LMFDB - Embedded newform 144.6.i.b.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,6,Mod(49,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("144.49");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	144.i (of order $3$, degree $2$, not 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:	$23.0952700531$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.47347183152.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331 $ x^6 - 3x^5 + 118x^4 - 231x^3 + 3700x^2 - 3585*x + 32331
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.3
Root			$0.500000 + 4.03013i$ of defining polynomial
Character	$\chi$	$=$	144.49
Dual form			144.6.i.b.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.58066 + 13.0143i) q^{3} +(-39.2420 + 67.9691i) q^{5} +(110.566 + 191.505i) q^{7} +(-95.7446 + 223.343i) q^{9} +O(q^{10})$	\(q+(8.58066 + 13.0143i) q^{3} +(-39.2420 + 67.9691i) q^{5} +(110.566 + 191.505i) q^{7} +(-95.7446 + 223.343i) q^{9} +(115.144 + 199.436i) q^{11} +(385.793 - 668.213i) q^{13} +(-1221.29 + 72.5123i) q^{15} -769.880 q^{17} +383.367 q^{19} +(-1543.58 + 3082.17i) q^{21} +(193.178 - 334.594i) q^{23} +(-1517.37 - 2628.15i) q^{25} +(-3728.20 + 670.377i) q^{27} +(394.883 + 683.958i) q^{29} +(1609.97 - 2788.54i) q^{31} +(-1607.51 + 3209.82i) q^{33} -17355.2 q^{35} +2465.33 q^{37} +(12006.7 - 712.877i) q^{39} +(4621.73 - 8005.07i) q^{41} +(5315.76 + 9207.16i) q^{43} +(-11423.2 - 15272.1i) q^{45} +(976.032 + 1690.54i) q^{47} +(-16046.0 + 27792.4i) q^{49} +(-6606.08 - 10019.5i) q^{51} -32589.2 q^{53} -18074.0 q^{55} +(3289.54 + 4989.25i) q^{57} +(-11916.1 + 20639.2i) q^{59} +(-18804.4 - 32570.2i) q^{61} +(-53357.3 + 6358.42i) q^{63} +(30278.5 + 52444.0i) q^{65} +(-11525.6 + 19962.9i) q^{67} +(6012.10 - 356.959i) q^{69} +66050.4 q^{71} +65130.0 q^{73} +(21183.6 - 42298.8i) q^{75} +(-25462.0 + 44101.5i) q^{77} +(-35433.7 - 61373.0i) q^{79} +(-40714.9 - 42767.7i) q^{81} +(27643.5 + 47880.0i) q^{83} +(30211.6 - 52328.0i) q^{85} +(-5512.88 + 11007.9i) q^{87} +10598.6 q^{89} +170622. q^{91} +(50105.6 - 2974.94i) q^{93} +(-15044.1 + 26057.1i) q^{95} +(41409.9 + 71724.1i) q^{97} +(-55567.0 + 6621.74i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9}+O(q^{10}) $ 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9	$ 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9} + 315 q^{11} - 744 q^{13} - 2286 q^{15} + 2898 q^{17} - 2262 q^{19} - 11076 q^{21} + 3168 q^{23} - 2883 q^{25} - 18144 q^{27} - 5148 q^{29} + 8610 q^{31} + 17469 q^{33} - 2700 q^{35} + 39936 q^{37} + 49026 q^{39} + 5049 q^{41} + 31389 q^{43} + 2538 q^{45} - 12924 q^{47} - 52857 q^{49} - 36837 q^{51} - 96048 q^{53} - 126252 q^{55} - 17469 q^{57} - 62955 q^{59} - 75966 q^{61} - 49578 q^{63} + 108702 q^{65} + 32991 q^{67} - 29250 q^{69} + 129672 q^{71} - 8466 q^{73} + 105483 q^{75} + 88740 q^{77} - 89202 q^{79} + 123435 q^{81} - 32634 q^{83} + 71388 q^{85} + 151524 q^{87} + 66132 q^{89} + 301836 q^{91} + 57678 q^{93} + 82944 q^{95} + 46245 q^{97} - 282168 q^{99}+O(q^{100}) $ 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9 + 315 * q^11 - 744 * q^13 - 2286 * q^15 + 2898 * q^17 - 2262 * q^19 - 11076 * q^21 + 3168 * q^23 - 2883 * q^25 - 18144 * q^27 - 5148 * q^29 + 8610 * q^31 + 17469 * q^33 - 2700 * q^35 + 39936 * q^37 + 49026 * q^39 + 5049 * q^41 + 31389 * q^43 + 2538 * q^45 - 12924 * q^47 - 52857 * q^49 - 36837 * q^51 - 96048 * q^53 - 126252 * q^55 - 17469 * q^57 - 62955 * q^59 - 75966 * q^61 - 49578 * q^63 + 108702 * q^65 + 32991 * q^67 - 29250 * q^69 + 129672 * q^71 - 8466 * q^73 + 105483 * q^75 + 88740 * q^77 - 89202 * q^79 + 123435 * q^81 - 32634 * q^83 + 71388 * q^85 + 151524 * q^87 + 66132 * q^89 + 301836 * q^91 + 57678 * q^93 + 82944 * q^95 + 46245 * q^97 - 282168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	8.58066	+	13.0143i	0.550449	+	0.834868i
$3$	8.58066	+	13.0143i	0.550449	+	0.834868i
$4$		0			0
$5$	−39.2420	+	67.9691i	−0.701982	+	1.21587i	0.265788	+	0.964032i	$0.414368\pi$
$5$	−39.2420	+	67.9691i	−0.701982	+	1.21587i	−0.967770	+	0.251837i	$0.918965\pi$
$6$		0			0
$7$	110.566	+	191.505i	0.852854	+	1.47719i	0.878622	+	0.477518i	$0.158464\pi$
$7$	110.566	+	191.505i	0.852854	+	1.47719i	−0.0257678	+	0.999668i	$0.508203\pi$
$8$		0			0
$9$	−95.7446	+	223.343i	−0.394011	+	0.919106i
$10$		0			0
$11$	115.144	+	199.436i	0.286920	+	0.496960i	0.973073	−	0.230497i	$-0.0740353\pi$
$11$	115.144	+	199.436i	0.286920	+	0.496960i	−0.686153	+	0.727457i	$0.740702\pi$
$12$		0			0
$13$	385.793	−	668.213i	0.633134	−	1.09662i	−0.353773	−	0.935331i	$-0.615101\pi$
$13$	385.793	−	668.213i	0.633134	−	1.09662i	0.986907	−	0.161289i	$-0.0515652\pi$
$14$		0			0
$15$	−1221.29	+	72.5123i	−1.40150	+	0.0832115i
$16$		0			0
$17$	−769.880			−0.646101			−0.323051	−	0.946382i	$-0.604708\pi$
$17$	−769.880			−0.646101			−0.323051	+	0.946382i	$0.604708\pi$
$18$		0			0
$19$	383.367			0.243630			0.121815	−	0.992553i	$-0.461129\pi$
$19$	383.367			0.243630			0.121815	+	0.992553i	$0.461129\pi$
$20$		0			0
$21$	−1543.58	+	3082.17i	−0.763803	+	1.52514i
$22$		0			0
$23$	193.178	−	334.594i	0.0761444	−	0.131886i	−0.825439	−	0.564491i	$-0.809072\pi$
$23$	193.178	−	334.594i	0.0761444	−	0.131886i	0.901583	+	0.432605i	$0.142406\pi$
$24$		0			0
$25$	−1517.37	−	2628.15i	−0.485557	−	0.841009i
$26$		0			0
$27$	−3728.20	+	670.377i	−0.984215	+	0.176974i
$28$		0			0
$29$	394.883	+	683.958i	0.0871914	+	0.151020i	0.906323	−	0.422586i	$-0.138877\pi$
$29$	394.883	+	683.958i	0.0871914	+	0.151020i	−0.819131	+	0.573606i	$0.805544\pi$
$30$		0			0
$31$	1609.97	−	2788.54i	0.300893	−	0.521163i	−0.675445	−	0.737410i	$-0.736048\pi$
$31$	1609.97	−	2788.54i	0.300893	−	0.521163i	0.976339	+	0.216247i	$0.0693818\pi$
$32$		0			0
$33$	−1607.51	+	3209.82i	−0.256961	+	0.513092i
$34$		0			0
$35$	−17355.2			−2.39475
$36$		0			0
$37$	2465.33			0.296054			0.148027	−	0.988983i	$-0.452708\pi$
$37$	2465.33			0.296054			0.148027	+	0.988983i	$0.452708\pi$
$38$		0			0
$39$	12006.7	−	712.877i	1.26404	−	0.0750505i
$40$		0			0
$41$	4621.73	−	8005.07i	0.429383	−	0.743713i	−0.567436	−	0.823418i	$-0.692064\pi$
$41$	4621.73	−	8005.07i	0.429383	−	0.743713i	0.996819	+	0.0797047i	$0.0253977\pi$
$42$		0			0
$43$	5315.76	+	9207.16i	0.438424	+	0.759372i	0.997568	−	0.0696983i	$-0.0222037\pi$
$43$	5315.76	+	9207.16i	0.438424	+	0.759372i	−0.559145	+	0.829070i	$0.688870\pi$
$44$		0			0
$45$	−11423.2	−	15272.1i	−0.840923	−	1.12426i
$46$		0			0
$47$	976.032	+	1690.54i	0.0644495	+	0.111630i	0.896450	−	0.443146i	$-0.146138\pi$
$47$	976.032	+	1690.54i	0.0644495	+	0.111630i	−0.832000	+	0.554775i	$0.812804\pi$
$48$		0			0
$49$	−16046.0	+	27792.4i	−0.954720	+	1.65362i
$50$		0			0
$51$	−6606.08	−	10019.5i	−0.355646	−	0.539410i
$52$		0			0
$53$	−32589.2			−1.59362			−0.796809	−	0.604231i	$-0.793480\pi$
$53$	−32589.2			−1.59362			−0.796809	+	0.604231i	$0.793480\pi$
$54$		0			0
$55$	−18074.0			−0.805651
$56$		0			0
$57$	3289.54	+	4989.25i	0.134106	+	0.203399i
$58$		0			0
