LMFDB - Embedded newform 845.2.b.f.339.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(339,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.339"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.6
Root			$-1.09445 + 0.895644i$ of defining polynomial
Character	$\chi$	$=$	845.339
Dual form			845.2.b.f.339.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.456850i q^{2} +1.00000i q^{3} +1.79129 q^{4} +(0.456850 + 2.18890i) q^{5} -0.456850 q^{6} +1.73205i q^{7} +1.73205i q^{8} +2.00000 q^{9} +(-1.00000 + 0.208712i) q^{10} +2.64575 q^{11} +1.79129i q^{12} -0.791288 q^{14} +(-2.18890 + 0.456850i) q^{15} +2.79129 q^{16} -4.58258i q^{17} +0.913701i q^{18} +1.73205 q^{19} +(0.818350 + 3.92095i) q^{20} -1.73205 q^{21} +1.20871i q^{22} -4.58258i q^{23} -1.73205 q^{24} +(-4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +3.10260i q^{28} -4.58258 q^{29} +(-0.208712 - 1.00000i) q^{30} -6.20520 q^{31} +4.73930i q^{32} +2.64575i q^{33} +2.09355 q^{34} +(-3.79129 + 0.791288i) q^{35} +3.58258 q^{36} -7.93725i q^{37} +0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +2.64575 q^{41} -0.791288i q^{42} -10.5826i q^{43} +4.73930 q^{44} +(0.913701 + 4.37780i) q^{45} +2.09355 q^{46} +1.82740i q^{47} +2.79129i q^{48} +4.00000 q^{49} +(-0.913701 - 2.09355i) q^{50} +4.58258 q^{51} +7.58258i q^{53} -2.28425 q^{54} +(1.20871 + 5.79129i) q^{55} -3.00000 q^{56} +1.73205i q^{57} -2.09355i q^{58} -13.9518 q^{59} +(-3.92095 + 0.818350i) q^{60} -1.41742 q^{61} -2.83485i q^{62} +3.46410i q^{63} +3.41742 q^{64} -1.20871 q^{66} -1.00905i q^{67} -8.20871i q^{68} +4.58258 q^{69} +(-0.361500 - 1.73205i) q^{70} -7.02355 q^{71} +3.46410i q^{72} +3.62614 q^{74} +(-2.00000 - 4.58258i) q^{75} +3.10260 q^{76} +4.58258i q^{77} +6.00000 q^{79} +(1.27520 + 6.10985i) q^{80} +1.00000 q^{81} +1.20871i q^{82} +6.01450i q^{83} -3.10260 q^{84} +(10.0308 - 2.09355i) q^{85} +4.83465 q^{86} -4.58258i q^{87} +4.58258i q^{88} -9.57395 q^{89} +(-2.00000 + 0.417424i) q^{90} -8.20871i q^{92} -6.20520i q^{93} -0.834849 q^{94} +(0.791288 + 3.79129i) q^{95} -4.73930 q^{96} -11.4014i q^{97} +1.82740i q^{98} +5.29150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 16 q^{9} - 8 q^{10} + 12 q^{14} + 4 q^{16} - 20 q^{30} - 12 q^{35} - 8 q^{36} - 12 q^{40} + 32 q^{49} + 28 q^{55} - 24 q^{56} - 48 q^{61} + 64 q^{64} - 28 q^{66} + 84 q^{74} - 16 q^{75}+ \cdots - 12 q^{95}+O(q^{100}) $ 8 * q - 4 * q^4 + 16 * q^9 - 8 * q^10 + 12 * q^14 + 4 * q^16 - 20 * q^30 - 12 * q^35 - 8 * q^36 - 12 * q^40 + 32 * q^49 + 28 * q^55 - 24 * q^56 - 48 * q^61 + 64 * q^64 - 28 * q^66 + 84 * q^74 - 16 * q^75 + 48 * q^79 + 8 * q^81 - 16 * q^90 - 80 * q^94 - 12 * q^95

Character values

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

$n$	$171$	$677$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.456850i			0.323042i	0.986869	+	0.161521i	$0.0516399\pi$
$2$			0.456850i			0.323042i	−0.986869	+	0.161521i	$0.948360\pi$
$3$			1.00000i			0.577350i	0.957427	+	0.288675i	$0.0932147\pi$
$3$			1.00000i			0.577350i	−0.957427	+	0.288675i	$0.906785\pi$
$4$	1.79129			0.895644
$5$	0.456850	+	2.18890i	0.204310	+	0.978906i
$5$	0.456850	+	2.18890i	0.204310	+	0.978906i
$6$	−0.456850			−0.186508
$7$			1.73205i			0.654654i	0.944911	+	0.327327i	$0.106148\pi$
$7$			1.73205i			0.654654i	−0.944911	+	0.327327i	$0.893852\pi$
$8$			1.73205i			0.612372i
$9$	2.00000			0.666667
$10$	−1.00000	+	0.208712i	−0.316228	+	0.0660006i
$11$	2.64575			0.797724			0.398862	−	0.917011i	$-0.369405\pi$
$11$	2.64575			0.797724			0.398862	+	0.917011i	$0.369405\pi$
$12$			1.79129i			0.517100i
$13$		0			0
$13$		0			0
$14$	−0.791288			−0.211481
$15$	−2.18890	+	0.456850i	−0.565172	+	0.117958i
$16$	2.79129			0.697822
$17$		−	4.58258i		−	1.11144i	−0.831370	−	0.555719i	$-0.812443\pi$
$17$		−	4.58258i		−	1.11144i	0.831370	−	0.555719i	$-0.187557\pi$
$18$			0.913701i			0.215361i
$19$	1.73205			0.397360			0.198680	−	0.980064i	$-0.436335\pi$
$19$	1.73205			0.397360			0.198680	+	0.980064i	$0.436335\pi$
$20$	0.818350	+	3.92095i	0.182989	+	0.876751i
$21$	−1.73205			−0.377964
$22$			1.20871i			0.257698i
$23$		−	4.58258i		−	0.955533i	−0.878487	−	0.477767i	$-0.841446\pi$
$23$		−	4.58258i		−	0.955533i	0.878487	−	0.477767i	$-0.158554\pi$
$24$	−1.73205			−0.353553
$25$	−4.58258	+	2.00000i	−0.916515	+	0.400000i
$26$		0			0
$27$			5.00000i			0.962250i
$28$			3.10260i			0.586337i
$29$	−4.58258			−0.850963			−0.425481	−	0.904967i	$-0.639895\pi$
$29$	−4.58258			−0.850963			−0.425481	+	0.904967i	$0.639895\pi$
$30$	−0.208712	−	1.00000i	−0.0381055	−	0.182574i
$31$	−6.20520			−1.11449			−0.557244	−	0.830349i	$-0.688141\pi$
$31$	−6.20520			−1.11449			−0.557244	+	0.830349i	$0.688141\pi$
$32$			4.73930i			0.837798i
$33$			2.64575i			0.460566i
$34$	2.09355			0.359041
$35$	−3.79129	+	0.791288i	−0.640845	+	0.133752i
$36$	3.58258			0.597096
$37$		−	7.93725i		−	1.30488i	−0.757842	−	0.652438i	$-0.773746\pi$
$37$		−	7.93725i		−	1.30488i	0.757842	−	0.652438i	$-0.226254\pi$
$38$			0.791288i			0.128364i
$39$		0			0
$40$	−3.79129	+	0.791288i	−0.599455	+	0.125114i
$41$	2.64575			0.413197			0.206598	−	0.978426i	$-0.433761\pi$
$41$	2.64575			0.413197			0.206598	+	0.978426i	$0.433761\pi$
$42$		−	0.791288i		−	0.122098i
$43$		−	10.5826i		−	1.61383i	−0.590669	−	0.806914i	$-0.701136\pi$
$43$		−	10.5826i		−	1.61383i	0.590669	−	0.806914i	$-0.298864\pi$
$44$	4.73930			0.714477
$45$	0.913701	+	4.37780i	0.136206	+	0.652604i
$46$	2.09355			0.308677
$47$			1.82740i			0.266554i	0.991079	+	0.133277i	$0.0425500\pi$
$47$			1.82740i			0.266554i	−0.991079	+	0.133277i	$0.957450\pi$
$48$			2.79129i			0.402888i
$49$	4.00000			0.571429
$50$	−0.913701	−	2.09355i	−0.129217	−	0.296073i
$51$	4.58258			0.641689
$52$		0			0
$53$			7.58258i			1.04155i	0.853695	+	0.520773i	$0.174356\pi$
$53$			7.58258i			1.04155i	−0.853695	+	0.520773i	$0.825644\pi$
$54$	−2.28425			−0.310847
$55$	1.20871	+	5.79129i	0.162983	+	0.780897i
$56$	−3.00000			−0.400892
$57$			1.73205i			0.229416i
$58$		−	2.09355i		−	0.274897i
$59$	−13.9518			−1.81636			−0.908182	−	0.418576i	$-0.862530\pi$
$59$	−13.9518			−1.81636			−0.908182	+	0.418576i	$0.862530\pi$
$60$	−3.92095	+	0.818350i	−0.506193	+	0.105649i
$61$	−1.41742			−0.181483			−0.0907413	−	0.995874i	$-0.528924\pi$
$61$	−1.41742			−0.181483			−0.0907413	+	0.995874i	$0.528924\pi$
$62$		−	2.83485i		−	0.360026i
$63$			3.46410i			0.436436i
$64$	3.41742			0.427178
$65$		0			0
$66$	−1.20871			−0.148782
$67$		−	1.00905i		−	0.123275i	−0.998099	−	0.0616376i	$-0.980368\pi$
$67$		−	1.00905i		−	0.123275i	0.998099	−	0.0616376i	$-0.0196323\pi$
$68$		−	8.20871i		−	0.995453i
$69$	4.58258			0.551677
$70$	−0.361500	−	1.73205i	−0.0432075	−	0.207020i
$71$	−7.02355			−0.833542			−0.416771	−	0.909011i	$-0.636838\pi$
$71$	−7.02355			−0.833542			−0.416771	+	0.909011i	$0.636838\pi$
$72$			3.46410i			0.408248i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	3.62614			0.421530
$75$	−2.00000	−	4.58258i	−0.230940	−	0.529150i
