LMFDB - Embedded newform 336.7.bh.f.241.3

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} - 2x^{7} + 193x^{6} + 306x^{5} + 29845x^{4} + 16988x^{3} + 1125468x^{2} + 214128x + 35378704 $ x^8 - 2x^7 + 193x^6 + 306x^5 + 29845x^4 + 16988x^3 + 1125468x^2 + 214128*x + 35378704
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			241.3
Root			$3.07067 + 5.31856i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.7.bh.f.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 + 7.79423i) q^{3} +(77.6900 - 44.8543i) q^{5} +(-204.220 - 275.578i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 + 7.79423i) q^{3} +(77.6900 - 44.8543i) q^{5} +(-204.220 - 275.578i) q^{7} +(121.500 + 210.444i) q^{9} +(1011.84 - 1752.56i) q^{11} +1764.65i q^{13} +1398.42 q^{15} +(3389.35 + 1956.84i) q^{17} +(1452.07 - 838.352i) q^{19} +(-609.061 - 5312.04i) q^{21} +(151.374 + 262.187i) q^{23} +(-3788.68 + 6562.18i) q^{25} +3788.00i q^{27} +31999.3 q^{29} +(-25554.3 - 14753.8i) q^{31} +(27319.7 - 15773.0i) q^{33} +(-28226.7 - 12249.5i) q^{35} +(-44308.1 - 76743.8i) q^{37} +(-13754.1 + 23822.8i) q^{39} -72254.7i q^{41} +12716.1 q^{43} +(18878.7 + 10899.6i) q^{45} +(13743.6 - 7934.88i) q^{47} +(-34237.0 + 112557. i) q^{49} +(30504.2 + 52834.8i) q^{51} +(136562. - 236533. i) q^{53} -181542. i q^{55} +26137.2 q^{57} +(-137947. - 79643.9i) q^{59} +(-341303. + 197051. i) q^{61} +(33180.9 - 76459.7i) q^{63} +(79152.4 + 137096. i) q^{65} +(136041. - 235629. i) q^{67} +4719.37i q^{69} -49541.8 q^{71} +(39955.8 + 23068.5i) q^{73} +(-102294. + 59059.6i) q^{75} +(-689604. + 79067.7i) q^{77} +(372231. + 644723. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -658103. i q^{83} +351092. q^{85} +(431991. + 249410. i) q^{87} +(1.00470e6 - 580061. i) q^{89} +(486299. - 360378. i) q^{91} +(-229988. - 398351. i) q^{93} +(75207.5 - 130263. i) q^{95} -686019. i q^{97} +491754. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q + 108 * q^3 + 462 * q^5 - 580 * q^7 + 972 * q^9	$ 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9} - 1806 q^{11} + 8316 q^{15} + 9564 q^{17} - 23022 q^{19} - 1350 q^{21} - 2400 q^{23} + 32762 q^{25} - 2484 q^{29} - 148416 q^{31} - 48762 q^{33} - 11412 q^{35} - 84046 q^{37} + 75222 q^{39} - 92972 q^{43} + 112266 q^{45} + 323124 q^{47} - 8644 q^{49} + 86076 q^{51} + 358086 q^{53} - 414396 q^{57} - 719382 q^{59} + 421536 q^{61} + 104490 q^{63} - 322740 q^{65} - 267010 q^{67} + 464664 q^{71} + 1944486 q^{73} + 884574 q^{75} - 1713498 q^{77} + 685904 q^{79} - 236196 q^{81} - 3876168 q^{85} - 33534 q^{87} + 4130604 q^{89} + 484266 q^{91} - 1335744 q^{93} + 2105232 q^{95} - 877716 q^{99}+O(q^{100}) $ 8 * q + 108 * q^3 + 462 * q^5 - 580 * q^7 + 972 * q^9 - 1806 * q^11 + 8316 * q^15 + 9564 * q^17 - 23022 * q^19 - 1350 * q^21 - 2400 * q^23 + 32762 * q^25 - 2484 * q^29 - 148416 * q^31 - 48762 * q^33 - 11412 * q^35 - 84046 * q^37 + 75222 * q^39 - 92972 * q^43 + 112266 * q^45 + 323124 * q^47 - 8644 * q^49 + 86076 * q^51 + 358086 * q^53 - 414396 * q^57 - 719382 * q^59 + 421536 * q^61 + 104490 * q^63 - 322740 * q^65 - 267010 * q^67 + 464664 * q^71 + 1944486 * q^73 + 884574 * q^75 - 1713498 * q^77 + 685904 * q^79 - 236196 * q^81 - 3876168 * q^85 - 33534 * q^87 + 4130604 * q^89 + 484266 * q^91 - 1335744 * q^93 + 2105232 * q^95 - 877716 * 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
$5$	77.6900	−	44.8543i	0.621520	−	0.358835i	−0.155941	−	0.987766i	$-0.549841\pi$
$5$	77.6900	−	44.8543i	0.621520	−	0.358835i	0.777461	+	0.628932i	$0.216507\pi$
$6$		0			0
$7$	−204.220	−	275.578i	−0.595395	−	0.803433i
$7$	−204.220	−	275.578i	−0.595395	−	0.803433i
$8$		0			0
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$		0			0
$11$	1011.84	−	1752.56i	0.760210	−	1.31672i	−0.182532	−	0.983200i	$-0.558429\pi$
$11$	1011.84	−	1752.56i	0.760210	−	1.31672i	0.942742	−	0.333522i	$-0.108237\pi$
$12$		0			0
$13$			1764.65i			0.803210i	0.915813	+	0.401605i	$0.131548\pi$
$13$			1764.65i			0.803210i	−0.915813	+	0.401605i	$0.868452\pi$
$14$		0			0
$15$	1398.42			0.414347
$16$		0			0
$17$	3389.35	+	1956.84i	0.689875	+	0.398299i	0.803565	−	0.595217i	$-0.202934\pi$
$17$	3389.35	+	1956.84i	0.689875	+	0.398299i	−0.113690	+	0.993516i	$0.536267\pi$
$18$		0			0
$19$	1452.07	−	838.352i	0.211703	−	0.122227i	−0.390400	−	0.920645i	$-0.627663\pi$
$19$	1452.07	−	838.352i	0.211703	−	0.122227i	0.602102	+	0.798419i	$0.294330\pi$
$20$		0			0
$21$	−609.061	−	5312.04i	−0.0657662	−	0.573592i
$22$		0			0
$23$	151.374	+	262.187i	0.0124413	+	0.0215490i	0.872179	−	0.489187i	$-0.162706\pi$
$23$	151.374	+	262.187i	0.0124413	+	0.0215490i	−0.859738	+	0.510736i	$0.829373\pi$
$24$		0			0
$25$	−3788.68	+	6562.18i	−0.242475	+	0.419979i
$26$		0			0
$27$			3788.00i			0.192450i
$28$		0			0
$29$	31999.3			1.31204			0.656019	−	0.754744i	$-0.272239\pi$
$29$	31999.3			1.31204			0.656019	+	0.754744i	$0.272239\pi$
$30$		0			0
$31$	−25554.3	−	14753.8i	−0.857784	−	0.495242i	0.00548542	−	0.999985i	$-0.498254\pi$
$31$	−25554.3	−	14753.8i	−0.857784	−	0.495242i	−0.863270	+	0.504743i	$0.831587\pi$
$32$		0			0
$33$	27319.7	−	15773.0i	0.760210	−	0.438907i
$34$		0			0
$35$	−28226.7	−	12249.5i	−0.658350	−	0.285702i
$36$		0			0
$37$	−44308.1	−	76743.8i	−0.874737	−	1.51509i	−0.857042	−	0.515246i	$-0.827701\pi$
$37$	−44308.1	−	76743.8i	−0.874737	−	1.51509i	−0.0176949	−	0.999843i	$-0.505633\pi$
$38$		0			0
$39$	−13754.1	+	23822.8i	−0.231867	+	0.401605i
$40$		0			0
$41$		−	72254.7i		−	1.04837i	−0.851604	−	0.524185i	$-0.824370\pi$
$41$		−	72254.7i		−	1.04837i	0.851604	−	0.524185i	$-0.175630\pi$
$42$		0			0
$43$	12716.1			0.159937			0.0799685	−	0.996797i	$-0.474518\pi$
$43$	12716.1			0.159937			0.0799685	+	0.996797i	$0.474518\pi$
$44$		0			0
$45$	18878.7	+	10899.6i	0.207173	+	0.119612i
$46$		0			0
$47$	13743.6	−	7934.88i	0.132375	−	0.0764270i	−0.432350	−	0.901706i	$-0.642315\pi$
$47$	13743.6	−	7934.88i	0.132375	−	0.0764270i	0.564725	+	0.825279i	$0.308982\pi$
$48$		0			0
$49$	−34237.0	+	112557.i	−0.291010	+	0.956720i
$50$		0			0
$51$	30504.2	+	52834.8i	0.229958	+	0.398299i
$52$		0			0
$53$	136562.	−	236533.i	0.917284	−	1.58878i	0.113761	−	0.993508i	$-0.463710\pi$
$53$	136562.	−	236533.i	0.917284	−	1.58878i	0.803523	−	0.595274i	$-0.202956\pi$
$54$		0			0
$55$		−	181542.i		−	1.09116i
$56$		0			0
$57$	26137.2			0.141135
$58$		0			0
$59$	−137947.	−	79643.9i	−0.671672	−	0.387790i	0.125038	−	0.992152i	$-0.460095\pi$
$59$	−137947.	−	79643.9i	−0.671672	−	0.387790i	−0.796710	+	0.604362i	$0.793428\pi$
$60$		0			0
$61$	−341303.	+	197051.i	−1.50366	+	0.868140i	−0.503671	+	0.863895i	$0.668018\pi$
$61$	−341303.	+	197051.i	−1.50366	+	0.868140i	−0.999991	+	0.00424442i	$0.998649\pi$
$62$		0			0
$63$	33180.9	−	76459.7i	0.132699	−	0.305781i
$64$		0			0
$65$	79152.4	+	137096.i	0.288220	+	0.499211i
$66$		0			0
$67$	136041.	−	235629.i	0.452319	−	0.783439i	−0.546211	−	0.837648i	$-0.683930\pi$
