LMFDB - Embedded newform 400.3.bg.a.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			353.2
Root			$-1.64599i$ of defining polynomial
Character	$\chi$	$=$	400.353
Dual form			400.3.bg.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.711697 + 4.49348i) q^{3} +(-4.53886 + 2.09733i) q^{5} +(-3.58690 + 3.58690i) q^{7} +(-11.1253 + 3.61484i) q^{9} +O(q^{10})$	\(q+(0.711697 + 4.49348i) q^{3} +(-4.53886 + 2.09733i) q^{5} +(-3.58690 + 3.58690i) q^{7} +(-11.1253 + 3.61484i) q^{9} +(-3.53728 + 10.8866i) q^{11} +(10.0537 - 19.7315i) q^{13} +(-12.6546 - 18.9026i) q^{15} +(-3.10698 + 19.6167i) q^{17} +(-15.8404 - 21.8024i) q^{19} +(-18.6705 - 13.5649i) q^{21} +(0.476846 - 0.242965i) q^{23} +(16.2024 - 19.0389i) q^{25} +(-5.57222 - 10.9361i) q^{27} +(-3.67470 + 5.05779i) q^{29} +(-5.42369 + 3.94054i) q^{31} +(-51.4362 - 8.14670i) q^{33} +(8.75753 - 23.8034i) q^{35} +(-5.24626 - 2.67310i) q^{37} +(95.8181 + 31.1332i) q^{39} +(7.33457 + 22.5735i) q^{41} +(-44.7386 - 44.7386i) q^{43} +(42.9147 - 39.7407i) q^{45} +(27.2676 - 4.31877i) q^{47} +23.2682i q^{49} -90.3585 q^{51} +(-13.6315 - 86.0658i) q^{53} +(-6.77762 - 56.8316i) q^{55} +(86.6950 - 86.6950i) q^{57} +(-20.7422 + 6.73954i) q^{59} +(-21.3293 + 65.6449i) q^{61} +(26.9394 - 52.8715i) q^{63} +(-4.24886 + 110.644i) q^{65} +(-14.4421 + 91.1840i) q^{67} +(1.43113 + 1.96978i) q^{69} +(-12.7283 - 9.24768i) q^{71} +(-60.4466 + 30.7991i) q^{73} +(97.0823 + 59.2553i) q^{75} +(-26.3614 - 51.7371i) q^{77} +(-71.8966 + 98.9571i) q^{79} +(-39.9985 + 29.0606i) q^{81} +(-60.8973 - 9.64518i) q^{83} +(-27.0406 - 95.5539i) q^{85} +(-25.3423 - 12.9126i) q^{87} +(75.7710 + 24.6195i) q^{89} +(34.7133 + 106.837i) q^{91} +(-21.5668 - 21.5668i) q^{93} +(117.624 + 65.7354i) q^{95} +(-134.309 + 21.2725i) q^{97} -133.904i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9	$ 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9} - 32 q^{11} - 8 q^{13} - 62 q^{17} - 30 q^{19} - 68 q^{21} + 18 q^{23} + 70 q^{25} + 40 q^{27} + 100 q^{29} - 132 q^{31} - 36 q^{33} - 150 q^{35} + 138 q^{37} + 320 q^{39} - 88 q^{41} + 78 q^{43} - 20 q^{45} + 22 q^{47} + 168 q^{51} + 182 q^{53} - 280 q^{55} + 280 q^{57} + 350 q^{59} + 372 q^{61} - 22 q^{63} - 910 q^{65} + 112 q^{67} - 30 q^{69} - 122 q^{71} - 248 q^{73} + 80 q^{75} + 16 q^{77} - 760 q^{79} - 144 q^{81} - 132 q^{83} - 30 q^{85} - 770 q^{87} + 550 q^{89} + 798 q^{91} + 54 q^{93} - 40 q^{95} - 292 q^{97}+O(q^{100}) $ 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9 - 32 * q^11 - 8 * q^13 - 62 * q^17 - 30 * q^19 - 68 * q^21 + 18 * q^23 + 70 * q^25 + 40 * q^27 + 100 * q^29 - 132 * q^31 - 36 * q^33 - 150 * q^35 + 138 * q^37 + 320 * q^39 - 88 * q^41 + 78 * q^43 - 20 * q^45 + 22 * q^47 + 168 * q^51 + 182 * q^53 - 280 * q^55 + 280 * q^57 + 350 * q^59 + 372 * q^61 - 22 * q^63 - 910 * q^65 + 112 * q^67 - 30 * q^69 - 122 * q^71 - 248 * q^73 + 80 * q^75 + 16 * q^77 - 760 * q^79 - 144 * q^81 - 132 * q^83 - 30 * q^85 - 770 * q^87 + 550 * q^89 + 798 * q^91 + 54 * q^93 - 40 * q^95 - 292 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.711697	+	4.49348i	0.237232	+	1.49783i	0.762555	+	0.646923i	$0.223945\pi$
$3$	0.711697	+	4.49348i	0.237232	+	1.49783i	−0.525323	+	0.850903i	$0.676055\pi$
$4$		0			0
$5$	−4.53886	+	2.09733i	−0.907771	+	0.419466i
$5$	−4.53886	+	2.09733i	−0.907771	+	0.419466i
$6$		0			0
$7$	−3.58690	+	3.58690i	−0.512415	+	0.512415i	−0.915266	−	0.402851i	$-0.868019\pi$
$7$	−3.58690	+	3.58690i	−0.512415	+	0.512415i	0.402851	+	0.915266i	$0.368019\pi$
$8$		0			0
$9$	−11.1253	+	3.61484i	−1.23615	+	0.401648i
$10$		0			0
$11$	−3.53728	+	10.8866i	−0.321571	+	0.989692i	0.651394	+	0.758739i	$0.274184\pi$
$11$	−3.53728	+	10.8866i	−0.321571	+	0.989692i	−0.972965	+	0.230953i	$0.925816\pi$
$12$		0			0
$13$	10.0537	−	19.7315i	0.773361	−	1.51781i	−0.0801805	−	0.996780i	$-0.525550\pi$
$13$	10.0537	−	19.7315i	0.773361	−	1.51781i	0.853541	−	0.521025i	$-0.174450\pi$
$14$		0			0
$15$	−12.6546	−	18.9026i	−0.843639	−	1.26017i
$16$		0			0
$17$	−3.10698	+	19.6167i	−0.182764	+	1.15392i	0.710268	+	0.703931i	$0.248574\pi$
$17$	−3.10698	+	19.6167i	−0.182764	+	1.15392i	−0.893032	+	0.449994i	$0.851426\pi$
$18$		0			0
$19$	−15.8404	−	21.8024i	−0.833703	−	1.14749i	−0.987222	−	0.159348i	$-0.949061\pi$
$19$	−15.8404	−	21.8024i	−0.833703	−	1.14749i	0.153520	−	0.988146i	$-0.450939\pi$
$20$		0			0
$21$	−18.6705	−	13.5649i	−0.889070	−	0.645947i
$22$		0			0
$23$	0.476846	−	0.242965i	0.0207324	−	0.0105637i	−0.443594	−	0.896228i	$-0.646297\pi$
$23$	0.476846	−	0.242965i	0.0207324	−	0.0105637i	0.464326	+	0.885664i	$0.346297\pi$
$24$		0			0
$25$	16.2024	−	19.0389i	0.648097	−	0.761558i
$26$		0			0
$27$	−5.57222	−	10.9361i	−0.206378	−	0.405041i
$28$		0			0
$29$	−3.67470	+	5.05779i	−0.126714	+	0.174406i	−0.867660	−	0.497157i	$-0.834377\pi$
$29$	−3.67470	+	5.05779i	−0.126714	+	0.174406i	0.740947	+	0.671564i	$0.234377\pi$
$30$		0			0
$31$	−5.42369	+	3.94054i	−0.174958	+	0.127114i	−0.671818	−	0.740716i	$-0.734486\pi$
$31$	−5.42369	+	3.94054i	−0.174958	+	0.127114i	0.496860	+	0.867831i	$0.334486\pi$
$32$		0			0
$33$	−51.4362	−	8.14670i	−1.55867	−	0.246870i
$34$		0			0
$35$	8.75753	−	23.8034i	0.250215	−	0.680096i
$36$		0			0
$37$	−5.24626	−	2.67310i	−0.141791	−	0.0722460i	0.381656	−	0.924305i	$-0.375354\pi$
$37$	−5.24626	−	2.67310i	−0.141791	−	0.0722460i	−0.523446	+	0.852059i	$0.675354\pi$
$38$		0			0
$39$	95.8181	+	31.1332i	2.45688	+	0.798287i
$40$		0			0
$41$	7.33457	+	22.5735i	0.178892	+	0.550573i	0.999790	−	0.0205022i	$-0.00652650\pi$
$41$	7.33457	+	22.5735i	0.178892	+	0.550573i	−0.820898	+	0.571075i	$0.806526\pi$
$42$		0			0
$43$	−44.7386	−	44.7386i	−1.04043	−	1.04043i	−0.999147	−	0.0412854i	$-0.986855\pi$
$43$	−44.7386	−	44.7386i	−1.04043	−	1.04043i	−0.0412854	−	0.999147i	$-0.513145\pi$
$44$		0			0
$45$	42.9147	−	39.7407i	0.953661	−	0.883126i
$46$		0			0
$47$	27.2676	−	4.31877i	0.580162	−	0.0918886i	0.140545	−	0.990074i	$-0.455114\pi$
$47$	27.2676	−	4.31877i	0.580162	−	0.0918886i	0.439616	+	0.898186i	$0.355114\pi$
$48$		0			0
$49$			23.2682i			0.474862i
$50$		0			0
$51$	−90.3585			−1.77174
$52$		0			0
$53$	−13.6315	−	86.0658i	−0.257198	−	1.62388i	−0.690986	−	0.722868i	$-0.742823\pi$
$53$	−13.6315	−	86.0658i	−0.257198	−	1.62388i	0.433788	−	0.901015i	$-0.357177\pi$
$54$		0			0
$55$	−6.77762	−	56.8316i	−0.123230	−	1.03330i
$56$		0			0
$57$	86.6950	−	86.6950i	1.52096	−	1.52096i
$58$		0			0
$59$	−20.7422	+	6.73954i	−0.351562	+	0.114229i	−0.479474	−	0.877556i	$-0.659173\pi$
$59$	−20.7422	+	6.73954i	−0.351562	+	0.114229i	0.127912	+	0.991786i	$0.459173\pi$
$60$		0			0
$61$	−21.3293	+	65.6449i	−0.349661	+	1.07615i	0.609380	+	0.792878i	$0.291418\pi$
$61$	−21.3293	+	65.6449i	−0.349661	+	1.07615i	−0.959041	+	0.283267i	$0.908582\pi$
$62$		0			0
$63$	26.9394	−	52.8715i	0.427609	−	0.839231i
$64$		0			0
$65$	−4.24886	+	110.644i	−0.0653671	+	1.70222i
$66$		0			0
$67$	−14.4421	+	91.1840i	−0.215554	+	1.36096i	0.608099	+	0.793861i	$0.291932\pi$
