LMFDB - Embedded newform 504.2.bf.b.115.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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([3, 3, 4, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bf (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:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.20
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14308 + 0.832691i) q^{2} +(-1.17641 + 1.27125i) q^{3} +(0.613252 - 1.90366i) q^{4} +(-1.57644 + 2.73047i) q^{5} +(0.286170 - 2.43272i) q^{6} +(-1.25267 - 2.33041i) q^{7} +(0.884165 + 2.68668i) q^{8} +(-0.232133 - 2.99101i) q^{9} +O(q^{10})$	\(q+(-1.14308 + 0.832691i) q^{2} +(-1.17641 + 1.27125i) q^{3} +(0.613252 - 1.90366i) q^{4} +(-1.57644 + 2.73047i) q^{5} +(0.286170 - 2.43272i) q^{6} +(-1.25267 - 2.33041i) q^{7} +(0.884165 + 2.68668i) q^{8} +(-0.232133 - 2.99101i) q^{9} +(-0.471646 - 4.43382i) q^{10} +(-0.814620 - 1.41096i) q^{11} +(1.69859 + 3.01907i) q^{12} +(0.0400258 + 0.0693267i) q^{13} +(3.37241 + 1.62075i) q^{14} +(-1.61656 - 5.21618i) q^{15} +(-3.24784 - 2.33485i) q^{16} +(-1.13969 - 0.658003i) q^{17} +(2.75593 + 3.22566i) q^{18} +(3.49599 - 2.01841i) q^{19} +(4.23113 + 4.67546i) q^{20} +(4.43618 + 1.14905i) q^{21} +(2.10607 + 0.934513i) q^{22} +(-3.67953 - 2.12438i) q^{23} +(-4.45557 - 2.03664i) q^{24} +(-2.47030 - 4.27868i) q^{25} +(-0.103480 - 0.0459167i) q^{26} +(4.07539 + 3.22354i) q^{27} +(-5.20451 + 0.955536i) q^{28} +(3.48772 + 2.01364i) q^{29} +(6.19132 + 4.61640i) q^{30} +3.97549 q^{31} +(5.65674 - 0.0355381i) q^{32} +(2.75200 + 0.624284i) q^{33} +(1.85067 - 0.196865i) q^{34} +(8.33787 + 0.253358i) q^{35} +(-5.83621 - 1.39234i) q^{36} +(-9.45599 + 5.45942i) q^{37} +(-2.31548 + 5.21829i) q^{38} +(-0.135218 - 0.0306738i) q^{39} +(-8.72972 - 1.82119i) q^{40} +(10.5992 - 6.11948i) q^{41} +(-6.02770 + 2.38051i) q^{42} +(5.79819 - 10.0428i) q^{43} +(-3.18556 + 0.685483i) q^{44} +(8.53278 + 4.08130i) q^{45} +(5.97494 - 0.635583i) q^{46} +0.848906 q^{47} +(6.78895 - 1.38208i) q^{48} +(-3.86162 + 5.83848i) q^{49} +(6.38656 + 2.83387i) q^{50} +(2.17723 - 0.674752i) q^{51} +(0.156520 - 0.0336808i) q^{52} +(-4.62915 - 2.67264i) q^{53} +(-7.34270 - 0.291223i) q^{54} +5.13678 q^{55} +(5.15350 - 5.42600i) q^{56} +(-1.54681 + 6.81875i) q^{57} +(-5.66347 + 0.602450i) q^{58} -4.33850i q^{59} +(-10.9212 - 0.121443i) q^{60} +5.27660 q^{61} +(-4.54429 + 3.31035i) q^{62} +(-6.67948 + 4.28772i) q^{63} +(-6.43650 + 4.75094i) q^{64} -0.252392 q^{65} +(-3.66559 + 1.57796i) q^{66} +6.21333 q^{67} +(-1.95153 + 1.76607i) q^{68} +(7.02924 - 2.17846i) q^{69} +(-9.74179 + 6.65326i) q^{70} -4.99349i q^{71} +(7.83063 - 3.26821i) q^{72} +(7.72355 + 4.45919i) q^{73} +(6.26292 - 14.1145i) q^{74} +(8.34534 + 1.89312i) q^{75} +(-1.69845 - 7.89298i) q^{76} +(-2.26767 + 3.66587i) q^{77} +(0.180106 - 0.0775322i) q^{78} -14.5396i q^{79} +(11.4952 - 5.18739i) q^{80} +(-8.89223 + 1.38862i) q^{81} +(-7.02012 + 15.8209i) q^{82} +(-2.34461 - 1.35366i) q^{83} +(4.90790 - 7.74031i) q^{84} +(3.59331 - 2.07460i) q^{85} +(1.73473 + 16.3077i) q^{86} +(-6.66280 + 2.06489i) q^{87} +(3.07055 - 3.43615i) q^{88} +(-5.04396 + 2.91213i) q^{89} +(-13.1521 + 2.43993i) q^{90} +(0.111420 - 0.180120i) q^{91} +(-6.30058 + 5.70180i) q^{92} +(-4.67679 + 5.05382i) q^{93} +(-0.970365 + 0.706876i) q^{94} +12.7276i q^{95} +(-6.60945 + 7.23292i) q^{96} +(-15.1154 - 8.72685i) q^{97} +(-0.447524 - 9.88937i) q^{98} +(-4.03110 + 2.76406i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.14308	+	0.832691i	−0.808278	+	0.588801i
$2$	−1.14308	+	0.832691i	−0.808278	+	0.588801i
$3$	−1.17641	+	1.27125i	−0.679199	+	0.733954i
$3$	−1.17641	+	1.27125i	−0.679199	+	0.733954i
$4$	0.613252	−	1.90366i	0.306626	−	0.951830i
$5$	−1.57644	+	2.73047i	−0.705003	+	1.22110i	0.261687	+	0.965153i	$0.415721\pi$
$5$	−1.57644	+	2.73047i	−0.705003	+	1.22110i	−0.966690	+	0.255949i	$0.917612\pi$
$6$	0.286170	−	2.43272i	0.116828	−	0.993152i
$7$	−1.25267	−	2.33041i	−0.473466	−	0.880812i
$7$	−1.25267	−	2.33041i	−0.473466	−	0.880812i
$8$	0.884165	+	2.68668i	0.312600	+	0.949885i
$9$	−0.232133	−	2.99101i	−0.0773775	−	0.997002i
$10$	−0.471646	−	4.43382i	−0.149148	−	1.40210i
$11$	−0.814620	−	1.41096i	−0.245617	−	0.425421i	0.716688	−	0.697394i	$-0.245657\pi$
$11$	−0.814620	−	1.41096i	−0.245617	−	0.425421i	−0.962305	+	0.271973i	$0.912324\pi$
$12$	1.69859	+	3.01907i	0.490340	+	0.871531i
$13$	0.0400258	+	0.0693267i	0.0111012	+	0.0192278i	0.871523	−	0.490355i	$-0.163133\pi$
$13$	0.0400258	+	0.0693267i	0.0111012	+	0.0192278i	−0.860421	+	0.509583i	$0.829800\pi$
$14$	3.37241	+	1.62075i	0.901315	+	0.433163i
$15$	−1.61656	−	5.21618i	−0.417395	−	1.34681i
$16$	−3.24784	−	2.33485i	−0.811961	−	0.583712i
$17$	−1.13969	−	0.658003i	−0.276416	−	0.159589i	0.355384	−	0.934721i	$-0.384350\pi$
$17$	−1.13969	−	0.658003i	−0.276416	−	0.159589i	−0.631800	+	0.775131i	$0.717684\pi$
$18$	2.75593	+	3.22566i	0.649579	+	0.760295i
$19$	3.49599	−	2.01841i	0.802036	−	0.463056i	−0.0421465	−	0.999111i	$-0.513420\pi$
$19$	3.49599	−	2.01841i	0.802036	−	0.463056i	0.844183	+	0.536056i	$0.180086\pi$
$20$	4.23113	+	4.67546i	0.946109	+	1.04547i
$21$	4.43618	+	1.14905i	0.968053	+	0.250744i
$22$	2.10607	+	0.934513i	0.449015	+	0.199239i
$23$	−3.67953	−	2.12438i	−0.767236	−	0.442964i	0.0646518	−	0.997908i	$-0.479406\pi$
$23$	−3.67953	−	2.12438i	−0.767236	−	0.442964i	−0.831888	+	0.554944i	$0.812740\pi$
$24$	−4.45557	−	2.03664i	−0.909489	−	0.415727i
$25$	−2.47030	−	4.27868i	−0.494060	−	0.855737i
$26$	−0.103480	−	0.0459167i	−0.0202942	−	0.00900501i
$27$	4.07539	+	3.22354i	0.784308	+	0.620371i
$28$	−5.20451	+	0.955536i	−0.983560	+	0.180579i
$29$	3.48772	+	2.01364i	0.647653	+	0.373923i	0.787556	−	0.616242i	$-0.211346\pi$
$29$	3.48772	+	2.01364i	0.647653	+	0.373923i	−0.139903	+	0.990165i	$0.544679\pi$
$30$	6.19132	+	4.61640i	1.13038	+	0.842835i
$31$	3.97549			0.714019			0.357009	−	0.934101i	$-0.383796\pi$
$31$	3.97549			0.714019			0.357009	+	0.934101i	$0.383796\pi$
$32$	5.65674	−	0.0355381i	0.999980	−	0.00628230i
$33$	2.75200	+	0.624284i	0.479062	+	0.108674i
$34$	1.85067	−	0.196865i	0.317387	−	0.0337620i
$35$	8.33787	+	0.253358i	1.40936	+	0.0428252i
$36$	−5.83621	−	1.39234i	−0.972702	−	0.232057i
$37$	−9.45599	+	5.45942i	−1.55456	+	0.897523i	−0.556794	+	0.830650i	$0.687969\pi$
$37$	−9.45599	+	5.45942i	−1.55456	+	0.897523i	−0.997762	+	0.0668728i	$0.978698\pi$
$38$	−2.31548	+	5.21829i	−0.375620	+	0.846518i
$39$	−0.135218	−	0.0306738i	−0.0216522	−	0.00491174i
$40$	−8.72972	−	1.82119i	−1.38029	−	0.287956i
$41$	10.5992	−	6.11948i	1.65532	−	0.955701i	0.680493	−	0.732755i	$-0.261766\pi$
$41$	10.5992	−	6.11948i	1.65532	−	0.955701i	0.974831	−	0.222947i	$-0.0715676\pi$
$42$	−6.02770	+	2.38051i	−0.930095	+	0.367320i
$43$	5.79819	−	10.0428i	0.884215	−	1.53151i	0.0376048	−	0.999293i	$-0.488027\pi$
$43$	5.79819	−	10.0428i	0.884215	−	1.53151i	0.846610	−	0.532213i	$-0.178639\pi$
$44$	−3.18556	+	0.685483i	−0.480241	+	0.103340i
$45$	8.53278	+	4.08130i	1.27199	+	0.608404i
$46$	5.97494	−	0.635583i	0.880957	−	0.0937116i
$47$	0.848906			0.123826			0.0619128	−	0.998082i	$-0.480280\pi$
$47$	0.848906			0.123826			0.0619128	+	0.998082i	$0.480280\pi$
$48$	6.78895	−	1.38208i	0.979901	−	0.199486i
$49$	−3.86162	+	5.83848i	−0.551660	+	0.834069i
$50$	6.38656	+	2.83387i	0.903196	+	0.400770i
$51$	2.17723	−	0.674752i	0.304873	−	0.0944842i
$52$	0.156520	−	0.0336808i	0.0217055	−	0.00467068i
$53$	−4.62915	−	2.67264i	−0.635862	−	0.367115i	0.147157	−	0.989113i	$-0.452988\pi$
$53$	−4.62915	−	2.67264i	−0.635862	−	0.367115i	−0.783019	+	0.621998i	$0.786321\pi$
$54$	−7.34270	−	0.291223i	−0.999214	−	0.0396304i
$55$	5.13678			0.692643
$56$	5.15350	−	5.42600i	0.688665	−	0.725080i
$57$	−1.54681	+	6.81875i	−0.204880	+	0.903165i
$58$	−5.66347	+	0.602450i	−0.743650	+	0.0791056i
$59$		−	4.33850i		−	0.564825i	−0.959293	−	0.282412i	$-0.908865\pi$
$59$		−	4.33850i		−	0.564825i	0.959293	−	0.282412i	$-0.0911347\pi$
$60$	−10.9212	−	0.121443i	−1.40992	−	0.0156782i
$61$	5.27660			0.675600			0.337800	−	0.941218i	$-0.390317\pi$
$61$	5.27660			0.675600			0.337800	+	0.941218i	$0.390317\pi$
$62$	−4.54429	+	3.31035i	−0.577125	+	0.420415i
$63$	−6.67948	+	4.28772i	−0.841536	+	0.540202i
$64$	−6.43650	+	4.75094i	−0.804563	+	0.593868i
$65$	−0.252392			−0.0313054
$66$	−3.66559	+	1.57796i	−0.451203	+	0.194234i
$67$	6.21333			0.759079			0.379539	−	0.925176i	$-0.376082\pi$
$67$	6.21333			0.759079			0.379539	+	0.925176i	$0.376082\pi$
$68$	−1.95153	+	1.76607i	−0.236658	+	0.214167i
$69$	7.02924	−	2.17846i	0.846221	−	0.262255i
$70$	−9.74179	+	6.65326i	−1.16437	+	0.795216i
$71$		−	4.99349i		−	0.592619i	−0.955092	−	0.296309i	$-0.904244\pi$
$71$		−	4.99349i		−	0.592619i	0.955092	−	0.296309i	$-0.0957559\pi$
$72$	7.83063	−	3.26821i	0.922849	−	0.385162i
$73$	7.72355	+	4.45919i	0.903973	+	0.521909i	0.878487	−	0.477766i	$-0.158553\pi$
$73$	7.72355	+	4.45919i	0.903973	+	0.521909i	0.0254859	+	0.999675i	$0.491887\pi$
$74$	6.26292	−	14.1145i	0.728050	−	1.64077i
$75$	8.34534	+	1.89312i	0.963636	+	0.218598i
$76$	−1.69845	−	7.89298i	−0.194825	−	0.905387i