$67$	136041.	−	235629.i	0.452319	−	0.783439i	0.998530	+	0.0542088i	$0.0172637\pi$
$68$		0			0
$69$			4719.37i			0.0143660i
$70$		0			0
$71$	−49541.8			−0.138419			−0.0692096	−	0.997602i	$-0.522048\pi$
$71$	−49541.8			−0.138419			−0.0692096	+	0.997602i	$0.522048\pi$
$72$		0			0
$73$	39955.8	+	23068.5i	0.102710	+	0.0592994i	0.550475	−	0.834852i	$-0.314447\pi$
$73$	39955.8	+	23068.5i	0.102710	+	0.0592994i	−0.447765	+	0.894151i	$0.647780\pi$
$74$		0			0
$75$	−102294.	+	59059.6i	−0.242475	+	0.139993i
$76$		0			0
$77$	−689604.	+	79067.7i	−1.51052	+	0.173192i
$78$		0			0
$79$	372231.	+	644723.i	0.754973	+	1.30765i	0.945388	+	0.325948i	$0.105684\pi$
$79$	372231.	+	644723.i	0.754973	+	1.30765i	−0.190414	+	0.981704i	$0.560983\pi$
$80$		0			0
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	658103.i		−	1.15096i	−0.817816	−	0.575479i	$-0.804816\pi$
$83$		−	658103.i		−	1.15096i	0.817816	−	0.575479i	$-0.195184\pi$
$84$		0			0
$85$	351092.			0.571695
$86$		0			0
$87$	431991.	+	249410.i	0.656019	+	0.378753i
$88$		0			0
$89$	1.00470e6	−	580061.i	1.42516	−	0.822818i	0.428429	−	0.903576i	$-0.359067\pi$
$89$	1.00470e6	−	580061.i	1.42516	−	0.822818i	0.996734	+	0.0807578i	$0.0257340\pi$
$90$		0			0
$91$	486299.	−	360378.i	0.645326	−	0.478227i
$92$		0			0
$93$	−229988.	−	398351.i	−0.285928	−	0.495242i
$94$		0			0
$95$	75207.5	−	130263.i	0.0877183	−	0.151933i
$96$		0			0
$97$		−	686019.i		−	0.751659i	−0.926689	−	0.375830i	$-0.877358\pi$
$97$		−	686019.i		−	0.751659i	0.926689	−	0.375830i	$-0.122642\pi$
$98$		0			0
$99$	491754.			0.506807
$100$		0			0
$101$	−208501.	−	120378.i	−0.202369	−	0.116838i	0.395391	−	0.918513i	$-0.370609\pi$
$101$	−208501.	−	120378.i	−0.202369	−	0.116838i	−0.597760	+	0.801675i	$0.703943\pi$
$102$		0			0
$103$	−848609.	+	489945.i	−0.776598	+	0.448369i	−0.835223	−	0.549911i	$-0.814662\pi$
$103$	−848609.	+	489945.i	−0.776598	+	0.448369i	0.0586256	+	0.998280i	$0.481328\pi$
$104$		0			0
$105$	−285586.	−	385373.i	−0.246700	−	0.332900i
$106$		0			0
$107$	−139826.	−	242186.i	−0.114140	−	0.197696i	0.803296	−	0.595580i	$-0.203078\pi$
$107$	−139826.	−	242186.i	−0.114140	−	0.197696i	−0.917436	+	0.397884i	$0.869745\pi$
$108$		0			0
$109$	703197.	−	1.21797e6i	0.542997	−	0.940498i	−0.455733	−	0.890116i	$-0.650623\pi$
$109$	703197.	−	1.21797e6i	0.542997	−	0.940498i	0.998730	−	0.0503816i	$-0.0160438\pi$
$110$		0			0
$111$		−	1.38139e6i		−	1.01006i
$112$		0			0
$113$	2.24575e6			1.55642			0.778208	−	0.628007i	$-0.216129\pi$
$113$	2.24575e6			1.55642			0.778208	+	0.628007i	$0.216129\pi$
$114$		0			0
$115$	23520.5	+	13579.5i	0.0154651	+	0.00892877i
$116$		0			0
$117$	−371361.	+	214405.i	−0.231867	+	0.133868i
$118$		0			0
$119$	−152913.	−	1.33366e6i	−0.0907409	−	0.791414i
$120$		0			0
$121$	−1.16186e6	−	2.01240e6i	−0.655838	−	1.13595i
$122$		0			0
$123$	563170.	−	975439.i	0.302638	−	0.524185i
$124$		0			0
$125$			2.08145e6i			1.06570i
$126$		0			0
$127$	−1.92780e6			−0.941133			−0.470567	−	0.882364i	$-0.655950\pi$
$127$	−1.92780e6			−0.941133			−0.470567	+	0.882364i	$0.655950\pi$
$128$		0			0
$129$	171668.	+	99112.3i	0.0799685	+	0.0461698i
$130$		0			0
$131$	−923072.	+	532936.i	−0.410602	+	0.237061i	−0.691049	−	0.722808i	$-0.742851\pi$
$131$	−923072.	+	532936.i	−0.410602	+	0.237061i	0.280446	+	0.959870i	$0.409518\pi$
$132$		0			0
$133$	−527573.	−	228949.i	−0.224248	−	0.0973159i
$134$		0			0
$135$	169908.	+	294289.i	0.0690578	+	0.119612i
$136$		0			0
$137$	−314874.	+	545378.i	−0.122455	+	0.212098i	−0.920735	−	0.390188i	$-0.872410\pi$
$137$	−314874.	+	545378.i	−0.122455	+	0.212098i	0.798280	+	0.602286i	$0.205743\pi$
$138$		0			0
$139$		−	4.85016e6i		−	1.80598i	−0.429667	−	0.902988i	$-0.641369\pi$
$139$		−	4.85016e6i		−	1.80598i	0.429667	−	0.902988i	$-0.358631\pi$
$140$		0			0
$141$	247385.			0.0882503
$142$		0			0
$143$	3.09266e6	+	1.78555e6i	1.05760	+	0.610608i
$144$		0			0
$145$	2.48603e6	−	1.43531e6i	0.815458	−	0.470805i
$146$		0			0
$147$	−1.33950e6	+	1.25267e6i	−0.421686	+	0.394353i
$148$		0			0
$149$	−1.46737e6	−	2.54156e6i	−0.443589	−	0.768318i	0.554364	−	0.832274i	$-0.312961\pi$
$149$	−1.46737e6	−	2.54156e6i	−0.443589	−	0.768318i	−0.997953	+	0.0639564i	$0.979628\pi$
$150$		0			0
$151$	856063.	−	1.48274e6i	0.248642	−	0.430661i	−0.714507	−	0.699628i	$-0.753349\pi$
$151$	856063.	−	1.48274e6i	0.248642	−	0.430661i	0.963149	+	0.268967i	$0.0866824\pi$
$152$		0			0
$153$			951027.i			0.265533i
$154$		0			0
$155$	−2.64708e6			−0.710840
$156$		0			0
$157$	285596.	+	164889.i	0.0737994	+	0.0426081i	0.536446	−	0.843935i	$-0.319767\pi$
$157$	285596.	+	164889.i	0.0737994	+	0.0426081i	−0.462646	+	0.886543i	$0.653100\pi$
$158$		0			0
$159$	3.68719e6	−	2.12880e6i	0.917284	−	0.529594i
$160$		0			0
$161$	41339.3	−	95259.2i	0.00990570	−	0.0228260i
$162$		0			0
$163$	873116.	+	1.51228e6i	0.201609	+	0.349196i	0.949047	−	0.315135i	$-0.102050\pi$
$163$	873116.	+	1.51228e6i	0.201609	+	0.349196i	−0.747438	+	0.664331i	$0.768716\pi$
$164$		0			0
$165$	1.41498e6	−	2.45081e6i	0.314990	−	0.545580i
$166$		0			0
$167$		−	2.55852e6i		−	0.549338i	−0.961539	−	0.274669i	$-0.911432\pi$
$167$		−	2.55852e6i		−	0.549338i	0.961539	−	0.274669i	$-0.0885682\pi$
$168$		0			0
$169$	1.71281e6			0.354853
$170$		0			0
$171$	352853.	+	203720.i	0.0705675	+	0.0407422i
$172$		0			0
$173$	6.49369e6	−	3.74913e6i	1.25416	−	0.724090i	0.282227	−	0.959348i	$-0.408927\pi$
$173$	6.49369e6	−	3.74913e6i	1.25416	−	0.724090i	0.971933	+	0.235258i	$0.0755934\pi$
$174$		0			0
$175$	2.58211e6	−	296057.i	0.481794	−	0.0552409i
$176$		0			0
$177$	−1.24153e6	−	2.15039e6i	−0.223891	−	0.387790i
$178$		0			0
$179$	−1.31679e6	+	2.28075e6i	−0.229592	+	0.397666i	−0.957687	−	0.287811i	$-0.907073\pi$
$179$	−1.31679e6	+	2.28075e6i	−0.229592	+	0.397666i	0.728095	+	0.685476i	$0.240406\pi$
$180$		0			0
$181$		−	6.75260e6i		−	1.13877i	−0.822071	−	0.569384i	$-0.807182\pi$
$181$		−	6.75260e6i		−	1.13877i	0.822071	−	0.569384i	$-0.192818\pi$
$182$		0			0
$183$	−6.14345e6			−1.00244
$184$		0			0
$185$	−6.88459e6	−	3.97482e6i	−1.08733	−	0.627772i
$186$		0			0
$187$	6.85897e6	−	3.96003e6i	1.04890	−	0.605582i
$188$		0			0
$189$	1.04389e6	−	773586.i	0.154621	−	0.114584i
$190$		0			0
$191$	−767421.	−	1.32921e6i	−0.110137	−	0.190763i	0.805688	−	0.592340i	$-0.201796\pi$
$191$	−767421.	−	1.32921e6i	−0.110137	−	0.190763i	−0.915825	+	0.401577i	$0.868462\pi$
$192$		0			0
$193$	−5.01947e6	+	8.69398e6i	−0.698210	+	1.20933i	0.270877	+	0.962614i	$0.412686\pi$
$193$	−5.01947e6	+	8.69398e6i	−0.698210	+	1.20933i	−0.969087	+	0.246721i	$0.920647\pi$
$194$		0			0
$195$			2.46773e6i			0.332808i
$196$		0			0
$197$	−1.22795e7			−1.60614			−0.803070	−	0.595885i	$-0.796802\pi$
$197$	−1.22795e7			−1.60614			−0.803070	+	0.595885i	$0.796802\pi$
$198$		0			0
$199$	−5.65170e6	−	3.26301e6i	−0.717167	−	0.414057i	0.0965421	−	0.995329i	$-0.469222\pi$
$199$	−5.65170e6	−	3.26301e6i	−0.717167	−	0.414057i	−0.813709	+	0.581272i	$0.802555\pi$
$200$		0			0
$201$	3.67310e6	−	2.12066e6i	0.452319	−	0.261146i
