LMFDB - Embedded newform 504.2.y.a.173.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(173,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1, 5]))

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

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

chi := DirichletCharacter("504.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.y (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.19
Character	$\chi$	$=$	504.173
Dual form			504.2.y.a.437.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14122 - 0.835238i) q^{2} +(-0.987509 + 1.42296i) q^{3} +(0.604756 + 1.90638i) q^{4} +0.709981i q^{5} +(2.31548 - 0.799106i) q^{6} +(-2.47476 - 0.935707i) q^{7} +(0.902119 - 2.68071i) q^{8} +(-1.04965 - 2.81038i) q^{9} +O(q^{10})$	\(q+(-1.14122 - 0.835238i) q^{2} +(-0.987509 + 1.42296i) q^{3} +(0.604756 + 1.90638i) q^{4} +0.709981i q^{5} +(2.31548 - 0.799106i) q^{6} +(-2.47476 - 0.935707i) q^{7} +(0.902119 - 2.68071i) q^{8} +(-1.04965 - 2.81038i) q^{9} +(0.593003 - 0.810243i) q^{10} -2.06516 q^{11} +(-3.30991 - 1.02202i) q^{12} +(1.34373 + 2.32741i) q^{13} +(2.04271 + 3.13486i) q^{14} +(-1.01028 - 0.701113i) q^{15} +(-3.26854 + 2.30579i) q^{16} +(-0.925683 - 1.60333i) q^{17} +(-1.14946 + 4.08396i) q^{18} +(-0.453561 + 0.785591i) q^{19} +(-1.35349 + 0.429365i) q^{20} +(3.77533 - 2.59748i) q^{21} +(2.35679 + 1.72490i) q^{22} -8.94020i q^{23} +(2.92370 + 3.93090i) q^{24} +4.49593 q^{25} +(0.410451 - 3.77842i) q^{26} +(5.03561 + 1.28166i) q^{27} +(0.287180 - 5.28370i) q^{28} +(3.23989 - 5.61165i) q^{29} +(0.567350 + 1.64394i) q^{30} +(-0.913241 - 0.527260i) q^{31} +(5.65599 + 0.0986046i) q^{32} +(2.03936 - 2.93864i) q^{33} +(-0.282756 + 2.60291i) q^{34} +(0.664334 - 1.75703i) q^{35} +(4.72286 - 3.70062i) q^{36} +(0.0827713 + 0.0477880i) q^{37} +(1.17377 - 0.517699i) q^{38} +(-4.63877 - 0.386259i) q^{39} +(1.90325 + 0.640487i) q^{40} +(-0.808217 - 1.39987i) q^{41} +(-6.47798 - 0.189007i) q^{42} +(-3.14459 - 1.81553i) q^{43} +(-1.24892 - 3.93697i) q^{44} +(1.99532 - 0.745232i) q^{45} +(-7.46719 + 10.2027i) q^{46} +(-4.28551 - 7.42271i) q^{47} +(-0.0533341 - 6.92800i) q^{48} +(5.24891 + 4.63130i) q^{49} +(-5.13083 - 3.75517i) q^{50} +(3.19560 + 0.266090i) q^{51} +(-3.62429 + 3.96917i) q^{52} +(-3.23163 - 5.59734i) q^{53} +(-4.67623 - 5.66858i) q^{54} -1.46622i q^{55} +(-4.74088 + 5.78999i) q^{56} +(-0.669971 - 1.42118i) q^{57} +(-8.38448 + 3.69804i) q^{58} +(8.76515 + 5.06056i) q^{59} +(0.725614 - 2.34997i) q^{60} +(-5.10189 - 8.83673i) q^{61} +(0.601819 + 1.36449i) q^{62} +(-0.0320548 + 7.93719i) q^{63} +(-6.37236 - 4.83663i) q^{64} +(-1.65242 + 0.954023i) q^{65} +(-4.78182 + 1.65028i) q^{66} +(-9.47786 - 5.47204i) q^{67} +(2.49674 - 2.73432i) q^{68} +(12.7216 + 8.82853i) q^{69} +(-2.22569 + 1.45028i) q^{70} -1.18064i q^{71} +(-8.48071 + 0.278507i) q^{72} +(7.22061 - 4.16882i) q^{73} +(-0.0545457 - 0.123670i) q^{74} +(-4.43977 + 6.39754i) q^{75} +(-1.77193 - 0.389567i) q^{76} +(5.11078 + 1.93238i) q^{77} +(4.97122 + 4.31528i) q^{78} +(5.34801 + 9.26302i) q^{79} +(-1.63706 - 2.32060i) q^{80} +(-6.79647 + 5.89983i) q^{81} +(-0.246875 + 2.27261i) q^{82} +(-7.97129 - 4.60223i) q^{83} +(7.23492 + 5.62635i) q^{84} +(1.13833 - 0.657217i) q^{85} +(2.07227 + 4.69840i) q^{86} +(4.78576 + 10.1518i) q^{87} +(-1.86302 + 5.53608i) q^{88} +(-3.98499 + 6.90221i) q^{89} +(-2.89954 - 0.816091i) q^{90} +(-1.14764 - 7.01713i) q^{91} +(17.0434 - 5.40664i) q^{92} +(1.65211 - 0.778834i) q^{93} +(-1.30903 + 12.0503i) q^{94} +(-0.557755 - 0.322020i) q^{95} +(-5.72566 + 7.95090i) q^{96} +(9.56123 + 5.52018i) q^{97} +(-2.12191 - 9.66941i) q^{98} +(2.16769 + 5.80388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.14122	−	0.835238i	−0.806963	−	0.590602i
$2$	−1.14122	−	0.835238i	−0.806963	−	0.590602i
$3$	−0.987509	+	1.42296i	−0.570139	+	0.821548i
$3$	−0.987509	+	1.42296i	−0.570139	+	0.821548i
$4$	0.604756	+	1.90638i	0.302378	+	0.953188i
$5$			0.709981i			0.317513i	0.987318	+	0.158757i	$0.0507485\pi$
$5$			0.709981i			0.317513i	−0.987318	+	0.158757i	$0.949251\pi$
$6$	2.31548	−	0.799106i	0.945289	−	0.326234i
$7$	−2.47476	−	0.935707i	−0.935373	−	0.353664i
$7$	−2.47476	−	0.935707i	−0.935373	−	0.353664i
$8$	0.902119	−	2.68071i	0.318947	−	0.947773i
$9$	−1.04965	−	2.81038i	−0.349883	−	0.936793i
$10$	0.593003	−	0.810243i	0.187524	−	0.256221i
$11$	−2.06516			−0.622668			−0.311334	−	0.950300i	$-0.600776\pi$
$11$	−2.06516			−0.622668			−0.311334	+	0.950300i	$0.600776\pi$
$12$	−3.30991	−	1.02202i	−0.955488	−	0.295031i
$13$	1.34373	+	2.32741i	0.372684	+	0.645507i	0.989977	−	0.141225i	$-0.0451043\pi$
$13$	1.34373	+	2.32741i	0.372684	+	0.645507i	−0.617294	+	0.786733i	$0.711771\pi$
$14$	2.04271	+	3.13486i	0.545936	+	0.837827i
$15$	−1.01028	−	0.701113i	−0.260852	−	0.181027i
$16$	−3.26854	+	2.30579i	−0.817135	+	0.576446i
$17$	−0.925683	−	1.60333i	−0.224511	−	0.388865i	0.731662	−	0.681668i	$-0.238745\pi$
$17$	−0.925683	−	1.60333i	−0.224511	−	0.388865i	−0.956173	+	0.292803i	$0.905412\pi$
$18$	−1.14946	+	4.08396i	−0.270929	+	0.962599i
$19$	−0.453561	+	0.785591i	−0.104054	+	0.180227i	−0.913351	−	0.407172i	$-0.866515\pi$
$19$	−0.453561	+	0.785591i	−0.104054	+	0.180227i	0.809297	+	0.587399i	$0.199848\pi$
$20$	−1.35349	+	0.429365i	−0.302650	+	0.0960090i
$21$	3.77533	−	2.59748i	0.823844	−	0.566816i
$22$	2.35679	+	1.72490i	0.502470	+	0.367749i
$23$		−	8.94020i		−	1.86416i	−0.362253	−	0.932080i	$-0.617992\pi$
$23$		−	8.94020i		−	1.86416i	0.362253	−	0.932080i	$-0.382008\pi$
$24$	2.92370	+	3.93090i	0.596797	+	0.802392i
$25$	4.49593			0.899185
$26$	0.410451	−	3.77842i	0.0804961	−	0.741008i
$27$	5.03561	+	1.28166i	0.969103	+	0.246656i
$28$	0.287180	−	5.28370i	0.0542720	−	0.998526i
$29$	3.23989	−	5.61165i	0.601632	−	1.04206i	−0.390942	−	0.920415i	$-0.627851\pi$
$29$	3.23989	−	5.61165i	0.601632	−	1.04206i	0.992574	−	0.121642i	$-0.0388161\pi$
$30$	0.567350	+	1.64394i	0.103583	+	0.300142i
$31$	−0.913241	−	0.527260i	−0.164023	−	0.0946986i	0.415742	−	0.909483i	$-0.363522\pi$
$31$	−0.913241	−	0.527260i	−0.164023	−	0.0946986i	−0.579764	+	0.814784i	$0.696855\pi$
$32$	5.65599	+	0.0986046i	0.999848	+	0.0174310i
$33$	2.03936	−	2.93864i	0.355007	−	0.511552i
$34$	−0.282756	+	2.60291i	−0.0484922	+	0.446396i
$35$	0.664334	−	1.75703i	0.112293	−	0.296993i
$36$	4.72286	−	3.70062i	0.787143	−	0.616770i
$37$	0.0827713	+	0.0477880i	0.0136075	+	0.00785630i	0.506788	−	0.862071i	$-0.330833\pi$
$37$	0.0827713	+	0.0477880i	0.0136075	+	0.00785630i	−0.493181	+	0.869927i	$0.664166\pi$
$38$	1.17377	−	0.517699i	0.190410	−	0.0839819i
$39$	−4.63877	−	0.386259i	−0.742797	−	0.0618510i
$40$	1.90325	+	0.640487i	0.300930	+	0.101270i
$41$	−0.808217	−	1.39987i	−0.126222	−	0.218623i	0.795988	−	0.605313i	$-0.206952\pi$
$41$	−0.808217	−	1.39987i	−0.126222	−	0.218623i	−0.922210	+	0.386689i	$0.873619\pi$
$42$	−6.47798	−	0.189007i	−0.999575	−	0.0291645i
$43$	−3.14459	−	1.81553i	−0.479546	−	0.276866i	0.240681	−	0.970604i	$-0.422629\pi$
$43$	−3.14459	−	1.81553i	−0.479546	−	0.276866i	−0.720227	+	0.693738i	$0.755963\pi$
$44$	−1.24892	−	3.93697i	−0.188281	−	0.593520i
$45$	1.99532	−	0.745232i	0.297444	−	0.111093i
$46$	−7.46719	+	10.2027i	−1.10098	+	1.50431i
$47$	−4.28551	−	7.42271i	−0.625105	−	1.08271i	−0.988521	−	0.151087i	$-0.951723\pi$
$47$	−4.28551	−	7.42271i	−0.625105	−	1.08271i	0.363415	−	0.931627i	$-0.381611\pi$
$48$	−0.0533341	−	6.92800i	−0.00769812	−	0.999970i
$49$	5.24891	+	4.63130i	0.749844	+	0.661615i
$50$	−5.13083	−	3.75517i	−0.725609	−	0.531061i
$51$	3.19560	+	0.266090i	0.447474	+	0.0372601i
$52$	−3.62429	+	3.96917i	−0.502599	+	0.550425i
$53$	−3.23163	−	5.59734i	−0.443898	−	0.768854i	0.554077	−	0.832466i	$-0.313071\pi$
$53$	−3.23163	−	5.59734i	−0.443898	−	0.768854i	−0.997975	+	0.0636116i	$0.979738\pi$
$54$	−4.67623	−	5.66858i	−0.636355	−	0.771397i
$55$		−	1.46622i		−	0.197705i
$56$	−4.74088	+	5.78999i	−0.633527	+	0.773720i
$57$	−0.669971	−	1.42118i	−0.0887399	−	0.188240i
$58$	−8.38448	+	3.69804i	−1.10094	+	0.485576i
$59$	8.76515	+	5.06056i	1.14112	+	0.658829i	0.946709	−	0.322091i	$-0.104386\pi$
$59$	8.76515	+	5.06056i	1.14112	+	0.658829i	0.194416	+	0.980919i	$0.437719\pi$
$60$	0.725614	−	2.34997i	0.0936763	−	0.303380i
$61$	−5.10189	−	8.83673i	−0.653230	−	1.13143i	−0.982334	−	0.187134i	$-0.940080\pi$
$61$	−5.10189	−	8.83673i	−0.653230	−	1.13143i	0.329104	−	0.944294i	$-0.393253\pi$
$62$	0.601819	+	1.36449i	0.0764311	+	0.173291i
$63$	−0.0320548	+	7.93719i	−0.00403852	+	0.999992i
$64$	−6.37236	−	4.83663i	−0.796545	−	0.604579i
$65$	−1.65242	+	0.954023i	−0.204957	+	0.118332i
$66$	−4.78182	+	1.65028i	−0.588602	+	0.203135i
$67$	−9.47786	−	5.47204i	−1.15790	−	0.668517i	−0.207104	−	0.978319i	$-0.566404\pi$
$67$	−9.47786	−	5.47204i	−1.15790	−	0.668517i	−0.950801	+	0.309802i	$0.899737\pi$
$68$	2.49674	−	2.73432i	0.302774	−	0.331585i
$69$	12.7216	+	8.82853i	1.53150	+	1.06283i
$70$	−2.22569	+	1.45028i	−0.266021	+	0.173342i
$71$		−	1.18064i		−	0.140116i	−0.997543	−	0.0700579i	$-0.977682\pi$
$71$		−	1.18064i		−	0.140116i	0.997543	−	0.0700579i	$-0.0223184\pi$
$72$	−8.48071	+	0.278507i	−0.999461	+	0.0328224i
