LMFDB - Embedded newform 44.3.b.a.23.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [44,3,Mod(23,44)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("44.23"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 44 = 2^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	44.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.19891316319$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 7x^{8} + 4x^{7} - 7x^{6} + 82x^{5} - 28x^{4} + 64x^{3} + 448x^{2} - 512x + 1024 $ x^10 - 2x^9 + 7x^8 + 4x^7 - 7x^6 + 82x^5 - 28x^4 + 64x^3 + 448x^2 - 512*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.9
Root			$1.34558 - 1.47967i$ of defining polynomial
Character	$\chi$	$=$	44.23
Dual form			44.3.b.a.23.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.82909 - 0.808964i) q^{2} -1.36518i q^{3} +(2.69116 - 2.95934i) q^{4} -4.78741 q^{5} +(-1.10438 - 2.49704i) q^{6} +13.2453i q^{7} +(2.52837 - 7.58995i) q^{8} +7.13628 q^{9} +(-8.75661 + 3.87284i) q^{10} -3.31662i q^{11} +(-4.04003 - 3.67391i) q^{12} -15.5629 q^{13} +(10.7149 + 24.2268i) q^{14} +6.53568i q^{15} +(-1.51536 - 15.9281i) q^{16} -3.60849 q^{17} +(13.0529 - 5.77299i) q^{18} -0.106690i q^{19} +(-12.8837 + 14.1676i) q^{20} +18.0822 q^{21} +(-2.68303 - 6.06641i) q^{22} -17.0293i q^{23} +(-10.3616 - 3.45169i) q^{24} -2.08070 q^{25} +(-28.4660 + 12.5898i) q^{26} -22.0289i q^{27} +(39.1972 + 35.6450i) q^{28} +12.8533 q^{29} +(5.28712 + 11.9544i) q^{30} -6.68834i q^{31} +(-15.6570 - 27.9080i) q^{32} -4.52779 q^{33} +(-6.60027 + 2.91914i) q^{34} -63.4105i q^{35} +(19.2048 - 21.1187i) q^{36} +34.3710 q^{37} +(-0.0863087 - 0.195147i) q^{38} +21.2462i q^{39} +(-12.1044 + 36.3362i) q^{40} +60.7610 q^{41} +(33.0739 - 14.6278i) q^{42} +41.8412i q^{43} +(-9.81501 - 8.92555i) q^{44} -34.1643 q^{45} +(-13.7761 - 31.1482i) q^{46} +55.9490i q^{47} +(-21.7447 + 2.06875i) q^{48} -126.437 q^{49} +(-3.80580 + 1.68321i) q^{50} +4.92624i q^{51} +(-41.8822 + 46.0559i) q^{52} -31.8236 q^{53} +(-17.8206 - 40.2929i) q^{54} +15.8780i q^{55} +(100.531 + 33.4890i) q^{56} -0.145652 q^{57} +(23.5098 - 10.3978i) q^{58} -25.7715i q^{59} +(19.3413 + 17.5885i) q^{60} -13.1325 q^{61} +(-5.41062 - 12.2336i) q^{62} +94.5219i q^{63} +(-51.2147 - 38.3805i) q^{64} +74.5061 q^{65} +(-8.28174 + 3.66282i) q^{66} +22.3757i q^{67} +(-9.71102 + 10.6788i) q^{68} -23.2481 q^{69} +(-51.2968 - 115.984i) q^{70} -103.875i q^{71} +(18.0432 - 54.1640i) q^{72} +39.0545 q^{73} +(62.8678 - 27.8049i) q^{74} +2.84054i q^{75} +(-0.315733 - 0.287121i) q^{76} +43.9295 q^{77} +(17.1874 + 38.8612i) q^{78} +125.098i q^{79} +(7.25467 + 76.2542i) q^{80} +34.1531 q^{81} +(111.138 - 49.1535i) q^{82} -73.0218i q^{83} +(48.6619 - 53.5112i) q^{84} +17.2753 q^{85} +(33.8480 + 76.5314i) q^{86} -17.5470i q^{87} +(-25.1730 - 8.38567i) q^{88} -67.0310 q^{89} +(-62.4897 + 27.6377i) q^{90} -206.135i q^{91} +(-50.3955 - 45.8286i) q^{92} -9.13078 q^{93} +(45.2607 + 102.336i) q^{94} +0.510771i q^{95} +(-38.0995 + 21.3746i) q^{96} +26.1827 q^{97} +(-231.265 + 102.283i) q^{98} -23.6684i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 4 q^{5} + 6 q^{6} - 12 q^{8} - 30 q^{9} - 2 q^{10} + 40 q^{12} - 4 q^{13} - 4 q^{14} - 40 q^{16} + 20 q^{17} - 22 q^{18} - 64 q^{20} + 32 q^{21} + 36 q^{24} - 10 q^{25} - 36 q^{26} + 40 q^{28}+ \cdots - 568 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 - 12 * q^8 - 30 * q^9 - 2 * q^10 + 40 * q^12 - 4 * q^13 - 4 * q^14 - 40 * q^16 + 20 * q^17 - 22 * q^18 - 64 * q^20 + 32 * q^21 + 36 * q^24 - 10 * q^25 - 36 * q^26 + 40 * q^28 + 28 * q^29 + 126 * q^30 + 80 * q^32 - 88 * q^34 - 4 * q^36 - 100 * q^37 + 40 * q^38 - 12 * q^40 + 100 * q^41 + 260 * q^42 - 44 * q^44 - 44 * q^45 - 130 * q^46 + 24 * q^48 - 22 * q^49 - 198 * q^50 - 176 * q^52 + 100 * q^53 - 350 * q^54 + 136 * q^56 - 112 * q^57 + 116 * q^58 - 136 * q^60 - 52 * q^61 + 134 * q^62 - 368 * q^64 - 184 * q^65 + 110 * q^66 + 176 * q^68 + 184 * q^69 - 36 * q^70 + 360 * q^72 + 84 * q^73 + 362 * q^74 + 504 * q^76 - 232 * q^78 - 120 * q^80 + 330 * q^81 + 220 * q^82 - 40 * q^84 - 216 * q^85 + 556 * q^86 - 132 * q^88 + 28 * q^89 - 520 * q^90 + 152 * q^92 - 72 * q^93 - 272 * q^94 - 704 * q^96 - 180 * q^97 - 568 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/44\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.82909	−	0.808964i	0.914546	−	0.404482i
$2$	1.82909	−	0.808964i	0.914546	−	0.404482i
$3$		−	1.36518i		−	0.455060i	−0.973771	−	0.227530i	$-0.926935\pi$
$3$		−	1.36518i		−	0.455060i	0.973771	−	0.227530i	$-0.0730650\pi$
$4$	2.69116	−	2.95934i	0.672789	−	0.739835i
$5$	−4.78741			−0.957482			−0.478741	−	0.877956i	$-0.658907\pi$
$5$	−4.78741			−0.957482			−0.478741	+	0.877956i	$0.658907\pi$
$6$	−1.10438	−	2.49704i	−0.184064	−	0.416173i
$7$			13.2453i			1.89218i	0.323905	+	0.946090i	$0.395004\pi$
$7$			13.2453i			1.89218i	−0.323905	+	0.946090i	$0.604996\pi$
$8$	2.52837	−	7.58995i	0.316047	−	0.948744i
$9$	7.13628			0.792920
$10$	−8.75661	+	3.87284i	−0.875661	+	0.387284i
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$	−4.04003	−	3.67391i	−0.336669	−	0.306159i
$13$	−15.5629			−1.19715			−0.598574	−	0.801068i	$-0.704266\pi$
$13$	−15.5629			−1.19715			−0.598574	+	0.801068i	$0.704266\pi$
$14$	10.7149	+	24.2268i	0.765352	+	1.73049i
$15$			6.53568i			0.435712i
$16$	−1.51536	−	15.9281i	−0.0947103	−	0.995505i
$17$	−3.60849			−0.212264			−0.106132	−	0.994352i	$-0.533847\pi$
$17$	−3.60849			−0.212264			−0.106132	+	0.994352i	$0.533847\pi$
$18$	13.0529	−	5.77299i	0.725162	−	0.320722i
$19$		−	0.106690i		−	0.00561529i	−0.999996	−	0.00280764i	$-0.999106\pi$
$19$		−	0.106690i		−	0.00561529i	0.999996	−	0.00280764i	$-0.000893702\pi$
$20$	−12.8837	+	14.1676i	−0.644183	+	0.708378i
$21$	18.0822			0.861055
$22$	−2.68303	−	6.06641i	−0.121956	−	0.275746i
$23$		−	17.0293i		−	0.740406i	−0.928951	−	0.370203i	$-0.879288\pi$
$23$		−	17.0293i		−	0.740406i	0.928951	−	0.370203i	$-0.120712\pi$
$24$	−10.3616	−	3.45169i	−0.431735	−	0.143820i
$25$	−2.08070			−0.0832282
$26$	−28.4660	+	12.5898i	−1.09485	+	0.484224i
$27$		−	22.0289i		−	0.815886i
$28$	39.1972	+	35.6450i	1.39990	+	1.27304i
$29$	12.8533			0.443216			0.221608	−	0.975136i	$-0.428869\pi$
$29$	12.8533			0.443216			0.221608	+	0.975136i	$0.428869\pi$
$30$	5.28712	+	11.9544i	0.176237	+	0.398478i
$31$		−	6.68834i		−	0.215753i	−0.994164	−	0.107876i	$-0.965595\pi$
$31$		−	6.68834i		−	0.215753i	0.994164	−	0.107876i	$-0.0344051\pi$
$32$	−15.6570	−	27.9080i	−0.489281	−	0.872126i
$33$	−4.52779			−0.137206
$34$	−6.60027	+	2.91914i	−0.194126	+	0.0858571i
$35$		−	63.4105i		−	1.81173i
$36$	19.2048	−	21.1187i	0.533468	−	0.586630i
$37$	34.3710			0.928947			0.464473	−	0.885587i	$-0.346244\pi$
$37$	34.3710			0.928947			0.464473	+	0.885587i	$0.346244\pi$
$38$	−0.0863087	−	0.195147i	−0.00227128	−	0.00513544i
$39$			21.2462i			0.544774i
$40$	−12.1044	+	36.3362i	−0.302609	+	0.908405i
$41$	60.7610			1.48198			0.740988	−	0.671518i	$-0.234357\pi$
$41$	60.7610			1.48198			0.740988	+	0.671518i	$0.234357\pi$
$42$	33.0739	−	14.6278i	0.787475	−	0.348281i
$43$			41.8412i			0.973051i	0.873666	+	0.486526i	$0.161736\pi$
$43$			41.8412i			0.973051i	−0.873666	+	0.486526i	$0.838264\pi$
$44$	−9.81501	−	8.92555i	−0.223069	−	0.202853i
$45$	−34.1643			−0.759207
$46$	−13.7761	−	31.1482i	−0.299481	−	0.677135i
$47$			55.9490i			1.19040i	0.803576	+	0.595202i	$0.202928\pi$
$47$			55.9490i			1.19040i	−0.803576	+	0.595202i	$0.797072\pi$
$48$	−21.7447	+	2.06875i	−0.453014	+	0.0430989i
$49$	−126.437			−2.58034
$50$	−3.80580	+	1.68321i	−0.0761160	+	0.0336643i
$51$			4.92624i			0.0965930i
$52$	−41.8822	+	46.0559i	−0.805428	+	0.885691i
$53$	−31.8236			−0.600445			−0.300222	−	0.953869i	$-0.597061\pi$
$53$	−31.8236			−0.600445			−0.300222	+	0.953869i	$0.597061\pi$
$54$	−17.8206	−	40.2929i	−0.330011	−	0.746166i
$55$			15.8780i			0.288692i
$56$	100.531	+	33.4890i	1.79519	+	0.598017i
$57$	−0.145652			−0.00255529
$58$	23.5098	−	10.3978i	0.405342	−	0.179273i