$202$		0			0
$203$	−6.53491e6	−	8.81829e6i	−0.781181	−	1.05414i
$204$		0			0
$205$	−3.24094e6	−	5.61347e6i	−0.376192	−	0.651583i
$206$		0			0
$207$	−36783.8	+	63711.4i	−0.00414711	+	0.00718301i
$208$		0			0
$209$		−	3.39311e6i		−	0.371671i
$210$		0			0
$211$	1.79844e7			1.91447			0.957237	−	0.289305i	$-0.0934242\pi$
$211$	1.79844e7			1.91447			0.957237	+	0.289305i	$0.0934242\pi$
$212$		0			0
$213$	−668814.	−	386140.i	−0.0692096	−	0.0399582i
$214$		0			0
$215$	987915.	−	570373.i	0.0994041	−	0.0573910i
$216$		0			0
$217$	1.15290e6	+	1.00552e7i	0.112826	+	0.984037i
$218$		0			0
$219$	359602.	+	622849.i	0.0342365	+	0.0592994i
$220$		0			0
$221$	−3.45315e6	+	5.98103e6i	−0.319918	+	0.554114i
$222$		0			0
$223$		−	1.04355e7i		−	0.941023i	−0.882394	−	0.470511i	$-0.844069\pi$
$223$		−	1.04355e7i		−	0.941023i	0.882394	−	0.470511i	$-0.155931\pi$
$224$		0			0
$225$	−1.84130e6			−0.161650
$226$		0			0
$227$	2.23300e6	+	1.28922e6i	0.190902	+	0.110217i	0.592405	−	0.805640i	$-0.298179\pi$
$227$	2.23300e6	+	1.28922e6i	0.190902	+	0.110217i	−0.401503	+	0.915858i	$0.631512\pi$
$228$		0			0
$229$	1.11391e7	−	6.43117e6i	0.927565	−	0.535530i	0.0415245	−	0.999137i	$-0.486779\pi$
$229$	1.11391e7	−	6.43117e6i	0.927565	−	0.535530i	0.886041	+	0.463607i	$0.153445\pi$
$230$		0			0
$231$	−9.92592e6	−	4.30752e6i	−0.805258	−	0.349455i
$232$		0			0
$233$	4.23377e6	+	7.33311e6i	0.334703	+	0.579723i	0.983428	−	0.181300i	$-0.0580306\pi$
$233$	4.23377e6	+	7.33311e6i	0.334703	+	0.579723i	−0.648725	+	0.761023i	$0.724697\pi$
$234$		0			0
$235$	711828.	−	1.23292e6i	0.0548493	−	0.0950019i
$236$		0			0
$237$			1.16050e7i			0.871768i
$238$		0			0
$239$	1.20479e7			0.882508			0.441254	−	0.897382i	$-0.354534\pi$
$239$	1.20479e7			0.882508			0.441254	+	0.897382i	$0.354534\pi$
$240$		0			0
$241$	2.21989e7	+	1.28165e7i	1.58591	+	0.915628i	0.993971	+	0.109648i	$0.0349722\pi$
$241$	2.21989e7	+	1.28165e7i	1.58591	+	0.915628i	0.591943	+	0.805980i	$0.298361\pi$
$242$		0			0
$243$	−797162.	+	460241.i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	2.38880e6	+	1.02802e7i	0.162436	+	0.699045i
$246$		0			0
$247$	1.47940e6	+	2.56240e6i	0.0981736	+	0.170042i
$248$		0			0
$249$	5.12941e6	−	8.88439e6i	0.332253	−	0.575479i
$250$		0			0
$251$			2.98235e7i			1.88598i	0.332817	+	0.942992i	$0.392001\pi$
$251$			2.98235e7i			1.88598i	−0.332817	+	0.942992i	$0.607999\pi$
$252$		0			0
$253$	612664.			0.0378321
$254$		0			0
$255$	4.73974e6	+	2.73649e6i	0.285847	+	0.165034i
$256$		0			0
$257$	−3.18946e6	+	1.84144e6i	−0.187896	+	0.108482i	−0.590997	−	0.806674i	$-0.701266\pi$
$257$	−3.18946e6	+	1.84144e6i	−0.187896	+	0.108482i	0.403101	+	0.915155i	$0.367932\pi$
$258$		0			0
$259$	−1.21003e7	+	2.78830e7i	−0.696459	+	1.60487i
$260$		0			0
$261$	3.88792e6	+	6.73407e6i	0.218673	+	0.378753i
$262$		0			0
$263$	−8.91969e6	+	1.54494e7i	−0.490323	+	0.849265i	−0.999938	−	0.0111379i	$-0.996455\pi$
$263$	−8.91969e6	+	1.54494e7i	−0.490323	+	0.849265i	0.509615	+	0.860403i	$0.329788\pi$
$264$		0			0
$265$		−	2.45017e7i		−	1.31661i
$266$		0			0
$267$	1.80845e7			0.950108
$268$		0			0
$269$	−1.81828e7	−	1.04979e7i	−0.934124	−	0.539317i	−0.0460105	−	0.998941i	$-0.514651\pi$
$269$	−1.81828e7	−	1.04979e7i	−0.934124	−	0.539317i	−0.888113	+	0.459624i	$0.847984\pi$
$270$		0			0
$271$	−3.25119e7	+	1.87708e7i	−1.63356	+	0.943136i	−0.650576	+	0.759441i	$0.725472\pi$
$271$	−3.25119e7	+	1.87708e7i	−1.63356	+	0.943136i	−0.982983	+	0.183695i	$0.941194\pi$
$272$		0			0
$273$	9.37390e6	−	1.07478e6i	0.460715	−	0.0528241i
$274$		0			0
$275$	7.66706e6	+	1.32797e7i	0.368664	+	0.638545i
$276$		0			0
$277$	−1.48976e7	+	2.58034e7i	−0.700935	+	1.21405i	0.267204	+	0.963640i	$0.413900\pi$
$277$	−1.48976e7	+	2.58034e7i	−0.700935	+	1.21405i	−0.968139	+	0.250415i	$0.919433\pi$
$278$		0			0
$279$		−	7.17032e6i		−	0.330161i
$280$		0			0
$281$	−9.41574e6			−0.424361			−0.212180	−	0.977230i	$-0.568056\pi$
$281$	−9.41574e6			−0.424361			−0.212180	+	0.977230i	$0.568056\pi$
$282$		0			0
$283$	−2.11534e7	−	1.22129e7i	−0.933298	−	0.538840i	−0.0454446	−	0.998967i	$-0.514470\pi$
$283$	−2.11534e7	−	1.22129e7i	−0.933298	−	0.538840i	−0.887853	+	0.460127i	$0.847804\pi$
$284$		0			0
$285$	2.03060e6	−	1.17237e6i	0.0877183	−	0.0506442i
$286$		0			0
$287$	−1.99118e7	+	1.47559e7i	−0.842295	+	0.624194i
$288$		0			0
$289$	−4.41030e6	−	7.63887e6i	−0.182715	−	0.316472i
$290$		0			0
$291$	5.34699e6	−	9.26126e6i	0.216985	−	0.375830i
$292$		0			0
$293$			2.21252e7i			0.879599i	0.898096	+	0.439800i	$0.144951\pi$
$293$			2.21252e7i			0.879599i	−0.898096	+	0.439800i	$0.855049\pi$
$294$		0			0
$295$	−1.42895e7			−0.556610
$296$		0			0
$297$	6.63868e6	+	3.83284e6i	0.253403	+	0.146302i
$298$		0			0
$299$	−462669.	+	267122.i	−0.0173084	+	0.00999301i
$300$		0			0
$301$	−2.59689e6	−	3.50428e6i	−0.0952257	−	0.128499i
$302$		0			0
$303$	−1.87651e6	−	3.25021e6i	−0.0674565	−	0.116838i
$304$		0			0
$305$	−1.76772e7	+	3.06178e7i	−0.623037	+	1.07913i
$306$		0			0
$307$			5.02266e7i			1.73588i	0.496672	+	0.867938i	$0.334555\pi$
$307$			5.02266e7i			1.73588i	−0.496672	+	0.867938i	$0.665445\pi$
$308$		0			0
$309$	−1.52750e7			−0.517732
$310$		0			0
$311$	−1.75549e7	−	1.01353e7i	−0.583602	−	0.336943i	0.178962	−	0.983856i	$-0.442726\pi$
$311$	−1.75549e7	−	1.01353e7i	−0.583602	−	0.336943i	−0.762563	+	0.646913i	$0.776060\pi$
$312$		0			0
$313$	−118863.	+	68625.7i	−0.00387627	+	0.00223797i	−0.501937	−	0.864904i	$-0.667379\pi$
$313$	−118863.	+	68625.7i	−0.00387627	+	0.00223797i	0.498061	+	0.867142i	$0.334046\pi$
$314$		0			0
$315$	−851723.	−	7.42846e6i	−0.0272500	−	0.237666i
$316$		0			0
$317$	2.72242e7	+	4.71537e7i	0.854629	+	1.48026i	0.876988	+	0.480511i	$0.159549\pi$
$317$	2.72242e7	+	4.71537e7i	0.854629	+	1.48026i	−0.0223592	+	0.999750i	$0.507118\pi$
$318$		0			0
$319$	3.23782e7	−	5.60806e7i	0.997425	−	1.72759i
$320$		0			0
$321$		−	4.35935e6i		−	0.131797i
$322$		0			0
$323$	6.56210e6			0.194731
$324$		0			0
$325$	−1.15800e7	−	6.68570e6i	−0.337332	−	0.194759i
$326$		0			0
$327$	1.89863e7	−	1.09618e7i	0.542997	−	0.313499i
$328$		0			0
$329$	−4.99340e6	−	2.16697e6i	−0.140220	−	0.0608506i
$330$		0			0
$331$	6.55778e6	+	1.13584e7i	0.180831	+	0.313209i	0.942164	−	0.335153i	$-0.108788\pi$
$331$	6.55778e6	+	1.13584e7i	0.180831	+	0.313209i	−0.761333	+	0.648361i	$0.775455\pi$
$332$		0			0
$333$	1.07669e7	−	1.86487e7i	0.291579	−	0.505030i
$334$		0			0
$335$		−	2.44081e7i		−	0.649231i
$336$		0			0
$337$	1.60491e7			0.419336			0.209668	−	0.977773i	$-0.432762\pi$
$337$	1.60491e7			0.419336			0.209668	+	0.977773i	$0.432762\pi$
$338$		0			0
$339$	3.03176e7	+	1.75039e7i	0.778208	+	0.449298i
$340$		0			0
$341$	−5.17136e7	+	2.98569e7i	−1.30419	+	0.752976i
$342$		0			0
$343$	3.80101e7	−	1.35515e7i	0.941927	−	0.335819i
$344$		0			0
$345$	211684.	+	366648.i	0.00515503	+	0.00892877i
$346$		0			0
$347$	−3.86721e6	+	6.69821e6i	−0.0925571	+	0.160314i	−0.908586	−	0.417697i	$-0.862837\pi$
