LMFDB - Embedded newform 75.3.k.a.13.1

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			13.1
Character	$\chi$	$=$	75.13
Dual form			75.3.k.a.52.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.44703 + 0.545956i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(7.77971 - 2.52778i) q^{4} +(-0.831800 + 4.93033i) q^{5} +(1.86796 - 5.74899i) q^{6} +(-0.992761 + 0.992761i) q^{7} +(-12.9984 + 6.62301i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(-3.44703 + 0.545956i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(7.77971 - 2.52778i) q^{4} +(-0.831800 + 4.93033i) q^{5} +(1.86796 - 5.74899i) q^{6} +(-0.992761 + 0.992761i) q^{7} +(-12.9984 + 6.62301i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(0.175498 - 17.4491i) q^{10} +(-12.5745 - 9.13588i) q^{11} +(-2.21641 + 13.9939i) q^{12} +(-21.5771 - 3.41748i) q^{13} +(2.88007 - 3.96408i) q^{14} +(-6.95474 - 5.16058i) q^{15} +(14.7187 - 10.6938i) q^{16} +(4.03639 + 7.92186i) q^{17} +(7.40340 + 7.40340i) q^{18} +(19.1510 + 6.22253i) q^{19} +(5.99162 + 40.4591i) q^{20} +(-0.751455 - 2.31274i) q^{21} +(48.3323 + 24.6265i) q^{22} +(-2.85577 - 18.0306i) q^{23} -25.2679i q^{24} +(-23.6162 - 8.20209i) q^{25} +76.2426 q^{26} +(5.13218 - 0.812857i) q^{27} +(-5.21391 + 10.2329i) q^{28} +(-30.2486 + 9.82836i) q^{29} +(26.7906 + 13.9917i) q^{30} +(-15.7354 + 48.4286i) q^{31} +(-3.63510 + 3.63510i) q^{32} +(23.9868 - 12.2219i) q^{33} +(-18.2385 - 25.1032i) q^{34} +(-4.06886 - 5.72041i) q^{35} +(-19.8535 - 14.4244i) q^{36} +(-0.839409 + 5.29982i) q^{37} +(-69.4112 - 10.9937i) q^{38} +(22.2409 - 30.6120i) q^{39} +(-21.8415 - 69.5953i) q^{40} +(13.3819 - 9.72252i) q^{41} +(3.85294 + 7.56182i) q^{42} +(-5.83292 - 5.83292i) q^{43} +(-120.919 - 39.2890i) q^{44} +(13.4329 - 6.67510i) q^{45} +(19.6879 + 60.5930i) q^{46} +(36.9193 + 18.8113i) q^{47} +(4.92952 + 31.1238i) q^{48} +47.0289i q^{49} +(85.8838 + 15.3794i) q^{50} -15.3995 q^{51} +(-176.502 + 27.9552i) q^{52} +(-16.2292 + 31.8515i) q^{53} +(-17.2470 + 5.60388i) q^{54} +(55.5023 - 54.3970i) q^{55} +(6.32923 - 19.4794i) q^{56} +(-24.6621 + 24.6621i) q^{57} +(98.9019 - 50.3930i) q^{58} +(49.4271 + 68.0306i) q^{59} +(-67.1507 - 22.5677i) q^{60} +(-82.7370 - 60.1119i) q^{61} +(27.8005 - 175.525i) q^{62} +(4.16007 + 0.658891i) q^{63} +(-32.2293 + 44.3599i) q^{64} +(34.7971 - 103.539i) q^{65} +(-76.0107 + 55.2250i) q^{66} +(-2.89032 - 5.67256i) q^{67} +(51.4267 + 51.4267i) q^{68} +(30.0717 + 9.77089i) q^{69} +(17.1486 + 17.4970i) q^{70} +(12.6579 + 38.9571i) q^{71} +(38.9952 + 19.8690i) q^{72} +(10.3074 + 65.0786i) q^{73} -18.7269i q^{74} +(31.2283 - 29.9966i) q^{75} +164.718 q^{76} +(21.5532 - 3.41369i) q^{77} +(-59.9522 + 117.663i) q^{78} +(94.9471 - 30.8502i) q^{79} +(40.4807 + 81.4630i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-40.8197 + 40.8197i) q^{82} +(-49.6409 + 25.2933i) q^{83} +(-11.6922 - 16.0929i) q^{84} +(-42.4148 + 13.3113i) q^{85} +(23.2908 + 16.9217i) q^{86} +(8.61771 - 54.4101i) q^{87} +(223.955 + 35.4710i) q^{88} +(-43.5166 + 59.8955i) q^{89} +(-42.6593 + 30.3430i) q^{90} +(24.8136 - 18.0282i) q^{91} +(-67.7946 - 133.054i) q^{92} +(-62.3650 - 62.3650i) q^{93} +(-137.532 - 44.6869i) q^{94} +(-46.6089 + 89.2447i) q^{95} +(-2.75153 - 8.46834i) q^{96} +(37.8699 + 19.2957i) q^{97} +(-25.6757 - 162.110i) q^{98} +46.6287i 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 $

$2$	−3.44703	+	0.545956i	−1.72351	+	0.272978i	−0.938193	−	0.346111i	$-0.887502\pi$
$2$	−3.44703	+	0.545956i	−1.72351	+	0.272978i	−0.785321	+	0.619089i	$0.787502\pi$
$3$	−0.786335	+	1.54327i	−0.262112	+	0.514423i
$3$	−0.786335	+	1.54327i	−0.262112	+	0.514423i
$4$	7.77971	−	2.52778i	1.94493	−	0.631945i
$5$	−0.831800	+	4.93033i	−0.166360	+	0.986065i
$5$	−0.831800	+	4.93033i	−0.166360	+	0.986065i
$6$	1.86796	−	5.74899i	0.311327	−	0.958166i
$7$	−0.992761	+	0.992761i	−0.141823	+	0.141823i	−0.774454	−	0.632631i	$-0.781975\pi$
$7$	−0.992761	+	0.992761i	−0.141823	+	0.141823i	0.632631	+	0.774454i	$0.281975\pi$
$8$	−12.9984	+	6.62301i	−1.62480	+	0.827877i
$9$	−1.76336	−	2.42705i	−0.195928	−	0.269672i
$10$	0.175498	−	17.4491i	0.0175498	−	1.74491i
$11$	−12.5745	−	9.13588i	−1.14313	−	0.830535i	−0.155580	−	0.987823i	$-0.549725\pi$
$11$	−12.5745	−	9.13588i	−1.14313	−	0.830535i	−0.987553	+	0.157289i	$0.949725\pi$
$12$	−2.21641	+	13.9939i	−0.184701	+	1.16616i
$13$	−21.5771	−	3.41748i	−1.65978	−	0.262883i	−0.745065	−	0.666991i	$-0.767582\pi$
$13$	−21.5771	−	3.41748i	−1.65978	−	0.262883i	−0.914711	+	0.404109i	$0.867582\pi$
$14$	2.88007	−	3.96408i	0.205719	−	0.283149i
$15$	−6.95474	−	5.16058i	−0.463650	−	0.344038i
$16$	14.7187	−	10.6938i	0.919918	−	0.668360i
$17$	4.03639	+	7.92186i	0.237435	+	0.465992i	0.978721	−	0.205198i	$-0.0657837\pi$
$17$	4.03639	+	7.92186i	0.237435	+	0.465992i	−0.741286	+	0.671189i	$0.765784\pi$
$18$	7.40340	+	7.40340i	0.411300	+	0.411300i
$19$	19.1510	+	6.22253i	1.00795	+	0.327502i	0.766037	−	0.642797i	$-0.222226\pi$
$19$	19.1510	+	6.22253i	1.00795	+	0.327502i	0.241910	+	0.970299i	$0.422226\pi$
$20$	5.99162	+	40.4591i	0.299581	+	2.02296i
$21$	−0.751455	−	2.31274i	−0.0357836	−	0.110130i
$22$	48.3323	+	24.6265i	2.19692	+	1.11939i
$23$	−2.85577	−	18.0306i	−0.124164	−	0.783941i	−0.968662	−	0.248382i	$-0.920101\pi$
$23$	−2.85577	−	18.0306i	−0.124164	−	0.783941i	0.844498	−	0.535559i	$-0.179899\pi$
$24$		−	25.2679i		−	1.05283i
$25$	−23.6162	−	8.20209i	−0.944649	−	0.328083i
$26$	76.2426			2.93241
$27$	5.13218	−	0.812857i	0.190081	−	0.0301058i
$28$	−5.21391	+	10.2329i	−0.186211	+	0.365460i
$29$	−30.2486	+	9.82836i	−1.04305	+	0.338909i	−0.779939	−	0.625855i	$-0.784750\pi$
$29$	−30.2486	+	9.82836i	−1.04305	+	0.338909i	−0.263116	+	0.964764i	$0.584750\pi$
$30$	26.7906	+	13.9917i	0.893021	+	0.466389i
$31$	−15.7354	+	48.4286i	−0.507593	+	1.56221i	0.288773	+	0.957397i	$0.406753\pi$
$31$	−15.7354	+	48.4286i	−0.507593	+	1.56221i	−0.796367	+	0.604814i	$0.793247\pi$
$32$	−3.63510	+	3.63510i	−0.113597	+	0.113597i
$33$	23.9868	−	12.2219i	0.726874	−	0.370361i
$34$	−18.2385	−	25.1032i	−0.536427	−	0.738329i
$35$	−4.06886	−	5.72041i	−0.116253	−	0.163440i
$36$	−19.8535	−	14.4244i	−0.551485	−	0.400677i
$37$	−0.839409	+	5.29982i	−0.0226867	+	0.143238i	−0.996432	−	0.0844035i	$-0.973102\pi$
$37$	−0.839409	+	5.29982i	−0.0226867	+	0.143238i	0.973745	+	0.227642i	$0.0731015\pi$
$38$	−69.4112	−	10.9937i	−1.82661	−	0.289307i
$39$	22.2409	−	30.6120i	0.570279	−	0.784922i
$40$	−21.8415	−	69.5953i	−0.546039	−	1.73988i
$41$	13.3819	−	9.72252i	0.326388	−	0.237135i	−0.412509	−	0.910954i	$-0.635347\pi$
$41$	13.3819	−	9.72252i	0.326388	−	0.237135i	0.738896	+	0.673819i	$0.235347\pi$
$42$	3.85294	+	7.56182i	0.0917366	+	0.180043i
$43$	−5.83292	−	5.83292i	−0.135649	−	0.135649i	0.636022	−	0.771671i	$-0.280579\pi$
$43$	−5.83292	−	5.83292i	−0.135649	−	0.135649i	−0.771671	+	0.636022i	$0.780579\pi$
$44$	−120.919	−	39.2890i	−2.74816	−	0.892932i
$45$	13.4329	−	6.67510i	0.298509	−	0.148336i
$46$	19.6879	+	60.5930i	0.427997	+	1.31724i
$47$	36.9193	+	18.8113i	0.785517	+	0.400241i	0.800262	−	0.599650i	$-0.204694\pi$
$47$	36.9193	+	18.8113i	0.785517	+	0.400241i	−0.0147448	+	0.999891i	$0.504694\pi$
$48$	4.92952	+	31.1238i	0.102698	+	0.648412i
$49$			47.0289i			0.959772i
$50$	85.8838	+	15.3794i	1.71768	+	0.307588i
$51$	−15.3995			−0.301951
$52$	−176.502	+	27.9552i	−3.39427	+	0.537600i
$53$	−16.2292	+	31.8515i	−0.306211	+	0.600972i	−0.991914	−	0.126908i	$-0.959495\pi$
$53$	−16.2292	+	31.8515i	−0.306211	+	0.600972i	0.685704	+	0.727881i	$0.259495\pi$
$54$	−17.2470	+	5.60388i	−0.319389	+	0.103776i
$55$	55.5023	−	54.3970i	1.00913	−	0.989036i
$56$	6.32923	−	19.4794i	0.113022	−	0.347846i
$57$	−24.6621	+	24.6621i	−0.432669	+	0.432669i
$58$	98.9019	−	50.3930i	1.70520	−	0.868845i
$59$	49.4271	+	68.0306i	0.837748	+	1.15306i	0.986431	+	0.164177i	$0.0524967\pi$
$59$	49.4271	+	68.0306i	0.837748	+	1.15306i	−0.148683	+	0.988885i	$0.547503\pi$
$60$	−67.1507	−	22.5677i	−1.11918	−	0.376129i
$61$	−82.7370	−	60.1119i	−1.35634	−	0.985441i	−0.998668	−	0.0515953i	$-0.983569\pi$
$61$	−82.7370	−	60.1119i	−1.35634	−	0.985441i	−0.357675	−	0.933846i	$-0.616431\pi$
$62$	27.8005	−	175.525i	0.448395	−	2.83106i
$63$	4.16007	+	0.658891i	0.0660329	+	0.0104586i
$64$	−32.2293	+	44.3599i	−0.503583	+	0.693123i
$65$	34.7971	−	103.539i	0.535340	−	1.59291i
$66$	−76.0107	+	55.2250i	−1.15168	+	0.836743i
$67$	−2.89032	−	5.67256i	−0.0431390	−	0.0846651i	0.868431	−	0.495810i	$-0.165129\pi$
$67$	−2.89032	−	5.67256i	−0.0431390	−	0.0846651i	−0.911570	+	0.411145i	$0.865129\pi$
$68$	51.4267	+	51.4267i	0.756275	+	0.756275i
$69$	30.0717	+	9.77089i	0.435822	+	0.141607i
$70$	17.1486	+	17.4970i	0.244979	+	0.249957i
$71$	12.6579	+	38.9571i	0.178281	+	0.548692i	0.999768	−	0.0215348i	$-0.00685527\pi$
$71$	12.6579	+	38.9571i	0.178281	+	0.548692i	−0.821487	+	0.570227i	$0.806855\pi$
$72$	38.9952	+	19.8690i	0.541600	+	0.275959i
$73$	10.3074	+	65.0786i	0.141198	+	0.891487i	0.951985	+	0.306146i	$0.0990395\pi$
$73$	10.3074	+	65.0786i	0.141198	+	0.891487i	−0.810787	+	0.585341i	$0.800961\pi$
$74$		−	18.7269i		−	0.253066i
$75$	31.2283	−	29.9966i	0.416377	−	0.399954i
$76$	164.718			2.16735
