LMFDB - Embedded newform 384.7.l.a.31.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,7,Mod(31,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("384.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	384.l (of order $4$, 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:	$88.3407681100$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.24
Character	$\chi$	$=$	384.31
Dual form			384.7.l.a.223.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.0227 + 11.0227i) q^{3} +(159.596 + 159.596i) q^{5} +527.602 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(11.0227 + 11.0227i) q^{3} +(159.596 + 159.596i) q^{5} +527.602 q^{7} +243.000i q^{9} +(-134.486 + 134.486i) q^{11} +(-1265.37 + 1265.37i) q^{13} +3518.36i q^{15} +8418.61 q^{17} +(-2553.03 - 2553.03i) q^{19} +(5815.60 + 5815.60i) q^{21} +8709.06 q^{23} +35316.9i q^{25} +(-2678.52 + 2678.52i) q^{27} +(-19317.9 + 19317.9i) q^{29} +16542.9i q^{31} -2964.80 q^{33} +(84203.3 + 84203.3i) q^{35} +(28820.7 + 28820.7i) q^{37} -27895.7 q^{39} -56876.6i q^{41} +(54549.8 - 54549.8i) q^{43} +(-38781.9 + 38781.9i) q^{45} -145597. i q^{47} +160715. q^{49} +(92795.8 + 92795.8i) q^{51} +(-84395.8 - 84395.8i) q^{53} -42926.9 q^{55} -56282.6i q^{57} +(-125938. + 125938. i) q^{59} +(52486.8 - 52486.8i) q^{61} +128207. i q^{63} -403898. q^{65} +(-142096. - 142096. i) q^{67} +(95997.4 + 95997.4i) q^{69} +25672.8 q^{71} -538587. i q^{73} +(-389288. + 389288. i) q^{75} +(-70955.1 + 70955.1i) q^{77} +122911. i q^{79} -59049.0 q^{81} +(539606. + 539606. i) q^{83} +(1.34358e6 + 1.34358e6i) q^{85} -425871. q^{87} -504858. i q^{89} +(-667614. + 667614. i) q^{91} +(-182348. + 182348. i) q^{93} -814908. i q^{95} -781168. q^{97} +(-32680.1 - 32680.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 2720 q^{11} - 3936 q^{19} - 26240 q^{23} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 340704 q^{43} + 806736 q^{49} + 80352 q^{51} - 443680 q^{53} - 232704 q^{55} - 886144 q^{59} + 326496 q^{61} - 372832 q^{65} - 962112 q^{67} - 541728 q^{69} - 534016 q^{71} - 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} - 2497760 q^{83} + 372000 q^{85} + 775008 q^{91} - 660960 q^{99}+O(q^{100}) $ 48 * q - 2720 * q^11 - 3936 * q^19 - 26240 * q^23 - 66400 * q^29 + 162336 * q^35 + 7200 * q^37 + 340704 * q^43 + 806736 * q^49 + 80352 * q^51 - 443680 * q^53 - 232704 * q^55 - 886144 * q^59 + 326496 * q^61 - 372832 * q^65 - 962112 * q^67 - 541728 * q^69 - 534016 * q^71 - 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 - 2497760 * q^83 + 372000 * q^85 + 775008 * q^91 - 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$4$		0			0
$5$	159.596	+	159.596i	1.27677	+	1.27677i	0.942465	+	0.334304i	$0.108501\pi$
$5$	159.596	+	159.596i	1.27677	+	1.27677i	0.334304	+	0.942465i	$0.391499\pi$
$6$		0			0
$7$	527.602			1.53820			0.769100	−	0.639129i	$-0.220705\pi$
$7$	527.602			1.53820			0.769100	+	0.639129i	$0.220705\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	−134.486	+	134.486i	−0.101041	+	0.101041i	−0.755820	−	0.654779i	$-0.772762\pi$
$11$	−134.486	+	134.486i	−0.101041	+	0.101041i	0.654779	+	0.755820i	$0.272762\pi$
$12$		0			0
$13$	−1265.37	+	1265.37i	−0.575955	+	0.575955i	−0.933786	−	0.357831i	$-0.883516\pi$
$13$	−1265.37	+	1265.37i	−0.575955	+	0.575955i	0.357831	+	0.933786i	$0.383516\pi$
$14$		0			0
$15$			3518.36i			1.04248i
$16$		0			0
$17$	8418.61			1.71354			0.856769	−	0.515701i	$-0.172468\pi$
$17$	8418.61			1.71354			0.856769	+	0.515701i	$0.172468\pi$
$18$		0			0
$19$	−2553.03	−	2553.03i	−0.372216	−	0.372216i	0.496068	−	0.868284i	$-0.334777\pi$
$19$	−2553.03	−	2553.03i	−0.372216	−	0.372216i	−0.868284	+	0.496068i	$0.834777\pi$
$20$		0			0
$21$	5815.60	+	5815.60i	0.627967	+	0.627967i
$22$		0			0
$23$	8709.06			0.715793			0.357897	−	0.933761i	$-0.383494\pi$
$23$	8709.06			0.715793			0.357897	+	0.933761i	$0.383494\pi$
$24$		0			0
$25$			35316.9i			2.26028i
$26$		0			0
$27$	−2678.52	+	2678.52i	−0.136083	+	0.136083i
$28$		0			0
$29$	−19317.9	+	19317.9i	−0.792075	+	0.792075i	−0.981831	−	0.189756i	$-0.939230\pi$
$29$	−19317.9	+	19317.9i	−0.792075	+	0.792075i	0.189756	+	0.981831i	$0.439230\pi$
$30$		0			0
$31$			16542.9i			0.555299i	0.960682	+	0.277650i	$0.0895554\pi$
$31$			16542.9i			0.555299i	−0.960682	+	0.277650i	$0.910445\pi$
$32$		0			0
$33$	−2964.80			−0.0824998
$34$		0			0
$35$	84203.3	+	84203.3i	1.96393	+	1.96393i
$36$		0			0
$37$	28820.7	+	28820.7i	0.568983	+	0.568983i	0.931844	−	0.362860i	$-0.118200\pi$
$37$	28820.7	+	28820.7i	0.568983	+	0.568983i	−0.362860	+	0.931844i	$0.618200\pi$
$38$		0			0
$39$	−27895.7			−0.470266
$40$		0			0
$41$		−	56876.6i		−	0.825244i	−0.910902	−	0.412622i	$-0.864613\pi$
$41$		−	56876.6i		−	0.825244i	0.910902	−	0.412622i	$-0.135387\pi$
$42$		0			0
$43$	54549.8	−	54549.8i	0.686101	−	0.686101i	−0.275267	−	0.961368i	$-0.588766\pi$
$43$	54549.8	−	54549.8i	0.686101	−	0.686101i	0.961368	+	0.275267i	$0.0887663\pi$
$44$		0			0
$45$	−38781.9	+	38781.9i	−0.425590	+	0.425590i
$46$		0			0
$47$		−	145597.i		−	1.40236i	−0.712985	−	0.701179i	$-0.752657\pi$
$47$		−	145597.i		−	1.40236i	0.712985	−	0.701179i	$-0.247343\pi$
$48$		0			0
$49$	160715.			1.36606
$50$		0			0
$51$	92795.8	+	92795.8i	0.699549	+	0.699549i
$52$		0			0
$53$	−84395.8	−	84395.8i	−0.566883	−	0.566883i	0.364371	−	0.931254i	$-0.381284\pi$
$53$	−84395.8	−	84395.8i	−0.566883	−	0.566883i	−0.931254	+	0.364371i	$0.881284\pi$
$54$		0			0
$55$	−42926.9			−0.258013
$56$		0			0
$57$		−	56282.6i		−	0.303913i
$58$		0			0
$59$	−125938.	+	125938.i	−0.613198	+	0.613198i	−0.943778	−	0.330580i	$-0.892756\pi$
$59$	−125938.	+	125938.i	−0.613198	+	0.613198i	0.330580	+	0.943778i	$0.392756\pi$
$60$		0			0
$61$	52486.8	−	52486.8i	0.231239	−	0.231239i	−0.581971	−	0.813210i	$-0.697718\pi$
$61$	52486.8	−	52486.8i	0.231239	−	0.231239i	0.813210	+	0.581971i	$0.197718\pi$
$62$		0			0
$63$			128207.i			0.512733i
$64$		0			0
$65$	−403898.			−1.47072
$66$		0			0
$67$	−142096.	−	142096.i	−0.472453	−	0.472453i	0.430255	−	0.902707i	$-0.358424\pi$
$67$	−142096.	−	142096.i	−0.472453	−	0.472453i	−0.902707	+	0.430255i	$0.858424\pi$
$68$		0			0
$69$	95997.4	+	95997.4i	0.292221	+	0.292221i
$70$		0			0
$71$	25672.8			0.0717295			0.0358647	−	0.999357i	$-0.488581\pi$
$71$	25672.8			0.0717295			0.0358647	+	0.999357i	$0.488581\pi$
$72$		0			0
$73$		−	538587.i		−	1.38448i	−0.721667	−	0.692240i	$-0.756624\pi$
