LMFDB - Embedded newform 1368.2.e.f.379.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (of order $2$, degree $1$, 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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.3
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.f.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39298 + 0.244153i) q^{2} +(1.88078 - 0.680200i) q^{4} -3.10261i q^{5} +4.34495i q^{7} +(-2.45381 + 1.40670i) q^{8} +O(q^{10})$	\(q+(-1.39298 + 0.244153i) q^{2} +(1.88078 - 0.680200i) q^{4} -3.10261i q^{5} +4.34495i q^{7} +(-2.45381 + 1.40670i) q^{8} +(0.757512 + 4.32187i) q^{10} +2.65647 q^{11} -5.10176 q^{13} +(-1.06083 - 6.05242i) q^{14} +(3.07466 - 2.55861i) q^{16} -3.48821 q^{17} +(1.86464 - 3.93994i) q^{19} +(-2.11040 - 5.83533i) q^{20} +(-3.70041 + 0.648586i) q^{22} -5.31965i q^{23} -4.62620 q^{25} +(7.10664 - 1.24561i) q^{26} +(2.95543 + 8.17189i) q^{28} +7.98077 q^{29} -3.19471 q^{31} +(-3.65824 + 4.31478i) q^{32} +(4.85901 - 0.851658i) q^{34} +13.4807 q^{35} +4.57585 q^{37} +(-1.63546 + 5.94351i) q^{38} +(4.36445 + 7.61322i) q^{40} -4.51800i q^{41} +6.28467 q^{43} +(4.99624 - 1.80693i) q^{44} +(1.29881 + 7.41015i) q^{46} -7.68246i q^{47} -11.8786 q^{49} +(6.44419 - 1.12950i) q^{50} +(-9.59527 + 3.47021i) q^{52} -9.81525 q^{53} -8.24201i q^{55} +(-6.11205 - 10.6617i) q^{56} +(-11.1170 + 1.94853i) q^{58} -4.94021i q^{59} -11.9988i q^{61} +(4.45016 - 0.779998i) q^{62} +(4.04238 - 6.90356i) q^{64} +15.8288i q^{65} +0.406143i q^{67} +(-6.56056 + 2.37268i) q^{68} +(-18.7783 + 3.29135i) q^{70} -2.40885 q^{71} +0.373802 q^{73} +(-6.37406 + 1.11721i) q^{74} +(0.827031 - 8.67848i) q^{76} +11.5422i q^{77} +17.2835 q^{79} +(-7.93838 - 9.53946i) q^{80} +(1.10308 + 6.29348i) q^{82} -12.2894 q^{83} +10.8226i q^{85} +(-8.75441 + 1.53442i) q^{86} +(-6.51849 + 3.73687i) q^{88} +1.95322i q^{89} -22.1669i q^{91} +(-3.61842 - 10.0051i) q^{92} +(1.87570 + 10.7015i) q^{94} +(-12.2241 - 5.78526i) q^{95} -4.87939i q^{97} +(16.5466 - 2.90019i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{4}+O(q^{10}) $ 24 * q + 20 * q^4	$ 24 q + 20 q^{4} - 12 q^{16} + 24 q^{19} - 40 q^{25} - 40 q^{28} - 72 q^{49} - 104 q^{58} + 20 q^{64} + 80 q^{73} - 12 q^{76} + 56 q^{82}+O(q^{100}) $ 24 * q + 20 * q^4 - 12 * q^16 + 24 * q^19 - 40 * q^25 - 40 * q^28 - 72 * q^49 - 104 * q^58 + 20 * q^64 + 80 * q^73 - 12 * q^76 + 56 * q^82

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.39298	+	0.244153i	−0.984985	+	0.172642i
$2$	−1.39298	+	0.244153i	−0.984985	+	0.172642i
$3$		0			0
$3$		0			0
$4$	1.88078	−	0.680200i	0.940389	−	0.340100i
$5$		−	3.10261i		−	1.38753i	−0.720201	−	0.693765i	$-0.755951\pi$
$5$		−	3.10261i		−	1.38753i	0.720201	−	0.693765i	$-0.244049\pi$
$6$		0			0
$7$			4.34495i			1.64224i	0.570758	+	0.821118i	$0.306650\pi$
$7$			4.34495i			1.64224i	−0.570758	+	0.821118i	$0.693350\pi$
$8$	−2.45381	+	1.40670i	−0.867553	+	0.497344i
$9$		0			0
$10$	0.757512	+	4.32187i	0.239546	+	1.36670i
$11$	2.65647			0.800957			0.400479	−	0.916306i	$-0.368844\pi$
$11$	2.65647			0.800957			0.400479	+	0.916306i	$0.368844\pi$
$12$		0			0
$13$	−5.10176			−1.41497			−0.707486	−	0.706727i	$-0.750171\pi$
$13$	−5.10176			−1.41497			−0.707486	+	0.706727i	$0.750171\pi$
$14$	−1.06083	−	6.05242i	−0.283520	−	1.61758i
$15$		0			0
$16$	3.07466	−	2.55861i	0.768664	−	0.639653i
$17$	−3.48821			−0.846016			−0.423008	−	0.906126i	$-0.639026\pi$
$17$	−3.48821			−0.846016			−0.423008	+	0.906126i	$0.639026\pi$
$18$		0			0
$19$	1.86464	−	3.93994i	0.427778	−	0.903884i
$19$	1.86464	−	3.93994i	0.427778	−	0.903884i
$20$	−2.11040	−	5.83533i	−0.471899	−	1.30482i
$21$		0			0
$22$	−3.70041	+	0.648586i	−0.788930	+	0.138279i
$23$		−	5.31965i		−	1.10922i	−0.832110	−	0.554611i	$-0.812867\pi$
$23$		−	5.31965i		−	1.10922i	0.832110	−	0.554611i	$-0.187133\pi$
$24$		0			0
$25$	−4.62620			−0.925240
$26$	7.10664	−	1.24561i	1.39373	−	0.244284i
$27$		0			0
$28$	2.95543	+	8.17189i	0.558525	+	1.54434i
$29$	7.98077			1.48199			0.740996	−	0.671510i	$-0.234354\pi$
$29$	7.98077			1.48199			0.740996	+	0.671510i	$0.234354\pi$
$30$		0			0
$31$	−3.19471			−0.573787			−0.286893	−	0.957963i	$-0.592623\pi$
$31$	−3.19471			−0.573787			−0.286893	+	0.957963i	$0.592623\pi$
$32$	−3.65824	+	4.31478i	−0.646691	+	0.762752i
$33$		0			0
$34$	4.85901	−	0.851658i	0.833313	−	0.146058i
$35$	13.4807			2.27865
$36$		0			0
$37$	4.57585			0.752265			0.376132	−	0.926566i	$-0.377254\pi$
$37$	4.57585			0.752265			0.376132	+	0.926566i	$0.377254\pi$
$38$	−1.63546	+	5.94351i	−0.265306	+	0.964164i
$39$		0			0
$40$	4.36445	+	7.61322i	0.690080	+	1.20376i
$41$		−	4.51800i		−	0.705593i	−0.935700	−	0.352797i	$-0.885231\pi$
$41$		−	4.51800i		−	0.705593i	0.935700	−	0.352797i	$-0.114769\pi$
$42$		0			0
$43$	6.28467			0.958403			0.479202	−	0.877705i	$-0.340926\pi$
$43$	6.28467			0.958403			0.479202	+	0.877705i	$0.340926\pi$
$44$	4.99624	−	1.80693i	0.753211	−	0.272405i
$45$		0			0
$46$	1.29881	+	7.41015i	0.191499	+	1.09257i
$47$		−	7.68246i		−	1.12060i	−0.828289	−	0.560301i	$-0.810685\pi$
$47$		−	7.68246i		−	1.12060i	0.828289	−	0.560301i	$-0.189315\pi$
$48$		0			0
$49$	−11.8786			−1.69694
$50$	6.44419	−	1.12950i	0.911347	−	0.159735i
$51$		0			0
$52$	−9.59527	+	3.47021i	−1.33062	+	0.481232i
$53$	−9.81525			−1.34823			−0.674114	−	0.738627i	$-0.735474\pi$
$53$	−9.81525			−1.34823			−0.674114	+	0.738627i	$0.735474\pi$
$54$		0			0
$55$		−	8.24201i		−	1.11135i
$56$	−6.11205	−	10.6617i	−0.816757	−	1.42473i
$57$		0			0
$58$	−11.1170	+	1.94853i	−1.45974	+	0.255854i
$59$		−	4.94021i		−	0.643161i	−0.946882	−	0.321580i	$-0.895786\pi$
$59$		−	4.94021i		−	0.643161i	0.946882	−	0.321580i	$-0.104214\pi$
$60$		0			0
$61$		−	11.9988i		−	1.53629i	−0.640274	−	0.768146i	$-0.721179\pi$
$61$		−	11.9988i		−	1.53629i	0.640274	−	0.768146i	$-0.278821\pi$
$62$	4.45016	−	0.779998i	0.565171	−	0.0990598i
$63$		0			0
$64$	4.04238	−	6.90356i	0.505298	−	0.862945i
$65$			15.8288i			1.96332i
$66$		0			0
$67$			0.406143i			0.0496183i	0.999692	+	0.0248092i	$0.00789781\pi$
$67$			0.406143i			0.0496183i	−0.999692	+	0.0248092i	$0.992102\pi$
$68$	−6.56056	+	2.37268i	−0.795584	+	0.287730i
$69$		0			0
$70$	−18.7783	+	3.29135i	−2.24444	+	0.393392i
$71$	−2.40885			−0.285878			−0.142939	−	0.989731i	$-0.545655\pi$
$71$	−2.40885			−0.285878			−0.142939	+	0.989731i	$0.545655\pi$
$72$		0			0
$73$	0.373802			0.0437502			0.0218751	−	0.999761i	$-0.493036\pi$
$73$	0.373802			0.0437502			0.0218751	+	0.999761i	$0.493036\pi$
$74$	−6.37406	+	1.11721i	−0.740969	+	0.129873i
$75$		0			0
$76$	0.827031	−	8.67848i	0.0948670	−	0.995490i
$77$			11.5422i			1.31536i
