LMFDB - Embedded newform 336.7.bh.h.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,7,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, 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:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.h.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 - 7.79423i) q^{3} +(-126.269 - 72.9015i) q^{5} +(-114.286 - 323.400i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 - 7.79423i) q^{3} +(-126.269 - 72.9015i) q^{5} +(-114.286 - 323.400i) q^{7} +(121.500 - 210.444i) q^{9} +(-1040.12 - 1801.54i) q^{11} -2134.45i q^{13} -2272.84 q^{15} +(2554.60 - 1474.90i) q^{17} +(-3678.74 - 2123.92i) q^{19} +(-4063.52 - 3475.13i) q^{21} +(1812.04 - 3138.54i) q^{23} +(2816.76 + 4878.77i) q^{25} -3788.00i q^{27} -257.072 q^{29} +(40538.8 - 23405.1i) q^{31} +(-28083.3 - 16213.9i) q^{33} +(-9145.56 + 49167.1i) q^{35} +(-36830.7 + 63792.7i) q^{37} +(-16636.4 - 28815.0i) q^{39} -89800.2i q^{41} +1885.78 q^{43} +(-30683.4 + 17715.1i) q^{45} +(69207.5 + 39957.0i) q^{47} +(-91526.4 + 73920.3i) q^{49} +(22991.4 - 39822.3i) q^{51} +(-32970.0 - 57105.7i) q^{53} +303306. i q^{55} -66217.4 q^{57} +(-130044. + 75081.2i) q^{59} +(-173828. - 100359. i) q^{61} +(-81943.4 - 15242.3i) q^{63} +(-155604. + 269515. i) q^{65} +(228278. + 395389. i) q^{67} -56493.8i q^{69} +365090. q^{71} +(-236879. + 136762. i) q^{73} +(76052.5 + 43908.9i) q^{75} +(-463748. + 542267. i) q^{77} +(306802. - 531397. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -490649. i q^{83} -430090. q^{85} +(-3470.47 + 2003.68i) q^{87} +(-617623. - 356585. i) q^{89} +(-690280. + 243937. i) q^{91} +(364849. - 631937. i) q^{93} +(309674. + 536372. i) q^{95} +294637. i q^{97} -505499. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) $ 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9	$ 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9} + 1190 q^{11} - 2268 q^{15} - 1500 q^{17} + 13446 q^{19} - 2106 q^{21} - 21504 q^{23} + 22542 q^{25} - 85484 q^{29} - 6264 q^{31} + 32130 q^{33} - 32268 q^{35} - 46938 q^{37} + 17010 q^{39} + 19548 q^{43} - 30618 q^{45} + 167004 q^{47} + 250644 q^{49} - 13500 q^{51} - 258982 q^{53} + 242028 q^{57} - 744834 q^{59} - 390096 q^{61} - 59778 q^{63} - 19388 q^{65} - 62742 q^{67} + 1102984 q^{71} - 663534 q^{73} + 608634 q^{75} + 404298 q^{77} + 271032 q^{79} - 708588 q^{81} + 2540040 q^{85} - 1154034 q^{87} - 433740 q^{89} + 2142270 q^{91} - 56376 q^{93} - 2205360 q^{95} + 578340 q^{99}+O(q^{100}) $ 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9 + 1190 * q^11 - 2268 * q^15 - 1500 * q^17 + 13446 * q^19 - 2106 * q^21 - 21504 * q^23 + 22542 * q^25 - 85484 * q^29 - 6264 * q^31 + 32130 * q^33 - 32268 * q^35 - 46938 * q^37 + 17010 * q^39 + 19548 * q^43 - 30618 * q^45 + 167004 * q^47 + 250644 * q^49 - 13500 * q^51 - 258982 * q^53 + 242028 * q^57 - 744834 * q^59 - 390096 * q^61 - 59778 * q^63 - 19388 * q^65 - 62742 * q^67 + 1102984 * q^71 - 663534 * q^73 + 608634 * q^75 + 404298 * q^77 + 271032 * q^79 - 708588 * q^81 + 2540040 * q^85 - 1154034 * q^87 - 433740 * q^89 + 2142270 * q^91 - 56376 * q^93 - 2205360 * q^95 + 578340 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$4$		0			0
$5$	−126.269	−	72.9015i	−1.01015	−	0.583212i	−0.0989165	−	0.995096i	$-0.531538\pi$
$5$	−126.269	−	72.9015i	−1.01015	−	0.583212i	−0.911236	+	0.411884i	$0.864871\pi$
$6$		0			0
$7$	−114.286	−	323.400i	−0.333196	−	0.942858i
$7$	−114.286	−	323.400i	−0.333196	−	0.942858i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	−1040.12	−	1801.54i	−0.781459	−	1.35353i	−0.931092	−	0.364785i	$-0.881143\pi$
$11$	−1040.12	−	1801.54i	−0.781459	−	1.35353i	0.149633	−	0.988742i	$-0.452191\pi$
$12$		0			0
$13$		−	2134.45i		−	0.971527i	−0.874090	−	0.485764i	$-0.838542\pi$
$13$		−	2134.45i		−	0.971527i	0.874090	−	0.485764i	$-0.161458\pi$
$14$		0			0
$15$	−2272.84			−0.673435
$16$		0			0
$17$	2554.60	−	1474.90i	0.519968	−	0.300204i	−0.216953	−	0.976182i	$-0.569612\pi$
$17$	2554.60	−	1474.90i	0.519968	−	0.300204i	0.736922	+	0.675978i	$0.236279\pi$
$18$		0			0
$19$	−3678.74	−	2123.92i	−0.536338	−	0.309655i	0.207255	−	0.978287i	$-0.433547\pi$
$19$	−3678.74	−	2123.92i	−0.536338	−	0.309655i	−0.743594	+	0.668632i	$0.766880\pi$
$20$		0			0
$21$	−4063.52	−	3475.13i	−0.438777	−	0.375244i
$22$		0			0
$23$	1812.04	−	3138.54i	0.148931	−	0.257955i	−0.781902	−	0.623401i	$-0.785750\pi$
$23$	1812.04	−	3138.54i	0.148931	−	0.257955i	0.930832	+	0.365446i	$0.119084\pi$
$24$		0			0
$25$	2816.76	+	4878.77i	0.180273	+	0.312241i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	−257.072			−0.0105405			−0.00527025	−	0.999986i	$-0.501678\pi$
$29$	−257.072			−0.0105405			−0.00527025	+	0.999986i	$0.501678\pi$
$30$		0			0
$31$	40538.8	−	23405.1i	1.36077	−	0.785642i	0.371046	−	0.928614i	$-0.378999\pi$
$31$	40538.8	−	23405.1i	1.36077	−	0.785642i	0.989727	+	0.142972i	$0.0456659\pi$
$32$		0			0
$33$	−28083.3	−	16213.9i	−0.781459	−	0.451176i
$34$		0			0
$35$	−9145.56	+	49167.1i	−0.213308	+	1.14675i
$36$		0			0
$37$	−36830.7	+	63792.7i	−0.727118	+	1.25941i	0.230978	+	0.972959i	$0.425808\pi$
$37$	−36830.7	+	63792.7i	−0.727118	+	1.25941i	−0.958096	+	0.286447i	$0.907526\pi$
$38$		0			0
$39$	−16636.4	−	28815.0i	−0.280456	−	0.485764i
$40$		0			0
$41$		−	89800.2i		−	1.30294i	−0.758673	−	0.651472i	$-0.774152\pi$
$41$		−	89800.2i		−	1.30294i	0.758673	−	0.651472i	$-0.225848\pi$
$42$		0			0
$43$	1885.78			0.0237184			0.0118592	−	0.999930i	$-0.496225\pi$
$43$	1885.78			0.0237184			0.0118592	+	0.999930i	$0.496225\pi$
$44$		0			0
$45$	−30683.4	+	17715.1i	−0.336718	+	0.194404i
$46$		0			0
$47$	69207.5	+	39957.0i	0.666591	+	0.384857i	0.794784	−	0.606893i	$-0.207584\pi$
$47$	69207.5	+	39957.0i	0.666591	+	0.384857i	−0.128192	+	0.991749i	$0.540918\pi$
$48$		0			0
$49$	−91526.4	+	73920.3i	−0.777961	+	0.628312i
$50$		0			0
$51$	22991.4	−	39822.3i	0.173323	−	0.300204i
$52$		0			0
$53$	−32970.0	−	57105.7i	−0.221458	−	0.383576i	0.733793	−	0.679373i	$-0.237748\pi$
$53$	−32970.0	−	57105.7i	−0.221458	−	0.383576i	−0.955251	+	0.295797i	$0.904415\pi$
$54$		0			0
$55$			303306.i			1.82303i
$56$		0			0
$57$	−66217.4			−0.357559
$58$		0			0
$59$	−130044.	+	75081.2i	−0.633193	+	0.365574i	−0.781987	−	0.623294i	$-0.785794\pi$
$59$	−130044.	+	75081.2i	−0.633193	+	0.365574i	0.148795	+	0.988868i	$0.452461\pi$
$60$		0			0
$61$	−173828.	−	100359.i	−0.765825	−	0.442149i	0.0655584	−	0.997849i	$-0.479117\pi$
$61$	−173828.	−	100359.i	−0.765825	−	0.442149i	−0.831383	+	0.555700i	$0.812450\pi$
$62$		0			0
$63$	−81943.4	−	15242.3i	−0.327712	−	0.0609577i
$64$		0			0
$65$	−155604.	+	269515.i	−0.566607	+	0.981391i
$66$		0			0
$67$	228278.	+	395389.i	0.758997	+	1.31462i	0.943363	+	0.331763i	$0.107644\pi$
$67$	228278.	+	395389.i	0.758997	+	1.31462i	−0.184366	+	0.982858i	$0.559023\pi$
$68$		0			0
$69$		−	56493.8i		−	0.171970i
