LMFDB - Embedded newform 845.2.e.m.191.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.3
Root			$-1.27597 - 0.609843i$ of defining polynomial
Character	$\chi$	$=$	845.191
Dual form			845.2.e.m.146.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.109843 - 0.190254i) q^{2} +(0.800098 - 1.38581i) q^{3} +(0.975869 + 1.69025i) q^{4} -1.00000 q^{5} +(-0.175771 - 0.304444i) q^{6} +(0.166123 + 0.287734i) q^{7} +0.868145 q^{8} +(0.219687 + 0.380509i) q^{9} +O(q^{10})$	\(q+(0.109843 - 0.190254i) q^{2} +(0.800098 - 1.38581i) q^{3} +(0.975869 + 1.69025i) q^{4} -1.00000 q^{5} +(-0.175771 - 0.304444i) q^{6} +(0.166123 + 0.287734i) q^{7} +0.868145 q^{8} +(0.219687 + 0.380509i) q^{9} +(-0.109843 + 0.190254i) q^{10} +(2.68591 - 4.65213i) q^{11} +3.12316 q^{12} +0.0729902 q^{14} +(-0.800098 + 1.38581i) q^{15} +(-1.85638 + 3.21534i) q^{16} +(2.53215 + 4.38581i) q^{17} +0.0965246 q^{18} +(-1.13397 - 1.96410i) q^{19} +(-0.975869 - 1.69025i) q^{20} +0.531659 q^{21} +(-0.590059 - 1.02201i) q^{22} +(1.41959 - 2.45880i) q^{23} +(0.694601 - 1.20308i) q^{24} +1.00000 q^{25} +5.50367 q^{27} +(-0.324229 + 0.561581i) q^{28} +(1.45174 - 2.51448i) q^{29} +(0.175771 + 0.304444i) q^{30} +5.46410 q^{31} +(1.27597 + 2.21004i) q^{32} +(-4.29798 - 7.44432i) q^{33} +1.11256 q^{34} +(-0.166123 - 0.287734i) q^{35} +(-0.428771 + 0.742653i) q^{36} +(-2.98601 + 5.17191i) q^{37} -0.498239 q^{38} -0.868145 q^{40} +(-1.86603 + 3.23205i) q^{41} +(0.0583993 - 0.101151i) q^{42} +(2.53215 + 4.38581i) q^{43} +10.4844 q^{44} +(-0.219687 - 0.380509i) q^{45} +(-0.311865 - 0.540166i) q^{46} +8.34285 q^{47} +(2.97057 + 5.14517i) q^{48} +(3.44481 - 5.96658i) q^{49} +(0.109843 - 0.190254i) q^{50} +8.10387 q^{51} -1.56063 q^{53} +(0.604542 - 1.04710i) q^{54} +(-2.68591 + 4.65213i) q^{55} +(0.144219 + 0.249795i) q^{56} -3.62916 q^{57} +(-0.318928 - 0.552399i) q^{58} +(-1.35366 - 2.34461i) q^{59} -3.12316 q^{60} +(-7.05193 - 12.2143i) q^{61} +(0.600196 - 1.03957i) q^{62} +(-0.0729902 + 0.126423i) q^{63} -6.86488 q^{64} -1.88842 q^{66} +(-5.16612 + 8.94799i) q^{67} +(-4.94209 + 8.55995i) q^{68} +(-2.27162 - 3.93456i) q^{69} -0.0729902 q^{70} +(-6.39866 - 11.0828i) q^{71} +(0.190720 + 0.330337i) q^{72} -9.68922 q^{73} +(0.655986 + 1.13620i) q^{74} +(0.800098 - 1.38581i) q^{75} +(2.21322 - 3.83341i) q^{76} +1.78477 q^{77} +4.51851 q^{79} +(1.85638 - 3.21534i) q^{80} +(3.74441 - 6.48552i) q^{81} +(0.409941 + 0.710039i) q^{82} -4.26371 q^{83} +(0.518830 + 0.898640i) q^{84} +(-2.53215 - 4.38581i) q^{85} +1.11256 q^{86} +(-2.32306 - 4.02367i) q^{87} +(2.33176 - 4.03872i) q^{88} +(-1.61292 + 2.79366i) q^{89} -0.0965246 q^{90} +5.54133 q^{92} +(4.37182 - 7.57221i) q^{93} +(0.916407 - 1.58726i) q^{94} +(1.13397 + 1.96410i) q^{95} +4.08359 q^{96} +(1.25396 + 2.17191i) q^{97} +(-0.756779 - 1.31078i) q^{98} +2.36023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} + 40 q^{18} - 16 q^{19} + 2 q^{20} + 8 q^{21} - 12 q^{22} + 10 q^{23} + 24 q^{24} + 8 q^{25} - 4 q^{27} - 8 q^{28} - 8 q^{29} - 4 q^{30} + 16 q^{31} - 4 q^{32} - 18 q^{33} - 8 q^{34} + 10 q^{35} - 20 q^{36} + 2 q^{37} + 16 q^{38} - 12 q^{40} - 8 q^{41} + 4 q^{42} + 2 q^{43} + 24 q^{44} + 4 q^{45} - 16 q^{46} + 16 q^{47} + 28 q^{48} - 12 q^{49} - 2 q^{50} + 8 q^{51} - 24 q^{53} + 16 q^{54} - 12 q^{56} - 28 q^{57} - 22 q^{58} - 12 q^{59} + 20 q^{60} - 28 q^{61} - 4 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} - 14 q^{68} + 16 q^{69} - 4 q^{70} - 4 q^{71} - 12 q^{72} - 16 q^{73} + 10 q^{74} + 2 q^{75} - 20 q^{76} + 36 q^{77} - 16 q^{79} + 2 q^{80} + 8 q^{81} - 4 q^{82} - 24 q^{83} + 28 q^{84} - 2 q^{85} - 8 q^{86} + 22 q^{87} + 18 q^{88} + 12 q^{89} - 40 q^{90} + 44 q^{92} - 8 q^{93} + 32 q^{94} + 16 q^{95} + 8 q^{96} - 2 q^{97} + 24 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 - 4 * q^9 + 2 * q^10 - 20 * q^12 + 4 * q^14 - 2 * q^15 - 2 * q^16 + 2 * q^17 + 40 * q^18 - 16 * q^19 + 2 * q^20 + 8 * q^21 - 12 * q^22 + 10 * q^23 + 24 * q^24 + 8 * q^25 - 4 * q^27 - 8 * q^28 - 8 * q^29 - 4 * q^30 + 16 * q^31 - 4 * q^32 - 18 * q^33 - 8 * q^34 + 10 * q^35 - 20 * q^36 + 2 * q^37 + 16 * q^38 - 12 * q^40 - 8 * q^41 + 4 * q^42 + 2 * q^43 + 24 * q^44 + 4 * q^45 - 16 * q^46 + 16 * q^47 + 28 * q^48 - 12 * q^49 - 2 * q^50 + 8 * q^51 - 24 * q^53 + 16 * q^54 - 12 * q^56 - 28 * q^57 - 22 * q^58 - 12 * q^59 + 20 * q^60 - 28 * q^61 - 4 * q^62 - 4 * q^63 + 8 * q^64 + 12 * q^66 - 30 * q^67 - 14 * q^68 + 16 * q^69 - 4 * q^70 - 4 * q^71 - 12 * q^72 - 16 * q^73 + 10 * q^74 + 2 * q^75 - 20 * q^76 + 36 * q^77 - 16 * q^79 + 2 * q^80 + 8 * q^81 - 4 * q^82 - 24 * q^83 + 28 * q^84 - 2 * q^85 - 8 * q^86 + 22 * q^87 + 18 * q^88 + 12 * q^89 - 40 * q^90 + 44 * q^92 - 8 * q^93 + 32 * q^94 + 16 * q^95 + 8 * q^96 - 2 * q^97 + 24 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.109843	−	0.190254i	0.0776710	−	0.134530i	−0.824574	−	0.565755i	$-0.808585\pi$
$2$	0.109843	−	0.190254i	0.0776710	−	0.134530i	0.902245	+	0.431224i	$0.141918\pi$
$3$	0.800098	−	1.38581i	0.461937	−	0.800098i	−0.537121	−	0.843505i	$-0.680488\pi$
$3$	0.800098	−	1.38581i	0.461937	−	0.800098i	0.999057	+	0.0434075i	$0.0138214\pi$
$4$	0.975869	+	1.69025i	0.487934	+	0.845127i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.175771	−	0.304444i	−0.0717582	−	0.124289i
$7$	0.166123	+	0.287734i	0.0627887	+	0.108753i	0.895711	−	0.444637i	$-0.146667\pi$
$7$	0.166123	+	0.287734i	0.0627887	+	0.108753i	−0.832922	+	0.553390i	$0.813334\pi$
$8$	0.868145			0.306936
$9$	0.219687	+	0.380509i	0.0732290	+	0.126836i
$10$	−0.109843	+	0.190254i	−0.0347355	+	0.0601637i
$11$	2.68591	−	4.65213i	0.809832	−	1.40267i	−0.103149	−	0.994666i	$-0.532892\pi$
$11$	2.68591	−	4.65213i	0.809832	−	1.40267i	0.912980	−	0.408004i	$-0.133775\pi$
$12$	3.12316			0.901579
$13$		0			0
$13$		0			0
$14$	0.0729902			0.0195074
$15$	−0.800098	+	1.38581i	−0.206584	+	0.357815i
$16$	−1.85638	+	3.21534i	−0.464094	+	0.803835i
$17$	2.53215	+	4.38581i	0.614136	+	1.06372i	0.990535	+	0.137258i	$0.0438288\pi$
$17$	2.53215	+	4.38581i	0.614136	+	1.06372i	−0.376399	+	0.926458i	$0.622838\pi$
$18$	0.0965246			0.0227511
$19$	−1.13397	−	1.96410i	−0.260152	−	0.450596i	0.706130	−	0.708082i	$-0.250439\pi$
$19$	−1.13397	−	1.96410i	−0.260152	−	0.450596i	−0.966282	+	0.257486i	$0.917106\pi$
$20$	−0.975869	−	1.69025i	−0.218211	−	0.377952i
$21$	0.531659			0.116018
$22$	−0.590059	−	1.02201i	−0.125801	−	0.217894i
$23$	1.41959	−	2.45880i	0.296005	−	0.512695i	−0.679213	−	0.733941i	$-0.737679\pi$
$23$	1.41959	−	2.45880i	0.296005	−	0.512695i	0.975218	+	0.221246i	$0.0710122\pi$
$24$	0.694601	−	1.20308i	0.141785	−	0.245578i
$25$	1.00000			0.200000
$26$		0			0
$27$	5.50367			1.05918
$28$	−0.324229	+	0.561581i	−0.0612735	+	0.106129i
$29$	1.45174	−	2.51448i	0.269581	−	0.466928i	−0.699173	−	0.714953i	$-0.746448\pi$
$29$	1.45174	−	2.51448i	0.269581	−	0.466928i	0.968754	+	0.248025i	$0.0797815\pi$
$30$	0.175771	+	0.304444i	0.0320912	+	0.0555837i
$31$	5.46410			0.981382			0.490691	−	0.871334i	$-0.336744\pi$
$31$	5.46410			0.981382			0.490691	+	0.871334i	$0.336744\pi$
$32$	1.27597	+	2.21004i	0.225561	+	0.390683i
$33$	−4.29798	−	7.44432i	−0.748182	−	1.29589i
$34$	1.11256			0.190802
$35$	−0.166123	−	0.287734i	−0.0280800	−	0.0486359i
$36$	−0.428771	+	0.742653i	−0.0714619	+	0.123776i
$37$	−2.98601	+	5.17191i	−0.490896	+	0.850257i	−0.999945	−	0.0104803i	$-0.996664\pi$
$37$	−2.98601	+	5.17191i	−0.490896	+	0.850257i	0.509049	+	0.860738i	$0.329997\pi$
$38$	−0.498239			−0.0808250
$39$		0			0
$40$	−0.868145			−0.137266
$41$	−1.86603	+	3.23205i	−0.291424	+	0.504762i	−0.974147	−	0.225916i	$-0.927462\pi$
$41$	−1.86603	+	3.23205i	−0.291424	+	0.504762i	0.682723	+	0.730678i	$0.260796\pi$
$42$	0.0583993	−	0.101151i	0.00901121	−	0.0156079i
$43$	2.53215	+	4.38581i	0.386149	+	0.668830i	0.991928	−	0.126803i	$-0.0404717\pi$
$43$	2.53215	+	4.38581i	0.386149	+	0.668830i	−0.605779	+	0.795633i	$0.707138\pi$
$44$	10.4844			1.58058
$45$	−0.219687	−	0.380509i	−0.0327490	−	0.0567229i
$46$	−0.311865	−	0.540166i	−0.0459820	−	0.0796432i
$47$	8.34285			1.21693			0.608465	−	0.793581i	$-0.291786\pi$
$47$	8.34285			1.21693			0.608465	+	0.793581i	$0.291786\pi$
$48$	2.97057	+	5.14517i	0.428764	+	0.742642i
$49$	3.44481	−	5.96658i	0.492115	−	0.852368i
$50$	0.109843	−	0.190254i	0.0155342	−	0.0269060i
$51$	8.10387			1.13477
$52$		0			0
$53$	−1.56063			−0.214369			−0.107184	−	0.994239i	$-0.534183\pi$
$53$	−1.56063			−0.214369			−0.107184	+	0.994239i	$0.534183\pi$
$54$	0.604542	−	1.04710i	0.0822678	−	0.142492i
$55$	−2.68591	+	4.65213i	−0.362168	+	0.627293i
$56$	0.144219	+	0.249795i	0.0192721	+	0.0333802i
$57$	−3.62916			−0.480694
$58$	−0.318928	−	0.552399i	−0.0418773	−	0.0725335i
