LMFDB - Embedded newform 370.2.h.c.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (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			253.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.c.117.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.41421	+	1.41421i	−0.816497	+	0.816497i	−0.985599	−	0.169102i	$-0.945913\pi$
$3$	−1.41421	+	1.41421i	−0.816497	+	0.816497i	0.169102	+	0.985599i	$0.445913\pi$
$4$	1.00000			0.500000
$5$	−0.707107	−	2.12132i	−0.316228	−	0.948683i
$5$	−0.707107	−	2.12132i	−0.316228	−	0.948683i
$6$	−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	$-0.00747000\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−0.707107	−	2.12132i	−0.223607	−	0.670820i
$11$		−	3.82843i		−	1.15431i	−0.816633	−	0.577157i	$-0.804162\pi$
$11$		−	3.82843i		−	1.15431i	0.816633	−	0.577157i	$-0.195838\pi$
$12$	−1.41421	+	1.41421i	−0.408248	+	0.408248i
$13$	2.24264			0.621997			0.310998	−	0.950410i	$-0.399337\pi$
$13$	2.24264			0.621997			0.310998	+	0.950410i	$0.399337\pi$
$14$	2.70711	−	2.70711i	0.723505	−	0.723505i
$15$	4.00000	+	2.00000i	1.03280	+	0.516398i
$16$	1.00000			0.250000
$17$			1.82843i			0.443459i	0.975108	+	0.221729i	$0.0711701\pi$
$17$			1.82843i			0.443459i	−0.975108	+	0.221729i	$0.928830\pi$
$18$		−	1.00000i		−	0.235702i
$19$	5.82843	+	5.82843i	1.33713	+	1.33713i	0.898825	+	0.438308i	$0.144422\pi$
$19$	5.82843	+	5.82843i	1.33713	+	1.33713i	0.438308	+	0.898825i	$0.355578\pi$
$20$	−0.707107	−	2.12132i	−0.158114	−	0.474342i
$21$			7.65685i			1.67086i
$22$		−	3.82843i		−	0.816223i
$23$	−2.58579			−0.539174			−0.269587	−	0.962976i	$-0.586887\pi$
$23$	−2.58579			−0.539174			−0.269587	+	0.962976i	$0.586887\pi$
$24$	−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	0.287783	−	0.957696i	$-0.407082\pi$
$29$	6.70711	−	6.70711i	1.24548	−	1.24548i	0.957696	−	0.287783i	$-0.0929181\pi$
$30$	4.00000	+	2.00000i	0.730297	+	0.365148i
$31$	−4.12132	−	4.12132i	−0.740211	−	0.740211i	0.232408	−	0.972619i	$-0.425340\pi$
$31$	−4.12132	−	4.12132i	−0.740211	−	0.740211i	−0.972619	+	0.232408i	$0.925340\pi$
$32$	1.00000			0.176777
$33$	5.41421	+	5.41421i	0.942494	+	0.942494i
$34$			1.82843i			0.313573i
$35$	−7.65685	−	3.82843i	−1.29424	−	0.647122i
$36$		−	1.00000i		−	0.166667i
$37$	3.53553	+	4.94975i	0.581238	+	0.813733i
$37$	3.53553	+	4.94975i	0.581238	+	0.813733i
$38$	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	$-0.815919\pi$
$41$		−	7.00000i		−	1.09322i	0.837389	−	0.546608i	$-0.184081\pi$
$42$			7.65685i			1.18148i
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$		−	3.82843i		−	0.577157i
$45$	−2.12132	+	0.707107i	−0.316228	+	0.105409i
$46$	−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
$50$	−4.00000	+	3.00000i	−0.565685	+	0.424264i
$51$	−2.58579	−	2.58579i	−0.362083	−	0.362083i
$52$	2.24264			0.310998
$53$	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
$55$	−8.12132	+	2.70711i	−1.09508	+	0.365026i
$56$	2.70711	−	2.70711i	0.361752	−	0.361752i
$57$	−16.4853			−2.18353
$58$	6.70711	−	6.70711i	0.880686	−	0.880686i
$59$	1.17157	+	1.17157i	0.152526	+	0.152526i	0.779245	−	0.626719i	$-0.215603\pi$
$59$	1.17157	+	1.17157i	0.152526	+	0.152526i	−0.626719	+	0.779245i	$0.715603\pi$
$60$	4.00000	+	2.00000i	0.516398	+	0.258199i
$61$	9.29289	+	9.29289i	1.18983	+	1.18983i	0.977113	+	0.212720i	$0.0682322\pi$
$61$	9.29289	+	9.29289i	1.18983	+	1.18983i	0.212720	+	0.977113i	$0.431768\pi$
$62$	−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	0.627114	−	0.778927i	$-0.284236\pi$
$67$	−1.24264	−	1.24264i	−0.151813	−	0.151813i	−0.778927	+	0.627114i	$0.784236\pi$
$68$			1.82843i			0.221729i
$69$	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	$0.506482\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−6.00000	+	6.00000i	−0.702247	+	0.702247i	−0.964892	−	0.262646i	$-0.915405\pi$
$73$	−6.00000	+	6.00000i	−0.702247	+	0.702247i	0.262646	+	0.964892i	$0.415405\pi$
$74$	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	−0.995888	−	0.0905930i	$-0.971124\pi$
$79$	−9.65685	−	9.65685i	−1.08648	−	1.08648i	−0.0905930	−	0.995888i	$-0.528876\pi$
$80$	−0.707107	−	2.12132i	−0.0790569	−	0.237171i
$81$	11.0000			1.22222
$82$		−	7.00000i		−	0.773021i
$83$	−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
$87$			18.9706i			2.03386i
$88$		−	3.82843i		−	0.408112i
$89$	−7.41421	+	7.41421i	−0.785905	+	0.785905i	−0.980820	−	0.194915i	$-0.937557\pi$
$89$	−7.41421	+	7.41421i	−0.785905	+	0.785905i	0.194915	+	0.980820i	$0.437557\pi$
$90$	−2.12132	+	0.707107i	−0.223607	+	0.0745356i
$91$	6.07107	−	6.07107i	0.636421	−	0.636421i
$92$	−2.58579			−0.269587
$93$	11.6569			1.20876
$94$	−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
$97$			7.00000i			0.710742i	0.934725	+	0.355371i	$0.115646\pi$
$97$			7.00000i			0.710742i	−0.934725	+	0.355371i	$0.884354\pi$
$98$		−	7.65685i		−	0.773459i
$99$	−3.82843			−0.384771
$100$	−4.00000	+	3.00000i	−0.400000	+	0.300000i
$101$			11.0711i			1.10161i	0.834633	+	0.550806i	$0.185680\pi$
$101$			11.0711i			1.10161i	−0.834633	+	0.550806i	$0.814320\pi$
$102$	−2.58579	−	2.58579i	−0.256031	−	0.256031i
$103$			13.5563i			1.33575i	0.744275	+	0.667873i	$0.232795\pi$
$103$			13.5563i			1.33575i	−0.744275	+	0.667873i	$0.767205\pi$
$104$	2.24264			0.219909
$105$	16.2426	−	5.41421i	1.58512	−	0.528373i
$106$	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	$-0.229511\pi$
$109$	0.949747	+	0.949747i	0.0909693	+	0.0909693i	−0.660158	+	0.751127i	$0.729511\pi$
