LMFDB - Embedded newform 750.2.g.f.151.1

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 $ x^16 - 4x^15 - 24x^14 + 94x^13 + 262x^12 - 936x^11 - 1584x^10 + 4642x^9 + 6259x^8 - 11958x^7 - 15752x^6 + 14670x^5 + 18271x^4 - 10440x^3 + 1135x^2 + 21080*x + 11105
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5^{6} $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			151.1
Root			$3.42137 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	750.151
Dual form			750.2.g.f.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} -3.52206 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} -3.52206 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(1.62388 + 4.99779i) q^{11} +(0.309017 - 0.951057i) q^{12} +(0.191313 - 0.588802i) q^{13} +(-1.08838 - 3.34968i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-2.78752 - 2.02525i) q^{17} +1.00000 q^{18} +(-1.83995 - 1.33680i) q^{19} +(2.84941 - 2.07022i) q^{21} +(-4.25137 + 3.08880i) q^{22} +(-2.76688 - 8.51557i) q^{23} +1.00000 q^{24} +0.619103 q^{26} +(0.309017 + 0.951057i) q^{27} +(2.84941 - 2.07022i) q^{28} +(2.16949 - 1.57623i) q^{29} +(-7.90309 - 5.74193i) q^{31} +1.00000 q^{32} +(-4.25137 - 3.08880i) q^{33} +(1.06474 - 3.27693i) q^{34} +(0.309017 + 0.951057i) q^{36} +(-0.309552 + 0.952702i) q^{37} +(0.702799 - 2.16299i) q^{38} +(0.191313 + 0.588802i) q^{39} +(1.94584 - 5.98868i) q^{41} +(2.84941 + 2.07022i) q^{42} -1.51251 q^{43} +(-4.25137 - 3.08880i) q^{44} +(7.24378 - 5.26291i) q^{46} +(-8.63710 + 6.27522i) q^{47} +(0.309017 + 0.951057i) q^{48} +5.40494 q^{49} +3.44557 q^{51} +(0.191313 + 0.588802i) q^{52} +(-0.447681 + 0.325260i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(2.84941 + 2.07022i) q^{56} +2.27431 q^{57} +(2.16949 + 1.57623i) q^{58} +(0.0861451 - 0.265127i) q^{59} +(1.13786 + 3.50196i) q^{61} +(3.01871 - 9.29064i) q^{62} +(-1.08838 + 3.34968i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.62388 - 4.99779i) q^{66} +(9.63710 + 7.00176i) q^{67} +3.44557 q^{68} +(7.24378 + 5.26291i) q^{69} +(-3.84168 + 2.79115i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(3.03890 + 9.35277i) q^{73} -1.00173 q^{74} +2.27431 q^{76} +(-5.71941 - 17.6025i) q^{77} +(-0.500865 + 0.363900i) q^{78} +(-5.27525 + 3.83269i) q^{79} +(-0.809017 - 0.587785i) q^{81} +6.29687 q^{82} +(-2.15177 - 1.56335i) q^{83} +(-1.08838 + 3.34968i) q^{84} +(-0.467392 - 1.43848i) q^{86} +(-0.828671 + 2.55039i) q^{87} +(1.62388 - 4.99779i) q^{88} +(-4.13649 - 12.7308i) q^{89} +(-0.673818 + 2.07380i) q^{91} +(7.24378 + 5.26291i) q^{92} +9.76875 q^{93} +(-8.63710 - 6.27522i) q^{94} +(-0.809017 + 0.587785i) q^{96} +(-3.53706 + 2.56983i) q^{97} +(1.67022 + 5.14040i) q^{98} +5.25498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	−3.52206			−1.33122			−0.665608	−	0.746302i	$-0.731828\pi$
$7$	−3.52206			−1.33122			−0.665608	+	0.746302i	$0.731828\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	1.62388	+	4.99779i	0.489618	+	1.50689i	0.825179	+	0.564871i	$0.191074\pi$
$11$	1.62388	+	4.99779i	0.489618	+	1.50689i	−0.335561	+	0.942018i	$0.608926\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	0.191313	−	0.588802i	0.0530608	−	0.163304i	−0.921015	−	0.389528i	$-0.872638\pi$
$13$	0.191313	−	0.588802i	0.0530608	−	0.163304i	0.974075	+	0.226224i	$0.0726381\pi$
$14$	−1.08838	−	3.34968i	−0.290881	−	0.895240i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.78752	−	2.02525i	−0.676073	−	0.491196i	0.195979	−	0.980608i	$-0.437211\pi$
$17$	−2.78752	−	2.02525i	−0.676073	−	0.491196i	−0.872053	+	0.489412i	$0.837211\pi$
$18$	1.00000			0.235702
$19$	−1.83995	−	1.33680i	−0.422114	−	0.306684i	0.356374	−	0.934343i	$-0.384013\pi$
$19$	−1.83995	−	1.33680i	−0.422114	−	0.306684i	−0.778488	+	0.627660i	$0.784013\pi$
$20$		0			0
$21$	2.84941	−	2.07022i	0.621792	−	0.451759i
$22$	−4.25137	+	3.08880i	−0.906395	+	0.658535i
$23$	−2.76688	−	8.51557i	−0.576934	−	1.77562i	−0.629498	−	0.777002i	$-0.716739\pi$
$23$	−2.76688	−	8.51557i	−0.576934	−	1.77562i	0.0525639	−	0.998618i	$-0.483261\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	0.619103			0.121416
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	2.84941	−	2.07022i	0.538488	−	0.391234i
$29$	2.16949	−	1.57623i	0.402864	−	0.292698i	−0.367843	−	0.929888i	$-0.619904\pi$
$29$	2.16949	−	1.57623i	0.402864	−	0.292698i	0.770706	+	0.637190i	$0.219904\pi$
$30$		0			0
$31$	−7.90309	−	5.74193i	−1.41944	−	1.03128i	−0.991864	−	0.127300i	$-0.959369\pi$
$31$	−7.90309	−	5.74193i	−1.41944	−	1.03128i	−0.427572	−	0.903981i	$-0.640631\pi$
$32$	1.00000			0.176777
$33$	−4.25137	−	3.08880i	−0.740069	−	0.537691i
$34$	1.06474	−	3.27693i	0.182601	−	0.561989i
$35$		0			0
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−0.309552	+	0.952702i	−0.0508900	+	0.156623i	−0.973272	−	0.229656i	$-0.926240\pi$
$37$	−0.309552	+	0.952702i	−0.0508900	+	0.156623i	0.922382	+	0.386279i	$0.126240\pi$
$38$	0.702799	−	2.16299i	0.114009	−	0.350884i
$39$	0.191313	+	0.588802i	0.0306347	+	0.0942838i
$40$		0			0
$41$	1.94584	−	5.98868i	0.303889	−	0.935274i	−0.676200	−	0.736718i	$-0.736375\pi$
$41$	1.94584	−	5.98868i	0.303889	−	0.935274i	0.980089	−	0.198557i	$-0.0636254\pi$
$42$	2.84941	+	2.07022i	0.439674	+	0.319442i
$43$	−1.51251			−0.230656			−0.115328	−	0.993327i	$-0.536792\pi$
$43$	−1.51251			−0.230656			−0.115328	+	0.993327i	$0.536792\pi$
$44$	−4.25137	−	3.08880i	−0.640918	−	0.465654i
$45$		0			0
$46$	7.24378	−	5.26291i	1.06804	−	0.775974i
$47$	−8.63710	+	6.27522i	−1.25985	+	0.915335i	−0.998750	−	0.0499772i	$-0.984085\pi$
$47$	−8.63710	+	6.27522i	−1.25985	+	0.915335i	−0.261100	+	0.965312i	$0.584085\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	5.40494			0.772134
$50$		0			0
$51$	3.44557			0.482476
$52$	0.191313	+	0.588802i	0.0265304	+	0.0816522i
$53$	−0.447681	+	0.325260i	−0.0614938	+	0.0446778i	−0.618107	−	0.786094i	$-0.712100\pi$
$53$	−0.447681	+	0.325260i	−0.0614938	+	0.0446778i	0.556614	+	0.830771i	$0.312100\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$		0			0
$56$	2.84941	+	2.07022i	0.380768	+	0.276644i
$57$	2.27431			0.301239
$58$	2.16949	+	1.57623i	0.284868	+	0.206968i
$59$	0.0861451	−	0.265127i	0.0112151	−	0.0345166i	−0.945292	−	0.326224i	$-0.894223\pi$
$59$	0.0861451	−	0.265127i	0.0112151	−	0.0345166i	0.956507	+	0.291708i	$0.0942235\pi$
$60$		0			0
$61$	1.13786	+	3.50196i	0.145688	+	0.448380i	0.997099	−	0.0761185i	$-0.0242527\pi$
$61$	1.13786	+	3.50196i	0.145688	+	0.448380i	−0.851411	+	0.524499i	$0.824253\pi$
$62$	3.01871	−	9.29064i	0.383377	−	1.17991i
$63$	−1.08838	+	3.34968i	−0.137123	+	0.422020i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$		0			0
$66$	1.62388	−	4.99779i	0.199886	−	0.615185i
$67$	9.63710	+	7.00176i	1.17736	+	0.855401i	0.991871	−	0.127245i	$-0.0406136\pi$
$67$	9.63710	+	7.00176i	1.17736	+	0.855401i	0.185487	+	0.982647i	$0.440614\pi$
$68$	3.44557			0.417836
$69$	7.24378	+	5.26291i	0.872049	+	0.633580i
$70$		0			0
$71$	−3.84168	+	2.79115i	−0.455924	+	0.331248i	−0.791930	−	0.610612i	$-0.790924\pi$
$71$	−3.84168	+	2.79115i	−0.455924	+	0.331248i	0.336006	+	0.941860i	$0.390924\pi$
$72$	−0.809017	+	0.587785i	−0.0953436	+	0.0692712i
$73$	3.03890	+	9.35277i	0.355676	+	1.09466i	0.955616	+	0.294614i	$0.0951911\pi$
$73$	3.03890	+	9.35277i	0.355676	+	1.09466i	−0.599940	+	0.800045i	$0.704809\pi$
$74$	−1.00173			−0.116449
$75$		0			0
$76$	2.27431			0.260881
$77$	−5.71941	−	17.6025i	−0.651787	−	2.00599i
$78$	−0.500865	+	0.363900i	−0.0567118	+	0.0412035i
$79$	−5.27525	+	3.83269i	−0.593512	+	0.431212i	−0.843570	−	0.537019i	$-0.819550\pi$
$79$	−5.27525	+	3.83269i	−0.593512	+	0.431212i	0.250058	+	0.968231i	$0.419550\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	6.29687			0.695373
$83$	−2.15177	−	1.56335i	−0.236187	−	0.171600i	0.463396	−	0.886151i	$-0.346631\pi$
$83$	−2.15177	−	1.56335i	−0.236187	−	0.171600i	−0.699583	+	0.714551i	$0.746631\pi$
$84$	−1.08838	+	3.34968i	−0.118752	+	0.365480i
$85$		0			0
$86$	−0.467392	−	1.43848i	−0.0504002	−	0.155116i
$87$	−0.828671	+	2.55039i	−0.0888428	+	0.273430i
$88$	1.62388	−	4.99779i	0.173106	−	0.532766i
