LMFDB - Embedded newform 208.4.i.d.81.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,4,Mod(81,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.81"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{217})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 55x^{2} + 54x + 2916 $ x^4 - x^3 + 55x^2 + 54x + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.2
Root			$-3.43273 + 5.94566i$ of defining polynomial
Character	$\chi$	$=$	208.81
Dual form			208.4.i.d.113.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.93273 + 5.07964i) q^{3} -10.8655 q^{5} +(-14.9327 + 25.8642i) q^{7} +(-3.70181 + 6.41172i) q^{9} +(-24.5291 - 42.4857i) q^{11} +(2.29819 - 46.8158i) q^{13} +(-31.8655 - 55.1926i) q^{15} +(3.03816 - 5.26225i) q^{17} +(-2.93273 + 5.07964i) q^{19} -175.175 q^{21} +(-2.79819 - 4.84661i) q^{23} -6.94178 q^{25} +114.942 q^{27} +(5.30724 + 9.19241i) q^{29} -316.771 q^{31} +(143.875 - 249.198i) q^{33} +(162.251 - 281.027i) q^{35} +(190.231 + 329.490i) q^{37} +(244.547 - 125.624i) q^{39} +(-134.155 - 232.363i) q^{41} +(-115.318 + 199.737i) q^{43} +(40.2219 - 69.6663i) q^{45} -524.466 q^{47} +(-274.473 - 475.401i) q^{49} +35.6404 q^{51} -274.865 q^{53} +(266.520 + 461.626i) q^{55} -34.4036 q^{57} +(-71.4709 + 123.791i) q^{59} +(-281.347 + 487.308i) q^{61} +(-110.556 - 191.489i) q^{63} +(-24.9709 + 508.675i) q^{65} +(-258.762 - 448.189i) q^{67} +(16.4127 - 28.4276i) q^{69} +(-72.2781 + 125.189i) q^{71} -201.018 q^{73} +(-20.3584 - 35.2617i) q^{75} +1465.15 q^{77} -26.4579 q^{79} +(437.042 + 756.979i) q^{81} +1147.16 q^{83} +(-33.0110 + 57.1767i) q^{85} +(-31.1294 + 53.9177i) q^{87} +(331.915 + 574.893i) q^{89} +(1176.54 + 758.529i) q^{91} +(-929.004 - 1609.08i) q^{93} +(31.8655 - 55.1926i) q^{95} +(68.7581 - 119.092i) q^{97} +363.208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{3} - 14 q^{5} - 45 q^{7} - 59 q^{9} + 5 q^{11} - 35 q^{13} - 98 q^{15} + 130 q^{17} + 3 q^{19} - 82 q^{21} + 33 q^{23} - 234 q^{25} + 666 q^{27} + 198 q^{29} - 560 q^{31} + 767 q^{33} + 266 q^{35}+ \cdots - 4852 q^{99}+O(q^{100}) $ 4 * q - 3 * q^3 - 14 * q^5 - 45 * q^7 - 59 * q^9 + 5 * q^11 - 35 * q^13 - 98 * q^15 + 130 * q^17 + 3 * q^19 - 82 * q^21 + 33 * q^23 - 234 * q^25 + 666 * q^27 + 198 * q^29 - 560 * q^31 + 767 * q^33 + 266 * q^35 + 702 * q^37 + 1317 * q^39 - 242 * q^41 - 93 * q^43 - 119 * q^45 - 448 * q^47 - 435 * q^49 - 2126 * q^51 - 1070 * q^53 + 742 * q^55 - 226 * q^57 - 389 * q^59 - 654 * q^61 - 1002 * q^63 - 203 * q^65 - 107 * q^67 + 375 * q^69 - 569 * q^71 - 1246 * q^73 + 935 * q^75 + 1294 * q^77 - 1520 * q^79 + 334 * q^81 + 3528 * q^83 + 413 * q^85 + 1599 * q^87 + 871 * q^89 + 1539 * q^91 - 2184 * q^93 + 98 * q^95 + 879 * q^97 - 4852 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	2.93273	+	5.07964i	0.564404	+	0.977577i	0.997105	+	0.0760390i	$0.0242274\pi$
$3$	2.93273	+	5.07964i	0.564404	+	0.977577i	−0.432701	+	0.901538i	$0.642439\pi$
$4$		0			0
$5$	−10.8655			−0.971836			−0.485918	−	0.874004i	$-0.661515\pi$
$5$	−10.8655			−0.971836			−0.485918	+	0.874004i	$0.661515\pi$
$6$		0			0
$7$	−14.9327	+	25.8642i	−0.806292	+	1.39654i	0.109124	+	0.994028i	$0.465195\pi$
$7$	−14.9327	+	25.8642i	−0.806292	+	1.39654i	−0.915416	+	0.402510i	$0.868138\pi$
$8$		0			0
$9$	−3.70181	+	6.41172i	−0.137104	+	0.237471i
$10$		0			0
$11$	−24.5291	−	42.4857i	−0.672346	−	1.16454i	−0.977237	−	0.212150i	$-0.931953\pi$
$11$	−24.5291	−	42.4857i	−0.672346	−	1.16454i	0.304891	−	0.952387i	$-0.401380\pi$
$12$		0			0
$13$	2.29819	−	46.8158i	0.0490310	−	0.998797i
$13$	2.29819	−	46.8158i	0.0490310	−	0.998797i
$14$		0			0
$15$	−31.8655	−	55.1926i	−0.548508	−	0.950044i
$16$		0			0
$17$	3.03816	−	5.26225i	0.0433448	−	0.0750754i	−0.843539	−	0.537068i	$-0.819532\pi$
$17$	3.03816	−	5.26225i	0.0433448	−	0.0750754i	0.886884	+	0.461992i	$0.152865\pi$
$18$		0			0
$19$	−2.93273	+	5.07964i	−0.0354113	+	0.0613341i	−0.883188	−	0.469019i	$-0.844607\pi$
$19$	−2.93273	+	5.07964i	−0.0354113	+	0.0613341i	0.847777	+	0.530353i	$0.177941\pi$
$20$		0			0
$21$	−175.175			−1.82030
$22$		0			0
$23$	−2.79819	−	4.84661i	−0.0253680	−	0.0439386i	0.853063	−	0.521808i	$-0.174742\pi$
$23$	−2.79819	−	4.84661i	−0.0253680	−	0.0439386i	−0.878431	+	0.477870i	$0.841409\pi$
$24$		0			0
$25$	−6.94178			−0.0555342
$26$		0			0
$27$	114.942			0.819280
$28$		0			0
$29$	5.30724	+	9.19241i	0.0339838	+	0.0588616i	0.882517	−	0.470280i	$-0.155847\pi$
$29$	5.30724	+	9.19241i	0.0339838	+	0.0588616i	−0.848533	+	0.529142i	$0.822514\pi$
$30$		0			0
$31$	−316.771			−1.83528			−0.917641	−	0.397410i	$-0.869909\pi$
$31$	−316.771			−1.83528			−0.917641	+	0.397410i	$0.869909\pi$
$32$		0			0
$33$	143.875	−	249.198i	0.758950	−	1.31454i
$34$		0			0
$35$	162.251	−	281.027i	0.783583	−	1.35721i
$36$		0			0
$37$	190.231	+	329.490i	0.845237	+	1.46399i	0.885415	+	0.464801i	$0.153874\pi$
$37$	190.231	+	329.490i	0.845237	+	1.46399i	−0.0401781	+	0.999193i	$0.512793\pi$
$38$		0			0
$39$	244.547	−	125.624i	1.00407	−	0.515794i
$40$		0			0
$41$	−134.155	−	232.363i	−0.511010	−	0.885096i	−0.999919	−	0.0127608i	$-0.995938\pi$
$41$	−134.155	−	232.363i	−0.511010	−	0.885096i	0.488908	−	0.872335i	$-0.337395\pi$
$42$		0			0
$43$	−115.318	+	199.737i	−0.408974	+	0.708363i	−0.994775	−	0.102091i	$-0.967447\pi$
$43$	−115.318	+	199.737i	−0.408974	+	0.708363i	0.585801	+	0.810455i	$0.300780\pi$
$44$		0			0
$45$	40.2219	−	69.6663i	0.133243	−	0.230783i
$46$		0			0
$47$	−524.466			−1.62768			−0.813842	−	0.581086i	$-0.802628\pi$
$47$	−524.466			−1.62768			−0.813842	+	0.581086i	$0.802628\pi$
$48$		0			0
$49$	−274.473	−	475.401i	−0.800212	−	1.38601i
$50$		0			0
$51$	35.6404			0.0978560
$52$		0			0
$53$	−274.865			−0.712371			−0.356186	−	0.934415i	$-0.615923\pi$
$53$	−274.865			−0.712371			−0.356186	+	0.934415i	$0.615923\pi$
$54$		0			0
$55$	266.520	+	461.626i	0.653410	+	1.13174i
$56$		0			0
$57$	−34.4036			−0.0799451
$58$		0			0
$59$	−71.4709	+	123.791i	−0.157707	+	0.273157i	−0.934041	−	0.357165i	$-0.883744\pi$
$59$	−71.4709	+	123.791i	−0.157707	+	0.273157i	0.776334	+	0.630321i	$0.217077\pi$
$60$		0			0
$61$	−281.347	+	487.308i	−0.590538	+	1.02284i	0.403622	+	0.914926i	$0.367751\pi$
$61$	−281.347	+	487.308i	−0.590538	+	1.02284i	−0.994160	+	0.107916i	$0.965582\pi$
$62$		0			0
$63$	−110.556	−	191.489i	−0.221092	−	0.382942i
$64$		0			0
$65$	−24.9709	+	508.675i	−0.0476501	+	0.970667i
$66$		0			0
$67$	−258.762	−	448.189i	−0.471833	−	0.817239i	0.527648	−	0.849463i	$-0.323074\pi$
$67$	−258.762	−	448.189i	−0.471833	−	0.817239i	−0.999481	+	0.0322247i	$0.989741\pi$
$68$		0			0