$77$	21.5532	−	3.41369i	0.279911	−	0.0443336i
$78$	−59.9522	+	117.663i	−0.768618	+	1.50850i
$79$	94.9471	−	30.8502i	1.20186	−	0.390509i	0.361416	−	0.932405i	$-0.382293\pi$
$79$	94.9471	−	30.8502i	1.20186	−	0.390509i	0.840445	+	0.541896i	$0.182293\pi$
$80$	40.4807	+	81.4630i	0.506009	+	1.01829i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	−40.8197	+	40.8197i	−0.497801	+	0.497801i
$83$	−49.6409	+	25.2933i	−0.598083	+	0.304738i	−0.726699	−	0.686956i	$-0.758946\pi$
$83$	−49.6409	+	25.2933i	−0.598083	+	0.304738i	0.128616	+	0.991694i	$0.458946\pi$
$84$	−11.6922	−	16.0929i	−0.139193	−	0.191583i
$85$	−42.4148	+	13.3113i	−0.498998	+	0.156604i
$86$	23.2908	+	16.9217i	0.270823	+	0.196764i
$87$	8.61771	−	54.4101i	0.0990541	−	0.625403i
$88$	223.955	+	35.4710i	2.54494	+	0.403079i
$89$	−43.5166	+	59.8955i	−0.488951	+	0.672983i	−0.980194	−	0.198040i	$-0.936543\pi$
$89$	−43.5166	+	59.8955i	−0.488951	+	0.672983i	0.491243	+	0.871022i	$0.336543\pi$
$90$	−42.6593	+	30.3430i	−0.473992	+	0.337145i
$91$	24.8136	−	18.0282i	0.272677	−	0.198112i
$92$	−67.7946	−	133.054i	−0.736898	−	1.44624i
$93$	−62.3650	−	62.3650i	−0.670591	−	0.670591i
$94$	−137.532	−	44.6869i	−1.46311	−	0.475392i
$95$	−46.6089	+	89.2447i	−0.490620	+	0.939418i
$96$	−2.75153	−	8.46834i	−0.0286618	−	0.0882118i
$97$	37.8699	+	19.2957i	0.390411	+	0.198925i	0.638167	−	0.769898i	$-0.279693\pi$
$97$	37.8699	+	19.2957i	0.390411	+	0.198925i	−0.247755	+	0.968823i	$0.579693\pi$
$98$	−25.6757	−	162.110i	−0.261997	−	1.65418i
$99$			46.6287i			0.470997i
$100$	−204.460	−	4.11322i	−2.04460	−	0.0411322i
$101$	−125.212			−1.23972			−0.619861	−	0.784712i	$-0.712811\pi$
$101$	−125.212			−1.23972			−0.619861	+	0.784712i	$0.712811\pi$
$102$	53.0825	−	8.40745i	0.520417	−	0.0824260i
$103$	58.0976	−	114.023i	0.564054	−	1.10702i	−0.416200	−	0.909273i	$-0.636638\pi$
$103$	58.0976	−	114.023i	0.564054	−	1.10702i	0.980254	−	0.197745i	$-0.0633617\pi$
$104$	303.102	−	98.4837i	2.91444	−	0.946958i
$105$	12.0276	−	1.78118i	0.114549	−	0.0169636i
$106$	38.5529	−	118.654i	0.363706	−	1.11937i
$107$	−6.02301	+	6.02301i	−0.0562898	+	0.0562898i	−0.734691	−	0.678402i	$-0.762673\pi$
$107$	−6.02301	+	6.02301i	−0.0562898	+	0.0562898i	0.678402	+	0.734691i	$0.262673\pi$
$108$	37.8721	−	19.2968i	0.350668	−	0.178674i
$109$	−31.5646	−	43.4449i	−0.289583	−	0.398577i	0.639296	−	0.768961i	$-0.279226\pi$
$109$	−31.5646	−	43.4449i	−0.289583	−	0.398577i	−0.928879	+	0.370384i	$0.879226\pi$
$110$	−161.620	+	217.810i	−1.46927	+	1.98009i
$111$	−7.51899	−	5.46287i	−0.0677387	−	0.0492150i
$112$	−3.99580	+	25.2285i	−0.0356768	+	0.225254i
$113$	−69.0588	−	10.9378i	−0.611139	−	0.0967950i	−0.156810	−	0.987629i	$-0.550121\pi$
$113$	−69.0588	−	10.9378i	−0.611139	−	0.0967950i	−0.454329	+	0.890834i	$0.650121\pi$
$114$	71.5466	−	98.4755i	0.627602	−	0.863820i
$115$	91.2723	+	0.917990i	0.793672	+	0.00798252i
$116$	−210.481	+	152.924i	−1.81449	+	1.31831i
$117$	29.7537	+	58.3949i	0.254305	+	0.499102i
$118$	−207.518	−	207.518i	−1.75863	−	1.75863i
$119$	−11.8717	−	3.85734i	−0.0997620	−	0.0324147i
$120$	124.579	+	21.0178i	1.03816	+	0.175149i
$121$	37.2617	+	114.680i	0.307948	+	0.947766i
$122$	318.015	+	162.037i	2.60668	+	1.32817i
$123$	4.48181	+	28.2970i	0.0364375	+	0.230057i
$124$			416.536i			3.35916i
$125$	60.0829	−	109.613i	0.480663	−	0.876905i
$126$	−14.6996			−0.116664
$127$	−103.307	+	16.3622i	−0.813439	+	0.128836i	−0.549275	−	0.835642i	$-0.685096\pi$
$127$	−103.307	+	16.3622i	−0.813439	+	0.128836i	−0.264164	+	0.964478i	$0.585096\pi$
$128$	96.2124	−	188.828i	0.751660	−	1.47522i
$129$	13.5884	−	4.41514i	0.105336	−	0.0342259i
$130$	−63.4186	+	375.901i	−0.487835	+	2.89155i
$131$	68.5992	−	211.127i	0.523658	−	1.61165i	−0.243296	−	0.969952i	$-0.578228\pi$
$131$	68.5992	−	211.127i	0.523658	−	1.61165i	0.766954	−	0.641702i	$-0.221772\pi$
$132$	155.716	−	155.716i	1.17967	−	1.17967i
$133$	−25.1898	+	12.8349i	−0.189397	+	0.0965028i
$134$	13.0600	+	17.9755i	0.0974625	+	0.134146i
$135$	−0.261294	+	25.9794i	−0.00193551	+	0.192440i
$136$	−104.933	−	76.2384i	−0.771567	−	0.560576i
$137$	−15.2431	+	96.2410i	−0.111263	+	0.702489i	0.867491	+	0.497453i	$0.165731\pi$
$137$	−15.2431	+	96.2410i	−0.111263	+	0.702489i	−0.978754	+	0.205036i	$0.934269\pi$
$138$	−108.992	−	17.2627i	−0.789801	−	0.125092i
$139$	112.284	−	154.546i	0.807798	−	1.11184i	−0.183861	−	0.982952i	$-0.558860\pi$
$139$	112.284	−	154.546i	0.807798	−	1.11184i	0.991659	−	0.128886i	$-0.0411403\pi$
$140$	−46.1145	−	34.2180i	−0.329389	−	0.244414i
$141$	−58.0619	+	42.1844i	−0.411786	+	0.299180i
$142$	−64.9012	−	127.376i	−0.457050	−	0.897012i
$143$	240.099	+	240.099i	1.67901	+	1.67901i
$144$	−51.9086	−	16.8661i	−0.360476	−	0.117126i
$145$	−23.2963	−	157.311i	−0.160664	−	1.08490i
$146$	−71.0600	−	218.700i	−0.486712	−	1.49795i
$147$	−72.5781	−	36.9804i	−0.493729	−	0.251567i
$148$	6.86643	+	43.3529i	0.0463948	+	0.292925i
$149$		−	15.4782i		−	0.103880i	−0.998650	−	0.0519402i	$-0.983459\pi$
$149$		−	15.4782i		−	0.103880i	0.998650	−	0.0519402i	$-0.0165405\pi$
$150$	−91.2679	+	120.448i	−0.608453	+	0.802989i
$151$	−113.852			−0.753986			−0.376993	−	0.926216i	$-0.623042\pi$
$151$	−113.852			−0.753986			−0.376993	+	0.926216i	$0.623042\pi$
$152$	−290.144	+	45.9543i	−1.90884	+	0.302331i
$153$	12.1092	−	23.7656i	0.0791449	−	0.155331i
$154$	−72.4307	+	23.5342i	−0.470329	+	0.152819i
$155$	−225.680	−	117.863i	−1.45600	−	0.760409i
$156$	95.6474	−	294.372i	0.613124	−	1.88700i
$157$	31.4873	−	31.4873i	0.200556	−	0.200556i	−0.599682	−	0.800238i	$-0.704706\pi$
$157$	31.4873	−	31.4873i	0.200556	−	0.200556i	0.800238	+	0.599682i	$0.204706\pi$
$158$	−310.442	+	158.178i	−1.96483	+	1.00113i
$159$	−36.3939	−	50.0919i	−0.228893	−	0.315044i
$160$	−14.8985	−	20.9459i	−0.0931159	−	0.130912i
$161$	20.7352	+	15.0650i	0.128790	+	0.0935715i
$162$	4.91360	−	31.0233i	0.0303309	−	0.191502i
$163$	−20.4361	−	3.23676i	−0.125375	−	0.0198574i	0.0934317	−	0.995626i	$-0.470216\pi$
$163$	−20.4361	−	3.23676i	−0.125375	−	0.0198574i	−0.218806	+	0.975768i	$0.570216\pi$
$164$	79.5309	−	109.465i	0.484945	−	0.667469i
$165$	40.3057	+	128.429i	0.244277	+	0.778358i
$166$	157.304	−	114.288i	0.947617	−	0.688484i
$167$	63.5031	+	124.632i	0.380258	+	0.746299i	0.999235	−	0.0391106i	$-0.0124525\pi$
$167$	63.5031	+	124.632i	0.380258	+	0.746299i	−0.618977	+	0.785409i	$0.712452\pi$
$168$	25.0850	+	25.0850i	0.149316	+	0.149316i
$169$	293.163	+	95.2545i	1.73469	+	0.563636i
$170$	138.938	−	69.0411i	0.817280	−	0.406124i
$171$	−18.6676	−	57.4530i	−0.109167	−	0.335982i
$172$	−60.1228	−	30.6341i	−0.349551	−	0.178105i
$173$	50.8293	+	320.924i	0.293811	+	1.85505i	0.486356	+	0.873761i	$0.338326\pi$
$173$	50.8293	+	320.924i	0.293811	+	1.85505i	−0.192545	+	0.981288i	$0.561674\pi$
$174$			192.258i			1.10493i
$175$	31.5880	−	15.3026i	0.180503	−	0.0874431i
$176$	−282.776			−1.60668
$177$	−143.856	+	22.7845i	−0.812745	+	0.128726i
$178$	117.303	−	230.220i	0.659004	−	1.29337i
$179$	−62.0827	+	20.1719i	−0.346831	+	0.112692i	−0.477252	−	0.878767i	$-0.658367\pi$
$179$	−62.0827	+	20.1719i	−0.346831	+	0.112692i	0.130421	+	0.991459i	$0.458367\pi$
$180$	87.6310	−	85.8858i	0.486839	−	0.477143i
$181$	−27.5629	+	84.8300i	−0.152281	+	0.468674i	−0.997875	−	0.0651527i	$-0.979247\pi$
$181$	−27.5629	+	84.8300i	−0.152281	+	0.468674i	0.845594	+	0.533827i	$0.179247\pi$
$182$	−75.6907	+	75.6907i	−0.415883	+	0.415883i
$183$	157.828	−	80.4173i	0.862447	−	0.439439i
$184$	156.538	+	215.455i	0.850748	+	1.17095i
$185$	−25.4316	−	8.54695i	−0.137468	−	0.0461997i
$186$	249.022	+	180.925i	1.33883	+	0.972717i
$187$	21.6177	−	136.489i	0.115603	−	0.729888i
$188$	334.773	+	53.0228i	1.78071	+	0.282036i
$189$	−4.28805	+	5.90200i	−0.0226881	+	0.0312275i
$190$	111.939	−	333.075i	0.589150	−	1.75303i
$191$	−14.7427	+	10.7112i	−0.0771871	+	0.0560797i	−0.625710	−	0.780056i	$-0.715190\pi$
$191$	−14.7427	+	10.7112i	−0.0771871	+	0.0560797i	0.548523	+	0.836136i	$0.315190\pi$
$192$	−43.1162	−	84.6202i	−0.224563	−	0.440730i
$193$	−85.3811	−	85.3811i	−0.442389	−	0.442389i	0.450425	−	0.892814i	$-0.351272\pi$
$193$	−85.3811	−	85.3811i	−0.442389	−	0.442389i	−0.892814	+	0.450425i	$0.851272\pi$
$194$	−141.073	−	45.8375i	−0.727182	−	0.236276i
$195$	132.427	+	135.118i	0.679113	+	0.692912i
$196$	118.879	+	365.871i	0.606524	+	1.86669i
$197$	0.0337489	+	0.0171959i	0.000171314	+	8.72889e-5i	0.454076	−	0.890963i	$-0.349969\pi$
$197$	0.0337489	+	0.0171959i	0.000171314	+	8.72889e-5i	−0.453905	+	0.891050i	$0.649969\pi$
$198$	−25.4572	−	160.730i	−0.128572	−	0.811769i
$199$		−	49.0100i		−	0.246282i	−0.992389	−	0.123141i	$-0.960703\pi$
$199$		−	49.0100i		−	0.246282i	0.992389	−	0.123141i	$-0.0392967\pi$
$200$	361.295	−	49.7966i	1.80648	−	0.248983i
$201$	11.0270			0.0548609
$202$	431.609	−	68.3602i	2.13668	−	0.338417i
$203$	20.2724	−	39.7868i	0.0998641	−	0.195994i
$204$	−119.804	+	38.9266i	−0.587273	+	0.190817i
$205$	36.8041	+	74.0643i	0.179532	+	0.361289i
$206$	−138.012	+	424.759i	−0.669964	+	2.06194i
$207$	−38.7255	+	38.7255i	−0.187080	+	0.187080i
$208$	−354.132	+	180.439i	−1.70256	+	0.867497i
$209$	−183.965	−	253.206i	−0.880215	−	1.21151i
$210$	−40.4871	+	12.7063i	−0.192796	+	0.0605063i
