LMFDB - Embedded newform 336.7.bh.b.241.4

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			241.4
Root			$4.15432 + 7.19549i$ of defining polynomial
Character	$\chi$	$=$	336.241
Dual form			336.7.bh.b.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.5000 - 7.79423i) q^{3} +(151.343 - 87.3778i) q^{5} +(271.614 + 209.463i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})$	\(q+(-13.5000 - 7.79423i) q^{3} +(151.343 - 87.3778i) q^{5} +(271.614 + 209.463i) q^{7} +(121.500 + 210.444i) q^{9} +(-92.6996 + 160.560i) q^{11} -3981.73i q^{13} -2724.17 q^{15} +(6101.23 + 3522.55i) q^{17} +(4064.58 - 2346.69i) q^{19} +(-2034.18 - 4944.78i) q^{21} +(-3322.00 - 5753.87i) q^{23} +(7457.27 - 12916.4i) q^{25} -3788.00i q^{27} +19385.8 q^{29} +(-20743.8 - 11976.4i) q^{31} +(2502.89 - 1445.04i) q^{33} +(59409.3 + 7967.73i) q^{35} +(19784.8 + 34268.3i) q^{37} +(-31034.5 + 53753.4i) q^{39} +46285.6i q^{41} +93128.7 q^{43} +(36776.3 + 21232.8i) q^{45} +(-129449. + 74737.3i) q^{47} +(29899.3 + 113786. i) q^{49} +(-54911.1 - 95108.8i) q^{51} +(50912.7 - 88183.4i) q^{53} +32399.5i q^{55} -73162.4 q^{57} +(-131933. - 76171.6i) q^{59} +(-145966. + 84273.5i) q^{61} +(-11079.2 + 82609.4i) q^{63} +(-347915. - 602606. i) q^{65} +(30552.0 - 52917.6i) q^{67} +103570. i q^{69} +485262. q^{71} +(-7732.72 - 4464.49i) q^{73} +(-201346. + 116247. i) q^{75} +(-58810.0 + 24193.3i) q^{77} +(221938. + 384409. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -559383. i q^{83} +1.23117e6 q^{85} +(-261708. - 151097. i) q^{87} +(-179055. + 103378. i) q^{89} +(834026. - 1.08149e6i) q^{91} +(186694. + 323364. i) q^{93} +(410097. - 710308. i) q^{95} -1.23197e6i q^{97} -45052.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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
$5$	151.343	−	87.3778i	1.21074	−	0.699023i	0.247821	−	0.968806i	$-0.420285\pi$
$5$	151.343	−	87.3778i	1.21074	−	0.699023i	0.962921	+	0.269783i	$0.0869520\pi$
$6$		0			0
$7$	271.614	+	209.463i	0.791877	+	0.610680i
$7$	271.614	+	209.463i	0.791877	+	0.610680i
$8$		0			0
$9$	121.500	+	210.444i	0.166667	+	0.288675i
$10$		0			0
$11$	−92.6996	+	160.560i	−0.0696466	+	0.120631i	−0.898746	−	0.438470i	$-0.855520\pi$
$11$	−92.6996	+	160.560i	−0.0696466	+	0.120631i	0.829099	+	0.559102i	$0.188854\pi$
$12$		0			0
$13$		−	3981.73i		−	1.81235i	−0.422904	−	0.906174i	$-0.638989\pi$
$13$		−	3981.73i		−	1.81235i	0.422904	−	0.906174i	$-0.361011\pi$
$14$		0			0
$15$	−2724.17			−0.807162
$16$		0			0
$17$	6101.23	+	3522.55i	1.24185	+	0.716985i	0.969471	−	0.245204i	$-0.0788550\pi$
$17$	6101.23	+	3522.55i	1.24185	+	0.716985i	0.272383	+	0.962189i	$0.412188\pi$
$18$		0			0
$19$	4064.58	−	2346.69i	0.592591	−	0.342132i	−0.173531	−	0.984828i	$-0.555518\pi$
$19$	4064.58	−	2346.69i	0.592591	−	0.342132i	0.766121	+	0.642696i	$0.222184\pi$
$20$		0			0
$21$	−2034.18	−	4944.78i	−0.219651	−	0.533935i
$22$		0			0
$23$	−3322.00	−	5753.87i	−0.273033	−	0.472908i	0.696604	−	0.717456i	$-0.254694\pi$
$23$	−3322.00	−	5753.87i	−0.273033	−	0.472908i	−0.969637	+	0.244549i	$0.921360\pi$
$24$		0			0
$25$	7457.27	−	12916.4i	0.477265	−	0.826647i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	19385.8			0.794857			0.397429	−	0.917633i	$-0.369903\pi$
$29$	19385.8			0.794857			0.397429	+	0.917633i	$0.369903\pi$
$30$		0			0
$31$	−20743.8	−	11976.4i	−0.696311	−	0.402015i	0.109661	−	0.993969i	$-0.465023\pi$
$31$	−20743.8	−	11976.4i	−0.696311	−	0.402015i	−0.805972	+	0.591954i	$0.798357\pi$
$32$		0			0
$33$	2502.89	−	1445.04i	0.0696466	−	0.0402105i
$34$		0			0
$35$	59409.3	+	7967.73i	1.38564	+	0.185836i
$36$		0			0
$37$	19784.8	+	34268.3i	0.390595	+	0.676531i	0.992528	−	0.122016i	$-0.0389359\pi$
$37$	19784.8	+	34268.3i	0.390595	+	0.676531i	−0.601933	+	0.798547i	$0.705603\pi$
$38$		0			0
$39$	−31034.5	+	53753.4i	−0.523180	+	0.906174i
$40$		0			0
$41$			46285.6i			0.671575i	0.941938	+	0.335787i	$0.109002\pi$
$41$			46285.6i			0.671575i	−0.941938	+	0.335787i	$0.890998\pi$
$42$		0			0
$43$	93128.7			1.17133			0.585664	−	0.810554i	$-0.300834\pi$
$43$	93128.7			1.17133			0.585664	+	0.810554i	$0.300834\pi$
$44$		0			0
$45$	36776.3	+	21232.8i	0.403581	+	0.233008i
$46$		0			0
$47$	−129449.	+	74737.3i	−1.24682	+	0.719853i	−0.970474	−	0.241205i	$-0.922457\pi$
$47$	−129449.	+	74737.3i	−1.24682	+	0.719853i	−0.276347	+	0.961058i	$0.589124\pi$
$48$		0			0
$49$	29899.3	+	113786.i	0.254140	+	0.967168i
$50$		0			0
$51$	−54911.1	−	95108.8i	−0.413951	−	0.716985i
$52$		0			0
$53$	50912.7	−	88183.4i	0.341978	−	0.592324i	−0.642822	−	0.766016i	$-0.722236\pi$
$53$	50912.7	−	88183.4i	0.341978	−	0.592324i	0.984800	+	0.173692i	$0.0555698\pi$
$54$		0			0
$55$			32399.5i			0.194738i
$56$		0			0
$57$	−73162.4			−0.395060
$58$		0			0
$59$	−131933.	−	76171.6i	−0.642388	−	0.370883i	0.143146	−	0.989702i	$-0.454278\pi$
$59$	−131933.	−	76171.6i	−0.642388	−	0.370883i	−0.785534	+	0.618819i	$0.787612\pi$
$60$		0			0
$61$	−145966.	+	84273.5i	−0.643076	+	0.371280i	−0.785798	−	0.618483i	$-0.787748\pi$
$61$	−145966.	+	84273.5i	−0.643076	+	0.371280i	0.142723	+	0.989763i	$0.454414\pi$
$62$		0			0
$63$	−11079.2	+	82609.4i	−0.0443086	+	0.330375i
$64$		0			0
$65$	−347915.	−	602606.i	−1.26687	−	2.19429i
$66$		0			0
$67$	30552.0	−	52917.6i	0.101582	−	0.175944i	−0.810755	−	0.585386i	$-0.800943\pi$
$67$	30552.0	−	52917.6i	0.101582	−	0.175944i	0.912336	+	0.409441i	$0.134276\pi$
$68$		0			0
$69$			103570.i			0.315272i
$70$		0			0
$71$	485262.			1.35582			0.677909	−	0.735146i	$-0.262886\pi$
$71$	485262.			1.35582			0.677909	+	0.735146i	$0.262886\pi$
$72$		0			0
$73$	−7732.72	−	4464.49i	−0.0198776	−	0.0114763i	0.490028	−	0.871707i	$-0.336986\pi$
$73$	−7732.72	−	4464.49i	−0.0198776	−	0.0114763i	−0.509906	+	0.860230i	$0.670320\pi$
$74$		0			0
$75$	−201346.	+	116247.i	−0.477265	+	0.275549i
$76$		0			0
$77$	−58810.0	+	24193.3i	−0.128819	+	0.0529935i
$78$		0			0
$79$	221938.	+	384409.i	0.450144	+	0.779672i	0.998395	−	0.0566422i	$-0.0180394\pi$
$79$	221938.	+	384409.i	0.450144	+	0.779672i	−0.548251	+	0.836314i	$0.684706\pi$
$80$		0			0
$81$	−29524.5	+	51137.9i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	559383.i		−	0.978306i	−0.872198	−	0.489153i	$-0.837306\pi$
$83$		−	559383.i		−	0.978306i	0.872198	−	0.489153i	$-0.162694\pi$
$84$		0			0
$85$	1.23117e6			2.00475
$86$		0			0
$87$	−261708.	−	151097.i	−0.397429	−	0.229456i
$88$		0			0
$89$	−179055.	+	103378.i	−0.253990	+	0.146641i	−0.621590	−	0.783343i	$-0.713513\pi$
$89$	−179055.	+	103378.i	−0.253990	+	0.146641i	0.367600	+	0.929984i	$0.380180\pi$
$90$		0			0
$91$	834026.	−	1.08149e6i	1.10677	−	1.43516i