$347$	−3.86721e6	+	6.69821e6i	−0.0925571	+	0.160314i	0.816029	+	0.578011i	$0.196171\pi$
$348$		0			0
$349$		−	3.41502e7i		−	0.803373i	−0.915777	−	0.401686i	$-0.868424\pi$
$349$		−	3.41502e7i		−	0.803373i	0.915777	−	0.401686i	$-0.131576\pi$
$350$		0			0
$351$	−6.68450e6			−0.154578
$352$		0			0
$353$	7.75351e6	+	4.47649e6i	0.176268	+	0.101769i	0.585538	−	0.810645i	$-0.300883\pi$
$353$	7.75351e6	+	4.47649e6i	0.176268	+	0.101769i	−0.409270	+	0.912413i	$0.634217\pi$
$354$		0			0
$355$	−3.84890e6	+	2.22216e6i	−0.0860303	+	0.0496696i
$356$		0			0
$357$	8.33051e6	−	1.91962e7i	0.183091	−	0.421901i
$358$		0			0
$359$	3.76091e7	+	6.51408e7i	0.812848	+	1.40789i	0.910863	+	0.412709i	$0.135417\pi$
$359$	3.76091e7	+	6.51408e7i	0.812848	+	1.40789i	−0.0980153	+	0.995185i	$0.531249\pi$
$360$		0			0
$361$	−2.21173e7	+	3.83082e7i	−0.470121	+	0.814274i
$362$		0			0
$363$		−	3.62231e7i		−	0.757297i
$364$		0			0
$365$	4.13889e6			0.0851148
$366$		0			0
$367$	−1.07122e7	−	6.18470e6i	−0.216711	−	0.125118i	0.387715	−	0.921779i	$-0.373264\pi$
$367$	−1.07122e7	−	6.18470e6i	−0.216711	−	0.125118i	−0.604426	+	0.796661i	$0.706598\pi$
$368$		0			0
$369$	1.52056e7	−	8.77895e6i	0.302638	−	0.174728i
$370$		0			0
$371$	−9.30721e7	+	1.06713e7i	−1.82263	+	0.208976i
$372$		0			0
$373$	1.00065e7	+	1.73318e7i	0.192822	+	0.333978i	0.946184	−	0.323628i	$-0.104903\pi$
$373$	1.00065e7	+	1.73318e7i	0.192822	+	0.333978i	−0.753362	+	0.657606i	$0.771569\pi$
$374$		0			0
$375$	−1.62233e7	+	2.80996e7i	−0.307642	+	0.532852i
$376$		0			0
$377$			5.64677e7i			1.05384i
$378$		0			0
$379$	6.96094e7			1.27865			0.639323	−	0.768939i	$-0.279215\pi$
$379$	6.96094e7			1.27865			0.639323	+	0.768939i	$0.279215\pi$
$380$		0			0
$381$	−2.60253e7	−	1.50257e7i	−0.470567	−	0.271682i
$382$		0			0
$383$	−4.99800e7	+	2.88560e7i	−0.889610	+	0.513617i	−0.873815	−	0.486259i	$-0.838361\pi$
$383$	−4.99800e7	+	2.88560e7i	−0.889610	+	0.513617i	−0.0157952	+	0.999875i	$0.505028\pi$
$384$		0			0
$385$	−5.00288e7	+	3.70745e7i	−0.876674	+	0.649670i
$386$		0			0
$387$	1.54501e6	+	2.67603e6i	0.0266562	+	0.0461698i
$388$		0			0
$389$	3.84399e7	−	6.65799e7i	0.653030	−	1.13108i	−0.329353	−	0.944207i	$-0.606831\pi$
$389$	3.84399e7	−	6.65799e7i	0.653030	−	1.13108i	0.982384	−	0.186875i	$-0.0598360\pi$
$390$		0			0
$391$			1.18486e6i			0.0198215i
$392$		0			0
$393$	−1.66153e7			−0.273735
$394$		0			0
$395$	5.78373e7	+	3.33924e7i	0.938462	+	0.541821i
$396$		0			0
$397$	6.81005e7	−	3.93178e7i	1.08838	−	0.628374i	0.155232	−	0.987878i	$-0.450388\pi$
$397$	6.81005e7	−	3.93178e7i	1.08838	−	0.628374i	0.933143	+	0.359504i	$0.117054\pi$
$398$		0			0
$399$	−5.33776e6	−	7.20284e6i	−0.0840311	−	0.113393i
$400$		0			0
$401$	−3.40877e7	−	5.90416e7i	−0.528646	−	0.915641i	−0.999442	−	0.0333993i	$-0.989367\pi$
$401$	−3.40877e7	−	5.90416e7i	−0.528646	−	0.915641i	0.470796	−	0.882242i	$-0.343967\pi$
$402$		0			0
$403$	2.60353e7	−	4.50944e7i	0.397783	−	0.688981i
$404$		0			0
$405$			5.29721e6i			0.0797411i
$406$		0			0
$407$	−1.79331e8			−2.65994
$408$		0			0
$409$	−4.77595e7	−	2.75740e7i	−0.698056	−	0.403023i	0.108567	−	0.994089i	$-0.465374\pi$
$409$	−4.77595e7	−	2.75740e7i	−0.698056	−	0.403023i	−0.806623	+	0.591066i	$0.798707\pi$
$410$		0			0
$411$	−8.50161e6	+	4.90840e6i	−0.122455	+	0.0706993i
$412$		0			0
$413$	6.22358e6	+	5.42801e7i	0.0883466	+	0.770532i
$414$		0			0
$415$	−2.95188e7	−	5.11280e7i	−0.413004	−	0.715344i
$416$		0			0
$417$	3.78033e7	−	6.54772e7i	0.521340	−	0.902988i
$418$		0			0
$419$			9.63639e7i			1.31000i	0.755627	+	0.655002i	$0.227332\pi$
$419$			9.63639e7i			1.31000i	−0.755627	+	0.655002i	$0.772668\pi$
$420$		0			0
$421$	6.77431e7			0.907859			0.453930	−	0.891037i	$-0.350022\pi$
$421$	6.77431e7			0.907859			0.453930	+	0.891037i	$0.350022\pi$
$422$		0			0
$423$	3.33970e6	+	1.92818e6i	0.0441252	+	0.0254757i
$424$		0			0
$425$	−2.56823e7	+	1.48277e7i	−0.334555	+	0.193155i
$426$		0			0
$427$	1.24004e8	+	5.38135e7i	1.59277	+	0.691206i
$428$		0			0
$429$	2.78339e7	+	4.82097e7i	0.352535	+	0.610608i
$430$		0			0
$431$	−1.12874e7	+	1.95504e7i	−0.140982	+	0.244188i	−0.927867	−	0.372912i	$-0.878359\pi$
$431$	−1.12874e7	+	1.95504e7i	−0.140982	+	0.244188i	0.786885	+	0.617100i	$0.211693\pi$
$432$		0			0
$433$			1.02792e8i			1.26618i	0.774078	+	0.633090i	$0.218214\pi$
$433$			1.02792e8i			1.26618i	−0.774078	+	0.633090i	$0.781786\pi$
$434$		0			0
$435$	4.47485e7			0.543639
$436$		0			0
$437$	439610.	+	253809.i	0.00526773	+	0.00304132i
$438$		0			0
$439$	8.39480e7	−	4.84674e7i	0.992240	−	0.572870i	0.0862971	−	0.996269i	$-0.472497\pi$
$439$	8.39480e7	−	4.84674e7i	0.992240	−	0.572870i	0.905943	+	0.423399i	$0.139163\pi$
$440$		0			0
$441$	−2.78468e7	+	6.47071e6i	−0.324683	+	0.0754460i
$442$		0			0
$443$	−2.17344e7	−	3.76451e7i	−0.249998	−	0.433010i	0.713527	−	0.700628i	$-0.247097\pi$
$443$	−2.17344e7	−	3.76451e7i	−0.249998	−	0.433010i	−0.963525	+	0.267618i	$0.913763\pi$
$444$		0			0
$445$	5.20365e7	−	9.01299e7i	0.590511	−	1.02280i
$446$		0			0
$447$		−	4.57480e7i		−	0.512212i
$448$		0			0
$449$	9.31403e6			0.102896			0.0514480	−	0.998676i	$-0.483616\pi$
$449$	9.31403e6			0.102896			0.0514480	+	0.998676i	$0.483616\pi$
$450$		0			0
$451$	−1.26631e8	−	7.31102e7i	−1.38041	−	0.796981i
$452$		0			0
$453$	2.31137e7	−	1.33447e7i	0.248642	−	0.143554i
$454$		0			0
$455$	2.16160e7	−	4.98104e7i	0.229478	−	0.528793i
$456$		0			0
$457$	−4.33472e7	−	7.50796e7i	−0.454164	−	0.786635i	0.544476	−	0.838777i	$-0.316729\pi$
$457$	−4.33472e7	−	7.50796e7i	−0.454164	−	0.786635i	−0.998640	+	0.0521415i	$0.983395\pi$
$458$		0			0
$459$	−7.41252e6	+	1.28389e7i	−0.0766527	+	0.132766i
$460$		0			0
$461$			1.02373e8i			1.04492i	0.852663	+	0.522461i	$0.174986\pi$
$461$			1.02373e8i			1.04492i	−0.852663	+	0.522461i	$0.825014\pi$
$462$		0			0
$463$	−7.51038e7			−0.756691			−0.378346	−	0.925664i	$-0.623507\pi$
$463$	−7.51038e7			−0.756691			−0.378346	+	0.925664i	$0.623507\pi$
$464$		0			0
$465$	−3.57356e7	−	2.06319e7i	−0.355420	−	0.205202i
$466$		0			0
$467$	1.02909e8	−	5.94147e7i	1.01042	−	0.583369i	0.0991085	−	0.995077i	$-0.468401\pi$
$467$	1.02909e8	−	5.94147e7i	1.01042	−	0.583369i	0.911316	+	0.411708i	$0.135068\pi$
$468$		0			0
$469$	−9.27165e7	+	1.06306e7i	−0.898749	+	0.103048i
$470$		0			0
$471$	2.57036e6	+	4.45200e6i	0.0245998	+	0.0426081i
$472$		0			0
$473$	1.28667e7	−	2.22857e7i	0.121586	−	0.210593i
$474$		0			0
$475$			1.27050e7i			0.118548i
$476$		0			0
$477$	6.63693e7			0.611522
$478$		0			0
$479$	−1.28812e8	−	7.43698e7i	−1.17206	−	0.676690i	−0.217897	−	0.975972i	$-0.569920\pi$
$479$	−1.28812e8	−	7.43698e7i	−1.17206	−	0.676690i	−0.954165	+	0.299281i	$0.903253\pi$
$480$		0			0
$481$	1.35426e8	−	7.81884e7i	1.21694	−	0.702598i
$482$		0			0
$483$	1.30055e6	−	963791.i	0.0115421	−	0.00855345i
$484$		0			0
$485$	−3.07709e7	−	5.32968e7i	−0.269721	−	0.467171i
$486$		0			0
$487$	−3.74920e7	+	6.49380e7i	−0.324602	+	0.562227i	−0.981432	−	0.191812i	$-0.938564\pi$