$77$	−2.26767	+	3.66587i	−0.258425	+	0.417765i
$78$	0.180106	−	0.0775322i	0.0203930	−	0.00877879i
$79$		−	14.5396i		−	1.63583i	−0.575340	−	0.817914i	$-0.695130\pi$
$79$		−	14.5396i		−	1.63583i	0.575340	−	0.817914i	$-0.304870\pi$
$80$	11.4952	−	5.18739i	1.28521	−	0.579968i
$81$	−8.89223	+	1.38862i	−0.988025	+	0.154291i
$82$	−7.02012	+	15.8209i	−0.775243	+	1.74713i
$83$	−2.34461	−	1.35366i	−0.257355	−	0.148584i	0.365773	−	0.930704i	$-0.380805\pi$
$83$	−2.34461	−	1.35366i	−0.257355	−	0.148584i	−0.623127	+	0.782120i	$0.714138\pi$
$84$	4.90790	−	7.74031i	0.535496	−	0.844538i
$85$	3.59331	−	2.07460i	0.389749	−	0.225022i
$86$	1.73473	+	16.3077i	0.187061	+	1.75851i
$87$	−6.66280	+	2.06489i	−0.714327	+	0.221380i
$88$	3.07055	−	3.43615i	0.327321	−	0.366294i
$89$	−5.04396	+	2.91213i	−0.534659	+	0.308685i	−0.742912	−	0.669390i	$-0.766556\pi$
$89$	−5.04396	+	2.91213i	−0.534659	+	0.308685i	0.208253	+	0.978075i	$0.433222\pi$
$90$	−13.1521	+	2.43993i	−1.38635	+	0.257191i
$91$	0.111420	−	0.180120i	0.0116800	−	0.0188817i
$92$	−6.30058	+	5.70180i	−0.656881	+	0.594454i
$93$	−4.67679	+	5.05382i	−0.484961	+	0.524057i
$94$	−0.970365	+	0.706876i	−0.100086	+	0.0729087i
$95$			12.7276i			1.30582i
$96$	−6.60945	+	7.23292i	−0.674575	+	0.738207i
$97$	−15.1154	−	8.72685i	−1.53473	−	0.886078i	−0.999134	−	0.0416045i	$-0.986753\pi$
$97$	−15.1154	−	8.72685i	−1.53473	−	0.886078i	−0.535598	−	0.844473i	$-0.679914\pi$
$98$	−0.447524	−	9.88937i	−0.0452067	−	0.998978i
$99$	−4.03110	+	2.76406i	−0.405140	+	0.277799i
$100$	−9.66008	+	2.07870i	−0.966008	+	0.207870i
$101$	−3.10321	−	5.37492i	−0.308781	−	0.534825i	0.669315	−	0.742979i	$-0.266588\pi$
$101$	−3.10321	−	5.37492i	−0.308781	−	0.534825i	−0.978096	+	0.208154i	$0.933254\pi$
$102$	−1.92688	+	2.58425i	−0.190789	+	0.255879i
$103$	−2.44406	+	4.23323i	−0.240820	+	0.417112i	−0.960948	−	0.276729i	$-0.910750\pi$
$103$	−2.44406	+	4.23323i	−0.240820	+	0.417112i	0.720128	+	0.693841i	$0.244083\pi$
$104$	−0.150869	+	0.168833i	−0.0147940	+	0.0165554i
$105$	−10.1308	+	10.3014i	−0.988665	+	1.00532i
$106$	7.51696	−	0.799614i	0.730111	−	0.0776654i
$107$	−6.31512	−	10.9381i	−0.610505	−	1.05743i	−0.991155	−	0.132707i	$-0.957633\pi$
$107$	−6.31512	−	10.9381i	−0.610505	−	1.05743i	0.380650	−	0.924719i	$-0.375700\pi$
$108$	8.63577	−	5.78131i	0.830977	−	0.556306i
$109$	−9.99835	−	5.77255i	−0.957668	−	0.552910i	−0.0622137	−	0.998063i	$-0.519816\pi$
$109$	−9.99835	−	5.77255i	−0.957668	−	0.552910i	−0.895455	+	0.445153i	$0.853149\pi$
$110$	−5.87174	+	4.27735i	−0.559848	+	0.407829i
$111$	4.18383	−	18.4434i	0.397112	−	1.75057i
$112$	−1.37266	+	10.4936i	−0.129704	+	0.991553i
$113$	2.58894	+	4.48417i	0.243547	+	0.421835i	0.961722	−	0.274027i	$-0.0883558\pi$
$113$	2.58894	+	4.48417i	0.243547	+	0.421835i	−0.718175	+	0.695862i	$0.755022\pi$
$114$	−3.90978	−	9.08237i	−0.366184	−	0.850642i
$115$	11.6011	−	6.69790i	1.08181	−	0.624582i
$116$	5.97213	−	5.40456i	0.554498	−	0.501801i
$117$	0.198065	−	0.135810i	0.0183111	−	0.0125557i
$118$	3.61263	+	4.95924i	0.332570	+	0.456535i
$119$	−0.105751	+	3.48022i	−0.00969420	+	0.319031i
$120$	12.5849	−	8.95516i	1.14884	−	0.817490i
$121$	4.17279	−	7.22748i	0.379345	−	0.657044i
$122$	−6.03157	+	4.39378i	−0.546072	+	0.397794i
$123$	−4.68967	+	20.6732i	−0.422853	+	1.86404i
$124$	2.43798	−	7.56798i	0.218937	−	0.679624i
$125$	−0.187286			−0.0167514
$126$	4.06482	−	10.4631i	0.362123	−	0.932130i
$127$		−	19.1471i		−	1.69903i	−0.527562	−	0.849516i	$-0.676894\pi$
$127$		−	19.1471i		−	1.69903i	0.527562	−	0.849516i	$-0.323106\pi$
$128$	3.40136	−	10.7903i	0.300640	−	0.953738i
$129$	5.94578	+	19.1853i	0.523497	+	1.68917i
$130$	0.288504	−	0.210165i	0.0253035	−	0.0184327i
$131$	−16.2141	−	9.36123i	−1.41663	−	0.817894i	−0.420633	−	0.907231i	$-0.638192\pi$
$131$	−16.2141	−	9.36123i	−1.41663	−	0.817894i	−0.996001	+	0.0893370i	$0.971525\pi$
$132$	2.87610	−	4.85604i	0.250332	−	0.422664i
$133$	−9.08307	−	5.61869i	−0.787602	−	0.487202i
$134$	−7.10231	+	5.17378i	−0.613546	+	0.446947i
$135$	−15.2264	+	6.04600i	−1.31048	+	0.520357i
$136$	0.760165	−	3.64378i	0.0651836	−	0.312451i
$137$	−3.47619	−	6.02094i	−0.296991	−	0.514404i	0.678455	−	0.734642i	$-0.262650\pi$
$137$	−3.47619	−	6.02094i	−0.296991	−	0.514404i	−0.975446	+	0.220238i	$0.929317\pi$
$138$	−6.22098	+	8.34333i	−0.529565	+	0.710231i
$139$	−11.7683	+	6.79440i	−0.998170	+	0.576294i	−0.907706	−	0.419606i	$-0.862168\pi$
$139$	−11.7683	+	6.79440i	−0.998170	+	0.576294i	−0.0904638	+	0.995900i	$0.528835\pi$
$140$	5.59552	−	15.7171i	0.472908	−	1.32834i
$141$	−0.998659	+	1.07917i	−0.0841023	+	0.0908824i
$142$	4.15804	+	5.70795i	0.348935	+	0.479000i
$143$	0.0652116	−	0.112950i	0.00545327	−	0.00944534i
$144$	−6.22961	+	10.2563i	−0.519134	+	0.854693i
$145$	−10.9963	+	6.34873i	−0.913195	+	0.527234i
$146$	−12.5417	+	1.33412i	−1.03796	+	0.110413i
$147$	−2.87932	−	11.7775i	−0.237482	−	0.971392i
$148$	4.59397	+	21.3490i	0.377622	+	1.75488i
$149$	−0.262277	−	0.151426i	−0.0214866	−	0.0124053i	0.489218	−	0.872161i	$-0.337282\pi$
$149$	−0.262277	−	0.151426i	−0.0214866	−	0.0124053i	−0.510705	+	0.859756i	$0.670615\pi$
$150$	−11.1157	+	4.78511i	−0.907597	+	0.390702i
$151$	2.63797	−	1.52303i	0.214675	−	0.123943i	−0.388807	−	0.921319i	$-0.627113\pi$
$151$	2.63797	−	1.52303i	0.214675	−	0.123943i	0.603482	+	0.797377i	$0.293779\pi$
$152$	8.51387	+	7.60801i	0.690566	+	0.617091i
$153$	−1.70353	+	3.56157i	−0.137722	+	0.287936i
$154$	−0.460418	−	6.07864i	−0.0371015	−	0.489831i
$155$	−6.26710	+	10.8549i	−0.503386	+	0.871889i
$156$	−0.141315	+	0.238598i	−0.0113143	+	0.0191031i
$157$	12.1464			0.969388			0.484694	−	0.874684i	$-0.338931\pi$
$157$	12.1464			0.969388			0.484694	+	0.874684i	$0.338931\pi$
$158$	12.1070	+	16.6198i	0.963178	+	1.32220i
$159$	8.84334	−	2.74067i	0.701323	−	0.217349i
$160$	−8.82046	+	15.5016i	−0.697318	+	1.22551i
$161$	−0.341421	+	11.2360i	−0.0269077	+	0.885519i
$162$	9.00822	−	8.99178i	0.707752	−	0.706461i
$163$	7.33302	+	12.7012i	0.574367	+	0.994832i	0.996110	+	0.0881170i	$0.0280849\pi$
$163$	7.33302	+	12.7012i	0.574367	+	0.994832i	−0.421743	+	0.906715i	$0.638582\pi$
$164$	−5.14939	−	23.9301i	−0.402100	−	1.86863i
$165$	−6.04295	+	6.53011i	−0.470443	+	0.508369i
$166$	3.80726	−	0.404996i	0.295500	−	0.0314338i
$167$	−0.0238525	−	0.0413137i	−0.00184576	−	0.00319695i	0.865101	−	0.501598i	$-0.167254\pi$
$167$	−0.0238525	−	0.0413137i	−0.00184576	−	0.00319695i	−0.866947	+	0.498401i	$0.833921\pi$
$168$	0.835174	+	12.9345i	0.0644350	+	0.997922i
$169$	6.49680	−	11.2528i	0.499754	−	0.865599i
$170$	−2.37993	+	5.36354i	−0.182532	+	0.411365i
$171$	−6.84862	−	9.98800i	−0.523727	−	0.763801i
$172$	−15.5622	−	17.1965i	−1.18661	−	1.31122i
$173$	21.5196			1.63611			0.818053	−	0.575142i	$-0.195053\pi$
$173$	21.5196			1.63611			0.818053	+	0.575142i	$0.195053\pi$
$174$	5.89668	−	7.90839i	0.447026	−	0.599533i
$175$	−6.87661	+	11.1166i	−0.519823	+	0.840336i
$176$	−0.648625	+	6.48460i	−0.0488919	+	0.488795i
$177$	5.51530	+	5.10385i	0.414556	+	0.383629i
$178$	3.34073	−	7.52885i	0.250399	−	0.564311i
$179$	−8.05382	+	13.9496i	−0.601971	+	1.04264i	0.390551	+	0.920581i	$0.372284\pi$
$179$	−8.05382	+	13.9496i	−0.601971	+	1.04264i	−0.992522	+	0.122063i	$0.961049\pi$
$180$	13.0022	−	13.7407i	0.969123	−	1.02417i
$181$	17.3344			1.28846			0.644230	−	0.764832i	$-0.277178\pi$
$181$	17.3344			1.28846			0.644230	+	0.764832i	$0.277178\pi$
$182$	0.0226223	+	0.298670i	0.00167688	+	0.0221389i
$183$	−6.20743	+	6.70786i	−0.458867	+	0.495859i
$184$	2.45421	−	11.7640i	0.180927	−	0.867256i
$185$		−	34.4257i		−	2.53103i
$186$	1.13766	−	9.67123i	0.0834176	−	0.709129i
$187$			2.14409i			0.156791i
$188$	0.520594	−	1.61603i	0.0379682	−	0.117861i
$189$	2.40705	−	13.5354i	0.175087	−	0.984553i
$190$	−10.5982	−	14.5486i	−0.768871	−	1.05547i
$191$			2.28810i			0.165561i	0.996568	+	0.0827807i	$0.0263801\pi$
$191$			2.28810i			0.165561i	−0.996568	+	0.0827807i	$0.973620\pi$
$192$	1.53233	−	13.7714i	0.110587	−	0.993866i
$193$	22.8602			1.64552			0.822758	−	0.568392i	$-0.192434\pi$
$193$	22.8602			1.64552			0.822758	+	0.568392i	$0.192434\pi$
$194$	24.5448	−	2.61095i	1.76221	−	0.187455i
$195$	0.296916	−	0.320853i	0.0212626	−	0.0229767i
$196$	8.74635	+	10.9317i	0.624739	+	0.780834i
$197$			10.0173i			0.713700i	0.934162	+	0.356850i	$0.116149\pi$
$197$			10.0173i			0.713700i	−0.934162	+	0.356850i	$0.883851\pi$
$198$	2.30625	−	6.51619i	0.163898	−	0.463086i
$199$	−4.29226	+	7.43441i	−0.304270	+	0.527011i	−0.977099	−	0.212787i	$-0.931746\pi$
$199$	−4.29226	+	7.43441i	−0.304270	+	0.527011i	0.672829	+	0.739798i	$0.265079\pi$
$200$	9.31130	−	10.4200i	0.658408	−	0.736803i
$201$	−7.30940	+	7.89867i	−0.515565	+	0.557129i
$202$	8.02286	+	3.55994i	0.564486	+	0.250476i
$203$	0.323622	−	10.6502i	0.0227138	−	0.747500i
$204$	0.0506902	−	4.55849i	0.00354902	−	0.319158i
$205$			38.5878i			2.69509i
$206$	−0.731226	−	6.87405i	−0.0509469	−	0.478938i
$207$	−5.49989	+	11.4986i	−0.382269	+	0.799211i
$208$	0.0318698	−	0.318616i	0.00220977	−	0.0220921i
$209$	−5.69581	−	3.28848i	−0.393987	−	0.227469i
$210$	3.00239	−	20.2112i	0.207185	−	1.39470i
