LMFDB - Embedded newform 550.2.j.c.81.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(81,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("550.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.11
Character	$\chi$	$=$	550.81
Dual form			550.2.j.c.421.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.487764 + 1.50118i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.30223 + 1.81775i) q^{5} +1.57844 q^{6} +(0.881273 + 2.71228i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.411412 - 0.298908i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.487764 + 1.50118i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.30223 + 1.81775i) q^{5} +1.57844 q^{6} +(0.881273 + 2.71228i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.411412 - 0.298908i) q^{9} +(2.13119 - 0.676779i) q^{10} +(-2.46498 + 2.21898i) q^{11} +(0.487764 - 1.50118i) q^{12} +(-2.96732 + 2.15588i) q^{13} +2.85186 q^{14} +(-2.09359 + 2.84152i) q^{15} +(0.309017 + 0.951057i) q^{16} -6.87947 q^{17} +(-0.157145 - 0.483644i) q^{18} +(4.74735 - 3.44915i) q^{19} +(0.0149191 - 2.23602i) q^{20} +(-3.64178 + 2.64591i) q^{21} +(1.34865 + 3.03004i) q^{22} +(-1.83472 - 5.64669i) q^{23} +(-1.27698 - 0.927783i) q^{24} +(-1.60840 + 4.73424i) q^{25} +(1.13341 + 3.48829i) q^{26} +(4.48034 + 3.25516i) q^{27} +(0.881273 - 2.71228i) q^{28} +(5.75878 + 4.18400i) q^{29} +(2.05549 + 2.86920i) q^{30} +(-1.26511 - 3.89362i) q^{31} +1.00000 q^{32} +(-4.53342 - 2.61806i) q^{33} +(-2.12587 + 6.54276i) q^{34} +(-3.78262 + 5.13394i) q^{35} -0.508533 q^{36} +8.70369 q^{37} +(-1.81333 - 5.58084i) q^{38} +(-4.68373 - 3.40293i) q^{39} +(-2.12197 - 0.705157i) q^{40} +(6.74324 + 4.89925i) q^{41} +(1.39103 + 4.28116i) q^{42} +1.18484 q^{43} +(3.29850 - 0.346309i) q^{44} +(1.07909 + 0.358595i) q^{45} -5.93728 q^{46} +(-0.00809888 - 0.0249258i) q^{47} +(-1.27698 + 0.927783i) q^{48} +(-0.916696 + 0.666019i) q^{49} +(4.00551 + 2.99264i) q^{50} +(-3.35556 - 10.3273i) q^{51} +3.66781 q^{52} +0.208818 q^{53} +(4.48034 - 3.25516i) q^{54} +(-7.24351 - 1.59110i) q^{55} +(-2.30720 - 1.67628i) q^{56} +(7.49339 + 5.44427i) q^{57} +(5.75878 - 4.18400i) q^{58} +6.99319 q^{59} +(3.36395 - 1.06825i) q^{60} +(5.41619 + 3.93510i) q^{61} -4.09399 q^{62} +(1.17329 + 0.852444i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-7.78297 - 2.58638i) q^{65} +(-3.89082 + 3.50252i) q^{66} +(-8.26158 - 6.00239i) q^{67} +(5.56561 + 4.04365i) q^{68} +(7.58181 - 5.50851i) q^{69} +(3.71377 + 5.18395i) q^{70} +(3.69399 - 11.3689i) q^{71} +(-0.157145 + 0.483644i) q^{72} +(-4.30682 + 3.12909i) q^{73} +(2.68959 - 8.27770i) q^{74} +(-7.89149 - 0.105311i) q^{75} -5.86804 q^{76} +(-8.19081 - 4.73020i) q^{77} +(-4.68373 + 3.40293i) q^{78} -3.42003 q^{79} +(-1.32637 + 1.80021i) q^{80} +(-2.22980 + 6.86263i) q^{81} +(6.74324 - 4.89925i) q^{82} -0.606929 q^{83} +4.50148 q^{84} +(-8.95864 - 12.5051i) q^{85} +(0.366135 - 1.12685i) q^{86} +(-3.47202 + 10.6858i) q^{87} +(0.689932 - 3.24407i) q^{88} +(-2.24065 - 6.89600i) q^{89} +(0.674502 - 0.915465i) q^{90} +(-8.46237 - 6.14827i) q^{91} +(-1.83472 + 5.64669i) q^{92} +(5.22796 - 3.79834i) q^{93} -0.0262085 q^{94} +(12.4518 + 4.13789i) q^{95} +(0.487764 + 1.50118i) q^{96} +17.1818 q^{97} +(0.350147 + 1.07764i) q^{98} +(-0.350853 + 1.64972i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 15 q^{2} + q^{3} - 15 q^{4} + 6 q^{6} - 3 q^{7} - 15 q^{8} - 12 q^{9}+O(q^{10}) $ 60 * q - 15 * q^2 + q^3 - 15 * q^4 + 6 * q^6 - 3 * q^7 - 15 * q^8 - 12 * q^9	\( 60 q - 15 q^{2} + q^{3} - 15 q^{4} + 6 q^{6} - 3 q^{7} - 15 q^{8} - 12 q^{9} - 5 q^{10} - 3 q^{11} + q^{12} - 8 q^{13} + 12 q^{14} - 3 q^{15} - 15 q^{16} + 6 q^{17} - 17 q^{18} - 22 q^{19} + 10 q^{20} - 4 q^{21} + 7 q^{22} - 3 q^{23} - 4 q^{24} + 18 q^{25} + 12 q^{26} - 8 q^{27} - 3 q^{28} - 22 q^{29} - 8 q^{30} + 15 q^{31} + 60 q^{32} + 25 q^{33} + q^{34} + 11 q^{35} + 58 q^{36} + 94 q^{37} + 3 q^{38} - 12 q^{39} - 5 q^{40} - 11 q^{41} - 19 q^{42} + 40 q^{43} + 7 q^{44} - 20 q^{45} + 2 q^{46} - 24 q^{47} - 4 q^{48} - 30 q^{49} - 27 q^{50} - 48 q^{51} - 8 q^{52} - 14 q^{53} - 8 q^{54} - 7 q^{55} - 3 q^{56} + 30 q^{57} - 22 q^{58} - 42 q^{59} + 12 q^{60} + 19 q^{61} - 20 q^{62} - 24 q^{63} - 15 q^{64} - 7 q^{65} + 10 q^{66} - 40 q^{67} - 4 q^{68} - 2 q^{69} - 19 q^{70} + 19 q^{71} - 17 q^{72} - 16 q^{73} - 11 q^{74} + 25 q^{75} + 38 q^{76} - 23 q^{77} - 12 q^{78} + 70 q^{79} - 86 q^{81} - 11 q^{82} - 14 q^{83} + 46 q^{84} - 31 q^{85} + 68 q^{87} - 8 q^{88} + q^{89} + 45 q^{90} - 25 q^{91} - 3 q^{92} - 40 q^{93} + 66 q^{94} + 19 q^{95} + q^{96} + 66 q^{97} - 30 q^{98} + 21 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 + q^3 - 15 * q^4 + 6 * q^6 - 3 * q^7 - 15 * q^8 - 12 * q^9 - 5 * q^10 - 3 * q^11 + q^12 - 8 * q^13 + 12 * q^14 - 3 * q^15 - 15 * q^16 + 6 * q^17 - 17 * q^18 - 22 * q^19 + 10 * q^20 - 4 * q^21 + 7 * q^22 - 3 * q^23 - 4 * q^24 + 18 * q^25 + 12 * q^26 - 8 * q^27 - 3 * q^28 - 22 * q^29 - 8 * q^30 + 15 * q^31 + 60 * q^32 + 25 * q^33 + q^34 + 11 * q^35 + 58 * q^36 + 94 * q^37 + 3 * q^38 - 12 * q^39 - 5 * q^40 - 11 * q^41 - 19 * q^42 + 40 * q^43 + 7 * q^44 - 20 * q^45 + 2 * q^46 - 24 * q^47 - 4 * q^48 - 30 * q^49 - 27 * q^50 - 48 * q^51 - 8 * q^52 - 14 * q^53 - 8 * q^54 - 7 * q^55 - 3 * q^56 + 30 * q^57 - 22 * q^58 - 42 * q^59 + 12 * q^60 + 19 * q^61 - 20 * q^62 - 24 * q^63 - 15 * q^64 - 7 * q^65 + 10 * q^66 - 40 * q^67 - 4 * q^68 - 2 * q^69 - 19 * q^70 + 19 * q^71 - 17 * q^72 - 16 * q^73 - 11 * q^74 + 25 * q^75 + 38 * q^76 - 23 * q^77 - 12 * q^78 + 70 * q^79 - 86 * q^81 - 11 * q^82 - 14 * q^83 + 46 * q^84 - 31 * q^85 + 68 * q^87 - 8 * q^88 + q^89 + 45 * q^90 - 25 * q^91 - 3 * q^92 - 40 * q^93 + 66 * q^94 + 19 * q^95 + q^96 + 66 * q^97 - 30 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.487764	+	1.50118i	0.281611	+	0.866709i	0.987394	+	0.158281i	$0.0505952\pi$
$3$	0.487764	+	1.50118i	0.281611	+	0.866709i	−0.705783	+	0.708428i	$0.749405\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.30223	+	1.81775i	0.582374	+	0.812921i
$5$	1.30223	+	1.81775i	0.582374	+	0.812921i
$6$	1.57844			0.644395
$7$	0.881273	+	2.71228i	0.333090	+	1.02515i	0.967655	+	0.252276i	$0.0811791\pi$
$7$	0.881273	+	2.71228i	0.333090	+	1.02515i	−0.634566	+	0.772869i	$0.718821\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.411412	−	0.298908i	0.137137	−	0.0996361i
$10$	2.13119	−	0.676779i	0.673941	−	0.214016i
$11$	−2.46498	+	2.21898i	−0.743220	+	0.669047i
$11$	−2.46498	+	2.21898i	−0.743220	+	0.669047i
$12$	0.487764	−	1.50118i	0.140805	−	0.433354i
$13$	−2.96732	+	2.15588i	−0.822986	+	0.597934i	−0.917566	−	0.397583i	$-0.869849\pi$
$13$	−2.96732	+	2.15588i	−0.822986	+	0.597934i	0.0945805	+	0.995517i	$0.469849\pi$
$14$	2.85186			0.762191
$15$	−2.09359	+	2.84152i	−0.540563	+	0.733676i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−6.87947			−1.66852			−0.834258	−	0.551374i	$-0.814104\pi$
$17$	−6.87947			−1.66852			−0.834258	+	0.551374i	$0.814104\pi$
$18$	−0.157145	−	0.483644i	−0.0370395	−	0.113996i
$19$	4.74735	−	3.44915i	1.08912	−	0.791289i	0.109866	−	0.993946i	$-0.464958\pi$
$19$	4.74735	−	3.44915i	1.08912	−	0.791289i	0.979250	+	0.202657i	$0.0649577\pi$
$20$	0.0149191	−	2.23602i	0.00333601	−	0.499989i
$21$	−3.64178	+	2.64591i	−0.794701	+	0.577384i
$22$	1.34865	+	3.03004i	0.287533	+	0.646007i
$23$	−1.83472	−	5.64669i	−0.382566	−	1.17742i	−0.938231	−	0.346010i	$-0.887536\pi$
$23$	−1.83472	−	5.64669i	−0.382566	−	1.17742i	0.555665	−	0.831406i	$-0.312464\pi$
$24$	−1.27698	−	0.927783i	−0.260663	−	0.189383i
$25$	−1.60840	+	4.73424i	−0.321680	+	0.946848i
$26$	1.13341	+	3.48829i	0.222281	+	0.684110i
$27$	4.48034	+	3.25516i	0.862241	+	0.626455i
$28$	0.881273	−	2.71228i	0.166545	−	0.512573i
$29$	5.75878	+	4.18400i	1.06938	+	0.776949i	0.975800	−	0.218663i	$-0.0701697\pi$
$29$	5.75878	+	4.18400i	1.06938	+	0.776949i	0.0935776	+	0.995612i	$0.470170\pi$
$30$	2.05549	+	2.86920i	0.375279	+	0.523842i
$31$	−1.26511	−	3.89362i	−0.227221	−	0.699314i	−0.998059	−	0.0622826i	$-0.980162\pi$
$31$	−1.26511	−	3.89362i	−0.227221	−	0.699314i	0.770838	−	0.637032i	$-0.219838\pi$
$32$	1.00000			0.176777
$33$	−4.53342	−	2.61806i	−0.789168	−	0.455745i
$34$	−2.12587	+	6.54276i	−0.364584	+	1.12207i
$35$	−3.78262	+	5.13394i	−0.639379	+	0.867794i
$36$	−0.508533			−0.0847555
$37$	8.70369			1.43088			0.715439	−	0.698675i	$-0.246227\pi$
$37$	8.70369			1.43088			0.715439	+	0.698675i	$0.246227\pi$
$38$	−1.81333	−	5.58084i	−0.294160	−	0.905332i
$39$	−4.68373	−	3.40293i	−0.749996	−	0.544904i
$40$	−2.12197	−	0.705157i	−0.335513	−	0.111495i
$41$	6.74324	+	4.89925i	1.05312	+	0.765134i	0.972803	−	0.231636i	$-0.0744077\pi$
$41$	6.74324	+	4.89925i	1.05312	+	0.765134i	0.0803140	+	0.996770i	$0.474408\pi$
$42$	1.39103	+	4.28116i	0.214641	+	0.660598i
$43$	1.18484			0.180686			0.0903431	−	0.995911i	$-0.471204\pi$
$43$	1.18484			0.180686			0.0903431	+	0.995911i	$0.471204\pi$
$44$	3.29850	−	0.346309i	0.497267	−	0.0522080i
$45$	1.07909	+	0.358595i	0.160861	+	0.0534562i
$46$	−5.93728			−0.875405
$47$	−0.00809888	−	0.0249258i	−0.00118134	−	0.00363580i	0.950464	−	0.310834i	$-0.100608\pi$
$47$	−0.00809888	−	0.0249258i	−0.00118134	−	0.00363580i	−0.951645	+	0.307199i	$0.900608\pi$
$48$	−1.27698	+	0.927783i	−0.184317	+	0.133914i
$49$	−0.916696	+	0.666019i	−0.130957	+	0.0951455i
$50$	4.00551	+	2.99264i	0.566464	+	0.423223i
$51$	−3.35556	−	10.3273i	−0.469872	−	1.44612i
$52$	3.66781			0.508633
$53$	0.208818			0.0286834			0.0143417	−	0.999897i	$-0.495435\pi$