$73$	7.22061	−	4.16882i	0.845109	−	0.487924i	−0.0138888	−	0.999904i	$-0.504421\pi$
$73$	7.22061	−	4.16882i	0.845109	−	0.487924i	0.858997	+	0.511980i	$0.171088\pi$
$74$	−0.0545457	−	0.123670i	−0.00634081	−	0.0143764i
$75$	−4.43977	+	6.39754i	−0.512661	+	0.738724i
$76$	−1.77193	−	0.389567i	−0.203254	−	0.0446864i
$77$	5.11078	+	1.93238i	0.582427	+	0.220215i
$78$	4.97122	+	4.31528i	0.562880	+	0.488609i
$79$	5.34801	+	9.26302i	0.601698	+	1.04217i	0.992564	+	0.121724i	$0.0388422\pi$
$79$	5.34801	+	9.26302i	0.601698	+	1.04217i	−0.390866	+	0.920447i	$0.627825\pi$
$80$	−1.63706	−	2.32060i	−0.183029	−	0.259451i
$81$	−6.79647	+	5.89983i	−0.755163	+	0.655537i
$82$	−0.246875	+	2.27261i	−0.0272628	+	0.250968i
$83$	−7.97129	−	4.60223i	−0.874963	−	0.505160i	−0.00596884	−	0.999982i	$-0.501900\pi$
$83$	−7.97129	−	4.60223i	−0.874963	−	0.505160i	−0.868994	+	0.494822i	$0.835233\pi$
$84$	7.23492	+	5.62635i	0.789395	+	0.613886i
$85$	1.13833	−	0.657217i	0.123470	−	0.0712852i
$86$	2.07227	+	4.69840i	0.223458	+	0.506642i
$87$	4.78576	+	10.1518i	0.513087	+	1.08839i
$88$	−1.86302	+	5.53608i	−0.198598	+	0.590148i
$89$	−3.98499	+	6.90221i	−0.422408	+	0.731633i	−0.996174	−	0.0873865i	$-0.972148\pi$
$89$	−3.98499	+	6.90221i	−0.422408	+	0.731633i	0.573766	+	0.819019i	$0.305482\pi$
$90$	−2.89954	−	0.816091i	−0.305638	−	0.0860236i
$91$	−1.14764	−	7.01713i	−0.120306	−	0.735595i
$92$	17.0434	−	5.40664i	1.77690	−	0.563681i
$93$	1.65211	−	0.778834i	0.171315	−	0.0807613i
$94$	−1.30903	+	12.0503i	−0.135017	+	1.24290i
$95$	−0.557755	−	0.322020i	−0.0572244	−	0.0330385i
$96$	−5.72566	+	7.95090i	−0.584373	+	0.811485i
$97$	9.56123	+	5.52018i	0.970796	+	0.560489i	0.899479	−	0.436965i	$-0.143946\pi$
$97$	9.56123	+	5.52018i	0.970796	+	0.560489i	0.0713170	+	0.997454i	$0.477280\pi$
$98$	−2.12191	−	9.66941i	−0.214345	−	0.976758i
$99$	2.16769	+	5.80388i	0.217861	+	0.583312i
$100$	2.71894	+	8.57093i	0.271894	+	0.857093i
$101$		−	9.49555i		−	0.944843i	−0.881373	−	0.472421i	$-0.843380\pi$
$101$		−	9.49555i		−	0.944843i	0.881373	−	0.472421i	$-0.156620\pi$
$102$	−3.42463	−	2.97275i	−0.339089	−	0.294346i
$103$		−	19.0732i		−	1.87934i	−0.342087	−	0.939668i	$-0.611134\pi$
$103$		−	19.0732i		−	1.87934i	0.342087	−	0.939668i	$-0.388866\pi$
$104$	7.45131	−	1.50255i	0.730661	−	0.147337i
$105$	1.84416	+	2.68041i	0.179972	+	0.261581i
$106$	−0.987121	+	9.08696i	−0.0958776	+	0.882604i
$107$	−3.78038	+	6.54780i	−0.365463	+	0.633000i	−0.988850	−	0.148913i	$-0.952423\pi$
$107$	−3.78038	+	6.54780i	−0.365463	+	0.633000i	0.623388	+	0.781913i	$0.285756\pi$
$108$	0.601984	+	10.3749i	0.0579259	+	0.998321i
$109$	1.11465	−	0.643544i	0.106764	−	0.0616403i	−0.445667	−	0.895199i	$-0.647033\pi$
$109$	1.11465	−	0.643544i	0.106764	−	0.0616403i	0.552431	+	0.833558i	$0.313700\pi$
$110$	−1.22464	+	1.67328i	−0.116765	+	0.159541i
$111$	−0.149738	+	0.0705894i	−0.0142125	+	0.00670005i
$112$	10.2464	−	2.64788i	0.968194	−	0.250201i
$113$	−10.5538	+	6.09326i	−0.992821	+	0.573206i	−0.906116	−	0.423028i	$-0.860967\pi$
$113$	−10.5538	+	6.09326i	−0.992821	+	0.573206i	−0.0867048	+	0.996234i	$0.527634\pi$
$114$	−0.422439	+	2.18146i	−0.0395651	+	0.204312i
$115$	6.34737			0.591895
$116$	12.6573	+	2.78277i	1.17520	+	0.258373i
$117$	5.13046	−	6.21936i	0.474311	−	0.574980i
$118$	−5.77617	−	13.0962i	−0.531740	−	1.20560i
$119$	0.790600	+	4.83403i	0.0724742	+	0.443135i
$120$	−2.79087	+	2.07577i	−0.254770	+	0.189491i
$121$	−6.73513			−0.612284
$122$	−1.55840	+	14.3459i	−0.141091	+	1.29882i
$123$	2.79009	+	0.232324i	0.251574	+	0.0209480i
$124$	0.452868	−	2.05984i	0.0406687	−	0.184979i
$125$			6.74193i			0.603016i
$126$	6.66602	−	9.03129i	0.593856	−	0.804571i
$127$	−12.1557			−1.07865			−0.539323	−	0.842099i	$-0.681320\pi$
$127$	−12.1557			−1.07865			−0.539323	+	0.842099i	$0.681320\pi$
$128$	3.23252	+	10.8421i	0.285717	+	0.958314i
$129$	5.68875	−	2.68179i	0.500867	−	0.236118i
$130$	2.68260	+	0.291412i	0.235280	+	0.0255586i
$131$			22.7019i			1.98348i	0.128276	+	0.991739i	$0.459056\pi$
$131$			22.7019i			1.98348i	−0.128276	+	0.991739i	$0.540944\pi$
$132$	6.83548	+	2.11063i	0.594952	+	0.183707i
$133$	1.85754	−	1.51975i	0.161069	−	0.131779i
$134$	6.24584	+	14.1611i	0.539559	+	1.22333i
$135$	−0.909956	+	3.57519i	−0.0783165	+	0.307703i
$136$	−5.13313	+	1.03509i	−0.440162	+	0.0887582i
$137$		−	20.0228i		−	1.71066i	−0.518080	−	0.855332i	$-0.673353\pi$
$137$		−	20.0228i		−	1.71066i	0.518080	−	0.855332i	$-0.326647\pi$
$138$	−7.14417	−	20.7008i	−0.608152	−	1.76217i
$139$	6.10135	+	10.5679i	0.517510	+	0.896354i	0.999793	+	0.0203383i	$0.00647432\pi$
$139$	6.10135	+	10.5679i	0.517510	+	0.896354i	−0.482283	+	0.876015i	$0.660192\pi$
$140$	3.75133	+	0.203893i	0.317045	+	0.0172321i
$141$	14.7942	+	1.23188i	1.24590	+	0.103743i
$142$	−0.986112	+	1.34736i	−0.0827527	+	0.113068i
$143$	−2.77502	−	4.80647i	−0.232058	−	0.401937i
$144$	9.91096	+	6.76557i	0.825913	+	0.563798i
$145$	3.98417	+	2.30026i	0.330867	+	0.191026i
$146$	−11.7222	−	1.27339i	−0.970140	−	0.105387i
$147$	−11.7735	+	2.89555i	−0.971064	+	0.238821i
$148$	−0.0410455	+	0.186693i	−0.00337392	+	0.0153461i
$149$	−10.0348			−0.822086			−0.411043	−	0.911616i	$-0.634835\pi$
$149$	−10.0348			−0.822086			−0.411043	+	0.911616i	$0.634835\pi$
$150$	10.4102	−	3.59272i	0.849990	−	0.293345i
$151$	2.74888			0.223701			0.111850	−	0.993725i	$-0.464322\pi$
$151$	2.74888			0.223701			0.111850	+	0.993725i	$0.464322\pi$
$152$	1.69677	+	1.92456i	0.137626	+	0.156102i
$153$	−3.53432	+	4.28446i	−0.285733	+	0.346378i
$154$	−4.21851	−	6.47398i	−0.339937	−	0.521688i
$155$	0.374344	−	0.648383i	0.0300681	−	0.0520794i
$156$	−2.06897	−	9.07683i	−0.165650	−	0.726728i
$157$	3.01634	−	5.22446i	0.240730	−	0.416957i	−0.720192	−	0.693775i	$-0.755946\pi$
$157$	3.01634	−	5.22446i	0.240730	−	0.416957i	0.960923	+	0.276817i	$0.0892797\pi$
$158$	1.63358	−	15.0380i	0.129961	−	1.19636i
$159$	11.1561	+	0.928941i	0.884734	+	0.0736698i
$160$	−0.0700074	+	4.01565i	−0.00553457	+	0.317465i
$161$	−8.36540	+	22.1249i	−0.659286	+	1.74368i
$162$	12.6840	−	1.05633i	0.996550	−	0.0829929i
$163$	−10.3497	−	5.97539i	−0.810650	−	0.468029i	0.0365317	−	0.999332i	$-0.488369\pi$
$163$	−10.3497	−	5.97539i	−0.810650	−	0.468029i	−0.847181	+	0.531304i	$0.821702\pi$
$164$	2.17991	−	2.38735i	0.170222	−	0.186421i
$165$	2.08638	+	1.44791i	0.162425	+	0.112720i
$166$	5.25303	+	11.9101i	0.407714	+	0.924401i
$167$	4.58409	+	7.93987i	0.354727	+	0.614406i	0.987071	−	0.160282i	$-0.0512404\pi$
$167$	4.58409	+	7.93987i	0.354727	+	0.614406i	−0.632344	+	0.774688i	$0.717907\pi$
$168$	−3.55728	−	12.4638i	−0.274450	−	0.961601i
$169$	2.88878	−	5.00351i	0.222213	−	0.384885i
$170$	−1.84802	−	0.200751i	−0.141737	−	0.0153969i
$171$	2.68389	+	0.450083i	0.205242	+	0.0344187i
$172$	1.55938	−	7.09274i	0.118901	−	0.540816i
$173$	−1.16572	+	0.673029i	−0.0886281	+	0.0511695i	−0.543659	−	0.839306i	$-0.682962\pi$
$173$	−1.16572	+	0.673029i	−0.0886281	+	0.0511695i	0.455031	+	0.890476i	$0.349628\pi$
$174$	3.01758	−	15.5827i	0.228762	−	1.18132i
$175$	−11.1264	−	4.20687i	−0.841073	−	0.318009i
$176$	6.75005	−	4.76181i	0.508804	−	0.358935i
$177$	−15.8567	+	7.47513i	−1.19186	+	0.561865i
$178$	10.3127	−	4.54851i	0.772972	−	0.340925i
$179$	−3.69397	−	6.39815i	−0.276100	−	0.478220i	0.694312	−	0.719674i	$-0.255709\pi$
$179$	−3.69397	−	6.39815i	−0.276100	−	0.478220i	−0.970412	+	0.241454i	$0.922376\pi$
$180$	2.62737	+	3.35314i	0.195833	+	0.249928i
$181$	−3.27523			−0.243446			−0.121723	−	0.992564i	$-0.538842\pi$
$181$	−3.27523			−0.243446			−0.121723	+	0.992564i	$0.538842\pi$
$182$	−4.55126	+	8.96662i	−0.337362	+	0.664650i
$183$	17.6125	+	1.46655i	1.30195	+	0.108411i
$184$	−23.9660	−	8.06512i	−1.76680	−	0.594568i
$185$	−0.0339286	+	0.0587660i	−0.00249448	+	0.00432056i
$186$	−2.53592	−	0.491081i	−0.185943	−	0.0360078i
$187$	1.91168	+	3.31113i	0.139796	+	0.242134i
$188$	11.5588	−	12.6587i	0.843012	−	0.923232i
$189$	−11.2627	−	7.88366i	−0.819239	−	0.573452i
$190$	0.367556	+	0.833352i	0.0266653	+	0.0604577i
$191$	3.31786	−	1.91557i	0.240072	−	0.138605i	−0.375138	−	0.926969i	$-0.622405\pi$
$191$	3.31786	−	1.91557i	0.240072	−	0.138605i	0.615210	+	0.788364i	$0.289071\pi$
$192$	13.1751	−	4.29142i	0.950832	−	0.309707i
$193$	−5.42920	+	9.40364i	−0.390802	+	0.676889i	−0.992556	−	0.121793i	$-0.961136\pi$
$193$	−5.42920	+	9.40364i	−0.390802	+	0.676889i	0.601753	+	0.798682i	$0.294469\pi$
$194$	−6.30078	−	14.2856i	−0.452370	−	1.02565i
$195$	0.274237	−	3.29344i	0.0196385	−	0.235848i
$196$	−5.65470	+	12.8072i	−0.403907	+	0.914800i
$197$	−11.3784			−0.810679			−0.405339	−	0.914166i	$-0.632847\pi$
$197$	−11.3784			−0.810679			−0.405339	+	0.914166i	$0.632847\pi$
$198$	2.37381	−	8.43403i	0.168699	−	0.599380i
$199$	2.23386	−	1.28972i	0.158354	−	0.0914256i	−0.418729	−	0.908111i	$-0.637524\pi$
$199$	2.23386	−	1.28972i	0.158354	−	0.0914256i	0.577083	+	0.816686i	$0.304191\pi$
$200$	4.05586	−	12.0523i	0.286793	−	0.852223i
$201$	17.1460	−	8.08295i	1.20939	−	0.570128i
$202$	−7.93104	+	10.8365i	−0.558026	+	0.762453i
$203$	−13.2688	+	10.8559i	−0.931288	+	0.761937i
$204$	1.42529	+	6.25294i	0.0997903	+	0.437793i
$205$	0.993883	−	0.573819i	0.0694158	−	0.0400772i
