LMFDB - Embedded newform 74.3.g.b.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,3,Mod(23,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("74.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	74.g (of order $12$, 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:	$2.01635395627$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 82x^{10} + 2505x^{8} + 34456x^{6} + 196096x^{4} + 262464x^{2} + 69696 $ x^12 + 82x^10 + 2505x^8 + 34456x^6 + 196096x^4 + 262464*x^2 + 69696
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.1
Root			$-3.64005i$ of defining polynomial
Character	$\chi$	$=$	74.23
Dual form			74.3.g.b.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(-3.15238 + 1.82002i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 + 3.23205i) q^{5} +(-3.64005 - 3.64005i) q^{6} +(-5.59738 - 9.69495i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.12498 - 3.68058i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(-3.15238 + 1.82002i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 + 3.23205i) q^{5} +(-3.64005 - 3.64005i) q^{6} +(-5.59738 - 9.69495i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.12498 - 3.68058i) q^{9} -4.73205 q^{10} +17.4995i q^{11} +(3.64005 - 6.30475i) q^{12} +(-5.11981 + 19.1074i) q^{13} +(11.1948 - 11.1948i) q^{14} +(-3.15238 - 11.7648i) q^{15} +(2.00000 - 3.46410i) q^{16} +(16.2014 - 4.34116i) q^{17} +(5.80556 + 1.55559i) q^{18} +(1.67724 - 6.25956i) q^{19} +(-1.73205 - 6.46410i) q^{20} +(35.2901 + 20.3748i) q^{21} +(-23.9048 + 6.40527i) q^{22} +(2.09462 + 2.09462i) q^{23} +(9.94480 + 2.66470i) q^{24} +(11.9545 + 6.90192i) q^{25} -27.9752 q^{26} -17.2904i q^{27} +(19.3899 + 11.1948i) q^{28} +(-28.8094 + 28.8094i) q^{29} +(14.9172 - 8.61245i) q^{30} +(-4.29768 + 4.29768i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-31.8496 - 55.1650i) q^{33} +(11.8603 + 20.5426i) q^{34} +(36.1820 - 9.69495i) q^{35} +8.49993i q^{36} +(-10.2486 + 35.5523i) q^{37} +9.16463 q^{38} +(-18.6364 - 69.5519i) q^{39} +(8.19615 - 4.73205i) q^{40} +(42.0018 - 24.2498i) q^{41} +(-14.9154 + 55.6649i) q^{42} +(-22.4138 - 22.4138i) q^{43} +(-17.4995 - 30.3101i) q^{44} +(10.0555 + 10.0555i) q^{45} +(-2.09462 + 3.62799i) q^{46} -13.2879 q^{47} +14.5602i q^{48} +(-38.1614 + 66.0974i) q^{49} +(-5.05256 + 18.8564i) q^{50} +(-43.1720 + 43.1720i) q^{51} +(-10.2396 - 38.2148i) q^{52} +(41.2891 - 71.5148i) q^{53} +(23.6191 - 6.32872i) q^{54} +(-56.5593 - 15.1550i) q^{55} +(-8.19514 + 30.5847i) q^{56} +(6.10525 + 22.7851i) q^{57} +(-49.8994 - 28.8094i) q^{58} +(4.02075 - 1.07736i) q^{59} +(17.2249 + 17.2249i) q^{60} +(23.2395 + 6.22701i) q^{61} +(-7.44381 - 4.29768i) q^{62} -47.5773 q^{63} +8.00000i q^{64} +(-57.3222 - 33.0950i) q^{65} +(63.6991 - 63.6991i) q^{66} +(-12.5276 + 7.23280i) q^{67} +(-23.7205 + 23.7205i) q^{68} +(-10.4153 - 2.79077i) q^{69} +(26.4871 + 45.8770i) q^{70} +(54.7866 + 94.8932i) q^{71} +(-11.6111 + 3.11119i) q^{72} -47.0811i q^{73} +(-52.3166 - 0.986866i) q^{74} -50.2467 q^{75} +(3.35449 + 12.5191i) q^{76} +(169.657 - 97.9515i) q^{77} +(88.1882 - 50.9155i) q^{78} +(-39.2697 + 146.556i) q^{79} +(9.46410 + 9.46410i) q^{80} +(50.5937 + 87.6309i) q^{81} +(48.4995 + 48.4995i) q^{82} +(16.4232 - 28.4457i) q^{83} -81.4990 q^{84} +56.1234i q^{85} +(22.4138 - 38.8218i) q^{86} +(38.3842 - 143.252i) q^{87} +(34.9990 - 34.9990i) q^{88} +(-12.0761 - 45.0687i) q^{89} +(-10.0555 + 17.4167i) q^{90} +(213.903 - 57.3151i) q^{91} +(-5.72261 - 1.53337i) q^{92} +(5.72602 - 21.3698i) q^{93} +(-4.86372 - 18.1516i) q^{94} +(18.7787 + 10.8419i) q^{95} +(-19.8896 + 5.32940i) q^{96} +(-50.0503 - 50.0503i) q^{97} +(-104.259 - 27.9361i) q^{98} +(64.4083 + 37.1861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 + 4 * q^6 - 8 * q^7 - 24 * q^8 + 28 * q^9	\( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9} - 36 q^{10} - 4 q^{12} + 16 q^{13} + 16 q^{14} + 24 q^{16} + 40 q^{17} + 28 q^{18} - 26 q^{19} + 66 q^{21} + 4 q^{22} - 80 q^{23} - 4 q^{24} - 54 q^{25} - 124 q^{26} - 12 q^{28} + 16 q^{29} - 6 q^{30} - 32 q^{31} + 24 q^{32} - 20 q^{33} - 10 q^{34} + 12 q^{35} - 148 q^{37} + 92 q^{38} + 216 q^{39} + 36 q^{40} + 66 q^{41} - 46 q^{42} + 152 q^{43} - 16 q^{44} + 84 q^{45} + 80 q^{46} - 112 q^{47} - 160 q^{49} + 168 q^{50} - 446 q^{51} + 32 q^{52} + 74 q^{53} + 230 q^{54} + 28 q^{56} + 50 q^{57} + 84 q^{58} - 114 q^{59} - 12 q^{60} + 448 q^{61} - 204 q^{62} - 784 q^{63} - 138 q^{65} + 40 q^{66} + 468 q^{67} + 20 q^{68} - 278 q^{69} + 18 q^{70} + 116 q^{71} - 56 q^{72} - 2 q^{74} + 76 q^{75} - 52 q^{76} + 60 q^{77} - 366 q^{78} + 114 q^{79} + 72 q^{80} + 14 q^{81} + 128 q^{82} - 20 q^{83} - 80 q^{84} - 152 q^{86} + 770 q^{87} + 32 q^{88} + 340 q^{89} - 84 q^{90} + 792 q^{91} + 68 q^{92} - 498 q^{93} + 20 q^{94} + 60 q^{95} + 8 q^{96} - 356 q^{97} - 160 q^{98} - 348 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 4 * q^6 - 8 * q^7 - 24 * q^8 + 28 * q^9 - 36 * q^10 - 4 * q^12 + 16 * q^13 + 16 * q^14 + 24 * q^16 + 40 * q^17 + 28 * q^18 - 26 * q^19 + 66 * q^21 + 4 * q^22 - 80 * q^23 - 4 * q^24 - 54 * q^25 - 124 * q^26 - 12 * q^28 + 16 * q^29 - 6 * q^30 - 32 * q^31 + 24 * q^32 - 20 * q^33 - 10 * q^34 + 12 * q^35 - 148 * q^37 + 92 * q^38 + 216 * q^39 + 36 * q^40 + 66 * q^41 - 46 * q^42 + 152 * q^43 - 16 * q^44 + 84 * q^45 + 80 * q^46 - 112 * q^47 - 160 * q^49 + 168 * q^50 - 446 * q^51 + 32 * q^52 + 74 * q^53 + 230 * q^54 + 28 * q^56 + 50 * q^57 + 84 * q^58 - 114 * q^59 - 12 * q^60 + 448 * q^61 - 204 * q^62 - 784 * q^63 - 138 * q^65 + 40 * q^66 + 468 * q^67 + 20 * q^68 - 278 * q^69 + 18 * q^70 + 116 * q^71 - 56 * q^72 - 2 * q^74 + 76 * q^75 - 52 * q^76 + 60 * q^77 - 366 * q^78 + 114 * q^79 + 72 * q^80 + 14 * q^81 + 128 * q^82 - 20 * q^83 - 80 * q^84 - 152 * q^86 + 770 * q^87 + 32 * q^88 + 340 * q^89 - 84 * q^90 + 792 * q^91 + 68 * q^92 - 498 * q^93 + 20 * q^94 + 60 * q^95 + 8 * q^96 - 356 * q^97 - 160 * q^98 - 348 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$3$	−3.15238	+	1.82002i	−1.05079	+	0.606675i	−0.922871	−	0.385109i	$-0.874164\pi$
$3$	−3.15238	+	1.82002i	−1.05079	+	0.606675i	−0.127921	+	0.991784i	$0.540830\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−0.866025	+	3.23205i	−0.173205	+	0.646410i	0.823645	+	0.567105i	$0.191937\pi$
$5$	−0.866025	+	3.23205i	−0.173205	+	0.646410i	−0.996850	+	0.0793049i	$0.974730\pi$
$6$	−3.64005	−	3.64005i	−0.606675	−	0.606675i
$7$	−5.59738	−	9.69495i	−0.799626	−	1.38499i	−0.919860	−	0.392247i	$-0.871698\pi$
$7$	−5.59738	−	9.69495i	−0.799626	−	1.38499i	0.120234	−	0.992746i	$-0.461636\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	2.12498	−	3.68058i	0.236109	−	0.408953i
$10$	−4.73205			−0.473205
$11$			17.4995i			1.59087i	0.606042	+	0.795433i	$0.292756\pi$
$11$			17.4995i			1.59087i	−0.606042	+	0.795433i	$0.707244\pi$
$12$	3.64005	−	6.30475i	0.303337	−	0.525396i
$13$	−5.11981	+	19.1074i	−0.393832	+	1.46980i	0.429930	+	0.902862i	$0.358538\pi$
$13$	−5.11981	+	19.1074i	−0.393832	+	1.46980i	−0.823761	+	0.566937i	$0.808128\pi$
$14$	11.1948	−	11.1948i	0.799626	−	0.799626i
$15$	−3.15238	−	11.7648i	−0.210158	−	0.784322i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	16.2014	−	4.34116i	0.953025	−	0.255362i	0.251379	−	0.967889i	$-0.419116\pi$
$17$	16.2014	−	4.34116i	0.953025	−	0.255362i	0.701645	+	0.712526i	$0.252449\pi$
$18$	5.80556	+	1.55559i	0.322531	+	0.0864219i
$19$	1.67724	−	6.25956i	0.0882760	−	0.329450i	−0.907638	−	0.419753i	$-0.862117\pi$
$19$	1.67724	−	6.25956i	0.0882760	−	0.329450i	0.995914	+	0.0903025i	$0.0287834\pi$
$20$	−1.73205	−	6.46410i	−0.0866025	−	0.323205i
$21$	35.2901	+	20.3748i	1.68048	+	0.970226i
$22$	−23.9048	+	6.40527i	−1.08658	+	0.291149i
$23$	2.09462	+	2.09462i	0.0910704	+	0.0910704i	0.751174	−	0.660104i	$-0.229488\pi$
$23$	2.09462	+	2.09462i	0.0910704	+	0.0910704i	−0.660104	+	0.751174i	$0.729488\pi$
$24$	9.94480	+	2.66470i	0.414367	+	0.111029i
$25$	11.9545	+	6.90192i	0.478179	+	0.276077i
$26$	−27.9752			−1.07597
$27$		−	17.2904i		−	0.640384i
$28$	19.3899	+	11.1948i	0.692496	+	0.399813i
$29$	−28.8094	+	28.8094i	−0.993428	+	0.993428i	−0.999979	−	0.00655068i	$-0.997915\pi$
$29$	−28.8094	+	28.8094i	−0.993428	+	0.993428i	0.00655068	+	0.999979i	$0.497915\pi$
$30$	14.9172	−	8.61245i	0.497240	−	0.287082i
$31$	−4.29768	+	4.29768i	−0.138635	+	0.138635i	−0.773018	−	0.634383i	$-0.781254\pi$
$31$	−4.29768	+	4.29768i	−0.138635	+	0.138635i	0.634383	+	0.773018i	$0.281254\pi$
$32$	5.46410	+	1.46410i	0.170753	+	0.0457532i
$33$	−31.8496	−	55.1650i	−0.965138	−	1.67167i
$34$	11.8603	+	20.5426i	0.348831	+	0.604194i
$35$	36.1820	−	9.69495i	1.03377	−	0.276999i
$36$			8.49993i			0.236109i
$37$	−10.2486	+	35.5523i	−0.276990	+	0.960873i
$37$	−10.2486	+	35.5523i	−0.276990	+	0.960873i
$38$	9.16463			0.241174
$39$	−18.6364	−	69.5519i	−0.477855	−	1.78338i
$40$	8.19615	−	4.73205i	0.204904	−	0.118301i
$41$	42.0018	−	24.2498i	1.02443	−	0.591458i	0.109049	−	0.994036i	$-0.465219\pi$
$41$	42.0018	−	24.2498i	1.02443	−	0.591458i	0.915385	+	0.402579i	$0.131886\pi$
$42$	−14.9154	+	55.6649i	−0.355127	+	1.32535i
$43$	−22.4138	−	22.4138i	−0.521250	−	0.521250i	0.396699	−	0.917949i	$-0.370156\pi$
$43$	−22.4138	−	22.4138i	−0.521250	−	0.521250i	−0.917949	+	0.396699i	$0.870156\pi$
$44$	−17.4995	−	30.3101i	−0.397716	−	0.688865i
$45$	10.0555	+	10.0555i	0.223456	+	0.223456i
$46$	−2.09462	+	3.62799i	−0.0455352	+	0.0788693i
$47$	−13.2879			−0.282722			−0.141361	−	0.989958i	$-0.545148\pi$
