LMFDB - Embedded newform 750.2.g.b.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(151,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("750.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.g (of order $5$, degree $4$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	750.301
Dual form			750.2.g.b.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.309017 - 0.951057i) q^{6} -2.61803 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.309017 - 0.951057i) q^{6} -2.61803 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-2.92705 + 2.12663i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(-5.23607 - 3.80423i) q^{13} +(-2.11803 + 1.53884i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.381966 - 1.17557i) q^{17} -1.00000 q^{18} +(-1.76393 - 5.42882i) q^{19} +(-0.809017 + 2.48990i) q^{21} +(-1.11803 + 3.44095i) q^{22} +(3.61803 - 2.62866i) q^{23} -1.00000 q^{24} -6.47214 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.809017 + 2.48990i) q^{28} +(2.61803 - 8.05748i) q^{29} +(2.04508 + 6.29412i) q^{31} -1.00000 q^{32} +(1.11803 + 3.44095i) q^{33} +(-1.00000 - 0.726543i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(6.47214 + 4.70228i) q^{37} +(-4.61803 - 3.35520i) q^{38} +(-5.23607 + 3.80423i) q^{39} +(-4.61803 - 3.35520i) q^{41} +(0.809017 + 2.48990i) q^{42} +7.70820 q^{43} +(1.11803 + 3.44095i) q^{44} +(1.38197 - 4.25325i) q^{46} +(-0.527864 + 1.62460i) q^{47} +(-0.809017 + 0.587785i) q^{48} -0.145898 q^{49} -1.23607 q^{51} +(-5.23607 + 3.80423i) q^{52} +(0.645898 - 1.98787i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(0.809017 + 2.48990i) q^{56} -5.70820 q^{57} +(-2.61803 - 8.05748i) q^{58} +(2.92705 + 2.12663i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(5.35410 + 3.88998i) q^{62} +(2.11803 + 1.53884i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.92705 + 2.12663i) q^{66} +(0.472136 + 1.45309i) q^{67} -1.23607 q^{68} +(-1.38197 - 4.25325i) q^{69} +(1.70820 - 5.25731i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(2.85410 - 2.07363i) q^{73} +8.00000 q^{74} -5.70820 q^{76} +(7.66312 - 5.56758i) q^{77} +(-2.00000 + 6.15537i) q^{78} +(-1.73607 + 5.34307i) q^{79} +(0.309017 + 0.951057i) q^{81} -5.70820 q^{82} +(-0.663119 - 2.04087i) q^{83} +(2.11803 + 1.53884i) q^{84} +(6.23607 - 4.53077i) q^{86} +(-6.85410 - 4.97980i) q^{87} +(2.92705 + 2.12663i) q^{88} +(-2.85410 + 2.07363i) q^{89} +(13.7082 + 9.95959i) q^{91} +(-1.38197 - 4.25325i) q^{92} +6.61803 q^{93} +(0.527864 + 1.62460i) q^{94} +(-0.309017 + 0.951057i) q^{96} +(1.04508 - 3.21644i) q^{97} +(-0.118034 + 0.0857567i) q^{98} +3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 6 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + q^6 - 6 * q^7 + q^8 - q^9	$ 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 6 q^{7} + q^{8} - q^{9} - 5 q^{11} - q^{12} - 12 q^{13} - 4 q^{14} - q^{16} - 6 q^{17} - 4 q^{18} - 16 q^{19} - q^{21} + 10 q^{23} - 4 q^{24} - 8 q^{26} - q^{27} - q^{28} + 6 q^{29} - 3 q^{31} - 4 q^{32} - 4 q^{34} - q^{36} + 8 q^{37} - 14 q^{38} - 12 q^{39} - 14 q^{41} + q^{42} + 4 q^{43} + 10 q^{46} - 20 q^{47} - q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} + 16 q^{53} + q^{54} + q^{56} + 4 q^{57} - 6 q^{58} + 5 q^{59} + 8 q^{62} + 4 q^{63} - q^{64} + 5 q^{66} - 16 q^{67} + 4 q^{68} - 10 q^{69} - 20 q^{71} + q^{72} - 2 q^{73} + 32 q^{74} + 4 q^{76} + 15 q^{77} - 8 q^{78} + 2 q^{79} - q^{81} + 4 q^{82} + 13 q^{83} + 4 q^{84} + 16 q^{86} - 14 q^{87} + 5 q^{88} + 2 q^{89} + 28 q^{91} - 10 q^{92} + 22 q^{93} + 20 q^{94} + q^{96} - 7 q^{97} + 4 q^{98} + 10 q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + q^6 - 6 * q^7 + q^8 - q^9 - 5 * q^11 - q^12 - 12 * q^13 - 4 * q^14 - q^16 - 6 * q^17 - 4 * q^18 - 16 * q^19 - q^21 + 10 * q^23 - 4 * q^24 - 8 * q^26 - q^27 - q^28 + 6 * q^29 - 3 * q^31 - 4 * q^32 - 4 * q^34 - q^36 + 8 * q^37 - 14 * q^38 - 12 * q^39 - 14 * q^41 + q^42 + 4 * q^43 + 10 * q^46 - 20 * q^47 - q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 + 16 * q^53 + q^54 + q^56 + 4 * q^57 - 6 * q^58 + 5 * q^59 + 8 * q^62 + 4 * q^63 - q^64 + 5 * q^66 - 16 * q^67 + 4 * q^68 - 10 * q^69 - 20 * q^71 + q^72 - 2 * q^73 + 32 * q^74 + 4 * q^76 + 15 * q^77 - 8 * q^78 + 2 * q^79 - q^81 + 4 * q^82 + 13 * q^83 + 4 * q^84 + 16 * q^86 - 14 * q^87 + 5 * q^88 + 2 * q^89 + 28 * q^91 - 10 * q^92 + 22 * q^93 + 20 * q^94 + q^96 - 7 * q^97 + 4 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−2.61803			−0.989524			−0.494762	−	0.869029i	$-0.664745\pi$
$7$	−2.61803			−0.989524			−0.494762	+	0.869029i	$0.664745\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−2.92705	+	2.12663i	−0.882539	+	0.641202i	−0.933922	−	0.357477i	$-0.883637\pi$
$11$	−2.92705	+	2.12663i	−0.882539	+	0.641202i	0.0513829	+	0.998679i	$0.483637\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	−5.23607	−	3.80423i	−1.45222	−	1.05510i	−0.985305	−	0.170802i	$-0.945364\pi$
$13$	−5.23607	−	3.80423i	−1.45222	−	1.05510i	−0.466919	−	0.884300i	$-0.654636\pi$
$14$	−2.11803	+	1.53884i	−0.566068	+	0.411273i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.381966	−	1.17557i	−0.0926404	−	0.285118i	0.893991	−	0.448085i	$-0.147894\pi$
$17$	−0.381966	−	1.17557i	−0.0926404	−	0.285118i	−0.986632	+	0.162967i	$0.947894\pi$
$18$	−1.00000			−0.235702
$19$	−1.76393	−	5.42882i	−0.404674	−	1.24546i	−0.921167	−	0.389167i	$-0.872763\pi$
$19$	−1.76393	−	5.42882i	−0.404674	−	1.24546i	0.516494	−	0.856291i	$-0.327237\pi$
$20$		0			0
$21$	−0.809017	+	2.48990i	−0.176542	+	0.543340i
$22$	−1.11803	+	3.44095i	−0.238366	+	0.733614i
$23$	3.61803	−	2.62866i	0.754412	−	0.548113i	−0.142779	−	0.989755i	$-0.545604\pi$
$23$	3.61803	−	2.62866i	0.754412	−	0.548113i	0.897191	+	0.441642i	$0.145604\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	−6.47214			−1.26929
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.809017	+	2.48990i	−0.152890	+	0.470547i
$29$	2.61803	−	8.05748i	0.486157	−	1.49624i	−0.344142	−	0.938918i	$-0.611830\pi$
$29$	2.61803	−	8.05748i	0.486157	−	1.49624i	0.830299	−	0.557319i	$-0.188170\pi$
$30$		0			0
$31$	2.04508	+	6.29412i	0.367308	+	1.13046i	0.948523	+	0.316708i	$0.102578\pi$
$31$	2.04508	+	6.29412i	0.367308	+	1.13046i	−0.581215	+	0.813750i	$0.697422\pi$
$32$	−1.00000			−0.176777
$33$	1.11803	+	3.44095i	0.194625	+	0.598993i
$34$	−1.00000	−	0.726543i	−0.171499	−	0.124601i
$35$		0			0
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	6.47214	+	4.70228i	1.06401	+	0.773050i	0.974827	−	0.222965i	$-0.0715734\pi$
$37$	6.47214	+	4.70228i	1.06401	+	0.773050i	0.0891861	+	0.996015i	$0.471573\pi$
$38$	−4.61803	−	3.35520i	−0.749144	−	0.544285i
$39$	−5.23607	+	3.80423i	−0.838442	+	0.609164i
$40$		0			0
$41$	−4.61803	−	3.35520i	−0.721216	−	0.523994i	0.165557	−	0.986200i	$-0.447058\pi$
$41$	−4.61803	−	3.35520i	−0.721216	−	0.523994i	−0.886772	+	0.462206i	$0.847058\pi$
$42$	0.809017	+	2.48990i	0.124834	+	0.384200i
$43$	7.70820			1.17549			0.587745	−	0.809046i	$-0.300016\pi$
$43$	7.70820			1.17549			0.587745	+	0.809046i	$0.300016\pi$
$44$	1.11803	+	3.44095i	0.168550	+	0.518743i
$45$		0			0
$46$	1.38197	−	4.25325i	0.203760	−	0.627108i
$47$	−0.527864	+	1.62460i	−0.0769969	+	0.236972i	−0.982145	−	0.188123i	$-0.939759\pi$
$47$	−0.527864	+	1.62460i	−0.0769969	+	0.236972i	0.905149	+	0.425096i	$0.139759\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	−0.145898			−0.0208426
$50$		0			0
$51$	−1.23607			−0.173084
$52$	−5.23607	+	3.80423i	−0.726112	+	0.527551i
$53$	0.645898	−	1.98787i	0.0887209	−	0.273055i	−0.896846	−	0.442344i	$-0.854147\pi$
$53$	0.645898	−	1.98787i	0.0887209	−	0.273055i	0.985566	+	0.169289i	$0.0541471\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$		0			0
$56$	0.809017	+	2.48990i	0.108109	+	0.332727i
$57$	−5.70820			−0.756070
$58$	−2.61803	−	8.05748i	−0.343765	−	1.05800i
$59$	2.92705	+	2.12663i	0.381070	+	0.276863i	0.761786	−	0.647829i	$-0.224323\pi$
$59$	2.92705	+	2.12663i	0.381070	+	0.276863i	−0.380717	+	0.924692i	$0.624323\pi$
$60$		0			0
$61$	−2.23607	+	1.62460i	−0.286299	+	0.208009i	−0.721660	−	0.692247i	$-0.756621\pi$
$61$	−2.23607	+	1.62460i	−0.286299	+	0.208009i	0.435361	+	0.900256i	$0.356621\pi$
$62$	5.35410	+	3.88998i	0.679972	+	0.494028i
