LMFDB - Embedded newform 1110.2.x.d.751.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 60x^{14} + 1362x^{12} + 15028x^{10} + 86441x^{8} + 260376x^{6} + 382684x^{4} + 224224x^{2} + 38416 $ x^16 + 60x^14 + 1362x^12 + 15028x^10 + 86441x^8 + 260376x^6 + 382684x^4 + 224224*x^2 + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.3
Root			$0.871333i$ of defining polynomial
Character	$\chi$	$=$	1110.751
Dual form			1110.2.x.d.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(0.435667 - 0.754597i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(0.435667 - 0.754597i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +1.12820 q^{11} +(0.500000 + 0.866025i) q^{12} +(-5.16160 - 2.98005i) q^{13} +0.871333i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.62062 + 0.935667i) q^{17} +(0.866025 + 0.500000i) q^{18} +(5.64541 + 3.25938i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(0.435667 + 0.754597i) q^{21} +(-0.977051 + 0.564101i) q^{22} +4.22805i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +5.96011 q^{26} +1.00000 q^{27} +(-0.435667 - 0.754597i) q^{28} +4.16204i q^{29} +(-0.500000 + 0.866025i) q^{30} +5.15096i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.564101 + 0.977051i) q^{33} +(0.935667 - 1.62062i) q^{34} +(-0.754597 + 0.435667i) q^{35} -1.00000 q^{36} +(-2.13754 - 5.69481i) q^{37} -6.51876 q^{38} +(5.16160 - 2.98005i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-5.31389 + 9.20392i) q^{41} +(-0.754597 - 0.435667i) q^{42} -9.37901i q^{43} +(0.564101 - 0.977051i) q^{44} +1.00000i q^{45} +(-2.11403 - 3.66160i) q^{46} +7.61359 q^{47} +1.00000 q^{48} +(3.12039 + 5.40467i) q^{49} +(-0.866025 - 0.500000i) q^{50} -1.87133i q^{51} +(-5.16160 + 2.98005i) q^{52} +(5.57432 + 9.65501i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.977051 - 0.564101i) q^{55} +(0.754597 + 0.435667i) q^{56} +(-5.64541 + 3.25938i) q^{57} +(-2.08102 - 3.60443i) q^{58} +(-1.96930 + 1.13698i) q^{59} -1.00000i q^{60} +(4.20441 + 2.42742i) q^{61} +(-2.57548 - 4.46086i) q^{62} -0.871333 q^{63} -1.00000 q^{64} +(2.98005 + 5.16160i) q^{65} -1.12820i q^{66} +(-7.07277 + 12.2504i) q^{67} +1.87133i q^{68} +(-3.66160 - 2.11403i) q^{69} +(0.435667 - 0.754597i) q^{70} +(-7.55813 + 13.0911i) q^{71} +(0.866025 - 0.500000i) q^{72} -4.43634 q^{73} +(4.69857 + 3.86308i) q^{74} -1.00000 q^{75} +(5.64541 - 3.25938i) q^{76} +(0.491520 - 0.851337i) q^{77} +(-2.98005 + 5.16160i) q^{78} +(-10.0774 - 5.81817i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -10.6278i q^{82} +(-2.47486 - 4.28659i) q^{83} +0.871333 q^{84} +1.87133 q^{85} +(4.68951 + 8.12246i) q^{86} +(-3.60443 - 2.08102i) q^{87} +1.12820i q^{88} +(7.87663 - 4.54758i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-4.49748 + 2.59662i) q^{91} +(3.66160 + 2.11403i) q^{92} +(-4.46086 - 2.57548i) q^{93} +(-6.59356 + 3.80679i) q^{94} +(-3.25938 - 5.64541i) q^{95} +(-0.866025 + 0.500000i) q^{96} +2.17225i q^{97} +(-5.40467 - 3.12039i) q^{98} +(-0.564101 - 0.977051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$		−	1.00000i		−	0.408248i
$7$	0.435667	−	0.754597i	0.164666	−	0.285211i	−0.771870	−	0.635780i	$-0.780679\pi$
$7$	0.435667	−	0.754597i	0.164666	−	0.285211i	0.936537	+	0.350569i	$0.114012\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	1.12820			0.340165			0.170083	−	0.985430i	$-0.445597\pi$
$11$	1.12820			0.340165			0.170083	+	0.985430i	$0.445597\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−5.16160	−	2.98005i	−1.43157	−	0.826518i	−0.434330	−	0.900754i	$-0.643015\pi$
$13$	−5.16160	−	2.98005i	−1.43157	−	0.826518i	−0.997241	+	0.0742358i	$0.976348\pi$
$14$			0.871333i			0.232874i
$15$	0.866025	−	0.500000i	0.223607	−	0.129099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.62062	+	0.935667i	−0.393059	+	0.226932i	−0.683485	−	0.729965i	$-0.739536\pi$
$17$	−1.62062	+	0.935667i	−0.393059	+	0.226932i	0.290426	+	0.956897i	$0.406203\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	5.64541	+	3.25938i	1.29515	+	0.747753i	0.979562	−	0.201144i	$-0.0644659\pi$
$19$	5.64541	+	3.25938i	1.29515	+	0.747753i	0.315585	+	0.948897i	$0.397799\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	0.435667	+	0.754597i	0.0950702	+	0.164666i
$22$	−0.977051	+	0.564101i	−0.208308	+	0.120267i
$23$			4.22805i			0.881610i	0.897603	+	0.440805i	$0.145307\pi$
$23$			4.22805i			0.881610i	−0.897603	+	0.440805i	$0.854693\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	5.96011			1.16887
$27$	1.00000			0.192450
$28$	−0.435667	−	0.754597i	−0.0823332	−	0.142605i
$29$			4.16204i			0.772872i	0.922316	+	0.386436i	$0.126294\pi$
$29$			4.16204i			0.772872i	−0.922316	+	0.386436i	$0.873706\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$			5.15096i			0.925140i	0.886583	+	0.462570i	$0.153073\pi$
$31$			5.15096i			0.925140i	−0.886583	+	0.462570i	$0.846927\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.564101	+	0.977051i	−0.0981973	+	0.170083i
$34$	0.935667	−	1.62062i	0.160465	−	0.277934i
$35$	−0.754597	+	0.435667i	−0.127550	+	0.0736411i
$36$	−1.00000			−0.166667
$37$	−2.13754	−	5.69481i	−0.351410	−	0.936222i
$37$	−2.13754	−	5.69481i	−0.351410	−	0.936222i
$38$	−6.51876			−1.05748
$39$	5.16160	−	2.98005i	0.826518	−	0.477190i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−5.31389	+	9.20392i	−0.829890	+	1.43741i	0.0682345	+	0.997669i	$0.478263\pi$
$41$	−5.31389	+	9.20392i	−0.829890	+	1.43741i	−0.898124	+	0.439742i	$0.855070\pi$
$42$	−0.754597	−	0.435667i	−0.116437	−	0.0672248i
$43$		−	9.37901i		−	1.43029i	−0.698978	−	0.715143i	$-0.746362\pi$
$43$		−	9.37901i		−	1.43029i	0.698978	−	0.715143i	$-0.253638\pi$
$44$	0.564101	−	0.977051i	0.0850414	−	0.147296i
$45$			1.00000i			0.149071i
$46$	−2.11403	−	3.66160i	−0.311696	−	0.539874i
$47$	7.61359			1.11056			0.555278	−	0.831665i	$-0.312612\pi$
$47$	7.61359			1.11056			0.555278	+	0.831665i	$0.312612\pi$
$48$	1.00000			0.144338
$49$	3.12039	+	5.40467i	0.445770	+	0.772096i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		−	1.87133i		−	0.262039i
$52$	−5.16160	+	2.98005i	−0.715786	+	0.413259i
$53$	5.57432	+	9.65501i	0.765692	+	1.32622i	0.939880	+	0.341505i	$0.110937\pi$
$53$	5.57432	+	9.65501i	0.765692	+	1.32622i	−0.174188	+	0.984712i	$0.555730\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−0.977051	−	0.564101i	−0.131746	−	0.0760633i
$56$	0.754597	+	0.435667i	0.100837	+	0.0582184i
$57$	−5.64541	+	3.25938i	−0.747753	+	0.431716i
$58$	−2.08102	−	3.60443i	−0.273251	−	0.473285i
$59$	−1.96930	+	1.13698i	−0.256381	+	0.148022i	−0.622683	−	0.782475i	$-0.713957\pi$
$59$	−1.96930	+	1.13698i	−0.256381	+	0.148022i	0.366301	+	0.930496i	$0.380624\pi$
$60$		−	1.00000i		−	0.129099i
$61$	4.20441	+	2.42742i	0.538319	+	0.310799i	0.744398	−	0.667737i	$-0.232737\pi$
$61$	4.20441	+	2.42742i	0.538319	+	0.310799i	−0.206078	+	0.978536i	$0.566070\pi$
$62$	−2.57548	−	4.46086i	−0.327086	−	0.566530i
$63$	−0.871333			−0.109778
$64$	−1.00000			−0.125000
$65$	2.98005	+	5.16160i	0.369630	+	0.640218i
$66$		−	1.12820i		−	0.138872i
$67$	−7.07277	+	12.2504i	−0.864076	+	1.49662i	0.00388486	+	0.999992i	$0.498763\pi$
$67$	−7.07277	+	12.2504i	−0.864076	+	1.49662i	−0.867961	+	0.496632i	$0.834570\pi$
$68$			1.87133i			0.226932i
$69$	−3.66160	−	2.11403i	−0.440805	−	0.254499i
$70$	0.435667	−	0.754597i	0.0520721	−	0.0901916i
$71$	−7.55813	+	13.0911i	−0.896985	+	1.55362i	−0.0656567	+	0.997842i	$0.520914\pi$
$71$	−7.55813	+	13.0911i	−0.896985	+	1.55362i	−0.831328	+	0.555782i	$0.812419\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−4.43634			−0.519234			−0.259617	−	0.965712i	$-0.583596\pi$
$73$	−4.43634			−0.519234			−0.259617	+	0.965712i	$0.583596\pi$
$74$	4.69857	+	3.86308i	0.546198	+	0.449074i
$75$	−1.00000			−0.115470
$76$	5.64541	−	3.25938i	0.647573	−	0.373877i
$77$	0.491520	−	0.851337i	0.0560139	−	0.0970188i
$78$	−2.98005	+	5.16160i	−0.337425	+	0.584436i
$79$	−10.0774	−	5.81817i	−1.13379	−	0.654596i	−0.188907	−	0.981995i	$-0.560494\pi$
$79$	−10.0774	−	5.81817i	−1.13379	−	0.654596i	−0.944886	+	0.327399i	$0.893828\pi$
$80$			1.00000i			0.111803i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	10.6278i		−	1.17364i
$83$	−2.47486	−	4.28659i	−0.271652	−	0.470515i	0.697633	−	0.716455i	$-0.254237\pi$
$83$	−2.47486	−	4.28659i	−0.271652	−	0.470515i	−0.969285	+	0.245941i	$0.920903\pi$
$84$	0.871333			0.0950702
$85$	1.87133			0.202975
$86$	4.68951	+	8.12246i	0.505683	+	0.875868i
$87$	−3.60443	−	2.08102i	−0.386436	−	0.223109i
$88$			1.12820i			0.120267i
