LMFDB - Embedded newform 36.3.f.c.31.3

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			31.3
Root			$1.63139 + 1.15696i$ of defining polynomial
Character	$\chi$	$=$	36.31
Dual form			36.3.f.c.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63139 - 1.15696i) q^{2} +(2.67178 + 1.36441i) q^{3} +(1.32286 + 3.77492i) q^{4} +(3.07403 - 5.32438i) q^{5} +(-2.78013 - 5.31703i) q^{6} +(-0.511543 + 0.295340i) q^{7} +(2.20934 - 7.68888i) q^{8} +(5.27677 + 7.29079i) q^{9} +O(q^{10})$	\(q+(-1.63139 - 1.15696i) q^{2} +(2.67178 + 1.36441i) q^{3} +(1.32286 + 3.77492i) q^{4} +(3.07403 - 5.32438i) q^{5} +(-2.78013 - 5.31703i) 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} +(-1.61614 + 11.8907i) q^{12} +(-0.892255 + 1.54543i) q^{13} +(1.17622 + 0.110024i) q^{14} +(15.4778 - 10.0313i) q^{15} +(-12.5001 + 9.98742i) q^{16} -16.9171 q^{17} +(-0.173276 - 17.9992i) q^{18} -19.5058i q^{19} +(24.1656 + 4.56079i) q^{20} +(-1.76969 + 0.0911265i) q^{21} +(34.7675 + 3.25214i) q^{22} +(6.86778 + 3.96511i) q^{23} +(16.3936 - 17.5285i) 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} +(-36.8561 - 1.54225i) q^{30} +(-27.6558 - 15.9671i) q^{31} +(31.9476 - 1.83125i) q^{32} +(-52.3096 + 2.69357i) q^{33} +(27.5984 + 19.5725i) q^{34} +3.63153i q^{35} +(-20.5417 + 29.5641i) q^{36} +58.2834 q^{37} +(-22.5675 + 31.8215i) q^{38} +(-4.49251 + 2.91164i) q^{39} +(-34.1469 - 35.3992i) q^{40} +(-2.66948 + 4.62368i) q^{41} +(2.99249 + 1.89881i) 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} +(-47.0243 + 9.62895i) q^{48} +(-24.3255 + 42.1331i) q^{49} +(-2.38396 + 25.4861i) q^{50} +(-45.1987 - 23.0819i) q^{51} +(-7.01421 - 1.32380i) q^{52} +35.8770 q^{53} +(24.0953 - 48.3262i) q^{54} +107.343i q^{55} +(1.14066 + 4.58570i) q^{56} +(26.6139 - 52.1151i) q^{57} +(1.18285 - 12.6455i) q^{58} +(20.8974 + 12.0651i) q^{59} +(58.3424 + 45.1572i) 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} +(88.4537 + 56.1261i) q^{66} +(31.8200 + 18.3713i) q^{67} +(-22.3790 - 63.8607i) q^{68} +(12.9391 + 19.9644i) q^{69} +(4.20156 - 5.92445i) q^{70} -87.8370i q^{71} +(67.7162 - 24.4646i) q^{72} -60.0423 q^{73} +(-95.0830 - 67.4319i) q^{74} +(-1.97450 - 38.3452i) q^{75} +(73.6328 - 25.8035i) q^{76} +(5.15652 - 8.93136i) q^{77} +(10.6977 + 0.447647i) 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} +(-2.68506 - 6.55991i) q^{84} +(-52.0037 + 90.0730i) q^{85} +(-78.0229 - 7.29823i) q^{86} +(0.979694 + 19.0258i) q^{87} +(33.7161 + 135.547i) q^{88} -27.5873 q^{89} +(-96.3670 - 54.4074i) q^{90} -1.05407i q^{91} +(-5.88285 + 31.1706i) q^{92} +(-52.1045 - 80.3944i) q^{93} +(-22.1686 - 2.07364i) q^{94} +(-103.856 - 59.9614i) q^{95} +(87.8553 + 38.6969i) 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 $

$2$	−1.63139	−	1.15696i	−0.815695	−	0.578482i
$2$	−1.63139	−	1.15696i	−0.815695	−	0.578482i
$3$	2.67178	+	1.36441i	0.890592	+	0.454803i
$3$	2.67178	+	1.36441i	0.890592	+	0.454803i
$4$	1.32286	+	3.77492i	0.330716	+	0.943730i
$5$	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	$-0.0440991\pi$
$6$	−2.78013	−	5.31703i	−0.463356	−	0.886172i
$7$	−0.511543	+	0.295340i	−0.0730776	+	0.0421914i	−0.536094	−	0.844159i	$-0.680101\pi$
$7$	−0.511543	+	0.295340i	−0.0730776	+	0.0421914i	0.463016	+	0.886350i	$0.346767\pi$
$8$	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	−0.991502	−	0.130092i	$-0.958473\pi$
$11$	−15.1205	+	8.72982i	−1.37459	+	0.793620i	−0.383088	+	0.923712i	$0.625139\pi$
$12$	−1.61614	+	11.8907i	−0.134678	+	0.990889i
$13$	−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	$0.188531\pi$
$14$	1.17622	+	0.110024i	0.0840160	+	0.00785882i
$15$	15.4778	−	10.0313i	1.03185	−	0.668754i
$16$	−12.5001	+	9.98742i	−0.781254	+	0.624214i
$17$	−16.9171			−0.995123			−0.497562	−	0.867429i	$-0.665771\pi$
$17$	−16.9171			−0.995123			−0.497562	+	0.867429i	$0.665771\pi$
$18$	−0.173276	−	17.9992i	−0.00962646	−	0.999954i
$19$		−	19.5058i		−	1.02662i	−0.858203	−	0.513310i	$-0.828419\pi$
$19$		−	19.5058i		−	1.02662i	0.858203	−	0.513310i	$-0.171581\pi$
$20$	24.1656	+	4.56079i	1.20828	+	0.228040i
$21$	−1.76969	+	0.0911265i	−0.0842711	+	0.00433936i
$22$	34.7675	+	3.25214i	1.58034	+	0.147824i
$23$	6.86778	+	3.96511i	0.298599	+	0.172396i	0.641813	−	0.766861i	$-0.278182\pi$
$23$	6.86778	+	3.96511i	0.298599	+	0.172396i	−0.343214	+	0.939257i	$0.611516\pi$
$24$	16.3936	−	17.5285i	0.683069	−	0.730354i
$25$	−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	$0.798412\pi$
$30$	−36.8561	−	1.54225i	−1.22854	−	0.0514084i
$31$	−27.6558	−	15.9671i	−0.892124	−	0.515068i	−0.0174873	−	0.999847i	$-0.505567\pi$
$31$	−27.6558	−	15.9671i	−0.892124	−	0.515068i	−0.874637	+	0.484779i	$0.838900\pi$
$32$	31.9476	−	1.83125i	0.998361	−	0.0572266i
$33$	−52.3096	+	2.69357i	−1.58514	+	0.0816233i
$34$	27.5984	+	19.5725i	0.811717	+	0.575661i
$35$			3.63153i			0.103758i
$36$	−20.5417	+	29.5641i	−0.570603	+	0.821226i
$37$	58.2834			1.57523			0.787614	−	0.616169i	$-0.211316\pi$
$37$	58.2834			1.57523			0.787614	+	0.616169i	$0.211316\pi$
$38$	−22.5675	+	31.8215i	−0.593881	+	0.837408i
$39$	−4.49251	+	2.91164i	−0.115192	+	0.0746575i
$40$	−34.1469	−	35.3992i	−0.853672	−	0.884980i
$41$	−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	$0.187406\pi$
$42$	2.99249	+	1.89881i	0.0712498	+	0.0452098i
$43$	33.9324	−	19.5909i	0.789126	−	0.455602i	−0.0505290	−	0.998723i	$-0.516091\pi$
$43$	33.9324	−	19.5909i	0.789126	−	0.455602i	0.839655	+	0.543121i	$0.182757\pi$
$44$	−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	−0.393915	−	0.919147i	$-0.628880\pi$
$47$	9.64117	−	5.56633i	0.205131	−	0.118433i	0.599047	+	0.800714i	$0.295546\pi$
$48$	−47.0243	+	9.62895i	−0.979673	+	0.200603i
$49$	−24.3255	+	42.1331i	−0.496440	+	0.859859i
$50$	−2.38396	+	25.4861i	−0.0476791	+	0.509721i
$51$	−45.1987	−	23.0819i	−0.886249	−	0.452585i
$52$	−7.01421	−	1.32380i	−0.134889	−	0.0254576i
$53$	35.8770			0.676925			0.338462	−	0.940980i	$-0.390093\pi$
$53$	35.8770			0.676925			0.338462	+	0.940980i	$0.390093\pi$
$54$	24.0953	−	48.3262i	0.446209	−	0.894929i
$55$			107.343i			1.95169i
$56$	1.14066	+	4.58570i	0.0203689	+	0.0818875i
$57$	26.6139	−	52.1151i	0.466910	−	0.914299i
$58$	1.18285	−	12.6455i	0.0203940	−	0.218026i
$59$	20.8974	+	12.0651i	0.354194	+	0.204494i	0.666531	−	0.745477i	$-0.267778\pi$
$59$	20.8974	+	12.0651i	0.354194	+	0.204494i	−0.312337	+	0.949971i	$0.601112\pi$
$60$	58.3424	+	45.1572i	0.972373	+	0.752621i
$61$	−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
$66$	88.4537	+	56.1261i	1.34021	+	0.850395i
$67$	31.8200	+	18.3713i	0.474925	+	0.274198i	0.718299	−	0.695734i	$-0.244921\pi$
$67$	31.8200	+	18.3713i	0.474925	+	0.274198i	−0.243374	+	0.969933i	$0.578254\pi$
$68$	−22.3790	−	63.8607i	−0.329103	−	0.939128i
$69$	12.9391	+	19.9644i	0.187524	+	0.289339i
$70$	4.20156	−	5.92445i	0.0600222	−	0.0846350i
$71$		−	87.8370i		−	1.23714i	−0.785730	−	0.618570i	$-0.787712\pi$
$71$		−	87.8370i		−	1.23714i	0.785730	−	0.618570i	$-0.212288\pi$
$72$	67.7162	−	24.4646i	0.940503	−	0.339786i
