LMFDB - Embedded newform 418.2.j.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (of order $9$, degree $6$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	418.23
Dual form			418.2.j.a.309.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.232600 - 1.31914i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.527700 - 0.442792i) q^{5} +(0.232600 - 1.31914i) q^{6} +(0.106944 - 0.185233i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.13305 - 0.412397i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.232600 - 1.31914i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.527700 - 0.442792i) q^{5} +(0.232600 - 1.31914i) q^{6} +(0.106944 - 0.185233i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.13305 - 0.412397i) q^{9} +(0.647319 - 0.235605i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.669744 - 1.16003i) q^{12} +(0.581469 - 3.29767i) q^{13} +(0.163848 - 0.137485i) q^{14} +(-0.706848 - 0.593116i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.626548 - 0.228045i) q^{17} +1.20577 q^{18} +(4.10521 - 1.46534i) q^{19} +0.688863 q^{20} +(-0.269224 - 0.0979894i) q^{21} +(0.173648 + 0.984808i) q^{22} +(-2.08279 - 1.74767i) q^{23} +(1.02611 - 0.861007i) q^{24} +(-0.785839 + 4.45672i) q^{25} +(1.67427 - 2.89993i) q^{26} +(-2.81679 - 4.87882i) q^{27} +(0.200990 - 0.0731543i) q^{28} +(-0.232416 + 0.0845926i) q^{29} +(-0.461362 - 0.799103i) q^{30} +(-0.155315 + 0.269013i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.02611 - 0.861007i) q^{33} +(-0.510766 - 0.428584i) q^{34} +(-0.0255853 - 0.145102i) q^{35} +(1.13305 + 0.412397i) q^{36} +4.31489 q^{37} +(4.35881 + 0.0271001i) q^{38} -4.48534 q^{39} +(0.647319 + 0.235605i) q^{40} +(0.261423 + 1.48261i) q^{41} +(-0.219473 - 0.184160i) q^{42} +(-6.33409 + 5.31493i) q^{43} +(-0.173648 + 0.984808i) q^{44} +(0.415305 - 0.719329i) q^{45} +(-1.35945 - 2.35463i) q^{46} +(-10.2638 + 3.73572i) q^{47} +(1.25871 - 0.458132i) q^{48} +(3.47713 + 6.02256i) q^{49} +(-2.26273 + 3.91917i) q^{50} +(-0.155088 + 0.879547i) q^{51} +(2.56514 - 2.15240i) q^{52} +(5.70567 + 4.78763i) q^{53} +(-0.978261 - 5.54799i) q^{54} +(0.647319 + 0.235605i) q^{55} +0.213889 q^{56} +(-2.88786 - 5.07451i) q^{57} -0.247332 q^{58} +(7.60286 + 2.76721i) q^{59} +(-0.160229 - 0.908706i) q^{60} +(-4.00867 - 3.36367i) q^{61} +(-0.237956 + 0.199669i) q^{62} +(0.0447840 - 0.253982i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.15334 - 1.99765i) q^{65} +(1.25871 - 0.458132i) q^{66} +(-14.4031 + 5.24230i) q^{67} +(-0.333379 - 0.577430i) q^{68} +(-1.82096 + 3.15400i) q^{69} +(0.0255853 - 0.145102i) q^{70} +(-6.85930 + 5.75564i) q^{71} +(0.923673 + 0.775054i) q^{72} +(-1.01277 - 5.74372i) q^{73} +(4.05467 + 1.47578i) q^{74} +6.06181 q^{75} +(4.08668 + 1.51627i) q^{76} +0.213889 q^{77} +(-4.21484 - 1.53408i) q^{78} +(-0.213330 - 1.20986i) q^{79} +(0.527700 + 0.442792i) q^{80} +(-3.00965 + 2.52539i) q^{81} +(-0.261423 + 1.48261i) q^{82} +(-4.00128 + 6.93041i) q^{83} +(-0.143251 - 0.248118i) q^{84} +(-0.431605 + 0.157092i) q^{85} +(-7.76991 + 2.82802i) q^{86} +(0.165649 + 0.286913i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-0.338582 + 1.92019i) q^{89} +(0.636284 - 0.533906i) q^{90} +(-0.548654 - 0.460375i) q^{91} +(-0.472131 - 2.67759i) q^{92} +(0.390992 + 0.142310i) q^{93} -10.9225 q^{94} +(1.51748 - 2.59102i) q^{95} +1.33949 q^{96} +(10.0645 + 3.66318i) q^{97} +(1.20759 + 6.84860i) q^{98} +(0.923673 + 0.775054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.232600	−	1.31914i	−0.134292	−	0.761605i	−0.975350	−	0.220662i	$-0.929178\pi$
$3$	−0.232600	−	1.31914i	−0.134292	−	0.761605i	0.841059	−	0.540944i	$-0.181933\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.527700	−	0.442792i	0.235994	−	0.198023i	−0.517119	−	0.855913i	$-0.672996\pi$
$5$	0.527700	−	0.442792i	0.235994	−	0.198023i	0.753113	+	0.657891i	$0.228551\pi$
$6$	0.232600	−	1.31914i	0.0949585	−	0.538536i
$7$	0.106944	−	0.185233i	0.0404212	−	0.0700116i	−0.845107	−	0.534597i	$-0.820463\pi$
$7$	0.106944	−	0.185233i	0.0404212	−	0.0700116i	0.885528	+	0.464586i	$0.153797\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	1.13305	−	0.412397i	0.377684	−	0.137466i
$10$	0.647319	−	0.235605i	0.204700	−	0.0745048i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.669744	−	1.16003i	0.193339	−	0.334872i
$13$	0.581469	−	3.29767i	0.161270	−	0.914610i	−0.791556	−	0.611096i	$-0.790729\pi$
$13$	0.581469	−	3.29767i	0.161270	−	0.914610i	0.952827	−	0.303514i	$-0.0981600\pi$
$14$	0.163848	−	0.137485i	0.0437903	−	0.0367444i
$15$	−0.706848	−	0.593116i	−0.182507	−	0.153142i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−0.626548	−	0.228045i	−0.151960	−	0.0553090i	0.264920	−	0.964270i	$-0.414654\pi$
$17$	−0.626548	−	0.228045i	−0.151960	−	0.0553090i	−0.416880	+	0.908961i	$0.636877\pi$
$18$	1.20577			0.284203
$19$	4.10521	−	1.46534i	0.941801	−	0.336171i
$19$	4.10521	−	1.46534i	0.941801	−	0.336171i
$20$	0.688863			0.154034
$21$	−0.269224	−	0.0979894i	−0.0587494	−	0.0213830i
$22$	0.173648	+	0.984808i	0.0370219	+	0.209962i
$23$	−2.08279	−	1.74767i	−0.434292	−	0.364414i	0.399276	−	0.916831i	$-0.369261\pi$
$23$	−2.08279	−	1.74767i	−0.434292	−	0.364414i	−0.833568	+	0.552416i	$0.813706\pi$
$24$	1.02611	−	0.861007i	0.209453	−	0.175752i
$25$	−0.785839	+	4.45672i	−0.157168	+	0.891343i
$26$	1.67427	−	2.89993i	0.328352	−	0.568722i
$27$	−2.81679	−	4.87882i	−0.542092	−	0.938930i
$28$	0.200990	−	0.0731543i	0.0379835	−	0.0138249i
$29$	−0.232416	+	0.0845926i	−0.0431586	+	0.0157084i	−0.363509	−	0.931591i	$-0.618421\pi$
$29$	−0.232416	+	0.0845926i	−0.0431586	+	0.0157084i	0.320351	+	0.947299i	$0.396199\pi$
$30$	−0.461362	−	0.799103i	−0.0842328	−	0.145895i
$31$	−0.155315	+	0.269013i	−0.0278954	+	0.0483162i	−0.879636	−	0.475647i	$-0.842214\pi$
$31$	−0.155315	+	0.269013i	−0.0278954	+	0.0483162i	0.851741	+	0.523964i	$0.175547\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	1.02611	−	0.861007i	0.178622	−	0.149882i
$34$	−0.510766	−	0.428584i	−0.0875957	−	0.0735015i
$35$	−0.0255853	−	0.145102i	−0.00432471	−	0.0245267i
$36$	1.13305	+	0.412397i	0.188842	+	0.0687329i
$37$	4.31489			0.709364			0.354682	−	0.934987i	$-0.384589\pi$
$37$	4.31489			0.709364			0.354682	+	0.934987i	$0.384589\pi$
$38$	4.35881	+	0.0271001i	0.707093	+	0.00439621i
$39$	−4.48534			−0.718229
$40$	0.647319	+	0.235605i	0.102350	+	0.0372524i
$41$	0.261423	+	1.48261i	0.0408275	+	0.231544i	0.998393	−	0.0566721i	$-0.0180490\pi$
$41$	0.261423	+	1.48261i	0.0408275	+	0.231544i	−0.957565	+	0.288216i	$0.906938\pi$
$42$	−0.219473	−	0.184160i	−0.0338654	−	0.0284165i
$43$	−6.33409	+	5.31493i	−0.965939	+	0.810519i	−0.981909	−	0.189353i	$-0.939361\pi$
$43$	−6.33409	+	5.31493i	−0.965939	+	0.810519i	0.0159696	+	0.999872i	$0.494916\pi$
$44$	−0.173648	+	0.984808i	−0.0261784	+	0.148465i
$45$	0.415305	−	0.719329i	0.0619100	−	0.107231i
$46$	−1.35945	−	2.35463i	−0.200439	−	0.347171i
$47$	−10.2638	+	3.73572i	−1.49713	+	0.544911i	−0.955316	−	0.295588i	$-0.904484\pi$
$47$	−10.2638	+	3.73572i	−1.49713	+	0.544911i	−0.541814	+	0.840498i	$0.682262\pi$
$48$	1.25871	−	0.458132i	0.181679	−	0.0661257i
$49$	3.47713	+	6.02256i	0.496732	+	0.860366i
$50$	−2.26273	+	3.91917i	−0.319999	+	0.554254i
$51$	−0.155088	+	0.879547i	−0.0217166	+	0.123161i
$52$	2.56514	−	2.15240i	0.355720	−	0.298485i
$53$	5.70567	+	4.78763i	0.783734	+	0.657631i	0.944186	−	0.329412i	$-0.106851\pi$
$53$	5.70567	+	4.78763i	0.783734	+	0.657631i	−0.160452	+	0.987044i	$0.551295\pi$
$54$	−0.978261	−	5.54799i	−0.133124	−	0.754986i
$55$	0.647319	+	0.235605i	0.0872845	+	0.0317690i
$56$	0.213889			0.0285821
$57$	−2.88786	−	5.07451i	−0.382506	−	0.672136i
$58$	−0.247332			−0.0324763
$59$	7.60286	+	2.76721i	0.989808	+	0.360261i	0.785646	−	0.618677i	$-0.212331\pi$
$59$	7.60286	+	2.76721i	0.989808	+	0.360261i	0.204162	+	0.978937i	$0.434553\pi$
$60$	−0.160229	−	0.908706i	−0.0206855	−	0.117313i
$61$	−4.00867	−	3.36367i	−0.513257	−	0.430674i	0.349016	−	0.937117i	$-0.386516\pi$
$61$	−4.00867	−	3.36367i	−0.513257	−	0.430674i	−0.862274	+	0.506443i	$0.830960\pi$
$62$	−0.237956	+	0.199669i	−0.0302205	+	0.0253580i
$63$	0.0447840	−	0.253982i	0.00564225	−	0.0319988i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.15334	−	1.99765i	−0.143055	−	0.247778i
$66$	1.25871	−	0.458132i	0.154936	−	0.0563922i
$67$	−14.4031	+	5.24230i	−1.75962	+	0.640449i	−0.999951	−	0.00986282i	$-0.996861\pi$
$67$	−14.4031	+	5.24230i	−1.75962	+	0.640449i	−0.759667	+	0.650312i	$0.774638\pi$
$68$	−0.333379	−	0.577430i	−0.0404282	−	0.0700236i
$69$	−1.82096	+	3.15400i	−0.219218	+	0.379697i
$70$	0.0255853	−	0.145102i	0.00305803	−	0.0173430i
$71$	−6.85930	+	5.75564i	−0.814050	+	0.683069i	−0.951571	−	0.307430i	$-0.900531\pi$
$71$	−6.85930	+	5.75564i	−0.814050	+	0.683069i	0.137521	+	0.990499i	$0.456087\pi$
$72$	0.923673	+	0.775054i	0.108856	+	0.0913409i
$73$	−1.01277	−	5.74372i	−0.118536	−	0.672252i	−0.984938	−	0.172905i	$-0.944685\pi$
$73$	−1.01277	−	5.74372i	−0.118536	−	0.672252i	0.866402	−	0.499347i	$-0.166427\pi$
$74$	4.05467	+	1.47578i	0.471346	+	0.171556i
$75$	6.06181			0.699958
$76$	4.08668	+	1.51627i	0.468774	+	0.173928i
$77$	0.213889			0.0243749
$78$	−4.21484	−	1.53408i	−0.477237	−	0.173700i