$47$	−13.2879			−0.282722			−0.141361	+	0.989958i	$0.545148\pi$
$48$			14.5602i			0.303337i
$49$	−38.1614	+	66.0974i	−0.778804	+	1.34893i
$50$	−5.05256	+	18.8564i	−0.101051	+	0.377128i
$51$	−43.1720	+	43.1720i	−0.846509	+	0.846509i
$52$	−10.2396	−	38.2148i	−0.196916	−	0.734900i
$53$	41.2891	−	71.5148i	0.779039	−	1.34934i	−0.153457	−	0.988155i	$-0.549041\pi$
$53$	41.2891	−	71.5148i	0.779039	−	1.34934i	0.932496	−	0.361180i	$-0.117626\pi$
$54$	23.6191	−	6.32872i	0.437390	−	0.117198i
$55$	−56.5593	−	15.1550i	−1.02835	−	0.275546i
$56$	−8.19514	+	30.5847i	−0.146342	+	0.546155i
$57$	6.10525	+	22.7851i	0.107110	+	0.399739i
$58$	−49.8994	−	28.8094i	−0.860334	−	0.496714i
$59$	4.02075	−	1.07736i	0.0681483	−	0.0182603i	−0.224584	−	0.974455i	$-0.572102\pi$
$59$	4.02075	−	1.07736i	0.0681483	−	0.0182603i	0.292732	+	0.956195i	$0.405436\pi$
$60$	17.2249	+	17.2249i	0.287082	+	0.287082i
$61$	23.2395	+	6.22701i	0.380976	+	0.102082i	0.444224	−	0.895916i	$-0.353479\pi$
$61$	23.2395	+	6.22701i	0.380976	+	0.102082i	−0.0632483	+	0.997998i	$0.520146\pi$
$62$	−7.44381	−	4.29768i	−0.120061	−	0.0693175i
$63$	−47.5773			−0.755196
$64$			8.00000i			0.125000i
$65$	−57.3222	−	33.0950i	−0.881880	−	0.509153i
$66$	63.6991	−	63.6991i	0.965138	−	0.965138i
$67$	−12.5276	+	7.23280i	−0.186979	+	0.107952i	−0.590567	−	0.806988i	$-0.701096\pi$
$67$	−12.5276	+	7.23280i	−0.186979	+	0.107952i	0.403589	+	0.914941i	$0.367763\pi$
$68$	−23.7205	+	23.7205i	−0.348831	+	0.348831i
$69$	−10.4153	−	2.79077i	−0.150946	−	0.0404459i
$70$	26.4871	+	45.8770i	0.378387	+	0.655386i
$71$	54.7866	+	94.8932i	0.771643	+	1.33652i	0.936662	+	0.350234i	$0.113898\pi$
$71$	54.7866	+	94.8932i	0.771643	+	1.33652i	−0.165019	+	0.986290i	$0.552769\pi$
$72$	−11.6111	+	3.11119i	−0.161265	+	0.0432110i
$73$		−	47.0811i		−	0.644946i	−0.946579	−	0.322473i	$-0.895486\pi$
$73$		−	47.0811i		−	0.644946i	0.946579	−	0.322473i	$-0.104514\pi$
$74$	−52.3166	−	0.986866i	−0.706981	−	0.0133360i
$75$	−50.2467			−0.669956
$76$	3.35449	+	12.5191i	0.0441380	+	0.164725i
$77$	169.657	−	97.9515i	2.20334	−	1.27210i
$78$	88.1882	−	50.9155i	1.13062	−	0.652763i
$79$	−39.2697	+	146.556i	−0.497085	+	1.85515i	0.0209413	+	0.999781i	$0.493334\pi$
$79$	−39.2697	+	146.556i	−0.497085	+	1.85515i	−0.518026	+	0.855365i	$0.673333\pi$
$80$	9.46410	+	9.46410i	0.118301	+	0.118301i
$81$	50.5937	+	87.6309i	0.624614	+	1.08186i
$82$	48.4995	+	48.4995i	0.591458	+	0.591458i
$83$	16.4232	−	28.4457i	0.197869	−	0.342720i	−0.749968	−	0.661474i	$-0.769931\pi$
$83$	16.4232	−	28.4457i	0.197869	−	0.342720i	0.947837	+	0.318754i	$0.103265\pi$
$84$	−81.4990			−0.970226
$85$			56.1234i			0.660275i
$86$	22.4138	−	38.8218i	0.260625	−	0.451416i
$87$	38.3842	−	143.252i	0.441198	−	1.64657i
$88$	34.9990	−	34.9990i	0.397716	−	0.397716i
$89$	−12.0761	−	45.0687i	−0.135687	−	0.506390i	−0.999994	−	0.00342574i	$-0.998910\pi$
$89$	−12.0761	−	45.0687i	−0.135687	−	0.506390i	0.864307	−	0.502964i	$-0.167757\pi$
$90$	−10.0555	+	17.4167i	−0.111728	+	0.193519i
$91$	213.903	−	57.3151i	2.35058	−	0.629836i
$92$	−5.72261	−	1.53337i	−0.0622023	−	0.0166670i
$93$	5.72602	−	21.3698i	0.0615701	−	0.229783i
$94$	−4.86372	−	18.1516i	−0.0517417	−	0.193103i
$95$	18.7787	+	10.8419i	0.197670	+	0.114125i
$96$	−19.8896	+	5.32940i	−0.207183	+	0.0555146i
$97$	−50.0503	−	50.0503i	−0.515982	−	0.515982i	0.400371	−	0.916353i	$-0.368881\pi$
$97$	−50.0503	−	50.0503i	−0.515982	−	0.515982i	−0.916353	+	0.400371i	$0.868881\pi$
$98$	−104.259	−	27.9361i	−1.06387	−	0.285062i
$99$	64.4083	+	37.1861i	0.650589	+	0.375618i
$100$	−27.6077			−0.276077
$101$			111.686i			1.10580i	0.833247	+	0.552901i	$0.186479\pi$
$101$			111.686i			1.10580i	−0.833247	+	0.552901i	$0.813521\pi$
$102$	−74.7760	−	43.1720i	−0.733098	−	0.423254i
$103$	−0.946984	+	0.946984i	−0.00919402	+	0.00919402i	−0.711689	−	0.702495i	$-0.752069\pi$
$103$	−0.946984	+	0.946984i	−0.00919402	+	0.00919402i	0.702495	+	0.711689i	$0.252069\pi$
$104$	48.4544	−	27.9752i	0.465908	−	0.268992i
$105$	−96.4144	+	96.4144i	−0.918232	+	0.918232i
$106$	112.804	+	30.2257i	1.06419	+	0.285148i
$107$	−10.8856	−	18.8543i	−0.101734	−	0.176209i	0.810665	−	0.585510i	$-0.199106\pi$
$107$	−10.8856	−	18.8543i	−0.101734	−	0.176209i	−0.912399	+	0.409301i	$0.865772\pi$
$108$	17.2904	+	29.9478i	0.160096	+	0.277294i
$109$	−13.5837	+	3.63975i	−0.124621	+	0.0333922i	−0.320591	−	0.947218i	$-0.603881\pi$
$109$	−13.5837	+	3.63975i	−0.124621	+	0.0333922i	0.195969	+	0.980610i	$0.437215\pi$
$110$		−	82.8086i		−	0.752805i
$111$	−32.3985	−	130.727i	−0.291878	−	1.17772i
$112$	−44.7791			−0.399813
$113$	18.5652	+	69.2862i	0.164294	+	0.613152i	0.998129	+	0.0611392i	$0.0194734\pi$
$113$	18.5652	+	69.2862i	0.164294	+	0.613152i	−0.833836	+	0.552013i	$0.813860\pi$
$114$	−28.8903	+	16.6799i	−0.253424	+	0.146314i
$115$	−8.58391	+	4.95592i	−0.0746427	+	0.0430950i
$116$	21.0900	−	78.7088i	0.181810	−	0.678524i
$117$	59.4467	+	59.4467i	0.508091	+	0.508091i
$118$	2.94339	+	5.09810i	0.0249440	+	0.0432043i
$119$	−132.773	−	132.773i	−1.11574	−	1.11574i
$120$	−17.2249	+	29.8344i	−0.143541	+	0.248620i
$121$	−185.233			−1.53085
$122$			34.0250i			0.278894i
$123$	−88.2704	+	152.889i	−0.717645	+	1.24300i
$124$	3.14612	−	11.7415i	0.0253720	−	0.0946895i
$125$	−91.8109	+	91.8109i	−0.734487	+	0.734487i
$126$	−17.4145	−	64.9918i	−0.138210	−	0.515808i
$127$	−64.5013	+	111.719i	−0.507884	+	0.879681i	0.492074	+	0.870553i	$0.336239\pi$
$127$	−64.5013	+	111.719i	−0.507884	+	0.879681i	−0.999958	+	0.00912775i	$0.997095\pi$
$128$	−10.9282	+	2.92820i	−0.0853766	+	0.0228766i
$129$	111.450	+	29.8630i	0.863955	+	0.231496i
$130$	24.2272	−	90.4171i	0.186363	−	0.695517i
$131$	29.6667	+	110.717i	0.226463	+	0.845171i	0.981813	+	0.189850i	$0.0608002\pi$
$131$	29.6667	+	110.717i	0.226463	+	0.845171i	−0.755350	+	0.655321i	$0.772533\pi$
$132$	110.330	+	63.6991i	0.835834	+	0.482569i
$133$	−70.0743	+	18.7763i	−0.526874	+	0.141176i
$134$	−14.4656	−	14.4656i	−0.107952	−	0.107952i
$135$	55.8834	+	14.9739i	0.413951	+	0.110918i
$136$	−41.0852	−	23.7205i	−0.302097	−	0.174416i
$137$	185.200			1.35183			0.675914	−	0.736981i	$-0.263749\pi$
$137$	185.200			1.35183			0.675914	+	0.736981i	$0.263749\pi$
$138$		−	15.2490i		−	0.110500i
$139$	200.316	+	115.653i	1.44112	+	0.832034i	0.997925	−	0.0643890i	$-0.0205098\pi$
$139$	200.316	+	115.653i	1.44112	+	0.832034i	0.443200	+	0.896423i	$0.353843\pi$
$140$	−52.9742	+	52.9742i	−0.378387	+	0.378387i
$141$	41.8885	−	24.1844i	0.297082	−	0.171520i
$142$	−109.573	+	109.573i	−0.771643	+	0.771643i
$143$	−334.370	−	89.5942i	−2.33825	−	0.626533i
$144$	−8.49993	−	14.7223i	−0.0590273	−	0.102238i
$145$	−68.1638	−	118.063i	−0.470095	−	0.814229i
$146$	64.3139	−	17.2329i	0.440506	−	0.118033i
$147$		−	277.819i		−	1.88992i
$148$	−17.8011	−	71.8270i	−0.120278	−	0.485318i
$149$	−115.914			−0.777948			−0.388974	−	0.921249i	$-0.627170\pi$
$149$	−115.914			−0.777948			−0.388974	+	0.921249i	$0.627170\pi$
$150$	−18.3916	−	68.6383i	−0.122610	−	0.457588i
$151$	100.888	−	58.2479i	0.668135	−	0.385748i	−0.127235	−	0.991873i	$-0.540610\pi$
$151$	100.888	−	58.2479i	0.668135	−	0.385748i	0.795369	+	0.606125i	$0.207277\pi$
$152$	−15.8736	+	9.16463i	−0.104432	+	0.0602936i
$153$	18.4498	−	68.8554i	0.120587	−	0.450036i
$154$	195.903	+	195.903i	1.27210	+	1.27210i
$155$	−10.1684	−	17.6122i	−0.0656028	−	0.113627i
$156$	101.831	+	101.831i	0.652763	+	0.652763i
$157$	93.8375	−	162.531i	0.597691	−	1.03523i	−0.395470	−	0.918479i	$-0.629418\pi$
$157$	93.8375	−	162.531i	0.597691	−	1.03523i	0.993161	−	0.116752i	$-0.0372484\pi$
$158$	−214.574			−1.35806
$159$			300.589i			1.89049i
$160$	−9.46410	+	16.3923i	−0.0591506	+	0.102452i
$161$	8.58285	−	32.0316i	0.0533096	−	0.198954i
$162$	−101.187	+	101.187i	−0.624614	+	0.624614i
$163$	−41.9851	−	156.691i	−0.257577	−	0.961292i	−0.966638	−	0.256145i	$-0.917548\pi$
$163$	−41.9851	−	156.691i	−0.257577	−	0.961292i	0.709061	−	0.705147i	$-0.249119\pi$
$164$	−48.4995	+	84.0037i	−0.295729	+	0.512217i
$165$	205.879	−	55.1650i	1.24775	−	0.334334i
$166$	44.8689	+	12.0226i	0.270294	+	0.0724252i
$167$	−11.9761	+	44.6953i	−0.0717130	+	0.267636i	−0.992468	−	0.122505i	$-0.960907\pi$
$167$	−11.9761	+	44.6953i	−0.0717130	+	0.267636i	0.920755	+	0.390141i	$0.127574\pi$
$168$	−29.8307	−	111.330i	−0.177564	−	0.662677i
$169$	−192.522	−	111.152i	−1.13918	−	0.657707i
$170$	−76.6659	+	20.5426i	−0.450976	+	0.120839i
$171$	−19.4747	−	19.4747i	−0.113887	−	0.113887i
$172$	61.2356	+	16.4080i	0.356021	+	0.0953955i
$173$	24.6561	+	14.2352i	0.142521	+	0.0822846i	0.569565	−	0.821946i	$-0.307112\pi$
$173$	24.6561	+	14.2352i	0.142521	+	0.0822846i	−0.427044	+	0.904231i	$0.640445\pi$
$174$	209.735			1.20538
$175$		−	154.531i		−	0.883033i
$176$	60.6201	+	34.9990i	0.344432	+	0.198858i
$177$	−10.7141	+	10.7141i	−0.0605316	+	0.0605316i
$178$	57.1448	−	32.9926i	0.321038	−	0.185351i
$179$	206.957	−	206.957i	1.15619	−	1.15619i	0.170897	−	0.985289i	$-0.445334\pi$
$179$	206.957	−	206.957i	1.15619	−	1.15619i	0.985289	−	0.170897i	$-0.0546665\pi$
$180$	−27.4722	−	7.36115i	−0.152623	−	0.0408953i
$181$	−176.589	−	305.861i	−0.975629	−	1.68984i	−0.677845	−	0.735205i	$-0.737086\pi$
$181$	−176.589	−	305.861i	−0.975629	−	1.68984i	−0.297784	−	0.954633i	$-0.596248\pi$
$182$	156.588	+	271.218i	0.860372	+	1.49021i
$183$	−84.5931	+	22.6666i	−0.462257	+	0.123861i
$184$		−	8.37848i		−	0.0455352i
$185$	−106.031	−	63.9133i	−0.573142	−	0.345477i
$186$	31.2876			0.168213
$187$	75.9682	+	283.517i	0.406247	+	1.51613i
$188$	23.0154	−	13.2879i	0.122422	−	0.0706805i
