LMFDB - Embedded newform 336.7.bh.h.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.1
Character	$\chi$	$=$	336.241
Dual form			336.7.bh.h.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 + 7.79423i) q^{3} +(-160.491 + 92.6595i) q^{5} +(338.827 - 53.3419i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 + 7.79423i) q^{3} +(-160.491 + 92.6595i) q^{5} +(338.827 - 53.3419i) q^{7} +(121.500 + 210.444i) q^{9} +(999.852 - 1731.80i) q^{11} +1997.85i q^{13} -2888.84 q^{15} +(-2442.52 - 1410.19i) q^{17} +(5356.39 - 3092.51i) q^{19} +(4989.92 + 1920.78i) q^{21} +(566.551 + 981.296i) q^{23} +(9359.05 - 16210.3i) q^{25} +3788.00i q^{27} -31206.3 q^{29} +(-46706.7 - 26966.2i) q^{31} +(26996.0 - 15586.2i) q^{33} +(-49436.0 + 39956.4i) q^{35} +(-17035.8 - 29506.9i) q^{37} +(-15571.7 + 26971.0i) q^{39} -12545.1i q^{41} +106268. q^{43} +(-38999.3 - 22516.2i) q^{45} +(119117. - 68772.1i) q^{47} +(111958. - 36147.3i) q^{49} +(-21982.6 - 38075.0i) q^{51} +(28441.0 - 49261.3i) q^{53} +370583. i q^{55} +96415.0 q^{57} +(166800. + 96302.3i) q^{59} +(327396. - 189022. i) q^{61} +(52393.0 + 64823.1i) q^{63} +(-185120. - 320637. i) q^{65} +(25424.5 - 44036.5i) q^{67} +17663.3i q^{69} -379429. q^{71} +(425878. + 245881. i) q^{73} +(252694. - 145893. i) q^{75} +(246400. - 640113. i) q^{77} +(445532. + 771685. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -719824. i q^{83} +522669. q^{85} +(-421285. - 243229. i) q^{87} +(118644. - 68499.1i) q^{89} +(106569. + 676927. i) q^{91} +(-420361. - 728086. i) q^{93} +(-573101. + 992640. i) q^{95} +502185. i q^{97} +485928. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) $ 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9	$ 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9} + 1190 q^{11} - 2268 q^{15} - 1500 q^{17} + 13446 q^{19} - 2106 q^{21} - 21504 q^{23} + 22542 q^{25} - 85484 q^{29} - 6264 q^{31} + 32130 q^{33} - 32268 q^{35} - 46938 q^{37} + 17010 q^{39} + 19548 q^{43} - 30618 q^{45} + 167004 q^{47} + 250644 q^{49} - 13500 q^{51} - 258982 q^{53} + 242028 q^{57} - 744834 q^{59} - 390096 q^{61} - 59778 q^{63} - 19388 q^{65} - 62742 q^{67} + 1102984 q^{71} - 663534 q^{73} + 608634 q^{75} + 404298 q^{77} + 271032 q^{79} - 708588 q^{81} + 2540040 q^{85} - 1154034 q^{87} - 433740 q^{89} + 2142270 q^{91} - 56376 q^{93} - 2205360 q^{95} + 578340 q^{99}+O(q^{100}) $ 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9 + 1190 * q^11 - 2268 * q^15 - 1500 * q^17 + 13446 * q^19 - 2106 * q^21 - 21504 * q^23 + 22542 * q^25 - 85484 * q^29 - 6264 * q^31 + 32130 * q^33 - 32268 * q^35 - 46938 * q^37 + 17010 * q^39 + 19548 * q^43 - 30618 * q^45 + 167004 * q^47 + 250644 * q^49 - 13500 * q^51 - 258982 * q^53 + 242028 * q^57 - 744834 * q^59 - 390096 * q^61 - 59778 * q^63 - 19388 * q^65 - 62742 * q^67 + 1102984 * q^71 - 663534 * q^73 + 608634 * q^75 + 404298 * q^77 + 271032 * q^79 - 708588 * q^81 + 2540040 * q^85 - 1154034 * q^87 - 433740 * q^89 + 2142270 * q^91 - 56376 * q^93 - 2205360 * q^95 + 578340 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	13.5000	+	7.79423i	0.500000	+	0.288675i
$3$	13.5000	+	7.79423i	0.500000	+	0.288675i
$4$		0			0
$5$	−160.491	+	92.6595i	−1.28393	+	0.741276i	−0.977564	−	0.210639i	$-0.932446\pi$
$5$	−160.491	+	92.6595i	−1.28393	+	0.741276i	−0.306363	+	0.951915i	$0.599112\pi$
$6$		0			0
$7$	338.827	−	53.3419i	0.987833	−	0.155516i
$7$	338.827	−	53.3419i	0.987833	−	0.155516i
$8$		0			0
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$		0			0
$11$	999.852	−	1731.80i	0.751204	−	1.30112i	−0.196036	−	0.980597i	$-0.562807\pi$
$11$	999.852	−	1731.80i	0.751204	−	1.30112i	0.947240	−	0.320527i	$-0.103860\pi$
$12$		0			0
$13$			1997.85i			0.909355i	0.890656	+	0.454678i	$0.150246\pi$
$13$			1997.85i			0.909355i	−0.890656	+	0.454678i	$0.849754\pi$
$14$		0			0
$15$	−2888.84			−0.855951
$16$		0			0
$17$	−2442.52	−	1410.19i	−0.497154	−	0.287032i	0.230384	−	0.973100i	$-0.426002\pi$
$17$	−2442.52	−	1410.19i	−0.497154	−	0.287032i	−0.727537	+	0.686068i	$0.759335\pi$
$18$		0			0
$19$	5356.39	−	3092.51i	0.780928	−	0.450869i	−0.0558308	−	0.998440i	$-0.517781\pi$
$19$	5356.39	−	3092.51i	0.780928	−	0.450869i	0.836759	+	0.547571i	$0.184447\pi$
$20$		0			0
$21$	4989.92	+	1920.78i	0.538810	+	0.207405i
$22$		0			0
$23$	566.551	+	981.296i	0.0465646	+	0.0806522i	0.888368	−	0.459132i	$-0.151839\pi$
$23$	566.551	+	981.296i	0.0465646	+	0.0806522i	−0.841804	+	0.539784i	$0.818506\pi$
$24$		0			0
$25$	9359.05	−	16210.3i	0.598979	−	1.03746i
$26$		0			0
$27$			3788.00i			0.192450i
$28$		0			0
$29$	−31206.3			−1.27952			−0.639761	−	0.768574i	$-0.720967\pi$
$29$	−31206.3			−1.27952			−0.639761	+	0.768574i	$0.720967\pi$
$30$		0			0
$31$	−46706.7	−	26966.2i	−1.56781	−	0.905178i	−0.996424	−	0.0844995i	$-0.973071\pi$
$31$	−46706.7	−	26966.2i	−1.56781	−	0.905178i	−0.571391	−	0.820678i	$-0.693596\pi$
$32$		0			0
$33$	26996.0	−	15586.2i	0.751204	−	0.433708i
$34$		0			0
$35$	−49436.0	+	39956.4i	−1.15303	+	0.931928i
$36$		0			0
$37$	−17035.8	−	29506.9i	−0.336324	−	0.582529i	0.647415	−	0.762138i	$-0.275850\pi$
$37$	−17035.8	−	29506.9i	−0.336324	−	0.582529i	−0.983738	+	0.179609i	$0.942517\pi$
$38$		0			0
$39$	−15571.7	+	26971.0i	−0.262508	+	0.454678i
$40$		0			0
$41$		−	12545.1i		−	0.182022i	−0.995850	−	0.0910111i	$-0.970990\pi$
$41$		−	12545.1i		−	0.182022i	0.995850	−	0.0910111i	$-0.0290099\pi$
$42$		0			0
$43$	106268.			1.33659			0.668294	−	0.743897i	$-0.267025\pi$
$43$	106268.			1.33659			0.668294	+	0.743897i	$0.267025\pi$
$44$		0			0
$45$	−38999.3	−	22516.2i	−0.427976	−	0.247092i
$46$		0			0
$47$	119117.	−	68772.1i	1.14731	−	0.662397i	0.199076	−	0.979984i	$-0.436206\pi$
$47$	119117.	−	68772.1i	1.14731	−	0.662397i	0.948229	+	0.317587i	$0.102872\pi$
$48$		0			0
$49$	111958.	−	36147.3i	0.951630	−	0.307247i
$50$		0			0
$51$	−21982.6	−	38075.0i	−0.165718	−	0.287032i
$52$		0			0
$53$	28441.0	−	49261.3i	0.191037	−	0.330886i	−0.754557	−	0.656234i	$-0.772148\pi$
$53$	28441.0	−	49261.3i	0.191037	−	0.330886i	0.945594	+	0.325348i	$0.105482\pi$
$54$		0			0
$55$			370583.i			2.22740i
$56$		0			0
$57$	96415.0			0.520619
$58$		0			0
$59$	166800.	+	96302.3i	0.812159	+	0.468900i	0.847705	−	0.530468i	$-0.177984\pi$
$59$	166800.	+	96302.3i	0.812159	+	0.468900i	−0.0355459	+	0.999368i	$0.511317\pi$
$60$		0			0
$61$	327396.	−	189022.i	1.44239	−	0.832767i	0.444386	−	0.895836i	$-0.353422\pi$
$61$	327396.	−	189022.i	1.44239	−	0.832767i	0.998009	+	0.0630685i	$0.0200887\pi$
$62$		0			0
$63$	52393.0	+	64823.1i	0.209532	+	0.259244i
$64$		0			0
$65$	−185120.	−	320637.i	−0.674083	−	1.16755i
$66$		0			0
$67$	25424.5	−	44036.5i	0.0845334	−	0.146416i	−0.820659	−	0.571418i	$-0.806393\pi$
$67$	25424.5	−	44036.5i	0.0845334	−	0.146416i	0.905192	+	0.425002i	$0.139727\pi$
$68$		0			0
$69$			17663.3i			0.0537681i
$70$		0			0
