LMFDB - Embedded newform 44.3.b.a.23.10

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

$q$-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	$0.0730650\pi$
$3$			1.36518i			0.455060i	−0.973771	+	0.227530i	$0.926935\pi$
$4$	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	$-0.604996\pi$
$7$		−	13.2453i		−	1.89218i	0.323905	−	0.946090i	$-0.395004\pi$
$8$	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	$0.000893702\pi$
$19$			0.106690i			0.00561529i	−0.999996	+	0.00280764i	$0.999106\pi$
$20$	−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	$0.120712\pi$
$23$			17.0293i			0.740406i	−0.928951	+	0.370203i	$0.879288\pi$
$24$	−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	$0.0344051\pi$
$31$			6.68834i			0.215753i	−0.994164	+	0.107876i	$0.965595\pi$
$32$	−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	$-0.838264\pi$
$43$		−	41.8412i		−	0.973051i	0.873666	−	0.486526i	$-0.161736\pi$
$44$	−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	$-0.797072\pi$
$47$		−	55.9490i		−	1.19040i	0.803576	−	0.595202i	$-0.202928\pi$
$48$	−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	$0.0700846\pi$
$59$			25.7715i			0.436805i	−0.975859	+	0.218402i	$0.929915\pi$
$60$	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	$-0.946598\pi$
$67$		−	22.3757i		−	0.333966i	0.985960	−	0.166983i	$-0.0534025\pi$
$68$	−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	$0.261186\pi$
$71$			103.875i			1.46303i	−0.681827	+	0.731513i	$0.738814\pi$
$72$	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	$-0.709166\pi$
$79$		−	125.098i		−	1.58352i	0.610835	−	0.791758i	$-0.290834\pi$
$80$	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	$0.144983\pi$
$83$			73.0218i			0.879781i	−0.898051	+	0.439891i	$0.855017\pi$
$84$	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	$-0.879209\pi$
$103$		−	76.3094i		−	0.740868i	0.928859	−	0.370434i	$-0.120791\pi$
$104$	−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	$-0.972084\pi$
$107$		−	18.7439i		−	0.175177i	0.996157	−	0.0875885i	$-0.0279161\pi$
$108$	−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	$0.0207576\pi$
$127$			16.5521i			0.130331i	−0.997874	+	0.0651657i	$0.979242\pi$
$128$	−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	$-0.856017\pi$
$131$		−	114.512i		−	0.874135i	0.899429	−	0.437068i	$-0.143983\pi$
$132$	−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	$0.142701\pi$
$139$			120.497i			0.866886i	−0.901181	+	0.433443i	$0.857299\pi$
$140$	−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	$0.404489\pi$
$151$			288.507i			1.91064i	−0.295573	+	0.955320i	$0.595511\pi$
$152$	−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	$-0.702815\pi$
$163$		−	262.034i		−	1.60757i	0.594918	−	0.803786i	$-0.297185\pi$
$164$	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	$-0.971101\pi$
$167$		−	30.2816i		−	0.181327i	0.995882	−	0.0906635i	$-0.0288988\pi$
$168$	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	$-0.879421\pi$
$179$		−	132.394i		−	0.739631i	0.929105	−	0.369816i	$-0.120579\pi$
$180$	−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	$0.0572675\pi$
$191$			68.3559i			0.357884i	−0.983860	+	0.178942i	$0.942732\pi$
$192$	−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	$0.109574\pi$
$199$			134.316i			0.674955i	−0.941334	+	0.337478i	$0.890426\pi$
$200$	−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	$-0.927911\pi$
$211$		−	94.7575i		−	0.449088i	0.974464	−	0.224544i	$-0.0720892\pi$
$212$	−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	$0.211283\pi$
$223$			274.775i			1.23217i	−0.787678	+	0.616087i	$0.788717\pi$
$224$	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	$-0.813511\pi$
$227$		−	251.028i		−	1.10585i	0.833231	−	0.552926i	$-0.186489\pi$
$228$	−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	$-0.871506\pi$
$239$		−	187.758i		−	0.785600i	0.919624	−	0.392800i	$-0.128494\pi$
$240$	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	$0.295484\pi$
$251$			401.899i			1.60119i	−0.599204	+	0.800596i	$0.704516\pi$
$252$	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	$0.195115\pi$
$263$			302.608i			1.15060i	−0.817943	+	0.575300i	$0.804885\pi$
