LMFDB - Embedded newform 370.2.g.c.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	370.43
Dual form			370.2.g.c.327.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 - 2.70711i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 - 2.70711i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-0.707107 - 2.12132i) q^{10} +3.82843i q^{11} +(-1.41421 + 1.41421i) q^{12} +2.24264i q^{13} +(-2.70711 - 2.70711i) q^{14} +(2.00000 - 4.00000i) q^{15} +1.00000 q^{16} -1.82843 q^{17} -1.00000 q^{18} +(-5.82843 + 5.82843i) q^{19} +(-2.12132 + 0.707107i) q^{20} -7.65685i q^{21} +3.82843 q^{22} -2.58579i q^{23} +(1.41421 + 1.41421i) q^{24} +(4.00000 - 3.00000i) q^{25} +2.24264 q^{26} +(2.82843 + 2.82843i) q^{27} +(-2.70711 + 2.70711i) q^{28} +(-6.70711 - 6.70711i) q^{29} +(-4.00000 - 2.00000i) q^{30} +(-4.12132 + 4.12132i) q^{31} -1.00000i q^{32} +(5.41421 + 5.41421i) q^{33} +1.82843i q^{34} +(3.82843 - 7.65685i) q^{35} +1.00000i q^{36} +(-4.94975 - 3.53553i) q^{37} +(5.82843 + 5.82843i) q^{38} +(3.17157 + 3.17157i) q^{39} +(0.707107 + 2.12132i) q^{40} +7.00000i q^{41} -7.65685 q^{42} -7.00000i q^{43} -3.82843i q^{44} +(-0.707107 - 2.12132i) q^{45} -2.58579 q^{46} +(-8.24264 + 8.24264i) q^{47} +(1.41421 - 1.41421i) q^{48} -7.65685i q^{49} +(-3.00000 - 4.00000i) q^{50} +(-2.58579 + 2.58579i) q^{51} -2.24264i q^{52} +(2.12132 + 2.12132i) q^{53} +(2.82843 - 2.82843i) q^{54} +(2.70711 + 8.12132i) q^{55} +(2.70711 + 2.70711i) q^{56} +16.4853i q^{57} +(-6.70711 + 6.70711i) q^{58} +(-1.17157 + 1.17157i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(9.29289 - 9.29289i) q^{61} +(4.12132 + 4.12132i) q^{62} +(-2.70711 - 2.70711i) q^{63} -1.00000 q^{64} +(1.58579 + 4.75736i) q^{65} +(5.41421 - 5.41421i) q^{66} +(1.24264 + 1.24264i) q^{67} +1.82843 q^{68} +(-3.65685 - 3.65685i) q^{69} +(-7.65685 - 3.82843i) q^{70} -0.343146 q^{71} +1.00000 q^{72} +(6.00000 - 6.00000i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(1.41421 - 9.89949i) q^{75} +(5.82843 - 5.82843i) q^{76} +(10.3640 + 10.3640i) q^{77} +(3.17157 - 3.17157i) q^{78} +(9.65685 - 9.65685i) q^{79} +(2.12132 - 0.707107i) q^{80} +11.0000 q^{81} +7.00000 q^{82} +(-0.828427 - 0.828427i) q^{83} +7.65685i q^{84} +(-3.87868 + 1.29289i) q^{85} -7.00000 q^{86} -18.9706 q^{87} -3.82843 q^{88} +(7.41421 + 7.41421i) q^{89} +(-2.12132 + 0.707107i) q^{90} +(6.07107 + 6.07107i) q^{91} +2.58579i q^{92} +11.6569i q^{93} +(8.24264 + 8.24264i) q^{94} +(-8.24264 + 16.4853i) q^{95} +(-1.41421 - 1.41421i) q^{96} -7.00000 q^{97} -7.65685 q^{98} +3.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 8 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 + 8 * q^7	$ 4 q - 4 q^{4} + 8 q^{7} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 4 q^{22} + 16 q^{25} - 8 q^{26} - 8 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} + 16 q^{33} + 4 q^{35} + 12 q^{38} + 24 q^{39} - 8 q^{42} - 16 q^{46} - 16 q^{47} - 12 q^{50} - 16 q^{51} + 8 q^{55} + 8 q^{56} - 24 q^{58} - 16 q^{59} - 8 q^{60} + 40 q^{61} + 8 q^{62} - 8 q^{63} - 4 q^{64} + 12 q^{65} + 16 q^{66} - 12 q^{67} - 4 q^{68} + 8 q^{69} - 8 q^{70} - 24 q^{71} + 4 q^{72} + 24 q^{73} + 12 q^{76} + 16 q^{77} + 24 q^{78} + 16 q^{79} + 44 q^{81} + 28 q^{82} + 8 q^{83} - 24 q^{85} - 28 q^{86} - 8 q^{87} - 4 q^{88} + 24 q^{89} - 4 q^{91} + 16 q^{94} - 16 q^{95} - 28 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 8 * q^7 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 4 * q^22 + 16 * q^25 - 8 * q^26 - 8 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 + 16 * q^33 + 4 * q^35 + 12 * q^38 + 24 * q^39 - 8 * q^42 - 16 * q^46 - 16 * q^47 - 12 * q^50 - 16 * q^51 + 8 * q^55 + 8 * q^56 - 24 * q^58 - 16 * q^59 - 8 * q^60 + 40 * q^61 + 8 * q^62 - 8 * q^63 - 4 * q^64 + 12 * q^65 + 16 * q^66 - 12 * q^67 - 4 * q^68 + 8 * q^69 - 8 * q^70 - 24 * q^71 + 4 * q^72 + 24 * q^73 + 12 * q^76 + 16 * q^77 + 24 * q^78 + 16 * q^79 + 44 * q^81 + 28 * q^82 + 8 * q^83 - 24 * q^85 - 28 * q^86 - 8 * q^87 - 4 * q^88 + 24 * q^89 - 4 * q^91 + 16 * q^94 - 16 * q^95 - 28 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.41421	−	1.41421i	0.816497	−	0.816497i	−0.169102	−	0.985599i	$-0.554087\pi$
$3$	1.41421	−	1.41421i	0.816497	−	0.816497i	0.985599	+	0.169102i	$0.0540867\pi$
$4$	−1.00000			−0.500000
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$6$	−1.41421	−	1.41421i	−0.577350	−	0.577350i
$7$	2.70711	−	2.70711i	1.02319	−	1.02319i	0.0234655	−	0.999725i	$-0.492530\pi$
$7$	2.70711	−	2.70711i	1.02319	−	1.02319i	0.999725	−	0.0234655i	$-0.00747000\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−0.707107	−	2.12132i	−0.223607	−	0.670820i
$11$			3.82843i			1.15431i	0.816633	+	0.577157i	$0.195838\pi$
$11$			3.82843i			1.15431i	−0.816633	+	0.577157i	$0.804162\pi$
$12$	−1.41421	+	1.41421i	−0.408248	+	0.408248i
$13$			2.24264i			0.621997i	0.950410	+	0.310998i	$0.100663\pi$
$13$			2.24264i			0.621997i	−0.950410	+	0.310998i	$0.899337\pi$
$14$	−2.70711	−	2.70711i	−0.723505	−	0.723505i
$15$	2.00000	−	4.00000i	0.516398	−	1.03280i
$16$	1.00000			0.250000
$17$	−1.82843			−0.443459			−0.221729	−	0.975108i	$-0.571170\pi$
$17$	−1.82843			−0.443459			−0.221729	+	0.975108i	$0.571170\pi$
$18$	−1.00000			−0.235702
$19$	−5.82843	+	5.82843i	−1.33713	+	1.33713i	−0.438308	+	0.898825i	$0.644422\pi$
$19$	−5.82843	+	5.82843i	−1.33713	+	1.33713i	−0.898825	+	0.438308i	$0.855578\pi$
$20$	−2.12132	+	0.707107i	−0.474342	+	0.158114i
$21$		−	7.65685i		−	1.67086i
$22$	3.82843			0.816223
$23$		−	2.58579i		−	0.539174i	−0.962976	−	0.269587i	$-0.913113\pi$
$23$		−	2.58579i		−	0.539174i	0.962976	−	0.269587i	$-0.0868871\pi$
$24$	1.41421	+	1.41421i	0.288675	+	0.288675i
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$	2.24264			0.439818
$27$	2.82843	+	2.82843i	0.544331	+	0.544331i
$28$	−2.70711	+	2.70711i	−0.511595	+	0.511595i
$29$	−6.70711	−	6.70711i	−1.24548	−	1.24548i	−0.957696	−	0.287783i	$-0.907082\pi$
$29$	−6.70711	−	6.70711i	−1.24548	−	1.24548i	−0.287783	−	0.957696i	$-0.592918\pi$
$30$	−4.00000	−	2.00000i	−0.730297	−	0.365148i
$31$	−4.12132	+	4.12132i	−0.740211	+	0.740211i	−0.972619	−	0.232408i	$-0.925340\pi$
$31$	−4.12132	+	4.12132i	−0.740211	+	0.740211i	0.232408	+	0.972619i	$0.425340\pi$
$32$		−	1.00000i		−	0.176777i
$33$	5.41421	+	5.41421i	0.942494	+	0.942494i
$34$			1.82843i			0.313573i
$35$	3.82843	−	7.65685i	0.647122	−	1.29424i
$36$			1.00000i			0.166667i
$37$	−4.94975	−	3.53553i	−0.813733	−	0.581238i
$37$	−4.94975	−	3.53553i	−0.813733	−	0.581238i
$38$	5.82843	+	5.82843i	0.945496	+	0.945496i
$39$	3.17157	+	3.17157i	0.507858	+	0.507858i
$40$	0.707107	+	2.12132i	0.111803	+	0.335410i
$41$			7.00000i			1.09322i	0.837389	+	0.546608i	$0.184081\pi$
$41$			7.00000i			1.09322i	−0.837389	+	0.546608i	$0.815919\pi$
$42$	−7.65685			−1.18148
$43$		−	7.00000i		−	1.06749i	−0.845645	−	0.533745i	$-0.820784\pi$
$43$		−	7.00000i		−	1.06749i	0.845645	−	0.533745i	$-0.179216\pi$
$44$		−	3.82843i		−	0.577157i
$45$	−0.707107	−	2.12132i	−0.105409	−	0.316228i
$46$	−2.58579			−0.381253
$47$	−8.24264	+	8.24264i	−1.20231	+	1.20231i	−0.228851	+	0.973461i	$0.573497\pi$
$47$	−8.24264	+	8.24264i	−1.20231	+	1.20231i	−0.973461	+	0.228851i	$0.926503\pi$
$48$	1.41421	−	1.41421i	0.204124	−	0.204124i
$49$		−	7.65685i		−	1.09384i
$50$	−3.00000	−	4.00000i	−0.424264	−	0.565685i
$51$	−2.58579	+	2.58579i	−0.362083	+	0.362083i
$52$		−	2.24264i		−	0.310998i
$53$	2.12132	+	2.12132i	0.291386	+	0.291386i	0.837628	−	0.546242i	$-0.183942\pi$
$53$	2.12132	+	2.12132i	0.291386	+	0.291386i	−0.546242	+	0.837628i	$0.683942\pi$
$54$	2.82843	−	2.82843i	0.384900	−	0.384900i
$55$	2.70711	+	8.12132i	0.365026	+	1.09508i
$56$	2.70711	+	2.70711i	0.361752	+	0.361752i
$57$			16.4853i			2.18353i
$58$	−6.70711	+	6.70711i	−0.880686	+	0.880686i
$59$	−1.17157	+	1.17157i	−0.152526	+	0.152526i	−0.779245	−	0.626719i	$-0.784397\pi$
$59$	−1.17157	+	1.17157i	−0.152526	+	0.152526i	0.626719	+	0.779245i	$0.284397\pi$
$60$	−2.00000	+	4.00000i	−0.258199	+	0.516398i
$61$	9.29289	−	9.29289i	1.18983	−	1.18983i	0.212720	−	0.977113i	$-0.431768\pi$
$61$	9.29289	−	9.29289i	1.18983	−	1.18983i	0.977113	−	0.212720i	$-0.0682322\pi$
$62$	4.12132	+	4.12132i	0.523408	+	0.523408i
$63$	−2.70711	−	2.70711i	−0.341063	−	0.341063i
$64$	−1.00000			−0.125000
$65$	1.58579	+	4.75736i	0.196693	+	0.590078i
$66$	5.41421	−	5.41421i	0.666444	−	0.666444i