$63$	2.11803	+	1.53884i	0.266847	+	0.193876i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$	2.92705	+	2.12663i	0.360295	+	0.261770i
$67$	0.472136	+	1.45309i	0.0576806	+	0.177523i	0.975746	−	0.218907i	$-0.0702491\pi$
$67$	0.472136	+	1.45309i	0.0576806	+	0.177523i	−0.918065	+	0.396430i	$0.870249\pi$
$68$	−1.23607			−0.149895
$69$	−1.38197	−	4.25325i	−0.166369	−	0.512032i
$70$		0			0
$71$	1.70820	−	5.25731i	0.202727	−	0.623928i	−0.797073	−	0.603884i	$-0.793619\pi$
$71$	1.70820	−	5.25731i	0.202727	−	0.623928i	0.999799	−	0.0200445i	$-0.00638080\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	2.85410	−	2.07363i	0.334047	−	0.242700i	−0.408099	−	0.912938i	$-0.633808\pi$
$73$	2.85410	−	2.07363i	0.334047	−	0.242700i	0.742146	+	0.670238i	$0.233808\pi$
$74$	8.00000			0.929981
$75$		0			0
$76$	−5.70820			−0.654776
$77$	7.66312	−	5.56758i	0.873293	−	0.634485i
$78$	−2.00000	+	6.15537i	−0.226455	+	0.696958i
$79$	−1.73607	+	5.34307i	−0.195323	+	0.601142i	0.804650	+	0.593750i	$0.202353\pi$
$79$	−1.73607	+	5.34307i	−0.195323	+	0.601142i	−0.999973	+	0.00739236i	$0.997647\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−5.70820			−0.630366
$83$	−0.663119	−	2.04087i	−0.0727868	−	0.224015i	0.908044	−	0.418874i	$-0.137575\pi$
$83$	−0.663119	−	2.04087i	−0.0727868	−	0.224015i	−0.980831	+	0.194859i	$0.937575\pi$
$84$	2.11803	+	1.53884i	0.231096	+	0.167901i
$85$		0			0
$86$	6.23607	−	4.53077i	0.672453	−	0.488565i
$87$	−6.85410	−	4.97980i	−0.734837	−	0.533890i
$88$	2.92705	+	2.12663i	0.312025	+	0.226699i
$89$	−2.85410	+	2.07363i	−0.302534	+	0.219804i	−0.728686	−	0.684848i	$-0.759869\pi$
$89$	−2.85410	+	2.07363i	−0.302534	+	0.219804i	0.426152	+	0.904651i	$0.359869\pi$
$90$		0			0
$91$	13.7082	+	9.95959i	1.43701	+	1.04405i
$92$	−1.38197	−	4.25325i	−0.144080	−	0.443432i
$93$	6.61803			0.686258
$94$	0.527864	+	1.62460i	0.0544450	+	0.167565i
$95$		0			0
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	1.04508	−	3.21644i	0.106112	−	0.326580i	−0.883878	−	0.467718i	$-0.845076\pi$
$97$	1.04508	−	3.21644i	0.106112	−	0.326580i	0.989990	+	0.141138i	$0.0450762\pi$
$98$	−0.118034	+	0.0857567i	−0.0119232	+	0.00866274i
$99$	3.61803			0.363626
$100$		0			0
$101$	4.38197			0.436022			0.218011	−	0.975946i	$-0.430043\pi$
$101$	4.38197			0.436022			0.218011	+	0.975946i	$0.430043\pi$
$102$	−1.00000	+	0.726543i	−0.0990148	+	0.0719384i
$103$	−4.42705	+	13.6251i	−0.436210	+	1.34252i	0.455631	+	0.890169i	$0.349414\pi$
$103$	−4.42705	+	13.6251i	−0.436210	+	1.34252i	−0.891841	+	0.452348i	$0.850586\pi$
$104$	−2.00000	+	6.15537i	−0.196116	+	0.603583i
$105$		0			0
$106$	−0.645898	−	1.98787i	−0.0627352	−	0.193079i
$107$	11.6180			1.12316			0.561579	−	0.827423i	$-0.310194\pi$
$107$	11.6180			1.12316			0.561579	+	0.827423i	$0.310194\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−13.9443	−	10.1311i	−1.33562	−	0.970384i	−0.999593	−	0.0285313i	$-0.990917\pi$
$109$	−13.9443	−	10.1311i	−1.33562	−	0.970384i	−0.336026	−	0.941853i	$-0.609083\pi$
$110$		0			0
$111$	6.47214	−	4.70228i	0.614308	−	0.446321i
$112$	2.11803	+	1.53884i	0.200135	+	0.145407i
$113$	−15.5623	−	11.3067i	−1.46398	−	1.06364i	−0.982304	−	0.187292i	$-0.940029\pi$
$113$	−15.5623	−	11.3067i	−1.46398	−	1.06364i	−0.481674	−	0.876350i	$-0.659971\pi$
$114$	−4.61803	+	3.35520i	−0.432519	+	0.314243i
$115$		0			0
$116$	−6.85410	−	4.97980i	−0.636387	−	0.462363i
$117$	2.00000	+	6.15537i	0.184900	+	0.569064i
$118$	3.61803			0.333067
$119$	1.00000	+	3.07768i	0.0916698	+	0.282131i
$120$		0			0
$121$	0.645898	−	1.98787i	0.0587180	−	0.180715i
$122$	−0.854102	+	2.62866i	−0.0773268	+	0.237987i
$123$	−4.61803	+	3.35520i	−0.416394	+	0.302528i
$124$	6.61803			0.594317
$125$		0			0
$126$	2.61803			0.233233
$127$	11.0172	−	8.00448i	0.977620	−	0.710283i	0.0204448	−	0.999791i	$-0.493492\pi$
$127$	11.0172	−	8.00448i	0.977620	−	0.710283i	0.957176	+	0.289508i	$0.0934918\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	2.38197	−	7.33094i	0.209720	−	0.645453i
$130$		0			0
$131$	−5.52786	−	17.0130i	−0.482972	−	1.48643i	−0.834897	−	0.550406i	$-0.814473\pi$
$131$	−5.52786	−	17.0130i	−0.482972	−	1.48643i	0.351925	−	0.936028i	$-0.385527\pi$
$132$	3.61803			0.314909
$133$	4.61803	+	14.2128i	0.400434	+	1.23241i
$134$	1.23607	+	0.898056i	0.106780	+	0.0775802i
$135$		0			0
$136$	−1.00000	+	0.726543i	−0.0857493	+	0.0623005i
$137$	−9.85410	−	7.15942i	−0.841893	−	0.611671i	0.0810060	−	0.996714i	$-0.474187\pi$
$137$	−9.85410	−	7.15942i	−0.841893	−	0.611671i	−0.922899	+	0.385043i	$0.874187\pi$
$138$	−3.61803	−	2.62866i	−0.307988	−	0.223766i
$139$	−8.47214	+	6.15537i	−0.718597	+	0.522091i	−0.885936	−	0.463808i	$-0.846483\pi$
$139$	−8.47214	+	6.15537i	−0.718597	+	0.522091i	0.167339	+	0.985899i	$0.446483\pi$
$140$		0			0
$141$	1.38197	+	1.00406i	0.116383	+	0.0845569i
$142$	−1.70820	−	5.25731i	−0.143349	−	0.441184i
$143$	23.4164			1.95818
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$		0			0
$146$	1.09017	−	3.35520i	0.0902231	−	0.277678i
$147$	−0.0450850	+	0.138757i	−0.00371855	+	0.0114445i
$148$	6.47214	−	4.70228i	0.532006	−	0.386525i
$149$	22.0902			1.80970			0.904849	−	0.425733i	$-0.139984\pi$
$149$	22.0902			1.80970			0.904849	+	0.425733i	$0.139984\pi$
$150$		0			0
$151$	18.3262			1.49137			0.745684	−	0.666300i	$-0.232123\pi$
$151$	18.3262			1.49137			0.745684	+	0.666300i	$0.232123\pi$
$152$	−4.61803	+	3.35520i	−0.374572	+	0.272143i
$153$	−0.381966	+	1.17557i	−0.0308801	+	0.0950392i
$154$	2.92705	−	9.00854i	0.235868	−	0.725929i
$155$		0			0
$156$	2.00000	+	6.15537i	0.160128	+	0.492824i
$157$	−8.65248			−0.690543			−0.345271	−	0.938503i	$-0.612213\pi$
$157$	−8.65248			−0.690543			−0.345271	+	0.938503i	$0.612213\pi$
$158$	1.73607	+	5.34307i	0.138114	+	0.425072i
$159$	−1.69098	−	1.22857i	−0.134104	−	0.0974320i
$160$		0			0
$161$	−9.47214	+	6.88191i	−0.746509	+	0.542370i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	−0.381966	−	0.277515i	−0.0299179	−	0.0217366i	0.572726	−	0.819747i	$-0.305886\pi$
$163$	−0.381966	−	0.277515i	−0.0299179	−	0.0217366i	−0.602644	+	0.798010i	$0.705886\pi$
$164$	−4.61803	+	3.35520i	−0.360608	+	0.261997i
$165$		0			0
$166$	−1.73607	−	1.26133i	−0.134745	−	0.0978980i
$167$	−3.61803	−	11.1352i	−0.279972	−	0.861665i	−0.987861	−	0.155341i	$-0.950352\pi$
$167$	−3.61803	−	11.1352i	−0.279972	−	0.861665i	0.707889	−	0.706324i	$-0.249648\pi$
$168$	2.61803			0.201986
$169$	8.92705	+	27.4746i	0.686696	+	2.11343i
$170$		0			0
$171$	−1.76393	+	5.42882i	−0.134891	+	0.415153i
$172$	2.38197	−	7.33094i	0.181623	−	0.558979i
$173$	4.11803	−	2.99193i	0.313088	−	0.227472i	−0.420132	−	0.907463i	$-0.638016\pi$
$173$	4.11803	−	2.99193i	0.313088	−	0.227472i	0.733221	+	0.679991i	$0.238016\pi$
$174$	−8.47214			−0.642271
$175$		0			0
$176$	3.61803			0.272720
$177$	2.92705	−	2.12663i	0.220011	−	0.159847i
$178$	−1.09017	+	3.35520i	−0.0817117	+	0.251483i
$179$	3.04508	−	9.37181i	0.227600	−	0.700482i	−0.770417	−	0.637540i	$-0.779952\pi$
$179$	3.04508	−	9.37181i	0.227600	−	0.700482i	0.998017	−	0.0629414i	$-0.0200481\pi$
$180$		0			0
$181$	−2.05573	−	6.32688i	−0.152801	−	0.470273i	0.845130	−	0.534560i	$-0.179523\pi$
$181$	−2.05573	−	6.32688i	−0.152801	−	0.470273i	−0.997931	+	0.0642869i	$0.979523\pi$
$182$	16.9443			1.25599
$183$	0.854102	+	2.62866i	0.0631370	+	0.194316i
$184$	−3.61803	−	2.62866i	−0.266725	−	0.193787i
$185$		0			0
$186$	5.35410	−	3.88998i	0.392582	−	0.285227i
$187$	3.61803	+	2.62866i	0.264577	+	0.192226i
$188$	1.38197	+	1.00406i	0.100790	+	0.0732284i
$189$	2.11803	−	1.53884i	0.154064	−	0.111934i
$190$		0			0
$191$	−3.47214	−	2.52265i	−0.251235	−	0.182533i	0.455039	−	0.890472i	$-0.349625\pi$
$191$	−3.47214	−	2.52265i	−0.251235	−	0.182533i	−0.706274	+	0.707939i	$0.749625\pi$
$192$	0.309017	+	0.951057i	0.0223014	+	0.0686366i
$193$	−17.8541			−1.28517			−0.642583	−	0.766216i	$-0.722137\pi$
$193$	−17.8541			−1.28517			−0.642583	+	0.766216i	$0.722137\pi$
$194$	−1.04508	−	3.21644i	−0.0750327	−	0.230927i
$195$		0			0
$196$	−0.0450850	+	0.138757i	−0.00322036	+	0.00991123i
$197$	5.28115	−	16.2537i	0.376267	−	1.15803i	−0.566354	−	0.824162i	$-0.691646\pi$
$197$	5.28115	−	16.2537i	0.376267	−	1.15803i	0.942620	−	0.333867i	$-0.108354\pi$
$198$	2.92705	−	2.12663i	0.208016	−	0.151133i
$199$	19.5066			1.38278			0.691392	−	0.722480i	$-0.256998\pi$
