LMFDB - Embedded newform 819.2.dt.a.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(337,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("819.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dt (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			337.1
Character	$\chi$	$=$	819.337
Dual form			819.2.dt.a.610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41651 + 1.39517i) q^{2} +(-0.424462 + 1.67924i) q^{3} +(2.89301 - 5.01083i) q^{4} +(-2.68905 - 1.55252i) q^{5} +(-1.31711 - 4.65008i) q^{6} +(-0.866025 + 0.500000i) q^{7} +10.5643i q^{8} +(-2.63966 - 1.42554i) q^{9} +O(q^{10})$	\(q+(-2.41651 + 1.39517i) q^{2} +(-0.424462 + 1.67924i) q^{3} +(2.89301 - 5.01083i) q^{4} +(-2.68905 - 1.55252i) q^{5} +(-1.31711 - 4.65008i) q^{6} +(-0.866025 + 0.500000i) q^{7} +10.5643i q^{8} +(-2.63966 - 1.42554i) q^{9} +8.66414 q^{10} +(-0.833992 + 0.481505i) q^{11} +(7.18640 + 6.98494i) q^{12} +(-3.25930 + 1.54174i) q^{13} +(1.39517 - 2.41651i) q^{14} +(3.74845 - 3.85656i) q^{15} +(-8.95295 - 15.5070i) q^{16} -7.70335 q^{17} +(8.36764 - 0.237949i) q^{18} -3.68043i q^{19} +(-15.5589 + 8.98291i) q^{20} +(-0.472023 - 1.66649i) q^{21} +(1.34356 - 2.32712i) q^{22} +(1.31520 - 2.27799i) q^{23} +(-17.7399 - 4.48413i) q^{24} +(2.32066 + 4.01949i) q^{25} +(5.72513 - 8.27291i) q^{26} +(3.51426 - 3.82753i) q^{27} +5.78601i q^{28} +(2.42876 + 4.20674i) q^{29} +(-3.67760 + 14.5491i) q^{30} +(4.22721 + 2.44058i) q^{31} +(24.9719 + 14.4175i) q^{32} +(-0.454563 - 1.60485i) q^{33} +(18.6152 - 10.7475i) q^{34} +3.10505 q^{35} +(-14.7797 + 9.10281i) q^{36} +1.58239i q^{37} +(5.13483 + 8.89380i) q^{38} +(-1.20550 - 6.12754i) q^{39} +(16.4013 - 28.4078i) q^{40} +(0.481150 + 0.277792i) q^{41} +(3.46569 + 3.36854i) q^{42} +(2.12352 + 3.67804i) q^{43} +5.57199i q^{44} +(4.88500 + 7.93149i) q^{45} +7.33971i q^{46} +(2.13913 - 1.23503i) q^{47} +(29.8400 - 8.45199i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-11.2158 - 6.47542i) q^{50} +(3.26978 - 12.9357i) q^{51} +(-1.70377 + 20.7921i) q^{52} +6.37047 q^{53} +(-3.15217 + 14.1522i) q^{54} +2.99019 q^{55} +(-5.28213 - 9.14892i) q^{56} +(6.18032 + 1.56220i) q^{57} +(-11.7382 - 6.77708i) q^{58} +(-1.06484 - 0.614788i) q^{59} +(-8.48029 - 29.9399i) q^{60} +(-5.90044 - 10.2199i) q^{61} -13.6201 q^{62} +(2.99879 - 0.0852758i) q^{63} -44.6478 q^{64} +(11.1580 + 0.914323i) q^{65} +(3.33750 + 3.24394i) q^{66} +(2.43494 + 1.40581i) q^{67} +(-22.2858 + 38.6002i) q^{68} +(3.26703 + 3.17545i) q^{69} +(-7.50337 + 4.33207i) q^{70} -7.30335i q^{71} +(15.0598 - 27.8861i) q^{72} +8.81549i q^{73} +(-2.20770 - 3.82385i) q^{74} +(-7.73471 + 2.19081i) q^{75} +(-18.4420 - 10.6475i) q^{76} +(0.481505 - 0.833992i) q^{77} +(11.4621 + 13.1254i) q^{78} +(4.57348 + 7.92151i) q^{79} +55.5986i q^{80} +(4.93566 + 7.52591i) q^{81} -1.55027 q^{82} +(3.10267 - 1.79133i) q^{83} +(-9.71607 - 2.45594i) q^{84} +(20.7147 + 11.9596i) q^{85} +(-10.2630 - 5.92533i) q^{86} +(-8.09503 + 2.29286i) q^{87} +(-5.08675 - 8.81051i) q^{88} +2.04612i q^{89} +(-22.8704 - 12.3511i) q^{90} +(2.05177 - 2.96484i) q^{91} +(-7.60976 - 13.1805i) q^{92} +(-5.89260 + 6.06255i) q^{93} +(-3.44616 + 5.96892i) q^{94} +(-5.71396 + 9.89687i) q^{95} +(-34.8100 + 35.8140i) q^{96} +(11.6816 - 6.74436i) q^{97} +2.79034i q^{98} +(2.88787 - 0.0821215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 84 q^{4} - 8 q^{9}+O(q^{10}) $ 168 * q + 84 * q^4 - 8 * q^9	$ 168 q + 84 q^{4} - 8 q^{9} - 24 q^{12} + 8 q^{14} - 84 q^{16} - 32 q^{23} + 84 q^{25} - 8 q^{26} + 48 q^{27} + 4 q^{29} + 80 q^{30} - 32 q^{35} + 4 q^{36} + 24 q^{38} + 24 q^{39} + 4 q^{48} + 84 q^{49} + 64 q^{51} + 18 q^{52} - 48 q^{53} - 24 q^{56} + 24 q^{62} - 240 q^{64} - 22 q^{65} - 132 q^{66} - 156 q^{68} - 52 q^{69} + 84 q^{74} - 60 q^{75} - 16 q^{77} - 148 q^{78} + 12 q^{79} - 8 q^{81} - 24 q^{82} + 88 q^{87} + 24 q^{88} - 164 q^{90} + 12 q^{91} + 128 q^{92} - 60 q^{94} - 96 q^{95}+O(q^{100}) $ 168 * q + 84 * q^4 - 8 * q^9 - 24 * q^12 + 8 * q^14 - 84 * q^16 - 32 * q^23 + 84 * q^25 - 8 * q^26 + 48 * q^27 + 4 * q^29 + 80 * q^30 - 32 * q^35 + 4 * q^36 + 24 * q^38 + 24 * q^39 + 4 * q^48 + 84 * q^49 + 64 * q^51 + 18 * q^52 - 48 * q^53 - 24 * q^56 + 24 * q^62 - 240 * q^64 - 22 * q^65 - 132 * q^66 - 156 * q^68 - 52 * q^69 + 84 * q^74 - 60 * q^75 - 16 * q^77 - 148 * q^78 + 12 * q^79 - 8 * q^81 - 24 * q^82 + 88 * q^87 + 24 * q^88 - 164 * q^90 + 12 * q^91 + 128 * q^92 - 60 * q^94 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	−2.41651	+	1.39517i	−1.70873	+	0.986535i	−0.772589	+	0.634906i	$0.781039\pi$
$2$	−2.41651	+	1.39517i	−1.70873	+	0.986535i	−0.936140	+	0.351629i	$0.885628\pi$
$3$	−0.424462	+	1.67924i	−0.245063	+	0.969507i
$3$	−0.424462	+	1.67924i	−0.245063	+	0.969507i
$4$	2.89301	−	5.01083i	1.44650	−	2.50542i
$5$	−2.68905	−	1.55252i	−1.20258	−	0.694309i	−0.241451	−	0.970413i	$-0.577623\pi$
$5$	−2.68905	−	1.55252i	−1.20258	−	0.694309i	−0.961128	+	0.276104i	$0.910957\pi$
$6$	−1.31711	−	4.65008i	−0.537706	−	1.89839i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			10.5643i			3.73503i
$9$	−2.63966	−	1.42554i	−0.879888	−	0.475181i
$10$	8.66414			2.73984
$11$	−0.833992	+	0.481505i	−0.251458	+	0.145179i	−0.620432	−	0.784260i	$-0.713043\pi$
$11$	−0.833992	+	0.481505i	−0.251458	+	0.145179i	0.368974	+	0.929440i	$0.379709\pi$
$12$	7.18640	+	6.98494i	2.07453	+	2.01638i
$13$	−3.25930	+	1.54174i	−0.903967	+	0.427602i
$13$	−3.25930	+	1.54174i	−0.903967	+	0.427602i
$14$	1.39517	−	2.41651i	0.372875	−	0.645839i
$15$	3.74845	−	3.85656i	0.967846	−	0.995759i
$16$	−8.95295	−	15.5070i	−2.23824	−	3.87674i
$17$	−7.70335			−1.86834			−0.934168	−	0.356833i	$-0.883857\pi$
$17$	−7.70335			−1.86834			−0.934168	+	0.356833i	$0.883857\pi$
$18$	8.36764	−	0.237949i	1.97227	−	0.0560850i
$19$		−	3.68043i		−	0.844349i	−0.906514	−	0.422175i	$-0.861267\pi$
$19$		−	3.68043i		−	0.844349i	0.906514	−	0.422175i	$-0.138733\pi$
$20$	−15.5589	+	8.98291i	−3.47907	+	2.00864i
$21$	−0.472023	−	1.66649i	−0.103004	−	0.363658i
$22$	1.34356	−	2.32712i	0.286449	−	0.496144i
$23$	1.31520	−	2.27799i	0.274238	−	0.474994i	−0.695705	−	0.718328i	$-0.744908\pi$
$23$	1.31520	−	2.27799i	0.274238	−	0.474994i	0.969943	+	0.243334i	$0.0782410\pi$
$24$	−17.7399	−	4.48413i	−3.62114	−	0.915319i
$25$	2.32066	+	4.01949i	0.464131	+	0.803899i
$26$	5.72513	−	8.27291i	1.12279	−	1.62245i
$27$	3.51426	−	3.82753i	0.676319	−	0.736608i
$28$			5.78601i			1.09345i
$29$	2.42876	+	4.20674i	0.451010	+	0.781172i	0.998449	−	0.0556733i	$-0.0177305\pi$
$29$	2.42876	+	4.20674i	0.451010	+	0.781172i	−0.547439	+	0.836846i	$0.684397\pi$
$30$	−3.67760	+	14.5491i	−0.671434	+	2.65630i
$31$	4.22721	+	2.44058i	0.759230	+	0.438341i	0.829019	−	0.559220i	$-0.188899\pi$
$31$	4.22721	+	2.44058i	0.759230	+	0.438341i	−0.0697894	+	0.997562i	$0.522233\pi$
$32$	24.9719	+	14.4175i	4.41445	+	2.54868i
$33$	−0.454563	−	1.60485i	−0.0791293	−	0.279368i
$34$	18.6152	−	10.7475i	3.19248	−	1.84318i
$35$	3.10505			0.524849
$36$	−14.7797	+	9.10281i	−2.46329	+	1.51714i
$37$			1.58239i			0.260143i	0.991505	+	0.130072i	$0.0415207\pi$
$37$			1.58239i			0.260143i	−0.991505	+	0.130072i	$0.958479\pi$
$38$	5.13483	+	8.89380i	0.832980	+	1.44276i
$39$	−1.20550	−	6.12754i	−0.193034	−	0.981192i
$40$	16.4013	−	28.4078i	2.59327	−	4.49167i
$41$	0.481150	+	0.277792i	0.0751430	+	0.0433838i	0.537101	−	0.843518i	$-0.319519\pi$
$41$	0.481150	+	0.277792i	0.0751430	+	0.0433838i	−0.461958	+	0.886902i	$0.652853\pi$
$42$	3.46569	+	3.36854i	0.534767	+	0.519776i
$43$	2.12352	+	3.67804i	0.323833	+	0.560895i	0.981275	−	0.192609i	$-0.0616951\pi$
$43$	2.12352	+	3.67804i	0.323833	+	0.560895i	−0.657442	+	0.753505i	$0.728362\pi$
$44$			5.57199i			0.840009i
$45$	4.88500	+	7.93149i	0.728213	+	1.18236i
$46$			7.33971i			1.08218i
$47$	2.13913	−	1.23503i	0.312025	−	0.180148i	−0.335807	−	0.941931i	$-0.609009\pi$
$47$	2.13913	−	1.23503i	0.312025	−	0.180148i	0.647832	+	0.761783i	$0.275676\pi$
$48$	29.8400	−	8.45199i	4.30704	−	1.21994i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−11.2158	−	6.47542i	−1.58615	−	0.915763i
$51$	3.26978	−	12.9357i	0.457861	−	1.81137i
$52$	−1.70377	+	20.7921i	−0.236270	+	2.88334i
$53$	6.37047			0.875051			0.437525	−	0.899206i	$-0.355855\pi$
$53$	6.37047			0.875051			0.437525	+	0.899206i	$0.355855\pi$
$54$	−3.15217	+	14.1522i	−0.428957	+	1.92588i
$55$	2.99019			0.403198
$56$	−5.28213	−	9.14892i	−0.705855	−	1.22258i
$57$	6.18032	+	1.56220i	0.818603	+	0.206919i
$58$	−11.7382	−	6.77708i	−1.54131	−	0.889874i
$59$	−1.06484	−	0.614788i	−0.138631	−	0.0800386i	0.429080	−	0.903266i	$-0.358838\pi$
$59$	−1.06484	−	0.614788i	−0.138631	−	0.0800386i	−0.567711	+	0.823228i	$0.692171\pi$
$60$	−8.48029	−	29.9399i	−1.09480	−	3.86522i
$61$	−5.90044	−	10.2199i	−0.755474	−	1.30852i	−0.945138	−	0.326670i	$-0.894073\pi$
$61$	−5.90044	−	10.2199i	−0.755474	−	1.30852i	0.189664	−	0.981849i	$-0.439260\pi$
$62$	−13.6201			−1.72976
