LMFDB - Embedded newform 110.3.h.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,3,Mod(41,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("110.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	110.h (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.99728290796$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 28 x^{14} + 336 x^{13} + 362 x^{12} - 6904 x^{11} - 3132 x^{10} + 87908 x^{9} + \cdots + 24267881 $ x^16 - 8x^15 - 28x^14 + 336x^13 + 362x^12 - 6904x^11 - 3132x^10 + 87908x^9 + 30150x^8 - 739436x^7 - 337806x^6 + 4062836x^5 + 2750033x^4 - 13356124x^3 - 12538020x^2 + 20049832*x + 24267881
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			61.4
Root			$3.46412 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	110.61
Dual form			110.3.h.a.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34500 - 0.437016i) q^{2} +(2.27262 + 1.65115i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 - 2.12663i) q^{5} +(3.77825 + 1.22763i) q^{6} +(0.859984 + 1.18367i) q^{7} +(1.66251 - 2.28825i) q^{8} +(-0.342665 - 1.05461i) q^{9} +O(q^{10})$	\(q+(1.34500 - 0.437016i) q^{2} +(2.27262 + 1.65115i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 - 2.12663i) q^{5} +(3.77825 + 1.22763i) q^{6} +(0.859984 + 1.18367i) q^{7} +(1.66251 - 2.28825i) q^{8} +(-0.342665 - 1.05461i) q^{9} -3.16228i q^{10} +(2.69824 + 10.6639i) q^{11} +5.61822 q^{12} +(-7.50754 + 2.43935i) q^{13} +(1.67396 + 1.21620i) q^{14} +(5.08173 - 3.69209i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-7.18045 - 2.33307i) q^{17} +(-0.921767 - 1.26870i) q^{18} +(-0.318363 + 0.438189i) q^{19} +(-1.38197 - 4.25325i) q^{20} +4.10999i q^{21} +(8.28944 + 13.1638i) q^{22} -21.5560 q^{23} +(7.55650 - 2.45525i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(-9.03159 + 6.56183i) q^{26} +(8.77516 - 27.0072i) q^{27} +(2.78297 + 0.904241i) q^{28} +(-14.6579 - 20.1748i) q^{29} +(5.22141 - 7.18665i) q^{30} +(1.82371 + 5.61280i) q^{31} -5.65685i q^{32} +(-11.4757 + 28.6903i) q^{33} -10.6773 q^{34} +(3.11145 - 1.01097i) q^{35} +(-1.79422 - 1.30358i) q^{36} +(-2.72160 + 1.97736i) q^{37} +(-0.236701 + 0.728492i) q^{38} +(-21.0895 - 6.85240i) q^{39} +(-3.71748 - 5.11667i) q^{40} +(-21.0666 + 28.9957i) q^{41} +(1.79613 + 5.52792i) q^{42} +65.2759i q^{43} +(16.9021 + 14.0826i) q^{44} -2.47955 q^{45} +(-28.9928 + 9.42032i) q^{46} +(-24.9072 - 18.0961i) q^{47} +(9.09048 - 6.60462i) q^{48} +(14.4803 - 44.5659i) q^{49} +(-6.72499 - 2.18508i) q^{50} +(-12.4662 - 17.1582i) q^{51} +(-9.27983 + 12.7726i) q^{52} +(17.3581 + 53.4228i) q^{53} -40.1594i q^{54} +(24.5426 + 1.63044i) q^{55} +4.13825 q^{56} +(-1.44703 + 0.470170i) q^{57} +(-28.5315 - 20.7294i) q^{58} +(89.8231 - 65.2603i) q^{59} +(3.88210 - 11.9479i) q^{60} +(-7.44578 - 2.41928i) q^{61} +(4.90577 + 6.75221i) q^{62} +(0.953625 - 1.31255i) q^{63} +(-2.47214 - 7.60845i) q^{64} +17.6513i q^{65} +(-2.89671 + 43.6034i) q^{66} +36.7187 q^{67} +(-14.3609 + 4.66614i) q^{68} +(-48.9886 - 35.5923i) q^{69} +(3.74308 - 2.71951i) q^{70} +(33.1029 - 101.880i) q^{71} +(-2.98290 - 0.969203i) q^{72} +(81.3232 + 111.932i) q^{73} +(-2.79641 + 3.84893i) q^{74} +(-4.34032 - 13.3581i) q^{75} +1.08326i q^{76} +(-10.3021 + 12.3646i) q^{77} -31.3600 q^{78} +(89.3392 - 29.0281i) q^{79} +(-7.23607 - 5.25731i) q^{80} +(56.4616 - 41.0218i) q^{81} +(-15.6629 + 48.2055i) q^{82} +(2.54710 + 0.827603i) q^{83} +(4.83158 + 6.65010i) q^{84} +(-9.92314 + 13.6580i) q^{85} +(28.5266 + 87.7959i) q^{86} -70.0522i q^{87} +(28.8875 + 11.5546i) q^{88} -3.30755 q^{89} +(-3.33498 + 1.08360i) q^{90} +(-9.34374 - 6.78862i) q^{91} +(-34.8783 + 25.3406i) q^{92} +(-5.12300 + 15.7670i) q^{93} +(-41.4084 - 13.4544i) q^{94} +(0.711881 + 0.979820i) q^{95} +(9.34034 - 12.8559i) q^{96} +(47.6046 + 146.512i) q^{97} -66.2691i q^{98} +(10.3217 - 6.49976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{3} + 8 q^{4} + 20 q^{5} + 20 q^{6} + 10 q^{7} - 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^3 + 8 * q^4 + 20 * q^5 + 20 * q^6 + 10 * q^7 - 10 * q^9	$ 16 q - 6 q^{3} + 8 q^{4} + 20 q^{5} + 20 q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{11} - 48 q^{12} + 40 q^{13} - 4 q^{14} - 30 q^{15} - 16 q^{16} + 70 q^{17} + 30 q^{19} - 40 q^{20} + 40 q^{22} - 12 q^{23} + 40 q^{24} - 20 q^{25} + 40 q^{26} - 72 q^{27} - 40 q^{28} + 30 q^{29} + 40 q^{30} - 68 q^{31} + 106 q^{33} - 176 q^{34} + 20 q^{36} - 136 q^{37} - 140 q^{38} - 110 q^{39} + 24 q^{42} + 20 q^{44} + 120 q^{46} - 216 q^{47} - 24 q^{48} + 6 q^{49} - 130 q^{51} - 20 q^{52} + 54 q^{53} + 70 q^{55} - 32 q^{56} + 210 q^{57} + 32 q^{58} - 130 q^{59} - 60 q^{60} - 180 q^{61} + 340 q^{62} + 430 q^{63} + 32 q^{64} + 128 q^{66} + 148 q^{67} + 140 q^{68} + 34 q^{69} - 20 q^{70} - 12 q^{71} - 80 q^{72} - 230 q^{73} + 240 q^{74} - 30 q^{75} + 400 q^{77} - 392 q^{78} + 190 q^{79} - 80 q^{80} - 64 q^{81} - 184 q^{82} + 230 q^{83} + 300 q^{84} + 100 q^{85} + 204 q^{86} - 80 q^{88} - 16 q^{89} - 40 q^{90} - 100 q^{91} - 56 q^{92} - 34 q^{93} - 320 q^{94} + 90 q^{95} - 304 q^{97} - 552 q^{99}+O(q^{100}) $ 16 * q - 6 * q^3 + 8 * q^4 + 20 * q^5 + 20 * q^6 + 10 * q^7 - 10 * q^9 - 10 * q^11 - 48 * q^12 + 40 * q^13 - 4 * q^14 - 30 * q^15 - 16 * q^16 + 70 * q^17 + 30 * q^19 - 40 * q^20 + 40 * q^22 - 12 * q^23 + 40 * q^24 - 20 * q^25 + 40 * q^26 - 72 * q^27 - 40 * q^28 + 30 * q^29 + 40 * q^30 - 68 * q^31 + 106 * q^33 - 176 * q^34 + 20 * q^36 - 136 * q^37 - 140 * q^38 - 110 * q^39 + 24 * q^42 + 20 * q^44 + 120 * q^46 - 216 * q^47 - 24 * q^48 + 6 * q^49 - 130 * q^51 - 20 * q^52 + 54 * q^53 + 70 * q^55 - 32 * q^56 + 210 * q^57 + 32 * q^58 - 130 * q^59 - 60 * q^60 - 180 * q^61 + 340 * q^62 + 430 * q^63 + 32 * q^64 + 128 * q^66 + 148 * q^67 + 140 * q^68 + 34 * q^69 - 20 * q^70 - 12 * q^71 - 80 * q^72 - 230 * q^73 + 240 * q^74 - 30 * q^75 + 400 * q^77 - 392 * q^78 + 190 * q^79 - 80 * q^80 - 64 * q^81 - 184 * q^82 + 230 * q^83 + 300 * q^84 + 100 * q^85 + 204 * q^86 - 80 * q^88 - 16 * q^89 - 40 * q^90 - 100 * q^91 - 56 * q^92 - 34 * q^93 - 320 * q^94 + 90 * q^95 - 304 * q^97 - 552 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	1.34500	−	0.437016i	0.672499	−	0.218508i
$2$	1.34500	−	0.437016i	0.672499	−	0.218508i
$3$	2.27262	+	1.65115i	0.757540	+	0.550385i	0.898155	−	0.439679i	$-0.144908\pi$
$3$	2.27262	+	1.65115i	0.757540	+	0.550385i	−0.140615	+	0.990064i	$0.544908\pi$
$4$	1.61803	−	1.17557i	0.404508	−	0.293893i
$5$	0.690983	−	2.12663i	0.138197	−	0.425325i
$5$	0.690983	−	2.12663i	0.138197	−	0.425325i
$6$	3.77825	+	1.22763i	0.629708	+	0.204605i
$7$	0.859984	+	1.18367i	0.122855	+	0.169095i	0.866014	−	0.500019i	$-0.166674\pi$
$7$	0.859984	+	1.18367i	0.122855	+	0.169095i	−0.743160	+	0.669114i	$0.766674\pi$
$8$	1.66251	−	2.28825i	0.207813	−	0.286031i
$9$	−0.342665	−	1.05461i	−0.0380739	−	0.117179i
$10$		−	3.16228i		−	0.316228i
$11$	2.69824	+	10.6639i	0.245295	+	0.969449i
$11$	2.69824	+	10.6639i	0.245295	+	0.969449i
$12$	5.61822			0.468185
$13$	−7.50754	+	2.43935i	−0.577503	+	0.187642i	−0.583182	−	0.812342i	$-0.698192\pi$
$13$	−7.50754	+	2.43935i	−0.577503	+	0.187642i	0.00567859	+	0.999984i	$0.498192\pi$
$14$	1.67396	+	1.21620i	0.119568	+	0.0868715i
$15$	5.08173	−	3.69209i	0.338782	−	0.246140i
$16$	1.23607	−	3.80423i	0.0772542	−	0.237764i
$17$	−7.18045	−	2.33307i	−0.422380	−	0.137239i	0.0901121	−	0.995932i	$-0.471277\pi$
$17$	−7.18045	−	2.33307i	−0.422380	−	0.137239i	−0.512492	+	0.858692i	$0.671277\pi$
$18$	−0.921767	−	1.26870i	−0.0512093	−	0.0704835i
$19$	−0.318363	+	0.438189i	−0.0167559	+	0.0230626i	−0.817313	−	0.576194i	$-0.804537\pi$
$19$	−0.318363	+	0.438189i	−0.0167559	+	0.0230626i	0.800557	+	0.599257i	$0.204537\pi$
$20$	−1.38197	−	4.25325i	−0.0690983	−	0.212663i
$21$			4.10999i			0.195714i
$22$	8.28944	+	13.1638i	0.376793	+	0.598354i
$23$	−21.5560			−0.937217			−0.468609	−	0.883406i	$-0.655245\pi$
$23$	−21.5560			−0.937217			−0.468609	+	0.883406i	$0.655245\pi$
$24$	7.55650	−	2.45525i	0.314854	−	0.102302i
$25$	−4.04508	−	2.93893i	−0.161803	−	0.117557i
$26$	−9.03159	+	6.56183i	−0.347369	+	0.252378i
$27$	8.77516	−	27.0072i	0.325006	−	1.00026i
$28$	2.78297	+	0.904241i	0.0993917	+	0.0322943i
$29$	−14.6579	−	20.1748i	−0.505444	−	0.695684i	0.477699	−	0.878524i	$-0.341471\pi$
$29$	−14.6579	−	20.1748i	−0.505444	−	0.695684i	−0.983143	+	0.182840i	$0.941471\pi$
$30$	5.22141	−	7.18665i	0.174047	−	0.239555i
$31$	1.82371	+	5.61280i	0.0588293	+	0.181058i	0.976153	−	0.217085i	$-0.0696548\pi$
$31$	1.82371	+	5.61280i	0.0588293	+	0.181058i	−0.917323	+	0.398143i	$0.869655\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−11.4757	+	28.6903i	−0.347749	+	0.869402i
$34$	−10.6773			−0.314038
$35$	3.11145	−	1.01097i	0.0888986	−	0.0288849i
$36$	−1.79422	−	1.30358i	−0.0498394	−	0.0362104i
$37$	−2.72160	+	1.97736i	−0.0735569	+	0.0534422i	−0.623956	−	0.781459i	$-0.714476\pi$
$37$	−2.72160	+	1.97736i	−0.0735569	+	0.0534422i	0.550399	+	0.834902i	$0.314476\pi$
$38$	−0.236701	+	0.728492i	−0.00622899	+	0.0191708i
$39$	−21.0895	−	6.85240i	−0.540757	−	0.175703i
$40$	−3.71748	−	5.11667i	−0.0929370	−	0.127917i
$41$	−21.0666	+	28.9957i	−0.513819	+	0.707211i	−0.984558	−	0.175061i	$-0.943988\pi$
$41$	−21.0666	+	28.9957i	−0.513819	+	0.707211i	0.470738	+	0.882273i	$0.343988\pi$
$42$	1.79613	+	5.52792i	0.0427650	+	0.131617i
$43$			65.2759i			1.51804i	0.651065	+	0.759022i	$0.274323\pi$
$43$			65.2759i			1.51804i	−0.651065	+	0.759022i	$0.725677\pi$
$44$	16.9021	+	14.0826i	0.384138	+	0.320060i
$45$	−2.47955			−0.0551011
