LMFDB - Embedded newform 400.3.bg.c.97.4

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:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	400.97
Dual form			400.3.bg.c.33.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.42692 - 0.701156i) q^{3} +(1.95091 + 4.60369i) q^{5} +(4.77540 + 4.77540i) q^{7} +(10.5465 - 3.42677i) q^{9} +O(q^{10})$	\(q+(4.42692 - 0.701156i) q^{3} +(1.95091 + 4.60369i) q^{5} +(4.77540 + 4.77540i) q^{7} +(10.5465 - 3.42677i) q^{9} +(-3.84423 + 11.8313i) q^{11} +(-1.05261 - 0.536333i) q^{13} +(11.8644 + 19.0123i) q^{15} +(-4.59461 - 0.727715i) q^{17} +(-12.8564 - 17.6953i) q^{19} +(24.4886 + 17.7920i) q^{21} +(4.03970 + 7.92835i) q^{23} +(-17.3879 + 17.9628i) q^{25} +(8.34369 - 4.25132i) q^{27} +(5.42781 - 7.47074i) q^{29} +(25.3215 - 18.3971i) q^{31} +(-8.72252 + 55.0718i) q^{33} +(-12.6681 + 31.3008i) q^{35} +(6.47182 - 12.7017i) q^{37} +(-5.03589 - 1.63626i) q^{39} +(-16.8825 - 51.9589i) q^{41} +(36.1728 - 36.1728i) q^{43} +(36.3511 + 41.8676i) q^{45} +(0.703158 + 4.43956i) q^{47} -3.39110i q^{49} -20.8502 q^{51} +(69.2402 - 10.9666i) q^{53} +(-61.9675 + 5.38424i) q^{55} +(-69.3215 - 69.3215i) q^{57} +(67.9339 - 22.0730i) q^{59} +(15.0860 - 46.4300i) q^{61} +(66.7281 + 33.9997i) q^{63} +(0.415555 - 5.89224i) q^{65} +(-79.5063 - 12.5926i) q^{67} +(23.4424 + 32.2657i) q^{69} +(34.9284 + 25.3769i) q^{71} +(27.3286 + 53.6354i) q^{73} +(-64.3801 + 91.7115i) q^{75} +(-74.8571 + 38.1416i) q^{77} +(27.4839 - 37.8283i) q^{79} +(-46.7867 + 33.9925i) q^{81} +(-17.1166 + 108.070i) q^{83} +(-5.61351 - 22.5719i) q^{85} +(18.7904 - 36.8782i) q^{87} +(63.0322 + 20.4804i) q^{89} +(-2.46544 - 7.58786i) q^{91} +(99.1969 - 99.1969i) q^{93} +(56.3820 - 93.7088i) q^{95} +(8.99168 + 56.7712i) q^{97} +137.953i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9}+O(q^{10}) $ 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9	$ 32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9} + 6 q^{11} - 10 q^{13} + 10 q^{15} + 60 q^{17} - 90 q^{19} - 6 q^{21} - 10 q^{23} - 40 q^{25} + 100 q^{27} - 110 q^{29} + 6 q^{31} - 190 q^{33} + 120 q^{35} + 50 q^{37} - 390 q^{39} - 86 q^{41} - 230 q^{43} + 310 q^{45} - 70 q^{47} + 16 q^{51} - 190 q^{53} + 250 q^{55} - 650 q^{57} + 260 q^{59} + 114 q^{61} + 20 q^{63} + 360 q^{65} - 270 q^{67} + 340 q^{69} + 66 q^{71} + 30 q^{73} + 90 q^{75} - 250 q^{77} + 210 q^{79} + 62 q^{81} + 600 q^{85} - 300 q^{87} - 10 q^{89} + 6 q^{91} + 520 q^{93} - 310 q^{95} + 270 q^{97}+O(q^{100}) $ 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9 + 6 * q^11 - 10 * q^13 + 10 * q^15 + 60 * q^17 - 90 * q^19 - 6 * q^21 - 10 * q^23 - 40 * q^25 + 100 * q^27 - 110 * q^29 + 6 * q^31 - 190 * q^33 + 120 * q^35 + 50 * q^37 - 390 * q^39 - 86 * q^41 - 230 * q^43 + 310 * q^45 - 70 * q^47 + 16 * q^51 - 190 * q^53 + 250 * q^55 - 650 * q^57 + 260 * q^59 + 114 * q^61 + 20 * q^63 + 360 * q^65 - 270 * q^67 + 340 * q^69 + 66 * q^71 + 30 * q^73 + 90 * q^75 - 250 * q^77 + 210 * q^79 + 62 * q^81 + 600 * q^85 - 300 * q^87 - 10 * q^89 + 6 * q^91 + 520 * q^93 - 310 * q^95 + 270 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$	$1$

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
$3$	4.42692	−	0.701156i	1.47564	−	0.233719i	0.633822	−	0.773479i	$-0.281485\pi$
$3$	4.42692	−	0.701156i	1.47564	−	0.233719i	0.841819	+	0.539760i	$0.181485\pi$
$4$		0			0
$5$	1.95091	+	4.60369i	0.390182	+	0.920738i
$5$	1.95091	+	4.60369i	0.390182	+	0.920738i
$6$		0			0
$7$	4.77540	+	4.77540i	0.682200	+	0.682200i	0.960496	−	0.278295i	$-0.0897694\pi$
$7$	4.77540	+	4.77540i	0.682200	+	0.682200i	−0.278295	+	0.960496i	$0.589769\pi$
$8$		0			0
$9$	10.5465	−	3.42677i	1.17184	−	0.380753i
$10$		0			0
$11$	−3.84423	+	11.8313i	−0.349476	+	1.07558i	0.609668	+	0.792657i	$0.291303\pi$
$11$	−3.84423	+	11.8313i	−0.349476	+	1.07558i	−0.959144	+	0.282919i	$0.908697\pi$
$12$		0			0
$13$	−1.05261	−	0.536333i	−0.0809703	−	0.0412564i	0.413036	−	0.910714i	$-0.364468\pi$
$13$	−1.05261	−	0.536333i	−0.0809703	−	0.0412564i	−0.494007	+	0.869458i	$0.664468\pi$
$14$		0			0
$15$	11.8644	+	19.0123i	0.790963	+	1.26749i
$16$		0			0
$17$	−4.59461	−	0.727715i	−0.270271	−	0.0428067i	0.0198278	−	0.999803i	$-0.493688\pi$
$17$	−4.59461	−	0.727715i	−0.270271	−	0.0428067i	−0.290099	+	0.956997i	$0.593688\pi$
$18$		0			0
$19$	−12.8564	−	17.6953i	−0.676652	−	0.931332i	0.323235	−	0.946319i	$-0.395229\pi$
$19$	−12.8564	−	17.6953i	−0.676652	−	0.931332i	−0.999888	+	0.0149865i	$0.995229\pi$
$20$		0			0
$21$	24.4886	+	17.7920i	1.16613	+	0.847240i
$22$		0			0
$23$	4.03970	+	7.92835i	0.175639	+	0.344711i	0.961997	−	0.273060i	$-0.0880358\pi$
$23$	4.03970	+	7.92835i	0.175639	+	0.344711i	−0.786358	+	0.617771i	$0.788036\pi$
$24$		0			0
$25$	−17.3879	+	17.9628i	−0.695515	+	0.718511i
$26$		0			0
$27$	8.34369	−	4.25132i	0.309025	−	0.157456i
$28$		0			0
$29$	5.42781	−	7.47074i	0.187166	−	0.257612i	−0.705114	−	0.709094i	$-0.749104\pi$
$29$	5.42781	−	7.47074i	0.187166	−	0.257612i	0.892280	+	0.451482i	$0.149104\pi$
$30$		0			0
$31$	25.3215	−	18.3971i	0.816821	−	0.593456i	−0.0989788	−	0.995090i	$-0.531558\pi$
$31$	25.3215	−	18.3971i	0.816821	−	0.593456i	0.915800	+	0.401634i	$0.131558\pi$
$32$		0			0
$33$	−8.72252	+	55.0718i	−0.264319	+	1.66884i
$34$		0			0
$35$	−12.6681	+	31.3008i	−0.361945	+	0.894310i
$36$		0			0
$37$	6.47182	−	12.7017i	0.174914	−	0.343288i	−0.786860	−	0.617131i	$-0.788295\pi$
$37$	6.47182	−	12.7017i	0.174914	−	0.343288i	0.961774	+	0.273843i	$0.0882948\pi$
$38$		0			0
$39$	−5.03589	−	1.63626i	−0.129125	−	0.0419554i
$40$		0			0
$41$	−16.8825	−	51.9589i	−0.411767	−	1.26729i	−0.915111	−	0.403203i	$-0.867897\pi$
$41$	−16.8825	−	51.9589i	−0.411767	−	1.26729i	0.503343	−	0.864086i	$-0.332103\pi$
$42$		0			0
$43$	36.1728	−	36.1728i	0.841228	−	0.841228i	−0.147791	−	0.989019i	$-0.547216\pi$
$43$	36.1728	−	36.1728i	0.841228	−	0.841228i	0.989019	+	0.147791i	$0.0472162\pi$
$44$		0			0
$45$	36.3511	+	41.8676i	0.807803	+	0.930390i
$46$		0			0
$47$	0.703158	+	4.43956i	0.0149608	+	0.0944588i	0.994039	−	0.109026i	$-0.0347732\pi$
$47$	0.703158	+	4.43956i	0.0149608	+	0.0944588i	−0.979078	+	0.203485i	$0.934773\pi$
$48$		0			0
$49$		−	3.39110i		−	0.0692062i
$50$		0			0
$51$	−20.8502			−0.408828
$52$		0			0
$53$	69.2402	−	10.9666i	1.30642	−	0.206916i	0.535872	−	0.844299i	$-0.319983\pi$
$53$	69.2402	−	10.9666i	1.30642	−	0.206916i	0.770547	+	0.637383i	$0.219983\pi$
$54$		0			0
$55$	−61.9675	+	5.38424i	−1.12668	+	0.0978953i
$56$		0			0
$57$	−69.3215	−	69.3215i	−1.21617	−	1.21617i
$58$		0			0
$59$	67.9339	−	22.0730i	1.15142	−	0.374119i	0.329743	−	0.944071i	$-0.393038\pi$
$59$	67.9339	−	22.0730i	1.15142	−	0.374119i	0.821678	+	0.569951i	$0.193038\pi$
$60$		0			0
$61$	15.0860	−	46.4300i	0.247312	−	0.761148i	−0.747936	−	0.663771i	$-0.768955\pi$
$61$	15.0860	−	46.4300i	0.247312	−	0.761148i	0.995248	−	0.0973769i	$-0.0310452\pi$
$62$		0			0
$63$	66.7281	+	33.9997i	1.05918	+	0.539677i
$64$		0			0
$65$	0.415555	−	5.89224i	0.00639315	−	0.0906499i
$66$		0			0
$67$	−79.5063	−	12.5926i	−1.18666	−	0.187949i	−0.468268	−	0.883586i	$-0.655122\pi$