$67$	−14.4421	+	91.1840i	−0.215554	+	1.36096i	−0.823653	+	0.567094i	$0.808068\pi$
$68$		0			0
$69$	1.43113	+	1.96978i	0.0207410	+	0.0285475i
$70$		0			0
$71$	−12.7283	−	9.24768i	−0.179272	−	0.130249i	0.494530	−	0.869161i	$-0.335340\pi$
$71$	−12.7283	−	9.24768i	−0.179272	−	0.130249i	−0.673803	+	0.738911i	$0.735340\pi$
$72$		0			0
$73$	−60.4466	+	30.7991i	−0.828036	+	0.421905i	−0.816021	−	0.578022i	$-0.803825\pi$
$73$	−60.4466	+	30.7991i	−0.828036	+	0.421905i	−0.0120152	+	0.999928i	$0.503825\pi$
$74$		0			0
$75$	97.0823	+	59.2553i	1.29443	+	0.790071i
$76$		0			0
$77$	−26.3614	−	51.7371i	−0.342356	−	0.671911i
$78$		0			0
$79$	−71.8966	+	98.9571i	−0.910083	+	1.25262i	0.0570551	+	0.998371i	$0.481829\pi$
$79$	−71.8966	+	98.9571i	−0.910083	+	1.25262i	−0.967138	+	0.254251i	$0.918171\pi$
$80$		0			0
$81$	−39.9985	+	29.0606i	−0.493809	+	0.358773i
$82$		0			0
$83$	−60.8973	−	9.64518i	−0.733702	−	0.116207i	−0.221607	−	0.975136i	$-0.571130\pi$
$83$	−60.8973	−	9.64518i	−0.733702	−	0.116207i	−0.512095	+	0.858929i	$0.671130\pi$
$84$		0			0
$85$	−27.0406	−	95.5539i	−0.318124	−	1.12416i
$86$		0			0
$87$	−25.3423	−	12.9126i	−0.291291	−	0.148420i
$88$		0			0
$89$	75.7710	+	24.6195i	0.851359	+	0.276623i	0.702015	−	0.712162i	$-0.252284\pi$
$89$	75.7710	+	24.6195i	0.851359	+	0.276623i	0.149344	+	0.988785i	$0.452284\pi$
$90$		0			0
$91$	34.7133	+	106.837i	0.381465	+	1.17403i
$92$		0			0
$93$	−21.5668	−	21.5668i	−0.231901	−	0.231901i
$94$		0			0
$95$	117.624	+	65.7354i	1.23815	+	0.691952i
$96$		0			0
$97$	−134.309	+	21.2725i	−1.38463	+	0.219304i	−0.803886	−	0.594783i	$-0.797238\pi$
$97$	−134.309	+	21.2725i	−1.38463	+	0.219304i	−0.580743	+	0.814087i	$0.697238\pi$
$98$		0			0
$99$		−	133.904i		−	1.35256i
$100$		0			0
$101$	60.2160			0.596198			0.298099	−	0.954535i	$-0.403648\pi$
$101$	60.2160			0.596198			0.298099	+	0.954535i	$0.403648\pi$
$102$		0			0
$103$	−11.2435	−	70.9888i	−0.109160	−	0.689211i	−0.980202	−	0.198002i	$-0.936555\pi$
$103$	−11.2435	−	70.9888i	−0.109160	−	0.689211i	0.871041	−	0.491210i	$-0.163445\pi$
$104$		0			0
$105$	113.193	+	22.4110i	1.07802	+	0.213438i
$106$		0			0
$107$	9.22591	−	9.22591i	0.0862234	−	0.0862234i	−0.662680	−	0.748903i	$-0.730581\pi$
$107$	9.22591	−	9.22591i	0.0862234	−	0.0862234i	0.748903	+	0.662680i	$0.230581\pi$
$108$		0			0
$109$	4.89779	−	1.59139i	0.0449339	−	0.0145999i	−0.286464	−	0.958091i	$-0.592480\pi$
$109$	4.89779	−	1.59139i	0.0449339	−	0.0145999i	0.331398	+	0.943491i	$0.392480\pi$
$110$		0			0
$111$	8.27778	−	25.4764i	0.0745746	−	0.229517i
$112$		0			0
$113$	−47.9858	+	94.1774i	−0.424653	+	0.833428i	0.575228	+	0.817993i	$0.304913\pi$
$113$	−47.9858	+	94.1774i	−0.424653	+	0.833428i	−0.999881	+	0.0154352i	$0.995087\pi$
$114$		0			0
$115$	−1.65476	+	2.10289i	−0.0143892	+	0.0182860i
$116$		0			0
$117$	−40.5245	+	255.861i	−0.346363	+	2.18685i
$118$		0			0
$119$	−59.2189	−	81.5078i	−0.497638	−	0.684939i
$120$		0			0
$121$	−8.11501	−	5.89590i	−0.0670662	−	0.0487265i
$122$		0			0
$123$	−96.2135	+	49.0232i	−0.782223	+	0.398563i
$124$		0			0
$125$	−33.6096	+	120.397i	−0.268877	+	0.963175i
$126$		0			0
$127$	27.8658	+	54.6898i	0.219416	+	0.430628i	0.974308	−	0.225221i	$-0.0723105\pi$
$127$	27.8658	+	54.6898i	0.219416	+	0.430628i	−0.754892	+	0.655850i	$0.772311\pi$
$128$		0			0
$129$	169.192	−	232.872i	1.31156	−	1.80521i
$130$		0			0
$131$	−58.9504	+	42.8300i	−0.450003	+	0.326947i	−0.789597	−	0.613626i	$-0.789710\pi$
$131$	−58.9504	+	42.8300i	−0.450003	+	0.326947i	0.339594	+	0.940572i	$0.389710\pi$
$132$		0			0
$133$	135.021	+	21.3852i	1.01519	+	0.160791i
$134$		0			0
$135$	48.2281	+	37.9506i	0.357245	+	0.281115i
$136$		0			0
$137$	140.901	+	71.7926i	1.02847	+	0.524033i	0.884985	−	0.465619i	$-0.154168\pi$
$137$	140.901	+	71.7926i	1.02847	+	0.524033i	0.143488	+	0.989652i	$0.454168\pi$
$138$		0			0
$139$	112.170	+	36.4463i	0.806981	+	0.262204i	0.683318	−	0.730120i	$-0.260536\pi$
$139$	112.170	+	36.4463i	0.806981	+	0.262204i	0.123662	+	0.992324i	$0.460536\pi$
$140$		0			0
$141$	38.8126	+	119.453i	0.275266	+	0.847183i
$142$		0			0
$143$	179.246	+	179.246i	1.25347	+	1.25347i
$144$		0			0
$145$	6.07108	−	30.6636i	0.0418695	−	0.211473i
$146$		0			0
$147$	−104.555	+	16.5599i	−0.711260	+	0.112653i
$148$		0			0
$149$			127.548i			0.856024i	0.903773	+	0.428012i	$0.140786\pi$
$149$			127.548i			0.856024i	−0.903773	+	0.428012i	$0.859214\pi$
$150$		0			0
$151$	89.8058			0.594741			0.297370	−	0.954762i	$-0.403890\pi$
$151$	89.8058			0.594741			0.297370	+	0.954762i	$0.403890\pi$
$152$		0			0
$153$	−36.3450	−	229.474i	−0.237549	−	1.49983i
$154$		0			0
$155$	16.3528	−	29.2608i	0.105502	−	0.188780i
$156$		0			0
$157$	−58.6460	+	58.6460i	−0.373541	+	0.373541i	−0.868765	−	0.495224i	$-0.835086\pi$
$157$	−58.6460	+	58.6460i	−0.373541	+	0.373541i	0.495224	+	0.868765i	$0.335086\pi$
$158$		0			0
$159$	377.033	−	122.506i	2.37128	−	0.770475i
$160$		0			0
$161$	−0.838909	+	2.58190i	−0.00521061	+	0.0160366i
$162$		0			0
$163$	86.5547	−	169.873i	0.531011	−	1.04217i	−0.457243	−	0.889342i	$-0.651163\pi$
$163$	86.5547	−	169.873i	0.531011	−	1.04217i	0.988253	−	0.152825i	$-0.0488371\pi$
$164$		0			0
$165$	250.548	−	70.9020i	1.51847	−	0.429709i
$166$		0			0
$167$	20.9891	−	132.520i	0.125683	−	0.793532i	−0.841650	−	0.540024i	$-0.818415\pi$
$167$	20.9891	−	132.520i	0.125683	−	0.793532i	0.967333	−	0.253509i	$-0.0815847\pi$
$168$		0			0
$169$	−188.919	−	260.024i	−1.11786	−	1.53861i
$170$		0			0
$171$	255.041	+	185.298i	1.49147	+	1.08362i
$172$		0			0
$173$	111.098	−	56.6075i	0.642187	−	0.327211i	−0.102393	−	0.994744i	$-0.532650\pi$
$173$	111.098	−	56.6075i	0.642187	−	0.327211i	0.744580	+	0.667533i	$0.232650\pi$
$174$		0			0
$175$	10.1743	+	126.407i	0.0581389	+	0.722328i
$176$		0			0
$177$	−45.0461	−	88.4080i	−0.254498	−	0.499480i
$178$		0			0
$179$	−103.351	+	142.251i	−0.577381	+	0.794697i	−0.993405	−	0.114656i	$-0.963423\pi$
$179$	−103.351	+	142.251i	−0.577381	+	0.794697i	0.416024	+	0.909354i	$0.363423\pi$
$180$		0			0
$181$	4.01656	−	2.91820i	0.0221909	−	0.0161227i	−0.576635	−	0.817002i	$-0.695634\pi$
$181$	4.01656	−	2.91820i	0.0221909	−	0.0161227i	0.598825	+	0.800880i	$0.295634\pi$
$182$		0			0
$183$	−310.154	−	49.1235i	−1.69483	−	0.268435i
$184$		0			0
$185$	29.4184	+	1.12970i	0.159018	+	0.00610648i
$186$		0			0
$187$	−202.569	−	103.214i	−1.08326	−	0.551948i
$188$		0			0
$189$	59.2138	+	19.2397i	0.313300	+	0.101797i
$190$		0			0
$191$	57.5605	+	177.153i	0.301364	+	0.927503i	0.981009	+	0.193962i	$0.0621337\pi$
$191$	57.5605	+	177.153i	0.301364	+	0.927503i	−0.679645	+	0.733541i	$0.737866\pi$
$192$		0			0
$193$	149.932	+	149.932i	0.776850	+	0.776850i	0.979294	−	0.202444i	$-0.0648883\pi$
$193$	149.932	+	149.932i	0.776850	+	0.776850i	−0.202444	+	0.979294i	$0.564888\pi$
$194$		0			0
$195$	−500.201	+	59.6530i	−2.56513	+	0.305913i
$196$		0			0
$197$	−297.815	+	47.1692i	−1.51175	+	0.239437i	−0.856568	−	0.516034i	$-0.827408\pi$
$197$	−297.815	+	47.1692i	−1.51175	+	0.239437i	−0.655181	+	0.755472i	$0.727408\pi$
$198$		0			0