$69$	16.4127	−	28.4276i	0.0286356	−	0.0495982i
$70$		0			0
$71$	−72.2781	+	125.189i	−0.120815	+	0.209257i	−0.920089	−	0.391709i	$-0.871884\pi$
$71$	−72.2781	+	125.189i	−0.120815	+	0.209257i	0.799275	+	0.600966i	$0.205217\pi$
$72$		0			0
$73$	−201.018			−0.322293			−0.161147	−	0.986930i	$-0.551519\pi$
$73$	−201.018			−0.322293			−0.161147	+	0.986930i	$0.551519\pi$
$74$		0			0
$75$	−20.3584	−	35.2617i	−0.0313438	−	0.0542890i
$76$		0			0
$77$	1465.15			2.16843
$78$		0			0
$79$	−26.4579			−0.0376804			−0.0188402	−	0.999823i	$-0.505997\pi$
$79$	−26.4579			−0.0376804			−0.0188402	+	0.999823i	$0.505997\pi$
$80$		0			0
$81$	437.042	+	756.979i	0.599509	+	1.03838i
$82$		0			0
$83$	1147.16			1.51707			0.758535	−	0.651632i	$-0.225916\pi$
$83$	1147.16			1.51707			0.758535	+	0.651632i	$0.225916\pi$
$84$		0			0
$85$	−33.0110	+	57.1767i	−0.0421241	+	0.0729610i
$86$		0			0
$87$	−31.1294	+	53.9177i	−0.0383612	+	0.0664435i
$88$		0			0
$89$	331.915	+	574.893i	0.395313	+	0.684703i	0.993141	−	0.116922i	$-0.0373027\pi$
$89$	331.915	+	574.893i	0.395313	+	0.684703i	−0.597828	+	0.801625i	$0.703969\pi$
$90$		0			0
$91$	1176.54	+	758.529i	1.35533	+	0.873796i
$92$		0			0
$93$	−929.004	−	1609.08i	−1.03584	−	1.79413i
$94$		0			0
$95$	31.8655	−	55.1926i	0.0344140	−	0.0596067i
$96$		0			0
$97$	68.7581	−	119.092i	0.0719724	−	0.124660i	−0.827793	−	0.561033i	$-0.810404\pi$
$97$	68.7581	−	119.092i	0.0719724	−	0.124660i	0.899766	+	0.436373i	$0.143737\pi$
$98$		0			0
$99$	363.208			0.368725
$100$		0			0
$101$	442.347	+	766.168i	0.435794	+	0.754818i	0.997360	−	0.0726144i	$-0.0231342\pi$
$101$	442.347	+	766.168i	0.435794	+	0.754818i	−0.561566	+	0.827432i	$0.689801\pi$
$102$		0			0
$103$	416.233			0.398181			0.199091	−	0.979981i	$-0.436201\pi$
$103$	416.233			0.398181			0.199091	+	0.979981i	$0.436201\pi$
$104$		0			0
$105$	1903.35			1.76903
$106$		0			0
$107$	211.587	+	366.480i	0.191167	+	0.331112i	0.945637	−	0.325223i	$-0.105439\pi$
$107$	211.587	+	366.480i	0.191167	+	0.331112i	−0.754470	+	0.656335i	$0.772106\pi$
$108$		0			0
$109$	−951.630			−0.836235			−0.418118	−	0.908393i	$-0.637310\pi$
$109$	−951.630			−0.836235			−0.418118	+	0.908393i	$0.637310\pi$
$110$		0			0
$111$	−1115.79	+	1932.61i	−0.954111	+	1.65257i
$112$		0			0
$113$	376.391	−	651.929i	0.313344	−	0.542729i	−0.665740	−	0.746184i	$-0.731884\pi$
$113$	376.391	−	651.929i	0.313344	−	0.542729i	0.979084	+	0.203456i	$0.0652172\pi$
$114$		0			0
$115$	30.4036	+	52.6606i	0.0246535	+	0.0427011i
$116$		0			0
$117$	291.662	+	188.039i	0.230463	+	0.148583i
$118$		0			0
$119$	90.7361	+	157.159i	0.0698971	+	0.121065i
$120$		0			0
$121$	−537.854	+	931.591i	−0.404098	+	0.699918i
$122$		0			0
$123$	786.878	−	1362.91i	0.576833	−	0.999104i
$124$		0			0
$125$	1433.61			1.02581
$126$		0			0
$127$	−665.802	−	1153.20i	−0.465200	−	0.805750i	0.534011	−	0.845478i	$-0.320684\pi$
$127$	−665.802	−	1153.20i	−0.465200	−	0.805750i	−0.999211	+	0.0397279i	$0.987351\pi$
$128$		0			0
$129$	−1352.79			−0.923306
$130$		0			0
$131$	−260.378			−0.173659			−0.0868294	−	0.996223i	$-0.527674\pi$
$131$	−260.378			−0.173659			−0.0868294	+	0.996223i	$0.527674\pi$
$132$		0			0
$133$	−87.5873	−	151.706i	−0.0571036	−	0.0989064i
$134$		0			0
$135$	−1248.90			−0.796206
$136$		0			0
$137$	−1205.97	+	2088.81i	−0.752068	+	1.30262i	0.194751	+	0.980853i	$0.437610\pi$
$137$	−1205.97	+	2088.81i	−0.752068	+	1.30262i	−0.946819	+	0.321767i	$0.895723\pi$
$138$		0			0
$139$	−203.965	+	353.278i	−0.124461	+	0.215573i	−0.921522	−	0.388326i	$-0.873054\pi$
$139$	−203.965	+	353.278i	−0.124461	+	0.215573i	0.797061	+	0.603899i	$0.206387\pi$
$140$		0			0
$141$	−1538.12	−	2664.10i	−0.918672	−	1.59119i
$142$		0			0
$143$	−2045.37	+	1050.71i	−1.19610	+	0.614439i
$144$		0			0
$145$	−57.6656	−	99.8798i	−0.0330267	−	0.0572039i
$146$		0			0
$147$	1609.91	−	2788.45i	0.903286	−	1.56454i
$148$		0			0
$149$	147.584	−	255.623i	0.0811447	−	0.140547i	−0.822597	−	0.568625i	$-0.807476\pi$
$149$	147.584	−	255.623i	0.0811447	−	0.140547i	0.903742	+	0.428078i	$0.140809\pi$
$150$		0			0
$151$	−2087.10			−1.12481			−0.562403	−	0.826863i	$-0.690123\pi$
$151$	−2087.10			−1.12481			−0.562403	+	0.826863i	$0.690123\pi$
$152$		0			0
$153$	22.4934	+	38.9597i	0.0118855	+	0.0205863i
$154$		0			0
$155$	3441.86			1.78359
$156$		0			0
$157$	557.512			0.283403			0.141702	−	0.989909i	$-0.454743\pi$
$157$	557.512			0.283403			0.141702	+	0.989909i	$0.454743\pi$
$158$		0			0
$159$	−806.106	−	1396.22i	−0.402065	−	0.696397i
$160$		0			0
$161$	167.138			0.0818159
$162$		0			0
$163$	−645.238	+	1117.59i	−0.310055	+	0.537031i	−0.978374	−	0.206844i	$-0.933681\pi$
$163$	−645.238	+	1117.59i	−0.310055	+	0.537031i	0.668319	+	0.743875i	$0.267014\pi$
$164$		0			0
$165$	−1563.26	+	2707.65i	−0.737575	+	1.27752i
$166$		0			0
$167$	1256.64	+	2176.56i	0.582284	+	1.00854i	0.995208	+	0.0977795i	$0.0311740\pi$
$167$	1256.64	+	2176.56i	0.582284	+	1.00854i	−0.412925	+	0.910765i	$0.635493\pi$
$168$		0			0
$169$	−2186.44	−	215.183i	−0.995192	−	0.0979441i
$170$		0			0
$171$	−21.7128	−	37.6077i	−0.00971006	−	0.0168183i
$172$		0			0
$173$	1700.26	−	2944.94i	0.747218	−	1.29422i	−0.201934	−	0.979399i	$-0.564723\pi$
$173$	1700.26	−	2944.94i	0.747218	−	1.29422i	0.949151	−	0.314820i	$-0.101944\pi$
$174$		0			0
$175$	103.660	−	179.544i	0.0447768	−	0.0775557i
$176$		0			0
$177$	−838.419			−0.356042
$178$		0			0
$179$	−785.111	−	1359.85i	−0.327832	−	0.567822i	0.654249	−	0.756279i	$-0.272985\pi$
$179$	−785.111	−	1359.85i	−0.327832	−	0.567822i	−0.982081	+	0.188457i	$0.939651\pi$
$180$		0			0
$181$	2921.99			1.19995			0.599973	−	0.800021i	$-0.295178\pi$
$181$	2921.99			1.19995			0.599973	+	0.800021i	$0.295178\pi$
$182$		0			0
$183$	−3300.46			−1.33321
$184$		0			0
$185$	−2066.95	−	3580.06i	−0.821432	−	1.42276i
$186$		0			0
$187$	−298.093			−0.116571
$188$		0			0
$189$	−1716.39	+	2972.88i	−0.660578	+	1.14416i
$190$		0			0
$191$	1954.35	−	3385.03i	0.740375	−	1.28237i	−0.211949	−	0.977281i	$-0.567981\pi$
$191$	1954.35	−	3385.03i	0.740375	−	1.28237i	0.952325	−	0.305087i	$-0.0986855\pi$
$192$		0			0
$193$	1059.66	+	1835.39i	0.395214	+	0.684531i	0.993128	−	0.117029i	$-0.0373371\pi$
$193$	1059.66	+	1835.39i	0.395214	+	0.684531i	−0.597914	+	0.801560i	$0.704004\pi$
$194$		0			0
$195$	−2657.12	+	1364.96i	−0.975796	+	0.501267i
$196$		0			0
$197$	−1555.25	−	2693.77i	−0.562472	−	0.974230i	−0.997280	−	0.0737067i	$-0.976517\pi$
$197$	−1555.25	−	2693.77i	−0.562472	−	0.974230i	0.434808	−	0.900523i	$-0.356816\pi$
$198$		0			0
$199$	−245.487	+	425.195i	−0.0874476	+	0.151464i	−0.906432	−	0.422353i	$-0.861204\pi$