$70$		0			0
$71$	365090.			1.02006			0.510029	−	0.860157i	$-0.329635\pi$
$71$	365090.			1.02006			0.510029	+	0.860157i	$0.329635\pi$
$72$		0			0
$73$	−236879.	+	136762.i	−0.608916	+	0.351558i	−0.772541	−	0.634965i	$-0.781015\pi$
$73$	−236879.	+	136762.i	−0.608916	+	0.351558i	0.163625	+	0.986523i	$0.447681\pi$
$74$		0			0
$75$	76052.5	+	43908.9i	0.180273	+	0.104080i
$76$		0			0
$77$	−463748.	+	542267.i	−1.01580	+	1.18779i
$78$		0			0
$79$	306802.	−	531397.i	0.622267	−	1.07780i	−0.366795	−	0.930302i	$-0.619545\pi$
$79$	306802.	−	531397.i	0.622267	−	1.07780i	0.989062	−	0.147497i	$-0.0471217\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	490649.i		−	0.858098i	−0.903281	−	0.429049i	$-0.858849\pi$
$83$		−	490649.i		−	0.858098i	0.903281	−	0.429049i	$-0.141151\pi$
$84$		0			0
$85$	−430090.			−0.700330
$86$		0			0
$87$	−3470.47	+	2003.68i	−0.00527025	+	0.00304278i
$88$		0			0
$89$	−617623.	−	356585.i	−0.876100	−	0.505816i	−0.00672936	−	0.999977i	$-0.502142\pi$
$89$	−617623.	−	356585.i	−0.876100	−	0.505816i	−0.869370	+	0.494161i	$0.835475\pi$
$90$		0			0
$91$	−690280.	+	243937.i	−0.916012	+	0.323709i
$92$		0			0
$93$	364849.	−	631937.i	0.453591	−	0.785642i
$94$		0			0
$95$	309674.	+	536372.i	0.361189	+	0.625598i
$96$		0			0
$97$			294637.i			0.322829i	0.986887	+	0.161415i	$0.0516056\pi$
$97$			294637.i			0.322829i	−0.986887	+	0.161415i	$0.948394\pi$
$98$		0			0
$99$	−505499.			−0.520973
$100$		0			0
$101$	1.65042e6	−	952870.i	1.60188	−	0.924846i	0.610769	−	0.791809i	$-0.290860\pi$
$101$	1.65042e6	−	952870.i	1.60188	−	0.924846i	0.991111	−	0.133037i	$-0.0424730\pi$
$102$		0			0
$103$	479472.	+	276823.i	0.438785	+	0.253333i	0.703082	−	0.711109i	$-0.251807\pi$
$103$	479472.	+	276823.i	0.438785	+	0.253333i	−0.264297	+	0.964441i	$0.585140\pi$
$104$		0			0
$105$	259754.	+	735038.i	0.224386	+	0.634954i
$106$		0			0
$107$	−325821.	+	564339.i	−0.265967	+	0.460669i	−0.967817	−	0.251657i	$-0.919025\pi$
$107$	−325821.	+	564339.i	−0.265967	+	0.460669i	0.701849	+	0.712325i	$0.252358\pi$
$108$		0			0
$109$	263320.	+	456083.i	0.203331	+	0.352180i	0.949600	−	0.313465i	$-0.101490\pi$
$109$	263320.	+	456083.i	0.203331	+	0.352180i	−0.746269	+	0.665645i	$0.768157\pi$
$110$		0			0
$111$			1.14827e6i			0.839604i
$112$		0			0
$113$	−802443.			−0.556133			−0.278067	−	0.960562i	$-0.589694\pi$
$113$	−802443.			−0.556133			−0.278067	+	0.960562i	$0.589694\pi$
$114$		0			0
$115$	−457609.	+	264201.i	−0.300885	+	0.173716i
$116$		0			0
$117$	−449182.	−	259335.i	−0.280456	−	0.161921i
$118$		0			0
$119$	−768939.	−	657599.i	−0.456300	−	0.390229i
$120$		0			0
$121$	−1.27793e6	+	2.21343e6i	−0.721356	+	1.24943i
$122$		0			0
$123$	−699923.	−	1.21230e6i	−0.376127	−	0.651472i
$124$		0			0
$125$			1.45679e6i			0.745876i
$126$		0			0
$127$	2.86800e6			1.40013			0.700064	−	0.714080i	$-0.253155\pi$
$127$	2.86800e6			1.40013			0.700064	+	0.714080i	$0.253155\pi$
$128$		0			0
$129$	25458.0	−	14698.2i	0.0118592	−	0.00684691i
$130$		0			0
$131$	−1.14686e6	−	662137.i	−0.510147	−	0.294533i	0.222747	−	0.974876i	$-0.428497\pi$
$131$	−1.14686e6	−	662137.i	−0.510147	−	0.294533i	−0.732894	+	0.680343i	$0.761831\pi$
$132$		0			0
$133$	−266448.	+	1.43244e6i	−0.113255	+	0.608866i
$134$		0			0
$135$	−276151.	+	478307.i	−0.112239	+	0.194404i
$136$		0			0
$137$	−563722.	−	976396.i	−0.219232	−	0.379721i	0.735342	−	0.677697i	$-0.237022\pi$
$137$	−563722.	−	976396.i	−0.219232	−	0.379721i	−0.954573	+	0.297976i	$0.903688\pi$
$138$		0			0
$139$			5.26387e6i			1.96002i	0.198946	+	0.980010i	$0.436248\pi$
$139$			5.26387e6i			1.96002i	−0.198946	+	0.980010i	$0.563752\pi$
$140$		0			0
$141$	1.24574e6			0.444394
$142$		0			0
$143$	−3.84530e6	+	2.22008e6i	−1.31499	+	0.759209i
$144$		0			0
$145$	32460.3	+	18740.9i	0.0106475	+	0.00614734i
$146$		0			0
$147$	−659455.	+	1.71130e6i	−0.207603	+	0.538734i
$148$		0			0
$149$	−280725.	+	486231.i	−0.0848639	+	0.146989i	−0.905333	−	0.424702i	$-0.860379\pi$
$149$	−280725.	+	486231.i	−0.0848639	+	0.146989i	0.820469	+	0.571691i	$0.193712\pi$
$150$		0			0
$151$	−2.97680e6	−	5.15598e6i	−0.864608	−	1.49755i	−0.867436	−	0.497550i	$-0.834233\pi$
$151$	−2.97680e6	−	5.15598e6i	−0.864608	−	1.49755i	0.00282714	−	0.999996i	$-0.499100\pi$
$152$		0			0
$153$		−	716802.i		−	0.200136i
$154$		0			0
$155$	−6.82506e6			−1.83278
$156$		0			0
$157$	−4.43609e6	+	2.56118e6i	−1.14631	+	0.661822i	−0.947985	−	0.318314i	$-0.896883\pi$
$157$	−4.43609e6	+	2.56118e6i	−1.14631	+	0.661822i	−0.198324	+	0.980136i	$0.563550\pi$
$158$		0			0
$159$	−890189.	−	513951.i	−0.221458	−	0.127859i
$160$		0			0
$161$	−1.22210e6	−	227322.i	−0.292838	−	0.0544708i
$162$		0			0
$163$	−1.37693e6	+	2.38491e6i	−0.317943	+	0.550693i	−0.980059	−	0.198709i	$-0.936325\pi$
$163$	−1.37693e6	+	2.38491e6i	−0.317943	+	0.550693i	0.662116	+	0.749401i	$0.269659\pi$
$164$		0			0
$165$	2.36403e6	+	4.09463e6i	0.526262	+	0.911513i
$166$		0			0
$167$			2.61488e6i			0.561439i	0.959790	+	0.280719i	$0.0905730\pi$
$167$			2.61488e6i			0.561439i	−0.959790	+	0.280719i	$0.909427\pi$
$168$		0			0
$169$	270950.			0.0561344
$170$		0			0
$171$	−893935.	+	516113.i	−0.178779	+	0.103218i
$172$		0			0
$173$	8.15365e6	+	4.70751e6i	1.57476	+	0.909186i	0.995573	+	0.0939893i	$0.0299619\pi$
$173$	8.15365e6	+	4.70751e6i	1.57476	+	0.909186i	0.579184	+	0.815197i	$0.303371\pi$
$174$		0			0
$175$	1.25588e6	−	1.46852e6i	0.234333	−	0.274009i
$176$		0			0
$177$	−1.17040e6	+	2.02719e6i	−0.211064	+	0.365574i
$178$		0			0
$179$	−2.13922e6	−	3.70524e6i	−0.372990	−	0.646037i	0.617034	−	0.786936i	$-0.288334\pi$
$179$	−2.13922e6	−	3.70524e6i	−0.372990	−	0.646037i	−0.990024	+	0.140899i	$0.955001\pi$
$180$		0			0
$181$			3.41324e6i			0.575614i	0.957688	+	0.287807i	$0.0929262\pi$
$181$			3.41324e6i			0.575614i	−0.957688	+	0.287807i	$0.907074\pi$
$182$		0			0
$183$	−3.12890e6			−0.510550
$184$		0			0
$185$	9.30117e6	−	5.37003e6i	1.46900	−	0.848128i
$186$		0			0
$187$	−5.31420e6	−	3.06815e6i	−0.812667	−	0.469194i
$188$		0			0
$189$	−1.22504e6	+	432915.i	−0.181453	+	0.0641235i
$190$		0			0
$191$	−5.32211e6	+	9.21816e6i	−0.763807	+	1.32295i	0.177068	+	0.984199i	$0.443339\pi$
$191$	−5.32211e6	+	9.21816e6i	−0.763807	+	1.32295i	−0.940875	+	0.338754i	$0.889995\pi$
$192$		0			0
$193$	−4.36347e6	−	7.55775e6i	−0.606960	−	1.05128i	−0.991739	−	0.128276i	$-0.959056\pi$
$193$	−4.36347e6	−	7.55775e6i	−0.606960	−	1.05128i	0.384779	−	0.923009i	$-0.374278\pi$
$194$		0			0
$195$			4.85126e6i			0.654261i
$196$		0			0
$197$	−9.33901e6			−1.22152			−0.610762	−	0.791814i	$-0.709137\pi$
$197$	−9.33901e6			−1.22152			−0.610762	+	0.791814i	$0.709137\pi$
$198$		0			0
$199$	4.71042e6	−	2.71956e6i	0.597724	−	0.345096i	−0.170422	−	0.985371i	$-0.554513\pi$
$199$	4.71042e6	−	2.71956e6i	0.597724	−	0.345096i	0.768145	+	0.640275i	$0.221180\pi$
$200$		0			0
$201$	6.16351e6	+	3.55850e6i	0.758997	+	0.438207i