$199$		−	137.629i		−	0.691604i	−0.938307	−	0.345802i	$-0.887607\pi$
$199$		−	137.629i		−	0.691604i	0.938307	−	0.345802i	$-0.112393\pi$
$200$		0			0
$201$	−420.012			−2.08961
$202$		0			0
$203$	−4.96101	−	31.3226i	−0.0244385	−	0.154298i
$204$		0			0
$205$	−80.6346	−	87.0748i	−0.393339	−	0.424755i
$206$		0			0
$207$	−4.42679	+	4.42679i	−0.0213854	+	0.0213854i
$208$		0			0
$209$	293.386	−	95.3268i	1.40376	−	0.456109i
$210$		0			0
$211$	−34.9377	+	107.527i	−0.165582	+	0.509608i	−0.999079	−	0.0429161i	$-0.986335\pi$
$211$	−34.9377	+	107.527i	−0.165582	+	0.509608i	0.833497	+	0.552524i	$0.186335\pi$
$212$		0			0
$213$	32.4955	−	63.7761i	0.152561	−	0.299418i
$214$		0			0
$215$	296.894	+	109.231i	1.38090	+	0.508049i
$216$		0			0
$217$	5.31992	−	33.5886i	0.0245157	−	0.154786i
$218$		0			0
$219$	−181.415	−	249.696i	−0.828378	−	1.14016i
$220$		0			0
$221$	355.830	+	258.526i	1.61009	+	1.16980i
$222$		0			0
$223$	213.575	−	108.822i	0.957738	−	0.487992i	0.0960197	−	0.995379i	$-0.469389\pi$
$223$	213.575	−	108.822i	0.957738	−	0.487992i	0.861718	+	0.507388i	$0.169389\pi$
$224$		0			0
$225$	−111.435	+	270.383i	−0.495265	+	1.20170i
$226$		0			0
$227$	−55.9856	−	109.878i	−0.246633	−	0.484044i	0.734190	−	0.678944i	$-0.237562\pi$
$227$	−55.9856	−	109.878i	−0.246633	−	0.484044i	−0.980823	+	0.194900i	$0.937562\pi$
$228$		0			0
$229$	−150.862	+	207.644i	−0.658787	+	0.906742i	−0.999440	−	0.0334469i	$-0.989352\pi$
$229$	−150.862	+	207.644i	−0.658787	+	0.906742i	0.340654	+	0.940189i	$0.389352\pi$
$230$		0			0
$231$	213.718	−	155.275i	0.925187	−	0.672188i
$232$		0			0
$233$	10.2744	+	1.62731i	0.0440962	+	0.00698416i	0.178444	−	0.983950i	$-0.442894\pi$
$233$	10.2744	+	1.62731i	0.0440962	+	0.00698416i	−0.134347	+	0.990934i	$0.542894\pi$
$234$		0			0
$235$	−114.706	+	76.7914i	−0.488110	+	0.326772i
$236$		0			0
$237$	−495.830	−	252.638i	−2.09211	−	1.06598i
$238$		0			0
$239$	−69.6575	−	22.6331i	−0.291454	−	0.0946992i	0.159641	−	0.987175i	$-0.448966\pi$
$239$	−69.6575	−	22.6331i	−0.291454	−	0.0946992i	−0.451095	+	0.892476i	$0.648966\pi$
$240$		0			0
$241$	−20.2934	−	62.4568i	−0.0842052	−	0.259157i	0.900085	−	0.435714i	$-0.143504\pi$
$241$	−20.2934	−	62.4568i	−0.0842052	−	0.259157i	−0.984290	+	0.176557i	$0.943504\pi$
$242$		0			0
$243$	−237.160	−	237.160i	−0.975969	−	0.975969i
$244$		0			0
$245$	−48.8011	−	105.611i	−0.199188	−	0.431066i
$246$		0			0
$247$	−589.447	+	93.3593i	−2.38643	+	0.377973i
$248$		0			0
$249$		−	280.505i		−	1.12653i
$250$		0			0
$251$	47.1625			0.187898			0.0939492	−	0.995577i	$-0.470051\pi$
$251$	47.1625			0.187898			0.0939492	+	0.995577i	$0.470051\pi$
$252$		0			0
$253$	0.958333	+	6.05068i	0.00378788	+	0.0239157i
$254$		0			0
$255$	410.124	−	189.512i	1.60833	−	0.743183i
$256$		0			0
$257$	−85.1375	+	85.1375i	−0.331274	+	0.331274i	−0.853070	−	0.521796i	$-0.825262\pi$
$257$	−85.1375	+	85.1375i	−0.331274	+	0.331274i	0.521796	+	0.853070i	$0.325262\pi$
$258$		0			0
$259$	28.4060	−	9.22967i	0.109676	−	0.0356358i
$260$		0			0
$261$	22.5991	−	69.5529i	0.0865866	−	0.266486i
$262$		0			0
$263$	−157.397	+	308.908i	−0.598467	+	1.17456i	0.370839	+	0.928697i	$0.379070\pi$
$263$	−157.397	+	308.908i	−0.598467	+	1.17456i	−0.969305	+	0.245860i	$0.920930\pi$
$264$		0			0
$265$	242.380	+	362.051i	0.914640	+	1.36623i
$266$		0			0
$267$	−56.7011	+	357.997i	−0.212364	+	1.34081i
$268$		0			0
$269$	−114.651	−	157.804i	−0.426212	−	0.586631i	0.540866	−	0.841109i	$-0.318097\pi$
$269$	−114.651	−	157.804i	−0.426212	−	0.586631i	−0.967079	+	0.254478i	$0.918097\pi$
$270$		0			0
$271$	−295.640	−	214.795i	−1.09092	−	0.792602i	−0.111368	−	0.993779i	$-0.535523\pi$
$271$	−295.640	−	214.795i	−1.09092	−	0.792602i	−0.979555	+	0.201177i	$0.935523\pi$
$272$		0			0
$273$	−455.362	+	232.019i	−1.66799	+	0.849885i
$274$		0			0
$275$	149.957	+	243.736i	0.545299	+	0.886311i
$276$		0			0
$277$	−46.0601	−	90.3980i	−0.166282	−	0.326346i	0.792797	−	0.609486i	$-0.208624\pi$
$277$	−46.0601	−	90.3980i	−0.166282	−	0.326346i	−0.959079	+	0.283139i	$0.908624\pi$
$278$		0			0
$279$	46.0959	−	63.4456i	0.165218	−	0.227404i
$280$		0			0
$281$	324.001	−	235.401i	1.15303	−	0.837725i	0.164149	−	0.986436i	$-0.447512\pi$
$281$	324.001	−	235.401i	1.15303	−	0.837725i	0.988881	+	0.148710i	$0.0475121\pi$
$282$		0			0
$283$	246.358	+	39.0193i	0.870523	+	0.137877i	0.575687	−	0.817670i	$-0.304735\pi$
$283$	246.358	+	39.0193i	0.870523	+	0.137877i	0.294837	+	0.955548i	$0.404735\pi$
$284$		0			0
$285$	−211.668	+	575.324i	−0.742695	+	2.01868i
$286$		0			0
$287$	−107.277	−	54.6606i	−0.373789	−	0.190455i
$288$		0			0
$289$	−100.307	−	32.5918i	−0.347084	−	0.112774i
$290$		0			0
$291$	−191.175	−	588.375i	−0.656957	−	2.02191i
$292$		0			0
$293$	−353.989	−	353.989i	−1.20815	−	1.20815i	−0.971624	−	0.236529i	$-0.923990\pi$
$293$	−353.989	−	353.989i	−1.20815	−	1.20815i	−0.236529	−	0.971624i	$-0.576010\pi$
$294$		0			0
$295$	80.0107	−	74.0930i	0.271223	−	0.251163i
$296$		0			0
$297$	138.768	−	21.9786i	0.467231	−	0.0740021i
$298$		0			0
$299$		−	11.8516i		−	0.0396374i
$300$		0			0
$301$	320.946			1.06627
$302$		0			0
$303$	42.8555	+	270.579i	0.141437	+	0.893000i
$304$		0			0
$305$	−40.8682	−	342.687i	−0.133994	−	1.12356i
$306$		0			0
$307$	235.076	−	235.076i	0.765718	−	0.765718i	−0.211631	−	0.977350i	$-0.567878\pi$
$307$	235.076	−	235.076i	0.765718	−	0.765718i	0.977350	+	0.211631i	$0.0678776\pi$
$308$		0			0
$309$	310.985	−	101.045i	1.00642	−	0.327006i
$310$		0			0
$311$	−73.4853	+	226.164i	−0.236287	+	0.727217i	0.760661	+	0.649149i	$0.224875\pi$
$311$	−73.4853	+	226.164i	−0.236287	+	0.727217i	−0.996948	+	0.0780676i	$0.975125\pi$
$312$		0			0
$313$	−17.1378	+	33.6349i	−0.0547535	+	0.107460i	−0.916762	−	0.399434i	$-0.869207\pi$
$313$	−17.1378	+	33.6349i	−0.0547535	+	0.107460i	0.862008	+	0.506894i	$0.169207\pi$
$314$		0			0
$315$	−11.3851	+	296.477i	−0.0361430	+	0.941197i
$316$		0			0
$317$	30.3237	−	191.456i	0.0956583	−	0.603963i	−0.892562	−	0.450925i	$-0.851094\pi$
$317$	30.3237	−	191.456i	0.0956583	−	0.603963i	0.988220	−	0.153038i	$-0.0489058\pi$
$318$		0			0
$319$	−42.0638	−	57.8958i	−0.131861	−	0.181492i
$320$		0			0
$321$	48.0225	+	34.8904i	0.149603	+	0.108693i
$322$		0			0
$323$	476.907	−	242.996i	1.47649	−	0.752310i
$324$		0			0
$325$	−212.772	−	511.109i	−0.654684	−	1.57264i
$326$		0			0
$327$	10.6366	+	20.8755i	0.0325279	+	0.0638396i
$328$		0			0
$329$	−82.3153	+	113.297i	−0.250199	+	0.344369i
$330$		0			0
$331$	−206.636	+	150.130i	−0.624279	+	0.453566i	−0.854414	−	0.519593i	$-0.826083\pi$
$331$	−206.636	+	150.130i	−0.624279	+	0.453566i	0.230134	+	0.973159i	$0.426083\pi$
$332$		0			0
$333$	68.0291	+	10.7748i	0.204292	+	0.0323566i
$334$		0			0
$335$	−125.692	−	444.161i	−0.375200	−	1.32585i
$336$		0			0
$337$	326.020	+	166.116i	0.967419	+	0.492925i	0.864975	−	0.501814i	$-0.167334\pi$
$337$	326.020	+	166.116i	0.967419	+	0.492925i	0.102444	+	0.994739i	$0.467334\pi$
$338$		0			0
$339$	−457.335	−	148.597i	−1.34907	−	0.438340i
$340$		0			0
$341$	−23.7141	−	72.9845i	−0.0695428	−	0.214031i