$189$	−167.629	+	96.7808i	−0.886927	+	0.512068i
$190$	−7.93680	+	29.6205i	−0.0417726	+	0.155898i
$191$	189.509	+	189.509i	0.992196	+	0.992196i	0.999970	−	0.00777363i	$-0.00247445\pi$
$191$	189.509	+	189.509i	0.992196	+	0.992196i	−0.00777363	+	0.999970i	$0.502474\pi$
$192$	−14.5602	−	25.2190i	−0.0758344	−	0.131349i
$193$	191.197	+	191.197i	0.990658	+	0.990658i	0.999957	−	0.00929913i	$-0.00296005\pi$
$193$	191.197	+	191.197i	0.990658	+	0.990658i	−0.00929913	+	0.999957i	$0.502960\pi$
$194$	50.0503	−	86.6896i	0.257991	−	0.446854i
$195$	240.935			1.23556
$196$		−	152.645i		−	0.778804i
$197$	−72.6283	+	125.796i	−0.368672	+	0.638558i	−0.989358	−	0.145501i	$-0.953521\pi$
$197$	−72.6283	+	125.796i	−0.368672	+	0.638558i	0.620687	+	0.784059i	$0.286854\pi$
$198$	−27.2221	+	101.594i	−0.137486	+	0.513103i
$199$	200.882	−	200.882i	1.00946	−	1.00946i	0.00950042	−	0.999955i	$-0.496976\pi$
$199$	200.882	−	200.882i	1.00946	−	1.00946i	0.999955	−	0.00950042i	$-0.00302412\pi$
$200$	−10.1051	−	37.7128i	−0.0505256	−	0.188564i
$201$	26.3277	−	45.6010i	0.130984	−	0.226871i
$202$	−152.566	+	40.8799i	−0.755277	+	0.202376i
$203$	440.563	+	118.049i	2.17026	+	0.581520i
$204$	31.6041	−	117.948i	0.154922	−	0.578176i
$205$	42.0018	+	156.753i	0.204887	+	0.764649i
$206$	−1.64022	−	0.946984i	−0.00796225	−	0.00459701i
$207$	12.1604	−	3.25838i	0.0587461	−	0.0157410i
$208$	55.9503	+	55.9503i	0.268992	+	0.268992i
$209$	109.539	+	29.3509i	0.524111	+	0.140435i
$210$	−166.995	−	96.4144i	−0.795212	−	0.459116i
$211$	−401.781			−1.90417			−0.952087	−	0.305826i	$-0.901067\pi$
$211$	−401.781			−1.90417			−0.952087	+	0.305826i	$0.901067\pi$
$212$			165.156i			0.779039i
$213$	−345.416	−	199.426i	−1.62167	−	0.936273i
$214$	21.7711	−	21.7711i	0.101734	−	0.101734i
$215$	91.8533	−	53.0315i	0.427225	−	0.246658i
$216$	−34.5807	+	34.5807i	−0.160096	+	0.160096i
$217$	65.7216	+	17.6101i	0.302865	+	0.0811523i
$218$	−9.94398	−	17.2235i	−0.0456146	−	0.0790068i
$219$	85.6887	+	148.417i	0.391273	+	0.677704i
$220$	113.119	−	30.3101i	0.514176	−	0.137773i
$221$			331.793i			1.50132i
$222$	166.718	−	92.1065i	0.750981	−	0.414894i
$223$	−122.537			−0.549492			−0.274746	−	0.961517i	$-0.588594\pi$
$223$	−122.537			−0.549492			−0.274746	+	0.961517i	$0.588594\pi$
$224$	−16.3903	−	61.1693i	−0.0731709	−	0.273077i
$225$	50.8061	−	29.3329i	0.225805	−	0.130369i
$226$	−87.8513	+	50.7210i	−0.388723	+	0.224429i
$227$	−86.5637	+	323.060i	−0.381338	+	1.42317i	0.462522	+	0.886608i	$0.346945\pi$
$227$	−86.5637	+	323.060i	−0.381338	+	1.42317i	−0.843859	+	0.536564i	$0.819722\pi$
$228$	−33.3597	−	33.3597i	−0.146314	−	0.146314i
$229$	−184.190	−	319.027i	−0.804324	−	1.39313i	−0.916747	−	0.399469i	$-0.869194\pi$
$229$	−184.190	−	319.027i	−0.804324	−	1.39313i	0.112423	−	0.993660i	$-0.464139\pi$
$230$	−9.91185	−	9.91185i	−0.0430950	−	0.0430950i
$231$	−356.548	+	617.560i	−1.54350	+	2.67342i
$232$	115.238			0.496714
$233$		−	178.031i		−	0.764082i	−0.924145	−	0.382041i	$-0.875221\pi$
$233$		−	178.031i		−	0.764082i	0.924145	−	0.382041i	$-0.124779\pi$
$234$	−59.4467	+	102.965i	−0.254046	+	0.440020i
$235$	11.5077	−	42.9473i	0.0489689	−	0.182754i
$236$	−5.88678	+	5.88678i	−0.0249440	+	0.0249440i
$237$	−142.944	−	533.473i	−0.603138	−	2.25094i
$238$	132.773	−	229.969i	0.557869	−	0.966258i
$239$	−143.454	+	38.4384i	−0.600226	+	0.160830i	−0.546123	−	0.837705i	$-0.683897\pi$
$239$	−143.454	+	38.4384i	−0.600226	+	0.160830i	−0.0541034	+	0.998535i	$0.517230\pi$
$240$	−47.0593	−	12.6095i	−0.196080	−	0.0525396i
$241$	81.4508	−	303.978i	0.337970	−	1.26132i	−0.562643	−	0.826700i	$-0.690216\pi$
$241$	81.4508	−	303.978i	0.337970	−	1.26132i	0.900613	−	0.434621i	$-0.143118\pi$
$242$	−67.8000	−	253.033i	−0.280165	−	1.04559i
$243$	−184.216	−	106.357i	−0.758090	−	0.437683i
$244$	−46.4791	+	12.4540i	−0.190488	+	0.0510411i
$245$	−180.582	−	180.582i	−0.737068	−	0.737068i
$246$	−241.159	−	64.6184i	−0.980322	−	0.262676i
$247$	111.017	+	64.0955i	0.449460	+	0.259496i
$248$	17.1907			0.0693175
$249$			119.562i			0.480169i
$250$	−159.021	−	91.8109i	−0.636084	−	0.367244i
$251$	40.6583	−	40.6583i	0.161985	−	0.161985i	−0.621460	−	0.783446i	$-0.713460\pi$
$251$	40.6583	−	40.6583i	0.161985	−	0.161985i	0.783446	+	0.621460i	$0.213460\pi$
$252$	82.4064	−	47.5773i	0.327009	−	0.188799i
$253$	−36.6548	+	36.6548i	−0.144881	+	0.144881i
$254$	−176.221	−	47.2182i	−0.693782	−	0.185898i
$255$	−102.146	−	176.922i	−0.400572	−	0.693812i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−39.8993	+	10.6910i	−0.155250	+	0.0415991i	−0.335607	−	0.942002i	$-0.608941\pi$
$257$	−39.8993	+	10.6910i	−0.155250	+	0.0415991i	0.180357	+	0.983601i	$0.442275\pi$
$258$			163.174i			0.632459i
$259$	402.043	−	99.6397i	1.55229	−	0.384709i
$260$	132.380			0.509153
$261$	44.8158	+	167.255i	0.171708	+	0.640823i
$262$	−140.384	+	81.0508i	−0.535817	+	0.309354i
$263$	85.2423	−	49.2147i	0.324115	−	0.187128i	−0.329110	−	0.944292i	$-0.606749\pi$
$263$	85.2423	−	49.2147i	0.324115	−	0.187128i	0.653225	+	0.757164i	$0.273415\pi$
$264$	−46.6310	+	174.029i	−0.176633	+	0.659202i
$265$	195.382	+	195.382i	0.737291	+	0.737291i
$266$	−51.2979	−	88.8506i	−0.192849	−	0.334025i
$267$	120.095	+	120.095i	0.449792	+	0.449792i
$268$	14.4656	−	25.0552i	0.0539761	−	0.0934894i
$269$	136.198			0.506311			0.253155	−	0.967426i	$-0.418532\pi$
$269$	136.198			0.506311			0.253155	+	0.967426i	$0.418532\pi$
$270$			81.8189i			0.303033i
$271$	5.21058	−	9.02498i	0.0192272	−	0.0333025i	−0.856252	−	0.516559i	$-0.827213\pi$
$271$	5.21058	−	9.02498i	0.0192272	−	0.0333025i	0.875479	+	0.483256i	$0.160546\pi$
$272$	17.3646	−	64.8057i	0.0638406	−	0.238256i
$273$	−569.987	+	569.987i	−2.08786	+	2.08786i
$274$	67.7880	+	252.988i	0.247402	+	0.923315i
$275$	−120.780	+	209.198i	−0.439201	+	0.760719i
$276$	20.8306	−	5.58154i	0.0754731	−	0.0202230i
$277$	236.539	+	63.3804i	0.853931	+	0.228810i	0.659127	−	0.752032i	$-0.270926\pi$
$277$	236.539	+	63.3804i	0.853931	+	0.228810i	0.194804	+	0.980842i	$0.437593\pi$
$278$	−84.6636	+	315.969i	−0.304546	+	1.13658i
$279$	6.68545	+	24.9505i	0.0239622	+	0.0894282i
$280$	−91.7540	−	52.9742i	−0.327693	−	0.189194i
$281$	429.645	−	115.123i	1.52899	−	0.409690i	0.606297	−	0.795238i	$-0.292654\pi$
$281$	429.645	−	115.123i	1.52899	−	0.409690i	0.922688	+	0.385548i	$0.125987\pi$
$282$	48.3687	+	48.3687i	0.171520	+	0.171520i
$283$	249.189	+	66.7700i	0.880527	+	0.235936i	0.670634	−	0.741788i	$-0.266022\pi$
$283$	249.189	+	66.7700i	0.880527	+	0.235936i	0.209892	+	0.977724i	$0.432689\pi$
$284$	−189.786	−	109.573i	−0.668262	−	0.385821i
$285$	−78.9299			−0.276947
$286$		−	489.552i		−	1.71172i
$287$	−470.201	−	271.470i	−1.63833	−	0.945890i
$288$	16.9999	−	16.9999i	0.0590273	−	0.0590273i
$289$	−6.64093	+	3.83414i	−0.0229790	+	0.0132669i
$290$	136.328	−	136.328i	0.470095	−	0.470095i
$291$	248.870	+	66.6845i	0.855223	+	0.229156i
$292$	47.0811	+	81.5468i	0.161237	+	0.279270i
$293$	−94.9513	−	164.461i	−0.324066	−	0.561299i	0.657257	−	0.753667i	$-0.271717\pi$
$293$	−94.9513	−	164.461i	−0.324066	−	0.561299i	−0.981323	+	0.192368i	$0.938383\pi$
$294$	379.507	−	101.689i	1.29084	−	0.345880i
$295$			13.9283i			0.0472145i
$296$	91.6019	−	50.6073i	0.309466	−	0.170971i
$297$	302.573			1.01876
$298$	−42.4276	−	158.342i	−0.142374	−	0.531348i
$299$	−50.7468	+	29.2987i	−0.169722	+	0.0979889i
$300$	87.0298	−	50.2467i	0.290099	−	0.167489i
$301$	−91.8419	+	342.759i	−0.305123	+	1.13873i
$302$	116.496	+	116.496i	0.385748	+	0.385748i
$303$	−203.271	−	352.076i	−0.670863	−	1.16197i
$304$	−18.3293	−	18.3293i	−0.0602936	−	0.0602936i
$305$	−40.2520	+	69.7186i	−0.131974	+	0.228586i
$306$	100.811			0.329449
$307$			87.9055i			0.286337i	0.989698	+	0.143169i	$0.0457291\pi$
$307$			87.9055i			0.286337i	−0.989698	+	0.143169i	$0.954271\pi$
$308$	−195.903	+	339.314i	−0.636049	+	1.10167i
$309$	1.26171	−	4.70878i	0.00408322	−	0.0152388i
$310$	20.3369	−	20.3369i	0.0656028	−	0.0656028i
$311$	70.8335	+	264.354i	0.227760	+	0.850013i	0.981280	+	0.192588i	$0.0616879\pi$
$311$	70.8335	+	264.354i	0.227760	+	0.850013i	−0.753519	+	0.657426i	$0.771645\pi$
$312$	−101.831	+	176.376i	−0.326381	+	0.565309i
$313$	162.767	−	43.6132i	0.520022	−	0.139339i	0.0107452	−	0.999942i	$-0.496580\pi$
$313$	162.767	−	43.6132i	0.520022	−	0.139339i	0.509277	+	0.860603i	$0.329913\pi$
$314$	256.369	+	68.6938i	0.816461	+	0.218770i
$315$	41.2032	−	153.772i	0.130804	−	0.488166i
$316$	−78.5394	−	293.113i	−0.248542	−	0.927573i
$317$	179.489	+	103.628i	0.566210	+	0.326902i	0.755634	−	0.654994i	$-0.227329\pi$
$317$	179.489	+	103.628i	0.566210	+	0.326902i	−0.189424	+	0.981895i	$0.560662\pi$
$318$	−410.612	+	110.023i	−1.29123	+	0.345985i
$319$	−504.151	−	504.151i	−1.58041	−	1.58041i
$320$	−25.8564	−	6.92820i	−0.0808013	−	0.0216506i
$321$	68.6307	+	39.6240i	0.213803	+	0.123439i
$322$	46.8976			0.145645
$323$		−	108.695i		−	0.336517i
$324$	−175.262	−	101.187i	−0.540932	−	0.312307i
$325$	−193.082	+	193.082i	−0.594100	+	0.594100i
$326$	198.676	−	114.705i	0.609435	−	0.351857i
$327$	36.1966	−	36.1966i	0.110693	−	0.110693i
$328$	−132.503	−	35.5041i	−0.403973	−	0.108244i
$329$	74.3776	+	128.826i	0.226072	+	0.391568i
$330$	150.714	+	261.044i	0.456708	+	0.791042i
$331$	385.148	−	103.200i	1.16359	−	0.311783i	0.375190	−	0.926948i	$-0.377577\pi$
$331$	385.148	−	103.200i	1.16359	−	0.311783i	0.788398	+	0.615165i	$0.210911\pi$
$332$			65.6926i			0.197869i
$333$	109.075	+	113.269i	0.327552	+	0.340147i
$334$	−65.4384			−0.195923
$335$	−12.5276	−	46.7535i	−0.0373957	−	0.139563i
