LMFDB - Embedded newform 336.7.bh.b.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 787x^{5} + 38792x^{4} - 92833x^{3} + 1563109x^{2} + 3107772x + 38787984 $ x^8 - x^7 + 212x^6 - 787x^5 + 38792x^4 - 92833x^3 + 1563109x^2 + 3107772x + 38787984
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$-2.30325 + 3.98935i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.b.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 + 7.79423i) q^{3} +(71.9311 + 41.5295i) q^{5} +(-77.0894 + 334.225i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 + 7.79423i) q^{3} +(71.9311 + 41.5295i) q^{5} +(-77.0894 + 334.225i) q^{7} +(121.500 - 210.444i) q^{9} +(-221.304 - 383.310i) q^{11} -696.494i q^{13} -1294.76 q^{15} +(-5447.24 + 3144.96i) q^{17} +(2327.56 + 1343.82i) q^{19} +(-1564.32 - 5112.89i) q^{21} +(7885.31 - 13657.8i) q^{23} +(-4363.11 - 7557.12i) q^{25} +3788.00i q^{27} -23274.5 q^{29} +(-41177.0 + 23773.6i) q^{31} +(5975.21 + 3449.79i) q^{33} +(-19425.3 + 20839.7i) q^{35} +(5079.89 - 8798.64i) q^{37} +(5428.63 + 9402.67i) q^{39} -38165.4i q^{41} +151197. q^{43} +(17479.3 - 10091.7i) q^{45} +(43543.1 + 25139.6i) q^{47} +(-105763. - 51530.4i) q^{49} +(49025.1 - 84914.0i) q^{51} +(99778.2 + 172821. i) q^{53} -36762.6i q^{55} -41896.1 q^{57} +(-335347. + 193612. i) q^{59} +(-10203.5 - 5890.98i) q^{61} +(60969.3 + 56831.3i) q^{63} +(28925.0 - 50099.6i) q^{65} +(-192138. - 332792. i) q^{67} +245840. i q^{69} -156126. q^{71} +(325227. - 187770. i) q^{73} +(117804. + 68014.1i) q^{75} +(145172. - 44416.2i) q^{77} +(16591.8 - 28737.9i) q^{79} +(-29524.5 - 51137.9i) q^{81} -984986. i q^{83} -522434. q^{85} +(314206. - 181407. i) q^{87} +(-227430. - 131307. i) q^{89} +(232786. + 53692.3i) q^{91} +(370593. - 641886. i) q^{93} +(111616. + 193325. i) q^{95} -575147. i q^{97} -107554. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9	$ 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99}+O(q^{100}) $ 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9 + 1070 * q^11 + 756 * q^15 + 7212 * q^17 + 24606 * q^19 + 8154 * q^21 + 15224 * q^23 + 22274 * q^25 + 32524 * q^29 - 40200 * q^31 - 28890 * q^33 + 242436 * q^35 - 45670 * q^37 - 93366 * q^39 + 445660 * q^43 - 10206 * q^45 - 82884 * q^47 + 24116 * q^49 - 64908 * q^51 - 13034 * q^53 - 442908 * q^57 - 1810362 * q^59 - 392856 * q^61 - 38394 * q^63 - 389004 * q^65 - 384094 * q^67 - 225688 * q^71 + 903078 * q^73 - 601398 * q^75 - 327674 * q^77 + 559592 * q^79 - 236196 * q^81 + 1953576 * q^85 - 439074 * q^87 - 1770036 * q^89 + 2960718 * q^91 + 361800 * q^93 - 1160112 * q^95 + 520020 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$4$		0			0
$5$	71.9311	+	41.5295i	0.575449	+	0.332236i	0.759323	−	0.650714i	$-0.225530\pi$
$5$	71.9311	+	41.5295i	0.575449	+	0.332236i	−0.183874	+	0.982950i	$0.558864\pi$
$6$		0			0
$7$	−77.0894	+	334.225i	−0.224750	+	0.974416i
$7$	−77.0894	+	334.225i	−0.224750	+	0.974416i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	−221.304	−	383.310i	−0.166269	−	0.287986i	0.770836	−	0.637033i	$-0.219839\pi$
$11$	−221.304	−	383.310i	−0.166269	−	0.287986i	−0.937105	+	0.349047i	$0.886505\pi$
$12$		0			0
$13$		−	696.494i		−	0.317020i	−0.987357	−	0.158510i	$-0.949331\pi$
$13$		−	696.494i		−	0.317020i	0.987357	−	0.158510i	$-0.0506691\pi$
$14$		0			0
$15$	−1294.76			−0.383633
$16$		0			0
$17$	−5447.24	+	3144.96i	−1.10874	+	0.640131i	−0.938503	−	0.345272i	$-0.887787\pi$
$17$	−5447.24	+	3144.96i	−1.10874	+	0.640131i	−0.170237	+	0.985403i	$0.554453\pi$
$18$		0			0
$19$	2327.56	+	1343.82i	0.339344	+	0.195920i	0.659982	−	0.751281i	$-0.270564\pi$
$19$	2327.56	+	1343.82i	0.339344	+	0.195920i	−0.320638	+	0.947202i	$0.603897\pi$
$20$		0			0
$21$	−1564.32	−	5112.89i	−0.168915	−	0.552088i
$22$		0			0
$23$	7885.31	−	13657.8i	0.648090	−	1.12252i	−0.335489	−	0.942044i	$-0.608902\pi$
$23$	7885.31	−	13657.8i	0.648090	−	1.12252i	0.983579	−	0.180480i	$-0.0577652\pi$
$24$		0			0
$25$	−4363.11	−	7557.12i	−0.279239	−	0.483656i
$26$		0			0
$27$			3788.00i			0.192450i
$28$		0			0
$29$	−23274.5			−0.954304			−0.477152	−	0.878821i	$-0.658331\pi$
$29$	−23274.5			−0.954304			−0.477152	+	0.878821i	$0.658331\pi$
$30$		0			0
$31$	−41177.0	+	23773.6i	−1.38220	+	0.798012i	−0.992419	−	0.122897i	$-0.960782\pi$
$31$	−41177.0	+	23773.6i	−1.38220	+	0.798012i	−0.389778	+	0.920909i	$0.627448\pi$
$32$		0			0
$33$	5975.21	+	3449.79i	0.166269	+	0.0959955i
$34$		0			0
$35$	−19425.3	+	20839.7i	−0.453068	+	0.486057i
$36$		0			0
$37$	5079.89	−	8798.64i	0.100288	−	0.173704i	−0.811515	−	0.584331i	$-0.801357\pi$
$37$	5079.89	−	8798.64i	0.100288	−	0.173704i	0.911803	+	0.410627i	$0.134690\pi$
$38$		0			0
$39$	5428.63	+	9402.67i	0.0915159	+	0.158510i
$40$		0			0
$41$		−	38165.4i		−	0.553756i	−0.960905	−	0.276878i	$-0.910700\pi$
$41$		−	38165.4i		−	0.553756i	0.960905	−	0.276878i	$-0.0892998\pi$
$42$		0			0
$43$	151197.			1.90168			0.950841	−	0.309679i	$-0.100221\pi$
$43$	151197.			1.90168			0.950841	+	0.309679i	$0.100221\pi$
$44$		0			0
$45$	17479.3	−	10091.7i	0.191816	−	0.110745i
$46$		0			0
$47$	43543.1	+	25139.6i	0.419397	+	0.242139i	0.694819	−	0.719184i	$-0.255484\pi$
$47$	43543.1	+	25139.6i	0.419397	+	0.242139i	−0.275422	+	0.961323i	$0.588818\pi$
$48$		0			0
$49$	−105763.	−	51530.4i	−0.898975	−	0.438001i
$50$		0			0
$51$	49025.1	−	84914.0i	0.369580	−	0.640131i
$52$		0			0
$53$	99778.2	+	172821.i	0.670206	+	1.16083i	0.977846	+	0.209328i	$0.0671275\pi$
$53$	99778.2	+	172821.i	0.670206	+	1.16083i	−0.307640	+	0.951503i	$0.599539\pi$
$54$		0			0
$55$		−	36762.6i		−	0.220962i
$56$		0			0
$57$	−41896.1			−0.226229
$58$		0			0
$59$	−335347.	+	193612.i	−1.63282	+	0.942708i	−0.649600	+	0.760277i	$0.725063\pi$
$59$	−335347.	+	193612.i	−1.63282	+	0.942708i	−0.983219	+	0.182431i	$0.941603\pi$
$60$		0			0
$61$	−10203.5	−	5890.98i	−0.0449530	−	0.0259536i	0.477355	−	0.878711i	$-0.341596\pi$
$61$	−10203.5	−	5890.98i	−0.0449530	−	0.0259536i	−0.522308	+	0.852757i	$0.674929\pi$
$62$		0			0
$63$	60969.3	+	56831.3i	0.243831	+	0.227283i
$64$		0			0
$65$	28925.0	−	50099.6i	0.105325	−	0.182429i
$66$		0			0
$67$	−192138.	−	332792.i	−0.638834	−	1.10649i	−0.985689	−	0.168575i	$-0.946084\pi$
$67$	−192138.	−	332792.i	−0.638834	−	1.10649i	0.346854	−	0.937919i	$-0.387250\pi$
$68$		0			0
$69$			245840.i			0.748350i
$70$		0			0
$71$	−156126.			−0.436213			−0.218107	−	0.975925i	$-0.569988\pi$
$71$	−156126.			−0.436213			−0.218107	+	0.975925i	$0.569988\pi$
$72$		0			0
$73$	325227.	−	187770.i	0.836022	−	0.482677i	−0.0198883	−	0.999802i	$-0.506331\pi$
$73$	325227.	−	187770.i	0.836022	−	0.482677i	0.855910	+	0.517125i	$0.172998\pi$
$74$		0			0
$75$	117804.	+	68014.1i	0.279239	+	0.161219i
$76$		0			0
$77$	145172.	−	44416.2i	0.317988	−	0.0972902i
$78$		0			0
