LMFDB - Embedded newform 750.2.g.f.451.1

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			451.1
Root			$-2.79002 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.451
Dual form			750.2.g.f.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} -4.80694 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(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} -4.80694 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.714027 + 0.518771i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(2.28564 - 1.66061i) q^{13} +(3.88890 + 2.82545i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.512289 - 1.57666i) q^{17} +1.00000 q^{18} +(1.66217 - 5.11563i) q^{19} +(-1.48543 - 4.57167i) q^{21} +(-0.272734 - 0.839389i) q^{22} +(-4.73553 - 3.44056i) q^{23} +1.00000 q^{24} -2.82520 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.48543 - 4.57167i) q^{28} +(1.10574 + 3.40313i) q^{29} +(3.22681 - 9.93109i) q^{31} +1.00000 q^{32} +(-0.272734 + 0.839389i) q^{33} +(-1.34119 + 0.974432i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(1.41260 - 1.02631i) q^{37} +(-4.35161 + 3.16163i) q^{38} +(2.28564 + 1.66061i) q^{39} +(1.40381 - 1.01993i) q^{41} +(-1.48543 + 4.57167i) q^{42} +2.27151 q^{43} +(-0.272734 + 0.839389i) q^{44} +(1.80881 + 5.56695i) q^{46} +(-2.69601 - 8.29746i) q^{47} +(-0.809017 - 0.587785i) q^{48} +16.1067 q^{49} +1.65780 q^{51} +(2.28564 + 1.66061i) q^{52} +(1.09681 + 3.37565i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-1.48543 + 4.57167i) q^{56} +5.37889 q^{57} +(1.10574 - 3.40313i) q^{58} +(-8.37628 + 6.08572i) q^{59} +(0.0697810 + 0.0506988i) q^{61} +(-8.44789 + 6.13775i) q^{62} +(3.88890 - 2.82545i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.714027 - 0.518771i) q^{66} +(3.69601 - 11.3751i) q^{67} +1.65780 q^{68} +(1.80881 - 5.56695i) q^{69} +(-1.08390 - 3.33591i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-5.84757 - 4.24851i) q^{73} -1.74607 q^{74} +5.37889 q^{76} +(-3.43228 - 2.49370i) q^{77} +(-0.873035 - 2.68693i) q^{78} +(-3.88627 - 11.9607i) q^{79} +(0.309017 - 0.951057i) q^{81} -1.73520 q^{82} +(-4.10192 + 12.6244i) q^{83} +(3.88890 - 2.82545i) q^{84} +(-1.83769 - 1.33516i) q^{86} +(-2.89488 + 2.10325i) q^{87} +(0.714027 - 0.518771i) q^{88} +(-15.1178 - 10.9837i) q^{89} +(-10.9869 + 7.98246i) q^{91} +(1.80881 - 5.56695i) q^{92} +10.4422 q^{93} +(-2.69601 + 8.29746i) q^{94} +(0.309017 + 0.951057i) q^{96} +(5.64593 + 17.3764i) q^{97} +(-13.0306 - 9.46727i) q^{98} -0.882586 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

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

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
$7$	−4.80694			−1.81685			−0.908426	−	0.418045i	$-0.862716\pi$
$7$	−4.80694			−1.81685			−0.908426	+	0.418045i	$0.862716\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	0.714027	+	0.518771i	0.215287	+	0.156415i	0.690203	−	0.723616i	$-0.257521\pi$
$11$	0.714027	+	0.518771i	0.215287	+	0.156415i	−0.474915	+	0.880031i	$0.657521\pi$
$12$	−0.809017	+	0.587785i	−0.233543	+	0.169679i
$13$	2.28564	−	1.66061i	0.633921	−	0.460571i	−0.223835	−	0.974627i	$-0.571858\pi$
$13$	2.28564	−	1.66061i	0.633921	−	0.460571i	0.857756	+	0.514056i	$0.171858\pi$
$14$	3.88890	+	2.82545i	1.03935	+	0.755133i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.512289	−	1.57666i	0.124248	−	0.382397i	−0.869515	−	0.493907i	$-0.835568\pi$
$17$	0.512289	−	1.57666i	0.124248	−	0.382397i	0.993763	+	0.111509i	$0.0355685\pi$
$18$	1.00000			0.235702
$19$	1.66217	−	5.11563i	0.381327	−	1.17361i	−0.557782	−	0.829987i	$-0.688348\pi$
$19$	1.66217	−	5.11563i	0.381327	−	1.17361i	0.939110	−	0.343618i	$-0.111652\pi$
$20$		0			0
$21$	−1.48543	−	4.57167i	−0.324147	−	0.997621i
$22$	−0.272734	−	0.839389i	−0.0581471	−	0.178958i
$23$	−4.73553	−	3.44056i	−0.987426	−	0.717407i	−0.0280705	−	0.999606i	$-0.508936\pi$
$23$	−4.73553	−	3.44056i	−0.987426	−	0.717407i	−0.959356	+	0.282199i	$0.908936\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	−2.82520			−0.554067
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−1.48543	−	4.57167i	−0.280719	−	0.863965i
$29$	1.10574	+	3.40313i	0.205332	+	0.631946i	0.999700	+	0.0245090i	$0.00780223\pi$
$29$	1.10574	+	3.40313i	0.205332	+	0.631946i	−0.794368	+	0.607437i	$0.792198\pi$
$30$		0			0
$31$	3.22681	−	9.93109i	0.579551	−	1.78368i	−0.0405785	−	0.999176i	$-0.512920\pi$
$31$	3.22681	−	9.93109i	0.579551	−	1.78368i	0.620130	−	0.784499i	$-0.287080\pi$
$32$	1.00000			0.176777
$33$	−0.272734	+	0.839389i	−0.0474769	+	0.146119i
$34$	−1.34119	+	0.974432i	−0.230012	+	0.167114i
$35$		0			0
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	1.41260	−	1.02631i	0.232230	−	0.168725i	−0.465585	−	0.885003i	$-0.654156\pi$
$37$	1.41260	−	1.02631i	0.232230	−	0.168725i	0.697815	+	0.716278i	$0.254156\pi$
$38$	−4.35161	+	3.16163i	−0.705925	+	0.512884i
$39$	2.28564	+	1.66061i	0.365995	+	0.265911i
$40$		0			0
$41$	1.40381	−	1.01993i	0.219238	−	0.159286i	−0.472746	−	0.881199i	$-0.656737\pi$
$41$	1.40381	−	1.01993i	0.219238	−	0.159286i	0.691984	+	0.721913i	$0.256737\pi$
$42$	−1.48543	+	4.57167i	−0.229206	+	0.705424i
$43$	2.27151			0.346403			0.173201	−	0.984886i	$-0.444589\pi$
$43$	2.27151			0.346403			0.173201	+	0.984886i	$0.444589\pi$
$44$	−0.272734	+	0.839389i	−0.0411162	+	0.126543i
$45$		0			0
$46$	1.80881	+	5.56695i	0.266695	+	0.820802i
$47$	−2.69601	−	8.29746i	−0.393253	−	1.21031i	−0.930314	−	0.366765i	$-0.880465\pi$
$47$	−2.69601	−	8.29746i	−0.393253	−	1.21031i	0.537060	−	0.843544i	$-0.319535\pi$
$48$	−0.809017	−	0.587785i	−0.116772	−	0.0848395i
$49$	16.1067			2.30095
$50$		0			0
$51$	1.65780			0.232139
$52$	2.28564	+	1.66061i	0.316961	+	0.230285i
$53$	1.09681	+	3.37565i	0.150659	+	0.463681i	0.997695	−	0.0678545i	$-0.0216154\pi$
$53$	1.09681	+	3.37565i	0.150659	+	0.463681i	−0.847036	+	0.531535i	$0.821615\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$		0			0
$56$	−1.48543	+	4.57167i	−0.198498	+	0.610915i
$57$	5.37889			0.712451
$58$	1.10574	−	3.40313i	0.145191	−	0.446853i
$59$	−8.37628	+	6.08572i	−1.09050	+	0.792293i	−0.979483	−	0.201525i	$-0.935410\pi$
$59$	−8.37628	+	6.08572i	−1.09050	+	0.792293i	−0.111015	+	0.993819i	$0.535410\pi$
$60$		0			0
$61$	0.0697810	+	0.0506988i	0.00893454	+	0.00649132i	0.592244	−	0.805759i	$-0.298242\pi$
$61$	0.0697810	+	0.0506988i	0.00893454	+	0.00649132i	−0.583309	+	0.812250i	$0.698242\pi$
$62$	−8.44789	+	6.13775i	−1.07288	+	0.779495i
$63$	3.88890	−	2.82545i	0.489955	−	0.355973i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	0.714027	−	0.518771i	0.0878906	−	0.0638563i
$67$	3.69601	−	11.3751i	0.451539	−	1.38969i	−0.423611	−	0.905844i	$-0.639238\pi$
$67$	3.69601	−	11.3751i	0.451539	−	1.38969i	0.875150	−	0.483851i	$-0.160762\pi$
$68$	1.65780			0.201038
$69$	1.80881	−	5.56695i	0.217755	−	0.670182i
$70$		0			0
$71$	−1.08390	−	3.33591i	−0.128636	−	0.395900i	0.865910	−	0.500199i	$-0.166740\pi$
$71$	−1.08390	−	3.33591i	−0.128636	−	0.395900i	−0.994546	+	0.104300i	$0.966740\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	−5.84757	−	4.24851i	−0.684407	−	0.497251i	0.190410	−	0.981705i	$-0.439018\pi$
$73$	−5.84757	−	4.24851i	−0.684407	−	0.497251i	−0.874817	+	0.484454i	$0.839018\pi$
$74$	−1.74607			−0.202977
$75$		0			0
$76$	5.37889			0.617001
$77$	−3.43228	−	2.49370i	−0.391145	−	0.284184i
$78$	−0.873035	−	2.68693i	−0.0988518	−	0.304234i
$79$	−3.88627	−	11.9607i	−0.437240	−	1.34569i	−0.890774	−	0.454447i	$-0.849837\pi$
$79$	−3.88627	−	11.9607i	−0.437240	−	1.34569i	0.453533	−	0.891239i	$-0.350163\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.73520			−0.191621
$83$	−4.10192	+	12.6244i	−0.450244	+	1.38571i	0.426386	+	0.904541i	$0.359787\pi$
$83$	−4.10192	+	12.6244i	−0.450244	+	1.38571i	−0.876629	+	0.481166i	$0.840213\pi$
$84$	3.88890	−	2.82545i	0.424313	−	0.308282i
$85$		0			0
