LMFDB - Embedded newform 675.2.k.c.424.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(199,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.199"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 $ x^16 - 12x^14 + 102x^12 - 406x^10 + 1167x^8 - 1842x^6 + 2023x^4 - 441*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.8
Root			$2.28087 + 1.31686i$ of defining polynomial
Character	$\chi$	$=$	675.424
Dual form			675.2.k.c.199.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.28087 + 1.31686i) q^{2} +(2.46825 + 4.27513i) q^{4} +(1.55662 + 0.898714i) q^{7} +7.73393i q^{8} +(0.904062 - 1.56588i) q^{11} +(-1.70765 + 0.985914i) q^{13} +(2.36696 + 4.09970i) q^{14} +(-5.24801 + 9.08982i) q^{16} -4.80812i q^{17} -2.96467 q^{19} +(4.12410 - 2.38105i) q^{22} +(-1.50162 + 0.866963i) q^{23} -5.19325 q^{26} +8.87300i q^{28} +(3.68382 - 6.38057i) q^{29} +(1.31151 + 2.27161i) q^{31} +(-10.5445 + 6.08789i) q^{32} +(6.33163 - 10.9667i) q^{34} +11.6351i q^{37} +(-6.76203 - 3.90406i) q^{38} +(-1.23324 - 2.13603i) q^{41} +(-6.30306 - 3.63907i) q^{43} +8.92580 q^{44} -4.56668 q^{46} +(5.44910 + 3.14604i) q^{47} +(-1.88463 - 3.26427i) q^{49} +(-8.42983 - 4.86696i) q^{52} +1.72540i q^{53} +(-6.95059 + 12.0388i) q^{56} +(16.8047 - 9.70218i) q^{58} +(-5.51300 - 9.54880i) q^{59} +(6.33521 - 10.9729i) q^{61} +6.90833i q^{62} -11.0756 q^{64} +(7.88407 - 4.55187i) q^{67} +(20.5554 - 11.8676i) q^{68} -1.27460 q^{71} +3.58770i q^{73} +(-15.3218 + 26.5382i) q^{74} +(-7.31755 - 12.6744i) q^{76} +(2.81456 - 1.62499i) q^{77} +(1.05545 - 1.82809i) q^{79} -6.49602i q^{82} +(-0.951614 - 0.549415i) q^{83} +(-9.58431 - 16.6005i) q^{86} +(12.1104 + 6.99195i) q^{88} -13.2935 q^{89} -3.54422 q^{91} +(-7.41277 - 4.27976i) q^{92} +(8.28580 + 14.3514i) q^{94} +(3.31926 + 1.91638i) q^{97} -9.92718i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74}+ \cdots + 6 q^{94}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.28087	+	1.31686i	1.61282	+	0.931162i	0.988713	+	0.149823i	$0.0478703\pi$
$2$	2.28087	+	1.31686i	1.61282	+	0.931162i	0.624107	+	0.781339i	$0.285463\pi$
$3$		0			0
$3$		0			0
$4$	2.46825	+	4.27513i	1.23412	+	2.13757i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.55662	+	0.898714i	0.588346	+	0.339682i	0.764443	−	0.644691i	$-0.223014\pi$
$7$	1.55662	+	0.898714i	0.588346	+	0.339682i	−0.176097	+	0.984373i	$0.556347\pi$
$8$			7.73393i			2.73436i
$9$		0			0
$10$		0			0
$11$	0.904062	−	1.56588i	0.272585	−	0.472131i	−0.696938	−	0.717131i	$-0.745455\pi$
$11$	0.904062	−	1.56588i	0.272585	−	0.472131i	0.969523	+	0.245000i	$0.0787881\pi$
$12$		0			0
$13$	−1.70765	+	0.985914i	−0.473618	+	0.273443i	−0.717753	−	0.696298i	$-0.754829\pi$
$13$	−1.70765	+	0.985914i	−0.473618	+	0.273443i	0.244135	+	0.969741i	$0.421496\pi$
$14$	2.36696	+	4.09970i	0.632598	+	1.09569i
$15$		0			0
$16$	−5.24801	+	9.08982i	−1.31200	+	2.27246i
$17$		−	4.80812i		−	1.16614i	−0.812421	−	0.583071i	$-0.801851\pi$
$17$		−	4.80812i		−	1.16614i	0.812421	−	0.583071i	$-0.198149\pi$
$18$		0			0
$19$	−2.96467			−0.680142			−0.340071	−	0.940400i	$-0.610451\pi$
$19$	−2.96467			−0.680142			−0.340071	+	0.940400i	$0.610451\pi$
$20$		0			0
$21$		0			0
$22$	4.12410	−	2.38105i	0.879261	−	0.507641i
$23$	−1.50162	+	0.866963i	−0.313110	+	0.180774i	−0.648317	−	0.761370i	$-0.724527\pi$
$23$	−1.50162	+	0.866963i	−0.313110	+	0.180774i	0.335207	+	0.942144i	$0.391194\pi$
$24$		0			0
$25$		0			0
$26$	−5.19325			−1.01848
$27$		0			0
$28$			8.87300i			1.67684i
$29$	3.68382	−	6.38057i	0.684069	−	1.18484i	−0.289659	−	0.957130i	$-0.593542\pi$
$29$	3.68382	−	6.38057i	0.684069	−	1.18484i	0.973728	−	0.227713i	$-0.0731247\pi$
$30$		0			0
$31$	1.31151	+	2.27161i	0.235555	+	0.407993i	0.959434	−	0.281934i	$-0.0909760\pi$
$31$	1.31151	+	2.27161i	0.235555	+	0.407993i	−0.723879	+	0.689927i	$0.757643\pi$
$32$	−10.5445	+	6.08789i	−1.86403	+	1.07620i
$33$		0			0
$34$	6.33163	−	10.9667i	1.08587	−	1.88078i
$35$		0			0
$36$		0			0
$37$			11.6351i			1.91280i	0.292063	+	0.956399i	$0.405658\pi$
$37$			11.6351i			1.91280i	−0.292063	+	0.956399i	$0.594342\pi$
$38$	−6.76203	−	3.90406i	−1.09695	−	0.633322i
$39$		0			0
$40$		0			0
$41$	−1.23324	−	2.13603i	−0.192600	−	0.333592i	0.753511	−	0.657435i	$-0.228359\pi$
$41$	−1.23324	−	2.13603i	−0.192600	−	0.333592i	−0.946111	+	0.323842i	$0.895025\pi$
$42$		0			0
$43$	−6.30306	−	3.63907i	−0.961207	−	0.554953i	−0.0646628	−	0.997907i	$-0.520597\pi$
$43$	−6.30306	−	3.63907i	−0.961207	−	0.554953i	−0.896544	+	0.442954i	$0.853931\pi$
$44$	8.92580			1.34562
$45$		0			0
$46$	−4.56668			−0.673321
$47$	5.44910	+	3.14604i	0.794833	+	0.458897i	0.841661	−	0.540006i	$-0.181578\pi$
$47$	5.44910	+	3.14604i	0.794833	+	0.458897i	−0.0468283	+	0.998903i	$0.514911\pi$
$48$		0			0
$49$	−1.88463	−	3.26427i	−0.269233	−	0.466324i
$50$		0			0
$51$		0			0
$52$	−8.42983	−	4.86696i	−1.16901	−	0.674926i
$53$			1.72540i			0.237001i	0.992954	+	0.118501i	$0.0378088\pi$
$53$			1.72540i			0.237001i	−0.992954	+	0.118501i	$0.962191\pi$
$54$		0			0
$55$		0			0
$56$	−6.95059	+	12.0388i	−0.928811	+	1.60875i
$57$		0			0
$58$	16.8047	−	9.70218i	2.20656	−	1.27396i
$59$	−5.51300	−	9.54880i	−0.717732	−	1.24315i	−0.961896	−	0.273414i	$-0.911847\pi$
$59$	−5.51300	−	9.54880i	−0.717732	−	1.24315i	0.244165	−	0.969734i	$-0.421486\pi$
$60$		0			0
$61$	6.33521	−	10.9729i	0.811141	−	1.40494i	−0.100925	−	0.994894i	$-0.532180\pi$
$61$	6.33521	−	10.9729i	0.811141	−	1.40494i	0.912066	−	0.410043i	$-0.134486\pi$
$62$			6.90833i			0.877358i
$63$		0			0
$64$	−11.0756			−1.38445
$65$		0			0
$66$		0			0
$67$	7.88407	−	4.55187i	0.963193	−	0.556100i	0.0660386	−	0.997817i	$-0.478964\pi$
$67$	7.88407	−	4.55187i	0.963193	−	0.556100i	0.897154	+	0.441717i	$0.145631\pi$
$68$	20.5554	−	11.8676i	2.49271	−	1.43916i
$69$		0			0
$70$		0			0
$71$	−1.27460			−0.151268			−0.0756338	−	0.997136i	$-0.524098\pi$
$71$	−1.27460			−0.151268			−0.0756338	+	0.997136i	$0.524098\pi$
$72$		0			0
$73$			3.58770i			0.419908i	0.977711	+	0.209954i	$0.0673315\pi$
$73$			3.58770i			0.419908i	−0.977711	+	0.209954i	$0.932669\pi$
$74$	−15.3218	+	26.5382i	−1.78112	+	3.08500i
$75$		0			0
$76$	−7.31755	−	12.6744i	−0.839380	−	1.45385i
$77$	2.81456	−	1.62499i	0.320749	−	0.185184i
$78$		0			0
$79$	1.05545	−	1.82809i	0.118747	−	0.205676i	−0.800524	−	0.599300i	$-0.795445\pi$
$79$	1.05545	−	1.82809i	0.118747	−	0.205676i	0.919272	+	0.393624i	$0.128779\pi$
$80$		0			0
$81$		0			0
$82$		−	6.49602i		−	0.717366i
$83$	−0.951614	−	0.549415i	−0.104453	−	0.0603061i	0.446863	−	0.894602i	$-0.352541\pi$
