LMFDB - Embedded newform 361.3.f.b.333.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,3,Mod(116,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("361.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.f (of order $18$, degree $6$, not 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:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			333.2
Root			$-1.89323i$ of defining polynomial
Character	$\chi$	$=$	361.333
Dual form			361.3.f.b.116.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86447 - 0.328757i) q^{2} +(-1.24899 - 1.48849i) q^{3} +(-0.390596 + 0.142165i) q^{4} +(2.62459 + 0.955274i) q^{5} +(-2.81806 - 2.36464i) q^{6} +(-1.20796 + 2.09224i) q^{7} +(-7.23987 + 4.17994i) q^{8} +(0.907209 - 5.14504i) q^{9} +O(q^{10})$	\(q+(1.86447 - 0.328757i) q^{2} +(-1.24899 - 1.48849i) q^{3} +(-0.390596 + 0.142165i) q^{4} +(2.62459 + 0.955274i) q^{5} +(-2.81806 - 2.36464i) q^{6} +(-1.20796 + 2.09224i) q^{7} +(-7.23987 + 4.17994i) q^{8} +(0.907209 - 5.14504i) q^{9} +(5.20754 + 0.918229i) q^{10} +(-9.60360 - 16.6339i) q^{11} +(0.699463 + 0.403835i) q^{12} +(9.33111 - 11.1204i) q^{13} +(-1.56436 + 4.29805i) q^{14} +(-1.85618 - 5.09982i) q^{15} +(-10.8507 + 9.10481i) q^{16} +(-2.97933 - 16.8966i) q^{17} -9.89103i q^{18} -1.16096 q^{20} +(4.62301 - 0.815162i) q^{21} +(-23.3742 - 27.8562i) q^{22} +(7.16888 - 2.60926i) q^{23} +(15.2644 + 5.55578i) q^{24} +(-13.1752 - 11.0553i) q^{25} +(13.7417 - 23.8013i) q^{26} +(-23.9363 + 13.8196i) q^{27} +(0.174379 - 0.988950i) q^{28} +(8.11247 + 1.43045i) q^{29} +(-5.13740 - 8.89824i) q^{30} +(-5.19837 - 3.00128i) q^{31} +(4.25698 - 5.07328i) q^{32} +(-12.7646 + 35.0706i) q^{33} +(-11.1098 - 30.5238i) q^{34} +(-5.16906 + 4.33736i) q^{35} +(0.377093 + 2.13860i) q^{36} +59.5153i q^{37} -28.2071 q^{39} +(-22.9947 + 4.05459i) q^{40} +(-19.8556 - 23.6630i) q^{41} +(8.35149 - 3.03969i) q^{42} +(-23.0914 - 8.40459i) q^{43} +(6.11589 + 5.13184i) q^{44} +(7.29598 - 12.6370i) q^{45} +(12.5084 - 7.22171i) q^{46} +(12.7064 - 72.0615i) q^{47} +(27.1049 + 4.77932i) q^{48} +(21.5817 + 37.3806i) q^{49} +(-28.1992 - 16.2808i) q^{50} +(-21.4293 + 25.5385i) q^{51} +(-2.06376 + 5.67013i) q^{52} +(9.58675 + 26.3394i) q^{53} +(-40.0853 + 33.6356i) q^{54} +(-9.31560 - 52.8314i) q^{55} -20.1968i q^{56} +15.5957 q^{58} +(9.07508 - 1.60018i) q^{59} +(1.45003 + 1.72808i) q^{60} +(57.9370 - 21.0873i) q^{61} +(-10.6789 - 3.88680i) q^{62} +(9.66879 + 8.11308i) q^{63} +(34.5983 - 59.9260i) q^{64} +(35.1134 - 20.2727i) q^{65} +(-12.2696 + 69.5845i) q^{66} +(-11.8649 - 2.09211i) q^{67} +(3.56583 + 6.17619i) q^{68} +(-12.8378 - 7.41188i) q^{69} +(-8.21163 + 9.78624i) q^{70} +(-13.1537 + 36.1396i) q^{71} +(14.9379 + 41.0415i) q^{72} +(38.9338 - 32.6693i) q^{73} +(19.5660 + 110.965i) q^{74} +33.4191i q^{75} +46.4029 q^{77} +(-52.5913 + 9.27327i) q^{78} +(69.0779 + 82.3239i) q^{79} +(-37.1763 + 13.5311i) q^{80} +(6.28271 + 2.28672i) q^{81} +(-44.7995 - 37.5913i) q^{82} +(-35.6336 + 61.7192i) q^{83} +(-1.68984 + 0.975631i) q^{84} +(8.32138 - 47.1929i) q^{85} +(-45.8164 - 8.07867i) q^{86} +(-8.00321 - 13.8620i) q^{87} +(139.058 + 80.2850i) q^{88} +(5.21087 - 6.21007i) q^{89} +(9.44864 - 25.9599i) q^{90} +(11.9950 + 32.9559i) q^{91} +(-2.42919 + 2.03833i) q^{92} +(2.02535 + 11.4863i) q^{93} -138.534i q^{94} -12.8685 q^{96} +(117.310 - 20.6849i) q^{97} +(52.5276 + 62.5999i) q^{98} +(-94.2946 + 34.3204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 9 q^{3} + 9 q^{4} + 3 q^{5} + 27 q^{6} + 6 q^{7} + 9 q^{8} - 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 + 3 * q^5 + 27 * q^6 + 6 * q^7 + 9 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} - 9 q^{3} + 9 q^{4} + 3 q^{5} + 27 q^{6} + 6 q^{7} + 9 q^{8} - 15 q^{9} + 21 q^{10} - 18 q^{11} - 63 q^{12} - 30 q^{13} - 81 q^{14} + 9 q^{15} - 39 q^{16} + 78 q^{17} - 90 q^{20} + 78 q^{21} - 111 q^{22} + 168 q^{23} + 78 q^{24} + 33 q^{25} + 21 q^{26} + 27 q^{27} - 6 q^{28} + 69 q^{29} + 24 q^{30} - 99 q^{31} - 57 q^{32} + 69 q^{33} + 66 q^{34} - 30 q^{35} + 162 q^{36} - 108 q^{39} + 3 q^{40} - 315 q^{41} + 114 q^{42} - 27 q^{43} + 174 q^{44} - 3 q^{45} + 54 q^{46} + 180 q^{47} - 75 q^{48} - 24 q^{49} - 72 q^{50} + 6 q^{51} - 30 q^{52} + 15 q^{53} - 231 q^{54} - 9 q^{55} - 132 q^{58} + 114 q^{59} + 201 q^{60} - 30 q^{61} + 63 q^{62} - 405 q^{63} + 27 q^{64} - 126 q^{65} - 237 q^{66} + 117 q^{67} - 30 q^{68} - 72 q^{69} + 99 q^{70} - 30 q^{71} + 12 q^{72} + 225 q^{73} - 240 q^{74} + 246 q^{77} - 288 q^{78} + 57 q^{79} - 285 q^{80} - 231 q^{81} + 243 q^{82} - 156 q^{83} - 99 q^{84} + 285 q^{85} - 72 q^{86} + 69 q^{87} + 405 q^{88} - 27 q^{89} - 159 q^{90} - 60 q^{91} - 60 q^{92} - 327 q^{93} + 558 q^{96} - 123 q^{97} + 618 q^{98} - 96 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 + 3 * q^5 + 27 * q^6 + 6 * q^7 + 9 * q^8 - 15 * q^9 + 21 * q^10 - 18 * q^11 - 63 * q^12 - 30 * q^13 - 81 * q^14 + 9 * q^15 - 39 * q^16 + 78 * q^17 - 90 * q^20 + 78 * q^21 - 111 * q^22 + 168 * q^23 + 78 * q^24 + 33 * q^25 + 21 * q^26 + 27 * q^27 - 6 * q^28 + 69 * q^29 + 24 * q^30 - 99 * q^31 - 57 * q^32 + 69 * q^33 + 66 * q^34 - 30 * q^35 + 162 * q^36 - 108 * q^39 + 3 * q^40 - 315 * q^41 + 114 * q^42 - 27 * q^43 + 174 * q^44 - 3 * q^45 + 54 * q^46 + 180 * q^47 - 75 * q^48 - 24 * q^49 - 72 * q^50 + 6 * q^51 - 30 * q^52 + 15 * q^53 - 231 * q^54 - 9 * q^55 - 132 * q^58 + 114 * q^59 + 201 * q^60 - 30 * q^61 + 63 * q^62 - 405 * q^63 + 27 * q^64 - 126 * q^65 - 237 * q^66 + 117 * q^67 - 30 * q^68 - 72 * q^69 + 99 * q^70 - 30 * q^71 + 12 * q^72 + 225 * q^73 - 240 * q^74 + 246 * q^77 - 288 * q^78 + 57 * q^79 - 285 * q^80 - 231 * q^81 + 243 * q^82 - 156 * q^83 - 99 * q^84 + 285 * q^85 - 72 * q^86 + 69 * q^87 + 405 * q^88 - 27 * q^89 - 159 * q^90 - 60 * q^91 - 60 * q^92 - 327 * q^93 + 558 * q^96 - 123 * q^97 + 618 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	1.86447	−	0.328757i	0.932236	−	0.164378i	0.313152	−	0.949703i	$-0.398615\pi$
$2$	1.86447	−	0.328757i	0.932236	−	0.164378i	0.619084	+	0.785325i	$0.287504\pi$
$3$	−1.24899	−	1.48849i	−0.416331	−	0.496164i	0.516596	−	0.856229i	$-0.327199\pi$
$3$	−1.24899	−	1.48849i	−0.416331	−	0.496164i	−0.932927	+	0.360065i	$0.882754\pi$
$4$	−0.390596	+	0.142165i	−0.0976490	+	0.0355413i
$5$	2.62459	+	0.955274i	0.524919	+	0.191055i	0.590868	−	0.806768i	$-0.298785\pi$
$5$	2.62459	+	0.955274i	0.524919	+	0.191055i	−0.0659493	+	0.997823i	$0.521008\pi$
$6$	−2.81806	−	2.36464i	−0.469677	−	0.394106i
$7$	−1.20796	+	2.09224i	−0.172565	+	0.298892i	−0.939316	−	0.343053i	$-0.888539\pi$
$7$	−1.20796	+	2.09224i	−0.172565	+	0.298892i	0.766751	+	0.641945i	$0.221872\pi$
$8$	−7.23987	+	4.17994i	−0.904984	+	0.522493i
$9$	0.907209	−	5.14504i	0.100801	−	0.571671i
$10$	5.20754	+	0.918229i	0.520754	+	0.0918229i
$11$	−9.60360	−	16.6339i	−0.873055	−	1.51218i	−0.858821	−	0.512277i	$-0.828802\pi$
$11$	−9.60360	−	16.6339i	−0.873055	−	1.51218i	−0.0142343	−	0.999899i	$-0.504531\pi$
$12$	0.699463	+	0.403835i	0.0582886	+	0.0336529i
$13$	9.33111	−	11.1204i	0.717778	−	0.855414i	−0.276635	−	0.960975i	$-0.589219\pi$
$13$	9.33111	−	11.1204i	0.717778	−	0.855414i	0.994413	+	0.105561i	$0.0336638\pi$
$14$	−1.56436	+	4.29805i	−0.111740	+	0.307004i
$15$	−1.85618	−	5.09982i	−0.123746	−	0.339988i
$16$	−10.8507	+	9.10481i	−0.678168	+	0.569051i
$17$	−2.97933	−	16.8966i	−0.175255	−	0.993919i	−0.937849	−	0.347042i	$-0.887186\pi$
$17$	−2.97933	−	16.8966i	−0.175255	−	0.993919i	0.762595	−	0.646877i	$-0.223925\pi$
$18$		−	9.89103i		−	0.549501i
$19$		0			0
$19$		0			0
$20$	−1.16096			−0.0580481
$21$	4.62301	−	0.815162i	0.220144	−	0.0388172i
$22$	−23.3742	−	27.8562i	−1.06246	−	1.26619i
$23$	7.16888	−	2.60926i	0.311691	−	0.113446i	−0.181438	−	0.983402i	$-0.558075\pi$
$23$	7.16888	−	2.60926i	0.311691	−	0.113446i	0.493129	+	0.869956i	$0.335853\pi$
$24$	15.2644	+	5.55578i	0.636015	+	0.231491i
$25$	−13.1752	−	11.0553i	−0.527007	−	0.442211i
$26$	13.7417	−	23.8013i	0.528527	−	0.915435i
$27$	−23.9363	+	13.8196i	−0.886530	+	0.511839i
$28$	0.174379	−	0.988950i	0.00622781	−	0.0353196i
$29$	8.11247	+	1.43045i	0.279740	+	0.0493258i	0.311758	−	0.950162i	$-0.399082\pi$
$29$	8.11247	+	1.43045i	0.279740	+	0.0493258i	−0.0320177	+	0.999487i	$0.510193\pi$
$30$	−5.13740	−	8.89824i	−0.171247	−	0.296608i
$31$	−5.19837	−	3.00128i	−0.167689	−	0.0968155i	0.413806	−	0.910365i	$-0.364199\pi$
$31$	−5.19837	−	3.00128i	−0.167689	−	0.0968155i	−0.581496	+	0.813549i	$0.697532\pi$
$32$	4.25698	−	5.07328i	0.133031	−	0.158540i
$33$	−12.7646	+	35.0706i	−0.386807	+	1.06274i
$34$	−11.1098	−	30.5238i	−0.326758	−	0.897759i
$35$	−5.16906	+	4.33736i	−0.147687	+	0.123924i
$36$	0.377093	+	2.13860i	0.0104748	+	0.0594056i
$37$			59.5153i			1.60852i	0.594277	+	0.804260i	$0.297438\pi$
$37$			59.5153i			1.60852i	−0.594277	+	0.804260i	$0.702562\pi$
$38$		0			0
$39$	−28.2071			−0.723259
$40$	−22.9947	+	4.05459i	−0.574868	+	0.101365i
$41$	−19.8556	−	23.6630i	−0.484282	−	0.577145i	0.467471	−	0.884008i	$-0.345165\pi$
$41$	−19.8556	−	23.6630i	−0.484282	−	0.577145i	−0.951754	+	0.306863i	$0.900721\pi$
$42$	8.35149	−	3.03969i	0.198845	−	0.0723737i
$43$	−23.0914	−	8.40459i	−0.537010	−	0.195456i	0.0592556	−	0.998243i	$-0.481127\pi$
$43$	−23.0914	−	8.40459i	−0.537010	−	0.195456i	−0.596266	+	0.802787i	$0.703350\pi$
$44$	6.11589	+	5.13184i	0.138998	+	0.116633i
$45$	7.29598	−	12.6370i	0.162133	−	0.280822i
$46$	12.5084	−	7.22171i	0.271921	−	0.156994i
$47$	12.7064	−	72.0615i	0.270349	−	1.53322i	−0.483011	−	0.875614i	$-0.660457\pi$
$47$	12.7064	−	72.0615i	0.270349	−	1.53322i	0.753360	−	0.657608i	$-0.228432\pi$
$48$	27.1049	+	4.77932i	0.564685	+	0.0995692i