$63$	2.99879	−	0.0852758i	0.377812	−	0.0107437i
$64$	−44.6478			−5.58098
$65$	11.1580	+	0.914323i	1.38398	+	0.113408i
$66$	3.33750	+	3.24394i	0.410817	+	0.399301i
$67$	2.43494	+	1.40581i	0.297475	+	0.171747i	0.641308	−	0.767284i	$-0.278392\pi$
$67$	2.43494	+	1.40581i	0.297475	+	0.171747i	−0.343833	+	0.939031i	$0.611725\pi$
$68$	−22.2858	+	38.6002i	−2.70255	+	4.68096i
$69$	3.26703	+	3.17545i	0.393305	+	0.382279i
$70$	−7.50337	+	4.33207i	−0.896824	+	0.517781i
$71$		−	7.30335i		−	0.866748i	−0.901214	−	0.433374i	$-0.857323\pi$
$71$		−	7.30335i		−	0.866748i	0.901214	−	0.433374i	$-0.142677\pi$
$72$	15.0598	−	27.8861i	1.77482	−	3.28641i
$73$			8.81549i			1.03177i	0.856656	+	0.515887i	$0.172538\pi$
$73$			8.81549i			1.03177i	−0.856656	+	0.515887i	$0.827462\pi$
$74$	−2.20770	−	3.82385i	−0.256640	−	0.444514i
$75$	−7.73471	+	2.19081i	−0.893127	+	0.252973i
$76$	−18.4420	−	10.6475i	−2.11545	−	1.22135i
$77$	0.481505	−	0.833992i	0.0548726	−	0.0950422i
$78$	11.4621	+	13.1254i	1.29782	+	1.48616i
$79$	4.57348	+	7.92151i	0.514557	+	0.891239i	0.999857	+	0.0168914i	$0.00537696\pi$
$79$	4.57348	+	7.92151i	0.514557	+	0.891239i	−0.485300	+	0.874348i	$0.661290\pi$
$80$			55.5986i			6.21611i
$81$	4.93566	+	7.52591i	0.548406	+	0.836212i
$82$	−1.55027			−0.171199
$83$	3.10267	−	1.79133i	0.340562	−	0.196624i	−0.319958	−	0.947432i	$-0.603669\pi$
$83$	3.10267	−	1.79133i	0.340562	−	0.196624i	0.660521	+	0.750808i	$0.270336\pi$
$84$	−9.71607	−	2.45594i	−1.06011	−	0.267965i
$85$	20.7147	+	11.9596i	2.24682	+	1.29720i
$86$	−10.2630	−	5.92533i	−1.10669	−	0.638945i
$87$	−8.09503	+	2.29286i	−0.867878	+	0.245821i
$88$	−5.08675	−	8.81051i	−0.542249	−	0.939204i
$89$			2.04612i			0.216888i	0.994103	+	0.108444i	$0.0345869\pi$
$89$			2.04612i			0.216888i	−0.994103	+	0.108444i	$0.965413\pi$
$90$	−22.8704	−	12.3511i	−2.41075	−	1.30192i
$91$	2.05177	−	2.96484i	0.215084	−	0.310799i
$92$	−7.60976	−	13.1805i	−0.793372	−	1.37416i
$93$	−5.89260	+	6.06255i	−0.611034	+	0.628657i
$94$	−3.44616	+	5.96892i	−0.355444	+	0.615647i
$95$	−5.71396	+	9.89687i	−0.586240	+	1.01540i
$96$	−34.8100	+	35.8140i	−3.55278	+	3.65525i
$97$	11.6816	−	6.74436i	1.18608	−	0.684786i	0.228670	−	0.973504i	$-0.426562\pi$
$97$	11.6816	−	6.74436i	1.18608	−	0.684786i	0.957414	+	0.288718i	$0.0932288\pi$
$98$			2.79034i			0.281867i
$99$	2.88787	−	0.0821215i	0.290241	−	0.00825352i
$100$	26.8547			2.68547
$101$	−2.45847	−	4.25819i	−0.244627	−	0.423706i	0.717400	−	0.696662i	$-0.245332\pi$
$101$	−2.45847	−	4.25819i	−0.244627	−	0.423706i	−0.962027	+	0.272956i	$0.911999\pi$
$102$	10.1461	+	35.8212i	1.00462	+	3.54683i
$103$	−5.75163	+	9.96211i	−0.566725	+	0.981596i	0.430162	+	0.902752i	$0.358456\pi$
$103$	−5.75163	+	9.96211i	−0.566725	+	0.981596i	−0.996887	+	0.0788444i	$0.974877\pi$
$104$	−16.2874	−	34.4321i	−1.59711	−	3.37635i
$105$	−1.31797	+	5.21410i	−0.128621	+	0.508844i
$106$	−15.3943	+	8.88789i	−1.49522	+	0.863268i
$107$	0.842813			0.0814778			0.0407389	−	0.999170i	$-0.487029\pi$
$107$	0.842813			0.0814778			0.0407389	+	0.999170i	$0.487029\pi$
$108$	−9.01234	−	28.6824i	−0.867213	−	2.75997i
$109$		−	6.17764i		−	0.591710i	−0.955233	−	0.295855i	$-0.904395\pi$
$109$		−	6.17764i		−	0.591710i	0.955233	−	0.295855i	$-0.0956045\pi$
$110$	−7.22582	+	4.17183i	−0.688955	+	0.397768i
$111$	−2.65720	−	0.671664i	−0.252211	−	0.0637515i
$112$	15.5070	+	8.95295i	1.46527	+	0.845974i
$113$	2.46088	−	4.26236i	0.231500	−	0.400970i	−0.726750	−	0.686902i	$-0.758970\pi$
$113$	2.46088	−	4.26236i	0.231500	−	0.400970i	0.958250	+	0.285933i	$0.0923034\pi$
$114$	−17.1143	+	4.84752i	−1.60290	+	0.454012i
$115$	−7.07327	+	4.08376i	−0.659586	+	0.380812i
$116$	28.1057			2.60955
$117$	10.8013	+	0.576595i	0.998578	+	0.0533062i
$118$	3.43094			0.315844
$119$	6.67130	−	3.85167i	0.611557	−	0.353082i
$120$	40.7417	+	39.5996i	3.71919	+	3.61493i
$121$	−5.03631	+	8.72314i	−0.457846	+	0.793012i
$122$	28.5169	+	16.4642i	2.58180	+	1.49060i
$123$	−0.670708	+	0.690052i	−0.0604757	+	0.0622199i
$124$	24.4587	−	14.1212i	2.19646	−	1.26812i
$125$			1.11374i			0.0996163i
$126$	−7.12762	+	4.38989i	−0.634979	+	0.391083i
$127$	4.65580			0.413136			0.206568	−	0.978432i	$-0.433771\pi$
$127$	4.65580			0.413136			0.206568	+	0.978432i	$0.433771\pi$
$128$	57.9481	−	33.4563i	5.12194	−	2.95715i
$129$	−7.07764	+	2.00470i	−0.623152	+	0.176504i
$130$	−28.2390	+	13.3579i	−2.47673	+	1.17156i
$131$	8.30876	−	14.3912i	0.725940	−	1.25736i	−0.232647	−	0.972561i	$-0.574739\pi$
$131$	8.30876	−	14.3912i	0.725940	−	1.25736i	0.958586	−	0.284803i	$-0.0919281\pi$
$132$	−9.35668	−	2.36510i	−0.814395	−	0.205855i
$133$	1.84022	+	3.18735i	0.159567	+	0.276378i
$134$	−7.84539			−0.677739
$135$	−15.3923	+	4.83645i	−1.32476	+	0.416255i
$136$		−	81.3802i		−	6.97830i
$137$	−5.13557	+	2.96502i	−0.438761	+	0.253319i	−0.703072	−	0.711119i	$-0.748189\pi$
$137$	−5.13557	+	2.96502i	−0.438761	+	0.253319i	0.264311	+	0.964438i	$0.414856\pi$
$138$	−12.3251	−	3.11543i	−1.04918	−	0.265203i
$139$	−10.8948	+	18.8703i	−0.924084	+	1.60056i	−0.131056	+	0.991375i	$0.541837\pi$
$139$	−10.8948	+	18.8703i	−0.924084	+	1.60056i	−0.793028	+	0.609185i	$0.791496\pi$
$140$	8.98291	−	15.5589i	0.759195	−	1.31496i
$141$	1.16593	+	4.11633i	0.0981886	+	0.346658i
$142$	10.1894	+	17.6486i	0.855077	+	1.48104i
$143$	1.97587	−	2.85517i	0.165231	−	0.238761i
$144$	1.52694	+	53.6960i	0.127245	+	4.47466i
$145$		−	15.0828i		−	1.25256i
$146$	−12.2991	−	21.3027i	−1.01788	−	1.76302i
$147$	1.24203	+	1.20721i	0.102441	+	0.0995692i
$148$	7.92909	+	4.57786i	0.651767	+	0.376298i
$149$	15.9745	+	9.22291i	1.30869	+	0.755570i	0.981877	−	0.189520i	$-0.0606933\pi$
$149$	15.9745	+	9.22291i	1.30869	+	0.755570i	0.326809	+	0.945090i	$0.394027\pi$
$150$	15.6344	−	16.0853i	1.27655	−	1.31336i
$151$	−20.9059	+	12.0701i	−1.70130	+	0.982247i	−0.756855	+	0.653582i	$0.773265\pi$
$151$	−20.9059	+	12.0701i	−1.70130	+	0.982247i	−0.944447	+	0.328665i	$0.893401\pi$
$152$	38.8811			3.15367
$153$	20.3343	+	10.9815i	1.64393	+	0.887798i
$154$			2.68713i			0.216535i
$155$	−7.57812	−	13.1257i	−0.608689	−	1.05428i
$156$	−34.1916	−	11.6865i	−2.73752	−	0.935666i
$157$	6.03317	−	10.4498i	0.481499	−	0.833981i	−0.518275	−	0.855214i	$-0.673426\pi$
$157$	6.03317	−	10.4498i	0.481499	−	0.833981i	0.999775	+	0.0212329i	$0.00675914\pi$
$158$	−22.1037	−	12.7616i	−1.75848	−	1.01526i
$159$	−2.70402	+	10.6975i	−0.214443	+	0.848368i
$160$	−44.7671	−	77.5388i	−3.53915	−	6.12998i
$161$			2.63040i			0.207304i
$162$	−22.4270	−	11.3003i	−1.76203	−	0.887838i
$163$		−	15.7403i		−	1.23287i	−0.787405	−	0.616436i	$-0.788576\pi$
$163$		−	15.7403i		−	1.23287i	0.787405	−	0.616436i	$-0.211424\pi$
$164$	2.78394	−	1.60731i	0.217389	−	0.125510i
$165$	−1.26922	+	5.02124i	−0.0988089	+	0.390903i
$166$	−4.99841	+	8.65751i	−0.387952	+	0.671953i
$167$	−6.63096	−	3.82839i	−0.513119	−	0.296250i	0.220996	−	0.975275i	$-0.429069\pi$
$167$	−6.63096	−	3.82839i	−0.513119	−	0.296250i	−0.734115	+	0.679025i	$0.762403\pi$
$168$	17.6053	−	4.98658i	1.35828	−	0.384723i
$169$	8.24607	−	10.0500i	0.634313	−	0.773076i
$170$	−66.7429			−5.11895
$171$	−5.24662	+	9.71511i	−0.401219	+	0.742933i
$172$	24.5734			1.87370
$173$	−5.32764	−	9.22775i	−0.405053	−	0.701573i	0.589274	−	0.807933i	$-0.299414\pi$
$173$	−5.32764	−	9.22775i	−0.405053	−	0.701573i	−0.994328	+	0.106360i	$0.966080\pi$
$174$	16.3628	−	16.8347i	1.24046	−	1.27623i
$175$	−4.01949	−	2.32066i	−0.303845	−	0.175425i
$176$	14.9334	+	8.62178i	1.12565	+	0.649891i
$177$	1.48436	−	1.52717i	0.111571	−	0.114789i
$178$	−2.85469	−	4.94447i	−0.213968	−	0.370604i
$179$	25.8852			1.93475			0.967376	−	0.253345i	$-0.0815307\pi$
$179$	25.8852			1.93475			0.967376	+	0.253345i	$0.0815307\pi$
$180$	53.8757	−	1.53205i	4.01566	−	0.114192i
$181$	9.04276			0.672143			0.336071	−	0.941837i	$-0.390902\pi$
$181$	9.04276			0.672143			0.336071	+	0.941837i	$0.390902\pi$
$182$	−0.821655	+	10.0271i	−0.0609051	+	0.743259i
$183$	19.6661	−	5.57029i	1.45376	−	0.411768i
$184$	24.0653	+	13.8941i	1.77412	+	1.02429i
$185$	2.45670	−	4.25512i	0.180620	−	0.312843i
$186$	5.78122	−	22.8714i	0.423900	−	1.67701i
$187$	6.42453	−	3.70920i	0.469808	−	0.271244i
$188$		−	14.2918i		−	1.04234i
$189$	−1.12967	+	5.07187i	−0.0821716	+	0.368924i
$190$		−	31.8878i		−	2.31338i
$191$	−4.56147	−	7.90070i	−0.330056	−	0.571674i	0.652466	−	0.757818i	$-0.273734\pi$
$191$	−4.56147	−	7.90070i	−0.330056	−	0.571674i	−0.982523	+	0.186143i	$0.940401\pi$
$192$	18.9513	−	74.9743i	1.36769	−	5.41080i
$193$	7.25102	+	4.18638i	0.521940	+	0.301342i	0.737728	−	0.675098i	$-0.235899\pi$
$193$	7.25102	+	4.18638i	0.521940	+	0.301342i	−0.215788	+	0.976440i	$0.569232\pi$
$194$	−18.8191	+	32.5956i	−1.35113	+	2.34023i
$195$	−6.27151	+	18.3488i	−0.449112	+	1.31399i
$196$	−2.89301	−	5.01083i	−0.206643	−	0.357917i
$197$			5.56235i			0.396301i	0.980172	+	0.198151i	$0.0634935\pi$
$197$			5.56235i			0.396301i	−0.980172	+	0.198151i	$0.936506\pi$
$198$	−6.86397	+	4.22751i	−0.487801	+	0.300436i