$73$	−60.0423			−0.822498			−0.411249	−	0.911523i	$-0.634907\pi$
$73$	−60.0423			−0.822498			−0.411249	+	0.911523i	$0.634907\pi$
$74$	−95.0830	−	67.4319i	−1.28490	−	0.911241i
$75$	−1.97450	−	38.3452i	−0.0263267	−	0.511269i
$76$	73.6328	−	25.8035i	0.968852	−	0.339520i
$77$	5.15652	−	8.93136i	0.0669678	−	0.115992i
$78$	10.6977	+	0.447647i	0.137150	+	0.00573907i
$79$	−32.1841	+	18.5815i	−0.407394	+	0.235209i	−0.689669	−	0.724124i	$-0.742244\pi$
$79$	−32.1841	+	18.5815i	−0.407394	+	0.235209i	0.282275	+	0.959333i	$0.408911\pi$
$80$	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	−0.0463824	−	0.998924i	$-0.514769\pi$
$83$	66.0281	−	38.1214i	0.795520	−	0.459294i	0.841902	+	0.539630i	$0.181436\pi$
$84$	−2.68506	−	6.55991i	−0.0319650	−	0.0780941i
$85$	−52.0037	+	90.0730i	−0.611808	+	1.05968i
$86$	−78.0229	−	7.29823i	−0.907243	−	0.0848632i
$87$	0.979694	+	19.0258i	0.0112609	+	0.218688i
$88$	33.7161	+	135.547i	0.383138	+	1.54030i
$89$	−27.5873			−0.309969			−0.154985	−	0.987917i	$-0.549533\pi$
$89$	−27.5873			−0.309969			−0.154985	+	0.987917i	$0.549533\pi$
$90$	−96.3670	−	54.4074i	−1.07074	−	0.604527i
$91$		−	1.05407i		−	0.0115832i
$92$	−5.88285	+	31.1706i	−0.0639440	+	0.338811i
$93$	−52.1045	−	80.3944i	−0.560264	−	0.864456i
$94$	−22.1686	−	2.07364i	−0.235836	−	0.0220600i
$95$	−103.856	−	59.9614i	−1.09322	−	0.631172i
$96$	87.8553	+	38.6969i	0.915159	+	0.403092i
$97$	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	$0.874047\pi$
$102$	47.0318	+	89.9488i	0.461096	+	0.881851i
$103$	16.9947	+	9.81187i	0.164997	+	0.0952609i	0.580225	−	0.814457i	$-0.302965\pi$
$103$	16.9947	+	9.81187i	0.164997	+	0.0952609i	−0.415228	+	0.909717i	$0.636298\pi$
$104$	9.91133	+	10.2748i	0.0953012	+	0.0987964i
$105$	−4.95490	+	9.70264i	−0.0471895	+	0.0924061i
$106$	−58.5294	−	41.5085i	−0.552164	−	0.391589i
$107$			183.200i			1.71215i	0.516850	+	0.856076i	$0.327105\pi$
$107$			183.200i			1.71215i	−0.516850	+	0.856076i	$0.672895\pi$
$108$	−95.2205	+	50.9614i	−0.881671	+	0.471865i
$109$	100.841			0.925147			0.462573	−	0.886581i	$-0.346926\pi$
$109$	100.841			0.925147			0.462573	+	0.886581i	$0.346926\pi$
$110$	124.192	−	175.118i	1.12902	−	1.59198i
$111$	155.720	+	79.5225i	1.40288	+	0.716419i
$112$	3.44464	−	8.80076i	0.0307557	−	0.0785782i
$113$	−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	$0.192398\pi$
$114$	−103.713	+	54.2286i	−0.909762	+	0.475690i
$115$	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
$120$	−42.9338	−	141.169i	−0.357782	−	1.17641i
$121$	91.9194	−	159.209i	0.759664	−	1.31578i
$122$	−14.1361	+	151.124i	−0.115870	+	1.23872i
$123$	−13.4408	+	8.71116i	−0.109275	+	0.0708224i
$124$	23.6896	−	125.521i	0.191045	−	1.01227i
$125$	75.0146			0.600117
$126$	5.40451	+	9.15618i	0.0428929	+	0.0726681i
$127$		−	164.386i		−	1.29438i	−0.762331	−	0.647188i	$-0.775945\pi$
$127$		−	164.386i		−	1.29438i	0.762331	−	0.647188i	$-0.224055\pi$
$128$	49.1751	+	118.177i	0.384181	+	0.923258i
$129$	117.390	−	6.04473i	0.909998	−	0.0468584i
$130$	2.04358	−	21.8472i	0.0157198	−	0.168055i
$131$	123.421	+	71.2570i	0.942143	+	0.543947i	0.890631	−	0.454726i	$-0.150263\pi$
$131$	123.421	+	71.2570i	0.942143	+	0.543947i	0.0515116	+	0.998672i	$0.483596\pi$
$132$	−79.3665	−	193.901i	−0.601262	−	1.46895i
$133$	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	$0.840494\pi$
$138$	1.98931	−	47.5398i	0.0144153	−	0.344491i
$139$	−103.168	−	59.5642i	−0.742218	−	0.428519i	0.0806575	−	0.996742i	$-0.474298\pi$
$139$	−103.168	−	59.5642i	−0.742218	−	0.428519i	−0.822875	+	0.568222i	$0.807631\pi$
$140$	−13.7088	+	4.80403i	−0.0979197	+	0.0343145i
$141$	33.3538	−	1.71748i	0.236552	−	0.0121807i
$142$	−101.624	+	143.296i	−0.715664	+	1.00913i
$143$		−	31.1569i		−	0.217880i
$144$	−138.776	−	38.4340i	−0.963723	−	0.266903i
$145$	39.0423			0.269257
$146$	97.9524	+	69.4669i	0.670907	+	0.475800i
$147$	−122.479	+	79.3801i	−0.833192	+	0.540001i
$148$	77.1011	+	220.015i	0.520953	+	1.48659i
$149$	−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	$0.922634\pi$
$150$	−41.1429	+	64.8404i	−0.274286	+	0.432269i
$151$	−127.422	+	73.5670i	−0.843853	+	0.487199i	−0.858572	−	0.512693i	$-0.828648\pi$
$151$	−127.422	+	73.5670i	−0.843853	+	0.487199i	0.0147190	+	0.999892i	$0.495315\pi$
$152$	−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
$156$	−16.9342	−	13.1071i	−0.108553	−	0.0840202i
$157$	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	$0.102491\pi$
$158$	74.0030	+	6.92221i	0.468373	+	0.0438115i
$159$	95.8554	+	48.9510i	0.602864	+	0.307868i
$160$	88.4575	−	175.730i	0.552859	−	1.09831i
$161$	−4.68422			−0.0290946
$162$	130.314	−	96.2408i	0.804407	−	0.594079i
$163$		−	143.325i		−	0.879292i	−0.898171	−	0.439646i	$-0.855104\pi$
$163$		−	143.325i		−	0.879292i	0.898171	−	0.439646i	$-0.144896\pi$
$164$	−20.9854	−	3.96058i	−0.127960	−	0.0241499i
$165$	−146.460	+	286.796i	−0.887635	+	1.73816i
$166$	−151.823	−	14.2014i	−0.914595	−	0.0855508i
$167$	−150.531	−	86.9089i	−0.901381	−	0.520413i	−0.0237332	−	0.999718i	$-0.507555\pi$
$167$	−150.531	−	86.9089i	−0.901381	−	0.520413i	−0.877648	+	0.479306i	$0.840889\pi$
$168$	−3.20920	+	13.8083i	−0.0191024	+	0.0821922i
$169$	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	$-0.425846\pi$
$174$	20.4140	−	32.1720i	0.117322	−	0.184897i
$175$	6.54707	+	3.77995i	0.0374118	+	0.0215997i
$176$	101.819	−	260.138i	0.578515	−	1.47806i
$177$	39.3715	+	60.7480i	0.222438	+	0.343209i
$178$	45.0056	+	31.9175i	0.252840	+	0.179312i
$179$			96.0059i			0.536346i	0.963371	+	0.268173i	$0.0864199\pi$
$179$			96.0059i			0.536346i	−0.963371	+	0.268173i	$0.913580\pi$
$180$	94.2647	+	200.253i	0.523693	+	1.11252i
$181$	−328.757			−1.81634			−0.908170	−	0.418603i	$-0.862520\pi$
$181$	−328.757			−1.81634			−0.908170	+	0.418603i	$0.862520\pi$
$182$	−1.21953	+	1.71960i	−0.00670069	+	0.00944838i
$183$	−11.7082	−	227.375i	−0.0639791	−	1.24249i
$184$	45.6605	−	44.0452i	0.248155	−	0.239376i
$185$	179.165	−	310.323i	0.968460	−	1.67742i
$186$	−8.01075	+	191.438i	−0.0430685	+	1.02924i
$187$	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	−0.499078	−	0.866557i	$-0.666328\pi$
$191$	0.351914	−	0.203178i	0.00184248	−	0.00106376i	0.500921	+	0.865493i	$0.332995\pi$
$192$	−98.5553	−	164.775i	−0.513309	−	0.858204i
$193$	−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	$0.218389\pi$
$194$	4.86472	−	52.0071i	0.0250759	−	0.268078i
$195$	1.69258	+	32.8703i	0.00867992	+	0.168566i
$196$	−191.228	−	36.0906i	−0.975656	−	0.184136i
$197$	−207.861			−1.05513			−0.527566	−	0.849514i	$-0.676895\pi$
$197$	−207.861			−1.05513			−0.527566	+	0.849514i	$0.676895\pi$
$198$	159.749	+	270.643i	0.806815	+	1.36689i
$199$			299.128i			1.50316i	0.659643	+	0.751579i	$0.270707\pi$
$199$			299.128i			1.50316i	−0.659643	+	0.751579i	$0.729293\pi$
$200$	−99.3616	+	24.7154i	−0.496808	+	0.123577i
$201$	59.9499	+	92.4995i	0.298258	+	0.460196i
$202$	−4.79938	+	51.3085i	−0.0237593	+	0.254003i
$203$	−3.24848	−	1.87551i	−0.0160024	−	0.00923896i
$204$	27.3404	−	201.156i	0.134022	−	0.986057i
