LMFDB - Embedded newform 845.2.m.a.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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, 1]))

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.361
Dual form			845.2.m.a.316.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.09808 - 0.633975i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.73205i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.09808 - 0.633975i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.73205i q^{8} +(1.23205 - 2.13397i) q^{9} +(-0.866025 - 1.50000i) q^{10} +(-1.09808 + 0.633975i) q^{11} +0.732051 q^{12} +3.46410 q^{14} +(-0.633975 + 0.366025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(1.73205 - 3.00000i) q^{17} +4.26795i q^{18} +(3.63397 + 2.09808i) q^{19} +(0.866025 + 0.500000i) q^{20} -1.46410i q^{21} +(1.09808 - 1.90192i) q^{22} +(2.36603 + 4.09808i) q^{23} +(1.09808 - 0.633975i) q^{24} -1.00000 q^{25} +4.00000 q^{27} +(-1.73205 + 1.00000i) q^{28} +(4.73205 + 8.19615i) q^{29} +(0.633975 - 1.09808i) q^{30} +0.196152i q^{31} +(-4.50000 - 2.59808i) q^{32} +(-0.803848 - 0.464102i) q^{33} +6.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(-1.23205 - 2.13397i) q^{36} +(-3.46410 + 2.00000i) q^{37} -7.26795 q^{38} +1.73205 q^{40} +(3.00000 - 1.73205i) q^{41} +(1.26795 + 2.19615i) q^{42} +(5.09808 - 8.83013i) q^{43} +1.26795i q^{44} +(2.13397 + 1.23205i) q^{45} +(-7.09808 - 4.09808i) q^{46} +6.00000i q^{47} +(-1.83013 + 3.16987i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(1.50000 - 0.866025i) q^{50} +2.53590 q^{51} -10.3923 q^{53} +(-6.00000 + 3.46410i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(-1.73205 + 3.00000i) q^{56} +3.07180i q^{57} +(-14.1962 - 8.19615i) q^{58} +(13.0981 + 7.56218i) q^{59} +0.732051i q^{60} +(-6.19615 + 10.7321i) q^{61} +(-0.169873 - 0.294229i) q^{62} +(-4.26795 + 2.46410i) q^{63} -1.00000 q^{64} +1.60770 q^{66} +(12.4641 - 7.19615i) q^{67} +(-1.73205 - 3.00000i) q^{68} +(-1.73205 + 3.00000i) q^{69} +3.46410i q^{70} +(1.09808 + 0.633975i) q^{71} +(-3.69615 - 2.13397i) q^{72} -4.00000i q^{73} +(3.46410 - 6.00000i) q^{74} +(-0.366025 - 0.633975i) q^{75} +(3.63397 - 2.09808i) q^{76} +2.53590 q^{77} +12.3923 q^{79} +(-4.33013 + 2.50000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-3.00000 + 5.19615i) q^{82} +6.00000i q^{83} +(-1.26795 - 0.732051i) q^{84} +(3.00000 + 1.73205i) q^{85} +17.6603i q^{86} +(-3.46410 + 6.00000i) q^{87} +(1.09808 + 1.90192i) q^{88} +(0.803848 - 0.464102i) q^{89} -4.26795 q^{90} +4.73205 q^{92} +(-0.124356 + 0.0717968i) q^{93} +(-5.19615 - 9.00000i) q^{94} +(-2.09808 + 3.63397i) q^{95} -3.80385i q^{96} +(1.73205 + 1.00000i) q^{97} +(4.50000 + 2.59808i) q^{98} +3.12436i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q - 6 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 - 2 * q^9	$ 4 q - 6 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} - 2 q^{9} + 6 q^{11} - 4 q^{12} - 6 q^{15} + 10 q^{16} + 18 q^{19} - 6 q^{22} + 6 q^{23} - 6 q^{24} - 4 q^{25} + 16 q^{27} + 12 q^{29} + 6 q^{30} - 18 q^{32} - 24 q^{33} + 4 q^{35} + 2 q^{36} - 36 q^{38} + 12 q^{41} + 12 q^{42} + 10 q^{43} + 12 q^{45} - 18 q^{46} + 10 q^{48} - 6 q^{49} + 6 q^{50} + 24 q^{51} - 24 q^{54} - 6 q^{55} - 36 q^{58} + 42 q^{59} - 4 q^{61} - 18 q^{62} - 24 q^{63} - 4 q^{64} + 48 q^{66} + 36 q^{67} - 6 q^{71} + 6 q^{72} + 2 q^{75} + 18 q^{76} + 24 q^{77} + 8 q^{79} - 2 q^{81} - 12 q^{82} - 12 q^{84} + 12 q^{85} - 6 q^{88} + 24 q^{89} - 24 q^{90} + 12 q^{92} + 48 q^{93} + 2 q^{95} + 18 q^{98}+O(q^{100}) $ 4 * q - 6 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 - 2 * q^9 + 6 * q^11 - 4 * q^12 - 6 * q^15 + 10 * q^16 + 18 * q^19 - 6 * q^22 + 6 * q^23 - 6 * q^24 - 4 * q^25 + 16 * q^27 + 12 * q^29 + 6 * q^30 - 18 * q^32 - 24 * q^33 + 4 * q^35 + 2 * q^36 - 36 * q^38 + 12 * q^41 + 12 * q^42 + 10 * q^43 + 12 * q^45 - 18 * q^46 + 10 * q^48 - 6 * q^49 + 6 * q^50 + 24 * q^51 - 24 * q^54 - 6 * q^55 - 36 * q^58 + 42 * q^59 - 4 * q^61 - 18 * q^62 - 24 * q^63 - 4 * q^64 + 48 * q^66 + 36 * q^67 - 6 * q^71 + 6 * q^72 + 2 * q^75 + 18 * q^76 + 24 * q^77 + 8 * q^79 - 2 * q^81 - 12 * q^82 - 12 * q^84 + 12 * q^85 - 6 * q^88 + 24 * q^89 - 24 * q^90 + 12 * q^92 + 48 * q^93 + 2 * q^95 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.135045	+	0.990839i	$0.543118\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	0.952129	−	0.305695i	$-0.0988889\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	−0.740805	+	0.671721i	$0.765556\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.09808	−	0.633975i	−0.448288	−	0.258819i
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$		−	1.73205i		−	0.612372i
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$	−0.866025	−	1.50000i	−0.273861	−	0.474342i
$11$	−1.09808	+	0.633975i	−0.331082	+	0.191151i	−0.656322	−	0.754481i	$-0.727889\pi$
$11$	−1.09808	+	0.633975i	−0.331082	+	0.191151i	0.325239	+	0.945632i	$0.394555\pi$
$12$	0.732051			0.211325
$13$		0			0
$13$		0			0
$14$	3.46410			0.925820
$15$	−0.633975	+	0.366025i	−0.163692	+	0.0945074i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	1.73205	−	3.00000i	0.420084	−	0.727607i	−0.575863	−	0.817546i	$-0.695334\pi$
$17$	1.73205	−	3.00000i	0.420084	−	0.727607i	0.995947	+	0.0899392i	$0.0286673\pi$
$18$			4.26795i			1.00597i
$19$	3.63397	+	2.09808i	0.833691	+	0.481332i	0.855115	−	0.518439i	$-0.173487\pi$
$19$	3.63397	+	2.09808i	0.833691	+	0.481332i	−0.0214238	+	0.999770i	$0.506820\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		−	1.46410i		−	0.319493i
$22$	1.09808	−	1.90192i	0.234111	−	0.405492i
$23$	2.36603	+	4.09808i	0.493350	+	0.854508i	0.999971	−	0.00766135i	$-0.00243871\pi$
$23$	2.36603	+	4.09808i	0.493350	+	0.854508i	−0.506620	+	0.862169i	$0.669105\pi$
$24$	1.09808	−	0.633975i	0.224144	−	0.129410i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	4.00000			0.769800
$28$	−1.73205	+	1.00000i	−0.327327	+	0.188982i
$29$	4.73205	+	8.19615i	0.878720	+	1.52199i	0.852747	+	0.522325i	$0.174935\pi$
$29$	4.73205	+	8.19615i	0.878720	+	1.52199i	0.0259731	+	0.999663i	$0.491732\pi$
$30$	0.633975	−	1.09808i	0.115747	−	0.200480i
$31$			0.196152i			0.0352300i	0.999845	+	0.0176150i	$0.00560732\pi$
$31$			0.196152i			0.0352300i	−0.999845	+	0.0176150i	$0.994393\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$	−0.803848	−	0.464102i	−0.139932	−	0.0807897i
$34$			6.00000i			1.02899i
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	−1.23205	−	2.13397i	−0.205342	−	0.355662i
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	−0.756948	−	0.653476i	$-0.773310\pi$
$37$	−3.46410	+	2.00000i	−0.569495	+	0.328798i	0.187453	+	0.982274i	$0.439977\pi$
$38$	−7.26795			−1.17902
$39$		0			0
$40$	1.73205			0.273861
$41$	3.00000	−	1.73205i	0.468521	−	0.270501i	−0.247099	−	0.968990i	$-0.579477\pi$
$41$	3.00000	−	1.73205i	0.468521	−	0.270501i	0.715621	+	0.698489i	$0.246144\pi$
$42$	1.26795	+	2.19615i	0.195649	+	0.338874i
$43$	5.09808	−	8.83013i	0.777449	−	1.34658i	−0.155958	−	0.987764i	$-0.549847\pi$
$43$	5.09808	−	8.83013i	0.777449	−	1.34658i	0.933408	−	0.358818i	$-0.116820\pi$
$44$			1.26795i			0.191151i
$45$	2.13397	+	1.23205i	0.318114	+	0.183663i
$46$	−7.09808	−	4.09808i	−1.04655	−	0.604228i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	−1.83013	+	3.16987i	−0.264156	+	0.457532i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	1.50000	−	0.866025i	0.212132	−	0.122474i
$51$	2.53590			0.355097
$52$		0			0
$53$	−10.3923			−1.42749			−0.713746	−	0.700404i	$-0.753003\pi$
$53$	−10.3923			−1.42749			−0.713746	+	0.700404i	$0.753003\pi$
$54$	−6.00000	+	3.46410i	−0.816497	+	0.471405i
$55$	−0.633975	−	1.09808i	−0.0854851	−	0.148065i
$56$	−1.73205	+	3.00000i	−0.231455	+	0.400892i
$57$			3.07180i			0.406869i
$58$	−14.1962	−	8.19615i	−1.86405	−	1.07621i
$59$	13.0981	+	7.56218i	1.70522	+	0.984512i	0.940272	+	0.340425i	$0.110571\pi$
$59$	13.0981	+	7.56218i	1.70522	+	0.984512i	0.764953	+	0.644086i	$0.222762\pi$
$60$			0.732051i			0.0945074i
$61$	−6.19615	+	10.7321i	−0.793336	+	1.37410i	0.130554	+	0.991441i	$0.458324\pi$
$61$	−6.19615	+	10.7321i	−0.793336	+	1.37410i	−0.923890	+	0.382657i	$0.875009\pi$
$62$	−0.169873	−	0.294229i	−0.0215739	−	0.0373671i
$63$	−4.26795	+	2.46410i	−0.537711	+	0.310448i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.60770			0.197894