$89$	−4.13649	−	12.7308i	−0.438467	−	1.34946i	−0.889491	−	0.456952i	$-0.848941\pi$
$89$	−4.13649	−	12.7308i	−0.438467	−	1.34946i	0.451024	−	0.892512i	$-0.351059\pi$
$90$		0			0
$91$	−0.673818	+	2.07380i	−0.0706353	+	0.217393i
$92$	7.24378	+	5.26291i	0.755216	+	0.548697i
$93$	9.76875			1.01297
$94$	−8.63710	−	6.27522i	−0.890848	−	0.647239i
$95$		0			0
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	−3.53706	+	2.56983i	−0.359134	+	0.260926i	−0.752691	−	0.658374i	$-0.771244\pi$
$97$	−3.53706	+	2.56983i	−0.359134	+	0.260926i	0.393557	+	0.919300i	$0.371244\pi$
$98$	1.67022	+	5.14040i	0.168717	+	0.519259i
$99$	5.25498			0.528146
$100$		0			0
$101$	−14.2687			−1.41979			−0.709893	−	0.704309i	$-0.751257\pi$
$101$	−14.2687			−1.41979			−0.709893	+	0.704309i	$0.751257\pi$
$102$	1.06474	+	3.27693i	0.105425	+	0.324464i
$103$	−14.2939	+	10.3852i	−1.40842	+	1.02328i	−0.414875	+	0.909879i	$0.636175\pi$
$103$	−14.2939	+	10.3852i	−1.40842	+	1.02328i	−0.993549	+	0.113401i	$0.963825\pi$
$104$	−0.500865	+	0.363900i	−0.0491138	+	0.0356833i
$105$		0			0
$106$	−0.447681	−	0.325260i	−0.0434827	−	0.0315920i
$107$	0.723713			0.0699640			0.0349820	−	0.999388i	$-0.488863\pi$
$107$	0.723713			0.0699640			0.0349820	+	0.999388i	$0.488863\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	−0.795198	+	2.44737i	−0.0761661	+	0.234415i	−0.981890	−	0.189454i	$-0.939328\pi$
$109$	−0.795198	+	2.44737i	−0.0761661	+	0.234415i	0.905724	+	0.423869i	$0.139328\pi$
$110$		0			0
$111$	−0.309552	−	0.952702i	−0.0293813	−	0.0904264i
$112$	−1.08838	+	3.34968i	−0.102842	+	0.316515i
$113$	4.69339	−	14.4448i	0.441517	−	1.35885i	−0.444741	−	0.895659i	$-0.646704\pi$
$113$	4.69339	−	14.4448i	0.441517	−	1.35885i	0.886258	−	0.463191i	$-0.153296\pi$
$114$	0.702799	+	2.16299i	0.0658232	+	0.202583i
$115$		0			0
$116$	−0.828671	+	2.55039i	−0.0769401	+	0.236797i
$117$	−0.500865	−	0.363900i	−0.0463050	−	0.0336425i
$118$	0.278771			0.0256630
$119$	9.81783	+	7.13307i	0.899999	+	0.653888i
$120$		0			0
$121$	−13.4417	+	9.76597i	−1.22197	+	0.887815i
$122$	−2.97895	+	2.16433i	−0.269701	+	0.195949i
$123$	1.94584	+	5.98868i	0.175450	+	0.539981i
$124$	9.76875			0.877260
$125$		0			0
$126$	−3.52206			−0.313770
$127$	−1.34850	−	4.15027i	−0.119660	−	0.368277i	0.873230	−	0.487308i	$-0.162021\pi$
$127$	−1.34850	−	4.15027i	−0.119660	−	0.368277i	−0.992891	+	0.119031i	$0.962021\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	1.22365	−	0.889032i	0.107736	−	0.0782749i
$130$		0			0
$131$	0.499797	+	0.363124i	0.0436675	+	0.0317263i	0.609405	−	0.792859i	$-0.291408\pi$
$131$	0.499797	+	0.363124i	0.0436675	+	0.0317263i	−0.565737	+	0.824585i	$0.691408\pi$
$132$	5.25498			0.457388
$133$	6.48043	+	4.70831i	0.561925	+	0.408262i
$134$	−3.68104	+	11.3291i	−0.317994	+	0.978684i
$135$		0			0
$136$	1.06474	+	3.27693i	0.0913006	+	0.280994i
$137$	2.86509	−	8.81784i	0.244781	−	0.753359i	−0.750891	−	0.660426i	$-0.770376\pi$
$137$	2.86509	−	8.81784i	0.244781	−	0.753359i	0.995672	−	0.0929329i	$-0.0296242\pi$
$138$	−2.76688	+	8.51557i	−0.235532	+	0.724894i
$139$	5.79774	+	17.8436i	0.491757	+	1.51347i	0.821950	+	0.569560i	$0.192886\pi$
$139$	5.79774	+	17.8436i	0.491757	+	1.51347i	−0.330192	+	0.943914i	$0.607114\pi$
$140$		0			0
$141$	3.29908	−	10.1535i	0.277832	−	0.855080i
$142$	−3.84168	−	2.79115i	−0.322387	−	0.234228i
$143$	3.25338			0.272061
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$		0			0
$146$	−7.95594	+	5.78033i	−0.658438	+	0.478383i
$147$	−4.37269	+	3.17694i	−0.360653	+	0.262030i
$148$	−0.309552	−	0.952702i	−0.0254450	−	0.0783116i
$149$	−16.8396			−1.37955			−0.689777	−	0.724022i	$-0.742291\pi$
$149$	−16.8396			−1.37955			−0.689777	+	0.724022i	$0.742291\pi$
$150$		0			0
$151$	16.7932			1.36661			0.683305	−	0.730133i	$-0.260542\pi$
$151$	16.7932			1.36661			0.683305	+	0.730133i	$0.260542\pi$
$152$	0.702799	+	2.16299i	0.0570045	+	0.175442i
$153$	−2.78752	+	2.02525i	−0.225358	+	0.163732i
$154$	14.9736	−	10.8790i	1.20661	−	0.876652i
$155$		0			0
$156$	−0.500865	−	0.363900i	−0.0401013	−	0.0291353i
$157$	4.55451			0.363489			0.181745	−	0.983346i	$-0.441826\pi$
$157$	4.55451			0.363489			0.181745	+	0.983346i	$0.441826\pi$
$158$	−5.27525	−	3.83269i	−0.419676	−	0.304913i
$159$	0.170999	−	0.526281i	0.0135611	−	0.0417368i
$160$		0			0
$161$	9.74512	+	29.9924i	0.768023	+	2.36373i
$162$	0.309017	−	0.951057i	0.0242787	−	0.0747221i
$163$	−6.24624	+	19.2239i	−0.489243	+	1.50574i	0.336497	+	0.941685i	$0.390758\pi$
$163$	−6.24624	+	19.2239i	−0.489243	+	1.50574i	−0.825740	+	0.564051i	$0.809242\pi$
$164$	1.94584	+	5.98868i	0.151945	+	0.467637i
$165$		0			0
$166$	0.821902	−	2.52955i	0.0637920	−	0.196331i
$167$	5.81831	+	4.22725i	0.450234	+	0.327114i	0.789688	−	0.613508i	$-0.210242\pi$
$167$	5.81831	+	4.22725i	0.450234	+	0.327114i	−0.339454	+	0.940623i	$0.610242\pi$
$168$	−3.52206			−0.271733
$169$	10.2071	+	7.41592i	0.785164	+	0.570455i
$170$		0			0
$171$	−1.83995	+	1.33680i	−0.140705	+	0.102228i
$172$	1.22365	−	0.889032i	0.0933023	−	0.0677881i
$173$	1.89475	+	5.83145i	0.144055	+	0.443357i	0.996888	−	0.0788271i	$-0.0251175\pi$
$173$	1.89475	+	5.83145i	0.144055	+	0.443357i	−0.852833	+	0.522184i	$0.825117\pi$
$174$	−2.68163			−0.203294
$175$		0			0
$176$	5.25498			0.396109
$177$	0.0861451	+	0.265127i	0.00647506	+	0.0199282i
$178$	10.8295	−	7.86808i	0.811704	−	0.589737i
$179$	−11.5930	+	8.42280i	−0.866501	+	0.629549i	−0.929646	−	0.368455i	$-0.879887\pi$
$179$	−11.5930	+	8.42280i	−0.866501	+	0.629549i	0.0631451	+	0.998004i	$0.479887\pi$
$180$		0			0
$181$	−12.7254	−	9.24554i	−0.945871	−	0.687215i	0.00395575	−	0.999992i	$-0.498741\pi$
$181$	−12.7254	−	9.24554i	−0.945871	−	0.687215i	−0.949827	+	0.312777i	$0.898741\pi$
$182$	−2.18052			−0.161631
$183$	−2.97895	−	2.16433i	−0.220210	−	0.159992i
$184$	−2.76688	+	8.51557i	−0.203977	+	0.627776i
$185$		0			0
$186$	3.01871	+	9.29064i	0.221343	+	0.681223i
$187$	5.59518	−	17.2202i	0.409160	−	1.25927i
$188$	3.29908	−	10.1535i	0.240610	−	0.740521i
$189$	−1.08838	−	3.34968i	−0.0791678	−	0.243654i
$190$		0			0
$191$	−1.11938	+	3.44511i	−0.0809958	+	0.249279i	−0.983352	−	0.181712i	$-0.941836\pi$
$191$	−1.11938	+	3.44511i	−0.0809958	+	0.249279i	0.902356	+	0.430992i	$0.141836\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	−9.72486			−0.700010			−0.350005	−	0.936748i	$-0.613820\pi$
$193$	−9.72486			−0.700010			−0.350005	+	0.936748i	$0.613820\pi$
$194$	−3.53706	−	2.56983i	−0.253946	−	0.184503i
$195$		0			0
$196$	−4.37269	+	3.17694i	−0.312335	+	0.226925i
$197$	5.72280	−	4.15786i	0.407732	−	0.296235i	−0.364951	−	0.931027i	$-0.618914\pi$
$197$	5.72280	−	4.15786i	0.407732	−	0.296235i	0.772683	+	0.634792i	$0.218914\pi$
$198$	1.62388	+	4.99779i	0.115404	+	0.355177i
$199$	−17.6745			−1.25291			−0.626455	−	0.779457i	$-0.715495\pi$
$199$	−17.6745			−1.25291			−0.626455	+	0.779457i	$0.715495\pi$
$200$		0			0
$201$	−11.9121			−0.840215
$202$	−4.40926	−	13.5703i	−0.310235	−	0.954804i
$203$	−7.64108	+	5.55157i	−0.536298	+	0.389644i
$204$	−2.78752	+	2.02525i	−0.195166	+	0.141796i
$205$		0			0
$206$	−14.2939	−	10.3852i	−0.995906	−	0.723568i
$207$	−8.95380			−0.622332
$208$	−0.500865	−	0.363900i	−0.0347287	−	0.0252319i
$209$	3.69320	−	11.3665i	0.255464	−	0.786237i
$210$		0			0
$211$	−3.63522	−	11.1881i	−0.250259	−	0.770218i	−0.994727	−	0.102559i	$-0.967297\pi$
$211$	−3.63522	−	11.1881i	−0.250259	−	0.770218i	0.744468	−	0.667658i	$-0.232703\pi$
$212$	0.170999	−	0.526281i	0.0117443	−	0.0361451i
$213$	1.46739	−	4.51617i	0.100544	−	0.309443i
$214$	0.223640	+	0.688292i	0.0152877	+	0.0470507i
$215$		0			0
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	27.8352	+	20.2234i	1.88958	+	1.37286i
$218$	−2.57331			−0.174287
$219$	−7.95594	−	5.78033i	−0.537613	−	0.390598i
$220$		0			0
$221$	−1.72576	+	1.25384i	−0.116087	+	0.0843424i
$222$	0.810416	−	0.588802i	0.0543916	−	0.0395178i
$223$	−3.92466	−	12.0789i	−0.262815	−	0.808860i	−0.992189	−	0.124745i	$-0.960189\pi$
$223$	−3.92466	−	12.0789i	−0.262815	−	0.808860i	0.729374	−	0.684115i	$-0.239811\pi$
$224$	−3.52206			−0.235328
$225$		0			0
$226$	15.1881			1.01030