$205$	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
$210$	19.3090	−	10.0961i	0.0919476	−	0.0480769i
$211$	141.744	+	81.8360i	0.671773	+	0.387848i	0.796748	−	0.604311i	$-0.206552\pi$
$211$	141.744	+	81.8360i	0.671773	+	0.387848i	−0.124975	+	0.992160i	$0.539885\pi$
$212$	47.4605	+	135.433i	0.223870	+	0.638835i
$213$	119.846	−	234.681i	0.562656	−	1.10179i
$214$	211.956	−	298.871i	0.990450	−	1.39659i
$215$		−	240.892i		−	1.12043i
$216$	214.302	+	27.0288i	0.992140	+	0.125133i
$217$	18.8629			0.0869257
$218$	−164.511	−	116.669i	−0.754637	−	0.535181i
$219$	−160.420	−	81.9223i	−0.732510	−	0.374075i
$220$	−405.211	+	142.000i	−1.84187	+	0.645455i
$221$	15.0944	−	26.1442i	0.0683003	−	0.118300i
$222$	−162.036	−	309.895i	−0.729890	−	1.39592i
$223$	−330.681	+	190.919i	−1.48287	+	0.856138i	−0.999811	−	0.0194478i	$-0.993809\pi$
$223$	−330.681	+	190.919i	−1.48287	+	0.856138i	−0.483063	+	0.875586i	$0.660476\pi$
$224$	−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	−0.382144	−	0.924103i	$-0.624814\pi$
$227$	51.5472	−	29.7608i	0.227080	−	0.131105i	0.609224	+	0.792998i	$0.291481\pi$
$228$	231.937	+	31.5241i	1.01727	+	0.138264i
$229$	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	$0.0758736\pi$
$230$	−97.0873	−	9.08150i	−0.422118	−	0.0394848i
$231$	25.9631	−	16.8270i	0.112394	−	0.0728441i
$232$	49.3005	−	12.2631i	0.212502	−	0.0528582i
$233$	14.9939			0.0643513			0.0321757	−	0.999482i	$-0.489756\pi$
$233$	14.9939			0.0643513			0.0321757	+	0.999482i	$0.489756\pi$
$234$	27.9711	+	15.7921i	0.119535	+	0.0674874i
$235$		−	68.4443i		−	0.291252i
$236$	−17.9005	+	94.8467i	−0.0758495	+	0.401893i
$237$	−111.342	+	5.73329i	−0.469796	+	0.0241911i
$238$	−19.8983	−	1.86128i	−0.0836063	−	0.00782050i
$239$	315.244	+	182.006i	1.31901	+	0.761532i	0.983570	−	0.180529i	$-0.0577811\pi$
$239$	315.244	+	182.006i	1.31901	+	0.761532i	0.335442	+	0.942061i	$0.391114\pi$
$240$	−93.2860	+	279.975i	−0.388691	+	1.16656i
$241$	−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
$246$	32.0058	+	1.33929i	0.130105	+	0.00544426i
$247$	30.1448	+	17.4041i	0.122044	+	0.0704620i
$248$	−183.870	+	177.366i	−0.741413	+	0.715184i
$249$	228.426	−	11.7623i	0.917372	−	0.0472381i
$250$	−122.378	−	86.7892i	−0.489512	−	0.347157i
$251$		−	281.883i		−	1.12304i	−0.827463	−	0.561520i	$-0.810217\pi$
$251$		−	281.883i		−	1.12304i	0.827463	−	0.561520i	$-0.189783\pi$
$252$	1.77652	−	21.1901i	0.00704968	−	0.0840878i
$253$	−138.459			−0.547268
$254$	−190.188	+	268.177i	−0.748773	+	1.05582i
$255$	−261.839	+	169.701i	−1.02682	+	0.665492i
$256$	56.5028	−	249.687i	0.220714	−	0.975339i
$257$	−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	$0.213475\pi$
$258$	−198.502	−	125.955i	−0.769388	−	0.488196i
$259$	−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	−0.284939	−	0.958546i	$-0.591973\pi$
$263$	105.914	−	61.1497i	0.402716	−	0.232508i	0.687655	+	0.726037i	$0.258640\pi$
$264$	−94.8593	+	408.153i	−0.359315	+	1.54603i
$265$	110.287	−	191.023i	0.416178	−	0.720841i
$266$	2.14609	−	22.9432i	0.00806802	−	0.0862525i
$267$	−73.7070	−	37.6403i	−0.276056	−	0.140975i
$268$	−27.2566	+	144.421i	−0.101704	+	0.538883i
$269$	280.452			1.04257			0.521287	−	0.853382i	$-0.325452\pi$
$269$	280.452			1.04257			0.521287	+	0.853382i	$0.325452\pi$
$270$	−183.237	−	276.848i	−0.678656	−	1.02536i
$271$			81.4468i			0.300542i	0.988645	+	0.150271i	$0.0480146\pi$
$271$			81.4468i			0.300542i	−0.988645	+	0.150271i	$0.951985\pi$
$272$	211.465	−	168.958i	0.777443	−	0.621170i
$273$	1.43819	−	2.81625i	0.00526809	−	0.0103159i
$274$	−1.14805	+	12.2735i	−0.00418998	+	0.0447937i
$275$	193.522	+	111.730i	0.703716	+	0.406291i
$276$	−58.2472	+	75.2543i	−0.211040	+	0.272661i
$277$	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	$0.876357\pi$
$282$	−56.4001	−	35.7873i	−0.200000	−	0.126905i
$283$	322.061	+	185.942i	1.13803	+	0.657039i	0.945941	−	0.324339i	$-0.105142\pi$
$283$	322.061	+	185.942i	1.13803	+	0.657039i	0.192084	+	0.981378i	$0.438475\pi$
$284$	331.578	−	116.196i	1.16753	−	0.409142i
$285$	−195.668	−	301.906i	−0.686556	−	1.05932i
$286$	−36.0474	+	50.8290i	−0.126040	+	0.177724i
$287$		−	3.15361i		−	0.0109882i
$288$	181.931	+	223.260i	0.631706	+	0.775208i
$289$	−2.81196			−0.00972996
$290$	−63.6932	−	45.1706i	−0.219632	−	0.155761i
$291$	4.02919	+	78.2475i	0.0138460	+	0.268892i
$292$	−79.4279	−	226.655i	−0.272013	−	0.776216i
$293$	−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	$0.239429\pi$
$294$	291.651	+	12.2042i	0.992011	+	0.0415109i
$295$	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
$300$	142.138	−	58.1791i	0.473794	−	0.193930i
$301$	−11.5719	+	20.0432i	−0.0384450	+	0.0665886i
$302$	292.989	+	27.4061i	0.970163	+	0.0907486i
$303$	−3.97507	−	77.1965i	−0.0131190	−	0.254774i
$304$	194.812	+	243.823i	0.640830	+	0.802050i
$305$	−466.589			−1.52980
$306$	2.93133	+	304.494i	0.00957952	+	0.995077i
$307$		−	336.514i		−	1.09614i	−0.836434	−	0.548068i	$-0.815363\pi$
$307$		−	336.514i		−	1.09614i	0.836434	−	0.548068i	$-0.184637\pi$
$308$	40.5366	+	7.65048i	0.131612	+	0.0248392i
$309$	32.0185	+	49.4028i	0.103620	+	0.159880i
$310$	390.960	+	36.5703i	1.26116	+	0.117969i
$311$	−304.206	−	175.634i	−0.978156	−	0.564738i	−0.0764428	−	0.997074i	$-0.524356\pi$
$311$	−304.206	−	175.634i	−0.978156	−	0.564738i	−0.901713	+	0.432336i	$0.857690\pi$
$312$	12.4618	+	40.9751i	0.0399416	+	0.131331i
$313$	−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	$-0.387624\pi$
$318$	−99.7429	−	190.759i	−0.313657	−	0.599872i
$319$	−96.0203	−	55.4374i	−0.301004	−	0.173785i
$320$	−347.622	+	184.342i	−1.08632	+	0.576069i
$321$	−249.960	+	489.470i	−0.778693	+	1.52483i
$322$	7.64179	+	5.41948i	0.0237323	+	0.0168307i
$323$			329.981i			1.02161i
$324$	−323.940	+	6.23766i	−0.999815	+	0.0192520i
$325$	22.8393			0.0702749
$326$	−165.821	+	233.818i	−0.508655	+	0.717234i
$327$	269.424	+	137.588i	0.823928	+	0.420760i
$328$	29.6531	+	30.7406i	0.0904057	+	0.0937213i
$329$	−3.28792	+	5.69484i	−0.00999368	+	0.0173096i
$330$	570.746	−	298.428i	1.72953	−	0.904326i
$331$	−384.104	+	221.763i	−1.16044	+	0.669978i	−0.951408	−	0.307932i	$-0.900363\pi$
$331$	−384.104	+	221.763i	−1.16044	+	0.669978i	−0.209027	+	0.977910i	$0.567030\pi$
$332$	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
$336$	21.2112	−	18.8138i	0.0631284	−	0.0559933i
$337$	−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	$0.894585\pi$
$338$	30.8858	−	330.190i	0.0913781	−	0.976893i
$339$	−45.9436	+	29.7766i	−0.135527	+	0.0878365i
$340$	−408.812	−	77.1553i	−1.20239	−	0.226927i
$341$	557.560			1.63507
$342$	−351.088	+	3.37989i	−1.02657	+	0.00988272i
$343$		−	57.6805i		−	0.168165i
$344$	−75.6636	−	304.185i	−0.219952	−	0.884259i
$345$	146.073	−	7.52172i	0.423400	−	0.0218021i
$346$	−46.8667	+	501.036i	−0.135453	+	1.44808i
$347$	−492.773	−	284.503i	−1.42010	−	0.819893i	−0.423790	−	0.905761i	$-0.639300\pi$
$347$	−492.773	−	284.503i	−1.42010	−	0.819893i	−0.996307	+	0.0858678i	$0.972634\pi$
$348$	−70.5250	+	28.8669i	−0.202658	+	0.0829508i