$67$	12.4641	−	7.19615i	1.52273	−	0.879150i	0.523094	−	0.852275i	$-0.324778\pi$
$67$	12.4641	−	7.19615i	1.52273	−	0.879150i	0.999639	−	0.0268747i	$-0.00855551\pi$
$68$	−1.73205	−	3.00000i	−0.210042	−	0.363803i
$69$	−1.73205	+	3.00000i	−0.208514	+	0.361158i
$70$			3.46410i			0.414039i
$71$	1.09808	+	0.633975i	0.130318	+	0.0752389i	0.563742	−	0.825951i	$-0.309361\pi$
$71$	1.09808	+	0.633975i	0.130318	+	0.0752389i	−0.433424	+	0.901190i	$0.642695\pi$
$72$	−3.69615	−	2.13397i	−0.435596	−	0.251491i
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$	3.46410	−	6.00000i	0.402694	−	0.697486i
$75$	−0.366025	−	0.633975i	−0.0422650	−	0.0732051i
$76$	3.63397	−	2.09808i	0.416845	−	0.240666i
$77$	2.53590			0.288992
$78$		0			0
$79$	12.3923			1.39424			0.697122	−	0.716953i	$-0.254464\pi$
$79$	12.3923			1.39424			0.697122	+	0.716953i	$0.254464\pi$
$80$	−4.33013	+	2.50000i	−0.484123	+	0.279508i
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	−1.26795	−	0.732051i	−0.138345	−	0.0798733i
$85$	3.00000	+	1.73205i	0.325396	+	0.187867i
$86$			17.6603i			1.90435i
$87$	−3.46410	+	6.00000i	−0.371391	+	0.643268i
$88$	1.09808	+	1.90192i	0.117055	+	0.202746i
$89$	0.803848	−	0.464102i	0.0852077	−	0.0491947i	−0.456791	−	0.889574i	$-0.651001\pi$
$89$	0.803848	−	0.464102i	0.0852077	−	0.0491947i	0.541998	+	0.840379i	$0.317668\pi$
$90$	−4.26795			−0.449881
$91$		0			0
$92$	4.73205			0.493350
$93$	−0.124356	+	0.0717968i	−0.0128951	+	0.00744498i
$94$	−5.19615	−	9.00000i	−0.535942	−	0.928279i
$95$	−2.09808	+	3.63397i	−0.215258	+	0.372838i
$96$		−	3.80385i		−	0.388229i
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	0.585348	−	0.810782i	$-0.300958\pi$
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	−0.409484	+	0.912317i	$0.634291\pi$
$98$	4.50000	+	2.59808i	0.454569	+	0.262445i
$99$			3.12436i			0.314010i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	6.46410	+	11.1962i	0.643202	+	1.11406i	0.984714	+	0.174181i	$0.0557278\pi$
$101$	6.46410	+	11.1962i	0.643202	+	1.11406i	−0.341511	+	0.939878i	$0.610939\pi$
$102$	−3.80385	+	2.19615i	−0.376637	+	0.217451i
$103$	−10.1962			−1.00466			−0.502328	−	0.864677i	$-0.667523\pi$
$103$	−10.1962			−1.00466			−0.502328	+	0.864677i	$0.667523\pi$
$104$		0			0
$105$	1.46410			0.142882
$106$	15.5885	−	9.00000i	1.51408	−	0.874157i
$107$	−0.169873	−	0.294229i	−0.0164222	−	0.0284442i	0.857697	−	0.514155i	$-0.171894\pi$
$107$	−0.169873	−	0.294229i	−0.0164222	−	0.0284442i	−0.874120	+	0.485710i	$0.838561\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$	1.90192	+	1.09808i	0.181341	+	0.104697i
$111$	−2.53590	−	1.46410i	−0.240697	−	0.138966i
$112$		−	10.0000i		−	0.944911i
$113$	−7.73205	+	13.3923i	−0.727370	+	1.25984i	0.230621	+	0.973044i	$0.425924\pi$
$113$	−7.73205	+	13.3923i	−0.727370	+	1.25984i	−0.957991	+	0.286798i	$0.907409\pi$
$114$	−2.66025	−	4.60770i	−0.249156	−	0.431550i
$115$	−4.09808	+	2.36603i	−0.382148	+	0.220633i
$116$	9.46410			0.878720
$117$		0			0
$118$	−26.1962			−2.41155
$119$	−6.00000	+	3.46410i	−0.550019	+	0.317554i
$120$	0.633975	+	1.09808i	0.0578737	+	0.100240i
$121$	−4.69615	+	8.13397i	−0.426923	+	0.739452i
$122$		−	21.4641i		−	1.94327i
$123$	2.19615	+	1.26795i	0.198020	+	0.114327i
$124$	0.169873	+	0.0980762i	0.0152550	+	0.00880750i
$125$		−	1.00000i		−	0.0894427i
$126$	4.26795	−	7.39230i	0.380219	−	0.658559i
$127$	2.90192	+	5.02628i	0.257504	+	0.446010i	0.965573	−	0.260134i	$-0.0837666\pi$
$127$	2.90192	+	5.02628i	0.257504	+	0.446010i	−0.708069	+	0.706144i	$0.750433\pi$
$128$	10.5000	−	6.06218i	0.928078	−	0.535826i
$129$	7.46410			0.657178
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−0.803848	+	0.464102i	−0.0699660	+	0.0403949i
$133$	−4.19615	−	7.26795i	−0.363853	−	0.630211i
$134$	−12.4641	+	21.5885i	−1.07673	+	1.86496i
$135$			4.00000i			0.344265i
$136$	−5.19615	−	3.00000i	−0.445566	−	0.257248i
$137$	11.1962	+	6.46410i	0.956552	+	0.552265i	0.895110	−	0.445845i	$-0.147097\pi$
$137$	11.1962	+	6.46410i	0.956552	+	0.552265i	0.0614418	+	0.998111i	$0.480430\pi$
$138$		−	6.00000i		−	0.510754i
$139$	4.19615	−	7.26795i	0.355913	−	0.616459i	−0.631361	−	0.775489i	$-0.717503\pi$
$139$	4.19615	−	7.26795i	0.355913	−	0.616459i	0.987274	+	0.159030i	$0.0508366\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$	−3.80385	+	2.19615i	−0.320342	+	0.184949i
$142$	−2.19615			−0.184297
$143$		0			0
$144$	12.3205			1.02671
$145$	−8.19615	+	4.73205i	−0.680653	+	0.392975i
$146$	3.46410	+	6.00000i	0.286691	+	0.496564i
$147$	1.09808	−	1.90192i	0.0905678	−	0.156868i
$148$			4.00000i			0.328798i
$149$	17.1962	+	9.92820i	1.40876	+	0.813350i	0.995269	−	0.0971565i	$-0.0309747\pi$
$149$	17.1962	+	9.92820i	1.40876	+	0.813350i	0.413495	+	0.910507i	$0.364308\pi$
$150$	1.09808	+	0.633975i	0.0896575	+	0.0517638i
$151$		−	12.1962i		−	0.992509i	−0.868177	−	0.496254i	$-0.834708\pi$
$151$		−	12.1962i		−	0.992509i	0.868177	−	0.496254i	$-0.165292\pi$
$152$	3.63397	−	6.29423i	0.294754	−	0.510529i
$153$	−4.26795	−	7.39230i	−0.345043	−	0.597632i
$154$	−3.80385	+	2.19615i	−0.306523	+	0.176971i
$155$	−0.196152			−0.0157553
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	−18.5885	+	10.7321i	−1.47882	+	0.853796i
$159$	−3.80385	−	6.58846i	−0.301665	−	0.522499i
$160$	2.59808	−	4.50000i	0.205396	−	0.355756i
$161$		−	9.46410i		−	0.745876i
$162$	6.69615	+	3.86603i	0.526099	+	0.303744i
$163$	−5.53590	−	3.19615i	−0.433605	−	0.250342i	0.267276	−	0.963620i	$-0.413876\pi$
$163$	−5.53590	−	3.19615i	−0.433605	−	0.250342i	−0.700881	+	0.713278i	$0.747210\pi$
$164$		−	3.46410i		−	0.270501i
$165$	0.464102	−	0.803848i	0.0361303	−	0.0625794i
$166$	−5.19615	−	9.00000i	−0.403300	−	0.698535i
$167$	11.1962	−	6.46410i	0.866384	−	0.500207i	0.000239271	−	1.00000i	$-0.499924\pi$
$167$	11.1962	−	6.46410i	0.866384	−	0.500207i	0.866145	+	0.499793i	$0.166591\pi$
$168$	−2.53590			−0.195649
$169$		0			0
$170$	−6.00000			−0.460179
$171$	8.95448	−	5.16987i	0.684766	−	0.395350i
$172$	−5.09808	−	8.83013i	−0.388725	−	0.673291i
$173$	7.73205	−	13.3923i	0.587857	−	1.01820i	−0.406656	−	0.913581i	$-0.633305\pi$
$173$	7.73205	−	13.3923i	0.587857	−	1.01820i	0.994513	−	0.104617i	$-0.0333615\pi$
$174$		−	12.0000i		−	0.909718i
$175$	1.73205	+	1.00000i	0.130931	+	0.0755929i
$176$	−5.49038	−	3.16987i	−0.413853	−	0.238938i
$177$			11.0718i			0.832207i
$178$	−0.803848	+	1.39230i	−0.0602509	+	0.104358i
$179$	−2.53590	−	4.39230i	−0.189542	−	0.328296i	0.755556	−	0.655084i	$-0.227367\pi$
$179$	−2.53590	−	4.39230i	−0.189542	−	0.328296i	−0.945098	+	0.326788i	$0.894034\pi$
$180$	2.13397	−	1.23205i	0.159057	−	0.0918316i
$181$	20.3923			1.51575			0.757874	−	0.652401i	$-0.226238\pi$
$181$	20.3923			1.51575			0.757874	+	0.652401i	$0.226238\pi$
$182$		0			0
$183$	−9.07180			−0.670607
$184$	7.09808	−	4.09808i	0.523277	−	0.302114i
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$	0.124356	−	0.215390i	0.00911820	−	0.0157932i
$187$			4.39230i			0.321197i
$188$	5.19615	+	3.00000i	0.378968	+	0.218797i
$189$	−6.92820	−	4.00000i	−0.503953	−	0.290957i
$190$		−	7.26795i		−	0.527272i
$191$	9.46410	−	16.3923i	0.684798	−	1.18611i	−0.288702	−	0.957419i	$-0.593224\pi$
$191$	9.46410	−	16.3923i	0.684798	−	1.18611i	0.973500	−	0.228686i	$-0.0734431\pi$
$192$	−0.366025	−	0.633975i	−0.0264156	−	0.0457532i
$193$	−8.66025	+	5.00000i	−0.623379	+	0.359908i	−0.778183	−	0.628037i	$-0.783859\pi$
$193$	−8.66025	+	5.00000i	−0.623379	+	0.359908i	0.154805	+	0.987945i	$0.450525\pi$
$194$	−3.46410			−0.248708
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−0.803848	+	0.464102i	−0.0572718	+	0.0330659i	−0.528362	−	0.849019i	$-0.677194\pi$
$197$	−0.803848	+	0.464102i	−0.0572718	+	0.0330659i	0.471091	+	0.882085i	$0.343860\pi$
$198$	−2.70577	−	4.68653i	−0.192291	−	0.333057i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$			1.73205i			0.122474i
$201$	9.12436	+	5.26795i	0.643582	+	0.371572i
$202$	−19.3923	−	11.1962i	−1.36444	−	0.787759i
$203$		−	18.9282i		−	1.32850i
$204$	1.26795	−	2.19615i	0.0887742	−	0.153761i
$205$	1.73205	+	3.00000i	0.120972	+	0.209529i
$206$	15.2942	−	8.83013i	1.06560	−	0.615224i
$207$	11.6603			0.810444
$208$		0			0
$209$	−5.32051			−0.368027
$210$	−2.19615	+	1.26795i	−0.151549	+	0.0874968i
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$	−5.19615	+	9.00000i	−0.356873	+	0.618123i
$213$			0.928203i			0.0635994i
$214$	0.509619	+	0.294229i	0.0348368	+	0.0201131i
