LMFDB - Embedded newform 4020.2.q.l.3781.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.4
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.l.841.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(-0.775137 - 1.34258i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(-0.775137 - 1.34258i) q^{7} +1.00000 q^{9} +(-0.262596 - 0.454829i) q^{11} +(-0.0526231 + 0.0911458i) q^{13} +1.00000 q^{15} +(1.53226 - 2.65395i) q^{17} +(-1.60844 + 2.78590i) q^{19} +(0.775137 + 1.34258i) q^{21} +(-4.09911 + 7.09986i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-3.20300 - 5.54777i) q^{29} +(1.70073 + 2.94575i) q^{31} +(0.262596 + 0.454829i) q^{33} +(0.775137 + 1.34258i) q^{35} +(-0.396101 + 0.686067i) q^{37} +(0.0526231 - 0.0911458i) q^{39} +(2.52857 + 4.37962i) q^{41} +4.99327 q^{43} -1.00000 q^{45} +(0.703919 + 1.21922i) q^{47} +(2.29832 - 3.98082i) q^{49} +(-1.53226 + 2.65395i) q^{51} -6.53926 q^{53} +(0.262596 + 0.454829i) q^{55} +(1.60844 - 2.78590i) q^{57} +3.21916 q^{59} +(2.81190 - 4.87035i) q^{61} +(-0.775137 - 1.34258i) q^{63} +(0.0526231 - 0.0911458i) q^{65} +(-7.78180 - 2.53843i) q^{67} +(4.09911 - 7.09986i) q^{69} +(2.92291 + 5.06262i) q^{71} +(-4.11127 + 7.12092i) q^{73} -1.00000 q^{75} +(-0.407095 + 0.705110i) q^{77} +(-0.910790 - 1.57753i) q^{79} +1.00000 q^{81} +(8.71382 - 15.0928i) q^{83} +(-1.53226 + 2.65395i) q^{85} +(3.20300 + 5.54777i) q^{87} -8.71903 q^{89} +0.163160 q^{91} +(-1.70073 - 2.94575i) q^{93} +(1.60844 - 2.78590i) q^{95} +(-1.03739 + 1.79682i) q^{97} +(-0.262596 - 0.454829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−0.775137	−	1.34258i	−0.292974	−	0.507446i	0.681537	−	0.731783i	$-0.261312\pi$
$7$	−0.775137	−	1.34258i	−0.292974	−	0.507446i	−0.974512	+	0.224337i	$0.927978\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.262596	−	0.454829i	−0.0791756	−	0.137136i	0.823719	−	0.566998i	$-0.191895\pi$
$11$	−0.262596	−	0.454829i	−0.0791756	−	0.137136i	−0.902894	+	0.429862i	$0.858562\pi$
$12$		0			0
$13$	−0.0526231	+	0.0911458i	−0.0145950	+	0.0252793i	−0.873231	−	0.487307i	$-0.837979\pi$
$13$	−0.0526231	+	0.0911458i	−0.0145950	+	0.0252793i	0.858636	+	0.512586i	$0.171313\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	1.53226	−	2.65395i	0.371627	−	0.643677i	−0.618189	−	0.786029i	$-0.712133\pi$
$17$	1.53226	−	2.65395i	0.371627	−	0.643677i	0.989816	+	0.142353i	$0.0454668\pi$
$18$		0			0
$19$	−1.60844	+	2.78590i	−0.369002	+	0.639130i	−0.989410	−	0.145150i	$-0.953634\pi$
$19$	−1.60844	+	2.78590i	−0.369002	+	0.639130i	0.620408	+	0.784279i	$0.286967\pi$
$20$		0			0
$21$	0.775137	+	1.34258i	0.169149	+	0.292974i
$22$		0			0
$23$	−4.09911	+	7.09986i	−0.854723	+	1.48042i	0.0221794	+	0.999754i	$0.492939\pi$
$23$	−4.09911	+	7.09986i	−0.854723	+	1.48042i	−0.876902	+	0.480669i	$0.840394\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.20300	−	5.54777i	−0.594783	−	1.03019i	−0.993577	−	0.113154i	$-0.963905\pi$
$29$	−3.20300	−	5.54777i	−0.594783	−	1.03019i	0.398794	−	0.917040i	$-0.369429\pi$
$30$		0			0
$31$	1.70073	+	2.94575i	0.305460	+	0.529072i	0.977364	−	0.211567i	$-0.0678565\pi$
$31$	1.70073	+	2.94575i	0.305460	+	0.529072i	−0.671904	+	0.740638i	$0.734523\pi$
$32$		0			0
$33$	0.262596	+	0.454829i	0.0457120	+	0.0791756i
$34$		0			0
$35$	0.775137	+	1.34258i	0.131022	+	0.226937i
$36$		0			0
$37$	−0.396101	+	0.686067i	−0.0651186	+	0.112789i	−0.896747	−	0.442544i	$-0.854076\pi$
$37$	−0.396101	+	0.686067i	−0.0651186	+	0.112789i	0.831628	+	0.555333i	$0.187409\pi$
$38$		0			0
$39$	0.0526231	−	0.0911458i	0.00842643	−	0.0145950i
$40$		0			0
$41$	2.52857	+	4.37962i	0.394897	+	0.683982i	0.993088	−	0.117372i	$-0.0374470\pi$
$41$	2.52857	+	4.37962i	0.394897	+	0.683982i	−0.598191	+	0.801353i	$0.704114\pi$
$42$		0			0
$43$	4.99327			0.761466			0.380733	−	0.924685i	$-0.375672\pi$
$43$	4.99327			0.761466			0.380733	+	0.924685i	$0.375672\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	0.703919	+	1.21922i	0.102677	+	0.177842i	0.912787	−	0.408436i	$-0.133926\pi$
$47$	0.703919	+	1.21922i	0.102677	+	0.177842i	−0.810110	+	0.586278i	$0.800592\pi$
$48$		0			0
$49$	2.29832	−	3.98082i	0.328332	−	0.568688i
$50$		0			0
$51$	−1.53226	+	2.65395i	−0.214559	+	0.371627i
$52$		0			0
$53$	−6.53926			−0.898236			−0.449118	−	0.893472i	$-0.648262\pi$
$53$	−6.53926			−0.898236			−0.449118	+	0.893472i	$0.648262\pi$
$54$		0			0
$55$	0.262596	+	0.454829i	0.0354084	+	0.0613291i
$56$		0			0
$57$	1.60844	−	2.78590i	0.213043	−	0.369002i
$58$		0			0
$59$	3.21916			0.419099			0.209550	−	0.977798i	$-0.432800\pi$
$59$	3.21916			0.419099			0.209550	+	0.977798i	$0.432800\pi$
$60$		0			0
$61$	2.81190	−	4.87035i	0.360027	−	0.623584i	−0.627938	−	0.778263i	$-0.716101\pi$
$61$	2.81190	−	4.87035i	0.360027	−	0.623584i	0.987965	+	0.154679i	$0.0494343\pi$
$62$		0			0
$63$	−0.775137	−	1.34258i	−0.0976581	−	0.169149i
$64$		0			0
$65$	0.0526231	−	0.0911458i	0.00652709	−	0.0113052i
$66$		0			0
$67$	−7.78180	−	2.53843i	−0.950698	−	0.310118i
$67$	−7.78180	−	2.53843i	−0.950698	−	0.310118i
$68$		0			0
$69$	4.09911	−	7.09986i	0.493474	−	0.854723i
$70$		0			0
$71$	2.92291	+	5.06262i	0.346885	+	0.600823i	0.985694	−	0.168542i	$-0.0539060\pi$
$71$	2.92291	+	5.06262i	0.346885	+	0.600823i	−0.638809	+	0.769365i	$0.720573\pi$
$72$		0			0
$73$	−4.11127	+	7.12092i	−0.481187	+	0.833441i	−0.999767	−	0.0215885i	$-0.993128\pi$
$73$	−4.11127	+	7.12092i	−0.481187	+	0.833441i	0.518580	+	0.855029i	$0.326461\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−0.407095	+	0.705110i	−0.0463928	+	0.0803547i
$78$		0			0
$79$	−0.910790	−	1.57753i	−0.102472	−	0.177486i	0.810231	−	0.586111i	$-0.199342\pi$
$79$	−0.910790	−	1.57753i	−0.102472	−	0.177486i	−0.912702	+	0.408625i	$0.866008\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	8.71382	−	15.0928i	0.956466	−	1.65665i	0.225488	−	0.974246i	$-0.427602\pi$
$83$	8.71382	−	15.0928i	0.956466	−	1.65665i	0.730977	−	0.682402i	$-0.239064\pi$
$84$		0			0
$85$	−1.53226	+	2.65395i	−0.166197	+	0.287861i
$86$		0			0
$87$	3.20300	+	5.54777i	0.343398	+	0.594783i
$88$		0			0
$89$	−8.71903			−0.924215			−0.462108	−	0.886824i	$-0.652907\pi$