$59$	−11916.1	+	20639.2i	−0.445659	+	0.771903i	−0.998098	−	0.0616498i	$-0.980364\pi$
$59$	−11916.1	+	20639.2i	−0.445659	+	0.771903i	0.552439	+	0.833553i	$0.313697\pi$
$60$		0			0
$61$	−18804.4	−	32570.2i	−0.647046	−	1.12072i	−0.983825	−	0.179133i	$-0.942671\pi$
$61$	−18804.4	−	32570.2i	−0.647046	−	1.12072i	0.336779	−	0.941584i	$-0.390663\pi$
$62$		0			0
$63$	−53357.3	+	6358.42i	−1.69372	+	0.201836i
$64$		0			0
$65$	30278.5	+	52444.0i	0.888897	+	1.53962i
$66$		0			0
$67$	−11525.6	+	19962.9i	−0.313672	+	0.543295i	−0.979154	−	0.203118i	$-0.934892\pi$
$67$	−11525.6	+	19962.9i	−0.313672	+	0.543295i	0.665483	+	0.746413i	$0.268226\pi$
$68$		0			0
$69$	6012.10	−	356.959i	0.152021	−	0.00902600i
$70$		0			0
$71$	66050.4			1.55500			0.777498	−	0.628885i	$-0.216489\pi$
$71$	66050.4			1.55500			0.777498	+	0.628885i	$0.216489\pi$
$72$		0			0
$73$	65130.0			1.43045			0.715227	−	0.698893i	$-0.246324\pi$
$73$	65130.0			1.43045			0.715227	+	0.698893i	$0.246324\pi$
$74$		0			0
$75$	21183.6	−	42298.8i	0.434858	−	0.868309i
$76$		0			0
$77$	−25462.0	+	44101.5i	−0.489402	+	0.847669i
$78$		0			0
$79$	−35433.7	−	61373.0i	−0.638776	−	1.10639i	−0.985702	−	0.168500i	$-0.946108\pi$
$79$	−35433.7	−	61373.0i	−0.638776	−	1.10639i	0.346925	−	0.937893i	$-0.387226\pi$
$80$		0			0
$81$	−40714.9	−	42767.7i	−0.689511	−	0.724275i
$82$		0			0
$83$	27643.5	+	47880.0i	0.440451	+	0.762884i	0.997723	−	0.0674462i	$-0.0214851\pi$
$83$	27643.5	+	47880.0i	0.440451	+	0.762884i	−0.557272	+	0.830330i	$0.688152\pi$
$84$		0			0
$85$	30211.6	−	52328.0i	0.453551	−	0.785574i
$86$		0			0
$87$	−5512.88	+	11007.9i	−0.0780873	+	0.155922i
$88$		0			0
$89$	10598.6			0.141831			0.0709156	−	0.997482i	$-0.477408\pi$
$89$	10598.6			0.141831			0.0709156	+	0.997482i	$0.477408\pi$
$90$		0			0
$91$	170622.			2.15988
$92$		0			0
$93$	50105.6	−	2974.94i	0.600729	−	0.0356673i
$94$		0			0
$95$	−15044.1	+	26057.1i	−0.171024	+	0.296222i
$96$		0			0
$97$	41409.9	+	71724.1i	0.446864	+	0.773991i	0.998180	−	0.0603057i	$-0.0192076\pi$
$97$	41409.9	+	71724.1i	0.446864	+	0.773991i	−0.551316	+	0.834296i	$0.685874\pi$
$98$		0			0
$99$	−55567.0	+	6621.74i	−0.569809	+	0.0679023i
$100$		0			0
$101$	−10604.1	−	18366.9i	−0.103436	−	0.179156i	0.809662	−	0.586896i	$-0.199650\pi$
$101$	−10604.1	−	18366.9i	−0.103436	−	0.179156i	−0.913098	+	0.407740i	$0.866317\pi$
$102$		0			0
$103$	65877.4	−	114103.i	0.611848	−	1.05975i	−0.379081	−	0.925363i	$-0.623760\pi$
$103$	65877.4	−	114103.i	0.611848	−	1.05975i	0.990929	−	0.134388i	$-0.0429068\pi$
$104$		0			0
$105$	−148919.	−	225866.i	−1.31819	−	1.99930i
$106$		0			0
$107$	−54796.5			−0.462693			−0.231347	−	0.972871i	$-0.574313\pi$
$107$	−54796.5			−0.462693			−0.231347	+	0.972871i	$0.574313\pi$
$108$		0			0
$109$	160570.			1.29448			0.647242	−	0.762284i	$-0.275922\pi$
$109$	160570.			1.29448			0.647242	+	0.762284i	$0.275922\pi$
$110$		0			0
$111$	21154.2	+	32084.6i	0.162963	+	0.247166i
$112$		0			0
$113$	33217.8	−	57534.9i	0.244723	−	0.423873i	−0.717331	−	0.696733i	$-0.754636\pi$
$113$	33217.8	−	57534.9i	0.244723	−	0.423873i	0.962054	+	0.272860i	$0.0879696\pi$
$114$		0			0
$115$	15161.4	+	26260.3i	0.106904	+	0.185163i
$116$		0			0
$117$	112303.	+	150142.i	0.758449	+	1.01400i
$118$		0			0
$119$	−85122.2	−	147436.i	−0.551030	−	0.954412i
$120$		0			0
$121$	54009.1	−	93546.4i	0.335354	−	0.580850i
$122$		0			0
$123$	143838.	−	8540.15i	0.857256	−	0.0508982i
$124$		0			0
$125$	−7084.72			−0.0405553
$126$		0			0
$127$	299603.			1.64830			0.824152	−	0.566368i	$-0.191652\pi$
$127$	299603.			1.64830			0.824152	+	0.566368i	$0.191652\pi$
$128$		0			0
$129$	−74212.1	+	148184.i	−0.392646	+	0.784022i
$130$		0			0
$131$	−166224.	+	287909.i	−0.846283	+	1.46581i	0.0382189	+	0.999269i	$0.487832\pi$
$131$	−166224.	+	287909.i	−0.846283	+	1.46581i	−0.884502	+	0.466536i	$0.845502\pi$
$132$		0			0
$133$	42387.1	+	73416.7i	0.207781	+	0.359887i
$134$		0			0
$135$	100737.	−	279710.i	0.475724	−	1.32091i
$136$		0			0
$137$	93601.3	+	162122.i	0.426070	+	0.737974i	0.996520	−	0.0833580i	$-0.0265645\pi$
$137$	93601.3	+	162122.i	0.426070	+	0.737974i	−0.570450	+	0.821332i	$0.693231\pi$
$138$		0			0
$139$	−105285.	+	182358.i	−0.462198	+	0.800550i	−0.999070	−	0.0431133i	$-0.986272\pi$
$139$	−105285.	+	182358.i	−0.462198	+	0.800550i	0.536872	+	0.843664i	$0.319606\pi$
$140$		0			0
$141$	−13626.2	+	27208.3i	−0.0577200	+	0.115253i
$142$		0			0
$143$	177687.			0.726635
$144$		0			0
$145$	−61984.0			−0.244827
$146$		0			0
$147$	−499385.	+	29650.1i	−1.90608	+	0.113171i
$148$		0			0
$149$	−242872.	+	420667.i	−0.896215	+	1.55229i	−0.0639212	+	0.997955i	$0.520361\pi$
$149$	−242872.	+	420667.i	−0.896215	+	1.55229i	−0.832294	+	0.554335i	$0.812973\pi$
$150$		0			0
$151$	105105.	+	182047.i	0.375130	+	0.649744i	0.990346	−	0.138614i	$-0.0442648\pi$
$151$	105105.	+	182047.i	0.375130	+	0.649744i	−0.615217	+	0.788358i	$0.710931\pi$
$152$		0			0
$153$	73711.8	−	171947.i	0.254571	−	0.593835i
$154$		0			0
$155$	126357.	+	218856.i	0.422443	+	0.731694i
$156$		0			0
$157$	196123.	−	339696.i	0.635009	−	1.09987i	−0.351504	−	0.936186i	$-0.614330\pi$
$157$	196123.	−	339696.i	0.635009	−	1.09987i	0.986513	−	0.163682i	$-0.0523371\pi$
$158$		0			0
$159$	−279637.	−	424126.i	−0.877206	−	1.33046i
$160$		0			0
$161$	85435.3			0.259760
$162$		0			0
$163$	−190208.			−0.560738			−0.280369	−	0.959892i	$-0.590457\pi$
$163$	−190208.			−0.560738			−0.280369	+	0.959892i	$0.590457\pi$
$164$		0			0
$165$	−155087.	−	235220.i	−0.443470	−	0.672612i
$166$		0			0
$167$	−200619.	+	347483.i	−0.556650	+	0.964145i	0.441123	+	0.897446i	$0.354580\pi$
$167$	−200619.	+	347483.i	−0.556650	+	0.964145i	−0.997773	+	0.0666991i	$0.978753\pi$
$168$		0			0
$169$	−112026.	−	194034.i	−0.301718	−	0.522590i
$170$		0			0
$171$	−36705.3	+	85622.1i	−0.0959927	+	0.223922i
$172$		0			0
$173$	−47391.9	−	82085.1i	−0.120389	−	0.208521i	0.799532	−	0.600624i	$-0.205081\pi$
$173$	−47391.9	−	82085.1i	−0.120389	−	0.208521i	−0.919921	+	0.392103i	$0.871748\pi$
$174$		0			0
$175$	335537.	−	581166.i	0.828218	−	1.43452i
$176$		0			0
$177$	−370853.	+	22018.8i	−0.889750	+	0.0528275i
$178$		0			0
$179$	218816.			0.510442			0.255221	−	0.966883i	$-0.417852\pi$
$179$	218816.			0.510442			0.255221	+	0.966883i	$0.417852\pi$
$180$		0			0
$181$	−344513.			−0.781645			−0.390823	−	0.920466i	$-0.627809\pi$
$181$	−344513.			−0.781645			−0.390823	+	0.920466i	$0.627809\pi$
$182$		0			0
$183$	262525.	−	524200.i	0.579485	−	1.15710i
$184$		0			0
$185$	−96744.5	+	167566.i	−0.207825	+	0.359963i
$186$		0			0
$187$	−88647.3	−	153542.i	−0.185379	−	0.321087i
$188$		0			0
$189$	−540592.	−	639849.i	−1.10082	−	1.30294i
$190$		0			0
$191$	−67476.5	−	116873.i	−0.133835	−	0.231809i	0.791317	−	0.611406i	$-0.209396\pi$
$191$	−67476.5	−	116873.i	−0.133835	−	0.231809i	−0.925152	+	0.379597i	$0.876062\pi$
$192$		0			0
$193$	−113675.	+	196892.i	−0.219671	+	0.380482i	−0.954707	−	0.297546i	$-0.903832\pi$
$193$	−113675.	+	196892.i	−0.219671	+	0.380482i	0.735036	+	0.678028i	$0.237165\pi$
$194$		0			0
$195$	−422712.	+	844058.i	−0.796083	+	1.58959i