$206$	−15.9306	+	21.7667i	−1.10994	+	1.51655i
$207$	−25.1253	+	9.38408i	−1.74633	+	0.652239i
$208$	−9.75855	−	4.50888i	−0.676633	−	0.312634i
$209$	0.936675	−	1.62237i	0.0647912	−	0.112222i
$210$	0.134192	−	4.59925i	0.00926010	−	0.317378i
$211$	−15.9661	+	9.21802i	−1.09915	+	0.634595i	−0.935998	−	0.352006i	$-0.885500\pi$
$211$	−15.9661	+	9.21802i	−1.09915	+	0.634595i	−0.163153	+	0.986601i	$0.552166\pi$
$212$	8.71629	−	9.54572i	0.598638	−	0.655603i
$213$	1.68000	+	1.16589i	0.115112	+	0.0798855i
$214$	9.78321	−	4.31496i	0.668766	−	0.294964i
$215$	1.28899	−	2.23260i	0.0879086	−	0.152262i
$216$	7.97848	−	12.3428i	0.542866	−	0.839819i
$217$	1.76669	+	2.15937i	0.119931	+	0.146587i
$218$	−1.80957	−	0.196575i	−0.122560	−	0.0133137i
$219$	−1.19834	+	14.3914i	−0.0809763	+	0.972482i
$220$	2.79517	−	0.886707i	0.188450	−	0.0597818i
$221$	2.48774	−	4.30889i	0.167343	−	0.289847i
$222$	0.229843	+	0.0445090i	0.0154260	+	0.00298725i
$223$	22.2383	+	12.8393i	1.48918	+	0.859781i	0.999924	−	0.0123575i	$-0.00393363\pi$
$223$	22.2383	+	12.8393i	1.48918	+	0.859781i	0.489260	+	0.872138i	$0.337267\pi$
$224$	−13.9050	−	5.53637i	−0.929066	−	0.369915i
$225$	−4.71915	−	12.6353i	−0.314610	−	0.842351i
$226$	17.1335	+	1.86122i	1.13971	+	0.123807i
$227$		−	3.52812i		−	0.234169i	−0.993122	−	0.117085i	$-0.962645\pi$
$227$		−	3.52812i		−	0.234169i	0.993122	−	0.117085i	$-0.0373549\pi$
$228$	2.30413	−	2.13668i	0.152595	−	0.141505i
$229$	−12.0633			−0.797163			−0.398581	−	0.917133i	$-0.630497\pi$
$229$	−12.0633			−0.797163			−0.398581	+	0.917133i	$0.630497\pi$
$230$	−7.24373	−	5.30156i	−0.477637	−	0.349575i
$231$	−7.79665	+	5.36420i	−0.512982	+	0.352939i
$232$	−12.1204	−	13.7476i	−0.795745	−	0.902572i
$233$	−2.93109	−	1.69226i	−0.192022	−	0.110864i	0.400907	−	0.916119i	$-0.368695\pi$
$233$	−2.93109	−	1.69226i	−0.192022	−	0.110864i	−0.592929	+	0.805255i	$0.702028\pi$
$234$	−11.0496	+	2.81249i	−0.722336	+	0.183858i
$235$	5.26998	−	3.04263i	0.343776	−	0.198479i
$236$	−4.34655	+	19.7701i	−0.282937	+	1.28692i
$237$	−18.4621	−	1.53730i	−1.19925	−	0.0998584i
$238$	3.13532	−	6.17702i	0.203232	−	0.400397i
$239$	17.3915	−	10.0410i	1.12496	−	0.649498i	0.182300	−	0.983243i	$-0.441646\pi$
$239$	17.3915	−	10.0410i	1.12496	−	0.649498i	0.942663	+	0.333746i	$0.108313\pi$
$240$	4.91875	−	0.0378662i	0.317504	−	0.00244425i
$241$		−	6.90959i		−	0.445086i	−0.974923	−	0.222543i	$-0.928564\pi$
$241$		−	6.90959i		−	0.445086i	0.974923	−	0.222543i	$-0.0714358\pi$
$242$	7.68624	+	5.62543i	0.494091	+	0.361616i
$243$	−1.68367	−	15.4973i	−0.108007	−	0.994150i
$244$	13.7607	−	15.0702i	0.880941	−	0.964770i
$245$	−3.28814	+	3.72662i	−0.210071	+	0.238085i
$246$	−2.99006	−	2.59552i	−0.190639	−	0.165484i
$247$	−2.43786			−0.155117
$248$	−2.23728	+	1.97248i	−0.142067	+	0.125252i
$249$	14.4205	−	6.79812i	0.913864	−	0.430813i
$250$	5.63111	−	7.69401i	0.356143	−	0.486612i
$251$		−	4.79484i		−	0.302648i	−0.988484	−	0.151324i	$-0.951646\pi$
$251$		−	4.79484i		−	0.302648i	0.988484	−	0.151324i	$-0.0483536\pi$
$252$	−15.1507	+	4.73896i	−0.954401	+	0.298526i
$253$			18.4629i			1.16075i
$254$	13.8723	+	10.1529i	0.870427	+	0.637050i
$255$	−0.188919	+	2.26882i	−0.0118306	+	0.142079i
$256$	5.36671	−	15.0731i	0.335419	−	0.942069i
$257$	−12.3148			−0.768179			−0.384090	−	0.923296i	$-0.625485\pi$
$257$	−12.3148			−0.768179			−0.384090	+	0.923296i	$0.625485\pi$
$258$	−8.73204	−	1.69096i	−0.543633	−	0.105274i
$259$	−0.160124	−	0.195714i	−0.00994960	−	0.0121611i
$260$	−2.81804	−	2.57318i	−0.174767	−	0.159582i
$261$	−19.1716	−	3.21505i	−1.18669	−	0.199006i
$262$	18.9615	−	25.9078i	1.17145	−	1.60059i
$263$		−	4.86985i		−	0.300288i	−0.988664	−	0.150144i	$-0.952026\pi$
$263$		−	4.86985i		−	0.300288i	0.988664	−	0.150144i	$-0.0479737\pi$
$264$	−6.03789	−	8.11793i	−0.371606	−	0.499624i
$265$	3.97401	−	2.29439i	0.244121	−	0.140943i
$266$	−3.38921	+	0.182881i	−0.207806	+	0.0112131i
$267$	−5.88637	−	12.4865i	−0.360240	−	0.764161i
$268$	4.69998	−	21.3776i	0.287097	−	1.30585i
$269$	−3.10632	+	1.79344i	−0.189396	+	0.109348i	−0.591700	−	0.806158i	$-0.701543\pi$
$269$	−3.10632	+	1.79344i	−0.189396	+	0.109348i	0.402304	+	0.915506i	$0.368210\pi$
$270$	4.02459	−	3.32004i	0.244929	−	0.202051i
$271$	−13.8378	−	7.98925i	−0.840586	−	0.485312i	0.0168777	−	0.999858i	$-0.494627\pi$
$271$	−13.8378	−	7.98925i	−0.840586	−	0.485312i	−0.857463	+	0.514545i	$0.827961\pi$
$272$	6.72257	+	3.10612i	0.407616	+	0.188336i
$273$	11.1184	+	5.29642i	0.672918	+	0.320554i
$274$	−16.7238	+	22.8504i	−1.01032	+	1.38044i
$275$	−9.28480			−0.559894
$276$	−9.13705	+	29.5912i	−0.549986	+	1.78118i
$277$		−	21.8716i		−	1.31414i	−0.753831	−	0.657068i	$-0.771796\pi$
$277$		−	21.8716i		−	1.31414i	0.753831	−	0.657068i	$-0.228204\pi$
$278$	1.86370	−	17.1563i	0.111777	−	1.02897i
$279$	−0.523217	+	3.11999i	−0.0313242	+	0.186789i
$280$	−4.11078	−	3.36594i	−0.245666	−	0.201153i
$281$	4.75177	+	2.74343i	0.283467	+	0.163660i	0.634992	−	0.772519i	$-0.281003\pi$
$281$	4.75177	+	2.74343i	0.283467	+	0.163660i	−0.351525	+	0.936178i	$0.614337\pi$
$282$	−15.8545	−	13.7625i	−0.944123	−	0.819547i
$283$	12.6161	−	21.8517i	0.749949	−	1.29895i	−0.197897	−	0.980223i	$-0.563411\pi$
$283$	12.6161	−	21.8517i	0.749949	−	1.29895i	0.947846	−	0.318727i	$-0.103255\pi$
$284$	2.25074	−	0.713997i	0.133557	−	0.0423679i
$285$	1.00901	−	0.475667i	0.0597686	−	0.0281761i
$286$	−0.847646	+	7.80302i	−0.0501223	+	0.461402i
$287$	0.690276	+	4.22061i	0.0407457	+	0.249135i
$288$	−5.65970	−	15.9990i	−0.333501	−	0.942750i
$289$	6.78622	−	11.7541i	0.399189	−	0.691416i
$290$	−2.62554	−	5.95282i	−0.154177	−	0.349562i
$291$	−17.2968	+	8.15405i	−1.01396	+	0.477999i
$292$	12.3141	+	11.2441i	0.720625	+	0.658010i
$293$	−25.3169	+	14.6167i	−1.47903	+	0.853919i	−0.999719	−	0.0237246i	$-0.992448\pi$
$293$	−25.3169	+	14.6167i	−1.47903	+	0.853919i	−0.479313	+	0.877644i	$0.659114\pi$
$294$	15.8546	+	6.52924i	0.924660	+	0.380793i
$295$	−3.59290	+	6.22309i	−0.209187	+	0.362322i
$296$	0.202775	−	0.178775i	0.0117861	−	0.0103911i
$297$	−10.3993	−	2.64683i	−0.603430	−	0.153585i
$298$	11.4519	+	8.38147i	0.663393	+	0.485526i
$299$	20.8075	−	12.0132i	1.20333	−	0.694742i
$300$	−14.8811	−	4.59492i	−0.859160	−	0.265288i
$301$	6.08332	+	7.43543i	0.350637	+	0.428571i
$302$	−3.13707	−	2.29597i	−0.180518	−	0.132118i
$303$	13.5118	+	9.37695i	0.776234	+	0.538692i
$304$	−0.328921	−	3.61355i	−0.0188649	−	0.207251i
$305$	6.27391	−	3.62224i	0.359243	−	0.207409i
$306$	7.61197	−	1.93750i	0.435148	−	0.110759i
$307$	8.86534			0.505972			0.252986	−	0.967470i	$-0.418587\pi$
$307$	8.86534			0.505972			0.252986	+	0.967470i	$0.418587\pi$
$308$	−0.593073	+	10.9117i	−0.0337935	+	0.621751i
$309$	27.1404	+	18.8349i	1.54397	+	1.07148i
$310$	−0.968763	+	0.427280i	−0.0550220	+	0.0242679i
$311$	5.91008	−	10.2366i	0.335130	−	0.580462i	−0.648380	−	0.761317i	$-0.724553\pi$
$311$	5.91008	−	10.2366i	0.335130	−	0.580462i	0.983510	+	0.180855i	$0.0578865\pi$
$312$	−5.22017	+	12.0867i	−0.295534	+	0.684275i
$313$	20.4645	−	11.8152i	1.15672	−	0.667832i	0.206204	−	0.978509i	$-0.433889\pi$
$313$	20.4645	−	11.8152i	1.15672	−	0.667832i	0.950516	+	0.310677i	$0.100556\pi$
$314$	−7.80597	+	3.44288i	−0.440516	+	0.194293i
$315$	−5.63525	−	0.0227583i	−0.317511	−	0.00128228i
$316$	−14.4246	+	15.7972i	−0.811445	+	0.888661i
$317$	14.2689	+	24.7145i	0.801424	+	1.38811i	0.918679	+	0.395005i	$0.129257\pi$
$317$	14.2689	+	24.7145i	0.801424	+	1.38811i	−0.117255	+	0.993102i	$0.537410\pi$
$318$	−11.9556	−	10.3781i	−0.670438	−	0.581975i
$319$	−6.69088	+	11.5889i	−0.374617	+	0.648856i
$320$	3.43391	−	4.52426i	0.191962	−	0.252914i
$321$	−5.58413	−	11.8454i	−0.311676	−	0.661143i
$322$	28.0263	−	18.2622i	1.56184	−	1.01771i
$323$	1.67942			0.0934452
$324$	−15.3575	−	9.38867i	−0.853195	−	0.521593i
$325$	6.04132	+	10.4639i	0.335112	+	0.580431i
$326$	6.82037	+	15.4637i	0.377745	+	0.856453i
$327$	−0.184989	+	2.22161i	−0.0102299	+	0.122856i
$328$	−4.48176	+	0.903740i	−0.247464	+	0.0499007i
$329$	3.66013	+	22.3794i	0.201789	+	1.23382i
$330$	−1.17167	−	3.39500i	−0.0644982	−	0.186889i
$331$	30.9316	−	17.8584i	1.70016	−	0.981585i	0.754566	−	0.656224i	$-0.227847\pi$
$331$	30.9316	−	17.8584i	1.70016	−	0.981585i	0.945590	−	0.325361i	$-0.105486\pi$
$332$	3.95289	−	17.9795i	0.216943	−	0.986754i
$333$	0.0474216	−	0.282779i	0.00259869	−	0.0154962i
$334$	1.40024	−	12.8899i	0.0766176	−	0.705305i
$335$	3.88505	−	6.72910i	0.212263	−	0.367650i
$336$	−6.35058	+	17.1951i	−0.346453	+	0.938067i
$337$	13.5198	+	23.4170i	0.736470	+	1.27560i	0.954075	+	0.299566i	$0.0968420\pi$
$337$	13.5198	+	23.4170i	0.736470	+	1.27560i	−0.217606	+	0.976037i	$0.569825\pi$
$338$	−7.47584	+	3.29728i	−0.406632	+	0.179348i
$339$	1.75153	−	21.0349i	0.0951298	−	1.14246i
$340$	1.94132	+	1.77264i	0.105283	+	0.0961347i
$341$	1.88599	+	1.08887i	0.102132	+	0.0589658i
$342$	−2.68698	−	2.75533i	−0.145295	−	0.148991i
$343$	−8.65626	−	16.3728i	−0.467394	−	0.884049i
$344$	−7.70371	+	6.79191i	−0.415356	+	0.366195i
$345$	−6.26809	+	9.03208i	−0.337462	+	0.486271i
$346$	1.89248	+	0.205581i	0.101740	+	0.0110521i