$73$		−	538587.i		−	1.38448i	0.721667	−	0.692240i	$-0.243376\pi$
$74$		0			0
$75$	−389288.	+	389288.i	−0.922756	+	0.922756i
$76$		0			0
$77$	−70955.1	+	70955.1i	−0.155422	+	0.155422i
$78$		0			0
$79$			122911.i			0.249293i	0.992201	+	0.124647i	$0.0397797\pi$
$79$			122911.i			0.249293i	−0.992201	+	0.124647i	$0.960220\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	539606.	+	539606.i	0.943719	+	0.943719i	0.998498	−	0.0547796i	$-0.0174456\pi$
$83$	539606.	+	539606.i	0.943719	+	0.943719i	−0.0547796	+	0.998498i	$0.517446\pi$
$84$		0			0
$85$	1.34358e6	+	1.34358e6i	2.18779	+	2.18779i
$86$		0			0
$87$	−425871.			−0.646727
$88$		0			0
$89$		−	504858.i		−	0.716142i	−0.933694	−	0.358071i	$-0.883435\pi$
$89$		−	504858.i		−	0.716142i	0.933694	−	0.358071i	$-0.116565\pi$
$90$		0			0
$91$	−667614.	+	667614.i	−0.885934	+	0.885934i
$92$		0			0
$93$	−182348.	+	182348.i	−0.226700	+	0.226700i
$94$		0			0
$95$		−	814908.i		−	0.950468i
$96$		0			0
$97$	−781168.			−0.855913			−0.427956	−	0.903799i	$-0.640766\pi$
$97$	−781168.			−0.855913			−0.427956	+	0.903799i	$0.640766\pi$
$98$		0			0
$99$	−32680.1	−	32680.1i	−0.0336804	−	0.0336804i
$100$		0			0
$101$	−1.12255e6	−	1.12255e6i	−1.08953	−	1.08953i	−0.995576	−	0.0939554i	$-0.970049\pi$
$101$	−1.12255e6	−	1.12255e6i	−1.08953	−	1.08953i	−0.0939554	−	0.995576i	$-0.529951\pi$
$102$		0			0
$103$	805137.			0.736814			0.368407	−	0.929665i	$-0.379903\pi$
$103$	805137.			0.736814			0.368407	+	0.929665i	$0.379903\pi$
$104$		0			0
$105$			1.85630e6i			1.60354i
$106$		0			0
$107$	1.18804e6	−	1.18804e6i	0.969796	−	0.969796i	−0.0297609	−	0.999557i	$-0.509475\pi$
$107$	1.18804e6	−	1.18804e6i	0.969796	−	0.969796i	0.999557	+	0.0297609i	$0.00947459\pi$
$108$		0			0
$109$	−1.29798e6	+	1.29798e6i	−1.00228	+	1.00228i	−0.00228452	+	0.999997i	$0.500727\pi$
$109$	−1.29798e6	+	1.29798e6i	−1.00228	+	1.00228i	−0.999997	+	0.00228452i	$0.999273\pi$
$110$		0			0
$111$			635364.i			0.464573i
$112$		0			0
$113$	−1.54963e6			−1.07397			−0.536987	−	0.843591i	$-0.680437\pi$
$113$	−1.54963e6			−1.07397			−0.536987	+	0.843591i	$0.680437\pi$
$114$		0			0
$115$	1.38993e6	+	1.38993e6i	0.913903	+	0.913903i
$116$		0			0
$117$	−307486.	−	307486.i	−0.191985	−	0.191985i
$118$		0			0
$119$	4.44168e6			2.63576
$120$		0			0
$121$			1.73539e6i			0.979581i
$122$		0			0
$123$	626934.	−	626934.i	0.336904	−	0.336904i
$124$		0			0
$125$	−3.14275e6	+	3.14275e6i	−1.60909	+	1.60909i
$126$		0			0
$127$			1.75836e6i			0.858413i	0.903206	+	0.429207i	$0.141207\pi$
$127$			1.75836e6i			0.858413i	−0.903206	+	0.429207i	$0.858793\pi$
$128$		0			0
$129$	1.20257e6			0.560199
$130$		0			0
$131$	1.27585e6	+	1.27585e6i	0.567526	+	0.567526i	0.931435	−	0.363908i	$-0.118558\pi$
$131$	1.27585e6	+	1.27585e6i	0.567526	+	0.567526i	−0.363908	+	0.931435i	$0.618558\pi$
$132$		0			0
$133$	−1.34698e6	−	1.34698e6i	−0.572542	−	0.572542i
$134$		0			0
$135$	−854962.			−0.347493
$136$		0			0
$137$		−	337811.i		−	0.131375i	−0.997840	−	0.0656874i	$-0.979076\pi$
$137$		−	337811.i		−	0.131375i	0.997840	−	0.0656874i	$-0.0209240\pi$
$138$		0			0
$139$	2.06015e6	−	2.06015e6i	0.767103	−	0.767103i	−0.210493	−	0.977595i	$-0.567507\pi$
$139$	2.06015e6	−	2.06015e6i	0.767103	−	0.767103i	0.977595	+	0.210493i	$0.0675069\pi$
$140$		0			0
$141$	1.60487e6	−	1.60487e6i	0.572510	−	0.572510i
$142$		0			0
$143$		−	340350.i		−	0.116390i
$144$		0			0
$145$	−6.16613e6			−2.02259
$146$		0			0
$147$	1.77152e6	+	1.77152e6i	0.557690	+	0.557690i
$148$		0			0
$149$	1.84110e6	+	1.84110e6i	0.556568	+	0.556568i	0.928329	−	0.371761i	$-0.121246\pi$
$149$	1.84110e6	+	1.84110e6i	0.556568	+	0.556568i	−0.371761	+	0.928329i	$0.621246\pi$
$150$		0			0
$151$	748278.			0.217336			0.108668	−	0.994078i	$-0.465341\pi$
$151$	748278.			0.217336			0.108668	+	0.994078i	$0.465341\pi$
$152$		0			0
$153$			2.04572e6i			0.571179i
$154$		0			0
$155$	−2.64019e6	+	2.64019e6i	−0.708989	+	0.708989i
$156$		0			0
$157$	−1.42496e6	+	1.42496e6i	−0.368217	+	0.368217i	−0.866827	−	0.498609i	$-0.833844\pi$
$157$	−1.42496e6	+	1.42496e6i	−0.368217	+	0.368217i	0.498609	+	0.866827i	$0.333844\pi$
$158$		0			0
$159$		−	1.86054e6i		−	0.462858i
$160$		0			0
$161$	4.59492e6			1.10103
$162$		0			0
$163$	−488683.	−	488683.i	−0.112840	−	0.112840i	0.648432	−	0.761272i	$-0.275425\pi$
$163$	−488683.	−	488683.i	−0.112840	−	0.112840i	−0.761272	+	0.648432i	$0.775425\pi$
$164$		0			0
$165$	−473170.	−	473170.i	−0.105333	−	0.105333i
$166$		0			0
$167$	−8.39552e6			−1.80260			−0.901298	−	0.433200i	$-0.857384\pi$
$167$	−8.39552e6			−1.80260			−0.901298	+	0.433200i	$0.857384\pi$
$168$		0			0
$169$			1.62447e6i			0.336551i
$170$		0			0
$171$	620386.	−	620386.i	0.124072	−	0.124072i
$172$		0			0
$173$	−626062.	+	626062.i	−0.120915	+	0.120915i	−0.764975	−	0.644060i	$-0.777249\pi$
$173$	−626062.	+	626062.i	−0.120915	+	0.120915i	0.644060	+	0.764975i	$0.277249\pi$
$174$		0			0
$175$			1.86333e7i			3.47676i
$176$		0			0
$177$	−2.77635e6			−0.500674
$178$		0			0
$179$	627061.	+	627061.i	0.109333	+	0.109333i	0.759657	−	0.650324i	$-0.225367\pi$
$179$	627061.	+	627061.i	0.109333	+	0.109333i	−0.650324	+	0.759657i	$0.725367\pi$
$180$		0			0
$181$	−6.94096e6	−	6.94096e6i	−1.17053	−	1.17053i	−0.982083	−	0.188450i	$-0.939653\pi$
$181$	−6.94096e6	−	6.94096e6i	−1.17053	−	1.17053i	−0.188450	−	0.982083i	$-0.560347\pi$
$182$		0			0
$183$	1.15709e6			0.188806
$184$		0			0
$185$			9.19935e6i			1.45292i
$186$		0			0
$187$	−1.13218e6	+	1.13218e6i	−0.173138	+	0.173138i
$188$		0			0
$189$	−1.41319e6	+	1.41319e6i	−0.209322	+	0.209322i
$190$		0			0
$191$			6.45958e6i			0.927051i	0.886083	+	0.463526i	$0.153416\pi$
$191$			6.45958e6i			0.927051i	−0.886083	+	0.463526i	$0.846584\pi$
$192$		0			0
$193$	5.10553e6			0.710181			0.355090	−	0.934832i	$-0.384450\pi$
$193$	5.10553e6			0.710181			0.355090	+	0.934832i	$0.384450\pi$
$194$		0			0
$195$	−4.45204e6	−	4.45204e6i	−0.600421	−	0.600421i
$196$		0			0
$197$	−1.12787e6	−	1.12787e6i	−0.147523	−	0.147523i	0.629487	−	0.777011i	$-0.283265\pi$
$197$	−1.12787e6	−	1.12787e6i	−0.147523	−	0.147523i	−0.777011	+	0.629487i	$0.783265\pi$
$198$		0			0
$199$	1.11015e7			1.40872			0.704359	−	0.709844i	$-0.251235\pi$
$199$	1.11015e7			1.40872			0.704359	+	0.709844i	$0.251235\pi$
$200$		0			0
$201$		−	3.13257e6i		−	0.385756i
$202$		0			0
$203$	−1.01922e7	+	1.01922e7i	−1.21837	+	1.21837i
$204$		0			0
$205$	9.07729e6	−	9.07729e6i	1.05365	−	1.05365i
$206$		0			0