$487$	−3.74920e7	+	6.49380e7i	−0.324602	+	0.562227i	0.656830	+	0.754039i	$0.271897\pi$
$488$		0			0
$489$			2.72211e7i			0.232798i
$490$		0			0
$491$	2.70620e7			0.228620			0.114310	−	0.993445i	$-0.463534\pi$
$491$	2.70620e7			0.228620			0.114310	+	0.993445i	$0.463534\pi$
$492$		0			0
$493$	1.08457e8	+	6.26177e7i	0.905142	+	0.522584i
$494$		0			0
$495$	3.82044e7	−	2.20573e7i	0.314990	−	0.181860i
$496$		0			0
$497$	1.01174e7	+	1.36526e7i	0.0824141	+	0.111211i
$498$		0			0
$499$	3.59690e7	+	6.23001e7i	0.289485	+	0.501403i	0.973687	−	0.227890i	$-0.0731825\pi$
$499$	3.59690e7	+	6.23001e7i	0.289485	+	0.501403i	−0.684202	+	0.729293i	$0.739849\pi$
$500$		0			0
$501$	1.99417e7	−	3.45400e7i	0.158580	−	0.274669i
$502$		0			0
$503$		−	1.01211e8i		−	0.795284i	−0.917541	−	0.397642i	$-0.869829\pi$
$503$		−	1.01211e8i		−	0.795284i	0.917541	−	0.397642i	$-0.130171\pi$
$504$		0			0
$505$	−2.15980e7			−0.167702
$506$		0			0
$507$	2.31229e7	+	1.33500e7i	0.177427	+	0.102437i
$508$		0			0
$509$	−1.56254e8	+	9.02134e7i	−1.18489	+	0.684097i	−0.957141	−	0.289623i	$-0.906470\pi$
$509$	−1.56254e8	+	9.02134e7i	−1.18489	+	0.684097i	−0.227750	+	0.973720i	$0.573137\pi$
$510$		0			0
$511$	−1.80263e6	−	1.57220e7i	−0.0135096	−	0.117827i
$512$		0			0
$513$	3.17567e6	+	5.50043e6i	0.0235225	+	0.0407422i
$514$		0			0
$515$	−4.39523e7	+	7.61276e7i	−0.321781	+	0.557340i
$516$		0			0
$517$		−	3.21153e7i		−	0.232402i
$518$		0			0
$519$	1.16886e8			0.836107
$520$		0			0
$521$	−1.68827e8	−	9.74725e7i	−1.19379	−	0.689237i	−0.234629	−	0.972085i	$-0.575388\pi$
$521$	−1.68827e8	−	9.74725e7i	−1.19379	−	0.689237i	−0.959165	+	0.282847i	$0.908721\pi$
$522$		0			0
$523$	1.28562e8	−	7.42252e7i	0.898684	−	0.518855i	0.0219109	−	0.999760i	$-0.493025\pi$
$523$	1.28562e8	−	7.42252e7i	0.898684	−	0.518855i	0.876773	+	0.480905i	$0.159692\pi$
$524$		0			0
$525$	3.71661e7	+	1.61288e7i	0.256844	+	0.111461i
$526$		0			0
$527$	−5.77416e7	−	1.00011e8i	−0.394509	−	0.683310i
$528$		0			0
$529$	7.39721e7	−	1.28123e8i	0.499690	−	0.865489i
$530$		0			0
$531$		−	3.87069e7i		−	0.258527i
$532$		0			0
$533$	1.27504e8			0.842062
$534$		0			0
$535$	−2.17262e7	−	1.25436e7i	−0.141880	−	0.0819146i
$536$		0			0
$537$	−3.55533e7	+	2.05267e7i	−0.229592	+	0.132555i
$538$		0			0
$539$	1.62620e8	+	1.73892e8i	1.03851	+	1.11049i
$540$		0			0
$541$	−1.05725e8	−	1.83121e8i	−0.667708	−	1.15650i	−0.978543	−	0.206041i	$-0.933942\pi$
$541$	−1.05725e8	−	1.83121e8i	−0.667708	−	1.15650i	0.310835	−	0.950464i	$-0.399391\pi$
$542$		0			0
$543$	5.26313e7	−	9.11602e7i	0.328734	−	0.569384i
$544$		0			0
$545$		−	1.26166e8i		−	0.779385i
$546$		0			0
$547$	8.83478e7			0.539801			0.269900	−	0.962888i	$-0.413009\pi$
$547$	8.83478e7			0.539801			0.269900	+	0.962888i	$0.413009\pi$
$548$		0			0
$549$	−8.29366e7	−	4.78835e7i	−0.501221	−	0.289380i
$550$		0			0
$551$	4.64652e7	−	2.68267e7i	0.277762	−	0.160366i
$552$		0			0
$553$	1.01654e8	−	2.34244e8i	0.601104	−	1.38514i
$554$		0			0
$555$	−6.19613e7	−	1.07320e8i	−0.362444	−	0.627772i
$556$		0			0
$557$	1.20720e7	−	2.09093e7i	0.0698576	−	0.120997i	−0.828981	−	0.559277i	$-0.811079\pi$
$557$	1.20720e7	−	2.09093e7i	0.0698576	−	0.120997i	0.898838	+	0.438280i	$0.144412\pi$
$558$		0			0
$559$			2.24395e7i			0.128463i
$560$		0			0
$561$	1.23461e8			0.699266
$562$		0			0
$563$	1.95701e8	+	1.12988e8i	1.09665	+	0.633151i	0.935339	−	0.353753i	$-0.115095\pi$
$563$	1.95701e8	+	1.12988e8i	1.09665	+	0.633151i	0.161310	+	0.986904i	$0.448428\pi$
$564$		0			0
$565$	1.74472e8	−	1.00732e8i	0.967343	−	0.558496i
$566$		0			0
$567$	2.01220e7	−	2.30712e6i	0.110388	−	0.0126567i
$568$		0			0
$569$	2.40641e7	+	4.16803e7i	0.130627	+	0.226253i	0.923919	−	0.382589i	$-0.124968\pi$
$569$	2.40641e7	+	4.16803e7i	0.130627	+	0.226253i	−0.793291	+	0.608842i	$0.791634\pi$
$570$		0			0
$571$	3.78268e7	−	6.55179e7i	0.203185	−	0.351926i	−0.746368	−	0.665533i	$-0.768204\pi$
$571$	3.78268e7	−	6.55179e7i	0.203185	−	0.351926i	0.949553	+	0.313607i	$0.101537\pi$
$572$		0			0
$573$		−	2.39258e7i		−	0.127175i
$574$		0			0
$575$	−2.29402e6			−0.0120669
$576$		0			0
$577$	1.57165e8	+	9.07391e7i	0.818140	+	0.472353i	0.849775	−	0.527146i	$-0.176738\pi$
$577$	1.57165e8	+	9.07391e7i	0.818140	+	0.472353i	−0.0316347	+	0.999499i	$0.510071\pi$
$578$		0			0
$579$	−1.35526e8	+	7.82458e7i	−0.698210	+	0.403112i
$580$		0			0
$581$	−1.81358e8	+	1.34398e8i	−0.924718	+	0.685275i
$582$		0			0
$583$	−2.76359e8	−	4.78667e8i	−1.39466	−	2.41562i
$584$		0			0
$585$	−1.92340e7	+	3.33143e7i	−0.0960733	+	0.166404i
$586$		0			0
$587$			1.85858e8i			0.918899i	0.888204	+	0.459450i	$0.151953\pi$
$587$			1.85858e8i			0.918899i	−0.888204	+	0.459450i	$0.848047\pi$
$588$		0			0
$589$	−4.94754e7			−0.242127
$590$		0			0
$591$	−1.65774e8	−	9.57096e7i	−0.803070	−	0.463653i
$592$		0			0
$593$	−2.60892e8	+	1.50626e8i	−1.25111	+	0.722330i	−0.971330	−	0.237734i	$-0.923596\pi$
$593$	−2.60892e8	+	1.50626e8i	−1.25111	+	0.722330i	−0.279782	+	0.960064i	$0.590262\pi$
$594$		0			0
$595$	−7.17001e7	−	9.67531e7i	−0.340384	−	0.459318i
$596$		0			0
$597$	−5.08653e7	−	8.81014e7i	−0.239056	−	0.414057i
$598$		0			0
$599$	1.46877e8	−	2.54399e8i	0.683398	−	1.18368i	−0.290540	−	0.956863i	$-0.593835\pi$
$599$	1.46877e8	−	2.54399e8i	0.683398	−	1.18368i	0.973937	−	0.226817i	$-0.0728318\pi$
$600$		0			0
$601$			1.88627e8i			0.868921i	0.900691	+	0.434460i	$0.143061\pi$
$601$			1.88627e8i			0.868921i	−0.900691	+	0.434460i	$0.856939\pi$
$602$		0			0
$603$	6.61158e7			0.301546
$604$		0			0
$605$	−1.80529e8	−	1.04229e8i	−0.815234	−	0.470675i
$606$		0			0
$607$	2.36778e7	−	1.36704e7i	0.105870	−	0.0611243i	−0.446130	−	0.894968i	$-0.647198\pi$
$607$	2.36778e7	−	1.36704e7i	0.105870	−	0.0611243i	0.552000	+	0.833844i	$0.313865\pi$
$608$		0			0
$609$	−1.94895e7	−	1.69982e8i	−0.0862878	−	0.752575i
$610$		0			0
$611$	1.40023e7	+	2.42527e7i	0.0613870	+	0.106325i
$612$		0			0
$613$	−1.45119e8	+	2.51354e8i	−0.630005	+	1.09120i	0.357545	+	0.933896i	$0.383614\pi$
$613$	−1.45119e8	+	2.51354e8i	−0.630005	+	1.09120i	−0.987550	+	0.157305i	$0.949719\pi$
$614$		0			0
$615$		−	1.01042e8i		−	0.434389i
$616$		0			0
$617$	3.11610e8			1.32665			0.663324	−	0.748332i	$-0.269145\pi$
$617$	3.11610e8			1.32665			0.663324	+	0.748332i	$0.269145\pi$
$618$		0			0
$619$	1.73249e8	+	1.00026e8i	0.730466	+	0.421734i	0.818592	−	0.574375i	$-0.194755\pi$
$619$	1.73249e8	+	1.00026e8i	0.730466	+	0.421734i	−0.0881269	+	0.996109i	$0.528088\pi$
$620$		0			0
$621$	−993163.	+	573403.i	−0.00414711	+	0.00239434i
$622$		0			0
$623$	−3.65031e8	−	1.58411e8i	−1.50961	−	0.655121i
$624$		0			0
$625$	3.41641e7	+	5.91740e7i	0.139936	+	0.242377i
$626$		0			0
$627$	2.64467e7	−	4.58070e7i	0.107292	−	0.185836i
$628$		0			0
$629$		−	3.46816e8i		−	1.39363i
$630$		0			0
$631$	−1.71182e7			−0.0681348			−0.0340674	−	0.999420i	$-0.510846\pi$
$631$	−1.71182e7			−0.0681348			−0.0340674	+	0.999420i	$0.510846\pi$
$632$		0			0