$196$		0			0
$197$	430437.			0.790213			0.395107	−	0.918635i	$-0.370708\pi$
$197$	430437.			0.790213			0.395107	+	0.918635i	$0.370708\pi$
$198$		0			0
$199$	−719704.			−1.28831			−0.644156	−	0.764894i	$-0.722791\pi$
$199$	−719704.			−1.28831			−0.644156	+	0.764894i	$0.722791\pi$
$200$		0			0
$201$	−358700.	+	21297.2i	−0.626241	+	0.0371820i
$202$		0			0
$203$	−87321.0	+	151244.i	−0.148723	+	0.257596i
$204$		0			0
$205$	362732.	+	628269.i	0.602838	+	1.04415i
$206$		0			0
$207$	56233.4	+	75180.4i	0.0912154	+	0.121949i
$208$		0			0
$209$	44142.5	+	76457.1i	0.0699023	+	0.121074i
$210$		0			0
$211$	30700.0	−	53174.0i	0.0474715	−	0.0822230i	−0.841313	−	0.540548i	$-0.818217\pi$
$211$	30700.0	−	53174.0i	0.0474715	−	0.0822230i	0.888785	+	0.458325i	$0.151550\pi$
$212$		0			0
$213$	566756.	+	859600.i	0.855947	+	1.29822i
$214$		0			0
$215$	−834403.			−1.23106
$216$		0			0
$217$	712027.			1.02647
$218$		0			0
$219$	558858.	+	847621.i	0.787392	+	1.19424i
$220$		0			0
$221$	−297014.	+	514443.i	−0.409069	+	0.708528i
$222$		0			0
$223$	329013.	+	569868.i	0.443049	+	0.767383i	0.997914	−	0.0645574i	$-0.0205636\pi$
$223$	329013.	+	569868.i	0.443049	+	0.767383i	−0.554865	+	0.831940i	$0.687230\pi$
$224$		0			0
$225$	732259.	−	87260.9i	0.964291	−	0.114912i
$226$		0			0
$227$	−5067.16	−	8776.57i	−0.00652679	−	0.0113047i	0.862744	−	0.505642i	$-0.168744\pi$
$227$	−5067.16	−	8776.57i	−0.00652679	−	0.0113047i	−0.869270	+	0.494337i	$0.835411\pi$
$228$		0			0
$229$	−611518.	+	1.05918e6i	−0.770584	+	1.33469i	0.166659	+	0.986015i	$0.446702\pi$
$229$	−611518.	+	1.05918e6i	−0.770584	+	1.33469i	−0.937243	+	0.348677i	$0.886631\pi$
$230$		0			0
$231$	−792431.	+	47049.3i	−0.977083	+	0.0580127i
$232$		0			0
$233$	−1.16513e6			−1.40599			−0.702996	−	0.711194i	$-0.748155\pi$
$233$	−1.16513e6			−1.40599			−0.702996	+	0.711194i	$0.748155\pi$
$234$		0			0
$235$	−153206.			−0.180969
$236$		0			0
$237$	494683.	−	987766.i	0.572079	−	1.14231i
$238$		0			0
$239$	659760.	−	1.14274e6i	0.747122	−	1.29405i	−0.202075	−	0.979370i	$-0.564769\pi$
$239$	659760.	−	1.14274e6i	0.747122	−	1.29405i	0.949197	−	0.314683i	$-0.101898\pi$
$240$		0			0
$241$	−265905.	−	460560.i	−0.294906	−	0.510792i	0.680057	−	0.733159i	$-0.261955\pi$
$241$	−265905.	−	460560.i	−0.294906	−	0.510792i	−0.974963	+	0.222367i	$0.928622\pi$
$242$		0			0
$243$	207231.	−	896852.i	0.225133	−	0.974328i
$244$		0			0
$245$	−1.25935e6	−	2.18126e6i	−1.34039	−	2.32163i
$246$		0			0
$247$	147900.	−	256170.i	0.154250	−	0.267169i
$248$		0			0
$249$	−385925.	+	770603.i	−0.394462	+	0.787648i
$250$		0			0
$251$	−475.750			−0.000476644			−0.000238322	−	1.00000i	$-0.500076\pi$
$251$	−475.750			−0.000476644			−0.000238322		1.00000i	$0.500076\pi$
$252$		0			0
$253$	88973.4			0.0873894
$254$		0			0
$255$	940249.	−	55825.7i	0.905508	−	0.0537631i
$256$		0			0
$257$	13603.3	−	23561.6i	0.0128473	−	0.0222522i	−0.859530	−	0.511085i	$-0.829244\pi$
$257$	13603.3	−	23561.6i	0.0128473	−	0.0222522i	0.872378	+	0.488833i	$0.162577\pi$
$258$		0			0
$259$	272581.	+	472124.i	0.252491	+	0.437327i
$260$		0			0
$261$	−190565.	+	22709.0i	−0.173158	+	0.0206347i
$262$		0			0
$263$	−69991.2	−	121228.i	−0.0623956	−	0.108072i	0.833140	−	0.553062i	$-0.186541\pi$
$263$	−69991.2	−	121228.i	−0.0623956	−	0.108072i	−0.895536	+	0.444990i	$0.853207\pi$
$264$		0			0
$265$	1.27887e6	−	2.21506e6i	1.11869	−	1.93763i
$266$		0			0
$267$	90942.6	+	137933.i	0.0780709	+	0.118410i
$268$		0			0
$269$	1.63842e6			1.38053			0.690263	−	0.723558i	$-0.257495\pi$
$269$	1.63842e6			1.38053			0.690263	+	0.723558i	$0.257495\pi$
$270$		0			0
$271$	280791.			0.232252			0.116126	−	0.993234i	$-0.462952\pi$
$271$	280791.			0.232252			0.116126	+	0.993234i	$0.462952\pi$
$272$		0			0
$273$	1.46405e6	+	2.22052e6i	1.18891	+	1.80322i
$274$		0			0
$275$	349432.	−	605234.i	0.278632	−	0.482605i
$276$		0			0
$277$	−346404.	−	599989.i	−0.271259	−	0.469834i	0.697926	−	0.716170i	$-0.254107\pi$
$277$	−346404.	−	599989.i	−0.271259	−	0.469834i	−0.969184	+	0.246336i	$0.920773\pi$
$278$		0			0
$279$	468656.	+	626563.i	0.360449	+	0.481897i
$280$		0			0
$281$	1.05464e6	+	1.82670e6i	0.796782	+	1.38007i	0.921701	+	0.387901i	$0.126800\pi$
$281$	1.05464e6	+	1.82670e6i	0.796782	+	1.38007i	−0.124919	+	0.992167i	$0.539867\pi$
$282$		0			0
$283$	−731346.	+	1.26673e6i	−0.542821	+	0.940193i	0.455920	+	0.890021i	$0.349310\pi$
$283$	−731346.	+	1.26673e6i	−0.542821	+	0.940193i	−0.998741	+	0.0501725i	$0.984023\pi$
$284$		0			0
$285$	−468203.	+	27798.8i	−0.341446	+	0.0202728i
$286$		0			0
$287$	2.04402e6			1.46480
$288$		0			0
$289$	−827142.			−0.582553
$290$		0			0
$291$	−578115.	+	1.15436e6i	−0.400204	+	0.799115i
$292$		0			0
$293$	1.27745e6	−	2.21261e6i	0.869313	−	1.50569i	0.00661216	−	0.999978i	$-0.497895\pi$
$293$	1.27745e6	−	2.21261e6i	0.869313	−	1.50569i	0.862700	−	0.505715i	$-0.168771\pi$
$294$		0			0
$295$	−935219.	−	1.61985e6i	−0.625688	−	1.08372i
$296$		0			0
$297$	−562979.	−	666347.i	−0.370340	−	0.438338i
$298$		0			0
$299$	−149053.	−	258168.i	−0.0964192	−	0.167003i
$300$		0			0
$301$	−1.17548e6	+	2.03599e6i	−0.747822	+	1.29527i
$302$		0			0
$303$	148042.	−	295605.i	0.0926357	−	0.184972i
$304$		0			0
$305$	2.95169e6			1.81686
$306$		0			0
$307$	2.14982e6			1.30183			0.650917	−	0.759149i	$-0.274385\pi$
$307$	2.14982e6			1.30183			0.650917	+	0.759149i	$0.274385\pi$
$308$		0			0
$309$	2.05024e6	−	121730.i	1.22154	−	0.0725272i
$310$		0			0
$311$	−183809.	+	318367.i	−0.107762	+	0.186650i	−0.914863	−	0.403763i	$-0.867702\pi$
$311$	−183809.	+	318367.i	−0.107762	+	0.186650i	0.807101	+	0.590413i	$0.201035\pi$
$312$		0			0
$313$	−91371.8	−	158261.i	−0.0527171	−	0.0913086i	0.838463	−	0.544959i	$-0.183455\pi$
$313$	−91371.8	−	158261.i	−0.0527171	−	0.0913086i	−0.891180	+	0.453650i	$0.850121\pi$
$314$		0			0
$315$	1.66167e6	−	3.87617e6i	0.943558	−	2.20103i
$316$		0			0
$317$	−432482.	−	749081.i	−0.241724	−	0.418679i	0.719481	−	0.694512i	$-0.244380\pi$
$317$	−432482.	−	749081.i	−0.241724	−	0.418679i	−0.961206	+	0.275833i	$0.911046\pi$
$318$		0			0
$319$	−90937.2	+	157508.i	−0.0500339	+	0.0866613i
$320$		0			0
$321$	−470190.	−	713139.i	−0.254689	−	0.386288i
$322$		0			0
$323$	−295146.			−0.157409
$324$		0			0
$325$	−2.34155e6			−1.22969
$326$		0			0
$327$	1.37779e6	+	2.08970e6i	0.712549	+	1.08072i
$328$		0			0
$329$	−215831.	+	373830.i	−0.109932	+	0.190408i
$330$		0			0
$331$	−1.49880e6	−	2.59600e6i	−0.751923	−	1.30237i	−0.946890	−	0.321559i	$-0.895793\pi$
$331$	−1.49880e6	−	2.59600e6i	−0.751923	−	1.30237i	0.194967	−	0.980810i	$-0.437540\pi$
$332$		0			0
$333$	−236042.	+	550614.i	−0.116648	+	0.272105i
$334$		0			0
$335$	−904572.	−	1.56676e6i	−0.440384	−	0.762767i
$336$		0			0
$337$	−359139.	+	622047.i	−0.172261	+	0.298365i	−0.939210	−	0.343343i	$-0.888441\pi$
$337$	−359139.	+	622047.i	−0.172261	+	0.298365i	0.766949	+	0.641708i	$0.221774\pi$
$338$		0			0
$339$	1.03381e6	−	61380.7i	0.488586	−	0.0290090i
$340$		0			0
$341$	741514.			0.345329
$342$		0			0
$343$	−3.37998e6			−1.55124