$67$	1.24264	+	1.24264i	0.151813	+	0.151813i	0.778927	−	0.627114i	$-0.215764\pi$
$67$	1.24264	+	1.24264i	0.151813	+	0.151813i	−0.627114	+	0.778927i	$0.715764\pi$
$68$	1.82843			0.221729
$69$	−3.65685	−	3.65685i	−0.440234	−	0.440234i
$70$	−7.65685	−	3.82843i	−0.915169	−	0.457585i
$71$	−0.343146			−0.0407239			−0.0203620	−	0.999793i	$-0.506482\pi$
$71$	−0.343146			−0.0407239			−0.0203620	+	0.999793i	$0.506482\pi$
$72$	1.00000			0.117851
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	−0.262646	−	0.964892i	$-0.584595\pi$
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	0.964892	+	0.262646i	$0.0845950\pi$
$74$	−3.53553	+	4.94975i	−0.410997	+	0.575396i
$75$	1.41421	−	9.89949i	0.163299	−	1.14310i
$76$	5.82843	−	5.82843i	0.668566	−	0.668566i
$77$	10.3640	+	10.3640i	1.18108	+	1.18108i
$78$	3.17157	−	3.17157i	0.359110	−	0.359110i
$79$	9.65685	−	9.65685i	1.08648	−	1.08648i	0.0905930	−	0.995888i	$-0.471124\pi$
$79$	9.65685	−	9.65685i	1.08648	−	1.08648i	0.995888	−	0.0905930i	$-0.0288762\pi$
$80$	2.12132	−	0.707107i	0.237171	−	0.0790569i
$81$	11.0000			1.22222
$82$	7.00000			0.773021
$83$	−0.828427	−	0.828427i	−0.0909317	−	0.0909317i	0.660178	−	0.751109i	$-0.270481\pi$
$83$	−0.828427	−	0.828427i	−0.0909317	−	0.0909317i	−0.751109	+	0.660178i	$0.770481\pi$
$84$			7.65685i			0.835431i
$85$	−3.87868	+	1.29289i	−0.420702	+	0.140234i
$86$	−7.00000			−0.754829
$87$	−18.9706			−2.03386
$88$	−3.82843			−0.408112
$89$	7.41421	+	7.41421i	0.785905	+	0.785905i	0.980820	−	0.194915i	$-0.0624431\pi$
$89$	7.41421	+	7.41421i	0.785905	+	0.785905i	−0.194915	+	0.980820i	$0.562443\pi$
$90$	−2.12132	+	0.707107i	−0.223607	+	0.0745356i
$91$	6.07107	+	6.07107i	0.636421	+	0.636421i
$92$			2.58579i			0.269587i
$93$			11.6569i			1.20876i
$94$	8.24264	+	8.24264i	0.850163	+	0.850163i
$95$	−8.24264	+	16.4853i	−0.845677	+	1.69135i
$96$	−1.41421	−	1.41421i	−0.144338	−	0.144338i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	−7.65685			−0.773459
$99$	3.82843			0.384771
$100$	−4.00000	+	3.00000i	−0.400000	+	0.300000i
$101$		−	11.0711i		−	1.10161i	−0.834633	−	0.550806i	$-0.814320\pi$
$101$		−	11.0711i		−	1.10161i	0.834633	−	0.550806i	$-0.185680\pi$
$102$	2.58579	+	2.58579i	0.256031	+	0.256031i
$103$	13.5563			1.33575			0.667873	−	0.744275i	$-0.267205\pi$
$103$	13.5563			1.33575			0.667873	+	0.744275i	$0.267205\pi$
$104$	−2.24264			−0.219909
$105$	−5.41421	−	16.2426i	−0.528373	−	1.58512i
$106$	2.12132	−	2.12132i	0.206041	−	0.206041i
$107$	−9.07107	+	9.07107i	−0.876933	+	0.876933i	−0.993216	−	0.116283i	$-0.962902\pi$
$107$	−9.07107	+	9.07107i	−0.876933	+	0.876933i	0.116283	+	0.993216i	$0.462902\pi$
$108$	−2.82843	−	2.82843i	−0.272166	−	0.272166i
$109$	−0.949747	+	0.949747i	−0.0909693	+	0.0909693i	−0.751127	−	0.660158i	$-0.770489\pi$
$109$	−0.949747	+	0.949747i	−0.0909693	+	0.0909693i	0.660158	+	0.751127i	$0.270489\pi$
$110$	8.12132	−	2.70711i	0.774338	−	0.258113i
$111$	−12.0000	+	2.00000i	−1.13899	+	0.189832i
$112$	2.70711	−	2.70711i	0.255798	−	0.255798i
$113$	−3.82843			−0.360148			−0.180074	−	0.983653i	$-0.557634\pi$
$113$	−3.82843			−0.360148			−0.180074	+	0.983653i	$0.557634\pi$
$114$	16.4853			1.54399
$115$	−1.82843	−	5.48528i	−0.170502	−	0.511505i
$116$	6.70711	+	6.70711i	0.622739	+	0.622739i
$117$	2.24264			0.207332
$118$	1.17157	+	1.17157i	0.107852	+	0.107852i
$119$	−4.94975	+	4.94975i	−0.453743	+	0.453743i
$120$	4.00000	+	2.00000i	0.365148	+	0.182574i
$121$	−3.65685			−0.332441
$122$	−9.29289	−	9.29289i	−0.841339	−	0.841339i
$123$	9.89949	+	9.89949i	0.892607	+	0.892607i
$124$	4.12132	−	4.12132i	0.370105	−	0.370105i
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$	−2.70711	+	2.70711i	−0.241168	+	0.241168i
$127$	2.58579	−	2.58579i	0.229451	−	0.229451i	−0.583012	−	0.812464i	$-0.698126\pi$
$127$	2.58579	−	2.58579i	0.229451	−	0.229451i	0.812464	+	0.583012i	$0.198126\pi$
$128$			1.00000i			0.0883883i
$129$	−9.89949	−	9.89949i	−0.871602	−	0.871602i
$130$	4.75736	−	1.58579i	0.417248	−	0.139083i
$131$	0.414214	−	0.414214i	0.0361900	−	0.0361900i	−0.688780	−	0.724970i	$-0.741853\pi$
$131$	0.414214	−	0.414214i	0.0361900	−	0.0361900i	0.724970	+	0.688780i	$0.241853\pi$
$132$	−5.41421	−	5.41421i	−0.471247	−	0.471247i
$133$			31.5563i			2.73628i
$134$	1.24264	−	1.24264i	0.107348	−	0.107348i
$135$	8.00000	+	4.00000i	0.688530	+	0.344265i
$136$		−	1.82843i		−	0.156786i
$137$	8.41421	−	8.41421i	0.718875	−	0.718875i	−0.249500	−	0.968375i	$-0.580266\pi$
$137$	8.41421	−	8.41421i	0.718875	−	0.718875i	0.968375	+	0.249500i	$0.0802663\pi$
$138$	−3.65685	+	3.65685i	−0.311292	+	0.311292i
$139$	−6.17157			−0.523466			−0.261733	−	0.965140i	$-0.584294\pi$
$139$	−6.17157			−0.523466			−0.261733	+	0.965140i	$0.584294\pi$
$140$	−3.82843	+	7.65685i	−0.323561	+	0.647122i
$141$			23.3137i			1.96337i
$142$			0.343146i			0.0287962i
$143$	−8.58579			−0.717980
$144$		−	1.00000i		−	0.0833333i
$145$	−18.9706	−	9.48528i	−1.57542	−	0.787710i
$146$	−6.00000	−	6.00000i	−0.496564	−	0.496564i
$147$	−10.8284	−	10.8284i	−0.893114	−	0.893114i
$148$	4.94975	+	3.53553i	0.406867	+	0.290619i
$149$			8.24264i			0.675263i	0.941278	+	0.337632i	$0.109626\pi$
$149$			8.24264i			0.675263i	−0.941278	+	0.337632i	$0.890374\pi$
$150$	−9.89949	−	1.41421i	−0.808290	−	0.115470i
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	−5.82843	−	5.82843i	−0.472748	−	0.472748i
$153$			1.82843i			0.147820i
$154$	10.3640	−	10.3640i	0.835152	−	0.835152i
$155$	−5.82843	+	11.6569i	−0.468151	+	0.936301i
$156$	−3.17157	−	3.17157i	−0.253929	−	0.253929i
$157$	5.87868	−	5.87868i	0.469170	−	0.469170i	−0.432476	−	0.901646i	$-0.642360\pi$
$157$	5.87868	−	5.87868i	0.469170	−	0.469170i	0.901646	+	0.432476i	$0.142360\pi$
$158$	−9.65685	−	9.65685i	−0.768258	−	0.768258i
$159$	6.00000			0.475831
$160$	−0.707107	−	2.12132i	−0.0559017	−	0.167705i
$161$	−7.00000	−	7.00000i	−0.551677	−	0.551677i
$162$		−	11.0000i		−	0.864242i
$163$	−14.6569			−1.14801			−0.574007	−	0.818851i	$-0.694612\pi$
$163$	−14.6569			−1.14801			−0.574007	+	0.818851i	$0.694612\pi$
$164$		−	7.00000i		−	0.546608i
$165$	15.3137	+	7.65685i	1.19217	+	0.596085i
$166$	−0.828427	+	0.828427i	−0.0642984	+	0.0642984i
$167$	−1.17157			−0.0906590			−0.0453295	−	0.998972i	$-0.514434\pi$
$167$	−1.17157			−0.0906590			−0.0453295	+	0.998972i	$0.514434\pi$
$168$	7.65685			0.590739
$169$	7.97056			0.613120
$170$	1.29289	+	3.87868i	0.0991604	+	0.297481i
$171$	5.82843	+	5.82843i	0.445711	+	0.445711i
$172$			7.00000i			0.533745i
$173$	6.02082	−	6.02082i	0.457754	−	0.457754i	−0.440164	−	0.897918i	$-0.645080\pi$
$173$	6.02082	−	6.02082i	0.457754	−	0.457754i	0.897918	+	0.440164i	$0.145080\pi$
$174$			18.9706i			1.43815i
$175$	2.70711	−	18.9497i	0.204638	−	1.43247i
$176$			3.82843i			0.288579i
$177$			3.31371i			0.249074i
$178$	7.41421	−	7.41421i	0.555719	−	0.555719i
$179$	−14.4853	−	14.4853i	−1.08268	−	1.08268i	−0.996259	−	0.0864222i	$-0.972457\pi$
$179$	−14.4853	−	14.4853i	−1.08268	−	1.08268i	−0.0864222	−	0.996259i	$-0.527543\pi$
$180$	0.707107	+	2.12132i	0.0527046	+	0.158114i
$181$	7.65685			0.569129			0.284565	−	0.958657i	$-0.408151\pi$
$181$	7.65685			0.569129			0.284565	+	0.958657i	$0.408151\pi$
$182$	6.07107	−	6.07107i	0.450017	−	0.450017i
$183$		−	26.2843i		−	1.94299i
$184$	2.58579			0.190627
$185$	−13.0000	−	4.00000i	−0.955779	−	0.294086i
$186$	11.6569			0.854722
$187$		−	7.00000i		−	0.511891i
$188$	8.24264	−	8.24264i	0.601156	−	0.601156i
$189$	15.3137			1.11391
$190$	16.4853	+	8.24264i	1.19597	+	0.597984i
$191$	1.53553	+	1.53553i	0.111107	+	0.111107i	0.760475	−	0.649367i	$-0.224966\pi$
$191$	1.53553	+	1.53553i	0.111107	+	0.111107i	−0.649367	+	0.760475i	$0.724966\pi$
$192$	−1.41421	+	1.41421i	−0.102062	+	0.102062i
$193$		−	20.4853i		−	1.47456i	−0.675586	−	0.737281i	$-0.736109\pi$
$193$		−	20.4853i		−	1.47456i	0.675586	−	0.737281i	$-0.263891\pi$
$194$			7.00000i			0.502571i
$195$	8.97056	+	4.48528i	0.642395	+	0.321198i
$196$			7.65685i			0.546918i
$197$	−2.00000	+	2.00000i	−0.142494	+	0.142494i	−0.774755	−	0.632261i	$-0.782127\pi$
$197$	−2.00000	+	2.00000i	−0.142494	+	0.142494i	0.632261	+	0.774755i	$0.282127\pi$
$198$		−	3.82843i		−	0.272074i
$199$	−3.89949	−	3.89949i	−0.276428	−	0.276428i	0.555253	−	0.831681i	$-0.312621\pi$
$199$	−3.89949	−	3.89949i	−0.276428	−	0.276428i	−0.831681	+	0.555253i	$0.812621\pi$
$200$	3.00000	+	4.00000i	0.212132	+	0.282843i