$342$		0			0
$343$	−259.219	−	259.219i	−0.755741	−	0.755741i
$344$		0			0
$345$	−10.6270	−	5.93900i	−0.0308028	−	0.0172145i
$346$		0			0
$347$	452.474	−	71.6649i	1.30396	−	0.206527i	0.534471	−	0.845187i	$-0.320511\pi$
$347$	452.474	−	71.6649i	1.30396	−	0.206527i	0.769489	+	0.638660i	$0.220511\pi$
$348$		0			0
$349$		−	98.1992i		−	0.281373i	−0.990054	−	0.140686i	$-0.955069\pi$
$349$		−	98.1992i		−	0.281373i	0.990054	−	0.140686i	$-0.0449310\pi$
$350$		0			0
$351$	−271.807			−0.774378
$352$		0			0
$353$	22.0875	+	139.455i	0.0625710	+	0.395058i	0.999020	+	0.0442546i	$0.0140913\pi$
$353$	22.0875	+	139.455i	0.0625710	+	0.395058i	−0.936449	+	0.350803i	$0.885909\pi$
$354$		0			0
$355$	77.1675	+	15.2784i	0.217373	+	0.0430377i
$356$		0			0
$357$	324.108	−	324.108i	0.907864	−	0.907864i
$358$		0			0
$359$	419.653	−	136.354i	1.16895	−	0.379815i	0.340699	−	0.940172i	$-0.389336\pi$
$359$	419.653	−	136.354i	1.16895	−	0.379815i	0.828251	+	0.560358i	$0.189336\pi$
$360$		0			0
$361$	−112.872	+	347.383i	−0.312664	+	0.962281i
$362$		0			0
$363$	20.7177	−	40.6607i	0.0570735	−	0.112013i
$364$		0			0
$365$	209.763	−	266.569i	0.574692	−	0.730326i
$366$		0			0
$367$	−53.9032	+	340.331i	−0.146875	+	0.927333i	0.798653	+	0.601792i	$0.205546\pi$
$367$	−53.9032	+	340.331i	−0.146875	+	0.927333i	−0.945528	+	0.325541i	$0.894454\pi$
$368$		0			0
$369$	−163.199	−	224.624i	−0.442274	−	0.608737i
$370$		0			0
$371$	357.605	+	259.815i	0.963894	+	0.700310i
$372$		0			0
$373$	316.871	−	161.454i	0.849520	−	0.432852i	0.0256771	−	0.999670i	$-0.491826\pi$
$373$	316.871	−	161.454i	0.849520	−	0.432852i	0.823843	+	0.566818i	$0.191826\pi$
$374$		0			0
$375$	−564.920	−	65.3378i	−1.50645	−	0.174234i
$376$		0			0
$377$	62.8533	+	123.357i	0.166720	+	0.327206i
$378$		0			0
$379$	155.812	−	214.457i	0.411115	−	0.565851i	−0.552375	−	0.833596i	$-0.686278\pi$
$379$	155.812	−	214.457i	0.411115	−	0.565851i	0.963490	+	0.267745i	$0.0862784\pi$
$380$		0			0
$381$	−225.915	+	164.137i	−0.592954	+	0.430806i
$382$		0			0
$383$	−380.286	−	60.2315i	−0.992915	−	0.157262i	−0.361221	−	0.932480i	$-0.617640\pi$
$383$	−380.286	−	60.2315i	−0.992915	−	0.157262i	−0.631694	+	0.775218i	$0.717640\pi$
$384$		0			0
$385$	228.160	+	179.539i	0.592624	+	0.466335i
$386$		0			0
$387$	659.454	+	336.009i	1.70402	+	0.868239i
$388$		0			0
$389$	607.465	+	197.377i	1.56161	+	0.507397i	0.957236	−	0.289307i	$-0.0934250\pi$
$389$	607.465	+	197.377i	1.56161	+	0.507397i	0.604370	+	0.796704i	$0.293425\pi$
$390$		0			0
$391$	3.28463	+	10.1090i	0.00840059	+	0.0258543i
$392$		0			0
$393$	−234.411	−	234.411i	−0.596464	−	0.596464i
$394$		0			0
$395$	118.783	−	599.943i	0.300715	−	1.51884i
$396$		0			0
$397$	−19.7208	+	3.12348i	−0.0496747	+	0.00786770i	−0.181222	−	0.983442i	$-0.558005\pi$
$397$	−19.7208	+	3.12348i	−0.0496747	+	0.00786770i	0.131548	+	0.991310i	$0.458005\pi$
$398$		0			0
$399$			621.933i			1.55873i
$400$		0			0
$401$	−546.371			−1.36252			−0.681261	−	0.732041i	$-0.738568\pi$
$401$	−546.371			−1.36252			−0.681261	+	0.732041i	$0.738568\pi$
$402$		0			0
$403$	23.2246	+	146.634i	0.0576293	+	0.363857i
$404$		0			0
$405$	120.598	−	215.792i	0.297772	−	0.532820i
$406$		0			0
$407$	47.6585	−	47.6585i	0.117097	−	0.117097i
$408$		0			0
$409$	−396.232	+	128.743i	−0.968782	+	0.314776i	−0.750324	−	0.661070i	$-0.770103\pi$
$409$	−396.232	+	128.743i	−0.968782	+	0.314776i	−0.218458	+	0.975846i	$0.570103\pi$
$410$		0			0
$411$	−222.320	+	684.229i	−0.540924	+	1.66479i
$412$		0			0
$413$	50.2261	−	98.5743i	0.121613	−	0.238679i
$414$		0			0
$415$	296.633	−	83.9435i	0.714779	−	0.202274i
$416$		0			0
$417$	−83.9396	+	529.974i	−0.201294	+	1.27092i
$418$		0			0
$419$	245.790	+	338.302i	0.586612	+	0.807402i	0.994401	−	0.105674i	$-0.0337000\pi$
$419$	245.790	+	338.302i	0.586612	+	0.807402i	−0.407789	+	0.913076i	$0.633700\pi$
$420$		0			0
$421$	−240.021	−	174.386i	−0.570122	−	0.414218i	0.265028	−	0.964241i	$-0.414619\pi$
$421$	−240.021	−	174.386i	−0.570122	−	0.414218i	−0.835149	+	0.550023i	$0.814619\pi$
$422$		0			0
$423$	−287.749	+	146.616i	−0.680258	+	0.346609i
$424$		0			0
$425$	323.141	+	376.992i	0.760332	+	0.887041i
$426$		0			0
$427$	−158.956	−	311.968i	−0.372262	−	0.730605i
$428$		0			0
$429$	−677.870	+	933.008i	−1.58012	+	2.17484i
$430$		0			0
$431$	319.131	−	231.862i	0.740442	−	0.537963i	−0.152408	−	0.988318i	$-0.548703\pi$
$431$	319.131	−	231.862i	0.740442	−	0.537963i	0.892850	+	0.450355i	$0.148703\pi$
$432$		0			0
$433$	−112.334	−	17.7920i	−0.259432	−	0.0410901i	0.0253633	−	0.999678i	$-0.491926\pi$
$433$	−112.334	−	17.7920i	−0.259432	−	0.0410901i	−0.284796	+	0.958588i	$0.591926\pi$
$434$		0			0
$435$	142.107	+	5.45707i	0.326683	+	0.0125450i
$436$		0			0
$437$	−12.8506	−	6.54773i	−0.0294065	−	0.0149834i
$438$		0			0
$439$	541.776	+	176.034i	1.23411	+	0.400988i	0.852203	−	0.523211i	$-0.175266\pi$
$439$	541.776	+	176.034i	1.23411	+	0.400988i	0.381911	+	0.924199i	$0.375266\pi$
$440$		0			0
$441$	−84.1108	−	258.867i	−0.190728	−	0.586999i
$442$		0			0
$443$	277.860	+	277.860i	0.627222	+	0.627222i	0.947368	−	0.320146i	$-0.103732\pi$
$443$	277.860	+	277.860i	0.627222	+	0.627222i	−0.320146	+	0.947368i	$0.603732\pi$
$444$		0			0
$445$	−395.549	+	47.1723i	−0.888874	+	0.106005i
$446$		0			0
$447$	−573.132	+	90.7752i	−1.28217	+	0.203077i
$448$		0			0
$449$			733.358i			1.63331i	0.577124	+	0.816657i	$0.304175\pi$
$449$			733.358i			1.63331i	−0.577124	+	0.816657i	$0.695825\pi$
$450$		0			0
$451$	−271.693			−0.602424
$452$		0			0
$453$	63.9145	+	403.540i	0.141092	+	0.890818i
$454$		0			0
$455$	−381.630	−	412.111i	−0.838747	−	0.905737i
$456$		0			0
$457$	637.278	−	637.278i	1.39448	−	1.39448i	0.579535	−	0.814948i	$-0.303234\pi$
$457$	637.278	−	637.278i	1.39448	−	1.39448i	0.814948	−	0.579535i	$-0.196766\pi$
$458$		0			0
$459$	231.843	−	75.3304i	0.505105	−	0.164119i
$460$		0			0
$461$	−199.771	+	614.831i	−0.433342	+	1.33369i	0.461434	+	0.887175i	$0.347335\pi$
$461$	−199.771	+	614.831i	−0.433342	+	1.33369i	−0.894776	+	0.446515i	$0.852665\pi$
$462$		0			0
$463$	152.915	−	300.113i	0.330271	−	0.648192i	−0.664837	−	0.746988i	$-0.731499\pi$
$463$	152.915	−	300.113i	0.330271	−	0.648192i	0.995108	+	0.0987958i	$0.0314991\pi$
$464$		0			0
$465$	143.121	+	52.6559i	0.307787	+	0.113238i
$466$		0			0
$467$	−88.2096	+	556.933i	−0.188886	+	1.19258i	0.692938	+	0.720997i	$0.256316\pi$
$467$	−88.2096	+	556.933i	−0.188886	+	1.19258i	−0.881824	+	0.471579i	$0.843684\pi$
$468$		0			0
$469$	−275.266	−	378.871i	−0.586921	−	0.807827i
$470$		0			0
$471$	−305.263	−	221.786i	−0.648116	−	0.470884i
$472$		0			0
$473$	645.305	−	328.799i	1.36428	−	0.695136i
$474$		0			0
$475$	−671.746	−	51.6678i	−1.41420	−	0.108774i
$476$		0			0
$477$	462.768	+	908.234i	0.970164	+	1.90405i
$478$		0			0
$479$	−478.041	+	657.967i	−0.997998	+	1.37363i	−0.0714519	+	0.997444i	$0.522763\pi$
$479$	−478.041	+	657.967i	−0.997998	+	1.37363i	−0.926546	+	0.376182i	$0.877237\pi$
$480$		0			0
$481$	−105.489	+	76.6419i	−0.219311	+	0.159339i
$482$		0			0