$83$	−0.951614	−	0.549415i	−0.104453	−	0.0603061i	−0.551317	+	0.834296i	$0.685874\pi$
$84$		0			0
$85$		0			0
$86$	−9.58431	−	16.6005i	−1.03350	−	1.79008i
$87$		0			0
$88$	12.1104	+	6.99195i	1.29097	+	0.745344i
$89$	−13.2935			−1.40910			−0.704552	−	0.709653i	$-0.748852\pi$
$89$	−13.2935			−1.40910			−0.704552	+	0.709653i	$0.748852\pi$
$90$		0			0
$91$	−3.54422			−0.371535
$92$	−7.41277	−	4.27976i	−0.772834	−	0.446196i
$93$		0			0
$94$	8.28580	+	14.3514i	0.854615	+	1.48024i
$95$		0			0
$96$		0			0
$97$	3.31926	+	1.91638i	0.337020	+	0.194579i	0.658954	−	0.752184i	$-0.270999\pi$
$97$	3.31926	+	1.91638i	0.337020	+	0.194579i	−0.321933	+	0.946762i	$0.604333\pi$
$98$		−	9.92718i		−	1.00280i
$99$		0			0
$100$		0			0
$101$	3.27618	−	5.67452i	0.325993	−	0.564636i	−0.655720	−	0.755004i	$-0.727635\pi$
$101$	3.27618	−	5.67452i	0.325993	−	0.564636i	0.981713	+	0.190368i	$0.0609682\pi$
$102$		0			0
$103$	6.99365	−	4.03779i	0.689105	−	0.397855i	−0.114172	−	0.993461i	$-0.536421\pi$
$103$	6.99365	−	4.03779i	0.689105	−	0.397855i	0.803277	+	0.595606i	$0.203088\pi$
$104$	−7.62499	−	13.2069i	−0.747691	−	1.29504i
$105$		0			0
$106$	−2.27211	+	3.93541i	−0.220687	+	0.382241i
$107$			8.97674i			0.867814i	0.900958	+	0.433907i	$0.142865\pi$
$107$			8.97674i			0.867814i	−0.900958	+	0.433907i	$0.857135\pi$
$108$		0			0
$109$	6.34164			0.607419			0.303710	−	0.952765i	$-0.401775\pi$
$109$	6.34164			0.607419			0.303710	+	0.952765i	$0.401775\pi$
$110$		0			0
$111$		0			0
$112$	−16.3383	+	9.43292i	−1.54382	+	0.891327i
$113$	−12.9060	+	7.45127i	−1.21409	+	0.700957i	−0.963648	−	0.267174i	$-0.913910\pi$
$113$	−12.9060	+	7.45127i	−1.21409	+	0.700957i	−0.250444	+	0.968131i	$0.580577\pi$
$114$		0			0
$115$		0			0
$116$	36.3704			3.37691
$117$		0			0
$118$		−	29.0394i		−	2.67330i
$119$	4.32113	−	7.48441i	0.396117	−	0.686095i
$120$		0			0
$121$	3.86534	+	6.69497i	0.351395	+	0.608634i
$122$	28.8996	−	16.6852i	2.61645	−	1.51061i
$123$		0			0
$124$	−6.47428	+	11.2138i	−0.581408	+	1.00703i
$125$		0			0
$126$		0			0
$127$			3.62303i			0.321492i	0.986996	+	0.160746i	$0.0513899\pi$
$127$			3.62303i			0.321492i	−0.986996	+	0.160746i	$0.948610\pi$
$128$	−4.17289	−	2.40922i	−0.368835	−	0.212947i
$129$		0			0
$130$		0			0
$131$	3.64673	+	6.31631i	0.318616	+	0.551859i	0.980200	−	0.198012i	$-0.0634486\pi$
$131$	3.64673	+	6.31631i	0.318616	+	0.551859i	−0.661584	+	0.749871i	$0.730115\pi$
$132$		0			0
$133$	−4.61486	−	2.66439i	−0.400159	−	0.231032i
$134$	23.9767			2.07127
$135$		0			0
$136$	37.1857			3.18865
$137$	−6.17148	−	3.56310i	−0.527265	−	0.304417i	0.212637	−	0.977131i	$-0.431795\pi$
$137$	−6.17148	−	3.56310i	−0.527265	−	0.304417i	−0.739902	+	0.672715i	$0.765128\pi$
$138$		0			0
$139$	−7.35533	−	12.7398i	−0.623871	−	1.08058i	−0.988758	−	0.149525i	$-0.952226\pi$
$139$	−7.35533	−	12.7398i	−0.623871	−	1.08058i	0.364887	−	0.931052i	$-0.381108\pi$
$140$		0			0
$141$		0			0
$142$	−2.90721	−	1.67848i	−0.243967	−	0.140855i
$143$			3.56531i			0.298146i
$144$		0			0
$145$		0			0
$146$	−4.72450	+	8.18308i	−0.391003	+	0.677236i
$147$		0			0
$148$	−49.7416	+	28.7183i	−4.08873	+	2.36063i
$149$	0.282655	+	0.489572i	0.0231560	+	0.0401073i	0.877371	−	0.479812i	$-0.159295\pi$
$149$	0.282655	+	0.489572i	0.0231560	+	0.0401073i	−0.854215	+	0.519920i	$0.825962\pi$
$150$		0			0
$151$	−0.0766925	+	0.132835i	−0.00624115	+	0.0108100i	−0.869129	−	0.494585i	$-0.835320\pi$
$151$	−0.0766925	+	0.132835i	−0.00624115	+	0.0108100i	0.862888	+	0.505395i	$0.168653\pi$
$152$		−	22.9285i		−	1.85975i
$153$		0			0
$154$	8.55953			0.689746
$155$		0			0
$156$		0			0
$157$	−9.92525	+	5.73035i	−0.792121	+	0.457332i	−0.840709	−	0.541487i	$-0.817861\pi$
$157$	−9.92525	+	5.73035i	−0.792121	+	0.457332i	0.0485874	+	0.998819i	$0.484528\pi$
$158$	4.81469	−	2.77976i	0.383036	−	0.221146i
$159$		0			0
$160$		0			0
$161$	−3.11661			−0.245623
$162$		0			0
$163$			22.0595i			1.72783i	0.503637	+	0.863915i	$0.331995\pi$
$163$			22.0595i			1.72783i	−0.503637	+	0.863915i	$0.668005\pi$
$164$	6.08789	−	10.5445i	0.475384	−	0.823389i
$165$		0			0
$166$	−1.44701	−	2.50629i	−0.112310	−	0.194526i
$167$	−14.7817	+	8.53421i	−1.14384	+	0.660397i	−0.947379	−	0.320115i	$-0.896279\pi$
$167$	−14.7817	+	8.53421i	−1.14384	+	0.660397i	−0.196462	+	0.980511i	$0.562945\pi$
$168$		0			0
$169$	−4.55595	+	7.89113i	−0.350457	+	0.607010i
$170$		0			0
$171$		0			0
$172$		−	35.9285i		−	2.73953i
$173$	−10.3444	−	5.97233i	−0.786468	−	0.454067i	0.0522497	−	0.998634i	$-0.483361\pi$
$173$	−10.3444	−	5.97233i	−0.786468	−	0.454067i	−0.838718	+	0.544567i	$0.816694\pi$
$174$		0			0
$175$		0			0
$176$	9.48906	+	16.4355i	0.715265	+	1.23887i
$177$		0			0
$178$	−30.3207	−	17.5056i	−2.27263	−	1.31210i
$179$	8.54921			0.638998			0.319499	−	0.947587i	$-0.396485\pi$
$179$	8.54921			0.638998			0.319499	+	0.947587i	$0.396485\pi$
$180$		0			0
$181$	−10.5524			−0.784351			−0.392176	−	0.919890i	$-0.628277\pi$
$181$	−10.5524			−0.784351			−0.392176	+	0.919890i	$0.628277\pi$
$182$	−8.08390	−	4.66724i	−0.599219	−	0.345959i
$183$		0			0
$184$	−6.70503	−	11.6135i	−0.494301	−	0.856155i
$185$		0			0
$186$		0			0
$187$	−7.52895	−	4.34684i	−0.550571	−	0.317873i
$188$			31.0608i			2.26534i
$189$		0			0
$190$		0			0
$191$	−8.66862	+	15.0145i	−0.627239	+	1.08641i	0.360864	+	0.932618i	$0.382482\pi$
$191$	−8.66862	+	15.0145i	−0.627239	+	1.08641i	−0.988103	+	0.153792i	$0.950852\pi$
$192$		0			0
$193$	−1.35059	+	0.779763i	−0.0972175	+	0.0561286i	−0.547821	−	0.836596i	$-0.684542\pi$
$193$	−1.35059	+	0.779763i	−0.0972175	+	0.0561286i	0.450603	+	0.892724i	$0.351209\pi$
$194$	5.04721	+	8.74202i	0.362369	+	0.627641i
$195$		0			0
$196$	9.30346	−	16.1141i	0.664533	−	1.15100i
$197$		−	17.9767i		−	1.28079i	−0.768046	−	0.640395i	$-0.778771\pi$
$197$		−	17.9767i		−	1.28079i	0.768046	−	0.640395i	$-0.221229\pi$
$198$		0			0
$199$	−11.0225			−0.781362			−0.390681	−	0.920526i	$-0.627760\pi$
$199$	−11.0225			−0.781362			−0.390681	+	0.920526i	$0.627760\pi$
$200$		0			0
$201$		0			0
$202$	14.9451	−	8.62856i	1.05153	−	0.607104i
$203$	11.4686	−	6.62141i	0.804939	−	0.464732i
$204$		0			0
$205$		0			0
$206$	21.2688			1.48187
$207$		0			0
$208$		−	20.6964i		−	1.43503i
$209$	−2.68025	+	4.64232i	−0.185397	+	0.321116i
$210$		0			0
$211$	11.9643	+	20.7227i	0.823655	+	1.42661i	0.902943	+	0.429760i	$0.141402\pi$
$211$	11.9643	+	20.7227i	0.823655	+	1.42661i	−0.0792886	+	0.996852i	$0.525265\pi$
$212$	−7.37630	+	4.25871i	−0.506606	+	0.292489i
$213$		0			0
$214$	−11.8211	+	20.4748i	−0.808076	+	1.39963i
$215$		0			0
$216$		0			0
$217$			4.71470i			0.320055i
$218$	14.4645	+	8.35107i	0.979658	+	0.565606i
