LMFDB - Embedded newform 75.3.k.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	75.13
Dual form			75.3.k.a.52.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.367346 - 0.0581819i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(-3.67267 + 1.19332i) q^{4} +(-3.52059 + 3.55042i) q^{5} +(-0.199067 + 0.612664i) q^{6} +(-1.57845 + 1.57845i) q^{7} +(-2.60526 + 1.32745i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(0.367346 - 0.0581819i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(-3.67267 + 1.19332i) q^{4} +(-3.52059 + 3.55042i) q^{5} +(-0.199067 + 0.612664i) q^{6} +(-1.57845 + 1.57845i) q^{7} +(-2.60526 + 1.32745i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(-1.08670 + 1.50906i) q^{10} +(9.51813 + 6.91533i) q^{11} +(1.04633 - 6.60626i) q^{12} +(-0.158460 - 0.0250976i) q^{13} +(-0.487999 + 0.671673i) q^{14} +(-2.71088 - 8.22503i) q^{15} +(11.6168 - 8.44012i) q^{16} +(6.98020 + 13.6994i) q^{17} +(-0.788972 - 0.788972i) q^{18} +(-17.4110 - 5.65719i) q^{19} +(8.69317 - 17.2407i) q^{20} +(-1.19478 - 3.67715i) q^{21} +(3.89879 + 1.98653i) q^{22} +(5.54091 + 34.9839i) q^{23} -5.06443i q^{24} +(-0.210906 - 24.9991i) q^{25} -0.0596699 q^{26} +(5.13218 - 0.812857i) q^{27} +(3.91351 - 7.68071i) q^{28} +(1.00211 - 0.325606i) q^{29} +(-1.47438 - 2.86371i) q^{30} +(13.5515 - 41.7072i) q^{31} +(12.0465 - 12.0465i) q^{32} +(-18.1566 + 9.25127i) q^{33} +(3.36120 + 4.62630i) q^{34} +(-0.0470801 - 11.1612i) q^{35} +(9.37247 + 6.80950i) q^{36} +(-11.1326 + 70.2885i) q^{37} +(-6.72501 - 1.06514i) q^{38} +(0.163335 - 0.224811i) q^{39} +(4.45906 - 13.9231i) q^{40} +(-9.47513 + 6.88408i) q^{41} +(-0.652841 - 1.28127i) q^{42} +(-14.9572 - 14.9572i) q^{43} +(-43.2092 - 14.0395i) q^{44} +(14.8251 + 2.28400i) q^{45} +(4.07086 + 12.5288i) q^{46} +(39.3212 + 20.0352i) q^{47} +(3.89066 + 24.5647i) q^{48} +44.0170i q^{49} +(-1.53197 - 9.17105i) q^{50} -26.6306 q^{51} +(0.611921 - 0.0969188i) q^{52} +(-18.2061 + 35.7314i) q^{53} +(1.83799 - 0.597200i) q^{54} +(-58.0617 + 9.44730i) q^{55} +(2.01696 - 6.20757i) q^{56} +(22.4215 - 22.4215i) q^{57} +(0.349178 - 0.177915i) q^{58} +(-27.8650 - 38.3529i) q^{59} +(19.7713 + 26.9728i) q^{60} +(45.4514 + 33.0224i) q^{61} +(2.55148 - 16.1094i) q^{62} +(6.61433 + 1.04761i) q^{63} +(-30.0361 + 41.3412i) q^{64} +(0.646980 - 0.474241i) q^{65} +(-6.13151 + 4.45480i) q^{66} +(-10.0539 - 19.7319i) q^{67} +(-41.9838 - 41.9838i) q^{68} +(-58.3466 - 18.9580i) q^{69} +(-0.666674 - 4.09728i) q^{70} +(-13.8403 - 42.5959i) q^{71} +(7.81578 + 3.98234i) q^{72} +(-2.13248 - 13.4640i) q^{73} +26.4679i q^{74} +(38.7462 + 19.3322i) q^{75} +70.6958 q^{76} +(-25.9393 + 4.10839i) q^{77} +(0.0469205 - 0.0920867i) q^{78} +(148.503 - 48.2515i) q^{79} +(-10.9321 + 70.9588i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-3.08012 + 3.08012i) q^{82} +(87.7020 - 44.6864i) q^{83} +(8.77606 + 12.0792i) q^{84} +(-73.2130 - 23.4474i) q^{85} +(-6.36472 - 4.62424i) q^{86} +(-0.285498 + 1.80256i) q^{87} +(-33.9769 - 5.38142i) q^{88} +(75.3521 - 103.713i) q^{89} +(5.57882 - 0.0235326i) q^{90} +(0.289736 - 0.210506i) q^{91} +(-62.0970 - 121.872i) q^{92} +(53.7094 + 53.7094i) q^{93} +(15.6102 + 5.07205i) q^{94} +(81.3824 - 41.8998i) q^{95} +(9.11842 + 28.0636i) q^{96} +(-34.6127 - 17.6360i) q^{97} +(2.56099 + 16.1695i) q^{98} -35.2952i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	0.367346	−	0.0581819i	0.183673	−	0.0290909i	−0.0639203	−	0.997955i	$-0.520360\pi$
$2$	0.367346	−	0.0581819i	0.183673	−	0.0290909i	0.247593	+	0.968864i	$0.420360\pi$
$3$	−0.786335	+	1.54327i	−0.262112	+	0.514423i
$3$	−0.786335	+	1.54327i	−0.262112	+	0.514423i
$4$	−3.67267	+	1.19332i	−0.918167	+	0.298331i
$5$	−3.52059	+	3.55042i	−0.704118	+	0.710083i
$5$	−3.52059	+	3.55042i	−0.704118	+	0.710083i
$6$	−0.199067	+	0.612664i	−0.0331778	+	0.102111i
$7$	−1.57845	+	1.57845i	−0.225492	+	0.225492i	−0.810807	−	0.585314i	$-0.800971\pi$
$7$	−1.57845	+	1.57845i	−0.225492	+	0.225492i	0.585314	+	0.810807i	$0.300971\pi$
$8$	−2.60526	+	1.32745i	−0.325657	+	0.165931i
$9$	−1.76336	−	2.42705i	−0.195928	−	0.269672i
$10$	−1.08670	+	1.50906i	−0.108670	+	0.150906i
$11$	9.51813	+	6.91533i	0.865285	+	0.628666i	0.929318	−	0.369282i	$-0.120396\pi$
$11$	9.51813	+	6.91533i	0.865285	+	0.628666i	−0.0640327	+	0.997948i	$0.520396\pi$
$12$	1.04633	−	6.60626i	0.0871941	−	0.550522i
$13$	−0.158460	−	0.0250976i	−0.0121892	−	0.00193059i	0.150337	−	0.988635i	$-0.451964\pi$
$13$	−0.158460	−	0.0250976i	−0.0121892	−	0.00193059i	−0.162526	+	0.986704i	$0.551964\pi$
$14$	−0.487999	+	0.671673i	−0.0348571	+	0.0479766i
$15$	−2.71088	−	8.22503i	−0.180726	−	0.548335i
$16$	11.6168	−	8.44012i	0.726052	−	0.527508i
$17$	6.98020	+	13.6994i	0.410600	+	0.805848i	0.999998	−	0.00199499i	$-0.000635027\pi$
$17$	6.98020	+	13.6994i	0.410600	+	0.805848i	−0.589398	+	0.807843i	$0.700635\pi$
$18$	−0.788972	−	0.788972i	−0.0438318	−	0.0438318i
$19$	−17.4110	−	5.65719i	−0.916370	−	0.297747i	−0.187393	−	0.982285i	$-0.560004\pi$
$19$	−17.4110	−	5.65719i	−0.916370	−	0.297747i	−0.728977	+	0.684538i	$0.760004\pi$
$20$	8.69317	−	17.2407i	0.434658	−	0.862035i
$21$	−1.19478	−	3.67715i	−0.0568943	−	0.175103i
$22$	3.89879	+	1.98653i	0.177218	+	0.0902970i
$23$	5.54091	+	34.9839i	0.240909	+	1.52104i	0.750643	+	0.660708i	$0.229744\pi$
$23$	5.54091	+	34.9839i	0.240909	+	1.52104i	−0.509734	+	0.860332i	$0.670256\pi$
$24$		−	5.06443i		−	0.211018i
$25$	−0.210906	−	24.9991i	−0.00843624	−	0.999964i
$26$	−0.0596699			−0.00229500
$27$	5.13218	−	0.812857i	0.190081	−	0.0301058i
$28$	3.91351	−	7.68071i	0.139768	−	0.274311i
$29$	1.00211	−	0.325606i	0.0345556	−	0.0112278i	−0.291688	−	0.956513i	$-0.594217\pi$
$29$	1.00211	−	0.325606i	0.0345556	−	0.0112278i	0.326244	+	0.945286i	$0.394217\pi$
$30$	−1.47438	−	2.86371i	−0.0491460	−	0.0954569i
$31$	13.5515	−	41.7072i	0.437145	−	1.34539i	−0.453727	−	0.891141i	$-0.649906\pi$
$31$	13.5515	−	41.7072i	0.437145	−	1.34539i	0.890872	−	0.454254i	$-0.150094\pi$
$32$	12.0465	−	12.0465i	0.376454	−	0.376454i
$33$	−18.1566	+	9.25127i	−0.550201	+	0.280342i
$34$	3.36120	+	4.62630i	0.0988590	+	0.136068i
$35$	−0.0470801	−	11.1612i	−0.00134515	−	0.318891i
$36$	9.37247	+	6.80950i	0.260347	+	0.189153i
$37$	−11.1326	+	70.2885i	−0.300881	+	1.89969i	0.120342	+	0.992732i	$0.461601\pi$
$37$	−11.1326	+	70.2885i	−0.300881	+	1.89969i	−0.421223	+	0.906957i	$0.638399\pi$
$38$	−6.72501	−	1.06514i	−0.176974	−	0.0280299i
$39$	0.163335	−	0.224811i	0.00418808	−	0.00576440i
$40$	4.45906	−	13.9231i	0.111477	−	0.348079i
$41$	−9.47513	+	6.88408i	−0.231101	+	0.167904i	−0.697309	−	0.716770i	$-0.745620\pi$
$41$	−9.47513	+	6.88408i	−0.231101	+	0.167904i	0.466209	+	0.884675i	$0.345620\pi$
$42$	−0.652841	−	1.28127i	−0.0155438	−	0.0305065i
$43$	−14.9572	−	14.9572i	−0.347843	−	0.347843i	0.511463	−	0.859305i	$-0.329104\pi$
$43$	−14.9572	−	14.9572i	−0.347843	−	0.347843i	−0.859305	+	0.511463i	$0.829104\pi$
$44$	−43.2092	−	14.0395i	−0.982026	−	0.319080i
$45$	14.8251	+	2.28400i	0.329446	+	0.0507556i
$46$	4.07086	+	12.5288i	0.0884970	+	0.272366i
$47$	39.3212	+	20.0352i	0.836622	+	0.426280i	0.819158	−	0.573567i	$-0.194441\pi$
$47$	39.3212	+	20.0352i	0.836622	+	0.426280i	0.0174635	+	0.999848i	$0.494441\pi$
$48$	3.89066	+	24.5647i	0.0810554	+	0.511764i
$49$			44.0170i			0.898306i
$50$	−1.53197	−	9.17105i	−0.0306394	−	0.183421i
$51$	−26.6306			−0.522169
$52$	0.611921	−	0.0969188i	0.0117677	−	0.00186382i
$53$	−18.2061	+	35.7314i	−0.343510	+	0.674177i	−0.996536	−	0.0831584i	$-0.973499\pi$
$53$	−18.2061	+	35.7314i	−0.343510	+	0.674177i	0.653026	+	0.757336i	$0.273499\pi$
$54$	1.83799	−	0.597200i	0.0340369	−	0.0110593i
$55$	−58.0617	+	9.44730i	−1.05567	+	0.171769i
$56$	2.01696	−	6.20757i	0.0360171	−	0.110849i
$57$	22.4215	−	22.4215i	0.393359	−	0.393359i
$58$	0.349178	−	0.177915i	0.00602030	−	0.00306750i
$59$	−27.8650	−	38.3529i	−0.472288	−	0.650049i	0.504712	−	0.863288i	$-0.331599\pi$
$59$	−27.8650	−	38.3529i	−0.472288	−	0.650049i	−0.977000	+	0.213239i	$0.931599\pi$
$60$	19.7713	+	26.9728i	0.329521	+	0.449547i
$61$	45.4514	+	33.0224i	0.745105	+	0.541351i	0.894306	−	0.447456i	$-0.147670\pi$
$61$	45.4514	+	33.0224i	0.745105	+	0.541351i	−0.149200	+	0.988807i	$0.547670\pi$
$62$	2.55148	−	16.1094i	0.0411530	−	0.259830i
$63$	6.61433	+	1.04761i	0.104989	+	0.0166287i
$64$	−30.0361	+	41.3412i	−0.469315	+	0.645956i
$65$	0.646980	−	0.474241i	0.00995354	−	0.00729602i
$66$	−6.13151	+	4.45480i	−0.0929017	+	0.0674970i
$67$	−10.0539	−	19.7319i	−0.150058	−	0.294506i	0.803725	−	0.595001i	$-0.202848\pi$
$67$	−10.0539	−	19.7319i	−0.150058	−	0.294506i	−0.953783	+	0.300495i	$0.902848\pi$
$68$	−41.9838	−	41.9838i	−0.617408	−	0.617408i
$69$	−58.3466	−	18.9580i	−0.845603	−	0.274753i
$70$	−0.666674	−	4.09728i	−0.00952392	−	0.0585326i
$71$	−13.8403	−	42.5959i	−0.194933	−	0.599943i	−0.999977	−	0.00672787i	$-0.997858\pi$
$71$	−13.8403	−	42.5959i	−0.194933	−	0.599943i	0.805044	−	0.593215i	$-0.202142\pi$
$72$	7.81578	+	3.98234i	0.108552	+	0.0553103i
$73$	−2.13248	−	13.4640i	−0.0292121	−	0.184438i	0.968768	−	0.247970i	$-0.0797635\pi$
$73$	−2.13248	−	13.4640i	−0.0292121	−	0.184438i	−0.997980	+	0.0635321i	$0.979763\pi$
$74$			26.4679i			0.357674i
$75$	38.7462	+	19.3322i	0.516616	+	0.257762i
$76$	70.6958			0.930208
$77$	−25.9393	+	4.10839i	−0.336875	+	0.0533557i