$46$	−28.9928	+	9.42032i	−0.630277	+	0.204790i
$47$	−24.9072	−	18.0961i	−0.529940	−	0.385024i	0.290395	−	0.956907i	$-0.406213\pi$
$47$	−24.9072	−	18.0961i	−0.529940	−	0.385024i	−0.820335	+	0.571883i	$0.806213\pi$
$48$	9.09048	−	6.60462i	0.189385	−	0.137596i
$49$	14.4803	−	44.5659i	0.295517	−	0.909508i
$50$	−6.72499	−	2.18508i	−0.134500	−	0.0437016i
$51$	−12.4662	−	17.1582i	−0.244435	−	0.336436i
$52$	−9.27983	+	12.7726i	−0.178458	+	0.245627i
$53$	17.3581	+	53.4228i	0.327512	+	1.00798i	0.970294	+	0.241928i	$0.0777799\pi$
$53$	17.3581	+	53.4228i	0.327512	+	1.00798i	−0.642782	+	0.766049i	$0.722220\pi$
$54$		−	40.1594i		−	0.743693i
$55$	24.5426	+	1.63044i	0.446230	+	0.0296444i
$56$	4.13825			0.0738973
$57$	−1.44703	+	0.470170i	−0.0253866	+	0.00824860i
$58$	−28.5315	−	20.7294i	−0.491923	−	0.357403i
$59$	89.8231	−	65.2603i	1.52243	−	1.10611i	0.562158	−	0.827030i	$-0.309971\pi$
$59$	89.8231	−	65.2603i	1.52243	−	1.10611i	0.960269	−	0.279077i	$-0.0900286\pi$
$60$	3.88210	−	11.9479i	0.0647016	−	0.199131i
$61$	−7.44578	−	2.41928i	−0.122062	−	0.0396603i	0.247349	−	0.968926i	$-0.420441\pi$
$61$	−7.44578	−	2.41928i	−0.122062	−	0.0396603i	−0.369411	+	0.929266i	$0.620441\pi$
$62$	4.90577	+	6.75221i	0.0791253	+	0.108907i
$63$	0.953625	−	1.31255i	0.0151369	−	0.0208342i
$64$	−2.47214	−	7.60845i	−0.0386271	−	0.118882i
$65$			17.6513i			0.271558i
$66$	−2.89671	+	43.6034i	−0.0438895	+	0.660658i
$67$	36.7187			0.548041			0.274021	−	0.961724i	$-0.411646\pi$
$67$	36.7187			0.548041			0.274021	+	0.961724i	$0.411646\pi$
$68$	−14.3609	+	4.66614i	−0.211190	+	0.0686197i
$69$	−48.9886	−	35.5923i	−0.709980	−	0.515830i
$70$	3.74308	−	2.71951i	0.0534726	−	0.0388501i
$71$	33.1029	−	101.880i	0.466238	−	1.43493i	−0.391180	−	0.920314i	$-0.627933\pi$
$71$	33.1029	−	101.880i	0.466238	−	1.43493i	0.857419	−	0.514620i	$-0.172067\pi$
$72$	−2.98290	−	0.969203i	−0.0414292	−	0.0134612i
$73$	81.3232	+	111.932i	1.11402	+	1.53331i	0.815363	+	0.578950i	$0.196537\pi$
$73$	81.3232	+	111.932i	1.11402	+	1.53331i	0.298653	+	0.954362i	$0.403463\pi$
$74$	−2.79641	+	3.84893i	−0.0377893	+	0.0520126i
$75$	−4.34032	−	13.3581i	−0.0578709	−	0.178108i
$76$			1.08326i			0.0142534i
$77$	−10.3021	+	12.3646i	−0.133793	+	0.160580i
$78$	−31.3600			−0.402051
$79$	89.3392	−	29.0281i	1.13088	−	0.367444i	0.316967	−	0.948437i	$-0.397336\pi$
$79$	89.3392	−	29.0281i	1.13088	−	0.367444i	0.813909	+	0.580993i	$0.197336\pi$
$80$	−7.23607	−	5.25731i	−0.0904508	−	0.0657164i
$81$	56.4616	−	41.0218i	0.697057	−	0.506441i
$82$	−15.6629	+	48.2055i	−0.191011	+	0.587872i
$83$	2.54710	+	0.827603i	0.0306879	+	0.00997112i	0.324321	−	0.945947i	$-0.394864\pi$
$83$	2.54710	+	0.827603i	0.0306879	+	0.00997112i	−0.293633	+	0.955918i	$0.594864\pi$
$84$	4.83158	+	6.65010i	0.0575188	+	0.0791679i
$85$	−9.92314	+	13.6580i	−0.116743	+	0.160683i
$86$	28.5266	+	87.7959i	0.331705	+	1.02088i
$87$		−	70.0522i		−	0.805197i
$88$	28.8875	+	11.5546i	0.328268	+	0.131303i
$89$	−3.30755			−0.0371635			−0.0185817	−	0.999827i	$-0.505915\pi$
$89$	−3.30755			−0.0371635			−0.0185817	+	0.999827i	$0.505915\pi$
$90$	−3.33498	+	1.08360i	−0.0370554	+	0.0120400i
$91$	−9.34374	−	6.78862i	−0.102678	−	0.0746003i
$92$	−34.8783	+	25.3406i	−0.379112	+	0.275441i
$93$	−5.12300	+	15.7670i	−0.0550861	+	0.169537i
$94$	−41.4084	−	13.4544i	−0.440515	−	0.143132i
$95$	0.711881	+	0.979820i	0.00749348	+	0.0103139i
$96$	9.34034	−	12.8559i	0.0972952	−	0.133915i
$97$	47.6046	+	146.512i	0.490769	+	1.51043i	0.823448	+	0.567392i	$0.192047\pi$
$97$	47.6046	+	146.512i	0.490769	+	1.51043i	−0.332679	+	0.943040i	$0.607953\pi$
$98$		−	66.2691i		−	0.676216i
$99$	10.3217	−	6.49976i	0.104260	−	0.0656542i
$100$	−10.0000			−0.100000
$101$	24.1142	−	7.83517i	0.238754	−	0.0775759i	−0.187196	−	0.982323i	$-0.559940\pi$
$101$	24.1142	−	7.83517i	0.238754	−	0.0775759i	0.425950	+	0.904747i	$0.359940\pi$
$102$	−24.2654	−	17.6298i	−0.237896	−	0.172842i
$103$	85.2970	−	61.9719i	0.828126	−	0.601669i	−0.0909026	−	0.995860i	$-0.528975\pi$
$103$	85.2970	−	61.9719i	0.828126	−	0.601669i	0.919029	+	0.394191i	$0.128975\pi$
$104$	−6.89952	+	21.2345i	−0.0663415	+	0.204178i
$105$	8.74042	+	2.83993i	0.0832421	+	0.0270470i
$106$	46.6932	+	64.2677i	0.440502	+	0.606299i
$107$	−34.4020	+	47.3502i	−0.321514	+	0.442526i	−0.938929	−	0.344112i	$-0.888180\pi$
$107$	−34.4020	+	47.3502i	−0.321514	+	0.442526i	0.617415	+	0.786638i	$0.288180\pi$
$108$	−17.5503	−	54.0143i	−0.162503	−	0.500132i
$109$			46.0539i			0.422513i	0.977431	+	0.211257i	$0.0677555\pi$
$109$			46.0539i			0.422513i	−0.977431	+	0.211257i	$0.932244\pi$
$110$	33.7223	−	8.53259i	0.306567	−	0.0775690i
$111$	−9.45010			−0.0851360
$112$	5.56593	−	1.80848i	0.0496958	−	0.0161472i
$113$	−149.729	−	108.784i	−1.32503	−	0.962693i	−0.999855	−	0.0170407i	$-0.994576\pi$
$113$	−149.729	−	108.784i	−1.32503	−	0.962693i	−0.325179	−	0.945653i	$-0.605424\pi$
$114$	−1.74079	+	1.26475i	−0.0152701	+	0.0110943i
$115$	−14.8948	+	45.8416i	−0.129520	+	0.398622i
$116$	−47.4339	−	15.4122i	−0.408913	−	0.132864i
$117$	5.14514	+	7.08168i	0.0439756	+	0.0605272i
$118$	92.2921	−	127.029i	0.782136	−	1.07652i
$119$	−3.41350	−	10.5057i	−0.0286849	−	0.0882829i
$120$		−	17.7664i		−	0.148053i
$121$	−106.439	+	57.5477i	−0.879661	+	0.475601i
$122$	−11.0718			−0.0907526
$123$	−95.7527	+	31.1119i	−0.778477	+	0.252943i
$124$	9.54907	+	6.93780i	0.0770086	+	0.0559500i
$125$	−9.04508	+	6.57164i	−0.0723607	+	0.0525731i
$126$	0.709017	−	2.18213i	0.00562712	−	0.0173185i
$127$	−145.651	−	47.3250i	−1.14686	−	0.372637i	−0.326901	−	0.945059i	$-0.606004\pi$
$127$	−145.651	−	47.3250i	−1.14686	−	0.372637i	−0.819960	+	0.572421i	$0.806004\pi$
$128$	−6.65003	−	9.15298i	−0.0519534	−	0.0715077i
$129$	−107.781	+	148.347i	−0.835509	+	1.14998i
$130$	7.71389	+	23.7409i	0.0593377	+	0.182623i
$131$		−	158.760i		−	1.21191i	−0.795501	−	0.605953i	$-0.792792\pi$
$131$		−	158.760i		−	1.21191i	0.795501	−	0.605953i	$-0.207208\pi$
$132$	15.1593	+	59.9124i	0.114843	+	0.453882i
$133$	−0.792456			−0.00595832
$134$	49.3866	−	16.0467i	0.368557	−	0.119751i
$135$	−51.3707	−	37.3230i	−0.380523	−	0.276466i
$136$	−17.2762	+	12.5519i	−0.127031	+	0.0922933i
$137$	−6.06205	+	18.6571i	−0.0442486	+	0.136183i	−0.970740	−	0.240132i	$-0.922809\pi$
$137$	−6.06205	+	18.6571i	−0.0442486	+	0.136183i	0.926492	+	0.376316i	$0.122809\pi$
$138$	−81.4439	−	26.4627i	−0.590173	−	0.191759i
$139$	94.7407	+	130.399i	0.681588	+	0.938125i	0.999952	−	0.00984335i	$-0.00313329\pi$
$139$	94.7407	+	130.399i	0.681588	+	0.938125i	−0.318364	+	0.947969i	$0.603133\pi$
$140$	3.84597	−	5.29352i	0.0274712	−	0.0378108i
$141$	−26.7250	−	82.2512i	−0.189539	−	0.583342i
$142$		−	151.495i		−	1.06687i
$143$	−46.2702	−	73.4780i	−0.323568	−	0.513832i
$144$	−4.43555			−0.0308024
$145$	−53.0327	+	17.2314i	−0.365743	+	0.118837i
$146$	158.295	+	115.008i	1.08422	+	0.787728i
$147$	106.494	−	77.3721i	0.724446	−	0.526341i
$148$	−2.07912	+	6.39888i	−0.0140481	+	0.0432356i
$149$	−224.225	−	72.8550i	−1.50486	−	0.488960i	−0.563431	−	0.826163i	$-0.690519\pi$
$149$	−224.225	−	72.8550i	−1.50486	−	0.488960i	−0.941432	+	0.337203i	$0.890519\pi$
$150$	−11.6754	−	16.0698i	−0.0778362	−	0.107132i
$151$	−118.097	+	162.547i	−0.782100	+	1.07647i	0.212947	+	0.977064i	$0.431694\pi$
$151$	−118.097	+	162.547i	−0.782100	+	1.07647i	−0.995047	+	0.0994042i	$0.968306\pi$
$152$	0.473403	+	1.45698i	0.00311449	+	0.00958542i
$153$			8.37207i			0.0547194i
$154$	−8.45275	+	21.1326i	−0.0548880	+	0.137224i
$155$	13.1965			0.0851386
$156$	−42.1790	+	13.7048i	−0.270379	+	0.0878513i
$157$	−22.1478	−	16.0913i	−0.141069	−	0.102492i	0.515013	−	0.857182i	$-0.327787\pi$
$157$	−22.1478	−	16.0913i	−0.141069	−	0.102492i	−0.656081	+	0.754690i	$0.727787\pi$
$158$	107.475	−	78.0853i	0.680223	−	0.494211i
$159$	−48.7609	+	150.071i	−0.306672	+	0.943840i
$160$	−12.0300	−	3.90879i	−0.0751876	−	0.0244299i
$161$	−18.5378	−	25.5151i	−0.115142	−	0.158479i
$162$	58.0135	−	79.8488i	0.358108	−	0.492894i
$163$	44.6827	+	137.519i	0.274127	+	0.843676i	0.989449	+	0.144881i	$0.0462800\pi$
$163$	44.6827	+	137.519i	0.274127	+	0.843676i	−0.715322	+	0.698795i	$0.753720\pi$
$164$			71.6812i			0.437081i
$165$	53.0840	+	44.2291i	0.321721	+	0.268055i
$166$	3.78752			0.0228164
$167$	−79.1771	+	25.7262i	−0.474114	+	0.154049i	−0.536321	−	0.844014i	$-0.680186\pi$
$167$	−79.1771	+	25.7262i	−0.474114	+	0.154049i	0.0622064	+	0.998063i	$0.480186\pi$
$168$	9.40467	+	6.83289i	0.0559802	+	0.0406720i
$169$	−86.3111	+	62.7087i	−0.510717	+	0.371057i
$170$	−7.37782	+	22.7066i	−0.0433989	+	0.133568i
$171$	0.571212	+	0.185598i	0.00334042	+	0.00108537i
$172$	76.7365	+	105.619i	0.446142	+	0.614062i
$173$	76.6326	−	105.476i	0.442963	−	0.609686i	−0.527905	−	0.849304i	$-0.677022\pi$
$173$	76.6326	−	105.476i	0.442963	−	0.609686i	0.970867	+	0.239618i	$0.0770221\pi$
$174$	−30.6139	−	94.2200i	−0.175942	−	0.541494i
$175$		−	7.31546i		−	0.0418026i
$176$	43.9032	+	2.91663i	0.249450	+	0.0165717i
$177$	311.889			1.76208
$178$	−4.44864	+	1.44545i	−0.0249924	+	0.00812052i
$179$	75.8603	+	55.1157i	0.423800	+	0.307909i	0.779165	−	0.626819i	$-0.215643\pi$
$179$	75.8603	+	55.1157i	0.423800	+	0.307909i	−0.355365	+	0.934728i	$0.615643\pi$
$180$	−4.01199	+	2.91488i	−0.0222888	+	0.0161938i
$181$	51.0056	−	156.979i	0.281799	−	0.867289i	−0.705541	−	0.708669i	$-0.749296\pi$
$181$	51.0056	−	156.979i	0.281799	−	0.867289i	0.987340	−	0.158619i	$-0.0507042\pi$
$182$	−15.5340	−	5.04731i	−0.0853519	−	0.0277325i
$183$	−12.9268	−	17.7922i	−0.0706384	−	0.0972254i
$184$	−35.8370	+	49.3254i	−0.194766	+	0.268073i
