LMFDB - Embedded newform 36.3.f.c.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,3,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.980928951697$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$0.186266 + 1.99131i$ of defining polynomial
Character	$\chi$	$=$	36.31
Dual form			36.3.f.c.7.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.186266 - 1.99131i) q^{2} +(-2.67178 - 1.36441i) q^{3} +(-3.93061 + 0.741826i) q^{4} +(3.07403 - 5.32438i) q^{5} +(-2.21930 + 5.57447i) q^{6} +(0.511543 - 0.295340i) q^{7} +(2.20934 + 7.68888i) q^{8} +(5.27677 + 7.29079i) q^{9} +O(q^{10})$	\(q+(-0.186266 - 1.99131i) q^{2} +(-2.67178 - 1.36441i) q^{3} +(-3.93061 + 0.741826i) q^{4} +(3.07403 - 5.32438i) q^{5} +(-2.21930 + 5.57447i) q^{6} +(0.511543 - 0.295340i) q^{7} +(2.20934 + 7.68888i) q^{8} +(5.27677 + 7.29079i) q^{9} +(-11.1751 - 5.12959i) q^{10} +(15.1205 - 8.72982i) q^{11} +(11.5139 + 3.38097i) q^{12} +(-0.892255 + 1.54543i) q^{13} +(-0.683395 - 0.963628i) q^{14} +(-15.4778 + 10.0313i) q^{15} +(14.8994 - 5.83166i) q^{16} -16.9171 q^{17} +(13.5353 - 11.8657i) q^{18} +19.5058i q^{19} +(-8.13306 + 23.2084i) q^{20} +(-1.76969 + 0.0911265i) q^{21} +(-20.2002 - 28.4835i) q^{22} +(-6.86778 - 3.96511i) q^{23} +(4.58791 - 23.5574i) q^{24} +(-6.39933 - 11.0840i) q^{25} +(3.24362 + 1.48889i) q^{26} +(-4.15071 - 26.6790i) q^{27} +(-1.79159 + 1.54034i) q^{28} +(3.17517 + 5.49956i) q^{29} +(22.8584 + 28.9525i) q^{30} +(27.6558 + 15.9671i) q^{31} +(-14.3879 - 28.5830i) q^{32} +(-52.3096 + 2.69357i) q^{33} +(3.15108 + 33.6871i) q^{34} -3.63153i q^{35} +(-26.1494 - 24.7428i) q^{36} +58.2834 q^{37} +(38.8420 - 3.63326i) q^{38} +(4.49251 - 2.91164i) q^{39} +(47.7301 + 11.8725i) q^{40} +(-2.66948 + 4.62368i) q^{41} +(0.511095 + 3.50703i) q^{42} +(-33.9324 + 19.5909i) q^{43} +(-52.9567 + 45.5303i) q^{44} +(55.0399 - 5.68339i) q^{45} +(-6.61653 + 14.4144i) q^{46} +(-9.64117 + 5.56633i) q^{47} +(-47.7646 - 4.74800i) q^{48} +(-24.3255 + 42.1331i) q^{49} +(-20.8796 + 14.8076i) q^{50} +(45.1987 + 23.0819i) q^{51} +(2.36067 - 6.73638i) q^{52} +35.8770 q^{53} +(-52.3530 + 13.2347i) q^{54} -107.343i q^{55} +(3.40100 + 3.28069i) q^{56} +(26.6139 - 52.1151i) q^{57} +(10.3599 - 7.34713i) q^{58} +(-20.8974 - 12.0651i) q^{59} +(53.3955 - 50.9109i) q^{60} +(-37.9460 - 65.7244i) q^{61} +(26.6441 - 58.0454i) q^{62} +(4.85256 + 2.17112i) q^{63} +(-54.2376 + 33.9747i) q^{64} +(5.48564 + 9.50141i) q^{65} +(15.1072 + 103.663i) q^{66} +(-31.8200 - 18.3713i) q^{67} +(66.4945 - 12.5495i) q^{68} +(12.9391 + 19.9644i) q^{69} +(-7.23150 + 0.676431i) q^{70} +87.8370i q^{71} +(-44.3998 + 56.6803i) q^{72} -60.0423 q^{73} +(-10.8562 - 116.060i) q^{74} +(1.97450 + 38.3452i) q^{75} +(-14.4699 - 76.6696i) q^{76} +(5.15652 - 8.93136i) q^{77} +(-6.63478 - 8.40362i) q^{78} +(32.1841 - 18.5815i) q^{79} +(14.7512 - 97.2567i) q^{80} +(-25.3114 + 76.9437i) q^{81} +(9.70439 + 4.45452i) q^{82} +(-66.0281 + 38.1214i) q^{83} +(6.88838 - 1.67099i) q^{84} +(-52.0037 + 90.0730i) q^{85} +(45.3319 + 63.9207i) q^{86} +(-0.979694 - 19.0258i) q^{87} +(100.529 + 96.9724i) q^{88} -27.5873 q^{89} +(-21.5694 - 108.543i) q^{90} +1.05407i q^{91} +(29.9360 + 10.4906i) q^{92} +(-52.1045 - 80.3944i) q^{93} +(12.8801 + 18.1617i) q^{94} +(103.856 + 59.9614i) q^{95} +(-0.557801 + 95.9984i) q^{96} +(13.0585 + 22.6180i) q^{97} +(88.4309 + 40.5917i) q^{98} +(143.435 + 64.1751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9	$ 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9} + 20 q^{10} - 36 q^{12} - 46 q^{13} - 12 q^{14} - 17 q^{16} + 12 q^{17} + 48 q^{18} + 36 q^{20} - 66 q^{21} + 33 q^{22} + 129 q^{24} - 30 q^{25} + 72 q^{26} + 12 q^{28} + 42 q^{29} + 84 q^{30} + 87 q^{32} - 168 q^{33} + 11 q^{34} - 81 q^{36} + 56 q^{37} - 99 q^{38} + 68 q^{40} + 84 q^{41} - 354 q^{42} - 222 q^{44} + 174 q^{45} - 264 q^{46} - 189 q^{48} + 58 q^{49} - 219 q^{50} + 110 q^{52} - 72 q^{53} - 105 q^{54} + 270 q^{56} + 366 q^{57} - 16 q^{58} + 432 q^{60} - 34 q^{61} + 516 q^{62} - 254 q^{64} - 30 q^{65} + 510 q^{66} + 375 q^{68} - 54 q^{69} + 150 q^{70} - 45 q^{72} + 116 q^{73} - 372 q^{74} - 15 q^{76} - 330 q^{77} - 294 q^{78} - 720 q^{80} - 102 q^{81} + 254 q^{82} - 714 q^{84} - 140 q^{85} - 273 q^{86} + 75 q^{88} - 384 q^{89} + 108 q^{90} + 258 q^{92} - 486 q^{93} + 36 q^{94} + 900 q^{96} - 148 q^{97} + 1170 q^{98}+O(q^{100}) $ 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9 + 20 * q^10 - 36 * q^12 - 46 * q^13 - 12 * q^14 - 17 * q^16 + 12 * q^17 + 48 * q^18 + 36 * q^20 - 66 * q^21 + 33 * q^22 + 129 * q^24 - 30 * q^25 + 72 * q^26 + 12 * q^28 + 42 * q^29 + 84 * q^30 + 87 * q^32 - 168 * q^33 + 11 * q^34 - 81 * q^36 + 56 * q^37 - 99 * q^38 + 68 * q^40 + 84 * q^41 - 354 * q^42 - 222 * q^44 + 174 * q^45 - 264 * q^46 - 189 * q^48 + 58 * q^49 - 219 * q^50 + 110 * q^52 - 72 * q^53 - 105 * q^54 + 270 * q^56 + 366 * q^57 - 16 * q^58 + 432 * q^60 - 34 * q^61 + 516 * q^62 - 254 * q^64 - 30 * q^65 + 510 * q^66 + 375 * q^68 - 54 * q^69 + 150 * q^70 - 45 * q^72 + 116 * q^73 - 372 * q^74 - 15 * q^76 - 330 * q^77 - 294 * q^78 - 720 * q^80 - 102 * q^81 + 254 * q^82 - 714 * q^84 - 140 * q^85 - 273 * q^86 + 75 * q^88 - 384 * q^89 + 108 * q^90 + 258 * q^92 - 486 * q^93 + 36 * q^94 + 900 * q^96 - 148 * q^97 + 1170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.186266	−	1.99131i	−0.0931330	−	0.995654i
$2$	−0.186266	−	1.99131i	−0.0931330	−	0.995654i
$3$	−2.67178	−	1.36441i	−0.890592	−	0.454803i
$3$	−2.67178	−	1.36441i	−0.890592	−	0.454803i
$4$	−3.93061	+	0.741826i	−0.982652	+	0.185456i
$5$	3.07403	−	5.32438i	0.614806	−	1.06488i	−0.375612	−	0.926777i	$-0.622568\pi$
$5$	3.07403	−	5.32438i	0.614806	−	1.06488i	0.990418	−	0.138099i	$-0.0440991\pi$
$6$	−2.21930	+	5.57447i	−0.369883	+	0.929078i
$7$	0.511543	−	0.295340i	0.0730776	−	0.0421914i	−0.463016	−	0.886350i	$-0.653233\pi$
$7$	0.511543	−	0.295340i	0.0730776	−	0.0421914i	0.536094	+	0.844159i	$0.319899\pi$
$8$	2.20934	+	7.68888i	0.276168	+	0.961109i
$9$	5.27677	+	7.29079i	0.586308	+	0.810088i
$10$	−11.1751	−	5.12959i	−1.11751	−	0.512959i
$11$	15.1205	−	8.72982i	1.37459	−	0.793620i	0.383088	−	0.923712i	$-0.374861\pi$
$11$	15.1205	−	8.72982i	1.37459	−	0.793620i	0.991502	+	0.130092i	$0.0415274\pi$
$12$	11.5139	+	3.38097i	0.959489	+	0.281748i
$13$	−0.892255	+	1.54543i	−0.0686350	+	0.118879i	−0.898301	−	0.439381i	$-0.855198\pi$
$13$	−0.892255	+	1.54543i	−0.0686350	+	0.118879i	0.829666	+	0.558261i	$0.188531\pi$
$14$	−0.683395	−	0.963628i	−0.0488140	−	0.0688306i
$15$	−15.4778	+	10.0313i	−1.03185	+	0.668754i
$16$	14.8994	−	5.83166i	0.931212	−	0.364479i
$17$	−16.9171			−0.995123			−0.497562	−	0.867429i	$-0.665771\pi$
$17$	−16.9171			−0.995123			−0.497562	+	0.867429i	$0.665771\pi$
$18$	13.5353	−	11.8657i	0.751963	−	0.659206i
$19$			19.5058i			1.02662i	0.858203	+	0.513310i	$0.171581\pi$
$19$			19.5058i			1.02662i	−0.858203	+	0.513310i	$0.828419\pi$
$20$	−8.13306	+	23.2084i	−0.406653	+	1.16042i
$21$	−1.76969	+	0.0911265i	−0.0842711	+	0.00433936i
$22$	−20.2002	−	28.4835i	−0.918190	−	1.29470i
$23$	−6.86778	−	3.96511i	−0.298599	−	0.172396i	0.343214	−	0.939257i	$-0.388484\pi$
$23$	−6.86778	−	3.96511i	−0.298599	−	0.172396i	−0.641813	+	0.766861i	$0.721818\pi$
$24$	4.58791	−	23.5574i	0.191163	−	0.981558i
$25$	−6.39933	−	11.0840i	−0.255973	−	0.443359i
$26$	3.24362	+	1.48889i	0.124755	+	0.0572651i
$27$	−4.15071	−	26.6790i	−0.153730	−	0.988113i
$28$	−1.79159	+	1.54034i	−0.0639852	+	0.0550122i
$29$	3.17517	+	5.49956i	0.109489	+	0.189640i	0.915563	−	0.402174i	$-0.131745\pi$
$29$	3.17517	+	5.49956i	0.109489	+	0.189640i	−0.806075	+	0.591814i	$0.798412\pi$
$30$	22.8584	+	28.9525i	0.761946	+	0.965083i
$31$	27.6558	+	15.9671i	0.892124	+	0.515068i	0.874637	−	0.484779i	$-0.161100\pi$
$31$	27.6558	+	15.9671i	0.892124	+	0.515068i	0.0174873	+	0.999847i	$0.494433\pi$
$32$	−14.3879	−	28.5830i	−0.449621	−	0.893219i
$33$	−52.3096	+	2.69357i	−1.58514	+	0.0816233i
$34$	3.15108	+	33.6871i	0.0926788	+	0.990798i
$35$		−	3.63153i		−	0.103758i
$36$	−26.1494	−	24.7428i	−0.726373	−	0.687301i
$37$	58.2834			1.57523			0.787614	−	0.616169i	$-0.211316\pi$
$37$	58.2834			1.57523			0.787614	+	0.616169i	$0.211316\pi$
$38$	38.8420	−	3.63326i	1.02216	−	0.0956122i
$39$	4.49251	−	2.91164i	0.115192	−	0.0746575i
$40$	47.7301	+	11.8725i	1.19325	+	0.296812i
$41$	−2.66948	+	4.62368i	−0.0651093	+	0.112773i	−0.896742	−	0.442553i	$-0.854073\pi$
$41$	−2.66948	+	4.62368i	−0.0651093	+	0.112773i	0.831633	+	0.555325i	$0.187406\pi$
$42$	0.511095	+	3.50703i	0.0121689	+	0.0835007i
$43$	−33.9324	+	19.5909i	−0.789126	+	0.455602i	−0.839655	−	0.543121i	$-0.817243\pi$
$43$	−33.9324	+	19.5909i	−0.789126	+	0.455602i	0.0505290	+	0.998723i	$0.483909\pi$
$44$	−52.9567	+	45.5303i	−1.20356	+	1.03478i
$45$	55.0399	−	5.68339i	1.22311	−	0.126298i
$46$	−6.61653	+	14.4144i	−0.143838	+	0.313357i
$47$	−9.64117	+	5.56633i	−0.205131	+	0.118433i	−0.599047	−	0.800714i	$-0.704454\pi$
$47$	−9.64117	+	5.56633i	−0.205131	+	0.118433i	0.393915	+	0.919147i	$0.371120\pi$
$48$	−47.7646	−	4.74800i	−0.995096	−	0.0989166i
$49$	−24.3255	+	42.1331i	−0.496440	+	0.859859i
$50$	−20.8796	+	14.8076i	−0.417592	+	0.296152i
$51$	45.1987	+	23.0819i	0.886249	+	0.452585i
$52$	2.36067	−	6.73638i	0.0453974	−	0.129546i
$53$	35.8770			0.676925			0.338462	−	0.940980i	$-0.390093\pi$
$53$	35.8770			0.676925			0.338462	+	0.940980i	$0.390093\pi$
$54$	−52.3530	+	13.2347i	−0.969501	+	0.245088i
$55$		−	107.343i		−	1.95169i
$56$	3.40100	+	3.28069i	0.0607322	+	0.0585837i
$57$	26.6139	−	52.1151i	0.466910	−	0.914299i
$58$	10.3599	−	7.34713i	0.178619	−	0.126675i
