LMFDB - Embedded newform 1110.2.o.b.253.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, 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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.12
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.b.487.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.161376 + 2.23024i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80704 - 1.80704i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.161376 + 2.23024i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80704 - 1.80704i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-0.161376 + 2.23024i) q^{10} -1.06354i q^{11} +(0.707107 - 0.707107i) q^{12} +5.30264 q^{13} +(1.80704 - 1.80704i) q^{14} +(1.46291 + 1.69113i) q^{15} +1.00000 q^{16} +0.822384i q^{17} -1.00000i q^{18} +(-0.279256 - 0.279256i) q^{19} +(-0.161376 + 2.23024i) q^{20} -2.55554i q^{21} -1.06354i q^{22} -6.71595 q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.94792 - 0.719812i) q^{25} +5.30264 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.80704 - 1.80704i) q^{28} +(-1.25223 + 1.25223i) q^{29} +(1.46291 + 1.69113i) q^{30} +(3.59810 + 3.59810i) q^{31} +1.00000 q^{32} +(-0.752035 - 0.752035i) q^{33} +0.822384i q^{34} +(3.73851 + 4.32174i) q^{35} -1.00000i q^{36} +(5.68089 - 2.17428i) q^{37} +(-0.279256 - 0.279256i) q^{38} +(3.74953 - 3.74953i) q^{39} +(-0.161376 + 2.23024i) q^{40} +2.48825i q^{41} -2.55554i q^{42} +9.11788 q^{43} -1.06354i q^{44} +(2.23024 + 0.161376i) q^{45} -6.71595 q^{46} +(6.22303 - 6.22303i) q^{47} +(0.707107 - 0.707107i) q^{48} +0.469223i q^{49} +(-4.94792 - 0.719812i) q^{50} +(0.581513 + 0.581513i) q^{51} +5.30264 q^{52} +(1.25857 + 1.25857i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(2.37194 + 0.171629i) q^{55} +(1.80704 - 1.80704i) q^{56} -0.394928 q^{57} +(-1.25223 + 1.25223i) q^{58} +(-10.0411 - 10.0411i) q^{59} +(1.46291 + 1.69113i) q^{60} +(5.97569 + 5.97569i) q^{61} +(3.59810 + 3.59810i) q^{62} +(-1.80704 - 1.80704i) q^{63} +1.00000 q^{64} +(-0.855717 + 11.8261i) q^{65} +(-0.752035 - 0.752035i) q^{66} +(-2.68826 - 2.68826i) q^{67} +0.822384i q^{68} +(-4.74890 + 4.74890i) q^{69} +(3.73851 + 4.32174i) q^{70} -6.33819 q^{71} -1.00000i q^{72} +(-9.12583 + 9.12583i) q^{73} +(5.68089 - 2.17428i) q^{74} +(-4.00769 + 2.98972i) q^{75} +(-0.279256 - 0.279256i) q^{76} +(-1.92186 - 1.92186i) q^{77} +(3.74953 - 3.74953i) q^{78} +(-10.8059 - 10.8059i) q^{79} +(-0.161376 + 2.23024i) q^{80} -1.00000 q^{81} +2.48825i q^{82} +(-2.66034 - 2.66034i) q^{83} -2.55554i q^{84} +(-1.83411 - 0.132713i) q^{85} +9.11788 q^{86} +1.77092i q^{87} -1.06354i q^{88} +(-1.96382 + 1.96382i) q^{89} +(2.23024 + 0.161376i) q^{90} +(9.58208 - 9.58208i) q^{91} -6.71595 q^{92} +5.08848 q^{93} +(6.22303 - 6.22303i) q^{94} +(0.667872 - 0.577742i) q^{95} +(0.707107 - 0.707107i) q^{96} +2.76938i q^{97} +0.469223i q^{98} -1.06354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	−0.161376	+	2.23024i	−0.0721694	+	0.997392i
$5$	−0.161376	+	2.23024i	−0.0721694	+	0.997392i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	1.80704	−	1.80704i	0.682996	−	0.682996i	−0.277678	−	0.960674i	$-0.589565\pi$
$7$	1.80704	−	1.80704i	0.682996	−	0.682996i	0.960674	+	0.277678i	$0.0895648\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−0.161376	+	2.23024i	−0.0510315	+	0.705263i
$11$		−	1.06354i		−	0.320669i	−0.987063	−	0.160334i	$-0.948743\pi$
$11$		−	1.06354i		−	0.320669i	0.987063	−	0.160334i	$-0.0512573\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	5.30264			1.47069			0.735344	−	0.677694i	$-0.237021\pi$
$13$	5.30264			1.47069			0.735344	+	0.677694i	$0.237021\pi$
$14$	1.80704	−	1.80704i	0.482951	−	0.482951i
$15$	1.46291	+	1.69113i	0.377721	+	0.436647i
$16$	1.00000			0.250000
$17$			0.822384i			0.199457i	0.995015	+	0.0997287i	$0.0317975\pi$
$17$			0.822384i			0.199457i	−0.995015	+	0.0997287i	$0.968203\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−0.279256	−	0.279256i	−0.0640657	−	0.0640657i	0.674348	−	0.738414i	$-0.264425\pi$
$19$	−0.279256	−	0.279256i	−0.0640657	−	0.0640657i	−0.738414	+	0.674348i	$0.764425\pi$
$20$	−0.161376	+	2.23024i	−0.0360847	+	0.498696i
$21$		−	2.55554i		−	0.557664i
$22$		−	1.06354i		−	0.226747i
$23$	−6.71595			−1.40037			−0.700187	−	0.713960i	$-0.746900\pi$
$23$	−6.71595			−1.40037			−0.700187	+	0.713960i	$0.746900\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	−4.94792	−	0.719812i	−0.989583	−	0.143962i
$26$	5.30264			1.03993
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.80704	−	1.80704i	0.341498	−	0.341498i
$29$	−1.25223	+	1.25223i	−0.232533	+	0.232533i	−0.813749	−	0.581216i	$-0.802577\pi$
$29$	−1.25223	+	1.25223i	−0.232533	+	0.232533i	0.581216	+	0.813749i	$0.302577\pi$
$30$	1.46291	+	1.69113i	0.267089	+	0.308756i
$31$	3.59810	+	3.59810i	0.646237	+	0.646237i	0.952082	−	0.305844i	$-0.0989387\pi$
$31$	3.59810	+	3.59810i	0.646237	+	0.646237i	−0.305844	+	0.952082i	$0.598939\pi$
$32$	1.00000			0.176777
$33$	−0.752035	−	0.752035i	−0.130913	−	0.130913i
$34$			0.822384i			0.141038i
$35$	3.73851	+	4.32174i	0.631924	+	0.730507i
$36$		−	1.00000i		−	0.166667i
$37$	5.68089	−	2.17428i	0.933933	−	0.357449i
$37$	5.68089	−	2.17428i	0.933933	−	0.357449i
$38$	−0.279256	−	0.279256i	−0.0453013	−	0.0453013i
$39$	3.74953	−	3.74953i	0.600406	−	0.600406i
$40$	−0.161376	+	2.23024i	−0.0255157	+	0.352631i
$41$			2.48825i			0.388599i	0.980942	+	0.194300i	$0.0622434\pi$
$41$			2.48825i			0.388599i	−0.980942	+	0.194300i	$0.937757\pi$
$42$		−	2.55554i		−	0.394328i
$43$	9.11788			1.39046			0.695232	−	0.718786i	$-0.255302\pi$
$43$	9.11788			1.39046			0.695232	+	0.718786i	$0.255302\pi$
$44$		−	1.06354i		−	0.160334i
$45$	2.23024	+	0.161376i	0.332464	+	0.0240565i
$46$	−6.71595			−0.990213
$47$	6.22303	−	6.22303i	0.907722	−	0.907722i	−0.0883657	−	0.996088i	$-0.528164\pi$
$47$	6.22303	−	6.22303i	0.907722	−	0.907722i	0.996088	+	0.0883657i	$0.0281644\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			0.469223i			0.0670318i
$50$	−4.94792	−	0.719812i	−0.699741	−	0.101797i
$51$	0.581513	+	0.581513i	0.0814282	+	0.0814282i
$52$	5.30264			0.735344
$53$	1.25857	+	1.25857i	0.172878	+	0.172878i	0.788243	−	0.615365i	$-0.210991\pi$
$53$	1.25857	+	1.25857i	0.172878	+	0.172878i	−0.615365	+	0.788243i	$0.710991\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	2.37194	+	0.171629i	0.319833	+	0.0231425i
$56$	1.80704	−	1.80704i	0.241476	−	0.241476i
$57$	−0.394928			−0.0523095
$58$	−1.25223	+	1.25223i	−0.164426	+	0.164426i
$59$	−10.0411	−	10.0411i	−1.30724	−	1.30724i	−0.923398	−	0.383845i	$-0.874600\pi$
$59$	−10.0411	−	10.0411i	−1.30724	−	1.30724i	−0.383845	−	0.923398i	$-0.625400\pi$
$60$	1.46291	+	1.69113i	0.188860	+	0.218323i
$61$	5.97569	+	5.97569i	0.765108	+	0.765108i	0.977241	−	0.212133i	$-0.0680409\pi$
$61$	5.97569	+	5.97569i	0.765108	+	0.765108i	−0.212133	+	0.977241i	$0.568041\pi$
$62$	3.59810	+	3.59810i	0.456959	+	0.456959i
$63$	−1.80704	−	1.80704i	−0.227665	−	0.227665i
$64$	1.00000			0.125000
$65$	−0.855717	+	11.8261i	−0.106139	+	1.46685i
$66$	−0.752035	−	0.752035i	−0.0925691	−	0.0925691i
$67$	−2.68826	−	2.68826i	−0.328423	−	0.328423i	0.523564	−	0.851987i	$-0.324602\pi$
$67$	−2.68826	−	2.68826i	−0.328423	−	0.328423i	−0.851987	+	0.523564i	$0.824602\pi$
$68$			0.822384i			0.0997287i
$69$	−4.74890	+	4.74890i	−0.571700	+	0.571700i
$70$	3.73851	+	4.32174i	0.446838	+	0.516546i
$71$	−6.33819			−0.752205			−0.376103	−	0.926578i	$-0.622736\pi$
$71$	−6.33819			−0.752205			−0.376103	+	0.926578i	$0.622736\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−9.12583	+	9.12583i	−1.06810	+	1.06810i	−0.0705921	+	0.997505i	$0.522489\pi$
$73$	−9.12583	+	9.12583i	−1.06810	+	1.06810i	−0.997505	+	0.0705921i	$0.977511\pi$
$74$	5.68089	−	2.17428i	0.660390	−	0.252755i
$75$	−4.00769	+	2.98972i	−0.462768	+	0.345223i
$76$	−0.279256	−	0.279256i	−0.0320329	−	0.0320329i
$77$	−1.92186	−	1.92186i	−0.219016	−	0.219016i
$78$	3.74953	−	3.74953i	0.424551	−	0.424551i
$79$	−10.8059	−	10.8059i	−1.21576	−	1.21576i	−0.969103	−	0.246656i	$-0.920668\pi$
$79$	−10.8059	−	10.8059i	−1.21576	−	1.21576i	−0.246656	−	0.969103i	$-0.579332\pi$
