LMFDB - Embedded newform 952.2.q.c.137.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(137,952)] 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("952.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 10 x^{10} - 11 x^{9} + 73 x^{8} - 77 x^{7} + 243 x^{6} - 236 x^{5} + 572 x^{4} + \cdots + 4 $ x^12 - x^11 + 10x^10 - 11x^9 + 73x^8 - 77x^7 + 243x^6 - 236x^5 + 572x^4 - 454x^3 + 493x^2 - 46x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			137.1
Root			$1.18253 - 2.04820i$ of defining polynomial
Character	$\chi$	$=$	952.137
Dual form			952.2.q.c.681.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18253 + 2.04820i) q^{3} +(0.949958 + 1.64538i) q^{5} +(-1.39834 + 2.24603i) q^{7} +(-1.29675 - 2.24603i) q^{9} +(-1.88435 + 3.26379i) q^{11} -0.189847 q^{13} -4.49341 q^{15} +(0.500000 - 0.866025i) q^{17} +(0.440306 + 0.762633i) q^{19} +(-2.94675 - 5.52007i) q^{21} +(1.98519 + 3.43845i) q^{23} +(0.695159 - 1.20405i) q^{25} -0.961410 q^{27} -6.30040 q^{29} +(2.94008 - 5.09238i) q^{31} +(-4.45660 - 7.71906i) q^{33} +(-5.02393 - 0.167151i) q^{35} +(5.44675 + 9.43405i) q^{37} +(0.224499 - 0.388844i) q^{39} +3.28277 q^{41} -0.477269 q^{43} +(2.46371 - 4.26727i) q^{45} +(-1.22232 - 2.11712i) q^{47} +(-3.08932 - 6.28141i) q^{49} +(1.18253 + 2.04820i) q^{51} +(3.58189 - 6.20402i) q^{53} -7.16022 q^{55} -2.08270 q^{57} +(2.26640 - 3.92552i) q^{59} +(-5.66136 - 9.80576i) q^{61} +(6.85795 + 0.228170i) q^{63} +(-0.180347 - 0.312370i) q^{65} +(-4.38157 + 7.58911i) q^{67} -9.39016 q^{69} -6.72185 q^{71} +(-0.347772 + 0.602358i) q^{73} +(1.64409 + 2.84765i) q^{75} +(-4.69563 - 8.79619i) q^{77} +(1.99036 + 3.44740i) q^{79} +(5.02714 - 8.70725i) q^{81} -7.77110 q^{83} +1.89992 q^{85} +(7.45040 - 12.9045i) q^{87} +(-0.118503 - 0.205254i) q^{89} +(0.265470 - 0.426402i) q^{91} +(6.95347 + 12.0438i) q^{93} +(-0.836545 + 1.44894i) q^{95} -6.81746 q^{97} +9.77411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} - q^{5} + 3 q^{7} - q^{9} + 6 q^{11} - 4 q^{13} + 6 q^{17} - 2 q^{19} + 14 q^{21} + 5 q^{23} - q^{25} - 16 q^{27} - 30 q^{29} - 8 q^{31} - 11 q^{33} + 7 q^{35} + 16 q^{37} + 2 q^{39} + 8 q^{41}+ \cdots + 4 q^{99}+O(q^{100}) $ 12 * q - q^3 - q^5 + 3 * q^7 - q^9 + 6 * q^11 - 4 * q^13 + 6 * q^17 - 2 * q^19 + 14 * q^21 + 5 * q^23 - q^25 - 16 * q^27 - 30 * q^29 - 8 * q^31 - 11 * q^33 + 7 * q^35 + 16 * q^37 + 2 * q^39 + 8 * q^41 + 48 * q^43 - 2 * q^45 + q^47 + 3 * q^49 + q^51 + 32 * q^53 - 50 * q^55 - 38 * q^57 + 6 * q^59 - 10 * q^61 + 45 * q^63 + 26 * q^65 - 27 * q^67 - 44 * q^69 - 24 * q^71 - 15 * q^73 - 24 * q^75 - 3 * q^77 + 21 * q^79 + 30 * q^81 - 40 * q^83 - 2 * q^85 + 9 * q^87 + 33 * q^89 + 25 * q^91 + 29 * q^93 + 15 * q^95 - 18 * q^97 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.18253	+	2.04820i	−0.682733	+	1.18253i	0.291410	+	0.956598i	$0.405875\pi$
$3$	−1.18253	+	2.04820i	−0.682733	+	1.18253i	−0.974143	+	0.225930i	$0.927458\pi$
$4$		0			0
$5$	0.949958	+	1.64538i	0.424834	+	0.735834i	0.996405	−	0.0847183i	$-0.0269990\pi$
$5$	0.949958	+	1.64538i	0.424834	+	0.735834i	−0.571571	+	0.820553i	$0.693666\pi$
$6$		0			0
$7$	−1.39834	+	2.24603i	−0.528521	+	0.848920i
$7$	−1.39834	+	2.24603i	−0.528521	+	0.848920i
$8$		0			0
$9$	−1.29675	−	2.24603i	−0.432249	−	0.748677i
$10$		0			0
$11$	−1.88435	+	3.26379i	−0.568154	+	0.984071i	0.428595	+	0.903497i	$0.359009\pi$
$11$	−1.88435	+	3.26379i	−0.568154	+	0.984071i	−0.996749	+	0.0805741i	$0.974325\pi$
$12$		0			0
$13$	−0.189847			−0.0526541			−0.0263270	−	0.999653i	$-0.508381\pi$
$13$	−0.189847			−0.0526541			−0.0263270	+	0.999653i	$0.508381\pi$
$14$		0			0
$15$	−4.49341			−1.16019
$16$		0			0
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$		0			0
$19$	0.440306	+	0.762633i	0.101013	+	0.174960i	0.912102	−	0.409963i	$-0.134458\pi$
$19$	0.440306	+	0.762633i	0.101013	+	0.174960i	−0.811089	+	0.584923i	$0.801125\pi$
$20$		0			0
$21$	−2.94675	−	5.52007i	−0.643033	−	1.20458i
$22$		0			0
$23$	1.98519	+	3.43845i	0.413940	+	0.716966i	0.995317	−	0.0966692i	$-0.0308189\pi$
$23$	1.98519	+	3.43845i	0.413940	+	0.716966i	−0.581376	+	0.813635i	$0.697486\pi$
$24$		0			0
$25$	0.695159	−	1.20405i	0.139032	−	0.240810i
$26$		0			0
$27$	−0.961410			−0.185023
$28$		0			0
$29$	−6.30040			−1.16996			−0.584978	−	0.811049i	$-0.698897\pi$
$29$	−6.30040			−1.16996			−0.584978	+	0.811049i	$0.698897\pi$
$30$		0			0
$31$	2.94008	−	5.09238i	0.528055	−	0.914618i	−0.471410	−	0.881914i	$-0.656255\pi$
$31$	2.94008	−	5.09238i	0.528055	−	0.914618i	0.999465	−	0.0327037i	$-0.0104118\pi$
$32$		0			0
$33$	−4.45660	−	7.71906i	−0.775794	−	1.34372i
$34$		0			0
$35$	−5.02393	−	0.167151i	−0.849199	−	0.0282537i
$36$		0			0
$37$	5.44675	+	9.43405i	0.895440	+	1.55095i	0.833259	+	0.552883i	$0.186472\pi$
$37$	5.44675	+	9.43405i	0.895440	+	1.55095i	0.0621811	+	0.998065i	$0.480194\pi$
$38$		0			0
$39$	0.224499	−	0.388844i	0.0359487	−	0.0622649i
$40$		0			0
$41$	3.28277			0.512683			0.256341	−	0.966586i	$-0.417483\pi$
$41$	3.28277			0.512683			0.256341	+	0.966586i	$0.417483\pi$
$42$		0			0
$43$	−0.477269			−0.0727828			−0.0363914	−	0.999338i	$-0.511586\pi$
$43$	−0.477269			−0.0727828			−0.0363914	+	0.999338i	$0.511586\pi$
$44$		0			0
$45$	2.46371	−	4.26727i	0.367268	−	0.636127i
$46$		0			0
$47$	−1.22232	−	2.11712i	−0.178293	−	0.308813i	0.763003	−	0.646395i	$-0.223724\pi$
$47$	−1.22232	−	2.11712i	−0.178293	−	0.308813i	−0.941296	+	0.337582i	$0.890391\pi$
$48$		0			0
$49$	−3.08932	−	6.28141i	−0.441331	−	0.897344i
$50$		0			0
$51$	1.18253	+	2.04820i	0.165587	+	0.286805i
$52$		0			0
$53$	3.58189	−	6.20402i	0.492011	−	0.852187i	−0.507947	−	0.861388i	$-0.669595\pi$
$53$	3.58189	−	6.20402i	0.492011	−	0.852187i	0.999958	+	0.00920100i	$0.00292881\pi$
$54$		0			0
$55$	−7.16022			−0.965484
$56$		0			0
$57$	−2.08270			−0.275860
$58$		0			0
$59$	2.26640	−	3.92552i	0.295061	−	0.511060i	−0.679938	−	0.733269i	$-0.737994\pi$
$59$	2.26640	−	3.92552i	0.295061	−	0.511060i	0.974999	+	0.222209i	$0.0713269\pi$
$60$		0			0
$61$	−5.66136	−	9.80576i	−0.724863	−	1.25550i	−0.959031	−	0.283303i	$-0.908570\pi$
$61$	−5.66136	−	9.80576i	−0.724863	−	1.25550i	0.234168	−	0.972196i	$-0.424763\pi$
$62$		0			0
$63$	6.85795	+	0.228170i	0.864020	+	0.0287468i
$64$		0			0
$65$	−0.180347	−	0.312370i	−0.0223692	−	0.0387447i
$66$		0			0
$67$	−4.38157	+	7.58911i	−0.535294	+	0.927157i	0.463855	+	0.885911i	$0.346466\pi$
$67$	−4.38157	+	7.58911i	−0.535294	+	0.927157i	−0.999149	+	0.0412455i	$0.986867\pi$
$68$		0			0