$215$	8.83013	+	5.09808i	0.602210	+	0.347686i
$216$		−	6.92820i		−	0.471405i
$217$	0.196152	−	0.339746i	0.0133157	−	0.0230635i
$218$	1.73205	+	3.00000i	0.117309	+	0.203186i
$219$	2.53590	−	1.46410i	0.171360	−	0.0989348i
$220$	−1.26795			−0.0854851
$221$		0			0
$222$	5.07180			0.340397
$223$	−1.73205	+	1.00000i	−0.115987	+	0.0669650i	−0.556871	−	0.830599i	$-0.687998\pi$
$223$	−1.73205	+	1.00000i	−0.115987	+	0.0669650i	0.440884	+	0.897564i	$0.354665\pi$
$224$	5.19615	+	9.00000i	0.347183	+	0.601338i
$225$	−1.23205	+	2.13397i	−0.0821367	+	0.142265i
$226$		−	26.7846i		−	1.78169i
$227$	3.00000	+	1.73205i	0.199117	+	0.114960i	0.596244	−	0.802804i	$-0.296659\pi$
$227$	3.00000	+	1.73205i	0.199117	+	0.114960i	−0.397127	+	0.917764i	$0.629993\pi$
$228$	2.66025	+	1.53590i	0.176180	+	0.101717i
$229$		−	14.3923i		−	0.951070i	−0.879697	−	0.475535i	$-0.842254\pi$
$229$		−	14.3923i		−	0.951070i	0.879697	−	0.475535i	$-0.157746\pi$
$230$	4.09808	−	7.09808i	0.270219	−	0.468033i
$231$	0.928203	+	1.60770i	0.0610713	+	0.105779i
$232$	14.1962	−	8.19615i	0.932023	−	0.538104i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$	13.0981	−	7.56218i	0.852612	−	0.492256i
$237$	4.53590	+	7.85641i	0.294638	+	0.510328i
$238$	6.00000	−	10.3923i	0.388922	−	0.673633i
$239$			3.80385i			0.246050i	0.992404	+	0.123025i	$0.0392596\pi$
$239$			3.80385i			0.246050i	−0.992404	+	0.123025i	$0.960740\pi$
$240$	−3.16987	−	1.83013i	−0.204614	−	0.118134i
$241$	−15.9282	−	9.19615i	−1.02603	−	0.592376i	−0.110182	−	0.993911i	$-0.535143\pi$
$241$	−15.9282	−	9.19615i	−1.02603	−	0.592376i	−0.915844	+	0.401535i	$0.868477\pi$
$242$		−	16.2679i		−	1.04574i
$243$	7.63397	−	13.2224i	0.489720	−	0.848219i
$244$	6.19615	+	10.7321i	0.396668	+	0.687049i
$245$	2.59808	−	1.50000i	0.165985	−	0.0958315i
$246$	−4.39230			−0.280043
$247$		0			0
$248$	0.339746			0.0215739
$249$	−3.80385	+	2.19615i	−0.241059	+	0.139176i
$250$	0.866025	+	1.50000i	0.0547723	+	0.0948683i
$251$	−7.26795	+	12.5885i	−0.458749	+	0.794576i	−0.998895	−	0.0469948i	$-0.985036\pi$
$251$	−7.26795	+	12.5885i	−0.458749	+	0.794576i	0.540146	+	0.841571i	$0.318369\pi$
$252$			4.92820i			0.310448i
$253$	−5.19615	−	3.00000i	−0.326679	−	0.188608i
$254$	−8.70577	−	5.02628i	−0.546249	−	0.315377i
$255$			2.53590i			0.158804i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−3.92820	−	6.80385i	−0.245035	−	0.424412i	0.717107	−	0.696963i	$-0.245466\pi$
$257$	−3.92820	−	6.80385i	−0.245035	−	0.424412i	−0.962141	+	0.272551i	$0.912133\pi$
$258$	−11.1962	+	6.46410i	−0.697042	+	0.402437i
$259$	8.00000			0.497096
$260$		0			0
$261$	23.3205			1.44350
$262$		0			0
$263$	−2.36603	−	4.09808i	−0.145895	−	0.252698i	0.783811	−	0.620999i	$-0.213273\pi$
$263$	−2.36603	−	4.09808i	−0.145895	−	0.252698i	−0.929707	+	0.368301i	$0.879940\pi$
$264$	−0.803848	+	1.39230i	−0.0494734	+	0.0856904i
$265$		−	10.3923i		−	0.638394i
$266$	12.5885	+	7.26795i	0.771848	+	0.445627i
$267$	0.588457	+	0.339746i	0.0360130	+	0.0207921i
$268$		−	14.3923i		−	0.879150i
$269$	−3.92820	+	6.80385i	−0.239507	+	0.414838i	−0.960573	−	0.278028i	$-0.910319\pi$
$269$	−3.92820	+	6.80385i	−0.239507	+	0.414838i	0.721066	+	0.692866i	$0.243652\pi$
$270$	−3.46410	−	6.00000i	−0.210819	−	0.365148i
$271$	−18.1699	+	10.4904i	−1.10374	+	0.637245i	−0.937201	−	0.348789i	$-0.886593\pi$
$271$	−18.1699	+	10.4904i	−1.10374	+	0.637245i	−0.166540	+	0.986035i	$0.553260\pi$
$272$	17.3205			1.05021
$273$		0			0
$274$	−22.3923			−1.35277
$275$	1.09808	−	0.633975i	0.0662165	−	0.0382301i
$276$	1.73205	+	3.00000i	0.104257	+	0.180579i
$277$	−2.80385	+	4.85641i	−0.168467	+	0.291793i	−0.937881	−	0.346957i	$-0.887215\pi$
$277$	−2.80385	+	4.85641i	−0.168467	+	0.291793i	0.769414	+	0.638750i	$0.220548\pi$
$278$			14.5359i			0.871805i
$279$	0.418584	+	0.241670i	0.0250600	+	0.0144684i
$280$	−3.00000	−	1.73205i	−0.179284	−	0.103510i
$281$			1.60770i			0.0959071i	0.998850	+	0.0479535i	$0.0152699\pi$
$281$			1.60770i			0.0959071i	−0.998850	+	0.0479535i	$0.984730\pi$
$282$	3.80385	−	6.58846i	0.226516	−	0.392337i
$283$	0.705771	+	1.22243i	0.0419538	+	0.0726660i	0.886240	−	0.463227i	$-0.153308\pi$
$283$	0.705771	+	1.22243i	0.0419538	+	0.0726660i	−0.844286	+	0.535893i	$0.819975\pi$
$284$	1.09808	−	0.633975i	0.0651588	−	0.0376195i
$285$	−3.07180			−0.181958
$286$		0			0
$287$	−6.92820			−0.408959
$288$	−11.0885	+	6.40192i	−0.653394	+	0.377237i
$289$	2.50000	+	4.33013i	0.147059	+	0.254713i
$290$	8.19615	−	14.1962i	0.481295	−	0.833627i
$291$			1.46410i			0.0858272i
$292$	−3.46410	−	2.00000i	−0.202721	−	0.117041i
$293$	16.3923	+	9.46410i	0.957649	+	0.552899i	0.895449	−	0.445165i	$-0.146855\pi$
$293$	16.3923	+	9.46410i	0.957649	+	0.552899i	0.0622001	+	0.998064i	$0.480188\pi$
$294$			3.80385i			0.221845i
$295$	−7.56218	+	13.0981i	−0.440287	+	0.762599i
$296$	3.46410	+	6.00000i	0.201347	+	0.348743i
$297$	−4.39230	+	2.53590i	−0.254867	+	0.147148i
$298$	−34.3923			−1.99229
$299$		0			0
$300$	−0.732051			−0.0422650
$301$	−17.6603	+	10.1962i	−1.01792	+	0.587696i
$302$	10.5622	+	18.2942i	0.607785	+	1.05271i
$303$	−4.73205	+	8.19615i	−0.271849	+	0.470857i
$304$			20.9808i			1.20333i
$305$	−10.7321	−	6.19615i	−0.614515	−	0.354791i
$306$	12.8038	+	7.39230i	0.731947	+	0.422590i
$307$			22.7846i			1.30039i	0.759769	+	0.650193i	$0.225312\pi$
$307$			22.7846i			1.30039i	−0.759769	+	0.650193i	$0.774688\pi$
$308$	1.26795	−	2.19615i	0.0722481	−	0.125137i
$309$	−3.73205	−	6.46410i	−0.212309	−	0.367730i
$310$	0.294229	−	0.169873i	0.0167111	−	0.00964814i
$311$	−4.39230			−0.249065			−0.124532	−	0.992216i	$-0.539743\pi$
$311$	−4.39230			−0.249065			−0.124532	+	0.992216i	$0.539743\pi$
$312$		0			0
$313$	6.39230			0.361314			0.180657	−	0.983546i	$-0.442178\pi$
$313$	6.39230			0.361314			0.180657	+	0.983546i	$0.442178\pi$
$314$	15.0000	−	8.66025i	0.846499	−	0.488726i
$315$	−2.46410	−	4.26795i	−0.138836	−	0.240472i
$316$	6.19615	−	10.7321i	0.348561	−	0.603725i
$317$		−	24.0000i		−	1.34797i	−0.738743	−	0.673987i	$-0.764580\pi$
$317$		−	24.0000i		−	1.34797i	0.738743	−	0.673987i	$-0.235420\pi$
$318$	11.4115	+	6.58846i	0.639928	+	0.369462i
$319$	−10.3923	−	6.00000i	−0.581857	−	0.335936i
$320$		−	1.00000i		−	0.0559017i
$321$	0.124356	−	0.215390i	0.00694086	−	0.0120219i
$322$	8.19615	+	14.1962i	0.456754	+	0.791121i
$323$	12.5885	−	7.26795i	0.700440	−	0.404400i
$324$	−4.46410			−0.248006
$325$		0			0
$326$	11.0718			0.613210
$327$	1.26795	−	0.732051i	0.0701178	−	0.0404825i
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$			1.60770i			0.0885007i
$331$	−24.7583	−	14.2942i	−1.36084	−	0.785682i	−0.371105	−	0.928591i	$-0.621021\pi$
$331$	−24.7583	−	14.2942i	−1.36084	−	0.785682i	−0.989736	+	0.142909i	$0.954354\pi$
$332$	5.19615	+	3.00000i	0.285176	+	0.164646i
$333$			9.85641i			0.540128i
$334$	−11.1962	+	19.3923i	−0.612626	+	1.06110i
$335$	7.19615	+	12.4641i	0.393168	+	0.680987i
$336$	6.33975	−	3.66025i	0.345861	−	0.199683i
$337$	5.60770			0.305471			0.152735	−	0.988267i	$-0.451192\pi$
$337$	5.60770			0.305471			0.152735	+	0.988267i	$0.451192\pi$
$338$		0			0
$339$	−11.3205			−0.614846
$340$	3.00000	−	1.73205i	0.162698	−	0.0939336i
$341$	−0.124356	−	0.215390i	−0.00673424	−	0.0116640i
$342$	−8.95448	+	15.5096i	−0.484203	+	0.838664i
$343$			20.0000i			1.07990i
$344$	−15.2942	−	8.83013i	−0.824610	−	0.476089i
$345$	−3.00000	−	1.73205i	−0.161515	−	0.0932505i
$346$			26.7846i			1.43995i
$347$	−5.83013	+	10.0981i	−0.312978	+	0.542093i	−0.979006	−	0.203834i	$-0.934660\pi$
$347$	−5.83013	+	10.0981i	−0.312978	+	0.542093i	0.666028	+	0.745927i	$0.267993\pi$
$348$	3.46410	+	6.00000i	0.185695	+	0.321634i
$349$	5.53590	−	3.19615i	0.296330	−	0.171086i	−0.344463	−	0.938800i	$-0.611939\pi$
$349$	5.53590	−	3.19615i	0.296330	−	0.171086i	0.640793	+	0.767714i	$0.278606\pi$
$350$	−3.46410			−0.185164
$351$		0			0
$352$	6.58846			0.351166
$353$	−24.0000	+	13.8564i	−1.27739	+	0.737502i	−0.976368	−	0.216115i	$-0.930661\pi$
$353$	−24.0000	+	13.8564i	−1.27739	+	0.737502i	−0.301023	+	0.953617i	$0.597328\pi$
$354$	−9.58846	−	16.6077i	−0.509621	−	0.882689i
$355$	−0.633975	+	1.09808i	−0.0336479	+	0.0582798i
$356$		−	0.928203i		−	0.0491947i
$357$	−4.39230	−	2.53590i	−0.232465	−	0.134214i
$358$	7.60770	+	4.39230i	0.402079	+	0.232141i
$359$			8.19615i			0.432576i	0.976330	+	0.216288i	$0.0693951\pi$
$359$			8.19615i			0.432576i	−0.976330	+	0.216288i	$0.930605\pi$
