LMFDB - Embedded newform 429.2.s.a.166.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.s (of order $6$, degree $2$, 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.2
Character	$\chi$	$=$	429.166
Dual form			429.2.s.a.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91936 + 1.10815i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.45597 - 2.52182i) q^{4} -0.692237i q^{5} +(-1.91936 - 1.10815i) q^{6} +(2.81071 + 1.62277i) q^{7} +2.02113i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.91936 + 1.10815i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.45597 - 2.52182i) q^{4} -0.692237i q^{5} +(-1.91936 - 1.10815i) q^{6} +(2.81071 + 1.62277i) q^{7} +2.02113i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.767100 + 1.32866i) q^{10} +(-0.866025 + 0.500000i) q^{11} +2.91194 q^{12} +(0.552093 - 3.56303i) q^{13} -7.19305 q^{14} +(0.599495 - 0.346119i) q^{15} +(0.672235 + 1.16434i) q^{16} +(2.74190 - 4.74912i) q^{17} -2.21629i q^{18} +(4.24831 + 2.45276i) q^{19} +(-1.74570 - 1.00788i) q^{20} +3.24553i q^{21} +(1.10815 - 1.91936i) q^{22} +(3.07703 + 5.32957i) q^{23} +(-1.75035 + 1.01057i) q^{24} +4.52081 q^{25} +(2.88869 + 7.45055i) q^{26} -1.00000 q^{27} +(8.18464 - 4.72541i) q^{28} +(-0.313126 - 0.542349i) q^{29} +(-0.767100 + 1.32866i) q^{30} -1.11589i q^{31} +(-6.08123 - 3.51100i) q^{32} +(-0.866025 - 0.500000i) q^{33} +12.1537i q^{34} +(1.12334 - 1.94568i) q^{35} +(1.45597 + 2.52182i) q^{36} +(-5.80260 + 3.35013i) q^{37} -10.8721 q^{38} +(3.36172 - 1.30339i) q^{39} +1.39910 q^{40} +(-5.53845 + 3.19762i) q^{41} +(-3.59652 - 6.22936i) q^{42} +(-0.752624 + 1.30358i) q^{43} +2.91194i q^{44} +(0.599495 + 0.346119i) q^{45} +(-11.8119 - 6.81959i) q^{46} +11.1846i q^{47} +(-0.672235 + 1.16434i) q^{48} +(1.76674 + 3.06009i) q^{49} +(-8.67707 + 5.00971i) q^{50} +5.48381 q^{51} +(-8.18148 - 6.57995i) q^{52} +3.70165 q^{53} +(1.91936 - 1.10815i) q^{54} +(0.346119 + 0.599495i) q^{55} +(-3.27983 + 5.68083i) q^{56} +4.90553i q^{57} +(1.20200 + 0.693977i) q^{58} +(3.35560 + 1.93735i) q^{59} -2.01576i q^{60} +(7.33077 - 12.6973i) q^{61} +(1.23657 + 2.14181i) q^{62} +(-2.81071 + 1.62277i) q^{63} +12.8739 q^{64} +(-2.46646 - 0.382179i) q^{65} +2.21629 q^{66} +(-10.4703 + 6.04506i) q^{67} +(-7.98427 - 13.8292i) q^{68} +(-3.07703 + 5.32957i) q^{69} +4.97930i q^{70} +(4.44548 + 2.56660i) q^{71} +(-1.75035 - 1.01057i) q^{72} +12.1349i q^{73} +(7.42486 - 12.8602i) q^{74} +(2.26040 + 3.91513i) q^{75} +(12.3708 - 7.14231i) q^{76} -3.24553 q^{77} +(-5.00802 + 6.22696i) q^{78} -2.59448 q^{79} +(0.806003 - 0.465346i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.08686 - 12.2748i) q^{82} -9.59617i q^{83} +(8.18464 + 4.72541i) q^{84} +(-3.28752 - 1.89805i) q^{85} -3.33607i q^{86} +(0.313126 - 0.542349i) q^{87} +(-1.01057 - 1.75035i) q^{88} +(11.9750 - 6.91375i) q^{89} -1.53420 q^{90} +(7.33374 - 9.11875i) q^{91} +17.9203 q^{92} +(0.966393 - 0.557947i) q^{93} +(-12.3942 - 21.4673i) q^{94} +(1.69790 - 2.94084i) q^{95} -7.02200i q^{96} +(-2.75197 - 1.58885i) q^{97} +(-6.78205 - 3.91562i) q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	−1.91936	+	1.10815i	−1.35720	+	0.783577i	−0.989245	−	0.146268i	$-0.953274\pi$
$2$	−1.91936	+	1.10815i	−1.35720	+	0.783577i	−0.367950	+	0.929845i	$0.619940\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.45597	−	2.52182i	0.727986	−	1.26091i
$5$		−	0.692237i		−	0.309578i	−0.987948	−	0.154789i	$-0.950530\pi$
$5$		−	0.692237i		−	0.309578i	0.987948	−	0.154789i	$-0.0494698\pi$
$6$	−1.91936	−	1.10815i	−0.783577	−	0.452398i
$7$	2.81071	+	1.62277i	1.06235	+	0.613348i	0.926081	−	0.377324i	$-0.123156\pi$
$7$	2.81071	+	1.62277i	1.06235	+	0.613348i	0.136269	+	0.990672i	$0.456489\pi$
$8$			2.02113i			0.714579i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.767100	+	1.32866i	0.242578	+	0.420158i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	2.91194			0.840606
$13$	0.552093	−	3.56303i	0.153123	−	0.988207i
$13$	0.552093	−	3.56303i	0.153123	−	0.988207i
$14$	−7.19305			−1.92242
$15$	0.599495	−	0.346119i	0.154789	−	0.0893675i
$16$	0.672235	+	1.16434i	0.168059	+	0.291086i
$17$	2.74190	−	4.74912i	0.665009	−	1.15183i	−0.314273	−	0.949333i	$-0.601761\pi$
$17$	2.74190	−	4.74912i	0.665009	−	1.15183i	0.979283	−	0.202497i	$-0.0649058\pi$
$18$		−	2.21629i		−	0.522385i
$19$	4.24831	+	2.45276i	0.974630	+	0.562703i	0.900645	−	0.434557i	$-0.143095\pi$
$19$	4.24831	+	2.45276i	0.974630	+	0.562703i	0.0739852	+	0.997259i	$0.476428\pi$
$20$	−1.74570	−	1.00788i	−0.390350	−	0.225368i
$21$			3.24553i			0.708234i
$22$	1.10815	−	1.91936i	0.236257	−	0.409210i
$23$	3.07703	+	5.32957i	0.641605	+	1.11129i	0.985074	+	0.172129i	$0.0550646\pi$
$23$	3.07703	+	5.32957i	0.641605	+	1.11129i	−0.343469	+	0.939164i	$0.611602\pi$
$24$	−1.75035	+	1.01057i	−0.357289	+	0.206281i
$25$	4.52081			0.904161
$26$	2.88869	+	7.45055i	0.566519	+	1.46117i
$27$	−1.00000			−0.192450
$28$	8.18464	−	4.72541i	1.54675	−	0.893018i
$29$	−0.313126	−	0.542349i	−0.0581460	−	0.100712i	0.835487	−	0.549510i	$-0.185186\pi$
$29$	−0.313126	−	0.542349i	−0.0581460	−	0.100712i	−0.893633	+	0.448798i	$0.851852\pi$
$30$	−0.767100	+	1.32866i	−0.140053	+	0.242578i
$31$		−	1.11589i		−	0.200421i	−0.994966	−	0.100210i	$-0.968048\pi$
$31$		−	1.11589i		−	0.200421i	0.994966	−	0.100210i	$-0.0319515\pi$
$32$	−6.08123	−	3.51100i	−1.07502	−	0.620663i
$33$	−0.866025	−	0.500000i	−0.150756	−	0.0870388i
$34$			12.1537i			2.08434i
$35$	1.12334	−	1.94568i	0.189879	−	0.328880i
$36$	1.45597	+	2.52182i	0.242662	+	0.420303i
$37$	−5.80260	+	3.35013i	−0.953941	+	0.550758i	−0.894303	−	0.447462i	$-0.852328\pi$
$37$	−5.80260	+	3.35013i	−0.953941	+	0.550758i	−0.0596379	+	0.998220i	$0.518995\pi$
$38$	−10.8721			−1.76368
$39$	3.36172	−	1.30339i	0.538306	−	0.208709i
$40$	1.39910			0.221218
$41$	−5.53845	+	3.19762i	−0.864960	+	0.499385i	−0.865670	−	0.500615i	$-0.833107\pi$
$41$	−5.53845	+	3.19762i	−0.864960	+	0.499385i	0.000710120		1.00000i	$0.499774\pi$
$42$	−3.59652	−	6.22936i	−0.554956	−	0.961211i
$43$	−0.752624	+	1.30358i	−0.114774	+	0.198795i	−0.917689	−	0.397299i	$-0.869948\pi$
$43$	−0.752624	+	1.30358i	−0.114774	+	0.198795i	0.802915	+	0.596093i	$0.203281\pi$
$44$			2.91194i			0.438992i
$45$	0.599495	+	0.346119i	0.0893675	+	0.0515963i
$46$	−11.8119	−	6.81959i	−1.74157	−	1.00549i
$47$			11.1846i			1.63144i	0.578445	+	0.815722i	$0.303660\pi$
$47$			11.1846i			1.63144i	−0.578445	+	0.815722i	$0.696340\pi$
$48$	−0.672235	+	1.16434i	−0.0970287	+	0.168059i
$49$	1.76674	+	3.06009i	0.252392	+	0.437156i
$50$	−8.67707	+	5.00971i	−1.22712	+	0.708480i
$51$	5.48381			0.767887
$52$	−8.18148	−	6.57995i	−1.13457	−	0.912475i
$53$	3.70165			0.508461			0.254231	−	0.967144i	$-0.418178\pi$
$53$	3.70165			0.508461			0.254231	+	0.967144i	$0.418178\pi$
$54$	1.91936	−	1.10815i	0.261192	−	0.150799i
$55$	0.346119	+	0.599495i	0.0466706	+	0.0808359i
$56$	−3.27983	+	5.68083i	−0.438285	+	0.759133i
$57$			4.90553i			0.649753i
$58$	1.20200	+	0.693977i	0.157831	+	0.0911237i
$59$	3.35560	+	1.93735i	0.436861	+	0.252222i	0.702265	−	0.711915i	$-0.252172\pi$
$59$	3.35560	+	1.93735i	0.436861	+	0.252222i	−0.265404	+	0.964137i	$0.585505\pi$
$60$		−	2.01576i		−	0.260233i
$61$	7.33077	−	12.6973i	0.938609	−	1.62572i	0.170541	−	0.985351i	$-0.445449\pi$
$61$	7.33077	−	12.6973i	0.938609	−	1.62572i	0.768068	−	0.640368i	$-0.221218\pi$
$62$	1.23657	+	2.14181i	0.157045	+	0.272010i
$63$	−2.81071	+	1.62277i	−0.354117	+	0.204449i
$64$	12.8739			1.60923
$65$	−2.46646	−	0.382179i	−0.305927	−	0.0474035i
$66$	2.21629			0.272807
$67$	−10.4703	+	6.04506i	−1.27916	+	0.738522i	−0.976693	−	0.214639i	$-0.931142\pi$
$67$	−10.4703	+	6.04506i	−1.27916	+	0.738522i	−0.302463	+	0.953161i	$0.597809\pi$
$68$	−7.98427	−	13.8292i	−0.968235	−	1.67703i
$69$	−3.07703	+	5.32957i	−0.370431	+	0.641605i
$70$			4.97930i			0.595140i
$71$	4.44548	+	2.56660i	0.527581	+	0.304599i	0.740031	−	0.672573i	$-0.234811\pi$
$71$	4.44548	+	2.56660i	0.527581	+	0.304599i	−0.212450	+	0.977172i	$0.568144\pi$
$72$	−1.75035	−	1.01057i	−0.206281	−	0.119096i
$73$			12.1349i			1.42028i	0.704062	+	0.710139i	$0.251368\pi$
$73$			12.1349i			1.42028i	−0.704062	+	0.710139i	$0.748632\pi$
$74$	7.42486	−	12.8602i	0.863123	−	1.49497i
$75$	2.26040	+	3.91513i	0.261009	+	0.452081i
$76$	12.3708	−	7.14231i	1.41903	−	0.819279i
$77$	−3.24553			−0.369863
$78$	−5.00802	+	6.22696i	−0.567047	+	0.705064i