$49$	21.5817	+	37.3806i	0.440443	+	0.762869i
$50$	−28.1992	−	16.2808i	−0.563984	−	0.325617i
$51$	−21.4293	+	25.5385i	−0.420183	+	0.500755i
$52$	−2.06376	+	5.67013i	−0.0396877	+	0.109041i
$53$	9.58675	+	26.3394i	0.180882	+	0.496969i	0.996685	−	0.0813610i	$-0.0259267\pi$
$53$	9.58675	+	26.3394i	0.180882	+	0.496969i	−0.815803	+	0.578330i	$0.803704\pi$
$54$	−40.0853	+	33.6356i	−0.742320	+	0.622881i
$55$	−9.31560	−	52.8314i	−0.169375	−	0.960571i
$56$		−	20.1968i		−	0.360656i
$57$		0			0
$58$	15.5957			0.268892
$59$	9.07508	−	1.60018i	0.153815	−	0.0271217i	−0.0962104	−	0.995361i	$-0.530672\pi$
$59$	9.07508	−	1.60018i	0.153815	−	0.0271217i	0.250025	+	0.968239i	$0.419561\pi$
$60$	1.45003	+	1.72808i	0.0241672	+	0.0288014i
$61$	57.9370	−	21.0873i	0.949787	−	0.345694i	0.179763	−	0.983710i	$-0.442467\pi$
$61$	57.9370	−	21.0873i	0.949787	−	0.345694i	0.770023	+	0.638016i	$0.220245\pi$
$62$	−10.6789	−	3.88680i	−0.172240	−	0.0626904i
$63$	9.66879	+	8.11308i	0.153473	+	0.128779i
$64$	34.5983	−	59.9260i	0.540598	−	0.936344i
$65$	35.1134	−	20.2727i	0.540206	−	0.311888i
$66$	−12.2696	+	69.5845i	−0.185903	+	1.05431i
$67$	−11.8649	−	2.09211i	−0.177089	−	0.0312255i	0.0844005	−	0.996432i	$-0.473102\pi$
$67$	−11.8649	−	2.09211i	−0.177089	−	0.0312255i	−0.261489	+	0.965206i	$0.584214\pi$
$68$	3.56583	+	6.17619i	0.0524386	+	0.0908264i
$69$	−12.8378	−	7.41188i	−0.186054	−	0.107419i
$70$	−8.21163	+	9.78624i	−0.117309	+	0.139803i
$71$	−13.1537	+	36.1396i	−0.185264	+	0.509009i	−0.997204	−	0.0747328i	$-0.976190\pi$
$71$	−13.1537	+	36.1396i	−0.185264	+	0.509009i	0.811940	+	0.583741i	$0.198412\pi$
$72$	14.9379	+	41.0415i	0.207471	+	0.570021i
$73$	38.9338	−	32.6693i	0.533339	−	0.447525i	−0.335914	−	0.941893i	$-0.609045\pi$
$73$	38.9338	−	32.6693i	0.533339	−	0.447525i	0.869253	+	0.494368i	$0.164601\pi$
$74$	19.5660	+	110.965i	0.264406	+	1.49952i
$75$			33.4191i			0.445588i
$76$		0			0
$77$	46.4029			0.602635
$78$	−52.5913	+	9.27327i	−0.674248	+	0.118888i
$79$	69.0779	+	82.3239i	0.874404	+	1.04207i	0.998757	+	0.0498365i	$0.0158700\pi$
$79$	69.0779	+	82.3239i	0.874404	+	1.04207i	−0.124353	+	0.992238i	$0.539686\pi$
$80$	−37.1763	+	13.5311i	−0.464703	+	0.169138i
$81$	6.28271	+	2.28672i	0.0775643	+	0.0282311i
$82$	−44.7995	−	37.5913i	−0.546336	−	0.458430i
$83$	−35.6336	+	61.7192i	−0.429321	+	0.743605i	−0.996813	−	0.0797735i	$-0.974580\pi$
$83$	−35.6336	+	61.7192i	−0.429321	+	0.743605i	0.567492	+	0.823379i	$0.307914\pi$
$84$	−1.68984	+	0.975631i	−0.0201172	+	0.0116147i
$85$	8.32138	−	47.1929i	0.0978985	−	0.555210i
$86$	−45.8164	−	8.07867i	−0.532749	−	0.0939380i
$87$	−8.00321	−	13.8620i	−0.0919909	−	0.159333i
$88$	139.058	+	80.2850i	1.58020	+	0.912330i
$89$	5.21087	−	6.21007i	0.0585491	−	0.0697761i	−0.735975	−	0.677009i	$-0.763276\pi$
$89$	5.21087	−	6.21007i	0.0585491	−	0.0697761i	0.794524	+	0.607233i	$0.207720\pi$
$90$	9.44864	−	25.9599i	0.104985	−	0.288444i
$91$	11.9950	+	32.9559i	0.131813	+	0.362152i
$92$	−2.42919	+	2.03833i	−0.0264042	+	0.0221558i
$93$	2.02535	+	11.4863i	0.0217779	+	0.123509i
$94$		−	138.534i		−	1.47376i
$95$		0			0
$96$	−12.8685			−0.134047
$97$	117.310	−	20.6849i	1.20938	−	0.213246i	0.467630	−	0.883924i	$-0.345108\pi$
$97$	117.310	−	20.6849i	1.20938	−	0.213246i	0.741748	+	0.670678i	$0.233997\pi$
$98$	52.5276	+	62.5999i	0.535995	+	0.638775i
$99$	−94.2946	+	34.3204i	−0.952471	+	0.346671i
$100$	6.71784	+	2.44509i	0.0671784	+	0.0244509i
$101$	100.664	+	84.4667i	0.996669	+	0.836304i	0.986519	−	0.163644i	$-0.0523249\pi$
$101$	100.664	+	84.4667i	0.996669	+	0.836304i	0.0101492	+	0.999948i	$0.496769\pi$
$102$	−31.5584	+	54.6608i	−0.309396	+	0.535890i
$103$	−11.4431	+	6.60670i	−0.111098	+	0.0641427i	−0.554520	−	0.832171i	$-0.687098\pi$
$103$	−11.4431	+	6.60670i	−0.111098	+	0.0641427i	0.443421	+	0.896313i	$0.353765\pi$
$104$	−21.0735	+	119.514i	−0.202630	+	1.14917i
$105$	12.9122	+	2.27678i	0.122974	+	0.0216836i
$106$	26.5335	+	45.9573i	0.250316	+	0.433560i
$107$	−94.8683	−	54.7722i	−0.886620	−	0.511890i	−0.0137844	−	0.999905i	$-0.504388\pi$
$107$	−94.8683	−	54.7722i	−0.886620	−	0.511890i	−0.872835	+	0.488015i	$0.837721\pi$
$108$	7.38475	−	8.80081i	0.0683774	−	0.0814890i
$109$	70.4905	−	193.671i	0.646702	−	1.77680i	0.0171346	−	0.999853i	$-0.494546\pi$
$109$	70.4905	−	193.671i	0.646702	−	1.77680i	0.629567	−	0.776946i	$-0.283232\pi$
$110$	−34.7374	−	95.4401i	−0.315794	−	0.867637i
$111$	88.5880	−	74.3342i	0.798090	−	0.669677i
$112$	−5.94230	−	33.7005i	−0.0530563	−	0.300897i
$113$		−	18.3671i		−	0.162541i	−0.996692	−	0.0812705i	$-0.974102\pi$
$113$		−	18.3671i		−	0.162541i	0.996692	−	0.0812705i	$-0.0258978\pi$
$114$		0			0
$115$	21.3080			0.185287
$116$	−3.37206	+	0.594584i	−0.0290694	+	0.00512573i
$117$	−48.7495	−	58.0974i	−0.416662	−	0.496559i
$118$	16.3942	−	5.96699i	0.138934	−	0.0505677i
$119$	38.9507	+	14.1769i	0.327317	+	0.119134i
$120$	34.7555	+	29.1633i	0.289629	+	0.243028i
$121$	−123.958	+	214.702i	−1.02445	+	1.77440i
$122$	101.089	−	58.3639i	0.828601	−	0.478393i
$123$	−10.4226	+	59.1098i	−0.0847370	+	0.480567i
$124$	2.45714	+	0.433260i	0.0198156	+	0.00349403i
$125$	−58.9316	−	102.072i	−0.471453	−	0.816580i
$126$	20.6944	+	11.9479i	0.164241	+	0.0948248i
$127$	−7.28329	+	8.67989i	−0.0573487	+	0.0683456i	−0.793956	−	0.607975i	$-0.791982\pi$
$127$	−7.28329	+	8.67989i	−0.0573487	+	0.0683456i	0.736607	+	0.676321i	$0.236427\pi$
$128$	35.7461	−	98.2116i	0.279266	−	0.767278i
$129$	16.3309	+	44.8687i	0.126596	+	0.347819i
$130$	58.8031	−	49.3417i	0.452332	−	0.379551i
$131$	1.94906	+	11.0537i	0.0148783	+	0.0843792i	0.991343	−	0.131299i	$-0.0419148\pi$
$131$	1.94906	+	11.0537i	0.0148783	+	0.0843792i	−0.976464	+	0.215678i	$0.930804\pi$
$132$		−	15.5131i		−	0.117523i
$133$		0			0
$134$	−22.8097			−0.170221
$135$	−76.0247	+	13.4052i	−0.563146	+	0.0992978i
$136$	92.1969	+	109.876i	0.677918	+	0.807912i
$137$	−151.985	+	55.3180i	−1.10938	+	0.403781i	−0.830765	−	0.556623i	$-0.812097\pi$
$137$	−151.985	+	55.3180i	−1.10938	+	0.403781i	−0.278613	+	0.960403i	$0.589875\pi$
$138$	−26.3723	−	9.59874i	−0.191104	−	0.0695561i
$139$	−147.124	−	123.452i	−1.05845	−	0.888143i	−0.0644911	−	0.997918i	$-0.520542\pi$
$139$	−147.124	−	123.452i	−1.05845	−	0.888143i	−0.993956	+	0.109775i	$0.964987\pi$
$140$	1.40239	−	2.42901i	0.0100171	−	0.0173501i
$141$	−123.133	+	71.0909i	−0.873284	+	0.504191i
$142$	−12.6436	+	71.7057i	−0.0890397	+	0.504969i
$143$	−274.588	−	48.4173i	−1.92020	−	0.338582i
$144$	37.0007	+	64.0872i	0.256950	+	0.445050i
$145$	19.9255	+	11.5040i	0.137417	+	0.0793378i
$146$	61.8506	−	73.7107i	0.423634	−	0.504868i
$147$	28.6853	−	78.8123i	0.195138	−	0.536138i
$148$	−8.46100	−	23.2464i	−0.0571689	−	0.157070i
$149$	107.680	−	90.3540i	0.722683	−	0.606403i	−0.205443	−	0.978669i	$-0.565864\pi$
$149$	107.680	−	90.3540i	0.722683	−	0.606403i	0.928126	+	0.372266i	$0.121419\pi$
$150$	10.9868	+	62.3090i	0.0732450	+	0.415393i
$151$			101.605i			0.672880i	0.941705	+	0.336440i	$0.109223\pi$
$151$			101.605i			0.672880i	−0.941705	+	0.336440i	$0.890777\pi$
$152$		0			0
$153$	−89.6366			−0.585860
$154$	86.5170	−	15.2553i	0.561798	−	0.0990602i
$155$	−10.7766	−	12.8430i	−0.0695262	−	0.0828581i
$156$	11.0176	−	4.01007i	0.0706255	−	0.0257056i
$157$	−157.259	−	57.2375i	−1.00165	−	0.364570i	−0.211428	−	0.977394i	$-0.567811\pi$
$157$	−157.259	−	57.2375i	−1.00165	−	0.364570i	−0.790220	+	0.612824i	$0.790034\pi$
$158$	155.858	+	130.781i	0.986446	+	0.827726i
$159$	27.2322	−	47.1675i	0.171272	−	0.296651i
$160$	16.0192	−	9.24871i	0.100120	−	0.0578044i
$161$	−3.20049	+	18.1509i	−0.0198788	+	0.112739i
$162$	12.4657	+	2.19804i	0.0769488	+	0.0135681i
$163$	16.9195	+	29.3054i	0.103801	+	0.179788i	0.913248	−	0.407405i	$-0.133566\pi$
$163$	16.9195	+	29.3054i	0.103801	+	0.179788i	−0.809447	+	0.587193i	$0.800233\pi$
$164$	11.1196	+	6.41988i	0.0678022	+	0.0391456i
$165$	−67.0040	+	79.8523i	−0.406085	+	0.483953i
$166$	−46.1473	+	126.789i	−0.277996	+	0.763787i
$167$	16.5120	+	45.3662i	0.0988740	+	0.271654i	0.979261	−	0.202601i	$-0.0649396\pi$
$167$	16.5120	+	45.3662i	0.0988740	+	0.271654i	−0.880387	+	0.474255i	$0.842717\pi$
$168$	−30.0627	+	25.2256i	−0.178945	+	0.150152i
$169$	−7.24677	−	41.0985i	−0.0428803	−	0.243186i
$170$		−	90.7255i		−	0.533679i
$171$		0			0
$172$	10.2143			0.0593852
$173$	50.9346	−	8.98115i	0.294420	−	0.0519142i	−0.0244872	−	0.999700i	$-0.507795\pi$
$173$	50.9346	−	8.98115i	0.294420	−	0.0519142i	0.318907	+	0.947786i	$0.396684\pi$
$174$	−19.4790	−	23.2141i	−0.111948	−	0.133415i
$175$	39.0453	−	14.2113i	0.223116	−	0.0812076i
$176$	255.654	+	93.0506i	1.45258	+	0.528697i
$177$	−13.7166	−	11.5096i	−0.0774948	−	0.0650258i
$178$	7.67391	−	13.2916i	0.0431119	−	0.0746719i
$179$	200.919	−	116.001i	1.12245	−	0.648048i	0.180426	−	0.983589i	$-0.442252\pi$
$179$	200.919	−	116.001i	1.12245	−	0.648048i	0.942026	+	0.335541i	$0.108919\pi$
$180$	−1.05324	+	5.97319i	−0.00585131	+	0.0331844i
$181$	266.290	+	46.9541i	1.47122	+	0.259415i	0.851062	−	0.525065i	$-0.175959\pi$
$181$	266.290	+	46.9541i	1.47122	+	0.259415i	0.620154	+	0.784480i	$0.287070\pi$
$182$	33.1987	+	57.5019i	0.182411	+	0.315944i
$183$	−103.751	−	59.9008i	−0.566947	−	0.327327i
$184$	−40.9953	+	48.8562i	−0.222800	+	0.265523i
$185$	−56.8534	+	156.203i	−0.307316	+	0.844343i
$186$	7.55240	+	20.7501i	0.0406043	+	0.111559i
$187$	−252.445	+	211.826i	−1.34997	+	1.13276i
$188$	5.28158	+	29.9533i	0.0280935	+	0.159326i
$189$		−	66.7741i		−	0.353302i
$190$		0			0
$191$	81.4552			0.426467			0.213233	−	0.977001i	$-0.431601\pi$
$191$	81.4552			0.426467			0.213233	+	0.977001i	$0.431601\pi$
$192$	−132.412	+	23.3479i	−0.689648	+	0.121604i
