LMFDB - Embedded newform 44.3.b.a.23.2

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			23.2
Root			$1.24026 - 1.56900i$ of defining polynomial
Character	$\chi$	$=$	44.23
Dual form			44.3.b.a.23.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80007 + 0.871632i) q^{2} +3.93920i q^{3} +(2.48051 - 3.13800i) q^{4} -7.32441 q^{5} +(-3.43354 - 7.09085i) q^{6} +5.80518i q^{7} +(-1.72992 + 7.81072i) q^{8} -6.51732 q^{9} +(13.1845 - 6.38420i) q^{10} +3.31662i q^{11} +(12.3612 + 9.77125i) q^{12} +13.3869 q^{13} +(-5.05998 - 10.4497i) q^{14} -28.8524i q^{15} +(-3.69410 - 15.5677i) q^{16} +18.5822 q^{17} +(11.7316 - 5.68071i) q^{18} +24.6869i q^{19} +(-18.1683 + 22.9840i) q^{20} -22.8678 q^{21} +(-2.89088 - 5.97016i) q^{22} -3.90291i q^{23} +(-30.7680 - 6.81451i) q^{24} +28.6470 q^{25} +(-24.0974 + 11.6685i) q^{26} +9.77977i q^{27} +(18.2167 + 14.3998i) q^{28} -17.7391 q^{29} +(25.1486 + 51.9363i) q^{30} -53.7292i q^{31} +(20.2190 + 24.8031i) q^{32} -13.0649 q^{33} +(-33.4493 + 16.1968i) q^{34} -42.5195i q^{35} +(-16.1663 + 20.4514i) q^{36} -41.7067 q^{37} +(-21.5179 - 44.4382i) q^{38} +52.7337i q^{39} +(12.6707 - 57.2090i) q^{40} +28.2740 q^{41} +(41.1637 - 19.9323i) q^{42} -10.8938i q^{43} +(10.4076 + 8.22694i) q^{44} +47.7356 q^{45} +(3.40190 + 7.02552i) q^{46} +21.6372i q^{47} +(61.3244 - 14.5518i) q^{48} +15.2999 q^{49} +(-51.5667 + 24.9697i) q^{50} +73.1990i q^{51} +(33.2064 - 42.0081i) q^{52} +58.4573 q^{53} +(-8.52436 - 17.6043i) q^{54} -24.2923i q^{55} +(-45.3427 - 10.0425i) q^{56} -97.2468 q^{57} +(31.9317 - 15.4620i) q^{58} -16.9088i q^{59} +(-90.5387 - 71.5687i) q^{60} +17.7938 q^{61} +(46.8321 + 96.7164i) q^{62} -37.8342i q^{63} +(-58.0148 - 27.0238i) q^{64} -98.0512 q^{65} +(23.5177 - 11.3878i) q^{66} +82.7612i q^{67} +(46.0934 - 58.3109i) q^{68} +15.3744 q^{69} +(37.0614 + 76.5382i) q^{70} -24.9700i q^{71} +(11.2744 - 50.9050i) q^{72} +67.7523 q^{73} +(75.0750 - 36.3529i) q^{74} +112.847i q^{75} +(77.4676 + 61.2363i) q^{76} -19.2536 q^{77} +(-45.9644 - 94.9244i) q^{78} +12.4825i q^{79} +(27.0571 + 114.024i) q^{80} -97.1804 q^{81} +(-50.8952 + 24.6445i) q^{82} -37.2108i q^{83} +(-56.7239 + 71.7591i) q^{84} -136.104 q^{85} +(9.49537 + 19.6096i) q^{86} -69.8781i q^{87} +(-25.9052 - 5.73750i) q^{88} +76.5448 q^{89} +(-85.9274 + 41.6079i) q^{90} +77.7134i q^{91} +(-12.2473 - 9.68123i) q^{92} +211.650 q^{93} +(-18.8597 - 38.9485i) q^{94} -180.817i q^{95} +(-97.7044 + 79.6466i) q^{96} -130.492 q^{97} +(-27.5409 + 13.3359i) q^{98} -21.6155i 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 $

$2$	−1.80007	+	0.871632i	−0.900036	+	0.435816i
$2$	−1.80007	+	0.871632i	−0.900036	+	0.435816i
$3$			3.93920i			1.31307i	0.754297	+	0.656534i	$0.227978\pi$
$3$			3.93920i			1.31307i	−0.754297	+	0.656534i	$0.772022\pi$
$4$	2.48051	−	3.13800i	0.620129	−	0.784500i
$5$	−7.32441			−1.46488			−0.732441	−	0.680830i	$-0.761619\pi$
$5$	−7.32441			−1.46488			−0.732441	+	0.680830i	$0.761619\pi$
$6$	−3.43354	−	7.09085i	−0.572256	−	1.18181i
$7$			5.80518i			0.829312i	0.909978	+	0.414656i	$0.136098\pi$
$7$			5.80518i			0.829312i	−0.909978	+	0.414656i	$0.863902\pi$
$8$	−1.72992	+	7.81072i	−0.216240	+	0.976340i
$9$	−6.51732			−0.724147
$10$	13.1845	−	6.38420i	1.31845	−	0.638420i
$11$			3.31662i			0.301511i
$11$			3.31662i			0.301511i
$12$	12.3612	+	9.77125i	1.03010	+	0.814271i
$13$	13.3869			1.02976			0.514881	−	0.857262i	$-0.327836\pi$
$13$	13.3869			1.02976			0.514881	+	0.857262i	$0.327836\pi$
$14$	−5.05998	−	10.4497i	−0.361427	−	0.746410i
$15$		−	28.8524i		−	1.92349i
$16$	−3.69410	−	15.5677i	−0.230881	−	0.972982i
$17$	18.5822			1.09307			0.546535	−	0.837436i	$-0.315947\pi$
$17$	18.5822			1.09307			0.546535	+	0.837436i	$0.315947\pi$
$18$	11.7316	−	5.68071i	0.651758	−	0.315595i
$19$			24.6869i			1.29931i	0.760229	+	0.649656i	$0.225087\pi$
$19$			24.6869i			1.29931i	−0.760229	+	0.649656i	$0.774913\pi$
$20$	−18.1683	+	22.9840i	−0.908416	+	1.14920i
$21$	−22.8678			−1.08894
$22$	−2.89088	−	5.97016i	−0.131404	−	0.271371i
$23$		−	3.90291i		−	0.169692i	−0.996394	−	0.0848459i	$-0.972960\pi$
$23$		−	3.90291i		−	0.169692i	0.996394	−	0.0848459i	$-0.0270398\pi$
$24$	−30.7680	−	6.81451i	−1.28200	−	0.283938i
$25$	28.6470			1.14588
$26$	−24.0974	+	11.6685i	−0.926822	+	0.448787i
$27$			9.77977i			0.362214i
$28$	18.2167	+	14.3998i	0.650595	+	0.514280i
$29$	−17.7391			−0.611695			−0.305847	−	0.952081i	$-0.598940\pi$
$29$	−17.7391			−0.611695			−0.305847	+	0.952081i	$0.598940\pi$
$30$	25.1486	+	51.9363i	0.838288	+	1.73121i
$31$		−	53.7292i		−	1.73320i	−0.499003	−	0.866600i	$-0.666300\pi$
$31$		−	53.7292i		−	1.73320i	0.499003	−	0.866600i	$-0.333700\pi$
$32$	20.2190	+	24.8031i	0.631842	+	0.775097i
$33$	−13.0649			−0.395905
$34$	−33.4493	+	16.1968i	−0.983802	+	0.476377i
$35$		−	42.5195i		−	1.21484i
$36$	−16.1663	+	20.4514i	−0.449064	+	0.568093i
$37$	−41.7067			−1.12721			−0.563604	−	0.826045i	$-0.690585\pi$
$37$	−41.7067			−1.12721			−0.563604	+	0.826045i	$0.690585\pi$
$38$	−21.5179	−	44.4382i	−0.566261	−	1.16943i
$39$			52.7337i			1.35215i
$40$	12.6707	−	57.2090i	0.316766	−	1.43022i
$41$	28.2740			0.689609			0.344805	−	0.938674i	$-0.387945\pi$
$41$	28.2740			0.689609			0.344805	+	0.938674i	$0.387945\pi$
$42$	41.1637	−	19.9323i	0.980087	−	0.474579i
$43$		−	10.8938i		−	0.253344i	−0.991945	−	0.126672i	$-0.959570\pi$
$43$		−	10.8938i		−	0.253344i	0.991945	−	0.126672i	$-0.0404295\pi$
$44$	10.4076	+	8.22694i	0.236536	+	0.186976i
$45$	47.7356			1.06079
$46$	3.40190	+	7.02552i	0.0739544	+	0.152729i
$47$			21.6372i			0.460365i	0.973147	+	0.230183i	$0.0739324\pi$
$47$			21.6372i			0.460365i	−0.973147	+	0.230183i	$0.926068\pi$
$48$	61.3244	−	14.5518i	1.27759	−	0.303163i
$49$	15.2999			0.312242
$50$	−51.5667	+	24.9697i	−1.03133	+	0.499394i
$51$			73.1990i			1.43527i
$52$	33.2064	−	42.0081i	0.638584	−	0.807848i
$53$	58.4573			1.10297			0.551484	−	0.834186i	$-0.314062\pi$
$53$	58.4573			1.10297			0.551484	+	0.834186i	$0.314062\pi$
$54$	−8.52436	−	17.6043i	−0.157859	−	0.326005i
$55$		−	24.2923i		−	0.441679i
$56$	−45.3427	−	10.0425i	−0.809690	−	0.179330i
$57$	−97.2468			−1.70608
$58$	31.9317	−	15.4620i	0.550547	−	0.266586i
$59$		−	16.9088i		−	0.286590i	−0.989680	−	0.143295i	$-0.954230\pi$
$59$		−	16.9088i		−	0.286590i	0.989680	−	0.143295i	$-0.0457697\pi$
$60$	−90.5387	−	71.5687i	−1.50898	−	1.19281i
$61$	17.7938			0.291702			0.145851	−	0.989307i	$-0.453408\pi$
$61$	17.7938			0.291702			0.145851	+	0.989307i	$0.453408\pi$
$62$	46.8321	+	96.7164i	0.755357	+	1.55994i
$63$		−	37.8342i		−	0.600544i
$64$	−58.0148	−	27.0238i	−0.906481	−	0.422248i
$65$	−98.0512			−1.50848
$66$	23.5177	−	11.3878i	0.356328	−	0.172542i
$67$			82.7612i			1.23524i	0.786476	+	0.617621i	$0.211904\pi$
$67$			82.7612i			1.23524i	−0.786476	+	0.617621i	$0.788096\pi$
$68$	46.0934	−	58.3109i	0.677844	−	0.857513i
$69$	15.3744			0.222817
$70$	37.0614	+	76.5382i	0.529449	+	1.09340i
$71$		−	24.9700i		−	0.351690i	−0.984418	−	0.175845i	$-0.943734\pi$
$71$		−	24.9700i		−	0.351690i	0.984418	−	0.175845i	$-0.0562658\pi$
$72$	11.2744	−	50.9050i	0.156590	−	0.707014i
$73$	67.7523			0.928113			0.464057	−	0.885806i	$-0.346393\pi$
$73$	67.7523			0.928113			0.464057	+	0.885806i	$0.346393\pi$
$74$	75.0750	−	36.3529i	1.01453	−	0.491255i
$75$			112.847i			1.50462i
$76$	77.4676	+	61.2363i	1.01931	+	0.805740i
$77$	−19.2536			−0.250047
$78$	−45.9644	−	94.9244i	−0.589287	−	1.21698i
$79$			12.4825i			0.158007i	0.996874	+	0.0790033i	$0.0251737\pi$
$79$			12.4825i			0.158007i	−0.996874	+	0.0790033i	$0.974826\pi$