$207$			2.11630e6i			0.238598i
$208$		0			0
$209$	686693.			0.0752184
$210$		0			0
$211$	2.86403e6	+	2.86403e6i	0.304881	+	0.304881i	0.842920	−	0.538039i	$-0.180835\pi$
$211$	2.86403e6	+	2.86403e6i	0.304881	+	0.304881i	−0.538039	+	0.842920i	$0.680835\pi$
$212$		0			0
$213$	282983.	+	282983.i	0.0292834	+	0.0292834i
$214$		0			0
$215$	1.74119e7			1.75199
$216$		0			0
$217$			8.72808e6i			0.854161i
$218$		0			0
$219$	5.93668e6	−	5.93668e6i	0.565212	−	0.565212i
$220$		0			0
$221$	−1.06527e7	+	1.06527e7i	−0.986921	+	0.986921i
$222$		0			0
$223$		−	1.62079e7i		−	1.46155i	−0.682620	−	0.730774i	$-0.739159\pi$
$223$		−	1.62079e7i		−	1.46155i	0.682620	−	0.730774i	$-0.260841\pi$
$224$		0			0
$225$	−8.58200e6			−0.753427
$226$		0			0
$227$	4.05438e6	+	4.05438e6i	0.346615	+	0.346615i	0.858847	−	0.512232i	$-0.171181\pi$
$227$	4.05438e6	+	4.05438e6i	0.346615	+	0.346615i	−0.512232	+	0.858847i	$0.671181\pi$
$228$		0			0
$229$	−865717.	−	865717.i	−0.0720890	−	0.0720890i	0.670143	−	0.742232i	$-0.266233\pi$
$229$	−865717.	−	865717.i	−0.0720890	−	0.0720890i	−0.742232	+	0.670143i	$0.766233\pi$
$230$		0			0
$231$	−1.56423e6			−0.126901
$232$		0			0
$233$		−	3.51049e6i		−	0.277524i	−0.990326	−	0.138762i	$-0.955688\pi$
$233$		−	3.51049e6i		−	0.277524i	0.990326	−	0.138762i	$-0.0443123\pi$
$234$		0			0
$235$	2.32367e7	−	2.32367e7i	1.79049	−	1.79049i
$236$		0			0
$237$	−1.35481e6	+	1.35481e6i	−0.101774	+	0.101774i
$238$		0			0
$239$		−	1.10471e6i		−	0.0809195i	−0.999181	−	0.0404598i	$-0.987118\pi$
$239$		−	1.10471e6i		−	0.0809195i	0.999181	−	0.0404598i	$-0.0128823\pi$
$240$		0			0
$241$	−1.84123e7			−1.31540			−0.657699	−	0.753281i	$-0.728470\pi$
$241$	−1.84123e7			−1.31540			−0.657699	+	0.753281i	$0.728470\pi$
$242$		0			0
$243$	−650880.	−	650880.i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	2.56495e7	+	2.56495e7i	1.74414	+	1.74414i
$246$		0			0
$247$	6.46107e6			0.428760
$248$		0			0
$249$			1.18958e7i			0.770543i
$250$		0			0
$251$	−1.63036e7	+	1.63036e7i	−1.03101	+	1.03101i	−0.0315063	+	0.999504i	$0.510030\pi$
$251$	−1.63036e7	+	1.63036e7i	−1.03101	+	1.03101i	−0.999504	+	0.0315063i	$0.989970\pi$
$252$		0			0
$253$	−1.17125e6	+	1.17125e6i	−0.0723247	+	0.0723247i
$254$		0			0
$255$			2.96197e7i			1.78632i
$256$		0			0
$257$	1.66324e6			0.0979840			0.0489920	−	0.998799i	$-0.484399\pi$
$257$	1.66324e6			0.0979840			0.0489920	+	0.998799i	$0.484399\pi$
$258$		0			0
$259$	1.52059e7	+	1.52059e7i	0.875209	+	0.875209i
$260$		0			0
$261$	−4.69425e6	−	4.69425e6i	−0.264025	−	0.264025i
$262$		0			0
$263$	−7.75539e6			−0.426321			−0.213160	−	0.977017i	$-0.568376\pi$
$263$	−7.75539e6			−0.426321			−0.213160	+	0.977017i	$0.568376\pi$
$264$		0			0
$265$		−	2.69385e7i		−	1.44756i
$266$		0			0
$267$	5.56490e6	−	5.56490e6i	0.292364	−	0.292364i
$268$		0			0
$269$	−1.26225e7	+	1.26225e7i	−0.648469	+	0.648469i	−0.952623	−	0.304154i	$-0.901626\pi$
$269$	−1.26225e7	+	1.26225e7i	−0.648469	+	0.648469i	0.304154	+	0.952623i	$0.401626\pi$
$270$		0			0
$271$		−	3.15459e7i		−	1.58502i	−0.609859	−	0.792510i	$-0.708774\pi$
$271$		−	3.15459e7i		−	1.58502i	0.609859	−	0.792510i	$-0.291226\pi$
$272$		0			0
$273$	−1.47178e7			−0.723362
$274$		0			0
$275$	−4.74962e6	−	4.74962e6i	−0.228382	−	0.228382i
$276$		0			0
$277$	8.67894e6	+	8.67894e6i	0.408345	+	0.408345i	0.881161	−	0.472816i	$-0.156762\pi$
$277$	8.67894e6	+	8.67894e6i	0.408345	+	0.408345i	−0.472816	+	0.881161i	$0.656762\pi$
$278$		0			0
$279$	−4.01993e6			−0.185100
$280$		0			0
$281$		−	9.81261e6i		−	0.442248i	−0.975246	−	0.221124i	$-0.929027\pi$
$281$		−	9.81261e6i		−	0.442248i	0.975246	−	0.221124i	$-0.0709725\pi$
$282$		0			0
$283$	−9.30687e6	+	9.30687e6i	−0.410624	+	0.410624i	−0.881956	−	0.471332i	$-0.843773\pi$
$283$	−9.30687e6	+	9.30687e6i	−0.410624	+	0.410624i	0.471332	+	0.881956i	$0.343773\pi$
$284$		0			0
$285$	8.98249e6	−	8.98249e6i	0.388027	−	0.388027i
$286$		0			0
$287$		−	3.00082e7i		−	1.26939i
$288$		0			0
$289$	4.67354e7			1.93621
$290$		0			0
$291$	−8.61059e6	−	8.61059e6i	−0.349425	−	0.349425i
$292$		0			0
$293$	−1.78308e7	−	1.78308e7i	−0.708871	−	0.708871i	0.257427	−	0.966298i	$-0.417125\pi$
$293$	−1.78308e7	−	1.78308e7i	−0.708871	−	0.708871i	−0.966298	+	0.257427i	$0.917125\pi$
$294$		0			0
$295$	−4.01984e7			−1.56582
$296$		0			0
$297$		−	720446.i		−	0.0274999i
$298$		0			0
$299$	−1.10202e7	+	1.10202e7i	−0.412265	+	0.412265i
$300$		0			0
$301$	2.87806e7	−	2.87806e7i	1.05536	−	1.05536i
$302$		0			0
$303$		−	2.47470e7i		−	0.889599i
$304$		0			0
$305$	1.67534e7			0.590477
$306$		0			0
$307$	1.44714e6	+	1.44714e6i	0.0500145	+	0.0500145i	0.731672	−	0.681657i	$-0.238740\pi$
$307$	1.44714e6	+	1.44714e6i	0.0500145	+	0.0500145i	−0.681657	+	0.731672i	$0.738740\pi$
$308$		0			0
$309$	8.87478e6	+	8.87478e6i	0.300803	+	0.300803i
$310$		0			0
$311$	−5.04892e7			−1.67849			−0.839243	−	0.543757i	$-0.817001\pi$
$311$	−5.04892e7			−1.67849			−0.839243	+	0.543757i	$0.817001\pi$
$312$		0			0
$313$		−	1.12021e7i		−	0.365314i	−0.983177	−	0.182657i	$-0.941530\pi$
$313$		−	1.12021e7i		−	0.365314i	0.983177	−	0.182657i	$-0.0584698\pi$
$314$		0			0
$315$	−2.04614e7	+	2.04614e7i	−0.654642	+	0.654642i
$316$		0			0
$317$	−2.16258e7	+	2.16258e7i	−0.678882	+	0.678882i	−0.959747	−	0.280866i	$-0.909378\pi$
$317$	−2.16258e7	+	2.16258e7i	−0.678882	+	0.678882i	0.280866	+	0.959747i	$0.409378\pi$
$318$		0			0
$319$		−	5.19598e6i		−	0.160065i
$320$		0			0
$321$	2.61909e7			0.791835
$322$		0			0
$323$	−2.14930e7	−	2.14930e7i	−0.637806	−	0.637806i
$324$		0			0
$325$	−4.46891e7	−	4.46891e7i	−1.30182	−	1.30182i
$326$		0			0
$327$	−2.86146e7			−0.818360
$328$		0			0
$329$		−	7.68173e7i		−	2.15711i
$330$		0			0
$331$	9.33730e6	−	9.33730e6i	0.257476	−	0.257476i	−0.566551	−	0.824027i	$-0.691722\pi$
$331$	9.33730e6	−	9.33730e6i	0.257476	−	0.257476i	0.824027	+	0.566551i	$0.191722\pi$
$332$		0			0
$333$	−7.00343e6	+	7.00343e6i	−0.189661	+	0.189661i
$334$		0			0
$335$		−	4.53561e7i		−	1.20643i
$336$		0			0
$337$	−1.44964e6			−0.0378765			−0.0189382	−	0.999821i	$-0.506029\pi$
$337$	−1.44964e6			−0.0378765			−0.0189382	+	0.999821i	$0.506029\pi$
$338$		0			0
$339$	−1.70811e7	−	1.70811e7i	−0.438448	−	0.438448i
$340$		0			0
$341$	−2.22479e6	−	2.22479e6i	−0.0561081	−	0.0561081i
$342$		0			0
$343$	2.27218e7			0.563067
$344$		0			0
$345$			3.06416e7i			0.746199i
$346$		0			0
$347$	5.79136e7	−	5.79136e7i	1.38609	−	1.38609i	0.552737	−	0.833356i	$-0.313583\pi$
