LMFDB - Embedded newform 384.7.l.a.31.7

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			31.7
Character	$\chi$	$=$	384.31
Dual form			384.7.l.a.223.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0227 - 11.0227i) q^{3} +(-45.7781 - 45.7781i) q^{5} +565.544 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(-11.0227 - 11.0227i) q^{3} +(-45.7781 - 45.7781i) q^{5} +565.544 q^{7} +243.000i q^{9} +(1291.95 - 1291.95i) q^{11} +(2882.93 - 2882.93i) q^{13} +1009.20i q^{15} -662.555 q^{17} +(1940.19 + 1940.19i) q^{19} +(-6233.83 - 6233.83i) q^{21} +15879.3 q^{23} -11433.7i q^{25} +(2678.52 - 2678.52i) q^{27} +(-11555.8 + 11555.8i) q^{29} +39097.9i q^{31} -28481.5 q^{33} +(-25889.6 - 25889.6i) q^{35} +(51336.5 + 51336.5i) q^{37} -63555.4 q^{39} +66520.0i q^{41} +(68923.6 - 68923.6i) q^{43} +(11124.1 - 11124.1i) q^{45} +107734. i q^{47} +202191. q^{49} +(7303.15 + 7303.15i) q^{51} +(108477. + 108477. i) q^{53} -118286. q^{55} -42772.3i q^{57} +(-67889.1 + 67889.1i) q^{59} +(99209.6 - 99209.6i) q^{61} +137427. i q^{63} -263951. q^{65} +(-105403. - 105403. i) q^{67} +(-175033. - 175033. i) q^{69} -266114. q^{71} +267965. i q^{73} +(-126031. + 126031. i) q^{75} +(730653. - 730653. i) q^{77} -557984. i q^{79} -59049.0 q^{81} +(-236224. - 236224. i) q^{83} +(30330.5 + 30330.5i) q^{85} +254751. q^{87} +419786. i q^{89} +(1.63043e6 - 1.63043e6i) q^{91} +(430964. - 430964. i) q^{93} -177637. i q^{95} +393308. q^{97} +(313943. + 313943. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−45.7781	−	45.7781i	−0.366225	−	0.366225i	0.499873	−	0.866098i	$-0.333380\pi$
$5$	−45.7781	−	45.7781i	−0.366225	−	0.366225i	−0.866098	+	0.499873i	$0.833380\pi$
$6$		0			0
$7$	565.544			1.64882			0.824408	−	0.565995i	$-0.191508\pi$
$7$	565.544			1.64882			0.824408	+	0.565995i	$0.191508\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	1291.95	−	1291.95i	0.970658	−	0.970658i	−0.0289233	−	0.999582i	$-0.509208\pi$
$11$	1291.95	−	1291.95i	0.970658	−	0.970658i	0.999582	+	0.0289233i	$0.00920786\pi$
$12$		0			0
$13$	2882.93	−	2882.93i	1.31221	−	1.31221i	0.392433	−	0.919781i	$-0.371634\pi$
$13$	2882.93	−	2882.93i	1.31221	−	1.31221i	0.919781	−	0.392433i	$-0.128366\pi$
$14$		0			0
$15$			1009.20i			0.299022i
$16$		0			0
$17$	−662.555			−0.134858			−0.0674288	−	0.997724i	$-0.521480\pi$
$17$	−662.555			−0.134858			−0.0674288	+	0.997724i	$0.521480\pi$
$18$		0			0
$19$	1940.19	+	1940.19i	0.282868	+	0.282868i	0.834252	−	0.551384i	$-0.185900\pi$
$19$	1940.19	+	1940.19i	0.282868	+	0.282868i	−0.551384	+	0.834252i	$0.685900\pi$
$20$		0			0
$21$	−6233.83	−	6233.83i	−0.673127	−	0.673127i
$22$		0			0
$23$	15879.3			1.30511			0.652557	−	0.757740i	$-0.273696\pi$
$23$	15879.3			1.30511			0.652557	+	0.757740i	$0.273696\pi$
$24$		0			0
$25$		−	11433.7i		−	0.731758i
$26$		0			0
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$		0			0
$29$	−11555.8	+	11555.8i	−0.473810	+	0.473810i	−0.903145	−	0.429335i	$-0.858748\pi$
$29$	−11555.8	+	11555.8i	−0.473810	+	0.473810i	0.429335	+	0.903145i	$0.358748\pi$
$30$		0			0
$31$			39097.9i			1.31241i	0.754585	+	0.656203i	$0.227838\pi$
$31$			39097.9i			1.31241i	−0.754585	+	0.656203i	$0.772162\pi$
$32$		0			0
$33$	−28481.5			−0.792539
$34$		0			0
$35$	−25889.6	−	25889.6i	−0.603838	−	0.603838i
$36$		0			0
$37$	51336.5	+	51336.5i	1.01349	+	1.01349i	0.999908	+	0.0135861i	$0.00432473\pi$
$37$	51336.5	+	51336.5i	1.01349	+	1.01349i	0.0135861	+	0.999908i	$0.495675\pi$
$38$		0			0
$39$	−63555.4			−1.07142
$40$		0			0
$41$			66520.0i			0.965163i	0.875851	+	0.482582i	$0.160301\pi$
$41$			66520.0i			0.965163i	−0.875851	+	0.482582i	$0.839699\pi$
$42$		0			0
$43$	68923.6	−	68923.6i	0.866887	−	0.866887i	−0.125239	−	0.992127i	$-0.539970\pi$
$43$	68923.6	−	68923.6i	0.866887	−	0.866887i	0.992127	+	0.125239i	$0.0399699\pi$
$44$		0			0
$45$	11124.1	−	11124.1i	0.122075	−	0.122075i
$46$		0			0
$47$			107734.i			1.03767i	0.854873	+	0.518837i	$0.173635\pi$
$47$			107734.i			1.03767i	−0.854873	+	0.518837i	$0.826365\pi$
$48$		0			0
$49$	202191.			1.71860
$50$		0			0
$51$	7303.15	+	7303.15i	0.0550554	+	0.0550554i
$52$		0			0
$53$	108477.	+	108477.i	0.728637	+	0.728637i	0.970348	−	0.241711i	$-0.0777086\pi$
$53$	108477.	+	108477.i	0.728637	+	0.728637i	−0.241711	+	0.970348i	$0.577709\pi$
$54$		0			0
$55$	−118286.			−0.710959
$56$		0			0
$57$		−	42772.3i		−	0.230961i
$58$		0			0
$59$	−67889.1	+	67889.1i	−0.330555	+	0.330555i	−0.852797	−	0.522242i	$-0.825096\pi$
$59$	−67889.1	+	67889.1i	−0.330555	+	0.330555i	0.522242	+	0.852797i	$0.325096\pi$
$60$		0			0
$61$	99209.6	−	99209.6i	0.437083	−	0.437083i	−0.453946	−	0.891029i	$-0.649984\pi$
$61$	99209.6	−	99209.6i	0.437083	−	0.437083i	0.891029	+	0.453946i	$0.149984\pi$
$62$		0			0
$63$			137427.i			0.549606i
$64$		0			0
$65$	−263951.			−0.961131
$66$		0			0
$67$	−105403.	−	105403.i	−0.350451	−	0.350451i	0.509826	−	0.860277i	$-0.329710\pi$
$67$	−105403.	−	105403.i	−0.350451	−	0.350451i	−0.860277	+	0.509826i	$0.829710\pi$
$68$		0			0
$69$	−175033.	−	175033.i	−0.532810	−	0.532810i
$70$		0			0
$71$	−266114.			−0.743520			−0.371760	−	0.928329i	$-0.621246\pi$
$71$	−266114.			−0.743520			−0.371760	+	0.928329i	$0.621246\pi$
$72$		0			0
$73$			267965.i			0.688826i	0.938818	+	0.344413i	$0.111922\pi$
$73$			267965.i			0.688826i	−0.938818	+	0.344413i	$0.888078\pi$
$74$		0			0
$75$	−126031.	+	126031.i	−0.298739	+	0.298739i
$76$		0			0
$77$	730653.	−	730653.i	1.60044	−	1.60044i
$78$		0			0
$79$		−	557984.i		−	1.13172i	−0.824500	−	0.565862i	$-0.808544\pi$
$79$		−	557984.i		−	1.13172i	0.824500	−	0.565862i	$-0.191456\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−236224.	−	236224.i	−0.413133	−	0.413133i	0.469695	−	0.882829i	$-0.344364\pi$
$83$	−236224.	−	236224.i	−0.413133	−	0.413133i	−0.882829	+	0.469695i	$0.844364\pi$
$84$		0			0
$85$	30330.5	+	30330.5i	0.0493882	+	0.0493882i
$86$		0			0
$87$	254751.			0.386864
$88$		0			0
$89$			419786.i			0.595467i	0.954649	+	0.297733i	$0.0962307\pi$
$89$			419786.i			0.595467i	−0.954649	+	0.297733i	$0.903769\pi$
$90$		0			0
$91$	1.63043e6	−	1.63043e6i	2.16360	−	2.16360i
$92$		0			0
$93$	430964.	−	430964.i	0.535787	−	0.535787i