$185$	2.32453	+	7.15416i	0.0125650	+	0.0386711i
$186$			23.4454i			0.126050i
$187$	5.50511	−	82.8671i	0.0294391	−	0.443139i
$188$	−61.5739			−0.327521
$189$	39.5140	−	12.8389i	0.209069	−	0.0679305i
$190$	1.38567	+	1.00675i	0.00729302	+	0.00529869i
$191$	144.252	−	104.805i	0.755245	−	0.548717i	−0.142203	−	0.989837i	$-0.545419\pi$
$191$	144.252	−	104.805i	0.755245	−	0.548717i	0.897448	+	0.441120i	$0.145419\pi$
$192$	6.94451	−	21.3730i	0.0361693	−	0.111318i
$193$	241.605	+	78.5021i	1.25184	+	0.406747i	0.858579	−	0.512682i	$-0.171348\pi$
$193$	241.605	+	78.5021i	1.25184	+	0.406747i	0.393258	+	0.919428i	$0.371348\pi$
$194$	128.056	+	176.254i	0.660083	+	0.908526i
$195$	−29.1450	+	40.1147i	−0.149462	+	0.205716i
$196$	−28.9607	−	89.1318i	−0.147759	−	0.454754i
$197$		−	269.113i		−	1.36606i	−0.730391	−	0.683029i	$-0.760662\pi$
$197$		−	269.113i		−	1.36606i	0.730391	−	0.683029i	$-0.239338\pi$
$198$	11.0422	−	13.2529i	0.0557688	−	0.0669340i
$199$	141.583			0.711473			0.355737	−	0.934586i	$-0.384230\pi$
$199$	141.583			0.711473			0.355737	+	0.934586i	$0.384230\pi$
$200$	−13.4500	+	4.37016i	−0.0672499	+	0.0218508i
$201$	83.4477	+	60.6283i	0.415163	+	0.301634i
$202$	29.0094	−	21.0765i	0.143611	−	0.104339i
$203$	11.2747	−	34.7001i	0.0555406	−	0.170936i
$204$	−40.3414	−	13.1077i	−0.197752	−	0.0642535i
$205$	47.1063	+	64.8363i	0.229787	+	0.316275i
$206$	87.6415	−	120.628i	0.425444	−	0.585573i
$207$	7.38649	+	22.7333i	0.0356835	+	0.109823i
$208$			31.5756i			0.151806i
$209$	−5.53184	−	2.21266i	−0.0264681	−	0.0105869i
$210$	12.9969			0.0618901
$211$	−16.1607	+	5.25091i	−0.0765908	+	0.0248859i	−0.347062	−	0.937842i	$-0.612821\pi$
$211$	−16.1607	+	5.25091i	−0.0765908	+	0.0248859i	0.270471	+	0.962728i	$0.412821\pi$
$212$	90.8883	+	66.0342i	0.428718	+	0.311482i
$213$	243.450	−	176.877i	1.14296	−	0.830409i
$214$	−25.5777	+	78.7201i	−0.119522	+	0.367851i
$215$	138.818	+	45.1046i	0.645663	+	0.209789i
$216$	−47.2102	−	64.9793i	−0.218566	−	0.300830i
$217$	−5.07532	+	6.98558i	−0.0233886	+	0.0321916i
$218$	20.1263	+	61.9424i	0.0923225	+	0.284139i
$219$			388.655i			1.77468i
$220$	41.6275	−	26.2135i	0.189216	−	0.119152i
$221$	59.5987			0.269677
$222$	−12.7104	+	4.12985i	−0.0572539	+	0.0186029i
$223$	−63.7069	−	46.2858i	−0.285681	−	0.207560i	0.435710	−	0.900087i	$-0.356497\pi$
$223$	−63.7069	−	46.2858i	−0.285681	−	0.207560i	−0.721392	+	0.692527i	$0.756497\pi$
$224$	6.69583	−	4.86480i	0.0298921	−	0.0217179i
$225$	−1.71333	+	5.27307i	−0.00761478	+	0.0234359i
$226$	−248.925	−	80.8807i	−1.10144	−	0.357879i
$227$	−184.642	−	254.138i	−0.813401	−	1.11955i	−0.990790	−	0.135410i	$-0.956765\pi$
$227$	−184.642	−	254.138i	−0.813401	−	1.11955i	0.177389	−	0.984141i	$-0.443235\pi$
$228$	−1.78863	+	2.46184i	−0.00784488	+	0.0107976i
$229$	−77.1967	−	237.587i	−0.337104	−	1.03750i	−0.965677	−	0.259747i	$-0.916361\pi$
$229$	−77.1967	−	237.587i	−0.337104	−	1.03750i	0.628573	−	0.777751i	$-0.283639\pi$
$230$			68.1661i			0.296374i
$231$	−43.8287	+	11.0897i	−0.189734	+	0.0480076i
$232$	−70.5338			−0.304025
$233$	−268.270	+	87.1663i	−1.15137	+	0.374104i	−0.821661	−	0.569977i	$-0.806952\pi$
$233$	−268.270	+	87.1663i	−1.15137	+	0.374104i	−0.329714	+	0.944081i	$0.606952\pi$
$234$	10.0150	+	7.27633i	0.0427992	+	0.0310954i
$235$	−55.6942	+	40.4642i	−0.236996	+	0.172188i
$236$	68.6188	−	211.187i	0.290758	−	0.894860i
$237$	250.964	+	81.5431i	1.05892	+	0.344064i
$238$	−9.18229	−	12.6383i	−0.0385810	−	0.0531023i
$239$	−243.302	+	334.877i	−1.01800	+	1.40116i	−0.104407	+	0.994535i	$0.533294\pi$
$239$	−243.302	+	334.877i	−1.01800	+	1.40116i	−0.913595	+	0.406625i	$0.866706\pi$
$240$	−7.76420	−	23.8957i	−0.0323508	−	0.0995656i
$241$		−	141.848i		−	0.588581i	−0.955716	−	0.294291i	$-0.904917\pi$
$241$		−	141.848i		−	0.588581i	0.955716	−	0.294291i	$-0.0950833\pi$
$242$	−118.011	+	123.917i	−0.487648	+	0.512054i
$243$	−59.5240			−0.244955
$244$	−14.8916	+	4.83856i	−0.0610310	+	0.0198302i
$245$	−84.7694	−	61.5886i	−0.345997	−	0.251382i
$246$	−115.191	+	83.6909i	−0.468255	+	0.340207i
$247$	1.32123	−	4.06632i	0.00534910	−	0.0164628i
$248$	15.8754	+	5.15823i	0.0640137	+	0.0207993i
$249$	4.42209	+	6.08648i	0.0177594	+	0.0244437i
$250$	−9.29370	+	12.7917i	−0.0371748	+	0.0511667i
$251$	61.1606	+	188.233i	0.243668	+	0.749932i	0.995853	+	0.0909798i	$0.0289999\pi$
$251$	61.1606	+	188.233i	0.243668	+	0.749932i	−0.752185	+	0.658952i	$0.771000\pi$
$252$		−	3.24481i		−	0.0128762i
$253$	−58.1633	−	229.872i	−0.229894	−	0.908584i
$254$	−216.582			−0.852686
$255$	−45.1031	+	14.6549i	−0.176875	+	0.0574701i
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	−379.127	+	275.452i	−1.47520	+	1.07180i	−0.496140	+	0.868243i	$0.665250\pi$
$257$	−379.127	+	275.452i	−1.47520	+	1.07180i	−0.979063	+	0.203555i	$0.934750\pi$
$258$	−80.1345	+	246.629i	−0.310599	+	0.955925i
$259$	−4.68107	−	1.52097i	−0.0180736	−	0.00587248i
$260$	20.7503	+	28.5604i	0.0798090	+	0.109848i
$261$	−16.2539	+	22.3716i	−0.0622756	+	0.0857151i
$262$	−69.3805	−	213.531i	−0.264811	−	0.815005i
$263$			231.641i			0.880766i	0.897810	+	0.440383i	$0.145157\pi$
$263$			231.641i			0.880766i	−0.897810	+	0.440383i	$0.854843\pi$
$264$	46.5719	+	73.9571i	0.176409	+	0.280141i
$265$	125.605			0.473979
$266$	−1.06585	+	0.346316i	−0.00400696	+	0.00130194i
$267$	−7.51680	−	5.46128i	−0.0281528	−	0.0204542i
$268$	59.4122	−	43.1655i	0.221687	−	0.161065i
$269$	142.661	−	439.065i	0.530337	−	1.63221i	−0.223176	−	0.974778i	$-0.571643\pi$
$269$	142.661	−	439.065i	0.530337	−	1.63221i	0.753514	−	0.657432i	$-0.228357\pi$
$270$	−85.4041	−	27.7495i	−0.316312	−	0.102776i
$271$	−149.063	−	205.168i	−0.550049	−	0.757078i	0.439970	−	0.898013i	$-0.354989\pi$
$271$	−149.063	−	205.168i	−0.550049	−	0.757078i	−0.990019	+	0.140935i	$0.954989\pi$
$272$	−17.7511	+	24.4322i	−0.0652612	+	0.0898244i
$273$	−10.0257	−	30.8559i	−0.0367242	−	0.113025i
$274$			27.7429i			0.101252i
$275$	20.4259	−	51.0665i	0.0742760	−	0.185696i
$276$	−121.106			−0.438791
$277$	−221.049	+	71.8230i	−0.798009	+	0.259289i	−0.679511	−	0.733665i	$-0.737808\pi$
$277$	−221.049	+	71.8230i	−0.798009	+	0.259289i	−0.118498	+	0.992954i	$0.537808\pi$
$278$	184.413	+	133.984i	0.663355	+	0.481955i
$279$	5.29442	−	3.84662i	0.0189764	−	0.0137872i
$280$	2.85946	−	8.80051i	0.0102124	−	0.0314304i
$281$	436.461	+	141.815i	1.55324	+	0.504679i	0.954993	−	0.296630i	$-0.0958626\pi$
$281$	436.461	+	141.815i	1.55324	+	0.504679i	0.598251	+	0.801309i	$0.295863\pi$
$282$	−71.8902	−	98.9484i	−0.254930	−	0.350881i
$283$	130.669	−	179.850i	0.461727	−	0.635513i	−0.513139	−	0.858306i	$-0.671517\pi$
$283$	130.669	−	179.850i	0.461727	−	0.635513i	0.974866	+	0.222793i	$0.0715174\pi$
$284$	−66.2058	−	203.761i	−0.233119	−	0.717467i
$285$			3.40218i			0.0119375i
$286$	−94.3443	−	78.6068i	−0.329875	−	0.274849i
$287$	−52.4381			−0.182711
$288$	−5.96580	+	1.93841i	−0.0207146	+	0.00673058i
$289$	−187.690	−	136.365i	−0.649447	−	0.471851i
$290$	−63.7985	+	46.3523i	−0.219995	+	0.159835i
$291$	−133.727	+	411.568i	−0.459542	+	1.41432i
$292$	263.167	+	85.5083i	0.901258	+	0.292836i
$293$	−172.082	−	236.850i	−0.587309	−	0.808362i	0.407164	−	0.913355i	$-0.366518\pi$
$293$	−172.082	−	236.850i	−0.587309	−	0.808362i	−0.994473	+	0.104993i	$0.966518\pi$
$294$	109.421	−	150.605i	0.372179	−	0.512260i
$295$	−76.7181	−	236.114i	−0.260061	−	0.800387i
$296$			9.51508i			0.0321455i
$297$	311.680	+	20.7059i	1.04943	+	0.0697167i
$298$	−333.420			−1.11886
$299$	161.833	−	52.5826i	0.541246	−	0.175861i
$300$	−22.7262	−	16.5115i	−0.0757540	−	0.0550385i
$301$	−77.2649	+	56.1362i	−0.256694	+	0.186499i
$302$	−87.8047	+	270.235i	−0.290744	+	0.894818i
$303$	67.7394	+	22.0099i	0.223562	+	0.0726398i
$304$	1.27345	+	1.75275i	0.00418898	+	0.00576564i
$305$	−10.2898	+	14.1627i	−0.0337371	+	0.0464351i
$306$	3.65873	+	11.2604i	0.0119566	+	0.0367987i
$307$		−	24.3489i		−	0.0793122i	−0.999213	−	0.0396561i	$-0.987374\pi$
$307$		−	24.3489i		−	0.0793122i	0.999213	−	0.0396561i	$-0.0126262\pi$
$308$	−2.13365	+	32.1172i	−0.00692742	+	0.104277i
$309$	296.173			0.958488
$310$	17.7492	−	5.76707i	0.0572556	−	0.0186035i
$311$	430.357	+	312.673i	1.38379	+	1.00538i	0.996515	+	0.0834123i	$0.0265819\pi$
$311$	430.357	+	312.673i	1.38379	+	1.00538i	0.387270	+	0.921966i	$0.373418\pi$
$312$	−50.7415	+	36.8658i	−0.162633	+	0.118160i
$313$	34.2363	−	105.369i	0.109381	−	0.336641i	−0.881353	−	0.472459i	$-0.843366\pi$
$313$	34.2363	−	105.369i	0.109381	−	0.336641i	0.990734	+	0.135818i	$0.0433664\pi$
$314$	−36.8208	−	11.9638i	−0.117264	−	0.0381013i
$315$	−2.13237	−	2.93496i	−0.00676943	−	0.00931732i
$316$	110.429	−	151.993i	0.349460	−	0.480990i
$317$	109.552	+	337.168i	0.345591	+	1.06362i	0.961267	+	0.275620i	$0.0888833\pi$
$317$	109.552	+	337.168i	0.345591	+	1.06362i	−0.615675	+	0.788000i	$0.711117\pi$
$318$			223.154i			0.701742i
$319$	175.593	−	210.747i	0.550447	−	0.660650i
$320$	−17.8885			−0.0559017
$321$	−156.365	+	50.8061i	−0.487119	+	0.158274i
$322$	−36.0838	−	26.2164i	−0.112062	−	0.0814175i
$323$	3.30831	−	2.40363i	0.0102425	−	0.00744158i
$324$	43.1328	−	132.749i	0.133126	−	0.409720i
$325$	37.5377	+	12.1967i	0.115501	+	0.0375284i
$326$	120.196	+	165.436i	0.368700	+	0.507472i
$327$	−76.0421	+	104.663i	−0.232545	+	0.320070i
$328$	31.3258	+	96.4110i	0.0955056	+	0.293936i
$329$		−	45.0442i		−	0.136912i
$330$	90.7266	+	36.2894i	0.274929	+	0.109968i
$331$	−398.211			−1.20306			−0.601528	−	0.798852i	$-0.705441\pi$
$331$	−398.211			−1.20306			−0.601528	+	0.798852i	$0.705441\pi$
$332$	5.09420	−	1.65521i	0.0153440	−	0.00498556i