$89$	−8.71903			−0.924215			−0.462108	+	0.886824i	$0.652907\pi$
$90$		0			0
$91$	0.163160			0.0171039
$92$		0			0
$93$	−1.70073	−	2.94575i	−0.176357	−	0.305460i
$94$		0			0
$95$	1.60844	−	2.78590i	0.165023	−	0.285827i
$96$		0			0
$97$	−1.03739	+	1.79682i	−0.105331	+	0.182439i	−0.913873	−	0.405999i	$-0.866924\pi$
$97$	−1.03739	+	1.79682i	−0.105331	+	0.182439i	0.808542	+	0.588438i	$0.200257\pi$
$98$		0			0
$99$	−0.262596	−	0.454829i	−0.0263919	−	0.0457120i
$100$		0			0
$101$	1.31323	+	2.27457i	0.130671	+	0.226328i	0.923935	−	0.382549i	$-0.124954\pi$
$101$	1.31323	+	2.27457i	0.130671	+	0.226328i	−0.793265	+	0.608877i	$0.791620\pi$
$102$		0			0
$103$	3.17348	+	5.49663i	0.312692	+	0.541599i	0.978944	−	0.204128i	$-0.0654358\pi$
$103$	3.17348	+	5.49663i	0.312692	+	0.541599i	−0.666252	+	0.745727i	$0.732102\pi$
$104$		0			0
$105$	−0.775137	−	1.34258i	−0.0756456	−	0.131022i
$106$		0			0
$107$	10.3184			0.997521			0.498761	−	0.866740i	$-0.333789\pi$
$107$	10.3184			0.997521			0.498761	+	0.866740i	$0.333789\pi$
$108$		0			0
$109$	6.42905			0.615792			0.307896	−	0.951420i	$-0.400375\pi$
$109$	6.42905			0.615792			0.307896	+	0.951420i	$0.400375\pi$
$110$		0			0
$111$	0.396101	−	0.686067i	0.0375962	−	0.0651186i
$112$		0			0
$113$	−1.66174	−	2.87821i	−0.156323	−	0.270759i	0.777217	−	0.629233i	$-0.216631\pi$
$113$	−1.66174	−	2.87821i	−0.156323	−	0.270759i	−0.933540	+	0.358473i	$0.883297\pi$
$114$		0			0
$115$	4.09911	−	7.09986i	0.382244	−	0.662065i
$116$		0			0
$117$	−0.0526231	+	0.0911458i	−0.00486500	+	0.00842643i
$118$		0			0
$119$	−4.75084			−0.435508
$120$		0			0
$121$	5.36209	−	9.28741i	0.487462	−	0.844310i
$122$		0			0
$123$	−2.52857	−	4.37962i	−0.227994	−	0.394897i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	10.8863	+	18.8556i	0.966001	+	1.67316i	0.706900	+	0.707313i	$0.250093\pi$
$127$	10.8863	+	18.8556i	0.966001	+	1.67316i	0.259101	+	0.965850i	$0.416574\pi$
$128$		0			0
$129$	−4.99327			−0.439633
$130$		0			0
$131$	14.8140			1.29431			0.647155	−	0.762359i	$-0.275959\pi$
$131$	14.8140			1.29431			0.647155	+	0.762359i	$0.275959\pi$
$132$		0			0
$133$	4.98705			0.432432
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−12.0569			−1.03009			−0.515044	−	0.857163i	$-0.672225\pi$
$137$	−12.0569			−1.03009			−0.515044	+	0.857163i	$0.672225\pi$
$138$		0			0
$139$	22.9507			1.94666			0.973328	−	0.229418i	$-0.0736821\pi$
$139$	22.9507			1.94666			0.973328	+	0.229418i	$0.0736821\pi$
$140$		0			0
$141$	−0.703919	−	1.21922i	−0.0592807	−	0.102677i
$142$		0			0
$143$	0.0552744			0.00462227
$144$		0			0
$145$	3.20300	+	5.54777i	0.265995	+	0.460717i
$146$		0			0
$147$	−2.29832	+	3.98082i	−0.189563	+	0.328332i
$148$		0			0
$149$	4.20473			0.344465			0.172232	−	0.985056i	$-0.444902\pi$
$149$	4.20473			0.344465			0.172232	+	0.985056i	$0.444902\pi$
$150$		0			0
$151$	1.97272	−	3.41684i	0.160537	−	0.278059i	−0.774524	−	0.632544i	$-0.782011\pi$
$151$	1.97272	−	3.41684i	0.160537	−	0.278059i	0.935062	+	0.354485i	$0.115344\pi$
$152$		0			0
$153$	1.53226	−	2.65395i	0.123876	−	0.214559i
$154$		0			0
$155$	−1.70073	−	2.94575i	−0.136606	−	0.236608i
$156$		0			0
$157$	6.28433	−	10.8848i	0.501544	−	0.868700i	−0.498454	−	0.866916i	$-0.666099\pi$
$157$	6.28433	−	10.8848i	0.501544	−	0.868700i	0.999998	−	0.00178402i	$-0.000567871\pi$
$158$		0			0
$159$	6.53926			0.518597
$160$		0			0
$161$	12.7095			1.00165
$162$		0			0
$163$	10.2750	+	17.7969i	0.804802	+	1.39396i	0.916425	+	0.400207i	$0.131062\pi$
$163$	10.2750	+	17.7969i	0.804802	+	1.39396i	−0.111623	+	0.993751i	$0.535605\pi$
$164$		0			0
$165$	−0.262596	−	0.454829i	−0.0204430	−	0.0354084i
$166$		0			0
$167$	−10.3299	−	17.8919i	−0.799353	−	1.38452i	−0.920038	−	0.391830i	$-0.871842\pi$
$167$	−10.3299	−	17.8919i	−0.799353	−	1.38452i	0.120685	−	0.992691i	$-0.461491\pi$
$168$		0			0
$169$	6.49446	+	11.2487i	0.499574	+	0.865288i
$170$		0			0
$171$	−1.60844	+	2.78590i	−0.123001	+	0.213043i
$172$		0			0
$173$	−0.847605	+	1.46810i	−0.0644422	+	0.111617i	−0.896446	−	0.443152i	$-0.853860\pi$
$173$	−0.847605	+	1.46810i	−0.0644422	+	0.111617i	0.832004	+	0.554769i	$0.187193\pi$
$174$		0			0
$175$	−0.775137	−	1.34258i	−0.0585949	−	0.101489i
$176$		0			0
$177$	−3.21916			−0.241967
$178$		0			0
$179$	16.2705			1.21612			0.608058	−	0.793893i	$-0.291949\pi$
$179$	16.2705			1.21612			0.608058	+	0.793893i	$0.291949\pi$
$180$		0			0
$181$	6.53860	+	11.3252i	0.486010	+	0.841794i	0.999871	−	0.0160795i	$-0.00511848\pi$
$181$	6.53860	+	11.3252i	0.486010	+	0.841794i	−0.513861	+	0.857874i	$0.671785\pi$
$182$		0			0
$183$	−2.81190	+	4.87035i	−0.207861	+	0.360027i
$184$		0			0
$185$	0.396101	−	0.686067i	0.0291219	−	0.0504407i
$186$		0			0
$187$	−1.60946			−0.117695
$188$		0			0
$189$	0.775137	+	1.34258i	0.0563829	+	0.0976581i
$190$		0			0
$191$	−7.38160	+	12.7853i	−0.534114	+	0.925112i	0.465092	+	0.885262i	$0.346021\pi$
$191$	−7.38160	+	12.7853i	−0.534114	+	0.925112i	−0.999206	+	0.0398496i	$0.987312\pi$
$192$		0			0
$193$	−0.212140			−0.0152702			−0.00763509	−	0.999971i	$-0.502430\pi$
$193$	−0.212140			−0.0152702			−0.00763509	+	0.999971i	$0.502430\pi$
$194$		0			0
$195$	−0.0526231	+	0.0911458i	−0.00376842	+	0.00652709i
$196$		0			0
$197$	12.3422	+	21.3774i	0.879348	+	1.52307i	0.852058	+	0.523447i	$0.175354\pi$
$197$	12.3422	+	21.3774i	0.879348	+	1.52307i	0.0272897	+	0.999628i	$0.491312\pi$
$198$		0			0
$199$	5.70515	−	9.88161i	0.404427	−	0.700489i	−0.589827	−	0.807529i	$-0.700804\pi$
$199$	5.70515	−	9.88161i	0.404427	−	0.700489i	0.994255	+	0.107041i	$0.0341375\pi$
$200$		0			0
$201$	7.78180	+	2.53843i	0.548886	+	0.179047i
$202$		0			0
$203$	−4.96554	+	8.60056i	−0.348512	+	0.603641i
$204$		0			0
$205$	−2.52857	−	4.37962i	−0.176603	−	0.305886i
$206$		0			0
$207$	−4.09911	+	7.09986i	−0.284908	+	0.493474i
$208$		0			0
$209$	1.68948			0.116864
$210$		0			0
$211$	11.2335	−	19.4570i	0.773346	−	1.33947i	−0.162374	−	0.986729i	$-0.551915\pi$
$211$	11.2335	−	19.4570i	0.773346	−	1.33947i	0.935720	−	0.352745i	$-0.114752\pi$
$212$		0			0
$213$	−2.92291	−	5.06262i	−0.200274	−	0.346885i
$214$		0			0
$215$	−4.99327			−0.340538
$216$		0			0
$217$	2.63659	−	4.56672i	0.178984	−	0.310009i
$218$		0			0