$76$	3.10260			0.355893
$77$			4.58258i			0.522233i
$78$		0			0
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$	1.27520	+	6.10985i	0.142572	+	0.683102i
$81$	1.00000			0.111111
$82$			1.20871i			0.133480i
$83$			6.01450i			0.660177i	0.943950	+	0.330089i	$0.107079\pi$
$83$			6.01450i			0.660177i	−0.943950	+	0.330089i	$0.892921\pi$
$84$	−3.10260			−0.338522
$85$	10.0308	−	2.09355i	1.08799	−	0.227077i
$86$	4.83465			0.521334
$87$		−	4.58258i		−	0.491304i
$88$			4.58258i			0.488504i
$89$	−9.57395			−1.01484			−0.507419	−	0.861700i	$-0.669400\pi$
$89$	−9.57395			−1.01484			−0.507419	+	0.861700i	$0.669400\pi$
$90$	−2.00000	+	0.417424i	−0.210819	+	0.0440004i
$91$		0			0
$92$		−	8.20871i		−	0.855817i
$93$		−	6.20520i		−	0.643450i
$94$	−0.834849			−0.0861081
$95$	0.791288	+	3.79129i	0.0811844	+	0.388978i
$96$	−4.73930			−0.483703
$97$		−	11.4014i		−	1.15763i	−0.815458	−	0.578816i	$-0.803515\pi$
$97$		−	11.4014i		−	1.15763i	0.815458	−	0.578816i	$-0.196485\pi$
$98$			1.82740i			0.184595i
$99$	5.29150			0.531816
$100$	−8.20871	+	3.58258i	−0.820871	+	0.358258i
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$			2.09355i			0.207292i
$103$		−	3.16515i		−	0.311872i	−0.987767	−	0.155936i	$-0.950161\pi$
$103$		−	3.16515i		−	0.311872i	0.987767	−	0.155936i	$-0.0498393\pi$
$104$		0			0
$105$	−0.791288	−	3.79129i	−0.0772218	−	0.369992i
$106$	−3.46410			−0.336463
$107$			10.5826i			1.02306i	0.859267	+	0.511528i	$0.170920\pi$
$107$			10.5826i			1.02306i	−0.859267	+	0.511528i	$0.829080\pi$
$108$			8.95644i			0.861834i
$109$	13.1334			1.25795			0.628976	−	0.777425i	$-0.283474\pi$
$109$	13.1334			1.25795			0.628976	+	0.777425i	$0.283474\pi$
$110$	−2.64575	+	0.552200i	−0.252262	+	0.0526502i
$111$	7.93725			0.753371
$112$			4.83465i			0.456832i
$113$		−	7.41742i		−	0.697773i	−0.937165	−	0.348886i	$-0.886560\pi$
$113$		−	7.41742i		−	0.697773i	0.937165	−	0.348886i	$-0.113440\pi$
$114$	−0.791288			−0.0741109
$115$	10.0308	−	2.09355i	0.935377	−	0.195225i
$116$	−8.20871			−0.762160
$117$		0			0
$118$		−	6.37386i		−	0.586762i
$119$	7.93725			0.727607
$120$	−0.791288	−	3.79129i	−0.0722344	−	0.346096i
$121$	−4.00000			−0.363636
$122$		−	0.647551i		−	0.0586265i
$123$			2.64575i			0.238559i
$124$	−11.1153			−0.998184
$125$	−6.47135	−	9.11710i	−0.578815	−	0.815459i
$126$	−1.58258			−0.140987
$127$			17.7477i			1.57486i	0.616407	+	0.787428i	$0.288588\pi$
$127$			17.7477i			1.57486i	−0.616407	+	0.787428i	$0.711412\pi$
$128$			11.0399i			0.975795i
$129$	10.5826			0.931744
$130$		0			0
$131$	−7.58258			−0.662493			−0.331246	−	0.943544i	$-0.607469\pi$
$131$	−7.58258			−0.662493			−0.331246	+	0.943544i	$0.607469\pi$
$132$			4.73930i			0.412503i
$133$			3.00000i			0.260133i
$134$	0.460985			0.0398230
$135$	−10.9445	+	2.28425i	−0.941953	+	0.196597i
$136$	7.93725			0.680614
$137$		−	10.4877i		−	0.896021i	−0.894028	−	0.448010i	$-0.852133\pi$
$137$		−	10.4877i		−	0.896021i	0.894028	−	0.448010i	$-0.147867\pi$
$138$			2.09355i			0.178215i
$139$	21.7477			1.84462			0.922309	−	0.386453i	$-0.126300\pi$
$139$	21.7477			1.84462			0.922309	+	0.386453i	$0.126300\pi$
$140$	−6.79129	+	1.41742i	−0.573969	+	0.119794i
$141$	−1.82740			−0.153895
$142$		−	3.20871i		−	0.269269i
$143$		0			0
$144$	5.58258			0.465215
$145$	−2.09355	−	10.0308i	−0.173860	−	0.833013i
$146$		0			0
$147$			4.00000i			0.329914i
$148$		−	14.2179i		−	1.16870i
$149$	16.6929			1.36753			0.683766	−	0.729701i	$-0.260341\pi$
$149$	16.6929			1.36753			0.683766	+	0.729701i	$0.260341\pi$
$150$	2.09355	−	0.913701i	0.170938	−	0.0746033i
$151$	−9.66930			−0.786877			−0.393438	−	0.919351i	$-0.628715\pi$
$151$	−9.66930			−0.786877			−0.393438	+	0.919351i	$0.628715\pi$
$152$			3.00000i			0.243332i
$153$		−	9.16515i		−	0.740959i
$154$	−2.09355			−0.168703
$155$	−2.83485	−	13.5826i	−0.227701	−	1.09098i
$156$		0			0
$157$		−	9.16515i		−	0.731459i	−0.930721	−	0.365729i	$-0.880820\pi$
$157$		−	9.16515i		−	0.731459i	0.930721	−	0.365729i	$-0.119180\pi$
$158$			2.74110i			0.218070i
$159$	−7.58258			−0.601337
$160$	−10.3739	+	2.16515i	−0.820126	+	0.171170i
$161$	7.93725			0.625543
$162$			0.456850i			0.0358935i
$163$		−	21.0707i		−	1.65038i	−0.564854	−	0.825191i	$-0.691068\pi$
$163$		−	21.0707i		−	1.65038i	0.564854	−	0.825191i	$-0.308932\pi$
$164$	4.73930			0.370077
$165$	−5.79129	+	1.20871i	−0.450851	+	0.0940981i
$166$	−2.74773			−0.213265
$167$			9.57395i			0.740855i	0.928861	+	0.370427i	$0.120789\pi$
$167$			9.57395i			0.740855i	−0.928861	+	0.370427i	$0.879211\pi$
$168$		−	3.00000i		−	0.231455i
$169$		0			0
$170$	0.956439	+	4.58258i	0.0733555	+	0.351468i
$171$	3.46410			0.264906
$172$		−	18.9564i		−	1.44541i
$173$			16.5826i			1.26075i	0.776291	+	0.630375i	$0.217099\pi$
$173$			16.5826i			1.26075i	−0.776291	+	0.630375i	$0.782901\pi$
$174$	2.09355			0.158712
$175$	−3.46410	−	7.93725i	−0.261861	−	0.600000i
$176$	7.38505			0.556669
$177$		−	13.9518i		−	1.04868i
$178$		−	4.37386i		−	0.327835i
$179$	18.1652			1.35773			0.678864	−	0.734264i	$-0.262473\pi$
$179$	18.1652			1.35773			0.678864	+	0.734264i	$0.262473\pi$
$180$	1.63670	+	7.84190i	0.121992	+	0.584501i
$181$	−8.74773			−0.650213			−0.325107	−	0.945677i	$-0.605400\pi$
$181$	−8.74773			−0.650213			−0.325107	+	0.945677i	$0.605400\pi$
$182$		0			0
$183$		−	1.41742i		−	0.104779i
$184$	7.93725			0.585142
$185$	17.3739	−	3.62614i	1.27735	−	0.266599i
$186$	2.83485			0.207861
$187$		−	12.1244i		−	0.886621i
$188$			3.27340i			0.238737i
$189$	−8.66025			−0.629941
$190$	−1.73205	+	0.361500i	−0.125656	+	0.0262260i
$191$	−16.5826			−1.19987			−0.599937	−	0.800048i	$-0.704808\pi$
$191$	−16.5826			−1.19987			−0.599937	+	0.800048i	$0.704808\pi$
$192$			3.41742i			0.246631i
$193$		−	14.8655i		−	1.07004i	−0.844840	−	0.535020i	$-0.820304\pi$
$193$		−	14.8655i		−	1.07004i	0.844840	−	0.535020i	$-0.179696\pi$
$194$	5.20871			0.373964
$195$		0			0
$196$	7.16515			0.511797
$197$		−	14.6748i		−	1.04553i	−0.852476	−	0.522767i	$-0.824900\pi$
$197$		−	14.6748i		−	1.04553i	0.852476	−	0.522767i	$-0.175100\pi$
$198$			2.41742i			0.171799i
$199$	10.5826			0.750179			0.375089	−	0.926989i	$-0.377612\pi$
$199$	10.5826			0.750179			0.375089	+	0.926989i	$0.377612\pi$
$200$	−3.46410	−	7.93725i	−0.244949	−	0.561249i
$201$	1.00905			0.0711729
$202$		−	4.11165i		−	0.289295i
$203$		−	7.93725i		−	0.557086i
$204$	8.20871			0.574725
$205$	1.20871	+	5.79129i	0.0844201	+	0.404481i
$206$	1.44600			0.100748
$207$		−	9.16515i		−	0.637022i
$208$		0			0
$209$	4.58258			0.316983
$210$	1.73205	−	0.361500i	0.119523	−	0.0249459i
$211$	−0.165151			−0.0113695			−0.00568475	−	0.999984i	$-0.501810\pi$
$211$	−0.165151			−0.0113695			−0.00568475	+	0.999984i	$0.501810\pi$
$212$			13.5826i			0.932855i
$213$		−	7.02355i		−	0.481246i
$214$	−4.83465			−0.330490
$215$	23.1642	−	4.83465i	1.57979	−	0.329721i
$216$	−8.66025			−0.589256
$217$		−	10.7477i		−	0.729603i
$218$			6.00000i			0.406371i
$219$		0			0