$92$		0			0
$93$	186694.	+	323364.i	0.232104	+	0.402015i
$94$		0			0
$95$	410097.	−	710308.i	0.478316	−	0.828468i
$96$		0			0
$97$		−	1.23197e6i		−	1.34984i	−0.737889	−	0.674922i	$-0.764177\pi$
$97$		−	1.23197e6i		−	1.34984i	0.737889	−	0.674922i	$-0.235823\pi$
$98$		0			0
$99$	−45052.0			−0.0464310
$100$		0			0
$101$	−776728.	−	448444.i	−0.753884	−	0.435255i	0.0732114	−	0.997316i	$-0.476675\pi$
$101$	−776728.	−	448444.i	−0.753884	−	0.435255i	−0.827096	+	0.562061i	$0.810009\pi$
$102$		0			0
$103$	1.15489e6	−	666775.i	1.05689	−	0.610194i	0.132317	−	0.991207i	$-0.457758\pi$
$103$	1.15489e6	−	666775.i	1.05689	−	0.610194i	0.924569	+	0.381014i	$0.124425\pi$
$104$		0			0
$105$	−739923.	−	570614.i	−0.639173	−	0.492918i
$106$		0			0
$107$	−50509.0	−	87484.1i	−0.0412304	−	0.0714131i	0.844674	−	0.535281i	$-0.179794\pi$
$107$	−50509.0	−	87484.1i	−0.0412304	−	0.0714131i	−0.885904	+	0.463868i	$0.846461\pi$
$108$		0			0
$109$	976298.	−	1.69100e6i	0.753881	−	1.30576i	−0.192047	−	0.981386i	$-0.561513\pi$
$109$	976298.	−	1.69100e6i	0.753881	−	1.30576i	0.945928	−	0.324375i	$-0.105154\pi$
$110$		0			0
$111$		−	616829.i		−	0.451020i
$112$		0			0
$113$	1.13981e6			0.789945			0.394972	−	0.918693i	$-0.370754\pi$
$113$	1.13981e6			0.789945			0.394972	+	0.918693i	$0.370754\pi$
$114$		0			0
$115$	−1.00552e6	−	580537.i	−0.661146	−	0.381713i
$116$		0			0
$117$	837932.	−	483780.i	0.523180	−	0.302058i
$118$		0			0
$119$	919335.	+	2.23476e6i	0.545548	+	1.32614i
$120$		0			0
$121$	868594.	+	1.50445e6i	0.490299	+	0.849222i
$122$		0			0
$123$	360760.	−	624855.i	0.193867	−	0.335787i
$124$		0			0
$125$			124158.i			0.0635691i
$126$		0			0
$127$	−3.37006e6			−1.64523			−0.822614	−	0.568600i	$-0.807485\pi$
$127$	−3.37006e6			−1.64523			−0.822614	+	0.568600i	$0.807485\pi$
$128$		0			0
$129$	−1.25724e6	−	725867.i	−0.585664	−	0.338133i
$130$		0			0
$131$	2.59143e6	−	1.49616e6i	1.15273	−	0.665527i	0.203176	−	0.979142i	$-0.434874\pi$
$131$	2.59143e6	−	1.49616e6i	1.15273	−	0.665527i	0.949550	+	0.313616i	$0.101540\pi$
$132$		0			0
$133$	1.59554e6	+	213987.i	0.678192	+	0.0909564i
$134$		0			0
$135$	−330987.	−	573286.i	−0.134527	−	0.233008i
$136$		0			0
$137$	1.27232e6	−	2.20372e6i	0.494804	−	0.857026i	−0.505178	−	0.863015i	$-0.668573\pi$
$137$	1.27232e6	−	2.20372e6i	0.494804	−	0.857026i	0.999982	+	0.00598920i	$0.00190643\pi$
$138$		0			0
$139$		−	1.61651e6i		−	0.601913i	−0.953638	−	0.300956i	$-0.902694\pi$
$139$		−	1.61651e6i		−	0.601913i	0.953638	−	0.300956i	$-0.0973059\pi$
$140$		0			0
$141$	2.33008e6			0.831214
$142$		0			0
$143$	639308.	+	369105.i	0.218626	+	0.126224i
$144$		0			0
$145$	2.93390e6	−	1.69389e6i	0.962368	−	0.555623i
$146$		0			0
$147$	483236.	−	1.76916e6i	0.152127	−	0.556948i
$148$		0			0
$149$	−570326.	−	987833.i	−0.172411	−	0.298624i	0.766851	−	0.641825i	$-0.221822\pi$
$149$	−570326.	−	987833.i	−0.172411	−	0.298624i	−0.939262	+	0.343201i	$0.888489\pi$
$150$		0			0
$151$	−218027.	+	377635.i	−0.0633258	+	0.109683i	−0.895950	−	0.444155i	$-0.853504\pi$
$151$	−218027.	+	377635.i	−0.0633258	+	0.109683i	0.832624	+	0.553838i	$0.186837\pi$
$152$		0			0
$153$			1.71196e6i			0.477990i
$154$		0			0
$155$	−4.18590e6			−1.12407
$156$		0			0
$157$	−4.62942e6	−	2.67280e6i	−1.19627	−	0.690664i	−0.236545	−	0.971621i	$-0.576015\pi$
$157$	−4.62942e6	−	2.67280e6i	−1.19627	−	0.690664i	−0.959721	+	0.280956i	$0.909348\pi$
$158$		0			0
$159$	−1.37464e6	+	793650.i	−0.341978	+	0.197441i
$160$		0			0
$161$	302923.	−	2.25867e6i	0.0725863	−	0.541221i
$162$		0			0
$163$	835252.	+	1.44670e6i	0.192866	+	0.334053i	0.946199	−	0.323586i	$-0.104889\pi$
$163$	835252.	+	1.44670e6i	0.192866	+	0.334053i	−0.753333	+	0.657639i	$0.771555\pi$
$164$		0			0
$165$	252529.	−	437394.i	0.0562160	−	0.0973690i
$166$		0			0
$167$		−	144090.i		−	0.0309375i	−0.999880	−	0.0154687i	$-0.995076\pi$
$167$		−	144090.i		−	0.0309375i	0.999880	−	0.0154687i	$-0.00492405\pi$
$168$		0			0
$169$	−1.10274e7			−2.28461
$170$		0			0
$171$	987693.	+	570245.i	0.197530	+	0.114044i
$172$		0			0
$173$	−1.52276e6	+	879168.i	−0.294100	+	0.169798i	−0.639789	−	0.768550i	$-0.720978\pi$
$173$	−1.52276e6	+	879168.i	−0.294100	+	0.169798i	0.345690	+	0.938349i	$0.387645\pi$
$174$		0			0
$175$	4.73100e6	−	1.94624e6i	0.882752	−	0.363147i
$176$		0			0
$177$	1.18740e6	+	2.05663e6i	0.214129	+	0.370883i
$178$		0			0
$179$	4.99233e6	−	8.64696e6i	0.870450	−	1.50766i	0.00891827	−	0.999960i	$-0.497161\pi$
$179$	4.99233e6	−	8.64696e6i	0.870450	−	1.50766i	0.861532	−	0.507704i	$-0.169505\pi$
$180$		0			0
$181$			7.80413e6i			1.31610i	0.752974	+	0.658050i	$0.228618\pi$
$181$			7.80413e6i			1.31610i	−0.752974	+	0.658050i	$0.771382\pi$
$182$		0			0
$183$	2.62739e6			0.428717
$184$		0			0
$185$	5.98858e6	+	3.45751e6i	0.945820	+	0.546070i
$186$		0			0
$187$	−1.13116e6	+	653077.i	−0.172982	+	0.0998710i
$188$		0			0
$189$	793446.	−	1.02887e6i	0.117525	−	0.152397i
$190$		0			0
$191$	−255812.	−	443079.i	−0.0367130	−	0.0635888i	0.847085	−	0.531457i	$-0.178355\pi$
$191$	−255812.	−	443079.i	−0.0367130	−	0.0635888i	−0.883798	+	0.467869i	$0.845022\pi$
$192$		0			0
$193$	4.35329e6	−	7.54012e6i	0.605544	−	1.04883i	−0.386421	−	0.922322i	$-0.626289\pi$
$193$	4.35329e6	−	7.54012e6i	0.605544	−	1.04883i	0.991965	−	0.126511i	$-0.0403778\pi$
$194$		0			0
$195$			1.08469e7i			1.46286i
$196$		0			0
$197$	4.44972e6			0.582015			0.291007	−	0.956721i	$-0.406010\pi$
$197$	4.44972e6			0.582015			0.291007	+	0.956721i	$0.406010\pi$
$198$		0			0
$199$	−6.16428e6	−	3.55895e6i	−0.782210	−	0.451609i	0.0550030	−	0.998486i	$-0.482483\pi$
$199$	−6.16428e6	−	3.55895e6i	−0.782210	−	0.451609i	−0.837213	+	0.546877i	$0.815816\pi$
$200$		0			0
$201$	−824903.	+	476258.i	−0.101582	+	0.0586482i
$202$		0			0
$203$	5.26545e6	+	4.06061e6i	0.629430	+	0.485404i
$204$		0			0
$205$	4.04433e6	+	7.00499e6i	0.469446	+	0.813104i
$206$		0			0
$207$	807245.	−	1.39819e6i	0.0910111	−	0.157636i
$208$		0			0
$209$			870147.i			0.0953134i
$210$		0			0
$211$	1.12917e7			1.20203			0.601013	−	0.799239i	$-0.294764\pi$
$211$	1.12917e7			1.20203			0.601013	+	0.799239i	$0.294764\pi$
$212$		0			0
$213$	−6.55104e6	−	3.78225e6i	−0.677909	−	0.391391i
$214$		0			0
$215$	1.40944e7	−	8.13738e6i	1.41818	−	0.818784i
$216$		0			0
$217$	−3.12568e6	−	7.59803e6i	−0.305890	−	0.743570i
$218$		0			0
$219$	69594.5	+	120541.i	0.00662586	+	0.0114763i
$220$		0			0
$221$	1.40258e7	−	2.42935e7i	1.29943	−	2.25067i
$222$		0			0
$223$		−	1.12380e6i		−	0.101338i	−0.998715	−	0.0506692i	$-0.983865\pi$
$223$		−	1.12380e6i		−	0.101338i	0.998715	−	0.0506692i	$-0.0161354\pi$
$224$		0			0