$110$	−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
$113$		−	3.82843i		−	0.360148i	−0.983653	−	0.180074i	$-0.942366\pi$
$113$		−	3.82843i		−	0.360148i	0.983653	−	0.180074i	$-0.0576337\pi$
$114$	−16.4853			−1.54399
$115$	1.82843	+	5.48528i	0.170502	+	0.511505i
$116$	6.70711	−	6.70711i	0.622739	−	0.622739i
$117$		−	2.24264i		−	0.207332i
$118$	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
$125$	9.19239	+	6.36396i	0.822192	+	0.569210i
$126$	−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	$0.198126\pi$
$128$	1.00000			0.0883883
$129$	9.89949	−	9.89949i	0.871602	−	0.871602i
$130$	−1.58579	−	4.75736i	−0.139083	−	0.417248i
$131$	0.414214	+	0.414214i	0.0361900	+	0.0361900i	0.724970	−	0.688780i	$-0.241853\pi$
$131$	0.414214	+	0.414214i	0.0361900	+	0.0361900i	−0.688780	+	0.724970i	$0.741853\pi$
$132$	5.41421	+	5.41421i	0.471247	+	0.471247i
$133$	31.5563			2.73628
$134$	−1.24264	−	1.24264i	−0.107348	−	0.107348i
$135$	−4.00000	+	8.00000i	−0.344265	+	0.688530i
$136$			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	$-0.415706\pi$
$139$	6.17157			0.523466			0.261733	+	0.965140i	$0.415706\pi$
$140$	−7.65685	−	3.82843i	−0.647122	−	0.323561i
$141$		−	23.3137i		−	1.96337i
$142$	−0.343146			−0.0287962
$143$		−	8.58579i		−	0.717980i
$144$		−	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
$148$	3.53553	+	4.94975i	0.290619	+	0.406867i
$149$			8.24264i			0.675263i	0.941278	+	0.337632i	$0.109626\pi$
$149$			8.24264i			0.675263i	−0.941278	+	0.337632i	$0.890374\pi$
$150$	1.41421	−	9.89949i	0.115470	−	0.808290i
$151$			12.0000i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$151$			12.0000i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$152$	5.82843	+	5.82843i	0.472748	+	0.472748i
$153$	1.82843			0.147820
$154$	−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
$162$	11.0000			0.864242
$163$		−	14.6569i		−	1.14801i	−0.818851	−	0.574007i	$-0.805388\pi$
$163$		−	14.6569i		−	1.14801i	0.818851	−	0.574007i	$-0.194612\pi$
$164$		−	7.00000i		−	0.546608i
$165$	7.65685	−	15.3137i	0.596085	−	1.19217i
$166$	−0.828427	−	0.828427i	−0.0642984	−	0.0642984i
$167$			1.17157i			0.0906590i	0.998972	+	0.0453295i	$0.0144338\pi$
$167$			1.17157i			0.0906590i	−0.998972	+	0.0453295i	$0.985566\pi$
$168$			7.65685i			0.590739i
$169$	−7.97056			−0.613120
$170$	3.87868	−	1.29289i	0.297481	−	0.0991604i
$171$	5.82843	−	5.82843i	0.445711	−	0.445711i
$172$	−7.00000			−0.533745
$173$	−6.02082	+	6.02082i	−0.457754	+	0.457754i	−0.897918	−	0.440164i	$-0.854920\pi$
$173$	−6.02082	+	6.02082i	−0.457754	+	0.457754i	0.440164	+	0.897918i	$0.354920\pi$
$174$			18.9706i			1.43815i
$175$	−2.70711	+	18.9497i	−0.204638	+	1.43247i
$176$		−	3.82843i		−	0.288579i
$177$	−3.31371			−0.249074
$178$	−7.41421	+	7.41421i	−0.555719	+	0.555719i
$179$	14.4853	−	14.4853i	1.08268	−	1.08268i	0.0864222	−	0.996259i	$-0.472457\pi$
$179$	14.4853	−	14.4853i	1.08268	−	1.08268i	0.996259	−	0.0864222i	$-0.0275434\pi$
$180$	−2.12132	+	0.707107i	−0.158114	+	0.0527046i
$181$	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
$183$	−26.2843			−1.94299
$184$	−2.58579			−0.190627
$185$	8.00000	−	11.0000i	0.588172	−	0.808736i
$186$	11.6569			0.854722
$187$	7.00000			0.511891
$188$	−8.24264	+	8.24264i	−0.601156	+	0.601156i
$189$	−15.3137			−1.11391
$190$	8.24264	−	16.4853i	0.597984	−	1.19597i
$191$	1.53553	−	1.53553i	0.111107	−	0.111107i	−0.649367	−	0.760475i	$-0.724966\pi$
$191$	1.53553	−	1.53553i	0.111107	−	0.111107i	0.760475	+	0.649367i	$0.224966\pi$
$192$	−1.41421	+	1.41421i	−0.102062	+	0.102062i
$193$	−20.4853			−1.47456			−0.737281	−	0.675586i	$-0.763891\pi$
$193$	−20.4853			−1.47456			−0.737281	+	0.675586i	$0.763891\pi$
$194$			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	$0.282127\pi$
$198$	−3.82843			−0.272074
$199$	3.89949	−	3.89949i	0.276428	−	0.276428i	−0.555253	−	0.831681i	$-0.687379\pi$
$199$	3.89949	−	3.89949i	0.276428	−	0.276428i	0.831681	+	0.555253i	$0.187379\pi$
$200$	−4.00000	+	3.00000i	−0.282843	+	0.212132i
$201$	3.51472			0.247909
$202$			11.0711i			0.778958i
$203$		−	36.3137i		−	2.54872i
$204$	−2.58579	−	2.58579i	−0.181041	−	0.181041i
$205$	−14.8492	+	4.94975i	−1.03712	+	0.345705i
$206$			13.5563i			0.944516i
$207$			2.58579i			0.179725i
$208$	2.24264			0.155499
$209$	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
$217$	−22.3137			−1.51475
$218$	0.949747	+	0.949747i	0.0643250	+	0.0643250i
$219$		−	16.9706i		−	1.14676i
$220$	−8.12132	+	2.70711i	−0.547539	+	0.182513i
$221$			4.10051i			0.275830i
$222$	−12.0000	−	2.00000i	−0.805387	−	0.134231i
$223$	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
$227$			7.48528i			0.496816i	0.968656	+	0.248408i	$0.0799073\pi$
$227$			7.48528i			0.496816i	−0.968656	+	0.248408i	$0.920093\pi$
$228$	−16.4853			−1.09176
$229$		−	1.41421i		−	0.0934539i	−0.998908	−	0.0467269i	$-0.985121\pi$
$229$		−	1.41421i		−	0.0934539i	0.998908	−	0.0467269i	$-0.0148791\pi$
$230$	1.82843	+	5.48528i	0.120563	+	0.361689i
$231$	29.3137			1.92870
$232$	6.70711	−	6.70711i	0.440343	−	0.440343i
$233$	−0.0710678	+	0.0710678i	−0.00465581	+	0.00465581i	−0.709431	−	0.704775i	$-0.751048\pi$
$233$	−0.0710678	+	0.0710678i	−0.00465581	+	0.00465581i	0.704775	+	0.709431i	$0.251048\pi$
$234$		−	2.24264i		−	0.146606i
$235$	23.3137	+	11.6569i	1.52082	+	0.760409i
$236$	1.17157	+	1.17157i	0.0762629	+	0.0762629i
$237$	27.3137			1.77422
$238$	4.94975	+	4.94975i	0.320844	+	0.320844i
$239$	−7.05025	−	7.05025i	−0.456043	−	0.456043i	0.441311	−	0.897354i	$-0.354513\pi$