$349$	−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	$0.776853\pi$
$354$	6.05312	−	144.655i	0.0170992	−	0.408630i
$355$	−467.677	−	270.014i	−1.31740	−	0.760602i
$356$	−36.4942	−	104.140i	−0.102512	−	0.292527i
$357$	29.9381	−	1.54160i	0.0838601	−	0.00431820i
$358$	111.076	−	156.623i	0.310267	−	0.437495i
$359$			303.196i			0.844557i	0.906466	+	0.422278i	$0.138770\pi$
$359$			303.196i			0.844557i	−0.906466	+	0.422278i	$0.861230\pi$
$360$	77.9031	−	435.752i	0.216398	−	1.21042i
$361$	−19.4752			−0.0539480
$362$	536.331	+	380.361i	1.48158	+	1.05072i
$363$	462.814	−	299.955i	1.27497	−	0.826323i
$364$	3.97904	−	1.39440i	0.0109314	−	0.00383076i
$365$	−184.572	+	319.688i	−0.505677	+	0.875858i
$366$	−243.964	+	384.483i	−0.666569	+	1.05050i
$367$	615.571	−	355.400i	1.67730	−	0.968392i	0.713936	−	0.700211i	$-0.246911\pi$
$367$	615.571	−	355.400i	1.67730	−	0.968392i	0.963369	−	0.268181i	$-0.0864224\pi$
$368$	−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
$372$	234.555	−	303.041i	0.630525	−	0.814628i
$373$	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	$0.0191501\pi$
$374$	−588.165	−	55.0167i	−1.57263	−	0.147103i
$375$	200.422	+	102.351i	0.534459	+	0.272935i
$376$	−21.4982	−	86.4277i	−0.0571761	−	0.229861i
$377$	−11.3323			−0.0300590
$378$	1.94685	+	31.8372i	0.00515039	+	0.0842255i
$379$			662.686i			1.74851i	0.485465	+	0.874256i	$0.338650\pi$
$379$			662.686i			1.74851i	−0.485465	+	0.874256i	$0.661350\pi$
$380$	88.9618	−	471.369i	0.234110	−	1.24045i
$381$	224.289	−	439.202i	0.588686	−	1.15276i
$382$	−0.809179	−	0.0756903i	−0.00211827	−	0.000198142i
$383$	69.9008	+	40.3572i	0.182509	+	0.105371i	0.588471	−	0.808518i	$-0.299730\pi$
$383$	69.9008	+	40.3572i	0.182509	+	0.105371i	−0.405962	+	0.913890i	$0.633064\pi$
$384$	−29.8570	+	382.838i	−0.0777526	+	0.996973i
$385$	−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	$-0.515597\pi$
$390$	35.2685	−	55.5825i	0.0904320	−	0.142519i
$391$	−116.183	−	67.0782i	−0.297143	−	0.171556i
$392$	270.213	+	280.123i	0.689318	+	0.714598i
$393$	232.529	+	358.779i	0.591676	+	0.912924i
$394$	339.102	+	240.488i	0.860665	+	0.610375i
$395$			228.481i			0.578432i
$396$	52.5114	−	626.349i	0.132604	−	1.58169i
$397$	657.713			1.65671			0.828354	−	0.560206i	$-0.189278\pi$
$397$	657.713			1.65671			0.828354	+	0.560206i	$0.189278\pi$
$398$	346.081	−	487.995i	0.869550	−	1.22612i
$399$	1.77749	+	34.5192i	0.00445487	+	0.0865144i
$400$	190.692	+	74.6374i	0.476731	+	0.186594i
$401$	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	$-0.0981459\pi$
$402$	9.21693	−	220.263i	0.0229277	−	0.547917i
$403$	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
$408$	−277.333	+	296.531i	−0.679737	+	0.726792i
$409$	−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	$0.295955\pi$
$410$	6.11405	−	65.3632i	0.0149123	−	0.159422i
$411$	−0.950872	−	18.4661i	−0.00231356	−	0.0449297i
$412$	−14.5574	+	77.1333i	−0.0353335	+	0.187217i
$413$	−14.2533			−0.0345115
$414$	70.1787	−	124.301i	0.169514	−	0.300245i
$415$		−	468.745i		−	1.12951i
$416$	−25.6753	+	51.0067i	−0.0617195	+	0.122612i
$417$	−194.372	−	299.906i	−0.466121	−	0.719199i
$418$	63.4354	−	678.167i	0.151759	−	1.62241i
$419$	222.744	+	128.601i	0.531608	+	0.306924i	0.741671	−	0.670764i	$-0.234033\pi$
$419$	222.744	+	128.601i	0.531608	+	0.306924i	−0.210063	+	0.977688i	$0.567367\pi$
$420$	−43.1814	−	5.86907i	−0.102813	−	0.0139740i
$421$	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
$426$	−467.032	+	244.198i	−1.09632	+	0.573236i
$427$	38.8221	+	22.4139i	0.0909182	+	0.0524917i
$428$	−691.567	+	242.349i	−1.61581	+	0.566237i
$429$	42.5108	−	83.2442i	0.0990927	−	0.194042i
$430$	−278.703	+	392.989i	−0.648148	+	0.913927i
$431$			144.348i			0.334914i	0.985879	+	0.167457i	$0.0535555\pi$
$431$			144.348i			0.334914i	−0.985879	+	0.167457i	$0.946445\pi$
$432$	−318.339	−	292.035i	−0.736896	−	0.676006i
$433$	395.353			0.913057			0.456528	−	0.889709i	$-0.349093\pi$
$433$	395.353			0.913057			0.456528	+	0.889709i	$0.349093\pi$
$434$	−30.7727	−	21.8237i	−0.0709049	−	0.0502850i
$435$	104.312	+	53.2697i	0.239798	+	0.122459i
$436$	133.399	+	380.667i	0.305961	+	0.873089i
$437$	77.3426	−	133.961i	0.176985	−	0.306548i
$438$	166.926	+	319.247i	0.381109	+	0.728875i
$439$	194.776	−	112.454i	0.443682	−	0.256160i	−0.261476	−	0.965210i	$-0.584209\pi$
$439$	194.776	−	112.454i	0.443682	−	0.256160i	0.705158	+	0.709050i	$0.250876\pi$
$440$	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	−0.0216335	−	0.999766i	$-0.506887\pi$
$443$	369.184	−	213.148i	0.833373	−	0.481148i	0.855006	+	0.518618i	$0.173553\pi$
$444$	−94.1943	+	693.029i	−0.212149	+	1.56088i
$445$	−84.8041	+	146.885i	−0.190571	+	0.330079i
$446$	760.356	+	71.1233i	1.70483	+	0.159469i
$447$	−520.444	+	337.306i	−1.16430	+	0.754599i
$448$	37.7790	+	1.36102i	0.0843281	+	0.00303799i
$449$	−406.744			−0.905888			−0.452944	−	0.891539i	$-0.649626\pi$
$449$	−406.744			−0.905888			−0.452944	+	0.891539i	$0.649626\pi$
$450$	−198.393	+	117.103i	−0.440874	+	0.260229i
$451$		−	93.2163i		−	0.206688i
$452$	−71.7324	−	13.5381i	−0.158700	−	0.0299515i
$453$	−440.818	+	22.6990i	−0.973108	+	0.0501081i
$454$	−118.526	−	11.0869i	−0.261070	−	0.0244204i
$455$	−5.61228	−	3.24025i	−0.0123347	−	0.00712144i
$456$	−341.907	−	319.771i	−0.749796	−	0.701252i
$457$	−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	$0.613302\pi$
$462$	−61.8242	−	2.58704i	−0.133819	−	0.00559966i
$463$	−230.088	−	132.841i	−0.496950	−	0.286914i	0.230503	−	0.973072i	$-0.425963\pi$
$463$	−230.088	−	132.841i	−0.496950	−	0.286914i	−0.727453	+	0.686157i	$0.759296\pi$
$464$	−94.6163	−	37.0330i	−0.203914	−	0.0798126i
$465$	−588.221	+	30.2892i	−1.26499	+	0.0651380i
$466$	−24.4608	−	17.3474i	−0.0524910	−	0.0372261i
$467$		−	794.598i		−	1.70149i	−0.525575	−	0.850747i	$-0.676150\pi$
$467$		−	794.598i		−	1.70149i	0.525575	−	0.850747i	$-0.323850\pi$
$468$	−27.3609	−	58.1246i	−0.0584634	−	0.124198i
$469$	−21.7031			−0.0462752
$470$	−79.1877	+	111.659i	−0.168484	+	0.237573i
$471$	158.298	−	102.595i	0.336089	−	0.217823i
$472$	138.937	−	134.022i	0.294358	−	0.283944i
$473$	−342.050	+	592.447i	−0.723149	+	1.25253i
$474$	188.275	+	119.465i	0.397204	+	0.252036i
$475$	−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	0.236468	−	0.971639i	$-0.424010\pi$
$479$	572.964	−	330.801i	1.19617	−	0.690607i	0.959698	+	0.281033i	$0.0906769\pi$
$480$	476.107	−	348.819i	0.991889	−	0.726707i
$481$	−52.0037	+	90.0730i	−0.108116	+	0.187262i
$482$	−15.0963	+	161.390i	−0.0313202	+	0.334833i
$483$	−12.5152	−	6.39120i	−0.0259114	−	0.0132323i
$484$	722.599	+	136.376i	1.49297	+	0.281769i
$485$	160.569			0.331071
$486$	479.481	−	79.3322i	0.986587	−	0.163235i
$487$		−	57.1525i		−	0.117356i	−0.998277	−	0.0586781i	$-0.981311\pi$
$487$		−	57.1525i		−	0.117356i	0.998277	−	0.0586781i	$-0.0186886\pi$
$488$	−589.183	+	146.554i	−1.20734	+	0.300317i
$489$	195.553	−	382.931i	0.399905	−	0.783090i
$490$	55.7140	−	595.620i	0.113702	−	1.21555i
$491$	−48.6600	−	28.0939i	−0.0991040	−	0.0572177i	0.449629	−	0.893215i	$-0.351556\pi$