$80$	27.0571	+	114.024i	0.338214	+	1.42530i
$81$	−97.1804			−1.19976
$82$	−50.8952	+	24.6445i	−0.620673	+	0.300543i
$83$		−	37.2108i		−	0.448323i	−0.974552	−	0.224162i	$-0.928036\pi$
$83$		−	37.2108i		−	0.448323i	0.974552	−	0.224162i	$-0.0719644\pi$
$84$	−56.7239	+	71.7591i	−0.675284	+	0.854275i
$85$	−136.104			−1.60122
$86$	9.49537	+	19.6096i	0.110411	+	0.228018i
$87$		−	69.8781i		−	0.803197i
$88$	−25.9052	−	5.73750i	−0.294378	−	0.0651988i
$89$	76.5448			0.860054			0.430027	−	0.902816i	$-0.358504\pi$
$89$	76.5448			0.860054			0.430027	+	0.902816i	$0.358504\pi$
$90$	−85.9274	+	41.6079i	−0.954749	+	0.462310i
$91$			77.7134i			0.853993i
$92$	−12.2473	−	9.68123i	−0.133123	−	0.105231i
$93$	211.650			2.27581
$94$	−18.8597	−	38.9485i	−0.200635	−	0.414345i
$95$		−	180.817i		−	1.90334i
$96$	−97.7044	+	79.6466i	−1.01775	+	0.829652i
$97$	−130.492			−1.34528			−0.672641	−	0.739969i	$-0.734840\pi$
$97$	−130.492			−1.34528			−0.672641	+	0.739969i	$0.734840\pi$
$98$	−27.5409	+	13.3359i	−0.281029	+	0.136080i
$99$		−	21.6155i		−	0.218339i
$100$	71.0594	−	89.8944i	0.710594	−	0.898944i
$101$	129.160			1.27881			0.639407	−	0.768869i	$-0.279180\pi$
$101$	129.160			1.27881			0.639407	+	0.768869i	$0.279180\pi$
$102$	−63.8026	−	131.763i	−0.625516	−	1.29180i
$103$			26.4552i			0.256847i	0.991719	+	0.128423i	$0.0409916\pi$
$103$			26.4552i			0.256847i	−0.991719	+	0.128423i	$0.959008\pi$
$104$	−23.1583	+	104.561i	−0.222676	+	1.00540i
$105$	167.493			1.59517
$106$	−105.227	+	50.9532i	−0.992710	+	0.480691i
$107$		−	92.4255i		−	0.863789i	−0.901924	−	0.431895i	$-0.857845\pi$
$107$		−	92.4255i		−	0.863789i	0.901924	−	0.431895i	$-0.142155\pi$
$108$	30.6889	+	24.2589i	0.284157	+	0.224619i
$109$	−22.2234			−0.203885			−0.101942	−	0.994790i	$-0.532506\pi$
$109$	−22.2234			−0.203885			−0.101942	+	0.994790i	$0.532506\pi$
$110$	21.1740	+	43.7279i	0.192491	+	0.397527i
$111$		−	164.291i		−	1.48010i
$112$	90.3734	−	21.4449i	0.806905	−	0.191472i
$113$	70.9385			0.627775			0.313887	−	0.949460i	$-0.398369\pi$
$113$	70.9385			0.627775			0.313887	+	0.949460i	$0.398369\pi$
$114$	175.051	−	84.7634i	1.53554	−	0.743539i
$115$			28.5865i			0.248579i
$116$	−44.0022	+	55.6655i	−0.379329	+	0.479875i
$117$	−87.2467			−0.745699
$118$	14.7383	+	30.4370i	0.124900	+	0.257941i
$119$			107.873i			0.906495i
$120$	225.358	+	49.9123i	1.87798	+	0.415936i
$121$	−11.0000			−0.0909091
$122$	−32.0302	+	15.5097i	−0.262543	+	0.127129i
$123$			111.377i			0.905504i
$124$	−168.602	−	133.276i	−1.35970	−	1.07481i
$125$	−26.7125			−0.213700
$126$	32.9775	+	68.1043i	0.261727	+	0.540511i
$127$			64.2837i			0.506171i	0.967444	+	0.253086i	$0.0814454\pi$
$127$			64.2837i			0.506171i	−0.967444	+	0.253086i	$0.918555\pi$
$128$	127.986	−	1.92267i	0.999887	−	0.0150209i
$129$	42.9128			0.332657
$130$	176.499	−	85.4646i	1.35769	−	0.657420i
$131$		−	169.921i		−	1.29711i	−0.761169	−	0.648554i	$-0.775374\pi$
$131$		−	169.921i		−	1.29711i	0.761169	−	0.648554i	$-0.224626\pi$
$132$	−32.4076	+	40.9975i	−0.245512	+	0.310587i
$133$	−143.312			−1.07753
$134$	−72.1374	−	148.976i	−0.538339	−	1.11176i
$135$		−	71.6311i		−	0.530601i
$136$	−32.1457	+	145.140i	−0.236365	+	1.06721i
$137$	−74.3855			−0.542960			−0.271480	−	0.962444i	$-0.587513\pi$
$137$	−74.3855			−0.542960			−0.271480	+	0.962444i	$0.587513\pi$
$138$	−27.6749	+	13.4008i	−0.200543	+	0.0971072i
$139$		−	79.5922i		−	0.572606i	−0.958139	−	0.286303i	$-0.907574\pi$
$139$		−	79.5922i		−	0.572606i	0.958139	−	0.286303i	$-0.0924263\pi$
$140$	−133.426	−	105.470i	−0.953046	−	0.753360i
$141$	−85.2332			−0.604491
$142$	21.7647	+	44.9478i	0.153272	+	0.316534i
$143$			44.3993i			0.310485i
$144$	24.0756	+	101.460i	0.167192	+	0.704582i
$145$	129.929			0.896061
$146$	−121.959	+	59.0551i	−0.835335	+	0.404487i
$147$			60.2693i			0.409995i
$148$	−103.454	+	130.876i	−0.699013	+	0.884294i
$149$	−171.827			−1.15320			−0.576600	−	0.817026i	$-0.695621\pi$
$149$	−171.827			−1.15320			−0.576600	+	0.817026i	$0.695621\pi$
$150$	−98.3607	−	203.132i	−0.655738	−	1.35421i
$151$			203.334i			1.34658i	0.739377	+	0.673292i	$0.235120\pi$
$151$			203.334i			1.34658i	−0.739377	+	0.673292i	$0.764880\pi$
$152$	−192.823	−	42.7064i	−1.26857	−	0.280963i
$153$	−121.106			−0.791543
$154$	34.6579	−	16.7821i	0.225051	−	0.108974i
$155$			393.535i			2.53894i
$156$	165.478	+	130.807i	1.06076	+	0.838505i
$157$	73.9277			0.470877			0.235439	−	0.971889i	$-0.424347\pi$
$157$	73.9277			0.470877			0.235439	+	0.971889i	$0.424347\pi$
$158$	−10.8802	−	22.4694i	−0.0688618	−	0.142211i
$159$			230.275i			1.44827i
$160$	−148.092	−	181.668i	−0.925575	−	1.13543i
$161$	22.6571			0.140727
$162$	174.932	−	84.7056i	1.07983	−	0.522874i
$163$		−	308.757i		−	1.89421i	−0.320921	−	0.947106i	$-0.603992\pi$
$163$		−	308.757i		−	1.89421i	0.320921	−	0.947106i	$-0.396008\pi$
$164$	70.1340	−	88.7238i	0.427646	−	0.540999i
$165$	95.6924			0.579954
$166$	32.4342	+	66.9822i	0.195387	+	0.403507i
$167$			209.003i			1.25151i	0.780018	+	0.625757i	$0.215210\pi$
$167$			209.003i			1.25151i	−0.780018	+	0.625757i	$0.784790\pi$
$168$	39.5594	−	178.614i	0.235473	−	1.06318i
$169$	10.2090			0.0604084
$170$	244.996	−	118.632i	1.44115	−	0.697837i
$171$		−	160.893i		−	0.940893i
$172$	−34.1847	−	27.0222i	−0.198748	−	0.157106i
$173$	−221.731			−1.28168			−0.640841	−	0.767674i	$-0.721414\pi$
$173$	−221.731			−1.28168			−0.640841	+	0.767674i	$0.721414\pi$
$174$	60.9080	+	125.786i	0.350046	+	0.722906i
$175$			166.301i			0.950293i
$176$	51.6323	−	12.2519i	0.293365	−	0.0696133i
$177$	66.6072			0.376312
$178$	−137.786	+	66.7189i	−0.774080	+	0.374826i
$179$		−	185.819i		−	1.03810i	−0.854745	−	0.519048i	$-0.826286\pi$
$179$		−	185.819i		−	1.03810i	0.854745	−	0.519048i	$-0.173714\pi$
$180$	118.409	−	149.794i	0.657827	−	0.832190i
$181$	222.314			1.22825			0.614127	−	0.789207i	$-0.289508\pi$
$181$	222.314			1.22825			0.614127	+	0.789207i	$0.289508\pi$
$182$	−67.7375	−	139.890i	−0.372184	−	0.768624i
$183$			70.0936i			0.383025i
$184$	30.4845	+	6.75172i	0.165677	+	0.0366941i
$185$	305.477			1.65123
$186$	−380.986	+	184.481i	−2.04831	+	0.991835i
$187$			61.6301i			0.329573i
$188$	67.8975	+	53.6713i	0.361157	+	0.285486i
$189$	−56.7733			−0.300388
$190$	157.606	+	325.484i	0.829506	+	1.71307i
$191$		−	147.914i		−	0.774419i	−0.921992	−	0.387210i	$-0.873439\pi$
$191$		−	147.914i		−	0.774419i	0.921992	−	0.387210i	$-0.126561\pi$
$192$	106.452	−	228.532i	0.554440	−	1.19027i
$193$	−44.4373			−0.230245			−0.115122	−	0.993351i	$-0.536726\pi$
$193$	−44.4373			−0.230245			−0.115122	+	0.993351i	$0.536726\pi$
$194$	234.895	−	113.741i	1.21080	−	0.586295i
$195$		−	386.244i		−	1.98074i
$196$	37.9516	−	48.0110i	0.193630	−	0.244954i
$197$	61.2376			0.310851			0.155425	−	0.987848i	$-0.450325\pi$
$197$	61.2376			0.310851			0.155425	+	0.987848i	$0.450325\pi$
$198$	18.8408	+	38.9095i	0.0951555	+	0.196512i
$199$		−	292.227i		−	1.46848i	−0.678892	−	0.734238i	$-0.737540\pi$
$199$		−	292.227i		−	1.46848i	0.678892	−	0.734238i	$-0.262460\pi$
$200$	−49.5571	+	223.754i	−0.247785	+	1.11877i
$201$	−326.013			−1.62196
$202$	−232.498	+	112.580i	−1.15098	+	0.557328i
$203$		−	102.979i		−	0.507286i
$204$	229.699	+	181.571i	1.12597	+	0.890055i
$205$	−207.090			−1.01020
$206$	−23.0592	−	47.6212i	−0.111938	−	0.231171i
$207$			25.4365i			0.122882i
$208$	−49.4525	−	208.403i	−0.237752	−	1.00194i
$209$	−81.8772			−0.391757
$210$	−301.500	+	145.992i	−1.43571	+	0.695202i
$211$		−	131.168i		−	0.621647i	−0.950468	−	0.310824i	$-0.899395\pi$
$211$		−	131.168i		−	0.621647i	0.950468	−	0.310824i	$-0.100605\pi$