$80$	−0.161376	+	2.23024i	−0.0180423	+	0.249348i
$81$	−1.00000			−0.111111
$82$			2.48825i			0.274781i
$83$	−2.66034	−	2.66034i	−0.292011	−	0.292011i	0.545864	−	0.837874i	$-0.316202\pi$
$83$	−2.66034	−	2.66034i	−0.292011	−	0.292011i	−0.837874	+	0.545864i	$0.816202\pi$
$84$		−	2.55554i		−	0.278832i
$85$	−1.83411	−	0.132713i	−0.198937	−	0.0143947i
$86$	9.11788			0.983206
$87$			1.77092i			0.189863i
$88$		−	1.06354i		−	0.113374i
$89$	−1.96382	+	1.96382i	−0.208164	+	0.208164i	−0.803487	−	0.595322i	$-0.797024\pi$
$89$	−1.96382	+	1.96382i	−0.208164	+	0.208164i	0.595322	+	0.803487i	$0.297024\pi$
$90$	2.23024	+	0.161376i	0.235088	+	0.0170105i
$91$	9.58208	−	9.58208i	1.00447	−	1.00447i
$92$	−6.71595			−0.700187
$93$	5.08848			0.527650
$94$	6.22303	−	6.22303i	0.641857	−	0.641857i
$95$	0.667872	−	0.577742i	0.0685223	−	0.0592751i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$			2.76938i			0.281188i	0.990067	+	0.140594i	$0.0449013\pi$
$97$			2.76938i			0.281188i	−0.990067	+	0.140594i	$0.955099\pi$
$98$			0.469223i			0.0473987i
$99$	−1.06354			−0.106890
$100$	−4.94792	−	0.719812i	−0.494792	−	0.0719812i
$101$			2.28701i			0.227566i	0.993506	+	0.113783i	$0.0362969\pi$
$101$			2.28701i			0.227566i	−0.993506	+	0.113783i	$0.963703\pi$
$102$	0.581513	+	0.581513i	0.0575784	+	0.0575784i
$103$			6.15995i			0.606958i	0.952838	+	0.303479i	$0.0981482\pi$
$103$			6.15995i			0.606958i	−0.952838	+	0.303479i	$0.901852\pi$
$104$	5.30264			0.519967
$105$	5.69946	+	0.412402i	0.556210	+	0.0402463i
$106$	1.25857	+	1.25857i	0.122243	+	0.122243i
$107$	−12.4413	+	12.4413i	−1.20274	+	1.20274i	−0.229413	+	0.973329i	$0.573681\pi$
$107$	−12.4413	+	12.4413i	−1.20274	+	1.20274i	−0.973329	+	0.229413i	$0.926319\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−9.15731	−	9.15731i	−0.877111	−	0.877111i	0.116124	−	0.993235i	$-0.462953\pi$
$109$	−9.15731	−	9.15731i	−0.877111	−	0.877111i	−0.993235	+	0.116124i	$0.962953\pi$
$110$	2.37194	+	0.171629i	0.226156	+	0.0163642i
$111$	2.47955	−	5.55444i	0.235348	−	0.527204i
$112$	1.80704	−	1.80704i	0.170749	−	0.170749i
$113$		−	8.83462i		−	0.831091i	−0.909572	−	0.415545i	$-0.863591\pi$
$113$		−	8.83462i		−	0.831091i	0.909572	−	0.415545i	$-0.136409\pi$
$114$	−0.394928			−0.0369884
$115$	1.08379	−	14.9782i	0.101064	−	1.39672i
$116$	−1.25223	+	1.25223i	−0.116267	+	0.116267i
$117$		−	5.30264i		−	0.490229i
$118$	−10.0411	−	10.0411i	−0.924360	−	0.924360i
$119$	1.48608	+	1.48608i	0.136229	+	0.136229i
$120$	1.46291	+	1.69113i	0.133544	+	0.154378i
$121$	9.86889			0.897171
$122$	5.97569	+	5.97569i	0.541013	+	0.541013i
$123$	1.75946	+	1.75946i	0.158645	+	0.158645i
$124$	3.59810	+	3.59810i	0.323119	+	0.323119i
$125$	2.40382	−	10.9189i	0.215005	−	0.976613i
$126$	−1.80704	−	1.80704i	−0.160984	−	0.160984i
$127$	−15.6868	+	15.6868i	−1.39198	+	1.39198i	−0.571102	+	0.820879i	$0.693484\pi$
$127$	−15.6868	+	15.6868i	−1.39198	+	1.39198i	−0.820879	+	0.571102i	$0.806516\pi$
$128$	1.00000			0.0883883
$129$	6.44731	−	6.44731i	0.567654	−	0.567654i
$130$	−0.855717	+	11.8261i	−0.0750514	+	1.03722i
$131$	9.31473	+	9.31473i	0.813832	+	0.813832i	0.985206	−	0.171374i	$-0.0548206\pi$
$131$	9.31473	+	9.31473i	0.813832	+	0.813832i	−0.171374	+	0.985206i	$0.554821\pi$
$132$	−0.752035	−	0.752035i	−0.0654563	−	0.0654563i
$133$	−1.00925			−0.0875133
$134$	−2.68826	−	2.68826i	−0.232230	−	0.232230i
$135$	1.69113	−	1.46291i	0.145549	−	0.125907i
$136$			0.822384i			0.0705189i
$137$	−4.28437	+	4.28437i	−0.366038	+	0.366038i	−0.866030	−	0.499992i	$-0.833336\pi$
$137$	−4.28437	+	4.28437i	−0.366038	+	0.366038i	0.499992	+	0.866030i	$0.333336\pi$
$138$	−4.74890	+	4.74890i	−0.404253	+	0.404253i
$139$	−14.4953			−1.22948			−0.614739	−	0.788731i	$-0.710739\pi$
$139$	−14.4953			−1.22948			−0.614739	+	0.788731i	$0.710739\pi$
$140$	3.73851	+	4.32174i	0.315962	+	0.365253i
$141$		−	8.80070i		−	0.741152i
$142$	−6.33819			−0.531889
$143$		−	5.63956i		−	0.471604i
$144$		−	1.00000i		−	0.0833333i
$145$	−2.59069	−	2.99485i	−0.215145	−	0.248709i
$146$	−9.12583	+	9.12583i	−0.755259	+	0.755259i
$147$	0.331791	+	0.331791i	0.0273656	+	0.0273656i
$148$	5.68089	−	2.17428i	0.466966	−	0.178725i
$149$			13.8394i			1.13377i	0.823797	+	0.566884i	$0.191851\pi$
$149$			13.8394i			1.13377i	−0.823797	+	0.566884i	$0.808149\pi$
$150$	−4.00769	+	2.98972i	−0.327226	+	0.244110i
$151$		−	21.0945i		−	1.71664i	−0.513112	−	0.858322i	$-0.671507\pi$
$151$		−	21.0945i		−	1.71664i	0.513112	−	0.858322i	$-0.328493\pi$
$152$	−0.279256	−	0.279256i	−0.0226507	−	0.0226507i
$153$	0.822384			0.0664858
$154$	−1.92186	−	1.92186i	−0.154868	−	0.154868i
$155$	−8.60525	+	7.44396i	−0.691191	+	0.597913i
$156$	3.74953	−	3.74953i	0.300203	−	0.300203i
$157$	−6.73511	+	6.73511i	−0.537520	+	0.537520i	−0.922800	−	0.385280i	$-0.874105\pi$
$157$	−6.73511	+	6.73511i	−0.537520	+	0.537520i	0.385280	+	0.922800i	$0.374105\pi$
$158$	−10.8059	−	10.8059i	−0.859672	−	0.859672i
$159$	1.77989			0.141154
$160$	−0.161376	+	2.23024i	−0.0127579	+	0.176316i
$161$	−12.1360	+	12.1360i	−0.956450	+	0.956450i
$162$	−1.00000			−0.0785674
$163$		−	9.31761i		−	0.729811i	−0.931045	−	0.364906i	$-0.881101\pi$
$163$		−	9.31761i		−	0.729811i	0.931045	−	0.364906i	$-0.118899\pi$
$164$			2.48825i			0.194300i
$165$	1.79858	−	1.55586i	0.140019	−	0.121123i
$166$	−2.66034	−	2.66034i	−0.206483	−	0.206483i
$167$		−	3.21570i		−	0.248838i	−0.992230	−	0.124419i	$-0.960293\pi$
$167$		−	3.21570i		−	0.248838i	0.992230	−	0.124419i	$-0.0397067\pi$
$168$		−	2.55554i		−	0.197164i
$169$	15.1180			1.16292
$170$	−1.83411	−	0.132713i	−0.140670	−	0.0101786i
$171$	−0.279256	+	0.279256i	−0.0213552	+	0.0213552i
$172$	9.11788			0.695232
$173$	0.505073	−	0.505073i	0.0384000	−	0.0384000i	−0.687646	−	0.726046i	$-0.741356\pi$
$173$	0.505073	−	0.505073i	0.0384000	−	0.0384000i	0.726046	+	0.687646i	$0.241356\pi$
$174$			1.77092i			0.134253i
$175$	−10.2418	+	7.64035i	−0.774208	+	0.577556i
$176$		−	1.06354i		−	0.0801672i
$177$	−14.2003			−1.06736
$178$	−1.96382	+	1.96382i	−0.147194	+	0.147194i
$179$	−6.04168	+	6.04168i	−0.451576	+	0.451576i	−0.895877	−	0.444301i	$-0.853452\pi$
$179$	−6.04168	+	6.04168i	−0.451576	+	0.451576i	0.444301	+	0.895877i	$0.353452\pi$
$180$	2.23024	+	0.161376i	0.166232	+	0.0120282i
$181$	−23.1096			−1.71772			−0.858860	−	0.512210i	$-0.828827\pi$
$181$	−23.1096			−1.71772			−0.858860	+	0.512210i	$0.828827\pi$
$182$	9.58208	−	9.58208i	0.710271	−	0.710271i
$183$	8.45090			0.624708
$184$	−6.71595			−0.495107
$185$	3.93240	+	13.0206i	0.289116	+	0.957294i
$186$	5.08848			0.373105
$187$	0.874637			0.0639598
$188$	6.22303	−	6.22303i	0.453861	−	0.453861i
$189$	−2.55554			−0.185888
$190$	0.667872	−	0.577742i	0.0484526	−	0.0419138i
$191$	7.76121	−	7.76121i	0.561581	−	0.561581i	−0.368175	−	0.929756i	$-0.620017\pi$
$191$	7.76121	−	7.76121i	0.561581	−	0.561581i	0.929756	+	0.368175i	$0.120017\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−14.5959			−1.05063			−0.525317	−	0.850907i	$-0.676053\pi$
$193$	−14.5959			−1.05063			−0.525317	+	0.850907i	$0.676053\pi$
$194$			2.76938i			0.198830i
$195$	7.75727	+	8.96743i	0.555509	+	0.642171i
$196$			0.469223i			0.0335159i
$197$	0.582703	−	0.582703i	0.0415158	−	0.0415158i	−0.686044	−	0.727560i	$-0.740654\pi$
$197$	0.582703	−	0.582703i	0.0415158	−	0.0415158i	0.727560	+	0.686044i	$0.240654\pi$
$198$	−1.06354			−0.0755824
$199$	6.47802	−	6.47802i	0.459215	−	0.459215i	−0.439183	−	0.898398i	$-0.644732\pi$
$199$	6.47802	−	6.47802i	0.459215	−	0.459215i	0.898398	+	0.439183i	$0.144732\pi$
$200$	−4.94792	−	0.719812i	−0.349870	−	0.0508984i
$201$	−3.80177			−0.268156
$202$			2.28701i			0.160914i
$203$			4.52566i			0.317639i
$204$	0.581513	+	0.581513i	0.0407141	+	0.0407141i
$205$	−5.54938	−	0.401543i	−0.387586	−	0.0280450i
$206$			6.15995i			0.429184i
$207$			6.71595i			0.466791i
$208$	5.30264			0.367672
$209$	−0.297000	+	0.297000i	−0.0205439	+	0.0205439i
$210$	5.69946	+	0.412402i	0.393300	+	0.0284584i
$211$	17.7152			1.21956			0.609782	−	0.792569i	$-0.291257\pi$
$211$	17.7152			1.21956			0.609782	+	0.792569i	$0.291257\pi$
$212$	1.25857	+	1.25857i	0.0864390	+	0.0864390i