$67$	−79.5063	−	12.5926i	−1.18666	−	0.187949i	−0.718393	+	0.695638i	$0.755122\pi$
$68$		0			0
$69$	23.4424	+	32.2657i	0.339745	+	0.467620i
$70$		0			0
$71$	34.9284	+	25.3769i	0.491949	+	0.357422i	0.805933	−	0.592006i	$-0.201664\pi$
$71$	34.9284	+	25.3769i	0.491949	+	0.357422i	−0.313985	+	0.949428i	$0.601664\pi$
$72$		0			0
$73$	27.3286	+	53.6354i	0.374364	+	0.734731i	0.998930	−	0.0462407i	$-0.0147241\pi$
$73$	27.3286	+	53.6354i	0.374364	+	0.734731i	−0.624566	+	0.780972i	$0.714724\pi$
$74$		0			0
$75$	−64.3801	+	91.7115i	−0.858402	+	1.22282i
$76$		0			0
$77$	−74.8571	+	38.1416i	−0.972170	+	0.495345i
$78$		0			0
$79$	27.4839	−	37.8283i	0.347898	−	0.478840i	−0.598830	−	0.800876i	$-0.704367\pi$
$79$	27.4839	−	37.8283i	0.347898	−	0.478840i	0.946727	+	0.322037i	$0.104367\pi$
$80$		0			0
$81$	−46.7867	+	33.9925i	−0.577613	+	0.419660i
$82$		0			0
$83$	−17.1166	+	108.070i	−0.206224	+	1.30205i	0.639650	+	0.768666i	$0.279079\pi$
$83$	−17.1166	+	108.070i	−0.206224	+	1.30205i	−0.845874	+	0.533382i	$0.820921\pi$
$84$		0			0
$85$	−5.61351	−	22.5719i	−0.0660413	−	0.265551i
$86$		0			0
$87$	18.7904	−	36.8782i	0.215981	−	0.423887i
$88$		0			0
$89$	63.0322	+	20.4804i	0.708227	+	0.230117i	0.640911	−	0.767615i	$-0.278557\pi$
$89$	63.0322	+	20.4804i	0.708227	+	0.230117i	0.0673154	+	0.997732i	$0.478557\pi$
$90$		0			0
$91$	−2.46544	−	7.58786i	−0.0270928	−	0.0833830i
$92$		0			0
$93$	99.1969	−	99.1969i	1.06663	−	1.06663i
$94$		0			0
$95$	56.3820	−	93.7088i	0.593495	−	0.986409i
$96$		0			0
$97$	8.99168	+	56.7712i	0.0926977	+	0.585270i	0.989690	+	0.143225i	$0.0457471\pi$
$97$	8.99168	+	56.7712i	0.0926977	+	0.585270i	−0.896993	+	0.442046i	$0.854253\pi$
$98$		0			0
$99$			137.953i			1.39346i
$100$		0			0
$101$	−4.10343			−0.0406280			−0.0203140	−	0.999794i	$-0.506467\pi$
$101$	−4.10343			−0.0406280			−0.0203140	+	0.999794i	$0.506467\pi$
$102$		0			0
$103$	93.2854	−	14.7750i	0.905683	−	0.143446i	0.313818	−	0.949483i	$-0.398392\pi$
$103$	93.2854	−	14.7750i	0.905683	−	0.143446i	0.591865	+	0.806037i	$0.298392\pi$
$104$		0			0
$105$	−34.1338	+	147.449i	−0.325084	+	1.40427i
$106$		0			0
$107$	−142.289	−	142.289i	−1.32980	−	1.32980i	−0.905538	−	0.424266i	$-0.860532\pi$
$107$	−142.289	−	142.289i	−1.32980	−	1.32980i	−0.424266	−	0.905538i	$-0.639468\pi$
$108$		0			0
$109$	−129.134	+	41.9581i	−1.18471	+	0.384936i	−0.834115	−	0.551590i	$-0.814021\pi$
$109$	−129.134	+	41.9581i	−1.18471	+	0.384936i	−0.350597	+	0.936526i	$0.614021\pi$
$110$		0			0
$111$	19.7444	−	60.7671i	0.177878	−	0.547451i
$112$		0			0
$113$	−82.9619	−	42.2712i	−0.734176	−	0.374081i	0.0465823	−	0.998914i	$-0.485167\pi$
$113$	−82.9619	−	42.2712i	−0.734176	−	0.374081i	−0.780758	+	0.624833i	$0.785167\pi$
$114$		0			0
$115$	−28.6186	+	34.0650i	−0.248857	+	0.296218i
$116$		0			0
$117$	−12.9393	−	2.04938i	−0.110592	−	0.0175161i
$118$		0			0
$119$	−18.4660	−	25.4162i	−0.155176	−	0.213582i
$120$		0			0
$121$	−27.3112	−	19.8428i	−0.225713	−	0.163990i
$122$		0			0
$123$	−111.169	−	218.181i	−0.903810	−	1.77383i
$124$		0			0
$125$	−116.617	−	45.0046i	−0.932938	−	0.360037i
$126$		0			0
$127$	43.9744	−	22.4061i	0.346255	−	0.176426i	−0.272210	−	0.962238i	$-0.587755\pi$
$127$	43.9744	−	22.4061i	0.346255	−	0.176426i	0.618465	+	0.785812i	$0.287755\pi$
$128$		0			0
$129$	134.771	−	185.497i	1.04474	−	1.43796i
$130$		0			0
$131$	−109.772	+	79.7539i	−0.837953	+	0.608809i	−0.921798	−	0.387670i	$-0.873280\pi$
$131$	−109.772	+	79.7539i	−0.837953	+	0.608809i	0.0838450	+	0.996479i	$0.473280\pi$
$132$		0			0
$133$	23.1078	−	145.897i	0.173743	−	1.09697i
$134$		0			0
$135$	35.8496	+	30.1178i	0.265552	+	0.223095i
$136$		0			0
$137$	84.2247	−	165.300i	0.614779	−	1.20657i	−0.348308	−	0.937380i	$-0.613243\pi$
$137$	84.2247	−	165.300i	0.614779	−	1.20657i	0.963087	−	0.269192i	$-0.0867565\pi$
$138$		0			0
$139$	−122.872	−	39.9236i	−0.883973	−	0.287220i	−0.168367	−	0.985724i	$-0.553849\pi$
$139$	−122.872	−	39.9236i	−0.883973	−	0.287220i	−0.715606	+	0.698504i	$0.753849\pi$
$140$		0			0
$141$	6.22565	+	19.1606i	0.0441535	+	0.135891i
$142$		0			0
$143$	10.3920	−	10.3920i	0.0726715	−	0.0726715i
$144$		0			0
$145$	44.9822	+	10.4132i	0.310222	+	0.0718151i
$146$		0			0
$147$	−2.37769	−	15.0122i	−0.0161748	−	0.102123i
$148$		0			0
$149$			232.485i			1.56030i	0.625592	+	0.780150i	$0.284857\pi$
$149$			232.485i			1.56030i	−0.625592	+	0.780150i	$0.715143\pi$
$150$		0			0
$151$	−172.702			−1.14372			−0.571861	−	0.820351i	$-0.693778\pi$
$151$	−172.702			−1.14372			−0.571861	+	0.820351i	$0.693778\pi$
$152$		0			0
$153$	−50.9509	+	8.06982i	−0.333012	+	0.0527439i
$154$		0			0
$155$	134.095	+	80.6810i	0.865126	+	0.520522i
$156$		0			0
$157$	−154.466	−	154.466i	−0.983858	−	0.983858i	0.0160139	−	0.999872i	$-0.494902\pi$
$157$	−154.466	−	154.466i	−0.983858	−	0.983858i	−0.999872	+	0.0160139i	$0.994902\pi$
$158$		0			0
$159$	298.832	−	97.0963i	1.87945	−	0.610669i
$160$		0			0
$161$	−18.5699	+	57.1522i	−0.115341	+	0.354983i
$162$		0			0
$163$	−32.1939	−	16.4036i	−0.197508	−	0.100636i	0.352439	−	0.935835i	$-0.385352\pi$
$163$	−32.1939	−	16.4036i	−0.197508	−	0.100636i	−0.549948	+	0.835199i	$0.685352\pi$
$164$		0			0
$165$	−270.550	+	67.2845i	−1.63970	+	0.407785i
$166$		0			0
$167$	11.3916	+	1.80425i	0.0682130	+	0.0108039i	0.190448	−	0.981697i	$-0.439006\pi$
$167$	11.3916	+	1.80425i	0.0682130	+	0.0108039i	−0.122235	+	0.992501i	$0.539006\pi$
$168$		0			0
$169$	−98.5154	−	135.595i	−0.582931	−	0.802336i
$170$		0			0
$171$	−196.228	−	142.568i	−1.14753	−	0.833731i
$172$		0			0
$173$	−44.0149	−	86.3841i	−0.254421	−	0.499330i	0.728102	−	0.685469i	$-0.240403\pi$
$173$	−44.0149	−	86.3841i	−0.254421	−	0.499330i	−0.982523	+	0.186139i	$0.940403\pi$
$174$		0			0
$175$	−168.814	+	2.74537i	−0.964649	+	0.0156878i
$176$		0			0
$177$	285.261	−	145.348i	1.61165	−	0.821175i
$178$		0			0
$179$	−119.212	+	164.081i	−0.665987	+	0.916653i	−0.999661	−	0.0260360i	$-0.991712\pi$
$179$	−119.212	+	164.081i	−0.665987	+	0.916653i	0.333674	+	0.942689i	$0.391712\pi$
$180$		0			0
$181$	−245.629	+	178.460i	−1.35707	+	0.985966i	−0.358440	+	0.933553i	$0.616691\pi$
$181$	−245.629	+	178.460i	−1.35707	+	0.985966i	−0.998625	+	0.0524129i	$0.983309\pi$
$182$		0			0
$183$	34.2300	−	216.120i	0.187049	−	1.18098i
$184$		0			0
$185$	71.1005	+	5.01441i	0.384327	+	0.0271049i
$186$		0			0
$187$	26.2726	−	51.5628i	0.140495	−	0.275737i
$188$		0			0
$189$	60.1462	+	19.5427i	0.318234	+	0.103400i
$190$		0			0
$191$	−28.3111	−	87.1326i	−0.148226	−	0.456192i	0.849186	−	0.528094i	$-0.177093\pi$
$191$	−28.3111	−	87.1326i	−0.148226	−	0.456192i	−0.997412	+	0.0719021i	$0.977093\pi$
$192$		0			0
$193$	129.347	−	129.347i	0.670189	−	0.670189i	−0.287570	−	0.957760i	$-0.592847\pi$
$193$	129.347	−	129.347i	0.670189	−	0.670189i	0.957760	+	0.287570i	$0.0928475\pi$
$194$		0			0
$195$	−2.29175	−	26.3759i	−0.0117526	−	0.135261i
$196$		0			0
$197$	19.2400	+	121.476i	0.0976648	+	0.616631i	0.987166	+	0.159698i	$0.0510521\pi$
$197$	19.2400	+	121.476i	0.0976648	+	0.616631i	−0.889501	+	0.456933i	$0.848948\pi$
$198$		0			0