$336$	141.160	−	81.4990i	0.420120	−	0.242557i
$337$	−144.907	+	83.6622i	−0.429992	+	0.248256i	−0.699343	−	0.714786i	$-0.746524\pi$
$337$	−144.907	+	83.6622i	−0.429992	+	0.248256i	0.269351	+	0.963042i	$0.413191\pi$
$338$	81.3692	−	303.674i	0.240737	−	0.898444i
$339$	−184.627	−	184.627i	−0.544622	−	0.544622i
$340$	−56.1234	−	97.2085i	−0.165069	−	0.285907i
$341$	−75.2074	−	75.2074i	−0.220550	−	0.220550i
$342$	19.4747	−	33.7311i	0.0569435	−	0.0986290i
$343$	305.872			0.891754
$344$			89.6551i			0.260625i
$345$	18.0398	−	31.2459i	0.0522893	−	0.0905677i
$346$	−10.4209	+	38.8914i	−0.0301183	+	0.112403i
$347$	−96.8879	+	96.8879i	−0.279216	+	0.279216i	−0.832796	−	0.553580i	$-0.813261\pi$
$347$	−96.8879	+	96.8879i	−0.279216	+	0.279216i	0.553580	+	0.832796i	$0.313261\pi$
$348$	76.7685	+	286.504i	0.220599	+	0.823287i
$349$	218.487	−	378.431i	0.626038	−	1.08433i	−0.362302	−	0.932061i	$-0.618009\pi$
$349$	218.487	−	378.431i	0.626038	−	1.08433i	0.988339	−	0.152268i	$-0.0486577\pi$
$350$	211.093	−	56.5622i	0.603123	−	0.161606i
$351$	330.374	+	88.5234i	0.941236	+	0.252203i
$352$	−25.6211	+	95.6191i	−0.0727871	+	0.271645i
$353$	38.9819	+	145.482i	0.110430	+	0.412131i	0.998905	−	0.0467952i	$-0.0149008\pi$
$353$	38.9819	+	145.482i	0.110430	+	0.412131i	−0.888474	+	0.458926i	$0.848234\pi$
$354$	−18.5573	−	10.7141i	−0.0524219	−	0.0302658i
$355$	−354.146	+	94.8932i	−0.997596	+	0.267305i
$356$	65.9851	+	65.9851i	0.185351	+	0.185351i
$357$	660.200	+	176.900i	1.84930	+	0.495518i
$358$	358.460	+	206.957i	1.00129	+	0.578093i
$359$	103.193			0.287446			0.143723	−	0.989618i	$-0.454093\pi$
$359$	103.193			0.287446			0.143723	+	0.989618i	$0.454093\pi$
$360$		−	40.2221i		−	0.111728i
$361$	276.266	+	159.502i	0.765281	+	0.441835i
$362$	353.178	−	353.178i	0.975629	−	0.975629i
$363$	583.924	−	337.129i	1.60861	−	0.928729i
$364$	−313.175	+	313.175i	−0.860372	+	0.860372i
$365$	152.168	+	40.7734i	0.416900	+	0.111708i
$366$	−61.9264	−	107.260i	−0.169198	−	0.293059i
$367$	−105.686	−	183.053i	−0.287972	−	0.498782i	0.685354	−	0.728211i	$-0.259648\pi$
$367$	−105.686	−	183.053i	−0.287972	−	0.498782i	−0.973326	+	0.229428i	$0.926314\pi$
$368$	11.4452	−	3.06674i	0.0311011	−	0.00833352i
$369$		−	206.121i		−	0.558594i
$370$	48.4971	−	168.235i	0.131073	−	0.454690i
$371$	−924.443			−2.49176
$372$	11.4520	+	42.7396i	0.0307851	+	0.114891i
$373$	−547.554	+	316.130i	−1.46797	+	0.847534i	−0.999357	−	0.0358684i	$-0.988580\pi$
$373$	−547.554	+	316.130i	−1.46797	+	0.847534i	−0.468615	+	0.883402i	$0.655247\pi$
$374$	−359.485	+	207.549i	−0.961190	+	0.554944i
$375$	122.324	−	456.521i	0.326198	−	1.21739i
$376$	26.5759	+	26.5759i	0.0706805	+	0.0706805i
$377$	−402.974	−	697.971i	−1.06890	−	1.85138i
$378$	−193.562	−	193.562i	−0.512068	−	0.512068i
$379$	−83.9680	+	145.437i	−0.221551	+	0.383738i	−0.955279	−	0.295705i	$-0.904445\pi$
$379$	−83.9680	+	145.437i	−0.221551	+	0.383738i	0.733728	+	0.679444i	$0.237779\pi$
$380$	−43.3675			−0.114125
$381$		−	469.576i		−	1.23248i
$382$	−189.509	+	328.240i	−0.496098	+	0.859267i
$383$	−11.1402	+	41.5758i	−0.0290867	+	0.108553i	−0.978943	−	0.204134i	$-0.934562\pi$
$383$	−11.1402	+	41.5758i	−0.0290867	+	0.108553i	0.949856	+	0.312687i	$0.101229\pi$
$384$	29.1204	−	29.1204i	0.0758344	−	0.0758344i
$385$	169.657	+	633.168i	0.440667	+	1.64459i
$386$	−191.197	+	331.163i	−0.495329	+	0.857935i
$387$	−130.124	+	34.8667i	−0.336239	+	0.0900949i
$388$	136.740	+	36.6393i	0.352422	+	0.0944313i
$389$	−10.7975	+	40.2970i	−0.0277572	+	0.103591i	−0.978415	−	0.206651i	$-0.933744\pi$
$389$	−10.7975	+	40.2970i	−0.0277572	+	0.103591i	0.950658	+	0.310242i	$0.100410\pi$
$390$	88.1882	+	329.123i	0.226124	+	0.843905i
$391$	43.0289	+	24.8427i	0.110048	+	0.0635364i
$392$	208.518	−	55.8721i	0.531933	−	0.142531i
$393$	−295.029	−	295.029i	−0.750710	−	0.750710i
$394$	−198.424	−	53.1676i	−0.503615	−	0.134943i
$395$	−439.669	−	253.843i	−1.11309	−	0.642641i
$396$	−148.745			−0.375618
$397$			275.702i			0.694465i	0.937779	+	0.347232i	$0.112878\pi$
$397$			275.702i			0.694465i	−0.937779	+	0.347232i	$0.887122\pi$
$398$	347.937	+	200.882i	0.874214	+	0.504728i
$399$	186.727	−	186.727i	0.467987	−	0.467987i
$400$	47.8179	−	27.6077i	0.119545	−	0.0690192i
$401$	−88.7433	+	88.7433i	−0.221305	+	0.221305i	−0.809048	−	0.587743i	$-0.800017\pi$
$401$	−88.7433	+	88.7433i	−0.221305	+	0.221305i	0.587743	+	0.809048i	$0.300017\pi$
$402$	71.9287	+	19.2732i	0.178927	+	0.0479434i
$403$	−60.1142	−	104.121i	−0.149167	−	0.258364i
$404$	−111.686	−	193.446i	−0.276451	−	0.478826i
$405$	−327.043	+	87.6309i	−0.807514	+	0.216373i
$406$			645.029i			1.58874i
$407$	−622.148	−	179.346i	−1.52862	−	0.440654i
$408$	172.688			0.423254
$409$	119.514	+	446.031i	0.292209	+	1.09054i	0.943408	+	0.331633i	$0.107600\pi$
$409$	119.514	+	446.031i	0.292209	+	1.09054i	−0.651199	+	0.758907i	$0.725734\pi$
$410$	−198.755	+	114.751i	−0.484768	+	0.279881i
$411$	−583.821	+	337.069i	−1.42049	+	0.820120i
$412$	0.693240	−	2.58721i	0.00168262	−	0.00627963i
$413$	−32.9506	−	32.9506i	−0.0797835	−	0.0797835i
$414$	8.90206	+	15.4188i	0.0215026	+	0.0372435i
$415$	77.7152	+	77.7152i	0.187266	+	0.187266i
$416$	−55.9503	+	96.9088i	−0.134496	+	0.232954i
$417$	−841.963			−2.01910
$418$			160.377i			0.383676i
$419$	190.205	−	329.445i	0.453951	−	0.786266i	−0.544676	−	0.838646i	$-0.683347\pi$
$419$	190.205	−	329.445i	0.453951	−	0.786266i	0.998627	+	0.0523804i	$0.0166808\pi$
$420$	70.5802	−	263.409i	0.168048	−	0.627164i
$421$	46.2121	−	46.2121i	0.109767	−	0.109767i	−0.650090	−	0.759857i	$-0.725269\pi$
$421$	46.2121	−	46.2121i	0.109767	−	0.109767i	0.759857	+	0.650090i	$0.225269\pi$
$422$	−147.062	−	548.843i	−0.348488	−	1.30058i
$423$	−28.2366	+	48.9072i	−0.0667532	+	0.115620i
$424$	−225.608	+	60.4514i	−0.532094	+	0.142574i
$425$	223.642	+	59.9247i	0.526216	+	0.140999i
$426$	145.990	−	544.842i	0.342700	−	1.27897i
$427$	−69.7100	−	260.161i	−0.163255	−	0.609277i
$428$	37.7087	+	21.7711i	0.0881044	+	0.0508671i
$429$	1217.12	−	326.127i	2.83712	−	0.760204i
$430$	106.063	+	106.063i	0.246658	+	0.246658i
$431$	−251.355	−	67.3503i	−0.583189	−	0.156265i	−0.0448507	−	0.998994i	$-0.514281\pi$
$431$	−251.355	−	67.3503i	−0.583189	−	0.156265i	−0.538339	+	0.842729i	$0.680948\pi$
$432$	−59.8956	−	34.5807i	−0.138647	−	0.0800480i
$433$	17.9052			0.0413515			0.0206758	−	0.999786i	$-0.493418\pi$
$433$	17.9052			0.0413515			0.0206758	+	0.999786i	$0.493418\pi$
$434$			96.2231i			0.221712i
$435$	429.756	+	248.120i	0.987944	+	0.570390i
$436$	19.8880	−	19.8880i	0.0456146	−	0.0456146i
$437$	16.6246	−	9.59821i	0.0380425	−	0.0219639i
$438$	−171.377	+	171.377i	−0.391273	+	0.391273i
$439$	−502.298	−	134.590i	−1.14419	−	0.306584i	−0.363554	−	0.931573i	$-0.618437\pi$
$439$	−502.298	−	134.590i	−1.14419	−	0.306584i	−0.780634	+	0.624989i	$0.785103\pi$
$440$	82.8086	+	143.429i	0.188201	+	0.325974i
$441$	162.184	+	280.912i	0.367765	+	0.636988i
$442$	−453.237	+	121.445i	−1.02542	+	0.274762i
$443$		−	376.468i		−	0.849814i	−0.905237	−	0.424907i	$-0.860307\pi$
$443$		−	376.468i		−	0.849814i	0.905237	−	0.424907i	$-0.139693\pi$
$444$	186.843	+	194.027i	0.420817	+	0.436998i
$445$	156.122			0.350837
$446$	−44.8515	−	167.388i	−0.100564	−	0.375310i
$447$	365.405	−	210.967i	0.817461	−	0.471962i
$448$	77.5596	−	44.7791i	0.173124	−	0.0999533i
$449$	6.48792	−	24.2132i	0.0144497	−	0.0539270i	−0.958325	−	0.285682i	$-0.907780\pi$
$449$	6.48792	−	24.2132i	0.0144497	−	0.0539270i	0.972774	+	0.231755i	$0.0744467\pi$
$450$	58.6658	+	58.6658i	0.130369	+	0.130369i
$451$	424.359	+	735.012i	0.940929	+	1.62974i
$452$	−101.442	−	101.442i	−0.224429	−	0.224429i
$453$	−212.025	+	367.238i	−0.468047	+	0.810681i
$454$	−472.993			−1.04183
$455$			740.981i			1.62853i
$456$	33.3597	−	57.7807i	0.0731572	−	0.126712i
$457$	−62.4258	+	232.976i	−0.136599	+	0.509795i	0.863387	+	0.504542i	$0.168339\pi$
$457$	−62.4258	+	232.976i	−0.136599	+	0.509795i	−0.999986	+	0.00525276i	$0.998328\pi$
$458$	368.380	−	368.380i	0.804324	−	0.804324i
$459$	−75.0602	−	280.129i	−0.163530	−	0.610302i
$460$	9.91185	−	17.1678i	0.0215475	−	0.0373214i
$461$	454.058	−	121.665i	0.984942	−	0.263914i	0.269818	−	0.962911i	$-0.413037\pi$
$461$	454.058	−	121.665i	0.984942	−	0.263914i	0.715125	+	0.698997i	$0.246370\pi$
$462$	−974.108	−	261.011i	−2.10846	−	0.564960i
$463$	14.3813	−	53.6719i	0.0310612	−	0.115922i	−0.948655	−	0.316314i	$-0.897555\pi$
$463$	14.3813	−	53.6719i	0.0310612	−	0.115922i	0.979716	+	0.200392i	$0.0642215\pi$
$464$	42.1799	+	157.418i	0.0909050	+	0.339262i
$465$	64.1094	+	37.0136i	0.137870	+	0.0795991i
$466$	243.195	−	65.1639i	0.521877	−	0.139837i
$467$	175.940	+	175.940i	0.376746	+	0.376746i	0.869927	−	0.493181i	$-0.164166\pi$
$467$	175.940	+	175.940i	0.376746	+	0.376746i	−0.493181	+	0.869927i	$0.664166\pi$
$468$	−162.411	−	43.5180i	−0.347033	−	0.0929872i
$469$	140.243	+	80.9695i	0.299026	+	0.172643i
$470$	62.8792			0.133785
$471$			683.146i			1.45042i
$472$	−10.1962	−	5.88678i	−0.0216021	−	0.0124720i
$473$	392.230	−	392.230i	0.829239	−	0.829239i
$474$	676.417	−	390.529i	1.42704	−	0.823902i
$475$	63.2536	−	63.2536i	0.133165	−	0.133165i
$476$	362.742	+	97.1965i	0.762063	+	0.204194i
$477$	−175.477	−	303.935i	−0.367876	−	0.637181i
$478$	−105.016	−	181.892i	−0.219698	−	0.380528i
$479$	−151.577	+	40.6149i	−0.316445	+	0.0847911i	−0.413545	−	0.910483i	$-0.635710\pi$
$479$	−151.577	+	40.6149i	−0.316445	+	0.0847911i	0.0971009	+	0.995275i	$0.469043\pi$
$480$		−	68.8996i		−	0.143541i