$79$	−2.59448			−0.291901			−0.145951	−	0.989292i	$-0.546624\pi$
$79$	−2.59448			−0.291901			−0.145951	+	0.989292i	$0.546624\pi$
$80$	0.806003	−	0.465346i	0.0901139	−	0.0520273i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.08686	−	12.2748i	0.782613	−	1.35553i
$83$		−	9.59617i		−	1.05332i	−0.850077	−	0.526658i	$-0.823445\pi$
$83$		−	9.59617i		−	1.05332i	0.850077	−	0.526658i	$-0.176555\pi$
$84$	8.18464	+	4.72541i	0.893018	+	0.515584i
$85$	−3.28752	−	1.89805i	−0.356581	−	0.205872i
$86$		−	3.33607i		−	0.359737i
$87$	0.313126	−	0.542349i	0.0335706	−	0.0581460i
$88$	−1.01057	−	1.75035i	−0.107727	−	0.186588i
$89$	11.9750	−	6.91375i	1.26934	−	0.732856i	0.294479	−	0.955658i	$-0.404854\pi$
$89$	11.9750	−	6.91375i	1.26934	−	0.732856i	0.974864	+	0.222802i	$0.0715204\pi$
$90$	−1.53420			−0.161719
$91$	7.33374	−	9.11875i	0.768785	−	0.955904i
$92$	17.9203			1.86832
$93$	0.966393	−	0.557947i	0.100210	−	0.0578564i
$94$	−12.3942	−	21.4673i	−1.27836	−	2.21419i
$95$	1.69790	−	2.94084i	0.174200	−	0.301724i
$96$		−	7.02200i		−	0.716680i
$97$	−2.75197	−	1.58885i	−0.279420	−	0.161323i	0.353741	−	0.935344i	$-0.384910\pi$
$97$	−2.75197	−	1.58885i	−0.279420	−	0.161323i	−0.633161	+	0.774020i	$0.718243\pi$
$98$	−6.78205	−	3.91562i	−0.685091	−	0.395537i
$99$		−	1.00000i		−	0.100504i
$100$	6.58217	−	11.4007i	0.658217	−	1.14007i
$101$	6.61180	+	11.4520i	0.657899	+	1.13951i	0.981159	+	0.193204i	$0.0618880\pi$
$101$	6.61180	+	11.4520i	0.657899	+	1.13951i	−0.323260	+	0.946310i	$0.604779\pi$
$102$	−10.5254	+	6.07686i	−1.04217	+	0.601698i
$103$	−8.01531			−0.789772			−0.394886	−	0.918730i	$-0.629216\pi$
$103$	−8.01531			−0.789772			−0.394886	+	0.918730i	$0.629216\pi$
$104$	7.20136	+	1.11585i	0.706152	+	0.109418i
$105$	2.24668			0.219254
$106$	−7.10482	+	4.10197i	−0.690081	+	0.398418i
$107$	−4.46785	−	7.73854i	−0.431923	−	0.748113i	0.565116	−	0.825012i	$-0.308831\pi$
$107$	−4.46785	−	7.73854i	−0.431923	−	0.748113i	−0.997039	+	0.0768988i	$0.975498\pi$
$108$	−1.45597	+	2.52182i	−0.140101	+	0.242662i
$109$		−	18.4472i		−	1.76692i	−0.468509	−	0.883459i	$-0.655209\pi$
$109$		−	18.4472i		−	1.76692i	0.468509	−	0.883459i	$-0.344791\pi$
$110$	−1.32866	−	0.767100i	−0.126682	−	0.0731401i
$111$	−5.80260	−	3.35013i	−0.550758	−	0.317980i
$112$			4.36352i			0.412314i
$113$	2.24564	−	3.88957i	0.211252	−	0.365900i	−0.740854	−	0.671666i	$-0.765579\pi$
$113$	2.24564	−	3.88957i	0.211252	−	0.365900i	0.952107	+	0.305766i	$0.0989125\pi$
$114$	−5.43604	−	9.41550i	−0.509132	−	0.881842i
$115$	3.68933	−	2.13004i	0.344032	−	0.198627i
$116$	−1.82361			−0.169318
$117$	2.80963	+	2.25964i	0.259750	+	0.208904i
$118$	−8.58748			−0.790542
$119$	15.4134	−	8.89894i	1.41295	−	0.815765i
$120$	0.699552	+	1.21166i	0.0638601	+	0.110609i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$			32.4942i			2.94189i
$123$	−5.53845	−	3.19762i	−0.499385	−	0.288320i
$124$	−2.81408	−	1.62471i	−0.252712	−	0.145903i
$125$		−	6.59066i		−	0.589486i
$126$	3.59652	−	6.22936i	0.320404	−	0.554956i
$127$	−6.02676	−	10.4386i	−0.534788	−	0.926280i	−0.999174	−	0.0406470i	$-0.987058\pi$
$127$	−6.02676	−	10.4386i	−0.534788	−	0.926280i	0.464385	−	0.885633i	$-0.346275\pi$
$128$	−12.5472	+	7.24410i	−1.10902	+	0.640294i
$129$	−1.50525			−0.132530
$130$	5.15755	−	1.99966i	0.452347	−	0.175382i
$131$	14.9458			1.30582			0.652909	−	0.757436i	$-0.273548\pi$
$131$	14.9458			1.30582			0.652909	+	0.757436i	$0.273548\pi$
$132$	−2.52182	+	1.45597i	−0.219496	+	0.126726i
$133$	7.96053	+	13.7880i	0.690265	+	1.19557i
$134$	13.3976	−	23.2053i	1.15738	−	2.00464i
$135$			0.692237i			0.0595783i
$136$	9.59860	+	5.54175i	0.823073	+	0.475201i
$137$	−14.0947	−	8.13757i	−1.20419	−	0.695240i	−0.242706	−	0.970100i	$-0.578035\pi$
$137$	−14.0947	−	8.13757i	−1.20419	−	0.695240i	−0.961484	+	0.274860i	$0.911368\pi$
$138$		−	13.6392i		−	1.16104i
$139$	2.62601	−	4.54839i	0.222735	−	0.385789i	−0.732902	−	0.680334i	$-0.761835\pi$
$139$	2.62601	−	4.54839i	0.222735	−	0.385789i	0.955638	+	0.294545i	$0.0951681\pi$
$140$	−3.27110	−	5.66572i	−0.276459	−	0.478840i
$141$	−9.68616	+	5.59231i	−0.815722	+	0.470957i
$142$	−11.3767			−0.954707
$143$	1.30339	+	3.36172i	0.108995	+	0.281121i
$144$	−1.34447			−0.112039
$145$	−0.375435	+	0.216757i	−0.0311781	+	0.0180007i
$146$	−13.4472	−	23.2912i	−1.11290	−	1.92759i
$147$	−1.76674	+	3.06009i	−0.145719	+	0.252392i
$148$			19.5108i			1.60378i
$149$	−8.26702	−	4.77297i	−0.677261	−	0.391017i	0.121562	−	0.992584i	$-0.461210\pi$
$149$	−8.26702	−	4.77297i	−0.677261	−	0.391017i	−0.798822	+	0.601567i	$0.794543\pi$
$150$	−8.67707	−	5.00971i	−0.708480	−	0.409041i
$151$			17.6961i			1.44009i	0.693927	+	0.720046i	$0.255879\pi$
$151$			17.6961i			1.44009i	−0.693927	+	0.720046i	$0.744121\pi$
$152$	−4.95736	+	8.58641i	−0.402095	+	0.696449i
$153$	2.74190	+	4.74912i	0.221670	+	0.383943i
$154$	6.22936	−	3.59652i	0.501976	−	0.289816i
$155$	−0.772464			−0.0620458
$156$	1.60766	−	10.3753i	0.128716	−	0.830693i
$157$	3.37268			0.269169			0.134585	−	0.990902i	$-0.457030\pi$
$157$	3.37268			0.269169			0.134585	+	0.990902i	$0.457030\pi$
$158$	4.97975	−	2.87506i	0.396167	−	0.228727i
$159$	1.85083	+	3.20573i	0.146780	+	0.254231i
$160$	−2.43045	+	4.20966i	−0.192144	+	0.332803i
$161$			19.9732i			1.57411i
$162$	1.91936	+	1.10815i	0.150799	+	0.0870641i
$163$	3.11456	+	1.79819i	0.243951	+	0.140845i	0.616991	−	0.786970i	$-0.288351\pi$
$163$	3.11456	+	1.79819i	0.243951	+	0.140845i	−0.373040	+	0.927815i	$0.621685\pi$
$164$			18.6226i			1.45418i
$165$	−0.346119	+	0.599495i	−0.0269453	+	0.0466706i
$166$	10.6340	+	18.4185i	0.825355	+	1.42956i
$167$	7.77828	−	4.49079i	0.601901	−	0.347508i	−0.167888	−	0.985806i	$-0.553695\pi$
$167$	7.77828	−	4.49079i	0.601901	−	0.347508i	0.769789	+	0.638298i	$0.220361\pi$
$168$	−6.55966			−0.506088
$169$	−12.3904	−	3.93425i	−0.953107	−	0.302634i
$170$	8.41325			0.645267
$171$	−4.24831	+	2.45276i	−0.324877	+	0.187568i
$172$	2.19160	+	3.79596i	0.167108	+	0.289439i
$173$	−0.421913	+	0.730775i	−0.0320775	+	0.0555598i	−0.881618	−	0.471963i	$-0.843546\pi$
$173$	−0.421913	+	0.730775i	−0.0320775	+	0.0555598i	0.849541	+	0.527523i	$0.176879\pi$
$174$			1.38795i			0.105221i
$175$	12.7067	+	7.33622i	0.960536	+	0.554566i
$176$	−1.16434	−	0.672235i	−0.0877658	−	0.0506716i
$177$			3.87471i			0.291241i
$178$	−15.3229	+	26.5400i	−1.14850	+	1.98926i
$179$	−5.66097	−	9.80509i	−0.423121	−	0.732867i	0.573122	−	0.819470i	$-0.305732\pi$
$179$	−5.66097	−	9.80509i	−0.423121	−	0.732867i	−0.996243	+	0.0866032i	$0.972399\pi$
$180$	1.74570	−	1.00788i	0.130117	−	0.0751228i
$181$	−14.0009			−1.04068			−0.520339	−	0.853960i	$-0.674195\pi$
$181$	−14.0009			−1.04068			−0.520339	+	0.853960i	$0.674195\pi$
$182$	−3.97123	+	25.6290i	−0.294367	+	1.89975i
$183$	14.6615			1.08381
$184$	−10.7718	+	6.21909i	−0.794106	+	0.458477i
$185$	2.31909	+	4.01677i	0.170503	+	0.295319i
$186$	−1.23657	+	2.14181i	−0.0906699	+	0.157045i
$187$			5.48381i			0.401016i
$188$	28.2055	+	16.2845i	2.05710	+	1.18767i
$189$	−2.81071	−	1.62277i	−0.204449	−	0.118039i
$190$			7.52606i			0.545998i
$191$	−1.92927	+	3.34159i	−0.139597	+	0.241789i	−0.927344	−	0.374210i	$-0.877914\pi$
$191$	−1.92927	+	3.34159i	−0.139597	+	0.241789i	0.787747	+	0.615999i	$0.211247\pi$
$192$	6.43693	+	11.1491i	0.464545	+	0.804616i
$193$	−22.2605	+	12.8521i	−1.60235	+	0.925115i	−0.611330	+	0.791376i	$0.709365\pi$
$193$	−22.2605	+	12.8521i	−1.60235	+	0.925115i	−0.991017	+	0.133739i	$0.957302\pi$
$194$	7.04271			0.505637
$195$	−0.902255	−	2.32711i	−0.0646118	−	0.166648i
$196$	10.2893			0.734952
$197$	1.93619	−	1.11786i	0.137948	−	0.0796443i	−0.429438	−	0.903096i	$-0.641288\pi$
$197$	1.93619	−	1.11786i	0.137948	−	0.0796443i	0.567386	+	0.823452i	$0.307955\pi$
$198$	1.10815	+	1.91936i	0.0787525	+	0.136403i
$199$	5.09506	−	8.82490i	0.361179	−	0.625581i	−0.626976	−	0.779039i	$-0.715708\pi$
$199$	5.09506	−	8.82490i	0.361179	−	0.625581i	0.988155	+	0.153458i	$0.0490409\pi$
$200$			9.13715i			0.646094i
$201$	−10.4703	−	6.04506i	−0.738522	−	0.426386i
$202$	−25.3809	−	14.6537i	−1.78580	−	1.03103i
$203$		−	2.03252i		−	0.142655i
$204$	7.98427	−	13.8292i	0.559011	−	0.968235i
$205$	2.21351	+	3.83392i	0.154599	+	0.267773i
$206$	15.3843	−	8.88213i	1.07188	−	0.618847i
$207$	−6.15406			−0.427737
$208$	4.51973	−	1.75237i	0.313387	−	0.121505i
$209$	−4.90553			−0.339323
$210$	−4.31220	+	2.48965i	−0.297570	+	0.171802i