$69$	−9.39016			−1.13044
$70$		0			0
$71$	−6.72185			−0.797737			−0.398868	−	0.917008i	$-0.630597\pi$
$71$	−6.72185			−0.797737			−0.398868	+	0.917008i	$0.630597\pi$
$72$		0			0
$73$	−0.347772	+	0.602358i	−0.0407036	+	0.0705007i	−0.885659	−	0.464335i	$-0.846293\pi$
$73$	−0.347772	+	0.602358i	−0.0407036	+	0.0705007i	0.844956	+	0.534836i	$0.179627\pi$
$74$		0			0
$75$	1.64409	+	2.84765i	0.189843	+	0.328818i
$76$		0			0
$77$	−4.69563	−	8.79619i	−0.535116	−	1.00242i
$78$		0			0
$79$	1.99036	+	3.44740i	0.223933	+	0.387863i	0.955999	−	0.293371i	$-0.0947771\pi$
$79$	1.99036	+	3.44740i	0.223933	+	0.387863i	−0.732066	+	0.681234i	$0.761444\pi$
$80$		0			0
$81$	5.02714	−	8.70725i	0.558571	−	0.967473i
$82$		0			0
$83$	−7.77110			−0.852989			−0.426495	−	0.904490i	$-0.640252\pi$
$83$	−7.77110			−0.852989			−0.426495	+	0.904490i	$0.640252\pi$
$84$		0			0
$85$	1.89992			0.206075
$86$		0			0
$87$	7.45040	−	12.9045i	0.798767	−	1.38351i
$88$		0			0
$89$	−0.118503	−	0.205254i	−0.0125613	−	0.0217569i	0.859676	−	0.510839i	$-0.170665\pi$
$89$	−0.118503	−	0.205254i	−0.0125613	−	0.0217569i	−0.872238	+	0.489082i	$0.837332\pi$
$90$		0			0
$91$	0.265470	−	0.426402i	0.0278288	−	0.0446991i
$92$		0			0
$93$	6.95347	+	12.0438i	0.721041	+	1.24888i
$94$		0			0
$95$	−0.836545	+	1.44894i	−0.0858277	+	0.148658i
$96$		0			0
$97$	−6.81746			−0.692208			−0.346104	−	0.938196i	$-0.612496\pi$
$97$	−6.81746			−0.692208			−0.346104	+	0.938196i	$0.612496\pi$
$98$		0			0
$99$	9.77411			0.982335
$100$		0			0
$101$	−8.47566	+	14.6803i	−0.843360	+	1.46074i	0.0436777	+	0.999046i	$0.486093\pi$
$101$	−8.47566	+	14.6803i	−0.843360	+	1.46074i	−0.887038	+	0.461697i	$0.847241\pi$
$102$		0			0
$103$	−1.23513	−	2.13930i	−0.121701	−	0.210791i	0.798738	−	0.601679i	$-0.205501\pi$
$103$	−1.23513	−	2.13930i	−0.121701	−	0.210791i	−0.920438	+	0.390888i	$0.872168\pi$
$104$		0			0
$105$	6.28329	−	10.0923i	0.613187	−	0.984912i
$106$		0			0
$107$	1.24395	+	2.15458i	0.120257	+	0.208291i	0.919869	−	0.392226i	$-0.128295\pi$
$107$	1.24395	+	2.15458i	0.120257	+	0.208291i	−0.799612	+	0.600517i	$0.794961\pi$
$108$		0			0
$109$	−3.90597	+	6.76534i	−0.374124	+	0.648002i	−0.990195	−	0.139689i	$-0.955390\pi$
$109$	−3.90597	+	6.76534i	−0.374124	+	0.648002i	0.616072	+	0.787690i	$0.288723\pi$
$110$		0			0
$111$	−25.7637			−2.44539
$112$		0			0
$113$	7.15811			0.673378			0.336689	−	0.941616i	$-0.390693\pi$
$113$	7.15811			0.673378			0.336689	+	0.941616i	$0.390693\pi$
$114$		0			0
$115$	−3.77169	+	6.53276i	−0.351712	+	0.609183i
$116$		0			0
$117$	0.246183	+	0.426402i	0.0227597	+	0.0394209i
$118$		0			0
$119$	1.24595	+	2.33401i	0.114216	+	0.213958i
$120$		0			0
$121$	−1.60156	−	2.77399i	−0.145597	−	0.252181i
$122$		0			0
$123$	−3.88197	+	6.72377i	−0.350026	+	0.606262i
$124$		0			0
$125$	12.1411			1.08593
$126$		0			0
$127$	5.32958			0.472924			0.236462	−	0.971641i	$-0.424012\pi$
$127$	5.32958			0.472924			0.236462	+	0.971641i	$0.424012\pi$
$128$		0			0
$129$	0.564384	−	0.977542i	0.0496912	−	0.0860677i
$130$		0			0
$131$	2.98396	+	5.16836i	0.260710	+	0.451562i	0.966431	−	0.256928i	$-0.0827102\pi$
$131$	2.98396	+	5.16836i	0.260710	+	0.451562i	−0.705721	+	0.708490i	$0.749377\pi$
$132$		0			0
$133$	−2.32859	−	0.0774745i	−0.201915	−	0.00671790i
$134$		0			0
$135$	−0.913299	−	1.58188i	−0.0786043	−	0.136147i
$136$		0			0
$137$	−8.50919	+	14.7383i	−0.726989	+	1.25918i	0.231161	+	0.972916i	$0.425748\pi$
$137$	−8.50919	+	14.7383i	−0.726989	+	1.25918i	−0.958150	+	0.286267i	$0.907586\pi$
$138$		0			0
$139$	8.57639			0.727440			0.363720	−	0.931508i	$-0.381506\pi$
$139$	8.57639			0.727440			0.363720	+	0.931508i	$0.381506\pi$
$140$		0			0
$141$	5.78170			0.486907
$142$		0			0
$143$	0.357738	−	0.619621i	0.0299156	−	0.0518153i
$144$		0			0
$145$	−5.98512	−	10.3665i	−0.497037	−	0.860893i
$146$		0			0
$147$	16.5188	+	1.10041i	1.36245	+	0.0907603i
$148$		0			0
$149$	10.5106	+	18.2049i	0.861063	+	1.49141i	0.870903	+	0.491454i	$0.163534\pi$
$149$	10.5106	+	18.2049i	0.861063	+	1.49141i	−0.00984000	+	0.999952i	$0.503132\pi$
$150$		0			0
$151$	11.7576	−	20.3647i	0.956817	−	1.65726i	0.226663	−	0.973973i	$-0.427219\pi$
$151$	11.7576	−	20.3647i	0.956817	−	1.65726i	0.730154	−	0.683282i	$-0.239448\pi$
$152$		0			0
$153$	−2.59349			−0.209672
$154$		0			0
$155$	11.1718			0.897343
$156$		0			0
$157$	9.41179	−	16.3017i	0.751143	−	1.30102i	−0.196127	−	0.980579i	$-0.562836\pi$
$157$	9.41179	−	16.3017i	0.751143	−	1.30102i	0.947269	−	0.320439i	$-0.103830\pi$
$158$		0			0
$159$	8.47138	+	14.6729i	0.671824	+	1.16363i
$160$		0			0
$161$	−10.4988	−	0.349306i	−0.827423	−	0.0275292i
$162$		0			0
$163$	8.40911	+	14.5650i	0.658652	+	1.14082i	0.980965	+	0.194186i	$0.0622064\pi$
$163$	8.40911	+	14.5650i	0.658652	+	1.14082i	−0.322313	+	0.946633i	$0.604460\pi$
$164$		0			0
$165$	8.46717	−	14.6656i	0.659168	−	1.14171i
$166$		0			0
$167$	−10.9092			−0.844182			−0.422091	−	0.906554i	$-0.638704\pi$
$167$	−10.9092			−0.844182			−0.422091	+	0.906554i	$0.638704\pi$
$168$		0			0
$169$	−12.9640			−0.997228
$170$		0			0
$171$	1.14193	−	1.97788i	0.0873257	−	0.151253i
$172$		0			0
$173$	5.67082	+	9.82215i	0.431145	+	0.746764i	0.996972	−	0.0777592i	$-0.0247765\pi$
$173$	5.67082	+	9.82215i	0.431145	+	0.746764i	−0.565827	+	0.824524i	$0.691443\pi$
$174$		0			0
$175$	1.73227	+	3.24501i	0.130947	+	0.245300i
$176$		0			0
$177$	5.36017	+	9.28409i	0.402895	+	0.697835i
$178$		0			0
$179$	−4.50993	+	7.81142i	−0.337088	+	0.583853i	−0.983884	−	0.178810i	$-0.942775\pi$
$179$	−4.50993	+	7.81142i	−0.337088	+	0.583853i	0.646796	+	0.762663i	$0.276109\pi$
$180$		0			0
$181$	3.13099			0.232725			0.116363	−	0.993207i	$-0.462877\pi$
$181$	3.13099			0.232725			0.116363	+	0.993207i	$0.462877\pi$
$182$		0			0
$183$	26.7789			1.97955
$184$		0			0
$185$	−10.3484	+	17.9239i	−0.760827	+	1.31779i
$186$		0			0
$187$	1.88435	+	3.26379i	0.137797	+	0.238672i
$188$		0			0
$189$	1.34437	−	2.15936i	0.0977888	−	0.157070i
$190$		0			0
$191$	10.0676	+	17.4376i	0.728466	+	1.26174i	0.957531	+	0.288329i	$0.0930997\pi$
$191$	10.0676	+	17.4376i	0.728466	+	1.26174i	−0.229065	+	0.973411i	$0.573567\pi$
$192$		0			0
$193$	−10.5515	+	18.2758i	−0.759517	+	1.31552i	0.183580	+	0.983005i	$0.441231\pi$
$193$	−10.5515	+	18.2758i	−0.759517	+	1.31552i	−0.943097	+	0.332517i	$0.892102\pi$
$194$		0			0
$195$	0.853060			0.0610889
$196$		0			0
$197$	16.8747			1.20227			0.601136	−	0.799147i	$-0.294715\pi$
$197$	16.8747			1.20227			0.601136	+	0.799147i	$0.294715\pi$
$198$		0			0