$79$	−0.213330	−	1.20986i	−0.0240015	−	0.136119i	0.970452	−	0.241293i	$-0.0775714\pi$
$79$	−0.213330	−	1.20986i	−0.0240015	−	0.136119i	−0.994454	+	0.105173i	$0.966460\pi$
$80$	0.527700	+	0.442792i	0.0589986	+	0.0495057i
$81$	−3.00965	+	2.52539i	−0.334405	+	0.280599i
$82$	−0.261423	+	1.48261i	−0.0288694	+	0.163726i
$83$	−4.00128	+	6.93041i	−0.439197	+	0.760712i	−0.997628	−	0.0688396i	$-0.978070\pi$
$83$	−4.00128	+	6.93041i	−0.439197	+	0.760712i	0.558431	+	0.829551i	$0.311404\pi$
$84$	−0.143251	−	0.248118i	−0.0156300	−	0.0270719i
$85$	−0.431605	+	0.157092i	−0.0468142	+	0.0170390i
$86$	−7.76991	+	2.82802i	−0.837851	+	0.304953i
$87$	0.165649	+	0.286913i	0.0177595	+	0.0307603i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−0.338582	+	1.92019i	−0.0358896	+	0.203540i	−0.997480	−	0.0709485i	$-0.977397\pi$
$89$	−0.338582	+	1.92019i	−0.0358896	+	0.203540i	0.961590	+	0.274488i	$0.0885085\pi$
$90$	0.636284	−	0.533906i	0.0670702	−	0.0562786i
$91$	−0.548654	−	0.460375i	−0.0575145	−	0.0482604i
$92$	−0.472131	−	2.67759i	−0.0492230	−	0.279158i
$93$	0.390992	+	0.142310i	0.0405440	+	0.0147568i
$94$	−10.9225			−1.12657
$95$	1.51748	−	2.59102i	0.155690	−	0.265833i
$96$	1.33949			0.136711
$97$	10.0645	+	3.66318i	1.02189	+	0.371939i	0.797989	−	0.602672i	$-0.205897\pi$
$97$	10.0645	+	3.66318i	1.02189	+	0.371939i	0.223905	+	0.974611i	$0.428119\pi$
$98$	1.20759	+	6.84860i	0.121985	+	0.691813i
$99$	0.923673	+	0.775054i	0.0928326	+	0.0778958i
$100$	−3.46671	+	2.90891i	−0.346671	+	0.290891i
$101$	−1.20764	+	6.84888i	−0.120165	+	0.681489i	0.863898	+	0.503667i	$0.168016\pi$
$101$	−1.20764	+	6.84888i	−0.120165	+	0.681489i	−0.984063	+	0.177822i	$0.943095\pi$
$102$	−0.446558	+	0.773460i	−0.0442158	+	0.0765840i
$103$	−2.02579	−	3.50876i	−0.199607	−	0.345729i	0.748794	−	0.662802i	$-0.230633\pi$
$103$	−2.02579	−	3.50876i	−0.199607	−	0.345729i	−0.948401	+	0.317074i	$0.897300\pi$
$104$	3.14660	−	1.14527i	0.308550	−	0.112303i
$105$	−0.185458	+	0.0675012i	−0.0180989	+	0.00658744i
$106$	3.72411	+	6.45035i	0.361718	+	0.626514i
$107$	−1.19513	+	2.07002i	−0.115537	+	0.200116i	−0.917994	−	0.396593i	$-0.870192\pi$
$107$	−1.19513	+	2.07002i	−0.115537	+	0.200116i	0.802457	+	0.596710i	$0.203526\pi$
$108$	0.978261	−	5.54799i	0.0941332	−	0.533856i
$109$	7.39305	−	6.20351i	0.708126	−	0.594188i	−0.215947	−	0.976405i	$-0.569284\pi$
$109$	7.39305	−	6.20351i	0.708126	−	0.594188i	0.924073	+	0.382217i	$0.124839\pi$
$110$	0.527700	+	0.442792i	0.0503142	+	0.0422186i
$111$	−1.00364	−	5.69194i	−0.0952616	−	0.540255i
$112$	0.200990	+	0.0731543i	0.0189917	+	0.00691243i
$113$	−6.41757			−0.603715			−0.301857	−	0.953353i	$-0.597607\pi$
$113$	−6.41757			−0.603715			−0.301857	+	0.953353i	$0.597607\pi$
$114$	−0.978111	−	5.75619i	−0.0916085	−	0.539116i
$115$	−1.87294			−0.174653
$116$	−0.232416	−	0.0845926i	−0.0215793	−	0.00785422i
$117$	−0.701117	−	3.97623i	−0.0648183	−	0.367603i
$118$	6.19791	+	5.20066i	0.570564	+	0.478760i
$119$	−0.109247	+	0.0916693i	−0.0100147	+	0.00840331i
$120$	0.160229	−	0.908706i	0.0146269	−	0.0829531i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−2.61647	−	4.53186i	−0.236884	−	0.410295i
$123$	1.89496	−	0.689707i	0.170862	−	0.0621888i
$124$	−0.291897	+	0.106242i	−0.0262131	+	0.00954079i
$125$	3.28087	+	5.68263i	0.293450	+	0.508270i
$126$	0.128950	−	0.223348i	0.0114878	−	0.0198975i
$127$	2.60701	−	14.7851i	0.231335	−	1.31197i	−0.618861	−	0.785500i	$-0.712406\pi$
$127$	2.60701	−	14.7851i	0.231335	−	1.31197i	0.850196	−	0.526466i	$-0.176483\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	8.48444	+	7.11929i	0.747013	+	0.626819i
$130$	−0.400552	−	2.27165i	−0.0351308	−	0.199236i
$131$	−16.1880	−	5.89196i	−1.41435	−	0.514783i	−0.481950	−	0.876199i	$-0.660071\pi$
$131$	−16.1880	−	5.89196i	−1.41435	−	0.514783i	−0.932405	+	0.361416i	$0.882293\pi$
$132$	1.33949			0.116588
$133$	0.167601	−	0.917131i	0.0145328	−	0.0795254i
$134$	−15.3275			−1.32409
$135$	−3.64673	−	1.32730i	−0.313860	−	0.114236i
$136$	−0.115781	−	0.656629i	−0.00992817	−	0.0563054i
$137$	−6.73245	−	5.64920i	−0.575192	−	0.482643i	0.308172	−	0.951331i	$-0.400283\pi$
$137$	−6.73245	−	5.64920i	−0.575192	−	0.482643i	−0.883364	+	0.468687i	$0.844727\pi$
$138$	−2.78988	+	2.34099i	−0.237490	+	0.199278i
$139$	2.84187	−	16.1171i	0.241045	−	1.36703i	−0.588458	−	0.808528i	$-0.700265\pi$
$139$	2.84187	−	16.1171i	0.241045	−	1.36703i	0.829502	−	0.558503i	$-0.188624\pi$
$140$	0.0736700	−	0.127600i	0.00622625	−	0.0107842i
$141$	7.31529	+	12.6705i	0.616059	+	1.06704i
$142$	−8.41418	+	3.06251i	−0.706103	+	0.257000i
$143$	3.14660	−	1.14527i	0.263132	−	0.0957723i
$144$	0.602885	+	1.04423i	0.0502404	+	0.0870189i
$145$	−0.0851889	+	0.147552i	−0.00707456	+	0.0122535i
$146$	1.01277	−	5.74372i	0.0838177	−	0.475354i
$147$	7.13581	−	5.98766i	0.588552	−	0.493854i
$148$	3.30540	+	2.77356i	0.271702	+	0.227985i
$149$	−1.24032	−	7.03420i	−0.101611	−	0.576264i	−0.992520	−	0.122082i	$-0.961043\pi$
$149$	−1.24032	−	7.03420i	−0.101611	−	0.576264i	0.890909	−	0.454182i	$-0.150068\pi$
$150$	5.69624	+	2.07326i	0.465096	+	0.169281i
$151$	8.56626			0.697112			0.348556	−	0.937288i	$-0.386672\pi$
$151$	8.56626			0.697112			0.348556	+	0.937288i	$0.386672\pi$
$152$	3.32163	+	2.82255i	0.269419	+	0.228939i
$153$	−0.803957			−0.0649960
$154$	0.200990	+	0.0731543i	0.0161962	+	0.00589494i
$155$	0.0371575	+	0.210731i	0.00298456	+	0.0169263i
$156$	−3.43597	−	2.88312i	−0.275098	−	0.230834i
$157$	2.26742	−	1.90259i	0.180960	−	0.151843i	−0.547808	−	0.836604i	$-0.684538\pi$
$157$	2.26742	−	1.90259i	0.180960	−	0.151843i	0.728768	+	0.684761i	$0.240093\pi$
$158$	0.213330	−	1.20986i	0.0169716	−	0.0962509i
$159$	4.98841	−	8.64018i	0.395607	−	0.685211i
$160$	0.344431	+	0.596573i	0.0272297	+	0.0471632i
$161$	−0.546470	+	0.198899i	−0.0430678	+	0.0156754i
$162$	−3.69188	+	1.34373i	−0.290061	+	0.105574i
$163$	9.27499	+	16.0648i	0.726473	+	1.25829i	0.958365	+	0.285547i	$0.0921752\pi$
$163$	9.27499	+	16.0648i	0.726473	+	1.25829i	−0.231891	+	0.972742i	$0.574491\pi$
$164$	−0.752738	+	1.30378i	−0.0587790	+	0.101808i
$165$	0.160229	−	0.908706i	0.0124738	−	0.0707427i
$166$	−6.13031	+	5.14394i	−0.475804	+	0.399247i
$167$	−8.27699	−	6.94522i	−0.640492	−	0.537437i	0.263677	−	0.964611i	$-0.415065\pi$
$167$	−8.27699	−	6.94522i	−0.640492	−	0.537437i	−0.904169	+	0.427174i	$0.859509\pi$
$168$	−0.0497505	−	0.282149i	−0.00383833	−	0.0217683i
$169$	1.67945	+	0.611271i	0.129189	+	0.0470209i
$170$	−0.459305			−0.0352271
$171$	4.04712	−	3.35328i	0.309491	−	0.256432i
$172$	−8.26857			−0.630472
$173$	20.2786	+	7.38079i	1.54175	+	0.561151i	0.966464	−	0.256801i	$-0.0826684\pi$
$173$	20.2786	+	7.38079i	1.54175	+	0.561151i	0.575286	+	0.817952i	$0.304891\pi$
$174$	0.0575294	+	0.326265i	0.00436129	+	0.0247341i
$175$	0.741490	+	0.622184i	0.0560514	+	0.0470327i
$176$	−0.766044	+	0.642788i	−0.0577428	+	0.0484519i
$177$	1.88192	−	10.6729i	0.141454	−	0.802223i
$178$	−0.974907	+	1.68859i	−0.0730723	+	0.126565i
$179$	0.648116	+	1.12257i	0.0484425	+	0.0839049i	0.889230	−	0.457461i	$-0.151241\pi$
$179$	0.648116	+	1.12257i	0.0484425	+	0.0839049i	−0.840787	+	0.541365i	$0.817908\pi$
$180$	0.780518	−	0.284085i	0.0581764	−	0.0211745i
$181$	0.734759	−	0.267431i	0.0546142	−	0.0198780i	−0.314569	−	0.949235i	$-0.601860\pi$
$181$	0.734759	−	0.267431i	0.0546142	−	0.0198780i	0.369183	+	0.929357i	$0.379638\pi$
$182$	−0.358108	−	0.620262i	−0.0265448	−	0.0459769i
$183$	−3.50473	+	6.07038i	−0.259077	+	0.448735i
$184$	0.472131	−	2.67759i	0.0348059	−	0.197394i
$185$	2.27697	−	1.91060i	0.167406	−	0.140470i
$186$	0.318740	+	0.267455i	0.0233711	+	0.0196107i
$187$	−0.115781	−	0.656629i	−0.00846677	−	0.0480174i
$188$	−10.2638	−	3.73572i	−0.748565	−	0.272455i
$189$	−1.20496			−0.0876480
$190$	2.31214	−	1.91575i	0.167741	−	0.138983i
$191$	−10.3812			−0.751160			−0.375580	−	0.926790i	$-0.622556\pi$
$191$	−10.3812			−0.751160			−0.375580	+	0.926790i	$0.622556\pi$
$192$	1.25871	+	0.458132i	0.0908394	+	0.0330628i
$193$	−1.37830	−	7.81671i	−0.0992119	−	0.562659i	−0.993375	−	0.114917i	$-0.963340\pi$
$193$	−1.37830	−	7.81671i	−0.0992119	−	0.562659i	0.894163	−	0.447741i	$-0.147771\pi$
$194$	8.20465	+	6.88452i	0.589060	+	0.494280i
$195$	−2.36691	+	1.98608i	−0.169498	+	0.142226i
$196$	−1.20759	+	6.84860i	−0.0862567	+	0.489186i
$197$	2.18000	−	3.77587i	0.155319	−	0.269020i	−0.777856	−	0.628442i	$-0.783693\pi$
$197$	2.18000	−	3.77587i	0.155319	−	0.269020i	0.933175	+	0.359422i	$0.117026\pi$
$198$	0.602885	+	1.04423i	0.0428451	+	0.0742100i
$199$	−0.715987	+	0.260598i	−0.0507550	+	0.0184733i	−0.367273	−	0.930113i	$-0.619708\pi$
$199$	−0.715987	+	0.260598i	−0.0507550	+	0.0184733i	0.316518	+	0.948587i	$0.397486\pi$
$200$	−4.25255	+	1.54780i	−0.300701	+	0.109446i
$201$	10.2655	+	17.7803i	0.724071	+	1.25413i
$202$	−3.47727	+	6.02281i	−0.244660	+	0.423763i
$203$	−0.00918626	+	0.0520979i	−0.000644749	+	0.00365655i
$204$	−0.684166	+	0.574083i	−0.0479012	+	0.0401939i
$205$	0.794439	+	0.666614i	0.0554861	+	0.0465583i
$206$	−0.703548	−	3.99002i	−0.0490185	−	0.277998i
$207$	−3.08065	−	1.12126i	−0.214120	−	0.0779332i
$208$	3.34855			0.232180
$209$	3.32163	+	2.82255i	0.229762	+	0.195240i
$210$	−0.197360			−0.0136192