$199$	15.5534			1.10255			0.551275	−	0.834324i	$-0.314141\pi$
$199$	15.5534			1.10255			0.551275	+	0.834324i	$0.314141\pi$
$200$	−42.4630	+	24.5160i	−3.00259	+	1.73354i
$201$	−3.39423	+	3.49212i	−0.239410	+	0.246315i
$202$	11.8818	+	6.85997i	0.836002	+	0.482666i
$203$	−4.20674	−	2.42876i	−0.295255	−	0.170466i
$204$	−55.3593	−	53.8075i	−3.87593	−	3.76728i
$205$	−0.862557	−	1.49399i	−0.0602436	−	0.104345i
$206$		−	32.0980i		−	2.23637i
$207$	−6.71906	+	4.13826i	−0.467007	+	0.287629i
$208$	53.0880	+	36.7387i	3.68099	+	2.54737i
$209$	1.77215	+	3.06945i	0.122582	+	0.212318i
$210$	−4.08967	−	14.4387i	−0.282214	−	0.996366i
$211$	−3.29864	+	5.71341i	−0.227088	+	0.393327i	−0.956944	−	0.290273i	$-0.906254\pi$
$211$	−3.29864	+	5.71341i	−0.227088	+	0.393327i	0.729856	+	0.683601i	$0.239587\pi$
$212$	18.4298	−	31.9213i	1.26576	−	2.19237i
$213$	12.2640	+	3.09999i	0.840318	+	0.212408i
$214$	−2.03666	+	1.17587i	−0.139223	+	0.0803807i
$215$		−	13.1872i		−	0.899361i
$216$	40.4350	+	37.1256i	2.75126	+	2.52607i
$217$	−4.88116			−0.331355
$218$	8.61886	+	14.9283i	0.583743	+	1.01107i
$219$	−14.8033	−	3.74184i	−1.00031	−	0.252850i
$220$	8.65064	−	14.9834i	0.583226	−	1.01018i
$221$	25.1075	−	11.8766i	1.68892	−	0.798904i
$222$	7.35824	−	2.08417i	0.493853	−	0.139881i
$223$	−9.86693	+	5.69668i	−0.660739	+	0.381478i	−0.792558	−	0.609796i	$-0.791251\pi$
$223$	−9.86693	+	5.69668i	−0.660739	+	0.381478i	0.131820	+	0.991274i	$0.457918\pi$
$224$	−28.8350			−1.92662
$225$	−0.395792	−	13.9183i	−0.0263861	−	0.927887i
$226$			13.7334i			0.913531i
$227$	−13.5024	+	7.79560i	−0.896184	+	0.517412i	−0.875960	−	0.482384i	$-0.839771\pi$
$227$	−13.5024	+	7.79560i	−0.896184	+	0.517412i	−0.0202236	+	0.999795i	$0.506438\pi$
$228$	25.7076	−	26.4491i	1.70253	−	1.75163i
$229$	−15.3875	−	8.88400i	−1.01684	−	0.587071i	−0.103651	−	0.994614i	$-0.533053\pi$
$229$	−15.3875	−	8.88400i	−1.01684	−	0.587071i	−0.913186	+	0.407542i	$0.866386\pi$
$230$	11.3951	−	19.7368i	0.751369	−	1.30141i
$231$	1.19609	+	1.16256i	0.0786968	+	0.0764908i
$232$	−44.4411	+	25.6581i	−2.91770	+	1.68454i
$233$	−9.58032			−0.627628			−0.313814	−	0.949485i	$-0.601607\pi$
$233$	−9.58032			−0.627628			−0.313814	+	0.949485i	$0.601607\pi$
$234$	−26.9058	+	13.6763i	−1.75889	+	0.894046i
$235$	−7.66965			−0.500313
$236$	−6.16120	+	3.55717i	−0.401060	+	0.231552i
$237$	−15.2433	+	4.31758i	−0.990161	+	0.280457i
$238$	−10.7475	+	18.6152i	−0.696656	+	1.20664i
$239$	2.77961	+	1.60481i	0.179798	+	0.103806i	0.587198	−	0.809444i	$-0.300231\pi$
$239$	2.77961	+	1.60481i	0.179798	+	0.103806i	−0.407400	+	0.913250i	$0.633564\pi$
$240$	−93.3632	−	23.5995i	−6.02657	−	1.52334i
$241$	19.5567	−	11.2910i	1.25976	−	0.727320i	0.286728	−	0.958012i	$-0.407432\pi$
$241$	19.5567	−	11.2910i	1.25976	−	0.727320i	0.973027	+	0.230692i	$0.0740989\pi$
$242$		−	28.1060i		−	1.80672i
$243$	−14.7328	+	5.09367i	−0.945108	+	0.326759i
$244$	−68.2800			−4.37118
$245$	−2.68905	+	1.55252i	−0.171797	+	0.0991871i
$246$	0.658030	−	2.60327i	0.0419545	−	0.165978i
$247$	5.67427	+	11.9956i	0.361045	+	0.763264i
$248$	−25.7830	+	44.6574i	−1.63722	+	2.83575i
$249$	1.69109	+	5.97046i	0.107169	+	0.378363i
$250$	−1.55386	−	2.69137i	−0.0982749	−	0.170217i
$251$	24.7645			1.56312			0.781562	−	0.623827i	$-0.214423\pi$
$251$	24.7645			1.56312			0.781562	+	0.623827i	$0.214423\pi$
$252$	8.24821	−	15.2731i	0.519588	−	0.962116i
$253$			2.53310i			0.159255i
$254$	−11.2508	+	6.49564i	−0.705937	+	0.407573i
$255$	−28.8756	+	29.7084i	−1.80826	+	1.86041i
$256$	−48.7068	+	84.3627i	−3.04418	+	5.27267i
$257$	0.103751	−	0.179702i	0.00647182	−	0.0112095i	−0.862771	−	0.505594i	$-0.831273\pi$
$257$	0.103751	−	0.179702i	0.00647182	−	0.0112095i	0.869243	+	0.494385i	$0.164607\pi$
$258$	14.3063	−	14.7189i	0.890670	−	0.916358i
$259$	−0.791195	−	1.37039i	−0.0491624	−	0.0851518i
$260$	36.8617	−	53.2657i	2.28606	−	3.30340i
$261$	−0.414229	−	14.5667i	−0.0256402	−	0.901655i
$262$			46.3686i			2.86466i
$263$	−5.59317	−	9.68766i	−0.344890	−	0.597366i	0.640444	−	0.768005i	$-0.278750\pi$
$263$	−5.59317	−	9.68766i	−0.344890	−	0.597366i	−0.985334	+	0.170638i	$0.945417\pi$
$264$	16.9541	−	4.80213i	1.04345	−	0.295550i
$265$	−17.1305	−	9.89030i	−1.05232	−	0.607556i
$266$	−8.89380	−	5.13483i	−0.545314	−	0.314837i
$267$	−3.43592	−	0.868501i	−0.210275	−	0.0531514i
$268$	14.0886	−	8.13404i	0.860597	−	0.496866i
$269$	10.4422			0.636673			0.318337	−	0.947978i	$-0.396876\pi$
$269$	10.4422			0.636673			0.318337	+	0.947978i	$0.396876\pi$
$270$	30.4480	−	33.1623i	1.85301	−	2.01819i
$271$			11.0864i			0.673448i	0.941603	+	0.336724i	$0.109319\pi$
$271$			11.0864i			0.673448i	−0.941603	+	0.336724i	$0.890681\pi$
$272$	68.9677	+	119.456i	4.18178	+	7.24305i
$273$	4.10776	+	4.70386i	0.248613	+	0.284691i
$274$	8.27343	−	14.3300i	0.499816	−	0.865707i
$275$	−3.87082	−	2.23482i	−0.233419	−	0.134765i
$276$	25.3632	−	7.18396i	1.52668	−	0.432424i
$277$	−4.16391	−	7.21210i	−0.250185	−	0.433333i	0.713392	−	0.700766i	$-0.247158\pi$
$277$	−4.16391	−	7.21210i	−0.250185	−	0.433333i	−0.963577	+	0.267432i	$0.913825\pi$
$278$		−	60.8004i		−	3.64656i
$279$	−7.67927	−	12.4684i	−0.459746	−	0.746463i
$280$			32.8025i			1.96033i
$281$	15.7639	−	9.10126i	0.940392	−	0.542936i	0.0503091	−	0.998734i	$-0.483979\pi$
$281$	15.7639	−	9.10126i	0.940392	−	0.542936i	0.890083	+	0.455798i	$0.150646\pi$
$282$	−8.56046	−	8.32049i	−0.509768	−	0.495478i
$283$	10.2184	−	17.6987i	0.607418	−	1.05208i	−0.384246	−	0.923231i	$-0.625539\pi$
$283$	10.2184	−	17.6987i	0.607418	−	1.05208i	0.991664	−	0.128848i	$-0.0411280\pi$
$284$	−36.5958	−	21.1286i	−2.17156	−	1.25375i
$285$	−14.1938	−	13.7959i	−0.840769	−	0.817200i
$286$	−0.791262	+	9.65622i	−0.0467883	+	0.570984i
$287$	−0.555584			−0.0327951
$288$	−45.3646	−	73.6559i	−2.67313	−	4.34022i
$289$	42.3416			2.49068
$290$	21.0431	+	36.4478i	1.23570	+	2.14029i
$291$	6.36699	+	22.4789i	0.373240	+	1.31773i
$292$	44.1729	+	25.5032i	2.58502	+	1.49246i
$293$	−5.67868	−	3.27859i	−0.331752	−	0.191537i	0.324867	−	0.945760i	$-0.394681\pi$
$293$	−5.67868	−	3.27859i	−0.331752	−	0.191537i	−0.656619	+	0.754223i	$0.728014\pi$
$294$	−4.68564	−	1.18439i	−0.273272	−	0.0690753i
$295$	1.90895	+	3.30639i	0.111143	+	0.192506i
$296$	−16.7168			−0.971643
$297$	−1.08789	+	4.88426i	−0.0631256	+	0.283414i
$298$	−51.4701			−2.98159
$299$	−0.774557	+	9.45236i	−0.0447938	+	0.546644i
$300$	−11.3988	+	45.0953i	−0.658109	+	2.60358i
$301$	−3.67804	−	2.12352i	−0.211998	−	0.122397i
$302$	33.6796	−	58.3348i	1.93804	−	3.35679i
$303$	8.19404	−	2.32091i	0.470735	−	0.133333i
$304$	−57.0723	+	32.9507i	−3.27332	+	1.88985i
$305$			36.6423i			2.09813i
$306$	−64.4589	+	1.83300i	−3.68487	+	0.104786i
$307$		−	25.2585i		−	1.44158i	−0.693154	−	0.720790i	$-0.743779\pi$
$307$		−	25.2585i		−	1.44158i	0.693154	−	0.720790i	$-0.256221\pi$
$308$	−2.78600	−	4.82549i	−0.158747	−	0.274958i
$309$	−14.2874	−	13.8869i	−0.812781	−	0.789997i
$310$	36.6252	+	21.1455i	2.08017	+	1.20099i
$311$	7.50758	−	13.0035i	0.425716	−	0.737362i	−0.570771	−	0.821109i	$-0.693356\pi$
$311$	7.50758	−	13.0035i	0.425716	−	0.737362i	0.996487	+	0.0837475i	$0.0266889\pi$
$312$	64.7330	−	12.7352i	3.66478	−	0.720988i
$313$	−7.48996	−	12.9730i	−0.423357	−	0.733277i	0.572908	−	0.819620i	$-0.305815\pi$
$313$	−7.48996	−	12.9730i	−0.423357	−	0.733277i	−0.996265	+	0.0863430i	$0.972482\pi$
$314$			33.6692i			1.90006i
$315$	−8.19628	−	4.42638i	−0.461808	−	0.249398i
$316$	52.9244			2.97723
$317$	−5.44936	+	3.14619i	−0.306067	+	0.176708i	−0.645165	−	0.764043i	$-0.723211\pi$
$317$	−5.44936	+	3.14619i	−0.306067	+	0.176708i	0.339098	+	0.940751i	$0.389878\pi$
$318$	−8.39058	−	29.6232i	−0.470520	−	1.66119i
$319$	−4.05114	−	2.33893i	−0.226820	−	0.130955i
$320$	120.060	+	69.3168i	6.71157	+	3.87493i
$321$	−0.357742	+	1.41528i	−0.0199672	+	0.0789933i
$322$	−3.66986	−	6.35638i	−0.204513	−	0.354227i
$323$			28.3517i			1.57753i
$324$	51.9899	−	2.95924i	2.88833	−	0.164402i
$325$	−13.7607	−	9.52289i	−0.763308	−	0.528235i
$326$	21.9604	+	38.0365i	1.21627	+	2.10664i
$327$	10.3737	+	2.62217i	0.573667	+	0.145006i
$328$	−2.93467	+	5.08299i	−0.162040	+	0.280661i
$329$	−1.23503	+	2.13913i	−0.0680894	+	0.117934i
$330$	−3.93840	−	13.9046i	−0.216802	−	0.765425i
$331$	24.1845	−	13.9629i	1.32930	−	0.767470i	0.344107	−	0.938931i	$-0.388182\pi$
$331$	24.1845	−	13.9629i	1.32930	−	0.767470i	0.985191	+	0.171460i	$0.0548485\pi$
$332$		−	20.7293i		−	1.13767i
$333$	2.25576	−	4.17698i	0.123615	−	0.228897i
$334$	21.3650			1.16904
$335$	−4.36511	−	7.56059i	−0.238491	−	0.413079i
$336$	−21.6162	+	22.2397i	−1.17926	+	1.21327i
$337$	−9.73962	+	16.8695i	−0.530551	+	0.918941i	0.468814	+	0.883297i	$0.344682\pi$
$337$	−9.73962	+	16.8695i	−0.530551	+	0.918941i	−0.999365	+	0.0356441i	$0.988652\pi$
$338$	−5.90524	+	35.7906i	−0.321203	+	1.94675i
$339$	6.11297	+	5.94160i	0.332011	+	0.322704i
$340$	119.855	−	69.1985i	6.50007	−	3.75282i
$341$	−4.70061			−0.254553
$342$	−0.875754	−	30.7966i	−0.0473554	−	1.66529i