$483$	−12.1987	−	1.93209i	−0.0252562	−	0.00400019i
$484$		0			0
$485$	564.994	−	378.243i	1.16494	−	0.779882i
$486$		0			0
$487$	106.854	+	54.4449i	0.219413	+	0.111796i	0.560243	−	0.828329i	$-0.310708\pi$
$487$	106.854	+	54.4449i	0.219413	+	0.111796i	−0.340830	+	0.940125i	$0.610708\pi$
$488$		0			0
$489$	824.922	+	268.033i	1.68696	+	0.548126i
$490$		0			0
$491$	47.2164	+	145.317i	0.0961637	+	0.295962i	0.987555	−	0.157273i	$-0.0502701\pi$
$491$	47.2164	+	145.317i	0.0961637	+	0.295962i	−0.891391	+	0.453234i	$0.850270\pi$
$492$		0			0
$493$	−87.8000	−	87.8000i	−0.178093	−	0.178093i
$494$		0			0
$495$	280.840	+	607.770i	0.567354	+	1.22782i
$496$		0			0
$497$	78.8259	−	12.4848i	0.158603	−	0.0251203i
$498$		0			0
$499$		−	424.984i		−	0.851671i	−0.904801	−	0.425836i	$-0.859980\pi$
$499$		−	424.984i		−	0.851671i	0.904801	−	0.425836i	$-0.140020\pi$
$500$		0			0
$501$	610.413			1.21839
$502$		0			0
$503$	93.9909	+	593.435i	0.186861	+	1.17979i	0.885611	+	0.464427i	$0.153740\pi$
$503$	93.9909	+	593.435i	0.186861	+	1.17979i	−0.698751	+	0.715365i	$0.746260\pi$
$504$		0			0
$505$	−273.312	+	126.293i	−0.541211	+	0.250084i
$506$		0			0
$507$	1033.96	−	1033.96i	2.03937	−	2.03937i
$508$		0			0
$509$	−103.142	+	33.5130i	−0.202637	+	0.0658408i	−0.408577	−	0.912724i	$-0.633975\pi$
$509$	−103.142	+	33.5130i	−0.202637	+	0.0658408i	0.205940	+	0.978565i	$0.433975\pi$
$510$		0			0
$511$	106.343	−	327.290i	0.208107	−	0.640489i
$512$		0			0
$513$	−150.167	+	294.719i	−0.292723	+	0.574501i
$514$		0			0
$515$	199.919	+	298.626i	0.388193	+	0.579857i
$516$		0			0
$517$	−49.4363	+	312.129i	−0.0956215	+	0.603730i
$518$		0			0
$519$	333.433	+	458.931i	0.642452	+	0.884260i
$520$		0			0
$521$	−161.044	−	117.005i	−0.309105	−	0.224578i	0.422407	−	0.906406i	$-0.361185\pi$
$521$	−161.044	−	117.005i	−0.309105	−	0.224578i	−0.731512	+	0.681828i	$0.761185\pi$
$522$		0			0
$523$	−565.327	+	288.049i	−1.08093	+	0.550762i	−0.901399	−	0.432990i	$-0.857459\pi$
$523$	−565.327	+	288.049i	−1.08093	+	0.550762i	−0.179533	+	0.983752i	$0.557459\pi$
$524$		0			0
$525$	−560.768	+	135.682i	−1.06813	+	0.258442i
$526$		0			0
$527$	−60.4492	−	118.638i	−0.114704	−	0.225120i
$528$		0			0
$529$	−310.770	+	427.738i	−0.587467	+	0.808579i
$530$		0			0
$531$	206.401	−	149.959i	0.388702	−	0.282409i
$532$		0			0
$533$	519.148	+	82.2249i	0.974011	+	0.154268i
$534$		0			0
$535$	−22.5253	+	61.2248i	−0.0421034	+	0.114439i
$536$		0			0
$537$	−712.756	−	363.167i	−1.32729	−	0.676289i
$538$		0			0
$539$	−253.312	−	82.3061i	−0.469967	−	0.152702i
$540$		0			0
$541$	−287.608	−	885.166i	−0.531622	−	1.63617i	−0.750836	−	0.660489i	$-0.770349\pi$
$541$	−287.608	−	885.166i	−0.531622	−	1.63617i	0.219214	−	0.975677i	$-0.429651\pi$
$542$		0			0
$543$	15.9714	+	15.9714i	0.0294133	+	0.0294133i
$544$		0			0
$545$	−18.8927	+	17.4954i	−0.0346655	+	0.0321016i
$546$		0			0
$547$	674.591	−	106.845i	1.23326	−	0.195328i	0.494425	−	0.869220i	$-0.335379\pi$
$547$	674.591	−	106.845i	1.23326	−	0.195328i	0.738830	+	0.673892i	$0.235379\pi$
$548$		0			0
$549$		−	807.422i		−	1.47071i
$550$		0			0
$551$	168.480			0.305772
$552$		0			0
$553$	−97.0637	−	612.836i	−0.175522	−	1.10820i
$554$		0			0
$555$	15.8607	+	132.995i	0.0285778	+	0.239630i
$556$		0			0
$557$	18.5591	−	18.5591i	0.0333198	−	0.0333198i	−0.690251	−	0.723570i	$-0.742500\pi$
$557$	18.5591	−	18.5591i	0.0333198	−	0.0333198i	0.723570	+	0.690251i	$0.242500\pi$
$558$		0			0
$559$	−1332.55	+	432.971i	−2.38380	+	0.774545i
$560$		0			0
$561$	319.623	−	983.699i	0.569738	−	1.75347i
$562$		0			0
$563$	428.520	−	841.019i	0.761138	−	1.49382i	−0.105251	−	0.994446i	$-0.533565\pi$
$563$	428.520	−	841.019i	0.761138	−	1.49382i	0.866388	−	0.499371i	$-0.166435\pi$
$564$		0			0
$565$	20.2796	−	528.100i	0.0358931	−	0.934690i
$566$		0			0
$567$	39.2332	−	247.709i	0.0691943	−	0.436876i
$568$		0			0
$569$	212.998	+	293.167i	0.374337	+	0.515231i	0.954073	−	0.299573i	$-0.0968443\pi$
$569$	212.998	+	293.167i	0.374337	+	0.515231i	−0.579736	+	0.814804i	$0.696844\pi$
$570$		0			0
$571$	908.751	+	660.246i	1.59151	+	1.15630i	0.901750	+	0.432258i	$0.142283\pi$
$571$	908.751	+	660.246i	1.59151	+	1.15630i	0.689758	+	0.724040i	$0.257717\pi$
$572$		0			0
$573$	−755.067	+	384.726i	−1.31774	+	0.671424i
$574$		0			0
$575$	3.10026	−	13.0153i	0.00539176	−	0.0226353i
$576$		0			0
$577$	42.7144	+	83.8317i	0.0740284	+	0.145289i	0.925054	−	0.379835i	$-0.124019\pi$
$577$	42.7144	+	83.8317i	0.0740284	+	0.145289i	−0.851026	+	0.525124i	$0.824019\pi$
$578$		0			0
$579$	−567.010	+	780.423i	−0.979292	+	1.34788i
$580$		0			0
$581$	253.029	−	183.836i	0.435506	−	0.316414i
$582$		0			0
$583$	985.183	+	156.038i	1.68985	+	0.267646i
$584$		0			0
$585$	−352.691	−	1246.31i	−0.602890	−	2.13045i
$586$		0			0
$587$	−349.794	−	178.229i	−0.595901	−	0.303627i	0.129905	−	0.991526i	$-0.458533\pi$
$587$	−349.794	−	178.229i	−0.595901	−	0.303627i	−0.725806	+	0.687900i	$0.758533\pi$
$588$		0			0
$589$	171.826	+	55.8298i	0.291726	+	0.0947875i
$590$		0			0
$591$	−423.907	−	1304.65i	−0.717271	−	2.20753i
$592$		0			0
$593$	730.554	+	730.554i	1.23196	+	1.23196i	0.963209	+	0.268754i	$0.0866120\pi$
$593$	730.554	+	730.554i	1.23196	+	1.23196i	0.268754	+	0.963209i	$0.413388\pi$
$594$		0			0
$595$	439.735	+	245.751i	0.739050	+	0.413026i
$596$		0			0
$597$	618.434	−	97.9503i	1.03590	−	0.164071i
$598$		0			0
$599$			287.501i			0.479968i	0.970777	+	0.239984i	$0.0771422\pi$
$599$			287.501i			0.479968i	−0.970777	+	0.239984i	$0.922858\pi$
$600$		0			0
$601$	481.352			0.800919			0.400459	−	0.916314i	$-0.368851\pi$
$601$	481.352			0.800919			0.400459	+	0.916314i	$0.368851\pi$
$602$		0			0
$603$	−168.942	−	1066.66i	−0.280169	−	1.76892i
$604$		0			0
$605$	49.1985	+	9.74080i	0.0813199	+	0.0161005i
$606$		0			0
$607$	431.854	−	431.854i	0.711456	−	0.711456i	−0.255383	−	0.966840i	$-0.582202\pi$
$607$	431.854	−	431.854i	0.711456	−	0.711456i	0.966840	+	0.255383i	$0.0822017\pi$
$608$		0			0
$609$	137.217	−	44.5844i	0.225315	−	0.0732092i
$610$		0			0
$611$	188.924	−	581.450i	0.309205	−	0.951636i
$612$		0			0
$613$	−136.550	+	267.994i	−0.222757	+	0.437185i	−0.975155	−	0.221524i	$-0.928897\pi$
$613$	−136.550	+	267.994i	−0.222757	+	0.437185i	0.752398	+	0.658709i	$0.228897\pi$
$614$		0			0
$615$	333.881	−	424.301i	0.542897	−	0.689920i
$616$		0			0
$617$	6.55430	−	41.3822i	0.0106228	−	0.0670700i	−0.981807	−	0.189879i	$-0.939190\pi$
$617$	6.55430	−	41.3822i	0.0106228	−	0.0670700i	0.992430	+	0.122809i	$0.0391903\pi$
$618$		0			0
$619$	−491.415	−	676.375i	−0.793885	−	1.09269i	−0.993613	−	0.112838i	$-0.964006\pi$
$619$	−491.415	−	676.375i	−0.793885	−	1.09269i	0.199728	−	0.979851i	$-0.435994\pi$
$620$		0			0
$621$	−5.31418	−	3.86098i	−0.00855746	−	0.00621736i
$622$		0			0
$623$	−360.091	+	183.476i	−0.577995	+	0.294503i
$624$		0			0
$625$	−99.9627	−	616.954i	−0.159940	−	0.987127i
$626$		0			0
$627$	637.151	+	1250.48i	1.01619	+	1.99438i
$628$		0			0
$629$	68.7376	−	94.6091i	0.109281	−	0.150412i
$630$		0			0
$631$	−559.824	+	406.736i	−0.887201	+	0.644589i	−0.935147	−	0.354261i	$-0.884732\pi$