$201$	3.51472			0.247909
$202$	−11.0711			−0.778958
$203$	−36.3137			−2.54872
$204$	2.58579	−	2.58579i	0.181041	−	0.181041i
$205$	4.94975	+	14.8492i	0.345705	+	1.03712i
$206$		−	13.5563i		−	0.944516i
$207$	−2.58579			−0.179725
$208$			2.24264i			0.155499i
$209$	−22.3137	−	22.3137i	−1.54347	−	1.54347i
$210$	−16.2426	+	5.41421i	−1.12085	+	0.373616i
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$	−2.12132	−	2.12132i	−0.145693	−	0.145693i
$213$	−0.485281	+	0.485281i	−0.0332509	+	0.0332509i
$214$	9.07107	+	9.07107i	0.620085	+	0.620085i
$215$	−4.94975	−	14.8492i	−0.337570	−	1.01271i
$216$	−2.82843	+	2.82843i	−0.192450	+	0.192450i
$217$			22.3137i			1.51475i
$218$	0.949747	+	0.949747i	0.0643250	+	0.0643250i
$219$		−	16.9706i		−	1.14676i
$220$	−2.70711	−	8.12132i	−0.182513	−	0.547539i
$221$		−	4.10051i		−	0.275830i
$222$	2.00000	+	12.0000i	0.134231	+	0.805387i
$223$	13.8787	+	13.8787i	0.929385	+	0.929385i	0.997666	−	0.0682810i	$-0.0217514\pi$
$223$	13.8787	+	13.8787i	0.929385	+	0.929385i	−0.0682810	+	0.997666i	$0.521751\pi$
$224$	−2.70711	−	2.70711i	−0.180876	−	0.180876i
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$			3.82843i			0.254663i
$227$	−7.48528			−0.496816			−0.248408	−	0.968656i	$-0.579907\pi$
$227$	−7.48528			−0.496816			−0.248408	+	0.968656i	$0.579907\pi$
$228$		−	16.4853i		−	1.09176i
$229$		−	1.41421i		−	0.0934539i	−0.998908	−	0.0467269i	$-0.985121\pi$
$229$		−	1.41421i		−	0.0934539i	0.998908	−	0.0467269i	$-0.0148791\pi$
$230$	−5.48528	+	1.82843i	−0.361689	+	0.120563i
$231$	29.3137			1.92870
$232$	6.70711	−	6.70711i	0.440343	−	0.440343i
$233$	0.0710678	−	0.0710678i	0.00465581	−	0.00465581i	−0.704775	−	0.709431i	$-0.748952\pi$
$233$	0.0710678	−	0.0710678i	0.00465581	−	0.00465581i	0.709431	+	0.704775i	$0.248952\pi$
$234$		−	2.24264i		−	0.146606i
$235$	−11.6569	+	23.3137i	−0.760409	+	1.52082i
$236$	1.17157	−	1.17157i	0.0762629	−	0.0762629i
$237$		−	27.3137i		−	1.77422i
$238$	4.94975	+	4.94975i	0.320844	+	0.320844i
$239$	7.05025	−	7.05025i	0.456043	−	0.456043i	−0.441311	−	0.897354i	$-0.645487\pi$
$239$	7.05025	−	7.05025i	0.456043	−	0.456043i	0.897354	+	0.441311i	$0.145487\pi$
$240$	2.00000	−	4.00000i	0.129099	−	0.258199i
$241$	0.757359	+	0.757359i	0.0487858	+	0.0487858i	0.731079	−	0.682293i	$-0.239017\pi$
$241$	0.757359	+	0.757359i	0.0487858	+	0.0487858i	−0.682293	+	0.731079i	$0.739017\pi$
$242$			3.65685i			0.235071i
$243$	7.07107	−	7.07107i	0.453609	−	0.453609i
$244$	−9.29289	+	9.29289i	−0.594917	+	0.594917i
$245$	−5.41421	−	16.2426i	−0.345901	−	1.03770i
$246$	9.89949	−	9.89949i	0.631169	−	0.631169i
$247$	−13.0711	−	13.0711i	−0.831692	−	0.831692i
$248$	−4.12132	−	4.12132i	−0.261704	−	0.261704i
$249$	−2.34315			−0.148491
$250$	−9.19239	−	6.36396i	−0.581378	−	0.402492i
$251$	−17.8995	+	17.8995i	−1.12981	+	1.12981i	−0.139598	+	0.990208i	$0.544581\pi$
$251$	−17.8995	+	17.8995i	−1.12981	+	1.12981i	−0.990208	+	0.139598i	$0.955419\pi$
$252$	2.70711	+	2.70711i	0.170532	+	0.170532i
$253$	9.89949			0.622376
$254$	−2.58579	−	2.58579i	−0.162247	−	0.162247i
$255$	−3.65685	+	7.31371i	−0.229001	+	0.458002i
$256$	1.00000			0.0625000
$257$	18.8284			1.17449			0.587243	−	0.809411i	$-0.300213\pi$
$257$	18.8284			1.17449			0.587243	+	0.809411i	$0.300213\pi$
$258$	−9.89949	+	9.89949i	−0.616316	+	0.616316i
$259$	−22.9706	+	3.82843i	−1.42732	+	0.237887i
$260$	−1.58579	−	4.75736i	−0.0983463	−	0.295039i
$261$	−6.70711	+	6.70711i	−0.415159	+	0.415159i
$262$	−0.414214	−	0.414214i	−0.0255902	−	0.0255902i
$263$	−14.6066	+	14.6066i	−0.900682	+	0.900682i	−0.995495	−	0.0948134i	$-0.969775\pi$
$263$	−14.6066	+	14.6066i	−0.900682	+	0.900682i	0.0948134	+	0.995495i	$0.469775\pi$
$264$	−5.41421	+	5.41421i	−0.333222	+	0.333222i
$265$	6.00000	+	3.00000i	0.368577	+	0.184289i
$266$	31.5563			1.93484
$267$	20.9706			1.28338
$268$	−1.24264	−	1.24264i	−0.0759064	−	0.0759064i
$269$			17.7990i			1.08522i	0.839984	+	0.542612i	$0.182565\pi$
$269$			17.7990i			1.08522i	−0.839984	+	0.542612i	$0.817435\pi$
$270$	4.00000	−	8.00000i	0.243432	−	0.486864i
$271$	−3.07107			−0.186554			−0.0932770	−	0.995640i	$-0.529734\pi$
$271$	−3.07107			−0.186554			−0.0932770	+	0.995640i	$0.529734\pi$
$272$	−1.82843			−0.110865
$273$	17.1716			1.03927
$274$	−8.41421	−	8.41421i	−0.508321	−	0.508321i
$275$	11.4853	+	15.3137i	0.692589	+	0.923451i
$276$	3.65685	+	3.65685i	0.220117	+	0.220117i
$277$		−	7.79899i		−	0.468596i	−0.972165	−	0.234298i	$-0.924721\pi$
$277$		−	7.79899i		−	0.468596i	0.972165	−	0.234298i	$-0.0752791\pi$
$278$			6.17157i			0.370146i
$279$	4.12132	+	4.12132i	0.246737	+	0.246737i
$280$	7.65685	+	3.82843i	0.457585	+	0.228792i
$281$	4.00000	+	4.00000i	0.238620	+	0.238620i	0.816279	−	0.577659i	$-0.196033\pi$
$281$	4.00000	+	4.00000i	0.238620	+	0.238620i	−0.577659	+	0.816279i	$0.696033\pi$
$282$	23.3137			1.38831
$283$	28.0000			1.66443			0.832214	−	0.554455i	$-0.187073\pi$
$283$	28.0000			1.66443			0.832214	+	0.554455i	$0.187073\pi$
$284$	0.343146			0.0203620
$285$	11.6569	+	34.9706i	0.690492	+	2.07148i
$286$			8.58579i			0.507688i
$287$	18.9497	+	18.9497i	1.11857	+	1.11857i
$288$	−1.00000			−0.0589256
$289$	−13.6569			−0.803344
$290$	−9.48528	+	18.9706i	−0.556995	+	1.11399i
$291$	−9.89949	+	9.89949i	−0.580319	+	0.580319i
$292$	−6.00000	+	6.00000i	−0.351123	+	0.351123i
$293$	−1.77817	−	1.77817i	−0.103882	−	0.103882i	0.653255	−	0.757138i	$-0.273403\pi$
$293$	−1.77817	−	1.77817i	−0.103882	−	0.103882i	−0.757138	+	0.653255i	$0.773403\pi$
$294$	−10.8284	+	10.8284i	−0.631527	+	0.631527i
$295$	−1.65685	+	3.31371i	−0.0964658	+	0.192932i
$296$	3.53553	−	4.94975i	0.205499	−	0.287698i
$297$	−10.8284	+	10.8284i	−0.628329	+	0.628329i
$298$	8.24264			0.477483
$299$	5.79899			0.335364
$300$	−1.41421	+	9.89949i	−0.0816497	+	0.571548i
$301$	−18.9497	−	18.9497i	−1.09225	−	1.09225i
$302$	−12.0000			−0.690522
$303$	−15.6569	−	15.6569i	−0.899463	−	0.899463i
$304$	−5.82843	+	5.82843i	−0.334283	+	0.334283i
$305$	13.1421	−	26.2843i	0.752516	−	1.50503i
$306$	1.82843			0.104524
$307$	−1.89949	−	1.89949i	−0.108410	−	0.108410i	0.650821	−	0.759231i	$-0.274425\pi$
$307$	−1.89949	−	1.89949i	−0.108410	−	0.108410i	−0.759231	+	0.650821i	$0.774425\pi$
$308$	−10.3640	−	10.3640i	−0.590541	−	0.590541i
$309$	19.1716	−	19.1716i	1.09063	−	1.09063i
$310$	11.6569	+	5.82843i	0.662065	+	0.331032i
$311$	−11.7782	+	11.7782i	−0.667879	+	0.667879i	−0.957225	−	0.289346i	$-0.906562\pi$
$311$	−11.7782	+	11.7782i	−0.667879	+	0.667879i	0.289346	+	0.957225i	$0.406562\pi$
$312$	−3.17157	+	3.17157i	−0.179555	+	0.179555i
$313$		−	0.686292i		−	0.0387915i	−0.999812	−	0.0193957i	$-0.993826\pi$
$313$		−	0.686292i		−	0.0387915i	0.999812	−	0.0193957i	$-0.00617424\pi$
$314$	−5.87868	−	5.87868i	−0.331753	−	0.331753i
$315$	−7.65685	−	3.82843i	−0.431415	−	0.215707i
$316$	−9.65685	+	9.65685i	−0.543240	+	0.543240i
$317$	15.5355	+	15.5355i	0.872563	+	0.872563i	0.992751	−	0.120189i	$-0.0383499\pi$
$317$	15.5355	+	15.5355i	0.872563	+	0.872563i	−0.120189	+	0.992751i	$0.538350\pi$
$318$		−	6.00000i		−	0.336463i
$319$	25.6777	−	25.6777i	1.43767	−	1.43767i
$320$	−2.12132	+	0.707107i	−0.118585	+	0.0395285i
$321$			25.6569i			1.43203i
$322$	−7.00000	+	7.00000i	−0.390095	+	0.390095i
$323$	10.6569	−	10.6569i	0.592963	−	0.592963i
$324$	−11.0000			−0.611111
$325$	6.72792	+	8.97056i	0.373198	+	0.497597i
$326$			14.6569i			0.811768i
$327$			2.68629i			0.148552i
$328$	−7.00000			−0.386510
$329$			44.6274i			2.46039i
$330$	7.65685	−	15.3137i	0.421496	−	0.842992i
$331$	2.58579	+	2.58579i	0.142128	+	0.142128i	0.774591	−	0.632463i	$-0.217956\pi$
$331$	2.58579	+	2.58579i	0.142128	+	0.142128i	−0.632463	+	0.774591i	$0.717956\pi$
$332$	0.828427	+	0.828427i	0.0454658	+	0.0454658i
$333$	−3.53553	+	4.94975i	−0.193746	+	0.271244i
$334$			1.17157i			0.0641056i
$335$	3.51472	+	1.75736i	0.192030	+	0.0960148i
$336$		−	7.65685i		−	0.417716i
$337$	5.65685	+	5.65685i	0.308148	+	0.308148i	0.844191	−	0.536043i	$-0.180081\pi$
$337$	5.65685	+	5.65685i	0.308148	+	0.308148i	−0.536043	+	0.844191i	$0.680081\pi$
$338$		−	7.97056i		−	0.433541i
$339$	−5.41421	+	5.41421i	−0.294060	+	0.294060i
$340$	3.87868	−	1.29289i	0.210351	−	0.0701170i
$341$	−15.7782	−	15.7782i	−0.854436	−	0.854436i
$342$	5.82843	−	5.82843i	0.315165	−	0.315165i
$343$	−1.77817	−	1.77817i	−0.0960124	−	0.0960124i
$344$	7.00000			0.377415
$345$	−10.3431	−	5.17157i	−0.556856	−	0.278428i