$59$	−1.35366	−	2.34461i	−0.176232	−	0.305242i	0.764355	−	0.644795i	$-0.223057\pi$
$59$	−1.35366	−	2.34461i	−0.176232	−	0.305242i	−0.940587	+	0.339553i	$0.889724\pi$
$60$	−3.12316			−0.403199
$61$	−7.05193	−	12.2143i	−0.902908	−	1.56388i	−0.823702	−	0.567023i	$-0.808095\pi$
$61$	−7.05193	−	12.2143i	−0.902908	−	1.56388i	−0.0792059	−	0.996858i	$-0.525238\pi$
$62$	0.600196	−	1.03957i	0.0762249	−	0.132025i
$63$	−0.0729902	+	0.126423i	−0.00919590	+	0.0159278i
$64$	−6.86488			−0.858111
$65$		0			0
$66$	−1.88842			−0.232448
$67$	−5.16612	+	8.94799i	−0.631142	+	1.09317i	0.356176	+	0.934419i	$0.384080\pi$
$67$	−5.16612	+	8.94799i	−0.631142	+	1.09317i	−0.987319	+	0.158752i	$0.949253\pi$
$68$	−4.94209	+	8.55995i	−0.599316	+	1.03805i
$69$	−2.27162	−	3.93456i	−0.273471	−	0.473666i
$70$	−0.0729902			−0.00872400
$71$	−6.39866	−	11.0828i	−0.759382	−	1.31529i	−0.943166	−	0.332321i	$-0.892168\pi$
$71$	−6.39866	−	11.0828i	−0.759382	−	1.31529i	0.183785	−	0.982967i	$-0.441165\pi$
$72$	0.190720	+	0.330337i	0.0224766	+	0.0389306i
$73$	−9.68922			−1.13404			−0.567019	−	0.823705i	$-0.691903\pi$
$73$	−9.68922			−1.13404			−0.567019	+	0.823705i	$0.691903\pi$
$74$	0.655986	+	1.13620i	0.0762569	+	0.132081i
$75$	0.800098	−	1.38581i	0.0923873	−	0.160020i
$76$	2.21322	−	3.83341i	0.253874	−	0.439722i
$77$	1.78477			0.203393
$78$		0			0
$79$	4.51851			0.508372			0.254186	−	0.967155i	$-0.418192\pi$
$79$	4.51851			0.508372			0.254186	+	0.967155i	$0.418192\pi$
$80$	1.85638	−	3.21534i	0.207549	−	0.359486i
$81$	3.74441	−	6.48552i	0.416046	−	0.720613i
$82$	0.409941	+	0.710039i	0.0452704	+	0.0784107i
$83$	−4.26371			−0.468003			−0.234001	−	0.972236i	$-0.575182\pi$
$83$	−4.26371			−0.468003			−0.234001	+	0.972236i	$0.575182\pi$
$84$	0.518830	+	0.898640i	0.0566090	+	0.0980496i
$85$	−2.53215	−	4.38581i	−0.274650	−	0.475708i
$86$	1.11256			0.119970
$87$	−2.32306	−	4.02367i	−0.249059	−	0.431382i
$88$	2.33176	−	4.03872i	0.248566	−	0.430529i
$89$	−1.61292	+	2.79366i	−0.170969	+	0.296127i	−0.938759	−	0.344575i	$-0.888023\pi$
$89$	−1.61292	+	2.79366i	−0.170969	+	0.296127i	0.767790	+	0.640702i	$0.221356\pi$
$90$	−0.0965246			−0.0101746
$91$		0			0
$92$	5.54133			0.577724
$93$	4.37182	−	7.57221i	0.453336	−	0.785201i
$94$	0.916407	−	1.58726i	0.0945202	−	0.163714i
$95$	1.13397	+	1.96410i	0.116343	+	0.201513i
$96$	4.08359			0.416780
$97$	1.25396	+	2.17191i	0.127320	+	0.220524i	0.922637	−	0.385669i	$-0.126029\pi$
$97$	1.25396	+	2.17191i	0.127320	+	0.220524i	−0.795318	+	0.606193i	$0.792696\pi$
$98$	−0.756779	−	1.31078i	−0.0764462	−	0.132409i
$99$	2.36023			0.237213
$100$	0.975869	+	1.69025i	0.0975869	+	0.169025i
$101$	−6.22336	+	10.7792i	−0.619247	+	1.07257i	0.370376	+	0.928882i	$0.379229\pi$
$101$	−6.22336	+	10.7792i	−0.619247	+	1.07257i	−0.989623	+	0.143686i	$0.954105\pi$
$102$	0.890157	−	1.54180i	0.0881386	−	0.152661i
$103$	−15.0247			−1.48043			−0.740215	−	0.672370i	$-0.765276\pi$
$103$	−15.0247			−1.48043			−0.740215	+	0.672370i	$0.765276\pi$
$104$		0			0
$105$	−0.531659			−0.0518846
$106$	−0.171425	+	0.296916i	−0.0166502	+	0.0288390i
$107$	6.53215	−	11.3140i	0.631487	−	1.09377i	−0.355761	−	0.934577i	$-0.615778\pi$
$107$	6.53215	−	11.3140i	0.631487	−	1.09377i	0.987248	−	0.159190i	$-0.0508883\pi$
$108$	5.37086	+	9.30260i	0.516811	+	0.895144i
$109$	−11.2325			−1.07587			−0.537937	−	0.842985i	$-0.680796\pi$
$109$	−11.2325			−1.07587			−0.537937	+	0.842985i	$0.680796\pi$
$110$	0.590059	+	1.02201i	0.0562599	+	0.0974450i
$111$	4.77819	+	8.27607i	0.453526	+	0.785530i
$112$	−1.23355			−0.116560
$113$	9.17191	+	15.8862i	0.862821	+	1.49445i	0.869195	+	0.494470i	$0.164638\pi$
$113$	9.17191	+	15.8862i	0.862821	+	1.49445i	−0.00637349	+	0.999980i	$0.502029\pi$
$114$	−0.398640	+	0.690464i	−0.0373360	+	0.0646679i
$115$	−1.41959	+	2.45880i	−0.132377	+	0.229284i
$116$	5.66682			0.526151
$117$		0			0
$118$	−0.594763			−0.0547524
$119$	−0.841298	+	1.45717i	−0.0771216	+	0.133579i
$120$	−0.694601	+	1.20308i	−0.0634081	+	0.109826i
$121$	−8.92820	−	15.4641i	−0.811655	−	1.40583i
$122$	−3.09843			−0.280519
$123$	2.98601	+	5.17191i	0.269239	+	0.466336i
$124$	5.33225	+	9.23572i	0.478850	+	0.829392i
$125$	−1.00000			−0.0894427
$126$	0.0160350	+	0.0277734i	0.00142851	+	0.00247425i
$127$	−1.61998	+	2.80589i	−0.143750	+	0.248982i	−0.928906	−	0.370316i	$-0.879249\pi$
$127$	−1.61998	+	2.80589i	−0.143750	+	0.248982i	0.785156	+	0.619298i	$0.212583\pi$
$128$	−3.30600	+	5.72615i	−0.292212	+	0.506125i
$129$	8.10387			0.713506
$130$		0			0
$131$	0.175664			0.0153478			0.00767390	−	0.999971i	$-0.497557\pi$
$131$	0.175664			0.0153478			0.00767390	+	0.999971i	$0.497557\pi$
$132$	8.38853	−	14.5294i	0.730127	−	1.26462i
$133$	0.376759	−	0.652566i	0.0326692	−	0.0565846i
$134$	1.13493	+	1.96576i	0.0980430	+	0.169815i
$135$	−5.50367			−0.473681
$136$	2.19827	+	3.80752i	0.188500	+	0.326492i
$137$	8.99144	+	15.5736i	0.768190	+	1.33054i	0.938543	+	0.345162i	$0.112176\pi$
$137$	8.99144	+	15.5736i	0.768190	+	1.33054i	−0.170353	+	0.985383i	$0.554491\pi$
$138$	−0.998090			−0.0849631
$139$	−5.99307	−	10.3803i	−0.508325	−	0.880445i	−0.999954	−	0.00964021i	$-0.996931\pi$
$139$	−5.99307	−	10.3803i	−0.508325	−	0.880445i	0.491628	−	0.870805i	$-0.336402\pi$
$140$	0.324229	−	0.561581i	0.0274024	−	0.0474623i
$141$	6.67510	−	11.5616i	0.562144	−	0.973663i
$142$	−2.81140			−0.235928
$143$		0			0
$144$	−1.63129			−0.135941
$145$	−1.45174	+	2.51448i	−0.120560	+	0.208816i
$146$	−1.06430	+	1.84342i	−0.0880819	+	0.152562i
$147$	−5.51236	−	9.54769i	−0.454652	−	0.787481i
$148$	−11.6558			−0.958101
$149$	1.70520	+	2.95350i	0.139696	+	0.241960i	0.927381	−	0.374117i	$-0.122054\pi$
$149$	1.70520	+	2.95350i	0.139696	+	0.241960i	−0.787686	+	0.616077i	$0.788721\pi$
$150$	−0.175771	−	0.304444i	−0.0143516	−	0.0248578i
$151$	7.96141			0.647890			0.323945	−	0.946076i	$-0.394991\pi$
$151$	7.96141			0.647890			0.323945	+	0.946076i	$0.394991\pi$
$152$	−0.984454	−	1.70512i	−0.0798498	−	0.138304i
$153$	−1.11256	+	1.92701i	−0.0899451	+	0.155790i
$154$	0.196045	−	0.339560i	0.0157978	−	0.0273625i
$155$	−5.46410			−0.438887
$156$		0			0
$157$	−16.4329			−1.31148			−0.655742	−	0.754985i	$-0.727644\pi$
$157$	−16.4329			−1.31148			−0.655742	+	0.754985i	$0.727644\pi$
$158$	0.496329	−	0.859667i	0.0394858	−	0.0683914i
$159$	−1.24865	+	2.16273i	−0.0990247	+	0.171516i
$160$	−1.27597	−	2.21004i	−0.100874	−	0.174719i
$161$	0.943307			0.0743430
$162$	−0.822599	−	1.42478i	−0.0646295	−	0.111942i
$163$	−8.90361	−	15.4215i	−0.697384	−	1.20791i	−0.969370	−	0.245604i	$-0.921014\pi$
$163$	−8.90361	−	15.4215i	−0.697384	−	1.20791i	0.271986	−	0.962301i	$-0.412320\pi$
$164$	−7.28398			−0.568784
$165$	4.29798	+	7.44432i	0.334597	+	0.579539i
$166$	−0.468341	+	0.811190i	−0.0363503	+	0.0629605i
$167$	3.14683	−	5.45047i	0.243509	−	0.421770i	−0.718202	−	0.695834i	$-0.755035\pi$
$167$	3.14683	−	5.45047i	0.243509	−	0.421770i	0.961711	+	0.274064i	$0.0883682\pi$
$168$	0.461557			0.0356099
$169$		0			0
$170$	−1.11256			−0.0853294
$171$	0.498239	−	0.862975i	0.0381013	−	0.0659933i
$172$	−4.94209	+	8.55995i	−0.376831	+	0.652690i
$173$	−7.98756	−	13.8349i	−0.607283	−	1.05184i	−0.991686	−	0.128679i	$-0.958926\pi$
$173$	−7.98756	−	13.8349i	−0.607283	−	1.05184i	0.384404	−	0.923165i	$-0.374407\pi$
$174$	−1.02069			−0.0773786
$175$	0.166123	+	0.287734i	0.0125577	+	0.0217506i
$176$	9.97212	+	17.2722i	0.751677	+	1.30194i
$177$	−4.33225			−0.325632
$178$	0.354337	+	0.613729i	0.0265587	+	0.0460010i
$179$	−11.8087	+	20.4533i	−0.882625	+	1.52875i	−0.0342123	+	0.999415i	$0.510892\pi$
$179$	−11.8087	+	20.4533i	−0.882625	+	1.52875i	−0.848412	+	0.529336i	$0.822441\pi$
$180$	0.428771	−	0.742653i	0.0319587	−	0.0553541i
$181$	−2.62590			−0.195182			−0.0975909	−	0.995227i	$-0.531114\pi$
$181$	−2.62590			−0.195182			−0.0975909	+	0.995227i	$0.531114\pi$
$182$		0			0
$183$	−22.5689			−1.66834
$184$	1.23241	−	2.13459i	0.0908544	−	0.157364i
$185$	2.98601	−	5.17191i	0.219536	−	0.380247i
$186$	−0.960431	−	1.66351i	−0.0704222	−	0.121975i
$187$	27.2045			1.98939
$188$	8.14153	+	14.1015i	0.593782	+	1.02846i
$189$	0.914288	+	1.58359i	0.0665046	+	0.115189i
$190$	0.498239			0.0361460
$191$	1.00791	+	1.74575i	0.0729298	+	0.126318i	0.900184	−	0.435509i	$-0.143432\pi$
$191$	1.00791	+	1.74575i	0.0729298	+	0.126318i	−0.827254	+	0.561828i	$0.810098\pi$
$192$	−5.49258	+	9.51343i	−0.396393	+	0.686572i
$193$	−11.4105	+	19.7636i	−0.821348	+	1.42262i	0.0833298	+	0.996522i	$0.473445\pi$
$193$	−11.4105	+	19.7636i	−0.821348	+	1.42262i	−0.904678	+	0.426095i	$0.859889\pi$
$194$	0.550955			0.0395563
$195$		0			0
$196$	13.4467			0.960480
$197$	0.321513	−	0.556877i	0.0229068	−	0.0396758i	−0.854345	−	0.519707i	$-0.826041\pi$
$197$	0.321513	−	0.556877i	0.0229068	−	0.0396758i	0.877252	+	0.480031i	$0.159375\pi$