$59$	−20.8974	−	12.0651i	−0.354194	−	0.204494i	0.312337	−	0.949971i	$-0.398888\pi$
$59$	−20.8974	−	12.0651i	−0.354194	−	0.204494i	−0.666531	+	0.745477i	$0.732222\pi$
$60$	53.3955	−	50.9109i	0.889926	−	0.848516i
$61$	−37.9460	−	65.7244i	−0.622066	−	1.07745i	−0.989100	−	0.147243i	$-0.952960\pi$
$61$	−37.9460	−	65.7244i	−0.622066	−	1.07745i	0.367034	−	0.930207i	$-0.380373\pi$
$62$	26.6441	−	58.0454i	0.429743	−	0.936216i
$63$	4.85256	+	2.17112i	0.0770247	+	0.0344622i
$64$	−54.2376	+	33.9747i	−0.847463	+	0.530855i
$65$	5.48564	+	9.50141i	0.0843944	+	0.146175i
$66$	15.1072	+	103.663i	0.228897	+	1.57065i
$67$	−31.8200	−	18.3713i	−0.474925	−	0.274198i	0.243374	−	0.969933i	$-0.421746\pi$
$67$	−31.8200	−	18.3713i	−0.474925	−	0.274198i	−0.718299	+	0.695734i	$0.755079\pi$
$68$	66.4945	−	12.5495i	0.977860	−	0.184552i
$69$	12.9391	+	19.9644i	0.187524	+	0.289339i
$70$	−7.23150	+	0.676431i	−0.103307	+	0.00966331i
$71$			87.8370i			1.23714i	0.785730	+	0.618570i	$0.212288\pi$
$71$			87.8370i			1.23714i	−0.785730	+	0.618570i	$0.787712\pi$
$72$	−44.3998	+	56.6803i	−0.616664	+	0.787226i
$73$	−60.0423			−0.822498			−0.411249	−	0.911523i	$-0.634907\pi$
$73$	−60.0423			−0.822498			−0.411249	+	0.911523i	$0.634907\pi$
$74$	−10.8562	−	116.060i	−0.146706	−	1.56838i
$75$	1.97450	+	38.3452i	0.0263267	+	0.511269i
$76$	−14.4699	−	76.6696i	−0.190393	−	1.00881i
$77$	5.15652	−	8.93136i	0.0669678	−	0.115992i
$78$	−6.63478	−	8.40362i	−0.0850613	−	0.107739i
$79$	32.1841	−	18.5815i	0.407394	−	0.235209i	−0.282275	−	0.959333i	$-0.591089\pi$
$79$	32.1841	−	18.5815i	0.407394	−	0.235209i	0.689669	+	0.724124i	$0.257756\pi$
$80$	14.7512	−	97.2567i	0.184391	−	1.21571i
$81$	−25.3114	+	76.9437i	−0.312486	+	0.949922i
$82$	9.70439	+	4.45452i	0.118346	+	0.0543234i
$83$	−66.0281	+	38.1214i	−0.795520	+	0.459294i	−0.841902	−	0.539630i	$-0.818564\pi$
$83$	−66.0281	+	38.1214i	−0.795520	+	0.459294i	0.0463824	+	0.998924i	$0.485231\pi$
$84$	6.88838	−	1.67099i	0.0820045	−	0.0198927i
$85$	−52.0037	+	90.0730i	−0.611808	+	1.05968i
$86$	45.3319	+	63.9207i	0.527115	+	0.743264i
$87$	−0.979694	−	19.0258i	−0.0112609	−	0.218688i
$88$	100.529	+	96.9724i	1.14237	+	1.10196i
$89$	−27.5873			−0.309969			−0.154985	−	0.987917i	$-0.549533\pi$
$89$	−27.5873			−0.309969			−0.154985	+	0.987917i	$0.549533\pi$
$90$	−21.5694	−	108.543i	−0.239660	−	1.20603i
$91$			1.05407i			0.0115832i
$92$	29.9360	+	10.4906i	0.325391	+	0.114028i
$93$	−52.1045	−	80.3944i	−0.560264	−	0.864456i
$94$	12.8801	+	18.1617i	0.137022	+	0.193210i
$95$	103.856	+	59.9614i	1.09322	+	0.631172i
$96$	−0.557801	+	95.9984i	−0.00581043	+	0.999983i
$97$	13.0585	+	22.6180i	0.134624	+	0.233176i	0.925454	−	0.378861i	$-0.123684\pi$
$97$	13.0585	+	22.6180i	0.134624	+	0.233176i	−0.790830	+	0.612036i	$0.790351\pi$
$98$	88.4309	+	40.5917i	0.902357	+	0.414201i
$99$	143.435	+	64.1751i	1.44883	+	0.648234i
$100$	33.3757	+	38.8196i	0.333757	+	0.388196i
$101$	−12.8831	−	22.3142i	−0.127556	−	0.220933i	0.795173	−	0.606382i	$-0.207380\pi$
$101$	−12.8831	−	22.3142i	−0.127556	−	0.220933i	−0.922729	+	0.385449i	$0.874047\pi$
$102$	37.5441	−	94.3038i	0.368079	−	0.924547i
$103$	−16.9947	−	9.81187i	−0.164997	−	0.0952609i	0.415228	−	0.909717i	$-0.363702\pi$
$103$	−16.9947	−	9.81187i	−0.164997	−	0.0952609i	−0.580225	+	0.814457i	$0.697035\pi$
$104$	−13.8539	−	3.44605i	−0.133211	−	0.0331351i
$105$	−4.95490	+	9.70264i	−0.0471895	+	0.0924061i
$106$	−6.68267	−	71.4422i	−0.0630441	−	0.673983i
$107$		−	183.200i		−	1.71215i	−0.516850	−	0.856076i	$-0.672895\pi$
$107$		−	183.200i		−	1.71215i	0.516850	−	0.856076i	$-0.327105\pi$
$108$	36.1060	+	101.786i	0.334315	+	0.942461i
$109$	100.841			0.925147			0.462573	−	0.886581i	$-0.346926\pi$
$109$	100.841			0.925147			0.462573	+	0.886581i	$0.346926\pi$
$110$	−213.753	+	19.9943i	−1.94321	+	0.181767i
$111$	−155.720	−	79.5225i	−1.40288	−	0.716419i
$112$	5.89936	−	7.38353i	0.0526729	−	0.0659243i
$113$	−9.12484	+	15.8047i	−0.0807508	+	0.139865i	−0.903573	−	0.428435i	$-0.859065\pi$
$113$	−9.12484	+	15.8047i	−0.0807508	+	0.139865i	0.822822	+	0.568299i	$0.192398\pi$
$114$	−108.734	−	43.2891i	−0.953810	−	0.379729i
$115$	−42.2235	+	24.3778i	−0.367161	+	0.211981i
$116$	−16.5601	−	19.2612i	−0.142759	−	0.166045i
$117$	−15.9756	+	1.64964i	−0.136544	+	0.0140995i
$118$	−20.1329	+	43.8606i	−0.170618	+	0.371700i
$119$	−8.65383	+	4.99629i	−0.0727212	+	0.0419856i
$120$	−111.325	−	96.8439i	−0.927709	−	0.807033i
$121$	91.9194	−	159.209i	0.759664	−	1.31578i
$122$	−123.810	+	87.8044i	−1.01483	+	0.719708i
$123$	13.4408	−	8.71116i	0.109275	−	0.0708224i
$124$	−120.549	−	42.2447i	−0.972170	−	0.340683i
$125$	75.0146			0.600117
$126$	3.41950	−	10.0673i	0.0271389	−	0.0798995i
$127$			164.386i			1.29438i	0.762331	+	0.647188i	$0.224055\pi$
$127$			164.386i			1.29438i	−0.762331	+	0.647188i	$0.775945\pi$
$128$	77.7567	+	101.675i	0.607474	+	0.794339i
$129$	117.390	−	6.04473i	0.909998	−	0.0468584i
$130$	17.8984	−	12.6934i	0.137680	−	0.0976414i
$131$	−123.421	−	71.2570i	−0.942143	−	0.543947i	−0.0515116	−	0.998672i	$-0.516404\pi$
$131$	−123.421	−	71.2570i	−0.942143	−	0.543947i	−0.890631	+	0.454726i	$0.849737\pi$
$132$	203.610	−	49.3920i	1.54250	−	0.374182i
$133$	5.76083	+	9.97805i	0.0433145	+	0.0750229i
$134$	−30.6559	+	66.7853i	−0.228775	+	0.498398i
$135$	−154.809	−	59.9122i	−1.14673	−	0.443794i
$136$	−37.3757	−	130.073i	−0.274821	−	0.956422i
$137$	−3.08176	−	5.33777i	−0.0224946	−	0.0389618i	0.854559	−	0.519354i	$-0.173828\pi$
$137$	−3.08176	−	5.33777i	−0.0224946	−	0.0389618i	−0.877054	+	0.480393i	$0.840494\pi$
$138$	37.3451	−	29.4845i	0.270616	−	0.213655i
$139$	103.168	+	59.5642i	0.742218	+	0.428519i	0.822875	−	0.568222i	$-0.192369\pi$
$139$	103.168	+	59.5642i	0.742218	+	0.428519i	−0.0806575	+	0.996742i	$0.525702\pi$
$140$	2.69397	+	14.2741i	0.0192426	+	0.101958i
$141$	33.3538	−	1.71748i	0.236552	−	0.0121807i
$142$	174.910	−	16.3610i	1.23176	−	0.115219i
$143$			31.1569i			0.217880i
$144$	121.138	+	77.8561i	0.841237	+	0.540667i
$145$	39.0423			0.269257
$146$	11.1838	+	119.563i	0.0766017	+	0.818923i
$147$	122.479	−	79.3801i	0.833192	−	0.540001i
$148$	−229.089	+	43.2361i	−1.54790	+	0.292136i
$149$	−103.365	+	179.034i	−0.693726	+	1.20157i	0.276882	+	0.960904i	$0.410699\pi$
$149$	−103.365	+	179.034i	−0.693726	+	1.20157i	−0.970608	+	0.240665i	$0.922634\pi$
$150$	75.9893	−	11.0742i	0.506595	−	0.0738283i
$151$	127.422	−	73.5670i	0.843853	−	0.487199i	−0.0147190	−	0.999892i	$-0.504685\pi$
$151$	127.422	−	73.5670i	0.843853	−	0.487199i	0.858572	+	0.512693i	$0.171352\pi$
$152$	−149.977	+	43.0949i	−0.986694	+	0.283519i
$153$	−89.2676	−	123.339i	−0.583449	−	0.806138i
$154$	−18.7456	−	8.60461i	−0.121724	−	0.0558741i
$155$	170.030	−	98.1668i	1.09697	−	0.633334i
$156$	−15.4984	+	14.7772i	−0.0993485	+	0.0947256i
$157$	31.4395	−	54.4548i	0.200251	−	0.346846i	−0.748358	−	0.663295i	$-0.769157\pi$
$157$	31.4395	−	54.4548i	0.200251	−	0.346846i	0.948609	+	0.316449i	$0.102491\pi$
$158$	−42.9963	−	60.6274i	−0.272129	−	0.383718i
$159$	−95.8554	−	48.9510i	−0.602864	−	0.307868i
$160$	−196.416	−	11.2586i	−1.22760	−	0.0703665i
$161$	−4.68422			−0.0290946
$162$	157.933	+	36.0707i	0.974896	+	0.222659i
$163$			143.325i			0.879292i	0.898171	+	0.439646i	$0.144896\pi$
$163$			143.325i			0.879292i	−0.898171	+	0.439646i	$0.855104\pi$
$164$	7.06272	−	20.1542i	0.0430654	−	0.122891i
$165$	−146.460	+	286.796i	−0.887635	+	1.73816i
$166$	88.2102	+	124.382i	0.531386	+	0.749287i
$167$	150.531	+	86.9089i	0.901381	+	0.520413i	0.877648	−	0.479306i	$-0.159111\pi$
$167$	150.531	+	86.9089i	0.901381	+	0.520413i	0.0237332	+	0.999718i	$0.492445\pi$
$168$	−4.61052	−	13.4056i	−0.0274436	−	0.0797954i
$169$	82.9078	+	143.600i	0.490578	+	0.849707i
$170$	189.050	+	86.7777i	1.11206	+	0.510457i
$171$	−142.213	+	102.927i	−0.831653	+	0.601915i
$172$	118.842	−	102.176i	0.690942	−	0.594047i
$173$	−125.806	−	217.902i	−0.727201	−	1.25955i	−0.958062	−	0.286562i	$-0.907488\pi$
$173$	−125.806	−	217.902i	−0.727201	−	1.25955i	0.230861	−	0.972987i	$-0.425846\pi$
$174$	−37.7038	+	5.49474i	−0.216688	+	0.0315790i
$175$	−6.54707	−	3.77995i	−0.0374118	−	0.0215997i
$176$	174.377	−	218.246i	0.990777	−	1.24004i
$177$	39.3715	+	60.7480i	0.222438	+	0.343209i
$178$	5.13857	+	54.9347i	0.0288684	+	0.308622i
$179$		−	96.0059i		−	0.536346i	−0.963371	−	0.268173i	$-0.913580\pi$
$179$		−	96.0059i		−	0.536346i	0.963371	−	0.268173i	$-0.0864199\pi$
$180$	−212.124	+	63.1692i	−1.17847	+	0.350940i
$181$	−328.757			−1.81634			−0.908170	−	0.418603i	$-0.862520\pi$
$181$	−328.757			−1.81634			−0.908170	+	0.418603i	$0.862520\pi$
$182$	2.09898	−	0.196338i	0.0115329	−	0.00107878i
$183$	11.7082	+	227.375i	0.0639791	+	1.24249i
$184$	15.3140	−	61.5658i	0.0832282	−	0.334597i
$185$	179.165	−	310.323i	0.968460	−	1.67742i
$186$	−150.385	+	118.731i	−0.808520	+	0.638338i
$187$	−255.795	+	147.683i	−1.36789	+	0.789749i
$188$	33.7664	−	29.0312i	0.179609	−	0.154421i
$189$	−10.0027	−	12.4216i	−0.0529241	−	0.0657229i
$190$	100.057	−	217.978i	0.526614	−	1.14725i
$191$	−0.351914	+	0.203178i	−0.00184248	+	0.00106376i	−0.500921	−	0.865493i	$-0.667005\pi$
$191$	−0.351914	+	0.203178i	−0.00184248	+	0.00106376i	0.499078	+	0.866557i	$0.333672\pi$
$192$	191.266	−	16.7705i	0.996178	−	0.0873463i
$193$	−31.2230	+	54.0798i	−0.161777	+	0.280206i	−0.935506	−	0.353311i	$-0.885056\pi$
$193$	−31.2230	+	54.0798i	−0.161777	+	0.280206i	0.773729	+	0.633517i	$0.218389\pi$
$194$	42.6071	−	30.2165i	0.219624	−	0.155755i
$195$	−1.69258	−	32.8703i	−0.00867992	−	0.168566i
$196$	64.3588	−	183.654i	0.328361	−	0.937010i