$239$	−7.05025	−	7.05025i	−0.456043	−	0.456043i	−0.897354	+	0.441311i	$0.854513\pi$
$240$	4.00000	+	2.00000i	0.258199	+	0.129099i
$241$	0.757359	−	0.757359i	0.0487858	−	0.0487858i	−0.682293	−	0.731079i	$-0.739017\pi$
$241$	0.757359	−	0.757359i	0.0487858	−	0.0487858i	0.731079	+	0.682293i	$0.239017\pi$
$242$	−3.65685			−0.235071
$243$	−7.07107	+	7.07107i	−0.453609	+	0.453609i
$244$	9.29289	+	9.29289i	0.594917	+	0.594917i
$245$	−16.2426	+	5.41421i	−1.03770	+	0.345901i
$246$	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	−0.990208	−	0.139598i	$-0.955419\pi$
$251$	−17.8995	−	17.8995i	−1.12981	−	1.12981i	−0.139598	−	0.990208i	$-0.544581\pi$
$252$	−2.70711	−	2.70711i	−0.170532	−	0.170532i
$253$			9.89949i			0.622376i
$254$	2.58579	−	2.58579i	0.162247	−	0.162247i
$255$	−3.65685	+	7.31371i	−0.229001	+	0.458002i
$256$	1.00000			0.0625000
$257$		−	18.8284i		−	1.17449i	−0.809411	−	0.587243i	$-0.800213\pi$
$257$		−	18.8284i		−	1.17449i	0.809411	−	0.587243i	$-0.199787\pi$
$258$	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	−0.0948134	−	0.995495i	$-0.530225\pi$
$263$	14.6066	−	14.6066i	0.900682	−	0.900682i	0.995495	+	0.0948134i	$0.0302254\pi$
$264$	5.41421	+	5.41421i	0.333222	+	0.333222i
$265$	3.00000	−	6.00000i	0.184289	−	0.368577i
$266$	31.5563			1.93484
$267$		−	20.9706i		−	1.28338i
$268$	−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	$0.529734\pi$
$272$			1.82843i			0.110865i
$273$			17.1716i			1.03927i
$274$	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
$277$	7.79899			0.468596			0.234298	−	0.972165i	$-0.424721\pi$
$277$	7.79899			0.468596			0.234298	+	0.972165i	$0.424721\pi$
$278$	6.17157			0.370146
$279$	−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	−0.577659	−	0.816279i	$-0.696033\pi$
$281$	4.00000	−	4.00000i	0.238620	−	0.238620i	0.816279	+	0.577659i	$0.196033\pi$
$282$		−	23.3137i		−	1.38831i
$283$			28.0000i			1.66443i	0.554455	+	0.832214i	$0.312927\pi$
$283$			28.0000i			1.66443i	−0.554455	+	0.832214i	$0.687073\pi$
$284$	−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
$288$		−	1.00000i		−	0.0589256i
$289$	13.6569			0.803344
$290$	−18.9706	−	9.48528i	−1.11399	−	0.556995i
$291$	−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
$298$			8.24264i			0.477483i
$299$	−5.79899			−0.335364
$300$	1.41421	−	9.89949i	0.0816497	−	0.571548i
$301$	−18.9497	+	18.9497i	−1.09225	+	1.09225i
$302$			12.0000i			0.690522i
$303$	−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	0.759231	−	0.650821i	$-0.225575\pi$
$307$	1.89949	+	1.89949i	0.108410	+	0.108410i	−0.650821	+	0.759231i	$0.725575\pi$
$308$	−10.3640	−	10.3640i	−0.590541	−	0.590541i
$309$	−19.1716	−	19.1716i	−1.09063	−	1.09063i
$310$	−5.82843	+	11.6569i	−0.331032	+	0.662065i
$311$	−11.7782	−	11.7782i	−0.667879	−	0.667879i	0.289346	−	0.957225i	$-0.406562\pi$
$311$	−11.7782	−	11.7782i	−0.667879	−	0.667879i	−0.957225	+	0.289346i	$0.906562\pi$
$312$	−3.17157	+	3.17157i	−0.179555	+	0.179555i
$313$	−0.686292			−0.0387915			−0.0193957	−	0.999812i	$-0.506174\pi$
$313$	−0.686292			−0.0387915			−0.0193957	+	0.999812i	$0.506174\pi$
$314$	5.87868	−	5.87868i	0.331753	−	0.331753i
$315$	−3.82843	+	7.65685i	−0.215707	+	0.431415i
$316$	−9.65685	−	9.65685i	−0.543240	−	0.543240i
$317$	−15.5355	−	15.5355i	−0.872563	−	0.872563i	0.120189	−	0.992751i	$-0.461650\pi$
$317$	−15.5355	−	15.5355i	−0.872563	−	0.872563i	−0.992751	+	0.120189i	$0.961650\pi$
$318$	−6.00000			−0.336463
$319$	−25.6777	−	25.6777i	−1.43767	−	1.43767i
$320$	−0.707107	−	2.12132i	−0.0395285	−	0.118585i
$321$		−	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
$325$	−8.97056	+	6.72792i	−0.497597	+	0.373198i
$326$		−	14.6569i		−	0.811768i
$327$	−2.68629			−0.148552
$328$		−	7.00000i		−	0.386510i
$329$			44.6274i			2.46039i
$330$	7.65685	−	15.3137i	0.421496	−	0.842992i
$331$	2.58579	−	2.58579i	0.142128	−	0.142128i	−0.632463	−	0.774591i	$-0.717956\pi$
$331$	2.58579	−	2.58579i	0.142128	−	0.142128i	0.774591	+	0.632463i	$0.217956\pi$
$332$	−0.828427	−	0.828427i	−0.0454658	−	0.0454658i
$333$	4.94975	−	3.53553i	0.271244	−	0.193746i
$334$			1.17157i			0.0641056i
$335$	−1.75736	+	3.51472i	−0.0960148	+	0.192030i
$336$			7.65685i			0.417716i
$337$	−5.65685	−	5.65685i	−0.308148	−	0.308148i	0.536043	−	0.844191i	$-0.319919\pi$
$337$	−5.65685	−	5.65685i	−0.308148	−	0.308148i	−0.844191	+	0.536043i	$0.819919\pi$
$338$	−7.97056			−0.433541
$339$	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
$347$	−17.3137			−0.929449			−0.464724	−	0.885455i	$-0.653847\pi$
$347$	−17.3137			−0.929449			−0.464724	+	0.885455i	$0.653847\pi$
$348$			18.9706i			1.01693i
$349$		−	4.14214i		−	0.221723i	−0.993836	−	0.110862i	$-0.964639\pi$
$349$		−	4.14214i		−	0.221723i	0.993836	−	0.110862i	$-0.0353611\pi$
$350$	−2.70711	+	18.9497i	−0.144701	+	1.01291i
$351$	−6.34315	−	6.34315i	−0.338572	−	0.338572i
$352$		−	3.82843i		−	0.204056i
$353$			7.34315i			0.390836i	0.980720	+	0.195418i	$0.0626064\pi$
$353$			7.34315i			0.390836i	−0.980720	+	0.195418i	$0.937394\pi$
$354$	−3.31371			−0.176122
$355$	0.242641	+	0.727922i	0.0128780	+	0.0386341i
$356$	−7.41421	+	7.41421i	−0.392953	+	0.392953i
$357$	−14.0000			−0.740959
$358$	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
$362$	7.65685			0.402435
$363$	5.17157	−	5.17157i	0.271437	−	0.271437i
$364$	6.07107	−	6.07107i	0.318210	−	0.318210i
$365$	16.9706	+	8.48528i	0.888280	+	0.444140i
$366$	−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	$0.0894634\pi$