$347$	4.09928	−	7.10016i	0.220061	−	0.381157i	−0.734765	−	0.678321i	$-0.762708\pi$
$347$	4.09928	−	7.10016i	0.220061	−	0.381157i	0.954826	+	0.297165i	$0.0960411\pi$
$348$	−16.4589	+	15.2628i	−0.882292	+	0.818173i
$349$	−16.1552	+	27.9816i	−0.864768	+	1.49782i	0.00250849	+	0.999997i	$0.499202\pi$
$349$	−16.1552	+	27.9816i	−0.864768	+	1.49782i	−0.867277	+	0.497826i	$0.834132\pi$
$350$	9.18386	+	14.0941i	0.490898	+	0.753362i
$351$	3.78355	+	13.4421i	0.201951	+	0.717488i
$352$	−11.6805	−	0.203634i	−0.622574	−	0.0108537i
$353$	−23.0788			−1.22836			−0.614181	−	0.789165i	$-0.710514\pi$
$353$	−23.0788			−1.22836			−0.614181	+	0.789165i	$0.710514\pi$
$354$	24.3394	+	4.71332i	1.29362	+	0.250510i
$355$	0.838230			0.0444886
$356$	−15.5682	−	3.42274i	−0.825111	−	0.181405i
$357$	−7.65937	−	3.64866i	−0.405377	−	0.193107i
$358$	−1.12835	+	10.3870i	−0.0596350	+	0.548971i
$359$	−7.96522	−	4.59872i	−0.420388	−	0.242711i	0.274855	−	0.961486i	$-0.411370\pi$
$359$	−7.96522	−	4.59872i	−0.420388	−	0.242711i	−0.695244	+	0.718774i	$0.744703\pi$
$360$	−0.197735	−	6.02114i	−0.0104215	−	0.317342i
$361$	9.08856	+	15.7419i	0.478346	+	0.828519i
$362$	3.73775	+	2.73559i	0.196452	+	0.143780i
$363$	6.65100	−	9.58384i	0.349087	−	0.503021i
$364$	12.6832	−	6.43149i	0.664782	−	0.337102i
$365$	2.95978	+	5.12650i	0.154922	+	0.268333i
$366$	−18.8748	−	16.3843i	−0.986601	−	0.856421i
$367$		−	24.5360i		−	1.28077i	−0.768055	−	0.640384i	$-0.778775\pi$
$367$		−	24.5360i		−	1.28077i	0.768055	−	0.640384i	$-0.221225\pi$
$368$	20.6142	+	29.2214i	1.07459	+	1.52327i
$369$	−3.08583	+	3.74078i	−0.160642	+	0.194737i
$370$	0.0878035	−	0.0387264i	0.00456469	−	0.00201329i
$371$	2.76004	+	16.8760i	0.143294	+	0.876156i
$372$	2.48387	+	2.67853i	0.128783	+	0.138875i
$373$		−	28.3099i		−	1.46583i	−0.680319	−	0.732916i	$-0.738159\pi$
$373$		−	28.3099i		−	1.46583i	0.680319	−	0.732916i	$-0.261841\pi$
$374$	0.583935	−	5.37543i	0.0301946	−	0.277957i
$375$	−9.59352	−	6.65772i	−0.495407	−	0.343803i
$376$	−23.7641	+	4.79201i	−1.22554	+	0.247129i
$377$	17.4142			0.896875
$378$	6.26844	+	18.4040i	0.322414	+	0.946599i
$379$		−	34.8946i		−	1.79241i	−0.443637	−	0.896207i	$-0.646312\pi$
$379$		−	34.8946i		−	1.79241i	0.443637	−	0.896207i	$-0.353688\pi$
$380$	0.276585	−	1.25803i	0.0141885	−	0.0645357i
$381$	12.0039	−	17.2971i	0.614977	−	0.886159i
$382$	−5.38635	−	0.585122i	−0.275590	−	0.0299374i
$383$	25.3288			1.29424			0.647121	−	0.762387i	$-0.275973\pi$
$383$	25.3288			1.29424			0.647121	+	0.762387i	$0.275973\pi$
$384$	−18.6200	−	6.10690i	−0.950200	−	0.311642i
$385$	−1.37195	+	3.62855i	−0.0699212	+	0.184928i
$386$	14.0502	−	6.19694i	0.715135	−	0.315416i
$387$	−1.80161	+	10.7432i	−0.0915811	+	0.546107i
$388$	−4.74132	+	21.5657i	−0.240704	+	1.09483i
$389$	15.7699			0.799566			0.399783	−	0.916610i	$-0.369086\pi$
$389$	15.7699			0.799566			0.399783	+	0.916610i	$0.369086\pi$
$390$	−3.06377	+	3.52947i	−0.155140	+	0.178722i
$391$	−14.3341	+	8.27579i	−0.724906	+	0.418525i
$392$	17.1503	−	9.89279i	0.866221	−	0.499661i
$393$	−32.3040	−	22.4184i	−1.62952	−	1.13086i
$394$	12.9853	+	9.50368i	0.654188	+	0.478789i
$395$	−6.57657	+	3.79698i	−0.330903	+	0.191047i
$396$	−9.75345	+	7.64237i	−0.490129	+	0.384043i
$397$	−10.3019	+	17.8434i	−0.517037	+	0.895534i	0.482768	+	0.875749i	$0.339632\pi$
$397$	−10.3019	+	17.8434i	−0.517037	+	0.895534i	−0.999804	+	0.0197853i	$0.993702\pi$
$398$	−3.62654	−	0.393952i	−0.181782	−	0.0197470i
$399$	0.328214	+	4.14398i	0.0164312	+	0.207458i
$400$	−14.6951	+	10.3666i	−0.734756	+	0.518332i
$401$		−	10.8296i		−	0.540802i	−0.962748	−	0.270401i	$-0.912844\pi$
$401$		−	10.8296i		−	0.540802i	0.962748	−	0.270401i	$-0.0871563\pi$
$402$	−26.3185	−	5.09657i	−1.31265	−	0.254194i
$403$		−	2.83398i		−	0.141171i
$404$	18.1021	−	5.74249i	0.900613	−	0.285700i
$405$	−4.18877	−	4.82536i	−0.208142	−	0.239774i
$406$	24.2099	−	1.30636i	1.20152	−	0.0648335i
$407$	−0.170936	−	0.0986897i	−0.00847297	−	0.00489187i
$408$	3.59612	−	8.32642i	0.178035	−	0.412219i
$409$	16.5367	+	9.54748i	0.817688	+	0.472093i	0.849619	−	0.527398i	$-0.176832\pi$
$409$	16.5367	+	9.54748i	0.817688	+	0.472093i	−0.0319303	+	0.999490i	$0.510165\pi$
$410$	−1.61351	−	0.175277i	−0.0796857	−	0.00865629i
$411$	28.4917	+	19.7727i	1.40539	+	0.975316i
$412$	36.3607	−	11.5346i	1.79136	−	0.568270i
$413$	−16.9565	−	20.7253i	−0.834373	−	1.01982i
$414$	36.5114	+	10.2764i	1.79444	+	0.505055i
$415$	3.26749	−	5.65947i	0.160395	−	0.277812i
$416$	7.37064	+	13.2963i	0.361375	+	0.651906i
$417$	−21.0628	−	1.75385i	−1.03145	−	0.0858865i
$418$	−2.42401	+	1.06913i	−0.118562	+	0.0522928i
$419$	19.2648	−	11.1225i	0.941148	−	0.543372i	0.0508280	−	0.998707i	$-0.483814\pi$
$419$	19.2648	−	11.1225i	0.941148	−	0.543372i	0.890320	+	0.455335i	$0.150481\pi$
$420$	−3.99460	+	5.13666i	−0.194917	+	0.250643i
$421$	13.0316	+	7.52380i	0.635122	+	0.366688i	0.782733	−	0.622358i	$-0.213825\pi$
$421$	13.0316	+	7.52380i	0.635122	+	0.366688i	−0.147611	+	0.989045i	$0.547158\pi$
$422$	25.9200	+	2.81570i	1.26177	+	0.137066i
$423$	−16.3624	+	19.8351i	−0.795565	+	0.964418i
$424$	−17.9201	+	3.61357i	−0.870279	+	0.175491i
$425$	−4.16180	−	7.20846i	−0.201877	−	0.349661i
$426$	−0.943454	−	2.73374i	−0.0457105	−	0.132450i
$427$	4.35738	+	26.6427i	0.210868	+	1.28933i
$428$	−14.7688	−	3.24700i	−0.713876	−	0.156949i
$429$	9.57978	+	0.797686i	0.462516	+	0.0385127i
$430$	−3.33578	+	1.47127i	−0.160865	+	0.0709509i
$431$	−13.8665	+	8.00586i	−0.667928	+	0.385629i	−0.795291	−	0.606228i	$-0.792682\pi$
$431$	−13.8665	+	8.00586i	−0.667928	+	0.385629i	0.127363	+	0.991856i	$0.459349\pi$
$432$	−19.4143	+	7.42186i	−0.934072	+	0.357085i
$433$		−	19.7250i		−	0.947924i	−0.880545	−	0.473962i	$-0.842823\pi$
$433$		−	19.7250i		−	0.947924i	0.880545	−	0.473962i	$-0.157177\pi$
$434$	−0.212597	−	3.93992i	−0.0102050	−	0.189122i
$435$	−7.20759	+	3.39780i	−0.345577	+	0.162912i
$436$	1.90093	+	1.73576i	0.0910380	+	0.0831277i
$437$	7.02334	+	4.05493i	0.335972	+	0.193973i
$438$	13.3878	−	15.4228i	0.639695	−	0.736932i
$439$	−20.3858	+	11.7698i	−0.972963	+	0.561741i	−0.900138	−	0.435604i	$-0.856535\pi$
$439$	−20.3858	+	11.7698i	−0.972963	+	0.561741i	−0.0728249	+	0.997345i	$0.523201\pi$
$440$	−3.93051	−	1.32271i	−0.187380	−	0.0630576i
$441$	7.50621	−	19.6127i	0.357438	−	0.933937i
$442$	−6.43800	+	2.83953i	−0.306224	+	0.135063i
$443$	17.1993	+	29.7901i	0.817165	+	1.41537i	0.907763	+	0.419484i	$0.137789\pi$
$443$	17.1993	+	29.7901i	0.817165	+	1.41537i	−0.0905976	+	0.995888i	$0.528878\pi$
$444$	−0.225125	−	0.242768i	−0.0106840	−	0.0115212i
$445$	−4.90044	−	2.82927i	−0.232303	−	0.134120i
$446$	−14.6549	−	33.2266i	−0.693927	−	1.57333i
$447$	9.90949	−	14.2792i	0.468703	−	0.675383i
$448$	11.2444	+	17.9322i	0.531249	+	0.847216i
$449$			25.7814i			1.21670i	0.793669	+	0.608350i	$0.208168\pi$
$449$			25.7814i			1.21670i	−0.793669	+	0.608350i	$0.791832\pi$
$450$	−5.16787	+	18.3612i	−0.243616	+	0.865555i
$451$	1.66910	+	2.89096i	0.0785947	+	0.136130i
$452$	−17.9985	−	16.4346i	−0.846580	−	0.773021i
$453$	−2.71455	+	3.91156i	−0.127541	+	0.183781i
$454$	−2.94682	+	4.02635i	−0.138301	+	0.188966i
$455$	4.98203	−	0.814804i	0.233561	−	0.0381986i
$456$	−4.41416	+	0.513923i	−0.206712	+	0.0240667i
$457$	1.03185	+	1.78722i	0.0482679	+	0.0836025i	0.889150	−	0.457616i	$-0.151297\pi$
$457$	1.03185	+	1.78722i	0.0482679	+	0.0836025i	−0.840882	+	0.541218i	$0.817963\pi$
$458$	13.7668	+	10.0757i	0.643281	+	0.470806i
$459$	−2.60645	−	9.26015i	−0.121659	−	0.432227i
$460$	3.83861	+	12.1005i	0.178976	+	0.564187i
$461$	−20.5154	−	11.8446i	−0.955499	−	0.551657i	−0.0607140	−	0.998155i	$-0.519338\pi$
$461$	−20.5154	−	11.8446i	−0.955499	−	0.551657i	−0.894785	+	0.446498i	$0.852671\pi$
$462$	13.3781	+	0.390330i	0.622403	+	0.0181598i
$463$	−0.269188	−	0.466247i	−0.0125102	−	0.0216683i	0.859703	−	0.510795i	$-0.170649\pi$
$463$	−0.269188	−	0.466247i	−0.0125102	−	0.0216683i	−0.872213	+	0.489127i	$0.837316\pi$
$464$	2.34956	+	25.8124i	0.109075	+	1.19831i
$465$	0.552957	+	1.17296i	0.0256428	+	0.0543949i
$466$	1.93157	+	4.37940i	0.0894781	+	0.202872i
$467$	25.1398	+	14.5145i	1.16333	+	0.671650i	0.952100	−	0.305787i	$-0.0989194\pi$
$467$	25.1398	+	14.5145i	1.16333	+	0.671650i	0.211231	+	0.977436i	$0.432253\pi$
$468$	14.9591	+	6.01939i	0.691485	+	0.278246i
$469$	18.3352	+	22.4105i	0.846642	+	1.03482i
$470$	−8.55552	−	0.929389i	−0.394637	−	0.0428695i
$471$	4.45555	+	9.45135i	0.205301	+	0.435495i
$472$	21.4731	−	18.9315i	0.988378	−	0.871395i
$473$	6.49408	+	3.74936i	0.298598	+	0.172396i
$474$	19.7853	+	17.1747i	0.908770	+	0.788859i
$475$	−2.03918	+	3.53196i	−0.0935639	+	0.162057i
$476$	−8.73736	+	4.43059i	−0.400476	+	0.203076i
$477$	−12.3386	+	14.9574i	−0.564945	+	0.684850i
$478$	−28.2341	−	3.06708i	−1.29140	−	0.140285i
$479$	−4.15650			−0.189915			−0.0949576	−	0.995481i	$-0.530272\pi$
$479$	−4.15650			−0.189915			−0.0949576	+	0.995481i	$0.530272\pi$
$480$	−5.64499	−	4.06511i	−0.257657	−	0.185546i
$481$			0.256857i			0.0117117i
$482$	−5.77115	+	7.88535i	−0.262869	+	0.359168i
$483$	−23.2220	−	33.7522i	−1.05664	−	1.53578i
$484$	−4.07311	−	12.8397i	−0.185141	−	0.583622i
$485$	−3.91922	+	6.78829i	−0.177963	+	0.308240i