$59$		−	25.7715i		−	0.436805i	−0.975859	−	0.218402i	$-0.929915\pi$
$59$		−	25.7715i		−	0.436805i	0.975859	−	0.218402i	$-0.0700846\pi$
$60$	19.3413	+	17.5885i	0.322355	+	0.293142i
$61$	−13.1325			−0.215288			−0.107644	−	0.994190i	$-0.534331\pi$
$61$	−13.1325			−0.215288			−0.107644	+	0.994190i	$0.534331\pi$
$62$	−5.41062	−	12.2336i	−0.0872681	−	0.197316i
$63$			94.5219i			1.50035i
$64$	−51.2147	−	38.3805i	−0.800229	−	0.599695i
$65$	74.5061			1.14625
$66$	−8.28174	+	3.66282i	−0.125481	+	0.0554972i
$67$			22.3757i			0.333966i	0.985960	+	0.166983i	$0.0534025\pi$
$67$			22.3757i			0.333966i	−0.985960	+	0.166983i	$0.946598\pi$
$68$	−9.71102	+	10.6788i	−0.142809	+	0.157041i
$69$	−23.2481			−0.336929
$70$	−51.2968	−	115.984i	−0.732811	−	1.65691i
$71$		−	103.875i		−	1.46303i	−0.681827	−	0.731513i	$-0.738814\pi$
$71$		−	103.875i		−	1.46303i	0.681827	−	0.731513i	$-0.261186\pi$
$72$	18.0432	−	54.1640i	0.250600	−	0.752278i
$73$	39.0545			0.534993			0.267497	−	0.963559i	$-0.413804\pi$
$73$	39.0545			0.534993			0.267497	+	0.963559i	$0.413804\pi$
$74$	62.8678	−	27.8049i	0.849564	−	0.375742i
$75$			2.84054i			0.0378738i
$76$	−0.315733	−	0.287121i	−0.00415438	−	0.00377790i
$77$	43.9295			0.570514
$78$	17.1874	+	38.8612i	0.220351	+	0.498221i
$79$			125.098i			1.58352i	0.610835	+	0.791758i	$0.290834\pi$
$79$			125.098i			1.58352i	−0.610835	+	0.791758i	$0.709166\pi$
$80$	7.25467	+	76.2542i	0.0906834	+	0.953178i
$81$	34.1531			0.421643
$82$	111.138	−	49.1535i	1.35534	−	0.599433i
$83$		−	73.0218i		−	0.879781i	−0.898051	−	0.439891i	$-0.855017\pi$
$83$		−	73.0218i		−	0.879781i	0.898051	−	0.439891i	$-0.144983\pi$
$84$	48.6619	−	53.5112i	0.579308	−	0.637038i
$85$	17.2753			0.203239
$86$	33.8480	+	76.5314i	0.393582	+	0.889900i
$87$		−	17.5470i		−	0.201690i
$88$	−25.1730	−	8.38567i	−0.286057	−	0.0952917i
$89$	−67.0310			−0.753157			−0.376578	−	0.926385i	$-0.622899\pi$
$89$	−67.0310			−0.753157			−0.376578	+	0.926385i	$0.622899\pi$
$90$	−62.4897	+	27.6377i	−0.694330	+	0.307085i
$91$		−	206.135i		−	2.26522i
$92$	−50.3955	−	45.8286i	−0.547778	−	0.498137i
$93$	−9.13078			−0.0981805
$94$	45.2607	+	102.336i	0.481497	+	1.08868i
$95$			0.510771i			0.00537654i
$96$	−38.0995	+	21.3746i	−0.396870	+	0.222652i
$97$	26.1827			0.269925			0.134963	−	0.990851i	$-0.456909\pi$
$97$	26.1827			0.269925			0.134963	+	0.990851i	$0.456909\pi$
$98$	−231.265	+	102.283i	−2.35984	+	1.04370i
$99$		−	23.6684i		−	0.239075i
$100$	−5.59950	+	6.15751i	−0.0559950	+	0.0615751i
$101$	−20.8702			−0.206636			−0.103318	−	0.994648i	$-0.532946\pi$
$101$	−20.8702			−0.206636			−0.103318	+	0.994648i	$0.532946\pi$
$102$	3.98515	+	9.01055i	0.0390701	+	0.0883388i
$103$			76.3094i			0.740868i	0.928859	+	0.370434i	$0.120791\pi$
$103$			76.3094i			0.740868i	−0.928859	+	0.370434i	$0.879209\pi$
$104$	−39.3489	+	118.122i	−0.378355	+	1.13579i
$105$	−86.5667			−0.824445
$106$	−58.2083	+	25.7441i	−0.549135	+	0.242869i
$107$			18.7439i			0.175177i	0.996157	+	0.0875885i	$0.0279161\pi$
$107$			18.7439i			0.175177i	−0.996157	+	0.0875885i	$0.972084\pi$
$108$	−65.1911	−	59.2833i	−0.603621	−	0.548919i
$109$	167.514			1.53682			0.768412	−	0.639956i	$-0.221047\pi$
$109$	167.514			1.53682			0.768412	+	0.639956i	$0.221047\pi$
$110$	12.8448	+	29.0424i	0.116771	+	0.264022i
$111$		−	46.9226i		−	0.422726i
$112$	210.971	−	20.0714i	1.88367	−	0.179209i
$113$	−70.4294			−0.623269			−0.311635	−	0.950202i	$-0.600876\pi$
$113$	−70.4294			−0.623269			−0.311635	+	0.950202i	$0.600876\pi$
$114$	−0.266410	+	0.117827i	−0.00233693	+	0.00103357i
$115$			81.5264i			0.708925i
$116$	34.5901	−	38.0372i	0.298191	−	0.327907i
$117$	−111.061			−0.949243
$118$	−20.8482	−	47.1384i	−0.176680	−	0.399478i
$119$		−	47.7954i		−	0.401642i
$120$	49.6054	+	16.5246i	0.413379	+	0.137705i
$121$	−11.0000			−0.0909091
$122$	−24.0206	+	10.6238i	−0.196890	+	0.0870799i
$123$		−	82.9498i		−	0.674388i
$124$	−19.7931	−	17.9994i	−0.159621	−	0.145156i
$125$	129.646			1.03717
$126$	76.4648	+	172.889i	0.606863	+	1.37214i
$127$		−	16.5521i		−	0.130331i	−0.997874	−	0.0651657i	$-0.979242\pi$
$127$		−	16.5521i		−	0.130331i	0.997874	−	0.0651657i	$-0.0207576\pi$
$128$	−124.725	−	28.7706i	−0.974412	−	0.224770i
$129$	57.1208			0.442797
$130$	136.278	−	60.2727i	1.04830	−	0.463636i
$131$			114.512i			0.874135i	0.899429	+	0.437068i	$0.143983\pi$
$131$			114.512i			0.874135i	−0.899429	+	0.437068i	$0.856017\pi$
$132$	−12.1850	+	13.3993i	−0.0923105	+	0.101510i
$133$	1.41314			0.0106251
$134$	18.1011	+	40.9272i	0.135083	+	0.305427i
$135$			105.462i			0.781196i
$136$	−9.12362	+	27.3883i	−0.0670855	+	0.201384i
$137$	32.4369			0.236766			0.118383	−	0.992968i	$-0.462229\pi$
$137$	32.4369			0.236766			0.118383	+	0.992968i	$0.462229\pi$
$138$	−42.5229	+	18.8069i	−0.308137	+	0.136282i
$139$		−	120.497i		−	0.866886i	−0.901181	−	0.433443i	$-0.857299\pi$
$139$		−	120.497i		−	0.866886i	0.901181	−	0.433443i	$-0.142701\pi$
$140$	−187.653	−	170.647i	−1.34038	−	1.21891i
$141$	76.3805			0.541706
$142$	−84.0310	−	189.997i	−0.591768	−	1.33801i
$143$			51.6164i			0.360954i
$144$	−10.8141	−	113.667i	−0.0750977	−	0.789356i
$145$	−61.5339			−0.424371
$146$	71.4343	−	31.5937i	0.489276	−	0.216395i
$147$			172.609i			1.17421i
$148$	92.4978	−	101.715i	0.624985	−	0.687267i
$149$	−175.284			−1.17640			−0.588202	−	0.808714i	$-0.700164\pi$
$149$	−175.284			−1.17640			−0.588202	+	0.808714i	$0.700164\pi$
$150$	2.29789	+	5.19560i	0.0153193	+	0.0346373i
$151$		−	288.507i		−	1.91064i	−0.295573	−	0.955320i	$-0.595511\pi$
$151$		−	288.507i		−	1.91064i	0.295573	−	0.955320i	$-0.404489\pi$
$152$	−0.809775	−	0.269753i	−0.00532747	−	0.00177469i
$153$	−25.7512			−0.168309
$154$	80.3512	−	35.5374i	0.521761	−	0.230762i
$155$			32.0198i			0.206579i
$156$	62.8746	+	57.1768i	0.403043	+	0.366518i
$157$	−160.775			−1.02405			−0.512023	−	0.858972i	$-0.671104\pi$
$157$	−160.775			−1.02405			−0.512023	+	0.858972i	$0.671104\pi$
$158$	101.200	+	228.815i	0.640504	+	1.44820i
$159$			43.4449i			0.273238i
$160$	74.9564	+	133.607i	0.468477	+	0.835045i
$161$	225.558			1.40098
$162$	62.4692	−	27.6286i	0.385612	−	0.170547i
$163$			262.034i			1.60757i	0.594918	+	0.803786i	$0.297185\pi$
$163$			262.034i			1.60757i	−0.594918	+	0.803786i	$0.702815\pi$
$164$	163.517	−	179.812i	0.997057	−	1.09642i
$165$	21.6764			0.131372
$166$	−59.0720	−	133.564i	−0.355856	−	0.804600i
$167$			30.2816i			0.181327i	0.995882	+	0.0906635i	$0.0288988\pi$
$167$			30.2816i			0.181327i	−0.995882	+	0.0906635i	$0.971101\pi$
$168$	45.7185	−	137.243i	0.272134	−	0.816921i
$169$	73.2044			0.433162
$170$	31.5982	−	13.9751i	0.185872	−	0.0822066i
$171$		−	0.761374i		−	0.00445248i
$172$	123.822	+	112.601i	0.719897	+	0.654658i
$173$	−322.712			−1.86539			−0.932693	−	0.360672i	$-0.882547\pi$
$173$	−322.712			−1.86539			−0.932693	+	0.360672i	$0.882547\pi$
$174$	−14.1949	−	32.0951i	−0.0815799	−	0.184455i
$175$		−	27.5595i		−	0.157483i
$176$	−52.8275	+	5.02590i	−0.300156	+	0.0285562i
$177$	−35.1827			−0.198772
$178$	−122.606	+	54.2256i	−0.688797	+	0.304638i
$179$			132.394i			0.739631i	0.929105	+	0.369816i	$0.120579\pi$
$179$			132.394i			0.739631i	−0.929105	+	0.369816i	$0.879421\pi$
$180$	−91.9415	+	101.104i	−0.510786	+	0.561688i
$181$	140.067			0.773853			0.386926	−	0.922111i	$-0.373537\pi$
$181$	140.067			0.773853			0.386926	+	0.922111i	$0.373537\pi$
$182$	−166.756	−	377.040i	−0.916240	−	2.07165i
$183$			17.9283i			0.0979688i
$184$	−129.252	−	43.0565i	−0.702455	−	0.234003i
$185$	−164.548			−0.889450
$186$	−16.7010	+	7.38647i	−0.0897906	+	0.0397122i
$187$			11.9680i			0.0640001i
$188$	165.572	+	150.568i	0.880702	+	0.800891i
$189$	291.779			1.54380
$190$	0.413195	+	0.934247i	0.00217471	+	0.00491709i
$191$		−	68.3559i		−	0.357884i	−0.983860	−	0.178942i	$-0.942732\pi$
$191$		−	68.3559i		−	0.357884i	0.983860	−	0.178942i	$-0.0572675\pi$
$192$	−52.3962	+	69.9172i	−0.272897	+	0.364152i
$193$	190.972			0.989494			0.494747	−	0.869037i	$-0.335261\pi$
$193$	190.972			0.989494			0.494747	+	0.869037i	$0.335261\pi$