$211$	14.1231	+	5.14037i	0.972272	+	0.353878i	0.778831	−	0.627234i	$-0.215813\pi$
$211$	14.1231	+	5.14037i	0.972272	+	0.353878i	0.193441	+	0.981112i	$0.438035\pi$
$212$	1.29337	+	7.33507i	0.0888291	+	0.503775i
$213$	9.18796	+	7.70962i	0.629549	+	0.528254i
$214$	−1.83104	+	1.53642i	−0.125167	+	0.105028i
$215$	−0.989084	+	5.60937i	−0.0674550	+	0.382556i
$216$	2.81679	−	4.87882i	0.191658	−	0.331962i
$217$	0.0332201	+	0.0575390i	0.00225513	+	0.00390600i
$218$	9.06892	−	3.30082i	0.614225	−	0.223560i
$219$	−7.34120	+	2.67198i	−0.496072	+	0.180556i
$220$	0.344431	+	0.596573i	0.0232216	+	0.0402209i
$221$	−1.11634	+	1.93355i	−0.0750928	+	0.130065i
$222$	1.00364	−	5.69194i	0.0673601	−	0.382018i
$223$	17.9046	−	15.0237i	1.19898	−	1.00606i	0.199321	−	0.979934i	$-0.436126\pi$
$223$	17.9046	−	15.0237i	1.19898	−	1.00606i	0.999659	−	0.0261290i	$-0.00831807\pi$
$224$	0.163848	+	0.137485i	0.0109476	+	0.00918611i
$225$	0.947541	+	5.37377i	0.0631694	+	0.358251i
$226$	−6.03055	−	2.19494i	−0.401146	−	0.146005i
$227$	1.87509			0.124454			0.0622272	−	0.998062i	$-0.480180\pi$
$227$	1.87509			0.124454			0.0622272	+	0.998062i	$0.480180\pi$
$228$	1.04961	−	5.74358i	0.0695120	−	0.380378i
$229$	26.0762			1.72316			0.861582	−	0.507618i	$-0.169474\pi$
$229$	26.0762			1.72316			0.861582	+	0.507618i	$0.169474\pi$
$230$	−1.75999	−	0.640585i	−0.116050	−	0.0422389i
$231$	−0.0497505	−	0.282149i	−0.00327334	−	0.0185640i
$232$	−0.189467	−	0.158982i	−0.0124391	−	0.0104377i
$233$	−14.2820	+	11.9840i	−0.935645	+	0.785099i	−0.976822	−	0.214053i	$-0.931334\pi$
$233$	−14.2820	+	11.9840i	−0.935645	+	0.785099i	0.0411775	+	0.999152i	$0.486889\pi$
$234$	0.701117	−	3.97623i	0.0458335	−	0.259935i
$235$	−3.76206	+	6.51607i	−0.245409	+	0.425062i
$236$	4.04540	+	7.00683i	0.263333	+	0.456106i
$237$	−1.54635	+	0.562824i	−0.100446	+	0.0365594i
$238$	−0.134012	+	0.0487762i	−0.00868668	+	0.00316169i
$239$	5.45731	+	9.45234i	0.353004	+	0.611421i	0.986774	−	0.162100i	$-0.0518268\pi$
$239$	5.45731	+	9.45234i	0.353004	+	0.611421i	−0.633770	+	0.773521i	$0.718493\pi$
$240$	0.461362	−	0.799103i	0.0297808	−	0.0515818i
$241$	2.08624	−	11.8317i	0.134387	−	0.762144i	−0.840898	−	0.541193i	$-0.817973\pi$
$241$	2.08624	−	11.8317i	0.134387	−	0.762144i	0.975285	−	0.220951i	$-0.0709161\pi$
$242$	−0.766044	+	0.642788i	−0.0492432	+	0.0413200i
$243$	−8.91534	−	7.48085i	−0.571919	−	0.479897i
$244$	−0.908691	−	5.15344i	−0.0581730	−	0.329915i
$245$	4.50162	+	1.63846i	0.287598	+	0.104677i
$246$	2.01657			0.128572
$247$	−2.44515	−	14.3897i	−0.155581	−	0.915595i
$248$	−0.310630			−0.0197250
$249$	10.0729	+	3.66623i	0.638343	+	0.232338i
$250$	1.13943	+	6.46205i	0.0720642	+	0.408696i
$251$	13.9500	+	11.7055i	0.880518	+	0.738842i	0.966285	−	0.257473i	$-0.0828899\pi$
$251$	13.9500	+	11.7055i	0.880518	+	0.738842i	−0.0857677	+	0.996315i	$0.527334\pi$
$252$	0.197563	−	0.165775i	0.0124453	−	0.0104429i
$253$	0.472131	−	2.67759i	0.0296826	−	0.168338i
$254$	7.50660	−	13.0018i	0.471006	−	0.815806i
$255$	0.307617	+	0.532808i	0.0192637	+	0.0333657i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−8.96948	+	3.26463i	−0.559501	+	0.203642i	−0.606263	−	0.795264i	$-0.707332\pi$
$257$	−8.96948	+	3.26463i	−0.559501	+	0.203642i	0.0467618	+	0.998906i	$0.485110\pi$
$258$	5.53783	+	9.59180i	0.344770	+	0.597159i
$259$	0.461454	−	0.799261i	0.0286733	−	0.0496637i
$260$	0.400552	−	2.27165i	0.0248412	−	0.140881i
$261$	−0.228454	+	0.191696i	−0.0141409	+	0.0118657i
$262$	−13.1966	−	11.0733i	−0.815289	−	0.684108i
$263$	−3.77777	−	21.4248i	−0.232947	−	1.32111i	−0.846894	−	0.531762i	$-0.821530\pi$
$263$	−3.77777	−	21.4248i	−0.232947	−	1.32111i	0.613946	−	0.789348i	$-0.289581\pi$
$264$	1.25871	+	0.458132i	0.0774681	+	0.0281961i
$265$	5.13081			0.315183
$266$	0.471171	−	0.804499i	0.0288893	−	0.0493270i
$267$	2.61175			0.159837
$268$	−14.4031	−	5.24230i	−0.879809	−	0.320224i
$269$	0.968804	+	5.49436i	0.0590690	+	0.334997i	0.999993	−	0.00361953i	$-0.00115213\pi$
$269$	0.968804	+	5.49436i	0.0590690	+	0.334997i	−0.940924	+	0.338617i	$0.890041\pi$
$270$	−2.97284	−	2.49451i	−0.180921	−	0.151811i
$271$	−3.02011	+	2.53417i	−0.183459	+	0.153940i	−0.729892	−	0.683563i	$-0.760430\pi$
$271$	−3.02011	+	2.53417i	−0.183459	+	0.153940i	0.546433	+	0.837503i	$0.315985\pi$
$272$	0.115781	−	0.656629i	0.00702028	−	0.0398140i
$273$	−0.479682	+	0.830834i	−0.0290317	+	0.0502844i
$274$	−4.39429	−	7.61114i	−0.265469	−	0.459806i
$275$	−4.25255	+	1.54780i	−0.256438	+	0.0933359i
$276$	−3.42229	+	1.24561i	−0.205998	+	0.0749770i
$277$	−4.49408	−	7.78397i	−0.270023	−	0.467693i	0.698845	−	0.715274i	$-0.253698\pi$
$277$	−4.49408	−	7.78397i	−0.270023	−	0.467693i	−0.968867	+	0.247580i	$0.920365\pi$
$278$	8.18285	−	14.1731i	0.490775	−	0.850046i
$279$	−0.0650396	+	0.368858i	−0.00389382	+	0.0220829i
$280$	0.112869	−	0.0947084i	0.00674521	−	0.00565991i
$281$	−15.1460	−	12.7090i	−0.903536	−	0.758157i	0.0673422	−	0.997730i	$-0.478548\pi$
$281$	−15.1460	−	12.7090i	−0.903536	−	0.758157i	−0.970878	+	0.239573i	$0.922993\pi$
$282$	2.54057	+	14.4083i	0.151289	+	0.858002i
$283$	14.9113	+	5.42727i	0.886385	+	0.322618i	0.744783	−	0.667306i	$-0.232553\pi$
$283$	14.9113	+	5.42727i	0.886385	+	0.322618i	0.141601	+	0.989924i	$0.454775\pi$
$284$	−8.95419			−0.531333
$285$	−3.77088	−	1.39910i	−0.223367	−	0.0828754i
$286$	3.34855			0.198004
$287$	0.302585	+	0.110132i	0.0178611	+	0.00650089i
$288$	0.209380	+	1.18745i	0.0123378	+	0.0699712i
$289$	−12.6822	−	10.6416i	−0.746012	−	0.625978i
$290$	−0.130517	+	0.109517i	−0.00766422	+	0.00643105i
$291$	2.49124	−	14.1285i	0.146039	−	0.828229i
$292$	2.91616	−	5.05095i	0.170656	−	0.295584i
$293$	−3.90839	−	6.76953i	−0.228331	−	0.395480i	0.728983	−	0.684532i	$-0.239993\pi$
$293$	−3.90839	−	6.76953i	−0.228331	−	0.395480i	−0.957314	+	0.289052i	$0.906660\pi$
$294$	8.75337	−	3.18597i	0.510507	−	0.185809i
$295$	5.23733	−	1.90623i	0.304929	−	0.110985i
$296$	2.15745	+	3.73681i	0.125399	+	0.217197i
$297$	2.81679	−	4.87882i	0.163447	−	0.283098i
$298$	1.24032	−	7.03420i	0.0718497	−	0.407480i
$299$	−6.97433	+	5.85216i	−0.403336	+	0.338439i
$300$	4.64362	+	3.89646i	0.268099	+	0.224962i
$301$	0.307106	+	1.74169i	0.0177013	+	0.100389i
$302$	8.04965	+	2.92983i	0.463205	+	0.168593i
$303$	9.31553			0.535163
$304$	2.15594	+	3.78839i	0.123652	+	0.217279i
$305$	−3.60478			−0.206409
$306$	−0.755472	−	0.274969i	−0.0431875	−	0.0157190i
$307$	−3.25292	−	18.4483i	−0.185654	−	1.05290i	−0.925112	−	0.379694i	$-0.876029\pi$
$307$	−3.25292	−	18.4483i	−0.185654	−	1.05290i	0.739458	−	0.673203i	$-0.235082\pi$
$308$	0.163848	+	0.137485i	0.00933613	+	0.00783394i
$309$	−4.15735	+	3.48843i	−0.236503	+	0.198450i
$310$	−0.0371575	+	0.210731i	−0.00211040	+	0.0119687i
$311$	5.91081	−	10.2378i	0.335171	−	0.580534i	−0.648346	−	0.761346i	$-0.724539\pi$
$311$	5.91081	−	10.2378i	0.335171	−	0.580534i	0.983518	+	0.180812i	$0.0578724\pi$
$312$	−2.24267	−	3.88442i	−0.126966	−	0.219912i
$313$	−21.4634	+	7.81204i	−1.21318	+	0.441563i	−0.867807	−	0.496902i	$-0.834471\pi$
$313$	−21.4634	+	7.81204i	−1.21318	+	0.441563i	−0.345376	+	0.938464i	$0.612249\pi$
$314$	2.78140	−	1.01235i	0.156964	−	0.0571301i
$315$	−0.0888291	−	0.153856i	−0.00500495	−	0.00866883i
$316$	0.614260	−	1.06393i	0.0345548	−	0.0598507i
$317$	2.03685	−	11.5515i	0.114401	−	0.648799i	−0.872644	−	0.488356i	$-0.837597\pi$
$317$	2.03685	−	11.5515i	0.114401	−	0.648799i	0.987045	−	0.160443i	$-0.0512922\pi$
$318$	7.64269	−	6.41297i	0.428581	−	0.359622i
$319$	−0.189467	−	0.158982i	−0.0106081	−	0.00890128i
$320$	0.119620	+	0.678397i	0.00668695	+	0.0379236i
$321$	3.00863	+	1.09505i	0.167925	+	0.0611198i
$322$	−0.581541			−0.0324080
$323$	−2.90628	−	0.0180692i	−0.161709	−	0.00100540i
$324$	−3.92881			−0.218267
$325$	14.2399	+	5.18288i	0.789885	+	0.287495i
$326$	3.22117	+	18.2682i	0.178404	+	1.01178i
$327$	−9.90291	−	8.30953i	−0.547632	−	0.459518i
$328$	−1.15326	+	0.967702i	−0.0636783	+	0.0534324i
$329$	−0.405677	+	2.30071i	−0.0223657	+	0.126842i
$330$	0.461362	−	0.799103i	0.0253971	−	0.0439891i
$331$	3.91015	+	6.77257i	0.214921	+	0.372254i	0.953248	−	0.302189i	$-0.0977172\pi$
$331$	3.91015	+	6.77257i	0.214921	+	0.372254i	−0.738327	+	0.674443i	$0.764384\pi$
$332$	−7.51994	+	2.73703i	−0.412710	+	0.150214i
$333$	4.88900	−	1.77945i	0.267915	−	0.0975133i
$334$	−5.40242	−	9.35726i	−0.295607	−	0.512007i
$335$	−5.27926	+	9.14394i	−0.288437	+	0.499587i
$336$	0.0497505	−	0.282149i	0.00271411	−	0.0153925i
$337$	−9.84741	+	8.26296i	−0.536422	+	0.450112i	−0.870312	−	0.492500i	$-0.836083\pi$
$337$	−9.84741	+	8.26296i	−0.536422	+	0.450112i	0.333890	+	0.942612i	$0.391639\pi$
$338$	1.36910	+	1.14881i	0.0744694	+	0.0624873i
$339$	1.49273	+	8.46567i	0.0810738	+	0.459792i
$340$	−0.431605	−	0.157092i	−0.0234071	−	0.00851948i
$341$	−0.310630			−0.0168216
$342$	4.94994	−	1.76686i	0.267662	−	0.0955407i
$343$	2.98466			0.161156
$344$	−7.76991	−	2.82802i	−0.418925	−	0.152476i
$345$	0.435646	+	2.47067i	0.0234544	+	0.133017i
$346$	16.5312	+	13.8714i	0.888725	+	0.745729i
$347$	−18.6318	+	15.6339i	−1.00021	+	0.839272i	−0.987013	−	0.160641i	$-0.948644\pi$
$347$	−18.6318	+	15.6339i	−1.00021	+	0.839272i	−0.0131925	+	0.999913i	$0.504199\pi$
$348$	−0.0575294	+	0.326265i	−0.00308390	+	0.0174897i