$53$	0.208818			0.0286834			0.0143417	+	0.999897i	$0.495435\pi$
$54$	4.48034	−	3.25516i	0.609697	−	0.442971i
$55$	−7.24351	−	1.59110i	−0.976714	−	0.214544i
$56$	−2.30720	−	1.67628i	−0.308313	−	0.224002i
$57$	7.49339	+	5.44427i	0.992524	+	0.721111i
$58$	5.75878	−	4.18400i	0.756164	−	0.549386i
$59$	6.99319			0.910436			0.455218	−	0.890380i	$-0.349561\pi$
$59$	6.99319			0.910436			0.455218	+	0.890380i	$0.349561\pi$
$60$	3.36395	−	1.06825i	0.434284	−	0.137911i
$61$	5.41619	+	3.93510i	0.693473	+	0.503837i	0.877800	−	0.479028i	$-0.159011\pi$
$61$	5.41619	+	3.93510i	0.693473	+	0.503837i	−0.184327	+	0.982865i	$0.559011\pi$
$62$	−4.09399			−0.519938
$63$	1.17329	+	0.852444i	0.147820	+	0.107398i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−7.78297	−	2.58638i	−0.965359	−	0.320801i
$66$	−3.89082	+	3.50252i	−0.478927	+	0.431130i
$67$	−8.26158	−	6.00239i	−1.00931	−	0.733309i	−0.0452478	−	0.998976i	$-0.514408\pi$
$67$	−8.26158	−	6.00239i	−1.00931	−	0.733309i	−0.964065	+	0.265667i	$0.914408\pi$
$68$	5.56561	+	4.04365i	0.674929	+	0.490365i
$69$	7.58181	−	5.50851i	0.912743	−	0.663147i
$70$	3.71377	+	5.18395i	0.443881	+	0.619601i
$71$	3.69399	−	11.3689i	0.438396	−	1.34924i	−0.451171	−	0.892438i	$-0.648994\pi$
$71$	3.69399	−	11.3689i	0.438396	−	1.34924i	0.889567	−	0.456806i	$-0.151006\pi$
$72$	−0.157145	+	0.483644i	−0.0185198	+	0.0569979i
$73$	−4.30682	+	3.12909i	−0.504075	+	0.366232i	−0.810571	−	0.585640i	$-0.800843\pi$
$73$	−4.30682	+	3.12909i	−0.504075	+	0.366232i	0.306496	+	0.951872i	$0.400843\pi$
$74$	2.68959	−	8.27770i	0.312658	−	0.962264i
$75$	−7.89149	−	0.105311i	−0.911231	−	0.0121603i
$76$	−5.86804			−0.673111
$77$	−8.19081	−	4.73020i	−0.933429	−	0.539056i
$78$	−4.68373	+	3.40293i	−0.530328	+	0.385306i
$79$	−3.42003			−0.384783			−0.192392	−	0.981318i	$-0.561624\pi$
$79$	−3.42003			−0.384783			−0.192392	+	0.981318i	$0.561624\pi$
$80$	−1.32637	+	1.80021i	−0.148292	+	0.201269i
$81$	−2.22980	+	6.86263i	−0.247756	+	0.762514i
$82$	6.74324	−	4.89925i	0.744666	−	0.541031i
$83$	−0.606929			−0.0666191			−0.0333096	−	0.999445i	$-0.510605\pi$
$83$	−0.606929			−0.0666191			−0.0333096	+	0.999445i	$0.510605\pi$
$84$	4.50148			0.491152
$85$	−8.95864	−	12.5051i	−0.971701	−	1.35637i
$86$	0.366135	−	1.12685i	0.0394814	−	0.121511i
$87$	−3.47202	+	10.6858i	−0.372240	+	1.14564i
$88$	0.689932	−	3.24407i	0.0735470	−	0.345819i
$89$	−2.24065	−	6.89600i	−0.237508	−	0.730974i	−0.996779	−	0.0801995i	$-0.974444\pi$
$89$	−2.24065	−	6.89600i	−0.237508	−	0.730974i	0.759271	−	0.650775i	$-0.225556\pi$
$90$	0.674502	−	0.915465i	0.0710988	−	0.0964985i
$91$	−8.46237	−	6.14827i	−0.887097	−	0.644514i
$92$	−1.83472	+	5.64669i	−0.191283	+	0.588708i
$93$	5.22796	−	3.79834i	0.542114	−	0.393869i
$94$	−0.0262085			−0.00270320
$95$	12.4518	+	4.13789i	1.27753	+	0.424539i
$96$	0.487764	+	1.50118i	0.0497822	+	0.153214i
$97$	17.1818			1.74455			0.872276	−	0.489014i	$-0.162643\pi$
$97$	17.1818			1.74455			0.872276	+	0.489014i	$0.162643\pi$
$98$	0.350147	+	1.07764i	0.0353702	+	0.108858i
$99$	−0.350853	+	1.64972i	−0.0352621	+	0.165803i
$100$	4.08394	−	2.88469i	0.408394	−	0.288469i
$101$	−1.65824	−	1.20478i	−0.165001	−	0.119880i	0.502221	−	0.864739i	$-0.332516\pi$
$101$	−1.65824	−	1.20478i	−0.165001	−	0.119880i	−0.667221	+	0.744859i	$0.732516\pi$
$102$	−10.8588			−1.07518
$103$	0.745189	+	0.541411i	0.0734256	+	0.0533468i	0.623893	−	0.781510i	$-0.285550\pi$
$103$	0.745189	+	0.541411i	0.0734256	+	0.0533468i	−0.550467	+	0.834857i	$0.685550\pi$
$104$	1.13341	−	3.48829i	0.111140	−	0.342055i
$105$	−9.55201	−	3.17425i	−0.932181	−	0.309775i
$106$	0.0645284	−	0.198598i	0.00626755	−	0.0192895i
$107$	−2.28278	+	7.02567i	−0.220685	+	0.679198i	0.778016	+	0.628244i	$0.216226\pi$
$107$	−2.28278	+	7.02567i	−0.220685	+	0.679198i	−0.998701	+	0.0509536i	$0.983774\pi$
$108$	−1.71134	−	5.26695i	−0.164673	−	0.506813i
$109$	4.06717	−	12.5175i	0.389565	−	1.19896i	−0.543550	−	0.839377i	$-0.682920\pi$
$109$	4.06717	−	12.5175i	0.389565	−	1.19896i	0.933114	−	0.359580i	$-0.117080\pi$
$110$	−3.75159	+	6.39731i	−0.357700	+	0.609959i
$111$	4.24535	+	13.0658i	0.402951	+	1.24015i
$112$	−2.30720	+	1.67628i	−0.218010	+	0.158394i
$113$	−5.59556	−	4.06541i	−0.526386	−	0.382442i	0.292618	−	0.956229i	$-0.405474\pi$
$113$	−5.59556	−	4.06541i	−0.526386	−	0.382442i	−0.819004	+	0.573788i	$0.805474\pi$
$114$	7.49339	−	5.44427i	0.701821	−	0.509903i
$115$	7.87503	−	10.6883i	0.734350	−	0.996693i
$116$	−2.19966	−	6.76985i	−0.204233	−	0.628565i
$117$	−0.576378	+	1.77391i	−0.0532862	+	0.163998i
$118$	2.16102	−	6.65092i	0.198938	−	0.612267i
$119$	−6.06269	−	18.6590i	−0.555766	−	1.71047i
$120$	0.0235488	−	3.52942i	0.00214970	−	0.322190i
$121$	1.15229	−	10.9395i	0.104753	−	0.994498i
$122$	5.41619	−	3.93510i	0.490359	−	0.356267i
$123$	−4.06556	+	12.5125i	−0.366579	+	1.12822i
$124$	−1.26511	+	3.89362i	−0.113611	+	0.349657i
$125$	−10.7002	+	3.24140i	−0.957051	+	0.289920i
$126$	1.17329	−	0.852444i	0.104525	−	0.0759417i
$127$	11.6167	+	8.44006i	1.03082	+	0.748934i	0.968472	−	0.249121i	$-0.0801415\pi$
$127$	11.6167	+	8.44006i	1.03082	+	0.748934i	0.0623467	+	0.998055i	$0.480142\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	0.577922	+	1.77866i	0.0508832	+	0.156602i
$130$	−4.86486	+	6.60281i	−0.426677	+	0.579105i
$131$	−8.55657	−	6.21671i	−0.747591	−	0.543157i	0.147488	−	0.989064i	$-0.452881\pi$
$131$	−8.55657	−	6.21671i	−0.747591	−	0.543157i	−0.895079	+	0.445907i	$0.852881\pi$
$132$	2.12876	+	4.78273i	0.185285	+	0.416283i
$133$	13.5388	+	9.83649i	1.17396	+	0.852932i
$134$	−8.26158	+	6.00239i	−0.713692	+	0.518527i
$135$	−0.0826219	+	12.3831i	−0.00711096	+	1.06577i
$136$	5.56561	−	4.04365i	0.477247	−	0.346740i
$137$	3.54196	+	10.9010i	0.302610	+	0.931338i	0.980558	+	0.196228i	$0.0628694\pi$
$137$	3.54196	+	10.9010i	0.302610	+	0.931338i	−0.677948	+	0.735110i	$0.737131\pi$
$138$	−2.89600	−	8.91296i	−0.246523	−	0.758721i
$139$	−6.77687	+	4.92369i	−0.574807	+	0.417622i	−0.836848	−	0.547435i	$-0.815604\pi$
$139$	−6.77687	+	4.92369i	−0.574807	+	0.417622i	0.262041	+	0.965057i	$0.415604\pi$
$140$	6.07785	−	1.93008i	0.513672	−	0.163121i
$141$	0.0334678	−	0.0243158i	0.00281850	−	0.00204776i
$142$	−9.67099	−	7.02638i	−0.811571	−	0.589641i
$143$	2.53054	−	11.8986i	0.211614	−	0.995013i
$144$	0.411412	+	0.298908i	0.0342843	+	0.0249090i
$145$	−0.106198	+	15.9165i	−0.00881923	+	1.32179i
$146$	1.64506	+	5.06297i	0.136146	+	0.419014i
$147$	−1.44695	−	1.05127i	−0.119342	−	0.0867072i
$148$	−7.04144	−	5.11590i	−0.578802	−	0.420525i
$149$	−18.2874	+	13.2866i	−1.49816	+	1.08848i	−0.527056	+	0.849831i	$0.676704\pi$
$149$	−18.2874	+	13.2866i	−1.49816	+	1.08848i	−0.971106	+	0.238648i	$0.923296\pi$
$150$	−2.53876	+	7.47271i	−0.207289	+	0.610144i
$151$	1.88170	−	5.79129i	0.153131	−	0.471288i	−0.844836	−	0.535026i	$-0.820302\pi$
$151$	1.88170	−	5.79129i	0.153131	−	0.471288i	0.997967	+	0.0637373i	$0.0203020\pi$
$152$	−1.81333	+	5.58084i	−0.147080	+	0.452666i
$153$	−2.83029	+	2.05633i	−0.228816	+	0.166244i
$154$	−7.02978	+	6.32821i	−0.566476	+	0.509942i
$155$	5.43014	−	7.37004i	0.436159	−	0.591976i
$156$	1.78902	+	5.50605i	0.143237	+	0.440837i
$157$	6.70064	−	20.6225i	0.534769	−	1.64585i	−0.209378	−	0.977835i	$-0.567144\pi$
$157$	6.70064	−	20.6225i	0.534769	−	1.64585i	0.744147	−	0.668016i	$-0.232856\pi$
$158$	−1.05685	+	3.25264i	−0.0840782	+	0.258766i
$159$	0.101854	+	0.313475i	0.00807756	+	0.0248602i
$160$	1.30223	+	1.81775i	0.102950	+	0.143705i
$161$	13.6985	−	9.95255i	1.07959	−	0.784371i
$162$	5.83770	+	4.24134i	0.458653	+	0.333231i
$163$	−8.74562	+	6.35407i	−0.685010	+	0.497689i	−0.875016	−	0.484094i	$-0.839149\pi$
$163$	−8.74562	+	6.35407i	−0.685010	+	0.497689i	0.190006	+	0.981783i	$0.439149\pi$
$164$	−2.57569	−	7.92715i	−0.201127	−	0.619006i
$165$	−1.14459	−	11.6499i	−0.0891064	−	0.906945i
$166$	−0.187551	+	0.577224i	−0.0145568	+	0.0448013i
$167$	−3.82062	−	11.7586i	−0.295648	−	0.909912i	−0.983003	−	0.183590i	$-0.941228\pi$
$167$	−3.82062	−	11.7586i	−0.295648	−	0.909912i	0.687355	−	0.726322i	$-0.258772\pi$
$168$	1.39103	−	4.28116i	0.107321	−	0.330299i
$169$	0.139922	−	0.430636i	0.0107633	−	0.0331259i
$170$	−14.6615	+	4.65588i	−1.12448	+	0.357090i
$171$	0.922136	−	2.83804i	0.0705175	−	0.217030i
$172$	−0.958554	−	0.696431i	−0.0730891	−	0.0531023i
$173$	−8.11283			−0.616807			−0.308404	−	0.951256i	$-0.599795\pi$
$173$	−8.11283			−0.616807			−0.308404	+	0.951256i	$0.599795\pi$
$174$	9.08987	+	6.60418i	0.689101	+	0.500661i
$175$	−14.2580	−	0.190272i	−1.07781	−	0.0143832i
$176$	−2.87209	−	1.65864i	−0.216492	−	0.125024i
$177$	3.41103	+	10.4981i	0.256389	+	0.789083i
$178$	−7.25088			−0.543476
$179$	−3.51260	−	10.8107i	−0.262544	−	0.808028i	−0.992249	−	0.124265i	$-0.960343\pi$
$179$	−3.51260	−	10.8107i	−0.262544	−	0.808028i	0.729705	−	0.683762i	$-0.239657\pi$
$180$	−0.662226	−	0.924384i	−0.0493594	−	0.0688995i
$181$	9.52714			0.708147			0.354073	−	0.935218i	$-0.384796\pi$
$181$	9.52714			0.708147			0.354073	+	0.935218i	$0.384796\pi$
$182$	−8.46237	+	6.14827i	−0.627273	+	0.455740i
$183$	−3.26548	+	10.0501i	−0.241391	+	0.742925i
$184$	4.80336	+	3.48985i	0.354109	+	0.257275i
$185$	11.3342	+	15.8211i	0.833307	+	1.16319i
$186$	−1.99690	−	6.14584i	−0.146420	−	0.450635i
$187$	16.9578	−	15.2654i	1.24008	−	1.11632i
$188$	−0.00809888	+	0.0249258i	−0.000590671	+	0.00181790i
$189$	−4.88049	+	15.0206i	−0.355003	+	1.09259i
$190$	7.78319	−	10.5637i	0.564652	−	0.766371i
$191$	−23.7497			−1.71847			−0.859235	−	0.511581i	$-0.829060\pi$
$191$	−23.7497			−1.71847			−0.859235	+	0.511581i	$0.829060\pi$