$344$		0			0
$345$	−211665.	+	422645.i	−0.0957416	+	0.191174i
$346$		0			0
$347$	−1.87463e6	+	3.24695e6i	−0.835779	+	1.44761i	0.0576157	+	0.998339i	$0.481650\pi$
$347$	−1.87463e6	+	3.24695e6i	−0.835779	+	1.44761i	−0.893395	+	0.449273i	$0.851683\pi$
$348$		0			0
$349$	1.16679e6	+	2.02094e6i	0.512778	+	0.888157i	0.999890	+	0.0148181i	$0.00471692\pi$
$349$	1.16679e6	+	2.02094e6i	0.512778	+	0.888157i	−0.487112	+	0.873339i	$0.661950\pi$
$350$		0			0
$351$	−990359.	+	2.74986e6i	−0.429067	+	1.19136i
$352$		0			0
$353$	−2.17285e6	−	3.76348e6i	−0.928094	−	1.60751i	−0.786508	−	0.617580i	$-0.788113\pi$
$353$	−2.17285e6	−	3.76348e6i	−0.928094	−	1.60751i	−0.141586	−	0.989926i	$-0.545220\pi$
$354$		0			0
$355$	−2.59195e6	+	4.48938e6i	−1.09158	+	1.89067i
$356$		0			0
$357$	1.18837e6	−	2.37290e6i	0.493494	−	0.985393i
$358$		0			0
$359$	2.71281e6			1.11092			0.555461	−	0.831542i	$-0.312542\pi$
$359$	2.71281e6			1.11092			0.555461	+	0.831542i	$0.312542\pi$
$360$		0			0
$361$	−2.32913e6			−0.940645
$362$		0			0
$363$	1.68088e6	−	99799.3i	0.669528	−	0.0397522i
$364$		0			0
$365$	−2.55583e6	+	4.42682e6i	−1.00415	+	1.73924i
$366$		0			0
$367$	1.95814e6	+	3.39160e6i	0.758889	+	1.31443i	0.943417	+	0.331608i	$0.107591\pi$
$367$	1.95814e6	+	3.39160e6i	0.758889	+	1.31443i	−0.184528	+	0.982827i	$0.559076\pi$
$368$		0			0
$369$	1.34537e6	+	1.79867e6i	0.514370	+	0.687679i
$370$		0			0
$371$	−3.60324e6	−	6.24100e6i	−1.35912	−	2.35407i
$372$		0			0
$373$	−890322.	+	1.54208e6i	−0.331341	+	0.573899i	−0.982775	−	0.184806i	$-0.940834\pi$
$373$	−890322.	+	1.54208e6i	−0.331341	+	0.573899i	0.651434	+	0.758705i	$0.274168\pi$
$374$		0			0
$375$	−60791.5	−	92202.7i	−0.0223236	−	0.0338583i
$376$		0			0
$377$	609373.			0.220815
$378$		0			0
$379$	631740.			0.225912			0.112956	−	0.993600i	$-0.463968\pi$
$379$	631740.			0.225912			0.112956	+	0.993600i	$0.463968\pi$
$380$		0			0
$381$	2.57079e6	+	3.89913e6i	0.907308	+	1.37612i
$382$		0			0
$383$	66803.0	−	115706.i	0.0232701	−	0.0403050i	−0.854156	−	0.520017i	$-0.825926\pi$
$383$	66803.0	−	115706.i	0.0232701	−	0.0403050i	0.877426	+	0.479712i	$0.159259\pi$
$384$		0			0
$385$	−1.99836e6	−	3.46126e6i	−0.687102	−	1.19010i
$386$		0			0
$387$	−2.56531e6	+	305700.i	−0.870687	+	0.103757i
$388$		0			0
$389$	−2.79735e6	−	4.84515e6i	−0.937286	−	1.62343i	−0.770505	−	0.637434i	$-0.779996\pi$
$389$	−2.79735e6	−	4.84515e6i	−0.937286	−	1.62343i	−0.166781	−	0.985994i	$-0.553337\pi$
$390$		0			0
$391$	−148724.	+	257597.i	−0.0491970	+	0.0852117i
$392$		0			0
$393$	−5.17324e6	+	307153.i	−1.68959	+	0.100317i
$394$		0			0
$395$	5.56195e6			1.79364
$396$		0			0
$397$	4.19051e6			1.33441			0.667206	−	0.744873i	$-0.267490\pi$
$397$	4.19051e6			1.33441			0.667206	+	0.744873i	$0.267490\pi$
$398$		0			0
$399$	−591758.	+	1.18160e6i	−0.186085	+	0.371569i
$400$		0			0
$401$	229109.	−	396829.i	0.0711511	−	0.123237i	−0.828255	−	0.560351i	$-0.810666\pi$
$401$	229109.	−	396829.i	0.0711511	−	0.123237i	0.899406	+	0.437114i	$0.143999\pi$
$402$		0			0
$403$	−1.24223e6	−	2.15160e6i	−0.381012	−	0.659932i
$404$		0			0
$405$	4.50462e6	−	1.08907e6i	1.36465	−	0.329927i
$406$		0			0
$407$	283869.	+	491675.i	0.0849438	+	0.147127i
$408$		0			0
$409$	−8467.95	+	14666.9i	−0.00250305	+	0.00433541i	−0.867274	−	0.497831i	$-0.834130\pi$
$409$	−8467.95	+	14666.9i	−0.00250305	+	0.00433541i	0.864771	+	0.502166i	$0.167463\pi$
$410$		0			0
$411$	−1.30675e6	+	2.60927e6i	−0.381582	+	0.761930i
$412$		0			0
$413$	−5.27002e6			−1.52033
$414$		0			0
$415$	−4.33914e6			−1.23676
$416$		0			0
$417$	−3.27668e6	+	194548.i	−0.922771	+	0.0547880i
$418$		0			0
$419$	2.24889e6	−	3.89520e6i	0.625798	−	1.08391i	−0.362588	−	0.931949i	$-0.618107\pi$
$419$	2.24889e6	−	3.89520e6i	0.625798	−	1.08391i	0.988386	−	0.151964i	$-0.0485598\pi$
$420$		0			0
$421$	217248.	+	376285.i	0.0597381	+	0.103469i	0.894348	−	0.447372i	$-0.147640\pi$
$421$	217248.	+	376285.i	0.0597381	+	0.103469i	−0.834610	+	0.550842i	$0.814307\pi$
$422$		0			0
$423$	−471019.	+	56129.8i	−0.127993	+	0.0152526i
$424$		0			0
$425$	1.16819e6	+	2.02336e6i	0.313719	+	0.543377i
$426$		0			0
$427$	4.15824e6	−	7.20229e6i	1.10367	−	1.91162i
$428$		0			0
$429$	1.52468e6	+	2.31248e6i	0.399976	+	0.606645i
$430$		0			0
$431$	−5.16700e6			−1.33982			−0.669908	−	0.742444i	$-0.733666\pi$
$431$	−5.16700e6			−1.33982			−0.669908	+	0.742444i	$0.733666\pi$
$432$		0			0
$433$	3.95066e6			1.01263			0.506314	−	0.862349i	$-0.331008\pi$
$433$	3.95066e6			1.01263			0.506314	+	0.862349i	$0.331008\pi$
$434$		0			0
$435$	−531864.	−	806679.i	−0.134765	−	0.204398i
$436$		0			0
$437$	74058.0	−	128272.i	0.0185510	−	0.0321313i
$438$		0			0
$439$	−243803.	−	422279.i	−0.0603778	−	0.104577i	0.834257	−	0.551377i	$-0.185897\pi$
$439$	−243803.	−	422279.i	−0.0603778	−	0.104577i	−0.894634	+	0.446799i	$0.852564\pi$
$440$		0			0
$441$	−4.67092e6	−	6.24473e6i	−1.14368	−	1.52903i
$442$		0			0
$443$	−4027.52	−	6975.87i	−0.000975053	−	0.00168884i	0.865537	−	0.500844i	$-0.166977\pi$
$443$	−4027.52	−	6975.87i	−0.000975053	−	0.00168884i	−0.866513	+	0.499155i	$0.833644\pi$
$444$		0			0
$445$	−415909.	+	720375.i	−0.0995630	+	0.172448i
$446$		0			0
$447$	−7.55870e6	+	448785.i	−1.78928	+	0.106236i
$448$		0			0
$449$	6.79644e6			1.59098			0.795492	−	0.605964i	$-0.207212\pi$
$449$	6.79644e6			1.59098			0.795492	+	0.605964i	$0.207212\pi$
$450$		0			0
$451$	2.12866e6			0.492794
$452$		0			0
$453$	−1.46735e6	+	2.92996e6i	−0.335961	+	0.670835i
$454$		0			0
$455$	−6.69553e6	+	1.15970e7i	−1.51620	+	2.62613i
$456$		0			0
$457$	−199059.	−	344780.i	−0.0445852	−	0.0772238i	0.842872	−	0.538115i	$-0.180863\pi$
$457$	−199059.	−	344780.i	−0.0445852	−	0.0772238i	−0.887457	+	0.460891i	$0.847530\pi$
$458$		0			0
$459$	2.87027e6	−	516110.i	0.635903	−	0.114343i
$460$		0			0
$461$	620959.	+	1.07553e6i	0.136085	+	0.235706i	0.926011	−	0.377495i	$-0.123215\pi$
$461$	620959.	+	1.07553e6i	0.136085	+	0.235706i	−0.789926	+	0.613202i	$0.789881\pi$
$462$		0			0
$463$	−1.21707e6	+	2.10802e6i	−0.263853	+	0.457007i	−0.967263	−	0.253778i	$-0.918327\pi$
$463$	−1.21707e6	+	2.10802e6i	−0.263853	+	0.457007i	0.703409	+	0.710785i	$0.251660\pi$
$464$		0			0
$465$	−1.76404e6	+	3.52237e6i	−0.378334	+	0.755445i
$466$		0			0
$467$	1.08309e6			0.229811			0.114906	−	0.993376i	$-0.463343\pi$
$467$	1.08309e6			0.229811			0.114906	+	0.993376i	$0.463343\pi$
$468$		0			0
$469$	−5.09732e6			−1.07006
$470$		0			0
$471$	6.10377e6	−	362402.i	1.26779	−	0.0752727i
$472$		0			0
$473$	−1.22416e6	+	2.12030e6i	−0.251585	+	0.435758i
$474$		0			0
$475$	−581707.	−	1.00755e6i	−0.118296	−	0.204895i
$476$		0			0
$477$	3.12024e6	−	7.27856e6i	0.627903	−	1.46470i
$478$		0			0
$479$	−1.66906e6	−	2.89090e6i	−0.332379	−	0.575698i	0.650599	−	0.759422i	$-0.274518\pi$
$479$	−1.66906e6	−	2.89090e6i	−0.332379	−	0.575698i	−0.982978	+	0.183724i	$0.941185\pi$
$480$		0			0
$481$	951107.	−	1.64737e6i	0.187442	−	0.324659i
$482$		0			0
$483$	733091.	+	1.11188e6i	0.142985	+	0.216866i
$484$		0			0
$485$	−6.50003e6			−1.25476