$349$	2.88937	−	5.00453i	0.154664	−	0.267886i	−0.778273	−	0.627927i	$-0.783904\pi$
$349$	2.88937	−	5.00453i	0.154664	−	0.267886i	0.932937	+	0.360040i	$0.117237\pi$
$350$	0.483974	+	0.838267i	0.0258695	+	0.0448072i
$351$	−17.7267	+	6.45197i	−0.946179	+	0.344381i
$352$	−0.939693	+	0.342020i	−0.0500858	+	0.0182297i
$353$	18.2320	+	31.5787i	0.970389	+	1.68076i	0.694381	+	0.719608i	$0.255678\pi$
$353$	18.2320	+	31.5787i	0.970389	+	1.68076i	0.276008	+	0.961155i	$0.410988\pi$
$354$	5.41876	−	9.38557i	0.288004	−	0.498838i
$355$	−1.07110	+	6.07450i	−0.0568480	+	0.322401i
$356$	−1.49364	+	1.25332i	−0.0791630	+	0.0664256i
$357$	0.146335	+	0.122790i	0.00774489	+	0.00649874i
$358$	0.225088	+	1.27654i	0.0118963	+	0.0674672i
$359$	−33.4230	−	12.1650i	−1.76400	−	0.642042i	−0.764002	−	0.645214i	$-0.776768\pi$
$359$	−33.4230	−	12.1650i	−1.76400	−	0.642042i	−0.999995	+	0.00317218i	$0.998990\pi$
$360$	0.830610			0.0437770
$361$	14.7056	−	12.0310i	0.773978	−	0.633213i
$362$	0.781915			0.0410965
$363$	1.25871	+	0.458132i	0.0660650	+	0.0240457i
$364$	−0.124370	−	0.705336i	−0.00651874	−	0.0369696i
$365$	−3.07772	−	2.58251i	−0.161095	−	0.135175i
$366$	−5.36957	+	4.50560i	−0.280672	+	0.235512i
$367$	2.56239	−	14.5320i	0.133756	−	0.758565i	−0.841963	−	0.539536i	$-0.818600\pi$
$367$	2.56239	−	14.5320i	0.133756	−	0.758565i	0.975718	−	0.219030i	$-0.0702891\pi$
$368$	1.35945	−	2.35463i	0.0708660	−	0.122744i
$369$	0.907629	+	1.57206i	0.0472493	+	0.0818381i
$370$	2.79311	−	1.01661i	0.145207	−	0.0528510i
$371$	1.49702	−	0.544870i	0.0777213	−	0.0282882i
$372$	0.208043	+	0.360341i	0.0107865	+	0.0186828i
$373$	−7.22031	+	12.5059i	−0.373854	+	0.647533i	−0.990155	−	0.139977i	$-0.955297\pi$
$373$	−7.22031	+	12.5059i	−0.373854	+	0.647533i	0.616301	+	0.787511i	$0.288630\pi$
$374$	0.115781	−	0.656629i	0.00598691	−	0.0339535i
$375$	6.73305	−	5.64970i	0.347693	−	0.291749i
$376$	−8.36713	−	7.02085i	−0.431502	−	0.362073i
$377$	0.143816	+	0.815621i	0.00740690	+	0.0420066i
$378$	−1.13229	−	0.412121i	−0.0582388	−	0.0211972i
$379$	4.36692			0.224314			0.112157	−	0.993691i	$-0.464224\pi$
$379$	4.36692			0.224314			0.112157	+	0.993691i	$0.464224\pi$
$380$	2.82793	−	1.00942i	0.145070	−	0.0517819i
$381$	−20.1100			−1.03027
$382$	−9.75517	−	3.55059i	−0.499118	−	0.181664i
$383$	0.458190	+	2.59852i	0.0234124	+	0.132778i	0.994274	−	0.106864i	$-0.0340809\pi$
$383$	0.458190	+	2.59852i	0.0234124	+	0.132778i	−0.970861	+	0.239642i	$0.922970\pi$
$384$	1.02611	+	0.861007i	0.0523634	+	0.0439381i
$385$	0.112869	−	0.0947084i	0.00575234	−	0.00482678i
$386$	1.37830	−	7.81671i	0.0701534	−	0.397860i
$387$	−4.98499	+	8.63426i	−0.253401	+	0.438904i
$388$	5.35521	+	9.27549i	0.271869	+	0.470892i
$389$	−8.85374	+	3.22250i	−0.448902	+	0.163387i	−0.556572	−	0.830800i	$-0.687884\pi$
$389$	−8.85374	+	3.22250i	−0.448902	+	0.163387i	0.107669	+	0.994187i	$0.465661\pi$
$390$	−2.90345	+	1.05677i	−0.147022	+	0.0535116i
$391$	0.906422	+	1.56997i	0.0458397	+	0.0793967i
$392$	−3.47713	+	6.02256i	−0.175621	+	0.304185i
$393$	−4.00698	+	22.7247i	−0.202126	+	1.14631i
$394$	3.33996	−	2.80256i	0.168265	−	0.141191i
$395$	−0.648289	−	0.543979i	−0.0326190	−	0.0273706i
$396$	0.209380	+	1.18745i	0.0105217	+	0.0596717i
$397$	−29.8755	−	10.8738i	−1.49941	−	0.545740i	−0.543500	−	0.839409i	$-0.682901\pi$
$397$	−29.8755	−	10.8738i	−1.49941	−	0.545740i	−0.955907	+	0.293670i	$0.905123\pi$
$398$	−0.761937			−0.0381925
$399$	−1.24881	−	0.00776422i	−0.0625186	−	0.000388697i
$400$	−4.52547			−0.226273
$401$	16.6404	+	6.05661i	0.830981	+	0.302452i	0.722262	−	0.691620i	$-0.243103\pi$
$401$	16.6404	+	6.05661i	0.830981	+	0.302452i	0.108720	+	0.994072i	$0.465325\pi$
$402$	3.56516	+	20.2191i	0.177814	+	1.00843i
$403$	0.796808	+	0.668601i	0.0396918	+	0.0333054i
$404$	−5.32749	+	4.47029i	−0.265052	+	0.222405i
$405$	−0.469964	+	2.66530i	−0.0233527	+	0.132440i
$406$	−0.0264508	+	0.0458141i	−0.00131273	+	0.00227372i
$407$	2.15745	+	3.73681i	0.106941	+	0.185227i
$408$	−0.839254	+	0.305463i	−0.0415493	+	0.0151227i
$409$	−5.13904	+	1.87046i	−0.254109	+	0.0924883i	−0.465934	−	0.884819i	$-0.654282\pi$
$409$	−5.13904	+	1.87046i	−0.254109	+	0.0924883i	0.211825	+	0.977308i	$0.432059\pi$
$410$	0.518533	+	0.898126i	0.0256085	+	0.0443553i
$411$	−5.88611	+	10.1950i	−0.290340	+	0.502884i
$412$	0.703548	−	3.99002i	0.0346613	−	0.196574i
$413$	1.32566	−	1.11236i	0.0652316	−	0.0547358i
$414$	−2.51137	−	2.10729i	−0.123427	−	0.103568i
$415$	0.957263	+	5.42891i	0.0469902	+	0.266495i
$416$	3.14660	+	1.14527i	0.154275	+	0.0561515i
$417$	−21.9217			−1.07351
$418$	2.15594	+	3.78839i	0.105450	+	0.185296i
$419$	10.9970			0.537239			0.268620	−	0.963246i	$-0.413433\pi$
$419$	10.9970			0.537239			0.268620	+	0.963246i	$0.413433\pi$
$420$	−0.185458	−	0.0675012i	−0.00904943	−	0.00329372i
$421$	2.65437	+	15.0537i	0.129366	+	0.733670i	0.978619	+	0.205684i	$0.0659418\pi$
$421$	2.65437	+	15.0537i	0.129366	+	0.733670i	−0.849253	+	0.527987i	$0.822947\pi$
$422$	11.5132	+	9.66074i	0.560455	+	0.470278i
$423$	−10.0888	+	8.46553i	−0.490536	+	0.411608i
$424$	−1.29337	+	7.33507i	−0.0628116	+	0.356223i
$425$	1.50870	−	2.61314i	0.0731825	−	0.126756i
$426$	5.99702	+	10.3871i	0.290556	+	0.503259i
$427$	−1.05177	+	0.382812i	−0.0508986	+	0.0185256i
$428$	−2.24610	+	0.817514i	−0.108569	+	0.0395160i
$429$	−2.24267	−	3.88442i	−0.108277	−	0.187542i
$430$	−2.84795	+	4.93280i	−0.137341	+	0.237881i
$431$	−3.42369	+	19.4167i	−0.164913	+	0.935270i	0.784240	+	0.620457i	$0.213053\pi$
$431$	−3.42369	+	19.4167i	−0.164913	+	0.935270i	−0.949154	+	0.314813i	$0.898058\pi$
$432$	4.31557	−	3.62120i	0.207633	−	0.174225i
$433$	−15.9603	−	13.3923i	−0.767005	−	0.643594i	0.172935	−	0.984933i	$-0.444675\pi$
$433$	−15.9603	−	13.3923i	−0.767005	−	0.643594i	−0.939940	+	0.341340i	$0.889119\pi$
$434$	0.0115372	+	0.0654309i	0.000553805	+	0.00314078i
$435$	0.214456	+	0.0780556i	0.0102824	+	0.00374248i
$436$	9.65095			0.462196
$437$	−11.1112	−	4.12257i	−0.531523	−	0.197209i
$438$	−7.81234			−0.373288
$439$	−15.4870	−	5.63681i	−0.739155	−	0.269030i	−0.0551201	−	0.998480i	$-0.517554\pi$
$439$	−15.4870	−	5.63681i	−0.739155	−	0.269030i	−0.684035	+	0.729449i	$0.739776\pi$
$440$	0.119620	+	0.678397i	0.00570265	+	0.0323413i
$441$	6.42345	+	5.38992i	0.305879	+	0.256663i
$442$	−1.71032	+	1.43513i	−0.0813519	+	0.0682623i
$443$	−0.328333	+	1.86207i	−0.0155996	+	0.0884697i	−0.991614	−	0.129238i	$-0.958747\pi$
$443$	−0.328333	+	1.86207i	−0.0155996	+	0.0884697i	0.976014	+	0.217708i	$0.0698580\pi$
$444$	2.88987	−	5.00541i	0.137147	−	0.237546i
$445$	0.671577	+	1.16321i	0.0318358	+	0.0551412i
$446$	21.9632	−	7.99396i	1.03999	−	0.378525i
$447$	−8.99059	+	3.27231i	−0.425240	+	0.154775i
$448$	0.106944	+	0.185233i	0.00505265	+	0.00875144i
$449$	−7.73941	+	13.4051i	−0.365245	+	0.632624i	−0.988816	−	0.149144i	$-0.952348\pi$
$449$	−7.73941	+	13.4051i	−0.365245	+	0.632624i	0.623570	+	0.781767i	$0.285682\pi$
$450$	−0.947541	+	5.37377i	−0.0446675	+	0.253322i
$451$	−1.15326	+	0.967702i	−0.0543050	+	0.0455673i
$452$	−4.91615	−	4.12514i	−0.231236	−	0.194030i
$453$	−1.99251	−	11.3001i	−0.0936163	−	0.530925i
$454$	1.76201	+	0.641320i	0.0826953	+	0.0300986i
$455$	−0.493375			−0.0231298
$456$	2.95073	−	5.03821i	0.138181	−	0.235936i
$457$	−18.9340			−0.885693			−0.442846	−	0.896597i	$-0.646031\pi$
$457$	−18.9340			−0.885693			−0.442846	+	0.896597i	$0.646031\pi$
$458$	24.5036	+	8.91859i	1.14498	+	0.416738i
$459$	0.652264	+	3.69917i	0.0304451	+	0.172663i
$460$	−1.43476	−	1.20391i	−0.0668959	−	0.0561324i
$461$	−3.12361	+	2.62102i	−0.145481	+	0.122073i	−0.712624	−	0.701546i	$-0.752493\pi$
$461$	−3.12361	+	2.62102i	−0.145481	+	0.122073i	0.567143	+	0.823620i	$0.308049\pi$
$462$	0.0497505	−	0.282149i	0.00231460	−	0.0131268i
$463$	−4.50125	+	7.79640i	−0.209191	+	0.362330i	−0.951460	−	0.307773i	$-0.900416\pi$
$463$	−4.50125	+	7.79640i	−0.209191	+	0.362330i	0.742269	+	0.670102i	$0.233750\pi$
$464$	−0.123666	−	0.214196i	−0.00574105	−	0.00994379i
$465$	0.269340	−	0.0980318i	0.0124903	−	0.00454612i
$466$	−17.5195	+	6.37656i	−0.811573	+	0.295389i
$467$	3.98825	+	6.90785i	0.184554	+	0.319657i	0.943426	−	0.331583i	$-0.107583\pi$
$467$	3.98825	+	6.90785i	0.184554	+	0.319657i	−0.758872	+	0.651240i	$0.774249\pi$
$468$	2.01879	−	3.49664i	0.0933185	−	0.161632i
$469$	−0.569283	+	3.22857i	−0.0262871	+	0.149081i
$470$	−5.76380	+	4.83641i	−0.265864	+	0.223087i
$471$	−3.03718	−	2.54850i	−0.139946	−	0.117429i
$472$	1.40495	+	7.96788i	0.0646681	+	0.366751i
$473$	−7.76991	−	2.82802i	−0.357261	−	0.130032i
$474$	−1.64559			−0.0755844
$475$	3.30455	+	19.4473i	0.151623	+	0.892303i
$476$	−0.142612			−0.00653662
$477$	8.43923	+	3.07163i	0.386406	+	0.140640i
$478$	1.89530	+	10.7488i	0.0866892	+	0.491639i
$479$	−5.92366	−	4.97054i	−0.270659	−	0.227110i	0.497348	−	0.867551i	$-0.334307\pi$
$479$	−5.92366	−	4.97054i	−0.270659	−	0.227110i	−0.768007	+	0.640441i	$0.778752\pi$
$480$	0.706848	−	0.593116i	0.0322630	−	0.0270719i
$481$	2.50898	−	14.2291i	0.114399	−	0.648791i
$482$	6.00709	−	10.4046i	0.273615	−	0.473916i
$483$	0.389484	+	0.674606i	0.0177221	+	0.0306956i
$484$	−0.939693	+	0.342020i	−0.0427133	+	0.0155464i
$485$	6.93306	−	2.52343i	0.314814	−	0.114583i
$486$	−5.81907	−	10.0789i	−0.263958	−	0.457189i