$199$	−4.71342	+	8.16388i	−0.334125	+	0.578722i	−0.983316	−	0.181903i	$-0.941774\pi$
$199$	−4.71342	+	8.16388i	−0.334125	+	0.578722i	0.649191	+	0.760625i	$0.275108\pi$
$200$		0			0
$201$	−10.3627	−	17.9487i	−0.730926	−	1.26600i
$202$		0			0
$203$	8.81007	−	14.1509i	0.618346	−	0.993199i
$204$		0			0
$205$	3.11850	+	5.40139i	0.217805	+	0.377250i
$206$		0			0
$207$	5.14857	−	8.91759i	0.357851	−	0.619815i
$208$		0			0
$209$	−3.31877			−0.229564
$210$		0			0
$211$	−0.0770744			−0.00530602			−0.00265301	−	0.999996i	$-0.500844\pi$
$211$	−0.0770744			−0.00530602			−0.00265301	+	0.999996i	$0.500844\pi$
$212$		0			0
$213$	7.94878	−	13.7677i	0.544641	−	0.943346i
$214$		0			0
$215$	−0.453385	−	0.785287i	−0.0309206	−	0.0535561i
$216$		0			0
$217$	7.32641	+	13.7244i	0.497349	+	0.931671i
$218$		0			0
$219$	−0.822500	−	1.42461i	−0.0555794	−	0.0962663i
$220$		0			0
$221$	−0.0949235	+	0.164412i	−0.00638524	+	0.0110596i
$222$		0			0
$223$	10.0086			0.670226			0.335113	−	0.942178i	$-0.391226\pi$
$223$	10.0086			0.670226			0.335113	+	0.942178i	$0.391226\pi$
$224$		0			0
$225$	−3.60578			−0.240385
$226$		0			0
$227$	−5.34431	+	9.25661i	−0.354714	+	0.614383i	−0.987069	−	0.160296i	$-0.948755\pi$
$227$	−5.34431	+	9.25661i	−0.354714	+	0.614383i	0.632355	+	0.774679i	$0.282089\pi$
$228$		0			0
$229$	7.87679	+	13.6430i	0.520513	+	0.901555i	0.999716	+	0.0238504i	$0.00759254\pi$
$229$	7.87679	+	13.6430i	0.520513	+	0.901555i	−0.479203	+	0.877704i	$0.659074\pi$
$230$		0			0
$231$	23.5691	+	0.784166i	1.55073	+	0.0515943i
$232$		0			0
$233$	−9.27108	−	16.0580i	−0.607369	−	1.05199i	−0.991672	−	0.128787i	$-0.958892\pi$
$233$	−9.27108	−	16.0580i	−0.607369	−	1.05199i	0.384304	−	0.923207i	$-0.374442\pi$
$234$		0			0
$235$	2.32230	−	4.02234i	0.151490	−	0.262389i
$236$		0			0
$237$	−9.41461			−0.611545
$238$		0			0
$239$	−13.8718			−0.897295			−0.448647	−	0.893709i	$-0.648094\pi$
$239$	−13.8718			−0.897295			−0.448647	+	0.893709i	$0.648094\pi$
$240$		0			0
$241$	−3.69105	+	6.39309i	−0.237762	+	0.411815i	−0.960072	−	0.279754i	$-0.909747\pi$
$241$	−3.69105	+	6.39309i	−0.237762	+	0.411815i	0.722310	+	0.691569i	$0.243080\pi$
$242$		0			0
$243$	10.4473	+	18.0953i	0.670198	+	1.16082i
$244$		0			0
$245$	7.40056	−	11.0502i	0.472804	−	0.705969i
$246$		0			0
$247$	−0.0835908	−	0.144783i	−0.00531875	−	0.00921235i
$248$		0			0
$249$	9.18955	−	15.9168i	0.582364	−	1.00868i
$250$		0			0
$251$	−25.1206			−1.58560			−0.792799	−	0.609484i	$-0.791377\pi$
$251$	−25.1206			−1.58560			−0.792799	+	0.609484i	$0.791377\pi$
$252$		0			0
$253$	−14.9632			−0.940727
$254$		0			0
$255$	−2.24671	+	3.89141i	−0.140694	+	0.243689i
$256$		0			0
$257$	12.5955	+	21.8160i	0.785684	+	1.36084i	0.928590	+	0.371108i	$0.121022\pi$
$257$	12.5955	+	21.8160i	0.785684	+	1.36084i	−0.142905	+	0.989736i	$0.545644\pi$
$258$		0			0
$259$	−28.8055	−	0.958389i	−1.78989	−	0.0595514i
$260$		0			0
$261$	8.17003	+	14.1509i	0.505712	+	0.875919i
$262$		0			0
$263$	2.63457	−	4.56321i	0.162455	−	0.281380i	−0.773294	−	0.634048i	$-0.781392\pi$
$263$	2.63457	−	4.56321i	0.162455	−	0.281380i	0.935748	+	0.352668i	$0.114726\pi$
$264$		0			0
$265$	13.6106			0.836092
$266$		0			0
$267$	0.560534			0.0343041
$268$		0			0
$269$	−6.90938	+	11.9674i	−0.421272	+	0.729665i	−0.996064	−	0.0886344i	$-0.971750\pi$
$269$	−6.90938	+	11.9674i	−0.421272	+	0.729665i	0.574792	+	0.818300i	$0.305083\pi$
$270$		0			0
$271$	−14.8763	−	25.7665i	−0.903669	−	1.56520i	−0.822694	−	0.568485i	$-0.807530\pi$
$271$	−14.8763	−	25.7665i	−0.903669	−	1.56520i	−0.0809757	−	0.996716i	$-0.525804\pi$
$272$		0			0
$273$	0.559431	+	1.04797i	0.0338583	+	0.0634259i
$274$		0			0
$275$	2.61985	+	4.53771i	0.157983	+	0.273634i
$276$		0			0
$277$	7.26340	−	12.5806i	0.436415	−	0.755893i	−0.560995	−	0.827819i	$-0.689581\pi$
$277$	7.26340	−	12.5806i	0.436415	−	0.755893i	0.997410	+	0.0719261i	$0.0229146\pi$
$278$		0			0
$279$	−15.2502			−0.913005
$280$		0			0
$281$	−17.3065			−1.03242			−0.516209	−	0.856462i	$-0.672657\pi$
$281$	−17.3065			−1.03242			−0.516209	+	0.856462i	$0.672657\pi$
$282$		0			0
$283$	11.5507	−	20.0065i	0.686621	−	1.18926i	−0.286304	−	0.958139i	$-0.592427\pi$
$283$	11.5507	−	20.0065i	0.686621	−	1.18926i	0.972925	−	0.231123i	$-0.0742399\pi$
$284$		0			0
$285$	−1.97848	−	3.42682i	−0.117195	−	0.202987i
$286$		0			0
$287$	−4.59042	+	7.37321i	−0.270964	+	0.435227i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	8.06184	−	13.9635i	0.472594	−	0.818556i
$292$		0			0
$293$	31.4518			1.83743			0.918717	−	0.394917i	$-0.129227\pi$
$293$	31.4518			1.83743			0.918717	+	0.394917i	$0.129227\pi$
$294$		0			0
$295$	8.61195			0.501407
$296$		0			0
$297$	1.81163	−	3.13784i	0.105122	−	0.182076i
$298$		0			0
$299$	−0.376882	−	0.652778i	−0.0217956	−	0.0377511i
$300$		0			0
$301$	0.667382	−	1.07196i	0.0384672	−	0.0617868i
$302$		0			0
$303$	−20.0454	−	34.7197i	−1.15158	−	1.99459i
$304$		0			0
$305$	10.7561	−	18.6301i	0.615893	−	1.06676i
$306$		0			0
$307$	−14.9725			−0.854527			−0.427263	−	0.904127i	$-0.640522\pi$
$307$	−14.9725			−0.854527			−0.427263	+	0.904127i	$0.640522\pi$
$308$		0			0
$309$	5.84228			0.332356
$310$		0			0
$311$	−0.206327	+	0.357368i	−0.0116997	+	0.0202645i	−0.871816	−	0.489834i	$-0.837058\pi$
$311$	−0.206327	+	0.357368i	−0.0116997	+	0.0202645i	0.860116	+	0.510098i	$0.170391\pi$
$312$		0			0
$313$	−2.16464	−	3.74927i	−0.122353	−	0.211921i	0.798342	−	0.602204i	$-0.205711\pi$
$313$	−2.16464	−	3.74927i	−0.122353	−	0.211921i	−0.920695	+	0.390283i	$0.872377\pi$
$314$		0			0
$315$	6.13934	+	11.5007i	0.345912	+	0.647988i
$316$		0			0
$317$	14.9896	+	25.9627i	0.841898	+	1.45821i	0.888288	+	0.459286i	$0.151895\pi$
$317$	14.9896	+	25.9627i	0.841898	+	1.45821i	−0.0463903	+	0.998923i	$0.514772\pi$
$318$		0			0
$319$	11.8722	−	20.5632i	0.664714	−	1.15132i
$320$		0			0
$321$	−5.88402			−0.328414
$322$		0			0
$323$	0.880612			0.0489986
$324$		0			0
$325$	−0.131974	+	0.228585i	−0.00732059	+	0.0126796i
$326$		0			0
$327$	−9.23784	−	16.0004i	−0.510854	−	0.884824i
$328$		0			0
$329$	6.46432	+	0.215074i	0.356389	+	0.0118574i
$330$		0			0
$331$	−11.8703	−	20.5599i	−0.652450	−	1.13008i	−0.982527	−	0.186122i	$-0.940408\pi$
$331$	−11.8703	−	20.5599i	−0.652450	−	1.13008i	0.330077	−	0.943954i	$-0.392925\pi$
$332$		0			0
$333$	14.1261	−	24.4671i	0.774106	−	1.34079i
$334$		0			0
$335$	−16.6492			−0.909645
$336$		0			0
$337$	−11.1783			−0.608921			−0.304460	−	0.952525i	$-0.598476\pi$
$337$	−11.1783			−0.608921			−0.304460	+	0.952525i	$0.598476\pi$