$212$	145.004	−	183.439i	0.683982	−	0.865278i
$213$	98.3620			0.461793
$214$	80.5610	+	166.372i	0.376453	+	0.777441i
$215$			79.7906i			0.371119i
$216$	−76.3870	−	16.9182i	−0.353644	−	0.0783251i
$217$	311.908			1.43736
$218$	40.0038	−	19.3707i	0.183504	−	0.0888563i
$219$			266.890i			1.21868i
$220$	−76.2294	−	60.2575i	−0.346497	−	0.273898i
$221$	248.758			1.12560
$222$	143.201	+	295.736i	0.645051	+	1.33214i
$223$		−	42.6819i		−	0.191399i	−0.995410	−	0.0956994i	$-0.969491\pi$
$223$		−	42.6819i		−	0.191399i	0.995410	−	0.0956994i	$-0.0305088\pi$
$224$	−143.986	+	117.375i	−0.642797	+	0.523994i
$225$	−186.702			−0.829787
$226$	−127.694	+	61.8323i	−0.565020	+	0.273594i
$227$			383.274i			1.68843i	0.536005	+	0.844215i	$0.319933\pi$
$227$			383.274i			1.68843i	−0.536005	+	0.844215i	$0.680067\pi$
$228$	−241.222	+	305.161i	−1.05799	+	1.33842i
$229$	172.329			0.752527			0.376263	−	0.926513i	$-0.377209\pi$
$229$	172.329			0.752527			0.376263	+	0.926513i	$0.377209\pi$
$230$	−24.9169	−	51.4578i	−0.108335	−	0.223730i
$231$		−	75.8439i		−	0.328328i
$232$	30.6873	−	138.556i	0.132273	−	0.597222i
$233$	−174.344			−0.748259			−0.374129	−	0.927377i	$-0.622058\pi$
$233$	−174.344			−0.748259			−0.374129	+	0.927377i	$0.622058\pi$
$234$	157.050	−	76.0471i	0.671155	−	0.324987i
$235$		−	158.480i		−	0.674381i
$236$	−53.0598	−	41.9425i	−0.224830	−	0.177723i
$237$	−49.1712			−0.207473
$238$	−94.0255	−	194.179i	−0.395065	−	0.815878i
$239$			124.374i			0.520394i	0.965556	+	0.260197i	$0.0837875\pi$
$239$			124.374i			0.520394i	−0.965556	+	0.260197i	$0.916212\pi$
$240$	−449.165	+	106.583i	−1.87152	+	0.444098i
$241$	171.826			0.712970			0.356485	−	0.934301i	$-0.383975\pi$
$241$	171.826			0.712970			0.356485	+	0.934301i	$0.383975\pi$
$242$	19.8008	−	9.58796i	0.0818214	−	0.0396196i
$243$		−	294.795i		−	1.21315i
$244$	44.1379	−	55.8371i	0.180893	−	0.228841i
$245$	−112.063			−0.457398
$246$	−97.0798	−	200.487i	−0.394633	−	0.814986i
$247$			330.481i			1.33798i
$248$	419.664	+	92.9473i	1.69219	+	0.374787i
$249$	146.581			0.588679
$250$	48.0843	−	23.2834i	0.192337	−	0.0931337i
$251$		−	4.25687i		−	0.0169596i	−0.999964	−	0.00847982i	$-0.997301\pi$
$251$		−	4.25687i		−	0.0169596i	0.999964	−	0.00847982i	$-0.00269924\pi$
$252$	−118.724	−	93.8484i	−0.471126	−	0.372414i
$253$	12.9445			0.0511640
$254$	−56.0318	−	115.715i	−0.220598	−	0.455572i
$255$		−	536.140i		−	2.10251i
$256$	−228.707	+	115.017i	−0.893388	+	0.449286i
$257$	414.591			1.61320			0.806598	−	0.591100i	$-0.201306\pi$
$257$	414.591			1.61320			0.806598	+	0.591100i	$0.201306\pi$
$258$	−77.2461	+	37.4042i	−0.299404	+	0.144977i
$259$		−	242.115i		−	0.934806i
$260$	−243.217	+	307.685i	−0.935451	+	1.18340i
$261$	115.612			0.442957
$262$	148.109	+	305.870i	0.565300	+	1.16744i
$263$			238.004i			0.904959i	0.891775	+	0.452479i	$0.149460\pi$
$263$			238.004i			0.904959i	−0.891775	+	0.452479i	$0.850540\pi$
$264$	22.6012	−	102.046i	0.0856105	−	0.386538i
$265$	−428.165			−1.61572
$266$	257.972	−	124.915i	0.969819	−	0.469607i
$267$			301.526i			1.12931i
$268$	259.705	+	205.290i	0.969048	+	0.766009i
$269$	−492.368			−1.83036			−0.915182	−	0.403042i	$-0.867953\pi$
$269$	−492.368			−1.83036			−0.915182	+	0.403042i	$0.867953\pi$
$270$	62.4360	+	128.941i	0.231244	+	0.477559i
$271$		−	219.809i		−	0.811103i	−0.914072	−	0.405551i	$-0.867080\pi$
$271$		−	219.809i		−	0.811103i	0.914072	−	0.405551i	$-0.132920\pi$
$272$	−68.6444	−	289.282i	−0.252369	−	1.06354i
$273$	−306.129			−1.12135
$274$	133.899	−	64.8368i	0.488683	−	0.236631i
$275$			95.0115i			0.345496i
$276$	38.1363	−	48.2447i	0.138175	−	0.174800i
$277$	−124.193			−0.448352			−0.224176	−	0.974549i	$-0.571969\pi$
$277$	−124.193			−0.448352			−0.224176	+	0.974549i	$0.571969\pi$
$278$	69.3751	+	143.272i	0.249551	+	0.515365i
$279$			350.171i			1.25509i
$280$	332.108	+	73.5554i	1.18610	+	0.262698i
$281$	−309.426			−1.10116			−0.550581	−	0.834782i	$-0.685594\pi$
$281$	−309.426			−1.10116			−0.550581	+	0.834782i	$0.685594\pi$
$282$	153.426	−	74.2920i	0.544063	−	0.263447i
$283$			315.046i			1.11324i	0.830768	+	0.556619i	$0.187902\pi$
$283$			315.046i			1.11324i	−0.830768	+	0.556619i	$0.812098\pi$
$284$	−78.3559	−	61.9385i	−0.275901	−	0.218093i
$285$	712.276			2.49921
$286$	−38.6999	−	79.9219i	−0.135314	−	0.279447i
$287$			164.136i			0.571901i
$288$	−131.774	−	161.650i	−0.457547	−	0.561284i
$289$	56.2975			0.194801
$290$	−233.881	+	113.250i	−0.806487	+	0.390518i
$291$		−	514.036i		−	1.76645i
$292$	168.060	−	212.607i	0.575550	−	0.728105i
$293$	52.9652			0.180768			0.0903842	−	0.995907i	$-0.471190\pi$
$293$	52.9652			0.180768			0.0903842	+	0.995907i	$0.471190\pi$
$294$	−52.5327	−	108.489i	−0.178683	−	0.369010i
$295$			123.847i			0.419821i
$296$	72.1492	−	325.759i	0.243747	−	1.10054i
$297$	−32.4358			−0.109212
$298$	309.301	−	149.770i	1.03792	−	0.502583i
$299$		−	52.2479i		−	0.174742i
$300$	354.112	+	279.917i	1.18037	+	0.933058i
$301$	63.2404			0.210101
$302$	−177.233	−	366.016i	−0.586863	−	1.21197i
$303$			508.788i			1.67917i
$304$	384.319	−	91.1959i	1.26421	−	0.299986i
$305$	−130.329			−0.427310
$306$	218.000	−	105.560i	0.712417	−	0.344967i
$307$		−	491.403i		−	1.60066i	−0.599558	−	0.800331i	$-0.704657\pi$
$307$		−	491.403i		−	1.60066i	0.599558	−	0.800331i	$-0.295343\pi$
$308$	−47.7588	+	60.4178i	−0.155061	+	0.196162i
$309$	−104.212			−0.337257
$310$	−343.018	−	708.391i	−1.10651	−	2.28513i
$311$		−	5.43852i		−	0.0174872i	−0.999962	−	0.00874360i	$-0.997217\pi$
$311$		−	5.43852i		−	0.0174872i	0.999962	−	0.00874360i	$-0.00278321\pi$
$312$	−411.888	−	91.2251i	−1.32015	−	0.292388i
$313$	−330.116			−1.05468			−0.527341	−	0.849653i	$-0.676811\pi$
$313$	−330.116			−1.05468			−0.527341	+	0.849653i	$0.676811\pi$
$314$	−133.075	+	64.4378i	−0.423806	+	0.205216i
$315$			277.114i			0.879726i
$316$	39.1701	+	30.9631i	0.123956	+	0.0979843i
$317$	−172.447			−0.543996			−0.271998	−	0.962298i	$-0.587684\pi$
$317$	−172.447			−0.543996			−0.271998	+	0.962298i	$0.587684\pi$
$318$	−200.715	−	414.512i	−0.631180	−	1.30350i
$319$		−	58.8341i		−	0.184433i
$320$	424.924	+	197.934i	1.32789	+	0.618543i
$321$	364.083			1.13421
$322$	−40.7844	+	19.7487i	−0.126660	+	0.0613312i
$323$			458.737i			1.42024i
$324$	−241.057	+	304.952i	−0.744004	+	0.941210i
$325$	383.495			1.17998
$326$	269.122	+	555.784i	0.825528	+	1.70486i
$327$		−	87.5426i		−	0.267715i
$328$	−48.9117	+	220.840i	−0.149121	+	0.673293i
$329$	−125.608			−0.381786
$330$	−172.253	+	83.4086i	−0.521979	+	0.252753i
$331$		−	163.853i		−	0.495024i	−0.968885	−	0.247512i	$-0.920387\pi$
$331$		−	163.853i		−	0.495024i	0.968885	−	0.247512i	$-0.0796129\pi$
$332$	−116.768	−	92.3020i	−0.351710	−	0.278018i
$333$	271.816			0.816264
$334$	−182.174	−	376.220i	−0.545430	−	1.12641i
$335$		−	606.178i		−	1.80949i
$336$	84.4758	+	355.999i	0.251416	+	1.05952i
$337$	412.255			1.22331			0.611654	−	0.791125i	$-0.290504\pi$
$337$	412.255			1.22331			0.611654	+	0.791125i	$0.290504\pi$
$338$	−18.3770	+	8.89851i	−0.0543697	+	0.0263269i
$339$			279.441i			0.824311i
$340$	−337.607	+	427.093i	−0.992962	+	1.25616i
$341$	178.200			0.522580
$342$	140.239	+	289.618i	0.410056	+	0.846837i
$343$			373.272i			1.08826i
$344$	85.0883	+	18.8454i	0.247350	+	0.0547830i
$345$	−112.608			−0.326400
$346$	399.131	−	193.268i	1.15356	−	0.558578i
$347$		−	378.806i		−	1.09166i	−0.837896	−	0.545831i	$-0.816214\pi$
$347$		−	378.806i		−	1.09166i	0.837896	−	0.545831i	$-0.183786\pi$
$348$	−219.278	−	173.334i	−0.630108	−	0.498085i
$349$	199.304			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$349$	199.304			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$350$	−144.954	−	299.354i	−0.414153	−	0.855298i