$192$	1.57844			0.113914
$193$	−21.9218	+	15.9271i	−1.57797	+	1.14646i	−0.658985	+	0.752157i	$0.729014\pi$
$193$	−21.9218	+	15.9271i	−1.57797	+	1.14646i	−0.918981	+	0.394302i	$0.870986\pi$
$194$	5.30948	−	16.3409i	0.381199	−	1.17321i
$195$	0.0863726	−	12.9452i	0.00618527	−	0.927026i
$196$	1.13310			0.0809356
$197$	−0.516992	+	0.375616i	−0.0368341	+	0.0267616i	−0.606050	−	0.795427i	$-0.707247\pi$
$197$	−0.516992	+	0.375616i	−0.0368341	+	0.0267616i	0.569216	+	0.822188i	$0.307247\pi$
$198$	1.46055	+	0.843472i	0.103797	+	0.0599429i
$199$	16.5514			1.17330			0.586648	−	0.809842i	$-0.300447\pi$
$199$	16.5514			1.17330			0.586648	+	0.809842i	$0.300447\pi$
$200$	−1.48149	−	4.77548i	−0.104757	−	0.337677i
$201$	4.98099	−	15.3299i	0.351332	−	1.08129i
$202$	−1.65824	+	1.20478i	−0.116673	+	0.0847680i
$203$	−6.27311	+	19.3066i	−0.440286	+	1.35506i
$204$	−3.35556	+	10.3273i	−0.234936	+	0.723059i
$205$	−0.124352	+	18.6374i	−0.00868512	+	1.30169i
$206$	0.745189	−	0.541411i	0.0519197	−	0.0377219i
$207$	−2.44267	−	1.77470i	−0.169777	−	0.123350i
$208$	−2.96732	−	2.15588i	−0.205746	−	0.149484i
$209$	−4.04855	+	19.0364i	−0.280044	+	1.31677i
$210$	−5.97062	+	8.10360i	−0.412012	+	0.559202i
$211$	4.30249	−	13.2417i	0.296196	−	0.911597i	−0.686621	−	0.727015i	$-0.740907\pi$
$211$	4.30249	−	13.2417i	0.296196	−	0.911597i	0.982817	−	0.184582i	$-0.0590930\pi$
$212$	−0.168938	−	0.122740i	−0.0116027	−	0.00842984i
$213$	18.8686			1.29286
$214$	5.97640	+	4.34211i	0.408538	+	0.296820i
$215$	1.54293	+	2.15374i	0.105227	+	0.146884i
$216$	−5.53800			−0.376813
$217$	9.44567	−	6.86268i	0.641214	−	0.465869i
$218$	−10.6480	−	7.73622i	−0.721174	−	0.523963i
$219$	−6.79804	−	4.93907i	−0.459369	−	0.333751i
$220$	4.92490	+	5.54485i	0.332036	+	0.373834i
$221$	20.4136	−	14.8313i	1.37316	−	0.997663i
$222$	13.7382			0.922050
$223$	−2.32765			−0.155871			−0.0779355	−	0.996958i	$-0.524833\pi$
$223$	−2.32765			−0.155871			−0.0779355	+	0.996958i	$0.524833\pi$
$224$	0.881273	+	2.71228i	0.0588825	+	0.181222i
$225$	0.753389	+	2.42849i	0.0502259	+	0.161899i
$226$	−5.59556	+	4.06541i	−0.372211	+	0.270427i
$227$	3.22815	−	2.34539i	0.214260	−	0.155669i	−0.475479	−	0.879727i	$-0.657725\pi$
$227$	3.22815	−	2.34539i	0.214260	−	0.155669i	0.689739	+	0.724058i	$0.257725\pi$
$228$	−2.86222	−	8.80901i	−0.189555	−	0.583391i
$229$	16.5012			1.09043			0.545214	−	0.838297i	$-0.316449\pi$
$229$	16.5012			1.09043			0.545214	+	0.838297i	$0.316449\pi$
$230$	−7.73170	−	10.7925i	−0.509813	−	0.711635i
$231$	3.10572	−	14.6031i	0.204341	−	0.960815i
$232$	−7.11824			−0.467335
$233$	−2.87096	−	8.83592i	−0.188083	−	0.578860i	0.811905	−	0.583790i	$-0.198431\pi$
$233$	−2.87096	−	8.83592i	−0.188083	−	0.578860i	−0.999988	+	0.00492957i	$0.998431\pi$
$234$	1.50898	+	1.09634i	0.0986450	+	0.0716698i
$235$	0.0347621	−	0.0471808i	0.00226763	−	0.00307773i
$236$	−5.65761	−	4.11050i	−0.368279	−	0.267570i
$237$	−1.66817	−	5.13409i	−0.108359	−	0.333495i
$238$	−19.6193			−1.27173
$239$	−8.44262			−0.546107			−0.273054	−	0.961999i	$-0.588034\pi$
$239$	−8.44262			−0.546107			−0.273054	+	0.961999i	$0.588034\pi$
$240$	−3.34940	−	1.11305i	−0.216203	−	0.0718468i
$241$	3.68366	−	11.3371i	0.237285	−	0.730289i	−0.759525	−	0.650478i	$-0.774569\pi$
$241$	3.68366	−	11.3371i	0.237285	−	0.730289i	0.996810	−	0.0798104i	$-0.0254315\pi$
$242$	−10.0480	−	4.47637i	−0.645909	−	0.287752i
$243$	5.22432			0.335140
$244$	−2.06880	−	6.36712i	−0.132441	−	0.407613i
$245$	−2.40440	−	0.799012i	−0.153612	−	0.0510470i
$246$	10.6438	+	7.73316i	0.678623	+	0.493048i
$247$	−6.65093	+	20.4694i	−0.423188	+	1.30244i
$248$	3.31211	+	2.40639i	0.210319	+	0.152806i
$249$	−0.296038	−	0.911112i	−0.0187607	−	0.0577394i
$250$	−0.223773	+	11.1781i	−0.0141526	+	0.706965i
$251$	7.18870	+	5.22289i	0.453747	+	0.329666i	0.791073	−	0.611721i	$-0.209523\pi$
$251$	7.18870	+	5.22289i	0.453747	+	0.329666i	−0.337327	+	0.941388i	$0.609523\pi$
$252$	−0.448156	−	1.37928i	−0.0282312	−	0.0868867i
$253$	17.0524	+	9.84780i	1.07208	+	0.619126i
$254$	11.6167	−	8.44006i	0.728899	−	0.529576i
$255$	14.4028	−	19.5481i	0.901938	−	1.22415i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	8.79561	+	27.0701i	0.548655	+	1.68859i	0.712137	+	0.702040i	$0.247727\pi$
$257$	8.79561	+	27.0701i	0.548655	+	1.68859i	−0.163482	+	0.986546i	$0.552273\pi$
$258$	1.87019			0.116433
$259$	7.67033	+	23.6068i	0.476611	+	1.46686i
$260$	4.77632	+	6.66714i	0.296215	+	0.413478i
$261$	3.61986			0.224064
$262$	−8.55657	+	6.21671i	−0.528627	+	0.384070i
$263$	−5.99185	+	18.4410i	−0.369473	+	1.13712i	0.577659	+	0.816278i	$0.303967\pi$
$263$	−5.99185	+	18.4410i	−0.369473	+	1.13712i	−0.947132	+	0.320844i	$0.896033\pi$
$264$	5.20647	−	0.546627i	0.320436	−	0.0336426i
$265$	0.271929	+	0.379579i	0.0167045	+	0.0233173i
$266$	13.5388	−	9.83649i	0.830115	−	0.603114i
$267$	9.25925	−	6.72724i	0.566657	−	0.411700i
$268$	3.15564	+	9.71207i	0.192762	+	0.593259i
$269$	−5.32222			−0.324502			−0.162251	−	0.986750i	$-0.551875\pi$
$269$	−5.32222			−0.324502			−0.162251	+	0.986750i	$0.551875\pi$
$270$	11.7515	+	3.90516i	0.715172	+	0.237660i
$271$	−3.06197	−	2.22465i	−0.186002	−	0.135138i	0.490888	−	0.871223i	$-0.336673\pi$
$271$	−3.06197	−	2.22465i	−0.186002	−	0.135138i	−0.676889	+	0.736085i	$0.736673\pi$
$272$	−2.12587	−	6.54276i	−0.128900	−	0.396713i
$273$	5.10204	−	15.7025i	0.308790	−	0.950357i
$274$	11.4620			0.692446
$275$	−6.54049	−	15.2388i	−0.394406	−	0.918936i
$276$	−9.37164			−0.564106
$277$	−3.02840	+	9.32044i	−0.181959	+	0.560011i	−0.999883	−	0.0153150i	$-0.995125\pi$
$277$	−3.02840	+	9.32044i	−0.181959	+	0.560011i	0.817924	+	0.575326i	$0.195125\pi$
$278$	2.58854	+	7.96669i	0.155250	+	0.477810i
$279$	−1.68432	−	1.22373i	−0.100837	−	0.0732627i
$280$	0.0425471	−	6.37681i	0.00254268	−	0.381087i
$281$	31.2553			1.86453			0.932267	−	0.361770i	$-0.117827\pi$
$281$	31.2553			1.86453			0.932267	+	0.361770i	$0.117827\pi$
$282$	−0.0127836	−	0.0393438i	−0.000761251	−	0.00234289i
$283$	17.3694	−	12.6196i	1.03250	−	0.750157i	0.0636948	−	0.997969i	$-0.479712\pi$
$283$	17.3694	−	12.6196i	1.03250	−	0.750157i	0.968808	+	0.247812i	$0.0797116\pi$
$284$	−9.67099	+	7.02638i	−0.573867	+	0.416939i
$285$	−0.138186	+	20.7108i	−0.00818541	+	1.22680i
$286$	−10.5343	−	6.08356i	−0.622905	−	0.359728i
$287$	−7.34550	+	22.6071i	−0.433591	+	1.33446i
$288$	0.411412	−	0.298908i	0.0242427	−	0.0176133i
$289$	30.3271			1.78395
$290$	15.1047	+	5.01947i	0.886978	+	0.294754i
$291$	8.38069	+	25.7931i	0.491285	+	1.51202i
$292$	5.32352			0.311535
$293$	−7.46308	−	22.9690i	−0.435998	−	1.34186i	−0.892061	−	0.451916i	$-0.850741\pi$
$293$	−7.46308	−	22.9690i	−0.435998	−	1.34186i	0.456063	−	0.889948i	$-0.349259\pi$
$294$	−1.44695	+	1.05127i	−0.0843877	+	0.0613113i
$295$	9.10674	+	12.7118i	0.530215	+	0.740112i
$296$	−7.04144	+	5.11590i	−0.409275	+	0.297356i
$297$	−18.2671	+	1.91786i	−1.05996	+	0.111285i
$298$	6.98517	+	21.4981i	0.404640	+	1.24535i
$299$	17.6178	+	12.8001i	1.01886	+	0.740248i
$300$	6.32245	+	4.72370i	0.365027	+	0.272723i
$301$	1.04417	+	3.21361i	0.0601847	+	0.185230i
$302$	−4.92636	−	3.57921i	−0.283480	−	0.205960i
$303$	0.999767	−	3.07697i	0.0574351	−	0.176767i
$304$	4.74735	+	3.44915i	0.272279	+	0.197822i
$305$	−0.0998800	+	14.9697i	−0.00571911	+	0.857160i
$306$	1.08108	+	3.32721i	0.0618010	+	0.190204i
$307$	16.2017			0.924679			0.462339	−	0.886703i	$-0.347010\pi$
$307$	16.2017			0.924679			0.462339	+	0.886703i	$0.347010\pi$
$308$	3.84616	+	8.64125i	0.219155	+	0.492381i
$309$	−0.449281	+	1.38275i	−0.0255587	+	0.0786617i
$310$	−5.33131	−	7.44184i	−0.302798	−	0.422668i
$311$	−18.5777			−1.05344			−0.526721	−	0.850038i	$-0.676579\pi$
$311$	−18.5777			−1.05344			−0.526721	+	0.850038i	$0.676579\pi$
$312$	5.78940			0.327760
$313$	−3.42374	−	10.5372i	−0.193521	−	0.595598i	−0.999991	−	0.00432166i	$-0.998624\pi$
$313$	−3.42374	−	10.5372i	−0.193521	−	0.595598i	0.806469	−	0.591276i	$-0.201376\pi$
$314$	−17.5425	−	12.7454i	−0.989981	−	0.719263i
$315$	−0.0216366	+	3.24282i	−0.00121908	+	0.182712i
$316$	2.76686	+	2.01024i	0.155648	+	0.113085i
$317$	−3.95680	−	12.1778i	−0.222236	−	0.683972i	−0.998560	−	0.0536382i	$-0.982918\pi$
$317$	−3.95680	−	12.1778i	−0.222236	−	0.683972i	0.776325	−	0.630333i	$-0.217082\pi$
$318$	0.329607			0.0184834
$319$	−23.4795	+	2.46511i	−1.31460	+	0.138020i
$320$	2.13119	−	0.676779i	0.119137	−	0.0378331i
$321$	−11.6603			−0.650814
$322$	−5.23237	−	16.1036i	−0.291588	−	0.897417i
$323$	−32.6592	+	23.7283i	−1.81721	+	1.32028i
$324$	5.83770	−	4.24134i	0.324317	−	0.235630i
$325$	−5.43383	−	17.5155i	−0.301415	−	0.971586i
$326$	3.34053	+	10.2811i	0.185015	+	0.569417i
$327$	20.7749			1.14885
$328$	−8.33510			−0.460229
$329$	0.0604683	−	0.0439328i	0.00333373	−	0.00242210i
$330$	−11.4334	−	2.51145i	−0.629390	−	0.138251i
$331$	−11.2671	−	8.18603i	−0.619296	−	0.449945i	0.233380	−	0.972386i	$-0.425022\pi$
$331$	−11.2671	−	8.18603i	−0.619296	−	0.449945i	−0.852676	+	0.522441i	$0.825022\pi$
$332$	0.491016	+	0.356744i	0.0269480	+	0.0195789i
$333$	3.58080	−	2.60160i	0.196227	−	0.142567i
$334$	−12.3638			−0.676516
$335$	0.152352	−	22.8339i	0.00832386	−	1.24755i
$336$	−3.64178	−	2.64591i	−0.198675	−	0.144346i
$337$	24.4315			1.33087			0.665434	−	0.746457i	$-0.268247\pi$
$337$	24.4315			1.33087			0.665434	+	0.746457i	$0.268247\pi$
$338$	−0.366321	−	0.266148i	−0.0199253	−	0.0144765i
$339$	3.37362	−	10.3829i	0.183230	−	0.563923i
$340$	−0.102635	+	15.3826i	−0.00556618	+	0.834240i
$341$	11.7583	+	6.79045i	0.636749	+	0.367723i
$342$	−2.41418	−	1.75401i	−0.130544	−	0.0948458i