$346$	−6.02082	−	6.02082i	−0.323681	−	0.323681i
$347$			17.3137i			0.929449i	0.885455	+	0.464724i	$0.153847\pi$
$347$			17.3137i			0.929449i	−0.885455	+	0.464724i	$0.846153\pi$
$348$	18.9706			1.01693
$349$		−	4.14214i		−	0.221723i	−0.993836	−	0.110862i	$-0.964639\pi$
$349$		−	4.14214i		−	0.221723i	0.993836	−	0.110862i	$-0.0353611\pi$
$350$	−18.9497	−	2.70711i	−1.01291	−	0.144701i
$351$	−6.34315	+	6.34315i	−0.338572	+	0.338572i
$352$	3.82843			0.204056
$353$	7.34315			0.390836			0.195418	−	0.980720i	$-0.437394\pi$
$353$	7.34315			0.390836			0.195418	+	0.980720i	$0.437394\pi$
$354$	3.31371			0.176122
$355$	−0.727922	+	0.242641i	−0.0386341	+	0.0128780i
$356$	−7.41421	−	7.41421i	−0.392953	−	0.392953i
$357$			14.0000i			0.740959i
$358$	−14.4853	+	14.4853i	−0.765571	+	0.765571i
$359$			30.5269i			1.61115i	0.592495	+	0.805574i	$0.298143\pi$
$359$			30.5269i			1.61115i	−0.592495	+	0.805574i	$0.701857\pi$
$360$	2.12132	−	0.707107i	0.111803	−	0.0372678i
$361$		−	48.9411i		−	2.57585i
$362$		−	7.65685i		−	0.402435i
$363$	−5.17157	+	5.17157i	−0.271437	+	0.271437i
$364$	−6.07107	−	6.07107i	−0.318210	−	0.318210i
$365$	8.48528	−	16.9706i	0.444140	−	0.888280i
$366$	−26.2843			−1.37390
$367$	13.0919	−	13.0919i	0.683391	−	0.683391i	−0.277372	−	0.960763i	$-0.589463\pi$
$367$	13.0919	−	13.0919i	0.683391	−	0.683391i	0.960763	+	0.277372i	$0.0894634\pi$
$368$		−	2.58579i		−	0.134793i
$369$	7.00000			0.364405
$370$	−4.00000	+	13.0000i	−0.207950	+	0.675838i
$371$	11.4853			0.596286
$372$		−	11.6569i		−	0.604380i
$373$	−10.8284	+	10.8284i	−0.560675	+	0.560675i	−0.929499	−	0.368824i	$-0.879760\pi$
$373$	−10.8284	+	10.8284i	−0.560675	+	0.560675i	0.368824	+	0.929499i	$0.379760\pi$
$374$	−7.00000			−0.361961
$375$	−4.00000	−	22.0000i	−0.206559	−	1.13608i
$376$	−8.24264	−	8.24264i	−0.425082	−	0.425082i
$377$	15.0416	−	15.0416i	0.774683	−	0.774683i
$378$		−	15.3137i		−	0.787652i
$379$			18.0000i			0.924598i	0.886724	+	0.462299i	$0.152975\pi$
$379$			18.0000i			0.924598i	−0.886724	+	0.462299i	$0.847025\pi$
$380$	8.24264	−	16.4853i	0.422839	−	0.845677i
$381$		−	7.31371i		−	0.374693i
$382$	1.53553	−	1.53553i	0.0785647	−	0.0785647i
$383$		−	16.5858i		−	0.847494i	−0.905781	−	0.423747i	$-0.860715\pi$
$383$		−	16.5858i		−	0.847494i	0.905781	−	0.423747i	$-0.139285\pi$
$384$	1.41421	+	1.41421i	0.0721688	+	0.0721688i
$385$	29.3137	+	14.6569i	1.49396	+	0.746982i
$386$	−20.4853			−1.04267
$387$	−7.00000			−0.355830
$388$	7.00000			0.355371
$389$	−3.77817	+	3.77817i	−0.191561	+	0.191561i	−0.796370	−	0.604809i	$-0.793249\pi$
$389$	−3.77817	+	3.77817i	−0.191561	+	0.191561i	0.604809	+	0.796370i	$0.293249\pi$
$390$	4.48528	−	8.97056i	0.227121	−	0.454242i
$391$			4.72792i			0.239101i
$392$	7.65685			0.386730
$393$		−	1.17157i		−	0.0590980i
$394$	2.00000	+	2.00000i	0.100759	+	0.100759i
$395$	13.6569	−	27.3137i	0.687151	−	1.37430i
$396$	−3.82843			−0.192386
$397$	8.48528	+	8.48528i	0.425864	+	0.425864i	0.887217	−	0.461353i	$-0.152636\pi$
$397$	8.48528	+	8.48528i	0.425864	+	0.425864i	−0.461353	+	0.887217i	$0.652636\pi$
$398$	−3.89949	+	3.89949i	−0.195464	+	0.195464i
$399$	44.6274	+	44.6274i	2.23417	+	2.23417i
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$	−7.07107	+	7.07107i	−0.353112	+	0.353112i	−0.861266	−	0.508154i	$-0.830328\pi$
$401$	−7.07107	+	7.07107i	−0.353112	+	0.353112i	0.508154	+	0.861266i	$0.330328\pi$
$402$		−	3.51472i		−	0.175298i
$403$	−9.24264	−	9.24264i	−0.460409	−	0.460409i
$404$			11.0711i			0.550806i
$405$	23.3345	−	7.77817i	1.15950	−	0.386501i
$406$			36.3137i			1.80222i
$407$	13.5355	−	18.9497i	0.670932	−	0.939304i
$408$	−2.58579	−	2.58579i	−0.128016	−	0.128016i
$409$	−19.7990	−	19.7990i	−0.978997	−	0.978997i	0.0207869	−	0.999784i	$-0.493383\pi$
$409$	−19.7990	−	19.7990i	−0.978997	−	0.978997i	−0.999784	+	0.0207869i	$0.993383\pi$
$410$	14.8492	−	4.94975i	0.733352	−	0.244451i
$411$		−	23.7990i		−	1.17392i
$412$	−13.5563			−0.667873
$413$			6.34315i			0.312126i
$414$			2.58579i			0.127084i
$415$	−2.34315	−	1.17157i	−0.115021	−	0.0575103i
$416$	2.24264			0.109955
$417$	−8.72792	+	8.72792i	−0.427408	+	0.427408i
$418$	−22.3137	+	22.3137i	−1.09140	+	1.09140i
$419$		−	26.9706i		−	1.31760i	−0.752319	−	0.658799i	$-0.771065\pi$
$419$		−	26.9706i		−	1.31760i	0.752319	−	0.658799i	$-0.228935\pi$
$420$	5.41421	+	16.2426i	0.264187	+	0.792560i
$421$	−25.3137	+	25.3137i	−1.23371	+	1.23371i	−0.271188	+	0.962526i	$0.587417\pi$
$421$	−25.3137	+	25.3137i	−1.23371	+	1.23371i	−0.962526	+	0.271188i	$0.912583\pi$
$422$			9.00000i			0.438113i
$423$	8.24264	+	8.24264i	0.400771	+	0.400771i
$424$	−2.12132	+	2.12132i	−0.103020	+	0.103020i
$425$	−7.31371	+	5.48528i	−0.354767	+	0.266075i
$426$	0.485281	+	0.485281i	0.0235120	+	0.0235120i
$427$		−	50.3137i		−	2.43485i
$428$	9.07107	−	9.07107i	0.438467	−	0.438467i
$429$	−12.1421	+	12.1421i	−0.586228	+	0.586228i
$430$	−14.8492	+	4.94975i	−0.716094	+	0.238698i
$431$	−20.5061	+	20.5061i	−0.987744	+	0.987744i	−0.999926	−	0.0121819i	$-0.996122\pi$
$431$	−20.5061	+	20.5061i	−0.987744	+	0.987744i	0.0121819	+	0.999926i	$0.496122\pi$
$432$	2.82843	+	2.82843i	0.136083	+	0.136083i
$433$	5.14214	+	5.14214i	0.247115	+	0.247115i	0.819786	−	0.572670i	$-0.194093\pi$
$433$	5.14214	+	5.14214i	0.247115	+	0.247115i	−0.572670	+	0.819786i	$0.694093\pi$
$434$	22.3137			1.07109
$435$	−40.2426	+	13.4142i	−1.92949	+	0.643162i
$436$	0.949747	−	0.949747i	0.0454847	−	0.0454847i
$437$	15.0711	+	15.0711i	0.720947	+	0.720947i
$438$	−16.9706			−0.810885
$439$	2.22183	+	2.22183i	0.106042	+	0.106042i	0.758137	−	0.652095i	$-0.226110\pi$
$439$	2.22183	+	2.22183i	0.106042	+	0.106042i	−0.652095	+	0.758137i	$0.726110\pi$
$440$	−8.12132	+	2.70711i	−0.387169	+	0.129056i
$441$	−7.65685			−0.364612
$442$	−4.10051			−0.195041
$443$	−5.34315	+	5.34315i	−0.253861	+	0.253861i	−0.822551	−	0.568691i	$-0.807450\pi$
$443$	−5.34315	+	5.34315i	−0.253861	+	0.253861i	0.568691	+	0.822551i	$0.307450\pi$
$444$	12.0000	−	2.00000i	0.569495	−	0.0949158i
$445$	20.9706	+	10.4853i	0.994100	+	0.497050i
$446$	13.8787	−	13.8787i	0.657175	−	0.657175i
$447$	11.6569	+	11.6569i	0.551350	+	0.551350i
$448$	−2.70711	+	2.70711i	−0.127899	+	0.127899i
$449$	−25.6274	+	25.6274i	−1.20943	+	1.20943i	−0.238222	+	0.971211i	$0.576565\pi$
$449$	−25.6274	+	25.6274i	−1.20943	+	1.20943i	−0.971211	+	0.238222i	$0.923435\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	−26.7990			−1.26192
$452$	3.82843			0.180074
$453$	−16.9706	−	16.9706i	−0.797347	−	0.797347i
$454$			7.48528i			0.351302i
$455$	17.1716	+	8.58579i	0.805016	+	0.402508i
$456$	−16.4853			−0.771994
$457$	−3.68629			−0.172437			−0.0862187	−	0.996276i	$-0.527478\pi$
$457$	−3.68629			−0.172437			−0.0862187	+	0.996276i	$0.527478\pi$
$458$	−1.41421			−0.0660819
$459$	−5.17157	−	5.17157i	−0.241388	−	0.241388i
$460$	1.82843	+	5.48528i	0.0852509	+	0.255753i
$461$	10.4645	+	10.4645i	0.487379	+	0.487379i	0.907478	−	0.420099i	$-0.138005\pi$
$461$	10.4645	+	10.4645i	0.487379	+	0.487379i	−0.420099	+	0.907478i	$0.638005\pi$
$462$		−	29.3137i		−	1.36380i
$463$			29.9411i			1.39148i	0.718293	+	0.695741i	$0.244924\pi$
$463$			29.9411i			1.39148i	−0.718293	+	0.695741i	$0.755076\pi$
$464$	−6.70711	−	6.70711i	−0.311370	−	0.311370i
$465$	8.24264	+	24.7279i	0.382243	+	1.14673i
$466$	−0.0710678	−	0.0710678i	−0.00329215	−	0.00329215i
$467$	2.31371			0.107066			0.0535328	−	0.998566i	$-0.482952\pi$
$467$	2.31371			0.107066			0.0535328	+	0.998566i	$0.482952\pi$
$468$	−2.24264			−0.103666
$469$	6.72792			0.310667
$470$	23.3137	+	11.6569i	1.07538	+	0.537691i
$471$		−	16.6274i		−	0.766151i
$472$	−1.17157	−	1.17157i	−0.0539260	−	0.0539260i
$473$	26.7990			1.23222
$474$	−27.3137			−1.25456
$475$	−5.82843	+	40.7990i	−0.267427	+	1.87199i
$476$	4.94975	−	4.94975i	0.226871	−	0.226871i
$477$	2.12132	−	2.12132i	0.0971286	−	0.0971286i
$478$	−7.05025	−	7.05025i	−0.322471	−	0.322471i
$479$	15.5563	−	15.5563i	0.710788	−	0.710788i	−0.255912	−	0.966700i	$-0.582376\pi$
$479$	15.5563	−	15.5563i	0.710788	−	0.710788i	0.966700	+	0.255912i	$0.0823758\pi$
$480$	−4.00000	−	2.00000i	−0.182574	−	0.0912871i
$481$	7.92893	−	11.1005i	0.361528	−	0.506139i
$482$	0.757359	−	0.757359i	0.0344968	−	0.0344968i
$483$	−19.7990			−0.900885
$484$	3.65685			0.166221
$485$	−14.8492	+	4.94975i	−0.674269	+	0.224756i
$486$	−7.07107	−	7.07107i	−0.320750	−	0.320750i