$71$	−379429.			−1.06012			−0.530061	−	0.847960i	$-0.677831\pi$
$71$	−379429.			−1.06012			−0.530061	+	0.847960i	$0.677831\pi$
$72$		0			0
$73$	425878.	+	245881.i	1.09475	+	0.632056i	0.934838	−	0.355074i	$-0.115544\pi$
$73$	425878.	+	245881.i	1.09475	+	0.632056i	0.159916	+	0.987131i	$0.448878\pi$
$74$		0			0
$75$	252694.	−	145893.i	0.598979	−	0.345821i
$76$		0			0
$77$	246400.	−	640113.i	0.539719	−	1.40212i
$78$		0			0
$79$	445532.	+	771685.i	0.903646	+	1.56516i	0.822725	+	0.568439i	$0.192453\pi$
$79$	445532.	+	771685.i	0.903646	+	1.56516i	0.0809204	+	0.996721i	$0.474214\pi$
$80$		0			0
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	719824.i		−	1.25890i	−0.777040	−	0.629451i	$-0.783280\pi$
$83$		−	719824.i		−	1.25890i	0.777040	−	0.629451i	$-0.216720\pi$
$84$		0			0
$85$	522669.			0.851079
$86$		0			0
$87$	−421285.	−	243229.i	−0.639761	−	0.369366i
$88$		0			0
$89$	118644.	−	68499.1i	0.168297	−	0.0971661i	−0.413486	−	0.910511i	$-0.635689\pi$
$89$	118644.	−	68499.1i	0.168297	−	0.0971661i	0.581782	+	0.813345i	$0.302356\pi$
$90$		0			0
$91$	106569.	+	676927.i	0.141419	+	0.898292i
$92$		0			0
$93$	−420361.	−	728086.i	−0.522605	−	0.905178i
$94$		0			0
$95$	−573101.	+	992640.i	−0.668437	+	1.15777i
$96$		0			0
$97$			502185.i			0.550235i	0.961411	+	0.275118i	$0.0887168\pi$
$97$			502185.i			0.550235i	−0.961411	+	0.275118i	$0.911283\pi$
$98$		0			0
$99$	485928.			0.500803
$100$		0			0
$101$	926392.	+	534852.i	0.899147	+	0.519122i	0.876923	−	0.480631i	$-0.159592\pi$
$101$	926392.	+	534852.i	0.899147	+	0.519122i	0.0222233	+	0.999753i	$0.492926\pi$
$102$		0			0
$103$	754307.	−	435499.i	0.690298	−	0.398543i	−0.113426	−	0.993546i	$-0.536182\pi$
$103$	754307.	−	435499.i	0.690298	−	0.398543i	0.803724	+	0.595003i	$0.202849\pi$
$104$		0			0
$105$	−978815.	+	154096.i	−0.845537	+	0.133114i
$106$		0			0
$107$	−157373.	−	272577.i	−0.128463	−	0.222504i	0.794618	−	0.607109i	$-0.207671\pi$
$107$	−157373.	−	272577.i	−0.128463	−	0.222504i	−0.923081	+	0.384605i	$0.874338\pi$
$108$		0			0
$109$	−287837.	+	498549.i	−0.222263	+	0.384971i	−0.955495	−	0.295008i	$-0.904678\pi$
$109$	−287837.	+	498549.i	−0.222263	+	0.384971i	0.733232	+	0.679979i	$0.238011\pi$
$110$		0			0
$111$		−	531124.i		−	0.388353i
$112$		0			0
$113$	−653003.			−0.452564			−0.226282	−	0.974062i	$-0.572657\pi$
$113$	−653003.			−0.452564			−0.226282	+	0.974062i	$0.572657\pi$
$114$		0			0
$115$	−181853.	−	104993.i	−0.119571	−	0.0690344i
$116$		0			0
$117$	−420437.	+	242739.i	−0.262508	+	0.151559i
$118$		0			0
$119$	−902812.	−	347521.i	−0.535743	−	0.206224i
$120$		0			0
$121$	−1.11363e6	−	1.92886e6i	−0.628615	−	1.08879i
$122$		0			0
$123$	97779.7	−	169359.i	0.0525453	−	0.0910111i
$124$		0			0
$125$			573210.i			0.293483i
$126$		0			0
$127$	149612.			0.0730389			0.0365194	−	0.999333i	$-0.488373\pi$
$127$	149612.			0.0730389			0.0365194	+	0.999333i	$0.488373\pi$
$128$		0			0
$129$	1.43462e6	+	828278.i	0.668294	+	0.385840i
$130$		0			0
$131$	3.30357e6	−	1.90732e6i	1.46950	−	0.848416i	0.470085	−	0.882621i	$-0.344223\pi$
$131$	3.30357e6	−	1.90732e6i	1.46950	−	0.848416i	0.999415	+	0.0342046i	$0.0108898\pi$
$132$		0			0
$133$	1.64993e6	−	1.33355e6i	0.701310	−	0.566830i
$134$		0			0
$135$	−350994.	−	607939.i	−0.142659	−	0.247092i
$136$		0			0
$137$	97751.6	−	169311.i	0.0380156	−	0.0658450i	−0.846392	−	0.532561i	$-0.821230\pi$
$137$	97751.6	−	169311.i	0.0380156	−	0.0658450i	0.884407	+	0.466716i	$0.154563\pi$
$138$		0			0
$139$		−	3.21163e6i		−	1.19586i	−0.801547	−	0.597932i	$-0.795989\pi$
$139$		−	3.21163e6i		−	1.19586i	0.801547	−	0.597932i	$-0.204011\pi$
$140$		0			0
$141$	2.14410e6			0.764870
$142$		0			0
$143$	3.45987e6	+	1.99756e6i	1.18318	+	0.683111i
$144$		0			0
$145$	5.00832e6	−	2.89156e6i	1.64281	−	0.948479i
$146$		0			0
$147$	1.79318e6	+	384639.i	0.564510	+	0.121088i
$148$		0			0
$149$	2.53285e6	+	4.38702e6i	0.765686	+	1.32621i	0.939883	+	0.341496i	$0.110933\pi$
$149$	2.53285e6	+	4.38702e6i	0.765686	+	1.32621i	−0.174198	+	0.984711i	$0.555733\pi$
$150$		0			0
$151$	−2.08480e6	+	3.61098e6i	−0.605526	+	1.04880i	0.386442	+	0.922314i	$0.373704\pi$
$151$	−2.08480e6	+	3.61098e6i	−0.605526	+	1.04880i	−0.991968	+	0.126489i	$0.959629\pi$
$152$		0			0
$153$		−	685351.i		−	0.191354i
$154$		0			0
$155$	9.99468e6			2.68395
$156$		0			0
$157$	5.49806e6	+	3.17431e6i	1.42073	+	0.820257i	0.996361	−	0.0852341i	$-0.0271638\pi$
$157$	5.49806e6	+	3.17431e6i	1.42073	+	0.820257i	0.424366	+	0.905491i	$0.360497\pi$
$158$		0			0
$159$	767908.	−	443352.i	0.191037	−	0.110295i
$160$		0			0
$161$	244307.	+	302268.i	0.0585407	+	0.0724294i
$162$		0			0
$163$	−882721.	−	1.52892e6i	−0.203827	−	0.353038i	0.745932	−	0.666022i	$-0.232005\pi$
$163$	−882721.	−	1.52892e6i	−0.203827	−	0.353038i	−0.949758	+	0.312985i	$0.898671\pi$
$164$		0			0
$165$	−2.88841e6	+	5.00287e6i	−0.642994	+	1.11370i
$166$		0			0
$167$		−	5.65725e6i		−	1.21466i	−0.794449	−	0.607331i	$-0.792240\pi$
$167$		−	5.65725e6i		−	1.21466i	0.794449	−	0.607331i	$-0.207760\pi$
$168$		0			0
$169$	835389.			0.173073
$170$		0			0
$171$	1.30160e6	+	751480.i	0.260309	+	0.150290i
$172$		0			0
$173$	−6.76175e6	+	3.90390e6i	−1.30593	+	0.753981i	−0.981415	−	0.191899i	$-0.938536\pi$
$173$	−6.76175e6	+	3.90390e6i	−1.30593	+	0.753981i	−0.324518	+	0.945879i	$0.605202\pi$
$174$		0			0
$175$	2.30641e6	−	5.99173e6i	0.430350	−	1.11799i
$176$		0			0
$177$	1.50120e6	+	2.60016e6i	0.270720	+	0.468900i
$178$		0			0
$179$	4.28458e6	−	7.42111e6i	0.747050	−	1.29393i	−0.202181	−	0.979348i	$-0.564803\pi$
$179$	4.28458e6	−	7.42111e6i	0.747050	−	1.29393i	0.949231	−	0.314580i	$-0.101864\pi$
$180$		0			0
$181$		−	5.65435e6i		−	0.953558i	−0.879023	−	0.476779i	$-0.841804\pi$
$181$		−	5.65435e6i		−	0.953558i	0.879023	−	0.476779i	$-0.158196\pi$
$182$		0			0
$183$	5.89313e6			0.961597
$184$		0			0
$185$	5.46818e6	+	3.15706e6i	0.863630	+	0.498617i
$186$		0			0
$187$	−4.88431e6	+	2.81996e6i	−0.746927	+	0.431239i
$188$		0			0
$189$	202059.	+	1.28347e6i	0.0299290	+	0.190109i
$190$		0			0
$191$	−3.54466e6	−	6.13953e6i	−0.508715	−	0.881120i	−0.999949	−	0.0100923i	$-0.996787\pi$
$191$	−3.54466e6	−	6.13953e6i	−0.508715	−	0.881120i	0.491234	−	0.871027i	$-0.336546\pi$
$192$		0			0
$193$	1.81840e6	−	3.14956e6i	0.252940	−	0.438104i	−0.711394	−	0.702793i	$-0.751936\pi$
$193$	1.81840e6	−	3.14956e6i	0.252940	−	0.438104i	0.964334	+	0.264689i	$0.0852692\pi$
$194$		0			0
$195$		−	5.77147e6i		−	0.778364i
$196$		0			0
$197$	−7.98407e6			−1.04430			−0.522150	−	0.852854i	$-0.674870\pi$
$197$	−7.98407e6			−1.04430			−0.522150	+	0.852854i	$0.674870\pi$
$198$		0			0
$199$	5.59246e6	+	3.22881e6i	0.709650	+	0.409716i	0.810931	−	0.585141i	$-0.198961\pi$
$199$	5.59246e6	+	3.22881e6i	0.709650	+	0.409716i	−0.101282	+	0.994858i	$0.532294\pi$
$200$		0			0
$201$	686462.	−	396329.i	0.0845334	−	0.0488054i
$202$		0			0
$203$	−1.05735e7	+	1.66460e6i	−1.26396	+	0.198986i