$213$	−4.48178	+	4.48178i	−0.307086	+	0.307086i
$214$	−12.4413	+	12.4413i	−0.850467	+	0.850467i
$215$	−1.47140	+	20.3350i	−0.100349	+	1.38684i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	13.0038			0.882755
$218$	−9.15731	−	9.15731i	−0.620211	−	0.620211i
$219$			12.9059i			0.872098i
$220$	2.37194	+	0.171629i	0.159916	+	0.0115712i
$221$			4.36081i			0.293340i
$222$	2.47955	−	5.55444i	0.166416	−	0.372790i
$223$	9.66780	+	9.66780i	0.647404	+	0.647404i	0.952365	−	0.304961i	$-0.0986435\pi$
$223$	9.66780	+	9.66780i	0.647404	+	0.647404i	−0.304961	+	0.952365i	$0.598644\pi$
$224$	1.80704	−	1.80704i	0.120738	−	0.120738i
$225$	−0.719812	+	4.94792i	−0.0479875	+	0.329861i
$226$		−	8.83462i		−	0.587670i
$227$		−	11.0930i		−	0.736266i	−0.929773	−	0.368133i	$-0.879997\pi$
$227$		−	11.0930i		−	0.736266i	0.929773	−	0.368133i	$-0.120003\pi$
$228$	−0.394928			−0.0261547
$229$			7.46941i			0.493592i	0.969067	+	0.246796i	$0.0793778\pi$
$229$			7.46941i			0.493592i	−0.969067	+	0.246796i	$0.920622\pi$
$230$	1.08379	−	14.9782i	0.0714631	−	0.987631i
$231$	−2.71791			−0.178826
$232$	−1.25223	+	1.25223i	−0.0822130	+	0.0822130i
$233$	−5.64417	+	5.64417i	−0.369762	+	0.369762i	−0.867390	−	0.497628i	$-0.834204\pi$
$233$	−5.64417	+	5.64417i	−0.369762	+	0.369762i	0.497628	+	0.867390i	$0.334204\pi$
$234$		−	5.30264i		−	0.346645i
$235$	12.8746	+	14.8831i	0.839846	+	0.970865i
$236$	−10.0411	−	10.0411i	−0.653621	−	0.653621i
$237$	−15.2819			−0.992663
$238$	1.48608	+	1.48608i	0.0963283	+	0.0963283i
$239$	−7.38903	−	7.38903i	−0.477957	−	0.477957i	0.426521	−	0.904478i	$-0.359739\pi$
$239$	−7.38903	−	7.38903i	−0.477957	−	0.477957i	−0.904478	+	0.426521i	$0.859739\pi$
$240$	1.46291	+	1.69113i	0.0944302	+	0.109162i
$241$	4.09152	−	4.09152i	0.263558	−	0.263558i	−0.562940	−	0.826498i	$-0.690330\pi$
$241$	4.09152	−	4.09152i	0.263558	−	0.263558i	0.826498	+	0.562940i	$0.190330\pi$
$242$	9.86889			0.634396
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	5.97569	+	5.97569i	0.382554	+	0.382554i
$245$	−1.04648	−	0.0757212i	−0.0668571	−	0.00483765i
$246$	1.75946	+	1.75946i	0.112179	+	0.112179i
$247$	−1.48079	−	1.48079i	−0.0942207	−	0.0942207i
$248$	3.59810	+	3.59810i	0.228479	+	0.228479i
$249$	−3.76229			−0.238426
$250$	2.40382	−	10.9189i	0.152031	−	0.690570i
$251$	10.0626	+	10.0626i	0.635148	+	0.635148i	0.949355	−	0.314207i	$-0.101739\pi$
$251$	10.0626	+	10.0626i	0.635148	+	0.635148i	−0.314207	+	0.949355i	$0.601739\pi$
$252$	−1.80704	−	1.80704i	−0.113833	−	0.113833i
$253$			7.14268i			0.449056i
$254$	−15.6868	+	15.6868i	−0.984279	+	0.984279i
$255$	−1.39075	+	1.20307i	−0.0870925	+	0.0753392i
$256$	1.00000			0.0625000
$257$			18.7819i			1.17158i	0.810463	+	0.585790i	$0.199216\pi$
$257$			18.7819i			1.17158i	−0.810463	+	0.585790i	$0.800784\pi$
$258$	6.44731	−	6.44731i	0.401392	−	0.401392i
$259$	6.33658	−	14.1946i	0.393736	−	0.882009i
$260$	−0.855717	+	11.8261i	−0.0530693	+	0.733427i
$261$	1.25223	+	1.25223i	0.0775111	+	0.0775111i
$262$	9.31473	+	9.31473i	0.575466	+	0.575466i
$263$	−5.85579	+	5.85579i	−0.361083	+	0.361083i	−0.864212	−	0.503128i	$-0.832182\pi$
$263$	−5.85579	+	5.85579i	−0.361083	+	0.361083i	0.503128	+	0.864212i	$0.332182\pi$
$264$	−0.752035	−	0.752035i	−0.0462846	−	0.0462846i
$265$	−3.01002	+	2.60381i	−0.184904	+	0.159951i
$266$	−1.00925			−0.0618813
$267$			2.77726i			0.169966i
$268$	−2.68826	−	2.68826i	−0.164212	−	0.164212i
$269$		−	15.7921i		−	0.962864i	−0.876483	−	0.481432i	$-0.840117\pi$
$269$		−	15.7921i		−	0.962864i	0.876483	−	0.481432i	$-0.159883\pi$
$270$	1.69113	−	1.46291i	0.102919	−	0.0890296i
$271$	16.3325			0.992127			0.496063	−	0.868286i	$-0.334778\pi$
$271$	16.3325			0.992127			0.496063	+	0.868286i	$0.334778\pi$
$272$			0.822384i			0.0498644i
$273$		−	13.5511i		−	0.820150i
$274$	−4.28437	+	4.28437i	−0.258828	+	0.258828i
$275$	−0.765548	+	5.26230i	−0.0461643	+	0.317329i
$276$	−4.74890	+	4.74890i	−0.285850	+	0.285850i
$277$	−15.9722			−0.959679			−0.479839	−	0.877356i	$-0.659305\pi$
$277$	−15.9722			−0.959679			−0.479839	+	0.877356i	$0.659305\pi$
$278$	−14.4953			−0.869372
$279$	3.59810	−	3.59810i	0.215412	−	0.215412i
$280$	3.73851	+	4.32174i	0.223419	+	0.258273i
$281$	3.15356	−	3.15356i	0.188126	−	0.188126i	−0.606760	−	0.794885i	$-0.707531\pi$
$281$	3.15356	−	3.15356i	0.188126	−	0.188126i	0.794885	+	0.606760i	$0.207531\pi$
$282$		−	8.80070i		−	0.524074i
$283$		−	20.7113i		−	1.23116i	−0.788074	−	0.615580i	$-0.788922\pi$
$283$		−	20.7113i		−	1.23116i	0.788074	−	0.615580i	$-0.211078\pi$
$284$	−6.33819			−0.376103
$285$	0.0637317	−	0.880782i	0.00377514	−	0.0521730i
$286$		−	5.63956i		−	0.333474i
$287$	4.49636	+	4.49636i	0.265412	+	0.265412i
$288$		−	1.00000i		−	0.0589256i
$289$	16.3237			0.960217
$290$	−2.59069	−	2.99485i	−0.152131	−	0.175864i
$291$	1.95825	+	1.95825i	0.114795	+	0.114795i
$292$	−9.12583	+	9.12583i	−0.534049	+	0.534049i
$293$	−14.7664	−	14.7664i	−0.862665	−	0.862665i	0.128982	−	0.991647i	$-0.458829\pi$
$293$	−14.7664	−	14.7664i	−0.862665	−	0.862665i	−0.991647	+	0.128982i	$0.958829\pi$
$294$	0.331791	+	0.331791i	0.0193504	+	0.0193504i
$295$	24.0145	−	20.7737i	1.39818	−	1.20949i
$296$	5.68089	−	2.17428i	0.330195	−	0.126377i
$297$	−0.752035	+	0.752035i	−0.0436375	+	0.0436375i
$298$			13.8394i			0.801695i
$299$	−35.6123			−2.05951
$300$	−4.00769	+	2.98972i	−0.231384	+	0.172612i
$301$	16.4764	−	16.4764i	0.949681	−	0.949681i
$302$		−	21.0945i		−	1.21385i
$303$	1.61716	+	1.61716i	0.0929035	+	0.0929035i
$304$	−0.279256	−	0.279256i	−0.0160164	−	0.0160164i
$305$	−14.2915	+	12.3629i	−0.818331	+	0.707896i
$306$	0.822384			0.0470126
$307$	1.44634	+	1.44634i	0.0825472	+	0.0825472i	0.747175	−	0.664628i	$-0.231410\pi$
$307$	1.44634	+	1.44634i	0.0825472	+	0.0825472i	−0.664628	+	0.747175i	$0.731410\pi$
$308$	−1.92186	−	1.92186i	−0.109508	−	0.109508i
$309$	4.35574	+	4.35574i	0.247790	+	0.247790i
$310$	−8.60525	+	7.44396i	−0.488746	+	0.422789i
$311$	5.97480	+	5.97480i	0.338800	+	0.338800i	0.855916	−	0.517116i	$-0.172994\pi$
$311$	5.97480	+	5.97480i	0.338800	+	0.338800i	−0.517116	+	0.855916i	$0.672994\pi$
$312$	3.74953	−	3.74953i	0.212276	−	0.212276i
$313$	−12.0851			−0.683089			−0.341545	−	0.939866i	$-0.610950\pi$
$313$	−12.0851			−0.683089			−0.341545	+	0.939866i	$0.610950\pi$
$314$	−6.73511	+	6.73511i	−0.380084	+	0.380084i
$315$	4.32174	−	3.73851i	0.243502	−	0.210641i
$316$	−10.8059	−	10.8059i	−0.607880	−	0.607880i
$317$	3.39821	+	3.39821i	0.190863	+	0.190863i	0.796069	−	0.605206i	$-0.206909\pi$
$317$	3.39821	+	3.39821i	0.190863	+	0.190863i	−0.605206	+	0.796069i	$0.706909\pi$
$318$	1.77989			0.0998112
$319$	1.33180	+	1.33180i	0.0745662	+	0.0745662i
$320$	−0.161376	+	2.23024i	−0.00902117	+	0.124674i
$321$			17.5946i			0.982035i
$322$	−12.1360	+	12.1360i	−0.676312	+	0.676312i
$323$	0.229656	−	0.229656i	0.0127784	−	0.0127784i
$324$	−1.00000			−0.0555556
$325$	−26.2370	−	3.81691i	−1.45537	−	0.211724i
$326$		−	9.31761i		−	0.516054i
$327$	−12.9504			−0.716158
$328$			2.48825i			0.137391i
$329$		−	22.4905i		−	1.23994i
$330$	1.79858	−	1.55586i	0.0990084	−	0.0856471i
$331$	−9.78568	+	9.78568i	−0.537870	+	0.537870i	−0.922903	−	0.385033i	$-0.874190\pi$
$331$	−9.78568	+	9.78568i	−0.537870	+	0.537870i	0.385033	+	0.922903i	$0.374190\pi$
$332$	−2.66034	−	2.66034i	−0.146005	−	0.146005i
$333$	−2.17428	−	5.68089i	−0.119150	−	0.311311i
$334$		−	3.21570i		−	0.175955i
$335$	6.42927	−	5.56164i	0.351269	−	0.303865i
$336$		−	2.55554i		−	0.139416i
$337$	−9.38432	−	9.38432i	−0.511196	−	0.511196i	0.403697	−	0.914893i	$-0.367725\pi$
$337$	−9.38432	−	9.38432i	−0.511196	−	0.511196i	−0.914893	+	0.403697i	$0.867725\pi$
$338$	15.1180			0.822312
$339$	−6.24702	−	6.24702i	−0.339291	−	0.339291i
$340$	−1.83411	−	0.132713i	−0.0994687	−	0.00719736i
$341$	3.82671	−	3.82671i	0.207228	−	0.207228i
$342$	−0.279256	+	0.279256i	−0.0151004	+	0.0151004i
$343$	13.4972	+	13.4972i	0.728779	+	0.728779i
$344$	9.11788			0.491603
$345$	−9.82481	−	11.3575i	−0.528950	−	0.611468i
$346$	0.505073	−	0.505073i	0.0271529	−	0.0271529i
$347$	−10.4542			−0.561210			−0.280605	−	0.959823i	$-0.590535\pi$