$227$	−4.40848	−	13.5679i	−0.292601	−	0.900533i	−0.984017	−	0.178076i	$-0.943013\pi$
$227$	−4.40848	−	13.5679i	−0.292601	−	0.900533i	0.691416	−	0.722457i	$-0.256987\pi$
$228$	−1.83995	+	1.33680i	−0.121854	+	0.0885320i
$229$	−7.12184	+	5.17432i	−0.470625	+	0.341929i	−0.797685	−	0.603075i	$-0.793942\pi$
$229$	−7.12184	+	5.17432i	−0.470625	+	0.341929i	0.327060	+	0.945004i	$0.393942\pi$
$230$		0			0
$231$	14.9736	+	10.8790i	0.985191	+	0.715783i
$232$	−2.68163			−0.176058
$233$	12.1969	+	8.86158i	0.799047	+	0.580542i	0.910634	−	0.413213i	$-0.135594\pi$
$233$	12.1969	+	8.86158i	0.799047	+	0.580542i	−0.111587	+	0.993755i	$0.535594\pi$
$234$	0.191313	−	0.588802i	0.0125065	−	0.0384912i
$235$		0			0
$236$	0.0861451	+	0.265127i	0.00560757	+	0.0172583i
$237$	2.01497	−	6.20143i	0.130886	−	0.402826i
$238$	−3.75008	+	11.5416i	−0.243081	+	0.748128i
$239$	−1.93007	−	5.94013i	−0.124846	−	0.384235i	0.869027	−	0.494764i	$-0.164746\pi$
$239$	−1.93007	−	5.94013i	−0.124846	−	0.384235i	−0.993873	+	0.110529i	$0.964746\pi$
$240$		0			0
$241$	−4.57636	+	14.0846i	−0.294790	+	0.907269i	0.688503	+	0.725234i	$0.258268\pi$
$241$	−4.57636	+	14.0846i	−0.294790	+	0.907269i	−0.983292	+	0.182035i	$0.941732\pi$
$242$	−13.4417	−	9.76597i	−0.864065	−	0.627780i
$243$	1.00000			0.0641500
$244$	−2.97895	−	2.16433i	−0.190708	−	0.138557i
$245$		0			0
$246$	−5.09427	+	3.70121i	−0.324799	+	0.235980i
$247$	−1.13912	+	0.827619i	−0.0724805	+	0.0526601i
$248$	3.01871	+	9.29064i	0.191688	+	0.589956i
$249$	2.65973			0.168554
$250$		0			0
$251$	18.2744			1.15347			0.576735	−	0.816931i	$-0.304327\pi$
$251$	18.2744			1.15347			0.576735	+	0.816931i	$0.304327\pi$
$252$	−1.08838	−	3.34968i	−0.0685614	−	0.211010i
$253$	38.0659	−	27.6565i	2.39319	−	1.73875i
$254$	3.53043	−	2.56501i	0.221519	−	0.160943i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.80149			−0.112374			−0.0561868	−	0.998420i	$-0.517894\pi$
$257$	−1.80149			−0.112374			−0.0561868	+	0.998420i	$0.517894\pi$
$258$	1.22365	+	0.889032i	0.0761810	+	0.0553487i
$259$	1.09026	−	3.35548i	0.0677455	−	0.208499i
$260$		0			0
$261$	−0.828671	−	2.55039i	−0.0512934	−	0.157865i
$262$	−0.190905	+	0.587547i	−0.0117942	+	0.0362987i
$263$	4.38923	−	13.5087i	0.270652	−	0.832981i	−0.719685	−	0.694300i	$-0.755714\pi$
$263$	4.38923	−	13.5087i	0.270652	−	0.832981i	0.990337	−	0.138680i	$-0.0442860\pi$
$264$	1.62388	+	4.99779i	0.0999429	+	0.307593i
$265$		0			0
$266$	−2.47530	+	7.61820i	−0.151771	+	0.467102i
$267$	10.8295	+	7.86808i	0.662753	+	0.481518i
$268$	−11.9121			−0.727648
$269$	5.05075	+	3.66959i	0.307950	+	0.223739i	0.731016	−	0.682360i	$-0.239046\pi$
$269$	5.05075	+	3.66959i	0.307950	+	0.223739i	−0.423066	+	0.906099i	$0.639046\pi$
$270$		0			0
$271$	19.2926	−	14.0169i	1.17194	−	0.851464i	0.180700	−	0.983538i	$-0.442164\pi$
$271$	19.2926	−	14.0169i	1.17194	−	0.851464i	0.991240	+	0.132074i	$0.0421637\pi$
$272$	−2.78752	+	2.02525i	−0.169018	+	0.122799i
$273$	−0.673818	−	2.07380i	−0.0407813	−	0.125512i
$274$	9.27162			0.560119
$275$		0			0
$276$	−8.95380			−0.538956
$277$	−2.15495	−	6.63226i	−0.129478	−	0.398494i	0.865212	−	0.501406i	$-0.167184\pi$
$277$	−2.15495	−	6.63226i	−0.129478	−	0.398494i	−0.994690	+	0.102913i	$0.967184\pi$
$278$	−15.1787	+	11.0279i	−0.910356	+	0.661412i
$279$	−7.90309	+	5.74193i	−0.473146	+	0.343760i
$280$		0			0
$281$	−9.41192	−	6.83816i	−0.561468	−	0.407931i	0.270528	−	0.962712i	$-0.412802\pi$
$281$	−9.41192	−	6.83816i	−0.561468	−	0.407931i	−0.831996	+	0.554782i	$0.812802\pi$
$282$	10.6760			0.635749
$283$	−7.77061	−	5.64568i	−0.461915	−	0.335601i	0.332367	−	0.943150i	$-0.392153\pi$
$283$	−7.77061	−	5.64568i	−0.461915	−	0.335601i	−0.794282	+	0.607549i	$0.792153\pi$
$284$	1.46739	−	4.51617i	0.0870737	−	0.267985i
$285$		0			0
$286$	1.00535	+	3.09415i	0.0594475	+	0.182961i
$287$	−6.85337	+	21.0925i	−0.404542	+	1.24505i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−1.58466	−	4.87709i	−0.0932154	−	0.286888i
$290$		0			0
$291$	1.35104	−	4.15806i	0.0791992	−	0.243750i
$292$	−7.95594	−	5.78033i	−0.465586	−	0.338268i
$293$	−8.52716			−0.498162			−0.249081	−	0.968483i	$-0.580129\pi$
$293$	−8.52716			−0.498162			−0.249081	+	0.968483i	$0.580129\pi$
$294$	−4.37269	−	3.17694i	−0.255020	−	0.185283i
$295$		0			0
$296$	0.810416	−	0.588802i	0.0471045	−	0.0342234i
$297$	−4.25137	+	3.08880i	−0.246690	+	0.179230i
$298$	−5.20372	−	16.0154i	−0.301444	−	0.927748i
$299$	−5.54333			−0.320579
$300$		0			0
$301$	5.32717			0.307053
$302$	5.18938	+	15.9713i	0.298615	+	0.919043i
$303$	11.5436	−	8.38692i	0.663163	−	0.481816i
$304$	−1.83995	+	1.33680i	−0.105528	+	0.0766709i
$305$		0			0
$306$	−2.78752	−	2.02525i	−0.159352	−	0.115776i
$307$	−2.85794			−0.163111			−0.0815557	−	0.996669i	$-0.525989\pi$
$307$	−2.85794			−0.163111			−0.0815557	+	0.996669i	$0.525989\pi$
$308$	14.9736	+	10.8790i	0.853200	+	0.619886i
$309$	5.45980	−	16.8035i	0.310597	−	0.955920i
$310$		0			0
$311$	−3.14017	−	9.66444i	−0.178063	−	0.548020i	0.821697	−	0.569924i	$-0.193027\pi$
$311$	−3.14017	−	9.66444i	−0.178063	−	0.548020i	−0.999760	+	0.0219035i	$0.993027\pi$
$312$	0.191313	−	0.588802i	0.0108310	−	0.0333344i
$313$	−5.62523	+	17.3127i	−0.317957	+	0.978570i	0.656564	+	0.754271i	$0.272009\pi$
$313$	−5.62523	+	17.3127i	−0.317957	+	0.978570i	−0.974520	+	0.224299i	$0.927991\pi$
$314$	1.40742	+	4.33159i	0.0794253	+	0.244446i
$315$		0			0
$316$	2.01497	−	6.20143i	0.113351	−	0.348857i
$317$	25.3031	+	18.3838i	1.42116	+	1.03254i	0.991578	+	0.129510i	$0.0413405\pi$
$317$	25.3031	+	18.3838i	1.42116	+	1.03254i	0.429586	+	0.903026i	$0.358660\pi$
$318$	0.553365			0.0310312
$319$	11.4006	+	8.28304i	0.638312	+	0.463761i
$320$		0			0
$321$	−0.585496	+	0.425388i	−0.0326792	+	0.0237428i
$322$	−25.5131	+	18.5363i	−1.42179	+	1.03299i
$323$	2.42154	+	7.45274i	0.134738	+	0.414681i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−20.2133			−1.11951
$327$	−0.795198	−	2.44737i	−0.0439745	−	0.135340i
$328$	−5.09427	+	3.70121i	−0.281284	+	0.204365i
$329$	30.4204	−	22.1017i	1.67713	−	1.21851i
$330$		0			0
$331$	−2.77650	−	2.01724i	−0.152610	−	0.110878i	0.508860	−	0.860849i	$-0.330067\pi$
$331$	−2.77650	−	2.01724i	−0.152610	−	0.110878i	−0.661470	+	0.749972i	$0.730067\pi$
$332$	2.65973			0.145972
$333$	0.810416	+	0.588802i	0.0444106	+	0.0322662i
$334$	−2.22240	+	6.83983i	−0.121604	+	0.374259i
$335$		0			0
$336$	−1.08838	−	3.34968i	−0.0593759	−	0.182740i
$337$	−3.62277	+	11.1497i	−0.197345	+	0.607365i	0.802596	+	0.596523i	$0.203451\pi$
$337$	−3.62277	+	11.1497i	−0.197345	+	0.607365i	−0.999941	+	0.0108427i	$0.996549\pi$
$338$	−3.89878	+	11.9992i	−0.212066	+	0.652671i
$339$	4.69339	+	14.4448i	0.254910	+	0.784533i
$340$		0			0
$341$	15.8633	−	48.8221i	0.859045	−	2.64387i
$342$	−1.83995	−	1.33680i	−0.0994932	−	0.0722861i
$343$	5.61791			0.303339
$344$	1.22365	+	0.889032i	0.0659747	+	0.0479334i
$345$		0			0
$346$	−4.96053	+	3.60403i	−0.266680	+	0.193754i
$347$	−26.2204	+	19.0502i	−1.40758	+	1.02267i	−0.413916	+	0.910315i	$0.635839\pi$
$347$	−26.2204	+	19.0502i	−1.40758	+	1.02267i	−0.993668	+	0.112355i	$0.964161\pi$
$348$	−0.828671	−	2.55039i	−0.0444214	−	0.136715i
$349$	−11.3708			−0.608665			−0.304333	−	0.952566i	$-0.598433\pi$
$349$	−11.3708			−0.608665			−0.304333	+	0.952566i	$0.598433\pi$
$350$		0			0
$351$	0.619103			0.0330453
$352$	1.62388	+	4.99779i	0.0865531	+	0.266383i
$353$	−1.68861	+	1.22685i	−0.0898756	+	0.0652984i	−0.631816	−	0.775119i	$-0.717690\pi$
$353$	−1.68861	+	1.22685i	−0.0898756	+	0.0652984i	0.541940	+	0.840417i	$0.317690\pi$
$354$	−0.225531	+	0.163858i	−0.0119868	+	0.00870894i
$355$		0			0
$356$	10.8295	+	7.86808i	0.573961	+	0.417007i
$357$	−12.1355			−0.642279
$358$	−11.5930	−	8.42280i	−0.612708	−	0.445159i
$359$	2.10507	−	6.47874i	0.111101	−	0.341935i	−0.880013	−	0.474950i	$-0.842466\pi$
$359$	2.10507	−	6.47874i	0.111101	−	0.341935i	0.991114	+	0.133015i	$0.0424660\pi$
$360$		0			0
$361$	−4.27294	−	13.1508i	−0.224892	−	0.692146i
$362$	4.86067	−	14.9596i	0.255471	−	0.786259i
$363$	5.13427	−	15.8017i	0.269479	−	0.829372i
$364$	−0.673818	−	2.07380i	−0.0353177	−	0.108697i