$204$		0			0
$205$	1.16243e6	+	2.01338e6i	0.134929	+	0.233703i
$206$		0			0
$207$	−137672.	+	238455.i	−0.0155215	+	0.0268841i
$208$		0			0
$209$		−	1.23682e7i		−	1.35478i
$210$		0			0
$211$	−8.18132e6			−0.870916			−0.435458	−	0.900209i	$-0.643413\pi$
$211$	−8.18132e6			−0.870916			−0.435458	+	0.900209i	$0.643413\pi$
$212$		0			0
$213$	−5.12229e6	−	2.95736e6i	−0.530061	−	0.306031i
$214$		0			0
$215$	−1.70551e7	+	9.84675e6i	−1.71608	+	0.990781i
$216$		0			0
$217$	−1.72639e7	−	6.64543e6i	−1.68951	−	0.650345i
$218$		0			0
$219$	3.83290e6	+	6.63878e6i	0.364918	+	0.632056i
$220$		0			0
$221$	2.81735e6	−	4.87979e6i	0.261014	−	0.452089i
$222$		0			0
$223$			6.09527e6i			0.549640i	0.961496	+	0.274820i	$0.0886183\pi$
$223$			6.09527e6i			0.549640i	−0.961496	+	0.274820i	$0.911382\pi$
$224$		0			0
$225$	4.54850e6			0.399319
$226$		0			0
$227$	−3.98383e6	−	2.30007e6i	−0.340583	−	0.196636i	0.319947	−	0.947436i	$-0.396335\pi$
$227$	−3.98383e6	−	2.30007e6i	−0.340583	−	0.196636i	−0.660530	+	0.750800i	$0.729668\pi$
$228$		0			0
$229$	1.72251e7	−	9.94490e6i	1.43435	−	0.828121i	0.436899	−	0.899510i	$-0.356077\pi$
$229$	1.72251e7	−	9.94490e6i	1.43435	−	0.828121i	0.997449	+	0.0713894i	$0.0227433\pi$
$230$		0			0
$231$	8.31558e6	−	6.72103e6i	0.674616	−	0.545255i
$232$		0			0
$233$	−4.60301e6	−	7.97265e6i	−0.363893	−	0.630282i	0.624705	−	0.780861i	$-0.285219\pi$
$233$	−4.60301e6	−	7.97265e6i	−0.363893	−	0.630282i	−0.988598	+	0.150579i	$0.951886\pi$
$234$		0			0
$235$	−1.27448e7	+	2.20746e7i	−0.982038	+	1.70094i
$236$		0			0
$237$			1.38903e7i			1.04344i
$238$		0			0
$239$	1.35437e7			0.992073			0.496036	−	0.868302i	$-0.334788\pi$
$239$	1.35437e7			0.992073			0.496036	+	0.868302i	$0.334788\pi$
$240$		0			0
$241$	7.96267e6	+	4.59725e6i	0.568863	+	0.328433i	0.756695	−	0.653768i	$-0.226813\pi$
$241$	7.96267e6	+	4.59725e6i	0.568863	+	0.328433i	−0.187832	+	0.982201i	$0.560146\pi$
$242$		0			0
$243$	−797162.	+	460241.i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−1.46189e7	+	1.61753e7i	−0.994068	+	1.09990i
$246$		0			0
$247$	6.17839e6	+	1.07013e7i	0.410000	+	0.710142i
$248$		0			0
$249$	5.61047e6	−	9.71762e6i	0.363414	−	0.629451i
$250$		0			0
$251$			1.71118e7i			1.08212i	0.840984	+	0.541060i	$0.181977\pi$
$251$			1.71118e7i			1.08212i	−0.840984	+	0.541060i	$0.818023\pi$
$252$		0			0
$253$	2.26587e6			0.139918
$254$		0			0
$255$	7.05603e6	+	4.07380e6i	0.425539	+	0.245685i
$256$		0			0
$257$	−1.88138e6	+	1.08622e6i	−0.110835	+	0.0639907i	−0.554393	−	0.832255i	$-0.687049\pi$
$257$	−1.88138e6	+	1.08622e6i	−0.110835	+	0.0639907i	0.443558	+	0.896246i	$0.353716\pi$
$258$		0			0
$259$	−7.34614e6	−	9.08900e6i	−0.422824	−	0.523138i
$260$		0			0
$261$	−3.79156e6	−	6.56718e6i	−0.213254	−	0.369366i
$262$		0			0
$263$	−1.34487e7	+	2.32939e7i	−0.739289	+	1.28049i	0.213527	+	0.976937i	$0.431505\pi$
$263$	−1.34487e7	+	2.32939e7i	−0.739289	+	1.28049i	−0.952816	+	0.303549i	$0.901828\pi$
$264$		0			0
$265$			1.05413e7i			0.566445i
$266$		0			0
$267$	2.13559e6			0.112198
$268$		0			0
$269$	5.03516e6	+	2.90705e6i	0.258676	+	0.149347i	0.623731	−	0.781639i	$-0.285616\pi$
$269$	5.03516e6	+	2.90705e6i	0.258676	+	0.149347i	−0.365054	+	0.930986i	$0.618950\pi$
$270$		0			0
$271$	8.90334e6	−	5.14035e6i	0.447348	−	0.258276i	−0.259362	−	0.965780i	$-0.583512\pi$
$271$	8.90334e6	−	5.14035e6i	0.447348	−	0.258276i	0.706709	+	0.707504i	$0.250179\pi$
$272$		0			0
$273$	−3.83743e6	+	9.96913e6i	−0.188605	+	0.489970i
$274$		0			0
$275$	−1.87153e7	−	3.24159e7i	−0.899911	−	1.55869i
$276$		0			0
$277$	1.17794e7	−	2.04026e7i	0.554224	−	0.959945i	−0.443739	−	0.896156i	$-0.646348\pi$
$277$	1.17794e7	−	2.04026e7i	0.554224	−	0.959945i	0.997963	−	0.0637887i	$-0.0203184\pi$
$278$		0			0
$279$		−	1.31056e7i		−	0.603452i
$280$		0			0
$281$	−3.16438e7			−1.42616			−0.713082	−	0.701081i	$-0.752701\pi$
$281$	−3.16438e7			−1.42616			−0.713082	+	0.701081i	$0.752701\pi$
$282$		0			0
$283$	1.97541e7	+	1.14050e7i	0.871561	+	0.503196i	0.867867	−	0.496797i	$-0.165491\pi$
$283$	1.97541e7	+	1.14050e7i	0.871561	+	0.503196i	0.00369436	+	0.999993i	$0.498824\pi$
$284$		0			0
$285$	−1.54737e7	+	8.93376e6i	−0.668437	+	0.385922i
$286$		0			0
$287$	−669182.	−	4.25063e6i	−0.0283073	−	0.179808i
$288$		0			0
$289$	−8.09153e6	−	1.40149e7i	−0.335226	−	0.580628i
$290$		0			0
$291$	−3.91414e6	+	6.77950e6i	−0.158839	+	0.275118i
$292$		0			0
$293$		−	4.31272e7i		−	1.71454i	−0.514864	−	0.857272i	$-0.672157\pi$
$293$		−	4.31272e7i		−	1.71454i	0.514864	−	0.857272i	$-0.327843\pi$
$294$		0			0
$295$	−3.56933e7			−1.39034
$296$		0			0
$297$	6.56003e6	+	3.78744e6i	0.250401	+	0.144569i
$298$		0			0
$299$	−1.96049e6	+	1.13189e6i	−0.0733415	+	0.0423438i
$300$		0			0
$301$	3.60065e7	−	5.66855e6i	1.32033	−	0.207861i
$302$		0			0
$303$	8.33752e6	+	1.44410e7i	0.299716	+	0.519122i
$304$		0			0
$305$	−3.50294e7	+	6.06727e7i	−1.23462	+	2.13842i
$306$		0			0
$307$			4.10405e7i			1.41840i	0.705010	+	0.709198i	$0.250943\pi$
$307$			4.10405e7i			1.41840i	−0.705010	+	0.709198i	$0.749057\pi$
$308$		0			0
$309$	1.35775e7			0.460198
$310$		0			0
$311$	−3.47644e7	−	2.00712e7i	−1.15572	−	0.667257i	−0.205448	−	0.978668i	$-0.565865\pi$
$311$	−3.47644e7	−	2.00712e7i	−1.15572	−	0.667257i	−0.950275	+	0.311411i	$0.899198\pi$
$312$		0			0
$313$	−7.55864e6	+	4.36398e6i	−0.246496	+	0.142315i	−0.618159	−	0.786053i	$-0.712121\pi$
$313$	−7.55864e6	+	4.36398e6i	−0.246496	+	0.142315i	0.371663	+	0.928368i	$0.378788\pi$
$314$		0			0
$315$	−1.44151e7	−	5.54881e6i	−0.461195	−	0.177529i
$316$		0			0
$317$	−2.02242e7	−	3.50294e7i	−0.634883	−	1.09965i	−0.986540	−	0.163521i	$-0.947715\pi$
$317$	−2.02242e7	−	3.50294e7i	−0.634883	−	1.09965i	0.351657	−	0.936129i	$-0.385618\pi$
$318$		0			0
$319$	−3.12017e7	+	5.40429e7i	−0.961182	+	1.66482i
$320$		0			0
$321$		−	4.90639e6i		−	0.148336i
$322$		0			0
$323$	−1.74441e7			−0.517655
$324$		0			0
$325$	3.23859e7	+	1.86980e7i	0.943422	+	0.544685i
$326$		0			0
$327$	−7.77161e6	+	4.48694e6i	−0.222263	+	0.128324i
$328$		0			0
$329$	3.66915e7	−	2.96557e7i	1.03033	−	0.832762i
$330$		0			0
$331$	−1.85686e7	−	3.21617e7i	−0.512029	−	0.886860i	−0.999903	−	0.0139462i	$-0.995561\pi$
$331$	−1.85686e7	−	3.21617e7i	−0.512029	−	0.886860i	0.487874	−	0.872914i	$-0.337773\pi$
$332$		0			0
$333$	4.13970e6	−	7.17017e6i	0.112108	−	0.194176i
$334$		0			0
$335$			9.42329e6i			0.250650i
$336$		0			0
$337$	−5.15757e7			−1.34758			−0.673791	−	0.738922i	$-0.735335\pi$
$337$	−5.15757e7			−1.34758			−0.673791	+	0.738922i	$0.735335\pi$
$338$		0			0
$339$	−8.81554e6	−	5.08966e6i	−0.226282	−	0.130644i
$340$		0			0
$341$	−9.33997e7	+	5.39243e7i	−2.35550	+	1.35995i
$342$		0			0
$343$	3.60063e7	−	1.82198e7i	0.892270	−	0.451503i
$344$		0			0
$345$	−1.63667e6	−	2.83480e6i	−0.0398570	−	0.0690344i
$346$		0			0
$347$	2.56672e7	−	4.44569e7i	0.614314	−	1.06402i	−0.376190	−	0.926542i	$-0.622766\pi$
