LMFDB - Embedded newform 1152.2.i.e.385.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			385.1
Root			$1.06839 - 1.36328i$ of defining polynomial
Character	$\chi$	$=$	1152.385
Dual form			1152.2.i.e.769.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71483 + 0.243611i) q^{3} +(-1.34011 - 2.32114i) q^{5} +(-2.48656 + 4.30684i) q^{7} +(2.88131 - 0.835506i) q^{9} +O(q^{10})$	\(q+(-1.71483 + 0.243611i) q^{3} +(-1.34011 - 2.32114i) q^{5} +(-2.48656 + 4.30684i) q^{7} +(2.88131 - 0.835506i) q^{9} +(1.26947 - 2.19879i) q^{11} +(2.21483 + 3.83620i) q^{13} +(2.86353 + 3.65391i) q^{15} -2.43417 q^{17} -4.18361 q^{19} +(3.21483 - 7.99127i) q^{21} +(0.570641 + 0.988379i) q^{23} +(-1.09180 + 1.89106i) q^{25} +(-4.73742 + 2.13467i) q^{27} +(3.00434 - 5.20366i) q^{29} +(2.65303 + 4.59518i) q^{31} +(-1.64128 + 4.07982i) q^{33} +13.3291 q^{35} +0.241556 q^{37} +(-4.73261 - 6.03889i) q^{39} +(-3.21105 - 5.56170i) q^{41} +(5.57273 - 9.65224i) q^{43} +(-5.80061 - 5.56825i) q^{45} +(2.37728 - 4.11757i) q^{47} +(-8.86592 - 15.3562i) q^{49} +(4.17419 - 0.592991i) q^{51} -9.38345 q^{53} -6.80494 q^{55} +(7.17419 - 1.01917i) q^{57} +(-5.40906 - 9.36876i) q^{59} +(4.16044 - 7.20610i) q^{61} +(-3.56614 + 14.4869i) q^{63} +(5.93625 - 10.2819i) q^{65} +(1.13269 + 1.96188i) q^{67} +(-1.21933 - 1.55589i) q^{69} +4.52639 q^{71} -3.34728 q^{73} +(1.41158 - 3.50883i) q^{75} +(6.31322 + 10.9348i) q^{77} +(3.14159 - 5.44139i) q^{79} +(7.60386 - 4.81470i) q^{81} +(0.738248 - 1.27868i) q^{83} +(3.26206 + 5.65005i) q^{85} +(-3.88426 + 9.65530i) q^{87} +14.8823 q^{89} -22.0292 q^{91} +(-5.66894 - 7.23366i) q^{93} +(5.60651 + 9.71076i) q^{95} +(5.89884 - 10.2171i) q^{97} +(1.82064 - 7.39604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} - 4 q^{7} - q^{9}+O(q^{10}) $ 10 * q - q^3 - 4 * q^7 - q^9	$ 10 q - q^{3} - 4 q^{7} - q^{9} + q^{11} + 6 q^{13} + 12 q^{15} - 6 q^{17} - 18 q^{19} + 16 q^{21} + 4 q^{23} + q^{25} + 2 q^{27} - 4 q^{29} - 8 q^{31} - 13 q^{33} + 24 q^{35} - 20 q^{37} - 18 q^{39} - 5 q^{41} + 13 q^{43} - 12 q^{45} - 6 q^{47} + 3 q^{49} - 3 q^{51} + 12 q^{55} + 27 q^{57} + 13 q^{59} + 10 q^{61} - 20 q^{63} + 17 q^{67} - 10 q^{69} + 8 q^{71} - 34 q^{73} + 29 q^{75} + 8 q^{77} - 6 q^{79} - q^{81} - 12 q^{83} + 18 q^{85} + 10 q^{87} + 44 q^{89} - 36 q^{91} + 26 q^{93} - 6 q^{95} + 27 q^{97} - 34 q^{99}+O(q^{100}) $ 10 * q - q^3 - 4 * q^7 - q^9 + q^11 + 6 * q^13 + 12 * q^15 - 6 * q^17 - 18 * q^19 + 16 * q^21 + 4 * q^23 + q^25 + 2 * q^27 - 4 * q^29 - 8 * q^31 - 13 * q^33 + 24 * q^35 - 20 * q^37 - 18 * q^39 - 5 * q^41 + 13 * q^43 - 12 * q^45 - 6 * q^47 + 3 * q^49 - 3 * q^51 + 12 * q^55 + 27 * q^57 + 13 * q^59 + 10 * q^61 - 20 * q^63 + 17 * q^67 - 10 * q^69 + 8 * q^71 - 34 * q^73 + 29 * q^75 + 8 * q^77 - 6 * q^79 - q^81 - 12 * q^83 + 18 * q^85 + 10 * q^87 + 44 * q^89 - 36 * q^91 + 26 * q^93 - 6 * q^95 + 27 * q^97 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.71483	+	0.243611i	−0.990060	+	0.140649i