$194$	47.8906	−	21.1809i	0.246859	−	0.109180i
$195$		−	101.714i		−	0.521611i
$196$	−340.261	+	374.169i	−1.73603	+	1.90903i
$197$	−121.722			−0.617878			−0.308939	−	0.951082i	$-0.599974\pi$
$197$	−121.722			−0.617878			−0.308939	+	0.951082i	$0.599974\pi$
$198$	−19.1469	−	43.2916i	−0.0967013	−	0.218645i
$199$		−	134.316i		−	0.674955i	−0.941334	−	0.337478i	$-0.890426\pi$
$199$		−	134.316i		−	0.674955i	0.941334	−	0.337478i	$-0.109574\pi$
$200$	−5.26080	+	15.7924i	−0.0263040	+	0.0789622i
$201$	30.5469			0.151975
$202$	−38.1736	+	16.8833i	−0.188978	+	0.0835805i
$203$			170.245i			0.838644i
$204$	14.5784	+	13.2573i	0.0714628	+	0.0649867i
$205$	−290.888			−1.41897
$206$	61.7316	+	139.577i	0.299668	+	0.677558i
$207$		−	121.526i		−	0.587083i
$208$	23.5835	+	247.887i	0.113382	+	1.19177i
$209$	−0.353852			−0.00169307
$210$	−158.338	+	70.0293i	−0.753993	+	0.333473i
$211$			94.7575i			0.449088i	0.974464	+	0.224544i	$0.0720892\pi$
$211$			94.7575i			0.449088i	−0.974464	+	0.224544i	$0.927911\pi$
$212$	−85.6422	+	94.1767i	−0.403973	+	0.444230i
$213$	−141.808			−0.665765
$214$	15.1632	+	34.2844i	0.0708559	+	0.160207i
$215$		−	200.311i		−	0.931679i
$216$	−167.198	−	55.6974i	−0.774067	−	0.257858i
$217$	88.5887			0.408243
$218$	306.398	−	135.513i	1.40550	−	0.621617i
$219$		−	53.3164i		−	0.243454i
$220$	46.9885	+	42.7303i	0.213584	+	0.194229i
$221$	56.1587			0.254112
$222$	−37.9587	−	85.8258i	−0.170985	−	0.386603i
$223$		−	274.775i		−	1.23217i	−0.787678	−	0.616087i	$-0.788717\pi$
$223$		−	274.775i		−	1.23217i	0.787678	−	0.616087i	$-0.211283\pi$
$224$	369.649	−	207.381i	1.65022	−	0.925807i
$225$	−14.8485			−0.0659933
$226$	−128.822	+	56.9748i	−0.570008	+	0.252101i
$227$			251.028i			1.10585i	0.833231	+	0.552926i	$0.186489\pi$
$227$			251.028i			1.10585i	−0.833231	+	0.552926i	$0.813511\pi$
$228$	−0.391971	+	0.431033i	−0.00171917	+	0.00189049i
$229$	261.081			1.14009			0.570045	−	0.821613i	$-0.306926\pi$
$229$	261.081			1.14009			0.570045	+	0.821613i	$0.306926\pi$
$230$	65.9519	+	149.119i	0.286747	+	0.648345i
$231$		−	59.9717i		−	0.259618i
$232$	32.4979	−	97.5556i	0.140077	−	0.420498i
$233$	64.5516			0.277045			0.138523	−	0.990359i	$-0.455765\pi$
$233$	64.5516			0.277045			0.138523	+	0.990359i	$0.455765\pi$
$234$	−203.142	+	89.8446i	−0.868126	+	0.383951i
$235$		−	267.851i		−	1.13979i
$236$	−76.2666	−	69.3551i	−0.323163	−	0.293878i
$237$	170.781			0.720595
$238$	−38.6648	−	87.4222i	−0.162457	−	0.367320i
$239$			187.758i			0.785600i	0.919624	+	0.392800i	$0.128494\pi$
$239$			187.758i			0.785600i	−0.919624	+	0.392800i	$0.871506\pi$
$240$	104.101	−	9.90393i	0.433753	−	0.0412664i
$241$	−258.284			−1.07172			−0.535859	−	0.844308i	$-0.680012\pi$
$241$	−258.284			−1.07172			−0.535859	+	0.844308i	$0.680012\pi$
$242$	−20.1200	+	8.89860i	−0.0831405	+	0.0367711i
$243$		−	244.886i		−	1.00776i
$244$	−35.3417	+	38.8636i	−0.144843	+	0.159277i
$245$	605.305			2.47063
$246$	−67.1033	−	151.723i	−0.272778	−	0.616759i
$247$			1.66042i			0.00672233i
$248$	−50.7641	−	16.9106i	−0.204694	−	0.0681880i
$249$	−99.6880			−0.400353
$250$	237.135	−	104.879i	0.948541	−	0.419517i
$251$		−	401.899i		−	1.60119i	−0.599204	−	0.800596i	$-0.704516\pi$
$251$		−	401.899i		−	1.60119i	0.599204	−	0.800596i	$-0.295484\pi$
$252$	279.722	+	254.373i	1.11001	+	1.00942i
$253$	−56.4799			−0.223241
$254$	−13.3900	−	30.2753i	−0.0527167	−	0.119194i
$255$		−	23.5839i		−	0.0924861i
$256$	−251.407	+	48.2737i	−0.982060	+	0.188569i
$257$	−177.029			−0.688830			−0.344415	−	0.938817i	$-0.611923\pi$
$257$	−177.029			−0.688830			−0.344415	+	0.938817i	$0.611923\pi$
$258$	104.479	−	46.2086i	0.404958	−	0.179103i
$259$			455.253i			1.75773i
$260$	200.507	−	220.489i	0.771182	−	0.848033i
$261$	91.7246			0.351435
$262$	92.6358	+	209.452i	0.353572	+	0.799437i
$263$		−	302.608i		−	1.15060i	−0.817943	−	0.575300i	$-0.804885\pi$
$263$		−	302.608i		−	1.15060i	0.817943	−	0.575300i	$-0.195115\pi$
$264$	−11.4479	+	34.3657i	−0.0433634	+	0.130173i
$265$	152.353			0.574915
$266$	2.58477	−	1.14318i	0.00971717	−	0.00429767i
$267$			91.5093i			0.342731i
$268$	66.2173	+	60.2165i	0.247080	+	0.224689i
$269$	−9.06122			−0.0336848			−0.0168424	−	0.999858i	$-0.505361\pi$
$269$	−9.06122			−0.0336848			−0.0168424	+	0.999858i	$0.505361\pi$
$270$	85.3145	+	192.899i	0.315980	+	0.714440i
$271$			23.0393i			0.0850158i	0.999096	+	0.0425079i	$0.0135348\pi$
$271$			23.0393i			0.0850158i	−0.999096	+	0.0425079i	$0.986465\pi$
$272$	5.46818	+	57.4764i	0.0201036	+	0.211310i
$273$	−281.411			−1.03081
$274$	59.3301	−	26.2403i	0.216533	−	0.0957674i
$275$			6.90092i			0.0250942i
$276$	−62.5643	+	68.7990i	−0.226682	+	0.249272i
$277$	−331.238			−1.19581			−0.597903	−	0.801569i	$-0.703999\pi$
$277$	−331.238			−1.19581			−0.597903	+	0.801569i	$0.703999\pi$
$278$	−97.4778	−	220.400i	−0.350640	−	0.792807i
$279$		−	47.7299i		−	0.171075i
$280$	−481.282	−	160.325i	−1.71887	−	0.572591i
$281$	59.7255			0.212546			0.106273	−	0.994337i	$-0.466108\pi$
$281$	59.7255			0.212546			0.106273	+	0.994337i	$0.466108\pi$
$282$	139.707	−	61.7890i	0.495415	−	0.219110i
$283$			501.669i			1.77268i	0.463032	+	0.886342i	$0.346762\pi$
$283$			501.669i			1.77268i	−0.463032	+	0.886342i	$0.653238\pi$
$284$	−307.401	−	279.543i	−1.08240	−	0.984308i
$285$	0.697295			0.00244665
$286$	41.7558	+	94.4111i	0.145999	+	0.330109i
$287$			804.796i			2.80417i
$288$	−111.733	−	199.160i	−0.387961	−	0.691527i
$289$	−275.979			−0.954944
$290$	−112.551	+	49.7787i	−0.388107	+	0.171651i
$291$		−	35.7441i		−	0.122832i
$292$	105.102	−	115.575i	0.359938	−	0.395806i
$293$	109.292			0.373009			0.186505	−	0.982454i	$-0.440284\pi$
$293$	109.292			0.373009			0.186505	+	0.982454i	$0.440284\pi$
$294$	139.634	+	315.718i	0.474947	+	1.07387i
$295$			123.379i			0.418233i
$296$	86.9028	−	260.874i	0.293591	−	0.881332i
$297$	−73.0617			−0.245999
$298$	−320.611	+	141.799i	−1.07588	+	0.475834i
$299$			265.026i			0.886375i
$300$	8.40611	+	7.64432i	0.0280204	+	0.0254811i
$301$	−554.198			−1.84119
$302$	−233.391	−	527.705i	−0.772819	−	1.74737i
$303$			28.4916i			0.0940318i
$304$	−1.69937	+	0.161675i	−0.00559005	+	0.000531826i
$305$	62.8709			0.206134
$306$	−47.1014	+	20.8318i	−0.153926	+	0.0680778i
$307$			13.4270i			0.0437360i	0.999761	+	0.0218680i	$0.00696136\pi$
$307$			13.4270i			0.0437360i	−0.999761	+	0.0218680i	$0.993039\pi$
$308$	118.221	−	130.002i	0.383835	−	0.422086i
$309$	104.176			0.337139
$310$	25.9029	+	58.5672i	0.0835576	+	0.188926i
$311$			125.527i			0.403623i	0.979424	+	0.201811i	$0.0646828\pi$
$311$			125.527i			0.403623i	−0.979424	+	0.201811i	$0.935317\pi$
$312$	161.257	+	53.7183i	0.516851	+	0.172174i
$313$	490.278			1.56638			0.783191	−	0.621781i	$-0.213591\pi$
$313$	490.278			1.56638			0.783191	+	0.621781i	$0.213591\pi$
$314$	−294.073	+	130.061i	−0.936537	+	0.414208i
$315$		−	452.515i		−	1.43656i
$316$	370.207	+	336.658i	1.17154	+	1.06537i
$317$	−61.8156			−0.195002			−0.0975010	−	0.995235i	$-0.531085\pi$
$317$	−61.8156			−0.195002			−0.0975010	+	0.995235i	$0.531085\pi$
$318$	35.1454	+	79.4648i	0.110520	+	0.249889i
$319$		−	42.6295i		−	0.133635i
$320$	245.186	+	183.743i	0.766205	+	0.574197i
$321$	25.5889			0.0797161
$322$	412.566	−	182.468i	1.28126	−	0.566671i
$323$			0.384992i			0.00119193i
$324$	91.9113	−	101.071i	0.283677	−	0.311946i
$325$	32.3818			0.0996364
$326$	211.976	+	479.285i	0.650234	+	1.47020i
$327$		−	228.686i		−	0.699347i
$328$	153.627	−	461.173i	0.468374	−	1.40602i
$329$	−741.059			−2.25246
$330$	39.6481	−	17.5354i	0.120146	−	0.0531376i
$331$			170.855i			0.516177i	0.966121	+	0.258089i	$0.0830927\pi$
$331$			170.855i			0.516177i	−0.966121	+	0.258089i	$0.916907\pi$
$332$	−216.096	−	196.513i	−0.650893	−	0.591907i
$333$	245.281			0.736581
$334$	24.4967	+	55.3879i	0.0733435	+	0.165832i
$335$		−	107.122i		−	0.319766i
$336$	−27.4011	−	288.014i	−0.0815508	−	0.857185i
$337$	322.479			0.956911			0.478456	−	0.878112i	$-0.341197\pi$
$337$	322.479			0.956911			0.478456	+	0.878112i	$0.341197\pi$