$347$	−10.4542			−0.561210			−0.280605	+	0.959823i	$0.590535\pi$
$348$			1.77092i			0.0949314i
$349$		−	34.0306i		−	1.82161i	−0.412832	−	0.910807i	$-0.635460\pi$
$349$		−	34.0306i		−	1.82161i	0.412832	−	0.910807i	$-0.364540\pi$
$350$	−10.2418	+	7.64035i	−0.547447	+	0.408394i
$351$	−3.74953	−	3.74953i	−0.200135	−	0.200135i
$352$		−	1.06354i		−	0.0566868i
$353$		−	1.70118i		−	0.0905448i	−0.998975	−	0.0452724i	$-0.985584\pi$
$353$		−	1.70118i		−	0.0905448i	0.998975	−	0.0452724i	$-0.0144156\pi$
$354$	−14.2003			−0.754737
$355$	1.02283	−	14.1357i	0.0542862	−	0.750244i
$356$	−1.96382	+	1.96382i	−0.104082	+	0.104082i
$357$	2.10163			0.111230
$358$	−6.04168	+	6.04168i	−0.319313	+	0.319313i
$359$			28.6844i			1.51390i	0.653471	+	0.756951i	$0.273312\pi$
$359$			28.6844i			1.51390i	−0.653471	+	0.756951i	$0.726688\pi$
$360$	2.23024	+	0.161376i	0.117544	+	0.00850524i
$361$		−	18.8440i		−	0.991791i
$362$	−23.1096			−1.21461
$363$	6.97836	−	6.97836i	0.366269	−	0.366269i
$364$	9.58208	−	9.58208i	0.502237	−	0.502237i
$365$	−18.8801	−	21.8254i	−0.988228	−	1.14240i
$366$	8.45090			0.441735
$367$	8.16152	−	8.16152i	0.426028	−	0.426028i	−0.461245	−	0.887273i	$-0.652597\pi$
$367$	8.16152	−	8.16152i	0.426028	−	0.426028i	0.887273	+	0.461245i	$0.152597\pi$
$368$	−6.71595			−0.350093
$369$	2.48825			0.129533
$370$	3.93240	+	13.0206i	0.204436	+	0.676909i
$371$	4.54857			0.236150
$372$	5.08848			0.263825
$373$	−14.4400	+	14.4400i	−0.747676	+	0.747676i	−0.974042	−	0.226366i	$-0.927315\pi$
$373$	−14.4400	+	14.4400i	−0.747676	+	0.747676i	0.226366	+	0.974042i	$0.427315\pi$
$374$	0.874637			0.0452264
$375$	−6.02104	−	9.42056i	−0.310925	−	0.486476i
$376$	6.22303	−	6.22303i	0.320928	−	0.320928i
$377$	−6.64013	+	6.64013i	−0.341984	+	0.341984i
$378$	−2.55554			−0.131443
$379$			5.16787i			0.265456i	0.991153	+	0.132728i	$0.0423736\pi$
$379$			5.16787i			0.265456i	−0.991153	+	0.132728i	$0.957626\pi$
$380$	0.667872	−	0.577742i	0.0342611	−	0.0296375i
$381$			22.1845i			1.13655i
$382$	7.76121	−	7.76121i	0.397098	−	0.397098i
$383$	29.7797			1.52167			0.760835	−	0.648945i	$-0.224790\pi$
$383$	29.7797			1.52167			0.760835	+	0.648945i	$0.224790\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	4.59633	−	3.97605i	0.234251	−	0.202638i
$386$	−14.5959			−0.742910
$387$		−	9.11788i		−	0.463488i
$388$			2.76938i			0.140594i
$389$	7.38126	+	7.38126i	0.374245	+	0.374245i	0.869021	−	0.494776i	$-0.164750\pi$
$389$	7.38126	+	7.38126i	0.374245	+	0.374245i	−0.494776	+	0.869021i	$0.664750\pi$
$390$	7.75727	+	8.96743i	0.392804	+	0.454084i
$391$		−	5.52309i		−	0.279315i
$392$			0.469223i			0.0236993i
$393$	13.1730			0.664491
$394$	0.582703	−	0.582703i	0.0293561	−	0.0293561i
$395$	25.8435	−	22.3559i	1.30033	−	1.12485i
$396$	−1.06354			−0.0534448
$397$	−6.00671	−	6.00671i	−0.301468	−	0.301468i	0.540120	−	0.841588i	$-0.318379\pi$
$397$	−6.00671	−	6.00671i	−0.301468	−	0.301468i	−0.841588	+	0.540120i	$0.818379\pi$
$398$	6.47802	−	6.47802i	0.324714	−	0.324714i
$399$	−0.713650	+	0.713650i	−0.0357272	+	0.0357272i
$400$	−4.94792	−	0.719812i	−0.247396	−	0.0359906i
$401$	13.2477	+	13.2477i	0.661556	+	0.661556i	0.955747	−	0.294191i	$-0.0950501\pi$
$401$	13.2477	+	13.2477i	0.661556	+	0.661556i	−0.294191	+	0.955747i	$0.595050\pi$
$402$	−3.80177			−0.189615
$403$	19.0794	+	19.0794i	0.950413	+	0.950413i
$404$			2.28701i			0.113783i
$405$	0.161376	−	2.23024i	0.00801882	−	0.110821i
$406$			4.52566i			0.224605i
$407$	−2.31243	−	6.04185i	−0.114623	−	0.299483i
$408$	0.581513	+	0.581513i	0.0287892	+	0.0287892i
$409$	28.4460	−	28.4460i	1.40656	−	1.40656i	0.629833	−	0.776731i	$-0.283123\pi$
$409$	28.4460	−	28.4460i	1.40656	−	1.40656i	0.776731	−	0.629833i	$-0.216877\pi$
$410$	−5.54938	−	0.401543i	−0.274065	−	0.0198308i
$411$			6.05901i			0.298869i
$412$			6.15995i			0.303479i
$413$	−36.2894			−1.78568
$414$			6.71595i			0.330071i
$415$	6.36251	−	5.50388i	0.312323	−	0.270175i
$416$	5.30264			0.259983
$417$	−10.2497	+	10.2497i	−0.501932	+	0.501932i
$418$	−0.297000	+	0.297000i	−0.0145267	+	0.0145267i
$419$			1.30795i			0.0638976i	0.999490	+	0.0319488i	$0.0101713\pi$
$419$			1.30795i			0.0638976i	−0.999490	+	0.0319488i	$0.989829\pi$
$420$	5.69946	+	0.412402i	0.278105	+	0.0201231i
$421$	10.3936	+	10.3936i	0.506553	+	0.506553i	0.913467	−	0.406914i	$-0.133395\pi$
$421$	10.3936	+	10.3936i	0.506553	+	0.506553i	−0.406914	+	0.913467i	$0.633395\pi$
$422$	17.7152			0.862361
$423$	−6.22303	−	6.22303i	−0.302574	−	0.302574i
$424$	1.25857	+	1.25857i	0.0611216	+	0.0611216i
$425$	0.591962	−	4.06909i	0.0287144	−	0.197380i
$426$	−4.48178	+	4.48178i	−0.217143	+	0.217143i
$427$	21.5966			1.04513
$428$	−12.4413	+	12.4413i	−0.601371	+	0.601371i
$429$	−3.98777	−	3.98777i	−0.192532	−	0.192532i
$430$	−1.47140	+	20.3350i	−0.0709574	+	0.980642i
$431$	15.1242	+	15.1242i	0.728508	+	0.728508i	0.970322	−	0.241815i	$-0.0777426\pi$
$431$	15.1242	+	15.1242i	0.728508	+	0.728508i	−0.241815	+	0.970322i	$0.577743\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	2.44455	+	2.44455i	0.117477	+	0.117477i	0.763402	−	0.645924i	$-0.223528\pi$
$433$	2.44455	+	2.44455i	0.117477	+	0.117477i	−0.645924	+	0.763402i	$0.723528\pi$
$434$	13.0038			0.624202
$435$	−3.94957	−	0.285784i	−0.189368	−	0.0137023i
$436$	−9.15731	−	9.15731i	−0.438556	−	0.438556i
$437$	1.87547	+	1.87547i	0.0897159	+	0.0897159i
$438$			12.9059i			0.616666i
$439$	7.81535	−	7.81535i	0.373007	−	0.373007i	−0.495565	−	0.868571i	$-0.665039\pi$
$439$	7.81535	−	7.81535i	0.373007	−	0.373007i	0.868571	+	0.495565i	$0.165039\pi$
$440$	2.37194	+	0.171629i	0.113078	+	0.00818210i
$441$	0.469223			0.0223439
$442$			4.36081i			0.207423i
$443$	9.14296	−	9.14296i	0.434395	−	0.434395i	−0.455725	−	0.890120i	$-0.650620\pi$
$443$	9.14296	−	9.14296i	0.434395	−	0.434395i	0.890120	+	0.455725i	$0.150620\pi$
$444$	2.47955	−	5.55444i	0.117674	−	0.263602i
$445$	−4.06287	−	4.69669i	−0.192598	−	0.222645i
$446$	9.66780	+	9.66780i	0.457783	+	0.457783i
$447$	9.78594	+	9.78594i	0.462859	+	0.462859i
$448$	1.80704	−	1.80704i	0.0853745	−	0.0853745i
$449$	20.5100	+	20.5100i	0.967926	+	0.967926i	0.999501	−	0.0315757i	$-0.0100525\pi$
$449$	20.5100	+	20.5100i	0.967926	+	0.967926i	−0.0315757	+	0.999501i	$0.510053\pi$
$450$	−0.719812	+	4.94792i	−0.0339323	+	0.233247i
$451$	2.64635			0.124612
$452$		−	8.83462i		−	0.415545i
$453$	−14.9160	−	14.9160i	−0.700817	−	0.700817i
$454$		−	11.0930i		−	0.520619i
$455$	19.8240	+	22.9166i	0.929363	+	1.07435i
$456$	−0.394928			−0.0184942
$457$			36.3219i			1.69907i	0.527534	+	0.849534i	$0.323117\pi$
$457$			36.3219i			1.69907i	−0.527534	+	0.849534i	$0.676883\pi$
$458$			7.46941i			0.349023i
$459$	0.581513	−	0.581513i	0.0271427	−	0.0271427i
$460$	1.08379	−	14.9782i	0.0505320	−	0.698361i
$461$	21.8487	−	21.8487i	1.01760	−	1.01760i	0.0177540	−	0.999842i	$-0.494348\pi$
$461$	21.8487	−	21.8487i	1.01760	−	1.01760i	0.999842	−	0.0177540i	$-0.00565159\pi$
$462$	−2.71791			−0.126449
$463$	−19.8482			−0.922425			−0.461212	−	0.887290i	$-0.652585\pi$
$463$	−19.8482			−0.922425			−0.461212	+	0.887290i	$0.652585\pi$
$464$	−1.25223	+	1.25223i	−0.0581333	+	0.0581333i
$465$	−0.821156	+	11.3485i	−0.0380802	+	0.526275i
$466$	−5.64417	+	5.64417i	−0.261461	+	0.261461i
$467$			6.15546i			0.284841i	0.989806	+	0.142420i	$0.0454885\pi$
$467$			6.15546i			0.284841i	−0.989806	+	0.142420i	$0.954512\pi$
$468$		−	5.30264i		−	0.245115i
$469$	−9.71557			−0.448624
$470$	12.8746	+	14.8831i	0.593861	+	0.686505i
$471$			9.52488i			0.438883i
$472$	−10.0411	−	10.0411i	−0.462180	−	0.462180i
$473$		−	9.69721i		−	0.445878i
$474$	−15.2819			−0.701919
$475$	1.18072	+	1.58275i	0.0541753	+	0.0726214i
$476$	1.48608	+	1.48608i	0.0681144	+	0.0681144i
$477$	1.25857	−	1.25857i	0.0576260	−	0.0576260i
$478$	−7.38903	−	7.38903i	−0.337966	−	0.337966i
$479$	−23.6189	−	23.6189i	−1.07918	−	1.07918i	−0.996583	−	0.0825916i	$-0.973680\pi$
$479$	−23.6189	−	23.6189i	−1.07918	−	1.07918i	−0.0825916	−	0.996583i	$-0.526320\pi$
$480$	1.46291	+	1.69113i	0.0667722	+	0.0771890i
$481$	30.1237	−	11.5294i	1.37352	−	0.525696i
$482$	4.09152	−	4.09152i	0.186364	−	0.186364i
$483$			17.1629i			0.780938i
$484$	9.86889			0.448586