$333$	3.01795	+	2.19267i	0.00906292	+	0.00658460i
$334$	−95.2502	+	69.2033i	−0.285180	+	0.207196i
$335$	25.3720	−	78.0871i	0.0757374	−	0.233096i
$336$	15.6353	+	5.08023i	0.0465337	+	0.0151197i
$337$	63.0438	+	86.7724i	0.187074	+	0.257485i	0.892244	−	0.451553i	$-0.149130\pi$
$337$	63.0438	+	86.7724i	0.187074	+	0.257485i	−0.705171	+	0.709037i	$0.749130\pi$
$338$	−88.6835	+	122.062i	−0.262377	+	0.361131i
$339$	−160.657	−	494.451i	−0.473914	−	1.45856i
$340$			33.7645i			0.0993074i
$341$	−54.9337	+	34.5926i	−0.161096	+	0.101445i
$342$	0.849388			0.00248359
$343$	133.387	−	43.3400i	0.388882	−	0.126356i
$344$	149.367	+	108.522i	0.434207	+	0.315470i
$345$	−109.542	+	79.5868i	−0.317513	+	0.230686i
$346$	56.9760	−	175.354i	0.164671	−	0.506804i
$347$	−109.196	−	35.4800i	−0.314686	−	0.102248i	0.147416	−	0.989075i	$-0.452905\pi$
$347$	−109.196	−	35.4800i	−0.314686	−	0.102248i	−0.462102	+	0.886827i	$0.652905\pi$
$348$	−82.3513	−	113.347i	−0.236642	−	0.325709i
$349$	209.005	−	287.671i	0.598868	−	0.824271i	−0.396736	−	0.917933i	$-0.629857\pi$
$349$	209.005	−	287.671i	0.598868	−	0.824271i	0.995604	+	0.0936614i	$0.0298571\pi$
$350$	−3.19697	−	9.83927i	−0.00913421	−	0.0281122i
$351$			224.163i			0.638641i
$352$	60.3243	−	15.2636i	0.171376	−	0.0433624i
$353$	−275.130			−0.779406			−0.389703	−	0.920941i	$-0.627422\pi$
$353$	−275.130			−0.779406			−0.389703	+	0.920941i	$0.627422\pi$
$354$	419.489	−	136.300i	1.18500	−	0.385029i
$355$	−193.788	−	140.795i	−0.545881	−	0.396606i
$356$	−5.35173	+	3.88826i	−0.0150329	+	0.0109221i
$357$	9.58890	−	29.5116i	0.0268597	−	0.0826655i
$358$	126.118	+	40.9783i	0.352286	+	0.114465i
$359$	89.9630	+	123.823i	0.250593	+	0.344912i	0.915719	−	0.401819i	$-0.131622\pi$
$359$	89.9630	+	123.823i	0.250593	+	0.344912i	−0.665126	+	0.746731i	$0.731622\pi$
$360$	−4.12227	+	5.67381i	−0.0114507	+	0.0157606i
$361$	111.464	+	343.052i	0.308766	+	0.950284i
$362$		−	233.427i		−	0.644826i
$363$	−336.916	−	44.9631i	−0.928142	−	0.123865i
$364$	−23.0990			−0.0634588
$365$	294.230	−	95.6011i	0.806110	−	0.261921i
$366$	−25.1620	−	18.2813i	−0.0687487	−	0.0499489i
$367$	−291.733	+	211.956i	−0.794913	+	0.577538i	−0.909417	−	0.415885i	$-0.863472\pi$
$367$	−291.733	+	211.956i	−0.794913	+	0.577538i	0.114504	+	0.993423i	$0.463472\pi$
$368$	−26.6447	+	82.0039i	−0.0724040	+	0.222837i
$369$	37.7980	+	12.2813i	0.102434	+	0.0332827i
$370$	6.25297	+	8.60647i	0.0168999	+	0.0232607i
$371$	−48.3071	+	66.4890i	−0.130208	+	0.179216i
$372$	10.2460	+	31.5340i	0.0275430	+	0.0847687i
$373$		−	48.5421i		−	0.130140i	−0.997881	−	0.0650698i	$-0.979273\pi$
$373$		−	48.5421i		−	0.130140i	0.997881	−	0.0650698i	$-0.0207270\pi$
$374$	−28.8099	−	113.862i	−0.0770318	−	0.304443i
$375$	−31.4068			−0.0837516
$376$	−82.8168	+	26.9088i	−0.220257	+	0.0715660i
$377$	159.258	+	115.708i	0.422435	+	0.306917i
$378$	47.5354	−	34.5365i	0.125755	−	0.0913663i
$379$	89.4197	−	275.206i	0.235936	−	0.726136i	−0.761060	−	0.648681i	$-0.775321\pi$
$379$	89.4197	−	275.206i	0.235936	−	0.726136i	0.996996	−	0.0774544i	$-0.0246792\pi$
$380$	2.30369	+	0.748516i	0.00606235	+	0.00196978i
$381$	−252.869	−	348.044i	−0.663698	−	0.913502i
$382$	148.217	−	204.003i	0.388002	−	0.534039i
$383$	168.884	+	519.771i	0.440950	+	1.35710i	0.886865	+	0.462028i	$0.152878\pi$
$383$	168.884	+	519.771i	0.440950	+	1.35710i	−0.445916	+	0.895075i	$0.647122\pi$
$384$		−	31.7815i		−	0.0827643i
$385$	19.1764	+	30.4525i	0.0498088	+	0.0790973i
$386$	359.264			0.930736
$387$	68.8409	−	22.3678i	0.177884	−	0.0577979i
$388$	249.261	+	181.099i	0.642425	+	0.466749i
$389$	−604.907	+	439.491i	−1.55503	+	1.12980i	−0.615090	+	0.788457i	$0.710880\pi$
$389$	−604.907	+	439.491i	−1.55503	+	1.12980i	−0.939940	+	0.341339i	$0.889120\pi$
$390$	−21.6692	+	66.6909i	−0.0555620	+	0.171002i
$391$	154.782	+	50.2917i	0.395862	+	0.128623i
$392$	−77.9041	−	107.226i	−0.198735	−	0.273535i
$393$	262.137	−	360.800i	0.667015	−	0.918067i
$394$	−117.607	−	361.957i	−0.298495	−	0.918672i
$395$		−	210.049i		−	0.531770i
$396$	9.06001	−	22.6508i	0.0228788	−	0.0571989i
$397$	277.155			0.698123			0.349061	−	0.937100i	$-0.386500\pi$
$397$	277.155			0.698123			0.349061	+	0.937100i	$0.386500\pi$
$398$	190.429	−	61.8741i	0.478465	−	0.155463i
$399$	−1.80095	−	1.30847i	−0.00451366	−	0.00327937i
$400$	−16.1803	+	11.7557i	−0.0404508	+	0.0293893i
$401$	−198.561	+	611.109i	−0.495165	+	1.52396i	0.321534	+	0.946898i	$0.395802\pi$
$401$	−198.561	+	611.109i	−0.495165	+	1.52396i	−0.816699	+	0.577064i	$0.804198\pi$
$402$	138.733	+	45.0769i	0.345106	+	0.112132i
$403$	−27.3831	−	37.6897i	−0.0679482	−	0.0935227i
$404$	29.8067	−	41.0255i	0.0737791	−	0.101548i
$405$	−48.2240	−	148.418i	−0.119072	−	0.366464i
$406$		−	51.5988i		−	0.127091i
$407$	−28.4300	−	23.6876i	−0.0698526	−	0.0582005i
$408$	−59.9874			−0.147028
$409$	658.661	−	214.012i	1.61042	−	0.523257i	0.640765	−	0.767737i	$-0.278617\pi$
$409$	658.661	−	214.012i	1.61042	−	0.523257i	0.969654	+	0.244481i	$0.0786175\pi$
$410$	91.6923	+	66.6184i	0.223640	+	0.162484i
$411$	−44.5825	+	32.3911i	−0.108473	+	0.0788104i
$412$	65.1611	−	200.545i	0.158158	−	0.486760i
$413$	154.493	+	50.1978i	0.374075	+	0.121544i
$414$	19.8696	+	27.3482i	0.0479942	+	0.0660584i
$415$	3.52000	−	4.84487i	0.00848194	−	0.0116744i
$416$	13.7990	+	42.4691i	0.0331708	+	0.102089i
$417$			452.780i			1.08580i
$418$	−8.40727	−	0.558521i	−0.0201131	−	0.00133617i
$419$	−36.7232			−0.0876448			−0.0438224	−	0.999039i	$-0.513954\pi$
$419$	−36.7232			−0.0876448			−0.0438224	+	0.999039i	$0.513954\pi$
$420$	17.4808	−	5.67987i	0.0416210	−	0.0135235i
$421$	−398.242	−	289.340i	−0.945944	−	0.687268i	0.00390038	−	0.999992i	$-0.498758\pi$
$421$	−398.242	−	289.340i	−0.945944	−	0.687268i	−0.949844	+	0.312724i	$0.898758\pi$
$422$	−19.4413	+	14.1249i	−0.0460694	+	0.0334714i
$423$	−10.5496	+	32.4684i	−0.0249400	+	0.0767574i
$424$	151.102	+	49.0962i	0.356374	+	0.115793i
$425$	22.1888	+	30.5403i	0.0522090	+	0.0718595i
$426$	250.142	−	344.291i	0.587188	−	0.808195i
$427$	−3.53963	−	10.8939i	−0.00828953	−	0.0255126i
$428$			117.056i			0.273496i
$429$	16.1689	−	243.387i	0.0376898	−	0.567335i
$430$	206.421			0.480048
$431$	754.220	−	245.061i	1.74993	−	0.568587i	0.753851	−	0.657046i	$-0.228194\pi$
$431$	754.220	−	245.061i	1.74993	−	0.568587i	0.996080	+	0.0884589i	$0.0281942\pi$
$432$	−91.8946	−	66.7654i	−0.212719	−	0.154549i
$433$	−388.221	+	282.059i	−0.896583	+	0.651406i	−0.937586	−	0.347753i	$-0.886945\pi$
$433$	−388.221	+	282.059i	−0.896583	+	0.651406i	0.0410029	+	0.999159i	$0.486945\pi$
$434$	−3.77348	+	11.6136i	−0.00869466	+	0.0267594i
$435$	−148.975	−	48.4049i	−0.342471	−	0.111276i
$436$	54.1396	+	74.5168i	0.124173	+	0.170910i
$437$	6.86263	−	9.44560i	0.0157040	−	0.0216146i
$438$	169.849	+	522.740i	0.387782	+	1.19347i
$439$			759.484i			1.73003i	0.501745	+	0.865016i	$0.332692\pi$
$439$			759.484i			1.73003i	−0.501745	+	0.865016i	$0.667308\pi$
$440$	44.5332	−	53.4490i	0.101212	−	0.121475i
$441$	−51.9618			−0.117827
$442$	80.1601	−	26.0456i	0.181358	−	0.0589267i
$443$	573.448	+	416.635i	1.29447	+	0.940485i	0.999885	−	0.0151421i	$-0.00482006\pi$
$443$	573.448	+	416.635i	1.29447	+	0.940485i	0.294581	+	0.955627i	$0.404820\pi$
$444$	−15.2906	+	11.1093i	−0.0344383	+	0.0250209i
$445$	−2.28546	+	7.03393i	−0.00513587	+	0.0158066i
$446$	−105.913	−	34.4133i	−0.237474	−	0.0771599i
$447$	−389.282	−	535.801i	−0.870878	−	1.19866i
$448$	6.87987	−	9.46933i	0.0153569	−	0.0211369i
$449$	−169.175	−	520.667i	−0.376782	−	1.15962i	−0.942269	−	0.334858i	$-0.891312\pi$
$449$	−169.175	−	520.667i	−0.376782	−	1.15962i	0.565487	−	0.824757i	$-0.308688\pi$
$450$			7.84102i			0.0174245i
$451$	−366.051	−	146.415i	−0.811642	−	0.324646i
$452$	−370.150			−0.818916
$453$	−536.779	+	174.410i	−1.18494	+	0.385011i
$454$	−359.405	−	261.123i	−0.791642	−	0.575161i
$455$	−20.8932	+	15.1798i	−0.0459192	+	0.0333622i
$456$	−1.32984	+	4.09283i	−0.00291632	+	0.00897551i
$457$	236.247	+	76.7614i	0.516952	+	0.167968i	0.555862	−	0.831275i	$-0.312388\pi$
$457$	236.247	+	76.7614i	0.516952	+	0.167968i	−0.0389095	+	0.999243i	$0.512388\pi$
$458$	−207.659	−	285.818i	−0.453403	−	0.624056i
$459$	−126.019	+	173.451i	−0.274552	+	0.377888i
$460$	29.7897	+	91.6831i	0.0647601	+	0.199311i
$461$		−	244.791i		−	0.531000i	−0.964111	−	0.265500i	$-0.914463\pi$
$461$		−	244.791i		−	0.531000i	0.964111	−	0.265500i	$-0.0855370\pi$
$462$	−54.1030	+	34.0695i	−0.117106	+	0.0737435i
$463$	−136.860			−0.295594			−0.147797	−	0.989018i	$-0.547218\pi$
$463$	−136.860			−0.295594			−0.147797	+	0.989018i	$0.547218\pi$
$464$	−94.8678	+	30.8244i	−0.204456	+	0.0664319i
$465$	29.9906	+	21.7894i	0.0644959	+	0.0468590i
$466$	−322.730	+	234.477i	−0.692553	+	0.503169i
$467$	−22.3538	+	68.7980i	−0.0478669	+	0.147319i	−0.972133	−	0.234429i	$-0.924678\pi$
$467$	−22.3538	+	68.7980i	−0.0478669	+	0.147319i	0.924266	+	0.381748i	$0.124678\pi$
$468$	16.6500	+	5.40992i	0.0355770	+	0.0115597i
$469$	31.5775	+	43.4627i	0.0673295	+	0.0926711i
$470$	−57.2250	+	78.7634i	−0.121755	+	0.167582i
$471$	−23.7642	−	73.1387i	−0.0504548	−	0.155284i
$472$		−	314.033i		−	0.665325i
$473$	−696.098	+	176.130i	−1.47167	+	0.372368i
$474$	373.181			0.787302
$475$	2.57561	−	0.836866i	0.00542233	−	0.00176182i
$476$	−17.8733	−	12.9857i	−0.0375490	−	0.0272809i
$477$	50.3924	−	36.6122i	0.105645	−	0.0767552i
$478$	−180.894	+	556.736i	−0.378440	+	1.16472i
$479$	−443.469	−	144.092i	−0.925822	−	0.300818i	−0.192969	−	0.981205i	$-0.561812\pi$
$479$	−443.469	−	144.092i	−0.925822	−	0.300818i	−0.732853	+	0.680387i	$0.761812\pi$