$202$		0			0
$203$	29379.8	+	83137.2i	0.00351204	+	0.00993818i
$204$		0			0
$205$	−6.54657e6	+	1.13390e7i	−0.759892	+	1.31617i
$206$		0			0
$207$	−440325.	−	762666.i	−0.0496435	−	0.0859851i
$208$		0			0
$209$			8.83656e6i			0.967931i
$210$		0			0
$211$	1.46831e7			1.56304			0.781519	−	0.623881i	$-0.214445\pi$
$211$	1.46831e7			1.56304			0.781519	+	0.623881i	$0.214445\pi$
$212$		0			0
$213$	4.92872e6	−	2.84560e6i	0.510029	−	0.294466i
$214$		0			0
$215$	−238115.	−	137476.i	−0.0239592	−	0.0138328i
$216$		0			0
$217$	−1.22022e7	−	1.04354e7i	−1.19415	−	1.02124i
$218$		0			0
$219$	−2.13191e6	+	3.69257e6i	−0.202972	+	0.351558i
$220$		0			0
$221$	−3.14810e6	−	5.45266e6i	−0.291656	−	0.505163i
$222$		0			0
$223$		−	7.20830e6i		−	0.650007i	−0.945713	−	0.325004i	$-0.894634\pi$
$223$		−	7.20830e6i		−	0.650007i	0.945713	−	0.325004i	$-0.105366\pi$
$224$		0			0
$225$	1.36894e6			0.120182
$226$		0			0
$227$	1.78651e7	−	1.03144e7i	1.52731	−	0.881794i	0.527839	−	0.849344i	$-0.323002\pi$
$227$	1.78651e7	−	1.03144e7i	1.52731	−	0.881794i	0.999473	−	0.0324501i	$-0.0103310\pi$
$228$		0			0
$229$	−1.10604e7	−	6.38574e6i	−0.921013	−	0.531747i	−0.0370548	−	0.999313i	$-0.511798\pi$
$229$	−1.10604e7	−	6.38574e6i	−0.921013	−	0.531747i	−0.883958	+	0.467566i	$0.845131\pi$
$230$		0			0
$231$	−2.03405e6	+	1.09352e7i	−0.165016	+	0.887134i
$232$		0			0
$233$	5.50728e6	−	9.53888e6i	0.435381	−	0.754101i	−0.561946	−	0.827174i	$-0.689947\pi$
$233$	5.50728e6	−	9.53888e6i	0.435381	−	0.754101i	0.997327	+	0.0730725i	$0.0232804\pi$
$234$		0			0
$235$	−5.82585e6	−	1.00907e7i	−0.448906	−	0.777528i
$236$		0			0
$237$		−	9.56514e6i		−	0.718533i
$238$		0			0
$239$	2.69616e7			1.97493			0.987467	−	0.157823i	$-0.0504476\pi$
$239$	2.69616e7			1.97493			0.987467	+	0.157823i	$0.0504476\pi$
$240$		0			0
$241$	2.40116e6	−	1.38631e6i	0.171542	−	0.0990398i	−0.411771	−	0.911287i	$-0.635090\pi$
$241$	2.40116e6	−	1.38631e6i	0.171542	−	0.0990398i	0.583313	+	0.812248i	$0.301756\pi$
$242$		0			0
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	1.69459e7	−	2.66144e6i	1.15230	−	0.180975i
$246$		0			0
$247$	−4.53340e6	+	7.85208e6i	−0.300838	+	0.521067i
$248$		0			0
$249$	−3.82423e6	−	6.62377e6i	−0.247712	−	0.429049i
$250$		0			0
$251$		−	1.81949e7i		−	1.15061i	−0.817939	−	0.575305i	$-0.804883\pi$
$251$		−	1.81949e7i		−	1.15061i	0.817939	−	0.575305i	$-0.195117\pi$
$252$		0			0
$253$	−7.53896e6			−0.465532
$254$		0			0
$255$	−5.80621e6	+	3.35222e6i	−0.350165	+	0.202168i
$256$		0			0
$257$	−1.12137e7	−	6.47425e6i	−0.660618	−	0.381408i	0.131894	−	0.991264i	$-0.457894\pi$
$257$	−1.12137e7	−	6.47425e6i	−0.660618	−	0.381408i	−0.792512	+	0.609856i	$0.791227\pi$
$258$		0			0
$259$	2.48398e7	+	4.62045e6i	1.42971	+	0.265941i
$260$		0			0
$261$	−31234.3	+	54099.3i	−0.00175675	+	0.00304278i
$262$		0			0
$263$	−1.43938e6	−	2.49307e6i	−0.0791238	−	0.137047i	0.823748	−	0.566956i	$-0.191879\pi$
$263$	−1.43938e6	−	2.49307e6i	−0.0791238	−	0.137047i	−0.902872	+	0.429909i	$0.858546\pi$
$264$		0			0
$265$			9.61424e6i			0.516628i
$266$		0			0
$267$	−1.11172e7			−0.584067
$268$		0			0
$269$	2.47256e7	−	1.42753e7i	1.27025	−	0.733380i	0.295216	−	0.955431i	$-0.404608\pi$
$269$	2.47256e7	−	1.42753e7i	1.27025	−	0.733380i	0.975035	+	0.222051i	$0.0712751\pi$
$270$		0			0
$271$	2.88491e7	+	1.66560e7i	1.44952	+	0.836881i	0.998453	−	0.0556083i	$-0.0177098\pi$
$271$	2.88491e7	+	1.66560e7i	1.44952	+	0.836881i	0.451068	+	0.892490i	$0.351043\pi$
$272$		0			0
$273$	−7.41748e6	+	8.67336e6i	−0.364559	+	0.426284i
$274$		0			0
$275$	5.85954e6	−	1.01490e7i	0.281751	−	0.488007i
$276$		0			0
$277$	1.14572e7	+	1.98445e7i	0.539064	+	0.933687i	0.998955	+	0.0457112i	$0.0145554\pi$
$277$	1.14572e7	+	1.98445e7i	0.539064	+	0.933687i	−0.459890	+	0.887976i	$0.652111\pi$
$278$		0			0
$279$		−	1.13749e7i		−	0.523762i
$280$		0			0
$281$	−3.06574e7			−1.38171			−0.690854	−	0.722994i	$-0.742765\pi$
$281$	−3.06574e7			−1.38171			−0.690854	+	0.722994i	$0.742765\pi$
$282$		0			0
$283$	4.21389e6	−	2.43289e6i	0.185919	−	0.107340i	−0.404152	−	0.914692i	$-0.632433\pi$
$283$	4.21389e6	−	2.43289e6i	0.185919	−	0.107340i	0.590071	+	0.807352i	$0.299100\pi$
$284$		0			0
$285$	8.36121e6	+	4.82735e6i	0.361189	+	0.208533i
$286$		0			0
$287$	−2.90414e7	+	1.02629e7i	−1.22849	+	0.434135i
$288$		0			0
$289$	−7.71812e6	+	1.33682e7i	−0.319755	+	0.553833i
$290$		0			0
$291$	2.29647e6	+	3.97761e6i	0.0931927	+	0.161415i
$292$		0			0
$293$		−	3.71690e7i		−	1.47767i	−0.673885	−	0.738836i	$-0.735376\pi$
$293$		−	3.71690e7i		−	1.47767i	0.673885	−	0.738836i	$-0.264624\pi$
$294$		0			0
$295$	2.18941e7			0.852828
$296$		0			0
$297$	−6.82424e6	+	3.93998e6i	−0.260486	+	0.150392i
$298$		0			0
$299$	−6.69905e6	−	3.86770e6i	−0.250611	−	0.144690i
$300$		0			0
$301$	−215518.	−	609861.i	−0.00790286	−	0.0223631i
$302$		0			0
$303$	1.48538e7	−	2.57275e7i	0.533960	−	0.924846i
$304$		0			0
$305$	1.46327e7	+	2.53446e7i	0.515733	+	0.893276i
$306$		0			0
$307$			4.12664e7i			1.42620i	0.701061	+	0.713102i	$0.252710\pi$
$307$			4.12664e7i			1.42620i	−0.701061	+	0.713102i	$0.747290\pi$
$308$		0			0
$309$	8.63050e6			0.292523
$310$		0			0
$311$	1.82448e7	−	1.05337e7i	0.606539	−	0.350185i	−0.165071	−	0.986282i	$-0.552785\pi$
$311$	1.82448e7	−	1.05337e7i	0.606539	−	0.350185i	0.771610	+	0.636096i	$0.219452\pi$
$312$		0			0
$313$	4.20771e6	+	2.42932e6i	0.137219	+	0.0792232i	0.567038	−	0.823692i	$-0.308089\pi$
$313$	4.20771e6	+	2.42932e6i	0.137219	+	0.0792232i	−0.429819	+	0.902915i	$0.641423\pi$
$314$		0			0
$315$	9.23574e6	+	7.89843e6i	0.295488	+	0.252702i
$316$		0			0
$317$	2.40298e7	−	4.16209e7i	0.754350	−	1.30657i	−0.191348	−	0.981522i	$-0.561286\pi$
$317$	2.40298e7	−	4.16209e7i	0.754350	−	1.30657i	0.945697	−	0.325049i	$-0.105381\pi$
$318$		0			0
$319$	267386.	+	463127.i	0.00823696	+	0.0142668i
$320$		0			0
$321$			1.01581e7i			0.307112i
$322$		0			0
$323$	−1.25303e7			−0.371838
$324$		0			0
$325$	1.04135e7	−	6.01222e6i	0.303351	−	0.175140i
$326$		0			0
$327$	7.10963e6	+	4.10475e6i	0.203331	+	0.117393i
$328$		0			0
$329$	5.01264e6	−	2.69483e7i	0.140760	−	0.756733i
$330$		0			0
$331$	2.32948e7	−	4.03478e7i	0.642355	−	1.11259i	−0.342551	−	0.939499i	$-0.611291\pi$
$331$	2.32948e7	−	4.03478e7i	0.642355	−	1.11259i	0.984906	−	0.173092i	$-0.0553757\pi$
$332$		0			0
$333$	8.94987e6	+	1.55016e7i	0.242373	+	0.419802i
$334$		0			0
$335$		−	6.65673e7i		−	1.77062i
$336$		0			0
$337$	5.13592e7			1.34193			0.670963	−	0.741491i	$-0.265881\pi$
$337$	5.13592e7			1.34193			0.670963	+	0.741491i	$0.265881\pi$
$338$		0			0
$339$	−1.08330e7	+	6.25442e6i	−0.278067	+	0.160542i
$340$		0			0
$341$	−8.43305e7	−	4.86883e7i	−2.12678	−	1.22789i
$342$		0			0
$343$	3.43660e7	+	2.11516e7i	0.851622	+	0.524156i
$344$		0			0
$345$	−4.11848e6	+	7.13342e6i	−0.100295	+	0.173716i
$346$		0			0
$347$	−2.64829e7	−	4.58697e7i	−0.633837	−	1.09784i	−0.986760	−	0.162185i	$-0.948146\pi$