$197$	−207.861			−1.05513			−0.527566	−	0.849514i	$-0.676895\pi$
$197$	−207.861			−1.05513			−0.527566	+	0.849514i	$0.676895\pi$
$198$	101.075	−	297.576i	0.510482	−	1.50291i
$199$		−	299.128i		−	1.50316i	−0.659643	−	0.751579i	$-0.729293\pi$
$199$		−	299.128i		−	1.50316i	0.659643	−	0.751579i	$-0.270707\pi$
$200$	71.0849	−	73.6919i	0.355425	−	0.368460i
$201$	59.9499	+	92.4995i	0.298258	+	0.460196i
$202$	−42.0348	+	29.8107i	−0.208093	+	0.147578i
$203$	3.24848	+	1.87551i	0.0160024	+	0.00923896i
$204$	−194.781	−	57.1962i	−0.954809	−	0.280374i
$205$	16.4121	+	28.4266i	0.0800592	+	0.138667i
$206$	−16.3729	+	35.6692i	−0.0794802	+	0.173152i
$207$	−7.33086	−	70.9946i	−0.0354148	−	0.342969i
$208$	−4.28163	+	28.2293i	−0.0205848	+	0.135718i
$209$	170.282	+	294.937i	0.814746	+	1.41118i
$210$	20.2439	+	8.05946i	0.0963994	+	0.0383784i
$211$	−141.744	−	81.8360i	−0.671773	−	0.387848i	0.124975	−	0.992160i	$-0.460115\pi$
$211$	−141.744	−	81.8360i	−0.671773	−	0.387848i	−0.796748	+	0.604311i	$0.793448\pi$
$212$	−141.019	+	26.6145i	−0.665182	+	0.125540i
$213$	119.846	−	234.681i	0.562656	−	1.10179i
$214$	−364.808	+	34.1240i	−1.70471	+	0.159458i
$215$			240.892i			1.12043i
$216$	195.962	−	90.8575i	0.907229	−	0.420636i
$217$	18.8629			0.0869257
$218$	−18.7833	−	200.805i	−0.0861617	−	0.921126i
$219$	160.420	+	81.9223i	0.732510	+	0.374075i
$220$	79.6297	+	421.923i	0.361953	+	1.91783i
$221$	15.0944	−	26.1442i	0.0683003	−	0.118300i
$222$	−129.348	+	324.899i	−0.582650	+	1.46351i
$223$	330.681	−	190.919i	1.48287	−	0.856138i	0.483063	−	0.875586i	$-0.339524\pi$
$223$	330.681	−	190.919i	1.48287	−	0.856138i	0.999811	+	0.0194478i	$0.00619081\pi$
$224$	−15.8017	−	10.3721i	−0.0705434	−	0.0463042i
$225$	47.0431	−	105.144i	0.209081	−	0.467306i
$226$	33.1717	+	15.2265i	0.146777	+	0.0673739i
$227$	−51.5472	+	29.7608i	−0.227080	+	0.131105i	−0.609224	−	0.792998i	$-0.708519\pi$
$227$	−51.5472	+	29.7608i	−0.227080	+	0.131105i	0.382144	+	0.924103i	$0.375186\pi$
$228$	−65.9485	+	224.587i	−0.289248	+	0.985030i
$229$	64.4366	−	111.608i	0.281383	−	0.487369i	−0.690343	−	0.723482i	$-0.742540\pi$
$229$	64.4366	−	111.608i	0.281383	−	0.487369i	0.971726	+	0.236113i	$0.0758736\pi$
$230$	56.4084	+	79.5393i	0.245254	+	0.345823i
$231$	−25.9631	+	16.8270i	−0.112394	+	0.0728441i
$232$	−35.2704	+	36.5639i	−0.152028	+	0.157603i
$233$	14.9939			0.0643513			0.0321757	−	0.999482i	$-0.489756\pi$
$233$	14.9939			0.0643513			0.0321757	+	0.999482i	$0.489756\pi$
$234$	6.26065	+	31.5051i	0.0267549	+	0.134637i
$235$			68.4443i			0.291252i
$236$	91.0899	+	31.9211i	0.385974	+	0.135259i
$237$	−111.342	+	5.73329i	−0.469796	+	0.0241911i
$238$	11.5611	+	16.3018i	0.0485759	+	0.0684949i
$239$	−315.244	−	182.006i	−1.31901	−	0.761532i	−0.335442	−	0.942061i	$-0.608886\pi$
$239$	−315.244	−	182.006i	−1.31901	−	0.761532i	−0.983570	+	0.180529i	$0.942219\pi$
$240$	−172.110	+	239.721i	−0.717125	+	0.998839i
$241$	−40.5235	−	70.1888i	−0.168147	−	0.291240i	0.769621	−	0.638501i	$-0.220445\pi$
$241$	−40.5235	−	70.1888i	−0.168147	−	0.291240i	−0.937769	+	0.347261i	$0.887112\pi$
$242$	−334.156	−	153.385i	−1.38081	−	0.633820i
$243$	172.609	−	171.041i	0.710326	−	0.703873i
$244$	197.907	+	230.188i	0.811095	+	0.943393i
$245$	149.555	+	259.037i	0.610428	+	1.05729i
$246$	−19.8502	−	25.1423i	−0.0806917	−	0.102204i
$247$	−30.1448	−	17.4041i	−0.122044	−	0.0704620i
$248$	−61.6679	+	247.919i	−0.248661	+	0.999674i
$249$	228.426	−	11.7623i	0.917372	−	0.0472381i
$250$	−13.9727	−	149.377i	−0.0558907	−	0.597508i
$251$			281.883i			1.12304i	0.827463	+	0.561520i	$0.189783\pi$
$251$			281.883i			1.12304i	−0.827463	+	0.561520i	$0.810217\pi$
$252$	−20.6841	−	4.93406i	−0.0820798	−	0.0195796i
$253$	−138.459			−0.547268
$254$	327.342	−	30.6195i	1.28875	−	0.120549i
$255$	261.839	−	169.701i	1.02682	−	0.665492i
$256$	187.984	−	173.776i	0.734311	−	0.678813i
$257$	−37.6564	+	65.2227i	−0.146523	+	0.253785i	−0.929940	−	0.367711i	$-0.880142\pi$
$257$	−37.6564	+	65.2227i	−0.146523	+	0.253785i	0.783417	+	0.621496i	$0.213475\pi$
$258$	−33.9026	−	232.633i	−0.131406	−	0.901679i
$259$	29.8145	−	17.2134i	0.115114	−	0.0664610i
$260$	−28.6103	−	33.2769i	−0.110040	−	0.127988i
$261$	−23.3415	+	52.1695i	−0.0894311	+	0.199883i
$262$	−118.905	+	259.041i	−0.453838	+	0.988708i
$263$	−105.914	+	61.1497i	−0.402716	+	0.232508i	−0.687655	−	0.726037i	$-0.741360\pi$
$263$	−105.914	+	61.1497i	−0.402716	+	0.232508i	0.284939	+	0.958546i	$0.408027\pi$
$264$	−136.280	−	396.251i	−0.516213	−	1.50095i
$265$	110.287	−	191.023i	0.416178	−	0.720841i
$266$	18.7963	−	13.3302i	0.0706628	−	0.0501134i
$267$	73.7070	+	37.6403i	0.276056	+	0.140975i
$268$	138.700	+	48.6054i	0.517538	+	0.181364i
$269$	280.452			1.04257			0.521287	−	0.853382i	$-0.325452\pi$
$269$	280.452			1.04257			0.521287	+	0.853382i	$0.325452\pi$
$270$	−90.4681	+	319.431i	−0.335067	+	1.18308i
$271$		−	81.4468i		−	0.300542i	−0.988645	−	0.150271i	$-0.951985\pi$
$271$		−	81.4468i		−	0.300542i	0.988645	−	0.150271i	$-0.0480146\pi$
$272$	−252.054	+	98.6547i	−0.926670	+	0.362701i
$273$	1.43819	−	2.81625i	0.00526809	−	0.0103159i
$274$	−10.0551	+	7.13098i	−0.0366975	+	0.0260255i
$275$	−193.522	−	111.730i	−0.703716	−	0.406291i
$276$	−65.6687	−	68.8735i	−0.237930	−	0.249542i
$277$	224.861	+	389.471i	0.811774	+	1.40603i	0.911622	+	0.411031i	$0.134831\pi$
$277$	224.861	+	389.471i	0.811774	+	1.40603i	−0.0998479	+	0.995003i	$0.531836\pi$
$278$	99.3939	−	216.534i	0.357532	−	0.778901i
$279$	29.5206	+	285.888i	0.105809	+	1.02469i
$280$	27.9224	−	8.02330i	0.0997229	−	0.0286546i
$281$	−37.8649	−	65.5838i	−0.134750	−	0.233394i	0.790752	−	0.612137i	$-0.209690\pi$
$281$	−37.8649	−	65.5838i	−0.134750	−	0.233394i	−0.925502	+	0.378743i	$0.876357\pi$
$282$	−9.63272	−	66.0978i	−0.0341586	−	0.234389i
$283$	−322.061	−	185.942i	−1.13803	−	0.657039i	−0.192084	−	0.981378i	$-0.561525\pi$
$283$	−322.061	−	185.942i	−1.13803	−	0.657039i	−0.945941	+	0.324339i	$0.894858\pi$
$284$	−65.1597	−	345.253i	−0.229436	−	1.21568i
$285$	−195.668	−	301.906i	−0.686556	−	1.05932i
$286$	62.0429	−	5.80347i	0.216933	−	0.0202919i
$287$			3.15361i			0.0109882i
$288$	132.471	−	255.725i	0.459970	−	0.887934i
$289$	−2.81196			−0.00972996
$290$	−7.27226	−	77.7453i	−0.0250768	−	0.268087i
$291$	−4.02919	−	78.2475i	−0.0138460	−	0.268892i
$292$	236.003	−	44.5409i	0.808229	−	0.152537i
$293$	−66.3946	+	114.999i	−0.226603	+	0.392488i	−0.956799	−	0.290750i	$-0.906095\pi$
$293$	−66.3946	+	114.999i	−0.226603	+	0.392488i	0.730196	+	0.683237i	$0.239429\pi$
$294$	−180.884	−	229.108i	−0.615252	−	0.779279i
$295$	−128.479	+	74.1772i	−0.435521	+	0.251448i
$296$	128.768	+	448.134i	0.435027	+	1.51397i
$297$	−295.664	−	367.165i	−0.995502	−	1.23625i
$298$	375.765	+	172.484i	1.26096	+	0.578806i
$299$	12.2556	−	7.07579i	0.0409887	−	0.0236648i
$300$	−36.2065	−	149.255i	−0.120688	−	0.497517i
$301$	−11.5719	+	20.0432i	−0.0384450	+	0.0665886i
$302$	−170.229	−	240.033i	−0.563672	−	0.794811i
$303$	3.97507	+	77.1965i	0.0131190	+	0.254774i
$304$	113.751	+	290.624i	0.374181	+	0.956000i
$305$	−466.589			−1.52980
$306$	−228.978	+	200.733i	−0.748296	+	0.655991i
$307$			336.514i			1.09614i	0.836434	+	0.548068i	$0.184637\pi$
$307$			336.514i			1.09614i	−0.836434	+	0.548068i	$0.815363\pi$
$308$	−13.6428	+	38.9309i	−0.0442947	+	0.126399i
$309$	32.0185	+	49.4028i	0.103620	+	0.159880i
$310$	−227.151	−	320.296i	−0.732745	−	1.03321i
$311$	304.206	+	175.634i	0.978156	+	0.564738i	0.901713	−	0.432336i	$-0.142310\pi$
$311$	304.206	+	175.634i	0.978156	+	0.564738i	0.0764428	+	0.997074i	$0.475644\pi$
$312$	32.3127	+	28.1095i	0.103567	+	0.0900946i
$313$	−95.4299	−	165.289i	−0.304888	−	0.528081i	0.672349	−	0.740235i	$-0.265286\pi$
$313$	−95.4299	−	165.289i	−0.304888	−	0.528081i	−0.977236	+	0.212154i	$0.931952\pi$
$314$	−114.292	−	52.4626i	−0.363988	−	0.167078i
$315$	26.4768	−	19.1628i	0.0840532	−	0.0608342i
$316$	−112.719	+	96.9117i	−0.356706	+	0.306683i
$317$	−202.797	−	351.255i	−0.639738	−	1.10806i	−0.985490	−	0.169733i	$-0.945709\pi$
$317$	−202.797	−	351.255i	−0.639738	−	1.10806i	0.345752	−	0.938326i	$-0.387624\pi$
$318$	−79.6218	+	199.995i	−0.250383	+	0.628916i
$319$	96.0203	+	55.4374i	0.301004	+	0.173785i
$320$	14.1661	+	393.221i	0.0442692	+	1.22882i
$321$	−249.960	+	489.470i	−0.778693	+	1.52483i
$322$	0.872512	+	9.32773i	0.00270966	+	0.0289681i
$323$		−	329.981i		−	1.02161i
$324$	42.4103	−	321.212i	0.130896	−	0.991396i
$325$	22.8393			0.0702749
$326$	285.403	−	26.6965i	0.875470	−	0.0818911i
$327$	−269.424	−	137.588i	−0.823928	−	0.420760i
$328$	−41.4487	−	10.3100i	−0.126368	−	0.0314330i
$329$	−3.28792	+	5.69484i	−0.00999368	+	0.0173096i
$330$	598.380	+	238.226i	1.81327	+	0.721897i
$331$	384.104	−	221.763i	1.16044	−	0.669978i	0.209027	−	0.977910i	$-0.432970\pi$
$331$	384.104	−	221.763i	1.16044	−	0.669978i	0.951408	+	0.307932i	$0.0996370\pi$
$332$	231.251	−	198.822i	0.696541	−	0.598860i
$333$	307.548	+	424.932i	0.923568	+	1.27607i
$334$	145.024	−	315.941i	0.434203	−	0.945931i
$335$	−195.631	+	112.948i	−0.583974	+	0.337158i
$336$	−25.8359	+	11.6780i	−0.0768927	+	0.0347559i
$337$	−254.239	+	440.356i	−0.754420	+	1.30669i	0.191243	+	0.981543i	$0.438748\pi$
$337$	−254.239	+	440.356i	−0.754420	+	1.30669i	−0.945662	+	0.325150i	$0.894585\pi$
$338$	270.510	−	191.843i	0.800325	−	0.567582i
$339$	45.9436	−	29.7766i	0.135527	−	0.0878365i
$340$	137.588	−	392.619i	0.404670	−	1.15476i
$341$	557.560			1.63507
$342$	231.450	+	264.017i	0.676753	+	0.771980i
$343$			57.6805i			0.168165i
$344$	−225.600	−	217.619i	−0.655814	−	0.632614i
$345$	146.073	−	7.52172i	0.423400	−	0.0218021i
$346$	−410.476	+	291.106i	−1.18635	+	0.841346i