$487$	18.7484	−	32.4732i	0.849570	−	1.47150i	−0.0320217	−	0.999487i	$-0.510195\pi$
$487$	18.7484	−	32.4732i	0.849570	−	1.47150i	0.881592	−	0.472012i	$-0.156472\pi$
$488$	0.908691	−	5.15344i	0.0411345	−	0.233285i
$489$	19.0343	−	15.9717i	0.860760	−	0.722263i
$490$	3.66976	+	3.07929i	0.165783	+	0.139108i
$491$	3.19527	+	18.1213i	0.144200	+	0.817802i	0.968006	+	0.250929i	$0.0807359\pi$
$491$	3.19527	+	18.1213i	0.144200	+	0.817802i	−0.823805	+	0.566873i	$0.808153\pi$
$492$	1.89496	+	0.689707i	0.0854312	+	0.0310944i
$493$	0.164911			0.00742720
$494$	2.62388	−	14.3582i	0.118054	−	0.646006i
$495$	0.830610			0.0373331
$496$	−0.291897	−	0.106242i	−0.0131065	−	0.00477039i
$497$	0.332571	+	1.88610i	0.0149179	+	0.0846033i
$498$	8.21148	+	6.89025i	0.367965	+	0.308760i
$499$	−13.6245	+	11.4323i	−0.609916	+	0.511780i	−0.894616	−	0.446836i	$-0.852551\pi$
$499$	−13.6245	+	11.4323i	−0.609916	+	0.511780i	0.284700	+	0.958617i	$0.408106\pi$
$500$	−1.13943	+	6.46205i	−0.0509570	+	0.288992i
$501$	−7.23648	+	12.5340i	−0.323302	+	0.559976i
$502$	9.10523	+	15.7707i	0.406386	+	0.703882i
$503$	−9.78163	+	3.56022i	−0.436141	+	0.158742i	−0.550754	−	0.834668i	$-0.685660\pi$
$503$	−9.78163	+	3.56022i	−0.436141	+	0.158742i	0.114612	+	0.993410i	$0.463437\pi$
$504$	0.242347	−	0.0882072i	0.0107950	−	0.00392906i
$505$	2.39536	+	4.14889i	0.106592	+	0.184623i
$506$	1.35945	−	2.35463i	0.0604348	−	0.104676i
$507$	0.415711	−	2.35762i	0.0184624	−	0.104705i
$508$	11.5008	−	9.65029i	0.510264	−	0.428163i
$509$	−28.3710	−	23.8061i	−1.25752	−	1.05519i	−0.995941	−	0.0900040i	$-0.971312\pi$
$509$	−28.3710	−	23.8061i	−1.25752	−	1.05519i	−0.261580	−	0.965182i	$-0.584244\pi$
$510$	0.106834	+	0.605887i	0.00473070	+	0.0268291i
$511$	−1.17224	−	0.426660i	−0.0518568	−	0.0188743i
$512$	−1.00000			−0.0441942
$513$	−18.7127	−	15.9011i	−0.826184	−	0.702050i
$514$	−9.54513			−0.421017
$515$	−2.62266	−	0.954570i	−0.115568	−	0.0420634i
$516$	1.92327	+	10.9074i	0.0846671	+	0.480171i
$517$	−8.36713	−	7.02085i	−0.367986	−	0.308777i
$518$	0.706988	−	0.593233i	0.0310633	−	0.0260652i
$519$	5.01950	−	28.4670i	0.220332	−	1.24956i
$520$	1.15334	−	1.99765i	0.0505775	−	0.0876028i
$521$	15.5746	+	26.9759i	0.682334	+	1.18184i	0.974267	+	0.225398i	$0.0723681\pi$
$521$	15.5746	+	26.9759i	0.682334	+	1.18184i	−0.291933	+	0.956439i	$0.594299\pi$
$522$	−0.280240	+	0.101999i	−0.0122658	+	0.00446438i
$523$	25.1798	−	9.16471i	1.10104	−	0.400745i	0.273339	−	0.961918i	$-0.411872\pi$
$523$	25.1798	−	9.16471i	1.10104	−	0.400745i	0.827698	+	0.561173i	$0.189650\pi$
$524$	−8.61347	−	14.9190i	−0.376281	−	0.651738i
$525$	0.648277	−	1.12285i	0.0282931	−	0.0490052i
$526$	3.77777	−	21.4248i	0.164719	−	0.934166i
$527$	0.158659	−	0.133131i	0.00691131	−	0.00579928i
$528$	1.02611	+	0.861007i	0.0446556	+	0.0374705i
$529$	−2.71024	−	15.3705i	−0.117836	−	0.668283i
$530$	4.82138	+	1.75484i	0.209427	+	0.0762253i
$531$	9.75563			0.423358
$532$	0.717910	−	0.594832i	0.0311254	−	0.0257892i
$533$	5.04116			0.218357
$534$	2.45425	+	0.893272i	0.106206	+	0.0386557i
$535$	0.285921	+	1.62154i	0.0123615	+	0.0701053i
$536$	−11.7415	−	9.85230i	−0.507156	−	0.425555i
$537$	1.33007	−	1.11607i	0.0573970	−	0.0481618i
$538$	−0.968804	+	5.49436i	−0.0417681	+	0.236879i
$539$	−3.47713	+	6.02256i	−0.149770	+	0.259410i
$540$	−1.94038	−	3.36084i	−0.0835008	−	0.144628i
$541$	11.6023	−	4.22289i	0.498821	−	0.181556i	−0.0803425	−	0.996767i	$-0.525601\pi$
$541$	11.6023	−	4.22289i	0.498821	−	0.181556i	0.579164	+	0.815211i	$0.303379\pi$
$542$	−3.70471	+	1.34841i	−0.159131	+	0.0579190i
$543$	−0.523683	−	0.907046i	−0.0224734	−	0.0389251i
$544$	0.333379	−	0.577430i	0.0142935	−	0.0247571i
$545$	1.15444	−	6.54718i	0.0494509	−	0.280450i
$546$	−0.734916	+	0.616667i	−0.0314515	+	0.0263909i
$547$	−9.85321	−	8.26783i	−0.421293	−	0.353507i	0.407362	−	0.913267i	$-0.366449\pi$
$547$	−9.85321	−	8.26783i	−0.421293	−	0.353507i	−0.828655	+	0.559760i	$0.810893\pi$
$548$	−1.52612	−	8.65507i	−0.0651927	−	0.369726i
$549$	−5.92920	−	2.15805i	−0.253052	−	0.0921034i
$550$	−4.52547			−0.192967
$551$	−0.830162	+	0.687838i	−0.0353661	+	0.0293029i
$552$	−3.64193			−0.155011
$553$	−0.246920	−	0.0898714i	−0.0105001	−	0.00382172i
$554$	−1.56078	−	8.85160i	−0.0663110	−	0.376069i
$555$	−3.04997	−	2.55923i	−0.129464	−	0.108633i
$556$	12.5368	−	10.5197i	0.531681	−	0.446133i
$557$	5.01246	−	28.4271i	0.212385	−	1.20449i	−0.673003	−	0.739640i	$-0.734996\pi$
$557$	5.01246	−	28.4271i	0.212385	−	1.20449i	0.885387	−	0.464854i	$-0.153893\pi$
$558$	−0.187274	+	0.324368i	−0.00792794	+	0.0137316i
$559$	13.8438	+	23.9782i	0.585532	+	1.01417i
$560$	0.138454	−	0.0503933i	0.00585076	−	0.00212950i
$561$	−0.839254	+	0.305463i	−0.0354333	+	0.0128967i
$562$	−9.88587	−	17.1228i	−0.417010	−	0.722283i
$563$	3.08426	−	5.34209i	0.129986	−	0.225142i	−0.793685	−	0.608329i	$-0.791840\pi$
$563$	3.08426	−	5.34209i	0.129986	−	0.225142i	0.923671	+	0.383187i	$0.125173\pi$
$564$	−2.54057	+	14.4083i	−0.106977	+	0.606699i
$565$	−3.38655	+	2.84165i	−0.142473	+	0.119549i
$566$	12.1558	+	10.1999i	0.510946	+	0.428735i
$567$	0.145922	+	0.827563i	0.00612813	+	0.0347544i
$568$	−8.41418	−	3.06251i	−0.353051	−	0.128500i
$569$	−2.39774			−0.100519			−0.0502593	−	0.998736i	$-0.516005\pi$
$569$	−2.39774			−0.100519			−0.0502593	+	0.998736i	$0.516005\pi$
$570$	−3.06494	−	2.60444i	−0.128376	−	0.109088i
$571$	24.6558			1.03181			0.515907	−	0.856645i	$-0.327455\pi$
$571$	24.6558			1.03181			0.515907	+	0.856645i	$0.327455\pi$
$572$	3.14660	+	1.14527i	0.131566	+	0.0478862i
$573$	2.41467	+	13.6943i	0.100874	+	0.572087i
$574$	0.246670	+	0.206981i	0.0102958	+	0.00863920i
$575$	9.42561	−	7.90903i	0.393075	−	0.329829i
$576$	−0.209380	+	1.18745i	−0.00872415	+	0.0494771i
$577$	20.2171	−	35.0171i	0.841651	−	1.45778i	−0.0468475	−	0.998902i	$-0.514917\pi$
$577$	20.2171	−	35.0171i	0.841651	−	1.45778i	0.888498	−	0.458880i	$-0.151749\pi$
$578$	−8.27772	−	14.3374i	−0.344308	−	0.596358i
$579$	−9.99073	+	3.63633i	−0.415201	+	0.151121i
$580$	−0.160103	+	0.0582727i	−0.00664791	+	0.00241964i
$581$	0.855828	+	1.48234i	0.0355057	+	0.0614977i
$582$	7.17324	−	12.4244i	0.297340	−	0.515009i
$583$	−1.29337	+	7.33507i	−0.0535660	+	0.303788i
$584$	4.46782	−	3.74895i	0.184880	−	0.155133i
$585$	−2.13063	−	1.78781i	−0.0880905	−	0.0739167i
$586$	−1.35737	−	7.69803i	−0.0560725	−	0.318003i
$587$	32.4041	+	11.7941i	1.33746	+	0.486796i	0.909012	−	0.416771i	$-0.136838\pi$
$587$	32.4041	+	11.7941i	1.33746	+	0.486796i	0.428448	+	0.903566i	$0.359060\pi$
$588$	9.31514			0.384150
$589$	−0.243406	+	1.33195i	−0.0100294	+	0.0548819i
$590$	5.57345			0.229455
$591$	−5.48797	−	1.99746i	−0.225745	−	0.0821644i
$592$	0.749273	+	4.24934i	0.0307949	+	0.174647i
$593$	−12.5396	−	10.5220i	−0.514940	−	0.432086i	0.347924	−	0.937523i	$-0.386887\pi$
$593$	−12.5396	−	10.5220i	−0.514940	−	0.432086i	−0.862863	+	0.505437i	$0.831331\pi$
$594$	4.31557	−	3.62120i	0.177070	−	0.148579i
$595$	−0.0170592	+	0.0967477i	−0.000699360	+	0.00396627i
$596$	3.57135	−	6.18577i	0.146288	−	0.253379i
$597$	0.510303	+	0.883871i	0.0208853	+	0.0361744i
$598$	−8.55528	+	3.11387i	−0.349851	+	0.127335i
$599$	19.7491	−	7.18808i	0.806926	−	0.293697i	0.0945725	−	0.995518i	$-0.469852\pi$
$599$	19.7491	−	7.18808i	0.806926	−	0.293697i	0.712353	+	0.701821i	$0.247629\pi$
$600$	3.03091	+	5.24969i	0.123736	+	0.214318i
$601$	10.5288	−	18.2364i	0.429479	−	0.743879i	−0.567348	−	0.823478i	$-0.692031\pi$
$601$	10.5288	−	18.2364i	0.429479	−	0.743879i	0.996827	+	0.0795991i	$0.0253640\pi$
$602$	−0.307106	+	1.74169i	−0.0125167	+	0.0709858i
$603$	−14.1576	+	11.8796i	−0.576540	+	0.483775i
$604$	6.56214	+	5.50629i	0.267010	+	0.224048i
$605$	0.119620	+	0.678397i	0.00486324	+	0.0275808i
$606$	8.75373	+	3.18610i	0.355596	+	0.129426i
$607$	44.4044			1.80232			0.901160	−	0.433487i	$-0.142717\pi$
$607$	44.4044			1.80232			0.901160	+	0.433487i	$0.142717\pi$
$608$	0.730212	+	4.29730i	0.0296140	+	0.174279i
$609$	0.0708611			0.00287144
$610$	−3.38739	−	1.23291i	−0.137151	−	0.0499190i
$611$	6.35110	+	36.0189i	0.256938	+	1.45717i
$612$	−0.615866	−	0.516773i	−0.0248949	−	0.0208893i
$613$	−17.8778	+	15.0013i	−0.722078	+	0.605895i	−0.927959	−	0.372682i	$-0.878438\pi$
$613$	−17.8778	+	15.0013i	−0.722078	+	0.605895i	0.205881	+	0.978577i	$0.433994\pi$
$614$	3.25292	−	18.4483i	0.131277	−	0.744511i
$615$	0.694570	−	1.20303i	0.0280078	−	0.0485109i
$616$	0.106944	+	0.185233i	0.00430891	+	0.00746326i
$617$	38.7929	−	14.1195i	1.56174	−	0.568428i	0.590608	−	0.806958i	$-0.298888\pi$
$617$	38.7929	−	14.1195i	1.56174	−	0.568428i	0.971135	+	0.238530i	$0.0766656\pi$
$618$	−5.09974	+	1.85616i	−0.205142	+	0.0746655i
$619$	16.2741	+	28.1875i	0.654110	+	1.13295i	0.982116	+	0.188276i	$0.0602900\pi$
$619$	16.2741	+	28.1875i	0.654110	+	1.13295i	−0.328006	+	0.944676i	$0.606377\pi$
$620$	−0.106991	+	0.185313i	−0.00429685	+	0.00744236i
$621$	−2.65979	+	15.0844i	−0.106734	+	0.605316i
$622$	9.05589	−	7.59880i	0.363108	−	0.304684i
$623$	0.319474	+	0.268070i	0.0127994	+	0.0107400i
$624$	−0.778871	−	4.41720i	−0.0311798	−	0.176829i
$625$	−17.0152	−	6.19303i	−0.680608	−	0.247721i
$626$	−22.8409			−0.912905
$627$	2.95073	−	5.03821i	0.117841	−	0.201207i
$628$	2.95991			0.118113
