LMFDB - Embedded newform 550.2.g.c.521.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(291,550)]

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([2, 4]))

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

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

chi := DirichletCharacter("550.291");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.g (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			521.5
Character	$\chi$	$=$	550.521
Dual form			550.2.g.c.531.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-1.27698 + 0.927783i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.32637 - 1.80021i) q^{5} +(0.487764 - 1.50118i) q^{6} +(0.881273 + 2.71228i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.157145 + 0.483644i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-1.27698 + 0.927783i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.32637 - 1.80021i) q^{5} +(0.487764 - 1.50118i) q^{6} +(0.881273 + 2.71228i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.157145 + 0.483644i) q^{9} +(2.13119 + 0.676779i) q^{10} +(3.29850 - 0.346309i) q^{11} +(0.487764 + 1.50118i) q^{12} +(1.13341 - 3.48829i) q^{13} +(-2.30720 - 1.67628i) q^{14} +(3.36395 + 1.06825i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.12587 + 6.54276i) q^{17} +(-0.157145 - 0.483644i) q^{18} +(-1.81333 - 5.58084i) q^{19} +(-2.12197 + 0.705157i) q^{20} +(-3.64178 - 2.64591i) q^{21} +(-2.46498 + 2.21898i) q^{22} +(-1.83472 + 5.64669i) q^{23} +(-1.27698 - 0.927783i) q^{24} +(-1.48149 + 4.77548i) q^{25} +(1.13341 + 3.48829i) q^{26} +(-1.71134 - 5.26695i) q^{27} +2.85186 q^{28} +(-2.19966 + 6.76985i) q^{29} +(-3.34940 + 1.11305i) q^{30} -4.09399 q^{31} +1.00000 q^{32} +(-3.89082 + 3.50252i) q^{33} +(-2.12587 - 6.54276i) q^{34} +(3.71377 - 5.18395i) q^{35} +(0.411412 + 0.298908i) q^{36} +(-7.04144 + 5.11590i) q^{37} +(4.74735 + 3.44915i) q^{38} +(1.78902 + 5.50605i) q^{39} +(1.30223 - 1.81775i) q^{40} -8.33510 q^{41} +4.50148 q^{42} +1.18484 q^{43} +(0.689932 - 3.24407i) q^{44} +(1.07909 - 0.358595i) q^{45} +(-1.83472 - 5.64669i) q^{46} +(0.0212031 - 0.0154050i) q^{47} +1.57844 q^{48} +(-0.916696 + 0.666019i) q^{49} +(-1.60840 - 4.73424i) q^{50} +(-3.35556 - 10.3273i) q^{51} +(-2.96732 - 2.15588i) q^{52} +(0.0645284 + 0.198598i) q^{53} +(4.48034 + 3.25516i) q^{54} +(-4.99845 - 5.47864i) q^{55} +(-2.30720 + 1.67628i) q^{56} +(7.49339 + 5.44427i) q^{57} +(-2.19966 - 6.76985i) q^{58} +(-5.65761 + 4.11050i) q^{59} +(2.05549 - 2.86920i) q^{60} +(-2.06880 - 6.36712i) q^{61} +(3.31211 - 2.40639i) q^{62} -1.45026 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.78297 + 2.58638i) q^{65} +(1.08901 - 5.12056i) q^{66} +(-8.26158 + 6.00239i) q^{67} +(5.56561 + 4.04365i) q^{68} +(-2.89600 - 8.91296i) q^{69} +(0.0425471 + 6.37681i) q^{70} +11.9540 q^{71} -0.508533 q^{72} +5.32352 q^{73} +(2.68959 - 8.27770i) q^{74} +(-2.53876 - 7.47271i) q^{75} -5.86804 q^{76} +(3.84616 + 8.64125i) q^{77} +(-4.68373 - 3.40293i) q^{78} +(-1.05685 - 3.25264i) q^{79} +(0.0149191 + 2.23602i) q^{80} +(5.83770 + 4.24134i) q^{81} +(6.74324 - 4.89925i) q^{82} +(-0.187551 + 0.577224i) q^{83} +(-3.64178 + 2.64591i) q^{84} +(14.5980 - 4.85110i) q^{85} +(-0.958554 + 0.696431i) q^{86} +(-3.47202 - 10.6858i) q^{87} +(1.34865 + 3.03004i) q^{88} +(-2.24065 + 6.89600i) q^{89} +(-0.662226 + 0.924384i) q^{90} +10.4601 q^{91} +(4.80336 + 3.48985i) q^{92} +(5.22796 - 3.79834i) q^{93} +(-0.00809888 + 0.0249258i) q^{94} +(-7.64154 + 10.6666i) q^{95} +(-1.27698 + 0.927783i) q^{96} +(5.30948 + 16.3409i) 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} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9}+O(q^{10}) $ 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9	\( 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21} - 3 q^{22} - 3 q^{23} - 4 q^{24} + 8 q^{25} + 12 q^{26} + 2 q^{27} + 12 q^{28} + 18 q^{29} + 2 q^{30} - 20 q^{31} + 60 q^{32} + 10 q^{33} + q^{34} - 19 q^{35} - 12 q^{36} - 36 q^{37} - 22 q^{38} + 13 q^{39} + 64 q^{41} + 46 q^{42} + 40 q^{43} - 8 q^{44} - 20 q^{45} - 3 q^{46} - 9 q^{47} + 6 q^{48} - 30 q^{49} + 18 q^{50} - 48 q^{51} - 8 q^{52} + 31 q^{53} - 8 q^{54} - 42 q^{55} - 3 q^{56} + 30 q^{57} + 18 q^{58} + 23 q^{59} - 8 q^{60} - 41 q^{61} - 5 q^{62} + 6 q^{63} - 15 q^{64} - 7 q^{65} - 30 q^{66} - 40 q^{67} - 4 q^{68} - 22 q^{69} - 4 q^{70} + 4 q^{71} + 58 q^{72} + 74 q^{73} - 11 q^{74} + 35 q^{75} + 38 q^{76} + 22 q^{77} - 12 q^{78} - 45 q^{79} + 10 q^{80} + 24 q^{81} - 11 q^{82} + 16 q^{83} - 4 q^{84} + 9 q^{85} - 20 q^{86} + 68 q^{87} + 7 q^{88} + q^{89} + 10 q^{90} + 10 q^{91} + 2 q^{92} - 40 q^{93} - 24 q^{94} + 24 q^{95} - 4 q^{96} + 6 q^{97} - 30 q^{98} + 21 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−1.27698	+	0.927783i	−0.737267	+	0.535656i	−0.891854	−	0.452324i	$-0.850595\pi$
$3$	−1.27698	+	0.927783i	−0.737267	+	0.535656i	0.154587	+	0.987979i	$0.450595\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.32637	−	1.80021i	−0.593170	−	0.805077i
$5$	−1.32637	−	1.80021i	−0.593170	−	0.805077i
$6$	0.487764	−	1.50118i	0.199129	−	0.612856i
$7$	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	$0.718821\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.157145	+	0.483644i	−0.0523818	+	0.161215i
$10$	2.13119	+	0.676779i	0.673941	+	0.214016i
$11$	3.29850	−	0.346309i	0.994534	−	0.104416i
$11$	3.29850	−	0.346309i	0.994534	−	0.104416i
$12$	0.487764	+	1.50118i	0.140805	+	0.433354i
$13$	1.13341	−	3.48829i	0.314353	−	0.967478i	−0.661668	−	0.749797i	$-0.730151\pi$
$13$	1.13341	−	3.48829i	0.314353	−	0.967478i	0.976020	−	0.217680i	$-0.0698490\pi$
$14$	−2.30720	−	1.67628i	−0.616626	−	0.448005i
$15$	3.36395	+	1.06825i	0.868569	+	0.275822i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.12587	+	6.54276i	−0.515600	+	1.58685i	0.266588	+	0.963811i	$0.414104\pi$
$17$	−2.12587	+	6.54276i	−0.515600	+	1.58685i	−0.782188	+	0.623043i	$0.785896\pi$
$18$	−0.157145	−	0.483644i	−0.0370395	−	0.113996i
$19$	−1.81333	−	5.58084i	−0.416005	−	1.28033i	−0.911349	−	0.411636i	$-0.864958\pi$
$19$	−1.81333	−	5.58084i	−0.416005	−	1.28033i	0.495343	−	0.868697i	$-0.335042\pi$
$20$	−2.12197	+	0.705157i	−0.474487	+	0.157678i
$21$	−3.64178	−	2.64591i	−0.794701	−	0.577384i
$22$	−2.46498	+	2.21898i	−0.525536	+	0.473087i
$23$	−1.83472	+	5.64669i	−0.382566	+	1.17742i	0.555665	+	0.831406i	$0.312464\pi$
$23$	−1.83472	+	5.64669i	−0.382566	+	1.17742i	−0.938231	+	0.346010i	$0.887536\pi$
$24$	−1.27698	−	0.927783i	−0.260663	−	0.189383i
$25$	−1.48149	+	4.77548i	−0.296299	+	0.955095i
$26$	1.13341	+	3.48829i	0.222281	+	0.684110i
$27$	−1.71134	−	5.26695i	−0.329347	−	1.01363i
$28$	2.85186			0.538951
$29$	−2.19966	+	6.76985i	−0.408466	+	1.25713i	0.509500	+	0.860471i	$0.329830\pi$
$29$	−2.19966	+	6.76985i	−0.408466	+	1.25713i	−0.917966	+	0.396659i	$0.870170\pi$
$30$	−3.34940	+	1.11305i	−0.611514	+	0.203213i
$31$	−4.09399			−0.735303			−0.367651	−	0.929964i	$-0.619838\pi$
$31$	−4.09399			−0.735303			−0.367651	+	0.929964i	$0.619838\pi$
$32$	1.00000			0.176777
$33$	−3.89082	+	3.50252i	−0.677305	+	0.609710i
$34$	−2.12587	−	6.54276i	−0.364584	−	1.12207i
$35$	3.71377	−	5.18395i	0.627742	−	0.876248i
$36$	0.411412	+	0.298908i	0.0685686	+	0.0498180i
$37$	−7.04144	+	5.11590i	−1.15760	+	0.841049i	−0.989473	−	0.144715i	$-0.953773\pi$
$37$	−7.04144	+	5.11590i	−1.15760	+	0.841049i	−0.168132	+	0.985765i	$0.553773\pi$
$38$	4.74735	+	3.44915i	0.770121	+	0.559526i
$39$	1.78902	+	5.50605i	0.286473	+	0.881674i
$40$	1.30223	−	1.81775i	0.205900	−	0.287411i
$41$	−8.33510			−1.30172			−0.650862	−	0.759196i	$-0.725592\pi$
$41$	−8.33510			−1.30172			−0.650862	+	0.759196i	$0.725592\pi$
$42$	4.50148			0.694594
$43$	1.18484			0.180686			0.0903431	−	0.995911i	$-0.471204\pi$
$43$	1.18484			0.180686			0.0903431	+	0.995911i	$0.471204\pi$
$44$	0.689932	−	3.24407i	0.104011	−	0.489062i
$45$	1.07909	−	0.358595i	0.160861	−	0.0534562i
$46$	−1.83472	−	5.64669i	−0.270515	−	0.832560i
$47$	0.0212031	−	0.0154050i	0.00309280	−	0.00224705i	−0.586238	−	0.810139i	$-0.699392\pi$
$47$	0.0212031	−	0.0154050i	0.00309280	−	0.00224705i	0.589331	+	0.807892i	$0.299392\pi$
$48$	1.57844			0.227828
$49$	−0.916696	+	0.666019i	−0.130957	+	0.0951455i
$50$	−1.60840	−	4.73424i	−0.227462	−	0.669523i
$51$	−3.35556	−	10.3273i	−0.469872	−	1.44612i
$52$	−2.96732	−	2.15588i	−0.411493	−	0.298967i
$53$	0.0645284	+	0.198598i	0.00886366	+	0.0272795i	0.955391	−	0.295345i	$-0.0954347\pi$
$53$	0.0645284	+	0.198598i	0.00886366	+	0.0272795i	−0.946527	+	0.322625i	$0.895435\pi$
$54$	4.48034	+	3.25516i	0.609697	+	0.442971i
$55$	−4.99845	−	5.47864i	−0.673990	−	0.738740i
$56$	−2.30720	+	1.67628i	−0.308313	+	0.224002i
$57$	7.49339	+	5.44427i	0.992524	+	0.721111i
$58$	−2.19966	−	6.76985i	−0.288829	−	0.888925i