$199$			390.191i			1.96076i	0.197114	+	0.980381i	$0.436843\pi$
$199$			390.191i			1.96076i	−0.197114	+	0.980381i	$0.563157\pi$
$200$		0			0
$201$	−360.798			−1.79501
$202$		0			0
$203$	61.5958	−	9.75581i	0.303427	−	0.0480582i
$204$		0			0
$205$	206.266	−	179.089i	1.00618	−	0.873604i
$206$		0			0
$207$	69.7734	+	69.7734i	0.337070	+	0.337070i
$208$		0			0
$209$	258.782	−	84.0834i	1.23819	−	0.402313i
$210$		0			0
$211$	34.5087	−	106.207i	0.163548	−	0.503350i	−0.835378	−	0.549676i	$-0.814751\pi$
$211$	34.5087	−	106.207i	0.163548	−	0.503350i	0.998926	+	0.0463257i	$0.0147512\pi$
$212$		0			0
$213$	172.418	+	87.8515i	0.809476	+	0.412449i
$214$		0			0
$215$	237.098	+	95.9583i	1.10278	+	0.446318i
$216$		0			0
$217$	208.774	+	33.0665i	0.962091	+	0.152380i
$218$		0			0
$219$	158.588	+	218.278i	0.724148	+	0.996704i
$220$		0			0
$221$	4.44605	+	3.23024i	0.0201179	+	0.0146165i
$222$		0			0
$223$	20.5207	+	40.2741i	0.0920209	+	0.180601i	0.932429	−	0.361352i	$-0.117685\pi$
$223$	20.5207	+	40.2741i	0.0920209	+	0.180601i	−0.840408	+	0.541954i	$0.817685\pi$
$224$		0			0
$225$	−121.827	+	249.029i	−0.541455	+	1.10680i
$226$		0			0
$227$	107.017	−	54.5277i	0.471439	−	0.240210i	−0.202096	−	0.979366i	$-0.564775\pi$
$227$	107.017	−	54.5277i	0.471439	−	0.240210i	0.673535	+	0.739156i	$0.264775\pi$
$228$		0			0
$229$	−71.1775	+	97.9675i	−0.310819	+	0.427806i	−0.935636	−	0.352965i	$-0.885173\pi$
$229$	−71.1775	+	97.9675i	−0.310819	+	0.427806i	0.624817	+	0.780771i	$0.285173\pi$
$230$		0			0
$231$	−304.643	+	221.336i	−1.31880	+	0.958166i
$232$		0			0
$233$	−30.8904	+	195.034i	−0.132577	+	0.837056i	0.828341	+	0.560224i	$0.189285\pi$
$233$	−30.8904	+	195.034i	−0.132577	+	0.837056i	−0.960918	+	0.276833i	$0.910715\pi$
$234$		0			0
$235$	−19.0666	+	11.8983i	−0.0811343	+	0.0506311i
$236$		0			0
$237$	95.1456	−	186.734i	0.401458	−	0.787906i
$238$		0			0
$239$	105.011	+	34.1201i	0.439375	+	0.142762i	0.520347	−	0.853955i	$-0.325802\pi$
$239$	105.011	+	34.1201i	0.439375	+	0.142762i	−0.0809720	+	0.996716i	$0.525802\pi$
$240$		0			0
$241$	21.0011	+	64.6348i	0.0871416	+	0.268194i	0.985126	−	0.171833i	$-0.0549689\pi$
$241$	21.0011	+	64.6348i	0.0871416	+	0.268194i	−0.897985	+	0.440027i	$0.854969\pi$
$242$		0			0
$243$	−242.881	+	242.881i	−0.999511	+	0.999511i
$244$		0			0
$245$	15.6116	−	6.61574i	0.0637207	−	0.0270030i
$246$		0			0
$247$	4.04223	+	25.5216i	0.0163653	+	0.103326i
$248$		0			0
$249$			490.419i			1.96955i
$250$		0			0
$251$	184.575			0.735358			0.367679	−	0.929953i	$-0.380153\pi$
$251$	184.575			0.735358			0.367679	+	0.929953i	$0.380153\pi$
$252$		0			0
$253$	−109.332	+	17.3166i	−0.432144	+	0.0684449i
$254$		0			0
$255$	−40.6770	−	95.9879i	−0.159517	−	0.376423i
$256$		0			0
$257$	110.251	+	110.251i	0.428992	+	0.428992i	0.888285	−	0.459293i	$-0.151897\pi$
$257$	110.251	+	110.251i	0.428992	+	0.428992i	−0.459293	+	0.888285i	$0.651897\pi$
$258$		0			0
$259$	91.5611	−	29.7500i	0.353518	−	0.114865i
$260$		0			0
$261$	31.6440	−	97.3903i	0.121241	−	0.373143i
$262$		0			0
$263$	295.330	+	150.478i	1.12293	+	0.572160i	0.913977	−	0.405766i	$-0.132995\pi$
$263$	295.330	+	150.478i	1.12293	+	0.572160i	0.208950	+	0.977926i	$0.432995\pi$
$264$		0			0
$265$	185.568	+	297.365i	0.700257	+	1.12213i
$266$		0			0
$267$	293.399	+	46.4698i	1.09887	+	0.174044i
$268$		0			0
$269$	306.607	+	422.008i	1.13980	+	1.56880i	0.767946	+	0.640515i	$0.221279\pi$
$269$	306.607	+	422.008i	1.13980	+	1.56880i	0.371857	+	0.928290i	$0.378721\pi$
$270$		0			0
$271$	−33.2207	−	24.1363i	−0.122586	−	0.0890638i	0.524803	−	0.851224i	$-0.324139\pi$
$271$	−33.2207	−	24.1363i	−0.122586	−	0.0890638i	−0.647389	+	0.762160i	$0.724139\pi$
$272$		0			0
$273$	−16.2346	−	31.8622i	−0.0594674	−	0.116711i
$274$		0			0
$275$	−145.681	−	274.775i	−0.529747	−	0.999182i
$276$		0			0
$277$	−471.855	+	240.422i	−1.70345	+	0.867950i	−0.718407	+	0.695623i	$0.755128\pi$
$277$	−471.855	+	240.422i	−1.70345	+	0.867950i	−0.985040	+	0.172327i	$0.944872\pi$
$278$		0			0
$279$	204.011	−	280.797i	0.731221	−	1.00644i
$280$		0			0
$281$	130.914	−	95.1145i	0.465886	−	0.338486i	−0.329950	−	0.943998i	$-0.607032\pi$
$281$	130.914	−	95.1145i	0.465886	−	0.338486i	0.795836	+	0.605513i	$0.207032\pi$
$282$		0			0
$283$	50.0186	−	315.805i	0.176744	−	1.11592i	−0.726618	−	0.687042i	$-0.758909\pi$
$283$	50.0186	−	315.805i	0.176744	−	1.11592i	0.903362	−	0.428878i	$-0.141091\pi$
$284$		0			0
$285$	183.894	−	454.374i	0.645243	−	1.59430i
$286$		0			0
$287$	167.504	−	328.745i	0.583637	−	1.14545i
$288$		0			0
$289$	−254.274	−	82.6188i	−0.879842	−	0.285878i
$290$		0			0
$291$	79.6109	+	245.017i	0.273577	+	0.841984i
$292$		0			0
$293$	252.694	−	252.694i	0.862436	−	0.862436i	−0.129184	−	0.991621i	$-0.541236\pi$
$293$	252.694	−	252.694i	0.862436	−	0.862436i	0.991621	+	0.129184i	$0.0412359\pi$
$294$		0			0
$295$	234.150	+	269.684i	0.793730	+	0.914182i
$296$		0			0
$297$	18.2237	+	115.060i	0.0613593	+	0.387407i
$298$		0			0
$299$		−	10.5121i		−	0.0351576i
$300$		0			0
$301$	345.479			1.14777
$302$		0			0
$303$	−18.1656	+	2.87714i	−0.0599524	+	0.00949552i
$304$		0			0
$305$	243.181	−	21.1295i	0.797315	−	0.0692772i
$306$		0			0
$307$	−260.783	−	260.783i	−0.849457	−	0.849457i	0.140609	−	0.990065i	$-0.455094\pi$
$307$	−260.783	−	260.783i	−0.849457	−	0.849457i	−0.990065	+	0.140609i	$0.955094\pi$
$308$		0			0
$309$	402.608	−	130.815i	1.30294	−	0.423350i
$310$		0			0
$311$	−117.574	+	361.855i	−0.378051	+	1.16352i	0.563347	+	0.826221i	$0.309514\pi$
$311$	−117.574	+	361.855i	−0.378051	+	1.16352i	−0.941397	+	0.337300i	$0.890486\pi$
$312$		0			0
$313$	−365.880	−	186.425i	−1.16895	−	0.595607i	−0.241806	−	0.970325i	$-0.577740\pi$
$313$	−365.880	−	186.425i	−1.16895	−	0.595607i	−0.927139	+	0.374717i	$0.877740\pi$
$314$		0			0
$315$	−26.3432	+	373.526i	−0.0836291	+	1.18580i
$316$		0			0
$317$	−171.773	−	27.2062i	−0.541872	−	0.0858241i	−0.120502	−	0.992713i	$-0.538450\pi$
$317$	−171.773	−	27.2062i	−0.541872	−	0.0858241i	−0.421370	+	0.906889i	$0.638450\pi$
$318$		0			0
$319$	67.5231	+	92.9375i	0.211671	+	0.291340i
$320$		0			0
$321$	−729.669	−	530.136i	−2.27311	−	1.65151i
$322$		0			0
$323$	46.1930	+	90.6588i	0.143012	+	0.280677i
$324$		0			0
$325$	27.9368	−	9.58216i	0.0859592	−	0.0294836i
$326$		0			0
$327$	−542.246	+	276.288i	−1.65824	+	0.844917i
$328$		0			0
$329$	−17.8428	+	24.5585i	−0.0542335	+	0.0746460i
$330$		0			0
$331$	−31.9665	+	23.2250i	−0.0965755	+	0.0701662i	−0.635025	−	0.772492i	$-0.719010\pi$
$331$	−31.9665	+	23.2250i	−0.0965755	+	0.0701662i	0.538450	+	0.842658i	$0.319010\pi$
$332$		0			0
$333$	24.7295	−	156.136i	0.0742628	−	0.468877i
$334$		0			0
$335$	−97.1376	−	390.589i	−0.289963	−	1.16594i
$336$		0			0
$337$	53.9081	−	105.801i	0.159965	−	0.313948i	−0.797088	−	0.603864i	$-0.793627\pi$
$337$	53.9081	−	105.801i	0.159965	−	0.313948i	0.957052	+	0.289915i	$0.0936271\pi$
$338$		0			0
$339$	−396.905	−	128.962i	−1.17081	−	0.380419i
$340$		0			0
$341$	120.321	+	370.309i	0.352847	+	1.08595i
$342$		0			0
$343$	250.188	−	250.188i	0.729413	−	0.729413i
$344$		0			0