$629$	−2.70349	−	0.983988i	−0.107795	−	0.0392342i
$630$	−0.0308500	−	0.174959i	−0.00122909	−	0.00697054i
$631$	−16.6043	−	13.9326i	−0.661005	−	0.554649i	0.249383	−	0.968405i	$-0.419772\pi$
$631$	−16.6043	−	13.9326i	−0.661005	−	0.554649i	−0.910388	+	0.413756i	$0.864217\pi$
$632$	0.941100	−	0.789677i	0.0374350	−	0.0314117i
$633$	3.49585	−	19.8259i	0.138947	−	0.788010i
$634$	5.86487	−	10.1583i	0.232924	−	0.403436i
$635$	−5.17102	−	8.95646i	−0.205205	−	0.355426i
$636$	9.37514	−	3.41227i	0.371749	−	0.135305i
$637$	21.8823	−	7.96450i	0.867007	−	0.315565i
$638$	−0.123666	−	0.214196i	−0.00489599	−	0.00848010i
$639$	−5.39834	+	9.35020i	−0.213555	+	0.369888i
$640$	−0.119620	+	0.678397i	−0.00472839	+	0.0268160i
$641$	1.69197	−	1.41973i	0.0668288	−	0.0560761i	−0.608761	−	0.793353i	$-0.708333\pi$
$641$	1.69197	−	1.41973i	0.0668288	−	0.0560761i	0.675590	+	0.737277i	$0.263889\pi$
$642$	2.45266	+	2.05802i	0.0967986	+	0.0812237i
$643$	−3.04712	−	17.2810i	−0.120166	−	0.681498i	−0.984062	−	0.177827i	$-0.943093\pi$
$643$	−3.04712	−	17.2810i	−0.120166	−	0.681498i	0.863895	−	0.503671i	$-0.168018\pi$
$644$	−0.546470	−	0.198899i	−0.0215339	−	0.00783770i
$645$	7.62960			0.300415
$646$	−2.72483	−	1.01098i	−0.107207	−	0.0397766i
$647$	−5.99419			−0.235656			−0.117828	−	0.993034i	$-0.537593\pi$
$647$	−5.99419			−0.235656			−0.117828	+	0.993034i	$0.537593\pi$
$648$	−3.69188	−	1.34373i	−0.145031	−	0.0527868i
$649$	1.40495	+	7.96788i	0.0551492	+	0.312766i
$650$	11.6084	+	9.74064i	0.455320	+	0.382059i
$651$	0.0681749	−	0.0572055i	0.00267199	−	0.00224206i
$652$	−3.22117	+	18.2682i	−0.126151	+	0.715436i
$653$	24.5179	−	42.4662i	0.959458	−	1.66183i	0.235639	−	0.971841i	$-0.424282\pi$
$653$	24.5179	−	42.4662i	0.959458	−	1.66183i	0.723819	−	0.689990i	$-0.242385\pi$
$654$	−6.46367	−	11.1954i	−0.252749	−	0.437775i
$655$	−11.1513	+	4.05875i	−0.435718	+	0.158589i
$656$	−1.41469	+	0.514903i	−0.0552342	+	0.0201036i
$657$	−3.51622	−	6.09027i	−0.137181	−	0.237604i
$658$	−1.16810	+	2.02321i	−0.0455373	+	0.0788730i
$659$	−3.27845	+	18.5930i	−0.127710	+	0.724281i	0.851951	+	0.523622i	$0.175419\pi$
$659$	−3.27845	+	18.5930i	−0.127710	+	0.724281i	−0.979661	+	0.200659i	$0.935692\pi$
$660$	0.706848	−	0.593116i	0.0275140	−	0.0230870i
$661$	18.1778	+	15.2530i	0.707036	+	0.593273i	0.923766	−	0.382958i	$-0.125095\pi$
$661$	18.1778	+	15.2530i	0.707036	+	0.593273i	−0.216730	+	0.976232i	$0.569539\pi$
$662$	1.35798	+	7.70149i	0.0527794	+	0.299327i
$663$	2.81028	+	1.02286i	0.109142	+	0.0397245i
$664$	−8.00255			−0.310559
$665$	−0.317656	−	0.558182i	−0.0123182	−	0.0216454i
$666$	5.20276			0.201603
$667$	0.631914	+	0.229998i	0.0244678	+	0.00890556i
$668$	−1.87624	−	10.6407i	−0.0725939	−	0.411701i
$669$	−23.9830	−	20.1241i	−0.927236	−	0.778043i
$670$	−8.08829	+	6.78688i	−0.312478	+	0.262200i
$671$	0.908691	−	5.15344i	0.0350796	−	0.198946i
$672$	0.143251	−	0.248118i	0.00552602	−	0.00957135i
$673$	15.8475	+	27.4486i	0.610875	+	1.05807i	0.991093	+	0.133170i	$0.0425155\pi$
$673$	15.8475	+	27.4486i	0.610875	+	1.05807i	−0.380218	+	0.924897i	$0.624151\pi$
$674$	−12.0796	+	4.39663i	−0.465290	+	0.169352i
$675$	23.9571	−	8.71966i	0.922108	−	0.335620i
$676$	0.893619	+	1.54779i	0.0343700	+	0.0595305i
$677$	6.79157	−	11.7633i	0.261021	−	0.452102i	−0.705492	−	0.708718i	$-0.749274\pi$
$677$	6.79157	−	11.7633i	0.261021	−	0.452102i	0.966514	+	0.256616i	$0.0826074\pi$
$678$	−1.49273	+	8.46567i	−0.0573278	+	0.325122i
$679$	1.75488	−	1.47252i	0.0673462	−	0.0565102i
$680$	−0.351848	−	0.295236i	−0.0134928	−	0.0113218i
$681$	−0.436146	−	2.47351i	−0.0167132	−	0.0947851i
$682$	−0.291897	−	0.106242i	−0.0111773	−	0.00406821i
$683$	20.5645			0.786877			0.393439	−	0.919351i	$-0.371285\pi$
$683$	20.5645			0.786877			0.393439	+	0.919351i	$0.371285\pi$
$684$	5.25572	+	0.0326764i	0.200958	+	0.00124942i
$685$	−6.05413			−0.231316
$686$	2.80466	+	1.02081i	0.107082	+	0.0389748i
$687$	−6.06532	−	34.3982i	−0.231407	−	1.31237i
$688$	−6.33409	−	5.31493i	−0.241485	−	0.202630i
$689$	19.1057	−	16.0316i	0.727869	−	0.610755i
$690$	−0.435646	+	2.47067i	−0.0165848	+	0.0940569i
$691$	−20.9053	+	36.2090i	−0.795275	+	1.37746i	0.127389	+	0.991853i	$0.459340\pi$
$691$	−20.9053	+	36.2090i	−0.795275	+	1.37746i	−0.922664	+	0.385604i	$0.873993\pi$
$692$	10.7900	+	18.6888i	0.410174	+	0.710443i
$693$	0.242347	−	0.0882072i	0.00920601	−	0.00335071i
$694$	−22.8552	+	8.31863i	−0.867573	+	0.315771i
$695$	−5.63686	−	9.76333i	−0.213818	−	0.370344i
$696$	−0.165649	+	0.286913i	−0.00627892	+	0.0108754i
$697$	0.174306	−	0.988539i	0.00660232	−	0.0374436i
$698$	4.42676	−	3.71450i	0.167556	−	0.140596i
$699$	19.1306	+	16.0525i	0.723585	+	0.607160i
$700$	0.168082	+	0.953242i	0.00635291	+	0.0360292i
$701$	35.5966	+	12.9561i	1.34447	+	0.489345i	0.911216	−	0.411929i	$-0.135145\pi$
$701$	35.5966	+	12.9561i	1.34447	+	0.489345i	0.433249	+	0.901274i	$0.357367\pi$
$702$	−18.8643			−0.711987
$703$	17.7136	−	6.32277i	0.668079	−	0.238468i
$704$	−1.00000			−0.0376889
$705$	9.47066	+	3.44704i	0.356686	+	0.129823i
$706$	6.33189	+	35.9099i	0.238304	+	1.35149i
$707$	1.13949	+	0.956145i	0.0428549	+	0.0359595i
$708$	8.30203	−	6.96623i	0.312009	−	0.261807i
$709$	−6.89820	+	39.1216i	−0.259067	+	1.46924i	0.526345	+	0.850271i	$0.323562\pi$
$709$	−6.89820	+	39.1216i	−0.259067	+	1.46924i	−0.785412	+	0.618973i	$0.787549\pi$
$710$	−3.08410	+	5.34182i	−0.115744	+	0.200475i
$711$	−0.740655	−	1.28285i	−0.0277767	−	0.0481107i
$712$	−1.83223	+	0.666875i	−0.0686655	+	0.0249922i
$713$	0.793636	−	0.288860i	0.0297219	−	0.0108179i
$714$	0.0955137	+	0.165435i	0.00357451	+	0.00619123i
$715$	1.15334	−	1.99765i	0.0431326	−	0.0747079i
$716$	−0.225088	+	1.27654i	−0.00841195	+	0.0477065i
$717$	11.1996	−	9.39757i	0.418256	−	0.350959i
$718$	−27.2466	−	22.8627i	−1.01684	−	0.853227i
$719$	−0.654566	−	3.71223i	−0.0244112	−	0.138443i	0.970166	−	0.242440i	$-0.0779478\pi$
$719$	−0.654566	−	3.71223i	−0.0244112	−	0.138443i	−0.994578	+	0.103997i	$0.966837\pi$
$720$	0.780518	+	0.284085i	0.0290882	+	0.0105872i
$721$	−0.866586			−0.0322733
$722$	17.9336	−	6.27588i	0.667419	−	0.233564i
$723$	−16.0929			−0.598500
$724$	0.734759	+	0.267431i	0.0273071	+	0.00993898i
$725$	−0.194363	−	1.10229i	−0.00721847	−	0.0409380i
$726$	1.02611	+	0.861007i	0.0380824	+	0.0319550i
$727$	−20.5326	+	17.2289i	−0.761511	+	0.638984i	−0.938520	−	0.345225i	$-0.887802\pi$
$727$	−20.5326	+	17.2289i	−0.761511	+	0.638984i	0.177008	+	0.984209i	$0.443358\pi$
$728$	0.124370	−	0.705336i	0.00460945	−	0.0261415i
$729$	−13.6878	+	23.7080i	−0.506956	+	0.878073i
$730$	−2.00884	−	3.47941i	−0.0743504	−	0.128779i
$731$	5.18065	−	1.88560i	0.191613	−	0.0697415i
$732$	−6.58675	+	2.39738i	−0.243453	+	0.0886097i
$733$	−3.68997	−	6.39121i	−0.136292	−	0.236065i	0.789798	−	0.613367i	$-0.210185\pi$
$733$	−3.68997	−	6.39121i	−0.136292	−	0.236065i	−0.926090	+	0.377302i	$0.876852\pi$
$734$	7.37810	−	12.7792i	0.272331	−	0.471691i
$735$	1.11428	−	6.31937i	0.0411007	−	0.233093i
$736$	2.08279	−	1.74767i	0.0767728	−	0.0644200i
$737$	−11.7415	−	9.85230i	−0.432504	−	0.362914i
$738$	0.315216	+	1.78768i	0.0116033	+	0.0658054i
$739$	27.2729	+	9.92653i	1.00325	+	0.365153i	0.790837	−	0.612026i	$-0.209645\pi$
$739$	27.2729	+	9.92653i	1.00325	+	0.365153i	0.212414	+	0.977180i	$0.431868\pi$
$740$	2.97237			0.109266
$741$	−18.4133	+	6.57253i	−0.676429	+	0.241448i
$742$	1.59309			0.0584843
$743$	18.7262	+	6.81579i	0.686998	+	0.250047i	0.661849	−	0.749637i	$-0.269772\pi$
$743$	18.7262	+	6.81579i	0.686998	+	0.250047i	0.0251489	+	0.999684i	$0.491994\pi$
$744$	0.0722525	+	0.409764i	0.00264890	+	0.0150227i
$745$	−3.76920	−	3.16274i	−0.138093	−	0.115874i
$746$	−11.0622	+	9.28225i	−0.405014	+	0.339847i
$747$	−1.67557	+	9.50264i	−0.0613059	+	0.347683i
$748$	0.333379	−	0.577430i	0.0121895	−	0.0211129i
$749$	0.255624	+	0.442754i	0.00934030	+	0.0161779i
$750$	8.25931	−	3.00614i	0.301588	−	0.109769i
$751$	13.9557	−	5.07945i	0.509250	−	0.185352i	−0.0746000	−	0.997214i	$-0.523768\pi$
$751$	13.9557	−	5.07945i	0.509250	−	0.185352i	0.583850	+	0.811862i	$0.301546\pi$
$752$	−5.46126	−	9.45917i	−0.199151	−	0.344940i
$753$	12.1964	−	21.1247i	0.444460	−	0.769827i
$754$	−0.143816	+	0.815621i	−0.00523747	+	0.0297032i
$755$	4.52041	−	3.79308i	0.164515	−	0.138044i
$756$	−0.923053	−	0.774533i	−0.0335711	−	0.0281695i
$757$	−5.68169	−	32.2225i	−0.206505	−	1.17115i	−0.895054	−	0.445957i	$-0.852863\pi$
$757$	−5.68169	−	32.2225i	−0.206505	−	1.17115i	0.688550	−	0.725189i	$-0.258248\pi$
$758$	4.10356	+	1.49357i	0.149048	+	0.0542491i
$759$	−3.64193			−0.132194
$760$	3.00263	+	0.0186682i	0.108917	+	0.000677168i
$761$	−27.0763			−0.981517			−0.490758	−	0.871296i	$-0.663280\pi$
$761$	−27.0763			−0.981517			−0.490758	+	0.871296i	$0.663280\pi$
$762$	−18.8972	−	6.87803i	−0.684574	−	0.249165i
$763$	−0.358450	−	2.03287i	−0.0129767	−	0.0735948i
$764$	−7.95249	−	6.67293i	−0.287711	−	0.241418i
$765$	−0.424247	+	0.355986i	−0.0153387	+	0.0128707i
$766$	−0.458190	+	2.59852i	−0.0165551	+	0.0938885i
$767$	13.5462	−	23.4627i	0.489125	−	0.847189i
$768$	0.669744	+	1.16003i	0.0241673	+	0.0418590i
$769$	−9.45269	+	3.44050i	−0.340873	+	0.124068i	−0.506784	−	0.862073i	$-0.669166\pi$
$769$	−9.45269	+	3.44050i	−0.340873	+	0.124068i	0.165911	+	0.986141i	$0.446944\pi$