$211$	4.22075	+	7.31056i	0.290569	+	0.503280i	0.973944	−	0.226787i	$-0.0728222\pi$
$211$	4.22075	+	7.31056i	0.290569	+	0.503280i	−0.683376	+	0.730067i	$0.739489\pi$
$212$	5.38950	−	9.33489i	0.370153	−	0.641123i
$213$			5.13320i			0.351721i
$214$	17.1509	+	9.90205i	1.17241	+	0.676890i
$215$	0.902389	+	0.520995i	0.0615424	+	0.0355315i
$216$		−	2.02113i		−	0.137521i
$217$	1.81084	−	3.13646i	0.122928	−	0.212917i
$218$	20.4421	+	35.4068i	1.38452	+	2.39805i
$219$	−10.5091	+	6.06743i	−0.710139	+	0.409999i
$220$	2.01576			0.135902
$221$	−15.4075	−	12.3914i	−1.03642	−	0.833539i
$222$	14.8497			0.996648
$223$	12.1286	−	7.00246i	0.812193	−	0.468920i	−0.0355241	−	0.999369i	$-0.511310\pi$
$223$	12.1286	−	7.00246i	0.812193	−	0.468920i	0.847717	+	0.530449i	$0.177977\pi$
$224$	−11.3951	−	19.7368i	−0.761365	−	1.31872i
$225$	−2.26040	+	3.91513i	−0.150694	+	0.261009i
$226$			9.95399i			0.662130i
$227$	−21.5290	−	12.4298i	−1.42893	−	0.824994i	−0.431895	−	0.901924i	$-0.642155\pi$
$227$	−21.5290	−	12.4298i	−1.42893	−	0.824994i	−0.997037	+	0.0769294i	$0.975488\pi$
$228$	12.3708	+	7.14231i	0.819279	+	0.473011i
$229$		−	10.0723i		−	0.665598i	−0.942998	−	0.332799i	$-0.892007\pi$
$229$		−	10.0723i		−	0.665598i	0.942998	−	0.332799i	$-0.107993\pi$
$230$	−4.72078	+	8.17663i	−0.311279	+	0.539151i
$231$	−1.62277	−	2.81071i	−0.106770	−	0.184931i
$232$	1.09616	−	0.632869i	0.0719665	−	0.0415499i
$233$	2.63682			0.172744			0.0863719	−	0.996263i	$-0.472473\pi$
$233$	2.63682			0.172744			0.0863719	+	0.996263i	$0.472473\pi$
$234$	−7.89671	−	1.22360i	−0.516224	−	0.0799891i
$235$	7.74241			0.505059
$236$	9.77131	−	5.64147i	0.636058	−	0.367228i
$237$	−1.29724	−	2.24688i	−0.0842647	−	0.145951i
$238$	−19.7226	+	34.1606i	−1.27843	+	2.21430i
$239$		−	22.8170i		−	1.47591i	−0.674852	−	0.737953i	$-0.735793\pi$
$239$		−	22.8170i		−	1.47591i	0.674852	−	0.737953i	$-0.264207\pi$
$240$	0.806003	+	0.465346i	0.0520273	+	0.0300380i
$241$	5.92776	+	3.42240i	0.381841	+	0.220456i	0.678619	−	0.734491i	$-0.262579\pi$
$241$	5.92776	+	3.42240i	0.381841	+	0.220456i	−0.296778	+	0.954946i	$0.595912\pi$
$242$			2.21629i			0.142469i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−21.3468	−	36.9737i	−1.36659	−	2.36700i
$245$	2.11831	−	1.22301i	0.135334	−	0.0781350i
$246$	14.1737			0.903684
$247$	11.0847	−	13.7827i	0.705305	−	0.876973i
$248$	2.25537			0.143216
$249$	8.31053	−	4.79809i	0.526658	−	0.304066i
$250$	7.30341	+	12.6499i	0.461908	+	0.800048i
$251$	−11.9857	+	20.7598i	−0.756531	+	1.31035i	0.188079	+	0.982154i	$0.439774\pi$
$251$	−11.9857	+	20.7598i	−0.756531	+	1.31035i	−0.944610	+	0.328196i	$0.893559\pi$
$252$			9.45081i			0.595345i
$253$	−5.32957	−	3.07703i	−0.335067	−	0.193451i
$254$	23.1351	+	13.3570i	1.45162	+	0.838095i
$255$		−	3.79610i		−	0.237721i
$256$	3.18118	−	5.50997i	0.198824	−	0.344373i
$257$	0.127745	+	0.221261i	0.00796851	+	0.0138019i	0.869982	−	0.493083i	$-0.164130\pi$
$257$	0.127745	+	0.221261i	0.00796851	+	0.0138019i	−0.862014	+	0.506885i	$0.830797\pi$
$258$	2.88912	−	1.66803i	0.179869	−	0.103847i
$259$	−21.7459			−1.35123
$260$	−4.55489	+	5.66353i	−0.282482	+	0.351237i
$261$	0.626251			0.0387640
$262$	−28.6864	+	16.5621i	−1.77225	+	1.02321i
$263$	0.0434967	+	0.0753385i	0.00268212	+	0.00464557i	0.867363	−	0.497675i	$-0.165813\pi$
$263$	0.0434967	+	0.0753385i	0.00268212	+	0.00464557i	−0.864681	+	0.502321i	$0.832480\pi$
$264$	1.01057	−	1.75035i	0.0621961	−	0.107727i
$265$		−	2.56242i		−	0.157408i
$266$	−30.5583	−	17.6428i	−1.87365	−	1.08175i
$267$	11.9750	+	6.91375i	0.732856	+	0.423114i
$268$			35.2057i			2.15053i
$269$	−6.74403	+	11.6810i	−0.411191	+	0.712204i	−0.995020	−	0.0996728i	$-0.968220\pi$
$269$	−6.74403	+	11.6810i	−0.411191	+	0.712204i	0.583829	+	0.811876i	$0.301554\pi$
$270$	−0.767100	−	1.32866i	−0.0466842	−	0.0808594i
$271$	7.15986	−	4.13375i	0.434930	−	0.251107i	−0.266514	−	0.963831i	$-0.585872\pi$
$271$	7.15986	−	4.13375i	0.434930	−	0.251107i	0.701445	+	0.712724i	$0.252539\pi$
$272$	7.37281			0.447042
$273$	11.5639	+	1.79183i	0.699881	+	0.108447i
$274$	36.0705			2.17910
$275$	−3.91513	+	2.26040i	−0.236091	+	0.136307i
$276$	8.96014	+	15.5194i	0.539337	+	0.934159i
$277$	−8.11632	+	14.0579i	−0.487662	+	0.844656i	−0.999899	−	0.0141883i	$-0.995484\pi$
$277$	−8.11632	+	14.0579i	−0.487662	+	0.844656i	0.512237	+	0.858844i	$0.328817\pi$
$278$			11.6400i			0.698121i
$279$	0.966393	+	0.557947i	0.0578564	+	0.0334034i
$280$	3.93248	+	2.27042i	0.235011	+	0.135684i
$281$			8.20700i			0.489588i	0.969575	+	0.244794i	$0.0787204\pi$
$281$			8.20700i			0.489588i	−0.969575	+	0.244794i	$0.921280\pi$
$282$	12.3942	−	21.4673i	0.738062	−	1.27836i
$283$	−14.8140	−	25.6585i	−0.880598	−	1.52524i	−0.850677	−	0.525689i	$-0.823808\pi$
$283$	−14.8140	−	25.6585i	−0.880598	−	1.52524i	−0.0299217	−	0.999552i	$-0.509526\pi$
$284$	12.9450	−	7.47379i	0.768143	−	0.443488i
$285$	3.39579			0.201149
$286$	−6.22696	−	5.00802i	−0.368208	−	0.296131i
$287$	−20.7560			−1.22519
$288$	6.08123	−	3.51100i	0.358340	−	0.206888i
$289$	−6.53607	−	11.3208i	−0.384475	−	0.665930i
$290$	0.480397	−	0.832072i	0.0282099	−	0.0488610i
$291$		−	3.17770i		−	0.186280i
$292$	30.6019	+	17.6680i	1.79084	+	1.03394i
$293$	7.97252	+	4.60294i	0.465760	+	0.268907i	0.714463	−	0.699673i	$-0.246671\pi$
$293$	7.97252	+	4.60294i	0.465760	+	0.268907i	−0.248703	+	0.968580i	$0.580004\pi$
$294$		−	7.83124i		−	0.456727i
$295$	1.34111	−	2.32287i	0.0780824	−	0.135243i
$296$	−6.77106	−	11.7278i	−0.393560	−	0.681666i
$297$	0.866025	−	0.500000i	0.0502519	−	0.0290129i
$298$	21.1566			1.22557
$299$	20.6882	−	8.02114i	1.19643	−	0.463875i
$300$	13.1643			0.760043
$301$	−4.23082	+	2.44267i	−0.243861	+	0.140793i
$302$	−19.6099	−	33.9653i	−1.12842	−	1.95449i
$303$	−6.61180	+	11.4520i	−0.379838	+	0.657899i
$304$			6.59533i			0.378268i
$305$	−8.78952	−	5.07463i	−0.503287	−	0.290573i
$306$	−10.5254	−	6.07686i	−0.601698	−	0.347391i
$307$		−	19.5936i		−	1.11827i	−0.829078	−	0.559133i	$-0.811134\pi$
$307$		−	19.5936i		−	1.11827i	0.829078	−	0.559133i	$-0.188866\pi$
$308$	−4.72541	+	8.18464i	−0.269255	+	0.466363i
$309$	−4.00766	−	6.94146i	−0.227988	−	0.394886i
$310$	1.48264	−	0.856002i	0.0842082	−	0.0486176i
$311$	5.55552			0.315024			0.157512	−	0.987517i	$-0.449653\pi$
$311$	5.55552			0.315024			0.157512	+	0.987517i	$0.449653\pi$
$312$	2.63432	+	6.79449i	0.149139	+	0.384662i
$313$	−26.5890			−1.50290			−0.751451	−	0.659789i	$-0.770645\pi$
$313$	−26.5890			−1.50290			−0.751451	+	0.659789i	$0.770645\pi$
$314$	−6.47340	+	3.73742i	−0.365315	+	0.210915i
$315$	1.12334	+	1.94568i	0.0632930	+	0.109627i
$316$	−3.77749	+	6.54280i	−0.212500	+	0.368061i
$317$			19.3444i			1.08649i	0.839575	+	0.543244i	$0.182804\pi$
$317$			19.3444i			1.08649i	−0.839575	+	0.543244i	$0.817196\pi$
$318$	−7.10482	−	4.10197i	−0.398418	−	0.230027i
$319$	0.542349	+	0.313126i	0.0303657	+	0.0175317i
$320$		−	8.91177i		−	0.498183i
$321$	4.46785	−	7.73854i	0.249371	−	0.431923i
$322$	−22.1332	−	38.3359i	−1.23344	−	2.13637i
$323$	23.2969	−	13.4505i	1.29628	−	0.748405i
$324$	−2.91194			−0.161775
$325$	2.49590	−	16.1078i	0.138448	−	0.893499i
$326$	−7.97063			−0.441452
$327$	15.9757	−	9.22358i	0.883459	−	0.510065i
$328$	−6.46282	−	11.1939i	−0.356850	−	0.618082i
$329$	−18.1500	+	31.4368i	−1.00064	+	1.73316i
$330$		−	1.53420i		−	0.0844549i
$331$	−7.38034	−	4.26104i	−0.405660	−	0.234208i	0.283263	−	0.959042i	$-0.408583\pi$
$331$	−7.38034	−	4.26104i	−0.405660	−	0.234208i	−0.688923	+	0.724834i	$0.741916\pi$
$332$	−24.1998	−	13.9718i	−1.32814	−	0.766800i
$333$		−	6.70026i		−	0.367172i
$334$	−9.95289	+	17.2389i	−0.544598	+	0.943272i
$335$	4.18462	+	7.24797i	0.228630	+	0.395999i
$336$	−3.77892	+	2.18176i	−0.206157	+	0.119025i
$337$	15.2980			0.833337			0.416668	−	0.909059i	$-0.363198\pi$
$337$	15.2980			0.833337			0.416668	+	0.909059i	$0.363198\pi$
$338$	28.1414	−	6.17910i	1.53069	−	0.336099i
$339$	4.49128			0.243933
$340$	−9.57306	+	5.52701i	−0.519172	+	0.299744i
$341$	0.557947	+	0.966393i	0.0302145	+	0.0523331i
$342$	5.43604	−	9.41550i	0.293947	−	0.509132i
$343$		−	11.2507i		−	0.607479i
$344$	−2.63472	−	1.52115i	−0.142054	−	0.0820151i
$345$	3.68933	+	2.13004i	0.198627	+	0.114677i
$346$		−	1.87016i		−	0.100541i
$347$	−7.16467	+	12.4096i	−0.384620	+	0.666181i	−0.991716	−	0.128447i	$-0.959001\pi$
$347$	−7.16467	+	12.4096i	−0.384620	+	0.666181i	0.607097	+	0.794628i	$0.292334\pi$
$348$	−0.911804	−	1.57929i	−0.0488778	−	0.0846589i