$347$	2.56672e7	−	4.44569e7i	0.614314	−	1.06402i	0.990504	−	0.137481i	$-0.0439006\pi$
$348$		0			0
$349$			7.97868e7i			1.87696i	0.345335	+	0.938480i	$0.387765\pi$
$349$			7.97868e7i			1.87696i	−0.345335	+	0.938480i	$0.612235\pi$
$350$		0			0
$351$	−7.56786e6			−0.175006
$352$		0			0
$353$	2.17460e7	+	1.25551e7i	0.494374	+	0.285427i	0.726387	−	0.687286i	$-0.241198\pi$
$353$	2.17460e7	+	1.25551e7i	0.494374	+	0.285427i	−0.232013	+	0.972713i	$0.574531\pi$
$354$		0			0
$355$	6.08949e7	−	3.51577e7i	1.36112	−	0.785842i
$356$		0			0
$357$	−9.47930e6	−	1.17283e7i	−0.208340	−	0.257768i
$358$		0			0
$359$	1.79417e7	+	3.10760e7i	0.387776	+	0.671648i	0.992150	−	0.125053i	$-0.0399100\pi$
$359$	1.79417e7	+	3.10760e7i	0.387776	+	0.671648i	−0.604374	+	0.796701i	$0.706577\pi$
$360$		0			0
$361$	−4.39568e6	+	7.61353e6i	−0.0934338	+	0.161832i
$362$		0			0
$363$		−	3.47195e7i		−	0.725862i
$364$		0			0
$365$	−9.11327e7			−1.87411
$366$		0			0
$367$	−6.88731e7	−	3.97639e7i	−1.39332	−	0.804435i	−0.399640	−	0.916672i	$-0.630865\pi$
$367$	−6.88731e7	−	3.97639e7i	−1.39332	−	0.804435i	−0.993681	+	0.112237i	$0.964198\pi$
$368$		0			0
$369$	2.64005e6	−	1.52424e6i	0.0525453	−	0.0303370i
$370$		0			0
$371$	7.00889e6	−	1.82082e7i	0.137255	−	0.356570i
$372$		0			0
$373$	−3.43975e7	−	5.95783e7i	−0.662828	−	1.14805i	−0.979869	−	0.199640i	$-0.936023\pi$
$373$	−3.43975e7	−	5.95783e7i	−0.662828	−	1.14805i	0.317041	−	0.948412i	$-0.397311\pi$
$374$		0			0
$375$	−4.46773e6	+	7.73833e6i	−0.0847214	+	0.146742i
$376$		0			0
$377$		−	6.23456e7i		−	1.16354i
$378$		0			0
$379$	7.44433e7			1.36744			0.683719	−	0.729745i	$-0.260361\pi$
$379$	7.44433e7			1.36744			0.683719	+	0.729745i	$0.260361\pi$
$380$		0			0
$381$	2.01976e6	+	1.16611e6i	0.0365194	+	0.0210845i
$382$		0			0
$383$	−2.40942e7	+	1.39108e7i	−0.428860	+	0.247603i	−0.698861	−	0.715257i	$-0.746309\pi$
$383$	−2.40942e7	+	1.39108e7i	−0.428860	+	0.247603i	0.270001	+	0.962860i	$0.412976\pi$
$384$		0			0
$385$	1.97676e7	+	1.25564e8i	0.346395	+	2.20030i
$386$		0			0
$387$	1.29116e7	+	2.23635e7i	0.222765	+	0.385840i
$388$		0			0
$389$	3.96552e7	−	6.86848e7i	0.673676	−	1.16684i	−0.303178	−	0.952934i	$-0.598048\pi$
$389$	3.96552e7	−	6.86848e7i	0.673676	−	1.16684i	0.976854	−	0.213907i	$-0.0686190\pi$
$390$		0			0
$391$		−	3.19577e6i		−	0.0534620i
$392$		0			0
$393$	5.94643e7			0.979667
$394$		0			0
$395$	−1.43008e8	−	8.25656e7i	−2.32043	−	1.33970i
$396$		0			0
$397$	−4.36840e7	+	2.52210e7i	−0.698153	+	0.403079i	−0.806659	−	0.591017i	$-0.798727\pi$
$397$	−4.36840e7	+	2.52210e7i	−0.698153	+	0.403079i	0.108506	+	0.994096i	$0.465393\pi$
$398$		0			0
$399$	3.26680e7	−	5.14296e6i	0.514285	−	0.0809645i
$400$		0			0
$401$	3.25487e7	+	5.63760e7i	0.504778	+	0.874301i	0.999985	+	0.00552593i	$0.00175897\pi$
$401$	3.25487e7	+	5.63760e7i	0.504778	+	0.874301i	−0.495207	+	0.868775i	$0.664908\pi$
$402$		0			0
$403$	5.38744e7	−	9.33133e7i	0.823128	−	1.42570i
$404$		0			0
$405$		−	1.09429e7i		−	0.164728i
$406$		0			0
$407$	−6.81331e7			−1.01059
$408$		0			0
$409$	−3.63616e7	−	2.09934e7i	−0.531464	−	0.306841i	0.210149	−	0.977669i	$-0.432605\pi$
$409$	−3.63616e7	−	2.09934e7i	−0.531464	−	0.306841i	−0.741612	+	0.670829i	$0.765939\pi$
$410$		0			0
$411$	2.63929e6	−	1.52380e6i	0.0380156	−	0.0219483i
$412$		0			0
$413$	6.16534e7	+	2.37323e7i	0.875200	+	0.336892i
$414$		0			0
$415$	6.66985e7	+	1.15525e8i	0.933193	+	1.61634i
$416$		0			0
$417$	2.50322e7	−	4.33571e7i	0.345216	−	0.597932i
$418$		0			0
$419$		−	3.38881e6i		−	0.0460687i	−0.999735	−	0.0230343i	$-0.992667\pi$
$419$		−	3.38881e6i		−	0.0460687i	0.999735	−	0.0230343i	$-0.00733270\pi$
$420$		0			0
$421$	5.10502e7			0.684149			0.342075	−	0.939673i	$-0.388870\pi$
$421$	5.10502e7			0.684149			0.342075	+	0.939673i	$0.388870\pi$
$422$		0			0
$423$	2.89454e7	+	1.67116e7i	0.382435	+	0.220799i
$424$		0			0
$425$	−4.57192e7	+	2.63960e7i	−0.595569	+	0.343852i
$426$		0			0
$427$	1.00848e8	−	8.15098e7i	1.29534	−	1.04695i
$428$		0			0
$429$	3.11389e7	+	5.39341e7i	0.394395	+	0.683111i
$430$		0			0
$431$	−7.10962e7	+	1.23142e8i	−0.888004	+	1.53807i	−0.0457722	+	0.998952i	$0.514575\pi$
$431$	−7.10962e7	+	1.23142e8i	−0.888004	+	1.53807i	−0.842232	+	0.539116i	$0.818758\pi$
$432$		0			0
$433$			3.33609e7i			0.410936i	0.978664	+	0.205468i	$0.0658716\pi$
$433$			3.33609e7i			0.410936i	−0.978664	+	0.205468i	$0.934128\pi$
$434$		0			0
$435$	9.01498e7			1.09521
$436$		0			0
$437$	6.06934e6	+	3.50413e6i	0.0727272	+	0.0419891i
$438$		0			0
$439$	1.15226e7	−	6.65258e6i	0.136194	−	0.0786315i	−0.430355	−	0.902660i	$-0.641612\pi$
$439$	1.15226e7	−	6.65258e6i	0.136194	−	0.0786315i	0.566549	+	0.824028i	$0.308278\pi$
$440$		0			0
$441$	2.12099e7	+	1.91691e7i	0.247300	+	0.223504i
$442$		0			0
$443$	7.16424e6	+	1.24088e7i	0.0824060	+	0.142731i	0.904283	−	0.426934i	$-0.140406\pi$
$443$	7.16424e6	+	1.24088e7i	0.0824060	+	0.142731i	−0.821877	+	0.569665i	$0.807073\pi$
$444$		0			0
$445$	−1.26942e7	+	2.19869e7i	−0.144054	+	0.249508i
$446$		0			0
$447$			7.89664e7i			0.884138i
$448$		0			0
$449$	−2.67415e7			−0.295425			−0.147712	−	0.989030i	$-0.547191\pi$
$449$	−2.67415e7			−0.295425			−0.147712	+	0.989030i	$0.547191\pi$
$450$		0			0
$451$	−2.17256e7	−	1.25433e7i	−0.236833	−	0.136736i
$452$		0			0
$453$	−5.62895e7	+	3.24988e7i	−0.605526	+	0.349601i
$454$		0			0
$455$	−7.98271e7	−	9.87659e7i	−0.847454	−	1.04851i
$456$		0			0
$457$	−9.89131e6	−	1.71323e7i	−0.103635	−	0.179501i	0.809545	−	0.587058i	$-0.199714\pi$
$457$	−9.89131e6	−	1.71323e7i	−0.103635	−	0.179501i	−0.913180	+	0.407557i	$0.866381\pi$
$458$		0			0
$459$	5.34178e6	−	9.25224e6i	0.0552393	−	0.0956772i
$460$		0			0
$461$			1.07290e8i			1.09511i	0.836769	+	0.547556i	$0.184442\pi$
$461$			1.07290e8i			1.09511i	−0.836769	+	0.547556i	$0.815558\pi$
$462$		0			0
$463$	−1.42791e6			−0.0143865			−0.00719327	−	0.999974i	$-0.502290\pi$
$463$	−1.42791e6			−0.0143865			−0.00719327	+	0.999974i	$0.502290\pi$
$464$		0			0
$465$	1.34928e8	+	7.79008e7i	1.34197	+	0.774788i
$466$		0			0
$467$	1.04411e7	−	6.02819e6i	0.102517	−	0.0591883i	−0.447865	−	0.894101i	$-0.647815\pi$
$467$	1.04411e7	−	6.02819e6i	0.102517	−	0.0591883i	0.550382	+	0.834913i	$0.314482\pi$
$468$		0			0
$469$	6.26551e6	−	1.62770e7i	0.0607349	−	0.157781i
$470$		0			0
$471$	4.94825e7	+	8.57063e7i	0.473576	+	0.820257i
$472$		0			0
$473$	1.06252e8	−	1.84035e8i	1.00405	−	1.73907i
$474$		0			0
$475$		−	1.15772e8i		−	1.08025i
$476$		0			0
$477$	1.38223e7			0.127358
$478$		0			0
$479$	6.11919e7	+	3.53292e7i	0.556785	+	0.321460i	0.751854	−	0.659329i	$-0.229160\pi$
$479$	6.11919e7	+	3.53292e7i	0.556785	+	0.321460i	−0.195069	+	0.980790i	$0.562493\pi$
$480$		0			0
$481$	5.89504e7	−	3.40350e7i	0.529726	−	0.305838i
$482$		0			0
$483$	942195.	+	5.98481e6i	0.00836180	+	0.0531140i
$484$		0			0
$485$	−4.65322e7	−	8.05961e7i	−0.407876	−	0.706462i