$365$		0			0
$366$	1.13786	−	3.50196i	0.0594767	−	0.183050i
$367$	0.125670	+	0.0913045i	0.00655991	+	0.00476606i	0.591060	−	0.806627i	$-0.298709\pi$
$367$	0.125670	+	0.0913045i	0.00655991	+	0.00476606i	−0.584500	+	0.811393i	$0.698709\pi$
$368$	−8.95380			−0.466749
$369$	−5.09427	−	3.70121i	−0.265197	−	0.192677i
$370$		0			0
$371$	1.57676	−	1.14559i	0.0818615	−	0.0594758i
$372$	−7.90309	+	5.74193i	−0.409756	+	0.297705i
$373$	−9.19203	−	28.2902i	−0.475945	−	1.46481i	−0.844679	−	0.535274i	$-0.820208\pi$
$373$	−9.19203	−	28.2902i	−0.475945	−	1.46481i	0.368733	−	0.929535i	$-0.379792\pi$
$374$	18.1064			0.936259
$375$		0			0
$376$	10.6760			0.550575
$377$	−0.513032	−	1.57895i	−0.0264225	−	0.0813201i
$378$	2.84941	−	2.07022i	0.146558	−	0.106481i
$379$	13.4962	−	9.80558i	0.693254	−	0.503679i	−0.184474	−	0.982837i	$-0.559058\pi$
$379$	13.4962	−	9.80558i	0.693254	−	0.503679i	0.877728	+	0.479159i	$0.159058\pi$
$380$		0			0
$381$	3.53043	+	2.56501i	0.180869	+	0.131409i
$382$	−3.62240			−0.185338
$383$	9.12503	+	6.62972i	0.466267	+	0.338763i	0.795985	−	0.605317i	$-0.206954\pi$
$383$	9.12503	+	6.62972i	0.466267	+	0.338763i	−0.329718	+	0.944080i	$0.606954\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$		0			0
$386$	−3.00515	−	9.24889i	−0.152958	−	0.470756i
$387$	−0.467392	+	1.43848i	−0.0237589	+	0.0731223i
$388$	1.35104	−	4.15806i	0.0685885	−	0.211094i
$389$	2.05849	+	6.33537i	0.104369	+	0.321216i	0.989582	−	0.143971i	$-0.0459872\pi$
$389$	2.05849	+	6.33537i	0.104369	+	0.321216i	−0.885213	+	0.465187i	$0.845987\pi$
$390$		0			0
$391$	−9.53346	+	29.3410i	−0.482128	+	1.48384i
$392$	−4.37269	−	3.17694i	−0.220854	−	0.160460i
$393$	−0.617783			−0.0311630
$394$	5.72280	+	4.15786i	0.288310	+	0.209470i
$395$		0			0
$396$	−4.25137	+	3.08880i	−0.213639	+	0.155218i
$397$	30.1144	−	21.8794i	1.51140	−	1.09810i	0.545849	−	0.837884i	$-0.316207\pi$
$397$	30.1144	−	21.8794i	1.51140	−	1.09810i	0.965551	−	0.260213i	$-0.0837927\pi$
$398$	−5.46171	−	16.8094i	−0.273771	−	0.842580i
$399$	−8.01025			−0.401014
$400$		0			0
$401$	19.6891			0.983228			0.491614	−	0.870813i	$-0.336407\pi$
$401$	19.6891			0.983228			0.491614	+	0.870813i	$0.336407\pi$
$402$	−3.68104	−	11.3291i	−0.183594	−	0.565043i
$403$	−4.89283	+	3.55485i	−0.243729	+	0.177080i
$404$	11.5436	−	8.38692i	0.574316	−	0.417265i
$405$		0			0
$406$	−7.64108	−	5.55157i	−0.379220	−	0.275520i
$407$	−5.26407			−0.260930
$408$	−2.78752	−	2.02525i	−0.138003	−	0.100265i
$409$	9.13460	−	28.1134i	0.451677	−	1.39012i	−0.423316	−	0.905982i	$-0.639134\pi$
$409$	9.13460	−	28.1134i	0.451677	−	1.39012i	0.874993	−	0.484136i	$-0.160866\pi$
$410$		0			0
$411$	2.86509	+	8.81784i	0.141324	+	0.434952i
$412$	5.45980	−	16.8035i	0.268985	−	0.827851i
$413$	−0.303409	+	0.933796i	−0.0149298	+	0.0459491i
$414$	−2.76688	−	8.51557i	−0.135985	−	0.418518i
$415$		0			0
$416$	0.191313	−	0.588802i	0.00937991	−	0.0288684i
$417$	−15.1787	−	11.0279i	−0.743303	−	0.540041i
$418$	11.9514			0.584564
$419$	0.946768	+	0.687867i	0.0462526	+	0.0336045i	0.610671	−	0.791884i	$-0.290900\pi$
$419$	0.946768	+	0.687867i	0.0462526	+	0.0336045i	−0.564419	+	0.825489i	$0.690900\pi$
$420$		0			0
$421$	−6.73922	+	4.89633i	−0.328449	+	0.238632i	−0.739772	−	0.672857i	$-0.765067\pi$
$421$	−6.73922	+	4.89633i	−0.328449	+	0.238632i	0.411323	+	0.911490i	$0.365067\pi$
$422$	9.51713	−	6.91460i	0.463287	−	0.336597i
$423$	3.29908	+	10.1535i	0.160407	+	0.493681i
$424$	0.553365			0.0268738
$425$		0			0
$426$	4.74858			0.230069
$427$	−4.00760	−	12.3341i	−0.193942	−	0.596891i
$428$	−0.585496	+	0.425388i	−0.0283010	+	0.0205619i
$429$	−2.63204	+	1.91229i	−0.127076	+	0.0923261i
$430$		0			0
$431$	15.1227	+	10.9873i	0.728435	+	0.529239i	0.889068	−	0.457775i	$-0.151354\pi$
$431$	15.1227	+	10.9873i	0.728435	+	0.529239i	−0.160633	+	0.987014i	$0.551354\pi$
$432$	1.00000			0.0481125
$433$	15.2972	+	11.1140i	0.735135	+	0.534107i	0.891184	−	0.453643i	$-0.149876\pi$
$433$	15.2972	+	11.1140i	0.735135	+	0.534107i	−0.156049	+	0.987749i	$0.549876\pi$
$434$	−10.6321	+	32.7222i	−0.510357	+	1.57072i
$435$		0			0
$436$	−0.795198	−	2.44737i	−0.0380831	−	0.117208i
$437$	−6.29273	+	19.3670i	−0.301022	+	0.926450i
$438$	3.03890	−	9.35277i	0.145204	−	0.446893i
$439$	−12.6264	−	38.8602i	−0.602627	−	1.85469i	−0.512348	−	0.858778i	$-0.671224\pi$
$439$	−12.6264	−	38.8602i	−0.602627	−	1.85469i	−0.0902783	−	0.995917i	$-0.528776\pi$
$440$		0			0
$441$	1.67022	−	5.14040i	0.0795342	−	0.244781i
$442$	−1.72576	−	1.25384i	−0.0820862	−	0.0596391i
$443$	5.99083			0.284633			0.142317	−	0.989821i	$-0.454545\pi$
$443$	5.99083			0.284633			0.142317	+	0.989821i	$0.454545\pi$
$444$	0.810416	+	0.588802i	0.0384607	+	0.0279433i
$445$		0			0
$446$	10.2749	−	7.46514i	0.486530	−	0.353485i
$447$	13.6235	−	9.89807i	0.644371	−	0.468163i
$448$	−1.08838	−	3.34968i	−0.0514210	−	0.158258i
$449$	12.4505			0.587574			0.293787	−	0.955871i	$-0.405084\pi$
$449$	12.4505			0.587574			0.293787	+	0.955871i	$0.405084\pi$
$450$		0			0
$451$	33.0899			1.55814
$452$	4.69339	+	14.4448i	0.220759	+	0.679425i
$453$	−13.5860	+	9.87079i	−0.638325	+	0.463770i
$454$	11.5415	−	8.38543i	0.541672	−	0.393548i
$455$		0			0
$456$	−1.83995	−	1.33680i	−0.0861637	−	0.0626016i
$457$	1.11807			0.0523011			0.0261506	−	0.999658i	$-0.491675\pi$
$457$	1.11807			0.0523011			0.0261506	+	0.999658i	$0.491675\pi$
$458$	−7.12184	−	5.17432i	−0.332782	−	0.241780i
$459$	1.06474	−	3.27693i	0.0496977	−	0.152954i
$460$		0			0
$461$	−9.29974	−	28.6216i	−0.433132	−	1.33304i	−0.894989	−	0.446089i	$-0.852817\pi$
$461$	−9.29974	−	28.6216i	−0.433132	−	1.33304i	0.461857	−	0.886954i	$-0.347183\pi$
$462$	−5.71941	+	17.6025i	−0.266091	+	0.818944i
$463$	−6.50042	+	20.0062i	−0.302100	+	0.929768i	0.678644	+	0.734468i	$0.262568\pi$
$463$	−6.50042	+	20.0062i	−0.302100	+	0.929768i	−0.980743	+	0.195300i	$0.937432\pi$
$464$	−0.828671	−	2.55039i	−0.0384701	−	0.118399i
$465$		0			0
$466$	−4.65881	+	14.3383i	−0.215815	+	0.664211i
$467$	2.86080	+	2.07849i	0.132382	+	0.0961812i	0.652006	−	0.758214i	$-0.273928\pi$
$467$	2.86080	+	2.07849i	0.132382	+	0.0961812i	−0.519624	+	0.854395i	$0.673928\pi$
$468$	0.619103			0.0286181
$469$	−33.9425	−	24.6607i	−1.56732	−	1.13872i
$470$		0			0
$471$	−3.68467	+	2.67707i	−0.169781	+	0.123353i
$472$	−0.225531	+	0.163858i	−0.0103809	+	0.00754216i
$473$	−2.45614	−	7.55921i	−0.112933	−	0.347573i
$474$	6.52057			0.299499
$475$		0			0
$476$	−12.1355			−0.556230
$477$	0.170999	+	0.526281i	0.00782951	+	0.0240968i
$478$	5.05298	−	3.67120i	0.231118	−	0.167917i
$479$	−32.7132	+	23.7675i	−1.49470	+	1.08597i	−0.522272	+	0.852779i	$0.674915\pi$
$479$	−32.7132	+	23.7675i	−1.49470	+	1.08597i	−0.972432	+	0.233187i	$0.925085\pi$
$480$		0			0
$481$	0.501731	+	0.364529i	0.0228770	+	0.0166211i
$482$	−14.8094			−0.674551
$483$	−25.5131	−	18.5363i	−1.16088	−	0.843432i
$484$	5.13427	−	15.8017i	0.233376	−	0.718258i
$485$		0			0
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	−8.25208	+	25.3973i	−0.373938	+	1.15086i	0.570255	+	0.821468i	$0.306844\pi$
$487$	−8.25208	+	25.3973i	−0.373938	+	1.15086i	−0.944193	+	0.329394i	$0.893156\pi$
$488$	1.13786	−	3.50196i	0.0515083	−	0.158526i
$489$	−6.24624	−	19.2239i	−0.282465	−	0.869337i
$490$		0			0
$491$	10.2314	−	31.4891i	0.461738	−	1.42108i	−0.401302	−	0.915946i	$-0.631442\pi$
$491$	10.2314	−	31.4891i	0.461738	−	1.42108i	0.863040	−	0.505136i	$-0.168558\pi$
$492$	−5.09427	−	3.70121i	−0.229668	−	0.166863i
$493$	−9.23975			−0.416137
$494$	−1.13912	−	0.827619i	−0.0512514	−	0.0372363i
$495$		0			0
$496$	−7.90309	+	5.74193i	−0.354859	+	0.257820i
$497$	13.5307	−	9.83059i	0.606933	−	0.440962i
$498$	0.821902	+	2.52955i	0.0368303	+	0.113352i
$499$	6.01303			0.269180			0.134590	−	0.990901i	$-0.457028\pi$
$499$	6.01303			0.269180			0.134590	+	0.990901i	$0.457028\pi$
$500$		0			0
$501$	−7.19183			−0.321307
$502$	5.64710	+	17.3800i	0.252042	+	0.775707i
$503$	−5.39391	+	3.91890i	−0.240502	+	0.174735i	−0.701507	−	0.712662i	$-0.747489\pi$
$503$	−5.39391	+	3.91890i	−0.240502	+	0.174735i	0.461005	+	0.887398i	$0.347489\pi$
$504$	2.84941	−	2.07022i	0.126923	−	0.0922148i