$94$		0			0
$95$		−	177637.i		−	0.207187i
$96$		0			0
$97$	393308.			0.430940			0.215470	−	0.976510i	$-0.430872\pi$
$97$	393308.			0.430940			0.215470	+	0.976510i	$0.430872\pi$
$98$		0			0
$99$	313943.	+	313943.i	0.323553	+	0.323553i
$100$		0			0
$101$	−670944.	−	670944.i	−0.651212	−	0.651212i	0.302073	−	0.953285i	$-0.402321\pi$
$101$	−670944.	−	670944.i	−0.651212	−	0.651212i	−0.953285	+	0.302073i	$0.902321\pi$
$102$		0			0
$103$	−456775.			−0.418013			−0.209007	−	0.977914i	$-0.567023\pi$
$103$	−456775.			−0.418013			−0.209007	+	0.977914i	$0.567023\pi$
$104$		0			0
$105$			570746.i			0.493032i
$106$		0			0
$107$	−498780.	+	498780.i	−0.407153	+	0.407153i	−0.880745	−	0.473592i	$-0.842957\pi$
$107$	−498780.	+	498780.i	−0.407153	+	0.407153i	0.473592	+	0.880745i	$0.342957\pi$
$108$		0			0
$109$	686021.	−	686021.i	0.529734	−	0.529734i	−0.390759	−	0.920493i	$-0.627787\pi$
$109$	686021.	−	686021.i	0.529734	−	0.529734i	0.920493	+	0.390759i	$0.127787\pi$
$110$		0			0
$111$		−	1.13173e6i		−	0.827514i
$112$		0			0
$113$	1.76590e6			1.22386			0.611930	−	0.790912i	$-0.290394\pi$
$113$	1.76590e6			1.22386			0.611930	+	0.790912i	$0.290394\pi$
$114$		0			0
$115$	−726926.	−	726926.i	−0.477965	−	0.477965i
$116$		0			0
$117$	700553.	+	700553.i	0.437404	+	0.437404i
$118$		0			0
$119$	−374704.			−0.222355
$120$		0			0
$121$		−	1.56669e6i		−	0.884355i
$122$		0			0
$123$	733230.	−	733230.i	0.394026	−	0.394026i
$124$		0			0
$125$	−1.23870e6	+	1.23870e6i	−0.634213	+	0.634213i
$126$		0			0
$127$			2.52519e6i			1.23277i	0.787445	+	0.616385i	$0.211404\pi$
$127$			2.52519e6i			1.23277i	−0.787445	+	0.616385i	$0.788596\pi$
$128$		0			0
$129$	−1.51945e6			−0.707810
$130$		0			0
$131$	−2.20532e6	−	2.20532e6i	−0.980976	−	0.980976i	0.0188466	−	0.999822i	$-0.494001\pi$
$131$	−2.20532e6	−	2.20532e6i	−0.980976	−	0.980976i	−0.999822	+	0.0188466i	$0.994001\pi$
$132$		0			0
$133$	1.09726e6	+	1.09726e6i	0.466398	+	0.466398i
$134$		0			0
$135$	−245235.			−0.0996738
$136$		0			0
$137$		−	210985.i		−	0.0820520i	−0.999158	−	0.0410260i	$-0.986937\pi$
$137$		−	210985.i		−	0.0820520i	0.999158	−	0.0410260i	$-0.0130626\pi$
$138$		0			0
$139$	−678952.	+	678952.i	−0.252810	+	0.252810i	−0.822122	−	0.569312i	$-0.807210\pi$
$139$	−678952.	+	678952.i	−0.252810	+	0.252810i	0.569312	+	0.822122i	$0.307210\pi$
$140$		0			0
$141$	1.18752e6	−	1.18752e6i	0.423629	−	0.423629i
$142$		0			0
$143$		−	7.44919e6i		−	2.54742i
$144$		0			0
$145$	1.05800e6			0.347042
$146$		0			0
$147$	−2.22869e6	−	2.22869e6i	−0.701614	−	0.701614i
$148$		0			0
$149$	2.62816e6	+	2.62816e6i	0.794497	+	0.794497i	0.982222	−	0.187724i	$-0.0601111\pi$
$149$	2.62816e6	+	2.62816e6i	0.794497	+	0.794497i	−0.187724	+	0.982222i	$0.560111\pi$
$150$		0			0
$151$	−2.88045e6			−0.836622			−0.418311	−	0.908304i	$-0.637378\pi$
$151$	−2.88045e6			−0.836622			−0.418311	+	0.908304i	$0.637378\pi$
$152$		0			0
$153$		−	161001.i		−	0.0449525i
$154$		0			0
$155$	1.78983e6	−	1.78983e6i	0.480636	−	0.480636i
$156$		0			0
$157$	501498.	−	501498.i	0.129590	−	0.129590i	−0.639337	−	0.768927i	$-0.720791\pi$
$157$	501498.	−	501498.i	0.129590	−	0.129590i	0.768927	+	0.639337i	$0.220791\pi$
$158$		0			0
$159$		−	2.39143e6i		−	0.594930i
$160$		0			0
$161$	8.98046e6			2.15189
$162$		0			0
$163$	1.30009e6	+	1.30009e6i	0.300199	+	0.300199i	0.841092	−	0.540893i	$-0.181913\pi$
$163$	1.30009e6	+	1.30009e6i	0.300199	+	0.300199i	−0.540893	+	0.841092i	$0.681913\pi$
$164$		0			0
$165$	1.30383e6	+	1.30383e6i	0.290248	+	0.290248i
$166$		0			0
$167$	8.60262e6			1.84706			0.923531	−	0.383524i	$-0.125290\pi$
$167$	8.60262e6			1.84706			0.923531	+	0.383524i	$0.125290\pi$
$168$		0			0
$169$		−	1.17958e7i		−	2.44381i
$170$		0			0
$171$	−471467.	+	471467.i	−0.0942894	+	0.0942894i
$172$		0			0
$173$	891920.	−	891920.i	0.172261	−	0.172261i	−0.615711	−	0.787972i	$-0.711131\pi$
$173$	891920.	−	891920.i	0.172261	−	0.172261i	0.787972	+	0.615711i	$0.211131\pi$
$174$		0			0
$175$		−	6.46628e6i		−	1.20654i
$176$		0			0
$177$	1.49664e6			0.269897
$178$		0			0
$179$	−2.89580e6	−	2.89580e6i	−0.504904	−	0.504904i	0.408054	−	0.912958i	$-0.366208\pi$
$179$	−2.89580e6	−	2.89580e6i	−0.504904	−	0.504904i	−0.912958	+	0.408054i	$0.866208\pi$
$180$		0			0
$181$	−2.14643e6	−	2.14643e6i	−0.361977	−	0.361977i	0.502563	−	0.864541i	$-0.332390\pi$
$181$	−2.14643e6	−	2.14643e6i	−0.361977	−	0.361977i	−0.864541	+	0.502563i	$0.832390\pi$
$182$		0			0
$183$	−2.18712e6			−0.356877
$184$		0			0
$185$		−	4.70018e6i		−	0.742334i
$186$		0			0
$187$	−855986.	+	855986.i	−0.130901	+	0.130901i
$188$		0			0
$189$	1.51482e6	−	1.51482e6i	0.224376	−	0.224376i
$190$		0			0
$191$			1.12449e6i			0.161382i	0.996739	+	0.0806912i	$0.0257128\pi$
$191$			1.12449e6i			0.161382i	−0.996739	+	0.0806912i	$0.974287\pi$
$192$		0			0
$193$	6.65489e6			0.925697			0.462848	−	0.886437i	$-0.346827\pi$
$193$	6.65489e6			0.925697			0.462848	+	0.886437i	$0.346827\pi$
$194$		0			0
$195$	2.90945e6	+	2.90945e6i	0.392380	+	0.392380i
$196$		0			0
$197$	−1.01919e6	−	1.01919e6i	−0.133307	−	0.133307i	0.637305	−	0.770612i	$-0.280049\pi$
$197$	−1.01919e6	−	1.01919e6i	−0.133307	−	0.133307i	−0.770612	+	0.637305i	$0.780049\pi$
$198$		0			0
$199$	−889727.			−0.112901			−0.0564505	−	0.998405i	$-0.517978\pi$
$199$	−889727.			−0.112901			−0.0564505	+	0.998405i	$0.517978\pi$
$200$		0			0
$201$			2.32365e6i			0.286142i
$202$		0			0
$203$	−6.53529e6	+	6.53529e6i	−0.781226	+	0.781226i
$204$		0			0
$205$	3.04516e6	−	3.04516e6i	0.353467	−	0.353467i
$206$		0			0
$207$			3.85867e6i			0.435038i
$208$		0			0
$209$	5.01325e6			0.549137
$210$		0			0
$211$	−6.10371e6	−	6.10371e6i	−0.649750	−	0.649750i	0.303182	−	0.952933i	$-0.401951\pi$
$211$	−6.10371e6	−	6.10371e6i	−0.649750	−	0.649750i	−0.952933	+	0.303182i	$0.901951\pi$
$212$		0			0
$213$	2.93330e6	+	2.93330e6i	0.303541	+	0.303541i
$214$		0			0
$215$	−6.31039e6			−0.634952
$216$		0			0
$217$			2.21116e7i			2.16392i
$218$		0			0
$219$	2.95370e6	−	2.95370e6i	0.281212	−	0.281212i
$220$		0			0
$221$	−1.91010e6	+	1.91010e6i	−0.176962	+	0.176962i
$222$		0			0
$223$		−	8.07405e6i		−	0.728077i	−0.931384	−	0.364038i	$-0.881398\pi$