$343$	13.5361	+	9.83457i	0.730882	+	0.531017i
$344$	−0.958554	+	0.696431i	−0.0516818	+	0.0375490i
$345$	19.8863	+	6.60847i	1.07064	+	0.355788i
$346$	−2.50700	+	7.71576i	−0.134777	+	0.414802i
$347$	6.07552	−	18.6985i	0.326151	−	1.00379i	−0.644768	−	0.764379i	$-0.723046\pi$
$347$	6.07552	−	18.6985i	0.326151	−	1.00379i	0.970918	−	0.239410i	$-0.0769541\pi$
$348$	9.08987	−	6.60418i	0.487268	−	0.354021i
$349$	−3.83021	+	11.7882i	−0.205026	+	0.631006i	0.794686	+	0.607021i	$0.207636\pi$
$349$	−3.83021	+	11.7882i	−0.205026	+	0.631006i	−0.999712	+	0.0239854i	$0.992364\pi$
$350$	−4.58693	+	13.5014i	−0.245182	+	0.721680i
$351$	−20.3123			−1.08419
$352$	−2.46498	+	2.21898i	−0.131384	+	0.118272i
$353$	−11.4769	+	8.33845i	−0.610853	+	0.443811i	−0.849715	−	0.527243i	$-0.823226\pi$
$353$	−11.4769	+	8.33845i	−0.610853	+	0.443811i	0.238862	+	0.971054i	$0.423226\pi$
$354$	11.0383			0.586680
$355$	25.4762	−	8.09021i	1.35214	−	0.429384i
$356$	−2.24065	+	6.89600i	−0.118754	+	0.365487i
$357$	25.0535	−	18.2024i	1.32597	−	0.963374i
$358$	−11.3670			−0.600765
$359$	−30.6549			−1.61791			−0.808953	−	0.587873i	$-0.799965\pi$
$359$	−30.6549			−1.61791			−0.808953	+	0.587873i	$0.799965\pi$
$360$	−1.08378	+	0.344164i	−0.0571202	+	0.0181391i
$361$	4.76935	−	14.6786i	0.251018	−	0.772555i
$362$	2.94405	−	9.06085i	0.154736	−	0.476228i
$363$	16.9842	−	3.60609i	0.891440	−	0.189271i
$364$	3.23234	+	9.94811i	0.169421	+	0.521423i
$365$	−11.2963	−	3.75391i	−0.591278	−	0.196489i
$366$	8.54913	+	6.21130i	0.446870	+	0.324670i
$367$	3.64586	−	11.2208i	0.190312	−	0.585721i	−0.809687	−	0.586862i	$-0.800363\pi$
$367$	3.64586	−	11.2208i	0.190312	−	0.585721i	0.999999	+	0.00114102i	$0.000363199\pi$
$368$	4.80336	−	3.48985i	0.250393	−	0.181921i
$369$	4.23867			0.220656
$370$	18.5492	−	5.89047i	0.964328	−	0.306231i
$371$	0.184026	+	0.566373i	0.00955415	+	0.0294046i
$372$	−6.46211			−0.335045
$373$	−1.98472	−	6.10833i	−0.102765	−	0.316278i	0.886435	−	0.462854i	$-0.153175\pi$
$373$	−1.98472	−	6.10833i	−0.102765	−	0.316278i	−0.989199	+	0.146576i	$0.953175\pi$
$374$	−9.27800	−	20.8451i	−0.479754	−	1.07787i
$375$	−10.0851	−	14.4819i	−0.520792	−	0.747840i
$376$	0.0212031	+	0.0154050i	0.00109347	+	0.000794451i
$377$	−26.1083			−1.34465
$378$	12.7773	+	9.28325i	0.657193	+	0.477479i
$379$	2.99341	−	9.21277i	0.153761	−	0.473228i	−0.844272	−	0.535915i	$-0.819967\pi$
$379$	2.99341	−	9.21277i	0.153761	−	0.473228i	0.998033	+	0.0626864i	$0.0199668\pi$
$380$	−7.64154	−	10.6666i	−0.392003	−	0.547186i
$381$	−7.00385	+	21.5556i	−0.358818	+	1.10433i
$382$	−7.33907	+	22.5873i	−0.375500	+	1.15567i
$383$	−8.60993	−	26.4986i	−0.439947	−	1.35402i	−0.887931	−	0.459976i	$-0.847858\pi$
$383$	−8.60993	−	26.4986i	−0.439947	−	1.35402i	0.447984	−	0.894041i	$-0.352142\pi$
$384$	0.487764	−	1.50118i	0.0248911	−	0.0766070i
$385$	−2.06800	−	21.0486i	−0.105395	−	1.07274i
$386$	8.37338	+	25.7706i	0.426194	+	1.31169i
$387$	0.487457	−	0.354158i	0.0247788	−	0.0180029i
$388$	−13.9004	−	10.0992i	−0.705686	−	0.512711i
$389$	−18.7425	+	13.6172i	−0.950284	+	0.690422i	−0.950874	−	0.309578i	$-0.899812\pi$
$389$	−18.7425	+	13.6172i	−0.950284	+	0.690422i	0.000589924		1.00000i	$0.499812\pi$
$390$	−12.2849	−	4.08244i	−0.622072	−	0.206722i
$391$	12.6219	+	38.8462i	0.638318	+	1.96454i
$392$	0.350147	−	1.07764i	0.0176851	−	0.0544291i
$393$	5.15884	−	15.8773i	0.260229	−	0.800903i
$394$	0.197473	+	0.607760i	0.00994856	+	0.0306185i
$395$	−4.45366	−	6.21674i	−0.224088	−	0.312798i
$396$	1.25353	−	1.12842i	0.0629920	−	0.0567054i
$397$	−10.9334	+	7.94355i	−0.548730	+	0.398675i	−0.827317	−	0.561736i	$-0.810134\pi$
$397$	−10.9334	+	7.94355i	−0.548730	+	0.398675i	0.278587	+	0.960411i	$0.410134\pi$
$398$	5.11466	−	15.7413i	0.256375	−	0.789040i
$399$	−8.16265	+	25.1221i	−0.408644	+	1.25768i
$400$	−4.99955	−	0.0667186i	−0.249978	−	0.00333593i
$401$	−25.5384	+	18.5547i	−1.27532	+	0.926577i	−0.999401	−	0.0346022i	$-0.988984\pi$
$401$	−25.5384	+	18.5547i	−1.27532	+	0.926577i	−0.275923	+	0.961180i	$0.588984\pi$
$402$	−13.0404	−	9.47440i	−0.650396	−	0.472540i
$403$	12.1482	+	8.82616i	0.605144	+	0.439663i
$404$	0.633390	+	1.94937i	0.0315123	+	0.0969850i
$405$	−15.3782	+	4.88350i	−0.764150	+	0.242663i
$406$	16.4232	+	11.9322i	0.815071	+	0.592183i
$407$	−21.4545	+	19.3133i	−1.06346	+	0.957324i
$408$	8.78497	+	6.38265i	0.434921	+	0.315988i
$409$	−20.1218	+	14.6193i	−0.994959	+	0.722880i	−0.961001	−	0.276543i	$-0.910811\pi$
$409$	−20.1218	+	14.6193i	−0.994959	+	0.722880i	−0.0339574	+	0.999423i	$0.510811\pi$
$410$	17.6868	+	5.87755i	0.873490	+	0.290271i
$411$	−14.6368	+	10.6343i	−0.721981	+	0.524550i
$412$	−0.284637	−	0.876022i	−0.0140230	−	0.0431585i
$413$	6.16291	+	18.9675i	0.303257	+	0.933329i
$414$	−2.44267	+	1.77470i	−0.120051	+	0.0872219i
$415$	−0.790361	−	1.10324i	−0.0387973	−	0.0541561i
$416$	−2.96732	+	2.15588i	−0.145485	+	0.105701i
$417$	−10.6969	−	7.77173i	−0.523828	−	0.380583i
$418$	16.8536	+	9.73296i	0.824335	+	0.476054i
$419$	11.6316	+	8.45088i	0.568243	+	0.412853i	0.834467	−	0.551059i	$-0.185776\pi$
$419$	11.6316	+	8.45088i	0.568243	+	0.412853i	−0.266224	+	0.963911i	$0.585776\pi$
$420$	5.86196	+	8.18255i	0.286034	+	0.399268i
$421$	−4.73803	−	14.5822i	−0.230917	−	0.710691i	−0.997637	−	0.0687084i	$-0.978112\pi$
$421$	−4.73803	−	14.5822i	−0.230917	−	0.710691i	0.766719	−	0.641982i	$-0.221888\pi$
$422$	−11.2641	−	8.18383i	−0.548326	−	0.398382i
$423$	−0.0107825	−	0.00783394i	−0.000524263	−	0.000380899i
$424$	−0.168938	+	0.122740i	−0.00820433	+	0.00596080i
$425$	11.0649	−	32.5691i	0.536729	−	1.57983i
$426$	5.83073	−	17.9451i	0.282500	−	0.869445i
$427$	−5.89993	+	18.1581i	−0.285518	+	0.878733i
$428$	5.97640	−	4.34211i	0.288880	−	0.209884i
$429$	19.0963	−	2.00492i	0.921979	−	0.0967986i
$430$	2.52512	−	0.801873i	0.121772	−	0.0386698i
$431$	−4.58559	−	14.1130i	−0.220880	−	0.679799i	−0.998684	−	0.0512914i	$-0.983666\pi$
$431$	−4.58559	−	14.1130i	−0.220880	−	0.679799i	0.777804	−	0.628507i	$-0.216334\pi$
$432$	−1.71134	+	5.26695i	−0.0823367	+	0.253406i
$433$	−8.11959	+	24.9895i	−0.390203	+	1.20092i	0.542432	+	0.840100i	$0.317504\pi$
$433$	−8.11959	+	24.9895i	−0.390203	+	1.20092i	−0.932635	+	0.360821i	$0.882496\pi$
$434$	−3.60792	−	11.1040i	−0.173186	−	0.533011i
$435$	−23.9454	+	7.60408i	−1.14809	+	0.364588i
$436$	−10.6480	+	7.73622i	−0.509947	+	0.370498i
$437$	−28.1864	−	20.4786i	−1.34834	−	0.979624i
$438$	−6.79804	+	4.93907i	−0.324823	+	0.235998i
$439$	2.31622	+	7.12859i	0.110547	+	0.340229i	0.990992	−	0.133919i	$-0.0427562\pi$
$439$	2.31622	+	7.12859i	0.110547	+	0.340229i	−0.880445	+	0.474148i	$0.842756\pi$
$440$	6.79535	−	2.97040i	0.323955	−	0.141608i
$441$	−0.178061	+	0.548016i	−0.00847910	+	0.0260960i
$442$	−7.79729	−	23.9976i	−0.370879	−	1.14145i
$443$	−4.66994	+	14.3726i	−0.221875	+	0.682862i	0.776718	+	0.629848i	$0.216883\pi$
$443$	−4.66994	+	14.3726i	−0.221875	+	0.682862i	−0.998594	+	0.0530141i	$0.983117\pi$
$444$	4.24535	−	13.0658i	0.201475	−	0.620077i
$445$	9.61734	−	13.0531i	0.455906	−	0.618776i
$446$	−0.719284	+	2.21373i	−0.0340591	+	0.104823i
$447$	−28.8655	−	20.9720i	−1.36529	−	0.991943i
$448$	2.85186			0.134738
$449$	19.6514	+	14.2776i	0.927405	+	0.673800i	0.945356	−	0.326039i	$-0.105714\pi$
$449$	19.6514	+	14.2776i	0.927405	+	0.673800i	−0.0179507	+	0.999839i	$0.505714\pi$
$450$	2.54244	+	0.0339286i	0.119852	+	0.00159941i
$451$	−27.4933	+	2.88652i	−1.29461	+	0.135921i
$452$	2.13731	+	6.57798i	0.100531	+	0.309402i
$453$	9.61161			0.451593
$454$	−1.23304	−	3.79491i	−0.0578695	−	0.178104i
$455$	0.156054	−	23.3889i	0.00731595	−	1.09649i
$456$	−9.26235			−0.433749
$457$	−12.9916	+	9.43897i	−0.607723	+	0.441537i	−0.848612	−	0.529016i	$-0.822561\pi$
$457$	−12.9916	+	9.43897i	−0.607723	+	0.441537i	0.240889	+	0.970553i	$0.422561\pi$
$458$	5.09914	−	15.6935i	0.238267	−	0.733311i
$459$	−30.8223	−	22.3937i	−1.43866	−	1.04525i
$460$	−12.6535	+	4.01823i	−0.589972	+	0.187351i
$461$	−9.54611	−	29.3799i	−0.444607	−	1.36836i	−0.882915	−	0.469533i	$-0.844422\pi$
$461$	−9.54611	−	29.3799i	−0.444607	−	1.36836i	0.438308	−	0.898825i	$-0.355578\pi$
$462$	−12.9287	−	7.46633i	−0.601497	−	0.347365i
$463$	6.89780	−	21.2293i	0.320568	−	0.986607i	−0.652833	−	0.757502i	$-0.726420\pi$
$463$	6.89780	−	21.2293i	0.320568	−	0.986607i	0.973402	−	0.229106i	$-0.0735802\pi$
$464$	−2.19966	+	6.76985i	−0.102117	+	0.314282i
$465$	13.7124	+	4.55680i	0.635898	+	0.211317i
$466$	−9.29064			−0.430380
$467$	14.9828			0.693322			0.346661	−	0.937991i	$-0.387315\pi$
$467$	14.9828			0.693322			0.346661	+	0.937991i	$0.387315\pi$
$468$	1.50898	−	1.09634i	0.0697526	−	0.0506782i
$469$	8.99945	−	27.6975i	0.415556	−	1.27895i
$470$	−0.0341295	−	0.0476404i	−0.00157428	−	0.00219749i
$471$	34.2264			1.57707
$472$	−5.65761	+	4.11050i	−0.260413	+	0.189201i
$473$	−2.92061	+	2.62913i	−0.134290	+	0.120887i
$474$	−5.39830			−0.247952
$475$	8.69347	+	28.0227i	0.398884	+	1.28577i
$476$	−6.06269	+	18.6590i	−0.277883	+	0.855236i
$477$	0.0859103	−	0.0624175i	0.00393356	−	0.00285790i
$478$	−2.60891	+	8.02941i	−0.119329	+	0.367256i
$479$	8.55111	−	26.3176i	0.390710	−	1.20248i	−0.541542	−	0.840674i	$-0.682159\pi$
$479$	8.55111	−	26.3176i	0.390710	−	1.20248i	0.932252	−	0.361809i	$-0.117841\pi$
$480$	−2.09359	+	2.84152i	−0.0955589	+	0.129697i
$481$	−25.8266	+	18.7641i	−1.17759	+	0.855571i
$482$	−9.64394	−	7.00673i	−0.439269	−	0.319148i
$483$	21.6223	+	15.7095i	0.983847	+	0.714807i
$484$	−7.36228	+	8.17293i	−0.334649	+	0.371497i
$485$	22.3747	+	31.2322i	1.01598	+	1.41818i