$631$	−559.824	+	406.736i	−0.887201	+	0.644589i	0.0479460	+	0.998850i	$0.484732\pi$
$632$		0			0
$633$	−508.036	−	80.4651i	−0.802585	−	0.127117i
$634$		0			0
$635$	−241.182	−	189.785i	−0.379813	−	0.298874i
$636$		0			0
$637$	459.116	+	233.932i	0.720748	+	0.367239i
$638$		0			0
$639$	175.036	+	56.8726i	0.273921	+	0.0890025i
$640$		0			0
$641$	353.774	+	1088.81i	0.551910	+	1.69860i	0.703967	+	0.710233i	$0.251410\pi$
$641$	353.774	+	1088.81i	0.551910	+	1.69860i	−0.152057	+	0.988372i	$0.548590\pi$
$642$		0			0
$643$	−160.690	−	160.690i	−0.249906	−	0.249906i	0.571026	−	0.820932i	$-0.306546\pi$
$643$	−160.690	−	160.690i	−0.249906	−	0.249906i	−0.820932	+	0.571026i	$0.806546\pi$
$644$		0			0
$645$	−279.527	+	1411.82i	−0.433375	+	2.18887i
$646$		0			0
$647$	−197.406	+	31.2660i	−0.305110	+	0.0483246i	−0.307112	−	0.951673i	$-0.599363\pi$
$647$	−197.406	+	31.2660i	−0.305110	+	0.0483246i	0.00200241	+	0.999998i	$0.499363\pi$
$648$		0			0
$649$		−	249.652i		−	0.384671i
$650$		0			0
$651$	154.716			0.237659
$652$		0			0
$653$	123.333	+	778.694i	0.188871	+	1.19249i	0.881850	+	0.471529i	$0.156298\pi$
$653$	123.333	+	778.694i	0.188871	+	1.19249i	−0.692979	+	0.720958i	$0.743702\pi$
$654$		0			0
$655$	177.739	−	318.038i	0.271357	−	0.485554i
$656$		0			0
$657$	561.155	−	561.155i	0.854117	−	0.854117i
$658$		0			0
$659$	−119.459	+	38.8147i	−0.181274	+	0.0588994i	−0.398247	−	0.917278i	$-0.630381\pi$
$659$	−119.459	+	38.8147i	−0.181274	+	0.0588994i	0.216974	+	0.976177i	$0.430381\pi$
$660$		0			0
$661$	−358.442	+	1103.17i	−0.542272	+	1.66894i	0.185118	+	0.982716i	$0.440733\pi$
$661$	−358.442	+	1103.17i	−0.542272	+	1.66894i	−0.727390	+	0.686224i	$0.759267\pi$
$662$		0			0
$663$	−908.437	+	1782.91i	−1.37019	+	2.68915i
$664$		0			0
$665$	−657.692	+	186.119i	−0.989011	+	0.279878i
$666$		0			0
$667$	−0.523399	+	3.30461i	−0.000784706	+	0.00495444i
$668$		0			0
$669$	640.991	+	882.248i	0.958133	+	1.31876i
$670$		0			0
$671$	−639.203	−	464.408i	−0.952612	−	0.692113i
$672$		0			0
$673$	210.697	−	107.355i	0.313071	−	0.159517i	−0.290394	−	0.956907i	$-0.593786\pi$
$673$	210.697	−	107.355i	0.313071	−	0.159517i	0.603465	+	0.797390i	$0.293786\pi$
$674$		0			0
$675$	−298.495	−	71.1021i	−0.442215	−	0.105336i
$676$		0			0
$677$	−349.807	−	686.535i	−0.516701	−	1.01408i	−0.991018	−	0.133729i	$-0.957305\pi$
$677$	−349.807	−	686.535i	−0.516701	−	1.01408i	0.474317	−	0.880354i	$-0.342695\pi$
$678$		0			0
$679$	405.451	−	558.056i	0.597130	−	0.821879i
$680$		0			0
$681$	453.890	−	329.770i	0.666504	−	0.484244i
$682$		0			0
$683$	442.682	+	70.1140i	0.648144	+	0.102656i	0.471846	−	0.881681i	$-0.343588\pi$
$683$	442.682	+	70.1140i	0.648144	+	0.102656i	0.176298	+	0.984337i	$0.443588\pi$
$684$		0			0
$685$	−790.101	−	30.3408i	−1.15343	−	0.0442931i
$686$		0			0
$687$	−1040.41	−	530.116i	−1.51443	−	0.771639i
$688$		0			0
$689$	−1835.25	−	596.309i	−2.66365	−	0.865471i
$690$		0			0
$691$	316.495	+	974.071i	0.458024	+	1.40965i	0.867547	+	0.497355i	$0.165695\pi$
$691$	316.495	+	974.071i	0.458024	+	1.40965i	−0.409523	+	0.912300i	$0.634305\pi$
$692$		0			0
$693$	480.300	+	480.300i	0.693074	+	0.693074i
$694$		0			0
$695$	−585.565	+	69.8333i	−0.842539	+	0.100480i
$696$		0			0
$697$	−465.606	+	73.7448i	−0.668015	+	0.105803i
$698$		0			0
$699$			47.3260i			0.0677054i
$700$		0			0
$701$	−1352.58			−1.92951			−0.964753	−	0.263156i	$-0.915237\pi$
$701$	−1352.58			−1.92951			−0.964753	+	0.263156i	$0.915237\pi$
$702$		0			0
$703$	24.8226	+	156.724i	0.0353095	+	0.222936i
$704$		0			0
$705$	−426.696	−	460.776i	−0.605243	−	0.653583i
$706$		0			0
$707$	−215.989	+	215.989i	−0.305501	+	0.305501i
$708$		0			0
$709$	−131.683	+	42.7865i	−0.185731	+	0.0603477i	−0.400406	−	0.916338i	$-0.631131\pi$
$709$	−131.683	+	42.7865i	−0.185731	+	0.0603477i	0.214675	+	0.976686i	$0.431131\pi$
$710$		0			0
$711$	442.159	−	1360.82i	0.621883	−	1.91396i
$712$		0			0
$713$	−1.62885	+	3.19680i	−0.00228451	+	0.00448359i
$714$		0			0
$715$	−1189.51	−	437.635i	−1.66365	−	0.612077i
$716$		0			0
$717$	52.1263	−	329.112i	0.0727005	−	0.459013i
$718$		0			0
$719$	−165.133	−	227.286i	−0.229670	−	0.316114i	0.678592	−	0.734515i	$-0.262590\pi$
$719$	−165.133	−	227.286i	−0.229670	−	0.316114i	−0.908262	+	0.418402i	$0.862590\pi$
$720$		0			0
$721$	294.959	+	214.301i	0.409098	+	0.297227i
$722$		0			0
$723$	266.205	−	135.638i	0.368196	−	0.187605i
$724$		0			0
$725$	36.7559	+	151.911i	0.0506978	+	0.209532i
$726$		0			0
$727$	83.8826	+	164.629i	0.115382	+	0.226449i	0.941474	−	0.337085i	$-0.109441\pi$
$727$	83.8826	+	164.629i	0.115382	+	0.226449i	−0.826092	+	0.563535i	$0.809441\pi$
$728$		0			0
$729$	635.343	−	874.475i	0.871527	−	1.19955i
$730$		0			0
$731$	1016.63	−	738.623i	1.39073	−	1.01043i
$732$		0			0
$733$	91.4234	+	14.4800i	0.124725	+	0.0197545i	0.218485	−	0.975840i	$-0.429889\pi$
$733$	91.4234	+	14.4800i	0.124725	+	0.0197545i	−0.0937599	+	0.995595i	$0.529889\pi$
$734$		0			0
$735$	439.830	−	294.450i	0.598408	−	0.400612i
$736$		0			0
$737$	−941.600	−	479.769i	−1.27761	−	0.650975i
$738$		0			0
$739$	−146.136	−	47.4824i	−0.197748	−	0.0642523i	0.208468	−	0.978029i	$-0.433152\pi$
$739$	−146.136	−	47.4824i	−0.197748	−	0.0642523i	−0.406217	+	0.913777i	$0.633152\pi$
$740$		0			0
$741$	−839.015	−	2582.22i	−1.13227	−	3.48478i
$742$		0			0
$743$	379.385	+	379.385i	0.510613	+	0.510613i	0.914714	−	0.404101i	$-0.132416\pi$
$743$	379.385	+	379.385i	0.510613	+	0.510613i	−0.404101	+	0.914714i	$0.632416\pi$
$744$		0			0
$745$	−267.509	−	578.920i	−0.359073	−	0.777074i
$746$		0			0
$747$	712.368	−	112.828i	0.953638	−	0.151041i
$748$		0			0
$749$			66.1849i			0.0883644i
$750$		0			0
$751$	−1091.70			−1.45366			−0.726829	−	0.686819i	$-0.759007\pi$
$751$	−1091.70			−1.45366			−0.726829	+	0.686819i	$0.759007\pi$
$752$		0			0
$753$	33.5654	+	211.924i	0.0445756	+	0.281439i
$754$		0			0
$755$	−407.616	+	188.352i	−0.539888	+	0.249473i
$756$		0			0
$757$	167.215	−	167.215i	0.220892	−	0.220892i	−0.587982	−	0.808874i	$-0.700077\pi$
$757$	167.215	−	167.215i	0.220892	−	0.220892i	0.808874	+	0.587982i	$0.200077\pi$
$758$		0			0
$759$	−26.5065	+	8.61250i	−0.0349230	+	0.0113472i
$760$		0			0
$761$	274.175	−	843.824i	0.360283	−	1.10884i	−0.592600	−	0.805497i	$-0.701899\pi$
$761$	274.175	−	843.824i	0.360283	−	1.10884i	0.952883	−	0.303339i	$-0.0981015\pi$
$762$		0			0
$763$	−11.8598	+	23.2761i	−0.0155436	+	0.0305060i
$764$		0			0
$765$	646.246	+	965.320i	0.844767	+	1.26186i
$766$		0			0
$767$	−75.5543	+	477.031i	−0.0985062	+	0.621944i
$768$		0			0
$769$	259.529	+	357.212i	0.337489	+	0.464514i	0.943706	−	0.330785i	$-0.107314\pi$
$769$	259.529	+	357.212i	0.337489	+	0.464514i	−0.606217	+	0.795300i	$0.707314\pi$
$770$		0			0
$771$	−443.156	−	321.971i	−0.574780	−	0.417602i
$772$		0			0
$773$	−674.908	+	343.883i	−0.873102	+	0.444868i	−0.832317	−	0.554300i	$-0.812986\pi$
$773$	−674.908	+	343.883i	−0.873102	+	0.444868i	−0.0407854	+	0.999168i	$0.512986\pi$
$774$		0			0
$775$	−12.8532	+	167.108i	−0.0165848	+	0.215623i