$223$		−	8.07405e6i		−	0.728077i	0.931384	−	0.364038i	$-0.118602\pi$
$224$		0			0
$225$	2.77840e6			0.243919
$226$		0			0
$227$	−4.13774e6	−	4.13774e6i	−0.353741	−	0.353741i	0.507758	−	0.861500i	$-0.330474\pi$
$227$	−4.13774e6	−	4.13774e6i	−0.353741	−	0.353741i	−0.861500	+	0.507758i	$0.830474\pi$
$228$		0			0
$229$	1.19667e7	+	1.19667e7i	0.996480	+	0.996480i	0.999994	−	0.00351356i	$-0.00111840\pi$
$229$	1.19667e7	+	1.19667e7i	0.996480	+	0.996480i	−0.00351356	+	0.999994i	$0.501118\pi$
$230$		0			0
$231$	−1.61075e7			−1.30675
$232$		0			0
$233$			1.46761e6i			0.116023i	0.998316	+	0.0580114i	$0.0184760\pi$
$233$			1.46761e6i			0.116023i	−0.998316	+	0.0580114i	$0.981524\pi$
$234$		0			0
$235$	4.93188e6	−	4.93188e6i	0.380022	−	0.380022i
$236$		0			0
$237$	−6.15049e6	+	6.15049e6i	−0.462024	+	0.462024i
$238$		0			0
$239$		−	1.28489e7i		−	0.941177i	−0.882353	−	0.470588i	$-0.844042\pi$
$239$		−	1.28489e7i		−	0.941177i	0.882353	−	0.470588i	$-0.155958\pi$
$240$		0			0
$241$	−1.87104e6			−0.133670			−0.0668348	−	0.997764i	$-0.521290\pi$
$241$	−1.87104e6			−0.133670			−0.0668348	+	0.997764i	$0.521290\pi$
$242$		0			0
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−9.25593e6	−	9.25593e6i	−0.629393	−	0.629393i
$246$		0			0
$247$	1.11869e7			0.742367
$248$		0			0
$249$			5.20766e6i			0.337322i
$250$		0			0
$251$	−2.06552e7	+	2.06552e7i	−1.30619	+	1.30619i	−0.382052	+	0.924141i	$0.624782\pi$
$251$	−2.06552e7	+	2.06552e7i	−1.30619	+	1.30619i	−0.924141	+	0.382052i	$0.875218\pi$
$252$		0			0
$253$	2.05152e7	−	2.05152e7i	1.26682	−	1.26682i
$254$		0			0
$255$		−	668649.i		−	0.0403253i
$256$		0			0
$257$	960591.			0.0565900			0.0282950	−	0.999600i	$-0.490992\pi$
$257$	960591.			0.0565900			0.0282950	+	0.999600i	$0.490992\pi$
$258$		0			0
$259$	2.90331e7	+	2.90331e7i	1.67107	+	1.67107i
$260$		0			0
$261$	−2.80805e6	−	2.80805e6i	−0.157937	−	0.157937i
$262$		0			0
$263$	2.66308e7			1.46392			0.731960	−	0.681348i	$-0.238606\pi$
$263$	2.66308e7			1.46392			0.731960	+	0.681348i	$0.238606\pi$
$264$		0			0
$265$		−	9.93178e6i		−	0.533690i
$266$		0			0
$267$	4.62717e6	−	4.62717e6i	0.243098	−	0.243098i
$268$		0			0
$269$	−2.00276e7	+	2.00276e7i	−1.02890	+	1.02890i	−0.0293254	+	0.999570i	$0.509336\pi$
$269$	−2.00276e7	+	2.00276e7i	−1.02890	+	1.02890i	−0.999570	+	0.0293254i	$0.990664\pi$
$270$		0			0
$271$			1.33995e7i			0.673256i	0.941638	+	0.336628i	$0.109286\pi$
$271$			1.33995e7i			0.673256i	−0.941638	+	0.336628i	$0.890714\pi$
$272$		0			0
$273$	−3.59434e7			−1.76657
$274$		0			0
$275$	−1.47718e7	−	1.47718e7i	−0.710287	−	0.710287i
$276$		0			0
$277$	1.43027e6	+	1.43027e6i	0.0672942	+	0.0672942i	0.739953	−	0.672659i	$-0.234848\pi$
$277$	1.43027e6	+	1.43027e6i	0.0672942	+	0.0672942i	−0.672659	+	0.739953i	$0.734848\pi$
$278$		0			0
$279$	−9.50078e6			−0.437469
$280$		0			0
$281$		−	1.75247e7i		−	0.789825i	−0.918719	−	0.394912i	$-0.870775\pi$
$281$		−	1.75247e7i		−	0.789825i	0.918719	−	0.394912i	$-0.129225\pi$
$282$		0			0
$283$	2.40129e7	−	2.40129e7i	1.05946	−	1.05946i	0.0613460	−	0.998117i	$-0.480461\pi$
$283$	2.40129e7	−	2.40129e7i	1.05946	−	1.05946i	0.998117	−	0.0613460i	$-0.0195393\pi$
$284$		0			0
$285$	−1.95804e6	+	1.95804e6i	−0.0845837	+	0.0845837i
$286$		0			0
$287$			3.76200e7i			1.59138i
$288$		0			0
$289$	−2.36986e7			−0.981813
$290$		0			0
$291$	−4.33531e6	−	4.33531e6i	−0.175931	−	0.175931i
$292$		0			0
$293$	−2.49680e7	−	2.49680e7i	−0.992617	−	0.992617i	0.00735615	−	0.999973i	$-0.497658\pi$
$293$	−2.49680e7	−	2.49680e7i	−0.992617	−	0.992617i	−0.999973	+	0.00735615i	$0.997658\pi$
$294$		0			0
$295$	6.21568e6			0.242115
$296$		0			0
$297$		−	6.92100e6i		−	0.264180i
$298$		0			0
$299$	4.57790e7	−	4.57790e7i	1.71259	−	1.71259i
$300$		0			0
$301$	3.89793e7	−	3.89793e7i	1.42934	−	1.42934i
$302$		0			0
$303$			1.47912e7i			0.531712i
$304$		0			0
$305$	−9.08326e6			−0.320142
$306$		0			0
$307$	3.13583e6	+	3.13583e6i	0.108377	+	0.108377i	0.759216	−	0.650839i	$-0.225583\pi$
$307$	3.13583e6	+	3.13583e6i	0.108377	+	0.108377i	−0.650839	+	0.759216i	$0.725583\pi$
$308$		0			0
$309$	5.03489e6	+	5.03489e6i	0.170653	+	0.170653i
$310$		0			0
$311$	−2.82703e7			−0.939830			−0.469915	−	0.882712i	$-0.655715\pi$
$311$	−2.82703e7			−0.939830			−0.469915	+	0.882712i	$0.655715\pi$
$312$		0			0
$313$		−	4.17098e6i		−	0.136021i	−0.997685	−	0.0680104i	$-0.978335\pi$
$313$		−	4.17098e6i		−	0.136021i	0.997685	−	0.0680104i	$-0.0216651\pi$
$314$		0			0
$315$	6.29116e6	−	6.29116e6i	0.201279	−	0.201279i
$316$		0			0
$317$	−3.49603e7	+	3.49603e7i	−1.09748	+	1.09748i	−0.102779	+	0.994704i	$0.532773\pi$
$317$	−3.49603e7	+	3.49603e7i	−1.09748	+	1.09748i	−0.994704	+	0.102779i	$0.967227\pi$
$318$		0			0
$319$			2.98588e7i			0.919815i
$320$		0			0
$321$	1.09958e7			0.332439
$322$		0			0
$323$	−1.28548e6	−	1.28548e6i	−0.0381469	−	0.0381469i
$324$		0			0
$325$	−3.29627e7	−	3.29627e7i	−0.960223	−	0.960223i
$326$		0			0
$327$	−1.51236e7			−0.432526
$328$		0			0
$329$			6.09286e7i			1.71093i
$330$		0			0
$331$	−2.32895e7	+	2.32895e7i	−0.642210	+	0.642210i	−0.951098	−	0.308888i	$-0.900043\pi$
$331$	−2.32895e7	+	2.32895e7i	−0.642210	+	0.642210i	0.308888	+	0.951098i	$0.400043\pi$
$332$		0			0
$333$	−1.24748e7	+	1.24748e7i	−0.337831	+	0.337831i
$334$		0			0
$335$			9.65029e6i			0.256688i
$336$		0			0
$337$	−1.28256e7			−0.335110			−0.167555	−	0.985863i	$-0.553587\pi$
$337$	−1.28256e7			−0.335110			−0.167555	+	0.985863i	$0.553587\pi$
$338$		0			0
$339$	−1.94650e7	−	1.94650e7i	−0.499638	−	0.499638i
$340$		0			0
$341$	5.05124e7	+	5.05124e7i	1.27390	+	1.27390i
$342$		0			0
$343$	4.78123e7			1.18483
$344$		0			0
$345$			1.60254e7i			0.390257i
$346$		0			0
$347$	−3.91869e7	+	3.91869e7i	−0.937891	+	0.937891i	−0.998181	−	0.0602903i	$-0.980797\pi$
$347$	−3.91869e7	+	3.91869e7i	−0.937891	+	0.937891i	0.0602903	+	0.998181i	$0.480797\pi$
$348$		0			0
$349$	−4.06672e7	+	4.06672e7i	−0.956682	+	0.956682i	−0.999100	−	0.0424175i	$-0.986494\pi$
$349$	−4.06672e7	+	4.06672e7i	−0.956682	+	0.956682i	0.0424175	+	0.999100i	$0.486494\pi$
$350$		0			0
$351$		−	1.54440e7i		−	0.357139i
$352$		0			0
$353$	−3.01960e7			−0.686475			−0.343237	−	0.939249i	$-0.611524\pi$