$338$	133.898	−	59.2197i	0.396147	−	0.175206i
$339$			96.1488i			0.283625i
$340$	46.4906	−	51.1236i	0.136737	−	0.150363i
$341$	−22.1827			−0.0650519
$342$	−0.615924	−	1.39262i	−0.00180095	−	0.00407200i
$343$		−	1025.67i		−	2.99029i
$344$	317.573	+	105.790i	0.923176	+	0.307530i
$345$	111.298			0.322603
$346$	−590.269	+	261.062i	−1.70598	+	0.754515i
$347$			33.6711i			0.0970348i	0.998822	+	0.0485174i	$0.0154496\pi$
$347$			33.6711i			0.0970348i	−0.998822	+	0.0485174i	$0.984550\pi$
$348$	−51.9276	−	47.2218i	−0.149217	−	0.135695i
$349$	−221.096			−0.633513			−0.316756	−	0.948507i	$-0.602594\pi$
$349$	−221.096			−0.633513			−0.316756	+	0.948507i	$0.602594\pi$
$350$	−22.2946	−	50.4088i	−0.0636989	−	0.144025i
$351$			342.834i			0.976736i
$352$	−92.5605	+	51.9283i	−0.262956	+	0.147524i
$353$	521.383			1.47700			0.738502	−	0.674251i	$-0.235533\pi$
$353$	521.383			1.47700			0.738502	+	0.674251i	$0.235533\pi$
$354$	−64.3524	+	28.4615i	−0.181787	+	0.0803999i
$355$			497.292i			1.40082i
$356$	−180.391	+	198.367i	−0.506715	+	0.557211i
$357$	−65.2494			−0.182771
$358$	107.102	+	242.161i	0.299167	+	0.676427i
$359$			125.540i			0.349693i	0.984596	+	0.174846i	$0.0559429\pi$
$359$			125.540i			0.349693i	−0.984596	+	0.174846i	$0.944057\pi$
$360$	−86.3802	+	259.305i	−0.239945	+	0.720293i
$361$	360.989			0.999968
$362$	256.196	−	113.309i	0.707724	−	0.313009i
$363$			15.0170i			0.0413691i
$364$	−610.023	−	554.741i	−1.67589	−	1.52401i
$365$	−186.970			−0.512246
$366$	14.5033	+	32.7925i	0.0396266	+	0.0895969i
$367$		−	567.667i		−	1.54678i	−0.633932	−	0.773389i	$-0.718560\pi$
$367$		−	567.667i		−	1.54678i	0.633932	−	0.773389i	$-0.281440\pi$
$368$	−271.245	+	25.8056i	−0.737077	+	0.0701240i
$369$	433.608			1.17509
$370$	−300.974	+	133.114i	−0.813443	+	0.359766i
$371$		−	421.512i		−	1.13615i
$372$	−24.5724	+	27.0211i	−0.0660547	+	0.0726373i
$373$	262.739			0.704395			0.352198	−	0.935926i	$-0.385434\pi$
$373$	262.739			0.704395			0.352198	+	0.935926i	$0.385434\pi$
$374$	9.68169	+	21.8906i	0.0258869	+	0.0585310i
$375$		−	176.991i		−	0.471975i
$376$	424.650	+	141.460i	1.12939	+	0.376223i
$377$	−200.034			−0.530595
$378$	533.690	−	236.038i	1.41188	−	0.624440i
$379$		−	422.129i		−	1.11380i	−0.830581	−	0.556898i	$-0.811991\pi$
$379$		−	422.129i		−	1.11380i	0.830581	−	0.556898i	$-0.188009\pi$
$380$	1.51154	+	1.37456i	0.00397775	+	0.00361728i
$381$	−22.5966			−0.0593086
$382$	−55.2975	−	125.029i	−0.144758	−	0.327302i
$383$			421.165i			1.09965i	0.835281	+	0.549823i	$0.185305\pi$
$383$			421.165i			1.09965i	−0.835281	+	0.549823i	$0.814695\pi$
$384$	−39.2770	+	170.272i	−0.102284	+	0.443416i
$385$	−210.309			−0.546257
$386$	349.306	−	154.490i	0.904937	−	0.400232i
$387$			298.591i			0.771552i
$388$	70.4618	−	77.4836i	0.181603	−	0.199700i
$389$	−453.286			−1.16526			−0.582630	−	0.812737i	$-0.697976\pi$
$389$	−453.286			−1.16526			−0.582630	+	0.812737i	$0.697976\pi$
$390$	−82.2831	−	186.045i	−0.210982	−	0.477037i
$391$			61.4502i			0.157162i
$392$	−319.680	+	959.649i	−0.815509	+	2.44808i
$393$	156.329			0.397784
$394$	−222.641	+	98.4686i	−0.565078	+	0.249920i
$395$		−	598.894i		−	1.51619i
$396$	−70.0427	−	63.6953i	−0.176876	−	0.160847i
$397$	207.363			0.522325			0.261163	−	0.965295i	$-0.415894\pi$
$397$	207.363			0.522325			0.261163	+	0.965295i	$0.415894\pi$
$398$	−108.657	−	245.677i	−0.273007	−	0.617278i
$399$		−	1.92919i		−	0.00483507i
$400$	3.15303	+	33.1416i	0.00788257	+	0.0828541i
$401$	−270.749			−0.675185			−0.337593	−	0.941292i	$-0.609613\pi$
$401$	−270.749			−0.675185			−0.337593	+	0.941292i	$0.609613\pi$
$402$	55.8731	−	24.7113i	0.138988	−	0.0614709i
$403$			104.090i			0.258288i
$404$	−56.1651	+	61.7621i	−0.139022	+	0.152876i
$405$	−163.505			−0.403716
$406$	137.722	+	311.393i	0.339216	+	0.766979i
$407$		−	113.996i		−	0.280088i
$408$	37.3899	+	12.4554i	0.0916420	+	0.0305279i
$409$	9.49821			0.0232230			0.0116115	−	0.999933i	$-0.496304\pi$
$409$	9.49821			0.0232230			0.0116115	+	0.999933i	$0.496304\pi$
$410$	−532.061	+	235.318i	−1.29771	+	0.573946i
$411$		−	44.2822i		−	0.107743i
$412$	225.825	+	205.361i	0.548120	+	0.498448i
$413$	341.350			0.826513
$414$	−98.3102	−	222.282i	−0.237464	−	0.536914i
$415$			349.586i			0.842375i
$416$	243.668	+	434.331i	0.585741	+	1.04406i
$417$	−164.500			−0.394485
$418$	−0.647228	+	0.286254i	−0.00154839	+	0.000684817i
$419$		−	692.742i		−	1.65332i	−0.562700	−	0.826661i	$-0.690237\pi$
$419$		−	692.742i		−	1.65332i	0.562700	−	0.826661i	$-0.309763\pi$
$420$	−232.964	+	256.180i	−0.554677	+	0.609953i
$421$	361.072			0.857652			0.428826	−	0.903387i	$-0.358927\pi$
$421$	361.072			0.857652			0.428826	+	0.903387i	$0.358927\pi$
$422$	76.6554	+	173.320i	0.181648	+	0.410711i
$423$			399.268i			0.943896i
$424$	−80.4619	+	241.539i	−0.189769	+	0.569668i
$425$	7.50821			0.0176664
$426$	−259.380	+	114.717i	−0.608873	+	0.269290i
$427$		−	173.944i		−	0.407363i
$428$	55.4697	+	50.4429i	0.129602	+	0.117857i
$429$	70.4656			0.164256
$430$	−162.044	−	366.387i	−0.376847	−	0.852064i
$431$			428.186i			0.993470i	0.867902	+	0.496735i	$0.165468\pi$
$431$			428.186i			0.993470i	−0.867902	+	0.496735i	$0.834532\pi$
$432$	−350.879	+	33.3819i	−0.812219	+	0.0772728i
$433$	440.752			1.01790			0.508951	−	0.860795i	$-0.330033\pi$
$433$	440.752			1.01790			0.508951	+	0.860795i	$0.330033\pi$
$434$	162.037	−	71.6651i	0.373357	−	0.165127i
$435$			84.0048i			0.193114i
$436$	450.806	−	495.730i	1.03396	−	1.13700i
$437$	−1.81687			−0.00415759
$438$	−43.1311	−	97.5207i	−0.0984727	−	0.222650i
$439$			100.780i			0.229568i	0.993390	+	0.114784i	$0.0366176\pi$
$439$			100.780i			0.229568i	−0.993390	+	0.114784i	$0.963382\pi$
$440$	120.514	+	40.1456i	0.273894	+	0.0912401i
$441$	−902.289			−2.04601
$442$	102.719	−	45.4303i	0.232397	−	0.102784i
$443$		−	218.191i		−	0.492530i	−0.969203	−	0.246265i	$-0.920797\pi$
$443$		−	218.191i		−	0.492530i	0.969203	−	0.246265i	$-0.0792033\pi$
$444$	−138.860	−	126.276i	−0.312748	−	0.284406i
$445$	320.905			0.721134
$446$	−222.283	−	502.589i	−0.498392	−	1.12688i
$447$			239.295i			0.535335i
$448$	508.359	−	678.351i	1.13473	−	1.51418i
$449$	−315.467			−0.702599			−0.351299	−	0.936263i	$-0.614260\pi$
$449$	−315.467			−0.702599			−0.351299	+	0.936263i	$0.614260\pi$
$450$	−27.1593	+	12.0119i	−0.0603539	+	0.0266931i
$451$		−	201.522i		−	0.446833i
$452$	−189.536	+	208.424i	−0.419329	+	0.461116i
$453$	−393.864			−0.869456
$454$	203.073	+	459.154i	0.447297	+	1.01135i
$455$			986.852i			2.16891i
$456$	−0.368262	+	1.10549i	−0.000807592	+	0.00242432i
$457$	−571.742			−1.25108			−0.625539	−	0.780193i	$-0.715121\pi$
$457$	−571.742			−1.25108			−0.625539	+	0.780193i	$0.715121\pi$
$458$	477.541	−	211.205i	1.04267	−	0.461146i
$459$			79.4913i			0.173184i
$460$	241.264	+	219.400i	0.524487	+	0.476957i
$461$	296.626			0.643440			0.321720	−	0.946835i	$-0.395739\pi$
$461$	296.626			0.643440			0.321720	+	0.946835i	$0.395739\pi$
$462$	−48.5150	−	109.694i	−0.105011	−	0.237433i
$463$			323.735i			0.699212i	0.936897	+	0.349606i	$0.113685\pi$
$463$			323.735i			0.699212i	−0.936897	+	0.349606i	$0.886315\pi$
$464$	−19.4774	−	204.728i	−0.0419771	−	0.441224i
$465$	43.7128			0.0940060
$466$	118.071	−	52.2199i	0.253371	−	0.112060i
$467$		−	120.058i		−	0.257084i	−0.991704	−	0.128542i	$-0.958970\pi$
$467$		−	120.058i		−	0.257084i	0.991704	−	0.128542i	$-0.0410297\pi$
$468$	−298.883	+	328.668i	−0.638640	+	0.702283i
$469$	−296.372			−0.631923
$470$	−216.682	−	489.924i	−0.461025	−	1.04239i
$471$			219.487i			0.466002i
$472$	−195.604	−	65.1600i	−0.414416	−	0.138051i
$473$	138.772			0.293386
$474$	312.374	−	138.156i	0.659017	−	0.291468i
$475$			0.221991i			0.000467350i
$476$	−141.443	−	128.625i	−0.297149	−	0.270220i
$477$	−227.102			−0.476105
$478$	151.890	+	343.427i	0.317761	+	0.718467i
$479$		−	284.576i		−	0.594104i	−0.954861	−	0.297052i	$-0.903997\pi$
$479$		−	284.576i		−	0.594104i	0.954861	−	0.297052i	$-0.0960034\pi$
$480$	182.398	−	102.329i	0.379996	−	0.213185i