$343$			1.00000i			0.0539949i
$344$	−38.8557	+	22.4334i	−2.09496	+	1.20953i
$345$	−3.85525	−	13.6111i	−0.207560	−	0.732796i
$346$	25.7486	+	14.8660i	1.38425	+	0.799198i
$347$	9.99526	−	17.3123i	0.536574	−	0.929373i	−0.462512	−	0.886613i	$-0.653052\pi$
$347$	9.99526	−	17.3123i	0.536574	−	0.929373i	0.999085	−	0.0427596i	$-0.0136150\pi$
$348$	−11.9298	+	47.1961i	−0.639504	+	2.52998i
$349$	−13.6453	+	7.87811i	−0.730415	+	0.421705i	−0.818574	−	0.574401i	$-0.805235\pi$
$349$	−13.6453	+	7.87811i	−0.730415	+	0.421705i	0.0881589	+	0.996106i	$0.471902\pi$
$350$	12.9508			0.692252
$351$	−5.55297	+	17.8931i	−0.296395	+	0.955065i
$352$	−27.7685			−1.48006
$353$	11.4343	−	6.60162i	0.608589	−	0.351369i	−0.163824	−	0.986490i	$-0.552383\pi$
$353$	11.4343	−	6.60162i	0.608589	−	0.351369i	0.772413	+	0.635121i	$0.219050\pi$
$354$	−1.45630	+	5.76136i	−0.0774016	+	0.306213i
$355$	−11.3386	+	19.6391i	−0.601791	+	1.04233i
$356$	10.2528	+	5.91944i	0.543396	+	0.313730i
$357$	3.63616	+	12.8376i	0.192446	+	0.679436i
$358$	−62.5518	+	36.1143i	−3.30597	+	1.90870i
$359$			10.7219i			0.565880i	0.959138	+	0.282940i	$0.0913097\pi$
$359$			10.7219i			0.565880i	−0.959138	+	0.282940i	$0.908690\pi$
$360$	−83.7904	+	51.6064i	−4.41614	+	2.71990i
$361$	5.45441			0.287074
$362$	−21.8519	+	12.6162i	−1.14851	+	0.663092i
$363$	−12.5105	−	12.1598i	−0.656630	−	0.638223i
$364$	−8.92053	−	18.8583i	−0.467563	−	0.988446i
$365$	13.6862	−	23.7053i	0.716371	−	1.24079i
$366$	−39.7517	+	40.8982i	−2.07785	+	2.13778i
$367$	−3.86409	−	6.69279i	−0.201704	−	0.349361i	0.747374	−	0.664404i	$-0.231314\pi$
$367$	−3.86409	−	6.69279i	−0.201704	−	0.349361i	−0.949077	+	0.315043i	$0.897981\pi$
$368$	−47.0996			−2.45524
$369$	−0.874070	−	1.41918i	−0.0455023	−	0.0738794i
$370$			13.7100i			0.712751i
$371$	−5.51699	+	3.18523i	−0.286428	+	0.165369i
$372$	13.3311	+	47.0658i	0.691185	+	2.44025i
$373$	7.64974	−	13.2497i	0.396089	−	0.686046i	−0.597151	−	0.802129i	$-0.703701\pi$
$373$	7.64974	−	13.2497i	0.396089	−	0.686046i	0.993239	+	0.116083i	$0.0370340\pi$
$374$	−10.3500	+	17.9266i	−0.535183	+	0.926965i
$375$	−1.87024	−	0.472742i	−0.0965787	−	0.0244123i
$376$	13.0472	+	22.5984i	0.672857	+	1.16542i
$377$	−14.4018	−	9.96651i	−0.741729	−	0.513301i
$378$	−4.34626	−	13.8323i	−0.223548	−	0.711456i
$379$		−	26.3635i		−	1.35420i	−0.735891	−	0.677100i	$-0.763236\pi$
$379$		−	26.3635i		−	1.35420i	0.735891	−	0.677100i	$-0.236764\pi$
$380$	33.0610	+	57.2634i	1.69599	+	2.93755i
$381$	−1.97621	+	7.81819i	−0.101244	+	0.400538i
$382$	22.0456	+	12.7281i	1.12795	+	0.651224i
$383$	2.93392	+	1.69390i	0.149917	+	0.0865544i	0.573082	−	0.819498i	$-0.305748\pi$
$383$	2.93392	+	1.69390i	0.149917	+	0.0865544i	−0.423165	+	0.906053i	$0.639081\pi$
$384$	31.5843	+	111.509i	1.61178	+	5.69044i
$385$	−2.58958	+	1.49510i	−0.131977	+	0.0761972i
$386$	−23.3629			−1.18914
$387$	−0.362169	−	12.7359i	−0.0184101	−	0.647404i
$388$		−	78.0459i		−	3.96218i
$389$	−12.2320	−	21.1864i	−0.620186	−	1.07419i	−0.989451	−	0.144870i	$-0.953724\pi$
$389$	−12.2320	−	21.1864i	−0.620186	−	1.07419i	0.369264	−	0.929324i	$-0.379610\pi$
$390$	−10.4446	−	53.0899i	−0.528883	−	2.68831i
$391$	−10.1314	+	17.5482i	−0.512369	+	0.887449i
$392$	9.14892	+	5.28213i	0.462090	+	0.266788i
$393$	20.6394	+	20.0609i	1.04112	+	1.01194i
$394$	−7.76044	−	13.4415i	−0.390965	−	0.677171i
$395$		−	28.4018i		−	1.42905i
$396$	7.94311	−	14.7082i	0.399156	−	0.739114i
$397$			21.6086i			1.08450i	0.840216	+	0.542252i	$0.182428\pi$
$397$			21.6086i			1.08450i	−0.840216	+	0.542252i	$0.817572\pi$
$398$	−37.5849	+	21.6996i	−1.88396	+	1.08770i
$399$	−6.13341	+	1.73725i	−0.307055	+	0.0869713i
$400$	41.5534	−	71.9726i	2.07767	−	3.59863i
$401$	−21.5328	−	12.4319i	−1.07529	−	0.620822i	−0.145672	−	0.989333i	$-0.546534\pi$
$401$	−21.5328	−	12.4319i	−1.07529	−	0.620822i	−0.929623	+	0.368511i	$0.879868\pi$
$402$	3.33007	−	13.1743i	0.166089	−	0.657073i
$403$	−17.5405	−	1.43733i	−0.873754	−	0.0715983i
$404$	−28.4495			−1.41541
$405$	−1.58807	−	27.9003i	−0.0789118	−	1.38637i
$406$	13.5542			0.672682
$407$	−0.761929	−	1.31970i	−0.0377674	−	0.0654151i
$408$	136.657	+	34.5428i	6.76551	+	1.71012i
$409$	16.5471	+	9.55346i	0.818201	+	0.472388i	0.849796	−	0.527112i	$-0.176725\pi$
$409$	16.5471	+	9.55346i	0.818201	+	0.472388i	−0.0315949	+	0.999501i	$0.510059\pi$
$410$	4.16875	+	2.40683i	0.205880	+	0.118865i
$411$	−2.79912	−	9.88237i	−0.138070	−	0.487461i
$412$	33.2790	+	57.6409i	1.63954	+	2.83976i
$413$	1.22958			0.0605035
$414$	10.4631	−	19.3744i	0.514232	−	0.952199i
$415$	−11.1243			−0.546071
$416$	−103.619	−	8.49087i	−5.08034	−	0.416299i
$417$	−27.0633	−	26.3047i	−1.32530	−	1.28814i
$418$	−8.56482	−	4.94490i	−0.418919	−	0.241863i
$419$	−13.9201	+	24.1103i	−0.680041	+	1.17787i	0.294927	+	0.955520i	$0.404705\pi$
$419$	−13.9201	+	24.1103i	−0.680041	+	1.17787i	−0.974968	+	0.222346i	$0.928629\pi$
$420$	22.3141	+	21.6886i	1.08882	+	1.05829i
$421$	11.6462	−	6.72393i	0.567601	−	0.327704i	−0.188590	−	0.982056i	$-0.560392\pi$
$421$	11.6462	−	6.72393i	0.567601	−	0.327704i	0.756190	+	0.654352i	$0.227058\pi$
$422$		−	18.4087i		−	0.896120i
$423$	−7.40719	+	0.210636i	−0.360150	+	0.0102415i
$424$			67.2993i			3.26834i
$425$	−17.8768	−	30.9636i	−0.867153	−	1.50195i
$426$	−33.9612	+	9.61928i	−1.64542	+	0.466056i
$427$	10.2199	+	5.90044i	0.494574	+	0.285542i
$428$	2.43826	−	4.22319i	0.117858	−	0.204136i
$429$	3.95582	+	4.52987i	0.190989	+	0.218704i
$430$	18.3984	+	31.8670i	0.887251	+	1.53676i
$431$		−	16.0443i		−	0.772829i	−0.922325	−	0.386414i	$-0.873713\pi$
$431$		−	16.0443i		−	0.772829i	0.922325	−	0.386414i	$-0.126287\pi$
$432$	−90.8163	−	20.2278i	−4.36940	−	0.973210i
$433$	1.20097			0.0577149			0.0288574	−	0.999584i	$-0.490813\pi$
$433$	1.20097			0.0577149			0.0288574	+	0.999584i	$0.490813\pi$
$434$	11.7954	−	6.81006i	0.566196	−	0.326893i
$435$	25.3276	+	6.40209i	1.21437	+	0.306957i
$436$	−30.9551	−	17.8719i	−1.48248	−	0.855910i
$437$	−8.38400	−	4.84050i	−0.401061	−	0.231553i
$438$	40.9927	−	11.6109i	1.95871	−	0.554792i
$439$	3.89234	+	6.74173i	0.185771	+	0.321765i	0.943836	−	0.330414i	$-0.107188\pi$
$439$	3.89234	+	6.74173i	0.185771	+	0.321765i	−0.758065	+	0.652179i	$0.773855\pi$
$440$			31.5892i			1.50596i
$441$	−2.55439	+	1.57324i	−0.121638	+	0.0749164i
$442$	−44.1027	+	63.7291i	−2.09775	+	3.03128i
$443$	10.0910	+	17.4780i	0.479436	+	0.830407i	0.999722	−	0.0235851i	$-0.00750806\pi$
$443$	10.0910	+	17.4780i	0.479436	+	0.830407i	−0.520286	+	0.853992i	$0.674175\pi$
$444$	−11.0529	+	11.3717i	−0.524547	+	0.539676i
$445$	3.17665	−	5.50212i	0.150588	−	0.260826i
$446$	15.8957	−	27.5321i	0.752682	−	1.30368i
$447$	−22.2680	+	22.9103i	−1.05324	+	1.08362i
$448$	38.6662	−	22.3239i	1.82680	−	1.05471i
$449$			37.9528i			1.79110i	0.444958	+	0.895551i	$0.353219\pi$
$449$			37.9528i			1.79110i	−0.444958	+	0.895551i	$0.646781\pi$
$450$	20.3749	+	33.0815i	0.960480	+	1.55948i
$451$	−0.535033			−0.0251937
$452$	−14.2387	−	24.6621i	−0.669730	−	1.16001i
$453$	−11.3947	−	40.2293i	−0.535369	−	1.89014i
$454$	21.7524	−	37.6762i	1.02089	−	1.76823i
$455$	−10.1203	+	4.78717i	−0.474446	+	0.224426i
$456$	−16.5035	+	65.2905i	−0.772849	+	3.05751i
$457$	−4.38626	+	2.53241i	−0.205180	+	0.118461i	−0.599070	−	0.800697i	$-0.704463\pi$
$457$	−4.38626	+	2.53241i	−0.205180	+	0.118461i	0.393889	+	0.919158i	$0.371129\pi$
$458$	49.5788			2.31667
$459$	−27.0716	+	29.4848i	−1.26359	+	1.37623i
$460$			47.2573i			2.20338i
$461$	−31.1357	+	17.9762i	−1.45013	+	0.837234i	−0.998488	−	0.0549641i	$-0.982496\pi$
$461$	−31.1357	+	17.9762i	−1.45013	+	0.837234i	−0.451644	+	0.892198i	$0.649162\pi$
$462$	−4.51232	−	1.14058i	−0.209932	−	0.0530648i
$463$	5.14908	+	2.97282i	0.239298	+	0.138159i	0.614854	−	0.788641i	$-0.289215\pi$
$463$	5.14908	+	2.97282i	0.239298	+	0.138159i	−0.375556	+	0.926800i	$0.622548\pi$
$464$	43.4892	−	75.3255i	2.01893	−	3.49690i
$465$	25.2577	−	7.15409i	1.17130	−	0.331763i
$466$	23.1509	−	13.3662i	1.07245	−	0.619177i
$467$	−9.60838			−0.444623			−0.222311	−	0.974976i	$-0.571360\pi$
$467$	−9.60838			−0.444623			−0.222311	+	0.974976i	$0.571360\pi$
$468$	34.1374	−	52.4553i	1.57800	−	2.42475i
$469$	−2.81162			−0.129829
$470$	18.5338	−	10.7005i	0.854899	−	0.493576i
$471$	14.9867	+	14.5666i	0.690553	+	0.671195i
$472$	6.49479	−	11.2493i	0.298947	−	0.517791i
$473$	−3.54199	−	2.04497i	−0.162861	−	0.0940277i
$474$	30.8119	−	31.7005i	1.41524	−	1.45605i
$475$	14.7935	−	8.54102i	0.678771	−	0.391889i
$476$		−	44.5717i		−	2.04294i
$477$	−16.8159	−	9.08137i	−0.769947	−	0.415807i
$478$	−8.95592			−0.409634
$479$	−6.51246	+	3.75997i	−0.297562	+	0.171798i	−0.641347	−	0.767251i	$-0.721624\pi$
$479$	−6.51246	+	3.75997i	−0.297562	+	0.171798i	0.343785	+	0.939048i	$0.388291\pi$
$480$	149.208	−	42.2622i	6.81038	−	1.92900i
$481$	−2.43963	−	5.15748i	−0.111238	−	0.235161i
$482$	−31.5059	+	54.5698i	−1.43505	+	2.48559i
$483$	−4.41706	−	1.11650i	−0.200983	−	0.0508027i