$3$	−1.71483	+	0.243611i	−0.990060	+	0.140649i
$4$		0			0
$5$	−1.34011	−	2.32114i	−0.599317	−	1.03805i	−0.992922	−	0.118767i	$-0.962106\pi$
$5$	−1.34011	−	2.32114i	−0.599317	−	1.03805i	0.393605	−	0.919279i	$-0.371228\pi$
$6$		0			0
$7$	−2.48656	+	4.30684i	−0.939830	+	1.62783i	−0.174043	+	0.984738i	$0.555683\pi$
$7$	−2.48656	+	4.30684i	−0.939830	+	1.62783i	−0.765786	+	0.643095i	$0.777650\pi$
$8$		0			0
$9$	2.88131	−	0.835506i	0.960436	−	0.278502i
$10$		0			0
$11$	1.26947	−	2.19879i	0.382760	−	0.662960i	−0.608696	−	0.793404i	$-0.708307\pi$
$11$	1.26947	−	2.19879i	0.382760	−	0.662960i	0.991456	+	0.130444i	$0.0416402\pi$
$12$		0			0
$13$	2.21483	+	3.83620i	0.614284	+	1.06397i	0.990510	+	0.137443i	$0.0438885\pi$
$13$	2.21483	+	3.83620i	0.614284	+	1.06397i	−0.376225	+	0.926528i	$0.622778\pi$
$14$		0			0
$15$	2.86353	+	3.65391i	0.739360	+	0.943435i
$16$		0			0
$17$	−2.43417			−0.590373			−0.295186	−	0.955440i	$-0.595382\pi$
$17$	−2.43417			−0.590373			−0.295186	+	0.955440i	$0.595382\pi$
$18$		0			0
$19$	−4.18361			−0.959786			−0.479893	−	0.877327i	$-0.659324\pi$
$19$	−4.18361			−0.959786			−0.479893	+	0.877327i	$0.659324\pi$
$20$		0			0
$21$	3.21483	−	7.99127i	0.701534	−	1.74384i
$22$		0			0
$23$	0.570641	+	0.988379i	0.118987	+	0.206091i	0.919366	−	0.393402i	$-0.128702\pi$
$23$	0.570641	+	0.988379i	0.118987	+	0.206091i	−0.800380	+	0.599494i	$0.795369\pi$
$24$		0			0
$25$	−1.09180	+	1.89106i	−0.218361	+	0.378212i
$26$		0			0
$27$	−4.73742	+	2.13467i	−0.911717	+	0.410818i
$28$		0			0
$29$	3.00434	−	5.20366i	0.557891	−	0.966296i	−0.439781	−	0.898105i	$-0.644944\pi$
$29$	3.00434	−	5.20366i	0.557891	−	0.966296i	0.997672	−	0.0681908i	$-0.0217227\pi$
$30$		0			0
$31$	2.65303	+	4.59518i	0.476498	+	0.825319i	0.999637	−	0.0269282i	$-0.00857256\pi$
$31$	2.65303	+	4.59518i	0.476498	+	0.825319i	−0.523139	+	0.852247i	$0.675239\pi$
$32$		0			0
$33$	−1.64128	+	4.07982i	−0.285711	+	0.710205i
$34$		0			0
$35$	13.3291			2.25302
$36$		0			0
$37$	0.241556			0.0397115			0.0198558	−	0.999803i	$-0.493679\pi$
$37$	0.241556			0.0397115			0.0198558	+	0.999803i	$0.493679\pi$
$38$		0			0
$39$	−4.73261	−	6.03889i	−0.757825	−	0.966997i
$40$		0			0
$41$	−3.21105	−	5.56170i	−0.501482	−	0.868592i	−0.999999	−	0.00171211i	$-0.999455\pi$