$491$	−48.6600	−	28.0939i	−0.0991040	−	0.0572177i	−0.548733	+	0.835998i	$0.684890\pi$
$492$	−50.6644	−	39.2144i	−0.102976	−	0.0797041i
$493$	−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
$498$	−386.260	−	245.091i	−0.775622	−	0.492152i
$499$	−522.225	−	301.507i	−1.04654	−	0.604222i	−0.124863	−	0.992174i	$-0.539849\pi$
$499$	−522.225	−	301.507i	−1.04654	−	0.604222i	−0.921679	+	0.387952i	$0.873183\pi$
$500$	99.2341	+	283.174i	0.198468	+	0.566348i
$501$	−283.605	−	437.587i	−0.566077	−	0.873427i
$502$	−326.129	+	459.861i	−0.649659	+	0.916058i
$503$			549.354i			1.09216i	0.837734	+	0.546078i	$0.183880\pi$
$503$			549.354i			1.09216i	−0.837734	+	0.546078i	$0.816120\pi$
$504$	−27.4144	+	32.5140i	−0.0543937	+	0.0645119i
$505$	−158.413			−0.313688
$506$	225.880	+	160.192i	0.446404	+	0.316585i
$507$	25.5810	+	496.788i	0.0504557	+	0.979859i
$508$	620.543	−	217.460i	1.22154	−	0.428071i
$509$	−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	$0.242079\pi$
$510$	623.498	+	26.0904i	1.22255	+	0.0511577i
$511$	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
$516$	178.109	+	435.141i	0.345173	+	0.843296i
$517$	−97.1862	+	168.331i	−0.187981	+	0.325593i
$518$	68.5544	+	6.41255i	0.132344	+	0.0123794i
$519$	−38.8171	−	753.836i	−0.0747922	−	1.45248i
$520$	85.1748	−	21.1865i	0.163798	−	0.0407433i
$521$	−567.711			−1.08966			−0.544828	−	0.838548i	$-0.683405\pi$
$521$	−567.711			−1.08966			−0.544828	+	0.838548i	$0.683405\pi$
$522$	98.4373	−	58.1034i	0.188577	−	0.111309i
$523$			941.999i			1.80114i	0.434706	+	0.900572i	$0.356852\pi$
$523$			941.999i			1.80114i	−0.434706	+	0.900572i	$0.643148\pi$
$524$	−105.721	+	560.167i	−0.201757	+	1.06902i
$525$	12.3349	+	19.0321i	0.0234950	+	0.0362516i
$526$	−243.536	−	22.7802i	−0.462996	−	0.0433084i
$527$	467.856	+	270.117i	0.887773	+	0.512556i
$528$	626.971	−	556.108i	1.18745	−	1.05323i
$529$	−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
$534$	76.6963	+	146.682i	0.143626	+	0.274686i
$535$	975.428	+	563.163i	1.82323	+	1.05264i
$536$	211.556	−	204.072i	0.394694	−	0.380730i
$537$	−130.991	+	256.506i	−0.243932	+	0.477665i
$538$	−457.527	−	324.473i	−0.850422	−	0.603110i
$539$		−	849.430i		−	1.57594i
$540$	−21.3729	+	663.647i	−0.0395795	+	1.22898i
$541$	−242.245			−0.447772			−0.223886	−	0.974615i	$-0.571874\pi$
$541$	−242.245			−0.447772			−0.223886	+	0.974615i	$0.571874\pi$
$542$	94.2311	−	132.871i	0.173858	−	0.245150i
$543$	−878.366	−	448.560i	−1.61762	−	0.826077i
$544$	−540.460	+	30.9794i	−0.993492	+	0.0569475i
$545$	309.988	−	536.915i	0.568786	−	0.985166i
$546$	−5.60454	+	2.93046i	−0.0102647	+	0.00536715i
$547$	170.503	−	98.4402i	0.311706	−	0.179964i	−0.335983	−	0.941868i	$-0.609069\pi$
$547$	170.503	−	98.4402i	0.311706	−	0.179964i	0.647690	+	0.761904i	$0.275735\pi$
$548$	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
$552$	182.090	−	55.3792i	0.329874	−	0.100325i
$553$	10.9757	−	19.0105i	0.0198476	−	0.0343770i
$554$	83.7681	−	895.536i	0.151206	−	1.61649i
$555$	902.096	−	584.659i	1.62540	−	1.05344i
$556$	88.3725	−	468.247i	0.158943	−	0.842171i
$557$	958.121			1.72015			0.860073	−	0.510171i	$-0.170418\pi$
$557$	958.121			1.72015			0.860073	+	0.510171i	$0.170418\pi$
$558$	−282.603	+	500.549i	−0.506456	+	0.897041i
$559$			69.9202i			0.125081i
$560$	−36.2697	−	45.3944i	−0.0647672	−	0.0810614i
$561$	884.926	−	45.5674i	1.57741	−	0.0812253i
$562$	−14.1059	+	150.801i	−0.0250994	+	0.268329i
$563$	−165.774	−	95.7097i	−0.294448	−	0.169999i	0.345498	−	0.938419i	$-0.387710\pi$
$563$	−165.774	−	95.7097i	−0.294448	−	0.169999i	−0.639946	+	0.768420i	$0.721043\pi$
$564$	50.6060	+	123.636i	0.0897269	+	0.219213i
$565$	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	$0.701968\pi$
$570$	−30.0828	+	718.907i	−0.0527768	+	1.26124i
$571$	842.764	+	486.570i	1.47594	+	0.852136i	0.999632	−	0.0271399i	$-0.00863995\pi$
$571$	842.764	+	486.570i	1.47594	+	0.852136i	0.476312	+	0.879276i	$0.341973\pi$
$572$	117.615	−	41.2164i	0.205620	−	0.0720566i
$573$	1.21745	−	0.0626902i	0.00212470	−	0.000109407i
$574$	−3.64862	+	5.14477i	−0.00635648	+	0.00896302i
$575$		−	101.496i		−	0.176515i
$576$	−38.4967	−	574.712i	−0.0668346	−	0.997764i
$577$	138.527			0.240081			0.120040	−	0.992769i	$-0.461698\pi$
$577$	138.527			0.240081			0.120040	+	0.992769i	$0.461698\pi$
$578$	4.58740	+	3.25334i	0.00793668	+	0.00562861i
$579$	−157.208	+	101.888i	−0.271516	+	0.175972i
$580$	51.6477	+	147.382i	0.0890478	+	0.254106i
$581$	−22.5175	+	39.0015i	−0.0387565	+	0.0671282i
$582$	83.9565	−	132.314i	0.144255	−	0.227343i
$583$	−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	−0.924766	−	0.380537i	$-0.875739\pi$
$587$	−620.808	+	358.424i	−1.05759	+	0.610602i	−0.132829	+	0.991139i	$0.542406\pi$
$588$	−461.677	−	357.340i	−0.785165	−	0.607721i
$589$	−311.451	+	539.449i	−0.528779	+	0.915872i
$590$	−295.419	−	27.6334i	−0.500711	−	0.0468363i
$591$	−555.358	−	283.607i	−0.939691	−	0.479877i
$592$	−728.546	+	582.101i	−1.23065	+	0.983279i
$593$	542.129			0.914214			0.457107	−	0.889412i	$-0.348886\pi$
$593$	542.129			0.914214			0.457107	+	0.889412i	$0.348886\pi$
$594$	57.5460	+	941.062i	0.0968788	+	1.58428i
$595$		−	61.4350i		−	0.103252i
$596$	−812.577	−	153.358i	−1.36338	−	0.257312i
$597$	−408.134	+	799.204i	−0.683641	+	1.33870i
$598$	28.1801	+	2.63596i	0.0471240	+	0.00440796i
$599$	245.527	+	141.755i	0.409895	+	0.236653i	0.690744	−	0.723099i	$-0.257283\pi$
$599$	245.527	+	141.755i	0.409895	+	0.236653i	−0.280850	+	0.959752i	$0.590616\pi$
$600$	−299.194	−	69.5359i	−0.498656	−	0.115893i
$601$	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
$606$	−82.8288	+	130.537i	−0.136681	+	0.215407i
$607$	−77.2227	−	44.5845i	−0.127220	−	0.0734506i	0.435039	−	0.900411i	$-0.356734\pi$
$607$	−77.2227	−	44.5845i	−0.127220	−	0.0734506i	−0.562260	+	0.826961i	$0.690068\pi$
$608$	−35.7200	−	623.162i	−0.0587499	−	1.02494i
$609$	−6.12024	−	9.44320i	−0.0100497	−	0.0155061i
$610$	761.189	+	539.827i	1.24785	+	0.884962i
$611$			19.8664i			0.0325145i
$612$	347.506	−	500.139i	0.567821	−	0.817221i
$613$	−316.779			−0.516769			−0.258385	−	0.966042i	$-0.583190\pi$
$613$	−316.779			−0.516769			−0.258385	+	0.966042i	$0.583190\pi$
$614$	−389.335	+	548.985i	−0.634096	+	0.894113i
$615$	5.06393	+	98.3425i	0.00823404	+	0.159907i
$616$	−57.2796	−	59.3803i	−0.0929863	−	0.0963966i
$617$	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	$-0.167283\pi$
$618$	4.92265	−	117.640i	0.00796545	−	0.190355i
$619$	−578.542	+	334.021i	−0.934640	+	0.539615i	−0.888276	−	0.459310i	$-0.848097\pi$
$619$	−578.542	+	334.021i	−0.934640	+	0.539615i	−0.0463638	+	0.998925i	$0.514763\pi$
$620$	−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
$624$	27.0768	−	81.2643i	0.0433923	−	0.130231i
$625$	390.580	−	676.505i	0.624929	−	1.08241i
$626$	−35.5507	+	380.060i	−0.0567902	+	0.607125i
$627$	52.5402	+	1020.34i	0.0837961	+	1.62734i
$628$	247.153	+	46.6452i	0.393555	+	0.0742759i
$629$	−985.986			−1.56755
$630$	65.3646	−	0.629259i	0.103753	−	0.000998824i