$199$	19.5066			1.38278			0.691392	+	0.722480i	$0.256998\pi$
$200$		0			0
$201$	1.52786			0.107767
$202$	3.54508	−	2.57565i	0.249431	−	0.181222i
$203$	−6.85410	+	21.0948i	−0.481064	+	1.48056i
$204$	−0.381966	+	1.17557i	−0.0267430	+	0.0823064i
$205$		0			0
$206$	4.42705	+	13.6251i	0.308447	+	0.949303i
$207$	−4.47214			−0.310835
$208$	2.00000	+	6.15537i	0.138675	+	0.426798i
$209$	16.7082	+	12.1392i	1.15573	+	0.839687i
$210$		0			0
$211$	2.76393	−	2.00811i	0.190277	−	0.138244i	−0.488568	−	0.872526i	$-0.662481\pi$
$211$	2.76393	−	2.00811i	0.190277	−	0.138244i	0.678845	+	0.734281i	$0.262481\pi$
$212$	−1.69098	−	1.22857i	−0.116137	−	0.0843786i
$213$	−4.47214	−	3.24920i	−0.306426	−	0.222631i
$214$	9.39919	−	6.82891i	0.642515	−	0.466815i
$215$		0			0
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−5.35410	−	16.4782i	−0.363460	−	1.11862i
$218$	−17.2361			−1.16737
$219$	−1.09017	−	3.35520i	−0.0736669	−	0.226723i
$220$		0			0
$221$	−2.47214	+	7.60845i	−0.166294	+	0.511800i
$222$	2.47214	−	7.60845i	0.165919	−	0.510646i
$223$	−6.54508	+	4.75528i	−0.438291	+	0.318437i	−0.784956	−	0.619552i	$-0.787314\pi$
$223$	−6.54508	+	4.75528i	−0.438291	+	0.318437i	0.346664	+	0.937989i	$0.387314\pi$
$224$	2.61803			0.174925
$225$		0			0
$226$	−19.2361			−1.27956
$227$	−18.0172	+	13.0903i	−1.19584	+	0.868832i	−0.993870	−	0.110558i	$-0.964736\pi$
$227$	−18.0172	+	13.0903i	−1.19584	+	0.868832i	−0.201975	+	0.979391i	$0.564736\pi$
$228$	−1.76393	+	5.42882i	−0.116819	+	0.359533i
$229$	−1.70820	+	5.25731i	−0.112881	+	0.347413i	−0.991499	−	0.130113i	$-0.958466\pi$
$229$	−1.70820	+	5.25731i	−0.112881	+	0.347413i	0.878618	+	0.477525i	$0.158466\pi$
$230$		0			0
$231$	−2.92705	−	9.00854i	−0.192586	−	0.592718i
$232$	−8.47214			−0.556223
$233$	−5.76393	−	17.7396i	−0.377608	−	1.16216i	−0.941702	−	0.336447i	$-0.890775\pi$
$233$	−5.76393	−	17.7396i	−0.377608	−	1.16216i	0.564095	−	0.825710i	$-0.309225\pi$
$234$	5.23607	+	3.80423i	0.342292	+	0.248690i
$235$		0			0
$236$	2.92705	−	2.12663i	0.190535	−	0.138432i
$237$	4.54508	+	3.30220i	0.295235	+	0.214501i
$238$	2.61803	+	1.90211i	0.169702	+	0.123296i
$239$	−9.94427	+	7.22494i	−0.643241	+	0.467342i	−0.860962	−	0.508669i	$-0.830138\pi$
$239$	−9.94427	+	7.22494i	−0.643241	+	0.467342i	0.217721	+	0.976011i	$0.430138\pi$
$240$		0			0
$241$	−7.73607	−	5.62058i	−0.498324	−	0.362054i	0.310052	−	0.950719i	$-0.399653\pi$
$241$	−7.73607	−	5.62058i	−0.498324	−	0.362054i	−0.808376	+	0.588666i	$0.799653\pi$
$242$	−0.645898	−	1.98787i	−0.0415199	−	0.127785i
$243$	1.00000			0.0641500
$244$	0.854102	+	2.62866i	0.0546783	+	0.168282i
$245$		0			0
$246$	−1.76393	+	5.42882i	−0.112464	+	0.346129i
$247$	−11.4164	+	35.1361i	−0.726409	+	2.23566i
$248$	5.35410	−	3.88998i	0.339986	−	0.247014i
$249$	−2.14590			−0.135991
$250$		0			0
$251$	13.5623			0.856045			0.428023	−	0.903768i	$-0.359210\pi$
$251$	13.5623			0.856045			0.428023	+	0.903768i	$0.359210\pi$
$252$	2.11803	−	1.53884i	0.133424	−	0.0969379i
$253$	−5.00000	+	15.3884i	−0.314347	+	0.967462i
$254$	4.20820	−	12.9515i	0.264046	−	0.812651i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	22.0000			1.37232			0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000			1.37232			0.686161	+	0.727450i	$0.259294\pi$
$258$	−2.38197	−	7.33094i	−0.148295	−	0.456404i
$259$	−16.9443	−	12.3107i	−1.05287	−	0.764952i
$260$		0			0
$261$	−6.85410	+	4.97980i	−0.424258	+	0.308242i
$262$	−14.4721	−	10.5146i	−0.894092	−	0.649596i
$263$	−9.47214	−	6.88191i	−0.584077	−	0.424357i	0.256115	−	0.966646i	$-0.417558\pi$
$263$	−9.47214	−	6.88191i	−0.584077	−	0.424357i	−0.840192	+	0.542290i	$0.817558\pi$
$264$	2.92705	−	2.12663i	0.180148	−	0.130885i
$265$		0			0
$266$	12.0902	+	8.78402i	0.741296	+	0.538583i
$267$	1.09017	+	3.35520i	0.0667173	+	0.205335i
$268$	1.52786			0.0933292
$269$	−2.80902	−	8.64527i	−0.171269	−	0.527111i	0.828175	−	0.560470i	$-0.189380\pi$
$269$	−2.80902	−	8.64527i	−0.171269	−	0.527111i	−0.999443	+	0.0333590i	$0.989380\pi$
$270$		0			0
$271$	−5.57295	+	17.1518i	−0.338533	+	1.04190i	0.626423	+	0.779483i	$0.284518\pi$
$271$	−5.57295	+	17.1518i	−0.338533	+	1.04190i	−0.964956	+	0.262413i	$0.915482\pi$
$272$	−0.381966	+	1.17557i	−0.0231601	+	0.0712794i
$273$	13.7082	−	9.95959i	0.829658	−	0.602782i
$274$	−12.1803			−0.735841
$275$		0			0
$276$	−4.47214			−0.269191
$277$	13.7082	−	9.95959i	0.823646	−	0.598414i	−0.0941084	−	0.995562i	$-0.530000\pi$
$277$	13.7082	−	9.95959i	0.823646	−	0.598414i	0.917755	+	0.397148i	$0.130000\pi$
$278$	−3.23607	+	9.95959i	−0.194086	+	0.597337i
$279$	2.04508	−	6.29412i	0.122436	−	0.376819i
$280$		0			0
$281$	1.81966	+	5.60034i	0.108552	+	0.334088i	0.990548	−	0.137169i	$-0.0438004\pi$
$281$	1.81966	+	5.60034i	0.108552	+	0.334088i	−0.881996	+	0.471257i	$0.843800\pi$
$282$	1.70820			0.101722
$283$	−1.41641	−	4.35926i	−0.0841967	−	0.259131i	0.900091	−	0.435701i	$-0.143500\pi$
$283$	−1.41641	−	4.35926i	−0.0841967	−	0.259131i	−0.984288	+	0.176571i	$0.943500\pi$
$284$	−4.47214	−	3.24920i	−0.265372	−	0.192804i
$285$		0			0
$286$	18.9443	−	13.7638i	1.12020	−	0.813872i
$287$	12.0902	+	8.78402i	0.713660	+	0.518504i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	12.5172	−	9.09429i	0.736307	−	0.534958i
$290$		0			0
$291$	−2.73607	−	1.98787i	−0.160391	−	0.116531i
$292$	−1.09017	−	3.35520i	−0.0637974	−	0.196348i
$293$	22.0902			1.29052			0.645261	−	0.763962i	$-0.276749\pi$
$293$	22.0902			1.29052			0.645261	+	0.763962i	$0.276749\pi$
$294$	0.0450850	+	0.138757i	0.00262941	+	0.00809249i
$295$		0			0
$296$	2.47214	−	7.60845i	0.143690	−	0.442232i
$297$	1.11803	−	3.44095i	0.0648749	−	0.199664i
$298$	17.8713	−	12.9843i	1.03526	−	0.752159i
$299$	−28.9443			−1.67389
$300$		0			0
$301$	−20.1803			−1.16318
$302$	14.8262	−	10.7719i	0.853154	−	0.619853i
$303$	1.35410	−	4.16750i	0.0777911	−	0.239416i
$304$	−1.76393	+	5.42882i	−0.101168	+	0.311364i
$305$		0			0
$306$	0.381966	+	1.17557i	0.0218355	+	0.0672029i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$	−2.92705	−	9.00854i	−0.166784	−	0.513309i
$309$	11.5902	+	8.42075i	0.659342	+	0.479040i
$310$		0			0
$311$	0.854102	−	0.620541i	0.0484317	−	0.0351877i	−0.563306	−	0.826248i	$-0.690471\pi$
$311$	0.854102	−	0.620541i	0.0484317	−	0.0351877i	0.611738	+	0.791061i	$0.290471\pi$
$312$	5.23607	+	3.80423i	0.296434	+	0.215372i
$313$	−13.1631	−	9.56357i	−0.744023	−	0.540565i	0.149945	−	0.988694i	$-0.452090\pi$
$313$	−13.1631	−	9.56357i	−0.744023	−	0.540565i	−0.893969	+	0.448130i	$0.852090\pi$
$314$	−7.00000	+	5.08580i	−0.395033	+	0.287008i
$315$		0			0
$316$	4.54508	+	3.30220i	0.255681	+	0.185763i
$317$	6.35410	+	19.5559i	0.356882	+	1.09837i	0.954910	+	0.296895i	$0.0959510\pi$
$317$	6.35410	+	19.5559i	0.356882	+	1.09837i	−0.598028	+	0.801475i	$0.704049\pi$
$318$	−2.09017			−0.117211
$319$	9.47214	+	29.1522i	0.530338	+	1.63221i
$320$		0			0
$321$	3.59017	−	11.0494i	0.200384	−	0.616718i
$322$	−3.61803	+	11.1352i	−0.201625	+	0.620538i
$323$	−5.70820	+	4.14725i	−0.317613	+	0.230759i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−0.472136			−0.0261492
$327$	−13.9443	+	10.1311i	−0.771120	+	0.560251i
$328$	−1.76393	+	5.42882i	−0.0973969	+	0.299757i
$329$	1.38197	−	4.25325i	0.0761903	−	0.234489i
$330$		0			0
$331$	−5.56231	−	17.1190i	−0.305732	−	0.940946i	−0.979403	−	0.201915i	$-0.935284\pi$
$331$	−5.56231	−	17.1190i	−0.305732	−	0.940946i	0.673671	−	0.739031i	$-0.264716\pi$
$332$	−2.14590			−0.117771
$333$	−2.47214	−	7.60845i	−0.135472	−	0.416941i
$334$	−9.47214	−	6.88191i	−0.518292	−	0.376561i
$335$		0			0
$336$	2.11803	−	1.53884i	0.115548	−	0.0839507i
$337$	0.736068	+	0.534785i	0.0400962	+	0.0291316i	0.607653	−	0.794203i	$-0.292111\pi$
$337$	0.736068	+	0.534785i	0.0400962	+	0.0291316i	−0.567557	+	0.823334i	$0.692111\pi$
$338$	23.3713	+	16.9803i	1.27123	+	0.923604i
$339$	−15.5623	+	11.3067i	−0.845228	+	0.614094i
$340$		0			0
$341$	−19.3713	−	14.0741i	−1.04902	−	0.762155i
$342$	1.76393	+	5.42882i	0.0953825	+	0.293557i
$343$	18.7082			1.01015
$344$	−2.38197	−	7.33094i	−0.128427	−	0.395258i
$345$		0			0
$346$	1.57295	−	4.84104i	0.0845623	−	0.260256i
$347$	−6.35410	+	19.5559i	−0.341106	+	1.04982i	0.622529	+	0.782596i	$0.286105\pi$
$347$	−6.35410	+	19.5559i	−0.341106	+	1.04982i	−0.963636	+	0.267220i	$0.913895\pi$