$219$	4.11127	−	7.12092i	0.277814	−	0.481187i
$220$		0			0
$221$	0.161264	+	0.279318i	0.0108478	+	0.0187889i
$222$		0			0
$223$	1.35718			0.0908833			0.0454416	−	0.998967i	$-0.485530\pi$
$223$	1.35718			0.0908833			0.0454416	+	0.998967i	$0.485530\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	4.01431	+	6.95299i	0.266439	+	0.461486i	0.967940	−	0.251183i	$-0.0808195\pi$
$227$	4.01431	+	6.95299i	0.266439	+	0.461486i	−0.701500	+	0.712669i	$0.747486\pi$
$228$		0			0
$229$	−3.22002	+	5.57724i	−0.212785	+	0.368555i	−0.952585	−	0.304272i	$-0.901587\pi$
$229$	−3.22002	+	5.57724i	−0.212785	+	0.368555i	0.739800	+	0.672827i	$0.234920\pi$
$230$		0			0
$231$	0.407095	−	0.705110i	0.0267849	−	0.0463928i
$232$		0			0
$233$	−13.8495	−	23.9880i	−0.907309	−	1.57151i	−0.817787	−	0.575521i	$-0.804799\pi$
$233$	−13.8495	−	23.9880i	−0.907309	−	1.57151i	−0.0895227	−	0.995985i	$-0.528534\pi$
$234$		0			0
$235$	−0.703919	−	1.21922i	−0.0459186	−	0.0795334i
$236$		0			0
$237$	0.910790	+	1.57753i	0.0591621	+	0.102472i
$238$		0			0
$239$	8.63210	+	14.9512i	0.558364	+	0.967115i	0.997633	+	0.0687593i	$0.0219040\pi$
$239$	8.63210	+	14.9512i	0.558364	+	0.967115i	−0.439269	+	0.898355i	$0.644763\pi$
$240$		0			0
$241$	10.2489			0.660192			0.330096	−	0.943947i	$-0.392919\pi$
$241$	10.2489			0.660192			0.330096	+	0.943947i	$0.392919\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−2.29832	+	3.98082i	−0.146835	+	0.254325i
$246$		0			0
$247$	−0.169282	−	0.293205i	−0.0107712	−	0.0186562i
$248$		0			0
$249$	−8.71382	+	15.0928i	−0.552216	+	0.956466i
$250$		0			0
$251$	−3.09480	+	5.36035i	−0.195342	+	0.338342i	−0.947013	−	0.321197i	$-0.895915\pi$
$251$	−3.09480	+	5.36035i	−0.195342	+	0.338342i	0.751671	+	0.659539i	$0.229248\pi$
$252$		0			0
$253$	4.30563			0.270693
$254$		0			0
$255$	1.53226	−	2.65395i	0.0959536	−	0.166197i
$256$		0			0
$257$	−7.92981	−	13.7348i	−0.494648	−	0.856755i	0.505333	−	0.862924i	$-0.331370\pi$
$257$	−7.92981	−	13.7348i	−0.494648	−	0.856755i	−0.999981	+	0.00616928i	$0.998036\pi$
$258$		0			0
$259$	1.22813			0.0763123
$260$		0			0
$261$	−3.20300	−	5.54777i	−0.198261	−	0.343398i
$262$		0			0
$263$	18.7400			1.15556			0.577780	−	0.816193i	$-0.303919\pi$
$263$	18.7400			1.15556			0.577780	+	0.816193i	$0.303919\pi$
$264$		0			0
$265$	6.53926			0.401703
$266$		0			0
$267$	8.71903			0.533596
$268$		0			0
$269$	−21.6742			−1.32150			−0.660750	−	0.750606i	$-0.729762\pi$
$269$	−21.6742			−1.32150			−0.660750	+	0.750606i	$0.729762\pi$
$270$		0			0
$271$	30.1382			1.83077			0.915384	−	0.402582i	$-0.131887\pi$
$271$	30.1382			1.83077			0.915384	+	0.402582i	$0.131887\pi$
$272$		0			0
$273$	−0.163160			−0.00987491
$274$		0			0
$275$	−0.262596	−	0.454829i	−0.0158351	−	0.0274272i
$276$		0			0
$277$	19.8633			1.19347			0.596734	−	0.802439i	$-0.296465\pi$
$277$	19.8633			1.19347			0.596734	+	0.802439i	$0.296465\pi$
$278$		0			0
$279$	1.70073	+	2.94575i	0.101820	+	0.176357i
$280$		0			0
$281$	16.1159	−	27.9135i	0.961393	−	1.66518i	0.242384	−	0.970180i	$-0.422071\pi$
$281$	16.1159	−	27.9135i	0.961393	−	1.66518i	0.719009	−	0.695001i	$-0.244596\pi$
$282$		0			0
$283$	−30.5884			−1.81829			−0.909147	−	0.416476i	$-0.863265\pi$
$283$	−30.5884			−1.81829			−0.909147	+	0.416476i	$0.863265\pi$
$284$		0			0
$285$	−1.60844	+	2.78590i	−0.0952758	+	0.165023i
$286$		0			0
$287$	3.91998	−	6.78961i	0.231389	−	0.400778i
$288$		0			0
$289$	3.80438	+	6.58938i	0.223787	+	0.387610i
$290$		0			0
$291$	1.03739	−	1.79682i	0.0608130	−	0.105331i
$292$		0			0
$293$	2.17227			0.126905			0.0634527	−	0.997985i	$-0.479789\pi$
$293$	2.17227			0.126905			0.0634527	+	0.997985i	$0.479789\pi$
$294$		0			0
$295$	−3.21916			−0.187427
$296$		0			0
$297$	0.262596	+	0.454829i	0.0152373	+	0.0263919i
$298$		0			0
$299$	−0.431415	−	0.747233i	−0.0249494	−	0.0432136i
$300$		0			0
$301$	−3.87047	−	6.70385i	−0.223090	−	0.386403i
$302$		0			0
$303$	−1.31323	−	2.27457i	−0.0754428	−	0.130671i
$304$		0			0
$305$	−2.81190	+	4.87035i	−0.161009	+	0.278875i
$306$		0			0
$307$	4.16325	−	7.21095i	0.237609	−	0.411551i	−0.722419	−	0.691456i	$-0.756970\pi$
$307$	4.16325	−	7.21095i	0.237609	−	0.411551i	0.960028	+	0.279905i	$0.0903030\pi$
$308$		0			0
$309$	−3.17348	−	5.49663i	−0.180533	−	0.312692i
$310$		0			0
$311$	−10.6902			−0.606187			−0.303094	−	0.952961i	$-0.598019\pi$
$311$	−10.6902			−0.606187			−0.303094	+	0.952961i	$0.598019\pi$
$312$		0			0
$313$	20.7113			1.17067			0.585335	−	0.810791i	$-0.300963\pi$
$313$	20.7113			1.17067			0.585335	+	0.810791i	$0.300963\pi$
$314$		0			0
$315$	0.775137	+	1.34258i	0.0436740	+	0.0756456i
$316$		0			0
$317$	10.5331	−	18.2438i	0.591596	−	1.02467i	−0.402421	−	0.915455i	$-0.631831\pi$
$317$	10.5331	−	18.2438i	0.591596	−	1.02467i	0.994018	−	0.109220i	$-0.0348354\pi$
$318$		0			0
$319$	−1.68219	+	2.91364i	−0.0941846	+	0.163132i
$320$		0			0
$321$	−10.3184			−0.575919
$322$		0			0
$323$	4.92909	+	8.53743i	0.274262	+	0.475035i
$324$		0			0
$325$	−0.0526231	+	0.0911458i	−0.00291900	+	0.00505586i
$326$		0			0
$327$	−6.42905			−0.355527
$328$		0			0
$329$	1.09127	−	1.89013i	0.0601635	−	0.104206i
$330$		0			0
$331$	16.6168	+	28.7812i	0.913344	+	1.58196i	0.809308	+	0.587385i	$0.199842\pi$
$331$	16.6168	+	28.7812i	0.913344	+	1.58196i	0.104036	+	0.994574i	$0.466824\pi$
$332$		0			0
$333$	−0.396101	+	0.686067i	−0.0217062	+	0.0375962i
$334$		0			0
$335$	7.78180	+	2.53843i	0.425165	+	0.138689i
$336$		0			0
$337$	0.722325	−	1.25110i	0.0393476	−	0.0681520i	−0.845681	−	0.533689i	$-0.820805\pi$
$337$	0.722325	−	1.25110i	0.0393476	−	0.0681520i	0.885029	+	0.465537i	$0.154139\pi$
$338$		0			0
$339$	1.66174	+	2.87821i	0.0902531	+	0.156323i
$340$		0			0
$341$	0.893208	−	1.54708i	0.0483699	−	0.0837791i
$342$		0			0
$343$	−17.9780			−0.970720
$344$		0			0
$345$	−4.09911	+	7.09986i	−0.220688	+	0.382244i
$346$		0			0
$347$	10.9030	+	18.8845i	0.585301	+	1.01377i	0.994838	+	0.101478i	$0.0323571\pi$
$347$	10.9030	+	18.8845i	0.585301	+	1.01377i	−0.409536	+	0.912294i	$0.634310\pi$
$348$		0			0
$349$	31.3545			1.67837			0.839184	−	0.543847i	$-0.183033\pi$
$349$	31.3545			1.67837			0.839184	+	0.543847i	$0.183033\pi$
$350$		0			0