$78$	0.0469205	−	0.0920867i	0.000601545	−	0.00118060i
$79$	148.503	−	48.2515i	1.87978	−	0.610779i	0.892683	−	0.450686i	$-0.148820\pi$
$79$	148.503	−	48.2515i	1.87978	−	0.610779i	0.987102	−	0.160093i	$-0.0511795\pi$
$80$	−10.9321	+	70.9588i	−0.136652	+	0.886985i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	−3.08012	+	3.08012i	−0.0375624	+	0.0375624i
$83$	87.7020	−	44.6864i	1.05665	−	0.538390i	0.162755	−	0.986666i	$-0.447962\pi$
$83$	87.7020	−	44.6864i	1.05665	−	0.538390i	0.893895	+	0.448276i	$0.147962\pi$
$84$	8.77606	+	12.0792i	0.104477	+	0.143800i
$85$	−73.2130	−	23.4474i	−0.861330	−	0.275852i
$86$	−6.36472	−	4.62424i	−0.0740084	−	0.0537702i
$87$	−0.285498	+	1.80256i	−0.00328159	+	0.0207191i
$88$	−33.9769	−	5.38142i	−0.386102	−	0.0611525i
$89$	75.3521	−	103.713i	0.846653	−	1.16532i	−0.137938	−	0.990441i	$-0.544047\pi$
$89$	75.3521	−	103.713i	0.846653	−	1.16532i	0.984590	−	0.174877i	$-0.0559527\pi$
$90$	5.57882	−	0.0235326i	0.0619869	−	0.000261473i
$91$	0.289736	−	0.210506i	0.00318391	−	0.00231325i
$92$	−62.0970	−	121.872i	−0.674968	−	1.32470i
$93$	53.7094	+	53.7094i	0.577521	+	0.577521i
$94$	15.6102	+	5.07205i	0.166066	+	0.0539580i
$95$	81.3824	−	41.8998i	0.856657	−	0.441050i
$96$	9.11842	+	28.0636i	0.0949835	+	0.292329i
$97$	−34.6127	−	17.6360i	−0.356832	−	0.181815i	0.266380	−	0.963868i	$-0.414172\pi$
$97$	−34.6127	−	17.6360i	−0.356832	−	0.181815i	−0.623211	+	0.782053i	$0.714172\pi$
$98$	2.56099	+	16.1695i	0.0261326	+	0.164995i
$99$		−	35.2952i		−	0.356517i
$100$	30.6066	+	91.5618i	0.306066	+	0.915618i
$101$	−138.856			−1.37481			−0.687404	−	0.726275i	$-0.741250\pi$
$101$	−138.856			−1.37481			−0.687404	+	0.726275i	$0.741250\pi$
$102$	−9.78266	+	1.54942i	−0.0959084	+	0.0151904i
$103$	57.3217	−	112.500i	0.556521	−	1.09223i	−0.425763	−	0.904835i	$-0.639994\pi$
$103$	57.3217	−	112.500i	0.556521	−	1.09223i	0.982284	−	0.187399i	$-0.0600058\pi$
$104$	0.446146	−	0.144961i	0.00428986	−	0.00139386i
$105$	17.2618	+	8.70378i	0.164398	+	0.0828932i
$106$	−4.60900	+	14.1850i	−0.0434811	+	0.133821i
$107$	9.22047	−	9.22047i	0.0861727	−	0.0861727i	−0.662707	−	0.748879i	$-0.730592\pi$
$107$	9.22047	−	9.22047i	0.0861727	−	0.0861727i	0.748879	+	0.662707i	$0.230592\pi$
$108$	−17.8788	+	9.10970i	−0.165544	+	0.0843491i
$109$	94.1660	+	129.608i	0.863908	+	1.18907i	0.980623	+	0.195903i	$0.0627636\pi$
$109$	94.1660	+	129.608i	0.863908	+	1.18907i	−0.116715	+	0.993165i	$0.537236\pi$
$110$	−20.7791	+	6.84857i	−0.188901	+	0.0622597i
$111$	−99.7201	−	72.4509i	−0.898379	−	0.652711i
$112$	−5.01427	+	31.6588i	−0.0447702	+	0.282668i
$113$	67.5205	+	10.6942i	0.597527	+	0.0946390i	0.447869	−	0.894099i	$-0.352183\pi$
$113$	67.5205	+	10.6942i	0.597527	+	0.0946390i	0.149657	+	0.988738i	$0.452183\pi$
$114$	6.93191	−	9.54095i	0.0608062	−	0.0836925i
$115$	−143.715	−	103.492i	−1.24969	−	0.899926i
$116$	−3.29187	+	2.39169i	−0.0283782	+	0.0206180i
$117$	0.218508	+	0.428847i	0.00186759	+	0.00366536i
$118$	−12.4675	−	12.4675i	−0.105657	−	0.105657i
$119$	−32.6417	−	10.6059i	−0.274300	−	0.0891254i
$120$	17.9808	+	17.8298i	0.149840	+	0.148582i
$121$	5.38204	+	16.5642i	0.0444797	+	0.136894i
$122$	18.6177	+	9.48619i	0.152604	+	0.0777557i
$123$	−3.17337	−	20.0359i	−0.0257997	−	0.162893i
$124$			169.348i			1.36571i
$125$	89.4998	+	87.2628i	0.715998	+	0.698102i
$126$	2.49070			0.0197675
$127$	−230.979	+	36.5835i	−1.81873	+	0.288059i	−0.970418	−	0.241433i	$-0.922383\pi$
$127$	−230.979	+	36.5835i	−1.81873	+	0.288059i	−0.848315	+	0.529492i	$0.822383\pi$
$128$	−39.5657	+	77.6521i	−0.309107	+	0.606657i
$129$	34.8444	−	11.3216i	0.270112	−	0.0877647i
$130$	0.210073	−	0.211853i	0.00161595	−	0.00162964i
$131$	−71.5894	+	220.329i	−0.546484	+	1.68190i	0.170952	+	0.985279i	$0.445316\pi$
$131$	−71.5894	+	220.329i	−0.546484	+	1.68190i	−0.717436	+	0.696625i	$0.754684\pi$
$132$	55.6436	−	55.6436i	0.421542	−	0.421542i
$133$	36.4119	−	18.5528i	0.273774	−	0.139495i
$134$	−4.84129	−	6.66347i	−0.0361291	−	0.0497274i
$135$	−15.1823	+	21.0831i	−0.112462	+	0.156171i
$136$	−36.3705	−	26.4247i	−0.267430	−	0.194299i
$137$	−8.83441	+	55.7783i	−0.0644848	+	0.407141i	0.934240	+	0.356646i	$0.116080\pi$
$137$	−8.83441	+	55.7783i	−0.0644848	+	0.407141i	−0.998724	+	0.0504947i	$0.983920\pi$
$138$	−22.5364	−	3.56941i	−0.163307	−	0.0258653i
$139$	91.3173	−	125.687i	0.656959	−	0.904226i	−0.342417	−	0.939548i	$-0.611246\pi$
$139$	91.3173	−	125.687i	0.656959	−	0.904226i	0.999376	+	0.0353216i	$0.0112456\pi$
$140$	13.4918	+	40.9352i	0.0963701	+	0.292394i
$141$	−61.8393	+	44.9289i	−0.438577	+	0.318644i
$142$	−7.56247	−	14.8422i	−0.0532569	−	0.104522i
$143$	−1.33469	−	1.33469i	−0.00933347	−	0.00933347i
$144$	−40.9692	−	13.3117i	−0.284509	−	0.0924424i
$145$	−2.37199	+	4.70424i	−0.0163585	+	0.0324430i
$146$	−1.56672	−	4.82186i	−0.0107309	−	0.0330264i
$147$	−67.9301	−	34.6121i	−0.462109	−	0.235456i
$148$	−42.9905	−	271.431i	−0.290476	−	1.83399i
$149$			279.322i			1.87465i	0.348460	+	0.937324i	$0.386705\pi$
$149$			279.322i			1.87465i	−0.348460	+	0.937324i	$0.613295\pi$
$150$	15.3580	+	4.84727i	0.102387	+	0.0323151i
$151$	8.72498			0.0577813			0.0288907	−	0.999583i	$-0.490803\pi$
$151$	8.72498			0.0577813			0.0288907	+	0.999583i	$0.490803\pi$
$152$	52.8699	−	8.37376i	0.347828	−	0.0550905i
$153$	20.9406	−	41.0982i	0.136867	−	0.268616i
$154$	−9.28968	+	3.01840i	−0.0603226	+	0.0196000i
$155$	100.369	+	194.948i	0.647540	+	1.25773i
$156$	−0.331603	+	1.02057i	−0.00212566	+	0.00654211i
$157$	92.1654	−	92.1654i	0.587041	−	0.587041i	−0.349788	−	0.936829i	$-0.613746\pi$
$157$	92.1654	−	92.1654i	0.587041	−	0.587041i	0.936829	+	0.349788i	$0.113746\pi$
$158$	51.7446	−	26.3652i	0.327497	−	0.166868i
$159$	−40.8271	−	56.1937i	−0.256774	−	0.353419i
$160$	0.359310	+	85.1810i	0.00224569	+	0.532381i
$161$	−63.9663	−	46.4742i	−0.397306	−	0.288660i
$162$	−0.523637	+	3.30611i	−0.00323233	+	0.0204081i
$163$	21.2651	+	3.36806i	0.130461	+	0.0206629i	0.221323	−	0.975200i	$-0.428962\pi$
$163$	21.2651	+	3.36806i	0.130461	+	0.0206629i	−0.0908626	+	0.995863i	$0.528962\pi$
$164$	26.5841	−	36.5898i	0.162098	−	0.223109i
$165$	31.0762	−	97.0336i	0.188341	−	0.588082i
$166$	29.6170	−	21.5180i	0.178416	−	0.129627i
$167$	−69.5781	−	136.555i	−0.416635	−	0.817693i	−0.999985	−	0.00547160i	$-0.998258\pi$
$167$	−69.5781	−	136.555i	−0.416635	−	0.817693i	0.583350	−	0.812221i	$-0.301742\pi$
$168$	7.99393	+	7.99393i	0.0475829	+	0.0475829i
$169$	−160.704	−	52.2159i	−0.950912	−	0.308970i
$170$	−28.2587	−	4.35363i	−0.166228	−	0.0256096i
$171$	16.9716	+	52.2331i	0.0992489	+	0.305457i
$172$	72.7818	+	37.0842i	0.423150	+	0.215606i
$173$	1.89520	+	11.9658i	0.0109549	+	0.0691666i	0.992560	−	0.121755i	$-0.0388523\pi$
$173$	1.89520	+	11.9658i	0.0109549	+	0.0691666i	−0.981605	+	0.190922i	$0.938852\pi$
$174$			0.678775i			0.00390101i
$175$	39.7927	+	39.1269i	0.227387	+	0.223582i
$176$	168.937			0.959868
$177$	81.1001	−	12.8450i	0.458192	−	0.0725705i
$178$	21.6460	−	42.4828i	0.121607	−	0.238667i
$179$	146.652	−	47.6501i	0.819284	−	0.266202i	0.130759	−	0.991414i	$-0.458259\pi$
$179$	146.652	−	47.6501i	0.819284	−	0.266202i	0.688525	+	0.725213i	$0.258259\pi$
$180$	−57.1732	+	9.30273i	−0.317629	+	0.0516818i
$181$	−5.32203	+	16.3795i	−0.0294035	+	0.0904946i	−0.964681	−	0.263420i	$-0.915150\pi$
$181$	−5.32203	+	16.3795i	−0.0294035	+	0.0904946i	0.935278	+	0.353914i	$0.115150\pi$
$182$	0.0941857	−	0.0941857i	0.000517504	−	0.000517504i
$183$	−86.7025	+	44.1771i	−0.473784	+	0.241405i
$184$	−60.8748	−	83.7870i	−0.330841	−	0.455364i
$185$	−210.360	−	286.982i	−1.13708	−	1.55126i
$186$	22.8549	+	16.6050i	0.122876	+	0.0892743i
$187$	−28.2975	+	178.663i	−0.151323	+	0.955418i
$188$	−168.322	−	26.6596i	−0.895331	−	0.141807i
$189$	−6.81782	+	9.38392i	−0.0360731	+	0.0496504i
$190$	27.4577	−	20.1267i	0.144514	−	0.105930i
$191$	130.936	−	95.1303i	0.685527	−	0.498065i	−0.189660	−	0.981850i	$-0.560738\pi$
$191$	130.936	−	95.1303i	0.685527	−	0.498065i	0.875187	+	0.483785i	$0.160738\pi$
$192$	−40.1821	−	78.8619i	−0.209282	−	0.410739i
$193$	137.301	+	137.301i	0.711405	+	0.711405i	0.966829	−	0.255424i	$-0.0822151\pi$
$193$	137.301	+	137.301i	0.711405	+	0.711405i	−0.255424	+	0.966829i	$0.582215\pi$
$194$	−13.7409	−	4.46469i	−0.0708294	−	0.0230139i
$195$	0.223138	+	1.37138i	0.00114430	+	0.00703270i
$196$	−52.5265	−	161.660i	−0.267992	−	0.824795i
$197$	288.764	+	147.133i	1.46581	+	0.746866i	0.991080	−	0.133266i	$-0.0425466\pi$
$197$	288.764	+	147.133i	1.46581	+	0.746866i	0.474727	+	0.880133i	$0.342547\pi$
$198$	−2.05354	−	12.9655i	−0.0103714	−	0.0654825i
$199$			90.1197i			0.452863i	0.974027	+	0.226431i	$0.0727059\pi$
$199$			90.1197i			0.452863i	−0.974027	+	0.226431i	$0.927294\pi$
$200$	33.7344	+	64.8492i	0.168672	+	0.324246i
$201$	38.3573			0.190832
$202$	−51.0080	+	8.07888i	−0.252515	+	0.0399944i
$203$	−1.06783	+	2.09573i	−0.00526024	+	0.0103238i
$204$	97.8055	−	31.7789i	0.479439	−	0.155779i
$205$	8.91667	−	57.8767i	0.0434960	−	0.282325i
$206$	14.5114	−	44.6615i	0.0704437	−	0.216803i
$207$	75.1372	−	75.1372i	0.362982	−	0.362982i
$208$	−2.05263	+	1.04587i	−0.00986842	+	0.00502821i
$209$	−126.599	−	174.249i	−0.605738	−	0.833727i
$210$	6.84744	+	2.19298i	0.0326068	+	0.0104427i
$211$	−2.00819	−	1.45903i	−0.00951748	−	0.00691485i	0.583016	−	0.812460i	$-0.301872\pi$