$78$		0			0
$79$	17.2835			1.94455			0.972273	−	0.233850i	$-0.0751324\pi$
$79$	17.2835			1.94455			0.972273	+	0.233850i	$0.0751324\pi$
$80$	−7.93838	−	9.53946i	−0.887537	−	1.06654i
$81$		0			0
$82$	1.10308	+	6.29348i	0.121815	+	0.694998i
$83$	−12.2894			−1.34893			−0.674467	−	0.738305i	$-0.735627\pi$
$83$	−12.2894			−1.34893			−0.674467	+	0.738305i	$0.735627\pi$
$84$		0			0
$85$			10.8226i			1.17387i
$86$	−8.75441	+	1.53442i	−0.944013	+	0.165461i
$87$		0			0
$88$	−6.51849	+	3.73687i	−0.694873	+	0.398351i
$89$			1.95322i			0.207041i	0.994627	+	0.103521i	$0.0330108\pi$
$89$			1.95322i			0.207041i	−0.994627	+	0.103521i	$0.966989\pi$
$90$		0			0
$91$		−	22.1669i		−	2.32372i
$92$	−3.61842	−	10.0051i	−0.377247	−	1.04310i
$93$		0			0
$94$	1.87570	+	10.7015i	0.193463	+	1.10378i
$95$	−12.2241	−	5.78526i	−1.25417	−	0.593555i
$96$		0			0
$97$		−	4.87939i		−	0.495427i	−0.968833	−	0.247713i	$-0.920321\pi$
$97$		−	4.87939i		−	0.495427i	0.968833	−	0.247713i	$-0.0796791\pi$
$98$	16.5466	−	2.90019i	1.67146	−	0.292964i
$99$		0			0
$100$	−8.70085	+	3.14674i	−0.870085	+	0.314674i
$101$			2.87407i			0.285981i	0.989724	+	0.142990i	$0.0456718\pi$
$101$			2.87407i			0.285981i	−0.989724	+	0.142990i	$0.954328\pi$
$102$		0			0
$103$	−10.6359			−1.04799			−0.523995	−	0.851721i	$-0.675559\pi$
$103$	−10.6359			−1.04799			−0.523995	+	0.851721i	$0.675559\pi$
$104$	12.5187	−	7.17665i	1.22756	−	0.703728i
$105$		0			0
$106$	13.6724	−	2.39642i	1.32798	−	0.232761i
$107$		−	10.7564i		−	1.03986i	−0.854210	−	0.519928i	$-0.825959\pi$
$107$		−	10.7564i		−	1.03986i	0.854210	−	0.519928i	$-0.174041\pi$
$108$		0			0
$109$	13.0593			1.25085			0.625425	−	0.780284i	$-0.284926\pi$
$109$	13.0593			1.25085			0.625425	+	0.780284i	$0.284926\pi$
$110$	2.01231	+	11.4809i	0.191866	+	1.09466i
$111$		0			0
$112$	11.1170	+	13.3592i	1.05046	+	1.26233i
$113$		−	14.9843i		−	1.40961i	−0.709402	−	0.704804i	$-0.751035\pi$
$113$		−	14.9843i		−	1.40961i	0.709402	−	0.704804i	$-0.248965\pi$
$114$		0			0
$115$	−16.5048			−1.53908
$116$	15.0101	−	5.42852i	1.39365	−	0.504025i
$117$		0			0
$118$	1.20617	+	6.88161i	0.111037	+	0.633503i
$119$		−	15.1561i		−	1.38936i
$120$		0			0
$121$	−3.94315			−0.358468
$122$	2.92955	+	16.7141i	0.265229	+	1.51322i
$123$		0			0
$124$	−6.00854	+	2.17304i	−0.539583	+	0.195145i
$125$		−	1.15976i		−	0.103732i
$126$		0			0
$127$	17.4704			1.55025			0.775126	−	0.631807i	$-0.217686\pi$
$127$	17.4704			1.55025			0.775126	+	0.631807i	$0.217686\pi$
$128$	−3.94542	+	10.6035i	−0.348730	+	0.937223i
$129$		0			0
$130$	−3.86464	−	22.0491i	−0.338951	−	1.93384i
$131$	−5.78511			−0.505447			−0.252724	−	0.967538i	$-0.581326\pi$
$131$	−5.78511			−0.505447			−0.252724	+	0.967538i	$0.581326\pi$
$132$		0			0
$133$	17.1188	+	8.10177i	1.48439	+	0.702513i
$134$	−0.0991612	−	0.565749i	−0.00856622	−	0.0488733i
$135$		0			0
$136$	8.55942	−	4.90688i	0.733964	−	0.420761i
$137$	−0.359578			−0.0307208			−0.0153604	−	0.999882i	$-0.504890\pi$
$137$	−0.359578			−0.0307208			−0.0153604	+	0.999882i	$0.504890\pi$
$138$		0			0
$139$	2.96772			0.251719			0.125860	−	0.992048i	$-0.459831\pi$
$139$	2.96772			0.251719			0.125860	+	0.992048i	$0.459831\pi$
$140$	25.3542	−	9.16957i	2.14282	−	0.774970i
$141$		0			0
$142$	3.35548	−	0.588129i	0.281586	−	0.0493547i
$143$	−13.5527			−1.13333
$144$		0			0
$145$		−	24.7612i		−	2.05631i
$146$	−0.520698	+	0.0912649i	−0.0430933	+	0.00755313i
$147$		0			0
$148$	8.60616	−	3.11249i	0.707422	−	0.255845i
$149$			9.69069i			0.793892i	0.917842	+	0.396946i	$0.129930\pi$
$149$			9.69069i			0.793892i	−0.917842	+	0.396946i	$0.870070\pi$
$150$		0			0
$151$	−9.32599			−0.758938			−0.379469	−	0.925204i	$-0.623893\pi$
$151$	−9.32599			−0.758938			−0.379469	+	0.925204i	$0.623893\pi$
$152$	0.966841	+	12.2909i	0.0784211	+	0.996920i
$153$		0			0
$154$	−2.81808	−	16.0781i	−0.227087	−	1.29561i
$155$			9.91194i			0.796146i
$156$		0			0
$157$		−	9.86616i		−	0.787405i	−0.919238	−	0.393703i	$-0.871194\pi$
$157$		−	9.86616i		−	0.787405i	0.919238	−	0.393703i	$-0.128806\pi$
$158$	−24.0755	+	4.21982i	−1.91535	+	0.335711i
$159$		0			0
$160$	13.3871	+	11.3501i	1.05834	+	0.897303i
$161$	23.1136			1.82161
$162$		0			0
$163$	−1.52311			−0.119300			−0.0596498	−	0.998219i	$-0.518998\pi$
$163$	−1.52311			−0.119300			−0.0596498	+	0.998219i	$0.518998\pi$
$164$	−3.07314	−	8.49736i	−0.239972	−	0.663532i
$165$		0			0
$166$	17.1188	−	3.00049i	1.32868	−	0.232883i
$167$	−2.40885			−0.186403			−0.0932013	−	0.995647i	$-0.529710\pi$
$167$	−2.40885			−0.186403			−0.0932013	+	0.995647i	$0.529710\pi$
$168$		0			0
$169$	13.0279			1.00215
$170$	−2.64236	−	15.0756i	−0.202660	−	1.15625i
$171$		0			0
$172$	11.8201	−	4.27483i	0.901272	−	0.325953i
$173$	14.6330			1.11252			0.556261	−	0.831007i	$-0.312235\pi$
$173$	14.6330			1.11252			0.556261	+	0.831007i	$0.312235\pi$
$174$		0			0
$175$		−	20.1006i		−	1.51946i
$176$	8.16774	−	6.79688i	0.615667	−	0.512334i
$177$		0			0
$178$	−0.476886	−	2.72080i	−0.0357441	−	0.203933i
$179$		−	4.70734i		−	0.351843i	−0.984404	−	0.175922i	$-0.943709\pi$
$179$		−	4.70734i		−	0.351843i	0.984404	−	0.175922i	$-0.0562906\pi$
$180$		0			0
$181$	−18.2196			−1.35425			−0.677124	−	0.735869i	$-0.736774\pi$
$181$	−18.2196			−1.35425			−0.677124	+	0.735869i	$0.736774\pi$
$182$	5.41211	+	30.8780i	0.401172	+	2.28883i
$183$		0			0
$184$	7.48315	+	13.0534i	0.551665	+	0.962310i
$185$		−	14.1971i		−	1.04379i
$186$		0			0
$187$	−9.26635			−0.677623
$188$	−5.22561	−	14.4490i	−0.381117	−	1.05380i
$189$		0			0
$190$	18.4404	+	5.07419i	1.33781	+	0.368120i
$191$			9.07076i			0.656337i	0.944619	+	0.328169i	$0.106431\pi$
$191$			9.07076i			0.656337i	−0.944619	+	0.328169i	$0.893569\pi$
$192$		0			0
$193$		−	25.5735i		−	1.84082i	−0.390953	−	0.920411i	$-0.627855\pi$
$193$		−	25.5735i		−	1.84082i	0.390953	−	0.920411i	$-0.372145\pi$
$194$	1.19132	+	6.79688i	0.0855316	+	0.487988i
$195$		0			0
$196$	−22.3410	+	8.07982i	−1.59579	+	0.577130i
$197$			24.0614i			1.71430i	0.515066	+	0.857151i	$0.327767\pi$
$197$			24.0614i			1.71430i	−0.515066	+	0.857151i	$0.672233\pi$
$198$		0			0
$199$			17.3002i			1.22638i	0.789936	+	0.613189i	$0.210114\pi$
$199$			17.3002i			1.22638i	−0.789936	+	0.613189i	$0.789886\pi$
$200$	11.3518	−	6.50768i	0.802695	−	0.460163i
$201$		0			0
$202$	−0.701713	−	4.00352i	−0.0493724	−	0.281687i
$203$			34.6760i			2.43378i
$204$		0			0
$205$	−14.0176			−0.979032
$206$	14.8156	−	2.59680i	1.03225	−	0.180927i
$207$		0			0
$208$	−15.6861	+	13.0534i	−1.08764	+	0.905091i
$209$	4.95337	−	10.4663i	0.342632	−	0.723972i
$210$		0			0
$211$		−	20.2880i		−	1.39668i	−0.715765	−	0.698341i	$-0.753922\pi$