$481$	−534.913			−1.11209
$482$	−472.425	+	208.942i	−0.980135	+	0.433490i
$483$		−	307.927i		−	0.637530i
$484$	−29.6027	+	32.5527i	−0.0611626	+	0.0672577i
$485$	−125.347			−0.258448
$486$	−198.103	−	447.918i	−0.407620	−	0.921642i
$487$		−	221.764i		−	0.455367i	−0.973735	−	0.227684i	$-0.926885\pi$
$487$		−	221.764i		−	0.455367i	0.973735	−	0.227684i	$-0.0731152\pi$
$488$	−33.2040	+	99.6753i	−0.0680409	+	0.204253i
$489$	357.724			0.731542
$490$	1107.16	−	489.670i	2.25951	−	0.999326i
$491$			125.352i			0.255300i	0.991819	+	0.127650i	$0.0407435\pi$
$491$			125.352i			0.255300i	−0.991819	+	0.127650i	$0.959257\pi$
$492$	−245.476	−	223.231i	−0.498936	−	0.453721i
$493$	−46.3809			−0.0940790
$494$	1.34322	+	3.03705i	0.00271906	+	0.00614788i
$495$			113.310i			0.228910i
$496$	−106.532	+	10.1353i	−0.214783	+	0.0204340i
$497$	1375.85			2.76831
$498$	−182.338	+	80.6439i	−0.366141	+	0.161936i
$499$			474.800i			0.951502i	0.879580	+	0.475751i	$0.157824\pi$
$499$			474.800i			0.951502i	−0.879580	+	0.475751i	$0.842176\pi$
$500$	348.899	−	383.668i	0.697797	−	0.767335i
$501$	41.3399			0.0825147
$502$	−325.122	−	735.111i	−0.647653	−	1.46436i
$503$		−	444.813i		−	0.884320i	−0.896936	−	0.442160i	$-0.854212\pi$
$503$		−	444.813i		−	0.884320i	0.896936	−	0.442160i	$-0.145788\pi$
$504$	717.416	+	238.987i	1.42345	+	0.474180i
$505$	99.9144			0.197850
$506$	−103.307	+	45.6902i	−0.204164	+	0.0902968i
$507$		−	99.9372i		−	0.197115i
$508$	−48.9832	−	44.5443i	−0.0964237	−	0.0876855i
$509$	741.308			1.45640			0.728201	−	0.685364i	$-0.240357\pi$
$509$	741.308			1.45640			0.728201	+	0.685364i	$0.240357\pi$
$510$	−19.0786	−	43.1372i	−0.0374089	−	0.0845828i
$511$			517.287i			1.01230i
$512$	−420.795	+	291.676i	−0.821866	+	0.569681i
$513$	−2.35028			−0.00458144
$514$	−323.803	+	143.210i	−0.629967	+	0.278619i
$515$		−	365.325i		−	0.709368i
$516$	153.721	−	169.040i	0.297909	−	0.327596i
$517$	185.562			0.358921
$518$	368.283	+	832.700i	0.710971	+	1.60753i
$519$			440.560i			0.848862i
$520$	188.379	−	565.497i	0.362268	−	1.08749i
$521$	602.117			1.15569			0.577847	−	0.816145i	$-0.303893\pi$
$521$	602.117			1.15569			0.577847	+	0.816145i	$0.303893\pi$
$522$	167.773	−	74.2018i	0.321404	−	0.142149i
$523$		−	157.486i		−	0.301120i	−0.988601	−	0.150560i	$-0.951892\pi$
$523$		−	157.486i		−	0.301120i	0.988601	−	0.150560i	$-0.0481076\pi$
$524$	338.879	+	308.169i	0.646715	+	0.588108i
$525$	−37.6236			−0.0716641
$526$	−244.799	−	553.497i	−0.465397	−	1.05228i
$527$			24.1348i			0.0457966i
$528$	6.86125	+	72.1190i	0.0129948	+	0.136589i
$529$	239.002			0.451799
$530$	278.667	−	123.248i	0.525786	−	0.232543i
$531$		−	183.913i		−	0.346352i
$532$	3.80299	−	4.18197i	0.00714847	−	0.00786084i
$533$	−945.619			−1.77414
$534$	74.0277	+	167.379i	0.138629	+	0.313444i
$535$		−	89.7350i		−	0.167729i
$536$	169.831	+	56.5742i	0.316848	+	0.105549i
$537$	180.742			0.336577
$538$	−16.5738	+	7.33020i	−0.0308063	+	0.0136249i
$539$			419.343i			0.778003i
$540$	312.096	+	283.813i	0.577956	+	0.525580i
$541$	−580.019			−1.07212			−0.536062	−	0.844178i	$-0.680089\pi$
$541$	−580.019			−1.07212			−0.536062	+	0.844178i	$0.680089\pi$
$542$	18.6379	+	42.1410i	0.0343873	+	0.0777509i
$543$		−	191.217i		−	0.352149i
$544$	56.4981	+	100.706i	0.103857	+	0.185121i
$545$	−801.957			−1.47148
$546$	−514.727	+	227.651i	−0.942723	+	0.416944i
$547$		−	320.297i		−	0.585551i	−0.956181	−	0.292776i	$-0.905421\pi$
$547$		−	320.297i		−	0.585551i	0.956181	−	0.292776i	$-0.0945789\pi$
$548$	87.2927	−	95.9917i	0.159293	−	0.175167i
$549$	−93.7176			−0.170706
$550$	5.58259	+	12.6224i	0.0101502	+	0.0229498i
$551$		−	1.37132i		−	0.00248879i
$552$	−58.7799	+	176.452i	−0.106485	+	0.319659i
$553$	−1656.95			−2.99630
$554$	−605.865	+	267.960i	−1.09362	+	0.483682i
$555$			224.638i			0.404753i
$556$	−356.592	−	324.277i	−0.641352	−	0.583231i
$557$	−568.258			−1.02021			−0.510106	−	0.860112i	$-0.670394\pi$
$557$	−568.258			−1.02021			−0.510106	+	0.860112i	$0.670394\pi$
$558$	−38.6117	−	87.3023i	−0.0691967	−	0.156456i
$559$		−	651.171i		−	1.16489i
$560$	−1010.01	+	96.0900i	−1.80358	+	0.171589i
$561$	16.3385			0.0291239
$562$	109.243	−	48.3158i	0.194383	−	0.0859711i
$563$		−	530.846i		−	0.942889i	−0.881896	−	0.471444i	$-0.843733\pi$
$563$		−	530.846i		−	0.942889i	0.881896	−	0.471444i	$-0.156267\pi$
$564$	205.552	−	226.036i	0.364453	−	0.400772i
$565$	337.174			0.596769
$566$	405.832	+	917.599i	0.717018	+	1.62120i
$567$			452.367i			0.797825i
$568$	−788.405	−	262.635i	−1.38804	−	0.462385i
$569$	520.132			0.914116			0.457058	−	0.889437i	$-0.348903\pi$
$569$	520.132			0.914116			0.457058	+	0.889437i	$0.348903\pi$
$570$	1.27542	−	0.564086i	0.00223757	−	0.000989624i
$571$			972.725i			1.70355i	0.523911	+	0.851773i	$0.324472\pi$
$571$			972.725i			1.70355i	−0.523911	+	0.851773i	$0.675528\pi$
$572$	152.750	+	138.908i	0.267046	+	0.242846i
$573$	−93.3181			−0.162859
$574$	651.050	+	1472.05i	1.13423	+	2.56454i
$575$			35.4330i			0.0616226i
$576$	−365.482	−	273.894i	−0.634518	−	0.475510i
$577$	353.203			0.612137			0.306068	−	0.952010i	$-0.400986\pi$
$577$	353.203			0.612137			0.306068	+	0.952010i	$0.400986\pi$
$578$	−504.791	+	223.257i	−0.873340	+	0.386257i
$579$		−	260.712i		−	0.450279i
$580$	−165.597	+	182.100i	−0.285512	+	0.313965i
$581$	967.193			1.66470
$582$	−28.9157	−	65.3793i	−0.0496834	−	0.112336i
$583$			105.547i			0.181041i
$584$	98.7444	−	296.422i	0.169083	−	0.507571i
$585$	531.696			0.908883
$586$	199.905	−	88.4131i	0.341134	−	0.150876i
$587$		−	941.422i		−	1.60379i	−0.597468	−	0.801893i	$-0.703826\pi$
$587$		−	941.422i		−	1.60379i	0.597468	−	0.801893i	$-0.296174\pi$
$588$	510.808	+	464.518i	0.868722	+	0.789996i
$589$	−0.713582			−0.00121151
$590$	99.8089	+	225.671i	0.169168	+	0.382493i
$591$			166.172i			0.281171i
$592$	−52.0846	−	547.464i	−0.0879808	−	0.924771i
$593$	−121.590			−0.205043			−0.102521	−	0.994731i	$-0.532691\pi$
$593$	−121.590			−0.205043			−0.102521	+	0.994731i	$0.532691\pi$
$594$	−133.637	+	59.1043i	−0.224977	+	0.0995021i
$595$			228.816i			0.384565i
$596$	−471.717	+	518.726i	−0.791472	+	0.870345i
$597$	−183.366			−0.307145
$598$	214.396	+	484.757i	0.358523	+	0.810631i
$599$		−	594.555i		−	0.992580i	−0.868157	−	0.496290i	$-0.834695\pi$
$599$		−	594.555i		−	0.992580i	0.868157	−	0.496290i	$-0.165305\pi$
$600$	21.5595	+	7.18194i	0.0359325	+	0.0119699i
$601$	823.664			1.37049			0.685245	−	0.728313i	$-0.259695\pi$
$601$	823.664			1.37049			0.685245	+	0.728313i	$0.259695\pi$
$602$	−1013.68	+	448.326i	−1.68385	+	0.744727i
$603$			159.679i			0.264808i
$604$	−853.789	−	776.416i	−1.41356	−	1.28546i
$605$	52.6615			0.0870438
$606$	23.0487	+	52.1138i	0.0380342	+	0.0859964i
$607$			261.313i			0.430499i	0.976559	+	0.215249i	$0.0690565\pi$
$607$			261.313i			0.430499i	−0.976559	+	0.215249i	$0.930944\pi$
$608$	−2.97752	+	1.67045i	−0.00489724	+	0.00274745i
$609$	232.415			0.381634
$610$	114.997	−	50.8603i	0.188519	−	0.0833775i
$611$		−	870.730i		−	1.42509i
$612$	−69.3006	+	76.2066i	−0.113236	+	0.124521i
$613$	223.335			0.364331			0.182165	−	0.983268i	$-0.441689\pi$
$613$	223.335			0.364331			0.182165	+	0.983268i	$0.441689\pi$
$614$	10.8619	+	24.5591i	0.0176904	+	0.0399986i
$615$			397.114i			0.645715i
$616$	111.070	−	333.423i	0.180309	−	0.541271i
$617$	−455.583			−0.738384			−0.369192	−	0.929353i	$-0.620366\pi$
$617$	−455.583			−0.738384			−0.369192	+	0.929353i	$0.620366\pi$
$618$	190.548	−	84.2747i	0.308330	−	0.136367i
$619$		−	408.196i		−	0.659445i	−0.944078	−	0.329722i	$-0.893045\pi$
$619$		−	408.196i		−	0.659445i	0.944078	−	0.329722i	$-0.106955\pi$
$620$	94.7575	+	86.1703i	0.152835	+	0.138984i
$621$	−375.138			−0.604087
$622$	101.547	+	229.600i	0.163258	+	0.369132i
$623$		−	887.842i		−	1.42511i
$624$	338.411	−	32.1957i	0.542325	−	0.0515957i
$625$	−568.653			−0.909845
$626$	896.763	−	396.617i	1.43253	−	0.633573i
$627$			0.483072i			0.000770450i
$628$	−432.671	+	475.788i	−0.688967	+	0.757624i
$629$	−124.028			−0.197182