$486$		0			0
$487$	−1.21936e7	+	2.11199e7i	−0.105571	+	0.182854i	−0.913971	−	0.405779i	$-0.867000\pi$
$487$	−1.21936e7	+	2.11199e7i	−0.105571	+	0.182854i	0.808401	+	0.588633i	$0.200334\pi$
$488$		0			0
$489$		−	2.75205e7i		−	0.235359i
$490$		0			0
$491$	1.48657e8			1.25586			0.627931	−	0.778269i	$-0.283902\pi$
$491$	1.48657e8			1.25586			0.627931	+	0.778269i	$0.283902\pi$
$492$		0			0
$493$	7.62218e7	+	4.40067e7i	0.636119	+	0.367264i
$494$		0			0
$495$	−7.79871e7	+	4.50258e7i	−0.642994	+	0.371233i
$496$		0			0
$497$	−1.28561e8	+	2.02395e7i	−1.04722	+	0.164866i
$498$		0			0
$499$	−9.65049e7	−	1.67151e8i	−0.776690	−	1.34527i	−0.933840	−	0.357692i	$-0.883564\pi$
$499$	−9.65049e7	−	1.67151e8i	−0.776690	−	1.34527i	0.157149	−	0.987575i	$-0.449770\pi$
$500$		0			0
$501$	4.40939e7	−	7.63728e7i	0.350643	−	0.607331i
$502$		0			0
$503$			7.31173e7i			0.574535i	0.957850	+	0.287267i	$0.0927468\pi$
$503$			7.31173e7i			0.574535i	−0.957850	+	0.287267i	$0.907253\pi$
$504$		0			0
$505$	−1.98237e8			−1.53925
$506$		0			0
$507$	1.12777e7	+	6.51121e6i	0.0865363	+	0.0499618i
$508$		0			0
$509$	3.77878e7	−	2.18168e7i	0.286549	−	0.165439i	−0.349836	−	0.936811i	$-0.613763\pi$
$509$	3.77878e7	−	2.18168e7i	0.286549	−	0.165439i	0.636384	+	0.771372i	$0.280429\pi$
$510$		0			0
$511$	1.57415e8	+	6.05938e7i	1.17973	+	0.454115i
$512$		0			0
$513$	1.17144e7	+	2.02900e7i	0.0867698	+	0.150290i
$514$		0			0
$515$	−8.07062e7	+	1.39787e8i	−0.590861	+	1.02340i
$516$		0			0
$517$		−	2.75048e8i		−	1.99038i
$518$		0			0
$519$	−1.21712e8			−0.870622
$520$		0			0
$521$	−1.53614e8	−	8.86894e7i	−1.08622	−	0.627131i	−0.153655	−	0.988125i	$-0.549104\pi$
$521$	−1.53614e8	−	8.86894e7i	−1.08622	−	0.627131i	−0.932568	+	0.360994i	$0.882438\pi$
$522$		0			0
$523$	−3.48534e7	+	2.01226e7i	−0.243635	+	0.140663i	−0.616846	−	0.787084i	$-0.711590\pi$
$523$	−3.48534e7	+	2.01226e7i	−0.243635	+	0.140663i	0.373211	+	0.927746i	$0.378257\pi$
$524$		0			0
$525$	7.78374e7	−	6.29117e7i	0.537911	−	0.434764i
$526$		0			0
$527$	7.60546e7	+	1.31730e8i	0.519630	+	0.900025i
$528$		0			0
$529$	7.33760e7	−	1.27091e8i	0.495663	−	0.858514i
$530$		0			0
$531$			4.68029e7i			0.312600i
$532$		0			0
$533$	2.50634e7			0.165523
$534$		0			0
$535$	5.05137e7	+	2.91641e7i	0.329874	+	0.190453i
$536$		0			0
$537$	1.15684e8	−	6.67900e7i	0.747050	−	0.431309i
$538$		0			0
$539$	4.93420e7	−	2.30031e8i	0.315101	−	1.46899i
$540$		0			0
$541$	5.88250e7	+	1.01888e8i	0.371510	+	0.643473i	0.989798	−	0.142478i	$-0.0455070\pi$
$541$	5.88250e7	+	1.01888e8i	0.371510	+	0.643473i	−0.618288	+	0.785951i	$0.712174\pi$
$542$		0			0
$543$	4.40713e7	−	7.63337e7i	0.275268	−	0.476779i
$544$		0			0
$545$		−	1.06683e8i		−	0.659033i
$546$		0			0
$547$	2.43639e8			1.48862			0.744311	−	0.667833i	$-0.232778\pi$
$547$	2.43639e8			1.48862			0.744311	+	0.667833i	$0.232778\pi$
$548$		0			0
$549$	7.95573e7	+	4.59324e7i	0.480798	+	0.277589i
$550$		0			0
$551$	−1.67153e8	+	9.65058e7i	−0.999216	+	0.576897i
$552$		0			0
$553$	1.92122e8	+	2.37702e8i	1.13606	+	1.40559i
$554$		0			0
$555$	4.92136e7	+	8.52405e7i	0.287877	+	0.498617i
$556$		0			0
$557$	1.26745e8	−	2.19529e8i	0.733443	−	1.27036i	−0.221961	−	0.975056i	$-0.571246\pi$
$557$	1.26745e8	−	2.19529e8i	0.733443	−	1.27036i	0.955403	−	0.295304i	$-0.0954210\pi$
$558$		0			0
$559$			2.12308e8i			1.21543i
$560$		0			0
$561$	−8.79176e7			−0.497952
$562$		0			0
$563$	−1.12968e8	−	6.52220e7i	−0.633038	−	0.365485i	0.148890	−	0.988854i	$-0.452430\pi$
$563$	−1.12968e8	−	6.52220e7i	−0.633038	−	0.365485i	−0.781928	+	0.623369i	$0.785763\pi$
$564$		0			0
$565$	1.04801e8	−	6.05069e7i	0.581059	−	0.335475i
$566$		0			0
$567$	−7.27590e6	+	1.89018e7i	−0.0399151	+	0.103694i
$568$		0			0
$569$	1.27324e8	+	2.20531e8i	0.691151	+	1.19711i	0.971461	+	0.237199i	$0.0762295\pi$
$569$	1.27324e8	+	2.20531e8i	0.691151	+	1.19711i	−0.280310	+	0.959910i	$0.590437\pi$
$570$		0			0
$571$	−1.20654e8	+	2.08979e8i	−0.648088	+	1.12252i	0.335490	+	0.942044i	$0.391098\pi$
$571$	−1.20654e8	+	2.08979e8i	−0.648088	+	1.12252i	−0.983579	+	0.180479i	$0.942235\pi$
$572$		0			0
$573$		−	1.10512e8i		−	0.587413i
$574$		0			0
$575$	2.12095e7			0.111565
$576$		0			0
$577$	1.24213e8	+	7.17141e7i	0.646603	+	0.373317i	0.787154	−	0.616757i	$-0.211554\pi$
$577$	1.24213e8	+	7.17141e7i	0.646603	+	0.373317i	−0.140550	+	0.990074i	$0.544887\pi$
$578$		0			0
$579$	4.90967e7	−	2.83460e7i	0.252940	−	0.146035i
$580$		0			0
$581$	−3.83968e7	−	2.43896e8i	−0.195779	−	1.24359i
$582$		0			0
$583$	−5.68737e7	−	9.85081e7i	−0.287016	−	0.497126i
$584$		0			0
$585$	4.49842e7	−	7.79149e7i	0.224694	−	0.389182i
$586$		0			0
$587$		−	2.03337e8i		−	1.00531i	−0.864486	−	0.502656i	$-0.832356\pi$
$587$		−	2.03337e8i		−	1.00531i	0.864486	−	0.502656i	$-0.167644\pi$
$588$		0			0
$589$	−3.33573e8			−1.63247
$590$		0			0
$591$	−1.07785e8	−	6.22296e7i	−0.522150	−	0.301464i
$592$		0			0
$593$	6.60555e7	−	3.81372e7i	0.316771	−	0.182888i	−0.333182	−	0.942863i	$-0.608122\pi$
$593$	6.60555e7	−	3.81372e7i	0.316771	−	0.182888i	0.649952	+	0.759975i	$0.274789\pi$
$594$		0			0
$595$	1.77094e8	−	2.78801e7i	0.840724	−	0.132356i
$596$		0			0
$597$	5.03322e7	+	8.71779e7i	0.236550	+	0.409716i
$598$		0			0
$599$	5.64433e7	−	9.77627e7i	0.262623	−	0.454876i	−0.704315	−	0.709887i	$-0.748746\pi$
$599$	5.64433e7	−	9.77627e7i	0.262623	−	0.454876i	0.966938	+	0.255012i	$0.0820793\pi$
$600$		0			0
$601$		−	1.92589e8i		−	0.887174i	−0.896231	−	0.443587i	$-0.853706\pi$
$601$		−	1.92589e8i		−	0.887174i	0.896231	−	0.443587i	$-0.146294\pi$
$602$		0			0
$603$	1.23563e7			0.0563556
$604$		0			0
$605$	3.57455e8	+	2.06377e8i	1.61419	+	0.931953i
$606$		0			0
$607$	3.24482e8	−	1.87340e8i	1.45086	−	0.837652i	0.452325	−	0.891853i	$-0.350595\pi$
$607$	3.24482e8	−	1.87340e8i	1.45086	−	0.837652i	0.998530	+	0.0542014i	$0.0172613\pi$
$608$		0			0
$609$	−1.55717e8	−	5.99403e7i	−0.689420	−	0.265379i
$610$		0			0
$611$	1.37397e8	+	2.37978e8i	0.602355	+	1.04331i
$612$		0			0
$613$	−1.51973e8	+	2.63225e8i	−0.659758	+	1.14274i	0.320920	+	0.947106i	$0.396008\pi$
$613$	−1.51973e8	+	2.63225e8i	−0.659758	+	1.14274i	−0.980678	+	0.195629i	$0.937325\pi$
$614$		0			0
$615$			3.62409e7i			0.155802i
$616$		0			0
$617$	−1.38304e8			−0.588815			−0.294408	−	0.955680i	$-0.595122\pi$
$617$	−1.38304e8			−0.588815			−0.294408	+	0.955680i	$0.595122\pi$
$618$		0			0
$619$	−1.10323e7	−	6.36951e6i	−0.0465152	−	0.0268556i	0.476562	−	0.879141i	$-0.341883\pi$
$619$	−1.10323e7	−	6.36951e6i	−0.0465152	−	0.0268556i	−0.523077	+	0.852285i	$0.675216\pi$
$620$		0			0
$621$	−3.71714e6	+	2.14609e6i	−0.0155215	+	0.00896136i
$622$		0			0
$623$	3.65459e7	−	2.95380e7i	0.151138	−	0.122157i
$624$		0			0
$625$	9.31218e7	+	1.61292e8i	0.381427	+	0.660651i
$626$		0			0
$627$	9.64008e7	−	1.66971e8i	0.391091	−	0.677390i
$628$		0			0
$629$			9.60946e7i			0.386142i
$630$		0			0