$211$	−2.00819	−	1.45903i	−0.00951748	−	0.00691485i	−0.592534	+	0.805546i	$0.701872\pi$
$212$	24.2257	−	152.955i	0.114272	−	0.721487i
$213$	76.6200	+	12.1354i	0.359719	+	0.0569738i
$214$	2.85064	−	3.92357i	0.0133207	−	0.0183344i
$215$	105.763	−	0.446128i	0.491920	−	0.00207501i
$216$	−12.2916	+	8.93040i	−0.0569057	+	0.0413444i
$217$	44.4423	+	87.2230i	0.204803	+	0.401949i
$218$	42.1324	+	42.1324i	0.193268	+	0.193268i
$219$	22.4554	+	7.29619i	0.102536	+	0.0333159i
$220$	201.968	−	103.983i	0.918035	−	0.472651i
$221$	−0.762261	−	2.34600i	−0.00344914	−	0.0106154i
$222$	−40.8471	−	20.8126i	−0.183996	−	0.0937506i
$223$	21.8714	+	138.090i	0.0980779	+	0.619240i	0.986943	+	0.161070i	$0.0514946\pi$
$223$	21.8714	+	138.090i	0.0980779	+	0.619240i	−0.888865	+	0.458169i	$0.848505\pi$
$224$			38.0296i			0.169775i
$225$	−60.3022	+	44.5942i	−0.268010	+	0.198196i
$226$	25.4256			0.112503
$227$	−294.930	+	46.7123i	−1.29925	+	0.205781i	−0.767461	−	0.641096i	$-0.778480\pi$
$227$	−294.930	+	46.7123i	−1.29925	+	0.205781i	−0.531789	+	0.846877i	$0.678480\pi$
$228$	−55.5905	+	109.103i	−0.243818	+	0.478520i
$229$	68.2329	−	22.1702i	0.297960	−	0.0968132i	−0.156222	−	0.987722i	$-0.549932\pi$
$229$	68.2329	−	22.1702i	0.297960	−	0.0968132i	0.454182	+	0.890909i	$0.349932\pi$
$230$	−58.8144	−	29.6556i	−0.255715	−	0.128937i
$231$	14.0567	−	43.2619i	0.0608513	−	0.187281i
$232$	−2.17854	+	2.17854i	−0.00939025	+	0.00939025i
$233$	−263.540	+	134.280i	−1.13107	+	0.576310i	−0.916355	−	0.400367i	$-0.868883\pi$
$233$	−263.540	+	134.280i	−1.13107	+	0.576310i	−0.214717	+	0.976676i	$0.568883\pi$
$234$	0.105219	+	0.144822i	0.000449655	+	0.000618897i
$235$	−209.567	+	69.0711i	−0.891775	+	0.293920i
$236$	148.106	+	107.606i	0.627569	+	0.455956i
$237$	−42.3079	+	267.122i	−0.178515	+	1.12710i
$238$	−12.6078	−	1.99689i	−0.0529742	−	0.00839028i
$239$	25.8655	−	35.6008i	0.108224	−	0.148957i	−0.751470	−	0.659768i	$-0.770655\pi$
$239$	25.8655	−	35.6008i	0.108224	−	0.148957i	0.859693	+	0.510811i	$0.170655\pi$
$240$	−100.912	−	72.6686i	−0.420467	−	0.302786i
$241$	48.4056	−	35.1688i	0.200853	−	0.145928i	−0.482812	−	0.875724i	$-0.660385\pi$
$241$	48.4056	−	35.1688i	0.200853	−	0.145928i	0.683666	+	0.729795i	$0.260385\pi$
$242$	2.94081	+	5.77166i	0.0121521	+	0.0238498i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$	−206.334	−	67.0421i	−0.845633	−	0.274763i
$245$	−156.279	−	154.966i	−0.637872	−	0.632514i
$246$	−2.33145	−	7.17546i	−0.00947743	−	0.0291685i
$247$	2.61697	+	1.33341i	0.0105950	+	0.00539844i
$248$	20.0589	+	126.647i	0.0808828	+	0.510674i
$249$			170.486i			0.684684i
$250$	37.9545	+	26.8484i	0.151818	+	0.107393i
$251$	−241.508			−0.962183			−0.481091	−	0.876671i	$-0.659759\pi$
$251$	−241.508			−0.962183			−0.481091	+	0.876671i	$0.659759\pi$
$252$	−25.5424	+	4.04552i	−0.101359	+	0.0160536i
$253$	−189.186	+	371.299i	−0.747772	+	1.46758i
$254$	−82.7207	+	26.8776i	−0.325672	+	0.105817i
$255$	93.7556	−	94.5499i	0.367669	−	0.370784i
$256$	53.1474	−	163.571i	0.207607	−	0.638949i
$257$	−107.085	+	107.085i	−0.416674	+	0.416674i	−0.884055	−	0.467382i	$-0.845197\pi$
$257$	−107.085	+	107.085i	−0.416674	+	0.416674i	0.467382	+	0.884055i	$0.345197\pi$
$258$	12.1412	−	6.18627i	0.0470591	−	0.0239778i
$259$	−93.3744	−	128.519i	−0.360519	−	0.496212i
$260$	−1.81022	+	2.51379i	−0.00696239	+	0.00966841i
$261$	−2.55734	−	1.85802i	−0.00979825	−	0.00711885i
$262$	−13.4789	+	85.1023i	−0.0514461	+	0.324818i
$263$	255.911	+	40.5323i	0.973044	+	0.154115i	0.622661	−	0.782492i	$-0.286051\pi$
$263$	255.911	+	40.5323i	0.973044	+	0.154115i	0.350383	+	0.936607i	$0.386051\pi$
$264$	35.0222	−	48.2039i	0.132660	−	0.182591i
$265$	−62.7653	−	190.435i	−0.236850	−	0.718621i
$266$	12.2963	−	8.93381i	0.0462268	−	0.0335858i
$267$	100.805	+	197.842i	0.377549	+	0.740981i
$268$	60.4711	+	60.4711i	0.225638	+	0.225638i
$269$	−313.786	−	101.955i	−1.16649	−	0.379015i	−0.339158	−	0.940730i	$-0.610142\pi$
$269$	−313.786	−	101.955i	−1.16649	−	0.379015i	−0.827331	+	0.561714i	$0.810142\pi$
$270$	−4.35050	+	8.62813i	−0.0161130	+	0.0319560i
$271$	102.300	+	314.847i	0.377491	+	1.16180i	0.941783	+	0.336223i	$0.109149\pi$
$271$	102.300	+	314.847i	0.377491	+	1.16180i	−0.564291	+	0.825576i	$0.690851\pi$
$272$	196.713	+	100.230i	0.723208	+	0.368493i
$273$	0.0970372	+	0.612668i	0.000355447	+	0.00224421i
$274$			21.0039i			0.0766567i
$275$	170.870	−	239.403i	0.621344	−	0.870558i
$276$	236.911			0.858372
$277$	357.818	−	56.6728i	1.29176	−	0.204595i	0.527530	−	0.849537i	$-0.323118\pi$
$277$	357.818	−	56.6728i	1.29176	−	0.204595i	0.764232	+	0.644942i	$0.223118\pi$
$278$	26.2323	−	51.4838i	0.0943608	−	0.185193i
$279$	−125.122	+	40.6545i	−0.448465	+	0.145715i
$280$	14.9386	+	29.0153i	0.0533520	+	0.103626i
$281$	106.524	−	327.848i	0.379090	−	1.16672i	−0.561588	−	0.827417i	$-0.689809\pi$
$281$	106.524	−	327.848i	0.379090	−	1.16672i	0.940678	−	0.339301i	$-0.110191\pi$
$282$	−20.1024	+	20.1024i	−0.0712850	+	0.0712850i
$283$	−233.777	+	119.115i	−0.826067	+	0.420902i	−0.815299	−	0.579040i	$-0.803428\pi$
$283$	−233.777	+	119.115i	−0.826067	+	0.420902i	−0.0107677	+	0.999942i	$0.503428\pi$
$284$	101.661	+	139.925i	0.357963	+	0.492693i
$285$	0.668762	+	158.542i	0.00234653	+	0.556288i
$286$	−0.567946	−	0.412637i	−0.00198583	−	0.00144279i
$287$	4.08982	−	25.8221i	0.0142503	−	0.0899726i
$288$	−50.4798	−	7.99522i	−0.175277	−	0.0277612i
$289$	30.9192	−	42.5567i	0.106987	−	0.147255i
$290$	−0.597639	+	1.86609i	−0.00206082	+	0.00643479i
$291$	54.4343	−	39.5488i	0.187059	−	0.135907i
$292$	23.8988	+	46.9039i	0.0818450	+	0.160630i
$293$	−285.593	−	285.593i	−0.974722	−	0.974722i	0.0249667	−	0.999688i	$-0.492052\pi$
$293$	−285.593	−	285.593i	−0.974722	−	0.974722i	−0.999688	+	0.0249667i	$0.992052\pi$
$294$	−26.9676	−	8.76231i	−0.0917266	−	0.0298038i
$295$	234.270	+	36.0924i	0.794136	+	0.122347i
$296$	−64.3009	−	197.898i	−0.217233	−	0.668573i
$297$	54.4699	+	27.7538i	0.183400	+	0.0934472i
$298$	16.2515	+	102.608i	0.0545352	+	0.344322i
$299$		−	5.68262i		−	0.0190054i
$300$	−165.371	−	24.7640i	−0.551238	−	0.0825467i
$301$	47.2184			0.156872
$302$	3.20509	−	0.507636i	0.0106129	−	0.00168091i
$303$	109.187	−	214.291i	0.360353	−	0.707233i
$304$	−250.008	+	81.2327i	−0.822396	+	0.267213i
$305$	−277.259	+	45.1132i	−0.909046	+	0.147912i
$306$	5.30127	−	16.3156i	0.0173244	−	0.0533190i
$307$	304.198	−	304.198i	0.990872	−	0.990872i	−0.00908665	−	0.999959i	$-0.502892\pi$
$307$	304.198	−	304.198i	0.990872	−	0.990872i	0.999959	+	0.00908665i	$0.00289241\pi$
$308$	90.3640	−	46.0427i	0.293389	−	0.149489i
$309$	128.544	+	176.925i	0.416000	+	0.572574i
$310$	48.2125	+	65.7735i	0.155524	+	0.212173i
$311$	262.116	+	190.438i	0.842816	+	0.612342i	0.923156	−	0.384426i	$-0.125600\pi$
$311$	262.116	+	190.438i	0.842816	+	0.612342i	−0.0803397	+	0.996768i	$0.525600\pi$
$312$	−0.127105	+	0.802511i	−0.000407388	+	0.00257215i
$313$	−53.7177	−	8.50805i	−0.171622	−	0.0271823i	0.0700319	−	0.997545i	$-0.477690\pi$
$313$	−53.7177	−	8.50805i	−0.171622	−	0.0271823i	−0.241654	+	0.970362i	$0.577690\pi$
$314$	28.4942	−	39.2189i	0.0907460	−	0.124901i
$315$	−27.0058	+	19.7954i	−0.0857327	+	0.0628427i
$316$	−487.823	+	354.424i	−1.54374	+	1.12159i
$317$	−25.3961	−	49.8427i	−0.0801139	−	0.157232i	0.847475	−	0.530836i	$-0.178122\pi$
$317$	−25.3961	−	49.8427i	−0.0801139	−	0.157232i	−0.927588	+	0.373604i	$0.878122\pi$
$318$	−18.2671	−	18.2671i	−0.0574437	−	0.0574437i
$319$	11.7899	+	3.83078i	0.0369590	+	0.0120087i
$320$	−41.0336	−	252.186i	−0.128230	−	0.788082i
$321$	6.97929	+	21.4800i	0.0217423	+	0.0669160i
$322$	−26.2017	−	13.3504i	−0.0813718	−	0.0414610i
$323$	−44.0323	−	278.009i	−0.136323	−	0.860709i
$324$		−	34.7550i		−	0.107269i
$325$	−0.593998	+	3.96666i	−0.00182769	+	0.0122051i
$326$	8.00760			0.0245632
$327$	−274.067	+	43.4079i	−0.838124	+	0.132746i
$328$	15.5469	−	30.5125i	0.0473991	−	0.0930260i
$329$	−93.6909	+	30.4420i	−0.284775	+	0.0925289i
$330$	5.77013	−	37.4530i	0.0174852	−	0.113494i
$331$	47.0770	−	144.888i	0.142226	−	0.437728i	−0.854417	−	0.519587i	$-0.826086\pi$
$331$	47.0770	−	144.888i	0.142226	−	0.437728i	0.996644	+	0.0818591i	$0.0260858\pi$
$332$	−268.775	+	268.775i	−0.809563	+	0.809563i
$333$	190.225	−	96.9242i	0.571245	−	0.291064i
$334$	−33.5042	−	46.1146i	−0.100312	−	0.138068i
$335$	105.452	+	33.7723i	0.314782	+	0.100813i
$336$	−44.9152	−	32.6328i	−0.133676	−	0.0971214i
$337$	73.1473	−	461.834i	0.217054	−	1.37043i	−0.602818	−	0.797879i	$-0.705955\pi$
$337$	73.1473	−	461.834i	0.217054	−	1.37043i	0.819872	−	0.572547i	$-0.194045\pi$
$338$	−62.0720	−	9.83124i	−0.183645	−	0.0290865i
$339$	−69.5978	+	95.7931i	−0.205303	+	0.282575i
$340$	296.867	−	1.25224i	0.873140	−	0.00368307i
$341$	417.404	−	303.262i	1.22406	−	0.889331i
$342$	9.27345	+	18.2002i	0.0271153	+	0.0532169i
$343$	−146.822	−	146.822i	−0.428054	−	0.428054i
$344$	58.8224	+	19.1126i	0.170995	+	0.0555598i
$345$	272.723	−	140.412i	0.790502	−	0.406990i
$346$	1.39239	+	4.28533i	0.00402424	+	0.0123853i
$347$	387.008	+	197.191i	1.11530	+	0.568273i	0.911731	−	0.410788i	$-0.134746\pi$
$347$	387.008	+	197.191i	1.11530	+	0.568273i	0.203567	+	0.979061i	$0.434746\pi$
$348$	−1.10250	−	6.96091i	−0.00316810	−	0.0200026i
$349$		−	364.641i		−	1.04482i	−0.852695	−	0.522409i	$-0.825033\pi$
$349$		−	364.641i		−	1.04482i	0.852695	−	0.522409i	$-0.174967\pi$