$630$	−366.068	−	827.692i	−0.581061	−	1.31380i
$631$			87.6592i			0.138921i	0.997585	+	0.0694605i	$0.0221278\pi$
$631$			87.6592i			0.138921i	−0.997585	+	0.0694605i	$0.977872\pi$
$632$	949.486	+	316.294i	1.50235	+	0.500465i
$633$	129.361			0.204362
$634$	−113.067	+	50.0066i	−0.178338	+	0.0788748i
$635$			79.2417i			0.124790i
$636$	128.568	+	116.917i	0.202151	+	0.183832i
$637$	1967.73			3.08905
$638$	−34.4857	−	77.9732i	−0.0540528	−	0.122215i
$639$		−	741.281i		−	1.16006i
$640$	597.108	+	137.737i	0.932982	+	0.215213i
$641$	−801.036			−1.24967			−0.624833	−	0.780759i	$-0.714833\pi$
$641$	−801.036			−1.24967			−0.624833	+	0.780759i	$0.714833\pi$
$642$	46.8044	−	20.7005i	0.0729040	−	0.0322437i
$643$			653.932i			1.01700i	0.861061	+	0.508501i	$0.169800\pi$
$643$			653.932i			1.01700i	−0.861061	+	0.508501i	$0.830200\pi$
$644$	607.011	−	667.502i	0.942564	−	1.03649i
$645$	−273.461			−0.423970
$646$	0.311445	+	0.704186i	0.000482112	+	0.00109007i
$647$			341.531i			0.527868i	0.964541	+	0.263934i	$0.0850202\pi$
$647$			341.531i			0.527868i	−0.964541	+	0.263934i	$0.914980\pi$
$648$	86.3518	−	259.220i	0.133259	−	0.400031i
$649$	−85.4744			−0.131702
$650$	59.2294	−	26.1957i	0.0911221	−	0.0403011i
$651$		−	120.940i		−	0.185775i
$652$	775.448	+	705.175i	1.18934	+	1.08156i
$653$	882.068			1.35079			0.675396	−	0.737455i	$-0.263973\pi$
$653$	882.068			1.35079			0.675396	+	0.737455i	$0.263973\pi$
$654$	−184.999	−	418.289i	−0.282873	−	0.639585i
$655$		−	548.215i		−	0.836969i
$656$	−92.0751	−	967.807i	−0.140358	−	1.47531i
$657$	278.704			0.424207
$658$	−1355.47	+	599.490i	−2.05998	+	0.911079i
$659$			551.843i			0.837394i	0.908126	+	0.418697i	$0.137513\pi$
$659$			551.843i			0.837394i	−0.908126	+	0.418697i	$0.862487\pi$
$660$	58.3345	−	64.1478i	0.0883856	−	0.0971936i
$661$	239.441			0.362240			0.181120	−	0.983461i	$-0.442028\pi$
$661$	239.441			0.362240			0.181120	+	0.983461i	$0.442028\pi$
$662$	138.215	+	312.509i	0.208784	+	0.472068i
$663$		−	76.6667i		−	0.115636i
$664$	−554.232	−	184.627i	−0.834687	−	0.278052i
$665$	−6.76529			−0.0101734
$666$	448.642	−	198.424i	0.673637	−	0.297934i
$667$		−	218.883i		−	0.328160i
$668$	89.6135	+	81.4925i	0.134152	+	0.121995i
$669$	−375.117			−0.560713
$670$	−86.6576	−	195.935i	−0.129340	−	0.292441i
$671$			43.5557i			0.0649117i
$672$	−283.112	−	504.638i	−0.421298	−	0.750949i
$673$	−900.739			−1.33839			−0.669197	−	0.743085i	$-0.733362\pi$
$673$	−900.739			−1.33839			−0.669197	+	0.743085i	$0.733362\pi$
$674$	589.844	−	260.874i	0.875140	−	0.387053i
$675$			45.8357i			0.0679047i
$676$	197.004	−	216.637i	0.291427	−	0.320468i
$677$	−596.622			−0.881273			−0.440636	−	0.897686i	$-0.645247\pi$
$677$	−596.622			−0.881273			−0.440636	+	0.897686i	$0.645247\pi$
$678$	77.7809	+	175.865i	0.114721	+	0.259388i
$679$			346.797i			0.510747i
$680$	43.6785	−	131.119i	0.0642331	−	0.192822i
$681$	342.699			0.503229
$682$	−40.5742	+	17.9450i	−0.0594930	+	0.0263123i
$683$			1132.25i			1.65775i	0.559431	+	0.828877i	$0.311020\pi$
$683$			1132.25i			1.65775i	−0.559431	+	0.828877i	$0.688980\pi$
$684$	−2.25316	−	2.04897i	−0.00329410	−	0.00299558i
$685$	−155.289			−0.226699
$686$	−829.730	−	1876.05i	−1.20952	−	2.73476i
$687$		−	356.422i		−	0.518809i
$688$	666.450	−	63.4047i	0.968677	−	0.0921580i
$689$	495.268			0.718821
$690$	203.575	−	90.0362i	0.295036	−	0.130487i
$691$			1061.26i			1.53583i	0.640553	+	0.767914i	$0.278705\pi$
$691$			1061.26i			1.53583i	−0.640553	+	0.767914i	$0.721295\pi$
$692$	−868.467	+	955.013i	−1.25501	+	1.38008i
$693$	313.494			0.452372
$694$	27.2387	+	61.5875i	0.0392488	+	0.0887428i
$695$			576.869i			0.830028i
$696$	−133.181	−	44.3654i	−0.191352	−	0.0637434i
$697$	−219.256			−0.314571
$698$	−404.405	+	178.859i	−0.579377	+	0.256244i
$699$		−	88.1245i		−	0.126072i
$700$	−81.5578	−	74.1668i	−0.116511	−	0.105953i
$701$	−716.278			−1.02179			−0.510897	−	0.859642i	$-0.670687\pi$
$701$	−716.278			−1.02179			−0.510897	+	0.859642i	$0.670687\pi$
$702$	277.341	+	627.076i	0.395072	+	0.893270i
$703$		−	3.66706i		−	0.00521630i
$704$	−127.294	+	169.860i	−0.180815	+	0.241278i
$705$	−365.665			−0.518673
$706$	953.657	−	421.780i	1.35079	−	0.597422i
$707$		−	276.432i		−	0.390992i
$708$	−94.6822	+	104.118i	−0.133732	+	0.147059i
$709$	−173.150			−0.244218			−0.122109	−	0.992517i	$-0.538966\pi$
$709$	−173.150			−0.244218			−0.122109	+	0.992517i	$0.538966\pi$
$710$	402.291	+	909.592i	0.566607	+	1.28112i
$711$			892.733i			1.25560i
$712$	−169.479	+	508.761i	−0.238033	+	0.714553i
$713$	−113.898			−0.159745
$714$	−119.347	+	52.7844i	−0.167153	+	0.0739277i
$715$		−	247.109i		−	0.345607i
$716$	391.799	+	356.293i	0.547205	+	0.497616i
$717$	256.324			0.357495
$718$	101.557	+	229.624i	0.141444	+	0.319810i
$719$		−	32.2510i		−	0.0448554i	−0.999748	−	0.0224277i	$-0.992860\pi$
$719$		−	32.2510i		−	0.0448554i	0.999748	−	0.0224277i	$-0.00713956\pi$
$720$	51.7714	+	544.172i	0.0719047	+	0.755794i
$721$	−1010.74			−1.40186
$722$	660.281	−	292.027i	0.914517	−	0.404469i
$723$			352.604i			0.487696i
$724$	376.943	−	414.507i	0.520640	−	0.572523i
$725$	−26.7439			−0.0368881
$726$	12.1482	+	27.4674i	0.0167330	+	0.0378339i
$727$		−	986.862i		−	1.35744i	−0.734395	−	0.678722i	$-0.762534\pi$
$727$		−	986.862i		−	1.35744i	0.734395	−	0.678722i	$-0.237466\pi$
$728$	−1564.55	−	521.186i	−2.14911	−	0.715915i
$729$	−26.9349			−0.0369477
$730$	−341.985	+	151.252i	−0.468473	+	0.207194i
$731$		−	150.984i		−	0.206544i
$732$	53.0559	+	48.2478i	0.0724807	+	0.0659123i
$733$	−1293.35			−1.76446			−0.882231	−	0.470816i	$-0.843959\pi$
$733$	−1293.35			−1.76446			−0.882231	+	0.470816i	$0.843959\pi$
$734$	−459.222	−	1038.32i	−0.625643	−	1.41460i
$735$		−	826.350i		−	1.12429i
$736$	−475.255	+	266.628i	−0.645727	+	0.362266i
$737$	74.2119			0.100695
$738$	793.109	−	350.773i	1.07467	−	0.475302i
$739$		−	167.702i		−	0.226931i	−0.993542	−	0.113466i	$-0.963805\pi$
$739$		−	167.702i		−	0.226931i	0.993542	−	0.113466i	$-0.0361952\pi$
$740$	−442.825	+	486.954i	−0.598412	+	0.658046i
$741$	2.26677			0.00305906
$742$	−340.988	−	770.983i	−0.459552	−	1.03906i
$743$			1020.16i			1.37302i	0.727118	+	0.686512i	$0.240859\pi$
$743$			1020.16i			1.37302i	−0.727118	+	0.686512i	$0.759141\pi$
$744$	−23.0860	+	69.3022i	−0.0310296	+	0.0931481i
$745$	839.158			1.12639
$746$	480.575	−	212.547i	0.644202	−	0.284915i
$747$		−	521.105i		−	0.697597i
$748$	35.4174	+	32.2078i	0.0473495	+	0.0430586i
$749$	−248.268			−0.331466
$750$	−143.179	−	323.732i	−0.190905	−	0.431643i
$751$		−	38.3346i		−	0.0510448i	−0.999674	−	0.0255224i	$-0.991875\pi$
$751$		−	38.3346i		−	0.0510448i	0.999674	−	0.0255224i	$-0.00812492\pi$
$752$	891.160	−	84.7832i	1.18505	−	0.112744i
$753$	−548.665			−0.728639
$754$	−365.881	+	161.821i	−0.485254	+	0.214616i
$755$			1381.20i			1.82940i
$756$	785.222	−	863.472i	1.03865	−	1.14216i
$757$	782.870			1.03417			0.517087	−	0.855933i	$-0.327016\pi$
$757$	782.870			1.03417			0.517087	+	0.855933i	$0.327016\pi$
$758$	−341.487	−	772.113i	−0.450510	−	1.01862i
$759$			77.1052i			0.101588i
$760$	3.87673	+	1.29142i	0.00510096	+	0.00169924i
$761$	184.768			0.242796			0.121398	−	0.992604i	$-0.461262\pi$
$761$	184.768			0.242796			0.121398	+	0.992604i	$0.461262\pi$
$762$	−41.3312	+	18.2798i	−0.0542405	+	0.0239893i
$763$			2218.76i			2.90795i
$764$	−202.288	−	183.956i	−0.264775	−	0.240781i
$765$	123.282			0.161153
$766$	340.707	+	770.349i	0.444787	+	1.00568i
$767$			401.080i			0.522920i
$768$	65.9023	+	343.216i	0.0858103	+	0.446896i
$769$	386.308			0.502351			0.251175	−	0.967942i	$-0.419183\pi$
$769$	386.308			0.502351			0.251175	+	0.967942i	$0.419183\pi$
$770$	−384.674	+	170.132i	−0.499577	+	0.220951i
$771$			241.677i			0.313459i
$772$	513.936	−	565.152i	0.665720	−	0.732062i
$773$	1200.83			1.55346			0.776732	−	0.629832i	$-0.216876\pi$
$773$	1200.83			1.55346			0.776732	+	0.629832i	$0.216876\pi$
$774$	241.549	+	546.150i	0.312079	+	0.705620i
$775$			13.9165i			0.0179567i
$776$	66.1997	−	198.726i	0.0853089	−	0.256090i