$79$	16591.8	−	28737.9i	0.0336521	−	0.0582872i	−0.848709	−	0.528860i	$-0.822620\pi$
$79$	16591.8	−	28737.9i	0.0336521	−	0.0582872i	0.882361	+	0.470573i	$0.155953\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	984986.i		−	1.72264i	−0.508059	−	0.861322i	$-0.669637\pi$
$83$		−	984986.i		−	1.72264i	0.508059	−	0.861322i	$-0.330363\pi$
$84$		0			0
$85$	−522434.			−0.850697
$86$		0			0
$87$	314206.	−	181407.i	0.477152	−	0.275484i
$88$		0			0
$89$	−227430.	−	131307.i	−0.322609	−	0.186259i	0.329946	−	0.944000i	$-0.392970\pi$
$89$	−227430.	−	131307.i	−0.322609	−	0.186259i	−0.652555	+	0.757741i	$0.726303\pi$
$90$		0			0
$91$	232786.	+	53692.3i	0.308910	+	0.0712505i
$92$		0			0
$93$	370593.	−	641886.i	0.460732	−	0.798012i
$94$		0			0
$95$	111616.	+	193325.i	0.130184	+	0.225484i
$96$		0			0
$97$		−	575147.i		−	0.630179i	−0.949062	−	0.315089i	$-0.897966\pi$
$97$		−	575147.i		−	0.630179i	0.949062	−	0.315089i	$-0.102034\pi$
$98$		0			0
$99$	−107554.			−0.110846
$100$		0			0
$101$	634688.	−	366437.i	0.616022	−	0.355661i	−0.159297	−	0.987231i	$-0.550923\pi$
$101$	634688.	−	366437.i	0.616022	−	0.355661i	0.775319	+	0.631570i	$0.217589\pi$
$102$		0			0
$103$	−908207.	−	524353.i	−0.831138	−	0.479858i	0.0231042	−	0.999733i	$-0.492645\pi$
$103$	−908207.	−	524353.i	−0.831138	−	0.479858i	−0.854242	+	0.519875i	$0.825978\pi$
$104$		0			0
$105$	99812.3	−	432741.i	0.0862216	−	0.373818i
$106$		0			0
$107$	587412.	−	1.01743e6i	0.479503	−	0.830524i	−0.520221	−	0.854032i	$-0.674150\pi$
$107$	587412.	−	1.01743e6i	0.479503	−	0.830524i	0.999724	+	0.0235083i	$0.00748363\pi$
$108$		0			0
$109$	−367045.	−	635741.i	−0.283426	−	0.490908i	0.688800	−	0.724951i	$-0.258138\pi$
$109$	−367045.	−	635741.i	−0.283426	−	0.490908i	−0.972226	+	0.234043i	$0.924804\pi$
$110$		0			0
$111$			158375.i			0.115803i
$112$		0			0
$113$	2.04925e6			1.42023			0.710116	−	0.704085i	$-0.248643\pi$
$113$	2.04925e6			1.42023			0.710116	+	0.704085i	$0.248643\pi$
$114$		0			0
$115$	1.13440e6	−	654945.i	0.745885	−	0.430637i
$116$		0			0
$117$	−146573.	−	84624.0i	−0.0915159	−	0.0528367i
$118$		0			0
$119$	−631201.	−	2.06304e6i	−0.374564	−	1.22424i
$120$		0			0
$121$	787829.	−	1.36456e6i	0.444709	−	0.770259i
$122$		0			0
$123$	297470.	+	515233.i	0.159856	+	0.276878i
$124$		0			0
$125$		−	2.02259e6i		−	1.03556i
$126$		0			0
$127$	1.64688e6			0.803991			0.401995	−	0.915642i	$-0.368317\pi$
$127$	1.64688e6			0.803991			0.401995	+	0.915642i	$0.368317\pi$
$128$		0			0
$129$	−2.04116e6	+	1.17846e6i	−0.950841	+	0.548968i
$130$		0			0
$131$	1.78472e6	+	1.03041e6i	0.793882	+	0.458348i	0.841327	−	0.540526i	$-0.181775\pi$
$131$	1.78472e6	+	1.03041e6i	0.793882	+	0.458348i	−0.0474457	+	0.998874i	$0.515108\pi$
$132$		0			0
$133$	−628568.	+	674335.i	−0.267176	+	0.286629i
$134$		0			0
$135$	−157313.	+	272475.i	−0.0639388	+	0.110745i
$136$		0			0
$137$	−1.61460e6	−	2.79657e6i	−0.627919	−	1.08759i	−0.987969	−	0.154654i	$-0.950574\pi$
$137$	−1.61460e6	−	2.79657e6i	−0.627919	−	1.08759i	0.360050	−	0.932933i	$-0.382760\pi$
$138$		0			0
$139$		−	4.06719e6i		−	1.51443i	−0.653163	−	0.757217i	$-0.726558\pi$
$139$		−	4.06719e6i		−	1.51443i	0.653163	−	0.757217i	$-0.273442\pi$
$140$		0			0
$141$	−783776.			−0.279598
$142$		0			0
$143$	−266973.	+	154137.i	−0.0912976	+	0.0527107i
$144$		0			0
$145$	−1.67416e6	−	966578.i	−0.549153	−	0.317054i
$146$		0			0
$147$	1.82945e6	−	128684.i	0.575927	−	0.0405111i
$148$		0			0
$149$	1.39737e6	−	2.42031e6i	0.422427	−	0.731666i	−0.573749	−	0.819031i	$-0.694511\pi$
$149$	1.39737e6	−	2.42031e6i	0.422427	−	0.731666i	0.996176	+	0.0873655i	$0.0278448\pi$
$150$		0			0
$151$	301549.	+	522299.i	0.0875846	+	0.151701i	0.906490	−	0.422228i	$-0.138752\pi$
$151$	301549.	+	522299.i	0.0875846	+	0.151701i	−0.818905	+	0.573929i	$0.805419\pi$
$152$		0			0
$153$			1.52845e6i			0.426754i
$154$		0			0
$155$	−3.94921e6			−1.06051
$156$		0			0
$157$	−1.23763e6	+	714546.i	−0.319810	+	0.184642i	−0.651308	−	0.758814i	$-0.725779\pi$
$157$	−1.23763e6	+	714546.i	−0.319810	+	0.184642i	0.331498	+	0.943456i	$0.392446\pi$
$158$		0			0
$159$	−2.69401e6	−	1.55539e6i	−0.670206	−	0.386943i
$160$		0			0
$161$	3.95689e6	+	3.68833e6i	0.948148	+	0.883797i
$162$		0			0
$163$	−2.78644e6	+	4.82625e6i	−0.643408	+	1.11442i	0.341259	+	0.939969i	$0.389147\pi$
$163$	−2.78644e6	+	4.82625e6i	−0.643408	+	1.11442i	−0.984667	+	0.174446i	$0.944186\pi$
$164$		0			0
$165$	286536.	+	496295.i	0.0637862	+	0.110481i
$166$		0			0
$167$			2.24388e6i			0.481781i	0.970552	+	0.240890i	$0.0774394\pi$
$167$			2.24388e6i			0.481781i	−0.970552	+	0.240890i	$0.922561\pi$
$168$		0			0
$169$	4.34171e6			0.899498
$170$		0			0
$171$	565597.	−	326548.i	0.113115	−	0.0653068i
$172$		0			0
$173$	−5.95864e6	−	3.44022e6i	−1.15082	−	0.664428i	−0.201736	−	0.979440i	$-0.564658\pi$
$173$	−5.95864e6	−	3.44022e6i	−1.15082	−	0.664428i	−0.949088	+	0.315012i	$0.897992\pi$
$174$		0			0
$175$	2.86213e6	−	875685.i	0.534041	−	0.163393i
$176$		0			0
$177$	3.01812e6	−	5.22754e6i	0.544273	−	0.942708i
$178$		0			0
$179$	−3.94643e6	−	6.83543e6i	−0.688091	−	1.19181i	−0.972455	−	0.233092i	$-0.925116\pi$
$179$	−3.94643e6	−	6.83543e6i	−0.688091	−	1.19181i	0.284364	−	0.958716i	$-0.408218\pi$
$180$		0			0
$181$		−	2.63639e6i		−	0.444604i	−0.974978	−	0.222302i	$-0.928643\pi$
$181$		−	2.63639e6i		−	0.444604i	0.974978	−	0.222302i	$-0.0713571\pi$
$182$		0			0
$183$	183663.			0.0299687
$184$		0			0
$185$	730805.	−	421931.i	0.115421	−	0.0666386i
$186$		0			0
$187$	2.41099e6	+	1.39199e6i	0.368698	+	0.212868i
$188$		0			0
$189$	−1.26604e6	−	292014.i	−0.187527	−	0.0432532i
$190$		0			0
$191$	6.17120e6	−	1.06888e7i	0.885665	−	1.53402i	0.0407156	−	0.999171i	$-0.487036\pi$
$191$	6.17120e6	−	1.06888e7i	0.885665	−	1.53402i	0.844949	−	0.534846i	$-0.179630\pi$
$192$		0			0
$193$	6.69614e6	+	1.15981e7i	0.931435	+	1.61329i	0.780871	+	0.624692i	$0.214776\pi$
$193$	6.69614e6	+	1.15981e7i	0.931435	+	1.61329i	0.150564	+	0.988600i	$0.451891\pi$
$194$		0			0
$195$			901793.i			0.121619i
$196$		0			0
$197$	−9.42468e6			−1.23273			−0.616365	−	0.787460i	$-0.711396\pi$
$197$	−9.42468e6			−1.23273			−0.616365	+	0.787460i	$0.711396\pi$
$198$		0			0
$199$	−4.91639e6	+	2.83848e6i	−0.623860	+	0.360186i	−0.778370	−	0.627805i	$-0.783953\pi$
$199$	−4.91639e6	+	2.83848e6i	−0.623860	+	0.360186i	0.154510	+	0.987991i	$0.450620\pi$
$200$		0			0
$201$	5.18772e6	+	2.99513e6i	0.638834	+	0.368831i
$202$		0			0
$203$	1.79422e6	−	7.77892e6i	0.214480	−	0.929890i
$204$		0			0
$205$	1.58499e6	−	2.74528e6i	0.183977	−	0.318658i
$206$		0			0
$207$	−1.91613e6	−	3.31883e6i	−0.216030	−	0.374175i
$208$		0			0
$209$		−	1.18957e6i		−	0.130302i
$210$		0			0
$211$	−1.05196e6			−0.111983			−0.0559914	−	0.998431i	$-0.517832\pi$
$211$	−1.05196e6			−0.111983			−0.0559914	+	0.998431i	$0.517832\pi$
$212$		0			0