$41$	−3.21105	−	5.56170i	−0.501482	−	0.868592i	0.498517	−	0.866880i	$-0.333878\pi$
$42$		0			0
$43$	5.57273	−	9.65224i	0.849833	−	1.47195i	−0.0315245	−	0.999503i	$-0.510036\pi$
$43$	5.57273	−	9.65224i	0.849833	−	1.47195i	0.881357	−	0.472451i	$-0.156630\pi$
$44$		0			0
$45$	−5.80061	−	5.56825i	−0.864703	−	0.830066i
$46$		0			0
$47$	2.37728	−	4.11757i	0.346762	−	0.600609i	−0.638910	−	0.769281i	$-0.720615\pi$
$47$	2.37728	−	4.11757i	0.346762	−	0.600609i	0.985672	+	0.168672i	$0.0539479\pi$
$48$		0			0
$49$	−8.86592	−	15.3562i	−1.26656	−	2.19375i
$50$		0			0
$51$	4.17419	−	0.592991i	0.584504	−	0.0830354i
$52$		0			0
$53$	−9.38345			−1.28892			−0.644458	−	0.764640i	$-0.722917\pi$
$53$	−9.38345			−1.28892			−0.644458	+	0.764640i	$0.722917\pi$
$54$		0			0
$55$	−6.80494			−0.917578
$56$		0			0
$57$	7.17419	−	1.01917i	0.950245	−	0.134993i
$58$		0			0
$59$	−5.40906	−	9.36876i	−0.704199	−	1.21971i	−0.966980	−	0.254853i	$-0.917973\pi$
$59$	−5.40906	−	9.36876i	−0.704199	−	1.21971i	0.262781	−	0.964856i	$-0.415360\pi$
$60$		0			0
$61$	4.16044	−	7.20610i	0.532690	−	0.922646i	−0.466581	−	0.884478i	$-0.654515\pi$
$61$	4.16044	−	7.20610i	0.532690	−	0.922646i	0.999271	−	0.0381677i	$-0.0121521\pi$
$62$		0			0
$63$	−3.56614	+	14.4869i	−0.449291	+	1.82517i
$64$		0			0
$65$	5.93625	−	10.2819i	0.736302	−	1.27531i
$66$		0			0
$67$	1.13269	+	1.96188i	0.138380	+	0.239682i	0.926884	−	0.375349i	$-0.122477\pi$
$67$	1.13269	+	1.96188i	0.138380	+	0.239682i	−0.788503	+	0.615030i	$0.789144\pi$
$68$		0			0
$69$	−1.21933	−	1.55589i	−0.146791	−	0.187307i
$70$		0			0
$71$	4.52639			0.537183			0.268592	−	0.963254i	$-0.413442\pi$
$71$	4.52639			0.537183			0.268592	+	0.963254i	$0.413442\pi$
$72$		0			0
$73$	−3.34728			−0.391769			−0.195885	−	0.980627i	$-0.562758\pi$
$73$	−3.34728			−0.391769			−0.195885	+	0.980627i	$0.562758\pi$
$74$		0			0
$75$	1.41158	−	3.50883i	0.162995	−	0.405165i
$76$		0			0
$77$	6.31322	+	10.9348i	0.719459	+	1.24614i
$78$		0			0
$79$	3.14159	−	5.44139i	0.353457	−	0.612205i	−0.633396	−	0.773828i	$-0.718340\pi$
$79$	3.14159	−	5.44139i	0.353457	−	0.612205i	0.986853	+	0.161623i	$0.0516729\pi$
$80$		0			0
$81$	7.60386	−	4.81470i	0.844873	−	0.534966i
$82$		0			0
$83$	0.738248	−	1.27868i	0.0810332	−	0.140354i	−0.822661	−	0.568533i	$-0.807511\pi$
$83$	0.738248	−	1.27868i	0.0810332	−	0.140354i	0.903694	+	0.428179i	$0.140845\pi$
$84$		0			0
$85$	3.26206	+	5.65005i	0.353820	+	0.612834i
$86$		0			0
$87$	−3.88426	+	9.65530i	−0.416437	+	1.03516i
$88$		0			0
$89$	14.8823			1.57752			0.788762	−	0.614698i	$-0.210722\pi$
$89$	14.8823			1.57752			0.788762	+	0.614698i	$0.210722\pi$