$484$	29.1401	+	50.4722i	1.32455	+	2.29419i
$485$	−41.8831			−1.90181
$486$	28.4953	−	32.8636i	1.29257	−	1.49072i
$487$		−	5.56743i		−	0.252284i	−0.992012	−	0.126142i	$-0.959740\pi$
$487$		−	5.56743i		−	0.252284i	0.992012	−	0.126142i	$-0.0402596\pi$
$488$	107.965	−	62.3338i	4.88736	−	2.82172i
$489$	26.4316	+	6.68114i	1.19528	+	0.302132i
$490$	4.33207	−	7.50337i	0.195703	−	0.338968i
$491$	−2.62581	+	4.54804i	−0.118501	+	0.205250i	−0.919174	−	0.393852i	$-0.871142\pi$
$491$	−2.62581	+	4.54804i	−0.118501	+	0.205250i	0.800673	+	0.599102i	$0.204476\pi$
$492$	1.51737	+	5.35713i	0.0684084	+	0.241518i
$493$	−18.7096	−	32.4060i	−0.842639	−	1.45949i
$494$	−30.4479	−	21.0710i	−1.36992	−	0.948028i
$495$	−7.89311	−	4.26265i	−0.354769	−	0.191592i
$496$		−	87.4016i		−	3.92445i
$497$	3.65167	+	6.32489i	0.163800	+	0.283710i
$498$	−12.4164	−	12.0683i	−0.556390	−	0.540793i
$499$	−20.1747	−	11.6479i	−0.903143	−	0.521430i	−0.0249244	−	0.999689i	$-0.507935\pi$
$499$	−20.1747	−	11.6479i	−0.903143	−	0.521430i	−0.878219	+	0.478259i	$0.841268\pi$
$500$	5.58078	+	3.22207i	0.249580	+	0.144095i
$501$	9.24336	−	9.50994i	0.412963	−	0.424873i
$502$	−59.8437	+	34.5508i	−2.67096	+	1.54208i
$503$	−3.80958			−0.169861			−0.0849303	−	0.996387i	$-0.527067\pi$
$503$	−3.80958			−0.169861			−0.0849303	+	0.996387i	$0.527067\pi$
$504$	0.900876	+	31.6800i	0.0401282	+	1.41114i
$505$			15.2673i			0.679387i
$506$	−3.53411	−	6.12126i	−0.157110	−	0.272123i
$507$	13.3762	+	18.1129i	0.594056	+	0.804424i
$508$	13.4693	−	23.3295i	0.597602	−	1.03508i
$509$	−9.65641	−	5.57513i	−0.428013	−	0.247113i	0.270487	−	0.962724i	$-0.412815\pi$
$509$	−9.65641	−	5.57513i	−0.428013	−	0.247113i	−0.698500	+	0.715610i	$0.746149\pi$
$510$	28.3298	−	112.077i	1.25447	−	4.96286i
$511$	−4.40774	−	7.63443i	−0.194987	−	0.337728i
$512$		−	137.992i		−	6.09844i
$513$	−14.0870	−	12.9340i	−0.621955	−	0.571050i
$514$			0.579003i			0.0255387i
$515$	30.9328	−	17.8591i	1.36306	−	0.786965i
$516$	−10.4305	+	41.2645i	−0.459175	+	1.81657i
$517$	−1.18935	+	2.06001i	−0.0523074	+	0.0905991i
$518$	3.82385	+	2.20770i	0.168011	+	0.0970009i
$519$	17.7569	−	5.02954i	0.779444	−	0.220772i
$520$	−9.65915	+	117.876i	−0.423582	+	5.16921i
$521$	11.0542			0.484295			0.242147	−	0.970240i	$-0.422148\pi$
$521$	11.0542			0.484295			0.242147	+	0.970240i	$0.422148\pi$
$522$	21.3240	+	34.6226i	0.933327	+	1.51539i
$523$	32.9692			1.44164			0.720821	−	0.693121i	$-0.243765\pi$
$523$	32.9692			1.44164			0.720821	+	0.693121i	$0.243765\pi$
$524$	−48.0746	−	83.2676i	−2.10015	−	3.63756i
$525$	5.60305	−	5.76465i	0.244537	−	0.251590i
$526$	27.0319	+	15.6069i	1.17865	+	0.680491i
$527$	−32.5637	−	18.8007i	−1.41850	−	0.818969i
$528$	−20.8167	+	21.4170i	−0.905929	+	0.932056i
$529$	8.04050	+	13.9266i	0.349587	+	0.605502i
$530$	55.1946			2.39750
$531$	1.93443	+	3.14082i	0.0839469	+	0.136300i
$532$	21.2950			0.923256
$533$	−1.99650	−	0.163599i	−0.0864778	−	0.00708627i
$534$	9.51463	−	2.69496i	0.411738	−	0.116622i
$535$	−2.26637	−	1.30849i	−0.0979835	−	0.0565708i
$536$	−14.8514	+	25.7233i	−0.641481	+	1.11108i
$537$	−10.9873	+	43.4674i	−0.474136	+	1.87576i
$538$	−25.2337	+	14.5687i	−1.08790	+	0.628101i
$539$			0.963011i			0.0414798i
$540$	−20.2955	+	91.1203i	−0.873380	+	3.92119i
$541$		−	21.0742i		−	0.906051i	−0.891498	−	0.453025i	$-0.850345\pi$
$541$		−	21.0742i		−	0.906051i	0.891498	−	0.453025i	$-0.149655\pi$
$542$	−15.4674	−	26.7903i	−0.664380	−	1.15074i
$543$	−3.83830	+	15.1849i	−0.164717	+	0.651647i
$544$	−192.367	−	111.063i	−8.24767	−	4.76180i
$545$	−9.59092	+	16.6120i	−0.410830	+	0.711578i
$546$	−16.4891	−	5.63588i	−0.705669	−	0.241193i
$547$	−5.77252	−	9.99830i	−0.246815	−	0.427496i	0.715825	−	0.698279i	$-0.246051\pi$
$547$	−5.77252	−	9.99830i	−0.246815	−	0.427496i	−0.962640	+	0.270783i	$0.912717\pi$
$548$			34.3113i			1.46571i
$549$	1.00633	+	35.3883i	0.0429491	+	1.51034i
$550$	12.4718			0.531800
$551$	15.4826	−	8.93890i	0.659582	−	0.380810i
$552$	−33.5463	+	34.5138i	−1.42783	+	1.46901i
$553$	−7.92151	−	4.57348i	−0.336857	−	0.194484i
$554$	20.1242	+	11.6187i	0.854996	+	0.493632i
$555$	6.10258	+	5.93151i	0.259040	+	0.251778i
$556$	63.0374	+	109.184i	2.67338	+	4.63043i
$557$		−	5.86891i		−	0.248674i	−0.992240	−	0.124337i	$-0.960320\pi$
$557$		−	5.86891i		−	0.248674i	0.992240	−	0.124337i	$-0.0396803\pi$
$558$	35.9525	+	19.4161i	1.52199	+	0.821947i
$559$	−12.5918	−	8.71392i	−0.532574	−	0.368559i
$560$	−27.7993	−	48.1498i	−1.17474	−	2.03470i
$561$	3.50166	+	12.3627i	0.147840	+	0.521954i
$562$	−25.3956	+	43.9865i	−1.07125	+	1.85546i
$563$	0.384127	−	0.665327i	0.0161890	−	0.0280402i	−0.857817	−	0.513955i	$-0.828180\pi$
$563$	0.384127	−	0.665327i	0.0161890	−	0.0280402i	0.874006	+	0.485914i	$0.161513\pi$
$564$	23.9993	+	6.06632i	1.01055	+	0.255438i
$565$	−13.2348	+	7.64114i	−0.556794	+	0.321465i
$566$			57.0254i			2.39696i
$567$	−8.03736	−	4.04980i	−0.337537	−	0.170076i
$568$	77.1545			3.23733
$569$	−1.61960	−	2.80524i	−0.0678974	−	0.117602i	0.830078	−	0.557647i	$-0.188296\pi$
$569$	−1.61960	−	2.80524i	−0.0678974	−	0.117602i	−0.897976	+	0.440045i	$0.854962\pi$
$570$	53.5471	+	13.5352i	2.24284	+	0.566925i
$571$	−9.61910	+	16.6608i	−0.402547	+	0.697231i	−0.994033	−	0.109084i	$-0.965208\pi$
$571$	−9.61910	+	16.6608i	−0.402547	+	0.697231i	0.591486	+	0.806315i	$0.298542\pi$
$572$	−8.59056	−	18.1608i	−0.359189	−	0.759341i
$573$	15.2033	−	4.30624i	0.635127	−	0.179896i
$574$	1.34257	−	0.775135i	0.0560379	−	0.0323535i
$575$	12.2085			0.509130
$576$	117.855	+	63.6474i	4.91064	+	2.65198i
$577$		−	31.6739i		−	1.31860i	−0.751880	−	0.659300i	$-0.770853\pi$
$577$		−	31.6739i		−	1.31860i	0.751880	−	0.659300i	$-0.229147\pi$
$578$	−102.319	+	59.0738i	−4.25590	+	2.45715i
$579$	−10.1077	+	10.3992i	−0.420062	+	0.432177i
$580$	−75.5776	−	43.6347i	−3.13819	−	1.81183i
$581$	−1.79133	+	3.10267i	−0.0743167	+	0.128720i
$582$	−46.7477	−	45.4373i	−1.93776	−	1.88344i
$583$	−5.31292	+	3.06741i	−0.220039	+	0.127039i
$584$	−93.1291			−3.85371
$585$	−28.1500	−	18.3197i	−1.16386	−	0.757427i
$586$	18.2968			0.755833
$587$	−0.280004	+	0.161660i	−0.0115570	+	0.00667243i	−0.505767	−	0.862670i	$-0.668791\pi$
$587$	−0.280004	+	0.161660i	−0.0115570	+	0.00667243i	0.494210	+	0.869342i	$0.335457\pi$
$588$	9.64234	−	2.73113i	0.397643	−	0.112630i
$589$	8.98240	−	15.5580i	0.370113	−	0.641055i
$590$	−9.22597	−	5.32661i	−0.379827	−	0.219293i
$591$	−9.34050	−	2.36101i	−0.384217	−	0.0971188i
$592$	24.5380	−	14.1670i	1.00851	−	0.582262i
$593$			21.1654i			0.869158i	0.900634	+	0.434579i	$0.143103\pi$
$593$			21.1654i			0.869158i	−0.900634	+	0.434579i	$0.856897\pi$
$594$	−4.18550	−	13.3206i	−0.171733	−	0.546553i
$595$	−23.9193			−0.980594
$596$	92.4289	−	53.3638i	3.78603	−	2.18587i
$597$	−6.60182	+	26.1178i	−0.270194	+	1.06893i
$598$	−11.3159	−	23.9223i	−0.462743	−	0.978257i
$599$	−3.16747	+	5.48622i	−0.129419	+	0.224161i	−0.923452	−	0.383715i	$-0.874645\pi$
$599$	−3.16747	+	5.48622i	−0.129419	+	0.224161i	0.794032	+	0.607875i	$0.207978\pi$
$600$	−23.1443	−	81.7115i	−0.944860	−	3.33586i
$601$	−3.85751	−	6.68141i	−0.157351	−	0.272540i	0.776561	−	0.630042i	$-0.216962\pi$
$601$	−3.85751	−	6.68141i	−0.157351	−	0.272540i	−0.933913	+	0.357501i	$0.883629\pi$
$602$	11.8507			0.482997
$603$	−4.42337	−	7.18198i	−0.180134	−	0.292473i
$604$			139.675i			5.68329i
$605$	27.0857	−	15.6380i	1.10119	−	0.635773i
$606$	−16.5629	+	17.0406i	−0.672821	+	0.692226i
$607$	−9.60134	+	16.6300i	−0.389706	+	0.674991i	−0.992410	−	0.122974i	$-0.960757\pi$
$607$	−9.60134	+	16.6300i	−0.389706	+	0.674991i	0.602704	+	0.797965i	$0.294090\pi$
$608$	53.0627	−	91.9073i	2.15198	−	3.72733i
$609$	5.86407	−	6.03319i	0.237624	−	0.244477i
$610$	−51.1222	−	88.5463i	−2.06988	−	3.58514i
$611$	−5.06799	+	7.32332i	−0.205029	+	0.296270i
$612$	113.853	−	70.1221i	4.60225	−	2.83452i
$613$		−	29.3138i		−	1.18397i	−0.805948	−	0.591986i	$-0.798344\pi$
$613$		−	29.3138i		−	1.18397i	0.805948	−	0.591986i	$-0.201656\pi$
$614$	35.2399	+	61.0374i	1.42217	+	2.46327i
$615$	2.87489	−	0.814294i	0.115927	−	0.0328355i
$616$	8.81051	+	5.08675i	0.354986	+	0.204951i
$617$	42.6853	+	24.6444i	1.71845	+	0.992146i	0.921767	+	0.387745i	$0.126746\pi$
$617$	42.6853	+	24.6444i	1.71845	+	0.992146i	0.796680	+	0.604401i	$0.206587\pi$
$618$	53.9001	+	13.6244i	2.16818	+	0.548053i
$619$	−19.0894	+	11.0212i	−0.767266	+	0.442981i	−0.831898	−	0.554928i	$-0.812746\pi$
$619$	−19.0894	+	11.0212i	−0.767266	+	0.442981i	0.0646325	+	0.997909i	$0.479412\pi$
$620$	−87.6942			−3.52188
$621$	−4.09713	−	13.0394i	−0.164412	−	0.523254i
$622$			41.8975i			1.67993i
$623$	−1.02306	−	1.77199i	−0.0409881	−	0.0709934i
$624$	−84.2268	+	73.5531i	−3.37177	+	2.94448i
$625$	13.3324	−	23.0924i	0.533296	−	0.923695i
$626$	36.1991	+	20.8995i	1.44681	+	0.835314i
$627$	−5.90654	+	1.67299i	−0.235885	+	0.0668128i
$628$	−34.9080	−	60.4624i	−1.39298	−	2.41271i
$629$		−	12.1897i		−	0.486035i
$630$	25.9819	−	0.738842i	1.03514	−	0.0294362i