$351$	0.0526231	−	0.0911458i	0.00280881	−	0.00486500i
$352$		0			0
$353$	−15.3212	+	26.5372i	−0.815467	+	1.41243i	0.0935249	+	0.995617i	$0.470187\pi$
$353$	−15.3212	+	26.5372i	−0.815467	+	1.41243i	−0.908992	+	0.416814i	$0.863147\pi$
$354$		0			0
$355$	−2.92291	−	5.06262i	−0.155132	−	0.268696i
$356$		0			0
$357$	4.75084			0.251441
$358$		0			0
$359$	−35.5977			−1.87877			−0.939387	−	0.342860i	$-0.888604\pi$
$359$	−35.5977			−1.87877			−0.939387	+	0.342860i	$0.888604\pi$
$360$		0			0
$361$	4.32583	+	7.49257i	0.227675	+	0.394346i
$362$		0			0
$363$	−5.36209	+	9.28741i	−0.281437	+	0.487462i
$364$		0			0
$365$	4.11127	−	7.12092i	0.215194	−	0.372726i
$366$		0			0
$367$	1.77266	+	3.07033i	0.0925319	+	0.160270i	0.908576	−	0.417720i	$-0.137171\pi$
$367$	1.77266	+	3.07033i	0.0925319	+	0.160270i	−0.816044	+	0.577990i	$0.803837\pi$
$368$		0			0
$369$	2.52857	+	4.37962i	0.131632	+	0.227994i
$370$		0			0
$371$	5.06882	+	8.77945i	0.263160	+	0.455807i
$372$		0			0
$373$	−16.5747	−	28.7082i	−0.858204	−	1.48645i	−0.873640	−	0.486572i	$-0.838247\pi$
$373$	−16.5747	−	28.7082i	−0.858204	−	1.48645i	0.0154362	−	0.999881i	$-0.495086\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	0.674208			0.0347235
$378$		0			0
$379$	5.35411	−	9.27360i	0.275022	−	0.476353i	−0.695118	−	0.718895i	$-0.744648\pi$
$379$	5.35411	−	9.27360i	0.275022	−	0.476353i	0.970141	+	0.242543i	$0.0779814\pi$
$380$		0			0
$381$	−10.8863	−	18.8556i	−0.557721	−	0.966001i
$382$		0			0
$383$	−12.3745	+	21.4332i	−0.632307	+	1.09519i	0.354772	+	0.934953i	$0.384559\pi$
$383$	−12.3745	+	21.4332i	−0.632307	+	1.09519i	−0.987079	+	0.160235i	$0.948775\pi$
$384$		0			0
$385$	0.407095	−	0.705110i	0.0207475	−	0.0359357i
$386$		0			0
$387$	4.99327			0.253822
$388$		0			0
$389$	10.2179	−	17.6979i	0.518068	−	0.897319i	−0.481712	−	0.876329i	$-0.659985\pi$
$389$	10.2179	−	17.6979i	0.518068	−	0.897319i	0.999780	−	0.0209898i	$-0.00668174\pi$
$390$		0			0
$391$	12.5618	+	21.7576i	0.635276	+	1.10033i
$392$		0			0
$393$	−14.8140			−0.747270
$394$		0			0
$395$	0.910790	+	1.57753i	0.0458268	+	0.0793743i
$396$		0			0
$397$	15.3340			0.769592			0.384796	−	0.923002i	$-0.374272\pi$
$397$	15.3340			0.769592			0.384796	+	0.923002i	$0.374272\pi$
$398$		0			0
$399$	−4.98705			−0.249665
$400$		0			0
$401$	26.8598			1.34132			0.670658	−	0.741767i	$-0.266012\pi$
$401$	26.8598			1.34132			0.670658	+	0.741767i	$0.266012\pi$
$402$		0			0
$403$	−0.357990			−0.0178328
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	0.416058			0.0206232
$408$		0			0
$409$	2.48655	+	4.30683i	0.122952	+	0.212959i	0.920931	−	0.389727i	$-0.127431\pi$
$409$	2.48655	+	4.30683i	0.122952	+	0.212959i	−0.797979	+	0.602686i	$0.794097\pi$
$410$		0			0
$411$	12.0569			0.594722
$412$		0			0
$413$	−2.49529	−	4.32197i	−0.122785	−	0.212670i
$414$		0			0
$415$	−8.71382	+	15.0928i	−0.427745	+	0.740875i
$416$		0			0
$417$	−22.9507			−1.12390
$418$		0			0
$419$	−17.0807	+	29.5846i	−0.834447	+	1.44530i	0.0600336	+	0.998196i	$0.480879\pi$
$419$	−17.0807	+	29.5846i	−0.834447	+	1.44530i	−0.894480	+	0.447108i	$0.852454\pi$
$420$		0			0
$421$	−4.93960	+	8.55564i	−0.240741	+	0.416976i	−0.960926	−	0.276806i	$-0.910724\pi$
$421$	−4.93960	+	8.55564i	−0.240741	+	0.416976i	0.720184	+	0.693783i	$0.244057\pi$
$422$		0			0
$423$	0.703919	+	1.21922i	0.0342257	+	0.0592807i
$424$		0			0
$425$	1.53226	−	2.65395i	0.0743254	−	0.128735i
$426$		0			0
$427$	−8.71843			−0.421914
$428$		0			0
$429$	−0.0552744			−0.00266867
$430$		0			0
$431$	3.23898	+	5.61007i	0.156016	+	0.270228i	0.933429	−	0.358763i	$-0.116802\pi$
$431$	3.23898	+	5.61007i	0.156016	+	0.270228i	−0.777413	+	0.628991i	$0.783468\pi$
$432$		0			0
$433$	−15.1428	−	26.2281i	−0.727716	−	1.26044i	−0.957846	−	0.287282i	$-0.907248\pi$
$433$	−15.1428	−	26.2281i	−0.727716	−	1.26044i	0.230130	−	0.973160i	$-0.426085\pi$
$434$		0			0
$435$	−3.20300	−	5.54777i	−0.153572	−	0.265995i
$436$		0			0
$437$	−13.1863	−	22.8394i	−0.630788	−	1.09256i
$438$		0			0
$439$	7.74874	−	13.4212i	0.369827	−	0.640560i	−0.619711	−	0.784830i	$-0.712750\pi$
$439$	7.74874	−	13.4212i	0.369827	−	0.640560i	0.989538	+	0.144270i	$0.0460835\pi$
$440$		0			0
$441$	2.29832	−	3.98082i	0.109444	−	0.189563i
$442$		0			0
$443$	−0.827526	−	1.43332i	−0.0393169	−	0.0680989i	0.845697	−	0.533663i	$-0.179185\pi$
$443$	−0.827526	−	1.43332i	−0.0393169	−	0.0680989i	−0.885014	+	0.465564i	$0.845852\pi$
$444$		0			0
$445$	8.71903			0.413322
$446$		0			0
$447$	−4.20473			−0.198877
$448$		0			0
$449$	−1.79139	−	3.10278i	−0.0845410	−	0.146429i	0.820655	−	0.571425i	$-0.193609\pi$
$449$	−1.79139	−	3.10278i	−0.0845410	−	0.146429i	−0.905196	+	0.424995i	$0.860276\pi$
$450$		0			0
$451$	1.32799	−	2.30014i	0.0625324	−	0.108309i
$452$		0			0
$453$	−1.97272	+	3.41684i	−0.0926863	+	0.160537i
$454$		0			0
$455$	−0.163160			−0.00764908
$456$		0			0
$457$	4.72189	+	8.17855i	0.220881	+	0.382577i	0.955076	−	0.296362i	$-0.0957735\pi$
$457$	4.72189	+	8.17855i	0.220881	+	0.382577i	−0.734195	+	0.678939i	$0.762440\pi$
$458$		0			0
$459$	−1.53226	+	2.65395i	−0.0715196	+	0.123876i
$460$		0			0
$461$	9.43538			0.439450			0.219725	−	0.975562i	$-0.429484\pi$
$461$	9.43538			0.439450			0.219725	+	0.975562i	$0.429484\pi$
$462$		0			0
$463$	4.77207	−	8.26546i	0.221777	−	0.384129i	−0.733571	−	0.679613i	$-0.762148\pi$
$463$	4.77207	−	8.26546i	0.221777	−	0.384129i	0.955348	+	0.295484i	$0.0954811\pi$
$464$		0			0
$465$	1.70073	+	2.94575i	0.0788694	+	0.136606i
$466$		0			0
$467$	−2.02364	+	3.50505i	−0.0936430	+	0.162194i	−0.909041	−	0.416706i	$-0.863185\pi$
$467$	−2.02364	+	3.50505i	−0.0936430	+	0.162194i	0.815398	+	0.578900i	$0.196518\pi$
$468$		0			0
$469$	2.62393	+	12.4153i	0.121162	+	0.573285i
$470$		0			0
$471$	−6.28433	+	10.8848i	−0.289567	+	0.501544i
$472$		0			0
$473$	−1.31121	−	2.27108i	−0.0602895	−	0.104425i
$474$		0			0
$475$	−1.60844	+	2.78590i	−0.0738003	+	0.127826i
$476$		0			0
$477$	−6.53926			−0.299412
$478$		0			0
$479$	−11.3259	+	19.6170i	−0.517494	+	0.896325i	0.482300	+	0.876006i	$0.339802\pi$
$479$	−11.3259	+	19.6170i	−0.517494	+	0.896325i	−0.999794	+	0.0203189i	$0.993532\pi$
$480$		0			0