$360$	2.13397	−	3.69615i	0.112470	−	0.194804i
$361$	−0.696152	−	1.20577i	−0.0366396	−	0.0634617i
$362$	−30.5885	+	17.6603i	−1.60769	+	0.928202i
$363$	−6.87564			−0.360878
$364$		0			0
$365$	4.00000			0.209370
$366$	13.6077	−	7.85641i	0.711286	−	0.410661i
$367$	−11.0981	−	19.2224i	−0.579315	−	1.00340i	−0.995558	−	0.0941495i	$-0.969987\pi$
$367$	−11.0981	−	19.2224i	−0.579315	−	1.00340i	0.416243	−	0.909253i	$-0.363346\pi$
$368$	−11.8301	+	20.4904i	−0.616688	+	1.06813i
$369$		−	8.53590i		−	0.444361i
$370$	6.00000	+	3.46410i	0.311925	+	0.180090i
$371$	18.0000	+	10.3923i	0.934513	+	0.539542i
$372$			0.143594i			0.00744498i
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−3.80385	−	6.58846i	−0.196692	−	0.340681i
$375$	0.633975	−	0.366025i	0.0327383	−	0.0189015i
$376$	10.3923			0.535942
$377$		0			0
$378$	13.8564			0.712697
$379$	28.5622	−	16.4904i	1.46714	−	0.847054i	0.467817	−	0.883825i	$-0.345041\pi$
$379$	28.5622	−	16.4904i	1.46714	−	0.847054i	0.999324	+	0.0367715i	$0.0117074\pi$
$380$	2.09808	+	3.63397i	0.107629	+	0.186419i
$381$	−2.12436	+	3.67949i	−0.108834	+	0.188506i
$382$			32.7846i			1.67741i
$383$	−0.803848	−	0.464102i	−0.0410747	−	0.0237145i	0.479322	−	0.877639i	$-0.340883\pi$
$383$	−0.803848	−	0.464102i	−0.0410747	−	0.0237145i	−0.520397	+	0.853925i	$0.674216\pi$
$384$	7.68653	+	4.43782i	0.392252	+	0.226467i
$385$			2.53590i			0.129241i
$386$	8.66025	−	15.0000i	0.440795	−	0.763480i
$387$	−12.5622	−	21.7583i	−0.638571	−	1.10604i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	16.3923			0.828994
$392$	−4.50000	+	2.59808i	−0.227284	+	0.131223i
$393$		0			0
$394$	0.803848	−	1.39230i	0.0404973	−	0.0701433i
$395$			12.3923i			0.623525i
$396$	2.70577	+	1.56218i	0.135970	+	0.0785024i
$397$	11.0718	+	6.39230i	0.555678	+	0.320821i	0.751409	−	0.659837i	$-0.229375\pi$
$397$	11.0718	+	6.39230i	0.555678	+	0.320821i	−0.195731	+	0.980658i	$0.562708\pi$
$398$			34.6410i			1.73640i
$399$	3.07180	−	5.32051i	0.153782	−	0.266359i
$400$	−2.50000	−	4.33013i	−0.125000	−	0.216506i
$401$	−19.9808	+	11.5359i	−0.997792	+	0.576075i	−0.907594	−	0.419849i	$-0.862083\pi$
$401$	−19.9808	+	11.5359i	−0.997792	+	0.576075i	−0.0901975	+	0.995924i	$0.528750\pi$
$402$	−18.2487			−0.910163
$403$		0			0
$404$	12.9282			0.643202
$405$	3.86603	−	2.23205i	0.192104	−	0.110911i
$406$	16.3923	+	28.3923i	0.813536	+	1.40909i
$407$	2.53590	−	4.39230i	0.125700	−	0.217718i
$408$		−	4.39230i		−	0.217451i
$409$	−33.2487	−	19.1962i	−1.64404	−	0.949189i	−0.979375	−	0.202049i	$-0.935240\pi$
$409$	−33.2487	−	19.1962i	−1.64404	−	0.949189i	−0.664668	−	0.747139i	$-0.731427\pi$
$410$	−5.19615	−	3.00000i	−0.256620	−	0.148159i
$411$			9.46410i			0.466830i
$412$	−5.09808	+	8.83013i	−0.251164	+	0.435029i
$413$	−15.1244	−	26.1962i	−0.744221	−	1.28903i
$414$	−17.4904	+	10.0981i	−0.859605	+	0.496293i
$415$	−6.00000			−0.294528
$416$		0			0
$417$	6.14359			0.300853
$418$	7.98076	−	4.60770i	0.390352	−	0.225370i
$419$	4.73205	+	8.19615i	0.231176	+	0.400408i	0.958154	−	0.286252i	$-0.0924094\pi$
$419$	4.73205	+	8.19615i	0.231176	+	0.400408i	−0.726979	+	0.686660i	$0.759076\pi$
$420$	0.732051	−	1.26795i	0.0357204	−	0.0618696i
$421$		−	10.7846i		−	0.525610i	−0.964849	−	0.262805i	$-0.915352\pi$
$421$		−	10.7846i		−	0.525610i	0.964849	−	0.262805i	$-0.0846475\pi$
$422$	12.0000	+	6.92820i	0.584151	+	0.337260i
$423$	12.8038	+	7.39230i	0.622544	+	0.359426i
$424$			18.0000i			0.874157i
$425$	−1.73205	+	3.00000i	−0.0840168	+	0.145521i
$426$	−0.803848	−	1.39230i	−0.0389465	−	0.0674574i
$427$	21.4641	−	12.3923i	1.03872	−	0.599706i
$428$	−0.339746			−0.0164222
$429$		0			0
$430$	−17.6603			−0.851653
$431$	−16.9019	+	9.75833i	−0.814137	+	0.470042i	−0.848390	−	0.529371i	$-0.822428\pi$
$431$	−16.9019	+	9.75833i	−0.814137	+	0.470042i	0.0342535	+	0.999413i	$0.489095\pi$
$432$	10.0000	+	17.3205i	0.481125	+	0.833333i
$433$	−3.39230	+	5.87564i	−0.163024	+	0.282365i	−0.935952	−	0.352128i	$-0.885458\pi$
$433$	−3.39230	+	5.87564i	−0.163024	+	0.282365i	0.772928	+	0.634494i	$0.218791\pi$
$434$			0.679492i			0.0326167i
$435$	−6.00000	−	3.46410i	−0.287678	−	0.166091i
$436$	−1.73205	−	1.00000i	−0.0829502	−	0.0478913i
$437$			19.8564i			0.949861i
$438$	−2.53590	+	4.39230i	−0.121170	+	0.209872i
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	0.940963	+	0.338508i	$0.109922\pi$
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	−0.177325	+	0.984152i	$0.556744\pi$
$440$	−1.90192	+	1.09808i	−0.0906707	+	0.0523487i
$441$	−7.39230			−0.352015
$442$		0			0
$443$	34.9808			1.66199			0.830993	−	0.556283i	$-0.187773\pi$
$443$	34.9808			1.66199			0.830993	+	0.556283i	$0.187773\pi$
$444$	−2.53590	+	1.46410i	−0.120348	+	0.0694832i
$445$	0.464102	+	0.803848i	0.0220005	+	0.0381060i
$446$	1.73205	−	3.00000i	0.0820150	−	0.142054i
$447$			14.5359i			0.687524i
$448$	1.73205	+	1.00000i	0.0818317	+	0.0472456i
$449$	−23.7846	−	13.7321i	−1.12247	−	0.648056i	−0.180436	−	0.983587i	$-0.557751\pi$
$449$	−23.7846	−	13.7321i	−1.12247	−	0.648056i	−0.942029	+	0.335531i	$0.891084\pi$
$450$		−	4.26795i		−	0.201193i
$451$	−2.19615	+	3.80385i	−0.103413	+	0.179116i
$452$	7.73205	+	13.3923i	0.363685	+	0.629921i
$453$	7.73205	−	4.46410i	0.363283	−	0.209742i
$454$	−6.00000			−0.281594
$455$		0			0
$456$	5.32051			0.249156
$457$	26.6603	−	15.3923i	1.24711	−	0.720022i	0.276581	−	0.960991i	$-0.410799\pi$
$457$	26.6603	−	15.3923i	1.24711	−	0.720022i	0.970533	+	0.240969i	$0.0774652\pi$
$458$	12.4641	+	21.5885i	0.582409	+	1.00876i
$459$	6.92820	−	12.0000i	0.323381	−	0.560112i
$460$			4.73205i			0.220633i
$461$	3.00000	+	1.73205i	0.139724	+	0.0806696i	0.568232	−	0.822868i	$-0.307627\pi$
$461$	3.00000	+	1.73205i	0.139724	+	0.0806696i	−0.428508	+	0.903538i	$0.640961\pi$
$462$	−2.78461	−	1.60770i	−0.129552	−	0.0747967i
$463$			18.3923i			0.854763i	0.904071	+	0.427381i	$0.140564\pi$
$463$			18.3923i			0.854763i	−0.904071	+	0.427381i	$0.859436\pi$
$464$	−23.6603	+	40.9808i	−1.09840	+	1.90248i
$465$	−0.0717968	−	0.124356i	−0.00332950	−	0.00576686i
$466$	−9.00000	+	5.19615i	−0.416917	+	0.240707i
$467$	−38.1962			−1.76751			−0.883754	−	0.467953i	$-0.844992\pi$
$467$	−38.1962			−1.76751			−0.883754	+	0.467953i	$0.844992\pi$
$468$		0			0
$469$	−28.7846			−1.32915
$470$	9.00000	−	5.19615i	0.415139	−	0.239681i
$471$	−3.66025	−	6.33975i	−0.168656	−	0.292120i
$472$	13.0981	−	22.6865i	0.602888	−	1.04423i
$473$			12.9282i			0.594439i
$474$	−13.6077	−	7.85641i	−0.625022	−	0.360857i
$475$	−3.63397	−	2.09808i	−0.166738	−	0.0962663i
$476$			6.92820i			0.317554i
$477$	−12.8038	+	22.1769i	−0.586248	+	1.01541i
$478$	−3.29423	−	5.70577i	−0.150675	−	0.260976i
$479$	15.8827	−	9.16987i	0.725698	−	0.418982i	−0.0911480	−	0.995837i	$-0.529054\pi$
$479$	15.8827	−	9.16987i	0.725698	−	0.418982i	0.816846	+	0.576855i	$0.195720\pi$
$480$	3.80385			0.173621
$481$		0			0
$482$	31.8564			1.45102
$483$	6.00000	−	3.46410i	0.273009	−	0.157622i
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$			26.4449i			1.19956i
$487$	−4.85641	−	2.80385i	−0.220065	−	0.127054i	0.385915	−	0.922534i	$-0.373886\pi$
$487$	−4.85641	−	2.80385i	−0.220065	−	0.127054i	−0.605980	+	0.795480i	$0.707219\pi$
$488$	18.5885	+	10.7321i	0.841460	+	0.485817i
$489$		−	4.67949i		−	0.211614i
$490$	−2.59808	+	4.50000i	−0.117369	+	0.203289i
$491$	−4.73205	−	8.19615i	−0.213554	−	0.369887i	0.739270	−	0.673409i	$-0.235171\pi$
$491$	−4.73205	−	8.19615i	−0.213554	−	0.369887i	−0.952824	+	0.303522i	$0.901837\pi$
$492$	2.19615	−	1.26795i	0.0990102	−	0.0571636i
$493$	32.7846			1.47654
$494$		0			0
$495$	−3.12436			−0.140429
$496$	−0.849365	+	0.490381i	−0.0381376	+	0.0220188i
$497$	−1.26795	−	2.19615i	−0.0568753	−	0.0985109i
$498$	3.80385	−	6.58846i	0.170454	−	0.295236i
$499$		−	12.9808i		−	0.581099i	−0.956860	−	0.290549i	$-0.906162\pi$
$499$		−	12.9808i		−	0.581099i	0.956860	−	0.290549i	$-0.0938380\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	8.19615	+	4.73205i	0.366177	+	0.211412i
$502$		−	25.1769i		−	1.12370i
$503$	12.7583	−	22.0981i	0.568866	−	0.985305i	−0.427813	−	0.903867i	$-0.640716\pi$
$503$	12.7583	−	22.0981i	0.568866	−	0.985305i	0.996678	−	0.0814371i	$-0.0259510\pi$
$504$	4.26795	+	7.39230i	0.190110	+	0.329279i
$505$	−11.1962	+	6.46410i	−0.498222	+	0.287649i
$506$	10.3923			0.461994
$507$		0			0
$508$	5.80385			0.257504
$509$	−28.1769	+	16.2679i	−1.24892	+	0.721064i	−0.970894	−	0.239509i	$-0.923013\pi$