$90$		0			0
$91$	−22.0292			−2.30929
$92$		0			0
$93$	−5.66894	−	7.23366i	−0.587842	−	0.750096i
$94$		0			0
$95$	5.60651	+	9.71076i	0.575216	+	0.996303i
$96$		0			0
$97$	5.89884	−	10.2171i	0.598937	−	1.03739i	−0.394042	−	0.919093i	$-0.628923\pi$
$97$	5.89884	−	10.2171i	0.598937	−	1.03739i	0.992978	−	0.118296i	$-0.0377432\pi$
$98$		0			0
$99$	1.82064	−	7.39604i	0.182981	−	0.743330i
$100$		0			0
$101$	−5.81211	+	10.0669i	−0.578326	+	1.00169i	0.417345	+	0.908748i	$0.362961\pi$
$101$	−5.81211	+	10.0669i	−0.578326	+	1.00169i	−0.995671	+	0.0929424i	$0.970373\pi$
$102$		0			0
$103$	−9.54962	−	16.5404i	−0.940952	−	1.62978i	−0.763660	−	0.645618i	$-0.776600\pi$
$103$	−9.54962	−	16.5404i	−0.940952	−	1.62978i	−0.177292	−	0.984158i	$-0.556734\pi$
$104$		0			0
$105$	−22.8571	+	3.24711i	−2.23063	+	0.316886i
$106$		0			0
$107$	−4.99694			−0.483072			−0.241536	−	0.970392i	$-0.577651\pi$
$107$	−4.99694			−0.483072			−0.241536	+	0.970392i	$0.577651\pi$
$108$		0			0
$109$	−2.15690			−0.206594			−0.103297	−	0.994651i	$-0.532939\pi$
$109$	−2.15690			−0.206594			−0.103297	+	0.994651i	$0.532939\pi$
$110$		0			0
$111$	−0.414228	+	0.0588457i	−0.0393168	+	0.00558539i
$112$		0			0
$113$	10.2451	+	17.7451i	0.963782	+	1.66932i	0.712853	+	0.701314i	$0.247403\pi$
$113$	10.2451	+	17.7451i	0.963782	+	1.66932i	0.250929	+	0.968005i	$0.419264\pi$
$114$		0			0
$115$	1.52945	−	2.64908i	0.142622	−	0.247028i
$116$		0			0
$117$	9.58679	+	9.20277i	0.886299	+	0.850797i
$118$		0			0
$119$	6.05270	−	10.4836i	0.554850	−	0.961028i
$120$		0			0
$121$	2.27688	+	3.94368i	0.206989	+	0.358516i
$122$		0			0
$123$	6.86131	+	8.75515i	0.618664	+	0.789425i
$124$		0			0
$125$	−7.54856			−0.675164
$126$		0			0
$127$	−9.71867			−0.862392			−0.431196	−	0.902258i	$-0.641908\pi$
$127$	−9.71867			−0.862392			−0.431196	+	0.902258i	$0.641908\pi$
$128$		0			0
$129$	−7.20490	+	17.9096i	−0.634356	+	1.57685i
$130$		0			0
$131$	−3.49219	−	6.04865i	−0.305114	−	0.528473i	0.672173	−	0.740394i	$-0.265361\pi$
$131$	−3.49219	−	6.04865i	−0.305114	−	0.528473i	−0.977287	+	0.211921i	$0.932028\pi$
$132$		0			0
$133$	10.4028	−	18.0181i	0.902035	−	1.56237i
$134$		0			0
$135$	11.3036	+	8.13554i	0.972856	+	0.700195i
$136$		0			0
$137$	11.2072	−	19.4114i	0.957493	−	1.65843i	0.228935	−	0.973442i	$-0.426476\pi$
$137$	11.2072	−	19.4114i	0.957493	−	1.65843i	0.728558	−	0.684984i	$-0.240191\pi$
$138$		0			0
$139$	−2.56822	−	4.44830i	−0.217834	−	0.377299i	0.736312	−	0.676643i	$-0.236566\pi$
$139$	−2.56822	−	4.44830i	−0.217834	−	0.377299i	−0.954146	+	0.299343i	$0.903232\pi$
$140$		0			0
$141$	−3.07355	+	7.64008i	−0.258840	+	0.643410i