$348$	−6.85410	+	4.97980i	−0.367418	+	0.266945i
$349$	−27.8885			−1.49284			−0.746420	−	0.665475i	$-0.768229\pi$
$349$	−27.8885			−1.49284			−0.746420	+	0.665475i	$0.768229\pi$
$350$		0			0
$351$	6.47214			0.345457
$352$	2.92705	−	2.12663i	0.156012	−	0.113350i
$353$	4.09017	−	12.5882i	0.217698	−	0.670005i	−0.781253	−	0.624214i	$-0.785419\pi$
$353$	4.09017	−	12.5882i	0.217698	−	0.670005i	0.998951	−	0.0457907i	$-0.0145807\pi$
$354$	1.11803	−	3.44095i	0.0594228	−	0.182885i
$355$		0			0
$356$	1.09017	+	3.35520i	0.0577789	+	0.177825i
$357$	3.23607			0.171271
$358$	−3.04508	−	9.37181i	−0.160938	−	0.495315i
$359$	−17.9443	−	13.0373i	−0.947062	−	0.688081i	0.00304782	−	0.999995i	$-0.499030\pi$
$359$	−17.9443	−	13.0373i	−0.947062	−	0.688081i	−0.950110	+	0.311914i	$0.899030\pi$
$360$		0			0
$361$	−10.9894	+	7.98424i	−0.578387	+	0.420223i
$362$	−5.38197	−	3.91023i	−0.282870	−	0.205517i
$363$	−1.69098	−	1.22857i	−0.0887536	−	0.0644833i
$364$	13.7082	−	9.95959i	0.718505	−	0.522025i
$365$		0			0
$366$	2.23607	+	1.62460i	0.116881	+	0.0849191i
$367$	9.46149	+	29.1195i	0.493886	+	1.52002i	0.818686	+	0.574242i	$0.194703\pi$
$367$	9.46149	+	29.1195i	0.493886	+	1.52002i	−0.324800	+	0.945783i	$0.605297\pi$
$368$	−4.47214			−0.233126
$369$	1.76393	+	5.42882i	0.0918266	+	0.282613i
$370$		0			0
$371$	−1.69098	+	5.20431i	−0.0877915	+	0.270194i
$372$	2.04508	−	6.29412i	0.106033	−	0.326335i
$373$	−9.32624	+	6.77591i	−0.482894	+	0.350843i	−0.802445	−	0.596726i	$-0.796468\pi$
$373$	−9.32624	+	6.77591i	−0.482894	+	0.350843i	0.319551	+	0.947569i	$0.396468\pi$
$374$	4.47214			0.231249
$375$		0			0
$376$	1.70820			0.0880939
$377$	−44.3607	+	32.2299i	−2.28469	+	1.65993i
$378$	0.809017	−	2.48990i	0.0416113	−	0.128067i
$379$	−6.23607	+	19.1926i	−0.320325	+	0.985860i	0.653181	+	0.757201i	$0.273434\pi$
$379$	−6.23607	+	19.1926i	−0.320325	+	0.985860i	−0.973507	+	0.228658i	$0.926566\pi$
$380$		0			0
$381$	−4.20820	−	12.9515i	−0.215593	−	0.663526i
$382$	−4.29180			−0.219587
$383$	6.18034	+	19.0211i	0.315801	+	0.971934i	0.975424	+	0.220338i	$0.0707160\pi$
$383$	6.18034	+	19.0211i	0.315801	+	0.971934i	−0.659623	+	0.751597i	$0.729284\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$		0			0
$386$	−14.4443	+	10.4944i	−0.735194	+	0.534150i
$387$	−6.23607	−	4.53077i	−0.316997	−	0.230312i
$388$	−2.73607	−	1.98787i	−0.138903	−	0.100919i
$389$	10.0172	−	7.27794i	0.507893	−	0.369006i	−0.304131	−	0.952630i	$-0.598366\pi$
$389$	10.0172	−	7.27794i	0.507893	−	0.369006i	0.812024	+	0.583624i	$0.198366\pi$
$390$		0			0
$391$	−4.47214	−	3.24920i	−0.226166	−	0.164319i
$392$	0.0450850	+	0.138757i	0.00227713	+	0.00700830i
$393$	−17.8885			−0.902358
$394$	−5.28115	−	16.2537i	−0.266061	−	0.818850i
$395$		0			0
$396$	1.11803	−	3.44095i	0.0561833	−	0.172914i
$397$	9.50658	−	29.2582i	0.477121	−	1.46843i	−0.365954	−	0.930633i	$-0.619257\pi$
$397$	9.50658	−	29.2582i	0.477121	−	1.46843i	0.843075	−	0.537796i	$-0.180743\pi$
$398$	15.7812	−	11.4657i	0.791038	−	0.574723i
$399$	14.9443			0.748149
$400$		0			0
$401$	25.7082			1.28381			0.641903	−	0.766786i	$-0.278145\pi$
$401$	25.7082			1.28381			0.641903	+	0.766786i	$0.278145\pi$
$402$	1.23607	−	0.898056i	0.0616495	−	0.0447910i
$403$	13.2361	−	40.7364i	0.659336	−	2.02923i
$404$	1.35410	−	4.16750i	0.0673691	−	0.207341i
$405$		0			0
$406$	6.85410	+	21.0948i	0.340163	+	1.04692i
$407$	−28.9443			−1.43471
$408$	0.381966	+	1.17557i	0.0189101	+	0.0581994i
$409$	−4.69098	−	3.40820i	−0.231954	−	0.168525i	0.465737	−	0.884923i	$-0.345789\pi$
$409$	−4.69098	−	3.40820i	−0.231954	−	0.168525i	−0.697691	+	0.716399i	$0.745789\pi$
$410$		0			0
$411$	−9.85410	+	7.15942i	−0.486067	+	0.353148i
$412$	11.5902	+	8.42075i	0.571007	+	0.414861i
$413$	−7.66312	−	5.56758i	−0.377077	−	0.273963i
$414$	−3.61803	+	2.62866i	−0.177817	+	0.129191i
$415$		0			0
$416$	5.23607	+	3.80423i	0.256719	+	0.186518i
$417$	3.23607	+	9.95959i	0.158471	+	0.487723i
$418$	20.6525			1.01015
$419$	−0.954915	−	2.93893i	−0.0466507	−	0.143576i	0.925018	−	0.379923i	$-0.124050\pi$
$419$	−0.954915	−	2.93893i	−0.0466507	−	0.143576i	−0.971669	+	0.236347i	$0.924050\pi$
$420$		0			0
$421$	−7.03444	+	21.6498i	−0.342838	+	1.05515i	0.619893	+	0.784686i	$0.287176\pi$
$421$	−7.03444	+	21.6498i	−0.342838	+	1.05515i	−0.962731	+	0.270460i	$0.912824\pi$
$422$	1.05573	−	3.24920i	0.0513920	−	0.158168i
$423$	1.38197	−	1.00406i	0.0671935	−	0.0488189i
$424$	−2.09017			−0.101508
$425$		0			0
$426$	−5.52786			−0.267826
$427$	5.85410	−	4.25325i	0.283300	−	0.205829i
$428$	3.59017	−	11.0494i	0.173537	−	0.534093i
$429$	7.23607	−	22.2703i	0.349361	−	1.07522i
$430$		0			0
$431$	5.20163	+	16.0090i	0.250554	+	0.771124i	0.994673	+	0.103078i	$0.0328692\pi$
$431$	5.20163	+	16.0090i	0.250554	+	0.771124i	−0.744120	+	0.668046i	$0.767131\pi$
$432$	1.00000			0.0481125
$433$	−4.79180	−	14.7476i	−0.230279	−	0.708726i	−0.997713	−	0.0675976i	$-0.978467\pi$
$433$	−4.79180	−	14.7476i	−0.230279	−	0.708726i	0.767434	−	0.641128i	$-0.221533\pi$
$434$	−14.0172	−	10.1841i	−0.672848	−	0.488853i
$435$		0			0
$436$	−13.9443	+	10.1311i	−0.667810	+	0.485192i
$437$	−20.6525	−	15.0049i	−0.987942	−	0.717782i
$438$	−2.85410	−	2.07363i	−0.136374	−	0.0990817i
$439$	19.0172	−	13.8168i	0.907642	−	0.659441i	−0.0327751	−	0.999463i	$-0.510434\pi$
$439$	19.0172	−	13.8168i	0.907642	−	0.659441i	0.940418	+	0.340022i	$0.110434\pi$
$440$		0			0
$441$	0.118034	+	0.0857567i	0.00562067	+	0.00408365i
$442$	2.47214	+	7.60845i	0.117588	+	0.361897i
$443$	−16.6180			−0.789547			−0.394773	−	0.918779i	$-0.629177\pi$
$443$	−16.6180			−0.789547			−0.394773	+	0.918779i	$0.629177\pi$
$444$	−2.47214	−	7.60845i	−0.117322	−	0.361081i
$445$		0			0
$446$	−2.50000	+	7.69421i	−0.118378	+	0.364331i
$447$	6.82624	−	21.0090i	0.322870	−	0.993692i
$448$	2.11803	−	1.53884i	0.100068	−	0.0727034i
$449$	−27.7082			−1.30763			−0.653815	−	0.756654i	$-0.726833\pi$
$449$	−27.7082			−1.30763			−0.653815	+	0.756654i	$0.726833\pi$
$450$		0			0
$451$	20.6525			0.972487
$452$	−15.5623	+	11.3067i	−0.731989	+	0.531821i
$453$	5.66312	−	17.4293i	0.266077	−	0.818899i
$454$	−6.88197	+	21.1805i	−0.322987	+	0.994051i
$455$		0			0
$456$	1.76393	+	5.42882i	0.0826037	+	0.254228i
$457$	4.09017			0.191330			0.0956650	−	0.995414i	$-0.469502\pi$
$457$	4.09017			0.191330			0.0956650	+	0.995414i	$0.469502\pi$
$458$	1.70820	+	5.25731i	0.0798191	+	0.245658i
$459$	1.00000	+	0.726543i	0.0466760	+	0.0339121i
$460$		0			0
$461$	−6.11803	+	4.44501i	−0.284945	+	0.207025i	−0.721072	−	0.692861i	$-0.756350\pi$
$461$	−6.11803	+	4.44501i	−0.284945	+	0.207025i	0.436126	+	0.899885i	$0.356350\pi$
$462$	−7.66312	−	5.56758i	−0.356521	−	0.259027i
$463$	−18.4721	−	13.4208i	−0.858473	−	0.623717i	0.0689961	−	0.997617i	$-0.478020\pi$
$463$	−18.4721	−	13.4208i	−0.858473	−	0.623717i	−0.927469	+	0.373900i	$0.878020\pi$
$464$	−6.85410	+	4.97980i	−0.318194	+	0.231181i
$465$		0			0
$466$	−15.0902	−	10.9637i	−0.699039	−	0.507881i
$467$	−3.29837	−	10.1514i	−0.152631	−	0.469749i	0.845283	−	0.534320i	$-0.179432\pi$
$467$	−3.29837	−	10.1514i	−0.152631	−	0.469749i	−0.997913	+	0.0645710i	$0.979432\pi$
$468$	6.47214			0.299175
$469$	−1.23607	−	3.80423i	−0.0570763	−	0.175663i
$470$		0			0
$471$	−2.67376	+	8.22899i	−0.123200	+	0.379172i
$472$	1.11803	−	3.44095i	0.0514617	−	0.158383i
$473$	−22.5623	+	16.3925i	−1.03742	+	0.753727i
$474$	5.61803			0.258045
$475$		0			0
$476$	3.23607			0.148325
$477$	−1.69098	+	1.22857i	−0.0774248	+	0.0562524i
$478$	−3.79837	+	11.6902i	−0.173734	+	0.534697i
$479$	−9.00000	+	27.6992i	−0.411220	+	1.26561i	0.504368	+	0.863489i	$0.331726\pi$
$479$	−9.00000	+	27.6992i	−0.411220	+	1.26561i	−0.915588	+	0.402117i	$0.868274\pi$
$480$		0			0
$481$	−16.0000	−	49.2429i	−0.729537	−	2.24528i
$482$	−9.56231			−0.435551
$483$	3.61803	+	11.1352i	0.164626	+	0.506667i
$484$	−1.69098	−	1.22857i	−0.0768629	−	0.0558441i
$485$		0			0
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	14.3992	+	10.4616i	0.652489	+	0.474061i	0.864118	−	0.503289i	$-0.167877\pi$
$487$	14.3992	+	10.4616i	0.652489	+	0.474061i	−0.211629	+	0.977350i	$0.567877\pi$
$488$	2.23607	+	1.62460i	0.101222	+	0.0735421i
$489$	−0.381966	+	0.277515i	−0.0172731	+	0.0125496i
$490$		0			0
$491$	20.4443	+	14.8536i	0.922637	+	0.670335i	0.944179	−	0.329433i	$-0.106858\pi$