$220$	2.16515	+	10.3739i	0.145974	+	0.699406i
$221$		0			0
$222$			3.62614i			0.243370i
$223$		−	8.66025i		−	0.579934i	−0.957037	−	0.289967i	$-0.906356\pi$
$223$		−	8.66025i		−	0.579934i	0.957037	−	0.289967i	$-0.0936443\pi$
$224$	−8.20871			−0.548468
$225$	−9.16515	+	4.00000i	−0.611010	+	0.266667i
$226$	3.38865			0.225410
$227$			0.818350i			0.0543158i	0.999631	+	0.0271579i	$0.00864569\pi$
$227$			0.818350i			0.0543158i	−0.999631	+	0.0271579i	$0.991354\pi$
$228$			3.10260i			0.205475i
$229$	26.2668			1.73576			0.867880	−	0.496774i	$-0.165482\pi$
$229$	26.2668			1.73576			0.867880	+	0.496774i	$0.165482\pi$
$230$	0.956439	+	4.58258i	0.0630657	+	0.302166i
$231$	−4.58258			−0.301511
$232$		−	7.93725i		−	0.521106i
$233$		−	2.83485i		−	0.185717i	−0.995679	−	0.0928586i	$-0.970400\pi$
$233$		−	2.83485i		−	0.185717i	0.995679	−	0.0928586i	$-0.0296004\pi$
$234$		0			0
$235$	−4.00000	+	0.834849i	−0.260931	+	0.0544595i
$236$	−24.9916			−1.62682
$237$			6.00000i			0.389742i
$238$			3.62614i			0.235048i
$239$	−0.190700			−0.0123354			−0.00616769	−	0.999981i	$-0.501963\pi$
$239$	−0.190700			−0.0123354			−0.00616769	+	0.999981i	$0.501963\pi$
$240$	−6.10985	+	1.27520i	−0.394389	+	0.0823138i
$241$	−1.73205			−0.111571			−0.0557856	−	0.998443i	$-0.517766\pi$
$241$	−1.73205			−0.111571			−0.0557856	+	0.998443i	$0.517766\pi$
$242$		−	1.82740i		−	0.117470i
$243$			16.0000i			1.02640i
$244$	−2.53901			−0.162544
$245$	1.82740	+	8.75560i	0.116748	+	0.559375i
$246$	−1.20871			−0.0770647
$247$		0			0
$248$		−	10.7477i		−	0.682481i
$249$	−6.01450			−0.381154
$250$	4.16515	−	2.95644i	0.263427	−	0.186982i
$251$	0.165151			0.0104243			0.00521213	−	0.999986i	$-0.498341\pi$
$251$	0.165151			0.0104243			0.00521213	+	0.999986i	$0.498341\pi$
$252$			6.20520i			0.390891i
$253$		−	12.1244i		−	0.762252i
$254$	−8.10805			−0.508745
$255$	2.09355	+	10.0308i	0.131103	+	0.628153i
$256$	1.79129			0.111955
$257$		−	18.1652i		−	1.13311i	−0.824024	−	0.566556i	$-0.808276\pi$
$257$		−	18.1652i		−	1.13311i	0.824024	−	0.566556i	$-0.191724\pi$
$258$			4.83465i			0.300992i
$259$	13.7477			0.854242
$260$		0			0
$261$	−9.16515			−0.567309
$262$		−	3.46410i		−	0.214013i
$263$			9.00000i			0.554964i	0.960731	+	0.277482i	$0.0894999\pi$
$263$			9.00000i			0.554964i	−0.960731	+	0.277482i	$0.910500\pi$
$264$	−4.58258			−0.282038
$265$	−16.5975	+	3.46410i	−1.01958	+	0.212798i
$266$	−1.37055			−0.0840339
$267$		−	9.57395i		−	0.585917i
$268$		−	1.80750i		−	0.110411i
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$	−1.04356	−	5.00000i	−0.0635091	−	0.304290i
$271$	−8.66025			−0.526073			−0.263036	−	0.964786i	$-0.584724\pi$
$271$	−8.66025			−0.526073			−0.263036	+	0.964786i	$0.584724\pi$
$272$		−	12.7913i		−	0.775586i
$273$		0			0
$274$	4.79129			0.289452
$275$	−12.1244	+	5.29150i	−0.731126	+	0.319090i
$276$	8.20871			0.494106
$277$		−	7.41742i		−	0.445670i	−0.974856	−	0.222835i	$-0.928469\pi$
$277$		−	7.41742i		−	0.445670i	0.974856	−	0.222835i	$-0.0715311\pi$
$278$			9.93545i			0.595889i
$279$	−12.4104			−0.742992
$280$	−1.37055	−	6.56670i	−0.0819061	−	0.392436i
$281$	3.65480			0.218027			0.109014	−	0.994040i	$-0.465231\pi$
$281$	3.65480			0.218027			0.109014	+	0.994040i	$0.465231\pi$
$282$		−	0.834849i		−	0.0497145i
$283$			27.7477i			1.64943i	0.565548	+	0.824716i	$0.308665\pi$
$283$			27.7477i			1.64943i	−0.565548	+	0.824716i	$0.691335\pi$
$284$	−12.5812			−0.746557
$285$	−3.79129	+	0.791288i	−0.224577	+	0.0468718i
$286$		0			0
$287$			4.58258i			0.270501i
$288$			9.47860i			0.558532i
$289$	−4.00000			−0.235294
$290$	4.58258	−	0.956439i	0.269098	−	0.0561640i
$291$	11.4014			0.668359
$292$		0			0
$293$			18.1389i			1.05968i	0.848097	+	0.529842i	$0.177749\pi$
$293$			18.1389i			1.05968i	−0.848097	+	0.529842i	$0.822251\pi$
$294$	−1.82740			−0.106576
$295$	−6.37386	−	30.5390i	−0.371101	−	1.77805i
$296$	13.7477			0.799070
$297$			13.2288i			0.767610i
$298$			7.62614i			0.441770i
$299$		0			0
$300$	−3.58258	−	8.20871i	−0.206840	−	0.473930i
$301$	18.3296			1.05650
$302$		−	4.41742i		−	0.254194i
$303$		−	9.00000i		−	0.517036i
$304$	4.83465			0.277286
$305$	−0.647551	−	3.10260i	−0.0370786	−	0.177654i
$306$	4.18710			0.239361
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$			8.20871i			0.467735i
$309$	3.16515			0.180059
$310$	6.20520	−	1.29510i	0.352432	−	0.0735568i
$311$	−7.58258			−0.429968			−0.214984	−	0.976618i	$-0.568970\pi$
$311$	−7.58258			−0.429968			−0.214984	+	0.976618i	$0.568970\pi$
$312$		0			0
$313$		−	3.25227i		−	0.183829i	−0.995767	−	0.0919147i	$-0.970701\pi$
$313$		−	3.25227i		−	0.183829i	0.995767	−	0.0919147i	$-0.0292987\pi$
$314$	4.18710			0.236292
$315$	−7.58258	+	1.58258i	−0.427230	+	0.0891680i
$316$	10.7477			0.604607
$317$			0.190700i			0.0107108i	0.999986	+	0.00535540i	$0.00170469\pi$
$317$			0.190700i			0.0107108i	−0.999986	+	0.00535540i	$0.998295\pi$
$318$		−	3.46410i		−	0.194257i
$319$	−12.1244			−0.678834
$320$	1.56125	+	7.48040i	0.0872766	+	0.418167i
$321$	−10.5826			−0.590662
$322$			3.62614i			0.202077i
$323$		−	7.93725i		−	0.441641i
$324$	1.79129			0.0995160
$325$		0			0
$326$	9.62614			0.533142
$327$			13.1334i			0.726279i
$328$			4.58258i			0.253030i
$329$	−3.16515			−0.174500
$330$	−0.552200	−	2.64575i	−0.0303976	−	0.145644i
$331$	4.47315			0.245867			0.122933	−	0.992415i	$-0.460770\pi$
$331$	4.47315			0.245867			0.122933	+	0.992415i	$0.460770\pi$
$332$			10.7737i			0.591284i
$333$		−	15.8745i		−	0.869918i
$334$	−4.37386			−0.239327
$335$	2.20871	−	0.460985i	0.120675	−	0.0251863i
$336$	−4.83465			−0.263752
$337$			30.7477i			1.67494i	0.546487	+	0.837468i	$0.315965\pi$
$337$			30.7477i			1.67494i	−0.546487	+	0.837468i	$0.684035\pi$
$338$		0			0
$339$	7.41742			0.402859
$340$	17.9681	−	3.75015i	0.974455	−	0.203381i
$341$	−16.4174			−0.889053
$342$			1.58258i			0.0855759i
$343$			19.0526i			1.02874i
$344$	18.3296			0.988264
$345$	2.09355	+	10.0308i	0.112713	+	0.540040i
$346$	−7.57575			−0.407275
$347$			21.3303i			1.14507i	0.819880	+	0.572535i	$0.194040\pi$
$347$			21.3303i			1.14507i	−0.819880	+	0.572535i	$0.805960\pi$
$348$		−	8.20871i		−	0.440033i
$349$	−2.45505			−0.131416			−0.0657079	−	0.997839i	$-0.520931\pi$
$349$	−2.45505			−0.131416			−0.0657079	+	0.997839i	$0.520931\pi$
$350$	3.62614	−	1.58258i	0.193825	−	0.0845922i
$351$		0			0
$352$			12.5390i			0.668332i
$353$			6.83285i			0.363676i	0.983328	+	0.181838i	$0.0582047\pi$
$353$			6.83285i			0.363676i	−0.983328	+	0.181838i	$0.941795\pi$
$354$	6.37386			0.338767
$355$	−3.20871	−	15.3739i	−0.170301	−	0.815960i
$356$	−17.1497			−0.908933
$357$			7.93725i			0.420084i
$358$			8.29875i			0.438603i
$359$	−19.5293			−1.03072			−0.515359	−	0.856975i	$-0.672341\pi$
$359$	−19.5293			−1.03072			−0.515359	+	0.856975i	$0.672341\pi$
$360$	−7.58258	+	1.58258i	−0.399637	+	0.0834091i
$361$	−16.0000			−0.842105
$362$		−	3.99640i		−	0.210046i
$363$		−	4.00000i		−	0.209946i
$364$		0			0
$365$		0			0
$366$	0.647551			0.0338480