$347$	5.79136e7	−	5.79136e7i	1.38609	−	1.38609i	0.833356	−	0.552737i	$-0.186417\pi$
$348$		0			0
$349$	2.49499e7	−	2.49499e7i	0.586938	−	0.586938i	−0.349863	−	0.936801i	$-0.613772\pi$
$349$	2.49499e7	−	2.49499e7i	0.586938	−	0.586938i	0.936801	+	0.349863i	$0.113772\pi$
$350$		0			0
$351$		−	6.77865e6i		−	0.156755i
$352$		0			0
$353$	−2.24022e7			−0.509292			−0.254646	−	0.967034i	$-0.581959\pi$
$353$	−2.24022e7			−0.509292			−0.254646	+	0.967034i	$0.581959\pi$
$354$		0			0
$355$	4.09728e6	+	4.09728e6i	0.0915820	+	0.0915820i
$356$		0			0
$357$	4.89593e7	+	4.89593e7i	1.07605	+	1.07605i
$358$		0			0
$359$	6.11369e7			1.32136			0.660679	−	0.750669i	$-0.270269\pi$
$359$	6.11369e7			1.32136			0.660679	+	0.750669i	$0.270269\pi$
$360$		0			0
$361$		−	3.40100e7i		−	0.722910i
$362$		0			0
$363$	−1.91287e7	+	1.91287e7i	−0.399912	+	0.399912i
$364$		0			0
$365$	8.59563e7	−	8.59563e7i	1.76766	−	1.76766i
$366$		0			0
$367$			2.51211e7i			0.508207i	0.967177	+	0.254104i	$0.0817804\pi$
$367$			2.51211e7i			0.508207i	−0.967177	+	0.254104i	$0.918220\pi$
$368$		0			0
$369$	1.38210e7			0.275081
$370$		0			0
$371$	−4.45274e7	−	4.45274e7i	−0.871978	−	0.871978i
$372$		0			0
$373$	−6.03278e6	−	6.03278e6i	−0.116249	−	0.116249i	0.646589	−	0.762838i	$-0.276195\pi$
$373$	−6.03278e6	−	6.03278e6i	−0.116249	−	0.116249i	−0.762838	+	0.646589i	$0.776195\pi$
$374$		0			0
$375$	−6.92832e7			−1.31381
$376$		0			0
$377$		−	4.88888e7i		−	0.912400i
$378$		0			0
$379$	−1.10680e7	+	1.10680e7i	−0.203306	+	0.203306i	−0.801415	−	0.598109i	$-0.795919\pi$
$379$	−1.10680e7	+	1.10680e7i	−0.203306	+	0.203306i	0.598109	+	0.801415i	$0.295919\pi$
$380$		0			0
$381$	−1.93819e7	+	1.93819e7i	−0.350446	+	0.350446i
$382$		0			0
$383$		−	1.89958e7i		−	0.338113i	−0.985606	−	0.169057i	$-0.945928\pi$
$383$		−	1.89958e7i		−	0.338113i	0.985606	−	0.169057i	$-0.0540721\pi$
$384$		0			0
$385$	−2.26483e7			−0.396875
$386$		0			0
$387$	1.32556e7	+	1.32556e7i	0.228700	+	0.228700i
$388$		0			0
$389$	3.85430e7	+	3.85430e7i	0.654782	+	0.654782i	0.954141	−	0.299359i	$-0.0967727\pi$
$389$	3.85430e7	+	3.85430e7i	0.654782	+	0.654782i	−0.299359	+	0.954141i	$0.596773\pi$
$390$		0			0
$391$	7.33182e7			1.22654
$392$		0			0
$393$			2.81266e7i			0.463383i
$394$		0			0
$395$	−1.96162e7	+	1.96162e7i	−0.318290	+	0.318290i
$396$		0			0
$397$	3.73215e7	−	3.73215e7i	0.596468	−	0.596468i	−0.342903	−	0.939371i	$-0.611410\pi$
$397$	3.73215e7	−	3.73215e7i	0.596468	−	0.596468i	0.939371	+	0.342903i	$0.111410\pi$
$398$		0			0
$399$		−	2.96948e7i		−	0.467479i
$400$		0			0
$401$	6.22774e6			0.0965822			0.0482911	−	0.998833i	$-0.484622\pi$
$401$	6.22774e6			0.0965822			0.0482911	+	0.998833i	$0.484622\pi$
$402$		0			0
$403$	−2.09330e7	−	2.09330e7i	−0.319828	−	0.319828i
$404$		0			0
$405$	−9.42399e6	−	9.42399e6i	−0.141863	−	0.141863i
$406$		0			0
$407$	−7.75196e6			−0.114982
$408$		0			0
$409$		−	2.45384e7i		−	0.358654i	−0.983790	−	0.179327i	$-0.942608\pi$
$409$		−	2.45384e7i		−	0.358654i	0.983790	−	0.179327i	$-0.0573920\pi$
$410$		0			0
$411$	3.72359e6	−	3.72359e6i	0.0536336	−	0.0536336i
$412$		0			0
$413$	−6.64451e7	+	6.64451e7i	−0.943220	+	0.943220i
$414$		0			0
$415$			1.72238e8i			2.40982i
$416$		0			0
$417$	4.54167e7			0.626337
$418$		0			0
$419$	2.00406e7	+	2.00406e7i	0.272439	+	0.272439i	0.830081	−	0.557642i	$-0.188294\pi$
$419$	2.00406e7	+	2.00406e7i	0.272439	+	0.272439i	−0.557642	+	0.830081i	$0.688294\pi$
$420$		0			0
$421$	4.69698e7	+	4.69698e7i	0.629466	+	0.629466i	0.947934	−	0.318468i	$-0.103168\pi$
$421$	4.69698e7	+	4.69698e7i	0.629466	+	0.629466i	−0.318468	+	0.947934i	$0.603168\pi$
$422$		0			0
$423$	3.53801e7			0.467453
$424$		0			0
$425$			2.97319e8i			3.87307i
$426$		0			0
$427$	2.76922e7	−	2.76922e7i	0.355691	−	0.355691i
$428$		0			0
$429$	3.75158e6	−	3.75158e6i	0.0475162	−	0.0475162i
$430$		0			0
$431$		−	3.47077e7i		−	0.433505i	−0.976227	−	0.216752i	$-0.930454\pi$
$431$		−	3.47077e7i		−	0.433505i	0.976227	−	0.216752i	$-0.0695464\pi$
$432$		0			0
$433$	7.60717e7			0.937042			0.468521	−	0.883452i	$-0.344787\pi$
$433$	7.60717e7			0.937042			0.468521	+	0.883452i	$0.344787\pi$
$434$		0			0
$435$	−6.79675e7	−	6.79675e7i	−0.825721	−	0.825721i
$436$		0			0
$437$	−2.22345e7	−	2.22345e7i	−0.266430	−	0.266430i
$438$		0			0
$439$	1.11886e8			1.32246			0.661230	−	0.750183i	$-0.270035\pi$
$439$	1.11886e8			1.32246			0.661230	+	0.750183i	$0.270035\pi$
$440$		0			0
$441$			3.90538e7i			0.455352i
$442$		0			0
$443$	−1.92485e7	+	1.92485e7i	−0.221404	+	0.221404i	−0.809089	−	0.587686i	$-0.800039\pi$
$443$	−1.92485e7	+	1.92485e7i	−0.221404	+	0.221404i	0.587686	+	0.809089i	$0.300039\pi$
$444$		0			0
$445$	8.05734e7	−	8.05734e7i	0.914348	−	0.914348i
$446$		0			0
$447$			4.05878e7i			0.454436i
$448$		0			0
$449$	1.01668e8			1.12317			0.561585	−	0.827419i	$-0.310192\pi$
$449$	1.01668e8			1.12317			0.561585	+	0.827419i	$0.310192\pi$
$450$		0			0
$451$	7.64911e6	+	7.64911e6i	0.0833837	+	0.0833837i
$452$		0			0
$453$	8.24805e6	+	8.24805e6i	0.0887272	+	0.0887272i
$454$		0			0
$455$	−2.13097e8			−2.26227
$456$		0			0
$457$		−	1.40168e8i		−	1.46859i	−0.678831	−	0.734294i	$-0.737513\pi$
$457$		−	1.40168e8i		−	1.46859i	0.678831	−	0.734294i	$-0.262487\pi$
$458$		0			0
$459$	−2.25494e7	+	2.25494e7i	−0.233183	+	0.233183i
$460$		0			0
$461$	5.42050e7	−	5.42050e7i	0.553269	−	0.553269i	−0.374114	−	0.927383i	$-0.622053\pi$
$461$	5.42050e7	−	5.42050e7i	0.553269	−	0.553269i	0.927383	+	0.374114i	$0.122053\pi$
$462$		0			0
$463$		−	9.65343e7i		−	0.972610i	−0.873789	−	0.486305i	$-0.838344\pi$
$463$		−	9.65343e7i		−	0.972610i	0.873789	−	0.486305i	$-0.161656\pi$
$464$		0			0
$465$	−5.82040e7			−0.578887
$466$		0			0
$467$	−9.46813e7	−	9.46813e7i	−0.929638	−	0.929638i	0.0680446	−	0.997682i	$-0.478324\pi$
$467$	−9.46813e7	−	9.46813e7i	−0.929638	−	0.929638i	−0.997682	+	0.0680446i	$0.978324\pi$
$468$		0			0
$469$	−7.49703e7	−	7.49703e7i	−0.726726	−	0.726726i
$470$		0			0
$471$	−3.14139e7			−0.300648
$472$		0			0
$473$			1.46724e7i			0.138649i
$474$		0			0
$475$	9.01651e7	−	9.01651e7i	0.841313	−	0.841313i
$476$		0			0
$477$	2.05082e7	−	2.05082e7i	0.188961	−	0.188961i
$478$		0			0
$479$			1.92049e8i			1.74746i	0.486415	+	0.873728i	$0.338304\pi$
$479$			1.92049e8i			1.74746i	−0.486415	+	0.873728i	$0.661696\pi$
$480$		0			0
$481$	−7.29379e7			−0.655418
$482$		0			0
$483$	5.06484e7	+	5.06484e7i	0.449495	+	0.449495i
$484$		0			0