$509$	−28.1769	+	16.2679i	−1.24892	+	0.721064i	−0.278026	+	0.960574i	$0.589680\pi$
$510$	−2.19615	−	3.80385i	−0.0972473	−	0.168437i
$511$	−4.00000	+	6.92820i	−0.176950	+	0.306486i
$512$		−	8.66025i		−	0.382733i
$513$	14.5359	+	8.39230i	0.641776	+	0.370529i
$514$	11.7846	+	6.80385i	0.519797	+	0.300105i
$515$		−	10.1962i		−	0.449296i
$516$	3.73205	−	6.46410i	0.164294	−	0.284566i
$517$	−3.80385	−	6.58846i	−0.167293	−	0.289760i
$518$	−12.0000	+	6.92820i	−0.527250	+	0.304408i
$519$	11.3205			0.496915
$520$		0			0
$521$	−7.60770			−0.333299			−0.166650	−	0.986016i	$-0.553295\pi$
$521$	−7.60770			−0.333299			−0.166650	+	0.986016i	$0.553295\pi$
$522$	−34.9808	+	20.1962i	−1.53107	+	0.883962i
$523$	6.90192	+	11.9545i	0.301800	+	0.522733i	0.976544	−	0.215319i	$-0.0690792\pi$
$523$	6.90192	+	11.9545i	0.301800	+	0.522733i	−0.674744	+	0.738052i	$0.735746\pi$
$524$		0			0
$525$			1.46410i			0.0638986i
$526$	7.09808	+	4.09808i	0.309491	+	0.178685i
$527$	0.588457	+	0.339746i	0.0256336	+	0.0147996i
$528$		−	4.64102i		−	0.201974i
$529$	0.303848	−	0.526279i	0.0132108	−	0.0228817i
$530$	9.00000	+	15.5885i	0.390935	+	0.677119i
$531$	32.2750	−	18.6340i	1.40062	−	0.808646i
$532$	−8.39230			−0.363853
$533$		0			0
$534$	−1.17691			−0.0509301
$535$	0.294229	−	0.169873i	0.0127206	−	0.00734425i
$536$	−12.4641	−	21.5885i	−0.538367	−	0.932479i
$537$	1.85641	−	3.21539i	0.0801099	−	0.138754i
$538$		−	13.6077i		−	0.586669i
$539$	3.29423	+	1.90192i	0.141892	+	0.0819217i
$540$	3.46410	+	2.00000i	0.149071	+	0.0860663i
$541$		−	5.60770i		−	0.241094i	−0.992708	−	0.120547i	$-0.961535\pi$
$541$		−	5.60770i		−	0.241094i	0.992708	−	0.120547i	$-0.0384648\pi$
$542$	18.1699	−	31.4711i	0.780463	−	1.35180i
$543$	7.46410	+	12.9282i	0.320315	+	0.554802i
$544$	−15.5885	+	9.00000i	−0.668350	+	0.385872i
$545$	2.00000			0.0856706
$546$		0			0
$547$	−1.80385			−0.0771270			−0.0385635	−	0.999256i	$-0.512278\pi$
$547$	−1.80385			−0.0771270			−0.0385635	+	0.999256i	$0.512278\pi$
$548$	11.1962	−	6.46410i	0.478276	−	0.276133i
$549$	15.2679	+	26.4449i	0.651620	+	1.12864i
$550$	−1.09808	+	1.90192i	−0.0468221	+	0.0810983i
$551$			39.7128i			1.69182i
$552$	5.19615	+	3.00000i	0.221163	+	0.127688i
$553$	−21.4641	−	12.3923i	−0.912746	−	0.526974i
$554$		−	9.71281i		−	0.412658i
$555$	1.46410	−	2.53590i	0.0621477	−	0.107643i
$556$	−4.19615	−	7.26795i	−0.177957	−	0.308230i
$557$	−22.3923	+	12.9282i	−0.948792	+	0.547786i	−0.892706	−	0.450640i	$-0.851196\pi$
$557$	−22.3923	+	12.9282i	−0.948792	+	0.547786i	−0.0560868	+	0.998426i	$0.517862\pi$
$558$	−0.837169			−0.0354402
$559$		0			0
$560$	10.0000			0.422577
$561$	−2.78461	+	1.60770i	−0.117566	+	0.0678769i
$562$	−1.39230	−	2.41154i	−0.0587308	−	0.101725i
$563$	8.02628	−	13.9019i	0.338267	−	0.585896i	−0.645840	−	0.763473i	$-0.723493\pi$
$563$	8.02628	−	13.9019i	0.338267	−	0.585896i	0.984107	+	0.177577i	$0.0568259\pi$
$564$			4.39230i			0.184949i
$565$	−13.3923	−	7.73205i	−0.563418	−	0.325290i
$566$	−2.11731	−	1.22243i	−0.0889973	−	0.0513826i
$567$			8.92820i			0.374949i
$568$	1.09808	−	1.90192i	0.0460743	−	0.0798029i
$569$	−4.73205	−	8.19615i	−0.198378	−	0.343601i	0.749625	−	0.661863i	$-0.230234\pi$
$569$	−4.73205	−	8.19615i	−0.198378	−	0.343601i	−0.948003	+	0.318263i	$0.896901\pi$
$570$	4.60770	−	2.66025i	0.192995	−	0.111426i
$571$	−15.6077			−0.653162			−0.326581	−	0.945169i	$-0.605897\pi$
$571$	−15.6077			−0.653162			−0.326581	+	0.945169i	$0.605897\pi$
$572$		0			0
$573$	13.8564			0.578860
$574$	10.3923	−	6.00000i	0.433766	−	0.250435i
$575$	−2.36603	−	4.09808i	−0.0986701	−	0.170902i
$576$	−1.23205	+	2.13397i	−0.0513355	+	0.0889156i
$577$			4.00000i			0.166522i	0.996528	+	0.0832611i	$0.0265335\pi$
$577$			4.00000i			0.166522i	−0.996528	+	0.0832611i	$0.973466\pi$
$578$	−7.50000	−	4.33013i	−0.311959	−	0.180110i
$579$	−6.33975	−	3.66025i	−0.263471	−	0.152115i
$580$			9.46410i			0.392975i
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−1.26795	−	2.19615i	−0.0525582	−	0.0910334i
$583$	11.4115	−	6.58846i	0.472618	−	0.272866i
$584$	−6.92820			−0.286691
$585$		0			0
$586$	−32.7846			−1.35432
$587$	13.3923	−	7.73205i	0.552760	−	0.319136i	−0.197475	−	0.980308i	$-0.563274\pi$
$587$	13.3923	−	7.73205i	0.552760	−	0.319136i	0.750234	+	0.661172i	$0.229941\pi$
$588$	−1.09808	−	1.90192i	−0.0452839	−	0.0784340i
$589$	−0.411543	+	0.712813i	−0.0169573	+	0.0293709i
$590$		−	26.1962i		−	1.07848i
$591$	−0.588457	−	0.339746i	−0.0242059	−	0.0139753i
$592$	−17.3205	−	10.0000i	−0.711868	−	0.410997i
$593$		−	14.7846i		−	0.607131i	−0.952811	−	0.303566i	$-0.901823\pi$
$593$		−	14.7846i		−	0.607131i	0.952811	−	0.303566i	$-0.0981771\pi$
$594$	4.39230	−	7.60770i	0.180218	−	0.312148i
$595$	−3.46410	−	6.00000i	−0.142014	−	0.245976i
$596$	17.1962	−	9.92820i	0.704382	−	0.406675i
$597$	14.6410			0.599217
$598$		0			0
$599$	−28.3923			−1.16008			−0.580039	−	0.814589i	$-0.696963\pi$
$599$	−28.3923			−1.16008			−0.580039	+	0.814589i	$0.696963\pi$
$600$	−1.09808	+	0.633975i	−0.0448288	+	0.0258819i
$601$	19.7846	+	34.2679i	0.807031	+	1.39782i	0.914911	+	0.403655i	$0.132260\pi$
$601$	19.7846	+	34.2679i	0.807031	+	1.39782i	−0.107880	+	0.994164i	$0.534406\pi$
$602$	17.6603	−	30.5885i	0.719778	−	1.24669i
$603$		−	35.4641i		−	1.44421i
$604$	−10.5622	−	6.09808i	−0.429769	−	0.248127i
$605$	−8.13397	−	4.69615i	−0.330693	−	0.190926i
$606$		−	16.3923i		−	0.665892i
$607$	13.4904	−	23.3660i	0.547558	−	0.948398i	−0.450883	−	0.892583i	$-0.648891\pi$
$607$	13.4904	−	23.3660i	0.547558	−	0.948398i	0.998441	−	0.0558149i	$-0.0177757\pi$
$608$	−10.9019	−	18.8827i	−0.442131	−	0.765794i
$609$	12.0000	−	6.92820i	0.486265	−	0.280745i
$610$	21.4641			0.869056
$611$		0			0
$612$	−8.53590			−0.345043
$613$	−22.5167	+	13.0000i	−0.909439	+	0.525065i	−0.880251	−	0.474509i	$-0.842626\pi$
$613$	−22.5167	+	13.0000i	−0.909439	+	0.525065i	−0.0291886	+	0.999574i	$0.509292\pi$
$614$	−19.7321	−	34.1769i	−0.796321	−	1.37927i
$615$	−1.26795	+	2.19615i	−0.0511286	+	0.0885574i
$616$		−	4.39230i		−	0.176971i
$617$	−18.8038	−	10.8564i	−0.757014	−	0.437062i	0.0712084	−	0.997461i	$-0.477314\pi$
$617$	−18.8038	−	10.8564i	−0.757014	−	0.437062i	−0.828223	+	0.560399i	$0.810648\pi$
$618$	11.1962	+	6.46410i	0.450375	+	0.260024i
$619$		−	44.9808i		−	1.80793i	−0.427607	−	0.903965i	$-0.640643\pi$
$619$		−	44.9808i		−	1.80793i	0.427607	−	0.903965i	$-0.359357\pi$
$620$	−0.0980762	+	0.169873i	−0.00393884	+	0.00682226i
$621$	9.46410	+	16.3923i	0.379781	+	0.657801i
$622$	6.58846	−	3.80385i	0.264173	−	0.152520i
$623$	−1.85641			−0.0743754
$624$		0			0
$625$	1.00000			0.0400000
$626$	−9.58846	+	5.53590i	−0.383232	+	0.221259i
$627$	−1.94744	−	3.37307i	−0.0777733	−	0.134707i
$628$	−5.00000	+	8.66025i	−0.199522	+	0.345582i
$629$			13.8564i			0.552491i
$630$	7.39230	+	4.26795i	0.294516	+	0.170039i
$631$	−14.0263	−	8.09808i	−0.558377	−	0.322379i	0.194117	−	0.980978i	$-0.437816\pi$
$631$	−14.0263	−	8.09808i	−0.558377	−	0.322379i	−0.752494	+	0.658599i	$0.771149\pi$
$632$		−	21.4641i		−	0.853796i
$633$	2.92820	−	5.07180i	0.116386	−	0.201586i
$634$	20.7846	+	36.0000i	0.825462	+	1.42974i
$635$	−5.02628	+	2.90192i	−0.199462	+	0.115159i
$636$	−7.60770			−0.301665
$637$		0			0
$638$	20.7846			0.822871
$639$	2.70577	−	1.56218i	0.107039	−	0.0617988i
$640$	6.06218	+	10.5000i	0.239629	+	0.415049i
$641$	−0.464102	+	0.803848i	−0.0183309	+	0.0317501i	−0.875045	−	0.484041i	$-0.839169\pi$
$641$	−0.464102	+	0.803848i	−0.0183309	+	0.0317501i	0.856714	+	0.515791i	$0.172502\pi$
$642$			0.430781i			0.0170016i
$643$	30.1244	+	17.3923i	1.18799	+	0.685886i	0.957849	−	0.287272i	$-0.0927484\pi$
$643$	30.1244	+	17.3923i	1.18799	+	0.685886i	0.230140	+	0.973158i	$0.426082\pi$
$644$	−8.19615	−	4.73205i	−0.322974	−	0.186469i
$645$			7.46410i			0.293899i
$646$	−12.5885	+	21.8038i	−0.495286	+	0.857861i
$647$	−8.02628	−	13.9019i	−0.315546	−	0.546541i	0.664008	−	0.747726i	$-0.268854\pi$
$647$	−8.02628	−	13.9019i	−0.315546	−	0.546541i	−0.979553	+	0.201185i	$0.935521\pi$
$648$	−6.69615	+	3.86603i	−0.263050	+	0.151872i
$649$	−19.1769			−0.752760
$650$		0			0
$651$	0.287187			0.0112557
$652$	−5.53590	+	3.19615i	−0.216803	+	0.125171i
$653$	9.92820	+	17.1962i	0.388521	+	0.672937i	0.992251	−	0.124251i	$-0.0396529\pi$
$653$	9.92820	+	17.1962i	0.388521	+	0.672937i	−0.603730	+	0.797189i	$0.706320\pi$
$654$	−1.26795	+	2.19615i	−0.0495807	+	0.0858764i