$368$	−2.58579			−0.134793
$369$	−7.00000			−0.364405
$370$	8.00000	−	11.0000i	0.415900	−	0.571863i
$371$	11.4853			0.596286
$372$	11.6569			0.604380
$373$	10.8284	−	10.8284i	0.560675	−	0.560675i	−0.368824	−	0.929499i	$-0.620240\pi$
$373$	10.8284	−	10.8284i	0.560675	−	0.560675i	0.929499	+	0.368824i	$0.120240\pi$
$374$	7.00000			0.361961
$375$	−22.0000	+	4.00000i	−1.13608	+	0.206559i
$376$	−8.24264	+	8.24264i	−0.425082	+	0.425082i
$377$	15.0416	−	15.0416i	0.774683	−	0.774683i
$378$	−15.3137			−0.787652
$379$			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
$383$	−16.5858			−0.847494			−0.423747	−	0.905781i	$-0.639285\pi$
$383$	−16.5858			−0.847494			−0.423747	+	0.905781i	$0.639285\pi$
$384$	−1.41421	+	1.41421i	−0.0721688	+	0.0721688i
$385$	−14.6569	+	29.3137i	−0.746982	+	1.49396i
$386$	−20.4853			−1.04267
$387$			7.00000i			0.355830i
$388$			7.00000i			0.355371i
$389$	3.77817	+	3.77817i	0.191561	+	0.191561i	0.796370	−	0.604809i	$-0.206751\pi$
$389$	3.77817	+	3.77817i	0.191561	+	0.191561i	−0.604809	+	0.796370i	$0.706751\pi$
$390$	8.97056	+	4.48528i	0.454242	+	0.227121i
$391$		−	4.72792i		−	0.239101i
$392$		−	7.65685i		−	0.386730i
$393$	−1.17157			−0.0590980
$394$	−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	0.461353	−	0.887217i	$-0.347364\pi$
$397$	−8.48528	−	8.48528i	−0.425864	−	0.425864i	−0.887217	+	0.461353i	$0.847364\pi$
$398$	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	0.508154	−	0.861266i	$-0.330328\pi$
$401$	−7.07107	−	7.07107i	−0.353112	−	0.353112i	−0.861266	+	0.508154i	$0.830328\pi$
$402$	3.51472			0.175298
$403$	−9.24264	−	9.24264i	−0.460409	−	0.460409i
$404$			11.0711i			0.550806i
$405$	−7.77817	−	23.3345i	−0.386501	−	1.15950i
$406$		−	36.3137i		−	1.80222i
$407$	18.9497	−	13.5355i	0.939304	−	0.670932i
$408$	−2.58579	−	2.58579i	−0.128016	−	0.128016i
$409$	19.7990	−	19.7990i	0.978997	−	0.978997i	−0.0207869	−	0.999784i	$-0.506617\pi$
$409$	19.7990	−	19.7990i	0.978997	−	0.978997i	0.999784	+	0.0207869i	$0.00661715\pi$
$410$	−14.8492	+	4.94975i	−0.733352	+	0.244451i
$411$			23.7990i			1.17392i
$412$			13.5563i			0.667873i
$413$	6.34315			0.312126
$414$			2.58579i			0.127084i
$415$	−1.17157	+	2.34315i	−0.0575103	+	0.115021i
$416$	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	$-0.228935\pi$
$420$	16.2426	−	5.41421i	0.792560	−	0.264187i
$421$	−25.3137	−	25.3137i	−1.23371	−	1.23371i	−0.962526	−	0.271188i	$-0.912583\pi$
$421$	−25.3137	−	25.3137i	−1.23371	−	1.23371i	−0.271188	−	0.962526i	$-0.587417\pi$
$422$	−9.00000			−0.438113
$423$	8.24264	+	8.24264i	0.400771	+	0.400771i
$424$	2.12132	+	2.12132i	0.103020	+	0.103020i
$425$	−5.48528	−	7.31371i	−0.266075	−	0.354767i
$426$	0.485281	−	0.485281i	0.0235120	−	0.0235120i
$427$	50.3137			2.43485
$428$	−9.07107	+	9.07107i	−0.438467	+	0.438467i
$429$	12.1421	+	12.1421i	0.586228	+	0.586228i
$430$	4.94975	+	14.8492i	0.238698	+	0.716094i
$431$	−20.5061	−	20.5061i	−0.987744	−	0.987744i	0.0121819	−	0.999926i	$-0.496122\pi$
$431$	−20.5061	−	20.5061i	−0.987744	−	0.987744i	−0.999926	+	0.0121819i	$0.996122\pi$
$432$	−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
$438$		−	16.9706i		−	0.810885i
$439$	−2.22183	+	2.22183i	−0.106042	+	0.106042i	−0.758137	−	0.652095i	$-0.773890\pi$
$439$	−2.22183	+	2.22183i	−0.106042	+	0.106042i	0.652095	+	0.758137i	$0.273890\pi$
$440$	−8.12132	+	2.70711i	−0.387169	+	0.129056i
$441$	−7.65685			−0.364612
$442$			4.10051i			0.195041i
$443$	5.34315	−	5.34315i	0.253861	−	0.253861i	−0.568691	−	0.822551i	$-0.692550\pi$
$443$	5.34315	−	5.34315i	0.253861	−	0.253861i	0.822551	+	0.568691i	$0.192550\pi$
$444$	−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	0.971211	+	0.238222i	$0.0765645\pi$
$449$	25.6274	+	25.6274i	1.20943	+	1.20943i	0.238222	+	0.971211i	$0.423435\pi$
$450$	3.00000	+	4.00000i	0.141421	+	0.188562i
$451$	−26.7990			−1.26192
$452$		−	3.82843i		−	0.180074i
$453$	−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
$457$			3.68629i			0.172437i	0.996276	+	0.0862187i	$0.0274784\pi$
$457$			3.68629i			0.172437i	−0.996276	+	0.0862187i	$0.972522\pi$
$458$		−	1.41421i		−	0.0660819i
$459$	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	−0.420099	−	0.907478i	$-0.638005\pi$
$461$	10.4645	−	10.4645i	0.487379	−	0.487379i	0.907478	+	0.420099i	$0.138005\pi$
$462$	29.3137			1.36380
$463$	29.9411			1.39148			0.695741	−	0.718293i	$-0.255076\pi$
$463$	29.9411			1.39148			0.695741	+	0.718293i	$0.255076\pi$
$464$	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
$467$		−	2.31371i		−	0.107066i	−0.998566	−	0.0535328i	$-0.982952\pi$
$467$		−	2.31371i		−	0.107066i	0.998566	−	0.0535328i	$-0.0170482\pi$
$468$		−	2.24264i		−	0.103666i
$469$	−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
$473$			26.7990i			1.23222i
$474$	27.3137			1.25456
$475$	−40.7990	−	5.82843i	−1.87199	−	0.267427i
$476$	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	$-0.417624\pi$
$479$	−15.5563	−	15.5563i	−0.710788	−	0.710788i	−0.966700	+	0.255912i	$0.917624\pi$
$480$	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
$483$		−	19.7990i		−	0.900885i
$484$	−3.65685			−0.166221
$485$	14.8492	−	4.94975i	0.674269	−	0.224756i
$486$	−7.07107	+	7.07107i	−0.320750	+	0.320750i
$487$		−	26.9706i		−	1.22215i	−0.791572	−	0.611076i	$-0.790737\pi$
$487$		−	26.9706i		−	1.22215i	0.791572	−	0.611076i	$-0.209263\pi$
$488$	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
$495$	2.70711	+	8.12132i	0.121675	+	0.365026i