$213$	2.10770e6	−	1.21688e6i	0.218107	−	0.125924i
$214$		0			0
$215$	1.08758e7	+	6.27913e6i	1.09432	+	0.631807i
$216$		0			0
$217$	−4.77141e6	−	1.55951e7i	−0.466946	−	1.52619i
$218$		0			0
$219$	−2.92704e6	+	5.06978e6i	−0.278674	+	0.482677i
$220$		0			0
$221$	2.19045e6	+	3.79397e6i	0.202935	+	0.351493i
$222$		0			0
$223$		−	9.96615e6i		−	0.898696i	−0.893357	−	0.449348i	$-0.851656\pi$
$223$		−	9.96615e6i		−	0.898696i	0.893357	−	0.449348i	$-0.148344\pi$
$224$		0			0
$225$	−2.12047e6			−0.186159
$226$		0			0
$227$	−1.59963e7	+	9.23545e6i	−1.36754	+	0.789552i	−0.990614	−	0.136690i	$-0.956354\pi$
$227$	−1.59963e7	+	9.23545e6i	−1.36754	+	0.789552i	−0.376930	+	0.926242i	$0.623020\pi$
$228$		0			0
$229$	1.17915e7	+	6.80784e6i	0.981892	+	0.566896i	0.902841	−	0.429975i	$-0.141478\pi$
$229$	1.17915e7	+	6.80784e6i	0.981892	+	0.566896i	0.0790512	+	0.996871i	$0.474811\pi$
$230$		0			0
$231$	−1.61363e6	+	1.73112e6i	−0.130909	+	0.140440i
$232$		0			0
$233$	−5103.02	+	8838.68i	−0.000403422	+	0.000698747i	−0.866227	−	0.499651i	$-0.833462\pi$
$233$	−5103.02	+	8838.68i	−0.000403422	+	0.000698747i	0.865824	+	0.500349i	$0.166795\pi$
$234$		0			0
$235$	2.08807e6	+	3.61664e6i	0.160895	+	0.278678i
$236$		0			0
$237$			517281.i			0.0388581i
$238$		0			0
$239$	−2.49567e6			−0.182807			−0.0914037	−	0.995814i	$-0.529135\pi$
$239$	−2.49567e6			−0.182807			−0.0914037	+	0.995814i	$0.529135\pi$
$240$		0			0
$241$	−4.73752e6	+	2.73521e6i	−0.338454	+	0.195407i	−0.659588	−	0.751627i	$-0.729269\pi$
$241$	−4.73752e6	+	2.73521e6i	−0.338454	+	0.195407i	0.321134	+	0.947034i	$0.395936\pi$
$242$		0			0
$243$	797162.	+	460241.i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−5.46766e6	−	8.09894e6i	−0.371795	−	0.550719i
$246$		0			0
$247$	935961.	−	1.62113e6i	0.0621108	−	0.107579i
$248$		0			0
$249$	7.67720e6	+	1.32973e7i	0.497285	+	0.861322i
$250$		0			0
$251$			2.18424e6i			0.138127i	0.997612	+	0.0690637i	$0.0220012\pi$
$251$			2.18424e6i			0.138127i	−0.997612	+	0.0690637i	$0.977999\pi$
$252$		0			0
$253$	−6.98020e6			−0.431029
$254$		0			0
$255$	7.05286e6	−	4.07197e6i	0.425349	−	0.245575i
$256$		0			0
$257$	−2.72638e7	−	1.57408e7i	−1.60615	−	0.927313i	−0.990220	−	0.139514i	$-0.955446\pi$
$257$	−2.72638e7	−	1.57408e7i	−1.60615	−	0.927313i	−0.615933	−	0.787799i	$-0.711221\pi$
$258$		0			0
$259$	2.54912e6	+	2.37611e6i	0.146720	+	0.136762i
$260$		0			0
$261$	−2.82785e6	+	4.89799e6i	−0.159051	+	0.275484i
$262$		0			0
$263$	3.28881e6	+	5.69639e6i	0.180789	+	0.313136i	0.942149	−	0.335193i	$-0.108802\pi$
$263$	3.28881e6	+	5.69639e6i	0.180789	+	0.313136i	−0.761360	+	0.648329i	$0.775468\pi$
$264$		0			0
$265$			1.65749e7i			0.890665i
$266$		0			0
$267$	4.09373e6			0.215073
$268$		0			0
$269$	190420.	−	109939.i	0.00978263	−	0.00564801i	−0.495101	−	0.868836i	$-0.664869\pi$
$269$	190420.	−	109939.i	0.00978263	−	0.00564801i	0.504883	+	0.863188i	$0.331536\pi$
$270$		0			0
$271$	2.41082e7	+	1.39189e7i	1.21132	+	0.699354i	0.963046	−	0.269337i	$-0.0868045\pi$
$271$	2.41082e7	+	1.39189e7i	1.21132	+	0.699354i	0.248270	+	0.968691i	$0.420138\pi$
$272$		0			0
$273$	−3.56109e6	+	1.08954e6i	−0.175023	+	0.0535494i
$274$		0			0
$275$	−1.93115e6	+	3.34485e6i	−0.0928576	+	0.160834i
$276$		0			0
$277$	2.87725e6	+	4.98354e6i	0.135375	+	0.234476i	0.925741	−	0.378159i	$-0.123443\pi$
$277$	2.87725e6	+	4.98354e6i	0.135375	+	0.234476i	−0.790366	+	0.612635i	$0.790109\pi$
$278$		0			0
$279$			1.15540e7i			0.532008i
$280$		0			0
$281$	1.75833e7			0.792467			0.396233	−	0.918150i	$-0.370317\pi$
$281$	1.75833e7			0.792467			0.396233	+	0.918150i	$0.370317\pi$
$282$		0			0
$283$	−1.27466e7	+	7.35922e6i	−0.562385	+	0.324693i	−0.754102	−	0.656757i	$-0.771928\pi$
$283$	−1.27466e7	+	7.35922e6i	−0.562385	+	0.324693i	0.191717	+	0.981450i	$0.438594\pi$
$284$		0			0
$285$	−3.01363e6	−	1.73992e6i	−0.130184	−	0.0751615i
$286$		0			0
$287$	1.27558e7	+	2.94215e6i	0.539589	+	0.124457i
$288$		0			0
$289$	7.71280e6	−	1.33590e7i	0.319535	−	0.553451i
$290$		0			0
$291$	4.48283e6	+	7.76448e6i	0.181917	+	0.315089i
$292$		0			0
$293$			3.49743e6i			0.139042i	0.997580	+	0.0695210i	$0.0221471\pi$
$293$			3.49743e6i			0.139042i	−0.997580	+	0.0695210i	$0.977853\pi$
$294$		0			0
$295$	−3.21625e7			−1.25280
$296$		0			0
$297$	1.45198e6	−	838299.i	0.0554230	−	0.0319985i
$298$		0			0
$299$	−9.51254e6	−	5.49207e6i	−0.355863	−	0.205458i
$300$		0			0
$301$	−1.16557e7	+	5.05338e7i	−0.427404	+	1.85303i
$302$		0			0
$303$	−5.71219e6	+	9.89381e6i	−0.205341	+	0.355661i
$304$		0			0
$305$	−489299.	−	847490.i	−0.0172455	−	0.0298700i
$306$		0			0
$307$			3.99694e7i			1.38138i	0.723152	+	0.690689i	$0.242692\pi$
$307$			3.99694e7i			1.38138i	−0.723152	+	0.690689i	$0.757308\pi$
$308$		0			0
$309$	1.63477e7			0.554092
$310$		0			0
$311$	2.88815e7	−	1.66747e7i	0.960148	−	0.554342i	0.0639296	−	0.997954i	$-0.479637\pi$
$311$	2.88815e7	−	1.66747e7i	0.960148	−	0.554342i	0.896219	+	0.443613i	$0.146303\pi$
$312$		0			0
$313$	1.62725e7	+	9.39495e6i	0.530667	+	0.306381i	0.741288	−	0.671187i	$-0.234215\pi$
$313$	1.62725e7	+	9.39495e6i	0.530667	+	0.306381i	−0.210621	+	0.977568i	$0.567549\pi$
$314$		0			0
$315$	2.02542e6	+	6.61996e6i	0.0648012	+	0.211799i
$316$		0			0
$317$	1.01986e7	−	1.76645e7i	0.320156	−	0.554527i	−0.660364	−	0.750946i	$-0.729598\pi$
$317$	1.01986e7	−	1.76645e7i	0.320156	−	0.554527i	0.980520	+	0.196419i	$0.0629312\pi$
$318$		0			0
$319$	5.15075e6	+	8.92136e6i	0.158671	+	0.274827i
$320$		0			0
$321$			1.83137e7i			0.553682i
$322$		0			0
$323$	−1.69050e7			−0.501659
$324$		0			0
$325$	−5.26349e6	+	3.03888e6i	−0.153329	+	0.0885244i
$326$		0			0
$327$	9.91021e6	+	5.72167e6i	0.283426	+	0.163636i
$328$		0			0
$329$	−1.17590e7	+	1.26152e7i	−0.330204	+	0.354247i
$330$		0			0
$331$	−1.06774e7	+	1.84939e7i	−0.294431	+	0.509969i	−0.974852	−	0.222852i	$-0.928463\pi$
$331$	−1.06774e7	+	1.84939e7i	−0.294431	+	0.509969i	0.680422	+	0.732821i	$0.261797\pi$
$332$		0			0
$333$	−1.23441e6	−	2.13807e6i	−0.0334294	−	0.0579014i
$334$		0			0
$335$		−	3.19175e7i		−	0.848974i
$336$		0			0
$337$	−1.98824e7			−0.519493			−0.259746	−	0.965677i	$-0.583639\pi$
$337$	−1.98824e7			−0.519493			−0.259746	+	0.965677i	$0.583639\pi$
$338$		0			0
$339$	−2.76649e7	+	1.59723e7i	−0.710116	+	0.409986i
$340$		0			0
$341$	1.82253e7	+	1.05224e7i	0.459633	+	0.265369i
$342$		0			0
$343$	2.53760e7	−	3.13763e7i	0.628840	−	0.777535i
$344$		0			0
$345$	−1.02096e7	+	1.76835e7i	−0.248628	+	0.430637i
$346$		0			0
$347$	−1.66198e7	−	2.87863e7i	−0.397774	−	0.688965i	0.595677	−	0.803224i	$-0.296884\pi$
$347$	−1.66198e7	−	2.87863e7i	−0.397774	−	0.688965i	−0.993451	+	0.114259i	$0.963551\pi$
$348$		0			0
$349$			2.57850e7i			0.606584i	0.952898	+	0.303292i	$0.0980858\pi$
$349$			2.57850e7i			0.606584i	−0.952898	+	0.303292i	$0.901914\pi$
$350$		0			0