$631$		−	29.1732i		−	1.16137i	−0.814129	−	0.580684i	$-0.802785\pi$
$631$		−	29.1732i		−	1.16137i	0.814129	−	0.580684i	$-0.197215\pi$
$632$	−83.6849	+	48.3155i	−3.32881	+	1.92189i
$633$	−8.19402	−	7.96432i	−0.325683	−	0.316553i
$634$	8.77895	−	15.2056i	0.348657	−	0.603891i
$635$	−12.5197	−	7.22824i	−0.496829	−	0.286844i
$636$	45.7807	+	44.4973i	1.81532	+	1.76443i
$637$	−0.294464	+	3.59351i	−0.0116671	+	0.142380i
$638$	13.0528			0.516765
$639$	−10.4112	+	19.2784i	−0.411862	+	0.762641i
$640$	−207.767			−8.21271
$641$	12.6029	+	21.8288i	0.497784	+	0.862187i	0.999997	−	0.00255726i	$-0.000814003\pi$
$641$	12.6029	+	21.8288i	0.497784	+	0.862187i	−0.502213	+	0.864744i	$0.667481\pi$
$642$	−1.11007	−	3.91915i	−0.0438111	−	0.154677i
$643$	25.4819	+	14.7120i	1.00491	+	0.580183i	0.909696	−	0.415274i	$-0.136314\pi$
$643$	25.4819	+	14.7120i	1.00491	+	0.580183i	0.0952105	+	0.995457i	$0.469648\pi$
$644$	13.1805	+	7.60976i	0.519384	+	0.299866i
$645$	22.1445	+	5.59747i	0.871937	+	0.220400i
$646$	−39.5554	−	68.5120i	−1.55629	−	2.69557i
$647$	−7.79894			−0.306608			−0.153304	−	0.988179i	$-0.548991\pi$
$647$	−7.79894			−0.306608			−0.153304	+	0.988179i	$0.548991\pi$
$648$	−79.5057	+	52.1416i	−3.12328	+	2.04831i
$649$	1.18410			0.0464798
$650$	46.5390	+	3.81356i	1.82541	+	0.149580i
$651$	2.07187	−	8.19662i	0.0812029	−	0.321251i
$652$	−78.8718	−	45.5367i	−3.08886	−	1.78335i
$653$	7.29372	−	12.6331i	0.285425	−	0.494371i	−0.687287	−	0.726386i	$-0.741198\pi$
$653$	7.29372	−	12.6331i	0.285425	−	0.494371i	0.972712	+	0.232015i	$0.0745318\pi$
$654$	−28.7265	+	8.13660i	−1.12330	+	0.318166i
$655$	−44.6853	+	25.7991i	−1.74600	+	1.00805i
$656$		−	9.94823i		−	0.388413i
$657$	12.5669	−	23.2699i	0.490280	−	0.907846i
$658$		−	6.89231i		−	0.268690i
$659$	−6.98279	−	12.0945i	−0.272011	−	0.471136i	0.697366	−	0.716715i	$-0.254355\pi$
$659$	−6.98279	−	12.0945i	−0.272011	−	0.471136i	−0.969377	+	0.245579i	$0.921022\pi$
$660$	21.4887	+	20.8863i	0.836447	+	0.812999i
$661$	25.4698	+	14.7050i	0.990661	+	0.571959i	0.905472	−	0.424406i	$-0.139517\pi$
$661$	25.4698	+	14.7050i	0.990661	+	0.571959i	0.0851894	+	0.996365i	$0.472850\pi$
$662$	−38.9613	+	67.4829i	−1.51427	+	2.62280i
$663$	9.28636	+	47.2026i	0.360652	+	1.83320i
$664$	18.9240	+	32.7774i	0.734395	+	1.27201i
$665$		−	11.4279i		−	0.443156i
$666$	0.376527	+	13.2409i	0.0145901	+	0.513073i
$667$	12.7772			0.494736
$668$	−38.3668	+	22.1511i	−1.48446	+	0.857052i
$669$	−5.37792	−	18.9869i	−0.207923	−	0.734077i
$670$	21.0966	+	12.1802i	0.815035	+	0.470560i
$671$	9.84184	+	5.68219i	0.379940	+	0.219358i
$672$	12.2394	−	48.4208i	0.472144	−	1.86787i
$673$	21.2756	+	36.8505i	0.820116	+	1.42048i	0.905596	+	0.424142i	$0.139424\pi$
$673$	21.2756	+	36.8505i	0.820116	+	1.42048i	−0.0854799	+	0.996340i	$0.527242\pi$
$674$		−	54.3538i		−	2.09363i
$675$	23.5401	+	5.24316i	0.906060	+	0.201809i
$676$	−26.5029	−	70.3944i	−1.01934	−	2.70748i
$677$	11.4050	+	19.7540i	0.438329	+	0.759208i	0.997561	−	0.0698031i	$-0.0222371\pi$
$677$	11.4050	+	19.7540i	0.438329	+	0.759208i	−0.559232	+	0.829011i	$0.688904\pi$
$678$	−23.0616	−	5.82930i	−0.885675	−	0.223873i
$679$	−6.74436	+	11.6816i	−0.258825	+	0.448298i
$680$	−126.345	+	218.835i	−4.84510	+	8.39195i
$681$	−7.35940	−	25.9826i	−0.282013	−	0.995655i
$682$	11.3591	−	6.55816i	0.434961	−	0.251125i
$683$			32.1993i			1.23207i	0.787717	+	0.616037i	$0.211263\pi$
$683$			32.1993i			1.23207i	−0.787717	+	0.616037i	$0.788737\pi$
$684$	33.5023	+	54.3958i	1.28099	+	2.07987i
$685$	18.4131			0.703527
$686$	−1.39517	−	2.41651i	−0.0532679	−	0.0922627i
$687$	21.4498	−	22.0684i	0.818359	−	0.841962i
$688$	38.0234	−	65.8585i	1.44963	−	2.51083i
$689$	−20.7633	+	9.82160i	−0.791017	+	0.374173i
$690$	28.3060	+	27.5126i	1.07759	+	1.04739i
$691$	−12.5112	+	7.22336i	−0.475950	+	0.274790i	−0.718727	−	0.695292i	$-0.755275\pi$
$691$	−12.5112	+	7.22336i	−0.475950	+	0.274790i	0.242777	+	0.970082i	$0.421942\pi$
$692$	−61.6516			−2.34364
$693$	−2.45990	+	1.51505i	−0.0934440	+	0.0575521i
$694$			55.7804i			2.11739i
$695$	58.5932	−	33.8288i	2.22257	−	1.28320i
$696$	−24.2224	−	85.5180i	−0.918149	−	3.24155i
$697$	−3.70647	−	2.13993i	−0.140392	−	0.0810556i
$698$	21.9826	−	38.0750i	0.832054	−	1.44116i
$699$	4.06648	−	16.0876i	0.153808	−	0.608490i
$700$	−23.2568	+	13.4273i	−0.879026	+	0.507506i
$701$	27.7025			1.04631			0.523155	−	0.852238i	$-0.324755\pi$
$701$	27.7025			1.04631			0.523155	+	0.852238i	$0.324755\pi$
$702$	−11.5452	−	50.9863i	−0.435746	−	1.92435i
$703$	5.82388			0.219652
$704$	37.2359	−	21.4982i	1.40338	−	0.810243i
$705$	3.25547	−	12.8791i	0.122608	−	0.485057i
$706$	−18.4208	+	31.9057i	−0.693275	+	1.20079i
$707$	4.25819	+	2.45847i	0.160146	+	0.0924603i
$708$	−3.35813	−	11.8560i	−0.126206	−	0.445576i
$709$	28.2889	−	16.3326i	1.06241	−	0.613384i	0.136313	−	0.990666i	$-0.456475\pi$
$709$	28.2889	−	16.3326i	1.06241	−	0.613384i	0.926098	+	0.377282i	$0.123141\pi$
$710$		−	63.2772i		−	2.37475i
$711$	−0.780015	−	27.4298i	−0.0292528	−	1.02870i
$712$	−21.6158			−0.810085
$713$	11.1193	−	6.41970i	0.416419	−	0.240420i
$714$	−26.6974	−	25.9490i	−0.999125	−	0.971117i
$715$	−9.74594	+	4.61010i	−0.364477	+	0.172408i
$716$	74.8861	−	129.706i	2.79862	−	4.84736i
$717$	−3.87468	+	3.98643i	−0.144703	+	0.148876i
$718$	−14.9589	−	25.9095i	−0.558260	−	0.966935i
$719$	5.00445			0.186634			0.0933172	−	0.995636i	$-0.470253\pi$
$719$	5.00445			0.186634			0.0933172	+	0.995636i	$0.470253\pi$
$720$	79.2582	−	146.762i	2.95378	−	5.46949i
$721$		−	11.5033i		−	0.428404i
$722$	−13.1806	+	7.60983i	−0.490532	+	0.283209i
$723$	10.6593	+	37.6329i	0.396422	+	1.39958i
$724$	26.1607	−	45.3117i	0.972256	−	1.68400i
$725$	−11.2726	+	19.5248i	−0.418656	+	0.725133i
$726$	47.1966	+	11.9299i	1.75163	+	0.442761i
$727$	−18.2855	−	31.6715i	−0.678173	−	1.17463i	−0.975531	−	0.219864i	$-0.929439\pi$
$727$	−18.2855	−	31.6715i	−0.678173	−	1.17463i	0.297357	−	0.954766i	$-0.403895\pi$
$728$	31.3213	+	21.6754i	1.16085	+	0.803344i
$729$	−2.29997	−	26.9019i	−0.0851839	−	0.996365i
$730$			76.3786i			2.82690i
$731$	−16.3582	−	28.3332i	−0.605029	−	1.04794i
$732$	28.9823	−	114.658i	1.07122	−	4.23789i
$733$	0.308620	+	0.178182i	0.0113991	+	0.00658129i	0.505689	−	0.862716i	$-0.331238\pi$
$733$	0.308620	+	0.178182i	0.0113991	+	0.00658129i	−0.494290	+	0.869297i	$0.664572\pi$
$734$	18.6752	+	10.7821i	0.689314	+	0.397975i
$735$	−1.46565	−	5.17453i	−0.0540614	−	0.190866i
$736$	65.6860	−	37.9238i	2.42122	−	1.39789i
$737$	−2.70762			−0.0997366
$738$	4.09219	+	2.20998i	0.150636	+	0.0813503i
$739$		−	13.2214i		−	0.486358i	−0.969981	−	0.243179i	$-0.921810\pi$
$739$		−	13.2214i		−	0.486358i	0.969981	−	0.243179i	$-0.0781902\pi$
$740$	−14.2145	−	24.6202i	−0.522534	−	0.905056i
$741$	−22.5520	+	4.43675i	−0.828469	+	0.162988i
$742$	8.88789	−	15.3943i	0.326285	−	0.565142i
$743$	16.2986	+	9.41001i	0.597938	+	0.345220i	0.768230	−	0.640174i	$-0.221138\pi$
$743$	16.2986	+	9.41001i	0.597938	+	0.345220i	−0.170292	+	0.985394i	$0.554471\pi$
$744$	−64.0464	−	62.2510i	−2.34805	−	2.28223i
$745$	−28.6376	−	49.6017i	−1.04920	−	1.81727i
$746$			42.6908i			1.56302i
$747$	−10.7436	+	0.305514i	−0.393088	+	0.0111782i
$748$		−	42.9230i		−	1.56942i
$749$	−0.729898	+	0.421407i	−0.0266699	+	0.0153979i
$750$	5.17900	−	1.46692i	0.189110	−	0.0535643i
$751$	−20.4158	+	35.3612i	−0.744983	+	1.29035i	0.205219	+	0.978716i	$0.434209\pi$
$751$	−20.4158	+	35.3612i	−0.744983	+	1.29035i	−0.950203	+	0.311633i	$0.899124\pi$
$752$	−38.3031	−	22.1143i	−1.39677	−	0.806426i
$753$	−10.5116	+	41.5855i	−0.383064	+	1.51546i
$754$	48.7070	+	3.99121i	1.77380	+	0.145351i
$755$	74.9562			2.72793
$756$	22.1461	+	20.3335i	0.805447	+	0.739524i
$757$	2.70234			0.0982182			0.0491091	−	0.998793i	$-0.484362\pi$
$757$	2.70234			0.0982182			0.0491091	+	0.998793i	$0.484362\pi$
$758$	36.7816	+	63.7075i	1.33597	+	2.31396i
$759$	−4.25368	−	1.07521i	−0.154399	−	0.0390275i
$760$	−104.553	−	60.3638i	−3.79254	−	2.18962i
$761$	8.51858	+	4.91821i	0.308798	+	0.178285i	0.646389	−	0.763008i	$-0.276278\pi$
$761$	8.51858	+	4.91821i	0.308798	+	0.178285i	−0.337590	+	0.941293i	$0.609612\pi$
$762$	−6.13219	−	21.6499i	−0.222146	−	0.784292i
$763$	3.08882	+	5.34999i	0.111823	+	0.193683i
$764$	−52.7854			−1.90971
$765$	−37.6308	−	61.0991i	−1.36055	−	2.20904i
$766$	−9.45313			−0.341556
$767$	4.41849	+	0.362066i	0.159543	+	0.0130734i
$768$	−120.991	−	117.599i	−4.36587	−	4.24349i
$769$	27.5370	+	15.8985i	0.993010	+	0.573315i	0.906173	−	0.422908i	$-0.138991\pi$
$769$	27.5370	+	15.8985i	0.993010	+	0.573315i	0.0868375	+	0.996222i	$0.472324\pi$
$770$	4.17183	−	7.22582i	0.150342	−	0.260401i
$771$	0.257724	+	0.250499i	0.00928171	+	0.00902152i
$772$	41.9545	−	24.2224i	1.50998	−	0.871785i
$773$		−	37.7896i		−	1.35920i	−0.733584	−	0.679599i	$-0.762154\pi$
$773$		−	37.7896i		−	1.35920i	0.733584	−	0.679599i	$-0.237846\pi$
$774$	18.6440	+	30.2712i	0.670145	+	1.08808i
$775$			22.6550i			0.813792i