$481$	−626.840	−	377.846i	−1.30320	−	0.785542i
$482$	445.055			0.923351
$483$	31.2420	+	116.597i	0.0646832	+	0.241401i
$484$	320.833	−	185.233i	0.662878	−	0.382713i
$485$	205.110	−	118.420i	0.422907	−	0.244165i
$486$	77.8588	−	290.573i	0.160203	−	0.597887i
$487$	61.9845	+	61.9845i	0.127278	+	0.127278i	0.767876	−	0.640598i	$-0.221314\pi$
$487$	61.9845	+	61.9845i	0.127278	+	0.127278i	−0.640598	+	0.767876i	$0.721314\pi$
$488$	−34.0250	−	58.9331i	−0.0697234	−	0.120765i
$489$	417.534	+	417.534i	0.853852	+	0.853852i
$490$	180.582	−	312.776i	0.368534	−	0.638319i
$491$	395.902			0.806318			0.403159	−	0.915130i	$-0.367912\pi$
$491$	395.902			0.806318			0.403159	+	0.915130i	$0.367912\pi$
$492$		−	353.081i		−	0.717645i
$493$	−341.687	+	591.820i	−0.693077	+	1.20045i
$494$	−46.9212	+	175.112i	−0.0949821	+	0.354478i
$495$	−175.967	+	175.967i	−0.355488	+	0.355488i
$496$	6.29225	+	23.4830i	0.0126860	+	0.0473447i
$497$	613.324	−	1062.31i	1.23405	−	2.13744i
$498$	−163.325	+	43.7628i	−0.327962	+	0.0878771i
$499$	−197.758	−	52.9890i	−0.396308	−	0.106190i	0.0551604	−	0.998478i	$-0.482433\pi$
$499$	−197.758	−	52.9890i	−0.396308	−	0.106190i	−0.451468	+	0.892287i	$0.649100\pi$
$500$	67.2102	−	250.832i	0.134420	−	0.501664i
$501$	−43.5935	−	162.693i	−0.0870129	−	0.324737i
$502$	70.4222	+	40.6583i	0.140283	+	0.0809926i
$503$	−71.1939	+	19.0764i	−0.141539	+	0.0379252i	−0.328893	−	0.944367i	$-0.606675\pi$
$503$	−71.1939	+	19.0764i	−0.141539	+	0.0379252i	0.187354	+	0.982292i	$0.440009\pi$
$504$	95.1547	+	95.1547i	0.188799	+	0.188799i
$505$	−360.975	−	96.7229i	−0.714802	−	0.191531i
$506$	−63.4880	−	36.6548i	−0.125470	−	0.0724404i
$507$	809.201			1.59606
$508$		−	258.005i		−	0.507884i
$509$	466.192	+	269.156i	0.915898	+	0.528794i	0.882324	−	0.470642i	$-0.155978\pi$
$509$	466.192	+	269.156i	0.915898	+	0.528794i	0.0335739	+	0.999436i	$0.489311\pi$
$510$	204.292	−	204.292i	0.400572	−	0.400572i
$511$	−456.449	+	263.531i	−0.893246	+	0.515716i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−108.230	−	29.0002i	−0.210975	−	0.0565305i
$514$	−29.2083	−	50.5903i	−0.0568255	−	0.0984246i
$515$	−2.24059	−	3.88081i	−0.00435066	−	0.00753556i
$516$	−222.900	+	59.7260i	−0.431978	+	0.115748i
$517$		−	232.532i		−	0.449772i
$518$	283.268	+	512.731i	0.546850	+	0.989828i
$519$	−103.634			−0.199680
$520$	48.4544	+	180.834i	0.0931815	+	0.347758i
$521$	−465.878	+	268.975i	−0.894200	+	0.516266i	−0.875314	−	0.483555i	$-0.839345\pi$
$521$	−465.878	+	268.975i	−0.894200	+	0.516266i	−0.0188857	+	0.999822i	$0.506012\pi$
$522$	−212.070	+	122.439i	−0.406265	+	0.234557i
$523$	138.929	−	518.492i	0.265640	−	0.991380i	−0.696218	−	0.717830i	$-0.745135\pi$
$523$	138.929	−	518.492i	0.265640	−	0.991380i	0.961858	−	0.273550i	$-0.0881979\pi$
$524$	−162.102	−	162.102i	−0.309354	−	0.309354i
$525$	281.250	+	487.139i	0.535714	+	0.927884i
$526$	98.4293	+	98.4293i	0.187128	+	0.187128i
$527$	−50.9717	+	88.2855i	−0.0967204	+	0.167525i
$528$	−254.796			−0.482569
$529$		−	520.225i		−	0.983412i
$530$	−195.382	+	338.412i	−0.368645	+	0.638513i
$531$	4.57872	−	17.0880i	0.00862283	−	0.0321808i
$532$	102.596	−	102.596i	0.192849	−	0.192849i
$533$	248.308	+	926.700i	0.465869	+	1.73865i
$534$	−120.095	+	208.010i	−0.224896	+	0.389532i
$535$	70.3653	−	18.8543i	0.131524	−	0.0352417i
$536$	39.5207	+	10.5896i	0.0737327	+	0.0197566i
$537$	−275.740	+	1029.07i	−0.513482	+	1.91634i
$538$	49.8518	+	186.049i	0.0926613	+	0.345817i
$539$	−1156.67	−	667.806i	−2.14596	−	1.23897i
$540$	−111.767	+	29.9478i	−0.206975	+	0.0554589i
$541$	−210.630	−	210.630i	−0.389334	−	0.389334i	0.485116	−	0.874450i	$-0.338777\pi$
$541$	−210.630	−	210.630i	−0.389334	−	0.389334i	−0.874450	+	0.485116i	$0.838777\pi$
$542$	14.2356	+	3.81441i	0.0262649	+	0.00703765i
$543$	1113.35	+	642.792i	2.05037	+	1.18378i
$544$	94.8821			0.174416
$545$		−	47.0554i		−	0.0863402i
$546$	−987.246	−	569.987i	−1.80814	−	1.04393i
$547$	−614.268	+	614.268i	−1.12298	+	1.12298i	−0.131684	+	0.991292i	$0.542038\pi$
$547$	−614.268	+	614.268i	−1.12298	+	1.12298i	−0.991292	+	0.131684i	$0.957962\pi$
$548$	−320.776	+	185.200i	−0.585358	+	0.337957i
$549$	72.3026	−	72.3026i	0.131699	−	0.131699i
$550$	−329.978	−	88.4173i	−0.599960	−	0.160759i
$551$	132.014	+	228.655i	0.239589	+	0.414981i
$552$	15.2490	+	26.4121i	0.0276251	+	0.0478480i
$553$	1640.67	−	439.615i	2.96685	−	0.794964i
$554$			346.317i			0.625121i
$555$	450.574	+	8.49934i	0.811845	+	0.0153141i
$556$	−462.611			−0.832034
$557$	−157.278	−	586.968i	−0.282366	−	1.05380i	−0.950743	−	0.309981i	$-0.899677\pi$
$557$	−157.278	−	586.968i	−0.282366	−	1.05380i	0.668377	−	0.743823i	$-0.266989\pi$
$558$	−31.6359	+	18.2650i	−0.0566952	+	0.0327330i
$559$	543.023	−	313.514i	0.971418	−	0.560849i
$560$	38.7798	−	144.728i	0.0692496	−	0.258443i
$561$	−755.488	−	755.488i	−1.34668	−	1.34668i
$562$	314.522	+	544.768i	0.559648	+	0.969338i
$563$	255.073	+	255.073i	0.453061	+	0.453061i	0.896369	−	0.443308i	$-0.146195\pi$
$563$	255.073	+	255.073i	0.453061	+	0.453061i	−0.443308	+	0.896369i	$0.646195\pi$
$564$	−48.3687	+	83.7771i	−0.0857602	+	0.148541i
$565$	−240.014			−0.424804
$566$			364.838i			0.644590i
$567$	566.385	−	981.008i	0.998915	−	1.73017i
$568$	80.2132	−	299.360i	0.141220	−	0.527042i
$569$	−163.070	+	163.070i	−0.286590	+	0.286590i	−0.835730	−	0.549140i	$-0.814955\pi$
$569$	−163.070	+	163.070i	−0.286590	+	0.286590i	0.549140	+	0.835730i	$0.314955\pi$
$570$	−28.8903	−	107.820i	−0.0506848	−	0.189158i
$571$	−101.824	+	176.364i	−0.178326	+	0.308869i	−0.941307	−	0.337551i	$-0.890401\pi$
$571$	−101.824	+	176.364i	−0.178326	+	0.308869i	0.762982	+	0.646420i	$0.223735\pi$
$572$	668.740	−	179.188i	1.16913	−	0.313266i
$573$	−942.317	−	252.493i	−1.64453	−	0.440651i
$574$	198.730	−	741.671i	0.346220	−	1.29211i
$575$	10.5832	+	39.4970i	0.0184056	+	0.0686905i
$576$	29.4446	+	16.9999i	0.0511191	+	0.0295136i
$577$	−576.370	+	154.438i	−0.998908	+	0.267657i	−0.720988	−	0.692947i	$-0.756312\pi$
$577$	−576.370	+	154.438i	−0.998908	+	0.267657i	−0.277920	+	0.960604i	$0.589645\pi$
$578$	−7.66829	−	7.66829i	−0.0132669	−	0.0132669i
$579$	−950.708	−	254.741i	−1.64198	−	0.439968i
$580$	236.126	+	136.328i	0.407114	+	0.235048i
$581$	−367.707			−0.632886
$582$			364.371i			0.626067i
$583$	1251.47	+	722.539i	2.14661	+	1.23935i
$584$	−94.1621	+	94.1621i	−0.161237	+	0.161237i
$585$	−243.617	+	140.652i	−0.416440	+	0.240431i
$586$	189.903	−	189.903i	0.324066	−	0.324066i
$587$	−753.173	−	201.812i	−1.28309	−	0.343802i	−0.448057	−	0.894005i	$-0.647884\pi$
$587$	−753.173	−	201.812i	−1.28309	−	0.343802i	−0.835031	+	0.550203i	$0.814550\pi$
$588$	277.819	+	481.196i	0.472481	+	0.818360i
$589$	19.6933	+	34.1099i	0.0334352	+	0.0579115i
$590$	−19.0264	+	5.09810i	−0.0322481	+	0.00864085i
$591$		−	528.741i		−	0.894655i
$592$	102.659	+	106.607i	0.173411	+	0.180079i
$593$	228.823			0.385873			0.192936	−	0.981211i	$-0.438199\pi$
$593$	228.823			0.385873			0.192936	+	0.981211i	$0.438199\pi$
$594$	110.749	+	413.323i	0.186447	+	0.695829i
$595$	544.113	−	314.144i	0.914476	−	0.527973i
$596$	200.769	−	115.914i	0.336861	−	0.194487i
$597$	−267.645	+	998.864i	−0.448316	+	1.67314i
$598$	−58.5973	−	58.5973i	−0.0979889	−	0.0979889i
$599$	254.582	+	440.948i	0.425011	+	0.736141i	0.996421	−	0.0845237i	$-0.0269369\pi$
$599$	254.582	+	440.948i	0.425011	+	0.736141i	−0.571410	+	0.820664i	$0.693604\pi$
$600$	100.493	+	100.493i	0.167489	+	0.167489i
$601$	−97.8619	+	169.502i	−0.162832	+	0.282033i	−0.935883	−	0.352310i	$-0.885396\pi$
$601$	−97.8619	+	169.502i	−0.162832	+	0.282033i	0.773051	+	0.634343i	$0.218729\pi$
$602$	−501.834			−0.833611
$603$			61.4783i			0.101954i
$604$	−116.496	+	201.777i	−0.192874	+	0.334067i
$605$	160.417	−	598.683i	0.265151	−	0.989558i
$606$	406.543	−	406.543i	0.670863	−	0.670863i
$607$	−2.75313	−	10.2748i	−0.00453564	−	0.0169272i	0.963621	−	0.267273i	$-0.0861225\pi$
$607$	−2.75313	−	10.2748i	−0.00453564	−	0.0169272i	−0.968157	+	0.250345i	$0.919456\pi$
$608$	18.3293	−	31.7472i	0.0301468	−	0.0522158i
$609$	−1603.67	+	429.702i	−2.63329	+	0.705587i
$610$	−109.971	−	29.4665i	−0.180280	−	0.0483058i
$611$	68.0317	−	253.898i	0.111345	−	0.415544i
$612$	36.8995	+	137.711i	0.0602933	+	0.225018i
$613$	149.361	+	86.2338i	0.243656	+	0.140675i	0.616856	−	0.787076i	$-0.288406\pi$
$613$	149.361	+	86.2338i	0.243656	+	0.140675i	−0.373200	+	0.927751i	$0.621739\pi$
$614$	−120.081	+	32.1756i	−0.195572	+	0.0524033i
$615$	−417.700	−	417.700i	−0.679187	−	0.679187i
$616$	−535.217	−	143.411i	−0.868858	−	0.232810i
$617$	−652.506	−	376.724i	−1.05755	−	0.610574i	−0.132794	−	0.991144i	$-0.542395\pi$
$617$	−652.506	−	376.724i	−1.05755	−	0.610574i	−0.924752	+	0.380569i	$0.875728\pi$
$618$	6.89414			0.0111556
$619$			863.281i			1.39464i	0.716761	+	0.697319i	$0.245624\pi$
$619$			863.281i			1.39464i	−0.716761	+	0.697319i	$0.754376\pi$
$620$	35.2245	+	20.3369i	0.0568137	+	0.0328014i
$621$	36.2168	−	36.2168i	0.0583201	−	0.0583201i
$622$	−335.188	+	193.521i	−0.538887	+	0.311126i
$623$	−369.344	+	369.344i	−0.592847	+	0.592847i
$624$	−278.207	−	74.5455i	−0.445845	−	0.119464i
$625$	−44.6788	−	77.3860i	−0.0714861	−	0.123818i
$626$	119.154	+	206.380i	0.190341	+	0.329681i
$627$	−398.728	+	106.839i	−0.635930	+	0.170397i
$628$			375.350i			0.597691i
$629$	−11.7045	+	620.489i	−0.0186081	+	0.986468i
$630$	225.138			0.357362
$631$	−319.555	−	1192.60i	−0.506427	−	1.89001i	−0.453160	−	0.891429i	$-0.649703\pi$
$631$	−319.555	−	1192.60i	−0.506427	−	1.89001i	−0.0532665	−	0.998580i	$-0.516963\pi$