$86$	−1.83769	−	1.33516i	−0.198164	−	0.143974i
$87$	−2.89488	+	2.10325i	−0.310363	+	0.225492i
$88$	0.714027	−	0.518771i	0.0761155	−	0.0553011i
$89$	−15.1178	−	10.9837i	−1.60248	−	1.16427i	−0.882542	−	0.470233i	$-0.844170\pi$
$89$	−15.1178	−	10.9837i	−1.60248	−	1.16427i	−0.719939	−	0.694037i	$-0.755830\pi$
$90$		0			0
$91$	−10.9869	+	7.98246i	−1.15174	+	0.836789i
$92$	1.80881	−	5.56695i	0.188582	−	0.580395i
$93$	10.4422			1.08280
$94$	−2.69601	+	8.29746i	−0.278072	+	0.855818i
$95$		0			0
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	5.64593	+	17.3764i	0.573257	+	1.76430i	0.642039	+	0.766672i	$0.278089\pi$
$97$	5.64593	+	17.3764i	0.573257	+	1.76430i	−0.0687822	+	0.997632i	$0.521911\pi$
$98$	−13.0306	−	9.46727i	−1.31629	−	0.956339i
$99$	−0.882586			−0.0887032
$100$		0			0
$101$	−5.46110			−0.543400			−0.271700	−	0.962382i	$-0.587586\pi$
$101$	−5.46110			−0.543400			−0.271700	+	0.962382i	$0.587586\pi$
$102$	−1.34119	−	0.974432i	−0.132798	−	0.0964831i
$103$	−2.05260	−	6.31725i	−0.202248	−	0.622457i	−0.999815	−	0.0192260i	$-0.993880\pi$
$103$	−2.05260	−	6.31725i	−0.202248	−	0.622457i	0.797567	−	0.603231i	$-0.206120\pi$
$104$	−0.873035	−	2.68693i	−0.0856081	−	0.263475i
$105$		0			0
$106$	1.09681	−	3.37565i	0.106532	−	0.327872i
$107$	14.5245			1.40414			0.702070	−	0.712108i	$-0.252259\pi$
$107$	14.5245			1.40414			0.702070	+	0.712108i	$0.252259\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−3.85954	+	2.80412i	−0.369676	+	0.268586i	−0.757077	−	0.653326i	$-0.773373\pi$
$109$	−3.85954	+	2.80412i	−0.369676	+	0.268586i	0.387400	+	0.921912i	$0.373373\pi$
$110$		0			0
$111$	1.41260	+	1.02631i	0.134078	+	0.0974134i
$112$	3.88890	−	2.82545i	0.367466	−	0.266980i
$113$	3.91206	−	2.84228i	0.368016	−	0.267379i	−0.388372	−	0.921503i	$-0.626962\pi$
$113$	3.91206	−	2.84228i	0.368016	−	0.267379i	0.756388	+	0.654124i	$0.226962\pi$
$114$	−4.35161	−	3.16163i	−0.407566	−	0.296114i
$115$		0			0
$116$	−2.89488	+	2.10325i	−0.268783	+	0.195282i
$117$	−0.873035	+	2.68693i	−0.0807121	+	0.248406i
$118$	10.3536			0.953131
$119$	−2.46254	+	7.57893i	−0.225741	+	0.694759i
$120$		0			0
$121$	−3.15848	−	9.72079i	−0.287134	−	0.883708i
$122$	−0.0266540	−	0.0820324i	−0.00241314	−	0.00742687i
$123$	1.40381	+	1.01993i	0.126577	+	0.0919637i
$124$	10.4422			0.937734
$125$		0			0
$126$	−4.80694			−0.428236
$127$	1.45769	+	1.05908i	0.129349	+	0.0939779i	0.650579	−	0.759439i	$-0.274526\pi$
$127$	1.45769	+	1.05908i	0.129349	+	0.0939779i	−0.521229	+	0.853417i	$0.674526\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	0.701936	+	2.16034i	0.0618021	+	0.190207i
$130$		0			0
$131$	−4.95400	+	15.2468i	−0.432833	+	1.33212i	0.462459	+	0.886641i	$0.346967\pi$
$131$	−4.95400	+	15.2468i	−0.432833	+	1.33212i	−0.895291	+	0.445481i	$0.853033\pi$
$132$	−0.882586			−0.0768192
$133$	−7.98994	+	24.5905i	−0.692816	+	2.13227i
$134$	−9.67628	+	7.03023i	−0.835903	+	0.607319i
$135$		0			0
$136$	−1.34119	−	0.974432i	−0.115006	−	0.0835569i
$137$	1.42968	−	1.03872i	0.122146	−	0.0887443i	−0.525035	−	0.851081i	$-0.675948\pi$
$137$	1.42968	−	1.03872i	0.122146	−	0.0887443i	0.647181	+	0.762336i	$0.275948\pi$
$138$	−4.73553	+	3.44056i	−0.403115	+	0.292880i
$139$	−8.89636	−	6.46359i	−0.754580	−	0.548234i	0.142663	−	0.989771i	$-0.454433\pi$
$139$	−8.89636	−	6.46359i	−0.754580	−	0.548234i	−0.897243	+	0.441537i	$0.854433\pi$
$140$		0			0
$141$	7.05824	−	5.12811i	0.594411	−	0.431865i
$142$	−1.08390	+	3.33591i	−0.0909591	+	0.279943i
$143$	2.49348			0.208515
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$		0			0
$146$	2.23357	+	6.87424i	0.184852	+	0.568916i
$147$	4.97724	+	15.3184i	0.410516	+	1.26344i
$148$	1.41260	+	1.02631i	0.116115	+	0.0843625i
$149$	2.90948			0.238354			0.119177	−	0.992873i	$-0.461974\pi$
$149$	2.90948			0.238354			0.119177	+	0.992873i	$0.461974\pi$
$150$		0			0
$151$	−1.34184			−0.109197			−0.0545986	−	0.998508i	$-0.517388\pi$
$151$	−1.34184			−0.109197			−0.0545986	+	0.998508i	$0.517388\pi$
$152$	−4.35161	−	3.16163i	−0.352962	−	0.256442i
$153$	0.512289	+	1.57666i	0.0414161	+	0.127466i
$154$	1.31102	+	4.03489i	0.105645	+	0.325141i
$155$		0			0
$156$	−0.873035	+	2.68693i	−0.0698987	+	0.215126i
$157$	−8.31169			−0.663345			−0.331673	−	0.943395i	$-0.607613\pi$
$157$	−8.31169			−0.663345			−0.331673	+	0.943395i	$0.607613\pi$
$158$	−3.88627	+	11.9607i	−0.309175	+	0.951544i
$159$	−2.87150	+	2.08626i	−0.227724	+	0.165451i
$160$		0			0
$161$	22.7634	+	16.5386i	1.79401	+	1.30342i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	5.04724	−	3.66704i	0.395331	−	0.287225i	−0.372306	−	0.928110i	$-0.621433\pi$
$163$	5.04724	−	3.66704i	0.395331	−	0.287225i	0.767636	+	0.640886i	$0.221433\pi$
$164$	1.40381	+	1.01993i	0.109619	+	0.0796429i
$165$		0			0
$166$	10.7390	−	7.80231i	0.833505	−	0.605576i
$167$	4.58483	−	14.1107i	0.354785	−	1.09192i	−0.601349	−	0.798986i	$-0.705370\pi$
$167$	4.58483	−	14.1107i	0.354785	−	1.09192i	0.956134	−	0.292929i	$-0.0946300\pi$
$168$	−4.80694			−0.370864
$169$	−1.55072	+	4.77263i	−0.119286	+	0.367125i
$170$		0			0
$171$	1.66217	+	5.11563i	0.127109	+	0.391202i
$172$	0.701936	+	2.16034i	0.0535221	+	0.164724i
$173$	12.9741	+	9.42623i	0.986402	+	0.716663i	0.959130	−	0.282965i	$-0.0913180\pi$
$173$	12.9741	+	9.42623i	0.986402	+	0.716663i	0.0272719	+	0.999628i	$0.491318\pi$
$174$	3.57827			0.271268
$175$		0			0
$176$	−0.882586			−0.0665274
$177$	−8.37628	−	6.08572i	−0.629600	−	0.457431i
$178$	5.77448	+	17.7720i	0.432815	+	1.33207i
$179$	3.63061	+	11.1739i	0.271365	+	0.835174i	0.990158	+	0.139951i	$0.0446945\pi$
$179$	3.63061	+	11.1739i	0.271365	+	0.835174i	−0.718794	+	0.695223i	$0.755306\pi$
$180$		0			0
$181$	−1.24658	+	3.83658i	−0.0926577	+	0.285171i	−0.986636	−	0.162939i	$-0.947903\pi$
$181$	−1.24658	+	3.83658i	−0.0926577	+	0.285171i	0.893979	+	0.448110i	$0.147903\pi$
$182$	13.5806			1.00666
$183$	−0.0266540	+	0.0820324i	−0.00197032	+	0.00606401i
$184$	−4.73553	+	3.44056i	−0.349108	+	0.253642i
$185$		0			0
$186$	−8.44789	−	6.13775i	−0.619429	−	0.450042i
$187$	1.18372	−	0.860020i	0.0865618	−	0.0628909i
$188$	7.05824	−	5.12811i	0.514775	−	0.374006i
$189$	3.88890	+	2.82545i	0.282876	+	0.205521i
$190$		0			0
$191$	−9.64472	+	7.00730i	−0.697867	+	0.507030i	−0.879237	−	0.476385i	$-0.841947\pi$
$191$	−9.64472	+	7.00730i	−0.697867	+	0.507030i	0.181370	+	0.983415i	$0.441947\pi$
$192$	0.309017	−	0.951057i	0.0223014	−	0.0686366i
$193$	11.8088			0.850019			0.425009	−	0.905189i	$-0.360271\pi$
$193$	11.8088			0.850019			0.425009	+	0.905189i	$0.360271\pi$
$194$	5.64593	−	17.3764i	0.405354	−	1.24755i
$195$		0			0
$196$	4.97724	+	15.3184i	0.355517	+	1.09417i
$197$	−2.24916	−	6.92219i	−0.160246	−	0.493186i	0.838409	−	0.545042i	$-0.183486\pi$
$197$	−2.24916	−	6.92219i	−0.160246	−	0.493186i	−0.998655	+	0.0518562i	$0.983486\pi$
$198$	0.714027	+	0.518771i	0.0507437	+	0.0368674i
$199$	2.27949			0.161589			0.0807944	−	0.996731i	$-0.474254\pi$
$199$	2.27949			0.161589			0.0807944	+	0.996731i	$0.474254\pi$
$200$		0			0
$201$	11.9605			0.843631
$202$	4.41813	+	3.20996i	0.310858	+	0.225852i
$203$	−5.31525	−	16.3587i	−0.373057	−	1.14815i
$204$	0.512289	+	1.57666i	0.0358674	+	0.110389i
$205$		0			0
$206$	−2.05260	+	6.31725i	−0.143011	+	0.440143i
$207$	5.85344			0.406842
$208$	−0.873035	+	2.68693i	−0.0605341	+	0.186305i
$209$	3.84067	−	2.79041i	0.265665	−	0.193017i
$210$		0			0
$211$	1.01062	+	0.734260i	0.0695741	+	0.0505485i	0.622029	−	0.782994i	$-0.286309\pi$
$211$	1.01062	+	0.734260i	0.0695741	+	0.0505485i	−0.552455	+	0.833543i	$0.686309\pi$
$212$	−2.87150	+	2.08626i	−0.197215	+	0.143285i
$213$	2.83769	−	2.06170i	0.194436	−	0.141266i
$214$	−11.7506	−	8.53731i	−0.803255	−	0.583599i
$215$		0			0
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	−15.5111	+	47.7381i	−1.05296	+	3.24068i
$218$	4.77065			0.323109
$219$	2.23357	−	6.87424i	0.150931	−	0.464518i
$220$		0			0