$633$	2.42790e8	+	1.40175e8i	0.957237	+	0.552661i
$634$		0			0
$635$	−1.49771e8	+	8.64703e7i	−0.584933	+	0.337711i
$636$		0			0
$637$	−1.98624e8	−	6.04165e7i	−0.768447	−	0.233742i
$638$		0			0
$639$	−6.01933e6	−	1.04258e7i	−0.0230699	−	0.0399582i
$640$		0			0
$641$	3.82406e6	−	6.62347e6i	0.0145195	−	0.0251485i	−0.858674	−	0.512522i	$-0.828711\pi$
$641$	3.82406e6	−	6.62347e6i	0.0145195	−	0.0251485i	0.873194	+	0.487373i	$0.162045\pi$
$642$		0			0
$643$			2.70679e8i			1.01817i	0.860715	+	0.509087i	$0.170017\pi$
$643$			2.70679e8i			1.01817i	−0.860715	+	0.509087i	$0.829983\pi$
$644$		0			0
$645$	1.77825e7			0.0662694
$646$		0			0
$647$	−1.02818e8	−	5.93622e7i	−0.379627	−	0.219178i	0.298029	−	0.954557i	$-0.403671\pi$
$647$	−1.02818e8	−	5.93622e7i	−0.379627	−	0.219178i	−0.677656	+	0.735379i	$0.737004\pi$
$648$		0			0
$649$	−2.79161e8	+	1.61174e8i	−1.02122	+	0.589604i
$650$		0			0
$651$	−6.28084e7	+	1.44731e8i	−0.227654	+	0.524589i
$652$		0			0
$653$	1.52658e8	+	2.64412e8i	0.548253	+	0.949602i	0.998394	+	0.0566447i	$0.0180402\pi$
$653$	1.52658e8	+	2.64412e8i	0.548253	+	0.949602i	−0.450141	+	0.892957i	$0.648626\pi$
$654$		0			0
$655$	−4.78090e7	+	8.28075e7i	−0.170132	+	0.294677i
$656$		0			0
$657$			1.12113e7i			0.0395330i
$658$		0			0
$659$	2.74462e8			0.959016			0.479508	−	0.877538i	$-0.340815\pi$
$659$	2.74462e8			0.959016			0.479508	+	0.877538i	$0.340815\pi$
$660$		0			0
$661$	−1.64530e8	−	9.49917e7i	−0.569694	−	0.328913i	0.187333	−	0.982296i	$-0.440016\pi$
$661$	−1.64530e8	−	9.49917e7i	−0.569694	−	0.328913i	−0.757027	+	0.653383i	$0.773349\pi$
$662$		0			0
$663$	−9.32351e7	+	5.38293e7i	−0.319918	+	0.184705i
$664$		0			0
$665$	−5.12565e7	+	5.87690e6i	−0.174295	+	0.0199840i
$666$		0			0
$667$	4.84385e6	+	8.38980e6i	0.0163235	+	0.0282732i
$668$		0			0
$669$	8.13369e7	−	1.40880e8i	0.271650	−	0.470511i
$670$		0			0
$671$			7.97537e8i			2.63987i
$672$		0			0
$673$	−1.08375e8			−0.355535			−0.177768	−	0.984072i	$-0.556888\pi$
$673$	−1.08375e8			−0.355535			−0.177768	+	0.984072i	$0.556888\pi$
$674$		0			0
$675$	−2.48575e7	−	1.43515e7i	−0.0808251	−	0.0466644i
$676$		0			0
$677$	2.14297e8	−	1.23724e8i	0.690637	−	0.398740i	−0.113214	−	0.993571i	$-0.536114\pi$
$677$	2.14297e8	−	1.23724e8i	0.690637	−	0.398740i	0.803851	+	0.594831i	$0.202781\pi$
$678$		0			0
$679$	−1.89051e8	+	1.40099e8i	−0.603908	+	0.447534i
$680$		0			0
$681$	2.00970e7	+	3.48090e7i	0.0636341	+	0.110217i
$682$		0			0
$683$	1.75114e7	−	3.03306e7i	0.0549615	−	0.0951961i	−0.837236	−	0.546842i	$-0.815830\pi$
$683$	1.75114e7	−	3.03306e7i	0.0549615	−	0.0951961i	0.892197	+	0.451646i	$0.149163\pi$
$684$		0			0
$685$			5.64939e7i			0.175764i
$686$		0			0
$687$	2.00504e8			0.618377
$688$		0			0
$689$	4.17399e8	+	2.40985e8i	1.27613	+	0.736772i
$690$		0			0
$691$	1.06856e8	−	6.16934e7i	0.323866	−	0.186984i	−0.329249	−	0.944243i	$-0.606795\pi$
$691$	1.06856e8	−	6.16934e7i	0.323866	−	0.186984i	0.653114	+	0.757259i	$0.273462\pi$
$692$		0			0
$693$	−1.00426e8	−	1.35516e8i	−0.301750	−	0.407185i
$694$		0			0
$695$	−2.17551e8	−	3.76809e8i	−0.648047	−	1.12245i
$696$		0			0
$697$	1.41391e8	−	2.44897e8i	0.417565	−	0.723244i
$698$		0			0
$699$			1.31996e8i			0.386482i
$700$		0			0
$701$	1.95528e8			0.567616			0.283808	−	0.958881i	$-0.408402\pi$
$701$	1.95528e8			0.567616			0.283808	+	0.958881i	$0.408402\pi$
$702$		0			0
$703$	−1.28677e8	−	7.42915e7i	−0.370368	−	0.213832i
$704$		0			0
$705$	1.92194e7	−	1.10963e7i	0.0548493	−	0.0316673i
$706$		0			0
$707$	9.40667e6	+	8.20420e7i	0.0266181	+	0.232155i
$708$		0			0
$709$	2.52353e8	+	4.37089e8i	0.708060	+	1.22640i	0.965576	+	0.260122i	$0.0837629\pi$
$709$	2.52353e8	+	4.37089e8i	0.708060	+	1.22640i	−0.257515	+	0.966274i	$0.582904\pi$
$710$		0			0
$711$	−9.04522e7	+	1.56668e8i	−0.251658	+	0.435884i
$712$		0			0
$713$		−	8.93332e6i		−	0.0246459i
$714$		0			0
$715$	3.20358e8			0.876430
$716$		0			0
$717$	1.62647e8	+	9.39043e7i	0.441254	+	0.254758i
$718$		0			0
$719$	−1.12251e8	+	6.48079e7i	−0.301996	+	0.174358i	−0.643339	−	0.765581i	$-0.722452\pi$
$719$	−1.12251e8	+	6.48079e7i	−0.301996	+	0.174358i	0.341343	+	0.939939i	$0.389118\pi$
$720$		0			0
$721$	3.08321e8	+	1.33801e8i	0.822617	+	0.356988i
$722$		0			0
$723$	1.99790e8	+	3.46046e8i	0.528638	+	0.915628i
$724$		0			0
$725$	−1.21235e8	+	2.09985e8i	−0.318137	+	0.551029i
$726$		0			0
$727$		−	4.16337e7i		−	0.108353i	−0.998531	−	0.0541766i	$-0.982747\pi$
$727$		−	4.16337e7i		−	0.108353i	0.998531	−	0.0541766i	$-0.0172534\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	4.30994e7	+	2.48835e7i	0.110337	+	0.0637028i
$732$		0			0
$733$	−1.48878e8	+	8.59549e7i	−0.378024	+	0.218252i	−0.676958	−	0.736021i	$-0.736702\pi$
$733$	−1.48878e8	+	8.59549e7i	−0.378024	+	0.218252i	0.298934	+	0.954274i	$0.403369\pi$
$734$		0			0
$735$	−4.78778e7	+	1.57402e8i	−0.120579	+	0.396414i
$736$		0			0
$737$	−2.75303e8	−	4.76838e8i	−0.687714	−	1.19116i
$738$		0			0
$739$	−3.33621e8	+	5.77848e8i	−0.826646	+	1.43179i	0.0740081	+	0.997258i	$0.476421\pi$
$739$	−3.33621e8	+	5.77848e8i	−0.826646	+	1.43179i	−0.900655	+	0.434536i	$0.856912\pi$
$740$		0			0
$741$			4.61231e7i			0.113361i
$742$		0			0
$743$	5.12549e8			1.24960			0.624798	−	0.780787i	$-0.285182\pi$
$743$	5.12549e8			1.24960			0.624798	+	0.780787i	$0.285182\pi$
$744$		0			0
$745$	−2.28000e8	−	1.31636e8i	−0.551398	−	0.318350i
$746$		0			0
$747$	1.38494e8	−	7.99595e7i	0.332253	−	0.191826i
$748$		0			0
$749$	−3.81857e7	+	8.79923e7i	−0.0908772	+	0.209411i
$750$		0			0
$751$	7.93513e7	+	1.37441e8i	0.187342	+	0.324485i	0.944363	−	0.328905i	$-0.106680\pi$
$751$	7.93513e7	+	1.37441e8i	0.187342	+	0.324485i	−0.757021	+	0.653390i	$0.773346\pi$
$752$		0			0
$753$	−2.32451e8	+	4.02618e8i	−0.544436	+	0.942992i
$754$		0			0
$755$		−	1.53592e8i		−	0.356886i
$756$		0			0
$757$	−3.57777e8			−0.824754			−0.412377	−	0.911013i	$-0.635301\pi$
$757$	−3.57777e8			−0.824754			−0.412377	+	0.911013i	$0.635301\pi$
$758$		0			0
$759$	8.27096e6	+	4.77524e6i	0.0189161	+	0.0109212i
$760$		0			0
$761$	3.19665e7	−	1.84559e7i	0.0725338	−	0.0418774i	−0.463294	−	0.886204i	$-0.653333\pi$
$761$	3.19665e7	−	1.84559e7i	0.0725338	−	0.0418774i	0.535828	+	0.844327i	$0.319999\pi$
$762$		0			0
$763$	−4.79253e8	+	5.49496e7i	−1.07892	+	0.123706i
$764$		0			0
$765$	4.26577e7	+	7.38853e7i	0.0952824	+	0.165034i
$766$		0			0
$767$	1.40544e8	−	2.43429e8i	0.311477	−	0.539494i
$768$		0			0
$769$			8.61346e8i			1.89408i	0.321114	+	0.947041i	$0.395943\pi$
$769$			8.61346e8i			1.89408i	−0.321114	+	0.947041i	$0.604057\pi$
$770$		0			0
$771$	−5.74103e7			−0.125264
$772$		0			0
$773$	7.64127e7	+	4.41169e7i	0.165435	+	0.0955139i	0.580432	−	0.814309i	$-0.302884\pi$
$773$	7.64127e7	+	4.41169e7i	0.165435	+	0.0955139i	−0.414997	+	0.909823i	$0.636217\pi$
$774$		0			0
$775$	1.93634e8	−	1.11794e8i	0.415983	−	0.240168i
$776$		0			0
$777$	−3.80680e8	+	2.82108e8i	−0.811515	+	0.601384i
$778$		0			0