$632$	371.652	−	214.574i	0.588058	−	0.339515i
$633$	1266.56	−	731.251i	2.00089	−	1.15522i
$634$	−75.8609	+	283.117i	−0.119654	+	0.446556i
$635$	−305.223	−	305.223i	−0.480667	−	0.480667i
$636$	−300.589	−	520.635i	−0.472624	−	0.818608i
$637$	−1067.57	−	1067.57i	−1.67594	−	1.67594i
$638$	504.151	−	873.215i	0.790205	−	1.36867i
$639$	465.682			0.728767
$640$		−	37.8564i		−	0.0591506i
$641$	512.608	−	887.863i	0.799700	−	1.38512i	−0.120111	−	0.992761i	$-0.538325\pi$
$641$	512.608	−	887.863i	0.799700	−	1.38512i	0.919811	−	0.392361i	$-0.128342\pi$
$642$	−29.0068	+	108.255i	−0.0451819	+	0.168621i
$643$	−21.2419	+	21.2419i	−0.0330356	+	0.0330356i	−0.723432	−	0.690396i	$-0.757436\pi$
$643$	−21.2419	+	21.2419i	−0.0330356	+	0.0330356i	0.690396	+	0.723432i	$0.257436\pi$
$644$	17.1657	+	64.0633i	0.0266548	+	0.0994771i
$645$	−193.037	+	334.351i	−0.299283	+	0.518373i
$646$	148.480	−	39.7851i	0.229845	−	0.0615868i
$647$	932.050	+	249.742i	1.44057	+	0.386000i	0.892734	−	0.450584i	$-0.148784\pi$
$647$	932.050	+	249.742i	1.44057	+	0.386000i	0.547838	+	0.836584i	$0.315451\pi$
$648$	74.0744	−	276.449i	0.114312	−	0.426619i
$649$	18.8532	+	70.3611i	0.0290496	+	0.108415i
$650$	−334.429	−	193.082i	−0.514506	−	0.297050i
$651$	−239.230	+	64.1015i	−0.367481	+	0.0984662i
$652$	229.411	+	229.411i	0.351857	+	0.351857i
$653$	899.742	+	241.085i	1.37786	+	0.369196i	0.870343	−	0.492446i	$-0.163897\pi$
$653$	899.742	+	241.085i	1.37786	+	0.369196i	0.507516	+	0.861642i	$0.330564\pi$
$654$	62.6943	+	36.1966i	0.0958629	+	0.0553465i
$655$	−383.537			−0.585552
$656$		−	193.998i		−	0.295729i
$657$	−173.285	−	100.046i	−0.263753	−	0.152278i
$658$	−148.755	+	148.755i	−0.226072	+	0.226072i
$659$	−651.722	+	376.272i	−0.988956	+	0.570974i	−0.904962	−	0.425492i	$-0.860101\pi$
$659$	−651.722	+	376.272i	−0.988956	+	0.570974i	−0.0839937	+	0.996466i	$0.526768\pi$
$660$	−301.427	+	301.427i	−0.456708	+	0.456708i
$661$	995.712	+	266.800i	1.50637	+	0.403631i	0.915229	−	0.402935i	$-0.132010\pi$
$661$	995.712	+	266.800i	1.50637	+	0.403631i	0.591144	+	0.806566i	$0.298676\pi$
$662$	281.948	+	488.348i	0.425903	+	0.737686i
$663$	−603.871	−	1045.94i	−0.910816	−	1.57758i
$664$	−89.7378	+	24.0452i	−0.135147	+	0.0362126i
$665$		−	242.744i		−	0.365029i
$666$	−114.804	+	190.458i	−0.172378	+	0.285973i
$667$	−120.690			−0.180944
$668$	−23.9521	−	89.3906i	−0.0358565	−	0.133818i
$669$	386.281	−	223.020i	0.577401	−	0.333363i
$670$	59.2811	−	34.2260i	0.0884793	−	0.0510835i
$671$	−108.970	+	406.681i	−0.162399	+	0.606081i
$672$	162.998	+	162.998i	0.242557	+	0.242557i
$673$	47.4100	+	82.1165i	0.0704458	+	0.122016i	0.899097	−	0.437750i	$-0.144224\pi$
$673$	47.4100	+	82.1165i	0.0704458	+	0.122016i	−0.828651	+	0.559766i	$0.810891\pi$
$674$	−167.324	−	167.324i	−0.248256	−	0.248256i
$675$	119.337	−	206.697i	0.176795	−	0.306218i
$676$	444.610			0.657707
$677$			936.626i			1.38350i	0.722139	+	0.691748i	$0.243159\pi$
$677$			936.626i			1.38350i	−0.722139	+	0.691748i	$0.756841\pi$
$678$	184.627	−	319.783i	0.272311	−	0.471657i
$679$	−205.084	+	765.385i	−0.302039	+	1.12722i
$680$	112.247	−	112.247i	0.165069	−	0.165069i
$681$	−315.096	−	1175.95i	−0.462696	−	1.72681i
$682$	75.2074	−	130.263i	0.110275	−	0.191002i
$683$	−449.954	+	120.565i	−0.658791	+	0.176523i	−0.572700	−	0.819765i	$-0.694104\pi$
$683$	−449.954	+	120.565i	−0.658791	+	0.176523i	−0.0860907	+	0.996287i	$0.527437\pi$
$684$	53.2058	+	14.2564i	0.0777862	+	0.0208428i
$685$	−160.388	+	598.577i	−0.234143	+	0.873835i
$686$	111.957	+	417.829i	0.163202	+	0.609079i
$687$	1161.27	+	670.461i	1.69035	+	0.975926i
$688$	−122.471	+	32.8160i	−0.178010	+	0.0476977i
$689$	1155.07	+	1155.07i	1.67644	+	1.67644i
$690$	49.2857	+	13.2061i	0.0714285	+	0.0191392i
$691$	−390.666	−	225.551i	−0.565363	−	0.326413i	0.189932	−	0.981797i	$-0.439173\pi$
$691$	−390.666	−	225.551i	−0.565363	−	0.326413i	−0.755295	+	0.655385i	$0.772507\pi$
$692$	−56.9409			−0.0822846
$693$		−	832.580i		−	1.20141i
$694$	−167.815	−	96.8879i	−0.241808	−	0.139608i
$695$	−547.274	+	547.274i	−0.787445	+	0.787445i
$696$	−363.272	+	209.735i	−0.521943	+	0.301344i
$697$	575.217	−	575.217i	0.825276	−	0.825276i
$698$	596.918	+	159.944i	0.855183	+	0.229146i
$699$	324.021	+	561.221i	0.463549	+	0.802891i
$700$	154.531	+	267.655i	0.220758	+	0.382365i
$701$	103.380	−	27.7006i	0.147475	−	0.0395159i	−0.184326	−	0.982865i	$-0.559010\pi$
$701$	103.380	−	27.7006i	0.147475	−	0.0395159i	0.331801	+	0.943349i	$0.392344\pi$
$702$			483.701i			0.689033i
$703$	205.352	+	123.782i	0.292108	+	0.176077i
$704$	−139.996			−0.198858
$705$	41.8885	+	156.330i	0.0594164	+	0.221745i
$706$	−184.464	+	106.500i	−0.261281	+	0.150850i
$707$	1082.79	−	625.149i	1.53153	−	0.884228i
$708$	7.84326	−	29.2714i	0.0110780	−	0.0413438i
$709$	−673.629	−	673.629i	−0.950112	−	0.950112i	0.0487014	−	0.998813i	$-0.484492\pi$
$709$	−673.629	−	673.629i	−0.950112	−	0.950112i	−0.998813	+	0.0487014i	$0.984492\pi$
$710$	−259.253	−	449.040i	−0.365145	−	0.632450i
$711$	455.965	+	455.965i	0.641301	+	0.641301i
$712$	−65.9851	+	114.290i	−0.0926757	+	0.160519i
$713$	−18.0040			−0.0252511
$714$			966.600i			1.35378i
$715$	579.146	−	1003.11i	0.809994	−	1.40295i
$716$	−151.503	+	565.418i	−0.211597	+	0.789690i
$717$	382.262	−	382.262i	0.533141	−	0.533141i
$718$	37.7713	+	140.964i	0.0526063	+	0.196329i
$719$	−19.5291	+	33.8254i	−0.0271615	+	0.0470450i	−0.879287	−	0.476293i	$-0.841980\pi$
$719$	−19.5291	+	33.8254i	−0.0271615	+	0.0470450i	0.852125	+	0.523338i	$0.175313\pi$
$720$	54.9444	−	14.7223i	0.0763116	−	0.0204476i
$721$	14.4816	+	3.88033i	0.0200854	+	0.00538187i
$722$	−116.764	+	435.769i	−0.161723	+	0.603558i
$723$	296.485	+	1106.50i	0.410076	+	1.53042i
$724$	611.722	+	353.178i	0.844919	+	0.487814i
$725$	−543.242	+	145.561i	−0.749299	+	0.200774i
$726$	674.258	+	674.258i	0.928729	+	0.928729i
$727$	180.487	+	48.3613i	0.248262	+	0.0665217i	0.380804	−	0.924656i	$-0.375647\pi$
$727$	180.487	+	48.3613i	0.248262	+	0.0665217i	−0.132542	+	0.991177i	$0.542314\pi$
$728$	−542.436	−	313.175i	−0.745104	−	0.430186i
$729$	−136.397			−0.187102
$730$			222.790i			0.305192i
$731$	−460.437	−	265.833i	−0.629872	−	0.363657i
$732$	123.853	−	123.853i	0.169198	−	0.169198i
$733$	395.268	−	228.208i	0.539247	−	0.311334i	−0.205527	−	0.978652i	$-0.565891\pi$
$733$	395.268	−	228.208i	0.539247	−	0.311334i	0.744774	+	0.667317i	$0.232557\pi$
$734$	211.371	−	211.371i	0.287972	−	0.287972i
$735$	897.924	+	240.598i	1.22167	+	0.327344i
$736$	8.37848	+	14.5120i	0.0113838	+	0.0197173i
$737$	−126.570	−	219.226i	−0.171737	−	0.297458i
$738$	281.567	−	75.4456i	0.381527	−	0.102230i
$739$		−	760.377i		−	1.02893i	−0.857512	−	0.514463i	$-0.827991\pi$
$739$		−	760.377i		−	1.02893i	0.857512	−	0.514463i	$-0.172009\pi$
$740$	247.565	+	4.66990i	0.334547	+	0.00631068i
$741$	−466.622			−0.629719
$742$	−338.370	−	1262.81i	−0.456024	−	1.70190i
$743$	−212.709	+	122.808i	−0.286284	+	0.165286i	−0.636265	−	0.771471i	$-0.719521\pi$
$743$	−212.709	+	122.808i	−0.286284	+	0.165286i	0.349981	+	0.936757i	$0.386188\pi$
$744$	−54.1917	+	31.2876i	−0.0728383	+	0.0420532i
$745$	100.385	−	374.641i	0.134745	−	0.502873i
$746$	−632.260	−	632.260i	−0.847534	−	0.847534i
$747$	−69.7978	−	120.893i	−0.0934375	−	0.161838i
$748$	−415.098	−	415.098i	−0.554944	−	0.554944i
$749$	−121.861	+	211.070i	−0.162699	+	0.281802i
$750$	668.392			0.891190
$751$		−	1062.89i		−	1.41530i	−0.706565	−	0.707648i	$-0.749756\pi$
$751$		−	1062.89i		−	1.41530i	0.706565	−	0.707648i	$-0.250244\pi$
$752$	−26.5759	+	46.0307i	−0.0353402	+	0.0612111i
$753$	−54.1711	+	202.169i	−0.0719403	+	0.268485i
$754$	805.948	−	805.948i	1.06890	−	1.06890i
$755$	100.888	+	376.520i	0.133627	+	0.498702i
$756$	193.562	−	335.259i	0.256034	−	0.443464i
$757$	848.035	−	227.230i	1.12026	−	0.300172i	0.349270	−	0.937022i	$-0.386430\pi$
$757$	848.035	−	227.230i	1.12026	−	0.300172i	0.770988	+	0.636850i	$0.219763\pi$
$758$	−229.405	−	61.4688i	−0.302645	−	0.0810935i
$759$	48.8371	−	182.263i	0.0643440	−	0.240135i
$760$	−15.8736	−	59.2411i	−0.0208863	−	0.0779488i
$761$	−207.217	−	119.637i	−0.272296	−	0.157210i	0.357635	−	0.933862i	$-0.383583\pi$
$761$	−207.217	−	119.637i	−0.272296	−	0.157210i	−0.629931	+	0.776652i	$0.716917\pi$
$762$	641.452	−	171.877i	0.841801	−	0.225560i
$763$	111.321	+	111.321i	0.145898	+	0.145898i
$764$	−517.749	−	138.731i	−0.677683	−	0.181584i
$765$	206.566	+	119.261i	0.270021	+	0.155897i
$766$	−60.8712			−0.0794663
$767$			82.3418i			0.107356i
$768$	50.4380	+	29.1204i	0.0656745	+	0.0379172i
$769$	−717.272	+	717.272i	−0.932733	+	0.932733i	−0.997876	−	0.0651431i	$-0.979250\pi$
$769$	−717.272	+	717.272i	−0.932733	+	0.932733i	0.0651431	+	0.997876i	$0.479250\pi$
$770$	−802.825	+	463.511i	−1.04263	+	0.601963i
$771$	106.320	−	106.320i	0.137898	−	0.137898i
$772$	−522.360	−	139.966i	−0.676632	−	0.181303i
$773$	−565.911	−	980.186i	−0.732097	−	1.26803i	−0.955986	−	0.293414i	$-0.905209\pi$
$773$	−565.911	−	980.186i	−0.732097	−	1.26803i	0.223889	−	0.974615i	$-0.428125\pi$
$774$	−95.2577	−	164.991i	−0.123072	−	0.213167i
$775$	−81.0389	+	21.7143i	−0.104566	+	0.0280185i
$776$			200.201i			0.257991i
$777$	−1086.04	+	1045.83i	−1.39774	+	1.34599i
$778$	−58.9989			−0.0758340
$779$	−81.3455	−	303.586i	−0.104423	−	0.389712i
$780$	−417.311	+	240.935i	−0.535014	+	0.308891i
$781$	−1660.59	+	958.740i	−2.12623	+	1.22758i
$782$	−18.1862	+	67.8717i	−0.0232560	+	0.0867924i
$783$	498.125	+	498.125i	0.636175	+	0.636175i
$784$	152.645	+	264.390i	0.194701	+	0.337232i