$347$	−2.64829e7	−	4.58697e7i	−0.633837	−	1.09784i	0.352924	−	0.935652i	$-0.385187\pi$
$348$		0			0
$349$			2.66336e7i			0.626547i	0.949663	+	0.313274i	$0.101426\pi$
$349$			2.66336e7i			0.626547i	−0.949663	+	0.313274i	$0.898574\pi$
$350$		0			0
$351$	−8.08527e6			−0.186971
$352$		0			0
$353$	6.99115e7	−	4.03634e7i	1.58937	−	0.917622i	0.595957	−	0.803016i	$-0.296773\pi$
$353$	6.99115e7	−	4.03634e7i	1.58937	−	0.917622i	0.993411	−	0.114606i	$-0.0365607\pi$
$354$		0			0
$355$	−4.60996e7	−	2.66156e7i	−1.03042	−	0.594910i
$356$		0			0
$357$	−1.55061e7	−	2.88430e6i	−0.340800	−	0.0633921i
$358$		0			0
$359$	3.70055e7	−	6.40954e7i	0.799803	−	1.38530i	−0.119941	−	0.992781i	$-0.538270\pi$
$359$	3.70055e7	−	6.40954e7i	0.799803	−	1.38530i	0.919744	−	0.392519i	$-0.128396\pi$
$360$		0			0
$361$	−1.45008e7	−	2.51162e7i	−0.308228	−	0.533866i
$362$		0			0
$363$			3.98418e7i			0.832950i
$364$		0			0
$365$	3.98806e7			0.820131
$366$		0			0
$367$	−5.49696e7	+	3.17367e7i	−1.11205	+	0.642043i	−0.939360	−	0.342933i	$-0.888580\pi$
$367$	−5.49696e7	+	3.17367e7i	−1.11205	+	0.642043i	−0.172691	+	0.984976i	$0.555246\pi$
$368$		0			0
$369$	−1.88979e7	−	1.09107e7i	−0.376127	−	0.217157i
$370$		0			0
$371$	−1.47000e7	+	1.71889e7i	−0.287869	+	0.336609i
$372$		0			0
$373$	−2.74298e7	+	4.75097e7i	−0.528562	+	0.915495i	0.470884	+	0.882195i	$0.343935\pi$
$373$	−2.74298e7	+	4.75097e7i	−0.528562	+	0.915495i	−0.999445	+	0.0333002i	$0.989398\pi$
$374$		0			0
$375$	1.13545e7	+	1.96666e7i	0.215316	+	0.372938i
$376$		0			0
$377$			548706.i			0.0102404i
$378$		0			0
$379$	−9.65749e7			−1.77397			−0.886986	−	0.461796i	$-0.847205\pi$
$379$	−9.65749e7			−1.77397			−0.886986	+	0.461796i	$0.847205\pi$
$380$		0			0
$381$	3.87180e7	−	2.23538e7i	0.700064	−	0.404182i
$382$		0			0
$383$	7.26301e6	+	4.19330e6i	0.129277	+	0.0746379i	0.563244	−	0.826291i	$-0.309553\pi$
$383$	7.26301e6	+	4.19330e6i	0.129277	+	0.0746379i	−0.433967	+	0.900929i	$0.642887\pi$
$384$		0			0
$385$	9.80892e7	−	3.46636e7i	1.71885	−	0.607424i
$386$		0			0
$387$	229122.	−	396851.i	0.00395306	−	0.00684691i
$388$		0			0
$389$	4.59894e6	+	7.96559e6i	0.0781283	+	0.135322i	0.902442	−	0.430811i	$-0.141772\pi$
$389$	4.59894e6	+	7.96559e6i	0.0781283	+	0.135322i	−0.824314	+	0.566133i	$0.808439\pi$
$390$		0			0
$391$		−	1.06903e7i		−	0.178838i
$392$		0			0
$393$	−2.06434e7			−0.340098
$394$		0			0
$395$	−7.74793e7	+	4.47327e7i	−1.25717	+	0.725828i
$396$		0			0
$397$	−2.31333e7	−	1.33560e7i	−0.369714	−	0.213454i	0.303620	−	0.952793i	$-0.401805\pi$
$397$	−2.31333e7	−	1.33560e7i	−0.369714	−	0.213454i	−0.673333	+	0.739339i	$0.735138\pi$
$398$		0			0
$399$	7.56772e6	+	2.14147e7i	0.119137	+	0.337127i
$400$		0			0
$401$	−7.64415e6	+	1.32401e7i	−0.118549	+	0.205332i	−0.919193	−	0.393808i	$-0.871157\pi$
$401$	−7.64415e6	+	1.32401e7i	−0.118549	+	0.205332i	0.800644	+	0.599140i	$0.204491\pi$
$402$		0			0
$403$	−4.99569e7	−	8.65278e7i	−0.763273	−	1.32203i
$404$		0			0
$405$			8.60952e6i			0.129603i
$406$		0			0
$407$	1.53234e8			2.27285
$408$		0			0
$409$	6.20022e7	−	3.57970e7i	0.906227	−	0.523210i	0.0270118	−	0.999635i	$-0.491401\pi$
$409$	6.20022e7	−	3.57970e7i	0.906227	−	0.523210i	0.879215	+	0.476425i	$0.158068\pi$
$410$		0			0
$411$	−1.52205e7	−	8.78756e6i	−0.219232	−	0.126574i
$412$		0			0
$413$	3.91435e7	+	3.34757e7i	0.555661	+	0.475203i
$414$		0			0
$415$	−3.57691e7	+	6.19538e7i	−0.500453	+	0.866810i
$416$		0			0
$417$	4.10278e7	+	7.10622e7i	0.565809	+	0.980010i
$418$		0			0
$419$		−	6.99639e7i		−	0.951112i	−0.879685	−	0.475556i	$-0.842247\pi$
$419$		−	6.99639e7i		−	0.951112i	0.879685	−	0.475556i	$-0.157753\pi$
$420$		0			0
$421$	−8.07271e7			−1.08187			−0.540933	−	0.841066i	$-0.681929\pi$
$421$	−8.07271e7			−1.08187			−0.540933	+	0.841066i	$0.681929\pi$
$422$		0			0
$423$	1.68174e7	−	9.70955e6i	0.222197	−	0.128286i
$424$		0			0
$425$	1.43914e7	+	8.30888e6i	0.187472	+	0.108237i
$426$		0			0
$427$	−1.25902e7	+	6.76856e7i	−0.161714	+	0.869386i
$428$		0			0
$429$	−3.46077e7	+	5.99423e7i	−0.438329	+	0.759209i
$430$		0			0
$431$	4.39988e6	+	7.62081e6i	0.0549552	+	0.0951852i	0.892194	−	0.451652i	$-0.149165\pi$
$431$	4.39988e6	+	7.62081e6i	0.0549552	+	0.0951852i	−0.837239	+	0.546837i	$0.815832\pi$
$432$		0			0
$433$			2.96339e7i			0.365027i	0.983203	+	0.182513i	$0.0584233\pi$
$433$			2.96339e7i			0.365027i	−0.983203	+	0.182513i	$0.941577\pi$
$434$		0			0
$435$	584285.			0.00709834
$436$		0			0
$437$	−1.33320e7	+	7.69726e6i	−0.159754	+	0.0922342i
$438$		0			0
$439$	1.76456e7	+	1.01877e7i	0.208566	+	0.120416i	0.600645	−	0.799516i	$-0.294911\pi$
$439$	1.76456e7	+	1.01877e7i	0.208566	+	0.120416i	−0.392079	+	0.919932i	$0.628244\pi$
$440$		0			0
$441$	4.43564e6	+	2.82425e7i	0.0517178	+	0.329297i
$442$		0			0
$443$	3.62846e7	−	6.28467e7i	0.417360	−	0.722888i	−0.578313	−	0.815815i	$-0.696289\pi$
$443$	3.62846e7	−	6.28467e7i	0.417360	−	0.722888i	0.995673	+	0.0929264i	$0.0296221\pi$
$444$		0			0
$445$	5.19912e7	+	9.00513e7i	0.589997	+	1.02190i
$446$		0			0
$447$			8.75215e6i			0.0979924i
$448$		0			0
$449$	−6.72959e7			−0.743446			−0.371723	−	0.928344i	$-0.621233\pi$
$449$	−6.72959e7			−0.743446			−0.371723	+	0.928344i	$0.621233\pi$
$450$		0			0
$451$	−1.61779e8	+	9.34031e7i	−1.76357	+	1.01820i
$452$		0			0
$453$	−8.03737e7	−	4.64038e7i	−0.864608	−	0.499182i
$454$		0			0
$455$	1.04944e8	+	1.95207e7i	1.11410	+	0.207234i
$456$		0			0
$457$	9.75464e6	−	1.68955e7i	0.102203	−	0.177020i	−0.810389	−	0.585892i	$-0.800744\pi$
$457$	9.75464e6	−	1.68955e7i	0.102203	−	0.177020i	0.912592	+	0.408872i	$0.134078\pi$
$458$		0			0
$459$	−5.58692e6	−	9.67683e6i	−0.0577742	−	0.100068i
$460$		0			0
$461$			8.53006e7i			0.870661i	0.900271	+	0.435331i	$0.143368\pi$
$461$			8.53006e7i			0.870661i	−0.900271	+	0.435331i	$0.856632\pi$
$462$		0			0
$463$	6.14259e7			0.618883			0.309441	−	0.950918i	$-0.399858\pi$
$463$	6.14259e7			0.618883			0.309441	+	0.950918i	$0.399858\pi$
$464$		0			0
$465$	−9.21383e7	+	5.31961e7i	−0.916392	+	0.529079i
$466$		0			0
$467$	−6.60424e6	−	3.81296e6i	−0.0648444	−	0.0374379i	0.467227	−	0.884137i	$-0.345253\pi$
$467$	−6.60424e6	−	3.81296e6i	−0.0648444	−	0.0374379i	−0.532072	+	0.846699i	$0.678586\pi$
$468$		0			0
$469$	1.01780e8	−	1.19013e8i	0.986606	−	1.15365i
$470$		0			0
$471$	−3.99249e7	+	6.91519e7i	−0.382103	+	0.661822i
$472$		0			0
$473$	−1.96144e6	−	3.39731e6i	−0.0185349	−	0.0321035i
$474$		0			0
$475$		−	2.39303e7i		−	0.223289i
$476$		0			0
$477$	−1.60234e7			−0.147639
$478$		0			0
$479$	−7.69512e6	+	4.44278e6i	−0.0700178	+	0.0404248i	−0.534600	−	0.845105i	$-0.679538\pi$
$479$	−7.69512e6	+	4.44278e6i	−0.0700178	+	0.0404248i	0.464582	+	0.885530i	$0.346204\pi$
$480$		0			0
$481$	1.36162e8	+	7.86132e7i	1.22355	+	0.706415i
$482$		0			0
$483$	−1.82701e7	+	6.45645e6i	−0.162143	+	0.0572997i
$484$		0			0