$487$	26.9706			1.22215			0.611076	−	0.791572i	$-0.290737\pi$
$487$	26.9706			1.22215			0.611076	+	0.791572i	$0.290737\pi$
$488$	9.29289	+	9.29289i	0.420670	+	0.420670i
$489$	−20.7279	+	20.7279i	−0.937349	+	0.937349i
$490$	−16.2426	+	5.41421i	−0.733768	+	0.244589i
$491$	17.7990			0.803257			0.401629	−	0.915803i	$-0.368444\pi$
$491$	17.7990			0.803257			0.401629	+	0.915803i	$0.368444\pi$
$492$	−9.89949	−	9.89949i	−0.446304	−	0.446304i
$493$	12.2635	+	12.2635i	0.552318	+	0.552318i
$494$	−13.0711	+	13.0711i	−0.588095	+	0.588095i
$495$	8.12132	−	2.70711i	0.365026	−	0.121675i
$496$	−4.12132	+	4.12132i	−0.185053	+	0.185053i
$497$	−0.928932	+	0.928932i	−0.0416683	+	0.0416683i
$498$			2.34315i			0.104999i
$499$	−10.2426	−	10.2426i	−0.458524	−	0.458524i	0.439647	−	0.898171i	$-0.355104\pi$
$499$	−10.2426	−	10.2426i	−0.458524	−	0.458524i	−0.898171	+	0.439647i	$0.855104\pi$
$500$	−6.36396	+	9.19239i	−0.284605	+	0.411096i
$501$	−1.65685	+	1.65685i	−0.0740228	+	0.0740228i
$502$	17.8995	+	17.8995i	0.798894	+	0.798894i
$503$		−	32.5858i		−	1.45293i	−0.687204	−	0.726464i	$-0.741162\pi$
$503$		−	32.5858i		−	1.45293i	0.687204	−	0.726464i	$-0.258838\pi$
$504$	2.70711	−	2.70711i	0.120584	−	0.120584i
$505$	−7.82843	−	23.4853i	−0.348360	−	1.04508i
$506$		−	9.89949i		−	0.440086i
$507$	11.2721	−	11.2721i	0.500611	−	0.500611i
$508$	−2.58579	+	2.58579i	−0.114726	+	0.114726i
$509$	1.27208			0.0563839			0.0281919	−	0.999603i	$-0.491025\pi$
$509$	1.27208			0.0563839			0.0281919	+	0.999603i	$0.491025\pi$
$510$	7.31371	+	3.65685i	0.323856	+	0.161928i
$511$		−	32.4853i		−	1.43706i
$512$		−	1.00000i		−	0.0441942i
$513$	−32.9706			−1.45569
$514$		−	18.8284i		−	0.830486i
$515$	28.7574	−	9.58579i	1.26720	−	0.422400i
$516$	9.89949	+	9.89949i	0.435801	+	0.435801i
$517$	−31.5563	−	31.5563i	−1.38785	−	1.38785i
$518$	3.82843	+	22.9706i	0.168211	+	1.00927i
$519$		−	17.0294i		−	0.747509i
$520$	−4.75736	+	1.58579i	−0.208624	+	0.0695413i
$521$		−	27.6274i		−	1.21038i	−0.796081	−	0.605190i	$-0.793097\pi$
$521$		−	27.6274i		−	1.21038i	0.796081	−	0.605190i	$-0.206903\pi$
$522$	6.70711	+	6.70711i	0.293562	+	0.293562i
$523$			43.6569i			1.90898i	0.298241	+	0.954490i	$0.403600\pi$
$523$			43.6569i			1.90898i	−0.298241	+	0.954490i	$0.596400\pi$
$524$	−0.414214	+	0.414214i	−0.0180950	+	0.0180950i
$525$	−22.9706	−	30.6274i	−1.00252	−	1.33669i
$526$	14.6066	+	14.6066i	0.636878	+	0.636878i
$527$	7.53553	−	7.53553i	0.328253	−	0.328253i
$528$	5.41421	+	5.41421i	0.235623	+	0.235623i
$529$	16.3137			0.709292
$530$	3.00000	−	6.00000i	0.130312	−	0.260623i
$531$	1.17157	+	1.17157i	0.0508419	+	0.0508419i
$532$		−	31.5563i		−	1.36814i
$533$	−15.6985			−0.679977
$534$		−	20.9706i		−	0.907485i
$535$	−12.8284	+	25.6569i	−0.554621	+	1.10924i
$536$	−1.24264	+	1.24264i	−0.0536739	+	0.0536739i
$537$	−40.9706			−1.76801
$538$	17.7990			0.767369
$539$	29.3137			1.26263
$540$	−8.00000	−	4.00000i	−0.344265	−	0.172133i
$541$	−27.7990	−	27.7990i	−1.19517	−	1.19517i	−0.975595	−	0.219577i	$-0.929532\pi$
$541$	−27.7990	−	27.7990i	−1.19517	−	1.19517i	−0.219577	−	0.975595i	$-0.570468\pi$
$542$			3.07107i			0.131914i
$543$	10.8284	−	10.8284i	0.464692	−	0.464692i
$544$			1.82843i			0.0783932i
$545$	−1.34315	+	2.68629i	−0.0575340	+	0.115068i
$546$		−	17.1716i		−	0.734875i
$547$			27.8284i			1.18986i	0.803778	+	0.594929i	$0.202820\pi$
$547$			27.8284i			1.18986i	−0.803778	+	0.594929i	$0.797180\pi$
$548$	−8.41421	+	8.41421i	−0.359437	+	0.359437i
$549$	−9.29289	−	9.29289i	−0.396611	−	0.396611i
$550$	15.3137	−	11.4853i	0.652979	−	0.489734i
$551$	78.1838			3.33074
$552$	3.65685	−	3.65685i	0.155646	−	0.155646i
$553$		−	52.2843i		−	2.22335i
$554$	−7.79899			−0.331347
$555$	−24.0416	+	12.7279i	−1.02051	+	0.540270i
$556$	6.17157			0.261733
$557$		−	23.2132i		−	0.983575i	−0.870715	−	0.491787i	$-0.836344\pi$
$557$		−	23.2132i		−	0.983575i	0.870715	−	0.491787i	$-0.163656\pi$
$558$	4.12132	−	4.12132i	0.174469	−	0.174469i
$559$	15.6985			0.663975
$560$	3.82843	−	7.65685i	0.161781	−	0.323561i
$561$	−9.89949	−	9.89949i	−0.417957	−	0.417957i
$562$	4.00000	−	4.00000i	0.168730	−	0.168730i
$563$		−	24.1127i		−	1.01623i	−0.861290	−	0.508115i	$-0.830343\pi$
$563$		−	24.1127i		−	1.01623i	0.861290	−	0.508115i	$-0.169657\pi$
$564$		−	23.3137i		−	0.981684i
$565$	−8.12132	+	2.70711i	−0.341667	+	0.113889i
$566$		−	28.0000i		−	1.17693i
$567$	29.7782	−	29.7782i	1.25057	−	1.25057i
$568$		−	0.343146i		−	0.0143981i
$569$	−1.68629	−	1.68629i	−0.0706930	−	0.0706930i	0.670876	−	0.741569i	$-0.265918\pi$
$569$	−1.68629	−	1.68629i	−0.0706930	−	0.0706930i	−0.741569	+	0.670876i	$0.765918\pi$
$570$	34.9706	−	11.6569i	1.46476	−	0.488252i
$571$	46.7990			1.95848			0.979238	−	0.202712i	$-0.0649755\pi$
$571$	46.7990			1.95848			0.979238	+	0.202712i	$0.0649755\pi$
$572$	8.58579			0.358990
$573$	4.34315			0.181438
$574$	18.9497	−	18.9497i	0.790947	−	0.790947i
$575$	−7.75736	−	10.3431i	−0.323504	−	0.431339i
$576$			1.00000i			0.0416667i
$577$	21.6569			0.901587			0.450793	−	0.892628i	$-0.351141\pi$
$577$	21.6569			0.901587			0.450793	+	0.892628i	$0.351141\pi$
$578$			13.6569i			0.568050i
$579$	−28.9706	−	28.9706i	−1.20398	−	1.20398i
$580$	18.9706	+	9.48528i	0.787710	+	0.393855i
$581$	−4.48528			−0.186081
$582$	9.89949	+	9.89949i	0.410347	+	0.410347i
$583$	−8.12132	+	8.12132i	−0.336351	+	0.336351i
$584$	6.00000	+	6.00000i	0.248282	+	0.248282i
$585$	4.75736	−	1.58579i	0.196693	−	0.0655642i
$586$	−1.77817	+	1.77817i	−0.0734557	+	0.0734557i
$587$			4.45584i			0.183912i	0.995763	+	0.0919562i	$0.0293120\pi$
$587$			4.45584i			0.183912i	−0.995763	+	0.0919562i	$0.970688\pi$
$588$	10.8284	+	10.8284i	0.446557	+	0.446557i
$589$		−	48.0416i		−	1.97952i
$590$	3.31371	+	1.65685i	0.136423	+	0.0682116i
$591$			5.65685i			0.232692i
$592$	−4.94975	−	3.53553i	−0.203433	−	0.145310i
$593$	−26.1421	−	26.1421i	−1.07353	−	1.07353i	−0.997073	−	0.0764559i	$-0.975640\pi$
$593$	−26.1421	−	26.1421i	−1.07353	−	1.07353i	−0.0764559	−	0.997073i	$-0.524360\pi$
$594$	10.8284	+	10.8284i	0.444296	+	0.444296i
$595$	−7.00000	+	14.0000i	−0.286972	+	0.573944i
$596$		−	8.24264i		−	0.337632i
$597$	−11.0294			−0.451405
$598$		−	5.79899i		−	0.237138i
$599$			33.7574i			1.37929i	0.724148	+	0.689644i	$0.242233\pi$
$599$			33.7574i			1.37929i	−0.724148	+	0.689644i	$0.757767\pi$
$600$	9.89949	+	1.41421i	0.404145	+	0.0577350i
$601$	−16.5147			−0.673649			−0.336825	−	0.941567i	$-0.609353\pi$
$601$	−16.5147			−0.673649			−0.336825	+	0.941567i	$0.609353\pi$
$602$	−18.9497	+	18.9497i	−0.772334	+	0.772334i
$603$	1.24264	−	1.24264i	0.0506042	−	0.0506042i
$604$			12.0000i			0.488273i
$605$	−7.75736	+	2.58579i	−0.315382	+	0.105127i
$606$	−15.6569	+	15.6569i	−0.636016	+	0.636016i
$607$			34.1838i			1.38748i	0.720227	+	0.693738i	$0.244037\pi$
$607$			34.1838i			1.38748i	−0.720227	+	0.693738i	$0.755963\pi$
$608$	5.82843	+	5.82843i	0.236374	+	0.236374i
$609$	−51.3553	+	51.3553i	−2.08102	+	2.08102i
$610$	−26.2843	−	13.1421i	−1.06422	−	0.532110i
$611$	−18.4853	−	18.4853i	−0.747834	−	0.747834i
$612$		−	1.82843i		−	0.0739098i
$613$	−12.1213	+	12.1213i	−0.489576	+	0.489576i	−0.908172	−	0.418597i	$-0.862522\pi$
$613$	−12.1213	+	12.1213i	−0.489576	+	0.489576i	0.418597	+	0.908172i	$0.362522\pi$
$614$	−1.89949	+	1.89949i	−0.0766574	+	0.0766574i
$615$	28.0000	+	14.0000i	1.12907	+	0.564534i
$616$	−10.3640	+	10.3640i	−0.417576	+	0.417576i
$617$	−27.7279	−	27.7279i	−1.11628	−	1.11628i	−0.992282	−	0.124002i	$-0.960427\pi$
$617$	−27.7279	−	27.7279i	−1.11628	−	1.11628i	−0.124002	−	0.992282i	$-0.539573\pi$
$618$	−19.1716	−	19.1716i	−0.771194	−	0.771194i
$619$	46.5980			1.87293			0.936465	−	0.350760i	$-0.114077\pi$
$619$	46.5980			1.87293			0.936465	+	0.350760i	$0.114077\pi$
$620$	5.82843	−	11.6569i	0.234075	−	0.468151i
$621$	7.31371	−	7.31371i	0.293489	−	0.293489i
$622$	11.7782	+	11.7782i	0.472262	+	0.472262i
$623$	40.1421			1.60826
$624$	3.17157	+	3.17157i	0.126965	+	0.126965i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	−0.686292			−0.0274297
$627$	−63.1127			−2.52048
$628$	−5.87868	+	5.87868i	−0.234585	+	0.234585i
$629$	9.05025	+	6.46447i	0.360857	+	0.257755i
$630$	−3.82843	+	7.65685i	−0.152528	+	0.305056i
$631$	−18.8492	+	18.8492i	−0.750376	+	0.750376i	−0.974549	−	0.224173i	$-0.928032\pi$
$631$	−18.8492	+	18.8492i	−0.750376	+	0.750376i	0.224173	+	0.974549i	$0.428032\pi$