$345$	−102.807	+	170.869i	−0.297992	+	0.495273i
$346$		0			0
$347$	67.0138	+	423.108i	0.193123	+	1.21933i	0.873630	+	0.486591i	$0.161760\pi$
$347$	67.0138	+	423.108i	0.193123	+	1.21933i	−0.680507	+	0.732742i	$0.738240\pi$
$348$		0			0
$349$			111.740i			0.320171i	0.987103	+	0.160085i	$0.0511769\pi$
$349$			111.740i			0.320171i	−0.987103	+	0.160085i	$0.948823\pi$
$350$		0			0
$351$	−11.0628			−0.0315180
$352$		0			0
$353$	329.586	−	52.2014i	0.933673	−	0.147879i	0.328979	−	0.944337i	$-0.393295\pi$
$353$	329.586	−	52.2014i	0.933673	−	0.147879i	0.604694	+	0.796458i	$0.293295\pi$
$354$		0			0
$355$	−48.6853	+	210.307i	−0.137142	+	0.592415i
$356$		0			0
$357$	−99.5682	−	99.5682i	−0.278902	−	0.278902i
$358$		0			0
$359$	111.358	−	36.1824i	0.310189	−	0.100787i	−0.149786	−	0.988718i	$-0.547858\pi$
$359$	111.358	−	36.1824i	0.310189	−	0.100787i	0.459975	+	0.887932i	$0.347858\pi$
$360$		0			0
$361$	−36.2820	+	111.664i	−0.100504	+	0.309320i
$362$		0			0
$363$	−134.818	−	68.6930i	−0.371398	−	0.189237i
$364$		0			0
$365$	−193.605	+	230.450i	−0.530424	+	0.631370i
$366$		0			0
$367$	−153.553	−	24.3204i	−0.418401	−	0.0662682i	−0.0563153	−	0.998413i	$-0.517935\pi$
$367$	−153.553	−	24.3204i	−0.418401	−	0.0662682i	−0.362086	+	0.932145i	$0.617935\pi$
$368$		0			0
$369$	−356.102	−	490.133i	−0.965047	−	1.32827i
$370$		0			0
$371$	383.019	+	278.280i	1.03240	+	0.750081i
$372$		0			0
$373$	160.733	+	315.456i	0.430919	+	0.845725i	0.999730	+	0.0232570i	$0.00740360\pi$
$373$	160.733	+	315.456i	0.430919	+	0.845725i	−0.568811	+	0.822468i	$0.692596\pi$
$374$		0			0
$375$	−547.811	−	117.465i	−1.46083	−	0.313240i
$376$		0			0
$377$	−9.72020	+	4.95269i	−0.0257830	+	0.0131371i
$378$		0			0
$379$	−210.869	+	290.236i	−0.556382	+	0.765794i	−0.990861	−	0.134888i	$-0.956933\pi$
$379$	−210.869	+	290.236i	−0.556382	+	0.765794i	0.434479	+	0.900682i	$0.356933\pi$
$380$		0			0
$381$	178.961	−	130.023i	0.469714	−	0.341267i
$382$		0			0
$383$	8.47845	−	53.5308i	0.0221370	−	0.139767i	−0.974144	−	0.225926i	$-0.927459\pi$
$383$	8.47845	−	53.5308i	0.0221370	−	0.139767i	0.996281	+	0.0861588i	$0.0274592\pi$
$384$		0			0
$385$	−321.632	−	270.208i	−0.835407	−	0.701838i
$386$		0			0
$387$	257.541	−	505.453i	0.665482	−	1.30608i
$388$		0			0
$389$	−340.490	−	110.632i	−0.875296	−	0.284401i	−0.163294	−	0.986578i	$-0.552212\pi$
$389$	−340.490	−	110.632i	−0.875296	−	0.284401i	−0.712003	+	0.702176i	$0.752212\pi$
$390$		0			0
$391$	−12.7912	−	39.3674i	−0.0327142	−	0.100684i
$392$		0			0
$393$	−430.032	+	430.032i	−1.09423	+	1.09423i
$394$		0			0
$395$	227.769	+	52.7275i	0.576629	+	0.133487i
$396$		0			0
$397$	−8.95869	−	56.5629i	−0.0225660	−	0.142476i	0.973833	−	0.227265i	$-0.0729784\pi$
$397$	−8.95869	−	56.5629i	−0.0225660	−	0.142476i	−0.996399	+	0.0847891i	$0.972978\pi$
$398$		0			0
$399$		−	662.075i		−	1.65934i
$400$		0			0
$401$	410.265			1.02310			0.511552	−	0.859252i	$-0.329071\pi$
$401$	410.265			1.02310			0.511552	+	0.859252i	$0.329071\pi$
$402$		0			0
$403$	−36.5207	+	5.78431i	−0.0906221	+	0.0143531i
$404$		0			0
$405$	−247.768	−	149.075i	−0.611772	−	0.368086i
$406$		0			0
$407$	125.398	+	125.398i	0.308104	+	0.308104i
$408$		0			0
$409$	230.995	−	75.0548i	0.564780	−	0.183508i	−0.0126910	−	0.999919i	$-0.504040\pi$
$409$	230.995	−	75.0548i	0.564780	−	0.183508i	0.577471	+	0.816411i	$0.304040\pi$
$410$		0			0
$411$	256.955	−	790.827i	0.625195	−	1.92415i
$412$		0			0
$413$	429.819	+	219.004i	1.04072	+	0.530275i
$414$		0			0
$415$	−530.914	+	132.036i	−1.27931	+	0.318158i
$416$		0			0
$417$	−571.939	−	90.5862i	−1.37156	−	0.217233i
$418$		0			0
$419$	−27.4988	−	37.8489i	−0.0656296	−	0.0903314i	0.774940	−	0.632034i	$-0.217780\pi$
$419$	−27.4988	−	37.8489i	−0.0656296	−	0.0903314i	−0.840570	+	0.541703i	$0.817780\pi$
$420$		0			0
$421$	516.008	+	374.902i	1.22567	+	0.890503i	0.996558	−	0.0828969i	$-0.0264172\pi$
$421$	516.008	+	374.902i	1.22567	+	0.890503i	0.229114	+	0.973400i	$0.426417\pi$
$422$		0			0
$423$	22.6292	+	44.4124i	0.0534970	+	0.104994i
$424$		0			0
$425$	92.9623	−	69.8785i	0.218735	−	0.164420i
$426$		0			0
$427$	293.764	−	149.680i	0.687972	−	0.350539i
$428$		0			0
$429$	38.7183	−	53.2911i	0.0902524	−	0.124222i
$430$		0			0
$431$	126.852	−	92.1635i	0.294321	−	0.213836i	−0.430819	−	0.902438i	$-0.641775\pi$
$431$	126.852	−	92.1635i	0.294321	−	0.213836i	0.725140	+	0.688602i	$0.241775\pi$
$432$		0			0
$433$	20.5870	−	129.981i	0.0475451	−	0.300188i	−0.952445	−	0.304712i	$-0.901440\pi$
$433$	20.5870	−	129.981i	0.0475451	−	0.300188i	0.999990	+	0.00452353i	$0.00143989\pi$
$434$		0			0
$435$	206.434	+	14.5589i	0.474561	+	0.0334687i
$436$		0			0
$437$	88.3587	−	173.414i	0.202194	−	0.396828i
$438$		0			0
$439$	−648.563	−	210.731i	−1.47736	−	0.480025i	−0.544040	−	0.839059i	$-0.683106\pi$
$439$	−648.563	−	210.731i	−1.47736	−	0.480025i	−0.933324	+	0.359034i	$0.883106\pi$
$440$		0			0
$441$	−11.6205	−	35.7644i	−0.0263504	−	0.0810983i
$442$		0			0
$443$	−3.05272	+	3.05272i	−0.00689102	+	0.00689102i	−0.710544	−	0.703653i	$-0.751551\pi$
$443$	−3.05272	+	3.05272i	−0.00689102	+	0.00689102i	0.703653	+	0.710544i	$0.251551\pi$
$444$		0			0
$445$	28.6849	+	330.136i	0.0644604	+	0.741878i
$446$		0			0
$447$	163.008	+	1029.19i	0.364671	+	2.30244i
$448$		0			0
$449$			68.8584i			0.153359i	0.997056	+	0.0766797i	$0.0244319\pi$
$449$			68.8584i			0.153359i	−0.997056	+	0.0766797i	$0.975568\pi$
$450$		0			0
$451$	679.643			1.50697
$452$		0			0
$453$	−764.538	+	121.091i	−1.68772	+	0.267309i
$454$		0			0
$455$	30.1223	−	26.1534i	0.0662028	−	0.0574799i
$456$		0			0
$457$	−133.432	−	133.432i	−0.291974	−	0.291974i	0.545886	−	0.837860i	$-0.316193\pi$
$457$	−133.432	−	133.432i	−0.291974	−	0.291974i	−0.837860	+	0.545886i	$0.816193\pi$
$458$		0			0
$459$	−41.4297	+	13.4613i	−0.0902608	+	0.0293275i
$460$		0			0
$461$	141.436	−	435.294i	0.306802	−	0.944239i	−0.672197	−	0.740372i	$-0.734649\pi$
$461$	141.436	−	435.294i	0.306802	−	0.944239i	0.978999	−	0.203866i	$-0.0653508\pi$
$462$		0			0
$463$	210.502	+	107.256i	0.454649	+	0.231655i	0.666291	−	0.745692i	$-0.267881\pi$
$463$	210.502	+	107.256i	0.454649	+	0.231655i	−0.211642	+	0.977347i	$0.567881\pi$
$464$		0			0
$465$	650.196	+	263.147i	1.39827	+	0.565908i
$466$		0			0
$467$	−375.182	−	59.4229i	−0.803387	−	0.127244i	−0.258781	−	0.965936i	$-0.583321\pi$
$467$	−375.182	−	59.4229i	−0.803387	−	0.127244i	−0.544606	+	0.838692i	$0.683321\pi$
$468$		0			0
$469$	−319.540	−	439.809i	−0.681322	−	0.937759i
$470$		0			0
$471$	−792.112	−	575.503i	−1.68177	−	1.22188i
$472$		0			0
$473$	288.916	+	567.029i	0.610816	+	1.19879i
$474$		0			0
$475$	541.403	+	76.7474i	1.13979	+	0.161573i
$476$		0			0
$477$	692.663	−	352.930i	1.45212	−	0.739894i
$478$		0			0
$479$	136.238	−	187.515i	0.284421	−	0.391472i	−0.642771	−	0.766058i	$-0.722215\pi$
$479$	136.238	−	187.515i	0.284421	−	0.391472i	0.927192	+	0.374587i	$0.122215\pi$
$480$		0			0
$481$	−13.6247	+	9.89889i	−0.0283257	+	0.0205798i
$482$		0			0
$483$	−42.1348	+	266.029i	−0.0872357	+	0.550784i
$484$		0			0
$485$	−243.815	+	152.151i	−0.502711	+	0.313712i
$486$		0			0