$485$	2.14795e7	−	3.72036e7i	0.188278	−	0.326107i
$486$		0			0
$487$	45255.3	+	78384.5i	0.000391816	+	0.000678646i	0.866221	−	0.499661i	$-0.166542\pi$
$487$	45255.3	+	78384.5i	0.000391816	+	0.000678646i	−0.865829	+	0.500339i	$0.833209\pi$
$488$		0			0
$489$			4.29284e7i			0.367129i
$490$		0			0
$491$	−1.03930e8			−0.878006			−0.439003	−	0.898486i	$-0.644668\pi$
$491$	−1.03930e8			−0.878006			−0.439003	+	0.898486i	$0.644668\pi$
$492$		0			0
$493$	−656717.	+	379156.i	−0.00548072	+	0.00316429i
$494$		0			0
$495$	6.38289e7	+	3.68517e7i	0.526262	+	0.303838i
$496$		0			0
$497$	−4.17247e7	−	1.18070e8i	−0.339879	−	0.961770i
$498$		0			0
$499$	−8.33230e7	+	1.44320e8i	−0.670600	+	1.16151i	0.307135	+	0.951666i	$0.400630\pi$
$499$	−8.33230e7	+	1.44320e8i	−0.670600	+	1.16151i	−0.977734	+	0.209847i	$0.932704\pi$
$500$		0			0
$501$	2.03810e7	+	3.53009e7i	0.162073	+	0.280719i
$502$		0			0
$503$			4.24779e7i			0.333779i	0.985976	+	0.166890i	$0.0533724\pi$
$503$			4.24779e7i			0.333779i	−0.985976	+	0.166890i	$0.946628\pi$
$504$		0			0
$505$	−2.77863e8			−2.15753
$506$		0			0
$507$	3.65783e6	−	2.11185e6i	0.0280672	−	0.0162046i
$508$		0			0
$509$	−9.02147e7	−	5.20855e7i	−0.684107	−	0.394969i	0.117294	−	0.993097i	$-0.462578\pi$
$509$	−9.02147e7	−	5.20855e7i	−0.684107	−	0.394969i	−0.801401	+	0.598128i	$0.795911\pi$
$510$		0			0
$511$	7.13008e7	+	6.09766e7i	0.534357	+	0.456984i
$512$		0			0
$513$	−8.04541e6	+	1.39351e7i	−0.0595931	+	0.103218i
$514$		0			0
$515$	−4.03617e7	−	6.99085e7i	−0.295493	−	0.511809i
$516$		0			0
$517$		−	1.66241e8i		−	1.20300i
$518$		0			0
$519$	1.46766e8			1.04984
$520$		0			0
$521$	−4.00720e7	+	2.31356e7i	−0.283353	+	0.163594i	−0.634940	−	0.772561i	$-0.718975\pi$
$521$	−4.00720e7	+	2.31356e7i	−0.283353	+	0.163594i	0.351587	+	0.936155i	$0.385642\pi$
$522$		0			0
$523$	5.24857e7	+	3.03026e7i	0.366890	+	0.211824i	0.672099	−	0.740461i	$-0.265393\pi$
$523$	5.24857e7	+	3.03026e7i	0.366890	+	0.211824i	−0.305209	+	0.952285i	$0.598726\pi$
$524$		0			0
$525$	5.50842e6	−	2.96136e7i	0.0380670	−	0.204651i
$526$		0			0
$527$	6.90403e7	−	1.19581e8i	0.471706	−	0.817018i
$528$		0			0
$529$	6.74510e7	+	1.16829e8i	0.455639	+	0.789191i
$530$		0			0
$531$			3.64895e7i			0.243716i
$532$		0			0
$533$	−1.91674e8			−1.26585
$534$		0			0
$535$	8.22823e7	−	4.75057e7i	0.537335	−	0.310231i
$536$		0			0
$537$	−5.77590e7	−	3.33472e7i	−0.372990	−	0.215346i
$538$		0			0
$539$	2.28369e8	+	8.80027e7i	1.45838	+	0.561992i
$540$		0			0
$541$	−7.43769e7	+	1.28825e8i	−0.469728	+	0.813593i	−0.999401	−	0.0346092i	$-0.988981\pi$
$541$	−7.43769e7	+	1.28825e8i	−0.469728	+	0.813593i	0.529673	+	0.848202i	$0.322315\pi$
$542$		0			0
$543$	2.66036e7	+	4.60788e7i	0.166166	+	0.287807i
$544$		0			0
$545$		−	7.67856e7i		−	0.474340i
$546$		0			0
$547$	−1.65159e8			−1.00911			−0.504557	−	0.863378i	$-0.668344\pi$
$547$	−1.65159e8			−1.00911			−0.504557	+	0.863378i	$0.668344\pi$
$548$		0			0
$549$	−4.22401e7	+	2.43873e7i	−0.255275	+	0.147383i
$550$		0			0
$551$	945702.	+	546001.i	0.00565327	+	0.00326392i
$552$		0			0
$553$	−2.06917e8	−	3.84886e7i	−1.22355	−	0.227592i
$554$		0			0
$555$	8.37105e7	−	1.44991e8i	0.489667	−	0.848128i
$556$		0			0
$557$	−7.50165e7	−	1.29932e8i	−0.434101	−	0.751886i	0.563120	−	0.826375i	$-0.309601\pi$
$557$	−7.50165e7	−	1.29932e8i	−0.434101	−	0.751886i	−0.997222	+	0.0744893i	$0.976267\pi$
$558$		0			0
$559$		−	4.02509e6i		−	0.0230431i
$560$		0			0
$561$	−9.56556e7			−0.541778
$562$		0			0
$563$	−1.65222e8	+	9.53911e7i	−0.925855	+	0.534543i	−0.885498	−	0.464642i	$-0.846183\pi$
$563$	−1.65222e8	+	9.53911e7i	−0.925855	+	0.534543i	−0.0403570	+	0.999185i	$0.512850\pi$
$564$		0			0
$565$	1.01324e8	+	5.84993e7i	0.561780	+	0.324344i
$566$		0			0
$567$	−1.31638e7	+	1.53926e7i	−0.0722157	+	0.0844427i
$568$		0			0
$569$	1.99753e6	−	3.45983e6i	0.0108432	−	0.0187809i	−0.860553	−	0.509361i	$-0.829882\pi$
$569$	1.99753e6	−	3.45983e6i	0.0108432	−	0.0187809i	0.871396	+	0.490580i	$0.163215\pi$
$570$		0			0
$571$	−1.19084e8	−	2.06260e8i	−0.639654	−	1.10791i	−0.985509	−	0.169625i	$-0.945744\pi$
$571$	−1.19084e8	−	2.06260e8i	−0.639654	−	1.10791i	0.345855	−	0.938288i	$-0.387589\pi$
$572$		0			0
$573$			1.65927e8i			0.881968i
$574$		0			0
$575$	2.04163e7			0.107392
$576$		0			0
$577$	−9.60002e7	+	5.54257e7i	−0.499741	+	0.288525i	−0.728606	−	0.684933i	$-0.759832\pi$
$577$	−9.60002e7	+	5.54257e7i	−0.499741	+	0.288525i	0.228866	+	0.973458i	$0.426498\pi$
$578$		0			0
$579$	−1.17814e8	−	6.80197e7i	−0.606960	−	0.350428i
$580$		0			0
$581$	−1.58676e8	+	5.60744e7i	−0.809064	+	0.285914i
$582$		0			0
$583$	−6.85856e7	+	1.18794e8i	−0.346120	+	0.599498i
$584$		0			0
$585$	3.78118e7	+	6.54920e7i	0.188869	+	0.327130i
$586$		0			0
$587$			2.18547e8i			1.08052i	0.841499	+	0.540258i	$0.181673\pi$
$587$			2.18547e8i			1.08052i	−0.841499	+	0.540258i	$0.818327\pi$
$588$		0			0
$589$	−1.98842e8			−0.973113
$590$		0			0
$591$	−1.26077e8	+	7.27903e7i	−0.610762	+	0.352624i
$592$		0			0
$593$	2.77768e6	+	1.60370e6i	0.0133204	+	0.00769056i	0.506645	−	0.862155i	$-0.330885\pi$
$593$	2.77768e6	+	1.60370e6i	0.0133204	+	0.00769056i	−0.493325	+	0.869845i	$0.664219\pi$
$594$		0			0
$595$	4.91533e7	+	1.39091e8i	0.233347	+	0.660311i
$596$		0			0
$597$	4.23938e7	−	7.34282e7i	0.199241	−	0.345096i
$598$		0			0
$599$	−1.21139e8	−	2.09819e8i	−0.563641	−	0.976255i	−0.997175	−	0.0751178i	$-0.976067\pi$
$599$	−1.21139e8	−	2.09819e8i	−0.563641	−	0.976255i	0.433533	−	0.901137i	$-0.357267\pi$
$600$		0			0
$601$			2.97265e8i			1.36937i	0.728839	+	0.684685i	$0.240060\pi$
$601$			2.97265e8i			1.36937i	−0.728839	+	0.684685i	$0.759940\pi$
$602$		0			0
$603$	1.10943e8			0.505998
$604$		0			0
$605$	3.22725e8	−	1.86326e8i	1.45736	−	0.841407i
$606$		0			0
$607$	2.24506e8	+	1.29619e8i	1.00383	+	0.579564i	0.909380	−	0.415966i	$-0.136556\pi$
$607$	2.24506e8	+	1.29619e8i	1.00383	+	0.579564i	0.0944532	+	0.995529i	$0.469890\pi$
$608$		0			0
$609$	1.04462e6	+	893359.i	0.00462493	+	0.00395525i
$610$		0			0
$611$	8.52860e7	−	1.47720e8i	0.373899	−	0.647612i
$612$		0			0
$613$	6.21469e7	+	1.07642e8i	0.269797	+	0.467303i	0.968809	−	0.247807i	$-0.0797099\pi$
$613$	6.21469e7	+	1.07642e8i	0.269797	+	0.467303i	−0.699012	+	0.715110i	$0.746377\pi$
$614$		0			0
$615$			2.04102e8i			0.877448i
$616$		0			0
$617$	−2.85625e7			−0.121602			−0.0608009	−	0.998150i	$-0.519365\pi$
$617$	−2.85625e7			−0.121602			−0.0608009	+	0.998150i	$0.519365\pi$
$618$		0			0
$619$	−1.40975e8	+	8.13918e7i	−0.594387	+	0.343170i	−0.766830	−	0.641850i	$-0.778167\pi$
$619$	−1.40975e8	+	8.13918e7i	−0.594387	+	0.343170i	0.172443	+	0.985019i	$0.444834\pi$
$620$		0			0
$621$	−1.18888e7	−	6.86399e6i	−0.0496435	−	0.0286617i
$622$		0			0
$623$	−4.47339e7	+	2.40492e8i	−0.185000	+	0.994573i
$624$		0			0
$625$	1.50214e8	−	2.60178e8i	0.615276	−	1.06569i
$626$		0			0
$627$	6.88742e7	+	1.19294e8i	0.279418	+	0.483965i