$485$	−6.17638	−	0.446911i	−0.280455	−	0.0202932i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$		−	3.98976i		−	0.180793i	−0.995906	−	0.0903967i	$-0.971187\pi$
$487$		−	3.98976i		−	0.180793i	0.995906	−	0.0903967i	$-0.0288135\pi$
$488$	5.97569	+	5.97569i	0.270507	+	0.270507i
$489$	−6.58854	−	6.58854i	−0.297944	−	0.297944i
$490$	−1.04648	−	0.0757212i	−0.0472751	−	0.00342073i
$491$	23.2276			1.04825			0.524123	−	0.851643i	$-0.324393\pi$
$491$	23.2276			1.04825			0.524123	+	0.851643i	$0.324393\pi$
$492$	1.75946	+	1.75946i	0.0793225	+	0.0793225i
$493$	−1.02981	−	1.02981i	−0.0463805	−	0.0463805i
$494$	−1.48079	−	1.48079i	−0.0666241	−	0.0666241i
$495$	0.171629	−	2.37194i	0.00771416	−	0.106611i
$496$	3.59810	+	3.59810i	0.161559	+	0.161559i
$497$	−11.4534	+	11.4534i	−0.513753	+	0.513753i
$498$	−3.76229			−0.168592
$499$	2.30443	−	2.30443i	0.103160	−	0.103160i	−0.653643	−	0.756803i	$-0.726760\pi$
$499$	2.30443	−	2.30443i	0.103160	−	0.103160i	0.756803	+	0.653643i	$0.226760\pi$
$500$	2.40382	−	10.9189i	0.107502	−	0.488307i
$501$	−2.27384	−	2.27384i	−0.101588	−	0.101588i
$502$	10.0626	+	10.0626i	0.449117	+	0.449117i
$503$	4.20658			0.187562			0.0937811	−	0.995593i	$-0.470105\pi$
$503$	4.20658			0.187562			0.0937811	+	0.995593i	$0.470105\pi$
$504$	−1.80704	−	1.80704i	−0.0804919	−	0.0804919i
$505$	−5.10058	−	0.369068i	−0.226973	−	0.0164233i
$506$			7.14268i			0.317531i
$507$	10.6900	−	10.6900i	0.474762	−	0.474762i
$508$	−15.6868	+	15.6868i	−0.695991	+	0.695991i
$509$	−31.5517			−1.39850			−0.699252	−	0.714876i	$-0.746483\pi$
$509$	−31.5517			−1.39850			−0.699252	+	0.714876i	$0.746483\pi$
$510$	−1.39075	+	1.20307i	−0.0615837	+	0.0532729i
$511$			32.9814i			1.45901i
$512$	1.00000			0.0441942
$513$			0.394928i			0.0174365i
$514$			18.7819i			0.828432i
$515$	−13.7381	−	0.994066i	−0.605375	−	0.0438038i
$516$	6.44731	−	6.44731i	0.283827	−	0.283827i
$517$	−6.61843	−	6.61843i	−0.291078	−	0.291078i
$518$	6.33658	−	14.1946i	0.278414	−	0.623675i
$519$		−	0.714281i		−	0.0313535i
$520$	−0.855717	+	11.8261i	−0.0375257	+	0.518611i
$521$		−	11.9791i		−	0.524814i	−0.964957	−	0.262407i	$-0.915484\pi$
$521$		−	11.9791i		−	0.524814i	0.964957	−	0.262407i	$-0.0845163\pi$
$522$	1.25223	+	1.25223i	0.0548086	+	0.0548086i
$523$	4.59086			0.200744			0.100372	−	0.994950i	$-0.467997\pi$
$523$	4.59086			0.200744			0.100372	+	0.994950i	$0.467997\pi$
$524$	9.31473	+	9.31473i	0.406916	+	0.406916i
$525$	−1.83951	+	12.6446i	−0.0802827	+	0.551855i
$526$	−5.85579	+	5.85579i	−0.255325	+	0.255325i
$527$	−2.95902	+	2.95902i	−0.128897	+	0.128897i
$528$	−0.752035	−	0.752035i	−0.0327281	−	0.0327281i
$529$	22.1040			0.961045
$530$	−3.01002	+	2.60381i	−0.130747	+	0.113102i
$531$	−10.0411	+	10.0411i	−0.435748	+	0.435748i
$532$	−1.00925			−0.0437567
$533$			13.1943i			0.571508i
$534$			2.77726i			0.120184i
$535$	−25.7392	−	29.7547i	−1.11280	−	1.28641i
$536$	−2.68826	−	2.68826i	−0.116115	−	0.116115i
$537$			8.54422i			0.368710i
$538$		−	15.7921i		−	0.680848i
$539$	0.499037			0.0214950
$540$	1.69113	−	1.46291i	0.0727745	−	0.0629535i
$541$	−24.1447	+	24.1447i	−1.03806	+	1.03806i	−0.0388161	+	0.999246i	$0.512359\pi$
$541$	−24.1447	+	24.1447i	−1.03806	+	1.03806i	−0.999246	+	0.0388161i	$0.987641\pi$
$542$	16.3325			0.701539
$543$	−16.3409	+	16.3409i	−0.701256	+	0.701256i
$544$			0.822384i			0.0352594i
$545$	21.9007	−	18.9452i	0.938124	−	0.811523i
$546$		−	13.5511i		−	0.579934i
$547$	33.1735			1.41840			0.709198	−	0.705009i	$-0.249057\pi$
$547$	33.1735			1.41840			0.709198	+	0.705009i	$0.249057\pi$
$548$	−4.28437	+	4.28437i	−0.183019	+	0.183019i
$549$	5.97569	−	5.97569i	0.255036	−	0.255036i
$550$	−0.765548	+	5.26230i	−0.0326431	+	0.224385i
$551$	0.699386			0.0297948
$552$	−4.74890	+	4.74890i	−0.202126	+	0.202126i
$553$	−39.0534			−1.66072
$554$	−15.9722			−0.678595
$555$	11.9876	+	6.42634i	0.508845	+	0.272783i
$556$	−14.4953			−0.614739
$557$	43.1483			1.82825			0.914127	−	0.405428i	$-0.132877\pi$
$557$	43.1483			1.82825			0.914127	+	0.405428i	$0.132877\pi$
$558$	3.59810	−	3.59810i	0.152320	−	0.152320i
$559$	48.3488			2.04494
$560$	3.73851	+	4.32174i	0.157981	+	0.182627i
$561$	0.618462	−	0.618462i	0.0261115	−	0.0261115i
$562$	3.15356	−	3.15356i	0.133025	−	0.133025i
$563$	30.3487			1.27905			0.639523	−	0.768772i	$-0.279132\pi$
$563$	30.3487			1.27905			0.639523	+	0.768772i	$0.279132\pi$
$564$		−	8.80070i		−	0.370576i
$565$	19.7033	+	1.42569i	0.828924	+	0.0599793i
$566$		−	20.7113i		−	0.870561i
$567$	−1.80704	+	1.80704i	−0.0758885	+	0.0758885i
$568$	−6.33819			−0.265945
$569$	23.4661	−	23.4661i	0.983752	−	0.983752i	−0.0161182	−	0.999870i	$-0.505131\pi$
$569$	23.4661	−	23.4661i	0.983752	−	0.983752i	0.999870	+	0.0161182i	$0.00513079\pi$
$570$	0.0637317	−	0.880782i	0.00266943	−	0.0368919i
$571$	−27.7114			−1.15969			−0.579844	−	0.814728i	$-0.696886\pi$
$571$	−27.7114			−1.15969			−0.579844	+	0.814728i	$0.696886\pi$
$572$		−	5.63956i		−	0.235802i
$573$		−	10.9760i		−	0.458529i
$574$	4.49636	+	4.49636i	0.187674	+	0.187674i
$575$	33.2300	+	4.83422i	1.38579	+	0.201601i
$576$		−	1.00000i		−	0.0416667i
$577$			3.00740i			0.125200i	0.998039	+	0.0625998i	$0.0199392\pi$
$577$			3.00740i			0.125200i	−0.998039	+	0.0625998i	$0.980061\pi$
$578$	16.3237			0.678976
$579$	−10.3208	+	10.3208i	−0.428919	+	0.428919i
$580$	−2.59069	−	2.99485i	−0.107573	−	0.124354i
$581$	−9.61468			−0.398884
$582$	1.95825	+	1.95825i	0.0811721	+	0.0811721i
$583$	1.33854	−	1.33854i	0.0554366	−	0.0554366i
$584$	−9.12583	+	9.12583i	−0.377629	+	0.377629i
$585$	11.8261	+	0.855717i	0.488951	+	0.0353796i
$586$	−14.7664	−	14.7664i	−0.609996	−	0.609996i
$587$	−44.3832			−1.83189			−0.915946	−	0.401302i	$-0.868558\pi$
$587$	−44.3832			−1.83189			−0.915946	+	0.401302i	$0.868558\pi$
$588$	0.331791	+	0.331791i	0.0136828	+	0.0136828i
$589$		−	2.00958i		−	0.0828033i
$590$	24.0145	−	20.7737i	0.988660	−	0.855239i
$591$		−	0.824066i		−	0.0338975i
$592$	5.68089	−	2.17428i	0.233483	−	0.0893623i
$593$	−19.7493	−	19.7493i	−0.811005	−	0.811005i	0.173779	−	0.984785i	$-0.444402\pi$
$593$	−19.7493	−	19.7493i	−0.811005	−	0.811005i	−0.984785	+	0.173779i	$0.944402\pi$
$594$	−0.752035	+	0.752035i	−0.0308564	+	0.0308564i
$595$	−3.55413	+	3.07449i	−0.145705	+	0.126042i
$596$			13.8394i			0.566884i
$597$		−	9.16131i		−	0.374947i
$598$	−35.6123			−1.45630
$599$		−	20.7918i		−	0.849531i	−0.905303	−	0.424766i	$-0.860356\pi$
$599$		−	20.7918i		−	0.849531i	0.905303	−	0.424766i	$-0.139644\pi$
$600$	−4.00769	+	2.98972i	−0.163613	+	0.122055i
$601$	8.39192			0.342313			0.171157	−	0.985244i	$-0.445250\pi$
$601$	8.39192			0.342313			0.171157	+	0.985244i	$0.445250\pi$
$602$	16.4764	−	16.4764i	0.671526	−	0.671526i
$603$	−2.68826	+	2.68826i	−0.109474	+	0.109474i
$604$		−	21.0945i		−	0.858322i
$605$	−1.59260	+	22.0100i	−0.0647483	+	0.894832i
$606$	1.61716	+	1.61716i	0.0656927	+	0.0656927i
$607$	−12.9350			−0.525014			−0.262507	−	0.964930i	$-0.584549\pi$
$607$	−12.9350			−0.525014			−0.262507	+	0.964930i	$0.584549\pi$
$608$	−0.279256	−	0.279256i	−0.0113253	−	0.0113253i
$609$	3.20012	+	3.20012i	0.129676	+	0.129676i
$610$	−14.2915	+	12.3629i	−0.578647	+	0.500558i
$611$	32.9985	−	32.9985i	1.33498	−	1.33498i
$612$	0.822384			0.0332429
$613$	−19.8672	+	19.8672i	−0.802430	+	0.802430i	−0.983475	−	0.181045i	$-0.942052\pi$
$613$	−19.8672	+	19.8672i	−0.802430	+	0.802430i	0.181045	+	0.983475i	$0.442052\pi$
$614$	1.44634	+	1.44634i	0.0583697	+	0.0583697i
$615$	−4.20794	+	3.64007i	−0.169681	+	0.146782i
$616$	−1.92186	−	1.92186i	−0.0774338	−	0.0774338i
$617$	19.5931	+	19.5931i	0.788789	+	0.788789i	0.981296	−	0.192507i	$-0.0616617\pi$
$617$	19.5931	+	19.5931i	0.788789	+	0.788789i	−0.192507	+	0.981296i	$0.561662\pi$
$618$	4.35574	+	4.35574i	0.175214	+	0.175214i
$619$	41.2199			1.65677			0.828384	−	0.560161i	$-0.189261\pi$
$619$	41.2199			1.65677			0.828384	+	0.560161i	$0.189261\pi$
$620$	−8.60525	+	7.44396i	−0.345595	+	0.298957i
$621$	4.74890	+	4.74890i	0.190567	+	0.190567i
$622$	5.97480	+	5.97480i	0.239568	+	0.239568i
$623$			7.09739i			0.284351i
$624$	3.74953	−	3.74953i	0.150101	−	0.150101i
$625$	23.9637	+	7.12314i	0.958550	+	0.284926i