$211$	−2.83896	−	4.91723i	−0.195442	−	0.338516i	0.751603	−	0.659616i	$-0.229281\pi$
$211$	−2.83896	−	4.91723i	−0.195442	−	0.338516i	−0.947045	+	0.321100i	$0.895948\pi$
$212$	−7.92663	+	7.17332i	−0.544403	+	0.492666i
$213$	6.34796	+	5.87438i	0.434955	+	0.402506i
$214$	16.3267	+	7.24456i	1.11607	+	0.495228i
$215$	18.2809	+	31.6635i	1.24675	+	2.15943i
$216$	−5.05731	+	13.7994i	−0.344107	+	0.938931i
$217$	−4.97999	−	9.26451i	−0.338064	−	0.628916i
$218$	16.2356	−	1.72706i	1.09962	−	0.116971i
$219$	−14.7548	+	4.57270i	−0.997035	+	0.308995i
$220$	3.15014	−	9.77869i	0.212383	−	0.659279i
$221$		−	0.105348i		−	0.00708650i
$222$	10.5752	+	24.5661i	0.709761	+	1.64877i
$223$	6.85163	−	11.8674i	0.458819	−	0.794698i	−0.540080	−	0.841614i	$-0.681606\pi$
$223$	6.85163	−	11.8674i	0.458819	−	0.794698i	0.998899	+	0.0469158i	$0.0149393\pi$
$224$	−7.16887	−	13.1380i	−0.478990	−	0.877820i
$225$	−12.2241	+	8.38190i	−0.814942	+	0.558793i
$226$	−6.69328	−	2.96997i	−0.445230	−	0.197559i
$227$	−11.4038	+	6.58401i	−0.756899	+	0.436996i	−0.828181	−	0.560460i	$-0.810624\pi$
$227$	−11.4038	+	6.58401i	−0.756899	+	0.436996i	0.0712822	+	0.997456i	$0.477291\pi$
$228$	12.0320	+	7.12622i	0.796838	+	0.471945i
$229$	−2.44088	+	4.22773i	−0.161298	+	0.279376i	−0.935334	−	0.353765i	$-0.884901\pi$
$229$	−2.44088	+	4.22773i	−0.161298	+	0.279376i	0.774037	+	0.633141i	$0.218235\pi$
$230$	−7.68368	+	17.3163i	−0.506647	+	1.14181i
$231$	−1.99252	−	7.19532i	−0.131098	−	0.473417i
$232$	−2.32627	+	11.1508i	−0.152727	+	0.732084i
$233$	1.93359	+	3.34907i	0.126674	+	0.219405i	0.922386	−	0.386270i	$-0.126237\pi$
$233$	1.93359	+	3.34907i	0.126674	+	0.219405i	−0.795712	+	0.605675i	$0.792903\pi$
$234$	−0.113316	+	0.320169i	−0.00740770	+	0.0209301i
$235$	−1.33825	+	2.31791i	−0.0872975	+	0.151204i
$236$	−8.25903	−	2.66060i	−0.537617	−	0.173190i
$237$	18.4834	+	17.1044i	1.20062	+	1.11105i
$238$	−2.77706	−	4.06621i	−0.180010	−	0.263574i
$239$	21.4576	−	12.3886i	1.38798	−	0.801350i	0.394892	−	0.918727i	$-0.370782\pi$
$239$	21.4576	−	12.3886i	1.38798	−	0.801350i	0.993087	+	0.117377i	$0.0374486\pi$
$240$	−6.92863	+	20.7158i	−0.447241	+	1.33720i
$241$	−0.753227	+	0.434876i	−0.0485196	+	0.0280128i	−0.524064	−	0.851679i	$-0.675585\pi$
$241$	−0.753227	+	0.434876i	−0.0485196	+	0.0280128i	0.475544	+	0.879692i	$0.342251\pi$
$242$	1.24844	+	11.7362i	0.0802526	+	0.754433i
$243$	8.69561	−	12.9378i	0.557823	−	0.829960i
$244$	3.23589	−	10.0449i	0.207157	−	0.643056i
$245$	−9.85420	−	19.7480i	−0.629562	−	1.26165i
$246$	−11.8538	−	27.5362i	−0.755768	−	1.75564i
$247$	0.279860	+	0.161577i	0.0178071	+	0.0102809i
$248$	3.51499	+	10.6809i	0.223202	+	0.678236i
$249$	4.47906	−	1.38812i	0.283849	−	0.0879686i
$250$	0.214082	−	0.155951i	0.0135398	−	0.00986322i
$251$		−	6.29865i		−	0.397567i	−0.980043	−	0.198784i	$-0.936301\pi$
$251$		−	6.29865i		−	0.397567i	0.980043	−	0.198784i	$-0.0636991\pi$
$252$	4.06615	+	15.3449i	0.256143	+	0.966639i
$253$			6.92225i			0.435198i
$254$	15.9436	+	21.8866i	1.00039	+	1.37329i
$255$	−1.58987	+	7.00855i	−0.0995615	+	0.438892i
$256$	5.09698	+	15.1664i	0.318561	+	0.947902i
$257$	−6.58189	−	3.80005i	−0.410567	−	0.237041i	0.280466	−	0.959864i	$-0.409511\pi$
$257$	−6.58189	−	3.80005i	−0.410567	−	0.237041i	−0.691033	+	0.722823i	$0.742844\pi$
$258$	−22.7719	−	16.9793i	−1.41772	−	1.05708i
$259$	24.5680	+	15.1975i	1.52658	+	0.944325i
$260$	−0.154780	+	0.480469i	−0.00959906	+	0.0297974i
$261$	5.21318	−	10.8992i	0.322688	−	0.674645i
$262$	26.3290	−	2.80074i	1.62661	−	0.173030i
$263$	−23.1028	+	13.3384i	−1.42458	+	0.822480i	−0.996686	−	0.0813497i	$-0.974077\pi$
$263$	−23.1028	+	13.3384i	−1.42458	+	0.822480i	−0.427892	+	0.903830i	$0.640744\pi$
$264$	0.755975	+	7.94573i	0.0465270	+	0.489026i
$265$	14.5951	−	8.42649i	0.896570	−	0.517635i
$266$	15.0613	−	1.14079i	0.923466	−	0.0699466i
$267$	2.23172	−	9.83797i	0.136579	−	0.602074i
$268$	3.81034	−	11.8281i	0.232753	−	0.722514i
$269$	3.84940	−	6.66735i	0.234702	−	0.406516i	−0.724484	−	0.689292i	$-0.757922\pi$
$269$	3.84940	−	6.66735i	0.234702	−	0.406516i	0.959186	+	0.282776i	$0.0912552\pi$
$270$	12.3705	−	19.5899i	0.752842	−	1.19220i
$271$	−3.10958	−	5.38595i	−0.188894	−	0.327173i	0.755988	−	0.654585i	$-0.227157\pi$
$271$	−3.10958	−	5.38595i	−0.188894	−	0.327173i	−0.944882	+	0.327412i	$0.893823\pi$
$272$	2.16521	+	4.79810i	0.131285	+	0.290928i
$273$	0.0979014	+	0.353537i	0.00592526	+	0.0213971i
$274$	8.98714	+	3.98781i	0.542933	+	0.240912i
$275$	−4.02471	+	6.97100i	−0.242699	+	0.420367i
$276$	0.163655	−	14.7172i	0.00985085	−	0.885873i
$277$	−3.08529	+	1.78129i	−0.185377	+	0.107028i	−0.589817	−	0.807537i	$-0.700800\pi$
$277$	−3.08529	+	1.78129i	−0.185377	+	0.107028i	0.404439	+	0.914565i	$0.367467\pi$
$278$	7.79439	−	17.5658i	0.467476	−	1.05353i
$279$	−0.922840	−	11.8907i	−0.0552490	−	0.711878i
$280$	6.69136	+	22.6252i	0.399885	+	1.35211i
$281$	−6.37653	+	11.0445i	−0.380392	+	0.658858i	−0.991118	−	0.132983i	$-0.957544\pi$
$281$	−6.37653	+	11.0445i	−0.380392	+	0.658858i	0.610726	+	0.791842i	$0.290878\pi$
$282$	0.242931	−	2.06515i	0.0144663	−	0.122978i
$283$			26.8312i			1.59495i	0.603352	+	0.797475i	$0.293832\pi$
$283$			26.8312i			1.59495i	−0.603352	+	0.797475i	$0.706168\pi$
$284$	−9.50591	−	3.06227i	−0.564072	−	0.181712i
$285$	−16.1799	−	14.9728i	−0.958415	−	0.886914i
$286$	0.0195103	+	0.183411i	0.00115367	+	0.0108453i
$287$	−27.5383	−	17.0349i	−1.62553	−	1.00554i
$288$	−1.41941	−	16.9111i	−0.0836394	−	0.996496i
$289$	−7.63407	−	13.2226i	−0.449063	−	0.777799i
$290$	7.28312	−	16.4136i	0.427680	−	0.963842i
$291$	28.8758	−	8.94900i	1.69273	−	0.524600i
$292$	13.2253	−	11.9684i	0.773950	−	0.700398i
$293$	−16.2805	−	28.1986i	−0.951116	−	1.64738i	−0.743016	−	0.669274i	$-0.766605\pi$
$293$	−16.2805	−	28.1986i	−0.951116	−	1.64738i	−0.208100	−	0.978108i	$-0.566728\pi$
$294$	13.0983	+	11.0650i	0.763908	+	0.645325i
$295$	11.8461	+	6.83937i	0.689709	+	0.398204i
$296$	−23.0284	−	20.5782i	−1.33850	−	1.19608i
$297$	1.22841	−	8.37618i	0.0712795	−	0.486035i
$298$	0.425894	−	0.0453044i	0.0246714	−	0.00262441i
$299$		−	0.340120i		−	0.0196697i
$300$	8.72165	−	14.7257i	0.503544	−	0.850190i
$301$	−30.6670	−	0.931858i	−1.76761	−	0.0537114i
$302$	−1.74719	+	3.93755i	−0.100539	+	0.226581i
$303$	10.4835	+	2.37815i	0.602261	+	0.136621i
$304$	−16.0671	−	1.60712i	−0.921513	−	0.0921748i
$305$	−8.31823	+	14.4076i	−0.476300	+	0.824976i
$306$	−1.01842	−	5.48967i	−0.0582194	−	0.313824i
$307$			8.23130i			0.469785i	0.972021	+	0.234892i	$0.0754738\pi$
$307$			8.23130i			0.469785i	−0.972021	+	0.234892i	$0.924526\pi$
$308$	5.58792	+	6.56497i	0.318401	+	0.374074i
$309$	−2.50627	−	8.08700i	−0.142577	−	0.460053i
$310$	−1.87502	−	17.6266i	−0.106494	−	1.00112i
$311$	4.97975			0.282376			0.141188	−	0.989983i	$-0.454908\pi$
$311$	4.97975			0.282376			0.141188	+	0.989983i	$0.454908\pi$
$312$	−0.0371443	−	0.390408i	−0.00210288	−	0.0221025i
$313$			15.0975i			0.853362i	0.904402	+	0.426681i	$0.140317\pi$
$313$			15.0975i			0.853362i	−0.904402	+	0.426681i	$0.859683\pi$
$314$	−13.8843	+	10.1142i	−0.783535	+	0.570777i
$315$	−1.17770	−	24.9974i	−0.0663556	−	1.40844i
$316$	−27.6784	−	8.91642i	−1.55703	−	0.501588i
$317$		−	24.8337i		−	1.39480i	−0.716683	−	0.697399i	$-0.754341\pi$
$317$		−	24.8337i		−	1.39480i	0.716683	−	0.697399i	$-0.245659\pi$
$318$	−7.82649	+	10.4966i	−0.438888	+	0.588619i
$319$		−	6.56139i		−	0.367367i
$320$	−2.82555	−	25.0642i	−0.157953	−	1.40113i
$321$	21.3342	+	4.83959i	1.19076	+	0.270120i
$322$	−8.96582	−	13.1279i	−0.499646	−	0.731589i
$323$	−5.31249			−0.295595
$324$	−2.80972	+	17.7794i	−0.156096	+	0.987742i
$325$	0.197751	−	0.342515i	0.0109693	−	0.0189993i
$326$	−18.9584	−	8.41228i	−1.05001	−	0.465913i
$327$	19.1005	−	5.91949i	1.05626	−	0.327349i
$328$	25.8126	+	23.0661i	1.42526	+	1.27361i
$329$	−1.06340	−	1.97830i	−0.0586273	−	0.109067i
$330$	1.46999	−	12.4963i	0.0809203	−	0.687900i
$331$	−0.767358			−0.0421778			−0.0210889	−	0.999778i	$-0.506713\pi$
$331$	−0.767358			−0.0421778			−0.0210889	+	0.999778i	$0.506713\pi$
$332$	−4.01475	+	3.63321i	−0.220338	+	0.199398i
$333$	18.5242	+	27.0156i	1.01512	+	1.48045i
$334$	0.0616668	+	0.0273630i	0.00337426	+	0.00149724i
$335$	−9.79491	+	16.9653i	−0.535153	+	0.926912i
$336$	−11.7251	−	14.0897i	−0.639659	−	0.768659i
$337$	−0.253412	−	0.438922i	−0.0138042	−	0.0239096i	0.859041	−	0.511907i	$-0.171061\pi$
$337$	−0.253412	−	0.438922i	−0.0138042	−	0.0239096i	−0.872845	+	0.487998i	$0.837727\pi$
$338$	1.94375	+	18.2726i	0.105726	+	0.993900i
$339$	−8.74612	−	1.98403i	−0.475024	−	0.107758i
$340$	−1.74572	−	8.11269i	−0.0946752	−	0.439972i
$341$	−3.23851	−	5.60926i	−0.175375	−	0.303759i
$342$	16.1454	+	5.71428i	0.873044	+	0.308993i
$343$	18.4434	+	1.68544i	0.995850	+	0.0910050i
$344$	32.1082	+	6.69842i	1.73116	+	0.361155i
$345$	−5.13294	+	22.6273i	−0.276348	+	1.21821i
$346$	−24.5986	+	17.9192i	−1.32243	+	0.963342i
$347$	16.3269			0.876474			0.438237	−	0.898860i	$-0.355603\pi$
$347$	16.3269			0.876474			0.438237	+	0.898860i	$0.355603\pi$
$348$	−0.155123	+	13.9500i	−0.00831548	+	0.747799i
$349$	−6.28314	+	10.8827i	−0.336329	+	0.582538i	−0.983739	−	0.179603i	$-0.942519\pi$