$193$	−19.1747	−	22.8515i	−0.0993508	−	0.118402i	0.714078	−	0.700066i	$-0.246846\pi$
$193$	−19.1747	−	22.8515i	−0.0993508	−	0.118402i	−0.813429	+	0.581664i	$0.802402\pi$
$194$	211.920	−	77.1327i	1.09237	−	0.397591i
$195$	−74.0322	−	26.9455i	−0.379652	−	0.138182i
$196$	−13.7439	−	11.5325i	−0.0701221	−	0.0588394i
$197$	90.0191	−	155.918i	0.456950	−	0.791461i	−0.541848	−	0.840476i	$-0.682275\pi$
$197$	90.0191	−	155.918i	0.456950	−	0.791461i	0.998798	+	0.0490159i	$0.0156085\pi$
$198$	−164.527	+	94.9895i	−0.830943	+	0.479745i
$199$	19.1234	−	108.454i	0.0960977	−	0.544997i	−0.898308	−	0.439367i	$-0.855203\pi$
$199$	19.1234	−	108.454i	0.0960977	−	0.544997i	0.994405	−	0.105630i	$-0.0336861\pi$
$200$	141.597	+	24.9674i	0.707985	+	0.124837i
$201$	11.7051	+	20.2739i	0.0582346	+	0.100865i
$202$	215.453	+	124.392i	1.06660	+	0.615802i
$203$	−12.7923	+	15.2453i	−0.0630165	+	0.0751001i
$204$	4.73952	−	13.0217i	0.0232330	−	0.0638320i
$205$	−29.5082	−	81.0732i	−0.143943	−	0.395479i
$206$	−19.1634	+	16.0800i	−0.0930263	+	0.0780583i
$207$	−6.92106	−	39.2513i	−0.0334351	−	0.189620i
$208$			205.622i			0.988566i
$209$		0			0
$210$	24.8230			0.118205
$211$	−151.572	+	26.7262i	−0.718350	+	0.126665i	−0.520862	−	0.853641i	$-0.674389\pi$
$211$	−151.572	+	26.7262i	−0.718350	+	0.126665i	−0.197488	+	0.980305i	$0.563278\pi$
$212$	−7.48909	−	8.92515i	−0.0353259	−	0.0420998i
$213$	70.2225	−	25.5589i	0.329683	−	0.119995i
$214$	−194.886	−	70.9327i	−0.910683	−	0.331461i
$215$	−52.5770	−	44.1173i	−0.244544	−	0.205197i
$216$	115.531	−	200.105i	0.534864	−	0.926412i
$217$	12.5588	−	7.25083i	0.0578747	−	0.0334140i
$218$	67.7569	−	384.269i	0.310812	−	1.76270i
$219$	−97.2560	−	17.1489i	−0.444091	−	0.0783053i
$220$	11.1494	+	19.3114i	0.0506792	+	0.0877789i
$221$	−215.697	−	124.533i	−0.976006	−	0.563497i
$222$	140.732	−	167.718i	0.633928	−	0.755486i
$223$	−53.2293	+	146.246i	−0.238696	+	0.655812i	0.761277	+	0.648427i	$0.224573\pi$
$223$	−53.2293	+	146.246i	−0.238696	+	0.655812i	−0.999973	+	0.00738504i	$0.997649\pi$
$224$	5.47227	+	15.0349i	0.0244298	+	0.0671202i
$225$	−68.8324	+	57.7572i	−0.305922	+	0.256699i
$226$	−6.03832	−	34.2450i	−0.0267182	−	0.151527i
$227$			67.0830i			0.295520i	0.989023	+	0.147760i	$0.0472063\pi$
$227$			67.0830i			0.295520i	−0.989023	+	0.147760i	$0.952794\pi$
$228$		0			0
$229$	69.2740			0.302506			0.151253	−	0.988495i	$-0.451669\pi$
$229$	69.2740			0.302506			0.151253	+	0.988495i	$0.451669\pi$
$230$	39.7281	−	7.00514i	0.172731	−	0.0304571i
$231$	−57.9569	−	69.0704i	−0.250896	−	0.299006i
$232$	−64.7124	+	23.5534i	−0.278933	+	0.101523i
$233$	153.369	+	55.8219i	0.658238	+	0.239579i	0.649475	−	0.760383i	$-0.274989\pi$
$233$	153.369	+	55.8219i	0.658238	+	0.239579i	0.00876257	+	0.999962i	$0.497211\pi$
$234$	−109.992	−	92.2942i	−0.470051	−	0.394420i
$235$	102.188	−	176.994i	0.434841	−	0.753166i
$236$	−3.31720	+	1.91519i	−0.0140559	+	0.00811519i
$237$	36.2606	−	205.644i	0.152998	−	0.867696i
$238$	77.2833	+	13.6271i	0.324720	+	0.0572568i
$239$	−152.816	−	264.685i	−0.639397	−	1.10747i	−0.985565	−	0.169296i	$-0.945851\pi$
$239$	−152.816	−	264.685i	−0.639397	−	1.10747i	0.346168	−	0.938172i	$-0.387483\pi$
$240$	66.5738	+	38.4364i	0.277391	+	0.160152i
$241$	−154.301	+	183.889i	−0.640253	+	0.763024i	−0.984410	−	0.175888i	$-0.943720\pi$
$241$	−154.301	+	183.889i	−0.640253	+	0.763024i	0.344157	+	0.938912i	$0.388165\pi$
$242$	−160.532	+	441.058i	−0.663356	+	1.82256i
$243$	80.6354	+	221.544i	0.331833	+	0.911704i
$244$	−19.6321	+	16.4733i	−0.0804592	+	0.0675133i
$245$	20.9345	+	118.725i	0.0854468	+	0.484593i
$246$			113.635i			0.461931i
$247$		0			0
$248$	50.1807			0.202342
$249$	136.375	−	24.0465i	0.547690	−	0.0965725i
$250$	−143.433	−	170.937i	−0.573733	−	0.683749i
$251$	300.110	−	109.231i	1.19566	−	0.435184i	0.333950	−	0.942591i	$-0.391618\pi$
$251$	300.110	−	109.231i	1.19566	−	0.435184i	0.861706	+	0.507407i	$0.169396\pi$
$252$	−4.92999	−	1.79437i	−0.0195634	−	0.00712051i
$253$	−112.249	−	94.1884i	−0.443673	−	0.372286i
$254$	−10.7259	+	18.5778i	−0.0422280	+	0.0731411i
$255$	−80.6396	+	46.5573i	−0.316234	+	0.182578i
$256$	−13.7036	+	77.7168i	−0.0535296	+	0.303581i
$257$	113.383	+	19.9925i	0.441179	+	0.0777917i	0.389825	−	0.920889i	$-0.372535\pi$
$257$	113.383	+	19.9925i	0.441179	+	0.0777917i	0.0513534	+	0.998681i	$0.483647\pi$
$258$	45.1993	+	78.2875i	0.175191	+	0.303440i
$259$	−124.520	−	71.8918i	−0.480773	−	0.277575i
$260$	−10.8331	+	12.9103i	−0.0416656	+	0.0496552i
$261$	14.7194	−	40.4412i	0.0563962	−	0.154947i
$262$	7.26794	+	19.9685i	0.0277402	+	0.0762156i
$263$	−17.4045	+	14.6041i	−0.0661767	+	0.0555289i	−0.675276	−	0.737565i	$-0.735976\pi$
$263$	−17.4045	+	14.6041i	−0.0661767	+	0.0555289i	0.609099	+	0.793094i	$0.291531\pi$
$264$	−54.1786	−	307.262i	−0.205222	−	1.16387i
$265$			78.2882i			0.295427i
$266$		0			0
$267$	−15.7520			−0.0589962
$268$	4.93182	−	0.869614i	0.0184023	−	0.00324483i
$269$	−178.579	−	212.822i	−0.663861	−	0.791159i	0.324073	−	0.946032i	$-0.394948\pi$
$269$	−178.579	−	212.822i	−0.663861	−	0.791159i	−0.987934	+	0.154873i	$0.950503\pi$
$270$	−137.339	+	49.9873i	−0.508662	+	0.185138i
$271$	−3.17967	−	1.15730i	−0.0117331	−	0.00427049i	0.336147	−	0.941810i	$-0.390876\pi$
$271$	−3.17967	−	1.15730i	−0.0117331	−	0.00427049i	−0.347880	+	0.937539i	$0.613098\pi$
$272$	186.168	+	156.214i	0.684442	+	0.574315i
$273$	34.0729	−	59.0161i	0.124809	−	0.216176i
$274$	−265.185	+	153.105i	−0.967830	+	0.558777i
$275$	−57.3636	+	325.325i	−0.208595	+	1.18300i
$276$	6.06808	+	1.06997i	0.0219858	+	0.00387669i
$277$	67.8848	+	117.580i	0.245072	+	0.424476i	0.962152	−	0.272514i	$-0.0878552\pi$
$277$	67.8848	+	117.580i	0.245072	+	0.424476i	−0.717080	+	0.696991i	$0.754522\pi$
$278$	−314.895	−	181.804i	−1.13271	−	0.653973i
$279$	−20.1577	+	24.0230i	−0.0722498	+	0.0861040i
$280$	19.2934	−	53.0083i	0.0689051	−	0.189315i
$281$	−168.694	−	463.482i	−0.600333	−	1.64940i	−0.750600	−	0.660757i	$-0.770236\pi$
$281$	−168.694	−	463.482i	−0.600333	−	1.64940i	0.150267	−	0.988645i	$-0.451987\pi$
$282$	−206.207	+	173.028i	−0.731229	+	0.613574i
$283$	−65.0602	−	368.975i	−0.229895	−	1.30380i	−0.853103	−	0.521742i	$-0.825282\pi$
$283$	−65.0602	−	368.975i	−0.229895	−	1.30380i	0.623209	−	0.782056i	$-0.285829\pi$
$284$		−	15.9860i		−	0.0562887i
$285$		0			0
$286$	−527.879			−1.84573
$287$	73.4933	−	12.9589i	0.256074	−	0.0451528i
$288$	−22.2402	−	26.5049i	−0.0772230	−	0.0920308i
$289$	−5.04832	+	1.83744i	−0.0174682	+	0.00635791i
$290$	40.9325	+	14.8982i	0.141147	+	0.0513731i
$291$	−177.308	−	148.779i	−0.609307	−	0.511269i
$292$	−10.5629	+	18.2955i	−0.0361744	+	0.0626559i
$293$	63.5500	−	36.6906i	0.216894	−	0.125224i	−0.387617	−	0.921820i	$-0.626702\pi$
$293$	63.5500	−	36.6906i	0.216894	−	0.125224i	0.604511	+	0.796597i	$0.293368\pi$
$294$	27.5729	−	156.374i	0.0937854	−	0.531883i
$295$	25.3470	+	4.46937i	0.0859221	+	0.0151504i
$296$	−248.770	−	430.883i	−0.840440	−	1.45569i
$297$	459.750	+	265.437i	1.54798	+	0.893726i
$298$	171.061	−	203.863i	0.574031	−	0.684104i
$299$	37.8777	−	104.068i	0.126681	−	0.348054i
$300$	−4.75103	−	13.0534i	−0.0158368	−	0.0435112i
$301$	45.4779	−	38.1605i	0.151089	−	0.126779i
$302$	33.4033	+	189.439i	0.110607	+	0.627283i
$303$		−	255.335i		−	0.842691i
$304$		0			0
$305$	172.205			0.564607
$306$	−167.125	+	29.4686i	−0.546160	+	0.0963027i
$307$	−59.4148	−	70.8079i	−0.193534	−	0.230644i	0.660547	−	0.750784i	$-0.270324\pi$
$307$	−59.4148	−	70.8079i	−0.193534	−	0.230644i	−0.854081	+	0.520140i	$0.825880\pi$
$308$	−18.1248	+	6.59688i	−0.0588467	+	0.0214185i
$309$	24.1264	+	8.78130i	0.0780791	+	0.0284185i
$310$	−24.3148	−	20.4026i	−0.0784350	−	0.0658147i
$311$	−99.6155	+	172.539i	−0.320307	+	0.554788i	−0.980551	−	0.196263i	$-0.937119\pi$
$311$	−99.6155	+	172.539i	−0.320307	+	0.554788i	0.660244	+	0.751051i	$0.270453\pi$
$312$	204.216	−	117.904i	0.654538	−	0.377898i
$313$	5.31322	−	30.1328i	0.0169751	−	0.0962708i	−0.975143	−	0.221576i	$-0.928880\pi$
$313$	5.31322	−	30.1328i	0.0169751	−	0.0962708i	0.992118	+	0.125305i	$0.0399910\pi$
$314$	−312.022	−	55.0178i	−0.993699	−	0.175216i
$315$	17.6264	+	30.5299i	0.0559569	+	0.0969203i
$316$	−38.6852	−	22.3349i	−0.122421	−	0.0706800i
$317$	366.328	−	436.573i	1.15561	−	1.37720i	0.242167	−	0.970234i	$-0.422142\pi$
$317$	366.328	−	436.573i	1.15561	−	1.37720i	0.913443	−	0.406968i	$-0.133414\pi$
$318$	35.2670	−	96.8953i	0.110902	−	0.304702i
$319$	−54.1150	−	148.680i	−0.169639	−	0.466080i
$320$	148.052	−	124.231i	0.462663	−	0.388221i
$321$	36.9618	+	209.621i	0.115146	+	0.653025i
$322$			34.8940i			0.108367i
$323$		0			0
$324$	−2.77909			−0.00857744
$325$	−245.878	+	43.3549i	−0.756547	+	0.133400i
$326$	41.1803	+	49.0767i	0.126320	+	0.150542i
$327$	−376.320	+	136.969i	−1.15083	+	0.418866i
$328$	242.662	+	88.3216i	0.739822	+	0.269273i
$329$	135.421	+	113.632i	0.411615	+	0.345386i
$330$	−98.6751	+	170.910i	−0.299015	+	0.517910i
$331$	−383.016	+	221.134i	−1.15715	+	0.668079i	−0.950619	−	0.310361i	$-0.899550\pi$
$331$	−383.016	+	221.134i	−1.15715	+	0.668079i	−0.206529	+	0.978441i	$0.566217\pi$
$332$	5.14401	−	29.1731i	0.0154940	−	0.0878709i
$333$	306.208	+	53.9928i	0.919544	+	0.162140i
$334$	45.7005	+	79.1556i	0.136828	+	0.236993i
$335$	−29.1421	−	16.8252i	−0.0869915	−	0.0502245i
$336$	−42.7410	+	50.9367i	−0.127205	+	0.151597i
$337$	151.257	−	415.575i	0.448834	−	1.23316i	−0.484703	−	0.874679i	$-0.661072\pi$
$337$	151.257	−	415.575i	0.448834	−	1.23316i	0.933537	−	0.358481i	$-0.116705\pi$
$338$	−27.0228	−	74.2445i	−0.0799491	−	0.219658i
$339$	−27.3393	+	22.9404i	−0.0806470	+	0.0676709i
$340$	3.45889	+	19.6163i	0.0101732	+	0.0576951i