$626$	−12.0851			−0.483017
$627$			0.420021i			0.0167740i
$628$	−6.73511	+	6.73511i	−0.268760	+	0.268760i
$629$	1.78809	+	4.67187i	0.0712959	+	0.186280i
$630$	4.32174	−	3.73851i	0.172182	−	0.148946i
$631$	−19.8995	−	19.8995i	−0.792187	−	0.792187i	0.189663	−	0.981849i	$-0.439261\pi$
$631$	−19.8995	−	19.8995i	−0.792187	−	0.792187i	−0.981849	+	0.189663i	$0.939261\pi$
$632$	−10.8059	−	10.8059i	−0.429836	−	0.429836i
$633$	12.5265	−	12.5265i	0.497885	−	0.497885i
$634$	3.39821	+	3.39821i	0.134960	+	0.134960i
$635$	−32.4539	−	37.5168i	−1.28789	−	1.48881i
$636$	1.77989			0.0705772
$637$			2.48812i			0.0985830i
$638$	1.33180	+	1.33180i	0.0527263	+	0.0527263i
$639$			6.33819i			0.250735i
$640$	−0.161376	+	2.23024i	−0.00637893	+	0.0881579i
$641$	2.45418			0.0969341			0.0484670	−	0.998825i	$-0.484566\pi$
$641$	2.45418			0.0969341			0.0484670	+	0.998825i	$0.484566\pi$
$642$			17.5946i			0.694403i
$643$			6.95487i			0.274273i	0.990552	+	0.137137i	$0.0437900\pi$
$643$			6.95487i			0.274273i	−0.990552	+	0.137137i	$0.956210\pi$
$644$	−12.1360	+	12.1360i	−0.478225	+	0.478225i
$645$	13.3386	+	15.4195i	0.525207	+	0.607141i
$646$	0.229656	−	0.229656i	0.00903569	−	0.00903569i
$647$	5.11832			0.201222			0.100611	−	0.994926i	$-0.467920\pi$
$647$	5.11832			0.201222			0.100611	+	0.994926i	$0.467920\pi$
$648$	−1.00000			−0.0392837
$649$	−10.6791	+	10.6791i	−0.419192	+	0.419192i
$650$	−26.2370	−	3.81691i	−1.02910	−	0.149711i
$651$	9.19507	−	9.19507i	0.360383	−	0.360383i
$652$		−	9.31761i		−	0.364906i
$653$		−	13.1975i		−	0.516459i	−0.966084	−	0.258229i	$-0.916861\pi$
$653$		−	13.1975i		−	0.516459i	0.966084	−	0.258229i	$-0.0831390\pi$
$654$	−12.9504			−0.506400
$655$	−22.2772	+	19.2709i	−0.870444	+	0.752976i
$656$			2.48825i			0.0971498i
$657$	9.12583	+	9.12583i	0.356032	+	0.356032i
$658$		−	22.4905i		−	0.876772i
$659$	31.5233			1.22797			0.613987	−	0.789316i	$-0.289565\pi$
$659$	31.5233			1.22797			0.613987	+	0.789316i	$0.289565\pi$
$660$	1.79858	−	1.55586i	0.0700095	−	0.0605616i
$661$	−8.62393	−	8.62393i	−0.335432	−	0.335432i	0.519213	−	0.854645i	$-0.326225\pi$
$661$	−8.62393	−	8.62393i	−0.335432	−	0.335432i	−0.854645	+	0.519213i	$0.826225\pi$
$662$	−9.78568	+	9.78568i	−0.380331	+	0.380331i
$663$	3.08356	+	3.08356i	0.119755	+	0.119755i
$664$	−2.66034	−	2.66034i	−0.103241	−	0.103241i
$665$	0.162869	−	2.25087i	0.00631578	−	0.0872851i
$666$	−2.17428	−	5.68089i	−0.0842516	−	0.220130i
$667$	8.40992	−	8.40992i	0.325633	−	0.325633i
$668$		−	3.21570i		−	0.124419i
$669$	13.6723			0.528603
$670$	6.42927	−	5.56164i	0.248385	−	0.214865i
$671$	6.35537	−	6.35537i	0.245346	−	0.245346i
$672$		−	2.55554i		−	0.0985820i
$673$	24.1094	+	24.1094i	0.929350	+	0.929350i	0.997664	−	0.0683141i	$-0.0217620\pi$
$673$	24.1094	+	24.1094i	0.929350	+	0.929350i	−0.0683141	+	0.997664i	$0.521762\pi$
$674$	−9.38432	−	9.38432i	−0.361470	−	0.361470i
$675$	2.98972	+	4.00769i	0.115074	+	0.154256i
$676$	15.1180			0.581462
$677$	−12.4278	−	12.4278i	−0.477641	−	0.477641i	0.426736	−	0.904376i	$-0.359663\pi$
$677$	−12.4278	−	12.4278i	−0.477641	−	0.477641i	−0.904376	+	0.426736i	$0.859663\pi$
$678$	−6.24702	−	6.24702i	−0.239915	−	0.239915i
$679$	5.00438	+	5.00438i	0.192051	+	0.192051i
$680$	−1.83411	−	0.132713i	−0.0703350	−	0.00508930i
$681$	−7.84392	−	7.84392i	−0.300580	−	0.300580i
$682$	3.82671	−	3.82671i	0.146532	−	0.146532i
$683$	20.6705			0.790936			0.395468	−	0.918480i	$-0.370582\pi$
$683$	20.6705			0.790936			0.395468	+	0.918480i	$0.370582\pi$
$684$	−0.279256	+	0.279256i	−0.0106776	+	0.0106776i
$685$	−8.86376	−	10.2465i	−0.338667	−	0.391500i
$686$	13.4972	+	13.4972i	0.515325	+	0.515325i
$687$	5.28167	+	5.28167i	0.201508	+	0.201508i
$688$	9.11788			0.347616
$689$	6.67375	+	6.67375i	0.254250	+	0.254250i
$690$	−9.82481	−	11.3575i	−0.374024	−	0.432373i
$691$			16.2532i			0.618302i	0.951013	+	0.309151i	$0.100045\pi$
$691$			16.2532i			0.618302i	−0.951013	+	0.309151i	$0.899955\pi$
$692$	0.505073	−	0.505073i	0.0192000	−	0.0192000i
$693$	−1.92186	+	1.92186i	−0.0730052	+	0.0730052i
$694$	−10.4542			−0.396836
$695$	2.33919	−	32.3280i	0.0887307	−	1.22627i
$696$			1.77092i			0.0671266i
$697$	−2.04630			−0.0775090
$698$		−	34.0306i		−	1.28808i
$699$			7.98207i			0.301910i
$700$	−10.2418	+	7.64035i	−0.387104	+	0.288778i
$701$	26.8591	−	26.8591i	1.01445	−	1.01445i	0.0145602	−	0.999894i	$-0.495365\pi$
$701$	26.8591	−	26.8591i	1.01445	−	1.01445i	0.999894	−	0.0145602i	$-0.00463483\pi$
$702$	−3.74953	−	3.74953i	−0.141517	−	0.141517i
$703$	−2.19360	−	0.979243i	−0.0827333	−	0.0369328i
$704$		−	1.06354i		−	0.0400836i
$705$	19.6276	+	1.42022i	0.739220	+	0.0534885i
$706$		−	1.70118i		−	0.0640248i
$707$	4.13272	+	4.13272i	0.155427	+	0.155427i
$708$	−14.2003			−0.533680
$709$	−3.54702	−	3.54702i	−0.133211	−	0.133211i	0.637357	−	0.770568i	$-0.280028\pi$
$709$	−3.54702	−	3.54702i	−0.133211	−	0.133211i	−0.770568	+	0.637357i	$0.780028\pi$
$710$	1.02283	−	14.1357i	0.0383861	−	0.530502i
$711$	−10.8059	+	10.8059i	−0.405253	+	0.405253i
$712$	−1.96382	+	1.96382i	−0.0735972	+	0.0735972i
$713$	−24.1646	−	24.1646i	−0.904973	−	0.904973i
$714$	2.10163			0.0786517
$715$	12.5776	+	0.910088i	0.470374	+	0.0340354i
$716$	−6.04168	+	6.04168i	−0.225788	+	0.225788i
$717$	−10.4497			−0.390250
$718$			28.6844i			1.07049i
$719$			30.1580i			1.12470i	0.826899	+	0.562351i	$0.190103\pi$
$719$			30.1580i			1.12470i	−0.826899	+	0.562351i	$0.809897\pi$
$720$	2.23024	+	0.161376i	0.0831160	+	0.00601412i
$721$	11.1313	+	11.1313i	0.414550	+	0.414550i
$722$		−	18.8440i		−	0.701302i
$723$		−	5.78628i		−	0.215194i
$724$	−23.1096			−0.858860
$725$	7.09730	−	5.29456i	0.263587	−	0.196635i
$726$	6.97836	−	6.97836i	0.258991	−	0.258991i
$727$	28.9822			1.07489			0.537445	−	0.843299i	$-0.319390\pi$
$727$	28.9822			1.07489			0.537445	+	0.843299i	$0.319390\pi$
$728$	9.58208	−	9.58208i	0.355135	−	0.355135i
$729$			1.00000i			0.0370370i
$730$	−18.8801	−	21.8254i	−0.698783	−	0.807796i
$731$			7.49840i			0.277338i
$732$	8.45090			0.312354
$733$	−29.0250	+	29.0250i	−1.07206	+	1.07206i	−0.0748691	+	0.997193i	$0.523854\pi$
$733$	−29.0250	+	29.0250i	−1.07206	+	1.07206i	−0.997193	+	0.0748691i	$0.976146\pi$
$734$	8.16152	−	8.16152i	0.301247	−	0.301247i
$735$	−0.793515	+	0.686429i	−0.0292692	+	0.0253193i
$736$	−6.71595			−0.247553
$737$	−2.85907	+	2.85907i	−0.105315	+	0.105315i
$738$	2.48825			0.0915937
$739$	33.3497			1.22679			0.613395	−	0.789777i	$-0.289804\pi$
$739$	33.3497			1.22679			0.613395	+	0.789777i	$0.289804\pi$
$740$	3.93240	+	13.0206i	0.144558	+	0.478647i
$741$	−2.09416			−0.0769309
$742$	4.54857			0.166983
$743$	−15.1228	+	15.1228i	−0.554801	+	0.554801i	−0.927823	−	0.373021i	$-0.878322\pi$
$743$	−15.1228	+	15.1228i	−0.554801	+	0.554801i	0.373021	+	0.927823i	$0.378322\pi$
$744$	5.08848			0.186553
$745$	−30.8652	−	2.23334i	−1.13081	−	0.0818234i
$746$	−14.4400	+	14.4400i	−0.528687	+	0.528687i
$747$	−2.66034	+	2.66034i	−0.0973368	+	0.0973368i
$748$	0.874637			0.0319799
$749$			44.9637i			1.64294i
$750$	−6.02104	−	9.42056i	−0.219857	−	0.343990i
$751$		−	14.7174i		−	0.537044i	−0.963274	−	0.268522i	$-0.913465\pi$
$751$		−	14.7174i		−	0.537044i	0.963274	−	0.268522i	$-0.0865352\pi$
$752$	6.22303	−	6.22303i	0.226931	−	0.226931i
$753$	14.2307			0.518596
$754$	−6.64013	+	6.64013i	−0.241819	+	0.241819i
$755$	47.0457	+	3.40413i	1.71217	+	0.123889i
$756$	−2.55554			−0.0929440
$757$		−	14.5848i		−	0.530092i	−0.964236	−	0.265046i	$-0.914613\pi$
$757$		−	14.5848i		−	0.530092i	0.964236	−	0.265046i	$-0.0853871\pi$
$758$			5.16787i			0.187706i
$759$	5.05063	+	5.05063i	0.183326	+	0.183326i
$760$	0.667872	−	0.577742i	0.0242263	−	0.0209569i
$761$		−	8.92275i		−	0.323449i	−0.986836	−	0.161725i	$-0.948294\pi$
$761$		−	8.92275i		−	0.323449i	0.986836	−	0.161725i	$-0.0517056\pi$
$762$			22.1845i			0.803661i
$763$	−33.0952			−1.19813
$764$	7.76121	−	7.76121i	0.280791	−	0.280791i
$765$	−0.132713	+	1.83411i	−0.00479824	+	0.0663125i
$766$	29.7797			1.07598
$767$	−53.2445	−	53.2445i	−1.92255	−	1.92255i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	10.6755	−	10.6755i	0.384969	−	0.384969i	−0.487919	−	0.872889i	$-0.662244\pi$