$347$	492.773	+	284.503i	1.42010	+	0.819893i	0.996307	−	0.0858678i	$-0.0273663\pi$
$347$	492.773	+	284.503i	1.42010	+	0.819893i	0.423790	+	0.905761i	$0.360700\pi$
$348$	17.9646	+	74.0564i	0.0516226	+	0.212806i
$349$	−206.901	−	358.363i	−0.592840	−	1.02683i	−0.993848	−	0.110754i	$-0.964673\pi$
$349$	−206.901	−	358.363i	−0.592840	−	1.02683i	0.401008	−	0.916074i	$-0.368660\pi$
$350$	−6.30755	+	13.7413i	−0.0180216	+	0.0392609i
$351$	44.9341	+	17.3899i	0.128017	+	0.0495438i
$352$	−467.076	−	306.586i	−1.32692	−	0.870982i
$353$	62.3070	+	107.919i	0.176507	+	0.305719i	0.940682	−	0.339290i	$-0.110187\pi$
$353$	62.3070	+	107.919i	0.176507	+	0.305719i	−0.764175	+	0.645009i	$0.776853\pi$
$354$	113.634	−	89.7160i	0.321001	−	0.253435i
$355$	467.677	+	270.014i	1.31740	+	0.760602i
$356$	108.435	−	20.4649i	0.304592	−	0.0574858i
$357$	29.9381	−	1.54160i	0.0838601	−	0.00431820i
$358$	−191.177	+	17.8826i	−0.534015	+	0.0499515i
$359$		−	303.196i		−	0.844557i	−0.906466	−	0.422278i	$-0.861230\pi$
$359$		−	303.196i		−	0.844557i	0.906466	−	0.422278i	$-0.138770\pi$
$360$	165.301	+	410.638i	0.459169	+	1.14066i
$361$	−19.4752			−0.0539480
$362$	61.2363	+	654.657i	0.169161	+	1.80844i
$363$	−462.814	+	299.955i	−1.27497	+	0.826323i
$364$	−0.781939	−	4.14315i	−0.00214818	−	0.0113823i
$365$	−184.572	+	319.688i	−0.505677	+	0.875858i
$366$	450.592	−	65.6668i	1.23113	−	0.179418i
$367$	−615.571	+	355.400i	−1.67730	+	0.968392i	−0.713936	+	0.700211i	$0.753089\pi$
$367$	−615.571	+	355.400i	−1.67730	+	0.968392i	−0.963369	+	0.268181i	$0.913578\pi$
$368$	−125.449	−	19.0273i	−0.340894	−	0.0517045i
$369$	−47.7965	+	4.93544i	−0.129530	+	0.0133752i
$370$	−651.321	−	298.970i	−1.76033	−	0.808027i
$371$	18.3527	−	10.5959i	0.0494681	−	0.0285604i
$372$	264.441	+	277.347i	0.710864	+	0.745556i
$373$	166.740	−	288.803i	0.447025	−	0.774271i	−0.551166	−	0.834396i	$-0.685817\pi$
$373$	166.740	−	288.803i	0.447025	−	0.774271i	0.998191	+	0.0601254i	$0.0191501\pi$
$374$	341.728	+	481.857i	0.913712	+	1.28839i
$375$	−200.422	−	102.351i	−0.534459	−	0.272935i
$376$	−64.0995	−	61.8318i	−0.170477	−	0.164446i
$377$	−11.3323			−0.0300590
$378$	−22.8721	+	22.2321i	−0.0605082	+	0.0588150i
$379$		−	662.686i		−	1.74851i	−0.485465	−	0.874256i	$-0.661350\pi$
$379$		−	662.686i		−	1.74851i	0.485465	−	0.874256i	$-0.338650\pi$
$380$	−452.699	−	158.642i	−1.19131	−	0.417478i
$381$	224.289	−	439.202i	0.588686	−	1.15276i
$382$	0.470139	+	0.662924i	0.00123073	+	0.00173540i
$383$	−69.9008	−	40.3572i	−0.182509	−	0.105371i	0.405962	−	0.913890i	$-0.366936\pi$
$383$	−69.9008	−	40.3572i	−0.182509	−	0.105371i	−0.588471	+	0.808518i	$0.700270\pi$
$384$	−69.0216	−	377.746i	−0.179744	−	0.983713i
$385$	−31.7026	−	54.9106i	−0.0823445	−	0.142625i
$386$	113.505	+	52.1013i	0.294055	+	0.134977i
$387$	−321.887	−	144.018i	−0.831748	−	0.372139i
$388$	−68.1066	−	79.2155i	−0.175533	−	0.204164i
$389$	−346.006	−	599.301i	−0.889476	−	1.54062i	−0.840495	−	0.541819i	$-0.817736\pi$
$389$	−346.006	−	599.301i	−0.889476	−	1.54062i	−0.0489809	−	0.998800i	$-0.515597\pi$
$390$	−65.1396	+	9.49307i	−0.167025	+	0.0243412i
$391$	116.183	+	67.0782i	0.297143	+	0.171556i
$392$	−377.700	−	93.9497i	−0.963519	−	0.239668i
$393$	232.529	+	358.779i	0.591676	+	0.912924i
$394$	38.7174	+	413.915i	0.0982675	+	1.05055i
$395$		−	228.481i		−	0.578432i
$396$	−611.392	−	145.844i	−1.54392	−	0.368293i
$397$	657.713			1.65671			0.828354	−	0.560206i	$-0.189278\pi$
$397$	657.713			1.65671			0.828354	+	0.560206i	$0.189278\pi$
$398$	−595.657	+	55.7175i	−1.49662	+	0.139994i
$399$	−1.77749	−	34.5192i	−0.00445487	−	0.0865144i
$400$	−159.984	−	127.826i	−0.399960	−	0.319564i
$401$	296.433	−	513.437i	0.739235	−	1.28039i	−0.213606	−	0.976920i	$-0.568521\pi$
$401$	296.433	−	513.437i	0.739235	−	1.28039i	0.952840	−	0.303472i	$-0.0981459\pi$
$402$	173.028	−	136.608i	0.430418	−	0.339821i
$403$	−49.3521	+	28.4935i	−0.122462	+	0.0707034i
$404$	67.1918	+	78.1515i	0.166316	+	0.193444i
$405$	331.869	+	371.295i	0.819431	+	0.916777i
$406$	3.12963	−	6.81806i	0.00770846	−	0.0167933i
$407$	881.274	−	508.804i	2.16529	−	1.25013i
$408$	−77.6141	+	398.523i	−0.190231	+	0.976771i
$409$	−161.594	+	279.889i	−0.395095	+	0.684325i	−0.993113	−	0.117157i	$-0.962622\pi$
$409$	−161.594	+	279.889i	−0.395095	+	0.684325i	0.598018	+	0.801483i	$0.295955\pi$
$410$	53.5492	−	37.9765i	0.130608	−	0.0926257i
$411$	0.950872	+	18.4661i	0.00231356	+	0.0449297i
$412$	74.0781	+	25.9596i	0.179801	+	0.0630086i
$413$	−14.2533			−0.0345115
$414$	−140.007	+	27.8219i	−0.338180	+	0.0672026i
$415$			468.745i			1.12951i
$416$	57.0107	+	3.26788i	0.137045	+	0.00785549i
$417$	−194.372	−	299.906i	−0.466121	−	0.719199i
$418$	555.592	−	394.020i	1.32917	−	0.942632i
$419$	−222.744	−	128.601i	−0.531608	−	0.306924i	0.210063	−	0.977688i	$-0.432633\pi$
$419$	−222.744	−	128.601i	−0.531608	−	0.306924i	−0.741671	+	0.670764i	$0.765967\pi$
$420$	12.2781	−	41.8130i	0.0292336	−	0.0995547i
$421$	41.9905	+	72.7297i	0.0997400	+	0.172755i	0.911577	−	0.411129i	$-0.134866\pi$
$421$	41.9905	+	72.7297i	0.0997400	+	0.172755i	−0.811837	+	0.583884i	$0.801532\pi$
$422$	−136.559	+	297.499i	−0.323598	+	0.704975i
$423$	−91.4573	−	40.9196i	−0.216211	−	0.0967365i
$424$	79.2646	+	275.854i	0.186945	+	0.650599i
$425$	108.258	+	187.509i	0.254725	+	0.441197i
$426$	−489.645	−	194.936i	−1.14940	−	0.457597i
$427$	−38.8221	−	22.4139i	−0.0909182	−	0.0524917i
$428$	135.903	+	720.089i	0.317530	+	1.68245i
$429$	42.5108	−	83.2442i	0.0990927	−	0.194042i
$430$	479.690	−	44.8700i	1.11556	−	0.104349i
$431$		−	144.348i		−	0.334914i	−0.985879	−	0.167457i	$-0.946445\pi$
$431$		−	144.348i		−	0.334914i	0.985879	−	0.167457i	$-0.0535555\pi$
$432$	−217.426	−	373.296i	−0.503301	−	0.864111i
$433$	395.353			0.913057			0.456528	−	0.889709i	$-0.349093\pi$
$433$	395.353			0.913057			0.456528	+	0.889709i	$0.349093\pi$
$434$	−3.51351	−	37.5618i	−0.00809566	−	0.0865479i
$435$	−104.312	−	53.2697i	−0.239798	−	0.122459i
$436$	−396.367	+	74.8065i	−0.909098	+	0.171574i
$437$	77.3426	−	133.961i	0.176985	−	0.306548i
$438$	133.252	−	334.704i	0.304228	−	0.764165i
$439$	−194.776	+	112.454i	−0.443682	+	0.256160i	−0.705158	−	0.709050i	$-0.749124\pi$
$439$	−194.776	+	112.454i	−0.443682	+	0.256160i	0.261476	+	0.965210i	$0.415791\pi$
$440$	825.346	−	237.157i	1.87579	−	0.538994i
$441$	−435.544	+	44.9740i	−0.987628	+	0.101982i
$442$	−54.8727	−	25.1877i	−0.124146	−	0.0569858i
$443$	−369.184	+	213.148i	−0.833373	+	0.481148i	−0.855006	−	0.518618i	$-0.826447\pi$
$443$	−369.184	+	213.148i	−0.833373	+	0.481148i	0.0216335	+	0.999766i	$0.493113\pi$
$444$	671.067	+	197.055i	1.51141	+	0.443817i
$445$	−84.8041	+	146.885i	−0.190571	+	0.330079i
$446$	−441.772	−	622.926i	−0.990521	−	1.39669i
$447$	520.444	−	337.306i	1.16430	−	0.754599i
$448$	−17.7108	+	33.3981i	−0.0395331	+	0.0745493i
$449$	−406.744			−0.905888			−0.452944	−	0.891539i	$-0.649626\pi$
$449$	−406.744			−0.905888			−0.452944	+	0.891539i	$0.649626\pi$
$450$	−218.136	−	74.0926i	−0.484747	−	0.164650i
$451$			93.2163i			0.206688i
$452$	24.1419	−	68.8911i	0.0534112	−	0.152414i
$453$	−440.818	+	22.6990i	−0.973108	+	0.0501081i
$454$	68.8644	+	97.1029i	0.151684	+	0.213883i
$455$	5.61228	+	3.24025i	0.0123347	+	0.00712144i
$456$	459.505	+	89.4908i	1.00769	+	0.196252i
$457$	−159.600	−	276.435i	−0.349234	−	0.604891i	0.636879	−	0.770963i	$-0.280225\pi$
$457$	−159.600	−	276.435i	−0.349234	−	0.604891i	−0.986114	+	0.166072i	$0.946892\pi$
$458$	−234.247	−	107.524i	−0.511457	−	0.234770i
$459$	70.2180	+	451.332i	0.152980	+	0.983294i
$460$	147.880	−	127.142i	0.321479	−	0.276396i
$461$	293.888	+	509.029i	0.637501	+	1.10418i	0.985979	+	0.166867i	$0.0533652\pi$
$461$	293.888	+	509.029i	0.637501	+	1.10418i	−0.348478	+	0.937317i	$0.613302\pi$
$462$	38.3437	+	48.5662i	0.0829951	+	0.105122i
$463$	230.088	+	132.841i	0.496950	+	0.286914i	0.727453	−	0.686157i	$-0.240704\pi$
$463$	230.088	+	132.841i	0.496950	+	0.286914i	−0.230503	+	0.973072i	$0.574037\pi$
$464$	79.3797	+	63.4236i	0.171077	+	0.136689i
$465$	−588.221	+	30.2892i	−1.26499	+	0.0651380i
$466$	−2.79285	−	29.8574i	−0.00599323	−	0.0640716i
$467$			794.598i			1.70149i	0.525575	+	0.850747i	$0.323850\pi$
$467$			794.598i			1.70149i	−0.525575	+	0.850747i	$0.676150\pi$
$468$	61.5703	−	18.3352i	0.131560	−	0.0391778i
$469$	−21.7031			−0.0462752
$470$	136.294	−	12.7489i	0.289987	−	0.0271252i
$471$	−158.298	+	102.595i	−0.336089	+	0.217823i
$472$	46.5978	−	187.334i	0.0987241	−	0.396894i
$473$	−342.050	+	592.447i	−0.723149	+	1.25253i
$474$	32.1559	+	220.647i	0.0678395	+	0.465501i
$475$	216.201	−	124.824i	0.455161	−	0.262787i
$476$	30.3084	−	26.0581i	0.0636732	−	0.0547439i
$477$	189.315	+	261.572i	0.396886	+	0.548369i
$478$	−303.711	+	661.649i	−0.635378	+	1.38420i
$479$	−572.964	+	330.801i	−1.19617	+	0.690607i	−0.959698	−	0.281033i	$-0.909323\pi$
$479$	−572.964	+	330.801i	−1.19617	+	0.690607i	−0.236468	+	0.971639i	$0.575990\pi$
$480$	509.417	+	298.072i	1.06129	+	0.620983i
$481$	−52.0037	+	90.0730i	−0.108116	+	0.187262i
$482$	−132.219	+	93.7686i	−0.274314	+	0.194541i
$483$	12.5152	+	6.39120i	0.0259114	+	0.0132323i
$484$	−243.194	+	693.977i	−0.502467	+	1.43384i
$485$	160.569			0.331071
$486$	−372.747	−	311.859i	−0.766969	−	0.641684i
$487$			57.1525i			0.117356i	0.998277	+	0.0586781i	$0.0186886\pi$
$487$			57.1525i			0.117356i	−0.998277	+	0.0586781i	$0.981311\pi$
$488$	421.511	−	436.970i	0.863753	−	0.895430i
$489$	195.553	−	382.931i	0.399905	−	0.783090i
$490$	487.965	−	346.060i	0.995847	−	0.706244i
$491$	48.6600	+	28.0939i	0.0991040	+	0.0572177i	0.548733	−	0.835998i	$-0.315110\pi$