$59$	−5.65761	+	4.11050i	−0.736558	+	0.535141i	−0.891631	−	0.452762i	$-0.850439\pi$
$59$	−5.65761	+	4.11050i	−0.736558	+	0.535141i	0.155073	+	0.987903i	$0.450439\pi$
$60$	2.05549	−	2.86920i	0.265362	−	0.370412i
$61$	−2.06880	−	6.36712i	−0.264883	−	0.815226i	−0.991720	−	0.128416i	$-0.959011\pi$
$61$	−2.06880	−	6.36712i	−0.264883	−	0.815226i	0.726837	−	0.686810i	$-0.240989\pi$
$62$	3.31211	−	2.40639i	0.420638	−	0.305612i
$63$	−1.45026			−0.182716
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−7.78297	+	2.58638i	−0.965359	+	0.320801i
$66$	1.08901	−	5.12056i	0.134048	−	0.630298i
$67$	−8.26158	+	6.00239i	−1.00931	+	0.733309i	−0.964065	−	0.265667i	$-0.914408\pi$
$67$	−8.26158	+	6.00239i	−1.00931	+	0.733309i	−0.0452478	+	0.998976i	$0.514408\pi$
$68$	5.56561	+	4.04365i	0.674929	+	0.490365i
$69$	−2.89600	−	8.91296i	−0.348637	−	1.07299i
$70$	0.0425471	+	6.37681i	0.00508535	+	0.762174i
$71$	11.9540			1.41868			0.709339	−	0.704867i	$-0.248994\pi$
$71$	11.9540			1.41868			0.709339	+	0.704867i	$0.248994\pi$
$72$	−0.508533			−0.0599312
$73$	5.32352			0.623071			0.311535	−	0.950235i	$-0.399157\pi$
$73$	5.32352			0.623071			0.311535	+	0.950235i	$0.399157\pi$
$74$	2.68959	−	8.27770i	0.312658	−	0.962264i
$75$	−2.53876	−	7.47271i	−0.293151	−	0.862874i
$76$	−5.86804			−0.673111
$77$	3.84616	+	8.64125i	0.438311	+	0.984761i
$78$	−4.68373	−	3.40293i	−0.530328	−	0.385306i
$79$	−1.05685	−	3.25264i	−0.118905	−	0.365950i	0.873837	−	0.486219i	$-0.161624\pi$
$79$	−1.05685	−	3.25264i	−0.118905	−	0.365950i	−0.992741	+	0.120269i	$0.961624\pi$
$80$	0.0149191	+	2.23602i	0.00166800	+	0.249994i
$81$	5.83770	+	4.24134i	0.648633	+	0.471260i
$82$	6.74324	−	4.89925i	0.744666	−	0.541031i
$83$	−0.187551	+	0.577224i	−0.0205864	+	0.0633586i	−0.960822	−	0.277166i	$-0.910605\pi$
$83$	−0.187551	+	0.577224i	−0.0205864	+	0.0633586i	0.940236	+	0.340525i	$0.110605\pi$
$84$	−3.64178	+	2.64591i	−0.397350	+	0.288692i
$85$	14.5980	−	4.85110i	1.58338	−	0.526176i
$86$	−0.958554	+	0.696431i	−0.103364	+	0.0750980i
$87$	−3.47202	−	10.6858i	−0.372240	−	1.14564i
$88$	1.34865	+	3.03004i	0.143767	+	0.323003i
$89$	−2.24065	+	6.89600i	−0.237508	+	0.730974i	0.759271	+	0.650775i	$0.225556\pi$
$89$	−2.24065	+	6.89600i	−0.237508	+	0.730974i	−0.996779	+	0.0801995i	$0.974444\pi$
$90$	−0.662226	+	0.924384i	−0.0698048	+	0.0974386i
$91$	10.4601			1.09651
$92$	4.80336	+	3.48985i	0.500785	+	0.363842i
$93$	5.22796	−	3.79834i	0.542114	−	0.393869i
$94$	−0.00809888	+	0.0249258i	−0.000835335	+	0.00257090i
$95$	−7.64154	+	10.6666i	−0.784005	+	1.09437i
$96$	−1.27698	+	0.927783i	−0.130332	+	0.0946914i
$97$	5.30948	+	16.3409i	0.539096	+	1.65917i	0.734628	+	0.678470i	$0.237357\pi$
$97$	5.30948	+	16.3409i	0.539096	+	1.65917i	−0.195532	+	0.980697i	$0.562643\pi$
$98$	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	$0.732516\pi$
$102$	8.78497	+	6.38265i	0.869841	+	0.631977i
$103$	−0.284637	+	0.876022i	−0.0280461	+	0.0863170i	−0.964100	−	0.265540i	$-0.914450\pi$
$103$	−0.284637	+	0.876022i	−0.0280461	+	0.0863170i	0.936054	+	0.351857i	$0.114450\pi$
$104$	3.66781			0.359658
$105$	0.0671580	+	10.0654i	0.00655395	+	0.982282i
$106$	−0.168938	−	0.122740i	−0.0164087	−	0.0119216i
$107$	−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	$0.983774\pi$
$108$	−5.53800			−0.532895
$109$	4.06717	+	12.5175i	0.389565	+	1.19896i	0.933114	+	0.359580i	$0.117080\pi$
$109$	4.06717	+	12.5175i	0.389565	+	1.19896i	−0.543550	+	0.839377i	$0.682920\pi$
$110$	7.26409	+	1.49430i	0.692604	+	0.142476i
$111$	4.24535	−	13.0658i	0.402951	−	1.24015i
$112$	0.881273	−	2.71228i	0.0832725	−	0.256286i
$113$	6.91649			0.650649			0.325324	−	0.945602i	$-0.394526\pi$
$113$	6.91649			0.650649			0.325324	+	0.945602i	$0.394526\pi$
$114$	−9.26235			−0.867498
$115$	12.5987	−	4.18671i	1.17484	−	0.390413i
$116$	5.75878	+	4.18400i	0.534689	+	0.388474i
$117$	1.50898	+	1.09634i	0.139505	+	0.101356i
$118$	2.16102	−	6.65092i	0.198938	−	0.612267i
$119$	−19.6193			−1.79850
$120$	0.0235488	+	3.52942i	0.00214970	+	0.322190i
$121$	10.7601	−	2.28460i	0.978195	−	0.207691i
$122$	5.41619	+	3.93510i	0.490359	+	0.356267i
$123$	10.6438	−	7.73316i	0.959718	−	0.697276i
$124$	−1.26511	+	3.89362i	−0.113611	+	0.349657i
$125$	10.5619	−	3.66704i	0.944681	−	0.327990i
$126$	1.17329	−	0.852444i	0.104525	−	0.0759417i
$127$	−4.43720	−	13.6563i	−0.393738	−	1.21180i	−0.929940	−	0.367711i	$-0.880142\pi$
$127$	−4.43720	−	13.6563i	−0.393738	−	1.21180i	0.536202	−	0.844090i	$-0.319858\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−1.51302	+	1.09927i	−0.133214	+	0.0967856i
$130$	4.77632	−	6.66714i	0.418911	−	0.584747i
$131$	−8.55657	+	6.21671i	−0.747591	+	0.543157i	−0.895079	−	0.445907i	$-0.852881\pi$
$131$	−8.55657	+	6.21671i	−0.747591	+	0.543157i	0.147488	+	0.989064i	$0.452881\pi$
$132$	2.12876	+	4.78273i	0.185285	+	0.416283i
$133$	13.5388	−	9.83649i	1.17396	−	0.852932i
$134$	3.15564	−	9.71207i	0.272606	−	0.838995i
$135$	−7.21175	+	10.0667i	−0.620688	+	0.866402i
$136$	−6.87947			−0.589910
$137$	−9.27297	−	6.73721i	−0.792243	−	0.575599i	0.116385	−	0.993204i	$-0.462869\pi$
$137$	−9.27297	−	6.73721i	−0.792243	−	0.575599i	−0.908628	+	0.417606i	$0.862869\pi$
$138$	7.58181	+	5.50851i	0.645407	+	0.468916i
$139$	8.37668			0.710500			0.355250	−	0.934771i	$-0.384396\pi$
$139$	8.37668			0.710500			0.355250	+	0.934771i	$0.384396\pi$
$140$	−3.78262	−	5.13394i	−0.319689	−	0.433897i
$141$	−0.0127836	+	0.0393438i	−0.00107657	+	0.00331335i
$142$	−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
$145$	15.1047	−	5.01947i	1.25438	−	0.416844i
$146$	−4.30682	+	3.12909i	−0.356435	+	0.258965i
$147$	0.552685	−	1.70099i	0.0455847	−	0.140295i
$148$	2.68959	+	8.27770i	0.221083	+	0.680423i
$149$	−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	$0.923296\pi$
$150$	6.44625	+	4.55330i	0.526334	+	0.371776i
$151$	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	$0.0203020\pi$
$152$	4.74735	−	3.44915i	0.385061	−	0.279763i
$153$	−2.83029	−	2.05633i	−0.228816	−	0.166244i
$154$	−8.19081	−	4.73020i	−0.660034	−	0.381170i
$155$	5.43014	+	7.37004i	0.436159	+	0.591976i
$156$	5.78940			0.463523
$157$	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	$-0.232856\pi$
$158$	2.76686	+	2.01024i	0.220120	+	0.159926i
$159$	−0.266657	−	0.193738i	−0.0211473	−	0.0153644i
$160$	−1.32637	−	1.80021i	−0.104859	−	0.142319i
$161$	−16.9323			−1.33445
$162$	−7.21580			−0.566926
$163$	3.34053	−	10.2811i	0.261651	−	0.805278i	−0.730796	−	0.682596i	$-0.760851\pi$
$163$	3.34053	−	10.2811i	0.261651	−	0.805278i	0.992446	−	0.122681i	$-0.0391493\pi$
$164$	−2.57569	+	7.92715i	−0.201127	+	0.619006i
$165$	11.4659	+	2.35866i	0.892621	+	0.183622i
$166$	−0.187551	−	0.577224i	−0.0145568	−	0.0448013i
$167$	−12.3638			−0.956738			−0.478369	−	0.878159i	$-0.658772\pi$
$167$	−12.3638			−0.956738			−0.478369	+	0.878159i	$0.658772\pi$
$168$	1.39103	−	4.28116i	0.107321	−	0.330299i
$169$	−0.366321	−	0.266148i	−0.0281786	−	0.0204729i
$170$	−8.95864	+	12.5051i	−0.687096	+	0.959099i
$171$	2.98409			0.228199
$172$	0.366135	−	1.12685i	0.0279175	−	0.0859214i
$173$	6.56342	+	4.76860i	0.499007	+	0.362550i	0.808638	−	0.588307i	$-0.200205\pi$
$173$	6.56342	+	4.76860i	0.499007	+	0.362550i	−0.309630	+	0.950857i	$0.600205\pi$
$174$	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
$178$	−2.24065	−	6.89600i	−0.167943	−	0.516877i
$179$	9.19611	−	6.68136i	0.687349	−	0.499389i	−0.188438	−	0.982085i	$-0.560343\pi$
$179$	9.19611	−	6.68136i	0.687349	−	0.499389i	0.875788	+	0.482696i	$0.160343\pi$
$180$	−0.00758684	−	1.13709i	−0.000565490	−	0.0847536i
$181$	2.94405	−	9.06085i	0.218829	−	0.673488i	−0.780030	−	0.625742i	$-0.784796\pi$
$181$	2.94405	−	9.06085i	0.218829	−	0.673488i	0.998860	−	0.0477457i	$-0.0152037\pi$
$182$	−8.46237	+	6.14827i	−0.627273	+	0.455740i
$183$	8.54913	+	6.21130i	0.631970	+	0.459153i
$184$	−5.93728			−0.437702
$185$	18.5492	+	5.89047i	1.36377	+	0.433076i
$186$	−1.99690	+	6.14584i	−0.146420	+	0.450635i
$187$	−4.74636	+	22.3175i	−0.347088	+	1.63202i
$188$	−0.00809888	−	0.0249258i	−0.000590671	−	0.00181790i
$189$	12.7773	−	9.28325i	0.929411	−	0.675257i
$190$	−0.0875458	−	13.1211i	−0.00635124	−	0.951901i
$191$	19.2139	−	13.9597i	1.39027	−	1.01009i	0.394436	−	0.918923i	$-0.370940\pi$
$191$	19.2139	−	13.9597i	1.39027	−	1.01009i	0.995836	−	0.0911682i	$-0.0290601\pi$
$192$	0.487764	−	1.50118i	0.0352014	−	0.108339i
$193$	−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	$0.870986\pi$
$194$	−13.9004	−	10.0992i	−0.997991	−	0.725083i
$195$	7.53913	−	10.5237i	0.539888	−	0.753615i
$196$	0.350147	+	1.07764i	0.0250105	+	0.0769743i
$197$	−0.516992	−	0.375616i	−0.0368341	−	0.0267616i	0.569216	−	0.822188i	$-0.307247\pi$
$197$	−0.516992	−	0.375616i	−0.0368341	−	0.0267616i	−0.606050	+	0.795427i	$0.707247\pi$