$486$		0			0
$487$	5.17210e6			0.988198			0.494099	−	0.869406i	$-0.335498\pi$
$487$	5.17210e6			0.988198			0.494099	+	0.869406i	$0.335498\pi$
$488$		0			0
$489$	−1.63211e6	−	2.47543e6i	−0.308658	−	0.468143i
$490$		0			0
$491$	303947.	−	526452.i	0.0568977	−	0.0985497i	−0.836174	−	0.548465i	$-0.815212\pi$
$491$	303947.	−	526452.i	0.0568977	−	0.0985497i	0.893071	+	0.449915i	$0.148546\pi$
$492$		0			0
$493$	−304013.	−	526565.i	−0.0563345	−	0.0975742i
$494$		0			0
$495$	1.73048e6	−	4.03669e6i	0.317435	−	0.740478i
$496$		0			0
$497$	7.30289e6	+	1.26490e7i	1.32618	+	2.29702i
$498$		0			0
$499$	1.75645e6	−	3.04226e6i	0.315780	−	0.546947i	−0.663823	−	0.747890i	$-0.731067\pi$
$499$	1.75645e6	−	3.04226e6i	0.315780	−	0.546947i	0.979603	+	0.200943i	$0.0644006\pi$
$500$		0			0
$501$	−6.24370e6	+	370710.i	−1.11134	+	0.0659841i
$502$		0			0
$503$	8.23500e6			1.45125			0.725627	−	0.688088i	$-0.241550\pi$
$503$	8.23500e6			1.45125			0.725627	+	0.688088i	$0.241550\pi$
$504$		0			0
$505$	1.66451e6			0.290440
$506$		0			0
$507$	1.56397e6	−	3.12288e6i	0.270214	−	0.539554i
$508$		0			0
$509$	5.30292e6	−	9.18492e6i	0.907236	−	1.57138i	0.0893495	−	0.996000i	$-0.471521\pi$
$509$	5.30292e6	−	9.18492e6i	0.907236	−	1.57138i	0.817887	−	0.575379i	$-0.195145\pi$
$510$		0			0
$511$	7.20113e6	+	1.24727e7i	1.21997	+	2.11305i
$512$		0			0
$513$	−1.42927e6	+	257000.i	−0.239784	+	0.0431162i
$514$		0			0
$515$	5.17032e6	+	8.95525e6i	0.859012	+	1.48785i
$516$		0			0
$517$	−224769.	+	389312.i	−0.0369837	+	0.0640576i
$518$		0			0
$519$	661628.	−	1.32112e6i	0.107819	−	0.215289i
$520$		0			0
$521$	1.03709e7			1.67388			0.836939	−	0.547297i	$-0.184343\pi$
$521$	1.03709e7			1.67388			0.836939	+	0.547297i	$0.184343\pi$
$522$		0			0
$523$	−8.86641e6			−1.41740			−0.708702	−	0.705508i	$-0.750719\pi$
$523$	−8.86641e6			−1.41740			−0.708702	+	0.705508i	$0.750719\pi$
$524$		0			0
$525$	1.04426e7	−	620013.i	1.65352	−	0.0981753i
$526$		0			0
$527$	−1.23948e6	+	2.14684e6i	−0.194408	+	0.336724i
$528$		0			0
$529$	3.14354e6	+	5.44476e6i	0.488404	+	0.845941i
$530$		0			0
$531$	−3.46872e6	−	4.63746e6i	−0.533867	−	0.713746i
$532$		0			0
$533$	−3.56606e6	−	6.17660e6i	−0.543714	−	0.941740i
$534$		0			0
$535$	2.15032e6	−	3.72447e6i	0.324802	−	0.562574i
$536$		0			0
$537$	1.87759e6	+	2.84774e6i	0.280973	+	0.426152i
$538$		0			0
$539$	−7.39041e6			−1.09571
$540$		0			0
$541$	−1.22530e6			−0.179990			−0.0899949	−	0.995942i	$-0.528685\pi$
$541$	−1.22530e6			−0.179990			−0.0899949	+	0.995942i	$0.528685\pi$
$542$		0			0
$543$	−2.95615e6	−	4.48360e6i	−0.430256	−	0.652571i
$544$		0			0
$545$	−6.30107e6	+	1.09138e7i	−0.908705	+	1.57392i
$546$		0			0
$547$	1.34505e6	+	2.32969e6i	0.192207	+	0.332913i	0.945981	−	0.324221i	$-0.105102\pi$
$547$	1.34505e6	+	2.32969e6i	0.192207	+	0.332913i	−0.753774	+	0.657134i	$0.771769\pi$
$548$		0			0
$549$	9.07474e6	−	1.08141e6i	1.28500	−	0.153129i
$550$		0			0
$551$	151385.	+	262207.i	0.0212424	+	0.0367930i
$552$		0			0
$553$	7.83549e6	−	1.35715e7i	1.08957	−	1.88718i
$554$		0			0
$555$	−3.01089e6	+	178767.i	−0.414918	+	0.0246351i
$556$		0			0
$557$	−5.82722e6			−0.795835			−0.397918	−	0.917421i	$-0.630267\pi$
$557$	−5.82722e6			−0.795835			−0.397918	+	0.917421i	$0.630267\pi$
$558$		0			0
$559$	8.20312e6			1.11032
$560$		0			0
$561$	1.23759e6	−	2.47117e6i	0.166023	−	0.331509i
$562$		0			0
$563$	4.66117e6	−	8.07338e6i	0.619760	−	1.07346i	−0.369769	−	0.929124i	$-0.620563\pi$
$563$	4.66117e6	−	8.07338e6i	0.619760	−	1.07346i	0.989529	−	0.144333i	$-0.0461035\pi$
$564$		0			0
$565$	2.60707e6	+	4.51557e6i	0.343582	+	0.595102i
$566$		0			0
$567$	3.68857e6	−	1.25258e7i	0.481837	−	1.63624i
$568$		0			0
$569$	−5.38674e6	−	9.33011e6i	−0.697502	−	1.20811i	−0.969330	−	0.245763i	$-0.920961\pi$
$569$	−5.38674e6	−	9.33011e6i	−0.697502	−	1.20811i	0.271828	−	0.962346i	$-0.412372\pi$
$570$		0			0
$571$	−1.66600e6	+	2.88559e6i	−0.213838	+	0.370378i	−0.952912	−	0.303246i	$-0.901930\pi$
$571$	−1.66600e6	+	2.88559e6i	−0.213838	+	0.370378i	0.739075	+	0.673623i	$0.235263\pi$
$572$		0			0
$573$	942025.	−	1.88101e6i	0.119860	−	0.239333i
$574$		0			0
$575$	−1.17249e6			−0.147890
$576$		0			0
$577$	3.94388e6			0.493156			0.246578	−	0.969123i	$-0.420694\pi$
$577$	3.94388e6			0.493156			0.246578	+	0.969123i	$0.420694\pi$
$578$		0			0
$579$	−3.53782e6	+	210052.i	−0.438570	+	0.0260394i
$580$		0			0
$581$	−6.11284e6	+	1.05877e7i	−0.751281	+	1.30126i
$582$		0			0
$583$	−3.75246e6	−	6.49946e6i	−0.457241	−	0.791965i
$584$		0			0
$585$	−1.46120e7	+	1.74126e6i	−1.76530	+	0.210366i
$586$		0			0
$587$	−817286.	−	1.41558e6i	−0.0978991	−	0.169566i	0.812916	−	0.582381i	$-0.197879\pi$
$587$	−817286.	−	1.41558e6i	−0.0978991	−	0.169566i	−0.910815	+	0.412815i	$0.864546\pi$
$588$		0			0
$589$	617208.	−	1.06904e6i	0.0733066	−	0.126971i
$590$		0			0
$591$	3.69344e6	+	5.60185e6i	0.434973	+	0.659724i
$592$		0			0
$593$	9.45304e6			1.10391			0.551957	−	0.833873i	$-0.313881\pi$
$593$	9.45304e6			1.10391			0.551957	+	0.833873i	$0.313881\pi$
$594$		0			0
$595$	1.33614e7			1.54725
$596$		0			0
$597$	−6.17553e6	−	9.36645e6i	−0.709151	−	1.07557i
$598$		0			0
$599$	−1.03628e6	+	1.79489e6i	−0.118008	+	0.204395i	−0.918978	−	0.394309i	$-0.870984\pi$
$599$	−1.03628e6	+	1.79489e6i	−0.118008	+	0.204395i	0.800970	+	0.598704i	$0.204317\pi$
$600$		0			0
$601$	−5.30513e6	−	9.18876e6i	−0.599115	−	1.03770i	−0.992952	−	0.118517i	$-0.962186\pi$
$601$	−5.30513e6	−	9.18876e6i	−0.599115	−	1.03770i	0.393838	−	0.919180i	$-0.371147\pi$
$602$		0			0
$603$	−3.35505e6	−	4.48549e6i	−0.375756	−	0.502362i
$604$		0			0
$605$	4.23884e6	+	7.34189e6i	0.470824	+	0.815492i
$606$		0			0
$607$	3.67761e6	−	6.36980e6i	0.405129	−	0.701704i	−0.589207	−	0.807982i	$-0.700560\pi$
$607$	3.67761e6	−	6.36980e6i	0.405129	−	0.701704i	0.994336	+	0.106278i	$0.0338932\pi$
$608$		0			0
$609$	−2.71761e6	+	161354.i	−0.296923	+	0.0176293i
$610$		0			0
$611$	1.50618e6			0.163221
$612$		0			0
$613$	1.09586e7			1.17789			0.588946	−	0.808173i	$-0.299543\pi$
$613$	1.09586e7			1.17789			0.588946	+	0.808173i	$0.299543\pi$
$614$		0			0
$615$	−5.06402e6	+	1.01117e7i	−0.539893	+	1.07804i
$616$		0			0
$617$	−1.88984e6	+	3.27330e6i	−0.199854	+	0.346157i	−0.948481	−	0.316835i	$-0.897380\pi$
$617$	−1.88984e6	+	3.27330e6i	−0.199854	+	0.346157i	0.748627	+	0.662991i	$0.230713\pi$
$618$		0			0
$619$	−246460.	−	426881.i	−0.0258535	−	0.0447796i	0.852809	−	0.522223i	$-0.174897\pi$
$619$	−246460.	−	426881.i	−0.0258535	−	0.0447796i	−0.878663	+	0.477443i	$0.841564\pi$
$620$		0			0
$621$	−495902.	+	1.37694e6i	−0.0516021	+	0.143280i
$622$		0			0
$623$	1.17184e6	+	2.02968e6i	0.120961	+	0.209511i
$624$		0			0
$625$	5.01978e6	−	8.69452e6i	0.514026	−	0.890319i
$626$		0			0
$627$	−616264.	+	1.23054e6i	−0.0626034	+	0.125004i
$628$		0			0
$629$	−1.89801e6			−0.191281
$630$		0			0
$631$	1.31134e6			0.131112			0.0655558	−	0.997849i	$-0.479118\pi$
$631$	1.31134e6			0.131112			0.0655558	+	0.997849i	$0.479118\pi$
$632$		0			0
$633$	955450.	−	56728.3i	0.0947761	−	0.00562718i