$491$	48.6600	+	28.0939i	0.0991040	+	0.0572177i	−0.449629	+	0.893215i	$0.648444\pi$
$492$	−46.3686	+	44.2109i	−0.0942450	+	0.0898596i
$493$	−53.7147	−	93.0366i	−0.108955	−	0.188715i
$494$	−29.0420	+	63.2694i	−0.0587895	+	0.128076i
$495$	782.615	−	566.424i	1.58104	−	1.14429i
$496$	505.170	+	76.6208i	1.01849	+	0.154477i
$497$	25.9417	+	44.9324i	0.0521967	+	0.0904073i
$498$	−65.9702	−	452.675i	−0.132470	−	0.908985i
$499$	522.225	+	301.507i	1.04654	+	0.604222i	0.921679	−	0.387952i	$-0.126817\pi$
$499$	522.225	+	301.507i	1.04654	+	0.604222i	0.124863	+	0.992174i	$0.460151\pi$
$500$	−294.853	+	55.6477i	−0.589706	+	0.111295i
$501$	−283.605	−	437.587i	−0.566077	−	0.873427i
$502$	561.316	−	52.5052i	1.11816	−	0.104592i
$503$		−	549.354i		−	1.09216i	−0.837734	−	0.546078i	$-0.816120\pi$
$503$		−	549.354i		−	1.09216i	0.837734	−	0.546078i	$-0.183880\pi$
$504$	−5.97249	+	42.1075i	−0.0118502	+	0.0835466i
$505$	−158.413			−0.313688
$506$	25.7902	+	275.714i	0.0509687	+	0.544890i
$507$	−25.5810	−	496.788i	−0.0504557	−	0.979859i
$508$	−121.946	−	646.136i	−0.240050	−	1.27192i
$509$	−119.464	+	206.918i	−0.234704	+	0.406519i	−0.959187	−	0.282774i	$-0.908745\pi$
$509$	−119.464	+	206.918i	−0.234704	+	0.406519i	0.724483	+	0.689293i	$0.242079\pi$
$510$	−386.698	−	489.792i	−0.758230	−	0.960376i
$511$	−30.7143	+	17.7329i	−0.0601062	+	0.0347023i
$512$	−381.057	−	341.964i	−0.744252	−	0.667899i
$513$	520.395	−	80.9629i	1.01442	−	0.157822i
$514$	136.893	+	62.8366i	0.266328	+	0.122250i
$515$	−104.484	+	60.3240i	−0.202882	+	0.117134i
$516$	−456.929	+	110.842i	−0.885522	+	0.214811i
$517$	−97.1862	+	168.331i	−0.187981	+	0.325593i
$518$	−39.8306	−	56.1636i	−0.0768931	−	0.108424i
$519$	38.8171	+	753.836i	0.0747922	+	1.45248i
$520$	−60.9355	+	63.1703i	−0.117184	+	0.121481i
$521$	−567.711			−1.08966			−0.544828	−	0.838548i	$-0.683405\pi$
$521$	−567.711			−1.08966			−0.544828	+	0.838548i	$0.683405\pi$
$522$	108.233	+	36.7627i	0.207343	+	0.0704267i
$523$		−	941.999i		−	1.80114i	−0.434706	−	0.900572i	$-0.643148\pi$
$523$		−	941.999i		−	1.80114i	0.434706	−	0.900572i	$-0.356852\pi$
$524$	537.979	+	188.527i	1.02668	+	0.359784i
$525$	12.3349	+	19.0321i	0.0234950	+	0.0362516i
$526$	141.496	+	199.518i	0.269004	+	0.379312i
$527$	−467.856	−	270.117i	−0.887773	−	0.512556i
$528$	−763.673	+	345.184i	−1.44635	+	0.653758i
$529$	−233.056	−	403.664i	−0.440559	−	0.763071i
$530$	−400.928	−	184.034i	−0.756468	−	0.347235i
$531$	−22.3065	−	216.024i	−0.0420085	−	0.406825i
$532$	−30.0456	−	34.9463i	−0.0564766	−	0.0656885i
$533$	−4.76372	−	8.25100i	−0.00893755	−	0.0154803i
$534$	61.2244	−	153.784i	0.114652	−	0.287986i
$535$	−975.428	−	563.163i	−1.82323	−	1.05264i
$536$	70.9532	−	285.248i	0.132375	−	0.532180i
$537$	−130.991	+	256.506i	−0.243932	+	0.477665i
$538$	−52.2387	−	558.467i	−0.0970980	−	1.03804i
$539$			849.430i			1.57594i
$540$	652.937	+	120.651i	1.20914	+	0.223427i
$541$	−242.245			−0.447772			−0.223886	−	0.974615i	$-0.571874\pi$
$541$	−242.245			−0.447772			−0.223886	+	0.974615i	$0.571874\pi$
$542$	−162.186	+	15.1708i	−0.299235	+	0.0279904i
$543$	878.366	+	448.560i	1.61762	+	0.826077i
$544$	243.401	+	483.542i	0.447428	+	0.888863i
$545$	309.988	−	536.915i	0.568786	−	0.985166i
$546$	−5.87590	−	2.33930i	−0.0107617	−	0.00428444i
$547$	−170.503	+	98.4402i	−0.311706	+	0.179964i	−0.647690	−	0.761904i	$-0.724265\pi$
$547$	−170.503	+	98.4402i	−0.311706	+	0.179964i	0.335983	+	0.941868i	$0.390931\pi$
$548$	16.0729	+	18.6945i	0.0293301	+	0.0341141i
$549$	278.951	−	623.470i	0.508107	−	1.13565i
$550$	−186.442	+	406.173i	−0.338986	+	0.738497i
$551$	−107.273	+	61.9342i	−0.194688	+	0.112403i
$552$	−124.917	+	143.595i	−0.226298	+	0.260137i
$553$	10.9757	−	19.0105i	0.0198476	−	0.0343770i
$554$	733.673	−	520.313i	1.32432	−	0.939194i
$555$	−902.096	+	584.659i	−1.62540	+	1.05344i
$556$	−449.700	−	157.591i	−0.808814	−	0.283437i
$557$	958.121			1.72015			0.860073	−	0.510171i	$-0.170418\pi$
$557$	958.121			1.72015			0.860073	+	0.510171i	$0.170418\pi$
$558$	563.792	−	112.036i	1.01038	−	0.200781i
$559$		−	69.9202i		−	0.125081i
$560$	−21.1779	−	54.1076i	−0.0378176	−	0.0966208i
$561$	884.926	−	45.5674i	1.57741	−	0.0812253i
$562$	−123.545	+	87.6166i	−0.219830	+	0.155901i
$563$	165.774	+	95.7097i	0.294448	+	0.169999i	0.639946	−	0.768420i	$-0.278957\pi$
$563$	165.774	+	95.7097i	0.294448	+	0.169999i	−0.345498	+	0.938419i	$0.612290\pi$
$564$	−129.827	+	31.4935i	−0.230189	+	0.0558395i
$565$	56.1001	+	97.1682i	0.0992922	+	0.171979i
$566$	−310.279	+	675.957i	−0.548196	+	1.19427i
$567$	9.77666	+	46.8355i	0.0172428	+	0.0826023i
$568$	−675.368	+	194.062i	−1.18903	+	0.341658i
$569$	228.215	+	395.280i	0.401081	+	0.694693i	0.993857	−	0.110675i	$-0.0353012\pi$
$569$	228.215	+	395.280i	0.401081	+	0.694693i	−0.592775	+	0.805368i	$0.701968\pi$
$570$	−564.740	+	445.871i	−0.990773	+	0.782229i
$571$	−842.764	−	486.570i	−1.47594	−	0.852136i	−0.476312	−	0.879276i	$-0.658027\pi$
$571$	−842.764	−	486.570i	−1.47594	−	0.852136i	−0.999632	+	0.0271399i	$0.991360\pi$
$572$	−23.1130	−	122.466i	−0.0404073	−	0.214101i
$573$	1.21745	−	0.0626902i	0.00212470	−	0.000109407i
$574$	6.27982	−	0.587411i	0.0109404	−	0.00102336i
$575$			101.496i			0.176515i
$576$	−533.902	−	216.159i	−0.926913	−	0.375275i
$577$	138.527			0.240081			0.120040	−	0.992769i	$-0.461698\pi$
$577$	138.527			0.240081			0.120040	+	0.992769i	$0.461698\pi$
$578$	0.523773	+	5.59948i	0.000906181	+	0.00968768i
$579$	157.208	−	101.888i	0.271516	−	0.175972i
$580$	−153.460	+	28.9626i	−0.264586	+	0.0499355i
$581$	−22.5175	+	39.0015i	−0.0387565	+	0.0671282i
$582$	−155.064	+	22.5982i	−0.266434	+	0.0388285i
$583$	542.478	−	313.200i	0.930494	−	0.537221i
$584$	−132.654	−	461.658i	−0.227147	−	0.790510i
$585$	−40.3263	+	90.1314i	−0.0689339	+	0.154071i
$586$	241.365	+	110.792i	0.411886	+	0.189064i
$587$	620.808	−	358.424i	1.05759	−	0.610602i	0.132829	−	0.991139i	$-0.457594\pi$
$587$	620.808	−	358.424i	1.05759	−	0.610602i	0.924766	+	0.380537i	$0.124261\pi$
$588$	−422.532	+	402.871i	−0.718591	+	0.685154i
$589$	−311.451	+	539.449i	−0.528779	+	0.915872i
$590$	171.641	+	242.024i	0.290917	+	0.410210i
$591$	555.358	+	283.607i	0.939691	+	0.479877i
$592$	868.387	−	339.889i	1.46687	−	0.574137i
$593$	542.129			0.914214			0.457107	−	0.889412i	$-0.348886\pi$
$593$	542.129			0.914214			0.457107	+	0.889412i	$0.348886\pi$
$594$	−676.067	+	657.148i	−1.13816	+	1.10631i
$595$			61.4350i			0.103252i
$596$	273.477	−	780.391i	0.458853	−	1.30938i
$597$	−408.134	+	799.204i	−0.683641	+	1.33870i
$598$	−16.3729	−	23.0867i	−0.0273794	−	0.0386066i
$599$	−245.527	−	141.755i	−0.409895	−	0.236653i	0.280850	−	0.959752i	$-0.409384\pi$
$599$	−245.527	−	141.755i	−0.409895	−	0.236653i	−0.690744	+	0.723099i	$0.742717\pi$
$600$	−290.469	+	99.8994i	−0.484115	+	0.166499i
$601$	377.424	+	653.717i	0.627993	+	1.08772i	0.987954	+	0.154748i	$0.0494567\pi$
$601$	377.424	+	653.717i	0.627993	+	1.08772i	−0.359961	+	0.932967i	$0.617210\pi$
$602$	42.0676	+	19.3099i	0.0698797	+	0.0320763i
$603$	−33.9656	−	328.934i	−0.0563276	−	0.545496i
$604$	−446.272	+	383.688i	−0.738860	+	0.635245i
$605$	−565.126	−	978.827i	−0.934093	−	1.61790i
$606$	152.982	−	22.2947i	0.252445	−	0.0367899i
$607$	77.2227	+	44.5845i	0.127220	+	0.0734506i	0.562260	−	0.826961i	$-0.309932\pi$
$607$	77.2227	+	44.5845i	0.127220	+	0.0734506i	−0.435039	+	0.900411i	$0.643266\pi$
$608$	557.534	−	280.647i	0.916997	−	0.461590i
$609$	−6.12024	−	9.44320i	−0.0100497	−	0.0155061i
$610$	86.9097	+	929.122i	0.142475	+	1.52315i
$611$		−	19.8664i		−	0.0325145i
$612$	442.372	+	418.577i	0.722831	+	0.683949i
$613$	−316.779			−0.516769			−0.258385	−	0.966042i	$-0.583190\pi$
$613$	−316.779			−0.516769			−0.258385	+	0.966042i	$0.583190\pi$
$614$	670.103	−	62.6811i	1.09137	−	0.102087i
$615$	−5.06393	−	98.3425i	−0.00823404	−	0.159907i
$616$	80.0646	+	19.9154i	0.129975	+	0.0323302i
$617$	534.934	−	926.533i	0.866992	−	1.50167i	0.00193565	−	0.999998i	$-0.499384\pi$
$617$	534.934	−	926.533i	0.866992	−	1.50167i	0.865056	−	0.501675i	$-0.167283\pi$
$618$	92.4122	−	72.9608i	0.149534	−	0.118059i
$619$	578.542	−	334.021i	0.934640	−	0.539615i	0.0463638	−	0.998925i	$-0.485237\pi$
$619$	578.542	−	334.021i	0.934640	−	0.539615i	0.888276	+	0.459310i	$0.151903\pi$
$620$	−595.498	+	511.988i	−0.960481	+	0.825787i
$621$	−77.2793	+	199.684i	−0.124443	+	0.321552i
$622$	293.077	−	638.483i	0.471185	−	1.02650i
$623$	−14.1121	+	8.14762i	−0.0226518	+	0.0130780i
$624$	49.9559	−	69.5805i	0.0800575	−	0.111507i
$625$	390.580	−	676.505i	0.624929	−	1.08241i
$626$	−311.367	+	220.818i	−0.497391	+	0.352744i
$627$	−52.5402	−	1020.34i	−0.0837961	−	1.62734i
$628$	−83.1804	+	237.363i	−0.132453	+	0.377967i
$629$	−985.986			−1.56755
$630$	−43.0907	−	49.1540i	−0.0683979	−	0.0780222i
$631$			150.631i			0.238718i	0.992851	+	0.119359i	$0.0380839\pi$
$631$			150.631i			0.238718i	−0.992851	+	0.119359i	$0.961916\pi$
$632$	213.977	+	206.407i	0.338571	+	0.326593i
$633$	267.051	+	412.045i	0.421881	+	0.650939i
$634$	−661.682	+	469.258i	−1.04366	+	0.740155i
$635$	875.252	+	505.327i	1.37835	+	0.795790i
$636$	413.083	+	121.299i	0.649502	+	0.190722i
$637$	−43.4092	−	75.1869i	−0.0681463	−	0.118033i
$638$	92.5075	−	201.532i	0.144996	−	0.315881i
$639$	−640.401	+	463.496i	−1.00219	+	0.725345i
$640$	780.385	−	101.453i	1.21935	−	0.158520i
$641$	351.521	+	608.852i	0.548395	+	0.949847i	0.998385	+	0.0568139i	$0.0180942\pi$
$641$	351.521	+	608.852i	0.548395	+	0.949847i	−0.449990	+	0.893034i	$0.648573\pi$
$642$	1021.24	+	406.576i	1.59072	+	0.633296i
$643$	742.057	+	428.427i	1.15405	+	0.666293i	0.949872	−	0.312639i	$-0.101213\pi$