$655$		0			0
$656$	15.0000	+	8.66025i	0.585652	+	0.338126i
$657$	−8.53590	−	4.92820i	−0.333017	−	0.192268i
$658$			20.7846i			0.810268i
$659$	7.26795	−	12.5885i	0.283119	−	0.490377i	−0.689032	−	0.724731i	$-0.741964\pi$
$659$	7.26795	−	12.5885i	0.283119	−	0.490377i	0.972151	+	0.234354i	$0.0752975\pi$
$660$	−0.464102	−	0.803848i	−0.0180651	−	0.0312897i
$661$	−26.6603	+	15.3923i	−1.03696	+	0.598691i	−0.918972	−	0.394323i	$-0.870979\pi$
$661$	−26.6603	+	15.3923i	−1.03696	+	0.598691i	−0.117992	+	0.993015i	$0.537646\pi$
$662$	49.5167			1.92452
$663$		0			0
$664$	10.3923			0.403300
$665$	7.26795	−	4.19615i	0.281839	−	0.162720i
$666$	−8.53590	−	14.7846i	−0.330759	−	0.572892i
$667$	−22.3923	+	38.7846i	−0.867034	+	1.50175i
$668$		−	12.9282i		−	0.500207i
$669$	−1.26795	−	0.732051i	−0.0490217	−	0.0283027i
$670$	−21.5885	−	12.4641i	−0.834035	−	0.481530i
$671$		−	15.7128i		−	0.606586i
$672$	−3.80385	+	6.58846i	−0.146737	+	0.254155i
$673$	3.19615	+	5.53590i	0.123203	+	0.213393i	0.921029	−	0.389494i	$-0.127350\pi$
$673$	3.19615	+	5.53590i	0.123203	+	0.213393i	−0.797826	+	0.602887i	$0.794017\pi$
$674$	−8.41154	+	4.85641i	−0.324001	+	0.187062i
$675$	−4.00000			−0.153960
$676$		0			0
$677$	−10.3923			−0.399409			−0.199704	−	0.979856i	$-0.563998\pi$
$677$	−10.3923			−0.399409			−0.199704	+	0.979856i	$0.563998\pi$
$678$	16.9808	−	9.80385i	0.652142	−	0.376514i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	3.00000	−	5.19615i	0.115045	−	0.199263i
$681$			2.53590i			0.0971758i
$682$	0.373067	+	0.215390i	0.0142855	+	0.00824772i
$683$	−34.1769	−	19.7321i	−1.30774	−	0.755026i	−0.326024	−	0.945361i	$-0.605709\pi$
$683$	−34.1769	−	19.7321i	−1.30774	−	0.755026i	−0.981719	+	0.190335i	$0.939042\pi$
$684$		−	10.3397i		−	0.395350i
$685$	−6.46410	+	11.1962i	−0.246981	+	0.427783i
$686$	−17.3205	−	30.0000i	−0.661300	−	1.14541i
$687$	9.12436	−	5.26795i	0.348116	−	0.200985i
$688$	50.9808			1.94362
$689$		0			0
$690$	6.00000			0.228416
$691$	−39.6340	+	22.8827i	−1.50775	+	0.870498i	−0.507788	+	0.861482i	$0.669537\pi$
$691$	−39.6340	+	22.8827i	−1.50775	+	0.870498i	−0.999959	+	0.00901639i	$0.997130\pi$
$692$	−7.73205	−	13.3923i	−0.293928	−	0.509099i
$693$	3.12436	−	5.41154i	0.118684	−	0.205568i
$694$		−	20.1962i		−	0.766635i
$695$	7.26795	+	4.19615i	0.275689	+	0.159169i
$696$	10.3923	+	6.00000i	0.393919	+	0.227429i
$697$		−	12.0000i		−	0.454532i
$698$	−5.53590	+	9.58846i	−0.209537	+	0.362928i
$699$	2.19615	+	3.80385i	0.0830661	+	0.143875i
$700$	1.73205	−	1.00000i	0.0654654	−	0.0377964i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	−16.7846			−0.633044
$704$	1.09808	−	0.633975i	0.0413853	−	0.0238938i
$705$	−2.19615	−	3.80385i	−0.0827119	−	0.143261i
$706$	24.0000	−	41.5692i	0.903252	−	1.56448i
$707$		−	25.8564i		−	0.972430i
$708$	9.58846	+	5.53590i	0.360356	+	0.208052i
$709$	−8.32051	−	4.80385i	−0.312483	−	0.180412i	0.335554	−	0.942021i	$-0.391077\pi$
$709$	−8.32051	−	4.80385i	−0.312483	−	0.180412i	−0.648037	+	0.761609i	$0.724410\pi$
$710$		−	2.19615i		−	0.0824201i
$711$	15.2679	−	26.4449i	0.572593	−	0.991760i
$712$	−0.803848	−	1.39230i	−0.0301255	−	0.0521788i
$713$	−0.803848	+	0.464102i	−0.0301043	+	0.0173807i
$714$	8.78461			0.328756
$715$		0			0
$716$	−5.07180			−0.189542
$717$	−2.41154	+	1.39230i	−0.0900607	+	0.0519966i
$718$	−7.09808	−	12.2942i	−0.264898	−	0.458817i
$719$	0.928203	−	1.60770i	0.0346161	−	0.0599569i	−0.848198	−	0.529679i	$-0.822312\pi$
$719$	0.928203	−	1.60770i	0.0346161	−	0.0599569i	0.882814	+	0.469722i	$0.155646\pi$
$720$			12.3205i			0.459158i
$721$	17.6603	+	10.1962i	0.657702	+	0.379725i
$722$	2.08846	+	1.20577i	0.0777243	+	0.0448742i
$723$		−	13.4641i		−	0.500735i
$724$	10.1962	−	17.6603i	0.378937	−	0.656338i
$725$	−4.73205	−	8.19615i	−0.175744	−	0.304397i
$726$	10.3135	−	5.95448i	0.382769	−	0.220992i
$727$	−13.4115			−0.497407			−0.248703	−	0.968580i	$-0.580004\pi$
$727$	−13.4115			−0.497407			−0.248703	+	0.968580i	$0.580004\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$	−6.00000	+	3.46410i	−0.222070	+	0.128212i
$731$	−17.6603	−	30.5885i	−0.653188	−	1.13135i
$732$	−4.53590	+	7.85641i	−0.167652	+	0.290381i
$733$		−	38.0000i		−	1.40356i	−0.712393	−	0.701781i	$-0.752388\pi$
$733$		−	38.0000i		−	1.40356i	0.712393	−	0.701781i	$-0.247612\pi$
$734$	33.2942	+	19.2224i	1.22891	+	0.709513i
$735$	1.90192	+	1.09808i	0.0701535	+	0.0405032i
$736$		−	24.5885i		−	0.906343i
$737$	−9.12436	+	15.8038i	−0.336100	+	0.582142i
$738$	7.39230	+	12.8038i	0.272115	+	0.471316i
$739$	−6.75833	+	3.90192i	−0.248609	+	0.143535i	−0.619127	−	0.785291i	$-0.712513\pi$
$739$	−6.75833	+	3.90192i	−0.248609	+	0.143535i	0.370518	+	0.928825i	$0.379180\pi$
$740$	−4.00000			−0.147043
$741$		0			0
$742$	−36.0000			−1.32160
$743$	37.9808	−	21.9282i	1.39338	−	0.804468i	0.399691	−	0.916650i	$-0.369117\pi$
$743$	37.9808	−	21.9282i	1.39338	−	0.804468i	0.993688	+	0.112182i	$0.0357840\pi$
$744$	0.124356	+	0.215390i	0.00455910	+	0.00789659i
$745$	−9.92820	+	17.1962i	−0.363741	+	0.630018i
$746$			17.3205i			0.634149i
$747$	12.8038	+	7.39230i	0.468468	+	0.270470i
$748$	3.80385	+	2.19615i	0.139082	+	0.0802993i
$749$			0.679492i			0.0248281i
$750$	−0.633975	+	1.09808i	−0.0231495	+	0.0400961i
$751$	7.80385	+	13.5167i	0.284766	+	0.493230i	0.972553	−	0.232683i	$-0.0747506\pi$
$751$	7.80385	+	13.5167i	0.284766	+	0.493230i	−0.687786	+	0.725913i	$0.741417\pi$
$752$	−25.9808	+	15.0000i	−0.947421	+	0.546994i
$753$	−10.6410			−0.387780
$754$		0			0
$755$	12.1962			0.443863
$756$	−6.92820	+	4.00000i	−0.251976	+	0.145479i
$757$	−9.19615	−	15.9282i	−0.334240	−	0.578920i	0.649099	−	0.760704i	$-0.275146\pi$
$757$	−9.19615	−	15.9282i	−0.334240	−	0.578920i	−0.983339	+	0.181784i	$0.941813\pi$
$758$	−28.5622	+	49.4711i	−1.03743	+	1.79687i
$759$		−	4.39230i		−	0.159431i
$760$	6.29423	+	3.63397i	0.228316	+	0.131818i
$761$	−6.80385	−	3.92820i	−0.246639	−	0.142397i	0.371585	−	0.928399i	$-0.378814\pi$
$761$	−6.80385	−	3.92820i	−0.246639	−	0.142397i	−0.618224	+	0.786002i	$0.712148\pi$
$762$		−	7.35898i		−	0.266588i
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	−9.46410	−	16.3923i	−0.342399	−	0.593053i
$765$	7.39230	−	4.26795i	0.267269	−	0.154308i
$766$	1.60770			0.0580884
$767$		0			0
$768$	−13.9090			−0.501897
$769$	5.87564	−	3.39230i	0.211881	−	0.122330i	−0.390304	−	0.920686i	$-0.627630\pi$
$769$	5.87564	−	3.39230i	0.211881	−	0.122330i	0.602185	+	0.798356i	$0.294297\pi$
$770$	−2.19615	−	3.80385i	−0.0791438	−	0.137081i
$771$	2.87564	−	4.98076i	0.103564	−	0.179378i
$772$			10.0000i			0.359908i
$773$	−6.00000	−	3.46410i	−0.215805	−	0.124595i	0.388201	−	0.921575i	$-0.373097\pi$
$773$	−6.00000	−	3.46410i	−0.215805	−	0.124595i	−0.604006	+	0.796980i	$0.706430\pi$
$774$	37.6865	+	21.7583i	1.35461	+	0.782087i
$775$		−	0.196152i		−	0.00704600i
$776$	1.73205	−	3.00000i	0.0621770	−	0.107694i
$777$	2.92820	+	5.07180i	0.105049	+	0.181950i
$778$	9.00000	−	5.19615i	0.322666	−	0.186291i
$779$	14.5359			0.520803
$780$		0			0
$781$	−1.60770			−0.0575279
$782$	−24.5885	+	14.1962i	−0.879281	+	0.507653i
$783$	18.9282	+	32.7846i	0.676439	+	1.17163i
$784$	7.50000	−	12.9904i	0.267857	−	0.463942i
$785$		−	10.0000i		−	0.356915i
$786$		0			0
$787$	44.6603	+	25.7846i	1.59197	+	0.919122i	0.992969	+	0.118371i	$0.0377671\pi$
$787$	44.6603	+	25.7846i	1.59197	+	0.919122i	0.598997	+	0.800752i	$0.295566\pi$
$788$			0.928203i			0.0330659i
$789$	1.73205	−	3.00000i	0.0616626	−	0.106803i
$790$	−10.7321	−	18.5885i	−0.381829	−	0.661348i
$791$	26.7846	−	15.4641i	0.952351	−	0.549840i
$792$	5.41154			0.192291
$793$		0			0
$794$	−22.1436			−0.785847
$795$	6.58846	−	3.80385i	0.233668	−	0.134909i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	14.3205	−	24.8038i	0.507258	−	0.878597i	−0.492706	−	0.870196i	$-0.663992\pi$
$797$	14.3205	−	24.8038i	0.507258	−	0.878597i	0.999965	−	0.00840168i	$-0.00267437\pi$
$798$			10.6410i			0.376688i
$799$	18.0000	+	10.3923i	0.636794	+	0.367653i
$800$	4.50000	+	2.59808i	0.159099	+	0.0918559i
$801$		−	2.28719i		−	0.0808138i
$802$	19.9808	−	34.6077i	0.705545	−	1.22204i
$803$	2.53590	+	4.39230i	0.0894899	+	0.155001i
$804$	9.12436	−	5.26795i	0.321791	−	0.185786i
$805$	9.46410			0.333566
$806$		0			0
$807$	−5.75129			−0.202455
$808$	19.3923	−	11.1962i	0.682219	−	0.393879i
$809$	4.73205	+	8.19615i	0.166370	+	0.288161i	0.937141	−	0.348951i	$-0.113462\pi$