$485$	−1.24671e8	−	1.24671e8i	−1.09280	−	1.09280i
$486$		0			0
$487$	−3.35207e7			−0.290219			−0.145109	−	0.989416i	$-0.546353\pi$
$487$	−3.35207e7			−0.290219			−0.145109	+	0.989416i	$0.546353\pi$
$488$		0			0
$489$		−	1.07732e7i		−	0.0921337i
$490$		0			0
$491$	−2.66828e7	+	2.66828e7i	−0.225417	+	0.225417i	−0.810775	−	0.585358i	$-0.800954\pi$
$491$	−2.66828e7	+	2.66828e7i	−0.225417	+	0.225417i	0.585358	+	0.810775i	$0.300954\pi$
$492$		0			0
$493$	−1.62630e8	+	1.62630e8i	−1.35725	+	1.35725i
$494$		0			0
$495$		−	1.04312e7i		−	0.0860043i
$496$		0			0
$497$	1.35450e7			0.110334
$498$		0			0
$499$	7.69399e7	+	7.69399e7i	0.619227	+	0.619227i	0.945333	−	0.326106i	$-0.105737\pi$
$499$	7.69399e7	+	7.69399e7i	0.619227	+	0.619227i	−0.326106	+	0.945333i	$0.605737\pi$
$500$		0			0
$501$	−9.25414e7	−	9.25414e7i	−0.735907	−	0.735907i
$502$		0			0
$503$	−1.07968e8			−0.848379			−0.424190	−	0.905573i	$-0.639441\pi$
$503$	−1.07968e8			−0.848379			−0.424190	+	0.905573i	$0.639441\pi$
$504$		0			0
$505$		−	3.58308e8i		−	2.78216i
$506$		0			0
$507$	−1.79060e7	+	1.79060e7i	−0.137396	+	0.137396i
$508$		0			0
$509$	1.11922e8	−	1.11922e8i	0.848718	−	0.848718i	−0.141255	−	0.989973i	$-0.545114\pi$
$509$	1.11922e8	−	1.11922e8i	0.848718	−	0.848718i	0.989973	+	0.141255i	$0.0451139\pi$
$510$		0			0
$511$		−	2.84159e8i		−	2.12961i
$512$		0			0
$513$	1.36767e7			0.101304
$514$		0			0
$515$	1.28497e8	+	1.28497e8i	0.940742	+	0.940742i
$516$		0			0
$517$	1.95807e7	+	1.95807e7i	0.141696	+	0.141696i
$518$		0			0
$519$	−1.38018e7			−0.0987264
$520$		0			0
$521$			2.62390e8i			1.85539i	0.373342	+	0.927694i	$0.378212\pi$
$521$			2.62390e8i			1.85539i	−0.373342	+	0.927694i	$0.621788\pi$
$522$		0			0
$523$	1.12853e8	−	1.12853e8i	0.788876	−	0.788876i	−0.192434	−	0.981310i	$-0.561638\pi$
$523$	1.12853e8	−	1.12853e8i	0.788876	−	0.788876i	0.981310	+	0.192434i	$0.0616381\pi$
$524$		0			0
$525$	−2.05389e8	+	2.05389e8i	−1.41938	+	1.41938i
$526$		0			0
$527$			1.39268e8i			0.951526i
$528$		0			0
$529$	−7.21882e7			−0.487640
$530$		0			0
$531$	−3.06029e7	−	3.06029e7i	−0.204399	−	0.204399i
$532$		0			0
$533$	7.19702e7	+	7.19702e7i	0.475304	+	0.475304i
$534$		0			0
$535$	3.79214e8			2.47641
$536$		0			0
$537$			1.38238e7i			0.0892698i
$538$		0			0
$539$	−2.16139e7	+	2.16139e7i	−0.138028	+	0.138028i
$540$		0			0
$541$	1.12563e8	−	1.12563e8i	0.710895	−	0.710895i	−0.255827	−	0.966722i	$-0.582348\pi$
$541$	1.12563e8	−	1.12563e8i	0.710895	−	0.710895i	0.966722	+	0.255827i	$0.0823479\pi$
$542$		0			0
$543$		−	1.53016e8i		−	0.955736i
$544$		0			0
$545$	−4.14307e8			−2.55937
$546$		0			0
$547$	−1.25472e8	−	1.25472e8i	−0.766629	−	0.766629i	0.210882	−	0.977511i	$-0.432366\pi$
$547$	−1.25472e8	−	1.25472e8i	−0.766629	−	0.766629i	−0.977511	+	0.210882i	$0.932366\pi$
$548$		0			0
$549$	1.27543e7	+	1.27543e7i	0.0770796	+	0.0770796i
$550$		0			0
$551$	9.86385e7			0.589646
$552$		0			0
$553$			6.48483e7i			0.383462i
$554$		0			0
$555$	−1.01402e8	+	1.01402e8i	−0.593152	+	0.593152i
$556$		0			0
$557$	−2.04700e8	+	2.04700e8i	−1.18455	+	1.18455i	−0.205994	+	0.978553i	$0.566043\pi$
$557$	−2.04700e8	+	2.04700e8i	−1.18455	+	1.18455i	−0.978553	+	0.205994i	$0.933957\pi$
$558$		0			0
$559$			1.38052e8i			0.790327i
$560$		0			0
$561$	−2.49595e7			−0.141367
$562$		0			0
$563$	−1.51024e8	−	1.51024e8i	−0.846294	−	0.846294i	0.143375	−	0.989668i	$-0.454205\pi$
$563$	−1.51024e8	−	1.51024e8i	−0.846294	−	0.846294i	−0.989668	+	0.143375i	$0.954205\pi$
$564$		0			0
$565$	−2.47315e8	−	2.47315e8i	−1.37122	−	1.37122i
$566$		0			0
$567$	−3.11544e7			−0.170911
$568$		0			0
$569$			3.90049e7i			0.211730i	0.994381	+	0.105865i	$0.0337612\pi$
$569$			3.90049e7i			0.211730i	−0.994381	+	0.105865i	$0.966239\pi$
$570$		0			0
$571$	−1.18656e8	+	1.18656e8i	−0.637356	+	0.637356i	−0.949903	−	0.312546i	$-0.898818\pi$
$571$	−1.18656e8	+	1.18656e8i	−0.637356	+	0.637356i	0.312546	+	0.949903i	$0.398818\pi$
$572$		0			0
$573$	−7.12020e7	+	7.12020e7i	−0.378467	+	0.378467i
$574$		0			0
$575$			3.07577e8i			1.61789i
$576$		0			0
$577$	3.34647e8			1.74205			0.871023	−	0.491243i	$-0.163457\pi$
$577$	3.34647e8			1.74205			0.871023	+	0.491243i	$0.163457\pi$
$578$		0			0
$579$	5.62768e7	+	5.62768e7i	0.289930	+	0.289930i
$580$		0			0
$581$	2.84697e8	+	2.84697e8i	1.45163	+	1.45163i
$582$		0			0
$583$	2.27001e7			0.114557
$584$		0			0
$585$		−	9.81471e7i		−	0.490241i
$586$		0			0
$587$	1.30966e8	−	1.30966e8i	0.647506	−	0.647506i	−0.304883	−	0.952390i	$-0.598618\pi$
$587$	1.30966e8	−	1.30966e8i	0.647506	−	0.647506i	0.952390	+	0.304883i	$0.0986175\pi$
$588$		0			0
$589$	4.22346e7	−	4.22346e7i	0.206691	−	0.206691i
$590$		0			0
$591$		−	2.48644e7i		−	0.120452i
$592$		0			0
$593$	1.59844e8			0.766535			0.383268	−	0.923637i	$-0.374799\pi$
$593$	1.59844e8			0.766535			0.383268	+	0.923637i	$0.374799\pi$
$594$		0			0
$595$	7.08875e8	+	7.08875e8i	3.36526	+	3.36526i
$596$		0			0
$597$	1.22369e8	+	1.22369e8i	0.575107	+	0.575107i
$598$		0			0
$599$	−2.88807e8			−1.34378			−0.671889	−	0.740652i	$-0.734517\pi$
$599$	−2.88807e8			−1.34378			−0.671889	+	0.740652i	$0.734517\pi$
$600$		0			0
$601$			2.91001e8i			1.34051i	0.742130	+	0.670256i	$0.233816\pi$
$601$			2.91001e8i			1.34051i	−0.742130	+	0.670256i	$0.766184\pi$
$602$		0			0
$603$	3.45294e7	−	3.45294e7i	0.157484	−	0.157484i
$604$		0			0
$605$	−2.76961e8	+	2.76961e8i	−1.25070	+	1.25070i
$606$		0			0
$607$		−	1.10595e8i		−	0.494504i	−0.968951	−	0.247252i	$-0.920472\pi$
$607$		−	1.10595e8i		−	0.494504i	0.968951	−	0.247252i	$-0.0795275\pi$
$608$		0			0
$609$	−2.24691e8			−0.994794
$610$		0			0
$611$	1.84235e8	+	1.84235e8i	0.807695	+	0.807695i
$612$		0			0
$613$	2.51990e8	+	2.51990e8i	1.09396	+	1.09396i	0.995101	+	0.0988588i	$0.0315192\pi$
$613$	2.51990e8	+	2.51990e8i	1.09396	+	1.09396i	0.0988588	+	0.995101i	$0.468481\pi$
$614$		0			0
$615$	2.00113e8			0.860299
$616$		0			0
$617$			1.50081e8i			0.638955i	0.947594	+	0.319478i	$0.103507\pi$
$617$			1.50081e8i			0.638955i	−0.947594	+	0.319478i	$0.896493\pi$
$618$		0			0
$619$	6.46406e7	−	6.46406e7i	0.272542	−	0.272542i	−0.557581	−	0.830123i	$-0.688270\pi$
$619$	6.46406e7	−	6.46406e7i	0.272542	−	0.272542i	0.830123	+	0.557581i	$0.188270\pi$
$620$		0			0
$621$	−2.33274e7	+	2.33274e7i	−0.0974072	+	0.0974072i
$622$		0			0
$623$		−	2.66364e8i		−	1.10157i
$624$		0			0
$625$	−4.51315e8			−1.84859
$626$		0			0
$627$	7.56922e6	+	7.56922e6i	0.0307078	+	0.0307078i