$338$		0			0
$339$	−8.46467	+	14.6612i	−0.459738	+	0.796289i
$340$		0			0
$341$	11.0803	+	19.1917i	0.600032	+	1.03929i
$342$		0			0
$343$	18.4281	+	1.84481i	0.995026	+	0.0996106i
$344$		0			0
$345$	−8.92026	−	15.4504i	−0.480251	−	0.831819i
$346$		0			0
$347$	6.15697	−	10.6642i	0.330523	−	0.572483i	−0.652091	−	0.758141i	$-0.726108\pi$
$347$	6.15697	−	10.6642i	0.330523	−	0.572483i	0.982615	+	0.185657i	$0.0594414\pi$
$348$		0			0
$349$	−20.2052			−1.08156			−0.540780	−	0.841164i	$-0.681871\pi$
$349$	−20.2052			−1.08156			−0.540780	+	0.841164i	$0.681871\pi$
$350$		0			0
$351$	0.182521			0.00974223
$352$		0			0
$353$	−0.128024	+	0.221744i	−0.00681402	+	0.0118022i	−0.869412	−	0.494087i	$-0.835502\pi$
$353$	−0.128024	+	0.221744i	−0.00681402	+	0.0118022i	0.862598	+	0.505890i	$0.168836\pi$
$354$		0			0
$355$	−6.38547	−	11.0600i	−0.338906	−	0.587002i
$356$		0			0
$357$	−6.25389	−	0.208073i	−0.330991	−	0.0110124i
$358$		0			0
$359$	7.69254	+	13.3239i	0.405997	+	0.703207i	0.994437	−	0.105334i	$-0.0335911\pi$
$359$	7.69254	+	13.3239i	0.405997	+	0.703207i	−0.588440	+	0.808541i	$0.700258\pi$
$360$		0			0
$361$	9.11226	−	15.7829i	0.479593	−	0.830679i
$362$		0			0
$363$	7.57558			0.397615
$364$		0			0
$365$	−1.32147			−0.0691691
$366$		0			0
$367$	1.21673	−	2.10743i	0.0635125	−	0.110007i	−0.832521	−	0.553994i	$-0.813103\pi$
$367$	1.21673	−	2.10743i	0.0635125	−	0.110007i	0.896033	+	0.443987i	$0.146436\pi$
$368$		0			0
$369$	−4.25693	−	7.37321i	−0.221607	−	0.383834i
$370$		0			0
$371$	8.92573	+	16.7203i	0.463401	+	0.868077i
$372$		0			0
$373$	10.1959	+	17.6599i	0.527926	+	0.914394i	0.999470	+	0.0325520i	$0.0103635\pi$
$373$	10.1959	+	17.6599i	0.527926	+	0.914394i	−0.471544	+	0.881842i	$0.656303\pi$
$374$		0			0
$375$	−14.3572	+	24.8673i	−0.741401	+	1.28414i
$376$		0			0
$377$	1.19611			0.0616029
$378$		0			0
$379$	−27.1309			−1.39362			−0.696810	−	0.717256i	$-0.745398\pi$
$379$	−27.1309			−1.39362			−0.696810	+	0.717256i	$0.745398\pi$
$380$		0			0
$381$	−6.30238	+	10.9160i	−0.322881	+	0.559246i
$382$		0			0
$383$	9.33746	+	16.1730i	0.477122	+	0.826399i	0.999656	−	0.0262189i	$-0.00834669\pi$
$383$	9.33746	+	16.1730i	0.477122	+	0.826399i	−0.522534	+	0.852618i	$0.675013\pi$
$384$		0			0
$385$	10.0124	−	16.0821i	0.510279	−	0.819619i
$386$		0			0
$387$	0.618897	+	1.07196i	0.0314603	+	0.0544908i
$388$		0			0
$389$	−1.57823	+	2.73358i	−0.0800195	+	0.138598i	−0.903258	−	0.429098i	$-0.858832\pi$
$389$	−1.57823	+	2.73358i	−0.0800195	+	0.138598i	0.823239	+	0.567696i	$0.192165\pi$
$390$		0			0
$391$	3.97038			0.200791
$392$		0			0
$393$	−14.1145			−0.711980
$394$		0			0
$395$	−3.78151	+	6.54977i	−0.190269	+	0.329555i
$396$		0			0
$397$	−14.3305	−	24.8211i	−0.719226	−	1.24574i	−0.961307	−	0.275480i	$-0.911163\pi$
$397$	−14.3305	−	24.8211i	−0.719226	−	1.24574i	0.242081	−	0.970256i	$-0.422170\pi$
$398$		0			0
$399$	2.91231	−	4.67781i	0.145798	−	0.234183i
$400$		0			0
$401$	6.18351	+	10.7102i	0.308790	+	0.534839i	0.978098	−	0.208145i	$-0.0667427\pi$
$401$	6.18351	+	10.7102i	0.308790	+	0.534839i	−0.669308	+	0.742985i	$0.733409\pi$
$402$		0			0
$403$	−0.558166	+	0.966772i	−0.0278042	+	0.0481583i
$404$		0			0
$405$	19.1023			0.949200
$406$		0			0
$407$	−41.0544			−2.03499
$408$		0			0
$409$	−13.8103	+	23.9202i	−0.682878	+	1.18278i	0.291221	+	0.956656i	$0.405938\pi$
$409$	−13.8103	+	23.9202i	−0.682878	+	1.18278i	−0.974099	+	0.226123i	$0.927395\pi$
$410$		0			0
$411$	−20.1247	−	34.8570i	−0.992679	−	1.71937i
$412$		0			0
$413$	5.64766	+	10.5796i	0.277903	+	0.520589i
$414$		0			0
$415$	−7.38222	−	12.7864i	−0.362379	−	0.627659i
$416$		0			0
$417$	−10.1418	+	17.5662i	−0.496648	+	0.860219i
$418$		0			0
$419$	−21.1268			−1.03211			−0.516055	−	0.856555i	$-0.672600\pi$
$419$	−21.1268			−1.03211			−0.516055	+	0.856555i	$0.672600\pi$
$420$		0			0
$421$	−4.03124			−0.196471			−0.0982353	−	0.995163i	$-0.531320\pi$
$421$	−4.03124			−0.196471			−0.0982353	+	0.995163i	$0.531320\pi$
$422$		0			0
$423$	−3.17007	+	5.49073i	−0.154134	+	0.266968i
$424$		0			0
$425$	−0.695159	−	1.20405i	−0.0337202	−	0.0584050i
$426$		0			0
$427$	29.9405	+	0.996150i	1.44892	+	0.0482071i
$428$		0			0
$429$	0.846072	+	1.46544i	0.0408487	+	0.0707521i
$430$		0			0
$431$	−5.58148	+	9.66740i	−0.268850	+	0.465662i	−0.968565	−	0.248760i	$-0.919977\pi$
$431$	−5.58148	+	9.66740i	−0.268850	+	0.465662i	0.699715	+	0.714422i	$0.253310\pi$
$432$		0			0
$433$	30.3717			1.45957			0.729785	−	0.683676i	$-0.239620\pi$
$433$	30.3717			1.45957			0.729785	+	0.683676i	$0.239620\pi$
$434$		0			0
$435$	28.3103			1.35737
$436$		0			0
$437$	−1.74818	+	3.02794i	−0.0836268	+	0.144846i
$438$		0			0
$439$	−8.73879	−	15.1360i	−0.417080	−	0.722404i	0.578564	−	0.815637i	$-0.303613\pi$
$439$	−8.73879	−	15.1360i	−0.417080	−	0.722404i	−0.995644	+	0.0932331i	$0.970280\pi$
$440$		0			0
$441$	−10.1022	+	15.0841i	−0.481056	+	0.718291i
$442$		0			0
$443$	4.52098	+	7.83057i	0.214798	+	0.372042i	0.953210	−	0.302308i	$-0.0977572\pi$
$443$	4.52098	+	7.83057i	0.214798	+	0.372042i	−0.738412	+	0.674350i	$0.764424\pi$
$444$		0			0
$445$	0.225146	−	0.389965i	0.0106730	−	0.0184861i
$446$		0			0
$447$	−49.7164			−2.35151
$448$		0			0
$449$	−20.6592			−0.974966			−0.487483	−	0.873132i	$-0.662085\pi$
$449$	−20.6592			−0.974966			−0.487483	+	0.873132i	$0.662085\pi$
$450$		0			0
$451$	−6.18590	+	10.7143i	−0.291283	+	0.504516i
$452$		0			0
$453$	27.8073	+	48.1637i	1.30650	+	2.26293i
$454$		0			0
$455$	0.953777	+	0.0317331i	0.0447138	+	0.00148767i
$456$		0			0
$457$	10.7505	+	18.6203i	0.502885	+	0.871023i	0.999994	+	0.00333478i	$0.00106149\pi$
$457$	10.7505	+	18.6203i	0.502885	+	0.871023i	−0.497109	+	0.867688i	$0.665605\pi$
$458$		0			0
$459$	−0.480705	+	0.832605i	−0.0224374	+	0.0388627i
$460$		0			0
$461$	15.7330			0.732758			0.366379	−	0.930466i	$-0.380597\pi$
$461$	15.7330			0.732758			0.366379	+	0.930466i	$0.380597\pi$
$462$		0			0
$463$	41.7714			1.94128			0.970640	−	0.240537i	$-0.0773236\pi$
$463$	41.7714			1.94128			0.970640	+	0.240537i	$0.0773236\pi$
$464$		0			0
$465$	−13.2110	+	22.8821i	−0.612646	+	1.06113i
$466$		0			0
$467$	−17.9496	−	31.0897i	−0.830611	−	1.43866i	−0.897555	−	0.440903i	$-0.854658\pi$
$467$	−17.9496	−	31.0897i	−0.830611	−	1.43866i	0.0669441	−	0.997757i	$-0.478675\pi$
$468$		0			0
$469$	−10.9185	−	20.4533i	−0.504168	−	0.944444i
$470$		0			0
$471$	22.2594	+	38.5544i	1.02566	+	1.77650i
$472$		0			0
$473$	0.899342	−	1.55771i	0.0413518	−	0.0716234i
$474$		0			0
$475$	1.22433			0.0561762