$225$	3.62423e6			0.318177
$226$		0			0
$227$	−8.63563e6	−	4.98578e6i	−0.738272	−	0.426241i	0.0831688	−	0.996535i	$-0.473496\pi$
$227$	−8.63563e6	−	4.98578e6i	−0.738272	−	0.426241i	−0.821441	+	0.570294i	$0.806829\pi$
$228$		0			0
$229$	−1.69249e7	+	9.77161e6i	−1.40936	+	0.813692i	−0.995326	−	0.0965721i	$-0.969212\pi$
$229$	−1.69249e7	+	9.77161e6i	−1.40936	+	0.813692i	−0.414029	+	0.910264i	$0.635879\pi$
$230$		0			0
$231$	982503.	+	131769.i	0.0797073	+	0.0106900i
$232$		0			0
$233$	1.60120e6	+	2.77335e6i	0.126583	+	0.219249i	0.922351	−	0.386354i	$-0.126266\pi$
$233$	1.60120e6	+	2.77335e6i	0.126583	+	0.219249i	−0.795767	+	0.605602i	$0.792932\pi$
$234$		0			0
$235$	−1.30608e7	+	2.26219e7i	−1.00639	+	1.74311i
$236$		0			0
$237$		−	6.91935e6i		−	0.519781i
$238$		0			0
$239$	−1.42350e7			−1.04271			−0.521355	−	0.853340i	$-0.674573\pi$
$239$	−1.42350e7			−1.04271			−0.521355	+	0.853340i	$0.674573\pi$
$240$		0			0
$241$	−4.38064e6	−	2.52916e6i	−0.312958	−	0.180686i	0.335291	−	0.942115i	$-0.391165\pi$
$241$	−4.38064e6	−	2.52916e6i	−0.312958	−	0.180686i	−0.648249	+	0.761428i	$0.724499\pi$
$242$		0			0
$243$	797162.	−	460241.i	0.0555556	−	0.0320750i
$244$		0			0
$245$	1.44674e7	+	1.46082e7i	0.983770	+	0.993342i
$246$		0			0
$247$	−9.34387e6	−	1.61841e7i	−0.620063	−	1.07398i
$248$		0			0
$249$	−4.35996e6	+	7.55167e6i	−0.282413	+	0.489153i
$250$		0			0
$251$			1.09278e7i			0.691050i	0.938409	+	0.345525i	$0.112299\pi$
$251$			1.09278e7i			0.691050i	−0.938409	+	0.345525i	$0.887701\pi$
$252$		0			0
$253$	1.23179e6			0.0760633
$254$		0			0
$255$	−1.66208e7	−	9.59602e6i	−1.00238	−	0.578723i
$256$		0			0
$257$	−8.37770e6	+	4.83687e6i	−0.493543	+	0.284947i	−0.726043	−	0.687649i	$-0.758643\pi$
$257$	−8.37770e6	+	4.83687e6i	−0.493543	+	0.284947i	0.232500	+	0.972596i	$0.425309\pi$
$258$		0			0
$259$	−1.80412e6	+	1.34519e7i	−0.103840	+	0.774258i
$260$		0			0
$261$	2.35537e6	+	4.07962e6i	0.132476	+	0.229456i
$262$		0			0
$263$	1.17936e7	−	2.04272e7i	0.648307	−	1.12290i	−0.335220	−	0.942140i	$-0.608811\pi$
$263$	1.17936e7	−	2.04272e7i	0.648307	−	1.12290i	0.983527	−	0.180760i	$-0.0578559\pi$
$264$		0			0
$265$		−	1.77946e7i		−	0.956202i
$266$		0			0
$267$	3.22300e6			0.169327
$268$		0			0
$269$	1.03935e7	+	6.00069e6i	0.533956	+	0.308280i	0.742626	−	0.669707i	$-0.233580\pi$
$269$	1.03935e7	+	6.00069e6i	0.533956	+	0.308280i	−0.208670	+	0.977986i	$0.566913\pi$
$270$		0			0
$271$	3.37870e6	−	1.95070e6i	0.169763	−	0.0980125i	−0.412711	−	0.910862i	$-0.635418\pi$
$271$	3.37870e6	−	1.95070e6i	0.169763	−	0.0980125i	0.582474	+	0.812849i	$0.302085\pi$
$272$		0			0
$273$	−1.96888e7	+	8.09957e6i	−0.967677	+	0.398083i
$274$		0			0
$275$	1.38257e6	+	2.39468e6i	0.0664797	+	0.115146i
$276$		0			0
$277$	−1.06268e7	+	1.84062e7i	−0.499992	+	0.866012i	−1.00000		9.05599e-6i	$-0.999997\pi$
$277$	−1.06268e7	+	1.84062e7i	−0.499992	+	0.866012i	0.500008	+	0.866021i	$0.333330\pi$
$278$		0			0
$279$		−	5.82055e6i		−	0.268010i
$280$		0			0
$281$	−1.01968e7			−0.459561			−0.229781	−	0.973242i	$-0.573801\pi$
$281$	−1.01968e7			−0.459561			−0.229781	+	0.973242i	$0.573801\pi$
$282$		0			0
$283$	3.34021e6	+	1.92847e6i	0.147372	+	0.0850851i	0.571873	−	0.820342i	$-0.306217\pi$
$283$	3.34021e6	+	1.92847e6i	0.147372	+	0.0850851i	−0.424501	+	0.905427i	$0.639550\pi$
$284$		0			0
$285$	−1.10726e7	+	6.39277e6i	−0.478316	+	0.276156i
$286$		0			0
$287$	−9.69513e6	+	1.25718e7i	−0.410117	+	0.531805i
$288$		0			0
$289$	1.27479e7	+	2.20800e7i	0.528134	+	0.914756i
$290$		0			0
$291$	−9.60222e6	+	1.66315e7i	−0.389666	+	0.674922i
$292$		0			0
$293$		−	2.88091e7i		−	1.14532i	−0.819793	−	0.572660i	$-0.805911\pi$
$293$		−	2.88091e7i		−	1.14532i	0.819793	−	0.572660i	$-0.194089\pi$
$294$		0			0
$295$	−2.66228e7			−1.03702
$296$		0			0
$297$	608202.	+	351145.i	0.0232155	+	0.0134035i
$298$		0			0
$299$	−2.29103e7	+	1.32273e7i	−0.857073	+	0.494832i
$300$		0			0
$301$	2.52951e7	+	1.95070e7i	0.927548	+	0.715306i
$302$		0			0
$303$	6.99055e6	+	1.21080e7i	0.251295	+	0.435255i
$304$		0			0
$305$	−1.47273e7	+	2.55084e7i	−0.519066	+	0.899049i
$306$		0			0
$307$			2.70175e7i			0.933747i	0.884324	+	0.466874i	$0.154620\pi$
$307$			2.70175e7i			0.933747i	−0.884324	+	0.466874i	$0.845380\pi$
$308$		0			0
$309$	−2.07880e7			−0.704591
$310$		0			0
$311$	4.85470e6	+	2.80286e6i	0.161392	+	0.0931795i	0.578520	−	0.815668i	$-0.303630\pi$
$311$	4.85470e6	+	2.80286e6i	0.161392	+	0.0931795i	−0.417129	+	0.908847i	$0.636964\pi$
$312$		0			0
$313$	2.49380e7	−	1.43979e7i	0.813257	−	0.469534i	−0.0348283	−	0.999393i	$-0.511088\pi$
$313$	2.49380e7	−	1.43979e7i	0.813257	−	0.469534i	0.848086	+	0.529859i	$0.177755\pi$
$314$		0			0
$315$	5.54146e6	+	1.34704e7i	0.177294	+	0.430972i
$316$		0			0
$317$	1.82746e7	+	3.16525e7i	0.573679	+	0.993641i	0.996184	+	0.0872807i	$0.0278177\pi$
$317$	1.82746e7	+	3.16525e7i	0.573679	+	0.993641i	−0.422505	+	0.906361i	$0.638849\pi$
$318$		0			0
$319$	−1.79705e6	+	3.11259e6i	−0.0553591	+	0.0958847i
$320$		0			0
$321$			1.57471e6i			0.0476087i
$322$		0			0
$323$	3.30652e7			0.981215
$324$		0			0
$325$	−5.14295e7	−	2.96928e7i	−1.49817	−	0.864971i
$326$		0			0
$327$	−2.63601e7	+	1.52190e7i	−0.753881	+	0.435254i
$328$		0			0
$329$	−5.08148e7	−	6.81507e6i	−1.42693	−	0.191374i
$330$		0			0
$331$	1.16042e7	+	2.00991e7i	0.319987	+	0.554234i	0.980485	−	0.196594i	$-0.0629881\pi$
$331$	1.16042e7	+	2.00991e7i	0.319987	+	0.554234i	−0.660498	+	0.750828i	$0.729655\pi$
$332$		0			0
$333$	−4.80771e6	+	8.32720e6i	−0.130198	+	0.225510i
$334$		0			0
$335$		−	1.06783e7i		−	0.284031i
$336$		0			0
$337$	2.11044e7			0.551421			0.275710	−	0.961241i	$-0.411087\pi$
$337$	2.11044e7			0.551421			0.275710	+	0.961241i	$0.411087\pi$
$338$		0			0
$339$	−1.53874e7	−	8.88393e6i	−0.394972	−	0.228037i
$340$		0			0
$341$	3.84588e6	−	2.22042e6i	0.0969913	−	0.0559979i
$342$		0			0
$343$	−1.57130e7	+	3.71687e7i	−0.389383	+	0.921076i
$344$		0			0
$345$	9.04968e6	+	1.56745e7i	0.220382	+	0.381713i
$346$		0			0
$347$	−403396.	+	698702.i	−0.00965479	+	0.0167226i	−0.870812	−	0.491615i	$-0.836407\pi$
$347$	−403396.	+	698702.i	−0.00965479	+	0.0167226i	0.861158	+	0.508338i	$0.169740\pi$
$348$		0			0
$349$			6.98266e7i			1.64265i	0.570462	+	0.821324i	$0.306764\pi$
$349$			6.98266e7i			1.64265i	−0.570462	+	0.821324i	$0.693236\pi$
$350$		0			0
$351$	−1.50828e7			−0.348787
$352$		0			0
$353$	2.32047e7	+	1.33972e7i	0.527535	+	0.304572i	0.740012	−	0.672594i	$-0.234820\pi$
$353$	2.32047e7	+	1.33972e7i	0.527535	+	0.304572i	−0.212477	+	0.977166i	$0.568153\pi$
$354$		0			0
$355$	7.34410e7	−	4.24012e7i	1.64155	−	0.947748i
$356$		0			0