$776$		0			0
$777$	61.6898	+	121.073i	0.0793948	+	0.155821i
$778$		0			0
$779$	375.974	−	517.483i	0.482636	−	0.664292i
$780$		0			0
$781$	145.700	−	105.857i	0.186555	−	0.135540i
$782$		0			0
$783$	75.7886	+	12.0037i	0.0967926	+	0.0153304i
$784$		0			0
$785$	143.186	−	389.186i	0.182402	−	0.495778i
$786$		0			0
$787$	−987.772	−	503.295i	−1.25511	−	0.639511i	−0.305276	−	0.952264i	$-0.598749\pi$
$787$	−987.772	−	503.295i	−1.25511	−	0.639511i	−0.949834	+	0.312753i	$0.898749\pi$
$788$		0			0
$789$	−1500.09	−	487.409i	−1.90126	−	0.617756i
$790$		0			0
$791$	−165.685	−	509.926i	−0.209463	−	0.644660i
$792$		0			0
$793$	1080.83	+	1080.83i	1.36297	+	1.36297i
$794$		0			0
$795$	−1454.37	+	1346.80i	−1.82939	+	1.69408i
$796$		0			0
$797$	292.105	−	46.2648i	0.366505	−	0.0580487i	0.0295343	−	0.999564i	$-0.490598\pi$
$797$	292.105	−	46.2648i	0.366505	−	0.0580487i	0.336971	+	0.941515i	$0.390598\pi$
$798$		0			0
$799$			548.320i			0.686257i
$800$		0			0
$801$	−931.972			−1.16351
$802$		0			0
$803$	−121.482	−	767.004i	−0.151285	−	0.955173i
$804$		0			0
$805$	−1.60740	−	13.4783i	−0.00199677	−	0.0167433i
$806$		0			0
$807$	627.491	−	627.491i	0.777560	−	0.777560i
$808$		0			0
$809$	−173.388	+	56.3370i	−0.214323	+	0.0696378i	−0.414211	−	0.910181i	$-0.635942\pi$
$809$	−173.388	+	56.3370i	−0.214323	+	0.0696378i	0.199887	+	0.979819i	$0.435942\pi$
$810$		0			0
$811$	−368.062	+	1132.78i	−0.453837	+	1.39677i	0.418659	+	0.908144i	$0.362500\pi$
$811$	−368.062	+	1132.78i	−0.453837	+	1.39677i	−0.872495	+	0.488622i	$0.837500\pi$
$812$		0			0
$813$	754.771	−	1481.32i	0.928377	−	1.82204i
$814$		0			0
$815$	−36.5795	+	952.564i	−0.0448828	+	1.16879i
$816$		0			0
$817$	−266.733	+	1684.08i	−0.326478	+	2.06130i
$818$		0			0
$819$	−772.393	−	1063.11i	−0.943093	−	1.29806i
$820$		0			0
$821$	388.310	+	282.124i	0.472972	+	0.343634i	0.798598	−	0.601864i	$-0.205575\pi$
$821$	388.310	+	282.124i	0.472972	+	0.343634i	−0.325626	+	0.945499i	$0.605575\pi$
$822$		0			0
$823$	156.554	−	79.7683i	0.190224	−	0.0969238i	−0.356285	−	0.934377i	$-0.615957\pi$
$823$	156.554	−	79.7683i	0.190224	−	0.0969238i	0.546508	+	0.837454i	$0.315957\pi$
$824$		0			0
$825$	−988.496	+	847.295i	−1.19818	+	1.02702i
$826$		0			0
$827$	73.1995	+	143.662i	0.0885121	+	0.173715i	0.931019	−	0.364971i	$-0.118921\pi$
$827$	73.1995	+	143.662i	0.0885121	+	0.173715i	−0.842507	+	0.538686i	$0.818921\pi$
$828$		0			0
$829$	920.375	−	1266.79i	1.11022	−	1.52809i	0.289136	−	0.957288i	$-0.406632\pi$
$829$	920.375	−	1266.79i	1.11022	−	1.52809i	0.821087	−	0.570803i	$-0.193368\pi$
$830$		0			0
$831$	373.420	−	271.306i	0.449363	−	0.326481i
$832$		0			0
$833$	−456.446	−	72.2940i	−0.547955	−	0.0867875i
$834$		0			0
$835$	182.671	+	645.510i	0.218768	+	0.773066i
$836$		0			0
$837$	73.3162	+	37.3565i	0.0875940	+	0.0446314i
$838$		0			0
$839$	1047.63	+	340.396i	1.24867	+	0.405717i	0.857443	−	0.514579i	$-0.172052\pi$
$839$	1047.63	+	340.396i	1.24867	+	0.405717i	0.391224	+	0.920295i	$0.372052\pi$
$840$		0			0
$841$	247.805	+	762.667i	0.294656	+	0.906857i
$842$		0			0
$843$	1288.36	+	1288.36i	1.52830	+	1.52830i
$844$		0			0
$845$	1402.83	+	783.988i	1.66016	+	0.927797i
$846$		0			0
$847$	50.2558	−	7.95974i	0.0593339	−	0.00939757i
$848$		0			0
$849$			1134.77i			1.33660i
$850$		0			0
$851$	−3.15113			−0.00370285
$852$		0			0
$853$	69.4424	+	438.442i	0.0814096	+	0.514000i	0.994371	+	0.105954i	$0.0337897\pi$
$853$	69.4424	+	438.442i	0.0814096	+	0.514000i	−0.912961	+	0.408046i	$0.866210\pi$
$854$		0			0
$855$	−1546.23	−	306.137i	−1.80845	−	0.358055i
$856$		0			0
$857$	155.970	−	155.970i	0.181996	−	0.181996i	−0.610229	−	0.792225i	$-0.708923\pi$
$857$	155.970	−	155.970i	0.181996	−	0.181996i	0.792225	+	0.610229i	$0.208923\pi$
$858$		0			0
$859$	−391.117	+	127.082i	−0.455316	+	0.147941i	−0.527691	−	0.849436i	$-0.676942\pi$
$859$	−391.117	+	127.082i	−0.455316	+	0.147941i	0.0723749	+	0.997377i	$0.476942\pi$
$860$		0			0
$861$	169.267	−	520.950i	0.196593	−	0.605053i
$862$		0			0
$863$	−140.246	+	275.247i	−0.162509	+	0.318943i	−0.957874	−	0.287189i	$-0.907279\pi$
$863$	−140.246	+	275.247i	−0.162509	+	0.318943i	0.795365	+	0.606131i	$0.207279\pi$
$864$		0			0
$865$	−385.535	+	489.943i	−0.445705	+	0.566408i
$866$		0			0
$867$	75.0621	−	473.924i	0.0865769	−	0.546625i
$868$		0			0
$869$	−822.990	−	1132.75i	−0.947054	−	1.30351i
$870$		0			0
$871$	1654.00	+	1201.70i	1.89897	+	1.37968i
$872$		0			0
$873$	1417.33	−	722.168i	1.62352	−	0.827225i
$874$		0			0
$875$	−311.298	−	552.406i	−0.355769	−	0.631321i
$876$		0			0
$877$	160.555	+	315.106i	0.183073	+	0.359300i	0.964244	−	0.265016i	$-0.0853774\pi$
$877$	160.555	+	315.106i	0.183073	+	0.359300i	−0.781171	+	0.624317i	$0.785377\pi$
$878$		0			0
$879$	1338.71	−	1842.57i	1.52299	−	2.09622i
$880$		0			0
$881$	1399.81	−	1017.02i	1.58889	−	1.15440i	0.683387	−	0.730056i	$-0.260506\pi$
$881$	1399.81	−	1017.02i	1.58889	−	1.15440i	0.905503	−	0.424340i	$-0.139494\pi$
$882$		0			0
$883$	1262.49	+	199.959i	1.42978	+	0.226454i	0.822830	−	0.568288i	$-0.192394\pi$
$883$	1262.49	+	199.959i	1.42978	+	0.226454i	0.606947	+	0.794742i	$0.292394\pi$
$884$		0			0
$885$	389.878	+	306.795i	0.440541	+	0.346661i
$886$		0			0
$887$	−1492.83	−	760.633i	−1.68301	−	0.857534i	−0.990721	−	0.135909i	$-0.956605\pi$
$887$	−1492.83	−	760.633i	−1.68301	−	0.857534i	−0.692284	−	0.721625i	$-0.743395\pi$
$888$		0			0
$889$	−296.119	−	96.2150i	−0.333092	−	0.108228i
$890$		0			0
$891$	−174.886	−	538.244i	−0.196281	−	0.604090i
$892$		0			0
$893$	−526.088	−	526.088i	−0.589124	−	0.589124i
$894$		0			0
$895$	170.750	−	862.418i	0.190782	−	0.963595i
$896$		0			0
$897$	53.2548	−	8.43473i	0.0593699	−	0.00940327i
$898$		0			0
$899$		−	41.9122i		−	0.0466209i
$900$		0			0
$901$	1730.68			1.92085
$902$		0			0
$903$	228.416	+	1442.16i	0.252953	+	1.59708i
$904$		0			0
$905$	−12.1102	+	21.6693i	−0.0133814	+	0.0239440i
$906$		0			0
$907$	−324.628	+	324.628i	−0.357914	+	0.357914i	−0.863044	−	0.505129i	$-0.831445\pi$
$907$	−324.628	+	324.628i	−0.357914	+	0.357914i	0.505129	+	0.863044i	$0.331445\pi$
$908$		0			0
$909$	−669.922	+	217.671i	−0.736988	+	0.239462i
$910$		0			0
$911$	−184.738	+	568.566i	−0.202786	+	0.624112i	0.797011	+	0.603965i	$0.206413\pi$
$911$	−184.738	+	568.566i	−0.202786	+	0.624112i	−0.999797	+	0.0201467i	$0.993587\pi$
$912$		0			0
$913$	320.414	−	628.848i	0.350946	−	0.688771i
$914$		0			0
$915$	1510.77	−	427.530i	1.65112	−	0.467246i
$916$		0			0
$917$	57.8225	−	365.077i	0.0630561	−	0.398121i
$918$		0			0
$919$	432.747	+	595.625i	0.470889	+	0.648123i	0.976722	−	0.214508i	$-0.0688149\pi$
$919$	432.747	+	595.625i	0.470889	+	0.648123i	−0.505833	+	0.862631i	$0.668815\pi$
$920$		0			0
$921$	1223.61	+	889.004i	1.32857	+	0.965260i
$922$		0			0
$923$	−310.437	+	158.176i	−0.336335	+	0.171371i
$924$		0			0
$925$	−135.895	+	56.5725i	−0.146914	+	0.0611594i
$926$		0			0
$927$	381.701	+	749.130i	0.411759	+	0.808122i
$928$		0			0
$929$	−469.300	+	645.936i	−0.505167	+	0.695303i	−0.983095	−	0.183096i	$-0.941388\pi$