$198$	−0.685833	−	1.54088i	−0.0487400	−	0.109505i
$199$	16.5514			1.17330			0.586648	−	0.809842i	$-0.300447\pi$
$199$	16.5514			1.17330			0.586648	+	0.809842i	$0.300447\pi$
$200$	−4.99955	+	0.0667186i	−0.353522	+	0.00471772i
$201$	4.98099	−	15.3299i	0.351332	−	1.08129i
$202$	2.04969			0.144216
$203$	−20.3002			−1.42480
$204$	−10.8588			−0.760269
$205$	11.0554	+	15.0049i	0.772143	+	1.04799i
$206$	−0.284637	−	0.876022i	−0.0198316	−	0.0610353i
$207$	−2.44267	−	1.77470i	−0.169777	−	0.123350i
$208$	−2.96732	+	2.15588i	−0.205746	+	0.149484i
$209$	−7.91394	−	17.7804i	−0.547419	−	1.22990i
$210$	−5.97062	−	8.10360i	−0.412012	−	0.559202i
$211$	−11.2641	+	8.18383i	−0.775451	+	0.563398i	−0.903610	−	0.428356i	$-0.859093\pi$
$211$	−11.2641	+	8.18383i	−0.775451	+	0.563398i	0.128160	+	0.991754i	$0.459093\pi$
$212$	0.208818			0.0143417
$213$	−15.2651	+	11.0907i	−1.04594	+	0.759923i
$214$	−2.28278	−	7.02567i	−0.156048	−	0.480265i
$215$	−1.57153	−	2.13296i	−0.107178	−	0.145466i
$216$	4.48034	−	3.25516i	0.304848	−	0.221485i
$217$	−3.60792	−	11.1040i	−0.244922	−	0.753792i
$218$	−10.6480	−	7.73622i	−0.721174	−	0.523963i
$219$	−6.79804	+	4.93907i	−0.459369	+	0.333751i
$220$	−6.75510	+	3.06081i	−0.455429	+	0.206360i
$221$	20.4136	+	14.8313i	1.37316	+	0.997663i
$222$	4.24535	+	13.0658i	0.284929	+	0.876922i
$223$	1.88311	+	1.36816i	0.126102	+	0.0916187i	0.649049	−	0.760747i	$-0.275167\pi$
$223$	1.88311	+	1.36816i	0.126102	+	0.0916187i	−0.522946	+	0.852366i	$0.675167\pi$
$224$	0.881273	+	2.71228i	0.0588825	+	0.181222i
$225$	−2.07682	−	1.46696i	−0.138455	−	0.0977973i
$226$	−5.59556	+	4.06541i	−0.372211	+	0.270427i
$227$	−3.99021			−0.264839			−0.132420	−	0.991194i	$-0.542275\pi$
$227$	−3.99021			−0.264839			−0.132420	+	0.991194i	$0.542275\pi$
$228$	7.49339	−	5.44427i	0.496262	−	0.360556i
$229$	5.09914	+	15.6935i	0.336960	+	1.03706i	0.965748	+	0.259481i	$0.0835514\pi$
$229$	5.09914	+	15.6935i	0.336960	+	1.03706i	−0.628788	+	0.777577i	$0.716449\pi$
$230$	−7.73170	+	10.7925i	−0.509813	+	0.711635i
$231$	−12.9287	−	7.46633i	−0.850645	−	0.491248i
$232$	−7.11824			−0.467335
$233$	−9.29064			−0.608650			−0.304325	−	0.952568i	$-0.598431\pi$
$233$	−9.29064			−0.608650			−0.304325	+	0.952568i	$0.598431\pi$
$234$	−1.86520			−0.121932
$235$	−0.0558553	−	0.0177374i	−0.00364360	−	0.00115706i
$236$	2.16102	+	6.65092i	0.140670	+	0.432938i
$237$	4.36732	+	3.17304i	0.283688	+	0.206111i
$238$	15.8723	−	11.5319i	1.02885	−	0.747503i
$239$	6.83022	+	4.96245i	0.441810	+	0.320994i	0.786354	−	0.617776i	$-0.211966\pi$
$239$	6.83022	+	4.96245i	0.441810	+	0.320994i	−0.344544	+	0.938770i	$0.611966\pi$
$240$	−2.09359	−	2.84152i	−0.135141	−	0.183419i
$241$	3.68366	+	11.3371i	0.237285	+	0.730289i	0.996810	+	0.0798104i	$0.0254315\pi$
$241$	3.68366	+	11.3371i	0.237285	+	0.730289i	−0.759525	+	0.650478i	$0.774569\pi$
$242$	−7.36228	+	8.17293i	−0.473266	+	0.525376i
$243$	5.22432			0.335140
$244$	−6.69478			−0.428590
$245$	2.41485	+	0.766857i	0.154279	+	0.0489927i
$246$	−4.06556	+	12.5125i	−0.259211	+	0.797769i
$247$	−21.5228			−1.36947
$248$	−1.26511	−	3.89362i	−0.0803348	−	0.247245i
$249$	−0.296038	−	0.911112i	−0.0187607	−	0.0577394i
$250$	−6.38929	+	9.17480i	−0.404094	+	0.580266i
$251$	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
$253$	−4.09632	+	19.2610i	−0.257534	+	1.21093i
$254$	11.6167	+	8.44006i	0.728899	+	0.529576i
$255$	−14.1407	+	19.7386i	−0.885523	+	1.23608i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	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	$0.552273\pi$
$258$	0.577922	−	1.77866i	0.0359798	−	0.110735i
$259$	−20.0812	−	14.5898i	−1.24778	−	0.906568i
$260$	0.0547203	+	8.20128i	0.00339361	+	0.508622i
$261$	−2.92853	−	2.12770i	−0.181271	−	0.131701i
$262$	3.26832	−	10.0589i	0.201917	−	0.621438i
$263$	−5.99185	−	18.4410i	−0.369473	−	1.13712i	−0.947132	−	0.320844i	$-0.896033\pi$
$263$	−5.99185	−	18.4410i	−0.369473	−	1.13712i	0.577659	−	0.816278i	$-0.303967\pi$
$264$	−4.53342	−	2.61806i	−0.279013	−	0.161130i
$265$	0.271929	−	0.379579i	0.0167045	−	0.0233173i
$266$	−5.17135	+	15.9158i	−0.317076	+	0.975859i
$267$	−3.53672	−	10.8849i	−0.216444	−	0.666145i
$268$	3.15564	+	9.71207i	0.192762	+	0.593259i
$269$	−1.64466	+	5.06173i	−0.100277	+	0.308619i	−0.988593	−	0.150613i	$-0.951875\pi$
$269$	−1.64466	+	5.06173i	−0.100277	+	0.308619i	0.888316	+	0.459232i	$0.151875\pi$
$270$	−0.0826219	−	12.3831i	−0.00502821	−	0.753610i
$271$	1.16957	−	3.59957i	0.0710463	−	0.218658i	−0.909228	−	0.416297i	$-0.863327\pi$
$271$	1.16957	−	3.59957i	0.0710463	−	0.218658i	0.980275	+	0.197639i	$0.0633275\pi$
$272$	5.56561	−	4.04365i	0.337464	−	0.245182i
$273$	−13.3573	+	9.70467i	−0.808422	+	0.587353i
$274$	11.4620			0.692446
$275$	−3.23291	+	16.2649i	−0.194952	+	0.980813i
$276$	−9.37164			−0.564106
$277$	7.92844	−	5.76035i	0.476374	−	0.346106i	−0.323546	−	0.946212i	$-0.604875\pi$
$277$	7.92844	−	5.76035i	0.476374	−	0.346106i	0.799920	+	0.600106i	$0.204875\pi$
$278$	−6.77687	+	4.92369i	−0.406450	+	0.295303i
$279$	0.643352	−	1.98003i	0.0385165	−	0.118541i
$280$	6.07785	+	1.93008i	0.363221	+	0.115344i
$281$	9.65842	−	29.7256i	0.576173	−	1.77328i	−0.0559771	−	0.998432i	$-0.517827\pi$
$281$	9.65842	−	29.7256i	0.576173	−	1.77328i	0.632150	−	0.774846i	$-0.282173\pi$
$282$	−0.0127836	−	0.0393438i	−0.000761251	−	0.00234289i
$283$	−6.63452	−	20.4189i	−0.394381	−	1.21378i	−0.929443	−	0.368967i	$-0.879712\pi$
$283$	−6.63452	−	20.4189i	−0.394381	−	1.21378i	0.535062	−	0.844813i	$-0.320288\pi$
$284$	3.69399	−	11.3689i	0.219198	−	0.674622i
$285$	−0.138186	−	20.7108i	−0.00818541	−	1.22680i
$286$	4.94659	+	11.1136i	0.292498	+	0.657161i
$287$	−7.34550	−	22.6071i	−0.433591	−	1.33446i
$288$	−0.157145	+	0.483644i	−0.00925988	+	0.0284990i
$289$	−24.5351	−	17.8258i	−1.44324	−	1.04858i
$290$	−9.26958	+	12.9391i	−0.544328	+	0.759813i
$291$	−21.9409	−	15.9410i	−1.28620	−	0.934479i
$292$	1.64506	−	5.06297i	0.0962697	−	0.296288i
$293$	−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	$-0.349259\pi$
$294$	0.552685	+	1.70099i	0.0322332	+	0.0992037i
$295$	14.9038	+	4.73284i	0.867734	+	0.275557i
$296$	−7.04144	−	5.11590i	−0.409275	−	0.297356i
$297$	−7.46883	−	16.7804i	−0.433385	−	0.973696i
$298$	6.98517	−	21.4981i	0.404640	−	1.24535i
$299$	17.6178	+	12.8001i	1.01886	+	0.740248i
$300$	−7.89149	+	0.105311i	−0.455615	+	0.00608015i
$301$	1.04417	+	3.21361i	0.0601847	+	0.185230i
$302$	1.88170	+	5.79129i	0.108280	+	0.333251i
$303$	3.23531			0.185864
$304$	−1.81333	+	5.58084i	−0.104001	+	0.320083i
$305$	−8.71814	+	12.1694i	−0.499199	+	0.696819i
$306$	3.49844			0.199992
$307$	16.2017			0.924679			0.462339	−	0.886703i	$-0.347010\pi$
$307$	16.2017			0.924679			0.462339	+	0.886703i	$0.347010\pi$
$308$	9.40684	−	0.987624i	0.536005	−	0.0562751i
$309$	−0.449281	−	1.38275i	−0.0255587	−	0.0786617i
$310$	−8.72508	−	2.77073i	−0.495551	−	0.157367i
$311$	15.0296	+	10.9197i	0.852253	+	0.619198i	0.925766	−	0.378096i	$-0.123421\pi$
$311$	15.0296	+	10.9197i	0.852253	+	0.619198i	−0.0735135	+	0.997294i	$0.523421\pi$
$312$	−4.68373	+	3.40293i	−0.265164	+	0.192653i
$313$	8.96348	+	6.51235i	0.506646	+	0.368100i	0.811550	−	0.584283i	$-0.198624\pi$
$313$	8.96348	+	6.51235i	0.506646	+	0.368100i	−0.304904	+	0.952383i	$0.598624\pi$
$314$	6.70064	+	20.6225i	0.378139	+	1.16379i
$315$	1.92358	+	2.61078i	0.108382	+	0.147101i
$316$	−3.42003			−0.192392
$317$	−12.8045			−0.719170			−0.359585	−	0.933112i	$-0.617082\pi$
$317$	−12.8045			−0.719170			−0.359585	+	0.933112i	$0.617082\pi$
$318$	0.329607			0.0184834
$319$	−4.91110	+	23.0921i	−0.274969	+	1.29291i
$320$	2.13119	+	0.676779i	0.119137	+	0.0378331i
$321$	−3.60323	−	11.0896i	−0.201113	−	0.618961i
$322$	13.6985	−	9.95255i	0.763388	−	0.554634i
$323$	40.3690			2.24619
$324$	5.83770	−	4.24134i	0.324317	−	0.235630i
$325$	14.9791	+	10.5805i	0.830891	+	0.586899i
$326$	3.34053	+	10.2811i	0.185015	+	0.569417i
$327$	−16.8072	−	12.2112i	−0.929441	−	0.675278i
$328$	−2.57569	−	7.92715i	−0.142219	−	0.437704i
$329$	0.0604683	+	0.0439328i	0.00333373	+	0.00242210i
$330$	−10.6625	+	4.83130i	−0.586952	+	0.265954i
$331$	−11.2671	+	8.18603i	−0.619296	+	0.449945i	−0.852676	−	0.522441i	$-0.825022\pi$
$331$	−11.2671	+	8.18603i	−0.619296	+	0.449945i	0.233380	+	0.972386i	$0.425022\pi$
$332$	0.491016	+	0.356744i	0.0269480	+	0.0195789i
$333$	−1.36774	−	4.20949i	−0.0749519	−	0.230678i
$334$	10.0025	−	7.26724i	0.547313	−	0.397646i
$335$	21.7634	+	6.91118i	1.18906	+	0.377598i
$336$	1.39103	+	4.28116i	0.0758872	+	0.233557i
$337$	−19.7655	+	14.3605i	−1.07669	+	0.782264i	−0.977104	−	0.212764i	$-0.931753\pi$
$337$	−19.7655	+	14.3605i	−1.07669	+	0.782264i	−0.0995907	+	0.995028i	$0.531753\pi$
$338$	0.452798			0.0246290