$809$	4.73205	+	8.19615i	0.166370	+	0.288161i	−0.770771	+	0.637112i	$0.780129\pi$
$810$	−3.86603	+	6.69615i	−0.135838	+	0.235279i
$811$		−	28.1962i		−	0.990101i	−0.868864	−	0.495050i	$-0.835150\pi$
$811$		−	28.1962i		−	0.990101i	0.868864	−	0.495050i	$-0.164850\pi$
$812$	−16.3923	−	9.46410i	−0.575257	−	0.332125i
$813$	−13.3013	−	7.67949i	−0.466496	−	0.269332i
$814$			8.78461i			0.307900i
$815$	3.19615	−	5.53590i	0.111956	−	0.193914i
$816$	6.33975	+	10.9808i	0.221936	+	0.384404i
$817$	37.0526	−	21.3923i	1.29630	−	0.748422i
$818$	66.4974			2.32503
$819$		0			0
$820$	3.46410			0.120972
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.261669	−	0.965158i	$-0.415727\pi$
$821$	35.1962	−	20.3205i	1.22835	−	0.709191i	0.966685	+	0.255967i	$0.0823939\pi$
$822$	−8.19615	−	14.1962i	−0.285874	−	0.495148i
$823$	−23.2942	+	40.3468i	−0.811986	+	1.40640i	0.0994864	+	0.995039i	$0.468280\pi$
$823$	−23.2942	+	40.3468i	−0.811986	+	1.40640i	−0.911472	+	0.411362i	$0.865053\pi$
$824$			17.6603i			0.615224i
$825$	0.803848	+	0.464102i	0.0279864	+	0.0161579i
$826$	45.3731	+	26.1962i	1.57873	+	0.911481i
$827$			18.0000i			0.625921i	0.949766	+	0.312961i	$0.101321\pi$
$827$			18.0000i			0.625921i	−0.949766	+	0.312961i	$0.898679\pi$
$828$	5.83013	−	10.0981i	0.202611	−	0.350932i
$829$	−10.1962	−	17.6603i	−0.354127	−	0.613366i	0.632841	−	0.774282i	$-0.281889\pi$
$829$	−10.1962	−	17.6603i	−0.354127	−	0.613366i	−0.986968	+	0.160916i	$0.948555\pi$
$830$	9.00000	−	5.19615i	0.312395	−	0.180361i
$831$	−4.10512			−0.142405
$832$		0			0
$833$	−10.3923			−0.360072
$834$	−9.21539	+	5.32051i	−0.319103	+	0.184234i
$835$	6.46410	+	11.1962i	0.223699	+	0.387459i
$836$	−2.66025	+	4.60770i	−0.0920068	+	0.159360i
$837$			0.784610i			0.0271201i
$838$	−14.1962	−	8.19615i	−0.490398	−	0.283131i
$839$	−15.2942	−	8.83013i	−0.528015	−	0.304850i	0.212193	−	0.977228i	$-0.431940\pi$
$839$	−15.2942	−	8.83013i	−0.528015	−	0.304850i	−0.740208	+	0.672378i	$0.765273\pi$
$840$		−	2.53590i		−	0.0874968i
$841$	−30.2846	+	52.4545i	−1.04430	+	1.80878i
$842$	9.33975	+	16.1769i	0.321869	+	0.557493i
$843$	−1.01924	+	0.588457i	−0.0351044	+	0.0202675i
$844$	−8.00000			−0.275371
$845$		0			0
$846$	−25.6077			−0.880411
$847$	16.2679	−	9.39230i	0.558973	−	0.322723i
$848$	−25.9808	−	45.0000i	−0.892183	−	1.54531i
$849$	−0.516660	+	0.894882i	−0.0177317	+	0.0307123i
$850$		−	6.00000i		−	0.205798i
$851$	−16.3923	−	9.46410i	−0.561921	−	0.324425i
$852$	0.803848	+	0.464102i	0.0275394	+	0.0158999i
$853$			8.00000i			0.273915i	0.990577	+	0.136957i	$0.0437323\pi$
$853$			8.00000i			0.273915i	−0.990577	+	0.136957i	$0.956268\pi$
$854$	−21.4641	+	37.1769i	−0.734486	+	1.27217i
$855$	5.16987	+	8.95448i	0.176806	+	0.306237i
$856$	−0.509619	+	0.294229i	−0.0174184	+	0.0100565i
$857$	−47.5692			−1.62493			−0.812467	−	0.583007i	$-0.801876\pi$
$857$	−47.5692			−1.62493			−0.812467	+	0.583007i	$0.801876\pi$
$858$		0			0
$859$	45.1769			1.54142			0.770708	−	0.637188i	$-0.219903\pi$
$859$	45.1769			1.54142			0.770708	+	0.637188i	$0.219903\pi$
$860$	8.83013	−	5.09808i	0.301105	−	0.173843i
$861$	−2.53590	−	4.39230i	−0.0864232	−	0.149689i
$862$	16.9019	−	29.2750i	0.575682	−	0.997110i
$863$		−	2.78461i		−	0.0947892i	−0.998876	−	0.0473946i	$-0.984908\pi$
$863$		−	2.78461i		−	0.0947892i	0.998876	−	0.0473946i	$-0.0150918\pi$
$864$	−18.0000	−	10.3923i	−0.612372	−	0.353553i
$865$	13.3923	+	7.73205i	0.455352	+	0.262898i
$866$		−	11.7513i		−	0.399325i
$867$	−1.83013	+	3.16987i	−0.0621544	+	0.107655i
$868$	−0.196152	−	0.339746i	−0.00665785	−	0.0115317i
$869$	−13.6077	+	7.85641i	−0.461609	+	0.266510i
$870$	12.0000			0.406838
$871$		0			0
$872$	−3.46410			−0.117309
$873$	4.26795	−	2.46410i	0.144448	−	0.0833972i
$874$	−17.1962	−	29.7846i	−0.581669	−	1.00748i
$875$	−1.00000	+	1.73205i	−0.0338062	+	0.0585540i
$876$		−	2.92820i		−	0.0989348i
$877$	1.73205	+	1.00000i	0.0584872	+	0.0337676i	0.528958	−	0.848648i	$-0.322583\pi$
$877$	1.73205	+	1.00000i	0.0584872	+	0.0337676i	−0.470471	+	0.882415i	$0.655916\pi$
$878$	−48.0000	−	27.7128i	−1.61992	−	0.935262i
$879$			13.8564i			0.467365i
$880$	3.16987	−	5.49038i	0.106856	−	0.185081i
$881$	−6.33975	−	10.9808i	−0.213591	−	0.369951i	0.739244	−	0.673437i	$-0.235183\pi$
$881$	−6.33975	−	10.9808i	−0.213591	−	0.369951i	−0.952836	+	0.303486i	$0.901849\pi$
$882$	11.0885	−	6.40192i	0.373368	−	0.215564i
$883$	−34.1962			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$883$	−34.1962			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$884$		0			0
$885$	−11.0718			−0.372174
$886$	−52.4711	+	30.2942i	−1.76280	+	1.01775i
$887$	−8.95448	−	15.5096i	−0.300662	−	0.520762i	0.675624	−	0.737246i	$-0.263874\pi$
$887$	−8.95448	−	15.5096i	−0.300662	−	0.520762i	−0.976286	+	0.216484i	$0.930541\pi$
$888$	−2.53590	+	4.39230i	−0.0850992	+	0.147396i
$889$		−	11.6077i		−	0.389310i
$890$	−1.39230	−	0.803848i	−0.0466702	−	0.0269450i
$891$	4.90192	+	2.83013i	0.164221	+	0.0948128i
$892$			2.00000i			0.0669650i
$893$	−12.5885	+	21.8038i	−0.421257	+	0.729638i
$894$	−12.5885	−	21.8038i	−0.421021	−	0.729230i
$895$	4.39230	−	2.53590i	0.146819	−	0.0847657i
$896$	−24.2487			−0.810093
$897$		0			0
$898$	47.5692			1.58741
$899$	−1.60770	+	0.928203i	−0.0536196	+	0.0309573i
$900$	1.23205	+	2.13397i	0.0410684	+	0.0711325i
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		−	7.60770i		−	0.253309i
$903$	−12.9282	−	7.46410i	−0.430224	−	0.248390i
$904$	23.1962	+	13.3923i	0.771493	+	0.445421i
$905$			20.3923i			0.677863i
$906$	−7.73205	+	13.3923i	−0.256880	+	0.444930i
$907$	19.8827	+	34.4378i	0.660194	+	1.14349i	0.980565	+	0.196197i	$0.0628592\pi$
$907$	19.8827	+	34.4378i	0.660194	+	1.14349i	−0.320371	+	0.947292i	$0.603807\pi$
$908$	3.00000	−	1.73205i	0.0995585	−	0.0574801i
$909$	31.8564			1.05661
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	−13.3013	+	7.67949i	−0.440449	+	0.254293i
$913$	−3.80385	−	6.58846i	−0.125889	−	0.218046i
$914$	−26.6603	+	46.1769i	−0.881843	+	1.52740i
$915$		−	9.07180i		−	0.299904i
$916$	−12.4641	−	7.19615i	−0.411826	−	0.237768i
$917$		0			0
$918$			24.0000i			0.792118i
$919$	26.5885	−	46.0526i	0.877072	−	1.51913i	0.0225335	−	0.999746i	$-0.492827\pi$
$919$	26.5885	−	46.0526i	0.877072	−	1.51913i	0.854539	−	0.519388i	$-0.173840\pi$
$920$	4.09808	+	7.09808i	0.135110	+	0.234017i
$921$	−14.4449	+	8.33975i	−0.475974	+	0.274804i
$922$	−6.00000			−0.197599
$923$		0			0
$924$	1.85641			0.0610713
$925$	3.46410	−	2.00000i	0.113899	−	0.0657596i
$926$	−15.9282	−	27.5885i	−0.523433	−	0.906613i
$927$	−12.5622	+	21.7583i	−0.412596	+	0.714637i
$928$		−	49.1769i		−	1.61431i
$929$	44.5692	+	25.7321i	1.46227	+	0.844241i	0.999116	−	0.0420373i	$-0.0133848\pi$
$929$	44.5692	+	25.7321i	1.46227	+	0.844241i	0.463153	+	0.886279i	$0.346718\pi$
$930$	0.215390	+	0.124356i	0.00706293	+	0.00407778i
$931$		−	12.5885i		−	0.412570i
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	−1.60770	−	2.78461i	−0.0526336	−	0.0911640i
$934$	57.2942	−	33.0788i	1.87472	−	1.08237i
$935$	−4.39230			−0.143644
$936$		0			0
$937$	−6.78461			−0.221644			−0.110822	−	0.993840i	$-0.535348\pi$
$937$	−6.78461			−0.221644			−0.110822	+	0.993840i	$0.535348\pi$
$938$	43.1769	−	24.9282i	1.40978	−	0.813935i
$939$	2.33975	+	4.05256i	0.0763547	+	0.132250i
$940$	−3.00000	+	5.19615i	−0.0978492	+	0.169480i
$941$			31.1769i			1.01634i	0.861257	+	0.508169i	$0.169678\pi$
$941$			31.1769i			1.01634i	−0.861257	+	0.508169i	$0.830322\pi$
$942$	10.9808	+	6.33975i	0.357773	+	0.206560i
$943$	14.1962	+	8.19615i	0.462290	+	0.266903i
$944$			75.6218i			2.46128i
$945$	4.00000	−	6.92820i	0.130120	−	0.225374i
$946$	−11.1962	−	19.3923i	−0.364018	−	0.630498i
$947$	−24.8038	+	14.3205i	−0.806017	+	0.465354i	−0.845571	−	0.533863i	$-0.820740\pi$
$947$	−24.8038	+	14.3205i	−0.806017	+	0.465354i	0.0395540	+	0.999217i	$0.487406\pi$
$948$	9.07180			0.294638
$949$		0			0
$950$	7.26795			0.235803
$951$	15.2154	−	8.78461i	0.493393	−	0.284860i
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	−6.46410	+	11.1962i	−0.209393	+	0.362679i	−0.951523	−	0.307576i	$-0.900482\pi$
$953$	−6.46410	+	11.1962i	−0.209393	+	0.362679i	0.742131	+	0.670255i	$0.233815\pi$
$954$		−	44.3538i		−	1.43601i
$955$	16.3923	+	9.46410i	0.530443	+	0.306251i
$956$	3.29423	+	1.90192i	0.106543	+	0.0615126i
$957$		−	8.78461i		−	0.283966i
$958$	−15.8827	+	27.5096i	−0.513146	+	0.888795i
$959$	−12.9282	−	22.3923i	−0.417473	−	0.723085i