$776$	71.2492	+	123.407i	2.55770	+	4.43006i
$777$	2.63704	−	0.746924i	0.0946032	−	0.0267958i
$778$	59.1174	+	34.1314i	2.11946	+	1.22367i
$779$	1.02240	−	1.77084i	0.0366311	−	0.0634469i
$780$	73.7993	+	84.5087i	2.64244	+	3.02590i
$781$	3.51660	+	6.09093i	0.125834	+	0.217951i
$782$		−	56.5404i		−	2.02188i
$783$	24.6367	+	5.48742i	0.880445	+	0.196104i
$784$	−17.9059			−0.639496
$785$	−32.4470	+	18.7333i	−1.15808	+	0.668619i
$786$	−77.8637	−	19.6817i	−2.77731	−	0.702022i
$787$	46.0724	+	26.5999i	1.64231	+	0.948185i	0.980011	+	0.198941i	$0.0637502\pi$
$787$	46.0724	+	26.5999i	1.64231	+	0.948185i	0.662294	+	0.749244i	$0.269583\pi$
$788$	27.8720	+	16.0919i	0.992900	+	0.573251i
$789$	18.6419	−	5.28021i	0.663671	−	0.187980i
$790$	39.6253	+	68.6330i	1.40981	+	2.44185i
$791$			4.92175i			0.174997i
$792$	0.867554	+	30.5082i	0.0308272	+	1.08406i
$793$	34.9877	+	24.2127i	1.24245	+	0.859816i
$794$	−30.1477	−	52.2173i	−1.06990	−	1.85312i
$795$	23.8794	−	24.5681i	0.846914	−	0.871340i
$796$	44.9960	−	77.9354i	1.59484	−	2.76235i
$797$	7.79933	−	13.5088i	0.276267	−	0.478508i	−0.694187	−	0.719794i	$-0.744236\pi$
$797$	7.79933	−	13.5088i	0.276267	−	0.478508i	0.970454	+	0.241287i	$0.0775694\pi$
$798$	12.3977	−	12.7552i	0.438873	−	0.451530i
$799$	−16.4785	+	9.51387i	−0.582968	+	0.336576i
$800$			133.832i			4.73169i
$801$	2.91683	−	5.40107i	0.103061	−	0.190838i
$802$	69.3788			2.44985
$803$	−4.24470	−	7.35204i	−0.149792	−	0.259448i
$804$	7.67891	+	27.1106i	0.270814	+	0.956118i
$805$	4.08376	−	7.07327i	0.143933	−	0.249300i
$806$	44.3921	−	20.9987i	1.56364	−	0.739647i
$807$	−4.43232	+	17.5349i	−0.156025	+	0.617259i
$808$	44.9847	−	25.9719i	1.58256	−	0.913689i
$809$	49.6205			1.74456			0.872282	−	0.489003i	$-0.162639\pi$
$809$	49.6205			1.74456			0.872282	+	0.489003i	$0.162639\pi$
$810$	42.7632	+	65.2055i	1.50255	+	2.29109i
$811$		−	35.9733i		−	1.26319i	−0.775297	−	0.631597i	$-0.782400\pi$
$811$		−	35.9733i		−	1.26319i	0.775297	−	0.631597i	$-0.217600\pi$
$812$	−24.3402	+	14.0528i	−0.854175	+	0.493158i
$813$	−18.6166	−	4.70574i	−0.652913	−	0.165037i
$814$	3.68241	+	2.12604i	0.129069	+	0.0745178i
$815$	−24.4371	+	42.3263i	−0.855995	+	1.48263i
$816$	−229.868	+	65.1087i	−8.04699	+	2.27926i
$817$	13.5368	−	7.81546i	0.473592	−	0.273428i
$818$	−53.3149			−1.86411
$819$	−9.64248	+	4.90129i	−0.336935	+	0.171265i
$820$	−9.98153			−0.348570
$821$	46.7472	−	26.9895i	1.63149	−	0.941941i	0.647855	−	0.761764i	$-0.275666\pi$
$821$	46.7472	−	26.9895i	1.63149	−	0.941941i	0.983634	−	0.180176i	$-0.0576669\pi$
$822$	20.5517	+	19.9756i	0.716822	+	0.696728i
$823$	−8.39407	+	14.5390i	−0.292599	+	0.506796i	−0.974423	−	0.224720i	$-0.927853\pi$
$823$	−8.39407	+	14.5390i	−0.292599	+	0.506796i	0.681825	+	0.731516i	$0.261187\pi$
$824$	−105.242	−	60.7617i	−3.66629	−	2.11673i
$825$	5.39580	−	5.55142i	0.187858	−	0.193276i
$826$	−2.97128	+	1.71547i	−0.103384	+	0.0596888i
$827$			39.5883i			1.37662i	0.725417	+	0.688309i	$0.241647\pi$
$827$			39.5883i			1.37662i	−0.725417	+	0.688309i	$0.758353\pi$
$828$	1.29786	+	45.6401i	0.0451036	+	1.58610i
$829$	−45.4725			−1.57933			−0.789663	−	0.613541i	$-0.789744\pi$
$829$	−45.4725			−1.57933			−0.789663	+	0.613541i	$0.789744\pi$
$830$	26.8820	−	15.5203i	0.933086	−	0.538718i
$831$	13.8782	−	3.93092i	0.481431	−	0.136362i
$832$	145.521	−	68.8354i	5.04502	−	2.38644i
$833$	−3.85167	+	6.67130i	−0.133453	+	0.231147i
$834$	102.098	+	25.8074i	3.53537	+	0.893639i
$835$	11.8873	+	20.5894i	0.411378	+	0.712527i
$836$	20.5073			0.709261
$837$	24.1969	−	7.60294i	0.836368	−	0.262796i
$838$		−	77.6836i		−	2.68354i
$839$	−26.4979	+	15.2986i	−0.914811	+	0.528166i	−0.881976	−	0.471295i	$-0.843787\pi$
$839$	−26.4979	+	15.2986i	−0.914811	+	0.528166i	−0.0328348	+	0.999461i	$0.510454\pi$
$840$	−55.0832	−	13.9234i	−1.90055	−	0.480404i
$841$	2.70222	−	4.68038i	0.0931800	−	0.161392i
$842$	−18.7621	+	32.4969i	−0.646584	+	1.11992i
$843$	8.59201	+	30.3344i	0.295925	+	1.04477i
$844$	19.0860	+	33.0579i	0.656966	+	1.13790i
$845$	−37.7769	+	14.2227i	−1.29957	+	0.489275i
$846$	17.6056	−	10.8433i	0.605295	−	0.372800i
$847$		−	10.0726i		−	0.346099i
$848$	−57.0344	−	98.7866i	−1.95857	−	3.39234i
$849$	25.3830	+	24.6714i	0.871142	+	0.846722i
$850$	86.3990	+	49.8825i	2.96346	+	1.71095i
$851$	3.60467	+	2.08116i	0.123567	+	0.0713412i
$852$	51.0135	−	52.4848i	1.74769	−	1.79810i
$853$	26.8129	−	15.4804i	0.918055	−	0.530039i	0.0350411	−	0.999386i	$-0.488844\pi$
$853$	26.8129	−	15.4804i	0.918055	−	0.530039i	0.883014	+	0.469346i	$0.155510\pi$
$854$	−32.9285			−1.12679
$855$	29.1913	−	17.9789i	0.998323	−	0.614866i
$856$			8.90370i			0.304322i
$857$	2.12921	+	3.68790i	0.0727324	+	0.125976i	0.900098	−	0.435688i	$-0.143495\pi$
$857$	2.12921	+	3.68790i	0.0727324	+	0.125976i	−0.827366	+	0.561664i	$0.810161\pi$
$858$	−15.8792	−	5.42741i	−0.542107	−	0.185289i
$859$	−17.5929	+	30.4719i	−0.600264	+	1.03969i	0.392517	+	0.919745i	$0.371604\pi$
$859$	−17.5929	+	30.4719i	−0.600264	+	1.03969i	−0.992781	+	0.119942i	$0.961729\pi$
$860$	−66.0790	−	38.1507i	−2.25327	−	1.30093i
$861$	0.235824	−	0.932957i	0.00803687	−	0.0317951i
$862$	22.3846	+	38.7713i	0.762423	+	1.32055i
$863$			35.3822i			1.20442i	0.798336	+	0.602212i	$0.205714\pi$
$863$			35.3822i			1.20442i	−0.798336	+	0.602212i	$0.794286\pi$
$864$	142.941	−	44.9137i	4.86296	−	1.52800i
$865$			33.0852i			1.12493i
$866$	−2.90215	+	1.67556i	−0.0986190	+	0.0569377i
$867$	−17.9724	+	71.1015i	−0.610374	+	2.41473i
$868$	−14.1212	+	24.4587i	−0.479306	+	0.830182i
$869$	−7.62850	−	4.40431i	−0.258779	−	0.149406i
$870$	−70.1365	+	19.8657i	−2.37785	+	0.673510i
$871$	−10.1036	−	0.827921i	−0.342347	−	0.0280530i
$872$	65.2622			2.21006
$873$	−40.4498	+	1.15026i	−1.36902	+	0.0389305i
$874$	27.0133			0.913740
$875$	−0.556872	−	0.964530i	−0.0188257	−	0.0326071i
$876$	−61.5757	+	63.3516i	−2.08045	+	2.14045i
$877$	−18.4018	−	10.6243i	−0.621384	−	0.358756i	0.156024	−	0.987753i	$-0.450132\pi$
$877$	−18.4018	−	10.6243i	−0.621384	−	0.358756i	−0.777408	+	0.628997i	$0.783466\pi$
$878$	−18.8117	−	10.8610i	−0.634865	−	0.366540i
$879$	7.91591	−	8.14421i	0.266997	−	0.274697i
$880$	−26.7710	−	46.3688i	−0.902452	−	1.56309i
$881$	39.7494			1.33919			0.669595	−	0.742726i	$-0.266468\pi$
$881$	39.7494			1.33919			0.669595	+	0.742726i	$0.266468\pi$
$882$	3.97775	−	7.36557i	0.133938	−	0.248012i
$883$	−2.79832			−0.0941710			−0.0470855	−	0.998891i	$-0.514993\pi$
$883$	−2.79832			−0.0941710			−0.0470855	+	0.998891i	$0.514993\pi$
$884$	13.1247	−	160.169i	0.441433	−	5.38705i
$885$	−6.36249	+	1.80213i	−0.213873	+	0.0605781i
$886$	−48.7697	−	28.1572i	−1.63845	−	0.945960i
$887$	−6.44994	+	11.1716i	−0.216568	+	0.375106i	−0.953756	−	0.300581i	$-0.902820\pi$
$887$	−6.44994	+	11.1716i	−0.216568	+	0.375106i	0.737189	+	0.675687i	$0.236153\pi$
$888$	7.09563	−	28.0714i	0.238114	−	0.942015i
$889$	−4.03204	+	2.32790i	−0.135230	+	0.0780753i
$890$			17.7279i			0.594240i
$891$	−7.74006	−	3.90000i	−0.259302	−	0.130655i
$892$			65.9220i			2.20723i
$893$	−4.54545	−	7.87294i	−0.152108	−	0.263458i
$894$	21.8471	−	86.4305i	0.730677	−	2.89067i
$895$	−69.6066	−	40.1874i	−2.32669	−	1.34332i
$896$	−33.4563	+	57.9481i	−1.11770	+	1.93591i
$897$	−15.5440	−	5.31283i	−0.518998	−	0.177390i
$898$	−52.9506	−	91.7132i	−1.76699	−	3.06051i
$899$			23.7104i			0.790785i
$900$	−70.8873	−	38.2825i	−2.36291	−	1.27608i
$901$	−49.0739			−1.63489
$902$	1.29291	−	0.746463i	0.0430493	−	0.0248545i
$903$	5.12707	−	5.27494i	0.170618	−	0.175539i
$904$	45.0287	+	25.9974i	1.49763	+	0.864659i
$905$	−24.3164	−	14.0391i	−0.808305	−	0.466675i
$906$	83.6621	+	81.3168i	2.77949	+	2.70157i
$907$	−14.5675	−	25.2317i	−0.483706	−	0.837803i	0.516119	−	0.856517i	$-0.327376\pi$
$907$	−14.5675	−	25.2317i	−0.483706	−	0.837803i	−0.999825	+	0.0187136i	$0.994043\pi$
$908$			90.2108i			2.99375i
$909$	0.419296	+	14.7449i	0.0139072	+	0.489056i
$910$	17.7768	−	25.6878i	0.589295	−	0.851541i
$911$	7.19399	+	12.4603i	0.238347	+	0.412830i	0.960240	−	0.279175i	$-0.0900610\pi$
$911$	7.19399	+	12.4603i	0.238347	+	0.412830i	−0.721893	+	0.692005i	$0.756728\pi$
$912$	−31.1070	−	109.824i	−1.03006	−	3.63664i
$913$	−1.72507	+	2.98790i	−0.0570914	+	0.0988852i
$914$	7.06628	−	12.2392i	0.233732	−	0.404835i
$915$	−61.5310	−	15.5532i	−2.03415	−	0.514175i
$916$	−89.0325	+	51.4029i	−2.94172	+	1.69840i
$917$			16.6175i			0.548759i
$918$	24.2823	−	109.020i	0.801435	−	3.59819i
$919$	−11.9239			−0.393334			−0.196667	−	0.980470i	$-0.563012\pi$
$919$	−11.9239			−0.393334			−0.196667	+	0.980470i	$0.563012\pi$
$920$	−43.1419	−	74.7239i	−1.42235	−	2.46357i
$921$	42.4150	+	10.7213i	1.39762	+	0.353278i
$922$	50.1597	−	86.8791i	1.65192	−	2.86121i
$923$	11.2599	+	23.8038i	0.370623	+	0.783512i
$924$	9.28568	−	2.63011i	0.305476	−	0.0865242i
$925$	−6.36040	+	3.67218i	−0.209129	+	0.120741i
$926$	−16.5904			−0.545194
$927$	29.3838	−	18.0974i	0.965090	−	0.594398i
$928$			140.067i			4.59792i