$367$			1.74773i			0.0912306i	0.998959	+	0.0456153i	$0.0145248\pi$
$367$			1.74773i			0.0912306i	−0.998959	+	0.0456153i	$0.985475\pi$
$368$		−	12.7913i		−	0.666792i
$369$	5.29150			0.275465
$370$	1.65660	+	7.93725i	0.0861226	+	0.412638i
$371$	−13.1334			−0.681852
$372$		−	11.1153i		−	0.576302i
$373$		−	13.0000i		−	0.673114i	−0.941663	−	0.336557i	$-0.890737\pi$
$373$		−	13.0000i		−	0.673114i	0.941663	−	0.336557i	$-0.109263\pi$
$374$	5.53901			0.286416
$375$	9.11710	−	6.47135i	0.470805	−	0.334179i
$376$	−3.16515			−0.163230
$377$		0			0
$378$		−	3.95644i		−	0.203497i
$379$	−10.6784			−0.548510			−0.274255	−	0.961657i	$-0.588431\pi$
$379$	−10.6784			−0.548510			−0.274255	+	0.961657i	$0.588431\pi$
$380$	1.41742	+	6.79129i	0.0727123	+	0.348386i
$381$	−17.7477			−0.909244
$382$		−	7.57575i		−	0.387609i
$383$			23.6211i			1.20698i	0.797371	+	0.603490i	$0.206224\pi$
$383$			23.6211i			1.20698i	−0.797371	+	0.603490i	$0.793776\pi$
$384$	−11.0399			−0.563375
$385$	−10.0308	+	2.09355i	−0.511217	+	0.106697i
$386$	6.79129			0.345667
$387$		−	21.1652i		−	1.07589i
$388$		−	20.4231i		−	1.03683i
$389$	−3.16515			−0.160480			−0.0802398	−	0.996776i	$-0.525569\pi$
$389$	−3.16515			−0.160480			−0.0802398	+	0.996776i	$0.525569\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$			6.92820i			0.349927i
$393$		−	7.58258i		−	0.382490i
$394$	6.70417			0.337751
$395$	2.74110	+	13.1334i	0.137920	+	0.660813i
$396$	9.47860			0.476318
$397$			20.3477i			1.02122i	0.859812	+	0.510610i	$0.170580\pi$
$397$			20.3477i			1.02122i	−0.859812	+	0.510610i	$0.829420\pi$
$398$			4.83465i			0.242339i
$399$	−3.00000			−0.150188
$400$	−12.7913	+	5.58258i	−0.639564	+	0.279129i
$401$	29.8263			1.48945			0.744726	−	0.667370i	$-0.232580\pi$
$401$	29.8263			1.48945			0.744726	+	0.667370i	$0.232580\pi$
$402$			0.460985i			0.0229918i
$403$		0			0
$404$	−16.1216			−0.802079
$405$	0.456850	+	2.18890i	0.0227011	+	0.108767i
$406$	3.62614			0.179962
$407$		−	21.0000i		−	1.04093i
$408$			7.93725i			0.392953i
$409$	−8.66025			−0.428222			−0.214111	−	0.976809i	$-0.568685\pi$
$409$	−8.66025			−0.428222			−0.214111	+	0.976809i	$0.568685\pi$
$410$	−2.64575	+	0.552200i	−0.130664	+	0.0272712i
$411$	10.4877			0.517318
$412$		−	5.66970i		−	0.279326i
$413$		−	24.1652i		−	1.18909i
$414$	4.18710			0.205785
$415$	−13.1652	+	2.74773i	−0.646252	+	0.134881i
$416$		0			0
$417$			21.7477i			1.06499i
$418$			2.09355i			0.102399i
$419$	5.83485			0.285051			0.142526	−	0.989791i	$-0.454478\pi$
$419$	5.83485			0.285051			0.142526	+	0.989791i	$0.454478\pi$
$420$	−1.41742	−	6.79129i	−0.0691632	−	0.331381i
$421$	−5.48220			−0.267186			−0.133593	−	0.991036i	$-0.542652\pi$
$421$	−5.48220			−0.267186			−0.133593	+	0.991036i	$0.542652\pi$
$422$		−	0.0754495i		−	0.00367282i
$423$			3.65480i			0.177703i
$424$	−13.1334			−0.637815
$425$	9.16515	+	21.0000i	0.444575	+	1.01865i
$426$	3.20871			0.155463
$427$		−	2.45505i		−	0.118808i
$428$			18.9564i			0.916294i
$429$		0			0
$430$	2.20871	+	10.5826i	0.106514	+	0.510337i
$431$	8.46955			0.407964			0.203982	−	0.978975i	$-0.434612\pi$
$431$	8.46955			0.407964			0.203982	+	0.978975i	$0.434612\pi$
$432$			13.9564i			0.671479i
$433$		−	9.74773i		−	0.468446i	−0.972183	−	0.234223i	$-0.924745\pi$
$433$		−	9.74773i		−	0.468446i	0.972183	−	0.234223i	$-0.0752546\pi$
$434$	4.91010			0.235692
$435$	10.0308	−	2.09355i	0.480940	−	0.100378i
$436$	23.5257			1.12668
$437$		−	7.93725i		−	0.379690i
$438$		0			0
$439$	−14.4955			−0.691830			−0.345915	−	0.938266i	$-0.612431\pi$
$439$	−14.4955			−0.691830			−0.345915	+	0.938266i	$0.612431\pi$
$440$	−10.0308	+	2.09355i	−0.478200	+	0.0998061i
$441$	8.00000			0.380952
$442$		0			0
$443$			19.9129i			0.946089i	0.881038	+	0.473045i	$0.156845\pi$
$443$			19.9129i			0.946089i	−0.881038	+	0.473045i	$0.843155\pi$
$444$	14.2179			0.674752
$445$	−4.37386	−	20.9564i	−0.207341	−	0.993430i
$446$	3.95644			0.187343
$447$			16.6929i			0.789545i
$448$			5.91915i			0.279654i
$449$	11.0200			0.520064			0.260032	−	0.965600i	$-0.416267\pi$
$449$	11.0200			0.520064			0.260032	+	0.965600i	$0.416267\pi$
$450$	−1.82740	−	4.18710i	−0.0861445	−	0.197382i
$451$	7.00000			0.329617
$452$		−	13.2867i		−	0.624956i
$453$		−	9.66930i		−	0.454304i
$454$	−0.373864			−0.0175463
$455$		0			0
$456$	−3.00000			−0.140488
$457$			1.73205i			0.0810219i	0.999179	+	0.0405110i	$0.0128986\pi$
$457$			1.73205i			0.0810219i	−0.999179	+	0.0405110i	$0.987101\pi$
$458$			12.0000i			0.560723i
$459$	22.9129			1.06948
$460$	17.9681	−	3.75015i	0.837765	−	0.174852i
$461$	−35.8408			−1.66927			−0.834635	−	0.550803i	$-0.814322\pi$
$461$	−35.8408			−1.66927			−0.834635	+	0.550803i	$0.814322\pi$
$462$		−	2.09355i		−	0.0974008i
$463$			39.4002i			1.83108i	0.402223	+	0.915542i	$0.368238\pi$
$463$			39.4002i			1.83108i	−0.402223	+	0.915542i	$0.631762\pi$
$464$	−12.7913			−0.593821
$465$	13.5826	−	2.83485i	0.629877	−	0.131463i
$466$	1.29510			0.0599944
$467$		−	24.3303i		−	1.12587i	−0.826500	−	0.562936i	$-0.809672\pi$
$467$		−	24.3303i		−	1.12587i	0.826500	−	0.562936i	$-0.190328\pi$
$468$		0			0
$469$	1.74773			0.0807025
$470$	−0.381401	−	1.82740i	−0.0175927	−	0.0842917i
$471$	9.16515			0.422308
$472$		−	24.1652i		−	1.11229i
$473$		−	27.9989i		−	1.28739i
$474$	−2.74110			−0.125903
$475$	−7.93725	+	3.46410i	−0.364186	+	0.158944i
$476$	14.2179			0.651677
$477$			15.1652i			0.694365i
$478$		−	0.0871215i		−	0.00398485i
$479$	−4.66385			−0.213097			−0.106548	−	0.994308i	$-0.533980\pi$
$479$	−4.66385			−0.213097			−0.106548	+	0.994308i	$0.533980\pi$
$480$	−2.16515	−	10.3739i	−0.0988252	−	0.473500i
$481$		0			0
$482$		−	0.791288i		−	0.0360422i
$483$			7.93725i			0.361158i
$484$	−7.16515			−0.325689
$485$	24.9564	−	5.20871i	1.13321	−	0.236515i
$486$	−7.30960			−0.331570
$487$			10.6784i			0.483882i	0.970291	+	0.241941i	$0.0777841\pi$
$487$			10.6784i			0.483882i	−0.970291	+	0.241941i	$0.922216\pi$
$488$		−	2.45505i		−	0.111135i
$489$	21.0707			0.952848
$490$	−4.00000	+	0.834849i	−0.180702	+	0.0377146i
$491$	−19.4174			−0.876296			−0.438148	−	0.898903i	$-0.644365\pi$
$491$	−19.4174			−0.876296			−0.438148	+	0.898903i	$0.644365\pi$
$492$			4.73930i			0.213664i
$493$			21.0000i			0.945792i
$494$		0			0
$495$	2.41742	+	11.5826i	0.108655	+	0.520598i
$496$	−17.3205			−0.777714
$497$		−	12.1652i		−	0.545682i
$498$		−	2.74773i		−	0.123129i
$499$	−0.723000			−0.0323659			−0.0161830	−	0.999869i	$-0.505151\pi$
$499$	−0.723000			−0.0323659			−0.0161830	+	0.999869i	$0.505151\pi$
$500$	−11.5921	−	16.3314i	−0.518413	−	0.730361i
$501$	−9.57395			−0.427733
$502$			0.0754495i			0.00336747i
$503$			0.165151i			0.00736374i	0.999993	+	0.00368187i	$0.00117198\pi$
$503$			0.165151i			0.00736374i	−0.999993	+	0.00368187i	$0.998828\pi$
$504$	−6.00000			−0.267261
$505$	−4.11165	−	19.7001i	−0.182966	−	0.876643i
$506$	5.53901			0.246239
$507$		0			0
$508$			31.7913i			1.41051i
$509$	−8.46955			−0.375406			−0.187703	−	0.982226i	$-0.560104\pi$