$221$	−1.44732	−	4.45439i	−0.0973573	−	0.299635i
$222$	−0.539565	−	1.66061i	−0.0362133	−	0.111453i
$223$	−7.15343	−	5.19727i	−0.479029	−	0.348035i	0.321921	−	0.946767i	$-0.395672\pi$
$223$	−7.15343	−	5.19727i	−0.479029	−	0.348035i	−0.800950	+	0.598732i	$0.795672\pi$
$224$	−4.80694			−0.321177
$225$		0			0
$226$	−4.83558			−0.321658
$227$	14.3170	+	10.4019i	0.950251	+	0.690398i	0.950866	−	0.309602i	$-0.100196\pi$
$227$	14.3170	+	10.4019i	0.950251	+	0.690398i	−0.000615300		1.00000i	$0.500196\pi$
$228$	1.66217	+	5.11563i	0.110080	+	0.338791i
$229$	−2.75446	−	8.47737i	−0.182020	−	0.560200i	0.817864	−	0.575411i	$-0.195158\pi$
$229$	−2.75446	−	8.47737i	−0.182020	−	0.560200i	−0.999884	+	0.0152110i	$0.995158\pi$
$230$		0			0
$231$	1.31102	−	4.03489i	0.0862585	−	0.265476i
$232$	3.57827			0.234925
$233$	−2.96367	+	9.12123i	−0.194156	+	0.597551i	0.805829	+	0.592148i	$0.201720\pi$
$233$	−2.96367	+	9.12123i	−0.194156	+	0.597551i	−0.999985	+	0.00540335i	$0.998280\pi$
$234$	2.28564	−	1.66061i	0.149417	−	0.108558i
$235$		0			0
$236$	−8.37628	−	6.08572i	−0.545249	−	0.396147i
$237$	10.1744	−	7.39213i	0.660898	−	0.480171i
$238$	6.44702	−	4.68404i	0.417898	−	0.303621i
$239$	7.41301	+	5.38587i	0.479508	+	0.348383i	0.801135	−	0.598483i	$-0.204230\pi$
$239$	7.41301	+	5.38587i	0.479508	+	0.348383i	−0.321627	+	0.946866i	$0.604230\pi$
$240$		0			0
$241$	2.01891	−	1.46682i	0.130049	−	0.0944864i	−0.520859	−	0.853643i	$-0.674388\pi$
$241$	2.01891	−	1.46682i	0.130049	−	0.0944864i	0.650908	+	0.759156i	$0.274388\pi$
$242$	−3.15848	+	9.72079i	−0.203035	+	0.624876i
$243$	1.00000			0.0641500
$244$	−0.0266540	+	0.0820324i	−0.00170634	+	0.00525159i
$245$		0			0
$246$	−0.536207	−	1.65028i	−0.0341873	−	0.105218i
$247$	−4.69596	−	14.4527i	−0.298797	−	0.919601i
$248$	−8.44789	−	6.13775i	−0.536441	−	0.389747i
$249$	−13.2741			−0.841211
$250$		0			0
$251$	8.71262			0.549936			0.274968	−	0.961453i	$-0.411333\pi$
$251$	8.71262			0.549936			0.274968	+	0.961453i	$0.411333\pi$
$252$	3.88890	+	2.82545i	0.244977	+	0.177987i
$253$	−1.59643	−	4.91331i	−0.100367	−	0.308897i
$254$	−0.556790	−	1.71362i	−0.0349361	−	0.107522i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−19.7871			−1.23429			−0.617143	−	0.786851i	$-0.711710\pi$
$257$	−19.7871			−1.23429			−0.617143	+	0.786851i	$0.711710\pi$
$258$	0.701936	−	2.16034i	0.0437007	−	0.134497i
$259$	−6.79029	+	4.93343i	−0.421928	+	0.306549i
$260$		0			0
$261$	−2.89488	−	2.10325i	−0.179188	−	0.130188i
$262$	12.9697	−	9.42306i	0.801272	−	0.582159i
$263$	−20.6813	+	15.0258i	−1.27526	+	0.926532i	−0.999399	−	0.0346651i	$-0.988964\pi$
$263$	−20.6813	+	15.0258i	−1.27526	+	0.926532i	−0.275863	+	0.961197i	$0.588964\pi$
$264$	0.714027	+	0.518771i	0.0439453	+	0.0319281i
$265$		0			0
$266$	20.9179	−	15.1978i	1.28256	−	0.931835i
$267$	5.77448	−	17.7720i	0.353392	−	1.08763i
$268$	11.9605			0.730606
$269$	7.54447	−	23.2195i	0.459994	−	1.41572i	−0.405176	−	0.914239i	$-0.632790\pi$
$269$	7.54447	−	23.2195i	0.459994	−	1.41572i	0.865170	−	0.501478i	$-0.167210\pi$
$270$		0			0
$271$	0.848720	+	2.61209i	0.0515561	+	0.158673i	0.973520	−	0.228603i	$-0.0734159\pi$
$271$	0.848720	+	2.61209i	0.0515561	+	0.158673i	−0.921964	+	0.387277i	$0.873416\pi$
$272$	0.512289	+	1.57666i	0.0310621	+	0.0955993i
$273$	−10.9869	−	7.98246i	−0.664958	−	0.483120i
$274$	−1.76718			−0.106760
$275$		0			0
$276$	5.85344			0.352336
$277$	−2.41151	−	1.75206i	−0.144893	−	0.105271i	0.512977	−	0.858402i	$-0.328543\pi$
$277$	−2.41151	−	1.75206i	−0.144893	−	0.105271i	−0.657870	+	0.753131i	$0.728543\pi$
$278$	3.39811	+	10.4583i	0.203805	+	0.627247i
$279$	3.22681	+	9.93109i	0.193184	+	0.594559i
$280$		0			0
$281$	1.19334	−	3.67274i	0.0711890	−	0.219097i	−0.909132	−	0.416509i	$-0.863254\pi$
$281$	1.19334	−	3.67274i	0.0711890	−	0.219097i	0.980321	+	0.197412i	$0.0632535\pi$
$282$	−8.72447			−0.519534
$283$	−5.16117	+	15.8844i	−0.306800	+	0.944232i	0.672200	+	0.740370i	$0.265350\pi$
$283$	−5.16117	+	15.8844i	−0.306800	+	0.944232i	−0.979000	+	0.203863i	$0.934650\pi$
$284$	2.83769	−	2.06170i	0.168386	−	0.122340i
$285$		0			0
$286$	−2.01727	−	1.46563i	−0.119284	−	0.0866646i
$287$	−6.74802	+	4.90273i	−0.398323	+	0.289399i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	11.5299	+	8.37693i	0.678227	+	0.492761i
$290$		0			0
$291$	−14.7812	+	10.7392i	−0.866491	+	0.629542i
$292$	2.23357	−	6.87424i	0.130710	−	0.402284i
$293$	−0.503153			−0.0293945			−0.0146972	−	0.999892i	$-0.504678\pi$
$293$	−0.503153			−0.0293945			−0.0146972	+	0.999892i	$0.504678\pi$
$294$	4.97724	−	15.3184i	0.290278	−	0.893385i
$295$		0			0
$296$	−0.539565	−	1.66061i	−0.0313616	−	0.0965211i
$297$	−0.272734	−	0.839389i	−0.0158256	−	0.0487063i
$298$	−2.35382	−	1.71015i	−0.136353	−	0.0990664i
$299$	−16.5371			−0.956367
$300$		0			0
$301$	−10.9190			−0.629363
$302$	1.08557	+	0.788713i	0.0624675	+	0.0453853i
$303$	−1.68757	−	5.19382i	−0.0969486	−	0.298377i
$304$	1.66217	+	5.11563i	0.0953319	+	0.293401i
$305$		0			0
$306$	0.512289	−	1.57666i	0.0292856	−	0.0901319i
$307$	−8.63375			−0.492754			−0.246377	−	0.969174i	$-0.579240\pi$
$307$	−8.63375			−0.492754			−0.246377	+	0.969174i	$0.579240\pi$
$308$	1.31102	−	4.03489i	0.0747021	−	0.229909i
$309$	5.37377	−	3.90427i	0.305703	−	0.222106i
$310$		0			0
$311$	−16.3967	−	11.9129i	−0.929771	−	0.675518i	0.0161660	−	0.999869i	$-0.494854\pi$
$311$	−16.3967	−	11.9129i	−0.929771	−	0.675518i	−0.945937	+	0.324351i	$0.894854\pi$
$312$	2.28564	−	1.66061i	0.129399	−	0.0940136i
$313$	13.7777	−	10.0101i	0.778763	−	0.565805i	−0.125844	−	0.992050i	$-0.540164\pi$
$313$	13.7777	−	10.0101i	0.778763	−	0.565805i	0.904608	+	0.426245i	$0.140164\pi$
$314$	6.72430	+	4.88549i	0.379474	+	0.275704i
$315$		0			0
$316$	10.1744	−	7.39213i	0.572355	−	0.415840i
$317$	−0.871912	+	2.68347i	−0.0489715	+	0.150719i	−0.972552	−	0.232686i	$-0.925249\pi$
$317$	−0.871912	+	2.68347i	−0.0489715	+	0.150719i	0.923580	+	0.383405i	$0.125249\pi$
$318$	3.54936			0.199038
$319$	−0.975914	+	3.00356i	−0.0546407	+	0.168167i
$320$		0			0
$321$	4.48833	+	13.8137i	0.250514	+	0.771003i
$322$	−8.69485	−	26.7600i	−0.484545	−	1.49128i
$323$	−7.21411	−	5.24136i	−0.401404	−	0.291637i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−6.23874			−0.345532
$327$	−3.85954	−	2.80412i	−0.213433	−	0.155068i
$328$	−0.536207	−	1.65028i	−0.0296071	−	0.0911212i
$329$	12.9596	+	39.8854i	0.714483	+	2.19895i
$330$		0			0
$331$	−1.25862	+	3.87364i	−0.0691802	+	0.212915i	−0.979670	−	0.200618i	$-0.935705\pi$
$331$	−1.25862	+	3.87364i	−0.0691802	+	0.212915i	0.910489	+	0.413532i	$0.135705\pi$
$332$	−13.2741			−0.728510
$333$	−0.539565	+	1.66061i	−0.0295680	+	0.0910009i
$334$	−12.0032	+	8.72086i	−0.656788	+	0.477184i
$335$		0			0
$336$	3.88890	+	2.82545i	0.212157	+	0.154141i
$337$	7.31984	−	5.31818i	0.398737	−	0.289700i	−0.370289	−	0.928917i	$-0.620741\pi$
$337$	7.31984	−	5.31818i	0.398737	−	0.289700i	0.769026	+	0.639217i	$0.220741\pi$
$338$	4.05984	−	2.94965i	0.220826	−	0.160440i
$339$	3.91206	+	2.84228i	0.212474	+	0.154371i
$340$		0			0
$341$	7.45598	−	5.41709i	0.403764	−	0.293352i
$342$	1.66217	−	5.11563i	0.0898797	−	0.276621i
$343$	−43.7753			−2.36364
$344$	0.701936	−	2.16034i	0.0378459	−	0.116478i
$345$		0			0
$346$	−4.95566	−	15.2520i	−0.266418	−	0.819951i
$347$	2.68429	+	8.26141i	0.144100	+	0.443495i	0.996894	−	0.0787523i	$-0.0250936\pi$
$347$	2.68429	+	8.26141i	0.144100	+	0.443495i	−0.852794	+	0.522248i	$0.825094\pi$
$348$	−2.89488	−	2.10325i	−0.155182	−	0.112746i
$349$	26.8305			1.43620			0.718101	−	0.695938i	$-0.245011\pi$
$349$	26.8305			1.43620			0.718101	+	0.695938i	$0.245011\pi$
$350$		0			0
$351$	−2.82520			−0.150798
$352$	0.714027	+	0.518771i	0.0380577	+	0.0276506i
$353$	−8.76060	−	26.9623i	−0.466279	−	1.43506i	−0.857366	−	0.514707i	$-0.827901\pi$
$353$	−8.76060	−	26.9623i	−0.466279	−	1.43506i	0.391087	−	0.920354i	$-0.372099\pi$