$353$	−3.01960e7			−0.686475			−0.343237	+	0.939249i	$0.611524\pi$
$354$		0			0
$355$	1.21822e7	+	1.21822e7i	0.272296	+	0.272296i
$356$		0			0
$357$	4.13025e6	+	4.13025e6i	0.0907762	+	0.0907762i
$358$		0			0
$359$	−6.27234e7			−1.35565			−0.677823	−	0.735225i	$-0.737076\pi$
$359$	−6.27234e7			−1.35565			−0.677823	+	0.735225i	$0.737076\pi$
$360$		0			0
$361$		−	3.95172e7i		−	0.839971i
$362$		0			0
$363$	−1.72691e7	+	1.72691e7i	−0.361036	+	0.361036i
$364$		0			0
$365$	1.22669e7	−	1.22669e7i	0.252265	−	0.252265i
$366$		0			0
$367$			7.63574e7i			1.54473i	0.635179	+	0.772365i	$0.280927\pi$
$367$			7.63574e7i			1.54473i	−0.635179	+	0.772365i	$0.719073\pi$
$368$		0			0
$369$	−1.61644e7			−0.321721
$370$		0			0
$371$	6.13487e7	+	6.13487e7i	1.20139	+	1.20139i
$372$		0			0
$373$	−3.70594e7	−	3.70594e7i	−0.714121	−	0.714121i	0.253274	−	0.967395i	$-0.418493\pi$
$373$	−3.70594e7	−	3.70594e7i	−0.714121	−	0.714121i	−0.967395	+	0.253274i	$0.918493\pi$
$374$		0			0
$375$	2.73076e7			0.517833
$376$		0			0
$377$			6.66289e7i			1.24348i
$378$		0			0
$379$	−4.65182e7	+	4.65182e7i	−0.854487	+	0.854487i	−0.990682	−	0.136195i	$-0.956513\pi$
$379$	−4.65182e7	+	4.65182e7i	−0.854487	+	0.854487i	0.136195	+	0.990682i	$0.456513\pi$
$380$		0			0
$381$	2.78344e7	−	2.78344e7i	0.503276	−	0.503276i
$382$		0			0
$383$		−	1.38162e7i		−	0.245919i	−0.992412	−	0.122959i	$-0.960762\pi$
$383$		−	1.38162e7i		−	0.245919i	0.992412	−	0.122959i	$-0.0392385\pi$
$384$		0			0
$385$	−6.68958e7			−1.17224
$386$		0			0
$387$	1.67484e7	+	1.67484e7i	0.288962	+	0.288962i
$388$		0			0
$389$	−3.29148e7	−	3.29148e7i	−0.559168	−	0.559168i	0.369902	−	0.929071i	$-0.379391\pi$
$389$	−3.29148e7	−	3.29148e7i	−0.559168	−	0.559168i	−0.929071	+	0.369902i	$0.879391\pi$
$390$		0			0
$391$	−1.05209e7			−0.176004
$392$		0			0
$393$			4.86172e7i			0.800963i
$394$		0			0
$395$	−2.55435e7	+	2.55435e7i	−0.414465	+	0.414465i
$396$		0			0
$397$	−9.09263e6	+	9.09263e6i	−0.145318	+	0.145318i	−0.776023	−	0.630705i	$-0.782766\pi$
$397$	−9.09263e6	+	9.09263e6i	−0.145318	+	0.145318i	0.630705	+	0.776023i	$0.282766\pi$
$398$		0			0
$399$		−	2.41896e7i		−	0.380812i
$400$		0			0
$401$	5.10274e7			0.791353			0.395677	−	0.918390i	$-0.370510\pi$
$401$	5.10274e7			0.791353			0.395677	+	0.918390i	$0.370510\pi$
$402$		0			0
$403$	1.12717e8	+	1.12717e8i	1.72216	+	1.72216i
$404$		0			0
$405$	2.70315e6	+	2.70315e6i	0.0406917	+	0.0406917i
$406$		0			0
$407$	1.32648e8			1.96751
$408$		0			0
$409$		−	8.06130e7i		−	1.17824i	−0.808044	−	0.589122i	$-0.799474\pi$
$409$		−	8.06130e7i		−	1.17824i	0.808044	−	0.589122i	$-0.200526\pi$
$410$		0			0
$411$	−2.32562e6	+	2.32562e6i	−0.0334976	+	0.0334976i
$412$		0			0
$413$	−3.83943e7	+	3.83943e7i	−0.545025	+	0.545025i
$414$		0			0
$415$			2.16278e7i			0.302599i
$416$		0			0
$417$	1.49678e7			0.206419
$418$		0			0
$419$	−8.05454e7	−	8.05454e7i	−1.09496	−	1.09496i	−0.994990	−	0.0999711i	$-0.968125\pi$
$419$	−8.05454e7	−	8.05454e7i	−1.09496	−	1.09496i	−0.0999711	−	0.994990i	$-0.531875\pi$
$420$		0			0
$421$	1.99109e7	+	1.99109e7i	0.266837	+	0.266837i	0.827824	−	0.560988i	$-0.189578\pi$
$421$	1.99109e7	+	1.99109e7i	0.266837	+	0.266837i	−0.560988	+	0.827824i	$0.689578\pi$
$422$		0			0
$423$	−2.61795e7			−0.345891
$424$		0			0
$425$			7.57548e6i			0.0986832i
$426$		0			0
$427$	5.61074e7	−	5.61074e7i	0.720670	−	0.720670i
$428$		0			0
$429$	−8.21102e7	+	8.21102e7i	−1.03998	+	1.03998i
$430$		0			0
$431$		−	5.56500e7i		−	0.695078i	−0.937666	−	0.347539i	$-0.887018\pi$
$431$		−	5.56500e7i		−	0.695078i	0.937666	−	0.347539i	$-0.112982\pi$
$432$		0			0
$433$	1.28922e8			1.58804			0.794022	−	0.607889i	$-0.207984\pi$
$433$	1.28922e8			1.58804			0.794022	+	0.607889i	$0.207984\pi$
$434$		0			0
$435$	−1.16620e7	−	1.16620e7i	−0.141679	−	0.141679i
$436$		0			0
$437$	3.08089e7	+	3.08089e7i	0.369175	+	0.369175i
$438$		0			0
$439$	1.16571e8			1.37784			0.688918	−	0.724839i	$-0.258086\pi$
$439$	1.16571e8			1.37784			0.688918	+	0.724839i	$0.258086\pi$
$440$		0			0
$441$			4.91325e7i			0.572865i
$442$		0			0
$443$	−8.56146e7	+	8.56146e7i	−0.984775	+	0.984775i	−0.999886	−	0.0151112i	$-0.995190\pi$
$443$	−8.56146e7	+	8.56146e7i	−0.984775	+	0.984775i	0.0151112	+	0.999886i	$0.495190\pi$
$444$		0			0
$445$	1.92170e7	−	1.92170e7i	0.218075	−	0.218075i
$446$		0			0
$447$		−	5.79388e7i		−	0.648704i
$448$		0			0
$449$	−1.62296e8			−1.79295			−0.896474	−	0.443096i	$-0.853880\pi$
$449$	−1.62296e8			−1.79295			−0.896474	+	0.443096i	$0.853880\pi$
$450$		0			0
$451$	8.59403e7	+	8.59403e7i	0.936844	+	0.936844i
$452$		0			0
$453$	3.17503e7	+	3.17503e7i	0.341550	+	0.341550i
$454$		0			0
$455$	−1.49276e8			−1.58473
$456$		0			0
$457$		−	1.31224e8i		−	1.37488i	−0.726241	−	0.687440i	$-0.758734\pi$
$457$		−	1.31224e8i		−	1.37488i	0.726241	−	0.687440i	$-0.241266\pi$
$458$		0			0
$459$	−1.77467e6	+	1.77467e6i	−0.0183518	+	0.0183518i
$460$		0			0
$461$	−3.76397e7	+	3.76397e7i	−0.384188	+	0.384188i	−0.872608	−	0.488421i	$-0.837573\pi$
$461$	−3.76397e7	+	3.76397e7i	−0.384188	+	0.384188i	0.488421	+	0.872608i	$0.337573\pi$
$462$		0			0
$463$			5.50458e6i			0.0554602i	0.999615	+	0.0277301i	$0.00882789\pi$
$463$			5.50458e6i			0.0554602i	−0.999615	+	0.0277301i	$0.991172\pi$
$464$		0			0
$465$	−3.94575e7			−0.392438
$466$		0			0
$467$	−9.63536e6	−	9.63536e6i	−0.0946057	−	0.0946057i	0.658220	−	0.752826i	$-0.271310\pi$
$467$	−9.63536e6	−	9.63536e6i	−0.0946057	−	0.0946057i	−0.752826	+	0.658220i	$0.771310\pi$
$468$		0			0
$469$	−5.96099e7	−	5.96099e7i	−0.577830	−	0.577830i
$470$		0			0
$471$	−1.10557e7			−0.105809
$472$		0			0
$473$		−	1.78091e8i		−	1.68290i
$474$		0			0
$475$	2.21836e7	−	2.21836e7i	0.206991	−	0.206991i
$476$		0			0
$477$	−2.63600e7	+	2.63600e7i	−0.242879	+	0.242879i
$478$		0			0
$479$		−	3.68794e6i		−	0.0335566i	−0.999859	−	0.0167783i	$-0.994659\pi$
$479$		−	3.68794e6i		−	0.0335566i	0.999859	−	0.0167783i	$-0.00534095\pi$
$480$		0			0
$481$	2.95999e8			2.65984
$482$		0			0
$483$	−9.89889e7	−	9.89889e7i	−0.878507	−	0.878507i
$484$		0			0
$485$	−1.80049e7	−	1.80049e7i	−0.157821	−	0.157821i
$486$		0			0
$487$	6.06471e7			0.525077			0.262539	−	0.964921i	$-0.415440\pi$