$349$	−19.3976	+	11.1992i	−1.03833	+	0.599479i	−0.919359	−	0.393419i	$-0.871292\pi$
$349$	−19.3976	+	11.1992i	−1.03833	+	0.599479i	−0.118969	+	0.992898i	$0.537959\pi$
$350$	−32.5184			−1.73818
$351$	−0.552093	+	3.56303i	−0.0294685	+	0.190181i
$352$	7.02200			0.374274
$353$	−19.8155	+	11.4405i	−1.05467	+	0.608917i	−0.923954	−	0.382503i	$-0.875062\pi$
$353$	−19.8155	+	11.4405i	−1.05467	+	0.608917i	−0.130720	+	0.991419i	$0.541729\pi$
$354$	−4.29374	−	7.43698i	−0.228210	−	0.395271i
$355$	1.77669	−	3.07733i	0.0942972	−	0.163327i
$356$		−	40.2649i		−	2.13403i
$357$	15.4134	+	8.89894i	0.815765	+	0.470982i
$358$	21.7309	+	12.5464i	1.14852	+	0.663096i
$359$		−	4.27489i		−	0.225620i	−0.993617	−	0.112810i	$-0.964015\pi$
$359$		−	4.27489i		−	0.225620i	0.993617	−	0.112810i	$-0.0359852\pi$
$360$	−0.699552	+	1.21166i	−0.0368696	+	0.0638601i
$361$	2.53211	+	4.38574i	0.133269	+	0.230828i
$362$	26.8728	−	15.5150i	1.41240	−	0.815452i
$363$	1.00000			0.0524864
$364$	−12.3181	−	31.7710i	−0.645643	−	1.66525i
$365$	8.40020			0.439687
$366$	−28.1408	+	16.2471i	−1.47094	+	0.849250i
$367$	−6.64575	−	11.5108i	−0.346905	−	0.600858i	0.638793	−	0.769379i	$-0.279434\pi$
$367$	−6.64575	−	11.5108i	−0.346905	−	0.600858i	−0.985698	+	0.168521i	$0.946101\pi$
$368$	−4.13697	+	7.16545i	−0.215655	+	0.373525i
$369$		−	6.39525i		−	0.332923i
$370$	−8.90234	−	5.13977i	−0.462810	−	0.267204i
$371$	10.4043	+	6.00692i	0.540164	+	0.311864i
$372$		−	3.24942i		−	0.168475i
$373$	0.743587	−	1.28793i	0.0385015	−	0.0666865i	−0.846133	−	0.532973i	$-0.821075\pi$
$373$	0.743587	−	1.28793i	0.0385015	−	0.0666865i	0.884634	+	0.466286i	$0.154408\pi$
$374$	−6.07686	−	10.5254i	−0.314227	−	0.544257i
$375$	5.70768	−	3.29533i	0.294743	−	0.170170i
$376$	−22.6056			−1.16579
$377$	−2.10528	+	0.816249i	−0.108428	+	0.0420390i
$378$	7.19305			0.369970
$379$	7.24124	−	4.18073i	0.371957	−	0.214750i	−0.302356	−	0.953195i	$-0.597773\pi$
$379$	7.24124	−	4.18073i	0.371957	−	0.214750i	0.674313	+	0.738445i	$0.264440\pi$
$380$	−4.94418	−	8.56356i	−0.253631	−	0.439302i
$381$	6.02676	−	10.4386i	0.308760	−	0.534788i
$382$		−	8.55164i		−	0.437540i
$383$	−2.64560	−	1.52744i	−0.135184	−	0.0780484i	0.430883	−	0.902408i	$-0.358202\pi$
$383$	−2.64560	−	1.52744i	−0.135184	−	0.0780484i	−0.566067	+	0.824359i	$0.691536\pi$
$384$	−12.5472	−	7.24410i	−0.640294	−	0.369674i
$385$			2.24668i			0.114501i
$386$	28.4840	−	49.3358i	1.44980	−	2.51112i
$387$	−0.752624	−	1.30358i	−0.0382580	−	0.0662649i
$388$	−8.01358	+	4.62664i	−0.406828	+	0.234882i
$389$	15.6067			0.791289			0.395645	−	0.918404i	$-0.370521\pi$
$389$	15.6067			0.791289			0.395645	+	0.918404i	$0.370521\pi$
$390$	4.31053	+	3.46674i	0.218272	+	0.175545i
$391$	33.7477			1.70669
$392$	−6.18485	+	3.57083i	−0.312382	+	0.180354i
$393$	7.47289	+	12.9434i	0.376957	+	0.652909i
$394$	−2.47750	+	4.29116i	−0.124815	+	0.216186i
$395$			1.79599i			0.0903663i
$396$	−2.52182	−	1.45597i	−0.126726	−	0.0731653i
$397$	1.83185	+	1.05762i	0.0919381	+	0.0530805i	0.545264	−	0.838264i	$-0.316429\pi$
$397$	1.83185	+	1.05762i	0.0919381	+	0.0530805i	−0.453326	+	0.891345i	$0.649763\pi$
$398$			22.5843i			1.13205i
$399$	−7.96053	+	13.7880i	−0.398525	+	0.690265i
$400$	3.03904	+	5.26378i	0.151952	+	0.263189i
$401$	33.0307	−	19.0703i	1.64948	−	0.952325i	0.672195	−	0.740374i	$-0.265352\pi$
$401$	33.0307	−	19.0703i	1.64948	−	0.952325i	0.977280	−	0.211950i	$-0.0679815\pi$
$402$	26.7952			1.33642
$403$	−3.97597	−	0.616077i	−0.198057	−	0.0306890i
$404$	38.5064			1.91577
$405$	−0.599495	+	0.346119i	−0.0297892	+	0.0171988i
$406$	2.25233	+	3.90114i	0.111781	+	0.193611i
$407$	3.35013	−	5.80260i	0.166060	−	0.287624i
$408$			11.0835i			0.548715i
$409$	−17.9804	−	10.3810i	−0.889075	−	0.513308i	−0.0154353	−	0.999881i	$-0.504913\pi$
$409$	−17.9804	−	10.3810i	−0.889075	−	0.513308i	−0.873640	+	0.486573i	$0.838247\pi$
$410$	−8.49708	−	4.90579i	−0.419641	−	0.242280i
$411$		−	16.2751i		−	0.802794i
$412$	−11.6701	+	20.2132i	−0.574943	+	0.995831i
$413$	6.28775	+	10.8907i	0.309400	+	0.535896i
$414$	11.8119	−	6.81959i	0.580522	−	0.335165i
$415$	−6.64283			−0.326084
$416$	−15.8672	+	19.7292i	−0.777954	+	0.967305i
$417$	5.25202			0.257193
$418$	9.41550	−	5.43604i	0.460527	−	0.265885i
$419$	−7.22830	−	12.5198i	−0.353125	−	0.611631i	0.633670	−	0.773604i	$-0.281548\pi$
$419$	−7.22830	−	12.5198i	−0.353125	−	0.611631i	−0.986795	+	0.161972i	$0.948214\pi$
$420$	3.27110	−	5.66572i	0.159613	−	0.276459i
$421$		−	1.98596i		−	0.0967895i	−0.998828	−	0.0483948i	$-0.984589\pi$
$421$		−	1.98596i		−	0.0967895i	0.998828	−	0.0483948i	$-0.0154106\pi$
$422$	−16.2023	−	9.35442i	−0.788717	−	0.455366i
$423$	−9.68616	−	5.59231i	−0.470957	−	0.271907i
$424$			7.48153i			0.363335i
$425$	12.3956	−	21.4698i	0.601276	−	1.04144i
$426$	−5.68833	−	9.85247i	−0.275600	−	0.477354i
$427$	41.2094	−	23.7923i	1.99426	−	1.15139i
$428$	−26.0202			−1.25774
$429$	−2.25964	+	2.80963i	−0.109097	+	0.135650i
$430$	−2.30935			−0.111367
$431$	−20.5043	+	11.8382i	−0.987658	+	0.570225i	−0.904573	−	0.426318i	$-0.859811\pi$
$431$	−20.5043	+	11.8382i	−0.987658	+	0.570225i	−0.0830846	+	0.996542i	$0.526477\pi$
$432$	−0.672235	−	1.16434i	−0.0323429	−	0.0560196i
$433$	−13.3241	+	23.0779i	−0.640313	+	1.10905i	0.345050	+	0.938584i	$0.387862\pi$
$433$	−13.3241	+	23.0779i	−0.640313	+	1.10905i	−0.985363	+	0.170470i	$0.945471\pi$
$434$			8.02668i			0.385293i
$435$	−0.375435	−	0.216757i	−0.0180007	−	0.0103927i
$436$	−46.5204	−	26.8586i	−2.22792	−	1.28629i
$437$			30.1889i			1.44413i
$438$	13.4472	−	23.2912i	0.642531	−	1.11290i
$439$	17.8146	+	30.8558i	0.850245	+	1.47267i	0.880987	+	0.473140i	$0.156880\pi$
$439$	17.8146	+	30.8558i	0.850245	+	1.47267i	−0.0307419	+	0.999527i	$0.509787\pi$
$440$	−1.21166	+	0.699552i	−0.0577636	+	0.0333498i
$441$	−3.53349			−0.168261
$442$	43.3041	+	6.70997i	2.05976	+	0.319161i
$443$	−26.7088			−1.26897			−0.634487	−	0.772933i	$-0.718789\pi$
$443$	−26.7088			−1.26897			−0.634487	+	0.772933i	$0.718789\pi$
$444$	−16.8968	+	9.75539i	−0.801888	+	0.462970i
$445$	−4.78595	−	8.28951i	−0.226876	−	0.392961i
$446$	−15.5195	+	26.8806i	−0.734869	+	1.27283i
$447$		−	9.54593i		−	0.451507i
$448$	36.1847	+	20.8913i	1.70957	+	0.987020i
$449$	9.11861	+	5.26463i	0.430334	+	0.248453i	0.699489	−	0.714644i	$-0.253411\pi$
$449$	9.11861	+	5.26463i	0.430334	+	0.248453i	−0.269155	+	0.963097i	$0.586744\pi$
$450$		−	10.0194i		−	0.472320i
$451$	3.19762	−	5.53845i	0.150570	−	0.260795i
$452$	−6.53919	−	11.3262i	−0.307577	−	0.532740i
$453$	−15.3253	+	8.84807i	−0.720046	+	0.415719i
$454$	55.0961			2.58579
$455$	−6.31234	−	5.07669i	−0.295927	−	0.237999i
$456$	−9.91473			−0.464300
$457$	11.6210	−	6.70938i	0.543607	−	0.313851i	−0.202933	−	0.979193i	$-0.565047\pi$
$457$	11.6210	−	6.70938i	0.543607	−	0.313851i	0.746539	+	0.665341i	$0.231714\pi$
$458$	11.1616	+	19.3324i	0.521547	+	0.903346i
$459$	−2.74190	+	4.74912i	−0.127981	+	0.221670i
$460$		−	12.4051i		−	0.578390i
$461$	−9.91731	−	5.72576i	−0.461895	−	0.266675i	0.250946	−	0.968001i	$-0.419258\pi$
$461$	−9.91731	−	5.72576i	−0.461895	−	0.266675i	−0.712841	+	0.701326i	$0.752592\pi$
$462$	6.22936	+	3.59652i	0.289816	+	0.167325i
$463$			33.5201i			1.55781i	0.627140	+	0.778906i	$0.284225\pi$
$463$			33.5201i			1.55781i	−0.627140	+	0.778906i	$0.715775\pi$
$464$	0.420988	−	0.729172i	0.0195439	−	0.0338510i
$465$	−0.386232	−	0.668973i	−0.0179111	−	0.0310229i
$466$	−5.06102	+	2.92198i	−0.234447	+	0.135358i
$467$	−3.65642			−0.169199			−0.0845995	−	0.996415i	$-0.526961\pi$
$467$	−3.65642			−0.169199			−0.0845995	+	0.996415i	$0.526961\pi$
$468$	9.78915	−	3.79540i	0.452503	−	0.175442i
$469$	−39.2389			−1.81188
$470$	−14.8605	+	8.57971i	−0.685464	+	0.395753i
$471$	1.68634	+	2.92083i	0.0777024	+	0.134585i
$472$	−3.91565	+	6.78211i	−0.180232	+	0.312172i
$473$		−	1.50525i		−	0.0692114i
$474$	4.97975	+	2.87506i	0.228727	+	0.132056i
$475$	19.2058	+	11.0885i	0.881223	+	0.508774i
$476$		−	51.8264i		−	2.37546i
$477$	−1.85083	+	3.20573i	−0.0847435	+	0.146780i
$478$	25.2845	+	43.7940i	1.15649	+	2.00309i
$479$	−34.5291	+	19.9354i	−1.57768	+	0.910872i	−0.582494	+	0.812835i	$0.697923\pi$
$479$	−34.5291	+	19.9354i	−1.57768	+	0.910872i	−0.995183	+	0.0980371i	$0.968744\pi$
$480$	−4.86089			−0.221868
$481$	8.73305	+	22.5244i	0.398193	+	1.02702i
$482$	−15.1700			−0.690977
$483$	−17.2973	+	9.98661i	−0.787055	+	0.454406i
$484$	−1.45597	−	2.52182i	−0.0661805	−	0.114628i