$354$	3.19945	+	9.84690i	0.170049	+	0.523357i
$355$		0			0
$356$	5.77448	−	17.7720i	0.306047	−	0.941915i
$357$	−7.96896			−0.421762
$358$	3.63061	−	11.1739i	0.191884	−	0.590557i
$359$	−7.02898	+	5.10686i	−0.370976	+	0.269530i	−0.757615	−	0.652701i	$-0.773636\pi$
$359$	−7.02898	+	5.10686i	−0.370976	+	0.269530i	0.386640	+	0.922231i	$0.373636\pi$
$360$		0			0
$361$	−8.03551	−	5.83814i	−0.422921	−	0.307270i
$362$	3.26359	−	2.37114i	0.171531	−	0.124624i
$363$	8.26900	−	6.00778i	0.434010	−	0.315327i
$364$	−10.9869	−	7.98246i	−0.575871	−	0.418395i
$365$		0			0
$366$	0.0697810	−	0.0506988i	0.00364751	−	0.00265007i
$367$	−3.85385	+	11.8609i	−0.201170	+	0.619136i	0.798679	+	0.601757i	$0.205532\pi$
$367$	−3.85385	+	11.8609i	−0.201170	+	0.619136i	−0.999849	+	0.0173794i	$0.994468\pi$
$368$	5.85344			0.305132
$369$	−0.536207	+	1.65028i	−0.0279138	+	0.0859099i
$370$		0			0
$371$	−5.27232	−	16.2265i	−0.273725	−	0.842439i
$372$	3.22681	+	9.93109i	0.167302	+	0.514903i
$373$	10.5162	+	7.64048i	0.544509	+	0.395609i	0.825757	−	0.564026i	$-0.190748\pi$
$373$	10.5162	+	7.64048i	0.544509	+	0.395609i	−0.281248	+	0.959635i	$0.590748\pi$
$374$	−1.46315			−0.0756578
$375$		0			0
$376$	−8.72447			−0.449930
$377$	8.17861	+	5.94211i	0.421220	+	0.306034i
$378$	−1.48543	−	4.57167i	−0.0764021	−	0.235141i
$379$	0.541481	+	1.66651i	0.0278140	+	0.0856027i	0.964000	−	0.265903i	$-0.0856699\pi$
$379$	0.541481	+	1.66651i	0.0278140	+	0.0856027i	−0.936186	+	0.351505i	$0.885670\pi$
$380$		0			0
$381$	−0.556790	+	1.71362i	−0.0285252	+	0.0877915i
$382$	11.9215			0.609958
$383$	10.5486	−	32.4652i	0.539007	−	1.65889i	−0.195822	−	0.980639i	$-0.562738\pi$
$383$	10.5486	−	32.4652i	0.539007	−	1.65889i	0.734829	−	0.678252i	$-0.237262\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$		0			0
$386$	−9.55355	−	6.94106i	−0.486263	−	0.353291i
$387$	−1.83769	+	1.33516i	−0.0934152	+	0.0678701i
$388$	−14.7812	+	10.7392i	−0.750403	+	0.545200i
$389$	−5.54704	−	4.03016i	−0.281246	−	0.204337i	0.438215	−	0.898870i	$-0.355611\pi$
$389$	−5.54704	−	4.03016i	−0.281246	−	0.204337i	−0.719461	+	0.694533i	$0.755611\pi$
$390$		0			0
$391$	−7.85058	+	5.70378i	−0.397021	+	0.288452i
$392$	4.97724	−	15.3184i	0.251388	−	0.773694i
$393$	−16.0315			−0.808680
$394$	−2.24916	+	6.92219i	−0.113311	+	0.348735i
$395$		0			0
$396$	−0.272734	−	0.839389i	−0.0137054	−	0.0421809i
$397$	−10.2466	−	31.5358i	−0.514262	−	1.58274i	−0.784621	−	0.619976i	$-0.787142\pi$
$397$	−10.2466	−	31.5358i	−0.514262	−	1.58274i	0.270359	−	0.962760i	$-0.412858\pi$
$398$	−1.84415	−	1.33985i	−0.0924387	−	0.0671607i
$399$	−25.8560			−1.29442
$400$		0			0
$401$	3.51432			0.175497			0.0877483	−	0.996143i	$-0.472033\pi$
$401$	3.51432			0.175497			0.0877483	+	0.996143i	$0.472033\pi$
$402$	−9.67628	−	7.03023i	−0.482609	−	0.350636i
$403$	−9.11637	−	28.0573i	−0.454119	−	1.39763i
$404$	−1.68757	−	5.19382i	−0.0839599	−	0.258402i
$405$		0			0
$406$	−5.31525	+	16.3587i	−0.263791	+	0.811866i
$407$	1.54106			0.0763873
$408$	0.512289	−	1.57666i	0.0253621	−	0.0780565i
$409$	13.1746	−	9.57194i	0.651444	−	0.473302i	−0.212318	−	0.977201i	$-0.568101\pi$
$409$	13.1746	−	9.57194i	0.651444	−	0.473302i	0.863763	+	0.503898i	$0.168101\pi$
$410$		0			0
$411$	1.42968	+	1.03872i	0.0705210	+	0.0512365i
$412$	5.37377	−	3.90427i	0.264747	−	0.192350i
$413$	40.2643	−	29.2537i	1.98128	−	1.43948i
$414$	−4.73553	−	3.44056i	−0.232739	−	0.169095i
$415$		0			0
$416$	2.28564	−	1.66061i	0.112062	−	0.0814182i
$417$	3.39811	−	10.4583i	0.166406	−	0.512145i
$418$	−4.74733			−0.232199
$419$	8.18528	−	25.1917i	0.399877	−	1.23070i	−0.525220	−	0.850966i	$-0.676017\pi$
$419$	8.18528	−	25.1917i	0.399877	−	1.23070i	0.925098	−	0.379730i	$-0.123983\pi$
$420$		0			0
$421$	−9.56476	−	29.4373i	−0.466158	−	1.43469i	−0.857520	−	0.514450i	$-0.827996\pi$
$421$	−9.56476	−	29.4373i	−0.466158	−	1.43469i	0.391362	−	0.920237i	$-0.372004\pi$
$422$	−0.386023	−	1.18806i	−0.0187913	−	0.0578337i
$423$	7.05824	+	5.12811i	0.343183	+	0.249337i
$424$	3.54936			0.172372
$425$		0			0
$426$	−3.50758			−0.169943
$427$	−0.335433	−	0.243706i	−0.0162327	−	0.0117938i
$428$	4.48833	+	13.8137i	0.216952	+	0.667708i
$429$	0.770528	+	2.37144i	0.0372014	+	0.114494i
$430$		0			0
$431$	−0.532381	+	1.63850i	−0.0256439	+	0.0789238i	−0.963059	−	0.269289i	$-0.913211\pi$
$431$	−0.532381	+	1.63850i	−0.0256439	+	0.0789238i	0.937416	+	0.348213i	$0.113211\pi$
$432$	1.00000			0.0481125
$433$	7.45911	−	22.9568i	0.358462	−	1.10323i	−0.595513	−	0.803346i	$-0.703051\pi$
$433$	7.45911	−	22.9568i	0.358462	−	1.10323i	0.953975	−	0.299886i	$-0.0969487\pi$
$434$	40.6085	−	29.5038i	1.94927	−	1.41623i
$435$		0			0
$436$	−3.85954	−	2.80412i	−0.184838	−	0.134293i
$437$	−25.4719	+	18.5064i	−1.21849	+	0.885282i
$438$	−5.84757	+	4.24851i	−0.279408	+	0.203002i
$439$	−6.66899	−	4.84531i	−0.318294	−	0.231254i	0.417153	−	0.908836i	$-0.363028\pi$
$439$	−6.66899	−	4.84531i	−0.318294	−	0.231254i	−0.735447	+	0.677582i	$0.763028\pi$
$440$		0			0
$441$	−13.0306	+	9.46727i	−0.620504	+	0.450822i
$442$	−1.44732	+	4.45439i	−0.0688420	+	0.211874i
$443$	22.4652			1.06735			0.533676	−	0.845689i	$-0.320810\pi$
$443$	22.4652			1.06735			0.533676	+	0.845689i	$0.320810\pi$
$444$	−0.539565	+	1.66061i	−0.0256066	+	0.0788091i
$445$		0			0
$446$	2.73237	+	8.40936i	0.129381	+	0.398195i
$447$	0.899079	+	2.76708i	0.0425250	+	0.130878i
$448$	3.88890	+	2.82545i	0.183733	+	0.133490i
$449$	30.4988			1.43933			0.719663	−	0.694323i	$-0.244296\pi$
$449$	30.4988			1.43933			0.719663	+	0.694323i	$0.244296\pi$
$450$		0			0
$451$	1.53146			0.0721139
$452$	3.91206	+	2.84228i	0.184008	+	0.133690i
$453$	−0.414651	−	1.27616i	−0.0194820	−	0.0599594i
$454$	−5.46860	−	16.8306i	−0.256654	−	0.789900i
$455$		0			0
$456$	1.66217	−	5.11563i	0.0778381	−	0.239561i
$457$	−6.65272			−0.311201			−0.155601	−	0.987820i	$-0.549731\pi$
$457$	−6.65272			−0.311201			−0.155601	+	0.987820i	$0.549731\pi$
$458$	−2.75446	+	8.47737i	−0.128708	+	0.396121i
$459$	−1.34119	+	0.974432i	−0.0626014	+	0.0454826i
$460$		0			0
$461$	19.1479	+	13.9118i	0.891808	+	0.647936i	0.936349	−	0.351071i	$-0.114183\pi$
$461$	19.1479	+	13.9118i	0.891808	+	0.647936i	−0.0445410	+	0.999008i	$0.514183\pi$
$462$	−3.43228	+	2.49370i	−0.159684	+	0.116017i
$463$	−21.1038	+	15.3328i	−0.980775	+	0.712575i	−0.957882	−	0.287163i	$-0.907288\pi$
$463$	−21.1038	+	15.3328i	−0.980775	+	0.712575i	−0.0228935	+	0.999738i	$0.507288\pi$
$464$	−2.89488	−	2.10325i	−0.134391	−	0.0976410i
$465$		0			0
$466$	7.75898	−	5.63723i	0.359428	−	0.261140i
$467$	−0.455993	+	1.40340i	−0.0211008	+	0.0649417i	−0.961052	−	0.276366i	$-0.910870\pi$
$467$	−0.455993	+	1.40340i	−0.0211008	+	0.0649417i	0.939952	+	0.341308i	$0.110870\pi$
$468$	−2.82520			−0.130595
$469$	−17.7665	+	54.6796i	−0.820380	+	2.52487i
$470$		0			0
$471$	−2.56845	−	7.90489i	−0.118348	−	0.364238i
$472$	3.19945	+	9.84690i	0.147267	+	0.453240i
$473$	1.62192	+	1.17839i	0.0745760	+	0.0541827i
$474$	−12.5762			−0.577646
$475$		0			0
$476$	−7.96896			−0.365257
$477$	−2.87150	−	2.08626i	−0.131477	−	0.0955235i
$478$	−2.83152	−	8.71452i	−0.129511	−	0.398593i
$479$	−4.14388	−	12.7536i	−0.189339	−	0.582725i	0.810657	−	0.585521i	$-0.199110\pi$
$479$	−4.14388	−	12.7536i	−0.189339	−	0.582725i	−0.999996	+	0.00279598i	$0.999110\pi$
$480$		0			0
$481$	1.52438	−	4.69156i	0.0695058	−	0.213917i
$482$	−2.49551			−0.113667
$483$	−8.69485	+	26.7600i	−0.395629	+	1.21762i
$484$	8.26900	−	6.00778i	0.375864	−	0.273081i
$485$		0			0
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	1.71518	−	1.24615i	0.0777224	−	0.0564686i	−0.548246	−	0.836317i	$-0.684704\pi$
$487$	1.71518	−	1.24615i	0.0777224	−	0.0564686i	0.625968	+	0.779849i	$0.284704\pi$
$488$	0.0697810	−	0.0506988i	0.00315884	−	0.00229503i
$489$	5.04724	+	3.66704i	0.228244	+	0.165829i
$490$		0			0
$491$	1.79947	−	1.30739i	0.0812091	−	0.0590019i	−0.546440	−	0.837498i	$-0.684017\pi$