$349$	−6.28314	+	10.8827i	−0.336329	+	0.582538i	0.647411	+	0.762141i	$0.275852\pi$
$350$	−1.39620	−	18.4332i	−0.0746299	−	0.985297i
$351$	−0.0603571	+	0.411558i	−0.00322162	+	0.0219673i
$352$	−4.65824	−	7.95250i	−0.248285	−	0.423870i
$353$	13.6055	−	7.85513i	0.724146	−	0.418086i	−0.0921304	−	0.995747i	$-0.529368\pi$
$353$	13.6055	−	7.85513i	0.724146	−	0.418086i	0.816277	+	0.577661i	$0.196034\pi$
$354$	−10.5543	−	1.24155i	−0.560957	−	0.0659875i
$355$	13.6346	+	7.87192i	0.723648	+	0.417798i
$356$	2.45049	+	11.3879i	0.129876	+	0.603555i
$357$	−4.29980	−	4.22859i	−0.227570	−	0.223801i
$358$	−2.40958	−	22.6519i	−0.127351	−	1.19719i
$359$	19.6776	−	11.3609i	1.03854	−	0.599604i	0.119123	−	0.992879i	$-0.461992\pi$
$359$	19.6776	−	11.3609i	1.03854	−	0.599604i	0.919421	+	0.393276i	$0.128658\pi$
$360$	−3.42075	+	26.5334i	−0.180289	+	1.39843i
$361$	−1.35201	+	2.34176i	−0.0711586	+	0.123250i
$362$	−19.8146	+	14.4342i	−1.04143	+	0.758646i
$363$	4.27901	+	13.8071i	0.224590	+	0.724685i
$364$	−0.274559	−	0.322566i	−0.0143908	−	0.0169070i
$365$	−24.3514	+	14.0593i	−1.27461	+	0.735895i
$366$	1.51000	−	12.8365i	0.0789292	−	0.670973i
$367$	3.76873	+	6.52763i	0.196726	+	0.340739i	0.947465	−	0.319860i	$-0.103636\pi$
$367$	3.76873	+	6.52763i	0.196726	+	0.340739i	−0.750739	+	0.660599i	$0.770302\pi$
$368$	6.99045	+	15.4908i	0.364402	+	0.807514i
$369$	−20.7638	−	30.2819i	−1.08092	−	1.57641i
$370$	28.6660	+	39.3512i	1.49027	+	2.04577i
$371$	−0.429534	+	14.1358i	−0.0223003	+	0.733892i
$372$	6.75271	+	12.0023i	0.350112	+	0.622290i
$373$	−24.7915	−	14.3134i	−1.28366	−	0.741120i	−0.306142	−	0.951986i	$-0.599038\pi$
$373$	−24.7915	−	14.3134i	−1.28366	−	0.741120i	−0.977515	+	0.210866i	$0.932372\pi$
$374$	−1.78536	−	2.45086i	−0.0923188	−	0.126731i
$375$	0.220324	−	0.238086i	0.0113775	−	0.0122947i
$376$	0.750574	+	2.28074i	0.0387079	+	0.117620i
$377$			0.322389i			0.0166039i
$378$	8.51933	+	17.4763i	0.438187	+	0.898884i
$379$	−15.0610			−0.773630			−0.386815	−	0.922157i	$-0.626425\pi$
$379$	−15.0610			−0.773630			−0.386815	+	0.922157i	$0.626425\pi$
$380$	24.2290	+	7.80523i	1.24292	+	0.400400i
$381$	24.3407	+	22.5248i	1.24701	+	1.15398i
$382$	−1.90528	−	2.61548i	−0.0974828	−	0.133820i
$383$	−4.47549	+	7.75177i	−0.228687	+	0.396097i	−0.957419	−	0.288702i	$-0.906776\pi$
$383$	−4.47549	+	7.75177i	−0.228687	+	0.396097i	0.728732	+	0.684798i	$0.240110\pi$
$384$	9.71576	+	17.0178i	0.495805	+	0.868434i
$385$	−6.43471	−	11.9708i	−0.327943	−	0.610089i
$386$	−26.1310	+	19.0355i	−1.33003	+	0.968882i
$387$	−31.3839	−	15.0112i	−1.59533	−	0.763060i
$388$	−25.8825	+	23.4227i	−1.31398	+	1.18911i
$389$	−3.08582	+	1.78160i	−0.156457	+	0.0903308i	−0.576185	−	0.817320i	$-0.695459\pi$
$389$	−3.08582	+	1.78160i	−0.156457	+	0.0903308i	0.419727	+	0.907650i	$0.362126\pi$
$390$	−0.0722271	+	0.613999i	−0.00365736	+	0.0310911i
$391$	2.79570	+	4.84229i	0.141384	+	0.244885i
$392$	−19.1005	−	5.21275i	−0.964719	−	0.263283i
$393$	30.9748	−	9.59952i	1.56247	−	0.484232i
$394$	−8.34128	−	11.4505i	−0.420228	−	0.576868i
$395$	39.6998	+	22.9207i	1.99751	+	1.15326i
$396$	2.78976	+	9.36890i	0.140190	+	0.470805i
$397$	5.23487	+	9.06706i	0.262731	+	0.455063i	0.966967	−	0.254903i	$-0.0820436\pi$
$397$	5.23487	+	9.06706i	0.262731	+	0.455063i	−0.704236	+	0.709966i	$0.748710\pi$
$398$	−1.28418	−	12.0722i	−0.0643701	−	0.605126i
$399$	17.8281	−	4.93695i	0.892522	−	0.247157i
$400$	−1.96693	+	19.6643i	−0.0983464	+	0.983213i
$401$	−3.83475	+	6.64198i	−0.191498	+	0.331685i	−0.945747	−	0.324904i	$-0.894668\pi$
$401$	−3.83475	+	6.64198i	−0.191498	+	0.331685i	0.754249	+	0.656589i	$0.228001\pi$
$402$	1.77807	−	15.1153i	0.0886819	−	0.753881i
$403$	0.159122	+	0.275608i	0.00792644	+	0.0137290i
$404$	−12.1351	+	2.61128i	−0.603743	+	0.129916i
$405$	10.2264	−	26.4690i	0.508156	−	1.31526i
$406$	8.49843	+	12.4435i	0.421770	+	0.617562i
$407$	15.4061	+	8.89470i	0.763651	+	0.440894i
$408$	3.73787	+	5.25292i	0.185052	+	0.260058i
$409$			12.9361i			0.639647i	0.947477	+	0.319824i	$0.103624\pi$
$409$			12.9361i			0.639647i	−0.947477	+	0.319824i	$0.896376\pi$
$410$	−32.1317	−	44.1089i	−1.58687	−	2.17838i
$411$	11.7435	+	2.66398i	0.579265	+	0.131405i
$412$	6.55981	+	7.24869i	0.323179	+	0.357117i
$413$	−10.1105	+	5.43473i	−0.497505	+	0.267425i
$414$	−3.28801	−	17.7236i	−0.161597	−	0.871065i
$415$	7.39226	−	4.26793i	0.362872	−	0.209504i
$416$	0.228879	+	0.390741i	0.0112217	+	0.0191577i
$417$	5.20690	−	22.9533i	0.254983	−	1.12403i
$418$	9.24904	−	0.983864i	0.452385	−	0.0481224i
$419$	−26.7404	+	15.4386i	−1.30636	+	0.754225i	−0.981486	−	0.191534i	$-0.938654\pi$
$419$	−26.7404	+	15.4386i	−1.30636	+	0.754225i	−0.324870	+	0.945759i	$0.605320\pi$
$420$	13.3977	+	25.6030i	0.653740	+	1.24930i
$421$	0.0295116	+	0.0170385i	0.00143831	+	0.000830406i	0.500719	−	0.865610i	$-0.333069\pi$
$421$	0.0295116	+	0.0170385i	0.00143831	+	0.000830406i	−0.499281	+	0.866440i	$0.666402\pi$
$422$	7.33969	+	3.25680i	0.357291	+	0.158538i
$423$	−0.197059	−	2.53908i	−0.00958132	−	0.123454i
$424$	3.08760	−	14.8001i	0.149947	−	0.718756i
$425$			6.50185i			0.315386i
$426$	−12.1478	−	1.42899i	−0.588560	−	0.0692346i
$427$	−6.60986	−	12.2966i	−0.319874	−	0.595076i
$428$	−24.6952	+	5.31402i	−1.19369	+	0.256863i
$429$	0.0668716	+	0.215775i	0.00322859	+	0.0104177i
$430$	−47.2624	−	20.9715i	−2.27920	−	1.01133i
$431$	0.136132	+	0.0785960i	0.00655726	+	0.00378584i	0.503275	−	0.864126i	$-0.332128\pi$
$431$	0.136132	+	0.0785960i	0.00655726	+	0.00378584i	−0.496718	+	0.867912i	$0.665462\pi$
$432$	−5.70974	−	19.9850i	−0.274710	−	0.961527i
$433$			20.9730i			1.00790i	0.863734	+	0.503949i	$0.168120\pi$
$433$			20.9730i			1.00790i	−0.863734	+	0.503949i	$0.831880\pi$
$434$	13.4070	+	6.44327i	0.643556	+	0.309287i
$435$	4.86536	−	21.4477i	0.233276	−	1.02834i
$436$	−17.1205	+	15.4934i	−0.819923	+	0.742001i
$437$	−17.1515			−0.820468
$438$	13.0582	−	17.5131i	0.623945	−	0.836809i
$439$	−18.0392			−0.860965			−0.430483	−	0.902599i	$-0.641657\pi$
$439$	−18.0392			−0.860965			−0.430483	+	0.902599i	$0.641657\pi$
$440$	4.54176	+	13.8009i	0.216520	+	0.657932i
$441$	18.3593	+	10.1948i	0.874255	+	0.485468i
$442$	0.0877226	+	0.120421i	0.00417254	+	0.00572786i
$443$	−21.2999			−1.01199			−0.505995	−	0.862536i	$-0.668875\pi$
$443$	−21.2999			−1.01199			−0.505995	+	0.862536i	$0.668875\pi$
$444$	−32.5442	−	19.2750i	−1.54448	−	0.914753i
$445$		−	18.3632i		−	0.870497i
$446$	2.04991	+	19.2706i	0.0970659	+	0.912490i
$447$	0.501045	−	0.155281i	0.0236986	−	0.00734452i
$448$	19.1345	+	9.04831i	0.904019	+	0.427493i
$449$	34.8408			1.64424			0.822120	−	0.569315i	$-0.192791\pi$
$449$	34.8408			1.64424			0.822120	+	0.569315i	$0.192791\pi$
$450$	6.99360	−	19.7601i	0.329681	−	0.931499i
$451$	−17.2687	−	9.97009i	−0.813151	−	0.469473i
$452$	10.1240	−	2.17853i	0.476193	−	0.102469i
$453$	−1.16718	+	5.14521i	−0.0548387	+	0.241743i
$454$	7.55302	−	17.0219i	0.354481	−	0.798877i
$455$	0.316165	+	0.588178i	0.0148221	+	0.0275742i
$456$	−19.6874	+	1.87311i	−0.921948	+	0.0877163i
$457$	−3.95677			−0.185090			−0.0925448	−	0.995709i	$-0.529500\pi$
$457$	−3.95677			−0.185090			−0.0925448	+	0.995709i	$0.529500\pi$
$458$	−0.730275	−	6.86511i	−0.0341235	−	0.320786i
$459$	−2.52359	−	6.35547i	−0.117791	−	0.296648i
$460$	−5.63612	−	26.1920i	−0.262786	−	1.22121i
$461$	−12.1460	+	21.0375i	−0.565696	+	0.979815i	0.431288	+	0.902214i	$0.358059\pi$
$461$	−12.1460	+	21.0375i	−0.565696	+	0.979815i	−0.996985	+	0.0776004i	$0.975274\pi$
$462$	8.26909	+	6.56565i	0.384713	+	0.305462i
$463$	8.76610	−	5.06111i	0.407395	−	0.235210i	−0.282275	−	0.959334i	$-0.591089\pi$
$463$	8.76610	−	5.06111i	0.407395	−	0.235210i	0.689670	+	0.724124i	$0.257756\pi$
$464$	−6.62603	−	14.6833i	−0.307606	−	0.681653i
$465$	−6.42663	−	20.7369i	−0.298028	−	0.961648i
$466$	−4.99898	−	2.21817i	−0.231573	−	0.102755i
$467$	2.47270	−	1.42762i	0.114423	−	0.0660622i	−0.441696	−	0.897165i	$-0.645623\pi$
$467$	2.47270	−	1.42762i	0.114423	−	0.0660622i	0.556119	+	0.831102i	$0.312290\pi$
$468$	−0.137073	−	0.460335i	−0.00633619	−	0.0212790i
$469$	−7.78327	−	14.4796i	−0.359398	−	0.668606i
$470$	−0.400383	−	3.76390i	−0.0184683	−	0.173616i
$471$	−14.2891	+	15.4411i	−0.658407	+	0.711486i
$472$	11.6562	−	3.83595i	0.536519	−	0.176564i
$473$	−18.8933			−0.868713
$474$	−35.3706	−	4.16078i	−1.62463	−	0.191111i
$475$	−17.2723	−	9.97217i	−0.792508	−	0.457555i
$476$	6.56030	+	2.33556i	0.300691	+	0.107050i
$477$	−6.91930	+	14.4662i	−0.316813	+	0.662362i
$478$	−14.2119	+	32.0287i	−0.650037	+	1.46496i
$479$	16.9602	+	29.3759i	0.774930	+	1.34222i	0.934834	+	0.355085i	$0.115548\pi$
$479$	16.9602	+	29.3759i	0.774930	+	1.34222i	−0.159904	+	0.987133i	$0.551118\pi$
$480$	−9.32986	−	29.4491i	−0.425848	−	1.34416i
$481$	−0.756967	−	0.437035i	−0.0345147	−	0.0199271i
$482$	0.498880	−	1.12430i	0.0227233	−	0.0512105i
$483$	−13.8820	−	13.6521i	−0.631655	−	0.621193i
$484$	−11.1997	−	12.3758i	−0.509077	−	0.562538i
$485$	47.6568	−	27.5147i	2.16398	−	1.24938i
$486$	0.833430	+	22.0296i	0.0378051	+	0.999285i
$487$	−27.3521	−	15.7917i	−1.23944	−	0.715591i	−0.270460	−	0.962731i	$-0.587176\pi$