$219$		0			0
$220$		0			0
$221$	4.74040	+	8.21061i	0.318874	+	0.552305i
$222$		0			0
$223$	18.8020	+	10.8553i	1.25907	+	0.726927i	0.972895	−	0.231249i	$-0.0742812\pi$
$223$	18.8020	+	10.8553i	1.25907	+	0.726927i	0.286180	+	0.958176i	$0.407615\pi$
$224$	−21.8851			−1.46226
$225$		0			0
$226$	−39.2492			−2.61082
$227$	12.2111	+	7.05010i	0.810481	+	0.467932i	0.847123	−	0.531397i	$-0.178333\pi$
$227$	12.2111	+	7.05010i	0.810481	+	0.467932i	−0.0366416	+	0.999328i	$0.511666\pi$
$228$		0			0
$229$	1.83879	+	3.18488i	0.121511	+	0.210463i	0.920364	−	0.391064i	$-0.127893\pi$
$229$	1.83879	+	3.18488i	0.121511	+	0.210463i	−0.798853	+	0.601526i	$0.794559\pi$
$230$		0			0
$231$		0			0
$232$	49.3469	+	28.4904i	3.23978	+	1.87049i
$233$		−	5.34164i		−	0.349943i	−0.984574	−	0.174971i	$-0.944017\pi$
$233$		−	5.34164i		−	0.349943i	0.984574	−	0.174971i	$-0.0559833\pi$
$234$		0			0
$235$		0			0
$236$	27.2149	−	47.1376i	1.77154	−	3.06840i
$237$		0			0
$238$	19.7119	−	11.3807i	1.27773	−	0.737698i
$239$	11.0167	+	19.0815i	0.712613	+	1.23428i	0.963873	+	0.266362i	$0.0858218\pi$
$239$	11.0167	+	19.0815i	0.712613	+	1.23428i	−0.251260	+	0.967920i	$0.580845\pi$
$240$		0			0
$241$	9.32358	−	16.1489i	0.600585	−	1.04024i	−0.392148	−	0.919902i	$-0.628268\pi$
$241$	9.32358	−	16.1489i	0.600585	−	1.04024i	0.992733	−	0.120341i	$-0.0383988\pi$
$242$			20.3605i			1.30882i
$243$		0			0
$244$	62.5475			4.00420
$245$		0			0
$246$		0			0
$247$	5.06263	−	2.92291i	0.322127	−	0.185980i
$248$	−17.5684	+	10.1431i	−1.11560	+	0.644091i
$249$		0			0
$250$		0			0
$251$	−14.6929			−0.927407			−0.463704	−	0.885990i	$-0.653480\pi$
$251$	−14.6929			−0.927407			−0.463704	+	0.885990i	$0.653480\pi$
$252$		0			0
$253$			3.13515i			0.197105i
$254$	−4.77103	+	8.26366i	−0.299361	+	0.518508i
$255$		0			0
$256$	4.73035	+	8.19320i	0.295647	+	0.512075i
$257$	−19.2335	+	11.1045i	−1.19975	+	0.692678i	−0.960500	−	0.278280i	$-0.910236\pi$
$257$	−19.2335	+	11.1045i	−1.19975	+	0.692678i	−0.239253	+	0.970957i	$0.576902\pi$
$258$		0			0
$259$	−10.4566	+	18.1114i	−0.649743	+	1.12539i
$260$		0			0
$261$		0			0
$262$			19.2089i			1.18673i
$263$	−4.97100	−	2.87001i	−0.306525	−	0.176972i	0.338846	−	0.940842i	$-0.389964\pi$
$263$	−4.97100	−	2.87001i	−0.306525	−	0.176972i	−0.645370	+	0.763870i	$0.723297\pi$
$264$		0			0
$265$		0			0
$266$	−7.01727	−	12.1543i	−0.430256	−	0.745226i
$267$		0			0
$268$	38.9197	+	22.4703i	2.37740	+	1.37259i
$269$	−15.6162			−0.952139			−0.476070	−	0.879408i	$-0.657939\pi$
$269$	−15.6162			−0.952139			−0.476070	+	0.879408i	$0.657939\pi$
$270$		0			0
$271$	−6.75315			−0.410225			−0.205112	−	0.978738i	$-0.565756\pi$
$271$	−6.75315			−0.410225			−0.205112	+	0.978738i	$0.565756\pi$
$272$	43.7050	+	25.2331i	2.65000	+	1.52998i
$273$		0			0
$274$	−9.38423	−	16.2540i	−0.566922	−	0.981938i
$275$		0			0
$276$		0			0
$277$	−26.2376	−	15.1483i	−1.57646	−	0.910172i	−0.995347	−	0.0963529i	$-0.969282\pi$
$277$	−26.2376	−	15.1483i	−1.57646	−	0.910172i	−0.581118	−	0.813820i	$-0.697384\pi$
$278$		−	38.7438i		−	2.32370i
$279$		0			0
$280$		0			0
$281$	9.31755	−	16.1385i	0.555838	−	0.962740i	−0.441999	−	0.897015i	$-0.645731\pi$
$281$	9.31755	−	16.1385i	0.555838	−	0.962740i	0.997838	−	0.0657249i	$-0.0209360\pi$
$282$		0			0
$283$	4.91354	−	2.83683i	0.292079	−	0.168632i	−0.346800	−	0.937939i	$-0.612732\pi$
$283$	4.91354	−	2.83683i	0.292079	−	0.168632i	0.638879	+	0.769307i	$0.279398\pi$
$284$	−3.14604	−	5.44910i	−0.186683	−	0.323345i
$285$		0			0
$286$	−4.69502	+	8.13201i	−0.277622	+	0.480856i
$287$		−	4.43332i		−	0.261690i
$288$		0			0
$289$	−6.11806			−0.359886
$290$		0			0
$291$		0			0
$292$	−15.3379	+	8.85533i	−0.897582	+	0.518219i
$293$	15.8286	−	9.13867i	0.924720	−	0.533887i	0.0395819	−	0.999216i	$-0.487397\pi$
$293$	15.8286	−	9.13867i	0.924720	−	0.533887i	0.885138	+	0.465329i	$0.154064\pi$
$294$		0			0
$295$		0			0
$296$	−89.9850			−5.23027
$297$		0			0
$298$			1.48887i			0.0862478i
$299$	1.70950	−	2.96094i	0.0988631	−	0.171236i
$300$		0			0
$301$	−6.54097	−	11.3293i	−0.377015	−	0.653009i
$302$	−0.349852	+	0.201987i	−0.0201317	+	0.0116230i
$303$		0			0
$304$	15.5586	−	26.9483i	0.892349	−	1.54559i
$305$		0			0
$306$		0			0
$307$		−	15.5050i		−	0.884915i	−0.896789	−	0.442458i	$-0.854107\pi$
$307$		−	15.5050i		−	0.884915i	0.896789	−	0.442458i	$-0.145893\pi$
$308$	13.8941	+	8.02174i	0.791688	+	0.457081i
$309$		0			0
$310$		0			0
$311$	15.2232	+	26.3673i	0.863228	+	1.49515i	0.868796	+	0.495170i	$0.164894\pi$
$311$	15.2232	+	26.3673i	0.863228	+	1.49515i	−0.00556798	+	0.999984i	$0.501772\pi$
$312$		0			0
$313$	−6.01832	−	3.47468i	−0.340176	−	0.196401i	0.320174	−	0.947359i	$-0.396259\pi$
$313$	−6.01832	−	3.47468i	−0.340176	−	0.196401i	−0.660350	+	0.750958i	$0.729592\pi$
$314$	−30.1843			−1.70340
$315$		0			0
$316$	10.4205			0.586196
$317$	−13.9820	−	8.07253i	−0.785309	−	0.453398i	0.0529995	−	0.998595i	$-0.483122\pi$
$317$	−13.9820	−	8.07253i	−0.785309	−	0.453398i	−0.838308	+	0.545196i	$0.816455\pi$
$318$		0			0
$319$	−6.66081	−	11.5369i	−0.372934	−	0.645940i
$320$		0			0
$321$		0			0
$322$	−7.10858	−	4.10414i	−0.396146	−	0.228715i
$323$			14.2545i			0.793142i
$324$		0			0
$325$		0			0
$326$	−29.0493	+	50.3148i	−1.60889	+	2.78668i
$327$		0			0
$328$	16.5199	−	9.53779i	0.912160	−	0.526636i
$329$	5.65478	+	9.79436i	0.311758	+	0.539981i
$330$		0			0
$331$	−6.31112	+	10.9312i	−0.346890	+	0.600832i	−0.985695	−	0.168537i	$-0.946096\pi$
$331$	−6.31112	+	10.9312i	−0.346890	+	0.600832i	0.638805	+	0.769369i	$0.279429\pi$
$332$		−	5.42437i		−	0.297701i
$333$		0			0
$334$	−44.9535			−2.45975
$335$		0			0
$336$		0			0
$337$	−5.99324	+	3.46020i	−0.326473	+	0.188489i	−0.654274	−	0.756258i	$-0.727026\pi$
$337$	−5.99324	+	3.46020i	−0.326473	+	0.188489i	0.327801	+	0.944747i	$0.393692\pi$
$338$	−20.7831	+	11.9991i	−1.13045	+	0.652665i
$339$		0			0
$340$		0			0
$341$	4.74276			0.256835
$342$		0			0
$343$		−	19.3570i		−	1.04518i
$344$	28.1443	−	48.7474i	1.51744	−	2.62828i
$345$		0			0
$346$	−15.7295	−	27.2442i	−0.845621	−	1.46466i
$347$	−11.9566	+	6.90317i	−0.641866	+	0.370581i	−0.785333	−	0.619074i	$-0.787508\pi$
$347$	−11.9566	+	6.90317i	−0.641866	+	0.370581i	0.143467	+	0.989655i	$0.454175\pi$
$348$		0			0
$349$	3.28384	−	5.68778i	0.175780	−	0.304460i	−0.764651	−	0.644445i	$-0.777089\pi$
$349$	3.28384	−	5.68778i	0.175780	−	0.304460i	0.940431	+	0.339985i	$0.110422\pi$
$350$		0			0
$351$		0			0
$352$			22.0153i			1.17342i
$353$	3.05273	+	1.76250i	0.162481	+	0.0938082i	0.579035	−	0.815302i	$-0.303429\pi$
$353$	3.05273	+	1.76250i	0.162481	+	0.0938082i	−0.416555	+	0.909111i	$0.636763\pi$