$481$	−0.0416881	−	0.0722059i	−0.00190081	−	0.00329231i
$482$		0			0
$483$	−12.7095			−0.578301
$484$		0			0
$485$	1.03739	−	1.79682i	0.0471055	−	0.0815892i
$486$		0			0
$487$	1.43999	−	2.49413i	0.0652520	−	0.113020i	−0.831554	−	0.555444i	$-0.812548\pi$
$487$	1.43999	−	2.49413i	0.0652520	−	0.113020i	0.896806	+	0.442425i	$0.145882\pi$
$488$		0			0
$489$	−10.2750	−	17.7969i	−0.464653	−	0.804802i
$490$		0			0
$491$	13.6498			0.616008			0.308004	−	0.951385i	$-0.400339\pi$
$491$	13.6498			0.616008			0.308004	+	0.951385i	$0.400339\pi$
$492$		0			0
$493$	−19.6313			−0.884149
$494$		0			0
$495$	0.262596	+	0.454829i	0.0118028	+	0.0204430i
$496$		0			0
$497$	4.53131	−	7.84846i	0.203257	−	0.352051i
$498$		0			0
$499$	2.10697	−	3.64938i	0.0943209	−	0.163369i	−0.815004	−	0.579455i	$-0.803265\pi$
$499$	2.10697	−	3.64938i	0.0943209	−	0.163369i	0.909325	+	0.416087i	$0.136599\pi$
$500$		0			0
$501$	10.3299	+	17.8919i	0.461507	+	0.799353i
$502$		0			0
$503$	−1.69612	−	2.93776i	−0.0756262	−	0.130988i	0.825732	−	0.564062i	$-0.190762\pi$
$503$	−1.69612	−	2.93776i	−0.0756262	−	0.130988i	−0.901358	+	0.433074i	$0.857429\pi$
$504$		0			0
$505$	−1.31323	−	2.27457i	−0.0584378	−	0.101217i
$506$		0			0
$507$	−6.49446	−	11.2487i	−0.288429	−	0.499574i
$508$		0			0
$509$	−14.0321			−0.621963			−0.310982	−	0.950416i	$-0.600658\pi$
$509$	−14.0321			−0.621963			−0.310982	+	0.950416i	$0.600658\pi$
$510$		0			0
$511$	12.7472			0.563902
$512$		0			0
$513$	1.60844	−	2.78590i	0.0710144	−	0.123001i
$514$		0			0
$515$	−3.17348	−	5.49663i	−0.139840	−	0.242210i
$516$		0			0
$517$	0.369692	−	0.640326i	0.0162590	−	0.0281615i
$518$		0			0
$519$	0.847605	−	1.46810i	0.0372057	−	0.0644422i
$520$		0			0
$521$	11.0180			0.482709			0.241355	−	0.970437i	$-0.422408\pi$
$521$	11.0180			0.482709			0.241355	+	0.970437i	$0.422408\pi$
$522$		0			0
$523$	13.0711	−	22.6398i	0.571559	−	0.989970i	−0.424847	−	0.905265i	$-0.639672\pi$
$523$	13.0711	−	22.6398i	0.571559	−	0.989970i	0.996406	−	0.0847044i	$-0.0269946\pi$
$524$		0			0
$525$	0.775137	+	1.34258i	0.0338298	+	0.0585949i
$526$		0			0
$527$	10.4238			0.454068
$528$		0			0
$529$	−22.1053	−	38.2876i	−0.961102	−	1.66468i
$530$		0			0
$531$	3.21916			0.139700
$532$		0			0
$533$	−0.532245			−0.0230541
$534$		0			0
$535$	−10.3184			−0.446105
$536$		0			0
$537$	−16.2705			−0.702125
$538$		0			0
$539$	−2.41412			−0.103984
$540$		0			0
$541$	22.0989			0.950105			0.475052	−	0.879957i	$-0.342429\pi$
$541$	22.0989			0.950105			0.475052	+	0.879957i	$0.342429\pi$
$542$		0			0
$543$	−6.53860	−	11.3252i	−0.280598	−	0.486010i
$544$		0			0
$545$	−6.42905			−0.275390
$546$		0			0
$547$	−15.6090	−	27.0356i	−0.667393	−	1.15596i	−0.978631	−	0.205626i	$-0.934077\pi$
$547$	−15.6090	−	27.0356i	−0.667393	−	1.15596i	0.311238	−	0.950332i	$-0.399257\pi$
$548$		0			0
$549$	2.81190	−	4.87035i	0.120009	−	0.207861i
$550$		0			0
$551$	20.6074			0.877904
$552$		0			0
$553$	−1.41197	+	2.44561i	−0.0600432	+	0.103998i
$554$		0			0
$555$	−0.396101	+	0.686067i	−0.0168136	+	0.0291219i
$556$		0			0
$557$	4.40764	+	7.63426i	0.186758	+	0.323474i	0.944167	−	0.329466i	$-0.106869\pi$
$557$	4.40764	+	7.63426i	0.186758	+	0.323474i	−0.757410	+	0.652940i	$0.773535\pi$
$558$		0			0
$559$	−0.262761	+	0.455116i	−0.0111136	+	0.0192493i
$560$		0			0
$561$	1.60946			0.0679513
$562$		0			0
$563$	−26.4203			−1.11348			−0.556741	−	0.830686i	$-0.687948\pi$
$563$	−26.4203			−1.11348			−0.556741	+	0.830686i	$0.687948\pi$
$564$		0			0
$565$	1.66174	+	2.87821i	0.0699098	+	0.121087i
$566$		0			0
$567$	−0.775137	−	1.34258i	−0.0325527	−	0.0563829i
$568$		0			0
$569$	−22.2680	−	38.5694i	−0.933524	−	1.61691i	−0.777245	−	0.629199i	$-0.783383\pi$
$569$	−22.2680	−	38.5694i	−0.933524	−	1.61691i	−0.156280	−	0.987713i	$-0.549950\pi$
$570$		0			0
$571$	−7.98314	−	13.8272i	−0.334084	−	0.578651i	0.649224	−	0.760597i	$-0.275094\pi$
$571$	−7.98314	−	13.8272i	−0.334084	−	0.578651i	−0.983308	+	0.181946i	$0.941760\pi$
$572$		0			0
$573$	7.38160	−	12.7853i	0.308371	−	0.534114i
$574$		0			0
$575$	−4.09911	+	7.09986i	−0.170945	+	0.296085i
$576$		0			0
$577$	2.46657	+	4.27223i	0.102685	+	0.177855i	0.912790	−	0.408429i	$-0.133923\pi$
$577$	2.46657	+	4.27223i	0.102685	+	0.177855i	−0.810105	+	0.586285i	$0.800590\pi$
$578$		0			0
$579$	0.212140			0.00881624
$580$		0			0
$581$	−27.0176			−1.12088
$582$		0			0
$583$	1.71718	+	2.97424i	0.0711183	+	0.123181i
$584$		0			0
$585$	0.0526231	−	0.0911458i	0.00217570	−	0.00376842i
$586$		0			0
$587$	10.9315	−	18.9338i	0.451189	−	0.781483i	−0.547271	−	0.836956i	$-0.684333\pi$
$587$	10.9315	−	18.9338i	0.451189	−	0.781483i	0.998460	+	0.0554725i	$0.0176665\pi$
$588$		0			0
$589$	−10.9421			−0.450861
$590$		0			0
$591$	−12.3422	−	21.3774i	−0.507692	−	0.879348i
$592$		0			0
$593$	−5.47607	+	9.48483i	−0.224875	+	0.389495i	−0.956282	−	0.292446i	$-0.905531\pi$
$593$	−5.47607	+	9.48483i	−0.224875	+	0.389495i	0.731407	+	0.681941i	$0.238864\pi$
$594$		0			0
$595$	4.75084			0.194765
$596$		0			0
$597$	−5.70515	+	9.88161i	−0.233496	+	0.404427i
$598$		0			0
$599$	−10.9642	−	18.9906i	−0.447985	−	0.775933i	0.550270	−	0.834987i	$-0.314525\pi$
$599$	−10.9642	−	18.9906i	−0.447985	−	0.775933i	−0.998255	+	0.0590539i	$0.981192\pi$
$600$		0			0
$601$	−15.1117	+	26.1742i	−0.616417	+	1.06767i	0.373717	+	0.927543i	$0.378083\pi$
$601$	−15.1117	+	26.1742i	−0.616417	+	1.06767i	−0.990134	+	0.140123i	$0.955250\pi$
$602$		0			0
$603$	−7.78180	−	2.53843i	−0.316899	−	0.103373i
$604$		0			0
$605$	−5.36209	+	9.28741i	−0.218000	+	0.377587i
$606$		0			0
$607$	22.5252	+	39.0148i	0.914271	+	1.58356i	0.807966	+	0.589229i	$0.200569\pi$
$607$	22.5252	+	39.0148i	0.914271	+	1.58356i	0.106305	+	0.994334i	$0.466098\pi$
$608$		0			0
$609$	4.96554	−	8.60056i	0.201214	−	0.348512i
$610$		0			0
$611$	−0.148169			−0.00599430
$612$		0			0
$613$	−7.17046	+	12.4196i	−0.289612	+	0.501623i	−0.973717	−	0.227760i	$-0.926860\pi$
$613$	−7.17046	+	12.4196i	−0.289612	+	0.501623i	0.684105	+	0.729384i	$0.260193\pi$
$614$		0			0
$615$	2.52857	+	4.37962i	0.101962	+	0.176603i
$616$		0			0
$617$	−43.9933			−1.77110			−0.885551	−	0.464542i	$-0.846219\pi$
$617$	−43.9933			−1.77110			−0.885551	+	0.464542i	$0.846219\pi$