$476$		0			0
$477$	−18.5792			−0.850684
$478$		0			0
$479$	−3.63726	+	6.29992i	−0.166191	+	0.287851i	−0.937078	−	0.349121i	$-0.886480\pi$
$479$	−3.63726	+	6.29992i	−0.166191	+	0.287851i	0.770887	+	0.636972i	$0.219813\pi$
$480$		0			0
$481$	−1.03405	−	1.79102i	−0.0471486	−	0.0816637i
$482$		0			0
$483$	13.1306	−	21.0906i	0.597463	−	0.959656i
$484$		0			0
$485$	−6.47630	−	11.2173i	−0.294074	−	0.509351i
$486$		0			0
$487$	5.86298	−	10.1550i	0.265677	−	0.460166i	−0.702064	−	0.712114i	$-0.747738\pi$
$487$	5.86298	−	10.1550i	0.265677	−	0.460166i	0.967741	+	0.251948i	$0.0810713\pi$
$488$		0			0
$489$	−39.7760			−1.79873
$490$		0			0
$491$	0.539527			0.0243485			0.0121742	−	0.999926i	$-0.496125\pi$
$491$	0.539527			0.0243485			0.0121742	+	0.999926i	$0.496125\pi$
$492$		0			0
$493$	−3.15020	+	5.45631i	−0.141878	+	0.245740i
$494$		0			0
$495$	9.28500	+	16.0821i	0.417330	+	0.722836i
$496$		0			0
$497$	9.39940	−	15.0975i	0.421621	−	0.677215i
$498$		0			0
$499$	−9.85972	−	17.0775i	−0.441382	−	0.764495i	0.556411	−	0.830907i	$-0.312178\pi$
$499$	−9.85972	−	17.0775i	−0.441382	−	0.764495i	−0.997792	+	0.0664120i	$0.978845\pi$
$500$		0			0
$501$	12.9005	−	22.3443i	0.576351	−	0.998269i
$502$		0			0
$503$	23.4213			1.04430			0.522152	−	0.852852i	$-0.325129\pi$
$503$	23.4213			1.04430			0.522152	+	0.852852i	$0.325129\pi$
$504$		0			0
$505$	−32.2061			−1.43315
$506$		0			0
$507$	15.3302	−	26.5528i	0.680840	−	1.17925i
$508$		0			0
$509$	10.2938	+	17.8294i	0.456266	+	0.790275i	0.998760	−	0.0497841i	$-0.0158533\pi$
$509$	10.2938	+	17.8294i	0.456266	+	0.790275i	−0.542494	+	0.840059i	$0.682520\pi$
$510$		0			0
$511$	−0.866614	−	1.62341i	−0.0383368	−	0.0718152i
$512$		0			0
$513$	−0.423315	−	0.733203i	−0.0186898	−	0.0323717i
$514$		0			0
$515$	2.34664	−	4.06449i	0.103405	−	0.179103i
$516$		0			0
$517$	9.21311			0.405192
$518$		0			0
$519$	−26.8236			−1.17743
$520$		0			0
$521$	−0.704286	+	1.21986i	−0.0308553	+	0.0534430i	−0.881041	−	0.473040i	$-0.843156\pi$
$521$	−0.704286	+	1.21986i	−0.0308553	+	0.0534430i	0.850185	+	0.526483i	$0.176490\pi$
$522$		0			0
$523$	−12.9386	−	22.4103i	−0.565766	−	0.979935i	−0.996978	−	0.0776844i	$-0.975247\pi$
$523$	−12.9386	−	22.4103i	−0.565766	−	0.979935i	0.431212	−	0.902250i	$-0.358086\pi$
$524$		0			0
$525$	−8.69490	−	0.289288i	−0.379476	−	0.0126255i
$526$		0			0
$527$	−2.94008	−	5.09238i	−0.128072	−	0.221827i
$528$		0			0
$529$	3.61806	−	6.26666i	0.157307	−	0.272463i
$530$		0			0
$531$	−11.7558			−0.510158
$532$		0			0
$533$	−0.623224			−0.0269948
$534$		0			0
$535$	−2.36340	+	4.09353i	−0.102179	+	0.176979i
$536$		0			0
$537$	−10.6662	−	18.4745i	−0.460282	−	0.797231i
$538$		0			0
$539$	26.3226	+	1.75350i	1.13379	+	0.0755285i
$540$		0			0
$541$	−13.5298	−	23.4343i	−0.581691	−	1.00752i	−0.995279	−	0.0970546i	$-0.969058\pi$
$541$	−13.5298	−	23.4343i	−0.581691	−	1.00752i	0.413588	−	0.910464i	$-0.364275\pi$
$542$		0			0
$543$	−3.70249	+	6.41290i	−0.158889	+	0.275204i
$544$		0			0
$545$	−14.8420			−0.635763
$546$		0			0
$547$	0.235008			0.0100482			0.00502410	−	0.999987i	$-0.498401\pi$
$547$	0.235008			0.0100482			0.00502410	+	0.999987i	$0.498401\pi$
$548$		0			0
$549$	−14.6827	+	25.4312i	−0.626642	+	1.08538i
$550$		0			0
$551$	−2.77411	−	4.80489i	−0.118181	−	0.204695i
$552$		0			0
$553$	−10.5262	−	0.350215i	−0.447618	−	0.0148927i
$554$		0			0
$555$	−24.4745	−	42.3910i	−1.03888	−	1.79940i
$556$		0			0
$557$	−14.1983	+	24.5921i	−0.601600	+	1.04200i	0.390978	+	0.920400i	$0.372137\pi$
$557$	−14.1983	+	24.5921i	−0.601600	+	1.04200i	−0.992579	+	0.121603i	$0.961197\pi$
$558$		0			0
$559$	0.0906080			0.00383231
$560$		0			0
$561$	−8.91320			−0.376316
$562$		0			0
$563$	−6.66425	+	11.5428i	−0.280865	+	0.486472i	−0.971598	−	0.236638i	$-0.923955\pi$
$563$	−6.66425	+	11.5428i	−0.280865	+	0.486472i	0.690733	+	0.723110i	$0.257288\pi$
$564$		0			0
$565$	6.79991	+	11.7778i	0.286074	+	0.495495i
$566$		0			0
$567$	12.5271	+	23.4668i	0.526091	+	0.985512i
$568$		0			0
$569$	−22.4200	−	38.8326i	−0.939896	−	1.62795i	−0.765662	−	0.643243i	$-0.777589\pi$
$569$	−22.4200	−	38.8326i	−0.939896	−	1.62795i	−0.174234	−	0.984704i	$-0.555745\pi$
$570$		0			0
$571$	−8.95179	+	15.5050i	−0.374621	+	0.648862i	−0.990270	−	0.139158i	$-0.955560\pi$
$571$	−8.95179	+	15.5050i	−0.374621	+	0.648862i	0.615649	+	0.788020i	$0.288894\pi$
$572$		0			0
$573$	−47.6209			−1.98939
$574$		0			0
$575$	5.52008			0.230203
$576$		0			0
$577$	−12.4993	+	21.6495i	−0.520353	+	0.901278i	0.479367	+	0.877615i	$0.340866\pi$
$577$	−12.4993	+	21.6495i	−0.520353	+	0.901278i	−0.999720	+	0.0236637i	$0.992467\pi$
$578$		0			0
$579$	−24.9550	−	43.2233i	−1.03709	−	1.79630i
$580$		0			0
$581$	10.8666	−	17.4541i	0.450823	−	0.724120i
$582$		0			0
$583$	13.4991	+	23.3811i	0.559075	+	0.968346i
$584$		0			0
$585$	−0.467728	+	0.810129i	−0.0193382	+	0.0334947i
$586$		0			0
$587$	40.3825			1.66676			0.833382	−	0.552697i	$-0.186401\pi$
$587$	40.3825			1.66676			0.833382	+	0.552697i	$0.186401\pi$
$588$		0			0
$589$	5.17815			0.213362
$590$		0			0
$591$	−19.9548	+	34.5627i	−0.820831	+	1.42172i
$592$		0			0
$593$	2.61105	+	4.52246i	0.107223	+	0.185715i	0.914644	−	0.404260i	$-0.132471\pi$
$593$	2.61105	+	4.52246i	0.107223	+	0.185715i	−0.807421	+	0.589975i	$0.799138\pi$
$594$		0			0
$595$	−2.65672	+	4.26727i	−0.108915	+	0.174941i
$596$		0			0
$597$	−11.1475	−	19.3080i	−0.456237	−	0.790225i
$598$		0			0
$599$	−0.548947	+	0.950804i	−0.0224294	+	0.0388488i	−0.877022	−	0.480450i	$-0.840473\pi$
$599$	−0.548947	+	0.950804i	−0.0224294	+	0.0388488i	0.854593	+	0.519299i	$0.173807\pi$
$600$		0			0
$601$	16.3752			0.667958			0.333979	−	0.942581i	$-0.391609\pi$
$601$	16.3752			0.667958			0.333979	+	0.942581i	$0.391609\pi$
$602$		0			0
$603$	22.7272			0.925522
$604$		0			0
$605$	3.04284	−	5.27035i	0.123709	−	0.214270i
$606$		0			0
$607$	−21.0993	−	36.5451i	−0.856396	−	1.48332i	−0.875344	−	0.483501i	$-0.839365\pi$
$607$	−21.0993	−	36.5451i	−0.856396	−	1.48332i	0.0189477	−	0.999820i	$-0.493968\pi$
$608$		0			0
$609$	18.5657	+	34.7786i	0.752320	+	1.40930i
$610$		0			0
$611$	0.232053	+	0.401928i	0.00938787	+	0.0162603i
$612$		0			0
$613$	−15.4561	+	26.7707i	−0.624265	+	1.08126i	0.364417	+	0.931236i	$0.381268\pi$
$613$	−15.4561	+	26.7707i	−0.624265	+	1.08126i	−0.988683	+	0.150023i	$0.952065\pi$
$614$		0			0
$615$	−14.7508			−0.594811
$616$		0			0
$617$	−11.2653			−0.453526			−0.226763	−	0.973950i	$-0.572814\pi$
$617$	−11.2653			−0.453526			−0.226763	+	0.973950i	$0.572814\pi$