$350$	16.8941	+	12.0579i	0.0482690	+	0.0344511i
$351$	−0.833647			−0.00237506
$352$	197.966	−	31.3547i	0.562403	−	0.0890759i
$353$	175.877	−	345.178i	0.498236	−	0.977842i	−0.495764	−	0.868457i	$-0.665112\pi$
$353$	175.877	−	345.178i	0.498236	−	0.977842i	0.993999	−	0.109385i	$-0.0348882\pi$
$354$	29.0444	−	9.43711i	0.0820464	−	0.0266585i
$355$	199.959	+	100.824i	0.563265	+	0.284012i
$356$	−152.980	+	470.824i	−0.429719	+	1.32254i
$357$	42.0350	−	42.0350i	0.117745	−	0.117745i
$358$	51.0996	−	26.0365i	0.142736	−	0.0727278i
$359$	150.002	+	206.460i	0.417832	+	0.575096i	0.965107	−	0.261857i	$-0.0843348\pi$
$359$	150.002	+	206.460i	0.417832	+	0.575096i	−0.547275	+	0.836953i	$0.684335\pi$
$360$	−41.6551	+	13.7291i	−0.115709	+	0.0381364i
$361$	−20.9150	−	15.1956i	−0.0579363	−	0.0420932i
$362$	−1.00203	+	6.32660i	−0.00276805	+	0.0174768i
$363$	−29.7951	−	4.71908i	−0.0820802	−	0.0130002i
$364$	−0.812904	+	1.11887i	−0.00223325	+	0.00307381i
$365$	55.3103	+	39.8299i	0.151535	+	0.109123i
$366$	−29.2795	+	21.2728i	−0.0799986	+	0.0581224i
$367$	−169.680	−	333.015i	−0.462342	−	0.907398i	−0.998015	−	0.0629723i	$-0.979942\pi$
$367$	−169.680	−	333.015i	−0.462342	−	0.907398i	0.535673	−	0.844426i	$-0.320058\pi$
$368$	359.637	+	359.637i	0.977273	+	0.977273i
$369$	33.4160	+	10.8575i	0.0905584	+	0.0294242i
$370$	−93.9721	−	93.1826i	−0.253979	−	0.251845i
$371$	−27.6628	−	85.1374i	−0.0745628	−	0.229481i
$372$	−261.350	−	133.164i	−0.702553	−	0.357969i
$373$	101.786	+	642.651i	0.272885	+	1.72293i	0.619567	+	0.784943i	$0.287308\pi$
$373$	101.786	+	642.651i	0.272885	+	1.72293i	−0.346683	+	0.937982i	$0.612692\pi$
$374$			67.2776i			0.179887i
$375$	−205.047	+	69.5044i	−0.546791	+	0.185345i
$376$	−129.038			−0.343185
$377$	−0.166967	+	0.0264449i	−0.000442883	+	7.01458e-5i
$378$	−1.95852	+	3.84382i	−0.00518128	+	0.0101688i
$379$	283.552	−	92.1317i	0.748159	−	0.243092i	0.0899703	−	0.995944i	$-0.471323\pi$
$379$	283.552	−	92.1317i	0.748159	−	0.243092i	0.658189	+	0.752853i	$0.271323\pi$
$380$	−248.891	+	250.999i	−0.654976	+	0.660525i
$381$	125.169	−	385.230i	0.328527	−	1.01110i
$382$	42.5638	−	42.5638i	0.111424	−	0.111424i
$383$	−10.5143	+	5.35729i	−0.0274524	+	0.0139877i	−0.467663	−	0.883907i	$-0.654904\pi$
$383$	−10.5143	+	5.35729i	−0.0274524	+	0.0139877i	0.440210	+	0.897895i	$0.354904\pi$
$384$	−88.7261	−	122.121i	−0.231058	−	0.318023i
$385$	76.7353	−	106.559i	0.199312	−	0.276778i
$386$	58.4254	+	42.4486i	0.151361	+	0.109970i
$387$	−9.92705	+	62.6769i	−0.0256513	+	0.161956i
$388$	148.166	+	23.4672i	0.381872	+	0.0604826i
$389$	−259.965	+	357.812i	−0.668291	+	0.919824i	−0.999720	−	0.0236561i	$-0.992469\pi$
$389$	−259.965	+	357.812i	−0.668291	+	0.919824i	0.331429	+	0.943480i	$0.392469\pi$
$390$	0.161758	+	0.490787i	0.000414765	+	0.00125843i
$391$	−440.583	+	320.102i	−1.12681	+	0.818675i
$392$	−58.4302	−	114.676i	−0.149057	−	0.292540i
$393$	−283.734	−	283.734i	−0.721970	−	0.721970i
$394$	114.637	+	37.2477i	0.290956	+	0.0945374i
$395$	−351.505	+	697.121i	−0.889886	+	1.76486i
$396$	42.1185	+	129.627i	0.106360	+	0.327342i
$397$	−585.087	−	298.117i	−1.47377	−	0.750924i	−0.481669	−	0.876353i	$-0.659969\pi$
$397$	−585.087	−	298.117i	−1.47377	−	0.750924i	−0.992103	+	0.125429i	$0.959969\pi$
$398$	5.24333	+	33.1051i	0.0131742	+	0.0831786i
$399$			70.7821i			0.177399i
$400$	−213.446	−	288.630i	−0.533614	−	0.721576i
$401$	−499.190			−1.24486			−0.622432	−	0.782674i	$-0.713855\pi$
$401$	−499.190			−1.24486			−0.622432	+	0.782674i	$0.713855\pi$
$402$	14.0904	−	2.23170i	0.0350507	−	0.00555149i
$403$	−3.19413	+	6.26882i	−0.00792587	+	0.0155554i
$404$	509.971	−	165.699i	1.26230	−	0.410147i
$405$	−20.5985	−	40.0088i	−0.0508605	−	0.0987871i
$406$	−0.270329	+	0.831987i	−0.000665835	+	0.00204923i
$407$	−592.030	+	592.030i	−1.45462	+	1.45462i
$408$	69.3797	−	35.3507i	0.170048	−	0.0866440i
$409$	−66.4164	−	91.4143i	−0.162387	−	0.223507i	0.720068	−	0.693904i	$-0.244111\pi$
$409$	−66.4164	−	91.4143i	−0.162387	−	0.223507i	−0.882455	+	0.470397i	$0.844111\pi$
$410$	−0.0918703	−	21.7795i	−0.000224074	−	0.0531208i
$411$	−79.1341	−	57.4943i	−0.192540	−	0.139889i
$412$	−76.2746	+	481.579i	−0.185132	+	1.16888i
$413$	104.521	+	16.5546i	0.253079	+	0.0400837i
$414$	23.2297	−	31.9730i	0.0561104	−	0.0772294i
$415$	−150.107	+	468.701i	−0.361705	+	1.12940i
$416$	−2.21123	+	1.60655i	−0.00531546	+	0.00386191i
$417$	122.164	+	239.760i	0.292958	+	0.574963i
$418$	−56.6438	−	56.6438i	−0.135512	−	0.135512i
$419$	610.071	+	198.224i	1.45602	+	0.473089i	0.926851	−	0.375429i	$-0.122505\pi$
$419$	610.071	+	198.224i	1.45602	+	0.473089i	0.529166	+	0.848518i	$0.322505\pi$
$420$	−73.7831	−	11.3673i	−0.175674	−	0.0270649i
$421$	63.0082	+	193.919i	0.149663	+	0.460616i	0.997581	−	0.0695117i	$-0.0221441\pi$
$421$	63.0082	+	193.919i	0.149663	+	0.460616i	−0.847918	+	0.530127i	$0.822144\pi$
$422$	−0.822589	−	0.419130i	−0.00194926	−	0.000993199i
$423$	−20.7109	−	130.764i	−0.0489620	−	0.309134i
$424$		−	117.257i		−	0.276550i
$425$	341.001	−	177.388i	0.802355	−	0.417384i
$426$	28.8521			0.0677280
$427$	−123.867	+	19.6186i	−0.290086	+	0.0459451i
$428$	−22.8607	+	44.8667i	−0.0534130	+	0.104829i
$429$	3.10929	−	1.01027i	0.00724776	−	0.00235494i
$430$	38.8255	−	6.31736i	0.0902919	−	0.0146915i
$431$	−115.718	+	356.142i	−0.268486	+	0.826316i	0.722383	+	0.691493i	$0.243047\pi$
$431$	−115.718	+	356.142i	−0.268486	+	0.826316i	−0.990870	+	0.134823i	$0.956953\pi$
$432$	52.7591	−	52.7591i	0.122127	−	0.122127i
$433$	128.238	−	65.3407i	0.296162	−	0.150902i	−0.299596	−	0.954066i	$-0.596852\pi$
$433$	128.238	−	65.3407i	0.296162	−	0.150902i	0.595758	+	0.803164i	$0.296852\pi$
$434$	21.4005	+	29.4553i	0.0493099	+	0.0678692i
$435$	−5.39473	−	7.35972i	−0.0124017	−	0.0169189i
$436$	−500.505	−	363.638i	−1.14795	−	0.834033i
$437$	101.438	−	640.452i	0.232123	−	1.46557i
$438$	8.67339	+	1.37373i	0.0198023	+	0.00313637i
$439$	86.1297	−	118.547i	0.196195	−	0.270040i	−0.699573	−	0.714561i	$-0.746626\pi$
$439$	86.1297	−	118.547i	0.196195	−	0.270040i	0.895768	+	0.444522i	$0.146626\pi$
$440$	138.725	−	101.686i	0.315284	−	0.231106i
$441$	106.832	−	77.6177i	0.242248	−	0.176004i
$442$	−0.416508	−	0.817443i	−0.000942325	−	0.00184942i
$443$	21.9869	+	21.9869i	0.0496319	+	0.0496319i	0.731487	−	0.681855i	$-0.238827\pi$
$443$	21.9869	+	21.9869i	0.0496319	+	0.0496319i	−0.681855	+	0.731487i	$0.738827\pi$
$444$	452.696	+	147.090i	1.01959	+	0.331283i
$445$	102.941	+	632.663i	0.231329	+	1.42171i
$446$	16.0687	+	49.4544i	0.0360285	+	0.110884i
$447$	−431.070	−	219.641i	−0.964361	−	0.491367i
$448$	−17.8444	−	112.665i	−0.0398313	−	0.251485i
$449$		−	379.318i		−	0.844806i	−0.906408	−	0.422403i	$-0.861187\pi$
$449$		−	379.318i		−	0.844806i	0.906408	−	0.422403i	$-0.138813\pi$
$450$	−19.5572	+	19.8900i	−0.0434604	+	0.0442000i
$451$	−137.791			−0.305524
$452$	−260.742	+	41.2975i	−0.576863	+	0.0913661i
$453$	−6.86076	+	13.4650i	−0.0151452	+	0.0297240i
$454$	−105.623	+	34.3191i	−0.232651	+	0.0755928i
$455$	−0.272659	+	1.76979i	−0.000599251	+	0.00388964i
$456$	−28.6504	+	88.1770i	−0.0628299	+	0.193371i
$457$	446.757	−	446.757i	0.977586	−	0.977586i	−0.0221682	−	0.999754i	$-0.507057\pi$
$457$	446.757	−	446.757i	0.977586	−	0.977586i	0.999754	+	0.0221682i	$0.00705695\pi$
$458$	23.7752	−	12.1141i	0.0519108	−	0.0264499i
$459$	46.9593	+	64.6339i	0.102308	+	0.140815i
$460$	651.315	+	208.592i	1.41590	+	0.453461i
$461$	143.090	+	103.961i	0.310390	+	0.225512i	0.732064	−	0.681236i	$-0.238557\pi$
$461$	143.090	+	103.961i	0.310390	+	0.225512i	−0.421674	+	0.906748i	$0.638557\pi$
$462$	2.64659	−	16.7099i	0.00572856	−	0.0361687i
$463$	−121.731	−	19.2803i	−0.262918	−	0.0416422i	0.0235835	−	0.999722i	$-0.492492\pi$
$463$	−121.731	−	19.2803i	−0.262918	−	0.0416422i	−0.286502	+	0.958080i	$0.592492\pi$
$464$	8.89322	−	12.2405i	0.0191664	−	0.0263803i
$465$	−379.780	+	1.60199i	−0.816731	+	0.00344513i
$466$	−88.9975	+	64.6605i	−0.190982	+	0.138756i
$467$	−128.195	−	251.596i	−0.274507	−	0.538750i	0.712058	−	0.702121i	$-0.247763\pi$
$467$	−128.195	−	251.596i	−0.274507	−	0.538750i	−0.986565	+	0.163371i	$0.947763\pi$
$468$	−1.31426	−	1.31426i	−0.00280825	−	0.00280825i
$469$	47.0152	+	15.2762i	0.100246	+	0.0325718i
$470$	−72.9649	+	37.5660i	−0.155244	+	0.0799276i
$471$	69.7631	+	214.709i	0.148117	+	0.455857i
$472$	123.507	+	62.9300i	0.261667	+	0.133326i
$473$	−38.9308	−	245.799i	−0.0823061	−	0.519660i
$474$			100.588i			0.212210i
$475$	−137.753	+	436.453i	−0.290005	+	0.918849i
$476$	132.538			0.278442
$477$	118.826	−	18.8201i	0.249110	−	0.0394552i
$478$	7.43025	−	14.5827i	0.0155445	−	0.0305077i
$479$	−150.078	+	48.7632i	−0.313315	+	0.101802i	−0.461453	−	0.887165i	$-0.652672\pi$
$479$	−150.078	+	48.7632i	−0.313315	+	0.101802i	0.148139	+	0.988967i	$0.452672\pi$
$480$	−131.740	−	66.4262i	−0.274458	−	0.138388i
$481$	3.52815	−	10.8585i	0.00733503	−	0.0225749i
$482$	15.7354	−	15.7354i	0.0326461	−	0.0326461i
$483$	122.021	−	62.1729i	0.252632	−	0.128722i
$484$	−39.5329	−	54.4124i	−0.0816795	−	0.112422i
$485$	184.472	−	60.8001i	0.380355	−	0.125361i
$486$	−4.69047	−	3.40782i	−0.00965116	−	0.00701198i
$487$	40.1061	−	253.220i	0.0823535	−	0.519959i	−0.911682	−	0.410898i	$-0.865215\pi$
$487$	40.1061	−	253.220i	0.0823535	−	0.519959i	0.994035	−	0.109062i	$-0.0347846\pi$