$631$	1.81591e8			0.722781			0.361390	−	0.932415i	$-0.382302\pi$
$631$	1.81591e8			0.722781			0.361390	+	0.932415i	$0.382302\pi$
$632$		0			0
$633$	−1.10448e8	−	6.37671e7i	−0.435458	−	0.251412i
$634$		0			0
$635$	−2.40113e7	+	1.38629e7i	−0.0937766	+	0.0541420i
$636$		0			0
$637$	7.22171e7	+	2.23676e8i	0.279397	+	0.865370i
$638$		0			0
$639$	−4.61006e7	−	7.98486e7i	−0.176687	−	0.306031i
$640$		0			0
$641$	−3.78572e7	+	6.55706e7i	−0.143739	+	0.248963i	−0.928902	−	0.370326i	$-0.879246\pi$
$641$	−3.78572e7	+	6.55706e7i	−0.143739	+	0.248963i	0.785163	+	0.619289i	$0.212579\pi$
$642$		0			0
$643$		−	3.40163e8i		−	1.27954i	−0.768566	−	0.639771i	$-0.779029\pi$
$643$		−	3.40163e8i		−	1.27954i	0.768566	−	0.639771i	$-0.220971\pi$
$644$		0			0
$645$	−3.06991e8			−1.14405
$646$		0			0
$647$	1.00798e8	+	5.81957e7i	0.372168	+	0.214871i	0.674405	−	0.738362i	$-0.264400\pi$
$647$	1.00798e8	+	5.81957e7i	0.372168	+	0.214871i	−0.302237	+	0.953233i	$0.597734\pi$
$648$		0			0
$649$	3.33552e8	−	1.92576e8i	1.22019	−	0.704480i
$650$		0			0
$651$	−1.81267e8	−	2.24272e8i	−0.657016	−	0.812892i
$652$		0			0
$653$	−1.71197e8	−	2.96523e8i	−0.614834	−	1.06492i	−0.990414	−	0.138133i	$-0.955890\pi$
$653$	−1.71197e8	−	2.96523e8i	−0.614834	−	1.06492i	0.375580	−	0.926790i	$-0.377444\pi$
$654$		0			0
$655$	−3.53462e8	+	6.12214e8i	−1.25782	+	2.17861i
$656$		0			0
$657$			1.19498e8i			0.421371i
$658$		0			0
$659$	−5.14540e8			−1.79789			−0.898944	−	0.438064i	$-0.855664\pi$
$659$	−5.14540e8			−1.79789			−0.898944	+	0.438064i	$0.855664\pi$
$660$		0			0
$661$	2.88588e8	+	1.66616e8i	0.999248	+	0.576916i	0.908026	−	0.418914i	$-0.137589\pi$
$661$	2.88588e8	+	1.66616e8i	0.999248	+	0.576916i	0.0912225	+	0.995831i	$0.470923\pi$
$662$		0			0
$663$	7.60684e7	−	4.39181e7i	0.261014	−	0.150696i
$664$		0			0
$665$	−1.41233e8	+	3.66903e8i	−0.480253	+	1.24763i
$666$		0			0
$667$	−1.76800e7	−	3.06226e7i	−0.0595804	−	0.103196i
$668$		0			0
$669$	−4.75079e7	+	8.22862e7i	−0.158667	+	0.274820i
$670$		0			0
$671$		−	7.55978e8i		−	2.50231i
$672$		0			0
$673$	−3.38288e7			−0.110979			−0.0554896	−	0.998459i	$-0.517672\pi$
$673$	−3.38288e7			−0.110979			−0.0554896	+	0.998459i	$0.517672\pi$
$674$		0			0
$675$	6.14047e7	+	3.54520e7i	0.199660	+	0.115274i
$676$		0			0
$677$	−3.43198e8	+	1.98145e8i	−1.10606	+	0.638584i	−0.937806	−	0.347160i	$-0.887146\pi$
$677$	−3.43198e8	+	1.98145e8i	−1.10606	+	0.638584i	−0.168254	+	0.985744i	$0.553813\pi$
$678$		0			0
$679$	2.67875e7	+	1.70154e8i	0.0855703	+	0.543541i
$680$		0			0
$681$	−3.58545e7	−	6.21018e7i	−0.113528	−	0.196636i
$682$		0			0
$683$	−2.53277e7	+	4.38688e7i	−0.0794938	+	0.137687i	−0.903032	−	0.429574i	$-0.858664\pi$
$683$	−2.53277e7	+	4.38688e7i	−0.0794938	+	0.137687i	0.823538	+	0.567261i	$0.191997\pi$
$684$		0			0
$685$			3.62304e7i			0.112720i
$686$		0			0
$687$	3.10051e8			0.956232
$688$		0			0
$689$	9.84169e7	+	5.68210e7i	0.300893	+	0.173721i
$690$		0			0
$691$	1.99858e8	−	1.15388e8i	0.605740	−	0.349724i	−0.165556	−	0.986200i	$-0.552942\pi$
$691$	1.99858e8	−	1.15388e8i	0.605740	−	0.349724i	0.771296	+	0.636476i	$0.219609\pi$
$692$		0			0
$693$	1.64646e8	−	2.59203e7i	0.494710	−	0.0778827i
$694$		0			0
$695$	2.97588e8	+	5.15438e8i	0.886464	+	1.53540i
$696$		0			0
$697$	−1.76910e7	+	3.06417e7i	−0.0522461	+	0.0904929i
$698$		0			0
$699$		−	1.43508e8i		−	0.420188i
$700$		0			0
$701$	1.99997e8			0.580591			0.290295	−	0.956937i	$-0.406246\pi$
$701$	1.99997e8			0.580591			0.290295	+	0.956937i	$0.406246\pi$
$702$		0			0
$703$	−1.82501e8	−	1.05367e8i	−0.525289	−	0.303276i
$704$		0			0
$705$	−3.44109e8	+	1.98671e8i	−0.982038	+	0.566980i
$706$		0			0
$707$	3.42416e8	+	1.31807e8i	0.968939	+	0.372975i
$708$		0			0
$709$	−1.91022e8	−	3.30860e8i	−0.535975	−	0.928335i	−0.999115	−	0.0420507i	$-0.986611\pi$
$709$	−1.91022e8	−	3.30860e8i	−0.535975	−	0.928335i	0.463141	−	0.886285i	$-0.346722\pi$
$710$		0			0
$711$	−1.08264e8	+	1.87519e8i	−0.301215	+	0.521720i
$712$		0			0
$713$		−	6.11108e7i		−	0.168597i
$714$		0			0
$715$	−7.40371e8			−2.02550
$716$		0			0
$717$	1.82840e8	+	1.05563e8i	0.496036	+	0.286387i
$718$		0			0
$719$	1.26655e8	−	7.31245e7i	0.340751	−	0.196733i	−0.319853	−	0.947467i	$-0.603634\pi$
$719$	1.26655e8	−	7.31245e7i	0.340751	−	0.196733i	0.660604	+	0.750735i	$0.270300\pi$
$720$		0			0
$721$	2.32349e8	−	1.87795e8i	0.619919	−	0.501047i
$722$		0			0
$723$	7.16640e7	+	1.24126e8i	0.189621	+	0.328433i
$724$		0			0
$725$	−2.92061e8	+	5.05865e8i	−0.766407	+	1.32746i
$726$		0			0
$727$			7.94751e7i			0.206837i	0.994638	+	0.103418i	$0.0329781\pi$
$727$			7.94751e7i			0.206837i	−0.994638	+	0.103418i	$0.967022\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	−2.59562e8	−	1.49858e8i	−0.664490	−	0.383643i
$732$		0			0
$733$	−2.11560e8	+	1.22144e8i	−0.537181	+	0.310142i	−0.743936	−	0.668251i	$-0.767043\pi$
$733$	−2.11560e8	+	1.22144e8i	−0.537181	+	0.310142i	0.206755	+	0.978393i	$0.433710\pi$
$734$		0			0
$735$	−3.23429e8	+	1.04424e8i	−0.814549	+	0.262989i
$736$		0			0
$737$	−5.08415e7	−	8.80601e7i	−0.127004	−	0.219977i
$738$		0			0
$739$	−6.11505e7	+	1.05916e8i	−0.151519	+	0.262438i	−0.931786	−	0.363008i	$-0.881750\pi$
$739$	−6.11505e7	+	1.05916e8i	−0.151519	+	0.262438i	0.780267	+	0.625446i	$0.215083\pi$
$740$		0			0
$741$			1.92623e8i			0.473428i
$742$		0			0
$743$	−5.14159e8			−1.25352			−0.626759	−	0.779213i	$-0.715619\pi$
$743$	−5.14159e8			−1.25352			−0.626759	+	0.779213i	$0.715619\pi$
$744$		0			0
$745$	−8.12998e8	−	4.69385e8i	−1.96617	−	1.13517i
$746$		0			0
$747$	1.51483e8	−	8.74586e7i	0.363414	−	0.209817i
$748$		0			0
$749$	−6.78619e7	−	8.39620e7i	−0.161503	−	0.199819i
$750$		0			0
$751$	−2.08037e8	−	3.60330e8i	−0.491157	−	0.850709i	0.508791	−	0.860890i	$-0.330092\pi$
$751$	−2.08037e8	−	3.60330e8i	−0.491157	−	0.850709i	−0.999948	+	0.0101813i	$0.996759\pi$
$752$		0			0
$753$	−1.33374e8	+	2.31010e8i	−0.312381	+	0.541060i
$754$		0			0
$755$		−	7.72705e8i		−	1.79545i
$756$		0			0
$757$	−4.98643e8			−1.14948			−0.574741	−	0.818335i	$-0.694897\pi$
$757$	−4.98643e8			−1.14948			−0.574741	+	0.818335i	$0.694897\pi$
$758$		0			0
$759$	3.05893e7	+	1.76607e7i	0.0699590	+	0.0403908i
$760$		0			0
$761$	7.89174e7	−	4.55630e7i	0.179068	−	0.103385i	−0.407787	−	0.913077i	$-0.633699\pi$
$761$	7.89174e7	−	4.55630e7i	0.179068	−	0.103385i	0.586855	+	0.809692i	$0.300366\pi$
$762$		0			0
$763$	−7.09335e7	+	1.84276e8i	−0.159690	+	0.414853i
$764$		0			0
$765$	6.35042e7	+	1.09993e8i	0.141846	+	0.245685i
$766$		0			0
$767$	−1.92398e8	+	3.33243e8i	−0.426397	+	0.738542i
$768$		0			0
$769$		−	5.37166e8i		−	1.18122i	−0.806959	−	0.590608i	$-0.798888\pi$
$769$		−	5.37166e8i		−	1.18122i	0.806959	−	0.590608i	$-0.201112\pi$
$770$		0			0
$771$	−3.38649e7			−0.0738901
$772$		0			0
$773$	2.04387e8	+	1.18003e8i	0.442502	+	0.255478i	0.704658	−	0.709547i	$-0.251100\pi$