$929$	−24.4346	+	14.1073i	−0.801672	+	0.462845i	−0.844055	−	0.536256i	$-0.819838\pi$
$929$	−24.4346	+	14.1073i	−0.801672	+	0.462845i	0.0423837	+	0.999101i	$0.486505\pi$
$930$	−51.0543	+	52.5268i	−1.67414	+	1.72242i
$931$	−3.18735	−	1.84022i	−0.104461	−	0.0603107i
$932$	−27.7159	+	48.0054i	−0.907865	+	1.57247i
$933$	18.6493	+	18.1265i	0.610550	+	0.593435i
$934$	23.2187	−	13.4053i	0.759739	−	0.438636i
$935$	−23.0345			−0.753309
$936$	−6.09130	+	114.108i	−0.199100	+	3.72972i
$937$	−20.4339			−0.667547			−0.333774	−	0.942653i	$-0.608322\pi$
$937$	−20.4339			−0.667547			−0.333774	+	0.942653i	$0.608322\pi$
$938$	6.79431	−	3.92270i	0.221842	−	0.128081i
$939$	24.9639	−	7.07087i	0.814666	−	0.230749i
$940$	−22.1883	+	38.4313i	−0.723704	+	1.25349i
$941$	−6.28179	−	3.62680i	−0.204781	−	0.118230i	0.394103	−	0.919066i	$-0.371055\pi$
$941$	−6.28179	−	3.62680i	−0.204781	−	0.118230i	−0.598883	+	0.800836i	$0.704389\pi$
$942$	−56.5385	−	14.2913i	−1.84212	−	0.465635i
$943$	1.26562	−	0.730704i	0.0412141	−	0.0237950i
$944$			22.0167i			0.716582i
$945$	10.9119	−	11.8847i	0.354965	−	0.386608i
$946$	11.4123			0.371047
$947$	−6.58650	+	3.80271i	−0.214032	+	0.123572i	−0.603184	−	0.797602i	$-0.706102\pi$
$947$	−6.58650	+	3.80271i	−0.214032	+	0.123572i	0.389152	+	0.921174i	$0.372768\pi$
$948$	−22.4644	+	88.8726i	−0.729610	+	2.88645i
$949$	−13.5912	−	28.7323i	−0.441189	−	0.932690i
$950$	−23.8324	+	41.2789i	−0.773224	+	1.33926i
$951$	−2.97015	−	10.4862i	−0.0963137	−	0.340038i
$952$	40.6901	+	70.4773i	1.31877	+	2.28418i
$953$	4.05582			0.131381			0.0656904	−	0.997840i	$-0.479075\pi$
$953$	4.05582			0.131381			0.0656904	+	0.997840i	$0.479075\pi$
$954$	53.3058	−	1.51584i	1.72584	−	0.0490773i
$955$			28.3271i			0.916645i
$956$	16.0828	−	9.28542i	0.520156	−	0.300312i
$957$	5.64716	−	5.81003i	0.182547	−	0.187812i
$958$	10.4916	−	18.1720i	0.338969	−	0.587111i
$959$	2.96502	−	5.13557i	0.0957456	−	0.165836i
$960$	−167.360	+	172.187i	−5.40153	+	5.55731i
$961$	−3.58712	−	6.21307i	−0.115714	−	0.200422i
$962$	13.0910	+	9.05938i	0.422069	+	0.292086i
$963$	−2.22474	−	1.20147i	−0.0716914	−	0.0387167i
$964$		−	130.660i		−	4.20828i
$965$	−12.9989	−	22.5148i	−0.418449	−	0.724776i
$966$	12.2316	−	3.46451i	0.393544	−	0.111469i
$967$	−39.6721	−	22.9047i	−1.27577	−	0.736565i	−0.299701	−	0.954033i	$-0.596887\pi$
$967$	−39.6721	−	22.9047i	−1.27577	−	0.736565i	−0.976068	+	0.217468i	$0.930220\pi$
$968$	−92.1535	−	53.2049i	−2.96193	−	1.71007i
$969$	−47.6091	−	12.0342i	−1.52943	−	0.386594i
$970$	101.211	−	58.4341i	3.24969	−	1.87621i
$971$	−22.0723			−0.708335			−0.354167	−	0.935182i	$-0.615236\pi$
$971$	−22.0723			−0.708335			−0.354167	+	0.935182i	$0.615236\pi$
$972$	−17.0985	+	88.5594i	−0.548434	+	2.84055i
$973$		−	21.7896i		−	0.698542i
$974$	7.76752	+	13.4537i	0.248887	+	0.431086i
$975$	21.8321	−	19.0654i	0.699186	−	0.610582i
$976$	−105.653	+	182.996i	−3.38186	+	5.85755i
$977$	34.8119	+	20.0987i	1.11373	+	0.643014i	0.939794	−	0.341743i	$-0.111017\pi$
$977$	34.8119	+	20.0987i	1.11373	+	0.643014i	0.173939	+	0.984756i	$0.444351\pi$
$978$	−73.1935	+	20.7316i	−2.34047	+	0.662923i
$979$	−0.985219	−	1.70645i	−0.0314877	−	0.0545383i
$980$			17.9658i			0.573897i
$981$	−8.80648	+	16.3069i	−0.281169	+	0.520639i
$982$		−	14.6538i		−	0.467623i
$983$	21.6501	−	12.4997i	0.690532	−	0.398679i	−0.113279	−	0.993563i	$-0.536135\pi$
$983$	21.6501	−	12.4997i	0.690532	−	0.398679i	0.803811	+	0.594884i	$0.202802\pi$
$984$	−7.28989	−	7.08554i	−0.232393	−	0.225879i
$985$	8.63568	−	14.9574i	0.275156	−	0.476584i
$986$	90.4238	+	52.2062i	2.87968	+	1.66258i
$987$	−3.06789	−	2.98189i	−0.0976519	−	0.0949145i
$988$	76.5238	+	6.27061i	2.43455	+	0.199495i
$989$	11.1714			0.355229
$990$	25.0209	−	0.711513i	0.795216	−	0.0226134i
$991$	9.75213			0.309786			0.154893	−	0.987931i	$-0.450497\pi$
$991$	9.75213			0.309786			0.154893	+	0.987931i	$0.450497\pi$
$992$	70.3743	+	121.892i	2.23439	+	3.87007i
$993$	13.1816	+	46.5381i	0.418306	+	1.47684i
$994$	−17.6486	−	10.1894i	−0.559779	−	0.323189i
$995$	−41.8238	−	24.1470i	−1.32590	−	0.765511i
$996$	34.8093	+	8.79878i	1.10298	+	0.278800i
$997$	−0.752195	−	1.30284i	−0.0238223	−	0.0412614i	0.853868	−	0.520489i	$-0.174250\pi$
$997$	−0.752195	−	1.30284i	−0.0238223	−	0.0412614i	−0.877691	+	0.479227i	$0.840917\pi$
$998$	65.0030			2.05764
$999$	6.05664	+	5.56093i	0.191624	+	0.175940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dt.a.337.1	✓	168
9.7	even	3	inner	819.2.dt.a.610.84	yes	168
13.12	even	2	inner	819.2.dt.a.337.84	yes	168
117.25	even	6	inner	819.2.dt.a.610.1	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.dt.a.337.1	✓	168	1.1	even	1	trivial
819.2.dt.a.337.84	yes	168	13.12	even	2	inner
819.2.dt.a.610.1	yes	168	117.25	even	6	inner
819.2.dt.a.610.84	yes	168	9.7	even	3	inner

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.41651 + 1.39517i) q^{2} +(-0.424462 + 1.67924i) q^{3} +(2.89301 - 5.01083i) q^{4} +(-2.68905 - 1.55252i) q^{5} +(-1.31711 - 4.65008i) q^{6} +(-0.866025 + 0.500000i) q^{7} +10.5643i q^{8} +(-2.63966 - 1.42554i) q^{9} +O(q^{10})\)	\(q+(-2.41651 + 1.39517i) q^{2} +(-0.424462 + 1.67924i) q^{3} +(2.89301 - 5.01083i) q^{4} +(-2.68905 - 1.55252i) q^{5} +(-1.31711 - 4.65008i) q^{6} +(-0.866025 + 0.500000i) q^{7} +10.5643i q^{8} +(-2.63966 - 1.42554i) q^{9} +8.66414 q^{10} +(-0.833992 + 0.481505i) q^{11} +(7.18640 + 6.98494i) q^{12} +(-3.25930 + 1.54174i) q^{13} +(1.39517 - 2.41651i) q^{14} +(3.74845 - 3.85656i) q^{15} +(-8.95295 - 15.5070i) q^{16} -7.70335 q^{17} +(8.36764 - 0.237949i) q^{18} -3.68043i q^{19} +(-15.5589 + 8.98291i) q^{20} +(-0.472023 - 1.66649i) q^{21} +(1.34356 - 2.32712i) q^{22} +(1.31520 - 2.27799i) q^{23} +(-17.7399 - 4.48413i) q^{24} +(2.32066 + 4.01949i) q^{25} +(5.72513 - 8.27291i) q^{26} +(3.51426 - 3.82753i) q^{27} +5.78601i q^{28} +(2.42876 + 4.20674i) q^{29} +(-3.67760 + 14.5491i) q^{30} +(4.22721 + 2.44058i) q^{31} +(24.9719 + 14.4175i) q^{32} +(-0.454563 - 1.60485i) q^{33} +(18.6152 - 10.7475i) q^{34} +3.10505 q^{35} +(-14.7797 + 9.10281i) q^{36} +1.58239i q^{37} +(5.13483 + 8.89380i) q^{38} +(-1.20550 - 6.12754i) q^{39} +(16.4013 - 28.4078i) q^{40} +(0.481150 + 0.277792i) q^{41} +(3.46569 + 3.36854i) q^{42} +(2.12352 + 3.67804i) q^{43} +5.57199i q^{44} +(4.88500 + 7.93149i) q^{45} +7.33971i q^{46} +(2.13913 - 1.23503i) q^{47} +(29.8400 - 8.45199i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-11.2158 - 6.47542i) q^{50} +(3.26978 - 12.9357i) q^{51} +(-1.70377 + 20.7921i) q^{52} +6.37047 q^{53} +(-3.15217 + 14.1522i) q^{54} +2.99019 q^{55} +(-5.28213 - 9.14892i) q^{56} +(6.18032 + 1.56220i) q^{57} +(-11.7382 - 6.77708i) q^{58} +(-1.06484 - 0.614788i) q^{59} +(-8.48029 - 29.9399i) q^{60} +(-5.90044 - 10.2199i) q^{61} -13.6201 q^{62} +(2.99879 - 0.0852758i) q^{63} -44.6478 q^{64} +(11.1580 + 0.914323i) q^{65} +(3.33750 + 3.24394i) q^{66} +(2.43494 + 1.40581i) q^{67} +(-22.2858 + 38.6002i) q^{68} +(3.26703 + 3.17545i) q^{69} +(-7.50337 + 4.33207i) q^{70} -7.30335i q^{71} +(15.0598 - 27.8861i) q^{72} +8.81549i q^{73} +(-2.20770 - 3.82385i) q^{74} +(-7.73471 + 2.19081i) q^{75} +(-18.4420 - 10.6475i) q^{76} +(0.481505 - 0.833992i) q^{77} +(11.4621 + 13.1254i) q^{78} +(4.57348 + 7.92151i) q^{79} +55.5986i q^{80} +(4.93566 + 7.52591i) q^{81} -1.55027 q^{82} +(3.10267 - 1.79133i) q^{83} +(-9.71607 - 2.45594i) q^{84} +(20.7147 + 11.9596i) q^{85} +(-10.2630 - 5.92533i) q^{86} +(-8.09503 + 2.29286i) q^{87} +(-5.08675 - 8.81051i) q^{88} +2.04612i q^{89} +(-22.8704 - 12.3511i) q^{90} +(2.05177 - 2.96484i) q^{91} +(-7.60976 - 13.1805i) q^{92} +(-5.89260 + 6.06255i) q^{93} +(-3.44616 + 5.96892i) q^{94} +(-5.71396 + 9.89687i) q^{95} +(-34.8100 + 35.8140i) q^{96} +(11.6816 - 6.74436i) q^{97} +2.79034i q^{98} +(2.88787 - 0.0821215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 84 q^{4} - 8 q^{9}+O(q^{10}) \) 168 * q + 84 * q^4 - 8 * q^9	\( 168 q + 84 q^{4} - 8 q^{9} - 24 q^{12} + 8 q^{14} - 84 q^{16} - 32 q^{23} + 84 q^{25} - 8 q^{26} + 48 q^{27} + 4 q^{29} + 80 q^{30} - 32 q^{35} + 4 q^{36} + 24 q^{38} + 24 q^{39} + 4 q^{48} + 84 q^{49} + 64 q^{51} + 18 q^{52} - 48 q^{53} - 24 q^{56} + 24 q^{62} - 240 q^{64} - 22 q^{65} - 132 q^{66} - 156 q^{68} - 52 q^{69} + 84 q^{74} - 60 q^{75} - 16 q^{77} - 148 q^{78} + 12 q^{79} - 8 q^{81} - 24 q^{82} + 88 q^{87} + 24 q^{88} - 164 q^{90} + 12 q^{91} + 128 q^{92} - 60 q^{94} - 96 q^{95}+O(q^{100}) \) 168 * q + 84 * q^4 - 8 * q^9 - 24 * q^12 + 8 * q^14 - 84 * q^16 - 32 * q^23 + 84 * q^25 - 8 * q^26 + 48 * q^27 + 4 * q^29 + 80 * q^30 - 32 * q^35 + 4 * q^36 + 24 * q^38 + 24 * q^39 + 4 * q^48 + 84 * q^49 + 64 * q^51 + 18 * q^52 - 48 * q^53 - 24 * q^56 + 24 * q^62 - 240 * q^64 - 22 * q^65 - 132 * q^66 - 156 * q^68 - 52 * q^69 + 84 * q^74 - 60 * q^75 - 16 * q^77 - 148 * q^78 + 12 * q^79 - 8 * q^81 - 24 * q^82 + 88 * q^87 + 24 * q^88 - 164 * q^90 + 12 * q^91 + 128 * q^92 - 60 * q^94 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more