$89$	7.87663	−	4.54758i	0.834921	−	0.482042i	−0.0206134	−	0.999788i	$-0.506562\pi$
$89$	7.87663	−	4.54758i	0.834921	−	0.482042i	0.855535	+	0.517745i	$0.173229\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−4.49748	+	2.59662i	−0.471464	+	0.272200i
$92$	3.66160	+	2.11403i	0.381748	+	0.220403i
$93$	−4.46086	−	2.57548i	−0.462570	−	0.267065i
$94$	−6.59356	+	3.80679i	−0.680074	+	0.392641i
$95$	−3.25938	−	5.64541i	−0.334405	−	0.579207i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$			2.17225i			0.220558i	0.993901	+	0.110279i	$0.0351745\pi$
$97$			2.17225i			0.220558i	−0.993901	+	0.110279i	$0.964826\pi$
$98$	−5.40467	−	3.12039i	−0.545954	−	0.315207i
$99$	−0.564101	−	0.977051i	−0.0566942	−	0.0981973i
$100$	1.00000			0.100000
$101$	−4.72751			−0.470405			−0.235202	−	0.971946i	$-0.575575\pi$
$101$	−4.72751			−0.470405			−0.235202	+	0.971946i	$0.575575\pi$
$102$	0.935667	+	1.62062i	0.0926448	+	0.160465i
$103$			5.43512i			0.535538i	0.963483	+	0.267769i	$0.0862864\pi$
$103$			5.43512i			0.535538i	−0.963483	+	0.267769i	$0.913714\pi$
$104$	2.98005	−	5.16160i	0.292218	−	0.506137i
$105$		−	0.871333i		−	0.0850334i
$106$	−9.65501	−	5.57432i	−0.937777	−	0.541426i
$107$	−8.33163	+	14.4308i	−0.805449	+	1.39508i	0.110539	+	0.993872i	$0.464742\pi$
$107$	−8.33163	+	14.4308i	−0.805449	+	1.39508i	−0.915988	+	0.401206i	$0.868591\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	14.5230	−	8.38487i	1.39105	−	0.803125i	0.397622	−	0.917549i	$-0.369836\pi$
$109$	14.5230	−	8.38487i	1.39105	−	0.803125i	0.993432	+	0.114424i	$0.0365023\pi$
$110$	1.12820			0.107570
$111$	6.00063	+	0.996242i	0.569554	+	0.0945591i
$112$	−0.871333			−0.0823332
$113$	−7.42944	+	4.28939i	−0.698903	+	0.403512i	−0.806939	−	0.590635i	$-0.798877\pi$
$113$	−7.42944	+	4.28939i	−0.698903	+	0.403512i	0.108036	+	0.994147i	$0.465544\pi$
$114$	3.25938	−	5.64541i	0.305269	−	0.528741i
$115$	2.11403	−	3.66160i	0.197134	−	0.341446i
$116$	3.60443	+	2.08102i	0.334663	+	0.193218i
$117$			5.96011i			0.551012i
$118$	1.13698	−	1.96930i	0.104667	−	0.181289i
$119$			1.63055i			0.149473i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−9.72716			−0.884287
$122$	−4.85483			−0.439536
$123$	−5.31389	−	9.20392i	−0.479137	−	0.829890i
$124$	4.46086	+	2.57548i	0.400597	+	0.231285i
$125$		−	1.00000i		−	0.0894427i
$126$	0.754597	−	0.435667i	0.0672248	−	0.0388123i
$127$	−8.08310	−	14.0003i	−0.717259	−	1.24233i	−0.962082	−	0.272761i	$-0.912063\pi$
$127$	−8.08310	−	14.0003i	−0.717259	−	1.24233i	0.244823	−	0.969568i	$-0.421270\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	8.12246	+	4.68951i	0.715143	+	0.412888i
$130$	−5.16160	−	2.98005i	−0.452703	−	0.261368i
$131$	−4.90282	+	2.83065i	−0.428361	+	0.247315i	−0.698648	−	0.715465i	$-0.746215\pi$
$131$	−4.90282	+	2.83065i	−0.428361	+	0.247315i	0.270287	+	0.962780i	$0.412881\pi$
$132$	0.564101	+	0.977051i	0.0490987	+	0.0850414i
$133$	4.91904	−	2.84001i	0.426535	−	0.246260i
$134$		−	14.1455i		−	1.22199i
$135$	−0.866025	−	0.500000i	−0.0745356	−	0.0430331i
$136$	−0.935667	−	1.62062i	−0.0802327	−	0.138967i
$137$	−16.5057			−1.41018			−0.705088	−	0.709120i	$-0.749093\pi$
$137$	−16.5057			−1.41018			−0.705088	+	0.709120i	$0.749093\pi$
$138$	4.22805			0.359916
$139$	8.84982	+	15.3283i	0.750632	+	1.30013i	0.947517	+	0.319706i	$0.103584\pi$
$139$	8.84982	+	15.3283i	0.750632	+	1.30013i	−0.196885	+	0.980427i	$0.563083\pi$
$140$			0.871333i			0.0736411i
$141$	−3.80679	+	6.59356i	−0.320590	+	0.555278i
$142$		−	15.1163i		−	1.26853i
$143$	−5.82333	−	3.36210i	−0.486971	−	0.281153i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	2.08102	−	3.60443i	0.172819	−	0.299332i
$146$	3.84198	−	2.21817i	0.317964	−	0.183577i
$147$	−6.24078			−0.514731
$148$	−6.00063	−	0.996242i	−0.493248	−	0.0818906i
$149$	16.5978			1.35975			0.679873	−	0.733330i	$-0.262035\pi$
$149$	16.5978			1.35975			0.679873	+	0.733330i	$0.262035\pi$
$150$	0.866025	−	0.500000i	0.0707107	−	0.0408248i
$151$	7.15224	−	12.3880i	0.582041	−	1.00812i	−0.413196	−	0.910642i	$-0.635588\pi$
$151$	7.15224	−	12.3880i	0.582041	−	1.00812i	0.995237	−	0.0974827i	$-0.0310791\pi$
$152$	−3.25938	+	5.64541i	−0.264371	+	0.457903i
$153$	1.62062	+	0.935667i	0.131020	+	0.0756442i
$154$			0.983039i			0.0792156i
$155$	2.57548	−	4.46086i	0.206868	−	0.358305i
$156$		−	5.96011i		−	0.477190i
$157$	9.11409	+	15.7861i	0.727383	+	1.25986i	0.957985	+	0.286817i	$0.0925971\pi$
$157$	9.11409	+	15.7861i	0.727383	+	1.25986i	−0.230602	+	0.973048i	$0.574070\pi$
$158$	11.6363			0.925738
$159$	−11.1486			−0.884145
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	3.19048	+	1.84202i	0.251445	+	0.145172i
$162$		−	1.00000i		−	0.0785674i
$163$	−5.43671	+	3.13889i	−0.425836	+	0.245857i	−0.697571	−	0.716516i	$-0.745736\pi$
$163$	−5.43671	+	3.13889i	−0.425836	+	0.245857i	0.271735	+	0.962372i	$0.412403\pi$
$164$	5.31389	+	9.20392i	0.414945	+	0.718706i
$165$	0.977051	−	0.564101i	0.0760633	−	0.0439152i
$166$	4.28659	+	2.47486i	0.332704	+	0.192087i
$167$	6.40836	+	3.69987i	0.495894	+	0.286304i	0.727016	−	0.686620i	$-0.240907\pi$
$167$	6.40836	+	3.69987i	0.495894	+	0.286304i	−0.231123	+	0.972925i	$0.574240\pi$
$168$	−0.754597	+	0.435667i	−0.0582184	+	0.0336124i
$169$	11.2614	+	19.5054i	0.866264	+	1.50041i
$170$	−1.62062	+	0.935667i	−0.124296	+	0.0717624i
$171$		−	6.51876i		−	0.498502i
$172$	−8.12246	−	4.68951i	−0.619332	−	0.357572i
$173$	5.21856	+	9.03881i	0.396760	+	0.687208i	0.993324	−	0.115357i	$-0.0368012\pi$
$173$	5.21856	+	9.03881i	0.396760	+	0.687208i	−0.596564	+	0.802565i	$0.703468\pi$
$174$	4.16204			0.315523
$175$	0.871333			0.0658666
$176$	−0.564101	−	0.977051i	−0.0425207	−	0.0736480i
$177$		−	2.27395i		−	0.170921i
$178$	−4.54758	+	7.87663i	−0.340855	+	0.590379i
$179$		−	8.74992i		−	0.653999i	−0.945024	−	0.327000i	$-0.893962\pi$
$179$		−	8.74992i		−	0.653999i	0.945024	−	0.327000i	$-0.106038\pi$
$180$	0.866025	+	0.500000i	0.0645497	+	0.0372678i
$181$	−7.65366	+	13.2565i	−0.568892	+	0.985350i	0.427784	+	0.903881i	$0.359295\pi$
$181$	−7.65366	+	13.2565i	−0.568892	+	0.985350i	−0.996676	+	0.0814692i	$0.974039\pi$
$182$	2.59662	−	4.49748i	0.192474	−	0.333375i
$183$	−4.20441	+	2.42742i	−0.310799	+	0.179440i
$184$	−4.22805			−0.311696
$185$	−0.996242	+	6.00063i	−0.0732452	+	0.441175i
$186$	5.15096			0.377687
$187$	−1.82839	+	1.05562i	−0.133705	+	0.0771946i
$188$	3.80679	−	6.59356i	0.277639	−	0.480885i
$189$	0.435667	−	0.754597i	0.0316901	−	0.0548888i
$190$	5.64541	+	3.25938i	0.409561	+	0.236460i
$191$		−	17.4079i		−	1.25959i	−0.776761	−	0.629796i	$-0.783139\pi$
$191$		−	17.4079i		−	1.25959i	0.776761	−	0.629796i	$-0.216861\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$			18.8491i			1.35679i	0.734698	+	0.678395i	$0.237324\pi$
$193$			18.8491i			1.35679i	−0.734698	+	0.678395i	$0.762676\pi$
$194$	−1.08612	−	1.88122i	−0.0779791	−	0.135064i
$195$	−5.96011			−0.426812
$196$	6.24078			0.445770
$197$	0.306829	+	0.531443i	0.0218607	+	0.0378638i	0.876749	−	0.480949i	$-0.159708\pi$
$197$	0.306829	+	0.531443i	0.0218607	+	0.0378638i	−0.854888	+	0.518812i	$0.826374\pi$
$198$	0.977051	+	0.564101i	0.0694360	+	0.0400889i
$199$		−	23.3952i		−	1.65844i	−0.558920	−	0.829222i	$-0.688784\pi$
$199$		−	23.3952i		−	1.65844i	0.558920	−	0.829222i	$-0.311216\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−7.07277	−	12.2504i	−0.498875	−	0.864076i
$202$	4.09414	−	2.36375i	0.288063	−	0.166313i
$203$	3.14066	+	1.81326i	0.220431	+	0.127266i
$204$	−1.62062	−	0.935667i	−0.113466	−	0.0655098i
$205$	9.20392	−	5.31389i	0.642830	−	0.371138i
$206$	−2.71756	−	4.70695i	−0.189341	−	0.327949i
$207$	3.66160	−	2.11403i	0.254499	−	0.146935i
$208$			5.96011i			0.413259i
$209$	6.36916	+	3.67724i	0.440564	+	0.254360i
$210$	0.435667	+	0.754597i	0.0300639	+	0.0520721i
$211$	21.1872			1.45859			0.729295	−	0.684199i	$-0.239848\pi$
$211$	21.1872			1.45859			0.729295	+	0.684199i	$0.239848\pi$
$212$	11.1486			0.765692
$213$	−7.55813	−	13.0911i	−0.517875	−	0.896985i
$214$		−	16.6633i		−	1.13908i
$215$	−4.68951	+	8.12246i	−0.319822	+	0.553947i
$216$			1.00000i			0.0680414i
$217$	3.88690	+	2.24410i	0.263860	+	0.152339i
$218$	−8.38487	+	14.5230i	−0.567895	+	0.983623i
$219$	2.21817	−	3.84198i	0.149890	−	0.259617i
$220$	−0.977051	+	0.564101i	−0.0658728	+	0.0380317i
$221$	11.1533			0.750255
$222$	−5.69481	+	2.13754i	−0.382211	+	0.143462i
$223$	15.4416			1.03405			0.517024	−	0.855971i	$-0.327040\pi$
$223$	15.4416			1.03405			0.517024	+	0.855971i	$0.327040\pi$