$643$	742.057	+	428.427i	1.15405	+	0.666293i	0.204182	+	0.978933i	$0.434546\pi$
$644$	18.4119	−	3.47488i	0.0285898	−	0.00539577i
$645$	328.675	−	643.609i	0.509574	−	0.997844i
$646$	−657.094	+	61.4643i	−1.01717	+	0.0951459i
$647$			156.257i			0.241510i	0.992682	+	0.120755i	$0.0385316\pi$
$647$			156.257i			0.241510i	−0.992682	+	0.120755i	$0.961468\pi$
$648$	−647.532	−	24.6211i	−0.999278	−	0.0379955i
$649$	−421.306			−0.649162
$650$	−4.25419	−	45.4802i	−0.00654491	−	0.0699695i
$651$	−50.3974	−	25.7367i	−0.0774154	−	0.0395341i
$652$	−106.322	−	563.353i	−0.163070	−	0.864038i
$653$	−441.773	+	765.173i	−0.676528	+	1.17178i	0.299492	+	0.954099i	$0.403183\pi$
$653$	−441.773	+	765.173i	−0.676528	+	1.17178i	−0.976020	+	0.217682i	$0.930151\pi$
$654$	−223.796	+	562.135i	−0.342196	+	0.859534i
$655$	−758.798	+	438.092i	−1.15847	+	0.668843i
$656$	−12.8099	+	84.4574i	−0.0195273	+	0.128746i
$657$	−316.830	−	437.756i	−0.482237	−	0.666296i
$658$	11.9526	+	5.48650i	0.0181651	+	0.00833815i
$659$	−379.533	+	219.123i	−0.575922	+	0.332509i	−0.759511	−	0.650494i	$-0.774562\pi$
$659$	−379.533	+	219.123i	−0.575922	+	0.332509i	0.183589	+	0.983003i	$0.441228\pi$
$660$	362.923	−	1235.93i	0.549884	−	1.87262i
$661$	233.924	−	405.168i	0.353894	−	0.612963i	−0.633034	−	0.774124i	$-0.718191\pi$
$661$	233.924	−	405.168i	0.353894	−	0.612963i	0.986928	+	0.161161i	$0.0515239\pi$
$662$	−513.143	−	723.562i	−0.775140	−	1.09299i
$663$	−76.0002	+	49.2565i	−0.114631	+	0.0742934i
$664$	−438.989	−	423.459i	−0.661128	−	0.637739i
$665$	70.8359			0.106520
$666$	788.885	−	691.573i	1.18451	−	1.03840i
$667$		−	50.3597i		−	0.0755018i
$668$	−656.149	−	229.938i	−0.982259	−	0.344218i
$669$	−1144.00	+	58.9076i	−1.71001	+	0.0880533i
$670$	261.353	+	368.524i	0.390079	+	0.550035i
$671$	−1147.52	−	662.524i	−1.71017	−	0.987368i
$672$	28.0668	+	49.2721i	0.0417661	+	0.0733215i
$673$	273.302	+	473.372i	0.406094	+	0.703376i	0.994448	−	0.105227i	$-0.0335571\pi$
$673$	273.302	+	473.372i	0.406094	+	0.703376i	−0.588354	+	0.808604i	$0.700224\pi$
$674$	924.240	+	424.246i	1.37128	+	0.629444i
$675$	−269.148	+	216.734i	−0.398738	+	0.321088i
$676$	−432.405	−	502.934i	−0.639652	−	0.743986i
$677$	227.606	+	394.225i	0.336198	+	0.582312i	0.983714	−	0.179740i	$-0.0575255\pi$
$677$	227.606	+	394.225i	0.336198	+	0.582312i	−0.647516	+	0.762052i	$0.724192\pi$
$678$	−67.8520	−	85.9415i	−0.100077	−	0.126757i
$679$	13.3600	+	7.71341i	0.0196760	+	0.0113600i
$680$	−807.454	−	200.848i	−1.18743	−	0.295364i
$681$	178.329	−	9.18264i	0.261863	−	0.0134841i
$682$	−103.854	−	1110.27i	−0.152279	−	1.62797i
$683$			123.214i			0.180400i	0.995924	+	0.0902002i	$0.0287507\pi$
$683$			123.214i			0.180400i	−0.995924	+	0.0902002i	$0.971249\pi$
$684$	482.628	−	510.065i	0.705596	−	0.745709i
$685$	−37.8937			−0.0553193
$686$	114.860	−	10.7439i	0.167434	−	0.0156617i
$687$	−324.439	+	210.272i	−0.472254	+	0.306073i
$688$	−391.325	+	489.774i	−0.568786	+	0.711881i
$689$	−32.0115	+	55.4455i	−0.0464607	+	0.0804724i
$690$	−42.1865	−	289.475i	−0.0611399	−	0.419529i
$691$	−163.326	+	94.2965i	−0.236362	+	0.136464i	−0.613504	−	0.789692i	$-0.710240\pi$
$691$	−163.326	+	94.2965i	−0.236362	+	0.136464i	0.377141	+	0.926156i	$0.376907\pi$
$692$	656.139	+	763.162i	0.948177	+	1.10283i
$693$	92.3265	−	9.53359i	0.133227	−	0.0137570i
$694$	474.746	−	1034.26i	0.684071	−	1.49028i
$695$	634.285	−	366.204i	0.912640	−	0.526913i
$696$	144.123	−	49.5673i	0.207073	−	0.0712174i
$697$	45.1599	−	78.2192i	0.0647918	−	0.112223i
$698$	−675.073	+	478.754i	−0.967153	+	0.685895i
$699$	−40.0602	−	20.4578i	−0.0573107	−	0.0292672i
$700$	28.5381	+	10.0007i	0.0407686	+	0.0142868i
$701$	−810.064			−1.15558			−0.577792	−	0.816184i	$-0.696085\pi$
$701$	−810.064			−1.15558			−0.577792	+	0.816184i	$0.696085\pi$
$702$	26.2589	−	92.7168i	0.0374058	−	0.132075i
$703$			1136.86i			1.61716i
$704$	−523.506	+	987.199i	−0.743616	+	1.40227i
$705$	93.3861	−	182.868i	0.132463	−	0.259387i
$706$	203.294	−	144.174i	0.287952	−	0.204212i
$707$	−13.1806	−	7.60980i	−0.0186429	−	0.0107635i
$708$	−199.818	−	209.570i	−0.282229	−	0.296003i
$709$	−651.819	−	1128.98i	−0.919349	−	1.59236i	−0.800406	−	0.599459i	$-0.795382\pi$
$709$	−651.819	−	1128.98i	−0.919349	−	1.59236i	−0.118944	−	0.992901i	$-0.537951\pi$
$710$	450.568	−	981.583i	0.634602	−	1.38251i
$711$	305.302	+	136.597i	0.429398	+	0.192120i
$712$	−60.9497	−	212.115i	−0.0856035	−	0.297914i
$713$	−126.623	−	219.317i	−0.177592	−	0.307598i
$714$	−8.64624	−	59.3288i	−0.0121096	−	0.0830935i
$715$	165.891	+	95.7772i	0.232015	+	0.133954i
$716$	71.2197	+	377.362i	0.0994688	+	0.527042i
$717$	593.930	+	916.401i	0.828354	+	1.27810i
$718$	−603.756	+	56.4751i	−0.840886	+	0.0786561i
$719$		−	788.981i		−	1.09733i	−0.836042	−	0.548666i	$-0.815136\pi$
$719$		−	788.981i		−	1.09733i	0.836042	−	0.548666i	$-0.184864\pi$
$720$	786.917	−	405.653i	1.09294	−	0.563407i
$721$	−11.5913			−0.0160768
$722$	3.62757	+	38.7812i	0.00502434	+	0.0537135i
$723$	12.5035	+	242.820i	0.0172939	+	0.335850i
$724$	1292.22	−	243.881i	1.78483	−	0.336852i
$725$	40.6380	−	70.3870i	0.0560524	−	0.0970856i
$726$	683.510	+	865.734i	0.941473	+	1.19247i
$727$	−232.676	+	134.335i	−0.320049	+	0.184780i	−0.651414	−	0.758722i	$-0.725824\pi$
$727$	−232.676	+	134.335i	−0.320049	+	0.184780i	0.331365	+	0.943502i	$0.392491\pi$
$728$	−8.10464	+	2.32881i	−0.0111327	+	0.00319891i
$729$	−694.543	+	221.474i	−0.952734	+	0.303805i
$730$	670.977	+	307.992i	0.919146	+	0.421907i
$731$	574.038	−	331.421i	0.785277	−	0.453380i
$732$	−214.693	−	885.037i	−0.293296	−	1.20907i
$733$	−36.8343	+	63.7989i	−0.0502514	+	0.0870380i	−0.890057	−	0.455849i	$-0.849336\pi$
$733$	−36.8343	+	63.7989i	−0.0502514	+	0.0870380i	0.839806	+	0.542887i	$0.182669\pi$
$734$	822.370	+	1159.59i	1.12040	+	1.57982i
$735$	−46.1449	−	896.143i	−0.0627822	−	1.21924i
$736$	−14.5222	+	253.351i	−0.0197313	+	0.344227i
$737$	−641.512			−0.870437
$738$	18.7309	+	94.2582i	0.0253806	+	0.127721i
$739$			448.249i			0.606562i	0.952901	+	0.303281i	$0.0980820\pi$
$739$			448.249i			0.606562i	−0.952901	+	0.303281i	$0.901918\pi$
$740$	−474.022	+	1352.67i	−0.640571	+	1.82793i
$741$	56.7939	+	87.6298i	0.0766449	+	0.118259i
$742$	−24.5182	−	34.5721i	−0.0330434	−	0.0465932i
$743$	656.602	+	379.089i	0.883718	+	0.510215i	0.871882	−	0.489715i	$-0.162899\pi$
$743$	656.602	+	379.089i	0.883718	+	0.510215i	0.0118352	+	0.999930i	$0.496233\pi$
$744$	503.026	−	578.244i	0.676110	−	0.777210i
$745$	635.496	+	1100.71i	0.853015	+	1.47746i
$746$	−606.153	−	278.237i	−0.812538	−	0.372972i
$747$	−626.350	−	280.240i	−0.838488	−	0.375154i
$748$	895.874	−	770.240i	1.19769	−	1.02973i
$749$	−54.1063	−	93.7149i	−0.0722381	−	0.125120i
$750$	−166.480	+	418.166i	−0.221973	+	0.557555i
$751$	1141.58	+	659.091i	1.52008	+	0.877618i	0.999720	+	0.0236697i	$0.00753501\pi$
$751$	1141.58	+	659.091i	1.52008	+	0.877618i	0.520358	+	0.853948i	$0.325798\pi$
$752$	−111.187	+	139.159i	−0.147855	+	0.185052i
$753$	384.604	−	753.128i	0.510762	−	1.00017i
$754$	2.11081	+	22.5660i	0.00279949	+	0.0299284i
$755$		−	904.589i		−	1.19813i
$756$	48.5312	+	41.4043i	0.0641947	+	0.0547676i
$757$	587.874			0.776583			0.388292	−	0.921537i	$-0.373065\pi$
$757$	587.874			0.776583			0.388292	+	0.921537i	$0.373065\pi$
$758$	−1319.61	+	123.436i	−1.74091	+	0.162844i
$759$	369.931	+	188.915i	0.487393	+	0.248899i
$760$	−231.582	+	931.012i	−0.304713	+	1.22502i
$761$	−188.496	+	326.485i	−0.247695	+	0.429021i	−0.962886	−	0.269908i	$-0.913007\pi$
$761$	−188.496	+	326.485i	−0.247695	+	0.429021i	0.715191	+	0.698929i	$0.246340\pi$
$762$	−916.363	−	364.821i	−1.20258	−	0.478768i
$763$	51.5845	−	29.7823i	0.0676075	−	0.0390332i
$764$	1.23252	−	1.05967i	0.00161324	−	0.00138701i
$765$	−931.115	+	96.1465i	−1.21714	+	0.125682i
$766$	−67.3435	+	146.711i	−0.0879158	+	0.191529i
$767$	37.2917	−	21.5304i	0.0486202	−	0.0280709i
$768$	−739.352	+	207.804i	−0.962698	+	0.270579i
$769$	643.939	−	1115.34i	0.837372	−	1.45037i	−0.0547122	−	0.998502i	$-0.517424\pi$
$769$	643.939	−	1115.34i	0.837372	−	1.45037i	0.892084	−	0.451869i	$-0.149243\pi$
$770$	−103.439	+	73.3576i	−0.134336	+	0.0952697i
$771$	189.600	−	122.882i	0.245914	−	0.159380i
$772$	82.6075	−	235.728i	0.107005	−	0.305348i
$773$	778.578			1.00722			0.503608	−	0.863932i	$-0.332006\pi$
$773$	778.578			1.00722			0.503608	+	0.863932i	$0.332006\pi$
$774$	−226.827	+	667.801i	−0.293058	+	0.862792i
$775$		−	408.715i		−	0.527375i
$776$	−145.057	+	150.376i	−0.186929	+	0.193784i
$777$	−103.144	+	5.31117i	−0.132746	+	0.00683548i
$778$	−1128.94	+	800.634i	−1.45108	+	1.02909i
$779$	−90.1884	−	52.0703i	−0.115775	−	0.0668425i
$780$	31.0369	+	127.945i	0.0397909	+	0.164032i
$781$	766.801	+	1328.14i	0.981819	+	1.70056i
$782$	111.932	−	243.850i	0.143136	−	0.311829i
$783$	133.544	−	107.538i	0.170554	−	0.137341i
$784$	−116.730	+	769.615i	−0.148890	+	0.981652i
$785$	−193.292	−	334.791i	−0.246232	−	0.426486i
$786$	671.127	−	529.865i	0.853852	−	0.674128i
$787$	−390.283	−	225.330i	−0.495913	−	0.286315i	0.231111	−	0.972927i	$-0.425764\pi$
$787$	−390.283	−	225.330i	−0.495913	−	0.286315i	−0.727024	+	0.686612i	$0.759097\pi$
$788$	817.020	−	154.197i	1.03683	−	0.195681i
$789$	366.413	−	18.8676i	0.464402	−	0.0239134i
$790$	−454.975	+	42.5582i	−0.575918	+	0.0538711i
$791$			10.7797i			0.0136280i
$792$	−176.538	+	1244.64i	−0.222902	+	1.57151i
$793$	135.430			0.170782
$794$	−122.510	−	1309.71i	−0.154294	−	1.64951i
$795$	−555.296	+	359.893i	−0.698485	+	0.452696i
$796$	221.901	+	1175.76i	0.278770	+	1.47708i
$797$	−182.891	+	316.776i	−0.229474	+	0.397461i	−0.957652	−	0.287927i	$-0.907034\pi$