$509$	−8.46955			−0.375406			−0.187703	+	0.982226i	$0.560104\pi$
$510$	−4.58258	+	0.956439i	−0.202920	+	0.0423518i
$511$		0			0
$512$			22.8981i			1.01196i
$513$			8.66025i			0.382360i
$514$	8.29875			0.366042
$515$	6.92820	−	1.44600i	0.305293	−	0.0637184i
$516$	18.9564			0.834511
$517$			4.83485i			0.212636i
$518$			6.28065i			0.275956i
$519$	−16.5826			−0.727894
$520$		0			0
$521$	27.4955			1.20460			0.602299	−	0.798271i	$-0.294252\pi$
$521$	27.4955			1.20460			0.602299	+	0.798271i	$0.294252\pi$
$522$		−	4.18710i		−	0.183264i
$523$			0.165151i			0.00722157i	0.999993	+	0.00361078i	$0.00114935\pi$
$523$			0.165151i			0.00722157i	−0.999993	+	0.00361078i	$0.998851\pi$
$524$	−13.5826			−0.593358
$525$	7.93725	−	3.46410i	0.346410	−	0.151186i
$526$	−4.11165			−0.179277
$527$			28.4358i			1.23868i
$528$			7.38505i			0.321393i
$529$	2.00000			0.0869565
$530$	−1.58258	−	7.58258i	−0.0687427	−	0.329366i
$531$	−27.9035			−1.21091
$532$			5.37386i			0.232987i
$533$		0			0
$534$	4.37386			0.189276
$535$	−23.1642	+	4.83465i	−1.00148	+	0.209020i
$536$	1.74773			0.0754903
$537$			18.1652i			0.783884i
$538$			6.85275i			0.295443i
$539$	10.5830			0.455842
$540$	−19.6048	+	4.09175i	−0.843655	+	0.176081i
$541$	−10.3923			−0.446800			−0.223400	−	0.974727i	$-0.571716\pi$
$541$	−10.3923			−0.446800			−0.223400	+	0.974727i	$0.571716\pi$
$542$		−	3.95644i		−	0.169944i
$543$		−	8.74773i		−	0.375401i
$544$	21.7182			0.931161
$545$	6.00000	+	28.7477i	0.257012	+	1.23142i
$546$		0			0
$547$		−	28.7477i		−	1.22916i	−0.788853	−	0.614582i	$-0.789325\pi$
$547$		−	28.7477i		−	1.22916i	0.788853	−	0.614582i	$-0.210675\pi$
$548$		−	18.7864i		−	0.802516i
$549$	−2.83485			−0.120988
$550$	−2.41742	−	5.53901i	−0.103079	−	0.236184i
$551$	−7.93725			−0.338138
$552$			7.93725i			0.337832i
$553$			10.3923i			0.441926i
$554$	3.38865			0.143970
$555$	3.62614	+	17.3739i	0.153921	+	0.737479i
$556$	38.9564			1.65212
$557$		−	7.74655i		−	0.328232i	−0.986441	−	0.164116i	$-0.947523\pi$
$557$		−	7.74655i		−	0.328232i	0.986441	−	0.164116i	$-0.0524771\pi$
$558$		−	5.66970i		−	0.240017i
$559$		0			0
$560$	−10.5826	+	2.20871i	−0.447195	+	0.0933351i
$561$	12.1244			0.511891
$562$			1.66970i			0.0704319i
$563$			9.00000i			0.379305i	0.981851	+	0.189652i	$0.0607361\pi$
$563$			9.00000i			0.379305i	−0.981851	+	0.189652i	$0.939264\pi$
$564$	−3.27340			−0.137835
$565$	16.2360	−	3.38865i	0.683054	−	0.142562i
$566$	−12.6766			−0.532835
$567$			1.73205i			0.0727393i
$568$		−	12.1652i		−	0.510438i
$569$	7.74773			0.324802			0.162401	−	0.986725i	$-0.448076\pi$
$569$	7.74773			0.324802			0.162401	+	0.986725i	$0.448076\pi$
$570$	−0.361500	−	1.73205i	−0.0151416	−	0.0725476i
$571$	35.0780			1.46797			0.733985	−	0.679166i	$-0.237658\pi$
$571$	35.0780			1.46797			0.733985	+	0.679166i	$0.237658\pi$
$572$		0			0
$573$		−	16.5826i		−	0.692747i
$574$	−2.09355			−0.0873831
$575$	9.16515	+	21.0000i	0.382213	+	0.875761i
$576$	6.83485			0.284785
$577$			6.92820i			0.288425i	0.989547	+	0.144212i	$0.0460649\pi$
$577$			6.92820i			0.288425i	−0.989547	+	0.144212i	$0.953935\pi$
$578$		−	1.82740i		−	0.0760099i
$579$	14.8655			0.617787
$580$	−3.75015	−	17.9681i	−0.155717	−	0.746083i
$581$	−10.4174			−0.432188
$582$			5.20871i			0.215908i
$583$			20.0616i			0.830867i
$584$		0			0
$585$		0			0
$586$	−8.28674			−0.342322
$587$			39.4956i			1.63016i	0.579351	+	0.815078i	$0.303306\pi$
$587$			39.4956i			1.63016i	−0.579351	+	0.815078i	$0.696694\pi$
$588$			7.16515i			0.295486i
$589$	−10.7477			−0.442852
$590$	13.9518	−	2.91190i	0.574385	−	0.119881i
$591$	14.6748			0.603639
$592$		−	22.1552i		−	0.910571i
$593$		−	21.1660i		−	0.869184i	−0.900627	−	0.434592i	$-0.856893\pi$
$593$		−	21.1660i		−	0.869184i	0.900627	−	0.434592i	$-0.143107\pi$
$594$	−6.04356			−0.247970
$595$	3.62614	+	17.3739i	0.148657	+	0.712259i
$596$	29.9017			1.22482
$597$			10.5826i			0.433116i
$598$		0			0
$599$	−15.4955			−0.633127			−0.316564	−	0.948571i	$-0.602529\pi$
$599$	−15.4955			−0.633127			−0.316564	+	0.948571i	$0.602529\pi$
$600$	7.93725	−	3.46410i	0.324037	−	0.141421i
$601$	16.9129			0.689891			0.344945	−	0.938623i	$-0.387897\pi$
$601$	16.9129			0.689891			0.344945	+	0.938623i	$0.387897\pi$
$602$			8.37386i			0.341293i
$603$		−	2.01810i		−	0.0821834i
$604$	−17.3205			−0.704761
$605$	−1.82740	−	8.75560i	−0.0742944	−	0.355966i
$606$	4.11165			0.167024
$607$		−	7.74773i		−	0.314471i	−0.987561	−	0.157235i	$-0.949742\pi$
$607$		−	7.74773i		−	0.314471i	0.987561	−	0.157235i	$-0.0502581\pi$
$608$			8.20871i			0.332907i
$609$	7.93725			0.321634
$610$	1.41742	−	0.295834i	0.0573898	−	0.0119780i
$611$		0			0
$612$		−	16.4174i		−	0.663635i
$613$		−	5.91915i		−	0.239072i	−0.992830	−	0.119536i	$-0.961859\pi$
$613$		−	5.91915i		−	0.239072i	0.992830	−	0.119536i	$-0.0381407\pi$
$614$	−11.0780			−0.447073
$615$	−5.79129	+	1.20871i	−0.233527	+	0.0487400i
$616$	−7.93725			−0.319801
$617$		−	13.9518i		−	0.561677i	−0.959755	−	0.280838i	$-0.909388\pi$
$617$		−	13.9518i		−	0.561677i	0.959755	−	0.280838i	$-0.0906125\pi$
$618$			1.44600i			0.0581667i
$619$	−29.7309			−1.19499			−0.597493	−	0.801874i	$-0.703836\pi$
$619$	−29.7309			−1.19499			−0.597493	+	0.801874i	$0.703836\pi$
$620$	−5.07803	−	24.3303i	−0.203939	−	0.977128i
$621$	22.9129			0.919462
$622$		−	3.46410i		−	0.138898i
$623$		−	16.5826i		−	0.664367i
$624$		0			0
$625$	17.0000	−	18.3303i	0.680000	−	0.733212i
$626$	1.48580			0.0593846
$627$			4.58258i			0.183010i
$628$		−	16.4174i		−	0.655127i
$629$	−36.3731			−1.45029
$630$	−0.723000	−	3.46410i	−0.0288050	−	0.138013i
$631$	−5.91915			−0.235638			−0.117819	−	0.993035i	$-0.537590\pi$
$631$	−5.91915			−0.235638			−0.117819	+	0.993035i	$0.537590\pi$
$632$			10.3923i			0.413384i
$633$		−	0.165151i		−	0.00656418i
$634$	−0.0871215			−0.00346004
$635$	−38.8480	+	8.10805i	−1.54164	+	0.321758i
$636$	−13.5826			−0.538584
$637$		0			0
$638$		−	5.53901i		−	0.219292i
$639$	−14.0471			−0.555695
$640$	−24.1652	+	5.04356i	−0.955211	+	0.199364i
$641$	−18.1652			−0.717480			−0.358740	−	0.933437i	$-0.616794\pi$
$641$	−18.1652			−0.717480			−0.358740	+	0.933437i	$0.616794\pi$
$642$		−	4.83465i		−	0.190809i
$643$		−	21.7937i		−	0.859458i	−0.902958	−	0.429729i	$-0.858609\pi$
$643$		−	21.7937i		−	0.859458i	0.902958	−	0.429729i	$-0.141391\pi$
$644$	14.2179			0.560264
$645$	4.83465	+	23.1642i	0.190364	+	0.912090i
$646$	3.62614			0.142668
$647$			27.0000i			1.06148i	0.847535	+	0.530740i	$0.178086\pi$
$647$			27.0000i			1.06148i	−0.847535	+	0.530740i	$0.821914\pi$
$648$			1.73205i			0.0680414i
$649$	−36.9129			−1.44896
$650$		0			0
$651$	10.7477			0.421237
$652$		−	37.7436i		−	1.47815i
$653$		−	42.8258i		−	1.67590i	−0.545746	−	0.837951i	$-0.683754\pi$
$653$		−	42.8258i		−	1.67590i	0.545746	−	0.837951i	$-0.316246\pi$
$654$	−6.00000			−0.234619
$655$	−3.46410	−	16.5975i	−0.135354	−	0.648518i
$656$	7.38505			0.288338
$657$		0			0
$658$		−	1.44600i		−	0.0563710i