$357$	5.00718e6	−	3.73347e7i	0.110050	−	0.820556i
$358$		0			0
$359$	1.28065e7	+	2.21815e7i	0.276787	+	0.479410i	0.970585	−	0.240761i	$-0.0773969\pi$
$359$	1.28065e7	+	2.21815e7i	0.276787	+	0.479410i	−0.693797	+	0.720171i	$0.744064\pi$
$360$		0			0
$361$	−1.25091e7	+	2.16664e7i	−0.265891	+	0.460537i
$362$		0			0
$363$		−	2.70801e7i		−	0.566148i
$364$		0			0
$365$	−1.56039e6			−0.0320889
$366$		0			0
$367$	2.41602e7	+	1.39489e7i	0.488767	+	0.282190i	0.724063	−	0.689734i	$-0.242273\pi$
$367$	2.41602e7	+	1.39489e7i	0.488767	+	0.282190i	−0.235296	+	0.971924i	$0.575606\pi$
$368$		0			0
$369$	−9.74053e6	+	5.62370e6i	−0.193867	+	0.111929i
$370$		0			0
$371$	3.22998e7	−	1.32875e7i	0.632525	−	0.260208i
$372$		0			0
$373$	−1.11791e7	−	1.93627e7i	−0.215416	−	0.373112i	0.737985	−	0.674817i	$-0.235778\pi$
$373$	−1.11791e7	−	1.93627e7i	−0.215416	−	0.373112i	−0.953401	+	0.301705i	$0.902444\pi$
$374$		0			0
$375$	967720.	−	1.67614e6i	0.0183508	−	0.0317846i
$376$		0			0
$377$		−	7.71889e7i		−	1.44056i
$378$		0			0
$379$	−5.91089e7			−1.08576			−0.542882	−	0.839809i	$-0.682667\pi$
$379$	−5.91089e7			−1.08576			−0.542882	+	0.839809i	$0.682667\pi$
$380$		0			0
$381$	4.54958e7	+	2.62670e7i	0.822614	+	0.474936i
$382$		0			0
$383$	3.98770e7	−	2.30230e7i	0.709785	−	0.409794i	−0.101197	−	0.994866i	$-0.532267\pi$
$383$	3.98770e7	−	2.30230e7i	0.709785	−	0.409794i	0.810981	+	0.585072i	$0.198934\pi$
$384$		0			0
$385$	−6.78651e6	+	8.80017e6i	−0.118923	+	0.154209i
$386$		0			0
$387$	1.13151e7	+	1.95984e7i	0.195221	+	0.338133i
$388$		0			0
$389$	2.16981e7	−	3.75821e7i	0.368614	−	0.638458i	−0.620735	−	0.784020i	$-0.713166\pi$
$389$	2.16981e7	−	3.75821e7i	0.368614	−	0.638458i	0.989349	+	0.145562i	$0.0464991\pi$
$390$		0			0
$391$		−	4.68075e7i		−	0.783043i
$392$		0			0
$393$	−4.66458e7			−0.768484
$394$		0			0
$395$	6.71776e7	+	3.87850e7i	1.09002	+	0.629321i
$396$		0			0
$397$	−3.39493e7	+	1.96007e7i	−0.542575	+	0.313256i	−0.746122	−	0.665809i	$-0.768086\pi$
$397$	−3.39493e7	+	1.96007e7i	−0.542575	+	0.313256i	0.203547	+	0.979065i	$0.434753\pi$
$398$		0			0
$399$	−1.98719e7	−	1.53248e7i	−0.312839	−	0.241256i
$400$		0			0
$401$	4.77624e7	+	8.27269e7i	0.740718	+	1.28296i	0.952169	+	0.305572i	$0.0988478\pi$
$401$	4.77624e7	+	8.27269e7i	0.740718	+	1.28296i	−0.211451	+	0.977389i	$0.567819\pi$
$402$		0			0
$403$	−4.76869e7	+	8.25962e7i	−0.728592	+	1.26196i
$404$		0			0
$405$			1.03191e7i			0.155338i
$406$		0			0
$407$	−7.33617e6			−0.108814
$408$		0			0
$409$	1.64736e7	+	9.51105e6i	0.240779	+	0.139014i	0.615535	−	0.788110i	$-0.288940\pi$
$409$	1.64736e7	+	9.51105e6i	0.240779	+	0.139014i	−0.374756	+	0.927124i	$0.622273\pi$
$410$		0			0
$411$	−3.43525e7	+	1.98334e7i	−0.494804	+	0.285675i
$412$		0			0
$413$	−1.98797e7	−	4.83244e7i	−0.282202	−	0.685988i
$414$		0			0
$415$	−4.88777e7	−	8.46586e7i	−0.683858	−	1.18448i
$416$		0			0
$417$	−1.25994e7	+	2.18229e7i	−0.173757	+	0.300956i
$418$		0			0
$419$		−	3.79635e7i		−	0.516089i	−0.966133	−	0.258044i	$-0.916922\pi$
$419$		−	3.79635e7i		−	0.516089i	0.966133	−	0.258044i	$-0.0830781\pi$
$420$		0			0
$421$	−1.18733e8			−1.59120			−0.795600	−	0.605823i	$-0.792844\pi$
$421$	−1.18733e8			−1.59120			−0.795600	+	0.605823i	$0.792844\pi$
$422$		0			0
$423$	−3.14560e7	−	1.81612e7i	−0.415607	−	0.239951i
$424$		0			0
$425$	9.09970e7	−	5.25371e7i	1.18539	−	0.684383i
$426$		0			0
$427$	−5.72986e7	−	7.68465e6i	−0.735970	−	0.0987053i
$428$		0			0
$429$	−5.75377e6	−	9.96583e6i	−0.0728754	−	0.126224i
$430$		0			0
$431$	−2.94287e7	+	5.09719e7i	−0.367569	+	0.636648i	−0.989185	−	0.146674i	$-0.953143\pi$
$431$	−2.94287e7	+	5.09719e7i	−0.367569	+	0.636648i	0.621616	+	0.783322i	$0.286476\pi$
$432$		0			0
$433$			5.48589e7i			0.675746i	0.941192	+	0.337873i	$0.109707\pi$
$433$			5.48589e7i			0.675746i	−0.941192	+	0.337873i	$0.890293\pi$
$434$		0			0
$435$	−5.28102e7			−0.641578
$436$		0			0
$437$	−2.70050e7	−	1.55914e7i	−0.323594	−	0.186827i
$438$		0			0
$439$	−6.23635e7	+	3.60056e7i	−0.737117	+	0.425575i	−0.821020	−	0.570899i	$-0.806595\pi$
$439$	−6.23635e7	+	3.60056e7i	−0.737117	+	0.425575i	0.0839029	+	0.996474i	$0.473261\pi$
$440$		0			0
$441$	−2.03129e7	+	2.01172e7i	−0.236841	+	0.234558i
$442$		0			0
$443$	6.73580e7	+	1.16667e8i	0.774779	+	1.34196i	0.934919	+	0.354862i	$0.115472\pi$
$443$	6.73580e7	+	1.16667e8i	0.774779	+	1.34196i	−0.160140	+	0.987094i	$0.551195\pi$
$444$		0			0
$445$	−1.80658e7	+	3.12909e7i	−0.205011	+	0.355090i
$446$		0			0
$447$			1.77810e7i			0.199083i
$448$		0			0
$449$	1.73542e8			1.91719			0.958594	−	0.284777i	$-0.0919196\pi$
$449$	1.73542e8			1.91719			0.958594	+	0.284777i	$0.0919196\pi$
$450$		0			0
$451$	−7.43163e6	−	4.29065e6i	−0.0810130	−	0.0467728i
$452$		0			0
$453$	5.88674e6	−	3.39871e6i	0.0633258	−	0.0365611i
$454$		0			0
$455$	3.17253e7	−	2.36552e8i	0.336800	−	2.51126i
$456$		0			0
$457$	−7.31723e7	−	1.26738e8i	−0.766652	−	1.32788i	−0.939369	−	0.342908i	$-0.888588\pi$
$457$	−7.31723e7	−	1.26738e8i	−0.766652	−	1.32788i	0.172717	−	0.984971i	$-0.444745\pi$
$458$		0			0
$459$	1.33434e7	−	2.31114e7i	0.137984	−	0.238995i
$460$		0			0
$461$		−	6.84094e7i		−	0.698254i	−0.937075	−	0.349127i	$-0.886478\pi$
$461$		−	6.84094e7i		−	0.698254i	0.937075	−	0.349127i	$-0.113522\pi$
$462$		0			0
$463$	−2.01813e7			−0.203332			−0.101666	−	0.994819i	$-0.532417\pi$
$463$	−2.01813e7			−0.203332			−0.101666	+	0.994819i	$0.532417\pi$
$464$		0			0
$465$	5.65096e7	+	3.26258e7i	0.562035	+	0.324491i
$466$		0			0
$467$	6.85001e7	−	3.95486e7i	0.672575	−	0.388311i	−0.124477	−	0.992223i	$-0.539725\pi$
$467$	6.85001e7	−	3.95486e7i	0.672575	−	0.388311i	0.797052	+	0.603911i	$0.206392\pi$
$468$		0			0
$469$	1.93826e7	−	7.97364e6i	0.187886	−	0.0772926i
$470$		0			0
$471$	4.16648e7	+	7.21655e7i	0.398755	+	0.690664i
$472$		0			0
$473$	−8.63299e6	+	1.49528e7i	−0.0815789	+	0.141299i
$474$		0			0
$475$		−	6.99994e7i		−	0.653151i
$476$		0			0
$477$	2.47436e7			0.227985
$478$		0			0
$479$	2.63942e6	+	1.52387e6i	0.0240161	+	0.0138657i	0.511960	−	0.859009i	$-0.328920\pi$
$479$	2.63942e6	+	1.52387e6i	0.0240161	+	0.0138657i	−0.487944	+	0.872875i	$0.662253\pi$
$480$		0			0
$481$	1.36447e8	−	7.87778e7i	1.22611	−	0.707895i
$482$		0			0
$483$	−2.16940e7	+	2.81309e7i	−0.192530	+	0.249657i
$484$		0			0
$485$	−1.07646e8	−	1.86449e8i	−0.943571	−	1.63431i
$486$		0			0
$487$	−3.68761e7	+	6.38713e7i	−0.319270	+	0.552992i	−0.980336	−	0.197336i	$-0.936771\pi$
$487$	−3.68761e7	+	6.38713e7i	−0.319270	+	0.552992i	0.661066	+	0.750328i	$0.270104\pi$
$488$		0			0
$489$		−	2.60406e7i		−	0.222702i
$490$		0			0