$354$		0			0
$355$		0			0
$356$	−32.8116	−	56.8313i	−1.73901	−	3.01205i
$357$		0			0
$358$	19.4996	+	11.2581i	1.03059	+	0.595010i
$359$	22.9285			1.21012			0.605061	−	0.796179i	$-0.293149\pi$
$359$	22.9285			1.21012			0.605061	+	0.796179i	$0.293149\pi$
$360$		0			0
$361$	−10.2107			−0.537407
$362$	−24.0686	−	13.8960i	−1.26502	−	0.730358i
$363$		0			0
$364$	−8.74801	−	15.1520i	−0.458520	−	0.794181i
$365$		0			0
$366$		0			0
$367$	−3.61939	−	2.08966i	−0.188931	−	0.109079i	0.402551	−	0.915397i	$-0.368124\pi$
$367$	−3.61939	−	2.08966i	−0.188931	−	0.109079i	−0.591482	+	0.806318i	$0.701457\pi$
$368$		−	18.1993i		−	0.948706i
$369$		0			0
$370$		0			0
$371$	−1.55064	+	2.68578i	−0.0805051	+	0.139439i
$372$		0			0
$373$	−5.92440	+	3.42045i	−0.306754	+	0.177104i	−0.645473	−	0.763783i	$-0.723340\pi$
$373$	−5.92440	+	3.42045i	−0.306754	+	0.177104i	0.338719	+	0.940888i	$0.390006\pi$
$374$	−11.4484	−	19.8292i	−0.591982	−	1.02534i
$375$		0			0
$376$	−24.3312	+	42.1429i	−1.25479	+	2.17336i
$377$			14.5277i			0.748217i
$378$		0			0
$379$	12.7764			0.656280			0.328140	−	0.944629i	$-0.393578\pi$
$379$	12.7764			0.656280			0.328140	+	0.944629i	$0.393578\pi$
$380$		0			0
$381$		0			0
$382$	−39.5440	+	22.8307i	−2.02325	+	1.16812i
$383$	6.52515	−	3.76730i	0.333420	−	0.192500i	−0.323939	−	0.946078i	$-0.605007\pi$
$383$	6.52515	−	3.76730i	0.333420	−	0.192500i	0.657358	+	0.753578i	$0.271674\pi$
$384$		0			0
$385$		0			0
$386$	−4.10736			−0.209059
$387$		0			0
$388$			18.9204i			0.960538i
$389$	−2.72588	+	4.72135i	−0.138207	+	0.239382i	−0.926818	−	0.375511i	$-0.877467\pi$
$389$	−2.72588	+	4.72135i	−0.138207	+	0.239382i	0.788611	+	0.614893i	$0.210801\pi$
$390$		0			0
$391$	4.16847	+	7.22000i	0.210808	+	0.365131i
$392$	25.2456	−	14.5756i	1.27510	−	0.736177i
$393$		0			0
$394$	23.6729	−	41.0026i	1.19262	−	2.06568i
$395$		0			0
$396$		0			0
$397$		−	5.64549i		−	0.283339i	−0.989914	−	0.141670i	$-0.954753\pi$
$397$		−	5.64549i		−	0.283339i	0.989914	−	0.141670i	$-0.0452470\pi$
$398$	−25.1408	−	14.5151i	−1.26020	−	0.727574i
$399$		0			0
$400$		0			0
$401$	−2.75209	−	4.76676i	−0.137433	−	0.238040i	0.789091	−	0.614276i	$-0.210552\pi$
$401$	−2.75209	−	4.76676i	−0.137433	−	0.238040i	−0.926524	+	0.376235i	$0.877218\pi$
$402$		0			0
$403$	−4.47922	−	2.58608i	−0.223126	−	0.128822i
$404$	32.3458			1.60926
$405$		0			0
$406$	34.8779			1.73096
$407$	18.2192	+	10.5188i	0.903091	+	0.521400i
$408$		0			0
$409$	16.4265	+	28.4515i	0.812238	+	1.40684i	0.911295	+	0.411755i	$0.135084\pi$
$409$	16.4265	+	28.4515i	0.812238	+	1.40684i	−0.0990570	+	0.995082i	$0.531583\pi$
$410$		0			0
$411$		0			0
$412$	34.5241	+	19.9325i	1.70088	+	0.982005i
$413$		−	19.8184i		−	0.975202i
$414$		0			0
$415$		0			0
$416$	12.0043	−	20.7920i	0.588558	−	1.01941i
$417$		0			0
$418$	−12.2266	+	7.05903i	−0.598022	+	0.345268i
$419$	−11.4295	−	19.7965i	−0.558369	−	0.967124i	−0.997633	−	0.0687656i	$-0.978094\pi$
$419$	−11.4295	−	19.7965i	−0.558369	−	0.967124i	0.439264	−	0.898358i	$-0.355239\pi$
$420$		0			0
$421$	−8.97071	+	15.5377i	−0.437205	+	0.757262i	−0.997473	−	0.0710498i	$-0.977365\pi$
$421$	−8.97071	+	15.5377i	−0.437205	+	0.757262i	0.560267	+	0.828312i	$0.310698\pi$
$422$			63.0212i			3.06782i
$423$		0			0
$424$	−13.3441			−0.648046
$425$		0			0
$426$		0			0
$427$	19.7230	−	11.3871i	0.954463	−	0.551060i
$428$	−38.3768	+	22.1568i	−1.85501	+	1.07099i
$429$		0			0
$430$		0			0
$431$	6.18871			0.298100			0.149050	−	0.988830i	$-0.452378\pi$
$431$	6.18871			0.298100			0.149050	+	0.988830i	$0.452378\pi$
$432$		0			0
$433$			3.11806i			0.149844i	0.997189	+	0.0749221i	$0.0238708\pi$
$433$			3.11806i			0.149844i	−0.997189	+	0.0749221i	$0.976129\pi$
$434$	−6.20861	+	10.7536i	−0.298023	+	0.516190i
$435$		0			0
$436$	15.6528	+	27.1114i	0.749631	+	1.29840i
$437$	4.45182	−	2.57026i	0.212960	−	0.122952i
$438$		0			0
$439$	6.75494	−	11.6999i	0.322396	−	0.558406i	−0.658586	−	0.752505i	$-0.728845\pi$
$439$	6.75494	−	11.6999i	0.322396	−	0.558406i	0.980982	+	0.194100i	$0.0621785\pi$
$440$		0			0
$441$		0			0
$442$			24.9698i			1.18769i
$443$	21.0248	+	12.1387i	0.998918	+	0.576726i	0.907928	−	0.419126i	$-0.137663\pi$
$443$	21.0248	+	12.1387i	0.998918	+	0.576726i	0.0909904	+	0.995852i	$0.470997\pi$
$444$		0			0
$445$		0			0
$446$	28.5899	+	49.5192i	1.35377	+	2.34480i
$447$		0			0
$448$	−17.2404	−	9.95377i	−0.814534	−	0.470271i
$449$	−24.1437			−1.13941			−0.569705	−	0.821849i	$-0.692943\pi$
$449$	−24.1437			−1.13941			−0.569705	+	0.821849i	$0.692943\pi$
$450$		0			0
$451$	−4.45970			−0.209999
$452$	−63.7104	−	36.7832i	−2.99668	−	1.73014i
$453$		0			0
$454$	18.5680	+	32.1607i	0.871440	+	1.50938i
$455$		0			0
$456$		0			0
$457$	2.44355	+	1.41078i	0.114304	+	0.0659937i	0.556062	−	0.831141i	$-0.312312\pi$
$457$	2.44355	+	1.41078i	0.114304	+	0.0659937i	−0.441758	+	0.897134i	$0.645645\pi$
$458$			9.68573i			0.452585i
$459$		0			0
$460$		0			0
$461$	10.7286	−	18.5825i	0.499681	−	0.865474i	−0.500318	−	0.865841i	$-0.666784\pi$
$461$	10.7286	−	18.5825i	0.499681	−	0.865474i	1.00000		0.000367761i	$0.000117062\pi$
$462$		0			0
$463$	17.1502	−	9.90167i	0.797037	−	0.460170i	−0.0453970	−	0.998969i	$-0.514455\pi$
$463$	17.1502	−	9.90167i	0.797037	−	0.460170i	0.842434	+	0.538799i	$0.181122\pi$
$464$	38.6655	+	66.9706i	1.79500	+	3.10903i
$465$		0			0
$466$	7.03421	−	12.1836i	0.325853	−	0.564395i
$467$		−	22.7210i		−	1.05140i	−0.850669	−	0.525701i	$-0.823803\pi$
$467$		−	22.7210i		−	1.05140i	0.850669	−	0.525701i	$-0.176197\pi$
$468$		0			0
$469$	16.3633			0.755588
$470$		0			0
$471$		0			0
$472$	73.8497	−	42.6372i	3.39921	−	1.96253i
$473$	−11.3967	+	6.57989i	−0.524021	+	0.302544i
$474$		0			0
$475$		0			0
$476$	42.6625			1.95543
$477$		0			0
$478$			58.0300i			2.65423i
$479$	−10.6440	+	18.4359i	−0.486336	+	0.842359i	−0.999877	−	0.0157065i	$-0.995000\pi$
$479$	−10.6440	+	18.4359i	−0.486336	+	0.842359i	0.513541	+	0.858065i	$0.328334\pi$
$480$		0			0
$481$	−11.4712	−	19.8687i	−0.523042	−	0.905935i
$482$	42.5318	−	24.5557i	1.93727	−	1.11848i
$483$		0			0
$484$	−19.0813	+	33.0497i	−0.867330	+	1.50226i
$485$		0			0
$486$		0			0
$487$		−	9.58690i		−	0.434424i	−0.976124	−	0.217212i	$-0.930304\pi$
$487$		−	9.58690i		−	0.434424i	0.976124	−	0.217212i	$-0.0696963\pi$
$488$	84.8637	+	48.9961i	3.84160	+	2.21795i
$489$		0			0
$490$		0			0
$491$	−18.9222	−	32.7742i	−0.853945	−	1.47908i	−0.877620	−	0.479357i	$-0.840870\pi$
$491$	−18.9222	−	32.7742i	−0.853945	−	1.47908i	0.0236745	−	0.999720i	$-0.492463\pi$
$492$		0			0
$493$	−30.6786	−	17.7123i	−1.38169	−	0.797721i