$618$		0			0
$619$	15.5012	−	26.8489i	0.623047	−	1.07915i	−0.365868	−	0.930667i	$-0.619228\pi$
$619$	15.5012	−	26.8489i	0.623047	−	1.07915i	0.988915	−	0.148483i	$-0.0474390\pi$
$620$		0			0
$621$	−1.90858	−	3.30576i	−0.0765886	−	0.132655i
$622$		0			0
$623$	0.626714	+	0.0208514i	0.0251088	+	0.000835393i
$624$		0			0
$625$	8.05772	+	13.9564i	0.322309	+	0.558255i
$626$		0			0
$627$	3.92454	−	6.79750i	0.156731	−	0.271466i
$628$		0			0
$629$	10.8935			0.434352
$630$		0			0
$631$	25.0599			0.997621			0.498810	−	0.866711i	$-0.333770\pi$
$631$	25.0599			0.997621			0.498810	+	0.866711i	$0.333770\pi$
$632$		0			0
$633$	0.0911427	−	0.157864i	0.00362260	−	0.00627452i
$634$		0			0
$635$	5.06288	+	8.76917i	0.200914	+	0.347994i
$636$		0			0
$637$	0.586497	+	1.19251i	0.0232379	+	0.0472488i
$638$		0			0
$639$	8.71654	+	15.0975i	0.344821	+	0.597247i
$640$		0			0
$641$	16.6285	−	28.8014i	0.656787	−	1.13759i	−0.324656	−	0.945832i	$-0.605249\pi$
$641$	16.6285	−	28.8014i	0.656787	−	1.13759i	0.981443	−	0.191756i	$-0.0614181\pi$
$642$		0			0
$643$	21.0140			0.828710			0.414355	−	0.910115i	$-0.364007\pi$
$643$	21.0140			0.828710			0.414355	+	0.910115i	$0.364007\pi$
$644$		0			0
$645$	2.14456			0.0844421
$646$		0			0
$647$	10.6395	−	18.4282i	0.418284	−	0.724489i	−0.577483	−	0.816403i	$-0.695965\pi$
$647$	10.6395	−	18.4282i	0.418284	−	0.724489i	0.995767	+	0.0919139i	$0.0292985\pi$
$648$		0			0
$649$	8.54140	+	14.7941i	0.335279	+	0.580721i
$650$		0			0
$651$	−36.7739	−	1.22350i	−1.44128	−	0.0479529i
$652$		0			0
$653$	−0.809444	−	1.40200i	−0.0316760	−	0.0548644i	0.849753	−	0.527181i	$-0.176751\pi$
$653$	−0.809444	−	1.40200i	−0.0316760	−	0.0548644i	−0.881429	+	0.472317i	$0.843418\pi$
$654$		0			0
$655$	−5.66927	+	9.81946i	−0.221517	+	0.383678i
$656$		0			0
$657$	1.80389			0.0703764
$658$		0			0
$659$	9.90958			0.386022			0.193011	−	0.981197i	$-0.438175\pi$
$659$	9.90958			0.386022			0.193011	+	0.981197i	$0.438175\pi$
$660$		0			0
$661$	6.08842	−	10.5455i	0.236812	−	0.410171i	−0.722986	−	0.690863i	$-0.757231\pi$
$661$	6.08842	−	10.5455i	0.236812	−	0.410171i	0.959798	+	0.280692i	$0.0905641\pi$
$662$		0			0
$663$	−0.224499	−	0.388844i	−0.00871883	−	0.0151015i
$664$		0			0
$665$	−2.08459	−	3.90501i	−0.0808370	−	0.151430i
$666$		0			0
$667$	−12.5075	−	21.6636i	−0.484292	−	0.838818i
$668$		0			0
$669$	−11.8355	+	20.4996i	−0.457585	+	0.792561i
$670$		0			0
$671$	42.6720			1.64733
$672$		0			0
$673$	4.19259			0.161612			0.0808062	−	0.996730i	$-0.474251\pi$
$673$	4.19259			0.161612			0.0808062	+	0.996730i	$0.474251\pi$
$674$		0			0
$675$	−0.668332	+	1.15759i	−0.0257241	+	0.0445555i
$676$		0			0
$677$	8.11027	+	14.0474i	0.311703	+	0.539885i	0.978731	−	0.205147i	$-0.0657673\pi$
$677$	8.11027	+	14.0474i	0.311703	+	0.539885i	−0.667028	+	0.745032i	$0.732434\pi$
$678$		0			0
$679$	9.53310	−	15.3122i	0.365847	−	0.587630i
$680$		0			0
$681$	−12.6396	−	21.8924i	−0.484350	−	0.838919i
$682$		0			0
$683$	−9.09220	+	15.7481i	−0.347903	+	0.602586i	−0.985877	−	0.167472i	$-0.946440\pi$
$683$	−9.09220	+	15.7481i	−0.347903	+	0.602586i	0.637974	+	0.770058i	$0.279773\pi$
$684$		0			0
$685$	−32.3335			−1.23540
$686$		0			0
$687$	−37.2581			−1.42149
$688$		0			0
$689$	−0.680011	+	1.17781i	−0.0259064	+	0.0448711i
$690$		0			0
$691$	−17.2688	−	29.9104i	−0.656936	−	1.13785i	−0.981405	−	0.191950i	$-0.938519\pi$
$691$	−17.2688	−	29.9104i	−0.656936	−	1.13785i	0.324469	−	0.945896i	$-0.394814\pi$
$692$		0			0
$693$	−13.6675	+	21.9530i	−0.519185	+	0.833924i
$694$		0			0
$695$	8.14722	+	14.1114i	0.309042	+	0.535276i
$696$		0			0
$697$	1.64139	−	2.84296i	0.0621719	−	0.107685i
$698$		0			0
$699$	43.8533			1.65868
$700$		0			0
$701$	−13.4147			−0.506665			−0.253333	−	0.967379i	$-0.581527\pi$
$701$	−13.4147			−0.506665			−0.253333	+	0.967379i	$0.581527\pi$
$702$		0			0
$703$	−4.79648	+	8.30774i	−0.180902	+	0.313332i
$704$		0			0
$705$	5.49237	+	9.51307i	0.206855	+	0.358283i
$706$		0			0
$707$	−21.1206	−	39.5646i	−0.794320	−	1.48798i
$708$		0			0
$709$	6.45422	+	11.1790i	0.242393	+	0.419837i	0.961395	−	0.275170i	$-0.0887343\pi$
$709$	6.45422	+	11.1790i	0.242393	+	0.419837i	−0.719002	+	0.695008i	$0.755401\pi$
$710$		0			0
$711$	5.16198	−	8.94081i	0.193589	−	0.335307i
$712$		0			0
$713$	23.3465			0.874333
$714$		0			0
$715$	1.35935			0.0508367
$716$		0			0
$717$	16.4038	−	28.4123i	0.612613	−	1.06108i
$718$		0			0
$719$	7.97727	+	13.8170i	0.297502	+	0.515289i	0.975564	−	0.219716i	$-0.0705132\pi$
$719$	7.97727	+	13.8170i	0.297502	+	0.515289i	−0.678062	+	0.735005i	$0.737180\pi$
$720$		0			0
$721$	6.53205	+	0.217328i	0.243266	+	0.00809371i
$722$		0			0
$723$	−8.72955	−	15.1200i	−0.324656	−	0.562320i
$724$		0			0
$725$	−4.37978	+	7.58600i	−0.162661	+	0.281737i
$726$		0			0
$727$	11.5506			0.428389			0.214195	−	0.976791i	$-0.431287\pi$
$727$	11.5506			0.428389			0.214195	+	0.976791i	$0.431287\pi$
$728$		0			0
$729$	−19.2543			−0.713123
$730$		0			0
$731$	−0.238634	+	0.413327i	−0.00882621	+	0.0152874i
$732$		0			0
$733$	−3.68030	−	6.37447i	−0.135935	−	0.235447i	0.790019	−	0.613082i	$-0.210071\pi$
$733$	−3.68030	−	6.37447i	−0.135935	−	0.235447i	−0.925954	+	0.377636i	$0.876737\pi$
$734$		0			0
$735$	13.8816	+	28.2250i	0.512029	+	1.04109i
$736$		0			0
$737$	−16.5128	−	28.6011i	−0.608259	−	1.05353i
$738$		0			0
$739$	−20.9898	+	36.3554i	−0.772122	+	1.33735i	0.164276	+	0.986414i	$0.447471\pi$
$739$	−20.9898	+	36.3554i	−0.772122	+	1.33735i	−0.936398	+	0.350940i	$0.885862\pi$
$740$		0			0
$741$	0.395394			0.0145252
$742$		0			0
$743$	33.2804			1.22094			0.610469	−	0.792040i	$-0.290981\pi$
$743$	33.2804			1.22094			0.610469	+	0.792040i	$0.290981\pi$
$744$		0			0
$745$	−19.9693	+	34.5878i	−0.731618	+	1.26720i
$746$		0			0
$747$	10.0772	+	17.4541i	0.368704	+	0.638614i
$748$		0			0
$749$	−6.57872	−	0.218880i	−0.240381	−	0.00799771i
$750$		0			0
$751$	10.2979	+	17.8364i	0.375774	+	0.650860i	0.990443	−	0.137926i	$-0.0440435\pi$
$751$	10.2979	+	17.8364i	0.375774	+	0.650860i	−0.614668	+	0.788786i	$0.710710\pi$
$752$		0			0
$753$	29.7058	−	51.4520i	1.08254	−	1.87501i
$754$		0			0
$755$	44.6768			1.62595
$756$		0			0
$757$	38.5859			1.40243			0.701214	−	0.712950i	$-0.252642\pi$
$757$	38.5859			1.40243			0.701214	+	0.712950i	$0.252642\pi$
$758$		0			0
$759$	17.6944	−	30.6476i	0.642265	−	1.11244i
$760$		0			0
$761$	−4.41939	−	7.65461i	−0.160203	−	0.277479i	0.774739	−	0.632282i	$-0.217881\pi$
$761$	−4.41939	−	7.65461i	−0.160203	−	0.277479i	−0.934941	+	0.354802i	$0.884548\pi$