$488$	−162.248	−	25.6976i	−0.332476	−	0.0526590i
$489$	−21.9193	+	30.1693i	−0.0448247	+	0.0616960i
$490$	−66.4245	−	47.8335i	−0.135560	−	0.0976193i
$491$	7.56809	−	5.49854i	0.0154136	−	0.0111987i	−0.580052	−	0.814580i	$-0.696968\pi$
$491$	7.56809	−	5.49854i	0.0154136	−	0.0111987i	0.595465	+	0.803381i	$0.296968\pi$
$492$	35.5640	+	69.7982i	0.0722845	+	0.141866i
$493$	11.4556	+	11.4556i	0.0232364	+	0.0232364i
$494$	1.03891	+	0.337564i	0.00210307	+	0.000683327i
$495$	125.313	+	124.260i	0.253157	+	0.251030i
$496$	−194.589	−	598.882i	−0.392316	−	1.20742i
$497$	89.0815	+	45.3893i	0.179238	+	0.0913266i
$498$	9.91921	+	62.6274i	0.0199181	+	0.125758i
$499$		−	167.764i		−	0.336200i	−0.985770	−	0.168100i	$-0.946237\pi$
$499$		−	167.764i		−	0.336200i	0.985770	−	0.168100i	$-0.0537632\pi$
$500$	−432.836	−	213.685i	−0.865671	−	0.427370i
$501$	265.452			0.529845
$502$	−88.7169	+	14.0514i	−0.176727	+	0.0279908i
$503$	228.314	−	448.092i	0.453905	−	0.890839i	−0.544730	−	0.838611i	$-0.683368\pi$
$503$	228.314	−	448.092i	0.453905	−	0.890839i	0.998635	−	0.0522276i	$-0.0166321\pi$
$504$	−18.6227	+	6.05088i	−0.0369498	+	0.0120057i
$505$	488.853	−	492.995i	0.968027	−	0.976228i
$506$	−47.8939	+	147.402i	−0.0946520	+	0.291309i
$507$	206.950	−	206.950i	0.408186	−	0.408186i
$508$	804.654	−	409.991i	1.58396	−	0.807070i
$509$	396.430	+	545.638i	0.778840	+	1.07198i	0.995409	+	0.0957139i	$0.0305134\pi$
$509$	396.430	+	545.638i	0.778840	+	1.07198i	−0.216569	+	0.976267i	$0.569487\pi$
$510$	28.9396	−	40.1874i	0.0567444	−	0.0787988i
$511$	24.6182	+	17.8861i	0.0481764	+	0.0350022i
$512$	64.5403	−	407.491i	0.126055	−	0.795881i
$513$	−93.9550	−	14.8810i	−0.183148	−	0.0290078i
$514$	−33.1069	+	45.5677i	−0.0644102	+	0.0886531i
$515$	197.616	+	599.582i	0.383721	+	1.16424i
$516$	−114.462	+	83.1613i	−0.221825	+	0.161165i
$517$	235.715	+	462.617i	0.455928	+	0.894810i
$518$	−41.7782	−	41.7782i	−0.0806528	−	0.0806528i
$519$	−19.9567	−	6.48433i	−0.0384523	−	0.0124939i
$520$	−1.05602	+	2.09435i	−0.00203081	+	0.00402760i
$521$	−105.124	−	323.539i	−0.201774	−	0.620995i	−0.999830	−	0.0184132i	$-0.994139\pi$
$521$	−105.124	−	323.539i	−0.201774	−	0.620995i	0.798057	−	0.602582i	$-0.205861\pi$
$522$	−1.04753	−	0.533744i	−0.00200677	−	0.00102250i
$523$	−72.8397	−	459.892i	−0.139273	−	0.879334i	−0.954069	−	0.299587i	$-0.903151\pi$
$523$	−72.8397	−	459.892i	−0.139273	−	0.879334i	0.814796	−	0.579747i	$-0.196849\pi$
$524$		−	894.626i		−	1.70730i
$525$	−91.6736	+	30.6440i	−0.174616	+	0.0583695i
$526$	96.3659			0.183205
$527$	665.957	−	105.477i	1.26368	−	0.200146i
$528$	−132.841	+	260.715i	−0.251593	+	0.493778i
$529$	−690.065	+	224.216i	−1.30447	+	0.423848i
$530$	−34.1364	−	66.3036i	−0.0644083	−	0.125101i
$531$	−43.9485	+	135.260i	−0.0827656	+	0.254726i
$532$	−111.589	+	111.589i	−0.209755	+	0.209755i
$533$	1.67420	−	0.853050i	0.00314110	−	0.00160047i
$534$	48.5413	+	66.8113i	0.0909013	+	0.125115i
$535$	0.275018	+	65.1980i	0.000514052	+	0.121865i
$536$	52.3860	+	38.0607i	0.0977351	+	0.0710087i
$537$	−41.7806	+	263.792i	−0.0778037	+	0.491233i
$538$	−121.200	−	19.1962i	−0.225278	−	0.0356806i
$539$	−304.392	+	418.960i	−0.564735	+	0.777291i
$540$	30.6007	−	95.5486i	0.0566679	−	0.176942i
$541$	637.841	−	463.419i	1.17900	−	0.856597i	0.186945	−	0.982370i	$-0.440141\pi$
$541$	637.841	−	463.419i	1.17900	−	0.856597i	0.992059	+	0.125774i	$0.0401413\pi$
$542$	55.8979	+	109.706i	0.103133	+	0.202409i
$543$	−21.0931	−	21.0931i	−0.0388455	−	0.0388455i
$544$	249.117	+	80.9431i	0.457936	+	0.148792i
$545$	−791.684	−	121.969i	−1.45263	−	0.223797i
$546$	0.0712924	+	0.219415i	0.000130572	+	0.000401860i
$547$	−584.989	−	298.067i	−1.06945	−	0.544912i	−0.171579	−	0.985170i	$-0.554887\pi$
$547$	−584.989	−	298.067i	−1.06945	−	0.544912i	−0.897871	+	0.440258i	$0.854887\pi$
$548$	−34.1156	−	215.397i	−0.0622548	−	0.393061i
$549$		−	168.543i		−	0.307000i
$550$	48.8393	−	97.8853i	0.0887988	−	0.177973i
$551$	−19.2898			−0.0350088
$552$	177.174	−	28.0616i	0.320967	−	0.0508362i
$553$	−158.242	+	310.566i	−0.286151	+	0.561603i
$554$	128.146	−	41.6370i	0.231310	−	0.0751571i
$555$	608.304	−	98.9780i	1.09604	−	0.178339i
$556$	−185.392	+	570.579i	−0.333440	+	1.02622i
$557$	−408.550	+	408.550i	−0.733484	+	0.733484i	−0.971308	−	0.237824i	$-0.923566\pi$
$557$	−408.550	+	408.550i	−0.733484	+	0.733484i	0.237824	+	0.971308i	$0.423566\pi$
$558$	−43.5976	+	22.2141i	−0.0781319	+	0.0398102i
$559$	1.99474	+	2.74552i	0.00356840	+	0.00491148i
$560$	−94.7489	−	129.260i	−0.169194	−	0.230822i
$561$	−253.474	−	184.160i	−0.451825	−	0.328270i
$562$	20.0564	−	126.631i	0.0356876	−	0.225323i
$563$	−718.156	−	113.745i	−1.27559	−	0.202033i	−0.518348	−	0.855170i	$-0.673453\pi$
$563$	−718.156	−	113.745i	−1.27559	−	0.202033i	−0.757240	+	0.653136i	$0.773453\pi$
$564$	173.501	−	238.803i	0.307625	−	0.423410i
$565$	−275.681	+	202.076i	−0.487931	+	0.357657i
$566$	−78.9466	+	57.3581i	−0.139482	+	0.101339i
$567$	−9.12082	−	17.9006i	−0.0160861	−	0.0315708i
$568$	92.6013	+	92.6013i	0.163030	+	0.163030i
$569$	−299.394	−	97.2791i	−0.526176	−	0.170965i	0.0338701	−	0.999426i	$-0.489217\pi$
$569$	−299.394	−	97.2791i	−0.526176	−	0.170965i	−0.560046	+	0.828461i	$0.689217\pi$
$570$	9.46995	+	58.2009i	0.0166139	+	0.102107i
$571$	263.725	+	811.662i	0.461865	+	1.42147i	0.862883	+	0.505404i	$0.168657\pi$
$571$	263.725	+	811.662i	0.461865	+	1.42147i	−0.401018	+	0.916070i	$0.631343\pi$
$572$	6.49457	+	3.30915i	0.0113541	+	0.00578523i
$573$	43.8524	+	276.873i	0.0765312	+	0.483199i
$574$		−	9.72361i		−	0.0169401i
$575$	873.399	−	145.896i	1.51895	−	0.253732i
$576$	153.302			0.266149
$577$	402.212	−	63.7042i	0.697075	−	0.110406i	0.202167	−	0.979351i	$-0.435202\pi$
$577$	402.212	−	63.7042i	0.697075	−	0.110406i	0.494908	+	0.868945i	$0.335202\pi$
$578$	8.88202	−	17.4320i	0.0153668	−	0.0301591i
$579$	−319.857	+	103.928i	−0.552430	+	0.179495i
$580$	3.09785	−	20.1077i	0.00534113	−	0.0346684i
$581$	−67.8978	+	208.968i	−0.116864	+	0.359670i
$582$	17.6952	−	17.6952i	0.0304041	−	0.0304041i
$583$	−420.382	+	214.195i	−0.721067	+	0.367402i
$584$	23.4284	+	32.2464i	0.0401171	+	0.0552164i
$585$	−2.29186	−	0.733998i	−0.00391771	−	0.00125470i
$586$	−121.528	−	88.2952i	−0.207386	−	0.150674i
$587$	45.6401	−	288.160i	0.0777515	−	0.490904i	−0.917828	−	0.396979i	$-0.870059\pi$
$587$	45.6401	−	288.160i	0.0777515	−	0.490904i	0.995579	−	0.0939249i	$-0.0299413\pi$
$588$	290.788	+	46.0563i	0.494537	+	0.0783270i
$589$	−471.891	+	649.502i	−0.801173	+	1.10272i
$590$	88.1580	−	0.371868i	0.149420	−	0.000630284i
$591$	−454.130	+	329.945i	−0.768410	+	0.558283i
$592$	463.918	+	910.491i	0.783645	+	1.53799i
$593$	296.439	+	296.439i	0.499897	+	0.499897i	0.911406	−	0.411509i	$-0.134998\pi$
$593$	296.439	+	296.439i	0.499897	+	0.499897i	−0.411509	+	0.911406i	$0.634998\pi$
$594$	21.6241	+	7.02609i	0.0364042	+	0.0118284i
$595$	152.573	−	78.5524i	0.256426	−	0.132021i
$596$	−333.322	−	1025.86i	−0.559265	−	1.72124i
$597$	−139.079	−	70.8642i	−0.232963	−	0.118701i
$598$	−0.330626	−	2.08749i	−0.000552886	−	0.00349078i
$599$		−	123.543i		−	0.206248i	−0.994668	−	0.103124i	$-0.967116\pi$
$599$		−	123.543i		−	0.206248i	0.994668	−	0.103124i	$-0.0328839\pi$
$600$	−126.606	+	1.06812i	−0.211010	+	0.00178020i
$601$	92.2454			0.153486			0.0767432	−	0.997051i	$-0.475548\pi$
$601$	92.2454			0.153486			0.0767432	+	0.997051i	$0.475548\pi$
$602$	17.3455	−	2.74725i	0.0288131	−	0.00456355i
$603$	−30.1617	+	59.1956i	−0.0500194	+	0.0981685i
$604$	−32.0440	+	10.4117i	−0.0530529	+	0.0172379i
$605$	−77.7578	−	39.2073i	−0.128525	−	0.0648055i
$606$	27.6415	−	85.0718i	0.0456130	−	0.140382i
$607$	−727.046	+	727.046i	−1.19777	+	1.19777i	−0.222937	+	0.974833i	$0.571564\pi$
$607$	−727.046	+	727.046i	−1.19777	+	1.19777i	−0.974833	+	0.222937i	$0.928436\pi$
$608$	−277.892	+	141.593i	−0.457059	+	0.232883i
$609$	−2.39461	−	3.29589i	−0.00393203	−	0.00541198i
$610$	−99.2252	+	32.7036i	−0.162664	+	0.0536124i
$611$	−5.72801	−	4.16164i	−0.00937482	−	0.00681120i
$612$	−27.8644	+	175.929i	−0.0455301	+	0.287466i
$613$	403.088	+	63.8429i	0.657566	+	0.104148i	0.476296	−	0.879285i	$-0.341979\pi$
$613$	403.088	+	63.8429i	0.657566	+	0.104148i	0.181270	+	0.983433i	$0.441979\pi$
$614$	94.0470	−	129.445i	0.153171	−	0.210822i
$615$	82.3078	+	59.2712i	0.133834	+	0.0963760i
$616$	62.1251	−	45.1365i	0.100852	−	0.0732735i
$617$	25.0146	+	49.0939i	0.0405423	+	0.0795687i	0.910389	−	0.413753i	$-0.135782\pi$
$617$	25.0146	+	49.0939i	0.0405423	+	0.0795687i	−0.869847	+	0.493322i	$0.835782\pi$
$618$	57.5139	+	57.5139i	0.0930646	+	0.0930646i
$619$	958.614	+	311.473i	1.54865	+	0.503187i	0.953747	−	0.300611i	$-0.0971906\pi$
$619$	958.614	+	311.473i	1.54865	+	0.503187i	0.594903	+	0.803798i	$0.297191\pi$
$620$	−601.256	−	596.205i	−0.969768	−	0.961621i
$621$	56.8739	+	175.040i	0.0915844	+	0.281868i
$622$	107.367	+	54.7063i	0.172616	+	0.0879523i
$623$	44.7666	+	282.645i	0.0718565	+	0.453684i
$624$		−	3.99017i		−	0.00639450i
$625$	−624.911	+	10.5449i	−0.999858	+	0.0168719i
$626$	−20.2280			−0.0323131
$627$	368.462	−	58.3587i	0.587659	−	0.0930760i
$628$	−228.510	+	448.476i	−0.363869	+	0.714134i
$629$	−1040.62	+	338.118i	−1.65440	+	0.537548i
$630$	−8.76873	+	8.84302i	−0.0139186	+	0.0140365i
$631$	170.573	−	524.970i	0.270322	−	0.831965i	−0.720098	−	0.693873i	$-0.755903\pi$