$487$	6.06471e7			0.525077			0.262539	+	0.964921i	$0.415440\pi$
$488$		0			0
$489$		−	2.86609e7i		−	0.245112i
$490$		0			0
$491$	2.63117e7	−	2.63117e7i	0.222282	−	0.222282i	−0.587177	−	0.809459i	$-0.699761\pi$
$491$	2.63117e7	−	2.63117e7i	0.222282	−	0.222282i	0.809459	+	0.587177i	$0.199761\pi$
$492$		0			0
$493$	7.65633e6	−	7.65633e6i	0.0638969	−	0.0638969i
$494$		0			0
$495$		−	2.87434e7i		−	0.236986i
$496$		0			0
$497$	−1.50499e8			−1.22593
$498$		0			0
$499$	−1.17267e8	−	1.17267e8i	−0.943788	−	0.943788i	0.0547144	−	0.998502i	$-0.482575\pi$
$499$	−1.17267e8	−	1.17267e8i	−0.943788	−	0.943788i	−0.998502	+	0.0547144i	$0.982575\pi$
$500$		0			0
$501$	−9.48241e7	−	9.48241e7i	−0.754060	−	0.754060i
$502$		0			0
$503$	−8.84245e7			−0.694814			−0.347407	−	0.937714i	$-0.612938\pi$
$503$	−8.84245e7			−0.694814			−0.347407	+	0.937714i	$0.612938\pi$
$504$		0			0
$505$			6.14291e7i			0.476980i
$506$		0			0
$507$	−1.30022e8	+	1.30022e8i	−0.997681	+	0.997681i
$508$		0			0
$509$	9.88133e7	−	9.88133e7i	0.749311	−	0.749311i	−0.225039	−	0.974350i	$-0.572251\pi$
$509$	9.88133e7	−	9.88133e7i	0.749311	−	0.749311i	0.974350	+	0.225039i	$0.0722509\pi$
$510$		0			0
$511$			1.51546e8i			1.13575i
$512$		0			0
$513$	1.03937e7			0.0769870
$514$		0			0
$515$	2.09103e7	+	2.09103e7i	0.153087	+	0.153087i
$516$		0			0
$517$	1.39187e8	+	1.39187e8i	1.00723	+	1.00723i
$518$		0			0
$519$	−1.96627e7			−0.140651
$520$		0			0
$521$			1.96978e8i			1.39285i	0.717629	+	0.696425i	$0.245227\pi$
$521$			1.96978e8i			1.39285i	−0.717629	+	0.696425i	$0.754773\pi$
$522$		0			0
$523$	7.96274e7	−	7.96274e7i	0.556618	−	0.556618i	−0.371725	−	0.928343i	$-0.621233\pi$
$523$	7.96274e7	−	7.96274e7i	0.556618	−	0.556618i	0.928343	+	0.371725i	$0.121233\pi$
$524$		0			0
$525$	−7.12758e7	+	7.12758e7i	−0.492566	+	0.492566i
$526$		0			0
$527$		−	2.59045e7i		−	0.176988i
$528$		0			0
$529$	1.04117e8			0.703322
$530$		0			0
$531$	−1.64971e7	−	1.64971e7i	−0.110185	−	0.110185i
$532$		0			0
$533$	1.91773e8	+	1.91773e8i	1.26650	+	1.26650i
$534$		0			0
$535$	4.56664e7			0.298219
$536$		0			0
$537$			6.38390e7i			0.412252i
$538$		0			0
$539$	2.61220e8	−	2.61220e8i	1.66817	−	1.66817i
$540$		0			0
$541$	1.92069e8	−	1.92069e8i	1.21302	−	1.21302i	0.242986	−	0.970030i	$-0.421873\pi$
$541$	1.92069e8	−	1.92069e8i	1.21302	−	1.21302i	0.970030	−	0.242986i	$-0.0781268\pi$
$542$		0			0
$543$			4.73190e7i			0.295553i
$544$		0			0
$545$	−6.28095e7			−0.388004
$546$		0			0
$547$	−7.48181e7	−	7.48181e7i	−0.457135	−	0.457135i	0.440579	−	0.897714i	$-0.354773\pi$
$547$	−7.48181e7	−	7.48181e7i	−0.457135	−	0.457135i	−0.897714	+	0.440579i	$0.854773\pi$
$548$		0			0
$549$	2.41079e7	+	2.41079e7i	0.145694	+	0.145694i
$550$		0			0
$551$	−4.48408e7			−0.268052
$552$		0			0
$553$		−	3.15564e8i		−	1.86600i
$554$		0			0
$555$	−5.18087e7	+	5.18087e7i	−0.303056	+	0.303056i
$556$		0			0
$557$	1.38814e8	−	1.38814e8i	0.803281	−	0.803281i	−0.180326	−	0.983607i	$-0.557715\pi$
$557$	1.38814e8	−	1.38814e8i	0.803281	−	0.803281i	0.983607	+	0.180326i	$0.0577152\pi$
$558$		0			0
$559$		−	3.97404e8i		−	2.27508i
$560$		0			0
$561$	1.88706e7			0.106880
$562$		0			0
$563$	−1.37839e8	−	1.37839e8i	−0.772411	−	0.772411i	0.206117	−	0.978527i	$-0.433917\pi$
$563$	−1.37839e8	−	1.37839e8i	−0.772411	−	0.772411i	−0.978527	+	0.206117i	$0.933917\pi$
$564$		0			0
$565$	−8.08397e7	−	8.08397e7i	−0.448208	−	0.448208i
$566$		0			0
$567$	−3.33948e7			−0.183202
$568$		0			0
$569$			1.94110e8i			1.05368i	0.849963	+	0.526842i	$0.176624\pi$
$569$			1.94110e8i			1.05368i	−0.849963	+	0.526842i	$0.823376\pi$
$570$		0			0
$571$	5.50758e7	−	5.50758e7i	0.295837	−	0.295837i	−0.543544	−	0.839381i	$-0.682918\pi$
$571$	5.50758e7	−	5.50758e7i	0.295837	−	0.295837i	0.839381	+	0.543544i	$0.182918\pi$
$572$		0			0
$573$	1.23949e7	−	1.23949e7i	0.0658841	−	0.0658841i
$574$		0			0
$575$		−	1.81560e8i		−	0.955028i
$576$		0			0
$577$	−1.62355e8			−0.845158			−0.422579	−	0.906326i	$-0.638875\pi$
$577$	−1.62355e8			−0.845158			−0.422579	+	0.906326i	$0.638875\pi$
$578$		0			0
$579$	−7.33548e7	−	7.33548e7i	−0.377914	−	0.377914i
$580$		0			0
$581$	−1.33595e8	−	1.33595e8i	−0.681181	−	0.681181i
$582$		0			0
$583$	2.80294e8			1.41452
$584$		0			0
$585$		−	6.41400e7i		−	0.320377i
$586$		0			0
$587$	1.11238e8	−	1.11238e8i	0.549968	−	0.549968i	−0.376464	−	0.926431i	$-0.622860\pi$
$587$	1.11238e8	−	1.11238e8i	0.549968	−	0.549968i	0.926431	+	0.376464i	$0.122860\pi$
$588$		0			0
$589$	−7.58574e7	+	7.58574e7i	−0.371238	+	0.371238i
$590$		0			0
$591$			2.24683e7i			0.108845i
$592$		0			0
$593$	3.77045e8			1.80813			0.904064	−	0.427397i	$-0.140569\pi$
$593$	3.77045e8			1.80813			0.904064	+	0.427397i	$0.140569\pi$
$594$		0			0
$595$	1.71533e7	+	1.71533e7i	0.0814321	+	0.0814321i
$596$		0			0
$597$	9.80720e6	+	9.80720e6i	0.0460916	+	0.0460916i
$598$		0			0
$599$	−3.55681e8			−1.65493			−0.827465	−	0.561517i	$-0.810218\pi$
$599$	−3.55681e8			−1.65493			−0.827465	+	0.561517i	$0.810218\pi$
$600$		0			0
$601$			1.48769e8i			0.685313i	0.939461	+	0.342656i	$0.111327\pi$
$601$			1.48769e8i			0.685313i	−0.939461	+	0.342656i	$0.888673\pi$
$602$		0			0
$603$	2.56129e7	−	2.56129e7i	0.116817	−	0.116817i
$604$		0			0
$605$	−7.17201e7	+	7.17201e7i	−0.323873	+	0.323873i
$606$		0			0
$607$		−	2.97217e7i		−	0.132894i	−0.997790	−	0.0664472i	$-0.978834\pi$
$607$		−	2.97217e7i		−	0.132894i	0.997790	−	0.0664472i	$-0.0211664\pi$
$608$		0			0
$609$	1.44073e8			0.637868
$610$		0			0
$611$	3.10591e8	+	3.10591e8i	1.36165	+	1.36165i
$612$		0			0
$613$	−1.04355e8	−	1.04355e8i	−0.453034	−	0.453034i	0.443326	−	0.896360i	$-0.353798\pi$
$613$	−1.04355e8	−	1.04355e8i	−0.453034	−	0.453034i	−0.896360	+	0.443326i	$0.853798\pi$
$614$		0			0
$615$	−6.71318e7			−0.288605
$616$		0			0
$617$		−	1.67053e8i		−	0.711213i	−0.934636	−	0.355606i	$-0.884274\pi$
$617$		−	1.67053e8i		−	0.711213i	0.934636	−	0.355606i	$-0.115726\pi$
$618$		0			0
$619$	−3.33498e7	+	3.33498e7i	−0.140612	+	0.140612i	−0.773909	−	0.633297i	$-0.781701\pi$
$619$	−3.33498e7	+	3.33498e7i	−0.140612	+	0.140612i	0.633297	+	0.773909i	$0.281701\pi$
$620$		0			0
$621$	4.25330e7	−	4.25330e7i	0.177603	−	0.177603i
$622$		0			0
$623$			2.37407e8i			0.981816i