$487$	−65.2171	+	127.996i	−0.133916	+	0.262825i	−0.948220	−	0.317613i	$-0.897119\pi$
$487$	−65.2171	+	127.996i	−0.133916	+	0.262825i	0.814304	+	0.580438i	$0.197119\pi$
$488$		0			0
$489$	−154.021	−	50.0446i	−0.314972	−	0.102341i
$490$		0			0
$491$	37.0190	+	113.933i	0.0753951	+	0.232042i	0.981651	−	0.190688i	$-0.0610718\pi$
$491$	37.0190	+	113.933i	0.0753951	+	0.232042i	−0.906256	+	0.422730i	$0.861072\pi$
$492$		0			0
$493$	−30.3752	+	30.3752i	−0.0616131	+	0.0616131i
$494$		0			0
$495$	−635.091	+	269.134i	−1.28301	+	0.543704i
$496$		0			0
$497$	45.6119	+	287.982i	0.0917743	+	0.579440i
$498$		0			0
$499$			274.256i			0.549612i	0.961500	+	0.274806i	$0.0886136\pi$
$499$			274.256i			0.549612i	−0.961500	+	0.274806i	$0.911386\pi$
$500$		0			0
$501$	51.6947			0.103183
$502$		0			0
$503$	379.704	−	60.1392i	0.754879	−	0.119561i	0.232878	−	0.972506i	$-0.425186\pi$
$503$	379.704	−	60.1392i	0.754879	−	0.119561i	0.522001	+	0.852945i	$0.325186\pi$
$504$		0			0
$505$	−8.00543	−	18.8909i	−0.0158523	−	0.0374077i
$506$		0			0
$507$	−531.193	−	531.193i	−1.04772	−	1.04772i
$508$		0			0
$509$	21.4135	−	6.95766i	0.0420697	−	0.0136693i	−0.287907	−	0.957659i	$-0.592959\pi$
$509$	21.4135	−	6.95766i	0.0420697	−	0.0136693i	0.329976	+	0.943989i	$0.392959\pi$
$510$		0			0
$511$	−125.625	+	386.635i	−0.245842	+	0.756625i
$512$		0			0
$513$	−182.498	−	92.9875i	−0.355747	−	0.181262i
$514$		0			0
$515$	250.011	+	400.632i	0.485458	+	0.777927i
$516$		0			0
$517$	−55.2290	−	8.74742i	−0.106826	−	0.0169196i
$518$		0			0
$519$	−255.419	−	351.554i	−0.492137	−	0.677369i
$520$		0			0
$521$	−189.989	−	138.035i	−0.364663	−	0.264943i	0.390332	−	0.920674i	$-0.372360\pi$
$521$	−189.989	−	138.035i	−0.364663	−	0.264943i	−0.754994	+	0.655731i	$0.772360\pi$
$522$		0			0
$523$	−27.0755	−	53.1387i	−0.0517696	−	0.101604i	0.863672	−	0.504054i	$-0.168159\pi$
$523$	−27.0755	−	53.1387i	−0.0517696	−	0.101604i	−0.915442	+	0.402450i	$0.868159\pi$
$524$		0			0
$525$	−745.400	+	130.518i	−1.41981	+	0.248606i
$526$		0			0
$527$	−129.730	+	66.1008i	−0.246167	+	0.125428i
$528$		0			0
$529$	264.399	−	363.914i	0.499809	−	0.687928i
$530$		0			0
$531$	640.827	−	465.588i	1.20683	−	0.876813i
$532$		0			0
$533$	−10.0966	+	63.7472i	−0.0189429	+	0.119601i
$534$		0			0
$535$	377.461	−	932.647i	0.705534	−	1.74327i
$536$		0			0
$537$	−412.695	+	809.959i	−0.768519	+	1.50830i
$538$		0			0
$539$	40.1213	+	13.0362i	0.0744365	+	0.0241859i
$540$		0			0
$541$	−127.378	−	392.030i	−0.235450	−	0.724640i	−0.997061	−	0.0766062i	$-0.975592\pi$
$541$	−127.378	−	392.030i	−0.235450	−	0.724640i	0.761612	−	0.648034i	$-0.224408\pi$
$542$		0			0
$543$	−962.252	+	962.252i	−1.77210	+	1.77210i
$544$		0			0
$545$	−445.090	−	512.635i	−0.816679	−	0.940614i
$546$		0			0
$547$	−64.7443	−	408.779i	−0.118362	−	0.747311i	−0.973462	−	0.228848i	$-0.926504\pi$
$547$	−64.7443	−	408.779i	−0.118362	−	0.747311i	0.855100	−	0.518463i	$-0.173496\pi$
$548$		0			0
$549$		−	541.372i		−	0.986106i
$550$		0			0
$551$	−201.979			−0.366569
$552$		0			0
$553$	311.892	−	49.3989i	0.564000	−	0.0893289i
$554$		0			0
$555$	318.272	−	27.6541i	0.573464	−	0.0498272i
$556$		0			0
$557$	−364.882	−	364.882i	−0.655084	−	0.655084i	0.299129	−	0.954213i	$-0.403304\pi$
$557$	−364.882	−	364.882i	−0.655084	−	0.655084i	−0.954213	+	0.299129i	$0.903304\pi$
$558$		0			0
$559$	−57.4767	+	18.6753i	−0.102820	+	0.0334084i
$560$		0			0
$561$	80.1531	−	246.686i	0.142875	−	0.439725i
$562$		0			0
$563$	−453.798	−	231.222i	−0.806036	−	0.410696i	0.00187651	−	0.999998i	$-0.499403\pi$
$563$	−453.798	−	231.222i	−0.806036	−	0.410696i	−0.807913	+	0.589302i	$0.799403\pi$
$564$		0			0
$565$	32.7520	−	464.398i	0.0579682	−	0.821943i
$566$		0			0
$567$	−385.753	−	61.0972i	−0.680340	−	0.107755i
$568$		0			0
$569$	−282.994	−	389.508i	−0.497353	−	0.684548i	0.484370	−	0.874863i	$-0.339049\pi$
$569$	−282.994	−	389.508i	−0.497353	−	0.684548i	−0.981723	+	0.190315i	$0.939049\pi$
$570$		0			0
$571$	−501.209	−	364.150i	−0.877775	−	0.637741i	0.0548871	−	0.998493i	$-0.482520\pi$
$571$	−501.209	−	364.150i	−0.877775	−	0.637741i	−0.932662	+	0.360752i	$0.882520\pi$
$572$		0			0
$573$	−186.425	−	365.879i	−0.325349	−	0.638532i
$574$		0			0
$575$	−212.657	−	65.2931i	−0.369838	−	0.113553i
$576$		0			0
$577$	296.742	−	151.197i	0.514284	−	0.262041i	−0.177532	−	0.984115i	$-0.556811\pi$
$577$	296.742	−	151.197i	0.514284	−	0.262041i	0.691815	+	0.722074i	$0.256811\pi$
$578$		0			0
$579$	481.915	−	663.299i	0.832323	−	1.14559i
$580$		0			0
$581$	−597.816	+	434.339i	−1.02894	+	0.747571i
$582$		0			0
$583$	−136.426	+	861.362i	−0.234007	+	1.47746i
$584$		0			0
$585$	−15.8087	−	63.5667i	−0.0270235	−	0.108661i
$586$		0			0
$587$	−313.341	+	614.967i	−0.533801	+	1.04764i	0.453865	+	0.891070i	$0.350045\pi$
$587$	−313.341	+	614.967i	−0.533801	+	1.04764i	−0.987666	+	0.156573i	$0.949955\pi$
$588$		0			0
$589$	−651.086	−	211.551i	−1.10541	−	0.359169i
$590$		0			0
$591$	170.348	+	524.276i	0.288236	+	0.887100i
$592$		0			0
$593$	−236.882	+	236.882i	−0.399464	+	0.399464i	−0.878044	−	0.478580i	$-0.841152\pi$
$593$	−236.882	+	236.882i	−0.399464	+	0.399464i	0.478580	+	0.878044i	$0.341152\pi$
$594$		0			0
$595$	80.9829	−	134.596i	0.136106	−	0.226212i
$596$		0			0
$597$	273.585	+	1727.35i	0.458266	+	2.89338i
$598$		0			0
$599$		−	120.628i		−	0.201382i	−0.994918	−	0.100691i	$-0.967895\pi$
$599$		−	120.628i		−	0.201382i	0.994918	−	0.100691i	$-0.0321053\pi$
$600$		0			0
$601$	1122.78			1.86819			0.934095	−	0.357025i	$-0.116209\pi$
$601$	1122.78			1.86819			0.934095	+	0.357025i	$0.116209\pi$
$602$		0			0
$603$	−881.667	+	139.642i	−1.46213	+	0.231579i
$604$		0			0
$605$	38.0681	−	164.444i	0.0629225	−	0.271808i
$606$		0			0
$607$	−125.125	−	125.125i	−0.206136	−	0.206136i	0.596487	−	0.802623i	$-0.296563\pi$
$607$	−125.125	−	125.125i	−0.206136	−	0.206136i	−0.802623	+	0.596487i	$0.796563\pi$
$608$		0			0
$609$	265.839	−	86.3765i	0.436518	−	0.141833i
$610$		0			0
$611$	1.64093	−	5.05027i	0.00268565	−	0.00826558i
$612$		0			0
$613$	−249.961	−	127.362i	−0.407767	−	0.207768i	0.238062	−	0.971250i	$-0.423488\pi$
$613$	−249.961	−	127.362i	−0.407767	−	0.207768i	−0.645829	+	0.763482i	$0.723488\pi$
$614$		0			0
$615$	787.555	−	937.437i	1.28058	−	1.52429i
$616$		0			0
$617$	−74.7801	−	11.8440i	−0.121200	−	0.0191961i	0.0955399	−	0.995426i	$-0.469542\pi$
$617$	−74.7801	−	11.8440i	−0.121200	−	0.0191961i	−0.216740	+	0.976229i	$0.569542\pi$
$618$		0			0
$619$	−131.262	−	180.667i	−0.212055	−	0.291868i	0.689719	−	0.724078i	$-0.257734\pi$
$619$	−131.262	−	180.667i	−0.212055	−	0.291868i	−0.901773	+	0.432209i	$0.857734\pi$
$620$		0			0
$621$	67.4119	+	48.9776i	0.108554	+	0.0788690i
$622$		0			0
$623$	203.202	+	398.806i	0.326167	+	0.640138i
$624$		0			0
$625$	−20.3230	−	624.669i	−0.0325168	−	0.999471i
$626$		0			0
$627$	1086.65	−	553.677i	1.73310	−	0.883058i
$628$		0			0
$629$	−38.9787	+	53.6496i	−0.0619693	+	0.0852934i
$630$		0			0
$631$	292.773	−	212.712i	0.463982	−	0.337103i	−0.331109	−	0.943592i	$-0.607423\pi$
$631$	292.773	−	212.712i	0.463982	−	0.337103i	0.795091	+	0.606490i	$0.207423\pi$