$211$	98.7367	+	71.7364i	0.467946	+	0.339983i	0.796640	−	0.604454i	$-0.206609\pi$
$211$	98.7367	+	71.7364i	0.467946	+	0.339983i	−0.328694	+	0.944436i	$0.606609\pi$
$212$	−45.7445	+	288.820i	−0.215776	+	1.36236i
$213$	−70.0747	−	11.0987i	−0.328989	−	0.0521068i
$214$	17.4732	−	24.0498i	0.0816504	−	0.112382i
$215$	33.6100	−	23.9064i	0.156326	−	0.111192i
$216$	−61.3265	+	44.5563i	−0.283919	+	0.206279i
$217$	−32.4565	−	63.6995i	−0.149569	−	0.293546i
$218$	132.523	+	132.523i	0.607903	+	0.607903i
$219$	−108.539	−	35.2664i	−0.495611	−	0.161034i
$220$	294.288	−	563.490i	1.33767	−	2.56132i
$221$	−60.0208	−	184.725i	−0.271587	−	0.835860i
$222$	28.9007	+	14.7256i	0.130183	+	0.0663316i
$223$	32.2311	+	203.499i	0.144534	+	0.912551i	0.948247	+	0.317534i	$0.102855\pi$
$223$	32.2311	+	203.499i	0.144534	+	0.912551i	−0.803713	+	0.595017i	$0.797145\pi$
$224$		−	7.21757i		−	0.0322213i
$225$	21.7369	+	71.7810i	0.0966085	+	0.319026i
$226$	244.019			1.07973
$227$	−122.117	+	19.3415i	−0.537962	+	0.0852048i	−0.419503	−	0.907754i	$-0.637796\pi$
$227$	−122.117	+	19.3415i	−0.537962	+	0.0852048i	−0.118459	+	0.992959i	$0.537796\pi$
$228$	−129.524	+	254.205i	−0.568087	+	1.11493i
$229$	−373.718	+	121.428i	−1.63196	+	0.530255i	−0.974720	−	0.223430i	$-0.928275\pi$
$229$	−373.718	+	121.428i	−1.63196	+	0.530255i	−0.657236	+	0.753684i	$0.728275\pi$
$230$	−315.120	+	46.6663i	−1.37008	+	0.202897i
$231$	−11.6798	+	35.9466i	−0.0505618	+	0.155613i
$232$	328.090	−	328.090i	1.41418	−	1.41418i
$233$	372.535	−	189.816i	1.59886	−	0.814661i	0.598959	−	0.800780i	$-0.295581\pi$
$233$	372.535	−	189.816i	1.59886	−	0.814661i	0.999904	−	0.0138818i	$-0.00441884\pi$
$234$	−134.443	−	185.045i	−0.574542	−	0.790790i
$235$	−123.455	+	166.377i	−0.525342	+	0.707987i
$236$	556.496	+	404.318i	2.35803	+	1.71321i
$237$	−27.0501	+	170.787i	−0.114135	+	0.720622i
$238$	43.0280	+	6.81496i	0.180790	+	0.0286343i
$239$	79.2731	−	109.110i	0.331686	−	0.456527i	−0.610304	−	0.792167i	$-0.708953\pi$
$239$	79.2731	−	109.110i	0.331686	−	0.456527i	0.941990	+	0.335640i	$0.108953\pi$
$240$	−157.551	−	1.58460i	−0.656461	−	0.00660249i
$241$	157.470	−	114.409i	0.653403	−	0.474725i	−0.211026	−	0.977481i	$-0.567680\pi$
$241$	157.470	−	114.409i	0.653403	−	0.474725i	0.864429	+	0.502755i	$0.167680\pi$
$242$	−191.052	−	374.961i	−0.789471	−	1.54942i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$	−795.619	−	258.512i	−3.26074	−	1.05948i
$245$	−231.868	−	39.1186i	−0.946398	−	0.159668i
$246$	−30.8978	−	95.0937i	−0.125601	−	0.386560i
$247$	−391.957	−	199.712i	−1.58687	−	0.808551i
$248$	−116.208	−	733.709i	−0.468581	−	2.95850i
$249$		−	96.4981i		−	0.387543i
$250$	−147.264	+	410.642i	−0.589054	+	1.64257i
$251$	−19.4389			−0.0774457			−0.0387228	−	0.999250i	$-0.512329\pi$
$251$	−19.4389			−0.0774457			−0.0387228	+	0.999250i	$0.512329\pi$
$252$	34.0297	−	5.38977i	0.135038	−	0.0213880i
$253$	−128.816	+	252.815i	−0.509154	+	0.999271i
$254$	347.168	−	112.802i	1.36680	−	0.444102i
$255$	12.8093	−	75.9246i	0.0502326	−	0.297743i
$256$	−160.780	+	494.829i	−0.628046	+	1.93293i
$257$	66.5349	−	66.5349i	0.258891	−	0.258891i	−0.565712	−	0.824603i	$-0.691399\pi$
$257$	66.5349	−	66.5349i	0.258891	−	0.258891i	0.824603	+	0.565712i	$0.191399\pi$
$258$	−44.4291	+	22.6378i	−0.172206	+	0.0877433i
$259$	−4.42812	−	6.09479i	−0.0170970	−	0.0235320i
$260$	8.98622	−	893.466i	0.0345624	−	3.43641i
$261$	77.1930	+	56.0840i	0.295758	+	0.214881i
$262$	−121.198	+	765.212i	−0.462587	+	2.92066i
$263$	−71.1177	−	11.2639i	−0.270409	−	0.0428286i	0.0197571	−	0.999805i	$-0.493711\pi$
$263$	−71.1177	−	11.2639i	−0.270409	−	0.0428286i	−0.290167	+	0.956976i	$0.593711\pi$
$264$	−230.845	+	317.730i	−0.874412	+	1.20352i
$265$	−143.539	−	106.509i	−0.541657	−	0.401921i
$266$	79.8228	−	57.9947i	0.300086	−	0.218025i
$267$	−58.2162	−	114.256i	−0.218038	−	0.427924i
$268$	−36.8248	−	36.8248i	−0.137406	−	0.137406i
$269$	−214.286	−	69.6259i	−0.796604	−	0.258832i	−0.117690	−	0.993050i	$-0.537549\pi$
$269$	−214.286	−	69.6259i	−0.796604	−	0.258832i	−0.678914	+	0.734218i	$0.737549\pi$
$270$	−13.2829	−	89.6946i	−0.0491961	−	0.332202i
$271$	22.4932	+	69.2270i	0.0830008	+	0.255450i	0.983941	−	0.178492i	$-0.0571220\pi$
$271$	22.4932	+	69.2270i	0.0830008	+	0.255450i	−0.900940	+	0.433943i	$0.857122\pi$
$272$	144.125	+	73.4352i	0.529871	+	0.269983i
$273$	8.31047	+	52.4703i	0.0304413	+	0.192199i
$274$		−	340.067i		−	1.24112i
$275$	222.028	+	318.892i	0.807374	+	1.15961i
$276$	258.648			0.937130
$277$	−64.9889	+	10.2932i	−0.234617	+	0.0371597i	−0.272636	−	0.962117i	$-0.587895\pi$
$277$	−64.9889	+	10.2932i	−0.234617	+	0.0371597i	0.0380187	+	0.999277i	$0.487895\pi$
$278$	−302.671	+	594.025i	−1.08874	+	2.13678i
$279$	145.286	−	47.2062i	0.520737	−	0.169198i
$280$	90.7750	+	47.4081i	0.324196	+	0.169315i
$281$	130.126	−	400.488i	0.463083	−	1.42522i	−0.398294	−	0.917258i	$-0.630398\pi$
$281$	130.126	−	400.488i	0.463083	−	1.42522i	0.861377	−	0.507965i	$-0.169602\pi$
$282$	177.110	−	177.110i	0.628050	−	0.628050i
$283$	−154.183	+	78.5602i	−0.544817	+	0.277598i	−0.704661	−	0.709544i	$-0.748901\pi$
$283$	−154.183	+	78.5602i	−0.544817	+	0.277598i	0.159844	+	0.987142i	$0.448901\pi$
$284$	196.950	+	271.079i	0.693487	+	0.954503i
$285$	−101.078	−	142.106i	−0.354661	−	0.498618i
$286$	−958.710	−	696.544i	−3.35213	−	2.43547i
$287$	−3.63289	+	22.9372i	−0.0126582	+	0.0799204i
$288$	15.2325	+	2.41260i	0.0528908	+	0.00837707i
$289$	123.407	−	169.855i	0.427012	−	0.587732i
$290$	166.187	+	529.535i	0.573060	+	1.82598i
$291$	−59.5568	+	43.2706i	−0.204663	+	0.148696i
$292$	244.693	+	480.237i	0.837990	+	1.64465i
$293$	−154.595	−	154.595i	−0.527627	−	0.527627i	0.392237	−	0.919864i	$-0.371701\pi$
$293$	−154.595	−	154.595i	−0.527627	−	0.527627i	−0.919864	+	0.392237i	$0.871701\pi$
$294$	270.369	+	87.8481i	0.919621	+	0.298803i
$295$	−376.527	+	187.104i	−1.27636	+	0.634251i
$296$	−24.1898	−	74.4486i	−0.0817223	−	0.251515i
$297$	−71.9605	−	36.6657i	−0.242291	−	0.123454i
$298$	8.45039	+	53.3537i	0.0283570	+	0.179039i
$299$			398.808i			1.33381i
$300$	167.122	−	312.303i	0.557074	−	1.04101i
$301$	11.5814			0.0384764
$302$	392.451	−	62.1581i	1.29951	−	0.205821i
$303$	98.4585	−	193.236i	0.324945	−	0.637741i
$304$	348.420	−	113.208i	1.14612	−	0.372396i
$305$	365.192	−	357.919i	1.19735	−	1.17351i
$306$	−28.7657	+	88.5317i	−0.0940055	+	0.289319i
$307$	28.1066	−	28.1066i	0.0915526	−	0.0915526i	−0.659847	−	0.751400i	$-0.729379\pi$
$307$	28.1066	−	28.1066i	0.0915526	−	0.0915526i	0.751400	+	0.659847i	$0.229379\pi$
$308$	159.048	−	81.0392i	0.516391	−	0.263114i
$309$	130.284	+	179.320i	0.421630	+	0.580324i
$310$	842.273	+	283.067i	2.71701	+	0.913121i
$311$	−28.9103	−	21.0046i	−0.0929592	−	0.0675388i	0.540335	−	0.841450i	$-0.318298\pi$
$311$	−28.9103	−	21.0046i	−0.0929592	−	0.0675388i	−0.633294	+	0.773911i	$0.718298\pi$
$312$	−86.3525	+	545.208i	−0.276771	+	1.74746i
$313$	104.153	+	16.4963i	0.332758	+	0.0527037i	0.320578	−	0.947222i	$-0.396123\pi$
$313$	104.153	+	16.4963i	0.332758	+	0.0527037i	0.0121801	+	0.999926i	$0.496123\pi$
$314$	−91.3469	+	125.728i	−0.290914	+	0.400408i
$315$	−6.70889	+	19.9624i	−0.0212981	+	0.0633728i
$316$	660.678	−	480.011i	2.09075	−	1.51902i
$317$	107.323	+	210.634i	0.338559	+	0.664460i	0.996030	−	0.0890203i	$-0.0283736\pi$
$317$	107.323	+	210.634i	0.338559	+	0.664460i	−0.657471	+	0.753480i	$0.728374\pi$
$318$	152.799	+	152.799i	0.480499	+	0.480499i
$319$	470.150	+	152.761i	1.47383	+	0.478875i
$320$	−191.900	−	195.800i	−0.599688	−	0.611874i
$321$	−4.55902	−	14.0312i	−0.0142025	−	0.0437110i
$322$	−79.6997	−	40.6090i	−0.247515	−	0.126115i
$323$	28.0068	+	176.828i	0.0867084	+	0.547455i
$324$			73.6207i			0.227224i
$325$	481.539	+	257.685i	1.48166	+	0.792877i
$326$	72.2108			0.221506
$327$	91.8674	−	14.5504i	0.280940	−	0.0444965i
$328$	−109.551	+	215.006i	−0.333996	+	0.655505i
$329$	−55.3272	+	17.9769i	−0.168168	+	0.0546410i
$330$	−209.052	−	420.694i	−0.633490	−	1.27483i
$331$	−125.432	+	386.039i	−0.378948	+	1.16628i	0.561829	+	0.827253i	$0.310098\pi$
$331$	−125.432	+	386.039i	−0.378948	+	1.16628i	−0.940777	+	0.339027i	$0.889902\pi$
$332$	−322.256	+	322.256i	−0.970650	+	0.970650i
$333$	14.3431	−	7.30818i	0.0430724	−	0.0219465i
$334$	−286.941	−	394.940i	−0.859103	−	1.18245i
$335$	30.3718	−	9.53176i	0.0906619	−	0.0284530i
$336$	−35.7923	−	26.0046i	−0.106525	−	0.0773947i
$337$	−66.2302	+	418.161i	−0.196529	+	1.24083i	0.670248	+	0.742137i	$0.266188\pi$
$337$	−66.2302	+	418.161i	−0.196529	+	1.24083i	−0.866777	+	0.498697i	$0.833812\pi$
$338$	−1062.55	−	168.291i	−3.14363	−	0.497902i
$339$	71.1833	−	97.9754i	0.209980	−	0.289013i
$340$	−296.327	+	210.774i	−0.871550	+	0.619922i
$341$	640.301	−	465.206i	1.87772	−	1.36424i
$342$	95.7145	+	187.850i	0.279867	+	0.549270i
$343$	−95.3337	−	95.3337i	−0.277941	−	0.277941i
$344$	114.450	+	37.1871i	0.332704	+	0.108102i
$345$	−73.1873	+	140.136i	−0.212137	+	0.406191i
$346$	−350.420	−	1078.48i	−1.01277	−	3.11700i
$347$	−137.014	−	69.8120i	−0.394852	−	0.201187i	0.245280	−	0.969452i	$-0.421120\pi$
$347$	−137.014	−	69.8120i	−0.394852	−	0.201187i	−0.640132	+	0.768265i	$0.721120\pi$
$348$	−70.4935	−	445.078i	−0.202567	−	1.27896i