$491$	20.4443	+	14.8536i	0.922637	+	0.670335i	−0.0215419	+	0.999768i	$0.506858\pi$
$492$	1.76393	+	5.42882i	0.0795242	+	0.244750i
$493$	−10.4721			−0.471641
$494$	11.4164	+	35.1361i	0.513648	+	1.58085i
$495$		0			0
$496$	2.04508	−	6.29412i	0.0918270	−	0.282615i
$497$	−4.47214	+	13.7638i	−0.200603	+	0.617392i
$498$	−1.73607	+	1.26133i	−0.0777951	+	0.0565214i
$499$	35.5967			1.59353			0.796765	−	0.604290i	$-0.206543\pi$
$499$	35.5967			1.59353			0.796765	+	0.604290i	$0.206543\pi$
$500$		0			0
$501$	−11.7082			−0.523084
$502$	10.9721	−	7.97172i	0.489710	−	0.355795i
$503$	−7.38197	+	22.7194i	−0.329146	+	1.01301i	0.640389	+	0.768051i	$0.278773\pi$
$503$	−7.38197	+	22.7194i	−0.329146	+	1.01301i	−0.969534	+	0.244955i	$0.921227\pi$
$504$	0.809017	−	2.48990i	0.0360365	−	0.110909i
$505$		0			0
$506$	5.00000	+	15.3884i	0.222277	+	0.684099i
$507$	28.8885			1.28299
$508$	−4.20820	−	12.9515i	−0.186709	−	0.574631i
$509$	14.1631	+	10.2901i	0.627769	+	0.456101i	0.855627	−	0.517593i	$-0.173172\pi$
$509$	14.1631	+	10.2901i	0.627769	+	0.456101i	−0.227857	+	0.973694i	$0.573172\pi$
$510$		0			0
$511$	−7.47214	+	5.42882i	−0.330548	+	0.240157i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	4.61803	+	3.35520i	0.203891	+	0.148136i
$514$	17.7984	−	12.9313i	0.785053	−	0.570374i
$515$		0			0
$516$	−6.23607	−	4.53077i	−0.274528	−	0.199456i
$517$	−1.90983	−	5.87785i	−0.0839942	−	0.258508i
$518$	−20.9443			−0.920238
$519$	−1.57295	−	4.84104i	−0.0690448	−	0.212498i
$520$		0			0
$521$	4.38197	−	13.4863i	0.191977	−	0.590846i	−0.808021	−	0.589153i	$-0.799461\pi$
$521$	4.38197	−	13.4863i	0.191977	−	0.590846i	0.999999	−	0.00169226i	$-0.000538663\pi$
$522$	−2.61803	+	8.05748i	−0.114588	+	0.352666i
$523$	8.94427	−	6.49839i	0.391106	−	0.284155i	−0.374803	−	0.927105i	$-0.622290\pi$
$523$	8.94427	−	6.49839i	0.391106	−	0.284155i	0.765908	+	0.642950i	$0.222290\pi$
$524$	−17.8885			−0.781465
$525$		0			0
$526$	−11.7082			−0.510502
$527$	6.61803	−	4.80828i	0.288286	−	0.209452i
$528$	1.11803	−	3.44095i	0.0486562	−	0.149748i
$529$	−0.927051	+	2.85317i	−0.0403066	+	0.124051i
$530$		0			0
$531$	−1.11803	−	3.44095i	−0.0485185	−	0.149325i
$532$	14.9443			0.647916
$533$	11.4164	+	35.1361i	0.494500	+	1.52191i
$534$	2.85410	+	2.07363i	0.123509	+	0.0897346i
$535$		0			0
$536$	1.23607	−	0.898056i	0.0533900	−	0.0387901i
$537$	−7.97214	−	5.79210i	−0.344023	−	0.249947i
$538$	−7.35410	−	5.34307i	−0.317058	−	0.230356i
$539$	0.427051	−	0.310271i	0.0183944	−	0.0133643i
$540$		0			0
$541$	21.1803	+	15.3884i	0.910614	+	0.661600i	0.941170	−	0.337933i	$-0.109728\pi$
$541$	21.1803	+	15.3884i	0.910614	+	0.661600i	−0.0305561	+	0.999533i	$0.509728\pi$
$542$	5.57295	+	17.1518i	0.239379	+	0.736732i
$543$	−6.65248			−0.285485
$544$	0.381966	+	1.17557i	0.0163767	+	0.0504022i
$545$		0			0
$546$	5.23607	−	16.1150i	0.224083	−	0.689657i
$547$	−3.00000	+	9.23305i	−0.128271	+	0.394777i	−0.994483	−	0.104900i	$-0.966548\pi$
$547$	−3.00000	+	9.23305i	−0.128271	+	0.394777i	0.866212	+	0.499677i	$0.166548\pi$
$548$	−9.85410	+	7.15942i	−0.420946	+	0.305835i
$549$	2.76393			0.117962
$550$		0			0
$551$	−48.3607			−2.06023
$552$	−3.61803	+	2.62866i	−0.153994	+	0.111883i
$553$	4.54508	−	13.9883i	0.193277	−	0.594844i
$554$	5.23607	−	16.1150i	0.222459	−	0.684659i
$555$		0			0
$556$	3.23607	+	9.95959i	0.137240	+	0.422381i
$557$	18.3262			0.776508			0.388254	−	0.921552i	$-0.373078\pi$
$557$	18.3262			0.776508			0.388254	+	0.921552i	$0.373078\pi$
$558$	−2.04508	−	6.29412i	−0.0865754	−	0.266452i
$559$	−40.3607	−	29.3238i	−1.70707	−	1.24026i
$560$		0			0
$561$	3.61803	−	2.62866i	0.152754	−	0.110982i
$562$	4.76393	+	3.46120i	0.200954	+	0.146002i
$563$	17.2082	+	12.5025i	0.725239	+	0.526917i	0.888054	−	0.459739i	$-0.152057\pi$
$563$	17.2082	+	12.5025i	0.725239	+	0.526917i	−0.162815	+	0.986657i	$0.552057\pi$
$564$	1.38197	−	1.00406i	0.0581913	−	0.0422784i
$565$		0			0
$566$	−3.70820	−	2.69417i	−0.155867	−	0.113244i
$567$	−0.809017	−	2.48990i	−0.0339755	−	0.104566i
$568$	−5.52786			−0.231944
$569$	−8.58359	−	26.4176i	−0.359843	−	1.10748i	−0.953148	−	0.302505i	$-0.902177\pi$
$569$	−8.58359	−	26.4176i	−0.359843	−	1.10748i	0.593305	−	0.804978i	$-0.297823\pi$
$570$		0			0
$571$	2.43769	−	7.50245i	0.102014	−	0.313968i	−0.887004	−	0.461762i	$-0.847217\pi$
$571$	2.43769	−	7.50245i	0.102014	−	0.313968i	0.989018	+	0.147794i	$0.0472174\pi$
$572$	7.23607	−	22.2703i	0.302555	−	0.931169i
$573$	−3.47214	+	2.52265i	−0.145051	+	0.105385i
$574$	14.9443			0.623762
$575$		0			0
$576$	1.00000			0.0416667
$577$	7.26393	−	5.27756i	0.302401	−	0.219708i	−0.426228	−	0.904616i	$-0.640158\pi$
$577$	7.26393	−	5.27756i	0.302401	−	0.219708i	0.728629	+	0.684908i	$0.240158\pi$
$578$	4.78115	−	14.7149i	0.198870	−	0.612058i
$579$	−5.51722	+	16.9803i	−0.229288	+	0.705676i
$580$		0			0
$581$	1.73607	+	5.34307i	0.0720242	+	0.221668i
$582$	−3.38197			−0.140187
$583$	2.33688	+	7.19218i	0.0967837	+	0.297870i
$584$	−2.85410	−	2.07363i	−0.118104	−	0.0858073i
$585$		0			0
$586$	17.8713	−	12.9843i	0.738258	−	0.536376i
$587$	−0.781153	−	0.567541i	−0.0322416	−	0.0234249i	0.571548	−	0.820569i	$-0.306343\pi$
$587$	−0.781153	−	0.567541i	−0.0322416	−	0.0234249i	−0.603789	+	0.797144i	$0.706343\pi$
$588$	0.118034	+	0.0857567i	0.00486764	+	0.00353655i
$589$	30.5623	−	22.2048i	1.25930	−	0.914933i
$590$		0			0
$591$	−13.8262	−	10.0453i	−0.568735	−	0.413210i
$592$	−2.47214	−	7.60845i	−0.101604	−	0.312705i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	−1.11803	−	3.44095i	−0.0458735	−	0.141184i
$595$		0			0
$596$	6.82624	−	21.0090i	0.279614	−	0.860562i
$597$	6.02786	−	18.5519i	0.246704	−	0.759277i
$598$	−23.4164	+	17.0130i	−0.957568	+	0.695714i
$599$	0.472136			0.0192910			0.00964548	−	0.999953i	$-0.496930\pi$
$599$	0.472136			0.0192910			0.00964548	+	0.999953i	$0.496930\pi$
$600$		0			0
$601$	−7.72949			−0.315292			−0.157646	−	0.987496i	$-0.550391\pi$
$601$	−7.72949			−0.315292			−0.157646	+	0.987496i	$0.550391\pi$
$602$	−16.3262	+	11.8617i	−0.665408	+	0.483447i
$603$	0.472136	−	1.45309i	0.0192269	−	0.0591742i
$604$	5.66312	−	17.4293i	0.230429	−	0.709188i
$605$		0			0
$606$	−1.35410	−	4.16750i	−0.0550066	−	0.169293i
$607$	−6.56231			−0.266356			−0.133178	−	0.991092i	$-0.542518\pi$
$607$	−6.56231			−0.266356			−0.133178	+	0.991092i	$0.542518\pi$
$608$	1.76393	+	5.42882i	0.0715369	+	0.220168i
$609$	17.9443	+	13.0373i	0.727139	+	0.528297i
$610$		0			0
$611$	8.94427	−	6.49839i	0.361847	−	0.262897i
$612$	1.00000	+	0.726543i	0.0404226	+	0.0293687i
$613$	39.0344	+	28.3602i	1.57659	+	1.14546i	0.920481	+	0.390788i	$0.127797\pi$
$613$	39.0344	+	28.3602i	1.57659	+	1.14546i	0.656105	+	0.754669i	$0.272203\pi$
$614$	−8.09017	+	5.87785i	−0.326493	+	0.237211i
$615$		0			0
$616$	−7.66312	−	5.56758i	−0.308756	−	0.224324i
$617$	−0.652476	−	2.00811i	−0.0262677	−	0.0808436i	0.937063	−	0.349160i	$-0.113533\pi$
$617$	−0.652476	−	2.00811i	−0.0262677	−	0.0808436i	−0.963331	+	0.268316i	$0.913533\pi$
$618$	14.3262			0.576286
$619$	−2.90983	−	8.95554i	−0.116956	−	0.359953i	0.875394	−	0.483410i	$-0.160602\pi$
$619$	−2.90983	−	8.95554i	−0.116956	−	0.359953i	−0.992350	+	0.123457i	$0.960602\pi$
$620$		0			0
$621$	−1.38197	+	4.25325i	−0.0554564	+	0.170677i
$622$	0.326238	−	1.00406i	0.0130809	−	0.0402590i
$623$	7.47214	−	5.42882i	0.299365	−	0.217501i
$624$	6.47214			0.259093
$625$		0			0
$626$	−16.2705			−0.650300
$627$	16.7082	−	12.1392i	0.667261	−	0.484794i
$628$	−2.67376	+	8.22899i	−0.106695	+	0.328373i
$629$	3.05573	−	9.40456i	0.121840	−	0.374985i
$630$		0			0
$631$	14.3607	+	44.1976i	0.571690	+	1.75948i	0.647184	+	0.762334i	$0.275946\pi$
$631$	14.3607	+	44.1976i	0.571690	+	1.75948i	−0.0754947	+	0.997146i	$0.524054\pi$
$632$	5.61803			0.223473
$633$	−1.05573	−	3.24920i	−0.0419614	−	0.129144i
$634$	16.6353	+	12.0862i	0.660670	+	0.480005i
$635$		0			0
$636$	−1.69098	+	1.22857i	−0.0670518	+	0.0487160i
$637$	0.763932	+	0.555029i	0.0302681	+	0.0219911i
$638$	24.7984	+	18.0171i	0.981777	+	0.713303i
$639$	−4.47214	+	3.24920i	−0.176915	+	0.128536i
$640$		0			0
$641$	11.1803	+	8.12299i	0.441597	+	0.320839i	0.786269	−	0.617884i	$-0.212010\pi$
$641$	11.1803	+	8.12299i	0.441597	+	0.320839i	−0.344672	+	0.938723i	$0.612010\pi$