$351$			130.921i			0.372994i
$352$	−82.2626	+	67.0587i	−0.233700	+	0.190508i
$353$	−9.83774			−0.0278690			−0.0139345	−	0.999903i	$-0.504436\pi$
$353$	−9.83774			−0.0278690			−0.0139345	+	0.999903i	$0.504436\pi$
$354$	−119.898	+	58.0570i	−0.338694	+	0.164003i
$355$			182.891i			0.515185i
$356$	189.871	−	240.198i	0.533344	−	0.674713i
$357$	−424.933			−1.19029
$358$	161.966	+	334.488i	0.452419	+	0.934324i
$359$			104.379i			0.290749i	0.989377	+	0.145375i	$0.0464387\pi$
$359$			104.379i			0.290749i	−0.989377	+	0.145375i	$0.953561\pi$
$360$	−82.5787	+	372.849i	−0.229385	+	1.03569i
$361$	−248.444			−0.688210
$362$	−400.181	+	193.776i	−1.10547	+	0.535293i
$363$		−	43.3312i		−	0.119370i
$364$	243.865	+	192.769i	0.669958	+	0.529585i
$365$	−496.246			−1.35958
$366$	−61.0958	−	126.173i	−0.166928	−	0.344736i
$367$		−	92.4715i		−	0.251966i	−0.992032	−	0.125983i	$-0.959792\pi$
$367$		−	92.4715i		−	0.251966i	0.992032	−	0.125983i	$-0.0402085\pi$
$368$	−60.7594	+	14.4177i	−0.165107	+	0.0391786i
$369$	−184.271			−0.499379
$370$	−549.880	+	266.263i	−1.48616	+	0.719631i
$371$			339.355i			0.914704i
$372$	525.002	−	664.159i	1.41129	−	1.78537i
$373$	−210.811			−0.565176			−0.282588	−	0.959241i	$-0.591193\pi$
$373$	−210.811			−0.565176			−0.282588	+	0.959241i	$0.591193\pi$
$374$	−53.7188	−	110.939i	−0.143633	−	0.296627i
$375$		−	105.226i		−	0.280602i
$376$	−169.002	−	37.4306i	−0.449473	−	0.0995494i
$377$	−237.472			−0.629900
$378$	102.196	−	49.4855i	0.270360	−	0.130914i
$379$		−	474.260i		−	1.25135i	−0.780085	−	0.625673i	$-0.784824\pi$
$379$		−	474.260i		−	1.25135i	0.780085	−	0.625673i	$-0.215176\pi$
$380$	−567.405	−	448.520i	−1.49317	−	1.18031i
$381$	−253.227			−0.664637
$382$	128.927	+	266.256i	0.337505	+	0.697005i
$383$		−	352.236i		−	0.919677i	−0.888003	−	0.459838i	$-0.847907\pi$
$383$		−	352.236i		−	0.919677i	0.888003	−	0.459838i	$-0.152093\pi$
$384$	7.57380	+	504.161i	0.0197234	+	1.31292i
$385$	141.021			0.366289
$386$	79.9903	−	38.7330i	0.207229	−	0.100344i
$387$			70.9983i			0.183458i
$388$	−323.688	+	409.485i	−0.834247	+	1.05537i
$389$	−183.305			−0.471220			−0.235610	−	0.971848i	$-0.575709\pi$
$389$	−183.305			−0.471220			−0.235610	+	0.971848i	$0.575709\pi$
$390$	336.662	+	695.266i	0.863237	+	1.78273i
$391$		−	72.5246i		−	0.185485i
$392$	−26.4676	+	119.503i	−0.0675193	+	0.304855i
$393$	669.354			1.70319
$394$	−110.232	+	53.3766i	−0.279777	+	0.135474i
$395$		−	91.4271i		−	0.231461i
$396$	−67.8295	−	53.6176i	−0.171287	−	0.135398i
$397$	−641.230			−1.61519			−0.807594	−	0.589739i	$-0.799231\pi$
$397$	−641.230			−1.61519			−0.807594	+	0.589739i	$0.799231\pi$
$398$	254.714	+	526.029i	0.639985	+	1.32168i
$399$		−	564.535i		−	1.41488i
$400$	−105.825	−	445.969i	−0.264562	−	1.11492i
$401$	493.400			1.23043			0.615213	−	0.788361i	$-0.289070\pi$
$401$	493.400			1.23043			0.615213	+	0.788361i	$0.289070\pi$
$402$	586.847	−	284.164i	1.45982	−	0.706875i
$403$		−	719.268i		−	1.78478i
$404$	320.384	−	405.305i	0.793029	−	1.00323i
$405$	711.790			1.75751
$406$	89.7598	+	185.369i	0.221083	+	0.456575i
$407$		−	138.325i		−	0.339866i
$408$	−571.737	−	126.628i	−1.40132	−	0.310364i
$409$	256.241			0.626507			0.313253	−	0.949670i	$-0.398581\pi$
$409$	256.241			0.626507			0.313253	+	0.949670i	$0.398581\pi$
$410$	372.777	−	180.507i	0.909213	−	0.440260i
$411$		−	293.020i		−	0.712943i
$412$	83.0164	+	65.6225i	0.201496	+	0.159278i
$413$	98.1586			0.237672
$414$	−22.1713	−	45.7876i	−0.0535539	−	0.110598i
$415$			272.548i			0.656741i
$416$	270.669	+	332.037i	0.650647	+	0.798165i
$417$	313.530			0.751870
$418$	147.385	−	71.3668i	0.352595	−	0.170734i
$419$			638.082i			1.52287i	0.648243	+	0.761434i	$0.275504\pi$
$419$			638.082i			1.52287i	−0.648243	+	0.761434i	$0.724496\pi$
$420$	415.469	−	525.594i	0.989212	−	1.25141i
$421$	638.939			1.51767			0.758835	−	0.651283i	$-0.225769\pi$
$421$	638.939			1.51767			0.758835	+	0.651283i	$0.225769\pi$
$422$	114.330	+	236.111i	0.270924	+	0.559505i
$423$		−	141.016i		−	0.333372i
$424$	−101.126	+	456.593i	−0.238506	+	1.07687i
$425$	532.325			1.25253
$426$	−177.059	+	85.7355i	−0.415630	+	0.201257i
$427$			103.296i			0.241912i
$428$	−290.031	−	229.263i	−0.677643	−	0.535661i
$429$	−174.898			−0.407687
$430$	−69.5480	−	143.629i	−0.161740	−	0.334020i
$431$		−	21.7364i		−	0.0504326i	−0.999682	−	0.0252163i	$-0.991973\pi$
$431$		−	21.7364i		−	0.0504326i	0.999682	−	0.0252163i	$-0.00802744\pi$
$432$	152.249	−	36.1274i	0.352427	−	0.0836283i
$433$	553.476			1.27823			0.639117	−	0.769109i	$-0.279300\pi$
$433$	553.476			1.27823			0.639117	+	0.769109i	$0.279300\pi$
$434$	−561.456	+	271.869i	−1.29368	+	0.626426i
$435$			511.816i			1.17659i
$436$	−55.1256	+	69.7372i	−0.126435	+	0.159948i
$437$	96.3508			0.220482
$438$	−232.630	−	480.421i	−0.531119	−	1.09685i
$439$			763.723i			1.73969i	0.493328	+	0.869844i	$0.335780\pi$
$439$			763.723i			1.73969i	−0.493328	+	0.869844i	$0.664220\pi$
$440$	189.741	+	42.0238i	0.431229	+	0.0955086i
$441$	−99.7142			−0.226109
$442$	−447.782	+	216.825i	−1.01308	+	0.490555i
$443$			23.5641i			0.0531921i	0.999646	+	0.0265961i	$0.00846679\pi$
$443$			23.5641i			0.0531921i	−0.999646	+	0.0265961i	$0.991533\pi$
$444$	−515.545	−	407.526i	−1.16114	−	0.917852i
$445$	−560.646			−1.25988
$446$	37.2030	+	76.8305i	0.0834147	+	0.172266i
$447$		−	676.861i		−	1.51423i
$448$	156.878	−	336.786i	0.350175	−	0.751755i
$449$	−387.403			−0.862814			−0.431407	−	0.902157i	$-0.641983\pi$
$449$	−387.403			−0.862814			−0.431407	+	0.902157i	$0.641983\pi$
$450$	336.077	−	162.736i	0.746838	−	0.361635i
$451$			93.7742i			0.207925i
$452$	175.964	−	222.605i	0.389301	−	0.492489i
$453$	−800.974			−1.76816
$454$	−334.074	−	689.920i	−0.735845	−	1.51965i
$455$		−	569.205i		−	1.25100i
$456$	168.229	−	759.568i	0.368924	−	1.66572i
$457$	−84.9126			−0.185804			−0.0929021	−	0.995675i	$-0.529614\pi$
$457$	−84.9126			−0.185804			−0.0929021	+	0.995675i	$0.529614\pi$
$458$	−310.204	+	150.207i	−0.677301	+	0.327963i
$459$			181.729i			0.395925i
$460$	89.7046	+	70.9093i	0.195010	+	0.154151i
$461$	661.135			1.43413			0.717066	−	0.697005i	$-0.245485\pi$
$461$	661.135			1.43413			0.717066	+	0.697005i	$0.245485\pi$
$462$	66.1080	+	136.524i	0.143091	+	0.295507i
$463$			170.691i			0.368663i	0.982864	+	0.184331i	$0.0590120\pi$
$463$			170.691i			0.368663i	−0.982864	+	0.184331i	$0.940988\pi$
$464$	65.5301	+	276.158i	0.141229	+	0.595168i
$465$	−1550.21			−3.33379
$466$	313.832	−	151.964i	0.673460	−	0.326103i
$467$			714.245i			1.52943i	0.644367	+	0.764717i	$0.277121\pi$
$467$			714.245i			1.52943i	−0.644367	+	0.764717i	$0.722879\pi$
$468$	−216.417	+	273.780i	−0.462429	+	0.585001i
$469$	−480.444			−1.02440
$470$	138.136	+	285.275i	0.293906	+	0.606967i
$471$			291.216i			0.618294i
$472$	132.070	+	29.2509i	0.279809	+	0.0619722i
$473$	36.1306			0.0763860
$474$	88.5116	−	42.8592i	0.186733	−	0.0904202i
$475$			707.207i			1.48886i
$476$	338.505	+	267.580i	0.711146	+	0.562144i
$477$	−380.985			−0.798711
$478$	−108.409	−	223.882i	−0.226796	−	0.468373i
$479$		−	801.041i		−	1.67232i	−0.548485	−	0.836160i	$-0.684795\pi$
$479$		−	801.041i		−	1.67232i	0.548485	−	0.836160i	$-0.315205\pi$
$480$	715.628	−	583.365i	1.49089	−	1.21534i
$481$	−558.323			−1.16075
$482$	−309.299	+	149.769i	−0.641698	+	0.310724i
$483$			89.2509i			0.184785i
$484$	−27.2857	+	34.5180i	−0.0563753	+	0.0713182i
$485$	955.780			1.97068
$486$	256.953	+	530.653i	0.528710	+	1.09188i
$487$			116.427i			0.239070i	0.992830	+	0.119535i	$0.0381404\pi$