$491$	8.29108e7			0.700433			0.350216	−	0.936669i	$-0.386108\pi$
$491$	8.29108e7			0.700433			0.350216	+	0.936669i	$0.386108\pi$
$492$		0			0
$493$	1.18277e8	+	6.82873e7i	0.987097	+	0.569901i
$494$		0			0
$495$	−6.81829e6	+	3.93654e6i	−0.0562160	+	0.0324563i
$496$		0			0
$497$	1.31804e8	+	1.01645e8i	1.07364	+	0.827971i
$498$		0			0
$499$	2.45539e7	+	4.25286e7i	0.197615	+	0.342279i	0.947755	−	0.319001i	$-0.103347\pi$
$499$	2.45539e7	+	4.25286e7i	0.197615	+	0.342279i	−0.750140	+	0.661279i	$0.770014\pi$
$500$		0			0
$501$	−1.12307e6	+	1.94522e6i	−0.00893088	+	0.0154687i
$502$		0			0
$503$		−	1.66557e8i		−	1.30875i	−0.756169	−	0.654377i	$-0.772931\pi$
$503$		−	1.66557e8i		−	1.30875i	0.756169	−	0.654377i	$-0.227069\pi$
$504$		0			0
$505$	−1.56736e8			−1.21701
$506$		0			0
$507$	1.48869e8	+	8.59498e7i	1.14230	+	0.659510i
$508$		0			0
$509$	8.07268e7	−	4.66076e7i	0.612159	−	0.353430i	−0.161651	−	0.986848i	$-0.551682\pi$
$509$	8.07268e7	−	4.66076e7i	0.612159	−	0.353430i	0.773810	+	0.633418i	$0.218348\pi$
$510$		0			0
$511$	−1.16517e6	−	2.83234e6i	−0.00873225	−	0.0212267i
$512$		0			0
$513$	−8.88923e6	−	1.53966e7i	−0.0658434	−	0.114044i
$514$		0			0
$515$	1.16523e8	−	2.01823e8i	0.853078	−	1.47757i
$516$		0			0
$517$		−	2.77124e7i		−	0.200541i
$518$		0			0
$519$	2.74098e7			0.196066
$520$		0			0
$521$	−1.07746e8	−	6.22072e7i	−0.761882	−	0.439873i	0.0680889	−	0.997679i	$-0.478310\pi$
$521$	−1.07746e8	−	6.22072e7i	−0.761882	−	0.439873i	−0.829971	+	0.557806i	$0.811643\pi$
$522$		0			0
$523$	5.54978e7	−	3.20417e7i	0.387945	−	0.223980i	−0.293324	−	0.956013i	$-0.594762\pi$
$523$	5.54978e7	−	3.20417e7i	0.387945	−	0.223980i	0.681269	+	0.732033i	$0.261428\pi$
$524$		0			0
$525$	−7.90380e7	−	1.06002e7i	−0.546208	−	0.0732551i
$526$		0			0
$527$	−8.43751e7	−	1.46142e8i	−0.576477	−	0.998488i
$528$		0			0
$529$	5.19466e7	−	8.99742e7i	0.350906	−	0.607786i
$530$		0			0
$531$		−	3.70194e7i		−	0.247255i
$532$		0			0
$533$	1.84297e8			1.21713
$534$		0			0
$535$	−1.52883e7	−	8.82673e6i	−0.0998387	−	0.0576419i
$536$		0			0
$537$	−1.34793e8	+	7.78227e7i	−0.870450	+	0.502555i
$538$		0			0
$539$	−2.10412e7	−	5.74730e6i	−0.134371	−	0.0367027i
$540$		0			0
$541$	−5.86026e7	−	1.01503e8i	−0.370105	−	0.641041i	0.619476	−	0.785015i	$-0.287345\pi$
$541$	−5.86026e7	−	1.01503e8i	−0.370105	−	0.641041i	−0.989581	+	0.143975i	$0.954012\pi$
$542$		0			0
$543$	6.08272e7	−	1.05356e8i	0.379925	−	0.658050i
$544$		0			0
$545$		−	3.41227e8i		−	2.10792i
$546$		0			0
$547$	1.64328e8			1.00403			0.502017	−	0.864858i	$-0.332591\pi$
$547$	1.64328e8			1.00403			0.502017	+	0.864858i	$0.332591\pi$
$548$		0			0
$549$	−3.54697e7	−	2.04785e7i	−0.214359	−	0.123760i
$550$		0			0
$551$	7.87950e7	−	4.54923e7i	0.471025	−	0.271946i
$552$		0			0
$553$	−2.02379e7	+	1.50899e8i	−0.119671	+	0.892298i
$554$		0			0
$555$	−5.38972e7	−	9.33527e7i	−0.315273	−	0.546070i
$556$		0			0
$557$	−1.01102e8	+	1.75114e8i	−0.585052	+	1.01334i	0.409817	+	0.912168i	$0.365593\pi$
$557$	−1.01102e8	+	1.75114e8i	−0.585052	+	1.01334i	−0.994869	+	0.101172i	$0.967741\pi$
$558$		0			0
$559$		−	3.70813e8i		−	2.12285i
$560$		0			0
$561$	2.03609e7			0.115321
$562$		0			0
$563$	1.22757e8	+	7.08737e7i	0.687892	+	0.397155i	0.802822	−	0.596219i	$-0.203331\pi$
$563$	1.22757e8	+	7.08737e7i	0.687892	+	0.397155i	−0.114930	+	0.993374i	$0.536664\pi$
$564$		0			0
$565$	1.72502e8	−	9.95940e7i	0.956419	−	0.552189i
$566$		0			0
$567$	−1.87308e7	+	7.70548e6i	−0.102756	+	0.0422718i
$568$		0			0
$569$	1.70801e8	+	2.95835e8i	0.927156	+	1.60588i	0.788057	+	0.615603i	$0.211087\pi$
$569$	1.70801e8	+	2.95835e8i	0.927156	+	1.60588i	0.139099	+	0.990278i	$0.455579\pi$
$570$		0			0
$571$	−1.31414e8	+	2.27616e8i	−0.705883	+	1.22263i	0.260488	+	0.965477i	$0.416116\pi$
$571$	−1.31414e8	+	2.27616e8i	−0.705883	+	1.22263i	−0.966372	+	0.257149i	$0.917217\pi$
$572$		0			0
$573$			7.97541e6i			0.0423925i
$574$		0			0
$575$	−9.90920e7			−0.521237
$576$		0			0
$577$	−1.79880e8	−	1.03854e8i	−0.936389	−	0.540625i	−0.0475627	−	0.998868i	$-0.515145\pi$
$577$	−1.79880e8	−	1.03854e8i	−0.936389	−	0.540625i	−0.888827	+	0.458244i	$0.848479\pi$
$578$		0			0
$579$	−1.17539e8	+	6.78611e7i	−0.605544	+	0.349611i
$580$		0			0
$581$	1.17170e8	−	1.51936e8i	0.597432	−	0.774699i
$582$		0			0
$583$	9.43917e6	+	1.63491e7i	0.0476352	+	0.0825066i
$584$		0			0
$585$	8.45433e7	−	1.46433e8i	0.422291	−	0.731429i
$586$		0			0
$587$			2.00752e8i			0.992537i	0.868169	+	0.496268i	$0.165297\pi$
$587$			2.00752e8i			0.992537i	−0.868169	+	0.496268i	$0.834703\pi$
$588$		0			0
$589$	−1.12420e8			−0.550169
$590$		0			0
$591$	−6.00712e7	−	3.46821e7i	−0.291007	−	0.168013i
$592$		0			0
$593$	−1.38061e8	+	7.97096e7i	−0.662075	+	0.382249i	−0.793067	−	0.609134i	$-0.791517\pi$
$593$	−1.38061e8	+	7.97096e7i	−0.662075	+	0.382249i	0.130992	+	0.991383i	$0.458184\pi$
$594$		0			0
$595$	3.34403e8	+	2.57885e8i	1.58752	+	1.22426i
$596$		0			0
$597$	5.54785e7	+	9.60917e7i	0.260737	+	0.451609i
$598$		0			0
$599$	4.27029e7	−	7.39635e7i	0.198690	−	0.344142i	−0.749414	−	0.662102i	$-0.769665\pi$
$599$	4.27029e7	−	7.39635e7i	0.198690	−	0.344142i	0.948104	+	0.317960i	$0.102998\pi$
$600$		0			0
$601$		−	1.61501e8i		−	0.743962i	−0.928240	−	0.371981i	$-0.878679\pi$
$601$		−	1.61501e8i		−	0.743962i	0.928240	−	0.371981i	$-0.121321\pi$
$602$		0			0
$603$	1.48483e7			0.0677211
$604$		0			0
$605$	2.62911e8	+	1.51792e8i	1.18725	+	0.685460i
$606$		0			0
$607$	2.02413e7	−	1.16863e7i	0.0905049	−	0.0522530i	−0.454064	−	0.890969i	$-0.650026\pi$
$607$	2.02413e7	−	1.16863e7i	0.0905049	−	0.0522530i	0.544569	+	0.838716i	$0.316693\pi$
$608$		0			0
$609$	−3.94342e7	−	9.58583e7i	−0.174591	−	0.424402i
$610$		0			0
$611$	2.97584e8	+	5.15430e8i	1.30462	+	2.25968i
$612$		0			0
$613$	−1.66743e8	+	2.88807e8i	−0.723878	+	1.25379i	0.235557	+	0.971861i	$0.424309\pi$
$613$	−1.66743e8	+	2.88807e8i	−0.723878	+	1.25379i	−0.959434	+	0.281932i	$0.909025\pi$
$614$		0			0
$615$		−	1.26090e8i		−	0.542069i
$616$		0			0
$617$	−1.74626e8			−0.743451			−0.371726	−	0.928343i	$-0.621234\pi$
$617$	−1.74626e8			−0.743451			−0.371726	+	0.928343i	$0.621234\pi$
$618$		0			0
$619$	4.50581e7	+	2.60143e7i	0.189977	+	0.109683i	0.591972	−	0.805959i	$-0.298350\pi$
$619$	4.50581e7	+	2.60143e7i	0.189977	+	0.109683i	−0.401995	+	0.915642i	$0.631683\pi$
$620$		0			0
$621$	−2.17956e7	+	1.25837e7i	−0.0910111	+	0.0525453i
$622$		0			0
$623$	−7.02877e7	−	9.42670e6i	−0.290680	−	0.0389848i
$624$		0			0
$625$	1.27368e8	+	2.20609e8i	0.521701	+	0.903613i
$626$		0			0
$627$	6.78212e6	−	1.17470e7i	0.0275146	−	0.0476567i
$628$		0			0
$629$			2.78772e8i			1.12020i