$769$	10.6755	−	10.6755i	0.384969	−	0.384969i	0.872889	+	0.487919i	$0.162244\pi$
$770$	4.59633	−	3.97605i	0.165640	−	0.143287i
$771$	13.2808	+	13.2808i	0.478295	+	0.478295i
$772$	−14.5959			−0.525317
$773$	28.2301	+	28.2301i	1.01536	+	1.01536i	0.999880	+	0.0154847i	$0.00492915\pi$
$773$	28.2301	+	28.2301i	1.01536	+	1.01536i	0.0154847	+	0.999880i	$0.495071\pi$
$774$		−	9.11788i		−	0.327735i
$775$	−15.2131	−	20.3930i	−0.546472	−	0.732539i
$776$			2.76938i			0.0994151i
$777$	−5.55645	−	14.5177i	−0.199337	−	0.520821i
$778$	7.38126	+	7.38126i	0.264631	+	0.264631i
$779$	0.694858	−	0.694858i	0.0248959	−	0.0248959i
$780$	7.75727	+	8.96743i	0.277755	+	0.321086i
$781$			6.74091i			0.241209i
$782$		−	5.52309i		−	0.197505i
$783$	1.77092			0.0632876
$784$			0.469223i			0.0167580i
$785$	−13.9340	−	16.1078i	−0.497326	−	0.574911i
$786$	13.1730			0.469866
$787$	8.25746	−	8.25746i	0.294347	−	0.294347i	−0.544448	−	0.838795i	$-0.683261\pi$
$787$	8.25746	−	8.25746i	0.294347	−	0.294347i	0.838795	+	0.544448i	$0.183261\pi$
$788$	0.582703	−	0.582703i	0.0207579	−	0.0207579i
$789$			8.28134i			0.294823i
$790$	25.8435	−	22.3559i	0.919472	−	0.795388i
$791$	−15.9645	−	15.9645i	−0.567632	−	0.567632i
$792$	−1.06354			−0.0377912
$793$	31.6869	+	31.6869i	1.12524	+	1.12524i
$794$	−6.00671	−	6.00671i	−0.213170	−	0.213170i
$795$	−0.287231	+	3.96957i	−0.0101870	+	0.140786i
$796$	6.47802	−	6.47802i	0.229607	−	0.229607i
$797$	−26.1069			−0.924753			−0.462377	−	0.886684i	$-0.653003\pi$
$797$	−26.1069			−0.924753			−0.462377	+	0.886684i	$0.653003\pi$
$798$	−0.713650	+	0.713650i	−0.0252629	+	0.0252629i
$799$	5.11772	+	5.11772i	0.181052	+	0.181052i
$800$	−4.94792	−	0.719812i	−0.174935	−	0.0254492i
$801$	1.96382	+	1.96382i	0.0693881	+	0.0693881i
$802$	13.2477	+	13.2477i	0.467791	+	0.467791i
$803$	9.70567	+	9.70567i	0.342506	+	0.342506i
$804$	−3.80177			−0.134078
$805$	−25.1077	−	29.0246i	−0.884929	−	1.02298i
$806$	19.0794	+	19.0794i	0.672044	+	0.672044i
$807$	−11.1667	−	11.1667i	−0.393088	−	0.393088i
$808$			2.28701i			0.0804568i
$809$	23.7338	−	23.7338i	0.834436	−	0.834436i	−0.153684	−	0.988120i	$-0.549114\pi$
$809$	23.7338	−	23.7338i	0.834436	−	0.834436i	0.988120	+	0.153684i	$0.0491137\pi$
$810$	0.161376	−	2.23024i	0.00567016	−	0.0783625i
$811$	−21.9695			−0.771454			−0.385727	−	0.922613i	$-0.626049\pi$
$811$	−21.9695			−0.771454			−0.385727	+	0.922613i	$0.626049\pi$
$812$			4.52566i			0.158819i
$813$	11.5488	−	11.5488i	0.405034	−	0.405034i
$814$	−2.31243	−	6.04185i	−0.0810506	−	0.211767i
$815$	20.7805	+	1.50363i	0.727908	+	0.0526700i
$816$	0.581513	+	0.581513i	0.0203570	+	0.0203570i
$817$	−2.54622	−	2.54622i	−0.0890811	−	0.0890811i
$818$	28.4460	−	28.4460i	0.994591	−	0.994591i
$819$	−9.58208	−	9.58208i	−0.334825	−	0.334825i
$820$	−5.54938	−	0.401543i	−0.193793	−	0.0140225i
$821$	−0.448348			−0.0156475			−0.00782373	−	0.999969i	$-0.502490\pi$
$821$	−0.448348			−0.0156475			−0.00782373	+	0.999969i	$0.502490\pi$
$822$			6.05901i			0.211332i
$823$	22.3962	+	22.3962i	0.780683	+	0.780683i	0.979946	−	0.199263i	$-0.0638549\pi$
$823$	22.3962	+	22.3962i	0.780683	+	0.780683i	−0.199263	+	0.979946i	$0.563855\pi$
$824$			6.15995i			0.214592i
$825$	3.17968	+	4.26233i	0.110702	+	0.148395i
$826$	−36.2894			−1.26267
$827$			33.9842i			1.18174i	0.806765	+	0.590872i	$0.201216\pi$
$827$			33.9842i			1.18174i	−0.806765	+	0.590872i	$0.798784\pi$
$828$			6.71595i			0.233396i
$829$	−0.497426	+	0.497426i	−0.0172763	+	0.0172763i	−0.715692	−	0.698416i	$-0.753889\pi$
$829$	−0.497426	+	0.497426i	−0.0172763	+	0.0172763i	0.698416	+	0.715692i	$0.253889\pi$
$830$	6.36251	−	5.50388i	0.220846	−	0.191042i
$831$	−11.2941	+	11.2941i	−0.391787	+	0.391787i
$832$	5.30264			0.183836
$833$	−0.385882			−0.0133700
$834$	−10.2497	+	10.2497i	−0.354920	+	0.354920i
$835$	7.17177	+	0.518936i	0.248189	+	0.0179585i
$836$	−0.297000	+	0.297000i	−0.0102719	+	0.0102719i
$837$		−	5.08848i		−	0.175883i
$838$			1.30795i			0.0451824i
$839$	−23.5526			−0.813128			−0.406564	−	0.913622i	$-0.633273\pi$
$839$	−23.5526			−0.813128			−0.406564	+	0.913622i	$0.633273\pi$
$840$	5.69946	+	0.412402i	0.196650	+	0.0142292i
$841$			25.8638i			0.891856i
$842$	10.3936	+	10.3936i	0.358187	+	0.358187i
$843$		−	4.45980i		−	0.153604i
$844$	17.7152			0.609782
$845$	−2.43968	+	33.7168i	−0.0839275	+	1.15989i
$846$	−6.22303	−	6.22303i	−0.213952	−	0.213952i
$847$	17.8335	−	17.8335i	0.612765	−	0.612765i
$848$	1.25857	+	1.25857i	0.0432195	+	0.0432195i
$849$	−14.6451	−	14.6451i	−0.502619	−	0.502619i
$850$	0.591962	−	4.06909i	0.0203041	−	0.139569i
$851$	−38.1526	+	14.6024i	−1.30785	+	0.500562i
$852$	−4.48178	+	4.48178i	−0.153543	+	0.153543i
$853$		−	17.3192i		−	0.592999i	−0.955033	−	0.296499i	$-0.904181\pi$
$853$		−	17.3192i		−	0.592999i	0.955033	−	0.296499i	$-0.0958193\pi$
$854$	21.5966			0.739020
$855$	−0.577742	−	0.667872i	−0.0197584	−	0.0228408i
$856$	−12.4413	+	12.4413i	−0.425234	+	0.425234i
$857$		−	12.2119i		−	0.417150i	−0.978006	−	0.208575i	$-0.933117\pi$
$857$		−	12.2119i		−	0.417150i	0.978006	−	0.208575i	$-0.0668826\pi$
$858$	−3.98777	−	3.98777i	−0.136140	−	0.136140i
$859$	−14.6801	−	14.6801i	−0.500879	−	0.500879i	0.410832	−	0.911711i	$-0.365238\pi$
$859$	−14.6801	−	14.6801i	−0.500879	−	0.500879i	−0.911711	+	0.410832i	$0.865238\pi$
$860$	−1.47140	+	20.3350i	−0.0501745	+	0.693419i
$861$	6.35881			0.216708
$862$	15.1242	+	15.1242i	0.515133	+	0.515133i
$863$	12.1402	+	12.1402i	0.413258	+	0.413258i	0.882872	−	0.469614i	$-0.155607\pi$
$863$	12.1402	+	12.1402i	0.413258	+	0.413258i	−0.469614	+	0.882872i	$0.655607\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	1.04493	+	1.20794i	0.0355286	+	0.0410712i
$866$	2.44455	+	2.44455i	0.0830691	+	0.0830691i
$867$	11.5426	−	11.5426i	0.392007	−	0.392007i
$868$	13.0038			0.441378
$869$	−11.4925	+	11.4925i	−0.389856	+	0.389856i
$870$	−3.94957	−	0.285784i	−0.133903	−	0.00968897i
$871$	−14.2549	−	14.2549i	−0.483008	−	0.483008i
$872$	−9.15731	−	9.15731i	−0.310106	−	0.310106i
$873$	2.76938			0.0937295
$874$	1.87547	+	1.87547i	0.0634387	+	0.0634387i
$875$	−15.3870	−	24.0746i	−0.520176	−	0.813871i
$876$			12.9059i			0.436049i
$877$	−31.1674	+	31.1674i	−1.05245	+	1.05245i	−0.0539030	+	0.998546i	$0.517166\pi$
$877$	−31.1674	+	31.1674i	−1.05245	+	1.05245i	−0.998546	+	0.0539030i	$0.982834\pi$
$878$	7.81535	−	7.81535i	0.263755	−	0.263755i
$879$	−20.8829			−0.704363
$880$	2.37194	+	0.171629i	0.0799582	+	0.00578562i
$881$		−	57.7813i		−	1.94670i	−0.229323	−	0.973350i	$-0.573651\pi$
$881$		−	57.7813i		−	1.94670i	0.229323	−	0.973350i	$-0.426349\pi$
$882$	0.469223			0.0157996
$883$			30.0024i			1.00966i	0.863218	+	0.504831i	$0.168445\pi$
$883$			30.0024i			1.00966i	−0.863218	+	0.504831i	$0.831555\pi$
$884$			4.36081i			0.146670i
$885$	2.29158	−	31.6700i	0.0770307	−	1.06458i
$886$	9.14296	−	9.14296i	0.307164	−	0.307164i
$887$	15.1524	+	15.1524i	0.508767	+	0.508767i	0.914148	−	0.405381i	$-0.132861\pi$
$887$	15.1524	+	15.1524i	0.508767	+	0.508767i	−0.405381	+	0.914148i	$0.632861\pi$
$888$	2.47955	−	5.55444i	0.0832082	−	0.186395i
$889$			56.6934i			1.90144i
$890$	−4.06287	−	4.69669i	−0.136188	−	0.157434i
$891$			1.06354i			0.0356299i
$892$	9.66780	+	9.66780i	0.323702	+	0.323702i
$893$	−3.47564			−0.116308
$894$	9.78594	+	9.78594i	0.327291	+	0.327291i
$895$	−12.4994	−	14.4494i	−0.417809	−	0.482989i
$896$	1.80704	−	1.80704i	0.0603689	−	0.0603689i
$897$	−25.1817	+	25.1817i	−0.840792	+	0.840792i
$898$	20.5100	+	20.5100i	0.684427	+	0.684427i
$899$	−9.01129			−0.300543
$900$	−0.719812	+	4.94792i	−0.0239937	+	0.164931i
$901$	−1.03503	+	1.03503i	−0.0344818	+	0.0344818i
$902$	2.64635			0.0881137
$903$		−	23.3011i		−	0.775412i
$904$		−	8.83462i		−	0.293835i
$905$	3.72932	−	51.5398i	0.123967	−	1.71324i
$906$	−14.9160	−	14.9160i	−0.495552	−	0.495552i
$907$			44.1175i			1.46490i	0.680822	+	0.732449i	$0.261623\pi$
$907$			44.1175i			1.46490i	−0.680822	+	0.732449i	$0.738377\pi$
$908$		−	11.0930i		−	0.368133i
$909$	2.28701			0.0758554
$910$	19.8240	+	22.9166i	0.657159	+	0.759679i
$911$	4.77567	−	4.77567i	0.158225	−	0.158225i	−0.623555	−	0.781780i	$-0.714312\pi$