$349$		−	125.270i		−	0.358939i	−0.983764	−	0.179469i	$-0.942562\pi$
$349$		−	125.270i		−	0.358939i	0.983764	−	0.179469i	$-0.0574381\pi$
$350$	−100.530	+	69.9940i	−0.287229	+	0.199983i
$351$	−113.515			−0.323406
$352$	78.9192	−	12.4996i	0.224202	−	0.0355102i
$353$	57.3537	−	112.563i	0.162475	−	0.318875i	−0.795388	−	0.606101i	$-0.792733\pi$
$353$	57.3537	−	112.563i	0.162475	−	0.318875i	0.957863	+	0.287226i	$0.0927329\pi$
$354$	483.436	−	157.078i	1.36564	−	0.443723i
$355$	−202.600	+	30.0032i	−0.570705	+	0.0845162i
$356$	−187.144	+	575.970i	−0.525685	+	1.61789i
$357$	15.2880	−	15.2880i	0.0428236	−	0.0428236i
$358$	202.988	−	103.428i	0.567005	−	0.288904i
$359$	−128.378	−	176.697i	−0.357599	−	0.492193i	0.591879	−	0.806027i	$-0.298387\pi$
$359$	−128.378	−	176.697i	−0.357599	−	0.492193i	−0.949478	+	0.313834i	$0.898387\pi$
$360$	−130.397	+	175.732i	−0.362214	+	0.488144i
$361$	35.9853	+	26.1448i	0.0996822	+	0.0724234i
$362$	48.6968	−	307.460i	0.134522	−	0.849336i
$363$	−206.282	−	32.6718i	−0.568269	−	0.0900050i
$364$	147.472	−	202.977i	0.405142	−	0.557630i
$365$	−329.432	−	3.31333i	−0.902554	−	0.00907762i
$366$	−500.133	+	363.368i	−1.36648	+	0.992808i
$367$	−109.369	−	214.649i	−0.298009	−	0.584875i	0.692645	−	0.721279i	$-0.256445\pi$
$367$	−109.369	−	214.649i	−0.298009	−	0.584875i	−0.990653	+	0.136404i	$0.956445\pi$
$368$	−234.848	−	234.848i	−0.638175	−	0.638175i
$369$	−47.1941	−	15.3343i	−0.127897	−	0.0415563i
$370$	92.3298	+	15.5770i	0.249540	+	0.0421001i
$371$	−15.5093	−	47.7326i	−0.0418040	−	0.128659i
$372$	−642.827	−	327.537i	−1.72803	−	0.880475i
$373$	56.9052	+	359.285i	0.152561	+	0.963232i	0.938588	+	0.345040i	$0.112135\pi$
$373$	56.9052	+	359.285i	0.152561	+	0.963232i	−0.786027	+	0.618192i	$0.787865\pi$
$374$			482.284i			1.28953i
$375$	121.917	+	178.917i	0.325113	+	0.477111i
$376$	−604.480			−1.60766
$377$	686.265	−	108.694i	1.82033	−	0.288312i
$378$	11.5588	−	22.6855i	0.0305789	−	0.0600144i
$379$	401.090	−	130.322i	1.05828	−	0.343857i	0.272370	−	0.962193i	$-0.412193\pi$
$379$	401.090	−	130.322i	1.05828	−	0.343857i	0.785914	+	0.618335i	$0.212193\pi$
$380$	−137.013	+	812.115i	−0.360560	+	2.13715i
$381$	55.9824	−	172.296i	0.146936	−	0.452221i
$382$	44.9708	−	44.9708i	0.117725	−	0.117725i
$383$	136.413	−	69.5058i	0.356169	−	0.181477i	−0.266746	−	0.963767i	$-0.585948\pi$
$383$	136.413	−	69.5058i	0.356169	−	0.181477i	0.622915	+	0.782290i	$0.285948\pi$
$384$	215.756	+	296.963i	0.561866	+	0.773342i
$385$	−1.09733	+	109.104i	−0.00285022	+	0.283386i
$386$	340.925	+	247.697i	0.883226	+	0.641702i
$387$	−3.87128	+	24.4423i	−0.0100033	+	0.0631584i
$388$	343.392	+	54.3880i	0.885032	+	0.140175i
$389$	22.3989	−	30.8295i	0.0575808	−	0.0792532i	−0.779256	−	0.626706i	$-0.784403\pi$
$389$	22.3989	−	30.8295i	0.0575808	−	0.0792532i	0.836836	+	0.547453i	$0.184403\pi$
$390$	−530.248	−	393.456i	−1.35961	−	1.00886i
$391$	131.309	−	95.4017i	0.335829	−	0.243994i
$392$	−311.473	−	611.300i	−0.794573	−	1.55944i
$393$	271.883	+	271.883i	0.691815	+	0.691815i
$394$	−0.125722	−	0.0408494i	−0.000319090	−	0.000103679i
$395$	73.1245	+	493.781i	0.185125	+	1.25008i
$396$	117.867	+	362.758i	0.297644	+	0.916054i
$397$	553.305	+	281.923i	1.39371	+	0.710133i	0.979762	−	0.200166i	$-0.0641480\pi$
$397$	553.305	+	281.923i	1.39371	+	0.710133i	0.413952	+	0.910299i	$0.364148\pi$
$398$	26.7573	+	168.939i	0.0672294	+	0.424470i
$399$		−	48.9672i		−	0.122725i
$400$	−435.311	+	131.822i	−1.08828	+	0.329555i
$401$	54.6342			0.136245			0.0681225	−	0.997677i	$-0.478299\pi$
$401$	54.6342			0.136245			0.0681225	+	0.997677i	$0.478299\pi$
$402$	−38.0105	+	6.02028i	−0.0945536	+	0.0149758i
$403$	505.027	−	991.172i	1.25317	−	2.45948i
$404$	−974.113	+	316.508i	−2.41117	+	0.783437i
$405$	−39.8878	−	20.8318i	−0.0984884	−	0.0514365i
$406$	−48.1577	+	148.214i	−0.118615	+	0.365060i
$407$	58.9736	−	58.9736i	0.144898	−	0.144898i
$408$	200.169	−	101.991i	0.490610	−	0.249978i
$409$	−220.403	−	303.358i	−0.538882	−	0.741707i	0.449570	−	0.893245i	$-0.351577\pi$
$409$	−220.403	−	303.358i	−0.538882	−	0.741707i	−0.988451	+	0.151538i	$0.951577\pi$
$410$	−167.301	−	235.208i	−0.408050	−	0.573679i
$411$	−136.540	−	99.2018i	−0.332213	−	0.241367i
$412$	163.757	−	1033.92i	0.397469	−	2.50952i
$413$	−116.608	−	18.4688i	−0.282343	−	0.0447187i
$414$	112.346	−	154.630i	0.271366	−	0.373503i
$415$	−83.4128	−	265.785i	−0.200995	−	0.640445i
$416$	90.8577	−	66.0120i	0.218408	−	0.158683i
$417$	150.213	+	294.809i	0.360222	+	0.706976i
$418$	772.372	+	772.372i	1.84778	+	1.84778i
$419$	126.156	+	40.9905i	0.301088	+	0.0978294i	0.455665	−	0.890151i	$-0.349401\pi$
$419$	126.156	+	40.9905i	0.301088	+	0.0978294i	−0.154577	+	0.987981i	$0.549401\pi$
$420$	89.0690	−	44.2603i	0.212069	−	0.105382i
$421$	200.215	+	616.198i	0.475570	+	1.46365i	0.845187	+	0.534470i	$0.179489\pi$
$421$	200.215	+	616.198i	0.475570	+	1.46365i	−0.369617	+	0.929184i	$0.620511\pi$
$422$	−379.513	−	193.372i	−0.899320	−	0.458226i
$423$	−19.4458	−	122.776i	−0.0459712	−	0.290251i
$424$		−	521.505i		−	1.22996i
$425$	−30.3485	−	220.191i	−0.0714082	−	0.518097i
$426$	247.609			0.581242
$427$	141.815	−	22.4613i	0.332119	−	0.0526025i
$428$	−31.6324	+	62.0821i	−0.0739075	+	0.145052i
$429$	−559.335	+	181.739i	−1.30381	+	0.423634i
$430$	−102.803	+	100.756i	−0.239076	+	0.234315i
$431$	−210.668	+	648.370i	−0.488789	+	1.50434i	0.337628	+	0.941280i	$0.390375\pi$
$431$	−210.668	+	648.370i	−0.488789	+	1.50434i	−0.826417	+	0.563058i	$0.809625\pi$
$432$	66.8465	−	66.8465i	0.154737	−	0.154737i
$433$	−463.923	+	236.381i	−1.07142	+	0.545914i	−0.898478	−	0.439019i	$-0.855326\pi$
$433$	−463.923	+	236.381i	−1.07142	+	0.545914i	−0.172938	+	0.984933i	$0.555326\pi$
$434$	146.656	+	201.854i	0.337916	+	0.465102i
$435$	261.091	+	87.7464i	0.600210	+	0.201716i
$436$	−355.382	−	258.200i	−0.815097	−	0.592203i
$437$	57.5054	−	363.075i	0.131591	−	0.830834i
$438$	393.390	+	62.3069i	0.898151	+	0.142253i
$439$	−385.509	+	530.608i	−0.878153	+	1.20867i	0.0987761	+	0.995110i	$0.468507\pi$
$439$	−385.509	+	530.608i	−0.878153	+	1.20867i	−0.976929	+	0.213564i	$0.931493\pi$
$440$	−361.169	+	1074.67i	−0.820838	+	2.44242i
$441$	114.141	−	82.9286i	0.258824	−	0.188047i
$442$	307.745	+	603.984i	0.696256	+	1.36648i
$443$	−604.817	−	604.817i	−1.36528	−	1.36528i	−0.867044	−	0.498231i	$-0.833983\pi$
$443$	−604.817	−	604.817i	−1.36528	−	1.36528i	−0.498231	−	0.867044i	$-0.666017\pi$
$444$	−72.3045	−	23.4932i	−0.162848	−	0.0529125i
$445$	−259.107	−	264.372i	−0.582263	−	0.594094i
$446$	−222.203	−	683.870i	−0.498213	−	1.53334i
$447$	23.8870	+	12.1710i	0.0534384	+	0.0272282i
$448$	−12.0427	−	76.0348i	−0.0268811	−	0.169721i
$449$			426.759i			0.950465i	0.879860	+	0.475232i	$0.157636\pi$
$449$			426.759i			0.950465i	−0.879860	+	0.475232i	$0.842364\pi$
$450$	−114.117	−	235.564i	−0.253593	−	0.523475i
$451$	−257.094			−0.570053
$452$	−564.906	+	89.4723i	−1.24979	+	0.197948i
$453$	89.5256	−	175.704i	0.197628	−	0.387867i
$454$	410.383	−	133.341i	0.903927	−	0.293704i
$455$	68.2447	+	137.335i	0.149988	+	0.301835i
$456$	157.230	−	483.906i	0.344804	−	1.06120i
$457$	544.727	−	544.727i	1.19196	−	1.19196i	0.215448	−	0.976515i	$-0.430879\pi$
$457$	544.727	−	544.727i	1.19196	−	1.19196i	0.976515	−	0.215448i	$-0.0691211\pi$
$458$	1221.92	−	622.600i	2.66795	−	1.35939i
$459$	27.1548	+	37.3754i	0.0591608	+	0.0814279i
$460$	712.393	−	223.575i	1.54868	−	0.486032i
$461$	524.080	+	380.767i	1.13683	+	0.825958i	0.986675	−	0.162704i	$-0.0520216\pi$
$461$	524.080	+	380.767i	1.13683	+	0.825958i	0.150158	+	0.988662i	$0.452022\pi$
$462$	20.6352	−	130.286i	0.0446650	−	0.282004i
$463$	−609.019	−	96.4591i	−1.31537	−	0.208335i	−0.540979	−	0.841036i	$-0.681946\pi$
$463$	−609.019	−	96.4591i	−1.31537	−	0.208335i	−0.774396	+	0.632701i	$0.781946\pi$
$464$	−340.118	+	468.132i	−0.733012	+	1.00890i
$465$	359.355	−	255.604i	0.772806	−	0.549687i
$466$	−1180.51	+	857.689i	−2.53328	+	1.84053i
$467$	−177.084	−	347.548i	−0.379196	−	0.744214i	0.619988	−	0.784611i	$-0.287138\pi$
$467$	−177.084	−	347.548i	−0.379196	−	0.744214i	−0.999184	+	0.0403976i	$0.987138\pi$
$468$	379.085	+	379.085i	0.810010	+	0.810010i
$469$	8.50089	+	2.76211i	0.0181256	+	0.00588936i
$470$	334.720	−	640.908i	0.712170	−	1.36363i
$471$	23.8338	+	73.3529i	0.0506025	+	0.155739i
$472$	−1093.04	−	556.932i	−2.31577	−	1.17994i
$473$	20.0570	+	126.635i	0.0424037	+	0.267727i
$474$		−	603.477i		−	1.27316i
$475$	−401.236	−	304.031i	−0.844708	−	0.640065i
$476$	−102.109			−0.214514
$477$	105.923	−	16.7766i	0.222061	−	0.0351710i
$478$	−213.687	+	419.385i	−0.447045	+	0.877374i
$479$	−814.769	+	264.734i	−1.70098	+	0.552681i	−0.988791	−	0.149308i	$-0.952295\pi$
$479$	−814.769	+	264.734i	−1.70098	+	0.552681i	−0.712187	+	0.701989i	$0.752295\pi$
$480$	44.0404	−	6.52197i	0.0917508	−	0.0135874i
$481$	36.2240	−	111.486i	0.0753098	−	0.231780i
$482$	−480.342	+	480.342i	−0.996560	+	0.996560i
$483$	−39.5542	+	20.1539i	−0.0818927	+	0.0417264i
$484$	579.770	+	797.985i	1.19787	+	1.64873i
$485$	−126.634	+	170.661i	−0.261101	+	0.351878i
$486$	44.0135	+	31.9777i	0.0905627	+	0.0657977i
$487$	28.4847	−	179.845i	0.0584902	−	0.369293i	−0.941030	−	0.338323i	$-0.890140\pi$
$487$	28.4847	−	179.845i	0.0584902	−	0.369293i	0.999520	−	0.0309698i	$-0.00985957\pi$