$487$			116.427i			0.239070i	−0.992830	+	0.119535i	$0.961860\pi$
$488$	−30.7819	+	138.983i	−0.0630777	+	0.284801i
$489$	1216.25			2.48723
$490$	201.721	−	97.6774i	0.411675	−	0.199342i
$491$			658.338i			1.34081i	0.741995	+	0.670406i	$0.233880\pi$
$491$			658.338i			1.34081i	−0.741995	+	0.670406i	$0.766120\pi$
$492$	349.501	+	276.272i	0.710368	+	0.561529i
$493$	−329.632			−0.668625
$494$	−288.058	−	594.890i	−0.583114	−	1.20423i
$495$			158.321i			0.319840i
$496$	−836.441	+	198.481i	−1.68637	+	0.400163i
$497$	144.955			0.291661
$498$	−263.856	+	127.765i	−0.529832	+	0.256556i
$499$			433.519i			0.868776i	0.900726	+	0.434388i	$0.143035\pi$
$499$			433.519i			0.868776i	−0.900726	+	0.434388i	$0.856965\pi$
$500$	−66.2606	+	83.8237i	−0.132521	+	0.167647i
$501$	−823.305			−1.64332
$502$	3.71042	+	7.66267i	0.00739128	+	0.0152643i
$503$		−	566.370i		−	1.12598i	−0.826462	−	0.562992i	$-0.809650\pi$
$503$		−	566.370i		−	1.12598i	0.826462	−	0.562992i	$-0.190350\pi$
$504$	295.513	+	65.4502i	0.586335	+	0.129862i
$505$	−946.023			−1.87331
$506$	−23.3010	+	11.2828i	−0.0460494	+	0.0222981i
$507$			40.2154i			0.0793203i
$508$	201.722	+	159.457i	0.397091	+	0.313891i
$509$	491.065			0.964764			0.482382	−	0.875961i	$-0.339772\pi$
$509$	491.065			0.964764			0.482382	+	0.875961i	$0.339772\pi$
$510$	467.317	+	965.090i	0.916307	+	1.89233i
$511$			393.314i			0.769695i
$512$	311.437	−	406.388i	0.608275	−	0.793727i
$513$	−241.432			−0.470628
$514$	−746.294	+	361.371i	−1.45193	+	0.703057i
$515$		−	193.769i		−	0.376250i
$516$	106.446	−	134.660i	0.206290	−	0.260970i
$517$	−71.7624			−0.138805
$518$	211.035	+	435.824i	0.407403	+	0.841359i
$519$		−	873.443i		−	1.68293i
$520$	169.621	−	765.850i	0.326194	−	1.47279i
$521$	103.457			0.198573			0.0992867	−	0.995059i	$-0.468344\pi$
$521$	103.457			0.198573			0.0992867	+	0.995059i	$0.468344\pi$
$522$	−208.109	+	100.771i	−0.398677	+	0.193048i
$523$			402.098i			0.768829i	0.923161	+	0.384415i	$0.125597\pi$
$523$			402.098i			0.768829i	−0.923161	+	0.384415i	$0.874403\pi$
$524$	−533.212	−	421.492i	−1.01758	−	0.804373i
$525$	−655.095			−1.24780
$526$	−207.452	−	428.424i	−0.394396	−	0.814495i
$527$		−	998.406i		−	1.89451i
$528$	48.2629	+	203.390i	0.0914069	+	0.385208i
$529$	513.767			0.971205
$530$	770.728	−	373.203i	1.45420	−	0.704156i
$531$			110.200i			0.207533i
$532$	−355.488	+	449.713i	−0.668210	+	0.845326i
$533$	378.501			0.710133
$534$	−262.819	−	542.768i	−0.492171	−	1.01642i
$535$			676.962i			1.26535i
$536$	−646.425	−	143.170i	−1.20602	−	0.267109i
$537$	731.980			1.36309
$538$	886.297	−	429.164i	1.64739	−	0.797702i
$539$			50.7439i			0.0941446i
$540$	−224.778	−	177.682i	−0.416256	−	0.329041i
$541$	1044.09			1.92992			0.964961	−	0.262394i	$-0.0845119\pi$
$541$	1044.09			1.92992			0.964961	+	0.262394i	$0.0845119\pi$
$542$	191.592	+	395.672i	0.353492	+	0.730021i
$543$			875.740i			1.61278i
$544$	375.712	+	460.896i	0.690648	+	0.847235i
$545$	162.774			0.298667
$546$	551.054	−	266.832i	1.00926	−	0.488703i
$547$		−	942.124i		−	1.72235i	−0.508312	−	0.861173i	$-0.669730\pi$
$547$		−	942.124i		−	1.72235i	0.508312	−	0.861173i	$-0.330270\pi$
$548$	−184.514	+	233.422i	−0.336705	+	0.425952i
$549$	−115.968			−0.211235
$550$	−82.8151	−	171.027i	−0.150573	−	0.310959i
$551$		−	437.925i		−	0.794782i
$552$	−26.5964	+	120.085i	−0.0481819	+	0.217545i
$553$	−72.4632			−0.131037
$554$	223.557	−	108.251i	0.403532	−	0.195399i
$555$			1203.34i			2.16817i
$556$	−249.760	−	197.430i	−0.449209	−	0.355089i
$557$	172.165			0.309094			0.154547	−	0.987985i	$-0.450608\pi$
$557$	172.165			0.309094			0.154547	+	0.987985i	$0.450608\pi$
$558$	−305.220	−	630.332i	−0.546989	−	1.12963i
$559$		−	145.834i		−	0.260884i
$560$	−661.932	+	157.071i	−1.18202	+	0.280485i
$561$	−242.774			−0.432752
$562$	556.990	−	269.706i	0.991085	−	0.479904i
$563$		−	837.976i		−	1.48841i	−0.667950	−	0.744206i	$-0.732828\pi$
$563$		−	837.976i		−	1.48841i	0.667950	−	0.744206i	$-0.267172\pi$
$564$	−211.422	+	267.462i	−0.374862	+	0.474223i
$565$	−519.583			−0.919616
$566$	−274.605	−	567.106i	−0.485167	−	1.00195i
$567$		−	564.150i		−	0.994973i
$568$	195.034	+	43.1961i	0.343369	+	0.0760495i
$569$	−538.014			−0.945542			−0.472771	−	0.881185i	$-0.656746\pi$
$569$	−538.014			−0.945542			−0.472771	+	0.881185i	$0.656746\pi$
$570$	−1282.15	+	620.843i	−2.24938	+	1.08920i
$571$			179.926i			0.315108i	0.987510	+	0.157554i	$0.0503608\pi$
$571$			179.926i			0.315108i	−0.987510	+	0.157554i	$0.949639\pi$
$572$	139.325	+	110.133i	0.243575	+	0.192540i
$573$	582.664			1.01687
$574$	−143.066	−	295.456i	−0.249244	−	0.514731i
$575$		−	111.807i		−	0.194447i
$576$	378.101	+	176.123i	0.656425	+	0.305769i
$577$	−450.823			−0.781322			−0.390661	−	0.920535i	$-0.627754\pi$
$577$	−450.823			−0.781322			−0.390661	+	0.920535i	$0.627754\pi$
$578$	−101.340	+	49.0707i	−0.175328	+	0.0848975i
$579$		−	175.047i		−	0.302327i
$580$	322.290	−	407.717i	0.555673	−	0.702960i
$581$	216.016			0.371800
$582$	448.050	+	925.301i	0.769846	+	1.58986i
$583$			193.881i			0.332557i
$584$	−117.206	+	529.194i	−0.200695	+	0.906154i
$585$	639.031			1.09236
$586$	−95.3411	+	46.1661i	−0.162698	+	0.0787818i
$587$		−	811.334i		−	1.38217i	−0.722773	−	0.691085i	$-0.757133\pi$
$587$		−	811.334i		−	1.38217i	0.722773	−	0.691085i	$-0.242867\pi$
$588$	189.125	+	149.499i	0.321641	+	0.254250i
$589$	1326.41			2.25197
$590$	−107.949	−	222.934i	−0.182965	−	0.377853i
$591$			241.227i			0.408168i
$592$	154.068	+	649.277i	0.260251	+	1.09675i
$593$	−624.543			−1.05319			−0.526596	−	0.850115i	$-0.676532\pi$
$593$	−624.543			−1.05319			−0.526596	+	0.850115i	$0.676532\pi$
$594$	58.3868	−	28.2721i	0.0982943	−	0.0475961i
$595$		−	790.106i		−	1.32791i
$596$	−426.219	+	539.193i	−0.715133	+	0.904686i
$597$	1151.14			1.92821
$598$	45.5409	+	94.0499i	0.0761554	+	0.157274i
$599$			302.388i			0.504822i	0.967620	+	0.252411i	$0.0812234\pi$
$599$			302.388i			0.504822i	−0.967620	+	0.252411i	$0.918777\pi$
$600$	−881.413	−	195.215i	−1.46902	−	0.325359i
$601$	−852.409			−1.41832			−0.709159	−	0.705049i	$-0.750925\pi$
$601$	−852.409			−1.41832			−0.709159	+	0.705049i	$0.750925\pi$
$602$	−113.837	+	55.1223i	−0.189098	+	0.0915653i
$603$		−	539.382i		−	0.894497i
$604$	638.063	+	504.373i	1.05640	+	0.835055i
$605$	80.5686			0.133171
$606$	−443.476	−	915.855i	−0.731809	−	1.51131i
$607$			633.424i			1.04353i	0.853088	+	0.521766i	$0.174727\pi$
$607$			633.424i			1.04353i	−0.853088	+	0.521766i	$0.825273\pi$
$608$	−612.312	+	499.144i	−1.00709	+	0.820960i
$609$	405.655			0.666100
$610$	234.602	−	113.599i	0.384594	−	0.186229i
$611$			289.655i			0.474066i
$612$	−300.405	+	380.031i	−0.490859	+	0.620966i
$613$	81.3226			0.132663			0.0663316	−	0.997798i	$-0.478870\pi$
$613$	81.3226			0.132663			0.0663316	+	0.997798i	$0.478870\pi$
$614$	428.323	+	884.561i	0.697594	+	1.44065i
$615$		−	815.771i		−	1.32646i
$616$	33.3072	−	150.385i	0.0540701	−	0.244131i
$617$	−798.403			−1.29401			−0.647004	−	0.762487i	$-0.723978\pi$
$617$	−798.403			−1.29401			−0.647004	+	0.762487i	$0.723978\pi$
$618$	187.590	−	90.8349i	0.303543	−	0.146982i
$619$		−	775.210i		−	1.25236i	−0.779679	−	0.626179i	$-0.784618\pi$
$619$		−	775.210i		−	1.25236i	0.779679	−	0.626179i	$-0.215382\pi$
$620$	1234.91	+	976.169i	1.99180	+	1.57447i
$621$	38.1696			0.0614647
$622$	4.74039	+	9.78972i	0.00762120	+	0.0157391i
$623$			444.357i			0.713253i
$624$	820.943	−	194.803i	1.31561	−	0.312185i
$625$	−520.523			−0.832837
$626$	594.232	−	287.740i	0.949252	−	0.459648i
$627$		−	322.531i		−	0.514404i