$487$	−27.3521	−	15.7917i	−1.23944	−	0.715591i	−0.968980	+	0.247140i	$0.920509\pi$
$488$	4.66539	+	14.1765i	0.211192	+	0.641742i
$489$	−24.7729	−	5.61967i	−1.12027	−	0.254130i
$490$	27.7081	+	14.3680i	1.25172	+	0.649081i
$491$	−13.9244	−	24.1177i	−0.628397	−	1.08842i	−0.987873	−	0.155262i	$-0.950378\pi$
$491$	−13.9244	−	24.1177i	−0.628397	−	1.08842i	0.359476	−	0.933154i	$-0.382955\pi$
$492$	36.4789	+	21.6054i	1.64459	+	0.974048i
$493$	−2.64995	−	4.58986i	−0.119348	−	0.206717i
$494$	−0.454446	+	0.0483415i	−0.0204465	+	0.00217499i
$495$	−1.19241	−	15.3641i	−0.0535950	−	0.690567i
$496$	−12.9118	−	9.28216i	−0.579755	−	0.416781i
$497$	−11.6369	+	6.25522i	−0.521986	+	0.280585i
$498$	−3.96404	+	5.31640i	−0.177633	+	0.238234i
$499$	5.16945	−	8.95375i	0.231416	−	0.400825i	−0.726809	−	0.686840i	$-0.758997\pi$
$499$	5.16945	−	8.95375i	0.231416	−	0.400825i	0.958225	+	0.286015i	$0.0923307\pi$
$500$	−0.114853	+	0.356529i	−0.00513640	+	0.0159444i
$501$	0.0805802	+	0.0182794i	0.00360006	+	0.000816663i
$502$	5.24483	+	7.19984i	0.234088	+	0.321345i
$503$	−22.8800			−1.02017			−0.510085	−	0.860124i	$-0.670386\pi$
$503$	−22.8800			−1.02017			−0.510085	+	0.860124i	$0.670386\pi$
$504$	−17.4255	−	14.1546i	−0.776193	−	0.630495i
$505$	19.5681			0.870767
$506$	−5.76409	−	7.91266i	−0.256245	−	0.351761i
$507$	6.66217	+	21.4969i	0.295878	+	0.954710i
$508$	−36.4496	−	11.7420i	−1.61719	−	0.520968i
$509$	15.6881	−	27.1725i	0.695361	−	1.20440i	−0.274698	−	0.961531i	$-0.588578\pi$
$509$	15.6881	−	27.1725i	0.695361	−	1.20440i	0.970059	−	0.242870i	$-0.0780888\pi$
$510$	−4.01861	−	9.33519i	−0.177947	−	0.413369i
$511$	0.716661	−	23.5849i	0.0317032	−	1.04334i
$512$	−18.4552	−	13.0922i	−0.815612	−	0.578599i
$513$	20.7540	+	3.04367i	0.916310	+	0.134382i
$514$	10.6879	−	1.13692i	0.471422	−	0.0501474i
$515$	−7.70580	−	13.3468i	−0.339558	−	0.588132i
$516$	40.1685	+	0.446671i	1.76832	+	0.0196636i
$517$	−0.691535	−	1.19777i	−0.0304137	−	0.0526781i
$518$	−40.7379	+	3.08563i	−1.78992	+	0.135575i
$519$	−25.3158	+	27.3567i	−1.11124	+	1.20083i
$520$	−0.223157	−	0.678098i	−0.00978607	−	0.0297366i
$521$	−0.825290	−	0.476481i	−0.0361566	−	0.0208750i	0.481813	−	0.876274i	$-0.339979\pi$
$521$	−0.825290	−	0.476481i	−0.0361566	−	0.0208750i	−0.517969	+	0.855399i	$0.673312\pi$
$522$	3.11661	+	16.7996i	0.136410	+	0.735299i
$523$	28.2674	−	16.3202i	1.23605	−	0.713633i	0.267765	−	0.963484i	$-0.413715\pi$
$523$	28.2674	−	16.3202i	1.23605	−	0.713633i	0.968284	+	0.249851i	$0.0803817\pi$
$524$	−27.7639	+	25.1254i	−1.21287	+	1.09761i
$525$	−6.04225	−	21.8195i	−0.263705	−	0.952281i
$526$	15.3015	−	34.4843i	0.667177	−	1.50359i
$527$	−4.53084	−	2.61588i	−0.197366	−	0.113950i
$528$	−7.48047	−	8.45309i	−0.325546	−	0.367873i
$529$	−2.47402	−	4.28513i	−0.107566	−	0.186310i
$530$	−9.66668	+	21.7853i	−0.419894	+	0.946295i
$531$	−12.9765	+	1.00711i	−0.563132	+	0.0437047i
$532$	−16.2663	+	13.8454i	−0.705233	+	0.600275i
$533$	0.848486	+	0.489874i	0.0367520	+	0.0212188i
$534$	5.64096	+	13.1039i	0.244108	+	0.567061i
$535$	39.8215			1.72163
$536$	5.49361	+	16.6932i	0.237288	+	0.721037i
$537$	−8.25884	−	26.6488i	−0.356395	−	1.14998i
$538$	1.15168	+	10.8267i	0.0496526	+	0.466771i
$539$	11.3836	+	0.692454i	0.490328	+	0.0298261i
$540$	2.17193	+	32.6935i	0.0934649	+	1.40691i
$541$	9.95401	−	5.74695i	0.427956	−	0.247081i	−0.270519	−	0.962715i	$-0.587195\pi$
$541$	9.95401	−	5.74695i	0.427956	−	0.247081i	0.698476	+	0.715634i	$0.253862\pi$
$542$	8.03932	+	3.56724i	0.345318	+	0.153226i
$543$	−20.3924	+	22.0363i	−0.875120	+	0.945670i
$544$	−6.47034	−	3.68165i	−0.277414	−	0.157849i
$545$	31.5235	−	18.2001i	1.35032	−	0.779607i
$546$	−0.406296	−	0.322599i	−0.0173879	−	0.0138060i
$547$	−15.9795	+	27.6773i	−0.683235	+	1.18340i	0.290753	+	0.956798i	$0.406094\pi$
$547$	−15.9795	+	27.6773i	−0.683235	+	1.18340i	−0.973988	+	0.226599i	$0.927239\pi$
$548$	−13.5936	+	2.92513i	−0.580690	+	0.124955i
$549$	−1.22487	−	15.7824i	−0.0522762	−	0.673574i
$550$	−1.20413	−	11.3197i	−0.0513444	−	0.482675i
$551$	16.2574			0.692588
$552$	12.0678	+	16.9592i	0.513641	+	0.721832i
$553$	−33.8831	+	18.2133i	−1.44086	+	0.774509i
$554$	2.04346	−	4.60525i	0.0868183	−	0.195658i
$555$	43.7635	+	40.4986i	1.85766	+	1.71907i
$556$	5.71733	+	26.5694i	0.242469	+	1.12680i
$557$	−23.0692	−	13.3190i	−0.977473	−	0.564344i	−0.0759668	−	0.997110i	$-0.524204\pi$
$557$	−23.0692	−	13.3190i	−0.977473	−	0.564344i	−0.901506	+	0.432766i	$0.857538\pi$
$558$	10.9562	+	12.8236i	0.463811	+	0.542864i
$559$	0.928308			0.0392633
$560$	−26.4885	−	20.2905i	−1.11934	−	0.857430i
$561$	−2.72566	−	2.52232i	−0.115078	−	0.106492i
$562$	−1.90776	−	17.9344i	−0.0804742	−	0.756516i
$563$			23.6890i			0.998371i	0.866495	+	0.499185i	$0.166367\pi$
$563$			23.6890i			0.998371i	−0.866495	+	0.499185i	$0.833633\pi$
$564$	1.44194	+	2.56291i	0.0607166	+	0.107918i
$565$	−16.3252			−0.686805
$566$	−22.3421	−	30.6702i	−0.939109	−	1.28916i
$567$	14.3751	+	18.9830i	0.603698	+	0.797213i
$568$	13.4159	−	4.41507i	0.562919	−	0.185252i
$569$	34.1153			1.43019			0.715094	−	0.699028i	$-0.246384\pi$
$569$	34.1153			1.43019			0.715094	+	0.699028i	$0.246384\pi$
$570$	30.9626	+	3.64225i	1.29688	+	0.152557i
$571$	−16.9315			−0.708560			−0.354280	−	0.935139i	$-0.615274\pi$
$571$	−16.9315			−0.708560			−0.354280	+	0.935139i	$0.615274\pi$
$572$	−0.175027	−	0.193407i	−0.00731824	−	0.00808677i
$573$	−2.90874	−	2.69174i	−0.121514	−	0.112449i
$574$	45.6632	−	3.45869i	1.90594	−	0.144363i
$575$			20.9914i			0.875403i
$576$	15.7042	+	18.1488i	0.654342	+	0.756199i
$577$	−33.2402	−	19.1913i	−1.38381	−	0.798943i	−0.391201	−	0.920305i	$-0.627940\pi$
$577$	−33.2402	−	19.1913i	−1.38381	−	0.798943i	−0.992608	+	0.121363i	$0.961274\pi$
$578$	19.7367	+	8.75763i	0.820937	+	0.364269i
$579$	−26.8929	+	29.0610i	−1.11763	+	1.20773i
$580$	5.34231	+	24.8266i	0.221827	+	1.03087i
$581$	−0.217555	+	7.15961i	−0.00902568	+	0.297031i
$582$	−25.5555	+	34.2740i	−1.05931	+	1.42070i
$583$			8.70874i			0.360679i
$584$	−5.15153	+	24.6934i	−0.213172	+	1.02182i
$585$	0.0585885	+	0.754907i	0.00242234	+	0.0312116i
$586$	42.0906	+	18.6766i	1.73875	+	0.771523i
$587$	−20.2432	−	11.6874i	−0.835526	−	0.482391i	0.0202148	−	0.999796i	$-0.493565\pi$
$587$	−20.2432	−	11.6874i	−0.835526	−	0.482391i	−0.855741	+	0.517404i	$0.826898\pi$
$588$	−24.1861	−	1.74134i	−0.997418	−	0.0718117i
$589$	13.8983	−	8.02418i	0.572669	−	0.330630i
$590$	−19.2361	+	2.04624i	−0.791939	+	0.0842423i
$591$	−12.7344	−	11.7844i	−0.523823	−	0.484744i
$592$	43.4585	+	4.34696i	1.78613	+	0.178659i
$593$	36.4016	−	21.0165i	1.49483	−	0.863042i	0.494851	−	0.868978i	$-0.335223\pi$
$593$	36.4016	−	21.0165i	1.49483	−	0.863042i	0.999982	+	0.00593582i	$0.00188944\pi$
$594$	5.57060	+	10.5975i	0.228564	+	0.434821i
$595$	−9.33590	−	5.77509i	−0.382735	−	0.236755i
$596$	−0.449106	+	0.406425i	−0.0183961	+	0.0166478i
$597$	−4.40152	−	14.2024i	−0.180142	−	0.581266i
$598$	0.283215	+	0.388784i	0.0115815	+	0.0158985i
$599$			10.2621i			0.419297i	0.977777	+	0.209649i	$0.0672320\pi$
$599$			10.2621i			0.419297i	−0.977777	+	0.209649i	$0.932768\pi$
$600$	2.29246	+	24.0951i	0.0935893	+	0.983678i
$601$	8.71209	+	5.02993i	0.355374	+	0.205175i	0.667049	−	0.745013i	$-0.267557\pi$
$601$	8.71209	+	5.02993i	0.355374	+	0.205175i	−0.311676	+	0.950188i	$0.600890\pi$
$602$	35.8307	−	24.4709i	1.46035	−	0.997360i
$603$	−1.44232	−	18.5841i	−0.0587356	−	0.756803i
$604$	−1.28159	−	5.95580i	−0.0521473	−	0.242338i
$605$	13.1563	+	22.7873i	0.534878	+	0.926437i
$606$	−13.9637	+	6.01109i	−0.567237	+	0.244184i
$607$	−14.8576	+	25.7342i	−0.603053	+	1.04452i	0.389303	+	0.921110i	$0.372716\pi$
$607$	−14.8576	+	25.7342i	−0.603053	+	1.04452i	−0.992356	+	0.123409i	$0.960617\pi$
$608$	19.7042	−	11.5419i	0.799111	−	0.468085i
$609$	13.1584	+	12.9404i	0.533204	+	0.524372i
$610$	−2.48869	−	23.3955i	−0.100764	−	0.947256i
$611$	0.0339781	+	0.0588519i	0.00137461	+	0.00238089i
$612$	5.73533	+	5.42708i	0.231837	+	0.219377i
$613$	15.1167	+	8.72763i	0.610558	+	0.352506i	0.773184	−	0.634182i	$-0.218663\pi$
$613$	15.1167	+	8.72763i	0.610558	+	0.352506i	−0.162626	+	0.986688i	$0.551996\pi$
$614$	−6.85412	−	9.40901i	−0.276610	−	0.379717i
$615$	−49.0546	−	45.3950i	−1.97807	−	1.83050i
$616$	−11.8540	−	2.85126i	−0.477612	−	0.114881i
$617$	2.93147	+	5.07745i	0.118017	+	0.204411i	0.918982	−	0.394301i	$-0.129013\pi$
$617$	2.93147	+	5.07745i	0.118017	+	0.204411i	−0.800965	+	0.598711i	$0.795680\pi$
$618$	9.59883	+	7.15712i	0.386122	+	0.287901i
$619$	10.6563	−	6.15242i	0.428313	−	0.247286i	−0.270315	−	0.962772i	$-0.587128\pi$
$619$	10.6563	−	6.15242i	0.428313	−	0.247286i	0.698628	+	0.715486i	$0.253794\pi$
$620$	16.8208	+	18.5872i	0.675539	+	0.746482i
$621$	−8.14749	−	20.5188i	−0.326948	−	0.823391i
$622$	−5.69224	+	4.14659i	−0.228238	+	0.166263i
$623$	13.1049	+	8.10655i	0.525037	+	0.324782i
$624$	0.367548	+	0.415337i	0.0147137	+	0.0166268i
$625$	12.6467	−	21.9048i	0.505870	−	0.876192i
$626$	−12.5716	−	17.2576i	−0.502461	−	0.689754i
$627$	10.8811	−	3.37219i	0.434548	−	0.134672i
$628$	7.44880	−	23.1226i	0.297240	−	0.922692i
$629$	14.3693			0.572940