$630$		0			0
$631$	−3.39999e8			−1.35329			−0.676643	−	0.736311i	$-0.736566\pi$
$631$	−3.39999e8			−1.35329			−0.676643	+	0.736311i	$0.736566\pi$
$632$		0			0
$633$	−1.52439e8	−	8.80105e7i	−0.601013	−	0.346995i
$634$		0			0
$635$	−5.10034e8	+	2.94468e8i	−1.99195	+	1.15005i
$636$		0			0
$637$	4.53066e8	−	1.19051e8i	1.75285	−	0.460590i
$638$		0			0
$639$	5.89594e7	+	1.02121e8i	0.225970	+	0.391391i
$640$		0			0
$641$	7.72851e6	−	1.33862e7i	0.0293441	−	0.0508256i	−0.850980	−	0.525197i	$-0.823991\pi$
$641$	7.72851e6	−	1.33862e7i	0.0293441	−	0.0508256i	0.880325	+	0.474372i	$0.157325\pi$
$642$		0			0
$643$			1.06911e8i			0.402152i	0.979576	+	0.201076i	$0.0644438\pi$
$643$			1.06911e8i			0.402152i	−0.979576	+	0.201076i	$0.935556\pi$
$644$		0			0
$645$	−2.53699e8			−0.945451
$646$		0			0
$647$	−4.33160e8	−	2.50085e8i	−1.59932	−	0.923369i	−0.991618	−	0.129205i	$-0.958757\pi$
$647$	−4.33160e8	−	2.50085e8i	−1.59932	−	0.923369i	−0.607704	−	0.794163i	$-0.707909\pi$
$648$		0			0
$649$	2.44603e7	−	1.41221e7i	0.0894803	−	0.0516615i
$650$		0			0
$651$	−1.70241e7	+	1.26936e8i	−0.0617051	+	0.460088i
$652$		0			0
$653$	−9.83335e7	−	1.70319e8i	−0.353152	−	0.611677i	0.633648	−	0.773622i	$-0.281557\pi$
$653$	−9.83335e7	−	1.70319e8i	−0.353152	−	0.611677i	−0.986800	+	0.161944i	$0.948224\pi$
$654$		0			0
$655$	2.61463e8	−	4.52867e8i	0.930436	−	1.61156i
$656$		0			0
$657$		−	2.16974e6i		−	0.00765089i
$658$		0			0
$659$	−2.58438e8			−0.903026			−0.451513	−	0.892264i	$-0.649116\pi$
$659$	−2.58438e8			−0.903026			−0.451513	+	0.892264i	$0.649116\pi$
$660$		0			0
$661$	4.01236e8	+	2.31654e8i	1.38930	+	0.802111i	0.993236	−	0.116112i	$-0.0370433\pi$
$661$	4.01236e8	+	2.31654e8i	1.38930	+	0.802111i	0.396062	+	0.918224i	$0.370377\pi$
$662$		0			0
$663$	−3.78697e8	+	2.18641e8i	−1.29943	+	0.750224i
$664$		0			0
$665$	2.60171e8	−	1.07029e8i	0.884697	−	0.363947i
$666$		0			0
$667$	−6.43995e7	−	1.11543e8i	−0.217023	−	0.375894i
$668$		0			0
$669$	−8.75915e6	+	1.51713e7i	−0.0292539	+	0.0506692i
$670$		0			0
$671$		−	3.12485e7i		−	0.103433i
$672$		0			0
$673$	−3.81262e8			−1.25077			−0.625385	−	0.780316i	$-0.715058\pi$
$673$	−3.81262e8			−1.25077			−0.625385	+	0.780316i	$0.715058\pi$
$674$		0			0
$675$	−4.89271e7	−	2.82481e7i	−0.159088	−	0.0918497i
$676$		0			0
$677$	−3.72384e8	+	2.14996e8i	−1.20012	+	0.692890i	−0.960582	−	0.277997i	$-0.910329\pi$
$677$	−3.72384e8	+	2.14996e8i	−1.20012	+	0.692890i	−0.239538	+	0.970887i	$0.576996\pi$
$678$		0			0
$679$	2.58052e8	−	3.34619e8i	0.824323	−	1.06891i
$680$		0			0
$681$	7.77206e7	+	1.34616e8i	0.246091	+	0.426241i
$682$		0			0
$683$	7.64651e7	−	1.32441e8i	0.239995	−	0.415683i	−0.720718	−	0.693228i	$-0.756188\pi$
$683$	7.64651e7	−	1.32441e8i	0.239995	−	0.415683i	0.960712	+	0.277546i	$0.0895210\pi$
$684$		0			0
$685$		−	4.44689e8i		−	1.38352i
$686$		0			0
$687$	3.04649e8			0.939570
$688$		0			0
$689$	−3.51122e8	−	2.02721e8i	−1.07350	−	0.619784i
$690$		0			0
$691$	−1.99349e8	+	1.15094e8i	−0.604198	+	0.348834i	−0.770691	−	0.637209i	$-0.780089\pi$
$691$	−1.99349e8	+	1.15094e8i	−0.604198	+	0.348834i	0.166493	+	0.986043i	$0.446756\pi$
$692$		0			0
$693$	−1.22367e7	−	9.43674e6i	−0.0367677	−	0.0283545i
$694$		0			0
$695$	−1.41247e8	−	2.44647e8i	−0.420751	−	0.728761i
$696$		0			0
$697$	−1.63043e8	+	2.82399e8i	−0.481509	+	0.833998i
$698$		0			0
$699$		−	4.99204e7i		−	0.146166i
$700$		0			0
$701$	8.76414e7			0.254422			0.127211	−	0.991876i	$-0.459397\pi$
$701$	8.76414e7			0.254422			0.127211	+	0.991876i	$0.459397\pi$
$702$		0			0
$703$	1.60834e8	+	9.28575e7i	0.462926	+	0.267270i
$704$		0			0
$705$	3.52640e8	−	2.03597e8i	1.00639	−	0.581037i
$706$		0			0
$707$	−1.17038e8	−	2.84500e8i	−0.331182	−	0.805051i
$708$		0			0
$709$	−1.56656e8	−	2.71336e8i	−0.439550	−	0.761324i	0.558104	−	0.829771i	$-0.311529\pi$
$709$	−1.56656e8	−	2.71336e8i	−0.439550	−	0.761324i	−0.997655	+	0.0684471i	$0.978196\pi$
$710$		0			0
$711$	−5.39310e7	+	9.34113e7i	−0.150048	+	0.259891i
$712$		0			0
$713$			1.59143e8i			0.439054i
$714$		0			0
$715$	1.29006e8			0.352933
$716$		0			0
$717$	1.92172e8	+	1.10951e8i	0.521355	+	0.301004i
$718$		0			0
$719$	6.19602e8	−	3.57727e8i	1.66696	−	0.962421i	0.697701	−	0.716389i	$-0.254207\pi$
$719$	6.19602e8	−	3.57727e8i	1.66696	−	0.962421i	0.969262	−	0.246032i	$-0.0791268\pi$
$720$		0			0
$721$	4.53349e8	+	6.08013e7i	1.20956	+	0.162221i
$722$		0			0
$723$	3.94257e7	+	6.82874e7i	0.104319	+	0.180686i
$724$		0			0
$725$	1.44565e8	−	2.50394e8i	0.379358	−	0.657067i
$726$		0			0
$727$			7.42437e8i			1.93222i	0.258132	+	0.966110i	$0.416893\pi$
$727$			7.42437e8i			1.93222i	−0.258132	+	0.966110i	$0.583107\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	5.68200e8	+	3.28050e8i	1.45462	+	0.839824i
$732$		0			0
$733$	−3.85053e8	+	2.22311e8i	−0.977707	+	0.564479i	−0.901577	−	0.432619i	$-0.857590\pi$
$733$	−3.85053e8	+	2.22311e8i	−0.977707	+	0.564479i	−0.0761299	+	0.997098i	$0.524256\pi$
$734$		0			0
$735$	−8.14507e7	−	3.09973e8i	−0.205132	−	0.780661i
$736$		0			0
$737$	5.66431e6	+	9.81087e6i	0.0141496	+	0.0245078i
$738$		0			0
$739$	−2.38987e8	+	4.13937e8i	−0.592162	+	1.02566i	0.401778	+	0.915737i	$0.368392\pi$
$739$	−2.38987e8	+	4.13937e8i	−0.592162	+	1.02566i	−0.993941	+	0.109918i	$0.964941\pi$
$740$		0			0
$741$			2.91313e8i			0.715987i
$742$		0			0
$743$	−4.11550e8			−1.00336			−0.501679	−	0.865054i	$-0.667284\pi$
$743$	−4.11550e8			−1.00336			−0.501679	+	0.865054i	$0.667284\pi$
$744$		0			0
$745$	−1.72629e8	−	9.96676e7i	−0.417490	−	0.241038i
$746$		0			0
$747$	1.17719e8	−	6.79650e7i	0.282413	−	0.163051i
$748$		0			0
$749$	4.60577e6	−	3.43417e7i	0.0109612	−	0.0817290i
$750$		0			0
$751$	4.02795e6	+	6.97662e6i	0.00950965	+	0.0164712i	0.870741	−	0.491742i	$-0.163640\pi$
$751$	4.02795e6	+	6.97662e6i	0.00950965	+	0.0164712i	−0.861231	+	0.508213i	$0.830306\pi$
$752$		0			0
$753$	8.51734e7	−	1.47525e8i	0.199489	−	0.345525i
$754$		0			0
$755$			7.62031e7i			0.177065i
$756$		0			0
$757$	−6.97539e7			−0.160798			−0.0803990	−	0.996763i	$-0.525619\pi$
$757$	−6.97539e7			−0.160798			−0.0803990	+	0.996763i	$0.525619\pi$
$758$		0			0
$759$	−1.66292e7	−	9.60086e6i	−0.0380317	−	0.0219576i
$760$		0			0
$761$	−3.33426e8	+	1.92503e8i	−0.756563	+	0.436802i	−0.828060	−	0.560639i	$-0.810556\pi$
$761$	−3.33426e8	+	1.92503e8i	−0.756563	+	0.436802i	0.0714973	+	0.997441i	$0.477222\pi$
$762$		0			0
$763$	6.19378e8	−	2.54800e8i	1.39438	−	0.573622i
$764$		0			0
$765$	1.49587e8	+	2.59092e8i	0.334126	+	0.578723i
$766$		0			0
$767$	−3.03295e8	+	5.25322e8i	−0.672170	+	1.16423i
$768$		0			0
$769$			5.19869e8i			1.14318i	0.820539	+	0.571590i	$0.193673\pi$