$631$	170.573	−	524.970i	0.270322	−	0.831965i	0.990419	−	0.138092i	$-0.0440969\pi$
$632$	−322.837	+	322.837i	−0.510819	+	0.510819i
$633$	3.83079	−	1.95188i	0.00605180	−	0.00308355i
$634$	−12.2291	−	16.8319i	−0.0192888	−	0.0265488i
$635$	683.296	−	948.867i	1.07606	−	1.49428i
$636$	217.001	+	157.661i	0.341197	+	0.247894i
$637$	1.10472	−	6.97494i	0.00173426	−	0.0109497i
$638$	4.55386	+	0.721260i	0.00713771	+	0.00113050i
$639$	−78.9772	+	108.703i	−0.123595	+	0.170114i
$640$	−136.403	−	413.856i	−0.213129	−	0.646650i
$641$	883.933	−	642.215i	1.37899	−	1.00190i	0.382016	−	0.924156i	$-0.375230\pi$
$641$	883.933	−	642.215i	1.37899	−	1.00190i	0.996974	−	0.0777395i	$-0.0247702\pi$
$642$	3.81356	+	7.48454i	0.00594013	+	0.0116582i
$643$	−229.214	−	229.214i	−0.356475	−	0.356475i	0.506037	−	0.862512i	$-0.331110\pi$
$643$	−229.214	−	229.214i	−0.356475	−	0.356475i	−0.862512	+	0.506037i	$0.831110\pi$
$644$	290.386	+	94.3520i	0.450909	+	0.146509i
$645$	−82.4764	+	163.571i	−0.127870	+	0.253599i
$646$	−32.3502	−	99.5636i	−0.0500777	−	0.154123i
$647$	220.633	+	112.418i	0.341009	+	0.173753i	0.616105	−	0.787664i	$-0.288710\pi$
$647$	220.633	+	112.418i	0.341009	+	0.173753i	−0.275096	+	0.961417i	$0.588710\pi$
$648$	−4.11666	−	25.9916i	−0.00635287	−	0.0401105i
$649$		−	557.744i		−	0.859390i
$650$	0.0125847	+	1.49169i	1.93611e−5	+	0.00229491i
$651$	−169.555			−0.260453
$652$	−82.1188	+	13.0063i	−0.125949	+	0.0199484i
$653$	−575.547	+	1129.57i	−0.881389	+	1.72982i	−0.226636	+	0.973979i	$0.572773\pi$
$653$	−575.547	+	1129.57i	−0.881389	+	1.72982i	−0.654752	+	0.755843i	$0.727227\pi$
$654$	−98.1517	+	31.8914i	−0.150079	+	0.0487636i
$655$	−530.224	−	1029.86i	−0.809503	−	1.57231i
$656$	−51.9685	+	159.943i	−0.0792202	+	0.243815i
$657$	−28.9174	+	28.9174i	−0.0440143	+	0.0440143i
$658$	−32.6458	+	16.6339i	−0.0496137	+	0.0252794i
$659$	−601.368	−	827.713i	−0.912547	−	1.25601i	−0.966289	−	0.257458i	$-0.917115\pi$
$659$	−601.368	−	827.713i	−0.912547	−	1.25601i	0.0537425	−	0.998555i	$-0.482885\pi$
$660$	1.65967	+	393.456i	0.00251466	+	0.596146i
$661$	201.806	+	146.621i	0.305304	+	0.221816i	0.729879	−	0.683577i	$-0.239576\pi$
$661$	201.806	+	146.621i	0.305304	+	0.221816i	−0.424575	+	0.905393i	$0.639576\pi$
$662$	8.86367	−	55.9630i	0.0133892	−	0.0845363i
$663$	4.21990	+	0.668366i	0.00636485	+	0.00100809i
$664$	−169.168	+	232.839i	−0.254771	+	0.350662i
$665$	−62.3213	+	194.594i	−0.0937162	+	0.292623i
$666$	64.2390	−	46.6723i	0.0964549	−	0.0700786i
$667$	16.9436	+	33.2537i	0.0254027	+	0.0498556i
$668$	418.491	+	418.491i	0.626483	+	0.626483i
$669$	−230.309	−	74.8319i	−0.344258	−	0.111856i
$670$	40.7023	+	6.27073i	0.0607497	+	0.00935930i
$671$	204.252	+	628.623i	0.304399	+	0.936845i
$672$	−58.6898	−	29.9040i	−0.0873361	−	0.0444999i
$673$	70.1889	+	443.155i	0.104293	+	0.658478i	0.983344	+	0.181752i	$0.0581766\pi$
$673$	70.1889	+	443.155i	0.104293	+	0.658478i	−0.879052	+	0.476726i	$0.841823\pi$
$674$		−	173.909i		−	0.258025i
$675$	−21.4031	−	128.128i	−0.0317083	−	0.189820i
$676$	652.523			0.965271
$677$	249.555	−	39.5256i	0.368619	−	0.0583835i	0.0306229	−	0.999531i	$-0.490251\pi$
$677$	249.555	−	39.5256i	0.368619	−	0.0583835i	0.337996	+	0.941147i	$0.390251\pi$
$678$	−19.9930	+	39.2385i	−0.0294882	+	0.0578739i
$679$	82.4718	−	26.7967i	0.121461	−	0.0394649i
$680$	221.864	−	36.0998i	0.326271	−	0.0530879i
$681$	159.824	−	491.887i	0.234690	−	0.722301i
$682$	135.687	−	135.687i	0.198955	−	0.198955i
$683$	−254.148	+	129.495i	−0.372105	+	0.189597i	−0.630035	−	0.776566i	$-0.716960\pi$
$683$	−254.148	+	129.495i	−0.372105	+	0.189597i	0.257930	+	0.966164i	$0.416960\pi$
$684$	−124.662	−	171.582i	−0.182254	−	0.250851i
$685$	−166.934	−	227.738i	−0.243699	−	0.332465i
$686$	−62.4770	−	45.3922i	−0.0910743	−	0.0661694i
$687$	−19.4393	+	122.735i	−0.0282959	+	0.178653i
$688$	−299.997	−	47.5148i	−0.436042	−	0.0690622i
$689$	3.78171	−	5.20507i	0.00548869	−	0.00755453i
$690$	92.0143	−	67.4471i	0.133354	−	0.0977495i
$691$	584.602	−	424.738i	0.846023	−	0.614672i	−0.0780238	−	0.996951i	$-0.524861\pi$
$691$	584.602	−	424.738i	0.846023	−	0.614672i	0.924047	+	0.382280i	$0.124861\pi$
$692$	−21.2395	−	41.6849i	−0.0306929	−	0.0602383i
$693$	55.7116	+	55.7116i	0.0803919	+	0.0803919i
$694$	153.639	+	49.9203i	0.221382	+	0.0719313i
$695$	124.752	+	766.708i	0.179499	+	1.10318i
$696$	−1.64901	−	5.07513i	−0.00236927	−	0.00729185i
$697$	−160.446	−	81.7514i	−0.230195	−	0.117290i
$698$	−21.2155	−	133.949i	−0.0303947	−	0.191905i
$699$		−	512.302i		−	0.732907i
$700$	−192.836	−	96.2145i	−0.275480	−	0.137449i
$701$	127.526			0.181920			0.0909598	−	0.995855i	$-0.471007\pi$
$701$	127.526			0.181920			0.0909598	+	0.995855i	$0.471007\pi$
$702$	−0.306237	+	0.0485031i	−0.000436235	+	6.90928e-5i
$703$	591.465	−	1160.82i	0.841345	−	1.65123i
$704$	−571.776	+	185.781i	−0.812182	+	0.263894i
$705$	58.1945	−	377.731i	0.0825454	−	0.535789i
$706$	44.5246	−	137.033i	0.0630660	−	0.194097i
$707$	219.176	−	219.176i	0.310009	−	0.310009i
$708$	−282.525	+	143.954i	−0.399047	+	0.203325i
$709$	49.5094	+	68.1438i	0.0698299	+	0.0961126i	0.842503	−	0.538691i	$-0.181081\pi$
$709$	49.5094	+	68.1438i	0.0698299	+	0.0961126i	−0.772674	+	0.634804i	$0.781081\pi$
$710$	79.3203	+	25.4033i	0.111719	+	0.0357793i
$711$	−378.973	−	275.340i	−0.533013	−	0.387257i
$712$	−58.6380	+	370.226i	−0.0823568	+	0.519980i
$713$	1534.17	+	242.989i	2.15171	+	0.340798i
$714$	12.9957	−	17.8871i	0.0182013	−	0.0250519i
$715$	9.43758	−	0.0398095i	0.0131994	−	5.56777e-5i
$716$	−481.742	+	350.006i	−0.672824	+	0.488835i
$717$	34.6026	+	67.9115i	0.0482603	+	0.0947161i
$718$	67.1147	+	67.1147i	0.0934745	+	0.0934745i
$719$	289.513	+	94.0683i	0.402660	+	0.130832i	0.503344	−	0.864086i	$-0.332103\pi$
$719$	289.513	+	94.0683i	0.402660	+	0.130832i	−0.100684	+	0.994918i	$0.532103\pi$
$720$	191.498	−	98.5927i	0.265969	−	0.136934i
$721$	87.0962	+	268.055i	0.120799	+	0.371782i
$722$	−8.56714	−	4.36518i	−0.0118658	−	0.00604595i
$723$	16.2118	+	102.357i	0.0224230	+	0.141573i
$724$		−	66.5075i		−	0.0918611i
$725$	−8.35121	−	24.9832i	−0.0115189	−	0.0344597i
$726$	−11.2197			−0.0154541
$727$	367.309	−	58.1760i	0.505239	−	0.0800220i	0.101388	−	0.994847i	$-0.467672\pi$
$727$	367.309	−	58.1760i	0.505239	−	0.0800220i	0.403851	+	0.914825i	$0.367672\pi$
$728$	−0.475403	+	0.933031i	−0.000653026	+	0.00128164i
$729$	25.6785	−	8.34346i	0.0352243	−	0.0114451i
$730$	22.6354	+	11.4133i	0.0310074	+	0.0156346i
$731$	100.501	−	309.310i	0.137484	−	0.423133i
$732$	265.712	−	265.712i	0.362994	−	0.362994i
$733$	−924.658	+	471.137i	−1.26147	+	0.642751i	−0.951399	−	0.307962i	$-0.900353\pi$
$733$	−924.658	+	471.137i	−1.26147	+	0.642751i	−0.310072	+	0.950713i	$0.600353\pi$
$734$	−81.7065	−	112.459i	−0.111317	−	0.153214i
$735$	362.041	−	119.325i	0.492573	−	0.162347i
$736$	488.183	+	354.686i	0.663292	+	0.481910i
$737$	40.7581	−	257.337i	0.0553027	−	0.349168i
$738$	12.9070	+	2.04426i	0.0174891	+	0.00277000i
$739$	320.162	−	440.665i	0.433237	−	0.596299i	−0.535456	−	0.844563i	$-0.679860\pi$
$739$	320.162	−	440.665i	0.433237	−	0.596299i	0.968692	+	0.248264i	$0.0798601\pi$
$740$	1115.05	+	802.964i	1.50682	+	1.08509i
$741$	−4.11563	+	2.99018i	−0.00555416	+	0.00403533i
$742$	−15.1153	−	29.6654i	−0.0203710	−	0.0399803i
$743$	−437.231	−	437.231i	−0.588467	−	0.588467i	0.348749	−	0.937216i	$-0.386606\pi$
$743$	−437.231	−	437.231i	−0.588467	−	0.588467i	−0.937216	+	0.348749i	$0.886606\pi$
$744$	−211.223	−	68.6307i	−0.283902	−	0.0922455i
$745$	−991.711	−	983.380i	−1.33116	−	1.31997i
$746$	74.7813	+	230.153i	0.100243	+	0.308516i
$747$	−263.106	−	134.059i	−0.352217	−	0.179463i
$748$	−109.276	−	689.939i	−0.146090	−	0.922378i
$749$			29.1080i			0.0388625i
$750$	−71.2791	+	37.4622i	−0.0950389	+	0.0499495i
$751$	573.177			0.763219			0.381609	−	0.924324i	$-0.375370\pi$
$751$	573.177			0.763219			0.381609	+	0.924324i	$0.375370\pi$
$752$	625.888	−	99.1308i	0.832297	−	0.131823i
$753$	189.906	−	372.711i	0.252199	−	0.494969i
$754$	−0.0597960	+	0.0194289i	−7.93050e−5	+	2.57678e-5i
$755$	−30.7171	+	30.9773i	−0.0406849	+	0.0410296i
$756$	13.8415	−	42.5999i	0.0183089	−	0.0563491i
$757$	176.152	−	176.152i	0.232698	−	0.232698i	−0.581120	−	0.813818i	$-0.697385\pi$
$757$	176.152	−	176.152i	0.232698	−	0.232698i	0.813818	+	0.581120i	$0.197385\pi$
$758$	98.8014	−	50.3418i	0.130345	−	0.0664140i
$759$	−424.250	−	583.930i	−0.558960	−	0.769342i
$760$	−156.403	+	217.191i	−0.205793	+	0.285777i
$761$	332.345	+	241.462i	0.436721	+	0.317296i	0.784331	−	0.620343i	$-0.213007\pi$
$761$	332.345	+	241.462i	0.436721	+	0.317296i	−0.347610	+	0.937639i	$0.613007\pi$
$762$	23.5668	−	148.795i	0.0309276	−	0.195269i
$763$	−353.216	−	55.9439i	−0.462930	−	0.0733210i
$764$	−367.362	+	505.631i	−0.480840	+	0.661820i
$765$	72.1926	+	219.038i	0.0943694	+	0.286324i
$766$	−3.55068	+	2.57972i	−0.00463535	+	0.00336778i
$767$	3.45293	+	6.77675i	0.00450186	+	0.00883540i
$768$	210.642	+	210.642i	0.274274	+	0.274274i
$769$	74.7164	+	24.2768i	0.0971605	+	0.0315693i	0.357194	−	0.934030i	$-0.383734\pi$
$769$	74.7164	+	24.2768i	0.0971605	+	0.0315693i	−0.260033	+	0.965600i	$0.583734\pi$
$770$	21.9886	−	43.6088i	0.0285566	−	0.0566347i
$771$	−81.0564	−	249.466i	−0.105131	−	0.323561i
$772$	−668.106	−	340.417i	−0.865422	−	0.440955i
$773$	58.2156	+	367.559i	0.0753113	+	0.475497i	0.996303	+	0.0859136i	$0.0273809\pi$