$911$	4.77567	−	4.77567i	0.158225	−	0.158225i	0.781780	+	0.623555i	$0.214312\pi$
$912$	−0.394928			−0.0130774
$913$	−2.82938	+	2.82938i	−0.0936387	+	0.0936387i
$914$			36.3219i			1.20142i
$915$	−1.36377	+	18.8475i	−0.0450848	+	0.623079i
$916$			7.46941i			0.246796i
$917$	33.6642			1.11169
$918$	0.581513	−	0.581513i	0.0191928	−	0.0191928i
$919$	−3.86720	+	3.86720i	−0.127567	+	0.127567i	−0.768008	−	0.640441i	$-0.778752\pi$
$919$	−3.86720	+	3.86720i	−0.127567	+	0.127567i	0.640441	+	0.768008i	$0.278752\pi$
$920$	1.08379	−	14.9782i	0.0357315	−	0.493816i
$921$	2.04544			0.0673995
$922$	21.8487	−	21.8487i	0.719549	−	0.719549i
$923$	−33.6092			−1.10626
$924$	−2.71791			−0.0894128
$925$	−29.6736	+	6.66897i	−0.975663	+	0.219274i
$926$	−19.8482			−0.652253
$927$	6.15995			0.202319
$928$	−1.25223	+	1.25223i	−0.0411065	+	0.0411065i
$929$	47.0627			1.54408			0.772038	−	0.635576i	$-0.219237\pi$
$929$	47.0627			1.54408			0.772038	+	0.635576i	$0.219237\pi$
$930$	−0.821156	+	11.3485i	−0.0269268	+	0.372132i
$931$	0.131033	−	0.131033i	0.00429444	−	0.00429444i
$932$	−5.64417	+	5.64417i	−0.184881	+	0.184881i
$933$	8.44965			0.276629
$934$			6.15546i			0.201413i
$935$	−0.141145	+	1.95065i	−0.00461594	+	0.0637930i
$936$		−	5.30264i		−	0.173322i
$937$	−3.14122	+	3.14122i	−0.102619	+	0.102619i	−0.756552	−	0.653933i	$-0.773118\pi$
$937$	−3.14122	+	3.14122i	−0.102619	+	0.102619i	0.653933	+	0.756552i	$0.273118\pi$
$938$	−9.71557			−0.317225
$939$	−8.54544	+	8.54544i	−0.278870	+	0.278870i
$940$	12.8746	+	14.8831i	0.419923	+	0.485433i
$941$	12.8303			0.418256			0.209128	−	0.977888i	$-0.432938\pi$
$941$	12.8303			0.418256			0.209128	+	0.977888i	$0.432938\pi$
$942$			9.52488i			0.310337i
$943$		−	16.7110i		−	0.544184i
$944$	−10.0411	−	10.0411i	−0.326811	−	0.326811i
$945$	0.412402	−	5.69946i	0.0134154	−	0.185403i
$946$		−	9.69721i		−	0.315284i
$947$		−	26.7213i		−	0.868324i	−0.900835	−	0.434162i	$-0.857044\pi$
$947$		−	26.7213i		−	0.868324i	0.900835	−	0.434162i	$-0.142956\pi$
$948$	−15.2819			−0.496332
$949$	−48.3910	+	48.3910i	−1.57084	+	1.57084i
$950$	1.18072	+	1.58275i	0.0383077	+	0.0513511i
$951$	4.80580			0.155839
$952$	1.48608	+	1.48608i	0.0481641	+	0.0481641i
$953$	9.96830	−	9.96830i	0.322905	−	0.322905i	−0.526976	−	0.849880i	$-0.676674\pi$
$953$	9.96830	−	9.96830i	0.322905	−	0.322905i	0.849880	+	0.526976i	$0.176674\pi$
$954$	1.25857	−	1.25857i	0.0407478	−	0.0407478i
$955$	16.0569	+	18.5618i	0.519588	+	0.600646i
$956$	−7.38903	−	7.38903i	−0.238978	−	0.238978i
$957$	1.88344			0.0608831
$958$	−23.6189	−	23.6189i	−0.763092	−	0.763092i
$959$			15.4840i			0.500006i
$960$	1.46291	+	1.69113i	0.0472151	+	0.0545808i
$961$		−	5.10741i		−	0.164755i
$962$	30.1237	−	11.5294i	0.971228	−	0.371723i
$963$	12.4413	+	12.4413i	0.400914	+	0.400914i
$964$	4.09152	−	4.09152i	0.131779	−	0.131779i
$965$	2.35542	−	32.5522i	0.0758236	−	1.04789i
$966$			17.1629i			0.552207i
$967$		−	33.0090i		−	1.06150i	−0.847529	−	0.530749i	$-0.821911\pi$
$967$		−	33.0090i		−	1.06150i	0.847529	−	0.530749i	$-0.178089\pi$
$968$	9.86889			0.317198
$969$		−	0.324782i		−	0.0104335i
$970$	−6.17638	−	0.446911i	−0.198312	−	0.0143495i
$971$	4.23427			0.135884			0.0679421	−	0.997689i	$-0.478357\pi$
$971$	4.23427			0.135884			0.0679421	+	0.997689i	$0.478357\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−26.1936	+	26.1936i	−0.839729	+	0.839729i
$974$		−	3.98976i		−	0.127840i
$975$	−21.2513	+	15.8534i	−0.680588	+	0.507716i
$976$	5.97569	+	5.97569i	0.191277	+	0.191277i
$977$	23.8838			0.764112			0.382056	−	0.924139i	$-0.375216\pi$
$977$	23.8838			0.764112			0.382056	+	0.924139i	$0.375216\pi$
$978$	−6.58854	−	6.58854i	−0.210678	−	0.210678i
$979$	2.08860	+	2.08860i	0.0667519	+	0.0667519i
$980$	−1.04648	−	0.0757212i	−0.0334285	−	0.00241882i
$981$	−9.15731	+	9.15731i	−0.292370	+	0.292370i
$982$	23.2276			0.741222
$983$	11.9445	−	11.9445i	0.380969	−	0.380969i	−0.490482	−	0.871451i	$-0.663179\pi$
$983$	11.9445	−	11.9445i	0.380969	−	0.380969i	0.871451	+	0.490482i	$0.163179\pi$
$984$	1.75946	+	1.75946i	0.0560894	+	0.0560894i
$985$	1.20553	+	1.39360i	0.0384114	+	0.0444038i
$986$	−1.02981	−	1.02981i	−0.0327960	−	0.0327960i
$987$	−15.9032	−	15.9032i	−0.506204	−	0.506204i
$988$	−1.48079	−	1.48079i	−0.0471104	−	0.0471104i
$989$	−61.2352			−1.94717
$990$	0.171629	−	2.37194i	0.00545474	−	0.0753853i
$991$	−39.3812	−	39.3812i	−1.25099	−	1.25099i	−0.955279	−	0.295707i	$-0.904445\pi$
$991$	−39.3812	−	39.3812i	−1.25099	−	1.25099i	−0.295707	−	0.955279i	$-0.595555\pi$
$992$	3.59810	+	3.59810i	0.114240	+	0.114240i
$993$			13.8390i			0.439169i
$994$	−11.4534	+	11.4534i	−0.363278	+	0.363278i
$995$	13.4021	+	15.4929i	0.424876	+	0.491159i
$996$	−3.76229			−0.119213
$997$			54.3738i			1.72204i	0.508574	+	0.861018i	$0.330173\pi$
$997$			54.3738i			1.72204i	−0.508574	+	0.861018i	$0.669827\pi$
$998$	2.30443	−	2.30443i	0.0729454	−	0.0729454i
$999$	−5.55444	−	2.47955i	−0.175735	−	0.0784495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.b.253.12	yes	40
5.2	odd	4		1110.2.l.b.697.9	yes	40
37.6	odd	4		1110.2.l.b.43.9	✓	40
185.117	even	4	inner	1110.2.o.b.487.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.9	✓	40	37.6	odd	4
1110.2.l.b.697.9	yes	40	5.2	odd	4
1110.2.o.b.253.12	yes	40	1.1	even	1	trivial
1110.2.o.b.487.12	yes	40	185.117	even	4	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.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.161376 + 2.23024i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80704 - 1.80704i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.161376 + 2.23024i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80704 - 1.80704i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-0.161376 + 2.23024i) q^{10} -1.06354i q^{11} +(0.707107 - 0.707107i) q^{12} +5.30264 q^{13} +(1.80704 - 1.80704i) q^{14} +(1.46291 + 1.69113i) q^{15} +1.00000 q^{16} +0.822384i q^{17} -1.00000i q^{18} +(-0.279256 - 0.279256i) q^{19} +(-0.161376 + 2.23024i) q^{20} -2.55554i q^{21} -1.06354i q^{22} -6.71595 q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.94792 - 0.719812i) q^{25} +5.30264 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.80704 - 1.80704i) q^{28} +(-1.25223 + 1.25223i) q^{29} +(1.46291 + 1.69113i) q^{30} +(3.59810 + 3.59810i) q^{31} +1.00000 q^{32} +(-0.752035 - 0.752035i) q^{33} +0.822384i q^{34} +(3.73851 + 4.32174i) q^{35} -1.00000i q^{36} +(5.68089 - 2.17428i) q^{37} +(-0.279256 - 0.279256i) q^{38} +(3.74953 - 3.74953i) q^{39} +(-0.161376 + 2.23024i) q^{40} +2.48825i q^{41} -2.55554i q^{42} +9.11788 q^{43} -1.06354i q^{44} +(2.23024 + 0.161376i) q^{45} -6.71595 q^{46} +(6.22303 - 6.22303i) q^{47} +(0.707107 - 0.707107i) q^{48} +0.469223i q^{49} +(-4.94792 - 0.719812i) q^{50} +(0.581513 + 0.581513i) q^{51} +5.30264 q^{52} +(1.25857 + 1.25857i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(2.37194 + 0.171629i) q^{55} +(1.80704 - 1.80704i) q^{56} -0.394928 q^{57} +(-1.25223 + 1.25223i) q^{58} +(-10.0411 - 10.0411i) q^{59} +(1.46291 + 1.69113i) q^{60} +(5.97569 + 5.97569i) q^{61} +(3.59810 + 3.59810i) q^{62} +(-1.80704 - 1.80704i) q^{63} +1.00000 q^{64} +(-0.855717 + 11.8261i) q^{65} +(-0.752035 - 0.752035i) q^{66} +(-2.68826 - 2.68826i) q^{67} +0.822384i q^{68} +(-4.74890 + 4.74890i) q^{69} +(3.73851 + 4.32174i) q^{70} -6.33819 q^{71} -1.00000i q^{72} +(-9.12583 + 9.12583i) q^{73} +(5.68089 - 2.17428i) q^{74} +(-4.00769 + 2.98972i) q^{75} +(-0.279256 - 0.279256i) q^{76} +(-1.92186 - 1.92186i) q^{77} +(3.74953 - 3.74953i) q^{78} +(-10.8059 - 10.8059i) q^{79} +(-0.161376 + 2.23024i) q^{80} -1.00000 q^{81} +2.48825i q^{82} +(-2.66034 - 2.66034i) q^{83} -2.55554i q^{84} +(-1.83411 - 0.132713i) q^{85} +9.11788 q^{86} +1.77092i q^{87} -1.06354i q^{88} +(-1.96382 + 1.96382i) q^{89} +(2.23024 + 0.161376i) q^{90} +(9.58208 - 9.58208i) q^{91} -6.71595 q^{92} +5.08848 q^{93} +(6.22303 - 6.22303i) q^{94} +(0.667872 - 0.577742i) q^{95} +(0.707107 - 0.707107i) q^{96} +2.76938i q^{97} +0.469223i q^{98} -1.06354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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