$624$		0			0
$625$	−6.52414e7			−0.267229
$626$		0			0
$627$	−5.52596e7	−	5.52596e7i	−0.224184	−	0.224184i
$628$		0			0
$629$	−3.40133e7	−	3.40133e7i	−0.136677	−	0.136677i
$630$		0			0
$631$	−1.26476e8			−0.503408			−0.251704	−	0.967804i	$-0.580991\pi$
$631$	−1.26476e8			−0.503408			−0.251704	+	0.967804i	$0.580991\pi$
$632$		0			0
$633$			1.34559e8i			0.530519i
$634$		0			0
$635$	1.15598e8	−	1.15598e8i	0.451471	−	0.451471i
$636$		0			0
$637$	5.82904e8	−	5.82904e8i	2.25517	−	2.25517i
$638$		0			0
$639$		−	6.46657e7i		−	0.247840i
$640$		0			0
$641$	−3.79771e8			−1.44194			−0.720971	−	0.692965i	$-0.756304\pi$
$641$	−3.79771e8			−1.44194			−0.720971	+	0.692965i	$0.756304\pi$
$642$		0			0
$643$	2.19573e8	+	2.19573e8i	0.825937	+	0.825937i	0.986952	−	0.161015i	$-0.0514768\pi$
$643$	2.19573e8	+	2.19573e8i	0.825937	+	0.825937i	−0.161015	+	0.986952i	$0.551477\pi$
$644$		0			0
$645$	6.95575e7	+	6.95575e7i	0.259218	+	0.259218i
$646$		0			0
$647$	−1.63625e8			−0.604139			−0.302069	−	0.953286i	$-0.597677\pi$
$647$	−1.63625e8			−0.604139			−0.302069	+	0.953286i	$0.597677\pi$
$648$		0			0
$649$			1.75418e8i			0.641713i
$650$		0			0
$651$	2.43729e8	−	2.43729e8i	0.883415	−	0.883415i
$652$		0			0
$653$	2.17072e8	−	2.17072e8i	0.779587	−	0.779587i	−0.200173	−	0.979761i	$-0.564151\pi$
$653$	2.17072e8	−	2.17072e8i	0.779587	−	0.779587i	0.979761	+	0.200173i	$0.0641505\pi$
$654$		0			0
$655$			2.01911e8i			0.718516i
$656$		0			0
$657$	−6.51155e7			−0.229609
$658$		0			0
$659$	−3.75232e8	−	3.75232e8i	−1.31112	−	1.31112i	−0.920588	−	0.390535i	$-0.872290\pi$
$659$	−3.75232e8	−	3.75232e8i	−1.31112	−	1.31112i	−0.390535	−	0.920588i	$-0.627710\pi$
$660$		0			0
$661$	9.25679e7	+	9.25679e7i	0.320521	+	0.320521i	0.848967	−	0.528446i	$-0.177225\pi$
$661$	9.25679e7	+	9.25679e7i	0.320521	+	0.320521i	−0.528446	+	0.848967i	$0.677225\pi$
$662$		0			0
$663$	4.21090e7			0.144489
$664$		0			0
$665$		−	1.00461e8i		−	0.341613i
$666$		0			0
$667$	−1.83498e8	+	1.83498e8i	−0.618376	+	0.618376i
$668$		0			0
$669$	−8.89979e7	+	8.89979e7i	−0.297236	+	0.297236i
$670$		0			0
$671$		−	2.56347e8i		−	0.848517i
$672$		0			0
$673$	5.35988e8			1.75837			0.879185	−	0.476481i	$-0.158088\pi$
$673$	5.35988e8			1.75837			0.879185	+	0.476481i	$0.158088\pi$
$674$		0			0
$675$	−3.06254e7	−	3.06254e7i	−0.0995797	−	0.0995797i
$676$		0			0
$677$	3.17164e8	+	3.17164e8i	1.02216	+	1.02216i	0.999749	+	0.0224072i	$0.00713303\pi$
$677$	3.17164e8	+	3.17164e8i	1.02216	+	1.02216i	0.0224072	+	0.999749i	$0.492867\pi$
$678$		0			0
$679$	2.22433e8			0.710542
$680$		0			0
$681$			9.12182e7i			0.288829i
$682$		0			0
$683$	−2.38997e8	+	2.38997e8i	−0.750121	+	0.750121i	−0.974502	−	0.224381i	$-0.927964\pi$
$683$	−2.38997e8	+	2.38997e8i	−0.750121	+	0.750121i	0.224381	+	0.974502i	$0.427964\pi$
$684$		0			0
$685$	−9.65848e6	+	9.65848e6i	−0.0300495	+	0.0300495i
$686$		0			0
$687$		−	2.63811e8i		−	0.813623i
$688$		0			0
$689$	6.25466e8			1.91226
$690$		0			0
$691$	−1.14977e8	−	1.14977e8i	−0.348478	−	0.348478i	0.511065	−	0.859542i	$-0.329251\pi$
$691$	−1.14977e8	−	1.14977e8i	−0.348478	−	0.348478i	−0.859542	+	0.511065i	$0.829251\pi$
$692$		0			0
$693$	1.77549e8	+	1.77549e8i	0.533479	+	0.533479i
$694$		0			0
$695$	6.21623e7			0.185171
$696$		0			0
$697$		−	4.40732e7i		−	0.130160i
$698$		0			0
$699$	1.61770e7	−	1.61770e7i	0.0473661	−	0.0473661i
$700$		0			0
$701$	−1.52614e8	+	1.52614e8i	−0.443036	+	0.443036i	−0.893031	−	0.449995i	$-0.851426\pi$
$701$	−1.52614e8	+	1.52614e8i	−0.443036	+	0.443036i	0.449995	+	0.893031i	$0.351426\pi$
$702$		0			0
$703$			1.99205e8i			0.573370i
$704$		0			0
$705$	−1.08725e8			−0.310287
$706$		0			0
$707$	−3.79448e8	−	3.79448e8i	−1.07373	−	1.07373i
$708$		0			0
$709$	−2.20534e8	−	2.20534e8i	−0.618780	−	0.618780i	0.326439	−	0.945218i	$-0.394151\pi$
$709$	−2.20534e8	−	2.20534e8i	−0.618780	−	0.618780i	−0.945218	+	0.326439i	$0.894151\pi$
$710$		0			0
$711$	1.35590e8			0.377241
$712$		0			0
$713$			6.20848e8i			1.71284i
$714$		0			0
$715$	−3.41010e8	+	3.41010e8i	−0.932930	+	0.932930i
$716$		0			0
$717$	−1.41629e8	+	1.41629e8i	−0.384234	+	0.384234i
$718$		0			0
$719$		−	1.10928e8i		−	0.298439i	−0.988804	−	0.149220i	$-0.952324\pi$
$719$		−	1.10928e8i		−	0.298439i	0.988804	−	0.149220i	$-0.0476762\pi$
$720$		0			0
$721$	−2.58326e8			−0.689228
$722$		0			0
$723$	2.06240e7	+	2.06240e7i	0.0545704	+	0.0545704i
$724$		0			0
$725$	1.32125e8	+	1.32125e8i	0.346714	+	0.346714i
$726$		0			0
$727$	−4.40388e8			−1.14613			−0.573063	−	0.819512i	$-0.694245\pi$
$727$	−4.40388e8			−1.14613			−0.573063	+	0.819512i	$0.694245\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	−4.56657e7	+	4.56657e7i	−0.116906	+	0.116906i
$732$		0			0
$733$	−8.77336e7	+	8.77336e7i	−0.222769	+	0.222769i	−0.809663	−	0.586895i	$-0.800350\pi$
$733$	−8.77336e7	+	8.77336e7i	−0.222769	+	0.222769i	0.586895	+	0.809663i	$0.300350\pi$
$734$		0			0
$735$			2.04051e8i			0.513897i
$736$		0			0
$737$	−2.72349e8			−0.680337
$738$		0			0
$739$	1.75595e8	+	1.75595e8i	0.435089	+	0.435089i	0.890355	−	0.455266i	$-0.150456\pi$
$739$	1.75595e8	+	1.75595e8i	0.435089	+	0.435089i	−0.455266	+	0.890355i	$0.650456\pi$
$740$		0			0
$741$	−1.23310e8	−	1.23310e8i	−0.303070	−	0.303070i
$742$		0			0
$743$	−1.99950e8			−0.487478			−0.243739	−	0.969841i	$-0.578374\pi$
$743$	−1.99950e8			−0.487478			−0.243739	+	0.969841i	$0.578374\pi$
$744$		0			0
$745$		−	2.40624e8i		−	0.581930i
$746$		0			0
$747$	5.74025e7	−	5.74025e7i	0.137711	−	0.137711i
$748$		0			0
$749$	−2.82082e8	+	2.82082e8i	−0.671320	+	0.671320i
$750$		0			0
$751$			4.31676e7i			0.101915i	0.998701	+	0.0509575i	$0.0162273\pi$
$751$			4.31676e7i			0.101915i	−0.998701	+	0.0509575i	$0.983773\pi$
$752$		0			0
$753$	4.55351e8			1.06650
$754$		0			0
$755$	1.31862e8	+	1.31862e8i	0.306392	+	0.306392i
$756$		0			0
$757$	3.04827e8	+	3.04827e8i	0.702692	+	0.702692i	0.964988	−	0.262295i	$-0.0844794\pi$
$757$	3.04827e8	+	3.04827e8i	0.702692	+	0.702692i	−0.262295	+	0.964988i	$0.584479\pi$
$758$		0			0
$759$	−4.52267e8			−1.03435
$760$		0			0
$761$		−	4.91137e8i		−	1.11442i	−0.830372	−	0.557209i	$-0.811872\pi$
$761$		−	4.91137e8i		−	1.11442i	0.830372	−	0.557209i	$-0.188128\pi$