$628$		0			0
$629$	2.42630e8	+	2.42630e8i	0.974974	+	0.974974i
$630$		0			0
$631$	4.45331e8			1.77254			0.886268	−	0.463172i	$-0.153289\pi$
$631$	4.45331e8			1.77254			0.886268	+	0.463172i	$0.153289\pi$
$632$		0			0
$633$			6.31387e7i			0.248934i
$634$		0			0
$635$	−2.80627e8	+	2.80627e8i	−1.09600	+	1.09600i
$636$		0			0
$637$	−2.03365e8	+	2.03365e8i	−0.786787	+	0.786787i
$638$		0			0
$639$			6.23848e6i			0.0239098i
$640$		0			0
$641$	−3.29718e8			−1.25190			−0.625949	−	0.779864i	$-0.715288\pi$
$641$	−3.29718e8			−1.25190			−0.625949	+	0.779864i	$0.715288\pi$
$642$		0			0
$643$	7.45261e6	+	7.45261e6i	0.0280334	+	0.0280334i	0.720985	−	0.692951i	$-0.243690\pi$
$643$	7.45261e6	+	7.45261e6i	0.0280334	+	0.0280334i	−0.692951	+	0.720985i	$0.743690\pi$
$644$		0			0
$645$	1.91926e8	+	1.91926e8i	0.715245	+	0.715245i
$646$		0			0
$647$	1.60945e8			0.594245			0.297123	−	0.954839i	$-0.403973\pi$
$647$	1.60945e8			0.594245			0.297123	+	0.954839i	$0.403973\pi$
$648$		0			0
$649$		−	3.38738e7i		−	0.123917i
$650$		0			0
$651$	−9.62071e7	+	9.62071e7i	−0.348710	+	0.348710i
$652$		0			0
$653$	8.93058e7	−	8.93058e7i	0.320731	−	0.320731i	−0.528317	−	0.849047i	$-0.677177\pi$
$653$	8.93058e7	−	8.93058e7i	0.320731	−	0.320731i	0.849047	+	0.528317i	$0.177177\pi$
$654$		0			0
$655$			4.07242e8i			1.44920i
$656$		0			0
$657$	1.30877e8			0.461494
$658$		0			0
$659$	2.27048e8	+	2.27048e8i	0.793345	+	0.793345i	0.982036	−	0.188691i	$-0.0604246\pi$
$659$	2.27048e8	+	2.27048e8i	0.793345	+	0.793345i	−0.188691	+	0.982036i	$0.560425\pi$
$660$		0			0
$661$	−2.60049e8	−	2.60049e8i	−0.900432	−	0.900432i	0.0950417	−	0.995473i	$-0.469702\pi$
$661$	−2.60049e8	−	2.60049e8i	−0.900432	−	0.900432i	−0.995473	+	0.0950417i	$0.969702\pi$
$662$		0			0
$663$	−2.34843e8			−0.805818
$664$		0			0
$665$		−	4.29947e8i		−	1.46201i
$666$		0			0
$667$	−1.68241e8	+	1.68241e8i	−0.566962	+	0.566962i
$668$		0			0
$669$	1.78655e8	−	1.78655e8i	0.596674	−	0.596674i
$670$		0			0
$671$			1.41175e7i			0.0467293i
$672$		0			0
$673$	−2.65424e8			−0.870752			−0.435376	−	0.900249i	$-0.643385\pi$
$673$	−2.65424e8			−0.870752			−0.435376	+	0.900249i	$0.643385\pi$
$674$		0			0
$675$	−9.45969e7	−	9.45969e7i	−0.307585	−	0.307585i
$676$		0			0
$677$	−1.15406e8	−	1.15406e8i	−0.371930	−	0.371930i	0.496250	−	0.868180i	$-0.334710\pi$
$677$	−1.15406e8	−	1.15406e8i	−0.371930	−	0.371930i	−0.868180	+	0.496250i	$0.834710\pi$
$678$		0			0
$679$	−4.12146e8			−1.31656
$680$		0			0
$681$			8.93805e7i			0.283010i
$682$		0			0
$683$	1.75669e8	−	1.75669e8i	0.551356	−	0.551356i	−0.375476	−	0.926832i	$-0.622521\pi$
$683$	1.75669e8	−	1.75669e8i	0.551356	−	0.551356i	0.926832	+	0.375476i	$0.122521\pi$
$684$		0			0
$685$	5.39134e7	−	5.39134e7i	0.167735	−	0.167735i
$686$		0			0
$687$		−	1.90851e7i		−	0.0588605i
$688$		0			0
$689$	2.13584e8			0.652998
$690$		0			0
$691$	−3.12963e8	−	3.12963e8i	−0.948548	−	0.948548i	0.0501919	−	0.998740i	$-0.484017\pi$
$691$	−3.12963e8	−	3.12963e8i	−0.948548	−	0.948548i	−0.998740	+	0.0501919i	$0.984017\pi$
$692$		0			0
$693$	−1.72421e7	−	1.72421e7i	−0.0518072	−	0.0518072i
$694$		0			0
$695$	6.57583e8			1.95883
$696$		0			0
$697$		−	4.78822e8i		−	1.41409i
$698$		0			0
$699$	3.86951e7	−	3.86951e7i	0.113299	−	0.113299i
$700$		0			0
$701$	7.91827e7	−	7.91827e7i	0.229867	−	0.229867i	−0.582770	−	0.812637i	$-0.698031\pi$
$701$	7.91827e7	−	7.91827e7i	0.229867	−	0.229867i	0.812637	+	0.582770i	$0.198031\pi$
$702$		0			0
$703$		−	1.47160e8i		−	0.423569i
$704$		0			0
$705$	5.12263e8			1.46193
$706$		0			0
$707$	−5.92258e8	−	5.92258e8i	−1.67592	−	1.67592i
$708$		0			0
$709$	−2.41686e8	−	2.41686e8i	−0.678129	−	0.678129i	0.281448	−	0.959577i	$-0.409185\pi$
$709$	−2.41686e8	−	2.41686e8i	−0.678129	−	0.678129i	−0.959577	+	0.281448i	$0.909185\pi$
$710$		0			0
$711$	−2.98674e7			−0.0830977
$712$		0			0
$713$			1.44073e8i			0.397480i
$714$		0			0
$715$	5.43185e7	−	5.43185e7i	0.148604	−	0.148604i
$716$		0			0
$717$	1.21769e7	−	1.21769e7i	0.0330352	−	0.0330352i
$718$		0			0
$719$		−	3.33237e7i		−	0.0896535i	−0.998995	−	0.0448267i	$-0.985726\pi$
$719$		−	3.33237e7i		−	0.0896535i	0.998995	−	0.0448267i	$-0.0142736\pi$
$720$		0			0
$721$	4.24792e8			1.13337
$722$		0			0
$723$	−2.02953e8	−	2.02953e8i	−0.537009	−	0.537009i
$724$		0			0
$725$	−6.82249e8	−	6.82249e8i	−1.79031	−	1.79031i
$726$		0			0
$727$	−3.18663e8			−0.829331			−0.414666	−	0.909974i	$-0.636101\pi$
$727$	−3.18663e8			−0.829331			−0.414666	+	0.909974i	$0.636101\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	4.59234e8	−	4.59234e8i	1.17566	−	1.17566i
$732$		0			0
$733$	−9.78519e7	+	9.78519e7i	−0.248461	+	0.248461i	−0.820339	−	0.571878i	$-0.806215\pi$
$733$	−9.78519e7	+	9.78519e7i	−0.248461	+	0.248461i	0.571878	+	0.820339i	$0.306215\pi$
$734$		0			0
$735$			5.65454e8i			1.42408i
$736$		0			0
$737$	3.82199e7			0.0954744
$738$		0			0
$739$	3.97007e8	+	3.97007e8i	0.983706	+	0.983706i	0.999869	−	0.0161635i	$-0.00514524\pi$
$739$	3.97007e8	+	3.97007e8i	0.983706	+	0.983706i	−0.0161635	+	0.999869i	$0.505145\pi$
$740$		0			0
$741$	7.12185e7	+	7.12185e7i	0.175040	+	0.175040i
$742$		0			0
$743$	−5.10776e7			−0.124527			−0.0622636	−	0.998060i	$-0.519832\pi$
$743$	−5.10776e7			−0.124527			−0.0622636	+	0.998060i	$0.519832\pi$
$744$		0			0
$745$			5.87665e8i			1.42122i
$746$		0			0
$747$	−1.31124e8	+	1.31124e8i	−0.314573	+	0.314573i
$748$		0			0
$749$	6.26814e8	−	6.26814e8i	1.49174	−	1.49174i
$750$		0			0
$751$			5.13098e8i			1.21138i	0.795700	+	0.605690i	$0.207103\pi$
$751$			5.13098e8i			1.21138i	−0.795700	+	0.605690i	$0.792897\pi$
$752$		0			0
$753$	−3.59420e8			−0.841816
$754$		0			0
$755$	1.19422e8	+	1.19422e8i	0.277488	+	0.277488i
$756$		0			0
$757$	8.20674e7	+	8.20674e7i	0.189183	+	0.189183i	0.795343	−	0.606160i	$-0.207291\pi$
$757$	8.20674e7	+	8.20674e7i	0.189183	+	0.189183i	−0.606160	+	0.795343i	$0.707291\pi$
$758$		0			0
$759$	−2.58206e7			−0.0590529
$760$		0			0
$761$		−	5.43029e8i		−	1.23217i	−0.787682	−	0.616083i	$-0.788719\pi$
$761$		−	5.43029e8i		−	1.23217i	0.787682	−	0.616083i	$-0.211281\pi$
$762$		0			0
$763$	−6.84819e8	+	6.84819e8i	−1.54171	+	1.54171i
$764$		0			0
$765$	−3.26489e8	+	3.26489e8i	−0.729264	+	0.729264i
$766$		0			0
$767$		−	3.18717e8i		−	0.706349i
$768$		0			0
$769$	6.28434e8			1.38191			0.690956	−	0.722897i	$-0.257190\pi$
$769$	6.28434e8			1.38191			0.690956	+	0.722897i	$0.257190\pi$
$770$		0			0