$351$	2.63832e6			0.0610106
$352$		0			0
$353$	−4.82036e7	+	2.78303e7i	−1.09586	+	0.632695i	−0.935130	−	0.354304i	$-0.884718\pi$
$353$	−4.82036e7	+	2.78303e7i	−1.09586	+	0.632695i	−0.160729	+	0.986999i	$0.551385\pi$
$354$		0			0
$355$	−1.12303e7	−	6.48381e6i	−0.251019	−	0.144926i
$356$		0			0
$357$	2.46010e7	+	2.29314e7i	0.540691	+	0.503994i
$358$		0			0
$359$	−8.08714e6	+	1.40073e7i	−0.174788	+	0.302742i	−0.940088	−	0.340932i	$-0.889257\pi$
$359$	−8.08714e6	+	1.40073e7i	−0.174788	+	0.302742i	0.765300	+	0.643674i	$0.222591\pi$
$360$		0			0
$361$	−1.99112e7	−	3.44873e7i	−0.423230	−	0.733056i
$362$		0			0
$363$			2.45621e7i			0.513506i
$364$		0			0
$365$	3.11919e7			0.641451
$366$		0			0
$367$	−9.72318e6	+	5.61368e6i	−0.196703	+	0.113566i	−0.595117	−	0.803639i	$-0.702894\pi$
$367$	−9.72318e6	+	5.61368e6i	−0.196703	+	0.113566i	0.398414	+	0.917206i	$0.369561\pi$
$368$		0			0
$369$	−8.03169e6	−	4.63710e6i	−0.159856	−	0.0922926i
$370$		0			0
$371$	−6.54529e7	+	2.00257e7i	−1.28176	+	0.392162i
$372$		0			0
$373$	−1.99988e7	+	3.46389e7i	−0.385369	+	0.667479i	−0.991820	−	0.127642i	$-0.959259\pi$
$373$	−1.99988e7	+	3.46389e7i	−0.385369	+	0.667479i	0.606451	+	0.795121i	$0.292593\pi$
$374$		0			0
$375$	1.57645e7	+	2.73049e7i	0.298942	+	0.517782i
$376$		0			0
$377$			1.62106e7i			0.302534i
$378$		0			0
$379$	−2.92098e7			−0.536551			−0.268276	−	0.963342i	$-0.586454\pi$
$379$	−2.92098e7			−0.536551			−0.268276	+	0.963342i	$0.586454\pi$
$380$		0			0
$381$	−2.22329e7	+	1.28362e7i	−0.401995	+	0.232092i
$382$		0			0
$383$	−3.97181e7	−	2.29312e7i	−0.706955	−	0.408161i	0.102978	−	0.994684i	$-0.467163\pi$
$383$	−3.97181e7	−	2.29312e7i	−0.706955	−	0.408161i	−0.809933	+	0.586523i	$0.800496\pi$
$384$		0			0
$385$	1.22870e7	+	2.83400e6i	0.215309	+	0.0496613i
$386$		0			0
$387$	1.83704e7	−	3.18185e7i	0.316947	−	0.548968i
$388$		0			0
$389$	−7.72431e6	−	1.33789e7i	−0.131223	−	0.227285i	0.792925	−	0.609319i	$-0.208557\pi$
$389$	−7.72431e6	−	1.33789e7i	−0.131223	−	0.227285i	−0.924148	+	0.382034i	$0.875224\pi$
$390$		0			0
$391$			9.91960e7i			1.65945i
$392$		0			0
$393$	−3.21249e7			−0.529254
$394$		0			0
$395$	2.38693e6	−	1.37810e6i	0.0387302	−	0.0223609i
$396$		0			0
$397$	2.54737e7	+	1.47073e7i	0.407118	+	0.235050i	0.689551	−	0.724237i	$-0.257808\pi$
$397$	2.54737e7	+	1.47073e7i	0.407118	+	0.235050i	−0.282433	+	0.959287i	$0.591141\pi$
$398$		0			0
$399$	3.22975e6	−	1.40027e7i	0.0508452	−	0.220442i
$400$		0			0
$401$	5.70055e7	−	9.87364e7i	0.884064	−	1.53124i	0.0372810	−	0.999305i	$-0.488130\pi$
$401$	5.70055e7	−	9.87364e7i	0.884064	−	1.53124i	0.846783	−	0.531939i	$-0.178536\pi$
$402$		0			0
$403$	1.65581e7	+	2.86796e7i	0.252986	+	0.438185i
$404$		0			0
$405$		−	4.90455e6i		−	0.0738302i
$406$		0			0
$407$	−4.49681e6			−0.0666992
$408$		0			0
$409$	2.99288e7	−	1.72794e7i	0.437442	−	0.252557i	−0.265070	−	0.964229i	$-0.585395\pi$
$409$	2.99288e7	−	1.72794e7i	0.437442	−	0.252557i	0.702512	+	0.711672i	$0.252062\pi$
$410$		0			0
$411$	4.35942e7	+	2.51691e7i	0.627919	+	0.362529i
$412$		0			0
$413$	−3.88584e7	−	1.27007e8i	−0.551614	−	1.80292i
$414$		0			0
$415$	4.09059e7	−	7.08511e7i	0.572324	−	0.991294i
$416$		0			0
$417$	3.17006e7	+	5.49071e7i	0.437180	+	0.757217i
$418$		0			0
$419$		−	3.73902e7i		−	0.508294i	−0.967166	−	0.254147i	$-0.918205\pi$
$419$		−	3.73902e7i		−	0.508294i	0.967166	−	0.254147i	$-0.0817948\pi$
$420$		0			0
$421$	−5.93910e7			−0.795929			−0.397965	−	0.917401i	$-0.630283\pi$
$421$	−5.93910e7			−0.795929			−0.397965	+	0.917401i	$0.630283\pi$
$422$		0			0
$423$	1.05810e7	−	6.10893e6i	0.139799	−	0.0807131i
$424$		0			0
$425$	4.75338e7	+	2.74436e7i	0.619206	+	0.357499i
$426$		0			0
$427$	2.75549e6	−	2.95612e6i	0.0353929	−	0.0379699i
$428$		0			0
$429$	2.40276e6	−	4.16170e6i	0.0304325	−	0.0527107i
$430$		0			0
$431$	−2.97697e7	−	5.15627e7i	−0.371829	−	0.644026i	0.618018	−	0.786164i	$-0.287936\pi$
$431$	−2.97697e7	−	5.15627e7i	−0.371829	−	0.644026i	−0.989847	+	0.142137i	$0.954603\pi$
$432$		0			0
$433$			6.40730e7i			0.789244i	0.918843	+	0.394622i	$0.129124\pi$
$433$			6.40730e7i			0.789244i	−0.918843	+	0.394622i	$0.870876\pi$
$434$		0			0
$435$	3.01349e7			0.366102
$436$		0			0
$437$	3.67071e7	−	2.11928e7i	0.439851	−	0.253948i
$438$		0			0
$439$	1.31778e8	+	7.60819e7i	1.55757	+	0.899265i	0.997488	+	0.0708286i	$0.0225643\pi$
$439$	1.31778e8	+	7.60819e7i	1.55757	+	0.899265i	0.560084	+	0.828436i	$0.310769\pi$
$440$		0			0
$441$	−2.36945e7	+	1.59964e7i	−0.276269	+	0.186511i
$442$		0			0
$443$	1.72920e7	−	2.99506e7i	0.198899	−	0.344504i	−0.749273	−	0.662262i	$-0.769597\pi$
$443$	1.72920e7	−	2.99506e7i	0.198899	−	0.344504i	0.948172	+	0.317758i	$0.102930\pi$
$444$		0			0
$445$	−1.09062e7	−	1.88901e7i	−0.123763	−	0.214365i
$446$		0			0
$447$			4.35656e7i			0.487777i
$448$		0			0
$449$	−1.33795e8			−1.47809			−0.739047	−	0.673654i	$-0.764724\pi$
$449$	−1.33795e8			−1.47809			−0.739047	+	0.673654i	$0.764724\pi$
$450$		0			0
$451$	−1.46292e7	+	8.44616e6i	−0.159474	+	0.0920724i
$452$		0			0
$453$	−8.14183e6	−	4.70069e6i	−0.0875846	−	0.0505670i
$454$		0			0
$455$	1.45147e7	+	1.35296e7i	0.154090	+	0.143632i
$456$		0			0
$457$	−7.62638e6	+	1.32093e7i	−0.0799043	+	0.138398i	−0.903208	−	0.429202i	$-0.858795\pi$
$457$	−7.62638e6	+	1.32093e7i	−0.0799043	+	0.138398i	0.823304	+	0.567600i	$0.192128\pi$
$458$		0			0
$459$	−1.19131e7	−	2.06341e7i	−0.123193	−	0.213377i
$460$		0			0
$461$			3.05013e7i			0.311326i	0.987810	+	0.155663i	$0.0497514\pi$
$461$			3.05013e7i			0.311326i	−0.987810	+	0.155663i	$0.950249\pi$
$462$		0			0
$463$	1.61661e8			1.62878			0.814388	−	0.580320i	$-0.197073\pi$
$463$	1.61661e8			1.62878			0.814388	+	0.580320i	$0.197073\pi$
$464$		0			0
$465$	5.33144e7	−	3.07811e7i	0.530256	−	0.306143i
$466$		0			0
$467$	−5.70833e7	−	3.29570e7i	−0.560478	−	0.323592i	0.192860	−	0.981226i	$-0.438224\pi$
$467$	−5.70833e7	−	3.29570e7i	−0.560478	−	0.323592i	−0.753337	+	0.657635i	$0.771557\pi$
$468$		0			0
$469$	1.26039e8	−	3.85624e7i	1.22176	−	0.373806i
$470$		0			0
$471$	1.11387e7	−	1.92927e7i	0.106603	−	0.184642i
$472$		0			0
$473$	−3.34605e7	−	5.79553e7i	−0.316191	−	0.547659i
$474$		0			0
$475$		−	2.34529e7i		−	0.218834i
$476$		0			0
$477$	4.84922e7			0.446804
$478$		0			0
$479$	7.96535e7	−	4.59880e7i	0.724767	−	0.418444i	−0.0917379	−	0.995783i	$-0.529242\pi$
$479$	7.96535e7	−	4.59880e7i	0.724767	−	0.418444i	0.816505	+	0.577339i	$0.195909\pi$
$480$		0			0
$481$	−6.12820e6	−	3.53812e6i	−0.0550678	−	0.0317934i
$482$		0			0
$483$	−8.21657e7	−	1.89516e7i	−0.729204	−	0.168192i
$484$		0			0
$485$	2.38855e7	−	4.13710e7i	0.209368	−	0.362636i
$486$		0			0
$487$	−9.53763e7	−	1.65197e8i	−0.825759	−	1.43026i	−0.901338	−	0.433117i	$-0.857414\pi$
$487$	−9.53763e7	−	1.65197e8i	−0.825759	−	1.43026i	0.0755785	−	0.997140i	$-0.475920\pi$