$264$	−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	$-0.986465\pi$
$271$		−	23.0393i		−	0.0850158i	0.999096	−	0.0425079i	$-0.0135348\pi$
$272$	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	$-0.653238\pi$
$283$		−	501.669i		−	1.77268i	0.463032	−	0.886342i	$-0.346762\pi$
$284$	−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	$-0.993039\pi$
$307$		−	13.4270i		−	0.0437360i	0.999761	−	0.0218680i	$-0.00696136\pi$
$308$	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	$-0.935317\pi$
$311$		−	125.527i		−	0.403623i	0.979424	−	0.201811i	$-0.0646828\pi$
$312$	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	$-0.916907\pi$
$331$		−	170.855i		−	0.516177i	0.966121	−	0.258089i	$-0.0830927\pi$
$332$	−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	$-0.984550\pi$
$347$		−	33.6711i		−	0.0970348i	0.998822	−	0.0485174i	$-0.0154496\pi$
$348$	−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	$-0.944057\pi$
$359$		−	125.540i		−	0.349693i	0.984596	−	0.174846i	$-0.0559429\pi$
$360$	−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	$0.281440\pi$
$367$			567.667i			1.54678i	−0.633932	+	0.773389i	$0.718560\pi$
$368$	−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	$0.188009\pi$
$379$			422.129i			1.11380i	−0.830581	+	0.556898i	$0.811991\pi$
$380$	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	$-0.814695\pi$
$383$		−	421.165i		−	1.09965i	0.835281	−	0.549823i	$-0.185305\pi$
$384$	−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	$0.309763\pi$
$419$			692.742i			1.65332i	−0.562700	+	0.826661i	$0.690237\pi$
$420$	−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	$-0.834532\pi$
$431$		−	428.186i		−	0.993470i	0.867902	−	0.496735i	$-0.165468\pi$
$432$	−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	$-0.963382\pi$
$439$		−	100.780i		−	0.229568i	0.993390	−	0.114784i	$-0.0366176\pi$
$440$	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	$0.0792033\pi$
$443$			218.191i			0.492530i	−0.969203	+	0.246265i	$0.920797\pi$
$444$	−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	$-0.886315\pi$
$463$		−	323.735i		−	0.699212i	0.936897	−	0.349606i	$-0.113685\pi$
$464$	−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	$0.0410297\pi$
$467$			120.058i			0.257084i	−0.991704	+	0.128542i	$0.958970\pi$
$468$	−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	$0.0960034\pi$
$479$			284.576i			0.594104i	−0.954861	+	0.297052i	$0.903997\pi$
$480$	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	$0.0731152\pi$
$487$			221.764i			0.455367i	−0.973735	+	0.227684i	$0.926885\pi$
$488$	−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	$-0.959257\pi$
$491$		−	125.352i		−	0.255300i	0.991819	−	0.127650i	$-0.0407435\pi$
$492$	−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	$-0.842176\pi$
$499$		−	474.800i		−	0.951502i	0.879580	−	0.475751i	$-0.157824\pi$
$500$	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	$0.145788\pi$
$503$			444.813i			0.884320i	−0.896936	+	0.442160i	$0.854212\pi$
$504$	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	$0.0481076\pi$
$523$			157.486i			0.301120i	−0.988601	+	0.150560i	$0.951892\pi$
$524$	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	$0.0945789\pi$
$547$			320.297i			0.585551i	−0.956181	+	0.292776i	$0.905421\pi$
$548$	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	$0.156267\pi$
$563$			530.846i			0.942889i	−0.881896	+	0.471444i	$0.843733\pi$
$564$	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	$-0.675528\pi$
$571$		−	972.725i		−	1.70355i	0.523911	−	0.851773i	$-0.324472\pi$
$572$	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	$0.296174\pi$
$587$			941.422i			1.60379i	−0.597468	+	0.801893i	$0.703826\pi$
$588$	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	$0.165305\pi$
$599$			594.555i			0.992580i	−0.868157	+	0.496290i	$0.834695\pi$
$600$	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	$-0.930944\pi$
$607$		−	261.313i		−	0.430499i	0.976559	−	0.215249i	$-0.0690565\pi$
$608$	−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	$0.106955\pi$
$619$			408.196i			0.659445i	−0.944078	+	0.329722i	$0.893045\pi$
$620$	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	$-0.977872\pi$
$631$		−	87.6592i		−	0.138921i	0.997585	−	0.0694605i	$-0.0221278\pi$