$341$			115.292i			0.338101i
$342$		0			0
$343$	−222.659			−0.649150
$344$	202.310	−	35.6727i	0.588110	−	0.103700i
$345$	−26.6135	−	31.7168i	−0.0771406	−	0.0919326i
$346$	92.0136	−	33.4902i	0.265935	−	0.0967925i
$347$	−3.29421	−	1.19900i	−0.00949341	−	0.00345532i	0.337269	−	0.941408i	$-0.390497\pi$
$347$	−3.29421	−	1.19900i	−0.00949341	−	0.00345532i	−0.346762	+	0.937953i	$0.612719\pi$
$348$	5.09671	+	4.27665i	0.0146457	+	0.0122892i
$349$	−44.1774	+	76.5174i	−0.126583	+	0.219248i	−0.922350	−	0.386354i	$-0.873734\pi$
$349$	−44.1774	+	76.5174i	−0.126583	+	0.219248i	0.795768	+	0.605602i	$0.207068\pi$
$350$	68.1268	−	39.3330i	0.194648	−	0.112380i
$351$	−69.6727	+	395.134i	−0.198498	+	1.12574i
$352$	−125.271	−	22.0886i	−0.355883	−	0.0627518i
$353$	62.9423	+	109.019i	0.178307	+	0.308837i	0.941301	−	0.337569i	$-0.109605\pi$
$353$	62.9423	+	109.019i	0.178307	+	0.308837i	−0.762994	+	0.646406i	$0.776271\pi$
$354$	−29.3580	−	16.9499i	−0.0829323	−	0.0478810i
$355$	−69.0465	+	82.2864i	−0.194497	+	0.231793i
$356$	−1.15249	+	3.16643i	−0.00323732	+	0.00889447i
$357$	−27.5470	−	75.6847i	−0.0771624	−	0.212002i
$358$	336.472	−	282.333i	0.939865	−	0.788640i
$359$	−10.4515	−	59.2733i	−0.0291128	−	0.165107i	0.966785	−	0.255590i	$-0.0822698\pi$
$359$	−10.4515	−	59.2733i	−0.0291128	−	0.165107i	−0.995898	+	0.0904837i	$0.971159\pi$
$360$			121.987i			0.338853i
$361$		0			0
$362$	511.927			1.41416
$363$	474.406	−	83.6505i	1.30690	−	0.230442i
$364$	−9.37036	−	11.1672i	−0.0257427	−	0.0306790i
$365$	133.393	−	48.5512i	0.365462	−	0.133017i
$366$	−213.134	−	77.5745i	−0.582333	−	0.211952i
$367$	117.496	+	98.5911i	0.320153	+	0.268641i	0.788674	−	0.614812i	$-0.210768\pi$
$367$	117.496	+	98.5911i	0.320153	+	0.268641i	−0.468520	+	0.883453i	$0.655213\pi$
$368$	−54.0305	+	93.5836i	−0.146822	+	0.254303i
$369$	−139.760	+	80.6904i	−0.378753	+	0.218673i
$370$	−54.6486	+	309.928i	−0.147699	+	0.837643i
$371$	−66.6887	−	11.7590i	−0.179754	−	0.0316955i
$372$	−2.42405	−	4.19857i	−0.00651625	−	0.0112865i
$373$	230.727	+	133.210i	0.618571	+	0.357132i	0.776313	−	0.630348i	$-0.217088\pi$
$373$	230.727	+	133.210i	0.618571	+	0.357132i	−0.157741	+	0.987480i	$0.550421\pi$
$374$	−401.037	+	477.937i	−1.07229	+	1.27791i
$375$	−78.3290	+	215.207i	−0.208877	+	0.573886i
$376$	209.220	+	574.828i	0.556437	+	1.52880i
$377$	91.6054	−	76.8661i	0.242985	−	0.203889i
$378$	−21.9524	−	124.498i	−0.0580752	−	0.329361i
$379$		−	670.093i		−	1.76806i	−0.467435	−	0.884028i	$-0.654822\pi$
$379$		−	670.093i		−	1.76806i	0.467435	−	0.884028i	$-0.345178\pi$
$380$		0			0
$381$	22.0167			0.0577867
$382$	151.871	−	26.7789i	0.397568	−	0.0701019i
$383$	443.456	+	528.490i	1.15785	+	1.37987i	0.911811	+	0.410610i	$0.134684\pi$
$383$	443.456	+	528.490i	1.15785	+	1.37987i	0.246037	+	0.969260i	$0.420871\pi$
$384$	−190.834	+	69.4578i	−0.496963	+	0.180880i
$385$	121.789	+	44.3275i	0.316335	+	0.115136i
$386$	−43.2633	−	36.3022i	−0.112081	−	0.0940472i
$387$	−64.1907	+	111.182i	−0.165867	+	0.287291i
$388$	−42.8800	+	24.7568i	−0.110515	+	0.0638061i
$389$	39.2149	−	222.399i	0.100810	−	0.571720i	−0.892002	−	0.452032i	$-0.850699\pi$
$389$	39.2149	−	222.399i	0.100810	−	0.571720i	0.992812	−	0.119688i	$-0.0381894\pi$
$390$	−146.889	−	25.9006i	−0.376640	−	0.0664117i
$391$	−65.4462	−	113.356i	−0.167381	−	0.289913i
$392$	−312.497	−	180.420i	−0.797187	−	0.460256i
$393$	14.0189	−	16.7071i	0.0356716	−	0.0425118i
$394$	116.579	−	320.299i	0.295886	−	0.812941i
$395$	102.660	+	282.055i	0.259898	+	0.714064i
$396$	31.9519	−	26.8108i	0.0806867	−	0.0677041i
$397$	104.985	+	595.401i	0.264447	+	1.49975i	0.770606	+	0.637312i	$0.219954\pi$
$397$	104.985	+	595.401i	0.264447	+	1.49975i	−0.506159	+	0.862440i	$0.668935\pi$
$398$		−	208.497i		−	0.523862i
$399$		0			0
$400$	243.616			0.609039
$401$	−319.251	+	56.2925i	−0.796137	+	0.140380i	−0.556899	−	0.830581i	$-0.688009\pi$
$401$	−319.251	+	56.2925i	−0.796137	+	0.140380i	−0.239238	+	0.970961i	$0.576898\pi$
$402$	28.4891	+	33.9520i	0.0708684	+	0.0844577i
$403$	−81.8819	+	29.8026i	−0.203181	+	0.0739518i
$404$	−51.3270	−	18.6815i	−0.127047	−	0.0462413i
$405$	14.3051	+	12.0034i	0.0353213	+	0.0296381i
$406$	−18.8390	+	32.6300i	−0.0464014	+	0.0803696i
$407$	989.972	−	571.561i	2.43236	−	1.40433i
$408$	48.3962	−	274.469i	0.118618	−	0.672718i
$409$	−257.465	−	45.3980i	−0.629499	−	0.110998i	−0.150209	−	0.988654i	$-0.547995\pi$
$409$	−257.465	−	45.3980i	−0.629499	−	0.110998i	−0.479290	+	0.877657i	$0.659106\pi$
$410$	−81.6706	−	141.458i	−0.199197	−	0.345019i
$411$	272.168	+	157.137i	0.662210	+	0.382327i
$412$	3.53040	−	4.20737i	0.00856893	−	0.0102121i
$413$	−7.61434	+	20.9202i	−0.0184366	+	0.0506543i
$414$	−25.8083	−	70.9076i	−0.0623388	−	0.171274i
$415$	−152.483	+	127.948i	−0.367428	+	0.308309i
$416$	−16.6944	−	94.6786i	−0.0401307	−	0.227593i
$417$			373.184i			0.894925i
$418$		0			0
$419$	−242.808			−0.579495			−0.289747	−	0.957103i	$-0.593571\pi$
$419$	−242.808			−0.579495			−0.289747	+	0.957103i	$0.593571\pi$
$420$	−5.36715	+	0.946373i	−0.0127789	+	0.00225327i
$421$	357.257	+	425.763i	0.848592	+	1.01131i	0.999740	+	0.0228015i	$0.00725857\pi$
$421$	357.257	+	425.763i	0.848592	+	1.01131i	−0.151148	+	0.988511i	$0.548297\pi$
$422$	−273.815	+	99.6606i	−0.648851	+	0.236162i
$423$	−359.231	−	130.750i	−0.849247	−	0.309101i
$424$	−179.504	−	150.622i	−0.423358	−	0.355240i
$425$	−147.544	+	255.553i	−0.347162	+	0.601301i
$426$	122.525	−	70.7399i	0.287618	−	0.166056i
$427$	−25.8655	+	146.691i	−0.0605750	+	0.343538i
$428$	44.8419	+	7.90683i	0.104771	+	0.0184739i
$429$	270.890	+	469.195i	0.631445	+	1.09369i
$430$	−112.532	−	64.9704i	−0.261703	−	0.151094i
$431$	4.11662	−	4.90599i	0.00955132	−	0.0113828i	−0.761248	−	0.648461i	$-0.775413\pi$
$431$	4.11662	−	4.90599i	0.00955132	−	0.0113828i	0.770799	+	0.637078i	$0.219857\pi$
$432$	133.900	−	367.888i	0.309955	−	0.851593i
$433$	19.5863	+	53.8130i	0.0452340	+	0.124279i	0.960253	−	0.279132i	$-0.0900466\pi$
$433$	19.5863	+	53.8130i	0.0452340	+	0.124279i	−0.915019	+	0.403411i	$0.867824\pi$
$434$	21.0318	−	17.6478i	0.0484603	−	0.0406630i
$435$	−7.76320	−	44.0273i	−0.0178464	−	0.101212i
$436$			85.6684i			0.196487i
$437$		0			0
$438$	−186.969			−0.426870
$439$	−515.607	+	90.9155i	−1.17450	+	0.207097i	−0.726649	−	0.687009i	$-0.758923\pi$
$439$	−515.607	+	90.9155i	−1.17450	+	0.207097i	−0.447855	+	0.894106i	$0.647812\pi$
$440$	288.276	+	343.554i	0.655173	+	0.780804i
$441$	211.903	−	77.1266i	0.480507	−	0.174890i
$442$	−443.103	−	161.276i	−1.00249	−	0.364878i
$443$	332.869	+	279.310i	0.751398	+	0.630497i	0.935872	−	0.352340i	$-0.114614\pi$
$443$	332.869	+	279.310i	0.751398	+	0.630497i	−0.184475	+	0.982837i	$0.559058\pi$
$444$	−24.0344	+	41.6287i	−0.0541315	+	0.0937584i
$445$	19.6087	−	11.3211i	0.0440646	−	0.0254407i
$446$	−51.1650	+	290.171i	−0.114720	+	0.650608i
$447$	−268.982	−	47.4289i	−0.601751	−	0.106105i
$448$	83.5864	+	144.776i	0.186577	+	0.323161i
$449$	272.280	+	157.201i	0.606415	+	0.350114i	0.771561	−	0.636155i	$-0.219476\pi$
$449$	272.280	+	157.201i	0.606415	+	0.350114i	−0.165146	+	0.986269i	$0.552810\pi$
$450$	−109.348	+	130.316i	−0.242996	+	0.289591i
$451$	−202.923	+	557.526i	−0.449940	+	1.23620i
$452$	2.61117	+	7.17413i	0.00577692	+	0.0158720i
$453$	151.238	−	126.904i	0.333859	−	0.280141i
$454$	22.0540	+	125.074i	0.0485771	+	0.275494i
$455$			97.9543i			0.215284i
$456$		0			0
$457$	525.189			1.14921			0.574606	−	0.818431i	$-0.305155\pi$
$457$	525.189			1.14921			0.574606	+	0.818431i	$0.305155\pi$
$458$	129.159	−	22.7743i	0.282007	−	0.0497255i
$459$	304.819	+	363.270i	0.664095	+	0.791437i
$460$	−8.32280	+	3.02925i	−0.0180931	+	0.00658533i
$461$	572.839	+	208.496i	1.24260	+	0.452269i	0.877895	−	0.478854i	$-0.158948\pi$
$461$	572.839	+	208.496i	1.24260	+	0.452269i	0.364705	+	0.931123i	$0.381170\pi$
$462$	−130.766	−	109.726i	−0.283044	−	0.237502i
$463$	381.720	−	661.158i	0.824449	−	1.42799i	−0.0778909	−	0.996962i	$-0.524819\pi$
$463$	381.720	−	661.158i	0.824449	−	1.42799i	0.902340	−	0.431025i	$-0.141848\pi$
$464$	−101.050	+	58.3411i	−0.217780	+	0.125735i
$465$	−5.65686	+	32.0817i	−0.0121653	+	0.0689928i
$466$	304.305	+	53.6572i	0.653015	+	0.115144i
$467$	224.311	+	388.519i	0.480324	+	0.831946i	0.999745	−	0.0225724i	$-0.00718563\pi$
$467$	224.311	+	388.519i	0.480324	+	0.831946i	−0.519421	+	0.854519i	$0.673852\pi$
$468$	27.3008	+	15.7621i	0.0583350	+	0.0336797i
$469$	18.7095	−	22.2972i	0.0398924	−	0.0475419i
$470$	132.338	−	363.595i	0.281570	−	0.773607i
$471$	111.217	+	305.568i	0.236131	+	0.648763i
$472$	−59.0138	+	49.5184i	−0.125029	+	0.104912i
$473$	81.9595	+	464.816i	0.173276	+	0.982697i
$474$		−	395.338i		−	0.834047i
$475$		0			0
$476$	−17.2294			−0.0361963
$477$	144.214	−	25.4289i	0.302336	−	0.0533100i
$478$	−371.938	−	443.258i	−0.778113	−	0.927318i
$479$	654.650	−	238.273i	1.36670	−	0.497439i	0.448582	−	0.893742i	$-0.351929\pi$
$479$	654.650	−	238.273i	1.36670	−	0.497439i	0.918120	+	0.396303i	$0.129707\pi$
$480$	−33.7745	−	12.2929i	−0.0703636	−	0.0256103i
$481$	661.832	+	555.343i	1.37595	+	1.15456i
$482$	−227.235	+	393.583i	−0.471442	+	0.816562i
$483$	31.0149	−	17.9064i	0.0642130	−	0.0370734i
$484$	17.8944	−	101.484i	0.0369720	−	0.209678i
$485$	327.650	+	57.7735i	0.675567	+	0.119121i
$486$	223.177	+	386.553i	0.459211	+	0.795377i
$487$	−16.8247	−	9.71373i	−0.0345476	−	0.0199461i	0.482627	−	0.875826i	$-0.339683\pi$
$487$	−16.8247	−	9.71373i	−0.0345476	−	0.0199461i	−0.517174	+	0.855880i	$0.673016\pi$
$488$	−331.313	+	394.843i	−0.678919	+	0.809104i
$489$	22.4886	−	61.7868i	0.0459889	−	0.126353i
$490$	78.0635	+	214.478i	0.159313	+	0.437709i