$339$	−8.83225	+	6.41700i	−0.479702	+	0.348524i
$340$	−0.102635	−	15.3826i	−0.00556618	−	0.834240i
$341$	−13.5040	+	1.41779i	−0.731283	+	0.0767774i
$342$	−2.41418	+	1.75401i	−0.130544	+	0.0948458i
$343$	13.5361	+	9.83457i	0.730882	+	0.531017i
$344$	0.366135	+	1.12685i	0.0197407	+	0.0607556i
$345$	−12.2040	+	17.0353i	−0.657042	+	0.917147i
$346$	−8.11283			−0.436148
$347$	19.6608			1.05545			0.527723	−	0.849416i	$-0.323046\pi$
$347$	19.6608			1.05545			0.527723	+	0.849416i	$0.323046\pi$
$348$	−11.2357			−0.602297
$349$	−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	$0.992364\pi$
$350$	11.4231	−	8.53459i	0.610593	−	0.456193i
$351$	−20.3123			−1.08419
$352$	3.29850	−	0.346309i	0.175810	−	0.0184583i
$353$	−11.4769	−	8.33845i	−0.610853	−	0.443811i	0.238862	−	0.971054i	$-0.423226\pi$
$353$	−11.4769	−	8.33845i	−0.610853	−	0.443811i	−0.849715	+	0.527243i	$0.823226\pi$
$354$	3.41103	+	10.4981i	0.181294	+	0.557966i
$355$	−15.8554	−	21.5197i	−0.841517	−	1.14215i
$356$	5.86608	+	4.26196i	0.310902	+	0.225883i
$357$	25.0535	−	18.2024i	1.32597	−	0.963374i
$358$	−3.51260	+	10.8107i	−0.185647	+	0.571362i
$359$	24.8004	−	18.0185i	1.30891	−	0.950981i	0.308913	−	0.951090i	$-0.400035\pi$
$359$	24.8004	−	18.0185i	1.30891	−	0.950981i	1.00000		0.000109073i	$3.47190e-5\pi$
$360$	0.674502	+	0.915465i	0.0355494	+	0.0482492i
$361$	−12.4863	+	9.07184i	−0.657175	+	0.477466i
$362$	2.94405	+	9.06085i	0.154736	+	0.476228i
$363$	−11.6209	+	12.9005i	−0.609940	+	0.677099i
$364$	3.23234	−	9.94811i	0.169421	−	0.521423i
$365$	−7.06095	−	9.58344i	−0.369587	−	0.501620i
$366$	−10.5673			−0.552362
$367$	−9.54498	−	6.93483i	−0.498244	−	0.361995i	0.310102	−	0.950703i	$-0.399637\pi$
$367$	−9.54498	−	6.93483i	−0.498244	−	0.361995i	−0.808346	+	0.588708i	$0.799637\pi$
$368$	4.80336	−	3.48985i	0.250393	−	0.181921i
$369$	1.30982	−	4.03122i	0.0681866	−	0.209857i
$370$	−18.4690	+	6.13747i	−0.960156	+	0.319072i
$371$	−0.481786	+	0.350038i	−0.0250131	+	0.0181731i
$372$	−1.99690	−	6.14584i	−0.103535	−	0.318647i
$373$	−1.98472	+	6.10833i	−0.102765	+	0.316278i	−0.989199	−	0.146576i	$-0.953175\pi$
$373$	−1.98472	+	6.10833i	−0.102765	+	0.316278i	0.886435	+	0.462854i	$0.153175\pi$
$374$	−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
$377$	21.1221	+	15.3461i	1.08784	+	0.790363i
$378$	−4.88049	+	15.0206i	−0.251025	+	0.772577i
$379$	9.68688			0.497582			0.248791	−	0.968557i	$-0.419967\pi$
$379$	9.68688			0.497582			0.248791	+	0.968557i	$0.419967\pi$
$380$	7.78319	+	10.5637i	0.399269	+	0.541906i
$381$	18.3363	+	13.3221i	0.939398	+	0.682512i
$382$	−7.33907	+	22.5873i	−0.375500	+	1.15567i
$383$	−27.8623			−1.42370			−0.711849	−	0.702332i	$-0.752142\pi$
$383$	−27.8623			−1.42370			−0.711849	+	0.702332i	$0.752142\pi$
$384$	0.487764	+	1.50118i	0.0248911	+	0.0766070i
$385$	10.4546	−	18.3854i	0.532816	−	0.937005i
$386$	8.37338	−	25.7706i	0.426194	−	1.31169i
$387$	−0.186192	+	0.573039i	−0.00946466	+	0.0291292i
$388$	17.1818			0.872276
$389$	23.1670			1.17462			0.587308	−	0.809364i	$-0.300188\pi$
$389$	23.1670			1.17462			0.587308	+	0.809364i	$0.300188\pi$
$390$	0.0863726	+	12.9452i	0.00437364	+	0.655506i
$391$	−33.0446	−	24.0083i	−1.67114	−	1.21415i
$392$	−0.916696	−	0.666019i	−0.0463001	−	0.0336390i
$393$	5.15884	−	15.8773i	0.260229	−	0.800903i
$394$	0.639037			0.0321942
$395$	−4.45366	+	6.21674i	−0.224088	+	0.312798i
$396$	1.46055	+	0.843472i	0.0733956	+	0.0423860i
$397$	−10.9334	−	7.94355i	−0.548730	−	0.398675i	0.278587	−	0.960411i	$-0.410134\pi$
$397$	−10.9334	−	7.94355i	−0.548730	−	0.398675i	−0.827317	+	0.561736i	$0.810134\pi$
$398$	−13.3903	+	9.72865i	−0.671197	+	0.487653i
$399$	−8.16265	+	25.1221i	−0.408644	+	1.25768i
$400$	4.00551	−	2.99264i	0.200275	−	0.149632i
$401$	−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	$0.588984\pi$
$402$	4.98099	+	15.3299i	0.248429	+	0.764586i
$403$	−4.64019	+	14.2810i	−0.231144	+	0.711389i
$404$	−1.65824	+	1.20478i	−0.0825003	+	0.0599400i
$405$	−0.107653	−	16.1346i	−0.00534932	−	0.801737i
$406$	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
$409$	7.68584	−	23.6546i	0.380040	−	1.16964i	−0.559974	−	0.828510i	$-0.689189\pi$
$409$	7.68584	−	23.6546i	0.380040	−	1.16964i	0.940015	−	0.341134i	$-0.110811\pi$
$410$	−17.7637	−	5.64102i	−0.877286	−	0.278590i
$411$	18.0921			0.892417
$412$	0.745189	+	0.541411i	0.0367128	+	0.0266734i
$413$	−16.1347	−	11.7226i	−0.793937	−	0.576829i
$414$	3.01930			0.148391
$415$	1.28789	−	0.427980i	0.0632198	−	0.0210087i
$416$	1.13341	−	3.48829i	0.0555702	−	0.171028i
$417$	−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	−0.266224	−	0.963911i	$-0.585776\pi$
$419$	11.6316	−	8.45088i	0.568243	−	0.412853i	0.834467	+	0.551059i	$0.185776\pi$
$420$	9.59351	+	3.04651i	0.468116	+	0.148654i
$421$	12.4043	−	9.01227i	0.604550	−	0.439231i	−0.242941	−	0.970041i	$-0.578112\pi$
$421$	12.4043	−	9.01227i	0.604550	−	0.439231i	0.847491	+	0.530810i	$0.178112\pi$
$422$	4.30249	−	13.2417i	0.209442	−	0.644596i
$423$	0.00411855	+	0.0126756i	0.000200251	+	0.000616308i
$424$	−0.168938	+	0.122740i	−0.00820433	+	0.00596080i
$425$	−28.0953	−	19.8451i	−1.36282	−	0.962630i
$426$	5.83073	−	17.9451i	0.282500	−	0.869445i
$427$	15.4462	−	11.2223i	0.747495	−	0.543087i
$428$	5.97640	+	4.34211i	0.288880	+	0.209884i
$429$	7.80788	+	17.5421i	0.376968	+	0.846942i
$430$	2.52512	+	0.801873i	0.121772	+	0.0386698i
$431$	−14.8393			−0.714783			−0.357391	−	0.933955i	$-0.616334\pi$
$431$	−14.8393			−0.714783			−0.357391	+	0.933955i	$0.616334\pi$
$432$	−1.71134	+	5.26695i	−0.0823367	+	0.253406i
$433$	21.2574	+	15.4444i	1.02156	+	0.742210i	0.966603	−	0.256279i	$-0.0824965\pi$
$433$	21.2574	+	15.4444i	1.02156	+	0.742210i	0.0549613	+	0.998488i	$0.482496\pi$
$434$	9.44567	+	6.86268i	0.453407	+	0.329419i
$435$	−14.6315	+	20.4236i	−0.701524	+	0.979239i
$436$	13.1617			0.630329
$437$	34.8402			1.66664
$438$	2.59662	−	7.99158i	0.124071	−	0.381852i
$439$	2.31622	−	7.12859i	0.110547	−	0.340229i	−0.880445	−	0.474148i	$-0.842756\pi$
$439$	2.31622	−	7.12859i	0.110547	−	0.340229i	0.990992	+	0.133919i	$0.0427562\pi$
$440$	3.66589	−	6.44680i	0.174765	−	0.307339i
$441$	−0.178061	−	0.548016i	−0.00847910	−	0.0260960i
$442$	−25.2326			−1.20019
$443$	−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	$0.983117\pi$
$444$	−11.1145	−	8.07514i	−0.527469	−	0.383229i
$445$	15.3861	−	5.11301i	0.729373	−	0.242380i
$446$	−2.32765			−0.110217
$447$	11.0257	−	33.9335i	0.521495	−	1.60500i
$448$	−2.30720	−	1.67628i	−0.109005	−	0.0791968i
$449$	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
$453$	2.97015	+	9.14119i	0.139550	+	0.429490i
$454$	3.22815	−	2.34539i	0.151504	−	0.110074i
$455$	−13.8739	−	18.8303i	−0.650418	−	0.882777i
$456$	−2.86222	+	8.80901i	−0.134036	+	0.412520i
$457$	−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	$0.422561\pi$
$458$	−13.3497	−	9.69914i	−0.623791	−	0.453211i
$459$	38.0985			1.77829
$460$	−0.0885788	−	13.2759i	−0.00413001	−	0.618991i
$461$	−9.54611	+	29.3799i	−0.444607	+	1.36836i	0.438308	+	0.898825i	$0.355578\pi$
$461$	−9.54611	+	29.3799i	−0.444607	+	1.36836i	−0.882915	+	0.469533i	$0.844422\pi$
$462$	14.8481	−	1.55890i	0.690797	−	0.0725268i
$463$	6.89780	+	21.2293i	0.320568	+	0.986607i	0.973402	+	0.229106i	$0.0735802\pi$
$463$	6.89780	+	21.2293i	0.320568	+	0.986607i	−0.652833	+	0.757502i	$0.726420\pi$
$464$	5.75878	−	4.18400i	0.267344	−	0.194237i
$465$	−13.7720	−	4.37342i	−0.638661	−	0.202813i
$466$	7.51628	−	5.46090i	0.348185	−	0.252971i
$467$	4.62994	−	14.2495i	0.214248	−	0.659388i	−0.784958	−	0.619549i	$-0.787315\pi$
$467$	4.62994	−	14.2495i	0.214248	−	0.659388i	0.999206	−	0.0398392i	$-0.0126846\pi$
$468$	1.50898	−	1.09634i	0.0697526	−	0.0506782i
$469$	−23.5609	−	17.1180i	−1.08794	−	0.790434i
$470$	0.0556137	−	0.0184811i	0.00256527	−	0.000852470i
$471$	10.5765	+	32.5513i	0.487342	+	1.49988i
$472$	−5.65761	−	4.11050i	−0.260413	−	0.189201i
$473$	3.90818	−	0.410320i	0.179698	−	0.0188665i
$474$	−5.39830			−0.247952
$475$	29.3376	−	0.391508i	1.34610	−	0.0179636i
$476$	−6.06269	+	18.6590i	−0.277883	+	0.855236i
$477$	−0.106191			−0.00486215
$478$	−8.44262			−0.386156
$479$	27.6720			1.26436			0.632182	−	0.774820i	$-0.282159\pi$
$479$	27.6720			1.26436			0.632182	+	0.774820i	$0.282159\pi$
$480$	3.36395	+	1.06825i	0.153543	+	0.0487589i
$481$	9.86489	+	30.3610i	0.449800	+	1.38434i
$482$	−9.64394	−	7.00673i	−0.439269	−	0.319148i
$483$	21.6223	−	15.7095i	0.983847	−	0.714807i
$484$	1.15229	−	10.9395i	0.0523766	−	0.497249i
$485$	22.3747	−	31.2322i	1.01598	−	1.41818i
$486$	−4.22656	+	3.07078i	−0.191721	+	0.139293i
$487$	34.2493			1.55199			0.775993	−	0.630742i	$-0.217249\pi$
$487$	34.2493			1.55199			0.775993	+	0.630742i	$0.217249\pi$
$488$	5.41619	−	3.93510i	0.245180	−	0.178133i
$489$	5.27282	+	16.2281i	0.238445	+	0.733859i