$762$		0			0
$763$	−9.73331	−	18.2331i	−0.352369	−	0.660084i
$764$		0			0
$765$	−2.46371	−	4.26727i	−0.0890757	−	0.154284i
$766$		0			0
$767$	−0.430270	+	0.745249i	−0.0155361	+	0.0269094i
$768$		0			0
$769$	−7.92516			−0.285789			−0.142894	−	0.989738i	$-0.545641\pi$
$769$	−7.92516			−0.285789			−0.142894	+	0.989738i	$0.545641\pi$
$770$		0			0
$771$	−59.5780			−2.14565
$772$		0			0
$773$	24.8690	−	43.0743i	0.894475	−	1.54928i	0.0600225	−	0.998197i	$-0.480883\pi$
$773$	24.8690	−	43.0743i	0.894475	−	1.54928i	0.834453	−	0.551080i	$-0.185784\pi$
$774$		0			0
$775$	−4.08765	−	7.08002i	−0.146833	−	0.254322i
$776$		0			0
$777$	36.0264	−	57.8662i	1.29244	−	2.07594i
$778$		0			0
$779$	1.44543	+	2.50355i	0.0517877	+	0.0896990i
$780$		0			0
$781$	12.6663	−	21.9387i	0.453237	−	0.785029i
$782$		0			0
$783$	6.05727			0.216469
$784$		0			0
$785$	35.7632			1.27644
$786$		0			0
$787$	−6.28276	+	10.8821i	−0.223956	+	0.387904i	−0.956006	−	0.293348i	$-0.905231\pi$
$787$	−6.28276	+	10.8821i	−0.223956	+	0.387904i	0.732049	+	0.681252i	$0.238564\pi$
$788$		0			0
$789$	6.23091	+	10.7923i	0.221826	+	0.384215i
$790$		0			0
$791$	−10.0094	+	16.0773i	−0.355895	+	0.571645i
$792$		0			0
$793$	1.07479	+	1.86159i	0.0381670	+	0.0661071i
$794$		0			0
$795$	−16.0949	+	27.8772i	−0.570827	+	0.988702i
$796$		0			0
$797$	−2.30988			−0.0818200			−0.0409100	−	0.999163i	$-0.513026\pi$
$797$	−2.30988			−0.0818200			−0.0409100	+	0.999163i	$0.513026\pi$
$798$		0			0
$799$	−2.44464			−0.0864850
$800$		0			0
$801$	−0.307338	+	0.532325i	−0.0108592	+	0.0188088i
$802$		0			0
$803$	−1.31065	−	2.27011i	−0.0462518	−	0.0801104i
$804$		0			0
$805$	−9.39870	−	17.6063i	−0.331261	−	0.620542i
$806$		0			0
$807$	−16.3411	−	28.3036i	−0.575233	−	0.996333i
$808$		0			0
$809$	24.8855	−	43.1030i	0.874928	−	1.51542i	0.0180879	−	0.999836i	$-0.494242\pi$
$809$	24.8855	−	43.1030i	0.874928	−	1.51542i	0.856840	−	0.515583i	$-0.172425\pi$
$810$		0			0
$811$	28.5230			1.00158			0.500789	−	0.865569i	$-0.333043\pi$
$811$	28.5230			1.00158			0.500789	+	0.865569i	$0.333043\pi$
$812$		0			0
$813$	70.3665			2.46786
$814$		0			0
$815$	−15.9766	+	27.6723i	−0.559636	+	0.969318i
$816$		0			0
$817$	−0.210144	−	0.363981i	−0.00735202	−	0.0127341i
$818$		0			0
$819$	−1.30196	−	0.0433175i	−0.0454942	−	0.00151363i
$820$		0			0
$821$	18.0649	+	31.2893i	0.630469	+	1.09200i	0.987456	+	0.157895i	$0.0504706\pi$
$821$	18.0649	+	31.2893i	0.630469	+	1.09200i	−0.356987	+	0.934109i	$0.616196\pi$
$822$		0			0
$823$	25.3144	−	43.8458i	0.882404	−	1.52837i	0.0337435	−	0.999431i	$-0.489257\pi$
$823$	25.3144	−	43.8458i	0.882404	−	1.52837i	0.848660	−	0.528938i	$-0.177410\pi$
$824$		0			0
$825$	−12.3922			−0.431440
$826$		0			0
$827$	−12.6809			−0.440957			−0.220479	−	0.975392i	$-0.570762\pi$
$827$	−12.6809			−0.440957			−0.220479	+	0.975392i	$0.570762\pi$
$828$		0			0
$829$	11.8010	−	20.4400i	0.409866	−	0.709909i	−0.585008	−	0.811027i	$-0.698909\pi$
$829$	11.8010	−	20.4400i	0.409866	−	0.709909i	0.994874	+	0.101118i	$0.0322420\pi$
$830$		0			0
$831$	17.1783	+	29.7538i	0.595910	+	1.03215i
$832$		0			0
$833$	−6.98452	−	0.465279i	−0.241999	−	0.0161209i
$834$		0			0
$835$	−10.3633	−	17.9498i	−0.358637	−	0.621178i
$836$		0			0
$837$	−2.82663	+	4.89586i	−0.0977025	+	0.169226i
$838$		0			0
$839$	−40.8581			−1.41058			−0.705290	−	0.708919i	$-0.749183\pi$
$839$	−40.8581			−1.41058			−0.705290	+	0.708919i	$0.749183\pi$
$840$		0			0
$841$	10.6951			0.368795
$842$		0			0
$843$	20.4654	−	35.4471i	0.704866	−	1.22086i
$844$		0			0
$845$	−12.3152	−	21.3306i	−0.423656	−	0.733794i
$846$		0			0
$847$	8.47000	+	0.281805i	0.291033	+	0.00968294i
$848$		0			0
$849$	27.3182	+	47.3165i	0.937557	+	1.62390i
$850$		0			0
$851$	−21.6256	+	37.4567i	−0.741317	+	1.28400i
$852$		0			0
$853$	−25.7967			−0.883261			−0.441630	−	0.897197i	$-0.645600\pi$
$853$	−25.7967			−0.883261			−0.441630	+	0.897197i	$0.645600\pi$
$854$		0			0
$855$	4.33915			0.148396
$856$		0			0
$857$	−20.7224	+	35.8923i	−0.707864	+	1.22606i	0.257784	+	0.966202i	$0.417008\pi$
$857$	−20.7224	+	35.8923i	−0.707864	+	1.22606i	−0.965648	+	0.259853i	$0.916326\pi$
$858$		0			0
$859$	23.3179	+	40.3879i	0.795598	+	1.37802i	0.922459	+	0.386095i	$0.126176\pi$
$859$	23.3179	+	40.3879i	0.795598	+	1.37802i	−0.126861	+	0.991920i	$0.540490\pi$
$860$		0			0
$861$	−9.67351	−	18.1211i	−0.329672	−	0.617566i
$862$		0			0
$863$	2.51419	+	4.35470i	0.0855839	+	0.148236i	0.905640	−	0.424048i	$-0.139391\pi$
$863$	2.51419	+	4.35470i	0.0855839	+	0.148236i	−0.820056	+	0.572283i	$0.806058\pi$
$864$		0			0
$865$	−10.7741	+	18.6613i	−0.366330	+	0.634502i
$866$		0			0
$867$	2.36506			0.0803215
$868$		0			0
$869$	−15.0021			−0.508912
$870$		0			0
$871$	0.831828	−	1.44077i	0.0281854	−	0.0488186i
$872$		0			0
$873$	8.84052	+	15.3122i	0.299206	+	0.518241i
$874$		0			0
$875$	−16.9773	+	27.2692i	−0.573937	+	0.921868i
$876$		0			0
$877$	18.6983	+	32.3864i	0.631396	+	1.09361i	0.987267	+	0.159074i	$0.0508510\pi$
$877$	18.6983	+	32.3864i	0.631396	+	1.09361i	−0.355871	+	0.934535i	$0.615816\pi$
$878$		0			0
$879$	−37.1926	+	64.4195i	−1.25448	+	2.17282i
$880$		0			0
$881$	52.7508			1.77722			0.888609	−	0.458665i	$-0.151672\pi$
$881$	52.7508			1.77722			0.888609	+	0.458665i	$0.151672\pi$
$882$		0			0
$883$	45.9674			1.54692			0.773462	−	0.633842i	$-0.218523\pi$
$883$	45.9674			1.54692			0.773462	+	0.633842i	$0.218523\pi$
$884$		0			0
$885$	−10.1839	+	17.6390i	−0.342327	+	0.592928i
$886$		0			0
$887$	−2.73443	−	4.73617i	−0.0918131	−	0.159025i	0.816461	−	0.577401i	$-0.195933\pi$
$887$	−2.73443	−	4.73617i	−0.0918131	−	0.159025i	−0.908274	+	0.418376i	$0.862600\pi$
$888$		0			0
$889$	−7.45254	+	11.9704i	−0.249950	+	0.401475i
$890$		0			0
$891$	18.9458	+	32.8151i	0.634708	+	1.09935i
$892$		0			0
$893$	1.07639	−	1.86436i	0.0360200	−	0.0623884i
$894$		0			0
$895$	−17.1370			−0.572826
$896$		0			0
$897$	1.78269			0.0595224
$898$		0			0
$899$	−18.5237	+	32.0840i	−0.617800	+	1.07006i
$900$		0			0
$901$	−3.58189	−	6.20402i	−0.119330	−	0.206686i
$902$		0			0
$903$	1.40639	+	2.63456i	0.0468018	+	0.0876725i
$904$		0			0
$905$	2.97431	+	5.15166i	0.0988696	+	0.171247i
$906$		0			0
$907$	−25.3835	+	43.9656i	−0.842846	+	1.45985i	0.0446322	+	0.999003i	$0.485788\pi$
$907$	−25.3835	+	43.9656i	−0.842846	+	1.45985i	−0.887478	+	0.460849i	$0.847545\pi$
$908$		0			0
$909$	43.9632			1.45817
$910$		0			0
$911$	15.2983			0.506856			0.253428	−	0.967354i	$-0.418442\pi$
$911$	15.2983			0.506856			0.253428	+	0.967354i	$0.418442\pi$