$634$		0			0
$635$	−1.17570e7	+	2.03638e7i	−1.15708	+	2.00412i
$636$		0			0
$637$	1.23808e7	+	2.14442e7i	1.20893	+	2.09393i
$638$		0			0
$639$	−6.32397e6	+	1.47519e7i	−0.612685	+	1.42921i
$640$		0			0
$641$	−692306.	−	1.19911e6i	−0.0665508	−	0.115269i	0.830830	−	0.556526i	$-0.187866\pi$
$641$	−692306.	−	1.19911e6i	−0.0665508	−	0.115269i	−0.897381	+	0.441257i	$0.854533\pi$
$642$		0			0
$643$	3.97132e6	−	6.87852e6i	0.378797	−	0.656096i	−0.612090	−	0.790788i	$-0.709671\pi$
$643$	3.97132e6	−	6.87852e6i	0.378797	−	0.656096i	0.990888	+	0.134692i	$0.0430044\pi$
$644$		0			0
$645$	−7.15973e6	−	1.08592e7i	−0.677637	−	1.02777i
$646$		0			0
$647$	2.30348e6			0.216334			0.108167	−	0.994133i	$-0.465502\pi$
$647$	2.30348e6			0.216334			0.108167	+	0.994133i	$0.465502\pi$
$648$		0			0
$649$	−5.48826e6			−0.511474
$650$		0			0
$651$	6.10966e6	+	9.26655e6i	0.565021	+	0.856970i
$652$		0			0
$653$	3.96246e6	−	6.86318e6i	0.363649	−	0.629858i	−0.624910	−	0.780697i	$-0.714864\pi$
$653$	3.96246e6	−	6.86318e6i	0.363649	−	0.629858i	0.988558	+	0.150839i	$0.0481975\pi$
$654$		0			0
$655$	−1.30459e7	−	2.25962e7i	−1.18815	−	2.05794i
$656$		0			0
$657$	−6.23584e6	+	1.45463e7i	−0.563614	+	1.31474i
$658$		0			0
$659$	4.75895e6	+	8.24275e6i	0.426872	+	0.739364i	0.996593	−	0.0824739i	$-0.0262821\pi$
$659$	4.75895e6	+	8.24275e6i	0.426872	+	0.739364i	−0.569721	+	0.821838i	$0.692949\pi$
$660$		0			0
$661$	−6.42742e6	+	1.11326e7i	−0.572181	+	0.991046i	0.424161	+	0.905587i	$0.360569\pi$
$661$	−6.42742e6	+	1.11326e7i	−0.572181	+	0.991046i	−0.996342	+	0.0854592i	$0.972764\pi$
$662$		0			0
$663$	−9.24370e6	+	548830.i	−0.816699	+	0.0484902i
$664$		0			0
$665$	−6.65342e6			−0.583433
$666$		0			0
$667$	305131.			0.0265565
$668$		0			0
$669$	−4.59329e6	+	9.17172e6i	−0.396788	+	0.792293i
$670$		0			0
$671$	4.33045e6	−	7.50055e6i	0.371301	−	0.643112i
$672$		0			0
$673$	−3.27549e6	−	5.67332e6i	−0.278766	−	0.482836i	0.692313	−	0.721598i	$-0.256592\pi$
$673$	−3.27549e6	−	5.67332e6i	−0.278766	−	0.482836i	−0.971078	+	0.238762i	$0.923259\pi$
$674$		0			0
$675$	7.41890e6	+	8.78108e6i	0.626730	+	0.741803i
$676$		0			0
$677$	−4.58192e6	−	7.93613e6i	−0.384217	−	0.665483i	0.607443	−	0.794363i	$-0.292195\pi$
$677$	−4.58192e6	−	7.93613e6i	−0.384217	−	0.665483i	−0.991660	+	0.128880i	$0.958862\pi$
$678$		0			0
$679$	−9.15702e6	+	1.58604e7i	−0.762219	+	1.32020i
$680$		0			0
$681$	70741.5	−	141254.i	0.00584530	−	0.0116717i
$682$		0			0
$683$	−8.96737e6			−0.735552			−0.367776	−	0.929914i	$-0.619881\pi$
$683$	−8.96737e6			−0.735552			−0.367776	+	0.929914i	$0.619881\pi$
$684$		0			0
$685$	−1.46924e7			−1.19637
$686$		0			0
$687$	−1.90317e7	+	1.12998e6i	−1.53846	+	0.0913435i
$688$		0			0
$689$	−1.25727e7	+	2.17765e7i	−1.00897	+	1.74759i
$690$		0			0
$691$	6.85931e6	+	1.18807e7i	0.546494	+	0.946555i	0.998511	+	0.0545458i	$0.0173711\pi$
$691$	6.85931e6	+	1.18807e7i	0.546494	+	0.946555i	−0.452018	+	0.892009i	$0.649296\pi$
$692$		0			0
$693$	−7.41189e6	−	9.90923e6i	−0.586268	−	0.783803i
$694$		0			0
$695$	−8.26315e6	−	1.43122e7i	−0.648909	−	1.12394i
$696$		0			0
$697$	−3.55818e6	+	6.16294e6i	−0.277425	+	0.480514i
$698$		0			0
$699$	−9.99754e6	−	1.51633e7i	−0.773927	−	1.17382i
$700$		0			0
$701$	3.42100e6			0.262941			0.131470	−	0.991320i	$-0.458030\pi$
$701$	3.42100e6			0.262941			0.131470	+	0.991320i	$0.458030\pi$
$702$		0			0
$703$	945126.			0.0721276
$704$		0			0
$705$	−1.31461e6	−	1.99387e6i	−0.0996145	−	0.151086i
$706$		0			0
$707$	2.34490e6	−	4.06149e6i	0.176431	−	0.305588i
$708$		0			0
$709$	−6.61125e6	−	1.14510e7i	−0.493933	−	0.855516i	0.506043	−	0.862508i	$-0.331108\pi$
$709$	−6.61125e6	−	1.14510e7i	−0.493933	−	0.855516i	−0.999976	+	0.00699191i	$0.997774\pi$
$710$		0			0
$711$	1.70998e7	−	2.03773e6i	1.26858	−	0.151172i
$712$		0			0
$713$	−622020.	−	1.07737e6i	−0.0458227	−	0.0793672i
$714$		0			0
$715$	−6.97281e6	+	1.20773e7i	−0.510085	+	0.883493i
$716$		0			0
$717$	2.05331e7	−	1.21912e6i	1.49162	−	0.0885623i
$718$		0			0
$719$	6.17969e6			0.445804			0.222902	−	0.974841i	$-0.428447\pi$
$719$	6.17969e6			0.445804			0.222902	+	0.974841i	$0.428447\pi$
$720$		0			0
$721$	2.91351e7			2.08727
$722$		0			0
$723$	3.71224e6	−	7.41248e6i	0.264113	−	0.527373i
$724$		0			0
$725$	1.19836e6	−	2.07563e6i	0.0846728	−	0.146658i
$726$		0			0
$727$	−4.83384e6	−	8.37245e6i	−0.339200	−	0.587512i	0.645082	−	0.764113i	$-0.276823\pi$
$727$	−4.83384e6	−	8.37245e6i	−0.339200	−	0.587512i	−0.984282	+	0.176601i	$0.943490\pi$
$728$		0			0
$729$	1.34501e7	−	4.99861e6i	0.937360	−	0.348362i
$730$		0			0
$731$	−4.09249e6	−	7.08841e6i	−0.283266	−	0.490631i
$732$		0			0
$733$	−1.13678e7	+	1.96895e7i	−0.781475	+	1.35355i	0.149608	+	0.988745i	$0.452199\pi$
$733$	−1.13678e7	+	1.96895e7i	−0.781475	+	1.35355i	−0.931082	+	0.364809i	$0.881134\pi$
$734$		0			0
$735$	1.75815e7	−	3.51062e7i	1.20043	−	2.39699i
$736$		0			0
$737$	−5.30842e6			−0.359995
$738$		0			0
$739$	−2.13860e7			−1.44052			−0.720260	−	0.693704i	$-0.755978\pi$
$739$	−2.13860e7			−1.44052			−0.720260	+	0.693704i	$0.755978\pi$
$740$		0			0
$741$	4.60296e6	−	273293.i	0.307958	−	0.0182845i
$742$		0			0
$743$	4.30567e6	−	7.45765e6i	0.286134	−	0.495598i	−0.686750	−	0.726894i	$-0.740963\pi$
$743$	4.30567e6	−	7.45765e6i	0.286134	−	0.495598i	0.972884	+	0.231296i	$0.0742965\pi$
$744$		0			0
$745$	−1.90616e7	−	3.30156e7i	−1.25825	−	2.17936i
$746$		0			0
$747$	−1.33404e7	+	1.58973e6i	−0.874714	+	0.104237i
$748$		0			0
$749$	−6.05860e6	−	1.04938e7i	−0.394610	−	0.683484i
$750$		0			0
$751$	−3.62736e6	+	6.28277e6i	−0.234688	+	0.406491i	−0.959182	−	0.282790i	$-0.908740\pi$
$751$	−3.62736e6	+	6.28277e6i	−0.234688	+	0.406491i	0.724494	+	0.689281i	$0.242073\pi$
$752$		0			0
$753$	−4082.25	−	6191.56i	−0.000262369	−	0.000397935i
$754$		0			0
$755$	−1.64981e7			−1.05334
$756$		0			0
$757$	−3.04305e6			−0.193005			−0.0965027	−	0.995333i	$-0.530766\pi$
$757$	−3.04305e6			−0.193005			−0.0965027	+	0.995333i	$0.530766\pi$
$758$		0			0
$759$	763450.	+	1.15793e6i	0.0481034	+	0.0729586i
$760$		0			0
$761$	1.33530e7	−	2.31282e7i	0.835832	−	1.44770i	−0.0575199	−	0.998344i	$-0.518319\pi$
$761$	1.33530e7	−	2.31282e7i	0.835832	−	1.44770i	0.893352	−	0.449359i	$-0.148347\pi$
$762$		0			0
$763$	1.77535e7	+	3.07499e7i	1.10401	+	1.91220i
$764$		0			0
$765$	8.79449e6	+	1.17577e7i	0.543322	+	0.726386i
$766$		0			0
$767$	9.19425e6	+	1.59249e7i	0.564323	+	0.977437i
$768$		0			0
$769$	−2.45064e6	+	4.24463e6i	−0.149439	+	0.258836i	−0.931020	−	0.364968i	$-0.881080\pi$
$769$	−2.45064e6	+	4.24463e6i	−0.149439	+	0.258836i	0.781581	+	0.623803i	$0.214413\pi$
$770$		0			0
$771$	423363.	−	25136.5i	0.0256494	−	0.00152289i
$772$		0			0
$773$	5.22612e6			0.314579			0.157290	−	0.987552i	$-0.449724\pi$
$773$	5.22612e6			0.314579			0.157290	+	0.987552i	$0.449724\pi$
$774$		0			0
$775$	−9.77163e6			−0.584404
$776$		0			0
$777$	−3.80544e6	+	7.59858e6i	−0.226127	+	0.451523i
$778$		0			0
$779$	1.77182e6	−	3.06888e6i	0.104610	−	0.181191i
$780$		0			0