$797$	−182.891	+	316.776i	−0.229474	+	0.397461i	0.728178	+	0.685388i	$0.240367\pi$
$798$	−68.4073	+	9.96930i	−0.0857235	+	0.0124929i
$799$	163.101	−	94.1662i	0.204131	−	0.117855i
$800$	−224.741	+	342.387i	−0.280926	+	0.427984i
$801$	−145.572	−	201.133i	−0.181737	−	0.251103i
$802$	−1077.63	−	494.653i	−1.34367	−	0.616775i
$803$	−907.869	+	524.158i	−1.13060	+	0.652750i
$804$	−304.258	−	319.107i	−0.378431	−	0.396899i
$805$	−14.3994	+	24.9406i	−0.0178875	+	0.0309821i
$806$	65.9319	+	92.9679i	0.0818013	+	0.115345i
$807$	−749.305	−	382.652i	−0.928507	−	0.474166i
$808$	143.108	−	148.357i	0.177114	−	0.183610i
$809$	1167.70			1.44339			0.721695	−	0.692212i	$-0.243364\pi$
$809$	1167.70			1.44339			0.721695	+	0.692212i	$0.243364\pi$
$810$	677.546	−	730.014i	0.836476	−	0.901251i
$811$			810.121i			0.998916i	0.866338	+	0.499458i	$0.166467\pi$
$811$			810.121i			0.998916i	−0.866338	+	0.499458i	$0.833533\pi$
$812$	−14.1598	−	4.96209i	−0.0174382	−	0.00611095i
$813$	−111.127	+	217.608i	−0.136687	+	0.267660i
$814$	−1177.34	−	1660.11i	−1.44636	−	2.03945i
$815$	763.114	+	440.584i	0.936336	+	0.540594i
$816$	808.038	+	80.3223i	0.990243	+	0.0984342i
$817$	−382.135	−	661.878i	−0.467730	−	0.810132i
$818$	587.445	+	269.650i	0.718148	+	0.329645i
$819$	−7.68503	+	5.56210i	−0.00938343	+	0.00679134i
$820$	−85.5973	−	99.5591i	−0.104387	−	0.121414i
$821$	−280.513	−	485.862i	−0.341672	−	0.591793i	0.643071	−	0.765806i	$-0.277660\pi$
$821$	−280.513	−	485.862i	−0.341672	−	0.591793i	−0.984743	+	0.174013i	$0.944327\pi$
$822$	36.5946	−	5.33308i	0.0445189	−	0.00648794i
$823$	−1016.04	−	586.612i	−1.23456	−	0.712773i	−0.266583	−	0.963812i	$-0.585895\pi$
$823$	−1016.04	−	586.612i	−1.23456	−	0.712773i	−0.967977	+	0.251039i	$0.919228\pi$
$824$	37.8952	−	152.348i	0.0459894	−	0.184888i
$825$	364.602	+	562.561i	0.441942	+	0.681892i
$826$	2.65490	+	28.3826i	0.00321416	+	0.0343615i
$827$			267.739i			0.323747i	0.986811	+	0.161874i	$0.0517537\pi$
$827$			267.739i			0.323747i	−0.986811	+	0.161874i	$0.948246\pi$
$828$	81.4804	+	273.614i	0.0984062	+	0.330451i
$829$	−432.474			−0.521682			−0.260841	−	0.965382i	$-0.584000\pi$
$829$	−432.474			−0.521682			−0.260841	+	0.965382i	$0.584000\pi$
$830$	933.415	−	87.3113i	1.12460	−	0.105194i
$831$	−69.3806	−	1347.38i	−0.0834904	−	1.62140i
$832$	−4.11180	−	114.135i	−0.00494207	−	0.137181i
$833$	411.518	−	712.769i	0.494019	−	0.855665i
$834$	−561.000	+	442.917i	−0.672662	+	0.531076i
$835$	925.472	−	534.321i	1.10835	−	0.639906i
$836$	−888.103	−	1032.96i	−1.06232	−	1.23560i
$837$	311.196	−	804.106i	0.371799	−	0.960701i
$838$	−214.595	+	467.506i	−0.256080	+	0.557883i
$839$	−459.103	+	265.063i	−0.547202	+	0.315927i	−0.747993	−	0.663707i	$-0.768982\pi$
$839$	−459.103	+	265.063i	−0.547202	+	0.315927i	0.200790	+	0.979634i	$0.435649\pi$
$840$	−85.5495	−	16.6612i	−0.101845	−	0.0198347i
$841$	400.337	−	693.403i	0.476024	−	0.824499i
$842$	137.006	−	97.1632i	0.162715	−	0.115396i
$843$	11.6831	+	226.889i	0.0138590	+	0.269144i
$844$	617.849	+	216.516i	0.732049	+	0.256536i
$845$	1019.44			1.20644
$846$	−64.4480	+	189.741i	−0.0761797	+	0.224281i
$847$		−	108.590i		−	0.128205i
$848$	534.546	−	209.222i	0.630361	−	0.246725i
$849$	606.774	+	936.219i	0.714692	+	1.10273i
$850$	353.222	−	250.502i	0.415556	−	0.294708i
$851$	−400.278	−	231.100i	−0.470361	−	0.271563i
$852$	−296.974	+	1011.34i	−0.348561	+	1.18702i
$853$	88.3868	+	153.090i	0.103619	+	0.179473i	0.913173	−	0.407572i	$-0.133624\pi$
$853$	88.3868	+	153.090i	0.103619	+	0.179473i	−0.809554	+	0.587045i	$0.800291\pi$
$854$	−37.4018	+	81.4816i	−0.0437960	+	0.0954118i
$855$	110.859	+	1073.60i	0.129660	+	1.25567i
$856$	1408.60	−	404.752i	1.64557	−	0.472841i
$857$	−194.859	−	337.505i	−0.227373	−	0.393821i	0.729656	−	0.683815i	$-0.239680\pi$
$857$	−194.859	−	337.505i	−0.227373	−	0.393821i	−0.957029	+	0.289993i	$0.906347\pi$
$858$	−173.683	−	69.1464i	−0.202428	−	0.0805903i
$859$	−503.279	−	290.568i	−0.585889	−	0.338263i	0.177581	−	0.984106i	$-0.443173\pi$
$859$	−503.279	−	290.568i	−0.585889	−	0.338263i	−0.763470	+	0.645843i	$0.776506\pi$
$860$	−178.700	−	946.852i	−0.207791	−	1.10099i
$861$	4.30282	−	8.42575i	0.00499747	−	0.00978601i
$862$	−287.441	+	26.8871i	−0.333458	+	0.0311915i
$863$		−	827.326i		−	0.958663i	−0.877634	−	0.479331i	$-0.840879\pi$
$863$		−	827.326i		−	0.958663i	0.877634	−	0.479331i	$-0.159121\pi$
$864$	−702.848	+	502.495i	−0.813481	+	0.581591i
$865$	−1546.92			−1.78835
$866$	−73.6409	−	787.270i	−0.0850357	−	0.909088i
$867$	7.51293	+	3.83667i	0.00866543	+	0.00442522i
$868$	−74.1426	+	13.9930i	−0.0854178	+	0.0161209i
$869$	324.426	−	561.923i	0.373333	−	0.646632i
$870$	−86.6466	+	217.640i	−0.0995938	+	0.250161i
$871$	56.7831	−	32.7837i	0.0651930	−	0.0376392i
$872$	222.792	+	775.354i	0.255496	+	0.889167i
$873$	−95.9966	+	214.557i	−0.109962	+	0.245770i
$874$	−281.165	−	129.060i	−0.321699	−	0.147666i
$875$	38.3732	−	22.1548i	0.0438551	−	0.0253198i
$876$	−691.319	−	203.001i	−0.789177	−	0.231737i
$877$	−279.815	+	484.653i	−0.319059	+	0.552626i	−0.980292	−	0.197554i	$-0.936700\pi$
$877$	−279.815	+	484.653i	−0.319059	+	0.552626i	0.661233	+	0.750181i	$0.270033\pi$
$878$	260.211	+	366.913i	0.296368	+	0.417897i
$879$	334.297	−	216.662i	0.380315	−	0.246487i
$880$	−625.987	−	1599.34i	−0.711349	−	1.81744i
$881$	−957.127			−1.08641			−0.543205	−	0.839600i	$-0.682789\pi$
$881$	−957.127			−1.08641			−0.543205	+	0.839600i	$0.682789\pi$
$882$	170.684	+	858.925i	0.193520	+	0.973838i
$883$		−	625.252i		−	0.708100i	−0.935227	−	0.354050i	$-0.884804\pi$
$883$		−	625.252i		−	0.708100i	0.935227	−	0.354050i	$-0.115196\pi$
$884$	−39.9356	+	113.960i	−0.0451760	+	0.128914i
$885$	444.475	−	22.8873i	0.502231	−	0.0258613i
$886$	493.211	+	695.457i	0.556671	+	0.784940i
$887$	921.187	+	531.847i	1.03854	+	0.599602i	0.919420	−	0.393277i	$-0.128659\pi$
$887$	921.187	+	531.847i	1.03854	+	0.599602i	0.119122	+	0.992880i	$0.461992\pi$
$888$	267.399	−	1373.01i	0.301125	−	1.54618i
$889$	48.5496	+	84.0904i	0.0546115	+	0.0945899i
$890$	308.289	+	141.511i	0.346393	+	0.159002i
$891$	288.984	+	1384.39i	0.324337	+	1.55375i
$892$	−1158.15	+	995.735i	−1.29837	+	1.11629i
$893$	−108.576	−	188.059i	−0.121585	−	0.210592i
$894$	−768.620	−	973.536i	−0.859754	−	1.08897i
$895$	−511.172	−	295.125i	−0.571142	−	0.329749i
$896$	69.8047	+	29.0467i	0.0779071	+	0.0324182i
$897$	−42.3985	+	2.18322i	−0.0472670	+	0.00243391i
$898$	75.7625	+	809.951i	0.0843681	+	0.901950i
$899$			202.793i			0.225577i
$900$	−106.910	+	448.177i	−0.118789	+	0.497974i
$901$	−606.935			−0.673624
$902$	185.622	−	17.3630i	0.205790	−	0.0192495i
$903$	58.2647	−	37.7620i	0.0645235	−	0.0418184i
$904$	−141.680	−	35.2418i	−0.156726	−	0.0389843i
$905$	−1010.61	+	1750.43i	−1.11670	+	1.93418i
$906$	127.310	+	873.576i	0.140519	+	0.964212i
$907$	207.207	−	119.631i	0.228453	−	0.131898i	−0.381405	−	0.924408i	$-0.624560\pi$
$907$	207.207	−	119.631i	0.228453	−	0.131898i	0.609858	+	0.792510i	$0.291226\pi$
$908$	180.535	−	155.217i	0.198827	−	0.170944i
$909$	94.7072	−	211.675i	0.104188	−	0.232866i
$910$	5.40696	−	11.7793i	0.00594172	−	0.0129443i
$911$	175.804	−	101.501i	0.192980	−	0.111417i	−0.400397	−	0.916342i	$-0.631128\pi$
$911$	175.804	−	101.501i	0.192980	−	0.111417i	0.593377	+	0.804925i	$0.297794\pi$
$912$	92.6134	−	931.685i	0.101550	−	1.02158i
$913$	−665.585	+	1152.83i	−0.729009	+	1.26268i
$914$	−520.740	+	369.303i	−0.569737	+	0.404052i
$915$	1246.62	+	636.619i	1.36243	+	0.695758i
$916$	−170.482	+	486.486i	−0.186116	+	0.531099i
$917$	−84.1801			−0.0917994
$918$	885.661	−	223.893i	0.964773	−	0.243893i
$919$		−	878.708i		−	0.956156i	−0.878317	−	0.478078i	$-0.841334\pi$
$919$		−	878.708i		−	0.956156i	0.878317	−	0.478078i	$-0.158666\pi$
$920$	−280.724	−	270.793i	−0.305135	−	0.294340i
$921$	459.143	−	899.090i	0.498527	−	0.976210i
$922$	958.892	−	680.036i	1.04001	−	0.737566i
$923$	−135.746	−	78.3730i	−0.147070	−	0.0849111i
$924$	89.5682	−	85.4004i	0.0969353	−	0.0924247i
$925$	−372.975	−	646.011i	−0.403216	−	0.698391i
$926$	221.670	−	482.920i	0.239385	−	0.521512i
$927$	−18.1406	−	175.680i	−0.0195691	−	0.189514i
$928$	111.510	−	169.883i	0.120162	−	0.183064i
$929$	300.259	+	520.064i	0.323207	+	0.559810i	0.981148	−	0.193259i	$-0.0619058\pi$
$929$	300.259	+	520.064i	0.323207	+	0.559810i	−0.657941	+	0.753069i	$0.728572\pi$
$930$	169.881	+	1165.69i	0.182667	+	1.25343i
$931$	−821.838	−	474.489i	−0.882748	−	0.509655i
$932$	−58.9350	+	11.1228i	−0.0632350	+	0.0119344i
$933$	−573.135	−	884.316i	−0.614293	−	0.947820i
$934$	1582.29	−	148.007i	1.69410	−	0.158465i
$935$			1815.93i			1.94217i
$936$	−47.9795	−	119.190i	−0.0512602	−	0.127340i
$937$	−184.325			−0.196718			−0.0983589	−	0.995151i	$-0.531359\pi$
$937$	−184.325			−0.196718			−0.0983589	+	0.995151i	$0.531359\pi$
$938$	4.04255	+	43.2175i	0.00430975	+	0.0460741i
$939$	29.4447	+	571.822i	0.0313575	+	0.608969i
$940$	−50.7738	−	269.028i	−0.0540147	−	0.286200i
$941$	−377.587	+	653.999i	−0.401261	+	0.695005i	−0.993878	−	0.110479i	$-0.964761\pi$
$941$	−377.587	+	653.999i	−0.401261	+	0.695005i	0.592617	+	0.805484i	$0.298095\pi$
$942$	233.783	+	296.110i	0.248177	+	0.314342i
$943$	36.6668	−	21.1696i	0.0388831	−	0.0224492i
$944$	−381.719	−	57.8966i	−0.404363	−	0.0613311i
$945$	−96.8859	+	15.0735i	−0.102525	+	0.0159507i
$946$	1243.46	+	570.773i	1.31444	+	0.603354i
$947$	−769.965	+	444.539i	−0.813057	+	0.469419i	−0.848016	−	0.529970i	$-0.822203\pi$
$947$	−769.965	+	444.539i	−0.813057	+	0.469419i	0.0349595	+	0.999389i	$0.488870\pi$
$948$	433.387	−	105.131i	0.457159	−	0.110898i