$912$		0			0
$913$	14.6435	−	25.3633i	0.484629	−	0.839402i
$914$		0			0
$915$	25.4388	+	44.0613i	0.840981	+	1.45662i
$916$		0			0
$917$	−15.7809	−	0.525045i	−0.521131	−	0.0173385i
$918$		0			0
$919$	16.3929	+	28.3933i	0.540750	+	0.936607i	0.998861	+	0.0477121i	$0.0151930\pi$
$919$	16.3929	+	28.3933i	0.540750	+	0.936607i	−0.458111	+	0.888895i	$0.651474\pi$
$920$		0			0
$921$	17.7054	−	30.6667i	0.583414	−	1.01050i
$922$		0			0
$923$	1.27612			0.0420041
$924$		0			0
$925$	15.1454			0.497978
$926$		0			0
$927$	−3.20329	+	5.54826i	−0.105210	+	0.182229i
$928$		0			0
$929$	5.15864	+	8.93502i	0.169249	+	0.293149i	0.938156	−	0.346212i	$-0.112532\pi$
$929$	5.15864	+	8.93502i	0.169249	+	0.293149i	−0.768907	+	0.639361i	$0.779199\pi$
$930$		0			0
$931$	3.43016	−	5.12176i	0.112419	−	0.167859i
$932$		0			0
$933$	−0.487974	−	0.845196i	−0.0159756	−	0.0276705i
$934$		0			0
$935$	−3.58011	+	6.20093i	−0.117082	+	0.202792i
$936$		0			0
$937$	−38.7047			−1.26443			−0.632214	−	0.774794i	$-0.717854\pi$
$937$	−38.7047			−1.26443			−0.632214	+	0.774794i	$0.717854\pi$
$938$		0			0
$939$	10.2390			0.334137
$940$		0			0
$941$	21.6898	−	37.5678i	0.707067	−	1.22468i	−0.258873	−	0.965911i	$-0.583351\pi$
$941$	21.6898	−	37.5678i	0.707067	−	1.22468i	0.965940	−	0.258765i	$-0.0833156\pi$
$942$		0			0
$943$	6.51692	+	11.2876i	0.212220	+	0.367576i
$944$		0			0
$945$	4.83005	+	0.160701i	0.157122	+	0.00522759i
$946$		0			0
$947$	26.6426	+	46.1463i	0.865768	+	1.49955i	0.866283	+	0.499554i	$0.166503\pi$
$947$	26.6426	+	46.1463i	0.865768	+	1.49955i	−0.000514495		1.00000i	$0.500164\pi$
$948$		0			0
$949$	0.0660234	−	0.114356i	0.00214321	−	0.00371215i
$950$		0			0
$951$	−70.9023			−2.29917
$952$		0			0
$953$	−54.3851			−1.76170			−0.880852	−	0.473391i	$-0.843030\pi$
$953$	−54.3851			−1.76170			−0.880852	+	0.473391i	$0.843030\pi$
$954$		0			0
$955$	−19.1276	+	33.1300i	−0.618955	+	1.07206i
$956$		0			0
$957$	28.0784	+	48.6332i	0.907645	+	1.57209i
$958$		0			0
$959$	−21.2041	−	39.7211i	−0.684716	−	1.28266i
$960$		0			0
$961$	−1.78819	−	3.09724i	−0.0576837	−	0.0999111i
$962$		0			0
$963$	3.22617	−	5.58790i	0.103962	−	0.180067i
$964$		0			0
$965$	−40.0941			−1.29068
$966$		0			0
$967$	38.2418			1.22977			0.614887	−	0.788615i	$-0.289202\pi$
$967$	38.2418			1.22977			0.614887	+	0.788615i	$0.289202\pi$
$968$		0			0
$969$	−1.04135	+	1.80367i	−0.0334530	+	0.0579422i
$970$		0			0
$971$	2.57515	+	4.46028i	0.0826404	+	0.143137i	0.904383	−	0.426721i	$-0.140331\pi$
$971$	2.57515	+	4.46028i	0.0826404	+	0.143137i	−0.821743	+	0.569858i	$0.806998\pi$
$972$		0			0
$973$	−11.9927	+	19.2629i	−0.384468	+	0.617539i
$974$		0			0
$975$	−0.312125	−	0.540617i	−0.00999601	−	0.0173136i
$976$		0			0
$977$	−9.72956	+	16.8521i	−0.311276	+	0.539146i	−0.978639	−	0.205587i	$-0.934090\pi$
$977$	−9.72956	+	16.8521i	−0.311276	+	0.539146i	0.667363	+	0.744733i	$0.267423\pi$
$978$		0			0
$979$	0.893208			0.0285471
$980$		0			0
$981$	20.2602			0.646859
$982$		0			0
$983$	−9.15008	+	15.8484i	−0.291842	+	0.505485i	−0.974245	−	0.225491i	$-0.927602\pi$
$983$	−9.15008	+	15.8484i	−0.291842	+	0.505485i	0.682403	+	0.730976i	$0.260935\pi$
$984$		0			0
$985$	16.0303	+	27.7652i	0.510766	+	0.884673i
$986$		0			0
$987$	−8.08476	+	12.9859i	−0.257341	+	0.413345i
$988$		0			0
$989$	−0.947468	−	1.64106i	−0.0301277	−	0.0521828i
$990$		0			0
$991$	−22.3497	+	38.7109i	−0.709963	+	1.22969i	0.254908	+	0.966965i	$0.417955\pi$
$991$	−22.3497	+	38.7109i	−0.709963	+	1.22969i	−0.964870	+	0.262726i	$0.915378\pi$
$992$		0			0
$993$	56.1478			1.78180
$994$		0			0
$995$	−17.9102			−0.567792
$996$		0			0
$997$	7.45316	−	12.9093i	0.236044	−	0.408840i	−0.723532	−	0.690291i	$-0.757482\pi$
$997$	7.45316	−	12.9093i	0.236044	−	0.408840i	0.959576	+	0.281451i	$0.0908157\pi$
$998$		0			0
$999$	−5.23656	−	9.06998i	−0.165677	−	0.286962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.q.c.137.1	✓	12
7.2	even	3	inner	952.2.q.c.681.1	yes	12
7.3	odd	6		6664.2.a.r.1.1		6
7.4	even	3		6664.2.a.s.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.q.c.137.1	✓	12	1.1	even	1	trivial
952.2.q.c.681.1	yes	12	7.2	even	3	inner
6664.2.a.r.1.1		6	7.3	odd	6
6664.2.a.s.1.6		6	7.4	even	3

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:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18253 + 2.04820i) q^{3} +(0.949958 + 1.64538i) q^{5} +(-1.39834 + 2.24603i) q^{7} +(-1.29675 - 2.24603i) q^{9} +(-1.88435 + 3.26379i) q^{11} -0.189847 q^{13} -4.49341 q^{15} +(0.500000 - 0.866025i) q^{17} +(0.440306 + 0.762633i) q^{19} +(-2.94675 - 5.52007i) q^{21} +(1.98519 + 3.43845i) q^{23} +(0.695159 - 1.20405i) q^{25} -0.961410 q^{27} -6.30040 q^{29} +(2.94008 - 5.09238i) q^{31} +(-4.45660 - 7.71906i) q^{33} +(-5.02393 - 0.167151i) q^{35} +(5.44675 + 9.43405i) q^{37} +(0.224499 - 0.388844i) q^{39} +3.28277 q^{41} -0.477269 q^{43} +(2.46371 - 4.26727i) q^{45} +(-1.22232 - 2.11712i) q^{47} +(-3.08932 - 6.28141i) q^{49} +(1.18253 + 2.04820i) q^{51} +(3.58189 - 6.20402i) q^{53} -7.16022 q^{55} -2.08270 q^{57} +(2.26640 - 3.92552i) q^{59} +(-5.66136 - 9.80576i) q^{61} +(6.85795 + 0.228170i) q^{63} +(-0.180347 - 0.312370i) q^{65} +(-4.38157 + 7.58911i) q^{67} -9.39016 q^{69} -6.72185 q^{71} +(-0.347772 + 0.602358i) q^{73} +(1.64409 + 2.84765i) q^{75} +(-4.69563 - 8.79619i) q^{77} +(1.99036 + 3.44740i) q^{79} +(5.02714 - 8.70725i) q^{81} -7.77110 q^{83} +1.89992 q^{85} +(7.45040 - 12.9045i) q^{87} +(-0.118503 - 0.205254i) q^{89} +(0.265470 - 0.426402i) q^{91} +(6.95347 + 12.0438i) q^{93} +(-0.836545 + 1.44894i) q^{95} -6.81746 q^{97} +9.77411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} - q^{5} + 3 q^{7} - q^{9} + 6 q^{11} - 4 q^{13} + 6 q^{17} - 2 q^{19} + 14 q^{21} + 5 q^{23} - q^{25} - 16 q^{27} - 30 q^{29} - 8 q^{31} - 11 q^{33} + 7 q^{35} + 16 q^{37} + 2 q^{39} + 8 q^{41}+ \cdots + 4 q^{99}+O(q^{100}) \) 12 * q - q^3 - q^5 + 3 * q^7 - q^9 + 6 * q^11 - 4 * q^13 + 6 * q^17 - 2 * q^19 + 14 * q^21 + 5 * q^23 - q^25 - 16 * q^27 - 30 * q^29 - 8 * q^31 - 11 * q^33 + 7 * q^35 + 16 * q^37 + 2 * q^39 + 8 * q^41 + 48 * q^43 - 2 * q^45 + q^47 + 3 * q^49 + q^51 + 32 * q^53 - 50 * q^55 - 38 * q^57 + 6 * q^59 - 10 * q^61 + 45 * q^63 + 26 * q^65 - 27 * q^67 - 44 * q^69 - 24 * q^71 - 15 * q^73 - 24 * q^75 - 3 * q^77 + 21 * q^79 + 30 * q^81 - 40 * q^83 - 2 * q^85 + 9 * q^87 + 33 * q^89 + 25 * q^91 + 29 * q^93 + 15 * q^95 - 18 * q^97 + 4 * q^99

Introduction

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