$618$		0			0
$619$	4.82126	−	8.35066i	0.193783	−	0.335641i	−0.752718	−	0.658343i	$-0.771258\pi$
$619$	4.82126	−	8.35066i	0.193783	−	0.335641i	0.946501	+	0.322702i	$0.104591\pi$
$620$		0			0
$621$	4.09911	−	7.09986i	0.164491	−	0.284908i
$622$		0			0
$623$	6.75844	+	11.7060i	0.270771	+	0.468990i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−1.68948			−0.0674713
$628$		0			0
$629$	1.21386	+	2.10246i	0.0483996	+	0.0838306i
$630$		0			0
$631$	−3.47163	+	6.01304i	−0.138203	+	0.239375i	−0.926817	−	0.375514i	$-0.877466\pi$
$631$	−3.47163	+	6.01304i	−0.138203	+	0.239375i	0.788613	+	0.614890i	$0.210799\pi$
$632$		0			0
$633$	−11.2335	+	19.4570i	−0.446491	+	0.773346i
$634$		0			0
$635$	−10.8863	−	18.8556i	−0.432009	−	0.748261i
$636$		0			0
$637$	0.241890	+	0.418965i	0.00958402	+	0.0166000i
$638$		0			0
$639$	2.92291	+	5.06262i	0.115628	+	0.200274i
$640$		0			0
$641$	−12.5610	−	21.7563i	−0.496131	−	0.859324i	0.503859	−	0.863786i	$-0.331913\pi$
$641$	−12.5610	−	21.7563i	−0.496131	−	0.859324i	−0.999990	+	0.00446177i	$0.998580\pi$
$642$		0			0
$643$	5.90010			0.232677			0.116339	−	0.993210i	$-0.462884\pi$
$643$	5.90010			0.232677			0.116339	+	0.993210i	$0.462884\pi$
$644$		0			0
$645$	4.99327			0.196610
$646$		0			0
$647$	−18.9350	+	32.7964i	−0.744413	+	1.28936i	0.206055	+	0.978540i	$0.433937\pi$
$647$	−18.9350	+	32.7964i	−0.744413	+	1.28936i	−0.950468	+	0.310821i	$0.899396\pi$
$648$		0			0
$649$	−0.845338	−	1.46417i	−0.0331824	−	0.0574736i
$650$		0			0
$651$	−2.63659	+	4.56672i	−0.103336	+	0.178984i
$652$		0			0
$653$	7.30803	−	12.6579i	0.285985	−	0.495341i	−0.686862	−	0.726788i	$-0.741012\pi$
$653$	7.30803	−	12.6579i	0.285985	−	0.495341i	0.972848	+	0.231446i	$0.0743458\pi$
$654$		0			0
$655$	−14.8140			−0.578833
$656$		0			0
$657$	−4.11127	+	7.12092i	−0.160396	+	0.277814i
$658$		0			0
$659$	12.9618	+	22.4506i	0.504922	+	0.874550i	0.999984	+	0.00569253i	$0.00181200\pi$
$659$	12.9618	+	22.4506i	0.504922	+	0.874550i	−0.495062	+	0.868858i	$0.664855\pi$
$660$		0			0
$661$	26.1006			1.01519			0.507597	−	0.861595i	$-0.330534\pi$
$661$	26.1006			1.01519			0.507597	+	0.861595i	$0.330534\pi$
$662$		0			0
$663$	−0.161264	−	0.279318i	−0.00626298	−	0.0108478i
$664$		0			0
$665$	−4.98705			−0.193389
$666$		0			0
$667$	52.5178			2.03350
$668$		0			0
$669$	−1.35718			−0.0524715
$670$		0			0
$671$	−2.95357			−0.114021
$672$		0			0
$673$	−5.13781			−0.198048			−0.0990240	−	0.995085i	$-0.531572\pi$
$673$	−5.13781			−0.198048			−0.0990240	+	0.995085i	$0.531572\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	24.0258	+	41.6138i	0.923385	+	1.59935i	0.794138	+	0.607737i	$0.207922\pi$
$677$	24.0258	+	41.6138i	0.923385	+	1.59935i	0.129246	+	0.991613i	$0.458744\pi$
$678$		0			0
$679$	3.21648			0.123437
$680$		0			0
$681$	−4.01431	−	6.95299i	−0.153829	−	0.266439i
$682$		0			0
$683$	4.21652	−	7.30323i	0.161341	−	0.279450i	−0.774009	−	0.633174i	$-0.781752\pi$
$683$	4.21652	−	7.30323i	0.161341	−	0.279450i	0.935350	+	0.353724i	$0.115085\pi$
$684$		0			0
$685$	12.0569			0.460670
$686$		0			0
$687$	3.22002	−	5.57724i	0.122852	−	0.212785i
$688$		0			0
$689$	0.344116	−	0.596026i	0.0131098	−	0.0227068i
$690$		0			0
$691$	3.27042	+	5.66453i	0.124413	+	0.215489i	0.921503	−	0.388371i	$-0.126962\pi$
$691$	3.27042	+	5.66453i	0.124413	+	0.215489i	−0.797091	+	0.603860i	$0.793629\pi$
$692$		0			0
$693$	−0.407095	+	0.705110i	−0.0154643	+	0.0267849i
$694$		0			0
$695$	−22.9507			−0.870571
$696$		0			0
$697$	15.4977			0.587017
$698$		0			0
$699$	13.8495	+	23.9880i	0.523835	+	0.907309i
$700$		0			0
$701$	−5.06428	−	8.77159i	−0.191275	−	0.331298i	0.754398	−	0.656417i	$-0.227929\pi$
$701$	−5.06428	−	8.77159i	−0.191275	−	0.331298i	−0.945673	+	0.325119i	$0.894596\pi$
$702$		0			0
$703$	−1.27421	−	2.20700i	−0.0480578	−	0.0832385i
$704$		0			0
$705$	0.703919	+	1.21922i	0.0265111	+	0.0459186i
$706$		0			0
$707$	2.03586	−	3.52621i	0.0765664	−	0.132617i
$708$		0			0
$709$	−12.9515	+	22.4327i	−0.486405	+	0.842479i	−0.999878	−	0.0156274i	$-0.995025\pi$
$709$	−12.9515	+	22.4327i	−0.486405	+	0.842479i	0.513473	+	0.858106i	$0.328359\pi$
$710$		0			0
$711$	−0.910790	−	1.57753i	−0.0341573	−	0.0591621i
$712$		0			0
$713$	−27.8859			−1.04433
$714$		0			0
$715$	−0.0552744			−0.00206714
$716$		0			0
$717$	−8.63210	−	14.9512i	−0.322372	−	0.558364i
$718$		0			0
$719$	−16.5293	+	28.6296i	−0.616440	+	1.06770i	0.373691	+	0.927553i	$0.378092\pi$
$719$	−16.5293	+	28.6296i	−0.616440	+	1.06770i	−0.990130	+	0.140151i	$0.955241\pi$
$720$		0			0
$721$	4.91976	−	8.52128i	0.183222	−	0.317349i
$722$		0			0
$723$	−10.2489			−0.381162
$724$		0			0
$725$	−3.20300	−	5.54777i	−0.118957	−	0.206039i
$726$		0			0
$727$	−12.0841	+	20.9303i	−0.448175	+	0.776262i	−0.998267	−	0.0588418i	$-0.981259\pi$
$727$	−12.0841	+	20.9303i	−0.448175	+	0.776262i	0.550092	+	0.835104i	$0.314593\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	7.65097	−	13.2519i	0.282981	−	0.490138i
$732$		0			0
$733$	−8.15456	−	14.1241i	−0.301196	−	0.521686i	0.675211	−	0.737624i	$-0.264052\pi$
$733$	−8.15456	−	14.1241i	−0.301196	−	0.521686i	−0.976407	+	0.215938i	$0.930719\pi$
$734$		0			0
$735$	2.29832	−	3.98082i	0.0847750	−	0.146835i
$736$		0			0
$737$	0.888916	+	4.20597i	0.0327436	+	0.154929i
$738$		0			0
$739$	−18.7995	+	32.5617i	−0.691552	+	1.19780i	0.279778	+	0.960065i	$0.409739\pi$
$739$	−18.7995	+	32.5617i	−0.691552	+	1.19780i	−0.971329	+	0.237738i	$0.923594\pi$
$740$		0			0
$741$	0.169282	+	0.293205i	0.00621874	+	0.0107712i
$742$		0			0
$743$	−7.81340	+	13.5332i	−0.286646	+	0.496485i	−0.973007	−	0.230776i	$-0.925874\pi$
$743$	−7.81340	+	13.5332i	−0.286646	+	0.496485i	0.686361	+	0.727261i	$0.259207\pi$
$744$		0			0
$745$	−4.20473			−0.154049
$746$		0			0
$747$	8.71382	−	15.0928i	0.318822	−	0.552216i
$748$		0			0
$749$	−7.99820	−	13.8533i	−0.292248	−	0.506188i
$750$		0			0
$751$	6.95650			0.253846			0.126923	−	0.991913i	$-0.459490\pi$
$751$	6.95650			0.253846			0.126923	+	0.991913i	$0.459490\pi$
$752$		0			0
$753$	3.09480	−	5.36035i	0.112781	−	0.195342i
$754$		0			0
$755$	−1.97272	+	3.41684i	−0.0717945	+	0.124352i
$756$		0			0