$659$	−30.4955			−1.18793			−0.593967	−	0.804489i	$-0.702439\pi$
$659$	−30.4955			−1.18793			−0.593967	+	0.804489i	$0.702439\pi$
$660$	−10.3739	+	2.16515i	−0.403802	+	0.0842784i
$661$	−18.3296			−0.712937			−0.356469	−	0.934307i	$-0.616019\pi$
$661$	−18.3296			−0.712937			−0.356469	+	0.934307i	$0.616019\pi$
$662$			2.04356i			0.0794252i
$663$		0			0
$664$	−10.4174			−0.404274
$665$	−6.56670	+	1.37055i	−0.254646	+	0.0531477i
$666$	7.25227			0.281020
$667$			21.0000i			0.813123i
$668$			17.1497i			0.663542i
$669$	8.66025			0.334825
$670$	0.210601	+	1.00905i	0.00813623	+	0.0389830i
$671$	−3.75015			−0.144773
$672$		−	8.20871i		−	0.316658i
$673$			24.1652i			0.931498i	0.884917	+	0.465749i	$0.154215\pi$
$673$			24.1652i			0.931498i	−0.884917	+	0.465749i	$0.845785\pi$
$674$	−14.0471			−0.541074
$675$	−10.0000	−	22.9129i	−0.384900	−	0.881917i
$676$		0			0
$677$			2.83485i			0.108952i	0.998515	+	0.0544760i	$0.0173489\pi$
$677$			2.83485i			0.108952i	−0.998515	+	0.0544760i	$0.982651\pi$
$678$			3.38865i			0.130140i
$679$	19.7477			0.757848
$680$	3.62614	+	17.3739i	0.139056	+	0.666257i
$681$	−0.818350			−0.0313593
$682$		−	7.50030i		−	0.287202i
$683$		−	33.0997i		−	1.26652i	−0.773938	−	0.633262i	$-0.781716\pi$
$683$		−	33.0997i		−	1.26652i	0.773938	−	0.633262i	$-0.218284\pi$
$684$	6.20520			0.237262
$685$	22.9564	−	4.79129i	0.877120	−	0.183066i
$686$	−8.70417			−0.332327
$687$			26.2668i			1.00214i
$688$		−	29.5390i		−	1.12616i
$689$		0			0
$690$	−4.58258	+	0.956439i	−0.174456	+	0.0364110i
$691$	19.7756			0.752298			0.376149	−	0.926559i	$-0.377248\pi$
$691$	19.7756			0.752298			0.376149	+	0.926559i	$0.377248\pi$
$692$			29.7042i			1.12918i
$693$			9.16515i			0.348155i
$694$	−9.74475			−0.369906
$695$	9.93545	+	47.6036i	0.376873	+	1.80571i
$696$	7.93725			0.300861
$697$		−	12.1244i		−	0.459243i
$698$		−	1.12159i		−	0.0424528i
$699$	2.83485			0.107224
$700$	−6.20520	−	14.2179i	−0.234535	−	0.537386i
$701$	21.1652			0.799397			0.399698	−	0.916647i	$-0.369115\pi$
$701$	21.1652			0.799397			0.399698	+	0.916647i	$0.369115\pi$
$702$		0			0
$703$		−	13.7477i		−	0.518505i
$704$	9.04165			0.340770
$705$	−0.834849	−	4.00000i	−0.0314422	−	0.150649i
$706$	−3.12159			−0.117483
$707$		−	15.5885i		−	0.586264i
$708$		−	24.9916i		−	0.939242i
$709$	36.3731			1.36602			0.683010	−	0.730409i	$-0.260671\pi$
$709$	36.3731			1.36602			0.683010	+	0.730409i	$0.260671\pi$
$710$	7.02355	−	1.46590i	0.263589	−	0.0550143i
$711$	12.0000			0.450035
$712$		−	16.5826i		−	0.621458i
$713$			28.4358i			1.06493i
$714$	−3.62614			−0.135705
$715$		0			0
$716$	32.5390			1.21604
$717$		−	0.190700i		−	0.00712184i
$718$		−	8.92197i		−	0.332965i
$719$	−24.4955			−0.913526			−0.456763	−	0.889588i	$-0.650991\pi$
$719$	−24.4955			−0.913526			−0.456763	+	0.889588i	$0.650991\pi$
$720$	2.55040	+	12.2197i	0.0950478	+	0.455402i
$721$	5.48220			0.204168
$722$		−	7.30960i		−	0.272035i
$723$		−	1.73205i		−	0.0644157i
$724$	−15.6697			−0.582360
$725$	21.0000	−	9.16515i	0.779920	−	0.340385i
$726$	1.82740			0.0678212
$727$		−	15.2523i		−	0.565675i	−0.959168	−	0.282838i	$-0.908724\pi$
$727$		−	15.2523i		−	0.565675i	0.959168	−	0.282838i	$-0.0912758\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−48.4955			−1.79367
$732$		−	2.53901i		−	0.0938447i
$733$		−	22.8027i		−	0.842237i	−0.907006	−	0.421119i	$-0.861638\pi$
$733$		−	22.8027i		−	0.842237i	0.907006	−	0.421119i	$-0.138362\pi$
$734$	−0.798450			−0.0294713
$735$	−8.75560	+	1.82740i	−0.322955	+	0.0674047i
$736$	21.7182			0.800544
$737$		−	2.66970i		−	0.0983396i
$738$			2.41742i			0.0889866i
$739$	17.0345			0.626623			0.313311	−	0.949650i	$-0.398562\pi$
$739$	17.0345			0.626623			0.313311	+	0.949650i	$0.398562\pi$
$740$	31.1216	−	6.49545i	1.14405	−	0.238778i
$741$		0			0
$742$		−	6.00000i		−	0.220267i
$743$			5.72845i			0.210157i	0.994464	+	0.105078i	$0.0335093\pi$
$743$			5.72845i			0.210157i	−0.994464	+	0.105078i	$0.966491\pi$
$744$	10.7477			0.394031
$745$	7.62614	+	36.5390i	0.279400	+	1.33869i
$746$	5.93905			0.217444
$747$			12.0290i			0.440118i
$748$		−	21.7182i		−	0.794096i
$749$	−18.3296			−0.669748
$750$	2.95644	+	4.16515i	0.107954	+	0.152090i
$751$	−11.7477			−0.428681			−0.214340	−	0.976759i	$-0.568760\pi$
$751$	−11.7477			−0.428681			−0.214340	+	0.976759i	$0.568760\pi$
$752$			5.10080i			0.186007i
$753$			0.165151i			0.00601845i
$754$		0			0
$755$	−4.41742	−	21.1652i	−0.160767	−	0.770279i
$756$	−15.5130			−0.564203
$757$		−	9.74773i		−	0.354287i	−0.984185	−	0.177144i	$-0.943314\pi$
$757$		−	9.74773i		−	0.354287i	0.984185	−	0.177144i	$-0.0566857\pi$
$758$		−	4.87841i		−	0.177192i
$759$	12.1244			0.440086
$760$	−6.56670	+	1.37055i	−0.238199	+	0.0497151i
$761$	−35.4594			−1.28540			−0.642701	−	0.766118i	$-0.722186\pi$
$761$	−35.4594			−1.28540			−0.642701	+	0.766118i	$0.722186\pi$
$762$		−	8.10805i		−	0.293724i
$763$			22.7477i			0.823523i
$764$	−29.7042			−1.07466
$765$	20.0616	−	4.18710i	0.725329	−	0.151385i
$766$	−10.7913			−0.389905
$767$		0			0
$768$			1.79129i			0.0646375i
$769$	−15.5885			−0.562134			−0.281067	−	0.959688i	$-0.590688\pi$
$769$	−15.5885			−0.562134			−0.281067	+	0.959688i	$0.590688\pi$
$770$	−0.956439	−	4.58258i	−0.0344677	−	0.165145i
$771$	18.1652			0.654202
$772$		−	26.6283i		−	0.958374i
$773$		−	24.1534i		−	0.868736i	−0.900735	−	0.434368i	$-0.856972\pi$
$773$		−	24.1534i		−	0.868736i	0.900735	−	0.434368i	$-0.143028\pi$
$774$	9.66930			0.347556
$775$	28.4358	−	12.4104i	1.02144	−	0.445795i
$776$	19.7477			0.708902
$777$			13.7477i			0.493197i
$778$		−	1.44600i		−	0.0518416i
$779$	4.58258			0.164188
$780$		0			0
$781$	−18.5826			−0.664937
$782$		−	9.59386i		−	0.343076i
$783$		−	22.9129i		−	0.818839i
$784$	11.1652			0.398755
$785$	20.0616	−	4.18710i	0.716030	−	0.149444i
$786$	3.46410			0.123560
$787$		−	16.3115i		−	0.581441i	−0.956808	−	0.290720i	$-0.906105\pi$
$787$		−	16.3115i		−	0.581441i	0.956808	−	0.290720i	$-0.0938949\pi$
$788$		−	26.2867i		−	0.936425i
$789$	−9.00000			−0.320408
$790$	−6.00000	+	1.25227i	−0.213470	+	0.0445539i
$791$	12.8474			0.456799
$792$			9.16515i			0.325669i
$793$		0			0
$794$	−9.29583			−0.329897
$795$	−3.46410	−	16.5975i	−0.122859	−	0.588653i
$796$	18.9564			0.671893
$797$			44.0780i			1.56132i	0.624954	+	0.780662i	$0.285118\pi$
$797$			44.0780i			1.56132i	−0.624954	+	0.780662i	$0.714882\pi$
$798$		−	1.37055i		−	0.0485170i
$799$	8.37420			0.296258
$800$	−9.47860	−	21.7182i	−0.335119	−	0.767855i
$801$	−19.1479			−0.676558
$802$			13.6261i			0.481156i
$803$		0			0
$804$	1.80750			0.0637456
$805$	3.62614	+	17.3739i	0.127805	+	0.612348i
$806$		0			0
$807$			15.0000i			0.528025i
$808$		−	15.5885i		−	0.548400i
$809$	54.8258			1.92757			0.963785	−	0.266679i	$-0.0859263\pi$
$809$	54.8258			1.92757			0.963785	+	0.266679i	$0.0859263\pi$
$810$	−1.00000	+	0.208712i	−0.0351364	+	0.00733340i
$811$	50.5155			1.77384			0.886920	−	0.461923i	$-0.152840\pi$
$811$	50.5155			1.77384			0.886920	+	0.461923i	$0.152840\pi$