$781$	7.60532e6	+	1.31728e7i	0.446160	+	0.772771i
$782$		0			0
$783$	−1.93072e6	−	2.28521e6i	−0.112542	−	0.133206i
$784$		0			0
$785$	1.53925e7	+	2.66607e7i	0.891530	+	1.54418i
$786$		0			0
$787$	−272112.	+	471312.i	−0.0156607	+	0.0271251i	−0.873750	−	0.486376i	$-0.838318\pi$
$787$	−272112.	+	471312.i	−0.0156607	+	0.0271251i	0.858089	+	0.513501i	$0.171652\pi$
$788$		0			0
$789$	977132.	−	1.95111e6i	0.0558806	−	0.111580i
$790$		0			0
$791$	1.46910e7			0.834852
$792$		0			0
$793$	−2.90184e7			−1.63867
$794$		0			0
$795$	3.98010e7	−	2.36312e6i	2.23345	−	0.132607i
$796$		0			0
$797$	8.60486e6	−	1.49041e7i	0.479842	−	0.831110i	−0.519891	−	0.854233i	$-0.674027\pi$
$797$	8.60486e6	−	1.49041e7i	0.479842	−	0.831110i	0.999733	+	0.0231224i	$0.00736074\pi$
$798$		0			0
$799$	−751427.	−	1.30151e6i	−0.0416409	−	0.0721241i
$800$		0			0
$801$	−1.01476e6	+	2.36711e6i	−0.0558830	+	0.130358i
$802$		0			0
$803$	7.49935e6	+	1.29892e7i	0.410426	+	0.710878i
$804$		0			0
$805$	−3.35265e6	+	5.80696e6i	−0.182347	+	0.315834i
$806$		0			0
$807$	1.40587e7	+	2.13229e7i	0.759910	+	1.15256i
$808$		0			0
$809$	−9.72387e6			−0.522357			−0.261179	−	0.965290i	$-0.584111\pi$
$809$	−9.72387e6			−0.522357			−0.261179	+	0.965290i	$0.584111\pi$
$810$		0			0
$811$	−1.04900e6			−0.0560045			−0.0280023	−	0.999608i	$-0.508915\pi$
$811$	−1.04900e6			−0.0560045			−0.0280023	+	0.999608i	$0.508915\pi$
$812$		0			0
$813$	2.40937e6	+	3.65430e6i	0.127843	+	0.193900i
$814$		0			0
$815$	7.46414e6	−	1.29283e7i	0.393628	−	0.681784i
$816$		0			0
$817$	2.03788e6	+	3.52972e6i	0.106813	+	0.185006i
$818$		0			0
$819$	−1.63361e7	+	3.81071e7i	−0.851017	+	1.98516i
$820$		0			0
$821$	2.86412e6	+	4.96080e6i	0.148297	+	0.256858i	0.930598	−	0.366042i	$-0.119287\pi$
$821$	2.86412e6	+	4.96080e6i	0.148297	+	0.256858i	−0.782301	+	0.622901i	$0.785954\pi$
$822$		0			0
$823$	1.60427e7	−	2.77868e7i	0.825617	−	1.43001i	−0.0758307	−	0.997121i	$-0.524161\pi$
$823$	1.60427e7	−	2.77868e7i	0.825617	−	1.43001i	0.901447	−	0.432889i	$-0.142506\pi$
$824$		0			0
$825$	1.08751e7	−	645689.i	0.556284	−	0.0330285i
$826$		0			0
$827$	5.90474e6			0.300218			0.150109	−	0.988669i	$-0.452037\pi$
$827$	5.90474e6			0.300218			0.150109	+	0.988669i	$0.452037\pi$
$828$		0			0
$829$	−1.24236e6			−0.0627859			−0.0313929	−	0.999507i	$-0.509994\pi$
$829$	−1.24236e6			−0.0627859			−0.0313929	+	0.999507i	$0.509994\pi$
$830$		0			0
$831$	4.83607e6	−	9.65652e6i	0.242935	−	0.485085i
$832$		0			0
$833$	1.23535e7	−	2.13968e7i	0.616846	−	1.06841i
$834$		0			0
$835$	−1.57454e7	−	2.72718e7i	−0.781516	−	1.35363i
$836$		0			0
$837$	−4.13291e6	+	1.14755e7i	−0.203912	+	0.566187i
$838$		0			0
$839$	−9.84453e6	−	1.70512e7i	−0.482825	−	0.836278i	0.516980	−	0.855997i	$-0.327056\pi$
$839$	−9.84453e6	−	1.70512e7i	−0.482825	−	0.836278i	−0.999806	+	0.0197194i	$0.993723\pi$
$840$		0			0
$841$	9.94371e6	−	1.72230e7i	0.484795	−	0.839690i
$842$		0			0
$843$	−1.47237e7	+	2.93997e7i	−0.713586	+	1.42487i
$844$		0			0
$845$	1.75844e7			0.847201
$846$		0			0
$847$	2.38862e7			1.14403
$848$		0			0
$849$	−2.27610e7	+	1.35140e6i	−1.08373	+	0.0643449i
$850$		0			0
$851$	476247.	−	824885.i	0.0225428	−	0.0390454i
$852$		0			0
$853$	−1.43299e7	−	2.48201e7i	−0.674327	−	1.16797i	−0.976665	−	0.214767i	$-0.931101\pi$
$853$	−1.43299e7	−	2.48201e7i	−0.674327	−	1.16797i	0.302339	−	0.953201i	$-0.402233\pi$
$854$		0			0
$855$	−4.37927e6	−	5.85481e6i	−0.204874	−	0.273903i
$856$		0			0
$857$	−3.69269e6	−	6.39594e6i	−0.171748	−	0.297476i	0.767283	−	0.641308i	$-0.221608\pi$
$857$	−3.69269e6	−	6.39594e6i	−0.171748	−	0.297476i	−0.939031	+	0.343832i	$0.888275\pi$
$858$		0			0
$859$	3.84152e6	−	6.65370e6i	0.177631	−	0.307667i	−0.763437	−	0.645882i	$-0.776490\pi$
$859$	3.84152e6	−	6.65370e6i	0.177631	−	0.307667i	0.941069	+	0.338215i	$0.109823\pi$
$860$		0			0
$861$	1.75390e7	+	2.66015e7i	0.806301	+	1.22292i
$862$		0			0
$863$	−3.40976e7			−1.55846			−0.779232	−	0.626735i	$-0.784391\pi$
$863$	−3.40976e7			−1.55846			−0.779232	+	0.626735i	$0.784391\pi$
$864$		0			0
$865$	7.43900e6			0.338045
$866$		0			0
$867$	−7.09742e6	−	1.07647e7i	−0.320666	−	0.486355i
$868$		0			0
$869$	8.15998e6	−	1.41335e7i	0.366556	−	0.634893i
$870$		0			0
$871$	8.89296e6	+	1.54031e7i	0.397193	+	0.687958i
$872$		0			0
$873$	−1.99838e7	+	2.38141e6i	−0.887448	+	0.105754i
$874$		0			0
$875$	−783325.	−	1.35676e6i	−0.0345877	−	0.0599077i
$876$		0			0
$877$	631848.	−	1.09439e6i	0.0277405	−	0.0480479i	−0.851822	−	0.523832i	$-0.824502\pi$
$877$	631848.	−	1.09439e6i	0.0277405	−	0.0480479i	0.879562	+	0.475784i	$0.157835\pi$
$878$		0			0
$879$	3.97570e7	−	2.36051e6i	1.73557	−	0.103047i
$880$		0			0
$881$	1.89395e7			0.822108			0.411054	−	0.911611i	$-0.365161\pi$
$881$	1.89395e7			0.822108			0.411054	+	0.911611i	$0.365161\pi$
$882$		0			0
$883$	−3.16414e7			−1.36570			−0.682848	−	0.730560i	$-0.739259\pi$
$883$	−3.16414e7			−1.36570			−0.682848	+	0.730560i	$0.739259\pi$
$884$		0			0
$885$	1.30564e7	−	2.60706e7i	0.560357	−	1.11890i
$886$		0			0
$887$	1.39213e7	−	2.41124e7i	0.594116	−	1.02904i	−0.399555	−	0.916709i	$-0.630835\pi$
$887$	1.39213e7	−	2.41124e7i	0.594116	−	1.02904i	0.993671	−	0.112330i	$-0.0358314\pi$
$888$		0			0
$889$	3.31258e7	+	5.73756e7i	1.40576	+	2.43485i
$890$		0			0
$891$	3.84132e6	−	1.30445e7i	0.162101	−	0.550469i
$892$		0			0
$893$	374178.	+	648096.i	0.0157018	+	0.0271963i
$894$		0			0
$895$	−8.58678e6	+	1.48727e7i	−0.358321	+	0.620631i
$896$		0			0
$897$	2.08090e6	−	4.15508e6i	0.0863516	−	0.172424i
$898$		0			0
$899$	2.54300e6			0.104941
$900$		0			0
$901$	2.50898e7			1.02964
$902$		0			0
$903$	−3.65834e7	+	2.17208e6i	−1.49302	+	0.0886454i
$904$		0			0
$905$	1.35194e7	−	2.34163e7i	0.548701	−	0.950377i
$906$		0			0
$907$	−4.48735e6	−	7.77232e6i	−0.181122	−	0.313713i	0.761141	−	0.648587i	$-0.224640\pi$
$907$	−4.48735e6	−	7.77232e6i	−0.181122	−	0.313713i	−0.942263	+	0.334874i	$0.891306\pi$
$908$		0			0
$909$	5.11740e6	−	609824.i	0.205418	−	0.0244791i
$910$		0			0
$911$	−4.43865e6	−	7.68797e6i	−0.177196	−	0.306913i	0.763723	−	0.645544i	$-0.223369\pi$
$911$	−4.43865e6	−	7.68797e6i	−0.177196	−	0.306913i	−0.940919	+	0.338631i	$0.890036\pi$
$912$		0			0
$913$	−6.36599e6	+	1.10262e7i	−0.252749	+	0.437773i
$914$		0			0
$915$	2.53274e7	+	3.84142e7i	1.00009	+	1.51684i
$916$		0			0
$917$	−7.35146e7			−2.88702
$918$		0			0
$919$	1.48072e7			0.578343			0.289172	−	0.957277i	$-0.406620\pi$
$919$	1.48072e7			0.578343			0.289172	+	0.957277i	$0.406620\pi$
$920$		0			0
$921$	1.84468e7	+	2.79784e7i	0.716594	+	1.08686i
$922$		0			0
$923$	2.54818e7	−	4.41357e7i	0.984521	−	1.70524i
$924$		0			0
$925$	−3.74081e6	−	6.47927e6i	−0.143751	−	0.248984i
$926$		0			0
$927$	1.91767e7	+	2.56380e7i	0.732949	+	0.979906i
$928$		0			0
$929$	7.13029e6	+	1.23500e7i	0.271062	+	0.469492i	0.969134	−	0.246535i	$-0.0792920\pi$
$929$	7.13029e6	+	1.23500e7i	0.271062	+	0.469492i	−0.698072	+	0.716027i	$0.745959\pi$
$930$		0			0
$931$	−6.15149e6	+	1.06547e7i	−0.232598	+	0.402872i
$932$		0			0
$933$	−5.72054e6	+	339648.i	−0.215146	+	0.0127739i