$632$	9.65685	+	9.65685i	0.384129	+	0.384129i
$633$	−12.7279	+	12.7279i	−0.505889	+	0.505889i
$634$	15.5355	−	15.5355i	0.616995	−	0.616995i
$635$	3.65685	−	7.31371i	0.145118	−	0.290236i
$636$	−6.00000			−0.237915
$637$	17.1716			0.680362
$638$	−25.6777	−	25.6777i	−1.01659	−	1.01659i
$639$			0.343146i			0.0135746i
$640$	0.707107	+	2.12132i	0.0279508	+	0.0838525i
$641$	25.2843			0.998669			0.499334	−	0.866409i	$-0.333578\pi$
$641$	25.2843			0.998669			0.499334	+	0.866409i	$0.333578\pi$
$642$	25.6569			1.01260
$643$	−24.5147			−0.966766			−0.483383	−	0.875409i	$-0.660592\pi$
$643$	−24.5147			−0.966766			−0.483383	+	0.875409i	$0.660592\pi$
$644$	7.00000	+	7.00000i	0.275839	+	0.275839i
$645$	−28.0000	−	14.0000i	−1.10250	−	0.551249i
$646$	−10.6569	−	10.6569i	−0.419288	−	0.419288i
$647$		−	27.3137i		−	1.07381i	−0.843642	−	0.536906i	$-0.819593\pi$
$647$		−	27.3137i		−	1.07381i	0.843642	−	0.536906i	$-0.180407\pi$
$648$			11.0000i			0.432121i
$649$	−4.48528	−	4.48528i	−0.176063	−	0.176063i
$650$	8.97056	−	6.72792i	0.351854	−	0.263891i
$651$	31.5563	+	31.5563i	1.23679	+	1.23679i
$652$	14.6569			0.574007
$653$	−19.6569			−0.769232			−0.384616	−	0.923077i	$-0.625666\pi$
$653$	−19.6569			−0.769232			−0.384616	+	0.923077i	$0.625666\pi$
$654$	2.68629			0.105042
$655$	0.585786	−	1.17157i	0.0228886	−	0.0457771i
$656$			7.00000i			0.273304i
$657$	−6.00000	−	6.00000i	−0.234082	−	0.234082i
$658$	44.6274			1.73976
$659$	−20.1421			−0.784626			−0.392313	−	0.919832i	$-0.628325\pi$
$659$	−20.1421			−0.784626			−0.392313	+	0.919832i	$0.628325\pi$
$660$	−15.3137	−	7.65685i	−0.596085	−	0.298043i
$661$	−20.2635	+	20.2635i	−0.788157	+	0.788157i	−0.981192	−	0.193035i	$-0.938167\pi$
$661$	−20.2635	+	20.2635i	−0.788157	+	0.788157i	0.193035	+	0.981192i	$0.438167\pi$
$662$	2.58579	−	2.58579i	0.100499	−	0.100499i
$663$	−5.79899	−	5.79899i	−0.225214	−	0.225214i
$664$	0.828427	−	0.828427i	0.0321492	−	0.0321492i
$665$	22.3137	+	66.9411i	0.865289	+	2.59587i
$666$	4.94975	+	3.53553i	0.191799	+	0.136999i
$667$	−17.3431	+	17.3431i	−0.671529	+	0.671529i
$668$	1.17157			0.0453295
$669$	39.2548			1.51768
$670$	1.75736	−	3.51472i	0.0678927	−	0.135785i
$671$	35.5772	+	35.5772i	1.37344	+	1.37344i
$672$	−7.65685			−0.295370
$673$	−10.5147	−	10.5147i	−0.405313	−	0.405313i	0.474788	−	0.880100i	$-0.342525\pi$
$673$	−10.5147	−	10.5147i	−0.405313	−	0.405313i	−0.880100	+	0.474788i	$0.842525\pi$
$674$	5.65685	−	5.65685i	0.217894	−	0.217894i
$675$	19.7990	+	2.82843i	0.762063	+	0.108866i
$676$	−7.97056			−0.306560
$677$	−13.5147	−	13.5147i	−0.519413	−	0.519413i	0.397981	−	0.917394i	$-0.369711\pi$
$677$	−13.5147	−	13.5147i	−0.519413	−	0.519413i	−0.917394	+	0.397981i	$0.869711\pi$
$678$	5.41421	+	5.41421i	0.207932	+	0.207932i
$679$	−18.9497	+	18.9497i	−0.727225	+	0.727225i
$680$	−1.29289	−	3.87868i	−0.0495802	−	0.148741i
$681$	−10.5858	+	10.5858i	−0.405648	+	0.405648i
$682$	−15.7782	+	15.7782i	−0.604178	+	0.604178i
$683$			12.3137i			0.471171i	0.971854	+	0.235585i	$0.0757008\pi$
$683$			12.3137i			0.471171i	−0.971854	+	0.235585i	$0.924299\pi$
$684$	−5.82843	−	5.82843i	−0.222855	−	0.222855i
$685$	11.8995	−	23.7990i	0.454656	−	0.909313i
$686$	−1.77817	+	1.77817i	−0.0678910	+	0.0678910i
$687$	−2.00000	−	2.00000i	−0.0763048	−	0.0763048i
$688$		−	7.00000i		−	0.266872i
$689$	−4.75736	+	4.75736i	−0.181241	+	0.181241i
$690$	−5.17157	+	10.3431i	−0.196878	+	0.393757i
$691$			9.97056i			0.379298i	0.981852	+	0.189649i	$0.0607350\pi$
$691$			9.97056i			0.379298i	−0.981852	+	0.189649i	$0.939265\pi$
$692$	−6.02082	+	6.02082i	−0.228877	+	0.228877i
$693$	10.3640	−	10.3640i	0.393694	−	0.393694i
$694$	17.3137			0.657219
$695$	−13.0919	+	4.36396i	−0.496603	+	0.165534i
$696$		−	18.9706i		−	0.719077i
$697$		−	12.7990i		−	0.484796i
$698$	−4.14214			−0.156782
$699$		−	0.201010i		−	0.00760290i
$700$	−2.70711	+	18.9497i	−0.102319	+	0.716233i
$701$	4.34315	+	4.34315i	0.164038	+	0.164038i	0.784353	−	0.620315i	$-0.212995\pi$
$701$	4.34315	+	4.34315i	0.164038	+	0.164038i	−0.620315	+	0.784353i	$0.712995\pi$
$702$	6.34315	+	6.34315i	0.239407	+	0.239407i
$703$	49.4558	−	8.24264i	1.86526	−	0.310877i
$704$		−	3.82843i		−	0.144289i
$705$	16.4853	+	49.4558i	0.620872	+	1.86261i
$706$		−	7.34315i		−	0.276363i
$707$	−29.9706	−	29.9706i	−1.12716	−	1.12716i
$708$		−	3.31371i		−	0.124537i
$709$	10.7071	−	10.7071i	0.402114	−	0.402114i	−0.476864	−	0.878977i	$-0.658226\pi$
$709$	10.7071	−	10.7071i	0.402114	−	0.402114i	0.878977	+	0.476864i	$0.158226\pi$
$710$	0.242641	+	0.727922i	0.00910614	+	0.0273184i
$711$	−9.65685	−	9.65685i	−0.362160	−	0.362160i
$712$	−7.41421	+	7.41421i	−0.277859	+	0.277859i
$713$	10.6569	+	10.6569i	0.399102	+	0.399102i
$714$	14.0000			0.523937
$715$	−18.2132	+	6.07107i	−0.681135	+	0.227045i
$716$	14.4853	+	14.4853i	0.541340	+	0.541340i
$717$		−	19.9411i		−	0.744715i
$718$	30.5269			1.13925
$719$			24.1421i			0.900350i	0.892940	+	0.450175i	$0.148638\pi$
$719$			24.1421i			0.900350i	−0.892940	+	0.450175i	$0.851362\pi$
$720$	−0.707107	−	2.12132i	−0.0263523	−	0.0790569i
$721$	36.6985	−	36.6985i	1.36672	−	1.36672i
$722$	−48.9411			−1.82140
$723$	2.14214			0.0796669
$724$	−7.65685			−0.284565
$725$	−46.9497	−	6.70711i	−1.74367	−	0.249096i
$726$	5.17157	+	5.17157i	0.191935	+	0.191935i
$727$			13.8579i			0.513960i	0.966417	+	0.256980i	$0.0827274\pi$
$727$			13.8579i			0.513960i	−0.966417	+	0.256980i	$0.917273\pi$
$728$	−6.07107	+	6.07107i	−0.225009	+	0.225009i
$729$			13.0000i			0.481481i
$730$	−16.9706	−	8.48528i	−0.628109	−	0.314054i
$731$			12.7990i			0.473388i
$732$			26.2843i			0.971495i
$733$	−22.7487	+	22.7487i	−0.840244	+	0.840244i	−0.988890	−	0.148647i	$-0.952508\pi$
$733$	−22.7487	+	22.7487i	−0.840244	+	0.840244i	0.148647	+	0.988890i	$0.452508\pi$
$734$	−13.0919	−	13.0919i	−0.483230	−	0.483230i
$735$	−30.6274	−	15.3137i	−1.12971	−	0.564855i
$736$	−2.58579			−0.0953134
$737$	−4.75736	+	4.75736i	−0.175240	+	0.175240i
$738$		−	7.00000i		−	0.257674i
$739$	−10.7990			−0.397247			−0.198624	−	0.980076i	$-0.563647\pi$
$739$	−10.7990			−0.397247			−0.198624	+	0.980076i	$0.563647\pi$
$740$	13.0000	+	4.00000i	0.477890	+	0.147043i
$741$	−36.9706			−1.35815
$742$		−	11.4853i		−	0.421638i
$743$	5.05025	−	5.05025i	0.185276	−	0.185276i	−0.608374	−	0.793650i	$-0.708178\pi$
$743$	5.05025	−	5.05025i	0.185276	−	0.185276i	0.793650	+	0.608374i	$0.208178\pi$
$744$	−11.6569			−0.427361
$745$	5.82843	+	17.4853i	0.213537	+	0.640611i
$746$	10.8284	+	10.8284i	0.396457	+	0.396457i
$747$	−0.828427	+	0.828427i	−0.0303106	+	0.0303106i
$748$			7.00000i			0.255945i
$749$			49.1127i			1.79454i
$750$	−22.0000	+	4.00000i	−0.803326	+	0.146059i
$751$		−	16.0416i		−	0.585367i	−0.956209	−	0.292684i	$-0.905452\pi$
$751$		−	16.0416i		−	0.585367i	0.956209	−	0.292684i	$-0.0945483\pi$
$752$	−8.24264	+	8.24264i	−0.300578	+	0.300578i
$753$			50.6274i			1.84497i
$754$	−15.0416	−	15.0416i	−0.547784	−	0.547784i
$755$	−8.48528	−	25.4558i	−0.308811	−	0.926433i
$756$	−15.3137			−0.556954
$757$	27.6569			1.00521			0.502603	−	0.864517i	$-0.332376\pi$
$757$	27.6569			1.00521			0.502603	+	0.864517i	$0.332376\pi$
$758$	18.0000			0.653789
$759$	14.0000	−	14.0000i	0.508168	−	0.508168i
$760$	−16.4853	−	8.24264i	−0.597984	−	0.298992i
$761$		−	11.6863i		−	0.423628i	−0.977310	−	0.211814i	$-0.932063\pi$
$761$		−	11.6863i		−	0.423628i	0.977310	−	0.211814i	$-0.0679371\pi$
$762$	−7.31371			−0.264948
$763$			5.14214i			0.186158i
$764$	−1.53553	−	1.53553i	−0.0555537	−	0.0555537i
$765$	1.29289	+	3.87868i	0.0467447	+	0.140234i
$766$	−16.5858			−0.599269
$767$	−2.62742	−	2.62742i	−0.0948705	−	0.0948705i
$768$	1.41421	−	1.41421i	0.0510310	−	0.0510310i
$769$	−19.1716	−	19.1716i	−0.691345	−	0.691345i	0.271183	−	0.962528i	$-0.412585\pi$
$769$	−19.1716	−	19.1716i	−0.691345	−	0.691345i	−0.962528	+	0.271183i	$0.912585\pi$
$770$	14.6569	−	29.3137i	0.528196	−	1.05639i
$771$	26.6274	−	26.6274i	0.958963	−	0.958963i
$772$			20.4853i			0.737281i
$773$	10.1213	+	10.1213i	0.364039	+	0.364039i	0.865297	−	0.501259i	$-0.167130\pi$
$773$	10.1213	+	10.1213i	0.364039	+	0.364039i	−0.501259	+	0.865297i	$0.667130\pi$
$774$			7.00000i			0.251610i
$775$	−4.12132	+	28.8492i	−0.148042	+	1.03630i
$776$		−	7.00000i		−	0.251285i
$777$	−27.0711	+	37.8995i	−0.971169	+	1.35964i
$778$	3.77817	+	3.77817i	0.135454	+	0.135454i
$779$	−40.7990	−	40.7990i	−1.46178	−	1.46178i