$770$	0.138454	−	0.0503933i	0.00498955	−	0.00181605i
$771$	6.39280	+	11.0726i	0.230231	+	0.398772i
$772$	3.96865	−	6.87390i	0.142835	−	0.247397i
$773$	−7.45547	+	42.2821i	−0.268155	+	1.52078i	0.491745	+	0.870740i	$0.336359\pi$
$773$	−7.45547	+	42.2821i	−0.268155	+	1.52078i	−0.759899	+	0.650041i	$0.774752\pi$
$774$	−7.63745	+	6.40858i	−0.274522	+	0.230352i
$775$	−1.07686	−	0.903596i	−0.0386821	−	0.0324581i
$776$	1.85984	+	10.5477i	0.0667645	+	0.378640i
$777$	−1.16167	−	0.422813i	−0.0416747	−	0.0151683i
$778$	−9.42195			−0.337793
$779$	3.24571	+	5.70334i	0.116290	+	0.204343i
$780$	−3.08978			−0.110632
$781$	−8.41418	−	3.06251i	−0.301083	−	0.109585i
$782$	0.314797	+	1.78530i	0.0112571	+	0.0638423i
$783$	1.06738	+	0.895638i	0.0381450	+	0.0320075i
$784$	−5.32727	+	4.47011i	−0.190259	+	0.159647i
$785$	0.354063	−	2.00799i	0.0126371	−	0.0716683i
$786$	−11.5376	+	19.9838i	−0.411534	+	0.712798i
$787$	11.0969	+	19.2204i	0.395562	+	0.685133i	0.993173	−	0.116653i	$-0.0372166\pi$
$787$	11.0969	+	19.2204i	0.395562	+	0.685133i	−0.597611	+	0.801786i	$0.703883\pi$
$788$	4.09706	−	1.49121i	0.145952	−	0.0531221i
$789$	−27.3836	+	9.96681i	−0.974882	+	0.354828i
$790$	−0.423141	−	0.732901i	−0.0150547	−	0.0260754i
$791$	−0.686324	+	1.18875i	−0.0244029	+	0.0422670i
$792$	−0.209380	+	1.18745i	−0.00743998	+	0.0421942i
$793$	−13.4232	+	11.2634i	−0.476672	+	0.399975i
$794$	−24.3547	−	20.4360i	−0.864316	−	0.725247i
$795$	−1.19342	−	6.76825i	−0.0423264	−	0.240045i
$796$	−0.715987	−	0.260598i	−0.0253775	−	0.00923665i
$797$	−17.6937			−0.626742			−0.313371	−	0.949631i	$-0.601458\pi$
$797$	−17.6937			−0.626742			−0.313371	+	0.949631i	$0.601458\pi$
$798$	−1.17084	−	0.434413i	−0.0414473	−	0.0153781i
$799$	7.28267			0.257642
$800$	−4.25255	−	1.54780i	−0.150350	−	0.0547230i
$801$	0.408251	+	2.31531i	0.0144248	+	0.0818074i
$802$	13.5654	+	11.3827i	0.479010	+	0.401937i
$803$	4.46782	−	3.74895i	0.157666	−	0.132298i
$804$	−3.56516	+	20.2191i	−0.125734	+	0.713071i
$805$	−0.200301	+	0.346931i	−0.00705968	+	0.0122277i
$806$	0.520079	+	0.900804i	0.0183190	+	0.0317295i
$807$	7.02248	−	2.55597i	0.247203	−	0.0899746i
$808$	−6.53513	+	2.37859i	−0.229905	+	0.0836786i
$809$	−18.9412	−	32.8070i	−0.665936	−	1.15343i	−0.979031	−	0.203713i	$-0.934699\pi$
$809$	−18.9412	−	32.8070i	−0.665936	−	1.15343i	0.313095	−	0.949722i	$-0.398634\pi$
$810$	−1.35321	+	2.34382i	−0.0475468	+	0.0823535i
$811$	7.14726	−	40.5341i	0.250974	−	1.42334i	−0.555225	−	0.831700i	$-0.687368\pi$
$811$	7.14726	−	40.5341i	0.250974	−	1.42334i	0.806199	−	0.591644i	$-0.201521\pi$
$812$	−0.0405250	+	0.0340045i	−0.00142215	+	0.00119332i
$813$	4.04541	+	3.39450i	0.141879	+	0.119050i
$814$	0.749273	+	4.24934i	0.0262620	+	0.148939i
$815$	12.0078	+	4.37047i	0.420613	+	0.153091i
$816$	−0.893115			−0.0312653
$817$	−18.2146	+	31.1005i	−0.637249	+	1.08807i
$818$	−5.46886			−0.191214
$819$	−0.811511	−	0.295366i	−0.0283565	−	0.0103209i
$820$	0.180085	+	1.02131i	0.00628883	+	0.0356657i
$821$	−21.0081	−	17.6279i	−0.733189	−	0.615219i	0.197810	−	0.980240i	$-0.436617\pi$
$821$	−21.0081	−	17.6279i	−0.733189	−	0.615219i	−0.930999	+	0.365022i	$0.881062\pi$
$822$	−9.01804	+	7.56704i	−0.314540	+	0.263931i
$823$	−1.40118	+	7.94650i	−0.0488421	+	0.276997i	−0.999441	−	0.0334237i	$-0.989359\pi$
$823$	−1.40118	+	7.94650i	−0.0488421	+	0.276997i	0.950599	+	0.310421i	$0.100470\pi$
$824$	2.02579	−	3.50876i	0.0705716	−	0.122234i
$825$	3.03091	+	5.24969i	0.105523	+	0.182771i
$826$	1.62617	−	0.591876i	0.0565816	−	0.0205940i
$827$	47.4114	−	17.2563i	1.64866	−	0.600061i	0.660135	−	0.751147i	$-0.270499\pi$
$827$	47.4114	−	17.2563i	1.64866	−	0.600061i	0.988521	+	0.151086i	$0.0482770\pi$
$828$	−1.63918	−	2.83914i	−0.0569654	−	0.0986670i
$829$	−4.29639	+	7.44157i	−0.149220	+	0.258456i	−0.930939	−	0.365174i	$-0.881010\pi$
$829$	−4.29639	+	7.44157i	−0.149220	+	0.258456i	0.781719	+	0.623630i	$0.214343\pi$
$830$	−0.957263	+	5.42891i	−0.0332271	+	0.188440i
$831$	−9.22282	+	7.73886i	−0.319936	+	0.268458i
$832$	2.56514	+	2.15240i	0.0889301	+	0.0746212i
$833$	−0.805173	−	4.56636i	−0.0278976	−	0.158215i
$834$	−20.5996	−	7.49765i	−0.713307	−	0.259622i
$835$	−7.44305			−0.257577
$836$	0.730212	+	4.29730i	0.0252549	+	0.148625i
$837$	1.74996			0.0604874
$838$	10.3338	+	3.76120i	0.356976	+	0.129929i
$839$	−5.12470	−	29.0636i	−0.176924	−	1.00339i	−0.935899	−	0.352267i	$-0.885411\pi$
$839$	−5.12470	−	29.0636i	−0.176924	−	1.00339i	0.758975	−	0.651119i	$-0.225700\pi$
$840$	−0.151187	−	0.126861i	−0.00521644	−	0.00437711i
$841$	−22.1684	+	18.6015i	−0.764429	+	0.641432i
$842$	−2.65437	+	15.0537i	−0.0914755	+	0.518783i
$843$	−13.2420	+	22.9358i	−0.456079	+	0.789952i
$844$	7.51472	+	13.0159i	0.258667	+	0.448025i
$845$	1.15691	−	0.421082i	0.0397990	−	0.0144857i
$846$	−12.3758	+	4.50441i	−0.425488	+	0.154865i
$847$	0.106944	+	0.185233i	0.00367465	+	0.00636469i
$848$	−3.72411	+	6.45035i	−0.127887	+	0.221506i
$849$	3.69096	−	20.9325i	0.126673	−	0.718400i
$850$	2.31146	−	1.93954i	0.0792823	−	0.0665258i
$851$	−8.98702	−	7.54101i	−0.308071	−	0.258502i
$852$	2.08274	+	11.8118i	0.0713536	+	0.404666i
$853$	−42.1897	−	15.3558i	−1.44455	−	0.525772i	−0.503485	−	0.864004i	$-0.667949\pi$
$853$	−42.1897	−	15.3558i	−1.44455	−	0.525772i	−0.941063	+	0.338232i	$0.890171\pi$
$854$	−1.11927			−0.0383006
$855$	0.650856	−	3.56156i	0.0222588	−	0.121803i
$856$	−2.39025			−0.0816971
$857$	48.5655	+	17.6764i	1.65896	+	0.603814i	0.990199	−	0.139660i	$-0.0446010\pi$
$857$	48.5655	+	17.6764i	1.65896	+	0.603814i	0.668765	+	0.743474i	$0.266823\pi$
$858$	−0.778871	−	4.41720i	−0.0265902	−	0.150801i
$859$	−3.41005	−	2.86138i	−0.116350	−	0.0976289i	0.582757	−	0.812647i	$-0.301974\pi$
$859$	−3.41005	−	2.86138i	−0.116350	−	0.0976289i	−0.699106	+	0.715018i	$0.746419\pi$
$860$	−4.36332	+	3.66126i	−0.148788	+	0.124848i
$861$	0.0748982	−	0.424769i	0.00255252	−	0.0144761i
$862$	−9.85812	+	17.0748i	−0.335769	+	0.581569i
$863$	−23.2708	−	40.3061i	−0.792146	−	1.37204i	−0.924636	−	0.380853i	$-0.875630\pi$
$863$	−23.2708	−	40.3061i	−0.792146	−	1.37204i	0.132490	−	0.991184i	$-0.457703\pi$
$864$	5.29384	−	1.92680i	0.180100	−	0.0655510i
$865$	13.9691	−	5.08435i	0.474965	−	0.172873i
$866$	−10.4174	−	18.0434i	−0.353997	−	0.613140i
$867$	−11.0879	+	19.2048i	−0.376565	+	0.652230i
$868$	−0.0115372	+	0.0654309i	−0.000391599	+	0.00222087i
$869$	0.941100	−	0.789677i	0.0319246	−	0.0267880i
$870$	0.174826	+	0.146697i	0.00592716	+	0.00497348i
$871$	8.91244	+	50.5450i	0.301987	+	1.71265i
$872$	9.06892	+	3.30082i	0.307112	+	0.111780i
$873$	12.9143			0.437082
$874$	−9.03114	−	7.67422i	−0.305483	−	0.259584i
$875$	1.40348			0.0474464
$876$	−7.34120	−	2.67198i	−0.248036	−	0.0902778i
$877$	−5.81418	−	32.9738i	−0.196331	−	1.11345i	−0.910511	−	0.413485i	$-0.864311\pi$
$877$	−5.81418	−	32.9738i	−0.196331	−	1.11345i	0.714180	−	0.699962i	$-0.246800\pi$
$878$	−12.6251	−	10.5937i	−0.426078	−	0.357522i
$879$	−8.02087	+	6.73031i	−0.270537	+	0.227008i
$880$	−0.119620	+	0.678397i	−0.00403238	+	0.0228688i
$881$	13.7259	−	23.7740i	0.462438	−	0.800966i	−0.536644	−	0.843809i	$-0.680308\pi$
$881$	13.7259	−	23.7740i	0.462438	−	0.800966i	0.999082	+	0.0428425i	$0.0136414\pi$
$882$	4.19261	+	7.26182i	0.141173	+	0.244518i
$883$	5.37928	−	1.95790i	0.181027	−	0.0658885i	−0.249916	−	0.968267i	$-0.580403\pi$
$883$	5.37928	−	1.95790i	0.181027	−	0.0658885i	0.430943	+	0.902379i	$0.358181\pi$
$884$	−2.09802	+	0.763618i	−0.0705642	+	0.0256833i
$885$	−3.73278	−	6.46537i	−0.125476	−	0.217331i
$886$	−0.945398	+	1.63748i	−0.0317613	+	0.0550121i
$887$	5.30746	−	30.1001i	0.178207	−	1.01066i	−0.756170	−	0.654376i	$-0.772932\pi$
$887$	5.30746	−	30.1001i	0.178207	−	1.01066i	0.934377	−	0.356287i	$-0.115957\pi$
$888$	4.42755	−	3.71515i	0.148579	−	0.124672i
$889$	−2.45989	−	2.06409i	−0.0825020	−	0.0692274i
$890$	0.233236	+	1.32275i	0.00781810	+	0.0443386i
$891$	−3.69188	−	1.34373i	−0.123683	−	0.0450168i
$892$	23.3728			0.782578
$893$	−36.6610	+	30.3759i	−1.22681	+	1.01649i
$894$	−9.56758			−0.319988
$895$	0.839076	+	0.305399i	0.0280472	+	0.0102084i
$896$	0.0371414	+	0.210639i	0.00124081	+	0.00703697i
$897$	9.34203	+	7.83890i	0.311921	+	0.261733i
$898$	−11.8575	+	9.94960i	−0.395689	+	0.332022i
$899$	0.0133412	−	0.0756616i	0.000444953	−	0.00252345i
$900$	−2.72834	+	4.72562i	−0.0909445	+	0.157521i
$901$	−2.48308	−	4.30083i	−0.0827235	−	0.143281i
$902$	−1.41469	+	0.514903i	−0.0471039	+	0.0171444i
$903$	2.22609	−	0.810231i	0.0740797	−	0.0269628i
$904$	−3.20879	−	5.55778i	−0.106723	−	0.184849i
$905$	0.269316	−	0.466469i	0.00895237	−	0.0155060i
$906$	1.99251	−	11.3001i	0.0661967	−	0.375420i
$907$	−15.0150	+	12.5991i	−0.498564	+	0.418345i	−0.857084	−	0.515177i	$-0.827726\pi$
$907$	−15.0150	+	12.5991i	−0.498564	+	0.418345i	0.358520	+	0.933522i	$0.383282\pi$
$908$	1.43640	+	1.20529i	0.0476688	+	0.0399988i
$909$	1.45614	+	8.25817i	0.0482971	+	0.273906i
$910$	−0.463621	−	0.168744i	−0.0153689	−	0.00559382i
$911$	−18.8411			−0.624232			−0.312116	−	0.950044i	$-0.601038\pi$
$911$	−18.8411			−0.624232			−0.312116	+	0.950044i	$0.601038\pi$
$912$	4.49595	−	3.72516i	0.148876	−	0.123352i
$913$	−8.00255			−0.264846
$914$	−17.7921	−	6.47579i	−0.588510	−	0.214200i