$785$	444.044	+	444.044i	0.565661	+	0.565661i
$786$	295.029	−	511.005i	0.375355	−	0.650134i
$787$	−208.881			−0.265415			−0.132707	−	0.991155i	$-0.542367\pi$
$787$	−208.881			−0.265415			−0.132707	+	0.991155i	$0.542367\pi$
$788$		−	290.513i		−	0.368672i
$789$	−179.144	+	310.286i	−0.227052	+	0.393265i
$790$	185.826	−	693.513i	0.235223	−	0.877864i
$791$	567.810	−	567.810i	0.717838	−	0.717838i
$792$	−54.4443	−	203.189i	−0.0687428	−	0.256552i
$793$	−237.964	+	412.166i	−0.300081	+	0.519755i
$794$	−376.617	+	100.914i	−0.474328	+	0.127096i
$795$	−971.518	−	260.317i	−1.22204	−	0.327443i
$796$	−147.056	+	548.819i	−0.184743	+	0.689471i
$797$	−6.05123	−	22.5835i	−0.00759251	−	0.0283356i	0.962026	−	0.272959i	$-0.0880023\pi$
$797$	−6.05123	−	22.5835i	−0.00759251	−	0.0283356i	−0.969618	+	0.244623i	$0.921336\pi$
$798$	323.421	+	186.727i	0.405289	+	0.233994i
$799$	−215.283	+	57.6850i	−0.269441	+	0.0721965i
$800$	55.2154	+	55.2154i	0.0690192	+	0.0690192i
$801$	−191.540	−	51.3230i	−0.239126	−	0.0640737i
$802$	−153.708	−	88.7433i	−0.191656	−	0.110652i
$803$	823.896			1.02602
$804$			105.311i			0.130984i
$805$	96.0949	+	55.4804i	0.119373	+	0.0689198i
$806$	120.228	−	120.228i	0.149167	−	0.149167i
$807$	−429.346	+	247.883i	−0.532027	+	0.307166i
$808$	223.372	−	223.372i	0.276451	−	0.276451i
$809$	659.267	+	176.650i	0.814916	+	0.218356i	0.642123	−	0.766602i	$-0.278054\pi$
$809$	659.267	+	176.650i	0.814916	+	0.218356i	0.172794	+	0.984958i	$0.444721\pi$
$810$	−239.412	−	414.674i	−0.295571	−	0.511943i
$811$	570.051	+	987.358i	0.702899	+	1.21746i	0.967444	+	0.253084i	$0.0814448\pi$
$811$	570.051	+	987.358i	0.702899	+	1.21746i	−0.264545	+	0.964373i	$0.585222\pi$
$812$	−881.126	+	236.097i	−1.08513	+	0.290760i
$813$			37.9335i			0.0466587i
$814$	17.2697	−	915.515i	0.0212158	−	1.12471i
$815$	542.792			0.666002
$816$	63.2081	+	235.896i	0.0774609	+	0.289088i
$817$	−177.894	+	102.707i	−0.217740	+	0.125712i
$818$	−565.545	+	326.517i	−0.691375	+	0.399166i
$819$	243.587	−	909.079i	0.297420	−	1.10999i
$820$	−229.502	−	229.502i	−0.279881	−	0.279881i
$821$	−354.106	−	613.329i	−0.431310	−	0.747051i	0.565676	−	0.824627i	$-0.308615\pi$
$821$	−354.106	−	613.329i	−0.431310	−	0.747051i	−0.996986	+	0.0775762i	$0.975282\pi$
$822$	−674.139	−	674.139i	−0.820120	−	0.820120i
$823$	328.580	−	569.117i	0.399247	−	0.691516i	−0.594386	−	0.804180i	$-0.702605\pi$
$823$	328.580	−	569.117i	0.399247	−	0.691516i	0.993633	+	0.112664i	$0.0359383\pi$
$824$	3.78794			0.00459701
$825$		−	879.293i		−	1.06581i
$826$	32.9506	−	57.0721i	0.0398917	−	0.0690945i
$827$	−207.344	+	773.818i	−0.250718	+	0.935693i	0.719704	+	0.694281i	$0.244277\pi$
$827$	−207.344	+	773.818i	−0.250718	+	0.935693i	−0.970423	+	0.241413i	$0.922389\pi$
$828$	−17.8041	+	17.8041i	−0.0215026	+	0.0215026i
$829$	26.7950	+	100.000i	0.0323221	+	0.120628i	0.980202	−	0.198000i	$-0.0634447\pi$
$829$	26.7950	+	100.000i	0.0323221	+	0.120628i	−0.947880	+	0.318628i	$0.896778\pi$
$830$	−77.7152	+	134.607i	−0.0936328	+	0.162177i
$831$	−861.013	+	230.708i	−1.03612	+	0.277627i
$832$	−152.859	−	40.9585i	−0.183725	−	0.0492289i
$833$	−331.329	+	1236.54i	−0.397754	+	1.48444i
$834$	−308.180	−	1150.14i	−0.369520	−	1.37907i
$835$	−134.086	−	77.4145i	−0.160582	−	0.0927120i
$836$	−219.078	+	58.7019i	−0.262056	+	0.0702176i
$837$	74.3086	+	74.3086i	0.0887796	+	0.0887796i
$838$	519.651	+	139.240i	0.620108	+	0.166158i
$839$	293.379	+	169.383i	0.349677	+	0.201886i	0.664543	−	0.747250i	$-0.268626\pi$
$839$	293.379	+	169.383i	0.349677	+	0.201886i	−0.314866	+	0.949136i	$0.601960\pi$
$840$	385.657			0.459116
$841$		−	818.964i		−	0.973798i
$842$	80.0416	+	46.2121i	0.0950613	+	0.0548837i
$843$	−1144.88	+	1144.88i	−1.35810	+	1.35810i
$844$	695.905	−	401.781i	0.824532	−	0.476044i
$845$	525.979	−	525.979i	0.622460	−	0.622460i
$846$	−77.1438	−	20.6706i	−0.0911866	−	0.0244334i
$847$	1036.82	+	1795.83i	1.22411	+	2.12022i
$848$	−165.156	−	286.059i	−0.194760	−	0.337334i
$849$	−907.061	+	243.046i	−1.06839	+	0.286273i
$850$			327.435i			0.385217i
$851$	−95.9356	+	53.0015i	−0.112733	+	0.0622815i
$852$	797.704			0.936273
$853$	1.47805	+	5.51616i	0.00173277	+	0.00646678i	0.966787	−	0.255584i	$-0.0822678\pi$
$853$	1.47805	+	5.51616i	0.00173277	+	0.00646678i	−0.965054	+	0.262051i	$0.915601\pi$
$854$	329.871	−	190.451i	0.386266	−	0.223011i
$855$	79.8087	−	46.0776i	0.0933435	−	0.0538919i
$856$	−15.9376	+	59.4798i	−0.0186186	+	0.0694857i
$857$	187.681	+	187.681i	0.218998	+	0.218998i	0.808076	−	0.589078i	$-0.200509\pi$
$857$	187.681	+	187.681i	0.218998	+	0.218998i	−0.589078	+	0.808076i	$0.700509\pi$
$858$	890.996	+	1543.25i	1.03846	+	1.79866i
$859$	38.0257	+	38.0257i	0.0442675	+	0.0442675i	0.728894	−	0.684627i	$-0.240035\pi$
$859$	38.0257	+	38.0257i	0.0442675	+	0.0442675i	−0.684627	+	0.728894i	$0.740035\pi$
$860$	−106.063	+	183.707i	−0.123329	+	0.213612i
$861$	1976.33			2.29539
$862$		−	368.009i		−	0.426924i
$863$	−310.264	+	537.393i	−0.359518	+	0.622704i	−0.987880	−	0.155217i	$-0.950392\pi$
$863$	−310.264	+	537.393i	−0.359518	+	0.622704i	0.628362	+	0.777921i	$0.283726\pi$
$864$	25.3149	−	94.4763i	0.0292996	−	0.109348i
$865$	−67.3619	+	67.3619i	−0.0778750	+	0.0778750i
$866$	6.55376	+	24.4590i	0.00756786	+	0.0282436i
$867$	13.9565	−	24.1733i	0.0160974	−	0.0278816i
$868$	−131.443	+	35.2201i	−0.151432	+	0.0405762i
$869$	−2564.67	−	687.201i	−2.95129	−	0.790795i
$870$	−181.636	+	677.875i	−0.208777	+	0.779167i
$871$	−74.0611	−	276.400i	−0.0850300	−	0.317336i
$872$	34.4470	+	19.8880i	0.0395034	+	0.0228073i
$873$	−290.570	+	77.8579i	−0.332840	+	0.0891843i
$874$	19.1964	+	19.1964i	0.0219639	+	0.0219639i
$875$	1404.00	+	376.201i	1.60457	+	0.429944i
$876$	−296.834	−	171.377i	−0.338852	−	0.195636i
$877$	−532.880			−0.607616			−0.303808	−	0.952733i	$-0.598258\pi$
$877$	−532.880			−0.607616			−0.303808	+	0.952733i	$0.598258\pi$
$878$		−	735.416i		−	0.837603i
$879$	598.645	+	345.628i	0.681052	+	0.393205i
$880$	−165.617	+	165.617i	−0.188201	+	0.188201i
$881$	−816.763	+	471.559i	−0.927087	+	0.535254i	−0.885889	−	0.463897i	$-0.846451\pi$
$881$	−816.763	+	471.559i	−0.927087	+	0.535254i	−0.0411978	+	0.999151i	$0.513117\pi$
$882$	−324.369	+	324.369i	−0.367765	+	0.367765i
$883$	−1513.59	−	405.564i	−1.71414	−	0.459303i	−0.737707	−	0.675121i	$-0.764091\pi$
$883$	−1513.59	−	405.564i	−1.71414	−	0.459303i	−0.976434	+	0.215818i	$0.930758\pi$
$884$	−331.793	−	574.682i	−0.375331	−	0.650093i
$885$	−25.3498	−	43.9072i	−0.0286439	−	0.0496126i
$886$	514.264	−	137.797i	0.580434	−	0.155527i
$887$		−	332.500i		−	0.374859i	−0.982278	−	0.187429i	$-0.939984\pi$
$887$		−	332.500i		−	0.374859i	0.982278	−	0.187429i	$-0.0600156\pi$
$888$	−196.657	+	326.251i	−0.221461	+	0.367400i
$889$	1444.15			1.62447
$890$	57.1448	+	213.267i	0.0642076	+	0.239626i
$891$	−1533.50	+	885.366i	−1.72110	+	0.993677i
$892$	212.240	−	122.537i	0.237937	−	0.137373i
$893$	−22.2871	+	83.1766i	−0.0249575	+	0.0931428i
$894$	421.934	+	421.934i	0.471962	+	0.471962i
$895$	489.666	+	848.127i	0.547113	+	0.947627i
$896$	89.5581	+	89.5581i	0.0999533	+	0.0999533i
$897$	106.649	−	184.721i	0.118895	−	0.205932i
$898$	35.4506			0.0394773
$899$		−	247.627i		−	0.275448i
$900$	−58.6658	+	101.612i	−0.0651843	+	0.112902i
$901$	358.485	−	1337.88i	0.397874	−	1.48489i
$902$	−848.718	+	848.718i	−0.940929	+	0.940929i
$903$	−334.309	−	1247.66i	−0.370221	−	1.38168i
$904$	101.442	−	175.703i	0.112215	−	0.194361i
$905$	1141.49	−	305.861i	1.26131	−	0.337968i
$906$	−579.264	−	155.213i	−0.639364	−	0.171317i
$907$	−43.8068	+	163.489i	−0.0482986	+	0.180253i	−0.985861	−	0.167564i	$-0.946410\pi$
$907$	−43.8068	+	163.489i	−0.0482986	+	0.180253i	0.937563	+	0.347816i	$0.113077\pi$
$908$	−173.127	−	646.120i	−0.190669	−	0.711586i
$909$	411.069	+	237.331i	0.452221	+	0.261090i
$910$	−1012.20	+	271.218i	−1.11231	+	0.298042i
$911$	575.316	+	575.316i	0.631522	+	0.631522i	0.948450	−	0.316928i	$-0.102651\pi$
$911$	575.316	+	575.316i	0.631522	+	0.631522i	−0.316928	+	0.948450i	$0.602651\pi$
$912$	91.1404	+	24.4210i	0.0999346	+	0.0267774i
$913$	497.787	+	287.397i	0.545221	+	0.314783i
$914$	−341.101			−0.373196
$915$		−	293.039i		−	0.320261i
$916$	638.053	+	368.380i	0.696565	+	0.402162i
$917$	907.345	−	907.345i	0.989471	−	0.989471i
$918$	355.189	−	205.068i	0.386916	−	0.223386i
$919$	1019.61	−	1019.61i	1.10948	−	1.10948i	0.116262	−	0.993219i	$-0.462909\pi$
$919$	1019.61	−	1019.61i	1.10948	−	1.10948i	0.993219	−	0.116262i	$-0.0370912\pi$
$920$	27.0797	+	7.25598i	0.0294344	+	0.00788693i
$921$	−159.990	−	277.111i	−0.173714	−	0.300881i
$922$	332.394	+	575.723i	0.360514	+	0.624428i
$923$	−2093.66	+	560.994i	−2.26832	+	0.607795i
$924$		−	1426.19i		−	1.54350i
$925$	−367.896	+	354.274i	−0.397726	+	0.382999i
$926$	78.5811			0.0848608
$927$	1.47312	+	5.49777i	0.00158913	+	0.00593071i
$928$	−199.597	+	115.238i	−0.215083	+	0.124178i
$929$	651.784	−	376.308i	0.701597	−	0.405067i	−0.106345	−	0.994329i	$-0.533915\pi$
$929$	651.784	−	376.308i	0.701597	−	0.405067i	0.807942	+	0.589262i	$0.200581\pi$
$930$	−27.0958	+	101.123i	−0.0291353	+	0.108734i
$931$	349.735	+	349.735i	0.375655	+	0.375655i
$932$	178.031	+	308.359i	0.191020	+	0.330857i
$933$	−704.425	−	704.425i	−0.755010	−	0.755010i
$934$	−175.940	+	304.738i	−0.188373	+	0.326272i
$935$	−982.132			−1.05041
$936$		−	237.787i		−	0.254046i
$937$	497.724	−	862.084i	0.531189	−	0.920047i	−0.468148	−	0.883650i	$-0.655079\pi$
$937$	497.724	−	862.084i	0.531189	−	0.920047i	0.999337	−	0.0363969i	$-0.0115881\pi$
$938$	−59.2738	+	221.213i	−0.0631917	+	0.235834i