$485$	−1.09986	+	1.90502i	−0.0499421	+	0.0865023i
$486$			2.21629i			0.100533i
$487$	10.1406	+	5.85468i	0.459515	+	0.265301i	0.711840	−	0.702341i	$-0.247862\pi$
$487$	10.1406	+	5.85468i	0.459515	+	0.265301i	−0.252325	+	0.967642i	$0.581195\pi$
$488$	25.6629	+	14.8165i	1.16170	+	0.670710i
$489$			3.59638i			0.162634i
$490$	−2.71054	+	4.69479i	−0.122450	+	0.212089i
$491$	4.60639	+	7.97850i	0.207883	+	0.360065i	0.951048	−	0.309045i	$-0.100009\pi$
$491$	4.60639	+	7.97850i	0.207883	+	0.360065i	−0.743164	+	0.669109i	$0.766676\pi$
$492$	−16.1276	+	9.31130i	−0.727090	+	0.419786i
$493$	−3.43424			−0.154670
$494$	−6.00239	+	38.7376i	−0.270060	+	1.74288i
$495$	−0.692237			−0.0311138
$496$	1.29929	−	0.750143i	0.0583396	−	0.0336824i
$497$	8.32998	+	14.4279i	0.373651	+	0.647182i
$498$	−10.6340	+	18.4185i	−0.476519	+	0.825355i
$499$		−	20.2285i		−	0.905552i	−0.891624	−	0.452776i	$-0.850434\pi$
$499$		−	20.2285i		−	0.905552i	0.891624	−	0.452776i	$-0.149566\pi$
$500$	−16.6204	−	9.59582i	−0.743289	−	0.429138i
$501$	7.77828	+	4.49079i	0.347508	+	0.200634i
$502$		−	53.1276i		−	2.37120i
$503$	−13.3940	+	23.1991i	−0.597210	+	1.03440i	0.396021	+	0.918241i	$0.370391\pi$
$503$	−13.3940	+	23.1991i	−0.597210	+	1.03440i	−0.993231	+	0.116157i	$0.962943\pi$
$504$	−3.27983	−	5.68083i	−0.146095	−	0.253044i
$505$	7.92749	−	4.57694i	0.352769	−	0.203671i
$506$	13.6392			0.606336
$507$	−2.78804	−	12.6975i	−0.123821	−	0.563916i
$508$	−35.0992			−1.55727
$509$	26.9286	−	15.5472i	1.19359	−	0.689119i	0.234471	−	0.972123i	$-0.424664\pi$
$509$	26.9286	−	15.5472i	1.19359	−	0.689119i	0.959119	+	0.283004i	$0.0913310\pi$
$510$	4.20663	+	7.28609i	0.186273	+	0.322634i
$511$	−19.6920	+	34.1076i	−0.871125	+	1.50883i
$512$		−	14.8756i		−	0.657414i
$513$	−4.24831	−	2.45276i	−0.187568	−	0.108292i
$514$	−0.490378	−	0.283120i	−0.0216297	−	0.0124879i
$515$			5.54850i			0.244496i
$516$	−2.19160	+	3.79596i	−0.0964798	+	0.167108i
$517$	−5.59231	−	9.68616i	−0.245949	−	0.425997i
$518$	41.7383	−	24.0976i	1.83388	−	1.05879i
$519$	−0.843826			−0.0370399
$520$	0.772435	−	4.98505i	0.0338735	−	0.218609i
$521$	−42.9644			−1.88231			−0.941153	−	0.337981i	$-0.890256\pi$
$521$	−42.9644			−1.88231			−0.941153	+	0.337981i	$0.890256\pi$
$522$	−1.20200	+	0.693977i	−0.0526103	+	0.0303746i
$523$	−10.6264	−	18.4055i	−0.464661	−	0.804817i	0.534525	−	0.845153i	$-0.320491\pi$
$523$	−10.6264	−	18.4055i	−0.464661	−	0.804817i	−0.999186	+	0.0403359i	$0.987157\pi$
$524$	21.7606	−	37.6905i	0.950617	−	1.64652i
$525$			14.6724i			0.640357i
$526$	−0.166972	−	0.0964013i	−0.00728032	−	0.00420330i
$527$	−5.29951	−	3.05967i	−0.230850	−	0.133282i
$528$		−	1.34447i		−	0.0585105i
$529$	−7.43624	+	12.8799i	−0.323315	+	0.559997i
$530$	2.83954	+	4.91822i	0.123342	+	0.213634i
$531$	−3.35560	+	1.93735i	−0.145620	+	0.0840740i
$532$	46.3612			2.01001
$533$	8.33550	+	21.4990i	0.361051	+	0.931227i
$534$	−30.6457			−1.32617
$535$	−5.35691	+	3.09281i	−0.231599	+	0.133714i
$536$	−12.2179	−	21.1620i	−0.527732	−	0.914058i
$537$	5.66097	−	9.80509i	0.244289	−	0.423121i
$538$		−	29.8935i		−	1.28880i
$539$	−3.06009	−	1.76674i	−0.131807	−	0.0760991i
$540$	1.74570	+	1.00788i	0.0751228	+	0.0433722i
$541$		−	5.16246i		−	0.221952i	−0.993823	−	0.110976i	$-0.964602\pi$
$541$		−	5.16246i		−	0.221952i	0.993823	−	0.110976i	$-0.0353976\pi$
$542$	−9.16158	+	15.8683i	−0.393524	+	0.681603i
$543$	−7.00045	−	12.1251i	−0.300418	−	0.520339i
$544$	−33.3483	+	19.2537i	−1.42980	+	0.825494i
$545$	−12.7698			−0.546999
$546$	−24.1810	+	9.37534i	−1.03485	+	0.401228i
$547$	−9.75753			−0.417202			−0.208601	−	0.978001i	$-0.566891\pi$
$547$	−9.75753			−0.417202			−0.208601	+	0.978001i	$0.566891\pi$
$548$	−41.0429	+	23.6962i	−1.75327	+	1.01225i
$549$	7.33077	+	12.6973i	0.312870	+	0.541906i
$550$	5.00971	−	8.67707i	0.213615	−	0.369992i
$551$		−	3.07209i		−	0.130876i
$552$	−10.7718	−	6.21909i	−0.458477	−	0.264702i
$553$	−7.29233	−	4.21023i	−0.310102	−	0.179037i
$554$		−	35.9762i		−	1.52848i
$555$	−2.31909	+	4.01677i	−0.0984397	+	0.170503i
$556$	−7.64680	−	13.2446i	−0.324297	−	0.561698i
$557$	27.4038	−	15.8216i	1.16113	−	0.670381i	0.209559	−	0.977796i	$-0.432797\pi$
$557$	27.4038	−	15.8216i	1.16113	−	0.670381i	0.951576	+	0.307415i	$0.0994638\pi$
$558$	−2.47315			−0.104697
$559$	4.22919	+	3.40132i	0.178876	+	0.143861i
$560$	3.02059			0.127643
$561$	−4.74912	+	2.74190i	−0.200508	+	0.115763i
$562$	−9.09455	−	15.7522i	−0.383630	−	0.664467i
$563$	15.0977	−	26.1499i	0.636291	−	1.10209i	−0.349949	−	0.936769i	$-0.613801\pi$
$563$	15.0977	−	26.1499i	0.636291	−	1.10209i	0.986240	−	0.165320i	$-0.0528657\pi$
$564$			32.5690i			1.37140i
$565$	−2.69250	−	1.55452i	−0.113274	−	0.0653991i
$566$	56.8668	+	32.8320i	2.39029	+	1.38003i
$567$		−	3.24553i		−	0.136300i
$568$	−5.18744	+	8.98490i	−0.217660	+	0.376998i
$569$	−5.80438	−	10.0535i	−0.243332	−	0.421464i	0.718329	−	0.695704i	$-0.244907\pi$
$569$	−5.80438	−	10.0535i	−0.243332	−	0.421464i	−0.961661	+	0.274239i	$0.911574\pi$
$570$	−6.51776	+	3.76303i	−0.272999	+	0.157616i
$571$	6.24136			0.261193			0.130596	−	0.991436i	$-0.458311\pi$
$571$	6.24136			0.261193			0.130596	+	0.991436i	$0.458311\pi$
$572$	10.3753	+	1.60766i	0.433815	+	0.0672198i
$573$	−3.85854			−0.161193
$574$	39.8383	−	23.0007i	1.66282	−	0.960029i
$575$	13.9107	+	24.0940i	0.580115	+	1.00479i
$576$	−6.43693	+	11.1491i	−0.268205	+	0.464545i
$577$		−	43.6609i		−	1.81763i	−0.417201	−	0.908814i	$-0.636989\pi$
$577$		−	43.6609i		−	1.81763i	0.417201	−	0.908814i	$-0.363011\pi$
$578$	25.0902	+	14.4858i	1.04361	+	0.602531i
$579$	−22.2605	−	12.8521i	−0.925115	−	0.534115i
$580$			1.26237i			0.0524171i
$581$	15.5724	−	26.9721i	0.646050	−	1.11899i
$582$	3.52135	+	6.09916i	0.145965	+	0.252818i
$583$	−3.20573	+	1.85083i	−0.132768	+	0.0766534i
$584$	−24.5262			−1.01490
$585$	1.56421	−	1.94493i	0.0646721	−	0.0804130i
$586$	−20.4029			−0.842836
$587$	−16.8019	+	9.70058i	−0.693488	+	0.400386i	−0.804918	−	0.593387i	$-0.797791\pi$
$587$	−16.8019	+	9.70058i	−0.693488	+	0.400386i	0.111429	+	0.993772i	$0.464457\pi$
$588$	5.14466	+	8.91082i	0.212162	+	0.367476i
$589$	2.73703	−	4.74067i	0.112777	−	0.195336i
$590$			5.94457i			0.244734i
$591$	1.93619	+	1.11786i	0.0796443	+	0.0459827i
$592$	−7.80141	−	4.50415i	−0.320636	−	0.185119i
$593$			36.9208i			1.51616i	0.652164	+	0.758078i	$0.273861\pi$
$593$			36.9208i			1.51616i	−0.652164	+	0.758078i	$0.726139\pi$
$594$	−1.10815	+	1.91936i	−0.0454678	+	0.0787525i
$595$	−6.16018	−	10.6697i	−0.252543	−	0.437417i
$596$	−24.0731	+	13.8986i	−0.986073	+	0.569309i
$597$	10.1901			0.417054
$598$	−30.8197	+	38.3211i	−1.26031	+	1.56707i
$599$	−2.58240			−0.105514			−0.0527570	−	0.998607i	$-0.516801\pi$
$599$	−2.58240			−0.105514			−0.0527570	+	0.998607i	$0.516801\pi$
$600$	−7.91301	+	4.56858i	−0.323047	+	0.186511i
$601$	8.75615	+	15.1661i	0.357171	+	0.618638i	0.987487	−	0.157700i	$-0.0504080\pi$
$601$	8.75615	+	15.1661i	0.357171	+	0.618638i	−0.630316	+	0.776339i	$0.717075\pi$
$602$	5.41366	−	9.37673i	0.220644	−	0.382167i
$603$		−	12.0901i		−	0.492348i
$604$	44.6264	+	25.7651i	1.81582	+	1.04837i
$605$	−0.599495	−	0.346119i	−0.0243729	−	0.0140717i
$606$		−	29.3074i		−	1.19053i
$607$	−7.50149	+	12.9930i	−0.304476	+	0.527368i	−0.977145	−	0.212576i	$-0.931815\pi$
$607$	−7.50149	+	12.9930i	−0.304476	+	0.527368i	0.672668	+	0.739944i	$0.265148\pi$
$608$	−17.2233	−	29.8317i	−0.698498	−	1.20983i
$609$	1.76021	−	1.01626i	0.0713274	−	0.0411809i
$610$	22.4937			0.910744
$611$	39.8511	+	6.17494i	1.61220	+	0.249811i
$612$	15.9685			0.645490
$613$	−10.9020	+	6.29429i	−0.440329	+	0.254224i	−0.703737	−	0.710460i	$-0.748487\pi$
$613$	−10.9020	+	6.29429i	−0.440329	+	0.254224i	0.263408	+	0.964684i	$0.415153\pi$
$614$	21.7126	+	37.6073i	0.876248	+	1.51771i
$615$	−2.21351	+	3.83392i	−0.0892575	+	0.154599i
$616$		−	6.55966i		−	0.264296i
$617$	−27.6627	−	15.9711i	−1.11366	−	0.642970i	−0.173883	−	0.984766i	$-0.555632\pi$
$617$	−27.6627	−	15.9711i	−1.11366	−	0.642970i	−0.939774	+	0.341796i	$0.888965\pi$
$618$	15.3843	+	8.88213i	0.618847	+	0.357292i
$619$			0.760511i			0.0305675i	0.999883	+	0.0152838i	$0.00486516\pi$
$619$			0.760511i			0.0305675i	−0.999883	+	0.0152838i	$0.995135\pi$
$620$	−1.12469	+	1.94801i	−0.0451685	+	0.0782341i
$621$	−3.07703	−	5.32957i	−0.123477	−	0.213868i
$622$	−10.6631	+	6.15632i	−0.427550	+	0.246846i
$623$	44.8776			1.79798
$624$	3.77746	+	3.03802i	0.151219	+	0.121618i
$625$	18.0417			0.721669