$628$		0			0
$629$			2.17287e8i			0.873135i
$630$		0			0
$631$	−3.03854e8			−1.20942			−0.604710	−	0.796446i	$-0.706711\pi$
$631$	−3.03854e8			−1.20942			−0.604710	+	0.796446i	$0.706711\pi$
$632$		0			0
$633$	1.98221e8	−	1.14443e8i	0.781519	−	0.451210i
$634$		0			0
$635$	−3.62140e8	−	2.09082e8i	−1.41434	−	0.816572i
$636$		0			0
$637$	1.57779e8	+	1.95358e8i	0.610422	+	0.755811i
$638$		0			0
$639$	4.43585e7	−	7.68311e7i	0.170010	−	0.294466i
$640$		0			0
$641$	1.72655e8	+	2.99048e8i	0.655550	+	1.13545i	0.981756	+	0.190147i	$0.0608966\pi$
$641$	1.72655e8	+	2.99048e8i	0.655550	+	1.13545i	−0.326205	+	0.945299i	$0.605770\pi$
$642$		0			0
$643$			4.59323e7i			0.172777i	0.996262	+	0.0863883i	$0.0275326\pi$
$643$			4.59323e7i			0.172777i	−0.996262	+	0.0863883i	$0.972467\pi$
$644$		0			0
$645$	−4.28608e6			−0.0159728
$646$		0			0
$647$	1.17029e8	−	6.75668e7i	0.432097	−	0.249471i	−0.268143	−	0.963379i	$-0.586410\pi$
$647$	1.17029e8	−	6.75668e7i	0.432097	−	0.249471i	0.700240	+	0.713908i	$0.253077\pi$
$648$		0			0
$649$	2.70524e8	+	1.56187e8i	0.989628	+	0.571362i
$650$		0			0
$651$	−2.46066e8	−	4.57706e7i	−0.891884	−	0.165899i
$652$		0			0
$653$	−1.41223e8	+	2.44605e8i	−0.507183	+	0.878467i	0.492783	+	0.870153i	$0.335980\pi$
$653$	−1.41223e8	+	2.44605e8i	−0.507183	+	0.878467i	−0.999965	+	0.00831407i	$0.997354\pi$
$654$		0			0
$655$	9.65416e7	+	1.67215e8i	0.343551	+	0.595047i
$656$		0			0
$657$			6.64663e7i			0.234372i
$658$		0			0
$659$	1.81490e8			0.634156			0.317078	−	0.948399i	$-0.397298\pi$
$659$	1.81490e8			0.634156			0.317078	+	0.948399i	$0.397298\pi$
$660$		0			0
$661$	4.32196e8	−	2.49529e8i	1.49650	−	0.864005i	0.496509	−	0.868032i	$-0.334615\pi$
$661$	4.32196e8	−	2.49529e8i	1.49650	−	0.864005i	0.999992	+	0.00402687i	$0.00128180\pi$
$662$		0			0
$663$	−8.49986e7	−	4.90740e7i	−0.291656	−	0.168388i
$664$		0			0
$665$	1.38071e8	−	1.61449e8i	0.469503	−	0.548996i
$666$		0			0
$667$	−465824.	+	806831.i	−0.00156980	+	0.00271898i
$668$		0			0
$669$	−5.61831e7	−	9.73120e7i	−0.187641	−	0.325004i
$670$		0			0
$671$			4.17544e8i			1.38209i
$672$		0			0
$673$	−5.50469e8			−1.80587			−0.902937	−	0.429773i	$-0.858593\pi$
$673$	−5.50469e8			−1.80587			−0.902937	+	0.429773i	$0.858593\pi$
$674$		0			0
$675$	1.84808e7	−	1.06699e7i	0.0600909	−	0.0346935i
$676$		0			0
$677$	−1.85942e8	−	1.07353e8i	−0.599253	−	0.345979i	0.169494	−	0.985531i	$-0.445787\pi$
$677$	−1.85942e8	−	1.07353e8i	−0.599253	−	0.345979i	−0.768748	+	0.639552i	$0.779120\pi$
$678$		0			0
$679$	9.52858e7	−	3.36730e7i	0.304382	−	0.107565i
$680$		0			0
$681$	1.60786e8	−	2.78489e8i	0.509104	−	0.881794i
$682$		0			0
$683$	−2.38402e8	−	4.12924e8i	−0.748251	−	1.29601i	−0.948661	−	0.316296i	$-0.897561\pi$
$683$	−2.38402e8	−	4.12924e8i	−0.748251	−	1.29601i	0.200410	−	0.979712i	$-0.435773\pi$
$684$		0			0
$685$			1.64385e8i			0.511434i
$686$		0			0
$687$	−1.99088e8			−0.614009
$688$		0			0
$689$	−1.21889e8	+	7.03726e7i	−0.372655	+	0.215152i
$690$		0			0
$691$	1.49390e6	+	862501.i	0.00452779	+	0.00261412i	0.502262	−	0.864715i	$-0.332501\pi$
$691$	1.49390e6	+	862501.i	0.00452779	+	0.00261412i	−0.497734	+	0.867330i	$0.665835\pi$
$692$		0			0
$693$	5.77715e7	+	1.63479e8i	0.173586	+	0.491203i
$694$		0			0
$695$	3.83744e8	−	6.64664e8i	1.14311	−	1.97992i
$696$		0			0
$697$	−1.32446e8	−	2.29404e8i	−0.391149	−	0.677489i
$698$		0			0
$699$		−	1.71700e8i		−	0.502734i
$700$		0			0
$701$	2.60769e8			0.757009			0.378505	−	0.925599i	$-0.376438\pi$
$701$	2.60769e8			0.757009			0.378505	+	0.925599i	$0.376438\pi$
$702$		0			0
$703$	2.70982e8	−	1.56451e8i	0.779963	−	0.450312i
$704$		0			0
$705$	−1.57298e8	−	9.08160e7i	−0.448906	−	0.259176i
$706$		0			0
$707$	−4.96778e8	−	4.24846e8i	−1.40574	−	1.20219i
$708$		0			0
$709$	1.75573e8	−	3.04101e8i	0.492627	−	0.853256i	−0.507337	−	0.861748i	$-0.669370\pi$
$709$	1.75573e8	−	3.04101e8i	0.492627	−	0.853256i	0.999964	+	0.00849234i	$0.00270323\pi$
$710$		0			0
$711$	−7.45529e7	−	1.29129e8i	−0.207422	−	0.359266i
$712$		0			0
$713$		−	1.69644e8i		−	0.468025i
$714$		0			0
$715$	6.47390e8			1.77112
$716$		0			0
$717$	3.63982e8	−	2.10145e8i	0.987467	−	0.570115i
$718$		0			0
$719$	2.90810e8	+	1.67899e8i	0.782389	+	0.451712i	0.837276	−	0.546780i	$-0.184147\pi$
$719$	2.90810e8	+	1.67899e8i	0.782389	+	0.451712i	−0.0548875	+	0.998493i	$0.517480\pi$
$720$		0			0
$721$	3.47277e7	−	1.86698e8i	0.0926554	−	0.498121i
$722$		0			0
$723$	2.16105e7	−	3.74304e7i	0.0571806	−	0.0990398i
$724$		0			0
$725$	−724110.	−	1.25420e6i	−0.00190016	−	0.00329118i
$726$		0			0
$727$		−	6.93214e7i		−	0.180412i	−0.995923	−	0.0902058i	$-0.971248\pi$
$727$		−	6.93214e7i		−	0.180412i	0.995923	−	0.0902058i	$-0.0287525\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	4.81741e6	−	2.78133e6i	0.0123328	−	0.00712035i
$732$		0			0
$733$	−695122.	−	401329.i	−0.00176502	−	0.00101903i	0.499117	−	0.866534i	$-0.333658\pi$
$733$	−695122.	−	401329.i	−0.00176502	−	0.00101903i	−0.500882	+	0.865515i	$0.666991\pi$
$734$		0			0
$735$	2.08025e8	−	1.68009e8i	0.523907	−	0.423127i
$736$		0			0
$737$	4.74874e8	−	8.22506e8i	1.18625	−	2.05464i
$738$		0			0
$739$	−2.89954e8	−	5.02214e8i	−0.718448	−	1.24439i	−0.961615	−	0.274404i	$-0.911520\pi$
$739$	−2.89954e8	−	5.02214e8i	−0.718448	−	1.24439i	0.243167	−	0.969984i	$-0.421814\pi$
$740$		0			0
$741$			1.41337e8i			0.347378i
$742$		0			0
$743$	−6.06555e8			−1.47878			−0.739391	−	0.673277i	$-0.764886\pi$
$743$	−6.06555e8			−1.47878			−0.739391	+	0.673277i	$0.764886\pi$
$744$		0			0
$745$	7.08939e7	−	4.09306e7i	0.171451	−	0.0989873i
$746$		0			0
$747$	−1.03254e8	−	5.96139e7i	−0.247712	−	0.143016i
$748$		0			0
$749$	2.19744e8	+	4.08746e7i	0.522964	+	0.0972765i
$750$		0			0
$751$	3.17721e8	−	5.50309e8i	0.750112	−	1.29923i	−0.197656	−	0.980271i	$-0.563333\pi$
$751$	3.17721e8	−	5.50309e8i	0.750112	−	1.29923i	0.947768	−	0.318961i	$-0.103334\pi$
$752$		0			0
$753$	−1.41815e8	−	2.45631e8i	−0.332152	−	0.575305i
$754$		0			0
$755$			8.68054e8i			2.01700i
$756$		0			0
$757$	2.47771e8			0.571167			0.285583	−	0.958354i	$-0.407813\pi$
$757$	2.47771e8			0.571167			0.285583	+	0.958354i	$0.407813\pi$
$758$		0			0
$759$	−1.01776e8	+	5.87604e7i	−0.232766	+	0.134388i
$760$		0			0
$761$	1.21702e8	+	7.02647e7i	0.276149	+	0.159435i	0.631679	−	0.775230i	$-0.282366\pi$
$761$	1.21702e8	+	7.02647e7i	0.276149	+	0.159435i	−0.355530	+	0.934665i	$0.615699\pi$
$762$		0			0
$763$	1.17404e8	−	1.37282e8i	0.264306	−	0.309057i
$764$		0			0
$765$	−5.22559e7	+	9.05099e7i	−0.116722	+	0.202168i
$766$		0			0
$767$	1.60257e8	+	2.77573e8i	0.355165	+	0.615164i
$768$		0			0
$769$			5.71522e8i			1.25677i	0.777904	+	0.628383i	$0.216283\pi$
$769$			5.71522e8i			1.25677i	−0.777904	+	0.628383i	$0.783717\pi$
$770$		0			0
$771$	−2.01847e8			−0.440412
$772$		0			0
$773$	5.92545e8	−	3.42106e8i	1.28287	−	0.740666i	0.305499	−	0.952192i	$-0.401177\pi$