$199$	−245.487	+	425.195i	−0.0874476	+	0.151464i	0.818984	+	0.573816i	$0.194538\pi$
$200$		0			0
$201$	1517.76	−	2628.83i	0.532609	−	0.922506i
$202$		0			0
$203$	−317.006			−0.109603
$204$		0			0
$205$	1457.65	+	2524.73i	0.496618	+	0.860168i
$206$		0			0
$207$	41.4335			0.0139122
$208$		0			0
$209$	287.749			0.0952345
$210$		0			0
$211$	−301.634	−	522.445i	−0.0984139	−	0.170458i	0.812614	−	0.582802i	$-0.198044\pi$
$211$	−301.634	−	522.445i	−0.0984139	−	0.170458i	−0.911028	+	0.412344i	$0.864710\pi$
$212$		0			0
$213$	−847.889			−0.272753
$214$		0			0
$215$	1252.99	−	2170.24i	0.397455	−	0.688413i
$216$		0			0
$217$	4730.26	−	8193.04i	1.47977	−	2.56304i
$218$		0			0
$219$	−589.532	−	1021.10i	−0.181904	−	0.315066i
$220$		0			0
$221$	−239.374	−	154.328i	−0.0728599	−	0.0469737i
$222$		0			0
$223$	−1567.57	−	2715.11i	−0.470727	−	0.815324i	0.528712	−	0.848801i	$-0.322675\pi$
$223$	−1567.57	−	2715.11i	−0.470727	−	0.815324i	−0.999439	+	0.0334775i	$0.989342\pi$
$224$		0			0
$225$	25.6972	−	44.5088i	0.00761397	−	0.0131878i
$226$		0			0
$227$	806.537	−	1396.96i	0.235823	−	0.408457i	−0.723689	−	0.690126i	$-0.757555\pi$
$227$	806.537	−	1396.96i	0.235823	−	0.408457i	0.959511	+	0.281670i	$0.0908882\pi$
$228$		0			0
$229$	−6156.40			−1.77653			−0.888267	−	0.459327i	$-0.848091\pi$
$229$	−6156.40			−1.77653			−0.888267	+	0.459327i	$0.848091\pi$
$230$		0			0
$231$	4296.88	+	7442.41i	1.22387	+	2.11980i
$232$		0			0
$233$	−3350.07			−0.941934			−0.470967	−	0.882151i	$-0.656095\pi$
$233$	−3350.07			−0.941934			−0.470967	+	0.882151i	$0.656095\pi$
$234$		0			0
$235$	5698.56			1.58184
$236$		0			0
$237$	−77.5939	−	134.397i	−0.0212670	−	0.0368354i
$238$		0			0
$239$	632.554			0.171199			0.0855994	−	0.996330i	$-0.472719\pi$
$239$	632.554			0.171199			0.0855994	+	0.996330i	$0.472719\pi$
$240$		0			0
$241$	−752.118	+	1302.71i	−0.201030	+	0.348194i	−0.948861	−	0.315696i	$-0.897762\pi$
$241$	−752.118	+	1302.71i	−0.201030	+	0.348194i	0.747831	+	0.663890i	$0.231096\pi$
$242$		0			0
$243$	−1011.74	+	1752.38i	−0.267091	+	0.462615i
$244$		0			0
$245$	2982.27	+	5165.45i	0.777675	+	1.34697i
$246$		0			0
$247$	231.067	+	148.972i	0.0595241	+	0.0383760i
$248$		0			0
$249$	3364.30	+	5827.14i	0.856240	+	1.48305i
$250$		0			0
$251$	518.384	−	897.868i	0.130359	−	0.225789i	−0.793456	−	0.608628i	$-0.791720\pi$
$251$	518.384	−	897.868i	0.130359	−	0.225789i	0.923815	+	0.382839i	$0.125054\pi$
$252$		0			0
$253$	−137.274	+	237.766i	−0.0341121	+	0.0590839i
$254$		0			0
$255$	−387.249			−0.0951000
$256$		0			0
$257$	−252.452	−	437.260i	−0.0612744	−	0.106130i	0.833761	−	0.552126i	$-0.186183\pi$
$257$	−252.452	−	437.260i	−0.0612744	−	0.106130i	−0.895035	+	0.445995i	$0.852850\pi$
$258$		0			0
$259$	−11362.7			−2.72603
$260$		0			0
$261$	−78.5856			−0.0186373
$262$		0			0
$263$	−84.6612	−	146.638i	−0.0198496	−	0.0343804i	0.855930	−	0.517092i	$-0.172985\pi$
$263$	−84.6612	−	146.638i	−0.0198496	−	0.0343804i	−0.875780	+	0.482711i	$0.839652\pi$
$264$		0			0
$265$	2986.54			0.692308
$266$		0			0
$267$	−1946.83	+	3372.01i	−0.446233	+	0.772898i
$268$		0			0
$269$	−771.017	+	1335.44i	−0.174757	+	0.302689i	−0.940077	−	0.340961i	$-0.889247\pi$
$269$	−771.017	+	1335.44i	−0.174757	+	0.302689i	0.765320	+	0.643650i	$0.222581\pi$
$270$		0			0
$271$	−589.678	−	1021.35i	−0.132179	−	0.228940i	0.792338	−	0.610083i	$-0.208864\pi$
$271$	−589.678	−	1021.35i	−0.132179	−	0.228940i	−0.924516	+	0.381143i	$0.875531\pi$
$272$		0			0
$273$	−402.585	+	8200.94i	−0.0892510	+	1.81811i
$274$		0			0
$275$	170.276	+	294.926i	0.0373382	+	0.0646717i
$276$		0			0
$277$	−1952.95	+	3382.61i	−0.423615	+	0.733723i	−0.996290	−	0.0860599i	$-0.972572\pi$
$277$	−1952.95	+	3382.61i	−0.423615	+	0.733723i	0.572675	+	0.819782i	$0.305906\pi$
$278$		0			0
$279$	1172.63	−	2031.05i	0.251625	−	0.435827i
$280$		0			0
$281$	58.9976			0.0125249			0.00626245	−	0.999980i	$-0.498007\pi$
$281$	58.9976			0.0125249			0.00626245	+	0.999980i	$0.498007\pi$
$282$		0			0
$283$	2347.79	+	4066.49i	0.493151	+	0.854163i	0.999969	−	0.00789055i	$-0.00251167\pi$
$283$	2347.79	+	4066.49i	0.493151	+	0.854163i	−0.506818	+	0.862053i	$0.669178\pi$
$284$		0			0
$285$	373.811			0.0776936
$286$		0			0
$287$	8013.18			1.64809
$288$		0			0
$289$	2438.04	+	4222.81i	0.496242	+	0.859517i
$290$		0			0
$291$	806.595			0.162486
$292$		0			0
$293$	4059.41	−	7031.11i	0.809397	−	1.40192i	−0.103885	−	0.994589i	$-0.533127\pi$
$293$	4059.41	−	7031.11i	0.809397	−	1.40192i	0.913282	−	0.407327i	$-0.133539\pi$
$294$		0			0
$295$	776.564	−	1345.05i	0.153265	−	0.265464i
$296$		0			0
$297$	−2819.42	−	4883.38i	−0.550839	−	0.954082i
$298$		0			0
$299$	−233.329	+	119.861i	−0.0451296	+	0.0231831i
$300$		0			0
$301$	−3444.03	−	5965.24i	−0.659504	−	1.14229i
$302$		0			0
$303$	−2594.57	+	4493.93i	−0.491928	+	0.852044i
$304$		0			0
$305$	3056.97	−	5294.82i	0.573907	−	0.994035i
$306$		0			0
$307$	1072.04			0.199298			0.0996492	−	0.995023i	$-0.468228\pi$
$307$	1072.04			0.199298			0.0996492	+	0.995023i	$0.468228\pi$
$308$		0			0
$309$	1220.70	+	2114.31i	0.224735	+	0.389252i
$310$		0			0
$311$	4528.41			0.825667			0.412834	−	0.910806i	$-0.364539\pi$
$311$	4528.41			0.825667			0.412834	+	0.910806i	$0.364539\pi$
$312$		0			0
$313$	−5396.13			−0.974464			−0.487232	−	0.873273i	$-0.661993\pi$
$313$	−5396.13			−0.974464			−0.487232	+	0.873273i	$0.661993\pi$
$314$		0			0
$315$	1201.24	+	2080.62i	0.214865	+	0.372157i
$316$		0			0
$317$	8222.40			1.45683			0.728417	−	0.685134i	$-0.240257\pi$
$317$	8222.40			1.45683			0.728417	+	0.685134i	$0.240257\pi$
$318$		0			0
$319$	260.364	−	450.963i	0.0456977	−	0.0791508i
$320$		0			0
$321$	−1241.06	+	2149.57i	−0.215791	+	0.373762i
$322$		0			0
$323$	17.8202	+	30.8655i	0.00306979	+	0.00531704i
$324$		0			0
$325$	−15.9535	+	324.985i	−0.00272290	+	0.0554675i
$326$		0			0
$327$	−2790.87	−	4833.94i	−0.471975	−	0.817484i
$328$		0			0
$329$	7831.71	−	13564.9i	1.31239	−	2.27312i
$330$		0			0
$331$	−304.177	+	526.851i	−0.0505109	+	0.0874874i	−0.890175	−	0.455618i	$-0.849418\pi$
$331$	−304.177	+	526.851i	−0.0505109	+	0.0874874i	0.839664	+	0.543105i	$0.182752\pi$
$332$		0			0
$333$	−2816.79			−0.463542
$334$		0			0
$335$	2811.57	+	4869.78i	0.458544	+	0.794222i
$336$		0			0
$337$	−8808.73			−1.42386			−0.711932	−	0.702248i	$-0.752180\pi$
$337$	−8808.73			−1.42386			−0.711932	+	0.702248i	$0.752180\pi$
$338$		0			0
$339$	4415.42			0.707412
$340$		0			0
$341$	7770.11	+	13458.2i	1.23394	+	2.13725i
$342$		0			0
$343$	6150.66			0.968235
$344$		0			0
$345$	−178.331	+	308.879i	−0.0278291	+	0.0482014i