$488$	1473.57	+	233.390i	3.01961	+	0.478259i
$489$	21.0648	−	28.9932i	0.0430772	−	0.0592907i
$490$	820.611	+	8.25347i	1.67472	+	0.0168438i
$491$	−600.160	+	436.042i	−1.22232	+	0.888068i	−0.996291	−	0.0860519i	$-0.972575\pi$
$491$	−600.160	+	436.042i	−1.22232	+	0.888068i	−0.226031	+	0.974120i	$0.572575\pi$
$492$	106.396	+	208.814i	0.216252	+	0.424418i
$493$	−199.954	−	199.954i	−0.405586	−	0.405586i
$494$	1460.12	+	474.422i	2.95571	+	0.960369i
$495$	−229.894	−	38.7857i	−0.464433	−	0.0783550i
$496$	286.279	+	881.075i	0.577175	+	1.77636i
$497$	−51.2414	−	26.1088i	−0.103101	−	0.0525328i
$498$	52.6837	+	332.632i	0.105791	+	0.667935i
$499$			269.815i			0.540710i	0.962761	+	0.270355i	$0.0871411\pi$
$499$			269.815i			0.540710i	−0.962761	+	0.270355i	$0.912859\pi$
$500$	190.350	−	1004.64i	0.380699	−	2.00927i
$501$	−242.275			−0.483583
$502$	67.0063	−	10.6128i	0.133479	−	0.0211410i
$503$	96.5289	−	189.449i	0.191906	−	0.376637i	−0.774925	−	0.632053i	$-0.782212\pi$
$503$	96.5289	−	189.449i	0.191906	−	0.376637i	0.966831	+	0.255416i	$0.0822124\pi$
$504$	−58.4381	+	18.9877i	−0.115949	+	0.0376740i
$505$	104.151	−	617.335i	0.206240	−	1.22245i
$506$	306.006	−	941.790i	0.604755	−	1.86125i
$507$	−377.528	+	377.528i	−0.744631	+	0.744631i
$508$	−762.337	+	388.430i	−1.50066	+	0.764626i
$509$	44.9987	+	61.9354i	0.0884061	+	0.121681i	0.850929	−	0.525280i	$-0.176040\pi$
$509$	44.9987	+	61.9354i	0.0884061	+	0.121681i	−0.762523	+	0.646961i	$0.776040\pi$
$510$	−2.70258	+	268.708i	−0.00529918	+	0.526878i
$511$	−74.8403	−	54.3746i	−0.146458	−	0.106408i
$512$	151.447	−	956.200i	0.295795	−	1.86758i
$513$	103.344	+	16.3681i	0.201451	+	0.0319067i
$514$	−193.023	+	265.673i	−0.375530	+	0.516873i
$515$	513.844	+	381.284i	0.997756	+	0.740357i
$516$	94.5533	−	68.6970i	0.183243	−	0.133134i
$517$	−292.382	−	573.833i	−0.565537	−	1.10993i
$518$	18.5914	+	18.5914i	0.0358906	+	0.0358906i
$519$	−535.240	−	173.910i	−1.03129	−	0.335087i
$520$	233.437	+	1576.31i	0.448917	+	3.03136i
$521$	7.96246	+	24.5059i	0.0152830	+	0.0470363i	0.958407	−	0.285404i	$-0.0921279\pi$
$521$	7.96246	+	24.5059i	0.0152830	+	0.0470363i	−0.943124	+	0.332441i	$0.892128\pi$
$522$	−296.706	−	151.179i	−0.568402	−	0.289615i
$523$	56.0773	+	354.058i	0.107222	+	0.676975i	0.981487	+	0.191527i	$0.0613438\pi$
$523$	56.0773	+	354.058i	0.107222	+	0.676975i	−0.874265	+	0.485449i	$0.838656\pi$
$524$		−	1815.91i		−	3.46548i
$525$	−1.22277	+	60.7817i	−0.00232909	+	0.115775i
$526$	251.294			0.477746
$527$	−447.158	+	70.8229i	−0.848498	+	0.134389i
$528$	222.357	−	436.400i	0.421131	−	0.826515i
$529$	186.161	−	60.4872i	0.351910	−	0.114343i
$530$	552.932	+	288.774i	1.04327	+	0.544857i
$531$	77.9562	−	239.924i	0.146810	−	0.451835i
$532$	−163.526	+	163.526i	−0.307380	+	0.307380i
$533$	−321.969	+	164.051i	−0.604069	+	0.307789i
$534$	263.051	+	362.059i	0.492606	+	0.678013i
$535$	−24.6854	−	34.7053i	−0.0461410	−	0.0648698i
$536$	75.1389	+	54.5916i	0.140185	+	0.101850i
$537$	17.6871	−	111.672i	0.0329369	−	0.207956i
$538$	776.664	+	123.012i	1.44361	+	0.228646i
$539$	429.650	−	591.362i	0.797124	−	1.09715i
$540$	63.6376	+	202.773i	0.117847	+	0.375506i
$541$	−363.412	+	264.034i	−0.671742	+	0.488049i	−0.870608	−	0.491978i	$-0.836274\pi$
$541$	−363.412	+	264.034i	−0.671742	+	0.488049i	0.198866	+	0.980027i	$0.436274\pi$
$542$	−115.330	−	226.347i	−0.212785	−	0.417615i
$543$	−109.242	−	109.242i	−0.201182	−	0.201182i
$544$	−43.4694	−	14.1241i	−0.0799070	−	0.0259634i
$545$	240.453	−	119.486i	0.441198	−	0.219241i
$546$	−57.2929	−	176.329i	−0.104932	−	0.322948i
$547$	400.436	+	204.032i	0.732059	+	0.373002i	0.779943	−	0.625850i	$-0.215248\pi$
$547$	400.436	+	204.032i	0.732059	+	0.373002i	−0.0478846	+	0.998853i	$0.515248\pi$
$548$	124.689	+	787.258i	0.227536	+	1.43660i
$549$			306.806i			0.558844i
$550$	−939.437	−	978.011i	−1.70807	−	1.77820i
$551$	−640.448			−1.16234
$552$	−455.597	+	72.1594i	−0.825356	+	0.130724i
$553$	−63.6329	+	124.887i	−0.115069	+	0.225835i
$554$	218.399	−	70.9621i	0.394222	−	0.128090i
$555$	33.1880	−	32.5271i	0.0597982	−	0.0586073i
$556$	482.879	−	1486.15i	0.868488	−	2.67293i
$557$	−490.042	+	490.042i	−0.879789	+	0.879789i	−0.993512	−	0.113724i	$-0.963722\pi$
$557$	−490.042	+	490.042i	−0.879789	+	0.879789i	0.113724	+	0.993512i	$0.463722\pi$
$558$	−475.031	+	242.041i	−0.851311	+	0.433764i
$559$	105.924	+	145.791i	0.189488	+	0.260807i
$560$	−121.061	−	40.6856i	−0.216180	−	0.0726529i
$561$	193.640	+	140.688i	0.345170	+	0.250781i
$562$	−229.901	+	1451.54i	−0.409076	+	2.58280i
$563$	706.500	+	111.899i	1.25488	+	0.198754i	0.748256	−	0.663410i	$-0.230892\pi$
$563$	706.500	+	111.899i	1.25488	+	0.198754i	0.506628	+	0.862165i	$0.330892\pi$
$564$	−345.072	+	474.950i	−0.611829	+	0.842111i
$565$	111.370	−	331.384i	0.197115	−	0.586521i
$566$	488.583	−	354.977i	0.863221	−	0.627167i
$567$	−5.73653	−	11.2586i	−0.0101173	−	0.0198564i
$568$	−422.547	−	422.547i	−0.743920	−	0.743920i
$569$	−143.653	−	46.6757i	−0.252466	−	0.0820312i	0.180050	−	0.983657i	$-0.442374\pi$
$569$	−143.653	−	46.6757i	−0.252466	−	0.0820312i	−0.432516	+	0.901626i	$0.642374\pi$
$570$	426.004	+	434.660i	0.747375	+	0.762561i
$571$	138.836	+	427.293i	0.243145	+	0.748325i	0.995936	+	0.0900645i	$0.0287073\pi$
$571$	138.836	+	427.293i	0.243145	+	0.748325i	−0.752791	+	0.658260i	$0.771293\pi$
$572$	2474.82	+	1260.98i	4.32660	+	2.20451i
$573$	−4.93757	−	31.1746i	−0.00861706	−	0.0544059i
$574$		−	81.0485i		−	0.141199i
$575$	−80.4463	+	449.239i	−0.139907	+	0.781285i
$576$	164.495			0.285582
$577$	319.422	−	50.5914i	0.553590	−	0.0876801i	0.126629	−	0.991950i	$-0.459584\pi$
$577$	319.422	−	50.5914i	0.553590	−	0.0876801i	0.426961	+	0.904270i	$0.359584\pi$
$578$	−332.653	+	652.868i	−0.575524	+	1.12953i
$579$	198.904	−	64.6279i	0.343530	−	0.111620i
$580$	−578.885	−	1164.94i	−0.998078	−	2.00852i
$581$	24.1713	−	74.3917i	0.0416030	−	0.128041i
$582$	181.670	−	181.670i	0.312148	−	0.312148i
$583$	495.065	−	252.248i	0.849168	−	0.432673i
$584$	−564.996	−	777.650i	−0.967459	−	1.33159i
$585$	−312.655	+	98.1226i	−0.534453	+	0.167731i
$586$	617.294	+	448.491i	1.05340	+	0.765342i
$587$	1.83345	−	11.5759i	0.00312342	−	0.0197205i	−0.986077	−	0.166287i	$-0.946822\pi$
$587$	1.83345	−	11.5759i	0.00312342	−	0.0197205i	0.989201	+	0.146566i	$0.0468222\pi$
$588$	−658.115	−	104.235i	−1.11924	−	0.177271i
$589$	−602.697	+	829.541i	−1.02325	+	1.40839i
$590$	1195.75	−	850.520i	2.02669	−	1.44156i
$591$	−0.0530758	+	0.0385619i	−8.98068e−5	+	6.52485e-5i
$592$	44.3200	+	86.9829i	0.0748648	+	0.146931i
$593$	−738.150	−	738.150i	−1.24477	−	1.24477i	−0.957998	−	0.286773i	$-0.907417\pi$
$593$	−738.150	−	738.150i	−1.24477	−	1.24477i	−0.286773	−	0.957998i	$-0.592583\pi$
$594$	268.068	+	87.1005i	0.451293	+	0.146634i
$595$	28.8928	−	55.3227i	0.0485594	−	0.0929794i
$596$	−39.1254	−	120.416i	−0.0656467	−	0.202040i
$597$	75.6357	+	38.5383i	0.126693	+	0.0645533i
$598$	−217.732	−	1374.70i	−0.364100	−	2.29884i
$599$			384.615i			0.642094i	0.947063	+	0.321047i	$0.104035\pi$
$599$			384.615i			0.642094i	−0.947063	+	0.321047i	$0.895965\pi$
$600$	−207.250	+	596.733i	−0.345416	+	0.994554i
$601$	248.449			0.413392			0.206696	−	0.978405i	$-0.433729\pi$
$601$	248.449			0.413392			0.206696	+	0.978405i	$0.433729\pi$
$602$	−39.9214	+	6.32293i	−0.0663146	+	0.0105032i
$603$	−8.67095	+	17.0177i	−0.0143797	+	0.0282217i
$604$	−885.734	+	287.793i	−1.46645	+	0.476478i
$605$	−596.402	+	88.3217i	−0.985789	+	0.145986i
$606$	−233.891	+	719.843i	−0.385959	+	1.18786i
$607$	635.251	−	635.251i	1.04654	−	1.04654i	0.0476797	−	0.998863i	$-0.484817\pi$
$607$	635.251	−	635.251i	1.04654	−	1.04654i	0.998863	−	0.0476797i	$-0.0151827\pi$
$608$	−92.2352	+	46.9962i	−0.151703	+	0.0772964i
$609$	45.4609	+	62.5715i	0.0746484	+	0.102745i
$610$	−1063.42	+	1433.14i	−1.74331	+	2.34940i
$611$	−732.324	−	532.065i	−1.19857	−	0.870810i
$612$	34.1316	−	215.499i	0.0557706	−	0.352122i
$613$	−874.395	−	138.491i	−1.42642	−	0.225923i	−0.604990	−	0.796233i	$-0.706823\pi$
$613$	−874.395	−	138.491i	−1.42642	−	0.225923i	−0.821429	+	0.570311i	$0.806823\pi$
$614$	−81.5394	+	112.229i	−0.132800	+	0.182784i
$615$	−143.241	−	1.44068i	−0.232913	−	0.00234257i
$616$	−257.548	+	187.119i	−0.418097	+	0.303765i
$617$	530.847	+	1041.85i	0.860368	+	1.68857i	0.714926	+	0.699200i	$0.246460\pi$
$617$	530.847	+	1041.85i	0.860368	+	1.68857i	0.145442	+	0.989367i	$0.453540\pi$
$618$	−546.993	−	546.993i	−0.885102	−	0.885102i
$619$	634.442	+	206.143i	1.02495	+	0.333025i	0.772790	−	0.634661i	$-0.218860\pi$
$619$	634.442	+	206.143i	1.02495	+	0.333025i	0.252156	+	0.967687i	$0.418860\pi$
$620$	−2053.66	−	346.474i	−3.31235	−	0.558830i
$621$	−29.3127	−	90.2151i	−0.0472024	−	0.145274i
$622$	111.122	+	56.6196i	0.178653	+	0.0910283i
$623$	−16.2603	−	102.663i	−0.0261000	−	0.164789i
$624$		−	688.407i		−	1.10322i
$625$	490.452	+	387.405i	0.784723	+	0.619847i
$626$	−368.026			−0.587900
$627$	535.423	−	84.8027i	0.853944	−	0.135251i
$628$	165.369	−	324.555i	0.263326	−	0.516807i
$629$	−45.3726	+	14.7425i	−0.0721345	+	0.0234379i
$630$	12.2271	−	72.4739i	0.0194081	−	0.115038i
$631$	360.150	−	1108.43i	0.570761	−	1.75662i	−0.0794168	−	0.996841i	$-0.525306\pi$