$915$	0.838471	+	4.75521i	0.0277190	+	0.157202i
$916$	19.9755	+	16.7615i	0.660010	+	0.553815i
$917$	−2.82261	+	2.36845i	−0.0932106	+	0.0782130i
$918$	−0.652264	+	3.69917i	−0.0215279	+	0.122091i
$919$	−24.1485	+	41.8265i	−0.796586	+	1.37973i	0.125241	+	0.992126i	$0.460030\pi$
$919$	−24.1485	+	41.8265i	−0.796586	+	1.37973i	−0.921827	+	0.387601i	$0.873304\pi$
$920$	−0.936472	−	1.62202i	−0.0308746	−	0.0534763i
$921$	−23.5792	+	8.58212i	−0.776961	+	0.282790i
$922$	−3.83168	+	1.39462i	−0.126190	+	0.0459293i
$923$	14.9918	+	25.9665i	0.493460	+	0.854697i
$924$	0.143251	−	0.248118i	0.00471261	−	0.00816248i
$925$	−3.39081	+	19.2302i	−0.111489	+	0.632287i
$926$	−6.89632	+	5.78670i	−0.226627	+	0.190163i
$927$	−3.74233	−	3.14018i	−0.122914	−	0.103137i
$928$	−0.0429488	−	0.243575i	−0.00140986	−	0.00799573i
$929$	−12.1681	−	4.42883i	−0.399223	−	0.145305i	0.134603	−	0.990900i	$-0.457024\pi$
$929$	−12.1681	−	4.42883i	−0.399223	−	0.145305i	−0.533826	+	0.845594i	$0.679246\pi$
$930$	0.286626			0.00939883
$931$	23.0994	+	19.6287i	0.757053	+	0.643306i
$932$	−18.6438			−0.610699
$933$	−14.8800	−	5.41587i	−0.487149	−	0.177308i
$934$	1.38510	+	7.85532i	0.0453220	+	0.257034i
$935$	−0.351848	−	0.295236i	−0.0115067	−	0.00965523i
$936$	3.09296	−	2.59530i	0.101097	−	0.0848301i
$937$	−4.23944	+	24.0431i	−0.138496	+	0.785452i	0.833864	+	0.551969i	$0.186123\pi$
$937$	−4.23944	+	24.0431i	−0.138496	+	0.785452i	−0.972361	+	0.233483i	$0.924988\pi$
$938$	−1.63919	+	2.83915i	−0.0535213	+	0.0927017i
$939$	15.2976	+	26.4961i	0.499217	+	0.864669i
$940$	−7.07035	+	2.57340i	−0.230609	+	0.0839350i
$941$	54.5186	−	19.8432i	1.77726	−	0.646868i	0.777416	−	0.628987i	$-0.216530\pi$
$941$	54.5186	−	19.8432i	1.77726	−	0.646868i	0.999840	−	0.0178818i	$-0.00569227\pi$
$942$	−1.98238	−	3.43358i	−0.0645894	−	0.111872i
$943$	2.04661	−	3.54484i	0.0666470	−	0.115436i
$944$	−1.40495	+	7.96788i	−0.0457273	+	0.259332i
$945$	−0.635857	+	0.533547i	−0.0206844	+	0.0173563i
$946$	−6.33409	−	5.31493i	−0.205939	−	0.172803i
$947$	−3.52636	−	19.9990i	−0.114591	−	0.649879i	−0.986952	−	0.161016i	$-0.948523\pi$
$947$	−3.52636	−	19.9990i	−0.114591	−	0.649879i	0.872361	−	0.488863i	$-0.162588\pi$
$948$	−1.54635	−	0.562824i	−0.0502230	−	0.0182797i
$949$	−19.5298			−0.633965
$950$	−3.54611	+	19.4047i	−0.115051	+	0.629572i
$951$	−15.7119			−0.509492
$952$	−0.134012	−	0.0487762i	−0.00434334	−	0.00158085i
$953$	2.19954	+	12.4742i	0.0712501	+	0.404079i	0.999485	+	0.0320851i	$0.0102147\pi$
$953$	2.19954	+	12.4742i	0.0712501	+	0.404079i	−0.928235	+	0.371994i	$0.878674\pi$
$954$	6.87972	+	5.77277i	0.222739	+	0.186900i
$955$	−5.47817	+	4.59673i	−0.177270	+	0.148747i
$956$	−1.89530	+	10.7488i	−0.0612985	+	0.347641i
$957$	−0.165649	+	0.286913i	−0.00535468	+	0.00927458i
$958$	−3.86639	−	6.69679i	−0.124918	−	0.216364i
$959$	−1.76642	+	0.642923i	−0.0570406	+	0.0207611i
$960$	0.867077	−	0.315590i	0.0279848	−	0.0101856i
$961$	15.4518	+	26.7632i	0.498444	+	0.863330i
$962$	7.22431	−	12.5129i	0.232921	−	0.403431i
$963$	−0.500470	+	2.83831i	−0.0161274	+	0.0914631i
$964$	9.20340	−	7.72257i	0.296421	−	0.248727i
$965$	−4.18850	−	3.51457i	−0.134833	−	0.113138i
$966$	0.135266	+	0.767133i	0.00435212	+	0.0246821i
$967$	36.7919	+	13.3912i	1.18315	+	0.430631i	0.857313	−	0.514796i	$-0.172132\pi$
$967$	36.7919	+	13.3912i	1.18315	+	0.430631i	0.325835	+	0.945427i	$0.394355\pi$
$968$	−1.00000			−0.0321412
$969$	0.652163	+	3.83798i	0.0209505	+	0.123294i
$970$	7.37800			0.236893
$971$	−38.8652	−	14.1458i	−1.24724	−	0.453959i	−0.367773	−	0.929915i	$-0.619880\pi$
$971$	−38.8652	−	14.1458i	−1.24724	−	0.453959i	−0.879469	+	0.475956i	$0.842102\pi$
$972$	−2.02094	−	11.4613i	−0.0648218	−	0.367622i
$973$	−2.68149	−	2.25004i	−0.0859647	−	0.0721329i
$974$	28.7242	−	24.1025i	0.920382	−	0.772293i
$975$	3.52476	−	19.9899i	0.112883	−	0.640189i
$976$	2.61647	−	4.53186i	0.0837512	−	0.145061i
$977$	−26.9209	−	46.6283i	−0.861274	−	1.49177i	−0.870700	−	0.491815i	$-0.836334\pi$
$977$	−26.9209	−	46.6283i	−0.861274	−	1.49177i	0.00942521	−	0.999956i	$-0.497000\pi$
$978$	23.3490	−	8.49834i	0.746619	−	0.271747i
$979$	−1.83223	+	0.666875i	−0.0585582	+	0.0213134i
$980$	2.39526	+	4.14872i	0.0765139	+	0.132526i
$981$	5.81841	−	10.0778i	0.185767	−	0.321759i
$982$	−3.19527	+	18.1213i	−0.101965	+	0.578273i
$983$	17.8367	−	14.9667i	0.568901	−	0.477365i	−0.312380	−	0.949957i	$-0.601126\pi$
$983$	17.8367	−	14.9667i	0.568901	−	0.477365i	0.881281	+	0.472593i	$0.156682\pi$
$984$	1.54478	+	1.29623i	0.0492459	+	0.0413222i
$985$	−0.521543	−	2.95782i	−0.0166177	−	0.0942438i
$986$	0.154965	+	0.0564028i	0.00493510	+	0.00179623i
$987$	3.12932			0.0996073
$988$	7.37643	−	12.5949i	0.234676	−	0.400696i
$989$	22.4813			0.714865
$990$	0.780518	+	0.284085i	0.0248065	+	0.00902882i
$991$	−3.58008	−	20.3036i	−0.113725	−	0.644966i	−0.987374	−	0.158409i	$-0.949364\pi$
$991$	−3.58008	−	20.3036i	−0.113725	−	0.644966i	0.873649	−	0.486557i	$-0.161747\pi$
$992$	−0.237956	−	0.199669i	−0.00755512	−	0.00633950i
$993$	8.02447	−	6.73333i	0.254649	−	0.213676i
$994$	−0.332571	+	1.88610i	−0.0105485	+	0.0598236i
$995$	−0.262435	+	0.454551i	−0.00831975	+	0.0144102i
$996$	5.35966	+	9.28321i	0.169827	+	0.294150i
$997$	−36.2041	+	13.1772i	−1.14659	+	0.417326i	−0.844291	−	0.535885i	$-0.819978\pi$
$997$	−36.2041	+	13.1772i	−1.14659	+	0.417326i	−0.302304	+	0.953212i	$0.597756\pi$
$998$	−16.7129	+	6.08300i	−0.529038	+	0.192554i
$999$	−12.1541	−	21.0516i	−0.384540	−	0.666043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.a.23.2	✓	24
19.5	even	9	inner	418.2.j.a.309.2	yes	24
19.9	even	9		7942.2.a.bt.1.4		12
19.10	odd	18		7942.2.a.bx.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.a.23.2	✓	24	1.1	even	1	trivial
418.2.j.a.309.2	yes	24	19.5	even	9	inner
7942.2.a.bt.1.4		12	19.9	even	9
7942.2.a.bx.1.9		12	19.10	odd	18

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.232600 - 1.31914i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.527700 - 0.442792i) q^{5} +(0.232600 - 1.31914i) q^{6} +(0.106944 - 0.185233i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.13305 - 0.412397i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.232600 - 1.31914i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.527700 - 0.442792i) q^{5} +(0.232600 - 1.31914i) q^{6} +(0.106944 - 0.185233i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.13305 - 0.412397i) q^{9} +(0.647319 - 0.235605i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.669744 - 1.16003i) q^{12} +(0.581469 - 3.29767i) q^{13} +(0.163848 - 0.137485i) q^{14} +(-0.706848 - 0.593116i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.626548 - 0.228045i) q^{17} +1.20577 q^{18} +(4.10521 - 1.46534i) q^{19} +0.688863 q^{20} +(-0.269224 - 0.0979894i) q^{21} +(0.173648 + 0.984808i) q^{22} +(-2.08279 - 1.74767i) q^{23} +(1.02611 - 0.861007i) q^{24} +(-0.785839 + 4.45672i) q^{25} +(1.67427 - 2.89993i) q^{26} +(-2.81679 - 4.87882i) q^{27} +(0.200990 - 0.0731543i) q^{28} +(-0.232416 + 0.0845926i) q^{29} +(-0.461362 - 0.799103i) q^{30} +(-0.155315 + 0.269013i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(1.02611 - 0.861007i) q^{33} +(-0.510766 - 0.428584i) q^{34} +(-0.0255853 - 0.145102i) q^{35} +(1.13305 + 0.412397i) q^{36} +4.31489 q^{37} +(4.35881 + 0.0271001i) q^{38} -4.48534 q^{39} +(0.647319 + 0.235605i) q^{40} +(0.261423 + 1.48261i) q^{41} +(-0.219473 - 0.184160i) q^{42} +(-6.33409 + 5.31493i) q^{43} +(-0.173648 + 0.984808i) q^{44} +(0.415305 - 0.719329i) q^{45} +(-1.35945 - 2.35463i) q^{46} +(-10.2638 + 3.73572i) q^{47} +(1.25871 - 0.458132i) q^{48} +(3.47713 + 6.02256i) q^{49} +(-2.26273 + 3.91917i) q^{50} +(-0.155088 + 0.879547i) q^{51} +(2.56514 - 2.15240i) q^{52} +(5.70567 + 4.78763i) q^{53} +(-0.978261 - 5.54799i) q^{54} +(0.647319 + 0.235605i) q^{55} +0.213889 q^{56} +(-2.88786 - 5.07451i) q^{57} -0.247332 q^{58} +(7.60286 + 2.76721i) q^{59} +(-0.160229 - 0.908706i) q^{60} +(-4.00867 - 3.36367i) q^{61} +(-0.237956 + 0.199669i) q^{62} +(0.0447840 - 0.253982i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.15334 - 1.99765i) q^{65} +(1.25871 - 0.458132i) q^{66} +(-14.4031 + 5.24230i) q^{67} +(-0.333379 - 0.577430i) q^{68} +(-1.82096 + 3.15400i) q^{69} +(0.0255853 - 0.145102i) q^{70} +(-6.85930 + 5.75564i) q^{71} +(0.923673 + 0.775054i) q^{72} +(-1.01277 - 5.74372i) q^{73} +(4.05467 + 1.47578i) q^{74} +6.06181 q^{75} +(4.08668 + 1.51627i) q^{76} +0.213889 q^{77} +(-4.21484 - 1.53408i) q^{78} +(-0.213330 - 1.20986i) q^{79} +(0.527700 + 0.442792i) q^{80} +(-3.00965 + 2.52539i) q^{81} +(-0.261423 + 1.48261i) q^{82} +(-4.00128 + 6.93041i) q^{83} +(-0.143251 - 0.248118i) q^{84} +(-0.431605 + 0.157092i) q^{85} +(-7.76991 + 2.82802i) q^{86} +(0.165649 + 0.286913i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-0.338582 + 1.92019i) q^{89} +(0.636284 - 0.533906i) q^{90} +(-0.548654 - 0.460375i) q^{91} +(-0.472131 - 2.67759i) q^{92} +(0.390992 + 0.142310i) q^{93} -10.9225 q^{94} +(1.51748 - 2.59102i) q^{95} +1.33949 q^{96} +(10.0645 + 3.66318i) q^{97} +(1.20759 + 6.84860i) q^{98} +(0.923673 + 0.775054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Introduction

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