$626$	51.0340	−	29.4645i	2.03973	−	1.17764i
$627$	−2.45276	−	4.24831i	−0.0979540	−	0.169661i
$628$	4.91053	−	8.50528i	0.195951	−	0.339398i
$629$			36.7429i			1.46504i
$630$	−4.31220	−	2.48965i	−0.171802	−	0.0991899i
$631$	4.63033	+	2.67332i	0.184331	+	0.106423i	0.589326	−	0.807896i	$-0.299393\pi$
$631$	4.63033	+	2.67332i	0.184331	+	0.106423i	−0.404995	+	0.914319i	$0.632727\pi$
$632$		−	5.24378i		−	0.208586i
$633$	−4.22075	+	7.31056i	−0.167760	+	0.290569i
$634$	−21.4364	−	37.1289i	−0.851348	−	1.47458i
$635$	−7.22602	+	4.17195i	−0.286756	+	0.165559i
$636$	10.7790			0.427415
$637$	11.8786	−	4.60551i	0.470648	−	0.182477i
$638$	−1.38795			−0.0549496
$639$	−4.44548	+	2.56660i	−0.175860	+	0.101533i
$640$	5.01464	+	8.68561i	0.198221	+	0.343329i
$641$	11.1868	−	19.3762i	0.441853	−	0.765313i	−0.555974	−	0.831200i	$-0.687654\pi$
$641$	11.1868	−	19.3762i	0.441853	−	0.765313i	0.997827	+	0.0658873i	$0.0209878\pi$
$642$			19.8041i			0.781605i
$643$	35.0206	+	20.2192i	1.38108	+	0.797366i	0.992287	−	0.123961i	$-0.0395597\pi$
$643$	35.0206	+	20.2192i	1.38108	+	0.797366i	0.388790	+	0.921326i	$0.372893\pi$
$644$	50.3688	+	29.0804i	1.98481	+	1.14593i
$645$			1.04199i			0.0410283i
$646$	−29.8102	+	51.6328i	−1.17287	+	2.03146i
$647$	−4.17171	−	7.22561i	−0.164007	−	0.284068i	0.772295	−	0.635264i	$-0.219109\pi$
$647$	−4.17171	−	7.22561i	−0.164007	−	0.284068i	−0.936302	+	0.351196i	$0.885775\pi$
$648$	1.75035	−	1.01057i	0.0687604	−	0.0396988i
$649$	−3.87471			−0.152096
$650$	13.0592	+	33.6825i	0.512224	+	1.32114i
$651$	3.62167			0.141945
$652$	9.06942	−	5.23623i	0.355186	−	0.205067i
$653$	12.0536	+	20.8775i	0.471695	+	0.817000i	0.999476	−	0.0323808i	$-0.0103089\pi$
$653$	12.0536	+	20.8775i	0.471695	+	0.817000i	−0.527780	+	0.849381i	$0.676976\pi$
$654$	−20.4421	+	35.4068i	−0.799351	+	1.38452i
$655$		−	10.3460i		−	0.404253i
$656$	−7.44627	−	4.29911i	−0.290728	−	0.167852i
$657$	−10.5091	−	6.06743i	−0.409999	−	0.236713i
$658$		−	80.4514i		−	3.13632i
$659$	9.58573	−	16.6030i	0.373407	−	0.646760i	−0.616680	−	0.787214i	$-0.711523\pi$
$659$	9.58573	−	16.6030i	0.373407	−	0.646760i	0.990087	+	0.140454i	$0.0448562\pi$
$660$	1.00788	+	1.74570i	0.0392316	+	0.0679511i
$661$	31.1434	−	17.9807i	1.21134	−	0.699367i	0.248288	−	0.968686i	$-0.420132\pi$
$661$	31.1434	−	17.9807i	1.21134	−	0.699367i	0.963051	+	0.269319i	$0.0867987\pi$
$662$	18.8874			0.734081
$663$	3.02757	−	19.5390i	0.117581	−	0.758831i
$664$	19.3951			0.752678
$665$	9.54460	−	5.51058i	0.370124	−	0.213691i
$666$	7.42486	+	12.8602i	0.287708	+	0.498324i
$667$	1.92699	−	3.33765i	0.0746135	−	0.129234i
$668$		−	26.1539i		−	1.01192i
$669$	12.1286	+	7.00246i	0.468920	+	0.270731i
$670$	−16.0636	−	9.27433i	−0.620591	−	0.358298i
$671$			14.6615i			0.566002i
$672$	11.3951	−	19.7368i	0.439574	−	0.761365i
$673$	−21.3242	−	36.9346i	−0.821988	−	1.42373i	−0.904199	−	0.427110i	$-0.859532\pi$
$673$	−21.3242	−	36.9346i	−0.821988	−	1.42373i	0.0822113	−	0.996615i	$-0.473802\pi$
$674$	−29.3625	+	16.9524i	−1.13100	+	0.652984i
$675$	−4.52081			−0.174006
$676$	−27.9615	+	25.5181i	−1.07544	+	0.981467i
$677$	−21.7686			−0.836633			−0.418317	−	0.908301i	$-0.637380\pi$
$677$	−21.7686			−0.836633			−0.418317	+	0.908301i	$0.637380\pi$
$678$	−8.62041	+	4.97700i	−0.331065	+	0.191140i
$679$	−5.15667	−	8.93161i	−0.197895	−	0.342764i
$680$	3.83621	−	6.64451i	0.147112	−	0.254805i
$681$		−	24.8596i		−	0.952621i
$682$	−2.14181	−	1.23657i	−0.0820140	−	0.0473508i
$683$	−31.9936	−	18.4715i	−1.22420	−	0.706792i	−0.258389	−	0.966041i	$-0.583192\pi$
$683$	−31.9936	−	18.4715i	−1.22420	−	0.706792i	−0.965811	+	0.259249i	$0.916525\pi$
$684$			14.2846i			0.546186i
$685$	−5.63313	+	9.75687i	−0.215231	+	0.372791i
$686$	12.4674	+	21.5941i	0.476007	+	0.824468i
$687$	8.72288	−	5.03616i	0.332799	−	0.192141i
$688$	−2.02376			−0.0771551
$689$	2.04365	−	13.1891i	0.0778571	−	0.502465i
$690$	−9.44156			−0.359434
$691$	44.5607	−	25.7272i	1.69517	−	0.978707i	0.744955	−	0.667115i	$-0.232471\pi$
$691$	44.5607	−	25.7272i	1.69517	−	0.978707i	0.950216	−	0.311592i	$-0.100862\pi$
$692$	1.22859	+	2.12798i	0.0467039	+	0.0808935i
$693$	1.62277	−	2.81071i	0.0616438	−	0.106770i
$694$		−	31.7580i		−	1.20552i
$695$	−3.14856	−	1.81782i	−0.119432	−	0.0689540i
$696$	1.09616	+	0.632869i	0.0415499	+	0.0239888i
$697$			35.0703i			1.32838i
$698$	24.8207	−	42.9907i	0.939476	−	1.62722i
$699$	1.31841	+	2.28355i	0.0498668	+	0.0863719i
$700$	37.0012	−	21.3627i	1.39851	−	0.807432i
$701$	−45.5437			−1.72016			−0.860081	−	0.510157i	$-0.829587\pi$
$701$	−45.5437			−1.72016			−0.860081	+	0.510157i	$0.829587\pi$
$702$	−2.88869	−	7.45055i	−0.109027	−	0.281203i
$703$	−32.8683			−1.23965
$704$	−11.1491	+	6.43693i	−0.420197	+	0.242601i
$705$	3.87120	+	6.70512i	0.145798	+	0.252529i
$706$	25.3555	−	43.9170i	0.954266	−	1.65284i
$707$			42.9177i			1.61408i
$708$	9.77131	+	5.64147i	0.367228	+	0.212019i
$709$	−18.4367	−	10.6444i	−0.692406	−	0.399761i	0.112107	−	0.993696i	$-0.464240\pi$
$709$	−18.4367	−	10.6444i	−0.692406	−	0.399761i	−0.804513	+	0.593935i	$0.797573\pi$
$710$			7.87534i			0.295556i
$711$	1.29724	−	2.24688i	0.0486502	−	0.0842647i
$712$	13.9736	+	24.2030i	0.523683	+	0.907045i
$713$	5.94724	−	3.43364i	0.222726	−	0.128591i
$714$	−39.4453			−1.47620
$715$	2.32711	−	0.902255i	0.0870290	−	0.0337424i
$716$	−32.9689			−1.23210
$717$	19.7601	−	11.4085i	0.737953	−	0.426057i
$718$	4.73720	+	8.20508i	0.176791	+	0.306211i
$719$	13.4899	−	23.3651i	0.503087	−	0.871373i	−0.496906	−	0.867804i	$-0.665531\pi$
$719$	13.4899	−	23.3651i	0.503087	−	0.871373i	0.999994	−	0.00356877i	$-0.00113598\pi$
$720$			0.930692i			0.0346848i
$721$	−22.5288	−	13.0070i	−0.839015	−	0.484405i
$722$	−9.72007	−	5.61188i	−0.361743	−	0.208853i
$723$			6.84479i			0.254561i
$724$	−20.3849	+	35.3077i	−0.757599	+	1.31220i
$725$	−1.41558	−	2.45186i	−0.0525733	−	0.0910597i
$726$	−1.91936	+	1.10815i	−0.0712343	+	0.0411271i
$727$	3.69979			0.137217			0.0686087	−	0.997644i	$-0.478144\pi$
$727$	3.69979			0.137217			0.0686087	+	0.997644i	$0.478144\pi$
$728$	18.4302	+	14.8225i	0.683069	+	0.549357i
$729$	1.00000			0.0370370
$730$	−16.1230	+	9.30865i	−0.596741	+	0.344528i
$731$	4.12725	+	7.14860i	0.152652	+	0.264400i
$732$	21.3468	−	36.9737i	0.789000	−	1.36659i
$733$			52.4477i			1.93720i	0.248624	+	0.968600i	$0.420022\pi$
$733$			52.4477i			1.93720i	−0.248624	+	0.968600i	$0.579978\pi$
$734$	25.5112	+	14.7289i	0.941636	+	0.543654i
$735$	2.11831	+	1.22301i	0.0781350	+	0.0451113i
$736$		−	43.2138i		−	1.59288i
$737$	6.04506	−	10.4703i	0.222673	−	0.385680i
$738$	7.08686	+	12.2748i	0.260871	+	0.451842i
$739$	2.88549	−	1.66594i	0.106144	−	0.0612825i	−0.445988	−	0.895039i	$-0.647148\pi$
$739$	2.88549	−	1.66594i	0.106144	−	0.0612825i	0.552132	+	0.833756i	$0.313814\pi$
$740$	13.5061			0.496494
$741$	17.4786	+	2.70831i	0.642091	+	0.0994921i
$742$	−26.6262			−0.977477
$743$	−13.6586	+	7.88582i	−0.501087	+	0.289303i	−0.729162	−	0.684341i	$-0.760090\pi$
$743$	−13.6586	+	7.88582i	−0.501087	+	0.289303i	0.228075	+	0.973644i	$0.426757\pi$
$744$	1.12769	+	1.95321i	0.0413430	+	0.0716081i
$745$	−3.30403	+	5.72274i	−0.121050	+	0.209665i
$746$			3.29601i			0.120675i
$747$	8.31053	+	4.79809i	0.304066	+	0.175553i
$748$	13.8292	+	7.98427i	0.505644	+	0.291934i
$749$		−	29.0011i		−	1.05968i
$750$	−7.30341	+	12.6499i	−0.266683	+	0.461908i
$751$	21.2483	+	36.8032i	0.775363	+	1.34297i	0.934590	+	0.355726i	$0.115766\pi$
$751$	21.2483	+	36.8032i	0.775363	+	1.34297i	−0.159228	+	0.987242i	$0.550900\pi$
$752$	−13.0227	+	7.51868i	−0.474891	+	0.274178i
$753$	−23.9714			−0.873567
$754$	3.13628	−	3.89964i	0.114217	−	0.142016i
$755$	12.2499			0.445821
$756$	−8.18464	+	4.72541i	−0.297673	+	0.171861i
$757$	16.5867	+	28.7289i	0.602852	+	1.04417i	0.992387	+	0.123159i	$0.0393026\pi$
$757$	16.5867	+	28.7289i	0.602852	+	1.04417i	−0.389535	+	0.921012i	$0.627364\pi$
$758$	−9.26571	+	16.0487i	−0.336546	+	0.582915i
$759$		−	6.15406i		−	0.223378i
$760$	5.94383	+	3.43167i	0.215605	+	0.124480i
$761$	45.5949	+	26.3242i	1.65281	+	0.954252i	0.975908	+	0.218181i	$0.0700124\pi$
$761$	45.5949	+	26.3242i	1.65281	+	0.954252i	0.676905	+	0.736071i	$0.263321\pi$
$762$			26.7141i			0.967749i
$763$	29.9354	−	51.8497i	1.08374	−	1.87709i
$764$	5.61792	+	9.73052i	0.203249	+	0.352038i
$765$	3.28752	−	1.89805i	0.118860	−	0.0686241i
$766$	6.77049			0.244628
$767$	8.75545	−	10.8865i	0.316141	−	0.393089i
$768$	6.36236			0.229582