$224$	0.754597	−	0.435667i	0.0504186	−	0.0291092i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	4.28939	−	7.42944i	0.285326	−	0.494199i
$227$	3.86623	+	2.23217i	0.256611	+	0.148154i	0.622788	−	0.782391i	$-0.286000\pi$
$227$	3.86623	+	2.23217i	0.256611	+	0.148154i	−0.366177	+	0.930545i	$0.619333\pi$
$228$			6.51876i			0.431716i
$229$	8.13293	−	14.0866i	0.537439	−	0.930872i	−0.461602	−	0.887087i	$-0.652725\pi$
$229$	8.13293	−	14.0866i	0.537439	−	0.930872i	0.999041	−	0.0437847i	$-0.0139416\pi$
$230$			4.22805i			0.278790i
$231$	0.491520	+	0.851337i	0.0323396	+	0.0560139i
$232$	−4.16204			−0.273251
$233$	3.64777			0.238973			0.119487	−	0.992836i	$-0.461875\pi$
$233$	3.64777			0.238973			0.119487	+	0.992836i	$0.461875\pi$
$234$	−2.98005	−	5.16160i	−0.194812	−	0.337425i
$235$	−6.59356	−	3.80679i	−0.430117	−	0.248328i
$236$			2.27395i			0.148022i
$237$	10.0774	−	5.81817i	0.654596	−	0.377931i
$238$	−0.815277	−	1.41210i	−0.0528466	−	0.0915330i
$239$	6.62403	−	3.82438i	0.428473	−	0.247379i	−0.270223	−	0.962798i	$-0.587097\pi$
$239$	6.62403	−	3.82438i	0.428473	−	0.247379i	0.698696	+	0.715419i	$0.253764\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	−18.8434	−	10.8793i	−1.21381	−	0.700794i	−0.250224	−	0.968188i	$-0.580504\pi$
$241$	−18.8434	−	10.8793i	−1.21381	−	0.700794i	−0.963587	+	0.267394i	$0.913838\pi$
$242$	8.42397	−	4.86358i	0.541513	−	0.312643i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	4.20441	−	2.42742i	0.269160	−	0.155399i
$245$		−	6.24078i		−	0.398709i
$246$	9.20392	+	5.31389i	0.586821	+	0.338801i
$247$	−19.4263	−	33.6473i	−1.23606	−	2.14092i
$248$	−5.15096			−0.327086
$249$	4.94973			0.313676
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$		−	0.241710i		−	0.0152566i	−0.999971	−	0.00762829i	$-0.997572\pi$
$251$		−	0.241710i		−	0.0152566i	0.999971	−	0.00762829i	$-0.00242818\pi$
$252$	−0.435667	+	0.754597i	−0.0274444	+	0.0475351i
$253$			4.77010i			0.299893i
$254$	14.0003	+	8.08310i	0.878459	+	0.507179i
$255$	−0.935667	+	1.62062i	−0.0585937	+	0.101487i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	21.5141	−	12.4212i	1.34201	−	0.774810i	0.354909	−	0.934901i	$-0.384512\pi$
$257$	21.5141	−	12.4212i	1.34201	−	0.774810i	0.987102	+	0.160091i	$0.0511787\pi$
$258$	−9.37901			−0.583912
$259$	−5.22854	−	0.868059i	−0.324886	−	0.0539385i
$260$	5.96011			0.369630
$261$	3.60443	−	2.08102i	0.223109	−	0.128812i
$262$	2.83065	−	4.90282i	0.174878	−	0.302897i
$263$	−1.71221	+	2.96564i	−0.105580	+	0.182869i	−0.913975	−	0.405771i	$-0.867003\pi$
$263$	−1.71221	+	2.96564i	−0.105580	+	0.182869i	0.808395	+	0.588640i	$0.200336\pi$
$264$	−0.977051	−	0.564101i	−0.0601333	−	0.0347180i
$265$		−	11.1486i		−	0.684856i
$266$	−2.84001	+	4.91904i	−0.174132	+	0.301605i
$267$			9.09515i			0.556614i
$268$	7.07277	+	12.2504i	0.432038	+	0.748312i
$269$	32.4772			1.98017			0.990084	−	0.140479i	$-0.0448644\pi$
$269$	32.4772			1.98017			0.990084	+	0.140479i	$0.0448644\pi$
$270$	1.00000			0.0608581
$271$	−3.74795	−	6.49164i	−0.227672	−	0.394339i	0.729446	−	0.684039i	$-0.239778\pi$
$271$	−3.74795	−	6.49164i	−0.227672	−	0.394339i	−0.957118	+	0.289699i	$0.906445\pi$
$272$	1.62062	+	0.935667i	0.0982646	+	0.0567331i
$273$		−	5.19324i		−	0.314309i
$274$	14.2943	−	8.25285i	0.863553	−	0.498573i
$275$	0.564101	+	0.977051i	0.0340165	+	0.0589184i
$276$	−3.66160	+	2.11403i	−0.220403	+	0.127249i
$277$	−4.86420	−	2.80834i	−0.292261	−	0.168737i	0.346700	−	0.937976i	$-0.387302\pi$
$277$	−4.86420	−	2.80834i	−0.292261	−	0.168737i	−0.638961	+	0.769239i	$0.720636\pi$
$278$	−15.3283	−	8.84982i	−0.919332	−	0.530777i
$279$	4.46086	−	2.57548i	0.267065	−	0.154190i
$280$	−0.435667	−	0.754597i	−0.0260361	−	0.0450958i
$281$	−17.9392	+	10.3572i	−1.07016	+	0.617860i	−0.928226	−	0.372016i	$-0.878667\pi$
$281$	−17.9392	+	10.3572i	−1.07016	+	0.617860i	−0.141938	+	0.989876i	$0.545333\pi$
$282$		−	7.61359i		−	0.453383i
$283$	8.44311	+	4.87463i	0.501891	+	0.289767i	0.729494	−	0.683987i	$-0.239756\pi$
$283$	8.44311	+	4.87463i	0.501891	+	0.289767i	−0.227603	+	0.973754i	$0.573089\pi$
$284$	7.55813	+	13.0911i	0.448493	+	0.776812i
$285$	6.51876			0.386138
$286$	6.72420			0.397610
$287$	4.63017	+	8.01968i	0.273310	+	0.473387i
$288$		−	1.00000i		−	0.0589256i
$289$	−6.74906	+	11.6897i	−0.397003	+	0.687630i
$290$			4.16204i			0.244403i
$291$	−1.88122	−	1.08612i	−0.110279	−	0.0636697i
$292$	−2.21817	+	3.84198i	−0.129808	+	0.224835i
$293$	9.36994	−	16.2292i	0.547398	−	0.948121i	−0.451054	−	0.892497i	$-0.648952\pi$
$293$	9.36994	−	16.2292i	0.547398	−	0.948121i	0.998452	−	0.0556243i	$-0.0177149\pi$
$294$	5.40467	−	3.12039i	0.315207	−	0.181985i
$295$	2.27395			0.132395
$296$	5.69481	−	2.13754i	0.331004	−	0.124242i
$297$	1.12820			0.0654649
$298$	−14.3741	+	8.29891i	−0.832671	+	0.480743i
$299$	12.5998	−	21.8235i	0.728667	−	1.26209i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−7.07737	−	4.08612i	−0.407933	−	0.235520i
$302$			14.3045i			0.823130i
$303$	2.36375	−	4.09414i	0.135794	−	0.235202i
$304$		−	6.51876i		−	0.373877i
$305$	−2.42742	−	4.20441i	−0.138993	−	0.240744i
$306$	−1.87133			−0.106977
$307$	26.2743			1.49955			0.749776	−	0.661692i	$-0.230161\pi$
$307$	26.2743			1.49955			0.749776	+	0.661692i	$0.230161\pi$
$308$	−0.491520	−	0.851337i	−0.0280069	−	0.0485094i
$309$	−4.70695	−	2.71756i	−0.267769	−	0.154597i
$310$			5.15096i			0.292555i
$311$	−28.9868	+	16.7355i	−1.64369	+	0.948984i	−0.664182	+	0.747571i	$0.731220\pi$
$311$	−28.9868	+	16.7355i	−1.64369	+	0.948984i	−0.979506	+	0.201414i	$0.935446\pi$
$312$	2.98005	+	5.16160i	0.168712	+	0.292218i
$313$	−1.72710	+	0.997143i	−0.0976216	+	0.0563619i	−0.548016	−	0.836468i	$-0.684617\pi$
$313$	−1.72710	+	0.997143i	−0.0976216	+	0.0563619i	0.450394	+	0.892830i	$0.351283\pi$
$314$	−15.7861	−	9.11409i	−0.890859	−	0.514338i
$315$	0.754597	+	0.435667i	0.0425167	+	0.0245470i
$316$	−10.0774	+	5.81817i	−0.566897	+	0.327298i
$317$	−2.99369	−	5.18523i	−0.168143	−	0.291232i	0.769624	−	0.638497i	$-0.220444\pi$
$317$	−2.99369	−	5.18523i	−0.168143	−	0.291232i	−0.937767	+	0.347266i	$0.887110\pi$
$318$	9.65501	−	5.57432i	0.541426	−	0.312592i
$319$			4.69562i			0.262904i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−8.33163	−	14.4308i	−0.465026	−	0.805449i
$322$	−3.68404			−0.205304
$323$	−12.1988			−0.678758
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$		−	5.96011i		−	0.330607i
$326$	3.13889	−	5.43671i	0.173847	−	0.301112i
$327$			16.7697i			0.927369i
$328$	−9.20392	−	5.31389i	−0.508202	−	0.293410i
$329$	3.31699	−	5.74519i	0.182871	−	0.316743i
$330$	−0.564101	+	0.977051i	−0.0310527	+	0.0537849i
$331$	−16.1475	+	9.32279i	−0.887549	+	0.512427i	−0.873140	−	0.487470i	$-0.837920\pi$
$331$	−16.1475	+	9.32279i	−0.887549	+	0.512427i	−0.0144090	+	0.999896i	$0.504587\pi$
$332$	−4.94973			−0.271652
$333$	−3.86308	+	4.69857i	−0.211696	+	0.257480i
$334$	−7.39973			−0.404895
$335$	12.2504	−	7.07277i	0.669311	−	0.386427i
$336$	0.435667	−	0.754597i	0.0237676	−	0.0411666i
$337$	0.597607	−	1.03509i	0.0325538	−	0.0563848i	−0.849290	−	0.527927i	$-0.822969\pi$
$337$	0.597607	−	1.03509i	0.0325538	−	0.0563848i	0.881843	+	0.471543i	$0.156303\pi$
$338$	−19.5054	−	11.2614i	−1.06095	−	0.612541i
$339$		−	8.57878i		−	0.465935i
$340$	0.935667	−	1.62062i	0.0507436	−	0.0878906i
$341$			5.81132i			0.314701i
$342$	3.25938	+	5.64541i	0.176247	+	0.305269i
$343$	11.5371			0.622946
$344$	9.37901			0.505683
$345$	2.11403	+	3.66160i	0.113815	+	0.197134i
$346$	−9.03881	−	5.21856i	−0.485930	−	0.280552i
$347$		−	5.89358i		−	0.316384i	−0.987408	−	0.158192i	$-0.949434\pi$
$347$		−	5.89358i		−	0.316384i	0.987408	−	0.158192i	$-0.0505665\pi$
$348$	−3.60443	+	2.08102i	−0.193218	+	0.111554i
$349$	7.13276	+	12.3543i	0.381808	+	0.661311i	0.991321	−	0.131465i	$-0.0419682\pi$
$349$	7.13276	+	12.3543i	0.381808	+	0.661311i	−0.609513	+	0.792776i	$0.708635\pi$
$350$	−0.754597	+	0.435667i	−0.0403349	+	0.0232874i
$351$	−5.16160	−	2.98005i	−0.275506	−	0.159063i
$352$	0.977051	+	0.564101i	0.0520770	+	0.0300667i
$353$	14.6158	−	8.43844i	0.777921	−	0.449133i	−0.0577722	−	0.998330i	$-0.518400\pi$
$353$	14.6158	−	8.43844i	0.777921	−	0.449133i	0.835693	+	0.549197i	$0.185066\pi$
$354$	1.13698	+	1.96930i	0.0604296	+	0.104667i
$355$	13.0911	−	7.55813i	0.694802	−	0.401144i
$356$		−	9.09515i		−	0.482042i
$357$	−1.41210	−	0.815277i	−0.0747364	−	0.0431491i
$358$	4.37496	+	7.57765i	0.231224	+	0.400491i
$359$	−8.99932			−0.474966			−0.237483	−	0.971392i	$-0.576322\pi$