$631$		−	150.631i		−	0.238718i	−0.992851	−	0.119359i	$-0.961916\pi$
$631$		−	150.631i		−	0.238718i	0.992851	−	0.119359i	$-0.0380839\pi$
$632$	71.7652	+	288.513i	0.113553	+	0.456507i
$633$	267.051	+	412.045i	0.421881	+	0.650939i
$634$	−75.5484	+	807.662i	−0.119162	+	1.27392i
$635$	−875.252	−	505.327i	−1.37835	−	0.795790i
$636$	−57.9824	+	426.602i	−0.0911672	+	0.670758i
$637$	−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	$0.648573\pi$
$642$	974.082	−	509.321i	1.51726	−	0.793335i
$643$	−742.057	−	428.427i	−1.15405	−	0.666293i	−0.204182	−	0.978933i	$-0.565454\pi$
$643$	−742.057	−	428.427i	−1.15405	−	0.666293i	−0.949872	+	0.312639i	$0.898787\pi$
$644$	−6.19659	−	17.6826i	−0.00962204	−	0.0274574i
$645$	328.675	−	643.609i	0.509574	−	0.997844i
$646$	381.776	−	538.328i	0.590985	−	0.833324i
$647$		−	156.257i		−	0.241510i	−0.992682	−	0.120755i	$-0.961468\pi$
$647$		−	156.257i		−	0.241510i	0.992682	−	0.120755i	$-0.0385316\pi$
$648$	535.689	+	364.611i	0.826681	+	0.562671i
$649$	−421.306			−0.649162
$650$	−37.2599	−	26.4243i	−0.0573229	−	0.0406528i
$651$	50.3974	+	25.7367i	0.0774154	+	0.0395341i
$652$	541.039	−	189.599i	0.829814	−	0.290796i
$653$	−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	$0.930151\pi$
$654$	−280.351	−	536.175i	−0.428672	−	0.819840i
$655$	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	−0.183589	−	0.983003i	$-0.558772\pi$
$659$	379.533	−	219.123i	0.575922	−	0.332509i	0.759511	+	0.650494i	$0.225438\pi$
$660$	−1276.38	−	173.481i	−1.93391	−	0.262851i
$661$	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	$0.0515239\pi$
$662$	883.195	+	82.6137i	1.33413	+	0.124794i
$663$	76.0002	−	49.2565i	0.114631	−	0.0742934i
$664$	−147.232	−	591.905i	−0.221734	−	0.891424i
$665$	70.8359			0.106520
$666$	−10.0991	−	1049.05i	−0.0151639	−	1.57515i
$667$			50.3597i			0.0755018i
$668$	128.943	−	683.210i	0.193028	−	1.02277i
$669$	−1144.00	+	58.9076i	−1.71001	+	0.0880533i
$670$	−449.827	−	42.0767i	−0.671384	−	0.0628010i
$671$	1147.52	+	662.524i	1.71017	+	0.987368i
$672$	−56.3705	+	6.15202i	−0.0838847	+	0.00915480i
$673$	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	$0.724192\pi$
$678$	109.402	+	4.57796i	0.161360	+	0.00675216i
$679$	−13.3600	−	7.71341i	−0.0196760	−	0.0113600i
$680$	577.666	+	598.852i	0.849509	+	0.880664i
$681$	178.329	−	9.18264i	0.261863	−	0.0134841i
$682$	−909.597	−	645.077i	−1.33372	−	0.945861i
$683$		−	123.214i		−	0.180400i	−0.995924	−	0.0902002i	$-0.971249\pi$
$683$		−	123.214i		−	0.180400i	0.995924	−	0.0902002i	$-0.0287507\pi$
$684$	576.671	+	400.682i	0.843087	+	0.585793i
$685$	−37.8937			−0.0553193
$686$	−66.7343	+	94.0994i	−0.0972803	+	0.137171i
$687$	324.439	−	210.272i	0.472254	−	0.306073i
$688$	−228.495	+	583.784i	−0.332114	+	0.848524i
$689$	−32.0115	+	55.4455i	−0.0464607	+	0.0804724i
$690$	−247.004	−	156.731i	−0.357977	−	0.227146i
$691$	163.326	−	94.2965i	0.236362	−	0.136464i	−0.377141	−	0.926156i	$-0.623093\pi$
$691$	163.326	−	94.2965i	0.236362	−	0.136464i	0.613504	+	0.789692i	$0.289760\pi$
$692$	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
$696$	148.452	+	34.5018i	0.213293	+	0.0495716i
$697$	45.1599	−	78.2192i	0.0647918	−	0.112223i
$698$	−77.0773	+	824.007i	−0.110426	+	1.18053i
$699$	40.0602	+	20.4578i	0.0573107	+	0.0292672i
$700$	−5.60814	+	29.7150i	−0.00801162	+	0.0424501i
$701$	−810.064			−1.15558			−0.577792	−	0.816184i	$-0.696085\pi$
$701$	−810.064			−1.15558			−0.577792	+	0.816184i	$0.696085\pi$
$702$	53.1856	+	80.3569i	0.0757630	+	0.114468i
$703$		−	1136.86i		−	1.61716i
$704$	1116.69	+	40.2298i	1.58621	+	0.0571447i
$705$	93.3861	−	182.868i	0.132463	−	0.259387i
$706$	23.2114	−	248.145i	0.0328773	−	0.351480i
$707$	13.1806	+	7.60980i	0.0186429	+	0.0107635i
$708$	−177.236	+	228.986i	−0.250333	+	0.323426i
$709$	−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
$714$	−50.6242	−	32.1224i	−0.0709023	−	0.0449893i
$715$	−165.891	−	95.7772i	−0.232015	−	0.133954i
$716$	−362.415	+	127.003i	−0.506166	+	0.177378i
$717$	593.930	+	916.401i	0.828354	+	1.27810i
$718$	350.787	−	494.631i	0.488561	−	0.688901i
$719$			788.981i			1.09733i	0.836042	+	0.548666i	$0.184864\pi$
$719$			788.981i			1.09733i	−0.836042	+	0.548666i	$0.815136\pi$
$720$	−631.239	+	620.749i	−0.876722	+	0.862152i
$721$	−11.5913			−0.0160768
$722$	31.7717	+	22.5321i	0.0440051	+	0.0312080i
$723$	−12.5035	−	242.820i	−0.0172939	−	0.335850i
$724$	−434.902	−	1241.03i	−0.600693	−	1.71413i
$725$	40.6380	−	70.3870i	0.0560524	−	0.0970856i
$726$	−1102.07	−	46.1163i	−1.51800	−	0.0635210i
$727$	232.676	−	134.335i	0.320049	−	0.184780i	−0.331365	−	0.943502i	$-0.607509\pi$
$727$	232.676	−	134.335i	0.320049	−	0.184780i	0.651414	+	0.758722i	$0.274176\pi$
$728$	−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
$732$	842.834	−	344.984i	1.15141	−	0.471289i
$733$	−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	$0.182669\pi$
$734$	−1415.42	−	132.398i	−1.92837	−	0.180379i
$735$	46.1449	+	896.143i	0.0627822	+	1.21924i
$736$	226.670	+	114.099i	0.307975	+	0.155026i
$737$	−641.512			−0.870437
$738$	83.6849	+	47.2473i	0.113394	+	0.0640207i
$739$		−	448.249i		−	0.606562i	−0.952901	−	0.303281i	$-0.901918\pi$
$739$		−	448.249i		−	0.606562i	0.952901	−	0.303281i	$-0.0980820\pi$
$740$	1408.46	+	265.818i	1.90332	+	0.359214i
$741$	56.7939	+	87.6298i	0.0766449	+	0.118259i
$742$	42.1994	+	3.94732i	0.0568725	+	0.00531983i
$743$	−656.602	−	379.089i	−0.883718	−	0.510215i	−0.0118352	−	0.999930i	$-0.503767\pi$
$743$	−656.602	−	379.089i	−0.883718	−	0.510215i	−0.871882	+	0.489715i	$0.837101\pi$
$744$	−733.260	+	223.006i	−0.985564	+	0.299740i
$745$	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
$750$	−208.550	−	398.855i	−0.278067	−	0.531807i
$751$	−1141.58	−	659.091i	−1.52008	−	0.877618i	−0.999720	−	0.0236697i	$-0.992465\pi$
$751$	−1141.58	−	659.091i	−1.52008	−	0.877618i	−0.520358	−	0.853948i	$-0.674202\pi$
$752$	−64.9219	+	165.870i	−0.0863323	+	0.220572i
$753$	384.604	−	753.128i	0.510762	−	1.00017i
$754$	18.4873	+	13.1110i	0.0245190	+	0.0173886i
$755$			904.589i			1.19813i
$756$	33.6585	−	54.1913i	0.0445218	−	0.0716817i
$757$	587.874			0.776583			0.388292	−	0.921537i	$-0.373065\pi$
$757$	587.874			0.776583			0.388292	+	0.921537i	$0.373065\pi$
$758$	766.705	−	1081.10i	1.01148	−	1.42625i
$759$	−369.931	−	188.915i	−0.487393	−	0.248899i
$760$	−690.489	+	666.062i	−0.908538	+	0.876397i
$761$	−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	$0.246340\pi$
$762$	−874.044	+	457.014i	−1.14704	+	0.599756i
$763$	−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
$768$	491.638	−	590.014i	0.640154	−	0.768247i
$769$	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	$-0.149243\pi$
$770$	−11.8102	+	126.259i	−0.0153380	+	0.163973i
$771$	−189.600	+	122.882i	−0.245914	+	0.159380i
$772$	−245.451	−	46.3240i	−0.317941	−	0.0600052i
$773$	778.578			1.00722			0.503608	−	0.863932i	$-0.332006\pi$
$773$	778.578			1.00722			0.503608	+	0.863932i	$0.332006\pi$
$774$	−358.499	−	607.360i	−0.463177	−	0.784703i