$486$	1.61440	−	4.96862i	0.0732308	−	0.225381i
$487$	−27.7083	−	20.1312i	−1.25558	−	0.912234i	−0.257050	−	0.966398i	$-0.582751\pi$
$487$	−27.7083	−	20.1312i	−1.25558	−	0.912234i	−0.998532	+	0.0541640i	$0.982751\pi$
$488$	−6.69478			−0.303059
$489$	−13.8044	−	10.0295i	−0.624258	−	0.453550i
$490$	−1.50291	+	2.03981i	−0.0678944	+	0.0921493i
$491$	−4.12398			−0.186113			−0.0930563	−	0.995661i	$-0.529664\pi$
$491$	−4.12398			−0.186113			−0.0930563	+	0.995661i	$0.529664\pi$
$492$	10.6438	−	7.73316i	0.479859	−	0.348638i
$493$	−39.6173	−	28.7837i	−1.78427	−	1.29635i
$494$	17.4123	+	12.6508i	0.783419	+	0.569187i
$495$	−3.45566	+	1.51055i	−0.155320	+	0.0678940i
$496$	3.31211	−	2.40639i	0.148718	−	0.108050i
$497$	34.0911			1.52920
$498$	−0.958000			−0.0429290
$499$	10.4091	+	32.0358i	0.465973	+	1.43412i	0.857754	+	0.514060i	$0.171859\pi$
$499$	10.4091	+	32.0358i	0.465973	+	1.43412i	−0.391781	+	0.920058i	$0.628141\pi$
$500$	10.5619	+	3.66704i	0.472341	+	0.163995i
$501$	15.7883	−	11.4709i	0.705371	−	0.512482i
$502$	7.18870	−	5.22289i	0.320847	−	0.233109i
$503$	−1.92582	−	5.92708i	−0.0858683	−	0.264275i	0.898898	−	0.438158i	$-0.144369\pi$
$503$	−1.92582	−	5.92708i	−0.0858683	−	0.264275i	−0.984766	+	0.173882i	$0.944369\pi$
$504$	−1.45026			−0.0645999
$505$	0.0305795	−	4.58315i	0.00136077	−	0.203948i
$506$	14.6353	−	13.1747i	0.650619	−	0.585687i
$507$	0.714714			0.0317415
$508$	−4.43720	−	13.6563i	−0.196869	−	0.605900i
$509$	2.66854	+	1.93881i	0.118281	+	0.0859362i	0.645353	−	0.763884i	$-0.276710\pi$
$509$	2.66854	+	1.93881i	0.118281	+	0.0859362i	−0.527072	+	0.849821i	$0.676710\pi$
$510$	−14.1407	−	19.7386i	−0.626159	−	0.874039i
$511$	−12.2824	−	8.92371i	−0.543343	−	0.394762i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	32.4972			1.43479
$514$	28.4632			1.25546
$515$	−0.0137420	+	2.05960i	−0.000605545	+	0.0907570i
$516$	0.577922	−	1.77866i	0.0254416	−	0.0783012i
$517$	0.0752733	+	0.0434704i	0.00331052	+	0.00191183i
$518$	24.8217			1.09060
$519$	−3.95715	−	12.1789i	−0.173700	−	0.534592i
$520$	7.81679	−	2.48229i	0.342789	−	0.108856i
$521$	18.2694	+	13.2735i	0.800395	+	0.581521i	0.911030	−	0.412340i	$-0.135288\pi$
$521$	18.2694	+	13.2735i	0.800395	+	0.581521i	−0.110635	+	0.993861i	$0.535288\pi$
$522$	1.11860	−	3.44269i	0.0489597	−	0.150682i
$523$	−7.60955	−	5.52866i	−0.332742	−	0.241751i	0.408851	−	0.912601i	$-0.365930\pi$
$523$	−7.60955	−	5.52866i	−0.332742	−	0.241751i	−0.741593	+	0.670850i	$0.765930\pi$
$524$	3.26832	+	10.0589i	0.142777	+	0.439423i
$525$	−6.66892	−	21.4967i	−0.291056	−	0.938194i
$526$	15.6869	+	11.3972i	0.683980	+	0.496941i
$527$	8.70331	+	26.7860i	0.379122	+	1.16682i
$528$	1.08901	−	5.12056i	0.0473933	−	0.222844i
$529$	−9.91155	+	7.20116i	−0.430937	+	0.313094i
$530$	0.445031	−	0.141324i	0.0193309	−	0.00613871i
$531$	2.87708	−	2.09032i	0.124855	−	0.0907123i
$532$	−5.17135	−	15.9158i	−0.224206	−	0.690036i
$533$	−30.5715			−1.32420
$534$	−3.53672	−	10.8849i	−0.153049	−	0.471036i
$535$	−15.7436	+	4.99952i	−0.680655	+	0.216148i
$536$	10.2119			0.441086
$537$	14.5155	−	10.5461i	0.626390	−	0.455099i
$538$	−1.64466	+	5.06173i	−0.0709062	+	0.218227i
$539$	0.781761	−	3.67585i	0.0336728	−	0.158330i
$540$	7.34543	−	9.96955i	0.316097	−	0.429021i
$541$	−7.82670	+	5.68643i	−0.336496	+	0.244479i	−0.743182	−	0.669089i	$-0.766684\pi$
$541$	−7.82670	+	5.68643i	−0.336496	+	0.244479i	0.406686	+	0.913568i	$0.366684\pi$
$542$	−3.06197	+	2.22465i	−0.131523	+	0.0955571i
$543$	4.64700	+	14.3020i	0.199422	+	0.613757i
$544$	−6.87947			−0.294955
$545$	28.0500	−	8.90753i	1.20153	−	0.381556i
$546$	−13.3573	−	9.70467i	−0.571641	−	0.415321i
$547$	−10.2783	−	31.6333i	−0.439467	−	1.35254i	−0.888439	−	0.458995i	$-0.848210\pi$
$547$	−10.2783	−	31.6333i	−0.439467	−	1.35254i	0.448972	−	0.893546i	$-0.351790\pi$
$548$	3.54196	−	10.9010i	0.151305	−	0.465669i
$549$	3.40452			0.145301
$550$	−16.5141	+	1.51132i	−0.704164	+	0.0644429i
$551$	41.7701			1.77947
$552$	−2.89600	+	8.91296i	−0.123262	+	0.379361i
$553$	−3.01398	−	9.27607i	−0.128167	−	0.394459i
$554$	7.92844	+	5.76035i	0.336847	+	0.244734i
$555$	−18.2220	+	24.7317i	−0.773479	+	1.04980i
$556$	8.37668			0.355250
$557$	3.05018	+	9.38748i	0.129240	+	0.397760i	0.994650	−	0.103305i	$-0.0329417\pi$
$557$	3.05018	+	9.38748i	0.129240	+	0.397760i	−0.865410	+	0.501065i	$0.832942\pi$
$558$	−1.68432	+	1.22373i	−0.0713028	+	0.0518045i
$559$	−3.51579	+	2.55437i	−0.148702	+	0.108038i
$560$	−6.05156	−	2.01101i	−0.255725	−	0.0849805i
$561$	31.1875	+	18.0108i	1.31674	+	0.760418i
$562$	9.65842	−	29.7256i	0.407416	−	1.25390i
$563$	17.6469	−	12.8212i	0.743727	−	0.540349i	−0.150149	−	0.988663i	$-0.547975\pi$
$563$	17.6469	−	12.8212i	0.743727	−	0.540349i	0.893876	+	0.448314i	$0.147975\pi$
$564$	−0.0413685			−0.00174193
$565$	0.103188	−	15.4654i	0.00434114	−	0.650634i
$566$	−6.63452	−	20.4189i	−0.278869	−	0.858272i
$567$	−20.5784			−0.864213
$568$	3.69399	+	11.3689i	0.154996	+	0.477029i
$569$	−5.93211	+	4.30993i	−0.248687	+	0.180682i	−0.705145	−	0.709064i	$-0.749118\pi$
$569$	−5.93211	+	4.30993i	−0.248687	+	0.180682i	0.456458	+	0.889745i	$0.349118\pi$
$570$	19.6544	+	6.53140i	0.823233	+	0.273570i
$571$	−25.0252	+	18.1818i	−1.04727	+	0.760886i	−0.971691	−	0.236254i	$-0.924080\pi$
$571$	−25.0252	+	18.1818i	−1.04727	+	0.760886i	−0.0755786	+	0.997140i	$0.524080\pi$
$572$	−9.04108	+	8.13877i	−0.378027	+	0.340299i
$573$	−11.5843	−	35.6527i	−0.483940	−	1.48941i
$574$	19.2308	+	13.9720i	0.802676	+	0.583179i
$575$	29.6838	+	0.396128i	1.23790	+	0.0165197i
$576$	−0.157145	−	0.483644i	−0.00654772	−	0.0201518i
$577$	19.8106	+	14.3933i	0.824727	+	0.599199i	0.918063	−	0.396435i	$-0.129753\pi$
$577$	19.8106	+	14.3933i	0.824727	+	0.599199i	−0.0933354	+	0.995635i	$0.529753\pi$
$578$	9.37159	−	28.8428i	0.389807	−	1.19970i
$579$	−34.6022	−	25.1400i	−1.43802	−	1.04478i
$580$	9.44141	−	12.8143i	0.392033	−	0.532085i
$581$	−0.534870	−	1.64616i	−0.0221902	−	0.0682943i
$582$	27.1205			1.12418
$583$	−0.514734	+	0.463363i	−0.0213181	+	0.0191905i
$584$	1.64506	−	5.06297i	0.0680730	−	0.209507i
$585$	−3.97510	+	1.26233i	−0.164350	+	0.0521908i
$586$	−24.1510			−0.997670
$587$	7.58885			0.313226			0.156613	−	0.987660i	$-0.449943\pi$
$587$	7.58885			0.313226			0.156613	+	0.987660i	$0.449943\pi$
$588$	0.552685	+	1.70099i	0.0227923	+	0.0701476i
$589$	−19.4356	−	14.1208i	−0.800830	−	0.581837i
$590$	14.9038	−	4.73284i	0.613581	−	0.194848i
$591$	−0.816039	−	0.592887i	−0.0335674	−	0.0243881i
$592$	2.68959	+	8.27770i	0.110541	+	0.340212i
$593$	23.1979			0.952623			0.476312	−	0.879276i	$-0.341973\pi$
$593$	23.1979			0.952623			0.476312	+	0.879276i	$0.341973\pi$
$594$	−3.82084	+	17.9657i	−0.156771	+	0.737140i
$595$	26.0224	−	35.3188i	1.06681	−	1.44793i
$596$	22.6045			0.925915
$597$	8.07317	+	24.8467i	0.330413	+	1.01691i
$598$	17.6178	−	12.8001i	0.720446	−	0.523434i
$599$	18.6577	−	13.5556i	0.762333	−	0.553868i	−0.137292	−	0.990531i	$-0.543840\pi$
$599$	18.6577	−	13.5556i	0.762333	−	0.553868i	0.899625	+	0.436663i	$0.143840\pi$
$600$	6.44625	−	4.55330i	0.263167	−	0.185888i
$601$	7.30371	+	22.4785i	0.297924	+	0.916917i	0.982223	+	0.187716i	$0.0601083\pi$
$601$	7.30371	+	22.4785i	0.297924	+	0.916917i	−0.684299	+	0.729202i	$0.739892\pi$
$602$	3.37899			0.137717
$603$	−5.19307			−0.211478
$604$	−4.92636	+	3.57921i	−0.200451	+	0.145636i
$605$	21.3857	−	12.1511i	0.869454	−	0.494014i
$606$	−2.61742	−	1.90167i	−0.106326	−	0.0772500i
$607$	−18.4049	−	13.3719i	−0.747032	−	0.542750i	0.147874	−	0.989006i	$-0.452757\pi$
$607$	−18.4049	−	13.3719i	−0.747032	−	0.542750i	−0.894905	+	0.446256i	$0.852757\pi$
$608$	4.74735	−	3.44915i	0.192530	−	0.139881i
$609$	−32.0426			−1.29843
$610$	14.2061	+	4.72087i	0.575189	+	0.191142i
$611$	0.0777690	+	0.0565025i	0.00314620	+	0.00228585i
$612$	3.49844			0.141416
$613$	2.24087	+	1.62809i	0.0905080	+	0.0657579i	0.632119	−	0.774871i	$-0.282185\pi$
$613$	2.24087	+	1.62809i	0.0905080	+	0.0657579i	−0.541611	+	0.840629i	$0.682185\pi$
$614$	5.00659	−	15.4087i	0.202050	−	0.621845i
$615$	−28.0389	+	8.90400i	−1.13064	+	0.359044i
$616$	9.40684	−	0.987624i	0.379012	−	0.0397925i
$617$	−11.0475	−	8.02650i	−0.444757	−	0.323135i	0.342765	−	0.939421i	$-0.388636\pi$
$617$	−11.0475	−	8.02650i	−0.444757	−	0.323135i	−0.787522	+	0.616286i	$0.788636\pi$
$618$	1.17623	+	0.854584i	0.0473151	+	0.0343764i
$619$	16.8605	−	12.2499i	0.677681	−	0.492364i	−0.194906	−	0.980822i	$-0.562440\pi$
$619$	16.8605	−	12.2499i	0.677681	−	0.492364i	0.872588	+	0.488458i	$0.162440\pi$
$620$	−8.72508	+	2.77073i	−0.350407	+	0.111275i
$621$	10.1607	−	31.2714i	0.407735	−	1.25488i
$622$	−5.74081	+	17.6684i	−0.230186	+	0.708438i
$623$	16.7292	−	12.1545i	0.670243	−	0.486960i
$624$	1.78902	−	5.50605i	0.0716183	−	0.220418i
$625$	−19.8261	−	15.2291i	−0.793044	−	0.609165i
$626$	−11.0795			−0.442825
$627$	−30.5518	+	3.20763i	−1.22012	+	0.128100i
$628$	−17.5425	+	12.7454i	−0.700022	+	0.508596i
$629$	−59.8768			−2.38744
$630$	3.07742	+	1.02266i	0.122607	+	0.0407439i
$631$	−10.9038	+	33.5584i	−0.434073	+	1.33594i	0.459960	+	0.887940i	$0.347864\pi$
$631$	−10.9038	+	33.5584i	−0.434073	+	1.33594i	−0.894033	+	0.448001i	$0.852136\pi$
$632$	2.76686	−	2.01024i	0.110060	−	0.0799631i
$633$	21.9768			0.873501
$634$	−12.8045			−0.508530
$635$	−0.214224	+	32.1072i	−0.00850123	+	1.27413i
$636$	0.101854	−	0.313475i	0.00403878	−	0.0124301i
$637$	1.28427	−	3.95258i	0.0508846	−	0.156607i
$638$	−4.91110	+	23.0921i	−0.194432	+	0.914224i
$639$	−1.87851	−	5.78147i	−0.0743129	−	0.228712i
$640$	0.0149191	−	2.23602i	0.000589728	−	0.0883864i