$490$	−2.40440	+	0.799012i	−0.108620	+	0.0360957i
$491$	3.33637	−	2.42401i	0.150568	−	0.109394i	−0.509951	−	0.860204i	$-0.670336\pi$
$491$	3.33637	−	2.42401i	0.150568	−	0.109394i	0.660519	+	0.750809i	$0.270336\pi$
$492$	−4.06556	−	12.5125i	−0.183290	−	0.564108i
$493$	−39.6173	−	28.7837i	−1.78427	−	1.29635i
$494$	17.4123	−	12.6508i	0.783419	−	0.569187i
$495$	3.43519	−	1.55652i	0.154400	−	0.0699605i
$496$	3.31211	+	2.40639i	0.148718	+	0.108050i
$497$	10.5347	+	32.4226i	0.472547	+	1.45435i
$498$	0.775038	+	0.563098i	0.0347303	+	0.0252330i
$499$	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	$0.628141\pi$
$500$	−0.223773	−	11.1781i	−0.0100074	−	0.499900i
$501$	15.7883	−	11.4709i	0.705371	−	0.512482i
$502$	−8.88572			−0.396589
$503$	5.04187	−	3.66314i	0.224806	−	0.163331i	−0.469681	−	0.882836i	$-0.655631\pi$
$503$	5.04187	−	3.66314i	0.224806	−	0.163331i	0.694487	+	0.719505i	$0.255631\pi$
$504$	−0.448156	−	1.37928i	−0.0199625	−	0.0614382i
$505$	0.0305795	+	4.58315i	0.00136077	+	0.203948i
$506$	−8.00732	−	17.9902i	−0.355969	−	0.799762i
$507$	0.714714			0.0317415
$508$	−14.3591			−0.637081
$509$	−3.29850			−0.146203			−0.0731017	−	0.997324i	$-0.523290\pi$
$509$	−3.29850			−0.146203			−0.0731017	+	0.997324i	$0.523290\pi$
$510$	−0.162003	−	24.2805i	−0.00717363	−	1.07516i
$511$	4.69147	+	14.4389i	0.207538	+	0.638738i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−26.2908	+	19.1014i	−1.16077	+	0.843347i
$514$	−23.0272	−	16.7302i	−1.01569	−	0.737939i
$515$	1.95455	−	0.649522i	0.0861279	−	0.0286214i
$516$	0.577922	+	1.77866i	0.0254416	+	0.0783012i
$517$	0.0646036	−	0.0581561i	0.00284126	−	0.00255770i
$518$	24.8217			1.09060
$519$	−12.8056			−0.562104
$520$	−4.86486	−	6.60281i	−0.213338	−	0.289552i
$521$	−6.97827	+	21.4769i	−0.305724	+	0.940921i	0.673682	+	0.739021i	$0.264712\pi$
$521$	−6.97827	+	21.4769i	−0.305724	+	0.940921i	−0.979406	+	0.201900i	$0.935288\pi$
$522$	3.61986			0.158437
$523$	2.90659	+	8.94556i	0.127096	+	0.391162i	0.994277	−	0.106831i	$-0.0340704\pi$
$523$	2.90659	+	8.94556i	0.127096	+	0.391162i	−0.867181	+	0.497993i	$0.834070\pi$
$524$	3.26832	+	10.0589i	0.142777	+	0.439423i
$525$	18.0307	−	13.4713i	0.786925	−	0.587937i
$526$	15.6869	+	11.3972i	0.683980	+	0.496941i
$527$	8.70331	−	26.7860i	0.379122	−	1.16682i
$528$	5.20647	−	0.546627i	0.226583	−	0.0237889i
$529$	−9.91155	−	7.20116i	−0.430937	−	0.313094i
$530$	0.00311538	+	0.466922i	0.000135323	+	0.0202818i
$531$	−1.09895	−	3.38221i	−0.0476903	−	0.146776i
$532$	−5.17135	−	15.9158i	−0.224206	−	0.690036i
$533$	−9.44712	+	29.0752i	−0.409200	+	1.25939i
$534$	9.25925	+	6.72724i	0.400687	+	0.291116i
$535$	15.6755	−	5.20915i	0.677710	−	0.225211i
$536$	−8.26158	−	6.00239i	−0.356846	−	0.259264i
$537$	−5.54442	+	17.0640i	−0.239260	+	0.736365i
$538$	−1.64466	−	5.06173i	−0.0709062	−	0.218227i
$539$	−2.79307	+	2.51432i	−0.120306	+	0.108299i
$540$	7.34543	+	9.96955i	0.316097	+	0.429021i
$541$	2.98953	−	9.20083i	0.128530	−	0.395575i	−0.865998	−	0.500048i	$-0.833316\pi$
$541$	2.98953	−	9.20083i	0.128530	−	0.395575i	0.994528	+	0.104473i	$0.0333157\pi$
$542$	1.16957	+	3.59957i	0.0502373	+	0.154615i
$543$	4.64700	+	14.3020i	0.199422	+	0.613757i
$544$	−2.12587	+	6.54276i	−0.0911460	+	0.280519i
$545$	17.1395	−	23.9245i	0.734175	−	1.02481i
$546$	5.10204	−	15.7025i	0.218347	−	0.672004i
$547$	26.9089	−	19.5504i	1.15054	−	0.835916i	0.161988	−	0.986793i	$-0.448210\pi$
$547$	26.9089	−	19.5504i	1.15054	−	0.835916i	0.988553	+	0.150876i	$0.0482095\pi$
$548$	−9.27297	+	6.73721i	−0.396122	+	0.287799i
$549$	3.40452			0.145301
$550$	−6.94481	−	15.0589i	−0.296128	−	0.642112i
$551$	41.7701			1.77947
$552$	7.58181	−	5.50851i	0.322703	−	0.234458i
$553$	7.89069	−	5.73292i	0.335546	−	0.243789i
$554$	−3.02840	+	9.32044i	−0.128664	+	0.395988i
$555$	−29.1521	+	9.68761i	−1.23744	+	0.411216i
$556$	2.58854	−	7.96669i	0.109778	−	0.337863i
$557$	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	$0.832942\pi$
$558$	0.643352	+	1.98003i	0.0272353	+	0.0838215i
$559$	1.34291	−	4.13306i	0.0567992	−	0.174810i
$560$	−6.05156	+	2.01101i	−0.255725	+	0.0849805i
$561$	−14.6447	−	32.9026i	−0.618302	−	1.38915i
$562$	9.65842	+	29.7256i	0.407416	+	1.25390i
$563$	−6.74050	+	20.7451i	−0.284078	+	0.874303i	0.702595	+	0.711590i	$0.252025\pi$
$563$	−6.74050	+	20.7451i	−0.284078	+	0.874303i	−0.986673	+	0.162713i	$0.947975\pi$
$564$	0.0334678	+	0.0243158i	0.00140925	+	0.00102388i
$565$	−9.17382	−	12.4511i	−0.385945	−	0.523823i
$566$	17.3694	+	12.6196i	0.730090	+	0.530441i
$567$	−6.35908	+	19.5712i	−0.267056	+	0.821915i
$568$	3.69399	+	11.3689i	0.154996	+	0.477029i
$569$	2.26586	+	6.97361i	0.0949899	+	0.292349i	0.987251	−	0.159171i	$-0.0508821\pi$
$569$	2.26586	+	6.97361i	0.0949899	+	0.292349i	−0.892261	+	0.451520i	$0.850882\pi$
$570$	12.2853	+	16.6741i	0.514574	+	0.698403i
$571$	−25.0252	−	18.1818i	−1.04727	−	0.760886i	−0.0755786	−	0.997140i	$-0.524080\pi$
$571$	−25.0252	−	18.1818i	−1.04727	−	0.760886i	−0.971691	+	0.236254i	$0.924080\pi$
$572$	−10.5343	−	6.08356i	−0.440460	−	0.254366i
$573$	−11.5843	+	35.6527i	−0.483940	+	1.48941i
$574$	19.2308	+	13.9720i	0.802676	+	0.583179i
$575$	−24.2475	−	17.1272i	−1.01119	−	0.714254i
$576$	−0.157145	−	0.483644i	−0.00654772	−	0.0201518i
$577$	−7.56699	−	23.2888i	−0.315018	−	0.969525i	−0.975747	−	0.218901i	$-0.929753\pi$
$577$	−7.56699	−	23.2888i	−0.315018	−	0.969525i	0.660729	−	0.750624i	$-0.270247\pi$
$578$	30.3271			1.26144
$579$	13.2169	−	40.6773i	0.549274	−	1.69049i
$580$	−0.106198	−	15.9165i	−0.00440961	−	0.660897i
$581$	−1.73088			−0.0718089
$582$	27.1205			1.12418
$583$	0.281623	+	0.632728i	0.0116636	+	0.0262049i
$584$	1.64506	+	5.06297i	0.0680730	+	0.209507i
$585$	−0.0278271	−	4.17062i	−0.00115051	−	0.172434i
$586$	19.5386	+	14.1956i	0.807132	+	0.586416i
$587$	−6.13951	+	4.46062i	−0.253405	+	0.184109i	−0.707234	−	0.706979i	$-0.750057\pi$
$587$	−6.13951	+	4.46062i	−0.253405	+	0.184109i	0.453830	+	0.891088i	$0.350057\pi$
$588$	−1.44695	−	1.05127i	−0.0596711	−	0.0433536i
$589$	7.42374	+	22.8479i	0.305890	+	0.941432i
$590$	−14.8393	+	4.93130i	−0.610926	+	0.203018i
$591$	1.00868			0.0414916
$592$	8.70369			0.357720
$593$	23.1979			0.952623			0.476312	−	0.879276i	$-0.341973\pi$
$593$	23.1979			0.952623			0.476312	+	0.879276i	$0.341973\pi$
$594$	15.9057	+	9.18554i	0.652617	+	0.376887i
$595$	26.0224	+	35.3188i	1.06681	+	1.44793i
$596$	6.98517	+	21.4981i	0.286124	+	0.880598i
$597$	−21.1358	+	15.3561i	−0.865032	+	0.628482i
$598$	−21.7768			−0.890520
$599$	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	$0.143840\pi$
$600$	6.32245	−	4.72370i	0.258113	−	0.192844i
$601$	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	$0.739892\pi$
$602$	−2.73366	−	1.98612i	−0.111416	−	0.0809483i
$603$	−1.60475	−	4.93891i	−0.0653504	−	0.201128i
$604$	−4.92636	−	3.57921i	−0.200451	−	0.145636i
$605$	−18.3847	−	16.3403i	−0.747443	−	0.664326i
$606$	−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	$0.852757\pi$
$608$	−1.81333	−	5.58084i	−0.0735401	−	0.226333i
$609$	25.9230	−	18.8342i	1.05045	−	0.763200i
$610$	−0.0998800	−	14.9697i	−0.00404402	−	0.606104i
$611$	−0.0297051	−	0.0914229i	−0.00120174	−	0.00369858i
$612$	−2.83029	+	2.05633i	−0.114408	+	0.0831222i
$613$	−2.76987			−0.111874			−0.0559370	−	0.998434i	$-0.517815\pi$
$613$	−2.76987			−0.111874			−0.0559370	+	0.998434i	$0.517815\pi$
$614$	−13.1074	+	9.52311i	−0.528973	+	0.384321i
$615$	−28.0389	−	8.90400i	−1.13064	−	0.359044i
$616$	−7.02978	+	6.32821i	−0.283238	+	0.254971i
$617$	−11.0475	+	8.02650i	−0.444757	+	0.323135i	−0.787522	−	0.616286i	$-0.788636\pi$
$617$	−11.0475	+	8.02650i	−0.444757	+	0.323135i	0.342765	+	0.939421i	$0.388636\pi$
$618$	1.17623	+	0.854584i	0.0473151	+	0.0343764i
$619$	−6.44014	−	19.8207i	−0.258851	−	0.796662i	−0.993046	−	0.117724i	$-0.962440\pi$
$619$	−6.44014	−	19.8207i	−0.258851	−	0.796662i	0.734195	−	0.678938i	$-0.237560\pi$
$620$	8.68733	−	2.88691i	0.348891	−	0.115941i
$621$	32.8807			1.31946
$622$	−18.5777			−0.744896
$623$	−20.6785			−0.828466
$624$	1.78902	−	5.50605i	0.0716183	−	0.220418i
$625$	−20.6103	−	14.1497i	−0.824414	−	0.565987i
$626$	−11.0795			−0.442825
$627$	26.6023	+	15.3629i	1.06239	+	0.613534i
$628$	−17.5425	−	12.7454i	−0.700022	−	0.508596i
$629$	−18.5029	−	56.9462i	−0.737761	−	2.27059i
$630$	−3.09079	−	0.981508i	−0.123140	−	0.0391042i
$631$	28.5465	+	20.7403i	1.13642	+	0.825657i	0.986616	−	0.163059i	$-0.0521362\pi$
$631$	28.5465	+	20.7403i	1.13642	+	0.825657i	0.149803	+	0.988716i	$0.452136\pi$
$632$	2.76686	−	2.01024i	0.110060	−	0.0799631i
$633$	6.79122	−	20.9012i	0.269927	−	0.830749i
$634$	10.3590	−	7.52627i	0.411410	−	0.298907i
$635$	−18.6988	+	26.1012i	−0.742040	+	1.03579i
$636$	−0.266657	+	0.193738i	−0.0105737	+	0.00768221i