$632$		0			0
$633$	78.2999	−	494.366i	0.123696	−	0.780989i
$634$		0			0
$635$	188.941	+	158.732i	0.297545	+	0.249972i
$636$		0			0
$637$	−1.81876	+	3.56952i	−0.00285520	+	0.00560364i
$638$		0			0
$639$	455.334	+	147.947i	0.712572	+	0.231529i
$640$		0			0
$641$	282.130	+	868.306i	0.440140	+	1.35461i	0.887727	+	0.460371i	$0.152284\pi$
$641$	282.130	+	868.306i	0.440140	+	1.35461i	−0.447587	+	0.894241i	$0.647716\pi$
$642$		0			0
$643$	520.582	−	520.582i	0.809615	−	0.809615i	−0.174960	−	0.984575i	$-0.555980\pi$
$643$	520.582	−	520.582i	0.809615	−	0.809615i	0.984575	+	0.174960i	$0.0559797\pi$
$644$		0			0
$645$	1116.90	+	258.557i	1.73162	+	0.400864i
$646$		0			0
$647$	167.501	+	1057.56i	0.258888	+	1.63456i	0.684048	+	0.729437i	$0.260218\pi$
$647$	167.501	+	1057.56i	0.258888	+	1.63456i	−0.425159	+	0.905118i	$0.639782\pi$
$648$		0			0
$649$			888.602i			1.36919i
$650$		0			0
$651$	947.410			1.45532
$652$		0			0
$653$	357.048	−	56.5509i	0.546781	−	0.0866016i	0.123068	−	0.992398i	$-0.460727\pi$
$653$	357.048	−	56.5509i	0.546781	−	0.0866016i	0.423713	+	0.905797i	$0.360727\pi$
$654$		0			0
$655$	−581.317	−	349.762i	−0.887508	−	0.533989i
$656$		0			0
$657$	472.018	+	472.018i	0.718444	+	0.718444i
$658$		0			0
$659$	−438.078	+	142.340i	−0.664762	+	0.215994i	−0.621912	−	0.783087i	$-0.713644\pi$
$659$	−438.078	+	142.340i	−0.664762	+	0.215994i	−0.0428503	+	0.999082i	$0.513644\pi$
$660$		0			0
$661$	42.7285	−	131.505i	0.0646422	−	0.198948i	−0.913519	−	0.406796i	$-0.866646\pi$
$661$	42.7285	−	131.505i	0.0646422	−	0.198948i	0.978161	+	0.207848i	$0.0666459\pi$
$662$		0			0
$663$	21.9472	+	11.1827i	0.0331029	+	0.0168668i
$664$		0			0
$665$	716.744	−	178.251i	1.07781	−	0.268046i
$666$		0			0
$667$	81.1574	+	12.8541i	0.121675	+	0.0192715i
$668$		0			0
$669$	119.082	+	163.902i	0.178000	+	0.244996i
$670$		0			0
$671$	491.335	+	356.976i	0.732243	+	0.532006i
$672$		0			0
$673$	−274.452	−	538.642i	−0.407803	−	0.800359i	0.592182	−	0.805804i	$-0.298267\pi$
$673$	−274.452	−	538.642i	−0.407803	−	0.800359i	−0.999985	+	0.00544506i	$0.998267\pi$
$674$		0			0
$675$	−68.7135	+	223.797i	−0.101798	+	0.331552i
$676$		0			0
$677$	222.931	−	113.589i	0.329293	−	0.167783i	−0.281526	−	0.959554i	$-0.590840\pi$
$677$	222.931	−	113.589i	0.329293	−	0.167783i	0.610819	+	0.791771i	$0.290840\pi$
$678$		0			0
$679$	−228.166	+	314.044i	−0.336033	+	0.462510i
$680$		0			0
$681$	435.522	−	316.425i	0.639533	−	0.464648i
$682$		0			0
$683$	59.7898	−	377.498i	0.0875400	−	0.552706i	−0.904469	−	0.426539i	$-0.859733\pi$
$683$	59.7898	−	377.498i	0.0875400	−	0.552706i	0.992009	−	0.126167i	$-0.0402674\pi$
$684$		0			0
$685$	925.306	+	65.2579i	1.35081	+	0.0952671i
$686$		0			0
$687$	−246.407	+	483.601i	−0.358671	+	0.703932i
$688$		0			0
$689$	−78.7649	−	25.5923i	−0.114318	−	0.0371441i
$690$		0			0
$691$	328.195	+	1010.08i	0.474957	+	1.46177i	0.846016	+	0.533158i	$0.178995\pi$
$691$	328.195	+	1010.08i	0.474957	+	1.46177i	−0.371059	+	0.928609i	$0.621005\pi$
$692$		0			0
$693$	−658.780	+	658.780i	−0.950620	+	0.950620i
$694$		0			0
$695$	−55.9171	−	643.553i	−0.0804562	−	0.925975i
$696$		0			0
$697$	39.7571	+	251.016i	0.0570403	+	0.360138i
$698$		0			0
$699$			885.060i			1.26618i
$700$		0			0
$701$	−709.732			−1.01246			−0.506228	−	0.862400i	$-0.668961\pi$
$701$	−709.732			−1.01246			−0.506228	+	0.862400i	$0.668961\pi$
$702$		0			0
$703$	−307.964	+	48.7768i	−0.438072	+	0.0693837i
$704$		0			0
$705$	−76.0636	+	66.0416i	−0.107892	+	0.0936760i
$706$		0			0
$707$	−19.5955	−	19.5955i	−0.0277164	−	0.0277164i
$708$		0			0
$709$	−1304.06	+	423.715i	−1.83930	+	0.597624i	−0.840889	+	0.541207i	$0.817968\pi$
$709$	−1304.06	+	423.715i	−1.83930	+	0.597624i	−0.998407	+	0.0564168i	$0.982032\pi$
$710$		0			0
$711$	160.230	−	493.139i	0.225359	−	0.693585i
$712$		0			0
$713$	248.150	+	126.439i	0.348036	+	0.177333i
$714$		0			0
$715$	68.1156	+	27.5677i	0.0952666	+	0.0385563i
$716$		0			0
$717$	488.798	+	77.4180i	0.681727	+	0.107975i
$718$		0			0
$719$	−182.262	−	250.863i	−0.253494	−	0.348905i	0.663237	−	0.748409i	$-0.269182\pi$
$719$	−182.262	−	250.863i	−0.253494	−	0.348905i	−0.916731	+	0.399505i	$0.869182\pi$
$720$		0			0
$721$	516.031	+	374.919i	0.715716	+	0.519998i
$722$		0			0
$723$	138.289	+	271.408i	0.191272	+	0.375392i
$724$		0			0
$725$	39.8172	+	227.399i	0.0549202	+	0.313654i
$726$		0			0
$727$	573.466	−	292.196i	0.788812	−	0.401920i	−0.0126843	−	0.999920i	$-0.504038\pi$
$727$	573.466	−	292.196i	0.788812	−	0.401920i	0.801496	+	0.598000i	$0.204038\pi$
$728$		0			0
$729$	−598.987	+	824.434i	−0.821655	+	1.13091i
$730$		0			0
$731$	−192.523	+	139.876i	−0.263370	+	0.191349i
$732$		0			0
$733$	−157.542	+	994.681i	−0.214928	+	1.35700i	0.610287	+	0.792181i	$0.291054\pi$
$733$	−157.542	+	994.681i	−0.214928	+	1.35700i	−0.825214	+	0.564820i	$0.808946\pi$
$734$		0			0
$735$	64.4726	−	40.2335i	0.0877178	−	0.0547395i
$736$		0			0
$737$	454.627	−	892.257i	0.616862	−	1.21066i
$738$		0			0
$739$	884.508	+	287.394i	1.19690	+	0.388896i	0.838619	−	0.544718i	$-0.183363\pi$
$739$	884.508	+	287.394i	1.19690	+	0.388896i	0.358280	+	0.933614i	$0.383363\pi$
$740$		0			0
$741$	35.7893	+	110.148i	0.0482986	+	0.148648i
$742$		0			0
$743$	527.824	−	527.824i	0.710395	−	0.710395i	−0.256223	−	0.966618i	$-0.582478\pi$
$743$	527.824	−	527.824i	0.710395	−	0.710395i	0.966618	+	0.256223i	$0.0824780\pi$
$744$		0			0
$745$	−1070.29	+	453.557i	−1.43663	+	0.608802i
$746$		0			0
$747$	189.811	+	1198.42i	0.254097	+	1.60431i
$748$		0			0
$749$		−	1358.97i		−	1.81438i
$750$		0			0
$751$	−166.431			−0.221612			−0.110806	−	0.993842i	$-0.535343\pi$
$751$	−166.431			−0.221612			−0.110806	+	0.993842i	$0.535343\pi$
$752$		0			0
$753$	817.099	−	129.416i	1.08512	−	0.171867i
$754$		0			0
$755$	−336.926	−	795.066i	−0.446260	−	1.05307i
$756$		0			0
$757$	317.868	+	317.868i	0.419905	+	0.419905i	0.885171	−	0.465266i	$-0.154041\pi$
$757$	317.868	+	317.868i	0.419905	+	0.419905i	−0.465266	+	0.885171i	$0.654041\pi$
$758$		0			0
$759$	−471.865	+	153.318i	−0.621693	+	0.202000i
$760$		0			0
$761$	−371.860	+	1144.47i	−0.488646	+	1.50390i	0.337983	+	0.941152i	$0.390255\pi$
$761$	−371.860	+	1144.47i	−0.488646	+	1.50390i	−0.826629	+	0.562747i	$0.809745\pi$
$762$		0			0
$763$	−817.032	−	416.298i	−1.07081	−	0.545607i
$764$		0			0
$765$	−136.552	−	218.818i	−0.178499	−	0.286037i
$766$		0			0
$767$	−83.3466	−	13.2008i	−0.108666	−	0.0172110i
$768$		0			0
$769$	827.508	+	1138.97i	1.07608	+	1.48110i	0.863761	+	0.503901i	$0.168102\pi$
$769$	827.508	+	1138.97i	1.07608	+	1.48110i	0.212321	+	0.977200i	$0.431898\pi$
$770$		0			0
$771$	565.376	+	410.770i	0.733302	+	0.532775i
$772$		0			0
$773$	−460.242	−	903.275i	−0.595397	−	1.16853i	−0.970399	−	0.241508i	$-0.922358\pi$
$773$	−460.242	−	903.275i	−0.595397	−	1.16853i	0.375002	−	0.927024i	$-0.377642\pi$
$774$		0			0
$775$	−109.823	+	774.731i	−0.141707	+	0.999653i
$776$		0			0
$777$	384.475	−	195.900i	0.494819	−	0.252123i
$778$		0			0
$779$	−702.381	+	966.744i	−0.901644	+	1.24101i
$780$		0			0
$781$	−434.516	+	315.694i	−0.556358	+	0.404218i