$488$		0			0
$489$		−	8.68725e7i		−	0.742944i
$490$		0			0
$491$	−8.85504e7			−0.748077			−0.374038	−	0.927413i	$-0.622027\pi$
$491$	−8.85504e7			−0.748077			−0.374038	+	0.927413i	$0.622027\pi$
$492$		0			0
$493$	1.26782e8	−	7.31975e7i	1.05807	−	0.610880i
$494$		0			0
$495$	−7.73647e6	−	4.46665e6i	−0.0637862	−	0.0368270i
$496$		0			0
$497$	1.20356e7	−	5.21810e7i	0.0980391	−	0.425053i
$498$		0			0
$499$	−2.61754e7	+	4.53371e7i	−0.210665	+	0.364882i	−0.951923	−	0.306338i	$-0.900896\pi$
$499$	−2.61754e7	+	4.53371e7i	−0.210665	+	0.364882i	0.741258	+	0.671220i	$0.234230\pi$
$500$		0			0
$501$	−1.74893e7	−	3.02923e7i	−0.139078	−	0.240890i
$502$		0			0
$503$		−	1.34114e8i		−	1.05383i	−0.849919	−	0.526914i	$-0.823349\pi$
$503$		−	1.34114e8i		−	1.05383i	0.849919	−	0.526914i	$-0.176651\pi$
$504$		0			0
$505$	6.08718e7			0.472653
$506$		0			0
$507$	−5.86130e7	+	3.38402e7i	−0.449749	+	0.259663i
$508$		0			0
$509$	−1.62222e8	−	9.36588e7i	−1.23014	−	0.710224i	−0.263084	−	0.964773i	$-0.584740\pi$
$509$	−1.62222e8	−	9.36588e7i	−1.23014	−	0.710224i	−0.967060	+	0.254549i	$0.918073\pi$
$510$		0			0
$511$	3.76858e7	+	1.23174e8i	0.282432	+	0.923115i
$512$		0			0
$513$	−5.09038e6	+	8.81679e6i	−0.0377049	+	0.0653068i
$514$		0			0
$515$	−4.35522e7	−	7.54347e7i	−0.318852	−	0.552267i
$516$		0			0
$517$		−	2.22540e7i		−	0.161041i
$518$		0			0
$519$	1.07255e8			0.767216
$520$		0			0
$521$	−3.89027e7	+	2.24605e7i	−0.275085	+	0.158820i	−0.631196	−	0.775623i	$-0.717436\pi$
$521$	−3.89027e7	+	2.24605e7i	−0.275085	+	0.158820i	0.356111	+	0.934444i	$0.384102\pi$
$522$		0			0
$523$	−1.43752e8	−	8.29951e7i	−1.00487	−	0.580160i	−0.0951815	−	0.995460i	$-0.530343\pi$
$523$	−1.43752e8	−	8.29951e7i	−1.00487	−	0.580160i	−0.909684	+	0.415300i	$0.863676\pi$
$524$		0			0
$525$	−3.18134e7	+	3.41298e7i	−0.219853	+	0.235861i
$526$		0			0
$527$	1.49534e8	−	2.59000e8i	1.02166	−	1.76957i
$528$		0			0
$529$	−5.03382e7	−	8.71883e7i	−0.340041	−	0.588967i
$530$		0			0
$531$			9.40956e7i			0.628472i
$532$		0			0
$533$	−2.65820e7			−0.175552
$534$		0			0
$535$	8.45064e7	−	4.87898e7i	0.551859	−	0.318616i
$536$		0			0
$537$	1.06554e8	+	6.15188e7i	0.688091	+	0.397269i
$538$		0			0
$539$	3.65378e6	+	5.19441e7i	0.0233333	+	0.331718i
$540$		0			0
$541$	−6.31514e7	+	1.09381e8i	−0.398833	+	0.690799i	−0.993582	−	0.113112i	$-0.963918\pi$
$541$	−6.31514e7	+	1.09381e8i	−0.398833	+	0.690799i	0.594749	+	0.803911i	$0.297251\pi$
$542$		0			0
$543$	2.05486e7	+	3.55912e7i	0.128346	+	0.222302i
$544$		0			0
$545$		−	6.09727e7i		−	0.376657i
$546$		0			0
$547$	−2.31931e8			−1.41709			−0.708545	−	0.705666i	$-0.750648\pi$
$547$	−2.31931e8			−1.41709			−0.708545	+	0.705666i	$0.750648\pi$
$548$		0			0
$549$	−2.47945e6	+	1.43151e6i	−0.0149843	+	0.00865121i
$550$		0			0
$551$	−5.41729e7	−	3.12767e7i	−0.323838	−	0.186968i
$552$		0			0
$553$	8.32585e6	+	7.76078e6i	0.0492327	+	0.0458912i
$554$		0			0
$555$	−6.57725e6	+	1.13921e7i	−0.0384738	+	0.0666386i
$556$		0			0
$557$	−1.20538e8	−	2.08779e8i	−0.697525	−	1.20815i	−0.969322	−	0.245794i	$-0.920951\pi$
$557$	−1.20538e8	−	2.08779e8i	−0.697525	−	1.20815i	0.271797	−	0.962355i	$-0.412382\pi$
$558$		0			0
$559$		−	1.05308e8i		−	0.602872i
$560$		0			0
$561$	−4.33978e7			−0.245799
$562$		0			0
$563$	1.01477e8	−	5.85878e7i	0.568647	−	0.328308i	−0.187962	−	0.982176i	$-0.560188\pi$
$563$	1.01477e8	−	5.85878e7i	0.568647	−	0.328308i	0.756609	+	0.653868i	$0.226855\pi$
$564$		0			0
$565$	1.47405e8	+	8.51042e7i	0.817271	+	0.471852i
$566$		0			0
$567$	1.93676e7	−	5.92563e6i	0.106249	−	0.0325076i
$568$		0			0
$569$	6.04302e7	−	1.04668e8i	0.328033	−	0.568170i	−0.654088	−	0.756418i	$-0.726948\pi$
$569$	6.04302e7	−	1.04668e8i	0.328033	−	0.568170i	0.982121	+	0.188248i	$0.0602809\pi$
$570$		0			0
$571$	5.39062e7	+	9.33683e7i	0.289555	+	0.501523i	0.973703	−	0.227819i	$-0.0731595\pi$
$571$	5.39062e7	+	9.33683e7i	0.289555	+	0.501523i	−0.684149	+	0.729342i	$0.739826\pi$
$572$		0			0
$573$			1.92399e8i			1.02268i
$574$		0			0
$575$	−1.37618e8			−0.723887
$576$		0			0
$577$	−6.79444e7	+	3.92277e7i	−0.353693	+	0.204205i	−0.666310	−	0.745674i	$-0.732127\pi$
$577$	−6.79444e7	+	3.92277e7i	−0.353693	+	0.204205i	0.312618	+	0.949879i	$0.398794\pi$
$578$		0			0
$579$	−1.80796e8	−	1.04382e8i	−0.931435	−	0.537764i
$580$		0			0
$581$	3.29207e8	+	7.59319e7i	1.67857	+	0.387165i
$582$		0			0
$583$	4.41627e7	−	7.64920e7i	0.222869	−	0.386020i
$584$		0			0
$585$	−7.02878e6	−	1.21742e7i	−0.0351085	−	0.0608097i
$586$		0			0
$587$			1.98030e8i			0.979075i	0.871982	+	0.489538i	$0.162834\pi$
$587$			1.98030e8i			0.979075i	−0.871982	+	0.489538i	$0.837166\pi$
$588$		0			0
$589$	−1.27789e8			−0.625387
$590$		0			0
$591$	1.27233e8	−	7.34581e7i	0.616365	−	0.355859i
$592$		0			0
$593$	−3.26564e6	−	1.88542e6i	−0.0156605	−	0.00904157i	0.492149	−	0.870511i	$-0.336211\pi$
$593$	−3.26564e6	−	1.88542e6i	−0.0156605	−	0.00904157i	−0.507810	+	0.861469i	$0.669545\pi$
$594$		0			0
$595$	4.02742e7	−	1.74611e8i	0.191195	−	0.828933i
$596$		0			0
$597$	4.42475e7	−	7.66389e7i	0.207953	−	0.360186i
$598$		0			0
$599$	1.33653e8	+	2.31493e8i	0.621867	+	1.07710i	0.989138	+	0.146991i	$0.0469588\pi$
$599$	1.33653e8	+	2.31493e8i	0.621867	+	1.07710i	−0.367271	+	0.930114i	$0.619708\pi$
$600$		0			0
$601$		−	9.26866e7i		−	0.426966i	−0.976947	−	0.213483i	$-0.931519\pi$
$601$		−	9.26866e7i		−	0.426966i	0.976947	−	0.213483i	$-0.0684809\pi$
$602$		0			0
$603$	−9.33790e7			−0.425890
$604$		0			0
$605$	1.13339e8	−	6.54363e7i	0.511815	−	0.295497i
$606$		0			0
$607$	−1.38921e8	−	8.02061e7i	−0.621158	−	0.358625i	0.156162	−	0.987731i	$-0.450088\pi$
$607$	−1.38921e8	−	8.02061e7i	−0.621158	−	0.358625i	−0.777320	+	0.629106i	$0.783421\pi$
$608$		0			0
$609$	3.64088e7	+	1.19000e8i	0.161196	+	0.526860i
$610$		0			0
$611$	1.75096e7	−	3.03275e7i	0.0767631	−	0.132958i
$612$		0			0
$613$	−3.60980e7	−	6.25236e7i	−0.156712	−	0.271433i	0.776969	−	0.629539i	$-0.216756\pi$
$613$	−3.60980e7	−	6.25236e7i	−0.156712	−	0.271433i	−0.933681	+	0.358106i	$0.883423\pi$
$614$		0			0
$615$			4.94151e7i			0.212439i
$616$		0			0
$617$	3.16720e6			0.0134841			0.00674203	−	0.999977i	$-0.497854\pi$
$617$	3.16720e6			0.0134841			0.00674203	+	0.999977i	$0.497854\pi$
$618$		0			0
$619$	−1.20117e8	+	6.93494e7i	−0.506444	+	0.292396i	−0.731371	−	0.681980i	$-0.761119\pi$
$619$	−1.20117e8	+	6.93494e7i	−0.506444	+	0.292396i	0.224927	+	0.974376i	$0.427786\pi$
$620$		0			0
$621$	5.17355e7	+	2.98695e7i	0.216030	+	0.124725i
$622$		0			0
$623$	6.14183e7	−	6.58903e7i	0.254000	−	0.272494i
$624$		0			0
$625$	1.58233e7	−	2.74068e7i	0.0648124	−	0.112258i
$626$		0			0
$627$	9.27178e6	+	1.60592e7i	0.0376150	+	0.0651510i
$628$		0			0
$629$			6.39043e7i			0.256790i
$630$		0			0
$631$	1.98716e8			0.790944			0.395472	−	0.918478i	$-0.370581\pi$