$491$	1.79947	−	1.30739i	0.0812091	−	0.0590019i	0.627649	+	0.778496i	$0.284017\pi$
$492$	−0.536207	+	1.65028i	−0.0241741	+	0.0744002i
$493$	5.93206			0.267166
$494$	−4.69596	+	14.4527i	−0.211281	+	0.650256i
$495$		0			0
$496$	3.22681	+	9.93109i	0.144888	+	0.445919i
$497$	5.21025	+	16.0355i	0.233712	+	0.719291i
$498$	10.7390	+	7.80231i	0.481224	+	0.349630i
$499$	14.5582			0.651715			0.325858	−	0.945419i	$-0.394347\pi$
$499$	14.5582			0.651715			0.325858	+	0.945419i	$0.394347\pi$
$500$		0			0
$501$	14.8368			0.662860
$502$	−7.04866	−	5.12115i	−0.314597	−	0.228568i
$503$	7.36734	+	22.6744i	0.328494	+	1.01100i	0.969839	+	0.243747i	$0.0783767\pi$
$503$	7.36734	+	22.6744i	0.328494	+	1.01100i	−0.641345	+	0.767252i	$0.721623\pi$
$504$	−1.48543	−	4.57167i	−0.0661662	−	0.203638i
$505$		0			0
$506$	−1.59643	+	4.91331i	−0.0709700	+	0.218423i
$507$	−5.01824			−0.222868
$508$	−0.556790	+	1.71362i	−0.0247035	+	0.0760297i
$509$	28.1543	−	20.4553i	1.24792	−	0.906664i	0.249817	−	0.968293i	$-0.419630\pi$
$509$	28.1543	−	20.4553i	1.24792	−	0.906664i	0.998099	+	0.0616289i	$0.0196295\pi$
$510$		0			0
$511$	28.1089	+	20.4223i	1.24347	+	0.903431i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−4.35161	+	3.16163i	−0.192128	+	0.139589i
$514$	16.0081	+	11.6306i	0.706088	+	0.513003i
$515$		0			0
$516$	−1.83769	+	1.33516i	−0.0808999	+	0.0587772i
$517$	2.37946	−	7.32322i	0.104648	−	0.322075i
$518$	8.39326			0.368778
$519$	−4.95566	+	15.2520i	−0.217529	+	0.669487i
$520$		0			0
$521$	−2.68575	−	8.26589i	−0.117665	−	0.362135i	0.874829	−	0.484433i	$-0.160974\pi$
$521$	−2.68575	−	8.26589i	−0.117665	−	0.362135i	−0.992494	+	0.122297i	$0.960974\pi$
$522$	1.10574	+	3.40313i	0.0483971	+	0.148951i
$523$	−26.2414	−	19.0655i	−1.14746	−	0.833676i	−0.159317	−	0.987228i	$-0.550929\pi$
$523$	−26.2414	−	19.0655i	−1.14746	−	0.833676i	−0.988141	+	0.153551i	$0.950929\pi$
$524$	−16.0315			−0.700338
$525$		0			0
$526$	25.5635			1.11462
$527$	−14.0049	−	10.1752i	−0.610064	−	0.443238i
$528$	−0.272734	−	0.839389i	−0.0118692	−	0.0365297i
$529$	3.48038	+	10.7115i	0.151321	+	0.465717i
$530$		0			0
$531$	3.19945	−	9.84690i	0.138844	−	0.427319i
$532$	−25.8560			−1.12100
$533$	1.51489	−	4.66236i	0.0656173	−	0.201949i
$534$	−15.1178	+	10.9837i	−0.654210	+	0.475312i
$535$		0			0
$536$	−9.67628	−	7.03023i	−0.417951	−	0.303659i
$537$	−9.50506	+	6.90583i	−0.410174	+	0.298009i
$538$	−19.7517	+	14.3504i	−0.851555	+	0.618691i
$539$	11.5006	+	8.35567i	0.495366	+	0.359904i
$540$		0			0
$541$	−25.0000	+	18.1636i	−1.07483	+	0.780913i	−0.976775	−	0.214268i	$-0.931264\pi$
$541$	−25.0000	+	18.1636i	−1.07483	+	0.780913i	−0.0980596	+	0.995181i	$0.531264\pi$
$542$	0.848720	−	2.61209i	0.0364557	−	0.112199i
$543$	−4.03402			−0.173116
$544$	0.512289	−	1.57666i	0.0219642	−	0.0675989i
$545$		0			0
$546$	4.19663	+	12.9159i	0.179599	+	0.552749i
$547$	−9.66035	−	29.7315i	−0.413047	−	1.27123i	−0.913986	−	0.405745i	$-0.867012\pi$
$547$	−9.66035	−	29.7315i	−0.413047	−	1.27123i	0.500940	−	0.865482i	$-0.332988\pi$
$548$	1.42968	+	1.03872i	0.0610730	+	0.0443721i
$549$	−0.0862540			−0.00368123
$550$		0			0
$551$	19.2471			0.819953
$552$	−4.73553	−	3.44056i	−0.201558	−	0.146440i
$553$	18.6811	+	57.4945i	0.794401	+	2.44491i
$554$	0.921114	+	2.83490i	0.0391344	+	0.120443i
$555$		0			0
$556$	3.39811	−	10.4583i	0.144112	−	0.443531i
$557$	34.8113			1.47500			0.737500	−	0.675347i	$-0.236006\pi$
$557$	34.8113			1.47500			0.737500	+	0.675347i	$0.236006\pi$
$558$	3.22681	−	9.93109i	0.136602	−	0.420416i
$559$	5.19185	−	3.77210i	0.219592	−	0.159543i
$560$		0			0
$561$	1.18372	+	0.860020i	0.0499765	+	0.0363101i
$562$	−3.12422	+	2.26988i	−0.131787	+	0.0957490i
$563$	−3.95734	+	2.87518i	−0.166782	+	0.121174i	−0.668045	−	0.744121i	$-0.732869\pi$
$563$	−3.95734	+	2.87518i	−0.166782	+	0.121174i	0.501263	+	0.865295i	$0.332869\pi$
$564$	7.05824	+	5.12811i	0.297206	+	0.215932i
$565$		0			0
$566$	13.5121	−	9.81713i	0.567957	−	0.412645i
$567$	−1.48543	+	4.57167i	−0.0623820	+	0.191992i
$568$	−3.50758			−0.147175
$569$	−0.906980	+	2.79140i	−0.0380226	+	0.117021i	−0.968266	−	0.249921i	$-0.919595\pi$
$569$	−0.906980	+	2.79140i	−0.0380226	+	0.117021i	0.930244	+	0.366942i	$0.119595\pi$
$570$		0			0
$571$	9.85310	+	30.3247i	0.412339	+	1.26905i	0.914609	+	0.404339i	$0.132499\pi$
$571$	9.85310	+	30.3247i	0.412339	+	1.26905i	−0.502270	+	0.864711i	$0.667501\pi$
$572$	0.770528	+	2.37144i	0.0322174	+	0.0991550i
$573$	−9.64472	−	7.00730i	−0.402914	−	0.292734i
$574$	8.34102			0.348147
$575$		0			0
$576$	1.00000			0.0416667
$577$	29.9024	+	21.7254i	1.24485	+	0.904439i	0.997912	−	0.0645913i	$-0.0205744\pi$
$577$	29.9024	+	21.7254i	1.24485	+	0.904439i	0.246942	+	0.969030i	$0.420574\pi$
$578$	−4.40401	−	13.5542i	−0.183183	−	0.563779i
$579$	3.64913	+	11.2309i	0.151653	+	0.466739i
$580$		0			0
$581$	19.7177	−	60.6847i	0.818027	−	2.51763i
$582$	18.2706			0.757341
$583$	−0.968032	+	2.97930i	−0.0400918	+	0.123390i
$584$	−5.84757	+	4.24851i	−0.241974	+	0.175805i
$585$		0			0
$586$	0.407059	+	0.295746i	0.0168155	+	0.0122171i
$587$	−22.7014	+	16.4935i	−0.936988	+	0.680761i	−0.947694	−	0.319181i	$-0.896592\pi$
$587$	−22.7014	+	16.4935i	−0.936988	+	0.680761i	0.0107059	+	0.999943i	$0.496592\pi$
$588$	−13.0306	+	9.46727i	−0.537372	+	0.390424i
$589$	−45.4402	−	33.0143i	−1.87233	−	1.36033i
$590$		0			0
$591$	5.88837	−	4.27815i	0.242215	−	0.175980i
$592$	−0.539565	+	1.66061i	−0.0221760	+	0.0682507i
$593$	−40.6263			−1.66832			−0.834161	−	0.551521i	$-0.814048\pi$
$593$	−40.6263			−1.66832			−0.834161	+	0.551521i	$0.814048\pi$
$594$	−0.272734	+	0.839389i	−0.0111904	+	0.0344405i
$595$		0			0
$596$	0.899079	+	2.76708i	0.0368277	+	0.113344i
$597$	0.704401	+	2.16792i	0.0288292	+	0.0887272i
$598$	13.3788	+	9.72029i	0.547101	+	0.397492i
$599$	−22.6989			−0.927451			−0.463725	−	0.885979i	$-0.653488\pi$
$599$	−22.6989			−0.927451			−0.463725	+	0.885979i	$0.653488\pi$
$600$		0			0
$601$	32.9640			1.34463			0.672316	−	0.740265i	$-0.265300\pi$
$601$	32.9640			1.34463			0.672316	+	0.740265i	$0.265300\pi$
$602$	8.83368	+	6.41805i	0.360034	+	0.261580i
$603$	3.69601	+	11.3751i	0.150513	+	0.463232i
$604$	−0.414651	−	1.27616i	−0.0168719	−	0.0519264i
$605$		0			0
$606$	−1.68757	+	5.19382i	−0.0685530	+	0.210984i
$607$	8.32854			0.338045			0.169023	−	0.985612i	$-0.445939\pi$
$607$	8.32854			0.338045			0.169023	+	0.985612i	$0.445939\pi$
$608$	1.66217	−	5.11563i	0.0674098	−	0.207466i
$609$	13.9155	−	10.1102i	0.563885	−	0.409686i
$610$		0			0
$611$	−19.9409	−	14.4879i	−0.806724	−	0.586120i
$612$	−1.34119	+	0.974432i	−0.0542144	+	0.0393891i
$613$	5.96457	−	4.33351i	0.240907	−	0.175029i	−0.460780	−	0.887514i	$-0.652430\pi$
$613$	5.96457	−	4.33351i	0.240907	−	0.175029i	0.701687	+	0.712485i	$0.252430\pi$
$614$	6.98485	+	5.07479i	0.281886	+	0.204802i
$615$		0			0
$616$	−3.43228	+	2.49370i	−0.138291	+	0.100474i
$617$	−2.73975	+	8.43210i	−0.110298	+	0.339463i	−0.990937	−	0.134324i	$-0.957114\pi$
$617$	−2.73975	+	8.43210i	−0.110298	+	0.339463i	0.880639	+	0.473788i	$0.157114\pi$
$618$	−6.64235			−0.267194
$619$	−0.139486	+	0.429292i	−0.00560640	+	0.0172547i	−0.953821	−	0.300377i	$-0.902888\pi$
$619$	−0.139486	+	0.429292i	−0.00560640	+	0.0172547i	0.948214	+	0.317632i	$0.102888\pi$
$620$		0			0
$621$	1.80881	+	5.56695i	0.0725851	+	0.223394i
$622$	6.26298	+	19.2755i	0.251122	+	0.772875i
$623$	72.6703	+	52.7980i	2.91147	+	2.11531i
$624$	−2.82520			−0.113099
$625$		0			0
$626$	−17.0302			−0.680664
$627$	3.84067	+	2.79041i	0.153382	+	0.111438i
$628$	−2.56845	−	7.90489i	−0.102492	−	0.315439i
$629$	−0.894493	−	2.75297i	−0.0356658	−	0.109768i
$630$		0			0
$631$	−9.74952	+	30.0059i	−0.388122	+	1.19452i	0.546068	+	0.837741i	$0.316124\pi$
$631$	−9.74952	+	30.0059i	−0.388122	+	1.19452i	−0.934190	+	0.356776i	$0.883876\pi$
$632$	−12.5762			−0.500256
$633$	−0.386023	+	1.18806i	−0.0153430	+	0.0472210i