$773$	2.04387e8	+	1.18003e8i	0.442502	+	0.255478i	−0.262157	+	0.965025i	$0.584434\pi$
$774$		0			0
$775$	−8.74262e8	+	5.04755e8i	−1.87818	+	1.08437i
$776$		0			0
$777$	−2.83311e7	−	1.79959e8i	−0.0603950	−	0.383628i
$778$		0			0
$779$	−3.87960e7	−	6.71967e7i	−0.0820682	−	0.142146i
$780$		0			0
$781$	−3.79373e8	+	6.57093e8i	−0.796367	+	1.37935i
$782$		0			0
$783$		−	1.18209e8i		−	0.246244i
$784$		0			0
$785$	−1.17652e9			−2.43215
$786$		0			0
$787$	−7.35575e7	−	4.24685e7i	−0.150905	−	0.0871249i	0.422646	−	0.906295i	$-0.361101\pi$
$787$	−7.35575e7	−	4.24685e7i	−0.150905	−	0.0871249i	−0.573551	+	0.819170i	$0.694435\pi$
$788$		0			0
$789$	−3.63116e8	+	2.09645e8i	−0.739289	+	0.426829i
$790$		0			0
$791$	−2.21255e8	+	3.48324e7i	−0.447058	+	0.0703808i
$792$		0			0
$793$	3.77639e8	+	6.54090e8i	0.757281	+	1.31165i
$794$		0			0
$795$	−8.21615e7	+	1.42308e8i	−0.163519	+	0.283222i
$796$		0			0
$797$		−	4.22019e8i		−	0.833599i	−0.908999	−	0.416799i	$-0.863152\pi$
$797$		−	4.22019e8i		−	0.833599i	0.908999	−	0.416799i	$-0.136848\pi$
$798$		0			0
$799$	−3.87926e8			−0.760516
$800$		0			0
$801$	2.88305e7	+	1.66453e7i	0.0560988	+	0.0323887i
$802$		0			0
$803$	8.51630e8	−	4.91689e8i	1.64477	−	0.949606i
$804$		0			0
$805$	−6.72171e7	−	2.58740e7i	−0.128852	−	0.0495993i
$806$		0			0
$807$	4.53164e7	+	7.84904e7i	0.0862254	+	0.149347i
$808$		0			0
$809$	−4.75061e8	+	8.22830e8i	−0.897230	+	1.55405i	−0.0662102	+	0.997806i	$0.521091\pi$
$809$	−4.75061e8	+	8.22830e8i	−0.897230	+	1.55405i	−0.831020	+	0.556243i	$0.812243\pi$
$810$		0			0
$811$		−	7.15589e8i		−	1.34153i	−0.741669	−	0.670766i	$-0.765965\pi$
$811$		−	7.15589e8i		−	1.34153i	0.741669	−	0.670766i	$-0.234035\pi$
$812$		0			0
$813$	1.60260e8			0.298232
$814$		0			0
$815$	2.83337e8	+	1.63585e8i	0.523397	+	0.302183i
$816$		0			0
$817$	5.69213e8	−	3.28636e8i	1.04378	−	0.602627i
$818$		0			0
$819$	−1.29507e8	+	1.04673e8i	−0.235745	+	0.190539i
$820$		0			0
$821$	2.17031e8	+	3.75909e8i	0.392186	+	0.679287i	0.992738	−	0.120300i	$-0.0383855\pi$
$821$	2.17031e8	+	3.75909e8i	0.392186	+	0.679287i	−0.600551	+	0.799586i	$0.705052\pi$
$822$		0			0
$823$	−8.84134e7	+	1.53137e8i	−0.158606	+	0.274713i	−0.934366	−	0.356315i	$-0.884033\pi$
$823$	−8.84134e7	+	1.53137e8i	−0.158606	+	0.274713i	0.775760	+	0.631028i	$0.217367\pi$
$824$		0			0
$825$		−	5.83486e8i		−	1.03913i
$826$		0			0
$827$	6.37823e8			1.12767			0.563837	−	0.825886i	$-0.309325\pi$
$827$	6.37823e8			1.12767			0.563837	+	0.825886i	$0.309325\pi$
$828$		0			0
$829$	3.44967e8	+	1.99167e8i	0.605500	+	0.349586i	0.771202	−	0.636590i	$-0.219656\pi$
$829$	3.44967e8	+	1.99167e8i	0.605500	+	0.349586i	−0.165702	+	0.986176i	$0.552989\pi$
$830$		0			0
$831$	3.18045e8	−	1.83623e8i	0.554224	−	0.319982i
$832$		0			0
$833$	−3.24434e8	−	6.95916e7i	−0.561296	−	0.120399i
$834$		0			0
$835$	5.24197e8	+	9.07937e8i	0.900400	+	1.55954i
$836$		0			0
$837$	1.02148e8	−	1.76925e8i	0.174202	−	0.301726i
$838$		0			0
$839$			1.10819e9i			1.87642i	0.346072	+	0.938208i	$0.387515\pi$
$839$			1.10819e9i			1.87642i	−0.346072	+	0.938208i	$0.612485\pi$
$840$		0			0
$841$	3.79008e8			0.637178
$842$		0			0
$843$	−4.27191e8	−	2.46639e8i	−0.713082	−	0.411698i
$844$		0			0
$845$	−1.34072e8	+	7.74066e7i	−0.222213	+	0.128295i
$846$		0			0
$847$	−4.80217e8	−	5.94147e8i	−0.790291	−	0.977786i
$848$		0			0
$849$	1.77787e8	+	3.07936e8i	0.290520	+	0.503196i
$850$		0			0
$851$	1.93033e7	−	3.34343e7i	0.0313215	−	0.0542505i
$852$		0			0
$853$		−	1.05321e9i		−	1.69695i	−0.529233	−	0.848477i	$-0.677520\pi$
$853$		−	1.05321e9i		−	1.69695i	0.529233	−	0.848477i	$-0.322480\pi$
$854$		0			0
$855$	−2.78527e8			−0.445625
$856$		0			0
$857$	8.17338e8	+	4.71890e8i	1.29855	+	0.749719i	0.980154	−	0.198239i	$-0.0635221\pi$
$857$	8.17338e8	+	4.71890e8i	1.29855	+	0.749719i	0.318397	+	0.947957i	$0.396855\pi$
$858$		0			0
$859$	−5.75620e8	+	3.32335e8i	−0.908148	+	0.524320i	−0.879835	−	0.475279i	$-0.842347\pi$
$859$	−5.75620e8	+	3.32335e8i	−0.908148	+	0.524320i	−0.0283134	+	0.999599i	$0.509014\pi$
$860$		0			0
$861$	2.40964e7	−	6.25993e7i	0.0377523	−	0.0980754i
$862$		0			0
$863$	4.33964e8	+	7.51648e8i	0.675183	+	1.16945i	0.976415	+	0.215901i	$0.0692688\pi$
$863$	4.33964e8	+	7.51648e8i	0.675183	+	1.16945i	−0.301232	+	0.953551i	$0.597398\pi$
$864$		0			0
$865$	7.23466e8	−	1.25308e9i	1.11782	−	1.93611i
$866$		0			0
$867$		−	2.52269e8i		−	0.387085i
$868$		0			0
$869$	1.78187e9			2.71529
$870$		0			0
$871$	8.79786e7	+	5.07945e7i	0.133144	+	0.0768709i
$872$		0			0
$873$	−1.05682e8	+	6.10155e7i	−0.158839	+	0.0917059i
$874$		0			0
$875$	3.05761e7	+	1.94219e8i	0.0456413	+	0.289913i
$876$		0			0
$877$	−3.46478e8	−	6.00117e8i	−0.513661	−	0.889687i	−0.999874	−	0.0158471i	$-0.994955\pi$
$877$	−3.46478e8	−	6.00117e8i	−0.513661	−	0.889687i	0.486213	−	0.873840i	$-0.338378\pi$
$878$		0			0
$879$	3.36143e8	−	5.82218e8i	0.494946	−	0.857272i
$880$		0			0
$881$		−	8.34200e8i		−	1.21995i	−0.792420	−	0.609975i	$-0.791179\pi$
$881$		−	8.34200e8i		−	1.21995i	0.792420	−	0.609975i	$-0.208821\pi$
$882$		0			0
$883$	−4.93052e8			−0.716161			−0.358081	−	0.933691i	$-0.616569\pi$
$883$	−4.93052e8			−0.716161			−0.358081	+	0.933691i	$0.616569\pi$
$884$		0			0
$885$	−4.81859e8	−	2.78202e8i	−0.695169	−	0.401356i
$886$		0			0
$887$	−2.07626e8	+	1.19873e8i	−0.297517	+	0.171772i	−0.641327	−	0.767268i	$-0.721616\pi$
$887$	−2.07626e8	+	1.19873e8i	−0.297517	+	0.171772i	0.343810	+	0.939039i	$0.388282\pi$
$888$		0			0
$889$	5.06924e7	−	7.98057e6i	0.0721503	−	0.0113587i
$890$		0			0
$891$	5.90403e7	+	1.02261e8i	0.0834671	+	0.144569i
$892$		0			0
$893$	4.25357e8	−	7.36740e8i	0.597309	−	1.03457i
$894$		0			0
$895$			1.58803e9i			2.21508i
$896$		0			0
$897$	−3.52887e7			−0.0488944
$898$		0			0
$899$	1.45754e9	+	8.41513e8i	2.00605	+	1.15820i
$900$		0			0
$901$	−1.38935e8	+	8.02144e7i	−0.189950	+	0.109667i
$902$		0			0
$903$	5.30270e8	+	2.04118e8i	0.720168	+	0.277215i
$904$		0			0
$905$	5.23929e8	+	9.07471e8i	0.706849	+	1.22430i
$906$		0			0
$907$	−1.09125e8	+	1.89010e8i	−0.146252	+	0.253316i	−0.929839	−	0.367966i	$-0.880054\pi$
$907$	−1.09125e8	+	1.89010e8i	−0.146252	+	0.253316i	0.783587	+	0.621282i	$0.213388\pi$
$908$		0			0
$909$			2.59938e8i			0.346082i
$910$		0			0
$911$	−4.52961e8			−0.599108			−0.299554	−	0.954079i	$-0.596838\pi$
$911$	−4.52961e8			−0.599108			−0.299554	+	0.954079i	$0.596838\pi$
$912$		0			0
$913$	−1.24659e9	−	7.19717e8i	−1.63799	−	0.945692i
$914$		0			0
$915$	−9.45794e8	+	5.46054e8i	−1.23462	+	0.712808i
$916$		0			0
$917$	1.01760e9	−	8.22469e8i	1.31968	−	1.06662i
$918$		0			0
$919$	−5.58754e8	−	9.67791e8i	−0.719904	−	1.24691i	−0.961038	−	0.276418i	$-0.910853\pi$
$919$	−5.58754e8	−	9.67791e8i	−0.719904	−	1.24691i	0.241134	−	0.970492i	$-0.422481\pi$
$920$		0			0
$921$	−3.19879e8	+	5.54047e8i	−0.409456	+	0.709198i
$922$		0			0
$923$		−	7.58044e8i		−	0.964027i
$924$		0			0
$925$	−6.37755e8			−0.805803