$637$	1.28427	+	3.95258i	0.0508846	+	0.156607i
$638$	−9.60002	−	21.5685i	−0.380068	−	0.853907i
$639$	−1.87851	+	5.78147i	−0.0743129	+	0.228712i
$640$	−2.12197	+	0.705157i	−0.0838782	+	0.0278738i
$641$	10.3172			0.407505			0.203752	−	0.979022i	$-0.434686\pi$
$641$	10.3172			0.407505			0.203752	+	0.979022i	$0.434686\pi$
$642$	9.43337	+	6.85375i	0.372305	+	0.270496i
$643$	−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	$0.468392\pi$
$644$	−5.23237	+	16.1036i	−0.206184	+	0.634570i
$645$	3.98574	+	1.26571i	0.156938	+	0.0498372i
$646$	−32.6592	+	23.7283i	−1.28496	+	0.933578i
$647$	−2.64660	−	8.14540i	−0.104049	−	0.320229i	0.885457	−	0.464721i	$-0.153845\pi$
$647$	−2.64660	−	8.14540i	−0.104049	−	0.320229i	−0.989506	+	0.144492i	$0.953845\pi$
$648$	−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
$652$	−8.74562	−	6.35407i	−0.342505	−	0.248844i
$653$	3.44068	−	10.5893i	0.134644	−	0.414392i	−0.860890	−	0.508790i	$-0.830093\pi$
$653$	3.44068	−	10.5893i	0.134644	−	0.414392i	0.995534	+	0.0943986i	$0.0300928\pi$
$654$	20.7749			0.812361
$655$	22.5405	+	7.15795i	0.880732	+	0.279684i
$656$	6.74324	+	4.89925i	0.263279	+	0.191284i
$657$	−0.836566	+	2.57469i	−0.0326375	+	0.100448i
$658$	−0.0747430			−0.00291379
$659$	−6.84080	−	21.0538i	−0.266480	−	0.820140i	−0.991349	−	0.131253i	$-0.958100\pi$
$659$	−6.84080	−	21.0538i	−0.266480	−	0.820140i	0.724869	−	0.688886i	$-0.241900\pi$
$660$	5.78639	−	10.1759i	0.225235	−	0.396095i
$661$	0.256745	−	0.790179i	0.00998621	−	0.0307344i	−0.945939	−	0.324344i	$-0.894857\pi$
$661$	0.256745	−	0.790179i	0.00998621	−	0.0307344i	0.955925	+	0.293609i	$0.0948565\pi$
$662$	4.30365	−	13.2453i	0.167266	−	0.514792i
$663$	−39.8280			−1.54679
$664$	−0.606929			−0.0235534
$665$	−35.6651	−	11.3258i	−1.38303	−	0.439195i
$666$	3.58080	+	2.60160i	0.138753	+	0.100810i
$667$	−34.1915	−	24.8416i	−1.32390	−	0.961870i
$668$	−3.82062	+	11.7586i	−0.147824	+	0.454956i
$669$	−3.67405			−0.142047
$670$	−21.6693	+	7.20097i	−0.837158	+	0.278198i
$671$	−9.02892	−	20.2855i	−0.348558	−	0.783112i
$672$	−3.64178	−	2.64591i	−0.140485	−	0.102068i
$673$	−3.09241	+	2.24677i	−0.119204	+	0.0866065i	−0.645790	−	0.763515i	$-0.723472\pi$
$673$	−3.09241	+	2.24677i	−0.119204	+	0.0866065i	0.526586	+	0.850122i	$0.323472\pi$
$674$	7.54974	−	23.2357i	0.290805	−	0.895006i
$675$	27.6875	−	0.369488i	1.06569	−	0.0142216i
$676$	−0.366321	+	0.266148i	−0.0140893	+	0.0102365i
$677$	10.7764	+	33.1663i	0.414170	+	1.27469i	0.912991	+	0.407980i	$0.133767\pi$
$677$	10.7764	+	33.1663i	0.414170	+	1.27469i	−0.498820	+	0.866705i	$0.666233\pi$
$678$	3.37362	−	10.3829i	0.129563	−	0.398754i
$679$	−39.6420	+	28.8016i	−1.52132	+	1.10530i
$680$	9.12471	+	12.3845i	0.349917	+	0.474923i
$681$	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	−0.661641	−	0.749821i	$-0.730140\pi$
$683$	−3.99795	+	2.90468i	−0.152977	+	0.111145i	0.508664	+	0.860965i	$0.330140\pi$
$684$	0.922136	−	2.83804i	0.0352587	−	0.108515i
$685$	0.171003	+	25.6293i	0.00653368	+	0.979245i
$686$	−16.7316			−0.638814
$687$	−21.0717	−	15.3095i	−0.803936	−	0.584093i
$688$	−0.958554	−	0.696431i	−0.0365445	−	0.0265512i
$689$	0.765905			0.0291787
$690$	−0.139816	−	20.9552i	−0.00532271	−	0.797749i
$691$	−10.5869	+	32.5832i	−0.402745	+	1.23952i	0.520018	+	0.854155i	$0.325925\pi$
$691$	−10.5869	+	32.5832i	−0.402745	+	1.23952i	−0.922763	+	0.385367i	$0.874075\pi$
$692$	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
$695$	−11.1106	−	15.0798i	−0.421447	−	0.572008i
$696$	9.08987	−	6.60418i	0.344551	−	0.250331i
$697$	17.7194	−	54.5346i	0.671169	−	2.06564i
$698$	−3.83021	−	11.7882i	−0.144976	−	0.446189i
$699$	11.8640	−	8.61969i	0.448737	−	0.326027i
$700$	−4.22501	+	13.6190i	−0.159690	+	0.514749i
$701$	−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	$0.115153\pi$
$702$	16.4330	−	11.9393i	0.620224	−	0.450619i
$703$	41.3195	+	30.0203i	1.55839	+	1.13224i
$704$	−2.46498	+	2.21898i	−0.0929026	+	0.0836308i
$705$	0.0877827	−	0.0291713i	0.00330609	−	0.00109865i
$706$	14.1862			0.533905
$707$	1.80634	−	5.55934i	0.0679343	−	0.209080i
$708$	−8.93019	−	6.48816i	−0.335617	−	0.243840i
$709$	−1.07686	−	0.782387i	−0.0404425	−	0.0293832i	0.567380	−	0.823456i	$-0.307957\pi$
$709$	−1.07686	−	0.782387i	−0.0404425	−	0.0293832i	−0.607823	+	0.794073i	$0.707957\pi$
$710$	25.4762	+	8.09021i	0.956106	+	0.303620i
$711$	1.73920			0.0652250
$712$	−7.25088			−0.271738
$713$	7.51134	−	23.1175i	0.281302	−	0.865758i
$714$	−9.56958	+	29.4521i	−0.358133	+	1.10222i
$715$	−24.7764	+	11.2265i	−0.926585	+	0.419846i
$716$	−3.51260	−	10.8107i	−0.131272	−	0.404014i
$717$	−13.3261			−0.497674
$718$	−9.47290	+	29.1546i	−0.353525	+	1.08804i
$719$	−23.5303	−	17.0958i	−0.877534	−	0.637566i	0.0550640	−	0.998483i	$-0.482464\pi$
$719$	−23.5303	−	17.0958i	−0.877534	−	0.637566i	−0.932598	+	0.360917i	$0.882464\pi$
$720$	−1.08378	−	0.344164i	−0.0403901	−	0.0128262i
$721$	−2.62686			−0.0978293
$722$	4.76935	−	14.6786i	0.177497	−	0.546279i
$723$	−15.2224	−	11.0597i	−0.566126	−	0.411314i
$724$	−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	−0.855427	−	0.517923i	$-0.826705\pi$
$727$	3.80327	−	11.7053i	0.141056	−	0.434124i	0.996483	+	0.0837989i	$0.0267053\pi$
$728$	3.23234	+	9.94811i	0.119798	+	0.368702i
$729$	−24.1845	+	17.5710i	−0.895721	+	0.650780i
$730$	11.3454	+	3.60284i	0.419913	+	0.133347i
$731$	−2.51882	+	7.75212i	−0.0931618	+	0.286722i
$732$	8.54913	−	6.21130i	0.315985	−	0.229576i
$733$	14.7375	+	10.7074i	0.544341	+	0.395487i	0.825695	−	0.564117i	$-0.190783\pi$
$733$	14.7375	+	10.7074i	0.544341	+	0.395487i	−0.281354	+	0.959604i	$0.590783\pi$
$734$	11.7982			0.435481
$735$	−3.79520	+	1.26119i	−0.139988	+	0.0465197i
$736$	−1.83472	+	5.64669i	−0.0676287	+	0.208140i
$737$	−25.1721	+	22.6599i	−0.927226	+	0.834689i
$738$	1.30982	+	4.03122i	0.0482152	+	0.148391i
$739$	−30.2328	+	21.9654i	−1.11213	+	0.808010i	−0.982998	−	0.183618i	$-0.941219\pi$
$739$	−30.2328	+	21.9654i	−1.11213	+	0.808010i	−0.129132	+	0.991627i	$0.541219\pi$
$740$	11.3342	−	15.8211i	0.416653	−	0.581595i
$741$	27.4843	−	19.9685i	1.00966	−	0.733562i
$742$	0.184026	−	0.566373i	0.00675580	−	0.0207922i
$743$	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	$0.200595\pi$
$744$	5.22796	+	3.79834i	0.191666	+	0.139254i
$745$	48.1744	+	15.2982i	1.76497	+	0.560484i
$746$	−1.98472	−	6.10833i	−0.0726657	−	0.223642i
$747$	−0.249698	−	0.181416i	−0.00913597	−	0.00663767i
$748$	19.7585	+	11.4105i	0.722442	+	0.417211i
$749$	−21.0673			−0.769784
$750$	−0.353212	−	17.6439i	−0.0128975	−	0.644266i
$751$	−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	$0.843653\pi$
$752$	−0.0262085			−0.000955726
$753$	−14.0256			−0.511120
$754$	−26.1083			−0.950809
$755$	−12.9213	+	4.29392i	−0.470256	+	0.156272i
$756$	−4.88049	−	15.0206i	−0.177502	−	0.546294i
$757$	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
$759$	−12.6391	−	28.3964i	−0.458769	−	1.03073i
$760$	−12.5059	−	3.97137i	−0.453637	−	0.144057i
$761$	25.7978	−	18.7432i	0.935171	−	0.679442i	−0.0120823	−	0.999927i	$-0.503846\pi$
$761$	25.7978	−	18.7432i	0.935171	−	0.679442i	0.947253	+	0.320485i	$0.103846\pi$
$762$	−22.6649			−0.821064
$763$	−30.3666	+	22.0626i	−1.09934	+	0.798720i
$764$	−7.33907	−	22.5873i	−0.265518	−	0.817181i
$765$	0.0521934	+	7.82257i	0.00188706	+	0.282826i
$766$	22.5411	−	16.3771i	0.814443	−	0.591727i
$767$	7.92619	+	24.3943i	0.286198	+	0.880827i
$768$	−1.27698	−	0.927783i	−0.0460792	−	0.0334785i
$769$	−21.8611	+	15.8830i	−0.788331	+	0.572756i	−0.907468	−	0.420122i	$-0.861987\pi$
$769$	−21.8611	+	15.8830i	−0.788331	+	0.572756i	0.119136	+	0.992878i	$0.461987\pi$
$770$	2.34869	+	21.0191i	0.0846408	+	0.757477i
$771$	−36.3470	−	26.4077i	−1.30901	−	0.951048i
$772$	8.37338	+	25.7706i	0.301365	+	0.927505i
$773$	−29.0191	−	21.0836i	−1.04374	−	0.758324i	−0.0727312	−	0.997352i	$-0.523172\pi$
$773$	−29.0191	−	21.0836i	−1.04374	−	0.758324i	−0.971013	+	0.239027i	$0.923172\pi$
$774$	−0.186192	−	0.573039i	−0.00669253	−	0.0205975i
$775$	6.06523	−	19.5508i	0.217869	−	0.702284i
$776$	−13.9004	+	10.0992i	−0.498995	+	0.362541i
$777$	39.1795			1.40556
$778$	−18.7425	+	13.6172i	−0.671952	+	0.488202i
$779$	15.1142	+	46.5169i	0.541524	+	1.66664i
$780$	−7.67888	−	10.4221i	−0.274948	−	0.373172i
$781$	39.4302	−	4.13977i	1.41092	−	0.148133i
$782$	40.8454			1.46063
$783$	39.4208			1.40879
$784$	1.13310			0.0404678
$785$	−46.0122	+	15.2904i	−1.64225	+	0.545739i
$786$	5.15884	+	15.8773i	0.184010	+	0.566324i
$787$	−33.1070	−	24.0536i	−1.18014	−	0.857419i	−0.187948	−	0.982179i	$-0.560184\pi$
$787$	−33.1070	−	24.0536i	−1.18014	−	0.857419i	−0.992187	+	0.124760i	$0.960184\pi$
$788$	−0.516992	+	0.375616i	−0.0184171	+	0.0133808i
$789$	24.7608	+	17.9897i	0.881506	+	0.640452i