$491$	507.388	−	425.749i	1.03338	−	0.867107i	0.0421287	−	0.999112i	$-0.486586\pi$
$491$	507.388	−	425.749i	1.03338	−	0.867107i	0.991249	+	0.132005i	$0.0421416\pi$
$492$	−4.33231	−	24.5698i	−0.00880551	−	0.0499385i
$493$		−	141.335i		−	0.286684i
$494$		0			0
$495$	−280.271			−0.566203
$496$	83.7320	−	14.7642i	0.168814	−	0.0297666i
$497$	−59.7236	−	71.1759i	−0.120168	−	0.143211i
$498$	246.361	−	89.6682i	0.494702	−	0.180057i
$499$	125.546	+	45.6950i	0.251595	+	0.0915732i	0.464739	−	0.885448i	$-0.346148\pi$
$499$	125.546	+	45.6950i	0.251595	+	0.0915732i	−0.213144	+	0.977021i	$0.568370\pi$
$500$	37.5296	+	31.4911i	0.0750592	+	0.0629821i
$501$	46.9040	−	81.2400i	0.0936207	−	0.162156i
$502$	523.636	−	302.321i	1.04310	−	0.602234i
$503$	−56.3915	+	319.812i	−0.112110	+	0.635810i	0.876030	+	0.482257i	$0.160183\pi$
$503$	−56.3915	+	319.812i	−0.112110	+	0.635810i	−0.988140	+	0.153553i	$0.950928\pi$
$504$	−103.913	−	18.3227i	−0.206177	−	0.0363545i
$505$	183.512	+	317.852i	0.363390	+	0.629410i
$506$	−240.251	−	138.709i	−0.474804	−	0.274128i
$507$	−52.1236	+	62.1185i	−0.102808	+	0.122522i
$508$	1.61084	−	4.42576i	0.00317095	−	0.00871212i
$509$	−167.095	−	459.089i	−0.328281	−	0.901944i	−0.988547	−	0.150912i	$-0.951779\pi$
$509$	−167.095	−	459.089i	−0.328281	−	0.901944i	0.660267	−	0.751031i	$-0.270443\pi$
$510$	−135.044	+	113.316i	−0.264793	+	0.222187i
$511$	21.3218	+	120.922i	0.0417256	+	0.236638i
$512$			567.464i			1.10833i
$513$		0			0
$514$	217.972			0.424070
$515$	−36.3448	+	6.40857i	−0.0705725	+	0.0124438i
$516$	−12.7575	−	15.2038i	−0.0247239	−	0.0294648i
$517$	−1320.69	+	480.693i	−2.55453	+	0.929773i
$518$	−255.799	−	93.1034i	−0.493821	−	0.179736i
$519$	−76.9854	−	64.5984i	−0.148334	−	0.124467i
$520$	−169.478	+	293.544i	−0.325919	+	0.564508i
$521$	−539.718	+	311.606i	−1.03593	+	0.598093i	−0.918677	−	0.395010i	$-0.870741\pi$
$521$	−539.718	+	311.606i	−1.03593	+	0.598093i	−0.117250	+	0.993102i	$0.537408\pi$
$522$	14.1486	−	80.2406i	0.0271046	−	0.153718i
$523$	−647.323	−	114.140i	−1.23771	−	0.218242i	−0.483777	−	0.875192i	$-0.660735\pi$
$523$	−647.323	−	114.140i	−1.23771	−	0.218242i	−0.753934	+	0.656950i	$0.771846\pi$
$524$	−2.33274	−	4.04043i	−0.00445180	−	0.00771074i
$525$	−69.9208	−	40.3688i	−0.133182	−	0.0768929i
$526$	−27.6490	+	32.9508i	−0.0525646	+	0.0626440i
$527$	−35.2238	+	96.7767i	−0.0668384	+	0.183637i
$528$	−180.806	−	496.759i	−0.342435	−	0.940832i
$529$	−360.653	+	302.624i	−0.681763	+	0.572067i
$530$	25.7378	+	145.966i	0.0485618	+	0.275408i
$531$		−	48.1433i		−	0.0906654i
$532$		0			0
$533$	−448.416			−0.841305
$534$	−29.3691	+	5.17857i	−0.0549983	+	0.00969769i
$535$	−196.668	−	234.380i	−0.367604	−	0.438094i
$536$	94.6456	−	34.4482i	0.176578	−	0.0642690i
$537$	−423.612	−	154.182i	−0.788849	−	0.287118i
$538$	−402.921	−	338.091i	−0.748924	−	0.628422i
$539$	414.524	−	717.976i	0.769061	−	1.33205i
$540$	27.7892	−	16.0441i	0.0514614	−	0.0297113i
$541$	15.5238	−	88.0397i	0.0286946	−	0.162735i	−0.967093	−	0.254422i	$-0.918115\pi$
$541$	15.5238	−	88.0397i	0.0286946	−	0.162735i	0.995788	+	0.0916869i	$0.0292259\pi$
$542$	−6.30887	−	1.11242i	−0.0116400	−	0.00205244i
$543$	−262.704	−	455.016i	−0.483800	−	0.837967i
$544$	−98.4042	−	56.8137i	−0.180890	−	0.104437i
$545$	370.018	−	440.970i	0.678932	−	0.809120i
$546$	44.1261	−	121.235i	0.0808170	−	0.222043i
$547$	239.692	+	658.549i	0.438194	+	1.20393i	0.940666	+	0.339334i	$0.110202\pi$
$547$	239.692	+	658.549i	0.438194	+	1.20393i	−0.502472	+	0.864594i	$0.667576\pi$
$548$	51.5004	−	43.2139i	0.0939787	−	0.0788575i
$549$	−55.9342	−	317.218i	−0.101884	−	0.577811i
$550$			625.418i			1.13712i
$551$		0			0
$552$	123.925			0.224502
$553$	−255.685	+	45.0841i	−0.462359	+	0.0815264i
$554$	165.225	+	196.907i	0.298239	+	0.355428i
$555$	303.517	−	110.471i	0.546878	−	0.199047i
$556$	75.0167	+	27.3038i	0.134922	+	0.0491076i
$557$	−161.372	−	135.407i	−0.289716	−	0.243101i	0.486332	−	0.873774i	$-0.338334\pi$
$557$	−161.372	−	135.407i	−0.289716	−	0.243101i	−0.776049	+	0.630673i	$0.782779\pi$
$558$	−29.6857	+	51.4172i	−0.0532003	+	0.0921455i
$559$	−308.931	+	178.361i	−0.552649	+	0.319072i
$560$	16.5971	−	94.1266i	0.0296376	−	0.168083i
$561$	630.604	+	111.193i	1.12407	+	0.198204i
$562$	−466.897	−	808.690i	−0.830778	−	1.43895i
$563$	461.855	+	266.652i	0.820347	+	0.473627i	0.850536	−	0.525917i	$-0.176278\pi$
$563$	461.855	+	266.652i	0.820347	+	0.473627i	−0.0301894	+	0.999544i	$0.509611\pi$
$564$	37.9886	−	45.2731i	0.0673557	−	0.0802714i
$565$	17.5457	−	48.2063i	0.0310543	−	0.0853209i
$566$	−242.606	−	666.554i	−0.428632	−	1.17766i
$567$	−12.3736	+	10.3827i	−0.0218229	+	0.0183116i
$568$	−55.8301	−	316.628i	−0.0982924	−	0.557444i
$569$		−	610.046i		−	1.07214i	−0.844174	−	0.536068i	$-0.819909\pi$
$569$		−	610.046i		−	1.07214i	0.844174	−	0.536068i	$-0.180091\pi$
$570$		0			0
$571$	−678.976			−1.18910			−0.594550	−	0.804059i	$-0.702670\pi$
$571$	−678.976			−1.18910			−0.594550	+	0.804059i	$0.702670\pi$
$572$	114.136	−	20.1253i	0.199539	−	0.0351841i
$573$	−101.737	−	121.245i	−0.177551	−	0.211598i
$574$	132.766	−	48.3228i	0.231299	−	0.0841861i
$575$	−123.297	−	44.8765i	−0.214430	−	0.0780462i
$576$	−276.934	−	232.375i	−0.480787	−	0.403429i
$577$	−363.669	+	629.894i	−0.630276	+	1.09167i	0.357219	+	0.934021i	$0.383725\pi$
$577$	−363.669	+	629.894i	−0.630276	+	1.09167i	−0.987495	+	0.157649i	$0.949608\pi$
$578$	−8.80838	+	5.08552i	−0.0152394	+	0.00879847i
$579$	−10.0652	+	57.0828i	−0.0173838	+	0.0985886i
$580$	−9.41827	−	1.66070i	−0.0162384	−	0.00286327i
$581$	−86.0877	−	149.108i	−0.148172	−	0.256641i
$582$	−379.498	−	219.104i	−0.652059	−	0.376467i
$583$	346.060	−	412.418i	0.593585	−	0.707407i
$584$	−145.320	+	399.262i	−0.248835	+	0.683669i
$585$	−72.4487	−	199.051i	−0.123844	−	0.340259i
$586$	106.425	−	89.3011i	0.181612	−	0.152391i
$587$	−170.141	−	964.916i	−0.289848	−	1.64381i	−0.687436	−	0.726245i	$-0.741264\pi$
$587$	−170.141	−	964.916i	−0.289848	−	1.64381i	0.397588	−	0.917564i	$-0.369847\pi$
$588$			34.8618i			0.0592888i
$589$		0			0
$590$	48.7282			0.0825901
$591$	−344.516	+	60.7474i	−0.582937	+	0.102787i
$592$	−541.875	−	645.782i	−0.915330	−	1.09085i
$593$	327.541	−	119.215i	0.552346	−	0.201037i	−0.0507426	−	0.998712i	$-0.516159\pi$
$593$	327.541	−	119.215i	0.552346	−	0.201037i	0.603088	+	0.797674i	$0.293937\pi$
$594$	944.455	+	343.753i	1.58999	+	0.578709i
$595$	88.6870	+	74.4172i	0.149054	+	0.125071i
$596$	−29.2140	+	50.6002i	−0.0490169	+	0.0848997i
$597$	−185.319	+	106.994i	−0.310417	+	0.179219i
$598$	36.4088	−	206.484i	0.0608842	−	0.345292i
$599$	−416.881	−	73.5073i	−0.695961	−	0.122717i	−0.185534	−	0.982638i	$-0.559401\pi$
$599$	−416.881	−	73.5073i	−0.695961	−	0.122717i	−0.510427	+	0.859921i	$0.670513\pi$
$600$	−139.690	−	241.950i	−0.232817	−	0.403250i
$601$	−437.051	−	252.331i	−0.727206	−	0.419853i	0.0901931	−	0.995924i	$-0.471252\pi$
$601$	−437.051	−	252.331i	−0.727206	−	0.419853i	−0.817399	+	0.576072i	$0.804585\pi$
$602$	72.2467	−	86.1003i	0.120011	−	0.143024i
$603$	−21.5280	+	59.1476i	−0.0357014	+	0.0980889i
$604$	−14.4447	−	39.6864i	−0.0239150	−	0.0657060i
$605$	−530.440	+	445.092i	−0.876760	+	0.735689i
$606$	−83.9432	−	476.065i	−0.138520	−	0.785587i
$607$			73.0072i			0.120275i	0.998190	+	0.0601377i	$0.0191540\pi$
$607$			73.0072i			0.120275i	−0.998190	+	0.0601377i	$0.980846\pi$
$608$		0			0
$609$	38.6701			0.0634977
$610$	321.072	−	56.6136i	0.526347	−	0.0928092i
$611$	−682.786	−	813.713i	−1.11749	−	1.33177i
$612$	35.0117	−	12.7432i	0.0572086	−	0.0208222i
$613$	965.219	+	351.311i	1.57458	+	0.573101i	0.974017	−	0.226474i	$-0.0727199\pi$
$613$	965.219	+	351.311i	1.57458	+	0.573101i	0.600566	+	0.799575i	$0.294942\pi$
$614$	−134.056	−	112.486i	−0.218332	−	0.183202i
$615$	−83.8212	+	145.183i	−0.136295	+	0.236069i
$616$	−335.951	+	193.962i	−0.545376	+	0.314873i
$617$	73.6558	−	417.723i	0.119377	−	0.677023i	−0.865112	−	0.501579i	$-0.832753\pi$
$617$	73.6558	−	417.723i	0.119377	−	0.677023i	0.984489	−	0.175444i	$-0.0561361\pi$
$618$	47.8700	+	8.44077i	0.0774595	+	0.0136582i
$619$	−164.352	−	284.665i	−0.265512	−	0.459879i	0.702186	−	0.711994i	$-0.252208\pi$
$619$	−164.352	−	284.665i	−0.265512	−	0.459879i	−0.967698	+	0.252114i	$0.918874\pi$
$620$	6.03511	+	3.48437i	0.00973405	+	0.00561996i
$621$	−135.538	+	161.527i	−0.218257	+	0.260109i
$622$	−129.007	+	354.444i	−0.207407	+	0.569845i
$623$	6.69847	+	18.4039i	0.0107520	+	0.0295407i
$624$	306.066	−	256.820i	0.490491	−	0.411571i
$625$	17.4999	+	99.2468i	0.0279998	+	0.158795i
$626$		−	57.9284i		−	0.0925375i
$627$		0			0
$628$	69.5618			0.110767
$629$	1005.61	−	177.316i	1.59874	−	0.281901i
$630$	42.9009	+	51.1273i	0.0680967	+	0.0811545i
$631$	−110.676	+	40.2829i	−0.175398	+	0.0638398i	−0.428227	−	0.903671i	$-0.640861\pi$
$631$	−110.676	+	40.2829i	−0.175398	+	0.0638398i	0.252828	+	0.967511i	$0.418639\pi$
$632$	−844.225	−	307.273i	−1.33580	−	0.486191i
$633$	229.094	+	192.233i	0.361918	+	0.303685i
$634$	539.483	−	934.411i	0.850919	−	1.47383i
$635$	−27.4074	+	15.8236i	−0.0431612	+	0.0249191i
$636$	−3.93119	+	22.2949i	−0.00618112	+	0.0350549i
$637$	617.067	+	108.806i	0.968708	+	0.170809i
$638$	−149.775	−	259.418i	−0.234757	−	0.406612i
$639$	174.006	+	100.463i	0.272310	+	0.157219i
$640$	187.638	−	223.618i	0.293184	−	0.349404i
$641$	−25.4507	+	69.9252i	−0.0397047	+	0.109088i	−0.957961	−	0.286900i	$-0.907375\pi$
$641$	−25.4507	+	69.9252i	−0.0397047	+	0.109088i	0.918256	+	0.395987i	$0.129598\pi$
$642$	137.829	+	378.681i	0.214686	+	0.589846i
$643$	−377.634	+	316.872i	−0.587300	+	0.492803i	−0.887335	−	0.461125i	$-0.847446\pi$
$643$	−377.634	+	316.872i	−0.587300	+	0.492803i	0.300036	+	0.953928i	$0.403001\pi$