$775$			408.715i			0.527375i
$776$	202.758	−	50.4344i	0.261286	−	0.0649928i
$777$	−103.144	+	5.31117i	−0.132746	+	0.00683548i
$778$	−128.898	+	1378.01i	−0.165679	+	1.77122i
$779$	90.1884	+	52.0703i	0.115775	+	0.0668425i
$780$	−121.844	+	49.8723i	−0.156210	+	0.0639389i
$781$	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
$786$	35.7499	−	854.336i	0.0454833	−	1.08694i
$787$	390.283	+	225.330i	0.495913	+	0.286315i	0.727024	−	0.686612i	$-0.240903\pi$
$787$	390.283	+	225.330i	0.495913	+	0.286315i	−0.231111	+	0.972927i	$0.574236\pi$
$788$	−274.972	−	784.658i	−0.348949	−	0.995759i
$789$	366.413	−	18.8676i	0.464402	−	0.0239134i
$790$	264.344	−	372.741i	0.334613	−	0.471824i
$791$		−	10.7797i		−	0.0136280i
$792$	−810.331	+	961.066i	−1.02314	+	1.21347i
$793$	135.430			0.170782
$794$	−1072.99	−	760.950i	−1.35137	−	0.958376i
$795$	555.296	−	359.893i	0.698485	−	0.452696i
$796$	−1129.19	+	395.707i	−1.41858	+	0.497119i
$797$	−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	$0.240367\pi$
$798$	37.0378	−	58.3708i	0.0464132	−	0.0731464i
$799$	−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
$804$	−269.873	+	348.671i	−0.335662	+	0.433670i
$805$	−14.3994	+	24.9406i	−0.0178875	+	0.0309821i
$806$	−113.478	−	10.6147i	−0.140792	−	0.0131696i
$807$	749.305	+	382.652i	0.928507	+	0.474166i
$808$	−200.035	+	49.7570i	−0.247568	+	0.0615804i
$809$	1167.70			1.44339			0.721695	−	0.692212i	$-0.243364\pi$
$809$	1167.70			1.44339			0.721695	+	0.692212i	$0.243364\pi$
$810$	−111.833	−	989.688i	−0.138066	−	1.22184i
$811$		−	810.121i		−	0.998916i	−0.866338	−	0.499458i	$-0.833533\pi$
$811$		−	810.121i		−	0.998916i	0.866338	−	0.499458i	$-0.166467\pi$
$812$	2.78260	−	14.7438i	0.00342685	−	0.0181574i
$813$	−111.127	+	217.608i	−0.136687	+	0.267660i
$814$	2026.37	+	189.546i	2.48940	+	0.232857i
$815$	−763.114	−	440.584i	−0.936336	−	0.540594i
$816$	795.514	−	162.894i	0.974895	−	0.199625i
$817$	−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	$0.944327\pi$
$822$	−19.8134	+	31.2255i	−0.0241039	+	0.0379873i
$823$	1016.04	+	586.612i	1.23456	+	0.712773i	0.967977	−	0.251039i	$-0.0807722\pi$
$823$	1016.04	+	586.612i	1.23456	+	0.712773i	0.266583	+	0.963812i	$0.414105\pi$
$824$	112.989	−	108.992i	0.137123	−	0.132272i
$825$	364.602	+	562.561i	0.441942	+	0.681892i
$826$	23.2526	+	16.4905i	0.0281509	+	0.0199643i
$827$		−	267.739i		−	0.323747i	−0.986811	−	0.161874i	$-0.948246\pi$
$827$		−	267.739i		−	0.323747i	0.986811	−	0.161874i	$-0.0517537\pi$
$828$	−258.301	+	121.590i	−0.311958	+	0.146847i
$829$	−432.474			−0.521682			−0.260841	−	0.965382i	$-0.584000\pi$
$829$	−432.474			−0.521682			−0.260841	+	0.965382i	$0.584000\pi$
$830$	−542.321	+	764.706i	−0.653399	+	0.921332i
$831$	69.3806	+	1347.38i	0.0834904	+	1.62140i
$832$	100.899	−	53.5064i	0.121273	−	0.0643105i
$833$	411.518	−	712.769i	0.494019	−	0.855665i
$834$	−29.8836	+	714.146i	−0.0358316	+	0.856290i
$835$	−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	−0.200790	−	0.979634i	$-0.564351\pi$
$839$	459.103	−	265.063i	0.547202	−	0.315927i	0.747993	+	0.663707i	$0.231018\pi$
$840$	63.6553	+	59.5341i	0.0757802	+	0.0708739i
$841$	400.337	−	693.403i	0.476024	−	0.824499i
$842$	15.6428	−	167.232i	0.0185782	−	0.198613i
$843$	−11.6831	−	226.889i	−0.0138590	−	0.269144i
$844$	−121.416	+	643.331i	−0.143858	+	0.762240i
$845$	1019.44			1.20644
$846$	−101.860	−	172.569i	−0.120402	−	0.203982i
$847$			108.590i			0.128205i
$848$	−448.465	+	358.319i	−0.528850	+	0.422546i
$849$	606.774	+	936.219i	0.714692	+	1.10273i
$850$	40.3296	−	431.150i	0.0474466	−	0.507236i
$851$	400.278	+	231.100i	0.470361	+	0.271563i
$852$	1044.44	+	141.957i	1.22587	+	0.166616i
$853$	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	$0.906347\pi$
$858$	−165.662	+	86.6203i	−0.193080	+	0.100956i
$859$	503.279	+	290.568i	0.585889	+	0.338263i	0.763470	−	0.645843i	$-0.223494\pi$
$859$	503.279	+	290.568i	0.585889	+	0.338263i	−0.177581	+	0.984106i	$0.556827\pi$
$860$	909.348	−	318.667i	1.05738	−	0.370544i
$861$	4.30282	−	8.42575i	0.00499747	−	0.00978601i
$862$	167.005	−	235.488i	0.193742	−	0.273187i
$863$			827.326i			0.958663i	0.877634	+	0.479331i	$0.159121\pi$
$863$			827.326i			0.958663i	−0.877634	+	0.479331i	$0.840879\pi$
$864$	181.461	+	844.729i	0.210025	+	0.977696i
$865$	−1546.92			−1.78835
$866$	−644.976	−	457.410i	−0.744776	−	0.528187i
$867$	−7.51293	−	3.83667i	−0.00866543	−	0.00442522i
$868$	24.9530	+	71.2059i	0.0287478	+	0.0820344i
$869$	324.426	−	561.923i	0.373333	−	0.646632i
$870$	−108.543	−	207.589i	−0.124762	−	0.238608i
$871$	−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
$876$	97.0369	−	713.944i	0.110773	−	0.815004i
$877$	−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	$0.270033\pi$
$878$	−447.862	−	41.8928i	−0.510093	−	0.0477139i
$879$	−334.297	+	216.662i	−0.380315	+	0.246487i
$880$	−1072.08	−	1341.79i	−1.21827	−	1.52476i
$881$	−957.127			−1.08641			−0.543205	−	0.839600i	$-0.682789\pi$
$881$	−957.127			−1.08641			−0.543205	+	0.839600i	$0.682789\pi$
$882$	762.575	+	430.539i	0.864598	+	0.488139i
$883$			625.252i			0.708100i	0.935227	+	0.354050i	$0.115196\pi$
$883$			625.252i			0.708100i	−0.935227	+	0.354050i	$0.884804\pi$
$884$	118.660	+	22.3948i	0.134231	+	0.0253335i
$885$	444.475	−	22.8873i	0.502231	−	0.0258613i
$886$	−848.888	−	79.4047i	−0.958113	−	0.0896215i
$887$	−921.187	−	531.847i	−1.03854	−	0.599602i	−0.119122	−	0.992880i	$-0.538008\pi$
$887$	−921.187	−	531.847i	−1.03854	−	0.599602i	−0.919420	+	0.393277i	$0.871341\pi$
$888$	955.478	−	1021.62i	1.07599	−	1.15047i
$889$	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
$894$	1239.30	+	51.8587i	1.38624	+	0.0580075i
$895$	511.172	+	295.125i	0.571142	+	0.329749i
$896$	−60.0576	−	45.9293i	−0.0670285	−	0.0512604i
$897$	−42.3985	+	2.18322i	−0.0472670	+	0.00243391i
$898$	663.557	+	470.588i	0.738928	+	0.524040i
$899$		−	202.793i		−	0.225577i
$900$	459.141	+	38.4931i	0.510157	+	0.0427701i
$901$	−606.935			−0.673624
$902$	−107.848	+	152.072i	−0.119565	+	0.168594i
$903$	−58.2647	+	37.7620i	−0.0645235	+	0.0418184i
$904$	101.360	+	105.078i	0.112124	+	0.116236i
$905$	−1010.61	+	1750.43i	−1.11670	+	1.93418i
$906$	745.408	+	472.980i	0.822746	+	0.522053i
$907$	−207.207	+	119.631i	−0.228453	+	0.131898i	−0.609858	−	0.792510i	$-0.708774\pi$
$907$	−207.207	+	119.631i	−0.228453	+	0.131898i	0.381405	+	0.924408i	$0.375440\pi$
$908$	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	−0.593377	−	0.804925i	$-0.702206\pi$
$911$	−175.804	+	101.501i	−0.192980	+	0.111417i	0.400397	+	0.916342i	$0.368872\pi$
$912$	187.820	+	917.245i	0.205943	+	1.00575i
$913$	−665.585	+	1152.83i	−0.729009	+	1.26268i
$914$	−59.4561	+	635.625i	−0.0650505	+	0.695433i
$915$	−1246.62	−	636.619i	−1.36243	−	0.695758i
$916$	506.551	+	95.6015i	0.553003	+	0.104368i
$917$	−84.1801			−0.0917994
$918$	−407.622	+	817.538i	−0.444033	+	0.890564i
$919$			878.708i			0.956156i	0.878317	+	0.478078i	$0.158666\pi$
$919$			878.708i			0.956156i	−0.878317	+	0.478078i	$0.841334\pi$
$920$	−94.1514	−	378.510i	−0.102338	−	0.411424i