$771$	1.83334e7	+	1.83334e7i	0.0400018	+	0.0400018i
$772$		0			0
$773$	−2.03425e8	−	2.03425e8i	−0.440419	−	0.440419i	0.451734	−	0.892153i	$-0.350806\pi$
$773$	−2.03425e8	−	2.03425e8i	−0.440419	−	0.440419i	−0.892153	+	0.451734i	$0.850806\pi$
$774$		0			0
$775$	−5.84244e8			−1.25513
$776$		0			0
$777$			3.35220e8i			0.714605i
$778$		0			0
$779$	−1.45208e8	+	1.45208e8i	−0.307169	+	0.307169i
$780$		0			0
$781$	−3.45263e6	+	3.45263e6i	−0.00724764	+	0.00724764i
$782$		0			0
$783$		−	1.03487e8i		−	0.215576i
$784$		0			0
$785$	−4.54837e8			−0.940257
$786$		0			0
$787$	1.31200e8	+	1.31200e8i	0.269159	+	0.269159i	0.828761	−	0.559602i	$-0.189046\pi$
$787$	1.31200e8	+	1.31200e8i	0.269159	+	0.269159i	−0.559602	+	0.828761i	$0.689046\pi$
$788$		0			0
$789$	−8.54853e7	−	8.54853e7i	−0.174045	−	0.174045i
$790$		0			0
$791$	−8.17590e8			−1.65198
$792$		0			0
$793$			1.32831e8i			0.266366i
$794$		0			0
$795$	2.96935e8	−	2.96935e8i	0.590963	−	0.590963i
$796$		0			0
$797$	−4.33506e8	+	4.33506e8i	−0.856288	+	0.856288i	−0.990899	−	0.134610i	$-0.957022\pi$
$797$	−4.33506e8	+	4.33506e8i	−0.856288	+	0.856288i	0.134610	+	0.990899i	$0.457022\pi$
$798$		0			0
$799$		−	1.22572e9i		−	2.40299i
$800$		0			0
$801$	1.22680e8			0.238714
$802$		0			0
$803$	7.24323e7	+	7.24323e7i	0.139890	+	0.139890i
$804$		0			0
$805$	7.33332e8	+	7.33332e8i	1.40577	+	1.40577i
$806$		0			0
$807$	−2.78269e8			−0.529473
$808$		0			0
$809$			6.44400e8i			1.21706i	0.793533	+	0.608528i	$0.208239\pi$
$809$			6.44400e8i			1.21706i	−0.793533	+	0.608528i	$0.791761\pi$
$810$		0			0
$811$	7.10034e8	−	7.10034e8i	1.33112	−	1.33112i	0.426748	−	0.904370i	$-0.359659\pi$
$811$	7.10034e8	−	7.10034e8i	1.33112	−	1.33112i	0.904370	−	0.426748i	$-0.140341\pi$
$812$		0			0
$813$	3.47721e8	−	3.47721e8i	0.647082	−	0.647082i
$814$		0			0
$815$		−	1.55984e8i		−	0.288142i
$816$		0			0
$817$	−2.78535e8			−0.510756
$818$		0			0
$819$	−1.62230e8	−	1.62230e8i	−0.295311	−	0.295311i
$820$		0			0
$821$	1.22452e8	+	1.22452e8i	0.221278	+	0.221278i	0.809036	−	0.587759i	$-0.199990\pi$
$821$	1.22452e8	+	1.22452e8i	0.221278	+	0.221278i	−0.587759	+	0.809036i	$0.699990\pi$
$822$		0			0
$823$	3.21527e8			0.576790			0.288395	−	0.957511i	$-0.406878\pi$
$823$	3.21527e8			0.576790			0.288395	+	0.957511i	$0.406878\pi$
$824$		0			0
$825$		−	1.04707e8i		−	0.186473i
$826$		0			0
$827$	4.75228e8	−	4.75228e8i	0.840205	−	0.840205i	−0.148681	−	0.988885i	$-0.547503\pi$
$827$	4.75228e8	−	4.75228e8i	0.840205	−	0.840205i	0.988885	+	0.148681i	$0.0475026\pi$
$828$		0			0
$829$	5.33510e8	−	5.33510e8i	0.936437	−	0.936437i	−0.0616601	−	0.998097i	$-0.519639\pi$
$829$	5.33510e8	−	5.33510e8i	0.936437	−	0.936437i	0.998097	+	0.0616601i	$0.0196395\pi$
$830$		0			0
$831$			1.91331e8i			0.333413i
$832$		0			0
$833$	1.35300e9			2.34079
$834$		0			0
$835$	−1.33989e9	−	1.33989e9i	−2.30150	−	2.30150i
$836$		0			0
$837$	−4.43105e7	−	4.43105e7i	−0.0755667	−	0.0755667i
$838$		0			0
$839$	9.03878e8			1.53047			0.765233	−	0.643753i	$-0.222624\pi$
$839$	9.03878e8			1.53047			0.765233	+	0.643753i	$0.222624\pi$
$840$		0			0
$841$		−	1.51541e8i		−	0.254766i
$842$		0			0
$843$	1.08162e8	−	1.08162e8i	0.180547	−	0.180547i
$844$		0			0
$845$	−2.59259e8	+	2.59259e8i	−0.429698	+	0.429698i
$846$		0			0
$847$			9.15595e8i			1.50679i
$848$		0			0
$849$	−2.05174e8			−0.335273
$850$		0			0
$851$	2.51001e8	+	2.51001e8i	0.407274	+	0.407274i
$852$		0			0
$853$	7.84622e7	+	7.84622e7i	0.126419	+	0.126419i	0.767486	−	0.641066i	$-0.221508\pi$
$853$	7.84622e7	+	7.84622e7i	0.126419	+	0.126419i	−0.641066	+	0.767486i	$0.721508\pi$
$854$		0			0
$855$	1.98023e8			0.316823
$856$		0			0
$857$			3.33726e8i			0.530209i	0.964220	+	0.265104i	$0.0854064\pi$
$857$			3.33726e8i			0.530209i	−0.964220	+	0.265104i	$0.914594\pi$
$858$		0			0
$859$	7.37537e8	−	7.37537e8i	1.16360	−	1.16360i	0.179921	−	0.983681i	$-0.442416\pi$
$859$	7.37537e8	−	7.37537e8i	1.16360	−	1.16360i	0.983681	−	0.179921i	$-0.0575843\pi$
$860$		0			0
$861$	3.30772e8	−	3.30772e8i	0.518226	−	0.518226i
$862$		0			0
$863$		−	1.77274e8i		−	0.275812i	−0.990445	−	0.137906i	$-0.955963\pi$
$863$		−	1.77274e8i		−	0.275812i	0.990445	−	0.137906i	$-0.0440372\pi$
$864$		0			0
$865$	−1.99834e8			−0.308760
$866$		0			0
$867$	5.15151e8	+	5.15151e8i	0.790455	+	0.790455i
$868$		0			0
$869$	−1.65298e7	−	1.65298e7i	−0.0251889	−	0.0251889i
$870$		0			0
$871$	3.59610e8			0.544223
$872$		0			0
$873$		−	1.89824e8i		−	0.285304i
$874$		0			0
$875$	−1.65812e9	+	1.65812e9i	−2.47510	+	2.47510i
$876$		0			0
$877$	8.15706e8	−	8.15706e8i	1.20930	−	1.20930i	0.238049	−	0.971253i	$-0.423492\pi$
$877$	8.15706e8	−	8.15706e8i	1.20930	−	1.20930i	0.971253	−	0.238049i	$-0.0765080\pi$
$878$		0			0
$879$		−	3.93087e8i		−	0.578791i
$880$		0			0
$881$	−6.07438e8			−0.888330			−0.444165	−	0.895945i	$-0.646500\pi$
$881$	−6.07438e8			−0.888330			−0.444165	+	0.895945i	$0.646500\pi$
$882$		0			0
$883$	−9.47786e8	−	9.47786e8i	−1.37666	−	1.37666i	−0.850192	−	0.526473i	$-0.823514\pi$
$883$	−9.47786e8	−	9.47786e8i	−1.37666	−	1.37666i	−0.526473	−	0.850192i	$-0.676486\pi$
$884$		0			0
$885$	−4.43095e8	−	4.43095e8i	−0.639245	−	0.639245i
$886$		0			0
$887$	−1.44775e7			−0.0207454			−0.0103727	−	0.999946i	$-0.503302\pi$
$887$	−1.44775e7			−0.0207454			−0.0103727	+	0.999946i	$0.503302\pi$
$888$		0			0
$889$			9.27714e8i			1.32041i
$890$		0			0
$891$	7.94126e6	−	7.94126e6i	0.0112268	−	0.0112268i
$892$		0			0
$893$	−3.71713e8	+	3.71713e8i	−0.521980	+	0.521980i
$894$		0			0
$895$			2.00153e8i			0.279186i
$896$		0			0
$897$	−2.42945e8			−0.336613
$898$		0			0
$899$	−3.19575e8	−	3.19575e8i	−0.439839	−	0.439839i
$900$		0			0
$901$	−7.10495e8	−	7.10495e8i	−0.971375	−	0.971375i
$902$		0			0
$903$	6.34480e8			0.861698
$904$		0			0
$905$		−	2.21550e9i		−	2.98900i
$906$		0			0
$907$	5.64289e8	−	5.64289e8i	0.756275	−	0.756275i	−0.219367	−	0.975642i	$-0.570399\pi$
$907$	5.64289e8	−	5.64289e8i	0.756275	−	0.756275i	0.975642	+	0.219367i	$0.0703992\pi$
$908$		0			0
$909$	2.72779e8	−	2.72779e8i	0.363177	−	0.363177i
$910$		0			0
$911$		−	8.97917e8i		−	1.18763i	−0.804601	−	0.593815i	$-0.797621\pi$
$911$		−	8.97917e8i		−	1.18763i	0.804601	−	0.593815i	$-0.202379\pi$
$912$		0			0
$913$	−1.45139e8			−0.190709
$914$		0			0
$915$	1.84668e8	+	1.84668e8i	0.241061	+	0.241061i
$916$		0			0
$917$	6.73142e8	+	6.73142e8i	0.872968	+	0.872968i
$918$		0			0
$919$	2.39406e8			0.308453			0.154226	−	0.988036i	$-0.450711\pi$