$211$		−	20.2880i		−	1.39668i	0.715765	−	0.698341i	$-0.246078\pi$
$212$	−18.4603	+	6.67633i	−1.26786	+	0.458532i
$213$		0			0
$214$	2.62620	+	14.9834i	0.179523	+	1.02424i
$215$		−	19.4989i		−	1.32981i
$216$		0			0
$217$		−	13.8809i		−	0.942294i
$218$	−18.1913	+	3.18846i	−1.23207	+	0.215950i
$219$		0			0
$220$	−5.60621	−	15.5014i	−0.377971	−	1.04510i
$221$	17.7960			1.19709
$222$		0			0
$223$	1.62662			0.108927			0.0544633	−	0.998516i	$-0.482655\pi$
$223$	1.62662			0.108927			0.0544633	+	0.998516i	$0.482655\pi$
$224$	−18.7475	−	15.8949i	−1.25262	−	1.06202i
$225$		0			0
$226$	3.65847	+	20.8729i	0.243358	+	1.38844i
$227$		−	19.8674i		−	1.31865i	−0.751860	−	0.659323i	$-0.770843\pi$
$227$		−	19.8674i		−	1.31865i	0.751860	−	0.659323i	$-0.229157\pi$
$228$		0			0
$229$		−	10.8226i		−	0.715176i	−0.933880	−	0.357588i	$-0.883599\pi$
$229$		−	10.8226i		−	0.715176i	0.933880	−	0.357588i	$-0.116401\pi$
$230$	22.9908	−	4.02970i	1.51597	−	0.265710i
$231$		0			0
$232$	−19.5833	+	11.2266i	−1.28571	+	0.737060i
$233$	−23.4732			−1.53778			−0.768889	−	0.639382i	$-0.779190\pi$
$233$	−23.4732			−1.53778			−0.768889	+	0.639382i	$0.779190\pi$
$234$		0			0
$235$	−23.8357			−1.55487
$236$	−3.36033	−	9.29144i	−0.218739	−	0.604821i
$237$		0			0
$238$	3.70041	+	21.1121i	0.239862	+	1.36850i
$239$		−	26.0413i		−	1.68447i	−0.539108	−	0.842237i	$-0.681239\pi$
$239$		−	26.0413i		−	1.68447i	0.539108	−	0.842237i	$-0.318761\pi$
$240$		0			0
$241$			14.6931i			0.946468i	0.880937	+	0.473234i	$0.156914\pi$
$241$			14.6931i			0.946468i	−0.880937	+	0.473234i	$0.843086\pi$
$242$	5.49272	−	0.962731i	0.353085	−	0.0618867i
$243$		0			0
$244$	−8.16160	−	22.5671i	−0.522493	−	1.44471i
$245$			36.8547i			2.35456i
$246$		0			0
$247$	−9.51294	+	20.1006i	−0.605294	+	1.27897i
$248$	7.83921	−	4.49400i	0.497791	−	0.285369i
$249$		0			0
$250$	0.283159	+	1.61552i	0.0179086	+	0.102175i
$251$	9.63290			0.608023			0.304012	−	0.952668i	$-0.401674\pi$
$251$	9.63290			0.608023			0.304012	+	0.952668i	$0.401674\pi$
$252$		0			0
$253$		−	14.1315i		−	0.888440i
$254$	−24.3360	+	4.26546i	−1.52697	+	0.267639i
$255$		0			0
$256$	2.90702	−	15.7337i	0.181689	−	0.983356i
$257$			21.5127i			1.34193i	0.741491	+	0.670963i	$0.234119\pi$
$257$			21.5127i			1.34193i	−0.741491	+	0.670963i	$0.765881\pi$
$258$		0			0
$259$			19.8818i			1.23540i
$260$	10.7667	+	29.7704i	0.667724	+	1.84628i
$261$		0			0
$262$	8.05853	−	1.41245i	0.497858	−	0.0872616i
$263$			3.50520i			0.216140i	0.994143	+	0.108070i	$0.0344670\pi$
$263$			3.50520i			0.216140i	−0.994143	+	0.108070i	$0.965533\pi$
$264$		0			0
$265$			30.4529i			1.87071i
$266$	−25.8242	−	7.10598i	−1.58339	−	0.435696i
$267$		0			0
$268$	0.276259	+	0.763866i	0.0168752	+	0.0466605i
$269$	3.48912			0.212736			0.106368	−	0.994327i	$-0.466078\pi$
$269$	3.48912			0.212736			0.106368	+	0.994327i	$0.466078\pi$
$270$		0			0
$271$		−	7.14536i		−	0.434050i	−0.976166	−	0.217025i	$-0.930365\pi$
$271$		−	7.14536i		−	0.434050i	0.976166	−	0.217025i	$-0.0696353\pi$
$272$	−10.7251	+	8.92498i	−0.650302	+	0.541156i
$273$		0			0
$274$	0.500884	−	0.0877921i	0.0302595	−	0.00530371i
$275$	−12.2894			−0.741077
$276$		0			0
$277$			5.38097i			0.323311i	0.986847	+	0.161656i	$0.0516834\pi$
$277$			5.38097i			0.323311i	−0.986847	+	0.161656i	$0.948317\pi$
$278$	−4.13398	+	0.724579i	−0.247939	+	0.0434574i
$279$		0			0
$280$	−33.0791	+	18.9633i	−1.97685	+	1.13327i
$281$			22.9687i			1.37020i	0.728450	+	0.685099i	$0.240241\pi$
$281$			22.9687i			1.37020i	−0.728450	+	0.685099i	$0.759759\pi$
$282$		0			0
$283$	−6.19221			−0.368089			−0.184044	−	0.982918i	$-0.558919\pi$
$283$	−6.19221			−0.368089			−0.184044	+	0.982918i	$0.558919\pi$
$284$	−4.53052	+	1.63850i	−0.268837	+	0.0972272i
$285$		0			0
$286$	18.8786	−	3.30893i	1.11631	−	0.195661i
$287$	19.6305			1.15875
$288$		0			0
$289$	−4.83237			−0.284257
$290$	6.04553	+	34.4918i	0.355006	+	2.02543i
$291$		0			0
$292$	0.703039	−	0.254260i	0.0411422	−	0.0148794i
$293$	1.32858			0.0776166			0.0388083	−	0.999247i	$-0.487644\pi$
$293$	1.32858			0.0776166			0.0388083	+	0.999247i	$0.487644\pi$
$294$		0			0
$295$	−15.3276			−0.892405
$296$	−11.2283	+	6.43685i	−0.652630	+	0.374134i
$297$		0			0
$298$	−2.36601	−	13.4989i	−0.137059	−	0.781971i
$299$			27.1395i			1.56952i
$300$		0			0
$301$			27.3066i			1.57393i
$302$	12.9909	−	2.27697i	0.747543	−	0.131025i
$303$		0			0
$304$	−4.34764	−	16.8848i	−0.249354	−	0.968412i
$305$	−37.2277			−2.13165
$306$		0			0
$307$			12.4081i			0.708167i	0.935214	+	0.354084i	$0.115207\pi$
$307$			12.4081i			0.708167i	−0.935214	+	0.354084i	$0.884793\pi$
$308$	7.85104	+	21.7084i	0.447354	+	1.23695i
$309$		0			0
$310$	−2.42003	−	13.8071i	−0.137449	−	0.784192i
$311$		−	2.11690i		−	0.120038i	−0.998197	−	0.0600191i	$-0.980884\pi$
$311$		−	2.11690i		−	0.120038i	0.998197	−	0.0600191i	$-0.0191162\pi$
$312$		0			0
$313$	31.0741			1.75641			0.878207	−	0.478281i	$-0.158740\pi$
$313$	31.0741			1.75641			0.878207	+	0.478281i	$0.158740\pi$
$314$	2.40885	+	13.7433i	0.135939	+	0.775582i
$315$		0			0
$316$	32.5064	−	11.7562i	1.82863	−	0.661340i
$317$	32.4290			1.82139			0.910696	−	0.413077i	$-0.135546\pi$
$317$	32.4290			1.82139			0.910696	+	0.413077i	$0.135546\pi$
$318$		0			0
$319$	21.2007			1.18701
$320$	−21.4191	−	12.5419i	−1.19736	−	0.701116i
$321$		0			0
$322$	−32.1967	+	5.64325i	−1.79425	+	0.314486i
$323$	−6.50427	+	13.7433i	−0.361907	+	0.764700i
$324$		0			0
$325$	23.6017			1.30919
$326$	2.12167	−	0.371873i	0.117508	−	0.0205961i
$327$		0			0
$328$	6.35548	+	11.0863i	0.350923	+	0.612140i
$329$	33.3799			1.84029
$330$		0			0
$331$			22.1669i			1.21840i	0.793016	+	0.609201i	$0.208510\pi$
$331$			22.1669i			1.21840i	−0.793016	+	0.609201i	$0.791490\pi$
$332$	−23.1136	+	8.35923i	−1.26852	+	0.458772i
$333$		0			0
$334$	3.35548	−	0.588129i	0.183604	−	0.0321810i
$335$	1.26011			0.0688469
$336$		0			0
$337$			9.00147i			0.490341i	0.969480	+	0.245171i	$0.0788440\pi$
$337$			9.00147i			0.490341i	−0.969480	+	0.245171i	$0.921156\pi$
$338$	−18.1476	+	3.18080i	−0.987099	+	0.173013i
$339$		0			0
$340$	7.36151	+	20.3549i	0.399234	+	1.10390i
$341$	−8.48666			−0.459579
$342$		0			0
$343$		−	21.1972i		−	1.14454i
$344$	−15.4214	+	8.84066i	−0.831466	+	0.476656i
$345$		0			0
$346$	−20.3834	+	3.57268i	−1.09582	+	0.192068i
$347$	9.63290			0.517121			0.258561	−	0.965995i	$-0.416752\pi$
$347$	9.63290			0.517121			0.258561	+	0.965995i	$0.416752\pi$
$348$		0			0
$349$			23.0412i			1.23337i	0.787210	+	0.616685i	$0.211525\pi$
$349$			23.0412i			1.23337i	−0.787210	+	0.616685i	$0.788475\pi$
$350$	4.90762	+	27.9997i	0.262323	+	1.49665i