$762$		0			0
$763$	3.87975e8	−	3.87975e8i	0.873434	−	0.873434i
$764$		0			0
$765$	−7.37032e6	+	7.37032e6i	−0.0164627	+	0.0164627i
$766$		0			0
$767$			3.91440e8i			0.867519i
$768$		0			0
$769$	−7.18352e8			−1.57964			−0.789820	−	0.613338i	$-0.789826\pi$
$769$	−7.18352e8			−1.57964			−0.789820	+	0.613338i	$0.789826\pi$
$770$		0			0
$771$	−1.05883e7	−	1.05883e7i	−0.0231028	−	0.0231028i
$772$		0			0
$773$	−4.46865e8	−	4.46865e8i	−0.967471	−	0.967471i	0.0320160	−	0.999487i	$-0.489807\pi$
$773$	−4.46865e8	−	4.46865e8i	−0.967471	−	0.967471i	−0.999487	+	0.0320160i	$0.989807\pi$
$774$		0			0
$775$	4.47034e8			0.960364
$776$		0			0
$777$		−	6.40046e8i		−	1.36442i
$778$		0			0
$779$	−1.29062e8	+	1.29062e8i	−0.273014	+	0.273014i
$780$		0			0
$781$	−3.43805e8	+	3.43805e8i	−0.721704	+	0.721704i
$782$		0			0
$783$			6.19046e7i			0.128955i
$784$		0			0
$785$	−4.59153e7			−0.0949179
$786$		0			0
$787$	1.27217e8	+	1.27217e8i	0.260989	+	0.260989i	0.825456	−	0.564467i	$-0.190918\pi$
$787$	1.27217e8	+	1.27217e8i	0.260989	+	0.260989i	−0.564467	+	0.825456i	$0.690918\pi$
$788$		0			0
$789$	−2.93544e8	−	2.93544e8i	−0.597643	−	0.597643i
$790$		0			0
$791$	9.98696e8			2.01792
$792$		0			0
$793$		−	5.72029e8i		−	1.14709i
$794$		0			0
$795$	−1.09475e8	+	1.09475e8i	−0.217878	+	0.217878i
$796$		0			0
$797$	−5.09748e7	+	5.09748e7i	−0.100689	+	0.100689i	−0.755657	−	0.654968i	$-0.772682\pi$
$797$	−5.09748e7	+	5.09748e7i	−0.100689	+	0.100689i	0.654968	+	0.755657i	$0.272682\pi$
$798$		0			0
$799$		−	7.13800e7i		−	0.139938i
$800$		0			0
$801$	−1.02008e8			−0.198489
$802$		0			0
$803$	3.46196e8	+	3.46196e8i	0.668615	+	0.668615i
$804$		0			0
$805$	−4.11109e8	−	4.11109e8i	−0.788077	−	0.788077i
$806$		0			0
$807$	4.41516e8			0.840090
$808$		0			0
$809$		−	9.47571e8i		−	1.78964i	−0.446424	−	0.894822i	$-0.647303\pi$
$809$		−	9.47571e8i		−	1.78964i	0.446424	−	0.894822i	$-0.352697\pi$
$810$		0			0
$811$	9.22998e7	−	9.22998e7i	0.173037	−	0.173037i	−0.615275	−	0.788312i	$-0.710955\pi$
$811$	9.22998e7	−	9.22998e7i	0.173037	−	0.173037i	0.788312	+	0.615275i	$0.210955\pi$
$812$		0			0
$813$	1.47699e8	−	1.47699e8i	0.274856	−	0.274856i
$814$		0			0
$815$		−	1.19031e8i		−	0.219881i
$816$		0			0
$817$	2.67450e8			0.490429
$818$		0			0
$819$	3.96193e8	+	3.96193e8i	0.721200	+	0.721200i
$820$		0			0
$821$	5.05480e8	+	5.05480e8i	0.913429	+	0.913429i	0.996540	−	0.0831113i	$-0.0264857\pi$
$821$	5.05480e8	+	5.05480e8i	0.913429	+	0.913429i	−0.0831113	+	0.996540i	$0.526486\pi$
$822$		0			0
$823$	3.69057e7			0.0662055			0.0331027	−	0.999452i	$-0.489461\pi$
$823$	3.69057e7			0.0662055			0.0331027	+	0.999452i	$0.489461\pi$
$824$		0			0
$825$			3.25649e8i			0.579947i
$826$		0			0
$827$	−1.45689e8	+	1.45689e8i	−0.257579	+	0.257579i	−0.824069	−	0.566490i	$-0.808301\pi$
$827$	−1.45689e8	+	1.45689e8i	−0.257579	+	0.257579i	0.566490	+	0.824069i	$0.308301\pi$
$828$		0			0
$829$	−6.21154e8	+	6.21154e8i	−1.09027	+	1.09027i	−0.0947757	+	0.995499i	$0.530213\pi$
$829$	−6.21154e8	+	6.21154e8i	−1.09027	+	1.09027i	−0.995499	+	0.0947757i	$0.969787\pi$
$830$		0			0
$831$		−	3.15308e7i		−	0.0549455i
$832$		0			0
$833$	−1.33963e8			−0.231766
$834$		0			0
$835$	−3.93812e8	−	3.93812e8i	−0.676440	−	0.676440i
$836$		0			0
$837$	1.04724e8	+	1.04724e8i	0.178596	+	0.178596i
$838$		0			0
$839$	7.28215e8			1.23303			0.616515	−	0.787343i	$-0.288544\pi$
$839$	7.28215e8			1.23303			0.616515	+	0.787343i	$0.288544\pi$
$840$		0			0
$841$			3.27752e8i			0.551008i
$842$		0			0
$843$	−1.93169e8	+	1.93169e8i	−0.322445	+	0.322445i
$844$		0			0
$845$	−5.39990e8	+	5.39990e8i	−0.894984	+	0.894984i
$846$		0			0
$847$		−	8.86032e8i		−	1.45814i
$848$		0			0
$849$	−5.29375e8			−0.865048
$850$		0			0
$851$	8.15189e8	+	8.15189e8i	1.32272	+	1.32272i
$852$		0			0
$853$	3.95707e8	+	3.95707e8i	0.637568	+	0.637568i	0.949955	−	0.312387i	$-0.101128\pi$
$853$	3.95707e8	+	3.95707e8i	0.637568	+	0.637568i	−0.312387	+	0.949955i	$0.601128\pi$
$854$		0			0
$855$	4.31657e7			0.0690623
$856$		0			0
$857$			7.60780e8i			1.20870i	0.796721	+	0.604348i	$0.206566\pi$
$857$			7.60780e8i			1.20870i	−0.796721	+	0.604348i	$0.793434\pi$
$858$		0			0
$859$	2.52493e8	−	2.52493e8i	0.398354	−	0.398354i	−0.479298	−	0.877652i	$-0.659109\pi$
$859$	2.52493e8	−	2.52493e8i	0.398354	−	0.398354i	0.877652	+	0.479298i	$0.159109\pi$
$860$		0			0
$861$	4.14674e8	−	4.14674e8i	0.649677	−	0.649677i
$862$		0			0
$863$		−	7.25728e7i		−	0.112912i	−0.998405	−	0.0564562i	$-0.982020\pi$
$863$		−	7.25728e7i		−	0.112912i	0.998405	−	0.0564562i	$-0.0179801\pi$
$864$		0			0
$865$	−8.16609e7			−0.126173
$866$		0			0
$867$	2.61223e8	+	2.61223e8i	0.400824	+	0.400824i
$868$		0			0
$869$	−7.20885e8	−	7.20885e8i	−1.09852	−	1.09852i
$870$		0			0
$871$	−6.07738e8			−0.919734
$872$		0			0
$873$			9.55738e7i			0.143647i
$874$		0			0
$875$	−7.00538e8	+	7.00538e8i	−1.04570	+	1.04570i
$876$		0			0
$877$	−5.64497e8	+	5.64497e8i	−0.836879	+	0.836879i	−0.988447	−	0.151568i	$-0.951568\pi$
$877$	−5.64497e8	+	5.64497e8i	−0.836879	+	0.836879i	0.151568	+	0.988447i	$0.451568\pi$
$878$		0			0
$879$			5.50431e8i			0.810468i
$880$		0			0
$881$	9.73736e7			0.142401			0.0712006	−	0.997462i	$-0.477317\pi$
$881$	9.73736e7			0.142401			0.0712006	+	0.997462i	$0.477317\pi$
$882$		0			0
$883$	−6.90645e7	−	6.90645e7i	−0.100317	−	0.100317i	0.655167	−	0.755484i	$-0.272598\pi$
$883$	−6.90645e7	−	6.90645e7i	−0.100317	−	0.100317i	−0.755484	+	0.655167i	$0.772598\pi$
$884$		0			0
$885$	−6.85136e7	−	6.85136e7i	−0.0988432	−	0.0988432i
$886$		0			0
$887$	4.66487e8			0.668450			0.334225	−	0.942493i	$-0.391526\pi$
$887$	4.66487e8			0.668450			0.334225	+	0.942493i	$0.391526\pi$
$888$		0			0
$889$			1.42810e9i			2.03261i
$890$		0			0
$891$	−7.62881e7	+	7.62881e7i	−0.107851	+	0.107851i
$892$		0			0
$893$	−2.09026e8	+	2.09026e8i	−0.293525	+	0.293525i
$894$		0			0
$895$			2.65128e8i			0.369817i
$896$		0			0
$897$	−1.00922e9			−1.39832
$898$		0			0
$899$	−4.51805e8	−	4.51805e8i	−0.621831	−	0.621831i
$900$		0			0
$901$	−7.18722e7	−	7.18722e7i	−0.0982623	−	0.0982623i
$902$		0			0
$903$	−8.59315e8			−1.16705
$904$		0			0
$905$			1.96519e8i			0.265130i
$906$		0			0