$757$	−11.2090	−	19.4146i	−0.407398	−	0.705634i	0.587199	−	0.809442i	$-0.300230\pi$
$757$	−11.2090	−	19.4146i	−0.407398	−	0.705634i	−0.994597	+	0.103808i	$0.966897\pi$
$758$		0			0
$759$	−4.30563			−0.156284
$760$		0			0
$761$	−7.91663			−0.286978			−0.143489	−	0.989652i	$-0.545832\pi$
$761$	−7.91663			−0.286978			−0.143489	+	0.989652i	$0.545832\pi$
$762$		0			0
$763$	−4.98340	−	8.63150i	−0.180411	−	0.312481i
$764$		0			0
$765$	−1.53226	+	2.65395i	−0.0553989	+	0.0959536i
$766$		0			0
$767$	−0.169402	+	0.293413i	−0.00611676	+	0.0105945i
$768$		0			0
$769$	7.32536	+	12.6879i	0.264159	+	0.457537i	0.967343	−	0.253471i	$-0.0815723\pi$
$769$	7.32536	+	12.6879i	0.264159	+	0.457537i	−0.703184	+	0.711008i	$0.748239\pi$
$770$		0			0
$771$	7.92981	+	13.7348i	0.285585	+	0.494648i
$772$		0			0
$773$	−23.9940	−	41.5588i	−0.863004	−	1.49477i	−0.869015	−	0.494785i	$-0.835247\pi$
$773$	−23.9940	−	41.5588i	−0.863004	−	1.49477i	0.00601145	−	0.999982i	$-0.498086\pi$
$774$		0			0
$775$	1.70073	+	2.94575i	0.0610920	+	0.105814i
$776$		0			0
$777$	−1.22813			−0.0440589
$778$		0			0
$779$	−16.2682			−0.582871
$780$		0			0
$781$	1.53509	−	2.65885i	0.0549297	−	0.0951410i
$782$		0			0
$783$	3.20300	+	5.54777i	0.114466	+	0.198261i
$784$		0			0
$785$	−6.28433	+	10.8848i	−0.224297	+	0.388494i
$786$		0			0
$787$	−14.2603	+	24.6996i	−0.508326	+	0.880447i	0.491627	+	0.870806i	$0.336402\pi$
$787$	−14.2603	+	24.6996i	−0.508326	+	0.880447i	−0.999954	+	0.00964096i	$0.996931\pi$
$788$		0			0
$789$	−18.7400			−0.667163
$790$		0			0
$791$	−2.57615	+	4.46202i	−0.0915972	+	0.158651i
$792$		0			0
$793$	0.295941	+	0.512585i	0.0105092	+	0.0182024i
$794$		0			0
$795$	−6.53926			−0.231924
$796$		0			0
$797$	4.24546	+	7.35336i	0.150382	+	0.260469i	0.931368	−	0.364079i	$-0.118616\pi$
$797$	4.24546	+	7.35336i	0.150382	+	0.260469i	−0.780986	+	0.624549i	$0.785283\pi$
$798$		0			0
$799$	4.31434			0.152630
$800$		0			0
$801$	−8.71903			−0.308072
$802$		0			0
$803$	4.31840			0.152393
$804$		0			0
$805$	−12.7095			−0.447950
$806$		0			0
$807$	21.6742			0.762968
$808$		0			0
$809$	−4.78307			−0.168164			−0.0840818	−	0.996459i	$-0.526796\pi$
$809$	−4.78307			−0.168164			−0.0840818	+	0.996459i	$0.526796\pi$
$810$		0			0
$811$	−24.2422	−	41.9887i	−0.851259	−	1.47442i	−0.880073	−	0.474839i	$-0.842506\pi$
$811$	−24.2422	−	41.9887i	−0.851259	−	1.47442i	0.0288136	−	0.999585i	$-0.490827\pi$
$812$		0			0
$813$	−30.1382			−1.05699
$814$		0			0
$815$	−10.2750	−	17.7969i	−0.359918	−	0.623397i
$816$		0			0
$817$	−8.03138	+	13.9108i	−0.280982	+	0.486676i
$818$		0			0
$819$	0.163160			0.00570128
$820$		0			0
$821$	16.3825	−	28.3753i	0.571754	−	0.990306i	−0.424633	−	0.905366i	$-0.639597\pi$
$821$	16.3825	−	28.3753i	0.571754	−	0.990306i	0.996386	−	0.0849404i	$-0.0270700\pi$
$822$		0			0
$823$	−11.2708	+	19.5217i	−0.392876	+	0.680482i	−0.992828	−	0.119555i	$-0.961853\pi$
$823$	−11.2708	+	19.5217i	−0.392876	+	0.680482i	0.599951	+	0.800037i	$0.295187\pi$
$824$		0			0
$825$	0.262596	+	0.454829i	0.00914241	+	0.0158351i
$826$		0			0
$827$	23.7232	−	41.0897i	0.824936	−	1.42883i	−0.0770328	−	0.997029i	$-0.524545\pi$
$827$	23.7232	−	41.0897i	0.824936	−	1.42883i	0.901968	−	0.431802i	$-0.142122\pi$
$828$		0			0
$829$	39.4233			1.36923			0.684613	−	0.728906i	$-0.259971\pi$
$829$	39.4233			1.36923			0.684613	+	0.728906i	$0.259971\pi$
$830$		0			0
$831$	−19.8633			−0.689049
$832$		0			0
$833$	−7.04325	−	12.1993i	−0.244034	−	0.422679i
$834$		0			0
$835$	10.3299	+	17.8919i	0.357482	+	0.619176i
$836$		0			0
$837$	−1.70073	−	2.94575i	−0.0587858	−	0.101820i
$838$		0			0
$839$	−8.81831	−	15.2738i	−0.304442	−	0.527309i	0.672695	−	0.739920i	$-0.265137\pi$
$839$	−8.81831	−	15.2738i	−0.304442	−	0.527309i	−0.977137	+	0.212611i	$0.931803\pi$
$840$		0			0
$841$	−6.01848	+	10.4243i	−0.207534	+	0.359459i
$842$		0			0
$843$	−16.1159	+	27.9135i	−0.555060	+	0.961393i
$844$		0			0
$845$	−6.49446	−	11.2487i	−0.223416	−	0.386968i
$846$		0			0
$847$	−16.6254			−0.571256
$848$		0			0
$849$	30.5884			1.04979
$850$		0			0
$851$	−3.24732	−	5.62452i	−0.111317	−	0.192806i
$852$		0			0
$853$	−15.6954	+	27.1852i	−0.537400	+	0.930805i	0.461643	+	0.887066i	$0.347260\pi$
$853$	−15.6954	+	27.1852i	−0.537400	+	0.930805i	−0.999043	+	0.0437386i	$0.986073\pi$
$854$		0			0
$855$	1.60844	−	2.78590i	0.0550075	−	0.0952758i
$856$		0			0
$857$	33.2972			1.13741			0.568706	−	0.822541i	$-0.307444\pi$
$857$	33.2972			1.13741			0.568706	+	0.822541i	$0.307444\pi$
$858$		0			0
$859$	0.331699	+	0.574519i	0.0113174	+	0.0196023i	0.871629	−	0.490167i	$-0.163064\pi$
$859$	0.331699	+	0.574519i	0.0113174	+	0.0196023i	−0.860311	+	0.509769i	$0.829731\pi$
$860$		0			0
$861$	−3.91998	+	6.78961i	−0.133593	+	0.231389i
$862$		0			0
$863$	−12.9776			−0.441763			−0.220882	−	0.975301i	$-0.570893\pi$
$863$	−12.9776			−0.441763			−0.220882	+	0.975301i	$0.570893\pi$
$864$		0			0
$865$	0.847605	−	1.46810i	0.0288194	−	0.0499167i
$866$		0			0
$867$	−3.80438	−	6.58938i	−0.129203	−	0.223787i
$868$		0			0
$869$	−0.478339	+	0.828507i	−0.0162265	+	0.0281052i
$870$		0			0
$871$	0.640869	−	0.575699i	0.0217150	−	0.0195068i
$872$		0			0
$873$	−1.03739	+	1.79682i	−0.0351104	+	0.0608130i
$874$		0			0
$875$	0.775137	+	1.34258i	0.0262044	+	0.0453874i
$876$		0			0
$877$	−20.6267	+	35.7265i	−0.696515	+	1.20640i	0.273153	+	0.961971i	$0.411934\pi$
$877$	−20.6267	+	35.7265i	−0.696515	+	1.20640i	−0.969667	+	0.244428i	$0.921400\pi$
$878$		0			0
$879$	−2.17227			−0.0732688
$880$		0			0
$881$	−0.741941	+	1.28508i	−0.0249966	+	0.0432954i	−0.878253	−	0.478196i	$-0.841291\pi$
$881$	−0.741941	+	1.28508i	−0.0249966	+	0.0432954i	0.853256	+	0.521491i	$0.174624\pi$
$882$		0			0
$883$	−11.9427	−	20.6854i	−0.401905	−	0.696120i	0.592051	−	0.805901i	$-0.298319\pi$
$883$	−11.9427	−	20.6854i	−0.401905	−	0.696120i	−0.993956	+	0.109781i	$0.964985\pi$
$884$		0			0
$885$	3.21916			0.108211
$886$		0			0
$887$	−1.24802	+	2.16163i	−0.0419044	+	0.0725805i	−0.886217	−	0.463271i	$-0.846676\pi$
$887$	−1.24802	+	2.16163i	−0.0419044	+	0.0725805i	0.844313	+	0.535851i	$0.180009\pi$
$888$		0			0
$889$	16.8767	−	29.2313i	0.566027	−	0.980388i
$890$		0			0
$891$	−0.262596	−	0.454829i	−0.00879729	−	0.0152373i