$777$	621.502			0.799874
$778$	−829.103	+	366.692i	−1.06568	+	0.471327i
$779$		−	6.48263i		−	0.00832173i
$780$	−301.007	−	273.729i	−0.385906	−	0.350934i
$781$	−344.514			−0.441119
$782$	49.7110	+	112.398i	0.0635691	+	0.143732i
$783$		−	283.144i		−	0.361614i
$784$	191.598	+	2013.90i	0.244385	+	2.56874i
$785$	769.697			0.980505
$786$	285.940	−	126.465i	0.363792	−	0.160896i
$787$		−	939.026i		−	1.19317i	−0.802549	−	0.596586i	$-0.796524\pi$
$787$		−	939.026i		−	1.19317i	0.802549	−	0.596586i	$-0.203476\pi$
$788$	−327.573	+	360.216i	−0.415701	+	0.457127i
$789$	−413.114			−0.523592
$790$	−484.484	−	1095.43i	−0.613271	−	1.38662i
$791$		−	932.856i		−	1.17934i
$792$	−179.642	−	59.8425i	−0.226820	−	0.0755587i
$793$	204.381			0.257731
$794$	379.286	−	167.749i	0.477691	−	0.211271i
$795$		−	207.989i		−	0.261621i
$796$	−397.487	−	361.466i	−0.499355	−	0.454102i
$797$	−1006.65			−1.26305			−0.631524	−	0.775356i	$-0.717570\pi$
$797$	−1006.65			−1.26305			−0.631524	+	0.775356i	$0.717570\pi$
$798$	−1.56065	−	3.52867i	−0.00195570	−	0.00442190i
$799$		−	201.892i		−	0.252680i
$800$	32.5775	+	58.0684i	0.0407219	+	0.0725855i
$801$	−478.352			−0.597193
$802$	−495.225	+	219.026i	−0.617488	+	0.273100i
$803$		−	129.529i		−	0.161307i
$804$	82.2064	−	90.3985i	0.102247	−	0.112436i
$805$	−1079.84			−1.34141
$806$	84.2051	+	190.390i	0.104473	+	0.236216i
$807$			12.3702i			0.0153286i
$808$	−52.7678	+	158.404i	−0.0653066	+	0.196045i
$809$	1299.27			1.60602			0.803009	−	0.595967i	$-0.203231\pi$
$809$	1299.27			1.60602			0.803009	+	0.595967i	$0.203231\pi$
$810$	−299.065	+	132.270i	−0.369217	+	0.163296i
$811$		−	384.909i		−	0.474610i	−0.971435	−	0.237305i	$-0.923736\pi$
$811$		−	384.909i		−	0.474610i	0.971435	−	0.237305i	$-0.0762642\pi$
$812$	503.812	+	458.155i	0.620458	+	0.564231i
$813$	31.4528			0.0386873
$814$	−92.2185	−	208.509i	−0.113290	−	0.256153i
$815$		−	1254.47i		−	1.53922i
$816$	78.4656	−	7.46506i	0.0961588	−	0.00914835i
$817$	4.46406			0.00546397
$818$	17.3731	−	7.68370i	0.0212385	−	0.00939328i
$819$		−	1471.04i		−	1.79614i
$820$	−782.825	+	860.836i	−0.954665	+	1.04980i
$821$	528.123			0.643268			0.321634	−	0.946864i	$-0.395768\pi$
$821$	528.123			0.643268			0.321634	+	0.946864i	$0.395768\pi$
$822$	−35.8227	−	80.9962i	−0.0435799	−	0.0985355i
$823$		−	930.833i		−	1.13102i	−0.824740	−	0.565512i	$-0.808679\pi$
$823$		−	930.833i		−	1.13102i	0.824740	−	0.565512i	$-0.191321\pi$
$824$	579.185	+	192.939i	0.702894	+	0.234149i
$825$	9.42099			0.0114194
$826$	624.361	−	276.140i	0.755885	−	0.334310i
$827$		−	847.952i		−	1.02534i	−0.858587	−	0.512668i	$-0.828657\pi$
$827$		−	847.952i		−	1.02534i	0.858587	−	0.512668i	$-0.171343\pi$
$828$	−359.637	−	327.046i	−0.434344	−	0.394983i
$829$	−776.118			−0.936210			−0.468105	−	0.883673i	$-0.655063\pi$
$829$	−776.118			−0.936210			−0.468105	+	0.883673i	$0.655063\pi$
$830$	282.802	+	639.424i	0.340725	+	0.770390i
$831$			452.200i			0.544163i
$832$	797.049	+	597.312i	0.957992	+	0.717923i
$833$	456.247			0.547715
$834$	−300.886	+	133.075i	−0.360775	+	0.159562i
$835$		−	144.971i		−	0.173617i
$836$	−0.952272	+	1.04717i	−0.00113908	+	0.00125259i
$837$	−147.337			−0.176030
$838$	−560.403	−	1267.09i	−0.668739	−	1.51204i
$839$			1285.70i			1.53242i	0.642588	+	0.766212i	$0.277861\pi$
$839$			1285.70i			1.53242i	−0.642588	+	0.766212i	$0.722139\pi$
$840$	−218.873	+	657.037i	−0.260563	+	0.782187i
$841$	−675.794			−0.803559
$842$	660.433	−	292.094i	0.784363	−	0.346905i
$843$		−	81.5361i		−	0.0967213i
$844$	280.420	+	255.007i	0.332251	+	0.302141i
$845$	−350.459			−0.414745
$846$	322.993	+	730.298i	0.381789	+	0.863236i
$847$		−	145.698i		−	0.172016i
$848$	48.2243	+	506.889i	0.0568683	+	0.597746i
$849$	684.869			0.806677
$850$	13.7332	−	6.07387i	0.0161567	−	0.00714573i
$851$		−	585.316i		−	0.687797i
$852$	−381.627	+	419.658i	−0.447919	+	0.492556i
$853$	195.207			0.228848			0.114424	−	0.993432i	$-0.463498\pi$
$853$	195.207			0.228848			0.114424	+	0.993432i	$0.463498\pi$
$854$	−140.714	−	318.159i	−0.164771	−	0.372552i
$855$			3.64501i			0.00426317i
$856$	142.266	+	47.3917i	0.166198	+	0.0553641i
$857$	−785.143			−0.916152			−0.458076	−	0.888913i	$-0.651461\pi$
$857$	−785.143			−0.916152			−0.458076	+	0.888913i	$0.651461\pi$
$858$	128.888	−	57.0041i	0.150219	−	0.0664384i
$859$			758.542i			0.883053i	0.897248	+	0.441526i	$0.145563\pi$
$859$			758.542i			0.883053i	−0.897248	+	0.441526i	$0.854437\pi$
$860$	−592.788	−	539.068i	−0.689289	−	0.626823i
$861$	1098.69			1.27606
$862$	346.387	+	783.191i	0.401841	+	0.908574i
$863$		−	1659.44i		−	1.92288i	−0.275021	−	0.961438i	$-0.588685\pi$
$863$		−	1659.44i		−	1.92288i	0.275021	−	0.961438i	$-0.411315\pi$
$864$	−614.784	+	344.906i	−0.711556	+	0.399197i
$865$	1544.95			1.78607
$866$	806.176	−	356.552i	0.930919	−	0.411723i
$867$			376.761i			0.434557i
$868$	238.406	−	262.164i	0.274661	−	0.302032i
$869$	414.902			0.477448
$870$	67.9568	+	153.653i	0.0781113	+	0.176612i
$871$		−	348.231i		−	0.399806i
$872$	423.537	−	1271.42i	0.485708	−	1.45805i
$873$	186.847			0.214029
$874$	−3.32322	+	1.46978i	−0.00380231	+	0.00168167i
$875$			1717.20i			1.96251i
$876$	−157.781	−	143.483i	−0.180116	−	0.163793i
$877$	1059.81			1.20845			0.604225	−	0.796814i	$-0.293483\pi$
$877$	1059.81			1.20845			0.604225	+	0.796814i	$0.293483\pi$
$878$	81.5276	+	184.336i	0.0928560	+	0.209950i
$879$		−	149.203i		−	0.169742i
$880$	252.907	−	24.0610i	0.287394	−	0.0273421i
$881$	−984.604			−1.11760			−0.558799	−	0.829303i	$-0.688738\pi$
$881$	−984.604			−1.11760			−0.558799	+	0.829303i	$0.688738\pi$
$882$	−1650.37	+	729.919i	−1.87117	+	0.827573i
$883$		−	38.3564i		−	0.0434388i	−0.999764	−	0.0217194i	$-0.993086\pi$
$883$		−	38.3564i		−	0.0434388i	0.999764	−	0.0217194i	$-0.00691404\pi$
$884$	151.132	−	166.193i	0.170964	−	0.188001i
$885$	168.434			0.190321
$886$	−176.508	−	399.091i	−0.199219	−	0.450441i
$887$		−	1436.26i		−	1.61923i	−0.586959	−	0.809617i	$-0.699675\pi$
$887$		−	1436.26i		−	1.61923i	0.586959	−	0.809617i	$-0.300325\pi$
$888$	−356.140	−	118.638i	−0.401059	−	0.133601i
$889$	219.237			0.246610
$890$	586.964	−	259.600i	0.659510	−	0.291686i
$891$		−	113.273i		−	0.127130i
$892$	−813.152	−	739.462i	−0.911605	−	0.828993i
$893$	5.96923			0.00668447
$894$	193.581	+	437.692i	0.216533	+	0.489588i
$895$		−	633.824i		−	0.708184i
$896$	381.074	−	1652.01i	0.425306	−	1.84376i
$897$	361.808			0.403354
$898$	−577.018	+	255.201i	−0.642559	+	0.284188i
$899$		−	85.9670i		−	0.0956251i
$900$	−39.9596	+	43.9417i	−0.0443996	+	0.0488241i
$901$	114.835			0.127453
$902$	−163.024	−	368.602i	−0.180736	−	0.408649i
$903$			756.579i			0.837851i
$904$	−178.072	+	534.556i	−0.196982	+	0.591323i
$905$	−670.560			−0.740950
$906$	−720.413	+	318.621i	−0.795157	+	0.351679i
$907$			1030.94i			1.13665i	0.822804	+	0.568325i	$0.192408\pi$
$907$			1030.94i			1.13665i	−0.822804	+	0.568325i	$0.807592\pi$
$908$	742.877	+	675.556i	0.818147	+	0.744004i
$909$	−148.936			−0.163846
$910$	798.327	+	1805.04i	0.877283	+	1.98356i
$911$			1702.49i			1.86882i	0.356202	+	0.934409i	$0.384072\pi$
$911$			1702.49i			1.86882i	−0.356202	+	0.934409i	$0.615928\pi$
$912$	0.220715	+	2.31995i	0.000242013	+	0.00254381i
$913$	−242.186			−0.265264
$914$	−1045.77	+	462.519i	−1.14417	+	0.506038i
$915$		−	85.8300i		−	0.0938033i
$916$	702.609	−	772.626i	0.767040	−	0.843478i
$917$	−1516.74			−1.65402
$918$	64.3056	+	145.397i	0.0700496	+	0.158384i
$919$		−	595.935i		−	0.648461i	−0.945978	−	0.324230i	$-0.894895\pi$
$919$		−	595.935i		−	0.648461i	0.945978	−	0.324230i	$-0.105105\pi$
$920$	618.781	+	206.129i	0.672588	+	0.224053i
$921$	18.3302			0.0199025
$922$	542.556	−	239.959i	0.588455	−	0.260260i
$923$			1616.60i			1.75146i
$924$	−177.477	−	161.393i	−0.192074	−	0.174668i
$925$	−71.5160			−0.0773145
$926$	261.890	+	592.142i	0.282819	+	0.639462i
$927$			544.566i			0.587450i
$928$	−201.243	−	358.710i	−0.216857	−	0.386540i
$929$	263.669			0.283820			0.141910	−	0.989880i	$-0.454676\pi$