$642$	−3.59017	−	11.0494i	−0.141693	−	0.436085i
$643$	−21.8885			−0.863200			−0.431600	−	0.902065i	$-0.642051\pi$
$643$	−21.8885			−0.863200			−0.431600	+	0.902065i	$0.642051\pi$
$644$	3.61803	+	11.1352i	0.142571	+	0.438787i
$645$		0			0
$646$	−2.18034	+	6.71040i	−0.0857843	+	0.264017i
$647$	7.09017	−	21.8213i	0.278743	−	0.857884i	−0.709461	−	0.704744i	$-0.751062\pi$
$647$	7.09017	−	21.8213i	0.278743	−	0.857884i	0.988205	−	0.153139i	$-0.0489383\pi$
$648$	0.809017	−	0.587785i	0.0317812	−	0.0230904i
$649$	−13.0902			−0.513834
$650$		0			0
$651$	−17.3262			−0.679069
$652$	−0.381966	+	0.277515i	−0.0149589	+	0.0108683i
$653$	1.19098	−	3.66547i	0.0466068	−	0.143441i	−0.925045	−	0.379858i	$-0.875973\pi$
$653$	1.19098	−	3.66547i	0.0466068	−	0.143441i	0.971652	+	0.236417i	$0.0759730\pi$
$654$	−5.32624	+	16.3925i	−0.208272	+	0.640996i
$655$		0			0
$656$	1.76393	+	5.42882i	0.0688700	+	0.211960i
$657$	−3.52786			−0.137635
$658$	−1.38197	−	4.25325i	−0.0538746	−	0.165809i
$659$	16.6803	+	12.1190i	0.649774	+	0.472088i	0.863194	−	0.504872i	$-0.168460\pi$
$659$	16.6803	+	12.1190i	0.649774	+	0.472088i	−0.213420	+	0.976960i	$0.568460\pi$
$660$		0			0
$661$	24.6525	−	17.9111i	0.958870	−	0.696660i	0.00598211	−	0.999982i	$-0.498096\pi$
$661$	24.6525	−	17.9111i	0.958870	−	0.696660i	0.952888	+	0.303322i	$0.0980958\pi$
$662$	−14.5623	−	10.5801i	−0.565980	−	0.411209i
$663$	6.47214	+	4.70228i	0.251357	+	0.182622i
$664$	−1.73607	+	1.26133i	−0.0673725	+	0.0489490i
$665$		0			0
$666$	−6.47214	−	4.70228i	−0.250790	−	0.182210i
$667$	−11.7082	−	36.0341i	−0.453343	−	1.39525i
$668$	−11.7082			−0.453004
$669$	2.50000	+	7.69421i	0.0966556	+	0.297475i
$670$		0			0
$671$	3.09017	−	9.51057i	0.119295	−	0.367151i
$672$	0.809017	−	2.48990i	0.0312085	−	0.0960499i
$673$	−25.4443	+	18.4863i	−0.980805	+	0.712596i	−0.957888	−	0.287141i	$-0.907295\pi$
$673$	−25.4443	+	18.4863i	−0.980805	+	0.712596i	−0.0229163	+	0.999737i	$0.507295\pi$
$674$	0.909830			0.0350453
$675$		0			0
$676$	28.8885			1.11110
$677$	23.5344	−	17.0988i	0.904502	−	0.657159i	−0.0351163	−	0.999383i	$-0.511180\pi$
$677$	23.5344	−	17.0988i	0.904502	−	0.657159i	0.939618	+	0.342224i	$0.111180\pi$
$678$	−5.94427	+	18.2946i	−0.228288	+	0.702599i
$679$	−2.73607	+	8.42075i	−0.105001	+	0.323159i
$680$		0			0
$681$	6.88197	+	21.1805i	0.263718	+	0.811639i
$682$	−23.9443			−0.916874
$683$	−10.3541	−	31.8666i	−0.396189	−	1.21934i	−0.928032	−	0.372501i	$-0.878500\pi$
$683$	−10.3541	−	31.8666i	−0.396189	−	1.21934i	0.531843	−	0.846843i	$-0.321500\pi$
$684$	4.61803	+	3.35520i	0.176575	+	0.128289i
$685$		0			0
$686$	15.1353	−	10.9964i	0.577867	−	0.419845i
$687$	4.47214	+	3.24920i	0.170623	+	0.123965i
$688$	−6.23607	−	4.53077i	−0.237748	−	0.172734i
$689$	−10.9443	+	7.95148i	−0.416944	+	0.302927i
$690$		0			0
$691$	−9.09017	−	6.60440i	−0.345806	−	0.251243i	0.401301	−	0.915946i	$-0.368558\pi$
$691$	−9.09017	−	6.60440i	−0.345806	−	0.251243i	−0.747108	+	0.664703i	$0.768558\pi$
$692$	−1.57295	−	4.84104i	−0.0597945	−	0.184029i
$693$	−9.47214			−0.359817
$694$	6.35410	+	19.5559i	0.241198	+	0.742332i
$695$		0			0
$696$	−2.61803	+	8.05748i	−0.0992363	+	0.305418i
$697$	−2.18034	+	6.71040i	−0.0825863	+	0.254174i
$698$	−22.5623	+	16.3925i	−0.853996	+	0.620464i
$699$	−18.6525			−0.705501
$700$		0			0
$701$	40.8328			1.54223			0.771117	−	0.636693i	$-0.219698\pi$
$701$	40.8328			1.54223			0.771117	+	0.636693i	$0.219698\pi$
$702$	5.23607	−	3.80423i	0.197623	−	0.143581i
$703$	14.1115	−	43.4306i	0.532224	−	1.63802i
$704$	1.11803	−	3.44095i	0.0421375	−	0.129686i
$705$		0			0
$706$	−4.09017	−	12.5882i	−0.153936	−	0.473765i
$707$	−11.4721			−0.431454
$708$	−1.11803	−	3.44095i	−0.0420183	−	0.129319i
$709$	35.3607	+	25.6910i	1.32800	+	0.964847i	0.999795	+	0.0202400i	$0.00644302\pi$
$709$	35.3607	+	25.6910i	1.32800	+	0.964847i	0.328203	+	0.944607i	$0.393557\pi$
$710$		0			0
$711$	4.54508	−	3.30220i	0.170454	−	0.123842i
$712$	2.85410	+	2.07363i	0.106962	+	0.0777124i
$713$	23.9443	+	17.3965i	0.896720	+	0.651505i
$714$	2.61803	−	1.90211i	0.0979775	−	0.0711848i
$715$		0			0
$716$	−7.97214	−	5.79210i	−0.297933	−	0.216461i
$717$	3.79837	+	11.6902i	0.141853	+	0.436578i
$718$	−22.1803			−0.827763
$719$	−5.12461	−	15.7719i	−0.191116	−	0.588194i	−1.00000		0.000225882i	$-0.999928\pi$
$719$	−5.12461	−	15.7719i	−0.191116	−	0.588194i	0.808884	−	0.587968i	$-0.200072\pi$
$720$		0			0
$721$	11.5902	−	35.6709i	0.431640	−	1.32845i
$722$	−4.19756	+	12.9188i	−0.156217	+	0.480787i
$723$	−7.73607	+	5.62058i	−0.287707	+	0.209032i
$724$	−6.65248			−0.247237
$725$		0			0
$726$	−2.09017			−0.0775735
$727$	−6.94427	+	5.04531i	−0.257549	+	0.187120i	−0.709066	−	0.705142i	$-0.750883\pi$
$727$	−6.94427	+	5.04531i	−0.257549	+	0.187120i	0.451517	+	0.892263i	$0.350883\pi$
$728$	5.23607	−	16.1150i	0.194062	−	0.597260i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−2.94427	−	9.06154i	−0.108898	−	0.335153i
$732$	2.76393			0.102158
$733$	11.0902	+	34.1320i	0.409625	+	1.26070i	0.916971	+	0.398953i	$0.130626\pi$
$733$	11.0902	+	34.1320i	0.409625	+	1.26070i	−0.507346	+	0.861742i	$0.669374\pi$
$734$	24.7705	+	17.9968i	0.914296	+	0.664275i
$735$		0			0
$736$	−3.61803	+	2.62866i	−0.133363	+	0.0968935i
$737$	−4.47214	−	3.24920i	−0.164733	−	0.119686i
$738$	4.61803	+	3.35520i	0.169992	+	0.123507i
$739$	38.9787	−	28.3197i	1.43386	−	1.04176i	0.444573	−	0.895743i	$-0.353356\pi$
$739$	38.9787	−	28.3197i	1.43386	−	1.04176i	0.989283	−	0.146014i	$-0.0466444\pi$
$740$		0			0
$741$	29.8885	+	21.7153i	1.09798	+	0.797731i
$742$	1.69098	+	5.20431i	0.0620779	+	0.191056i
$743$	39.0132			1.43125			0.715627	−	0.698483i	$-0.246141\pi$
$743$	39.0132			1.43125			0.715627	+	0.698483i	$0.246141\pi$
$744$	−2.04508	−	6.29412i	−0.0749765	−	0.230754i
$745$		0			0
$746$	−3.56231	+	10.9637i	−0.130425	+	0.401408i
$747$	−0.663119	+	2.04087i	−0.0242623	+	0.0746715i
$748$	3.61803	−	2.62866i	0.132288	−	0.0961132i
$749$	−30.4164			−1.11139
$750$		0			0
$751$	24.7984			0.904906			0.452453	−	0.891788i	$-0.350549\pi$
$751$	24.7984			0.904906			0.452453	+	0.891788i	$0.350549\pi$
$752$	1.38197	−	1.00406i	0.0503951	−	0.0366142i
$753$	4.19098	−	12.8985i	0.152728	−	0.470048i
$754$	−16.9443	+	52.1491i	−0.617074	+	1.89916i
$755$		0			0
$756$	−0.809017	−	2.48990i	−0.0294237	−	0.0905567i
$757$	17.1246			0.622405			0.311202	−	0.950344i	$-0.399268\pi$
$757$	17.1246			0.622405			0.311202	+	0.950344i	$0.399268\pi$
$758$	6.23607	+	19.1926i	0.226504	+	0.697108i
$759$	13.0902	+	9.51057i	0.475143	+	0.345212i
$760$		0			0
$761$	−1.14590	+	0.832544i	−0.0415388	+	0.0301797i	−0.608361	−	0.793661i	$-0.708173\pi$
$761$	−1.14590	+	0.832544i	−0.0415388	+	0.0301797i	0.566822	+	0.823840i	$0.308173\pi$
$762$	−11.0172	−	8.00448i	−0.399112	−	0.289972i
$763$	36.5066	+	26.5236i	1.32163	+	0.960218i
$764$	−3.47214	+	2.52265i	−0.125617	+	0.0912664i
$765$		0			0
$766$	16.1803	+	11.7557i	0.584619	+	0.424751i
$767$	−7.23607	−	22.2703i	−0.261279	−	0.804135i
$768$	1.00000			0.0360844
$769$	7.62868	+	23.4787i	0.275097	+	0.846662i	0.989194	+	0.146615i	$0.0468377\pi$
$769$	7.62868	+	23.4787i	0.275097	+	0.846662i	−0.714097	+	0.700047i	$0.753162\pi$
$770$		0			0
$771$	6.79837	−	20.9232i	0.244837	−	0.753532i
$772$	−5.51722	+	16.9803i	−0.198569	+	0.611133i
$773$	−0.927051	+	0.673542i	−0.0333437	+	0.0242256i	−0.604332	−	0.796732i	$-0.706560\pi$
$773$	−0.927051	+	0.673542i	−0.0333437	+	0.0242256i	0.570989	+	0.820958i	$0.306560\pi$
$774$	−7.70820			−0.277066
$775$		0			0
$776$	−3.38197			−0.121406
$777$	−16.9443	+	12.3107i	−0.607872	+	0.441645i
$778$	3.82624	−	11.7759i	0.137177	−	0.422188i
$779$	−10.0689	+	30.9888i	−0.360755	+	1.11029i
$780$		0			0
$781$	6.18034	+	19.0211i	0.221150	+	0.680630i
$782$	−5.52786			−0.197676
$783$	2.61803	+	8.05748i	0.0935609	+	0.287951i
$784$	0.118034	+	0.0857567i	0.00421550	+	0.00306274i
$785$		0			0
$786$	−14.4721	+	10.5146i	−0.516204	+	0.375044i
$787$	22.7082	+	16.4985i	0.809460	+	0.588107i	0.913674	−	0.406448i	$-0.133233\pi$
$787$	22.7082	+	16.4985i	0.809460	+	0.588107i	−0.104214	+	0.994555i	$0.533233\pi$
$788$	−13.8262	−	10.0453i	−0.492539	−	0.357851i
$789$	−9.47214	+	6.88191i	−0.337217	+	0.245002i
$790$		0			0
$791$	40.7426	+	29.6013i	1.44864	+	1.05250i
$792$	−1.11803	−	3.44095i	−0.0397276	−	0.122269i
$793$	17.8885			0.635241