$480$	−20.8856	−	28.7466i	−0.0435118	−	0.0598888i
$481$	15.6091	−	21.4841i	0.0324513	−	0.0446654i
$482$	−61.9899	−	190.785i	−0.128610	−	0.395820i
$483$		−	88.5949i		−	0.183426i
$484$	−104.570	+	218.241i	−0.216055	+	0.450911i
$485$	344.470			0.710248
$486$	−80.0596	+	26.0129i	−0.164732	+	0.0535246i
$487$	−83.5191	−	60.6802i	−0.171497	−	0.124600i	0.498726	−	0.866760i	$-0.333801\pi$
$487$	−83.5191	−	60.6802i	−0.171497	−	0.124600i	−0.670223	+	0.742160i	$0.733801\pi$
$488$	−17.9146	+	13.0157i	−0.0367102	+	0.0266715i
$489$	−125.519	+	386.307i	−0.256685	+	0.789994i
$490$	−140.930	−	45.7909i	−0.287612	−	0.0934507i
$491$	−74.6823	−	102.791i	−0.152102	−	0.209351i	0.726165	−	0.687520i	$-0.241301\pi$
$491$	−74.6823	−	102.791i	−0.152102	−	0.209351i	−0.878268	+	0.478169i	$0.841301\pi$
$492$	−118.357	+	162.904i	−0.240563	+	0.331106i
$493$	58.1809	+	179.062i	0.118014	+	0.363210i
$494$		−	6.04658i		−	0.0122400i
$495$	−6.69042	−	26.4417i	−0.0135160	−	0.0534176i
$496$	23.6066			0.0475939
$497$	149.060	−	48.4326i	0.299920	−	0.0974499i
$498$	8.60758	+	6.25378i	0.0172843	+	0.0125578i
$499$	−119.418	+	86.7624i	−0.239315	+	0.173873i	−0.700978	−	0.713183i	$-0.747253\pi$
$499$	−119.418	+	86.7624i	−0.239315	+	0.173873i	0.461663	+	0.887055i	$0.347253\pi$
$500$	−6.90983	+	21.2663i	−0.0138197	+	0.0425325i
$501$	−222.417	−	72.2678i	−0.443947	−	0.144247i
$502$	164.522	+	226.444i	0.327732	+	0.451085i
$503$	131.335	−	180.768i	0.261104	−	0.359379i	−0.658257	−	0.752793i	$-0.728706\pi$
$503$	131.335	−	180.768i	0.261104	−	0.359379i	0.919361	+	0.393414i	$0.128706\pi$
$504$	−1.41803	−	4.36426i	−0.00281356	−	0.00865924i
$505$		−	56.6958i		−	0.112269i
$506$	−178.687	−	283.759i	−0.353137	−	0.560788i
$507$	−299.694			−0.591113
$508$	−291.303	+	94.6499i	−0.573430	+	0.186319i
$509$	−172.014	−	124.975i	−0.337945	−	0.245531i	0.405849	−	0.913940i	$-0.366976\pi$
$509$	−172.014	−	124.975i	−0.337945	−	0.245531i	−0.743794	+	0.668409i	$0.766976\pi$
$510$	−54.2591	+	39.4215i	−0.106390	+	0.0772971i
$511$	−62.5532	+	192.519i	−0.122413	+	0.376750i
$512$	−21.5200	−	6.99226i	−0.0420312	−	0.0136568i
$513$	9.04055	+	12.4432i	0.0176229	+	0.0242558i
$514$	−389.548	+	536.167i	−0.757876	+	1.04313i
$515$	−72.8523	−	224.216i	−0.141461	−	0.435372i
$516$			366.735i			0.710726i
$517$	125.770	−	314.436i	0.243269	−	0.608194i
$518$	−6.96072			−0.0134377
$519$	348.313	−	113.174i	0.671124	−	0.218061i
$520$	40.3905	+	29.3454i	0.0776740	+	0.0564335i
$521$	429.326	−	311.924i	0.824043	−	0.598702i	−0.0938246	−	0.995589i	$-0.529909\pi$
$521$	429.326	−	311.924i	0.824043	−	0.598702i	0.917868	+	0.396886i	$0.129909\pi$
$522$	−12.0847	+	37.1930i	−0.0231508	+	0.0712510i
$523$	254.184	+	82.5895i	0.486012	+	0.157915i	0.541766	−	0.840530i	$-0.317756\pi$
$523$	254.184	+	82.5895i	0.486012	+	0.157915i	−0.0557533	+	0.998445i	$0.517756\pi$
$524$	−186.633	−	256.879i	−0.356170	−	0.490226i
$525$	12.0790	−	16.6253i	0.0230075	−	0.0316672i
$526$	101.231	+	311.557i	0.192454	+	0.592314i
$527$		−	44.5573i		−	0.0845489i
$528$	94.9595	+	79.1194i	0.179848	+	0.149847i
$529$	−64.3389			−0.121624
$530$	168.938	−	54.8912i	0.318750	−	0.103568i
$531$	−99.6038	−	72.3664i	−0.187578	−	0.136283i
$532$	−1.28222	+	0.931588i	−0.00241019	+	0.00175111i
$533$	87.4277	−	269.075i	0.164029	−	0.504831i
$534$	−12.4967	−	4.06044i	−0.0234021	−	0.00760382i
$535$	76.9251	+	105.878i	0.143785	+	0.197903i
$536$	61.0452	−	84.0215i	0.113890	−	0.156757i
$537$	81.3970	+	250.514i	0.151577	+	0.466507i
$538$		−	652.886i		−	1.21354i
$539$	514.319	+	34.1678i	0.954210	+	0.0633911i
$540$	−126.995			−0.235176
$541$	−302.152	+	98.1752i	−0.558507	+	0.181470i	−0.574649	−	0.818400i	$-0.694861\pi$
$541$	−302.152	+	98.1752i	−0.558507	+	0.181470i	0.0161425	+	0.999870i	$0.494861\pi$
$542$	−290.151	−	210.807i	−0.535335	−	0.388943i
$543$	375.113	−	272.536i	0.690817	−	0.501908i
$544$	−13.1978	+	40.6188i	−0.0242607	+	0.0746669i
$545$	97.9395	+	31.8225i	0.179706	+	0.0583899i
$546$	−26.9691	−	37.1197i	−0.0493939	−	0.0679848i
$547$	491.757	−	676.845i	0.899007	−	1.23738i	−0.0717767	−	0.997421i	$-0.522867\pi$
$547$	491.757	−	676.845i	0.899007	−	1.23738i	0.970784	−	0.239956i	$-0.0771331\pi$
$548$	12.1241	+	37.3142i	0.0221243	+	0.0680916i
$549$			8.68143i			0.0158132i
$550$	5.15591	−	77.6107i	0.00937439	−	0.141110i
$551$	13.5069			0.0245135
$552$	−162.888	+	52.9255i	−0.295087	+	0.0958795i
$553$	111.190	+	80.7841i	0.201066	+	0.146083i
$554$	−265.922	+	193.204i	−0.480003	+	0.348743i
$555$	−6.52986	+	20.0968i	−0.0117655	+	0.0362105i
$556$	306.587	+	99.6163i	0.551416	+	0.179166i
$557$	−63.2277	−	87.0254i	−0.113515	−	0.156240i	0.748479	−	0.663158i	$-0.230784\pi$
$557$	−63.2277	−	87.0254i	−0.113515	−	0.156240i	−0.861994	+	0.506919i	$0.830784\pi$
$558$	5.43994	−	7.48744i	0.00974900	−	0.0134184i
$559$	−159.231	−	490.062i	−0.284849	−	0.876676i
$560$		−	13.0863i		−	0.0233684i
$561$	149.337	−	179.236i	0.266199	−	0.319493i
$562$	649.015			1.15483
$563$	469.409	−	152.520i	0.833763	−	0.270906i	0.139134	−	0.990274i	$-0.455568\pi$
$563$	469.409	−	152.520i	0.833763	−	0.270906i	0.694630	+	0.719368i	$0.255568\pi$
$564$	−139.934	−	101.668i	−0.248110	−	0.180263i
$565$	−334.804	+	243.249i	−0.592573	+	0.430530i
$566$	97.1517	−	299.002i	0.171646	−	0.528272i
$567$	97.1121	+	31.5536i	0.171274	+	0.0556502i
$568$	−178.093	−	245.124i	−0.313544	−	0.431557i
$569$	−585.307	+	805.605i	−1.02866	+	1.41583i	−0.122708	+	0.992443i	$0.539158\pi$
$569$	−585.307	+	805.605i	−1.02866	+	1.41583i	−0.905950	+	0.423384i	$0.860842\pi$
$570$	1.48681	+	4.57593i	0.00260844	+	0.00802794i
$571$			706.234i			1.23684i	0.785849	+	0.618419i	$0.212226\pi$
$571$			706.234i			1.23684i	−0.785849	+	0.618419i	$0.787774\pi$
$572$	−161.245	−	64.4960i	−0.281897	−	0.112755i
$573$	500.879			0.874134
$574$	−70.5291	+	22.9163i	−0.122873	+	0.0399239i
$575$	87.1958	+	63.3515i	0.151645	+	0.110177i
$576$	−7.17687	+	5.21430i	−0.0124598	+	0.00905261i
$577$	−84.6069	+	260.393i	−0.146632	+	0.451288i	−0.997217	−	0.0745496i	$-0.976248\pi$
$577$	−84.6069	+	260.393i	−0.146632	+	0.451288i	0.850585	+	0.525838i	$0.176248\pi$
$578$	−312.036	−	101.387i	−0.539855	−	0.175410i
$579$	419.456	+	577.332i	0.724449	+	0.997119i
$580$	−65.5520	+	90.2246i	−0.113021	+	0.155560i
$581$	1.21086	+	3.72664i	0.00208409	+	0.00641418i
$582$			611.999i			1.05154i
$583$	−522.861	+	329.253i	−0.896845	+	0.564757i
$584$	391.328			0.670082
$585$	18.6153	−	6.04848i	0.0318210	−	0.0103393i
$586$	−334.957	−	243.360i	−0.571598	−	0.415290i
$587$	562.362	−	408.580i	0.958028	−	0.696048i	0.00533594	−	0.999986i	$-0.498302\pi$
$587$	562.362	−	408.580i	0.958028	−	0.696048i	0.952692	+	0.303938i	$0.0983015\pi$
$588$	81.3538	−	250.381i	0.138357	−	0.425818i
$589$	−3.04007	−	0.987778i	−0.00516140	−	0.00167704i
$590$	−206.371	−	284.046i	−0.349782	−	0.481433i
$591$	444.348	−	611.592i	0.751858	−	1.03484i
$592$	4.15824	+	12.7978i	0.00702406	+	0.0216178i
$593$		−	1075.43i		−	1.81354i	−0.421626	−	0.906770i	$-0.638541\pi$
$593$		−	1075.43i		−	1.81354i	0.421626	−	0.906770i	$-0.361459\pi$
$594$	428.257	−	108.360i	0.720972	−	0.182424i
$595$	−24.7003			−0.0415131
$596$	−448.449	+	145.710i	−0.752432	+	0.244480i
$597$	321.765	+	233.776i	0.538969	+	0.391584i
$598$	194.685	−	141.447i	0.325560	−	0.236533i
$599$	−110.666	+	340.595i	−0.184751	+	0.568605i	−0.999944	−	0.0105841i	$-0.996631\pi$
$599$	−110.666	+	340.595i	−0.184751	+	0.568605i	0.815193	+	0.579190i	$0.196631\pi$
$600$	−37.7825	−	12.2763i	−0.0629708	−	0.0204605i
$601$	253.867	+	349.418i	0.422408	+	0.581395i	0.966190	−	0.257832i	$-0.0830081\pi$
$601$	253.867	+	349.418i	0.422408	+	0.581395i	−0.543782	+	0.839227i	$0.683008\pi$
$602$	−79.3886	+	109.269i	−0.131875	+	0.181510i
$603$	−12.5822	−	38.7241i	−0.0208661	−	0.0642191i
$604$			401.837i			0.665294i
$605$	48.8351	+	266.121i	0.0807191	+	0.439869i
$606$	100.728			0.166218
$607$	−225.890	+	73.3961i	−0.372141	+	0.120916i	−0.489116	−	0.872219i	$-0.662680\pi$
$607$	−225.890	+	73.3961i	−0.372141	+	0.120916i	0.116974	+	0.993135i	$0.462680\pi$
$608$	2.47877	+	1.80093i	0.00407692	+	0.00296206i
$609$	82.9184	−	60.2437i	0.136155	−	0.0989224i
$610$	−7.65044	+	23.5456i	−0.0125417	+	0.0385994i
$611$	231.134	+	75.1001i	0.378289	+	0.122913i
$612$	9.84196	+	13.5463i	0.0160816	+	0.0221345i
$613$	392.977	−	540.887i	0.641072	−	0.882360i	−0.357600	−	0.933875i	$-0.616405\pi$
$613$	392.977	−	540.887i	0.641072	−	0.882360i	0.998672	+	0.0515145i	$0.0164048\pi$
$614$	−10.6408	−	32.7491i	−0.0173304	−	0.0533374i
$615$			225.128i			0.366062i
$616$	11.1660	+	44.1300i	0.0181266	+	0.0716396i
$617$	−348.051			−0.564103			−0.282051	−	0.959399i	$-0.591015\pi$
$617$	−348.051			−0.564103			−0.282051	+	0.959399i	$0.591015\pi$
$618$	398.351	−	129.432i	0.644582	−	0.209437i
$619$	340.079	+	247.082i	0.549400	+	0.399163i	0.827564	−	0.561371i	$-0.189726\pi$
$619$	340.079	+	247.082i	0.549400	+	0.399163i	−0.278164	+	0.960534i	$0.589726\pi$
$620$	21.3524	−	15.5134i	0.0344393	−	0.0250216i
$621$	−189.157	+	582.166i	−0.304601	+	0.937466i
$622$	715.472	+	232.471i	1.15028	+	0.373748i
$623$	−2.84444	−	3.91504i	−0.00456571	−	0.00628417i
$624$	−52.1362	+	71.7593i	−0.0835516	+	0.114999i
$625$	7.72542	+	23.7764i	0.0123607	+	0.0380423i
$626$		−	156.682i		−	0.250291i
$627$	−8.91831	−	14.1625i	−0.0142238	−	0.0225876i
$628$	−54.7523			−0.0871851
$629$	24.1557	−	7.84866i	0.0384033	−	0.0124780i
$630$	−4.15066	−	3.01563i	−0.00658834	−	0.00478671i
$631$	889.716	−	646.417i	1.41001	−	1.02443i	0.416689	−	0.909049i	$-0.363190\pi$