$769$			5.19869e8i			1.14318i	−0.820539	+	0.571590i	$0.806327\pi$
$770$		0			0
$771$	1.50799e8			0.329029
$772$		0			0
$773$	3.28958e8	+	1.89924e8i	0.712199	+	0.411188i	0.811875	−	0.583832i	$-0.198447\pi$
$773$	3.28958e8	+	1.89924e8i	0.712199	+	0.411188i	−0.0996756	+	0.995020i	$0.531781\pi$
$774$		0			0
$775$	−3.09384e8	+	1.78623e8i	−0.664649	+	0.383735i
$776$		0			0
$777$	1.29203e8	−	1.67539e8i	0.275429	−	0.357153i
$778$		0			0
$779$	1.08618e8	+	1.88131e8i	0.229767	+	0.397969i
$780$		0			0
$781$	−4.49836e7	+	7.79139e7i	−0.0944281	+	0.163554i
$782$		0			0
$783$		−	7.34332e7i		−	0.152970i
$784$		0			0
$785$	−9.34173e8			−1.93116
$786$		0			0
$787$	−5.10557e8	−	2.94770e8i	−1.04742	−	0.604727i	−0.125492	−	0.992095i	$-0.540051\pi$
$787$	−5.10557e8	−	2.94770e8i	−1.04742	−	0.604727i	−0.921925	+	0.387368i	$0.873384\pi$
$788$		0			0
$789$	−3.18428e8	+	1.83845e8i	−0.648307	+	0.374300i
$790$		0			0
$791$	3.09588e8	+	2.38748e8i	0.625539	+	0.482403i
$792$		0			0
$793$	3.35554e8	+	5.81197e8i	0.672889	+	1.16548i
$794$		0			0
$795$	−1.38695e8	+	2.40227e8i	−0.276032	+	0.478101i
$796$		0			0
$797$		−	6.68330e8i		−	1.32013i	−0.751210	−	0.660063i	$-0.770529\pi$
$797$		−	6.68330e8i		−	1.32013i	0.751210	−	0.660063i	$-0.229471\pi$
$798$		0			0
$799$	−1.05306e9			−2.06449
$800$		0			0
$801$	−4.35104e7	−	2.51208e7i	−0.0846634	−	0.0488805i
$802$		0			0
$803$	1.43364e6	−	827712.i	0.00276881	−	0.00159857i
$804$		0			0
$805$	−1.51512e8	−	3.68302e8i	−0.290442	−	0.706018i
$806$		0			0
$807$	−9.35416e7	−	1.62019e8i	−0.177985	−	0.308280i
$808$		0			0
$809$	2.51863e8	−	4.36240e8i	0.475685	−	0.823910i	−0.523927	−	0.851763i	$-0.675534\pi$
$809$	2.51863e8	−	4.36240e8i	0.475685	−	0.823910i	0.999612	+	0.0278529i	$0.00886700\pi$
$810$		0			0
$811$		−	7.44534e7i		−	0.139580i	−0.997562	−	0.0697898i	$-0.977767\pi$
$811$		−	7.44534e7i		−	0.139580i	0.997562	−	0.0697898i	$-0.0222329\pi$
$812$		0			0
$813$	−6.08167e7			−0.113175
$814$		0			0
$815$	2.52819e8	+	1.45965e8i	0.467021	+	0.269635i
$816$		0			0
$817$	3.78529e8	−	2.18544e8i	0.694118	−	0.400749i
$818$		0			0
$819$	3.28928e8	+	4.41145e7i	0.598755	+	0.0803026i
$820$		0			0
$821$	9.26917e7	+	1.60547e8i	0.167499	+	0.290116i	0.937540	−	0.347878i	$-0.113098\pi$
$821$	9.26917e7	+	1.60547e8i	0.167499	+	0.290116i	−0.770041	+	0.637994i	$0.779764\pi$
$822$		0			0
$823$	−128632.	+	222798.i	−0.000230755	+	0.000399679i	−0.866141	−	0.499800i	$-0.833407\pi$
$823$	−128632.	+	222798.i	−0.000230755	+	0.000399679i	0.865910	+	0.500200i	$0.166740\pi$
$824$		0			0
$825$		−	4.31043e7i		−	0.0767642i
$826$		0			0
$827$	−4.71800e8			−0.834144			−0.417072	−	0.908873i	$-0.636944\pi$
$827$	−4.71800e8			−0.834144			−0.417072	+	0.908873i	$0.636944\pi$
$828$		0			0
$829$	−1.11055e8	−	6.41175e7i	−0.194928	−	0.112542i	0.399360	−	0.916794i	$-0.369232\pi$
$829$	−1.11055e8	−	6.41175e7i	−0.194928	−	0.112542i	−0.594287	+	0.804253i	$0.702566\pi$
$830$		0			0
$831$	2.86924e8	−	1.65655e8i	0.499992	−	0.288671i
$832$		0			0
$833$	−2.18395e8	+	7.99558e8i	−0.377840	+	1.38330i
$834$		0			0
$835$	−1.25903e7	−	2.18070e7i	−0.0216260	−	0.0374573i
$836$		0			0
$837$	−4.53667e7	+	7.85774e7i	−0.0773678	+	0.134005i
$838$		0			0
$839$			1.11310e9i			1.88473i	0.334590	+	0.942364i	$0.391402\pi$
$839$			1.11310e9i			1.88473i	−0.334590	+	0.942364i	$0.608598\pi$
$840$		0			0
$841$	−2.19015e8			−0.368202
$842$		0			0
$843$	1.37656e8	+	7.94759e7i	0.229781	+	0.132664i
$844$		0			0
$845$	−1.66891e9	+	9.63548e8i	−2.76607	+	1.59699i
$846$		0			0
$847$	−7.92046e7	+	5.90568e8i	−0.130347	+	0.971896i
$848$		0			0
$849$	−3.00619e7	−	5.20687e7i	−0.0491239	−	0.0850851i
$850$		0			0
$851$	1.31450e8	−	2.27678e8i	0.213291	−	0.369431i
$852$		0			0
$853$			2.87514e8i			0.463247i	0.972806	+	0.231623i	$0.0744037\pi$
$853$			2.87514e8i			0.463247i	−0.972806	+	0.231623i	$0.925596\pi$
$854$		0			0
$855$	1.99307e8			0.318878
$856$		0			0
$857$	1.00459e8	+	5.79999e7i	0.159605	+	0.0921478i	0.577675	−	0.816267i	$-0.303960\pi$
$857$	1.00459e8	+	5.79999e7i	0.159605	+	0.0921478i	−0.418070	+	0.908415i	$0.637293\pi$
$858$		0			0
$859$	1.44237e8	−	8.32755e7i	0.227561	−	0.131382i	−0.381885	−	0.924210i	$-0.624725\pi$
$859$	1.44237e8	−	8.32755e7i	0.227561	−	0.131382i	0.609446	+	0.792827i	$0.291392\pi$
$860$		0			0
$861$	2.28872e8	−	9.41534e7i	0.358577	−	0.147512i
$862$		0			0
$863$	4.27084e8	+	7.39732e8i	0.664479	+	1.15091i	0.979426	+	0.201802i	$0.0646798\pi$
$863$	4.27084e8	+	7.39732e8i	0.664479	+	1.15091i	−0.314947	+	0.949109i	$0.601987\pi$
$864$		0			0
$865$	−1.53640e8	+	2.66112e8i	−0.237386	+	0.411164i
$866$		0			0
$867$		−	3.97440e8i		−	0.609837i
$868$		0			0
$869$	−8.22944e7			−0.125404
$870$		0			0
$871$	−2.10704e8	−	1.21650e8i	−0.318873	−	0.184101i
$872$		0			0
$873$	2.59260e8	−	1.49684e8i	0.389666	−	0.224974i
$874$		0			0
$875$	−2.60066e7	+	3.37232e7i	−0.0388204	+	0.0503390i
$876$		0			0
$877$	8.49474e7	+	1.47133e8i	0.125936	+	0.218128i	0.922099	−	0.386955i	$-0.126473\pi$
$877$	8.49474e7	+	1.47133e8i	0.125936	+	0.218128i	−0.796162	+	0.605083i	$0.793140\pi$
$878$		0			0
$879$	−2.24545e8	+	3.88923e8i	−0.330626	+	0.572660i
$880$		0			0
$881$			8.77883e7i			0.128383i	0.997938	+	0.0641917i	$0.0204469\pi$
$881$			8.77883e7i			0.128383i	−0.997938	+	0.0641917i	$0.979553\pi$
$882$		0			0
$883$	1.75158e8			0.254417			0.127209	−	0.991876i	$-0.459398\pi$
$883$	1.75158e8			0.254417			0.127209	+	0.991876i	$0.459398\pi$
$884$		0			0
$885$	3.59408e8	+	2.07504e8i	0.518511	+	0.299363i
$886$		0			0
$887$	−9.61516e8	+	5.55132e8i	−1.37780	+	0.795473i	−0.991894	−	0.127066i	$-0.959444\pi$
$887$	−9.61516e8	+	5.55132e8i	−1.37780	+	0.795473i	−0.385905	+	0.922539i	$0.626111\pi$
$888$		0			0
$889$	−9.15354e8	−	7.05903e8i	−1.30282	−	1.00471i
$890$		0			0
$891$	−5.47382e6	−	9.48093e6i	−0.00773851	−	0.0134035i
$892$		0			0
$893$	−3.50770e8	+	6.07551e8i	−0.492570	+	0.853156i
$894$		0			0
$895$		−	1.74487e9i		−	2.43386i
$896$		0			0
$897$	4.12386e8			0.571382
$898$		0			0
$899$	−4.02134e8	−	2.32172e8i	−0.553468	−	0.319545i
$900$		0			0
$901$	6.21260e8	−	3.58685e8i	0.849374	−	0.490386i
$902$		0			0
$903$	−1.89441e8	−	4.60501e8i	−0.257283	−	0.625413i
$904$		0			0
$905$	6.81908e8	+	1.18110e9i	0.919983	+	1.59346i
$906$		0			0
$907$	−3.54463e8	+	6.13948e8i	−0.475060	+	0.822829i	−0.999592	−	0.0285622i	$-0.990907\pi$
$907$	−3.54463e8	+	6.13948e8i	−0.475060	+	0.822829i	0.524532	+	0.851391i	$0.324240\pi$
$908$		0			0
$909$		−	2.17944e8i		−	0.290170i
$910$		0			0
$911$	−9.81055e8			−1.29759			−0.648796	−	0.760962i	$-0.724727\pi$
$911$	−9.81055e8			−1.29759			−0.648796	+	0.760962i	$0.724727\pi$