$631$	360.150	−	1108.43i	0.570761	−	1.75662i	0.650178	−	0.759782i	$-0.274694\pi$
$632$	−1029.84	+	1029.84i	−1.62949	+	1.62949i
$633$	−188.349	+	95.9684i	−0.297549	+	0.151609i
$634$	−484.943	−	667.467i	−0.764894	−	1.05279i
$635$	5.25964	−	522.946i	0.00828289	−	0.823537i
$636$	−409.756	−	297.705i	−0.644270	−	0.468089i
$637$	160.720	−	1014.75i	0.252308	−	1.59301i
$638$	−1704.02	−	269.891i	−2.67088	−	0.423026i
$639$	72.2305	−	99.4168i	0.113037	−	0.155582i
$640$	850.952	+	631.425i	1.32961	+	0.986602i
$641$	−238.996	+	173.640i	−0.372848	+	0.270890i	−0.758391	−	0.651800i	$-0.774014\pi$
$641$	−238.996	+	173.640i	−0.372848	+	0.270890i	0.385543	+	0.922690i	$0.374014\pi$
$642$	23.3755	+	45.8770i	0.0364104	+	0.0714595i
$643$	−401.574	−	401.574i	−0.624532	−	0.624532i	0.322155	−	0.946687i	$-0.395593\pi$
$643$	−401.574	−	401.574i	−0.624532	−	0.624532i	−0.946687	+	0.322155i	$0.895593\pi$
$644$	199.395	+	64.7874i	0.309620	+	0.100602i
$645$	10.4652	+	70.6677i	0.0162252	+	0.109562i
$646$	−193.080	−	594.241i	−0.298886	−	0.919877i
$647$	448.446	+	228.494i	0.693115	+	0.353160i	0.764800	−	0.644267i	$-0.222838\pi$
$647$	448.446	+	228.494i	0.693115	+	0.353160i	−0.0716849	+	0.997427i	$0.522838\pi$
$648$	−20.5392	−	129.679i	−0.0316963	−	0.200123i
$649$		−	1307.01i		−	2.01388i
$650$	−1800.56	−	625.349i	−2.77010	−	0.962075i
$651$	123.827			0.190211
$652$	−167.169	+	26.4769i	−0.256393	+	0.0406087i
$653$	−3.36743	+	6.60895i	−0.00515686	+	0.0101209i	−0.893571	−	0.448923i	$-0.851808\pi$
$653$	−3.36743	+	6.60895i	−0.00515686	+	0.0101209i	0.888414	+	0.459044i	$0.151808\pi$
$654$	−308.726	+	100.311i	−0.472058	+	0.153381i
$655$	983.863	+	513.832i	1.50208	+	0.784476i
$656$	92.9938	−	286.205i	0.141759	−	0.436289i
$657$	139.773	−	139.773i	0.212745	−	0.212745i
$658$	180.900	−	92.1731i	0.274924	−	0.140081i
$659$	−99.3342	−	136.722i	−0.150735	−	0.207468i	0.726972	−	0.686668i	$-0.240927\pi$
$659$	−99.3342	−	136.722i	−0.150735	−	0.207468i	−0.877706	+	0.479199i	$0.840927\pi$
$660$	638.208	+	897.258i	0.966982	+	1.35948i
$661$	428.561	+	311.368i	0.648352	+	0.471055i	0.862709	−	0.505700i	$-0.168766\pi$
$661$	428.561	+	311.368i	0.648352	+	0.471055i	−0.214357	+	0.976755i	$0.568766\pi$
$662$	221.606	−	1399.17i	0.334753	−	2.11355i
$663$	332.277	+	52.6274i	0.501171	+	0.0793777i
$664$	477.734	−	657.544i	0.719478	−	0.990277i
$665$	−42.3272	−	134.870i	−0.0636499	−	0.202812i
$666$	−45.4512	+	33.0222i	−0.0682450	+	0.0495829i
$667$	263.595	+	517.334i	0.395194	+	0.775613i
$668$	809.078	+	809.078i	1.21119	+	1.21119i
$669$	−339.398	−	110.277i	−0.507321	−	0.164839i
$670$	−99.4884	+	49.4379i	−0.148490	+	0.0737879i
$671$	491.197	+	1511.75i	0.732038	+	2.25298i
$672$	11.1386	+	5.67542i	0.0165754	+	0.00844557i
$673$	142.895	+	902.203i	0.212325	+	1.34057i	0.831592	+	0.555388i	$0.187430\pi$
$673$	142.895	+	902.203i	0.212325	+	1.34057i	−0.619266	+	0.785181i	$0.712570\pi$
$674$		−	1477.57i		−	2.19224i
$675$	−127.870	−	22.8980i	−0.189437	−	0.0339229i
$676$	2521.51			3.73004
$677$	−750.052	+	118.797i	−1.10791	+	0.175475i	−0.683467	−	0.729982i	$-0.739529\pi$
$677$	−750.052	+	118.797i	−1.10791	+	0.175475i	−0.424439	+	0.905457i	$0.639529\pi$
$678$	−191.881	+	376.587i	−0.283010	+	0.555438i
$679$	−56.7518	+	18.4398i	−0.0835814	+	0.0271572i
$680$	463.163	−	453.940i	0.681123	−	0.667558i
$681$	66.1760	−	203.669i	0.0971748	−	0.299073i
$682$	−1953.16	+	1953.16i	−2.86386	+	2.86386i
$683$	−253.148	+	128.985i	−0.370641	+	0.188851i	−0.629383	−	0.777095i	$-0.716692\pi$
$683$	−253.148	+	128.985i	−0.370641	+	0.188851i	0.258742	+	0.965947i	$0.416692\pi$
$684$	−290.457	−	399.780i	−0.424645	−	0.584474i
$685$	−461.820	−	155.207i	−0.674190	−	0.226579i
$686$	380.666	+	276.570i	0.554907	+	0.403163i
$687$	106.471	−	672.231i	0.154979	−	0.978502i
$688$	−148.229	−	23.4771i	−0.215449	−	0.0341237i
$689$	459.030	−	631.801i	0.666226	−	0.916982i
$690$	175.771	−	523.009i	0.254740	−	0.757985i
$691$	550.945	−	400.285i	0.797315	−	0.579283i	−0.112810	−	0.993617i	$-0.535985\pi$
$691$	550.945	−	400.285i	0.797315	−	0.579283i	0.910125	+	0.414333i	$0.135985\pi$
$692$	1206.66	+	2368.21i	1.74373	+	3.42226i
$693$	−46.2911	−	46.2911i	−0.0667982	−	0.0667982i
$694$	510.404	+	165.840i	0.735453	+	0.238963i
$695$	668.562	+	682.147i	0.961960	+	0.981507i
$696$	248.342	+	764.319i	0.356814	+	1.09816i
$697$	131.035	+	66.7656i	0.187999	+	0.0957900i
$698$	68.3916	+	431.808i	0.0979823	+	0.618636i
$699$			724.181i			1.03602i
$700$	207.064	−	198.897i	0.295805	−	0.284138i
$701$	311.439			0.444278			0.222139	−	0.975015i	$-0.428696\pi$
$701$	311.439			0.444278			0.222139	+	0.975015i	$0.428696\pi$
$702$	391.291	−	61.9744i	0.557394	−	0.0882826i
$703$	−49.0538	+	96.2736i	−0.0697778	+	0.136947i
$704$	810.533	−	263.358i	1.15133	−	0.374088i
$705$	−159.687	−	321.353i	−0.226507	−	0.455820i
$706$	−136.245	+	419.320i	−0.192982	+	0.593938i
$707$	124.306	−	124.306i	0.175821	−	0.175821i
$708$	−1061.56	+	540.893i	−1.49938	+	0.763973i
$709$	68.9496	+	94.9010i	0.0972491	+	0.133852i	0.854869	−	0.518845i	$-0.173638\pi$
$709$	68.9496	+	94.9010i	0.0972491	+	0.133852i	−0.757619	+	0.652697i	$0.773638\pi$
$710$	681.988	−	214.033i	0.960547	−	0.301455i
$711$	−242.300	−	176.042i	−0.340788	−	0.247597i
$712$	168.958	−	1066.76i	0.237300	−	1.49825i
$713$	918.134	+	145.418i	1.28771	+	0.203953i
$714$	−44.3517	+	61.0449i	−0.0621172	+	0.0854970i
$715$	−1383.48	+	984.050i	−1.93493	+	1.37629i
$716$	−431.995	+	313.863i	−0.603346	+	0.438356i
$717$	106.051	+	208.137i	0.147909	+	0.290288i
$718$	538.992	+	538.992i	0.750686	+	0.750686i
$719$	1166.19	+	378.919i	1.62197	+	0.527008i	0.972405	−	0.233301i	$-0.0749528\pi$
$719$	1166.19	+	378.919i	1.62197	+	0.527008i	0.649561	+	0.760310i	$0.274953\pi$
$720$	126.333	−	241.897i	0.175463	−	0.335968i
$721$	55.5205	+	170.874i	0.0770048	+	0.236996i
$722$	−138.316	−	70.4756i	−0.191574	−	0.0976117i
$723$	52.7392	+	332.982i	0.0729450	+	0.460556i
$724$			729.626i			1.00777i
$725$	794.970	+	15.9928i	1.09651	+	0.0220590i
$726$	728.896			1.00399
$727$	−1231.81	+	195.100i	−1.69438	+	0.268363i	−0.927608	−	0.373556i	$-0.878138\pi$
$727$	−1231.81	+	195.100i	−1.69438	+	0.268363i	−0.766772	+	0.641919i	$0.778138\pi$
$728$	−203.137	+	398.678i	−0.279034	+	0.547635i
$729$	25.6785	−	8.34346i	0.0352243	−	0.0114451i
$730$	1137.37	−	168.434i	1.55804	−	0.230732i
$731$	22.6636	−	69.7515i	0.0310036	−	0.0954193i
$732$	1024.58	−	1024.58i	1.39970	−	1.39970i
$733$	195.621	−	99.6740i	0.266877	−	0.135981i	−0.315432	−	0.948948i	$-0.602149\pi$
$733$	195.621	−	99.6740i	0.266877	−	0.135981i	0.582309	+	0.812967i	$0.302149\pi$
$734$	494.188	+	680.191i	0.673280	+	0.926691i
$735$	242.696	−	327.074i	0.330199	−	0.444998i
$736$	75.9241	+	55.1621i	0.103158	+	0.0749485i
$737$	−15.4797	+	97.7350i	−0.0210037	+	0.132612i
$738$	171.051	+	27.0919i	0.231777	+	0.0367098i
$739$	−152.284	+	209.601i	−0.206068	+	0.283628i	−0.899524	−	0.436870i	$-0.856087\pi$
$739$	−152.284	+	209.601i	−0.206068	+	0.283628i	0.693457	+	0.720498i	$0.256087\pi$
$740$	−219.456	−	2.20722i	−0.296561	−	0.00298273i
$741$	616.419	−	447.855i	0.831875	−	0.604392i
$742$	79.5208	+	156.068i	0.107171	+	0.210335i
$743$	408.589	+	408.589i	0.549918	+	0.549918i	0.926417	−	0.376499i	$-0.122872\pi$
$743$	408.589	+	408.589i	0.549918	+	0.549918i	−0.376499	+	0.926417i	$0.622872\pi$
$744$	1223.69	+	397.601i	1.64474	+	0.534409i
$745$	76.3124	+	12.8747i	0.102433	+	0.0172815i
$746$	−392.308	−	1207.40i	−0.525882	−	1.61850i
$747$	148.923	+	75.8798i	0.199361	+	0.101579i
$748$	−176.835	−	1116.49i	−0.236410	−	1.49263i
$749$		−	11.9588i		−	0.0159664i
$750$	−517.933	−	550.170i	−0.690577	−	0.733559i
$751$	−520.835			−0.693522			−0.346761	−	0.937954i	$-0.612718\pi$
$751$	−520.835			−0.693522			−0.346761	+	0.937954i	$0.612718\pi$
$752$	744.568	−	117.928i	0.990117	−	0.156819i
$753$	15.2855	−	29.9994i	0.0202994	−	0.0398398i
$754$	−2306.23	+	749.340i	−3.05866	+	0.993820i
$755$	94.7019	−	561.327i	0.125433	−	0.743479i
$756$	−18.4409	+	56.7551i	−0.0243927	+	0.0750729i
$757$	−891.828	+	891.828i	−1.17811	+	1.17811i	−0.197883	+	0.980226i	$0.563407\pi$
$757$	−891.828	+	891.828i	−1.17811	+	1.17811i	−0.980226	+	0.197883i	$0.936593\pi$
$758$	−1311.42	+	668.201i	−1.73010	+	0.881531i
$759$	−288.870	−	397.595i	−0.380593	−	0.523841i
$760$	14.7720	−	1468.73i	0.0194369	−	1.93254i
$761$	−887.776	−	645.007i	−1.16659	−	0.847579i	−0.175995	−	0.984391i	$-0.556314\pi$
$761$	−887.776	−	645.007i	−1.16659	−	0.847579i	−0.990597	+	0.136813i	$0.956314\pi$
$762$	−98.9070	+	624.474i	−0.129799	+	0.819520i
$763$	74.4664	+	11.7943i	0.0975969	+	0.0154578i
$764$	−87.6186	+	120.597i	−0.114684	+	0.157849i
$765$	107.100	+	79.4703i	0.140000	+	0.103883i
$766$	−432.272	+	314.064i	−0.564324	+	0.410005i
$767$	−834.001	−	1636.82i	−1.08735	−	2.13405i
$768$	−637.227	−	637.227i	−0.829723	−	0.829723i
$769$	−1054.97	−	342.779i	−1.37187	−	0.445747i	−0.471880	−	0.881663i	$-0.656424\pi$
$769$	−1054.97	−	342.779i	−1.37187	−	0.445747i	−0.899987	+	0.435916i	$0.856424\pi$
$770$	−55.7832	−	376.683i	−0.0724458	−	0.489198i
$771$	50.3625	+	155.000i	0.0653210	+	0.201037i
$772$	−880.065	−	448.416i	−1.13998	−	0.580849i