$631$	1.98716e8			0.790944			0.395472	+	0.918478i	$0.370581\pi$
$632$		0			0
$633$	1.42014e7	−	8.19920e6i	0.0559914	−	0.0323266i
$634$		0			0
$635$	1.18462e8	+	6.83941e7i	0.462656	+	0.267114i
$636$		0			0
$637$	−3.58906e7	+	7.36636e7i	−0.138855	+	0.284993i
$638$		0			0
$639$	−1.89693e7	+	3.28557e7i	−0.0727022	+	0.125924i
$640$		0			0
$641$	−7.21736e7	−	1.25008e8i	−0.274034	−	0.474641i	0.695857	−	0.718180i	$-0.255025\pi$
$641$	−7.21736e7	−	1.25008e8i	−0.274034	−	0.474641i	−0.969891	+	0.243540i	$0.921691\pi$
$642$		0			0
$643$			2.68271e8i			1.00911i	0.863378	+	0.504557i	$0.168344\pi$
$643$			2.68271e8i			1.00911i	−0.863378	+	0.504557i	$0.831656\pi$
$644$		0			0
$645$	−1.95764e8			−0.729548
$646$		0			0
$647$	3.38971e8	−	1.95705e8i	1.25155	−	0.722585i	0.280136	−	0.959960i	$-0.409620\pi$
$647$	3.38971e8	−	1.95705e8i	1.25155	−	0.722585i	0.971418	+	0.237375i	$0.0762871\pi$
$648$		0			0
$649$	1.48427e8	+	8.56944e7i	0.542974	+	0.313486i
$650$		0			0
$651$	1.85966e8	+	1.73344e8i	0.674046	+	0.628299i
$652$		0			0
$653$	−2.30591e8	+	3.99396e8i	−0.828139	+	1.43438i	0.0713566	+	0.997451i	$0.477267\pi$
$653$	−2.30591e8	+	3.99396e8i	−0.828139	+	1.43438i	−0.899496	+	0.436929i	$0.856066\pi$
$654$		0			0
$655$	8.55845e7	+	1.48237e8i	0.304559	+	0.527512i
$656$		0			0
$657$		−	9.12561e7i		−	0.321785i
$658$		0			0
$659$	−2.90612e8			−1.01545			−0.507724	−	0.861520i	$-0.669513\pi$
$659$	−2.90612e8			−1.01545			−0.507724	+	0.861520i	$0.669513\pi$
$660$		0			0
$661$	−2.43164e8	+	1.40391e8i	−0.841965	+	0.486109i	−0.857932	−	0.513764i	$-0.828251\pi$
$661$	−2.43164e8	+	1.40391e8i	−0.841965	+	0.486109i	0.0159666	+	0.999873i	$0.494917\pi$
$662$		0			0
$663$	−5.91421e7	−	3.41457e7i	−0.202935	−	0.117164i
$664$		0			0
$665$	−7.32183e7	+	2.24016e7i	−0.248975	+	0.0761752i
$666$		0			0
$667$	−1.83527e8	+	3.17878e8i	−0.618475	+	1.07123i
$668$		0			0
$669$	7.76784e7	+	1.34543e8i	0.259431	+	0.449348i
$670$		0			0
$671$			5.21480e6i			0.0172611i
$672$		0			0
$673$	−2.35293e8			−0.771904			−0.385952	−	0.922519i	$-0.626127\pi$
$673$	−2.35293e8			−0.771904			−0.385952	+	0.922519i	$0.626127\pi$
$674$		0			0
$675$	2.86264e7	−	1.65274e7i	0.0930796	−	0.0537396i
$676$		0			0
$677$	−5.35332e8	−	3.09074e8i	−1.72527	−	0.996085i	−0.906835	−	0.421486i	$-0.861509\pi$
$677$	−5.35332e8	−	3.09074e8i	−1.72527	−	0.996085i	−0.818435	−	0.574599i	$-0.805158\pi$
$678$		0			0
$679$	1.92228e8	+	4.43377e7i	0.614056	+	0.141633i
$680$		0			0
$681$	1.43966e8	−	2.49357e8i	0.455848	−	0.789552i
$682$		0			0
$683$	6.53722e6	+	1.13228e7i	0.0205178	+	0.0355379i	0.876102	−	0.482126i	$-0.160135\pi$
$683$	6.53722e6	+	1.13228e7i	0.0205178	+	0.0355379i	−0.855584	+	0.517664i	$0.826802\pi$
$684$		0			0
$685$		−	2.68214e8i		−	0.834468i
$686$		0			0
$687$	−2.12248e8			−0.654595
$688$		0			0
$689$	1.20369e8	−	6.94949e7i	0.368007	−	0.212469i
$690$		0			0
$691$	−2.37346e8	−	1.37032e8i	−0.719362	−	0.415324i	0.0951555	−	0.995462i	$-0.469665\pi$
$691$	−2.37346e8	−	1.37032e8i	−0.719362	−	0.415324i	−0.814518	+	0.580138i	$0.802998\pi$
$692$		0			0
$693$	8.29126e6	−	3.59471e7i	0.0249127	−	0.108010i
$694$		0			0
$695$	1.68908e8	−	2.92558e8i	0.503149	−	0.871480i
$696$		0			0
$697$	1.20029e8	+	2.07896e8i	0.354476	+	0.613971i
$698$		0			0
$699$		−	159096.i		−	0.000465831i
$700$		0			0
$701$	4.35624e8			1.26461			0.632307	−	0.774718i	$-0.282108\pi$
$701$	4.35624e8			1.26461			0.632307	+	0.774718i	$0.282108\pi$
$702$		0			0
$703$	2.36475e7	−	1.36529e7i	0.0680644	−	0.0392970i
$704$		0			0
$705$	−5.63779e7	−	3.25498e7i	−0.160895	−	0.0928925i
$706$		0			0
$707$	7.35448e7	+	2.40377e8i	0.208110	+	0.680197i
$708$		0			0
$709$	1.80906e8	−	3.13339e8i	0.507592	−	0.879176i	−0.492369	−	0.870387i	$-0.663869\pi$
$709$	1.80906e8	−	3.13339e8i	0.507592	−	0.879176i	0.999961	−	0.00878924i	$-0.00279774\pi$
$710$		0			0
$711$	−4.03181e6	−	6.98330e6i	−0.0112174	−	0.0194291i
$712$		0			0
$713$			7.49848e8i			2.06873i
$714$		0			0
$715$	−2.56049e7			−0.0700495
$716$		0			0
$717$	3.36916e7	−	1.94518e7i	0.0914037	−	0.0527720i
$718$		0			0
$719$	2.12503e8	+	1.22689e8i	0.571713	+	0.330079i	0.757833	−	0.652448i	$-0.226258\pi$
$719$	2.12503e8	+	1.22689e8i	0.571713	+	0.330079i	−0.186120	+	0.982527i	$0.559591\pi$
$720$		0			0
$721$	2.45265e8	−	2.63123e8i	0.654380	−	0.702026i
$722$		0			0
$723$	4.26377e7	−	7.38506e7i	0.112818	−	0.195407i
$724$		0			0
$725$	1.01549e8	+	1.75888e8i	0.266479	+	0.461555i
$726$		0			0
$727$			2.59949e8i			0.676526i	0.941052	+	0.338263i	$0.109839\pi$
$727$			2.59949e8i			0.676526i	−0.941052	+	0.338263i	$0.890161\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	−8.23606e8	+	4.75509e8i	−2.10847	+	1.21733i
$732$		0			0
$733$	−1.08280e8	−	6.25152e7i	−0.274938	−	0.158735i	0.356192	−	0.934413i	$-0.384075\pi$
$733$	−1.08280e8	−	6.25152e7i	−0.274938	−	0.158735i	−0.631129	+	0.775678i	$0.717408\pi$
$734$		0			0
$735$	1.36938e8	+	6.67195e7i	0.344876	+	0.168031i
$736$		0			0
$737$	−8.50418e7	+	1.47297e8i	−0.212437	+	0.367951i
$738$		0			0
$739$	−2.82361e8	−	4.89063e8i	−0.699634	−	1.21180i	−0.968593	−	0.248650i	$-0.920013\pi$
$739$	−2.82361e8	−	4.89063e8i	−0.699634	−	1.21180i	0.268960	−	0.963151i	$-0.413320\pi$
$740$		0			0
$741$			2.91804e7i			0.0717194i
$742$		0			0
$743$	−2.68677e8			−0.655035			−0.327518	−	0.944845i	$-0.606212\pi$
$743$	−2.68677e8			−0.655035			−0.327518	+	0.944845i	$0.606212\pi$
$744$		0			0
$745$	2.01029e8	−	1.16064e8i	0.486171	−	0.280691i
$746$		0			0
$747$	−2.07284e8	−	1.19676e8i	−0.497285	−	0.287107i
$748$		0			0
$749$	2.94766e8	+	2.74760e8i	0.701507	+	0.653896i
$750$		0			0
$751$	1.95480e8	−	3.38581e8i	0.461512	−	0.799362i	−0.537525	−	0.843248i	$-0.680641\pi$
$751$	1.95480e8	−	3.38581e8i	0.461512	−	0.799362i	0.999037	+	0.0438862i	$0.0139739\pi$
$752$		0			0
$753$	−1.70245e7	−	2.94873e7i	−0.0398740	−	0.0690637i
$754$		0			0
$755$			5.00927e7i			0.116395i
$756$		0			0
$757$	−5.67872e8			−1.30907			−0.654535	−	0.756031i	$-0.727136\pi$
$757$	−5.67872e8			−1.30907			−0.654535	+	0.756031i	$0.727136\pi$
$758$		0			0
$759$	9.42327e7	−	5.44053e7i	0.215515	−	0.124427i
$760$		0			0
$761$	−1.66316e8	−	9.60225e7i	−0.377381	−	0.217881i	0.299297	−	0.954160i	$-0.403248\pi$
$761$	−1.66316e8	−	9.60225e7i	−0.377381	−	0.217881i	−0.676678	+	0.736279i	$0.736581\pi$
$762$		0			0
$763$	2.40776e8	−	7.36667e7i	0.542049	−	0.165843i
$764$		0			0
$765$	−6.34758e7	+	1.09943e8i	−0.141783	+	0.245575i
$766$		0			0
$767$	1.34850e8	+	2.33567e8i	0.298858	+	0.517637i
$768$		0			0
$769$			7.75766e8i			1.70589i	0.521999	+	0.852946i	$0.325187\pi$
$769$			7.75766e8i			1.70589i	−0.521999	+	0.852946i	$0.674813\pi$
$770$		0			0
$771$	4.90748e8			1.07077
$772$		0			0
$773$	2.34180e7	−	1.35204e7i	0.0507005	−	0.0292719i	−0.474436	−	0.880290i	$-0.657348\pi$