$773$	5.92545e8	−	3.42106e8i	1.28287	−	0.740666i	0.977372	+	0.211526i	$0.0678433\pi$
$774$		0			0
$775$	2.28376e8	+	1.31853e8i	0.490620	+	0.283260i
$776$		0			0
$777$	3.71350e8	−	1.31231e8i	0.791627	−	0.279752i
$778$		0			0
$779$	−1.90729e8	+	3.30352e8i	−0.403463	+	0.698818i
$780$		0			0
$781$	−3.79738e8	−	6.57726e8i	−0.797134	−	1.38068i
$782$		0			0
$783$			973788.i			0.00202852i
$784$		0			0
$785$	7.46856e8			1.54393
$786$		0			0
$787$	1.47920e8	−	8.54015e7i	0.303460	−	0.175203i	−0.340536	−	0.940231i	$-0.610609\pi$
$787$	1.47920e8	−	8.54015e7i	0.303460	−	0.175203i	0.643996	+	0.765029i	$0.277275\pi$
$788$		0			0
$789$	−3.88632e7	−	2.24377e7i	−0.0791238	−	0.0456822i
$790$		0			0
$791$	9.17080e7	+	2.59510e8i	0.185301	+	0.524354i
$792$		0			0
$793$	−2.14212e8	+	3.71026e8i	−0.429560	+	0.744020i
$794$		0			0
$795$	7.49356e7	+	1.29792e8i	0.149138	+	0.258314i
$796$		0			0
$797$			3.35735e8i			0.663165i	0.943426	+	0.331583i	$0.107583\pi$
$797$			3.35735e8i			0.663165i	−0.943426	+	0.331583i	$0.892417\pi$
$798$		0			0
$799$	2.35730e8			0.462142
$800$		0			0
$801$	−1.50082e8	+	8.66501e7i	−0.292033	+	0.168605i
$802$		0			0
$803$	4.92765e8	+	2.84498e8i	0.951685	+	0.549456i
$804$		0			0
$805$	1.37741e8	+	1.17796e8i	0.264043	+	0.225811i
$806$		0			0
$807$	2.22530e8	−	3.85434e8i	0.423417	−	0.733380i
$808$		0			0
$809$	2.00668e8	+	3.47567e8i	0.378994	+	0.656438i	0.990916	−	0.134481i	$-0.0429366\pi$
$809$	2.00668e8	+	3.47567e8i	0.378994	+	0.656438i	−0.611922	+	0.790918i	$0.709603\pi$
$810$		0			0
$811$		−	6.88767e8i		−	1.29125i	−0.763655	−	0.645624i	$-0.776597\pi$
$811$		−	6.88767e8i		−	1.29125i	0.763655	−	0.645624i	$-0.223403\pi$
$812$		0			0
$813$	5.19284e8			0.966347
$814$		0			0
$815$	3.47727e8	−	2.00760e8i	0.642341	−	0.370856i
$816$		0			0
$817$	−6.93729e6	−	4.00525e6i	−0.0127211	−	0.00734452i
$818$		0			0
$819$	−3.25338e7	+	1.74904e8i	−0.0592221	+	0.318381i
$820$		0			0
$821$	−4.44407e8	+	7.69736e8i	−0.803067	+	1.39095i	0.114522	+	0.993421i	$0.463466\pi$
$821$	−4.44407e8	+	7.69736e8i	−0.803067	+	1.39095i	−0.917588	+	0.397532i	$0.869867\pi$
$822$		0			0
$823$	−3.35501e8	−	5.81105e8i	−0.601858	−	1.04245i	−0.992540	−	0.121923i	$-0.961094\pi$
$823$	−3.35501e8	−	5.81105e8i	−0.601858	−	1.04245i	0.390681	−	0.920526i	$-0.372239\pi$
$824$		0			0
$825$		−	1.82683e8i		−	0.325338i
$826$		0			0
$827$	−5.77797e8			−1.02155			−0.510774	−	0.859715i	$-0.670641\pi$
$827$	−5.77797e8			−1.02155			−0.510774	+	0.859715i	$0.670641\pi$
$828$		0			0
$829$	−7.19049e8	+	4.15143e8i	−1.26210	+	0.728676i	−0.973481	−	0.228767i	$-0.926531\pi$
$829$	−7.19049e8	+	4.15143e8i	−1.26210	+	0.728676i	−0.288623	+	0.957443i	$0.593197\pi$
$830$		0			0
$831$	3.09345e8	+	1.78601e8i	0.539064	+	0.311229i
$832$		0			0
$833$	−1.24789e8	+	3.23829e8i	−0.215894	+	0.560249i
$834$		0			0
$835$	1.90629e8	−	3.30179e8i	0.327438	−	0.567139i
$836$		0			0
$837$	−8.86583e7	−	1.53561e8i	−0.151197	−	0.261881i
$838$		0			0
$839$			7.31636e8i			1.23882i	0.785067	+	0.619411i	$0.212629\pi$
$839$			7.31636e8i			1.23882i	−0.785067	+	0.619411i	$0.787371\pi$
$840$		0			0
$841$	−5.94757e8			−0.999889
$842$		0			0
$843$	−4.13875e8	+	2.38951e8i	−0.690854	+	0.398865i
$844$		0			0
$845$	−3.42126e7	−	1.97527e7i	−0.0567043	−	0.0327383i
$846$		0			0
$847$	8.61874e8	+	1.60317e8i	1.41838	+	0.263833i
$848$		0			0
$849$	3.79250e7	−	6.56880e7i	0.0619730	−	0.107340i
$850$		0			0
$851$	1.33477e8	+	2.31190e8i	0.216580	+	0.375128i
$852$		0			0
$853$		−	6.20436e8i		−	0.999655i	−0.866125	−	0.499828i	$-0.833397\pi$
$853$		−	6.20436e8i		−	0.999655i	0.866125	−	0.499828i	$-0.166603\pi$
$854$		0			0
$855$	1.50502e8			0.240793
$856$		0			0
$857$	−8.99465e7	+	5.19306e7i	−0.142903	+	0.0825051i	−0.569747	−	0.821820i	$-0.692959\pi$
$857$	−8.99465e7	+	5.19306e7i	−0.142903	+	0.0825051i	0.426844	+	0.904325i	$0.359625\pi$
$858$		0			0
$859$	−5.08441e8	−	2.93549e8i	−0.802161	−	0.463128i	0.0420654	−	0.999115i	$-0.486606\pi$
$859$	−5.08441e8	−	2.93549e8i	−0.802161	−	0.463128i	−0.844226	+	0.535987i	$0.819940\pi$
$860$		0			0
$861$	−3.12067e8	+	3.64905e8i	−0.488921	+	0.571702i
$862$		0			0
$863$	1.25582e8	−	2.17515e8i	0.195387	−	0.338421i	−0.751640	−	0.659574i	$-0.770737\pi$
$863$	1.25582e8	−	2.17515e8i	0.195387	−	0.338421i	0.947027	+	0.321153i	$0.104070\pi$
$864$		0			0
$865$	−6.86369e8	−	1.18883e9i	−1.06050	−	1.83683i
$866$		0			0
$867$			2.40627e8i			0.369222i
$868$		0			0
$869$	−1.27645e9			−1.94511
$870$		0			0
$871$	8.43937e8	−	4.87247e8i	1.27719	−	0.737386i
$872$		0			0
$873$	6.20047e7	+	3.57984e7i	0.0931927	+	0.0538049i
$874$		0			0
$875$	4.71126e8	−	1.66491e8i	0.703255	−	0.248522i
$876$		0			0
$877$	4.63228e8	−	8.02335e8i	0.686746	−	1.18948i	−0.286138	−	0.958188i	$-0.592372\pi$
$877$	4.63228e8	−	8.02335e8i	0.686746	−	1.18948i	0.972885	−	0.231291i	$-0.0742950\pi$
$878$		0			0
$879$	−2.89704e8	−	5.01782e8i	−0.426567	−	0.738836i
$880$		0			0
$881$			5.06838e8i			0.741210i	0.928791	+	0.370605i	$0.120850\pi$
$881$			5.06838e8i			0.741210i	−0.928791	+	0.370605i	$0.879150\pi$
$882$		0			0
$883$	−8.94286e8			−1.29896			−0.649478	−	0.760381i	$-0.725012\pi$
$883$	−8.94286e8			−1.29896			−0.649478	+	0.760381i	$0.725012\pi$
$884$		0			0
$885$	2.95571e8	−	1.70648e8i	0.426414	−	0.246190i
$886$		0			0
$887$	1.88522e8	+	1.08843e8i	0.270142	+	0.155967i	0.628952	−	0.777444i	$-0.283484\pi$
$887$	1.88522e8	+	1.08843e8i	0.270142	+	0.155967i	−0.358810	+	0.933411i	$0.616817\pi$
$888$		0			0
$889$	−3.27772e8	−	9.27512e8i	−0.466517	−	1.32012i
$890$		0			0
$891$	−6.14182e7	+	1.06379e8i	−0.0868288	+	0.150392i
$892$		0			0
$893$	−1.69731e8	−	2.93983e8i	−0.238346	−	0.412827i
$894$		0			0
$895$			6.23810e8i			0.870129i
$896$		0			0
$897$	−1.20583e8			−0.167074
$898$		0			0
$899$	−1.04214e7	+	6.01679e6i	−0.0143432	+	0.00828106i
$900$		0			0
$901$	−1.68450e8	−	9.72549e7i	−0.230302	−	0.132965i
$902$		0			0
$903$	−7.66289e6	−	6.55332e6i	−0.0104071	−	0.00890017i
$904$		0			0
$905$	2.48831e8	−	4.30987e8i	0.335705	−	0.581459i
$906$		0			0
$907$	5.14799e8	+	8.91658e8i	0.689947	+	1.19502i	0.971855	+	0.235582i	$0.0756995\pi$
$907$	5.14799e8	+	8.91658e8i	0.689947	+	1.19502i	−0.281908	+	0.959442i	$0.590967\pi$
$908$		0			0
$909$		−	4.63095e8i		−	0.616564i
$910$		0			0
$911$	−9.31773e8			−1.23241			−0.616205	−	0.787586i	$-0.711331\pi$
$911$	−9.31773e8			−1.23241			−0.616205	+	0.787586i	$0.711331\pi$
$912$		0			0
$913$	−8.83926e8	+	5.10335e8i	−1.16146	+	0.670568i
$914$		0			0
$915$	3.95083e8	+	2.28101e8i	0.515733	+	0.297759i
$916$		0			0
$917$	−8.30658e7	+	4.46566e8i	−0.107724	+	0.579133i
$918$		0			0
$919$	−2.59405e8	+	4.49302e8i	−0.334219	+	0.578884i	−0.983334	−	0.181806i	$-0.941806\pi$
$919$	−2.59405e8	+	4.49302e8i	−0.334219	+	0.578884i	0.649115	+	0.760690i	$0.275139\pi$
$920$		0			0
$921$	3.21640e8	+	5.57096e8i	0.411709	+	0.713102i
$922$		0			0
$923$		−	7.79265e8i		−	0.991015i