$641$	−8.34678	−	6.06429i	−0.329678	−	0.239525i	0.410616	−	0.911808i	$-0.365314\pi$
$641$	−8.34678	−	6.06429i	−0.329678	−	0.239525i	−0.740294	+	0.672283i	$0.765314\pi$
$642$	−3.60323	+	11.0896i	−0.142208	+	0.437671i
$643$	−20.7068	+	15.0444i	−0.816598	+	0.593293i	−0.915736	−	0.401780i	$-0.868392\pi$
$643$	−20.7068	+	15.0444i	−0.816598	+	0.593293i	0.0991378	+	0.995074i	$0.468392\pi$
$644$	−16.9323			−0.667226
$645$	−2.48057	+	3.36674i	−0.0976722	+	0.132565i
$646$	12.4747	+	38.3932i	0.490811	+	1.51056i
$647$	−8.56458			−0.336708			−0.168354	−	0.985727i	$-0.553845\pi$
$647$	−8.56458			−0.336708			−0.168354	+	0.985727i	$0.553845\pi$
$648$	−2.22980	−	6.86263i	−0.0875950	−	0.269590i
$649$	−17.2381	+	15.5177i	−0.676655	+	0.609124i
$650$	−18.3374	−	0.244711i	−0.719252	−	0.00959836i
$651$	14.9094	+	10.8323i	0.584346	+	0.424552i
$652$	10.8102			0.423360
$653$	−9.00781	−	6.54455i	−0.352503	−	0.256108i	0.397415	−	0.917639i	$-0.369907\pi$
$653$	−9.00781	−	6.54455i	−0.352503	−	0.256108i	−0.749918	+	0.661531i	$0.769907\pi$
$654$	6.41978	−	19.7581i	0.251033	−	0.772601i
$655$	0.157792	−	23.6493i	0.00616543	−	0.924053i
$656$	−2.57569	+	7.92715i	−0.100564	+	0.309503i
$657$	−0.836566	+	2.57469i	−0.0326375	+	0.100448i
$658$	−0.0230969	−	0.0710848i	−0.000900409	−	0.00277117i
$659$	−6.84080	+	21.0538i	−0.266480	+	0.820140i	0.724869	+	0.688886i	$0.241900\pi$
$659$	−6.84080	+	21.0538i	−0.266480	+	0.820140i	−0.991349	+	0.131253i	$0.958100\pi$
$660$	−5.92166	+	10.0978i	−0.230500	+	0.393055i
$661$	0.256745	+	0.790179i	0.00998621	+	0.0307344i	0.955925	−	0.293609i	$-0.0948565\pi$
$661$	0.256745	+	0.790179i	0.00998621	+	0.0307344i	−0.945939	+	0.324344i	$0.894857\pi$
$662$	−11.2671	+	8.18603i	−0.437908	+	0.318159i
$663$	32.2215	+	23.4103i	1.25138	+	0.909182i
$664$	0.491016	−	0.356744i	0.0190551	−	0.0138444i
$665$	−0.249668	+	37.4194i	−0.00968172	+	1.45106i
$666$	−1.36774	−	4.20949i	−0.0529990	−	0.163114i
$667$	13.0600	−	40.1945i	0.505685	−	1.55634i
$668$	−3.82062	+	11.7586i	−0.147824	+	0.454956i
$669$	−1.13534	−	3.49423i	−0.0438950	−	0.135095i
$670$	−21.6693	−	7.20097i	−0.837158	−	0.278198i
$671$	−22.0827	+	2.31846i	−0.852494	+	0.0895033i
$672$	−3.64178	+	2.64591i	−0.140485	+	0.102068i
$673$	1.18119	−	3.63534i	0.0455317	−	0.140132i	−0.925706	−	0.378243i	$-0.876528\pi$
$673$	1.18119	−	3.63534i	0.0455317	−	0.140132i	0.971238	+	0.238111i	$0.0765283\pi$
$674$	7.54974	−	23.2357i	0.290805	−	0.895006i
$675$	−22.6169	+	15.9754i	−0.870524	+	0.614894i
$676$	−0.366321	+	0.266148i	−0.0140893	+	0.0102365i
$677$	−28.2130	−	20.4979i	−1.08431	−	0.787799i	−0.105883	−	0.994379i	$-0.533767\pi$
$677$	−28.2130	−	20.4979i	−1.08431	−	0.787799i	−0.978430	+	0.206580i	$0.933767\pi$
$678$	−8.83225	−	6.41700i	−0.339200	−	0.246443i
$679$	15.1419	+	46.6019i	0.581092	+	1.78842i
$680$	14.5980	+	4.85110i	0.559809	+	0.186031i
$681$	5.09543	+	3.70205i	0.195257	+	0.141863i
$682$	10.0916	−	9.08447i	0.386428	−	0.347862i
$683$	−3.99795	−	2.90468i	−0.152977	−	0.111145i	0.508664	−	0.860965i	$-0.330140\pi$
$683$	−3.99795	−	2.90468i	−0.152977	−	0.111145i	−0.661641	+	0.749821i	$0.730140\pi$
$684$	−2.41418	+	1.75401i	−0.0923086	+	0.0670661i
$685$	−15.2029	+	20.6340i	−0.580872	+	0.788385i
$686$	13.5361	−	9.83457i	0.516812	−	0.375486i
$687$	8.04867	+	24.7713i	0.307076	+	0.945083i
$688$	0.366135	+	1.12685i	0.0139588	+	0.0429607i
$689$	−0.619630	+	0.450188i	−0.0236060	+	0.0171508i
$690$	12.4302	−	16.8709i	0.473211	−	0.642264i
$691$	27.7169	−	20.1375i	1.05440	−	0.766067i	0.0813563	−	0.996685i	$-0.474075\pi$
$691$	27.7169	−	20.1375i	1.05440	−	0.766067i	0.973044	+	0.230618i	$0.0740748\pi$
$692$	6.56342	+	4.76860i	0.249504	+	0.181275i
$693$	−4.78369	+	0.502239i	−0.181717	+	0.0190785i
$694$	−15.9059	−	11.5563i	−0.603780	−	0.438672i
$695$	−17.7750	−	5.90687i	−0.674246	−	0.224060i
$696$	−3.47202	−	10.6858i	−0.131607	−	0.405044i
$697$	−46.3899	−	33.7042i	−1.75714	−	1.27664i
$698$	10.0276	+	7.28549i	0.379551	+	0.275760i
$699$	11.8640	−	8.61969i	0.448737	−	0.326027i
$700$	11.4231	+	8.53459i	0.431754	+	0.322577i
$701$	−0.778685	+	2.39655i	−0.0294105	+	0.0905163i	−0.964684	−	0.263409i	$-0.915153\pi$
$701$	−0.778685	+	2.39655i	−0.0294105	+	0.0905163i	0.935274	+	0.353925i	$0.115153\pi$
$702$	−6.27685	+	19.3182i	−0.236904	+	0.729117i
$703$	41.3195	−	30.0203i	1.55839	−	1.13224i
$704$	1.34865	+	3.03004i	0.0508292	+	0.114199i
$705$	0.0877827	+	0.0291713i	0.00330609	+	0.00109865i
$706$	4.38378	+	13.4919i	0.164986	+	0.507774i
$707$	1.80634	−	5.55934i	0.0679343	−	0.209080i
$708$	3.41103	−	10.4981i	0.128194	−	0.394542i
$709$	0.411325	+	1.26593i	0.0154477	+	0.0475430i	0.958483	−	0.285149i	$-0.0920431\pi$
$709$	0.411325	+	1.26593i	0.0154477	+	0.0475430i	−0.943036	+	0.332692i	$0.892043\pi$
$710$	0.178343	−	26.7294i	0.00669308	−	1.00313i
$711$	−1.40704	+	1.02227i	−0.0527681	+	0.0383383i
$712$	5.86608	+	4.26196i	0.219841	+	0.159724i
$713$	−19.6649	+	14.2874i	−0.736458	+	0.535068i
$714$	−9.56958	−	29.4521i	−0.358133	−	1.10222i
$715$	24.9240	−	10.8949i	0.932105	−	0.407444i
$716$	−3.51260	+	10.8107i	−0.131272	+	0.404014i
$717$	−4.11801	−	12.6739i	−0.153790	−	0.473316i
$718$	−9.47290	+	29.1546i	−0.353525	+	1.08804i
$719$	8.98779	−	27.6616i	0.335188	−	1.03160i	−0.631441	−	0.775424i	$-0.717536\pi$
$719$	8.98779	−	27.6616i	0.335188	−	1.03160i	0.966629	−	0.256179i	$-0.0824637\pi$
$720$	−0.00758684	+	1.13709i	−0.000282745	+	0.0423768i
$721$	−0.811744	+	2.49829i	−0.0302309	+	0.0930412i
$722$	−12.4863	−	9.07184i	−0.464693	−	0.337619i
$723$	18.8159			0.699770
$724$	−7.70762	−	5.59991i	−0.286451	−	0.208119i
$725$	−29.0705	+	20.5339i	−1.07965	+	0.762610i
$726$	1.81881	−	17.2673i	0.0675025	−	0.640849i
$727$	3.80327	+	11.7053i	0.141056	+	0.434124i	0.996483	−	0.0837989i	$-0.0267053\pi$
$727$	3.80327	+	11.7053i	0.141056	+	0.434124i	−0.855427	+	0.517923i	$0.826705\pi$
$728$	10.4601			0.387676
$729$	9.23765	+	28.4306i	0.342135	+	1.05298i
$730$	−7.06095	+	9.58344i	−0.261337	+	0.354699i
$731$	−8.15106			−0.301478
$732$	8.54913	−	6.21130i	0.315985	−	0.229576i
$733$	−5.62922	+	17.3249i	−0.207920	+	0.639911i	0.791661	+	0.610961i	$0.209217\pi$
$733$	−5.62922	+	17.3249i	−0.207920	+	0.639911i	−0.999581	+	0.0289509i	$0.990783\pi$
$734$	−9.54498	−	6.93483i	−0.352312	−	0.255969i
$735$	0.0266832	−	3.99918i	0.000984223	−	0.147512i
$736$	−1.83472	−	5.64669i	−0.0676287	−	0.208140i
$737$	33.6838	−	3.53646i	1.24076	−	0.130267i
$738$	1.30982	−	4.03122i	0.0482152	−	0.148391i
$739$	11.5479	−	35.5407i	0.424796	−	1.30739i	−0.478394	−	0.878145i	$-0.658781\pi$
$739$	11.5479	−	35.5407i	0.424796	−	1.30739i	0.903190	−	0.429242i	$-0.141219\pi$
$740$	0.129851	−	19.4616i	0.00477342	−	0.715423i
$741$	−33.9725			−1.24801
$742$	0.595520			0.0218622
$743$	13.5506	−	9.84510i	0.497124	−	0.361182i	−0.310793	−	0.950478i	$-0.600595\pi$
$743$	13.5506	−	9.84510i	0.497124	−	0.361182i	0.807917	+	0.589296i	$0.200595\pi$
$744$	−1.99690	+	6.14584i	−0.0732100	+	0.225317i
$745$	−47.9660	−	15.9397i	−1.75734	−	0.583985i
$746$	−6.42268			−0.235151
$747$	−0.249698	+	0.181416i	−0.00913597	+	0.00663767i
$748$	−22.6919	+	2.38242i	−0.829698	+	0.0871099i
$749$	−21.0673			−0.769784
$750$	−16.8895	+	5.11635i	−0.616719	+	0.186823i
$751$	−12.2126	+	37.5864i	−0.445643	+	1.37155i	0.436134	+	0.899882i	$0.356347\pi$
$751$	−12.2126	+	37.5864i	−0.445643	+	1.37155i	−0.881777	+	0.471667i	$0.843653\pi$
$752$	0.0212031	−	0.0154050i	0.000773199	−	0.000561762i
$753$	−4.33414	+	13.3391i	−0.157945	+	0.486104i
$754$	−8.06791	+	24.8305i	−0.293816	+	0.904273i
$755$	12.9775	−	4.12112i	0.472299	−	0.149983i
$756$	12.7773	−	9.28325i	0.464706	−	0.337628i
$757$	17.6737	+	12.8407i	0.642360	+	0.466702i	0.860660	−	0.509180i	$-0.170051\pi$
$757$	17.6737	+	12.8407i	0.642360	+	0.466702i	−0.218300	+	0.975882i	$0.570051\pi$
$758$	−7.83685	−	5.69381i	−0.284647	−	0.206808i
$759$	−6.46579	+	30.4023i	−0.234693	+	1.10353i
$760$	−12.5059	+	3.97137i	−0.453637	+	0.144057i
$761$	−9.85390	+	30.3272i	−0.357204	+	1.09936i	0.597517	+	0.801856i	$0.296154\pi$
$761$	−9.85390	+	30.3272i	−0.357204	+	1.09936i	−0.954721	+	0.297504i	$0.903846\pi$
$762$	18.3363	+	13.3221i	0.664254	+	0.482609i
$763$	37.5352			1.35886
$764$	19.2139	+	13.9597i	0.695136	+	0.505046i
$765$	−7.42358	−	2.46695i	−0.268400	−	0.0891926i
$766$	−27.8623			−1.00671
$767$	−20.7510	+	15.0765i	−0.749276	+	0.544381i
$768$	−1.27698	−	0.927783i	−0.0460792	−	0.0334785i
$769$	−21.8611	−	15.8830i	−0.788331	−	0.572756i	0.119136	−	0.992878i	$-0.461987\pi$
$769$	−21.8611	−	15.8830i	−0.788331	−	0.572756i	−0.907468	+	0.420122i	$0.861987\pi$
$770$	−20.6575	−	4.53759i	−0.744443	−	0.163523i
$771$	−36.3470	+	26.4077i	−1.30901	+	0.951048i
$772$	27.0968			0.975236
$773$	35.8696			1.29014			0.645069	−	0.764124i	$-0.276828\pi$
$773$	35.8696			1.29014			0.645069	+	0.764124i	$0.276828\pi$
$774$	−0.186192	−	0.573039i	−0.00669253	−	0.0205975i
$775$	20.4681	+	0.273146i	0.735237	+	0.00981168i
$776$	−13.9004	+	10.0992i	−0.498995	+	0.362541i
$777$	−31.6969	+	23.0291i	−1.13712	+	0.826166i
$778$	7.15901	+	22.0332i	0.256663	+	0.789927i
$779$	48.9107			1.75241
$780$	−7.67888	+	10.4221i	−0.274948	+	0.373172i
$781$	16.1218	+	36.2211i	0.576882	+	1.29609i
$782$	40.8454			1.46063
$783$	12.1817	+	37.4914i	0.435339	+	1.33983i
$784$	−0.916696	−	0.666019i	−0.0327391	−	0.0237864i
$785$	46.2121	−	14.6751i	1.64938	−	0.523776i
$786$	−13.5060	−	9.81270i	−0.481744	−	0.350007i
$787$	12.6457	+	38.9196i	0.450772	+	1.38733i	0.876028	+	0.482260i	$0.160184\pi$
$787$	12.6457	+	38.9196i	0.450772	+	1.38733i	−0.425257	+	0.905073i	$0.639816\pi$