$929$	263.669			0.283820			0.141910	+	0.989880i	$0.454676\pi$
$930$	79.9548	−	35.3621i	0.0859729	−	0.0380237i
$931$			13.4896i			0.0144894i
$932$	173.718	−	191.030i	0.186393	−	0.204968i
$933$	171.367			0.183673
$934$	−97.1227	−	219.597i	−0.103986	−	0.235115i
$935$		−	57.2958i		−	0.0612790i
$936$	−280.805	+	842.950i	−0.300005	+	0.900588i
$937$	−1022.74			−1.09151			−0.545754	−	0.837946i	$-0.683757\pi$
$937$	−1022.74			−1.09151			−0.545754	+	0.837946i	$0.683757\pi$
$938$	−542.092	+	239.754i	−0.577923	+	0.255602i
$939$		−	669.317i		−	0.712798i
$940$	−792.661	−	720.828i	−0.843257	−	0.766839i
$941$	218.644			0.232352			0.116176	−	0.993229i	$-0.462936\pi$
$941$	218.644			0.232352			0.116176	+	0.993229i	$0.462936\pi$
$942$	177.557	+	401.462i	0.188489	+	0.426180i
$943$		−	1034.72i		−	1.09726i
$944$	−410.490	+	39.0532i	−0.434841	+	0.0413699i
$945$	−1396.86			−1.47816
$946$	253.826	−	112.261i	0.268315	−	0.118669i
$947$		−	192.307i		−	0.203070i	−0.994832	−	0.101535i	$-0.967625\pi$
$947$		−	192.307i		−	0.203070i	0.994832	−	0.101535i	$-0.0323754\pi$
$948$	459.598	−	505.399i	0.484808	−	0.533121i
$949$	−607.802			−0.640466
$950$	0.179583	+	0.406043i	0.000189035	+	0.000427413i
$951$			84.3895i			0.0887376i
$952$	−362.765	−	120.845i	−0.381056	−	0.126938i
$953$	−1023.56			−1.07404			−0.537021	−	0.843569i	$-0.680450\pi$
$953$	−1023.56			−1.07404			−0.537021	+	0.843569i	$0.680450\pi$
$954$	−415.391	+	183.717i	−0.435420	+	0.192576i
$955$			327.248i			0.342668i
$956$	555.641	+	505.287i	0.581214	+	0.528543i
$957$	−58.1969			−0.0608118
$958$	−230.211	−	520.515i	−0.240304	−	0.543335i
$959$			429.635i			0.448003i
$960$	250.842	−	334.722i	0.261294	−	0.348669i
$961$	916.266			0.953451
$962$	−978.406	+	432.726i	−1.01705	+	0.449819i
$963$			133.762i			0.138901i
$964$	−695.082	+	764.350i	−0.721040	+	0.792894i
$965$	−914.263			−0.947422
$966$	−249.102	−	563.227i	−0.257869	−	0.583051i
$967$			470.231i			0.486278i	0.969991	+	0.243139i	$0.0781771\pi$
$967$			470.231i			0.486278i	−0.969991	+	0.243139i	$0.921823\pi$
$968$	−27.8121	+	83.4894i	−0.0287315	+	0.0862494i
$969$	0.525583			0.000542398
$970$	−229.272	+	101.402i	−0.236363	+	0.104538i
$971$			1584.01i			1.63132i	0.578531	+	0.815660i	$0.303626\pi$
$971$			1584.01i			1.63132i	−0.578531	+	0.815660i	$0.696374\pi$
$972$	−724.699	−	659.025i	−0.745575	−	0.678009i
$973$	1596.02			1.64030
$974$	−179.399	−	405.627i	−0.184188	−	0.416454i
$975$		−	44.2070i		−	0.0453405i
$976$	19.9006	+	209.176i	0.0203900	+	0.214320i
$977$	−1203.34			−1.23166			−0.615832	−	0.787877i	$-0.711180\pi$
$977$	−1203.34			−1.23166			−0.615832	+	0.787877i	$0.711180\pi$
$978$	654.310	−	289.386i	0.669029	−	0.295896i
$979$			222.317i			0.227085i
$980$	1628.97	−	1791.30i	1.66221	−	1.82786i
$981$	1195.43			1.21858
$982$	101.406	+	229.281i	0.103264	+	0.233484i
$983$			69.7530i			0.0709593i	0.999370	+	0.0354797i	$0.0112959\pi$
$983$			69.7530i			0.0709593i	−0.999370	+	0.0354797i	$0.988704\pi$
$984$	−629.584	−	209.728i	−0.639822	−	0.213138i
$985$	582.733			0.591607
$986$	−84.8350	+	37.5205i	−0.0860396	+	0.0380532i
$987$			1011.68i			1.02500i
$988$	4.91373	+	4.46844i	0.00497341	+	0.00452271i
$989$	712.528			0.720453
$990$	91.6639	+	207.255i	0.0925898	+	0.209348i
$991$		−	646.046i		−	0.651913i	−0.945385	−	0.325956i	$-0.894314\pi$
$991$		−	646.046i		−	0.651913i	0.945385	−	0.325956i	$-0.105686\pi$
$992$	−186.658	+	104.719i	−0.188164	+	0.105564i
$993$	233.247			0.234892
$994$	2516.56	−	1113.01i	2.53175	−	1.11973i
$995$			643.026i			0.646258i
$996$	−268.276	+	295.010i	−0.269353	+	0.296195i
$997$	−572.771			−0.574495			−0.287247	−	0.957856i	$-0.592740\pi$
$997$	−572.771			−0.574495			−0.287247	+	0.957856i	$0.592740\pi$
$998$	384.096	+	868.452i	0.384865	+	0.870193i
$999$		−	757.157i		−	0.757915i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.3.b.a.23.9	✓	10
3.2	odd	2		396.3.g.c.199.2		10
4.3	odd	2	inner	44.3.b.a.23.10	yes	10
8.3	odd	2		704.3.d.d.639.5		10
8.5	even	2		704.3.d.d.639.6		10
11.10	odd	2		484.3.b.h.243.2		10
12.11	even	2		396.3.g.c.199.1		10
44.43	even	2		484.3.b.h.243.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.b.a.23.9	✓	10	1.1	even	1	trivial
44.3.b.a.23.10	yes	10	4.3	odd	2	inner
396.3.g.c.199.1		10	12.11	even	2
396.3.g.c.199.2		10	3.2	odd	2
484.3.b.h.243.1		10	44.43	even	2
484.3.b.h.243.2		10	11.10	odd	2
704.3.d.d.639.5		10	8.3	odd	2
704.3.d.d.639.6		10	8.5	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	44.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82909 - 0.808964i) q^{2} -1.36518i q^{3} +(2.69116 - 2.95934i) q^{4} -4.78741 q^{5} +(-1.10438 - 2.49704i) q^{6} +13.2453i q^{7} +(2.52837 - 7.58995i) q^{8} +7.13628 q^{9} +(-8.75661 + 3.87284i) q^{10} -3.31662i q^{11} +(-4.04003 - 3.67391i) q^{12} -15.5629 q^{13} +(10.7149 + 24.2268i) q^{14} +6.53568i q^{15} +(-1.51536 - 15.9281i) q^{16} -3.60849 q^{17} +(13.0529 - 5.77299i) q^{18} -0.106690i q^{19} +(-12.8837 + 14.1676i) q^{20} +18.0822 q^{21} +(-2.68303 - 6.06641i) q^{22} -17.0293i q^{23} +(-10.3616 - 3.45169i) q^{24} -2.08070 q^{25} +(-28.4660 + 12.5898i) q^{26} -22.0289i q^{27} +(39.1972 + 35.6450i) q^{28} +12.8533 q^{29} +(5.28712 + 11.9544i) q^{30} -6.68834i q^{31} +(-15.6570 - 27.9080i) q^{32} -4.52779 q^{33} +(-6.60027 + 2.91914i) q^{34} -63.4105i q^{35} +(19.2048 - 21.1187i) q^{36} +34.3710 q^{37} +(-0.0863087 - 0.195147i) q^{38} +21.2462i q^{39} +(-12.1044 + 36.3362i) q^{40} +60.7610 q^{41} +(33.0739 - 14.6278i) q^{42} +41.8412i q^{43} +(-9.81501 - 8.92555i) q^{44} -34.1643 q^{45} +(-13.7761 - 31.1482i) q^{46} +55.9490i q^{47} +(-21.7447 + 2.06875i) q^{48} -126.437 q^{49} +(-3.80580 + 1.68321i) q^{50} +4.92624i q^{51} +(-41.8822 + 46.0559i) q^{52} -31.8236 q^{53} +(-17.8206 - 40.2929i) q^{54} +15.8780i q^{55} +(100.531 + 33.4890i) q^{56} -0.145652 q^{57} +(23.5098 - 10.3978i) q^{58} -25.7715i q^{59} +(19.3413 + 17.5885i) q^{60} -13.1325 q^{61} +(-5.41062 - 12.2336i) q^{62} +94.5219i q^{63} +(-51.2147 - 38.3805i) q^{64} +74.5061 q^{65} +(-8.28174 + 3.66282i) q^{66} +22.3757i q^{67} +(-9.71102 + 10.6788i) q^{68} -23.2481 q^{69} +(-51.2968 - 115.984i) q^{70} -103.875i q^{71} +(18.0432 - 54.1640i) q^{72} +39.0545 q^{73} +(62.8678 - 27.8049i) q^{74} +2.84054i q^{75} +(-0.315733 - 0.287121i) q^{76} +43.9295 q^{77} +(17.1874 + 38.8612i) q^{78} +125.098i q^{79} +(7.25467 + 76.2542i) q^{80} +34.1531 q^{81} +(111.138 - 49.1535i) q^{82} -73.0218i q^{83} +(48.6619 - 53.5112i) q^{84} +17.2753 q^{85} +(33.8480 + 76.5314i) q^{86} -17.5470i q^{87} +(-25.1730 - 8.38567i) q^{88} -67.0310 q^{89} +(-62.4897 + 27.6377i) q^{90} -206.135i q^{91} +(-50.3955 - 45.8286i) q^{92} -9.13078 q^{93} +(45.2607 + 102.336i) q^{94} +0.510771i q^{95} +(-38.0995 + 21.3746i) q^{96} +26.1827 q^{97} +(-231.265 + 102.283i) q^{98} -23.6684i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 4 q^{5} + 6 q^{6} - 12 q^{8} - 30 q^{9} - 2 q^{10} + 40 q^{12} - 4 q^{13} - 4 q^{14} - 40 q^{16} + 20 q^{17} - 22 q^{18} - 64 q^{20} + 32 q^{21} + 36 q^{24} - 10 q^{25} - 36 q^{26} + 40 q^{28}+ \cdots - 568 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 - 12 * q^8 - 30 * q^9 - 2 * q^10 + 40 * q^12 - 4 * q^13 - 4 * q^14 - 40 * q^16 + 20 * q^17 - 22 * q^18 - 64 * q^20 + 32 * q^21 + 36 * q^24 - 10 * q^25 - 36 * q^26 + 40 * q^28 + 28 * q^29 + 126 * q^30 + 80 * q^32 - 88 * q^34 - 4 * q^36 - 100 * q^37 + 40 * q^38 - 12 * q^40 + 100 * q^41 + 260 * q^42 - 44 * q^44 - 44 * q^45 - 130 * q^46 + 24 * q^48 - 22 * q^49 - 198 * q^50 - 176 * q^52 + 100 * q^53 - 350 * q^54 + 136 * q^56 - 112 * q^57 + 116 * q^58 - 136 * q^60 - 52 * q^61 + 134 * q^62 - 368 * q^64 - 184 * q^65 + 110 * q^66 + 176 * q^68 + 184 * q^69 - 36 * q^70 + 360 * q^72 + 84 * q^73 + 362 * q^74 + 504 * q^76 - 232 * q^78 - 120 * q^80 + 330 * q^81 + 220 * q^82 - 40 * q^84 - 216 * q^85 + 556 * q^86 - 132 * q^88 + 28 * q^89 - 520 * q^90 + 152 * q^92 - 72 * q^93 - 272 * q^94 - 704 * q^96 - 180 * q^97 - 568 * q^98

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