$780$	−8.97056	−	4.48528i	−0.321198	−	0.160599i
$781$		−	1.31371i		−	0.0470082i
$782$	4.72792			0.169070
$783$		−	37.9411i		−	1.35591i
$784$		−	7.65685i		−	0.273459i
$785$	8.31371	−	16.6274i	0.296729	−	0.593458i
$786$	−1.17157			−0.0417886
$787$	16.2426	−	16.2426i	0.578988	−	0.578988i	−0.355637	−	0.934624i	$-0.615736\pi$
$787$	16.2426	−	16.2426i	0.578988	−	0.578988i	0.934624	+	0.355637i	$0.115736\pi$
$788$	2.00000	−	2.00000i	0.0712470	−	0.0712470i
$789$			41.3137i			1.47081i
$790$	−27.3137	−	13.6569i	−0.971778	−	0.485889i
$791$	−10.3640	+	10.3640i	−0.368500	+	0.368500i
$792$			3.82843i			0.136037i
$793$	20.8406	+	20.8406i	0.740072	+	0.740072i
$794$	8.48528	−	8.48528i	0.301131	−	0.301131i
$795$	12.7279	−	4.24264i	0.451413	−	0.150471i
$796$	3.89949	+	3.89949i	0.138214	+	0.138214i
$797$			51.2548i			1.81554i	0.419469	+	0.907770i	$0.362216\pi$
$797$			51.2548i			1.81554i	−0.419469	+	0.907770i	$0.637784\pi$
$798$	44.6274	−	44.6274i	1.57979	−	1.57979i
$799$	15.0711	−	15.0711i	0.533176	−	0.533176i
$800$	−3.00000	−	4.00000i	−0.106066	−	0.141421i
$801$	7.41421	−	7.41421i	0.261968	−	0.261968i
$802$	7.07107	+	7.07107i	0.249688	+	0.249688i
$803$	22.9706	+	22.9706i	0.810614	+	0.810614i
$804$	−3.51472			−0.123955
$805$	−19.7990	−	9.89949i	−0.697823	−	0.348911i
$806$	−9.24264	+	9.24264i	−0.325558	+	0.325558i
$807$	25.1716	+	25.1716i	0.886081	+	0.886081i
$808$	11.0711			0.389479
$809$	39.9706	+	39.9706i	1.40529	+	1.40529i	0.781954	+	0.623336i	$0.214223\pi$
$809$	39.9706	+	39.9706i	1.40529	+	1.40529i	0.623336	+	0.781954i	$0.285777\pi$
$810$	−7.77817	−	23.3345i	−0.273297	−	0.819892i
$811$	−24.9706			−0.876835			−0.438418	−	0.898771i	$-0.644461\pi$
$811$	−24.9706			−0.876835			−0.438418	+	0.898771i	$0.644461\pi$
$812$	36.3137			1.27436
$813$	−4.34315	+	4.34315i	−0.152321	+	0.152321i
$814$	−18.9497	−	13.5355i	−0.664188	−	0.474420i
$815$	−31.0919	+	10.3640i	−1.08910	+	0.363034i
$816$	−2.58579	+	2.58579i	−0.0905206	+	0.0905206i
$817$	40.7990	+	40.7990i	1.42738	+	1.42738i
$818$	−19.7990	+	19.7990i	−0.692255	+	0.692255i
$819$	6.07107	−	6.07107i	0.212140	−	0.212140i
$820$	−4.94975	−	14.8492i	−0.172853	−	0.518558i
$821$	−41.5563			−1.45033			−0.725163	−	0.688577i	$-0.758236\pi$
$821$	−41.5563			−1.45033			−0.725163	+	0.688577i	$0.758236\pi$
$822$	−23.7990			−0.830085
$823$	−28.9706	−	28.9706i	−1.00985	−	1.00985i	−0.999951	−	0.00989933i	$-0.996849\pi$
$823$	−28.9706	−	28.9706i	−1.00985	−	1.00985i	−0.00989933	−	0.999951i	$-0.503151\pi$
$824$			13.5563i			0.472258i
$825$	37.8995	+	5.41421i	1.31949	+	0.188499i
$826$	6.34315			0.220706
$827$	3.82843			0.133127			0.0665637	−	0.997782i	$-0.478796\pi$
$827$	3.82843			0.133127			0.0665637	+	0.997782i	$0.478796\pi$
$828$	2.58579			0.0898623
$829$	−24.7487	−	24.7487i	−0.859559	−	0.859559i	0.131727	−	0.991286i	$-0.457948\pi$
$829$	−24.7487	−	24.7487i	−0.859559	−	0.859559i	−0.991286	+	0.131727i	$0.957948\pi$
$830$	−1.17157	+	2.34315i	−0.0406659	+	0.0813318i
$831$	−11.0294	−	11.0294i	−0.382607	−	0.382607i
$832$		−	2.24264i		−	0.0777496i
$833$			14.0000i			0.485071i
$834$	8.72792	+	8.72792i	0.302223	+	0.302223i
$835$	−2.48528	+	0.828427i	−0.0860067	+	0.0286689i
$836$	22.3137	+	22.3137i	0.771736	+	0.771736i
$837$	−23.3137			−0.805840
$838$	−26.9706			−0.931683
$839$	25.3553			0.875364			0.437682	−	0.899130i	$-0.355800\pi$
$839$	25.3553			0.875364			0.437682	+	0.899130i	$0.355800\pi$
$840$	16.2426	−	5.41421i	0.560424	−	0.186808i
$841$			60.9706i			2.10243i
$842$	25.3137	+	25.3137i	0.872368	+	0.872368i
$843$	11.3137			0.389665
$844$	9.00000			0.309793
$845$	16.9081	−	5.63604i	0.581657	−	0.193886i
$846$	8.24264	−	8.24264i	0.283388	−	0.283388i
$847$	−9.89949	+	9.89949i	−0.340151	+	0.340151i
$848$	2.12132	+	2.12132i	0.0728464	+	0.0728464i
$849$	39.5980	−	39.5980i	1.35900	−	1.35900i
$850$	5.48528	+	7.31371i	0.188144	+	0.250858i
$851$	−9.14214	+	12.7990i	−0.313388	+	0.438744i
$852$	0.485281	−	0.485281i	0.0166255	−	0.0166255i
$853$	−27.1716			−0.930337			−0.465168	−	0.885222i	$-0.654006\pi$
$853$	−27.1716			−0.930337			−0.465168	+	0.885222i	$0.654006\pi$
$854$	−50.3137			−1.72170
$855$	16.4853	+	8.24264i	0.563785	+	0.281892i
$856$	−9.07107	−	9.07107i	−0.310043	−	0.310043i
$857$	13.1421			0.448927			0.224463	−	0.974483i	$-0.427937\pi$
$857$	13.1421			0.448927			0.224463	+	0.974483i	$0.427937\pi$
$858$	12.1421	+	12.1421i	0.414526	+	0.414526i
$859$	−36.5563	+	36.5563i	−1.24729	+	1.24729i	−0.290373	+	0.956914i	$0.593779\pi$
$859$	−36.5563	+	36.5563i	−1.24729	+	1.24729i	−0.956914	+	0.290373i	$0.906221\pi$
$860$	4.94975	+	14.8492i	0.168785	+	0.506355i
$861$	53.5980			1.82661
$862$	20.5061	+	20.5061i	0.698440	+	0.698440i
$863$	20.7071	+	20.7071i	0.704878	+	0.704878i	0.965454	−	0.260575i	$-0.0839123\pi$
$863$	20.7071	+	20.7071i	0.704878	+	0.704878i	−0.260575	+	0.965454i	$0.583912\pi$
$864$	2.82843	−	2.82843i	0.0962250	−	0.0962250i
$865$	8.51472	−	17.0294i	0.289509	−	0.579018i
$866$	5.14214	−	5.14214i	0.174737	−	0.174737i
$867$	−19.3137	+	19.3137i	−0.655928	+	0.655928i
$868$		−	22.3137i		−	0.757377i
$869$	36.9706	+	36.9706i	1.25414	+	1.25414i
$870$	13.4142	+	40.2426i	0.454784	+	1.36435i
$871$	−2.78680	+	2.78680i	−0.0944270	+	0.0944270i
$872$	−0.949747	−	0.949747i	−0.0321625	−	0.0321625i
$873$			7.00000i			0.236914i
$874$	15.0711	−	15.0711i	0.509786	−	0.509786i
$875$	−7.65685	−	42.1127i	−0.258849	−	1.42367i
$876$			16.9706i			0.573382i
$877$	−14.0208	+	14.0208i	−0.473449	+	0.473449i	−0.903029	−	0.429580i	$-0.858662\pi$
$877$	−14.0208	+	14.0208i	−0.473449	+	0.473449i	0.429580	+	0.903029i	$0.358662\pi$
$878$	2.22183	−	2.22183i	0.0749830	−	0.0749830i
$879$	−5.02944			−0.169639
$880$	2.70711	+	8.12132i	0.0912566	+	0.273770i
$881$		−	9.48528i		−	0.319567i	−0.987152	−	0.159784i	$-0.948920\pi$
$881$		−	9.48528i		−	0.319567i	0.987152	−	0.159784i	$-0.0510797\pi$
$882$			7.65685i			0.257820i
$883$	8.37258			0.281760			0.140880	−	0.990027i	$-0.455007\pi$
$883$	8.37258			0.281760			0.140880	+	0.990027i	$0.455007\pi$
$884$			4.10051i			0.137915i
$885$	2.34315	+	7.02944i	0.0787640	+	0.236292i
$886$	5.34315	+	5.34315i	0.179506	+	0.179506i
$887$	−34.0624	−	34.0624i	−1.14370	−	1.14370i	−0.987767	−	0.155938i	$-0.950160\pi$
$887$	−34.0624	−	34.0624i	−1.14370	−	1.14370i	−0.155938	−	0.987767i	$-0.549840\pi$
$888$	−2.00000	−	12.0000i	−0.0671156	−	0.402694i
$889$		−	14.0000i		−	0.469545i
$890$	10.4853	−	20.9706i	0.351467	−	0.702935i
$891$			42.1127i			1.41083i
$892$	−13.8787	−	13.8787i	−0.464693	−	0.464693i
$893$		−	96.0833i		−	3.21530i
$894$	11.6569	−	11.6569i	0.389864	−	0.389864i
$895$	−40.9706	−	20.4853i	−1.36949	−	0.684747i
$896$	2.70711	+	2.70711i	0.0904381	+	0.0904381i
$897$	8.20101	−	8.20101i	0.273824	−	0.273824i
$898$	25.6274	+	25.6274i	0.855198	+	0.855198i
$899$	55.2843			1.84383
$900$	3.00000	+	4.00000i	0.100000	+	0.133333i
$901$	−3.87868	−	3.87868i	−0.129218	−	0.129218i
$902$			26.7990i			0.892309i
$903$	−53.5980			−1.78363
$904$		−	3.82843i		−	0.127332i
$905$	16.2426	−	5.41421i	0.539924	−	0.179975i
$906$	−16.9706	+	16.9706i	−0.563809	+	0.563809i
$907$	−14.0000			−0.464862			−0.232431	−	0.972613i	$-0.574668\pi$
$907$	−14.0000			−0.464862			−0.232431	+	0.972613i	$0.574668\pi$
$908$	7.48528			0.248408
$909$	−11.0711			−0.367204
$910$	8.58579	−	17.1716i	0.284616	−	0.569232i
$911$	24.5858	+	24.5858i	0.814563	+	0.814563i	0.985314	−	0.170751i	$-0.0546193\pi$
$911$	24.5858	+	24.5858i	0.814563	+	0.814563i	−0.170751	+	0.985314i	$0.554619\pi$
$912$			16.4853i			0.545882i
$913$	3.17157	−	3.17157i	0.104964	−	0.104964i
$914$			3.68629i			0.121932i
$915$	−18.5858	−	55.7574i	−0.614427	−	1.84328i
$916$			1.41421i			0.0467269i
$917$		−	2.24264i		−	0.0740585i
$918$	−5.17157	+	5.17157i	−0.170687	+	0.170687i
$919$	−34.6274	−	34.6274i	−1.14225	−	1.14225i	−0.988037	−	0.154216i	$-0.950715\pi$
$919$	−34.6274	−	34.6274i	−1.14225	−	1.14225i	−0.154216	−	0.988037i	$-0.549285\pi$
$920$	5.48528	−	1.82843i	0.180844	−	0.0602815i
$921$	−5.37258			−0.177033
$922$	10.4645	−	10.4645i	0.344629	−	0.344629i
$923$		−	0.769553i		−	0.0253301i
$924$	−29.3137			−0.964350
$925$	−30.4056	+	0.707107i	−0.999730	+	0.0232495i
$926$	29.9411			0.983926
$927$		−	13.5563i		−	0.445249i
$928$	−6.70711	+	6.70711i	−0.220172	+	0.220172i
$929$	9.34315			0.306539			0.153269	−	0.988184i	$-0.451020\pi$
$929$	9.34315			0.306539			0.153269	+	0.988184i	$0.451020\pi$