$628$	183.379	−	231.985i	0.292004	−	0.369403i
$629$	−775.001			−1.23212
$630$	−241.541	−	498.824i	−0.383399	−	0.791785i
$631$		−	916.853i		−	1.45302i	−0.687158	−	0.726508i	$-0.741142\pi$
$631$		−	916.853i		−	1.45302i	0.687158	−	0.726508i	$-0.258858\pi$
$632$	−97.4974	−	21.5938i	−0.154268	−	0.0341673i
$633$	516.696			0.816265
$634$	310.416	−	150.310i	0.489616	−	0.237082i
$635$		−	470.841i		−	0.741481i
$636$	722.603	+	571.201i	1.13617	+	0.898114i
$637$	204.818			0.321535
$638$	51.2817	+	105.906i	0.0803788	+	0.165996i
$639$			162.738i			0.254676i
$640$	−937.419	+	14.0824i	−1.46472	+	0.0220038i
$641$	−401.005			−0.625592			−0.312796	−	0.949820i	$-0.601266\pi$
$641$	−401.005			−0.625592			−0.312796	+	0.949820i	$0.601266\pi$
$642$	−655.375	+	317.346i	−1.02083	+	0.494309i
$643$		−	227.345i		−	0.353569i	−0.984250	−	0.176785i	$-0.943430\pi$
$643$		−	227.345i		−	0.353569i	0.984250	−	0.176785i	$-0.0565696\pi$
$644$	56.2013	−	71.0980i	0.0872690	−	0.110401i
$645$	−314.311			−0.487304
$646$	−399.850	−	825.759i	−0.618963	−	1.27826i
$647$			273.880i			0.423307i	0.977345	+	0.211654i	$0.0678849\pi$
$647$			273.880i			0.423307i	−0.977345	+	0.211654i	$0.932115\pi$
$648$	168.114	−	759.049i	0.259436	−	1.17137i
$649$	56.0801			0.0864101
$650$	−690.318	+	334.267i	−1.06203	+	0.514256i
$651$			1228.67i			1.88736i
$652$	−968.878	−	765.875i	−1.48601	−	1.17465i
$653$	−751.947			−1.15153			−0.575764	−	0.817616i	$-0.695295\pi$
$653$	−751.947			−1.15153			−0.575764	+	0.817616i	$0.695295\pi$
$654$	76.3050	+	157.583i	0.116674	+	0.240953i
$655$			1244.57i			1.90011i
$656$	−104.447	−	440.161i	−0.159218	−	0.670977i
$657$	−441.564			−0.672091
$658$	226.103	−	109.484i	0.343621	−	0.166389i
$659$			1125.72i			1.70822i	0.520090	+	0.854112i	$0.325899\pi$
$659$			1125.72i			1.70822i	−0.520090	+	0.854112i	$0.674101\pi$
$660$	237.366	−	300.283i	0.359646	−	0.454974i
$661$	−886.587			−1.34128			−0.670641	−	0.741782i	$-0.733981\pi$
$661$	−886.587			−1.34128			−0.670641	+	0.741782i	$0.733981\pi$
$662$	142.819	+	294.947i	0.215739	+	0.445539i
$663$			979.907i			1.47799i
$664$	290.644	+	64.3718i	0.437716	+	0.0969454i
$665$	1049.68			1.57846
$666$	−489.288	+	236.923i	−0.734666	+	0.355741i
$667$			69.2343i			0.103800i
$668$	655.851	+	518.435i	0.981813	+	0.776100i
$669$	168.133			0.251320
$670$	528.364	+	1091.16i	0.788603	+	1.62860i
$671$			59.0155i			0.0879516i
$672$	−462.363	−	567.192i	−0.688040	−	0.844036i
$673$	1253.65			1.86278			0.931392	−	0.364018i	$-0.118595\pi$
$673$	1253.65			1.86278			0.931392	+	0.364018i	$0.118595\pi$
$674$	−742.088	+	359.335i	−1.10102	+	0.533138i
$675$			280.161i			0.415054i
$676$	25.3236	−	32.0359i	0.0374610	−	0.0473904i
$677$	−829.568			−1.22536			−0.612679	−	0.790332i	$-0.709908\pi$
$677$	−829.568			−1.22536			−0.612679	+	0.790332i	$0.709908\pi$
$678$	−243.570	−	503.014i	−0.359248	−	0.741909i
$679$		−	757.531i		−	1.11566i
$680$	235.448	−	1063.07i	0.346248	−	1.56333i
$681$	−1509.79			−2.21702
$682$	−320.772	+	155.325i	−0.470340	+	0.227749i
$683$		−	596.596i		−	0.873493i	−0.899585	−	0.436746i	$-0.856131\pi$
$683$		−	596.596i		−	0.873493i	0.899585	−	0.436746i	$-0.143869\pi$
$684$	−504.881	−	399.096i	−0.738130	−	0.583474i
$685$	544.830			0.795372
$686$	−325.356	−	671.917i	−0.474280	−	0.979471i
$687$			678.838i			0.988119i
$688$	−169.591	+	40.2427i	−0.246499	+	0.0584923i
$689$	782.561			1.13579
$690$	202.703	−	98.1529i	0.293772	−	0.142251i
$691$			138.107i			0.199865i	0.994994	+	0.0999323i	$0.0318626\pi$
$691$			138.107i			0.199865i	−0.994994	+	0.0999323i	$0.968137\pi$
$692$	−550.007	+	695.792i	−0.794807	+	1.00548i
$693$	125.482			0.181071
$694$	330.180	+	681.879i	0.475764	+	0.982534i
$695$			582.966i			0.838800i
$696$	545.798	+	120.884i	0.784193	+	0.173683i
$697$	525.392			0.753791
$698$	−358.762	+	173.720i	−0.513986	+	0.248883i
$699$		−	686.778i		−	0.982514i
$700$	521.853	+	412.513i	0.745505	+	0.589304i
$701$	192.374			0.274427			0.137214	−	0.990541i	$-0.456185\pi$
$701$	192.374			0.274427			0.137214	+	0.990541i	$0.456185\pi$
$702$	−114.115	−	235.667i	−0.162557	−	0.335708i
$703$		−	1029.61i		−	1.46459i
$704$	89.6280	−	192.413i	0.127312	−	0.273314i
$705$	624.283			0.885508
$706$	17.7086	−	8.57489i	0.0250831	−	0.0121457i
$707$			749.798i			1.06054i
$708$	165.220	−	209.013i	0.233362	−	0.295217i
$709$	622.551			0.878069			0.439035	−	0.898470i	$-0.355321\pi$
$709$	622.551			0.878069			0.439035	+	0.898470i	$0.355321\pi$
$710$	−159.413	−	329.216i	−0.224526	−	0.463685i
$711$		−	81.3526i		−	0.114420i
$712$	−132.416	+	597.870i	−0.185978	+	0.839706i
$713$	−209.700			−0.294110
$714$	764.911	−	370.386i	1.07130	−	0.518747i
$715$		−	325.199i		−	0.454824i
$716$	−583.101	−	460.927i	−0.814387	−	0.643753i
$717$	−489.935			−0.683313
$718$	−90.9801	−	187.890i	−0.126713	−	0.261685i
$719$			1004.18i			1.39664i	0.715788	+	0.698318i	$0.246068\pi$
$719$			1004.18i			1.39664i	−0.715788	+	0.698318i	$0.753932\pi$
$720$	−176.340	−	743.134i	−0.244917	−	1.03213i
$721$	−153.577			−0.213006
$722$	447.217	−	216.552i	0.619414	−	0.299933i
$723$			676.856i			0.936178i
$724$	551.453	−	697.621i	0.761675	−	0.963565i
$725$	−508.174			−0.700930
$726$	37.7689	+	77.9993i	0.0520233	+	0.107437i
$727$			454.468i			0.625128i	0.949897	+	0.312564i	$0.101188\pi$
$727$			454.468i			0.625128i	−0.949897	+	0.312564i	$0.898812\pi$
$728$	−606.997	−	134.438i	−0.833788	−	0.184667i
$729$	286.636			0.393190
$730$	893.278	−	432.544i	1.22367	−	0.592526i
$731$		−	202.430i		−	0.276922i
$732$	219.954	+	173.868i	0.300483	+	0.237525i
$733$	−929.155			−1.26761			−0.633803	−	0.773495i	$-0.718507\pi$
$733$	−929.155			−1.26761			−0.633803	+	0.773495i	$0.718507\pi$
$734$	80.6011	+	166.455i	0.109811	+	0.226778i
$735$		−	441.437i		−	0.600595i
$736$	96.8043	−	78.9128i	0.131528	−	0.107218i
$737$	−274.488			−0.372440
$738$	331.700	−	160.616i	0.449459	−	0.217637i
$739$		−	953.768i		−	1.29062i	−0.763921	−	0.645310i	$-0.776728\pi$
$739$		−	953.768i		−	1.29062i	0.763921	−	0.645310i	$-0.223272\pi$
$740$	757.740	−	958.587i	1.02397	−	1.29539i
$741$	−1301.83			−1.75686
$742$	−295.793	−	610.863i	−0.398643	−	0.823266i
$743$		−	610.718i		−	0.821962i	−0.911644	−	0.410981i	$-0.865186\pi$
$743$		−	610.718i		−	0.821962i	0.911644	−	0.410981i	$-0.134814\pi$
$744$	−366.138	+	1653.14i	−0.492121	+	2.22196i
$745$	1258.53			1.68930
$746$	379.474	−	183.749i	0.508679	−	0.246313i
$747$			242.515i			0.324652i
$748$	193.395	+	152.874i	0.258550	+	0.204378i
$749$	536.547			0.716351
$750$	91.7182	+	189.414i	0.122291	+	0.252552i
$751$			737.978i			0.982660i	0.870974	+	0.491330i	$0.163489\pi$
$751$			737.978i			0.982660i	−0.870974	+	0.491330i	$0.836511\pi$
$752$	336.841	−	79.9298i	0.447927	−	0.106290i
$753$	16.7687			0.0222692
$754$	427.467	−	206.988i	0.566932	−	0.274520i
$755$		−	1489.30i		−	1.97259i
$756$	−140.827	+	178.155i	−0.186279	+	0.235654i
$757$	314.110			0.414940			0.207470	−	0.978241i	$-0.433477\pi$
$757$	314.110			0.414940			0.207470	+	0.978241i	$0.433477\pi$
$758$	413.381	+	853.702i	0.545357	+	1.12626i
$759$			50.9910i			0.0671818i
$760$	1412.31	+	312.799i	1.85831	+	0.411578i
$761$	−582.044			−0.764841			−0.382421	−	0.923988i	$-0.624910\pi$
$761$	−582.044			−0.764841			−0.382421	+	0.923988i	$0.624910\pi$
$762$	455.826	−	220.721i	0.598197	−	0.289660i
$763$		−	129.011i		−	0.169084i
$764$	−464.155	−	366.903i	−0.607532	−	0.480240i
$765$	887.031			1.15952
$766$	307.021	+	634.050i	0.400810	+	0.827742i
$767$		−	226.356i		−	0.295119i
$768$	−453.077	−	900.925i	−0.589943	−	1.17308i
$769$	−940.119			−1.22252			−0.611260	−	0.791429i	$-0.709337\pi$