$486$	−11.0225	+	19.0920i	−0.499989	+	0.866032i
$487$	13.7344	+	23.7887i	0.622366	+	1.07797i	0.989044	+	0.147622i	$0.0471619\pi$
$487$	13.7344	+	23.7887i	0.622366	+	1.07797i	−0.366678	+	0.930348i	$0.619505\pi$
$488$	−28.2912	+	5.70488i	−1.28068	+	0.258248i
$489$	18.7232	−	8.82647i	0.846691	−	0.399147i
$490$	6.86510	−	1.50651i	0.310134	−	0.0680573i
$491$	−15.0246	−	26.0234i	−0.678051	−	1.17442i	−0.975567	−	0.219702i	$-0.929491\pi$
$491$	−15.0246	−	26.0234i	−0.678051	−	1.17442i	0.297516	−	0.954717i	$-0.403842\pi$
$492$	1.24443	+	5.45946i	0.0561031	+	0.246132i
$493$	−11.9964			−0.540293
$494$	2.78212	+	2.03619i	0.125174	+	0.0916125i
$495$	−4.12064	+	1.53902i	−0.185209	+	0.0691738i
$496$	4.20071	−	0.382367i	0.188618	−	0.0171688i
$497$	−1.10473	+	2.92180i	−0.0495539	+	0.131060i
$498$	−22.1350	−	4.28644i	−0.991894	−	0.192080i
$499$			1.70335i			0.0762525i	0.999273	+	0.0381263i	$0.0121389\pi$
$499$			1.70335i			0.0762525i	−0.999273	+	0.0381263i	$0.987861\pi$
$500$	−12.8526	+	4.07722i	−0.574788	+	0.182339i
$501$	−15.8250	−	1.31771i	−0.707008	−	0.0588709i
$502$	−4.00483	+	5.47196i	−0.178744	+	0.244225i
$503$	11.5079			0.513112			0.256556	−	0.966529i	$-0.417412\pi$
$503$	11.5079			0.513112			0.256556	+	0.966529i	$0.417412\pi$
$504$	21.2483	+	7.24622i	0.946477	+	0.322772i
$505$	6.74166			0.300000
$506$	15.4209	−	21.0702i	0.685544	−	0.936685i
$507$	4.26711	+	9.05163i	0.189509	+	0.401997i
$508$	−7.35124	−	23.1734i	−0.326159	−	1.02815i
$509$		−	19.8134i		−	0.878212i	−0.898435	−	0.439106i	$-0.855295\pi$
$509$		−	19.8134i		−	0.878212i	0.898435	−	0.439106i	$-0.144705\pi$
$510$	2.11060	−	2.43142i	0.0934589	−	0.107665i
$511$	−21.7701	+	3.56047i	−0.963052	+	0.157506i
$512$	−18.7142	+	12.7192i	−0.827059	+	0.562115i
$513$	−3.29082	+	3.37461i	−0.145293	+	0.148993i
$514$	14.0539	+	10.2858i	0.619892	+	0.453688i
$515$	13.5416			0.596714
$516$	8.55281	+	9.22308i	0.376516	+	0.406023i
$517$	8.85024	+	15.3291i	0.389233	+	0.674172i
$518$	0.0192686	+	0.357093i	0.000846616	+	0.0156898i
$519$	0.193464	−	2.32340i	0.00849214	−	0.101986i
$520$	1.06678	+	5.29028i	0.0467814	+	0.231994i
$521$	−15.9625	−	27.6478i	−0.699329	−	1.21127i	−0.968699	−	0.248237i	$-0.920149\pi$
$521$	−15.9625	−	27.6478i	−0.699329	−	1.21127i	0.269370	−	0.963037i	$-0.413185\pi$
$522$	19.1937	+	19.6819i	0.840084	+	0.861455i
$523$	−1.10121	+	1.90735i	−0.0481524	+	0.0834024i	−0.889097	−	0.457719i	$-0.848667\pi$
$523$	−1.10121	+	1.90735i	−0.0481524	+	0.0834024i	0.840945	+	0.541121i	$0.182000\pi$
$524$	−43.2784	+	13.7291i	−1.89063	+	0.599760i
$525$	16.9736	−	11.6781i	0.740789	−	0.509673i
$526$	−4.06748	+	5.55756i	−0.177351	+	0.242321i
$527$			1.95230i			0.0850436i
$528$	0.110143	+	14.3074i	0.00479338	+	0.622650i
$529$	−56.9271			−2.47509
$530$	−6.45157	−	0.700837i	−0.280238	−	0.0304424i
$531$	5.02175	−	29.9452i	0.217926	−	1.29951i
$532$	4.02058	+	2.62209i	0.174314	+	0.113682i
$533$	2.17205	−	3.76211i	0.0940821	−	0.162955i
$534$	−3.71156	+	19.1663i	−0.160615	+	0.829408i
$535$	−4.64882	−	2.68400i	−0.200986	−	0.116039i
$536$	−23.2191	+	20.4709i	−1.00291	+	0.884209i
$537$	12.7522	+	1.06184i	0.550296	+	0.0458219i
$538$	5.04294	+	0.547817i	0.217417	+	0.0236180i
$539$	−10.8398	−	9.56437i	−0.466904	−	0.411967i
$540$	−7.36595	+	0.427397i	−0.316980	+	0.0183922i
$541$	7.19050	+	4.15144i	0.309144	+	0.178484i	0.646543	−	0.762877i	$-0.276214\pi$
$541$	7.19050	+	4.15144i	0.309144	+	0.178484i	−0.337399	+	0.941362i	$0.609547\pi$
$542$	9.11900	+	20.6753i	0.391695	+	0.888081i
$543$	3.23432	−	4.66053i	0.138798	−	0.200003i
$544$	−5.07756	−	9.15970i	−0.217699	−	0.392719i
$545$	0.456904	+	0.791381i	0.0195716	+	0.0338990i
$546$	−8.26477	−	15.3309i	−0.353699	−	0.656102i
$547$	−16.0160	−	9.24685i	−0.684795	−	0.395367i	0.116864	−	0.993148i	$-0.462716\pi$
$547$	−16.0160	−	9.24685i	−0.684795	−	0.395367i	−0.801659	+	0.597781i	$0.796049\pi$
$548$	38.1710	−	12.1089i	1.63058	−	0.517267i
$549$	−19.4794	+	23.6137i	−0.831359	+	1.00781i
$550$	10.5960	+	7.75501i	0.451814	+	0.330675i
$551$	2.93898	+	5.09045i	0.125205	+	0.216861i
$552$	35.1431	−	26.1384i	1.49579	−	1.11252i
$553$	−4.56758	−	27.9279i	−0.194233	−	1.18762i
$554$	−18.2680	+	24.9602i	−0.776132	+	1.06046i
$555$	−0.0501171	−	0.106311i	−0.00212735	−	0.00451266i
$556$	−16.4565	+	18.0224i	−0.697910	+	0.764322i
$557$	−7.40431	−	12.8246i	−0.313730	−	0.543397i	0.665436	−	0.746455i	$-0.268246\pi$
$557$	−7.40431	−	12.8246i	−0.313730	−	0.543397i	−0.979167	+	0.203057i	$0.934912\pi$
$558$	3.20304	−	3.12358i	0.135595	−	0.132232i
$559$		−	9.75835i		−	0.412734i
$560$	1.87994	+	7.27475i	0.0794421	+	0.307414i
$561$	−6.59942	−	0.549518i	−0.278628	−	0.0232007i
$562$	−3.13138	−	7.09971i	−0.132089	−	0.299483i
$563$	23.9216	+	13.8111i	1.00817	+	0.582069i	0.910656	−	0.413164i	$-0.135577\pi$
$563$	23.9216	+	13.8111i	1.00817	+	0.582069i	0.0975173	+	0.995234i	$0.468910\pi$
$564$	6.59847	+	28.9483i	0.277846	+	1.21895i
$565$	−4.32610	−	7.49302i	−0.182000	−	0.315234i
$566$	−32.6491	+	14.4001i	−1.37234	+	0.605283i
$567$	22.3402	−	8.24119i	0.938199	−	0.346097i
$568$	−3.16494	−	1.06507i	−0.132798	−	0.0446895i
$569$	1.44931	−	0.836759i	0.0607582	−	0.0350787i	−0.469313	−	0.883032i	$-0.655498\pi$
$569$	1.44931	−	0.836759i	0.0607582	−	0.0350787i	0.530071	+	0.847953i	$0.322165\pi$
$570$	−1.54880	−	0.299924i	−0.0648719	−	0.0125624i
$571$	32.5170	+	18.7737i	1.36079	+	0.785655i	0.989730	−	0.142952i	$-0.0456596\pi$
$571$	32.5170	+	18.7737i	1.36079	+	0.785655i	0.371064	+	0.928607i	$0.378993\pi$
$572$	7.48473	−	8.19696i	0.312952	−	0.342732i
$573$	−0.550635	+	6.61283i	−0.0230031	+	0.276255i
$574$	2.73746	−	5.39318i	0.114259	−	0.225107i
$575$		−	40.1945i		−	1.67623i
$576$	−6.90401	+	22.9855i	−0.287667	+	0.957730i
$577$	−21.9106	+	12.6501i	−0.912148	+	0.526629i	−0.881122	−	0.472889i	$-0.843211\pi$
$577$	−21.9106	+	12.6501i	−0.912148	+	0.526629i	−0.0310266	+	0.999519i	$0.509878\pi$
$578$	−17.5620	+	7.74586i	−0.730483	+	0.322185i
$579$	−8.01966	−	17.0117i	−0.333286	−	0.706983i
$580$	−1.97571	+	8.98642i	−0.0820369	+	0.373141i
$581$	15.4207	+	18.8482i	0.639760	+	0.781956i
$582$	26.5500	+	5.14140i	1.10053	+	0.213118i
$583$	6.67382	+	11.5594i	0.276401	+	0.478741i
$584$	−4.66153	−	23.1171i	−0.192896	−	0.956593i
$585$	4.41563	+	3.64253i	0.182564	+	0.150600i
$586$	41.1006	+	4.46478i	1.69785	+	0.184438i
$587$	−14.9955	−	8.65763i	−0.618929	−	0.357339i	0.157523	−	0.987515i	$-0.449649\pi$
$587$	−14.9955	−	8.65763i	−0.618929	−	0.357339i	−0.776452	+	0.630177i	$0.782982\pi$
$588$	−12.6401	−	20.6937i	−0.521269	−	0.853392i
$589$	0.828421	−	0.478289i	0.0341345	−	0.0197076i
$590$	9.29804	−	4.10097i	0.382794	−	0.168834i
$591$	11.2363	−	16.1911i	0.462199	−	0.666012i
$592$	−0.380730	+	0.0346557i	−0.0156479	+	0.00142434i
$593$	−19.6284	+	33.9974i	−0.806042	+	1.39611i	0.109543	+	0.993982i	$0.465061\pi$
$593$	−19.6284	+	33.9974i	−0.806042	+	1.39611i	−0.915585	+	0.402124i	$0.868272\pi$
$594$	9.65715	+	11.7065i	0.396238	+	0.480324i
$595$	−3.43207	+	0.561311i	−0.140701	+	0.0230115i
$596$	−6.06863	−	19.1302i	−0.248581	−	0.783602i
$597$	−0.370733	+	4.45230i	−0.0151731	+	0.182221i
$598$	−33.7798	−	3.66951i	−1.38136	−	0.150058i
$599$	11.7199	+	6.76646i	0.478860	+	0.276470i	0.719941	−	0.694035i	$-0.244169\pi$
$599$	11.7199	+	6.76646i	0.478860	+	0.276470i	−0.241081	+	0.970505i	$0.577502\pi$
$600$	13.1447	+	17.6731i	0.536631	+	0.721500i
$601$	−18.1204	−	10.4618i	−0.739147	−	0.426747i	0.0826120	−	0.996582i	$-0.473674\pi$
$601$	−18.1204	−	10.4618i	−0.739147	−	0.426747i	−0.821759	+	0.569835i	$0.807007\pi$
$602$	−0.732043	−	13.5665i	−0.0298358	−	0.552928i
$603$	−5.43009	+	32.3801i	−0.221130	+	1.31862i
$604$	1.66240	+	5.24040i	0.0676422	+	0.213229i
$605$		−	4.78181i		−	0.194408i
$606$	−7.58796	−	21.9867i	−0.308240	−	0.893150i
$607$		−	5.83438i		−	0.236810i	−0.992965	−	0.118405i	$-0.962222\pi$
$607$		−	5.83438i		−	0.236810i	0.992965	−	0.118405i	$-0.0377782\pi$
$608$	−2.64280	+	4.39857i	−0.107180	+	0.178386i
$609$	−2.34450	−	29.6014i	−0.0950041	−	1.19951i
$610$	−10.1853	−	1.10644i	−0.412392	−	0.0447983i
$611$	11.5171	−	19.9483i	0.465933	−	0.807020i
$612$	−10.3052	−	4.14670i	−0.416563	−	0.167620i
$613$	7.54385	−	4.35544i	0.304693	−	0.175915i	−0.339856	−	0.940477i	$-0.610378\pi$
$613$	7.54385	−	4.35544i	0.304693	−	0.175915i	0.644549	+	0.764563i	$0.277045\pi$
$614$	−10.1173	−	7.40466i	−0.408300	−	0.298828i
$615$	−0.164946	+	1.98091i	−0.00665126	+	0.0798781i
$616$	9.79067	−	11.9572i	0.394477	−	0.481771i
$617$	−2.90616	+	1.67787i	−0.116998	+	0.0675487i	−0.557357	−	0.830273i	$-0.688184\pi$
$617$	−2.90616	+	1.67787i	−0.116998	+	0.0675487i	0.440359	+	0.897822i	$0.354851\pi$
$618$	−15.2415	−	44.1635i	−0.613103	−	1.77652i
$619$	21.1935			0.851838			0.425919	−	0.904761i	$-0.359951\pi$
$619$	21.1935			0.851838			0.425919	+	0.904761i	$0.359951\pi$
$620$	1.46245	+	0.321527i	0.0587334	+	0.0129128i
$621$	11.4583	−	45.0193i	0.459806	−	1.80656i
$622$	−15.2946	+	6.74582i	−0.613259	+	0.270483i
$623$	16.3204	−	13.3526i	0.653861	−	0.534959i
$624$	16.0526	−	9.43349i	0.642619	−	0.377642i
$625$	17.6930			0.707720
$626$	−33.2229	−	3.60901i	−1.32785	−	0.144245i