$794$	−9.50658	−	29.2582i	−0.337376	−	1.03834i
$795$		0			0
$796$	6.02786	−	18.5519i	0.213652	−	0.657553i
$797$	−0.465558	+	1.43284i	−0.0164909	+	0.0507538i	−0.958963	−	0.283530i	$-0.908494\pi$
$797$	−0.465558	+	1.43284i	−0.0164909	+	0.0507538i	0.942472	+	0.334284i	$0.108494\pi$
$798$	12.0902	−	8.78402i	0.427987	−	0.310951i
$799$	2.11146			0.0746979
$800$		0			0
$801$	3.52786			0.124651
$802$	20.7984	−	15.1109i	0.734416	−	0.533585i
$803$	−3.94427	+	12.1392i	−0.139190	+	0.428384i
$804$	0.472136	−	1.45309i	0.0166510	−	0.0512464i
$805$		0			0
$806$	−13.2361	−	40.7364i	−0.466221	−	1.43488i
$807$	−9.09017			−0.319989
$808$	−1.35410	−	4.16750i	−0.0476371	−	0.146612i
$809$	24.9443	+	18.1231i	0.876994	+	0.637173i	0.932454	−	0.361288i	$-0.117663\pi$
$809$	24.9443	+	18.1231i	0.876994	+	0.637173i	−0.0554606	+	0.998461i	$0.517663\pi$
$810$		0			0
$811$	4.61803	−	3.35520i	0.162161	−	0.117817i	−0.503745	−	0.863852i	$-0.668045\pi$
$811$	4.61803	−	3.35520i	0.162161	−	0.117817i	0.665906	+	0.746035i	$0.268045\pi$
$812$	17.9443	+	13.0373i	0.629720	+	0.457519i
$813$	14.5902	+	10.6004i	0.511700	+	0.371772i
$814$	−23.4164	+	17.0130i	−0.820745	+	0.596306i
$815$		0			0
$816$	1.00000	+	0.726543i	0.0350070	+	0.0254341i
$817$	−13.5967	−	41.8465i	−0.475690	−	1.46402i
$818$	−5.79837			−0.202735
$819$	−5.23607	−	16.1150i	−0.182963	−	0.563102i
$820$		0			0
$821$	−13.9336	+	42.8833i	−0.486287	+	1.49664i	0.343821	+	0.939035i	$0.388279\pi$
$821$	−13.9336	+	42.8833i	−0.486287	+	1.49664i	−0.830108	+	0.557602i	$0.811721\pi$
$822$	−3.76393	+	11.5842i	−0.131282	+	0.404045i
$823$	2.39919	−	1.74311i	0.0836304	−	0.0607610i	−0.545184	−	0.838316i	$-0.683540\pi$
$823$	2.39919	−	1.74311i	0.0836304	−	0.0607610i	0.628815	+	0.777555i	$0.283540\pi$
$824$	14.3262			0.499078
$825$		0			0
$826$	−9.47214			−0.329578
$827$	35.6803	−	25.9233i	1.24073	−	0.901441i	0.243080	−	0.970006i	$-0.421842\pi$
$827$	35.6803	−	25.9233i	1.24073	−	0.901441i	0.997647	+	0.0685652i	$0.0218421\pi$
$828$	−1.38197	+	4.25325i	−0.0480266	+	0.147811i
$829$	8.00000	−	24.6215i	0.277851	−	0.855139i	−0.710599	−	0.703597i	$-0.751576\pi$
$829$	8.00000	−	24.6215i	0.277851	−	0.855139i	0.988451	−	0.151542i	$-0.0484239\pi$
$830$		0			0
$831$	−5.23607	−	16.1150i	−0.181637	−	0.559022i
$832$	6.47214			0.224381
$833$	0.0557281	+	0.171513i	0.00193086	+	0.00594259i
$834$	8.47214	+	6.15537i	0.293366	+	0.213143i
$835$		0			0
$836$	16.7082	−	12.1392i	0.577865	−	0.419844i
$837$	−5.35410	−	3.88998i	−0.185065	−	0.134457i
$838$	−2.50000	−	1.81636i	−0.0863611	−	0.0627450i
$839$	−5.14590	+	3.73871i	−0.177656	+	0.129075i	−0.673060	−	0.739588i	$-0.735020\pi$
$839$	−5.14590	+	3.73871i	−0.177656	+	0.129075i	0.495403	+	0.868663i	$0.335020\pi$
$840$		0			0
$841$	−34.6074	−	25.1437i	−1.19336	−	0.867026i
$842$	7.03444	+	21.6498i	0.242423	+	0.746101i
$843$	5.88854			0.202812
$844$	−1.05573	−	3.24920i	−0.0363397	−	0.111842i
$845$		0			0
$846$	0.527864	−	1.62460i	0.0181483	−	0.0558548i
$847$	−1.69098	+	5.20431i	−0.0581029	+	0.178822i
$848$	−1.69098	+	1.22857i	−0.0580686	+	0.0421893i
$849$	−4.58359			−0.157308
$850$		0			0
$851$	35.7771			1.22642
$852$	−4.47214	+	3.24920i	−0.153213	+	0.111316i
$853$	13.4721	−	41.4630i	0.461277	−	1.41967i	−0.402328	−	0.915496i	$-0.631799\pi$
$853$	13.4721	−	41.4630i	0.461277	−	1.41967i	0.863605	−	0.504169i	$-0.168201\pi$
$854$	2.23607	−	6.88191i	0.0765167	−	0.235494i
$855$		0			0
$856$	−3.59017	−	11.0494i	−0.122709	−	0.377661i
$857$	16.0689			0.548903			0.274451	−	0.961601i	$-0.411504\pi$
$857$	16.0689			0.548903			0.274451	+	0.961601i	$0.411504\pi$
$858$	−7.23607	−	22.2703i	−0.247035	−	0.760296i
$859$	1.85410	+	1.34708i	0.0632611	+	0.0459619i	0.618966	−	0.785417i	$-0.287552\pi$
$859$	1.85410	+	1.34708i	0.0632611	+	0.0459619i	−0.555705	+	0.831379i	$0.687552\pi$
$860$		0			0
$861$	12.0902	−	8.78402i	0.412032	−	0.299359i
$862$	13.6180	+	9.89408i	0.463832	+	0.336994i
$863$	−8.23607	−	5.98385i	−0.280359	−	0.203693i	0.438715	−	0.898626i	$-0.355434\pi$
$863$	−8.23607	−	5.98385i	−0.280359	−	0.203693i	−0.719074	+	0.694934i	$0.755434\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$		0			0
$866$	−12.5451	−	9.11454i	−0.426299	−	0.309725i
$867$	−4.78115	−	14.7149i	−0.162376	−	0.499743i
$868$	−17.3262			−0.588091
$869$	−6.28115	−	19.3314i	−0.213074	−	0.655773i
$870$		0			0
$871$	3.05573	−	9.40456i	0.103539	−	0.318661i
$872$	−5.32624	+	16.3925i	−0.180369	+	0.555119i
$873$	−2.73607	+	1.98787i	−0.0926019	+	0.0672792i
$874$	−25.5279			−0.863493
$875$		0			0
$876$	−3.52786			−0.119195
$877$	−30.0344	+	21.8213i	−1.01419	+	0.736853i	−0.965084	−	0.261941i	$-0.915638\pi$
$877$	−30.0344	+	21.8213i	−1.01419	+	0.736853i	−0.0491070	+	0.998794i	$0.515638\pi$
$878$	7.26393	−	22.3561i	0.245146	−	0.754481i
$879$	6.82624	−	21.0090i	0.230243	−	0.708616i
$880$		0			0
$881$	−7.29180	−	22.4418i	−0.245667	−	0.756085i	−0.995526	−	0.0944874i	$-0.969879\pi$
$881$	−7.29180	−	22.4418i	−0.245667	−	0.756085i	0.749859	−	0.661597i	$-0.230121\pi$
$882$	0.145898			0.00491264
$883$	9.29180	+	28.5972i	0.312694	+	0.962373i	0.976693	+	0.214640i	$0.0688577\pi$
$883$	9.29180	+	28.5972i	0.312694	+	0.962373i	−0.663999	+	0.747733i	$0.731142\pi$
$884$	6.47214	+	4.70228i	0.217681	+	0.158155i
$885$		0			0
$886$	−13.4443	+	9.76784i	−0.451669	+	0.328157i
$887$	18.9443	+	13.7638i	0.636086	+	0.462144i	0.858503	−	0.512808i	$-0.171395\pi$
$887$	18.9443	+	13.7638i	0.636086	+	0.462144i	−0.222417	+	0.974952i	$0.571395\pi$
$888$	−6.47214	−	4.70228i	−0.217191	−	0.157798i
$889$	−28.8435	+	20.9560i	−0.967379	+	0.702842i
$890$		0			0
$891$	−2.92705	−	2.12663i	−0.0980599	−	0.0712447i
$892$	2.50000	+	7.69421i	0.0837062	+	0.257621i
$893$	9.75078			0.326297
$894$	−6.82624	−	21.0090i	−0.228304	−	0.702646i
$895$		0			0
$896$	0.809017	−	2.48990i	0.0270274	−	0.0831817i
$897$	−8.94427	+	27.5276i	−0.298641	+	0.919121i
$898$	−22.4164	+	16.2865i	−0.748045	+	0.543487i
$899$	56.0689			1.87000
$900$		0			0
$901$	−2.58359			−0.0860719
$902$	16.7082	−	12.1392i	0.556322	−	0.404192i
$903$	−6.23607	+	19.1926i	−0.207523	+	0.638691i
$904$	−5.94427	+	18.2946i	−0.197704	+	0.608469i
$905$		0			0
$906$	−5.66312	−	17.4293i	−0.188145	−	0.579049i
$907$	−30.4721			−1.01181			−0.505905	−	0.862589i	$-0.668841\pi$
$907$	−30.4721			−1.01181			−0.505905	+	0.862589i	$0.668841\pi$
$908$	6.88197	+	21.1805i	0.228386	+	0.702900i
$909$	−3.54508	−	2.57565i	−0.117583	−	0.0854291i
$910$		0			0
$911$	−14.7082	+	10.6861i	−0.487305	+	0.354047i	−0.804147	−	0.594431i	$-0.797377\pi$
$911$	−14.7082	+	10.6861i	−0.487305	+	0.354047i	0.316842	+	0.948478i	$0.397377\pi$
$912$	4.61803	+	3.35520i	0.152918	+	0.111102i
$913$	6.28115	+	4.56352i	0.207876	+	0.151031i
$914$	3.30902	−	2.40414i	0.109453	−	0.0795219i
$915$		0			0
$916$	4.47214	+	3.24920i	0.147764	+	0.107356i
$917$	14.4721	+	44.5407i	0.477912	+	1.47086i
$918$	1.23607			0.0407963
$919$	−12.5836	−	38.7283i	−0.415094	−	1.27753i	−0.912166	−	0.409820i	$-0.865592\pi$
$919$	−12.5836	−	38.7283i	−0.415094	−	1.27753i	0.497072	−	0.867709i	$-0.334408\pi$
$920$		0			0
$921$	−3.09017	+	9.51057i	−0.101825	+	0.313384i
$922$	−2.33688	+	7.19218i	−0.0769611	+	0.236862i
$923$	−28.9443	+	21.0292i	−0.952712	+	0.692186i
$924$	−9.47214			−0.311610
$925$		0			0
$926$	−22.8328			−0.750333
$927$	11.5902	−	8.42075i	0.380671	−	0.276574i
$928$	−2.61803	+	8.05748i	−0.0859412	+	0.264500i
$929$	−5.87539	+	18.0826i	−0.192765	+	0.593270i	0.807230	+	0.590237i	$0.200966\pi$
$929$	−5.87539	+	18.0826i	−0.192765	+	0.593270i	−0.999995	+	0.00303360i	$0.999034\pi$
$930$		0			0
$931$	0.257354	+	0.792055i	0.00843444	+	0.0259585i
$932$	−18.6525			−0.610982
$933$	−0.326238	−	1.00406i	−0.0106806	−	0.0328714i
$934$	−8.63525	−	6.27388i	−0.282554	−	0.205288i
$935$		0			0
$936$	5.23607	−	3.80423i	0.171146	−	0.124345i
$937$	−7.02786	−	5.10604i	−0.229590	−	0.166807i	0.467043	−	0.884235i	$-0.345319\pi$
$937$	−7.02786	−	5.10604i	−0.229590	−	0.166807i	−0.696633	+	0.717428i	$0.745319\pi$
$938$	−3.23607	−	2.35114i	−0.105661	−	0.0767675i
$939$	−13.1631	+	9.56357i	−0.429562	+	0.312095i
$940$		0			0
$941$	3.59017	+	2.60841i	0.117036	+	0.0850318i	0.644764	−	0.764382i	$-0.276956\pi$
$941$	3.59017	+	2.60841i	0.117036	+	0.0850318i	−0.527728	+	0.849414i	$0.676956\pi$
$942$	2.67376	+	8.22899i	0.0871159	+	0.268115i