$930$	24.7279	−	8.24264i	0.810861	−	0.270287i
$931$	44.6274	+	44.6274i	1.46260	+	1.46260i
$932$	−0.0710678	+	0.0710678i	−0.00232790	+	0.00232790i
$933$			33.3137i			1.09064i
$934$		−	2.31371i		−	0.0757069i
$935$	−4.94975	−	14.8492i	−0.161874	−	0.485622i
$936$			2.24264i			0.0733030i
$937$	4.58579	−	4.58579i	0.149811	−	0.149811i	−0.628223	−	0.778034i	$-0.716217\pi$
$937$	4.58579	−	4.58579i	0.149811	−	0.149811i	0.778034	+	0.628223i	$0.216217\pi$
$938$		−	6.72792i		−	0.219674i
$939$	−0.970563	−	0.970563i	−0.0316731	−	0.0316731i
$940$	11.6569	−	23.3137i	0.380205	−	0.760409i
$941$	20.9289			0.682264			0.341132	−	0.940015i	$-0.389190\pi$
$941$	20.9289			0.682264			0.341132	+	0.940015i	$0.389190\pi$
$942$	−16.6274			−0.541751
$943$	18.1005			0.589434
$944$	−1.17157	+	1.17157i	−0.0381314	+	0.0381314i
$945$	32.4853	−	10.8284i	1.05675	−	0.352249i
$946$		−	26.7990i		−	0.871310i
$947$	−8.79899			−0.285929			−0.142964	−	0.989728i	$-0.545663\pi$
$947$	−8.79899			−0.285929			−0.142964	+	0.989728i	$0.545663\pi$
$948$			27.3137i			0.887108i
$949$	13.4558	+	13.4558i	0.436795	+	0.436795i
$950$	40.7990	+	5.82843i	1.32369	+	0.189099i
$951$	43.9411			1.42489
$952$	−4.94975	−	4.94975i	−0.160422	−	0.160422i
$953$	20.3431	−	20.3431i	0.658979	−	0.658979i	−0.296159	−	0.955139i	$-0.595706\pi$
$953$	20.3431	−	20.3431i	0.658979	−	0.658979i	0.955139	+	0.296159i	$0.0957060\pi$
$954$	−2.12132	−	2.12132i	−0.0686803	−	0.0686803i
$955$	4.34315	+	2.17157i	0.140541	+	0.0702704i
$956$	−7.05025	+	7.05025i	−0.228021	+	0.228021i
$957$		−	72.6274i		−	2.34771i
$958$	−15.5563	−	15.5563i	−0.502603	−	0.502603i
$959$		−	45.5563i		−	1.47109i
$960$	−2.00000	+	4.00000i	−0.0645497	+	0.129099i
$961$		−	2.97056i		−	0.0958246i
$962$	−11.1005	−	7.92893i	−0.357895	−	0.255639i
$963$	9.07107	+	9.07107i	0.292311	+	0.292311i
$964$	−0.757359	−	0.757359i	−0.0243929	−	0.0243929i
$965$	−14.4853	−	43.4558i	−0.466298	−	1.39889i
$966$			19.7990i			0.637022i
$967$	−53.9411			−1.73463			−0.867315	−	0.497760i	$-0.834156\pi$
$967$	−53.9411			−1.73463			−0.867315	+	0.497760i	$0.834156\pi$
$968$		−	3.65685i		−	0.117536i
$969$		−	30.1421i		−	0.968305i
$970$	4.94975	+	14.8492i	0.158927	+	0.476780i
$971$	−53.7696			−1.72555			−0.862774	−	0.505591i	$-0.831275\pi$
$971$	−53.7696			−1.72555			−0.862774	+	0.505591i	$0.831275\pi$
$972$	−7.07107	+	7.07107i	−0.226805	+	0.226805i
$973$	−16.7071	+	16.7071i	−0.535605	+	0.535605i
$974$		−	26.9706i		−	0.864193i
$975$	22.2010	+	3.17157i	0.711001	+	0.101572i
$976$	9.29289	−	9.29289i	0.297458	−	0.297458i
$977$		−	32.5147i		−	1.04024i	−0.854094	−	0.520119i	$-0.825888\pi$
$977$		−	32.5147i		−	1.04024i	0.854094	−	0.520119i	$-0.174112\pi$
$978$	20.7279	+	20.7279i	0.662806	+	0.662806i
$979$	−28.3848	+	28.3848i	−0.907181	+	0.907181i
$980$	5.41421	+	16.2426i	0.172951	+	0.518852i
$981$	0.949747	+	0.949747i	0.0303231	+	0.0303231i
$982$		−	17.7990i		−	0.567989i
$983$	30.6066	−	30.6066i	0.976199	−	0.976199i	−0.0235243	−	0.999723i	$-0.507489\pi$
$983$	30.6066	−	30.6066i	0.976199	−	0.976199i	0.999723	+	0.0235243i	$0.00748870\pi$
$984$	−9.89949	+	9.89949i	−0.315584	+	0.315584i
$985$	−2.82843	+	5.65685i	−0.0901212	+	0.180242i
$986$	12.2635	−	12.2635i	0.390548	−	0.390548i
$987$	63.1127	+	63.1127i	2.00890	+	2.00890i
$988$	13.0711	+	13.0711i	0.415846	+	0.415846i
$989$	−18.1005			−0.575563
$990$	−2.70711	−	8.12132i	−0.0860375	−	0.258113i
$991$	38.8492	−	38.8492i	1.23409	−	1.23409i	0.271707	−	0.962380i	$-0.412412\pi$
$991$	38.8492	−	38.8492i	1.23409	−	1.23409i	0.962380	−	0.271707i	$-0.0875881\pi$
$992$	4.12132	+	4.12132i	0.130852	+	0.130852i
$993$	7.31371			0.232094
$994$	0.928932	+	0.928932i	0.0294639	+	0.0294639i
$995$	−11.0294	−	5.51472i	−0.349657	−	0.174828i
$996$	2.34315			0.0742454
$997$	37.4558			1.18624			0.593119	−	0.805115i	$-0.297896\pi$
$997$	37.4558			1.18624			0.593119	+	0.805115i	$0.297896\pi$
$998$	−10.2426	+	10.2426i	−0.324225	+	0.324225i
$999$	−4.00000	−	24.0000i	−0.126554	−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.g.c.43.2	✓	4
5.2	odd	4		370.2.h.c.117.1	yes	4
37.31	odd	4		370.2.h.c.253.1	yes	4
185.142	even	4	inner	370.2.g.c.327.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.c.43.2	✓	4	1.1	even	1	trivial
370.2.g.c.327.2	yes	4	185.142	even	4	inner
370.2.h.c.117.1	yes	4	5.2	odd	4
370.2.h.c.253.1	yes	4	37.31	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 - 2.70711i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 - 2.70711i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-0.707107 - 2.12132i) q^{10} +3.82843i q^{11} +(-1.41421 + 1.41421i) q^{12} +2.24264i q^{13} +(-2.70711 - 2.70711i) q^{14} +(2.00000 - 4.00000i) q^{15} +1.00000 q^{16} -1.82843 q^{17} -1.00000 q^{18} +(-5.82843 + 5.82843i) q^{19} +(-2.12132 + 0.707107i) q^{20} -7.65685i q^{21} +3.82843 q^{22} -2.58579i q^{23} +(1.41421 + 1.41421i) q^{24} +(4.00000 - 3.00000i) q^{25} +2.24264 q^{26} +(2.82843 + 2.82843i) q^{27} +(-2.70711 + 2.70711i) q^{28} +(-6.70711 - 6.70711i) q^{29} +(-4.00000 - 2.00000i) q^{30} +(-4.12132 + 4.12132i) q^{31} -1.00000i q^{32} +(5.41421 + 5.41421i) q^{33} +1.82843i q^{34} +(3.82843 - 7.65685i) q^{35} +1.00000i q^{36} +(-4.94975 - 3.53553i) q^{37} +(5.82843 + 5.82843i) q^{38} +(3.17157 + 3.17157i) q^{39} +(0.707107 + 2.12132i) q^{40} +7.00000i q^{41} -7.65685 q^{42} -7.00000i q^{43} -3.82843i q^{44} +(-0.707107 - 2.12132i) q^{45} -2.58579 q^{46} +(-8.24264 + 8.24264i) q^{47} +(1.41421 - 1.41421i) q^{48} -7.65685i q^{49} +(-3.00000 - 4.00000i) q^{50} +(-2.58579 + 2.58579i) q^{51} -2.24264i q^{52} +(2.12132 + 2.12132i) q^{53} +(2.82843 - 2.82843i) q^{54} +(2.70711 + 8.12132i) q^{55} +(2.70711 + 2.70711i) q^{56} +16.4853i q^{57} +(-6.70711 + 6.70711i) q^{58} +(-1.17157 + 1.17157i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(9.29289 - 9.29289i) q^{61} +(4.12132 + 4.12132i) q^{62} +(-2.70711 - 2.70711i) q^{63} -1.00000 q^{64} +(1.58579 + 4.75736i) q^{65} +(5.41421 - 5.41421i) q^{66} +(1.24264 + 1.24264i) q^{67} +1.82843 q^{68} +(-3.65685 - 3.65685i) q^{69} +(-7.65685 - 3.82843i) q^{70} -0.343146 q^{71} +1.00000 q^{72} +(6.00000 - 6.00000i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(1.41421 - 9.89949i) q^{75} +(5.82843 - 5.82843i) q^{76} +(10.3640 + 10.3640i) q^{77} +(3.17157 - 3.17157i) q^{78} +(9.65685 - 9.65685i) q^{79} +(2.12132 - 0.707107i) q^{80} +11.0000 q^{81} +7.00000 q^{82} +(-0.828427 - 0.828427i) q^{83} +7.65685i q^{84} +(-3.87868 + 1.29289i) q^{85} -7.00000 q^{86} -18.9706 q^{87} -3.82843 q^{88} +(7.41421 + 7.41421i) q^{89} +(-2.12132 + 0.707107i) q^{90} +(6.07107 + 6.07107i) q^{91} +2.58579i q^{92} +11.6569i q^{93} +(8.24264 + 8.24264i) q^{94} +(-8.24264 + 16.4853i) q^{95} +(-1.41421 - 1.41421i) q^{96} -7.00000 q^{97} -7.65685 q^{98} +3.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 8 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 + 8 * q^7	\( 4 q - 4 q^{4} + 8 q^{7} - 8 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 4 q^{22} + 16 q^{25} - 8 q^{26} - 8 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} + 16 q^{33} + 4 q^{35} + 12 q^{38} + 24 q^{39} - 8 q^{42} - 16 q^{46} - 16 q^{47} - 12 q^{50} - 16 q^{51} + 8 q^{55} + 8 q^{56} - 24 q^{58} - 16 q^{59} - 8 q^{60} + 40 q^{61} + 8 q^{62} - 8 q^{63} - 4 q^{64} + 12 q^{65} + 16 q^{66} - 12 q^{67} - 4 q^{68} + 8 q^{69} - 8 q^{70} - 24 q^{71} + 4 q^{72} + 24 q^{73} + 12 q^{76} + 16 q^{77} + 24 q^{78} + 16 q^{79} + 44 q^{81} + 28 q^{82} + 8 q^{83} - 24 q^{85} - 28 q^{86} - 8 q^{87} - 4 q^{88} + 24 q^{89} - 4 q^{91} + 16 q^{94} - 16 q^{95} - 28 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 8 * q^7 - 8 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 4 * q^22 + 16 * q^25 - 8 * q^26 - 8 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 + 16 * q^33 + 4 * q^35 + 12 * q^38 + 24 * q^39 - 8 * q^42 - 16 * q^46 - 16 * q^47 - 12 * q^50 - 16 * q^51 + 8 * q^55 + 8 * q^56 - 24 * q^58 - 16 * q^59 - 8 * q^60 + 40 * q^61 + 8 * q^62 - 8 * q^63 - 4 * q^64 + 12 * q^65 + 16 * q^66 - 12 * q^67 - 4 * q^68 + 8 * q^69 - 8 * q^70 - 24 * q^71 + 4 * q^72 + 24 * q^73 + 12 * q^76 + 16 * q^77 + 24 * q^78 + 16 * q^79 + 44 * q^81 + 28 * q^82 + 8 * q^83 - 24 * q^85 - 28 * q^86 - 8 * q^87 - 4 * q^88 + 24 * q^89 - 4 * q^91 + 16 * q^94 - 16 * q^95 - 28 * q^97 - 8 * q^98 + 4 * q^99

Introduction

L-functions

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