$773$	2.34180e7	−	1.35204e7i	0.0507005	−	0.0292719i	0.525136	+	0.851018i	$0.324014\pi$
$774$		0			0
$775$	3.59320e8	+	2.07453e8i	0.771926	+	0.445672i
$776$		0			0
$777$	−5.29330e7	−	1.22091e7i	−0.112840	−	0.0260267i
$778$		0			0
$779$	5.12874e7	−	8.88323e7i	0.108492	−	0.187914i
$780$		0			0
$781$	3.45512e7	+	5.98445e7i	0.0725288	+	0.125624i
$782$		0			0
$783$		−	8.81638e7i		−	0.183656i
$784$		0			0
$785$	−1.18699e8			−0.245379
$786$		0			0
$787$	3.68573e8	−	2.12796e8i	0.756136	−	0.436555i	−0.0717707	−	0.997421i	$-0.522865\pi$
$787$	3.68573e8	−	2.12796e8i	0.756136	−	0.436555i	0.827907	+	0.560866i	$0.189532\pi$
$788$		0			0
$789$	−8.87979e7	−	5.12675e7i	−0.180789	−	0.104379i
$790$		0			0
$791$	−1.57975e8	+	6.84910e8i	−0.319198	+	1.38390i
$792$		0			0
$793$	−4.10303e6	+	7.10666e6i	−0.00822783	+	0.0142510i
$794$		0			0
$795$	−1.29189e8	−	2.23762e8i	−0.257113	−	0.445333i
$796$		0			0
$797$		−	7.51386e7i		−	0.148419i	−0.997243	−	0.0742093i	$-0.976357\pi$
$797$		−	7.51386e7i		−	0.148419i	0.997243	−	0.0742093i	$-0.0236433\pi$
$798$		0			0
$799$	−3.16253e8			−0.620003
$800$		0			0
$801$	−5.52654e7	+	3.19075e7i	−0.107536	+	0.0620862i
$802$		0			0
$803$	−1.43948e8	−	8.31084e7i	−0.278009	−	0.160509i
$804$		0			0
$805$	1.31449e8	+	4.29633e8i	0.251982	+	0.823589i
$806$		0			0
$807$	−1.71378e6	+	2.96835e6i	−0.00326088	+	0.00564801i
$808$		0			0
$809$	3.91158e8	+	6.77506e8i	0.738766	+	1.27958i	0.953051	+	0.302810i	$0.0979246\pi$
$809$	3.91158e8	+	6.77506e8i	0.738766	+	1.27958i	−0.214285	+	0.976771i	$0.568742\pi$
$810$		0			0
$811$			8.00635e8i			1.50097i	0.660888	+	0.750485i	$0.270180\pi$
$811$			8.00635e8i			1.50097i	−0.660888	+	0.750485i	$0.729820\pi$
$812$		0			0
$813$	−4.33948e8			−0.807544
$814$		0			0
$815$	−4.00863e8	+	2.31439e8i	−0.740497	+	0.427526i
$816$		0			0
$817$	3.51921e8	+	2.03181e8i	0.645325	+	0.372579i
$818$		0			0
$819$	3.95827e7	−	4.24647e7i	0.0720532	−	0.0772995i
$820$		0			0
$821$	1.37831e8	−	2.38730e8i	0.249067	−	0.431397i	−0.714200	−	0.699942i	$-0.753209\pi$
$821$	1.37831e8	−	2.38730e8i	0.249067	−	0.431397i	0.963267	+	0.268544i	$0.0865426\pi$
$822$		0			0
$823$	−3.78952e8	−	6.56364e8i	−0.679806	−	1.17746i	−0.975039	−	0.222033i	$-0.928731\pi$
$823$	−3.78952e8	−	6.56364e8i	−0.679806	−	1.17746i	0.295233	−	0.955425i	$-0.404603\pi$
$824$		0			0
$825$		−	6.02072e7i		−	0.107223i
$826$		0			0
$827$	−3.06595e8			−0.542061			−0.271030	−	0.962571i	$-0.587364\pi$
$827$	−3.06595e8			−0.542061			−0.271030	+	0.962571i	$0.587364\pi$
$828$		0			0
$829$	1.07092e8	−	6.18296e7i	0.187972	−	0.108526i	−0.403061	−	0.915173i	$-0.632054\pi$
$829$	1.07092e8	−	6.18296e7i	0.187972	−	0.108526i	0.591033	+	0.806647i	$0.298720\pi$
$830$		0			0
$831$	−7.76858e7	−	4.48519e7i	−0.135375	−	0.0781588i
$832$		0			0
$833$	7.38180e8	−	5.19240e7i	1.27711	−	0.0898325i
$834$		0			0
$835$	−9.31869e7	+	1.61405e8i	−0.160065	+	0.277240i
$836$		0			0
$837$	−9.00542e7	−	1.55978e8i	−0.153577	−	0.266004i
$838$		0			0
$839$			2.04720e8i			0.346637i	0.984866	+	0.173318i	$0.0554489\pi$
$839$			2.04720e8i			0.346637i	−0.984866	+	0.173318i	$0.944551\pi$
$840$		0			0
$841$	−5.31198e7			−0.0893035
$842$		0			0
$843$	−2.37374e8	+	1.37048e8i	−0.396233	+	0.228765i
$844$		0			0
$845$	3.12304e8	+	1.80309e8i	0.517615	+	0.298845i
$846$		0			0
$847$	3.95337e8	+	3.68505e8i	0.650604	+	0.606448i
$848$		0			0
$849$	1.14719e8	−	1.98699e8i	0.187462	−	0.324693i
$850$		0			0
$851$	−8.01131e7	−	1.38760e8i	−0.129991	−	0.225152i
$852$		0			0
$853$			1.81851e8i			0.293001i	0.989211	+	0.146500i	$0.0468010\pi$
$853$			1.81851e8i			0.293001i	−0.989211	+	0.146500i	$0.953199\pi$
$854$		0			0
$855$	5.42454e7			0.0867890
$856$		0			0
$857$	−5.32176e8	+	3.07252e8i	−0.845499	+	0.488149i	−0.859130	−	0.511758i	$-0.828994\pi$
$857$	−5.32176e8	+	3.07252e8i	−0.845499	+	0.488149i	0.0136307	+	0.999907i	$0.495661\pi$
$858$		0			0
$859$	1.89532e8	+	1.09426e8i	0.299022	+	0.172640i	0.642003	−	0.766702i	$-0.278103\pi$
$859$	1.89532e8	+	1.09426e8i	0.299022	+	0.172640i	−0.342981	+	0.939342i	$0.611437\pi$
$860$		0			0
$861$	−1.95135e8	+	5.97028e7i	−0.305722	+	0.0935374i
$862$		0			0
$863$	−3.29715e8	+	5.71084e8i	−0.512988	+	0.888521i	0.486899	+	0.873458i	$0.338128\pi$
$863$	−3.29715e8	+	5.71084e8i	−0.512988	+	0.888521i	−0.999887	+	0.0150623i	$0.995205\pi$
$864$		0			0
$865$	−2.85741e8	−	4.94918e8i	−0.441494	−	0.764689i
$866$		0			0
$867$			2.40461e8i			0.368967i
$868$		0			0
$869$	−1.46873e7			−0.0223812
$870$		0			0
$871$	−2.31788e8	+	1.33823e8i	−0.350781	+	0.202524i
$872$		0			0
$873$	−1.21036e8	−	6.98804e7i	−0.181917	−	0.105030i
$874$		0			0
$875$	6.75998e8	+	1.55920e8i	1.00907	+	0.232743i
$876$		0			0
$877$	−8.11828e7	+	1.40613e8i	−0.120355	+	0.208462i	−0.919908	−	0.392135i	$-0.871737\pi$
$877$	−8.11828e7	+	1.40613e8i	−0.120355	+	0.208462i	0.799552	+	0.600596i	$0.205070\pi$
$878$		0			0
$879$	−2.72598e7	−	4.72153e7i	−0.0401380	−	0.0695210i
$880$		0			0
$881$			8.48365e8i			1.24067i	0.784338	+	0.620333i	$0.213003\pi$
$881$			8.48365e8i			1.24067i	−0.784338	+	0.620333i	$0.786997\pi$
$882$		0			0
$883$	−3.14592e8			−0.456947			−0.228473	−	0.973550i	$-0.573373\pi$
$883$	−3.14592e8			−0.456947			−0.228473	+	0.973550i	$0.573373\pi$
$884$		0			0
$885$	4.34193e8	−	2.50682e8i	0.626402	−	0.361654i
$886$		0			0
$887$	7.25058e8	+	4.18612e8i	1.03897	+	0.599848i	0.919540	−	0.392995i	$-0.128561\pi$
$887$	7.25058e8	+	4.18612e8i	1.03897	+	0.599848i	0.119426	+	0.992843i	$0.461894\pi$
$888$		0			0
$889$	−1.26957e8	+	5.50429e8i	−0.180697	+	0.783422i
$890$		0			0
$891$	−1.30678e7	+	2.26341e7i	−0.0184743	+	0.0319985i
$892$		0			0
$893$	6.75662e7	+	1.17028e8i	0.0948800	+	0.164337i
$894$		0			0
$895$		−	6.55573e8i		−	0.914433i
$896$		0			0
$897$	1.71226e8			0.237242
$898$		0			0
$899$	9.58376e8	−	5.53319e8i	1.31904	−	0.761546i
$900$		0			0
$901$	−1.08703e9	−	6.27598e8i	−1.48617	−	0.858039i
$902$		0			0
$903$	−2.36520e8	−	7.73054e8i	−0.321222	−	1.04990i
$904$		0			0
$905$	1.09488e8	−	1.89638e8i	0.147713	−	0.255847i
$906$		0			0
$907$	3.44024e8	+	5.95867e8i	0.461070	+	0.798596i	0.999015	−	0.0443839i	$-0.0141325\pi$
$907$	3.44024e8	+	5.95867e8i	0.461070	+	0.798596i	−0.537945	+	0.842980i	$0.680799\pi$
$908$		0			0
$909$		−	1.78089e8i		−	0.237107i
$910$		0			0
$911$	−2.31613e8			−0.306343			−0.153171	−	0.988200i	$-0.548949\pi$
$911$	−2.31613e8			−0.306343			−0.153171	+	0.988200i	$0.548949\pi$
$912$		0			0
$913$	−3.77555e8	+	2.17981e8i	−0.496098	+	0.286422i
$914$		0			0
$915$	1.32111e7	+	7.62741e6i	0.0172455	+	0.00995667i
$916$		0			0
$917$	−4.81971e8	+	5.17064e8i	−0.625047	+	0.670557i
$918$		0			0
$919$	−5.62582e8	+	9.74420e8i	−0.724835	+	1.25545i	0.234207	+	0.972187i	$0.424751\pi$
$919$	−5.62582e8	+	9.74420e8i	−0.724835	+	1.25545i	−0.959042	+	0.283264i	$0.908583\pi$
$920$		0			0
$921$	−3.11530e8	−	5.39587e8i	−0.398769	−	0.690689i