$142$		0			0
$143$	11.2467			0.940494
$144$		0			0
$145$	−16.1046			−1.33741
$146$		0			0
$147$	18.9445	+	24.1735i	1.56252	+	1.99380i
$148$		0			0
$149$	−1.08562	−	1.88034i	−0.0889372	−	0.154044i	0.818125	−	0.575040i	$-0.195014\pi$
$149$	−1.08562	−	1.88034i	−0.0889372	−	0.154044i	−0.907062	+	0.420997i	$0.861680\pi$
$150$		0			0
$151$	3.10508	−	5.37816i	0.252688	−	0.437669i	−0.711577	−	0.702608i	$-0.752019\pi$
$151$	3.10508	−	5.37816i	0.252688	−	0.437669i	0.964265	+	0.264940i	$0.0853520\pi$
$152$		0			0
$153$	−7.01359	+	2.03376i	−0.567015	+	0.164420i
$154$		0			0
$155$	7.11072	−	12.3161i	0.571147	−	0.989255i
$156$		0			0
$157$	7.97578	+	13.8144i	0.636536	+	1.10251i	0.986187	+	0.165633i	$0.0529667\pi$
$157$	7.97578	+	13.8144i	0.636536	+	1.10251i	−0.349651	+	0.936880i	$0.613700\pi$
$158$		0			0
$159$	16.0911	−	2.28592i	1.27610	−	0.181285i
$160$		0			0
$161$	−5.67572			−0.447310
$162$		0			0
$163$	4.72991			0.370475			0.185237	−	0.982694i	$-0.440695\pi$
$163$	4.72991			0.370475			0.185237	+	0.982694i	$0.440695\pi$
$164$		0			0
$165$	11.6693	−	1.65776i	0.908457	−	0.129057i
$166$		0			0
$167$	−1.18611	−	2.05440i	−0.0917836	−	0.158974i	0.816478	−	0.577376i	$-0.195923\pi$
$167$	−1.18611	−	2.05440i	−0.0917836	−	0.158974i	−0.908262	+	0.418403i	$0.862590\pi$
$168$		0			0
$169$	−3.31097	+	5.73477i	−0.254690	+	0.441137i
$170$		0			0
$171$	−12.0543	+	3.49543i	−0.921813	+	0.267302i
$172$		0			0
$173$	1.19528	−	2.07028i	0.0908752	−	0.157400i	−0.817004	−	0.576631i	$-0.804367\pi$
$173$	1.19528	−	2.07028i	0.0908752	−	0.157400i	0.907880	+	0.419231i	$0.137700\pi$
$174$		0			0
$175$	−5.42967	−	9.40446i	−0.410444	−	0.710910i
$176$		0			0
$177$	11.5580	+	14.7482i	0.868750	+	1.10854i
$178$		0			0
$179$	1.19567			0.0893689			0.0446845	−	0.999001i	$-0.485772\pi$
$179$	1.19567			0.0893689			0.0446845	+	0.999001i	$0.485772\pi$
$180$		0			0
$181$	5.17390			0.384573			0.192287	−	0.981339i	$-0.438410\pi$
$181$	5.17390			0.384573			0.192287	+	0.981339i	$0.438410\pi$
$182$		0			0
$183$	−5.37898	+	13.3708i	−0.397625	+	0.988397i
$184$		0			0
$185$	−0.323712	−	0.560686i	−0.0237998	−	0.0412224i
$186$		0			0
$187$	−3.09011	+	5.35222i	−0.225971	+	0.391393i
$188$		0			0
$189$	2.58617	−	25.7113i	0.188116	−	1.87022i
$190$		0			0
$191$	−0.654726	+	1.13402i	−0.0473743	+	0.0820548i	−0.888740	−	0.458411i	$-0.848419\pi$
$191$	−0.654726	+	1.13402i	−0.0473743	+	0.0820548i	0.841366	+	0.540466i	$0.181752\pi$
$192$		0			0
$193$	10.0726	+	17.4463i	0.725043	+	1.25581i	0.958956	+	0.283554i	$0.0915135\pi$
$193$	10.0726	+	17.4463i	0.725043	+	1.25581i	−0.233913	+	0.972257i	$0.575153\pi$