$496$	−4.12132	−	4.12132i	−0.185053	−	0.185053i
$497$	−0.928932	+	0.928932i	−0.0416683	+	0.0416683i
$498$	2.34315			0.104999
$499$	10.2426	−	10.2426i	0.458524	−	0.458524i	−0.439647	−	0.898171i	$-0.644896\pi$
$499$	10.2426	−	10.2426i	0.458524	−	0.458524i	0.898171	+	0.439647i	$0.144896\pi$
$500$	9.19239	+	6.36396i	0.411096	+	0.284605i
$501$	−1.65685	−	1.65685i	−0.0740228	−	0.0740228i
$502$	−17.8995	−	17.8995i	−0.798894	−	0.798894i
$503$	−32.5858			−1.45293			−0.726464	−	0.687204i	$-0.758838\pi$
$503$	−32.5858			−1.45293			−0.726464	+	0.687204i	$0.758838\pi$
$504$	−2.70711	−	2.70711i	−0.120584	−	0.120584i
$505$	23.4853	−	7.82843i	1.04508	−	0.348360i
$506$			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	$-0.508975\pi$
$509$	−1.27208			−0.0563839			−0.0281919	+	0.999603i	$0.508975\pi$
$510$	−3.65685	+	7.31371i	−0.161928	+	0.323856i
$511$			32.4853i			1.43706i
$512$	1.00000			0.0441942
$513$		−	32.9706i		−	1.45569i
$514$		−	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
$518$	22.9706	+	3.82843i	1.00927	+	0.168211i
$519$		−	17.0294i		−	0.747509i
$520$	−1.58579	−	4.75736i	−0.0695413	−	0.208624i
$521$			27.6274i			1.21038i	0.796081	+	0.605190i	$0.206903\pi$
$521$			27.6274i			1.21038i	−0.796081	+	0.605190i	$0.793097\pi$
$522$	−6.70711	−	6.70711i	−0.293562	−	0.293562i
$523$	43.6569			1.90898			0.954490	−	0.298241i	$-0.0964000\pi$
$523$	43.6569			1.90898			0.954490	+	0.298241i	$0.0964000\pi$
$524$	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
$532$	31.5563			1.36814
$533$		−	15.6985i		−	0.679977i
$534$		−	20.9706i		−	0.907485i
$535$	25.6569	+	12.8284i	1.10924	+	0.554621i
$536$	−1.24264	−	1.24264i	−0.0536739	−	0.0536739i
$537$			40.9706i			1.76801i
$538$			17.7990i			0.767369i
$539$	−29.3137			−1.26263
$540$	−4.00000	+	8.00000i	−0.172133	+	0.344265i
$541$	−27.7990	+	27.7990i	−1.19517	+	1.19517i	−0.219577	+	0.975595i	$0.570468\pi$
$541$	−27.7990	+	27.7990i	−1.19517	+	1.19517i	−0.975595	+	0.219577i	$0.929532\pi$
$542$	−3.07107			−0.131914
$543$	−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
$547$	−27.8284			−1.18986			−0.594929	−	0.803778i	$-0.702820\pi$
$547$	−27.8284			−1.18986			−0.594929	+	0.803778i	$0.702820\pi$
$548$	8.41421	−	8.41421i	0.359437	−	0.359437i
$549$	9.29289	−	9.29289i	0.396611	−	0.396611i
$550$	11.4853	+	15.3137i	0.489734	+	0.652979i
$551$	78.1838			3.33074
$552$	3.65685	−	3.65685i	0.155646	−	0.155646i
$553$	−52.2843			−2.22335
$554$	7.79899			0.331347
$555$	4.24264	+	26.8701i	0.180090	+	1.14057i
$556$	6.17157			0.261733
$557$	23.2132			0.983575			0.491787	−	0.870715i	$-0.336344\pi$
$557$	23.2132			0.983575			0.491787	+	0.870715i	$0.336344\pi$
$558$	−4.12132	+	4.12132i	−0.174469	+	0.174469i
$559$	−15.6985			−0.663975
$560$	−7.65685	−	3.82843i	−0.323561	−	0.161781i
$561$	−9.89949	+	9.89949i	−0.417957	+	0.417957i
$562$	4.00000	−	4.00000i	0.168730	−	0.168730i
$563$	−24.1127			−1.01623			−0.508115	−	0.861290i	$-0.669657\pi$
$563$	−24.1127			−1.01623			−0.508115	+	0.861290i	$0.669657\pi$
$564$		−	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
$568$	−0.343146			−0.0143981
$569$	1.68629	−	1.68629i	0.0706930	−	0.0706930i	−0.670876	−	0.741569i	$-0.734082\pi$
$569$	1.68629	−	1.68629i	0.0706930	−	0.0706930i	0.741569	+	0.670876i	$0.234082\pi$
$570$	11.6569	+	34.9706i	0.488252	+	1.46476i
$571$	46.7990			1.95848			0.979238	−	0.202712i	$-0.0649755\pi$
$571$	46.7990			1.95848			0.979238	+	0.202712i	$0.0649755\pi$
$572$		−	8.58579i		−	0.358990i
$573$			4.34315i			0.181438i
$574$	−18.9497	−	18.9497i	−0.790947	−	0.790947i
$575$	10.3431	−	7.75736i	0.431339	−	0.323504i
$576$		−	1.00000i		−	0.0416667i
$577$		−	21.6569i		−	0.901587i	−0.892628	−	0.450793i	$-0.851141\pi$
$577$		−	21.6569i		−	0.901587i	0.892628	−	0.450793i	$-0.148859\pi$
$578$	13.6569			0.568050
$579$	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
$587$	−4.45584			−0.183912			−0.0919562	−	0.995763i	$-0.529312\pi$
$587$	−4.45584			−0.183912			−0.0919562	+	0.995763i	$0.529312\pi$
$588$	10.8284	+	10.8284i	0.446557	+	0.446557i
$589$		−	48.0416i		−	1.97952i
$590$	1.65685	−	3.31371i	0.0682116	−	0.136423i
$591$		−	5.65685i		−	0.232692i
$592$	3.53553	+	4.94975i	0.145310	+	0.203433i
$593$	−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
$597$			11.0294i			0.451405i
$598$	−5.79899			−0.237138
$599$			33.7574i			1.37929i	0.724148	+	0.689644i	$0.242233\pi$
$599$			33.7574i			1.37929i	−0.724148	+	0.689644i	$0.757767\pi$
$600$	1.41421	−	9.89949i	0.0577350	−	0.404145i
$601$	−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
$605$	2.58579	+	7.75736i	0.105127	+	0.315382i
$606$	−15.6569	−	15.6569i	−0.636016	−	0.636016i
$607$	−34.1838			−1.38748			−0.693738	−	0.720227i	$-0.744037\pi$
$607$	−34.1838			−1.38748			−0.693738	+	0.720227i	$0.744037\pi$
$608$	5.82843	+	5.82843i	0.236374	+	0.236374i
$609$	51.3553	+	51.3553i	2.08102	+	2.08102i
$610$	13.1421	−	26.2843i	0.532110	−	1.06422i
$611$	−18.4853	+	18.4853i	−0.747834	+	0.747834i
$612$	1.82843			0.0739098
$613$	12.1213	−	12.1213i	0.489576	−	0.489576i	−0.418597	−	0.908172i	$-0.637478\pi$
$613$	12.1213	−	12.1213i	0.489576	−	0.489576i	0.908172	+	0.418597i	$0.137478\pi$
$614$	1.89949	+	1.89949i	0.0766574	+	0.0766574i
$615$	14.0000	−	28.0000i	0.564534	−	1.12907i
$616$	−10.3640	−	10.3640i	−0.417576	−	0.417576i
$617$	27.7279	+	27.7279i	1.11628	+	1.11628i	0.992282	+	0.124002i	$0.0395730\pi$
$617$	27.7279	+	27.7279i	1.11628	+	1.11628i	0.124002	+	0.992282i	$0.460427\pi$
$618$	−19.1716	−	19.1716i	−0.771194	−	0.771194i