$634$	2.28270	−	1.65848i	0.0906575	−	0.0658665i
$635$		0			0
$636$	−2.87150	−	2.08626i	−0.113862	−	0.0827257i
$637$	36.8140	−	26.7469i	1.45862	−	1.05975i
$638$	2.55498	−	1.85630i	0.101153	−	0.0734916i
$639$	2.83769	+	2.06170i	0.112257	+	0.0815598i
$640$		0			0
$641$	−15.1110	+	10.9788i	−0.596848	+	0.433635i	−0.844759	−	0.535147i	$-0.820256\pi$
$641$	−15.1110	+	10.9788i	−0.596848	+	0.433635i	0.247911	+	0.968783i	$0.420256\pi$
$642$	4.48833	−	13.8137i	0.177140	−	0.545182i
$643$	15.5969			0.615083			0.307541	−	0.951535i	$-0.400494\pi$
$643$	15.5969			0.615083			0.307541	+	0.951535i	$0.400494\pi$
$644$	−8.69485	+	26.7600i	−0.342625	+	1.05449i
$645$		0			0
$646$	2.75555	+	8.48070i	0.108416	+	0.333669i
$647$	8.14520	+	25.0683i	0.320221	+	0.985538i	0.973552	+	0.228466i	$0.0733710\pi$
$647$	8.14520	+	25.0683i	0.320221	+	0.985538i	−0.653331	+	0.757072i	$0.726629\pi$
$648$	−0.809017	−	0.587785i	−0.0317812	−	0.0230904i
$649$	−9.13798			−0.358697
$650$		0			0
$651$	−50.1948			−1.96729
$652$	5.04724	+	3.66704i	0.197665	+	0.143612i
$653$	6.06245	+	18.6583i	0.237242	+	0.730156i	0.996816	+	0.0797351i	$0.0254074\pi$
$653$	6.06245	+	18.6583i	0.237242	+	0.730156i	−0.759574	+	0.650421i	$0.774593\pi$
$654$	1.47421	+	4.53716i	0.0576462	+	0.177417i
$655$		0			0
$656$	−0.536207	+	1.65028i	−0.0209354	+	0.0644324i
$657$	7.22800			0.281991
$658$	12.9596	−	39.8854i	0.505216	−	1.55489i
$659$	−18.7179	+	13.5993i	−0.729145	+	0.529755i	−0.889293	−	0.457338i	$-0.848803\pi$
$659$	−18.7179	+	13.5993i	−0.729145	+	0.529755i	0.160148	+	0.987093i	$0.448803\pi$
$660$		0			0
$661$	−14.1554	−	10.2845i	−0.550581	−	0.400021i	0.277419	−	0.960749i	$-0.410521\pi$
$661$	−14.1554	−	10.2845i	−0.550581	−	0.400021i	−0.828000	+	0.560729i	$0.810521\pi$
$662$	3.29512	−	2.39404i	0.128068	−	0.0930472i
$663$	3.78913	−	2.75297i	0.147158	−	0.106916i
$664$	10.7390	+	7.80231i	0.416752	+	0.302788i
$665$		0			0
$666$	1.41260	−	1.02631i	0.0547372	−	0.0397689i
$667$	6.47241	−	19.9200i	0.250613	−	0.771306i
$668$	14.8368			0.574054
$669$	2.73237	−	8.40936i	0.105639	−	0.325125i
$670$		0			0
$671$	0.0235244	+	0.0724006i	0.000908149	+	0.00279500i
$672$	−1.48543	−	4.57167i	−0.0573016	−	0.176356i
$673$	−0.836959	−	0.608086i	−0.0322624	−	0.0234400i	0.571537	−	0.820576i	$-0.306347\pi$
$673$	−0.836959	−	0.608086i	−0.0322624	−	0.0234400i	−0.603800	+	0.797136i	$0.706347\pi$
$674$	−9.04782			−0.348509
$675$		0			0
$676$	−5.01824			−0.193009
$677$	7.61625	+	5.53353i	0.292716	+	0.212671i	0.724445	−	0.689333i	$-0.242096\pi$
$677$	7.61625	+	5.53353i	0.292716	+	0.212671i	−0.431729	+	0.902004i	$0.642096\pi$
$678$	−1.49428	−	4.59891i	−0.0573873	−	0.176620i
$679$	−27.1396	−	83.5272i	−1.04152	−	3.20548i
$680$		0			0
$681$	−5.46860	+	16.8306i	−0.209557	+	0.644950i
$682$	−9.21610			−0.352903
$683$	4.28318	−	13.1823i	0.163891	−	0.504405i	−0.835062	−	0.550156i	$-0.814568\pi$
$683$	4.28318	−	13.1823i	0.163891	−	0.504405i	0.998953	+	0.0457510i	$0.0145681\pi$
$684$	−4.35161	+	3.16163i	−0.166388	+	0.120888i
$685$		0			0
$686$	35.4149	+	25.7305i	1.35215	+	0.982394i
$687$	7.21128	−	5.23930i	0.275128	−	0.199892i
$688$	−1.83769	+	1.33516i	−0.0700614	+	0.0509026i
$689$	8.11255	+	5.89411i	0.309064	+	0.224548i
$690$		0			0
$691$	7.36726	−	5.35263i	0.280264	−	0.203624i	−0.438769	−	0.898600i	$-0.644585\pi$
$691$	7.36726	−	5.35263i	0.280264	−	0.203624i	0.719032	+	0.694977i	$0.244585\pi$
$692$	−4.95566	+	15.2520i	−0.188386	+	0.579793i
$693$	4.24254			0.161161
$694$	2.68429	−	8.26141i	0.101894	−	0.313599i
$695$		0			0
$696$	1.10574	+	3.40313i	0.0419131	+	0.128995i
$697$	−0.888926	−	2.73583i	−0.0336705	−	0.103627i
$698$	−21.7063	−	15.7706i	−0.821596	−	0.596925i
$699$	−9.59063			−0.362751
$700$		0			0
$701$	−22.6848			−0.856791			−0.428396	−	0.903591i	$-0.640921\pi$
$701$	−22.6848			−0.856791			−0.428396	+	0.903591i	$0.640921\pi$
$702$	2.28564	+	1.66061i	0.0862657	+	0.0626757i
$703$	−2.90226	−	8.93224i	−0.109461	−	0.336886i
$704$	−0.272734	−	0.839389i	−0.0102790	−	0.0316357i
$705$		0			0
$706$	−8.76060	+	26.9623i	−0.329709	+	1.01474i
$707$	26.2512			0.987278
$708$	3.19945	−	9.84690i	0.120243	−	0.370069i
$709$	−18.1615	+	13.1951i	−0.682069	+	0.495552i	−0.874043	−	0.485848i	$-0.838511\pi$
$709$	−18.1615	+	13.1951i	−0.682069	+	0.495552i	0.191974	+	0.981400i	$0.438511\pi$
$710$		0			0
$711$	10.1744	+	7.39213i	0.381570	+	0.277227i
$712$	−15.1178	+	10.9837i	−0.566563	+	0.411632i
$713$	−49.4492	+	35.9269i	−1.85189	+	1.34547i
$714$	6.44702	+	4.68404i	0.241274	+	0.175296i
$715$		0			0
$716$	−9.50506	+	6.90583i	−0.355221	+	0.258083i
$717$	−2.83152	+	8.71452i	−0.105745	+	0.325450i
$718$	8.68830			0.324245
$719$	14.1238	−	43.4684i	0.526727	−	1.62110i	−0.234148	−	0.972201i	$-0.575230\pi$
$719$	14.1238	−	43.4684i	0.526727	−	1.62110i	0.760875	−	0.648898i	$-0.224770\pi$
$720$		0			0
$721$	9.86672	+	30.3666i	0.367456	+	1.13091i
$722$	3.06929	+	9.44630i	0.114227	+	0.351555i
$723$	2.01891	+	1.46682i	0.0750840	+	0.0545517i
$724$	−4.03402			−0.149923
$725$		0			0
$726$	−10.2210			−0.379338
$727$	−1.77517	−	1.28973i	−0.0658373	−	0.0478336i	0.554380	−	0.832264i	$-0.312956\pi$
$727$	−1.77517	−	1.28973i	−0.0658373	−	0.0478336i	−0.620217	+	0.784430i	$0.712956\pi$
$728$	4.19663	+	12.9159i	0.155537	+	0.478695i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	1.16367	−	3.58141i	0.0430400	−	0.132463i
$732$	−0.0862540			−0.00318804
$733$	2.83618	−	8.72887i	0.104757	−	0.322408i	−0.884917	−	0.465750i	$-0.845785\pi$
$733$	2.83618	−	8.72887i	0.104757	−	0.322408i	0.989673	+	0.143342i	$0.0457847\pi$
$734$	10.0895	−	7.33046i	0.372411	−	0.270572i
$735$		0			0
$736$	−4.73553	−	3.44056i	−0.174554	−	0.126821i
$737$	8.54014	−	6.20478i	0.314580	−	0.228556i
$738$	1.40381	−	1.01993i	0.0516749	−	0.0375440i
$739$	35.2025	+	25.5761i	1.29495	+	0.940833i	0.999893	−	0.0146478i	$-0.00466270\pi$
$739$	35.2025	+	25.5761i	1.29495	+	0.940833i	0.295053	+	0.955481i	$0.404663\pi$
$740$		0			0
$741$	12.2942	−	8.93224i	0.451638	−	0.328134i
$742$	−5.27232	+	16.2265i	−0.193553	+	0.595695i
$743$	−8.61668			−0.316115			−0.158058	−	0.987430i	$-0.550523\pi$
$743$	−8.61668			−0.316115			−0.158058	+	0.987430i	$0.550523\pi$
$744$	3.22681	−	9.93109i	0.118300	−	0.364091i
$745$		0			0
$746$	−4.01684	−	12.3626i	−0.147067	−	0.452625i
$747$	−4.10192	−	12.6244i	−0.150081	−	0.461903i
$748$	1.18372	+	0.860020i	0.0432809	+	0.0314454i
$749$	−69.8186			−2.55112
$750$		0			0
$751$	1.11603			0.0407245			0.0203623	−	0.999793i	$-0.493518\pi$
$751$	1.11603			0.0407245			0.0203623	+	0.999793i	$0.493518\pi$
$752$	7.05824	+	5.12811i	0.257388	+	0.187003i
$753$	2.69235	+	8.28619i	0.0981146	+	0.301966i
$754$	−3.12395	−	9.61453i	−0.113768	−	0.350141i
$755$		0			0
$756$	−1.48543	+	4.57167i	−0.0540244	+	0.166270i
$757$	−37.2729			−1.35471			−0.677354	−	0.735658i	$-0.736873\pi$
$757$	−37.2729			−1.35471			−0.677354	+	0.735658i	$0.736873\pi$
$758$	0.541481	−	1.66651i	0.0196675	−	0.0605302i
$759$	4.17951	−	3.03659i	0.151707	−	0.110221i
$760$		0			0
$761$	16.1999	+	11.7699i	0.587245	+	0.426659i	0.841329	−	0.540524i	$-0.181774\pi$
$761$	16.1999	+	11.7699i	0.587245	+	0.426659i	−0.254084	+	0.967182i	$0.581774\pi$
$762$	1.45769	−	1.05908i	0.0528067	−	0.0383663i
$763$	18.5526	−	13.4792i	0.671648	−	0.487981i
$764$	−9.64472	−	7.00730i	−0.348934	−	0.253515i
$765$		0			0
$766$	−27.6165	+	20.0646i	−0.997825	+	0.724962i
$767$	−9.03910	+	27.8195i	−0.326383	+	1.00450i
$768$	1.00000			0.0360844
$769$	−4.78043	+	14.7126i	−0.172387	+	0.530552i	−0.999504	−	0.0314770i	$-0.989979\pi$
$769$	−4.78043	+	14.7126i	−0.172387	+	0.530552i	0.827118	+	0.562029i	$0.189979\pi$
$770$		0			0
$771$	−6.11455	−	18.8187i	−0.220210	−	0.677738i
$772$	3.64913	+	11.2309i	0.131335	+	0.404208i
$773$	19.4632	+	14.1408i	0.700042	+	0.508610i	0.879946	−	0.475074i	$-0.157579\pi$
$773$	19.4632	+	14.1408i	0.700042	+	0.508610i	−0.179904	+	0.983684i	$0.557579\pi$