$351$		0			0
$352$	−9.71801	+	11.4621i	−0.517972	+	0.610932i
$353$	−23.8328			−1.26849			−0.634245	−	0.773132i	$-0.718689\pi$
$353$	−23.8328			−1.26849			−0.634245	+	0.773132i	$0.718689\pi$
$354$		0			0
$355$			7.47373i			0.396665i
$356$	1.32858	+	3.67358i	0.0704148	+	0.194699i
$357$		0			0
$358$	1.14931	+	6.55723i	0.0607430	+	0.346560i
$359$			21.8641i			1.15394i	0.816765	+	0.576971i	$0.195765\pi$
$359$			21.8641i			1.15394i	−0.816765	+	0.576971i	$0.804235\pi$
$360$		0			0
$361$	−12.0462	−	14.6931i	−0.634012	−	0.773323i
$362$	25.3794	−	4.44836i	1.33391	−	0.233801i
$363$		0			0
$364$	−15.0779	−	41.6910i	−0.790297	−	2.18520i
$365$		−	1.15976i		−	0.0607047i
$366$		0			0
$367$		−	33.0558i		−	1.72550i	−0.505630	−	0.862751i	$-0.668740\pi$
$367$		−	33.0558i		−	1.72550i	0.505630	−	0.862751i	$-0.331260\pi$
$368$	−13.6109	−	16.3561i	−0.709517	−	0.852620i
$369$		0			0
$370$	3.46626	+	19.7762i	0.180202	+	1.02812i
$371$		−	42.6468i		−	2.21411i
$372$		0			0
$373$	−9.95803			−0.515607			−0.257804	−	0.966197i	$-0.582999\pi$
$373$	−9.95803			−0.515607			−0.257804	+	0.966197i	$0.582999\pi$
$374$	12.9078	−	2.26241i	0.667448	−	0.116986i
$375$		0			0
$376$	10.8069	+	18.8513i	0.557325	+	0.972182i
$377$	−40.7159			−2.09698
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−26.9260	−	2.56596i	−1.38127	−	0.131631i
$381$		0			0
$382$	−2.21465	−	12.6354i	−0.113312	−	0.646482i
$383$	27.1054			1.38502			0.692510	−	0.721409i	$-0.256505\pi$
$383$	27.1054			1.38502			0.692510	+	0.721409i	$0.256505\pi$
$384$		0			0
$385$	35.8111			1.82510
$386$	6.24385	+	35.6233i	0.317804	+	1.81318i
$387$		0			0
$388$	−3.31896	−	9.17705i	−0.168495	−	0.465894i
$389$			30.0380i			1.52299i	0.648171	+	0.761495i	$0.275534\pi$
$389$			30.0380i			1.52299i	−0.648171	+	0.761495i	$0.724466\pi$
$390$		0			0
$391$			18.5561i			0.938420i
$392$	29.1478	−	16.7096i	1.47219	−	0.843964i
$393$		0			0
$394$	−5.87465	−	33.5170i	−0.295961	−	1.68856i
$395$		−	53.6240i		−	2.69812i
$396$		0			0
$397$		−	28.4828i		−	1.42951i	−0.699373	−	0.714756i	$-0.746538\pi$
$397$		−	28.4828i		−	1.42951i	0.699373	−	0.714756i	$-0.253462\pi$
$398$	−4.22389	−	24.0988i	−0.211725	−	1.20796i
$399$		0			0
$400$	−14.2240	+	11.8366i	−0.711198	+	0.591832i
$401$			5.94834i			0.297046i	0.988909	+	0.148523i	$0.0474519\pi$
$401$			5.94834i			0.297046i	−0.988909	+	0.148523i	$0.952548\pi$
$402$		0			0
$403$	16.2986			0.811892
$404$	1.95494	+	5.40549i	0.0972621	+	0.268933i
$405$		0			0
$406$	−8.46626	−	48.3030i	−0.420173	−	2.39724i
$407$	12.1556			0.602532
$408$		0			0
$409$			14.9475i			0.739105i	0.929210	+	0.369552i	$0.120489\pi$
$409$			14.9475i			0.739105i	−0.929210	+	0.369552i	$0.879511\pi$
$410$	19.5262	−	3.42244i	0.964331	−	0.169022i
$411$		0			0
$412$	−20.0039	+	7.23457i	−0.985519	+	0.356422i
$413$	21.4650			1.05622
$414$		0			0
$415$			38.1292i			1.87169i
$416$	18.6634	−	22.0129i	0.915050	−	1.07927i
$417$		0			0
$418$	−4.34455	+	15.7888i	−0.212499	+	0.772254i
$419$	7.69558			0.375954			0.187977	−	0.982173i	$-0.439807\pi$
$419$	7.69558			0.375954			0.187977	+	0.982173i	$0.439807\pi$
$420$		0			0
$421$	1.48425			0.0723379			0.0361689	−	0.999346i	$-0.488485\pi$
$421$	1.48425			0.0723379			0.0361689	+	0.999346i	$0.488485\pi$
$422$	4.95337	+	28.2607i	0.241126	+	1.37571i
$423$		0			0
$424$	24.0848	−	13.8071i	1.16966	−	0.670533i
$425$	16.1372			0.782768
$426$		0			0
$427$	52.1343			2.52296
$428$	−7.31648	−	20.2303i	−0.353655	−	0.977870i
$429$		0			0
$430$	4.76071	+	27.1615i	0.229582	+	1.30985i
$431$	−33.1832			−1.59838			−0.799189	−	0.601080i	$-0.794737\pi$
$431$	−33.1832			−1.59838			−0.799189	+	0.601080i	$0.794737\pi$
$432$		0			0
$433$			23.6946i			1.13869i	0.822099	+	0.569345i	$0.192803\pi$
$433$			23.6946i			1.13869i	−0.822099	+	0.569345i	$0.807197\pi$
$434$	3.38905	+	19.3357i	0.162680	+	0.928145i
$435$		0			0
$436$	24.5616	−	8.88291i	1.17629	−	0.425414i
$437$	−20.9591	−	9.91923i	−1.00261	−	0.474501i
$438$		0			0
$439$	−18.8516			−0.899737			−0.449869	−	0.893095i	$-0.648529\pi$
$439$	−18.8516			−0.899737			−0.449869	+	0.893095i	$0.648529\pi$
$440$	11.5940	+	20.2243i	0.552724	+	0.964157i
$441$		0			0
$442$	−24.7895	+	4.34495i	−1.17911	+	0.206668i
$443$	9.63290			0.457673			0.228836	−	0.973465i	$-0.426508\pi$
$443$	9.63290			0.457673			0.228836	+	0.973465i	$0.426508\pi$
$444$		0			0
$445$	6.06010			0.287276
$446$	−2.26585	+	0.397145i	−0.107291	+	0.0188053i
$447$		0			0
$448$	29.9956	+	17.5639i	1.41716	+	0.829818i
$449$			19.1808i			0.905198i	0.891714	+	0.452599i	$0.149503\pi$
$449$			19.1808i			0.905198i	−0.891714	+	0.452599i	$0.850497\pi$
$450$		0			0
$451$		−	12.0020i		−	0.565150i
$452$	−10.1924	−	28.1822i	−0.479408	−	1.32558i
$453$		0			0
$454$	4.85069	+	27.6749i	0.227654	+	1.29885i
$455$	−68.7752			−3.22423
$456$		0			0
$457$	−21.9894			−1.02862			−0.514310	−	0.857604i	$-0.671952\pi$
$457$	−21.9894			−1.02862			−0.514310	+	0.857604i	$0.671952\pi$
$458$	2.64236	+	15.0756i	0.123470	+	0.704437i
$459$		0			0
$460$	−31.0419	+	11.2266i	−1.44733	+	0.523441i
$461$			13.4851i			0.628064i	0.949412	+	0.314032i	$0.101680\pi$
$461$			13.4851i			0.628064i	−0.949412	+	0.314032i	$0.898320\pi$
$462$		0			0
$463$		−	0.816179i		−	0.0379310i	−0.999820	−	0.0189655i	$-0.993963\pi$
$463$		−	0.816179i		−	0.0379310i	0.999820	−	0.0189655i	$-0.00603727\pi$
$464$	24.5381	−	20.4197i	1.13915	−	0.947960i
$465$		0			0
$466$	32.6976	−	5.73105i	1.51469	−	0.265486i
$467$	41.1881			1.90596			0.952979	−	0.303038i	$-0.0980009\pi$
$467$	41.1881			1.90596			0.952979	+	0.303038i	$0.0980009\pi$
$468$		0			0
$469$	−1.76467			−0.0814850
$470$	33.2026	−	5.81956i	1.53152	−	0.268436i
$471$		0			0
$472$	6.94940	+	12.1223i	0.319872	+	0.557976i
$473$	16.6951			0.767640
$474$		0			0
$475$	−8.62620	+	18.2269i	−0.395797	+	0.836309i
$476$	−10.3092	−	28.5053i	−0.472521	−	1.30654i
$477$		0			0
$478$	6.35807	+	36.2750i	0.290811	+	1.65918i
$479$		−	29.3354i		−	1.34037i	−0.742195	−	0.670184i	$-0.766215\pi$
$479$		−	29.3354i		−	1.34037i	0.742195	−	0.670184i	$-0.233785\pi$
$480$		0			0
$481$	−23.3449			−1.06443
$482$	−3.58737	−	20.4672i	−0.163400	−	0.932257i
$483$		0			0
$484$	−7.41618	+	2.68213i	−0.337099	+	0.121915i
$485$	−15.1388			−0.687420
$486$		0			0
$487$	31.8174			1.44178			0.720891	−	0.693048i	$-0.243733\pi$
$487$	31.8174			1.44178			0.720891	+	0.693048i	$0.243733\pi$
$488$	16.8788	+	29.4429i	0.764066	+	1.33282i
$489$		0			0
$490$	−8.99818	−	51.3378i	−0.406496	−	2.31920i
$491$	2.18431			0.0985767			0.0492883	−	0.998785i	$-0.484305\pi$
$491$	2.18431			0.0985767			0.0492883	+	0.998785i	$0.484305\pi$
$492$		0			0