$627$	1.38360	+	2.93496i	0.0552555	+	0.117211i
$628$	11.7839	+	2.59076i	0.470230	+	0.103383i
$629$		−	0.176946i		−	0.00705531i
$630$	6.41204	+	4.73275i	0.255462	+	0.188557i
$631$	12.2898			0.489248			0.244624	−	0.969618i	$-0.421336\pi$
$631$	12.2898			0.489248			0.244624	+	0.969618i	$0.421336\pi$
$632$	29.6560	−	5.98009i	1.17965	−	0.237875i
$633$	2.64975	−	31.8220i	0.105318	−	1.26481i
$634$	4.35854	−	40.1226i	0.173100	−	1.59347i
$635$		−	8.63032i		−	0.342484i
$636$	4.97579	+	21.8295i	0.197303	+	0.865594i
$637$	−3.72583	+	18.4396i	−0.147623	+	0.730603i
$638$	17.3153	−	7.63703i	0.685518	−	0.302353i
$639$	−3.31804	+	1.23926i	−0.131260	+	0.0490242i
$640$	−7.69767	+	2.29503i	−0.304277	+	0.0907189i
$641$		−	3.78637i		−	0.149553i	−0.997200	−	0.0747763i	$-0.976176\pi$
$641$		−	3.78637i		−	0.149553i	0.997200	−	0.0747763i	$-0.0238243\pi$
$642$	−3.52098	+	18.1822i	−0.138962	+	0.717594i
$643$	5.43661	+	9.41649i	0.214399	+	0.371350i	0.953087	−	0.302698i	$-0.0978873\pi$
$643$	5.43661	+	9.41649i	0.214399	+	0.371350i	−0.738687	+	0.674048i	$0.764554\pi$
$644$	−47.2374	−	2.56745i	−1.86141	−	0.101172i
$645$	1.90402	+	4.03891i	0.0749707	+	0.159032i
$646$	−1.91658	−	1.40271i	−0.0754068	−	0.0551889i
$647$	15.1157	+	26.1811i	0.594259	+	1.02929i	0.993651	+	0.112507i	$0.0358879\pi$
$647$	15.1157	+	26.1811i	0.594259	+	1.02929i	−0.399392	+	0.916780i	$0.630779\pi$
$648$	9.68449	+	23.5417i	0.380443	+	0.924804i
$649$	−18.1014	−	10.4509i	−0.710542	−	0.410232i
$650$	1.84536	−	16.9875i	0.0723809	−	0.666304i
$651$	−4.81733	+	0.381545i	−0.188806	+	0.0149539i
$652$	5.13231	−	23.3440i	0.200997	−	0.914223i
$653$	1.96259			0.0768022			0.0384011	−	0.999262i	$-0.487774\pi$
$653$	1.96259			0.0768022			0.0384011	+	0.999262i	$0.487774\pi$
$654$	2.06669	−	2.38084i	0.0808139	−	0.0930980i
$655$	−16.1179			−0.629780
$656$	5.86950	+	2.71197i	0.229165	+	0.105885i
$657$	−19.2951	−	15.9169i	−0.752773	−	0.620976i
$658$	14.5151	−	28.5969i	0.565859	−	1.11482i
$659$	25.0514	−	43.3903i	0.975865	−	1.69025i	0.298813	−	0.954312i	$-0.403409\pi$
$659$	25.0514	−	43.3903i	0.975865	−	1.69025i	0.677052	−	0.735936i	$-0.263257\pi$
$660$	−1.49851	+	4.85306i	−0.0583293	+	0.188905i
$661$	15.0559	−	26.0776i	0.585607	−	1.01430i	−0.409193	−	0.912448i	$-0.634190\pi$
$661$	15.0559	−	26.0776i	0.585607	−	1.01430i	0.994799	−	0.101853i	$-0.0324770\pi$
$662$	−50.2157	−	5.45495i	−1.95169	−	0.212013i
$663$	3.67473	+	7.79503i	0.142715	+	0.302734i
$664$	−19.5283	+	17.2169i	−0.757844	+	0.668147i
$665$	1.07899	+	1.31882i	0.0418416	+	0.0511415i
$666$	−0.290306	+	0.283105i	−0.0112491	+	0.0109701i
$667$	−50.1693	−	28.9652i	−1.94256	−	1.12154i
$668$	−12.3641	+	13.5407i	−0.478382	+	0.523905i
$669$	−40.2303	+	18.9653i	−1.55539	+	0.733242i
$670$	−10.0541	+	4.43443i	−0.388423	+	0.171317i
$671$	10.5362	+	18.2492i	0.406746	+	0.704504i
$672$	21.6094	−	14.3191i	0.833599	−	0.552370i
$673$	1.79494	−	3.10893i	0.0691899	−	0.119840i	−0.829355	−	0.558722i	$-0.811292\pi$
$673$	1.79494	−	3.10893i	0.0691899	−	0.119840i	0.898545	+	0.438882i	$0.144625\pi$
$674$	4.12970	−	38.0161i	0.159070	−	1.46433i
$675$	22.6397	+	5.76226i	0.871403	+	0.221790i
$676$	11.2856	+	2.48119i	0.434060	+	0.0954305i
$677$	9.86475	−	5.69541i	0.379133	−	0.218893i	−0.298308	−	0.954470i	$-0.596422\pi$
$677$	9.86475	−	5.69541i	0.379133	−	0.218893i	0.677441	+	0.735577i	$0.263089\pi$
$678$	−19.5680	+	22.5424i	−0.751504	+	0.865737i
$679$	−18.4965	−	22.6076i	−0.709831	−	0.867602i
$680$	−0.734894	−	3.64443i	−0.0281819	−	0.139757i
$681$	5.02038	+	3.48405i	0.192381	+	0.133509i
$682$	−1.24285	−	2.81789i	−0.0475912	−	0.107903i
$683$	−13.8176	−	23.9327i	−0.528715	−	0.915761i	−0.999439	−	0.0334808i	$-0.989341\pi$
$683$	−13.8176	−	23.9327i	−0.528715	−	0.915761i	0.470725	−	0.882280i	$-0.343993\pi$
$684$	0.765070	+	5.38869i	0.0292532	+	0.206042i
$685$	14.2158			0.543158
$686$	−3.79652	+	25.9150i	−0.144952	+	0.989439i
$687$	11.9126	−	17.1656i	0.454493	−	0.654908i
$688$	14.4645	−	1.31662i	0.551452	−	0.0501956i
$689$	8.68487	−	15.0426i	0.330867	−	0.573079i
$690$	14.6972	−	5.07222i	0.559512	−	0.193096i
$691$	16.0273	+	27.7601i	0.609707	+	1.05604i	0.991289	+	0.131708i	$0.0420461\pi$
$691$	16.0273	+	27.7601i	0.609707	+	1.05604i	−0.381582	+	0.924335i	$0.624621\pi$
$692$	−1.98802	−	1.81528i	−0.0755733	−	0.0690068i
$693$	0.0661981	−	16.3915i	0.00251466	−	0.622663i
$694$	−10.6085	+	4.67896i	−0.402693	+	0.177611i
$695$	−7.50298	+	4.33184i	−0.284604	+	0.164316i
$696$	31.5313	−	3.67107i	1.19519	−	0.139152i
$697$	−1.49631	+	2.59168i	−0.0566766	+	0.0981668i
$698$	41.8079	−	18.4397i	1.58245	−	0.697953i
$699$	5.30250	−	2.49970i	0.200559	−	0.0945474i
$700$	1.29114	−	23.7551i	0.0488006	−	0.897860i
$701$	34.3902			1.29890			0.649450	−	0.760404i	$-0.274999\pi$
$701$	34.3902			1.29890			0.649450	+	0.760404i	$0.274999\pi$
$702$	6.90952	−	18.5006i	0.260783	−	0.698259i
$703$	−0.0750836	+	0.0433496i	−0.00283183	+	0.00163496i
$704$	13.1599	+	9.98840i	0.495984	+	0.376452i
$705$	−0.874612	+	10.5036i	−0.0329398	+	0.395589i
$706$	26.3380	+	19.2763i	0.991243	+	0.725473i
$707$	−8.88505	+	23.4992i	−0.334157	+	0.883780i
$708$	−23.8398	−	25.7081i	−0.895955	−	0.966170i
$709$	−35.7815	+	20.6585i	−1.34380	+	0.775845i	−0.987363	−	0.158473i	$-0.949343\pi$
$709$	−35.7815	+	20.6585i	−1.34380	+	0.775845i	−0.356440	+	0.934318i	$0.616010\pi$
$710$	−0.956603	−	0.700121i	−0.0359007	−	0.0262751i
$711$	20.4191	−	24.7529i	0.765775	−	0.928305i
$712$	14.9079	+	16.9092i	0.558695	+	0.633699i
$713$	−4.71381	+	8.16455i	−0.176533	+	0.305765i
$714$	5.69352	+	10.5613i	0.213075	+	0.395247i
$715$	3.41250	−	1.97021i	0.127620	−	0.0736816i
$716$	9.96332	−	10.9114i	0.372347	−	0.407779i
$717$	−2.88631	+	34.6630i	−0.107791	+	1.29452i
$718$	5.24903	+	11.9010i	0.195892	+	0.444141i
$719$	−24.6491	+	42.6936i	−0.919258	+	1.59220i	−0.118713	+	0.992929i	$0.537877\pi$
$719$	−24.6491	+	42.6936i	−0.919258	+	1.59220i	−0.800545	+	0.599273i	$0.795457\pi$
$720$	−4.80343	+	7.03659i	−0.179013	+	0.262238i
$721$	−17.8469	+	47.2016i	−0.664653	+	1.75788i
$722$	2.77616	−	25.5560i	0.103318	−	0.951096i
$723$	9.83210	+	6.82329i	0.365660	+	0.253761i
$724$	−1.98071	−	6.24382i	−0.0736127	−	0.232050i
$725$	14.5663	−	25.2296i	0.540979	−	0.937003i
$726$	−15.5950	+	5.38208i	−0.578786	+	0.199748i
$727$	13.5657	+	7.83218i	0.503125	+	0.290479i	0.730003	−	0.683444i	$-0.239519\pi$
$727$	13.5657	+	7.83218i	0.503125	+	0.290479i	−0.226878	+	0.973923i	$0.572852\pi$
$728$	−19.8462	−	3.25379i	−0.735548	−	0.120593i
$729$	23.7147	+	12.9079i	0.878322	+	0.478070i
$730$	0.904085	−	8.32257i	0.0334617	−	0.308032i
$731$			6.72243i			0.248638i
$732$	7.85547	+	34.4630i	0.290347	+	1.27379i
$733$	3.93621			0.145387			0.0726936	−	0.997354i	$-0.476840\pi$
$733$	3.93621			0.145387			0.0726936	+	0.997354i	$0.476840\pi$
$734$	−20.4934	+	28.0009i	−0.756424	+	1.03353i
$735$	−2.05578	−	8.35898i	−0.0758287	−	0.308325i
$736$	0.881545	−	50.5657i	0.0324942	−	1.86388i
$737$	19.5733	+	11.3006i	0.720991	+	0.416264i
$738$	6.64604	−	1.69164i	0.244644	−	0.0622700i
$739$	−11.3964	+	6.57971i	−0.419223	+	0.242039i	−0.694745	−	0.719256i	$-0.744483\pi$
$739$	−11.3964	+	6.57971i	−0.419223	+	0.242039i	0.275522	+	0.961295i	$0.411149\pi$
$740$	−0.132549	−	0.0291415i	−0.00487258	−	0.00107126i
$741$	2.40741	−	3.46898i	0.0884383	−	0.127436i
$742$	10.9456	−	21.5644i	0.401826	−	0.791655i
$743$	4.76281	−	2.74981i	0.174731	−	0.100881i	−0.410084	−	0.912048i	$-0.634501\pi$
$743$	4.76281	−	2.74981i	0.174731	−	0.100881i	0.584815	+	0.811167i	$0.301167\pi$
$744$	−0.597430	−	5.13141i	−0.0219028	−	0.188127i
$745$		−	7.12454i		−	0.261023i
$746$	−23.6455	+	32.3078i	−0.865724	+	1.18287i
$747$	−4.56694	+	27.2331i	−0.167096	+	0.996407i
$748$	−5.15616	+	5.64681i	−0.188528	+	0.206468i
$749$	15.4824	−	12.6669i	0.565713	−	0.462840i
$750$	5.38752	+	15.6108i	0.196724	+	0.570025i
$751$	19.2460			0.702296			0.351148	−	0.936320i	$-0.385791\pi$
$751$	19.2460			0.702296			0.351148	+	0.936320i	$0.385791\pi$
$752$	31.1225	+	14.3800i	1.13492	+	0.524384i
$753$	6.82288	+	4.73495i	0.248640	+	0.172551i
$754$	−19.8733	−	14.5450i	−0.723744	−	0.529696i
$755$			1.95165i			0.0710280i
$756$	8.21805	−	26.2386i	0.298888	−	0.954288i
$757$			6.30862i			0.229291i	0.993406	+	0.114645i	$0.0365732\pi$
$757$			6.30862i			0.229291i	−0.993406	+	0.114645i	$0.963427\pi$
$758$	−29.1452	+	39.8223i	−1.05860	+	1.44641i
$759$	−26.2721	−	18.2323i	−0.953615	−	0.661791i
$760$	−1.36640	+	1.20468i	−0.0495646	+	0.0436982i
$761$	33.9444			1.23048			0.615242	−	0.788338i	$-0.289058\pi$
$761$	33.9444			1.23048			0.615242	+	0.788338i	$0.289058\pi$
$762$	−28.1463	+	9.71371i	−1.01963	+	0.351890i
$763$	−3.36067	+	0.549633i	−0.121664	+	0.0198980i
$764$	5.65828	+	5.16663i	0.204709	+	0.186922i
$765$	−3.04188	−	2.50930i	−0.109980	−	0.0907240i
$766$	−28.9057	−	21.1556i	−1.04440	−	0.764382i
$767$			27.2001i			0.982139i
$768$	16.1488	+	22.5215i	0.582720	+	0.812673i
$769$	−36.1605	+	20.8773i	−1.30398	+	0.752854i	−0.981085	−	0.193580i	$-0.937990\pi$
$769$	−36.1605	+	20.8773i	−1.30398	+	0.752854i	−0.322898	+	0.946434i	$0.604657\pi$
$770$	4.59640	−	2.99506i	0.165643	−	0.107935i
$771$	12.1610	−	17.5236i	0.437969	−	0.631096i