$790$	−0.0510236	−	7.64724i	−0.00181534	−	0.272077i
$791$	6.09532	+	18.7595i	0.216725	+	0.667009i
$792$	−1.67739	+	0.176109i	−0.0596036	+	0.00625778i
$793$	−24.5552			−0.871980
$794$	13.5144			0.479607
$795$	0.00491743	+	0.737007i	0.000174403	+	0.0261389i
$796$	5.11466	−	15.7413i	0.181284	−	0.557935i
$797$	0.143278			0.00507515			0.00253758	−	0.999997i	$-0.499192\pi$
$797$	0.143278			0.00507515			0.00253758	+	0.999997i	$0.499192\pi$
$798$	−8.16265	−	25.1221i	−0.288955	−	0.889311i
$799$	0.0557160	+	0.171476i	0.00197109	+	0.00606639i
$800$	−1.48149	+	4.77548i	−0.0523787	+	0.168839i
$801$	−2.98310	−	2.16735i	−0.105403	−	0.0765794i
$802$	9.75478	−	30.0221i	0.344453	−	1.06012i
$803$	17.5596	−	1.84358i	0.619665	−	0.0650586i
$804$	−13.0404	−	9.47440i	−0.459899	−	0.334136i
$805$	22.4585	+	30.4816i	0.791557	+	1.07434i
$806$	−4.64019	−	14.2810i	−0.163444	−	0.503028i
$807$	−2.59599	−	7.98963i	−0.0913832	−	0.281248i
$808$	0.633390	−	1.94937i	0.0222826	−	0.0685787i
$809$	−8.96106	−	6.51059i	−0.315054	−	0.228900i	0.419008	−	0.907983i	$-0.362378\pi$
$809$	−8.96106	−	6.51059i	−0.315054	−	0.228900i	−0.734062	+	0.679082i	$0.762378\pi$
$810$	9.57080	+	12.9899i	0.336284	+	0.456420i
$811$	−9.69975	−	7.04728i	−0.340604	−	0.247464i	0.404312	−	0.914621i	$-0.367511\pi$
$811$	−9.69975	−	7.04728i	−0.340604	−	0.247464i	−0.744917	+	0.667157i	$0.767511\pi$
$812$	−6.27311	+	19.3066i	−0.220143	+	0.677531i
$813$	1.84609	+	5.68169i	0.0647453	+	0.199266i
$814$	6.00495	−	28.2354i	0.210474	−	0.989650i
$815$	−22.9389	+	7.62287i	−0.803514	+	0.267018i
$816$	−3.35556	+	10.3273i	−0.117468	+	0.361529i
$817$	−2.14850	−	6.61240i	−0.0751664	−	0.231338i
$818$	7.68584	+	23.6546i	0.268729	+	0.827063i
$819$	−1.64375	+	5.05894i	−0.0574373	+	0.176774i
$820$	17.6868	−	5.87755i	0.617651	−	0.205253i
$821$	−1.05128	+	3.23551i	−0.0366900	+	0.112920i	−0.967724	−	0.252012i	$-0.918908\pi$
$821$	−1.05128	+	3.23551i	−0.0366900	+	0.112920i	0.931034	+	0.364932i	$0.118908\pi$
$822$	−14.6368	+	10.6343i	−0.510517	+	0.370913i
$823$	28.8933	−	20.9922i	1.00716	−	0.731743i	0.0435473	−	0.999051i	$-0.486134\pi$
$823$	28.8933	−	20.9922i	1.00716	−	0.731743i	0.963611	+	0.267308i	$0.0861341\pi$
$824$	−0.921104			−0.0320882
$825$	−10.9620	−	23.7695i	−0.381646	−	0.827548i
$826$	19.9436			0.693927
$827$	−17.8039	+	12.9353i	−0.619102	+	0.449804i	−0.852608	−	0.522552i	$-0.824980\pi$
$827$	−17.8039	+	12.9353i	−0.619102	+	0.449804i	0.233506	+	0.972355i	$0.424980\pi$
$828$	−2.44267	+	1.77470i	−0.0848886	+	0.0616752i
$829$	−1.16518	+	3.58607i	−0.0404685	+	0.124549i	−0.969250	−	0.246079i	$-0.920858\pi$
$829$	−1.16518	+	3.58607i	−0.0404685	+	0.124549i	0.928781	+	0.370628i	$0.120858\pi$
$830$	−0.790361	+	1.10324i	−0.0274338	+	0.0382941i
$831$	−4.78014	+	14.7117i	−0.165821	+	0.510345i
$832$	1.13341	+	3.48829i	0.0392941	+	0.120935i
$833$	−2.40882	−	7.41360i	−0.0834608	−	0.256866i
$834$	4.08584	−	12.5749i	0.141481	−	0.435434i
$835$	16.3989	+	22.2574i	0.567508	+	0.770248i
$836$	−19.3557	+	2.03216i	−0.669431	+	0.0702836i
$837$	7.00620	+	21.5629i	0.242170	+	0.745322i
$838$	−4.44289	+	13.6738i	−0.153477	+	0.472354i
$839$	−14.8859	−	10.8152i	−0.513917	−	0.373383i	0.300390	−	0.953816i	$-0.402883\pi$
$839$	−14.8859	−	10.8152i	−0.513917	−	0.373383i	−0.814308	+	0.580434i	$0.802883\pi$
$840$	−9.55201	+	3.17425i	−0.329576	+	0.109522i
$841$	−17.5309	−	12.7369i	−0.604512	−	0.439204i
$842$	−4.73803	+	14.5822i	−0.163283	+	0.502534i
$843$	15.2452	+	46.9200i	0.525073	+	1.61601i
$844$	4.30249	+	13.2417i	0.148098	+	0.455798i
$845$	0.00675533	+	1.01246i	0.000232390	+	0.0348298i
$846$	−0.0107825	−	0.00783394i	−0.000370710	−	0.000269336i
$847$	15.6791	+	27.1711i	0.538740	+	0.933612i
$848$	0.0645284	−	0.198598i	0.00221591	−	0.00681988i
$849$	27.4165	+	19.9193i	0.940932	+	0.683627i
$850$	34.3943	−	0.458989i	1.17971	−	0.0157432i
$851$	−15.9689	−	49.1471i	−0.547405	−	1.68474i
$852$	5.83073	+	17.9451i	0.199758	+	0.614791i
$853$	31.1244			1.06568			0.532840	−	0.846216i	$-0.321125\pi$
$853$	31.1244			1.06568			0.532840	+	0.846216i	$0.321125\pi$
$854$	−5.89993	+	18.1581i	−0.201891	+	0.621358i
$855$	−3.95801	−	5.37199i	−0.135361	−	0.183718i
$856$	−7.38723			−0.252490
$857$	7.09992			0.242529			0.121264	−	0.992620i	$-0.461305\pi$
$857$	7.09992			0.242529			0.121264	+	0.992620i	$0.461305\pi$
$858$	−16.6277	−	9.60252i	−0.567661	−	0.327825i
$859$	13.6251	+	41.9338i	0.464883	+	1.43076i	0.859129	+	0.511759i	$0.171006\pi$
$859$	13.6251	+	41.9338i	0.464883	+	1.43076i	−0.394246	+	0.919005i	$0.628994\pi$
$860$	−2.51419	+	0.835497i	−0.0857332	+	0.0284902i
$861$	30.3546	+	22.0539i	1.03448	+	0.751594i
$862$	12.0052	−	8.72231i	0.408900	−	0.297083i
$863$	−21.1894	−	15.3950i	−0.721294	−	0.524051i	0.165503	−	0.986209i	$-0.447075\pi$
$863$	−21.1894	−	15.3950i	−0.721294	−	0.524051i	−0.886797	+	0.462158i	$0.847075\pi$
$864$	−1.71134	−	5.26695i	−0.0582209	−	0.179185i
$865$	−0.121036	−	18.1404i	−0.00411534	−	0.616793i
$866$	−26.2756			−0.892880
$867$	47.8694			1.62573
$868$	−11.6755			−0.396292
$869$	−4.61242	−	10.3628i	−0.156466	−	0.351535i
$870$	−0.167626	−	25.1232i	−0.00568306	−	0.851757i
$871$	11.5743	+	35.6220i	0.392180	+	1.20700i
$872$	−10.6480	+	7.73622i	−0.360587	+	0.261982i
$873$	−8.73753			−0.295721
$874$	−28.1864	+	20.4786i	−0.953418	+	0.692698i
$875$	19.2539	+	25.4150i	0.650901	+	0.859185i
$876$	2.59662	+	7.99158i	0.0877317	+	0.270010i
$877$	−8.71910	−	6.33479i	−0.294423	−	0.213911i	0.430761	−	0.902466i	$-0.358245\pi$
$877$	−8.71910	−	6.33479i	−0.294423	−	0.213911i	−0.725184	+	0.688555i	$0.758245\pi$
$878$	2.31622	+	7.12859i	0.0781686	+	0.240578i
$879$	30.8405	+	22.4069i	1.04022	+	0.755766i
$880$	0.823563	+	7.37033i	0.0277623	+	0.248454i
$881$	−2.24052	+	1.62784i	−0.0754852	+	0.0548432i	−0.624888	−	0.780715i	$-0.714855\pi$
$881$	−2.24052	+	1.62784i	−0.0754852	+	0.0548432i	0.549403	+	0.835558i	$0.314855\pi$
$882$	0.466170	+	0.338692i	0.0156968	+	0.0114044i
$883$	2.46349	+	7.58184i	0.0829030	+	0.255149i	0.983913	−	0.178650i	$-0.0571728\pi$
$883$	2.46349	+	7.58184i	0.0829030	+	0.255149i	−0.901010	+	0.433799i	$0.857173\pi$
$884$	20.4136	−	14.8313i	0.686582	−	0.498831i
$885$	−23.4230	+	7.78375i	−0.787355	+	0.261648i
$886$	−4.66994	−	14.3726i	−0.156890	−	0.482856i
$887$	12.3763	−	8.99192i	0.415556	−	0.301919i	−0.360291	−	0.932840i	$-0.617323\pi$
$887$	12.3763	−	8.99192i	0.415556	−	0.301919i	0.775847	+	0.630921i	$0.217323\pi$
$888$	13.7382			0.461025
$889$	33.1293	−	24.0699i	1.11112	−	0.807277i
$890$	−9.44230	+	13.1803i	−0.316507	+	0.441803i
$891$	20.7244	+	11.9684i	0.694295	+	0.400956i
$892$	1.88311	−	1.36816i	0.0630511	−	0.0458093i
$893$	−0.124421	−	0.0903971i	−0.00416359	−	0.00302502i
$894$	11.0257	+	33.9335i	0.368753	+	1.13490i
$895$	−24.2253	−	7.69295i	−0.809761	−	0.257147i
$896$	2.85186			0.0952739
$897$	−34.3733			−1.14769
$898$	−24.2904			−0.810582
$899$	9.00538	−	27.7157i	0.300346	−	0.924370i
$900$	−2.03693	+	1.52186i	−0.0678978	+	0.0507286i
$901$	−1.43656			−0.0478587
$902$	20.5459	−	18.4954i	0.684103	−	0.615829i
$903$	−4.31492	−	3.13497i	−0.143591	−	0.104325i
$904$	2.13731	+	6.57798i	0.0710860	+	0.218780i
$905$	−20.2163	+	6.71813i	−0.672013	+	0.223318i
$906$	−7.77596	−	5.64956i	−0.258339	−	0.187694i
$907$	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	$0.139050\pi$
$908$	−1.23304	+	3.79491i	−0.0409199	+	0.125939i
$909$	0.843268	−	0.612670i	0.0279694	−	0.0203210i
$910$	22.2924	+	7.07915i	0.738985	+	0.234671i
$911$	6.93372	−	5.03764i	0.229724	−	0.166904i	−0.466969	−	0.884274i	$-0.654654\pi$
$911$	6.93372	−	5.03764i	0.229724	−	0.166904i	0.696693	+	0.717369i	$0.254654\pi$
$912$	−2.86222	−	8.80901i	−0.0947776	−	0.291696i
$913$	−0.418740	+	1.96892i	−0.0138583	+	0.0651618i
$914$	4.96236	−	15.2726i	0.164140	−	0.505172i
$915$	−0.157654	−	23.6287i	−0.00521189	−	0.781140i
$916$	16.5012			0.545214
$917$	−24.4021	−	17.7292i	−0.805830	−	0.585469i
$918$	−30.8223	+	22.3937i	−1.01729	+	0.739104i
$919$	3.42847	−	10.5518i	0.113095	−	0.348070i	−0.878450	−	0.477834i	$-0.841422\pi$
$919$	3.42847	−	10.5518i	0.113095	−	0.348070i	0.991545	+	0.129764i	$0.0414220\pi$
$920$	7.87503	+	10.6883i	0.259632	+	0.352384i
$921$	−20.6893	+	15.0316i	−0.681735	+	0.495309i
$922$	−9.54611	−	29.3799i	−0.314384	−	0.967575i
$923$	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
$927$	−0.378953	−	0.275325i	−0.0124464	−	0.00904287i
$928$	−2.19966	+	6.76985i	−0.0722073	+	0.222231i
$929$	8.59258			0.281913			0.140957	−	0.990016i	$-0.454982\pi$
$929$	8.59258			0.281913			0.140957	+	0.990016i	$0.454982\pi$
$930$	13.7124	−	4.55680i	0.449648	−	0.149423i
$931$	5.37921	+	3.90823i	0.176297	+	0.128087i
$932$	−2.87096	+	8.83592i	−0.0940416	+	0.289430i
$933$	−29.3237			−0.960014
$934$	4.62994	+	14.2495i	0.151496	+	0.466258i
$935$	46.4715	−	21.0568i	1.51978	−	0.688630i