$198$	0.259256	−	0.449045i	0.0184245	−	0.0319122i
$199$	−1.53342	−	2.65596i	−0.108701	−	0.188276i	0.806543	−	0.591175i	$-0.201336\pi$
$199$	−1.53342	−	2.65596i	−0.108701	−	0.188276i	−0.915244	+	0.402899i	$0.868003\pi$
$200$	0.868145			0.0613871
$201$	8.26681	+	14.3185i	0.583096	+	1.00995i
$202$	1.36719	+	2.36804i	0.0961952	+	0.166615i
$203$	0.964670			0.0677065
$204$	7.90831	+	13.6976i	0.553693	+	0.959024i
$205$	1.86603	−	3.23205i	0.130329	−	0.225736i
$206$	−1.65037	+	2.85852i	−0.114987	+	0.199163i
$207$	1.24746			0.0867045
$208$		0			0
$209$	−12.1830			−0.842716
$210$	−0.0583993	+	0.101151i	−0.00402993	+	0.00698005i
$211$	4.10020	−	7.10175i	0.282269	−	0.488904i	−0.689674	−	0.724120i	$-0.742246\pi$
$211$	4.10020	−	7.10175i	0.282269	−	0.488904i	0.971943	+	0.235215i	$0.0755796\pi$
$212$	−1.52297	−	2.63786i	−0.104598	−	0.181169i
$213$	−20.4782			−1.40314
$214$	−1.43503	−	2.48554i	−0.0980964	−	0.169908i
$215$	−2.53215	−	4.38581i	−0.172691	−	0.299110i
$216$	4.77798			0.325101
$217$	0.907714	+	1.57221i	0.0616197	+	0.106728i
$218$	−1.23381	+	2.13703i	−0.0835643	+	0.144738i
$219$	−7.75232	+	13.4274i	−0.523854	+	0.907341i
$220$	−10.4844			−0.706856
$221$		0			0
$222$	2.09941			0.140903
$223$	−5.12210	+	8.87174i	−0.343001	+	0.594095i	−0.984989	−	0.172620i	$-0.944777\pi$
$223$	−5.12210	+	8.87174i	−0.343001	+	0.594095i	0.641987	+	0.766715i	$0.278110\pi$
$224$	−0.423935	+	0.734278i	−0.0283254	+	0.0490610i
$225$	0.219687	+	0.380509i	0.0146458	+	0.0253673i
$226$	4.02990			0.268065
$227$	−3.52190	−	6.10012i	−0.233757	−	0.404879i	0.725154	−	0.688587i	$-0.241769\pi$
$227$	−3.52190	−	6.10012i	−0.233757	−	0.404879i	−0.958911	+	0.283708i	$0.908435\pi$
$228$	−3.54159	−	6.13421i	−0.234547	−	0.406248i
$229$	1.32899			0.0878219			0.0439109	−	0.999035i	$-0.486018\pi$
$229$	1.32899			0.0878219			0.0439109	+	0.999035i	$0.486018\pi$
$230$	0.311865	+	0.540166i	0.0205638	+	0.0356175i
$231$	1.42799	−	2.47335i	0.0939547	−	0.162734i
$232$	1.26032	−	2.18294i	0.0827440	−	0.143317i
$233$	−1.24746			−0.0817238			−0.0408619	−	0.999165i	$-0.513010\pi$
$233$	−1.24746			−0.0817238			−0.0408619	+	0.999165i	$0.513010\pi$
$234$		0			0
$235$	−8.34285			−0.544227
$236$	2.64199	−	4.57606i	0.171979	−	0.297876i
$237$	3.61525	−	6.26180i	0.234836	−	0.406748i
$238$	0.184822	+	0.320121i	0.0119802	+	0.0207504i
$239$	−9.94207			−0.643099			−0.321549	−	0.946893i	$-0.604204\pi$
$239$	−9.94207			−0.643099			−0.321549	+	0.946893i	$0.604204\pi$
$240$	−2.97057	−	5.14517i	−0.191749	−	0.332120i
$241$	11.2934	+	19.5608i	0.727475	+	1.26002i	0.957947	+	0.286944i	$0.0926395\pi$
$241$	11.2934	+	19.5608i	0.727475	+	1.26002i	−0.230472	+	0.973079i	$0.574027\pi$
$242$	−3.92282			−0.252168
$243$	2.26371	+	3.92086i	0.145217	+	0.251523i
$244$	13.7635	−	23.8391i	0.881119	−	1.52614i
$245$	−3.44481	+	5.96658i	−0.220081	+	0.381191i
$246$	1.31197			0.0836483
$247$		0			0
$248$	4.74363			0.301221
$249$	−3.41139	+	5.90869i	−0.216188	+	0.374448i
$250$	−0.109843	+	0.190254i	−0.00694711	+	0.0120327i
$251$	3.38418	+	5.86157i	0.213608	+	0.369979i	0.952841	−	0.303470i	$-0.0981453\pi$
$251$	3.38418	+	5.86157i	0.213608	+	0.369979i	−0.739233	+	0.673449i	$0.764812\pi$
$252$	−0.284915			−0.0179480
$253$	−7.62577	−	13.2082i	−0.479428	−	0.830394i
$254$	0.355888	+	0.616417i	0.0223304	+	0.0386774i
$255$	−8.10387			−0.507484
$256$	−6.13860	−	10.6324i	−0.383663	−	0.664523i
$257$	5.12691	−	8.88007i	0.319808	−	0.553924i	−0.660640	−	0.750703i	$-0.729715\pi$
$257$	5.12691	−	8.88007i	0.319808	−	0.553924i	0.980448	+	0.196779i	$0.0630483\pi$
$258$	0.890157	−	1.54180i	0.0554187	−	0.0959881i
$259$	−1.98418			−0.123291
$260$		0			0
$261$	1.27571			0.0789645
$262$	0.0192955	−	0.0334208i	0.00119208	−	0.00206474i
$263$	−9.32850	+	16.1574i	−0.575220	+	0.996310i	0.420798	+	0.907154i	$0.361750\pi$
$263$	−9.32850	+	16.1574i	−0.575220	+	0.996310i	−0.996018	+	0.0891555i	$0.971583\pi$
$264$	−3.73127	−	6.46275i	−0.229644	−	0.397754i
$265$	1.56063			0.0958685
$266$	−0.0827690	−	0.143360i	−0.00507489	−	0.00878998i
$267$	2.58098	+	4.47040i	0.157954	+	0.273584i
$268$	−20.1658			−1.23182
$269$	−8.97894	−	15.5520i	−0.547456	−	0.948221i	−0.998448	−	0.0556934i	$-0.982263\pi$
$269$	−8.97894	−	15.5520i	−0.547456	−	0.948221i	0.450992	−	0.892528i	$-0.351070\pi$
$270$	−0.604542	+	1.04710i	−0.0367913	+	0.0637243i
$271$	−15.4488	+	26.7582i	−0.938450	+	1.62544i	−0.170086	+	0.985429i	$0.554405\pi$
$271$	−15.4488	+	26.7582i	−0.938450	+	1.62544i	−0.768363	+	0.640014i	$0.778929\pi$
$272$	−18.8025			−1.14007
$273$		0			0
$274$	3.95060			0.238665
$275$	2.68591	−	4.65213i	0.161966	−	0.280534i
$276$	4.43361	−	7.67923i	0.266872	−	0.462235i
$277$	−13.2522	−	22.9536i	−0.796250	−	1.37915i	−0.922042	−	0.387089i	$-0.873481\pi$
$277$	−13.2522	−	22.9536i	−0.796250	−	1.37915i	0.125792	−	0.992057i	$-0.459853\pi$
$278$	−2.63320			−0.157929
$279$	1.20039	+	2.07914i	0.0718656	+	0.124475i
$280$	−0.144219	−	0.249795i	−0.00861874	−	0.0149281i
$281$	4.97766			0.296942			0.148471	−	0.988917i	$-0.452565\pi$
$281$	4.97766			0.296942			0.148471	+	0.988917i	$0.452565\pi$
$282$	−1.46643	−	2.53993i	−0.0873247	−	0.151251i
$283$	6.29317	−	10.9001i	0.374090	−	0.647943i	−0.616100	−	0.787668i	$-0.711288\pi$
$283$	6.29317	−	10.9001i	0.374090	−	0.647943i	0.990190	+	0.139725i	$0.0446218\pi$
$284$	12.4885	−	21.6307i	0.741057	−	1.28355i
$285$	3.62916			0.214973
$286$		0			0
$287$	−1.23996			−0.0731926
$288$	−0.560626	+	0.971033i	−0.0330352	+	0.0572187i
$289$	−4.32355	+	7.48861i	−0.254327	+	0.440507i
$290$	0.318928	+	0.552399i	0.0187281	+	0.0324380i
$291$	4.01315			0.235255
$292$	−9.45541	−	16.3772i	−0.553336	−	0.958406i
$293$	−8.45880	−	14.6511i	−0.494168	−	0.855925i	0.505809	−	0.862645i	$-0.331194\pi$
$293$	−8.45880	−	14.6511i	−0.494168	−	0.855925i	−0.999977	+	0.00672072i	$0.997861\pi$
$294$	−2.42199			−0.141253
$295$	1.35366	+	2.34461i	0.0788132	+	0.136508i
$296$	−2.59229	+	4.48997i	−0.150674	+	0.260974i
$297$	14.7824	−	25.6038i	0.857759	−	1.48568i
$298$	0.749222			0.0434012
$299$		0			0
$300$	3.12316			0.180316
$301$	−0.841298	+	1.45717i	−0.0484916	+	0.0839899i
$302$	0.874509	−	1.51469i	0.0503223	−	0.0871608i
$303$	9.95859	+	17.2488i	0.572106	+	0.990917i
$304$	8.42034			0.482940
$305$	7.05193	+	12.2143i	0.403793	+	0.699389i
$306$	0.244415	+	0.423339i	0.0139723	+	0.0242007i
$307$	−4.30426			−0.245657			−0.122828	−	0.992428i	$-0.539197\pi$
$307$	−4.30426			−0.245657			−0.122828	+	0.992428i	$0.539197\pi$
$308$	1.74170	+	3.01671i	0.0992425	+	0.171893i
$309$	−12.0213	+	20.8214i	−0.683865	+	1.18449i
$310$	−0.600196	+	1.03957i	−0.0340888	+	0.0590436i
$311$	−2.22512			−0.126175			−0.0630875	−	0.998008i	$-0.520095\pi$
$311$	−2.22512			−0.126175			−0.0630875	+	0.998008i	$0.520095\pi$
$312$		0			0
$313$	7.20887			0.407469			0.203735	−	0.979026i	$-0.434692\pi$
$313$	7.20887			0.407469			0.203735	+	0.979026i	$0.434692\pi$
$314$	−1.80504	+	3.12642i	−0.101864	+	0.176434i
$315$	0.0729902	−	0.126423i	0.00411253	−	0.00712311i
$316$	4.40948	+	7.63744i	0.248052	+	0.429639i
$317$	−0.321644			−0.0180653			−0.00903266	−	0.999959i	$-0.502875\pi$
$317$	−0.321644			−0.0180653			−0.00903266	+	0.999959i	$0.502875\pi$
$318$	0.274313	+	0.475124i	0.0153827	+	0.0266436i
$319$	−7.79847	−	13.5073i	−0.436630	−	0.756266i
$320$	6.86488			0.383759
$321$	−10.4527	−	18.1046i	−0.583414	−	1.01050i
$322$	0.103616	−	0.179468i	0.00577430	−	0.0100014i
$323$	5.74278	−	9.94679i	0.319537	−	0.553454i
$324$	14.6162			0.812013
$325$		0			0
$326$	−3.91201			−0.216666
$327$	−8.98707	+	15.5661i	−0.496986	+	0.860805i
$328$	−1.61998	+	2.80589i	−0.0894485	+	0.154929i
$329$	1.38594	+	2.40052i	0.0764094	+	0.132345i
$330$	1.88842			0.103954
$331$	−8.31600	−	14.4037i	−0.457089	−	0.791701i	0.541717	−	0.840561i	$-0.317775\pi$
$331$	−8.31600	−	14.4037i	−0.457089	−	0.791701i	−0.998806	+	0.0488600i	$0.984441\pi$
$332$	−4.16082	−	7.20676i	−0.228355	−	0.395522i
$333$	−2.62395			−0.143791
$334$	−0.691317	−	1.19740i	−0.0378272	−	0.0655186i
$335$	5.16612	−	8.94799i	0.282255	−	0.488881i
$336$	−0.986961	+	1.70947i	−0.0538431	+	0.0932590i
$337$	24.2186			1.31927			0.659636	−	0.751586i	$-0.270711\pi$
$337$	24.2186			1.31927			0.659636	+	0.751586i	$0.270711\pi$
$338$		0			0
$339$	29.3537			1.59427
$340$	4.94209	−	8.55995i	0.268022	−	0.464229i
$341$	14.6761	−	25.4197i	0.794754	−	1.37655i
$342$	−0.109456	−	0.189584i	−0.00591873	−	0.0102515i
$343$	4.61478			0.249174
$344$	2.19827	+	3.80752i	0.118523	+	0.205288i
$345$	2.27162	+	3.93456i	0.122300	+	0.211830i
$346$	−3.50952			−0.188673
$347$	3.13680	+	5.43309i	0.168392	+	0.291664i	0.937855	−	0.347028i	$-0.112809\pi$
$347$	3.13680	+	5.43309i	0.168392	+	0.291664i	−0.769463	+	0.638692i	$0.779476\pi$