$631$	889.716	−	646.417i	1.41001	−	1.02443i	0.993321	−	0.115383i	$-0.0368096\pi$
$632$	82.1037	−	252.689i	0.129911	−	0.399825i
$633$	−45.3971	−	14.7504i	−0.0717174	−	0.0233024i
$634$	294.695	+	405.613i	0.464819	+	0.639769i
$635$	−201.285	+	277.045i	−0.316984	+	0.436292i
$636$	97.5218	+	300.141i	0.153336	+	0.471920i
$637$			369.903i			0.580695i
$638$	144.072	−	360.191i	0.225818	−	0.564563i
$639$	−118.788			−0.185896
$640$	−24.0600	+	7.81758i	−0.0375938	+	0.0122150i
$641$	242.452	+	176.151i	0.378240	+	0.274807i	0.760619	−	0.649198i	$-0.224895\pi$
$641$	242.452	+	176.151i	0.378240	+	0.274807i	−0.382380	+	0.924005i	$0.624895\pi$
$642$	−188.108	+	136.668i	−0.293002	+	0.212879i
$643$	385.964	−	1187.87i	0.600255	−	1.84739i	0.0736504	−	0.997284i	$-0.476535\pi$
$643$	385.964	−	1187.87i	0.600255	−	1.84739i	0.526604	−	0.850110i	$-0.323465\pi$
$644$	−59.9896	−	19.4918i	−0.0931516	−	0.0302668i
$645$	241.005	+	331.715i	0.373651	+	0.514286i
$646$	3.39925	−	4.67866i	0.00526199	−	0.00724251i
$647$	−103.202	−	317.622i	−0.159508	−	0.490914i	0.839082	−	0.544005i	$-0.183093\pi$
$647$	−103.202	−	317.622i	−0.159508	−	0.490914i	−0.998590	+	0.0530906i	$0.983093\pi$
$648$		−	197.397i		−	0.304625i
$649$	938.297	+	781.780i	1.44576	+	1.20459i
$650$	55.8183			0.0858743
$651$	−23.0686	+	7.49543i	−0.0354356	+	0.0115137i
$652$	233.962	+	169.983i	0.358837	+	0.260710i
$653$	−426.222	+	309.669i	−0.652714	+	0.474225i	−0.864195	−	0.503158i	$-0.832172\pi$
$653$	−426.222	+	309.669i	−0.652714	+	0.474225i	0.211481	+	0.977382i	$0.432172\pi$
$654$	−56.5370	+	174.003i	−0.0864481	+	0.266060i
$655$	−337.623	−	109.700i	−0.515454	−	0.167481i
$656$	84.2663	+	115.983i	0.128455	+	0.176803i
$657$	90.1783	−	124.120i	0.137258	−	0.188919i
$658$	−19.6850	−	60.5843i	−0.0299165	−	0.0920734i
$659$		−	13.3676i		−	0.0202847i	−0.999949	−	0.0101424i	$-0.996772\pi$
$659$		−	13.3676i		−	0.0202847i	0.999949	−	0.0101424i	$-0.00322847\pi$
$660$	137.886	+	9.16020i	0.208918	+	0.0138791i
$661$	−421.870			−0.638231			−0.319115	−	0.947716i	$-0.603386\pi$
$661$	−421.870			−0.638231			−0.319115	+	0.947716i	$0.603386\pi$
$662$	−535.593	+	174.025i	−0.809053	+	0.262877i
$663$	135.445	+	98.4067i	0.204291	+	0.148426i
$664$	6.12833	−	4.45249i	0.00922941	−	0.00670556i
$665$	−0.547574	+	1.68526i	−0.000823419	+	0.00253422i
$666$	5.01737	+	1.63024i	0.00753359	+	0.00244781i
$667$	315.965	+	434.889i	0.473711	+	0.652007i
$668$	−97.8683	+	134.704i	−0.146509	+	0.201653i
$669$	−68.3566	−	210.380i	−0.102177	−	0.314469i
$670$		−	116.115i		−	0.173306i
$671$	5.70853	−	85.9291i	0.00850750	−	0.128061i
$672$	23.2496			0.0345976
$673$	−1174.65	+	381.668i	−1.74540	+	0.567115i	−0.995528	−	0.0944677i	$-0.969885\pi$
$673$	−1174.65	+	381.668i	−1.74540	+	0.567115i	−0.749872	+	0.661583i	$0.769885\pi$
$674$	122.715	+	89.1574i	0.182069	+	0.132281i
$675$	−114.868	+	83.4567i	−0.170175	+	0.123640i
$676$	−65.9358	+	202.930i	−0.0975382	+	0.300192i
$677$	−830.341	−	269.794i	−1.22650	−	0.398514i	−0.377055	−	0.926191i	$-0.623063\pi$
$677$	−830.341	−	269.794i	−1.22650	−	0.398514i	−0.849445	+	0.527677i	$0.823063\pi$
$678$	−432.166	−	594.825i	−0.637413	−	0.877323i
$679$	−132.482	+	182.346i	−0.195113	+	0.268551i
$680$	14.7556	+	45.4132i	0.0216995	+	0.0667841i
$681$		−	882.432i		−	1.29579i
$682$	−58.7682	+	70.5339i	−0.0861703	+	0.103422i
$683$	−90.8680			−0.133043			−0.0665213	−	0.997785i	$-0.521190\pi$
$683$	−90.8680			−0.133043			−0.0665213	+	0.997785i	$0.521190\pi$
$684$	1.14242	−	0.371196i	0.00167021	−	0.000542684i
$685$	35.4879	+	25.7835i	0.0518071	+	0.0376401i
$686$	160.464	−	116.584i	0.233913	−	0.169948i
$687$	216.854	−	667.409i	0.315654	−	0.971483i
$688$	248.324	+	80.6855i	0.360937	+	0.117275i
$689$	−260.634	−	358.731i	−0.378278	−	0.520655i
$690$	−112.553	+	154.916i	−0.163120	+	0.224515i
$691$	−44.8083	−	137.906i	−0.0648456	−	0.199574i	0.913384	−	0.407098i	$-0.133459\pi$
$691$	−44.8083	−	137.906i	−0.0648456	−	0.199574i	−0.978230	+	0.207524i	$0.933459\pi$
$692$		−	260.750i		−	0.376807i
$693$	16.5701	+	6.62781i	0.0239107	+	0.00956394i
$694$	−162.374			−0.233968
$695$	342.775	−	111.374i	0.493202	−	0.160251i
$696$	−160.297	−	116.462i	−0.230311	−	0.167331i
$697$	218.917	−	159.052i	0.314084	−	0.228195i
$698$	155.394	−	478.255i	0.222628	−	0.685179i
$699$	−753.601	−	244.860i	−1.07811	−	0.350300i
$700$	−8.59984	−	11.8367i	−0.0122855	−	0.0169095i
$701$	43.7586	−	60.2285i	0.0624231	−	0.0859180i	−0.776664	−	0.629915i	$-0.783090\pi$
$701$	43.7586	−	60.2285i	0.0624231	−	0.0859180i	0.839087	+	0.543997i	$0.183090\pi$
$702$	97.9628	+	301.499i	0.139548	+	0.429485i
$703$		−	1.82209i		−	0.00259188i
$704$	74.4656	−	46.8921i	0.105775	−	0.0666082i
$705$	−193.384			−0.274304
$706$	−370.049	+	120.236i	−0.524149	+	0.170306i
$707$	30.0120	+	21.8050i	0.0424498	+	0.0308416i
$708$	504.647	−	366.647i	0.712778	−	0.517863i
$709$	−56.7700	+	174.720i	−0.0800705	+	0.246432i	−0.983076	−	0.183197i	$-0.941355\pi$
$709$	−56.7700	+	174.720i	−0.0800705	+	0.246432i	0.903006	+	0.429628i	$0.141355\pi$
$710$	−322.174	−	104.681i	−0.453766	−	0.147437i
$711$	−61.2268	−	84.2715i	−0.0861137	−	0.118525i
$712$	−5.49883	+	7.56849i	−0.00772307	+	0.0106299i
$713$	−39.3119	−	120.990i	−0.0551359	−	0.169691i
$714$		−	43.8835i		−	0.0614615i
$715$	−188.232	+	47.6274i	−0.263262	+	0.0666118i
$716$	187.537			0.261923
$717$	−1105.87	+	359.318i	−1.54235	+	0.501141i
$718$	175.113	+	127.227i	0.243890	+	0.177196i
$719$	−147.799	+	107.383i	−0.205562	+	0.149350i	−0.685804	−	0.727787i	$-0.740549\pi$
$719$	−147.799	+	107.383i	−0.205562	+	0.149350i	0.480241	+	0.877136i	$0.340549\pi$
$720$	−3.06489	+	9.43276i	−0.00425679	+	0.0131011i
$721$	146.708	+	47.6683i	0.203479	+	0.0661142i
$722$	299.839	+	412.693i	0.415289	+	0.571597i
$723$	234.213	−	322.367i	0.323946	−	0.445874i
$724$	−102.011	−	313.958i	−0.140900	−	0.433644i
$725$			124.687i			0.171983i
$726$	−472.800	+	86.7623i	−0.651240	+	0.119507i
$727$	−1204.32			−1.65655			−0.828277	−	0.560318i	$-0.810679\pi$
$727$	−1204.32			−1.65655			−0.828277	+	0.560318i	$0.810679\pi$
$728$	−31.0681	+	10.0946i	−0.0426759	+	0.0138662i
$729$	−643.430	−	467.479i	−0.882620	−	0.641261i
$730$	353.959	−	257.166i	0.484876	−	0.352283i
$731$	152.293	−	468.711i	0.208336	−	0.641191i
$732$	−41.8321	−	13.5921i	−0.0571476	−	0.0185684i
$733$	606.462	+	834.723i	0.827369	+	1.13878i	0.988407	+	0.151828i	$0.0485159\pi$
$733$	606.462	+	834.723i	0.827369	+	1.13878i	−0.161038	+	0.986948i	$0.551484\pi$
$734$	−299.752	+	412.573i	−0.408381	+	0.562088i
$735$	−90.9563	−	279.935i	−0.123750	−	0.380864i
$736$			121.939i			0.165678i
$737$	99.0761	+	391.566i	0.134432	+	0.531298i
$738$	56.2054			0.0761591
$739$	−560.538	+	182.130i	−0.758508	+	0.246454i	−0.662638	−	0.748940i	$-0.730563\pi$
$739$	−560.538	+	182.130i	−0.758508	+	0.246454i	−0.0958700	+	0.995394i	$0.530563\pi$
$740$	12.1714	+	8.84303i	0.0164478	+	0.0119500i
$741$	9.71676	−	7.05964i	0.0131130	−	0.00952718i
$742$	−35.9161	+	110.538i	−0.0484045	+	0.148974i
$743$	−80.9333	−	26.2968i	−0.108928	−	0.0353928i	0.254046	−	0.967192i	$-0.418239\pi$
$743$	−80.9333	−	26.2968i	−0.108928	−	0.0353928i	−0.362974	+	0.931799i	$0.618239\pi$
$744$	27.5617	+	37.9354i	0.0370453	+	0.0509885i
$745$	−309.871	+	426.501i	−0.415934	+	0.572484i
$746$	−21.2137	−	65.2890i	−0.0284366	−	0.0875187i
$747$		−	2.96980i		−	0.00397563i
$748$	−88.5086	−	140.553i	−0.118327	−	0.187906i
$749$	−85.6320			−0.114328
$750$	−42.2421	+	13.7253i	−0.0563228	+	0.0183004i
$751$	−442.671	−	321.619i	−0.589441	−	0.428254i	0.252674	−	0.967551i	$-0.418690\pi$
$751$	−442.671	−	321.619i	−0.589441	−	0.428254i	−0.842116	+	0.539297i	$0.818690\pi$
$752$	−99.6287	+	72.3845i	−0.132485	+	0.0962560i
$753$	−171.807	+	528.767i	−0.228163	+	0.702214i
$754$	264.768	+	86.0283i	0.351151	+	0.114096i
$755$	264.073	+	363.465i	0.349766	+	0.481411i
$756$	48.8419	−	67.2251i	0.0646057	−	0.0889222i
$757$	114.617	+	352.756i	0.151410	+	0.465992i	0.997779	−	0.0666040i	$-0.0212164\pi$
$757$	114.617	+	352.756i	0.151410	+	0.465992i	−0.846369	+	0.532596i	$0.821216\pi$
$758$		−	409.228i		−	0.539879i
$759$	247.371	−	618.448i	0.325917	−	0.814819i
$760$	3.42558			0.00450734
$761$	−714.408	+	232.125i	−0.938776	+	0.305027i	−0.738146	−	0.674640i	$-0.764299\pi$
$761$	−714.408	+	232.125i	−0.938776	+	0.305027i	−0.200629	+	0.979667i	$0.564299\pi$
$762$	−492.209	−	357.611i	−0.645944	−	0.469306i
$763$	−54.5125	+	39.6056i	−0.0714449	+	0.0519078i
$764$	110.199	−	339.156i	0.144239	−	0.443922i
$765$	17.8043	+	5.78496i	0.0232736	+	0.00756204i
$766$	454.296	+	625.285i	0.593076	+	0.816299i
$767$	−515.158	+	709.055i	−0.671654	+	0.924452i
$768$	−13.8890	−	42.7460i	−0.0180847	−	0.0556588i
$769$		−	369.638i		−	0.480674i	−0.970690	−	0.240337i	$-0.922742\pi$
$769$		−	369.638i		−	0.480674i	0.970690	−	0.240337i	$-0.0772580\pi$
$770$	39.1004	+	32.5781i	0.0507797	+	0.0423092i
$771$	−1316.43			−1.70743
$772$	483.209	−	157.004i	0.625919	−	0.203373i
$773$	1065.14	+	773.868i	1.37793	+	1.00112i	0.997070	+	0.0764897i	$0.0243712\pi$
$773$	1065.14	+	773.868i	1.37793	+	1.00112i	0.380858	+	0.924634i	$0.375629\pi$
$774$	82.8158	−	60.1692i	0.106997	−	0.0777380i
$775$	9.11855	−	28.0640i	0.0117659	−	0.0362116i
$776$	414.398	+	134.646i	0.534018	+	0.173513i
$777$	−8.12694	−	11.1858i	−0.0104594	−	0.0143961i
$778$	−621.534	+	855.467i	−0.798886	+	1.09957i
$779$	−5.99876	−	18.4623i	−0.00770059	−	0.0237000i
$780$			99.1689i			0.127140i
$781$	1175.76	+	78.1096i	1.50546	+	0.100012i
$782$	230.159			0.294322
$783$	−673.490	+	218.830i	−0.860141	+	0.279477i
$784$	−151.640	−	110.173i	−0.193418	−	0.140527i