$812$		−	14.2179i		−	0.498951i
$813$		−	8.66025i		−	0.303728i
$814$	9.59386			0.336264
$815$	46.1216	−	9.62614i	1.61557	−	0.337189i
$816$	12.7913			0.447785
$817$		−	18.3296i		−	0.641270i
$818$		−	3.95644i		−	0.138334i
$819$		0			0
$820$	2.16515	+	10.3739i	0.0756104	+	0.362271i
$821$	18.1389			0.633051			0.316525	−	0.948584i	$-0.397484\pi$
$821$	18.1389			0.633051			0.316525	+	0.948584i	$0.397484\pi$
$822$			4.79129i			0.167115i
$823$			31.4174i			1.09514i	0.836759	+	0.547571i	$0.184448\pi$
$823$			31.4174i			1.09514i	−0.836759	+	0.547571i	$0.815552\pi$
$824$	5.48220			0.190982
$825$	−5.29150	−	12.1244i	−0.184226	−	0.422116i
$826$	11.0399			0.384126
$827$			10.7737i			0.374638i	0.982299	+	0.187319i	$0.0599799\pi$
$827$			10.7737i			0.374638i	−0.982299	+	0.187319i	$0.940020\pi$
$828$		−	16.4174i		−	0.570545i
$829$	−33.3303			−1.15761			−0.578805	−	0.815466i	$-0.696481\pi$
$829$	−33.3303			−1.15761			−0.578805	+	0.815466i	$0.696481\pi$
$830$	−1.25530	−	6.01450i	−0.0435721	−	0.208766i
$831$	7.41742			0.257308
$832$		0			0
$833$		−	18.3303i		−	0.635107i
$834$	−9.93545			−0.344037
$835$	−20.9564	+	4.37386i	−0.725227	+	0.151364i
$836$	8.20871			0.283904
$837$		−	31.0260i		−	1.07242i
$838$			2.66565i			0.0920834i
$839$	43.6827			1.50809			0.754047	−	0.656821i	$-0.228099\pi$
$839$	43.6827			1.50809			0.754047	+	0.656821i	$0.228099\pi$
$840$	6.56670	−	1.37055i	0.226573	−	0.0472885i
$841$	−8.00000			−0.275862
$842$		−	2.50455i		−	0.0863123i
$843$			3.65480i			0.125878i
$844$	−0.295834			−0.0101830
$845$		0			0
$846$	−1.66970			−0.0574054
$847$		−	6.92820i		−	0.238056i
$848$			21.1652i			0.726814i
$849$	−27.7477			−0.952300
$850$	−9.59386	+	4.18710i	−0.329067	+	0.143616i
$851$	−36.3731			−1.24685
$852$		−	12.5812i		−	0.431025i
$853$		−	5.63310i		−	0.192874i	−0.995339	−	0.0964369i	$-0.969255\pi$
$853$		−	5.63310i		−	0.192874i	0.995339	−	0.0964369i	$-0.0307446\pi$
$854$	1.12159			0.0383800
$855$	1.58258	+	7.58258i	0.0541229	+	0.259319i
$856$	−18.3296			−0.626491
$857$		−	4.74773i		−	0.162179i	−0.996707	−	0.0810896i	$-0.974160\pi$
$857$		−	4.74773i		−	0.162179i	0.996707	−	0.0810896i	$-0.0258400\pi$
$858$		0			0
$859$	44.2432			1.50956			0.754779	−	0.655979i	$-0.227744\pi$
$859$	44.2432			1.50956			0.754779	+	0.655979i	$0.227744\pi$
$860$	41.4938	−	8.66025i	1.41493	−	0.295312i
$861$	−4.58258			−0.156174
$862$			3.86932i			0.131789i
$863$		−	13.6657i		−	0.465186i	−0.972574	−	0.232593i	$-0.925279\pi$
$863$		−	13.6657i		−	0.465186i	0.972574	−	0.232593i	$-0.0747210\pi$
$864$	−23.6965			−0.806172
$865$	−36.2976	+	7.57575i	−1.23416	+	0.257583i
$866$	4.45325			0.151328
$867$		−	4.00000i		−	0.135847i
$868$		−	19.2523i		−	0.653465i
$869$	15.8745			0.538506
$870$	0.956439	+	4.58258i	0.0324263	+	0.155364i
$871$		0			0
$872$			22.7477i			0.770335i
$873$		−	22.8027i		−	0.771755i
$874$	3.62614			0.122656
$875$	15.7913	−	11.2087i	0.533843	−	0.378924i
$876$		0			0
$877$		−	7.93725i		−	0.268022i	−0.990980	−	0.134011i	$-0.957214\pi$
$877$		−	7.93725i		−	0.268022i	0.990980	−	0.134011i	$-0.0427858\pi$
$878$		−	6.62225i		−	0.223490i
$879$	−18.1389			−0.611809
$880$	3.37386	+	16.1652i	0.113733	+	0.544927i
$881$	−36.4955			−1.22956			−0.614782	−	0.788697i	$-0.710756\pi$
$881$	−36.4955			−1.22956			−0.614782	+	0.788697i	$0.710756\pi$
$882$			3.65480i			0.123064i
$883$		−	36.2432i		−	1.21968i	−0.792524	−	0.609840i	$-0.791234\pi$
$883$		−	36.2432i		−	1.21968i	0.792524	−	0.609840i	$-0.208766\pi$
$884$		0			0
$885$	30.5390	−	6.37386i	1.02656	−	0.214255i
$886$	−9.09720			−0.305627
$887$		−	54.4955i		−	1.82978i	−0.403705	−	0.914889i	$-0.632278\pi$
$887$		−	54.4955i		−	1.82978i	0.403705	−	0.914889i	$-0.367722\pi$
$888$			13.7477i			0.461344i
$889$	−30.7400			−1.03099
$890$	9.57395	−	1.99820i	0.320920	−	0.0669798i
$891$	2.64575			0.0886360
$892$		−	15.5130i		−	0.519414i
$893$			3.16515i			0.105918i
$894$	−7.62614			−0.255056
$895$	8.29875	+	39.7617i	0.277397	+	1.32909i
$896$	−19.1216			−0.638808
$897$		0			0
$898$			5.03447i			0.168002i
$899$	28.4358			0.948387
$900$	−16.4174	+	7.16515i	−0.547247	+	0.238838i
$901$	34.7477			1.15761
$902$			3.19795i			0.106480i
$903$			18.3296i			0.609970i
$904$	12.8474			0.427297
$905$	−3.99640	−	19.1479i	−0.132845	−	0.636498i
$906$	4.41742			0.146759
$907$		−	6.25227i		−	0.207603i	−0.994598	−	0.103802i	$-0.966899\pi$
$907$		−	6.25227i		−	0.207603i	0.994598	−	0.103802i	$-0.0331007\pi$
$908$			1.46590i			0.0486476i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	−7.91288			−0.262165			−0.131083	−	0.991371i	$-0.541845\pi$
$911$	−7.91288			−0.262165			−0.131083	+	0.991371i	$0.541845\pi$
$912$			4.83465i			0.160091i
$913$			15.9129i			0.526639i
$914$	−0.791288			−0.0261735
$915$	3.10260	−	0.647551i	0.102569	−	0.0214074i
$916$	47.0514			1.55462
$917$		−	13.1334i		−	0.433703i
$918$			10.4678i			0.345487i
$919$	−54.1652			−1.78674			−0.893372	−	0.449318i	$-0.851667\pi$
$919$	−54.1652			−1.78674			−0.893372	+	0.449318i	$0.851667\pi$
$920$	3.62614	+	17.3739i	0.119550	+	0.572799i
$921$	−24.2487			−0.799022
$922$		−	16.3739i		−	0.539244i
$923$		0			0
$924$	−8.20871			−0.270047
$925$	15.8745	+	36.3731i	0.521951	+	1.19594i
$926$	−18.0000			−0.591517
$927$		−	6.33030i		−	0.207914i
$928$		−	21.7182i		−	0.712935i
$929$	−26.3622			−0.864915			−0.432457	−	0.901654i	$-0.642353\pi$
$929$	−26.3622			−0.864915			−0.432457	+	0.901654i	$0.642353\pi$
$930$	1.29510	+	6.20520i	0.0424680	+	0.203477i
$931$	6.92820			0.227063
$932$		−	5.07803i		−	0.166336i
$933$		−	7.58258i		−	0.248242i
$934$	11.1153			0.363704
$935$	26.5390	−	5.53901i	0.867919	−	0.181145i
$936$		0			0
$937$		−	31.4955i		−	1.02891i	−0.857517	−	0.514456i	$-0.827994\pi$
$937$		−	31.4955i		−	1.02891i	0.857517	−	0.514456i	$-0.172006\pi$
$938$			0.798450i			0.0260703i
$939$	3.25227			0.106134
$940$	−7.16515	+	1.49545i	−0.233701	+	0.0487763i
$941$	26.4575			0.862490			0.431245	−	0.902235i	$-0.358074\pi$
$941$	26.4575			0.862490			0.431245	+	0.902235i	$0.358074\pi$
$942$			4.18710i			0.136423i
$943$		−	12.1244i		−	0.394823i
$944$	−38.9434			−1.26750
$945$	−3.95644	−	18.9564i	−0.128703	−	0.616653i
$946$	12.7913			0.415881
$947$		−	14.3332i		−	0.465765i	−0.972505	−	0.232883i	$-0.925184\pi$
$947$		−	14.3332i		−	0.465765i	0.972505	−	0.232883i	$-0.0748158\pi$
$948$			10.7477i			0.349070i
$949$		0			0
$950$	−1.58258	−	3.62614i	−0.0513455	−	0.117647i
$951$	−0.190700			−0.00618388
$952$			13.7477i			0.445566i
$953$			8.07803i			0.261673i	0.991404	+	0.130837i	$0.0417663\pi$
$953$			8.07803i			0.261673i	−0.991404	+	0.130837i	$0.958234\pi$
$954$	−6.92820			−0.224309
$955$	−7.57575	−	36.2976i	−0.245146	−	1.17456i
$956$	−0.341599			−0.0110481
$957$		−	12.1244i		−	0.391925i
$958$		−	2.13068i		−	0.0688392i
$959$	18.1652			0.586583
$960$	−7.48040	+	1.56125i	−0.241429	+	0.0503892i
$961$	7.50455			0.242082
$962$		0			0
$963$			21.1652i			0.682037i
$964$	−3.10260			−0.0999281
$965$	32.5390	−	6.79129i	1.04747	−	0.218619i