$348$	4.53401	−	7.85314i	0.243049	−	0.420972i
$349$	−3.53497	+	6.12275i	−0.189223	+	0.327743i	−0.944991	−	0.327095i	$-0.893930\pi$
$349$	−3.53497	+	6.12275i	−0.189223	+	0.327743i	0.755769	+	0.654839i	$0.227263\pi$
$350$	0.0729902			0.00390149
$351$		0			0
$352$	13.7085			0.730666
$353$	10.8949	−	18.8705i	0.579878	−	1.00438i	−0.415615	−	0.909541i	$-0.636434\pi$
$353$	10.8949	−	18.8705i	0.579878	−	1.00438i	0.995493	−	0.0948371i	$-0.0302330\pi$
$354$	−0.475869	+	0.824229i	−0.0252921	+	0.0438073i
$355$	6.39866	+	11.0828i	0.339606	+	0.588214i
$356$	−6.29598			−0.333687
$357$	1.34624	+	2.33176i	0.0712506	+	0.123410i
$358$	2.59422	+	4.49332i	0.137109	+	0.237479i
$359$	23.9737			1.26528			0.632642	−	0.774444i	$-0.281971\pi$
$359$	23.9737			1.26528			0.632642	+	0.774444i	$0.281971\pi$
$360$	−0.190720	−	0.330337i	−0.0100518	−	0.0174103i
$361$	6.92820	−	12.0000i	0.364642	−	0.631579i
$362$	−0.288438	+	0.499589i	−0.0151600	+	0.0262578i
$363$	−28.5737			−1.49973
$364$		0			0
$365$	9.68922			0.507157
$366$	−2.47905	+	4.29384i	−0.129582	+	0.224443i
$367$	−3.19566	+	5.53505i	−0.166812	+	0.288927i	−0.937297	−	0.348531i	$-0.886681\pi$
$367$	−3.19566	+	5.53505i	−0.166812	+	0.288927i	0.770485	+	0.637458i	$0.220014\pi$
$368$	5.27059	+	9.12892i	0.274748	+	0.475878i
$369$	−1.63977			−0.0853628
$370$	−0.655986	−	1.13620i	−0.0341031	−	0.0590683i
$371$	−0.259256	−	0.449045i	−0.0134599	−	0.0233133i
$372$	17.0653			0.884793
$373$	10.0401	+	17.3899i	0.519855	+	0.900414i	0.999734	+	0.0230798i	$0.00734719\pi$
$373$	10.0401	+	17.3899i	0.519855	+	0.900414i	−0.479879	+	0.877335i	$0.659319\pi$
$374$	2.98823	−	5.17577i	0.154518	−	0.267633i
$375$	−0.800098	+	1.38581i	−0.0413169	+	0.0715629i
$376$	7.24280			0.373519
$377$		0			0
$378$	0.401714			0.0206619
$379$	2.73091	−	4.73007i	0.140277	−	0.242968i	−0.787324	−	0.616540i	$-0.788534\pi$
$379$	2.73091	−	4.73007i	0.140277	−	0.242968i	0.927601	+	0.373572i	$0.121867\pi$
$380$	−2.21322	+	3.83341i	−0.113536	+	0.196650i
$381$	2.59229	+	4.48997i	0.132807	+	0.230028i
$382$	0.442849			0.0226581
$383$	2.83388	+	4.90842i	0.144804	+	0.250808i	0.929300	−	0.369326i	$-0.120411\pi$
$383$	2.83388	+	4.90842i	0.144804	+	0.250808i	−0.784496	+	0.620134i	$0.787078\pi$
$384$	5.29024	+	9.16297i	0.269966	+	0.467596i
$385$	−1.78477			−0.0909602
$386$	2.50675	+	4.34181i	0.127590	+	0.220992i
$387$	−1.11256	+	1.92701i	−0.0565546	+	0.0979554i
$388$	−2.44739	+	4.23901i	−0.124247	+	0.215203i
$389$	10.6174			0.538325			0.269162	−	0.963095i	$-0.413253\pi$
$389$	10.6174			0.538325			0.269162	+	0.963095i	$0.413253\pi$
$390$		0			0
$391$	14.3784			0.727149
$392$	2.99059	−	5.17986i	0.151048	−	0.261622i
$393$	0.140548	−	0.243436i	0.00708971	−	0.0122797i
$394$	−0.0706321	−	0.122338i	−0.00355840	−	0.00616332i
$395$	−4.51851			−0.227351
$396$	2.30328	+	3.98940i	0.115744	+	0.200475i
$397$	−14.0169	−	24.2780i	−0.703487	−	1.21848i	−0.967235	−	0.253884i	$-0.918292\pi$
$397$	−14.0169	−	24.2780i	−0.703487	−	1.21848i	0.263748	−	0.964592i	$-0.415041\pi$
$398$	−0.673745			−0.0337718
$399$	−0.602888	−	1.04423i	−0.0301822	−	0.0522770i
$400$	−1.85638	+	3.21534i	−0.0928189	+	0.160767i
$401$	11.2571	−	19.4979i	0.562155	−	0.973680i	−0.435154	−	0.900356i	$-0.643306\pi$
$401$	11.2571	−	19.4979i	0.562155	−	0.973680i	0.997308	−	0.0733241i	$-0.0233607\pi$
$402$	3.63222			0.181159
$403$		0			0
$404$	−24.2927			−1.20861
$405$	−3.74441	+	6.48552i	−0.186061	+	0.322268i
$406$	0.105963	−	0.183533i	0.00525884	−	0.00910857i
$407$	16.0403	+	27.7826i	0.795087	+	1.37713i
$408$	7.03533			0.348301
$409$	−2.14386	−	3.71328i	−0.106007	−	0.183610i	0.808142	−	0.588988i	$-0.200473\pi$
$409$	−2.14386	−	3.71328i	−0.106007	−	0.183610i	−0.914149	+	0.405378i	$0.867140\pi$
$410$	−0.409941	−	0.710039i	−0.0202456	−	0.0350663i
$411$	28.7761			1.41942
$412$	−14.6622	−	25.3956i	−0.722353	−	1.25115i
$413$	0.449749	−	0.778989i	0.0221307	−	0.0383315i
$414$	0.137025	−	0.237335i	0.00673443	−	0.0116644i
$415$	4.26371			0.209297
$416$		0			0
$417$	−19.1802			−0.939257
$418$	−1.33822	+	2.31787i	−0.0654546	+	0.113371i
$419$	−8.85578	+	15.3387i	−0.432633	+	0.749343i	−0.997099	−	0.0761137i	$-0.975749\pi$
$419$	−8.85578	+	15.3387i	−0.432633	+	0.749343i	0.564466	+	0.825456i	$0.309082\pi$
$420$	−0.518830	−	0.898640i	−0.0253163	−	0.0438491i
$421$	12.8787			0.627672			0.313836	−	0.949477i	$-0.398386\pi$
$421$	12.8787			0.627672			0.313836	+	0.949477i	$0.398386\pi$
$422$	−0.900759	−	1.56016i	−0.0438483	−	0.0759474i
$423$	1.83281	+	3.17453i	0.0891145	+	0.154351i
$424$	−1.35485			−0.0657973
$425$	2.53215	+	4.38581i	0.122827	+	0.212743i
$426$	−2.24940	+	3.89607i	−0.108984	+	0.188765i
$427$	2.34298	−	4.05816i	0.113385	−	0.196388i
$428$	25.4981			1.23250
$429$		0			0
$430$	−1.11256			−0.0536524
$431$	−4.74923	+	8.22590i	−0.228762	+	0.396228i	−0.957442	−	0.288627i	$-0.906801\pi$
$431$	−4.74923	+	8.22590i	−0.228762	+	0.396228i	0.728679	+	0.684855i	$0.240134\pi$
$432$	−10.2169	+	17.6962i	−0.491560	+	0.851408i
$433$	0.698141	+	1.20922i	0.0335505	+	0.0581112i	0.882313	−	0.470663i	$-0.155985\pi$
$433$	0.698141	+	1.20922i	0.0335505	+	0.0581112i	−0.848763	+	0.528774i	$0.822652\pi$
$434$	0.398826			0.0191443
$435$	2.32306	+	4.02367i	0.111382	+	0.192920i
$436$	−10.9614	−	18.9857i	−0.524956	−	0.909251i
$437$	−6.43911			−0.308024
$438$	1.70308	+	2.94983i	0.0813765	+	0.140948i
$439$	−2.08090	+	3.60422i	−0.0993159	+	0.172020i	−0.911402	−	0.411518i	$-0.864999\pi$
$439$	−2.08090	+	3.60422i	−0.0993159	+	0.172020i	0.812086	+	0.583538i	$0.198332\pi$
$440$	−2.33176	+	4.03872i	−0.111162	+	0.192539i
$441$	3.02711			0.144148
$442$		0			0
$443$	9.54563			0.453526			0.226763	−	0.973950i	$-0.427186\pi$
$443$	9.54563			0.453526			0.226763	+	0.973950i	$0.427186\pi$
$444$	−9.32578	+	16.1527i	−0.442582	+	0.766574i
$445$	1.61292	−	2.79366i	0.0764596	−	0.132432i
$446$	1.12526	+	1.94900i	0.0532825	+	0.0922880i
$447$	5.45732			0.258122
$448$	−1.14042	−	1.97526i	−0.0538796	−	0.0933223i
$449$	−10.8585	−	18.8075i	−0.512446	−	0.887582i	−0.999896	−	0.0144310i	$-0.995406\pi$
$449$	−10.8585	−	18.8075i	−0.512446	−	0.887582i	0.487450	−	0.873151i	$-0.337927\pi$
$450$	0.0965246			0.00455022
$451$	10.0239	+	17.3620i	0.472009	+	0.817544i
$452$	−17.9012	+	31.0057i	−0.842000	+	1.45839i
$453$	6.36991	−	11.0330i	0.299284	−	0.518376i
$454$	−1.54743			−0.0726246
$455$		0			0
$456$	−3.15064			−0.147542
$457$	−2.36130	+	4.08989i	−0.110457	+	0.191317i	−0.915955	−	0.401282i	$-0.868565\pi$
$457$	−2.36130	+	4.08989i	−0.110457	+	0.191317i	0.805498	+	0.592599i	$0.201898\pi$
$458$	0.145980	−	0.252845i	0.00682122	−	0.0118147i
$459$	13.9361	+	24.1381i	0.650482	+	1.12667i
$460$	−5.54133			−0.258366
$461$	0.890753	+	1.54283i	0.0414865	+	0.0718568i	0.886023	−	0.463641i	$-0.153457\pi$
$461$	0.890753	+	1.54283i	0.0414865	+	0.0718568i	−0.844537	+	0.535498i	$0.820124\pi$
$462$	−0.313710	−	0.543362i	−0.0145951	−	0.0252795i
$463$	6.80200			0.316116			0.158058	−	0.987430i	$-0.449477\pi$
$463$	6.80200			0.316116			0.158058	+	0.987430i	$0.449477\pi$
$464$	5.38995	+	9.33566i	0.250222	+	0.433397i
$465$	−4.37182	+	7.57221i	−0.202738	+	0.351153i
$466$	−0.137025	+	0.237335i	−0.00634758	+	0.0109943i
$467$	18.2374			0.843927			0.421963	−	0.906613i	$-0.361341\pi$
$467$	18.2374			0.843927			0.421963	+	0.906613i	$0.361341\pi$
$468$		0			0
$469$	−3.43285			−0.158514
$470$	−0.916407	+	1.58726i	−0.0422707	+	0.0732150i
$471$	−13.1479	+	22.7728i	−0.605823	+	1.04932i
$472$	−1.17517	−	2.03546i	−0.0540918	−	0.0936897i
$473$	27.2045			1.25086
$474$	−0.794223	−	1.37564i	−0.0364799	−	0.0631850i
$475$	−1.13397	−	1.96410i	−0.0520303	−	0.0901192i
$476$	−3.28398			−0.150521
$477$	−0.342849	−	0.593832i	−0.0156980	−	0.0271897i
$478$	−1.09207	+	1.89152i	−0.0499502	+	0.0865162i
$479$	17.5904	−	30.4674i	0.803724	−	1.39209i	−0.113425	−	0.993547i	$-0.536182\pi$
$479$	17.5904	−	30.4674i	0.803724	−	1.39209i	0.917149	−	0.398544i	$-0.130485\pi$
$480$	−4.08359			−0.186390
$481$		0			0
$482$	4.96204			0.226015
$483$	0.754738	−	1.30724i	0.0343418	−	0.0594817i
$484$	17.4255	−	30.1819i	0.792069	−	1.37190i
$485$	−1.25396	−	2.17191i	−0.0569392	−	0.0986215i
$486$	0.994615			0.0451166
$487$	5.15200	+	8.92352i	0.233459	+	0.404363i	0.958824	−	0.284002i	$-0.0916621\pi$
$487$	5.15200	+	8.92352i	0.233459	+	0.404363i	−0.725364	+	0.688365i	$0.758329\pi$
$488$	−6.12210	−	10.6038i	−0.277134	−	0.480011i
$489$	−28.4950			−1.28859
$490$	0.756779	+	1.31078i	0.0341878	+	0.0592150i
$491$	−4.66599	+	8.08174i	−0.210573	+	0.364724i	−0.951894	−	0.306427i	$-0.900866\pi$
$491$	−4.66599	+	8.08174i	−0.210573	+	0.364724i	0.741321	+	0.671151i	$0.234200\pi$
$492$	−5.82790	+	10.0942i	−0.262742	+	0.455083i
$493$	14.7041			0.662238
$494$		0			0
$495$	−2.36023			−0.106085