$921$	459.143	−	899.090i	0.498527	−	0.976210i
$922$	109.483	−	1170.44i	0.118745	−	1.26946i
$923$	135.746	+	78.3730i	0.147070	+	0.0849111i
$924$	97.8662	+	75.7489i	0.105916	+	0.0819793i
$925$	−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	$0.728572\pi$
$930$	994.662	+	631.138i	1.06953	+	0.678643i
$931$	821.838	+	474.489i	0.882748	+	0.509655i
$932$	19.8348	+	56.6006i	0.0212820	+	0.0607303i
$933$	−573.135	−	884.316i	−0.614293	−	0.947820i
$934$	−919.322	+	1296.30i	−0.984284	+	1.38790i
$935$		−	1815.93i		−	1.94217i
$936$	−22.6118	+	126.479i	−0.0241579	+	0.135128i
$937$	−184.325			−0.196718			−0.0983589	−	0.995151i	$-0.531359\pi$
$937$	−184.325			−0.196718			−0.0983589	+	0.995151i	$0.531359\pi$
$938$	35.4062	+	25.1097i	0.0377465	+	0.0267694i
$939$	−29.4447	−	571.822i	−0.0313575	−	0.608969i
$940$	258.372	−	90.5426i	0.274864	−	0.0963219i
$941$	−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	$0.298095\pi$
$942$	−376.944	−	15.7733i	−0.400153	−	0.0167445i
$943$	−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	−0.0349595	−	0.999389i	$-0.511130\pi$
$947$	769.965	−	444.539i	0.813057	−	0.469419i	0.848016	+	0.529970i	$0.177797\pi$
$948$	−168.933	−	412.721i	−0.178199	−	0.435360i
$949$	53.5731	−	92.7913i	0.0564521	−	0.0977779i
$950$	497.126	+	46.5009i	0.523290	+	0.0489483i
$951$	−62.5727	−	1215.17i	−0.0657967	−	1.27778i
$952$	−19.2966	−	77.5767i	−0.0202695	−	0.0814881i
$953$	15.5920			0.0163610			0.00818050	−	0.999967i	$-0.497396\pi$
$953$	15.5920			0.0163610			0.00818050	+	0.999967i	$0.497396\pi$
$954$	−6.21664	−	645.757i	−0.00651639	−	0.676894i
$955$		−	2.49830i		−	0.00261602i
$956$	−270.034	+	1430.79i	−0.282462	+	1.49664i
$957$	−180.905	−	279.127i	−0.189034	−	0.291669i
$958$	−1317.45	−	123.234i	−1.37521	−	0.128637i
$959$	3.15291	+	1.82033i	0.00328770	+	0.00189816i
$960$	−1180.29	+	18.2216i	−1.22947	+	0.0189809i
$961$	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
$966$	13.0228	+	24.9062i	0.0134811	+	0.0257828i
$967$	−847.921	−	489.548i	−0.876858	−	0.506254i	−0.00723669	−	0.999974i	$-0.502304\pi$
$967$	−847.921	−	489.548i	−0.876858	−	0.506254i	−0.869621	+	0.493720i	$0.835637\pi$
$968$	−1021.06	−	1058.50i	−1.05481	−	1.09350i
$969$	−450.229	+	881.635i	−0.464633	+	0.909840i
$970$	−261.951	−	185.773i	−0.270053	−	0.191519i
$971$			67.3838i			0.0693963i	0.999398	+	0.0346982i	$0.0110470\pi$
$971$			67.3838i			0.0693963i	−0.999398	+	0.0346982i	$0.988953\pi$
$972$	−874.006	−	425.321i	−0.899183	−	0.437573i
$973$	70.3667			0.0723193
$974$	−66.1234	+	93.2379i	−0.0678885	+	0.0957268i
$975$	61.0216	+	31.1622i	0.0625863	+	0.0319613i
$976$	1130.75	+	442.576i	1.15855	+	0.453459i
$977$	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	$0.0487480\pi$
$978$	−762.062	+	398.461i	−0.779204	+	0.407425i
$979$	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	−0.317655	−	0.948206i	$-0.602895\pi$
$983$	338.829	−	195.623i	0.344689	−	0.199006i	0.662343	+	0.749200i	$0.269562\pi$
$984$	37.2836	+	122.591i	0.0378898	+	0.124584i
$985$	−638.971	+	1106.73i	−0.648701	+	1.12358i
$986$	−20.0104	+	213.925i	−0.0202946	+	0.216962i
$987$	−16.5547	+	10.7293i	−0.0167727	+	0.0108706i
$988$	−25.8217	+	136.818i	−0.0261353	+	0.138479i
$989$	310.720			0.314176
$990$	1932.08	−	18.6000i	1.95160	−	0.0187879i
$991$			104.988i			0.105941i	0.998596	+	0.0529706i	$0.0168690\pi$
$991$			104.988i			0.105941i	−0.998596	+	0.0529706i	$0.983131\pi$
$992$	−912.776	−	459.465i	−0.920137	−	0.463171i
$993$	−1328.81	+	68.4244i	−1.33818	+	0.0689068i
$994$	9.66413	−	103.316i	0.00972247	−	0.103940i
$995$	1592.67	+	919.530i	1.60068	+	0.924151i
$996$	346.578	+	846.728i	0.347970	+	0.850129i
$997$	−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.31.3	yes	16
3.2	odd	2		108.3.f.c.91.6		16
4.3	odd	2	inner	36.3.f.c.31.4	yes	16
8.3	odd	2		576.3.o.g.319.7		16
8.5	even	2		576.3.o.g.319.2		16
9.2	odd	6		108.3.f.c.19.5		16
9.4	even	3		324.3.d.i.163.7		8
9.5	odd	6		324.3.d.g.163.2		8
9.7	even	3	inner	36.3.f.c.7.4	yes	16
12.11	even	2		108.3.f.c.91.5		16
24.5	odd	2		1728.3.o.g.1279.7		16
24.11	even	2		1728.3.o.g.1279.8		16
36.7	odd	6	inner	36.3.f.c.7.3	✓	16
36.11	even	6		108.3.f.c.19.6		16
36.23	even	6		324.3.d.g.163.1		8
36.31	odd	6		324.3.d.i.163.8		8
72.11	even	6		1728.3.o.g.127.7		16
72.29	odd	6		1728.3.o.g.127.8		16
72.43	odd	6		576.3.o.g.511.2		16
72.61	even	6		576.3.o.g.511.7		16

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

\(f(q)\)	\(=\)	\(q+(-1.63139 - 1.15696i) q^{2} +(2.67178 + 1.36441i) q^{3} +(1.32286 + 3.77492i) q^{4} +(3.07403 - 5.32438i) q^{5} +(-2.78013 - 5.31703i) q^{6} +(-0.511543 + 0.295340i) q^{7} +(2.20934 - 7.68888i) q^{8} +(5.27677 + 7.29079i) q^{9} +O(q^{10})\)	\(q+(-1.63139 - 1.15696i) q^{2} +(2.67178 + 1.36441i) q^{3} +(1.32286 + 3.77492i) q^{4} +(3.07403 - 5.32438i) q^{5} +(-2.78013 - 5.31703i) 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} +(-1.61614 + 11.8907i) q^{12} +(-0.892255 + 1.54543i) q^{13} +(1.17622 + 0.110024i) q^{14} +(15.4778 - 10.0313i) q^{15} +(-12.5001 + 9.98742i) q^{16} -16.9171 q^{17} +(-0.173276 - 17.9992i) q^{18} -19.5058i q^{19} +(24.1656 + 4.56079i) q^{20} +(-1.76969 + 0.0911265i) q^{21} +(34.7675 + 3.25214i) q^{22} +(6.86778 + 3.96511i) q^{23} +(16.3936 - 17.5285i) 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} +(-36.8561 - 1.54225i) q^{30} +(-27.6558 - 15.9671i) q^{31} +(31.9476 - 1.83125i) q^{32} +(-52.3096 + 2.69357i) q^{33} +(27.5984 + 19.5725i) q^{34} +3.63153i q^{35} +(-20.5417 + 29.5641i) q^{36} +58.2834 q^{37} +(-22.5675 + 31.8215i) q^{38} +(-4.49251 + 2.91164i) q^{39} +(-34.1469 - 35.3992i) q^{40} +(-2.66948 + 4.62368i) q^{41} +(2.99249 + 1.89881i) 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} +(-47.0243 + 9.62895i) q^{48} +(-24.3255 + 42.1331i) q^{49} +(-2.38396 + 25.4861i) q^{50} +(-45.1987 - 23.0819i) q^{51} +(-7.01421 - 1.32380i) q^{52} +35.8770 q^{53} +(24.0953 - 48.3262i) q^{54} +107.343i q^{55} +(1.14066 + 4.58570i) q^{56} +(26.6139 - 52.1151i) q^{57} +(1.18285 - 12.6455i) q^{58} +(20.8974 + 12.0651i) q^{59} +(58.3424 + 45.1572i) 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} +(88.4537 + 56.1261i) q^{66} +(31.8200 + 18.3713i) q^{67} +(-22.3790 - 63.8607i) q^{68} +(12.9391 + 19.9644i) q^{69} +(4.20156 - 5.92445i) q^{70} -87.8370i q^{71} +(67.7162 - 24.4646i) q^{72} -60.0423 q^{73} +(-95.0830 - 67.4319i) q^{74} +(-1.97450 - 38.3452i) q^{75} +(73.6328 - 25.8035i) q^{76} +(5.15652 - 8.93136i) q^{77} +(10.6977 + 0.447647i) 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} +(-2.68506 - 6.55991i) q^{84} +(-52.0037 + 90.0730i) q^{85} +(-78.0229 - 7.29823i) q^{86} +(0.979694 + 19.0258i) q^{87} +(33.7161 + 135.547i) q^{88} -27.5873 q^{89} +(-96.3670 - 54.4074i) q^{90} -1.05407i q^{91} +(-5.88285 + 31.1706i) q^{92} +(-52.1045 - 80.3944i) q^{93} +(-22.1686 - 2.07364i) q^{94} +(-103.856 - 59.9614i) q^{95} +(87.8553 + 38.6969i) 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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