$359$	−8.99932			−0.474966			−0.237483	+	0.971392i	$0.576322\pi$
$360$	−1.00000			−0.0527046
$361$	11.7471	+	20.3466i	0.618270	+	1.07087i
$362$		−	15.3073i		−	0.804535i
$363$	4.86358	−	8.42397i	0.255272	−	0.442144i
$364$			5.19324i			0.272200i
$365$	3.84198	+	2.21817i	0.201098	+	0.116104i
$366$	2.42742	−	4.20441i	0.126883	−	0.219768i
$367$	6.20181	−	10.7419i	0.323732	−	0.560720i	−0.657523	−	0.753435i	$-0.728396\pi$
$367$	6.20181	−	10.7419i	0.323732	−	0.560720i	0.981255	+	0.192714i	$0.0617290\pi$
$368$	3.66160	−	2.11403i	0.190874	−	0.110201i
$369$	10.6278			0.553260
$370$	−2.13754	−	5.69481i	−0.111126	−	0.296059i
$371$	9.71418			0.504335
$372$	−4.46086	+	2.57548i	−0.231285	+	0.133532i
$373$	−5.45850	+	9.45441i	−0.282631	+	0.489531i	−0.972032	−	0.234849i	$-0.924540\pi$
$373$	−5.45850	+	9.45441i	−0.282631	+	0.489531i	0.689401	+	0.724380i	$0.257874\pi$
$374$	1.05562	−	1.82839i	0.0545848	−	0.0945437i
$375$	0.866025	+	0.500000i	0.0447214	+	0.0258199i
$376$			7.61359i			0.392641i
$377$	12.4031	−	21.4828i	0.638792	−	1.10642i
$378$			0.871333i			0.0448165i
$379$	11.4000	+	19.7454i	0.585578	+	1.01425i	0.994803	+	0.101818i	$0.0324659\pi$
$379$	11.4000	+	19.7454i	0.585578	+	1.01425i	−0.409225	+	0.912434i	$0.634201\pi$
$380$	−6.51876			−0.334405
$381$	16.1662			0.828219
$382$	8.70395	+	15.0757i	0.445333	+	0.771339i
$383$	−22.5335	−	13.0097i	−1.15141	−	0.664767i	−0.202180	−	0.979348i	$-0.564802\pi$
$383$	−22.5335	−	13.0097i	−1.15141	−	0.664767i	−0.949230	+	0.314582i	$0.898136\pi$
$384$			1.00000i			0.0510310i
$385$	−0.851337	+	0.491520i	−0.0433881	+	0.0250502i
$386$	−9.42456	−	16.3238i	−0.479697	−	0.830860i
$387$	−8.12246	+	4.68951i	−0.412888	+	0.238381i
$388$	1.88122	+	1.08612i	0.0955045	+	0.0551395i
$389$	−31.1670	−	17.9943i	−1.58023	−	0.912345i	−0.994825	−	0.101602i	$-0.967603\pi$
$389$	−31.1670	−	17.9943i	−1.58023	−	0.912345i	−0.585403	−	0.810743i	$-0.699064\pi$
$390$	5.16160	−	2.98005i	0.261368	−	0.150901i
$391$	−3.95605	−	6.85208i	−0.200066	−	0.346525i
$392$	−5.40467	+	3.12039i	−0.272977	+	0.157603i
$393$		−	5.66129i		−	0.285574i
$394$	−0.531443	−	0.306829i	−0.0267737	−	0.0154578i
$395$	5.81817	+	10.0774i	0.292744	+	0.507048i
$396$	−1.12820			−0.0566942
$397$	−16.2648			−0.816306			−0.408153	−	0.912914i	$-0.633827\pi$
$397$	−16.2648			−0.816306			−0.408153	+	0.912914i	$0.633827\pi$
$398$	11.6976	+	20.2609i	0.586348	+	1.01559i
$399$			5.68001i			0.284356i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			33.5429i			1.67505i	0.546397	+	0.837527i	$0.315999\pi$
$401$			33.5429i			1.67505i	−0.546397	+	0.837527i	$0.684001\pi$
$402$	12.2504	+	7.07277i	0.610994	+	0.352758i
$403$	15.3501	−	26.5872i	0.764644	−	1.32440i
$404$	−2.36375	+	4.09414i	−0.117601	+	0.203691i
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	−3.62652			−0.179981
$407$	−2.41158	−	6.42490i	−0.119537	−	0.318470i
$408$	1.87133			0.0926448
$409$	−9.51451	+	5.49320i	−0.470462	+	0.271621i	−0.716433	−	0.697656i	$-0.754227\pi$
$409$	−9.51451	+	5.49320i	−0.470462	+	0.271621i	0.245971	+	0.969277i	$0.420893\pi$
$410$	−5.31389	+	9.20392i	−0.262434	+	0.454549i
$411$	8.25285	−	14.2943i	0.407083	−	0.705088i
$412$	4.70695	+	2.71756i	0.231895	+	0.133885i
$413$			1.98137i			0.0974969i
$414$	−2.11403	+	3.66160i	−0.103899	+	0.179958i
$415$			4.94973i			0.242973i
$416$	−2.98005	−	5.16160i	−0.146109	−	0.253068i
$417$	−17.6996			−0.866755
$418$	−7.35448			−0.359719
$419$	−16.6045	−	28.7598i	−0.811181	−	1.40501i	−0.912038	−	0.410105i	$-0.865492\pi$
$419$	−16.6045	−	28.7598i	−0.811181	−	1.40501i	0.100858	−	0.994901i	$-0.467841\pi$
$420$	−0.754597	−	0.435667i	−0.0368205	−	0.0212584i
$421$			17.5126i			0.853512i	0.904367	+	0.426756i	$0.140344\pi$
$421$			17.5126i			0.853512i	−0.904367	+	0.426756i	$0.859656\pi$
$422$	−18.3487	+	10.5936i	−0.893200	+	0.515689i
$423$	−3.80679	−	6.59356i	−0.185093	−	0.320590i
$424$	−9.65501	+	5.57432i	−0.468889	+	0.270713i
$425$	−1.62062	−	0.935667i	−0.0786117	−	0.0453865i
$426$	13.0911	+	7.55813i	0.634264	+	0.366193i
$427$	3.66344	−	2.11509i	0.177286	−	0.102356i
$428$	8.33163	+	14.4308i	0.402724	+	0.697539i
$429$	5.82333	−	3.36210i	0.281153	−	0.162324i
$430$		−	9.37901i		−	0.452296i
$431$	−20.2700	−	11.7029i	−0.976372	−	0.563709i	−0.0751993	−	0.997169i	$-0.523959\pi$
$431$	−20.2700	−	11.7029i	−0.976372	−	0.563709i	−0.901173	+	0.433460i	$0.857293\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	8.47827			0.407439			0.203720	−	0.979029i	$-0.434697\pi$
$433$	8.47827			0.407439			0.203720	+	0.979029i	$0.434697\pi$
$434$	−4.48820			−0.215441
$435$	2.08102	+	3.60443i	0.0997773	+	0.172819i
$436$		−	16.7697i		−	0.803125i
$437$	−13.7808	+	23.8691i	−0.659227	+	1.14181i
$438$			4.43634i			0.211976i
$439$	−2.06183	−	1.19040i	−0.0984056	−	0.0568145i	0.449990	−	0.893034i	$-0.351428\pi$
$439$	−2.06183	−	1.19040i	−0.0984056	−	0.0568145i	−0.548395	+	0.836219i	$0.684761\pi$
$440$	0.564101	−	0.977051i	0.0268924	−	0.0465791i
$441$	3.12039	−	5.40467i	0.148590	−	0.257365i
$442$	−9.65908	+	5.57667i	−0.459436	+	0.265255i
$443$	−3.83814			−0.182355			−0.0911777	−	0.995835i	$-0.529063\pi$
$443$	−3.83814			−0.182355			−0.0911777	+	0.995835i	$0.529063\pi$
$444$	3.86308	−	4.69857i	0.183334	−	0.222984i
$445$	−9.09515			−0.431151
$446$	−13.3728	+	7.72081i	−0.633222	+	0.365591i
$447$	−8.29891	+	14.3741i	−0.392525	+	0.679873i
$448$	−0.435667	+	0.754597i	−0.0205833	+	0.0356513i
$449$	−12.2708	−	7.08457i	−0.579097	−	0.334342i	0.181678	−	0.983358i	$-0.441847\pi$
$449$	−12.2708	−	7.08457i	−0.579097	−	0.334342i	−0.760774	+	0.649017i	$0.775181\pi$
$450$			1.00000i			0.0471405i
$451$	−5.99513	+	10.3839i	−0.282300	+	0.488958i
$452$			8.57878i			0.403512i
$453$	7.15224	+	12.3880i	0.336042	+	0.582041i
$454$	−4.46434			−0.209522
$455$	5.19324			0.243463
$456$	−3.25938	−	5.64541i	−0.152634	−	0.264371i
$457$	10.7010	+	6.17825i	0.500574	+	0.289006i	0.728950	−	0.684566i	$-0.240008\pi$
$457$	10.7010	+	6.17825i	0.500574	+	0.289006i	−0.228377	+	0.973573i	$0.573342\pi$
$458$			16.2659i			0.760054i
$459$	−1.62062	+	0.935667i	−0.0756442	+	0.0436732i
$460$	−2.11403	−	3.66160i	−0.0985670	−	0.170723i
$461$	31.2722	−	18.0550i	1.45649	−	0.840905i	0.457654	−	0.889130i	$-0.348690\pi$
$461$	31.2722	−	18.0550i	1.45649	−	0.840905i	0.998837	+	0.0482247i	$0.0153564\pi$
$462$	−0.851337	−	0.491520i	−0.0396078	−	0.0228676i
$463$	−21.4520	−	12.3853i	−0.996960	−	0.575595i	−0.0896122	−	0.995977i	$-0.528563\pi$
$463$	−21.4520	−	12.3853i	−0.996960	−	0.575595i	−0.907347	+	0.420382i	$0.861896\pi$
$464$	3.60443	−	2.08102i	0.167332	−	0.0966089i
$465$	2.57548	+	4.46086i	0.119435	+	0.206868i
$466$	−3.15906	+	1.82389i	−0.146341	+	0.0844899i
$467$		−	0.754892i		−	0.0349322i	−0.999847	−	0.0174661i	$-0.994440\pi$
$467$		−	0.754892i		−	0.0349322i	0.999847	−	0.0174661i	$-0.00555992\pi$
$468$	5.16160	+	2.98005i	0.238595	+	0.137753i
$469$	6.16274	+	10.6742i	0.284569	+	0.492888i
$470$	7.61359			0.351189
$471$	−18.2282			−0.839910
$472$	−1.13698	−	1.96930i	−0.0523336	−	0.0906444i
$473$		−	10.5814i		−	0.486534i
$474$	−5.81817	+	10.0774i	−0.267238	+	0.462869i
$475$			6.51876i			0.299101i
$476$	1.41210	+	0.815277i	0.0647236	+	0.0373682i
$477$	5.57432	−	9.65501i	0.255231	−	0.442072i
$478$	−3.82438	+	6.62403i	−0.174923	+	0.302976i
$479$	−13.3889	+	7.73007i	−0.611753	+	0.353196i	−0.773651	−	0.633611i	$-0.781572\pi$
$479$	−13.3889	+	7.73007i	−0.611753	+	0.353196i	0.161898	+	0.986808i	$0.448238\pi$
$480$	1.00000			0.0456435
$481$	−5.93771	+	35.7644i	−0.270736	+	1.63071i
$482$	21.7585			0.991073
$483$	−3.19048	+	1.84202i	−0.145172	+	0.0838149i
$484$	−4.86358	+	8.42397i	−0.221072	+	0.382908i
$485$	1.08612	−	1.88122i	0.0493183	−	0.0854218i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$			33.7547i			1.52957i	0.644283	+	0.764787i	$0.277156\pi$
$487$			33.7547i			1.52957i	−0.644283	+	0.764787i	$0.722844\pi$
$488$	−2.42742	+	4.20441i	−0.109884	+	0.190325i
$489$		−	6.27777i		−	0.283891i
$490$	3.12039	+	5.40467i	0.140965	+	0.244158i
$491$	−9.71651			−0.438500			−0.219250	−	0.975669i	$-0.570361\pi$
$491$	−9.71651			−0.438500			−0.219250	+	0.975669i	$0.570361\pi$
$492$	−10.6278			−0.479137
$493$	−3.89428	−	6.74509i	−0.175390	−	0.303784i
$494$	33.6473	+	19.4263i	1.51386	+	0.874029i
$495$			1.12820i			0.0507089i
$496$	4.46086	−	2.57548i	0.200299	−	0.115642i
$497$	6.58565	+	11.4067i	0.295407	+	0.511660i
$498$	−4.28659	+	2.47486i	−0.192087	+	0.110901i
$499$	8.26563	+	4.77216i	0.370020	+	0.213631i	0.673467	−	0.739217i	$-0.264804\pi$