$346$		0			0
$347$	−3583.04	+	6206.01i	−0.554317	+	0.960105i	0.443640	+	0.896205i	$0.353687\pi$
$347$	−3583.04	+	6206.01i	−0.554317	+	0.960105i	−0.997956	+	0.0638994i	$0.979646\pi$
$348$		0			0
$349$	942.489	+	1632.44i	0.144557	+	0.250380i	0.929207	−	0.369559i	$-0.120491\pi$
$349$	942.489	+	1632.44i	0.144557	+	0.250380i	−0.784651	+	0.619938i	$0.787158\pi$
$350$		0			0
$351$	264.158	−	5381.09i	0.0401701	−	0.818294i
$352$		0			0
$353$	5977.01	+	10352.5i	0.901202	+	1.56093i	0.825936	+	0.563764i	$0.190647\pi$
$353$	5977.01	+	10352.5i	0.901202	+	1.56093i	0.0752661	+	0.997163i	$0.476019\pi$
$354$		0			0
$355$	785.335	−	1360.24i	0.117412	−	0.203364i
$356$		0			0
$357$	−532.209	+	921.812i	−0.0789005	+	0.136660i
$358$		0			0
$359$	−9068.77			−1.33324			−0.666618	−	0.745400i	$-0.732259\pi$
$359$	−9068.77			−1.33324			−0.666618	+	0.745400i	$0.732259\pi$
$360$		0			0
$361$	3412.30	+	5910.27i	0.497492	+	0.861682i
$362$		0			0
$363$	−6309.53			−0.912298
$364$		0			0
$365$	2184.15			0.313216
$366$		0			0
$367$	3922.06	+	6793.21i	0.557847	+	0.966220i	0.997676	+	0.0681380i	$0.0217058\pi$
$367$	3922.06	+	6793.21i	0.557847	+	0.966220i	−0.439829	+	0.898082i	$0.644961\pi$
$368$		0			0
$369$	1986.46			0.280246
$370$		0			0
$371$	4104.49	−	7109.19i	0.574379	−	0.994854i
$372$		0			0
$373$	−723.844	+	1253.74i	−0.100481	+	0.174037i	−0.911883	−	0.410451i	$-0.865371\pi$
$373$	−723.844	+	1253.74i	−0.100481	+	0.174037i	0.811402	+	0.584488i	$0.198705\pi$
$374$		0			0
$375$	4204.39	+	7282.21i	0.578969	+	1.00280i
$376$		0			0
$377$	442.547	−	227.337i	0.0604571	−	0.0310569i
$378$		0			0
$379$	−5909.48	−	10235.5i	−0.800922	−	1.38724i	−0.919010	−	0.394234i	$-0.871010\pi$
$379$	−5909.48	−	10235.5i	−0.800922	−	1.38724i	0.118088	−	0.993003i	$-0.462323\pi$
$380$		0			0
$381$	3905.24	−	6764.07i	0.525121	−	0.909537i
$382$		0			0
$383$	3625.40	−	6279.38i	0.483680	−	0.837758i	−0.516145	−	0.856501i	$-0.672633\pi$
$383$	3625.40	−	6279.38i	0.483680	−	0.837758i	0.999824	+	0.0187436i	$0.00596662\pi$
$384$		0			0
$385$	−15919.5			−2.10736
$386$		0			0
$387$	−853.773	−	1478.78i	−0.112144	−	0.194239i
$388$		0			0
$389$	−9331.29			−1.21623			−0.608117	−	0.793847i	$-0.708075\pi$
$389$	−9331.29			−1.21623			−0.608117	+	0.793847i	$0.708075\pi$
$390$		0			0
$391$	−34.0054			−0.00439828
$392$		0			0
$393$	−763.617	−	1322.62i	−0.0980138	−	0.169765i
$394$		0			0
$395$	287.478			0.0366191
$396$		0			0
$397$	3847.13	−	6663.42i	0.486352	−	0.842386i	−0.513525	−	0.858075i	$-0.671661\pi$
$397$	3847.13	−	6663.42i	0.486352	−	0.842386i	0.999877	+	0.0156884i	$0.00499397\pi$
$398$		0			0
$399$	513.740	−	889.824i	0.0644591	−	0.111646i
$400$		0			0
$401$	−928.729	−	1608.61i	−0.115657	−	0.200324i	0.802385	−	0.596807i	$-0.203564\pi$
$401$	−928.729	−	1608.61i	−0.115657	−	0.200324i	−0.918042	+	0.396483i	$0.870231\pi$
$402$		0			0
$403$	−728.000	+	14829.9i	−0.0899858	+	1.83308i
$404$		0			0
$405$	−4748.66	−	8224.93i	−0.582625	−	1.00914i
$406$		0			0
$407$	9332.39	−	16164.2i	1.13658	−	1.96862i
$408$		0			0
$409$	269.235	−	466.328i	0.0325496	−	0.0563776i	−0.849292	−	0.527924i	$-0.822971\pi$
$409$	269.235	−	466.328i	0.0325496	−	0.0563776i	0.881841	+	0.471546i	$0.156304\pi$
$410$		0			0
$411$	−14147.2			−1.69788
$412$		0			0
$413$	−2134.51	−	3697.08i	−0.254316	−	0.440488i
$414$		0			0
$415$	−12464.4			−1.47434
$416$		0			0
$417$	−2392.70			−0.280985
$418$		0			0
$419$	2418.69	+	4189.30i	0.282007	+	0.488450i	0.971879	−	0.235481i	$-0.0756666\pi$
$419$	2418.69	+	4189.30i	0.282007	+	0.488450i	−0.689872	+	0.723931i	$0.742333\pi$
$420$		0			0
$421$	−1392.34			−0.161184			−0.0805918	−	0.996747i	$-0.525681\pi$
$421$	−1392.34			−0.161184			−0.0805918	+	0.996747i	$0.525681\pi$
$422$		0			0
$423$	1941.47	−	3362.73i	0.223162	−	0.386528i
$424$		0			0
$425$	−21.0902	+	36.5294i	−0.00240712	+	0.00416926i
$426$		0			0
$427$	−8402.57	−	14553.7i	−0.952292	−	1.64942i
$428$		0			0
$429$	−11335.7	−	7308.30i	−1.27575	−	0.822490i
$430$		0			0
$431$	3953.78	+	6848.14i	0.441872	+	0.765344i	0.997828	−	0.0658670i	$-0.0209813\pi$
$431$	3953.78	+	6848.14i	0.441872	+	0.765344i	−0.555957	+	0.831211i	$0.687648\pi$
$432$		0			0
$433$	−4816.28	+	8342.04i	−0.534539	+	0.925850i	0.464646	+	0.885497i	$0.346182\pi$
$433$	−4816.28	+	8342.04i	−0.534539	+	0.925850i	−0.999185	+	0.0403530i	$0.987152\pi$
$434$		0			0
$435$	338.235	−	585.841i	0.0372808	−	0.0645722i
$436$		0			0
$437$	32.8253			0.00359325
$438$		0			0
$439$	−323.735	−	560.725i	−0.0351959	−	0.0609611i	0.847891	−	0.530171i	$-0.177872\pi$
$439$	−323.735	−	560.725i	−0.0351959	−	0.0609611i	−0.883087	+	0.469210i	$0.844539\pi$
$440$		0			0
$441$	4064.19			0.438850
$442$		0			0
$443$	−16862.3			−1.80847			−0.904233	−	0.427039i	$-0.859557\pi$
$443$	−16862.3			−1.80847			−0.904233	+	0.427039i	$0.859557\pi$
$444$		0			0
$445$	−3606.41	−	6246.48i	−0.384180	−	0.665419i
$446$		0			0
$447$	1731.30			0.183194
$448$		0			0
$449$	−6240.44	+	10808.8i	−0.655912	+	1.13607i	0.325752	+	0.945455i	$0.394383\pi$
$449$	−6240.44	+	10808.8i	−0.655912	+	1.13607i	−0.981664	+	0.190618i	$0.938951\pi$
$450$		0			0
$451$	−6581.39	+	11399.3i	−0.687152	+	1.19018i
$452$		0			0
$453$	−6120.90	−	10601.7i	−0.634845	−	1.09958i
$454$		0			0
$455$	−12783.6	−	8241.76i	−1.31715	−	0.849186i
$456$		0			0
$457$	−6268.52	−	10857.4i	−0.641639	−	1.11135i	−0.985067	−	0.172172i	$-0.944921\pi$
$457$	−6268.52	−	10857.4i	−0.641639	−	1.11135i	0.343428	−	0.939179i	$-0.388412\pi$
$458$		0			0
$459$	349.212	−	604.852i	0.0355115	−	0.0615078i
$460$		0			0
$461$	−726.957	+	1259.13i	−0.0734442	+	0.127209i	−0.900409	−	0.435045i	$-0.856732\pi$
$461$	−726.957	+	1259.13i	−0.0734442	+	0.127209i	0.826964	+	0.562254i	$0.190066\pi$
$462$		0			0
$463$	7154.47			0.718135			0.359068	−	0.933312i	$-0.383095\pi$
$463$	7154.47			0.718135			0.359068	+	0.933312i	$0.383095\pi$
$464$		0			0
$465$	10094.1	+	17483.4i	1.00667	+	1.74360i
$466$		0			0
$467$	5823.27			0.577021			0.288510	−	0.957477i	$-0.406840\pi$
$467$	5823.27			0.577021			0.288510	+	0.957477i	$0.406840\pi$
$468$		0			0
$469$	15456.1			1.52174
$470$		0			0
$471$	1635.03	+	2831.96i	0.159954	+	0.277048i
$472$		0			0
$473$	11314.6			1.09989
$474$		0			0
$475$	20.3584	−	35.2617i	0.00196654	−	0.00340615i
$476$		0			0
$477$	1017.50	−	1762.36i	0.0976690	−	0.169168i
$478$		0			0
$479$	1460.09	+	2528.94i	0.139276	+	0.241233i	0.927223	−	0.374511i	$-0.122189\pi$
$479$	1460.09	+	2528.94i	0.139276	+	0.241233i	−0.787947	+	0.615743i	$0.788856\pi$
$480$		0			0
$481$	15862.5	−	8148.58i	1.50368	−	0.772439i
$482$		0			0
$483$	490.172	+	849.003i	0.0461772	+	0.0799813i