$773$	−128.684	−	812.477i	−0.166473	−	1.05107i	−0.919503	−	0.393083i	$-0.871408\pi$
$773$	−128.684	−	812.477i	−0.166473	−	1.05107i	0.753030	−	0.657987i	$-0.228592\pi$
$774$		−	86.3669i		−	0.111585i
$775$	768.826	−	1014.64i	0.992033	−	1.30921i
$776$	−620.044			−0.799025
$777$	12.8879	−	2.04124i	0.0165867	−	0.00262708i
$778$	−60.3783	+	118.499i	−0.0776070	+	0.152312i
$779$	316.775	−	102.927i	0.406643	−	0.132126i
$780$	1371.79	+	716.432i	1.75871	+	0.918502i
$781$	196.741	−	605.506i	0.251909	−	0.775296i
$782$	−400.541	+	400.541i	−0.512201	+	0.512201i
$783$	−147.252	+	75.0287i	−0.188061	+	0.0958221i
$784$	502.915	+	692.203i	0.641473	+	0.882912i
$785$	129.051	+	181.434i	0.164397	+	0.231126i
$786$	−1085.63	−	788.753i	−1.38120	−	1.00350i
$787$	−135.941	+	858.298i	−0.172733	+	1.09059i	0.737150	+	0.675729i	$0.236171\pi$
$787$	−135.941	+	858.298i	−0.172733	+	1.09059i	−0.909883	+	0.414865i	$0.863829\pi$
$788$	0.306024	+	0.0484695i	0.000388356	+	6.15095e-5i
$789$	73.3056	−	100.896i	0.0929095	−	0.127879i
$790$	−521.645	−	1662.15i	−0.660310	−	2.10399i
$791$	79.4175	−	57.7002i	0.100401	−	0.0729459i
$792$	−308.822	−	606.098i	−0.389927	−	0.765275i
$793$	1579.79	+	1579.79i	1.99217	+	1.99217i
$794$	−2061.17	−	669.716i	−2.59594	−	0.843471i
$795$	277.242	−	137.767i	0.348732	−	0.173292i
$796$	−123.887	−	381.284i	−0.155637	−	0.479000i
$797$	−942.402	−	480.178i	−1.18244	−	0.602481i	−0.251569	−	0.967839i	$-0.580947\pi$
$797$	−942.402	−	480.178i	−1.18244	−	0.602481i	−0.930867	+	0.365358i	$0.880947\pi$
$798$	26.7339	+	168.791i	0.0335012	+	0.211518i
$799$			368.400i			0.461076i
$800$	115.663	−	56.0319i	0.144578	−	0.0700398i
$801$	222.105			0.277284
$802$	−188.326	+	29.8279i	−0.234820	+	0.0371919i
$803$	464.939	−	912.495i	0.579003	−	1.13636i
$804$	85.7872	−	27.8740i	0.106701	−	0.0346691i
$805$	−91.5230	+	89.7003i	−0.113693	+	0.111429i
$806$	−1199.71	+	3692.32i	−1.48847	+	4.58104i
$807$	275.952	−	275.952i	0.341948	−	0.341948i
$808$	1627.55	−	829.280i	2.01430	−	1.02634i
$809$	311.920	+	429.320i	0.385562	+	0.530680i	0.957047	−	0.289932i	$-0.0936326\pi$
$809$	311.920	+	429.320i	0.385562	+	0.530680i	−0.571485	+	0.820612i	$0.693633\pi$
$810$	148.868	+	50.0308i	0.183787	+	0.0617664i
$811$	290.130	+	210.792i	0.357743	+	0.259916i	0.752110	−	0.659037i	$-0.229036\pi$
$811$	290.130	+	210.792i	0.357743	+	0.259916i	−0.394367	+	0.918953i	$0.629036\pi$
$812$	57.1410	−	360.774i	0.0703707	−	0.444303i
$813$	−124.523	−	19.7225i	−0.153165	−	0.0242589i
$814$	−171.087	+	235.481i	−0.210180	+	0.289288i
$815$	32.9570	−	98.0641i	0.0404380	−	0.120324i
$816$	−226.661	+	164.679i	−0.277770	+	0.201812i
$817$	−75.4107	−	148.002i	−0.0923019	−	0.181153i
$818$	925.354	+	925.354i	1.13124	+	1.13124i
$819$	−87.5105	−	28.4339i	−0.106850	−	0.0347178i
$820$	473.544	+	483.166i	0.577492	+	0.589227i
$821$	183.123	+	563.593i	0.223048	+	0.686472i	0.998484	+	0.0550453i	$0.0175303\pi$
$821$	183.123	+	563.593i	0.223048	+	0.686472i	−0.775436	+	0.631427i	$0.782470\pi$
$822$	524.815	+	267.407i	0.638462	+	0.325312i
$823$	−169.524	−	1070.33i	−0.205983	−	1.30052i	−0.846421	−	0.532514i	$-0.821247\pi$
$823$	−169.524	−	1070.33i	−0.205983	−	1.30052i	0.640438	−	0.768010i	$-0.278753\pi$
$824$			1866.89i			2.26565i
$825$	−666.724	+	91.8931i	−0.808150	+	0.111386i
$826$	412.033			0.498829
$827$	687.012	−	108.812i	0.830727	−	0.131574i	0.273435	−	0.961891i	$-0.411840\pi$
$827$	687.012	−	108.812i	0.830727	−	0.131574i	0.557293	+	0.830316i	$0.311840\pi$
$828$	−203.384	+	399.163i	−0.245633	+	0.482081i
$829$	−562.317	+	182.708i	−0.678308	+	0.220396i	−0.627854	−	0.778331i	$-0.716067\pi$
$829$	−562.317	+	182.708i	−0.678308	+	0.220396i	−0.0504536	+	0.998726i	$0.516067\pi$
$830$	432.633	+	870.627i	0.521245	+	1.04895i
$831$	35.2178	−	108.389i	0.0423800	−	0.130432i
$832$	847.014	−	847.014i	1.01805	−	1.01805i
$833$	−372.556	+	189.827i	−0.447246	+	0.227883i
$834$	−678.740	−	934.205i	−0.813836	−	1.12015i
$835$	−667.298	+	209.422i	−0.799159	+	0.250805i
$836$	−2071.24	−	1504.85i	−2.47757	−	1.80006i
$837$	−41.3913	+	261.335i	−0.0494520	+	0.312228i
$838$	−457.242	−	72.4200i	−0.545635	−	0.0864201i
$839$	117.412	−	161.604i	0.139943	−	0.192615i	−0.733293	−	0.679913i	$-0.762017\pi$
$839$	117.412	−	161.604i	0.139943	−	0.192615i	0.873236	+	0.487298i	$0.162017\pi$
$840$	−144.543	+	102.812i	−0.172075	+	0.122395i
$841$	137.997	−	100.261i	0.164087	−	0.119216i
$842$	−1026.56	−	2014.74i	−1.21920	−	2.39281i
$843$	515.737	+	515.737i	0.611788	+	0.611788i
$844$	949.477	+	308.504i	1.12497	+	0.365526i
$845$	−713.489	+	1366.16i	−0.844366	+	1.61675i
$846$	134.061	+	412.596i	0.158464	+	0.487703i
$847$	−150.841	−	76.8576i	−0.178089	−	0.0907409i
$848$	101.740	+	642.364i	0.119977	+	0.757504i
$849$		−	299.721i		−	0.353028i
$850$	224.827	+	742.436i	0.264502	+	0.873454i
$851$	97.9563			0.115107
$852$	−573.216	+	90.7885i	−0.672789	+	0.106559i
$853$	−554.905	+	1089.06i	−0.650533	+	1.27674i	0.296324	+	0.955088i	$0.404239\pi$
$853$	−554.905	+	1089.06i	−0.650533	+	1.27674i	−0.946857	+	0.321655i	$0.895761\pi$
$854$	−476.577	+	154.849i	−0.558052	+	0.181322i
$855$	298.790	−	44.2480i	0.349461	−	0.0517520i
$856$	38.3990	−	118.180i	0.0448586	−	0.138061i
$857$	−777.143	+	777.143i	−0.906818	+	0.906818i	−0.996014	−	0.0891961i	$-0.971570\pi$
$857$	−777.143	+	777.143i	−0.906818	+	0.906818i	0.0891961	+	0.996014i	$0.471570\pi$
$858$	1828.82	−	931.831i	2.13149	−	1.08605i
$859$	−394.567	−	543.075i	−0.459333	−	0.632218i	0.515037	−	0.857168i	$-0.327778\pi$
$859$	−394.567	−	543.075i	−0.459333	−	0.632218i	−0.974370	+	0.224950i	$0.927778\pi$
$860$	201.046	−	270.944i	0.233775	−	0.315051i
$861$	−32.5415	−	23.6428i	−0.0377950	−	0.0274597i
$862$	372.198	−	2349.96i	0.431784	−	2.72618i
$863$	−211.133	−	33.4401i	−0.244650	−	0.0387487i	0.0329052	−	0.999458i	$-0.489524\pi$
$863$	−211.133	−	33.4401i	−0.244650	−	0.0387487i	−0.277555	+	0.960710i	$0.589524\pi$
$864$	−15.7012	+	21.6108i	−0.0181726	+	0.0250125i
$865$	−1624.54	−	16.3391i	−1.87808	−	0.0188892i
$866$	1470.10	−	1068.09i	1.69758	−	1.23336i
$867$	165.092	+	324.012i	0.190418	+	0.373716i
$868$	−413.521	−	413.521i	−0.476406	−	0.476406i
$869$	−1475.75	−	479.501i	−1.69822	−	0.551785i
$870$	−947.894	−	159.920i	−1.08953	−	0.183816i
$871$	42.9788	+	132.275i	0.0493442	+	0.151866i
$872$	698.024	+	355.661i	0.800487	+	0.407868i
$873$	−19.9465	−	125.937i	−0.0228482	−	0.144258i
$874$			1282.92i			1.46788i
$875$	49.1717	+	168.468i	0.0561962	+	0.192534i
$876$	−933.546			−1.06569
$877$	1205.12	−	190.872i	1.37414	−	0.217642i	0.574686	−	0.818374i	$-0.305124\pi$
$877$	1205.12	−	190.872i	1.37414	−	0.217642i	0.799451	+	0.600732i	$0.205124\pi$
$878$	1039.17	−	2039.49i	1.18357	−	2.32288i
$879$	360.144	−	117.018i	0.409721	−	0.133126i
$880$	235.213	−	1394.18i	0.267288	−	1.58430i
$881$	−101.816	+	313.357i	−0.115568	+	0.355683i	−0.992065	−	0.125725i	$-0.959874\pi$
$881$	−101.816	+	313.357i	−0.115568	+	0.355683i	0.876497	+	0.481408i	$0.159874\pi$
$882$	−348.173	+	348.173i	−0.394754	+	0.394754i
$883$	340.430	−	173.458i	0.385538	−	0.196441i	−0.250469	−	0.968125i	$-0.580585\pi$
$883$	340.430	−	173.458i	0.385538	−	0.196441i	0.636007	+	0.771683i	$0.280585\pi$
$884$	−933.889	−	1285.39i	−1.05644	−	1.45406i
$885$	7.32410	−	728.208i	0.00827582	−	0.822834i
$886$	2415.02	+	1754.62i	2.72576	+	1.98038i
$887$	−101.952	+	643.702i	−0.114941	+	0.725707i	0.861151	+	0.508349i	$0.169744\pi$
$887$	−101.952	+	643.702i	−0.114941	+	0.725707i	−0.976092	+	0.217358i	$0.930256\pi$
$888$	133.915	+	21.2101i	0.150806	+	0.0238853i
$889$	86.3152	−	118.803i	0.0970925	−	0.133636i
$890$	1037.48	+	769.837i	1.16571	+	0.864985i
$891$	113.170	−	82.2229i	0.127015	−	0.0922816i
$892$	765.149	+	1501.69i	0.857791	+	1.68351i
$893$	589.987	+	589.987i	0.660680	+	0.660680i
$894$	−88.9839	−	28.9126i	−0.0995346	−	0.0323407i
$895$	−47.8136	−	322.867i	−0.0534231	−	0.360745i
$896$	91.9447	+	282.977i	0.102617	+	0.315822i
$897$	−615.468	−	313.597i	−0.686141	−	0.349606i
$898$	−232.991	−	1471.05i	−0.259456	−	1.63814i
$899$		−	1619.55i		−	1.80150i
$900$	350.554	+	503.489i	0.389504	+	0.559432i
$901$	−317.831			−0.352753
$902$	886.210	−	140.362i	0.982494	−	0.155612i
$903$	−9.10685	+	17.8732i	−0.0100851	+	0.0197931i
$904$	970.094	−	315.203i	1.07311	−	0.348676i
$905$	−395.313	−	206.456i	−0.436810	−	0.228128i
$906$	−212.671	+	654.534i	−0.234736	+	0.722443i
$907$	114.860	−	114.860i	0.126638	−	0.126638i	−0.640947	−	0.767585i	$-0.721458\pi$
$907$	114.860	−	114.860i	0.126638	−	0.126638i	0.767585	+	0.640947i	$0.221458\pi$
$908$	−901.147	+	459.157i	−0.992453	+	0.505680i
$909$	220.793	+	303.896i	0.242897	+	0.334319i
$910$	−310.220	−	436.139i	−0.340902	−	0.479274i
$911$	390.109	+	283.431i	0.428221	+	0.311120i	0.780937	−	0.624610i	$-0.214742\pi$
$911$	390.109	+	283.431i	0.428221	+	0.311120i	−0.352716	+	0.935730i	$0.614742\pi$
$912$	−99.2635	+	626.725i	−0.108842	+	0.687198i
$913$	855.283	+	135.464i	0.936783	+	0.148372i
$914$	−1580.29	+	2175.09i	−1.72899	+	2.37975i
$915$	265.202	+	845.033i	0.289838	+	0.923534i
$916$	−2600.47	+	1889.36i	−2.83895	+	2.06261i
$917$	141.496	+	277.701i	0.154303	+	0.302836i
$918$	−114.009	−	114.009i	−0.124193	−	0.124193i
$919$	1553.99	+	504.921i	1.69096	+	0.549425i	0.986986	−	0.160806i	$-0.0514094\pi$