$494$	15.3963			0.692711
$495$		0			0
$496$	−27.5314			−1.23619
$497$	−1.98407	−	1.14550i	−0.0889977	−	0.0513829i
$498$		0			0
$499$	8.46266	+	14.6577i	0.378840	+	0.656171i	0.990894	−	0.134646i	$-0.0429896\pi$
$499$	8.46266	+	14.6577i	0.378840	+	0.656171i	−0.612053	+	0.790816i	$0.709656\pi$
$500$		0			0
$501$		0			0
$502$	−33.5126	−	19.3485i	−1.49574	−	0.863566i
$503$			40.4168i			1.80210i	0.433719	+	0.901048i	$0.357201\pi$
$503$			40.4168i			1.80210i	−0.433719	+	0.901048i	$0.642799\pi$
$504$		0			0
$505$		0			0
$506$	−4.12856	+	7.15088i	−0.183537	+	0.317896i
$507$		0			0
$508$	−15.4889	+	8.94253i	−0.687210	+	0.396761i
$509$	20.7034	+	35.8593i	0.917660	+	1.58943i	0.802959	+	0.596034i	$0.203258\pi$
$509$	20.7034	+	35.8593i	0.917660	+	1.58943i	0.114701	+	0.993400i	$0.463409\pi$
$510$		0			0
$511$	−3.22431	+	5.58467i	−0.142635	+	0.247051i
$512$			34.5537i			1.52707i
$513$		0			0
$514$	−58.4922			−2.57998
$515$		0			0
$516$		0			0
$517$	9.85265	−	5.68843i	0.433319	−	0.250177i
$518$	−47.7004	+	27.5398i	−2.09584	+	1.21003i
$519$		0			0
$520$		0			0
$521$	17.0301			0.746103			0.373052	−	0.927811i	$-0.378311\pi$
$521$	17.0301			0.746103			0.373052	+	0.927811i	$0.378311\pi$
$522$		0			0
$523$		−	9.57651i		−	0.418751i	−0.977835	−	0.209376i	$-0.932857\pi$
$523$		−	9.57651i		−	0.418751i	0.977835	−	0.209376i	$-0.0671432\pi$
$524$	−18.0021	+	31.1805i	−0.786424	+	1.36213i
$525$		0			0
$526$	−7.55880	−	13.0922i	−0.329579	−	0.570848i
$527$	10.9222	−	6.30592i	0.475777	−	0.274690i
$528$		0			0
$529$	−9.99675	+	17.3149i	−0.434641	+	0.752821i
$530$		0			0
$531$		0			0
$532$		−	26.3055i		−	1.14049i
$533$	4.21189	+	2.43174i	0.182437	+	0.105330i
$534$		0			0
$535$		0			0
$536$	35.2038	+	60.9748i	1.52057	+	2.63371i
$537$		0			0
$538$	−35.6187	−	20.5644i	−1.53563	−	0.886596i
$539$	−6.81528			−0.293555
$540$		0			0
$541$	−0.833751			−0.0358458			−0.0179229	−	0.999839i	$-0.505705\pi$
$541$	−0.833751			−0.0358458			−0.0179229	+	0.999839i	$0.505705\pi$
$542$	−15.4031	−	8.89297i	−0.661619	−	0.381986i
$543$		0			0
$544$	29.2713	+	50.6994i	1.25500	+	2.17372i
$545$		0			0
$546$		0			0
$547$	24.5319	+	14.1635i	1.04891	+	0.605587i	0.922343	−	0.386371i	$-0.126272\pi$
$547$	24.5319	+	14.1635i	1.04891	+	0.605587i	0.126565	+	0.991958i	$0.459605\pi$
$548$		−	35.1785i		−	1.50275i
$549$		0			0
$550$		0			0
$551$	−10.9213	+	18.9163i	−0.465264	+	0.805861i
$552$		0			0
$553$	3.28586	−	1.89709i	0.139729	−	0.0806727i
$554$	−39.8964	−	69.1026i	−1.69504	−	2.93589i
$555$		0			0
$556$	36.3096	−	62.8901i	1.53987	−	2.66713i
$557$		−	11.5042i		−	0.487448i	−0.969845	−	0.243724i	$-0.921631\pi$
$557$		−	11.5042i		−	0.487448i	0.969845	−	0.243724i	$-0.0783690\pi$
$558$		0			0
$559$	14.3512			0.606993
$560$		0			0
$561$		0			0
$562$	42.5043	−	24.5398i	1.79293	−	1.03515i
$563$	28.5840	−	16.5030i	1.20467	−	0.695517i	0.243080	−	0.970006i	$-0.421842\pi$
$563$	28.5840	−	16.5030i	1.20467	−	0.695517i	0.961590	+	0.274490i	$0.0885089\pi$
$564$		0			0
$565$		0			0
$566$	14.9429			0.628095
$567$		0			0
$568$		−	9.85769i		−	0.413619i
$569$	13.5044	−	23.3903i	0.566135	−	0.980574i	−0.430809	−	0.902443i	$-0.641772\pi$
$569$	13.5044	−	23.3903i	0.566135	−	0.980574i	0.996943	−	0.0781305i	$-0.0248951\pi$
$570$		0			0
$571$	12.2122	+	21.1521i	0.511064	+	0.885189i	0.999918	+	0.0128232i	$0.00408185\pi$
$571$	12.2122	+	21.1521i	0.511064	+	0.885189i	−0.488854	+	0.872366i	$0.662585\pi$
$572$	−15.2422	+	8.80007i	−0.637307	+	0.367950i
$573$		0			0
$574$	5.83807	−	10.1118i	0.243676	−	0.422060i
$575$		0			0
$576$		0			0
$577$			14.7976i			0.616033i	0.951381	+	0.308017i	$0.0996653\pi$
$577$			14.7976i			0.616033i	−0.951381	+	0.308017i	$0.900335\pi$
$578$	−13.9545	−	8.05663i	−0.580431	−	0.335112i
$579$		0			0
$580$		0			0
$581$	−0.987533	−	1.71046i	−0.0409698	−	0.0709617i
$582$		0			0
$583$	2.70177	+	1.55987i	0.111896	+	0.0646030i
$584$	−27.7470			−1.14818
$585$		0			0
$586$	48.1375			1.98854
$587$	26.4813	+	15.2890i	1.09300	+	0.631044i	0.934374	−	0.356295i	$-0.115960\pi$
$587$	26.4813	+	15.2890i	1.09300	+	0.631044i	0.158626	+	0.987339i	$0.449294\pi$
$588$		0			0
$589$	−3.88821	−	6.73457i	−0.160211	−	0.277493i
$590$		0			0
$591$		0			0
$592$	−105.761	−	61.0611i	−4.34675	−	2.50960i
$593$		−	5.09990i		−	0.209428i	−0.994502	−	0.104714i	$-0.966607\pi$
$593$		−	5.09990i		−	0.209428i	0.994502	−	0.104714i	$-0.0333927\pi$
$594$		0			0
$595$		0			0
$596$	−1.39532	+	2.41677i	−0.0571547	+	0.0989949i
$597$		0			0
$598$	7.79831	−	4.50236i	0.318897	−	0.184115i
$599$	0.282655	+	0.489572i	0.0115490	+	0.0200034i	0.871742	−	0.489965i	$-0.162990\pi$
$599$	0.282655	+	0.489572i	0.0115490	+	0.0200034i	−0.860193	+	0.509968i	$0.829657\pi$
$600$		0			0
$601$	5.50480	−	9.53459i	0.224546	−	0.388924i	−0.731637	−	0.681694i	$-0.761244\pi$
$601$	5.50480	−	9.53459i	0.224546	−	0.388924i	0.956183	+	0.292770i	$0.0945769\pi$
$602$		−	34.4542i		−	1.40425i
$603$		0			0
$604$	−0.757185			−0.0308094
$605$		0			0
$606$		0			0
$607$	−16.5396	+	9.54913i	−0.671321	+	0.387587i	−0.796577	−	0.604537i	$-0.793358\pi$
$607$	−16.5396	+	9.54913i	−0.671321	+	0.387587i	0.125256	+	0.992124i	$0.460025\pi$
$608$	31.2611	−	18.0486i	1.26780	−	0.731967i
$609$		0			0
$610$		0			0
$611$	−12.4069			−0.501929
$612$		0			0
$613$		−	9.33918i		−	0.377206i	−0.982053	−	0.188603i	$-0.939604\pi$
$613$		−	9.33918i		−	0.377206i	0.982053	−	0.188603i	$-0.0603959\pi$
$614$	20.4179	−	35.3648i	0.823999	−	1.42721i
$615$		0			0
$616$	12.5675	+	21.7676i	0.506360	+	0.877041i
$617$	21.1444	−	12.2077i	0.851241	−	0.491464i	−0.00982861	−	0.999952i	$-0.503129\pi$
$617$	21.1444	−	12.2077i	0.851241	−	0.491464i	0.861069	+	0.508488i	$0.169795\pi$
$618$		0			0
$619$	19.7431	−	34.1961i	0.793544	−	1.37446i	−0.130216	−	0.991486i	$-0.541567\pi$
$619$	19.7431	−	34.1961i	0.793544	−	1.37446i	0.923760	−	0.382973i	$-0.125100\pi$
$620$		0			0
$621$		0			0
$622$			80.1874i			3.21522i
$623$	−20.6928	−	11.9470i	−0.829040	−	0.478647i
$624$		0			0
$625$		0			0
$626$	−9.15135	−	15.8506i	−0.365761	−	0.633517i
$627$		0			0
$628$	−48.9960	−	28.2879i	−1.95515	−	1.12881i
$629$	55.9430			2.23059
$630$		0			0
$631$	42.1634			1.67850			0.839249	−	0.543747i	$-0.182995\pi$
$631$	42.1634			1.67850			0.839249	+	0.543747i	$0.182995\pi$
$632$	14.1383	+	8.16277i	0.562393	+	0.324698i
$633$		0			0
$634$	−21.2608	−	36.8248i	−0.844375	−	1.46250i
$635$		0			0
$636$		0			0
$637$	6.43658	+	3.71616i	0.255027	+	0.147240i
$638$		−	35.0855i		−	1.38905i
$639$		0			0
$640$		0			0
$641$	17.6577	−	30.5841i	0.697438	−	1.20800i	−0.271913	−	0.962322i	$-0.587656\pi$