$939$	−433.725	+	433.725i	−0.461901	+	0.461901i
$940$	23.0154	+	85.8945i	0.0244844	+	0.0913772i
$941$	420.473	−	728.280i	0.446836	−	0.773942i	−0.551342	−	0.834279i	$-0.685884\pi$
$941$	420.473	−	728.280i	0.446836	−	0.773942i	0.998178	+	0.0603368i	$0.0192175\pi$
$942$	−933.195	+	250.049i	−0.990653	+	0.265445i
$943$	138.772	+	37.1838i	0.147160	+	0.0394314i
$944$	4.30942	−	16.0830i	0.00456507	−	0.0170371i
$945$	−167.629	−	625.601i	−0.177385	−	0.662012i
$946$	679.362	+	392.230i	0.718142	+	0.414620i
$947$	981.074	−	262.878i	1.03598	−	0.277590i	0.299534	−	0.954086i	$-0.403169\pi$
$947$	981.074	−	262.878i	1.03598	−	0.277590i	0.736447	+	0.676495i	$0.236502\pi$
$948$	781.059	+	781.059i	0.823902	+	0.823902i
$949$	899.596	+	241.046i	0.947941	+	0.254000i
$950$	109.558	+	63.2536i	0.115325	+	0.0665827i
$951$	−754.421			−0.793292
$952$			531.091i			0.557869i
$953$	407.682	+	235.375i	0.427788	+	0.246984i	0.698404	−	0.715704i	$-0.253894\pi$
$953$	407.682	+	235.375i	0.427788	+	0.246984i	−0.270616	+	0.962687i	$0.587227\pi$
$954$	350.954	−	350.954i	0.367876	−	0.367876i
$955$	−776.624	+	448.384i	−0.813219	+	0.469512i
$956$	210.031	−	210.031i	0.219698	−	0.219698i
$957$	2506.84	+	671.706i	2.61948	+	0.701887i
$958$	−110.962	−	192.192i	−0.115827	−	0.200618i
$959$	−1036.64	−	1795.51i	−1.08096	−	1.87227i
$960$	94.1186	−	25.2190i	0.0980402	−	0.0262698i
$961$			924.060i			0.961561i
$962$	286.707	−	994.581i	0.298033	−	1.03387i
$963$	−92.5264			−0.0960814
$964$	162.902	+	607.957i	0.168985	+	0.630661i
$965$	−783.540	+	452.377i	−0.811958	+	0.468784i
$966$	−147.839	+	85.3547i	−0.153042	+	0.0883589i
$967$	229.277	−	855.675i	0.237102	−	0.884876i	−0.740088	−	0.672510i	$-0.765216\pi$
$967$	229.277	−	855.675i	0.237102	−	0.884876i	0.977190	−	0.212366i	$-0.0681170\pi$
$968$	370.466	+	370.466i	0.382713	+	0.382713i
$969$	197.827	+	342.647i	0.204156	+	0.353609i
$970$	236.840	+	236.840i	0.244165	+	0.244165i
$971$	917.295	−	1588.80i	0.944691	−	1.63625i	0.188321	−	0.982107i	$-0.439695\pi$
$971$	917.295	−	1588.80i	0.944691	−	1.63625i	0.756369	−	0.654145i	$-0.226971\pi$
$972$	425.428			0.437683
$973$		−	2589.41i		−	2.66126i
$974$	−61.9845	+	107.360i	−0.0636391	+	0.110226i
$975$	257.254	−	960.083i	0.263850	−	0.984701i
$976$	68.0501	−	68.0501i	0.0697234	−	0.0697234i
$977$	349.888	+	1305.80i	0.358125	+	1.33654i	0.876506	+	0.481390i	$0.159868\pi$
$977$	349.888	+	1305.80i	0.358125	+	1.33654i	−0.518382	+	0.855149i	$0.673465\pi$
$978$	−417.534	+	723.189i	−0.426926	+	0.739457i
$979$	788.680	−	211.326i	0.805598	−	0.215859i
$980$	493.358	+	132.195i	0.503427	+	0.134893i
$981$	−15.4688	+	57.7304i	−0.0157684	+	0.0588485i
$982$	144.910	+	540.813i	0.147566	+	0.550726i
$983$	−166.616	−	96.1956i	−0.169497	−	0.0978592i	0.412852	−	0.910798i	$-0.364533\pi$
$983$	−166.616	−	96.1956i	−0.169497	−	0.0978592i	−0.582349	+	0.812939i	$0.697866\pi$
$984$	482.318	−	129.237i	0.490161	−	0.131338i
$985$	−343.681	−	343.681i	−0.348915	−	0.348915i
$986$	−933.507	−	250.132i	−0.946761	−	0.253684i
$987$	−468.932	−	270.738i	−0.475109	−	0.274304i
$988$	−256.382			−0.259496
$989$		−	93.8967i		−	0.0949410i
$990$	−304.783	−	175.967i	−0.307862	−	0.177744i
$991$	1187.28	−	1187.28i	1.19806	−	1.19806i	0.223315	−	0.974746i	$-0.428312\pi$
$991$	1187.28	−	1187.28i	1.19806	−	1.19806i	0.974746	−	0.223315i	$-0.0716879\pi$
$992$	−29.7752	+	17.1907i	−0.0300154	+	0.0173294i
$993$	−1026.30	+	1026.30i	−1.03354	+	1.03354i
$994$	1675.63	+	448.984i	1.68575	+	0.451694i
$995$	475.291	+	823.228i	0.477679	+	0.827365i
$996$	−119.562	−	207.088i	−0.120042	−	0.207919i
$997$	−1628.75	+	436.421i	−1.63365	+	0.437734i	−0.954970	−	0.296703i	$-0.904113\pi$
$997$	−1628.75	+	436.421i	−1.63365	+	0.437734i	−0.678677	+	0.734437i	$0.737446\pi$
$998$		−	289.537i		−	0.290118i
$999$	614.712	+	177.203i	0.615328	+	0.177380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.3.g.b.23.1	✓	12
37.29	odd	12	inner	74.3.g.b.29.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.3.g.b.23.1	✓	12	1.1	even	1	trivial
74.3.g.b.29.1	yes	12	37.29	odd	12	inner

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	74.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-3.15238 + 1.82002i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 + 3.23205i) q^{5} +(-3.64005 - 3.64005i) q^{6} +(-5.59738 - 9.69495i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.12498 - 3.68058i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(-3.15238 + 1.82002i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-0.866025 + 3.23205i) q^{5} +(-3.64005 - 3.64005i) q^{6} +(-5.59738 - 9.69495i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(2.12498 - 3.68058i) q^{9} -4.73205 q^{10} +17.4995i q^{11} +(3.64005 - 6.30475i) q^{12} +(-5.11981 + 19.1074i) q^{13} +(11.1948 - 11.1948i) q^{14} +(-3.15238 - 11.7648i) q^{15} +(2.00000 - 3.46410i) q^{16} +(16.2014 - 4.34116i) q^{17} +(5.80556 + 1.55559i) q^{18} +(1.67724 - 6.25956i) q^{19} +(-1.73205 - 6.46410i) q^{20} +(35.2901 + 20.3748i) q^{21} +(-23.9048 + 6.40527i) q^{22} +(2.09462 + 2.09462i) q^{23} +(9.94480 + 2.66470i) q^{24} +(11.9545 + 6.90192i) q^{25} -27.9752 q^{26} -17.2904i q^{27} +(19.3899 + 11.1948i) q^{28} +(-28.8094 + 28.8094i) q^{29} +(14.9172 - 8.61245i) q^{30} +(-4.29768 + 4.29768i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-31.8496 - 55.1650i) q^{33} +(11.8603 + 20.5426i) q^{34} +(36.1820 - 9.69495i) q^{35} +8.49993i q^{36} +(-10.2486 + 35.5523i) q^{37} +9.16463 q^{38} +(-18.6364 - 69.5519i) q^{39} +(8.19615 - 4.73205i) q^{40} +(42.0018 - 24.2498i) q^{41} +(-14.9154 + 55.6649i) q^{42} +(-22.4138 - 22.4138i) q^{43} +(-17.4995 - 30.3101i) q^{44} +(10.0555 + 10.0555i) q^{45} +(-2.09462 + 3.62799i) q^{46} -13.2879 q^{47} +14.5602i q^{48} +(-38.1614 + 66.0974i) q^{49} +(-5.05256 + 18.8564i) q^{50} +(-43.1720 + 43.1720i) q^{51} +(-10.2396 - 38.2148i) q^{52} +(41.2891 - 71.5148i) q^{53} +(23.6191 - 6.32872i) q^{54} +(-56.5593 - 15.1550i) q^{55} +(-8.19514 + 30.5847i) q^{56} +(6.10525 + 22.7851i) q^{57} +(-49.8994 - 28.8094i) q^{58} +(4.02075 - 1.07736i) q^{59} +(17.2249 + 17.2249i) q^{60} +(23.2395 + 6.22701i) q^{61} +(-7.44381 - 4.29768i) q^{62} -47.5773 q^{63} +8.00000i q^{64} +(-57.3222 - 33.0950i) q^{65} +(63.6991 - 63.6991i) q^{66} +(-12.5276 + 7.23280i) q^{67} +(-23.7205 + 23.7205i) q^{68} +(-10.4153 - 2.79077i) q^{69} +(26.4871 + 45.8770i) q^{70} +(54.7866 + 94.8932i) q^{71} +(-11.6111 + 3.11119i) q^{72} -47.0811i q^{73} +(-52.3166 - 0.986866i) q^{74} -50.2467 q^{75} +(3.35449 + 12.5191i) q^{76} +(169.657 - 97.9515i) q^{77} +(88.1882 - 50.9155i) q^{78} +(-39.2697 + 146.556i) q^{79} +(9.46410 + 9.46410i) q^{80} +(50.5937 + 87.6309i) q^{81} +(48.4995 + 48.4995i) q^{82} +(16.4232 - 28.4457i) q^{83} -81.4990 q^{84} +56.1234i q^{85} +(22.4138 - 38.8218i) q^{86} +(38.3842 - 143.252i) q^{87} +(34.9990 - 34.9990i) q^{88} +(-12.0761 - 45.0687i) q^{89} +(-10.0555 + 17.4167i) q^{90} +(213.903 - 57.3151i) q^{91} +(-5.72261 - 1.53337i) q^{92} +(5.72602 - 21.3698i) q^{93} +(-4.86372 - 18.1516i) q^{94} +(18.7787 + 10.8419i) q^{95} +(-19.8896 + 5.32940i) q^{96} +(-50.0503 - 50.0503i) q^{97} +(-104.259 - 27.9361i) q^{98} +(64.4083 + 37.1861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 + 4 * q^6 - 8 * q^7 - 24 * q^8 + 28 * q^9	\( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9} - 36 q^{10} - 4 q^{12} + 16 q^{13} + 16 q^{14} + 24 q^{16} + 40 q^{17} + 28 q^{18} - 26 q^{19} + 66 q^{21} + 4 q^{22} - 80 q^{23} - 4 q^{24} - 54 q^{25} - 124 q^{26} - 12 q^{28} + 16 q^{29} - 6 q^{30} - 32 q^{31} + 24 q^{32} - 20 q^{33} - 10 q^{34} + 12 q^{35} - 148 q^{37} + 92 q^{38} + 216 q^{39} + 36 q^{40} + 66 q^{41} - 46 q^{42} + 152 q^{43} - 16 q^{44} + 84 q^{45} + 80 q^{46} - 112 q^{47} - 160 q^{49} + 168 q^{50} - 446 q^{51} + 32 q^{52} + 74 q^{53} + 230 q^{54} + 28 q^{56} + 50 q^{57} + 84 q^{58} - 114 q^{59} - 12 q^{60} + 448 q^{61} - 204 q^{62} - 784 q^{63} - 138 q^{65} + 40 q^{66} + 468 q^{67} + 20 q^{68} - 278 q^{69} + 18 q^{70} + 116 q^{71} - 56 q^{72} - 2 q^{74} + 76 q^{75} - 52 q^{76} + 60 q^{77} - 366 q^{78} + 114 q^{79} + 72 q^{80} + 14 q^{81} + 128 q^{82} - 20 q^{83} - 80 q^{84} - 152 q^{86} + 770 q^{87} + 32 q^{88} + 340 q^{89} - 84 q^{90} + 792 q^{91} + 68 q^{92} - 498 q^{93} + 20 q^{94} + 60 q^{95} + 8 q^{96} - 356 q^{97} - 160 q^{98} - 348 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 4 * q^6 - 8 * q^7 - 24 * q^8 + 28 * q^9 - 36 * q^10 - 4 * q^12 + 16 * q^13 + 16 * q^14 + 24 * q^16 + 40 * q^17 + 28 * q^18 - 26 * q^19 + 66 * q^21 + 4 * q^22 - 80 * q^23 - 4 * q^24 - 54 * q^25 - 124 * q^26 - 12 * q^28 + 16 * q^29 - 6 * q^30 - 32 * q^31 + 24 * q^32 - 20 * q^33 - 10 * q^34 + 12 * q^35 - 148 * q^37 + 92 * q^38 + 216 * q^39 + 36 * q^40 + 66 * q^41 - 46 * q^42 + 152 * q^43 - 16 * q^44 + 84 * q^45 + 80 * q^46 - 112 * q^47 - 160 * q^49 + 168 * q^50 - 446 * q^51 + 32 * q^52 + 74 * q^53 + 230 * q^54 + 28 * q^56 + 50 * q^57 + 84 * q^58 - 114 * q^59 - 12 * q^60 + 448 * q^61 - 204 * q^62 - 784 * q^63 - 138 * q^65 + 40 * q^66 + 468 * q^67 + 20 * q^68 - 278 * q^69 + 18 * q^70 + 116 * q^71 - 56 * q^72 - 2 * q^74 + 76 * q^75 - 52 * q^76 + 60 * q^77 - 366 * q^78 + 114 * q^79 + 72 * q^80 + 14 * q^81 + 128 * q^82 - 20 * q^83 - 80 * q^84 - 152 * q^86 + 770 * q^87 + 32 * q^88 + 340 * q^89 - 84 * q^90 + 792 * q^91 + 68 * q^92 - 498 * q^93 + 20 * q^94 + 60 * q^95 + 8 * q^96 - 356 * q^97 - 160 * q^98 - 348 * q^99

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