$484$		0			0
$485$	−747.088	+	1293.99i	−0.0699454	+	0.121149i
$486$		0			0
$487$	−1681.12	+	2911.79i	−0.156425	+	0.270936i	−0.933577	−	0.358377i	$-0.883330\pi$
$487$	−1681.12	+	2911.79i	−0.156425	+	0.270936i	0.777152	+	0.629313i	$0.216664\pi$
$488$		0			0
$489$	−7569.24			−0.699985
$490$		0			0
$491$	7434.83	+	12877.5i	0.683359	+	1.18361i	0.973950	+	0.226764i	$0.0728147\pi$
$491$	7434.83	+	12877.5i	0.683359	+	1.18361i	−0.290591	+	0.956847i	$0.593852\pi$
$492$		0			0
$493$	64.4970			0.00589209
$494$		0			0
$495$	−3946.43			−0.358341
$496$		0			0
$497$	−2158.62	−	3738.84i	−0.194824	−	0.337444i
$498$		0			0
$499$	18693.3			1.67701			0.838503	−	0.544896i	$-0.183431\pi$
$499$	18693.3			1.67701			0.838503	+	0.544896i	$0.183431\pi$
$500$		0			0
$501$	−7370.74	+	12766.5i	−0.657287	+	1.13845i
$502$		0			0
$503$	7359.24	−	12746.6i	0.652350	−	1.12990i	−0.330201	−	0.943911i	$-0.607116\pi$
$503$	7359.24	−	12746.6i	0.652350	−	1.12990i	0.982551	−	0.185993i	$-0.0595502\pi$
$504$		0			0
$505$	−4806.31	−	8324.77i	−0.423521	−	0.733559i
$506$		0			0
$507$	−5319.18	−	11737.4i	−0.465943	−	1.02816i
$508$		0			0
$509$	−7939.46	−	13751.6i	−0.691376	−	1.19750i	−0.971387	−	0.237502i	$-0.923671\pi$
$509$	−7939.46	−	13751.6i	−0.691376	−	1.19750i	0.280011	−	0.959997i	$-0.409662\pi$
$510$		0			0
$511$	3001.75	−	5199.18i	0.259862	−	0.450094i
$512$		0			0
$513$	−337.093	+	583.863i	−0.0290118	+	0.0502498i
$514$		0			0
$515$	−4522.56			−0.386967
$516$		0			0
$517$	12864.7	+	22282.3i	1.09437	+	1.89550i
$518$		0			0
$519$	19945.7			1.68693
$520$		0			0
$521$	−9618.86			−0.808848			−0.404424	−	0.914572i	$-0.632528\pi$
$521$	−9618.86			−0.808848			−0.404424	+	0.914572i	$0.632528\pi$
$522$		0			0
$523$	−5177.94	−	8968.45i	−0.432917	−	0.749834i	0.564206	−	0.825634i	$-0.309182\pi$
$523$	−5177.94	−	8968.45i	−0.432917	−	0.749834i	−0.997123	+	0.0758002i	$0.975849\pi$
$524$		0			0
$525$	1216.02			0.101089
$526$		0			0
$527$	−962.401	+	1666.93i	−0.0795500	+	0.137785i
$528$		0			0
$529$	6067.84	−	10509.8i	0.498713	−	0.863796i
$530$		0			0
$531$	−529.143	−	916.503i	−0.0432446	−	0.0749018i
$532$		0			0
$533$	−11186.6	+	5746.54i	−0.909087	+	0.466999i
$534$		0			0
$535$	−2298.99	−	3981.97i	−0.185783	−	0.321786i
$536$		0			0
$537$	4605.04	−	7976.16i	0.370060	−	0.640962i
$538$		0			0
$539$	−13465.1	+	23322.3i	−1.07604	+	1.86375i
$540$		0			0
$541$	14130.6			1.12296			0.561479	−	0.827491i	$-0.310232\pi$
$541$	14130.6			1.12296			0.561479	+	0.827491i	$0.310232\pi$
$542$		0			0
$543$	8569.42	+	14842.7i	0.677254	+	1.17304i
$544$		0			0
$545$	10339.9			0.812684
$546$		0			0
$547$	−6505.59			−0.508517			−0.254259	−	0.967136i	$-0.581831\pi$
$547$	−6505.59			−0.508517			−0.254259	+	0.967136i	$0.581831\pi$
$548$		0			0
$549$	−2082.99	−	3607.84i	−0.161930	−	0.280472i
$550$		0			0
$551$	−62.2588			−0.00481364
$552$		0			0
$553$	395.089	−	684.314i	0.0303814	−	0.0526221i
$554$		0			0
$555$	12123.6	−	20998.7i	0.927239	−	1.60603i
$556$		0			0
$557$	9162.49	+	15869.9i	0.696996	+	1.20723i	0.969503	+	0.245079i	$0.0788140\pi$
$557$	9162.49	+	15869.9i	0.696996	+	1.20723i	−0.272507	+	0.962154i	$0.587853\pi$
$558$		0			0
$559$	9085.83	+	5857.75i	0.687459	+	0.443214i
$560$		0			0
$561$	−874.228	−	1514.21i	−0.0657931	−	0.113957i
$562$		0			0
$563$	12087.1	−	20935.5i	0.904815	−	1.56719i	0.0836495	−	0.996495i	$-0.473342\pi$
$563$	12087.1	−	20935.5i	0.904815	−	1.56719i	0.821165	−	0.570690i	$-0.193324\pi$
$564$		0			0
$565$	−4089.67	+	7083.51i	−0.304520	+	0.527443i
$566$		0			0
$567$	−26104.9			−1.93352
$568$		0			0
$569$	−4816.74	−	8342.84i	−0.354883	−	0.614675i	0.632215	−	0.774793i	$-0.282146\pi$
$569$	−4816.74	−	8342.84i	−0.354883	−	0.614675i	−0.987098	+	0.160118i	$0.948813\pi$
$570$		0			0
$571$	8221.17			0.602531			0.301266	−	0.953540i	$-0.402591\pi$
$571$	8221.17			0.602531			0.301266	+	0.953540i	$0.402591\pi$
$572$		0			0
$573$	22926.3			1.67148
$574$		0			0
$575$	19.4244	+	33.6441i	0.00140879	+	0.00244010i
$576$		0			0
$577$	−7986.09			−0.576196			−0.288098	−	0.957601i	$-0.593023\pi$
$577$	−7986.09			−0.576196			−0.288098	+	0.957601i	$0.593023\pi$
$578$		0			0
$579$	−6215.42	+	10765.4i	−0.446121	+	0.772704i
$580$		0			0
$581$	−17130.2	+	29670.3i	−1.22320	+	2.11865i
$582$		0			0
$583$	6742.21	+	11677.8i	0.478960	+	0.829583i
$584$		0			0
$585$	−3169.05	−	2043.13i	−0.223973	−	0.144398i
$586$		0			0
$587$	3722.38	+	6447.35i	0.261736	+	0.453340i	0.966703	−	0.255900i	$-0.0823717\pi$
$587$	3722.38	+	6447.35i	0.261736	+	0.453340i	−0.704967	+	0.709240i	$0.749038\pi$
$588$		0			0
$589$	929.004	−	1609.08i	0.0649897	−	0.112565i
$590$		0			0
$591$	9122.26	−	15800.2i	0.634923	−	1.09972i
$592$		0			0
$593$	−6806.49			−0.471347			−0.235674	−	0.971832i	$-0.575730\pi$
$593$	−6806.49			−0.471347			−0.235674	+	0.971832i	$0.575730\pi$
$594$		0			0
$595$	−985.889	−	1707.61i	−0.0679286	−	0.117656i
$596$		0			0
$597$	−2879.78			−0.197423
$598$		0			0
$599$	−22251.5			−1.51782			−0.758909	−	0.651196i	$-0.774267\pi$
$599$	−22251.5			−1.51782			−0.758909	+	0.651196i	$0.774267\pi$
$600$		0			0
$601$	10608.1	+	18373.7i	0.719988	+	1.24706i	0.961004	+	0.276535i	$0.0891862\pi$
$601$	10608.1	+	18373.7i	0.719988	+	1.24706i	−0.241016	+	0.970521i	$0.577480\pi$
$602$		0			0
$603$	3831.55			0.258761
$604$		0			0
$605$	5844.04	−	10122.2i	0.392717	−	0.680206i
$606$		0			0
$607$	−8895.83	+	15408.0i	−0.594844	+	1.03030i	0.398724	+	0.917071i	$0.369453\pi$
$607$	−8895.83	+	15408.0i	−0.594844	+	1.03030i	−0.993569	+	0.113230i	$0.963880\pi$
$608$		0			0
$609$	−929.694	−	1610.28i	−0.0618606	−	0.107146i
$610$		0			0
$611$	−1205.32	+	24553.3i	−0.0798070	+	1.62573i
$612$		0			0
$613$	5487.29	+	9504.27i	0.361549	+	0.626221i	0.988216	−	0.153066i	$-0.0489146\pi$
$613$	5487.29	+	9504.27i	0.361549	+	0.626221i	−0.626667	+	0.779287i	$0.715581\pi$
$614$		0			0
$615$	−8549.80	+	14808.7i	−0.560587	+	0.970965i
$616$		0			0
$617$	1530.46	−	2650.84i	0.0998609	−	0.172964i	−0.811766	−	0.583983i	$-0.801494\pi$
$617$	1530.46	−	2650.84i	0.0998609	−	0.172964i	0.911627	+	0.411019i	$0.134827\pi$
$618$		0			0
$619$	8387.51			0.544625			0.272312	−	0.962209i	$-0.412212\pi$
$619$	8387.51			0.544625			0.272312	+	0.962209i	$0.412212\pi$
$620$		0			0
$621$	−321.629	−	557.078i	−0.0207835	−	0.0359980i
$622$		0			0
$623$	−19825.6			−1.27495
$624$		0			0
$625$	−14709.1			−0.941382
$626$		0			0
$627$	843.890	+	1461.66i	0.0537508	+	0.0930990i
$628$		0			0
$629$	2311.81			0.146547
$630$		0			0
$631$	−13105.5	+	22699.4i	−0.826818	+	1.43209i	0.0737032	+	0.997280i	$0.476518\pi$