$769$	−940.119			−1.22252			−0.611260	+	0.791429i	$0.709337\pi$
$770$	−253.849	+	122.919i	−0.329673	+	0.159635i
$771$			1633.16i			2.11824i
$772$	−110.227	+	139.444i	−0.142781	+	0.180627i
$773$	189.525			0.245181			0.122591	−	0.992457i	$-0.460880\pi$
$773$	189.525			0.245181			0.122591	+	0.992457i	$0.460880\pi$
$774$	−61.8844	−	127.802i	−0.0799540	−	0.165119i
$775$		−	1539.18i		−	1.98604i
$776$	225.741	−	1019.24i	0.290904	−	1.31345i
$777$	953.739			1.22746
$778$	329.962	−	159.774i	0.424115	−	0.205365i
$779$			697.997i			0.896017i
$780$	−1212.03	−	958.083i	−1.55389	−	1.22831i
$781$	82.8162			0.106039
$782$	63.2148	+	130.549i	0.0808373	+	0.166943i
$783$		−	173.485i		−	0.221564i
$784$	−56.5192	−	238.184i	−0.0720909	−	0.303806i
$785$	−541.477			−0.689780
$786$	−1204.88	+	583.430i	−1.53293	+	0.742278i
$787$			1475.76i			1.87517i	0.347757	+	0.937585i	$0.386943\pi$
$787$			1475.76i			1.87517i	−0.347757	+	0.937585i	$0.613057\pi$
$788$	151.901	−	192.163i	0.192767	−	0.243862i
$789$	−937.547			−1.18827
$790$	79.6908	+	164.575i	0.100874	+	0.208323i
$791$			411.811i			0.520621i
$792$	168.833	+	37.3931i	0.213173	+	0.0472135i
$793$	238.204			0.300384
$794$	1154.26	−	558.916i	1.45373	−	0.703925i
$795$		−	1686.63i		−	2.12155i
$796$	−917.007	−	724.872i	−1.15202	−	0.910644i
$797$	275.208			0.345305			0.172653	−	0.984983i	$-0.444766\pi$
$797$	275.208			0.345305			0.172653	+	0.984983i	$0.444766\pi$
$798$	492.067	+	1016.20i	0.616625	+	1.27344i
$799$			402.066i			0.503211i
$800$	579.213	+	710.535i	0.724017	+	0.888169i
$801$	−498.867			−0.622806
$802$	−888.156	+	430.064i	−1.10743	+	0.536239i
$803$			224.709i			0.279837i
$804$	−808.681	+	1023.03i	−1.00582	+	1.27243i
$805$	−165.950			−0.206149
$806$	626.937	+	1294.73i	0.777837	+	1.60637i
$807$		−	1939.54i		−	2.40339i
$808$	−223.437	+	1008.83i	−0.276531	+	1.24856i
$809$	−210.974			−0.260783			−0.130392	−	0.991463i	$-0.541624\pi$
$809$	−210.974			−0.260783			−0.130392	+	0.991463i	$0.541624\pi$
$810$	−1281.27	+	620.419i	−1.58182	+	0.765949i
$811$			1139.50i			1.40506i	0.711655	+	0.702529i	$0.247946\pi$
$811$			1139.50i			1.40506i	−0.711655	+	0.702529i	$0.752054\pi$
$812$	−323.148	−	255.441i	−0.397966	−	0.314582i
$813$	865.872			1.06503
$814$	120.569	+	248.996i	0.148119	+	0.305891i
$815$			2261.46i			2.77480i
$816$	1139.54	−	270.404i	1.39650	−	0.331378i
$817$	268.934			0.329172
$818$	−461.253	+	223.348i	−0.563879	+	0.273042i
$819$		−	506.483i		−	0.618416i
$820$	−513.691	+	649.850i	−0.626452	+	0.792500i
$821$	583.985			0.711310			0.355655	−	0.934617i	$-0.384258\pi$
$821$	583.985			0.711310			0.355655	+	0.934617i	$0.384258\pi$
$822$	255.405	+	527.456i	0.310712	+	0.641674i
$823$			184.871i			0.224631i	0.993673	+	0.112315i	$0.0358267\pi$
$823$			184.871i			0.224631i	−0.993673	+	0.112315i	$0.964173\pi$
$824$	−206.634	−	45.7654i	−0.250770	−	0.0555405i
$825$	−374.270			−0.453660
$826$	−176.693	+	85.5582i	−0.213914	+	0.103581i
$827$		−	1127.50i		−	1.36336i	−0.731652	−	0.681678i	$-0.761251\pi$
$827$		−	1127.50i		−	1.36336i	0.731652	−	0.681678i	$-0.238749\pi$
$828$	79.8198	+	63.0957i	0.0964008	+	0.0762025i
$829$	−708.255			−0.854349			−0.427174	−	0.904169i	$-0.640491\pi$
$829$	−708.255			−0.854349			−0.427174	+	0.904169i	$0.640491\pi$
$830$	−237.561	−	490.605i	−0.286218	−	0.591091i
$831$		−	489.223i		−	0.588716i
$832$	−776.638	−	361.765i	−0.933459	−	0.434814i
$833$	284.305			0.341303
$834$	−564.376	+	273.283i	−0.676710	+	0.327677i
$835$		−	1530.82i		−	1.83332i
$836$	−203.098	+	256.931i	−0.242940	+	0.307334i
$837$	525.459			0.627789
$838$	−556.173	−	1148.59i	−0.663690	−	1.37064i
$839$			396.430i			0.472503i	0.971692	+	0.236252i	$0.0759189\pi$
$839$			396.430i			0.472503i	−0.971692	+	0.236252i	$0.924081\pi$
$840$	−289.750	+	1308.24i	−0.344940	+	1.55743i
$841$	−526.323			−0.625830
$842$	−1150.14	+	556.920i	−1.36596	+	0.661425i
$843$		−	1218.89i		−	1.44590i
$844$	−411.604	−	325.363i	−0.487683	−	0.385501i
$845$	−74.7750			−0.0884912
$846$	122.914	+	253.840i	0.145289	+	0.300047i
$847$		−	63.8570i		−	0.0753920i
$848$	−215.947	−	910.046i	−0.254654	−	1.07317i
$849$	−1241.03			−1.46176
$850$	−958.222	+	463.991i	−1.12732	+	0.545872i
$851$			162.777i			0.191278i
$852$	243.988	−	308.660i	0.286371	−	0.362277i
$853$	467.329			0.547866			0.273933	−	0.961749i	$-0.411675\pi$
$853$	467.329			0.547866			0.273933	+	0.961749i	$0.411675\pi$
$854$	−90.0366	−	185.941i	−0.105429	−	0.217730i
$855$			1178.44i			1.37830i
$856$	721.910	+	159.889i	0.843352	+	0.186786i
$857$	1539.00			1.79580			0.897902	−	0.440195i	$-0.145091\pi$
$857$	1539.00			1.79580			0.897902	+	0.440195i	$0.145091\pi$
$858$	314.829	−	152.447i	0.366933	−	0.177677i
$859$		−	1510.20i		−	1.75809i	−0.476735	−	0.879047i	$-0.658180\pi$
$859$		−	1510.20i		−	1.75809i	0.476735	−	0.879047i	$-0.341820\pi$
$860$	250.383	+	197.922i	0.291143	+	0.230141i
$861$	−646.563			−0.750945
$862$	18.9462	+	39.1271i	0.0219793	+	0.0453911i
$863$		−	547.962i		−	0.634950i	−0.948267	−	0.317475i	$-0.897165\pi$
$863$		−	547.962i		−	0.634950i	0.948267	−	0.317475i	$-0.102835\pi$
$864$	−242.569	+	197.737i	−0.280751	+	0.228862i
$865$	1624.05			1.87751
$866$	−996.296	+	482.427i	−1.15046	+	0.557075i
$867$			221.767i			0.255787i
$868$	773.692	−	978.767i	0.891350	−	1.12761i
$869$	−41.3998			−0.0476408
$870$	−446.116	−	921.306i	−0.512776	−	1.05897i
$871$			1107.92i			1.27200i
$872$	38.4448	−	173.581i	0.0440880	−	0.199061i
$873$	850.460			0.974181
$874$	−173.438	+	83.9825i	−0.198442	+	0.0960898i
$875$		−	155.071i		−	0.177224i
$876$	837.501	+	662.024i	0.956051	+	0.755736i
$877$	−1265.34			−1.44281			−0.721404	−	0.692515i	$-0.756503\pi$
$877$	−1265.34			−1.44281			−0.721404	+	0.692515i	$0.756503\pi$
$878$	−665.685	−	1374.76i	−0.758184	−	1.56578i
$879$			208.641i			0.237361i
$880$	−378.176	+	89.7383i	−0.429746	+	0.101975i
$881$	1328.16			1.50756			0.753781	−	0.657126i	$-0.228228\pi$
$881$	1328.16			1.50756			0.753781	+	0.657126i	$0.228228\pi$
$882$	179.493	−	86.9141i	0.203507	−	0.0985421i
$883$		−	383.184i		−	0.433957i	−0.976176	−	0.216978i	$-0.930380\pi$
$883$		−	383.184i		−	0.433957i	0.976176	−	0.216978i	$-0.0696201\pi$
$884$	617.047	−	780.602i	0.698017	−	0.883034i
$885$	−487.859			−0.551253
$886$	−20.5392	−	42.4171i	−0.0231820	−	0.0478748i
$887$			74.5488i			0.0840460i	0.999117	+	0.0420230i	$0.0133803\pi$
$887$			74.5488i			0.0840460i	−0.999117	+	0.0420230i	$0.986620\pi$
$888$	1283.23	+	284.210i	1.44508	+	0.320057i
$889$	−373.179			−0.419774
$890$	1009.20	−	488.677i	1.13394	−	0.549075i
$891$		−	322.311i		−	0.361741i
$892$	−133.936	−	105.873i	−0.150152	−	0.118692i
$893$	−534.155			−0.598158
$894$	589.974	+	1218.40i	0.659926	+	1.36286i
$895$			1361.02i			1.52069i
$896$	11.1615	+	742.979i	0.0124570	+	0.829218i
$897$	205.815			0.229448
$898$	697.354	−	337.673i	0.776563	−	0.376028i
$899$			953.111i			1.06019i
$900$	−463.117	+	585.871i	−0.514575	+	0.650968i
$901$	1086.26			1.20562
$902$	−81.7366	−	168.800i	−0.0906171	−	0.187140i
$903$			249.117i			0.275877i
$904$	−122.718	+	554.081i	−0.135750	+	0.612922i
$905$	−1628.32			−1.79925
$906$	1441.81	−	698.155i	1.59140	−	0.770591i
$907$			32.7978i			0.0361607i	0.999837	+	0.0180804i	$0.00575547\pi$
$907$			32.7978i			0.0361607i	−0.999837	+	0.0180804i	$0.994245\pi$
$908$	1202.71	+	950.716i	1.32457	+	1.04704i
$909$	−841.779			−0.926049
$910$	496.137	+	1024.61i	0.545206	+	1.12594i
$911$		−	59.0963i		−	0.0648697i	−0.999474	−	0.0324349i	$-0.989674\pi$
$911$		−	59.0963i		−	0.0648697i	0.999474	−	0.0324349i	$-0.0103261\pi$
$912$	359.239	+	1513.91i	0.393903	+	1.65999i
$913$	123.414			0.135175