$505$		0			0
$506$	38.0659	+	27.6565i	1.69224	+	1.22948i
$507$	−12.6167			−0.560328
$508$	3.53043	+	2.56501i	0.156638	+	0.113804i
$509$	−5.43941	+	16.7408i	−0.241098	+	0.742022i	0.755156	+	0.655545i	$0.227561\pi$
$509$	−5.43941	+	16.7408i	−0.241098	+	0.742022i	−0.996254	+	0.0864773i	$0.972439\pi$
$510$		0			0
$511$	−10.7032	−	32.9411i	−0.473482	−	1.45723i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	0.702799	−	2.16299i	0.0310293	−	0.0954985i
$514$	−0.556690	−	1.71331i	−0.0245545	−	0.0755711i
$515$		0			0
$516$	−0.467392	+	1.43848i	−0.0205758	+	0.0633258i
$517$	−45.3878	−	32.9762i	−1.99615	−	1.45029i
$518$	3.52816			0.155018
$519$	−4.96053	−	3.60403i	−0.217743	−	0.158199i
$520$		0			0
$521$	−14.9188	+	10.8391i	−0.653605	+	0.474872i	−0.864497	−	0.502638i	$-0.832363\pi$
$521$	−14.9188	+	10.8391i	−0.653605	+	0.474872i	0.210892	+	0.977509i	$0.432363\pi$
$522$	2.16949	−	1.57623i	0.0949559	−	0.0689895i
$523$	−3.18752	−	9.81016i	−0.139380	−	0.428968i	0.856865	−	0.515540i	$-0.172409\pi$
$523$	−3.18752	−	9.81016i	−0.139380	−	0.428968i	−0.996246	+	0.0865719i	$0.972409\pi$
$524$	−0.617783			−0.0269880
$525$		0			0
$526$	14.2039			0.619318
$527$	10.4012	+	32.0115i	0.453082	+	1.39444i
$528$	−4.25137	+	3.08880i	−0.185017	+	0.134423i
$529$	−46.2520	+	33.6040i	−2.01096	+	1.46105i
$530$		0			0
$531$	−0.225531	−	0.163858i	−0.00978720	−	0.00711082i
$532$	−8.01025			−0.347288
$533$	−3.15388	−	2.29143i	−0.136610	−	0.0992528i
$534$	−4.13649	+	12.7308i	−0.179004	+	0.550916i
$535$		0			0
$536$	−3.68104	−	11.3291i	−0.158997	−	0.489342i
$537$	4.42813	−	13.6284i	0.191088	−	0.588108i
$538$	−1.92922	+	5.93752i	−0.0831744	+	0.255985i
$539$	8.77697	+	27.0127i	0.378051	+	1.16352i
$540$		0			0
$541$	−11.5756	+	35.6262i	−0.497676	+	1.53169i	0.315069	+	0.949069i	$0.397972\pi$
$541$	−11.5756	+	35.6262i	−0.497676	+	1.53169i	−0.812745	+	0.582620i	$0.802028\pi$
$542$	19.2926	+	14.0169i	0.828687	+	0.602076i
$543$	15.7294			0.675015
$544$	−2.78752	−	2.02525i	−0.119514	−	0.0868320i
$545$		0			0
$546$	1.76408	−	1.28168i	0.0754956	−	0.0548508i
$547$	−8.93631	+	6.49261i	−0.382089	+	0.277604i	−0.762206	−	0.647334i	$-0.775884\pi$
$547$	−8.93631	+	6.49261i	−0.382089	+	0.277604i	0.380117	+	0.924938i	$0.375884\pi$
$548$	2.86509	+	8.81784i	0.122391	+	0.376679i
$549$	3.68218			0.157152
$550$		0			0
$551$	−6.09886			−0.259820
$552$	−2.76688	−	8.51557i	−0.117766	−	0.362447i
$553$	18.5798	−	13.4990i	0.790092	−	0.574035i
$554$	5.64173	−	4.09896i	0.239694	−	0.174148i
$555$		0			0
$556$	−15.1787	−	11.0279i	−0.643719	−	0.467689i
$557$	29.7087			1.25880			0.629400	−	0.777082i	$-0.283301\pi$
$557$	29.7087			1.25880			0.629400	+	0.777082i	$0.283301\pi$
$558$	−7.90309	−	5.74193i	−0.334564	−	0.243075i
$559$	−0.289364	+	0.890570i	−0.0122388	+	0.0376671i
$560$		0			0
$561$	5.59518	+	17.2202i	0.236229	+	0.727038i
$562$	3.59504	−	11.0644i	0.151647	−	0.466723i
$563$	5.66439	−	17.4332i	0.238726	−	0.734722i	−0.757880	−	0.652394i	$-0.773765\pi$
$563$	5.66439	−	17.4332i	0.238726	−	0.734722i	0.996605	−	0.0823274i	$-0.0262353\pi$
$564$	3.29908	+	10.1535i	0.138916	+	0.427540i
$565$		0			0
$566$	2.96811	−	9.13490i	0.124759	−	0.383969i
$567$	2.84941	+	2.07022i	0.119664	+	0.0869410i
$568$	4.74858			0.199246
$569$	17.7915	+	12.9263i	0.745859	+	0.541898i	0.894541	−	0.446987i	$-0.147503\pi$
$569$	17.7915	+	12.9263i	0.745859	+	0.541898i	−0.148681	+	0.988885i	$0.547503\pi$
$570$		0			0
$571$	−20.2890	+	14.7408i	−0.849069	+	0.616885i	−0.924889	−	0.380237i	$-0.875843\pi$
$571$	−20.2890	+	14.7408i	−0.849069	+	0.616885i	0.0758199	+	0.997122i	$0.475843\pi$
$572$	−2.63204	+	1.91229i	−0.110051	+	0.0799567i
$573$	−1.11938	−	3.44511i	−0.0467629	−	0.143922i
$574$	−22.1780			−0.925691
$575$		0			0
$576$	1.00000			0.0416667
$577$	10.8117	+	33.2751i	0.450099	+	1.38526i	0.876794	+	0.480866i	$0.159678\pi$
$577$	10.8117	+	33.2751i	0.450099	+	1.38526i	−0.426695	+	0.904395i	$0.640322\pi$
$578$	4.14870	−	3.01421i	0.172563	−	0.125374i
$579$	7.86757	−	5.71613i	0.326965	−	0.237554i
$580$		0			0
$581$	7.57866	+	5.50622i	0.314416	+	0.228437i
$582$	4.37205			0.181227
$583$	−2.35256	−	1.70923i	−0.0974330	−	0.0707892i
$584$	3.03890	−	9.35277i	0.125751	−	0.387020i
$585$		0			0
$586$	−2.63504	−	8.10981i	−0.108852	−	0.335013i
$587$	3.20936	−	9.87738i	0.132464	−	0.407683i	−0.862723	−	0.505677i	$-0.831243\pi$
$587$	3.20936	−	9.87738i	0.132464	−	0.407683i	0.995187	+	0.0979941i	$0.0312426\pi$
$588$	1.67022	−	5.14040i	0.0688786	−	0.211987i
$589$	6.86547	+	21.1298i	0.282887	+	0.870636i
$590$		0			0
$591$	−2.18591	+	6.72755i	−0.0899165	+	0.276734i
$592$	0.810416	+	0.588802i	0.0333079	+	0.0241996i
$593$	−0.948200			−0.0389379			−0.0194690	−	0.999810i	$-0.506198\pi$
$593$	−0.948200			−0.0389379			−0.0194690	+	0.999810i	$0.506198\pi$
$594$	−4.25137	−	3.08880i	−0.174436	−	0.126735i
$595$		0			0
$596$	13.6235	−	9.89807i	0.558041	−	0.405441i
$597$	14.2990	−	10.3888i	0.585217	−	0.425185i
$598$	−1.71298	−	5.27202i	−0.0700491	−	0.215589i
$599$	25.4901			1.04150			0.520748	−	0.853710i	$-0.325653\pi$
$599$	25.4901			1.04150			0.520748	+	0.853710i	$0.325653\pi$
$600$		0			0
$601$	−16.6409			−0.678797			−0.339399	−	0.940643i	$-0.610224\pi$
$601$	−16.6409			−0.678797			−0.339399	+	0.940643i	$0.610224\pi$
$602$	1.64618	+	5.06644i	0.0670935	+	0.206492i
$603$	9.63710	−	7.00176i	0.392453	−	0.285134i
$604$	−13.5860	+	9.87079i	−0.552805	+	0.401637i
$605$		0			0
$606$	11.5436	+	8.38692i	0.468927	+	0.340695i
$607$	−33.2662			−1.35023			−0.675116	−	0.737712i	$-0.735906\pi$
$607$	−33.2662			−1.35023			−0.675116	+	0.737712i	$0.735906\pi$
$608$	−1.83995	−	1.33680i	−0.0746199	−	0.0542145i
$609$	2.91863	−	8.98262i	0.118269	−	0.363994i
$610$		0			0
$611$	2.04247	+	6.28607i	0.0826295	+	0.254307i
$612$	1.06474	−	3.27693i	0.0430395	−	0.132462i
$613$	5.03144	−	15.4852i	0.203218	−	0.625440i	−0.796564	−	0.604554i	$-0.793351\pi$
$613$	5.03144	−	15.4852i	0.203218	−	0.625440i	0.999782	−	0.0208859i	$-0.00664867\pi$
$614$	−0.883153	−	2.71807i	−0.0356412	−	0.109692i
$615$		0			0
$616$	−5.71941	+	17.6025i	−0.230442	+	0.709226i
$617$	−39.2603	−	28.5243i	−1.58056	−	1.14834i	−0.916050	−	0.401063i	$-0.868641\pi$
$617$	−39.2603	−	28.5243i	−1.58056	−	1.14834i	−0.664509	−	0.747280i	$-0.731359\pi$
$618$	17.6683			0.710723
$619$	19.9552	+	14.4983i	0.802066	+	0.582735i	0.911519	−	0.411257i	$-0.134910\pi$
$619$	19.9552	+	14.4983i	0.802066	+	0.582735i	−0.109454	+	0.993992i	$0.534910\pi$
$620$		0			0
$621$	7.24378	−	5.26291i	0.290683	−	0.211193i
$622$	8.22107	−	5.97296i	0.329635	−	0.239494i
$623$	14.5690	+	44.8388i	0.583694	+	1.79643i
$624$	0.619103			0.0247840
$625$		0			0
$626$	−18.2036			−0.727563
$627$	3.69320	+	11.3665i	0.147492	+	0.453934i
$628$	−3.68467	+	2.67707i	−0.147034	+	0.106827i
$629$	2.79234	−	2.02876i	0.111338	−	0.0808918i
$630$		0			0
$631$	9.54099	+	6.93194i	0.379821	+	0.275956i	0.761272	−	0.648433i	$-0.224575\pi$
$631$	9.54099	+	6.93194i	0.379821	+	0.275956i	−0.381451	+	0.924389i	$0.624575\pi$
$632$	6.52057			0.259374
$633$	9.51713	+	6.91460i	0.378272	+	0.274831i
$634$	−9.66493	+	29.7456i	−0.383843	+	1.18135i
$635$		0			0
$636$	0.170999	+	0.526281i	0.00678056	+	0.0208684i
$637$	1.03404	−	3.18244i	0.0409700	−	0.126093i
$638$	−4.35465	+	13.4022i	−0.172402	+	0.530600i
$639$	1.46739	+	4.51617i	0.0580491	+	0.178657i
$640$		0			0
$641$	−4.20359	+	12.9373i	−0.166032	+	0.510994i	−0.999111	−	0.0421603i	$-0.986576\pi$
$641$	−4.20359	+	12.9373i	−0.166032	+	0.510994i	0.833079	+	0.553154i	$0.186576\pi$
$642$	−0.585496	−	0.425388i	−0.0231077	−	0.0167887i
$643$	−20.9102			−0.824617			−0.412308	−	0.911044i	$-0.635277\pi$
$643$	−20.9102			−0.824617			−0.412308	+	0.911044i	$0.635277\pi$
$644$	−25.5131	−	18.5363i	−1.00536	−	0.730433i
$645$		0			0
$646$	−6.33968	+	4.60604i	−0.249431	+	0.181222i
$647$	37.1240	−	26.9722i	1.45950	−	1.06039i	0.476002	−	0.879444i	$-0.342086\pi$
$647$	37.1240	−	26.9722i	1.45950	−	1.06039i	0.983494	−	0.180941i	$-0.0579144\pi$
$648$	0.309017	+	0.951057i	0.0121393	+	0.0373610i
$649$	1.46494			0.0575039
$650$		0			0
$651$	−34.4062			−1.34848
$652$	−6.24624	−	19.2239i	−0.244622	−	0.752868i