$631$	−13105.5	+	22699.4i	−0.826818	+	1.43209i	−0.900522	+	0.434811i	$0.856815\pi$
$632$		0			0
$633$	1769.22	−	3064.38i	0.111090	−	0.192414i
$634$		0			0
$635$	7234.25	+	12530.1i	0.452098	+	0.783057i
$636$		0			0
$637$	−22887.1	+	11757.1i	−1.42358	+	0.731293i
$638$		0			0
$639$	−535.120	−	926.855i	−0.0331283	−	0.0573800i
$640$		0			0
$641$	12229.5	−	21182.1i	0.753565	−	1.30521i	−0.192520	−	0.981293i	$-0.561666\pi$
$641$	12229.5	−	21182.1i	0.753565	−	1.30521i	0.946085	−	0.323919i	$-0.105001\pi$
$642$		0			0
$643$	14490.9	−	25099.0i	0.888750	−	1.53936i	0.0473946	−	0.998876i	$-0.484908\pi$
$643$	14490.9	−	25099.0i	0.888750	−	1.53936i	0.841355	−	0.540483i	$-0.181758\pi$
$644$		0			0
$645$	14698.7			0.897302
$646$		0			0
$647$	−4423.15	−	7661.11i	−0.268766	−	0.465517i	0.699777	−	0.714361i	$-0.253283\pi$
$647$	−4423.15	−	7661.11i	−0.268766	−	0.465517i	−0.968544	+	0.248844i	$0.919949\pi$
$648$		0			0
$649$	7012.47			0.424135
$650$		0			0
$651$	55490.3			3.34076
$652$		0			0
$653$	−13153.7	−	22782.9i	−0.788275	−	1.36533i	−0.927023	−	0.375005i	$-0.877641\pi$
$653$	−13153.7	−	22782.9i	−0.788275	−	1.36533i	0.138748	−	0.990328i	$-0.455692\pi$
$654$		0			0
$655$	2829.12			0.168768
$656$		0			0
$657$	744.131	−	1288.87i	0.0441877	−	0.0765353i
$658$		0			0
$659$	−1653.40	+	2863.78i	−0.0977352	+	0.169282i	−0.910747	−	0.412965i	$-0.864493\pi$
$659$	−1653.40	+	2863.78i	−0.0977352	+	0.169282i	0.813012	+	0.582247i	$0.197826\pi$
$660$		0			0
$661$	11801.3	+	20440.5i	0.694432	+	1.20279i	0.970372	+	0.241616i	$0.0776774\pi$
$661$	11801.3	+	20440.5i	0.694432	+	1.20279i	−0.275940	+	0.961175i	$0.588989\pi$
$662$		0			0
$663$	81.9084	−	1668.53i	0.00479798	−	0.0977383i
$664$		0			0
$665$	951.677	+	1648.35i	0.0554954	+	0.0961208i
$666$		0			0
$667$	29.7013	−	51.4442i	0.00172420	−	0.00298640i
$668$		0			0
$669$	9194.51	−	15925.4i	0.531361	−	0.920344i
$670$		0			0
$671$	27604.8			1.58818
$672$		0			0
$673$	1887.77	+	3269.72i	0.108125	+	0.187278i	0.915011	−	0.403429i	$-0.132182\pi$
$673$	1887.77	+	3269.72i	0.108125	+	0.187278i	−0.806886	+	0.590708i	$0.798849\pi$
$674$		0			0
$675$	−797.901			−0.0454981
$676$		0			0
$677$	−11395.4			−0.646916			−0.323458	−	0.946242i	$-0.604845\pi$
$677$	−11395.4			−0.646916			−0.323458	+	0.946242i	$0.604845\pi$
$678$		0			0
$679$	2053.49	+	3556.75i	0.116062	+	0.201024i
$680$		0			0
$681$	9461.42			0.532397
$682$		0			0
$683$	118.213	−	204.751i	0.00662269	−	0.0114708i	−0.862695	−	0.505724i	$-0.831225\pi$
$683$	118.213	−	204.751i	0.00662269	−	0.0114708i	0.869318	+	0.494254i	$0.164559\pi$
$684$		0			0
$685$	13103.5	−	22695.9i	0.730887	−	1.26593i
$686$		0			0
$687$	−18055.1	−	31272.3i	−1.00268	−	1.73670i
$688$		0			0
$689$	−631.693	+	12868.0i	−0.0349283	+	0.711514i
$690$		0			0
$691$	4720.82	+	8176.70i	0.259897	+	0.450154i	0.966214	−	0.257741i	$-0.0829782\pi$
$691$	4720.82	+	8176.70i	0.259897	+	0.450154i	−0.706317	+	0.707895i	$0.749645\pi$
$692$		0			0
$693$	−5423.69	+	9394.11i	−0.297300	+	0.514939i
$694$		0			0
$695$	2216.17	−	3838.53i	0.120956	−	0.209502i
$696$		0			0
$697$	−1630.33			−0.0885986
$698$		0			0
$699$	−9824.86	−	17017.2i	−0.531631	−	0.920812i
$700$		0			0
$701$	−145.814			−0.00785638			−0.00392819	−	0.999992i	$-0.501250\pi$
$701$	−145.814			−0.00785638			−0.00392819	+	0.999992i	$0.501250\pi$
$702$		0			0
$703$	−2231.58			−0.119724
$704$		0			0
$705$	16712.3	+	28946.6i	0.892799	+	1.54637i
$706$		0			0
$707$	−26421.8			−1.40551
$708$		0			0
$709$	5445.77	−	9432.35i	0.288463	−	0.499632i	−0.684980	−	0.728562i	$-0.740189\pi$
$709$	5445.77	−	9432.35i	0.288463	−	0.499632i	0.973443	+	0.228929i	$0.0735225\pi$
$710$		0			0
$711$	97.9422	−	169.641i	0.00516613	−	0.00894800i
$712$		0			0
$713$	886.386	+	1535.26i	0.0465574	+	0.0806397i
$714$		0			0
$715$	22223.9	−	11416.4i	1.16242	−	0.597134i
$716$		0			0
$717$	1855.11	+	3213.14i	0.0966253	+	0.167360i
$718$		0			0
$719$	−3447.89	+	5971.91i	−0.178838	+	0.309756i	−0.941483	−	0.337061i	$-0.890567\pi$
$719$	−3447.89	+	5971.91i	−0.178838	+	0.309756i	0.762645	+	0.646817i	$0.223900\pi$
$720$		0			0
$721$	−6215.49	+	10765.5i	−0.321050	+	0.556075i
$722$		0			0
$723$	−8823.04			−0.453848
$724$		0			0
$725$	−36.8417	−	63.8117i	−0.00188726	−	0.00326884i
$726$		0			0
$727$	−12841.0			−0.655086			−0.327543	−	0.944836i	$-0.606221\pi$
$727$	−12841.0			−0.655086			−0.327543	+	0.944836i	$0.606221\pi$
$728$		0			0
$729$	11731.6			0.596029
$730$		0			0
$731$	700.711	+	1213.67i	0.0354538	+	0.0614078i
$732$		0			0
$733$	−26005.8			−1.31043			−0.655216	−	0.755441i	$-0.727423\pi$
$733$	−26005.8			−1.31043			−0.655216	+	0.755441i	$0.727423\pi$
$734$		0			0
$735$	−17492.4	+	30297.7i	−0.877846	+	1.52047i
$736$		0			0
$737$	−12694.4	+	21987.3i	−0.634470	+	1.09893i
$738$		0			0
$739$	−8885.01	−	15389.3i	−0.442274	−	0.766041i	0.555584	−	0.831460i	$-0.312495\pi$
$739$	−8885.01	−	15389.3i	−0.442274	−	0.766041i	−0.997858	+	0.0654195i	$0.979161\pi$
$740$		0			0
$741$	−79.0661	+	1610.63i	−0.00391979	+	0.0798489i
$742$		0			0
$743$	−14420.9	−	24977.7i	−0.712046	−	1.23330i	−0.964088	−	0.265583i	$-0.914436\pi$
$743$	−14420.9	−	24977.7i	−0.712046	−	1.23330i	0.252043	−	0.967716i	$-0.418898\pi$
$744$		0			0
$745$	−1603.57	+	2777.46i	−0.0788594	+	0.136588i
$746$		0			0
$747$	−4246.56	+	7355.25i	−0.207996	+	0.360260i
$748$		0			0
$749$	−12638.3			−0.616547
$750$		0			0
$751$	−4216.12	−	7302.54i	−0.204858	−	0.354825i	0.745229	−	0.666808i	$-0.232340\pi$
$751$	−4216.12	−	7302.54i	−0.204858	−	0.354825i	−0.950088	+	0.311983i	$0.899007\pi$
$752$		0			0
$753$	6081.12			0.294301
$754$		0			0
$755$	22677.3			1.09313
$756$		0			0
$757$	−19480.8	−	33741.7i	−0.935325	−	1.62003i	−0.774053	−	0.633121i	$-0.781774\pi$
$757$	−19480.8	−	33741.7i	−0.935325	−	1.62003i	−0.161272	−	0.986910i	$-0.551560\pi$
$758$		0			0
$759$	−1610.35			−0.0770120
$760$		0			0
$761$	−4012.86	+	6950.47i	−0.191151	+	0.331083i	−0.945632	−	0.325239i	$-0.894555\pi$
$761$	−4012.86	+	6950.47i	−0.191151	+	0.331083i	0.754481	+	0.656322i	$0.227889\pi$
$762$		0			0
$763$	14210.4	−	24613.2i	0.674249	−	1.16783i
$764$		0			0
$765$	−244.401	−	423.315i	−0.0115508	−	0.0200065i
$766$		0			0
$767$	5631.13	+	3630.46i	0.265096	+	0.170911i
$768$		0			0
$769$	−11295.1	−	19563.8i	−0.529666	−	0.917408i	−0.999401	−	0.0346010i	$-0.988984\pi$
$769$	−11295.1	−	19563.8i	−0.529666	−	0.917408i	0.469735	−	0.882807i	$-0.344349\pi$
$770$		0			0
$771$	1480.75	−	2564.73i	0.0691671	−	0.119801i
$772$		0			0
$773$	20460.0	−	35437.7i	0.951997	−	1.64891i	0.210901	−	0.977508i	$-0.432360\pi$
$773$	20460.0	−	35437.7i	0.951997	−	1.64891i	0.741096	−	0.671399i	$-0.234306\pi$