$934$		0			0
$935$	1.39148e7			0.520532
$936$		0			0
$937$	−3.54753e7			−1.32001			−0.660006	−	0.751261i	$-0.729446\pi$
$937$	−3.54753e7			−1.32001			−0.660006	+	0.751261i	$0.729446\pi$
$938$		0			0
$939$	1.27562e6	−	2.54712e6i	0.0472126	−	0.0942726i
$940$		0			0
$941$	−1.30008e7	+	2.25180e7i	−0.478624	+	0.829001i	−0.999700	−	0.0245095i	$-0.992198\pi$
$941$	−1.30008e7	+	2.25180e7i	−0.478624	+	0.829001i	0.521076	+	0.853511i	$0.325531\pi$
$942$		0			0
$943$	−1.78563e6	−	3.09280e6i	−0.0653902	−	0.113259i
$944$		0			0
$945$	6.47039e7	−	1.16346e7i	2.35695	−	0.423809i
$946$		0			0
$947$	1.11889e7	+	1.93797e7i	0.405426	+	0.702218i	0.994371	−	0.105955i	$-0.0337899\pi$
$947$	1.11889e7	+	1.93797e7i	0.405426	+	0.702218i	−0.588945	+	0.808173i	$0.700457\pi$
$948$		0			0
$949$	2.51267e7	−	4.35207e7i	0.905669	−	1.56866i
$950$		0			0
$951$	6.03779e6	−	1.20561e7i	0.216485	−	0.432269i
$952$		0			0
$953$	−4.62557e7			−1.64981			−0.824903	−	0.565275i	$-0.808770\pi$
$953$	−4.62557e7			−1.64981			−0.824903	+	0.565275i	$0.808770\pi$
$954$		0			0
$955$	1.05916e7			0.375798
$956$		0			0
$957$	−2.83016e6	+	168036.i	−0.0998920	+	0.00593092i
$958$		0			0
$959$	−2.06982e7	+	3.58503e7i	−0.726750	+	1.25877i
$960$		0			0
$961$	9.13059e6	+	1.58146e7i	0.318926	+	0.552396i
$962$		0			0
$963$	5.24647e6	−	1.22384e7i	0.182306	−	0.425264i
$964$		0			0
$965$	−8.92170e6	−	1.54528e7i	−0.308411	−	0.534183i
$966$		0			0
$967$	−2.04313e7	+	3.53880e7i	−0.702634	+	1.21700i	0.264905	+	0.964274i	$0.414659\pi$
$967$	−2.04313e7	+	3.53880e7i	−0.702634	+	1.21700i	−0.967539	+	0.252723i	$0.918674\pi$
$968$		0			0
$969$	−2.53255e6	−	3.84112e6i	−0.0866460	−	0.131416i
$970$		0			0
$971$	3.69663e7			1.25822			0.629112	−	0.777315i	$-0.283419\pi$
$971$	3.69663e7			1.25822			0.629112	+	0.777315i	$0.283419\pi$
$972$		0			0
$973$	−4.65634e7			−1.57675
$974$		0			0
$975$	−2.00921e7	−	3.04737e7i	−0.676882	−	1.02663i
$976$		0			0
$977$	2.95829e7	−	5.12390e7i	0.991525	−	1.71737i	0.383253	−	0.923643i	$-0.374804\pi$
$977$	2.95829e7	−	5.12390e7i	0.991525	−	1.71737i	0.608272	−	0.793729i	$-0.291863\pi$
$978$		0			0
$979$	1.22036e6	+	2.11373e6i	0.0406942	+	0.0704845i
$980$		0			0
$981$	−1.53737e7	+	3.58620e7i	−0.510041	+	1.18977i
$982$		0			0
$983$	−9.12629e6	−	1.58072e7i	−0.301238	−	0.521760i	0.675178	−	0.737655i	$-0.264067\pi$
$983$	−9.12629e6	−	1.58072e7i	−0.301238	−	0.521760i	−0.976417	+	0.215894i	$0.930733\pi$
$984$		0			0
$985$	−1.68912e7	+	2.92564e7i	−0.554715	+	0.960795i
$986$		0			0
$987$	−6.71712e6	+	398818.i	−0.219477	+	0.0130311i
$988$		0			0
$989$	4.10755e6			0.133534
$990$		0			0
$991$	−4.10661e7			−1.32831			−0.664154	−	0.747596i	$-0.731208\pi$
$991$	−4.10661e7			−1.32831			−0.664154	+	0.747596i	$0.731208\pi$
$992$		0			0
$993$	2.09244e7	−	4.17812e7i	0.673411	−	1.34465i
$994$		0			0
$995$	2.82426e7	−	4.89176e7i	0.904372	−	1.56642i
$996$		0			0
$997$	−9.35086e6	−	1.61962e7i	−0.297930	−	0.516029i	0.677732	−	0.735309i	$-0.262963\pi$
$997$	−9.35086e6	−	1.61962e7i	−0.297930	−	0.516029i	−0.975662	+	0.219279i	$0.929629\pi$
$998$		0			0
$999$	−9.19126e6	+	1.65270e6i	−0.291381	+	0.0523939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.6.i.b.49.3		6
3.2	odd	2		432.6.i.b.145.3		6
4.3	odd	2		18.6.c.b.13.1	yes	6
9.2	odd	6		432.6.i.b.289.3		6
9.7	even	3	inner	144.6.i.b.97.3		6
12.11	even	2		54.6.c.b.37.3		6
36.7	odd	6		18.6.c.b.7.1	✓	6
36.11	even	6		54.6.c.b.19.3		6
36.23	even	6		162.6.a.i.1.1		3
36.31	odd	6		162.6.a.j.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.b.7.1	✓	6	36.7	odd	6
18.6.c.b.13.1	yes	6	4.3	odd	2
54.6.c.b.19.3		6	36.11	even	6
54.6.c.b.37.3		6	12.11	even	2
144.6.i.b.49.3		6	1.1	even	1	trivial
144.6.i.b.97.3		6	9.7	even	3	inner
162.6.a.i.1.1		3	36.23	even	6
162.6.a.j.1.3		3	36.31	odd	6
432.6.i.b.145.3		6	3.2	odd	2
432.6.i.b.289.3		6	9.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.58066 + 13.0143i) q^{3} +(-39.2420 + 67.9691i) q^{5} +(110.566 + 191.505i) q^{7} +(-95.7446 + 223.343i) q^{9} +O(q^{10})\)	\(q+(8.58066 + 13.0143i) q^{3} +(-39.2420 + 67.9691i) q^{5} +(110.566 + 191.505i) q^{7} +(-95.7446 + 223.343i) q^{9} +(115.144 + 199.436i) q^{11} +(385.793 - 668.213i) q^{13} +(-1221.29 + 72.5123i) q^{15} -769.880 q^{17} +383.367 q^{19} +(-1543.58 + 3082.17i) q^{21} +(193.178 - 334.594i) q^{23} +(-1517.37 - 2628.15i) q^{25} +(-3728.20 + 670.377i) q^{27} +(394.883 + 683.958i) q^{29} +(1609.97 - 2788.54i) q^{31} +(-1607.51 + 3209.82i) q^{33} -17355.2 q^{35} +2465.33 q^{37} +(12006.7 - 712.877i) q^{39} +(4621.73 - 8005.07i) q^{41} +(5315.76 + 9207.16i) q^{43} +(-11423.2 - 15272.1i) q^{45} +(976.032 + 1690.54i) q^{47} +(-16046.0 + 27792.4i) q^{49} +(-6606.08 - 10019.5i) q^{51} -32589.2 q^{53} -18074.0 q^{55} +(3289.54 + 4989.25i) q^{57} +(-11916.1 + 20639.2i) q^{59} +(-18804.4 - 32570.2i) q^{61} +(-53357.3 + 6358.42i) q^{63} +(30278.5 + 52444.0i) q^{65} +(-11525.6 + 19962.9i) q^{67} +(6012.10 - 356.959i) q^{69} +66050.4 q^{71} +65130.0 q^{73} +(21183.6 - 42298.8i) q^{75} +(-25462.0 + 44101.5i) q^{77} +(-35433.7 - 61373.0i) q^{79} +(-40714.9 - 42767.7i) q^{81} +(27643.5 + 47880.0i) q^{83} +(30211.6 - 52328.0i) q^{85} +(-5512.88 + 11007.9i) q^{87} +10598.6 q^{89} +170622. q^{91} +(50105.6 - 2974.94i) q^{93} +(-15044.1 + 26057.1i) q^{95} +(41409.9 + 71724.1i) q^{97} +(-55567.0 + 6621.74i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9}+O(q^{10}) \) 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9	\( 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9} + 315 q^{11} - 744 q^{13} - 2286 q^{15} + 2898 q^{17} - 2262 q^{19} - 11076 q^{21} + 3168 q^{23} - 2883 q^{25} - 18144 q^{27} - 5148 q^{29} + 8610 q^{31} + 17469 q^{33} - 2700 q^{35} + 39936 q^{37} + 49026 q^{39} + 5049 q^{41} + 31389 q^{43} + 2538 q^{45} - 12924 q^{47} - 52857 q^{49} - 36837 q^{51} - 96048 q^{53} - 126252 q^{55} - 17469 q^{57} - 62955 q^{59} - 75966 q^{61} - 49578 q^{63} + 108702 q^{65} + 32991 q^{67} - 29250 q^{69} + 129672 q^{71} - 8466 q^{73} + 105483 q^{75} + 88740 q^{77} - 89202 q^{79} + 123435 q^{81} - 32634 q^{83} + 71388 q^{85} + 151524 q^{87} + 66132 q^{89} + 301836 q^{91} + 57678 q^{93} + 82944 q^{95} + 46245 q^{97} - 282168 q^{99}+O(q^{100}) \) 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9 + 315 * q^11 - 744 * q^13 - 2286 * q^15 + 2898 * q^17 - 2262 * q^19 - 11076 * q^21 + 3168 * q^23 - 2883 * q^25 - 18144 * q^27 - 5148 * q^29 + 8610 * q^31 + 17469 * q^33 - 2700 * q^35 + 39936 * q^37 + 49026 * q^39 + 5049 * q^41 + 31389 * q^43 + 2538 * q^45 - 12924 * q^47 - 52857 * q^49 - 36837 * q^51 - 96048 * q^53 - 126252 * q^55 - 17469 * q^57 - 62955 * q^59 - 75966 * q^61 - 49578 * q^63 + 108702 * q^65 + 32991 * q^67 - 29250 * q^69 + 129672 * q^71 - 8466 * q^73 + 105483 * q^75 + 88740 * q^77 - 89202 * q^79 + 123435 * q^81 - 32634 * q^83 + 71388 * q^85 + 151524 * q^87 + 66132 * q^89 + 301836 * q^91 + 57678 * q^93 + 82944 * q^95 + 46245 * q^97 - 282168 * q^99

Introduction

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