$653$	2.10838	−	1.53183i	0.0825072	−	0.0599450i	−0.545767	−	0.837937i	$-0.683762\pi$
$653$	2.10838	−	1.53183i	0.0825072	−	0.0599450i	0.628274	+	0.777992i	$0.283762\pi$
$654$	2.08185	−	1.51256i	0.0814069	−	0.0591456i
$655$		0			0
$656$	−5.09427	−	3.70121i	−0.198898	−	0.144508i
$657$	9.83408			0.383664
$658$	30.4204	+	22.1017i	1.18591	+	0.861615i
$659$	7.39977	−	22.7742i	0.288254	−	0.887155i	−0.697150	−	0.716925i	$-0.745549\pi$
$659$	7.39977	−	22.7742i	0.288254	−	0.887155i	0.985404	−	0.170230i	$-0.0544511\pi$
$660$		0			0
$661$	8.01908	+	24.6802i	0.311906	+	0.959948i	0.977009	+	0.213196i	$0.0683874\pi$
$661$	8.01908	+	24.6802i	0.311906	+	0.959948i	−0.665103	+	0.746751i	$0.731613\pi$
$662$	1.06053	−	3.26397i	0.0412186	−	0.126858i
$663$	0.659183	−	2.02876i	0.0256005	−	0.0787904i
$664$	0.821902	+	2.52955i	0.0318960	+	0.0981657i
$665$		0			0
$666$	−0.309552	+	0.952702i	−0.0119949	+	0.0369164i
$667$	−19.4252	−	14.1132i	−0.752145	−	0.546466i
$668$	−7.19183			−0.278260
$669$	10.2749	+	7.46514i	0.397250	+	0.288619i
$670$		0			0
$671$	−15.6543	+	11.3735i	−0.604328	+	0.439070i
$672$	2.84941	−	2.07022i	0.109918	−	0.0798604i
$673$	4.57632	+	14.0845i	0.176404	+	0.542916i	0.999695	−	0.0247037i	$-0.00786423\pi$
$673$	4.57632	+	14.0845i	0.176404	+	0.542916i	−0.823291	+	0.567620i	$0.807864\pi$
$674$	−11.7235			−0.451574
$675$		0			0
$676$	−12.6167			−0.485258
$677$	−10.7946	−	33.2224i	−0.414870	−	1.27684i	−0.912367	−	0.409373i	$-0.865747\pi$
$677$	−10.7946	−	33.2224i	−0.414870	−	1.27684i	0.497497	−	0.867466i	$-0.334253\pi$
$678$	−12.2875	+	8.92737i	−0.471897	+	0.342853i
$679$	12.4578	−	9.05109i	0.478085	−	0.347349i
$680$		0			0
$681$	11.5415	+	8.38543i	0.442273	+	0.321330i
$682$	51.3346			1.96571
$683$	−16.9963	−	12.3485i	−0.650346	−	0.472504i	0.213043	−	0.977043i	$-0.431662\pi$
$683$	−16.9963	−	12.3485i	−0.650346	−	0.472504i	−0.863389	+	0.504539i	$0.831662\pi$
$684$	0.702799	−	2.16299i	0.0268722	−	0.0827041i
$685$		0			0
$686$	1.73603	+	5.34295i	0.0662819	+	0.203995i
$687$	2.72030	−	8.37223i	0.103786	−	0.319421i
$688$	−0.467392	+	1.43848i	−0.0178192	+	0.0548417i
$689$	0.105866	+	0.325822i	0.00403318	+	0.0124128i
$690$		0			0
$691$	−7.23231	+	22.2588i	−0.275130	+	0.846763i	0.714055	+	0.700090i	$0.246857\pi$
$691$	−7.23231	+	22.2588i	−0.275130	+	0.846763i	−0.989185	+	0.146673i	$0.953143\pi$
$692$	−4.96053	−	3.60403i	−0.188571	−	0.137005i
$693$	−18.5084			−0.703076
$694$	−26.2204	−	19.0502i	−0.995312	−	0.723137i
$695$		0			0
$696$	2.16949	−	1.57623i	0.0822342	−	0.0597467i
$697$	−17.5527	+	12.7528i	−0.664854	+	0.483045i
$698$	−3.51377	−	10.8143i	−0.132998	−	0.409326i
$699$	−15.0762			−0.570235
$700$		0			0
$701$	−43.2849			−1.63485			−0.817424	−	0.576037i	$-0.804598\pi$
$701$	−43.2849			−1.63485			−0.817424	+	0.576037i	$0.804598\pi$
$702$	0.191313	+	0.588802i	0.00722066	+	0.0222229i
$703$	1.84314	−	1.33912i	0.0695152	−	0.0505057i
$704$	−4.25137	+	3.08880i	−0.160230	+	0.116414i
$705$		0			0
$706$	−1.68861	−	1.22685i	−0.0635516	−	0.0461730i
$707$	50.2552			1.89004
$708$	−0.225531	−	0.163858i	−0.00847597	−	0.00615815i
$709$	−7.72993	+	23.7903i	−0.290303	+	0.893462i	0.694455	+	0.719536i	$0.255645\pi$
$709$	−7.72993	+	23.7903i	−0.290303	+	0.893462i	−0.984759	+	0.173926i	$0.944355\pi$
$710$		0			0
$711$	2.01497	+	6.20143i	0.0755671	+	0.232572i
$712$	−4.13649	+	12.7308i	−0.155022	+	0.477108i
$713$	−27.0289	+	83.1865i	−1.01224	+	3.11536i
$714$	−3.75008	−	11.5416i	−0.140343	−	0.431932i
$715$		0			0
$716$	4.42813	−	13.6284i	0.165487	−	0.509316i
$717$	5.05298	+	3.67120i	0.188707	+	0.137104i
$718$	6.81215			0.254227
$719$	24.9533	+	18.1296i	0.930601	+	0.676121i	0.946140	−	0.323758i	$-0.104946\pi$
$719$	24.9533	+	18.1296i	0.930601	+	0.676121i	−0.0155391	+	0.999879i	$0.504946\pi$
$720$		0			0
$721$	50.3442	−	36.5772i	1.87492	−	1.36221i
$722$	11.1867	−	8.12762i	0.416326	−	0.302479i
$723$	−4.57636	−	14.0846i	−0.170197	−	0.523812i
$724$	15.7294			0.584580
$725$		0			0
$726$	16.6149			0.616635
$727$	−0.202574	−	0.623458i	−0.00751304	−	0.0231228i	0.947230	−	0.320556i	$-0.103870\pi$
$727$	−0.202574	−	0.623458i	−0.00751304	−	0.0231228i	−0.954743	+	0.297433i	$0.903870\pi$
$728$	1.76408	−	1.28168i	0.0653811	−	0.0475022i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	4.21616	+	3.06322i	0.155940	+	0.113297i
$732$	3.68218			0.136097
$733$	11.0933	+	8.05975i	0.409740	+	0.297694i	0.773497	−	0.633800i	$-0.218506\pi$
$733$	11.0933	+	8.05975i	0.409740	+	0.297694i	−0.363756	+	0.931494i	$0.618506\pi$
$734$	−0.0480016	+	0.147734i	−0.00177177	+	0.00545295i
$735$		0			0
$736$	−2.76688	−	8.51557i	−0.101988	−	0.313888i
$737$	−19.3438	+	59.5342i	−0.712539	+	2.19297i
$738$	1.94584	−	5.98868i	0.0716273	−	0.220446i
$739$	−3.38589	−	10.4207i	−0.124552	−	0.383332i	0.869267	−	0.494343i	$-0.164591\pi$
$739$	−3.38589	−	10.4207i	−0.124552	−	0.383332i	−0.993819	+	0.111011i	$0.964591\pi$
$740$		0			0
$741$	0.435105	−	1.33912i	0.0159840	−	0.0491937i
$742$	1.57676	+	1.14559i	0.0578848	+	0.0420558i
$743$	−5.67053			−0.208032			−0.104016	−	0.994576i	$-0.533169\pi$
$743$	−5.67053			−0.208032			−0.104016	+	0.994576i	$0.533169\pi$
$744$	−7.90309	−	5.74193i	−0.289741	−	0.210509i
$745$		0			0
$746$	24.0650	−	17.4843i	0.881084	−	0.640145i
$747$	−2.15177	+	1.56335i	−0.0787290	+	0.0572000i
$748$	5.59518	+	17.2202i	0.204580	+	0.629633i
$749$	−2.54896			−0.0931371
$750$		0			0
$751$	−22.2909			−0.813408			−0.406704	−	0.913560i	$-0.633322\pi$
$751$	−22.2909			−0.813408			−0.406704	+	0.913560i	$0.633322\pi$
$752$	3.29908	+	10.1535i	0.120305	+	0.370261i
$753$	−14.7843	+	10.7414i	−0.538770	+	0.391439i
$754$	1.34314	−	0.975846i	0.0489141	−	0.0355382i
$755$		0			0
$756$	2.84941	+	2.07022i	0.103632	+	0.0752931i
$757$	17.3894			0.632030			0.316015	−	0.948754i	$-0.397655\pi$
$757$	17.3894			0.632030			0.316015	+	0.948754i	$0.397655\pi$
$758$	13.4962	+	9.80558i	0.490205	+	0.356155i
$759$	−14.5399	+	44.7492i	−0.527765	+	1.62429i
$760$		0			0
$761$	4.78812	+	14.7363i	0.173569	+	0.534191i	0.999565	−	0.0294850i	$-0.00938672\pi$
$761$	4.78812	+	14.7363i	0.173569	+	0.534191i	−0.825996	+	0.563676i	$0.809387\pi$
$762$	−1.34850	+	4.15027i	−0.0488512	+	0.150348i
$763$	2.80074	−	8.61978i	0.101393	−	0.312057i
$764$	−1.11938	−	3.44511i	−0.0404979	−	0.124640i
$765$		0			0
$766$	−3.48545	+	10.7271i	−0.125934	+	0.387586i
$767$	−0.139627	−	0.101445i	−0.00504163	−	0.00366296i
$768$	1.00000			0.0360844
$769$	39.5215	+	28.7140i	1.42518	+	1.03545i	0.990889	+	0.134683i	$0.0430015\pi$
$769$	39.5215	+	28.7140i	1.42518	+	1.03545i	0.434292	+	0.900772i	$0.356998\pi$
$770$		0			0
$771$	1.45743	−	1.05889i	0.0524881	−	0.0381349i
$772$	7.86757	−	5.71613i	0.283160	−	0.205728i
$773$	−0.332330	−	1.02281i	−0.0119531	−	0.0367878i	0.944902	−	0.327353i	$-0.106157\pi$
$773$	−0.332330	−	1.02281i	−0.0119531	−	0.0367878i	−0.956855	+	0.290565i	$0.906157\pi$
$774$	−1.51251			−0.0543661
$775$		0			0
$776$	4.37205			0.156947
$777$	1.09026	+	3.35548i	0.0391129	+	0.120377i
$778$	−5.38919	+	3.91547i	−0.193212	+	0.140377i
$779$	−11.5859	+	8.41768i	−0.415109	+	0.301595i
$780$		0			0
$781$	−20.1880	−	14.6674i	−0.722383	−	0.524842i
$782$	−30.8509			−1.10323
$783$	2.16949	+	1.57623i	0.0775312	+	0.0563297i
$784$	1.67022	−	5.14040i	0.0596506	−	0.183586i
$785$		0			0
$786$	−0.190905	−	0.587547i	−0.00680937	−	0.0209571i
$787$	11.6956	−	35.9953i	0.416903	−	1.28310i	−0.493635	−	0.869669i	$-0.664332\pi$
$787$	11.6956	−	35.9953i	0.416903	−	1.28310i	0.910538	−	0.413426i	$-0.135668\pi$
$788$	−2.18591	+	6.72755i	−0.0778700	+	0.239659i
$789$	4.38923	+	13.5087i	0.156261	+	0.480922i
$790$		0			0
$791$	−16.5304	+	50.8755i	−0.587755	+	1.80892i
$792$	−4.25137	−	3.08880i	−0.151066	−	0.109756i
$793$	2.27965			0.0809527
$794$	30.1144	+	21.8794i	1.06872	+	0.776471i
$795$		0			0
$796$	14.2990	−	10.3888i	0.506813	−	0.368221i
$797$	9.35037	−	6.79344i	0.331207	−	0.240636i	−0.409736	−	0.912204i	$-0.634379\pi$
$797$	9.35037	−	6.79344i	0.331207	−	0.240636i	0.740943	+	0.671568i	$0.234379\pi$
$798$	−2.47530	−	7.61820i	−0.0876248	−	0.269681i
$799$	36.7850			1.30136
$800$		0			0