$914$	152.849	−	74.0125i	0.167231	−	0.0809765i
$915$		−	513.394i		−	0.561087i
$916$	427.464	−	540.767i	0.466663	−	0.590358i
$917$	986.423			1.07571
$918$	−158.401	−	327.126i	−0.172550	−	0.356346i
$919$		−	544.818i		−	0.592837i	−0.955058	−	0.296419i	$-0.904208\pi$
$919$		−	544.818i		−	0.592837i	0.955058	−	0.296419i	$-0.0957924\pi$
$920$	−223.281	−	49.4524i	−0.242697	−	0.0537526i
$921$	1935.74			2.10178
$922$	−1190.09	+	576.266i	−1.29077	+	0.625018i
$923$		−	334.271i		−	0.362157i
$924$	−237.998	−	188.132i	−0.257574	−	0.203606i
$925$	−1194.77			−1.29165
$926$	−148.780	−	307.256i	−0.160669	−	0.331810i
$927$		−	172.417i		−	0.185995i
$928$	−358.667	−	439.986i	−0.386495	−	0.474123i
$929$	−1027.49			−1.10601			−0.553006	−	0.833177i	$-0.686520\pi$
$929$	−1027.49			−1.10601			−0.553006	+	0.833177i	$0.686520\pi$
$930$	2790.50	−	1351.22i	3.00053	−	1.45292i
$931$			377.707i			0.405700i
$932$	−432.463	+	547.092i	−0.464017	+	0.587009i
$933$	21.4234			0.0229619
$934$	−622.559	−	1285.69i	−0.666552	−	1.37654i
$935$		−	451.405i		−	0.482786i
$936$	150.930	−	681.460i	0.161250	−	0.728056i
$937$	318.343			0.339747			0.169873	−	0.985466i	$-0.445664\pi$
$937$	318.343			0.339747			0.169873	+	0.985466i	$0.445664\pi$
$938$	864.834	−	418.771i	0.921997	−	0.446450i
$939$		−	1300.39i		−	1.38487i
$940$	−497.309	−	393.111i	−0.529052	−	0.418203i
$941$	112.117			0.119147			0.0595735	−	0.998224i	$-0.481026\pi$
$941$	112.117			0.119147			0.0595735	+	0.998224i	$0.481026\pi$
$942$	−253.834	−	524.210i	−0.269462	−	0.556487i
$943$		−	110.351i		−	0.117021i
$944$	−263.231	+	62.4628i	−0.278847	+	0.0661682i
$945$	415.831			0.440033
$946$	−65.0376	+	31.4926i	−0.0687501	+	0.0332903i
$947$		−	1761.09i		−	1.85965i	−0.368005	−	0.929824i	$-0.619959\pi$
$947$		−	1761.09i		−	1.85965i	0.368005	−	0.929824i	$-0.380041\pi$
$948$	−121.970	+	154.299i	−0.128660	+	0.162763i
$949$	906.993			0.955735
$950$	−616.425	−	1273.02i	−0.648868	−	1.34002i
$951$		−	679.303i		−	0.714304i
$952$	−842.565	−	186.612i	−0.885048	−	0.196021i
$953$	−1392.57			−1.46125			−0.730625	−	0.682779i	$-0.760771\pi$
$953$	−1392.57			−1.46125			−0.730625	+	0.682779i	$0.760771\pi$
$954$	685.800	−	332.079i	0.718868	−	0.348091i
$955$			1083.38i			1.13443i
$956$	390.286	+	308.512i	0.408249	+	0.322711i
$957$	231.759			0.242173
$958$	698.214	+	1441.93i	0.728824	+	1.50515i
$959$		−	431.821i		−	0.450283i
$960$	−779.702	+	1673.86i	−0.812189	+	1.74361i
$961$	−1925.83			−2.00398
$962$	1005.02	−	486.652i	1.04472	−	0.505875i
$963$			602.367i			0.625511i
$964$	426.216	−	539.189i	0.442133	−	0.559325i
$965$	325.477			0.337282
$966$	−77.7940	−	160.658i	−0.0805321	−	0.166313i
$967$			373.578i			0.386326i	0.981167	+	0.193163i	$0.0618747\pi$
$967$			373.578i			0.386326i	−0.981167	+	0.193163i	$0.938125\pi$
$968$	19.0291	−	85.9179i	0.0196582	−	0.0887582i
$969$	−1807.06			−1.86487
$970$	−1720.47	+	833.088i	−1.77368	+	0.858854i
$971$			516.552i			0.531979i	0.963976	+	0.265990i	$0.0856987\pi$
$971$			516.552i			0.531979i	−0.963976	+	0.265990i	$0.914301\pi$
$972$	−925.068	−	731.244i	−0.951716	−	0.752309i
$973$	462.047			0.474868
$974$	−101.482	−	209.577i	−0.104191	−	0.215172i
$975$			1510.66i			1.54940i
$976$	−65.7322	−	277.009i	−0.0673486	−	0.283821i
$977$	295.602			0.302560			0.151280	−	0.988491i	$-0.451660\pi$
$977$	295.602			0.302560			0.151280	+	0.988491i	$0.451660\pi$
$978$	−2189.35	+	1060.13i	−2.23859	+	1.08397i
$979$			253.870i			0.259316i
$980$	−277.973	+	351.653i	−0.283646	+	0.358829i
$981$	144.837			0.147643
$982$	−573.829	−	1185.06i	−0.584347	−	1.20678i
$983$			1511.98i			1.53813i	0.639169	+	0.769066i	$0.279278\pi$
$983$			1511.98i			1.53813i	−0.639169	+	0.769066i	$0.720722\pi$
$984$	−869.935	−	192.673i	−0.884080	−	0.195806i
$985$	−448.529			−0.455360
$986$	593.361	−	287.318i	0.601786	−	0.291398i
$987$		−	494.794i		−	0.501311i
$988$	1037.05	+	819.763i	1.04965	+	0.829720i
$989$	−42.5174			−0.0429903
$990$	−137.998	−	284.989i	−0.139392	−	0.287868i
$991$		−	462.791i		−	0.466994i	−0.972358	−	0.233497i	$-0.924983\pi$
$991$		−	462.791i		−	0.466994i	0.972358	−	0.233497i	$-0.0750168\pi$
$992$	1332.65	−	1086.35i	1.34340	−	1.09511i
$993$	645.450			0.650000
$994$	−260.930	+	126.348i	−0.262505	+	0.127111i
$995$			2140.39i			2.15114i
$996$	363.596	−	459.971i	0.365057	−	0.461819i
$997$	−361.841			−0.362930			−0.181465	−	0.983397i	$-0.558084\pi$
$997$	−361.841			−0.362930			−0.181465	+	0.983397i	$0.558084\pi$
$998$	−377.870	−	780.366i	−0.378627	−	0.781930i
$999$		−	407.881i		−	0.408290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.3.b.a.23.2	yes	10
3.2	odd	2		396.3.g.c.199.9		10
4.3	odd	2	inner	44.3.b.a.23.1	✓	10
8.3	odd	2		704.3.d.d.639.9		10
8.5	even	2		704.3.d.d.639.2		10
11.10	odd	2		484.3.b.h.243.9		10
12.11	even	2		396.3.g.c.199.10		10
44.43	even	2		484.3.b.h.243.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.b.a.23.1	✓	10	4.3	odd	2	inner
44.3.b.a.23.2	yes	10	1.1	even	1	trivial
396.3.g.c.199.9		10	3.2	odd	2
396.3.g.c.199.10		10	12.11	even	2
484.3.b.h.243.9		10	11.10	odd	2
484.3.b.h.243.10		10	44.43	even	2
704.3.d.d.639.2		10	8.5	even	2
704.3.d.d.639.9		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+(-1.80007 + 0.871632i) q^{2} +3.93920i q^{3} +(2.48051 - 3.13800i) q^{4} -7.32441 q^{5} +(-3.43354 - 7.09085i) q^{6} +5.80518i q^{7} +(-1.72992 + 7.81072i) q^{8} -6.51732 q^{9} +(13.1845 - 6.38420i) q^{10} +3.31662i q^{11} +(12.3612 + 9.77125i) q^{12} +13.3869 q^{13} +(-5.05998 - 10.4497i) q^{14} -28.8524i q^{15} +(-3.69410 - 15.5677i) q^{16} +18.5822 q^{17} +(11.7316 - 5.68071i) q^{18} +24.6869i q^{19} +(-18.1683 + 22.9840i) q^{20} -22.8678 q^{21} +(-2.89088 - 5.97016i) q^{22} -3.90291i q^{23} +(-30.7680 - 6.81451i) q^{24} +28.6470 q^{25} +(-24.0974 + 11.6685i) q^{26} +9.77977i q^{27} +(18.2167 + 14.3998i) q^{28} -17.7391 q^{29} +(25.1486 + 51.9363i) q^{30} -53.7292i q^{31} +(20.2190 + 24.8031i) q^{32} -13.0649 q^{33} +(-33.4493 + 16.1968i) q^{34} -42.5195i q^{35} +(-16.1663 + 20.4514i) q^{36} -41.7067 q^{37} +(-21.5179 - 44.4382i) q^{38} +52.7337i q^{39} +(12.6707 - 57.2090i) q^{40} +28.2740 q^{41} +(41.1637 - 19.9323i) q^{42} -10.8938i q^{43} +(10.4076 + 8.22694i) q^{44} +47.7356 q^{45} +(3.40190 + 7.02552i) q^{46} +21.6372i q^{47} +(61.3244 - 14.5518i) q^{48} +15.2999 q^{49} +(-51.5667 + 24.9697i) q^{50} +73.1990i q^{51} +(33.2064 - 42.0081i) q^{52} +58.4573 q^{53} +(-8.52436 - 17.6043i) q^{54} -24.2923i q^{55} +(-45.3427 - 10.0425i) q^{56} -97.2468 q^{57} +(31.9317 - 15.4620i) q^{58} -16.9088i q^{59} +(-90.5387 - 71.5687i) q^{60} +17.7938 q^{61} +(46.8321 + 96.7164i) q^{62} -37.8342i q^{63} +(-58.0148 - 27.0238i) q^{64} -98.0512 q^{65} +(23.5177 - 11.3878i) q^{66} +82.7612i q^{67} +(46.0934 - 58.3109i) q^{68} +15.3744 q^{69} +(37.0614 + 76.5382i) q^{70} -24.9700i q^{71} +(11.2744 - 50.9050i) q^{72} +67.7523 q^{73} +(75.0750 - 36.3529i) q^{74} +112.847i q^{75} +(77.4676 + 61.2363i) q^{76} -19.2536 q^{77} +(-45.9644 - 94.9244i) q^{78} +12.4825i q^{79} +(27.0571 + 114.024i) q^{80} -97.1804 q^{81} +(-50.8952 + 24.6445i) q^{82} -37.2108i q^{83} +(-56.7239 + 71.7591i) q^{84} -136.104 q^{85} +(9.49537 + 19.6096i) q^{86} -69.8781i q^{87} +(-25.9052 - 5.73750i) q^{88} +76.5448 q^{89} +(-85.9274 + 41.6079i) q^{90} +77.7134i q^{91} +(-12.2473 - 9.68123i) q^{92} +211.650 q^{93} +(-18.8597 - 38.9485i) q^{94} -180.817i q^{95} +(-97.7044 + 79.6466i) q^{96} -130.492 q^{97} +(-27.5409 + 13.3359i) q^{98} -21.6155i 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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