$769$	−33.8961	+	19.5699i	−1.22233	+	0.705710i	−0.965413	−	0.260725i	$-0.916039\pi$
$769$	−33.8961	+	19.5699i	−1.22233	+	0.705710i	−0.256913	+	0.966435i	$0.582705\pi$
$770$	−2.48965	−	4.31220i	−0.0897207	−	0.155401i
$771$	−0.127745	+	0.221261i	−0.00460062	+	0.00796851i
$772$			74.8492i			2.69388i
$773$	−15.7910	−	9.11692i	−0.567962	−	0.327913i	0.188373	−	0.982098i	$-0.439679\pi$
$773$	−15.7910	−	9.11692i	−0.567962	−	0.327913i	−0.756335	+	0.654185i	$0.773012\pi$
$774$	2.88912	+	1.66803i	0.103847	+	0.0599562i
$775$		−	5.04474i		−	0.181213i
$776$	3.21128	−	5.56210i	0.115278	−	0.199668i
$777$	−10.8730	−	18.8325i	−0.390065	−	0.675613i
$778$	−29.9549	+	17.2945i	−1.07393	+	0.620036i
$779$	−31.3721			−1.12402
$780$	−7.18220	−	1.11288i	−0.257164	−	0.0398476i
$781$	−5.13320			−0.183680
$782$	−64.7741	+	37.3973i	−2.31632	+	1.33733i
$783$	0.313126	+	0.542349i	0.0111902	+	0.0193820i
$784$	−2.37533	+	4.11420i	−0.0848334	+	0.146936i
$785$		−	2.33469i		−	0.0833288i
$786$	−28.6864	−	16.5621i	−1.02321	−	0.590750i
$787$	−4.31812	−	2.49307i	−0.153924	−	0.0888683i	0.421060	−	0.907033i	$-0.361658\pi$
$787$	−4.31812	−	2.49307i	−0.153924	−	0.0888683i	−0.574984	+	0.818165i	$0.694992\pi$
$788$		−	6.51030i		−	0.231920i
$789$	−0.0434967	+	0.0753385i	−0.00154852	+	0.00268212i
$790$	−1.99022	−	3.44717i	−0.0708089	−	0.122645i
$791$	12.6237	−	7.28831i	0.448848	−	0.259142i
$792$	2.02113			0.0718178
$793$	−41.1935	−	33.1298i	−1.46282	−	1.17647i
$794$	−4.68799			−0.166371
$795$	2.21912	−	1.28121i	0.0787042	−	0.0454399i
$796$	−14.8365	−	25.6976i	−0.525867	−	0.910828i
$797$	9.27694	−	16.0681i	0.328606	−	0.569162i	−0.653630	−	0.756815i	$-0.726755\pi$
$797$	9.27694	−	16.0681i	0.328606	−	0.569162i	0.982235	+	0.187652i	$0.0600879\pi$
$798$		−	35.2857i		−	1.24910i
$799$	53.1170	+	30.6671i	1.87915	+	1.08492i
$800$	−27.4921	−	15.8726i	−0.971992	−	0.561180i
$801$			13.8275i			0.488570i
$802$	−42.2653	+	73.2057i	−1.49244	+	2.58498i
$803$	−6.06743	−	10.5091i	−0.214115	−	0.370858i
$804$	−30.4891	+	17.6029i	−1.07527	+	0.620806i
$805$	13.8262			0.487310
$806$	8.31403	−	3.22347i	0.292849	−	0.113542i
$807$	−13.4881			−0.474802
$808$	−23.1460	+	13.3633i	−0.814273	+	0.470121i
$809$	0.436301	+	0.755696i	0.0153395	+	0.0265689i	0.873593	−	0.486657i	$-0.161784\pi$
$809$	0.436301	+	0.755696i	0.0153395	+	0.0265689i	−0.858254	+	0.513226i	$0.828450\pi$
$810$	0.767100	−	1.32866i	0.0269531	−	0.0466842i
$811$		−	43.3483i		−	1.52216i	−0.648656	−	0.761081i	$-0.724669\pi$
$811$		−	43.3483i		−	1.52216i	0.648656	−	0.761081i	$-0.275331\pi$
$812$	−5.12564	−	2.95929i	−0.179875	−	0.103851i
$813$	7.15986	+	4.13375i	0.251107	+	0.144977i
$814$			14.8497i			0.520483i
$815$	1.24478	−	2.15601i	0.0436026	−	0.0755219i
$816$	3.68641	+	6.38504i	0.129050	+	0.223521i
$817$	−6.39476	+	3.69202i	−0.223724	+	0.129167i
$818$	46.0147			1.60886
$819$	4.23020	+	10.9106i	0.147815	+	0.381247i
$820$	12.8913			0.450182
$821$	−33.8636	+	19.5512i	−1.18185	+	0.682340i	−0.956441	−	0.291925i	$-0.905704\pi$
$821$	−33.8636	+	19.5512i	−1.18185	+	0.682340i	−0.225406	+	0.974265i	$0.572371\pi$
$822$	18.0352	+	31.2379i	0.629051	+	1.08955i
$823$	−22.5527	+	39.0625i	−0.786138	+	1.36163i	0.142178	+	0.989841i	$0.454589\pi$
$823$	−22.5527	+	39.0625i	−0.786138	+	1.36163i	−0.928317	+	0.371790i	$0.878744\pi$
$824$		−	16.2000i		−	0.564354i
$825$	−3.91513	−	2.26040i	−0.136307	−	0.0786972i
$826$	−24.1370	−	13.9355i	−0.839832	−	0.484877i
$827$			29.5732i			1.02836i	0.857682	+	0.514180i	$0.171904\pi$
$827$			29.5732i			1.02836i	−0.857682	+	0.514180i	$0.828096\pi$
$828$	−8.96014	+	15.5194i	−0.311386	+	0.539337i
$829$	0.578101	+	1.00130i	0.0200783	+	0.0347766i	0.875890	−	0.482511i	$-0.160275\pi$
$829$	0.578101	+	1.00130i	0.0200783	+	0.0347766i	−0.855812	+	0.517287i	$0.826942\pi$
$830$	12.7500	−	7.36122i	0.442559	−	0.255512i
$831$	−16.2326			−0.563104
$832$	7.10756	−	45.8700i	0.246410	−	1.59025i
$833$	19.3770			0.671372
$834$	−10.0805	+	5.82001i	−0.349061	+	0.201530i
$835$	−3.10869	−	5.38441i	−0.107581	−	0.186335i
$836$	−7.14231	+	12.3708i	−0.247022	+	0.427855i
$837$			1.11589i			0.0385709i
$838$	27.7475	+	16.0200i	0.958521	+	0.553402i
$839$	14.6126	+	8.43656i	0.504481	+	0.291263i	0.730562	−	0.682846i	$-0.239258\pi$
$839$	14.6126	+	8.43656i	0.504481	+	0.291263i	−0.226081	+	0.974109i	$0.572591\pi$
$840$			4.54084i			0.156674i
$841$	14.3039	−	24.7751i	0.493238	−	0.854313i
$842$	2.20073	+	3.81177i	0.0758421	+	0.131362i
$843$	−7.10747	+	4.10350i	−0.244794	+	0.141332i
$844$	24.5812			0.846120
$845$	−2.72343	+	8.57709i	−0.0936889	+	0.295061i
$846$	24.7883			0.852241
$847$	2.81071	−	1.62277i	0.0965773	−	0.0557589i
$848$	2.48838	+	4.31000i	0.0854513	+	0.148006i
$849$	14.8140	−	25.6585i	0.508414	−	0.880598i
$850$			54.9446i			1.88458i
$851$	−35.7095	−	20.6169i	−1.22411	−	0.706738i
$852$	12.9450	+	7.47379i	0.443488	+	0.256048i
$853$		−	21.4477i		−	0.734357i	−0.930151	−	0.367178i	$-0.880324\pi$
$853$		−	21.4477i		−	0.734357i	0.930151	−	0.367178i	$-0.119676\pi$
$854$	−52.7306	+	91.3320i	−1.80440	+	3.12532i
$855$	1.69790	+	2.94084i	0.0580668	+	0.100575i
$856$	15.6406	−	9.03011i	0.534585	−	0.308643i
$857$	−26.9558			−0.920792			−0.460396	−	0.887714i	$-0.652293\pi$
$857$	−26.9558			−0.920792			−0.460396	+	0.887714i	$0.652293\pi$
$858$	1.22360	−	7.89671i	0.0417729	−	0.269589i
$859$	−15.3959			−0.525301			−0.262651	−	0.964891i	$-0.584597\pi$
$859$	−15.3959			−0.525301			−0.262651	+	0.964891i	$0.584597\pi$
$860$	2.62771	−	1.51711i	0.0896040	−	0.0517329i
$861$	−10.3780	−	17.9752i	−0.353681	−	0.612594i
$862$	26.2368	−	45.4435i	0.893630	−	1.54781i
$863$		−	26.3009i		−	0.895294i	−0.894210	−	0.447647i	$-0.852262\pi$
$863$		−	26.3009i		−	0.895294i	0.894210	−	0.447647i	$-0.147738\pi$
$864$	6.08123	+	3.51100i	0.206888	+	0.119447i
$865$	0.505870	+	0.292064i	0.0172001	+	0.00993047i
$866$		−	59.0599i		−	2.00694i
$867$	6.53607	−	11.3208i	0.221977	−	0.384475i
$868$	−5.27305	−	9.13320i	−0.178979	−	0.310001i
$869$	2.24688	−	1.29724i	0.0762203	−	0.0440058i
$870$	0.960794			0.0325740
$871$	15.7581	+	40.6436i	0.533944	+	1.37716i
$872$	37.2842			1.26260
$873$	2.75197	−	1.58885i	0.0931400	−	0.0537744i
$874$	−33.4537	−	57.9435i	−1.13159	−	1.95997i
$875$	10.6951	−	18.5245i	0.361560	−	0.626241i
$876$			35.3360i			1.19389i
$877$	16.3878	+	9.46150i	0.553377	+	0.319492i	0.750483	−	0.660890i	$-0.229821\pi$
$877$	16.3878	+	9.46150i	0.553377	+	0.319492i	−0.197106	+	0.980382i	$0.563154\pi$
$878$	−68.3855	−	39.4824i	−2.30790	−	1.33247i
$879$			9.20588i			0.310507i
$880$	−0.465346	+	0.806003i	−0.0156868	+	0.0271704i
$881$	6.84633	+	11.8582i	0.230659	+	0.399513i	0.958002	−	0.286761i	$-0.0925786\pi$
$881$	6.84633	+	11.8582i	0.230659	+	0.399513i	−0.727343	+	0.686274i	$0.759245\pi$
$882$	6.78205	−	3.91562i	0.228364	−	0.131846i
$883$	23.2710			0.783130			0.391565	−	0.920150i	$-0.371934\pi$
$883$	23.2710			0.783130			0.391565	+	0.920150i	$0.371934\pi$
$884$	−53.6818	+	20.8132i	−1.80551	+	0.700025i
$885$	2.68222			0.0901618
$886$	51.2640	−	29.5973i	1.72225	−	0.994339i
$887$	2.57606	+	4.46187i	0.0864956	+	0.149815i	0.906028	−	0.423219i	$-0.139100\pi$
$887$	2.57606	+	4.46187i	0.0864956	+	0.149815i	−0.819532	+	0.573034i	$0.805766\pi$
$888$	6.77106	−	11.7278i	0.227222	−	0.393560i
$889$		−	39.1201i		−	1.31205i
$890$	18.3720	+	10.6071i	0.615830	+	0.355550i
$891$	0.866025	+	0.500000i	0.0290129	+	0.0167506i
$892$		−	40.7816i		−	1.36547i
$893$	−27.4332	+	47.5157i	−0.918018	+	1.59005i
$894$	10.5783	+	18.3221i	0.353791	+	0.612783i
$895$	−6.78745	+	3.91874i	−0.226879	+	0.130989i
$896$	−47.0220			−1.57089
$897$	17.2906	+	13.9060i	0.577317	+	0.464307i
$898$	−23.3359			−0.778729
$899$	−0.605205	+	0.349415i	−0.0201847	+	0.0116536i
$900$	6.58217	+	11.4007i	0.219406	+	0.380022i
$901$	10.1496	−	17.5796i	0.338131	−	0.585661i
$902$			14.1737i			0.471933i
$903$	−4.23082	−	2.44267i	−0.140793	−	0.0812869i
$904$	7.86133	+	4.53874i	0.261464	+	0.150956i
$905$			9.69195i			0.322171i
$906$	19.6099	−	33.9653i	0.651495	−	1.12842i
$907$	15.1743	+	26.2826i	0.503853	+	0.872700i	0.999990	+	0.00445515i	$0.00141812\pi$
$907$	15.1743	+	26.2826i	0.503853	+	0.872700i	−0.496137	+	0.868244i	$0.665249\pi$
$908$	−62.6913	+	36.1949i	−2.08049	+	1.20117i
$909$	−13.2236			−0.438599
$910$	17.7414	+	2.74903i	0.588121	+	0.0911295i
$911$	−46.8985			−1.55382			−0.776909	−	0.629613i	$-0.783213\pi$
$911$	−46.8985			−1.55382			−0.776909	+	0.629613i	$0.783213\pi$