$919$	2.39406e8			0.308453			0.154226	+	0.988036i	$0.450711\pi$
$920$		0			0
$921$			3.19028e7i			0.0408367i
$922$		0			0
$923$	−3.24856e7	+	3.24856e7i	−0.0413130	+	0.0413130i
$924$		0			0
$925$	−1.01786e9	+	1.01786e9i	−1.28606	+	1.28606i
$926$		0			0
$927$			1.95648e8i			0.245605i
$928$		0			0
$929$	8.39266e8			1.04677			0.523387	−	0.852095i	$-0.324668\pi$
$929$	8.39266e8			1.04677			0.523387	+	0.852095i	$0.324668\pi$
$930$		0			0
$931$	−4.10311e8	−	4.10311e8i	−0.508468	−	0.508468i
$932$		0			0
$933$	−5.56528e8	−	5.56528e8i	−0.685239	−	0.685239i
$934$		0			0
$935$	−3.61385e8			−0.442115
$936$		0			0
$937$		−	7.10866e8i		−	0.864110i	−0.901847	−	0.432055i	$-0.857789\pi$
$937$		−	7.10866e8i		−	0.864110i	0.901847	−	0.432055i	$-0.142211\pi$
$938$		0			0
$939$	1.23477e8	−	1.23477e8i	0.149139	−	0.149139i
$940$		0			0
$941$	5.49078e8	−	5.49078e8i	0.658969	−	0.658969i	−0.296167	−	0.955136i	$-0.595709\pi$
$941$	5.49078e8	−	5.49078e8i	0.658969	−	0.658969i	0.955136	+	0.296167i	$0.0957086\pi$
$942$		0			0
$943$		−	4.95342e8i		−	0.590704i
$944$		0			0
$945$	−4.51080e8			−0.534513
$946$		0			0
$947$	−9.93248e8	−	9.93248e8i	−1.16952	−	1.16952i	−0.982322	−	0.187198i	$-0.940059\pi$
$947$	−9.93248e8	−	9.93248e8i	−1.16952	−	1.16952i	−0.187198	−	0.982322i	$-0.559941\pi$
$948$		0			0
$949$	6.81513e8	+	6.81513e8i	0.797399	+	0.797399i
$950$		0			0
$951$	−4.76749e8			−0.554304
$952$		0			0
$953$		−	1.04368e9i		−	1.20584i	−0.797803	−	0.602918i	$-0.794005\pi$
$953$		−	1.04368e9i		−	1.20584i	0.797803	−	0.602918i	$-0.205995\pi$
$954$		0			0
$955$	−1.03092e9	+	1.03092e9i	−1.18363	+	1.18363i
$956$		0			0
$957$	5.72737e7	−	5.72737e7i	0.0653461	−	0.0653461i
$958$		0			0
$959$		−	1.78230e8i		−	0.202081i
$960$		0			0
$961$	6.13835e8			0.691643
$962$		0			0
$963$	2.88694e8	+	2.88694e8i	0.323265	+	0.323265i
$964$		0			0
$965$	8.14823e8	+	8.14823e8i	0.906737	+	0.906737i
$966$		0			0
$967$	−1.72023e9			−1.90243			−0.951214	−	0.308533i	$-0.900162\pi$
$967$	−1.72023e9			−1.90243			−0.951214	+	0.308533i	$0.900162\pi$
$968$		0			0
$969$		−	4.73821e8i		−	0.520767i
$970$		0			0
$971$	−1.04392e8	+	1.04392e8i	−0.114028	+	0.114028i	−0.761818	−	0.647791i	$-0.775693\pi$
$971$	−1.04392e8	+	1.04392e8i	−0.114028	+	0.114028i	0.647791	+	0.761818i	$0.275693\pi$
$972$		0			0
$973$	1.08694e9	−	1.08694e9i	1.17996	−	1.17996i
$974$		0			0
$975$		−	9.85188e8i		−	1.06293i
$976$		0			0
$977$	2.78618e8			0.298762			0.149381	−	0.988780i	$-0.452272\pi$
$977$	2.78618e8			0.298762			0.149381	+	0.988780i	$0.452272\pi$
$978$		0			0
$979$	6.78963e7	+	6.78963e7i	0.0723599	+	0.0723599i
$980$		0			0
$981$	−3.15410e8	−	3.15410e8i	−0.334094	−	0.334094i
$982$		0			0
$983$	−3.52152e8			−0.370740			−0.185370	−	0.982669i	$-0.559348\pi$
$983$	−3.52152e8			−0.370740			−0.185370	+	0.982669i	$0.559348\pi$
$984$		0			0
$985$		−	3.60008e8i		−	0.376706i
$986$		0			0
$987$	8.46734e8	−	8.46734e8i	0.880634	−	0.880634i
$988$		0			0
$989$	4.75078e8	−	4.75078e8i	0.491107	−	0.491107i
$990$		0			0
$991$		−	2.24796e8i		−	0.230976i	−0.993309	−	0.115488i	$-0.963157\pi$
$991$		−	2.24796e8i		−	0.230976i	0.993309	−	0.115488i	$-0.0368432\pi$
$992$		0			0
$993$	2.05845e8			0.210229
$994$		0			0
$995$	1.77176e9	+	1.77176e9i	1.79861	+	1.79861i
$996$		0			0
$997$	5.42120e8	+	5.42120e8i	0.547028	+	0.547028i	0.925580	−	0.378552i	$-0.123578\pi$
$997$	5.42120e8	+	5.42120e8i	0.547028	+	0.547028i	−0.378552	+	0.925580i	$0.623578\pi$
$998$		0			0
$999$	−1.54393e8			−0.154858

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.a.31.24		48
4.3	odd	2		384.7.l.b.31.1		48
8.3	odd	2		48.7.l.a.43.21	yes	48
8.5	even	2		192.7.l.a.79.1		48
16.3	odd	4	inner	384.7.l.a.223.24		48
16.5	even	4		48.7.l.a.19.21	✓	48
16.11	odd	4		192.7.l.a.175.1		48
16.13	even	4		384.7.l.b.223.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.21	✓	48	16.5	even	4
48.7.l.a.43.21	yes	48	8.3	odd	2
192.7.l.a.79.1		48	8.5	even	2
192.7.l.a.175.1		48	16.11	odd	4
384.7.l.a.31.24		48	1.1	even	1	trivial
384.7.l.a.223.24		48	16.3	odd	4	inner
384.7.l.b.31.1		48	4.3	odd	2
384.7.l.b.223.1		48	16.13	even	4

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	384.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(11.0227 + 11.0227i) q^{3} +(159.596 + 159.596i) q^{5} +527.602 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(11.0227 + 11.0227i) q^{3} +(159.596 + 159.596i) q^{5} +527.602 q^{7} +243.000i q^{9} +(-134.486 + 134.486i) q^{11} +(-1265.37 + 1265.37i) q^{13} +3518.36i q^{15} +8418.61 q^{17} +(-2553.03 - 2553.03i) q^{19} +(5815.60 + 5815.60i) q^{21} +8709.06 q^{23} +35316.9i q^{25} +(-2678.52 + 2678.52i) q^{27} +(-19317.9 + 19317.9i) q^{29} +16542.9i q^{31} -2964.80 q^{33} +(84203.3 + 84203.3i) q^{35} +(28820.7 + 28820.7i) q^{37} -27895.7 q^{39} -56876.6i q^{41} +(54549.8 - 54549.8i) q^{43} +(-38781.9 + 38781.9i) q^{45} -145597. i q^{47} +160715. q^{49} +(92795.8 + 92795.8i) q^{51} +(-84395.8 - 84395.8i) q^{53} -42926.9 q^{55} -56282.6i q^{57} +(-125938. + 125938. i) q^{59} +(52486.8 - 52486.8i) q^{61} +128207. i q^{63} -403898. q^{65} +(-142096. - 142096. i) q^{67} +(95997.4 + 95997.4i) q^{69} +25672.8 q^{71} -538587. i q^{73} +(-389288. + 389288. i) q^{75} +(-70955.1 + 70955.1i) q^{77} +122911. i q^{79} -59049.0 q^{81} +(539606. + 539606. i) q^{83} +(1.34358e6 + 1.34358e6i) q^{85} -425871. q^{87} -504858. i q^{89} +(-667614. + 667614. i) q^{91} +(-182348. + 182348. i) q^{93} -814908. i q^{95} -781168. q^{97} +(-32680.1 - 32680.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 2720 q^{11} - 3936 q^{19} - 26240 q^{23} - 66400 q^{29} + 162336 q^{35} + 7200 q^{37} + 340704 q^{43} + 806736 q^{49} + 80352 q^{51} - 443680 q^{53} - 232704 q^{55} - 886144 q^{59} + 326496 q^{61} - 372832 q^{65} - 962112 q^{67} - 541728 q^{69} - 534016 q^{71} - 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} - 2497760 q^{83} + 372000 q^{85} + 775008 q^{91} - 660960 q^{99}+O(q^{100}) \) 48 * q - 2720 * q^11 - 3936 * q^19 - 26240 * q^23 - 66400 * q^29 + 162336 * q^35 + 7200 * q^37 + 340704 * q^43 + 806736 * q^49 + 80352 * q^51 - 443680 * q^53 - 232704 * q^55 - 886144 * q^59 + 326496 * q^61 - 372832 * q^65 - 962112 * q^67 - 541728 * q^69 - 534016 * q^71 - 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 - 2497760 * q^83 + 372000 * q^85 + 775008 * q^91 - 660960 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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