$924$		0			0
$925$	−4.14973e8			−0.524318
$926$		0			0
$927$	1.16512e8	−	6.72681e7i	0.146262	−	0.0844442i
$928$		0			0
$929$	2.79957e8	+	1.61633e8i	0.349176	+	0.201597i	0.664322	−	0.747446i	$-0.268720\pi$
$929$	2.79957e8	+	1.61633e8i	0.349176	+	0.201597i	−0.315146	+	0.949043i	$0.602054\pi$
$930$		0			0
$931$	4.93703e8	−	7.75387e7i	0.611810	−	0.0960881i
$932$		0			0
$933$	1.64203e8	−	2.84409e8i	0.202180	−	0.350185i
$934$		0			0
$935$	4.47346e8	+	7.74826e8i	0.547279	+	0.947915i
$936$		0			0
$937$			1.40282e9i			1.70523i	0.522542	+	0.852613i	$0.324984\pi$
$937$			1.40282e9i			1.70523i	−0.522542	+	0.852613i	$0.675016\pi$
$938$		0			0
$939$	7.57388e7			0.0914791
$940$		0			0
$941$	−9.59524e8	+	5.53981e8i	−1.15156	+	0.664854i	−0.949267	−	0.314471i	$-0.898173\pi$
$941$	−9.59524e8	+	5.53981e8i	−1.15156	+	0.664854i	−0.202293	+	0.979325i	$0.564839\pi$
$942$		0			0
$943$	−2.81842e8	−	1.62721e8i	−0.336101	−	0.194048i
$944$		0			0
$945$	1.86245e8	+	3.46433e7i	0.220693	+	0.0410511i
$946$		0			0
$947$	−2.48846e8	+	4.31014e8i	−0.293009	+	0.507506i	−0.974520	−	0.224302i	$-0.927990\pi$
$947$	−2.48846e8	+	4.31014e8i	−0.293009	+	0.507506i	0.681511	+	0.731808i	$0.261323\pi$
$948$		0			0
$949$	2.91911e8	+	5.05605e8i	0.341548	+	0.591578i
$950$		0			0
$951$		−	7.49175e8i		−	0.871048i
$952$		0			0
$953$	−9.34286e8			−1.07945			−0.539723	−	0.841843i	$-0.681471\pi$
$953$	−9.34286e8			−1.07945			−0.539723	+	0.841843i	$0.681471\pi$
$954$		0			0
$955$	1.34404e9	−	7.75979e8i	1.54312	−	0.890923i
$956$		0			0
$957$	7.21943e6	+	4.16814e6i	0.00823696	+	0.00475561i
$958$		0			0
$959$	−2.51341e8	+	2.93896e8i	−0.284975	+	0.333226i
$960$		0			0
$961$	6.51843e8	−	1.12903e9i	0.734468	−	1.27214i
$962$		0			0
$963$	7.91746e7	+	1.37134e8i	0.0886557	+	0.153556i
$964$		0			0
$965$			1.27241e9i			1.41594i
$966$		0			0
$967$	−7.10460e8			−0.785706			−0.392853	−	0.919601i	$-0.628512\pi$
$967$	−7.10460e8			−0.785706			−0.392853	+	0.919601i	$0.628512\pi$
$968$		0			0
$969$	−1.69159e8	+	9.76641e7i	−0.185919	+	0.107340i
$970$		0			0
$971$	3.05909e8	+	1.76617e8i	0.334144	+	0.192918i	0.657680	−	0.753298i	$-0.271538\pi$
$971$	3.05909e8	+	1.76617e8i	0.334144	+	0.192918i	−0.323535	+	0.946216i	$0.604871\pi$
$972$		0			0
$973$	1.70234e9	−	6.01587e8i	1.84802	−	0.653070i
$974$		0			0
$975$	9.37212e7	−	1.62330e8i	0.101117	−	0.175140i
$976$		0			0
$977$	−8.78288e8	−	1.52124e9i	−0.941788	−	1.63122i	−0.762058	−	0.647508i	$-0.775811\pi$
$977$	−8.78288e8	−	1.52124e9i	−0.941788	−	1.63122i	−0.179729	−	0.983716i	$-0.557522\pi$
$978$		0			0
$979$			1.48357e9i			1.58110i
$980$		0			0
$981$	1.27973e8			0.135554
$982$		0			0
$983$	−1.38481e8	+	7.99519e7i	−0.145790	+	0.0841722i	−0.571121	−	0.820866i	$-0.693491\pi$
$983$	−1.38481e8	+	7.99519e7i	−0.145790	+	0.0841722i	0.425330	+	0.905038i	$0.360158\pi$
$984$		0			0
$985$	1.17923e9	+	6.80828e8i	1.23393	+	0.712407i
$986$		0			0
$987$	−1.42370e8	−	4.02871e8i	−0.148070	−	0.419001i
$988$		0			0
$989$	3.41710e6	−	5.91859e6i	0.00353239	−	0.00611828i
$990$		0			0
$991$	−2.34805e8	−	4.06694e8i	−0.241260	−	0.417875i	0.719813	−	0.694168i	$-0.244227\pi$
$991$	−2.34805e8	−	4.06694e8i	−0.241260	−	0.417875i	−0.961074	+	0.276293i	$0.910894\pi$
$992$		0			0
$993$		−	7.26260e8i		−	0.741727i
$994$		0			0
$995$	−7.93041e8			−0.805056
$996$		0			0
$997$	−1.16551e9	+	6.72905e8i	−1.17606	+	0.678998i	−0.955100	−	0.296285i	$-0.904252\pi$
$997$	−1.16551e9	+	6.72905e8i	−1.17606	+	0.678998i	−0.220959	+	0.975283i	$0.570919\pi$
$998$		0			0
$999$	2.41646e8	+	1.39515e8i	0.242373	+	0.139934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.h.145.3		24
4.3	odd	2		168.7.z.a.145.3	yes	24
7.3	odd	6	inner	336.7.bh.h.241.3		24
28.3	even	6		168.7.z.a.73.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.7.z.a.73.3	✓	24	28.3	even	6
168.7.z.a.145.3	yes	24	4.3	odd	2
336.7.bh.h.145.3		24	1.1	even	1	trivial
336.7.bh.h.241.3		24	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(13.5000 - 7.79423i) q^{3} +(-126.269 - 72.9015i) q^{5} +(-114.286 - 323.400i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 - 7.79423i) q^{3} +(-126.269 - 72.9015i) q^{5} +(-114.286 - 323.400i) q^{7} +(121.500 - 210.444i) q^{9} +(-1040.12 - 1801.54i) q^{11} -2134.45i q^{13} -2272.84 q^{15} +(2554.60 - 1474.90i) q^{17} +(-3678.74 - 2123.92i) q^{19} +(-4063.52 - 3475.13i) q^{21} +(1812.04 - 3138.54i) q^{23} +(2816.76 + 4878.77i) q^{25} -3788.00i q^{27} -257.072 q^{29} +(40538.8 - 23405.1i) q^{31} +(-28083.3 - 16213.9i) q^{33} +(-9145.56 + 49167.1i) q^{35} +(-36830.7 + 63792.7i) q^{37} +(-16636.4 - 28815.0i) q^{39} -89800.2i q^{41} +1885.78 q^{43} +(-30683.4 + 17715.1i) q^{45} +(69207.5 + 39957.0i) q^{47} +(-91526.4 + 73920.3i) q^{49} +(22991.4 - 39822.3i) q^{51} +(-32970.0 - 57105.7i) q^{53} +303306. i q^{55} -66217.4 q^{57} +(-130044. + 75081.2i) q^{59} +(-173828. - 100359. i) q^{61} +(-81943.4 - 15242.3i) q^{63} +(-155604. + 269515. i) q^{65} +(228278. + 395389. i) q^{67} -56493.8i q^{69} +365090. q^{71} +(-236879. + 136762. i) q^{73} +(76052.5 + 43908.9i) q^{75} +(-463748. + 542267. i) q^{77} +(306802. - 531397. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -490649. i q^{83} -430090. q^{85} +(-3470.47 + 2003.68i) q^{87} +(-617623. - 356585. i) q^{89} +(-690280. + 243937. i) q^{91} +(364849. - 631937. i) q^{93} +(309674. + 536372. i) q^{95} +294637. i q^{97} -505499. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) \) 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9} + 1190 q^{11} - 2268 q^{15} - 1500 q^{17} + 13446 q^{19} - 2106 q^{21} - 21504 q^{23} + 22542 q^{25} - 85484 q^{29} - 6264 q^{31} + 32130 q^{33} - 32268 q^{35} - 46938 q^{37} + 17010 q^{39} + 19548 q^{43} - 30618 q^{45} + 167004 q^{47} + 250644 q^{49} - 13500 q^{51} - 258982 q^{53} + 242028 q^{57} - 744834 q^{59} - 390096 q^{61} - 59778 q^{63} - 19388 q^{65} - 62742 q^{67} + 1102984 q^{71} - 663534 q^{73} + 608634 q^{75} + 404298 q^{77} + 271032 q^{79} - 708588 q^{81} + 2540040 q^{85} - 1154034 q^{87} - 433740 q^{89} + 2142270 q^{91} - 56376 q^{93} - 2205360 q^{95} + 578340 q^{99}+O(q^{100}) \) 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9 + 1190 * q^11 - 2268 * q^15 - 1500 * q^17 + 13446 * q^19 - 2106 * q^21 - 21504 * q^23 + 22542 * q^25 - 85484 * q^29 - 6264 * q^31 + 32130 * q^33 - 32268 * q^35 - 46938 * q^37 + 17010 * q^39 + 19548 * q^43 - 30618 * q^45 + 167004 * q^47 + 250644 * q^49 - 13500 * q^51 - 258982 * q^53 + 242028 * q^57 - 744834 * q^59 - 390096 * q^61 - 59778 * q^63 - 19388 * q^65 - 62742 * q^67 + 1102984 * q^71 - 663534 * q^73 + 608634 * q^75 + 404298 * q^77 + 271032 * q^79 - 708588 * q^81 + 2540040 * q^85 - 1154034 * q^87 - 433740 * q^89 + 2142270 * q^91 - 56376 * q^93 - 2205360 * q^95 + 578340 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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