$943$	−25.5279			−0.831302
$944$	−1.11803	−	3.44095i	−0.0363889	−	0.111994i
$945$		0			0
$946$	−8.61803	+	26.5236i	−0.280196	+	0.862356i
$947$	10.3713	−	31.9196i	0.337023	−	1.03725i	−0.628694	−	0.777652i	$-0.716410\pi$
$947$	10.3713	−	31.9196i	0.337023	−	1.03725i	0.965717	−	0.259597i	$-0.0835897\pi$
$948$	4.54508	−	3.30220i	0.147617	−	0.107250i
$949$	−22.8328			−0.741185
$950$		0			0
$951$	20.5623			0.666778
$952$	2.61803	−	1.90211i	0.0848510	−	0.0616478i
$953$	−1.63932	+	5.04531i	−0.0531028	+	0.163434i	−0.974091	−	0.226157i	$-0.927384\pi$
$953$	−1.63932	+	5.04531i	−0.0531028	+	0.163434i	0.920988	+	0.389591i	$0.127384\pi$
$954$	−0.645898	+	1.98787i	−0.0209117	+	0.0643597i
$955$		0			0
$956$	3.79837	+	11.6902i	0.122848	+	0.378088i
$957$	30.6525			0.990854
$958$	9.00000	+	27.6992i	0.290777	+	0.894919i
$959$	25.7984	+	18.7436i	0.833073	+	0.605263i
$960$		0			0
$961$	−10.3541	+	7.52270i	−0.334003	+	0.242668i
$962$	−41.8885	−	30.4338i	−1.35054	−	0.981225i
$963$	−9.39919	−	6.82891i	−0.302885	−	0.220059i
$964$	−7.73607	+	5.62058i	−0.249162	+	0.181027i
$965$		0			0
$966$	9.47214	+	6.88191i	0.304761	+	0.221422i
$967$	−3.37132	−	10.3759i	−0.108414	−	0.333665i	0.882102	−	0.471058i	$-0.156128\pi$
$967$	−3.37132	−	10.3759i	−0.108414	−	0.333665i	−0.990517	+	0.137393i	$0.956128\pi$
$968$	−2.09017			−0.0671806
$969$	2.18034	+	6.71040i	0.0700426	+	0.215569i
$970$		0			0
$971$	−4.39261	+	13.5191i	−0.140966	+	0.433847i	−0.996470	−	0.0839479i	$-0.973247\pi$
$971$	−4.39261	+	13.5191i	−0.140966	+	0.433847i	0.855505	+	0.517795i	$0.173247\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	22.1803	−	16.1150i	0.711069	−	0.516622i
$974$	17.7984			0.570297
$975$		0			0
$976$	2.76393			0.0884713
$977$	−0.618034	+	0.449028i	−0.0197727	+	0.0143657i	−0.597628	−	0.801774i	$-0.703890\pi$
$977$	−0.618034	+	0.449028i	−0.0197727	+	0.0143657i	0.577855	+	0.816139i	$0.303890\pi$
$978$	−0.145898	+	0.449028i	−0.00466530	+	0.0143583i
$979$	3.94427	−	12.1392i	0.126059	−	0.387971i
$980$		0			0
$981$	5.32624	+	16.3925i	0.170054	+	0.523371i
$982$	25.2705			0.806414
$983$	−12.4164	−	38.2138i	−0.396022	−	1.21883i	−0.928163	−	0.372174i	$-0.878612\pi$
$983$	−12.4164	−	38.2138i	−0.396022	−	1.21883i	0.532141	−	0.846656i	$-0.321388\pi$
$984$	4.61803	+	3.35520i	0.147218	+	0.106960i
$985$		0			0
$986$	−8.47214	+	6.15537i	−0.269808	+	0.196027i
$987$	−3.61803	−	2.62866i	−0.115163	−	0.0836710i
$988$	29.8885	+	21.7153i	0.950881	+	0.690856i
$989$	27.8885	−	20.2622i	0.886804	−	0.644301i
$990$		0			0
$991$	−23.8262	−	17.3108i	−0.756865	−	0.549895i	0.141082	−	0.989998i	$-0.454942\pi$
$991$	−23.8262	−	17.3108i	−0.756865	−	0.549895i	−0.897947	+	0.440103i	$0.854942\pi$
$992$	−2.04508	−	6.29412i	−0.0649315	−	0.199839i
$993$	−18.0000			−0.571213
$994$	4.47214	+	13.7638i	0.141848	+	0.436562i
$995$		0			0
$996$	−0.663119	+	2.04087i	−0.0210117	+	0.0646675i
$997$	1.72949	−	5.32282i	0.0547735	−	0.168576i	−0.919927	−	0.392089i	$-0.871753\pi$
$997$	1.72949	−	5.32282i	0.0547735	−	0.168576i	0.974701	+	0.223513i	$0.0717526\pi$
$998$	28.7984	−	20.9232i	0.911597	−	0.662314i
$999$	−8.00000			−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.b.301.1		4
5.2	odd	4		750.2.h.b.199.2		8
5.3	odd	4		750.2.h.b.199.1		8
5.4	even	2		150.2.g.a.61.1	✓	4
15.14	odd	2		450.2.h.c.361.1		4
25.3	odd	20		3750.2.c.b.1249.4		4
25.4	even	10		3750.2.a.f.1.2		2
25.9	even	10		150.2.g.a.91.1	yes	4
25.12	odd	20		750.2.h.b.49.1		8
25.13	odd	20		750.2.h.b.49.2		8
25.16	even	5	inner	750.2.g.b.451.1		4
25.21	even	5		3750.2.a.d.1.1		2
25.22	odd	20		3750.2.c.b.1249.1		4
75.59	odd	10		450.2.h.c.91.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.61.1	✓	4	5.4	even	2
150.2.g.a.91.1	yes	4	25.9	even	10
450.2.h.c.91.1		4	75.59	odd	10
450.2.h.c.361.1		4	15.14	odd	2
750.2.g.b.301.1		4	1.1	even	1	trivial
750.2.g.b.451.1		4	25.16	even	5	inner
750.2.h.b.49.1		8	25.12	odd	20
750.2.h.b.49.2		8	25.13	odd	20
750.2.h.b.199.1		8	5.3	odd	4
750.2.h.b.199.2		8	5.2	odd	4
3750.2.a.d.1.1		2	25.21	even	5
3750.2.a.f.1.2		2	25.4	even	10
3750.2.c.b.1249.1		4	25.22	odd	20
3750.2.c.b.1249.4		4	25.3	odd	20

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.309017 - 0.951057i) q^{6} -2.61803 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.309017 - 0.951057i) q^{6} -2.61803 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-2.92705 + 2.12663i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(-5.23607 - 3.80423i) q^{13} +(-2.11803 + 1.53884i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-0.381966 - 1.17557i) q^{17} -1.00000 q^{18} +(-1.76393 - 5.42882i) q^{19} +(-0.809017 + 2.48990i) q^{21} +(-1.11803 + 3.44095i) q^{22} +(3.61803 - 2.62866i) q^{23} -1.00000 q^{24} -6.47214 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.809017 + 2.48990i) q^{28} +(2.61803 - 8.05748i) q^{29} +(2.04508 + 6.29412i) q^{31} -1.00000 q^{32} +(1.11803 + 3.44095i) q^{33} +(-1.00000 - 0.726543i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(6.47214 + 4.70228i) q^{37} +(-4.61803 - 3.35520i) q^{38} +(-5.23607 + 3.80423i) q^{39} +(-4.61803 - 3.35520i) q^{41} +(0.809017 + 2.48990i) q^{42} +7.70820 q^{43} +(1.11803 + 3.44095i) q^{44} +(1.38197 - 4.25325i) q^{46} +(-0.527864 + 1.62460i) q^{47} +(-0.809017 + 0.587785i) q^{48} -0.145898 q^{49} -1.23607 q^{51} +(-5.23607 + 3.80423i) q^{52} +(0.645898 - 1.98787i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(0.809017 + 2.48990i) q^{56} -5.70820 q^{57} +(-2.61803 - 8.05748i) q^{58} +(2.92705 + 2.12663i) q^{59} +(-2.23607 + 1.62460i) q^{61} +(5.35410 + 3.88998i) q^{62} +(2.11803 + 1.53884i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.92705 + 2.12663i) q^{66} +(0.472136 + 1.45309i) q^{67} -1.23607 q^{68} +(-1.38197 - 4.25325i) q^{69} +(1.70820 - 5.25731i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(2.85410 - 2.07363i) q^{73} +8.00000 q^{74} -5.70820 q^{76} +(7.66312 - 5.56758i) q^{77} +(-2.00000 + 6.15537i) q^{78} +(-1.73607 + 5.34307i) q^{79} +(0.309017 + 0.951057i) q^{81} -5.70820 q^{82} +(-0.663119 - 2.04087i) q^{83} +(2.11803 + 1.53884i) q^{84} +(6.23607 - 4.53077i) q^{86} +(-6.85410 - 4.97980i) q^{87} +(2.92705 + 2.12663i) q^{88} +(-2.85410 + 2.07363i) q^{89} +(13.7082 + 9.95959i) q^{91} +(-1.38197 - 4.25325i) q^{92} +6.61803 q^{93} +(0.527864 + 1.62460i) q^{94} +(-0.309017 + 0.951057i) q^{96} +(1.04508 - 3.21644i) q^{97} +(-0.118034 + 0.0857567i) q^{98} +3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 6 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 6 * q^7 + q^8 - q^9	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 6 q^{7} + q^{8} - q^{9} - 5 q^{11} - q^{12} - 12 q^{13} - 4 q^{14} - q^{16} - 6 q^{17} - 4 q^{18} - 16 q^{19} - q^{21} + 10 q^{23} - 4 q^{24} - 8 q^{26} - q^{27} - q^{28} + 6 q^{29} - 3 q^{31} - 4 q^{32} - 4 q^{34} - q^{36} + 8 q^{37} - 14 q^{38} - 12 q^{39} - 14 q^{41} + q^{42} + 4 q^{43} + 10 q^{46} - 20 q^{47} - q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} + 16 q^{53} + q^{54} + q^{56} + 4 q^{57} - 6 q^{58} + 5 q^{59} + 8 q^{62} + 4 q^{63} - q^{64} + 5 q^{66} - 16 q^{67} + 4 q^{68} - 10 q^{69} - 20 q^{71} + q^{72} - 2 q^{73} + 32 q^{74} + 4 q^{76} + 15 q^{77} - 8 q^{78} + 2 q^{79} - q^{81} + 4 q^{82} + 13 q^{83} + 4 q^{84} + 16 q^{86} - 14 q^{87} + 5 q^{88} + 2 q^{89} + 28 q^{91} - 10 q^{92} + 22 q^{93} + 20 q^{94} + q^{96} - 7 q^{97} + 4 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 6 * q^7 + q^8 - q^9 - 5 * q^11 - q^12 - 12 * q^13 - 4 * q^14 - q^16 - 6 * q^17 - 4 * q^18 - 16 * q^19 - q^21 + 10 * q^23 - 4 * q^24 - 8 * q^26 - q^27 - q^28 + 6 * q^29 - 3 * q^31 - 4 * q^32 - 4 * q^34 - q^36 + 8 * q^37 - 14 * q^38 - 12 * q^39 - 14 * q^41 + q^42 + 4 * q^43 + 10 * q^46 - 20 * q^47 - q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 + 16 * q^53 + q^54 + q^56 + 4 * q^57 - 6 * q^58 + 5 * q^59 + 8 * q^62 + 4 * q^63 - q^64 + 5 * q^66 - 16 * q^67 + 4 * q^68 - 10 * q^69 - 20 * q^71 + q^72 - 2 * q^73 + 32 * q^74 + 4 * q^76 + 15 * q^77 - 8 * q^78 + 2 * q^79 - q^81 + 4 * q^82 + 13 * q^83 + 4 * q^84 + 16 * q^86 - 14 * q^87 + 5 * q^88 + 2 * q^89 + 28 * q^91 - 10 * q^92 + 22 * q^93 + 20 * q^94 + q^96 - 7 * q^97 + 4 * q^98 + 10 * q^99

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