$772$	−21.2102	−	4.66318i	−0.763372	−	0.167831i
$773$	−13.4656	+	7.77434i	−0.484322	+	0.279624i	−0.722216	−	0.691668i	$-0.756876\pi$
$773$	−13.4656	+	7.77434i	−0.484322	+	0.279624i	0.237894	+	0.971291i	$0.423543\pi$
$774$	11.0291	−	10.7555i	0.396434	−	0.386600i
$775$	−4.10586	−	2.37052i	−0.147487	−	0.0851516i
$776$	23.4233	−	20.6510i	0.840849	−	0.741327i
$777$	0.436617	−	0.0345812i	0.0156635	−	0.00124059i
$778$	−17.9969	−	13.1716i	−0.645220	−	0.472225i
$779$	1.46630			0.0525358
$780$	6.44437	−	1.46893i	0.230746	−	0.0525960i
$781$			2.43820i			0.0872457i
$782$	23.2706	+	2.52789i	0.832154	+	0.0903972i
$783$	23.5071	−	24.1056i	0.840074	−	0.861465i
$784$	−27.8351	−	3.03475i	−0.994109	−	0.108384i
$785$	3.70927	+	2.14155i	0.132389	+	0.0764351i
$786$	18.1413	+	52.5658i	0.647077	+	1.87496i
$787$	−24.0500	+	41.6558i	−0.857290	+	1.48487i	0.0172132	+	0.999852i	$0.494521\pi$
$787$	−24.0500	+	41.6558i	−0.857290	+	1.48487i	−0.874504	+	0.485019i	$0.838813\pi$
$788$	−6.88117	−	21.6915i	−0.245131	−	0.772729i
$789$	6.92962	+	4.80903i	0.246701	+	0.171206i
$790$	10.6767	+	1.15981i	0.379859	+	0.0412643i
$791$	31.8197	−	5.20408i	1.13138	−	0.185036i
$792$	17.5140	−	0.575161i	0.622333	−	0.0204375i
$793$	13.7111	−	23.7484i	0.486897	−	0.843330i
$794$	26.6602	−	11.7587i	0.946134	−	0.417299i
$795$	−0.659530	+	7.92060i	−0.0233911	+	0.280915i
$796$	3.80962	+	3.47860i	0.135029	+	0.123296i
$797$	8.79621	−	5.07849i	0.311578	−	0.179889i	−0.336055	−	0.941843i	$-0.609093\pi$
$797$	8.79621	−	5.07849i	0.311578	−	0.179889i	0.647632	+	0.761953i	$0.275759\pi$
$798$	3.08664	−	5.00332i	0.109266	−	0.177116i
$799$	−7.93404	+	13.7422i	−0.280686	+	0.486163i
$800$	25.4289	+	0.443319i	0.899049	+	0.0156737i
$801$	23.5807	+	3.95444i	0.833182	+	0.139723i
$802$	−9.04525	+	12.3589i	−0.319399	+	0.436407i
$803$	−14.9117	+	8.60927i	−0.526222	+	0.303815i
$804$	25.7783	+	27.7985i	0.909130	+	0.980378i
$805$	−15.7082	−	5.93928i	−0.553643	−	0.209332i
$806$	−2.36705	+	3.23419i	−0.0833757	+	0.113919i
$807$	0.515529	−	6.19122i	0.0181475	−	0.217941i
$808$	−25.4548	−	8.56612i	−0.895496	−	0.301355i
$809$	21.3713	−	12.3387i	0.751376	−	0.433807i	−0.0748147	−	0.997197i	$-0.523837\pi$
$809$	21.3713	−	12.3387i	0.751376	−	0.433807i	0.826191	+	0.563390i	$0.190503\pi$
$810$	0.749972	+	9.00541i	0.0263513	+	0.316418i
$811$	2.72577			0.0957147			0.0478574	−	0.998854i	$-0.484761\pi$
$811$	2.72577			0.0957147			0.0478574	+	0.998854i	$0.484761\pi$
$812$	−28.7199	−	18.7302i	−1.00787	−	0.657300i
$813$	25.0334	−	11.8012i	0.877958	−	0.413886i
$814$	0.112645	+	0.255398i	0.00394822	+	0.00895171i
$815$	4.24241	−	7.34808i	0.148605	−	0.257392i
$816$	−11.0585	+	6.49864i	−0.387125	+	0.227498i
$817$	2.85253	−	1.64691i	0.0997975	−	0.0576181i
$818$	−10.8976	−	24.7078i	−0.381025	−	0.863890i
$819$	−18.5162	+	10.5908i	−0.647007	+	0.370074i
$820$	1.69497	+	1.54770i	0.0591910	+	0.0540479i
$821$	3.46544	+	6.00233i	0.120945	+	0.209483i	0.920141	−	0.391588i	$-0.128074\pi$
$821$	3.46544	+	6.00233i	0.120945	+	0.209483i	−0.799196	+	0.601071i	$0.794741\pi$
$822$	−16.0004	−	46.3623i	−0.558076	−	1.61707i
$823$	6.16716	−	10.6818i	0.214974	−	0.372345i	−0.738291	−	0.674483i	$-0.764367\pi$
$823$	6.16716	−	10.6818i	0.214974	−	0.372345i	0.953264	+	0.302137i	$0.0977001\pi$
$824$	−51.1296	−	17.2063i	−1.78118	−	0.599409i
$825$	9.16882	−	13.2119i	0.319217	−	0.459980i
$826$	2.04047	+	37.8147i	0.0709971	+	1.31574i
$827$	−37.4584			−1.30256			−0.651279	−	0.758839i	$-0.725767\pi$
$827$	−37.4584			−1.30256			−0.651279	+	0.758839i	$0.725767\pi$
$828$	−33.0843	−	42.2233i	−1.14976	−	1.46736i
$829$	−10.8796	−	18.8440i	−0.377863	−	0.654478i	0.612888	−	0.790170i	$-0.290008\pi$
$829$	−10.8796	−	18.8440i	−0.377863	−	0.654478i	−0.990751	+	0.135692i	$0.956674\pi$
$830$	−8.45592	+	3.72955i	−0.293509	+	0.129455i
$831$	31.1225	+	21.5984i	1.07963	+	0.749240i
$832$	2.69408	−	21.3302i	0.0934003	−	0.739493i
$833$	2.56669	−	12.7029i	0.0889304	−	0.440128i
$834$	22.5724	+	19.5940i	0.781617	+	0.678484i
$835$	−5.63716	+	3.25461i	−0.195082	+	0.112631i
$836$	3.65930	+	0.804517i	0.126560	+	0.0278248i
$837$	−3.92295	−	3.82554i	−0.135597	−	0.132230i
$838$	−31.2753	−	3.39745i	−1.08039	−	0.117363i
$839$	−24.6800	+	42.7469i	−0.852047	+	1.47579i	0.0273111	+	0.999627i	$0.491306\pi$
$839$	−24.6800	+	42.7469i	−0.852047	+	1.47579i	−0.879358	+	0.476161i	$0.842028\pi$
$840$	8.84904	−	2.52560i	0.305321	−	0.0871415i
$841$	−6.49376	−	11.2475i	−0.223923	−	0.387846i
$842$	−8.58774	−	19.4708i	−0.295953	−	0.671008i
$843$	−8.59622	+	4.05243i	−0.296070	+	0.139573i
$844$	−27.2286	−	24.8627i	−0.937247	−	0.855810i
$845$	3.55239	+	2.05098i	0.122206	+	0.0705557i
$846$	35.2401	−	8.96977i	1.21158	−	0.308387i
$847$	16.6678	+	6.30210i	0.572714	+	0.216543i
$848$	23.4690	+	10.8437i	0.805928	+	0.372374i
$849$	18.6357	+	39.5310i	0.639575	+	1.35670i
$850$	−1.27125	+	11.7025i	−0.0436035	+	0.401393i
$851$	0.427234	−	0.739991i	0.0146454	−	0.0253666i
$852$	−1.20663	+	3.90780i	−0.0413386	+	0.133879i
$853$	−14.6400	+	25.3573i	−0.501265	+	0.868216i	0.498734	+	0.866755i	$0.333798\pi$
$853$	−14.6400	+	25.3573i	−0.501265	+	0.868216i	−0.999999	+	0.00146097i	$0.999535\pi$
$854$	17.2803	−	34.0446i	0.591318	−	1.16498i
$855$	−0.319551	+	1.90551i	−0.0109284	+	0.0651671i
$856$	14.1424	+	16.0410i	0.483377	+	0.548269i
$857$	−1.40239			−0.0479048			−0.0239524	−	0.999713i	$-0.507625\pi$
$857$	−1.40239			−0.0479048			−0.0239524	+	0.999713i	$0.507625\pi$
$858$	−10.2664	−	8.91173i	−0.350488	−	0.304241i
$859$	−48.0956			−1.64100			−0.820500	−	0.571647i	$-0.806305\pi$
$859$	−48.0956			−1.64100			−0.820500	+	0.571647i	$0.806305\pi$
$860$	5.03571	+	1.10713i	0.171716	+	0.0377527i
$861$	−6.68743	−	3.18565i	−0.227907	−	0.108567i
$862$	22.5115	+	2.44544i	0.766746	+	0.0832920i
$863$	−31.3503	−	18.1001i	−1.06718	−	0.616135i	−0.139768	−	0.990184i	$-0.544636\pi$
$863$	−31.3503	−	18.1001i	−1.06718	−	0.616135i	−0.927409	+	0.374049i	$0.877969\pi$
$864$	28.3550	+	7.74561i	0.964656	+	0.263511i
$865$	−0.477838	−	0.827640i	−0.0162470	−	0.0281406i
$866$	−16.4751	+	22.5105i	−0.559846	+	0.764940i
$867$	10.0242	+	21.2638i	0.340439	+	0.722157i
$868$	−3.04815	+	4.67387i	−0.103461	+	0.158642i
$869$	−11.0445	−	19.1296i	−0.374658	−	0.648927i
$870$	11.0634	+	2.14242i	0.375084	+	0.0726350i
$871$		−	29.4118i		−	0.996582i
$872$	−0.719605	−	3.56860i	−0.0243689	−	0.120848i
$873$	5.47785	−	32.6649i	0.185397	−	1.10554i
$874$	−4.62833	−	10.4937i	−0.156556	−	0.354955i
$875$	6.30847	−	16.6847i	0.213265	−	0.564045i
$876$	−28.1602	+	6.41881i	−0.951444	+	0.216871i
$877$		−	47.1496i		−	1.59213i	−0.605211	−	0.796065i	$-0.706911\pi$
$877$		−	47.1496i		−	1.59213i	0.605211	−	0.796065i	$-0.293089\pi$
$878$	33.0952	+	3.59515i	1.11691	+	0.121330i
$879$	4.20163	−	50.4593i	0.141717	−	1.70195i
$880$	3.38079	+	4.79241i	0.113967	+	0.161552i
$881$	−21.6654			−0.729927			−0.364964	−	0.931022i	$-0.618919\pi$
$881$	−21.6654			−0.729927			−0.364964	+	0.931022i	$0.618919\pi$
$882$	−24.9475	+	16.1129i	−0.840025	+	0.542548i
$883$		−	13.8995i		−	0.467757i	−0.972266	−	0.233878i	$-0.924858\pi$
$883$		−	13.8995i		−	0.467757i	0.972266	−	0.233878i	$-0.0751417\pi$
$884$	9.71884	+	2.13674i	0.326880	+	0.0718663i
$885$	−5.30720	−	11.2579i	−0.178400	−	0.378431i
$886$	5.25365	−	48.3626i	0.176500	−	1.62477i
$887$	−48.6187			−1.63246			−0.816229	−	0.577729i	$-0.803939\pi$
$887$	−48.6187			−1.63246			−0.816229	+	0.577729i	$0.803939\pi$
$888$	0.0541479	+	0.465083i	0.00181708	+	0.0156072i
$889$	30.0825	+	11.3742i	1.00894	+	0.381478i
$890$	3.22935	+	7.32184i	0.108248	+	0.245429i
$891$	14.0358	−	12.1841i	0.470216	−	0.408182i
$892$	−11.0277	+	50.1591i	−0.369236	+	1.67945i
$893$	7.77495			0.260179
$894$	−23.2354	+	8.01890i	−0.777109	+	0.268192i
$895$	4.54256	−	2.62265i	0.151841	−	0.0876655i
$896$	2.14529	−	29.8563i	0.0716691	−	0.997428i
$897$	−3.45324	+	41.4715i	−0.115300	+	1.38469i
$898$	21.5336	−	29.4222i	0.718586	−	0.981832i
$899$	−5.91760	+	3.41653i	−0.197363	+	0.113948i
$900$	21.2336	−	16.6377i	0.707788	−	0.554591i
$901$	−5.98293	+	10.3627i	−0.199320	+	0.345233i
$902$	0.509836	−	4.69331i	0.0169757	−	0.156270i
$903$	−16.5877	+	1.31379i	−0.552004	+	0.0437201i
$904$	6.81342	+	33.7886i	0.226611	+	1.12379i
$905$		−	2.32535i		−	0.0772972i
$906$	6.36497	−	2.19665i	0.211462	−	0.0729788i
$907$			51.9053i			1.72349i	0.507344	+	0.861744i	$0.330627\pi$
$907$			51.9053i			1.72349i	−0.507344	+	0.861744i	$0.669373\pi$
$908$	6.72592	−	2.13365i	0.223207	−	0.0708077i
$909$	−26.6861	+	9.96701i	−0.885122	+	0.330585i
$910$	−6.36613	−	3.23131i	−0.211035	−	0.107117i
$911$	−47.5896	−	27.4758i	−1.57671	−	0.910315i	−0.995314	−	0.0966964i	$-0.969172\pi$
$911$	−47.5896	−	27.4758i	−1.57671	−	0.910315i	−0.581398	−	0.813619i	$-0.697494\pi$
$912$	5.46676	+	3.10037i	0.181023	+	0.102664i
$913$	16.4620	+	9.50433i	0.544812	+	0.314547i
$914$	0.315185	−	2.90144i	0.0104254	−	0.0959713i
$915$	−1.04122	+	12.5045i	−0.0344218	+	0.413388i
$916$	−7.29533	−	22.9971i	−0.241044	−	0.759846i
$917$	21.2423	−	56.1819i	0.701484	−	1.85529i
$918$	−4.75990	+	12.7449i	−0.157100	+	0.420643i
$919$	2.51085	−	4.34891i	0.0828252	−	0.143457i	−0.821637	−	0.570011i	$-0.806939\pi$