$912$	−5.71173	+	3.29767i	−0.189134	+	0.109197i
$913$	4.79809	+	8.31053i	0.158793	+	0.275038i
$914$	−14.8699	+	25.7555i	−0.491854	+	0.851915i
$915$		−	10.1493i		−	0.335524i
$916$	−25.4006	−	14.6650i	−0.839258	−	0.484546i
$917$	42.0083	+	24.2535i	1.38724	+	0.800921i
$918$		−	12.1537i		−	0.401132i
$919$	−16.5527	+	28.6701i	−0.546023	+	0.945740i	0.452519	+	0.891755i	$0.350526\pi$
$919$	−16.5527	+	28.6701i	−0.546023	+	0.945740i	−0.998542	+	0.0539848i	$0.982808\pi$
$920$	4.30509	+	7.45663i	0.141934	+	0.245838i
$921$	16.9686	−	9.79680i	0.559133	−	0.322816i
$922$	25.3799			0.835842
$923$	11.5992	−	14.4224i	0.381792	−	0.474718i
$924$	−9.45081			−0.310909
$925$	−26.2324	+	15.1453i	−0.862516	+	0.497974i
$926$	−37.1452	−	64.3373i	−1.22067	−	2.11426i
$927$	4.00766	−	6.94146i	0.131629	−	0.227988i
$928$			4.39754i			0.144356i
$929$	18.8910	+	10.9067i	0.619794	+	0.357838i	0.776789	−	0.629761i	$-0.216847\pi$
$929$	18.8910	+	10.9067i	0.619794	+	0.357838i	−0.156995	+	0.987599i	$0.550181\pi$
$930$	1.48264	+	0.856002i	0.0486176	+	0.0280694i
$931$			17.3336i			0.568087i
$932$	3.83914	−	6.64958i	0.125755	−	0.217814i
$933$	2.77776	+	4.81122i	0.0909397	+	0.157512i
$934$	7.01800	−	4.05184i	0.229636	−	0.132580i
$935$	3.79610			0.124146
$936$	−4.56704	+	5.67864i	−0.149278	+	0.185612i
$937$	−7.10452			−0.232094			−0.116047	−	0.993244i	$-0.537022\pi$
$937$	−7.10452			−0.232094			−0.116047	+	0.993244i	$0.537022\pi$
$938$	75.3137	−	43.4824i	2.45908	−	1.41975i
$939$	−13.2945	−	23.0268i	−0.433850	−	0.751451i
$940$	11.2727	−	19.5249i	0.367676	−	0.636833i
$941$			26.5720i			0.866221i	0.901341	+	0.433111i	$0.142584\pi$
$941$			26.5720i			0.866221i	−0.901341	+	0.433111i	$0.857416\pi$
$942$	−6.47340	−	3.73742i	−0.210915	−	0.121772i
$943$	−34.0839	−	19.6784i	−1.10993	−	0.640816i
$944$			5.20943i			0.169552i
$945$	−1.12334	+	1.94568i	−0.0365423	+	0.0632930i
$946$	1.66803	+	2.88912i	0.0542325	+	0.0939334i
$947$	23.4759	−	13.5538i	0.762864	−	0.440440i	−0.0674593	−	0.997722i	$-0.521489\pi$
$947$	23.4759	−	13.5538i	0.762864	−	0.440440i	0.830323	+	0.557282i	$0.188156\pi$
$948$	−7.55497			−0.245374
$949$	43.2369	+	6.69957i	1.40353	+	0.217477i
$950$	−49.1506			−1.59465
$951$	−16.7527	+	9.67219i	−0.543244	+	0.313642i
$952$	17.9859	+	31.1526i	0.582928	+	1.00966i
$953$	29.7421	−	51.5148i	0.963441	−	1.66873i	0.249696	−	0.968324i	$-0.419669\pi$
$953$	29.7421	−	51.5148i	0.963441	−	1.66873i	0.713745	−	0.700405i	$-0.246997\pi$
$954$		−	8.20394i		−	0.265612i
$955$	2.31317	+	1.33551i	0.0748525	+	0.0432161i
$956$	−57.5402	−	33.2208i	−1.86098	−	1.07444i
$957$			0.626251i			0.0202438i
$958$	44.1827	−	76.5266i	1.42748	−	2.47246i
$959$	−26.4108	−	45.7448i	−0.852848	−	1.47718i
$960$	7.71782	−	4.45588i	0.249091	−	0.143813i
$961$	29.7548			0.959832
$962$	−41.7222	−	33.5551i	−1.34518	−	1.08186i
$963$	8.93569			0.287949
$964$	17.2613	−	9.96583i	0.555950	−	0.320978i
$965$	8.89671	+	15.4096i	0.286395	+	0.496051i
$966$	22.1332	−	38.3359i	0.712125	−	1.23344i
$967$		−	27.3736i		−	0.880274i	−0.897931	−	0.440137i	$-0.854930\pi$
$967$		−	27.3736i		−	0.880274i	0.897931	−	0.440137i	$-0.145070\pi$
$968$	1.75035	+	1.01057i	0.0562585	+	0.0324808i
$969$	23.2969	+	13.4505i	0.748405	+	0.432092i
$970$		−	4.87523i		−	0.156534i
$971$	9.70080	−	16.8023i	0.311314	−	0.539211i	−0.667333	−	0.744759i	$-0.732564\pi$
$971$	9.70080	−	16.8023i	0.311314	−	0.539211i	0.978647	+	0.205548i	$0.0658977\pi$
$972$	−1.45597	−	2.52182i	−0.0467003	−	0.0808873i
$973$	14.7619	−	8.52281i	0.473246	−	0.273229i
$974$	−25.9514			−0.831535
$975$	15.1977	−	5.89237i	0.486716	−	0.188707i
$976$	19.7120			0.630966
$977$	21.7852	−	12.5777i	0.696969	−	0.402395i	−0.109249	−	0.994014i	$-0.534844\pi$
$977$	21.7852	−	12.5777i	0.696969	−	0.402395i	0.806217	+	0.591619i	$0.201511\pi$
$978$	−3.98532	−	6.90277i	−0.127436	−	0.220726i
$979$	−6.91375	+	11.9750i	−0.220964	+	0.382721i
$980$		−	7.12265i		−	0.227525i
$981$	15.9757	+	9.22358i	0.510065	+	0.294486i
$982$	−17.6827	−	10.2091i	−0.564277	−	0.325785i
$983$		−	7.79769i		−	0.248708i	−0.992238	−	0.124354i	$-0.960314\pi$
$983$		−	7.79769i		−	0.248708i	0.992238	−	0.124354i	$-0.0396858\pi$
$984$	6.46282	−	11.1939i	0.206027	−	0.356850i
$985$	−0.773825	−	1.34030i	−0.0246561	−	0.0427057i
$986$	6.59156	−	3.80564i	0.209918	−	0.121196i
$987$	−36.3000			−1.15544
$988$	−18.6184	−	48.0209i	−0.592331	−	1.52775i
$989$	−9.26339			−0.294559
$990$	1.32866	−	0.767100i	0.0422274	−	0.0243800i
$991$	30.6282	+	53.0496i	0.972937	+	1.68518i	0.686581	+	0.727054i	$0.259111\pi$
$991$	30.6282	+	53.0496i	0.972937	+	1.68518i	0.286357	+	0.958123i	$0.407556\pi$
$992$	−3.91791	+	6.78601i	−0.124394	+	0.215456i
$993$		−	8.52209i		−	0.270440i
$994$	−31.9765	−	18.4617i	−1.01423	−	0.585568i
$995$	−6.10893	−	3.52699i	−0.193666	−	0.111813i
$996$		−	27.9435i		−	0.885424i
$997$	15.4528	−	26.7650i	0.489395	−	0.847657i	−0.510531	−	0.859860i	$-0.670551\pi$
$997$	15.4528	−	26.7650i	0.489395	−	0.847657i	0.999926	+	0.0122027i	$0.00388435\pi$
$998$	22.4161	+	38.8258i	0.709570	+	1.22901i
$999$	5.80260	−	3.35013i	0.183586	−	0.105993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.a.166.2	✓	24
13.2	odd	12		5577.2.a.z.1.3		12
13.4	even	6	inner	429.2.s.a.199.2	yes	24
13.11	odd	12		5577.2.a.be.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.a.166.2	✓	24	1.1	even	1	trivial
429.2.s.a.199.2	yes	24	13.4	even	6	inner
5577.2.a.z.1.3		12	13.2	odd	12
5577.2.a.be.1.10		12	13.11	odd	12

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91936 + 1.10815i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.45597 - 2.52182i) q^{4} -0.692237i q^{5} +(-1.91936 - 1.10815i) q^{6} +(2.81071 + 1.62277i) q^{7} +2.02113i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.91936 + 1.10815i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.45597 - 2.52182i) q^{4} -0.692237i q^{5} +(-1.91936 - 1.10815i) q^{6} +(2.81071 + 1.62277i) q^{7} +2.02113i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.767100 + 1.32866i) q^{10} +(-0.866025 + 0.500000i) q^{11} +2.91194 q^{12} +(0.552093 - 3.56303i) q^{13} -7.19305 q^{14} +(0.599495 - 0.346119i) q^{15} +(0.672235 + 1.16434i) q^{16} +(2.74190 - 4.74912i) q^{17} -2.21629i q^{18} +(4.24831 + 2.45276i) q^{19} +(-1.74570 - 1.00788i) q^{20} +3.24553i q^{21} +(1.10815 - 1.91936i) q^{22} +(3.07703 + 5.32957i) q^{23} +(-1.75035 + 1.01057i) q^{24} +4.52081 q^{25} +(2.88869 + 7.45055i) q^{26} -1.00000 q^{27} +(8.18464 - 4.72541i) q^{28} +(-0.313126 - 0.542349i) q^{29} +(-0.767100 + 1.32866i) q^{30} -1.11589i q^{31} +(-6.08123 - 3.51100i) q^{32} +(-0.866025 - 0.500000i) q^{33} +12.1537i q^{34} +(1.12334 - 1.94568i) q^{35} +(1.45597 + 2.52182i) q^{36} +(-5.80260 + 3.35013i) q^{37} -10.8721 q^{38} +(3.36172 - 1.30339i) q^{39} +1.39910 q^{40} +(-5.53845 + 3.19762i) q^{41} +(-3.59652 - 6.22936i) q^{42} +(-0.752624 + 1.30358i) q^{43} +2.91194i q^{44} +(0.599495 + 0.346119i) q^{45} +(-11.8119 - 6.81959i) q^{46} +11.1846i q^{47} +(-0.672235 + 1.16434i) q^{48} +(1.76674 + 3.06009i) q^{49} +(-8.67707 + 5.00971i) q^{50} +5.48381 q^{51} +(-8.18148 - 6.57995i) q^{52} +3.70165 q^{53} +(1.91936 - 1.10815i) q^{54} +(0.346119 + 0.599495i) q^{55} +(-3.27983 + 5.68083i) q^{56} +4.90553i q^{57} +(1.20200 + 0.693977i) q^{58} +(3.35560 + 1.93735i) q^{59} -2.01576i q^{60} +(7.33077 - 12.6973i) q^{61} +(1.23657 + 2.14181i) q^{62} +(-2.81071 + 1.62277i) q^{63} +12.8739 q^{64} +(-2.46646 - 0.382179i) q^{65} +2.21629 q^{66} +(-10.4703 + 6.04506i) q^{67} +(-7.98427 - 13.8292i) q^{68} +(-3.07703 + 5.32957i) q^{69} +4.97930i q^{70} +(4.44548 + 2.56660i) q^{71} +(-1.75035 - 1.01057i) q^{72} +12.1349i q^{73} +(7.42486 - 12.8602i) q^{74} +(2.26040 + 3.91513i) q^{75} +(12.3708 - 7.14231i) q^{76} -3.24553 q^{77} +(-5.00802 + 6.22696i) q^{78} -2.59448 q^{79} +(0.806003 - 0.465346i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.08686 - 12.2748i) q^{82} -9.59617i q^{83} +(8.18464 + 4.72541i) q^{84} +(-3.28752 - 1.89805i) q^{85} -3.33607i q^{86} +(0.313126 - 0.542349i) q^{87} +(-1.01057 - 1.75035i) q^{88} +(11.9750 - 6.91375i) q^{89} -1.53420 q^{90} +(7.33374 - 9.11875i) q^{91} +17.9203 q^{92} +(0.966393 - 0.557947i) q^{93} +(-12.3942 - 21.4673i) q^{94} +(1.69790 - 2.94084i) q^{95} -7.02200i q^{96} +(-2.75197 - 1.58885i) q^{97} +(-6.78205 - 3.91562i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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