$194$		0			0
$195$	−7.67490	+	19.0779i	−0.549611	+	1.36619i
$196$		0			0
$197$	−7.46023			−0.531520			−0.265760	−	0.964039i	$-0.585623\pi$
$197$	−7.46023			−0.531520			−0.265760	+	0.964039i	$0.585623\pi$
$198$		0			0
$199$	3.47361			0.246238			0.123119	−	0.992392i	$-0.460710\pi$
$199$	3.47361			0.246238			0.123119	+	0.992392i	$0.460710\pi$
$200$		0			0
$201$	−2.42031	−	3.08836i	−0.170716	−	0.217836i
$202$		0			0
$203$	14.9409	+	25.8784i	1.04865	+	1.81631i
$204$		0			0
$205$	−8.60634	+	14.9066i	−0.601093	+	1.04112i
$206$		0			0
$207$	2.46999	+	2.37105i	0.171676	+	0.164799i
$208$		0			0
$209$	−5.31097	+	9.19888i	−0.367368	+	0.636300i
$210$		0			0
$211$	−4.38878	−	7.60159i	−0.302136	−	0.523315i	0.674483	−	0.738290i	$-0.264366\pi$
$211$	−4.38878	−	7.60159i	−0.302136	−	0.523315i	−0.976620	+	0.214975i	$0.931033\pi$
$212$		0			0
$213$	−7.76200	+	1.10268i	−0.531843	+	0.0755543i
$214$		0			0
$215$	−29.8723			−2.03728
$216$		0			0
$217$	−26.3876			−1.79131
$218$		0			0
$219$	5.74002	−	0.815435i	0.387875	−	0.0551020i
$220$		0			0
$221$	−5.39128	−	9.33797i	−0.362657	−	0.628140i
$222$		0			0
$223$	−7.42411	+	12.8589i	−0.497155	+	0.861098i	−0.999995	−	0.00328197i	$-0.998955\pi$
$223$	−7.42411	+	12.8589i	−0.497155	+	0.861098i	0.502840	+	0.864380i	$0.332289\pi$
$224$		0			0
$225$	−1.56583	+	6.36094i	−0.104389	+	0.424062i
$226$		0			0
$227$	−9.49314	+	16.4426i	−0.630082	+	1.09133i	0.357453	+	0.933931i	$0.383645\pi$
$227$	−9.49314	+	16.4426i	−0.630082	+	1.09133i	−0.987535	+	0.157403i	$0.949688\pi$
$228$		0			0
$229$	−1.17194	−	2.02986i	−0.0774441	−	0.134137i	0.824702	−	0.565567i	$-0.191343\pi$
$229$	−1.17194	−	2.02986i	−0.0774441	−	0.134137i	−0.902147	+	0.431430i	$0.858009\pi$
$230$		0			0
$231$	−13.4900	−	17.2134i	−0.887575	−	1.13256i
$232$		0			0
$233$	12.0912			0.792120			0.396060	−	0.918225i	$-0.370377\pi$
$233$	12.0912			0.792120			0.396060	+	0.918225i	$0.370377\pi$
$234$		0			0
$235$	−12.7433			−0.831281
$236$		0			0
$237$	−4.06172	+	10.0964i	−0.263837	+	0.655832i
$238$		0			0
$239$	−7.54375	−	13.0662i	−0.487965	−	0.845180i	0.511939	−	0.859022i	$-0.328927\pi$
$239$	−7.54375	−	13.0662i	−0.487965	−	0.845180i	−0.999904	+	0.0138417i	$0.995594\pi$
$240$		0			0
$241$	1.01095	−	1.75101i	0.0651208	−	0.112793i	−0.831627	−	0.555335i	$-0.812590\pi$
$241$	1.01095	−	1.75101i	0.0651208	−	0.112793i	0.896748	+	0.442542i	$0.145923\pi$
$242$		0			0
$243$	−11.8664	+	10.1088i	−0.761232	+	0.648479i
$244$		0			0
$245$	−23.7627	+	41.1581i	−1.51814	+	2.62950i
$246$		0			0
$247$	−9.26600	−	16.0492i	−0.589581	−	1.02118i
$248$		0			0
$249$	−0.954470	+	2.37257i	−0.0604871	+	0.150356i