$774$		0			0
$775$	2198.96			0.101921
$776$		0			0
$777$	−33323.6	−	57718.2i	−1.53858	−	2.66490i
$778$		0			0
$779$	1573.76			0.0723821
$780$		0			0
$781$	7091.67			0.324917
$782$		0			0
$783$	610.024	+	1056.59i	0.0278422	+	0.0482242i
$784$		0			0
$785$	−6057.63			−0.275422
$786$		0			0
$787$	7807.21	−	13522.5i	0.353618	−	0.612484i	−0.633263	−	0.773937i	$-0.718285\pi$
$787$	7807.21	−	13522.5i	0.353618	−	0.612484i	0.986880	+	0.161453i	$0.0516181\pi$
$788$		0			0
$789$	496.577	−	860.097i	0.0224063	−	0.0388089i
$790$		0			0
$791$	11241.1	+	19470.2i	0.505294	+	0.875195i
$792$		0			0
$793$	22167.1	+	14291.4i	0.992657	+	0.639979i
$794$		0			0
$795$	8758.71	+	15170.5i	0.390742	+	0.676784i
$796$		0			0
$797$	−8934.79	+	15475.5i	−0.397097	+	0.687793i	−0.993366	−	0.114992i	$-0.963316\pi$
$797$	−8934.79	+	15475.5i	−0.397097	+	0.687793i	0.596269	+	0.802785i	$0.296649\pi$
$798$		0			0
$799$	−1593.41	+	2759.87i	−0.0705517	+	0.122199i
$800$		0			0
$801$	−4914.74			−0.216796
$802$		0			0
$803$	4930.80	+	8540.39i	0.216692	+	0.375322i
$804$		0			0
$805$	−1816.04			−0.0795116
$806$		0			0
$807$	−9044.74			−0.394535
$808$		0			0
$809$	4056.59	+	7026.23i	0.176294	+	0.305351i	0.940608	−	0.339493i	$-0.110256\pi$
$809$	4056.59	+	7026.23i	0.176294	+	0.305351i	−0.764314	+	0.644844i	$0.776922\pi$
$810$		0			0
$811$	−22750.9			−0.985073			−0.492536	−	0.870292i	$-0.663930\pi$
$811$	−22750.9			−0.985073			−0.492536	+	0.870292i	$0.663930\pi$
$812$		0			0
$813$	3458.73	−	5990.70i	0.149204	−	0.258429i
$814$		0			0
$815$	7010.81	−	12143.1i	0.301323	−	0.521906i
$816$		0			0
$817$	−676.395	−	1171.55i	−0.0289646	−	0.0501681i
$818$		0			0
$819$	−9218.79	+	4735.70i	−0.393322	+	0.202050i
$820$		0			0
$821$	2997.11	+	5191.15i	0.127406	+	0.220673i	0.922671	−	0.385589i	$-0.126002\pi$
$821$	2997.11	+	5191.15i	0.127406	+	0.220673i	−0.795265	+	0.606262i	$0.792668\pi$
$822$		0			0
$823$	−17094.1	+	29607.9i	−0.724015	+	1.25403i	0.235363	+	0.971907i	$0.424372\pi$
$823$	−17094.1	+	29607.9i	−0.724015	+	1.25403i	−0.959378	+	0.282123i	$0.908961\pi$
$824$		0			0
$825$	−998.745	+	1729.88i	−0.0421477	+	0.0730019i
$826$		0			0
$827$	−39546.0			−1.66282			−0.831409	−	0.555661i	$-0.812465\pi$
$827$	−39546.0			−1.66282			−0.831409	+	0.555661i	$0.812465\pi$
$828$		0			0
$829$	−12104.0	−	20964.7i	−0.507104	−	0.878329i	−0.999966	−	0.00822196i	$-0.997383\pi$
$829$	−12104.0	−	20964.7i	−0.507104	−	0.878329i	0.492863	−	0.870107i	$-0.335950\pi$
$830$		0			0
$831$	−22909.9			−0.956360
$832$		0			0
$833$	−3335.57			−0.138740
$834$		0			0
$835$	−13653.9	−	23649.3i	−0.565884	−	0.980140i
$836$		0			0
$837$	−36410.2			−1.50361
$838$		0			0
$839$	17071.8	−	29569.1i	0.702482	−	1.21673i	−0.265111	−	0.964218i	$-0.585408\pi$
$839$	17071.8	−	29569.1i	0.702482	−	1.21673i	0.967593	−	0.252516i	$-0.0812582\pi$
$840$		0			0
$841$	12138.2	−	21023.9i	0.497690	−	0.862025i
$842$		0			0
$843$	173.024	+	299.686i	0.00706911	+	0.0122441i
$844$		0			0
$845$	23756.6	+	2338.06i	0.967164	+	0.0951856i
$846$		0			0
$847$	−16063.3	−	27822.4i	−0.651642	−	1.12868i
$848$		0			0
$849$	−13770.9	+	23851.9i	−0.556673	+	0.964186i
$850$		0			0
$851$	1064.60	−	1843.95i	0.0428839	−	0.0742770i
$852$		0			0
$853$	13008.1			0.522145			0.261072	−	0.965319i	$-0.415924\pi$
$853$	13008.1			0.522145			0.261072	+	0.965319i	$0.415924\pi$
$854$		0			0
$855$	235.920	+	408.625i	0.00943659	+	0.0163447i
$856$		0			0
$857$	−35075.0			−1.39806			−0.699031	−	0.715091i	$-0.746385\pi$
$857$	−35075.0			−1.39806			−0.699031	+	0.715091i	$0.746385\pi$
$858$		0			0
$859$	2869.77			0.113988			0.0569939	−	0.998375i	$-0.481848\pi$
$859$	2869.77			0.113988			0.0569939	+	0.998375i	$0.481848\pi$
$860$		0			0
$861$	23500.5	+	40704.0i	0.930191	+	1.61114i
$862$		0			0
$863$	−29617.3			−1.16823			−0.584117	−	0.811670i	$-0.698559\pi$
$863$	−29617.3			−1.16823			−0.584117	+	0.811670i	$0.698559\pi$
$864$		0			0
$865$	−18474.1	+	31998.2i	−0.726173	+	1.25777i
$866$		0			0
$867$	−14300.2	+	24768.7i	−0.560163	+	0.970230i
$868$		0			0
$869$	648.989	+	1124.08i	0.0253342	+	0.0438802i
$870$		0			0
$871$	−21577.0	+	11084.1i	−0.839390	+	0.431195i
$872$		0			0
$873$	509.059	+	881.715i	0.0197354	+	0.0341828i
$874$		0			0
$875$	−21407.7	+	37079.2i	−0.827099	+	1.43258i
$876$		0			0
$877$	7675.09	−	13293.6i	0.295518	−	0.511852i	−0.679587	−	0.733595i	$-0.737841\pi$
$877$	7675.09	−	13293.6i	0.295518	−	0.511852i	0.975105	+	0.221743i	$0.0711744\pi$
$878$		0			0
$879$	47620.6			1.82731
$880$		0			0
$881$	−3181.94	−	5511.28i	−0.121682	−	0.210760i	0.798749	−	0.601665i	$-0.205496\pi$
$881$	−3181.94	−	5511.28i	−0.121682	−	0.210760i	−0.920431	+	0.390904i	$0.872162\pi$
$882$		0			0
$883$	32249.9			1.22910			0.614550	−	0.788878i	$-0.289338\pi$
$883$	32249.9			1.22910			0.614550	+	0.788878i	$0.289338\pi$
$884$		0			0
$885$	9109.81			0.346015
$886$		0			0
$887$	14244.7	+	24672.5i	0.539221	+	0.933959i	0.998946	+	0.0458972i	$0.0146147\pi$
$887$	14244.7	+	24672.5i	0.539221	+	0.933959i	−0.459725	+	0.888061i	$0.652052\pi$
$888$		0			0
$889$	39769.0			1.50035
$890$		0			0
$891$	21440.5	−	37136.0i	0.806155	−	1.39630i
$892$		0			0
$893$	1538.12	−	2664.10i	0.0576384	−	0.0998327i
$894$		0			0
$895$	8530.60	+	14775.4i	0.318599	+	0.551830i
$896$		0			0
$897$	−1293.14	−	833.704i	−0.0481346	−	0.0310330i
$898$		0			0
$899$	−1681.18	−	2911.89i	−0.0623698	−	0.108028i
$900$		0			0
$901$	−835.085	+	1446.41i	−0.0308776	+	0.0534816i
$902$		0			0
$903$	20200.8	−	34988.9i	0.744454	−	1.28943i
$904$		0			0
$905$	−31748.8			−1.16615
$906$		0			0
$907$	3592.78	+	6222.88i	0.131529	+	0.227814i	0.924266	−	0.381749i	$-0.124678\pi$
$907$	3592.78	+	6222.88i	0.131529	+	0.227814i	−0.792737	+	0.609563i	$0.791345\pi$
$908$		0			0
$909$	−6549.94			−0.238997
$910$		0			0
$911$	−27000.2			−0.981949			−0.490975	−	0.871174i	$-0.663359\pi$
$911$	−27000.2			−0.981949			−0.490975	+	0.871174i	$0.663359\pi$
$912$		0			0
$913$	−28138.7	−	48737.7i	−1.02000	−	1.76668i
$914$		0			0
$915$	35861.1			1.29566
$916$		0			0
$917$	3888.15	−	6734.47i	0.140020	−	0.242521i
$918$		0			0
$919$	10592.5	−	18346.8i	0.380213	−	0.658548i	−0.610879	−	0.791724i	$-0.709184\pi$
$919$	10592.5	−	18346.8i	0.380213	−	0.658548i	0.991092	+	0.133175i	$0.0425173\pi$
$920$		0			0
$921$	3144.01	+	5445.58i	0.112485	+	0.194829i
$922$		0			0
$923$	5694.73	+	3671.47i	0.203082	+	0.130929i
$924$		0			0
$925$	−1320.54	−	2287.24i	−0.0469396	−	0.0813018i
$926$		0			0
$927$	−1540.82	+	2668.77i	−0.0545922	+	0.0945565i
$928$		0			0
$929$	−12021.9	+	20822.5i	−0.424570	+	0.735377i	−0.996380	−	0.0850093i	$-0.972908\pi$