$779$	−6.05749e7	−	1.04919e8i	−0.128139	−	0.221943i
$780$		0			0
$781$	−5.01283e7	+	8.68248e7i	−0.105228	+	0.182260i
$782$		0			0
$783$			1.21213e8i			0.252502i
$784$		0			0
$785$	2.95839e7			0.0611570
$786$		0			0
$787$	5.19289e8	+	2.99812e8i	1.06533	+	0.615070i	0.926902	−	0.375302i	$-0.122461\pi$
$787$	5.19289e8	+	2.99812e8i	1.06533	+	0.615070i	0.138430	+	0.990372i	$0.455794\pi$
$788$		0			0
$789$	−2.40832e8	+	1.39044e8i	−0.490323	+	0.283088i
$790$		0			0
$791$	−4.58627e8	−	6.18878e8i	−0.926682	−	1.25048i
$792$		0			0
$793$	−3.47727e8	−	6.02281e8i	−0.697299	−	1.20776i
$794$		0			0
$795$	1.90972e8	−	3.30773e8i	0.380073	−	0.658307i
$796$		0			0
$797$			5.37114e8i			1.06094i	0.847703	+	0.530471i	$0.177985\pi$
$797$			5.37114e8i			1.06094i	−0.847703	+	0.530471i	$0.822015\pi$
$798$		0			0
$799$	6.21093e7			0.121763
$800$		0			0
$801$	2.44141e8	+	1.40955e8i	0.475054	+	0.274273i
$802$		0			0
$803$	8.08577e7	−	4.66832e7i	0.156162	−	0.0901600i
$804$		0			0
$805$	−1.06114e6	−	9.25493e6i	−0.00203416	−	0.0177413i
$806$		0			0
$807$	−1.63645e8	−	2.83442e8i	−0.311375	−	0.539317i
$808$		0			0
$809$	−1.20486e7	+	2.08688e7i	−0.0227558	+	0.0394142i	−0.877179	−	0.480163i	$-0.840577\pi$
$809$	−1.20486e7	+	2.08688e7i	−0.0227558	+	0.0394142i	0.854423	+	0.519578i	$0.173911\pi$
$810$		0			0
$811$			1.15668e8i			0.216846i	0.994105	+	0.108423i	$0.0345801\pi$
$811$			1.15668e8i			0.216846i	−0.994105	+	0.108423i	$0.965420\pi$
$812$		0			0
$813$	−5.85215e8			−1.08904
$814$		0			0
$815$	1.35665e8	+	7.83261e7i	0.250608	+	0.144688i
$816$		0			0
$817$	1.84647e7	−	1.06606e7i	0.0338591	−	0.0195486i
$818$		0			0
$819$	1.34925e8	+	5.85528e7i	0.245607	+	0.106585i
$820$		0			0
$821$	−2.22737e8	−	3.85792e8i	−0.402497	−	0.697145i	0.591530	−	0.806283i	$-0.298524\pi$
$821$	−2.22737e8	−	3.85792e8i	−0.402497	−	0.697145i	−0.994027	+	0.109138i	$0.965191\pi$
$822$		0			0
$823$	5.71152e7	−	9.89264e7i	0.102460	−	0.177465i	−0.810238	−	0.586101i	$-0.800662\pi$
$823$	5.71152e7	−	9.89264e7i	0.102460	−	0.177465i	0.912697	+	0.408636i	$0.133995\pi$
$824$		0			0
$825$			2.39035e8i			0.425697i
$826$		0			0
$827$	−2.90474e8			−0.513560			−0.256780	−	0.966470i	$-0.582662\pi$
$827$	−2.90474e8			−0.513560			−0.256780	+	0.966470i	$0.582662\pi$
$828$		0			0
$829$	3.17366e8	+	1.83231e8i	0.557054	+	0.321615i	0.751962	−	0.659206i	$-0.229108\pi$
$829$	3.17366e8	+	1.83231e8i	0.557054	+	0.321615i	−0.194908	+	0.980821i	$0.562441\pi$
$830$		0			0
$831$	−4.02236e8	+	2.32231e8i	−0.700935	+	0.404685i
$832$		0			0
$833$	−3.36298e8	+	3.14500e8i	−0.581821	+	0.544108i
$834$		0			0
$835$	−1.14761e8	−	1.98771e8i	−0.197121	−	0.341424i
$836$		0			0
$837$	5.58871e7	−	9.67994e7i	0.0953094	−	0.165081i
$838$		0			0
$839$			9.03137e8i			1.52921i	0.644498	+	0.764606i	$0.277066\pi$
$839$			9.03137e8i			1.52921i	−0.644498	+	0.764606i	$0.722934\pi$
$840$		0			0
$841$	4.29132e8			0.721445
$842$		0			0
$843$	−1.27112e8	−	7.33884e7i	−0.212180	−	0.122502i
$844$		0			0
$845$	1.33068e8	−	7.68269e7i	0.220548	−	0.127334i
$846$		0			0
$847$	−3.17296e8	+	7.31155e8i	−0.522174	+	1.20326i
$848$		0			0
$849$	−1.90380e8	−	3.29748e8i	−0.311099	−	0.538840i
$850$		0			0
$851$	1.34142e7	−	2.32340e7i	0.0217658	−	0.0376995i
$852$		0			0
$853$			1.02501e9i			1.65151i	0.564027	+	0.825756i	$0.309251\pi$
$853$			1.02501e9i			1.65151i	−0.564027	+	0.825756i	$0.690749\pi$
$854$		0			0
$855$	3.65508e7			0.0584789
$856$		0			0
$857$	−6.70184e7	−	3.86931e7i	−0.106476	−	0.0614739i	0.445816	−	0.895124i	$-0.352913\pi$
$857$	−6.70184e7	−	3.86931e7i	−0.106476	−	0.0614739i	−0.552292	+	0.833651i	$0.686247\pi$
$858$		0			0
$859$	−6.95223e8	+	4.01387e8i	−1.09684	+	0.633263i	−0.935390	−	0.353618i	$-0.884951\pi$
$859$	−6.95223e8	+	4.01387e8i	−1.09684	+	0.633263i	−0.161453	+	0.986880i	$0.551618\pi$
$860$		0			0
$861$	−3.83820e8	+	4.40075e7i	−0.601337	+	0.0689473i
$862$		0			0
$863$	1.26911e8	+	2.19817e8i	0.197455	+	0.342002i	0.947703	−	0.319155i	$-0.103399\pi$
$863$	1.26911e8	+	2.19817e8i	0.197455	+	0.342002i	−0.750248	+	0.661157i	$0.770066\pi$
$864$		0			0
$865$	3.36330e8	−	5.82540e8i	0.519657	−	0.900073i
$866$		0			0
$867$		−	1.37500e8i		−	0.210981i
$868$		0			0
$869$	1.50655e9			2.29575
$870$		0			0
$871$	4.15804e8	+	2.40065e8i	0.629266	+	0.363307i
$872$		0			0
$873$	1.44369e8	−	8.33513e7i	0.216985	−	0.125277i
$874$		0			0
$875$	5.73602e8	−	4.25075e8i	0.856222	−	0.634514i
$876$		0			0
$877$	−6.55708e8	−	1.13572e9i	−0.972101	−	1.68373i	−0.689187	−	0.724583i	$-0.742032\pi$
$877$	−6.55708e8	−	1.13572e9i	−0.972101	−	1.68373i	−0.282914	−	0.959145i	$-0.591301\pi$
$878$		0			0
$879$	−1.72449e8	+	2.98690e8i	−0.253918	+	0.439800i
$880$		0			0
$881$		−	3.21715e8i		−	0.470483i	−0.971937	−	0.235241i	$-0.924412\pi$
$881$		−	3.21715e8i		−	0.470483i	0.971937	−	0.235241i	$-0.0755880\pi$
$882$		0			0
$883$	6.04235e8			0.877656			0.438828	−	0.898571i	$-0.355394\pi$
$883$	6.04235e8			0.877656			0.438828	+	0.898571i	$0.355394\pi$
$884$		0			0
$885$	−1.92908e8	−	1.11376e8i	−0.278305	−	0.160679i
$886$		0			0
$887$	2.46051e8	−	1.42058e8i	0.352577	−	0.203561i	−0.313243	−	0.949673i	$-0.601415\pi$
$887$	2.46051e8	−	1.42058e8i	0.352577	−	0.203561i	0.665820	+	0.746113i	$0.268082\pi$
$888$		0			0
$889$	3.93696e8	+	5.31259e8i	0.560346	+	0.756138i
$890$		0			0
$891$	5.97481e7	+	1.03487e8i	0.0844678	+	0.146302i
$892$		0			0
$893$	1.33045e7	−	2.30440e7i	0.0186828	−	0.0323596i
$894$		0			0
$895$			2.36255e8i			0.329543i
$896$		0			0
$897$	−8.32804e6			−0.0115389
$898$		0			0
$899$	−8.17718e8	−	4.72110e8i	−1.12545	−	0.649777i
$900$		0			0
$901$	9.25717e8	−	5.34463e8i	1.26562	−	0.730707i
$902$		0			0
$903$	−7.74488e6	−	6.75485e7i	−0.0105184	−	0.0917386i
$904$		0			0
$905$	−3.02884e8	−	5.24610e8i	−0.408630	−	0.707768i
$906$		0			0
$907$	−3.02132e8	+	5.23309e8i	−0.404926	+	0.701352i	−0.994313	−	0.106499i	$-0.966036\pi$
$907$	−3.02132e8	+	5.23309e8i	−0.404926	+	0.701352i	0.589387	+	0.807851i	$0.299369\pi$
$908$		0			0
$909$		−	5.85039e7i		−	0.0778920i
$910$		0			0
$911$	−1.48125e8			−0.195918			−0.0979591	−	0.995190i	$-0.531231\pi$
$911$	−1.48125e8			−0.195918			−0.0979591	+	0.995190i	$0.531231\pi$
$912$		0			0
$913$	−1.15336e9	−	6.65895e8i	−1.51549	−	0.874970i
$914$		0			0
$915$	−4.77285e8	+	2.75560e8i	−0.623037	+	0.359711i
$916$		0			0
$917$	3.35375e8	+	1.45542e8i	0.434934	+	0.188747i
$918$		0			0
$919$	−5.97977e8	−	1.03573e9i	−0.770439	−	1.33444i	−0.937323	−	0.348463i	$-0.886704\pi$
$919$	−5.97977e8	−	1.03573e9i	−0.770439	−	1.33444i	0.166884	−	0.985977i	$-0.446629\pi$
$920$		0			0
$921$	−3.91478e8	+	6.78059e8i	−0.501104	+	0.867938i
$922$		0			0
$923$		−	8.74240e7i		−	0.111180i
$924$		0			0
$925$	6.71476e8			0.848408
$926$		0			0
$927$	−2.06212e8	−	1.19057e8i	−0.258866	−	0.149456i
$928$		0			0
$929$	1.46476e8	−	8.45678e7i	0.182692	−	0.105477i	−0.405865	−	0.913933i	$-0.633030\pi$
$929$	1.46476e8	−	8.45678e7i	0.182692	−	0.105477i	0.588557	+	0.808456i	$0.299696\pi$
$930$		0			0