$641$	17.6577	−	30.5841i	0.697438	−	1.20800i	0.969352	−	0.245677i	$-0.0790103\pi$
$642$		0			0
$643$	−12.2936	+	7.09771i	−0.484812	+	0.279906i	−0.722420	−	0.691455i	$-0.756970\pi$
$643$	−12.2936	+	7.09771i	−0.484812	+	0.279906i	0.237608	+	0.971361i	$0.423637\pi$
$644$	−7.69256	−	13.3239i	−0.303129	−	0.525036i
$645$		0			0
$646$	−18.7712	+	32.5127i	−0.738544	+	1.27919i
$647$		−	17.4897i		−	0.687593i	−0.939044	−	0.343796i	$-0.888287\pi$
$647$		−	17.4897i		−	0.687593i	0.939044	−	0.343796i	$-0.111713\pi$
$648$		0			0
$649$	−19.9364			−0.782572
$650$		0			0
$651$		0			0
$652$	−94.3072	+	54.4483i	−3.69335	+	2.13236i
$653$	−9.50650	+	5.48858i	−0.372018	+	0.214785i	−0.674340	−	0.738421i	$-0.735572\pi$
$653$	−9.50650	+	5.48858i	−0.372018	+	0.214785i	0.302322	+	0.953206i	$0.402238\pi$
$654$		0			0
$655$		0			0
$656$	25.8882			1.01077
$657$		0			0
$658$			29.7862i			1.16119i
$659$	7.89381	−	13.6725i	0.307499	−	0.532604i	−0.670316	−	0.742076i	$-0.733841\pi$
$659$	7.89381	−	13.6725i	0.307499	−	0.532604i	0.977815	+	0.209472i	$0.0671746\pi$
$660$		0			0
$661$	−24.9466	−	43.2088i	−0.970311	−	1.68063i	−0.694614	−	0.719383i	$-0.744425\pi$
$661$	−24.9466	−	43.2088i	−0.970311	−	1.68063i	−0.275697	−	0.961245i	$-0.588909\pi$
$662$	−28.7897	+	16.6217i	−1.11894	+	0.646022i
$663$		0			0
$664$	4.24913	−	7.35972i	0.164898	−	0.285612i
$665$		0			0
$666$		0			0
$667$			12.7750i			0.494649i
$668$	−72.9698	−	42.1291i	−2.82328	−	1.63002i
$669$		0			0
$670$		0			0
$671$	−11.4549	−	19.8404i	−0.442210	−	0.765929i
$672$		0			0
$673$	24.9757	+	14.4197i	0.962743	+	0.555840i	0.897016	−	0.441998i	$-0.145730\pi$
$673$	24.9757	+	14.4197i	0.962743	+	0.555840i	0.0657266	+	0.997838i	$0.479063\pi$
$674$	−18.2264			−0.702055
$675$		0			0
$676$	−44.9809			−1.73003
$677$	9.06176	+	5.23181i	0.348272	+	0.201075i	0.663924	−	0.747800i	$-0.268890\pi$
$677$	9.06176	+	5.23181i	0.348272	+	0.201075i	−0.315652	+	0.948875i	$0.602223\pi$
$678$		0			0
$679$	3.44455	+	5.96614i	0.132190	+	0.228959i
$680$		0			0
$681$		0			0
$682$	10.8176	+	6.24556i	0.414228	+	0.239155i
$683$		−	16.1875i		−	0.619396i	−0.950835	−	0.309698i	$-0.899772\pi$
$683$		−	16.1875i		−	0.619396i	0.950835	−	0.309698i	$-0.100228\pi$
$684$		0			0
$685$		0			0
$686$	25.4904	−	44.1507i	0.973229	−	1.68568i
$687$		0			0
$688$	66.1570	−	38.1958i	2.52221	−	1.45620i
$689$	−1.70109	−	2.94638i	−0.0648065	−	0.112248i
$690$		0			0
$691$	−4.94181	+	8.55946i	−0.187995	+	0.325617i	−0.944582	−	0.328276i	$-0.893532\pi$
$691$	−4.94181	+	8.55946i	−0.187995	+	0.325617i	0.756586	+	0.653894i	$0.226866\pi$
$692$		−	58.9648i		−	2.24150i
$693$		0			0
$694$	−36.3621			−1.38029
$695$		0			0
$696$		0			0
$697$	−10.2703	+	5.92957i	−0.389016	+	0.224598i
$698$	14.9800	−	8.64872i	0.567002	−	0.327359i
$699$		0			0
$700$		0			0
$701$	−43.9692			−1.66069			−0.830346	−	0.557248i	$-0.811857\pi$
$701$	−43.9692			−1.66069			−0.830346	+	0.557248i	$0.811857\pi$
$702$		0			0
$703$		−	34.4942i		−	1.30097i
$704$	−10.0130	+	17.3430i	−0.377379	+	0.653640i
$705$		0			0
$706$	4.64193	+	8.04005i	0.174701	+	0.302591i
$707$	10.1995	−	5.88870i	0.383593	−	0.221467i
$708$		0			0
$709$	12.6130	−	21.8464i	0.473692	−	0.820458i	−0.525855	−	0.850574i	$-0.676254\pi$
$709$	12.6130	−	21.8464i	0.473692	−	0.820458i	0.999546	+	0.0301162i	$0.00958774\pi$
$710$		0			0
$711$		0			0
$712$		−	102.811i		−	3.85299i
$713$	−3.93880	−	2.27407i	−0.147509	−	0.0851645i
$714$		0			0
$715$		0			0
$716$	21.1016	+	36.5490i	0.788603	+	1.36590i
$717$		0			0
$718$	52.2971	+	30.1937i	1.95171	+	1.12682i
$719$	−36.8600			−1.37465			−0.687323	−	0.726352i	$-0.741214\pi$
$719$	−36.8600			−1.37465			−0.687323	+	0.726352i	$0.741214\pi$
$720$		0			0
$721$	14.5153			0.540576
$722$	−23.2893	−	13.4461i	−0.866740	−	0.500412i
$723$		0			0
$724$	−26.0459	−	45.1128i	−0.967988	−	1.67660i
$725$		0			0
$726$		0			0
$727$	33.1213	+	19.1226i	1.22840	+	0.709217i	0.966695	−	0.255931i	$-0.0823820\pi$
$727$	33.1213	+	19.1226i	1.22840	+	0.709217i	0.261705	+	0.965148i	$0.415715\pi$
$728$		−	27.4107i		−	1.01591i
$729$		0			0
$730$		0			0
$731$	−17.4971	+	30.3059i	−0.647154	+	1.12090i
$732$		0			0
$733$	−34.2801	+	19.7916i	−1.26616	+	0.731020i	−0.974260	−	0.225428i	$-0.927622\pi$
$733$	−34.2801	+	19.7916i	−1.26616	+	0.731020i	−0.291903	+	0.956448i	$0.594289\pi$
$734$	−5.50358	−	9.53248i	−0.203141	−	0.351850i
$735$		0			0
$736$	10.5559	−	18.2834i	0.389097	−	0.673936i
$737$		−	16.4607i		−	0.606338i
$738$		0			0
$739$	8.24773			0.303398			0.151699	−	0.988427i	$-0.451526\pi$
$739$	8.24773			0.303398			0.151699	+	0.988427i	$0.451526\pi$
$740$		0			0
$741$		0			0
$742$	−7.07361	+	4.08395i	−0.259680	+	0.149927i
$743$	1.13292	−	0.654091i	0.0415627	−	0.0239963i	−0.479075	−	0.877774i	$-0.659028\pi$
$743$	1.13292	−	0.654091i	0.0415627	−	0.0239963i	0.520637	+	0.853778i	$0.325694\pi$
$744$		0			0
$745$		0			0
$746$	−18.0171			−0.659651
$747$		0			0
$748$		−	42.9164i		−	1.56918i
$749$	−8.06752	+	13.9734i	−0.294781	+	0.510575i
$750$		0			0
$751$	−14.2234	−	24.6357i	−0.519020	−	0.898969i	−0.999756	−	0.0221034i	$-0.992964\pi$
$751$	−14.2234	−	24.6357i	−0.519020	−	0.898969i	0.480736	−	0.876866i	$-0.340370\pi$
$752$	−57.1939	+	33.0209i	−2.08565	+	1.20415i
$753$		0			0
$754$	−19.1310	+	33.1359i	−0.696711	+	1.20674i
$755$		0			0
$756$		0			0
$757$		−	38.2012i		−	1.38845i	−0.719760	−	0.694223i	$-0.755748\pi$
$757$		−	38.2012i		−	1.38845i	0.719760	−	0.694223i	$-0.244252\pi$
$758$	29.1414	+	16.8248i	1.05846	+	0.611103i
$759$		0			0
$760$		0			0
$761$	11.0952	+	19.2174i	0.402200	+	0.696632i	0.993991	−	0.109460i	$-0.0349121\pi$
$761$	11.0952	+	19.2174i	0.402200	+	0.696632i	−0.591791	+	0.806092i	$0.701579\pi$
$762$		0			0
$763$	9.87152	+	5.69932i	0.357373	+	0.206329i
$764$	−85.5852			−3.09637
$765$		0			0
$766$	19.8440			0.716994
$767$	18.8286	+	10.8707i	0.679861	+	0.392518i
$768$		0			0
$769$	−8.45652	−	14.6471i	−0.304950	−	0.528189i	0.672300	−	0.740279i	$-0.265306\pi$
$769$	−8.45652	−	14.6471i	−0.304950	−	0.528189i	−0.977250	+	0.212090i	$0.931973\pi$
$770$		0			0
$771$		0			0
$772$	−6.66718	−	3.84930i	−0.239957	−	0.138539i
$773$		−	38.6464i		−	1.39001i	−0.719003	−	0.695007i	$-0.755401\pi$
$773$		−	38.6464i		−	1.39001i	0.719003	−	0.695007i	$-0.244599\pi$
$774$		0			0
$775$		0			0
$776$	−14.8211	+	25.6709i	−0.532047	+	0.921533i
$777$		0			0
$778$	−12.4347	+	7.17920i	−0.445807	+	0.257387i
$779$	3.65615	+	6.33264i	0.130995	+	0.226890i
$780$		0			0
$781$	−1.15232	+	1.99588i	−0.0412333	+	0.0714181i
$782$			21.9572i			0.785187i
$783$		0			0
$784$	39.5622			1.41294
$785$		0			0
$786$		0			0