$619$	−46.5980			−1.87293			−0.936465	−	0.350760i	$-0.885923\pi$
$619$	−46.5980			−1.87293			−0.936465	+	0.350760i	$0.885923\pi$
$620$	−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
$623$			40.1421i			1.60826i
$624$	−3.17157	+	3.17157i	−0.126965	+	0.126965i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	−0.686292			−0.0274297
$627$			63.1127i			2.52048i
$628$	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	0.224173	−	0.974549i	$-0.428032\pi$
$631$	−18.8492	−	18.8492i	−0.750376	−	0.750376i	−0.974549	+	0.224173i	$0.928032\pi$
$632$	−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
$635$	−7.31371	−	3.65685i	−0.290236	−	0.145118i
$636$	−6.00000			−0.237915
$637$		−	17.1716i		−	0.680362i
$638$	−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	$0.333578\pi$
$642$		−	25.6569i		−	1.01260i
$643$		−	24.5147i		−	0.966766i	−0.875409	−	0.483383i	$-0.839408\pi$
$643$		−	24.5147i		−	0.966766i	0.875409	−	0.483383i	$-0.160592\pi$
$644$	−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
$647$	27.3137			1.07381			0.536906	−	0.843642i	$-0.319593\pi$
$647$	27.3137			1.07381			0.536906	+	0.843642i	$0.319593\pi$
$648$	11.0000			0.432121
$649$	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
$652$		−	14.6569i		−	0.574007i
$653$		−	19.6569i		−	0.769232i	−0.923077	−	0.384616i	$-0.874334\pi$
$653$		−	19.6569i		−	0.769232i	0.923077	−	0.384616i	$-0.125666\pi$
$654$	−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
$658$			44.6274i			1.73976i
$659$	20.1421			0.784626			0.392313	−	0.919832i	$-0.371675\pi$
$659$	20.1421			0.784626			0.392313	+	0.919832i	$0.371675\pi$
$660$	7.65685	−	15.3137i	0.298043	−	0.596085i
$661$	−20.2635	−	20.2635i	−0.788157	−	0.788157i	0.193035	−	0.981192i	$-0.438167\pi$
$661$	−20.2635	−	20.2635i	−0.788157	−	0.788157i	−0.981192	+	0.193035i	$0.938167\pi$
$662$	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
$668$			1.17157i			0.0453295i
$669$	−39.2548			−1.51768
$670$	−1.75736	+	3.51472i	−0.0678927	+	0.135785i
$671$	35.5772	−	35.5772i	1.37344	−	1.37344i
$672$			7.65685i			0.295370i
$673$	−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	0.917394	−	0.397981i	$-0.130289\pi$
$677$	13.5147	+	13.5147i	0.519413	+	0.519413i	−0.397981	+	0.917394i	$0.630289\pi$
$678$	5.41421	+	5.41421i	0.207932	+	0.207932i
$679$	18.9497	+	18.9497i	0.727225	+	0.727225i
$680$	3.87868	−	1.29289i	0.148741	−	0.0495802i
$681$	−10.5858	−	10.5858i	−0.405648	−	0.405648i
$682$	−15.7782	+	15.7782i	−0.604178	+	0.604178i
$683$	12.3137			0.471171			0.235585	−	0.971854i	$-0.424299\pi$
$683$	12.3137			0.471171			0.235585	+	0.971854i	$0.424299\pi$
$684$	5.82843	−	5.82843i	0.222855	−	0.222855i
$685$	−23.7990	−	11.8995i	−0.909313	−	0.454656i
$686$	−1.77817	−	1.77817i	−0.0678910	−	0.0678910i
$687$	2.00000	+	2.00000i	0.0763048	+	0.0763048i
$688$	−7.00000			−0.266872
$689$	4.75736	+	4.75736i	0.181241	+	0.181241i
$690$	−10.3431	−	5.17157i	−0.393757	−	0.196878i
$691$		−	9.97056i		−	0.379298i	−0.981852	−	0.189649i	$-0.939265\pi$
$691$		−	9.97056i		−	0.379298i	0.981852	−	0.189649i	$-0.0607350\pi$
$692$	−6.02082	+	6.02082i	−0.228877	+	0.228877i
$693$	−10.3640	+	10.3640i	−0.393694	+	0.393694i
$694$	−17.3137			−0.657219
$695$	−4.36396	−	13.0919i	−0.165534	−	0.496603i
$696$			18.9706i			0.719077i
$697$	12.7990			0.484796
$698$		−	4.14214i		−	0.156782i
$699$		−	0.201010i		−	0.00760290i
$700$	−2.70711	+	18.9497i	−0.102319	+	0.716233i
$701$	4.34315	−	4.34315i	0.164038	−	0.164038i	−0.620315	−	0.784353i	$-0.712995\pi$
$701$	4.34315	−	4.34315i	0.164038	−	0.164038i	0.784353	+	0.620315i	$0.212995\pi$
$702$	−6.34315	−	6.34315i	−0.239407	−	0.239407i
$703$	−8.24264	+	49.4558i	−0.310877	+	1.86526i
$704$		−	3.82843i		−	0.144289i
$705$	−49.4558	+	16.4853i	−1.86261	+	0.620872i
$706$			7.34315i			0.276363i
$707$	29.9706	+	29.9706i	1.12716	+	1.12716i
$708$	−3.31371			−0.124537
$709$	−10.7071	−	10.7071i	−0.402114	−	0.402114i	0.476864	−	0.878977i	$-0.341774\pi$
$709$	−10.7071	−	10.7071i	−0.402114	−	0.402114i	−0.878977	+	0.476864i	$0.841774\pi$
$710$	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
$717$	19.9411			0.744715
$718$			30.5269i			1.13925i
$719$			24.1421i			0.900350i	0.892940	+	0.450175i	$0.148638\pi$
$719$			24.1421i			0.900350i	−0.892940	+	0.450175i	$0.851362\pi$
$720$	−2.12132	+	0.707107i	−0.0790569	+	0.0263523i
$721$	36.6985	+	36.6985i	1.36672	+	1.36672i
$722$			48.9411i			1.82140i
$723$			2.14214i			0.0796669i
$724$	7.65685			0.284565
$725$	−6.70711	+	46.9497i	−0.249096	+	1.74367i
$726$	5.17157	−	5.17157i	0.191935	−	0.191935i
$727$	−13.8579			−0.513960			−0.256980	−	0.966417i	$-0.582727\pi$
$727$	−13.8579			−0.513960			−0.256980	+	0.966417i	$0.582727\pi$
$728$	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
$732$	−26.2843			−0.971495
$733$	22.7487	−	22.7487i	0.840244	−	0.840244i	−0.148647	−	0.988890i	$-0.547492\pi$
$733$	22.7487	−	22.7487i	0.840244	−	0.840244i	0.988890	+	0.148647i	$0.0474917\pi$
$734$	13.0919	−	13.0919i	0.483230	−	0.483230i
$735$	15.3137	−	30.6274i	0.564855	−	1.12971i
$736$	−2.58579			−0.0953134
$737$	−4.75736	+	4.75736i	−0.175240	+	0.175240i
$738$	−7.00000			−0.257674
$739$	10.7990			0.397247			0.198624	−	0.980076i	$-0.436353\pi$
$739$	10.7990			0.397247			0.198624	+	0.980076i	$0.436353\pi$
$740$	8.00000	−	11.0000i	0.294086	−	0.404368i
$741$	−36.9706			−1.35815
$742$	11.4853			0.421638
$743$	−5.05025	+	5.05025i	−0.185276	+	0.185276i	−0.793650	−	0.608374i	$-0.791822\pi$