$493$	−27.8386			−1.25379
$494$	8.34370	−	30.3223i	0.375401	−	1.36427i
$495$		0			0
$496$	−9.82263	+	8.17402i	−0.441049	+	0.367024i
$497$		−	10.4663i		−	0.469480i
$498$		0			0
$499$	35.0881			1.57076			0.785379	−	0.619015i	$-0.212468\pi$
$499$	35.0881			1.57076			0.785379	+	0.619015i	$0.212468\pi$
$500$	−0.788870	−	2.18126i	−0.0352793	−	0.0975487i
$501$		0			0
$502$	−13.4184	+	2.35190i	−0.598894	+	0.104971i
$503$			11.2681i			0.502418i	0.967933	+	0.251209i	$0.0808282\pi$
$503$			11.2681i			0.502418i	−0.967933	+	0.251209i	$0.919172\pi$
$504$		0			0
$505$	8.91713			0.396807
$506$	3.45025	+	19.6849i	0.153382	+	0.875100i
$507$		0			0
$508$	32.8580	−	11.8834i	1.45784	−	0.527240i
$509$	−22.7936			−1.01031			−0.505153	−	0.863030i	$-0.668564\pi$
$509$	−22.7936			−1.01031			−0.505153	+	0.863030i	$0.668564\pi$
$510$		0			0
$511$			1.62415i			0.0718482i
$512$	−0.207989	+	22.6265i	−0.00919190	+	0.999958i
$513$		0			0
$514$	−5.25240	−	29.9668i	−0.231673	−	1.32178i
$515$			32.9992i			1.45412i
$516$		0			0
$517$		−	20.4083i		−	0.897554i
$518$	−4.85421	−	27.6950i	−0.213282	−	1.21685i
$519$		0			0
$520$	−22.2663	−	38.8408i	−0.976444	−	1.70328i
$521$			41.2795i			1.80849i	0.427019	+	0.904243i	$0.359564\pi$
$521$			41.2795i			1.80849i	−0.427019	+	0.904243i	$0.640436\pi$
$522$		0			0
$523$			22.5730i			0.987049i	0.869732	+	0.493525i	$0.164292\pi$
$523$			22.5730i			0.987049i	−0.869732	+	0.493525i	$0.835708\pi$
$524$	−10.8805	+	3.93503i	−0.475317	+	0.171903i
$525$		0			0
$526$	−0.855805	−	4.88267i	−0.0373149	−	0.212894i
$527$	11.1438			0.485433
$528$		0			0
$529$	−5.29862			−0.230375
$530$	−7.43517	−	42.4202i	−0.322963	−	1.84262i
$531$		0			0
$532$	37.7076	+	3.59341i	1.63483	+	0.155794i
$533$			23.0497i			0.998395i
$534$		0			0
$535$	−33.3728			−1.44283
$536$	−0.571323	−	0.996599i	−0.0246774	−	0.0430465i
$537$		0			0
$538$	−4.86027	+	0.851880i	−0.209541	+	0.0367271i
$539$	−31.5552			−1.35918
$540$		0			0
$541$			13.0159i			0.559596i	0.960059	+	0.279798i	$0.0902675\pi$
$541$			13.0159i			0.559596i	−0.960059	+	0.279798i	$0.909733\pi$
$542$	1.74456	+	9.95333i	0.0749353	+	0.427532i
$543$		0			0
$544$	12.7607	−	15.0509i	0.547111	−	0.645300i
$545$		−	40.5178i		−	1.73559i
$546$		0			0
$547$		−	27.1012i		−	1.15877i	−0.815056	−	0.579383i	$-0.803294\pi$
$547$		−	27.1012i		−	1.15877i	0.815056	−	0.579383i	$-0.196706\pi$
$548$	−0.676287	+	0.244585i	−0.0288895	+	0.0104481i
$549$		0			0
$550$	17.1188	−	3.00049i	0.729950	−	0.127941i
$551$	14.8813	−	31.4437i	0.633963	−	1.33955i
$552$		0			0
$553$			75.0959i			3.19340i
$554$	−1.31378	−	7.49558i	−0.0558172	−	0.318457i
$555$		0			0
$556$	5.58163	−	2.01865i	0.236714	−	0.0856097i
$557$		−	27.1183i		−	1.14904i	−0.818490	−	0.574520i	$-0.805189\pi$
$557$		−	27.1183i		−	1.14904i	0.818490	−	0.574520i	$-0.194811\pi$
$558$		0			0
$559$	−32.0629			−1.35611
$560$	41.4485	−	34.4918i	1.75152	−	1.45755i
$561$		0			0
$562$	−5.60788	−	31.9949i	−0.236554	−	1.34962i
$563$			4.40370i			0.185594i	0.995685	+	0.0927969i	$0.0295807\pi$
$563$			4.40370i			0.185594i	−0.995685	+	0.0927969i	$0.970419\pi$
$564$		0			0
$565$	−46.4906			−1.95587
$566$	8.62562	−	1.51185i	0.362562	−	0.0635477i
$567$		0			0
$568$	5.91087	−	3.38854i	0.248015	−	0.142180i
$569$		−	17.8135i		−	0.746781i	−0.927674	−	0.373391i	$-0.878195\pi$
$569$		−	17.8135i		−	0.746781i	0.927674	−	0.373391i	$-0.121805\pi$
$570$		0			0
$571$	27.4219			1.14757			0.573786	−	0.819005i	$-0.305474\pi$
$571$	27.4219			1.14757			0.573786	+	0.819005i	$0.305474\pi$
$572$	−25.4896	+	9.21853i	−1.06577	+	0.385446i
$573$		0			0
$574$	−27.3449	+	4.79284i	−1.14135	+	0.200049i
$575$			24.6097i			1.02630i
$576$		0			0
$577$	−28.3651			−1.18085			−0.590427	−	0.807091i	$-0.701040\pi$
$577$	−28.3651			−1.18085			−0.590427	+	0.807091i	$0.701040\pi$
$578$	6.73138	−	1.17984i	0.279989	−	0.0490747i
$579$		0			0
$580$	−16.8426	−	46.5704i	−0.699350	−	1.93373i
$581$		−	53.3967i		−	2.21527i
$582$		0			0
$583$	−26.0739			−1.07987
$584$	−0.917239	+	0.525828i	−0.0379556	+	0.0217589i
$585$		0			0
$586$	−1.85069	+	0.324378i	−0.0764512	+	0.0133999i
$587$	2.85480			0.117830			0.0589150	−	0.998263i	$-0.481236\pi$
$587$	2.85480			0.117830			0.0589150	+	0.998263i	$0.481236\pi$
$588$		0			0
$589$	−5.95699	+	12.5870i	−0.245453	+	0.518637i
$590$	21.3510	−	3.74227i	0.879005	−	0.154067i
$591$		0			0
$592$	14.0692	−	11.7078i	0.578239	−	0.481188i
$593$	14.4737			0.594363			0.297182	−	0.954821i	$-0.403953\pi$
$593$	14.4737			0.594363			0.297182	+	0.954821i	$0.403953\pi$
$594$		0			0
$595$	−47.0235			−1.92778
$596$	6.59160	+	18.2260i	0.270003	+	0.746568i
$597$		0			0
$598$	−6.62620	−	37.8048i	−0.270965	−	1.54595i
$599$	−3.91727			−0.160055			−0.0800277	−	0.996793i	$-0.525501\pi$
$599$	−3.91727			−0.160055			−0.0800277	+	0.996793i	$0.525501\pi$
$600$		0			0
$601$		−	0.0549752i		−	0.00224249i	−0.999999	−	0.00112124i	$-0.999643\pi$
$601$		−	0.0549752i		−	0.00224249i	0.999999	−	0.00112124i	$-0.000356903\pi$
$602$	−6.66699	−	38.0375i	−0.271726	−	1.55029i
$603$		0			0
$604$	−17.5401	+	6.34354i	−0.713698	+	0.258115i
$605$			12.2340i			0.497385i
$606$		0			0
$607$	29.9200			1.21441			0.607207	−	0.794544i	$-0.292290\pi$
$607$	29.9200			1.21441			0.607207	+	0.794544i	$0.292290\pi$
$608$	10.1787	+	22.4587i	0.412799	+	0.910822i
$609$		0			0
$610$	51.8574	−	9.08926i	2.09964	−	0.368013i
$611$			39.1940i			1.58562i
$612$		0			0
$613$			31.5719i			1.27518i	0.770377	+	0.637589i	$0.220068\pi$
$613$			31.5719i			1.27518i	−0.770377	+	0.637589i	$0.779932\pi$
$614$	−3.02947	−	17.2842i	−0.122260	−	0.697534i
$615$		0			0
$616$	−16.2365	−	28.3225i	−0.654187	−	1.14115i
$617$	−42.9373			−1.72859			−0.864295	−	0.502985i	$-0.832235\pi$
$617$	−42.9373			−1.72859			−0.864295	+	0.502985i	$0.832235\pi$
$618$		0			0
$619$	−27.3169			−1.09796			−0.548980	−	0.835835i	$-0.684984\pi$
$619$	−27.3169			−1.09796			−0.548980	+	0.835835i	$0.684984\pi$
$620$	6.74210	+	18.6422i	0.270769	+	0.748687i
$621$		0			0
$622$	0.516846	+	2.94879i	0.0207237	+	0.118236i
$623$	−8.48666			−0.340011
$624$		0			0
$625$	−26.7293			−1.06917
$626$	−43.2856	+	7.58684i	−1.73004	+	0.303231i
$627$		0			0
$628$	−6.71096	−	18.5561i	−0.267796	−	0.740467i
$629$	−15.9615			−0.636428
$630$		0			0
$631$		−	11.8586i		−	0.472083i	−0.971743	−	0.236042i	$-0.924150\pi$
$631$		−	11.8586i		−	0.472083i	0.971743	−	0.236042i	$-0.0758502\pi$
$632$	−42.4104	+	24.3127i	−1.68700	+	0.967108i
$633$		0			0
$634$	−45.1729	+	7.91763i	−1.79404	+	0.314449i
$635$		−	54.2040i		−	2.15102i
$636$		0			0
$637$	60.6017			2.40113
$638$	−29.5321	+	5.17622i	−1.16919	+	0.204928i
$639$		0			0