$788$	0.639037			0.0227647
$789$	−30.6060			−1.08960
$790$	−7.28873	+	2.31460i	−0.259321	+	0.0823498i
$791$	6.09532	−	18.7595i	0.216725	−	0.667009i
$792$	−0.685833	−	1.54088i	−0.0243700	−	0.0547526i
$793$	−24.5552			−0.871980
$794$	4.17617	+	12.8529i	0.148207	+	0.456134i
$795$	−0.437180	+	0.593361i	−0.0155052	+	0.0210443i
$796$	−13.3903	−	9.72865i	−0.474608	−	0.344823i
$797$	0.0442752	−	0.136265i	0.00156831	−	0.00482676i	−0.950269	−	0.311429i	$-0.899192\pi$
$797$	0.0442752	−	0.136265i	0.00156831	−	0.00482676i	0.951838	+	0.306603i	$0.0991923\pi$
$798$	21.3701	+	15.5263i	0.756493	+	0.549625i
$799$	0.0557160	+	0.171476i	0.00197109	+	0.00606639i
$800$	−1.60840	+	4.73424i	−0.0568655	+	0.167381i
$801$	−2.98310	−	2.16735i	−0.105403	−	0.0765794i
$802$	9.75478	+	30.0221i	0.344453	+	1.06012i
$803$	3.67286	−	17.2699i	0.129613	−	0.609440i
$804$	−13.0404	+	9.47440i	−0.459899	+	0.334136i
$805$	35.9298	+	11.9399i	1.26636	+	0.420827i
$806$	12.1482	−	8.82616i	0.427901	−	0.310888i
$807$	−2.59599	−	7.98963i	−0.0913832	−	0.281248i
$808$	2.04969			0.0721079
$809$	3.42282	+	10.5344i	0.120340	+	0.370368i	0.993023	−	0.117918i	$-0.0376221\pi$
$809$	3.42282	+	10.5344i	0.120340	+	0.370368i	−0.872683	+	0.488287i	$0.837622\pi$
$810$	−0.107653	+	16.1346i	−0.00378254	+	0.566914i
$811$	11.9896			0.421010			0.210505	−	0.977593i	$-0.432489\pi$
$811$	11.9896			0.421010			0.210505	+	0.977593i	$0.432489\pi$
$812$	16.4232	−	11.9322i	0.576342	−	0.418737i
$813$	1.84609	−	5.68169i	0.0647453	−	0.199266i
$814$	11.7382	+	26.3725i	0.411425	+	0.924357i
$815$	−22.9389	−	7.62287i	−0.803514	−	0.267018i
$816$	8.78497	−	6.38265i	0.307535	−	0.223438i
$817$	5.62484	−	4.08669i	0.196788	−	0.142975i
$818$	7.68584	+	23.6546i	0.268729	+	0.827063i
$819$	−5.31929			−0.185871
$820$	11.0554	−	15.0049i	0.386072	−	0.523994i
$821$	2.75229	+	1.99966i	0.0960557	+	0.0697885i	0.634776	−	0.772696i	$-0.281092\pi$
$821$	2.75229	+	1.99966i	0.0960557	+	0.0697885i	−0.538721	+	0.842484i	$0.681092\pi$
$822$	5.59076	+	17.2066i	0.195000	+	0.600149i
$823$	−11.0363	+	33.9662i	−0.384700	+	1.18399i	0.551997	+	0.833846i	$0.313866\pi$
$823$	−11.0363	+	33.9662i	−0.384700	+	1.18399i	−0.936697	+	0.350140i	$0.886134\pi$
$824$	−0.921104			−0.0320882
$825$	19.6861	−	17.2514i	0.685381	−	0.600618i
$826$	19.9436			0.693927
$827$	6.80048	−	20.9297i	0.236476	−	0.727798i	−0.760446	−	0.649401i	$-0.775020\pi$
$827$	6.80048	−	20.9297i	0.236476	−	0.727798i	0.996922	−	0.0783971i	$-0.0249802\pi$
$828$	0.933017	+	2.87153i	0.0324246	+	0.0997926i
$829$	3.05049	+	2.21631i	0.105948	+	0.0769757i	0.639498	−	0.768793i	$-0.279142\pi$
$829$	3.05049	+	2.21631i	0.105948	+	0.0769757i	−0.533550	+	0.845769i	$0.679142\pi$
$830$	−1.29348	+	0.410757i	−0.0448974	+	0.0142576i
$831$	−15.4688			−0.536608
$832$	1.13341	+	3.48829i	0.0392941	+	0.120935i
$833$	6.30638	−	4.58185i	0.218503	−	0.158752i
$834$	−10.6969	+	7.77173i	−0.370402	+	0.269113i
$835$	16.3989	−	22.2574i	0.567508	−	0.770248i
$836$	14.4646	−	13.0211i	0.500270	−	0.450343i
$837$	7.00620	−	21.5629i	0.242170	−	0.745322i
$838$	11.6316	−	8.45088i	0.401808	−	0.291931i
$839$	18.3999			0.635237			0.317618	−	0.948219i	$-0.397117\pi$
$839$	18.3999			0.635237			0.317618	+	0.948219i	$0.397117\pi$
$840$	9.59351	−	3.04651i	0.331008	−	0.105115i
$841$	6.69619	+	20.6088i	0.230903	+	0.710647i
$842$	−15.3326			−0.528396
$843$	15.2452	+	46.9200i	0.525073	+	1.61601i
$844$	−11.2641	+	8.18383i	−0.387725	+	0.281699i
$845$	0.964999	−	0.306444i	0.0331970	−	0.0105420i
$846$	−0.0107825	+	0.00783394i	−0.000370710	+	0.000269336i
$847$	30.6864	−	6.51535i	1.05440	−	0.223870i
$848$	0.0645284	+	0.198598i	0.00221591	+	0.00681988i
$849$	27.4165	+	19.9193i	0.940932	+	0.683627i
$850$	−27.5558	−	20.5878i	−0.945155	−	0.706155i
$851$	−15.9689	−	49.1471i	−0.547405	−	1.68474i
$852$	−15.2651	−	11.0907i	−0.522972	−	0.379961i
$853$	9.61798	−	29.6011i	0.329313	−	1.01352i	−0.640143	−	0.768256i	$-0.721125\pi$
$853$	9.61798	−	29.6011i	0.329313	−	1.01352i	0.969456	−	0.245266i	$-0.0788753\pi$
$854$	15.4462	+	11.2223i	0.528559	+	0.384020i
$855$	6.35967	−	2.01957i	0.217496	−	0.0690679i
$856$	−2.28278	−	7.02567i	−0.0780238	−	0.240133i
$857$	7.09992			0.242529			0.121264	−	0.992620i	$-0.461305\pi$
$857$	7.09992			0.242529			0.121264	+	0.992620i	$0.461305\pi$
$858$	3.99429	−	18.7812i	0.136363	−	0.641181i
$859$	13.6251	−	41.9338i	0.464883	−	1.43076i	−0.394246	−	0.919005i	$-0.628994\pi$
$859$	13.6251	−	41.9338i	0.464883	−	1.43076i	0.859129	−	0.511759i	$-0.171006\pi$
$860$	0.0176767	−	2.64932i	0.000602770	−	0.0903411i
$861$	−37.5203			−1.27869
$862$	−14.8393			−0.505428
$863$	8.09362	+	24.9096i	0.275510	+	0.847932i	0.989084	+	0.147353i	$0.0470752\pi$
$863$	8.09362	+	24.9096i	0.275510	+	0.847932i	−0.713574	+	0.700580i	$0.752925\pi$
$864$	4.48034	+	3.25516i	0.152424	+	0.110743i
$865$	−10.5648	−	14.7471i	−0.359213	−	0.501415i
$866$	21.2574	+	15.4444i	0.722355	+	0.524822i
$867$	14.7925	+	45.5265i	0.502379	+	1.54616i
$868$	−11.6755			−0.396292
$869$	8.43031	−	7.58896i	0.285979	−	0.257438i
$870$	−0.167626	+	25.1232i	−0.00568306	+	0.851757i
$871$	37.4552			1.26912
$872$	4.06717	+	12.5175i	0.137732	+	0.423895i
$873$	7.06881	−	5.13579i	0.239243	−	0.173820i
$874$	−28.1864	+	20.4786i	−0.953418	+	0.692698i
$875$	−18.2213	−	26.1652i	−0.615994	−	0.884547i
$876$	2.59662	+	7.99158i	0.0877317	+	0.270010i
$877$	10.7774			0.363927			0.181963	−	0.983305i	$-0.441755\pi$
$877$	10.7774			0.363927			0.181963	+	0.983305i	$0.441755\pi$
$878$	7.49544			0.252959
$879$	30.8405	−	22.4069i	1.04022	−	0.755766i
$880$	−0.725142	−	7.38066i	−0.0244445	−	0.248802i
$881$	−2.24052	−	1.62784i	−0.0754852	−	0.0548432i	0.549403	−	0.835558i	$-0.314855\pi$
$881$	−2.24052	−	1.62784i	−0.0754852	−	0.0548432i	−0.624888	+	0.780715i	$0.714855\pi$
$882$	0.466170	+	0.338692i	0.0156968	+	0.0114044i
$883$	−6.44950	+	4.68584i	−0.217043	+	0.157691i	−0.690995	−	0.722860i	$-0.742827\pi$
$883$	−6.44950	+	4.68584i	−0.217043	+	0.157691i	0.473952	+	0.880551i	$0.342827\pi$
$884$	−25.2326			−0.848663
$885$	−14.6409	+	19.8713i	−0.492148	+	0.667966i
$886$	12.2261	+	8.88275i	0.410742	+	0.298422i
$887$	−15.2980			−0.513655			−0.256828	−	0.966457i	$-0.582677\pi$
$887$	−15.2980			−0.513655			−0.256828	+	0.966457i	$0.582677\pi$
$888$	−11.1145	−	8.07514i	−0.372977	−	0.270984i
$889$	−12.6543	+	38.9458i	−0.424411	+	1.30620i
$890$	−9.44230	−	13.1803i	−0.316507	−	0.441803i
$891$	−9.73159	−	21.8641i	−0.326020	−	0.732477i
$892$	1.88311	+	1.36816i	0.0630511	+	0.0458093i
$893$	−0.124421	−	0.0903971i	−0.00416359	−	0.00302502i
$894$	−28.8655	+	20.9720i	−0.965408	+	0.701410i
$895$	15.0768	−	20.4630i	0.503963	−	0.684002i
$896$	0.881273	−	2.71228i	0.0294413	−	0.0906109i
$897$	−10.6219	+	32.6910i	−0.354656	+	1.09152i
$898$	19.6514	−	14.2776i	0.655775	−	0.476448i
$899$	9.00538	−	27.7157i	0.300346	−	0.924370i
$900$	0.817925	−	2.40752i	0.0272642	−	0.0802506i
$901$	−1.43656			−0.0478587
$902$	−5.75065	+	27.0397i	−0.191476	+	0.900322i
$903$	−4.31492	+	3.13497i	−0.143591	+	0.104325i
$904$	6.91649			0.230039
$905$	12.4065	+	17.3179i	0.412407	+	0.575667i
$906$	2.97015	−	9.14119i	0.0986767	−	0.303696i
$907$	23.6029	−	17.1485i	0.783721	−	0.569407i	−0.122372	−	0.992484i	$-0.539050\pi$
$907$	23.6029	−	17.1485i	0.783721	−	0.569407i	0.906094	+	0.423077i	$0.139050\pi$
$908$	−3.99021			−0.132420
$909$	−1.04234			−0.0345721
$910$	−22.1959	−	7.37598i	−0.735788	−	0.244511i
$911$	−2.64844	+	8.15107i	−0.0877469	+	0.270057i	−0.985296	−	0.170858i	$-0.945346\pi$
$911$	−2.64844	+	8.15107i	−0.0877469	+	0.270057i	0.897549	+	0.440915i	$0.145346\pi$
$912$	−2.86222	+	8.80901i	−0.0947776	+	0.291696i
$913$	1.49607	−	1.34676i	0.0495127	−	0.0445713i
$914$	4.96236	+	15.2726i	0.164140	+	0.505172i
$915$	−22.5209	+	7.15173i	−0.744519	+	0.236429i
$916$	−13.3497	−	9.69914i	−0.441087	−	0.320468i
$917$	9.32079	−	28.6864i	0.307800	−	0.947310i
$918$	−30.8223	+	22.3937i	−1.01729	+	0.739104i
$919$	11.0948			0.365983			0.182991	−	0.983115i	$-0.441422\pi$
$919$	11.0948			0.365983			0.182991	+	0.983115i	$0.441422\pi$
$920$	−0.0885788	+	13.2759i	−0.00292036	+	0.437693i
$921$	7.90260	+	24.3217i	0.260400	+	0.801427i
$922$	−30.8919			−1.01737
$923$	13.5488	+	41.6990i	0.445965	+	1.37254i
$924$	−11.0961	+	9.98868i	−0.365034	+	0.328604i
$925$	−13.9990	+	41.2054i	−0.460285	+	1.35482i
$926$	−18.0587	−	13.1204i	−0.593445	−	0.431163i
$927$	0.468412			0.0153847
$928$	5.75878	+	4.18400i	0.189041	+	0.137346i
$929$	2.65525	−	8.17203i	0.0871160	−	0.268116i	−0.898003	−	0.439989i	$-0.854982\pi$
$929$	2.65525	−	8.17203i	0.0871160	−	0.268116i	0.985119	+	0.171874i	$0.0549822\pi$
$930$	8.57114	−	11.6331i	0.281059	−	0.381466i
$931$	−2.05468	+	6.32364i	−0.0673393	+	0.207249i
$932$	−2.87096	+	8.83592i	−0.0940416	+	0.289430i
$933$	−9.06152	−	27.8885i	−0.296661	−	0.913028i
$934$	4.62994	−	14.2495i	0.151496	−	0.466258i
$935$	49.8315	+	10.9459i	1.62966	+	0.357970i
$936$	−0.576378	−	1.77391i	−0.0188395	−	0.0579821i
$937$	5.47031	−	3.97441i	0.178707	−	0.129838i	−0.494836	−	0.868987i	$-0.664772\pi$
$937$	5.47031	−	3.97441i	0.178707	−	0.129838i	0.673543	+	0.739148i	$0.264772\pi$
$938$	−23.5609	−	17.1180i	−0.769289	−	0.558921i
$939$	14.1483	−	10.2793i	0.461712	−	0.335454i
$940$	−0.0558553	+	0.0177374i	−0.00182180	+	0.000578529i
$941$	4.59914	+	14.1547i	0.149928	+	0.461430i	0.997612	−	0.0690717i	$-0.0220037\pi$
$941$	4.59914	+	14.1547i	0.149928	+	0.461430i	−0.847684	+	0.530501i	$0.822004\pi$
$942$	10.5765	−	32.5513i	0.344603	−	1.06058i
$943$	15.2926	−	47.0657i	0.497995	−	1.53267i