$919$	2.51085	−	4.34891i	0.0828252	−	0.143457i	0.904462	+	0.426553i	$0.140272\pi$
$920$	5.72608	−	17.0154i	0.188783	−	0.560982i
$921$	−8.75461	+	12.6151i	−0.288474	+	0.415680i
$922$	13.5195	+	30.6525i	0.445242	+	1.00949i
$923$	2.74783	−	1.58646i	0.0904458	−	0.0522189i
$924$	−14.9413	−	11.6193i	−0.491531	−	0.382247i
$925$	0.372134	+	0.214851i	0.0122357	+	0.00706427i
$926$	−0.0822251	+	0.756925i	−0.00270209	+	0.0248741i
$927$	−53.6029	+	20.0202i	−1.76055	+	0.657549i
$928$	18.8781	−	31.4200i	0.619705	−	1.03141i
$929$	9.00989	+	15.6056i	0.295605	+	0.512002i	0.975125	−	0.221654i	$-0.0711455\pi$
$929$	9.00989	+	15.6056i	0.295605	+	0.512002i	−0.679521	+	0.733656i	$0.737812\pi$
$930$	0.348658	−	1.80046i	0.0114330	−	0.0590393i
$931$	−6.01901	+	2.02291i	−0.197265	+	0.0662983i
$932$	1.45350	−	6.61116i	0.0476109	−	0.216556i
$933$	8.72998	+	18.5185i	0.285807	+	0.606269i
$934$	−16.5670	−	37.5619i	−0.542087	−	1.22906i
$935$	−2.35084	+	1.35726i	−0.0768806	+	0.0443871i
$936$	−12.0440	−	19.3638i	−0.393670	−	0.632927i
$937$			19.4889i			0.636675i	0.947977	+	0.318337i	$0.103124\pi$
$937$			19.4889i			0.636675i	−0.947977	+	0.318337i	$0.896876\pi$
$938$	−2.20639	−	40.8895i	−0.0720411	−	1.33509i
$939$	−3.39630	+	40.7878i	−0.110834	+	1.33106i
$940$	8.98745	+	8.20653i	0.293138	+	0.267667i
$941$	3.94192	+	2.27587i	0.128503	+	0.0741911i	0.562873	−	0.826543i	$-0.309696\pi$
$941$	3.94192	+	2.27587i	0.128503	+	0.0741911i	−0.434371	+	0.900734i	$0.643029\pi$
$942$	2.80937	−	14.5075i	0.0915343	−	0.472680i
$943$	−12.5151	+	7.22562i	−0.407549	+	0.235299i
$944$	−40.3178	+	3.66990i	−1.31223	+	0.119445i
$945$	5.59725	−	7.99629i	0.182079	−	0.260119i
$946$	−4.27956	−	9.70294i	−0.139140	−	0.315470i
$947$	−6.74535	−	11.6833i	−0.219195	−	0.379656i	0.735367	−	0.677669i	$-0.237010\pi$
$947$	−6.74535	−	11.6833i	−0.219195	−	0.379656i	−0.954562	+	0.298013i	$0.903676\pi$
$948$	−8.23442	−	36.1255i	−0.267442	−	1.17330i
$949$	19.4051	+	11.2035i	0.629917	+	0.363683i
$950$	5.27717	−	2.32754i	0.171214	−	0.0755153i
$951$	−49.2586	−	4.10165i	−1.59732	−	0.133005i
$952$	13.6718	+	2.24150i	0.443106	+	0.0726476i
$953$		−	39.6231i		−	1.28352i	−0.766906	−	0.641759i	$-0.778205\pi$
$953$		−	39.6231i		−	1.28352i	0.766906	−	0.641759i	$-0.221795\pi$
$954$	26.5740	−	6.76395i	0.860363	−	0.218991i
$955$	1.36002	+	2.35562i	0.0440091	+	0.0762259i
$956$	29.6595	+	27.0824i	0.959257	+	0.875907i
$957$	−9.88334	−	20.9651i	−0.319483	−	0.677705i
$958$	4.74347	+	3.47166i	0.153255	+	0.112164i
$959$	−18.7355	+	49.5517i	−0.605000	+	1.60011i
$960$	3.04683	+	9.35408i	0.0983360	+	0.301902i
$961$	−14.9440	−	25.8838i	−0.482064	−	0.834960i
$962$	0.214537	−	0.293130i	0.00691693	−	0.00945088i
$963$	22.3699	+	3.75139i	0.720860	+	0.120887i
$964$	13.1723	−	4.17862i	0.424251	−	0.134584i
$965$	−6.67641	−	3.85463i	−0.214921	−	0.124085i
$966$	−1.68976	+	57.9145i	−0.0543672	+	1.86337i
$967$	24.5755	+	42.5659i	0.790293	+	1.36883i	0.925785	+	0.378050i	$0.123405\pi$
$967$	24.5755	+	42.5659i	0.790293	+	1.36883i	−0.135492	+	0.990778i	$0.543262\pi$
$968$	−6.07588	+	18.0549i	−0.195286	+	0.580306i
$969$	−1.65844	+	2.38975i	−0.0532767	+	0.0767697i
$970$	10.1425	−	4.47344i	0.325657	−	0.143633i
$971$	2.21663	+	1.27977i	0.0711351	+	0.0410699i	0.535146	−	0.844760i	$-0.320257\pi$
$971$	2.21663	+	1.27977i	0.0711351	+	0.0410699i	−0.464011	+	0.885830i	$0.653590\pi$
$972$	28.5254	−	12.5818i	0.914953	−	0.403561i
$973$	−5.21099	−	31.8620i	−0.167057	−	1.02145i
$974$	4.19527	−	38.6196i	0.134425	−	1.23745i
$975$	−20.8556	−	1.73659i	−0.667912	−	0.0556155i
$976$	37.0513	+	17.1194i	1.18598	+	0.547977i
$977$	45.7232	+	26.3983i	1.46282	+	0.844557i	0.999141	−	0.0414483i	$-0.0131972\pi$
$977$	45.7232	+	26.3983i	1.46282	+	0.844557i	0.463675	+	0.886005i	$0.346531\pi$
$978$	−28.7394	−	5.56538i	−0.918985	−	0.177961i
$979$	8.22964	−	14.2541i	0.263020	−	0.455565i
$980$	−9.09287	−	4.01473i	−0.290461	−	0.128246i
$981$	−2.97860	−	2.45710i	−0.0950993	−	0.0784491i
$982$	−4.58936	+	42.2475i	−0.146452	+	1.34817i
$983$	13.4428			0.428757			0.214379	−	0.976751i	$-0.431227\pi$
$983$	13.4428			0.428757			0.214379	+	0.976751i	$0.431227\pi$
$984$	3.13979	−	7.26983i	0.100093	−	0.231754i
$985$		−	8.07846i		−	0.257401i
$986$	13.6906	+	10.0199i	0.435996	+	0.319098i
$987$	−35.4595	−	16.8917i	−1.12869	−	0.537668i
$988$	−1.47431	−	4.64747i	−0.0469040	−	0.147856i
$989$	−16.2312	+	28.1133i	−0.516123	+	0.893951i
$990$	5.98800	+	1.68536i	0.190311	+	0.0535642i
$991$	19.6314	+	34.0025i	0.623611	+	1.08013i	0.988808	+	0.149195i	$0.0476684\pi$
$991$	19.6314	+	34.0025i	0.623611	+	1.08013i	−0.365197	+	0.930930i	$0.618998\pi$
$992$	−5.11329	−	3.07223i	−0.162347	−	0.0975433i
$993$	−5.13344	+	61.6499i	−0.162905	+	1.95640i
$994$	3.70113	−	2.41169i	0.117393	−	0.0764943i
$995$	0.915675	+	1.58599i	0.0290288	+	0.0502794i
$996$	21.6807	+	23.3798i	0.686978	+	0.740816i
$997$	−48.6800			−1.54171			−0.770855	−	0.637011i	$-0.780171\pi$
$997$	−48.6800			−1.54171			−0.770855	+	0.637011i	$0.780171\pi$
$998$	1.42270	−	1.94390i	0.0450349	−	0.0615330i
$999$	0.355555	+	0.346726i	0.0112493	+	0.0109699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.y.a.173.19	✓	184
7.3	odd	6		504.2.ca.a.101.81	yes	184
8.5	even	2	inner	504.2.y.a.173.51	yes	184
9.5	odd	6		504.2.ca.a.5.12	yes	184
56.45	odd	6		504.2.ca.a.101.12	yes	184
63.59	even	6	inner	504.2.y.a.437.51	yes	184
72.5	odd	6		504.2.ca.a.5.81	yes	184
504.437	even	6	inner	504.2.y.a.437.19	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.y.a.173.19	✓	184	1.1	even	1	trivial
504.2.y.a.173.51	yes	184	8.5	even	2	inner
504.2.y.a.437.19	yes	184	504.437	even	6	inner
504.2.y.a.437.51	yes	184	63.59	even	6	inner
504.2.ca.a.5.12	yes	184	9.5	odd	6
504.2.ca.a.5.81	yes	184	72.5	odd	6
504.2.ca.a.101.12	yes	184	56.45	odd	6
504.2.ca.a.101.81	yes	184	7.3	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14122 - 0.835238i) q^{2} +(-0.987509 + 1.42296i) q^{3} +(0.604756 + 1.90638i) q^{4} +0.709981i q^{5} +(2.31548 - 0.799106i) q^{6} +(-2.47476 - 0.935707i) q^{7} +(0.902119 - 2.68071i) q^{8} +(-1.04965 - 2.81038i) q^{9} +O(q^{10})\)	\(q+(-1.14122 - 0.835238i) q^{2} +(-0.987509 + 1.42296i) q^{3} +(0.604756 + 1.90638i) q^{4} +0.709981i q^{5} +(2.31548 - 0.799106i) q^{6} +(-2.47476 - 0.935707i) q^{7} +(0.902119 - 2.68071i) q^{8} +(-1.04965 - 2.81038i) q^{9} +(0.593003 - 0.810243i) q^{10} -2.06516 q^{11} +(-3.30991 - 1.02202i) q^{12} +(1.34373 + 2.32741i) q^{13} +(2.04271 + 3.13486i) q^{14} +(-1.01028 - 0.701113i) q^{15} +(-3.26854 + 2.30579i) q^{16} +(-0.925683 - 1.60333i) q^{17} +(-1.14946 + 4.08396i) q^{18} +(-0.453561 + 0.785591i) q^{19} +(-1.35349 + 0.429365i) q^{20} +(3.77533 - 2.59748i) q^{21} +(2.35679 + 1.72490i) q^{22} -8.94020i q^{23} +(2.92370 + 3.93090i) q^{24} +4.49593 q^{25} +(0.410451 - 3.77842i) q^{26} +(5.03561 + 1.28166i) q^{27} +(0.287180 - 5.28370i) q^{28} +(3.23989 - 5.61165i) q^{29} +(0.567350 + 1.64394i) q^{30} +(-0.913241 - 0.527260i) q^{31} +(5.65599 + 0.0986046i) q^{32} +(2.03936 - 2.93864i) q^{33} +(-0.282756 + 2.60291i) q^{34} +(0.664334 - 1.75703i) q^{35} +(4.72286 - 3.70062i) q^{36} +(0.0827713 + 0.0477880i) q^{37} +(1.17377 - 0.517699i) q^{38} +(-4.63877 - 0.386259i) q^{39} +(1.90325 + 0.640487i) q^{40} +(-0.808217 - 1.39987i) q^{41} +(-6.47798 - 0.189007i) q^{42} +(-3.14459 - 1.81553i) q^{43} +(-1.24892 - 3.93697i) q^{44} +(1.99532 - 0.745232i) q^{45} +(-7.46719 + 10.2027i) q^{46} +(-4.28551 - 7.42271i) q^{47} +(-0.0533341 - 6.92800i) q^{48} +(5.24891 + 4.63130i) q^{49} +(-5.13083 - 3.75517i) q^{50} +(3.19560 + 0.266090i) q^{51} +(-3.62429 + 3.96917i) q^{52} +(-3.23163 - 5.59734i) q^{53} +(-4.67623 - 5.66858i) q^{54} -1.46622i q^{55} +(-4.74088 + 5.78999i) q^{56} +(-0.669971 - 1.42118i) q^{57} +(-8.38448 + 3.69804i) q^{58} +(8.76515 + 5.06056i) q^{59} +(0.725614 - 2.34997i) q^{60} +(-5.10189 - 8.83673i) q^{61} +(0.601819 + 1.36449i) q^{62} +(-0.0320548 + 7.93719i) q^{63} +(-6.37236 - 4.83663i) q^{64} +(-1.65242 + 0.954023i) q^{65} +(-4.78182 + 1.65028i) q^{66} +(-9.47786 - 5.47204i) q^{67} +(2.49674 - 2.73432i) q^{68} +(12.7216 + 8.82853i) q^{69} +(-2.22569 + 1.45028i) q^{70} -1.18064i q^{71} +(-8.48071 + 0.278507i) q^{72} +(7.22061 - 4.16882i) q^{73} +(-0.0545457 - 0.123670i) q^{74} +(-4.43977 + 6.39754i) q^{75} +(-1.77193 - 0.389567i) q^{76} +(5.11078 + 1.93238i) q^{77} +(4.97122 + 4.31528i) q^{78} +(5.34801 + 9.26302i) q^{79} +(-1.63706 - 2.32060i) q^{80} +(-6.79647 + 5.89983i) q^{81} +(-0.246875 + 2.27261i) q^{82} +(-7.97129 - 4.60223i) q^{83} +(7.23492 + 5.62635i) q^{84} +(1.13833 - 0.657217i) q^{85} +(2.07227 + 4.69840i) q^{86} +(4.78576 + 10.1518i) q^{87} +(-1.86302 + 5.53608i) q^{88} +(-3.98499 + 6.90221i) q^{89} +(-2.89954 - 0.816091i) q^{90} +(-1.14764 - 7.01713i) q^{91} +(17.0434 - 5.40664i) q^{92} +(1.65211 - 0.778834i) q^{93} +(-1.30903 + 12.0503i) q^{94} +(-0.557755 - 0.322020i) q^{95} +(-5.72566 + 7.95090i) q^{96} +(9.56123 + 5.52018i) q^{97} +(-2.12191 - 9.66941i) q^{98} +(2.16769 + 5.80388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

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