$931$	4.46480e7	+	1.92143e8i	0.0553290	+	0.238109i
$932$		0			0
$933$	−1.57994e8	−	2.73653e8i	−0.194534	−	0.336943i
$934$		0			0
$935$	3.55249e8	−	6.15309e8i	0.434608	−	0.752763i
$936$		0			0
$937$			1.14529e9i			1.39218i	0.717953	+	0.696091i	$0.245079\pi$
$937$			1.14529e9i			1.39218i	−0.717953	+	0.696091i	$0.754921\pi$
$938$		0			0
$939$	−2.13954e6			−0.00258418
$940$		0			0
$941$	−8.22353e8	−	4.74786e8i	−0.986937	−	0.569808i	−0.0825796	−	0.996584i	$-0.526316\pi$
$941$	−8.22353e8	−	4.74786e8i	−0.986937	−	0.569808i	−0.904357	+	0.426776i	$0.859649\pi$
$942$		0			0
$943$	1.89442e7	−	1.09375e7i	0.0225914	−	0.0130431i
$944$		0			0
$945$	4.64009e7	−	1.06923e8i	0.0549833	−	0.126699i
$946$		0			0
$947$	1.52542e7	+	2.64211e7i	0.0179614	+	0.0311100i	0.874866	−	0.484364i	$-0.160949\pi$
$947$	1.52542e7	+	2.64211e7i	0.0179614	+	0.0311100i	−0.856905	+	0.515474i	$0.827616\pi$
$948$		0			0
$949$	−4.07079e7	+	7.05081e7i	−0.0476299	+	0.0824974i
$950$		0			0
$951$			8.48767e8i			0.986841i
$952$		0			0
$953$	1.33990e9			1.54808			0.774039	−	0.633138i	$-0.218234\pi$
$953$	1.33990e9			1.54808			0.774039	+	0.633138i	$0.218234\pi$
$954$		0			0
$955$	−1.19242e8	−	6.88444e7i	−0.136905	−	0.0790421i
$956$		0			0
$957$	8.74210e8	−	5.04726e8i	0.997425	−	0.575863i
$958$		0			0
$959$	2.14598e8	−	2.46051e7i	0.243315	−	0.0278977i
$960$		0			0
$961$	−8.40536e6	−	1.45585e7i	−0.00947079	−	0.0164039i
$962$		0			0
$963$	3.39777e7	−	5.88512e7i	0.0380466	−	0.0658986i
$964$		0			0
$965$			9.00580e8i			1.00217i
$966$		0			0
$967$	5.28612e8			0.584599			0.292299	−	0.956327i	$-0.405580\pi$
$967$	5.28612e8			0.584599			0.292299	+	0.956327i	$0.405580\pi$
$968$		0			0
$969$	8.85883e7	+	5.11465e7i	0.0973655	+	0.0562140i
$970$		0			0
$971$	7.40804e8	−	4.27703e8i	0.809181	−	0.467181i	−0.0374907	−	0.999297i	$-0.511936\pi$
$971$	7.40804e8	−	4.27703e8i	0.809181	−	0.467181i	0.846671	+	0.532116i	$0.178603\pi$
$972$		0			0
$973$	−1.33660e9	+	9.90502e8i	−1.45098	+	1.07527i
$974$		0			0
$975$	−1.04220e8	−	1.80514e8i	−0.112444	−	0.194759i
$976$		0			0
$977$	3.23616e8	−	5.60519e8i	0.347013	−	0.601044i	−0.638704	−	0.769452i	$-0.720529\pi$
$977$	3.23616e8	−	5.60519e8i	0.347013	−	0.601044i	0.985717	+	0.168408i	$0.0538626\pi$
$978$		0			0
$979$		−	2.34771e9i		−	2.50206i
$980$		0			0
$981$	3.41754e8			0.361998
$982$		0			0
$983$	8.15767e8	+	4.70983e8i	0.858827	+	0.495844i	0.863619	−	0.504145i	$-0.168192\pi$
$983$	8.15767e8	+	4.70983e8i	0.858827	+	0.495844i	−0.00479238	+	0.999989i	$0.501525\pi$
$984$		0			0
$985$	−9.53998e8	+	5.50791e8i	−0.998248	+	0.576339i
$986$		0			0
$987$	−5.05211e7	−	6.81738e7i	−0.0525438	−	0.0709033i
$988$		0			0
$989$	1.92489e6	+	3.33400e6i	0.00198983	+	0.00344649i
$990$		0			0
$991$	3.68293e8	−	6.37902e8i	0.378418	−	0.655440i	−0.612414	−	0.790537i	$-0.709801\pi$
$991$	3.68293e8	−	6.37902e8i	0.378418	−	0.655440i	0.990832	+	0.135098i	$0.0431348\pi$
$992$		0			0
$993$			2.04451e8i			0.208806i
$994$		0			0
$995$	−5.85441e8			−0.594311
$996$		0			0
$997$	−6.63710e8	−	3.83193e8i	−0.669720	−	0.386663i	0.126251	−	0.991998i	$-0.459706\pi$
$997$	−6.63710e8	−	3.83193e8i	−0.669720	−	0.386663i	−0.795970	+	0.605336i	$0.793039\pi$
$998$		0			0
$999$	2.90705e8	−	1.67839e8i	0.291579	−	0.168343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.f.241.3		8
4.3	odd	2		42.7.g.a.31.4	yes	8
7.5	odd	6	inner	336.7.bh.f.145.3		8
12.11	even	2		126.7.n.a.73.1		8
28.3	even	6		294.7.c.b.97.1		8
28.11	odd	6		294.7.c.b.97.4		8
28.19	even	6		42.7.g.a.19.4	✓	8
28.23	odd	6		294.7.g.d.19.3		8
28.27	even	2		294.7.g.d.31.3		8
84.47	odd	6		126.7.n.a.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.7.g.a.19.4	✓	8	28.19	even	6
42.7.g.a.31.4	yes	8	4.3	odd	2
126.7.n.a.19.1		8	84.47	odd	6
126.7.n.a.73.1		8	12.11	even	2
294.7.c.b.97.1		8	28.3	even	6
294.7.c.b.97.4		8	28.11	odd	6
294.7.g.d.19.3		8	28.23	odd	6
294.7.g.d.31.3		8	28.27	even	2
336.7.bh.f.145.3		8	7.5	odd	6	inner
336.7.bh.f.241.3		8	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)

\(f(q)\)	\(=\)	\(q+(13.5000 + 7.79423i) q^{3} +(77.6900 - 44.8543i) q^{5} +(-204.220 - 275.578i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 + 7.79423i) q^{3} +(77.6900 - 44.8543i) q^{5} +(-204.220 - 275.578i) q^{7} +(121.500 + 210.444i) q^{9} +(1011.84 - 1752.56i) q^{11} +1764.65i q^{13} +1398.42 q^{15} +(3389.35 + 1956.84i) q^{17} +(1452.07 - 838.352i) q^{19} +(-609.061 - 5312.04i) q^{21} +(151.374 + 262.187i) q^{23} +(-3788.68 + 6562.18i) q^{25} +3788.00i q^{27} +31999.3 q^{29} +(-25554.3 - 14753.8i) q^{31} +(27319.7 - 15773.0i) q^{33} +(-28226.7 - 12249.5i) q^{35} +(-44308.1 - 76743.8i) q^{37} +(-13754.1 + 23822.8i) q^{39} -72254.7i q^{41} +12716.1 q^{43} +(18878.7 + 10899.6i) q^{45} +(13743.6 - 7934.88i) q^{47} +(-34237.0 + 112557. i) q^{49} +(30504.2 + 52834.8i) q^{51} +(136562. - 236533. i) q^{53} -181542. i q^{55} +26137.2 q^{57} +(-137947. - 79643.9i) q^{59} +(-341303. + 197051. i) q^{61} +(33180.9 - 76459.7i) q^{63} +(79152.4 + 137096. i) q^{65} +(136041. - 235629. i) q^{67} +4719.37i q^{69} -49541.8 q^{71} +(39955.8 + 23068.5i) q^{73} +(-102294. + 59059.6i) q^{75} +(-689604. + 79067.7i) q^{77} +(372231. + 644723. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -658103. i q^{83} +351092. q^{85} +(431991. + 249410. i) q^{87} +(1.00470e6 - 580061. i) q^{89} +(486299. - 360378. i) q^{91} +(-229988. - 398351. i) q^{93} +(75207.5 - 130263. i) q^{95} -686019. i q^{97} +491754. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q + 108 * q^3 + 462 * q^5 - 580 * q^7 + 972 * q^9	\( 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9} - 1806 q^{11} + 8316 q^{15} + 9564 q^{17} - 23022 q^{19} - 1350 q^{21} - 2400 q^{23} + 32762 q^{25} - 2484 q^{29} - 148416 q^{31} - 48762 q^{33} - 11412 q^{35} - 84046 q^{37} + 75222 q^{39} - 92972 q^{43} + 112266 q^{45} + 323124 q^{47} - 8644 q^{49} + 86076 q^{51} + 358086 q^{53} - 414396 q^{57} - 719382 q^{59} + 421536 q^{61} + 104490 q^{63} - 322740 q^{65} - 267010 q^{67} + 464664 q^{71} + 1944486 q^{73} + 884574 q^{75} - 1713498 q^{77} + 685904 q^{79} - 236196 q^{81} - 3876168 q^{85} - 33534 q^{87} + 4130604 q^{89} + 484266 q^{91} - 1335744 q^{93} + 2105232 q^{95} - 877716 q^{99}+O(q^{100}) \) 8 * q + 108 * q^3 + 462 * q^5 - 580 * q^7 + 972 * q^9 - 1806 * q^11 + 8316 * q^15 + 9564 * q^17 - 23022 * q^19 - 1350 * q^21 - 2400 * q^23 + 32762 * q^25 - 2484 * q^29 - 148416 * q^31 - 48762 * q^33 - 11412 * q^35 - 84046 * q^37 + 75222 * q^39 - 92972 * q^43 + 112266 * q^45 + 323124 * q^47 - 8644 * q^49 + 86076 * q^51 + 358086 * q^53 - 414396 * q^57 - 719382 * q^59 + 421536 * q^61 + 104490 * q^63 - 322740 * q^65 - 267010 * q^67 + 464664 * q^71 + 1944486 * q^73 + 884574 * q^75 - 1713498 * q^77 + 685904 * q^79 - 236196 * q^81 - 3876168 * q^85 - 33534 * q^87 + 4130604 * q^89 + 484266 * q^91 - 1335744 * q^93 + 2105232 * q^95 - 877716 * q^99

Introduction

L-functions

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