$929$	−12021.9	+	20822.5i	−0.424570	+	0.735377i	0.571810	+	0.820386i	$0.306241\pi$
$930$		0			0
$931$	3219.82			0.113346
$932$		0			0
$933$	13280.6	+	23002.7i	0.466010	+	0.807153i
$934$		0			0
$935$	3238.92			0.113288
$936$		0			0
$937$	6308.48			0.219946			0.109973	−	0.993935i	$-0.464924\pi$
$937$	6308.48			0.219946			0.109973	+	0.993935i	$0.464924\pi$
$938$		0			0
$939$	−15825.4	−	27410.4i	−0.549991	−	0.952613i
$940$		0			0
$941$	1549.84			0.0536912			0.0268456	−	0.999640i	$-0.491454\pi$
$941$	1549.84			0.0536912			0.0268456	+	0.999640i	$0.491454\pi$
$942$		0			0
$943$	−750.780	+	1300.39i	−0.0259266	+	0.0449062i
$944$		0			0
$945$	18649.4	−	32301.7i	0.641974	−	1.11193i
$946$		0			0
$947$	6586.00	+	11407.3i	0.225994	+	0.391433i	0.956617	−	0.291348i	$-0.0941037\pi$
$947$	6586.00	+	11407.3i	0.225994	+	0.391433i	−0.730623	+	0.682781i	$0.760770\pi$
$948$		0			0
$949$	−461.978	+	9410.82i	−0.0158024	+	0.321905i
$950$		0			0
$951$	24114.1	+	41766.8i	0.822243	+	1.42417i
$952$		0			0
$953$	−14012.7	+	24270.7i	−0.476303	+	0.824980i	−0.999631	−	0.0271505i	$-0.991357\pi$
$953$	−14012.7	+	24270.7i	−0.476303	+	0.824980i	0.523329	+	0.852131i	$0.324690\pi$
$954$		0			0
$955$	−21234.9	+	36779.9i	−0.719523	+	1.24625i
$956$		0			0
$957$	3054.31			0.103168
$958$		0			0
$959$	−36017.0	−	62383.2i	−1.21277	−	2.10058i
$960$		0			0
$961$	70552.9			2.36826
$962$		0			0
$963$	−3133.02			−0.104839
$964$		0			0
$965$	−11513.7	−	19942.4i	−0.384083	−	0.665252i
$966$		0			0
$967$	4250.06			0.141337			0.0706684	−	0.997500i	$-0.477487\pi$
$967$	4250.06			0.141337			0.0706684	+	0.997500i	$0.477487\pi$
$968$		0			0
$969$	−104.524	+	181.040i	−0.00346521	+	0.00600191i
$970$		0			0
$971$	−2356.03	+	4080.76i	−0.0778667	+	0.134869i	−0.902329	−	0.431047i	$-0.858144\pi$
$971$	−2356.03	+	4080.76i	−0.0778667	+	0.134869i	0.824463	+	0.565916i	$0.191478\pi$
$972$		0			0
$973$	−6091.51	−	10550.8i	−0.200704	−	0.347629i
$974$		0			0
$975$	−1697.59	+	872.055i	−0.0557605	+	0.0286442i
$976$		0			0
$977$	26478.0	+	45861.2i	0.867047	+	1.50177i	0.865000	+	0.501771i	$0.167318\pi$
$977$	26478.0	+	45861.2i	0.867047	+	1.50177i	0.00204652	+	0.999998i	$0.499349\pi$
$978$		0			0
$979$	16283.1	−	28203.2i	0.531574	−	0.920714i
$980$		0			0
$981$	3522.75	−	6101.59i	0.114651	−	0.198582i
$982$		0			0
$983$	10772.6			0.349534			0.174767	−	0.984610i	$-0.444083\pi$
$983$	10772.6			0.349534			0.174767	+	0.984610i	$0.444083\pi$
$984$		0			0
$985$	16898.5	+	29269.1i	0.546631	+	0.946792i
$986$		0			0
$987$	91873.1			2.96287
$988$		0			0
$989$	1290.73			0.0414993
$990$		0			0
$991$	7696.24	+	13330.3i	0.246700	+	0.427296i	0.962608	−	0.270898i	$-0.0873206\pi$
$991$	7696.24	+	13330.3i	0.246700	+	0.427296i	−0.715909	+	0.698194i	$0.753987\pi$
$992$		0			0
$993$	−3568.28			−0.114034
$994$		0			0
$995$	2667.32	−	4619.94i	0.0849848	−	0.147198i
$996$		0			0
$997$	−860.917	+	1491.15i	−0.0273475	+	0.0473673i	−0.879375	−	0.476129i	$-0.842039\pi$
$997$	−860.917	+	1491.15i	−0.0273475	+	0.0473673i	0.852028	+	0.523497i	$0.175373\pi$
$998$		0			0
$999$	21865.5	+	37872.1i	0.692486	+	1.19942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.i.d.81.2		4
4.3	odd	2		26.4.c.b.3.1	✓	4
12.11	even	2		234.4.h.h.55.2		4
13.9	even	3	inner	208.4.i.d.113.2		4
52.3	odd	6		338.4.a.h.1.2		2
52.7	even	12		338.4.e.f.147.1		8
52.11	even	12		338.4.b.e.337.4		4
52.15	even	12		338.4.b.e.337.2		4
52.19	even	12		338.4.e.f.147.3		8
52.23	odd	6		338.4.a.g.1.2		2
52.31	even	4		338.4.e.f.23.1		8
52.35	odd	6		26.4.c.b.9.1	yes	4
52.43	odd	6		338.4.c.j.191.1		4
52.47	even	4		338.4.e.f.23.3		8
52.51	odd	2		338.4.c.j.315.1		4
156.35	even	6		234.4.h.h.217.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.c.b.3.1	✓	4	4.3	odd	2
26.4.c.b.9.1	yes	4	52.35	odd	6
208.4.i.d.81.2		4	1.1	even	1	trivial
208.4.i.d.113.2		4	13.9	even	3	inner
234.4.h.h.55.2		4	12.11	even	2
234.4.h.h.217.2		4	156.35	even	6
338.4.a.g.1.2		2	52.23	odd	6
338.4.a.h.1.2		2	52.3	odd	6
338.4.b.e.337.2		4	52.15	even	12
338.4.b.e.337.4		4	52.11	even	12
338.4.c.j.191.1		4	52.43	odd	6
338.4.c.j.315.1		4	52.51	odd	2
338.4.e.f.23.1		8	52.31	even	4
338.4.e.f.23.3		8	52.47	even	4
338.4.e.f.147.1		8	52.7	even	12
338.4.e.f.147.3		8	52.19	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.93273 + 5.07964i) q^{3} -10.8655 q^{5} +(-14.9327 + 25.8642i) q^{7} +(-3.70181 + 6.41172i) q^{9} +(-24.5291 - 42.4857i) q^{11} +(2.29819 - 46.8158i) q^{13} +(-31.8655 - 55.1926i) q^{15} +(3.03816 - 5.26225i) q^{17} +(-2.93273 + 5.07964i) q^{19} -175.175 q^{21} +(-2.79819 - 4.84661i) q^{23} -6.94178 q^{25} +114.942 q^{27} +(5.30724 + 9.19241i) q^{29} -316.771 q^{31} +(143.875 - 249.198i) q^{33} +(162.251 - 281.027i) q^{35} +(190.231 + 329.490i) q^{37} +(244.547 - 125.624i) q^{39} +(-134.155 - 232.363i) q^{41} +(-115.318 + 199.737i) q^{43} +(40.2219 - 69.6663i) q^{45} -524.466 q^{47} +(-274.473 - 475.401i) q^{49} +35.6404 q^{51} -274.865 q^{53} +(266.520 + 461.626i) q^{55} -34.4036 q^{57} +(-71.4709 + 123.791i) q^{59} +(-281.347 + 487.308i) q^{61} +(-110.556 - 191.489i) q^{63} +(-24.9709 + 508.675i) q^{65} +(-258.762 - 448.189i) q^{67} +(16.4127 - 28.4276i) q^{69} +(-72.2781 + 125.189i) q^{71} -201.018 q^{73} +(-20.3584 - 35.2617i) q^{75} +1465.15 q^{77} -26.4579 q^{79} +(437.042 + 756.979i) q^{81} +1147.16 q^{83} +(-33.0110 + 57.1767i) q^{85} +(-31.1294 + 53.9177i) q^{87} +(331.915 + 574.893i) q^{89} +(1176.54 + 758.529i) q^{91} +(-929.004 - 1609.08i) q^{93} +(31.8655 - 55.1926i) q^{95} +(68.7581 - 119.092i) q^{97} +363.208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{3} - 14 q^{5} - 45 q^{7} - 59 q^{9} + 5 q^{11} - 35 q^{13} - 98 q^{15} + 130 q^{17} + 3 q^{19} - 82 q^{21} + 33 q^{23} - 234 q^{25} + 666 q^{27} + 198 q^{29} - 560 q^{31} + 767 q^{33} + 266 q^{35}+ \cdots - 4852 q^{99}+O(q^{100}) \) 4 * q - 3 * q^3 - 14 * q^5 - 45 * q^7 - 59 * q^9 + 5 * q^11 - 35 * q^13 - 98 * q^15 + 130 * q^17 + 3 * q^19 - 82 * q^21 + 33 * q^23 - 234 * q^25 + 666 * q^27 + 198 * q^29 - 560 * q^31 + 767 * q^33 + 266 * q^35 + 702 * q^37 + 1317 * q^39 - 242 * q^41 - 93 * q^43 - 119 * q^45 - 448 * q^47 - 435 * q^49 - 2126 * q^51 - 1070 * q^53 + 742 * q^55 - 226 * q^57 - 389 * q^59 - 654 * q^61 - 1002 * q^63 - 203 * q^65 - 107 * q^67 + 375 * q^69 - 569 * q^71 - 1246 * q^73 + 935 * q^75 + 1294 * q^77 - 1520 * q^79 + 334 * q^81 + 3528 * q^83 + 413 * q^85 + 1599 * q^87 + 871 * q^89 + 1539 * q^91 - 2184 * q^93 + 98 * q^95 + 879 * q^97 - 4852 * q^99

Introduction

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