$743$	−5.05025	+	5.05025i	−0.185276	+	0.185276i	0.608374	+	0.793650i	$0.291822\pi$
$744$	11.6569			0.427361
$745$	17.4853	−	5.82843i	0.640611	−	0.213537i
$746$	10.8284	−	10.8284i	0.396457	−	0.396457i
$747$	−0.828427	+	0.828427i	−0.0303106	+	0.0303106i
$748$	7.00000			0.255945
$749$			49.1127i			1.79454i
$750$	−22.0000	+	4.00000i	−0.803326	+	0.146059i
$751$			16.0416i			0.585367i	0.956209	+	0.292684i	$0.0945483\pi$
$751$			16.0416i			0.585367i	−0.956209	+	0.292684i	$0.905452\pi$
$752$	−8.24264	+	8.24264i	−0.300578	+	0.300578i
$753$	50.6274			1.84497
$754$	15.0416	−	15.0416i	0.547784	−	0.547784i
$755$	25.4558	−	8.48528i	0.926433	−	0.308811i
$756$	−15.3137			−0.556954
$757$		−	27.6569i		−	1.00521i	−0.864517	−	0.502603i	$-0.832376\pi$
$757$		−	27.6569i		−	1.00521i	0.864517	−	0.502603i	$-0.167624\pi$
$758$			18.0000i			0.653789i
$759$	−14.0000	−	14.0000i	−0.508168	−	0.508168i
$760$	8.24264	−	16.4853i	0.298992	−	0.597984i
$761$			11.6863i			0.423628i	0.977310	+	0.211814i	$0.0679371\pi$
$761$			11.6863i			0.423628i	−0.977310	+	0.211814i	$0.932063\pi$
$762$			7.31371i			0.264948i
$763$	5.14214			0.186158
$764$	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	$-0.587415\pi$
$769$	19.1716	−	19.1716i	0.691345	−	0.691345i	0.962528	+	0.271183i	$0.0874149\pi$
$770$	−14.6569	+	29.3137i	−0.528196	+	1.05639i
$771$	26.6274	+	26.6274i	0.958963	+	0.958963i
$772$	−20.4853			−0.737281
$773$	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
$775$	28.8492	+	4.12132i	1.03630	+	0.148042i
$776$			7.00000i			0.251285i
$777$	−37.8995	+	27.0711i	−1.35964	+	0.971169i
$778$	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
$782$		−	4.72792i		−	0.169070i
$783$	−37.9411			−1.35591
$784$		−	7.65685i		−	0.273459i
$785$	−16.6274	−	8.31371i	−0.593458	−	0.296729i
$786$	−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
$790$	−13.6569	+	27.3137i	−0.485889	+	0.971778i
$791$	−10.3640	−	10.3640i	−0.368500	−	0.368500i
$792$	−3.82843			−0.136037
$793$	20.8406	+	20.8406i	0.740072	+	0.740072i
$794$	−8.48528	−	8.48528i	−0.301131	−	0.301131i
$795$	4.24264	+	12.7279i	0.150471	+	0.451413i
$796$	3.89949	−	3.89949i	0.138214	−	0.138214i
$797$	−51.2548			−1.81554			−0.907770	−	0.419469i	$-0.862216\pi$
$797$	−51.2548			−1.81554			−0.907770	+	0.419469i	$0.862216\pi$
$798$	−44.6274	+	44.6274i	−1.57979	+	1.57979i
$799$	−15.0711	−	15.0711i	−0.533176	−	0.533176i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	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
$808$			11.0711i			0.389479i
$809$	−39.9706	+	39.9706i	−1.40529	+	1.40529i	−0.623336	+	0.781954i	$0.714223\pi$
$809$	−39.9706	+	39.9706i	−1.40529	+	1.40529i	−0.781954	+	0.623336i	$0.785777\pi$
$810$	−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	$0.644461\pi$
$812$		−	36.3137i		−	1.27436i
$813$	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
$820$	−14.8492	+	4.94975i	−0.518558	+	0.172853i
$821$	−41.5563			−1.45033			−0.725163	−	0.688577i	$-0.758236\pi$
$821$	−41.5563			−1.45033			−0.725163	+	0.688577i	$0.758236\pi$
$822$			23.7990i			0.830085i
$823$	−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
$827$		−	3.82843i		−	0.133127i	−0.997782	−	0.0665637i	$-0.978796\pi$
$827$		−	3.82843i		−	0.133127i	0.997782	−	0.0665637i	$-0.0212036\pi$
$828$			2.58579i			0.0898623i
$829$	24.7487	−	24.7487i	0.859559	−	0.859559i	−0.131727	−	0.991286i	$-0.542052\pi$
$829$	24.7487	−	24.7487i	0.859559	−	0.859559i	0.991286	+	0.131727i	$0.0420522\pi$
$830$	−1.17157	+	2.34315i	−0.0406659	+	0.0813318i
$831$	−11.0294	+	11.0294i	−0.382607	+	0.382607i
$832$	2.24264			0.0777496
$833$	14.0000			0.485071
$834$	−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
$837$			23.3137i			0.805840i
$838$		−	26.9706i		−	0.931683i
$839$	−25.3553			−0.875364			−0.437682	−	0.899130i	$-0.644200\pi$
$839$	−25.3553			−0.875364			−0.437682	+	0.899130i	$0.644200\pi$
$840$	16.2426	−	5.41421i	0.560424	−	0.186808i
$841$		−	60.9706i		−	2.10243i
$842$	−25.3137	−	25.3137i	−0.872368	−	0.872368i
$843$			11.3137i			0.389665i
$844$	−9.00000			−0.309793
$845$	5.63604	+	16.9081i	0.193886	+	0.581657i
$846$	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
$853$		−	27.1716i		−	0.930337i	−0.885222	−	0.465168i	$-0.845994\pi$
$853$		−	27.1716i		−	0.930337i	0.885222	−	0.465168i	$-0.154006\pi$
$854$	50.3137			1.72170
$855$	−16.4853	−	8.24264i	−0.563785	−	0.281892i
$856$	−9.07107	+	9.07107i	−0.310043	+	0.310043i
$857$		−	13.1421i		−	0.448927i	−0.974483	−	0.224463i	$-0.927937\pi$
$857$		−	13.1421i		−	0.448927i	0.974483	−	0.224463i	$-0.0720629\pi$
$858$	12.1421	+	12.1421i	0.414526	+	0.414526i
$859$	36.5563	+	36.5563i	1.24729	+	1.24729i	0.956914	+	0.290373i	$0.0937794\pi$
$859$	36.5563	+	36.5563i	1.24729	+	1.24729i	0.290373	+	0.956914i	$0.406221\pi$
$860$	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
$865$	17.0294	+	8.51472i	0.579018	+	0.289509i
$866$	5.14214	+	5.14214i	0.174737	+	0.174737i
$867$	−19.3137	+	19.3137i	−0.655928	+	0.655928i
$868$	−22.3137			−0.757377
$869$	−36.9706	+	36.9706i	−1.25414	+	1.25414i
$870$	40.2426	−	13.4142i	1.36435	−	0.454784i
$871$	−2.78680	−	2.78680i	−0.0944270	−	0.0944270i
$872$	0.949747	+	0.949747i	0.0321625	+	0.0321625i
$873$	7.00000			0.236914
$874$	−15.0711	−	15.0711i	−0.509786	−	0.509786i
$875$	42.1127	−	7.65685i	1.42367	−	0.258849i
$876$		−	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
$880$	−8.12132	+	2.70711i	−0.273770	+	0.0912566i
$881$			9.48528i			0.319567i	0.987152	+	0.159784i	$0.0510797\pi$