$782$		0			0
$783$	13.5274	−	85.4089i	0.0172764	−	0.109079i
$784$		0			0
$785$	409.763	−	1012.46i	0.521991	−	1.28976i
$786$		0			0
$787$	574.499	−	1127.52i	0.729986	−	1.43268i	−0.164866	−	0.986316i	$-0.552719\pi$
$787$	574.499	−	1127.52i	0.729986	−	1.43268i	0.894852	−	0.446363i	$-0.147281\pi$
$788$		0			0
$789$	1412.91	+	459.083i	1.79076	+	0.581854i
$790$		0			0
$791$	−194.314	−	598.038i	−0.245657	−	0.756053i
$792$		0			0
$793$	−40.7817	+	40.7817i	−0.0514272	+	0.0514272i
$794$		0			0
$795$	1030.00	+	1186.30i	1.29559	+	1.49220i
$796$		0			0
$797$	153.706	+	970.462i	0.192856	+	1.21764i	0.874158	+	0.485641i	$0.161414\pi$
$797$	153.706	+	970.462i	0.192856	+	1.21764i	−0.681302	+	0.732002i	$0.738586\pi$
$798$		0			0
$799$		−	20.9097i		−	0.0261699i
$800$		0			0
$801$	734.952			0.917543
$802$		0			0
$803$	−739.636	+	117.147i	−0.921090	+	0.145886i
$804$		0			0
$805$	−299.339	+	26.0090i	−0.371850	+	0.0323093i
$806$		0			0
$807$	1653.22	+	1653.22i	2.04860	+	2.04860i
$808$		0			0
$809$	−748.876	+	243.325i	−0.925681	+	0.300772i	−0.732795	−	0.680449i	$-0.761785\pi$
$809$	−748.876	+	243.325i	−0.925681	+	0.300772i	−0.192886	+	0.981221i	$0.561785\pi$
$810$		0			0
$811$	0.441685	−	1.35937i	0.000544618	−	0.00167616i	−0.950784	−	0.309855i	$-0.899720\pi$
$811$	0.441685	−	1.35937i	0.000544618	−	0.00167616i	0.951328	+	0.308179i	$0.0997195\pi$
$812$		0			0
$813$	−163.989	−	83.5565i	−0.201708	−	0.102776i
$814$		0			0
$815$	12.7096	−	180.213i	0.0155946	−	0.221120i
$816$		0			0
$817$	−1105.14	−	175.037i	−1.35268	−	0.214244i
$818$		0			0
$819$	−52.0037	−	71.5770i	−0.0634966	−	0.0873956i
$820$		0			0
$821$	−266.252	−	193.444i	−0.324303	−	0.235620i	0.413707	−	0.910410i	$-0.364234\pi$
$821$	−266.252	−	193.444i	−0.324303	−	0.235620i	−0.738009	+	0.674791i	$0.764234\pi$
$822$		0			0
$823$	−384.423	−	754.474i	−0.467100	−	0.916736i	−0.997613	−	0.0690586i	$-0.978000\pi$
$823$	−384.423	−	754.474i	−0.467100	−	0.916736i	0.530512	−	0.847677i	$-0.322000\pi$
$824$		0			0
$825$	−837.577	−	1114.26i	−1.01524	−	1.35062i
$826$		0			0
$827$	308.853	−	157.369i	0.373462	−	0.190289i	−0.257177	−	0.966364i	$-0.582792\pi$
$827$	308.853	−	157.369i	0.373462	−	0.190289i	0.630640	+	0.776076i	$0.282792\pi$
$828$		0			0
$829$	172.734	−	237.748i	0.208364	−	0.286789i	−0.692026	−	0.721873i	$-0.743281\pi$
$829$	172.734	−	237.748i	0.208364	−	0.286789i	0.900390	+	0.435084i	$0.143281\pi$
$830$		0			0
$831$	−1920.29	+	1395.17i	−2.31082	+	1.67891i
$832$		0			0
$833$	−2.46775	+	15.5808i	−0.00296249	+	0.0187044i
$834$		0			0
$835$	13.9178	+	55.9632i	0.0166680	+	0.0670218i
$836$		0			0
$837$	133.062	−	261.149i	0.158975	−	0.312007i
$838$		0			0
$839$	613.225	+	199.249i	0.730900	+	0.237484i	0.650743	−	0.759298i	$-0.274458\pi$
$839$	613.225	+	199.249i	0.730900	+	0.237484i	0.0801576	+	0.996782i	$0.474458\pi$
$840$		0			0
$841$	233.532	+	718.739i	0.277684	+	0.854624i
$842$		0			0
$843$	512.856	−	512.856i	0.608370	−	0.608370i
$844$		0			0
$845$	432.041	−	718.067i	0.511291	−	0.849784i
$846$		0			0
$847$	−35.6649	−	225.179i	−0.0421073	−	0.265855i
$848$		0			0
$849$		−	1433.12i		−	1.68801i
$850$		0			0
$851$	126.847			0.149057
$852$		0			0
$853$	−959.328	+	151.943i	−1.12465	+	0.178127i	−0.690931	−	0.722920i	$-0.742799\pi$
$853$	−959.328	+	151.943i	−1.12465	+	0.178127i	−0.433720	+	0.901048i	$0.642799\pi$
$854$		0			0
$855$	273.515	−	1181.51i	0.319901	−	1.38188i
$856$		0			0
$857$	−41.2739	−	41.2739i	−0.0481609	−	0.0481609i	0.682616	−	0.730777i	$-0.260842\pi$
$857$	−41.2739	−	41.2739i	−0.0481609	−	0.0481609i	−0.730777	+	0.682616i	$0.760842\pi$
$858$		0			0
$859$	−1517.56	+	493.085i	−1.76666	+	0.574023i	−0.997855	−	0.0654608i	$-0.979148\pi$
$859$	−1517.56	+	493.085i	−1.76666	+	0.574023i	−0.768805	+	0.639483i	$0.779148\pi$
$860$		0			0
$861$	511.025	−	1572.77i	0.593525	−	1.82668i
$862$		0			0
$863$	179.583	+	91.5021i	0.208092	+	0.106028i	0.554930	−	0.831897i	$-0.312745\pi$
$863$	179.583	+	91.5021i	0.208092	+	0.106028i	−0.346839	+	0.937925i	$0.612745\pi$
$864$		0			0
$865$	311.816	−	371.158i	0.360481	−	0.429085i
$866$		0			0
$867$	−1183.58	−	187.461i	−1.36515	−	0.216218i
$868$		0			0
$869$	341.905	+	470.592i	0.393447	+	0.541533i
$870$		0			0
$871$	76.9356	+	55.8970i	0.0883302	+	0.0641756i
$872$		0			0
$873$	289.373	+	567.927i	0.331470	+	0.650546i
$874$		0			0
$875$	−341.979	−	771.809i	−0.390833	−	0.882067i
$876$		0			0
$877$	1256.66	−	640.303i	1.43291	−	0.730106i	0.446561	−	0.894753i	$-0.352649\pi$
$877$	1256.66	−	640.303i	1.43291	−	0.730106i	0.986352	+	0.164647i	$0.0526487\pi$
$878$		0			0
$879$	941.479	−	1295.83i	1.07108	−	1.47421i
$880$		0			0
$881$	640.260	−	465.176i	0.726742	−	0.528009i	−0.161789	−	0.986825i	$-0.551726\pi$
$881$	640.260	−	465.176i	0.726742	−	0.528009i	0.888531	+	0.458816i	$0.151726\pi$
$882$		0			0
$883$	−196.982	+	1243.69i	−0.223082	+	1.40849i	0.580969	+	0.813925i	$0.302674\pi$
$883$	−196.982	+	1243.69i	−0.223082	+	1.40849i	−0.804051	+	0.594560i	$0.797326\pi$
$884$		0			0
$885$	1225.66	+	1029.69i	1.38492	+	1.16350i
$886$		0			0
$887$	−417.143	+	818.690i	−0.470286	+	0.922988i	0.527036	+	0.849843i	$0.323303\pi$
$887$	−417.143	+	818.690i	−0.470286	+	0.922988i	−0.997321	+	0.0731444i	$0.976697\pi$
$888$		0			0
$889$	316.993	+	102.997i	0.356573	+	0.115858i
$890$		0			0
$891$	−222.318	−	684.224i	−0.249515	−	0.767928i
$892$		0			0
$893$	69.5194	−	69.5194i	0.0778492	−	0.0778492i
$894$		0			0
$895$	−987.948	−	228.706i	−1.10385	−	0.255538i
$896$		0			0
$897$	−7.37063	−	46.5363i	−0.00821698	−	0.0518800i
$898$		0			0
$899$		−	289.026i		−	0.321498i
$900$		0			0
$901$	−326.112			−0.361945
$902$		0			0
$903$	1529.41	−	242.235i	1.69370	−	0.268256i
$904$		0			0
$905$	−1300.77	−	782.639i	−1.43732	−	0.864795i
$906$		0			0
$907$	718.126	+	718.126i	0.791759	+	0.791759i	0.981780	−	0.190021i	$-0.0608555\pi$
$907$	718.126	+	718.126i	0.791759	+	0.791759i	−0.190021	+	0.981780i	$0.560855\pi$
$908$		0			0
$909$	−43.2769	+	14.0615i	−0.0476094	+	0.0154692i
$910$		0			0
$911$	253.082	−	778.907i	0.277807	−	0.855002i	−0.710656	−	0.703540i	$-0.751602\pi$
$911$	253.082	−	778.907i	0.277807	−	0.855002i	0.988463	−	0.151462i	$-0.0483982\pi$
$912$		0			0
$913$	−1212.81	−	617.959i	−1.32838	−	0.676844i
$914$		0			0
$915$	1061.73	−	264.047i	1.16036	−	0.288576i
$916$		0			0
$917$	−905.062	−	143.348i	−0.986981	−	0.156322i
$918$		0			0
$919$	−879.635	−	1210.71i	−0.957165	−	1.31742i	−0.948270	−	0.317464i	$-0.897169\pi$
$919$	−879.635	−	1210.71i	−0.957165	−	1.31742i	−0.00889471	−	0.999960i	$-0.502831\pi$
$920$		0			0
$921$	−1337.32	−	971.617i	−1.45203	−	1.05496i
$922$		0			0
$923$	−23.1556	−	45.4453i	−0.0250873	−	0.0492366i
$924$		0			0
$925$	115.626	+	337.107i	0.125001	+	0.364440i
$926$		0			0
$927$	933.206	−	475.492i	1.00669	−	0.512937i
$928$		0			0
$929$	−648.674	+	892.823i	−0.698250	+	0.961058i	0.301721	+	0.953396i	$0.402439\pi$
$929$	−648.674	+	892.823i	−0.698250	+	0.961058i	−0.999971	+	0.00766213i	$0.997561\pi$
$930$		0			0
$931$	−60.0066	+	43.5974i	−0.0644539	+	0.0468285i
$932$		0			0
$933$	−266.773	+	1684.34i	−0.285931	+	1.80530i