$499$	8.26563	+	4.77216i	0.370020	+	0.213631i	−0.303447	+	0.952848i	$0.598138\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	−6.40836	+	3.69987i	−0.286304	+	0.165298i
$502$	0.120855	+	0.209327i	0.00539402	+	0.00934271i
$503$	−6.69477	+	3.86523i	−0.298505	+	0.172342i	−0.641771	−	0.766896i	$-0.721800\pi$
$503$	−6.69477	+	3.86523i	−0.298505	+	0.172342i	0.343266	+	0.939238i	$0.388467\pi$
$504$		−	0.871333i		−	0.0388123i
$505$	4.09414	+	2.36375i	0.182187	+	0.105186i
$506$	−2.38505	−	4.13102i	−0.106028	−	0.183646i
$507$	−22.5229			−1.00028
$508$	−16.1662			−0.717259
$509$	−10.0860	−	17.4694i	−0.447052	−	0.774317i	0.551140	−	0.834412i	$-0.314193\pi$
$509$	−10.0860	−	17.4694i	−0.447052	−	0.774317i	−0.998193	+	0.0600954i	$0.980859\pi$
$510$		−	1.87133i		−	0.0828640i
$511$	−1.93276	+	3.34764i	−0.0855004	+	0.148091i
$512$		−	1.00000i		−	0.0441942i
$513$	5.64541	+	3.25938i	0.249251	+	0.143905i
$514$	−12.4212	+	21.5141i	−0.547874	+	0.948945i
$515$	2.71756	−	4.70695i	0.119750	−	0.207413i
$516$	8.12246	−	4.68951i	0.357572	−	0.206444i
$517$	8.58966			0.377773
$518$	4.96208	−	1.86251i	0.218021	−	0.0818340i
$519$	−10.4371			−0.458139
$520$	−5.16160	+	2.98005i	−0.226351	+	0.130684i
$521$	−6.83008	+	11.8301i	−0.299231	+	0.518284i	−0.975960	−	0.217948i	$-0.930064\pi$
$521$	−6.83008	+	11.8301i	−0.299231	+	0.518284i	0.676729	+	0.736232i	$0.263397\pi$
$522$	−2.08102	+	3.60443i	−0.0910838	+	0.157762i
$523$	−16.6298	−	9.60120i	−0.727169	−	0.419831i	0.0902166	−	0.995922i	$-0.471244\pi$
$523$	−16.6298	−	9.60120i	−0.727169	−	0.419831i	−0.817386	+	0.576091i	$0.804577\pi$
$524$			5.66129i			0.247315i
$525$	−0.435667	+	0.754597i	−0.0190140	+	0.0329333i
$526$		−	3.42443i		−	0.149312i
$527$	−4.81958	−	8.34776i	−0.209944	−	0.363634i
$528$	1.12820			0.0490987
$529$	5.12355			0.222763
$530$	5.57432	+	9.65501i	0.242133	+	0.419387i
$531$	1.96930	+	1.13698i	0.0854604	+	0.0493406i
$532$		−	5.68001i		−	0.246260i
$533$	54.8563	−	31.6713i	2.37609	−	1.37184i
$534$	−4.54758	−	7.87663i	−0.196793	−	0.340855i
$535$	14.4308	−	8.33163i	0.623898	−	0.360208i
$536$	−12.2504	−	7.07277i	−0.529137	−	0.305497i
$537$	7.57765	+	4.37496i	0.327000	+	0.188793i
$538$	−28.1260	+	16.2386i	−1.21260	+	0.700095i
$539$	3.52043	+	6.09756i	0.151636	+	0.262640i
$540$	−0.866025	+	0.500000i	−0.0372678	+	0.0215166i
$541$		−	29.5852i		−	1.27197i	−0.771702	−	0.635984i	$-0.780594\pi$
$541$		−	29.5852i		−	1.27197i	0.771702	−	0.635984i	$-0.219406\pi$
$542$	6.49164	+	3.74795i	0.278840	+	0.160988i
$543$	−7.65366	−	13.2565i	−0.328450	−	0.568892i
$544$	−1.87133			−0.0802327
$545$	−16.7697			−0.718337
$546$	2.59662	+	4.49748i	0.111125	+	0.192474i
$547$		−	9.36718i		−	0.400512i	−0.979744	−	0.200256i	$-0.935823\pi$
$547$		−	9.36718i		−	0.400512i	0.979744	−	0.200256i	$-0.0641774\pi$
$548$	−8.25285	+	14.2943i	−0.352544	+	0.610624i
$549$		−	4.85483i		−	0.207199i
$550$	−0.977051	−	0.564101i	−0.0416616	−	0.0240533i
$551$	−13.5657	+	23.4964i	−0.577917	+	1.00098i
$552$	2.11403	−	3.66160i	0.0899790	−	0.155848i
$553$	−8.78075	+	5.06957i	−0.373395	+	0.215580i
$554$	5.61669			0.238630
$555$	−4.69857	−	3.86308i	−0.199443	−	0.163979i
$556$	17.6996			0.750632
$557$	−28.3100	+	16.3448i	−1.19953	+	0.692551i	−0.960451	−	0.278448i	$-0.910180\pi$
$557$	−28.3100	+	16.3448i	−1.19953	+	0.692551i	−0.239082	+	0.970999i	$0.576847\pi$
$558$	−2.57548	+	4.46086i	−0.109029	+	0.188843i
$559$	−27.9500	+	48.4107i	−1.18216	+	2.04756i
$560$	0.754597	+	0.435667i	0.0318875	+	0.0184103i
$561$		−	2.11124i		−	0.0891366i
$562$	10.3572	−	17.9392i	0.436893	−	0.756721i
$563$			29.2451i			1.23253i	0.787538	+	0.616267i	$0.211356\pi$
$563$			29.2451i			1.23253i	−0.787538	+	0.616267i	$0.788644\pi$
$564$	3.80679	+	6.59356i	0.160295	+	0.277639i
$565$	8.57878			0.360912
$566$	−9.74927			−0.409792
$567$	0.435667	+	0.754597i	0.0182963	+	0.0316901i
$568$	−13.0911	−	7.55813i	−0.549289	−	0.317132i
$569$			2.76558i			0.115939i	0.998318	+	0.0579696i	$0.0184626\pi$
$569$			2.76558i			0.115939i	−0.998318	+	0.0579696i	$0.981537\pi$
$570$	−5.64541	+	3.25938i	−0.236460	+	0.136520i
$571$	−8.17459	−	14.1588i	−0.342096	−	0.592528i	0.642726	−	0.766096i	$-0.277804\pi$
$571$	−8.17459	−	14.1588i	−0.342096	−	0.592528i	−0.984822	+	0.173569i	$0.944470\pi$
$572$	−5.82333	+	3.36210i	−0.243486	+	0.140576i
$573$	15.0757	+	8.70395i	0.629796	+	0.363613i
$574$	−8.01968	−	4.63017i	−0.334735	−	0.193259i
$575$	−3.66160	+	2.11403i	−0.152699	+	0.0881610i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	14.5112	−	8.37802i	0.604107	−	0.348782i	−0.166548	−	0.986033i	$-0.553262\pi$
$577$	14.5112	−	8.37802i	0.604107	−	0.348782i	0.770656	+	0.637252i	$0.219929\pi$
$578$		−	13.4981i		−	0.561447i
$579$	−16.3238	−	9.42456i	−0.678395	−	0.391671i
$580$	−2.08102	−	3.60443i	−0.0864097	−	0.149666i
$581$	−4.31286			−0.178928
$582$	2.17225			0.0900425
$583$	6.28895	+	10.8928i	0.260462	+	0.451133i
$584$		−	4.43634i		−	0.183577i
$585$	2.98005	−	5.16160i	0.123210	−	0.213406i
$586$			18.7399i			0.774138i
$587$	9.82117	+	5.67026i	0.405363	+	0.234037i	0.688796	−	0.724956i	$-0.258140\pi$
$587$	9.82117	+	5.67026i	0.405363	+	0.234037i	−0.283432	+	0.958992i	$0.591473\pi$
$588$	−3.12039	+	5.40467i	−0.128683	+	0.222885i
$589$	−16.7889	+	29.0793i	−0.691776	+	1.19819i
$590$	−1.96930	+	1.13698i	−0.0810748	+	0.0468086i
$591$	−0.613658			−0.0252425
$592$	−3.86308	+	4.69857i	−0.158772	+	0.193110i
$593$	−37.1864			−1.52706			−0.763531	−	0.645771i	$-0.776536\pi$
$593$	−37.1864			−1.52706			−0.763531	+	0.645771i	$0.776536\pi$
$594$	−0.977051	+	0.564101i	−0.0400889	+	0.0231453i
$595$	0.815277	−	1.41210i	0.0334231	−	0.0578905i
$596$	8.29891	−	14.3741i	0.339937	−	0.588788i
$597$	20.2609	+	11.6976i	0.829222	+	0.478751i
$598$			25.1997i			1.03049i
$599$	7.12050	−	12.3331i	0.290936	−	0.503915i	−0.683096	−	0.730329i	$-0.739367\pi$
$599$	7.12050	−	12.3331i	0.290936	−	0.503915i	0.974031	+	0.226414i	$0.0727001\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−11.1396	−	19.2944i	−0.454395	−	0.787036i	0.544258	−	0.838918i	$-0.316811\pi$
$601$	−11.1396	−	19.2944i	−0.454395	−	0.787036i	−0.998653	+	0.0518822i	$0.983478\pi$
$602$	8.17225			0.333076
$603$	14.1455			0.576051
$604$	−7.15224	−	12.3880i	−0.291021	−	0.504062i
$605$	8.42397	+	4.86358i	0.342483	+	0.197733i
$606$			4.72751i			0.192042i
$607$	20.6605	−	11.9284i	0.838585	−	0.484157i	−0.0181978	−	0.999834i	$-0.505793\pi$
$607$	20.6605	−	11.9284i	0.838585	−	0.484157i	0.856783	+	0.515677i	$0.172460\pi$
$608$	3.25938	+	5.64541i	0.132185	+	0.228952i
$609$	−3.14066	+	1.81326i	−0.127266	+	0.0734771i
$610$	4.20441	+	2.42742i	0.170232	+	0.0982832i
$611$	−39.2983	−	22.6889i	−1.58984	−	0.917895i
$612$	1.62062	−	0.935667i	0.0655098	−	0.0378221i
$613$	16.6580	+	28.8526i	0.672812	+	1.16534i	0.977103	+	0.212765i	$0.0682470\pi$
$613$	16.6580	+	28.8526i	0.672812	+	1.16534i	−0.304291	+	0.952579i	$0.598420\pi$
$614$	−22.7542	+	13.1371i	−0.918284	+	0.530172i
$615$			10.6278i			0.428553i
$616$	0.851337	+	0.491520i	0.0343013	+	0.0198039i
$617$	−0.0901992	−	0.156230i	−0.00363128	−	0.00628956i	0.864204	−	0.503141i	$-0.167823\pi$
$617$	−0.0901992	−	0.156230i	−0.00363128	−	0.00628956i	−0.867835	+	0.496852i	$0.834489\pi$
$618$	5.43512			0.218632
$619$	19.6346			0.789181			0.394590	−	0.918857i	$-0.370886\pi$
$619$	19.6346			0.789181			0.394590	+	0.918857i	$0.370886\pi$
$620$	−2.57548	−	4.46086i	−0.103434	−	0.179153i
$621$			4.22805i			0.169666i
$622$	16.7355	−	28.9868i	0.671033	−	1.16226i
$623$		−	7.92491i		−	0.317505i
$624$	−5.16160	−	2.98005i	−0.206629	−	0.119298i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.997143	−	1.72710i	0.0398539	−	0.0690289i
$627$	−6.36916	+	3.67724i	−0.254360	+	0.146855i
$628$	18.2282			0.727383
$629$	8.79260	+	7.22912i	0.350584	+	0.288244i
$630$	−0.871333			−0.0347147
$631$	26.8143	−	15.4812i	1.06746	−	0.616298i	0.139973	−	0.990155i	$-0.455298\pi$
$631$	26.8143	−	15.4812i	1.06746	−	0.616298i	0.927486	+	0.373857i	$0.121965\pi$
$632$	5.81817	−	10.0774i	0.231435	−	0.400856i
$633$	−10.5936	+	18.3487i	−0.421059	+	0.729295i
$634$	5.18523	+	2.99369i	0.205932	+	0.118895i
$635$			16.1662i			0.641536i
$636$	−5.57432	+	9.65501i	−0.221036	+	0.382846i
$637$		−	37.1957i		−	1.47375i
$638$	−2.34781	−	4.06653i	−0.0929507	−	0.160995i
$639$	15.1163			0.597990
$640$	−1.00000			−0.0395285
$641$	5.04530	+	8.73872i	0.199277	+	0.345159i	0.948294	−	0.317392i	$-0.102807\pi$
$641$	5.04530	+	8.73872i	0.199277	+	0.345159i	−0.749017	+	0.662551i	$0.769474\pi$
$642$	14.4308	+	8.33163i	0.569538	+	0.328823i