$960$	0.633975	−	0.366025i	0.0204614	−	0.0118134i
$961$	30.9615			0.998759
$962$		0			0
$963$	−0.837169			−0.0269774
$964$	−15.9282	+	9.19615i	−0.513013	+	0.296188i
$965$	−5.00000	−	8.66025i	−0.160956	−	0.278783i
$966$	−6.00000	+	10.3923i	−0.193047	+	0.334367i
$967$			29.6077i			0.952119i	0.879413	+	0.476060i	$0.157935\pi$
$967$			29.6077i			0.952119i	−0.879413	+	0.476060i	$0.842065\pi$
$968$	14.0885	+	8.13397i	0.452820	+	0.261436i
$969$	9.21539	+	5.32051i	0.296041	+	0.170919i
$970$		−	3.46410i		−	0.111226i
$971$	−2.53590	+	4.39230i	−0.0813809	+	0.140956i	−0.903843	−	0.427864i	$-0.859266\pi$
$971$	−2.53590	+	4.39230i	−0.0813809	+	0.140956i	0.822462	+	0.568819i	$0.192600\pi$
$972$	−7.63397	−	13.2224i	−0.244860	−	0.424110i
$973$	−14.5359	+	8.39230i	−0.466000	+	0.269045i
$974$	9.71281			0.311219
$975$		0			0
$976$	−61.9615			−1.98334
$977$	−34.3923	+	19.8564i	−1.10031	+	0.635263i	−0.936302	−	0.351197i	$-0.885775\pi$
$977$	−34.3923	+	19.8564i	−1.10031	+	0.635263i	−0.164006	+	0.986459i	$0.552442\pi$
$978$	4.05256	+	7.01924i	0.129587	+	0.224450i
$979$	−0.588457	+	1.01924i	−0.0188072	+	0.0325750i
$980$		−	3.00000i		−	0.0958315i
$981$	−4.26795	−	2.46410i	−0.136265	−	0.0786727i
$982$	14.1962	+	8.19615i	0.453017	+	0.261550i
$983$		−	13.6077i		−	0.434018i	−0.976170	−	0.217009i	$-0.930370\pi$
$983$		−	13.6077i		−	0.434018i	0.976170	−	0.217009i	$-0.0696301\pi$
$984$	2.19615	−	3.80385i	0.0700108	−	0.121262i
$985$	−0.464102	−	0.803848i	−0.0147875	−	0.0256127i
$986$	−49.1769	+	28.3923i	−1.56611	+	0.904195i
$987$	8.78461			0.279617
$988$		0			0
$989$	48.2487			1.53422
$990$	4.68653	−	2.70577i	0.148948	−	0.0859951i
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	0.509619	−	0.882686i	0.0161804	−	0.0280253i
$993$		−	20.9282i		−	0.664136i
$994$	3.80385	+	2.19615i	0.120651	+	0.0696577i
$995$	17.3205	+	10.0000i	0.549097	+	0.317021i
$996$			4.39230i			0.139176i
$997$	−27.1962	+	47.1051i	−0.861311	+	1.49183i	0.00935346	+	0.999956i	$0.497023\pi$
$997$	−27.1962	+	47.1051i	−0.861311	+	1.49183i	−0.870664	+	0.491878i	$0.836311\pi$
$998$	11.2417	+	19.4711i	0.355849	+	0.616348i
$999$	−13.8564	+	8.00000i	−0.438397	+	0.253109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.a.361.2		4
13.2	odd	12		845.2.a.d.1.1		2
13.3	even	3		845.2.c.e.506.1		4
13.4	even	6	inner	845.2.m.a.316.2		4
13.5	odd	4		845.2.e.f.146.2		4
13.6	odd	12		845.2.e.f.191.2		4
13.7	odd	12		845.2.e.e.191.1		4
13.8	odd	4		845.2.e.e.146.1		4
13.9	even	3		845.2.m.c.316.2		4
13.10	even	6		845.2.c.e.506.3		4
13.11	odd	12		65.2.a.c.1.2	✓	2
13.12	even	2		845.2.m.c.361.2		4
39.2	even	12		7605.2.a.be.1.2		2
39.11	even	12		585.2.a.k.1.1		2
52.11	even	12		1040.2.a.h.1.2		2
65.24	odd	12		325.2.a.g.1.1		2
65.37	even	12		325.2.b.e.274.3		4
65.54	odd	12		4225.2.a.w.1.2		2
65.63	even	12		325.2.b.e.274.2		4
91.76	even	12		3185.2.a.k.1.2		2
104.11	even	12		4160.2.a.bj.1.1		2
104.37	odd	12		4160.2.a.y.1.2		2
143.76	even	12		7865.2.a.h.1.1		2
156.11	odd	12		9360.2.a.cm.1.2		2
195.89	even	12		2925.2.a.z.1.2		2
195.128	odd	12		2925.2.c.v.2224.3		4
195.167	odd	12		2925.2.c.v.2224.2		4
260.219	even	12		5200.2.a.ca.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.c.1.2	✓	2	13.11	odd	12
325.2.a.g.1.1		2	65.24	odd	12
325.2.b.e.274.2		4	65.63	even	12
325.2.b.e.274.3		4	65.37	even	12
585.2.a.k.1.1		2	39.11	even	12
845.2.a.d.1.1		2	13.2	odd	12
845.2.c.e.506.1		4	13.3	even	3
845.2.c.e.506.3		4	13.10	even	6
845.2.e.e.146.1		4	13.8	odd	4
845.2.e.e.191.1		4	13.7	odd	12
845.2.e.f.146.2		4	13.5	odd	4
845.2.e.f.191.2		4	13.6	odd	12
845.2.m.a.316.2		4	13.4	even	6	inner
845.2.m.a.361.2		4	1.1	even	1	trivial
845.2.m.c.316.2		4	13.9	even	3
845.2.m.c.361.2		4	13.12	even	2
1040.2.a.h.1.2		2	52.11	even	12
2925.2.a.z.1.2		2	195.89	even	12
2925.2.c.v.2224.2		4	195.167	odd	12
2925.2.c.v.2224.3		4	195.128	odd	12
3185.2.a.k.1.2		2	91.76	even	12
4160.2.a.y.1.2		2	104.37	odd	12
4160.2.a.bj.1.1		2	104.11	even	12
4225.2.a.w.1.2		2	65.54	odd	12
5200.2.a.ca.1.1		2	260.219	even	12
7605.2.a.be.1.2		2	39.2	even	12
7865.2.a.h.1.1		2	143.76	even	12
9360.2.a.cm.1.2		2	156.11	odd	12

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.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.09808 - 0.633975i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.73205i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} +(0.366025 + 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-1.09808 - 0.633975i) q^{6} +(-1.73205 - 1.00000i) q^{7} -1.73205i q^{8} +(1.23205 - 2.13397i) q^{9} +(-0.866025 - 1.50000i) q^{10} +(-1.09808 + 0.633975i) q^{11} +0.732051 q^{12} +3.46410 q^{14} +(-0.633975 + 0.366025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(1.73205 - 3.00000i) q^{17} +4.26795i q^{18} +(3.63397 + 2.09808i) q^{19} +(0.866025 + 0.500000i) q^{20} -1.46410i q^{21} +(1.09808 - 1.90192i) q^{22} +(2.36603 + 4.09808i) q^{23} +(1.09808 - 0.633975i) q^{24} -1.00000 q^{25} +4.00000 q^{27} +(-1.73205 + 1.00000i) q^{28} +(4.73205 + 8.19615i) q^{29} +(0.633975 - 1.09808i) q^{30} +0.196152i q^{31} +(-4.50000 - 2.59808i) q^{32} +(-0.803848 - 0.464102i) q^{33} +6.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(-1.23205 - 2.13397i) q^{36} +(-3.46410 + 2.00000i) q^{37} -7.26795 q^{38} +1.73205 q^{40} +(3.00000 - 1.73205i) q^{41} +(1.26795 + 2.19615i) q^{42} +(5.09808 - 8.83013i) q^{43} +1.26795i q^{44} +(2.13397 + 1.23205i) q^{45} +(-7.09808 - 4.09808i) q^{46} +6.00000i q^{47} +(-1.83013 + 3.16987i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(1.50000 - 0.866025i) q^{50} +2.53590 q^{51} -10.3923 q^{53} +(-6.00000 + 3.46410i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(-1.73205 + 3.00000i) q^{56} +3.07180i q^{57} +(-14.1962 - 8.19615i) q^{58} +(13.0981 + 7.56218i) q^{59} +0.732051i q^{60} +(-6.19615 + 10.7321i) q^{61} +(-0.169873 - 0.294229i) q^{62} +(-4.26795 + 2.46410i) q^{63} -1.00000 q^{64} +1.60770 q^{66} +(12.4641 - 7.19615i) q^{67} +(-1.73205 - 3.00000i) q^{68} +(-1.73205 + 3.00000i) q^{69} +3.46410i q^{70} +(1.09808 + 0.633975i) q^{71} +(-3.69615 - 2.13397i) q^{72} -4.00000i q^{73} +(3.46410 - 6.00000i) q^{74} +(-0.366025 - 0.633975i) q^{75} +(3.63397 - 2.09808i) q^{76} +2.53590 q^{77} +12.3923 q^{79} +(-4.33013 + 2.50000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-3.00000 + 5.19615i) q^{82} +6.00000i q^{83} +(-1.26795 - 0.732051i) q^{84} +(3.00000 + 1.73205i) q^{85} +17.6603i q^{86} +(-3.46410 + 6.00000i) q^{87} +(1.09808 + 1.90192i) q^{88} +(0.803848 - 0.464102i) q^{89} -4.26795 q^{90} +4.73205 q^{92} +(-0.124356 + 0.0717968i) q^{93} +(-5.19615 - 9.00000i) q^{94} +(-2.09808 + 3.63397i) q^{95} -3.80385i q^{96} +(1.73205 + 1.00000i) q^{97} +(4.50000 + 2.59808i) q^{98} +3.12436i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q - 6 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 - 2 * q^9	\( 4 q - 6 q^{2} - 2 q^{3} + 2 q^{4} + 6 q^{6} - 2 q^{9} + 6 q^{11} - 4 q^{12} - 6 q^{15} + 10 q^{16} + 18 q^{19} - 6 q^{22} + 6 q^{23} - 6 q^{24} - 4 q^{25} + 16 q^{27} + 12 q^{29} + 6 q^{30} - 18 q^{32} - 24 q^{33} + 4 q^{35} + 2 q^{36} - 36 q^{38} + 12 q^{41} + 12 q^{42} + 10 q^{43} + 12 q^{45} - 18 q^{46} + 10 q^{48} - 6 q^{49} + 6 q^{50} + 24 q^{51} - 24 q^{54} - 6 q^{55} - 36 q^{58} + 42 q^{59} - 4 q^{61} - 18 q^{62} - 24 q^{63} - 4 q^{64} + 48 q^{66} + 36 q^{67} - 6 q^{71} + 6 q^{72} + 2 q^{75} + 18 q^{76} + 24 q^{77} + 8 q^{79} - 2 q^{81} - 12 q^{82} - 12 q^{84} + 12 q^{85} - 6 q^{88} + 24 q^{89} - 24 q^{90} + 12 q^{92} + 48 q^{93} + 2 q^{95} + 18 q^{98}+O(q^{100}) \) 4 * q - 6 * q^2 - 2 * q^3 + 2 * q^4 + 6 * q^6 - 2 * q^9 + 6 * q^11 - 4 * q^12 - 6 * q^15 + 10 * q^16 + 18 * q^19 - 6 * q^22 + 6 * q^23 - 6 * q^24 - 4 * q^25 + 16 * q^27 + 12 * q^29 + 6 * q^30 - 18 * q^32 - 24 * q^33 + 4 * q^35 + 2 * q^36 - 36 * q^38 + 12 * q^41 + 12 * q^42 + 10 * q^43 + 12 * q^45 - 18 * q^46 + 10 * q^48 - 6 * q^49 + 6 * q^50 + 24 * q^51 - 24 * q^54 - 6 * q^55 - 36 * q^58 + 42 * q^59 - 4 * q^61 - 18 * q^62 - 24 * q^63 - 4 * q^64 + 48 * q^66 + 36 * q^67 - 6 * q^71 + 6 * q^72 + 2 * q^75 + 18 * q^76 + 24 * q^77 + 8 * q^79 - 2 * q^81 - 12 * q^82 - 12 * q^84 + 12 * q^85 - 6 * q^88 + 24 * q^89 - 24 * q^90 + 12 * q^92 + 48 * q^93 + 2 * q^95 + 18 * q^98

Introduction

L-functions

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Database

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