$801$	−13.3860			−0.472970
$802$	6.08427	+	18.7255i	0.214843	+	0.661219i
$803$	−41.8083	+	30.3755i	−1.47538	+	1.07193i
$804$	9.63710	−	7.00176i	0.339874	−	0.246933i
$805$		0			0
$806$	−4.89283	−	3.55485i	−0.172342	−	0.125214i
$807$	−6.24307			−0.219767
$808$	11.5436	+	8.38692i	0.406103	+	0.295051i
$809$	−6.24192	+	19.2106i	−0.219454	+	0.675410i	0.779353	+	0.626585i	$0.215548\pi$
$809$	−6.24192	+	19.2106i	−0.219454	+	0.675410i	−0.998807	+	0.0488254i	$0.984452\pi$
$810$		0			0
$811$	−12.8802	−	39.6412i	−0.452285	−	1.39199i	−0.874293	−	0.485399i	$-0.838674\pi$
$811$	−12.8802	−	39.6412i	−0.452285	−	1.39199i	0.422008	−	0.906592i	$-0.361326\pi$
$812$	2.91863	−	8.98262i	0.102424	−	0.315228i
$813$	−7.36910	+	22.6798i	−0.258446	+	0.795414i
$814$	−1.62669	−	5.00643i	−0.0570154	−	0.175475i
$815$		0			0
$816$	1.06474	−	3.27693i	0.0372733	−	0.114715i
$817$	2.78295	+	2.02193i	0.0973631	+	0.0707384i
$818$	29.5602			1.03355
$819$	1.76408	+	1.28168i	0.0616419	+	0.0447855i
$820$		0			0
$821$	26.4710	−	19.2323i	0.923844	−	0.671212i	−0.0206340	−	0.999787i	$-0.506568\pi$
$821$	26.4710	−	19.2323i	0.923844	−	0.671212i	0.944478	+	0.328575i	$0.106568\pi$
$822$	−7.50090	+	5.44972i	−0.261624	+	0.190081i
$823$	10.3474	+	31.8460i	0.360687	+	1.11008i	0.952638	+	0.304107i	$0.0983581\pi$
$823$	10.3474	+	31.8460i	0.360687	+	1.11008i	−0.591950	+	0.805974i	$0.701642\pi$
$824$	17.6683			0.615504
$825$		0			0
$826$	−0.981851			−0.0341630
$827$	−2.70350	−	8.32052i	−0.0940100	−	0.289333i	0.892984	−	0.450088i	$-0.148607\pi$
$827$	−2.70350	−	8.32052i	−0.0940100	−	0.289333i	−0.986994	+	0.160755i	$0.948607\pi$
$828$	7.24378	−	5.26291i	0.251739	−	0.182899i
$829$	−15.3302	+	11.1381i	−0.532441	+	0.386841i	−0.821270	−	0.570539i	$-0.806734\pi$
$829$	−15.3302	+	11.1381i	−0.532441	+	0.386841i	0.288829	+	0.957381i	$0.406734\pi$
$830$		0			0
$831$	5.64173	+	4.09896i	0.195710	+	0.142191i
$832$	0.619103			0.0214635
$833$	−15.0664	−	10.9464i	−0.522019	−	0.379269i
$834$	5.79774	−	17.8436i	0.200759	−	0.617873i
$835$		0			0
$836$	3.69320	+	11.3665i	0.127732	+	0.393118i
$837$	3.01871	−	9.29064i	0.104342	−	0.321131i
$838$	−0.361633	+	1.11299i	−0.0124924	+	0.0384477i
$839$	−3.54657	−	10.9152i	−0.122441	−	0.376835i	0.870985	−	0.491309i	$-0.163482\pi$
$839$	−3.54657	−	10.9152i	−0.122441	−	0.376835i	−0.993426	+	0.114474i	$0.963482\pi$
$840$		0			0
$841$	−6.73930	+	20.7414i	−0.232390	+	0.715222i
$842$	−6.73922	−	4.89633i	−0.232249	−	0.168739i
$843$	11.6338			0.400689
$844$	9.51713	+	6.91460i	0.327593	+	0.238010i
$845$		0			0
$846$	−8.63710	+	6.27522i	−0.296949	+	0.215746i
$847$	47.3425	−	34.3964i	1.62671	−	1.18187i
$848$	0.170999	+	0.526281i	0.00587213	+	0.0180726i
$849$	9.60500			0.329643
$850$		0			0
$851$	8.96929			0.307463
$852$	1.46739	+	4.51617i	0.0502720	+	0.154721i
$853$	8.39899	−	6.10223i	0.287576	−	0.208936i	−0.434639	−	0.900605i	$-0.643124\pi$
$853$	8.39899	−	6.10223i	0.287576	−	0.208936i	0.722215	+	0.691668i	$0.243124\pi$
$854$	10.4920	−	7.62292i	0.359030	−	0.260851i
$855$		0			0
$856$	−0.585496	−	0.425388i	−0.0200119	−	0.0145395i
$857$	−32.7252			−1.11787			−0.558936	−	0.829211i	$-0.688790\pi$
$857$	−32.7252			−1.11787			−0.558936	+	0.829211i	$0.688790\pi$
$858$	−2.63204	−	1.91229i	−0.0898563	−	0.0652844i
$859$	6.38693	−	19.6569i	0.217919	−	0.670686i	−0.781014	−	0.624513i	$-0.785297\pi$
$859$	6.38693	−	19.6569i	0.217919	−	0.670686i	0.998933	−	0.0461730i	$-0.0147026\pi$
$860$		0			0
$861$	−6.85337	−	21.0925i	−0.233562	−	0.718831i
$862$	−5.77636	+	17.7778i	−0.196744	+	0.605515i
$863$	17.4041	−	53.5643i	0.592443	−	1.82335i	0.0253777	−	0.999678i	$-0.491921\pi$
$863$	17.4041	−	53.5643i	0.592443	−	1.82335i	0.567065	−	0.823673i	$-0.308079\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$		0			0
$866$	−5.84299	+	17.9829i	−0.198553	+	0.611083i
$867$	4.14870	+	3.01421i	0.140897	+	0.102368i
$868$	−34.4062			−1.16782
$869$	−27.7213	−	20.1407i	−0.940382	−	0.683228i
$870$		0			0
$871$	5.96636	−	4.33481i	0.202162	−	0.146879i
$872$	2.08185	−	1.51256i	0.0705005	−	0.0512216i
$873$	1.35104	+	4.15806i	0.0457257	+	0.140729i
$874$	−20.3637			−0.688812
$875$		0			0
$876$	9.83408			0.332263
$877$	13.9318	+	42.8777i	0.470443	+	1.44788i	0.852006	+	0.523533i	$0.175386\pi$
$877$	13.9318	+	42.8777i	0.470443	+	1.44788i	−0.381562	+	0.924343i	$0.624614\pi$
$878$	33.0564	−	24.0169i	1.11560	−	0.810531i
$879$	6.89862	−	5.01214i	0.232685	−	0.169055i
$880$		0			0
$881$	−25.2754	−	18.3636i	−0.851550	−	0.618687i	0.0740232	−	0.997257i	$-0.476416\pi$
$881$	−25.2754	−	18.3636i	−0.851550	−	0.618687i	−0.925573	+	0.378569i	$0.876416\pi$
$882$	5.40494			0.181994
$883$	21.7253	+	15.7843i	0.731113	+	0.531185i	0.889915	−	0.456126i	$-0.150763\pi$
$883$	21.7253	+	15.7843i	0.731113	+	0.531185i	−0.158802	+	0.987310i	$0.550763\pi$
$884$	0.659183	−	2.02876i	0.0221707	−	0.0682345i
$885$		0			0
$886$	1.85127	+	5.69762i	0.0621946	+	0.191415i
$887$	4.50825	−	13.8750i	0.151372	−	0.465876i	−0.846403	−	0.532543i	$-0.821237\pi$
$887$	4.50825	−	13.8750i	0.151372	−	0.465876i	0.997775	+	0.0666671i	$0.0212366\pi$
$888$	−0.309552	+	0.952702i	−0.0103879	+	0.0319706i
$889$	4.74952	+	14.6175i	0.159294	+	0.490256i
$890$		0			0
$891$	1.62388	−	4.99779i	0.0544020	−	0.167432i
$892$	10.2749	+	7.46514i	0.344029	+	0.249952i
$893$	24.2806			0.812519
$894$	13.6235	+	9.89807i	0.455639	+	0.331041i
$895$		0			0
$896$	2.84941	−	2.07022i	0.0951921	−	0.0691611i
$897$	4.48465	−	3.25829i	0.149738	−	0.108791i
$898$	3.84740	+	11.8411i	0.128390	+	0.395142i
$899$	−26.1962			−0.873693
$900$		0			0
$901$	1.90665			0.0635199
$902$	10.2254	+	31.4704i	0.340467	+	1.04785i
$903$	−4.30977	+	3.13123i	−0.143420	+	0.104201i
$904$	−12.2875	+	8.92737i	−0.408675	+	0.296920i
$905$		0			0
$906$	−13.5860	−	9.87079i	−0.451364	−	0.327935i
$907$	−29.5506			−0.981211			−0.490606	−	0.871382i	$-0.663224\pi$
$907$	−29.5506			−0.981211			−0.490606	+	0.871382i	$0.663224\pi$
$908$	11.5415	+	8.38543i	0.383020	+	0.278280i
$909$	−4.40926	+	13.5703i	−0.146246	+	0.450099i
$910$		0			0
$911$	1.30316	+	4.01073i	0.0431757	+	0.132881i	0.970321	−	0.241821i	$-0.0777448\pi$
$911$	1.30316	+	4.01073i	0.0431757	+	0.132881i	−0.927145	+	0.374703i	$0.877745\pi$
$912$	0.702799	−	2.16299i	0.0232720	−	0.0716239i
$913$	4.31908	−	13.2928i	0.142941	−	0.439926i
$914$	0.345503	+	1.06335i	0.0114282	+	0.0351724i
$915$		0			0
$916$	2.72030	−	8.37223i	0.0898813	−	0.276626i
$917$	−1.76032	−	1.27895i	−0.0581308	−	0.0422345i
$918$	3.44557			0.113721
$919$	−23.0230	−	16.7272i	−0.759459	−	0.551779i	0.139286	−	0.990252i	$-0.455519\pi$
$919$	−23.0230	−	16.7272i	−0.759459	−	0.551779i	−0.898744	+	0.438473i	$0.855519\pi$
$920$		0			0
$921$	2.31212	−	1.67986i	0.0761871	−	0.0553532i
$922$	24.3470	−	17.6892i	0.801827	−	0.582561i
$923$	0.908467	+	2.79597i	0.0299026	+	0.0920306i
$924$	−18.5084			−0.608881
$925$		0			0
$926$	−21.0358			−0.691279
$927$	5.45980	+	16.8035i	0.179323	+	0.551901i
$928$	2.16949	−	1.57623i	0.0712169	−	0.0517421i
$929$	21.2379	−	15.4302i	0.696792	−	0.506249i	−0.182094	−	0.983281i	$-0.558288\pi$
$929$	21.2379	−	15.4302i	0.696792	−	0.506249i	0.878886	+	0.477032i	$0.158288\pi$
$930$		0			0
$931$	−9.94483	−	7.22534i	−0.325929	−	0.236801i
$932$	−15.0762			−0.493838
$933$	8.22107	+	5.97296i	0.269146	+	0.195546i
$934$	−1.09273	+	3.36307i	−0.0357552	+	0.110043i
$935$		0			0
$936$	0.191313	+	0.588802i	0.00625327	+	0.0192456i
$937$	1.64774	−	5.07121i	0.0538292	−	0.165669i	−0.920528	−	0.390677i	$-0.872241\pi$
$937$	1.64774	−	5.07121i	0.0538292	−	0.165669i	0.974357	+	0.225008i	$0.0722408\pi$
$938$	12.9649	−	39.9018i	0.423318	−	1.30284i
$939$	−5.62523	−	17.3127i	−0.183572	−	0.564978i
$940$		0			0
$941$	−2.62746	+	8.08650i	−0.0856529	+	0.263612i	−0.984705	−	0.174229i	$-0.944257\pi$
$941$	−2.62746	+	8.08650i	−0.0856529	+	0.263612i	0.899052	+	0.437841i	$0.144257\pi$
$942$	−3.68467	−	2.67707i	−0.120053	−	0.0872237i
$943$	−56.3809			−1.83602
$944$	−0.225531	−	0.163858i	−0.00734040	−	0.00533311i
$945$		0			0
$946$	6.43025	−	4.67185i	0.209065	−	0.151895i
$947$	−18.0650	+	13.1250i	−0.587033	+	0.426504i	−0.841253	−	0.540642i	$-0.818181\pi$