$643$			19.4671i			0.767706i	0.923394	+	0.383853i	$0.125403\pi$
$643$			19.4671i			0.767706i	−0.923394	+	0.383853i	$0.874597\pi$
$644$	3.19048	−	1.84202i	0.125722	−	0.0725858i
$645$	−4.68951	−	8.12246i	−0.184649	−	0.319822i
$646$	10.5644	−	6.09939i	0.415653	−	0.239977i
$647$	−11.4187	−	6.59257i	−0.448914	−	0.259181i	0.258458	−	0.966023i	$-0.416786\pi$
$647$	−11.4187	−	6.59257i	−0.448914	−	0.259181i	−0.707371	+	0.706842i	$0.750119\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−2.22177	+	1.28274i	−0.0872120	+	0.0503519i
$650$	2.98005	+	5.16160i	0.116887	+	0.202455i
$651$	−3.88690	+	2.24410i	−0.152339	+	0.0879532i
$652$			6.27777i			0.245857i
$653$	−20.1410	−	11.6284i	−0.788180	−	0.455056i	0.0511414	−	0.998691i	$-0.483714\pi$
$653$	−20.1410	−	11.6284i	−0.788180	−	0.455056i	−0.839321	+	0.543635i	$0.817047\pi$
$654$	−8.38487	−	14.5230i	−0.327874	−	0.567895i
$655$	5.66129			0.221205
$656$	10.6278			0.414945
$657$	2.21817	+	3.84198i	0.0865390	+	0.149890i
$658$			6.63397i			0.258619i
$659$	14.9905	−	25.9644i	0.583949	−	1.01143i	−0.411057	−	0.911610i	$-0.634840\pi$
$659$	14.9905	−	25.9644i	0.583949	−	1.01143i	0.995006	−	0.0998192i	$-0.0318265\pi$
$660$		−	1.12820i		−	0.0439152i
$661$	11.5053	+	6.64256i	0.447503	+	0.258366i	0.706775	−	0.707439i	$-0.250149\pi$
$661$	11.5053	+	6.64256i	0.447503	+	0.258366i	−0.259272	+	0.965804i	$0.583483\pi$
$662$	9.32279	−	16.1475i	0.362340	−	0.627592i
$663$	−5.57667	+	9.65908i	−0.216580	+	0.375128i
$664$	4.28659	−	2.47486i	0.166352	−	0.0960434i
$665$	−5.68001			−0.220261
$666$	0.996242	−	6.00063i	0.0386036	−	0.232520i
$667$	−17.5973			−0.681372
$668$	6.40836	−	3.69987i	0.247947	−	0.143152i
$669$	−7.72081	+	13.3728i	−0.298504	+	0.517024i
$670$	−7.07277	+	12.2504i	−0.273245	+	0.473274i
$671$	4.74342	+	2.73861i	0.183118	+	0.105723i
$672$			0.871333i			0.0336124i
$673$	−6.35737	+	11.0113i	−0.245058	+	0.424454i	−0.962148	−	0.272527i	$-0.912140\pi$
$673$	−6.35737	+	11.0113i	−0.245058	+	0.424454i	0.717090	+	0.696981i	$0.245474\pi$
$674$			1.19521i			0.0460380i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	22.5229			0.866264
$677$	−12.3800			−0.475801			−0.237901	−	0.971290i	$-0.576459\pi$
$677$	−12.3800			−0.475801			−0.237901	+	0.971290i	$0.576459\pi$
$678$	4.28939	+	7.42944i	0.164733	+	0.285326i
$679$	1.63917	+	0.946375i	0.0629056	+	0.0363185i
$680$			1.87133i			0.0717624i
$681$	−3.86623	+	2.23217i	−0.148154	+	0.0855370i
$682$	−2.90566	−	5.03275i	−0.111263	−	0.192714i
$683$	−8.49785	+	4.90623i	−0.325161	+	0.187732i	−0.653691	−	0.756762i	$-0.726780\pi$
$683$	−8.49785	+	4.90623i	−0.325161	+	0.187732i	0.328530	+	0.944494i	$0.393447\pi$
$684$	−5.64541	−	3.25938i	−0.215858	−	0.124626i
$685$	14.2943	+	8.25285i	0.546159	+	0.315325i
$686$	−9.99145	+	5.76856i	−0.381475	+	0.220245i
$687$	8.13293	+	14.0866i	0.310291	+	0.537439i
$688$	−8.12246	+	4.68951i	−0.309666	+	0.178786i
$689$		−	66.4471i		−	2.53143i
$690$	−3.66160	−	2.11403i	−0.139395	−	0.0804796i
$691$	10.7731	+	18.6595i	0.409828	+	0.709842i	0.994870	−	0.101160i	$-0.0322555\pi$
$691$	10.7731	+	18.6595i	0.409828	+	0.709842i	−0.585043	+	0.811003i	$0.698922\pi$
$692$	10.4371			0.396760
$693$	−0.983039			−0.0373426
$694$	2.94679	+	5.10399i	0.111859	+	0.193745i
$695$		−	17.6996i		−	0.671385i
$696$	2.08102	−	3.60443i	0.0788809	−	0.136626i
$697$		−	19.8881i		−	0.753316i
$698$	−12.3543	−	7.13276i	−0.467617	−	0.269979i
$699$	−1.82389	+	3.15906i	−0.0689857	+	0.119487i
$700$	0.435667	−	0.754597i	0.0164666	−	0.0285211i
$701$	38.8616	−	22.4368i	1.46778	−	0.847426i	0.468435	−	0.883498i	$-0.344818\pi$
$701$	38.8616	−	22.4368i	1.46778	−	0.847426i	0.999349	+	0.0360723i	$0.0114847\pi$
$702$	5.96011			0.224950
$703$	6.49426	−	39.1166i	0.244936	−	1.47531i
$704$	−1.12820			−0.0425207
$705$	6.59356	−	3.80679i	0.248328	−	0.143372i
$706$	−8.43844	+	14.6158i	−0.317585	+	0.550073i
$707$	−2.05962	+	3.56736i	−0.0774599	+	0.134164i
$708$	−1.96930	−	1.13698i	−0.0740109	−	0.0427302i
$709$		−	23.4849i		−	0.881995i	−0.897508	−	0.440998i	$-0.854625\pi$
$709$		−	23.4849i		−	0.881995i	0.897508	−	0.440998i	$-0.145375\pi$
$710$	−7.55813	+	13.0911i	−0.283652	+	0.491299i
$711$			11.6363i			0.436397i
$712$	4.54758	+	7.87663i	0.170428	+	0.295189i
$713$	−21.7785			−0.815613
$714$	1.63055			0.0610220
$715$	3.36210	+	5.82333i	0.125735	+	0.217780i
$716$	−7.57765	−	4.37496i	−0.283190	−	0.163500i
$717$			7.64877i			0.285648i
$718$	7.79364	−	4.49966i	0.290856	−	0.167926i
$719$	−14.6060	−	25.2983i	−0.544710	−	0.943466i	−0.998625	−	0.0524210i	$-0.983306\pi$
$719$	−14.6060	−	25.2983i	−0.544710	−	0.943466i	0.453915	−	0.891045i	$-0.350027\pi$
$720$	0.866025	−	0.500000i	0.0322749	−	0.0186339i
$721$	4.10132	+	2.36790i	0.152741	+	0.0881852i
$722$	−20.3466	−	11.7471i	−0.757223	−	0.437183i
$723$	18.8434	−	10.8793i	0.700794	−	0.404604i
$724$	7.65366	+	13.2565i	0.284446	+	0.492675i
$725$	−3.60443	+	2.08102i	−0.133865	+	0.0772872i
$726$			9.72716i			0.361009i
$727$	23.3477	+	13.4798i	0.865917	+	0.499938i	0.865989	−	0.500062i	$-0.166690\pi$
$727$	23.3477	+	13.4798i	0.865917	+	0.499938i	−7.19505e−5		1.00000i	$0.500023\pi$
$728$	−2.59662	−	4.49748i	−0.0962371	−	0.166688i
$729$	1.00000			0.0370370
$730$	−4.43634			−0.164196
$731$	8.77563	+	15.1998i	0.324578	+	0.562186i
$732$			4.85483i			0.179440i
$733$	−15.1833	+	26.2982i	−0.560806	+	0.971345i	0.436620	+	0.899646i	$0.356175\pi$
$733$	−15.1833	+	26.2982i	−0.560806	+	0.971345i	−0.997426	+	0.0716990i	$0.977158\pi$
$734$			12.4036i			0.457826i
$735$	5.40467	+	3.12039i	0.199354	+	0.115097i
$736$	−2.11403	+	3.66160i	−0.0779241	+	0.134968i
$737$	−7.97951	+	13.8209i	−0.293929	+	0.509100i
$738$	−9.20392	+	5.31389i	−0.338801	+	0.195607i
$739$	−13.9985			−0.514942			−0.257471	−	0.966286i	$-0.582889\pi$
$739$	−13.9985			−0.514942			−0.257471	+	0.966286i	$0.582889\pi$
$740$	4.69857	+	3.86308i	0.172723	+	0.142010i
$741$	38.8525			1.42728
$742$	−8.41273	+	4.85709i	−0.308841	+	0.178309i
$743$	10.1124	−	17.5151i	0.370986	−	0.642567i	−0.618731	−	0.785603i	$-0.712353\pi$
$743$	10.1124	−	17.5151i	0.370986	−	0.642567i	0.989718	+	0.143036i	$0.0456864\pi$
$744$	2.57548	−	4.46086i	0.0944217	−	0.163543i
$745$	−14.3741	−	8.29891i	−0.526628	−	0.304049i
$746$		−	10.9170i		−	0.399700i
$747$	−2.47486	+	4.28659i	−0.0905506	+	0.156838i
$748$			2.11124i			0.0771946i
$749$	7.25962	+	12.5740i	0.265261	+	0.459445i
$750$	−1.00000			−0.0365148
$751$	−48.7420			−1.77862			−0.889311	−	0.457302i	$-0.848816\pi$
$751$	−48.7420			−1.77862			−0.889311	+	0.457302i	$0.848816\pi$
$752$	−3.80679	−	6.59356i	−0.138820	−	0.240442i
$753$	0.209327	+	0.120855i	0.00762829	+	0.00440420i
$754$			24.8062i			0.903389i
$755$	−12.3880	+	7.15224i	−0.450847	+	0.260297i
$756$	−0.435667	−	0.754597i	−0.0158450	−	0.0274444i
$757$	−24.5161	+	14.1544i	−0.891051	+	0.514449i	−0.874286	−	0.485411i	$-0.838670\pi$
$757$	−24.5161	+	14.1544i	−0.891051	+	0.514449i	−0.0167650	+	0.999859i	$0.505337\pi$
$758$	−19.7454	−	11.4000i	−0.717184	−	0.414067i
$759$	−4.13102	−	2.38505i	−0.149947	−	0.0865718i
$760$	5.64541	−	3.25938i	0.204781	−	0.118230i
$761$	14.3149	+	24.7942i	0.518916	+	0.898790i	0.999758	+	0.0219824i	$0.00699777\pi$
$761$	14.3149	+	24.7942i	0.518916	+	0.898790i	−0.480842	+	0.876807i	$0.659669\pi$
$762$	−14.0003	+	8.08310i	−0.507179	+	0.292820i
$763$		−	14.6120i		−	0.528991i
$764$	−15.0757	−	8.70395i	−0.545419	−	0.314898i
$765$	−0.935667	−	1.62062i	−0.0338291	−	0.0585937i
$766$	26.0195			0.940122
$767$	13.5530			0.489370
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$			53.0077i			1.91151i	0.294168	+	0.955754i	$0.404957\pi$
$769$			53.0077i			1.91151i	−0.294168	+	0.955754i	$0.595043\pi$
$770$	0.491520	−	0.851337i	0.0177131	−	0.0306801i
$771$			24.8423i			0.894674i
$772$	16.3238	+	9.42456i	0.587507	+	0.339197i
$773$	4.26473	−	7.38673i	0.153392	−	0.265682i	−0.779080	−	0.626924i	$-0.784314\pi$
$773$	4.26473	−	7.38673i	0.153392	−	0.265682i	0.932472	+	0.361242i	$0.117647\pi$
$774$	4.68951	−	8.12246i	0.168561	−	0.291956i
$775$	−4.46086	+	2.57548i	−0.160239	+	0.0925140i
$776$	−2.17225			−0.0779791
$777$	3.36603	−	4.09402i	0.120756	−	0.146872i
$778$	35.9885			1.29025
$779$	−59.9982	+	34.6400i	−2.14966	+	1.24111i
$780$	−2.98005	+	5.16160i	−0.106703	+	0.184815i
$781$	−8.52709	+	14.7694i	−0.305123	+	0.528489i
$782$	6.85208	+	3.95605i	0.245030	+	0.141468i
$783$			4.16204i			0.148739i
$784$	3.12039	−	5.40467i	0.111442	−	0.193024i
$785$		−	18.2282i		−	0.650591i
$786$	2.83065	+	4.90282i	0.100966	+	0.174878i