$966$	−3.62614			−0.116669
$967$			37.3821i			1.20213i	0.799201	+	0.601064i	$0.205256\pi$
$967$			37.3821i			1.20213i	−0.799201	+	0.601064i	$0.794744\pi$
$968$		−	6.92820i		−	0.222681i
$969$	7.93725			0.254981
$970$	2.37960	+	11.4014i	0.0764044	+	0.366075i
$971$	−18.4955			−0.593547			−0.296774	−	0.954948i	$-0.595911\pi$
$971$	−18.4955			−0.593547			−0.296774	+	0.954948i	$0.595911\pi$
$972$			28.6606i			0.919289i
$973$			37.6682i			1.20759i
$974$	−4.87841			−0.156314
$975$		0			0
$976$	−3.95644			−0.126643
$977$		−	35.3085i		−	1.12962i	−0.825222	−	0.564809i	$-0.808950\pi$
$977$		−	35.3085i		−	1.12962i	0.825222	−	0.564809i	$-0.191050\pi$
$978$			9.62614i			0.307810i
$979$	−25.3303			−0.809560
$980$	3.27340	+	15.6838i	0.104565	+	0.501001i
$981$	26.2668			0.838635
$982$		−	8.87086i		−	0.283080i
$983$			55.0840i			1.75691i	0.477827	+	0.878454i	$0.341424\pi$
$983$			55.0840i			1.75691i	−0.477827	+	0.878454i	$0.658576\pi$
$984$	−4.58258			−0.146087
$985$	32.1216	−	6.70417i	1.02348	−	0.213613i
$986$	−9.59386			−0.305531
$987$		−	3.16515i		−	0.100748i
$988$		0			0
$989$	−48.4955			−1.54207
$990$	−5.29150	+	1.10440i	−0.168175	+	0.0351002i
$991$	−13.0000			−0.412959			−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000			−0.412959			−0.206479	+	0.978451i	$0.566201\pi$
$992$		−	29.4083i		−	0.933715i
$993$			4.47315i			0.141951i
$994$	5.55765			0.176278
$995$	4.83465	+	23.1642i	0.153269	+	0.734355i
$996$	−10.7737			−0.341378
$997$		−	0.165151i		−	0.00523040i	−0.999997	−	0.00261520i	$-0.999168\pi$
$997$		−	0.165151i		−	0.00523040i	0.999997	−	0.00261520i	$-0.000832444\pi$
$998$		−	0.330303i		−	0.0104556i
$999$	39.6863			1.25562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.b.f.339.6		8
5.2	odd	4		4225.2.a.bk.1.2		4
5.3	odd	4		4225.2.a.bj.1.3		4
5.4	even	2	inner	845.2.b.f.339.3		8
13.2	odd	12		65.2.l.a.4.2	✓	8
13.3	even	3		845.2.n.d.529.1		8
13.4	even	6		845.2.n.d.484.2		8
13.5	odd	4		845.2.d.c.844.6		8
13.6	odd	12		845.2.l.c.699.2		8
13.7	odd	12		65.2.l.a.49.3	yes	8
13.8	odd	4		845.2.d.c.844.4		8
13.9	even	3		845.2.n.c.484.4		8
13.10	even	6		845.2.n.c.529.3		8
13.11	odd	12		845.2.l.c.654.3		8
13.12	even	2	inner	845.2.b.f.339.4		8
39.2	even	12		585.2.bf.a.199.3		8
39.20	even	12		585.2.bf.a.244.2		8
52.7	even	12		1040.2.df.b.49.1		8
52.15	even	12		1040.2.df.b.849.4		8
65.2	even	12		325.2.n.c.251.1		4
65.4	even	6		845.2.n.c.484.3		8
65.7	even	12		325.2.n.c.101.1		4
65.9	even	6		845.2.n.d.484.1		8
65.12	odd	4		4225.2.a.bk.1.3		4
65.19	odd	12		845.2.l.c.699.3		8
65.24	odd	12		845.2.l.c.654.2		8
65.28	even	12		325.2.n.b.251.2		4
65.29	even	6		845.2.n.c.529.4		8
65.33	even	12		325.2.n.b.101.2		4
65.34	odd	4		845.2.d.c.844.5		8
65.38	odd	4		4225.2.a.bj.1.2		4
65.44	odd	4		845.2.d.c.844.3		8
65.49	even	6		845.2.n.d.529.2		8
65.54	odd	12		65.2.l.a.4.3	yes	8
65.59	odd	12		65.2.l.a.49.2	yes	8
65.64	even	2	inner	845.2.b.f.339.5		8
195.59	even	12		585.2.bf.a.244.3		8
195.119	even	12		585.2.bf.a.199.2		8
260.59	even	12		1040.2.df.b.49.4		8
260.119	even	12		1040.2.df.b.849.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.l.a.4.2	✓	8	13.2	odd	12
65.2.l.a.4.3	yes	8	65.54	odd	12
65.2.l.a.49.2	yes	8	65.59	odd	12
65.2.l.a.49.3	yes	8	13.7	odd	12
325.2.n.b.101.2		4	65.33	even	12
325.2.n.b.251.2		4	65.28	even	12
325.2.n.c.101.1		4	65.7	even	12
325.2.n.c.251.1		4	65.2	even	12
585.2.bf.a.199.2		8	195.119	even	12
585.2.bf.a.199.3		8	39.2	even	12
585.2.bf.a.244.2		8	39.20	even	12
585.2.bf.a.244.3		8	195.59	even	12
845.2.b.f.339.3		8	5.4	even	2	inner
845.2.b.f.339.4		8	13.12	even	2	inner
845.2.b.f.339.5		8	65.64	even	2	inner
845.2.b.f.339.6		8	1.1	even	1	trivial
845.2.d.c.844.3		8	65.44	odd	4
845.2.d.c.844.4		8	13.8	odd	4
845.2.d.c.844.5		8	65.34	odd	4
845.2.d.c.844.6		8	13.5	odd	4
845.2.l.c.654.2		8	65.24	odd	12
845.2.l.c.654.3		8	13.11	odd	12
845.2.l.c.699.2		8	13.6	odd	12
845.2.l.c.699.3		8	65.19	odd	12
845.2.n.c.484.3		8	65.4	even	6
845.2.n.c.484.4		8	13.9	even	3
845.2.n.c.529.3		8	13.10	even	6
845.2.n.c.529.4		8	65.29	even	6
845.2.n.d.484.1		8	65.9	even	6
845.2.n.d.484.2		8	13.4	even	6
845.2.n.d.529.1		8	13.3	even	3
845.2.n.d.529.2		8	65.49	even	6
1040.2.df.b.49.1		8	52.7	even	12
1040.2.df.b.49.4		8	260.59	even	12
1040.2.df.b.849.1		8	260.119	even	12
1040.2.df.b.849.4		8	52.15	even	12
4225.2.a.bj.1.2		4	65.38	odd	4
4225.2.a.bj.1.3		4	5.3	odd	4
4225.2.a.bk.1.2		4	5.2	odd	4
4225.2.a.bk.1.3		4	65.12	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.456850i q^{2} +1.00000i q^{3} +1.79129 q^{4} +(0.456850 + 2.18890i) q^{5} -0.456850 q^{6} +1.73205i q^{7} +1.73205i q^{8} +2.00000 q^{9} +(-1.00000 + 0.208712i) q^{10} +2.64575 q^{11} +1.79129i q^{12} -0.791288 q^{14} +(-2.18890 + 0.456850i) q^{15} +2.79129 q^{16} -4.58258i q^{17} +0.913701i q^{18} +1.73205 q^{19} +(0.818350 + 3.92095i) q^{20} -1.73205 q^{21} +1.20871i q^{22} -4.58258i q^{23} -1.73205 q^{24} +(-4.58258 + 2.00000i) q^{25} +5.00000i q^{27} +3.10260i q^{28} -4.58258 q^{29} +(-0.208712 - 1.00000i) q^{30} -6.20520 q^{31} +4.73930i q^{32} +2.64575i q^{33} +2.09355 q^{34} +(-3.79129 + 0.791288i) q^{35} +3.58258 q^{36} -7.93725i q^{37} +0.791288i q^{38} +(-3.79129 + 0.791288i) q^{40} +2.64575 q^{41} -0.791288i q^{42} -10.5826i q^{43} +4.73930 q^{44} +(0.913701 + 4.37780i) q^{45} +2.09355 q^{46} +1.82740i q^{47} +2.79129i q^{48} +4.00000 q^{49} +(-0.913701 - 2.09355i) q^{50} +4.58258 q^{51} +7.58258i q^{53} -2.28425 q^{54} +(1.20871 + 5.79129i) q^{55} -3.00000 q^{56} +1.73205i q^{57} -2.09355i q^{58} -13.9518 q^{59} +(-3.92095 + 0.818350i) q^{60} -1.41742 q^{61} -2.83485i q^{62} +3.46410i q^{63} +3.41742 q^{64} -1.20871 q^{66} -1.00905i q^{67} -8.20871i q^{68} +4.58258 q^{69} +(-0.361500 - 1.73205i) q^{70} -7.02355 q^{71} +3.46410i q^{72} +3.62614 q^{74} +(-2.00000 - 4.58258i) q^{75} +3.10260 q^{76} +4.58258i q^{77} +6.00000 q^{79} +(1.27520 + 6.10985i) q^{80} +1.00000 q^{81} +1.20871i q^{82} +6.01450i q^{83} -3.10260 q^{84} +(10.0308 - 2.09355i) q^{85} +4.83465 q^{86} -4.58258i q^{87} +4.58258i q^{88} -9.57395 q^{89} +(-2.00000 + 0.417424i) q^{90} -8.20871i q^{92} -6.20520i q^{93} -0.834849 q^{94} +(0.791288 + 3.79129i) q^{95} -4.73930 q^{96} -11.4014i q^{97} +1.82740i q^{98} +5.29150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 16 q^{9} - 8 q^{10} + 12 q^{14} + 4 q^{16} - 20 q^{30} - 12 q^{35} - 8 q^{36} - 12 q^{40} + 32 q^{49} + 28 q^{55} - 24 q^{56} - 48 q^{61} + 64 q^{64} - 28 q^{66} + 84 q^{74} - 16 q^{75}+ \cdots - 12 q^{95}+O(q^{100}) \) 8 * q - 4 * q^4 + 16 * q^9 - 8 * q^10 + 12 * q^14 + 4 * q^16 - 20 * q^30 - 12 * q^35 - 8 * q^36 - 12 * q^40 + 32 * q^49 + 28 * q^55 - 24 * q^56 - 48 * q^61 + 64 * q^64 - 28 * q^66 + 84 * q^74 - 16 * q^75 + 48 * q^79 + 8 * q^81 - 16 * q^90 - 80 * q^94 - 12 * q^95

Introduction

L-functions

Modular forms

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Database

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