$632$	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	$-0.830200\pi$
$643$		−	653.932i		−	1.01700i	0.861061	−	0.508501i	$-0.169800\pi$
$644$	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	$-0.914980\pi$
$647$		−	341.531i		−	0.527868i	0.964541	−	0.263934i	$-0.0850202\pi$
$648$	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	$-0.862487\pi$
$659$		−	551.843i		−	0.837394i	0.908126	−	0.418697i	$-0.137513\pi$
$660$	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	$-0.688980\pi$
$683$		−	1132.25i		−	1.65775i	0.559431	−	0.828877i	$-0.311020\pi$
$684$	−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	$-0.721295\pi$
$691$		−	1061.26i		−	1.53583i	0.640553	−	0.767914i	$-0.278705\pi$
$692$	−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	$0.00713956\pi$
$719$			32.2510i			0.0448554i	−0.999748	+	0.0224277i	$0.992860\pi$
$720$	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	$0.237466\pi$
$727$			986.862i			1.35744i	−0.734395	+	0.678722i	$0.762534\pi$
$728$	−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	$0.0361952\pi$
$739$			167.702i			0.226931i	−0.993542	+	0.113466i	$0.963805\pi$
$740$	−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	$-0.759141\pi$
$743$		−	1020.16i		−	1.37302i	0.727118	−	0.686512i	$-0.240859\pi$
$744$	−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	$0.00812492\pi$
$751$			38.3346i			0.0510448i	−0.999674	+	0.0255224i	$0.991875\pi$
$752$	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	$0.203476\pi$
$787$			939.026i			1.19317i	−0.802549	+	0.596586i	$0.796524\pi$
$788$	−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	$0.0762642\pi$
$811$			384.909i			0.474610i	−0.971435	+	0.237305i	$0.923736\pi$
$812$	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	$0.191321\pi$
$823$			930.833i			1.13102i	−0.824740	+	0.565512i	$0.808679\pi$
$824$	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	$0.171343\pi$
$827$			847.952i			1.02534i	−0.858587	+	0.512668i	$0.828657\pi$
$828$	−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	$-0.722139\pi$
$839$		−	1285.70i		−	1.53242i	0.642588	−	0.766212i	$-0.277861\pi$
$840$	−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	$-0.854437\pi$
$859$		−	758.542i		−	0.883053i	0.897248	−	0.441526i	$-0.145563\pi$
$860$	−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	$0.411315\pi$
$863$			1659.44i			1.92288i	−0.275021	+	0.961438i	$0.588685\pi$
$864$	−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	$0.00691404\pi$
$883$			38.3564i			0.0434388i	−0.999764	+	0.0217194i	$0.993086\pi$
$884$	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	$0.300325\pi$
$887$			1436.26i			1.61923i	−0.586959	+	0.809617i	$0.699675\pi$
$888$	−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	$-0.807592\pi$
$907$		−	1030.94i		−	1.13665i	0.822804	−	0.568325i	$-0.192408\pi$
$908$	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	$-0.615928\pi$
$911$		−	1702.49i		−	1.86882i	0.356202	−	0.934409i	$-0.384072\pi$
$912$	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	$0.105105\pi$
$919$			595.935i			0.648461i	−0.945978	+	0.324230i	$0.894895\pi$
$920$	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	$0.0323754\pi$
$947$			192.307i			0.203070i	−0.994832	+	0.101535i	$0.967625\pi$
$948$	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	$-0.921823\pi$
$967$		−	470.231i		−	0.486278i	0.969991	−	0.243139i	$-0.0781771\pi$
$968$	−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	$-0.696374\pi$
$971$		−	1584.01i		−	1.63132i	0.578531	−	0.815660i	$-0.303626\pi$
$972$	−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	$-0.988704\pi$
$983$		−	69.7530i		−	0.0709593i	0.999370	−	0.0354797i	$-0.0112959\pi$
$984$	−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	$0.105686\pi$
$991$			646.046i			0.651913i	−0.945385	+	0.325956i	$0.894314\pi$
$992$	−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.23.10	yes	10
3.2	odd	2		396.3.g.c.199.1		10
4.3	odd	2	inner	44.3.b.a.23.9	✓	10
8.3	odd	2		704.3.d.d.639.6		10
8.5	even	2		704.3.d.d.639.5		10
11.10	odd	2		484.3.b.h.243.1		10
12.11	even	2		396.3.g.c.199.2		10
44.43	even	2		484.3.b.h.243.2		10

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more