$640$	32.8985	+	12.2411i	1.30043	+	0.483873i
$641$		−	26.6994i		−	1.05456i	−0.849690	−	0.527282i	$-0.823211\pi$
$641$		−	26.6994i		−	1.05456i	0.849690	−	0.527282i	$-0.176789\pi$
$642$		0			0
$643$	35.7711			1.41068			0.705338	−	0.708871i	$-0.250795\pi$
$643$	35.7711			1.41068			0.705338	+	0.708871i	$0.250795\pi$
$644$	43.4716	−	15.7219i	1.71302	−	0.619528i
$645$		0			0
$646$	5.70482	−	20.7322i	0.224453	−	0.815698i
$647$			6.84253i			0.269008i	0.990913	+	0.134504i	$0.0429440\pi$
$647$			6.84253i			0.269008i	−0.990913	+	0.134504i	$0.957056\pi$
$648$		0			0
$649$		−	13.1235i		−	0.515144i
$650$	−32.8767	+	5.76243i	−1.28953	+	0.226021i
$651$		0			0
$652$	−2.86464	+	1.03602i	−0.112188	+	0.0405738i
$653$		−	10.1996i		−	0.399141i	−0.979883	−	0.199570i	$-0.936045\pi$
$653$		−	10.1996i		−	0.399141i	0.979883	−	0.199570i	$-0.0639547\pi$
$654$		0			0
$655$			17.9489i			0.701323i
$656$	−11.5598	−	13.8913i	−0.451335	−	0.542364i
$657$		0			0
$658$	−46.4975	+	8.14981i	−1.81266	+	0.317713i
$659$			14.8086i			0.576862i	0.957501	+	0.288431i	$0.0931336\pi$
$659$			14.8086i			0.576862i	−0.957501	+	0.288431i	$0.906866\pi$
$660$		0			0
$661$	−8.06062			−0.313522			−0.156761	−	0.987637i	$-0.550105\pi$
$661$	−8.06062			−0.313522			−0.156761	+	0.987637i	$0.550105\pi$
$662$	−5.41211	−	30.8780i	−0.210348	−	1.20011i
$663$		0			0
$664$	30.1558	−	17.2875i	1.17027	−	0.670885i
$665$	25.1367	−	53.1131i	0.974758	−	2.05964i
$666$		0			0
$667$		−	42.4548i		−	1.64386i
$668$	−4.53052	+	1.63850i	−0.175291	+	0.0633955i
$669$		0			0
$670$	−1.75530	+	0.307659i	−0.0678131	+	0.0118859i
$671$		−	31.8746i		−	1.23050i
$672$		0			0
$673$		−	11.6927i		−	0.450719i	−0.974276	−	0.225359i	$-0.927644\pi$
$673$		−	11.6927i		−	0.450719i	0.974276	−	0.225359i	$-0.0723556\pi$
$674$	−2.19774	−	12.5388i	−0.0846536	−	0.482978i
$675$		0			0
$676$	24.5026	−	8.86158i	0.942408	−	0.340830i
$677$	−7.98077			−0.306726			−0.153363	−	0.988170i	$-0.549010\pi$
$677$	−7.98077			−0.306726			−0.153363	+	0.988170i	$0.549010\pi$
$678$		0			0
$679$	21.2007			0.813608
$680$	−15.2241	−	26.5566i	−0.583819	−	1.01840i
$681$		0			0
$682$	11.8217	−	2.07204i	0.452678	−	0.0793427i
$683$			23.1580i			0.886118i	0.896493	+	0.443059i	$0.146107\pi$
$683$			23.1580i			0.886118i	−0.896493	+	0.443059i	$0.853893\pi$
$684$		0			0
$685$			1.11563i			0.0426261i
$686$	5.17537	+	29.5273i	0.197597	+	1.12736i
$687$		0			0
$688$	19.3232	−	16.0800i	0.736690	−	0.613045i
$689$	50.0750			1.90770
$690$		0			0
$691$	11.4446			0.435373			0.217687	−	0.976019i	$-0.430149\pi$
$691$	11.4446			0.435373			0.217687	+	0.976019i	$0.430149\pi$
$692$	27.5213	−	9.95333i	1.04620	−	0.378369i
$693$		0			0
$694$	−13.4184	+	2.35190i	−0.509356	+	0.0892770i
$695$		−	9.20770i		−	0.349268i
$696$		0			0
$697$			15.7598i			0.596943i
$698$	−5.62559	−	32.0960i	−0.212932	−	1.21485i
$699$		0			0
$700$	−13.6724	−	37.8048i	−0.516769	−	1.42889i
$701$		−	11.4506i		−	0.432485i	−0.976340	−	0.216242i	$-0.930620\pi$
$701$		−	11.4506i		−	0.432485i	0.976340	−	0.216242i	$-0.0693801\pi$
$702$		0			0
$703$	8.53231	−	18.0286i	0.321802	−	0.679960i
$704$	10.7385	−	18.3391i	0.404722	−	0.691182i
$705$		0			0
$706$	33.1985	−	5.81884i	1.24944	−	0.218995i
$707$	−12.4877			−0.469648
$708$		0			0
$709$		−	45.3623i		−	1.70362i	−0.523852	−	0.851809i	$-0.675506\pi$
$709$		−	45.3623i		−	1.70362i	0.523852	−	0.851809i	$-0.324494\pi$
$710$	−1.82473	−	10.4108i	−0.0684811	−	0.390708i
$711$		0			0
$712$	−2.74760	−	4.79284i	−0.102971	−	0.179619i
$713$			16.9947i			0.636457i
$714$		0			0
$715$			42.0487i			1.57253i
$716$	−3.20194	−	8.85347i	−0.119662	−	0.330870i
$717$		0			0
$718$	−5.33818	−	30.4562i	−0.199219	−	1.13661i
$719$			12.4081i			0.462744i	0.972865	+	0.231372i	$0.0743214\pi$
$719$			12.4081i			0.462744i	−0.972865	+	0.231372i	$0.925679\pi$
$720$		0			0
$721$		−	46.2126i		−	1.72105i
$722$	20.3675	+	17.5261i	0.758000	+	0.652254i
$723$		0			0
$724$	−34.2669	+	12.3929i	−1.27352	+	0.460580i
$725$	−36.9206			−1.37120
$726$		0			0
$727$			14.0519i			0.521156i	0.965453	+	0.260578i	$0.0839131\pi$
$727$			14.0519i			0.521156i	−0.965453	+	0.260578i	$0.916087\pi$
$728$	31.1822	+	54.3933i	1.15569	+	2.01595i
$729$		0			0
$730$	0.283159	+	1.61552i	0.0104802	+	0.0597932i
$731$	−21.9223			−0.810825
$732$		0			0
$733$			19.7323i			0.728830i	0.931237	+	0.364415i	$0.118731\pi$
$733$			19.7323i			0.728830i	−0.931237	+	0.364415i	$0.881269\pi$
$734$	8.07068	+	46.0461i	0.297894	+	1.69959i
$735$		0			0
$736$	22.9531	+	19.4605i	0.846062	+	0.717325i
$737$			1.07891i			0.0397421i
$738$		0			0
$739$	31.2297			1.14880			0.574402	−	0.818574i	$-0.305235\pi$
$739$	31.2297			1.14880			0.574402	+	0.818574i	$0.305235\pi$
$740$	−9.65685	−	26.7016i	−0.354993	−	0.981569i
$741$		0			0
$742$	10.4123	+	59.4060i	0.382249	+	2.18086i
$743$	5.06602			0.185854			0.0929271	−	0.995673i	$-0.470378\pi$
$743$	5.06602			0.185854			0.0929271	+	0.995673i	$0.470378\pi$
$744$		0			0
$745$	30.0664			1.10155
$746$	13.8713	−	2.43128i	0.507865	−	0.0890156i
$747$		0			0
$748$	−17.4280	+	6.30297i	−0.637229	+	0.230459i
$749$	46.7359			1.70769
$750$		0			0
$751$	4.05958			0.148136			0.0740680	−	0.997253i	$-0.476402\pi$
$751$	4.05958			0.148136			0.0740680	+	0.997253i	$0.476402\pi$
$752$	−19.6564	−	23.6209i	−0.716796	−	0.861367i
$753$		0			0
$754$	56.7164	−	9.94092i	2.06549	−	0.362027i
$755$			28.9349i			1.05305i
$756$		0			0
$757$		−	0.219844i		−	0.00799035i	−0.999992	−	0.00399518i	$-0.998728\pi$
$757$		−	0.219844i		−	0.00799035i	0.999992	−	0.00399518i	$-0.00127171\pi$
$758$		0			0
$759$		0			0
$760$	38.1338	−	2.99973i	1.38326	−	0.108812i
$761$	30.9704			1.12268			0.561339	−	0.827586i	$-0.310287\pi$
$761$	30.9704			1.12268			0.561339	+	0.827586i	$0.310287\pi$
$762$		0			0
$763$			56.7418i			2.05419i
$764$	6.16993	+	17.0601i	0.223220	+	0.617213i
$765$		0			0
$766$	−37.7572	+	6.61786i	−1.36422	+	0.239113i
$767$			25.2037i			0.910054i
$768$		0			0
$769$	27.5770			0.994453			0.497227	−	0.867621i	$-0.334352\pi$
$769$	27.5770			0.994453			0.497227	+	0.867621i	$0.334352\pi$
$770$	−49.8841	+	8.74339i	−1.79770	+	0.315090i
$771$		0			0
$772$	−17.3951	−	48.0981i	−0.626063	−	1.73109i
$773$	17.9758			0.646546			0.323273	−	0.946306i	$-0.395217\pi$
$773$	17.9758			0.646546			0.323273	+	0.946306i	$0.395217\pi$
$774$		0			0
$775$	14.7794			0.530890
$776$	6.86384	+	11.9731i	0.246398	+	0.429809i
$777$		0			0
$778$	−7.33388	−	41.8424i	−0.262932	−	1.50012i
$779$	−17.8006	−	8.42445i	−0.637774	−	0.301837i
$780$		0			0
$781$	−6.39905			−0.228976
$782$	−4.53052	−	25.8482i	−0.162011	−	0.924329i
$783$		0			0
$784$	−36.5226	+	30.3927i	−1.30438	+	1.08545i