$787$	9.45240	−	5.45734i	0.336942	−	0.194533i	−0.321977	−	0.946747i	$-0.604347\pi$
$787$	9.45240	−	5.45734i	0.336942	−	0.194533i	0.658919	+	0.752214i	$0.271014\pi$
$788$	76.8530	−	44.3711i	2.73777	−	1.58065i
$789$		0			0
$790$		0			0
$791$	−26.7862			−0.952409
$792$		0			0
$793$			24.9839i			0.887204i
$794$	7.43433	−	12.8766i	0.263835	−	0.456975i
$795$		0			0
$796$	−27.2062	−	47.1225i	−0.964298	−	1.67021i
$797$	2.53356	−	1.46275i	0.0897432	−	0.0518133i	−0.454457	−	0.890769i	$-0.650167\pi$
$797$	2.53356	−	1.46275i	0.0897432	−	0.0518133i	0.544200	+	0.838956i	$0.316833\pi$
$798$		0			0
$799$	15.1265	−	26.1999i	0.535139	−	0.926888i
$800$		0			0
$801$		0			0
$802$		−	14.4965i		−	0.511888i
$803$	5.61791	+	3.24350i	0.198252	+	0.114461i
$804$		0			0
$805$		0			0
$806$	−6.81102	−	11.7970i	−0.239908	−	0.415532i
$807$		0			0
$808$	43.8863	+	25.3378i	1.54391	+	0.891380i
$809$	−37.9241			−1.33334			−0.666671	−	0.745352i	$-0.732281\pi$
$809$	−37.9241			−1.33334			−0.666671	+	0.745352i	$0.732281\pi$
$810$		0			0
$811$	19.5050			0.684912			0.342456	−	0.939534i	$-0.388741\pi$
$811$	19.5050			0.684912			0.342456	+	0.939534i	$0.388741\pi$
$812$	56.6148	+	32.6866i	1.98679	+	1.14707i
$813$		0			0
$814$	27.7037	+	47.9843i	0.971016	+	1.68185i
$815$		0			0
$816$		0			0
$817$	18.6865	+	10.7887i	0.653758	+	0.377447i
$818$			86.5257i			3.02530i
$819$		0			0
$820$		0			0
$821$	22.3762	−	38.7567i	0.780934	−	1.35262i	−0.150464	−	0.988615i	$-0.548077\pi$
$821$	22.3762	−	38.7567i	0.780934	−	1.35262i	0.931398	−	0.364002i	$-0.118590\pi$
$822$		0			0
$823$	31.0898	−	17.9497i	1.08372	−	0.625687i	0.151824	−	0.988408i	$-0.451485\pi$
$823$	31.0898	−	17.9497i	1.08372	−	0.625687i	0.931898	+	0.362721i	$0.118152\pi$
$824$	31.2279	+	54.0884i	1.08788	+	1.88426i
$825$		0			0
$826$	26.0981	−	45.2033i	0.908071	−	1.57282i
$827$			16.2717i			0.565822i	0.959146	+	0.282911i	$0.0913001\pi$
$827$			16.2717i			0.565822i	−0.959146	+	0.282911i	$0.908700\pi$
$828$		0			0
$829$	20.6592			0.717525			0.358762	−	0.933429i	$-0.383199\pi$
$829$	20.6592			0.717525			0.358762	+	0.933429i	$0.383199\pi$
$830$		0			0
$831$		0			0
$832$	18.9132	−	10.9196i	0.655698	−	0.378568i
$833$	−15.6950	+	9.06152i	−0.543800	+	0.313963i
$834$		0			0
$835$		0			0
$836$	−26.4621			−0.915210
$837$		0			0
$838$		−	60.2044i		−	2.07973i
$839$	6.11836	−	10.5973i	0.211229	−	0.365860i	−0.740870	−	0.671648i	$-0.765587\pi$
$839$	6.11836	−	10.5973i	0.211229	−	0.365860i	0.952100	+	0.305788i	$0.0989200\pi$
$840$		0			0
$841$	−12.6411	−	21.8951i	−0.435901	−	0.755003i
$842$	−40.9221	+	23.6264i	−1.41027	+	0.814218i
$843$		0			0
$844$	−59.0616	+	102.298i	−2.03299	+	3.52123i
$845$		0			0
$846$		0			0
$847$			13.8953i			0.477450i
$848$	−15.6836	−	9.05490i	−0.538575	−	0.310947i
$849$		0			0
$850$		0			0
$851$	−10.0872	−	17.4715i	−0.345785	−	0.598917i
$852$		0			0
$853$	14.2282	+	8.21464i	0.487164	+	0.281264i	0.723397	−	0.690432i	$-0.242580\pi$
$853$	14.2282	+	8.21464i	0.487164	+	0.281264i	−0.236233	+	0.971696i	$0.575913\pi$
$854$	59.9809			2.05250
$855$		0			0
$856$	−69.4255			−2.37291
$857$	42.5129	+	24.5449i	1.45221	+	0.838436i	0.998607	−	0.0527655i	$-0.0168036\pi$
$857$	42.5129	+	24.5449i	1.45221	+	0.838436i	0.453607	+	0.891202i	$0.350137\pi$
$858$		0			0
$859$	20.5454	+	35.5856i	0.700999	+	1.21417i	0.968116	+	0.250502i	$0.0805958\pi$
$859$	20.5454	+	35.5856i	0.700999	+	1.21417i	−0.267117	+	0.963664i	$0.586071\pi$
$860$		0			0
$861$		0			0
$862$	14.1157	+	8.14968i	0.480781	+	0.277579i
$863$			47.8366i			1.62838i	0.580601	+	0.814188i	$0.302817\pi$
$863$			47.8366i			1.62838i	−0.580601	+	0.814188i	$0.697183\pi$
$864$		0			0
$865$		0			0
$866$	−4.10605	+	7.11189i	−0.139529	+	0.241672i
$867$		0			0
$868$	−20.1560	+	11.6371i	−0.684138	+	0.394987i
$869$	−1.90838	−	3.30542i	−0.0647375	−	0.112129i
$870$		0			0
$871$	−8.97551	+	15.5460i	−0.304123	+	0.526757i
$872$			49.0458i			1.66090i
$873$		0			0
$874$	13.5387			0.457954
$875$		0			0
$876$		0			0
$877$	−9.85292	+	5.68859i	−0.332710	+	0.192090i	−0.657043	−	0.753853i	$-0.728193\pi$
$877$	−9.85292	+	5.68859i	−0.332710	+	0.192090i	0.324334	+	0.945943i	$0.394860\pi$
$878$	30.8143	−	17.7906i	1.03993	−	0.600405i
$879$		0			0
$880$		0			0
$881$	43.9924			1.48214			0.741071	−	0.671426i	$-0.234318\pi$
$881$	43.9924			1.48214			0.741071	+	0.671426i	$0.234318\pi$
$882$		0			0
$883$		−	37.6820i		−	1.26810i	−0.773291	−	0.634051i	$-0.781391\pi$
$883$		−	37.6820i		−	1.26810i	0.773291	−	0.634051i	$-0.218609\pi$
$884$	−23.4010	+	40.5317i	−0.787060	+	1.36323i
$885$		0			0
$886$	31.9699	+	55.3735i	1.07405	+	1.86031i
$887$	28.8241	−	16.6416i	0.967820	−	0.558771i	0.0692492	−	0.997599i	$-0.477940\pi$
$887$	28.8241	−	16.6416i	0.967820	−	0.558771i	0.898571	+	0.438828i	$0.144606\pi$
$888$		0			0
$889$	−3.25606	+	5.63967i	−0.109205	+	0.189148i
$890$		0			0
$891$		0			0
$892$			107.175i			3.58847i
$893$	−16.1548	−	9.32697i	−0.540599	−	0.312115i
$894$		0			0
$895$		0			0
$896$	−4.33040	−	7.50047i	−0.144669	−	0.250573i
$897$		0			0
$898$	−55.0686	−	31.7939i	−1.83766	−	1.06098i
$899$	19.3255			0.644543
$900$		0			0
$901$	8.29592			0.276377
$902$	−10.1720	−	5.87281i	−0.338691	−	0.195543i
$903$		0			0
$904$	−57.6276	−	99.8139i	−1.91667	−	3.31976i
$905$		0			0
$906$		0			0
$907$	12.1922	+	7.03918i	0.404836	+	0.233732i	0.688568	−	0.725171i	$-0.258239\pi$
$907$	12.1922	+	7.03918i	0.404836	+	0.233732i	−0.283733	+	0.958903i	$0.591573\pi$
$908$			69.6056i			2.30994i
$909$		0			0
$910$		0			0
$911$	3.65761	−	6.33517i	0.121182	−	0.209894i	−0.799052	−	0.601262i	$-0.794665\pi$
$911$	3.65761	−	6.33517i	0.121182	−	0.209894i	0.920234	+	0.391368i	$0.127998\pi$
$912$		0			0
$913$	−1.72064	+	0.993410i	−0.0569448	+	0.0328771i
$914$	3.71561	+	6.43563i	0.122902	+	0.212872i
$915$		0			0
$916$	−9.07719	+	15.7222i	−0.299919	+	0.519475i
$917$			13.1094i			0.432912i
$918$		0			0
$919$	−4.44684			−0.146688			−0.0733438	−	0.997307i	$-0.523367\pi$
$919$	−4.44684			−0.146688			−0.0733438	+	0.997307i	$0.523367\pi$
$920$		0			0
$921$		0			0
$922$	48.9412	−	28.2562i	1.61179	−	0.930569i
$923$	2.17658	−	1.25665i	0.0716430	−	0.0413631i
$924$		0			0
$925$		0			0
$926$	52.1565			1.71397
$927$		0			0
$928$			89.7068i			2.94477i
$929$	−6.55663	+	11.3564i	−0.215116	+	0.372592i	−0.953309	−	0.301998i	$-0.902346\pi$
$929$	−6.55663	+	11.3564i	−0.215116	+	0.372592i	0.738192	+	0.674590i	$0.235680\pi$
$930$		0			0
$931$	5.58730	+	9.67749i	0.183116	+	0.317167i
$932$	22.8362	−	13.1845i	0.748026	−	0.431873i
$933$		0			0
$934$	29.9204	−	51.8236i	0.979025	−	1.69572i
$935$		0			0
$936$		0			0