$630$	22.1613	+	27.5933i	0.882928	+	1.09934i
$631$			27.5446i			1.09653i	0.836304	+	0.548266i	$0.184712\pi$
$631$			27.5446i			1.09653i	−0.836304	+	0.548266i	$0.815288\pi$
$632$	39.0632	−	12.8554i	1.55385	−	0.511360i
$633$	9.59079	+	2.17564i	0.381200	+	0.0864741i
$634$	20.6788	+	28.3868i	0.821259	+	1.12738i
$635$	52.2806	+	30.1842i	2.07469	+	1.19782i
$636$	0.205891	−	18.5154i	0.00816409	−	0.734185i
$637$	−0.559327	−	0.0340233i	−0.0221614	−	0.00134805i
$638$	5.46361	+	7.50017i	0.216306	+	0.296935i
$639$	−14.9356	+	1.15915i	−0.590842	+	0.0458553i
$640$	24.1006	+	26.2975i	0.952658	+	1.03950i
$641$	16.4201	+	28.4405i	0.648556	+	1.12333i	0.983468	+	0.181083i	$0.0579602\pi$
$641$	16.4201	+	28.4405i	0.648556	+	1.12333i	−0.334912	+	0.942250i	$0.608706\pi$
$642$	−28.4165	+	12.2327i	−1.12151	+	0.482787i
$643$	−4.33664	+	2.50376i	−0.171021	+	0.0987388i	−0.583067	−	0.812424i	$-0.698147\pi$
$643$	−4.33664	+	2.50376i	−0.171021	+	0.0987388i	0.412046	+	0.911163i	$0.364814\pi$
$644$	21.1801	+	7.54044i	0.834613	+	0.297135i
$645$	−61.7579	−	14.0096i	−2.43172	−	0.551628i
$646$	6.07258	−	4.42366i	0.238923	−	0.174046i
$647$	21.3640	−	37.0035i	0.839905	−	1.45476i	−0.0500677	−	0.998746i	$-0.515944\pi$
$647$	21.3640	−	37.0035i	0.839905	−	1.45476i	0.889973	−	0.456013i	$-0.150723\pi$
$648$	−11.5930	−	22.6628i	−0.455415	−	0.890279i
$649$	−6.12146	+	3.53423i	−0.240288	+	0.138731i
$650$	0.0591643	+	0.556188i	0.00232062	+	0.0218155i
$651$	17.6360	+	4.56805i	0.691208	+	0.179036i
$652$	28.6757	−	6.17056i	1.12303	−	0.241658i
$653$	31.6123	+	18.2514i	1.23708	+	0.714231i	0.968497	−	0.249024i	$-0.0801098\pi$
$653$	31.6123	+	18.2514i	1.23708	+	0.714231i	0.268588	+	0.963255i	$0.413443\pi$
$654$	−16.9042	+	22.6712i	−0.661007	+	0.886515i
$655$	51.1210	−	29.5147i	1.99746	−	1.15324i
$656$	−48.7127	−	4.87251i	−1.90191	−	0.190240i
$657$	11.5446	−	24.1363i	0.450397	−	0.941647i
$658$	2.86286	+	1.37586i	0.111606	+	0.0536368i
$659$	4.57831	−	7.92986i	0.178346	−	0.308903i	−0.762968	−	0.646436i	$-0.776259\pi$
$659$	4.57831	−	7.92986i	0.178346	−	0.308903i	0.941314	+	0.337532i	$0.109592\pi$
$660$	8.72526	+	15.5083i	0.339630	+	0.603661i
$661$	−5.84883			−0.227493			−0.113747	−	0.993510i	$-0.536285\pi$
$661$	−5.84883			−0.227493			−0.113747	+	0.993510i	$0.536285\pi$
$662$	0.877150	−	0.638972i	0.0340914	−	0.0248344i
$663$	0.133924	+	0.123933i	0.00520116	+	0.00481314i
$664$	1.56383	−	7.49609i	0.0606885	−	0.290905i
$665$	29.6605	−	15.9435i	1.15019	−	0.618263i
$666$	−43.6703	−	15.4560i	−1.69219	−	0.598908i
$667$	−8.55545	−	14.8185i	−0.331269	−	0.573774i
$668$	−0.0932749	+	0.0200713i	−0.00360891	+	0.000776582i
$669$	7.02604	+	22.6710i	0.271642	+	0.876510i
$670$	−2.93049	−	27.5488i	−0.113215	−	1.06430i
$671$	−4.29842	−	7.44509i	−0.165939	−	0.287414i
$672$	25.1352	+	6.34225i	0.969610	+	0.244658i
$673$	−12.9937	+	22.5058i	−0.500872	+	0.867536i	0.499128	+	0.866529i	$0.333654\pi$
$673$	−12.9937	+	22.5058i	−0.500872	+	0.867536i	−0.999999	+	0.00100715i	$0.999679\pi$
$674$	0.655155	+	0.290708i	0.0252356	+	0.0111977i
$675$	3.72510	−	25.4004i	0.143379	−	0.977662i
$676$	−17.4373	−	19.2685i	−0.670665	−	0.741095i
$677$	−4.94364			−0.190000			−0.0949998	−	0.995477i	$-0.530285\pi$
$677$	−4.94364			−0.190000			−0.0949998	+	0.995477i	$0.530285\pi$
$678$	11.6496	−	5.01491i	0.447400	−	0.192597i
$679$	−1.40254	+	46.1569i	−0.0538246	+	1.77134i
$680$	8.75086	+	7.81978i	0.335580	+	0.299875i
$681$	5.04566	−	22.2426i	0.193350	−	0.852336i
$682$	8.37265	+	3.71515i	0.320605	+	0.142260i
$683$	12.1201	−	20.9926i	0.463762	−	0.803260i	−0.535382	−	0.844610i	$-0.679832\pi$
$683$	12.1201	−	20.9926i	0.463762	−	0.803260i	0.999145	+	0.0413497i	$0.0131658\pi$
$684$	−23.2137	+	6.91228i	−0.887598	+	0.264298i
$685$	21.9200			0.837519
$686$	−22.4857	+	13.4311i	−0.858508	+	0.512801i
$687$	−2.50301	−	8.07648i	−0.0954959	−	0.308137i
$688$	−42.2799	+	19.0794i	−1.61191	+	0.727396i
$689$		−	0.427898i		−	0.0163016i
$690$	−12.9742	−	30.1389i	−0.493919	−	1.14737i
$691$			26.6014i			1.01197i	0.862544	+	0.505983i	$0.168870\pi$
$691$			26.6014i			1.01197i	−0.862544	+	0.505983i	$0.831130\pi$
$692$	13.1970	−	40.9660i	0.501673	−	1.55730i
$693$	11.4910	+	5.93164i	0.436509	+	0.225324i
$694$	−18.6629	+	13.5953i	−0.708434	+	0.516069i
$695$		−	42.8438i		−	1.62516i
$696$	−11.4387	−	16.0751i	−0.433584	−	0.609326i
$697$	−16.1065			−0.610078
$698$	−1.87982	−	17.6717i	−0.0711523	−	0.668883i
$699$	−6.53218	−	1.48181i	−0.247070	−	0.0560471i
$700$	16.9451	+	19.9080i	0.640466	+	0.752452i
$701$			5.20314i			0.196520i	0.995161	+	0.0982600i	$0.0313277\pi$
$701$			5.20314i			0.196520i	−0.995161	+	0.0982600i	$0.968672\pi$
$702$	−0.273708	−	0.520701i	−0.0103304	−	0.0196526i
$703$	−22.0387	+	38.1722i	−0.831207	+	1.43969i
$704$	11.9467	+	5.21145i	0.450258	+	0.196414i
$705$	−1.37231	−	4.42805i	−0.0516842	−	0.166770i
$706$	−9.01122	+	20.3082i	−0.339142	+	0.764308i
$707$	−8.63846	+	13.9648i	−0.324883	+	0.525199i
$708$	13.0983	−	7.36932i	0.492263	−	0.276956i
$709$			21.8206i			0.819490i	0.912200	+	0.409745i	$0.134382\pi$
$709$			21.8206i			0.819490i	−0.912200	+	0.409745i	$0.865618\pi$
$710$	−22.1402	+	2.35516i	−0.830908	+	0.0883877i
$711$	−43.4879	+	3.37511i	−1.63092	+	0.126576i
$712$	−12.2837	−	10.9767i	−0.460350	−	0.411369i
$713$	−14.6279	−	8.44545i	−0.547821	−	0.316284i
$714$	8.43611	+	1.25320i	0.315714	+	0.0468996i
$715$	0.205604	+	0.356116i	0.00768915	+	0.0133180i
$716$	21.6163	+	23.8864i	0.807840	+	0.892676i
$717$	−9.49400	+	41.8520i	−0.354560	+	1.56299i
$718$	−13.0329	+	29.3717i	−0.486385	+	1.09614i
$719$	−1.57964	−	2.73601i	−0.0589105	−	0.102036i	0.835066	−	0.550150i	$-0.185429\pi$
$719$	−1.57964	−	2.73601i	−0.0589105	−	0.102036i	−0.893977	+	0.448114i	$0.852096\pi$
$720$	−18.1839	−	33.1782i	−0.677675	−	1.23648i
$721$	12.9268	+	0.392798i	0.481418	+	0.0146285i
$722$	−0.404503	−	3.80262i	−0.0150540	−	0.141519i
$723$	0.333267	−	1.46913i	0.0123943	−	0.0546374i
$724$	10.6304	−	32.9989i	0.395075	−	1.22639i
$725$		−	19.8971i		−	0.738961i
$726$	−16.3883	−	12.2195i	−0.608227	−	0.453508i
$727$	1.42958	−	2.47610i	0.0530201	−	0.0918335i	−0.838297	−	0.545213i	$-0.816449\pi$
$727$	1.42958	−	2.47610i	0.0530201	−	0.0918335i	0.891317	+	0.453380i	$0.149782\pi$
$728$	0.582440	+	0.140095i	0.0215866	+	0.00519226i
$729$	6.21754	+	26.2744i	0.230279	+	0.973125i
$730$	16.1285	−	36.3480i	0.596941	−	1.34530i
$731$	−13.2163	+	7.63044i	−0.488823	+	0.282222i
$732$	8.96276	+	15.9305i	0.331273	+	0.588807i
$733$	15.2324	−	26.3833i	0.562622	−	0.974490i	−0.434645	−	0.900602i	$-0.643126\pi$
$733$	15.2324	−	26.3833i	0.562622	−	0.974490i	0.997267	−	0.0738877i	$-0.0235406\pi$
$734$	−9.74344	−	4.32340i	−0.359637	−	0.159580i
$735$	36.6971	+	10.7046i	1.35359	+	0.394845i
$736$	−20.8897	−	11.8863i	−0.770004	−	0.438135i
$737$	−5.06150	−	8.76677i	−0.186443	−	0.322928i
$738$	48.9501	+	17.3247i	1.80188	+	0.637730i
$739$	14.2279	−	24.6434i	0.523380	−	0.906521i	−0.476250	−	0.879310i	$-0.658004\pi$
$739$	14.2279	−	24.6434i	0.523380	−	0.906521i	0.999630	−	0.0272108i	$-0.00866253\pi$
$740$	−65.5348	−	21.1116i	−2.40911	−	0.776079i
$741$	−0.534634	+	0.165690i	−0.0196403	+	0.00608678i
$742$	−11.2797	−	16.5159i	−0.414092	−	0.606319i
$743$	24.3731	−	14.0718i	0.894164	−	0.516246i	0.0188617	−	0.999822i	$-0.493996\pi$
$743$	24.3731	−	14.0718i	0.894164	−	0.516246i	0.875302	+	0.483576i	$0.160662\pi$
$744$	−17.7131	−	8.09663i	−0.649392	−	0.296837i
$745$	0.826927	−	0.477427i	0.0302963	−	0.0174916i
$746$	40.2573	−	4.28236i	1.47392	−	0.156788i
$747$	−3.50455	+	7.32698i	−0.128225	+	0.268080i
$748$	4.08161	+	1.31487i	0.149239	+	0.0480763i
$749$	−17.5795	+	28.4187i	−0.642340	+	1.03840i
$750$	−0.0535956	+	0.455613i	−0.00195703	+	0.0166367i
$751$	17.4414	+	10.0698i	0.636444	+	0.367451i	0.783243	−	0.621715i	$-0.213564\pi$
$751$	17.4414	+	10.0698i	0.636444	+	0.367451i	−0.146799	+	0.989166i	$0.546897\pi$
$752$	−2.75711	−	1.98207i	−0.100542	−	0.0722785i
$753$	8.00713	+	7.40978i	0.291796	+	0.270027i
$754$	−0.268451	−	0.368516i	−0.00977640	−	0.0134206i
$755$			9.60384i			0.349520i
$756$	−24.2906	−	12.8828i	−0.883441	−	0.468543i
$757$		−	14.6951i		−	0.534104i	−0.963682	−	0.267052i	$-0.913950\pi$
$757$		−	14.6951i		−	0.534104i	0.963682	−	0.267052i	$-0.0860496\pi$
$758$	17.2159	−	12.5411i	0.625308	−	0.455515i
$759$	−8.79988	−	8.14338i	−0.319415	−	0.295586i
$760$	−34.1950	+	11.2533i	−1.24038	+	0.408200i
$761$	32.7523	+	18.9095i	1.18727	+	0.685470i	0.957685	−	0.287818i	$-0.0929300\pi$
$761$	32.7523	+	18.9095i	1.18727	+	0.685470i	0.229584	+	0.973289i	$0.426263\pi$
$762$	−46.5795	−	5.47933i	−1.68740	−	0.198495i
$763$	−0.927738	+	30.5314i	−0.0335864	+	1.10531i
$764$	4.35577	+	1.40318i	0.157586	+	0.0507654i
$765$	−7.03926	−	10.2660i	−0.254505	−	0.371169i
$766$	−1.33900	−	12.5876i	−0.0483800	−	0.454807i
$767$	0.300774	−	0.173652i	0.0108603	−	0.00627021i
$768$	−25.2764	−	11.3624i	−0.912083	−	0.410005i
$769$	30.8752	−	17.8258i	1.11339	−	0.642815i	0.173683	−	0.984802i	$-0.444433\pi$
$769$	30.8752	−	17.8258i	1.11339	−	0.642815i	0.939705	+	0.341987i	$0.111100\pi$
$770$	17.3234	+	8.32543i	0.624290	+	0.300028i
$771$	12.5738	−	3.89679i	0.452834	−	0.140339i