$929$	−469.300	+	645.936i	−0.505167	+	0.695303i	0.477928	+	0.878399i	$0.341388\pi$
$930$		0			0
$931$	507.303	−	368.577i	0.544901	−	0.395894i
$932$		0			0
$933$	−1068.56	−	169.244i	−1.14530	−	0.181398i
$934$		0			0
$935$	1135.91	+	43.6201i	1.21487	+	0.0466526i
$936$		0			0
$937$	−1258.08	−	641.022i	−1.34266	−	0.684122i	−0.372833	−	0.927898i	$-0.621614\pi$
$937$	−1258.08	−	641.022i	−1.34266	−	0.684122i	−0.969831	+	0.243776i	$0.921614\pi$
$938$		0			0
$939$	−163.335	−	53.0706i	−0.173945	−	0.0565182i
$940$		0			0
$941$	−135.437	−	416.831i	−0.143928	−	0.442966i	0.852943	−	0.522004i	$-0.174815\pi$
$941$	−135.437	−	416.831i	−0.143928	−	0.442966i	−0.996872	+	0.0790378i	$0.974815\pi$
$942$		0			0
$943$	8.98204	+	8.98204i	0.00952496	+	0.00952496i
$944$		0			0
$945$	−309.115	+	36.8644i	−0.327105	+	0.0390099i
$946$		0			0
$947$	941.730	−	149.155i	0.994435	−	0.157503i	0.362051	−	0.932158i	$-0.382077\pi$
$947$	941.730	−	149.155i	0.994435	−	0.157503i	0.632384	+	0.774655i	$0.282077\pi$
$948$		0			0
$949$			1502.35i			1.58308i
$950$		0			0
$951$	881.886			0.927325
$952$		0			0
$953$	7.52363	+	47.5024i	0.00789468	+	0.0498451i	0.991321	−	0.131462i	$-0.0419672\pi$
$953$	7.52363	+	47.5024i	0.00789468	+	0.0498451i	−0.983427	+	0.181307i	$0.941967\pi$
$954$		0			0
$955$	−632.807	−	683.349i	−0.662625	−	0.715548i
$956$		0			0
$957$	230.217	−	230.217i	0.240561	−	0.240561i
$958$		0			0
$959$	−762.911	+	247.885i	−0.795528	+	0.258483i
$960$		0			0
$961$	−283.077	+	871.221i	−0.294565	+	0.906577i
$962$		0			0
$963$	−69.2910	+	135.991i	−0.0719533	+	0.141216i
$964$		0			0
$965$	−994.977	−	366.063i	−1.03106	−	0.379340i
$966$		0			0
$967$	157.289	−	993.084i	0.162657	−	1.02697i	−0.762389	−	0.647119i	$-0.775974\pi$
$967$	157.289	−	993.084i	0.162657	−	1.02697i	0.925046	−	0.379856i	$-0.124026\pi$
$968$		0			0
$969$	1431.31	+	1970.03i	1.47710	+	2.03306i
$970$		0			0
$971$	−722.828	−	525.165i	−0.744416	−	0.540850i	0.149675	−	0.988735i	$-0.452177\pi$
$971$	−722.828	−	525.165i	−0.744416	−	0.540850i	−0.894091	+	0.447885i	$0.852177\pi$
$972$		0			0
$973$	−533.074	+	271.615i	−0.547866	+	0.279152i
$974$		0			0
$975$	2145.23	−	1319.84i	2.20024	−	1.35368i
$976$		0			0
$977$	319.212	+	626.489i	0.326727	+	0.641237i	0.994685	−	0.102961i	$-0.0328317\pi$
$977$	319.212	+	626.489i	0.326727	+	0.641237i	−0.667959	+	0.744198i	$0.732832\pi$
$978$		0			0
$979$	−536.046	+	737.804i	−0.547544	+	0.753630i
$980$		0			0
$981$	−48.7369	+	35.4094i	−0.0496809	+	0.0360953i
$982$		0			0
$983$	−1496.27	−	236.985i	−1.52214	−	0.241084i	−0.661364	−	0.750065i	$-0.730022\pi$
$983$	−1496.27	−	236.985i	−1.52214	−	0.241084i	−0.860777	+	0.508981i	$0.830022\pi$
$984$		0			0
$985$	1252.81	−	838.709i	1.27189	−	0.851481i
$986$		0			0
$987$	−567.683	−	289.249i	−0.575160	−	0.293058i
$988$		0			0
$989$	−32.2034	−	10.4635i	−0.0325615	−	0.0105799i
$990$		0			0
$991$	−349.037	−	1074.23i	−0.352207	−	1.08398i	−0.957611	−	0.288063i	$-0.906989\pi$
$991$	−349.037	−	1074.23i	−0.352207	−	1.08398i	0.605404	−	0.795918i	$-0.293011\pi$
$992$		0			0
$993$	−821.669	−	821.669i	−0.827461	−	0.827461i
$994$		0			0
$995$	288.654	+	624.679i	0.290104	+	0.627819i
$996$		0			0
$997$	1358.50	−	215.165i	1.36259	−	0.215813i	0.568033	−	0.823006i	$-0.307705\pi$
$997$	1358.50	−	215.165i	1.36259	−	0.215813i	0.794554	+	0.607194i	$0.207705\pi$
$998$		0			0
$999$			72.2687i			0.0723410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.a.353.2		16
4.3	odd	2		50.3.f.a.3.1	✓	16
20.3	even	4		250.3.f.c.7.2		16
20.7	even	4		250.3.f.a.7.1		16
20.19	odd	2		250.3.f.b.243.2		16
25.17	odd	20	inner	400.3.bg.a.17.2		16
100.19	odd	10		250.3.f.c.143.2		16
100.31	odd	10		250.3.f.a.143.1		16
100.67	even	20		50.3.f.a.17.1	yes	16
100.83	even	20		250.3.f.b.107.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.3.1	✓	16	4.3	odd	2
50.3.f.a.17.1	yes	16	100.67	even	20
250.3.f.a.7.1		16	20.7	even	4
250.3.f.a.143.1		16	100.31	odd	10
250.3.f.b.107.2		16	100.83	even	20
250.3.f.b.243.2		16	20.19	odd	2
250.3.f.c.7.2		16	20.3	even	4
250.3.f.c.143.2		16	100.19	odd	10
400.3.bg.a.17.2		16	25.17	odd	20	inner
400.3.bg.a.353.2		16	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.711697 + 4.49348i) q^{3} +(-4.53886 + 2.09733i) q^{5} +(-3.58690 + 3.58690i) q^{7} +(-11.1253 + 3.61484i) q^{9} +O(q^{10})\)	\(q+(0.711697 + 4.49348i) q^{3} +(-4.53886 + 2.09733i) q^{5} +(-3.58690 + 3.58690i) q^{7} +(-11.1253 + 3.61484i) q^{9} +(-3.53728 + 10.8866i) q^{11} +(10.0537 - 19.7315i) q^{13} +(-12.6546 - 18.9026i) q^{15} +(-3.10698 + 19.6167i) q^{17} +(-15.8404 - 21.8024i) q^{19} +(-18.6705 - 13.5649i) q^{21} +(0.476846 - 0.242965i) q^{23} +(16.2024 - 19.0389i) q^{25} +(-5.57222 - 10.9361i) q^{27} +(-3.67470 + 5.05779i) q^{29} +(-5.42369 + 3.94054i) q^{31} +(-51.4362 - 8.14670i) q^{33} +(8.75753 - 23.8034i) q^{35} +(-5.24626 - 2.67310i) q^{37} +(95.8181 + 31.1332i) q^{39} +(7.33457 + 22.5735i) q^{41} +(-44.7386 - 44.7386i) q^{43} +(42.9147 - 39.7407i) q^{45} +(27.2676 - 4.31877i) q^{47} +23.2682i q^{49} -90.3585 q^{51} +(-13.6315 - 86.0658i) q^{53} +(-6.77762 - 56.8316i) q^{55} +(86.6950 - 86.6950i) q^{57} +(-20.7422 + 6.73954i) q^{59} +(-21.3293 + 65.6449i) q^{61} +(26.9394 - 52.8715i) q^{63} +(-4.24886 + 110.644i) q^{65} +(-14.4421 + 91.1840i) q^{67} +(1.43113 + 1.96978i) q^{69} +(-12.7283 - 9.24768i) q^{71} +(-60.4466 + 30.7991i) q^{73} +(97.0823 + 59.2553i) q^{75} +(-26.3614 - 51.7371i) q^{77} +(-71.8966 + 98.9571i) q^{79} +(-39.9985 + 29.0606i) q^{81} +(-60.8973 - 9.64518i) q^{83} +(-27.0406 - 95.5539i) q^{85} +(-25.3423 - 12.9126i) q^{87} +(75.7710 + 24.6195i) q^{89} +(34.7133 + 106.837i) q^{91} +(-21.5668 - 21.5668i) q^{93} +(117.624 + 65.7354i) q^{95} +(-134.309 + 21.2725i) q^{97} -133.904i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9	\( 16 q - 2 q^{3} + 2 q^{7} - 40 q^{9} - 32 q^{11} - 8 q^{13} - 62 q^{17} - 30 q^{19} - 68 q^{21} + 18 q^{23} + 70 q^{25} + 40 q^{27} + 100 q^{29} - 132 q^{31} - 36 q^{33} - 150 q^{35} + 138 q^{37} + 320 q^{39} - 88 q^{41} + 78 q^{43} - 20 q^{45} + 22 q^{47} + 168 q^{51} + 182 q^{53} - 280 q^{55} + 280 q^{57} + 350 q^{59} + 372 q^{61} - 22 q^{63} - 910 q^{65} + 112 q^{67} - 30 q^{69} - 122 q^{71} - 248 q^{73} + 80 q^{75} + 16 q^{77} - 760 q^{79} - 144 q^{81} - 132 q^{83} - 30 q^{85} - 770 q^{87} + 550 q^{89} + 798 q^{91} + 54 q^{93} - 40 q^{95} - 292 q^{97}+O(q^{100}) \) 16 * q - 2 * q^3 + 2 * q^7 - 40 * q^9 - 32 * q^11 - 8 * q^13 - 62 * q^17 - 30 * q^19 - 68 * q^21 + 18 * q^23 + 70 * q^25 + 40 * q^27 + 100 * q^29 - 132 * q^31 - 36 * q^33 - 150 * q^35 + 138 * q^37 + 320 * q^39 - 88 * q^41 + 78 * q^43 - 20 * q^45 + 22 * q^47 + 168 * q^51 + 182 * q^53 - 280 * q^55 + 280 * q^57 + 350 * q^59 + 372 * q^61 - 22 * q^63 - 910 * q^65 + 112 * q^67 - 30 * q^69 - 122 * q^71 - 248 * q^73 + 80 * q^75 + 16 * q^77 - 760 * q^79 - 144 * q^81 - 132 * q^83 - 30 * q^85 - 770 * q^87 + 550 * q^89 + 798 * q^91 + 54 * q^93 - 40 * q^95 - 292 * q^97

Introduction

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