$937$		−	33.5187i		−	1.09501i	−0.836803	−	0.547504i	$-0.815578\pi$
$937$		−	33.5187i		−	1.09501i	0.836803	−	0.547504i	$-0.184422\pi$
$938$	37.3226	+	21.5482i	1.21863	+	0.703574i
$939$		0			0
$940$		0			0
$941$	0.895381	+	1.55085i	0.0291886	+	0.0505561i	0.880251	−	0.474509i	$-0.157374\pi$
$941$	0.895381	+	1.55085i	0.0291886	+	0.0505561i	−0.851062	+	0.525065i	$0.824041\pi$
$942$		0			0
$943$	3.70373	+	2.13835i	0.120610	+	0.0696342i
$944$	115.729			3.76667
$945$		0			0
$946$	−34.6592			−1.12687
$947$	−45.5832	−	26.3175i	−1.48126	−	0.855204i	−0.481482	−	0.876456i	$-0.659901\pi$
$947$	−45.5832	−	26.3175i	−1.48126	−	0.855204i	−0.999774	+	0.0212525i	$0.993235\pi$
$948$		0			0
$949$	−3.53716	−	6.12654i	−0.114821	−	0.198876i
$950$		0			0
$951$		0			0
$952$	57.8839	+	33.4193i	1.87603	+	1.08312i
$953$		−	18.4072i		−	0.596268i	−0.954524	−	0.298134i	$-0.903636\pi$
$953$		−	18.4072i		−	0.596268i	0.954524	−	0.298134i	$-0.0963642\pi$
$954$		0			0
$955$		0			0
$956$	−54.3841	+	94.1960i	−1.75891	+	3.04652i
$957$		0			0
$958$	−48.5551	+	28.0333i	−1.56874	+	0.905715i
$959$	−6.40442	−	11.0928i	−0.206810	−	0.358205i
$960$		0			0
$961$	12.0599	−	20.8883i	0.389028	−	0.673816i
$962$		−	60.4240i		−	1.94815i
$963$		0			0
$964$	92.0517			2.96479
$965$		0			0
$966$		0			0
$967$	−5.27911	+	3.04790i	−0.169765	+	0.0980137i	−0.582475	−	0.812849i	$-0.697916\pi$
$967$	−5.27911	+	3.04790i	−0.169765	+	0.0980137i	0.412710	+	0.910862i	$0.364582\pi$
$968$	−51.7784	+	29.8943i	−1.66422	+	0.960839i
$969$		0			0
$970$		0			0
$971$	34.1077			1.09457			0.547283	−	0.836947i	$-0.315662\pi$
$971$	34.1077			1.09457			0.547283	+	0.836947i	$0.315662\pi$
$972$		0			0
$973$		−	26.4414i		−	0.847671i
$974$	12.6246	−	21.8665i	0.404519	−	0.700648i
$975$		0			0
$976$	66.4945	+	115.172i	2.12844	+	3.68656i
$977$	−42.2546	+	24.3957i	−1.35184	+	0.780488i	−0.988508	−	0.151170i	$-0.951696\pi$
$977$	−42.2546	+	24.3957i	−1.35184	+	0.780488i	−0.363337	+	0.931658i	$0.618363\pi$
$978$		0			0
$979$	−12.0181	+	20.8160i	−0.384100	+	0.665281i
$980$		0			0
$981$		0			0
$982$		−	99.6715i		−	3.18065i
$983$	−28.9402	−	16.7086i	−0.923048	−	0.532922i	−0.0384416	−	0.999261i	$-0.512239\pi$
$983$	−28.9402	−	16.7086i	−0.923048	−	0.532922i	−0.884606	+	0.466339i	$0.845573\pi$
$984$		0			0
$985$		0			0
$986$	−46.6493	−	80.7989i	−1.48562	−	2.57316i
$987$		0			0
$988$	24.9917	+	14.4289i	0.795091	+	0.459046i
$989$	12.6198			0.401285
$990$		0			0
$991$	−19.3512			−0.614713			−0.307356	−	0.951595i	$-0.599444\pi$
$991$	−19.3512			−0.614713			−0.307356	+	0.951595i	$0.599444\pi$
$992$	−27.6586	−	15.9687i	−0.878161	−	0.507006i
$993$		0			0
$994$	−3.01694	−	5.22549i	−0.0956915	−	0.165743i
$995$		0			0
$996$		0			0
$997$	−34.2463	−	19.7721i	−1.08459	−	0.626189i	−0.152460	−	0.988310i	$-0.548719\pi$
$997$	−34.2463	−	19.7721i	−1.08459	−	0.626189i	−0.932131	+	0.362121i	$0.882053\pi$
$998$			44.5766i			1.41105i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.k.c.424.8		16
3.2	odd	2		225.2.k.c.124.1		16
5.2	odd	4		675.2.e.c.451.1		8
5.3	odd	4		675.2.e.e.451.4		8
5.4	even	2	inner	675.2.k.c.424.1		16
9.2	odd	6		2025.2.b.n.649.8		8
9.4	even	3	inner	675.2.k.c.199.1		16
9.5	odd	6		225.2.k.c.49.8		16
9.7	even	3		2025.2.b.o.649.1		8
15.2	even	4		225.2.e.e.151.4	yes	8
15.8	even	4		225.2.e.c.151.1	yes	8
15.14	odd	2		225.2.k.c.124.8		16
45.2	even	12		2025.2.a.q.1.1		4
45.4	even	6	inner	675.2.k.c.199.8		16
45.7	odd	12		2025.2.a.z.1.4		4
45.13	odd	12		675.2.e.e.226.4		8
45.14	odd	6		225.2.k.c.49.1		16
45.22	odd	12		675.2.e.c.226.1		8
45.23	even	12		225.2.e.c.76.1	✓	8
45.29	odd	6		2025.2.b.n.649.1		8
45.32	even	12		225.2.e.e.76.4	yes	8
45.34	even	6		2025.2.b.o.649.8		8
45.38	even	12		2025.2.a.y.1.4		4
45.43	odd	12		2025.2.a.p.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.e.c.76.1	✓	8	45.23	even	12
225.2.e.c.151.1	yes	8	15.8	even	4
225.2.e.e.76.4	yes	8	45.32	even	12
225.2.e.e.151.4	yes	8	15.2	even	4
225.2.k.c.49.1		16	45.14	odd	6
225.2.k.c.49.8		16	9.5	odd	6
225.2.k.c.124.1		16	3.2	odd	2
225.2.k.c.124.8		16	15.14	odd	2
675.2.e.c.226.1		8	45.22	odd	12
675.2.e.c.451.1		8	5.2	odd	4
675.2.e.e.226.4		8	45.13	odd	12
675.2.e.e.451.4		8	5.3	odd	4
675.2.k.c.199.1		16	9.4	even	3	inner
675.2.k.c.199.8		16	45.4	even	6	inner
675.2.k.c.424.1		16	5.4	even	2	inner
675.2.k.c.424.8		16	1.1	even	1	trivial
2025.2.a.p.1.1		4	45.43	odd	12
2025.2.a.q.1.1		4	45.2	even	12
2025.2.a.y.1.4		4	45.38	even	12
2025.2.a.z.1.4		4	45.7	odd	12
2025.2.b.n.649.1		8	45.29	odd	6
2025.2.b.n.649.8		8	9.2	odd	6
2025.2.b.o.649.1		8	9.7	even	3
2025.2.b.o.649.8		8	45.34	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.28087 + 1.31686i) q^{2} +(2.46825 + 4.27513i) q^{4} +(1.55662 + 0.898714i) q^{7} +7.73393i q^{8} +(0.904062 - 1.56588i) q^{11} +(-1.70765 + 0.985914i) q^{13} +(2.36696 + 4.09970i) q^{14} +(-5.24801 + 9.08982i) q^{16} -4.80812i q^{17} -2.96467 q^{19} +(4.12410 - 2.38105i) q^{22} +(-1.50162 + 0.866963i) q^{23} -5.19325 q^{26} +8.87300i q^{28} +(3.68382 - 6.38057i) q^{29} +(1.31151 + 2.27161i) q^{31} +(-10.5445 + 6.08789i) q^{32} +(6.33163 - 10.9667i) q^{34} +11.6351i q^{37} +(-6.76203 - 3.90406i) q^{38} +(-1.23324 - 2.13603i) q^{41} +(-6.30306 - 3.63907i) q^{43} +8.92580 q^{44} -4.56668 q^{46} +(5.44910 + 3.14604i) q^{47} +(-1.88463 - 3.26427i) q^{49} +(-8.42983 - 4.86696i) q^{52} +1.72540i q^{53} +(-6.95059 + 12.0388i) q^{56} +(16.8047 - 9.70218i) q^{58} +(-5.51300 - 9.54880i) q^{59} +(6.33521 - 10.9729i) q^{61} +6.90833i q^{62} -11.0756 q^{64} +(7.88407 - 4.55187i) q^{67} +(20.5554 - 11.8676i) q^{68} -1.27460 q^{71} +3.58770i q^{73} +(-15.3218 + 26.5382i) q^{74} +(-7.31755 - 12.6744i) q^{76} +(2.81456 - 1.62499i) q^{77} +(1.05545 - 1.82809i) q^{79} -6.49602i q^{82} +(-0.951614 - 0.549415i) q^{83} +(-9.58431 - 16.6005i) q^{86} +(12.1104 + 6.99195i) q^{88} -13.2935 q^{89} -3.54422 q^{91} +(-7.41277 - 4.27976i) q^{92} +(8.28580 + 14.3514i) q^{94} +(3.31926 + 1.91638i) q^{97} -9.92718i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{11} - 6 q^{14} - 8 q^{16} - 8 q^{19} + 40 q^{26} - 2 q^{29} + 8 q^{31} + 18 q^{34} - 10 q^{41} + 88 q^{44} - 6 q^{49} - 60 q^{56} - 34 q^{59} + 26 q^{61} - 76 q^{64} + 32 q^{71} - 80 q^{74}+ \cdots + 6 q^{94}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^11 - 6 * q^14 - 8 * q^16 - 8 * q^19 + 40 * q^26 - 2 * q^29 + 8 * q^31 + 18 * q^34 - 10 * q^41 + 88 * q^44 - 6 * q^49 - 60 * q^56 - 34 * q^59 + 26 * q^61 - 76 * q^64 + 32 * q^71 - 80 * q^74 - 22 * q^76 - 14 * q^79 - 68 * q^86 - 36 * q^89 - 68 * q^91 + 6 * q^94

Introduction

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