$922$		0			0
$923$			1.08740e8i			0.138289i
$924$		0			0
$925$	−8.86565e7			−0.112017
$926$		0			0
$927$	−2.20694e8	+	1.27418e8i	−0.277046	+	0.159953i
$928$		0			0
$929$	−5.93421e8	−	3.42612e8i	−0.740143	−	0.427322i	0.0819782	−	0.996634i	$-0.473876\pi$
$929$	−5.93421e8	−	3.42612e8i	−0.740143	−	0.427322i	−0.822121	+	0.569312i	$0.807210\pi$
$930$		0			0
$931$	−1.76923e8	−	2.62067e8i	−0.219248	−	0.324761i
$932$		0			0
$933$	−2.59933e8	+	4.50218e8i	−0.320049	+	0.554342i
$934$		0			0
$935$	1.15617e8	+	2.00254e8i	0.141445	+	0.244989i
$936$		0			0
$937$		−	7.87984e8i		−	0.957852i	−0.877855	−	0.478926i	$-0.841026\pi$
$937$		−	7.87984e8i		−	0.957852i	0.877855	−	0.478926i	$-0.158974\pi$
$938$		0			0
$939$	−2.92905e8			−0.353778
$940$		0			0
$941$	1.79551e8	−	1.03664e8i	0.215486	−	0.124411i	−0.388372	−	0.921503i	$-0.626963\pi$
$941$	1.79551e8	−	1.03664e8i	0.215486	−	0.124411i	0.603859	+	0.797092i	$0.293629\pi$
$942$		0			0
$943$	−5.21254e8	−	3.00946e8i	−0.621604	−	0.358883i
$944$		0			0
$945$	−7.89406e7	−	7.35830e7i	−0.0935417	−	0.0871930i
$946$		0			0
$947$	−1.77030e8	+	3.06624e8i	−0.208447	+	0.361041i	−0.951226	−	0.308496i	$-0.900174\pi$
$947$	−1.77030e8	+	3.06624e8i	−0.208447	+	0.361041i	0.742778	+	0.669537i	$0.233508\pi$
$948$		0			0
$949$	−1.30780e8	−	2.26518e8i	−0.153019	−	0.265036i
$950$		0			0
$951$			3.17960e8i			0.369685i
$952$		0			0
$953$	−4.28652e8			−0.495252			−0.247626	−	0.968856i	$-0.579650\pi$
$953$	−4.28652e8			−0.495252			−0.247626	+	0.968856i	$0.579650\pi$
$954$		0			0
$955$	8.87803e8	−	5.12573e8i	1.01931	−	0.588499i
$956$		0			0
$957$	−1.39070e8	−	8.02922e7i	−0.158671	−	0.0916089i
$958$		0			0
$959$	1.05915e9	−	3.24054e8i	1.20089	−	0.367419i
$960$		0			0
$961$	6.86614e8	−	1.18925e9i	0.773646	−	1.33999i
$962$		0			0
$963$	−1.42741e8	−	2.47235e8i	−0.159834	−	0.276841i
$964$		0			0
$965$			1.11235e9i			1.23782i
$966$		0			0
$967$	−1.16972e9			−1.29361			−0.646805	−	0.762655i	$-0.723895\pi$
$967$	−1.16972e9			−1.29361			−0.646805	+	0.762655i	$0.723895\pi$
$968$		0			0
$969$	2.28218e8	−	1.31762e8i	0.250829	−	0.144816i
$970$		0			0
$971$	−6.09512e8	−	3.51902e8i	−0.665770	−	0.384383i	0.128702	−	0.991683i	$-0.458919\pi$
$971$	−6.09512e8	−	3.51902e8i	−0.665770	−	0.384383i	−0.794472	+	0.607301i	$0.792252\pi$
$972$		0			0
$973$	1.35936e9	+	3.13537e8i	1.47569	+	0.340370i
$974$		0			0
$975$	4.73714e7	−	8.20497e7i	0.0511096	−	0.0885244i
$976$		0			0
$977$	−2.21206e8	−	3.83140e8i	−0.237199	−	0.410841i	0.722710	−	0.691151i	$-0.242896\pi$
$977$	−2.21206e8	−	3.83140e8i	−0.237199	−	0.410841i	−0.959910	+	0.280310i	$0.909563\pi$
$978$		0			0
$979$			1.16235e8i			0.123876i
$980$		0			0
$981$	−1.78384e8			−0.188951
$982$		0			0
$983$	1.01182e9	−	5.84175e8i	1.06523	−	0.615011i	0.138355	−	0.990383i	$-0.455818\pi$
$983$	1.01182e9	−	5.84175e8i	1.06523	−	0.615011i	0.926874	+	0.375372i	$0.122485\pi$
$984$		0			0
$985$	−6.77928e8	−	3.91402e8i	−0.709374	−	0.409557i
$986$		0			0
$987$	6.04208e7	−	2.61957e8i	0.0628398	−	0.272445i
$988$		0			0
$989$	1.19224e9	−	2.06501e9i	1.23246	−	2.13468i
$990$		0			0
$991$	−5.01818e8	−	8.69174e8i	−0.515615	−	0.893071i	−0.999836	−	0.0181249i	$-0.994230\pi$
$991$	−5.01818e8	−	8.69174e8i	−0.515615	−	0.893071i	0.484221	−	0.874946i	$-0.339103\pi$
$992$		0			0
$993$		−	3.32890e8i		−	0.339979i
$994$		0			0
$995$	−4.71522e8			−0.478666
$996$		0			0
$997$	1.60115e9	−	9.24424e8i	1.61565	−	0.932794i	0.627619	−	0.778521i	$-0.284030\pi$
$997$	1.60115e9	−	9.24424e8i	1.61565	−	0.932794i	0.988028	−	0.154274i	$-0.0493037\pi$
$998$		0			0
$999$	3.33292e7	+	1.92426e7i	0.0334294	+	0.0193005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.b.145.3		8
4.3	odd	2		21.7.f.b.19.3	yes	8
7.3	odd	6	inner	336.7.bh.b.241.3		8
12.11	even	2		63.7.m.c.19.2		8
28.3	even	6		21.7.f.b.10.3	✓	8
28.11	odd	6		147.7.f.a.31.3		8
28.19	even	6		147.7.d.a.97.3		8
28.23	odd	6		147.7.d.a.97.4		8
28.27	even	2		147.7.f.a.19.3		8
84.23	even	6		441.7.d.d.244.6		8
84.47	odd	6		441.7.d.d.244.5		8
84.59	odd	6		63.7.m.c.10.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.3	✓	8	28.3	even	6
21.7.f.b.19.3	yes	8	4.3	odd	2
63.7.m.c.10.2		8	84.59	odd	6
63.7.m.c.19.2		8	12.11	even	2
147.7.d.a.97.3		8	28.19	even	6
147.7.d.a.97.4		8	28.23	odd	6
147.7.f.a.19.3		8	28.27	even	2
147.7.f.a.31.3		8	28.11	odd	6
336.7.bh.b.145.3		8	1.1	even	1	trivial
336.7.bh.b.241.3		8	7.3	odd	6	inner
441.7.d.d.244.5		8	84.47	odd	6
441.7.d.d.244.6		8	84.23	even	6

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)

\(f(q)\)	\(=\)	\(q+(-13.5000 + 7.79423i) q^{3} +(71.9311 + 41.5295i) q^{5} +(-77.0894 + 334.225i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 + 7.79423i) q^{3} +(71.9311 + 41.5295i) q^{5} +(-77.0894 + 334.225i) q^{7} +(121.500 - 210.444i) q^{9} +(-221.304 - 383.310i) q^{11} -696.494i q^{13} -1294.76 q^{15} +(-5447.24 + 3144.96i) q^{17} +(2327.56 + 1343.82i) q^{19} +(-1564.32 - 5112.89i) q^{21} +(7885.31 - 13657.8i) q^{23} +(-4363.11 - 7557.12i) q^{25} +3788.00i q^{27} -23274.5 q^{29} +(-41177.0 + 23773.6i) q^{31} +(5975.21 + 3449.79i) q^{33} +(-19425.3 + 20839.7i) q^{35} +(5079.89 - 8798.64i) q^{37} +(5428.63 + 9402.67i) q^{39} -38165.4i q^{41} +151197. q^{43} +(17479.3 - 10091.7i) q^{45} +(43543.1 + 25139.6i) q^{47} +(-105763. - 51530.4i) q^{49} +(49025.1 - 84914.0i) q^{51} +(99778.2 + 172821. i) q^{53} -36762.6i q^{55} -41896.1 q^{57} +(-335347. + 193612. i) q^{59} +(-10203.5 - 5890.98i) q^{61} +(60969.3 + 56831.3i) q^{63} +(28925.0 - 50099.6i) q^{65} +(-192138. - 332792. i) q^{67} +245840. i q^{69} -156126. q^{71} +(325227. - 187770. i) q^{73} +(117804. + 68014.1i) q^{75} +(145172. - 44416.2i) q^{77} +(16591.8 - 28737.9i) q^{79} +(-29524.5 - 51137.9i) q^{81} -984986. i q^{83} -522434. q^{85} +(314206. - 181407. i) q^{87} +(-227430. - 131307. i) q^{89} +(232786. + 53692.3i) q^{91} +(370593. - 641886. i) q^{93} +(111616. + 193325. i) q^{95} -575147. i q^{97} -107554. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9	\( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99}+O(q^{100}) \) 8 * q - 108 * q^3 - 42 * q^5 - 748 * q^7 + 972 * q^9 + 1070 * q^11 + 756 * q^15 + 7212 * q^17 + 24606 * q^19 + 8154 * q^21 + 15224 * q^23 + 22274 * q^25 + 32524 * q^29 - 40200 * q^31 - 28890 * q^33 + 242436 * q^35 - 45670 * q^37 - 93366 * q^39 + 445660 * q^43 - 10206 * q^45 - 82884 * q^47 + 24116 * q^49 - 64908 * q^51 - 13034 * q^53 - 442908 * q^57 - 1810362 * q^59 - 392856 * q^61 - 38394 * q^63 - 389004 * q^65 - 384094 * q^67 - 225688 * q^71 + 903078 * q^73 - 601398 * q^75 - 327674 * q^77 + 559592 * q^79 - 236196 * q^81 + 1953576 * q^85 - 439074 * q^87 - 1770036 * q^89 + 2960718 * q^91 + 361800 * q^93 - 1160112 * q^95 + 520020 * q^99

Introduction

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