$774$	2.27151			0.0816479
$775$		0			0
$776$	18.2706			0.655876
$777$	−6.79029	−	4.93343i	−0.243600	−	0.176986i
$778$	2.11878	+	6.52094i	0.0759620	+	0.233787i
$779$	−2.88420	−	8.87665i	−0.103337	−	0.318039i
$780$		0			0
$781$	0.956637	−	2.94422i	0.0342311	−	0.105353i
$782$	9.70385			0.347009
$783$	1.10574	−	3.40313i	0.0395161	−	0.121618i
$784$	−13.0306	+	9.46727i	−0.465378	+	0.338117i
$785$		0			0
$786$	12.9697	+	9.42306i	0.462615	+	0.336109i
$787$	26.9857	−	19.6062i	0.961935	−	0.698887i	0.00833555	−	0.999965i	$-0.497347\pi$
$787$	26.9857	−	19.6062i	0.961935	−	0.698887i	0.953599	+	0.301079i	$0.0973467\pi$
$788$	5.88837	−	4.27815i	0.209764	−	0.152403i
$789$	−20.6813	−	15.0258i	−0.736273	−	0.534933i
$790$		0			0
$791$	−18.8051	+	13.6627i	−0.668631	+	0.485789i
$792$	−0.272734	+	0.839389i	−0.00969118	+	0.0298264i
$793$	0.243685			0.00865350
$794$	−10.2466	+	31.5358i	−0.363638	+	1.11916i
$795$		0			0
$796$	0.704401	+	2.16792i	0.0249668	+	0.0768400i
$797$	−10.0916	−	31.0587i	−0.357462	−	1.10016i	−0.954568	−	0.297993i	$-0.903683\pi$
$797$	−10.0916	−	31.0587i	−0.357462	−	1.10016i	0.597106	−	0.802162i	$-0.296317\pi$
$798$	20.9179	+	15.1978i	0.740487	+	0.537995i
$799$	−14.4634			−0.511680
$800$		0			0
$801$	18.6866			0.660259
$802$	−2.84314	−	2.06566i	−0.100395	−	0.0729411i
$803$	−1.97132	−	6.06710i	−0.0695664	−	0.214103i
$804$	3.69601	+	11.3751i	0.130348	+	0.401170i
$805$		0			0
$806$	−9.11637	+	28.0573i	−0.321111	+	0.988277i
$807$	24.4144			0.859428
$808$	−1.68757	+	5.19382i	−0.0593686	+	0.182718i
$809$	−8.36995	+	6.08113i	−0.294272	+	0.213801i	−0.725118	−	0.688624i	$-0.758215\pi$
$809$	−8.36995	+	6.08113i	−0.294272	+	0.213801i	0.430847	+	0.902425i	$0.358215\pi$
$810$		0			0
$811$	30.7731	+	22.3580i	1.08059	+	0.785094i	0.977786	−	0.209607i	$-0.0672186\pi$
$811$	30.7731	+	22.3580i	1.08059	+	0.785094i	0.102804	+	0.994702i	$0.467219\pi$
$812$	13.9155	−	10.1102i	0.488338	−	0.354799i
$813$	−2.22198	+	1.61436i	−0.0779282	+	0.0566181i
$814$	−1.24674	−	0.905810i	−0.0436982	−	0.0317486i
$815$		0			0
$816$	−1.34119	+	0.974432i	−0.0469511	+	0.0341119i
$817$	3.77564	−	11.6202i	0.132093	−	0.406540i
$818$	−16.2848			−0.569383
$819$	4.19663	−	12.9159i	0.146642	−	0.451318i
$820$		0			0
$821$	−6.18062	−	19.0220i	−0.215705	−	0.663872i	−0.999103	−	0.0423510i	$-0.986515\pi$
$821$	−6.18062	−	19.0220i	−0.215705	−	0.663872i	0.783398	−	0.621521i	$-0.213485\pi$
$822$	−0.546090	−	1.68069i	−0.0190471	−	0.0586209i
$823$	31.7381	+	23.0591i	1.10632	+	0.803790i	0.982080	−	0.188462i	$-0.0603502\pi$
$823$	31.7381	+	23.0591i	1.10632	+	0.803790i	0.124242	+	0.992252i	$0.460350\pi$
$824$	−6.64235			−0.231397
$825$		0			0
$826$	−49.7694			−1.73170
$827$	−44.4208	−	32.2736i	−1.54466	−	1.12226i	−0.947326	−	0.320271i	$-0.896226\pi$
$827$	−44.4208	−	32.2736i	−1.54466	−	1.12226i	−0.597336	−	0.801991i	$-0.703774\pi$
$828$	1.80881	+	5.56695i	0.0628606	+	0.193465i
$829$	−2.01553	−	6.20315i	−0.0700021	−	0.215444i	0.909935	−	0.414751i	$-0.136131\pi$
$829$	−2.01553	−	6.20315i	−0.0700021	−	0.215444i	−0.979937	+	0.199306i	$0.936131\pi$
$830$		0			0
$831$	0.921114	−	2.83490i	0.0319531	−	0.0983415i
$832$	−2.82520			−0.0979462
$833$	8.25128	−	25.3948i	0.285890	−	0.879879i
$834$	−8.89636	+	6.46359i	−0.308056	+	0.223816i
$835$		0			0
$836$	3.84067	+	2.79041i	0.132832	+	0.0965083i
$837$	−8.44789	+	6.13775i	−0.292002	+	0.212152i
$838$	−21.4294	+	15.5693i	−0.740265	+	0.537834i
$839$	35.1557	+	25.5421i	1.21371	+	0.881811i	0.995562	−	0.0941047i	$-0.0299988\pi$
$839$	35.1557	+	25.5421i	1.21371	+	0.881811i	0.218147	+	0.975916i	$0.429999\pi$
$840$		0			0
$841$	13.1029	−	9.51978i	0.451823	−	0.328268i
$842$	−9.56476	+	29.4373i	−0.329624	+	1.01448i
$843$	3.86174			0.133006
$844$	−0.386023	+	1.18806i	−0.0132875	+	0.0408946i
$845$		0			0
$846$	−2.69601	−	8.29746i	−0.0926907	−	0.285273i
$847$	15.1826	+	46.7273i	0.521681	+	1.60557i
$848$	−2.87150	−	2.08626i	−0.0986076	−	0.0716426i
$849$	−16.7019			−0.573208
$850$		0			0
$851$	−10.2205			−0.350355
$852$	2.83769	+	2.06170i	0.0972178	+	0.0706328i
$853$	6.44673	+	19.8410i	0.220732	+	0.679343i	0.998697	+	0.0510350i	$0.0162520\pi$
$853$	6.44673	+	19.8410i	0.220732	+	0.679343i	−0.777965	+	0.628307i	$0.783748\pi$
$854$	0.128124	+	0.394325i	0.00438431	+	0.0134935i
$855$		0			0
$856$	4.48833	−	13.8137i	0.153408	−	0.472141i
$857$	−10.2125			−0.348854			−0.174427	−	0.984670i	$-0.555807\pi$
$857$	−10.2125			−0.348854			−0.174427	+	0.984670i	$0.555807\pi$
$858$	0.770528	−	2.37144i	0.0263054	−	0.0809597i
$859$	−2.14672	+	1.55969i	−0.0732453	+	0.0532158i	−0.623805	−	0.781580i	$-0.714414\pi$
$859$	−2.14672	+	1.55969i	−0.0732453	+	0.0532158i	0.550560	+	0.834796i	$0.314414\pi$
$860$		0			0
$861$	−6.74802	−	4.90273i	−0.229972	−	0.167084i
$862$	1.39379	−	1.01265i	0.0474727	−	0.0344910i
$863$	−1.81361	+	1.31766i	−0.0617360	+	0.0448538i	−0.618225	−	0.786001i	$-0.712148\pi$
$863$	−1.81361	+	1.31766i	−0.0617360	+	0.0448538i	0.556489	+	0.830855i	$0.312148\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$		0			0
$866$	−19.5282	+	14.1881i	−0.663595	+	0.482130i
$867$	−4.40401	+	13.5542i	−0.149568	+	0.460323i
$868$	−50.1948			−1.70372
$869$	3.42997	−	10.5564i	0.116354	−	0.358100i
$870$		0			0
$871$	−10.4420	−	32.1371i	−0.353812	−	1.08892i
$872$	1.47421	+	4.53716i	0.0499231	+	0.153648i
$873$	−14.7812	−	10.7392i	−0.500269	−	0.363467i
$874$	31.4850			1.06500
$875$		0			0
$876$	7.22800			0.244211
$877$	41.3556	+	30.0466i	1.39648	+	1.01460i	0.995119	+	0.0986803i	$0.0314621\pi$
$877$	41.3556	+	30.0466i	1.39648	+	1.01460i	0.401359	+	0.915921i	$0.368538\pi$
$878$	2.54733	+	7.83987i	0.0859682	+	0.264583i
$879$	−0.155483	−	0.478527i	−0.00524430	−	0.0161403i
$880$		0			0
$881$	−14.5343	+	44.7321i	−0.489674	+	1.50706i	0.335422	+	0.942068i	$0.391121\pi$
$881$	−14.5343	+	44.7321i	−0.489674	+	1.50706i	−0.825096	+	0.564993i	$0.808879\pi$
$882$	16.1067			0.542340
$883$	8.21666	−	25.2883i	0.276513	−	0.851018i	−0.712303	−	0.701873i	$-0.752348\pi$
$883$	8.21666	−	25.2883i	0.276513	−	0.851018i	0.988815	−	0.149146i	$-0.0476524\pi$
$884$	3.78913	−	2.75297i	0.127442	−	0.0925923i
$885$		0			0
$886$	−18.1747	−	13.2047i	−0.610591	−	0.443621i
$887$	38.7797	−	28.1751i	1.30209	−	0.946027i	0.302121	−	0.953270i	$-0.402305\pi$
$887$	38.7797	−	28.1751i	1.30209	−	0.946027i	0.999974	+	0.00724276i	$0.00230546\pi$
$888$	1.41260	−	1.02631i	0.0474038	−	0.0344409i
$889$	−7.00705	−	5.09092i	−0.235009	−	0.170744i
$890$		0			0
$891$	0.714027	−	0.518771i	0.0239208	−	0.0173795i
$892$	2.73237	−	8.40936i	0.0914864	−	0.281566i
$893$	−46.9279			−1.57038
$894$	0.899079	−	2.76708i	0.0300697	−	0.0925451i
$895$		0			0
$896$	−1.48543	−	4.57167i	−0.0496246	−	0.152729i
$897$	−5.11026	−	15.7278i	−0.170627	−	0.525134i
$898$	−24.6740	−	17.9267i	−0.823383	−	0.598223i
$899$	37.3648			1.24619
$900$		0			0
$901$	5.88415			0.196029
$902$	−1.23898	−	0.900172i	−0.0412536	−	0.0299725i
$903$	−3.37417	−	10.3846i	−0.112285	−	0.345578i
$904$	−1.49428	−	4.59891i	−0.0496989	−	0.152957i
$905$		0			0
$906$	−0.414651	+	1.27616i	−0.0137759	+	0.0423977i
$907$	5.35392			0.177774			0.0888870	−	0.996042i	$-0.471669\pi$
$907$	5.35392			0.177774			0.0888870	+	0.996042i	$0.471669\pi$
$908$	−5.46860	+	16.8306i	−0.181482	+	0.558543i
$909$	4.41813	−	3.20996i	0.146540	−	0.106468i
$910$		0			0
$911$	10.9464	+	7.95304i	0.362671	+	0.263496i	0.754165	−	0.656685i	$-0.228042\pi$
$911$	10.9464	+	7.95304i	0.362671	+	0.263496i	−0.391494	+	0.920181i	$0.628042\pi$
$912$	−4.35161	+	3.16163i	−0.144096	+	0.104692i
$913$	−9.47805	+	6.88620i	−0.313678	+	0.227900i
$914$	5.38217	+	3.91037i	0.178026	+	0.129344i
$915$		0			0
$916$	7.21128	−	5.23930i	0.238267	−	0.173111i
$917$	23.8136	−	73.2906i	0.786393	−	2.42027i
$918$	1.65780			0.0547156
$919$	−17.2285	+	53.0240i	−0.568317	+	1.74910i	0.0895666	+	0.995981i	$0.471452\pi$