$787$	−15.9288			−0.567799			−0.283900	−	0.958854i	$-0.591628\pi$
$787$	−15.9288			−0.567799			−0.283900	+	0.958854i	$0.591628\pi$
$788$	0.613658			0.0218607
$789$	−1.71221	−	2.96564i	−0.0609564	−	0.105580i
$790$	−10.0774	−	5.81817i	−0.358537	−	0.207001i
$791$			7.47497i			0.265779i
$792$	0.977051	−	0.564101i	0.0347180	−	0.0200444i
$793$	−14.4677	−	25.0587i	−0.513762	−	0.889861i
$794$	14.0857	−	8.13239i	0.499883	−	0.288608i
$795$	9.65501	+	5.57432i	0.342428	+	0.197701i
$796$	−20.2609	−	11.6976i	−0.718127	−	0.414611i
$797$	9.49762	−	5.48345i	0.336423	−	0.194234i	−0.322266	−	0.946649i	$-0.604445\pi$
$797$	9.49762	−	5.48345i	0.336423	−	0.194234i	0.658689	+	0.752415i	$0.271111\pi$
$798$	−2.84001	−	4.91904i	−0.100535	−	0.174132i
$799$	−12.3388	+	7.12378i	−0.436514	+	0.252021i
$800$			1.00000i			0.0353553i
$801$	−7.87663	−	4.54758i	−0.278307	−	0.160681i
$802$	−16.7715	−	29.0490i	−0.592221	−	1.02576i
$803$	−5.00508			−0.176625
$804$	−14.1455			−0.498875
$805$	−1.84202	−	3.19048i	−0.0649227	−	0.112450i
$806$			30.7003i			1.08137i
$807$	−16.2386	+	28.1260i	−0.571625	+	0.990084i
$808$		−	4.72751i		−	0.166313i
$809$	1.23771	+	0.714591i	0.0435155	+	0.0251237i	0.521600	−	0.853190i	$-0.325335\pi$
$809$	1.23771	+	0.714591i	0.0435155	+	0.0251237i	−0.478084	+	0.878314i	$0.658669\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	10.0462	−	17.4006i	0.352770	−	0.611016i	−0.633963	−	0.773363i	$-0.718573\pi$
$811$	10.0462	−	17.4006i	0.352770	−	0.611016i	0.986734	+	0.162347i	$0.0519063\pi$
$812$	3.14066	−	1.81326i	0.110216	−	0.0636330i
$813$	7.49590			0.262893
$814$	5.30094	+	4.35834i	0.185798	+	0.152760i
$815$	6.27777			0.219901
$816$	−1.62062	+	0.935667i	−0.0567331	+	0.0327549i
$817$	30.5698	−	52.9484i	1.06950	−	1.85243i
$818$	5.49320	−	9.51451i	0.192065	−	0.332667i
$819$	4.49748	+	2.59662i	0.157155	+	0.0907332i
$820$		−	10.6278i		−	0.371138i
$821$	1.62602	−	2.81636i	0.0567486	−	0.0982915i	−0.836255	−	0.548340i	$-0.815260\pi$
$821$	1.62602	−	2.81636i	0.0567486	−	0.0982915i	0.893004	+	0.450048i	$0.148593\pi$
$822$			16.5057i			0.575702i
$823$	9.77530	+	16.9313i	0.340746	+	0.590189i	0.984571	−	0.174983i	$-0.0559872\pi$
$823$	9.77530	+	16.9313i	0.340746	+	0.590189i	−0.643826	+	0.765172i	$0.722654\pi$
$824$	−5.43512			−0.189341
$825$	−1.12820			−0.0392789
$826$	−0.990685	−	1.71592i	−0.0344703	−	0.0597044i
$827$	3.60118	+	2.07914i	0.125225	+	0.0722988i	0.561304	−	0.827610i	$-0.310300\pi$
$827$	3.60118	+	2.07914i	0.125225	+	0.0722988i	−0.436079	+	0.899908i	$0.643633\pi$
$828$		−	4.22805i		−	0.146935i
$829$	−23.9113	+	13.8052i	−0.830472	+	0.479474i	−0.854014	−	0.520249i	$-0.825839\pi$
$829$	−23.9113	+	13.8052i	−0.830472	+	0.479474i	0.0235419	+	0.999723i	$0.492506\pi$
$830$	−2.47486	−	4.28659i	−0.0859038	−	0.148790i
$831$	4.86420	−	2.80834i	0.168737	−	0.0974204i
$832$	5.16160	+	2.98005i	0.178946	+	0.103315i
$833$	−10.1139	−	5.83929i	−0.350427	−	0.202319i
$834$	15.3283	−	8.84982i	0.530777	−	0.306444i
$835$	−3.69987	−	6.40836i	−0.128039	−	0.221770i
$836$	6.36916	−	3.67724i	0.220282	−	0.127180i
$837$			5.15096i			0.178043i
$838$	28.7598	+	16.6045i	0.993489	+	0.573591i
$839$	−11.7345	−	20.3247i	−0.405120	−	0.701688i	0.589216	−	0.807976i	$-0.299437\pi$
$839$	−11.7345	−	20.3247i	−0.405120	−	0.701688i	−0.994335	+	0.106288i	$0.966103\pi$
$840$	0.871333			0.0300639
$841$	11.6774			0.402670
$842$	−8.75630	−	15.1664i	−0.301762	−	0.522667i
$843$		−	20.7144i		−	0.713443i
$844$	10.5936	−	18.3487i	0.364647	−	0.631588i
$845$		−	22.5229i		−	0.774810i
$846$	6.59356	+	3.80679i	0.226691	+	0.130880i
$847$	−4.23780	+	7.34008i	−0.145613	+	0.252208i
$848$	5.57432	−	9.65501i	0.191423	−	0.331554i
$849$	−8.44311	+	4.87463i	−0.289767	+	0.167297i
$850$	1.87133			0.0641862
$851$	24.0780	−	9.03764i	0.825383	−	0.309806i
$852$	−15.1163			−0.517875
$853$	15.1900	−	8.76996i	0.520096	−	0.300278i	−0.216878	−	0.976199i	$-0.569587\pi$
$853$	15.1900	−	8.76996i	0.520096	−	0.300278i	0.736974	+	0.675921i	$0.236254\pi$
$854$	−2.11509	+	3.66344i	−0.0723768	+	0.125360i
$855$	−3.25938	+	5.64541i	−0.111468	+	0.193069i
$856$	−14.4308	−	8.33163i	−0.493235	−	0.284769i
$857$			2.44958i			0.0836759i	0.999124	+	0.0418380i	$0.0133213\pi$
$857$			2.44958i			0.0836759i	−0.999124	+	0.0418380i	$0.986679\pi$
$858$	−3.36210	+	5.82333i	−0.114780	+	0.198805i
$859$			26.8029i			0.914505i	0.889337	+	0.457252i	$0.151166\pi$
$859$			26.8029i			0.914505i	−0.889337	+	0.457252i	$0.848834\pi$
$860$	4.68951	+	8.12246i	0.159911	+	0.276974i
$861$	−9.26033			−0.315591
$862$	23.4058			0.797205
$863$	−19.1575	−	33.1818i	−0.652131	−	1.12952i	−0.982605	−	0.185708i	$-0.940542\pi$
$863$	−19.1575	−	33.1818i	−0.652131	−	1.12952i	0.330474	−	0.943815i	$-0.392791\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		−	10.4371i		−	0.354873i
$866$	−7.34239	+	4.23913i	−0.249505	+	0.144052i
$867$	−6.74906	−	11.6897i	−0.229210	−	0.397003i
$868$	3.88690	−	2.24410i	0.131930	−	0.0761697i
$869$	−11.3693	−	6.56407i	−0.385677	−	0.222671i
$870$	−3.60443	−	2.08102i	−0.122202	−	0.0705532i
$871$	73.0137	−	42.1545i	2.47397	−	1.42835i
$872$	8.38487	+	14.5230i	0.283948	+	0.491812i
$873$	1.88122	−	1.08612i	0.0636697	−	0.0367597i
$874$		−	27.5617i		−	0.932288i
$875$	−0.754597	−	0.435667i	−0.0255100	−	0.0147282i
$876$	−2.21817	−	3.84198i	−0.0749449	−	0.129808i
$877$	−43.2267			−1.45966			−0.729830	−	0.683628i	$-0.760401\pi$
$877$	−43.2267			−1.45966			−0.729830	+	0.683628i	$0.760401\pi$
$878$	2.38079			0.0803479
$879$	9.36994	+	16.2292i	0.316040	+	0.547398i
$880$			1.12820i			0.0380317i
$881$	3.46842	−	6.00748i	0.116854	−	0.202397i	−0.801665	−	0.597773i	$-0.796052\pi$
$881$	3.46842	−	6.00748i	0.116854	−	0.202397i	0.918519	+	0.395376i	$0.129386\pi$
$882$			6.24078i			0.210138i
$883$	−2.30101	−	1.32849i	−0.0774352	−	0.0447073i	0.460782	−	0.887513i	$-0.347569\pi$
$883$	−2.30101	−	1.32849i	−0.0774352	−	0.0447073i	−0.538218	+	0.842806i	$0.680902\pi$
$884$	5.57667	−	9.65908i	0.187564	−	0.324870i
$885$	−1.13698	+	1.96930i	−0.0382190	+	0.0661973i
$886$	3.32392	−	1.91907i	0.111669	−	0.0644724i
$887$	33.3061			1.11831			0.559155	−	0.829063i	$-0.311126\pi$
$887$	33.3061			1.11831			0.559155	+	0.829063i	$0.311126\pi$
$888$	−0.996242	+	6.00063i	−0.0334317	+	0.201368i
$889$	−14.0861			−0.472434
$890$	7.87663	−	4.54758i	0.264025	−	0.152435i
$891$	−0.564101	+	0.977051i	−0.0188981	+	0.0327324i
$892$	7.72081	−	13.3728i	0.258512	−	0.447756i
$893$	42.9819	+	24.8156i	1.43833	+	0.830422i
$894$		−	16.5978i		−	0.555114i
$895$	−4.37496	+	7.57765i	−0.146239	+	0.253293i
$896$		−	0.871333i		−	0.0291092i
$897$	12.5998	+	21.8235i	0.420696	+	0.728667i
$898$	14.1691			0.472830
$899$	−21.4385			−0.715014
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−18.0677	−	10.4314i	−0.601923	−	0.347521i
$902$		−	11.9903i		−	0.399232i
$903$	7.07737	−	4.08612i	0.235520	−	0.135978i
$904$	−4.28939	−	7.42944i	−0.142663	−	0.247099i
$905$	13.2565	−	7.65366i	0.440662	−	0.254416i
$906$	−12.3880	−	7.15224i	−0.411565	−	0.237617i
$907$	−28.8307	−	16.6454i	−0.957306	−	0.552701i	−0.0619632	−	0.998078i	$-0.519736\pi$
$907$	−28.8307	−	16.6454i	−0.957306	−	0.552701i	−0.895343	+	0.445378i	$0.853069\pi$
$908$	3.86623	−	2.23217i	0.128305	−	0.0740772i
$909$	2.36375	+	4.09414i	0.0784008	+	0.135794i
$910$	−4.49748	+	2.59662i	−0.149090	+	0.0860771i
$911$			2.03305i			0.0673578i	0.999433	+	0.0336789i	$0.0107224\pi$
$911$			2.03305i			0.0673578i	−0.999433	+	0.0336789i	$0.989278\pi$
$912$	5.64541	+	3.25938i	0.186938	+	0.107929i
$913$	−2.79215	−	4.83614i	−0.0924065	−	0.160053i
$914$	−12.3565			−0.408717
$915$	4.85483			0.160496
$916$	−8.13293	−	14.0866i	−0.268720	−	0.465436i
$917$			4.93287i			0.162898i
$918$	0.935667	−	1.62062i	0.0308816	−	0.0534885i
$919$		−	42.9444i		−	1.41661i	−0.705909	−	0.708303i	$-0.749461\pi$
$919$		−	42.9444i		−	1.41661i	0.705909	−	0.708303i	$-0.250539\pi$
$920$	3.66160	+	2.11403i	0.120719	+	0.0696974i
$921$	−13.1371	+	22.7542i	−0.432883	+	0.749776i
$922$	−18.0550	+	31.2722i	−0.594610	+	1.02989i
$923$	78.0241	−	45.0473i	2.56820	−	1.48275i
$924$	0.983039			0.0323396
$925$	3.86308	−	4.69857i	0.127017	−	0.154488i
$926$	24.7706			0.814014
$927$	4.70695	−	2.71756i	0.154597	−	0.0892563i
$928$	−2.08102	+	3.60443i	−0.0683128	+	0.118321i
$929$	−16.9494	+	29.3572i	−0.556091	+	0.963179i	0.441726	+	0.897150i	$0.354366\pi$
$929$	−16.9494	+	29.3572i	−0.556091	+	0.963179i	−0.997818	+	0.0660287i	$0.978967\pi$
$930$	−4.46086	−	2.57548i	−0.146277	−	0.0844533i
$931$			40.6821i			1.33330i