$785$	−49.5239	+	35.9812i	−0.0630878	+	0.0458359i
$786$	194.898	−	599.833i	0.247961	−	0.763147i
$787$	−701.711	−	228.000i	−0.891628	−	0.289708i	−0.172851	−	0.984948i	$-0.555298\pi$
$787$	−701.711	−	228.000i	−0.891628	−	0.289708i	−0.718777	+	0.695240i	$0.755298\pi$
$788$	−316.362	−	435.435i	−0.401474	−	0.552582i
$789$	−382.476	+	526.433i	−0.484760	+	0.667215i
$790$	−91.7948	−	282.515i	−0.116196	−	0.357614i
$791$		−	270.782i		−	0.342328i
$792$	2.28693	−	34.4246i	0.00288754	−	0.0434654i
$793$	61.8010			0.0779331
$794$	372.772	−	121.121i	0.469486	−	0.152545i
$795$	285.451	+	207.393i	0.359058	+	0.260871i
$796$	229.086	−	166.441i	0.287797	−	0.209097i
$797$	−28.1073	+	86.5053i	−0.0352664	+	0.108539i	−0.967140	−	0.254244i	$-0.918173\pi$
$797$	−28.1073	+	86.5053i	−0.0352664	+	0.108539i	0.931874	+	0.362783i	$0.118173\pi$
$798$	−2.99410	−	0.972841i	−0.00375200	−	0.00121910i
$799$	136.625	+	188.049i	0.170995	+	0.235355i
$800$	−16.6251	+	22.8825i	−0.0207813	+	0.0286031i
$801$	1.13338	+	3.48819i	0.00141496	+	0.00435479i
$802$			908.714i			1.13306i
$803$	−974.203	+	1169.24i	−1.21320	+	1.45609i
$804$	206.294			0.256585
$805$	−67.0704	+	21.7925i	−0.0833173	+	0.0270714i
$806$	−53.3012	−	38.7256i	−0.0661306	−	0.0480467i
$807$	1049.18	−	762.272i	1.30010	−	0.944575i
$808$	22.1612	−	68.2051i	0.0274272	−	0.0844123i
$809$	−74.5304	−	24.2164i	−0.0921266	−	0.0299337i	0.262591	−	0.964907i	$-0.415423\pi$
$809$	−74.5304	−	24.2164i	−0.0921266	−	0.0299337i	−0.354718	+	0.934973i	$0.615423\pi$
$810$	−129.722	−	178.547i	−0.160151	−	0.220429i
$811$	248.151	−	341.551i	0.305982	−	0.421148i	−0.628141	−	0.778100i	$-0.716184\pi$
$811$	248.151	−	341.551i	0.305982	−	0.421148i	0.934123	+	0.356952i	$0.116184\pi$
$812$	−22.5495	−	69.4002i	−0.0277703	−	0.0854682i
$813$		−	712.395i		−	0.876255i
$814$	−48.5901	−	19.4354i	−0.0596930	−	0.0238764i
$815$	323.327			0.396720
$816$	−80.6828	+	26.2154i	−0.0988760	+	0.0321268i
$817$	−28.6032	−	20.7814i	−0.0350100	−	0.0254363i
$818$	792.371	−	575.691i	0.968668	−	0.703779i
$819$	−3.95761	+	12.1803i	−0.00483224	+	0.0148721i
$820$	152.439	+	49.5305i	0.185902	+	0.0604031i
$821$	−519.994	−	715.710i	−0.633367	−	0.871754i	0.364873	−	0.931057i	$-0.381112\pi$
$821$	−519.994	−	715.710i	−0.633367	−	0.871754i	−0.998240	+	0.0593028i	$0.981112\pi$
$822$	−45.8079	+	63.0492i	−0.0557274	+	0.0767021i
$823$	286.154	+	880.693i	0.347697	+	1.07010i	0.960124	+	0.279574i	$0.0901932\pi$
$823$	286.154	+	880.693i	0.347697	+	1.07010i	−0.612427	+	0.790527i	$0.709807\pi$
$824$		−	298.209i		−	0.361904i
$825$	130.739	−	82.3283i	0.158471	−	0.0997919i
$826$	229.730			0.278123
$827$	1016.93	−	330.419i	1.22966	−	0.399540i	0.379067	−	0.925369i	$-0.376245\pi$
$827$	1016.93	−	330.419i	1.22966	−	0.399540i	0.850590	+	0.525829i	$0.176245\pi$
$828$	38.6762	+	28.0999i	0.0467103	+	0.0339370i
$829$	−149.615	+	108.701i	−0.180476	+	0.131123i	−0.674355	−	0.738407i	$-0.735578\pi$
$829$	−149.615	+	108.701i	−0.180476	+	0.131123i	0.493879	+	0.869530i	$0.335578\pi$
$830$	2.61711	−	8.05463i	0.00315314	−	0.00970438i
$831$	−620.950	−	201.759i	−0.747233	−	0.242791i
$832$	37.1193	+	51.0904i	0.0446146	+	0.0614067i
$833$	−207.951	+	286.220i	−0.249641	+	0.343601i
$834$	197.872	+	608.988i	0.237257	+	0.730201i
$835$			186.157i			0.222942i
$836$	−11.5518	+	2.92290i	−0.0138180	+	0.00349630i
$837$	167.589			0.200226
$838$	−49.3926	+	16.0486i	−0.0589410	+	0.0191511i
$839$	379.816	+	275.952i	0.452700	+	0.328906i	0.790661	−	0.612254i	$-0.209737\pi$
$839$	379.816	+	275.952i	0.452700	+	0.328906i	−0.337961	+	0.941160i	$0.609737\pi$
$840$	21.0295	−	15.2788i	0.0250351	−	0.0181891i
$841$	67.7125	−	208.398i	0.0805142	−	0.247797i
$842$	−662.081	−	215.123i	−0.786319	−	0.255491i
$843$	757.752	+	1042.96i	0.898876	+	1.23720i
$844$	−19.9757	+	27.4941i	−0.0236679	+	0.0325760i
$845$	73.7185	+	226.882i	0.0872408	+	0.268500i
$846$			48.2802i			0.0570688i
$847$	−159.653	−	76.4981i	−0.188492	−	0.0903165i
$848$	224.688			0.264962
$849$	593.921	−	192.976i	0.699553	−	0.227299i
$850$	43.1905	+	31.3797i	0.0508124	+	0.0369173i
$851$	58.6669	−	42.6240i	0.0689388	−	0.0500870i
$852$	185.980	−	572.386i	0.218286	−	0.671815i
$853$	329.712	+	107.130i	0.386532	+	0.125592i	0.495835	−	0.868417i	$-0.334862\pi$
$853$	329.712	+	107.130i	0.386532	+	0.125592i	−0.109303	+	0.994008i	$0.534862\pi$
$854$	−9.52159	−	13.1053i	−0.0111494	−	0.0153458i
$855$	0.789396	−	1.08651i	0.000923270	−	0.00127077i
$856$	51.1554	+	157.440i	0.0597610	+	0.183926i
$857$		−	1210.35i		−	1.41231i	−0.708057	−	0.706155i	$-0.750428\pi$
$857$		−	1210.35i		−	1.41231i	0.708057	−	0.706155i	$-0.249572\pi$
$858$	−84.6167	−	334.421i	−0.0986209	−	0.389768i
$859$	1346.17			1.56714			0.783570	−	0.621304i	$-0.213397\pi$
$859$	1346.17			1.56714			0.783570	+	0.621304i	$0.213397\pi$
$860$	277.635	−	90.2091i	0.322832	−	0.104894i
$861$	−119.172	−	86.5835i	−0.138411	−	0.100561i
$862$	907.328	−	659.213i	1.05258	−	0.764748i
$863$	242.612	−	746.682i	0.281126	−	0.865217i	−0.706407	−	0.707806i	$-0.749685\pi$
$863$	242.612	−	746.682i	0.281126	−	0.865217i	0.987533	−	0.157411i	$-0.0503148\pi$
$864$	−152.776	−	49.6398i	−0.176824	−	0.0574534i
$865$	−171.356	−	235.851i	−0.198099	−	0.272660i
$866$	−398.891	+	549.027i	−0.460613	+	0.633980i
$867$	−201.389	−	619.811i	−0.232282	−	0.714892i
$868$			17.2693i			0.0198955i
$869$	550.612	+	874.382i	0.633616	+	1.00619i
$870$	−221.524			−0.254626
$871$	−275.667	+	89.5698i	−0.316495	+	0.102836i
$872$	105.383	+	76.5650i	0.120852	+	0.0878039i
$873$	138.201	−	100.409i	0.158306	−	0.115016i
$874$	5.10234	−	15.7034i	0.00583791	−	0.0179673i
$875$	−15.5573	−	5.05486i	−0.0177797	−	0.00577698i
$876$	456.892	+	628.858i	0.521566	+	0.717874i
$877$	293.276	−	403.660i	0.334409	−	0.460274i	−0.608389	−	0.793639i	$-0.708184\pi$
$877$	293.276	−	403.660i	0.334409	−	0.460274i	0.942798	+	0.333365i	$0.108184\pi$
$878$	331.907	+	1021.50i	0.378026	+	1.16344i
$879$		−	822.403i		−	0.935613i
$880$	36.5390	−	91.3504i	0.0415215	−	0.103807i
$881$	772.928			0.877330			0.438665	−	0.898651i	$-0.355451\pi$
$881$	772.928			0.877330			0.438665	+	0.898651i	$0.355451\pi$
$882$	−69.8884	+	22.7081i	−0.0792386	+	0.0257462i
$883$	−653.044	−	474.464i	−0.739574	−	0.537332i	0.153004	−	0.988226i	$-0.451105\pi$
$883$	−653.044	−	474.464i	−0.739574	−	0.537332i	−0.892578	+	0.450894i	$0.851105\pi$
$884$	96.4328	−	70.0625i	0.109087	−	0.0792562i
$885$	215.510	−	663.271i	0.243514	−	0.749459i
$886$	953.362	+	309.766i	1.07603	+	0.349623i
$887$	593.300	+	816.607i	0.668884	+	0.920639i	0.999734	−	0.0230438i	$-0.00733573\pi$
$887$	593.300	+	816.607i	0.668884	+	0.920639i	−0.330851	+	0.943683i	$0.607336\pi$
$888$	−15.7109	+	21.6242i	−0.0176924	+	0.0243515i
$889$	−69.2408	−	213.101i	−0.0778861	−	0.239709i
$890$			10.4594i			0.0117521i
$891$	589.800	+	491.416i	0.661953	+	0.551533i
$892$	−157.492			−0.176561
$893$	15.8590	−	5.15291i	0.0177593	−	0.00577034i
$894$	−757.737	−	550.528i	−0.847581	−	0.615804i
$895$	169.629	−	123.242i	0.189529	−	0.137701i
$896$	5.11516	−	15.7428i	0.00570888	−	0.0175701i
$897$	454.606	+	147.710i	0.506807	+	0.164672i
$898$	−455.080	−	626.364i	−0.506770	−	0.697510i
$899$	86.5056	−	119.065i	0.0962243	−	0.132441i
$900$	3.42665	+	10.5461i	0.00380739	+	0.0117179i
$901$		−	424.098i		−	0.470697i
$902$	−556.323	−	36.9582i	−0.616766	−	0.0409736i
$903$	−268.283			−0.297102
$904$	−497.851	+	161.761i	−0.550720	+	0.178940i
$905$	−298.592	−	216.940i	−0.329936	−	0.239713i
$906$	−645.747	+	469.162i	−0.712745	+	0.517839i
$907$	−330.836	+	1018.21i	−0.364758	+	1.12261i	0.585374	+	0.810763i	$0.300948\pi$
$907$	−330.836	+	1018.21i	−0.364758	+	1.12261i	−0.950132	+	0.311847i	$0.899052\pi$
$908$	−597.514	−	194.144i	−0.658055	−	0.213815i
$909$	−16.5262	−	22.7463i	−0.0181806	−	0.0250234i
$910$	−21.4675	+	29.5475i	−0.0235907	+	0.0324698i
$911$	135.755	+	417.810i	0.149017	+	0.458628i	0.997506	−	0.0705858i	$-0.0224868\pi$
$911$	135.755	+	417.810i	0.149017	+	0.458628i	−0.848488	+	0.529214i	$0.822487\pi$
$912$			6.08601i			0.00667326i
$913$	−1.95281	+	29.3952i	−0.00213889	+	0.0321962i
$914$	351.298			0.384352
$915$	−46.7697	+	15.1964i	−0.0511144	+	0.0166081i
$916$	−404.207	−	293.674i	−0.441274	−	0.320604i
$917$	187.918	−	136.531i	0.204927	−	0.148888i
$918$	−93.6948	+	288.363i	−0.102064	+	0.314121i
$919$	−325.164	−	105.652i	−0.353824	−	0.114964i	0.126712	−	0.991940i	$-0.459558\pi$
$919$	−325.164	−	105.652i	−0.353824	−	0.114964i	−0.480535	+	0.876975i	$0.659558\pi$
$920$	80.1340	+	110.295i	0.0871022	+	0.119886i
$921$	40.2037	−	55.3357i	0.0436523	−	0.0600822i
$922$	−106.978	−	329.243i	−0.116028	−	0.357097i
$923$			845.620i			0.916164i
$924$	−57.8795	+	69.4673i	−0.0626401	+	0.0751810i
$925$	16.8204			0.0181843
$926$	−184.076	+	59.8100i	−0.198787	+	0.0645897i
$927$	−94.5847	−	68.7198i	−0.102033	−	0.0741314i
$928$	−114.126	+	82.9175i	−0.122981	+	0.0893508i
$929$	49.1789	−	151.357i	0.0529375	−	0.162925i	−0.921093	−	0.389344i	$-0.872702\pi$
$929$	49.1789	−	151.357i	0.0529375	−	0.162925i	0.974030	+	0.226419i	$0.0727018\pi$
$930$	49.8596	+	16.2004i	0.0536125	+	0.0174197i
$931$	14.9183	+	20.5332i	0.0160239	+	0.0220550i
$932$	−331.600	+	456.409i	−0.355794	+	0.489709i
$933$	461.767	+	1421.17i	0.494927	+	1.52323i
$934$			102.302i			0.109531i
$935$	−172.423	−	68.9671i	−0.184410	−	0.0737616i
$936$	24.7585			0.0264514
$937$	1087.77	−	353.437i	1.16091	−	0.377201i	0.335664	−	0.941982i	$-0.391039\pi$
$937$	1087.77	−	353.437i	1.16091	−	0.377201i	0.825241	+	0.564781i	$0.191039\pi$
$938$	61.4656	+	44.6574i	0.0655284	+	0.0476091i