$926$		0			0
$927$	1.83297e8	+	1.05826e8i	0.230099	+	0.132848i
$928$		0			0
$929$	1.09553e8	−	6.32505e7i	0.136640	−	0.0788891i	−0.430122	−	0.902771i	$-0.641529\pi$
$929$	1.09553e8	−	6.32505e7i	0.136640	−	0.0788891i	0.566762	+	0.823882i	$0.308196\pi$
$930$		0			0
$931$	4.87906e8	−	5.39852e8i	0.604626	−	0.668999i
$932$		0			0
$933$	−3.12880e8	−	5.41924e8i	−0.385241	−	0.667257i
$934$		0			0
$935$	5.22591e8	−	9.05155e8i	0.639333	−	1.10736i
$936$		0			0
$937$			1.67547e8i			0.203665i	0.994802	+	0.101833i	$0.0324706\pi$
$937$			1.67547e8i			0.203665i	−0.994802	+	0.101833i	$0.967529\pi$
$938$		0			0
$939$	−1.36056e8			−0.164331
$940$		0			0
$941$	−2.71400e8	−	1.56693e8i	−0.325717	−	0.188053i	0.328221	−	0.944601i	$-0.393551\pi$
$941$	−2.71400e8	−	1.56693e8i	−0.325717	−	0.188053i	−0.653938	+	0.756548i	$0.726884\pi$
$942$		0			0
$943$	1.23105e7	−	7.10747e6i	0.0146805	−	0.00847578i
$944$		0			0
$945$	−1.51355e8	−	1.87263e8i	−0.179350	−	0.221900i
$946$		0			0
$947$	1.07686e8	+	1.86517e8i	0.126797	+	0.219618i	0.922434	−	0.386155i	$-0.126197\pi$
$947$	1.07686e8	+	1.86517e8i	0.126797	+	0.219618i	−0.795637	+	0.605774i	$0.792864\pi$
$948$		0			0
$949$	−4.91234e8	+	8.50842e8i	−0.574764	+	0.995520i
$950$		0			0
$951$		−	6.30529e8i		−	0.733100i
$952$		0			0
$953$	−2.21964e8			−0.256451			−0.128226	−	0.991745i	$-0.540928\pi$
$953$	−2.21964e8			−0.256451			−0.128226	+	0.991745i	$0.540928\pi$
$954$		0			0
$955$	1.13777e9	+	6.56892e8i	1.30631	+	0.754196i
$956$		0			0
$957$	−8.42445e8	+	4.86386e8i	−0.961182	+	0.554939i
$958$		0			0
$959$	2.40895e7	−	6.25813e7i	0.0273132	−	0.0709559i
$960$		0			0
$961$	1.01060e9	+	1.75040e9i	1.13869	+	1.97228i
$962$		0			0
$963$	3.82415e7	−	6.62363e7i	0.0428210	−	0.0741681i
$964$		0			0
$965$			6.73967e8i			0.749992i
$966$		0			0
$967$	−8.94588e8			−0.989336			−0.494668	−	0.869082i	$-0.664710\pi$
$967$	−8.94588e8			−0.989336			−0.494668	+	0.869082i	$0.664710\pi$
$968$		0			0
$969$	−2.35495e8	−	1.35963e8i	−0.258828	−	0.149434i
$970$		0			0
$971$	−5.30082e8	+	3.06043e8i	−0.579009	+	0.334291i	−0.760739	−	0.649057i	$-0.775163\pi$
$971$	−5.30082e8	+	3.06043e8i	−0.579009	+	0.334291i	0.181731	+	0.983348i	$0.441830\pi$
$972$		0			0
$973$	−1.71315e8	−	1.08819e9i	−0.185976	−	1.18131i
$974$		0			0
$975$	2.91473e8	+	5.04846e8i	0.314474	+	0.544685i
$976$		0			0
$977$	2.90190e8	−	5.02623e8i	0.311170	−	0.538963i	−0.667446	−	0.744658i	$-0.732612\pi$
$977$	2.90190e8	−	5.02623e8i	0.311170	−	0.538963i	0.978616	+	0.205696i	$0.0659457\pi$
$978$		0			0
$979$		−	2.73956e8i		−	0.291966i
$980$		0			0
$981$	−1.39889e8			−0.148175
$982$		0			0
$983$	2.35488e8	+	1.35959e8i	0.247918	+	0.143136i	0.618811	−	0.785540i	$-0.287615\pi$
$983$	2.35488e8	+	1.35959e8i	0.247918	+	0.143136i	−0.370892	+	0.928676i	$0.620948\pi$
$984$		0			0
$985$	1.28137e9	−	7.39799e8i	1.34081	−	0.774115i
$986$		0			0
$987$	7.26479e8	−	1.14370e8i	0.755565	−	0.118949i
$988$		0			0
$989$	6.02063e7	+	1.04280e8i	0.0622377	+	0.107799i
$990$		0			0
$991$	4.26662e8	−	7.39001e8i	0.438393	−	0.759319i	−0.559173	−	0.829051i	$-0.688881\pi$
$991$	4.26662e8	−	7.39001e8i	0.438393	−	0.759319i	0.997566	+	0.0697323i	$0.0222145\pi$
$992$		0			0
$993$		−	5.78911e8i		−	0.591240i
$994$		0			0
$995$	−1.19672e9			−1.21485
$996$		0			0
$997$	−1.06621e9	−	6.15576e8i	−1.07586	−	0.621150i	−0.146085	−	0.989272i	$-0.546667\pi$
$997$	−1.06621e9	−	6.15576e8i	−1.07586	−	0.621150i	−0.929777	+	0.368122i	$0.880001\pi$
$998$		0			0
$999$	1.11772e8	−	6.45315e7i	0.112108	−	0.0647255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.h.241.1		24
4.3	odd	2		168.7.z.a.73.1	✓	24
7.5	odd	6	inner	336.7.bh.h.145.1		24
28.19	even	6		168.7.z.a.145.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.7.z.a.73.1	✓	24	4.3	odd	2
168.7.z.a.145.1	yes	24	28.19	even	6
336.7.bh.h.145.1		24	7.5	odd	6	inner
336.7.bh.h.241.1		24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(13.5000 + 7.79423i) q^{3} +(-160.491 + 92.6595i) q^{5} +(338.827 - 53.3419i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 + 7.79423i) q^{3} +(-160.491 + 92.6595i) q^{5} +(338.827 - 53.3419i) q^{7} +(121.500 + 210.444i) q^{9} +(999.852 - 1731.80i) q^{11} +1997.85i q^{13} -2888.84 q^{15} +(-2442.52 - 1410.19i) q^{17} +(5356.39 - 3092.51i) q^{19} +(4989.92 + 1920.78i) q^{21} +(566.551 + 981.296i) q^{23} +(9359.05 - 16210.3i) q^{25} +3788.00i q^{27} -31206.3 q^{29} +(-46706.7 - 26966.2i) q^{31} +(26996.0 - 15586.2i) q^{33} +(-49436.0 + 39956.4i) q^{35} +(-17035.8 - 29506.9i) q^{37} +(-15571.7 + 26971.0i) q^{39} -12545.1i q^{41} +106268. q^{43} +(-38999.3 - 22516.2i) q^{45} +(119117. - 68772.1i) q^{47} +(111958. - 36147.3i) q^{49} +(-21982.6 - 38075.0i) q^{51} +(28441.0 - 49261.3i) q^{53} +370583. i q^{55} +96415.0 q^{57} +(166800. + 96302.3i) q^{59} +(327396. - 189022. i) q^{61} +(52393.0 + 64823.1i) q^{63} +(-185120. - 320637. i) q^{65} +(25424.5 - 44036.5i) q^{67} +17663.3i q^{69} -379429. q^{71} +(425878. + 245881. i) q^{73} +(252694. - 145893. i) q^{75} +(246400. - 640113. i) q^{77} +(445532. + 771685. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -719824. i q^{83} +522669. q^{85} +(-421285. - 243229. i) q^{87} +(118644. - 68499.1i) q^{89} +(106569. + 676927. i) q^{91} +(-420361. - 728086. i) q^{93} +(-573101. + 992640. i) q^{95} +502185. i q^{97} +485928. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9}+O(q^{10}) \) 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9	\( 24 q + 324 q^{3} - 126 q^{5} + 12 q^{7} + 2916 q^{9} + 1190 q^{11} - 2268 q^{15} - 1500 q^{17} + 13446 q^{19} - 2106 q^{21} - 21504 q^{23} + 22542 q^{25} - 85484 q^{29} - 6264 q^{31} + 32130 q^{33} - 32268 q^{35} - 46938 q^{37} + 17010 q^{39} + 19548 q^{43} - 30618 q^{45} + 167004 q^{47} + 250644 q^{49} - 13500 q^{51} - 258982 q^{53} + 242028 q^{57} - 744834 q^{59} - 390096 q^{61} - 59778 q^{63} - 19388 q^{65} - 62742 q^{67} + 1102984 q^{71} - 663534 q^{73} + 608634 q^{75} + 404298 q^{77} + 271032 q^{79} - 708588 q^{81} + 2540040 q^{85} - 1154034 q^{87} - 433740 q^{89} + 2142270 q^{91} - 56376 q^{93} - 2205360 q^{95} + 578340 q^{99}+O(q^{100}) \) 24 * q + 324 * q^3 - 126 * q^5 + 12 * q^7 + 2916 * q^9 + 1190 * q^11 - 2268 * q^15 - 1500 * q^17 + 13446 * q^19 - 2106 * q^21 - 21504 * q^23 + 22542 * q^25 - 85484 * q^29 - 6264 * q^31 + 32130 * q^33 - 32268 * q^35 - 46938 * q^37 + 17010 * q^39 + 19548 * q^43 - 30618 * q^45 + 167004 * q^47 + 250644 * q^49 - 13500 * q^51 - 258982 * q^53 + 242028 * q^57 - 744834 * q^59 - 390096 * q^61 - 59778 * q^63 - 19388 * q^65 - 62742 * q^67 + 1102984 * q^71 - 663534 * q^73 + 608634 * q^75 + 404298 * q^77 + 271032 * q^79 - 708588 * q^81 + 2540040 * q^85 - 1154034 * q^87 - 433740 * q^89 + 2142270 * q^91 - 56376 * q^93 - 2205360 * q^95 + 578340 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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