$773$	58.2156	+	367.559i	0.0753113	+	0.475497i	−0.920991	+	0.389583i	$0.872619\pi$
$774$			23.6017i			0.0304931i
$775$	−1045.50	−	329.979i	−1.34903	−	0.425780i
$776$	113.586			0.146373
$777$	271.763	−	43.0430i	0.349759	−	0.0553964i
$778$	−74.6790	+	146.566i	−0.0959885	+	0.188388i
$779$	203.916	−	66.2564i	0.261767	−	0.0850531i
$780$	−2.45601	−	4.77033i	−0.00314873	−	0.00611581i
$781$	162.831	−	501.144i	0.208491	−	0.641669i
$782$	−143.222	+	143.222i	−0.183148	+	0.183148i
$783$	4.87835	−	2.48564i	0.00623033	−	0.00317451i
$784$	371.509	+	511.338i	0.473864	+	0.652217i
$785$	2.74901	+	651.702i	0.00350192	+	0.830194i
$786$	−120.737	−	87.7204i	−0.153609	−	0.111604i
$787$	−92.2818	+	582.644i	−0.117258	+	0.740336i	0.857070	+	0.515200i	$0.172282\pi$
$787$	−92.2818	+	582.644i	−0.117258	+	0.740336i	−0.974327	+	0.225136i	$0.927718\pi$
$788$	−1236.11	−	195.781i	−1.56867	−	0.248453i
$789$	−263.783	+	363.067i	−0.334326	+	0.460161i
$790$	−88.5641	+	276.536i	−0.112106	+	0.350045i
$791$	−123.458	+	89.6973i	−0.156078	+	0.113397i
$792$	46.8524	+	91.9531i	0.0591571	+	0.116102i
$793$	−6.37346	−	6.37346i	−0.00803715	−	0.00803715i
$794$	−232.274	−	75.4705i	−0.292537	−	0.0950510i
$795$	343.246	+	52.8817i	0.431756	+	0.0665178i
$796$	−107.542	−	330.980i	−0.135103	−	0.415804i
$797$	1388.99	+	707.724i	1.74277	+	0.887985i	0.966136	+	0.258032i	$0.0830741\pi$
$797$	1388.99	+	707.724i	1.74277	+	0.887985i	0.776633	+	0.629953i	$0.216926\pi$
$798$	4.11824	+	26.0015i	0.00516070	+	0.0325834i
$799$			678.527i			0.849221i
$800$	−303.693	−	298.612i	−0.379616	−	0.373264i
$801$	−384.590			−0.480137
$802$	−183.376	+	29.0438i	−0.228648	+	0.0362143i
$803$	72.8105	−	142.899i	0.0906731	−	0.177956i
$804$	−140.874	+	45.7726i	−0.175216	+	0.0569311i
$805$	390.202	−	63.4903i	0.484723	−	0.0788699i
$806$	−0.808617	+	2.48867i	−0.00100325	+	0.00308768i
$807$	404.085	−	404.085i	0.500724	−	0.500724i
$808$	361.755	−	184.323i	0.447716	−	0.228123i
$809$	−211.651	−	291.312i	−0.261620	−	0.360089i	0.657918	−	0.753089i	$-0.271437\pi$
$809$	−211.651	−	291.312i	−0.261620	−	0.360089i	−0.919538	+	0.393000i	$0.871437\pi$
$810$	−9.89456	−	13.4986i	−0.0122155	−	0.0166649i
$811$	7.84334	+	5.69852i	0.00967119	+	0.00702653i	0.592610	−	0.805489i	$-0.298097\pi$
$811$	7.84334	+	5.69852i	0.00967119	+	0.00702653i	−0.582939	+	0.812516i	$0.698097\pi$
$812$	1.42090	−	8.97120i	0.00174987	−	0.0110483i
$813$	−566.336	−	89.6988i	−0.696600	−	0.110331i
$814$	−183.034	+	251.925i	−0.224858	+	0.309490i
$815$	−86.8237	+	63.6424i	−0.106532	+	0.0780888i
$816$	−309.364	+	224.766i	−0.379122	+	0.275448i
$817$	175.805	+	345.037i	0.215184	+	0.422322i
$818$	−29.7164	−	29.7164i	−0.0363282	−	0.0363282i
$819$	−1.02182	−	0.332008i	−0.00124764	−	0.000405382i
$820$	36.3175	+	223.202i	0.0442897	+	0.272198i
$821$	−171.369	−	527.420i	−0.208732	−	0.642412i	−0.999539	−	0.0303464i	$-0.990339\pi$
$821$	−171.369	−	527.420i	−0.208732	−	0.642412i	0.790807	−	0.612065i	$-0.209661\pi$
$822$	−32.4147	−	16.5161i	−0.0394339	−	0.0200926i
$823$	−99.7775	−	629.970i	−0.121236	−	0.765456i	−0.971139	−	0.238516i	$-0.923339\pi$
$823$	−99.7775	−	629.970i	−0.121236	−	0.765456i	0.849902	−	0.526940i	$-0.176661\pi$
$824$			369.183i			0.448038i
$825$	235.103	+	451.949i	0.284973	+	0.547817i
$826$	39.3587			0.0476497
$827$	−783.247	+	124.054i	−0.947094	+	0.150005i	−0.610829	−	0.791763i	$-0.709164\pi$
$827$	−783.247	+	124.054i	−0.947094	+	0.150005i	−0.336265	+	0.941767i	$0.609164\pi$
$828$	−186.291	+	365.617i	−0.224989	+	0.441566i
$829$	−586.777	+	190.656i	−0.707814	+	0.229983i	−0.640732	−	0.767765i	$-0.721369\pi$
$829$	−586.777	+	190.656i	−0.707814	+	0.229983i	−0.0670819	+	0.997747i	$0.521369\pi$
$830$	−27.8714	+	180.909i	−0.0335800	+	0.217963i
$831$	−193.903	+	596.773i	−0.233337	+	0.718138i
$832$	5.79710	−	5.79710i	0.00696767	−	0.00696767i
$833$	−603.007	+	307.248i	−0.723898	+	0.368845i
$834$	58.8259	+	80.9670i	0.0705347	+	0.0970827i
$835$	729.782	+	233.722i	0.873990	+	0.279906i
$836$	672.892	+	488.885i	0.804895	+	0.584790i
$837$	35.6467	−	225.064i	0.0425887	−	0.268894i
$838$	235.640	+	37.3217i	0.281194	+	0.0445367i
$839$	503.455	−	692.947i	0.600066	−	0.825920i	−0.395649	−	0.918402i	$-0.629480\pi$
$839$	503.455	−	692.947i	0.600066	−	0.825920i	0.995714	+	0.0924824i	$0.0294802\pi$
$840$	−56.5252	+	0.238434i	−0.0672918	+	0.000283850i
$841$	−679.485	+	493.675i	−0.807949	+	0.587009i
$842$	34.4284	+	67.5695i	0.0408888	+	0.0802488i
$843$	422.194	+	422.194i	0.500823	+	0.500823i
$844$	9.11651	+	2.96213i	0.0108015	+	0.00350964i
$845$	751.161	−	386.736i	0.888948	−	0.457675i
$846$	−15.2162	−	46.8305i	−0.0179860	−	0.0553552i
$847$	−34.6410	−	17.6505i	−0.0408985	−	0.0208388i
$848$	90.0807	+	568.747i	0.106227	+	0.670692i
$849$		−	454.445i		−	0.535271i
$850$	114.945	−	85.0028i	0.135229	−	0.100003i
$851$	−2520.65			−2.96199
$852$	−295.881	+	46.8630i	−0.347279	+	0.0550035i
$853$	561.230	−	1101.48i	0.657948	−	1.29130i	−0.285055	−	0.958511i	$-0.592012\pi$
$853$	561.230	−	1101.48i	0.657948	−	1.29130i	0.943003	−	0.332785i	$-0.107988\pi$
$854$	−44.3605	+	14.4136i	−0.0519444	+	0.0168777i
$855$	−245.199	−	123.635i	−0.286783	−	0.144602i
$856$	−11.7820	+	36.2614i	−0.0137641	+	0.0423615i
$857$	−937.167	+	937.167i	−1.09354	+	1.09354i	−0.0983960	+	0.995147i	$0.531371\pi$
$857$	−937.167	+	937.167i	−1.09354	+	1.09354i	−0.995147	+	0.0983960i	$0.968629\pi$
$858$	1.08341	−	0.552023i	0.00126271	−	0.000643383i
$859$	676.207	+	930.719i	0.787202	+	1.08349i	0.994451	+	0.105203i	$0.0335492\pi$
$859$	676.207	+	930.719i	0.787202	+	1.08349i	−0.207248	+	0.978288i	$0.566451\pi$
$860$	−387.899	+	127.847i	−0.451045	+	0.148660i
$861$	36.6345	+	26.6165i	0.0425488	+	0.0309135i
$862$	−21.7874	+	137.560i	−0.0252754	+	0.159582i
$863$	1095.11	+	173.449i	1.26896	+	0.200984i	0.754369	−	0.656451i	$-0.227943\pi$
$863$	1095.11	+	173.449i	1.26896	+	0.200984i	0.514593	+	0.857435i	$0.327943\pi$
$864$	52.0328	−	71.6170i	0.0602231	−	0.0828900i
$865$	−49.1558	−	35.3980i	−0.0568276	−	0.0409225i
$866$	43.3062	−	31.4638i	0.0500071	−	0.0363323i
$867$	41.3635	+	81.1805i	0.0477088	+	0.0936337i
$868$	−267.307	−	267.307i	−0.307957	−	0.307957i
$869$	1747.15	+	567.682i	2.01053	+	0.653259i
$870$	−2.40993	−	2.38969i	−0.00277004	−	0.00274677i
$871$	1.09792	+	3.37904i	0.00126053	+	0.00387950i
$872$	−417.375	−	212.663i	−0.478641	−	0.243880i
$873$	18.2309	+	115.105i	0.0208830	+	0.131850i
$874$		−	241.169i		−	0.275937i
$875$	−279.010	+	3.53093i	−0.318869	+	0.00403534i
$876$	−91.1778			−0.104084
$877$	−653.320	+	103.476i	−0.744949	+	0.117988i	−0.517358	−	0.855769i	$-0.673085\pi$
$877$	−653.320	+	103.476i	−0.744949	+	0.117988i	−0.227590	+	0.973757i	$0.573085\pi$
$878$	24.7421	−	48.5591i	0.0281801	−	0.0553065i
$879$	665.319	−	216.175i	0.756905	−	0.245933i
$880$	−594.757	+	599.796i	−0.675860	+	0.681586i
$881$	−89.6904	+	276.039i	−0.101805	+	0.313324i	−0.988967	−	0.148134i	$-0.952673\pi$
$881$	−89.6904	+	276.039i	−0.101805	+	0.313324i	0.887162	+	0.461458i	$0.152673\pi$
$882$	34.7282	−	34.7282i	0.0393744	−	0.0393744i
$883$	−80.1173	+	40.8218i	−0.0907331	+	0.0462308i	−0.498768	−	0.866735i	$-0.666214\pi$
$883$	−80.1173	+	40.8218i	−0.0907331	+	0.0462308i	0.408035	+	0.912966i	$0.366214\pi$
$884$	5.59906	+	7.70645i	0.00633378	+	0.00871770i
$885$	−239.915	+	333.161i	−0.271090	+	0.376453i
$886$	9.35605	+	6.79757i	0.0105599	+	0.00767220i
$887$	215.969	−	1363.57i	0.243482	−	1.53729i	−0.498514	−	0.866882i	$-0.666121\pi$
$887$	215.969	−	1363.57i	0.243482	−	1.53729i	0.741996	−	0.670404i	$-0.233879\pi$
$888$	355.971	+	56.3803i	0.400869	+	0.0634914i
$889$	306.843	−	422.333i	0.345155	−	0.475065i
$890$	74.6246	+	226.417i	0.0838479	+	0.254401i
$891$	−85.6632	+	62.2380i	−0.0961428	+	0.0698518i
$892$	−245.113	−	481.061i	−0.274790	−	0.539306i
$893$	−571.280	−	571.280i	−0.639732	−	0.639732i
$894$	−171.131	−	55.6037i	−0.191421	−	0.0621966i
$895$	−347.123	+	688.432i	−0.387847	+	0.769197i
$896$	−60.1173	−	185.022i	−0.0670952	−	0.206498i
$897$	8.76981	+	4.46844i	0.00977683	+	0.00498154i
$898$	−22.0694	−	139.341i	−0.0245762	−	0.155168i
$899$		−	46.2078i		−	0.0513991i
$900$	168.255	−	235.740i	0.186950	−	0.261933i
$901$	−616.581			−0.684330
$902$	−50.6170	+	8.01695i	−0.0561164	+	0.00888797i
$903$	−37.1295	+	72.8707i	−0.0411179	+	0.0806984i
$904$	−190.104	+	61.7687i	−0.210293	+	0.0683282i
$905$	−39.4175	−	76.5610i	−0.0435552	−	0.0845978i
$906$	−1.73685	+	5.34548i	−0.00191705	+	0.00590009i
$907$	−572.229	+	572.229i	−0.630903	+	0.630903i	−0.948295	−	0.317391i	$-0.897193\pi$
$907$	−572.229	+	572.229i	−0.630903	+	0.630903i	0.317391	+	0.948295i	$0.397193\pi$
$908$	1027.44	−	523.505i	1.13154	−	0.576547i
$909$	244.852	+	337.010i	0.269364	+	0.370748i
$910$	0.00280927	+	0.665988i	3.08711e−6	+	0.000731855i
$911$	−142.730	−	103.700i	−0.156674	−	0.113831i	0.506686	−	0.862131i	$-0.330870\pi$
$911$	−142.730	−	103.700i	−0.156674	−	0.113831i	−0.663360	+	0.748300i	$0.730870\pi$
$912$	71.2265	−	449.706i	0.0780992	−	0.493099i
$913$	1143.78	+	181.157i	1.25277	+	0.198420i
$914$	138.121	−	190.107i	0.151117	−	0.207995i
$915$	148.397	−	463.359i	0.162182	−	0.506404i
$916$	−224.141	+	162.848i	−0.244695	+	0.177781i
$917$	−234.778	−	460.778i	−0.256029	−	0.502484i
$918$	21.0108	+	21.0108i	0.0228876	+	0.0228876i