$932$	1.82389	−	3.15906i	0.0597433	−	0.103479i
$933$		−	33.4710i		−	1.09579i
$934$	0.377446	+	0.653756i	0.0123504	+	0.0213915i
$935$	2.11124			0.0690449
$936$	−5.96011			−0.194812
$937$	−20.8577	−	36.1266i	−0.681391	−	1.18020i	−0.974556	−	0.224142i	$-0.928042\pi$
$937$	−20.8577	−	36.1266i	−0.681391	−	1.18020i	0.293165	−	0.956062i	$-0.405291\pi$
$938$	−10.6742	−	6.16274i	−0.348524	−	0.201221i
$939$		−	1.99429i		−	0.0650811i
$940$	−6.59356	+	3.80679i	−0.215058	+	0.124164i
$941$	−19.3792	−	33.5658i	−0.631744	−	1.09421i	−0.987195	−	0.159518i	$-0.949006\pi$
$941$	−19.3792	−	33.5658i	−0.631744	−	1.09421i	0.355451	−	0.934695i	$-0.384327\pi$
$942$	15.7861	−	9.11409i	0.514338	−	0.296953i
$943$	−38.9147	−	22.4674i	−1.26724	−	0.731639i
$944$	1.96930	+	1.13698i	0.0640953	+	0.0370054i
$945$	−0.754597	+	0.435667i	−0.0245470	+	0.0141722i
$946$	5.29071	+	9.16377i	0.172016	+	0.297940i
$947$	9.02357	−	5.20976i	0.293227	−	0.169294i	−0.346169	−	0.938172i	$-0.612518\pi$
$947$	9.02357	−	5.20976i	0.293227	−	0.169294i	0.639396	+	0.768878i	$0.279184\pi$
$948$		−	11.6363i		−	0.377931i
$949$	22.8986	+	13.2205i	0.743320	+	0.429156i
$950$	−3.25938	−	5.64541i	−0.105748	−	0.183161i
$951$	5.98739			0.194154
$952$	−1.63055			−0.0528466
$953$	26.0984	+	45.2037i	0.845410	+	1.46429i	0.885265	+	0.465087i	$0.153977\pi$
$953$	26.0984	+	45.2037i	0.845410	+	1.46429i	−0.0398554	+	0.999205i	$0.512690\pi$
$954$			11.1486i			0.360951i
$955$	−8.70395	+	15.0757i	−0.281653	+	0.487838i
$956$		−	7.64877i		−	0.247379i
$957$	−4.06653	−	2.34781i	−0.131452	−	0.0758939i
$958$	7.73007	−	13.3889i	0.249747	−	0.432575i
$959$	−7.19098	+	12.4551i	−0.232209	+	0.402197i
$960$	−0.866025	+	0.500000i	−0.0279508	+	0.0161374i
$961$	4.46762			0.144117
$962$	−12.7400	−	33.9417i	−0.410753	−	1.09432i
$963$	16.6633			0.536966
$964$	−18.8434	+	10.8793i	−0.606906	+	0.350397i
$965$	9.42456	−	16.3238i	0.303387	−	0.525482i
$966$	1.84202	−	3.19048i	0.0592661	−	0.102652i
$967$	3.10303	+	1.79154i	0.0997867	+	0.0576119i	0.549063	−	0.835781i	$-0.314985\pi$
$967$	3.10303	+	1.79154i	0.0997867	+	0.0576119i	−0.449276	+	0.893393i	$0.648318\pi$
$968$		−	9.72716i		−	0.312643i
$969$	6.09939	−	10.5644i	0.195941	−	0.339379i
$970$			2.17225i			0.0697466i
$971$	−0.682493	−	1.18211i	−0.0219022	−	0.0379358i	0.854867	−	0.518848i	$-0.173639\pi$
$971$	−0.682493	−	1.18211i	−0.0219022	−	0.0379358i	−0.876769	+	0.480912i	$0.840306\pi$
$972$	−1.00000			−0.0320750
$973$	15.4223			0.494415
$974$	−16.8774	−	29.2325i	−0.540786	−	0.936669i
$975$	5.16160	+	2.98005i	0.165304	+	0.0954381i
$976$		−	4.85483i		−	0.155399i
$977$	22.0377	−	12.7235i	0.705048	−	0.407059i	−0.104177	−	0.994559i	$-0.533221\pi$
$977$	22.0377	−	12.7235i	0.705048	−	0.407059i	0.809225	+	0.587499i	$0.199888\pi$
$978$	3.13889	+	5.43671i	0.100371	+	0.173847i
$979$	8.88643	−	5.13058i	0.284011	−	0.163974i
$980$	−5.40467	−	3.12039i	−0.172646	−	0.0996772i
$981$	−14.5230	−	8.38487i	−0.463685	−	0.267708i
$982$	8.41474	−	4.85825i	0.268525	−	0.155033i
$983$	18.9236	+	32.7766i	0.603569	+	1.04541i	0.992276	+	0.124051i	$0.0395886\pi$
$983$	18.9236	+	32.7766i	0.603569	+	1.04541i	−0.388707	+	0.921362i	$0.627078\pi$
$984$	9.20392	−	5.31389i	0.293410	−	0.169401i
$985$		−	0.613658i		−	0.0195528i
$986$	6.74509	+	3.89428i	0.214808	+	0.124019i
$987$	3.31699	+	5.74519i	0.105581	+	0.182871i
$988$	−38.8525			−1.23606
$989$	39.6550			1.26096
$990$	−0.564101	−	0.977051i	−0.0179283	−	0.0310527i
$991$			17.1176i			0.543759i	0.962331	+	0.271880i	$0.0876453\pi$
$991$			17.1176i			0.543759i	−0.962331	+	0.271880i	$0.912355\pi$
$992$	−2.57548	+	4.46086i	−0.0817716	+	0.141632i
$993$		−	18.6456i		−	0.591699i
$994$	−11.4067	−	6.58565i	−0.361798	−	0.208884i
$995$	−11.6976	+	20.2609i	−0.370839	+	0.642312i
$996$	2.47486	−	4.28659i	0.0784191	−	0.135826i
$997$	43.5000	−	25.1147i	1.37766	−	0.795391i	0.385781	−	0.922591i	$-0.373932\pi$
$997$	43.5000	−	25.1147i	1.37766	−	0.795391i	0.991877	+	0.127199i	$0.0405988\pi$
$998$	−9.54433			−0.302120
$999$	−2.13754	−	5.69481i	−0.0676288	−	0.180176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.d.751.3	✓	16
37.27	even	6	inner	1110.2.x.d.841.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.d.751.3	✓	16	1.1	even	1	trivial
1110.2.x.d.841.3	yes	16	37.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(0.435667 - 0.754597i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(0.435667 - 0.754597i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +1.12820 q^{11} +(0.500000 + 0.866025i) q^{12} +(-5.16160 - 2.98005i) q^{13} +0.871333i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.62062 + 0.935667i) q^{17} +(0.866025 + 0.500000i) q^{18} +(5.64541 + 3.25938i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(0.435667 + 0.754597i) q^{21} +(-0.977051 + 0.564101i) q^{22} +4.22805i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +5.96011 q^{26} +1.00000 q^{27} +(-0.435667 - 0.754597i) q^{28} +4.16204i q^{29} +(-0.500000 + 0.866025i) q^{30} +5.15096i q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.564101 + 0.977051i) q^{33} +(0.935667 - 1.62062i) q^{34} +(-0.754597 + 0.435667i) q^{35} -1.00000 q^{36} +(-2.13754 - 5.69481i) q^{37} -6.51876 q^{38} +(5.16160 - 2.98005i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-5.31389 + 9.20392i) q^{41} +(-0.754597 - 0.435667i) q^{42} -9.37901i q^{43} +(0.564101 - 0.977051i) q^{44} +1.00000i q^{45} +(-2.11403 - 3.66160i) q^{46} +7.61359 q^{47} +1.00000 q^{48} +(3.12039 + 5.40467i) q^{49} +(-0.866025 - 0.500000i) q^{50} -1.87133i q^{51} +(-5.16160 + 2.98005i) q^{52} +(5.57432 + 9.65501i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.977051 - 0.564101i) q^{55} +(0.754597 + 0.435667i) q^{56} +(-5.64541 + 3.25938i) q^{57} +(-2.08102 - 3.60443i) q^{58} +(-1.96930 + 1.13698i) q^{59} -1.00000i q^{60} +(4.20441 + 2.42742i) q^{61} +(-2.57548 - 4.46086i) q^{62} -0.871333 q^{63} -1.00000 q^{64} +(2.98005 + 5.16160i) q^{65} -1.12820i q^{66} +(-7.07277 + 12.2504i) q^{67} +1.87133i q^{68} +(-3.66160 - 2.11403i) q^{69} +(0.435667 - 0.754597i) q^{70} +(-7.55813 + 13.0911i) q^{71} +(0.866025 - 0.500000i) q^{72} -4.43634 q^{73} +(4.69857 + 3.86308i) q^{74} -1.00000 q^{75} +(5.64541 - 3.25938i) q^{76} +(0.491520 - 0.851337i) q^{77} +(-2.98005 + 5.16160i) q^{78} +(-10.0774 - 5.81817i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} -10.6278i q^{82} +(-2.47486 - 4.28659i) q^{83} +0.871333 q^{84} +1.87133 q^{85} +(4.68951 + 8.12246i) q^{86} +(-3.60443 - 2.08102i) q^{87} +1.12820i q^{88} +(7.87663 - 4.54758i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-4.49748 + 2.59662i) q^{91} +(3.66160 + 2.11403i) q^{92} +(-4.46086 - 2.57548i) q^{93} +(-6.59356 + 3.80679i) q^{94} +(-3.25938 - 5.64541i) q^{95} +(-0.866025 + 0.500000i) q^{96} +2.17225i q^{97} +(-5.40467 - 3.12039i) q^{98} +(-0.564101 - 0.977051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} + 16 q^{10} - 8 q^{11} + 8 q^{12} - 6 q^{13} - 8 q^{16} + 6 q^{17} - 12 q^{19} - 2 q^{21} + 8 q^{25} + 4 q^{26} + 16 q^{27} + 2 q^{28} - 8 q^{30} + 4 q^{33} + 6 q^{34} + 6 q^{35} - 16 q^{36} + 12 q^{37} - 4 q^{38} + 6 q^{39} + 8 q^{40} + 4 q^{41} + 6 q^{42} - 4 q^{44} - 2 q^{46} + 68 q^{47} + 16 q^{48} - 4 q^{49} - 6 q^{52} - 12 q^{53} - 6 q^{56} + 12 q^{57} - 6 q^{58} + 6 q^{59} + 12 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{64} + 2 q^{65} - 36 q^{67} + 18 q^{69} - 2 q^{70} + 6 q^{71} - 16 q^{73} + 14 q^{74} - 16 q^{75} - 12 q^{76} + 26 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} + 24 q^{89} - 8 q^{90} + 60 q^{91} - 18 q^{92} - 30 q^{93} + 6 q^{94} - 2 q^{95} - 12 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 + 16 * q^10 - 8 * q^11 + 8 * q^12 - 6 * q^13 - 8 * q^16 + 6 * q^17 - 12 * q^19 - 2 * q^21 + 8 * q^25 + 4 * q^26 + 16 * q^27 + 2 * q^28 - 8 * q^30 + 4 * q^33 + 6 * q^34 + 6 * q^35 - 16 * q^36 + 12 * q^37 - 4 * q^38 + 6 * q^39 + 8 * q^40 + 4 * q^41 + 6 * q^42 - 4 * q^44 - 2 * q^46 + 68 * q^47 + 16 * q^48 - 4 * q^49 - 6 * q^52 - 12 * q^53 - 6 * q^56 + 12 * q^57 - 6 * q^58 + 6 * q^59 + 12 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^64 + 2 * q^65 - 36 * q^67 + 18 * q^69 - 2 * q^70 + 6 * q^71 - 16 * q^73 + 14 * q^74 - 16 * q^75 - 12 * q^76 + 26 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 12 * q^83 - 4 * q^84 + 12 * q^85 - 2 * q^86 + 24 * q^89 - 8 * q^90 + 60 * q^91 - 18 * q^92 - 30 * q^93 + 6 * q^94 - 2 * q^95 - 12 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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