$881$			9.48528i			0.319567i	−0.987152	+	0.159784i	$0.948920\pi$
$882$	−7.65685			−0.257820
$883$			8.37258i			0.281760i	0.990027	+	0.140880i	$0.0449931\pi$
$883$			8.37258i			0.281760i	−0.990027	+	0.140880i	$0.955007\pi$
$884$			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	$0.0498401\pi$
$887$	34.0624	+	34.0624i	1.14370	+	1.14370i	0.155938	+	0.987767i	$0.450160\pi$
$888$	−12.0000	−	2.00000i	−0.402694	−	0.0671156i
$889$		−	14.0000i		−	0.469545i
$890$	20.9706	+	10.4853i	0.702935	+	0.351467i
$891$		−	42.1127i		−	1.41083i
$892$	13.8787	+	13.8787i	0.464693	+	0.464693i
$893$	−96.0833			−3.21530
$894$	−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
$902$	−26.7990			−0.892309
$903$		−	53.5980i		−	1.78363i
$904$		−	3.82843i		−	0.127332i
$905$	−5.41421	−	16.2426i	−0.179975	−	0.539924i
$906$	−16.9706	−	16.9706i	−0.563809	−	0.563809i
$907$			14.0000i			0.464862i	0.972613	+	0.232431i	$0.0746680\pi$
$907$			14.0000i			0.464862i	−0.972613	+	0.232431i	$0.925332\pi$
$908$			7.48528i			0.248408i
$909$	11.0711			0.367204
$910$	−17.1716	−	8.58579i	−0.569232	−	0.284616i
$911$	24.5858	−	24.5858i	0.814563	−	0.814563i	−0.170751	−	0.985314i	$-0.554619\pi$
$911$	24.5858	−	24.5858i	0.814563	−	0.814563i	0.985314	+	0.170751i	$0.0546193\pi$
$912$	−16.4853			−0.545882
$913$	−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
$917$	2.24264			0.0740585
$918$	5.17157	−	5.17157i	0.170687	−	0.170687i
$919$	34.6274	−	34.6274i	1.14225	−	1.14225i	0.154216	−	0.988037i	$-0.450715\pi$
$919$	34.6274	−	34.6274i	1.14225	−	1.14225i	0.988037	−	0.154216i	$-0.0492851\pi$
$920$	1.82843	+	5.48528i	0.0602815	+	0.180844i
$921$	−5.37258			−0.177033
$922$	10.4645	−	10.4645i	0.344629	−	0.344629i
$923$	−0.769553			−0.0253301
$924$	29.3137			0.964350
$925$	−28.9914	−	9.19239i	−0.953231	−	0.302244i
$926$	29.9411			0.983926
$927$	13.5563			0.445249
$928$	6.70711	−	6.70711i	0.220172	−	0.220172i
$929$	−9.34315			−0.306539			−0.153269	−	0.988184i	$-0.548980\pi$
$929$	−9.34315			−0.306539			−0.153269	+	0.988184i	$0.548980\pi$
$930$	−8.24264	−	24.7279i	−0.270287	−	0.810861i
$931$	44.6274	−	44.6274i	1.46260	−	1.46260i
$932$	−0.0710678	+	0.0710678i	−0.00232790	+	0.00232790i
$933$	33.3137			1.09064
$934$		−	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	$0.216217\pi$
$938$	−6.72792			−0.219674
$939$	0.970563	−	0.970563i	0.0316731	−	0.0316731i
$940$	23.3137	+	11.6569i	0.760409	+	0.380205i
$941$	20.9289			0.682264			0.341132	−	0.940015i	$-0.389190\pi$
$941$	20.9289			0.682264			0.341132	+	0.940015i	$0.389190\pi$
$942$			16.6274i			0.541751i
$943$			18.1005i			0.589434i
$944$	1.17157	+	1.17157i	0.0381314	+	0.0381314i
$945$	10.8284	+	32.4853i	0.352249	+	1.05675i
$946$			26.7990i			0.871310i
$947$			8.79899i			0.285929i	0.989728	+	0.142964i	$0.0456634\pi$
$947$			8.79899i			0.285929i	−0.989728	+	0.142964i	$0.954337\pi$
$948$	27.3137			0.887108
$949$	−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	−0.955139	−	0.296159i	$-0.904294\pi$
$953$	−20.3431	+	20.3431i	−0.658979	+	0.658979i	0.296159	+	0.955139i	$0.404294\pi$
$954$	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
$957$	72.6274			2.34771
$958$	−15.5563	−	15.5563i	−0.502603	−	0.502603i
$959$		−	45.5563i		−	1.47109i
$960$	4.00000	+	2.00000i	0.129099	+	0.0645497i
$961$			2.97056i			0.0958246i
$962$	7.92893	+	11.1005i	0.255639	+	0.357895i
$963$	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
$967$			53.9411i			1.73463i	0.497760	+	0.867315i	$0.334156\pi$
$967$			53.9411i			1.73463i	−0.497760	+	0.867315i	$0.665844\pi$
$968$	−3.65685			−0.117536
$969$		−	30.1421i		−	0.968305i
$970$	14.8492	−	4.94975i	0.476780	−	0.158927i
$971$	−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
$975$	3.17157	−	22.2010i	0.101572	−	0.711001i
$976$	9.29289	+	9.29289i	0.297458	+	0.297458i
$977$	32.5147			1.04024			0.520119	−	0.854094i	$-0.325888\pi$
$977$	32.5147			1.04024			0.520119	+	0.854094i	$0.325888\pi$
$978$	20.7279	+	20.7279i	0.662806	+	0.662806i
$979$	28.3848	+	28.3848i	0.907181	+	0.907181i
$980$	−16.2426	+	5.41421i	−0.518852	+	0.172951i
$981$	0.949747	−	0.949747i	0.0303231	−	0.0303231i
$982$	17.7990			0.567989
$983$	−30.6066	+	30.6066i	−0.976199	+	0.976199i	−0.999723	−	0.0235243i	$-0.992511\pi$
$983$	−30.6066	+	30.6066i	−0.976199	+	0.976199i	0.0235243	+	0.999723i	$0.492511\pi$
$984$	9.89949	+	9.89949i	0.315584	+	0.315584i
$985$	5.65685	+	2.82843i	0.180242	+	0.0901212i
$986$	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	0.962380	+	0.271707i	$0.0875881\pi$
$991$	38.8492	+	38.8492i	1.23409	+	1.23409i	0.271707	+	0.962380i	$0.412412\pi$
$992$	−4.12132	−	4.12132i	−0.130852	−	0.130852i
$993$			7.31371i			0.232094i
$994$	−0.928932	+	0.928932i	−0.0294639	+	0.0294639i
$995$	−11.0294	−	5.51472i	−0.349657	−	0.174828i
$996$	2.34315			0.0742454
$997$		−	37.4558i		−	1.18624i	−0.805115	−	0.593119i	$-0.797896\pi$
$997$		−	37.4558i		−	1.18624i	0.805115	−	0.593119i	$-0.202104\pi$
$998$	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.h.c.253.1	yes	4
5.2	odd	4		370.2.g.c.327.2	yes	4
37.6	odd	4		370.2.g.c.43.2	✓	4
185.117	even	4	inner	370.2.h.c.117.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.c.43.2	✓	4	37.6	odd	4
370.2.g.c.327.2	yes	4	5.2	odd	4
370.2.h.c.117.1	yes	4	185.117	even	4	inner
370.2.h.c.253.1	yes	4	1.1	even	1	trivial

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.h (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

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