$496$	−10.1434	+	17.5689i	−0.455454	+	0.788869i
$497$	2.12593	−	3.68222i	0.0953611	−	0.165170i
$498$	0.749437	+	1.29806i	0.0335831	+	0.0581676i
$499$	23.9421			1.07179			0.535897	−	0.844283i	$-0.319974\pi$
$499$	23.9421			1.07179			0.535897	+	0.844283i	$0.319974\pi$
$500$	−0.975869	−	1.69025i	−0.0436422	−	0.0755905i
$501$	−5.03554	−	8.72181i	−0.224971	−	0.389662i
$502$	1.48692			0.0663645
$503$	−21.0721	−	36.4980i	−0.939560	−	1.62737i	−0.766294	−	0.642490i	$-0.777901\pi$
$503$	−21.0721	−	36.4980i	−0.939560	−	1.62737i	−0.173266	−	0.984875i	$-0.555432\pi$
$504$	−0.0633661	+	0.109753i	−0.00282255	+	0.00488880i
$505$	6.22336	−	10.7792i	0.276936	−	0.479667i
$506$	−3.35056			−0.148951
$507$		0			0
$508$	−6.32355			−0.280562
$509$	16.7801	−	29.0640i	0.743765	−	1.28824i	−0.207005	−	0.978340i	$-0.566371\pi$
$509$	16.7801	−	29.0640i	0.743765	−	1.28824i	0.950770	−	0.309899i	$-0.100295\pi$
$510$	−0.890157	+	1.54180i	−0.0394168	+	0.0682719i
$511$	−1.60960	−	2.78792i	−0.0712047	−	0.123330i
$512$	−15.9211			−0.703621
$513$	−6.24102	−	10.8098i	−0.275548	−	0.477263i
$514$	−1.12632	−	1.95084i	−0.0496796	−	0.0860477i
$515$	15.0247			0.662069
$516$	7.90831	+	13.6976i	0.348144	+	0.603003i
$517$	22.4081	−	38.8120i	0.985508	−	1.70695i
$518$	−0.217949	+	0.377499i	−0.00957614	+	0.0165864i
$519$	−25.5633			−1.12210
$520$		0			0
$521$	12.4649			0.546098			0.273049	−	0.962000i	$-0.411968\pi$
$521$	12.4649			0.546098			0.273049	+	0.962000i	$0.411968\pi$
$522$	0.140128	−	0.242710i	0.00613326	−	0.0106231i
$523$	2.82978	−	4.90132i	0.123738	−	0.214320i	−0.797501	−	0.603317i	$-0.793845\pi$
$523$	2.82978	−	4.90132i	0.123738	−	0.214320i	0.921239	+	0.388998i	$0.127179\pi$
$524$	0.171425	+	0.296916i	0.00748872	+	0.0129708i
$525$	0.531659			0.0232035
$526$	2.04935	+	3.54958i	0.0893558	+	0.154769i
$527$	13.8359	+	23.9645i	0.602702	+	1.04391i
$528$	31.9147			1.38891
$529$	7.46953	+	12.9376i	0.324762	+	0.562505i
$530$	0.171425	−	0.296916i	0.00744621	−	0.0128972i
$531$	0.594763	−	1.03016i	0.0258105	−	0.0447051i
$532$	1.47067			0.0637616
$533$		0			0
$534$	1.13402			0.0490737
$535$	−6.53215	+	11.3140i	−0.282409	+	0.489147i
$536$	−4.48494	+	7.76815i	−0.193720	+	0.335533i
$537$	18.8963	+	32.7293i	0.815433	+	1.41237i
$538$	−3.94511			−0.170086
$539$	−18.5049	−	32.0514i	−0.797061	−	1.38055i
$540$	−5.37086	−	9.30260i	−0.231125	−	0.400320i
$541$	−15.4750			−0.665321			−0.332660	−	0.943047i	$-0.607946\pi$
$541$	−15.4750			−0.665321			−0.332660	+	0.943047i	$0.607946\pi$
$542$	3.39391	+	5.87842i	0.145781	+	0.252500i
$543$	−2.10098	+	3.63900i	−0.0901616	+	0.156165i
$544$	−6.46187	+	11.1923i	−0.277051	+	0.479866i
$545$	11.2325			0.481146
$546$		0			0
$547$	25.1765			1.07647			0.538234	−	0.842795i	$-0.319092\pi$
$547$	25.1765			1.07647			0.538234	+	0.842795i	$0.319092\pi$
$548$	−17.5489	+	30.3956i	−0.749653	+	1.29844i
$549$	3.09843	−	5.36665i	0.132238	−	0.229043i
$550$	−0.590059	−	1.02201i	−0.0251602	−	0.0435787i
$551$	−6.58493			−0.280528
$552$	−1.97210	−	3.41577i	−0.0839380	−	0.145385i
$553$	0.750630	+	1.30013i	0.0319200	+	0.0552871i
$554$	−5.82269			−0.247382
$555$	−4.77819	−	8.27607i	−0.202823	−	0.351300i
$556$	11.6969	−	20.2596i	0.496059	−	0.859199i
$557$	−21.1744	+	36.6752i	−0.897190	+	1.55398i	−0.0661194	+	0.997812i	$0.521062\pi$
$557$	−21.1744	+	36.6752i	−0.897190	+	1.55398i	−0.831071	+	0.556167i	$0.812272\pi$
$558$	0.527420			0.0223275
$559$		0			0
$560$	1.23355			0.0521270
$561$	21.7662	−	37.7002i	0.918971	−	1.59171i
$562$	0.546763	−	0.947022i	0.0230638	−	0.0399477i
$563$	−11.8953	−	20.6032i	−0.501326	−	0.868322i	−0.999999	−	0.00153173i	$-0.999512\pi$
$563$	−11.8953	−	20.6032i	−0.501326	−	0.868322i	0.498673	−	0.866790i	$-0.333821\pi$
$564$	26.0561			1.09716
$565$	−9.17191	−	15.8862i	−0.385865	−	0.668338i
$566$	−1.38253	−	2.39461i	−0.0581119	−	0.100653i
$567$	2.48814			0.104492
$568$	−5.55497	−	9.62148i	−0.233081	−	0.403709i
$569$	13.3710	−	23.1593i	0.560543	−	0.970889i	−0.436906	−	0.899507i	$-0.643926\pi$
$569$	13.3710	−	23.1593i	0.560543	−	0.970889i	0.997449	−	0.0713817i	$-0.0227408\pi$
$570$	0.398640	−	0.690464i	0.0166972	−	0.0289204i
$571$	−16.7159			−0.699539			−0.349769	−	0.936836i	$-0.613740\pi$
$571$	−16.7159			−0.699539			−0.349769	+	0.936836i	$0.613740\pi$
$572$		0			0
$573$	3.22571			0.134756
$574$	−0.136202	+	0.235908i	−0.00568494	+	0.00984661i
$575$	1.41959	−	2.45880i	0.0592010	−	0.102539i
$576$	−1.50812	−	2.61215i	−0.0628385	−	0.108840i
$577$	−20.6768			−0.860786			−0.430393	−	0.902642i	$-0.641625\pi$
$577$	−20.6768			−0.860786			−0.430393	+	0.902642i	$0.641625\pi$
$578$	0.949828	+	1.64515i	0.0395076	+	0.0684292i
$579$	18.2591	+	31.6257i	0.758822	+	1.31432i
$580$	−5.66682			−0.235302
$581$	−0.708301	−	1.22681i	−0.0293853	−	0.0508968i
$582$	0.440818	−	0.763519i	0.0182725	−	0.0316489i
$583$	−4.19170	+	7.26023i	−0.173602	+	0.300688i
$584$	−8.41165			−0.348076
$585$		0			0
$586$	−3.71657			−0.153530
$587$	−10.3986	+	18.0109i	−0.429196	+	0.743388i	−0.996802	−	0.0799116i	$-0.974536\pi$
$587$	−10.3986	+	18.0109i	−0.429196	+	0.743388i	0.567606	+	0.823300i	$0.307870\pi$
$588$	10.7587	−	18.6346i	0.443681	−	0.768478i
$589$	−6.19615	−	10.7321i	−0.255308	−	0.442206i
$590$	0.594763			0.0244860
$591$	−0.514483	−	0.891111i	−0.0211630	−	0.0366554i
$592$	−11.0863	−	19.2021i	−0.455644	−	0.789199i
$593$	−21.8475			−0.897169			−0.448585	−	0.893740i	$-0.648072\pi$
$593$	−21.8475			−0.897169			−0.448585	+	0.893740i	$0.648072\pi$
$594$	−3.24749	−	5.62482i	−0.133246	−	0.230789i
$595$	0.841298	−	1.45717i	0.0344898	−	0.0597381i
$596$	−3.32811	+	5.76446i	−0.136325	+	0.236121i
$597$	−4.90755			−0.200853
$598$		0			0
$599$	−3.58040			−0.146291			−0.0731456	−	0.997321i	$-0.523304\pi$
$599$	−3.58040			−0.146291			−0.0731456	+	0.997321i	$0.523304\pi$
$600$	0.694601	−	1.20308i	0.0283570	−	0.0491157i
$601$	−10.6743	+	18.4885i	−0.435414	+	0.754160i	−0.997329	−	0.0730352i	$-0.976731\pi$
$601$	−10.6743	+	18.4885i	−0.435414	+	0.754160i	0.561915	+	0.827195i	$0.310065\pi$
$602$	0.184822	+	0.320121i	0.00753278	+	0.0130472i
$603$	−4.53972			−0.184872
$604$	7.76929	+	13.4568i	0.316128	+	0.547550i
$605$	8.92820	+	15.4641i	0.362983	+	0.628705i
$606$	4.37554			0.177744
$607$	1.64988	+	2.85767i	0.0669665	+	0.115989i	0.897565	−	0.440883i	$-0.145335\pi$
$607$	1.64988	+	2.85767i	0.0669665	+	0.115989i	−0.830598	+	0.556872i	$0.812001\pi$
$608$	2.89383	−	5.01226i	0.117360	−	0.203274i
$609$	0.771830	−	1.33685i	0.0312761	−	0.0541718i
$610$	3.09843			0.125452
$611$		0			0
$612$	−4.34285			−0.175549
$613$	−4.94318	+	8.56183i	−0.199653	+	0.345809i	−0.948416	−	0.317029i	$-0.897315\pi$
$613$	−4.94318	+	8.56183i	−0.199653	+	0.345809i	0.748763	+	0.662838i	$0.230648\pi$
$614$	−0.472795	+	0.818904i	−0.0190804	+	0.0330483i
$615$	−2.98601	−	5.17191i	−0.120407	−	0.208552i
$616$	1.54944			0.0624286
$617$	22.8584	+	39.5920i	0.920246	+	1.59391i	0.799033	+	0.601287i	$0.205345\pi$
$617$	22.8584	+	39.5920i	0.920246	+	1.59391i	0.121213	+	0.992626i	$0.461321\pi$
$618$	2.64091	+	4.57419i	0.106233	+	0.184001i
$619$	19.9143			0.800425			0.400212	−	0.916422i	$-0.368936\pi$
$619$	19.9143			0.800425			0.400212	+	0.916422i	$0.368936\pi$
$620$	−5.33225	−	9.23572i	−0.214148	−	0.370916i
$621$	7.81295	−	13.5324i	0.313523	−	0.543038i
$622$	−0.244415	+	0.423339i	−0.00980014	+	0.0169743i
$623$	−1.07177			−0.0429397
$624$		0			0
$625$	1.00000			0.0400000
$626$	0.791847	−	1.37152i	0.0316486	−	0.0548169i
$627$	−9.74760	+	16.8833i	−0.389282	+	0.674255i
$628$	−16.0363	−	27.7757i	−0.639918	−	1.10837i
$629$	−30.2440			−1.20591
$630$	−0.0160350	−	0.0277734i	−0.000638849	−	0.00110652i
$631$	−7.29790	−	12.6403i	−0.290525	−	0.503204i	0.683409	−	0.730036i	$-0.260497\pi$
$631$	−7.29790	−	12.6403i	−0.290525	−	0.503204i	−0.973934	+	0.226832i	$0.927163\pi$
$632$	3.92272			0.156038
$633$	−6.56112	−	11.3642i	−0.260781	−	0.451686i
$634$	−0.0353305	+	0.0611942i	−0.00140315	+	0.00243033i
$635$	1.61998	−	2.80589i	0.0642870	−	0.111348i
$636$	−4.87409			−0.193270
$637$		0			0
$638$	−3.42644			−0.135654
$639$	2.81140	−	4.86950i	0.111217	−	0.192634i
$640$	3.30600	−	5.72615i	0.130681	−	0.226346i
$641$	7.08183	+	12.2661i	0.279716	+	0.484482i	0.971314	−	0.237801i	$-0.0764265\pi$
$641$	7.08183	+	12.2661i	0.279716	+	0.484482i	−0.691598	+	0.722282i	$0.743093\pi$
$642$	−4.59265			−0.181257
$643$	−8.38581	−	14.5246i	−0.330704	−	0.572796i	0.651946	−	0.758265i	$-0.273953\pi$
$643$	−8.38581	−	14.5246i	−0.330704	−	0.572796i	−0.982650	+	0.185469i	$0.940620\pi$
$644$	0.920544	+	1.59443i	0.0362745	+	0.0628293i
$645$	−8.10387			−0.319089
$646$	−1.26161	−	2.18518i	−0.0496376	−	0.0859748i
$647$	1.49584	−	2.59087i	0.0588075	−	0.101858i	−0.835123	−	0.550063i	$-0.814604\pi$