$947$	−18.0650	+	13.1250i	−0.587033	+	0.426504i	0.254220	+	0.967146i	$0.418181\pi$
$948$	2.01497	+	6.20143i	0.0654430	+	0.201413i
$949$	6.08831			0.197635
$950$		0			0
$951$	−31.2764			−1.01421
$952$	−3.75008	−	11.5416i	−0.121541	−	0.374064i
$953$	11.0509	−	8.02894i	0.357973	−	0.260083i	−0.394233	−	0.919011i	$-0.628990\pi$
$953$	11.0509	−	8.02894i	0.357973	−	0.260083i	0.752206	+	0.658928i	$0.228990\pi$
$954$	−0.447681	+	0.325260i	−0.0144942	+	0.0105307i
$955$		0			0
$956$	5.05298	+	3.67120i	0.163425	+	0.118735i
$957$	−14.0919			−0.455528
$958$	−32.7132	−	23.7675i	−1.05692	−	0.767894i
$959$	−10.0910	+	31.0570i	−0.325856	+	1.00288i
$960$		0			0
$961$	19.9095	+	61.2752i	0.642243	+	1.97662i
$962$	−0.191644	+	0.589821i	−0.00617886	+	0.0190166i
$963$	0.223640	−	0.688292i	0.00720669	−	0.0221799i
$964$	−4.57636	−	14.0846i	−0.147395	−	0.453634i
$965$		0			0
$966$	9.74512	−	29.9924i	0.313544	−	0.964990i
$967$	−25.4414	−	18.4843i	−0.818141	−	0.594414i	0.0980386	−	0.995183i	$-0.468743\pi$
$967$	−25.4414	−	18.4843i	−0.818141	−	0.594414i	−0.916179	+	0.400769i	$0.868743\pi$
$968$	16.6149			0.534022
$969$	−6.33968	−	4.60604i	−0.203660	−	0.147967i
$970$		0			0
$971$	3.40793	−	2.47601i	0.109366	−	0.0794589i	−0.531758	−	0.846896i	$-0.678468\pi$
$971$	3.40793	−	2.47601i	0.109366	−	0.0794589i	0.641124	+	0.767437i	$0.278468\pi$
$972$	−0.809017	+	0.587785i	−0.0259492	+	0.0188532i
$973$	−20.4200	−	62.8463i	−0.654635	−	2.01476i
$974$	−26.7043			−0.855661
$975$		0			0
$976$	3.68218			0.117864
$977$	4.38892	+	13.5077i	0.140414	+	0.432149i	0.996393	−	0.0848613i	$-0.0270447\pi$
$977$	4.38892	+	13.5077i	0.140414	+	0.432149i	−0.855979	+	0.517011i	$0.827045\pi$
$978$	16.3529	−	11.8811i	0.522907	−	0.379914i
$979$	56.9087	−	41.3466i	1.81881	−	1.32144i
$980$		0			0
$981$	2.08185	+	1.51256i	0.0664685	+	0.0482922i
$982$	33.1096			1.05657
$983$	−26.0353	−	18.9158i	−0.830398	−	0.603319i	0.0892742	−	0.996007i	$-0.471545\pi$
$983$	−26.0353	−	18.9158i	−0.830398	−	0.603319i	−0.919672	+	0.392688i	$0.871545\pi$
$984$	1.94584	−	5.98868i	0.0620311	−	0.190912i
$985$		0			0
$986$	−2.85524	−	8.78752i	−0.0909293	−	0.279852i
$987$	−11.6196	+	35.7613i	−0.369855	+	1.13830i
$988$	0.435105	−	1.33912i	0.0138425	−	0.0426030i
$989$	4.18494	+	12.8799i	0.133073	+	0.409557i
$990$		0			0
$991$	12.2198	−	37.6086i	0.388174	−	1.19468i	−0.545978	−	0.837799i	$-0.683842\pi$
$991$	12.2198	−	37.6086i	0.388174	−	1.19468i	0.934152	−	0.356876i	$-0.116158\pi$
$992$	−7.90309	−	5.74193i	−0.250923	−	0.182306i
$993$	3.43194			0.108909
$994$	13.5307	+	9.83059i	0.429166	+	0.311808i
$995$		0			0
$996$	−2.15177	+	1.56335i	−0.0681813	+	0.0495366i
$997$	−2.29512	+	1.66750i	−0.0726873	+	0.0528104i	−0.623535	−	0.781795i	$-0.714304\pi$
$997$	−2.29512	+	1.66750i	−0.0726873	+	0.0528104i	0.550848	+	0.834605i	$0.314304\pi$
$998$	1.85813	+	5.71873i	0.0588181	+	0.181023i
$999$	−1.00173			−0.0316933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.f.151.1		16
5.2	odd	4		150.2.h.b.19.2	✓	16
5.3	odd	4		750.2.h.d.349.4		16
5.4	even	2		750.2.g.g.151.4		16
15.2	even	4		450.2.l.c.19.3		16
25.2	odd	20		3750.2.c.k.1249.10		16
25.3	odd	20		150.2.h.b.79.2	yes	16
25.4	even	10		750.2.g.g.601.4		16
25.11	even	5		3750.2.a.v.1.2		8
25.14	even	10		3750.2.a.u.1.7		8
25.21	even	5	inner	750.2.g.f.601.1		16
25.22	odd	20		750.2.h.d.649.3		16
25.23	odd	20		3750.2.c.k.1249.7		16
75.53	even	20		450.2.l.c.379.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.19.2	✓	16	5.2	odd	4
150.2.h.b.79.2	yes	16	25.3	odd	20
450.2.l.c.19.3		16	15.2	even	4
450.2.l.c.379.3		16	75.53	even	20
750.2.g.f.151.1		16	1.1	even	1	trivial
750.2.g.f.601.1		16	25.21	even	5	inner
750.2.g.g.151.4		16	5.4	even	2
750.2.g.g.601.4		16	25.4	even	10
750.2.h.d.349.4		16	5.3	odd	4
750.2.h.d.649.3		16	25.22	odd	20
3750.2.a.u.1.7		8	25.14	even	10
3750.2.a.v.1.2		8	25.11	even	5
3750.2.c.k.1249.7		16	25.23	odd	20
3750.2.c.k.1249.10		16	25.2	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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} -3.52206 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} -3.52206 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(1.62388 + 4.99779i) q^{11} +(0.309017 - 0.951057i) q^{12} +(0.191313 - 0.588802i) q^{13} +(-1.08838 - 3.34968i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-2.78752 - 2.02525i) q^{17} +1.00000 q^{18} +(-1.83995 - 1.33680i) q^{19} +(2.84941 - 2.07022i) q^{21} +(-4.25137 + 3.08880i) q^{22} +(-2.76688 - 8.51557i) q^{23} +1.00000 q^{24} +0.619103 q^{26} +(0.309017 + 0.951057i) q^{27} +(2.84941 - 2.07022i) q^{28} +(2.16949 - 1.57623i) q^{29} +(-7.90309 - 5.74193i) q^{31} +1.00000 q^{32} +(-4.25137 - 3.08880i) q^{33} +(1.06474 - 3.27693i) q^{34} +(0.309017 + 0.951057i) q^{36} +(-0.309552 + 0.952702i) q^{37} +(0.702799 - 2.16299i) q^{38} +(0.191313 + 0.588802i) q^{39} +(1.94584 - 5.98868i) q^{41} +(2.84941 + 2.07022i) q^{42} -1.51251 q^{43} +(-4.25137 - 3.08880i) q^{44} +(7.24378 - 5.26291i) q^{46} +(-8.63710 + 6.27522i) q^{47} +(0.309017 + 0.951057i) q^{48} +5.40494 q^{49} +3.44557 q^{51} +(0.191313 + 0.588802i) q^{52} +(-0.447681 + 0.325260i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(2.84941 + 2.07022i) q^{56} +2.27431 q^{57} +(2.16949 + 1.57623i) q^{58} +(0.0861451 - 0.265127i) q^{59} +(1.13786 + 3.50196i) q^{61} +(3.01871 - 9.29064i) q^{62} +(-1.08838 + 3.34968i) q^{63} +(0.309017 + 0.951057i) q^{64} +(1.62388 - 4.99779i) q^{66} +(9.63710 + 7.00176i) q^{67} +3.44557 q^{68} +(7.24378 + 5.26291i) q^{69} +(-3.84168 + 2.79115i) q^{71} +(-0.809017 + 0.587785i) q^{72} +(3.03890 + 9.35277i) q^{73} -1.00173 q^{74} +2.27431 q^{76} +(-5.71941 - 17.6025i) q^{77} +(-0.500865 + 0.363900i) q^{78} +(-5.27525 + 3.83269i) q^{79} +(-0.809017 - 0.587785i) q^{81} +6.29687 q^{82} +(-2.15177 - 1.56335i) q^{83} +(-1.08838 + 3.34968i) q^{84} +(-0.467392 - 1.43848i) q^{86} +(-0.828671 + 2.55039i) q^{87} +(1.62388 - 4.99779i) q^{88} +(-4.13649 - 12.7308i) q^{89} +(-0.673818 + 2.07380i) q^{91} +(7.24378 + 5.26291i) q^{92} +9.76875 q^{93} +(-8.63710 - 6.27522i) q^{94} +(-0.809017 + 0.587785i) q^{96} +(-3.53706 + 2.56983i) q^{97} +(1.67022 + 5.14040i) q^{98} +5.25498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{6} + 8 q^{7} - 4 q^{8} - 4 q^{9} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} + 16 q^{18} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 16 q^{24} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 10 q^{29} - 18 q^{31} + 16 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} - 2 q^{42} + 4 q^{43} - 8 q^{44} - 6 q^{46} - 2 q^{47} - 4 q^{48} + 52 q^{49} + 28 q^{51} + 4 q^{52} - 16 q^{53} - 4 q^{54} - 2 q^{56} + 20 q^{57} + 10 q^{58} - 20 q^{59} + 12 q^{61} + 2 q^{62} - 2 q^{63} - 4 q^{64} + 2 q^{66} + 18 q^{67} + 28 q^{68} - 6 q^{69} - 28 q^{71} - 4 q^{72} + 24 q^{73} - 12 q^{74} + 20 q^{76} - 14 q^{77} - 6 q^{78} + 20 q^{79} - 4 q^{81} + 12 q^{82} - 36 q^{83} - 2 q^{84} - 6 q^{86} - 20 q^{87} + 2 q^{88} - 70 q^{89} + 12 q^{91} - 6 q^{92} + 32 q^{93} - 2 q^{94} - 4 q^{96} + 28 q^{97} - 38 q^{98} + 12 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^6 + 8 * q^7 - 4 * q^8 - 4 * q^9 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 + 16 * q^18 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 16 * q^24 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 10 * q^29 - 18 * q^31 + 16 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 2 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 - 2 * q^42 + 4 * q^43 - 8 * q^44 - 6 * q^46 - 2 * q^47 - 4 * q^48 + 52 * q^49 + 28 * q^51 + 4 * q^52 - 16 * q^53 - 4 * q^54 - 2 * q^56 + 20 * q^57 + 10 * q^58 - 20 * q^59 + 12 * q^61 + 2 * q^62 - 2 * q^63 - 4 * q^64 + 2 * q^66 + 18 * q^67 + 28 * q^68 - 6 * q^69 - 28 * q^71 - 4 * q^72 + 24 * q^73 - 12 * q^74 + 20 * q^76 - 14 * q^77 - 6 * q^78 + 20 * q^79 - 4 * q^81 + 12 * q^82 - 36 * q^83 - 2 * q^84 - 6 * q^86 - 20 * q^87 + 2 * q^88 - 70 * q^89 + 12 * q^91 - 6 * q^92 + 32 * q^93 - 2 * q^94 - 4 * q^96 + 28 * q^97 - 38 * q^98 + 12 * q^99

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