$785$	−30.6109			−1.09255
$786$		0			0
$787$			26.6951i			0.951577i	0.879560	+	0.475789i	$0.157837\pi$
$787$			26.6951i			0.951577i	−0.879560	+	0.475789i	$0.842163\pi$
$788$	16.3665	+	45.2541i	0.583034	+	1.61211i
$789$		0			0
$790$	13.0925	+	74.6971i	0.465809	+	2.65760i
$791$	65.1062			2.31491
$792$		0			0
$793$			61.2151i			2.17381i
$794$	6.95417	+	39.6760i	0.246794	+	1.40805i
$795$		0			0
$796$	11.7676	+	32.5378i	0.417091	+	1.15327i
$797$	5.82023			0.206163			0.103082	−	0.994673i	$-0.467130\pi$
$797$	5.82023			0.206163			0.103082	+	0.994673i	$0.467130\pi$
$798$		0			0
$799$			26.7981i			0.948047i
$800$	16.9237	−	19.9610i	0.598344	−	0.705728i
$801$		0			0
$802$	−1.45231	−	8.28591i	−0.0512827	−	0.292586i
$803$	0.992995			0.0350420
$804$		0			0
$805$		−	71.7125i		−	2.52753i
$806$	−22.7036	+	3.97936i	−0.799701	+	0.140167i
$807$		0			0
$808$	−4.04296	−	7.05243i	−0.142231	−	0.248104i
$809$	48.0519			1.68942			0.844708	−	0.535228i	$-0.179774\pi$
$809$	48.0519			1.68942			0.844708	+	0.535228i	$0.179774\pi$
$810$		0			0
$811$		−	36.8600i		−	1.29433i	−0.762350	−	0.647165i	$-0.775954\pi$
$811$		−	36.8600i		−	1.29433i	0.762350	−	0.647165i	$-0.224046\pi$
$812$	23.5866	+	65.2179i	0.827729	+	2.28870i
$813$		0			0
$814$	−16.9325	+	2.96783i	−0.593484	+	0.104022i
$815$			4.72563i			0.165532i
$816$		0			0
$817$	11.7187	−	24.7612i	0.409984	−	0.866285i
$818$	−3.64947	−	20.8215i	−0.127601	−	0.728007i
$819$		0			0
$820$	−26.3640	+	9.53477i	−0.920671	+	0.332969i
$821$		−	36.1520i		−	1.26171i	−0.775900	−	0.630856i	$-0.782704\pi$
$821$		−	36.1520i		−	1.26171i	0.775900	−	0.630856i	$-0.217296\pi$
$822$		0			0
$823$			15.3874i			0.536370i	0.963367	+	0.268185i	$0.0864238\pi$
$823$			15.3874i			0.536370i	−0.963367	+	0.268185i	$0.913576\pi$
$824$	26.0986	−	14.9616i	0.909188	−	0.521212i
$825$		0			0
$826$	−29.9002	+	5.24074i	−1.04036	+	0.182349i
$827$			1.84666i			0.0642147i	0.999484	+	0.0321073i	$0.0102218\pi$
$827$			1.84666i			0.0642147i	−0.999484	+	0.0321073i	$0.989778\pi$
$828$		0			0
$829$	−20.3039			−0.705184			−0.352592	−	0.935777i	$-0.614700\pi$
$829$	−20.3039			−0.705184			−0.352592	+	0.935777i	$0.614700\pi$
$830$	−9.30935	−	53.1131i	−0.323132	−	1.84358i
$831$		0			0
$832$	−20.6232	+	35.2203i	−0.714982	+	1.22104i
$833$	41.4351			1.43564
$834$		0			0
$835$			7.47373i			0.258639i
$836$	2.19699	−	23.0542i	0.0759844	−	0.797345i
$837$		0			0
$838$	−10.7198	+	1.87890i	−0.370309	+	0.0649055i
$839$	−53.7141			−1.85442			−0.927208	−	0.374546i	$-0.877799\pi$
$839$	−53.7141			−1.85442			−0.927208	+	0.374546i	$0.877799\pi$
$840$		0			0
$841$	34.6926			1.19630
$842$	−2.06753	+	0.362384i	−0.0712517	+	0.0124886i
$843$		0			0
$844$	−13.7999	−	38.1572i	−0.475011	−	1.31342i
$845$		−	40.4205i		−	1.39051i
$846$		0			0
$847$		−	17.1328i		−	0.588689i
$848$	−30.1785	+	25.1134i	−1.03633	+	0.862397i
$849$		0			0
$850$	−22.4787	+	3.93994i	−0.771014	+	0.135139i
$851$		−	24.3419i		−	0.834429i
$852$		0			0
$853$			39.1842i			1.34164i	0.741620	+	0.670820i	$0.234058\pi$
$853$			39.1842i			1.34164i	−0.741620	+	0.670820i	$0.765942\pi$
$854$	−72.6220	+	12.7288i	−2.48507	+	0.435569i
$855$		0			0
$856$	15.1310	+	26.3941i	0.517167	+	0.902131i
$857$			37.5744i			1.28352i	0.766907	+	0.641758i	$0.221795\pi$
$857$			37.5744i			1.28352i	−0.766907	+	0.641758i	$0.778205\pi$
$858$		0			0
$859$	−33.0235			−1.12675			−0.563374	−	0.826202i	$-0.690497\pi$
$859$	−33.0235			−1.12675			−0.563374	+	0.826202i	$0.690497\pi$
$860$	−13.2631	−	36.6731i	−0.452270	−	1.25054i
$861$		0			0
$862$	46.2234	−	8.10177i	1.57438	−	0.275947i
$863$	34.0836			1.16022			0.580110	−	0.814538i	$-0.303010\pi$
$863$	34.0836			1.16022			0.580110	+	0.814538i	$0.303010\pi$
$864$		0			0
$865$		−	45.4004i		−	1.54366i
$866$	−5.78511	−	33.0061i	−0.196586	−	1.12159i
$867$		0			0
$868$	−9.44176	−	26.1068i	−0.320474	−	0.886123i
$869$	45.9132			1.55750
$870$		0			0
$871$		−	2.07204i		−	0.0702085i
$872$	−32.0450	+	18.3705i	−1.08518	+	0.622103i
$873$		0			0
$874$	31.6174	+	8.70005i	1.06947	+	0.294284i
$875$	5.03911			0.170353
$876$		0			0
$877$	20.8395			0.703698			0.351849	−	0.936057i	$-0.385553\pi$
$877$	20.8395			0.703698			0.351849	+	0.936057i	$0.385553\pi$
$878$	26.2599	−	4.60267i	0.886227	−	0.155333i
$879$		0			0
$880$	−21.0881	−	25.3413i	−0.710879	−	0.854256i
$881$	4.20737			0.141750			0.0708749	−	0.997485i	$-0.477421\pi$
$881$	4.20737			0.141750			0.0708749	+	0.997485i	$0.477421\pi$
$882$		0			0
$883$	4.68449			0.157646			0.0788228	−	0.996889i	$-0.474884\pi$
$883$	4.68449			0.157646			0.0788228	+	0.996889i	$0.474884\pi$
$884$	33.4704	−	12.1048i	1.12573	−	0.407130i
$885$		0			0
$886$	−13.4184	+	2.35190i	−0.450801	+	0.0790137i
$887$	42.8186			1.43771			0.718854	−	0.695161i	$-0.244667\pi$
$887$	42.8186			1.43771			0.718854	+	0.695161i	$0.244667\pi$
$888$		0			0
$889$			75.9082i			2.54588i
$890$	−8.44158	+	1.47959i	−0.282963	+	0.0495960i
$891$		0			0
$892$	3.05931	−	1.10643i	0.102433	−	0.0370459i
$893$	−30.2684	−	14.3250i	−1.01289	−	0.479369i
$894$		0			0
$895$	−14.6051			−0.488193
$896$	−46.0716	−	17.1427i	−1.53914	−	0.572697i
$897$		0			0
$898$	−4.68305	−	26.7185i	−0.156276	−	0.891606i
$899$	−25.4962			−0.850347
$900$		0			0
$901$	34.2377			1.14062
$902$	2.93031	+	16.7185i	0.0975688	+	0.556664i
$903$		0			0
$904$	21.0785	+	36.7688i	0.701061	+	1.22291i
$905$			56.5282i			1.87906i
$906$		0			0
$907$		−	56.3357i		−	1.87060i	−0.353861	−	0.935298i	$-0.615131\pi$
$907$		−	56.3357i		−	1.87060i	0.353861	−	0.935298i	$-0.384869\pi$
$908$	−13.5138	−	37.3662i	−0.448471	−	1.24004i
$909$		0			0
$910$	95.8024	−	16.7917i	3.17582	−	0.556639i
$911$	−21.1389			−0.700363			−0.350182	−	0.936682i	$-0.613880\pi$
$911$	−21.1389			−0.700363			−0.350182	+	0.936682i	$0.613880\pi$
$912$		0			0
$913$	−32.6464			−1.08044
$914$	30.6307	−	5.36877i	1.01317	−	0.177583i
$915$		0			0
$916$	−7.36151	−	20.3549i	−0.243231	−	0.672544i
$917$		−	25.1360i		−	0.830064i
$918$		0			0
$919$		−	27.6142i		−	0.910910i	−0.890259	−	0.455455i	$-0.849477\pi$
$919$		−	27.6142i		−	0.910910i	0.890259	−	0.455455i	$-0.150523\pi$
$920$	40.4996	−	23.2173i	1.33523	−	0.765452i
$921$		0			0
$922$	−3.29243	−	18.7845i	−0.108430	−	0.618633i
$923$	12.2894			0.404510
$924$		0			0
$925$	−21.1688			−0.696025
$926$	0.199272	+	1.13692i	0.00654850	+	0.0373615i
$927$		0			0
$928$	−29.1955	+	34.4352i	−0.958391	+	1.13039i
$929$	−43.2969			−1.42052			−0.710262	−	0.703937i	$-0.751424\pi$
$929$	−43.2969			−1.42052			−0.710262	+	0.703937i	$0.751424\pi$
$930$		0			0
$931$	−22.1493	+	46.8009i	−0.725914	+	1.53384i
$932$	−44.1478	+	15.9664i	−1.44611	+	0.522998i