$644$	−1.33033	−	7.54467i	−0.00206573	−	0.0117153i
$645$			133.363i			0.206764i
$646$		0			0
$647$	989.083			1.52872			0.764361	−	0.644789i	$-0.223055\pi$
$647$	989.083			1.52872			0.764361	+	0.644789i	$0.223055\pi$
$648$	−55.0444	+	9.70581i	−0.0849450	+	0.0149781i
$649$	−113.771	−	135.587i	−0.175302	−	0.208916i
$650$	−444.179	+	161.668i	−0.683352	+	0.248720i
$651$	−26.4787	−	9.63745i	−0.0406738	−	0.0148041i
$652$	−10.7749	−	9.04121i	−0.0165259	−	0.0138669i
$653$	79.5099	−	137.715i	0.121761	−	0.210896i	−0.798701	−	0.601728i	$-0.794479\pi$
$653$	79.5099	−	137.715i	0.121761	−	0.210896i	0.920462	+	0.390832i	$0.127813\pi$
$654$	−656.609	+	379.093i	−1.00399	+	0.579653i
$655$	−5.44379	+	30.8733i	−0.00831114	+	0.0471348i
$656$	430.894	+	75.9782i	0.656850	+	0.115820i
$657$	−132.764	−	229.953i	−0.202076	−	0.350005i
$658$	289.846	+	167.343i	0.440496	+	0.254320i
$659$	478.449	−	570.194i	0.726023	−	0.865241i	−0.269178	−	0.963090i	$-0.586752\pi$
$659$	478.449	−	570.194i	0.726023	−	0.865241i	0.995201	+	0.0978498i	$0.0311965\pi$
$660$	14.8193	−	40.7156i	0.0224534	−	0.0616903i
$661$	−262.170	−	720.307i	−0.396627	−	1.08972i	−0.963917	−	0.266205i	$-0.914230\pi$
$661$	−262.170	−	720.307i	−0.396627	−	1.08972i	0.567290	−	0.823518i	$-0.307992\pi$
$662$	−641.423	+	538.218i	−0.968917	+	0.813017i
$663$	84.0383	+	476.605i	0.126755	+	0.718861i
$664$		−	595.786i		−	0.897268i
$665$		0			0
$666$	588.667			0.883884
$667$	61.8897	−	10.9128i	0.0927882	−	0.0163611i
$668$	−12.8990	−	15.3724i	−0.0193099	−	0.0230126i
$669$	284.169	−	103.429i	0.424767	−	0.154603i
$670$	−59.8661	−	21.7895i	−0.0893524	−	0.0325216i
$671$	−907.169	−	761.205i	−1.35197	−	1.13443i
$672$	15.5446	−	26.9240i	0.0231318	−	0.0400654i
$673$	−695.119	+	401.327i	−1.03287	+	0.596326i	−0.917804	−	0.397033i	$-0.870040\pi$
$673$	−695.119	+	401.327i	−1.03287	+	0.596326i	−0.115062	+	0.993358i	$0.536707\pi$
$674$	145.391	−	824.555i	0.215714	−	1.22337i
$675$	468.145	+	82.5466i	0.693548	+	0.122291i
$676$	8.67333	+	15.0227i	0.0128304	+	0.0222229i
$677$	432.884	+	249.926i	0.639415	+	0.369166i	0.784389	−	0.620269i	$-0.212977\pi$
$677$	432.884	+	249.926i	0.639415	+	0.369166i	−0.144974	+	0.989435i	$0.546310\pi$
$678$	−43.4316	+	51.7598i	−0.0640584	+	0.0763419i
$679$	−98.4272	+	270.427i	−0.144959	+	0.398272i
$680$	137.018	+	376.453i	0.201497	+	0.553608i
$681$	99.8525	−	83.7862i	0.146626	−	0.123034i
$682$	37.9032	+	214.959i	0.0555765	+	0.315190i
$683$		−	52.2603i		−	0.0765159i	−0.999268	−	0.0382579i	$-0.987819\pi$
$683$		−	52.2603i		−	0.0765159i	0.999268	−	0.0382579i	$-0.0121808\pi$
$684$		0			0
$685$	−451.742			−0.659478
$686$	−415.141	+	73.2005i	−0.605161	+	0.106706i
$687$	−86.5227	−	103.114i	−0.125943	−	0.150093i
$688$	327.080	−	119.047i	0.475407	−	0.173034i
$689$	382.359	+	139.167i	0.554948	+	0.201984i
$690$	−60.0472	−	50.3856i	−0.0870250	−	0.0730226i
$691$	130.083	−	225.311i	0.188253	−	0.326065i	−0.756415	−	0.654093i	$-0.773051\pi$
$691$	130.083	−	225.311i	0.188253	−	0.326065i	0.944668	+	0.328028i	$0.106384\pi$
$692$	−18.6180	+	10.7491i	−0.0269047	+	0.0155334i
$693$	42.0971	−	238.745i	0.0607462	−	0.344509i
$694$	−6.53614	−	1.15250i	−0.00941808	−	0.00166066i
$695$	−268.211	−	464.555i	−0.385915	−	0.668425i
$696$	115.884	+	66.9059i	0.166501	+	0.0961292i
$697$	−340.668	+	405.992i	−0.488763	+	0.582485i
$698$	−57.2118	+	157.188i	−0.0819654	+	0.225198i
$699$	−108.467	−	298.010i	−0.155174	−	0.426338i
$700$	−13.2306	+	11.1018i	−0.0189008	+	0.0158597i
$701$	83.3601	+	472.759i	0.118916	+	0.674406i	0.984737	+	0.174051i	$0.0556859\pi$
$701$	83.3601	+	472.759i	0.118916	+	0.674406i	−0.865821	+	0.500355i	$0.833203\pi$
$702$			759.621i			1.08208i
$703$		0			0
$704$	−1329.07			−1.88789
$705$	−391.086	+	68.9590i	−0.554732	+	0.0978142i
$706$	153.195	+	182.571i	0.216990	+	0.258599i
$707$	−298.322	+	108.580i	−0.421955	+	0.153579i
$708$	6.99390	+	2.54557i	0.00987839	+	0.00359544i
$709$	326.161	+	273.682i	0.460030	+	0.386011i	0.843142	−	0.537691i	$-0.180703\pi$
$709$	326.161	+	273.682i	0.460030	+	0.386011i	−0.383112	+	0.923702i	$0.625148\pi$
$710$	−101.683	+	176.120i	−0.143216	+	0.248057i
$711$	486.227	−	280.724i	0.683864	−	0.394829i
$712$	−11.7683	+	66.7412i	−0.0165285	+	0.0937377i
$713$	−45.0976	−	7.95193i	−0.0632505	−	0.0111528i
$714$	−76.2424	−	132.056i	−0.106782	−	0.184952i
$715$	−674.430	−	389.382i	−0.943259	−	0.544591i
$716$	−61.9868	+	73.8730i	−0.0865738	+	0.103175i
$717$	−203.115	+	558.055i	−0.283285	+	0.778319i
$718$	−38.9730	−	107.077i	−0.0542799	−	0.149133i
$719$	430.573	−	361.294i	0.598850	−	0.502495i	−0.292226	−	0.956349i	$-0.594396\pi$
$719$	430.573	−	361.294i	0.598850	−	0.502495i	0.891076	+	0.453855i	$0.149951\pi$
$720$	35.8911	+	203.549i	0.0498488	+	0.282706i
$721$		−	31.9224i		−	0.0442752i
$722$		0			0
$723$	466.438			0.645142
$724$	−110.687	+	19.5171i	−0.152883	+	0.0269573i
$725$	−91.0691	−	108.532i	−0.125613	−	0.149699i
$726$	857.016	−	311.928i	1.18046	−	0.429653i
$727$	−249.763	−	90.9062i	−0.343553	−	0.125043i	0.164481	−	0.986380i	$-0.447405\pi$
$727$	−249.763	−	90.9062i	−0.343553	−	0.125043i	−0.508033	+	0.861337i	$0.669627\pi$
$728$	−224.596	−	188.458i	−0.308510	−	0.258871i
$729$	259.140	−	448.844i	0.355473	−	0.615698i
$730$	232.747	−	134.376i	0.318831	−	0.184077i
$731$	−73.2123	+	415.207i	−0.100154	+	0.567999i
$732$	49.0406	+	8.64718i	0.0669954	+	0.0118131i
$733$	354.455	+	613.934i	0.483567	+	0.837563i	0.999822	−	0.0188721i	$-0.00600753\pi$
$733$	354.455	+	613.934i	0.483567	+	0.837563i	−0.516255	+	0.856435i	$0.672674\pi$
$734$	251.481	+	145.193i	0.342617	+	0.197810i
$735$	150.575	−	179.448i	0.204863	−	0.244147i
$736$	17.2803	−	47.4773i	0.0234787	−	0.0645072i
$737$	79.1462	+	217.452i	0.107390	+	0.295051i
$738$	−234.051	+	196.392i	−0.317142	+	0.266114i
$739$	−108.007	−	612.536i	−0.146153	−	0.828872i	−0.966435	−	0.256913i	$-0.917295\pi$
$739$	−108.007	−	612.536i	−0.146153	−	0.828872i	0.820282	−	0.571959i	$-0.193816\pi$
$740$		−	69.0950i		−	0.0933716i
$741$		0			0
$742$	−128.205			−0.172783
$743$	−501.290	+	88.3909i	−0.674683	+	0.118965i	−0.500484	−	0.865746i	$-0.666845\pi$
$743$	−501.290	+	88.3909i	−0.674683	+	0.118965i	−0.174199	+	0.984710i	$0.555734\pi$
$744$	−62.6754	−	74.6936i	−0.0842411	−	0.100395i
$745$	368.928	−	134.279i	0.495206	−	0.180240i
$746$	473.978	+	172.514i	0.635359	+	0.231252i
$747$	285.221	+	239.328i	0.381821	+	0.320386i
$748$	68.4896	−	118.627i	0.0915636	−	0.158593i
$749$	229.194	−	132.325i	0.305999	−	0.176669i
$750$	−75.2914	+	426.999i	−0.100389	+	0.569332i
$751$	−534.824	−	94.3040i	−0.712150	−	0.125571i	−0.194175	−	0.980967i	$-0.562203\pi$
$751$	−534.824	−	94.3040i	−0.712150	−	0.125571i	−0.517975	+	0.855396i	$0.673314\pi$
$752$	518.233	+	897.606i	0.689140	+	1.19362i
$753$	−537.425	−	310.282i	−0.713712	−	0.412062i
$754$	145.526	−	173.431i	0.193005	−	0.230014i
$755$	−97.0606	+	266.672i	−0.128557	+	0.353208i
$756$	9.49295	+	26.0817i	0.0125568	+	0.0344996i
$757$	−471.663	+	395.772i	−0.623068	+	0.522816i	−0.898766	−	0.438428i	$-0.855535\pi$
$757$	−471.663	+	395.772i	−0.623068	+	0.522816i	0.275698	+	0.961244i	$0.411091\pi$
$758$	−220.298	−	1249.37i	−0.290630	−	1.64824i
$759$			284.723i			0.375129i
$760$		0			0
$761$	841.391			1.10564			0.552819	−	0.833301i	$-0.313552\pi$
$761$	841.391			1.10564			0.552819	+	0.833301i	$0.313552\pi$
$762$	41.0496	−	7.23815i	0.0538708	−	0.00949888i
$763$	320.057	+	381.429i	0.419472	+	0.499907i
$764$	−31.8160	+	11.5801i	−0.0416440	+	0.0151572i
$765$	−235.260	−	85.6276i	−0.307529	−	0.111931i
$766$	1000.56	+	839.566i	1.30621	+	1.09604i
$767$	66.8860	−	115.850i	0.0872046	−	0.151043i
$768$	132.797	−	76.6701i	0.172912	−	0.0998309i
$769$	135.914	−	770.809i	0.176742	−	1.00235i	−0.759372	−	0.650656i	$-0.774494\pi$
$769$	135.914	−	770.809i	0.176742	−	1.00235i	0.936114	−	0.351696i	$-0.114395\pi$
$770$	241.645	+	42.6085i	0.313825	+	0.0553357i
$771$	−111.856	−	193.740i	−0.145079	−	0.251284i
$772$	10.7383	+	6.19973i	0.0139097	+	0.00803074i
$773$	−620.250	+	739.185i	−0.802393	+	0.956255i	−0.999710	−	0.0240846i	$-0.992333\pi$
$773$	−620.250	+	739.185i	−0.802393	+	0.956255i	0.197317	+	0.980340i	$0.436777\pi$
$774$	−83.1301	+	228.398i	−0.107403	+	0.295088i
$775$	35.3094	+	97.0118i	0.0455605	+	0.125176i
$776$	−762.846	+	640.103i	−0.983048	+	0.824876i
$777$	48.5146	+	275.140i	0.0624383	+	0.354105i
$778$		−	427.549i		−	0.549548i
$779$		0			0
$780$	32.7474			0.0419838
$781$	727.467	−	128.272i	0.931456	−	0.164241i
$782$	−159.289	−	189.833i	−0.203695	−	0.242754i
$783$	−213.951	+	77.8718i	−0.273245	+	0.0994531i
$784$	−574.519	−	209.108i	−0.732805	−	0.266719i
$785$	−358.063	−	300.450i	−0.456131	−	0.382739i
$786$	20.6453	−	35.7588i	0.0262663	−	0.0454946i
$787$	1163.29	−	671.627i	1.47814	−	0.853402i	0.478441	−	0.878120i	$-0.341202\pi$
$787$	1163.29	−	671.627i	1.47814	−	0.853402i	0.999694	+	0.0247177i	$0.00786869\pi$
$788$	−12.9950	+	73.6984i	−0.0164911	+	0.0935259i
$789$	43.4762	+	7.66602i	0.0551029	+	0.00971612i
$790$	284.134	+	492.134i	0.359663	+	0.622954i
$791$	38.4285	+	22.1867i	0.0485822	+	0.0280489i
$792$	539.224	−	642.622i	0.680838	−	0.811391i
$793$	306.117	−	841.050i	0.386024	−	1.06059i
$794$	391.484	+	1075.59i	0.493053	+	1.35465i
$795$	116.531	−	97.7814i	0.146580	−	0.122995i
$796$	7.94892	+	45.0805i	0.00998608	+	0.0566339i
$797$			1393.79i			1.74880i	0.485209	+	0.874398i	$0.338743\pi$
$797$			1393.79i			1.74880i	−0.485209	+	0.874398i	$0.661257\pi$
$798$		0			0
$799$	−1255.45			−1.57128
$800$	−112.173	+	19.7791i	−0.140216	+	0.0247239i
$801$	−27.2237	−	32.4439i	−0.0339871	−	0.0405043i
$802$	−576.728	+	209.912i	−0.719112	+	0.261735i