$647$	1.49584	−	2.59087i	0.0588075	−	0.101858i	0.893930	+	0.448206i	$0.147937\pi$
$648$	3.25069	−	5.63037i	0.127699	−	0.221182i
$649$	−14.5432			−0.570872
$650$		0			0
$651$	2.90504			0.113858
$652$	17.3775	−	30.0987i	0.680556	−	1.17876i
$653$	5.83217	−	10.1016i	0.228230	−	0.395307i	−0.729053	−	0.684457i	$-0.760039\pi$
$653$	5.83217	−	10.1016i	0.228230	−	0.395307i	0.957284	+	0.289150i	$0.0933727\pi$
$654$	1.97434	+	3.41966i	0.0772028	+	0.133719i
$655$	−0.175664			−0.00686374
$656$	−6.92810	−	11.9998i	−0.270497	−	0.468514i
$657$	−2.12859	−	3.68683i	−0.0830444	−	0.143837i
$658$	0.608946			0.0237392
$659$	0.905237	+	1.56792i	0.0352630	+	0.0610773i	0.883118	−	0.469150i	$-0.155440\pi$
$659$	0.905237	+	1.56792i	0.0352630	+	0.0610773i	−0.847855	+	0.530228i	$0.822106\pi$
$660$	−8.38853	+	14.5294i	−0.326523	+	0.565554i
$661$	6.17028	−	10.6872i	0.239996	−	0.415686i	−0.720717	−	0.693230i	$-0.756187\pi$
$661$	6.17028	−	10.6872i	0.239996	−	0.415686i	0.960713	+	0.277544i	$0.0895205\pi$
$662$	−3.65383			−0.142010
$663$		0			0
$664$	−3.70152			−0.143647
$665$	−0.376759	+	0.652566i	−0.0146101	+	0.0253054i
$666$	−0.288223	+	0.499217i	−0.0111684	+	0.0193443i
$667$	−4.12174	−	7.13907i	−0.159594	−	0.276426i
$668$	12.2836			0.475265
$669$	8.19636	+	14.1965i	0.316890	+	0.548869i
$670$	−1.13493	−	1.96576i	−0.0438461	−	0.0759438i
$671$	−75.7634			−2.92481
$672$	0.678380	+	1.17499i	0.0261691	+	0.0453262i
$673$	−4.63313	+	8.02481i	−0.178594	+	0.309334i	−0.941399	−	0.337295i	$-0.890488\pi$
$673$	−4.63313	+	8.02481i	−0.178594	+	0.309334i	0.762805	+	0.646628i	$0.223822\pi$
$674$	2.66025	−	4.60770i	0.102469	−	0.177482i
$675$	5.50367			0.211836
$676$		0			0
$677$	13.8984			0.534158			0.267079	−	0.963675i	$-0.413941\pi$
$677$	13.8984			0.534158			0.267079	+	0.963675i	$0.413941\pi$
$678$	3.22431	−	5.58467i	0.123829	−	0.214478i
$679$	−0.416622	+	0.721611i	−0.0159885	+	0.0276929i
$680$	−2.19827	−	3.80752i	−0.0842999	−	0.146012i
$681$	−11.2715			−0.431924
$682$	−3.22414	−	5.58438i	−0.123459	−	0.213837i
$683$	18.8756	+	32.6935i	0.722255	+	1.25098i	0.960094	+	0.279678i	$0.0902278\pi$
$683$	18.8756	+	32.6935i	0.722255	+	1.25098i	−0.237838	+	0.971305i	$0.576439\pi$
$684$	1.94486			0.0743637
$685$	−8.99144	−	15.5736i	−0.343545	−	0.595038i
$686$	0.506903	−	0.877981i	0.0193536	−	0.0335215i
$687$	1.06332	−	1.84172i	0.0405681	−	0.0702661i
$688$	−18.8025			−0.716838
$689$		0			0
$690$	0.998090			0.0379966
$691$	0.826456	−	1.43146i	0.0314399	−	0.0544554i	−0.849877	−	0.526981i	$-0.823324\pi$
$691$	0.826456	−	1.43146i	0.0314399	−	0.0544554i	0.881317	+	0.472525i	$0.156657\pi$
$692$	15.5896	−	27.0020i	0.592628	−	1.02646i
$693$	0.392090	+	0.679120i	0.0148943	+	0.0257976i
$694$	1.37823			0.0523168
$695$	5.99307	+	10.3803i	0.227330	+	0.393747i
$696$	−2.01676	−	3.49312i	−0.0764450	−	0.132407i
$697$	−18.9002			−0.715897
$698$	0.776587	+	1.34509i	0.0293943	+	0.0509123i
$699$	−0.998090	+	1.72874i	−0.0377512	+	0.0653871i
$700$	−0.324229	+	0.561581i	−0.0122547	+	0.0212258i
$701$	20.4819			0.773590			0.386795	−	0.922166i	$-0.373582\pi$
$701$	20.4819			0.773590			0.386795	+	0.922166i	$0.373582\pi$
$702$		0			0
$703$	13.5442			0.510830
$704$	−18.4384	+	31.9363i	−0.694925	+	1.20365i
$705$	−6.67510	+	11.5616i	−0.251399	+	0.435435i
$706$	−2.39347	−	4.14561i	−0.0900794	−	0.156022i
$707$	−4.13538			−0.155527
$708$	−4.22770	−	7.32260i	−0.158887	−	0.275200i
$709$	−10.9709	−	19.0021i	−0.412020	−	0.713639i	0.583091	−	0.812407i	$-0.301843\pi$
$709$	−10.9709	−	19.0021i	−0.412020	−	0.713639i	−0.995110	+	0.0987679i	$0.968510\pi$
$710$	2.81140			0.105510
$711$	0.992658	+	1.71933i	0.0372276	+	0.0644801i
$712$	−1.40025	+	2.42530i	−0.0524764	+	0.0908919i
$713$	7.75678	−	13.4351i	0.290494	−	0.503150i
$714$	0.591503			0.0221364
$715$		0			0
$716$	−46.0950			−1.72265
$717$	−7.95463	+	13.7778i	−0.297071	+	0.514542i
$718$	2.63335	−	4.56110i	0.0982759	−	0.170219i
$719$	−19.4237	−	33.6429i	−0.724384	−	1.25467i	−0.959227	−	0.282636i	$-0.908791\pi$
$719$	−19.4237	−	33.6429i	−0.724384	−	1.25467i	0.234844	−	0.972033i	$-0.424542\pi$
$720$	1.63129			0.0607945
$721$	−2.49596	−	4.32312i	−0.0929543	−	0.161002i
$722$	−1.52204	−	2.63624i	−0.0566443	−	0.0981108i
$723$	36.1434			1.34419
$724$	−2.56254	−	4.43844i	−0.0952359	−	0.164953i
$725$	1.45174	−	2.51448i	0.0539162	−	0.0933856i
$726$	−3.13864	+	5.43628i	−0.116486	+	0.201759i
$727$	−30.6598			−1.13711			−0.568555	−	0.822645i	$-0.692497\pi$
$727$	−30.6598			−1.13711			−0.568555	+	0.822645i	$0.692497\pi$
$728$		0			0
$729$	29.7112			1.10042
$730$	1.06430	−	1.84342i	0.0393914	−	0.0682279i
$731$	−12.8236	+	22.2110i	−0.474296	+	0.821505i
$732$	−22.0243	−	38.1473i	−0.814043	−	1.40996i
$733$	24.3858			0.900709			0.450355	−	0.892850i	$-0.351298\pi$
$733$	24.3858			0.900709			0.450355	+	0.892850i	$0.351298\pi$
$734$	0.702045	+	1.21598i	0.0259130	+	0.0448826i
$735$	5.51236	+	9.54769i	0.203327	+	0.352172i
$736$	7.24539			0.267069
$737$	27.7515	+	48.0669i	1.02224	+	1.77057i
$738$	−0.180117	+	0.311973i	−0.00663021	+	0.0114839i
$739$	−19.1394	+	33.1504i	−0.704054	+	1.21946i	0.262977	+	0.964802i	$0.415296\pi$
$739$	−19.1394	+	33.1504i	−0.704054	+	1.21946i	−0.967032	+	0.254656i	$0.918038\pi$
$740$	11.6558			0.428476
$741$		0			0
$742$	−0.113910			−0.00418178
$743$	20.0040	−	34.6479i	0.733874	−	1.27111i	−0.221342	−	0.975196i	$-0.571044\pi$
$743$	20.0040	−	34.6479i	0.733874	−	1.27111i	0.955216	−	0.295910i	$-0.0956230\pi$
$744$	3.79537	−	6.57377i	0.139145	−	0.241006i
$745$	−1.70520	−	2.95350i	−0.0624738	−	0.108208i
$746$	4.41134			0.161511
$747$	−0.936681	−	1.62238i	−0.0342714	−	0.0593598i
$748$	26.5480	+	45.9825i	0.970691	+	1.68129i
$749$	4.34057			0.158601
$750$	0.175771	+	0.304444i	0.00641825	+	0.0111167i
$751$	−12.8010	+	22.1720i	−0.467115	+	0.809067i	−0.999294	−	0.0375648i	$-0.988040\pi$
$751$	−12.8010	+	22.1720i	−0.467115	+	0.809067i	0.532179	+	0.846632i	$0.321373\pi$
$752$	−15.4875	+	26.8251i	−0.564770	+	0.978211i
$753$	10.8307			0.394693
$754$		0			0
$755$	−7.96141			−0.289745
$756$	−1.78445	+	3.09076i	−0.0648998	+	0.112410i
$757$	0.924239	−	1.60083i	0.0335920	−	0.0581831i	−0.848741	−	0.528809i	$-0.822639\pi$
$757$	0.924239	−	1.60083i	0.0335920	−	0.0581831i	0.882333	+	0.470626i	$0.155972\pi$
$758$	−0.599945	−	1.03914i	−0.0217910	−	0.0377431i
$759$	−24.4055			−0.885862
$760$	0.984454	+	1.70512i	0.0357099	+	0.0618514i
$761$	−13.1062	−	22.7006i	−0.475099	−	0.822896i	0.524494	−	0.851414i	$-0.324255\pi$
$761$	−13.1062	−	22.7006i	−0.475099	−	0.822896i	−0.999593	+	0.0285179i	$0.990921\pi$
$762$	1.13898			0.0412610
$763$	−1.86597	−	3.23196i	−0.0675528	−	0.117005i
$764$	−1.96718	+	3.40725i	−0.0711699	+	0.123270i
$765$	1.11256	−	1.92701i	0.0402247	−	0.0696712i
$766$	1.24513			0.0449884
$767$		0			0
$768$	−19.6459			−0.708911
$769$	22.1747	−	38.4078i	0.799641	−	1.38502i	−0.120208	−	0.992749i	$-0.538356\pi$
$769$	22.1747	−	38.4078i	0.799641	−	1.38502i	0.919850	−	0.392271i	$-0.128310\pi$
$770$	−0.196045	+	0.339560i	−0.00706497	+	0.0122369i
$771$	−8.20406	−	14.2099i	−0.295462	−	0.511755i
$772$	−44.5408			−1.60306
$773$	11.6319	+	20.1471i	0.418371	+	0.724640i	0.995776	−	0.0918181i	$-0.0292678\pi$
$773$	11.6319	+	20.1471i	0.418371	+	0.724640i	−0.577405	+	0.816458i	$0.695935\pi$
$774$	0.244415	+	0.423339i	0.00878531	+	0.0152166i
$775$	5.46410			0.196276
$776$	1.08861	+	1.88554i	0.0390790	+	0.0676868i
$777$	−1.58754	+	2.74970i	−0.0569526	+	0.0986448i
$778$	1.16625	−	2.02001i	0.0418122	−	0.0724209i
$779$	8.46410			0.303258
$780$		0			0
$781$	−68.7449			−2.45989
$782$	1.57938	−	2.73556i	0.0564784	−	0.0978235i
$783$	7.98989	−	13.8389i	0.285535	−	0.494562i
$784$	12.7897	+	22.1524i	0.456776	+	0.791159i
$785$	16.4329			0.586514
$786$	−0.0308766	−	0.0534798i	−0.00110133	−	0.00190756i
$787$	23.9567	+	41.4942i	0.853963	+	1.47911i	0.877604	+	0.479387i	$0.159141\pi$
$787$	23.9567	+	41.4942i	0.853963	+	1.47911i	−0.0236408	+	0.999721i	$0.507526\pi$
$788$	1.25502			0.0447081
$789$	14.9274	+	25.8551i	0.531430	+	0.920464i
$790$	−0.496329	+	0.859667i	−0.0176586	+	0.0305856i
$791$	−3.04734	+	5.27814i	−0.108351	+	0.187669i
$792$	2.04903			0.0728090
$793$		0			0
$794$	−6.15865			−0.218562
$795$	1.24865	−	2.16273i	0.0442852	−	0.0767042i
$796$	2.99284	−	5.18374i	0.106078	−	0.183733i
$797$	10.3476	+	17.9225i	0.366530	+	0.634849i	0.989020	−	0.147779i	$-0.0472124\pi$
$797$	10.3476	+	17.9225i	0.366530	+	0.634849i	−0.622490	+	0.782627i	$0.713879\pi$
$798$	−0.264893			−0.00937712
$799$	21.1253	+	36.5902i	0.747361	+	1.29447i
$800$	1.27597	+	2.21004i	0.0451122	+	0.0781367i
$801$	−1.41735			−0.0500795
$802$	−2.47305	−	4.28344i	−0.0873263	−	0.151254i
$803$	−26.0244	+	45.0755i	−0.918380	+	1.59068i
$804$	−16.1346	+	27.9460i	−0.569025	+	0.985580i