$919$	1553.99	+	504.921i	1.69096	+	0.549425i	0.703969	+	0.710231i	$0.251409\pi$
$920$	−1192.47	+	592.565i	−1.29617	+	0.644093i
$921$	21.2749	+	65.4773i	0.0230998	+	0.0710937i
$922$	−2014.40	−	1026.39i	−2.18482	−	1.11322i
$923$	−139.987	−	883.840i	−0.151665	−	0.957573i
$924$			309.178i			0.334609i
$925$	63.2933	−	118.277i	0.0684251	−	0.127867i
$926$	2151.97			2.32394
$927$	−379.186	+	60.0572i	−0.409046	+	0.0647866i
$928$	74.2295	−	145.684i	0.0799887	−	0.156987i
$929$	1047.87	−	340.472i	1.12795	−	0.366494i	0.315154	−	0.949041i	$-0.397944\pi$
$929$	1047.87	−	340.472i	1.12795	−	0.366494i	0.812797	+	0.582547i	$0.197944\pi$
$930$	−1099.16	+	1077.27i	−1.18189	+	1.15835i
$931$	−292.639	+	900.649i	−0.314327	+	0.967400i
$932$	2418.40	−	2418.40i	2.59485	−	2.59485i
$933$	55.1489	−	28.0997i	0.0591092	−	0.0301176i
$934$	800.161	+	1101.33i	0.856703	+	1.17915i
$935$	654.954	+	220.114i	0.700485	+	0.235416i
$936$	−773.501	−	561.981i	−0.826390	−	0.600407i
$937$	−139.604	+	881.422i	−0.148990	+	0.940685i	0.794013	+	0.607901i	$0.207988\pi$
$937$	−139.604	+	881.422i	−0.148990	+	0.940685i	−0.943003	+	0.332784i	$0.892012\pi$
$938$	−30.8108	−	4.87995i	−0.0328473	−	0.00520251i
$939$	−107.358	+	147.765i	−0.114332	+	0.157364i
$940$	−539.883	+	1606.43i	−0.574344	+	1.70897i
$941$	1074.47	−	780.646i	1.14184	−	0.829592i	0.154461	−	0.987999i	$-0.450636\pi$
$941$	1074.47	−	780.646i	1.14184	−	0.829592i	0.987374	+	0.158407i	$0.0506357\pi$
$942$	−122.203	−	239.837i	−0.129727	−	0.254604i
$943$	−213.519	−	213.519i	−0.226425	−	0.226425i
$944$	1455.01	+	472.760i	1.54132	+	0.500805i
$945$	−25.5320	−	26.0508i	−0.0270180	−	0.0275670i
$946$	−138.274	−	425.563i	−0.146167	−	0.449855i
$947$	−208.557	−	106.265i	−0.220229	−	0.112212i	0.340396	−	0.940282i	$-0.389439\pi$
$947$	−208.557	−	106.265i	−0.220229	−	0.112212i	−0.560625	+	0.828070i	$0.689439\pi$
$948$	221.272	+	1397.05i	0.233409	+	1.47368i
$949$		−	1439.43i		−	1.51679i
$950$	1549.06	+	828.946i	1.63059	+	0.872574i
$951$	−409.457			−0.430554
$952$	179.860	−	28.4870i	0.188929	−	0.0299234i
$953$	−475.434	+	933.091i	−0.498881	+	0.979109i	0.495025	+	0.868879i	$0.335159\pi$
$953$	−475.434	+	933.091i	−0.498881	+	0.979109i	−0.993906	+	0.110231i	$0.964841\pi$
$954$	−355.961	+	115.659i	−0.373124	+	0.121235i
$955$	−40.5468	−	81.5961i	−0.0424574	−	0.0854409i
$956$	340.915	−	1049.23i	0.356606	−	1.09752i
$957$	−605.447	+	605.447i	−0.632651	+	0.632651i
$958$	2664.00	−	1357.37i	2.78079	−	1.41688i
$959$	−80.4116	−	110.677i	−0.0838494	−	0.115409i
$960$	453.069	−	142.190i	0.471947	−	0.148114i
$961$	−1320.26	−	959.223i	−1.37384	−	0.998151i
$962$	−63.9988	+	404.072i	−0.0665268	+	0.420034i
$963$	25.2388	+	3.99744i	0.0262086	+	0.00415103i
$964$	935.872	−	1288.12i	0.970822	−	1.33622i
$965$	491.977	−	349.937i	0.509820	−	0.362629i
$966$	125.341	−	91.0658i	0.129753	−	0.0942710i
$967$	−307.636	−	603.770i	−0.318134	−	0.624374i	0.675458	−	0.737399i	$-0.263946\pi$
$967$	−307.636	−	603.770i	−0.318134	−	0.624374i	−0.993592	+	0.113025i	$0.963946\pi$
$968$	−1243.87	−	1243.87i	−1.28499	−	1.28499i
$969$	−294.916	−	95.8240i	−0.304351	−	0.0988895i
$970$	343.338	−	657.409i	0.353957	−	0.677742i
$971$	−457.886	−	1409.23i	−0.471561	−	1.45132i	−0.850540	−	0.525911i	$-0.823725\pi$
$971$	−457.886	−	1409.23i	−0.471561	−	1.45132i	0.378979	−	0.925405i	$-0.376275\pi$
$972$	−113.616	−	57.8905i	−0.116889	−	0.0595581i
$973$	41.9557	+	264.898i	0.0431200	+	0.272249i
$974$			635.484i			0.652448i
$975$	−776.328	+	540.517i	−0.796234	+	0.554377i
$976$	−1860.60			−1.90635
$977$	−409.523	+	64.8620i	−0.419164	+	0.0663890i	−0.362454	−	0.932002i	$-0.618061\pi$
$977$	−409.523	+	64.8620i	−0.419164	+	0.0663890i	−0.0567097	+	0.998391i	$0.518061\pi$
$978$	−56.7819	+	111.441i	−0.0580592	+	0.113948i
$979$	1094.40	−	355.591i	1.11787	−	0.363218i
$980$	−1902.75	+	281.779i	−1.94158	+	0.287530i
$981$	−49.7834	+	153.218i	−0.0507476	+	0.156185i
$982$	1830.71	−	1830.71i	1.86427	−	1.86427i
$983$	266.636	−	135.858i	0.271247	−	0.138207i	−0.313077	−	0.949728i	$-0.601360\pi$
$983$	266.636	−	135.858i	0.271247	−	0.138207i	0.584324	+	0.811520i	$0.301360\pi$
$984$	−245.668	−	338.133i	−0.249662	−	0.343631i
$985$	−0.112854	+	0.152089i	−0.000114572	+	0.000154406i
$986$	798.413	+	580.081i	0.809749	+	0.588317i
$987$	15.7625	−	99.5206i	0.0159701	−	0.100831i
$988$	−3554.14	−	562.921i	−3.59731	−	0.569758i
$989$	−88.5138	+	121.829i	−0.0894983	+	0.123184i
$990$	813.628	+	8.18323i	0.821847	+	0.00826589i
$991$	−376.064	+	273.226i	−0.379479	+	0.275708i	−0.761131	−	0.648599i	$-0.775355\pi$
$991$	−376.064	+	273.226i	−0.379479	+	0.275708i	0.381652	+	0.924306i	$0.375355\pi$
$992$	−118.843	−	233.242i	−0.119801	−	0.235123i
$993$	−497.130	−	497.130i	−0.500635	−	0.500635i
$994$	190.885	+	62.0223i	0.192037	+	0.0623967i
$995$	241.635	+	40.7665i	0.242850	+	0.0409714i
$996$	−243.926	−	750.728i	−0.244906	−	0.753743i
$997$	1501.75	+	765.180i	1.50627	+	0.767483i	0.995725	−	0.0923684i	$-0.0294437\pi$
$997$	1501.75	+	765.180i	1.50627	+	0.767483i	0.510545	+	0.859851i	$0.329444\pi$
$998$	−147.307	−	930.058i	−0.147602	−	0.931922i
$999$			27.8819i			0.0279099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.13.1	✓	80
3.2	odd	2		225.3.r.b.163.10		80
5.2	odd	4		375.3.k.c.82.1		80
5.3	odd	4		375.3.k.b.82.10		80
5.4	even	2		375.3.k.a.43.10		80
25.2	odd	20	inner	75.3.k.a.52.1	yes	80
25.11	even	5		375.3.k.c.343.1		80
25.14	even	10		375.3.k.b.343.10		80
25.23	odd	20		375.3.k.a.157.10		80
75.2	even	20		225.3.r.b.127.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.13.1	✓	80	1.1	even	1	trivial
75.3.k.a.52.1	yes	80	25.2	odd	20	inner
225.3.r.b.127.10		80	75.2	even	20
225.3.r.b.163.10		80	3.2	odd	2
375.3.k.a.43.10		80	5.4	even	2
375.3.k.a.157.10		80	25.23	odd	20
375.3.k.b.82.10		80	5.3	odd	4
375.3.k.b.343.10		80	25.14	even	10
375.3.k.c.82.1		80	5.2	odd	4
375.3.k.c.343.1		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)

\(f(q)\)	\(=\)	\(q+(-3.44703 + 0.545956i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(7.77971 - 2.52778i) q^{4} +(-0.831800 + 4.93033i) q^{5} +(1.86796 - 5.74899i) q^{6} +(-0.992761 + 0.992761i) q^{7} +(-12.9984 + 6.62301i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(-3.44703 + 0.545956i) q^{2} +(-0.786335 + 1.54327i) q^{3} +(7.77971 - 2.52778i) q^{4} +(-0.831800 + 4.93033i) q^{5} +(1.86796 - 5.74899i) q^{6} +(-0.992761 + 0.992761i) q^{7} +(-12.9984 + 6.62301i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(0.175498 - 17.4491i) q^{10} +(-12.5745 - 9.13588i) q^{11} +(-2.21641 + 13.9939i) q^{12} +(-21.5771 - 3.41748i) q^{13} +(2.88007 - 3.96408i) q^{14} +(-6.95474 - 5.16058i) q^{15} +(14.7187 - 10.6938i) q^{16} +(4.03639 + 7.92186i) q^{17} +(7.40340 + 7.40340i) q^{18} +(19.1510 + 6.22253i) q^{19} +(5.99162 + 40.4591i) q^{20} +(-0.751455 - 2.31274i) q^{21} +(48.3323 + 24.6265i) q^{22} +(-2.85577 - 18.0306i) q^{23} -25.2679i q^{24} +(-23.6162 - 8.20209i) q^{25} +76.2426 q^{26} +(5.13218 - 0.812857i) q^{27} +(-5.21391 + 10.2329i) q^{28} +(-30.2486 + 9.82836i) q^{29} +(26.7906 + 13.9917i) q^{30} +(-15.7354 + 48.4286i) q^{31} +(-3.63510 + 3.63510i) q^{32} +(23.9868 - 12.2219i) q^{33} +(-18.2385 - 25.1032i) q^{34} +(-4.06886 - 5.72041i) q^{35} +(-19.8535 - 14.4244i) q^{36} +(-0.839409 + 5.29982i) q^{37} +(-69.4112 - 10.9937i) q^{38} +(22.2409 - 30.6120i) q^{39} +(-21.8415 - 69.5953i) q^{40} +(13.3819 - 9.72252i) q^{41} +(3.85294 + 7.56182i) q^{42} +(-5.83292 - 5.83292i) q^{43} +(-120.919 - 39.2890i) q^{44} +(13.4329 - 6.67510i) q^{45} +(19.6879 + 60.5930i) q^{46} +(36.9193 + 18.8113i) q^{47} +(4.92952 + 31.1238i) q^{48} +47.0289i q^{49} +(85.8838 + 15.3794i) q^{50} -15.3995 q^{51} +(-176.502 + 27.9552i) q^{52} +(-16.2292 + 31.8515i) q^{53} +(-17.2470 + 5.60388i) q^{54} +(55.5023 - 54.3970i) q^{55} +(6.32923 - 19.4794i) q^{56} +(-24.6621 + 24.6621i) q^{57} +(98.9019 - 50.3930i) q^{58} +(49.4271 + 68.0306i) q^{59} +(-67.1507 - 22.5677i) q^{60} +(-82.7370 - 60.1119i) q^{61} +(27.8005 - 175.525i) q^{62} +(4.16007 + 0.658891i) q^{63} +(-32.2293 + 44.3599i) q^{64} +(34.7971 - 103.539i) q^{65} +(-76.0107 + 55.2250i) q^{66} +(-2.89032 - 5.67256i) q^{67} +(51.4267 + 51.4267i) q^{68} +(30.0717 + 9.77089i) q^{69} +(17.1486 + 17.4970i) q^{70} +(12.6579 + 38.9571i) q^{71} +(38.9952 + 19.8690i) q^{72} +(10.3074 + 65.0786i) q^{73} -18.7269i q^{74} +(31.2283 - 29.9966i) q^{75} +164.718 q^{76} +(21.5532 - 3.41369i) q^{77} +(-59.9522 + 117.663i) q^{78} +(94.9471 - 30.8502i) q^{79} +(40.4807 + 81.4630i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-40.8197 + 40.8197i) q^{82} +(-49.6409 + 25.2933i) q^{83} +(-11.6922 - 16.0929i) q^{84} +(-42.4148 + 13.3113i) q^{85} +(23.2908 + 16.9217i) q^{86} +(8.61771 - 54.4101i) q^{87} +(223.955 + 35.4710i) q^{88} +(-43.5166 + 59.8955i) q^{89} +(-42.6593 + 30.3430i) q^{90} +(24.8136 - 18.0282i) q^{91} +(-67.7946 - 133.054i) q^{92} +(-62.3650 - 62.3650i) q^{93} +(-137.532 - 44.6869i) q^{94} +(-46.6089 + 89.2447i) q^{95} +(-2.75153 - 8.46834i) q^{96} +(37.8699 + 19.2957i) q^{97} +(-25.6757 - 162.110i) q^{98} +46.6287i 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

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