$912$		0			0
$913$	8.98147e7	+	5.18545e7i	0.118014	+	0.0681357i
$914$		0			0
$915$	3.97636e8	−	2.29575e8i	0.519066	−	0.299683i
$916$		0			0
$917$	1.01726e9	+	1.36431e8i	1.31924	+	0.176931i
$918$		0			0
$919$	2.56762e8	+	4.44725e8i	0.330814	+	0.572987i	0.982672	−	0.185354i	$-0.0593433\pi$
$919$	2.56762e8	+	4.44725e8i	0.330814	+	0.572987i	−0.651858	+	0.758341i	$0.726010\pi$
$920$		0			0
$921$	2.10580e8	−	3.64736e8i	0.269550	−	0.466874i
$922$		0			0
$923$		−	1.93218e9i		−	2.45722i
$924$		0			0
$925$	5.90162e8			0.745670
$926$		0			0
$927$	2.80638e8	+	1.62026e8i	0.352295	+	0.203398i
$928$		0			0
$929$	1.62459e8	−	9.37957e7i	0.202627	−	0.116987i	−0.395253	−	0.918572i	$-0.629343\pi$
$929$	1.62459e8	−	9.37957e7i	0.202627	−	0.116987i	0.597880	+	0.801586i	$0.296010\pi$
$930$		0			0
$931$	3.88549e8	+	3.92329e8i	0.481500	+	0.486185i
$932$		0			0
$933$	−4.36923e7	−	7.56772e7i	−0.0537972	−	0.0931795i
$934$		0			0
$935$	−1.14129e8	+	1.97677e8i	−0.139624	+	0.241836i
$936$		0			0
$937$		−	7.38833e8i		−	0.898106i	−0.893505	−	0.449053i	$-0.851761\pi$
$937$		−	7.38833e8i		−	0.898106i	0.893505	−	0.449053i	$-0.148239\pi$
$938$		0			0
$939$	−4.48883e8			−0.542172
$940$		0			0
$941$	−1.15564e9	−	6.67210e8i	−1.38693	−	0.800744i	−0.393961	−	0.919127i	$-0.628895\pi$
$941$	−1.15564e9	−	6.67210e8i	−1.38693	−	0.800744i	−0.992968	+	0.118384i	$0.962229\pi$
$942$		0			0
$943$	2.66321e8	−	1.53761e8i	0.317593	−	0.183362i
$944$		0			0
$945$	3.01817e7	−	2.25042e8i	0.0357642	−	0.266666i
$946$		0			0
$947$	3.19069e7	+	5.52644e7i	0.0375695	+	0.0650722i	0.884199	−	0.467111i	$-0.154705\pi$
$947$	3.19069e7	+	5.52644e7i	0.0375695	+	0.0650722i	−0.846629	+	0.532183i	$0.821372\pi$
$948$		0			0
$949$	−1.77764e7	+	3.07896e7i	−0.0207991	+	0.0360251i
$950$		0			0
$951$		−	5.69744e8i		−	0.662428i
$952$		0			0
$953$	5.83137e8			0.673740			0.336870	−	0.941551i	$-0.390632\pi$
$953$	5.83137e8			0.673740			0.336870	+	0.941551i	$0.390632\pi$
$954$		0			0
$955$	−7.74305e7	−	4.47045e7i	−0.0889000	−	0.0513264i
$956$		0			0
$957$	4.85204e7	−	2.80133e7i	0.0553591	−	0.0319616i
$958$		0			0
$959$	8.07177e8	−	3.32057e8i	0.915193	−	0.376492i
$960$		0			0
$961$	−1.56882e8	−	2.71728e8i	−0.176768	−	0.306171i
$962$		0			0
$963$	1.22737e7	−	2.12586e7i	0.0137435	−	0.0238044i
$964$		0			0
$965$		−	1.52152e9i		−	1.69316i
$966$		0			0
$967$	1.30054e9			1.43828			0.719140	−	0.694865i	$-0.244536\pi$
$967$	1.30054e9			1.43828			0.719140	+	0.694865i	$0.244536\pi$
$968$		0			0
$969$	−4.46381e8	−	2.57718e8i	−0.490607	−	0.283252i
$970$		0			0
$971$	−1.32683e9	+	7.66045e8i	−1.44930	+	0.836752i	−0.998439	−	0.0558447i	$-0.982215\pi$
$971$	−1.32683e9	+	7.66045e8i	−1.44930	+	0.836752i	−0.450857	+	0.892596i	$0.648882\pi$
$972$		0			0
$973$	3.38599e8	−	4.39066e8i	0.367576	−	0.476641i
$974$		0			0
$975$	4.62865e8	+	8.01706e8i	0.499391	+	0.864971i
$976$		0			0
$977$	−3.03013e8	+	5.24833e8i	−0.324920	+	0.562778i	−0.981496	−	0.191481i	$-0.938671\pi$
$977$	−3.03013e8	+	5.24833e8i	−0.324920	+	0.562778i	0.656576	+	0.754260i	$0.272004\pi$
$978$		0			0
$979$		−	3.83322e7i		−	0.0408523i
$980$		0			0
$981$	4.74481e8			0.502588
$982$		0			0
$983$	1.19815e9	+	6.91751e8i	1.26139	+	0.728265i	0.973344	−	0.229351i	$-0.0736605\pi$
$983$	1.19815e9	+	6.91751e8i	1.26139	+	0.728265i	0.288048	+	0.957616i	$0.406994\pi$
$984$		0			0
$985$	6.73433e8	−	3.88807e8i	0.704670	−	0.406841i
$986$		0			0
$987$	6.32881e8	+	4.88066e8i	0.658220	+	0.507606i
$988$		0			0
$989$	−3.09373e8	−	5.35850e8i	−0.319811	−	0.553929i
$990$		0			0
$991$	1.02203e8	−	1.77020e8i	0.105013	−	0.181887i	−0.808731	−	0.588179i	$-0.799845\pi$
$991$	1.02203e8	−	1.77020e8i	0.105013	−	0.181887i	0.913743	+	0.406292i	$0.133178\pi$
$992$		0			0
$993$		−	3.61784e8i		−	0.369489i
$994$		0			0
$995$	−1.24389e9			−1.26274
$996$		0			0
$997$	1.32391e9	+	7.64362e8i	1.33590	+	0.771283i	0.986197	−	0.165578i	$-0.0529489\pi$
$997$	1.32391e9	+	7.64362e8i	1.33590	+	0.771283i	0.349704	+	0.936860i	$0.386282\pi$
$998$		0			0
$999$	1.29808e8	−	7.49448e7i	0.130198	−	0.0751701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.b.241.4		8
4.3	odd	2		21.7.f.b.10.2	✓	8
7.5	odd	6	inner	336.7.bh.b.145.4		8
12.11	even	2		63.7.m.c.10.3		8
28.3	even	6		147.7.d.a.97.6		8
28.11	odd	6		147.7.d.a.97.5		8
28.19	even	6		21.7.f.b.19.2	yes	8
28.23	odd	6		147.7.f.a.19.2		8
28.27	even	2		147.7.f.a.31.2		8
84.11	even	6		441.7.d.d.244.3		8
84.47	odd	6		63.7.m.c.19.3		8
84.59	odd	6		441.7.d.d.244.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.b.10.2	✓	8	4.3	odd	2
21.7.f.b.19.2	yes	8	28.19	even	6
63.7.m.c.10.3		8	12.11	even	2
63.7.m.c.19.3		8	84.47	odd	6
147.7.d.a.97.5		8	28.11	odd	6
147.7.d.a.97.6		8	28.3	even	6
147.7.f.a.19.2		8	28.23	odd	6
147.7.f.a.31.2		8	28.27	even	2
336.7.bh.b.145.4		8	7.5	odd	6	inner
336.7.bh.b.241.4		8	1.1	even	1	trivial
441.7.d.d.244.3		8	84.11	even	6
441.7.d.d.244.4		8	84.59	odd	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)

\(f(q)\)	\(=\)	\(q+(-13.5000 - 7.79423i) q^{3} +(151.343 - 87.3778i) q^{5} +(271.614 + 209.463i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\)	\(q+(-13.5000 - 7.79423i) q^{3} +(151.343 - 87.3778i) q^{5} +(271.614 + 209.463i) q^{7} +(121.500 + 210.444i) q^{9} +(-92.6996 + 160.560i) q^{11} -3981.73i q^{13} -2724.17 q^{15} +(6101.23 + 3522.55i) q^{17} +(4064.58 - 2346.69i) q^{19} +(-2034.18 - 4944.78i) q^{21} +(-3322.00 - 5753.87i) q^{23} +(7457.27 - 12916.4i) q^{25} -3788.00i q^{27} +19385.8 q^{29} +(-20743.8 - 11976.4i) q^{31} +(2502.89 - 1445.04i) q^{33} +(59409.3 + 7967.73i) q^{35} +(19784.8 + 34268.3i) q^{37} +(-31034.5 + 53753.4i) q^{39} +46285.6i q^{41} +93128.7 q^{43} +(36776.3 + 21232.8i) q^{45} +(-129449. + 74737.3i) q^{47} +(29899.3 + 113786. i) q^{49} +(-54911.1 - 95108.8i) q^{51} +(50912.7 - 88183.4i) q^{53} +32399.5i q^{55} -73162.4 q^{57} +(-131933. - 76171.6i) q^{59} +(-145966. + 84273.5i) q^{61} +(-11079.2 + 82609.4i) q^{63} +(-347915. - 602606. i) q^{65} +(30552.0 - 52917.6i) q^{67} +103570. i q^{69} +485262. q^{71} +(-7732.72 - 4464.49i) q^{73} +(-201346. + 116247. i) q^{75} +(-58810.0 + 24193.3i) q^{77} +(221938. + 384409. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -559383. i q^{83} +1.23117e6 q^{85} +(-261708. - 151097. i) q^{87} +(-179055. + 103378. i) q^{89} +(834026. - 1.08149e6i) q^{91} +(186694. + 323364. i) q^{93} +(410097. - 710308. i) q^{95} -1.23197e6i q^{97} -45052.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9}+O(q^{10}) \) 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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