$933$		0			0
$934$	−57.3741	+	10.0562i	−1.87734	+	0.329049i
$935$			28.7499i			0.940222i
$936$		0			0
$937$	27.8603			0.910155			0.455078	−	0.890452i	$-0.349611\pi$
$937$	27.8603			0.910155			0.455078	+	0.890452i	$0.349611\pi$
$938$	2.45815	−	0.430850i	0.0802615	−	0.0140678i
$939$		0			0
$940$	−44.8297	+	16.2130i	−1.46218	+	0.528811i
$941$	3.98575			0.129932			0.0649658	−	0.997887i	$-0.479306\pi$
$941$	3.98575			0.129932			0.0649658	+	0.997887i	$0.479306\pi$
$942$		0			0
$943$	−24.0342			−0.782660
$944$	−12.6401	−	15.1894i	−0.411399	−	0.494374i
$945$		0			0
$946$	−23.2559	+	4.07615i	−0.756114	+	0.132527i
$947$	−9.87990			−0.321053			−0.160527	−	0.987031i	$-0.551319\pi$
$947$	−9.87990			−0.321053			−0.160527	+	0.987031i	$0.551319\pi$
$948$		0			0
$949$	−1.90705			−0.0619053
$950$	7.56595	−	27.4958i	0.245472	−	0.892083i
$951$		0			0
$952$	21.3201	+	37.1902i	0.690989	+	1.20534i
$953$		−	52.2372i		−	1.69213i	−0.533082	−	0.846064i	$-0.678966\pi$
$953$		−	52.2372i		−	1.69213i	0.533082	−	0.846064i	$-0.321034\pi$
$954$		0			0
$955$	28.1431			0.910688
$956$	−17.7133	−	48.9780i	−0.572889	−	1.58406i
$957$		0			0
$958$	7.16232	+	40.8635i	0.231404	+	1.32024i
$959$		−	1.56235i		−	0.0504509i
$960$		0			0
$961$	−20.7938			−0.670769
$962$	32.5189	−	5.69972i	1.04845	−	0.183766i
$963$		0			0
$964$	9.99427	+	27.6345i	0.321894	+	0.890049i
$965$	−79.3447			−2.55419
$966$		0			0
$967$		−	23.4702i		−	0.754749i	−0.926061	−	0.377375i	$-0.876827\pi$
$967$		−	23.4702i		−	0.754749i	0.926061	−	0.377375i	$-0.123173\pi$
$968$	9.67573	−	5.54683i	0.310990	−	0.178282i
$969$		0			0
$970$	21.0881	−	3.69620i	0.677098	−	0.118678i
$971$		−	23.8446i		−	0.765211i	−0.923912	−	0.382605i	$-0.875027\pi$
$971$		−	23.8446i		−	0.765211i	0.923912	−	0.382605i	$-0.124973\pi$
$972$		0			0
$973$			12.8946i			0.413382i
$974$	−44.3209	+	7.76831i	−1.42013	+	0.248913i
$975$		0			0
$976$	−30.7003	−	36.8923i	−0.982694	−	1.18089i
$977$			43.5227i			1.39241i	0.717841	+	0.696207i	$0.245131\pi$
$977$			43.5227i			1.39241i	−0.717841	+	0.696207i	$0.754869\pi$
$978$		0			0
$979$			5.18869i			0.165831i
$980$	25.0685	+	69.3155i	0.800785	+	2.21420i
$981$		0			0
$982$	−3.04270	+	0.533307i	−0.0970965	+	0.0170185i
$983$	28.1172			0.896798			0.448399	−	0.893834i	$-0.351994\pi$
$983$	28.1172			0.896798			0.448399	+	0.893834i	$0.351994\pi$
$984$		0			0
$985$	74.6531			2.37864
$986$	38.7786	−	6.79688i	1.23496	−	0.216457i
$987$		0			0
$988$	−4.21931	+	44.2755i	−0.134234	+	1.40859i
$989$		−	33.4322i		−	1.06308i
$990$		0			0
$991$	−37.7810			−1.20015			−0.600076	−	0.799943i	$-0.704863\pi$
$991$	−37.7810			−1.20015			−0.600076	+	0.799943i	$0.704863\pi$
$992$	11.6870	−	13.7845i	0.371063	−	0.437657i
$993$		0			0
$994$	2.55539	+	14.5794i	0.0810520	+	0.462430i
$995$	53.6758			1.70164
$996$		0			0
$997$			46.5992i			1.47581i	0.674904	+	0.737906i	$0.264185\pi$
$997$			46.5992i			1.47581i	−0.674904	+	0.737906i	$0.735815\pi$
$998$	−48.8770	+	8.56686i	−1.54717	+	0.271179i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.f.379.3	yes	24
3.2	odd	2	inner	1368.2.e.f.379.21	yes	24
4.3	odd	2		5472.2.e.f.5167.5		24
8.3	odd	2	inner	1368.2.e.f.379.24	yes	24
8.5	even	2		5472.2.e.f.5167.16		24
12.11	even	2		5472.2.e.f.5167.4		24
19.18	odd	2	inner	1368.2.e.f.379.22	yes	24
24.5	odd	2		5472.2.e.f.5167.23		24
24.11	even	2	inner	1368.2.e.f.379.2	yes	24
57.56	even	2	inner	1368.2.e.f.379.4	yes	24
76.75	even	2		5472.2.e.f.5167.15		24
152.37	odd	2		5472.2.e.f.5167.6		24
152.75	even	2	inner	1368.2.e.f.379.1	✓	24
228.227	odd	2		5472.2.e.f.5167.24		24
456.227	odd	2	inner	1368.2.e.f.379.23	yes	24
456.341	even	2		5472.2.e.f.5167.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.e.f.379.1	✓	24	152.75	even	2	inner
1368.2.e.f.379.2	yes	24	24.11	even	2	inner
1368.2.e.f.379.3	yes	24	1.1	even	1	trivial
1368.2.e.f.379.4	yes	24	57.56	even	2	inner
1368.2.e.f.379.21	yes	24	3.2	odd	2	inner
1368.2.e.f.379.22	yes	24	19.18	odd	2	inner
1368.2.e.f.379.23	yes	24	456.227	odd	2	inner
1368.2.e.f.379.24	yes	24	8.3	odd	2	inner
5472.2.e.f.5167.3		24	456.341	even	2
5472.2.e.f.5167.4		24	12.11	even	2
5472.2.e.f.5167.5		24	4.3	odd	2
5472.2.e.f.5167.6		24	152.37	odd	2
5472.2.e.f.5167.15		24	76.75	even	2
5472.2.e.f.5167.16		24	8.5	even	2
5472.2.e.f.5167.23		24	24.5	odd	2
5472.2.e.f.5167.24		24	228.227	odd	2

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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39298 + 0.244153i) q^{2} +(1.88078 - 0.680200i) q^{4} -3.10261i q^{5} +4.34495i q^{7} +(-2.45381 + 1.40670i) q^{8} +O(q^{10})\)	\(q+(-1.39298 + 0.244153i) q^{2} +(1.88078 - 0.680200i) q^{4} -3.10261i q^{5} +4.34495i q^{7} +(-2.45381 + 1.40670i) q^{8} +(0.757512 + 4.32187i) q^{10} +2.65647 q^{11} -5.10176 q^{13} +(-1.06083 - 6.05242i) q^{14} +(3.07466 - 2.55861i) q^{16} -3.48821 q^{17} +(1.86464 - 3.93994i) q^{19} +(-2.11040 - 5.83533i) q^{20} +(-3.70041 + 0.648586i) q^{22} -5.31965i q^{23} -4.62620 q^{25} +(7.10664 - 1.24561i) q^{26} +(2.95543 + 8.17189i) q^{28} +7.98077 q^{29} -3.19471 q^{31} +(-3.65824 + 4.31478i) q^{32} +(4.85901 - 0.851658i) q^{34} +13.4807 q^{35} +4.57585 q^{37} +(-1.63546 + 5.94351i) q^{38} +(4.36445 + 7.61322i) q^{40} -4.51800i q^{41} +6.28467 q^{43} +(4.99624 - 1.80693i) q^{44} +(1.29881 + 7.41015i) q^{46} -7.68246i q^{47} -11.8786 q^{49} +(6.44419 - 1.12950i) q^{50} +(-9.59527 + 3.47021i) q^{52} -9.81525 q^{53} -8.24201i q^{55} +(-6.11205 - 10.6617i) q^{56} +(-11.1170 + 1.94853i) q^{58} -4.94021i q^{59} -11.9988i q^{61} +(4.45016 - 0.779998i) q^{62} +(4.04238 - 6.90356i) q^{64} +15.8288i q^{65} +0.406143i q^{67} +(-6.56056 + 2.37268i) q^{68} +(-18.7783 + 3.29135i) q^{70} -2.40885 q^{71} +0.373802 q^{73} +(-6.37406 + 1.11721i) q^{74} +(0.827031 - 8.67848i) q^{76} +11.5422i q^{77} +17.2835 q^{79} +(-7.93838 - 9.53946i) q^{80} +(1.10308 + 6.29348i) q^{82} -12.2894 q^{83} +10.8226i q^{85} +(-8.75441 + 1.53442i) q^{86} +(-6.51849 + 3.73687i) q^{88} +1.95322i q^{89} -22.1669i q^{91} +(-3.61842 - 10.0051i) q^{92} +(1.87570 + 10.7015i) q^{94} +(-12.2241 - 5.78526i) q^{95} -4.87939i q^{97} +(16.5466 - 2.90019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4}+O(q^{10}) \) 24 * q + 20 * q^4	\( 24 q + 20 q^{4} - 12 q^{16} + 24 q^{19} - 40 q^{25} - 40 q^{28} - 72 q^{49} - 104 q^{58} + 20 q^{64} + 80 q^{73} - 12 q^{76} + 56 q^{82}+O(q^{100}) \) 24 * q + 20 * q^4 - 12 * q^16 + 24 * q^19 - 40 * q^25 - 40 * q^28 - 72 * q^49 - 104 * q^58 + 20 * q^64 + 80 * q^73 - 12 * q^76 + 56 * q^82

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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