$907$	−1.99657e8	+	1.99657e8i	−0.267585	+	0.267585i	−0.828126	−	0.560541i	$-0.810593\pi$
$907$	−1.99657e8	+	1.99657e8i	−0.267585	+	0.267585i	0.560541	+	0.828126i	$0.310593\pi$
$908$		0			0
$909$	1.63039e8	−	1.63039e8i	0.217071	−	0.217071i
$910$		0			0
$911$			7.71797e8i			1.02082i	0.859932	+	0.510409i	$0.170506\pi$
$911$			7.71797e8i			1.02082i	−0.859932	+	0.510409i	$0.829494\pi$
$912$		0			0
$913$	−6.10378e8			−0.802022
$914$		0			0
$915$	1.00122e8	+	1.00122e8i	0.130697	+	0.130697i
$916$		0			0
$917$	−1.24721e9	−	1.24721e9i	−1.61745	−	1.61745i
$918$		0			0
$919$	−8.94727e8			−1.15277			−0.576387	−	0.817177i	$-0.695538\pi$
$919$	−8.94727e8			−1.15277			−0.576387	+	0.817177i	$0.695538\pi$
$920$		0			0
$921$		−	6.91307e7i		−	0.0884896i
$922$		0			0
$923$	−7.67189e8	+	7.67189e8i	−0.975658	+	0.975658i
$924$		0			0
$925$	5.86967e8	−	5.86967e8i	0.741633	−	0.741633i
$926$		0			0
$927$		−	1.10996e8i		−	0.139338i
$928$		0			0
$929$	5.16188e8			0.643814			0.321907	−	0.946771i	$-0.395676\pi$
$929$	5.16188e8			0.643814			0.321907	+	0.946771i	$0.395676\pi$
$930$		0			0
$931$	3.92290e8	+	3.92290e8i	0.486136	+	0.486136i
$932$		0			0
$933$	3.11615e8	+	3.11615e8i	0.383684	+	0.383684i
$934$		0			0
$935$	7.83709e7			0.0958782
$936$		0			0
$937$			5.89366e8i			0.716418i	0.933641	+	0.358209i	$0.116612\pi$
$937$			5.89366e8i			0.716418i	−0.933641	+	0.358209i	$0.883388\pi$
$938$		0			0
$939$	−4.59755e7	+	4.59755e7i	−0.0555303	+	0.0555303i
$940$		0			0
$941$	−4.11063e7	+	4.11063e7i	−0.0493333	+	0.0493333i	−0.731343	−	0.682010i	$-0.761106\pi$
$941$	−4.11063e7	+	4.11063e7i	−0.0493333	+	0.0493333i	0.682010	+	0.731343i	$0.261106\pi$
$942$		0			0
$943$			1.05629e9i			1.25965i
$944$		0			0
$945$	−1.38691e8			−0.164344
$946$		0			0
$947$	−1.82225e8	−	1.82225e8i	−0.214565	−	0.214565i	0.591639	−	0.806203i	$-0.298481\pi$
$947$	−1.82225e8	−	1.82225e8i	−0.214565	−	0.214565i	−0.806203	+	0.591639i	$0.798481\pi$
$948$		0			0
$949$	7.72525e8	+	7.72525e8i	0.903887	+	0.903887i
$950$		0			0
$951$	7.70715e8			0.896091
$952$		0			0
$953$			1.41084e9i			1.63004i	0.579433	+	0.815020i	$0.303274\pi$
$953$			1.41084e9i			1.63004i	−0.579433	+	0.815020i	$0.696726\pi$
$954$		0			0
$955$	5.14771e7	−	5.14771e7i	0.0591023	−	0.0591023i
$956$		0			0
$957$	3.29125e8	−	3.29125e8i	0.375513	−	0.375513i
$958$		0			0
$959$		−	1.19321e8i		−	0.135289i
$960$		0			0
$961$	−6.41141e8			−0.722409
$962$		0			0
$963$	−1.21203e8	−	1.21203e8i	−0.135718	−	0.135718i
$964$		0			0
$965$	−3.04648e8	−	3.04648e8i	−0.339013	−	0.339013i
$966$		0			0
$967$	−9.62310e8			−1.06423			−0.532115	−	0.846672i	$-0.678603\pi$
$967$	−9.62310e8			−1.06423			−0.532115	+	0.846672i	$0.678603\pi$
$968$		0			0
$969$			2.83390e7i			0.0311468i
$970$		0			0
$971$	8.97286e8	−	8.97286e8i	0.980106	−	0.980106i	−0.0196995	−	0.999806i	$-0.506271\pi$
$971$	8.97286e8	−	8.97286e8i	0.980106	−	0.980106i	0.999806	+	0.0196995i	$0.00627094\pi$
$972$		0			0
$973$	−3.83977e8	+	3.83977e8i	−0.416838	+	0.416838i
$974$		0			0
$975$			7.26675e8i			0.784019i
$976$		0			0
$977$	−1.56733e8			−0.168065			−0.0840324	−	0.996463i	$-0.526780\pi$
$977$	−1.56733e8			−0.168065			−0.0840324	+	0.996463i	$0.526780\pi$
$978$		0			0
$979$	5.42341e8	+	5.42341e8i	0.577995	+	0.577995i
$980$		0			0
$981$	1.66703e8	+	1.66703e8i	0.176578	+	0.176578i
$982$		0			0
$983$	−2.49727e7			−0.0262909			−0.0131454	−	0.999914i	$-0.504184\pi$
$983$	−2.49727e7			−0.0262909			−0.0131454	+	0.999914i	$0.504184\pi$
$984$		0			0
$985$			9.33128e7i			0.0976411i
$986$		0			0
$987$	6.71598e8	−	6.71598e8i	0.698486	−	0.698486i
$988$		0			0
$989$	1.09446e9	−	1.09446e9i	1.13139	−	1.13139i
$990$		0			0
$991$			4.63587e8i			0.476333i	0.971224	+	0.238166i	$0.0765463\pi$
$991$			4.63587e8i			0.476333i	−0.971224	+	0.238166i	$0.923454\pi$
$992$		0			0
$993$	5.13428e8			0.524362
$994$		0			0
$995$	4.07300e7	+	4.07300e7i	0.0413472	+	0.0413472i
$996$		0			0
$997$	9.19997e7	+	9.19997e7i	0.0928327	+	0.0928327i	0.751998	−	0.659165i	$-0.229090\pi$
$997$	9.19997e7	+	9.19997e7i	0.0928327	+	0.0928327i	−0.659165	+	0.751998i	$0.729090\pi$
$998$		0			0
$999$	2.75011e8			0.275838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.a.31.7		48
4.3	odd	2		384.7.l.b.31.18		48
8.3	odd	2		48.7.l.a.43.18	yes	48
8.5	even	2		192.7.l.a.79.18		48
16.3	odd	4	inner	384.7.l.a.223.7		48
16.5	even	4		48.7.l.a.19.18	✓	48
16.11	odd	4		192.7.l.a.175.18		48
16.13	even	4		384.7.l.b.223.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.18	✓	48	16.5	even	4
48.7.l.a.43.18	yes	48	8.3	odd	2
192.7.l.a.79.18		48	8.5	even	2
192.7.l.a.175.18		48	16.11	odd	4
384.7.l.a.31.7		48	1.1	even	1	trivial
384.7.l.a.223.7		48	16.3	odd	4	inner
384.7.l.b.31.18		48	4.3	odd	2
384.7.l.b.223.18		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)

\(f(q)\)	\(=\)	\(q+(-11.0227 - 11.0227i) q^{3} +(-45.7781 - 45.7781i) q^{5} +565.544 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(-11.0227 - 11.0227i) q^{3} +(-45.7781 - 45.7781i) q^{5} +565.544 q^{7} +243.000i q^{9} +(1291.95 - 1291.95i) q^{11} +(2882.93 - 2882.93i) q^{13} +1009.20i q^{15} -662.555 q^{17} +(1940.19 + 1940.19i) q^{19} +(-6233.83 - 6233.83i) q^{21} +15879.3 q^{23} -11433.7i q^{25} +(2678.52 - 2678.52i) q^{27} +(-11555.8 + 11555.8i) q^{29} +39097.9i q^{31} -28481.5 q^{33} +(-25889.6 - 25889.6i) q^{35} +(51336.5 + 51336.5i) q^{37} -63555.4 q^{39} +66520.0i q^{41} +(68923.6 - 68923.6i) q^{43} +(11124.1 - 11124.1i) q^{45} +107734. i q^{47} +202191. q^{49} +(7303.15 + 7303.15i) q^{51} +(108477. + 108477. i) q^{53} -118286. q^{55} -42772.3i q^{57} +(-67889.1 + 67889.1i) q^{59} +(99209.6 - 99209.6i) q^{61} +137427. i q^{63} -263951. q^{65} +(-105403. - 105403. i) q^{67} +(-175033. - 175033. i) q^{69} -266114. q^{71} +267965. i q^{73} +(-126031. + 126031. i) q^{75} +(730653. - 730653. i) q^{77} -557984. i q^{79} -59049.0 q^{81} +(-236224. - 236224. i) q^{83} +(30330.5 + 30330.5i) q^{85} +254751. q^{87} +419786. i q^{89} +(1.63043e6 - 1.63043e6i) q^{91} +(430964. - 430964. i) q^{93} -177637. i q^{95} +393308. q^{97} +(313943. + 313943. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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