$772$	14.0191	−	43.5181i	0.504558	−	1.56625i
$773$	9.35820	−	16.2089i	0.336591	−	0.582993i	−0.647198	−	0.762322i	$-0.724059\pi$
$773$	9.35820	−	16.2089i	0.336591	−	0.582993i	0.983789	+	0.179329i	$0.0573926\pi$
$774$	48.3739	−	8.97415i	1.73876	−	0.322569i
$775$	−9.82064	−	17.0099i	−0.352768	−	0.611012i
$776$	10.0818	−	48.3261i	0.361915	−	1.73481i
$777$	−48.2216	+	13.3535i	−1.72994	+	0.479054i
$778$	2.04381	−	4.60605i	0.0732742	−	0.165135i
$779$	24.7033	−	42.7873i	0.885086	−	1.53301i
$780$	−0.428710	−	0.761991i	−0.0153503	−	0.0272837i
$781$	−7.04563	+	4.06780i	−0.252112	+	0.145557i
$782$	−7.22782	−	3.20716i	−0.258466	−	0.114688i
$783$	7.72276	+	19.4492i	0.275989	+	0.695056i
$784$	26.1739	−	9.94620i	0.934782	−	0.355221i
$785$	−19.1480	+	33.1653i	−0.683422	+	1.18372i
$786$	−27.4132	+	36.7654i	−0.977796	+	1.31138i
$787$		−	42.3204i		−	1.50856i	−0.656552	−	0.754280i	$-0.727986\pi$
$787$		−	42.3204i		−	1.50856i	0.656552	−	0.754280i	$-0.272014\pi$
$788$	19.0695	+	6.14310i	0.679321	+	0.218839i
$789$	10.2219	−	45.0607i	0.363909	−	1.60420i
$790$	−64.4658	+	6.85753i	−2.29359	+	0.243980i
$791$	7.20686	−	11.6505i	0.256246	−	0.414243i
$792$	−10.9903	−	8.38638i	−0.390524	−	0.297997i
$793$	0.211200	+	0.365810i	0.00749994	+	0.0129903i
$794$	−13.5339	−	6.00533i	−0.480301	−	0.213121i
$795$	−6.45765	+	28.4670i	−0.229029	+	1.00962i
$796$	11.5203	+	12.7302i	0.408328	+	0.451209i
$797$	1.88556	+	3.26589i	0.0667901	+	0.115684i	0.897487	−	0.441042i	$-0.145391\pi$
$797$	1.88556	+	3.26589i	0.0667901	+	0.115684i	−0.830697	+	0.556725i	$0.812058\pi$
$798$	−16.2680	+	20.4886i	−0.575880	+	0.725290i
$799$	−0.967493	−	0.558582i	−0.0342274	−	0.0197612i
$800$	−14.1259	−	24.1156i	−0.499426	−	0.852616i
$801$	9.88107	+	14.4105i	0.349131	+	0.509171i
$802$	−1.14730	−	10.7855i	−0.0405126	−	0.380848i
$803$		−	14.5302i		−	0.512759i
$804$	10.5539	+	18.7585i	0.372206	+	0.661561i
$805$	−30.1412	−	18.6450i	−1.06234	−	0.657151i
$806$	−0.411385	−	0.182541i	−0.0144904	−	0.00642974i
$807$	3.94739	+	12.7371i	0.138955	+	0.448366i
$808$	11.6969	−	13.0897i	0.411497	−	0.460493i
$809$	−4.06036	+	7.03274i	−0.142755	+	0.247258i	−0.928533	−	0.371250i	$-0.878929\pi$
$809$	−4.06036	+	7.03274i	−0.142755	+	0.247258i	0.785778	+	0.618508i	$0.212263\pi$
$810$	10.3509	+	38.7716i	0.363693	+	1.36229i
$811$			18.0366i			0.633350i	0.948534	+	0.316675i	$0.102566\pi$
$811$			18.0366i			0.633350i	−0.948534	+	0.316675i	$0.897434\pi$
$812$	−20.0760	−	7.14735i	−0.704529	−	0.250823i
$813$	10.5050	+	2.38303i	0.368426	+	0.0835765i
$814$	−25.0169	+	2.66116i	−0.876841	+	0.0932737i
$815$	−46.2402			−1.61972
$816$	−8.64674	−	2.89200i	−0.302696	−	0.101240i
$817$		−	46.8126i		−	1.63776i
$818$	−10.7717	−	14.7869i	−0.376625	−	0.517013i
$819$	−0.564605	−	0.291447i	−0.0197289	−	0.0101840i
$820$	73.4581	+	23.6641i	2.56527	+	0.826385i
$821$		−	49.9486i		−	1.74322i	−0.490202	−	0.871609i	$-0.663077\pi$
$821$		−	49.9486i		−	1.74322i	0.490202	−	0.871609i	$-0.336923\pi$
$822$	−15.6420	+	6.73358i	−0.545578	+	0.234860i
$823$			14.0138i			0.488491i	0.969713	+	0.244246i	$0.0785403\pi$
$823$			14.0138i			0.488491i	−0.969713	+	0.244246i	$0.921460\pi$
$824$	−13.5343	−	2.82352i	−0.471489	−	0.0983621i
$825$	−4.12716	−	13.3171i	−0.143689	−	0.463643i
$826$	7.03162	−	14.6312i	0.244661	−	0.509085i
$827$	−35.7576			−1.24341			−0.621707	−	0.783250i	$-0.713561\pi$
$827$	−35.7576			−1.24341			−0.621707	+	0.783250i	$0.713561\pi$
$828$	18.5167	+	17.5215i	0.643499	+	0.608914i
$829$	−22.6167	+	39.1733i	−0.785512	+	1.36055i	0.143181	+	0.989697i	$0.454267\pi$
$829$	−22.6167	+	39.1733i	−0.785512	+	1.36055i	−0.928693	+	0.370850i	$0.879066\pi$
$830$	−4.89607	+	11.0340i	−0.169945	+	0.382997i
$831$	1.36510	−	6.01769i	0.0473546	−	0.208751i
$832$	−0.586993	−	0.256061i	−0.0203503	−	0.00887733i
$833$	8.24280	−	4.11313i	0.285596	−	0.142512i
$834$	13.1611	+	30.5732i	0.455733	+	1.05866i
$835$	0.150408			0.00520507
$836$	−9.75311	+	8.82622i	−0.337318	+	0.305261i
$837$	16.2016	+	12.8152i	0.560011	+	0.442957i
$838$	17.7108	−	39.9140i	0.611810	−	1.37881i
$839$	10.0994	−	17.4927i	0.348671	−	0.603915i	−0.637343	−	0.770580i	$-0.719967\pi$
$839$	10.0994	−	17.4927i	0.348671	−	0.603915i	0.986014	+	0.166665i	$0.0532999\pi$
$840$	−36.6339	−	18.1101i	−1.26399	−	0.624857i
$841$	−6.39054	−	11.0687i	−0.220364	−	0.381681i
$842$	−0.0479218	+	0.00509767i	−0.00165149	+	0.000175677i
$843$	−6.53885	−	21.0989i	−0.225210	−	0.726686i
$844$	−11.1017	+	2.38892i	−0.382138	+	0.0822301i
$845$	20.4836	+	35.4786i	0.704656	+	1.22050i
$846$	2.33952	+	2.73828i	0.0804345	+	0.0941440i
$847$	−22.0701	−	0.670632i	−0.758339	−	0.0230432i
$848$	8.79454	+	19.4887i	0.302006	+	0.669244i
$849$	−34.1091	−	31.5644i	−1.17062	−	1.08329i
$850$	−5.41403	−	7.43212i	−0.185700	−	0.254920i
$851$	46.3915			1.59028
$852$	15.0757	−	8.48188i	0.516486	−	0.290584i
$853$	−2.30945	+	4.00008i	−0.0790740	+	0.136960i	−0.902851	−	0.429954i	$-0.858530\pi$
$853$	−2.30945	+	4.00008i	−0.0790740	+	0.136960i	0.823777	+	0.566915i	$0.191863\pi$
$854$	17.7949	+	8.55205i	0.608929	+	0.292645i
$855$	38.0683	−	2.95449i	1.30191	−	0.101041i
$856$	23.8036	−	26.6378i	0.813589	−	0.910461i
$857$	−18.6265	+	10.7540i	−0.636270	+	0.367351i	−0.783176	−	0.621800i	$-0.786402\pi$
$857$	−18.6265	+	10.7540i	−0.636270	+	0.367351i	0.146906	+	0.989150i	$0.453068\pi$
$858$	−0.256113	−	0.190964i	−0.00874356	−	0.00651941i
$859$	−24.5803	−	14.1914i	−0.838668	−	0.484205i	0.0181430	−	0.999835i	$-0.494225\pi$
$859$	−24.5803	−	14.1914i	−0.838668	−	0.484205i	−0.856811	+	0.515630i	$0.827558\pi$
$860$	71.4874	−	15.3830i	2.43770	−	0.524555i
$861$	54.0517	−	14.9680i	1.84208	−	0.510107i
$862$	−0.221056	+	0.0235148i	−0.00752920	+	0.000800916i
$863$	20.2470	−	11.6896i	0.689216	−	0.397919i	−0.114102	−	0.993469i	$-0.536399\pi$
$863$	20.2470	−	11.6896i	0.689216	−	0.397919i	0.803318	+	0.595550i	$0.203066\pi$
$864$	23.1680	+	18.0899i	0.788190	+	0.615432i
$865$	−33.9243	+	58.7586i	−1.15346	+	1.99785i
$866$	−17.4640	−	23.9737i	−0.593451	−	0.814661i
$867$	25.7899	+	5.85037i	0.875872	+	0.198689i
$868$	−20.6905	+	3.79872i	−0.702280	+	0.128937i
$869$	−20.5148	+	11.8442i	−0.695916	+	0.401787i
$870$	12.2978	+	28.5678i	0.416936	+	0.968538i
$871$	0.248693	+	0.430750i	0.00842665	+	0.0145954i
$872$	6.66880	−	31.9663i	0.225834	−	1.08251i
$873$	−22.5933	+	47.2359i	−0.764668	+	1.59869i
$874$	19.6055	−	14.2819i	0.663166	−	0.483093i
$875$	0.234608	+	0.436453i	0.00793120	+	0.0147548i
$876$	−0.343520	+	30.8923i	−0.0116065	+	1.04375i
$877$	37.5397	+	21.6736i	1.26763	+	0.731865i	0.974538	−	0.224220i	$-0.0719836\pi$
$877$	37.5397	+	21.6736i	1.26763	+	0.731865i	0.293089	+	0.956085i	$0.405317\pi$
$878$	20.6202	−	15.0211i	0.695899	−	0.506937i
$879$	54.9999	+	12.4766i	1.85510	+	0.420824i
$880$	−16.6835	−	11.9936i	−0.562399	−	0.404304i
$881$			25.2180i			0.849616i	0.905284	+	0.424808i	$0.139658\pi$
$881$			25.2180i			0.849616i	−0.905284	+	0.424808i	$0.860342\pi$
$882$	−29.4753	+	3.63419i	−0.992485	+	0.122370i
$883$	0.109495			0.00368482			0.00184241	−	0.999998i	$-0.499414\pi$
$883$	0.109495			0.00368482			0.00184241	+	0.999998i	$0.499414\pi$
$884$	−0.200547	−	0.0646051i	−0.00674514	−	0.00217290i
$885$	−22.6304	+	7.01347i	−0.760713	+	0.235755i
$886$	24.3475	−	17.7363i	0.817970	−	0.595862i
$887$	−10.6962	+	18.5264i	−0.359144	+	0.622056i	−0.987818	−	0.155613i	$-0.950265\pi$
$887$	−10.6962	+	18.5264i	−0.359144	+	0.622056i	0.628674	+	0.777669i	$0.283598\pi$
$888$	53.2507	−	5.06639i	1.78698	−	0.170017i
$889$	−44.6206	+	23.9851i	−1.49653	+	0.804434i
$890$	15.2908	+	20.9905i	0.512550	+	0.703604i
$891$	9.20307	+	11.4154i	0.308315	+	0.382430i
$892$	−18.3897	−	20.3209i	−0.615732	−	0.680393i
$893$	2.96777	−	1.71344i	0.0993127	−	0.0573382i
$894$	−0.443432	+	0.594713i	−0.0148306	+	0.0198902i
$895$	−25.3927	−	43.9814i	−0.848783	−	1.47014i
$896$	−29.4066	+	5.59018i	−0.982407	+	0.186755i
$897$	0.432376	+	0.400120i	0.0144366	+	0.0133596i
$898$	−39.8257	+	29.0116i	−1.32900	+	0.968130i
$899$	13.8654	+	8.00518i	0.462436	+	0.266988i
$900$	8.45981	+	28.4108i	0.281994	+	0.947027i
$901$	3.51721	+	6.09198i	0.117175	+	0.202953i
$902$	28.0415	−	2.98290i	0.933678	−	0.0993198i
$903$	37.2615	−	37.8890i	1.23998	−	1.26087i
$904$	−9.75848	+	10.9204i	−0.324562	+	0.363207i
$905$	−27.3266	+	47.3311i	−0.908368	+	1.57334i
$906$	−2.95020	−	6.85327i	−0.0980137	−	0.227685i
$907$	−21.8295	−	37.8098i	−0.724836	−	1.25545i	−0.959041	−	0.283266i	$-0.908582\pi$
$907$	−21.8295	−	37.8098i	−0.724836	−	1.25545i	0.234206	−	0.972187i	$-0.424751\pi$
$908$	5.54029	+	25.7467i	0.183861	+	0.854434i
$909$	−15.3561	+	10.5294i	−0.509328	+	0.349239i
$910$	−0.851172	−	0.409065i	−0.0282161	−	0.0135604i
$911$	−40.4047	−	23.3277i	−1.33867	−	0.772880i	−0.352057	−	0.935978i	$-0.614518\pi$
$911$	−40.4047	−	23.3277i	−1.33867	−	0.772880i	−0.986610	+	0.163099i	$0.947851\pi$
$912$	20.9445	−	18.5346i	0.693543	−	0.613743i
$913$			4.41088i			0.145979i
$914$	4.52289	−	3.29476i	0.149604	−	0.108981i
$915$	−8.52997	−	27.5237i	−0.281992	−	0.909906i
$916$	6.55128	+	7.23926i	0.216460	+	0.239192i
$917$	−1.50449	+	49.5121i	−0.0496828	+	1.63503i