$939$	251.786	−	182.933i	0.268143	−	0.194817i
$940$	−42.5465	+	130.945i	−0.0452623	+	0.139303i
$941$	−1097.17	−	356.491i	−1.16596	−	0.378843i	−0.338826	−	0.940849i	$-0.610030\pi$
$941$	−1097.17	−	356.491i	−1.16596	−	0.378843i	−0.827133	+	0.562006i	$0.810030\pi$
$942$	−63.9256	−	87.9860i	−0.0678616	−	0.0934034i
$943$	454.111	−	625.031i	0.481560	−	0.662811i
$944$	−137.238	−	422.374i	−0.145379	−	0.447430i
$945$		−	92.9029i		−	0.0983099i
$946$	−859.278	+	541.101i	−0.908328	+	0.571988i
$947$	681.693			0.719845			0.359922	−	0.932982i	$-0.382803\pi$
$947$	681.693			0.719845			0.359922	+	0.932982i	$0.382803\pi$
$948$	501.927	−	163.086i	0.529459	−	0.172032i
$949$	−883.578	−	641.957i	−0.931062	−	0.676456i
$950$	3.09846	−	2.25116i	0.00326154	−	0.00236965i
$951$	−307.745	+	947.142i	−0.323601	+	0.995943i
$952$	−29.7145	−	9.65483i	−0.0312127	−	0.0101416i
$953$	−119.206	−	164.073i	−0.125085	−	0.172165i	0.741882	−	0.670531i	$-0.233934\pi$
$953$	−119.206	−	164.073i	−0.125085	−	0.172165i	−0.866967	+	0.498366i	$0.833934\pi$
$954$	51.7775	−	71.2657i	0.0542741	−	0.0747020i
$955$	−123.206	−	379.188i	−0.129011	−	0.397056i
$956$			827.862i			0.865964i
$957$	747.032	−	189.018i	0.780598	−	0.197511i
$958$	−659.435			−0.688345
$959$	−27.2970	+	8.86934i	−0.0284641	+	0.00924853i
$960$	−40.6539	−	29.5368i	−0.0423478	−	0.0307675i
$961$	749.288	−	544.389i	0.779696	−	0.566482i
$962$	11.6053	−	35.7174i	0.0120637	−	0.0371283i
$963$	61.7246	+	20.0555i	0.0640962	+	0.0208261i
$964$	−166.752	−	229.515i	−0.172980	−	0.238086i
$965$	333.889	−	459.559i	0.345999	−	0.476227i
$966$	−38.7174	−	119.160i	−0.0400801	−	0.123354i
$967$			1229.94i			1.27192i	0.771723	+	0.635958i	$0.219395\pi$
$967$			1229.94i			1.27192i	−0.771723	+	0.635958i	$0.780605\pi$
$968$	−45.2723	+	339.232i	−0.0467689	+	0.350446i
$969$	11.4873			0.0118548
$970$	463.311	−	150.539i	0.477640	−	0.155195i
$971$	594.550	+	431.966i	0.612307	+	0.444867i	0.850226	−	0.526418i	$-0.176465\pi$
$971$	594.550	+	431.966i	0.612307	+	0.444867i	−0.237919	+	0.971285i	$0.576465\pi$
$972$	−96.3118	+	69.9746i	−0.0990862	+	0.0719904i
$973$	−72.8739	+	224.283i	−0.0748961	+	0.230506i
$974$	−138.851	−	45.1155i	−0.142558	−	0.0463198i
$975$	65.1702	+	89.6991i	0.0668412	+	0.0919991i
$976$	−18.4070	+	25.3350i	−0.0188596	+	0.0259580i
$977$	−146.201	−	449.962i	−0.149643	−	0.460554i	0.847936	−	0.530099i	$-0.177845\pi$
$977$	−146.201	−	449.962i	−0.149643	−	0.460554i	−0.997579	+	0.0695448i	$0.977845\pi$
$978$			574.435i			0.587357i
$979$	−8.92457	−	35.2715i	−0.00911601	−	0.0360281i
$980$	−209.561			−0.213838
$981$	48.5691	−	15.7811i	0.0495098	−	0.0160867i
$982$	−145.369	−	105.617i	−0.148034	−	0.107553i
$983$	−889.956	+	646.591i	−0.905347	+	0.657773i	−0.939834	−	0.341632i	$-0.889020\pi$
$983$	−889.956	+	646.591i	−0.905347	+	0.657773i	0.0344865	+	0.999405i	$0.489020\pi$
$984$	−87.9978	+	270.829i	−0.0894287	+	0.275233i
$985$	−572.304	−	185.953i	−0.581019	−	0.188785i
$986$	156.506	+	215.412i	0.158728	+	0.218471i
$987$	74.3749	−	102.368i	0.0753545	−	0.103717i
$988$	−2.64245	−	8.13263i	−0.00267455	−	0.00823141i
$989$		−	1407.09i		−	1.42274i
$990$	−20.5541	−	32.6402i	−0.0207617	−	0.0329699i
$991$	−129.253			−0.130427			−0.0652133	−	0.997871i	$-0.520773\pi$
$991$	−129.253			−0.130427			−0.0652133	+	0.997871i	$0.520773\pi$
$992$	31.7508	−	10.3165i	0.0320068	−	0.0103997i
$993$	−904.983	−	657.509i	−0.911362	−	0.662144i
$994$	179.320	−	130.283i	0.180402	−	0.131070i
$995$	97.8316	−	301.095i	0.0983232	−	0.302608i
$996$	14.3102	+	4.64966i	0.0143676	+	0.00466833i
$997$	−549.620	−	756.487i	−0.551274	−	0.758763i	0.438911	−	0.898531i	$-0.355364\pi$
$997$	−549.620	−	756.487i	−0.551274	−	0.758763i	−0.990184	+	0.139768i	$0.955364\pi$
$998$	−122.701	+	168.883i	−0.122946	+	0.169221i
$999$	29.5204	+	90.8544i	0.0295499	+	0.0909454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.3.h.a.61.4	✓	16
11.2	odd	10	inner	110.3.h.a.101.4	yes	16
11.3	even	5		1210.3.d.f.241.1		16
11.8	odd	10		1210.3.d.f.241.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.h.a.61.4	✓	16	1.1	even	1	trivial
110.3.h.a.101.4	yes	16	11.2	odd	10	inner
1210.3.d.f.241.1		16	11.3	even	5
1210.3.d.f.241.9		16	11.8	odd	10

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34500 - 0.437016i) q^{2} +(2.27262 + 1.65115i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 - 2.12663i) q^{5} +(3.77825 + 1.22763i) q^{6} +(0.859984 + 1.18367i) q^{7} +(1.66251 - 2.28825i) q^{8} +(-0.342665 - 1.05461i) q^{9} +O(q^{10})\)	\(q+(1.34500 - 0.437016i) q^{2} +(2.27262 + 1.65115i) q^{3} +(1.61803 - 1.17557i) q^{4} +(0.690983 - 2.12663i) q^{5} +(3.77825 + 1.22763i) q^{6} +(0.859984 + 1.18367i) q^{7} +(1.66251 - 2.28825i) q^{8} +(-0.342665 - 1.05461i) q^{9} -3.16228i q^{10} +(2.69824 + 10.6639i) q^{11} +5.61822 q^{12} +(-7.50754 + 2.43935i) q^{13} +(1.67396 + 1.21620i) q^{14} +(5.08173 - 3.69209i) q^{15} +(1.23607 - 3.80423i) q^{16} +(-7.18045 - 2.33307i) q^{17} +(-0.921767 - 1.26870i) q^{18} +(-0.318363 + 0.438189i) q^{19} +(-1.38197 - 4.25325i) q^{20} +4.10999i q^{21} +(8.28944 + 13.1638i) q^{22} -21.5560 q^{23} +(7.55650 - 2.45525i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(-9.03159 + 6.56183i) q^{26} +(8.77516 - 27.0072i) q^{27} +(2.78297 + 0.904241i) q^{28} +(-14.6579 - 20.1748i) q^{29} +(5.22141 - 7.18665i) q^{30} +(1.82371 + 5.61280i) q^{31} -5.65685i q^{32} +(-11.4757 + 28.6903i) q^{33} -10.6773 q^{34} +(3.11145 - 1.01097i) q^{35} +(-1.79422 - 1.30358i) q^{36} +(-2.72160 + 1.97736i) q^{37} +(-0.236701 + 0.728492i) q^{38} +(-21.0895 - 6.85240i) q^{39} +(-3.71748 - 5.11667i) q^{40} +(-21.0666 + 28.9957i) q^{41} +(1.79613 + 5.52792i) q^{42} +65.2759i q^{43} +(16.9021 + 14.0826i) q^{44} -2.47955 q^{45} +(-28.9928 + 9.42032i) q^{46} +(-24.9072 - 18.0961i) q^{47} +(9.09048 - 6.60462i) q^{48} +(14.4803 - 44.5659i) q^{49} +(-6.72499 - 2.18508i) q^{50} +(-12.4662 - 17.1582i) q^{51} +(-9.27983 + 12.7726i) q^{52} +(17.3581 + 53.4228i) q^{53} -40.1594i q^{54} +(24.5426 + 1.63044i) q^{55} +4.13825 q^{56} +(-1.44703 + 0.470170i) q^{57} +(-28.5315 - 20.7294i) q^{58} +(89.8231 - 65.2603i) q^{59} +(3.88210 - 11.9479i) q^{60} +(-7.44578 - 2.41928i) q^{61} +(4.90577 + 6.75221i) q^{62} +(0.953625 - 1.31255i) q^{63} +(-2.47214 - 7.60845i) q^{64} +17.6513i q^{65} +(-2.89671 + 43.6034i) q^{66} +36.7187 q^{67} +(-14.3609 + 4.66614i) q^{68} +(-48.9886 - 35.5923i) q^{69} +(3.74308 - 2.71951i) q^{70} +(33.1029 - 101.880i) q^{71} +(-2.98290 - 0.969203i) q^{72} +(81.3232 + 111.932i) q^{73} +(-2.79641 + 3.84893i) q^{74} +(-4.34032 - 13.3581i) q^{75} +1.08326i q^{76} +(-10.3021 + 12.3646i) q^{77} -31.3600 q^{78} +(89.3392 - 29.0281i) q^{79} +(-7.23607 - 5.25731i) q^{80} +(56.4616 - 41.0218i) q^{81} +(-15.6629 + 48.2055i) q^{82} +(2.54710 + 0.827603i) q^{83} +(4.83158 + 6.65010i) q^{84} +(-9.92314 + 13.6580i) q^{85} +(28.5266 + 87.7959i) q^{86} -70.0522i q^{87} +(28.8875 + 11.5546i) q^{88} -3.30755 q^{89} +(-3.33498 + 1.08360i) q^{90} +(-9.34374 - 6.78862i) q^{91} +(-34.8783 + 25.3406i) q^{92} +(-5.12300 + 15.7670i) q^{93} +(-41.4084 - 13.4544i) q^{94} +(0.711881 + 0.979820i) q^{95} +(9.34034 - 12.8559i) q^{96} +(47.6046 + 146.512i) q^{97} -66.2691i q^{98} +(10.3217 - 6.49976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{3} + 8 q^{4} + 20 q^{5} + 20 q^{6} + 10 q^{7} - 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^3 + 8 * q^4 + 20 * q^5 + 20 * q^6 + 10 * q^7 - 10 * q^9	\( 16 q - 6 q^{3} + 8 q^{4} + 20 q^{5} + 20 q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{11} - 48 q^{12} + 40 q^{13} - 4 q^{14} - 30 q^{15} - 16 q^{16} + 70 q^{17} + 30 q^{19} - 40 q^{20} + 40 q^{22} - 12 q^{23} + 40 q^{24} - 20 q^{25} + 40 q^{26} - 72 q^{27} - 40 q^{28} + 30 q^{29} + 40 q^{30} - 68 q^{31} + 106 q^{33} - 176 q^{34} + 20 q^{36} - 136 q^{37} - 140 q^{38} - 110 q^{39} + 24 q^{42} + 20 q^{44} + 120 q^{46} - 216 q^{47} - 24 q^{48} + 6 q^{49} - 130 q^{51} - 20 q^{52} + 54 q^{53} + 70 q^{55} - 32 q^{56} + 210 q^{57} + 32 q^{58} - 130 q^{59} - 60 q^{60} - 180 q^{61} + 340 q^{62} + 430 q^{63} + 32 q^{64} + 128 q^{66} + 148 q^{67} + 140 q^{68} + 34 q^{69} - 20 q^{70} - 12 q^{71} - 80 q^{72} - 230 q^{73} + 240 q^{74} - 30 q^{75} + 400 q^{77} - 392 q^{78} + 190 q^{79} - 80 q^{80} - 64 q^{81} - 184 q^{82} + 230 q^{83} + 300 q^{84} + 100 q^{85} + 204 q^{86} - 80 q^{88} - 16 q^{89} - 40 q^{90} - 100 q^{91} - 56 q^{92} - 34 q^{93} - 320 q^{94} + 90 q^{95} - 304 q^{97} - 552 q^{99}+O(q^{100}) \) 16 * q - 6 * q^3 + 8 * q^4 + 20 * q^5 + 20 * q^6 + 10 * q^7 - 10 * q^9 - 10 * q^11 - 48 * q^12 + 40 * q^13 - 4 * q^14 - 30 * q^15 - 16 * q^16 + 70 * q^17 + 30 * q^19 - 40 * q^20 + 40 * q^22 - 12 * q^23 + 40 * q^24 - 20 * q^25 + 40 * q^26 - 72 * q^27 - 40 * q^28 + 30 * q^29 + 40 * q^30 - 68 * q^31 + 106 * q^33 - 176 * q^34 + 20 * q^36 - 136 * q^37 - 140 * q^38 - 110 * q^39 + 24 * q^42 + 20 * q^44 + 120 * q^46 - 216 * q^47 - 24 * q^48 + 6 * q^49 - 130 * q^51 - 20 * q^52 + 54 * q^53 + 70 * q^55 - 32 * q^56 + 210 * q^57 + 32 * q^58 - 130 * q^59 - 60 * q^60 - 180 * q^61 + 340 * q^62 + 430 * q^63 + 32 * q^64 + 128 * q^66 + 148 * q^67 + 140 * q^68 + 34 * q^69 - 20 * q^70 - 12 * q^71 - 80 * q^72 - 230 * q^73 + 240 * q^74 - 30 * q^75 + 400 * q^77 - 392 * q^78 + 190 * q^79 - 80 * q^80 - 64 * q^81 - 184 * q^82 + 230 * q^83 + 300 * q^84 + 100 * q^85 + 204 * q^86 - 80 * q^88 - 16 * q^89 - 40 * q^90 - 100 * q^91 - 56 * q^92 - 34 * q^93 - 320 * q^94 + 90 * q^95 - 304 * q^97 - 552 * q^99

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