$934$		0			0
$935$	288.635	+	20.3562i	0.308700	+	0.0217713i
$936$		0			0
$937$	−26.6874	+	52.3769i	−0.0284817	+	0.0558985i	−0.904809	−	0.425818i	$-0.859986\pi$
$937$	−26.6874	+	52.3769i	−0.0284817	+	0.0558985i	0.876327	+	0.481716i	$0.159986\pi$
$938$		0			0
$939$	−1750.43	−	568.751i	−1.86415	−	0.605698i
$940$		0			0
$941$	−455.101	−	1400.66i	−0.483635	−	1.48848i	−0.833948	−	0.551844i	$-0.813925\pi$
$941$	−455.101	−	1400.66i	−0.483635	−	1.48848i	0.350312	−	0.936633i	$-0.386075\pi$
$942$		0			0
$943$	343.748	−	343.748i	0.364526	−	0.364526i
$944$		0			0
$945$	27.3715	+	315.020i	0.0289646	+	0.333355i
$946$		0			0
$947$	−214.634	−	1355.15i	−0.226646	−	1.43099i	−0.794202	−	0.607654i	$-0.792111\pi$
$947$	−214.634	−	1355.15i	−0.226646	−	1.43099i	0.567555	−	0.823335i	$-0.307889\pi$
$948$		0			0
$949$		−	71.1146i		−	0.0749363i
$950$		0			0
$951$	−779.503			−0.819667
$952$		0			0
$953$	−1007.09	+	159.507i	−1.05676	+	0.167374i	−0.660546	−	0.750786i	$-0.729675\pi$
$953$	−1007.09	+	159.507i	−1.05676	+	0.167374i	−0.396211	+	0.918159i	$0.629675\pi$
$954$		0			0
$955$	345.899	−	300.324i	0.362198	−	0.314475i
$956$		0			0
$957$	364.083	+	364.083i	0.380442	+	0.380442i
$958$		0			0
$959$	1191.58	−	387.169i	1.24253	−	0.403721i
$960$		0			0
$961$	5.75717	−	17.7188i	0.00599082	−	0.0184378i
$962$		0			0
$963$	−1988.25	−	1013.06i	−2.06464	−	1.05199i
$964$		0			0
$965$	847.815	+	343.127i	0.878565	+	0.355572i
$966$		0			0
$967$	−461.511	−	73.0962i	−0.477261	−	0.0755907i	−0.0868303	−	0.996223i	$-0.527674\pi$
$967$	−461.511	−	73.0962i	−0.477261	−	0.0755907i	−0.390430	+	0.920632i	$0.627674\pi$
$968$		0			0
$969$	268.059	+	368.951i	0.276634	+	0.380755i
$970$		0			0
$971$	−805.523	−	585.247i	−0.829581	−	0.602726i	0.0898601	−	0.995954i	$-0.471358\pi$
$971$	−805.523	−	585.247i	−0.829581	−	0.602726i	−0.919441	+	0.393229i	$0.871358\pi$
$972$		0			0
$973$	−396.113	−	777.415i	−0.407105	−	0.798988i
$974$		0			0
$975$	116.955	−	62.0075i	0.119954	−	0.0635975i
$976$		0			0
$977$	−1580.72	+	805.418i	−1.61793	+	0.824378i	−0.618684	+	0.785640i	$0.712334\pi$
$977$	−1580.72	+	805.418i	−1.61793	+	0.824378i	−0.999249	+	0.0387385i	$0.987666\pi$
$978$		0			0
$979$	−484.621	+	667.023i	−0.495016	+	0.681331i
$980$		0			0
$981$	−1218.13	+	885.024i	−1.24172	+	0.902165i
$982$		0			0
$983$	113.706	−	717.913i	0.115673	−	0.730329i	−0.859869	−	0.510515i	$-0.829455\pi$
$983$	113.706	−	717.913i	0.115673	−	0.730329i	0.975542	−	0.219814i	$-0.0705451\pi$
$984$		0			0
$985$	−521.704	+	325.564i	−0.529648	+	0.330522i
$986$		0			0
$987$	−61.7695	+	121.229i	−0.0625831	+	0.122826i
$988$		0			0
$989$	432.918	+	140.664i	0.437733	+	0.142228i
$990$		0			0
$991$	468.726	+	1442.59i	0.472983	+	1.45569i	0.848658	+	0.528941i	$0.177411\pi$
$991$	468.726	+	1442.59i	0.472983	+	1.45569i	−0.375675	+	0.926751i	$0.622589\pi$
$992$		0			0
$993$	−125.229	+	125.229i	−0.126112	+	0.126112i
$994$		0			0
$995$	−1796.32	+	761.229i	−1.80535	+	0.765055i
$996$		0			0
$997$	−125.911	−	794.973i	−0.126290	−	0.797365i	−0.966794	−	0.255559i	$-0.917741\pi$
$997$	−125.911	−	794.973i	−0.126290	−	0.797365i	0.840503	−	0.541806i	$-0.182259\pi$
$998$		0			0
$999$		−	133.493i		−	0.133626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.c.97.4		32
4.3	odd	2		25.3.f.a.22.4	yes	32
12.11	even	2		225.3.r.a.172.1		32
20.3	even	4		125.3.f.a.118.1		32
20.7	even	4		125.3.f.b.118.4		32
20.19	odd	2		125.3.f.c.7.1		32
25.8	odd	20	inner	400.3.bg.c.33.4		32
100.19	odd	10		125.3.f.b.107.4		32
100.31	odd	10		125.3.f.a.107.1		32
100.67	even	20		125.3.f.c.18.1		32
100.83	even	20		25.3.f.a.8.4	✓	32
300.83	odd	20		225.3.r.a.208.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.8.4	✓	32	100.83	even	20
25.3.f.a.22.4	yes	32	4.3	odd	2
125.3.f.a.107.1		32	100.31	odd	10
125.3.f.a.118.1		32	20.3	even	4
125.3.f.b.107.4		32	100.19	odd	10
125.3.f.b.118.4		32	20.7	even	4
125.3.f.c.7.1		32	20.19	odd	2
125.3.f.c.18.1		32	100.67	even	20
225.3.r.a.172.1		32	12.11	even	2
225.3.r.a.208.1		32	300.83	odd	20
400.3.bg.c.33.4		32	25.8	odd	20	inner
400.3.bg.c.97.4		32	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)

\(f(q)\)	\(=\)	\(q+(4.42692 - 0.701156i) q^{3} +(1.95091 + 4.60369i) q^{5} +(4.77540 + 4.77540i) q^{7} +(10.5465 - 3.42677i) q^{9} +O(q^{10})\)	\(q+(4.42692 - 0.701156i) q^{3} +(1.95091 + 4.60369i) q^{5} +(4.77540 + 4.77540i) q^{7} +(10.5465 - 3.42677i) q^{9} +(-3.84423 + 11.8313i) q^{11} +(-1.05261 - 0.536333i) q^{13} +(11.8644 + 19.0123i) q^{15} +(-4.59461 - 0.727715i) q^{17} +(-12.8564 - 17.6953i) q^{19} +(24.4886 + 17.7920i) q^{21} +(4.03970 + 7.92835i) q^{23} +(-17.3879 + 17.9628i) q^{25} +(8.34369 - 4.25132i) q^{27} +(5.42781 - 7.47074i) q^{29} +(25.3215 - 18.3971i) q^{31} +(-8.72252 + 55.0718i) q^{33} +(-12.6681 + 31.3008i) q^{35} +(6.47182 - 12.7017i) q^{37} +(-5.03589 - 1.63626i) q^{39} +(-16.8825 - 51.9589i) q^{41} +(36.1728 - 36.1728i) q^{43} +(36.3511 + 41.8676i) q^{45} +(0.703158 + 4.43956i) q^{47} -3.39110i q^{49} -20.8502 q^{51} +(69.2402 - 10.9666i) q^{53} +(-61.9675 + 5.38424i) q^{55} +(-69.3215 - 69.3215i) q^{57} +(67.9339 - 22.0730i) q^{59} +(15.0860 - 46.4300i) q^{61} +(66.7281 + 33.9997i) q^{63} +(0.415555 - 5.89224i) q^{65} +(-79.5063 - 12.5926i) q^{67} +(23.4424 + 32.2657i) q^{69} +(34.9284 + 25.3769i) q^{71} +(27.3286 + 53.6354i) q^{73} +(-64.3801 + 91.7115i) q^{75} +(-74.8571 + 38.1416i) q^{77} +(27.4839 - 37.8283i) q^{79} +(-46.7867 + 33.9925i) q^{81} +(-17.1166 + 108.070i) q^{83} +(-5.61351 - 22.5719i) q^{85} +(18.7904 - 36.8782i) q^{87} +(63.0322 + 20.4804i) q^{89} +(-2.46544 - 7.58786i) q^{91} +(99.1969 - 99.1969i) q^{93} +(56.3820 - 93.7088i) q^{95} +(8.99168 + 56.7712i) q^{97} +137.953i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9}+O(q^{10}) \) 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9	\( 32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9} + 6 q^{11} - 10 q^{13} + 10 q^{15} + 60 q^{17} - 90 q^{19} - 6 q^{21} - 10 q^{23} - 40 q^{25} + 100 q^{27} - 110 q^{29} + 6 q^{31} - 190 q^{33} + 120 q^{35} + 50 q^{37} - 390 q^{39} - 86 q^{41} - 230 q^{43} + 310 q^{45} - 70 q^{47} + 16 q^{51} - 190 q^{53} + 250 q^{55} - 650 q^{57} + 260 q^{59} + 114 q^{61} + 20 q^{63} + 360 q^{65} - 270 q^{67} + 340 q^{69} + 66 q^{71} + 30 q^{73} + 90 q^{75} - 250 q^{77} + 210 q^{79} + 62 q^{81} + 600 q^{85} - 300 q^{87} - 10 q^{89} + 6 q^{91} + 520 q^{93} - 310 q^{95} + 270 q^{97}+O(q^{100}) \) 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9 + 6 * q^11 - 10 * q^13 + 10 * q^15 + 60 * q^17 - 90 * q^19 - 6 * q^21 - 10 * q^23 - 40 * q^25 + 100 * q^27 - 110 * q^29 + 6 * q^31 - 190 * q^33 + 120 * q^35 + 50 * q^37 - 390 * q^39 - 86 * q^41 - 230 * q^43 + 310 * q^45 - 70 * q^47 + 16 * q^51 - 190 * q^53 + 250 * q^55 - 650 * q^57 + 260 * q^59 + 114 * q^61 + 20 * q^63 + 360 * q^65 - 270 * q^67 + 340 * q^69 + 66 * q^71 + 30 * q^73 + 90 * q^75 - 250 * q^77 + 210 * q^79 + 62 * q^81 + 600 * q^85 - 300 * q^87 - 10 * q^89 + 6 * q^91 + 520 * q^93 - 310 * q^95 + 270 * q^97

Introduction

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