$803$	−917.323	−	333.878i	−1.14237	−	0.415789i
$804$	−7.45423	−	6.25484i	−0.00927143	−	0.00777965i
$805$	−25.7391	+	44.5814i	−0.0319740	+	0.0553806i
$806$	−142.869	+	82.4853i	−0.177257	+	0.102339i
$807$	−93.7400	+	531.626i	−0.116159	+	0.658768i
$808$	−1081.86	−	190.761i	−1.33893	−	0.236090i
$809$	650.512	+	1126.72i	0.804095	+	1.39273i	0.916901	+	0.399116i	$0.130683\pi$
$809$	650.512	+	1126.72i	0.804095	+	1.39273i	−0.112806	+	0.993617i	$0.535984\pi$
$810$	30.6177	+	17.6771i	0.0377996	+	0.0218236i
$811$	−949.330	+	1131.37i	−1.17057	+	1.39503i	−0.268585	+	0.963256i	$0.586556\pi$
$811$	−949.330	+	1131.37i	−1.17057	+	1.39503i	−0.901983	+	0.431772i	$0.857889\pi$
$812$	2.82928	−	7.77339i	0.00348434	−	0.00957314i
$813$	2.24874	+	6.17837i	0.00276598	+	0.00759947i
$814$	1657.87	−	1391.12i	2.03670	−	1.70899i
$815$	16.4121	+	93.0776i	0.0201375	+	0.114206i
$816$		−	472.220i		−	0.578701i
$817$		0			0
$818$	−494.961			−0.605087
$819$	180.441	−	31.8166i	0.220319	−	0.0388481i
$820$	23.0516	+	27.4718i	0.0281117	+	0.0335022i
$821$	111.775	−	40.6826i	0.136144	−	0.0495525i	−0.273049	−	0.962000i	$-0.588032\pi$
$821$	111.775	−	40.6826i	0.136144	−	0.0495525i	0.409194	+	0.912448i	$0.365810\pi$
$822$	559.110	+	203.499i	0.680183	+	0.247566i
$823$	−804.244	−	674.841i	−0.977210	−	0.819977i	0.00645612	−	0.999979i	$-0.497945\pi$
$823$	−804.244	−	674.841i	−0.977210	−	0.819977i	−0.983666	+	0.180003i	$0.942389\pi$
$824$	55.2313	−	95.6634i	0.0670282	−	0.116096i
$825$	555.891	−	320.944i	0.673807	−	0.389023i
$826$	−7.31905	+	41.5084i	−0.00886084	+	0.0502523i
$827$	361.306	+	63.7079i	0.436887	+	0.0770350i	0.387766	−	0.921758i	$-0.373247\pi$
$827$	361.306	+	63.7079i	0.436887	+	0.0770350i	0.0491211	+	0.998793i	$0.484358\pi$
$828$	8.28351	+	14.3475i	0.0100042	+	0.0173279i
$829$	−290.861	−	167.929i	−0.350858	−	0.202568i	0.314205	−	0.949355i	$-0.398262\pi$
$829$	−290.861	−	167.929i	−0.350858	−	0.202568i	−0.665063	+	0.746787i	$0.731595\pi$
$830$	−242.236	+	288.685i	−0.291850	+	0.347814i
$831$	90.2292	−	247.903i	0.108579	−	0.298318i
$832$	−343.560	−	943.922i	−0.412932	−	1.13452i
$833$	567.307	−	476.027i	0.681040	−	0.571461i
$834$	122.687	+	695.791i	0.147106	+	0.834281i
$835$			134.841i			0.161487i
$836$		0			0
$837$	165.906			0.198216
$838$	−452.709	+	79.8249i	−0.540226	+	0.0952564i
$839$	678.105	+	808.134i	0.808230	+	0.963211i	0.999833	−	0.0182617i	$-0.00581319\pi$
$839$	678.105	+	808.134i	0.808230	+	0.963211i	−0.191603	+	0.981472i	$0.561369\pi$
$840$	−103.000	+	37.4889i	−0.122619	+	0.0446296i
$841$	−726.516	−	264.430i	−0.863871	−	0.314423i
$842$	806.068	+	676.372i	0.957326	+	0.803292i
$843$	−479.192	+	829.985i	−0.568437	+	0.984561i
$844$	55.4038	−	31.9874i	0.0656443	−	0.0378998i
$845$	20.2405	−	114.789i	0.0239532	−	0.135846i
$846$	−712.762	−	125.679i	−0.842508	−	0.148557i
$847$	−299.473	−	518.702i	−0.353569	−	0.612399i
$848$	−343.838	−	198.515i	−0.405469	−	0.234098i
$849$	−467.956	+	557.688i	−0.551185	+	0.656877i
$850$	−191.076	+	524.978i	−0.224796	+	0.617621i
$851$	155.291	+	426.658i	0.182480	+	0.501361i
$852$	−23.7950	+	19.9664i	−0.0279284	+	0.0234347i
$853$	93.2238	+	528.699i	0.109289	+	0.619811i	0.989420	+	0.145079i	$0.0463437\pi$
$853$	93.2238	+	528.699i	0.109289	+	0.619811i	−0.880131	+	0.474731i	$0.842545\pi$
$854$			282.004i			0.330216i
$855$		0			0
$856$	915.780			1.06984
$857$	−1229.23	+	216.746i	−1.43434	+	0.252912i	−0.836175	−	0.548463i	$-0.815213\pi$
$857$	−1229.23	+	216.746i	−1.43434	+	0.252912i	−0.598162	+	0.801375i	$0.704102\pi$
$858$	659.317	+	785.744i	0.768435	+	0.915785i
$859$	475.756	−	173.161i	0.553849	−	0.201585i	−0.0499068	−	0.998754i	$-0.515892\pi$
$859$	475.756	−	173.161i	0.553849	−	0.201585i	0.603756	+	0.797169i	$0.293670\pi$
$860$	26.8083	+	9.75742i	0.0311724	+	0.0113458i
$861$	−111.082	−	93.2087i	−0.129015	−	0.108256i
$862$	6.06244	−	10.5005i	0.00703299	−	0.0121815i
$863$	−1102.47	+	636.511i	−1.27748	+	0.737556i	−0.976385	−	0.216037i	$-0.930687\pi$
$863$	−1102.47	+	636.511i	−1.27748	+	0.737556i	−0.301099	+	0.953593i	$0.597354\pi$
$864$	−31.7857	+	180.266i	−0.0367890	+	0.208641i
$865$	142.262	+	25.0847i	0.164465	+	0.0289996i
$866$	54.2095	+	93.8937i	0.0625976	+	0.108422i
$867$	9.04032	+	5.21943i	0.0104271	+	0.00602011i
$868$	−3.87460	+	4.61757i	−0.00446383	+	0.00531978i
$869$	705.973	−	1939.64i	0.812396	−	2.23204i
$870$	−28.9485	−	79.5354i	−0.0332742	−	0.0914201i
$871$	−133.978	+	112.421i	−0.153821	+	0.129071i
$872$	299.192	+	1696.80i	0.343110	+	1.94587i
$873$		−	622.328i		−	0.712861i
$874$		0			0
$875$	284.747			0.325425
$876$	40.4258	−	7.12815i	0.0461481	−	0.00813716i
$877$	197.866	+	235.807i	0.225617	+	0.268879i	0.866963	−	0.498372i	$-0.166068\pi$
$877$	197.866	+	235.807i	0.225617	+	0.268879i	−0.641347	+	0.767251i	$0.721624\pi$
$878$	−931.446	+	339.019i	−1.06087	+	0.386126i
$879$	−133.987	−	48.7674i	−0.152431	−	0.0554805i
$880$	582.101	+	488.440i	0.661478	+	0.555046i
$881$	−117.273	+	203.123i	−0.133113	+	0.230559i	−0.924875	−	0.380271i	$-0.875831\pi$
$881$	−117.273	+	203.123i	−0.133113	+	0.230559i	0.791762	+	0.610830i	$0.209164\pi$
$882$	369.732	−	213.465i	0.419198	−	0.242024i
$883$	−47.8272	+	271.242i	−0.0541645	+	0.307182i	−0.999839	−	0.0179323i	$-0.994292\pi$
$883$	−47.8272	+	271.242i	−0.0541645	+	0.307182i	0.945675	+	0.325114i	$0.105403\pi$
$884$	101.955	+	17.9774i	0.115333	+	0.0203364i
$885$	−25.0057	−	43.3111i	−0.0282550	−	0.0489391i
$886$	712.450	+	411.333i	0.804120	+	0.464259i
$887$	216.820	−	258.396i	0.244442	−	0.291314i	−0.629848	−	0.776718i	$-0.716883\pi$
$887$	216.820	−	258.396i	0.244442	−	0.291314i	0.874290	+	0.485404i	$0.161327\pi$
$888$	−330.653	+	908.463i	−0.372357	+	1.02304i
$889$	−9.36252	−	25.7233i	−0.0105315	−	0.0289351i
$890$	32.8380	−	27.5544i	0.0368967	−	0.0309600i
$891$	−22.2995	−	126.467i	−0.0250275	−	0.141938i
$892$		−	64.6905i		−	0.0725230i
$893$		0			0
$894$	−517.103			−0.578415
$895$	638.143	−	112.522i	0.713009	−	0.125723i
$896$	162.303	+	193.425i	0.181141	+	0.215876i
$897$	−202.213	+	73.5996i	−0.225433	+	0.0820509i
$898$	559.340	+	203.583i	0.622873	+	0.226707i
$899$	−37.8784	−	31.7838i	−0.0421340	−	0.0353546i
$900$	18.6746	−	32.3453i	0.0207495	−	0.0359392i
$901$	416.485	−	240.457i	0.462247	−	0.266878i
$902$	−195.054	+	1106.20i	−0.216246	+	1.22639i
$903$	−113.603	−	20.0313i	−0.125806	−	0.0221831i
$904$	76.7736	+	132.976i	0.0849266	+	0.147097i
$905$	654.049	+	377.616i	0.722706	+	0.417255i
$906$	240.259	−	286.329i	0.265186	−	0.316037i
$907$	87.3998	−	240.129i	0.0963614	−	0.264751i	−0.882141	−	0.470985i	$-0.843899\pi$
$907$	87.3998	−	240.129i	0.0963614	−	0.264751i	0.978503	+	0.206234i	$0.0661209\pi$
$908$	−9.53687	−	26.2023i	−0.0105032	−	0.0288572i
$909$	525.907	−	441.289i	0.578556	−	0.485466i
$910$	32.2031	+	182.633i	0.0353880	+	0.200696i
$911$		−	598.961i		−	0.657477i	−0.944421	−	0.328738i	$-0.893377\pi$
$911$		−	598.961i		−	0.657477i	0.944421	−	0.328738i	$-0.106623\pi$
$912$		0			0
$913$	1368.84			1.49928
$914$	979.201	−	172.660i	1.07134	−	0.188905i
$915$	−215.083	−	256.326i	−0.235064	−	0.280138i
$916$	−27.0581	+	9.84835i	−0.0295394	+	0.0107515i
$917$	−25.4813	−	9.27444i	−0.0277877	−	0.0101139i
$918$	687.755	+	577.095i	0.749188	+	0.628644i
$919$	−724.843	+	1255.46i	−0.788730	+	1.36612i	0.138015	+	0.990430i	$0.455928\pi$
$919$	−724.843	+	1255.46i	−0.788730	+	1.36612i	−0.926745	+	0.375691i	$0.877406\pi$
$920$	−154.267	+	89.0661i	−0.167682	+	0.0968110i
$921$	−31.1882	+	176.877i	−0.0338634	+	0.192049i
$922$	1136.59	+	200.411i	1.23274	+	0.217365i
$923$	279.147	+	483.497i	0.302435	+	0.523832i
$924$	32.4571	+	18.7391i	0.0351268	+	0.0202805i
$925$	657.957	−	784.123i	0.711305	−	0.847701i
$926$	494.346	−	1358.20i	0.533851	−	1.46674i
$927$	23.6104	+	64.8690i	0.0254697	+	0.0699774i
$928$	41.7917	−	35.0674i	0.0450342	−	0.0377881i
$929$	−307.523	−	1744.05i	−0.331026	−	1.87734i	−0.463408	−	0.886145i	$-0.653374\pi$
$929$	−307.523	−	1744.05i	−0.331026	−	1.87734i	0.132382	−	0.991199i	$-0.457737\pi$
$930$			61.6751i			0.0663173i
$931$		0			0
$932$	−67.8414			−0.0727912
$933$	381.242	−	67.2233i	0.408620	−	0.0720507i
$934$	545.951	+	650.639i	0.584530	+	0.696615i
$935$	−864.918	+	314.804i	−0.925046	+	0.336689i
$936$	595.784	+	216.848i	0.636521	+	0.231675i
$937$	−496.117	−	416.291i	−0.529474	−	0.444281i	0.338446	−	0.940986i	$-0.390099\pi$
$937$	−496.117	−	416.291i	−0.529474	−	0.444281i	−0.867920	+	0.496705i	$0.834543\pi$
$938$	27.5531	−	47.7233i	0.0293743	−	0.0508777i
$939$	−51.4886	+	29.7269i	−0.0548334	+	0.0316581i
$940$	−14.7516	+	83.6607i	−0.0156932	+	0.0890007i
$941$	−1334.60	−	235.326i	−1.41828	−	0.250081i	−0.588646	−	0.808391i	$-0.700339\pi$
$941$	−1334.60	−	235.326i	−1.41828	−	0.250081i	−0.829632	+	0.558310i	$0.811450\pi$
$942$	307.819	+	533.159i	0.326772	+	0.565986i
$943$	−204.085	−	117.829i	−0.216421	−	0.124951i
$944$	−83.9016	+	99.9900i	−0.0888788	+	0.105922i
$945$	63.7876	−	175.255i	0.0675001	−	0.185455i
$946$	305.623	+	839.691i	0.323068	+	0.887623i
$947$	−243.675	+	204.468i	−0.257313	+	0.215911i	−0.762314	−	0.647208i	$-0.775937\pi$
$947$	−243.675	+	204.468i	−0.257313	+	0.215911i	0.505001	+	0.863119i	$0.331492\pi$
$948$	15.0722	+	85.4787i	0.0158989	+	0.0901674i
$949$		−	737.799i		−	0.777449i
$950$		0			0
$951$	−1107.38			−1.16443
$952$	−341.257	+	60.1728i	−0.358463	+	0.0632067i
$953$	−590.113	−	703.270i	−0.619216	−	0.737953i	0.361719	−	0.932287i	$-0.382190\pi$
$953$	−590.113	−	703.270i	−0.619216	−	0.737953i	−0.980935	+	0.194334i	$0.937746\pi$
$954$	260.524	−	94.8228i	0.273085	−	0.0993950i
$955$	213.787	+	77.8120i	0.223861	+	0.0814786i
$956$	97.3182	+	81.6597i	0.101797	+	0.0854181i
$957$	−153.719	+	266.250i	−0.160626	+	0.278213i