$918$	8.17680	+	5.16342i	0.269875	+	0.170418i
$919$	−26.1413	+	15.0927i	−0.862323	+	0.497862i	−0.864789	−	0.502135i	$-0.832548\pi$
$919$	−26.1413	+	15.0927i	−0.862323	+	0.497862i	0.00246672	+	0.999997i	$0.499215\pi$
$920$	28.2524	+	25.2464i	0.931454	+	0.832349i
$921$	−10.4640	−	9.68335i	−0.344801	−	0.319077i
$922$	−3.63391	−	34.1614i	−0.119676	−	1.12505i
$923$	0.346183	−	0.199869i	0.0113947	−	0.00657875i
$924$	−14.9194	−	0.619457i	−0.490811	−	0.0203786i
$925$	46.7183	+	26.9728i	1.53609	+	0.886860i
$926$	−5.80599	+	13.0847i	−0.190797	+	0.429990i
$927$	13.2290	+	6.32752i	0.434496	+	0.207823i
$928$	19.8007	+	11.2667i	0.649989	+	0.369847i
$929$		−	40.8824i		−	1.34131i	−0.741771	−	0.670653i	$-0.766014\pi$
$929$		−	40.8824i		−	1.34131i	0.741771	−	0.670653i	$-0.233986\pi$
$930$	24.6135	+	18.3524i	0.807109	+	0.601800i
$931$	−1.71572	+	28.2057i	−0.0562304	+	0.924403i
$932$	7.56128	−	1.62707i	0.247678	−	0.0532964i
$933$	−5.85821	+	6.33049i	−0.191789	+	0.207251i
$934$	−1.63773	+	3.69087i	−0.0535881	+	0.120769i
$935$	−5.85436	−	3.38002i	−0.191458	−	0.110538i
$936$	0.540002	+	0.412059i	0.0176505	+	0.0134686i
$937$		−	2.09716i		−	0.0685113i	−0.999413	−	0.0342556i	$-0.989094\pi$
$937$		−	2.09716i		−	0.0685113i	0.999413	−	0.0342556i	$-0.0109060\pi$
$938$	20.9539	+	10.0702i	0.684169	+	0.328805i
$939$	−19.1927	−	17.7608i	−0.626329	−	0.579603i
$940$	3.59183	+	3.96903i	0.117153	+	0.129455i
$941$	35.9990			1.17354			0.586768	−	0.809755i	$-0.300400\pi$
$941$	35.9990			1.17354			0.586768	+	0.809755i	$0.300400\pi$
$942$	3.47593	−	29.5487i	0.113252	−	0.962749i
$943$	−52.0004			−1.69336
$944$	−10.1297	+	14.0908i	−0.329695	+	0.458616i
$945$	33.1633	+	27.9100i	1.07880	+	0.907912i
$946$	21.5965	−	15.7322i	0.702162	−	0.511499i
$947$	25.0978			0.815568			0.407784	−	0.913078i	$-0.366302\pi$
$947$	25.0978			0.815568			0.407784	+	0.913078i	$0.366302\pi$
$948$	43.8960	−	24.6967i	1.42568	−	0.802111i
$949$			0.713931i			0.0231752i
$950$	28.0473	−	2.98353i	0.909975	−	0.0967984i
$951$	31.5697	+	29.2145i	1.02372	+	0.947345i
$952$	−9.44373	+	2.79297i	−0.306073	+	0.0905206i
$953$	15.8364			0.512990			0.256495	−	0.966546i	$-0.417432\pi$
$953$	15.8364			0.512990			0.256495	+	0.966546i	$0.417432\pi$
$954$	−4.13658	−	22.2976i	−0.133927	−	0.721913i
$955$	−6.24759	−	3.60705i	−0.202167	−	0.116721i
$956$	−10.4247	−	48.4454i	−0.337159	−	1.56684i
$957$	8.34114	+	7.71886i	0.269631	+	0.249515i
$958$	−43.8478	−	19.4563i	−1.41666	−	0.628605i
$959$	−9.67673	+	15.6432i	−0.312478	+	0.505146i
$960$	35.1868	+	25.8937i	1.13565	+	0.835717i
$961$	−15.1955			−0.490177
$962$	1.22919	−	0.130755i	0.0396306	−	0.00421570i
$963$	−31.2500	+	21.4276i	−1.00702	+	0.690496i
$964$	0.365938	+	1.70058i	0.0117861	+	0.0547719i
$965$	−36.0377	+	62.4191i	−1.16009	+	2.00934i
$966$	27.2362	+	4.04598i	0.876312	+	0.130177i
$967$	43.8994	−	25.3454i	1.41171	−	0.815052i	0.416161	−	0.909291i	$-0.363375\pi$
$967$	43.8994	−	25.3454i	1.41171	−	0.815052i	0.995550	+	0.0942394i	$0.0300419\pi$
$968$	23.1074	+	4.82066i	0.742699	+	0.154942i
$969$	6.24965	−	6.75348i	0.200768	−	0.216953i
$970$	−31.5642	+	71.1347i	−1.01346	+	2.28400i
$971$	−12.7651	+	7.36992i	−0.409651	+	0.236512i	−0.690640	−	0.723199i	$-0.742671\pi$
$971$	−12.7651	+	7.36992i	−0.409651	+	0.236512i	0.280989	+	0.959711i	$0.409338\pi$
$972$	−19.2966	−	24.4876i	−0.618937	−	0.785440i
$973$	30.5755	+	18.9137i	0.980206	+	0.606345i
$974$	44.4151	−	4.72465i	1.42315	−	0.151387i
$975$	0.202785	+	0.654328i	0.00649433	+	0.0209553i
$976$	−17.1376	−	12.3201i	−0.548561	−	0.394356i
$977$	−31.5328			−1.00882			−0.504412	−	0.863463i	$-0.668291\pi$
$977$	−31.5328			−1.00882			−0.504412	+	0.863463i	$0.668291\pi$
$978$	32.9968	−	14.2045i	1.05512	−	0.454209i
$979$	8.21782	+	4.74456i	0.262643	+	0.151637i
$980$	−43.6366	+	6.64853i	−1.39392	+	0.212379i
$981$	−14.9448	+	31.2451i	−0.477150	+	0.997580i
$982$	35.9992	+	15.9737i	1.14878	+	0.509741i
$983$	−24.5033	−	42.4409i	−0.781532	−	1.35365i	−0.931049	−	0.364895i	$-0.881105\pi$
$983$	−24.5033	−	42.4409i	−0.781532	−	1.35365i	0.149516	−	0.988759i	$-0.452228\pi$
$984$	−59.6888	+	5.67893i	−1.90281	+	0.181038i
$985$	−27.3518	−	15.7916i	−0.871500	−	0.503161i
$986$	6.85103	+	3.03997i	0.218181	+	0.0968123i
$987$	3.76590	+	0.975439i	0.119870	+	0.0310486i
$988$	0.479213	−	0.433671i	0.0152458	−	0.0137969i
$989$	−42.6693	+	24.6351i	−1.35680	+	0.783351i
$990$	14.1566	+	16.5695i	0.449926	+	0.526613i
$991$	1.40027	+	0.808447i	0.0444811	+	0.0256812i	0.522076	−	0.852899i	$-0.325158\pi$
$991$	1.40027	+	0.808447i	0.0444811	+	0.0256812i	−0.477595	+	0.878580i	$0.658491\pi$
$992$	22.4883	−	0.141281i	0.714005	−	0.00448568i
$993$	0.902726	−	0.975501i	0.0286471	−	0.0309566i
$994$	8.09320	−	16.8401i	0.256701	−	0.534136i
$995$	−13.5329	−	23.4397i	−0.429023	−	0.743089i
$996$	0.104281	−	9.37787i	0.00330428	−	0.297149i
$997$	−22.0008	−	38.1064i	−0.696771	−	1.20684i	−0.969580	−	0.244774i	$-0.921286\pi$
$997$	−22.0008	−	38.1064i	−0.696771	−	1.20684i	0.272809	−	0.962068i	$-0.412047\pi$
$998$	1.54662	+	14.5394i	0.0489575	+	0.460236i
$999$	−56.1355	−	8.23255i	−1.77605	−	0.260466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bf.b.115.20	yes	180
7.5	odd	6		504.2.cz.b.187.78	yes	180
8.3	odd	2	inner	504.2.bf.b.115.19	✓	180
9.4	even	3		504.2.cz.b.283.43	yes	180
56.19	even	6		504.2.cz.b.187.43	yes	180
63.40	odd	6	inner	504.2.bf.b.355.20	yes	180
72.67	odd	6		504.2.cz.b.283.78	yes	180
504.355	even	6	inner	504.2.bf.b.355.19	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.19	✓	180	8.3	odd	2	inner
504.2.bf.b.115.20	yes	180	1.1	even	1	trivial
504.2.bf.b.355.19	yes	180	504.355	even	6	inner
504.2.bf.b.355.20	yes	180	63.40	odd	6	inner
504.2.cz.b.187.43	yes	180	56.19	even	6
504.2.cz.b.187.78	yes	180	7.5	odd	6
504.2.cz.b.283.43	yes	180	9.4	even	3
504.2.cz.b.283.78	yes	180	72.67	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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14308 + 0.832691i) q^{2} +(-1.17641 + 1.27125i) q^{3} +(0.613252 - 1.90366i) q^{4} +(-1.57644 + 2.73047i) q^{5} +(0.286170 - 2.43272i) q^{6} +(-1.25267 - 2.33041i) q^{7} +(0.884165 + 2.68668i) q^{8} +(-0.232133 - 2.99101i) q^{9} +O(q^{10})\)	\(q+(-1.14308 + 0.832691i) q^{2} +(-1.17641 + 1.27125i) q^{3} +(0.613252 - 1.90366i) q^{4} +(-1.57644 + 2.73047i) q^{5} +(0.286170 - 2.43272i) q^{6} +(-1.25267 - 2.33041i) q^{7} +(0.884165 + 2.68668i) q^{8} +(-0.232133 - 2.99101i) q^{9} +(-0.471646 - 4.43382i) q^{10} +(-0.814620 - 1.41096i) q^{11} +(1.69859 + 3.01907i) q^{12} +(0.0400258 + 0.0693267i) q^{13} +(3.37241 + 1.62075i) q^{14} +(-1.61656 - 5.21618i) q^{15} +(-3.24784 - 2.33485i) q^{16} +(-1.13969 - 0.658003i) q^{17} +(2.75593 + 3.22566i) q^{18} +(3.49599 - 2.01841i) q^{19} +(4.23113 + 4.67546i) q^{20} +(4.43618 + 1.14905i) q^{21} +(2.10607 + 0.934513i) q^{22} +(-3.67953 - 2.12438i) q^{23} +(-4.45557 - 2.03664i) q^{24} +(-2.47030 - 4.27868i) q^{25} +(-0.103480 - 0.0459167i) q^{26} +(4.07539 + 3.22354i) q^{27} +(-5.20451 + 0.955536i) q^{28} +(3.48772 + 2.01364i) q^{29} +(6.19132 + 4.61640i) q^{30} +3.97549 q^{31} +(5.65674 - 0.0355381i) q^{32} +(2.75200 + 0.624284i) q^{33} +(1.85067 - 0.196865i) q^{34} +(8.33787 + 0.253358i) q^{35} +(-5.83621 - 1.39234i) q^{36} +(-9.45599 + 5.45942i) q^{37} +(-2.31548 + 5.21829i) q^{38} +(-0.135218 - 0.0306738i) q^{39} +(-8.72972 - 1.82119i) q^{40} +(10.5992 - 6.11948i) q^{41} +(-6.02770 + 2.38051i) q^{42} +(5.79819 - 10.0428i) q^{43} +(-3.18556 + 0.685483i) q^{44} +(8.53278 + 4.08130i) q^{45} +(5.97494 - 0.635583i) q^{46} +0.848906 q^{47} +(6.78895 - 1.38208i) q^{48} +(-3.86162 + 5.83848i) q^{49} +(6.38656 + 2.83387i) q^{50} +(2.17723 - 0.674752i) q^{51} +(0.156520 - 0.0336808i) q^{52} +(-4.62915 - 2.67264i) q^{53} +(-7.34270 - 0.291223i) q^{54} +5.13678 q^{55} +(5.15350 - 5.42600i) q^{56} +(-1.54681 + 6.81875i) q^{57} +(-5.66347 + 0.602450i) q^{58} -4.33850i q^{59} +(-10.9212 - 0.121443i) q^{60} +5.27660 q^{61} +(-4.54429 + 3.31035i) q^{62} +(-6.67948 + 4.28772i) q^{63} +(-6.43650 + 4.75094i) q^{64} -0.252392 q^{65} +(-3.66559 + 1.57796i) q^{66} +6.21333 q^{67} +(-1.95153 + 1.76607i) q^{68} +(7.02924 - 2.17846i) q^{69} +(-9.74179 + 6.65326i) q^{70} -4.99349i q^{71} +(7.83063 - 3.26821i) q^{72} +(7.72355 + 4.45919i) q^{73} +(6.26292 - 14.1145i) q^{74} +(8.34534 + 1.89312i) q^{75} +(-1.69845 - 7.89298i) q^{76} +(-2.26767 + 3.66587i) q^{77} +(0.180106 - 0.0775322i) q^{78} -14.5396i q^{79} +(11.4952 - 5.18739i) q^{80} +(-8.89223 + 1.38862i) q^{81} +(-7.02012 + 15.8209i) q^{82} +(-2.34461 - 1.35366i) q^{83} +(4.90790 - 7.74031i) q^{84} +(3.59331 - 2.07460i) q^{85} +(1.73473 + 16.3077i) q^{86} +(-6.66280 + 2.06489i) q^{87} +(3.07055 - 3.43615i) q^{88} +(-5.04396 + 2.91213i) q^{89} +(-13.1521 + 2.43993i) q^{90} +(0.111420 - 0.180120i) q^{91} +(-6.30058 + 5.70180i) q^{92} +(-4.67679 + 5.05382i) q^{93} +(-0.970365 + 0.706876i) q^{94} +12.7276i q^{95} +(-6.60945 + 7.23292i) q^{96} +(-15.1154 - 8.72685i) q^{97} +(-0.447524 - 9.88937i) q^{98} +(-4.03110 + 2.76406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

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