$944$	2.16102	+	6.65092i	0.0703351	+	0.216469i
$945$	−33.6592	+	10.6888i	−1.09493	+	0.347706i
$946$	1.59793	+	3.59011i	0.0519533	+	0.116724i
$947$	10.6046	−	7.70471i	0.344604	−	0.250370i	−0.401998	−	0.915641i	$-0.631684\pi$
$947$	10.6046	−	7.70471i	0.344604	−	0.250370i	0.746602	+	0.665271i	$0.231684\pi$
$948$	−1.66817	+	5.13409i	−0.0541795	+	0.166747i
$949$	6.03375	−	18.5700i	0.195864	−	0.602807i
$950$	29.3376	+	0.391508i	0.951838	+	0.0127022i
$951$	16.3511	−	11.8798i	0.530220	−	0.385228i
$952$	15.8723	+	11.5319i	0.514425	+	0.373752i
$953$	34.1703	+	24.8262i	1.10689	+	0.804200i	0.982170	−	0.187993i	$-0.0601981\pi$
$953$	34.1703	+	24.8262i	1.10689	+	0.804200i	0.124716	+	0.992193i	$0.460198\pi$
$954$	−0.0328148	−	0.100994i	−0.00106242	−	0.00326979i
$955$	−30.9276	−	43.1710i	−1.00079	−	1.39698i
$956$	6.83022	+	4.96245i	0.220905	+	0.160497i
$957$	−15.1530	−	34.0446i	−0.489828	−	1.10051i
$958$	−22.3871	−	16.2652i	−0.723294	−	0.525504i
$959$	−26.4452	+	19.2136i	−0.853960	+	0.620438i
$960$	2.05549	+	2.86920i	0.0663406	+	0.0926030i
$961$	11.5198	−	8.36961i	0.371606	−	0.269987i
$962$	9.86489	+	30.3610i	0.318057	+	0.978878i
$963$	1.16087	+	3.57279i	0.0374085	+	0.115131i
$964$	−9.64394	+	7.00673i	−0.310610	+	0.225672i
$965$	−57.4986	−	19.1075i	−1.85095	−	0.615092i
$966$	21.6223	−	15.7095i	0.695685	−	0.505445i
$967$	27.4140	+	19.9174i	0.881575	+	0.640501i	0.933668	−	0.358141i	$-0.116589\pi$
$967$	27.4140	+	19.9174i	0.881575	+	0.640501i	−0.0520930	+	0.998642i	$0.516589\pi$
$968$	5.49785	+	9.52752i	0.176707	+	0.306226i
$969$	−51.5506	−	37.4537i	−1.65604	−	1.20319i
$970$	36.6178	−	11.6283i	1.17573	−	0.373362i
$971$	16.7175	+	51.4512i	0.536490	+	1.65115i	0.740407	+	0.672158i	$0.234633\pi$
$971$	16.7175	+	51.4512i	0.536490	+	1.65115i	−0.203918	+	0.978988i	$0.565367\pi$
$972$	−4.22656	−	3.07078i	−0.135567	−	0.0984953i
$973$	−19.3267	−	14.0417i	−0.619585	−	0.450155i
$974$	−27.7083	+	20.1312i	−0.887831	+	0.645047i
$975$	23.6436	−	16.7006i	0.757201	−	0.534848i
$976$	−2.06880	+	6.36712i	−0.0662207	+	0.203806i
$977$	−8.38176	+	25.7964i	−0.268156	+	0.825300i	0.722793	+	0.691064i	$0.242858\pi$
$977$	−8.38176	+	25.7964i	−0.268156	+	0.825300i	−0.990949	+	0.134236i	$0.957142\pi$
$978$	−13.8044	+	10.0295i	−0.441417	+	0.320708i
$979$	20.8252	+	12.0266i	0.665577	+	0.384371i
$980$	1.47555	+	2.05969i	0.0471348	+	0.0657942i
$981$	−2.06829	−	6.36555i	−0.0660355	−	0.203236i
$982$	−1.27438	+	3.92214i	−0.0406671	+	0.125160i
$983$	−16.7820	+	51.6495i	−0.535261	+	1.64736i	0.207823	+	0.978166i	$0.433362\pi$
$983$	−16.7820	+	51.6495i	−0.535261	+	1.64736i	−0.743084	+	0.669198i	$0.766638\pi$
$984$	−4.06556	−	12.5125i	−0.129605	−	0.398884i
$985$	−1.35602	−	0.450621i	−0.0432063	−	0.0143580i
$986$	−39.6173	+	28.7837i	−1.26167	+	0.916659i
$987$	0.0954456	+	0.0693453i	0.00303807	+	0.00220728i
$988$	17.4123	−	12.6508i	0.553961	−	0.402476i
$989$	−2.17385	−	6.69042i	−0.0691244	−	0.212743i
$990$	0.368759	+	3.75331i	0.0117199	+	0.119288i
$991$	14.3826	−	44.2650i	0.456877	−	1.40612i	−0.412040	−	0.911166i	$-0.635183\pi$
$991$	14.3826	−	44.2650i	0.456877	−	1.40612i	0.868917	−	0.494958i	$-0.164817\pi$
$992$	−1.26511	−	3.89362i	−0.0401674	−	0.123622i
$993$	6.79305	−	20.9068i	0.215571	−	0.663459i
$994$	10.5347	−	32.4226i	0.334141	−	1.02838i
$995$	21.5537	+	30.0862i	0.683297	+	0.953796i
$996$	−0.296038	+	0.911112i	−0.00938033	+	0.0288697i
$997$	−7.80571	−	5.67118i	−0.247209	−	0.179608i	0.457280	−	0.889323i	$-0.348824\pi$
$997$	−7.80571	−	5.67118i	−0.247209	−	0.179608i	−0.704489	+	0.709715i	$0.748824\pi$
$998$	33.6844			1.06626
$999$	38.9955	+	28.3319i	1.23376	+	0.896381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.j.c.81.11	yes	60
11.3	even	5		550.2.g.c.531.5	yes	60
25.21	even	5		550.2.g.c.521.5	✓	60
275.146	even	5	inner	550.2.j.c.421.11	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.g.c.521.5	✓	60	25.21	even	5
550.2.g.c.531.5	yes	60	11.3	even	5
550.2.j.c.81.11	yes	60	1.1	even	1	trivial
550.2.j.c.421.11	yes	60	275.146	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.487764 + 1.50118i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.30223 + 1.81775i) q^{5} +1.57844 q^{6} +(0.881273 + 2.71228i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.411412 - 0.298908i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.487764 + 1.50118i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.30223 + 1.81775i) q^{5} +1.57844 q^{6} +(0.881273 + 2.71228i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.411412 - 0.298908i) q^{9} +(2.13119 - 0.676779i) q^{10} +(-2.46498 + 2.21898i) q^{11} +(0.487764 - 1.50118i) q^{12} +(-2.96732 + 2.15588i) q^{13} +2.85186 q^{14} +(-2.09359 + 2.84152i) q^{15} +(0.309017 + 0.951057i) q^{16} -6.87947 q^{17} +(-0.157145 - 0.483644i) q^{18} +(4.74735 - 3.44915i) q^{19} +(0.0149191 - 2.23602i) q^{20} +(-3.64178 + 2.64591i) q^{21} +(1.34865 + 3.03004i) q^{22} +(-1.83472 - 5.64669i) q^{23} +(-1.27698 - 0.927783i) q^{24} +(-1.60840 + 4.73424i) q^{25} +(1.13341 + 3.48829i) q^{26} +(4.48034 + 3.25516i) q^{27} +(0.881273 - 2.71228i) q^{28} +(5.75878 + 4.18400i) q^{29} +(2.05549 + 2.86920i) q^{30} +(-1.26511 - 3.89362i) q^{31} +1.00000 q^{32} +(-4.53342 - 2.61806i) q^{33} +(-2.12587 + 6.54276i) q^{34} +(-3.78262 + 5.13394i) q^{35} -0.508533 q^{36} +8.70369 q^{37} +(-1.81333 - 5.58084i) q^{38} +(-4.68373 - 3.40293i) q^{39} +(-2.12197 - 0.705157i) q^{40} +(6.74324 + 4.89925i) q^{41} +(1.39103 + 4.28116i) q^{42} +1.18484 q^{43} +(3.29850 - 0.346309i) q^{44} +(1.07909 + 0.358595i) q^{45} -5.93728 q^{46} +(-0.00809888 - 0.0249258i) q^{47} +(-1.27698 + 0.927783i) q^{48} +(-0.916696 + 0.666019i) q^{49} +(4.00551 + 2.99264i) q^{50} +(-3.35556 - 10.3273i) q^{51} +3.66781 q^{52} +0.208818 q^{53} +(4.48034 - 3.25516i) q^{54} +(-7.24351 - 1.59110i) q^{55} +(-2.30720 - 1.67628i) q^{56} +(7.49339 + 5.44427i) q^{57} +(5.75878 - 4.18400i) q^{58} +6.99319 q^{59} +(3.36395 - 1.06825i) q^{60} +(5.41619 + 3.93510i) q^{61} -4.09399 q^{62} +(1.17329 + 0.852444i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-7.78297 - 2.58638i) q^{65} +(-3.89082 + 3.50252i) q^{66} +(-8.26158 - 6.00239i) q^{67} +(5.56561 + 4.04365i) q^{68} +(7.58181 - 5.50851i) q^{69} +(3.71377 + 5.18395i) q^{70} +(3.69399 - 11.3689i) q^{71} +(-0.157145 + 0.483644i) q^{72} +(-4.30682 + 3.12909i) q^{73} +(2.68959 - 8.27770i) q^{74} +(-7.89149 - 0.105311i) q^{75} -5.86804 q^{76} +(-8.19081 - 4.73020i) q^{77} +(-4.68373 + 3.40293i) q^{78} -3.42003 q^{79} +(-1.32637 + 1.80021i) q^{80} +(-2.22980 + 6.86263i) q^{81} +(6.74324 - 4.89925i) q^{82} -0.606929 q^{83} +4.50148 q^{84} +(-8.95864 - 12.5051i) q^{85} +(0.366135 - 1.12685i) q^{86} +(-3.47202 + 10.6858i) q^{87} +(0.689932 - 3.24407i) q^{88} +(-2.24065 - 6.89600i) q^{89} +(0.674502 - 0.915465i) q^{90} +(-8.46237 - 6.14827i) q^{91} +(-1.83472 + 5.64669i) q^{92} +(5.22796 - 3.79834i) q^{93} -0.0262085 q^{94} +(12.4518 + 4.13789i) q^{95} +(0.487764 + 1.50118i) q^{96} +17.1818 q^{97} +(0.350147 + 1.07764i) q^{98} +(-0.350853 + 1.64972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} + q^{3} - 15 q^{4} + 6 q^{6} - 3 q^{7} - 15 q^{8} - 12 q^{9}+O(q^{10}) \) 60 * q - 15 * q^2 + q^3 - 15 * q^4 + 6 * q^6 - 3 * q^7 - 15 * q^8 - 12 * q^9	\( 60 q - 15 q^{2} + q^{3} - 15 q^{4} + 6 q^{6} - 3 q^{7} - 15 q^{8} - 12 q^{9} - 5 q^{10} - 3 q^{11} + q^{12} - 8 q^{13} + 12 q^{14} - 3 q^{15} - 15 q^{16} + 6 q^{17} - 17 q^{18} - 22 q^{19} + 10 q^{20} - 4 q^{21} + 7 q^{22} - 3 q^{23} - 4 q^{24} + 18 q^{25} + 12 q^{26} - 8 q^{27} - 3 q^{28} - 22 q^{29} - 8 q^{30} + 15 q^{31} + 60 q^{32} + 25 q^{33} + q^{34} + 11 q^{35} + 58 q^{36} + 94 q^{37} + 3 q^{38} - 12 q^{39} - 5 q^{40} - 11 q^{41} - 19 q^{42} + 40 q^{43} + 7 q^{44} - 20 q^{45} + 2 q^{46} - 24 q^{47} - 4 q^{48} - 30 q^{49} - 27 q^{50} - 48 q^{51} - 8 q^{52} - 14 q^{53} - 8 q^{54} - 7 q^{55} - 3 q^{56} + 30 q^{57} - 22 q^{58} - 42 q^{59} + 12 q^{60} + 19 q^{61} - 20 q^{62} - 24 q^{63} - 15 q^{64} - 7 q^{65} + 10 q^{66} - 40 q^{67} - 4 q^{68} - 2 q^{69} - 19 q^{70} + 19 q^{71} - 17 q^{72} - 16 q^{73} - 11 q^{74} + 25 q^{75} + 38 q^{76} - 23 q^{77} - 12 q^{78} + 70 q^{79} - 86 q^{81} - 11 q^{82} - 14 q^{83} + 46 q^{84} - 31 q^{85} + 68 q^{87} - 8 q^{88} + q^{89} + 45 q^{90} - 25 q^{91} - 3 q^{92} - 40 q^{93} + 66 q^{94} + 19 q^{95} + q^{96} + 66 q^{97} - 30 q^{98} + 21 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 + q^3 - 15 * q^4 + 6 * q^6 - 3 * q^7 - 15 * q^8 - 12 * q^9 - 5 * q^10 - 3 * q^11 + q^12 - 8 * q^13 + 12 * q^14 - 3 * q^15 - 15 * q^16 + 6 * q^17 - 17 * q^18 - 22 * q^19 + 10 * q^20 - 4 * q^21 + 7 * q^22 - 3 * q^23 - 4 * q^24 + 18 * q^25 + 12 * q^26 - 8 * q^27 - 3 * q^28 - 22 * q^29 - 8 * q^30 + 15 * q^31 + 60 * q^32 + 25 * q^33 + q^34 + 11 * q^35 + 58 * q^36 + 94 * q^37 + 3 * q^38 - 12 * q^39 - 5 * q^40 - 11 * q^41 - 19 * q^42 + 40 * q^43 + 7 * q^44 - 20 * q^45 + 2 * q^46 - 24 * q^47 - 4 * q^48 - 30 * q^49 - 27 * q^50 - 48 * q^51 - 8 * q^52 - 14 * q^53 - 8 * q^54 - 7 * q^55 - 3 * q^56 + 30 * q^57 - 22 * q^58 - 42 * q^59 + 12 * q^60 + 19 * q^61 - 20 * q^62 - 24 * q^63 - 15 * q^64 - 7 * q^65 + 10 * q^66 - 40 * q^67 - 4 * q^68 - 2 * q^69 - 19 * q^70 + 19 * q^71 - 17 * q^72 - 16 * q^73 - 11 * q^74 + 25 * q^75 + 38 * q^76 - 23 * q^77 - 12 * q^78 + 70 * q^79 - 86 * q^81 - 11 * q^82 - 14 * q^83 + 46 * q^84 - 31 * q^85 + 68 * q^87 - 8 * q^88 + q^89 + 45 * q^90 - 25 * q^91 - 3 * q^92 - 40 * q^93 + 66 * q^94 + 19 * q^95 + q^96 + 66 * q^97 - 30 * q^98 + 21 * q^99

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