$919$	373.118	+	121.233i	0.406004	+	0.131919i	0.504898	−	0.863179i	$-0.331530\pi$
$919$	373.118	+	121.233i	0.406004	+	0.131919i	−0.0988933	+	0.995098i	$0.531530\pi$
$920$	511.794	+	78.8486i	0.556297	+	0.0857050i
$921$	230.258	+	708.660i	0.250008	+	0.769446i
$922$	58.6121	+	29.8644i	0.0635706	+	0.0323908i
$923$	1.12407	+	7.09712i	0.00121785	+	0.00768918i
$924$			175.661i			0.190109i
$925$	1759.50	+	263.481i	1.90216	+	0.284844i
$926$	−45.8392			−0.0495024
$927$	−374.122	+	59.2551i	−0.403584	+	0.0639214i
$928$	8.14955	−	15.9944i	0.00878184	−	0.0172353i
$929$	26.5924	−	8.64041i	0.0286248	−	0.00930076i	−0.294670	−	0.955599i	$-0.595210\pi$
$929$	26.5924	−	8.64041i	0.0286248	−	0.00930076i	0.323294	+	0.946298i	$0.395210\pi$
$930$	−139.417	+	22.6848i	−0.149911	+	0.0243922i
$931$	249.012	−	766.381i	0.267468	−	0.823181i
$932$	807.654	−	807.654i	0.866582	−	0.866582i
$933$	−500.008	+	254.767i	−0.535915	+	0.273062i
$934$	−61.7301	−	84.9642i	−0.0660922	−	0.0909681i
$935$	−534.705	−	729.468i	−0.571877	−	0.780179i
$936$	−1.13854	−	0.827199i	−0.00121639	−	0.000883760i
$937$	−125.553	+	792.709i	−0.133994	+	0.846008i	0.825525	+	0.564365i	$0.190879\pi$
$937$	−125.553	+	792.709i	−0.133994	+	0.846008i	−0.959520	+	0.281642i	$0.909121\pi$
$938$	18.1596	+	2.87621i	0.0193600	+	0.00306632i
$939$	55.3703	−	76.2107i	0.0589673	−	0.0811616i
$940$	687.246	−	503.756i	0.731113	−	0.535911i
$941$	−476.294	+	346.048i	−0.506157	+	0.367745i	−0.811364	−	0.584541i	$-0.801274\pi$
$941$	−476.294	+	346.048i	−0.506157	+	0.367745i	0.305207	+	0.952286i	$0.401274\pi$
$942$	38.1194	+	74.8135i	0.0404664	+	0.0794198i
$943$	−293.333	−	293.333i	−0.311064	−	0.311064i
$944$	−647.407	−	210.355i	−0.685812	−	0.222834i
$945$	−9.31409	−	57.2430i	−0.00985618	−	0.0605746i
$946$	−28.6021	−	88.0283i	−0.0302348	−	0.0930531i
$947$	−1065.80	−	543.054i	−1.12545	−	0.573447i	−0.210736	−	0.977543i	$-0.567586\pi$
$947$	−1065.80	−	543.054i	−1.12545	−	0.573447i	−0.914716	+	0.404096i	$0.867586\pi$
$948$	−163.379	−	1031.54i	−0.172341	−	1.08812i
$949$			2.18702i			0.00230455i
$950$	−25.2091	+	168.344i	−0.0265359	+	0.177204i
$951$	96.8905			0.101883
$952$	99.1188	−	15.6989i	0.104116	−	0.0164904i
$953$	−97.5332	+	191.420i	−0.102343	+	0.200860i	−0.936500	−	0.350667i	$-0.885955\pi$
$953$	−97.5332	+	191.420i	−0.102343	+	0.200860i	0.834157	+	0.551527i	$0.185955\pi$
$954$	42.5551	−	13.8270i	0.0446070	−	0.0144937i
$955$	−123.218	+	799.791i	−0.129025	+	0.837477i
$956$	−52.5121	+	161.616i	−0.0549290	+	0.169054i
$957$	−15.1827	+	15.1827i	−0.0158649	+	0.0158649i
$958$	−52.2933	+	26.6448i	−0.0545859	+	0.0278129i
$959$	−74.0984	−	101.988i	−0.0772663	−	0.106348i
$960$	421.457	+	134.977i	0.439018	+	0.140601i
$961$	−778.385	−	565.530i	−0.809974	−	0.588480i
$962$	0.664282	−	4.19411i	0.000690521	−	0.00435978i
$963$	−38.6375	−	6.11958i	−0.0401221	−	0.00635471i
$964$	−135.810	+	186.927i	−0.140882	+	0.193907i
$965$	−970.857	+	4.09526i	−1.00607	+	0.00424380i
$966$	41.2066	−	29.9384i	0.0426570	−	0.0309921i
$967$	97.6273	+	191.604i	0.100959	+	0.198143i	0.935961	−	0.352104i	$-0.114534\pi$
$967$	97.6273	+	191.604i	0.100959	+	0.198143i	−0.835002	+	0.550247i	$0.814534\pi$
$968$	−36.0097	−	36.0097i	−0.0372001	−	0.0372001i
$969$	463.667	+	150.655i	0.478500	+	0.155474i
$970$	64.2276	−	33.0676i	0.0662140	−	0.0340903i
$971$	66.8653	+	205.790i	0.0688623	+	0.211936i	0.979566	−	0.201125i	$-0.0644596\pi$
$971$	66.8653	+	205.790i	0.0688623	+	0.211936i	−0.910703	+	0.413061i	$0.864460\pi$
$972$	53.6364	+	27.3291i	0.0551815	+	0.0281164i
$973$	54.2515	+	342.530i	0.0557569	+	0.352035i
$974$		−	95.3528i		−	0.0978982i
$975$	−5.65453	−	4.03582i	−0.00579952	−	0.00413930i
$976$	806.715			0.826552
$977$	894.819	−	141.725i	0.915885	−	0.145062i	0.319339	−	0.947641i	$-0.396539\pi$
$977$	894.819	−	141.725i	0.915885	−	0.145062i	0.596546	+	0.802579i	$0.296539\pi$
$978$	−6.29665	+	12.3579i	−0.00643830	+	0.0126359i
$979$	1434.42	−	466.072i	1.46519	−	0.476070i
$980$	758.884	+	382.647i	0.774371	+	0.390456i
$981$	148.518	−	457.091i	0.151395	−	0.465944i
$982$	2.46019	−	2.46019i	0.00250529	−	0.00250529i
$983$	1037.36	−	528.563i	1.05530	−	0.537704i	0.161830	−	0.986819i	$-0.448260\pi$
$983$	1037.36	−	528.563i	1.05530	−	0.537704i	0.893474	+	0.449114i	$0.148260\pi$
$984$	34.8640	+	47.9861i	0.0354309	+	0.0487664i
$985$	−1539.00	+	507.239i	−1.56244	+	0.514964i
$986$	4.87466	+	3.54165i	0.00494387	+	0.00359193i
$987$	26.6922	−	168.528i	0.0270438	−	0.170748i
$988$	−11.2025	−	1.77430i	−0.0113385	−	0.00179585i
$989$	440.386	−	606.140i	0.445284	−	0.612881i
$990$	53.2627	+	38.3554i	0.0538007	+	0.0387428i
$991$	233.201	−	169.431i	0.235319	−	0.170969i	−0.463876	−	0.885900i	$-0.653542\pi$
$991$	233.201	−	169.431i	0.235319	−	0.170969i	0.699195	+	0.714931i	$0.253542\pi$
$992$	−339.179	−	665.675i	−0.341914	−	0.671044i
$993$	186.583	+	186.583i	0.187898	+	0.187898i
$994$	35.3646	+	11.4906i	0.0355780	+	0.0115600i
$995$	−319.962	−	317.274i	−0.321570	−	0.318869i
$996$	−203.445	−	626.139i	−0.204262	−	0.628654i
$997$	−688.190	−	350.650i	−0.690261	−	0.351705i	0.0734185	−	0.997301i	$-0.476609\pi$
$997$	−688.190	−	350.650i	−0.690261	−	0.351705i	−0.763679	+	0.645596i	$0.776609\pi$
$998$	−9.76081	−	61.6274i	−0.00978037	−	0.0617509i
$999$			369.782i			0.370153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.13.6	✓	80
3.2	odd	2		225.3.r.b.163.5		80
5.2	odd	4		375.3.k.c.82.6		80
5.3	odd	4		375.3.k.b.82.5		80
5.4	even	2		375.3.k.a.43.5		80
25.2	odd	20	inner	75.3.k.a.52.6	yes	80
25.11	even	5		375.3.k.c.343.6		80
25.14	even	10		375.3.k.b.343.5		80
25.23	odd	20		375.3.k.a.157.5		80
75.2	even	20		225.3.r.b.127.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.13.6	✓	80	1.1	even	1	trivial
75.3.k.a.52.6	yes	80	25.2	odd	20	inner
225.3.r.b.127.5		80	75.2	even	20
225.3.r.b.163.5		80	3.2	odd	2
375.3.k.a.43.5		80	5.4	even	2
375.3.k.a.157.5		80	25.23	odd	20
375.3.k.b.82.5		80	5.3	odd	4
375.3.k.b.343.5		80	25.14	even	10
375.3.k.c.82.6		80	5.2	odd	4
375.3.k.c.343.6		80	25.11	even	5

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.367346 - 0.0581819i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(-3.67267 + 1.19332i) q^{4} +(-3.52059 + 3.55042i) q^{5} +(-0.199067 + 0.612664i) q^{6} +(-1.57845 + 1.57845i) q^{7} +(-2.60526 + 1.32745i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(0.367346 - 0.0581819i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(-3.67267 + 1.19332i) q^{4} +(-3.52059 + 3.55042i) q^{5} +(-0.199067 + 0.612664i) q^{6} +(-1.57845 + 1.57845i) q^{7} +(-2.60526 + 1.32745i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(-1.08670 + 1.50906i) q^{10} +(9.51813 + 6.91533i) q^{11} +(1.04633 - 6.60626i) q^{12} +(-0.158460 - 0.0250976i) q^{13} +(-0.487999 + 0.671673i) q^{14} +(-2.71088 - 8.22503i) q^{15} +(11.6168 - 8.44012i) q^{16} +(6.98020 + 13.6994i) q^{17} +(-0.788972 - 0.788972i) q^{18} +(-17.4110 - 5.65719i) q^{19} +(8.69317 - 17.2407i) q^{20} +(-1.19478 - 3.67715i) q^{21} +(3.89879 + 1.98653i) q^{22} +(5.54091 + 34.9839i) q^{23} -5.06443i q^{24} +(-0.210906 - 24.9991i) q^{25} -0.0596699 q^{26} +(5.13218 - 0.812857i) q^{27} +(3.91351 - 7.68071i) q^{28} +(1.00211 - 0.325606i) q^{29} +(-1.47438 - 2.86371i) q^{30} +(13.5515 - 41.7072i) q^{31} +(12.0465 - 12.0465i) q^{32} +(-18.1566 + 9.25127i) q^{33} +(3.36120 + 4.62630i) q^{34} +(-0.0470801 - 11.1612i) q^{35} +(9.37247 + 6.80950i) q^{36} +(-11.1326 + 70.2885i) q^{37} +(-6.72501 - 1.06514i) q^{38} +(0.163335 - 0.224811i) q^{39} +(4.45906 - 13.9231i) q^{40} +(-9.47513 + 6.88408i) q^{41} +(-0.652841 - 1.28127i) q^{42} +(-14.9572 - 14.9572i) q^{43} +(-43.2092 - 14.0395i) q^{44} +(14.8251 + 2.28400i) q^{45} +(4.07086 + 12.5288i) q^{46} +(39.3212 + 20.0352i) q^{47} +(3.89066 + 24.5647i) q^{48} +44.0170i q^{49} +(-1.53197 - 9.17105i) q^{50} -26.6306 q^{51} +(0.611921 - 0.0969188i) q^{52} +(-18.2061 + 35.7314i) q^{53} +(1.83799 - 0.597200i) q^{54} +(-58.0617 + 9.44730i) q^{55} +(2.01696 - 6.20757i) q^{56} +(22.4215 - 22.4215i) q^{57} +(0.349178 - 0.177915i) q^{58} +(-27.8650 - 38.3529i) q^{59} +(19.7713 + 26.9728i) q^{60} +(45.4514 + 33.0224i) q^{61} +(2.55148 - 16.1094i) q^{62} +(6.61433 + 1.04761i) q^{63} +(-30.0361 + 41.3412i) q^{64} +(0.646980 - 0.474241i) q^{65} +(-6.13151 + 4.45480i) q^{66} +(-10.0539 - 19.7319i) q^{67} +(-41.9838 - 41.9838i) q^{68} +(-58.3466 - 18.9580i) q^{69} +(-0.666674 - 4.09728i) q^{70} +(-13.8403 - 42.5959i) q^{71} +(7.81578 + 3.98234i) q^{72} +(-2.13248 - 13.4640i) q^{73} +26.4679i q^{74} +(38.7462 + 19.3322i) q^{75} +70.6958 q^{76} +(-25.9393 + 4.10839i) q^{77} +(0.0469205 - 0.0920867i) q^{78} +(148.503 - 48.2515i) q^{79} +(-10.9321 + 70.9588i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-3.08012 + 3.08012i) q^{82} +(87.7020 - 44.6864i) q^{83} +(8.77606 + 12.0792i) q^{84} +(-73.2130 - 23.4474i) q^{85} +(-6.36472 - 4.62424i) q^{86} +(-0.285498 + 1.80256i) q^{87} +(-33.9769 - 5.38142i) q^{88} +(75.3521 - 103.713i) q^{89} +(5.57882 - 0.0235326i) q^{90} +(0.289736 - 0.210506i) q^{91} +(-62.0970 - 121.872i) q^{92} +(53.7094 + 53.7094i) q^{93} +(15.6102 + 5.07205i) q^{94} +(81.3824 - 41.8998i) q^{95} +(9.11842 + 28.0636i) q^{96} +(-34.6127 - 17.6360i) q^{97} +(2.56099 + 16.1695i) q^{98} -35.2952i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

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