$958$	1142.24	−	659.474i	1.19232	−	0.688387i
$959$	67.8525	−	384.811i	0.0707534	−	0.401262i
$960$	−369.833	−	65.2115i	−0.385242	−	0.0679286i
$961$	−462.485	−	801.047i	−0.481254	−	0.833556i
$962$	1416.54	+	817.840i	1.47250	+	0.850146i
$963$	−367.871	+	438.411i	−0.382005	+	0.455256i
$964$	34.1267	−	93.7624i	0.0354012	−	0.0972639i
$965$	−28.4964	−	78.2931i	−0.0295299	−	0.0811328i
$966$	51.9395	−	43.5824i	0.0537676	−	0.0451164i
$967$	68.1381	+	386.430i	0.0704634	+	0.399618i	0.999557	+	0.0297724i	$0.00947825\pi$
$967$	68.1381	+	386.430i	0.0704634	+	0.399618i	−0.929093	+	0.369845i	$0.879411\pi$
$968$		−	2072.56i		−	2.14107i
$969$		0			0
$970$	629.888			0.649369
$971$	463.909	−	81.7996i	0.477764	−	0.0842427i	0.0704198	−	0.997517i	$-0.477566\pi$
$971$	463.909	−	81.7996i	0.477764	−	0.0842427i	0.407344	+	0.913275i	$0.366455\pi$
$972$	−62.9917	−	75.0706i	−0.0648063	−	0.0772331i
$973$	436.011	−	158.695i	0.448110	−	0.163099i
$974$	−34.5626	−	12.5798i	−0.0354852	−	0.0129156i
$975$	371.633	+	311.837i	0.381162	+	0.319833i
$976$	−436.660	+	756.317i	−0.447398	+	0.774915i
$977$	−170.882	+	98.6590i	−0.174905	+	0.100982i	−0.584897	−	0.811108i	$-0.698865\pi$
$977$	−170.882	+	98.6590i	−0.174905	+	0.100982i	0.409991	+	0.912089i	$0.365532\pi$
$978$	21.6165	−	122.593i	0.0221027	−	0.125351i
$979$	−153.341	−	27.0381i	−0.156630	−	0.0276181i
$980$	−25.0555	−	43.3974i	−0.0255669	−	0.0442831i
$981$	−932.495	−	538.376i	−0.950556	−	0.548804i
$982$	806.044	−	960.605i	0.820818	−	0.978213i
$983$	262.990	−	722.560i	0.267538	−	0.735056i	−0.731069	−	0.682303i	$-0.760978\pi$
$983$	262.990	−	722.560i	0.267538	−	0.735056i	0.998608	−	0.0527523i	$-0.0167994\pi$
$984$	−171.617	−	471.513i	−0.174407	−	0.479180i
$985$	385.208	−	323.228i	0.391074	−	0.328150i
$986$	−46.4649	−	263.515i	−0.0471246	−	0.267257i
$987$		−	343.499i		−	0.348023i
$988$		0			0
$989$	−187.470			−0.189555
$990$	−522.557	+	92.1408i	−0.527835	+	0.0930716i
$991$	1121.81	+	1336.92i	1.13199	+	1.34906i	0.929088	+	0.369858i	$0.120594\pi$
$991$	1121.81	+	1336.92i	1.13199	+	1.34906i	0.202905	+	0.979198i	$0.434962\pi$
$992$	−37.3557	+	13.5964i	−0.0376570	+	0.0137060i
$993$	807.541	+	293.921i	0.813233	+	0.295993i
$994$	−134.753	−	113.071i	−0.135566	−	0.113753i
$995$	153.795	−	266.381i	0.154568	−	0.267719i
$996$	−49.8488	+	28.7802i	−0.0500490	+	0.0288958i
$997$	−214.134	+	1214.42i	−0.214779	+	1.21807i	0.666512	+	0.745495i	$0.267787\pi$
$997$	−214.134	+	1214.42i	−0.214779	+	1.21807i	−0.881290	+	0.472576i	$0.843324\pi$
$998$	249.100	+	43.9230i	0.249599	+	0.0440110i
$999$	−822.479	−	1424.58i	−0.823303	−	1.42600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.f.b.333.2		12
19.2	odd	18	inner	361.3.f.b.116.2		12
19.3	odd	18		361.3.f.g.299.1		12
19.4	even	9		361.3.d.f.293.5		12
19.5	even	9		361.3.f.e.307.2		12
19.6	even	9		361.3.b.c.360.4		12
19.7	even	3		361.3.f.g.262.1		12
19.8	odd	6		361.3.f.e.127.2		12
19.9	even	9		361.3.d.d.69.2		12
19.10	odd	18		361.3.d.f.69.5		12
19.11	even	3		361.3.f.c.127.1		12
19.12	odd	6		19.3.f.a.15.2	yes	12
19.13	odd	18		361.3.b.c.360.9		12
19.14	odd	18		361.3.f.c.307.1		12
19.15	odd	18		361.3.d.d.293.2		12
19.16	even	9		19.3.f.a.14.2	✓	12
19.17	even	9		361.3.f.f.116.1		12
19.18	odd	2		361.3.f.f.333.1		12
57.35	odd	18		171.3.ba.b.109.1		12
57.50	even	6		171.3.ba.b.91.1		12
76.31	even	6		304.3.z.a.129.2		12
76.35	odd	18		304.3.z.a.33.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.14.2	✓	12	19.16	even	9
19.3.f.a.15.2	yes	12	19.12	odd	6
171.3.ba.b.91.1		12	57.50	even	6
171.3.ba.b.109.1		12	57.35	odd	18
304.3.z.a.33.2		12	76.35	odd	18
304.3.z.a.129.2		12	76.31	even	6
361.3.b.c.360.4		12	19.6	even	9
361.3.b.c.360.9		12	19.13	odd	18
361.3.d.d.69.2		12	19.9	even	9
361.3.d.d.293.2		12	19.15	odd	18
361.3.d.f.69.5		12	19.10	odd	18
361.3.d.f.293.5		12	19.4	even	9
361.3.f.b.116.2		12	19.2	odd	18	inner
361.3.f.b.333.2		12	1.1	even	1	trivial
361.3.f.c.127.1		12	19.11	even	3
361.3.f.c.307.1		12	19.14	odd	18
361.3.f.e.127.2		12	19.8	odd	6
361.3.f.e.307.2		12	19.5	even	9
361.3.f.f.116.1		12	19.17	even	9
361.3.f.f.333.1		12	19.18	odd	2
361.3.f.g.262.1		12	19.7	even	3
361.3.f.g.299.1		12	19.3	odd	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.86447 - 0.328757i) q^{2} +(-1.24899 - 1.48849i) q^{3} +(-0.390596 + 0.142165i) q^{4} +(2.62459 + 0.955274i) q^{5} +(-2.81806 - 2.36464i) q^{6} +(-1.20796 + 2.09224i) q^{7} +(-7.23987 + 4.17994i) q^{8} +(0.907209 - 5.14504i) q^{9} +O(q^{10})\)	\(q+(1.86447 - 0.328757i) q^{2} +(-1.24899 - 1.48849i) q^{3} +(-0.390596 + 0.142165i) q^{4} +(2.62459 + 0.955274i) q^{5} +(-2.81806 - 2.36464i) q^{6} +(-1.20796 + 2.09224i) q^{7} +(-7.23987 + 4.17994i) q^{8} +(0.907209 - 5.14504i) q^{9} +(5.20754 + 0.918229i) q^{10} +(-9.60360 - 16.6339i) q^{11} +(0.699463 + 0.403835i) q^{12} +(9.33111 - 11.1204i) q^{13} +(-1.56436 + 4.29805i) q^{14} +(-1.85618 - 5.09982i) q^{15} +(-10.8507 + 9.10481i) q^{16} +(-2.97933 - 16.8966i) q^{17} -9.89103i q^{18} -1.16096 q^{20} +(4.62301 - 0.815162i) q^{21} +(-23.3742 - 27.8562i) q^{22} +(7.16888 - 2.60926i) q^{23} +(15.2644 + 5.55578i) q^{24} +(-13.1752 - 11.0553i) q^{25} +(13.7417 - 23.8013i) q^{26} +(-23.9363 + 13.8196i) q^{27} +(0.174379 - 0.988950i) q^{28} +(8.11247 + 1.43045i) q^{29} +(-5.13740 - 8.89824i) q^{30} +(-5.19837 - 3.00128i) q^{31} +(4.25698 - 5.07328i) q^{32} +(-12.7646 + 35.0706i) q^{33} +(-11.1098 - 30.5238i) q^{34} +(-5.16906 + 4.33736i) q^{35} +(0.377093 + 2.13860i) q^{36} +59.5153i q^{37} -28.2071 q^{39} +(-22.9947 + 4.05459i) q^{40} +(-19.8556 - 23.6630i) q^{41} +(8.35149 - 3.03969i) q^{42} +(-23.0914 - 8.40459i) q^{43} +(6.11589 + 5.13184i) q^{44} +(7.29598 - 12.6370i) q^{45} +(12.5084 - 7.22171i) q^{46} +(12.7064 - 72.0615i) q^{47} +(27.1049 + 4.77932i) q^{48} +(21.5817 + 37.3806i) q^{49} +(-28.1992 - 16.2808i) q^{50} +(-21.4293 + 25.5385i) q^{51} +(-2.06376 + 5.67013i) q^{52} +(9.58675 + 26.3394i) q^{53} +(-40.0853 + 33.6356i) q^{54} +(-9.31560 - 52.8314i) q^{55} -20.1968i q^{56} +15.5957 q^{58} +(9.07508 - 1.60018i) q^{59} +(1.45003 + 1.72808i) q^{60} +(57.9370 - 21.0873i) q^{61} +(-10.6789 - 3.88680i) q^{62} +(9.66879 + 8.11308i) q^{63} +(34.5983 - 59.9260i) q^{64} +(35.1134 - 20.2727i) q^{65} +(-12.2696 + 69.5845i) q^{66} +(-11.8649 - 2.09211i) q^{67} +(3.56583 + 6.17619i) q^{68} +(-12.8378 - 7.41188i) q^{69} +(-8.21163 + 9.78624i) q^{70} +(-13.1537 + 36.1396i) q^{71} +(14.9379 + 41.0415i) q^{72} +(38.9338 - 32.6693i) q^{73} +(19.5660 + 110.965i) q^{74} +33.4191i q^{75} +46.4029 q^{77} +(-52.5913 + 9.27327i) q^{78} +(69.0779 + 82.3239i) q^{79} +(-37.1763 + 13.5311i) q^{80} +(6.28271 + 2.28672i) q^{81} +(-44.7995 - 37.5913i) q^{82} +(-35.6336 + 61.7192i) q^{83} +(-1.68984 + 0.975631i) q^{84} +(8.32138 - 47.1929i) q^{85} +(-45.8164 - 8.07867i) q^{86} +(-8.00321 - 13.8620i) q^{87} +(139.058 + 80.2850i) q^{88} +(5.21087 - 6.21007i) q^{89} +(9.44864 - 25.9599i) q^{90} +(11.9950 + 32.9559i) q^{91} +(-2.42919 + 2.03833i) q^{92} +(2.02535 + 11.4863i) q^{93} -138.534i q^{94} -12.8685 q^{96} +(117.310 - 20.6849i) q^{97} +(52.5276 + 62.5999i) q^{98} +(-94.2946 + 34.3204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 9 q^{3} + 9 q^{4} + 3 q^{5} + 27 q^{6} + 6 q^{7} + 9 q^{8} - 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 + 3 * q^5 + 27 * q^6 + 6 * q^7 + 9 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} - 9 q^{3} + 9 q^{4} + 3 q^{5} + 27 q^{6} + 6 q^{7} + 9 q^{8} - 15 q^{9} + 21 q^{10} - 18 q^{11} - 63 q^{12} - 30 q^{13} - 81 q^{14} + 9 q^{15} - 39 q^{16} + 78 q^{17} - 90 q^{20} + 78 q^{21} - 111 q^{22} + 168 q^{23} + 78 q^{24} + 33 q^{25} + 21 q^{26} + 27 q^{27} - 6 q^{28} + 69 q^{29} + 24 q^{30} - 99 q^{31} - 57 q^{32} + 69 q^{33} + 66 q^{34} - 30 q^{35} + 162 q^{36} - 108 q^{39} + 3 q^{40} - 315 q^{41} + 114 q^{42} - 27 q^{43} + 174 q^{44} - 3 q^{45} + 54 q^{46} + 180 q^{47} - 75 q^{48} - 24 q^{49} - 72 q^{50} + 6 q^{51} - 30 q^{52} + 15 q^{53} - 231 q^{54} - 9 q^{55} - 132 q^{58} + 114 q^{59} + 201 q^{60} - 30 q^{61} + 63 q^{62} - 405 q^{63} + 27 q^{64} - 126 q^{65} - 237 q^{66} + 117 q^{67} - 30 q^{68} - 72 q^{69} + 99 q^{70} - 30 q^{71} + 12 q^{72} + 225 q^{73} - 240 q^{74} + 246 q^{77} - 288 q^{78} + 57 q^{79} - 285 q^{80} - 231 q^{81} + 243 q^{82} - 156 q^{83} - 99 q^{84} + 285 q^{85} - 72 q^{86} + 69 q^{87} + 405 q^{88} - 27 q^{89} - 159 q^{90} - 60 q^{91} - 60 q^{92} - 327 q^{93} + 558 q^{96} - 123 q^{97} + 618 q^{98} - 96 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 + 3 * q^5 + 27 * q^6 + 6 * q^7 + 9 * q^8 - 15 * q^9 + 21 * q^10 - 18 * q^11 - 63 * q^12 - 30 * q^13 - 81 * q^14 + 9 * q^15 - 39 * q^16 + 78 * q^17 - 90 * q^20 + 78 * q^21 - 111 * q^22 + 168 * q^23 + 78 * q^24 + 33 * q^25 + 21 * q^26 + 27 * q^27 - 6 * q^28 + 69 * q^29 + 24 * q^30 - 99 * q^31 - 57 * q^32 + 69 * q^33 + 66 * q^34 - 30 * q^35 + 162 * q^36 - 108 * q^39 + 3 * q^40 - 315 * q^41 + 114 * q^42 - 27 * q^43 + 174 * q^44 - 3 * q^45 + 54 * q^46 + 180 * q^47 - 75 * q^48 - 24 * q^49 - 72 * q^50 + 6 * q^51 - 30 * q^52 + 15 * q^53 - 231 * q^54 - 9 * q^55 - 132 * q^58 + 114 * q^59 + 201 * q^60 - 30 * q^61 + 63 * q^62 - 405 * q^63 + 27 * q^64 - 126 * q^65 - 237 * q^66 + 117 * q^67 - 30 * q^68 - 72 * q^69 + 99 * q^70 - 30 * q^71 + 12 * q^72 + 225 * q^73 - 240 * q^74 + 246 * q^77 - 288 * q^78 + 57 * q^79 - 285 * q^80 - 231 * q^81 + 243 * q^82 - 156 * q^83 - 99 * q^84 + 285 * q^85 - 72 * q^86 + 69 * q^87 + 405 * q^88 - 27 * q^89 - 159 * q^90 - 60 * q^91 - 60 * q^92 - 327 * q^93 + 558 * q^96 - 123 * q^97 + 618 * q^98 - 96 * q^99

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