$919$	−17.2285	+	53.0240i	−0.568317	+	1.74910i	−0.657884	+	0.753119i	$0.728548\pi$
$920$		0			0
$921$	−2.66798	−	8.21118i	−0.0879128	−	0.270568i
$922$	−7.31386	−	22.5097i	−0.240869	−	0.741319i
$923$	−8.01705	−	5.82473i	−0.263885	−	0.191723i
$924$	4.24254			0.139569
$925$		0			0
$926$	26.0857			0.857229
$927$	5.37377	+	3.90427i	0.176498	+	0.128233i
$928$	1.10574	+	3.40313i	0.0362979	+	0.111713i
$929$	−16.0123	−	49.2807i	−0.525346	−	1.61685i	−0.763631	−	0.645653i	$-0.776585\pi$
$929$	−16.0123	−	49.2807i	−0.525346	−	1.61685i	0.238284	−	0.971195i	$-0.423415\pi$
$930$		0			0
$931$	26.7720	−	82.3958i	0.877417	−	2.70041i
$932$	−9.59063			−0.314151
$933$	6.26298	−	19.2755i	0.205041	−	0.631050i
$934$	1.19380	−	0.867350i	0.0390625	−	0.0283805i
$935$		0			0
$936$	2.28564	+	1.66061i	0.0747083	+	0.0542788i
$937$	−32.3322	+	23.4907i	−1.05625	+	0.767409i	−0.973391	−	0.229152i	$-0.926405\pi$
$937$	−32.3322	+	23.4907i	−1.05625	+	0.767409i	−0.0828575	+	0.996561i	$0.526405\pi$
$938$	46.5133	−	33.7939i	1.51871	−	1.10341i
$939$	13.7777	+	10.0101i	0.449619	+	0.326667i
$940$		0			0
$941$	12.2262	−	8.88288i	0.398564	−	0.289574i	−0.370392	−	0.928876i	$-0.620777\pi$
$941$	12.2262	−	8.88288i	0.398564	−	0.289574i	0.768956	+	0.639302i	$0.220777\pi$
$942$	−2.56845	+	7.90489i	−0.0836848	+	0.257555i
$943$	−10.1569			−0.330754
$944$	3.19945	−	9.84690i	0.104133	−	0.320489i
$945$		0			0
$946$	−0.619519	−	1.90668i	−0.0201423	−	0.0619916i
$947$	10.5272	+	32.3992i	0.342087	+	1.05283i	0.963125	+	0.269054i	$0.0867110\pi$
$947$	10.5272	+	32.3992i	0.342087	+	1.05283i	−0.621039	+	0.783780i	$0.713289\pi$
$948$	10.1744	+	7.39213i	0.330449	+	0.240085i
$949$	−20.4205			−0.662879
$950$		0			0
$951$	−2.82157			−0.0914956
$952$	6.44702	+	4.68404i	0.208949	+	0.151811i
$953$	−10.3122	−	31.7376i	−0.334044	−	1.02808i	−0.967191	−	0.254050i	$-0.918237\pi$
$953$	−10.3122	−	31.7376i	−0.334044	−	1.02808i	0.633147	−	0.774031i	$-0.281763\pi$
$954$	1.09681	+	3.37565i	0.0355107	+	0.109291i
$955$		0			0
$956$	−2.83152	+	8.71452i	−0.0915779	+	0.281848i
$957$	−3.15813			−0.102088
$958$	−4.14388	+	12.7536i	−0.133883	+	0.412049i
$959$	−6.87240	+	4.99309i	−0.221921	+	0.161235i
$960$		0			0
$961$	−63.1347	−	45.8700i	−2.03660	−	1.47968i
$962$	−3.99088	+	2.89954i	−0.128671	+	0.0934850i
$963$	−11.7506	+	8.53731i	−0.378658	+	0.275111i
$964$	2.01891	+	1.46682i	0.0650247	+	0.0472432i
$965$		0			0
$966$	22.7634	−	16.5386i	0.732401	−	0.532120i
$967$	8.17697	−	25.1661i	0.262954	−	0.809288i	−0.729204	−	0.684296i	$-0.760110\pi$
$967$	8.17697	−	25.1661i	0.262954	−	0.809288i	0.992158	−	0.124992i	$-0.0398904\pi$
$968$	−10.2210			−0.328517
$969$	2.75555	−	8.48070i	0.0885209	−	0.272439i
$970$		0			0
$971$	9.76352	+	30.0490i	0.313326	+	0.964319i	0.976438	+	0.215798i	$0.0692354\pi$
$971$	9.76352	+	30.0490i	0.313326	+	0.964319i	−0.663112	+	0.748520i	$0.730765\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	42.7643	+	31.0701i	1.37096	+	0.996061i
$974$	−2.12008			−0.0679318
$975$		0			0
$976$	−0.0862540			−0.00276092
$977$	3.75428	+	2.72764i	0.120110	+	0.0872650i	0.646219	−	0.763152i	$-0.276349\pi$
$977$	3.75428	+	2.72764i	0.120110	+	0.0872650i	−0.526109	+	0.850417i	$0.676349\pi$
$978$	−1.92788	−	5.93339i	−0.0616467	−	0.189729i
$979$	−5.09647	−	15.6853i	−0.162884	−	0.501305i
$980$		0			0
$981$	1.47421	−	4.53716i	0.0470679	−	0.144860i
$982$	−2.22427			−0.0709793
$983$	10.5031	−	32.3253i	0.334998	−	1.03102i	−0.631725	−	0.775192i	$-0.717653\pi$
$983$	10.5031	−	32.3253i	0.334998	−	1.03102i	0.966723	−	0.255825i	$-0.0823470\pi$
$984$	1.40381	−	1.01993i	0.0447518	−	0.0325141i
$985$		0			0
$986$	−4.79914	−	3.48678i	−0.152836	−	0.111042i
$987$	−33.9285	+	24.6505i	−1.07996	+	0.784635i
$988$	12.2942	−	8.93224i	0.391130	−	0.284172i
$989$	−10.7568	−	7.81529i	−0.342047	−	0.248512i
$990$		0			0
$991$	44.5440	−	32.3631i	1.41499	−	1.02805i	0.422411	−	0.906404i	$-0.361184\pi$
$991$	44.5440	−	32.3631i	1.41499	−	1.02805i	0.992574	−	0.121643i	$-0.0388162\pi$
$992$	3.22681	−	9.93109i	0.102451	−	0.315312i
$993$	−4.07299			−0.129252
$994$	5.21025	−	16.0355i	0.165259	−	0.508616i
$995$		0			0
$996$	−4.10192	−	12.6244i	−0.129974	−	0.400019i
$997$	−0.225852	−	0.695101i	−0.00715280	−	0.0220141i	0.947416	−	0.320003i	$-0.103684\pi$
$997$	−0.225852	−	0.695101i	−0.00715280	−	0.0220141i	−0.954569	+	0.297989i	$0.903684\pi$
$998$	−11.7778	−	8.55710i	−0.372821	−	0.270870i
$999$	−1.74607			−0.0552432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.f.451.1		16
5.2	odd	4		750.2.h.d.49.3		16
5.3	odd	4		150.2.h.b.109.2	✓	16
5.4	even	2		750.2.g.g.451.4		16
15.8	even	4		450.2.l.c.109.3		16
25.2	odd	20		150.2.h.b.139.2	yes	16
25.6	even	5		3750.2.a.v.1.1		8
25.8	odd	20		3750.2.c.k.1249.8		16
25.11	even	5	inner	750.2.g.f.301.1		16
25.14	even	10		750.2.g.g.301.4		16
25.17	odd	20		3750.2.c.k.1249.9		16
25.19	even	10		3750.2.a.u.1.8		8
25.23	odd	20		750.2.h.d.199.4		16
75.2	even	20		450.2.l.c.289.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.b.109.2	✓	16	5.3	odd	4
150.2.h.b.139.2	yes	16	25.2	odd	20
450.2.l.c.109.3		16	15.8	even	4
450.2.l.c.289.3		16	75.2	even	20
750.2.g.f.301.1		16	25.11	even	5	inner
750.2.g.f.451.1		16	1.1	even	1	trivial
750.2.g.g.301.4		16	25.14	even	10
750.2.g.g.451.4		16	5.4	even	2
750.2.h.d.49.3		16	5.2	odd	4
750.2.h.d.199.4		16	25.23	odd	20
3750.2.a.u.1.8		8	25.19	even	10
3750.2.a.v.1.1		8	25.6	even	5
3750.2.c.k.1249.8		16	25.8	odd	20
3750.2.c.k.1249.9		16	25.17	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.309017 - 0.951057i) q^{6} -4.80694 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(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} -4.80694 q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.714027 + 0.518771i) q^{11} +(-0.809017 + 0.587785i) q^{12} +(2.28564 - 1.66061i) q^{13} +(3.88890 + 2.82545i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.512289 - 1.57666i) q^{17} +1.00000 q^{18} +(1.66217 - 5.11563i) q^{19} +(-1.48543 - 4.57167i) q^{21} +(-0.272734 - 0.839389i) q^{22} +(-4.73553 - 3.44056i) q^{23} +1.00000 q^{24} -2.82520 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-1.48543 - 4.57167i) q^{28} +(1.10574 + 3.40313i) q^{29} +(3.22681 - 9.93109i) q^{31} +1.00000 q^{32} +(-0.272734 + 0.839389i) q^{33} +(-1.34119 + 0.974432i) q^{34} +(-0.809017 - 0.587785i) q^{36} +(1.41260 - 1.02631i) q^{37} +(-4.35161 + 3.16163i) q^{38} +(2.28564 + 1.66061i) q^{39} +(1.40381 - 1.01993i) q^{41} +(-1.48543 + 4.57167i) q^{42} +2.27151 q^{43} +(-0.272734 + 0.839389i) q^{44} +(1.80881 + 5.56695i) q^{46} +(-2.69601 - 8.29746i) q^{47} +(-0.809017 - 0.587785i) q^{48} +16.1067 q^{49} +1.65780 q^{51} +(2.28564 + 1.66061i) q^{52} +(1.09681 + 3.37565i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-1.48543 + 4.57167i) q^{56} +5.37889 q^{57} +(1.10574 - 3.40313i) q^{58} +(-8.37628 + 6.08572i) q^{59} +(0.0697810 + 0.0506988i) q^{61} +(-8.44789 + 6.13775i) q^{62} +(3.88890 - 2.82545i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.714027 - 0.518771i) q^{66} +(3.69601 - 11.3751i) q^{67} +1.65780 q^{68} +(1.80881 - 5.56695i) q^{69} +(-1.08390 - 3.33591i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-5.84757 - 4.24851i) q^{73} -1.74607 q^{74} +5.37889 q^{76} +(-3.43228 - 2.49370i) q^{77} +(-0.873035 - 2.68693i) q^{78} +(-3.88627 - 11.9607i) q^{79} +(0.309017 - 0.951057i) q^{81} -1.73520 q^{82} +(-4.10192 + 12.6244i) q^{83} +(3.88890 - 2.82545i) q^{84} +(-1.83769 - 1.33516i) q^{86} +(-2.89488 + 2.10325i) q^{87} +(0.714027 - 0.518771i) q^{88} +(-15.1178 - 10.9837i) q^{89} +(-10.9869 + 7.98246i) q^{91} +(1.80881 - 5.56695i) q^{92} +10.4422 q^{93} +(-2.69601 + 8.29746i) q^{94} +(0.309017 + 0.951057i) q^{96} +(5.64593 + 17.3764i) q^{97} +(-13.0306 - 9.46727i) q^{98} -0.882586 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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