$949$	53.5731	−	92.7913i	0.0564521	−	0.0977779i
$950$	−288.834	−	407.273i	−0.304036	−	0.428708i
$951$	62.5727	+	1215.17i	0.0657967	+	1.27778i
$952$	−57.5351	−	55.4997i	−0.0604360	−	0.0582980i
$953$	15.5920			0.0163610			0.00818050	−	0.999967i	$-0.497396\pi$
$953$	15.5920			0.0163610			0.00818050	+	0.999967i	$0.497396\pi$
$954$	485.607	−	425.706i	0.509022	−	0.446233i
$955$			2.49830i			0.00261602i
$956$	1374.12	+	481.539i	1.43736	+	0.503702i
$957$	−180.905	−	279.127i	−0.189034	−	0.291669i
$958$	765.449	+	1079.33i	0.799008	+	1.12665i
$959$	−3.15291	−	1.82033i	−0.00328770	−	0.00189816i
$960$	498.666	−	1069.93i	0.519443	−	1.11451i
$961$	29.3970	+	50.9172i	0.0305900	+	0.0529835i
$962$	189.050	+	86.7777i	0.196517	+	0.0902056i
$963$	1335.68	−	966.706i	1.38699	−	1.00385i
$964$	211.350	+	245.824i	0.219243	+	0.255004i
$965$	191.961	+	332.486i	0.198923	+	0.344545i
$966$	10.3957	−	26.1121i	0.0107616	−	0.0270311i
$967$	847.921	+	489.548i	0.876858	+	0.506254i	0.869621	−	0.493720i	$-0.164363\pi$
$967$	847.921	+	489.548i	0.876858	+	0.506254i	0.00723669	+	0.999974i	$0.497696\pi$
$968$	1427.22	+	355.009i	1.47440	+	0.366745i
$969$	−450.229	+	881.635i	−0.464633	+	0.909840i
$970$	−29.9086	−	319.743i	−0.0308336	−	0.329632i
$971$		−	67.3838i		−	0.0693963i	−0.999398	−	0.0346982i	$-0.988953\pi$
$971$		−	67.3838i		−	0.0693963i	0.999398	−	0.0346982i	$-0.0110470\pi$
$972$	−551.576	+	800.342i	−0.567465	+	0.823397i
$973$	70.3667			0.0723193
$974$	113.808	−	10.6456i	0.116846	−	0.0109297i
$975$	−61.0216	−	31.1622i	−0.0625863	−	0.0319613i
$976$	−948.655	−	757.966i	−0.971983	−	0.776604i
$977$	353.710	−	612.644i	0.362037	−	0.627067i	−0.626259	−	0.779615i	$-0.715415\pi$
$977$	353.710	−	612.644i	0.362037	−	0.627067i	0.988296	+	0.152549i	$0.0487480\pi$
$978$	−798.959	−	318.080i	−0.816931	−	0.325235i
$979$	−417.133	+	240.832i	−0.426081	+	0.245998i
$980$	−780.002	−	907.229i	−0.795921	−	0.925744i
$981$	532.115	+	735.211i	0.542421	+	0.749451i
$982$	46.8799	−	102.130i	0.0477392	−	0.104002i
$983$	−338.829	+	195.623i	−0.344689	+	0.199006i	−0.662343	−	0.749200i	$-0.730438\pi$
$983$	−338.829	+	195.623i	−0.344689	+	0.199006i	0.317655	+	0.948206i	$0.397105\pi$
$984$	96.6744	+	84.0990i	0.0982464	+	0.0854665i
$985$	−638.971	+	1106.73i	−0.648701	+	1.12358i
$986$	−175.259	+	124.292i	−0.177748	+	0.126057i
$987$	16.5547	−	10.7293i	0.0167727	−	0.0108706i
$988$	131.398	+	46.0466i	0.132994	+	0.0466059i
$989$	310.720			0.314176
$990$	−1273.70	−	1452.92i	−1.28656	−	1.46760i
$991$		−	104.988i		−	0.105941i	−0.998596	−	0.0529706i	$-0.983131\pi$
$991$		−	104.988i		−	0.105941i	0.998596	−	0.0529706i	$-0.0168690\pi$
$992$	58.4795	−	1020.22i	0.0589512	−	1.02845i
$993$	−1328.81	+	68.4244i	−1.33818	+	0.0689068i
$994$	84.6422	−	60.0274i	0.0851531	−	0.0603897i
$995$	−1592.67	−	919.530i	−1.60068	−	0.924151i
$996$	−889.126	+	215.685i	−0.892697	+	0.216551i
$997$	−39.0028	−	67.5547i	−0.0391201	−	0.0677580i	0.845802	−	0.533496i	$-0.179122\pi$
$997$	−39.0028	−	67.5547i	−0.0391201	−	0.0677580i	−0.884923	+	0.465738i	$0.845789\pi$
$998$	503.120	−	1096.07i	0.504128	−	1.09827i
$999$	−241.918	−	1554.95i	−0.242160	−	1.55650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.3.f.c.31.4	yes	16
3.2	odd	2		108.3.f.c.91.5		16
4.3	odd	2	inner	36.3.f.c.31.3	yes	16
8.3	odd	2		576.3.o.g.319.2		16
8.5	even	2		576.3.o.g.319.7		16
9.2	odd	6		108.3.f.c.19.6		16
9.4	even	3		324.3.d.i.163.8		8
9.5	odd	6		324.3.d.g.163.1		8
9.7	even	3	inner	36.3.f.c.7.3	✓	16
12.11	even	2		108.3.f.c.91.6		16
24.5	odd	2		1728.3.o.g.1279.8		16
24.11	even	2		1728.3.o.g.1279.7		16
36.7	odd	6	inner	36.3.f.c.7.4	yes	16
36.11	even	6		108.3.f.c.19.5		16
36.23	even	6		324.3.d.g.163.2		8
36.31	odd	6		324.3.d.i.163.7		8
72.11	even	6		1728.3.o.g.127.8		16
72.29	odd	6		1728.3.o.g.127.7		16
72.43	odd	6		576.3.o.g.511.7		16
72.61	even	6		576.3.o.g.511.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.3	✓	16	9.7	even	3	inner
36.3.f.c.7.4	yes	16	36.7	odd	6	inner
36.3.f.c.31.3	yes	16	4.3	odd	2	inner
36.3.f.c.31.4	yes	16	1.1	even	1	trivial
108.3.f.c.19.5		16	36.11	even	6
108.3.f.c.19.6		16	9.2	odd	6
108.3.f.c.91.5		16	3.2	odd	2
108.3.f.c.91.6		16	12.11	even	2
324.3.d.g.163.1		8	9.5	odd	6
324.3.d.g.163.2		8	36.23	even	6
324.3.d.i.163.7		8	36.31	odd	6
324.3.d.i.163.8		8	9.4	even	3
576.3.o.g.319.2		16	8.3	odd	2
576.3.o.g.319.7		16	8.5	even	2
576.3.o.g.511.2		16	72.61	even	6
576.3.o.g.511.7		16	72.43	odd	6
1728.3.o.g.127.7		16	72.29	odd	6
1728.3.o.g.127.8		16	72.11	even	6
1728.3.o.g.1279.7		16	24.11	even	2
1728.3.o.g.1279.8		16	24.5	odd	2

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.186266 - 1.99131i) q^{2} +(-2.67178 - 1.36441i) q^{3} +(-3.93061 + 0.741826i) q^{4} +(3.07403 - 5.32438i) q^{5} +(-2.21930 + 5.57447i) q^{6} +(0.511543 - 0.295340i) q^{7} +(2.20934 + 7.68888i) q^{8} +(5.27677 + 7.29079i) q^{9} +O(q^{10})\)	\(q+(-0.186266 - 1.99131i) q^{2} +(-2.67178 - 1.36441i) q^{3} +(-3.93061 + 0.741826i) q^{4} +(3.07403 - 5.32438i) q^{5} +(-2.21930 + 5.57447i) q^{6} +(0.511543 - 0.295340i) q^{7} +(2.20934 + 7.68888i) q^{8} +(5.27677 + 7.29079i) q^{9} +(-11.1751 - 5.12959i) q^{10} +(15.1205 - 8.72982i) q^{11} +(11.5139 + 3.38097i) q^{12} +(-0.892255 + 1.54543i) q^{13} +(-0.683395 - 0.963628i) q^{14} +(-15.4778 + 10.0313i) q^{15} +(14.8994 - 5.83166i) q^{16} -16.9171 q^{17} +(13.5353 - 11.8657i) q^{18} +19.5058i q^{19} +(-8.13306 + 23.2084i) q^{20} +(-1.76969 + 0.0911265i) q^{21} +(-20.2002 - 28.4835i) q^{22} +(-6.86778 - 3.96511i) q^{23} +(4.58791 - 23.5574i) q^{24} +(-6.39933 - 11.0840i) q^{25} +(3.24362 + 1.48889i) q^{26} +(-4.15071 - 26.6790i) q^{27} +(-1.79159 + 1.54034i) q^{28} +(3.17517 + 5.49956i) q^{29} +(22.8584 + 28.9525i) q^{30} +(27.6558 + 15.9671i) q^{31} +(-14.3879 - 28.5830i) q^{32} +(-52.3096 + 2.69357i) q^{33} +(3.15108 + 33.6871i) q^{34} -3.63153i q^{35} +(-26.1494 - 24.7428i) q^{36} +58.2834 q^{37} +(38.8420 - 3.63326i) q^{38} +(4.49251 - 2.91164i) q^{39} +(47.7301 + 11.8725i) q^{40} +(-2.66948 + 4.62368i) q^{41} +(0.511095 + 3.50703i) q^{42} +(-33.9324 + 19.5909i) q^{43} +(-52.9567 + 45.5303i) q^{44} +(55.0399 - 5.68339i) q^{45} +(-6.61653 + 14.4144i) q^{46} +(-9.64117 + 5.56633i) q^{47} +(-47.7646 - 4.74800i) q^{48} +(-24.3255 + 42.1331i) q^{49} +(-20.8796 + 14.8076i) q^{50} +(45.1987 + 23.0819i) q^{51} +(2.36067 - 6.73638i) q^{52} +35.8770 q^{53} +(-52.3530 + 13.2347i) q^{54} -107.343i q^{55} +(3.40100 + 3.28069i) q^{56} +(26.6139 - 52.1151i) q^{57} +(10.3599 - 7.34713i) q^{58} +(-20.8974 - 12.0651i) q^{59} +(53.3955 - 50.9109i) q^{60} +(-37.9460 - 65.7244i) q^{61} +(26.6441 - 58.0454i) q^{62} +(4.85256 + 2.17112i) q^{63} +(-54.2376 + 33.9747i) q^{64} +(5.48564 + 9.50141i) q^{65} +(15.1072 + 103.663i) q^{66} +(-31.8200 - 18.3713i) q^{67} +(66.4945 - 12.5495i) q^{68} +(12.9391 + 19.9644i) q^{69} +(-7.23150 + 0.676431i) q^{70} +87.8370i q^{71} +(-44.3998 + 56.6803i) q^{72} -60.0423 q^{73} +(-10.8562 - 116.060i) q^{74} +(1.97450 + 38.3452i) q^{75} +(-14.4699 - 76.6696i) q^{76} +(5.15652 - 8.93136i) q^{77} +(-6.63478 - 8.40362i) q^{78} +(32.1841 - 18.5815i) q^{79} +(14.7512 - 97.2567i) q^{80} +(-25.3114 + 76.9437i) q^{81} +(9.70439 + 4.45452i) q^{82} +(-66.0281 + 38.1214i) q^{83} +(6.88838 - 1.67099i) q^{84} +(-52.0037 + 90.0730i) q^{85} +(45.3319 + 63.9207i) q^{86} +(-0.979694 - 19.0258i) q^{87} +(100.529 + 96.9724i) q^{88} -27.5873 q^{89} +(-21.5694 - 108.543i) q^{90} +1.05407i q^{91} +(29.9360 + 10.4906i) q^{92} +(-52.1045 - 80.3944i) q^{93} +(12.8801 + 18.1617i) q^{94} +(103.856 + 59.9614i) q^{95} +(-0.557801 + 95.9984i) q^{96} +(13.0585 + 22.6180i) q^{97} +(88.4309 + 40.5917i) q^{98} +(143.435 + 64.1751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9	\( 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9} + 20 q^{10} - 36 q^{12} - 46 q^{13} - 12 q^{14} - 17 q^{16} + 12 q^{17} + 48 q^{18} + 36 q^{20} - 66 q^{21} + 33 q^{22} + 129 q^{24} - 30 q^{25} + 72 q^{26} + 12 q^{28} + 42 q^{29} + 84 q^{30} + 87 q^{32} - 168 q^{33} + 11 q^{34} - 81 q^{36} + 56 q^{37} - 99 q^{38} + 68 q^{40} + 84 q^{41} - 354 q^{42} - 222 q^{44} + 174 q^{45} - 264 q^{46} - 189 q^{48} + 58 q^{49} - 219 q^{50} + 110 q^{52} - 72 q^{53} - 105 q^{54} + 270 q^{56} + 366 q^{57} - 16 q^{58} + 432 q^{60} - 34 q^{61} + 516 q^{62} - 254 q^{64} - 30 q^{65} + 510 q^{66} + 375 q^{68} - 54 q^{69} + 150 q^{70} - 45 q^{72} + 116 q^{73} - 372 q^{74} - 15 q^{76} - 330 q^{77} - 294 q^{78} - 720 q^{80} - 102 q^{81} + 254 q^{82} - 714 q^{84} - 140 q^{85} - 273 q^{86} + 75 q^{88} - 384 q^{89} + 108 q^{90} + 258 q^{92} - 486 q^{93} + 36 q^{94} + 900 q^{96} - 148 q^{97} + 1170 q^{98}+O(q^{100}) \) 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9 + 20 * q^10 - 36 * q^12 - 46 * q^13 - 12 * q^14 - 17 * q^16 + 12 * q^17 + 48 * q^18 + 36 * q^20 - 66 * q^21 + 33 * q^22 + 129 * q^24 - 30 * q^25 + 72 * q^26 + 12 * q^28 + 42 * q^29 + 84 * q^30 + 87 * q^32 - 168 * q^33 + 11 * q^34 - 81 * q^36 + 56 * q^37 - 99 * q^38 + 68 * q^40 + 84 * q^41 - 354 * q^42 - 222 * q^44 + 174 * q^45 - 264 * q^46 - 189 * q^48 + 58 * q^49 - 219 * q^50 + 110 * q^52 - 72 * q^53 - 105 * q^54 + 270 * q^56 + 366 * q^57 - 16 * q^58 + 432 * q^60 - 34 * q^61 + 516 * q^62 - 254 * q^64 - 30 * q^65 + 510 * q^66 + 375 * q^68 - 54 * q^69 + 150 * q^70 - 45 * q^72 + 116 * q^73 - 372 * q^74 - 15 * q^76 - 330 * q^77 - 294 * q^78 - 720 * q^80 - 102 * q^81 + 254 * q^82 - 714 * q^84 - 140 * q^85 - 273 * q^86 + 75 * q^88 - 384 * q^89 + 108 * q^90 + 258 * q^92 - 486 * q^93 + 36 * q^94 + 900 * q^96 - 148 * q^97 + 1170 * q^98

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