$805$	−0.943307			−0.0332472
$806$		0			0
$807$	−28.7361			−1.01156
$808$	−5.40278	+	9.35788i	−0.190069	+	0.329209i
$809$	−7.94574	+	13.7624i	−0.279357	+	0.483861i	−0.971225	−	0.238163i	$-0.923455\pi$
$809$	−7.94574	+	13.7624i	−0.279357	+	0.483861i	0.691868	+	0.722024i	$0.256788\pi$
$810$	0.822599	+	1.42478i	0.0289032	+	0.0500618i
$811$	−23.8796			−0.838525			−0.419263	−	0.907865i	$-0.637711\pi$
$811$	−23.8796			−0.838525			−0.419263	+	0.907865i	$0.637711\pi$
$812$	0.941391	+	1.63054i	0.0330363	+	0.0572206i
$813$	24.7212	+	42.8183i	0.867009	+	1.50170i
$814$	7.04768			0.247021
$815$	8.90361	+	15.4215i	0.311880	+	0.540192i
$816$	−15.0438	+	26.0567i	−0.526640	+	0.912167i
$817$	5.74278	−	9.94679i	0.200915	−	0.347994i
$818$	−0.941956			−0.0329347
$819$		0			0
$820$	7.28398			0.254368
$821$	−7.95484	+	13.7782i	−0.277626	+	0.480862i	−0.970794	−	0.239914i	$-0.922881\pi$
$821$	−7.95484	+	13.7782i	−0.277626	+	0.480862i	0.693169	+	0.720776i	$0.256214\pi$
$822$	3.16087	−	5.47478i	0.110248	−	0.190955i
$823$	7.40573	+	12.8271i	0.258147	+	0.447124i	0.965746	−	0.259491i	$-0.0835547\pi$
$823$	7.40573	+	12.8271i	0.258147	+	0.447124i	−0.707598	+	0.706615i	$0.750221\pi$
$824$	−13.0436			−0.454397
$825$	−4.29798	−	7.44432i	−0.149636	−	0.259178i
$826$	−0.0988040	−	0.171134i	−0.00343783	−	0.00595450i
$827$	33.9498			1.18055			0.590275	−	0.807202i	$-0.299019\pi$
$827$	33.9498			1.18055			0.590275	+	0.807202i	$0.299019\pi$
$828$	1.21736	+	2.10853i	0.0423061	+	0.0732763i
$829$	−11.6573	+	20.1910i	−0.404875	+	0.701264i	−0.994307	−	0.106554i	$-0.966018\pi$
$829$	−11.6573	+	20.1910i	−0.404875	+	0.701264i	0.589432	+	0.807818i	$0.299352\pi$
$830$	0.468341	−	0.811190i	0.0162563	−	0.0281568i
$831$	−42.4124			−1.47127
$832$		0			0
$833$	34.8910			1.20890
$834$	−2.10682	+	3.64911i	−0.0729530	+	0.126358i
$835$	−3.14683	+	5.45047i	−0.108900	+	0.188621i
$836$	−11.8890	−	20.5924i	−0.411190	−	0.712202i
$837$	30.0726			1.03946
$838$	1.94550	+	3.36970i	0.0672061	+	0.116404i
$839$	7.39649	+	12.8111i	0.255355	+	0.442288i	0.964992	−	0.262280i	$-0.0844742\pi$
$839$	7.39649	+	12.8111i	0.255355	+	0.442288i	−0.709637	+	0.704568i	$0.751141\pi$
$840$	−0.461557			−0.0159252
$841$	10.2849	+	17.8140i	0.354652	+	0.614276i
$842$	1.41465	−	2.45024i	0.0487519	−	0.0844408i
$843$	3.98261	−	6.89809i	0.137169	−	0.237583i
$844$	16.0050			0.550915
$845$		0			0
$846$	0.805291			0.0276865
$847$	2.96636	−	5.13789i	0.101925	−	0.176540i
$848$	2.89711	−	5.01794i	0.0994872	−	0.172317i
$849$	−10.0703	−	17.4423i	−0.345612	−	0.598617i
$850$	1.11256			0.0381605
$851$	8.47780	+	14.6840i	0.290615	+	0.503360i
$852$	−19.9841	−	34.6134i	−0.684643	−	1.18584i
$853$	−16.3452			−0.559650			−0.279825	−	0.960051i	$-0.590276\pi$
$853$	−16.3452			−0.559650			−0.279825	+	0.960051i	$0.590276\pi$
$854$	−0.514722	−	0.891525i	−0.0176134	−	0.0305073i
$855$	−0.498239	+	0.862975i	−0.0170394	+	0.0295131i
$856$	5.67085	−	9.82220i	0.193826	−	0.335716i
$857$	−34.1418			−1.16626			−0.583132	−	0.812378i	$-0.698173\pi$
$857$	−34.1418			−1.16626			−0.583132	+	0.812378i	$0.698173\pi$
$858$		0			0
$859$	−45.1996			−1.54219			−0.771096	−	0.636719i	$-0.780291\pi$
$859$	−45.1996			−1.54219			−0.771096	+	0.636719i	$0.780291\pi$
$860$	4.94209	−	8.55995i	0.168524	−	0.291892i
$861$	−0.992090	+	1.71835i	−0.0338103	+	0.0585612i
$862$	1.04334	+	1.80712i	0.0355364	+	0.0615508i
$863$	4.75058			0.161712			0.0808559	−	0.996726i	$-0.474235\pi$
$863$	4.75058			0.161712			0.0808559	+	0.996726i	$0.474235\pi$
$864$	7.02250	+	12.1633i	0.238910	+	0.413805i
$865$	7.98756	+	13.8349i	0.271585	+	0.470399i
$866$	0.306745			0.0104236
$867$	6.91853	+	11.9832i	0.234966	+	0.406972i
$868$	−1.77162	+	3.06854i	−0.0601327	+	0.104153i
$869$	12.1363	−	21.0207i	0.411696	−	0.713079i
$870$	1.02069			0.0346048
$871$		0			0
$872$	−9.75140			−0.330224
$873$	−0.550955	+	0.954282i	−0.0186470	+	0.0322975i
$874$	−0.707294	+	1.22507i	−0.0239246	+	0.0414386i
$875$	−0.166123	−	0.287734i	−0.00561599	−	0.00972718i
$876$	−30.2610			−1.02242
$877$	−1.12753	−	1.95294i	−0.0380741	−	0.0659462i	0.846360	−	0.532611i	$-0.178789\pi$
$877$	−1.12753	−	1.95294i	−0.0380741	−	0.0659462i	−0.884434	+	0.466664i	$0.845456\pi$
$878$	0.457146	+	0.791801i	0.0154279	+	0.0267220i
$879$	−27.0715			−0.913098
$880$	−9.97212	−	17.2722i	−0.336160	−	0.582246i
$881$	1.49152	−	2.58339i	0.0502507	−	0.0870367i	−0.839806	−	0.542887i	$-0.817331\pi$
$881$	1.49152	−	2.58339i	0.0502507	−	0.0870367i	0.890057	+	0.455850i	$0.150665\pi$
$882$	0.332509	−	0.575922i	0.0111961	−	0.0193923i
$883$	28.2874			0.951947			0.475973	−	0.879460i	$-0.342096\pi$
$883$	28.2874			0.951947			0.475973	+	0.879460i	$0.342096\pi$
$884$		0			0
$885$	4.33225			0.145627
$886$	1.04852	−	1.81610i	0.0352259	−	0.0610130i
$887$	13.9908	−	24.2328i	0.469766	−	0.813658i	−0.529637	−	0.848225i	$-0.677672\pi$
$887$	13.9908	−	24.2328i	0.469766	−	0.813658i	0.999402	+	0.0345665i	$0.0110051\pi$
$888$	4.14816	+	7.18483i	0.139203	+	0.241107i
$889$	−1.07647			−0.0361035
$890$	−0.354337	−	0.613729i	−0.0118774	−	0.0205723i
$891$	−20.1143	−	34.8390i	−0.673855	−	1.16715i
$892$	−19.9940			−0.669448
$893$	−9.46058	−	16.3862i	−0.316586	−	0.548343i
$894$	0.599451	−	1.03828i	0.0200486	−	0.0347252i
$895$	11.8087	−	20.4533i	0.394722	−	0.683678i
$896$	−2.19681			−0.0733903
$897$		0			0
$898$	−4.77095			−0.159209
$899$	7.93244	−	13.7394i	0.264562	−	0.458234i
$900$	−0.428771	+	0.742653i	−0.0142924	+	0.0247551i
$901$	−3.95174	−	6.84461i	−0.131651	−	0.228027i
$902$	4.40426			0.146646
$903$	1.34624	+	2.33176i	0.0448001	+	0.0775960i
$904$	7.96255	+	13.7915i	0.264830	+	0.458700i
$905$	2.62590			0.0872879
$906$	−1.39938	−	2.42381i	−0.0464914	−	0.0805255i
$907$	−8.27600	+	14.3344i	−0.274800	+	0.475967i	−0.970085	−	0.242767i	$-0.921945\pi$
$907$	−8.27600	+	14.3344i	−0.274800	+	0.475967i	0.695285	+	0.718734i	$0.255278\pi$
$908$	6.87383	−	11.9058i	0.228116	−	0.395109i
$909$	−5.46876			−0.181387
$910$		0			0
$911$	7.04863			0.233532			0.116766	−	0.993159i	$-0.462747\pi$
$911$	7.04863			0.233532			0.116766	+	0.993159i	$0.462747\pi$
$912$	6.73710	−	11.6690i	0.223088	−	0.386399i
$913$	−11.4519	+	19.8353i	−0.379004	+	0.656454i
$914$	0.518746	+	0.898494i	0.0171586	+	0.0297196i
$915$	22.5689			0.746106
$916$	1.29692	+	2.24632i	0.0428513	+	0.0742206i
$917$	0.0291818	+	0.0505443i	0.000963668	+	0.00166912i
$918$	6.12316			0.202094
$919$	−8.27188	−	14.3273i	−0.272864	−	0.472615i	0.696730	−	0.717334i	$-0.254638\pi$
$919$	−8.27188	−	14.3273i	−0.272864	−	0.472615i	−0.969594	+	0.244719i	$0.921304\pi$
$920$	−1.23241	+	2.13459i	−0.0406313	+	0.0703755i
$921$	−3.44383	+	5.96488i	−0.113478	+	0.196550i
$922$	0.391374			0.0128892
$923$		0			0
$924$	5.57412			0.183375
$925$	−2.98601	+	5.17191i	−0.0981793	+	0.170051i
$926$	0.747155	−	1.29411i	0.0245530	−	0.0425271i
$927$	−3.30074	−	5.71704i	−0.108410	−	0.187772i
$928$	7.40948			0.243228
$929$	−16.9184	−	29.3035i	−0.555074	−	0.961416i	−0.997898	−	0.0648073i	$-0.979357\pi$
$929$	−16.9184	−	29.3035i	−0.555074	−	0.961416i	0.442824	−	0.896609i	$-0.353977\pi$
$930$	0.960431	+	1.66351i	0.0314938	+	0.0545488i
$931$	−15.6253			−0.512098
$932$	−1.21736	−	2.10853i	−0.0398759	−	0.0690670i
$933$	−1.78031	+	3.08359i	−0.0582848	+	0.100952i
$934$	2.00326	−	3.46975i	0.0655487	−	0.113534i
$935$	−27.2045			−0.889681
$936$		0			0
$937$	−30.4606			−0.995104			−0.497552	−	0.867434i	$-0.665768\pi$
$937$	−30.4606			−0.995104			−0.497552	+	0.867434i	$0.665768\pi$
$938$	−0.377076	+	0.653115i	−0.0123120	+	0.0213250i
$939$	5.76780	−	9.99012i	0.188225	−	0.326015i
$940$	−8.14153	−	14.1015i	−0.265547	−	0.459941i
$941$	−38.2101			−1.24561			−0.622807	−	0.782375i	$-0.714008\pi$
$941$	−38.2101			−1.24561			−0.622807	+	0.782375i	$0.714008\pi$
$942$	2.88842	+	5.00289i	0.0941098	+	0.163003i
$943$	5.29798	+	9.17637i	0.172526	+	0.298824i
$944$	10.0516			0.327153
$945$	−0.914288	−	1.58359i	−0.0297418	−	0.0515143i
$946$	2.98823	−	5.17577i	0.0971558	−	0.168279i
$947$	−26.2241	+	45.4215i	−0.852169	+	1.47600i	0.0270773	+	0.999633i	$0.491380\pi$
$947$	−26.2241	+	45.4215i	−0.852169	+	1.47600i	−0.879247	+	0.476367i	$0.841953\pi$
$948$	14.1120			0.458338
$949$		0			0
$950$	−0.498239			−0.0161650
$951$	−0.257347	+	0.445737i	−0.00834504	+	0.0144540i
$952$	−0.730368	+	1.26503i	−0.0236714	+	0.0410000i
$953$	−19.8750	−	34.4245i	−0.643814	−	1.11512i	−0.984574	−	0.174969i	$-0.944018\pi$
$953$	−19.8750	−	34.4245i	−0.643814	−	1.11512i	0.340760	−	0.940150i	$-0.389316\pi$
$954$	−0.150639			−0.00487711
$955$	−1.00791	−	1.74575i	−0.0326152	−	0.0564912i
$956$	−9.70215	−	16.8046i	−0.313790	−	0.543500i
$957$	−24.9581			−0.806782
$958$	−3.86437	−	6.69329i	−0.124852	−	0.216250i
$959$	−2.98737	+	5.17428i	−0.0964673	+	0.167086i