$892$		0			0
$893$	−4.52885			−0.151552
$894$		0			0
$895$	−16.2705			−0.543864
$896$		0			0
$897$	0.431415	+	0.747233i	0.0144045	+	0.0249494i
$898$		0			0
$899$	10.8949	−	18.8705i	0.363365	−	0.629366i
$900$		0			0
$901$	−10.0198	+	17.3548i	−0.333809	+	0.578173i
$902$		0			0
$903$	3.87047	+	6.70385i	0.128801	+	0.223090i
$904$		0			0
$905$	−6.53860	−	11.3252i	−0.217350	−	0.376462i
$906$		0			0
$907$	−15.0591	−	26.0831i	−0.500028	−	0.866074i	−1.00000		3.22262e-5i	$-0.999990\pi$
$907$	−15.0591	−	26.0831i	−0.500028	−	0.866074i	0.499972	−	0.866042i	$-0.333344\pi$
$908$		0			0
$909$	1.31323	+	2.27457i	0.0435569	+	0.0754428i
$910$		0			0
$911$	18.5596			0.614907			0.307454	−	0.951563i	$-0.400523\pi$
$911$	18.5596			0.614907			0.307454	+	0.951563i	$0.400523\pi$
$912$		0			0
$913$	−9.15284			−0.302915
$914$		0			0
$915$	2.81190	−	4.87035i	0.0929585	−	0.161009i
$916$		0			0
$917$	−11.4829	−	19.8890i	−0.379199	−	0.656792i
$918$		0			0
$919$	4.49216	−	7.78064i	0.148183	−	0.256660i	−0.782373	−	0.622810i	$-0.785991\pi$
$919$	4.49216	−	7.78064i	0.148183	−	0.256660i	0.930556	+	0.366150i	$0.119324\pi$
$920$		0			0
$921$	−4.16325	+	7.21095i	−0.137184	+	0.237609i
$922$		0			0
$923$	−0.615249			−0.0202512
$924$		0			0
$925$	−0.396101	+	0.686067i	−0.0130237	+	0.0225577i
$926$		0			0
$927$	3.17348	+	5.49663i	0.104231	+	0.180533i
$928$		0			0
$929$	−33.5743			−1.10154			−0.550769	−	0.834658i	$-0.685666\pi$
$929$	−33.5743			−1.10154			−0.550769	+	0.834658i	$0.685666\pi$
$930$		0			0
$931$	7.39344	+	12.8058i	0.242310	+	0.419694i
$932$		0			0
$933$	10.6902			0.349982
$934$		0			0
$935$	1.60946			0.0526348
$936$		0			0
$937$	7.89342			0.257867			0.128933	−	0.991653i	$-0.458845\pi$
$937$	7.89342			0.257867			0.128933	+	0.991653i	$0.458845\pi$
$938$		0			0
$939$	−20.7113			−0.675887
$940$		0			0
$941$	−22.8789			−0.745830			−0.372915	−	0.927866i	$-0.621642\pi$
$941$	−22.8789			−0.745830			−0.372915	+	0.927866i	$0.621642\pi$
$942$		0			0
$943$	−41.4596			−1.35011
$944$		0			0
$945$	−0.775137	−	1.34258i	−0.0252152	−	0.0436740i
$946$		0			0
$947$	−32.4028			−1.05295			−0.526475	−	0.850191i	$-0.676487\pi$
$947$	−32.4028			−1.05295			−0.526475	+	0.850191i	$0.676487\pi$
$948$		0			0
$949$	−0.432695	−	0.749449i	−0.0140459	−	0.0243282i
$950$		0			0
$951$	−10.5331	+	18.2438i	−0.341558	+	0.591596i
$952$		0			0
$953$	45.3592			1.46933			0.734664	−	0.678432i	$-0.237340\pi$
$953$	45.3592			1.46933			0.734664	+	0.678432i	$0.237340\pi$
$954$		0			0
$955$	7.38160	−	12.7853i	0.238863	−	0.413723i
$956$		0			0
$957$	1.68219	−	2.91364i	0.0543775	−	0.0941846i
$958$		0			0
$959$	9.34574	+	16.1873i	0.301790	+	0.522715i
$960$		0			0
$961$	9.71505	−	16.8270i	0.313389	−	0.542805i
$962$		0			0
$963$	10.3184			0.332507
$964$		0			0
$965$	0.212140			0.00682903
$966$		0			0
$967$	−12.6946	−	21.9877i	−0.408231	−	0.707077i	0.586461	−	0.809978i	$-0.300521\pi$
$967$	−12.6946	−	21.9877i	−0.408231	−	0.707077i	−0.994692	+	0.102901i	$0.967187\pi$
$968$		0			0
$969$	−4.92909	−	8.53743i	−0.158345	−	0.274262i
$970$		0			0
$971$	26.9116	+	46.6122i	0.863634	+	1.49586i	0.868397	+	0.495869i	$0.165150\pi$
$971$	26.9116	+	46.6122i	0.863634	+	1.49586i	−0.00476379	+	0.999989i	$0.501516\pi$
$972$		0			0
$973$	−17.7900	−	30.8131i	−0.570320	−	0.987824i
$974$		0			0
$975$	0.0526231	−	0.0911458i	0.00168529	−	0.00291900i
$976$		0			0
$977$	−4.21136	+	7.29429i	−0.134733	+	0.233365i	−0.925496	−	0.378758i	$-0.876351\pi$
$977$	−4.21136	+	7.29429i	−0.134733	+	0.233365i	0.790762	+	0.612124i	$0.209684\pi$
$978$		0			0
$979$	2.28958	+	3.96567i	0.0731753	+	0.126743i
$980$		0			0
$981$	6.42905			0.205264
$982$		0			0
$983$	1.92197			0.0613013			0.0306507	−	0.999530i	$-0.490242\pi$
$983$	1.92197			0.0613013			0.0306507	+	0.999530i	$0.490242\pi$
$984$		0			0
$985$	−12.3422	−	21.3774i	−0.393256	−	0.681140i
$986$		0			0
$987$	−1.09127	+	1.89013i	−0.0347354	+	0.0601635i
$988$		0			0
$989$	−20.4679	+	35.4515i	−0.650843	+	1.12729i
$990$		0			0
$991$	18.2784			0.580633			0.290317	−	0.956931i	$-0.406239\pi$
$991$	18.2784			0.580633			0.290317	+	0.956931i	$0.406239\pi$
$992$		0			0
$993$	−16.6168	−	28.7812i	−0.527319	−	0.913344i
$994$		0			0
$995$	−5.70515	+	9.88161i	−0.180865	+	0.313268i
$996$		0			0
$997$	19.7744			0.626260			0.313130	−	0.949710i	$-0.398622\pi$
$997$	19.7744			0.626260			0.313130	+	0.949710i	$0.398622\pi$
$998$		0			0
$999$	0.396101	−	0.686067i	0.0125321	−	0.0217062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.3781.4	yes	22
67.37	even	3	inner	4020.2.q.l.841.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.4	✓	22	67.37	even	3	inner
4020.2.q.l.3781.4	yes	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-0.775137 - 1.34258i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(-0.775137 - 1.34258i) q^{7} +1.00000 q^{9} +(-0.262596 - 0.454829i) q^{11} +(-0.0526231 + 0.0911458i) q^{13} +1.00000 q^{15} +(1.53226 - 2.65395i) q^{17} +(-1.60844 + 2.78590i) q^{19} +(0.775137 + 1.34258i) q^{21} +(-4.09911 + 7.09986i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-3.20300 - 5.54777i) q^{29} +(1.70073 + 2.94575i) q^{31} +(0.262596 + 0.454829i) q^{33} +(0.775137 + 1.34258i) q^{35} +(-0.396101 + 0.686067i) q^{37} +(0.0526231 - 0.0911458i) q^{39} +(2.52857 + 4.37962i) q^{41} +4.99327 q^{43} -1.00000 q^{45} +(0.703919 + 1.21922i) q^{47} +(2.29832 - 3.98082i) q^{49} +(-1.53226 + 2.65395i) q^{51} -6.53926 q^{53} +(0.262596 + 0.454829i) q^{55} +(1.60844 - 2.78590i) q^{57} +3.21916 q^{59} +(2.81190 - 4.87035i) q^{61} +(-0.775137 - 1.34258i) q^{63} +(0.0526231 - 0.0911458i) q^{65} +(-7.78180 - 2.53843i) q^{67} +(4.09911 - 7.09986i) q^{69} +(2.92291 + 5.06262i) q^{71} +(-4.11127 + 7.12092i) q^{73} -1.00000 q^{75} +(-0.407095 + 0.705110i) q^{77} +(-0.910790 - 1.57753i) q^{79} +1.00000 q^{81} +(8.71382 - 15.0928i) q^{83} +(-1.53226 + 2.65395i) q^{85} +(3.20300 + 5.54777i) q^{87} -8.71903 q^{89} +0.163160 q^{91} +(-1.70073 - 2.94575i) q^{93} +(1.60844 - 2.78590i) q^{95} +(-1.03739 + 1.79682i) q^{97} +(-0.262596 - 0.454829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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