$936$	−0.576378	+	1.77391i	−0.0188395	+	0.0579821i
$937$	−2.08947	+	6.43073i	−0.0682601	+	0.210083i	−0.979368	−	0.202085i	$-0.935228\pi$
$937$	−2.08947	+	6.43073i	−0.0682601	+	0.210083i	0.911108	+	0.412168i	$0.135228\pi$
$938$	29.1228			0.950894
$939$	−17.4883			−0.570708
$940$	−0.0341295	+	0.0476404i	−0.00111318	+	0.00155386i
$941$	−12.0407	−	8.74808i	−0.392515	−	0.285179i	0.373970	−	0.927441i	$-0.377996\pi$
$941$	−12.0407	−	8.74808i	−0.392515	−	0.285179i	−0.766485	+	0.642262i	$0.777996\pi$
$942$	−27.6898	−	20.1178i	−0.902181	−	0.655473i
$943$	15.2926	−	47.0657i	0.497995	−	1.53267i
$944$	6.99319			0.227609
$945$	−33.6592	−	10.6888i	−1.09493	−	0.347706i
$946$	−2.92061	+	2.62913i	−0.0949571	+	0.0854803i
$947$	10.6046	+	7.70471i	0.344604	+	0.250370i	0.746602	−	0.665271i	$-0.231684\pi$
$947$	10.6046	+	7.70471i	0.344604	+	0.250370i	−0.401998	+	0.915641i	$0.631684\pi$
$948$	4.36732	−	3.17304i	0.141844	−	0.103056i
$949$	6.03375	−	18.5700i	0.195864	−	0.602807i
$950$	−23.5045	+	17.5610i	−0.762587	+	0.569752i
$951$	16.3511	−	11.8798i	0.530220	−	0.385228i
$952$	−6.06269	−	18.6590i	−0.196493	−	0.604743i
$953$	−13.0519	+	40.1697i	−0.422793	+	1.30122i	0.482299	+	0.876007i	$0.339802\pi$
$953$	−13.0519	+	40.1697i	−0.422793	+	1.30122i	−0.905092	+	0.425216i	$0.860198\pi$
$954$	0.0859103	−	0.0624175i	0.00278145	−	0.00202084i
$955$	−50.6152	−	16.0733i	−1.63787	−	0.520120i
$956$	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
$959$	10.1012	−	31.0882i	0.326184	−	1.00389i
$960$	−3.34940	+	1.11305i	−0.108101	+	0.0359234i
$961$	−14.2392			−0.459330
$962$	−25.8266	−	18.7641i	−0.832684	−	0.604980i
$963$	−3.03919	−	2.20810i	−0.0979367	−	0.0711552i
$964$	11.9206			0.383935
$965$	57.7485	+	18.3386i	1.85899	+	0.590339i
$966$	−8.25897	+	25.4185i	−0.265728	+	0.817827i
$967$	27.4140	−	19.9174i	0.881575	−	0.640501i	−0.0520930	−	0.998642i	$-0.516589\pi$
$967$	27.4140	−	19.9174i	0.881575	−	0.640501i	0.933668	+	0.358141i	$0.116589\pi$
$968$	5.49785	+	9.52752i	0.176707	+	0.306226i
$969$	−51.5506	+	37.4537i	−1.65604	+	1.20319i
$970$	0.256337	+	38.4189i	0.00823049	+	1.23356i
$971$	−43.7670	+	31.7986i	−1.40455	+	1.02046i	−0.410462	+	0.911878i	$0.634633\pi$
$971$	−43.7670	+	31.7986i	−1.40455	+	1.02046i	−0.994087	+	0.108587i	$0.965367\pi$
$972$	1.61440	−	4.96862i	0.0517820	−	0.159369i
$973$	7.38214	+	22.7199i	0.236660	+	0.728366i
$974$	−27.7083	+	20.1312i	−0.887831	+	0.645047i
$975$	−28.9444	+	0.386261i	−0.926964	+	0.0123703i
$976$	−2.06880	+	6.36712i	−0.0662207	+	0.203806i
$977$	21.9437	−	15.9431i	0.702042	−	0.510063i	−0.178555	−	0.983930i	$-0.557142\pi$
$977$	21.9437	−	15.9431i	0.702042	−	0.510063i	0.880597	+	0.473867i	$0.157142\pi$
$978$	−13.8044	−	10.0295i	−0.441417	−	0.320708i
$979$	−5.00261	+	23.5224i	−0.159884	+	0.751778i
$980$	1.47555	−	2.05969i	0.0471348	−	0.0657942i
$981$	−6.69313			−0.213695
$982$	−1.27438	+	3.92214i	−0.0406671	+	0.125160i
$983$	43.9357	+	31.9212i	1.40133	+	1.01813i	0.994512	+	0.104619i	$0.0333623\pi$
$983$	43.9357	+	31.9212i	1.40133	+	1.01813i	0.406820	+	0.913508i	$0.366638\pi$
$984$	10.6438	+	7.73316i	0.339311	+	0.246524i
$985$	0.00953384	+	1.42890i	0.000303773	+	0.0455285i
$986$	48.9697			1.55951
$987$	−0.117977			−0.00375526
$988$	−6.65093	+	20.4694i	−0.211594	+	0.651220i
$989$	−2.17385	+	6.69042i	−0.0691244	+	0.212743i
$990$	−1.86423	+	3.27841i	−0.0592490	+	0.104195i
$991$	14.3826	+	44.2650i	0.456877	+	1.40612i	0.868917	+	0.494958i	$0.164817\pi$
$991$	14.3826	+	44.2650i	0.456877	+	1.40612i	−0.412040	+	0.911166i	$0.635183\pi$
$992$	−4.09399			−0.129984
$993$	6.79305	−	20.9068i	0.215571	−	0.663459i
$994$	−27.5803	−	20.0382i	−0.874793	−	0.635575i
$995$	−21.9532	−	29.7959i	−0.695964	−	0.944594i
$996$	−0.958000			−0.0303554
$997$	2.98151	−	9.17616i	0.0944255	−	0.290612i	−0.892678	−	0.450695i	$-0.851176\pi$
$997$	2.98151	−	9.17616i	0.0944255	−	0.290612i	0.987104	+	0.160083i	$0.0511762\pi$
$998$	−27.2513	−	19.7992i	−0.862623	−	0.626733i
$999$	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.g.c.521.5	✓	60
11.3	even	5		550.2.j.c.421.11	yes	60
25.6	even	5		550.2.j.c.81.11	yes	60
275.256	even	5	inner	550.2.g.c.531.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.g.c.521.5	✓	60	1.1	even	1	trivial
550.2.g.c.531.5	yes	60	275.256	even	5	inner
550.2.j.c.81.11	yes	60	25.6	even	5
550.2.j.c.421.11	yes	60	11.3	even	5

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.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-1.27698 + 0.927783i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.32637 - 1.80021i) q^{5} +(0.487764 - 1.50118i) q^{6} +(0.881273 + 2.71228i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.157145 + 0.483644i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-1.27698 + 0.927783i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.32637 - 1.80021i) q^{5} +(0.487764 - 1.50118i) q^{6} +(0.881273 + 2.71228i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.157145 + 0.483644i) q^{9} +(2.13119 + 0.676779i) q^{10} +(3.29850 - 0.346309i) q^{11} +(0.487764 + 1.50118i) q^{12} +(1.13341 - 3.48829i) q^{13} +(-2.30720 - 1.67628i) q^{14} +(3.36395 + 1.06825i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.12587 + 6.54276i) q^{17} +(-0.157145 - 0.483644i) q^{18} +(-1.81333 - 5.58084i) q^{19} +(-2.12197 + 0.705157i) q^{20} +(-3.64178 - 2.64591i) q^{21} +(-2.46498 + 2.21898i) q^{22} +(-1.83472 + 5.64669i) q^{23} +(-1.27698 - 0.927783i) q^{24} +(-1.48149 + 4.77548i) q^{25} +(1.13341 + 3.48829i) q^{26} +(-1.71134 - 5.26695i) q^{27} +2.85186 q^{28} +(-2.19966 + 6.76985i) q^{29} +(-3.34940 + 1.11305i) q^{30} -4.09399 q^{31} +1.00000 q^{32} +(-3.89082 + 3.50252i) q^{33} +(-2.12587 - 6.54276i) q^{34} +(3.71377 - 5.18395i) q^{35} +(0.411412 + 0.298908i) q^{36} +(-7.04144 + 5.11590i) q^{37} +(4.74735 + 3.44915i) q^{38} +(1.78902 + 5.50605i) q^{39} +(1.30223 - 1.81775i) q^{40} -8.33510 q^{41} +4.50148 q^{42} +1.18484 q^{43} +(0.689932 - 3.24407i) q^{44} +(1.07909 - 0.358595i) q^{45} +(-1.83472 - 5.64669i) q^{46} +(0.0212031 - 0.0154050i) q^{47} +1.57844 q^{48} +(-0.916696 + 0.666019i) q^{49} +(-1.60840 - 4.73424i) q^{50} +(-3.35556 - 10.3273i) q^{51} +(-2.96732 - 2.15588i) q^{52} +(0.0645284 + 0.198598i) q^{53} +(4.48034 + 3.25516i) q^{54} +(-4.99845 - 5.47864i) q^{55} +(-2.30720 + 1.67628i) q^{56} +(7.49339 + 5.44427i) q^{57} +(-2.19966 - 6.76985i) q^{58} +(-5.65761 + 4.11050i) q^{59} +(2.05549 - 2.86920i) q^{60} +(-2.06880 - 6.36712i) q^{61} +(3.31211 - 2.40639i) q^{62} -1.45026 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.78297 + 2.58638i) q^{65} +(1.08901 - 5.12056i) q^{66} +(-8.26158 + 6.00239i) q^{67} +(5.56561 + 4.04365i) q^{68} +(-2.89600 - 8.91296i) q^{69} +(0.0425471 + 6.37681i) q^{70} +11.9540 q^{71} -0.508533 q^{72} +5.32352 q^{73} +(2.68959 - 8.27770i) q^{74} +(-2.53876 - 7.47271i) q^{75} -5.86804 q^{76} +(3.84616 + 8.64125i) q^{77} +(-4.68373 - 3.40293i) q^{78} +(-1.05685 - 3.25264i) q^{79} +(0.0149191 + 2.23602i) q^{80} +(5.83770 + 4.24134i) q^{81} +(6.74324 - 4.89925i) q^{82} +(-0.187551 + 0.577224i) q^{83} +(-3.64178 + 2.64591i) q^{84} +(14.5980 - 4.85110i) q^{85} +(-0.958554 + 0.696431i) q^{86} +(-3.47202 - 10.6858i) q^{87} +(1.34865 + 3.03004i) q^{88} +(-2.24065 + 6.89600i) q^{89} +(-0.662226 + 0.924384i) q^{90} +10.4601 q^{91} +(4.80336 + 3.48985i) q^{92} +(5.22796 - 3.79834i) q^{93} +(-0.00809888 + 0.0249258i) q^{94} +(-7.64154 + 10.6666i) q^{95} +(-1.27698 + 0.927783i) q^{96} +(5.30948 + 16.3409i) q^{97} +(0.350147 - 1.07764i) q^{98} +(-0.350853 + 1.64972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9}+O(q^{10}) \) 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9	\( 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21} - 3 q^{22} - 3 q^{23} - 4 q^{24} + 8 q^{25} + 12 q^{26} + 2 q^{27} + 12 q^{28} + 18 q^{29} + 2 q^{30} - 20 q^{31} + 60 q^{32} + 10 q^{33} + q^{34} - 19 q^{35} - 12 q^{36} - 36 q^{37} - 22 q^{38} + 13 q^{39} + 64 q^{41} + 46 q^{42} + 40 q^{43} - 8 q^{44} - 20 q^{45} - 3 q^{46} - 9 q^{47} + 6 q^{48} - 30 q^{49} + 18 q^{50} - 48 q^{51} - 8 q^{52} + 31 q^{53} - 8 q^{54} - 42 q^{55} - 3 q^{56} + 30 q^{57} + 18 q^{58} + 23 q^{59} - 8 q^{60} - 41 q^{61} - 5 q^{62} + 6 q^{63} - 15 q^{64} - 7 q^{65} - 30 q^{66} - 40 q^{67} - 4 q^{68} - 22 q^{69} - 4 q^{70} + 4 q^{71} + 58 q^{72} + 74 q^{73} - 11 q^{74} + 35 q^{75} + 38 q^{76} + 22 q^{77} - 12 q^{78} - 45 q^{79} + 10 q^{80} + 24 q^{81} - 11 q^{82} + 16 q^{83} - 4 q^{84} + 9 q^{85} - 20 q^{86} + 68 q^{87} + 7 q^{88} + q^{89} + 10 q^{90} + 10 q^{91} + 2 q^{92} - 40 q^{93} - 24 q^{94} + 24 q^{95} - 4 q^{96} + 6 q^{97} - 30 q^{98} + 21 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

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