$960$	5.49258	−	9.51343i	0.177272	−	0.307045i
$961$	−1.14359			−0.0368901
$962$		0			0
$963$	5.74011			0.184972
$964$	−22.0418	+	38.1776i	−0.709920	+	1.22962i
$965$	11.4105	−	19.7636i	0.367318	−	0.636214i
$966$	−0.165806	−	0.287184i	−0.00533472	−	0.00924001i
$967$	25.7857			0.829214			0.414607	−	0.910001i	$-0.363919\pi$
$967$	25.7857			0.829214			0.414607	+	0.910001i	$0.363919\pi$
$968$	−7.75097	−	13.4251i	−0.249126	−	0.431498i
$969$	−9.18958	−	15.9168i	−0.295212	−	0.511322i
$970$	−0.550955			−0.0176901
$971$	27.7626	+	48.0863i	0.890945	+	1.54316i	0.838744	+	0.544525i	$0.183290\pi$
$971$	27.7626	+	48.0863i	0.890945	+	1.54316i	0.0522005	+	0.998637i	$0.483377\pi$
$972$	−4.41817	+	7.65249i	−0.141713	+	0.245454i
$973$	1.99118	−	3.44882i	0.0638342	−	0.110564i
$974$	2.26365			0.0725321
$975$		0			0
$976$	52.3642			1.67614
$977$	20.2580	−	35.0879i	0.648112	−	1.12256i	−0.335461	−	0.942054i	$-0.608892\pi$
$977$	20.2580	−	35.0879i	0.648112	−	1.12256i	0.983573	−	0.180509i	$-0.0577745\pi$
$978$	−3.12999	+	5.42130i	−0.100086	+	0.173354i
$979$	8.66430	+	15.0070i	0.276912	+	0.479626i
$980$	−13.4467			−0.429540
$981$	−2.46762	−	4.27405i	−0.0787852	−	0.136460i
$982$	1.02506	+	1.77545i	0.0327109	+	0.0566569i
$983$	34.8059			1.11014			0.555068	−	0.831805i	$-0.312692\pi$
$983$	34.8059			1.11014			0.555068	+	0.831805i	$0.312692\pi$
$984$	2.59229	+	4.48997i	0.0826390	+	0.143135i
$985$	−0.321513	+	0.556877i	−0.0102443	+	0.0177436i
$986$	1.61514	−	2.79751i	0.0514367	−	0.0890910i
$987$	4.43555			0.141185
$988$		0			0
$989$	14.3784			0.457208
$990$	−0.259256	+	0.449045i	−0.00823971	+	0.0142716i
$991$	−21.9427	+	38.0059i	−0.697034	+	1.20730i	0.272456	+	0.962168i	$0.412164\pi$
$991$	−21.9427	+	38.0059i	−0.697034	+	1.20730i	−0.969490	+	0.245130i	$0.921169\pi$
$992$	6.97201	+	12.0759i	0.221362	+	0.383410i
$993$	−26.6145			−0.844584
$994$	−0.467040	−	0.808936i	−0.0148136	−	0.0256579i
$995$	1.53342	+	2.65596i	0.0486127	+	0.0841997i
$996$	−13.3163			−0.421942
$997$	2.74569	+	4.75567i	0.0869568	+	0.150614i	0.906223	−	0.422799i	$-0.138952\pi$
$997$	2.74569	+	4.75567i	0.0869568	+	0.150614i	−0.819267	+	0.573413i	$0.805619\pi$
$998$	2.62988	−	4.55508i	0.0832474	−	0.144189i
$999$	−16.4340	+	28.4645i	−0.519949	+	0.900577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.m.191.3		8
13.2	odd	12		845.2.m.g.361.3		8
13.3	even	3	inner	845.2.e.m.146.3		8
13.4	even	6		845.2.a.l.1.3		4
13.5	odd	4		65.2.m.a.56.2	yes	8
13.6	odd	12		845.2.c.g.506.5		8
13.7	odd	12		845.2.c.g.506.4		8
13.8	odd	4		845.2.m.g.316.3		8
13.9	even	3		845.2.a.m.1.2		4
13.10	even	6		845.2.e.n.146.2		8
13.11	odd	12		65.2.m.a.36.2	✓	8
13.12	even	2		845.2.e.n.191.2		8
39.5	even	4		585.2.bu.c.316.3		8
39.11	even	12		585.2.bu.c.361.3		8
39.17	odd	6		7605.2.a.cj.1.2		4
39.35	odd	6		7605.2.a.cf.1.3		4
52.11	even	12		1040.2.da.b.881.2		8
52.31	even	4		1040.2.da.b.641.2		8
65.4	even	6		4225.2.a.bl.1.2		4
65.9	even	6		4225.2.a.bi.1.3		4
65.18	even	4		325.2.m.c.199.2		8
65.24	odd	12		325.2.n.d.101.3		8
65.37	even	12		325.2.m.c.49.2		8
65.44	odd	4		325.2.n.d.251.3		8
65.57	even	4		325.2.m.b.199.3		8
65.63	even	12		325.2.m.b.49.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.2	✓	8	13.11	odd	12
65.2.m.a.56.2	yes	8	13.5	odd	4
325.2.m.b.49.3		8	65.63	even	12
325.2.m.b.199.3		8	65.57	even	4
325.2.m.c.49.2		8	65.37	even	12
325.2.m.c.199.2		8	65.18	even	4
325.2.n.d.101.3		8	65.24	odd	12
325.2.n.d.251.3		8	65.44	odd	4
585.2.bu.c.316.3		8	39.5	even	4
585.2.bu.c.361.3		8	39.11	even	12
845.2.a.l.1.3		4	13.4	even	6
845.2.a.m.1.2		4	13.9	even	3
845.2.c.g.506.4		8	13.7	odd	12
845.2.c.g.506.5		8	13.6	odd	12
845.2.e.m.146.3		8	13.3	even	3	inner
845.2.e.m.191.3		8	1.1	even	1	trivial
845.2.e.n.146.2		8	13.10	even	6
845.2.e.n.191.2		8	13.12	even	2
845.2.m.g.316.3		8	13.8	odd	4
845.2.m.g.361.3		8	13.2	odd	12
1040.2.da.b.641.2		8	52.31	even	4
1040.2.da.b.881.2		8	52.11	even	12
4225.2.a.bi.1.3		4	65.9	even	6
4225.2.a.bl.1.2		4	65.4	even	6
7605.2.a.cf.1.3		4	39.35	odd	6
7605.2.a.cj.1.2		4	39.17	odd	6

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.109843 - 0.190254i) q^{2} +(0.800098 - 1.38581i) q^{3} +(0.975869 + 1.69025i) q^{4} -1.00000 q^{5} +(-0.175771 - 0.304444i) q^{6} +(0.166123 + 0.287734i) q^{7} +0.868145 q^{8} +(0.219687 + 0.380509i) q^{9} +O(q^{10})\)	\(q+(0.109843 - 0.190254i) q^{2} +(0.800098 - 1.38581i) q^{3} +(0.975869 + 1.69025i) q^{4} -1.00000 q^{5} +(-0.175771 - 0.304444i) q^{6} +(0.166123 + 0.287734i) q^{7} +0.868145 q^{8} +(0.219687 + 0.380509i) q^{9} +(-0.109843 + 0.190254i) q^{10} +(2.68591 - 4.65213i) q^{11} +3.12316 q^{12} +0.0729902 q^{14} +(-0.800098 + 1.38581i) q^{15} +(-1.85638 + 3.21534i) q^{16} +(2.53215 + 4.38581i) q^{17} +0.0965246 q^{18} +(-1.13397 - 1.96410i) q^{19} +(-0.975869 - 1.69025i) q^{20} +0.531659 q^{21} +(-0.590059 - 1.02201i) q^{22} +(1.41959 - 2.45880i) q^{23} +(0.694601 - 1.20308i) q^{24} +1.00000 q^{25} +5.50367 q^{27} +(-0.324229 + 0.561581i) q^{28} +(1.45174 - 2.51448i) q^{29} +(0.175771 + 0.304444i) q^{30} +5.46410 q^{31} +(1.27597 + 2.21004i) q^{32} +(-4.29798 - 7.44432i) q^{33} +1.11256 q^{34} +(-0.166123 - 0.287734i) q^{35} +(-0.428771 + 0.742653i) q^{36} +(-2.98601 + 5.17191i) q^{37} -0.498239 q^{38} -0.868145 q^{40} +(-1.86603 + 3.23205i) q^{41} +(0.0583993 - 0.101151i) q^{42} +(2.53215 + 4.38581i) q^{43} +10.4844 q^{44} +(-0.219687 - 0.380509i) q^{45} +(-0.311865 - 0.540166i) q^{46} +8.34285 q^{47} +(2.97057 + 5.14517i) q^{48} +(3.44481 - 5.96658i) q^{49} +(0.109843 - 0.190254i) q^{50} +8.10387 q^{51} -1.56063 q^{53} +(0.604542 - 1.04710i) q^{54} +(-2.68591 + 4.65213i) q^{55} +(0.144219 + 0.249795i) q^{56} -3.62916 q^{57} +(-0.318928 - 0.552399i) q^{58} +(-1.35366 - 2.34461i) q^{59} -3.12316 q^{60} +(-7.05193 - 12.2143i) q^{61} +(0.600196 - 1.03957i) q^{62} +(-0.0729902 + 0.126423i) q^{63} -6.86488 q^{64} -1.88842 q^{66} +(-5.16612 + 8.94799i) q^{67} +(-4.94209 + 8.55995i) q^{68} +(-2.27162 - 3.93456i) q^{69} -0.0729902 q^{70} +(-6.39866 - 11.0828i) q^{71} +(0.190720 + 0.330337i) q^{72} -9.68922 q^{73} +(0.655986 + 1.13620i) q^{74} +(0.800098 - 1.38581i) q^{75} +(2.21322 - 3.83341i) q^{76} +1.78477 q^{77} +4.51851 q^{79} +(1.85638 - 3.21534i) q^{80} +(3.74441 - 6.48552i) q^{81} +(0.409941 + 0.710039i) q^{82} -4.26371 q^{83} +(0.518830 + 0.898640i) q^{84} +(-2.53215 - 4.38581i) q^{85} +1.11256 q^{86} +(-2.32306 - 4.02367i) q^{87} +(2.33176 - 4.03872i) q^{88} +(-1.61292 + 2.79366i) q^{89} -0.0965246 q^{90} +5.54133 q^{92} +(4.37182 - 7.57221i) q^{93} +(0.916407 - 1.58726i) q^{94} +(1.13397 + 1.96410i) q^{95} +4.08359 q^{96} +(1.25396 + 2.17191i) q^{97} +(-0.756779 - 1.31078i) q^{98} +2.36023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} + 40 q^{18} - 16 q^{19} + 2 q^{20} + 8 q^{21} - 12 q^{22} + 10 q^{23} + 24 q^{24} + 8 q^{25} - 4 q^{27} - 8 q^{28} - 8 q^{29} - 4 q^{30} + 16 q^{31} - 4 q^{32} - 18 q^{33} - 8 q^{34} + 10 q^{35} - 20 q^{36} + 2 q^{37} + 16 q^{38} - 12 q^{40} - 8 q^{41} + 4 q^{42} + 2 q^{43} + 24 q^{44} + 4 q^{45} - 16 q^{46} + 16 q^{47} + 28 q^{48} - 12 q^{49} - 2 q^{50} + 8 q^{51} - 24 q^{53} + 16 q^{54} - 12 q^{56} - 28 q^{57} - 22 q^{58} - 12 q^{59} + 20 q^{60} - 28 q^{61} - 4 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} - 14 q^{68} + 16 q^{69} - 4 q^{70} - 4 q^{71} - 12 q^{72} - 16 q^{73} + 10 q^{74} + 2 q^{75} - 20 q^{76} + 36 q^{77} - 16 q^{79} + 2 q^{80} + 8 q^{81} - 4 q^{82} - 24 q^{83} + 28 q^{84} - 2 q^{85} - 8 q^{86} + 22 q^{87} + 18 q^{88} + 12 q^{89} - 40 q^{90} + 44 q^{92} - 8 q^{93} + 32 q^{94} + 16 q^{95} + 8 q^{96} - 2 q^{97} + 24 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 4 * q^6 - 10 * q^7 + 12 * q^8 - 4 * q^9 + 2 * q^10 - 20 * q^12 + 4 * q^14 - 2 * q^15 - 2 * q^16 + 2 * q^17 + 40 * q^18 - 16 * q^19 + 2 * q^20 + 8 * q^21 - 12 * q^22 + 10 * q^23 + 24 * q^24 + 8 * q^25 - 4 * q^27 - 8 * q^28 - 8 * q^29 - 4 * q^30 + 16 * q^31 - 4 * q^32 - 18 * q^33 - 8 * q^34 + 10 * q^35 - 20 * q^36 + 2 * q^37 + 16 * q^38 - 12 * q^40 - 8 * q^41 + 4 * q^42 + 2 * q^43 + 24 * q^44 + 4 * q^45 - 16 * q^46 + 16 * q^47 + 28 * q^48 - 12 * q^49 - 2 * q^50 + 8 * q^51 - 24 * q^53 + 16 * q^54 - 12 * q^56 - 28 * q^57 - 22 * q^58 - 12 * q^59 + 20 * q^60 - 28 * q^61 - 4 * q^62 - 4 * q^63 + 8 * q^64 + 12 * q^66 - 30 * q^67 - 14 * q^68 + 16 * q^69 - 4 * q^70 - 4 * q^71 - 12 * q^72 - 16 * q^73 + 10 * q^74 + 2 * q^75 - 20 * q^76 + 36 * q^77 - 16 * q^79 + 2 * q^80 + 8 * q^81 - 4 * q^82 - 24 * q^83 + 28 * q^84 - 2 * q^85 - 8 * q^86 + 22 * q^87 + 18 * q^88 + 12 * q^89 - 40 * q^90 + 44 * q^92 - 8 * q^93 + 32 * q^94 + 16 * q^95 + 8 * q^96 - 2 * q^97 + 24 * q^98 + 48 * q^99

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