$250$		0			0
$251$	18.7796			1.18536			0.592679	−	0.805438i	$-0.298070\pi$
$251$	18.7796			1.18536			0.592679	+	0.805438i	$0.298070\pi$
$252$		0			0
$253$	2.89765			0.182174
$254$		0			0
$255$	−6.97031	−	8.89423i	−0.436498	−	0.556978i
$256$		0			0
$257$	−11.5006	−	19.9197i	−0.717389	−	1.24255i	−0.962031	−	0.272940i	$-0.912004\pi$
$257$	−11.5006	−	19.9197i	−0.717389	−	1.24255i	0.244642	−	0.969613i	$-0.421329\pi$
$258$		0			0
$259$	−0.600642	+	1.04034i	−0.0373221	+	0.0646437i
$260$		0			0
$261$	4.30872	−	17.5035i	0.266703	−	1.08344i
$262$		0			0
$263$	9.77774	−	16.9356i	0.602922	−	1.04429i	−0.389455	−	0.921046i	$-0.627337\pi$
$263$	9.77774	−	16.9356i	0.602922	−	1.04429i	0.992376	−	0.123245i	$-0.0393302\pi$
$264$		0			0
$265$	12.5749	+	21.7803i	0.772469	+	1.33796i
$266$		0			0
$267$	−25.5207	+	3.62551i	−1.56184	+	0.221877i
$268$		0			0
$269$	−13.2107			−0.805468			−0.402734	−	0.915317i	$-0.631940\pi$
$269$	−13.2107			−0.805468			−0.402734	+	0.915317i	$0.631940\pi$
$270$		0			0
$271$	8.63055			0.524268			0.262134	−	0.965031i	$-0.415574\pi$
$271$	8.63055			0.524268			0.262134	+	0.965031i	$0.415574\pi$
$272$		0			0
$273$	37.7765	−	5.36657i	2.28634	−	0.324800i
$274$		0			0
$275$	2.77203	+	4.80130i	0.167160	+	0.289529i
$276$		0			0
$277$	−1.21650	+	2.10705i	−0.0730927	+	0.126600i	−0.900255	−	0.435362i	$-0.856620\pi$
$277$	−1.21650	+	2.10705i	−0.0730927	+	0.126600i	0.827163	+	0.561963i	$0.189954\pi$
$278$		0			0
$279$	11.4835	+	11.0235i	0.687499	+	0.659960i
$280$		0			0
$281$	−4.75715	+	8.23962i	−0.283787	+	0.491534i	−0.972314	−	0.233676i	$-0.924924\pi$
$281$	−4.75715	+	8.23962i	−0.283787	+	0.491534i	0.688527	+	0.725211i	$0.258258\pi$
$282$		0			0
$283$	5.27042	+	9.12864i	0.313294	+	0.542641i	0.979073	−	0.203507i	$-0.0652341\pi$
$283$	5.27042	+	9.12864i	0.313294	+	0.542641i	−0.665779	+	0.746149i	$0.731901\pi$
$284$		0			0
$285$	−11.9799	−	15.2865i	−0.709627	−	0.905495i
$286$		0			0
$287$	31.9378			1.88523
$288$		0			0
$289$	−11.0748			−0.651460
$290$		0			0
$291$	−7.62653	+	18.9576i	−0.447075	+	1.11132i
$292$		0			0
$293$	3.10888	+	5.38474i	0.181623	+	0.314580i	0.942433	−	0.334394i	$-0.108532\pi$
$293$	3.10888	+	5.38474i	0.181623	+	0.314580i	−0.760811	+	0.648974i	$0.775198\pi$
$294$		0			0
$295$	−14.4975	+	25.1104i	−0.844077	+	1.46198i
$296$		0			0
$297$	−1.32033	+	13.1265i	−0.0766132	+	0.761677i
$298$		0			0
$299$	−2.52775	+	4.37819i	−0.146184	+	0.253197i
$300$		0			0
$301$	27.7138	+	48.0017i	1.59740	+	2.76677i
$302$		0			0
$303$	7.51439	−	18.6789i	0.431691	−	1.07307i
$304$		0			0
$305$	−22.3018			−1.27700
$306$		0			0
$307$	−2.45594			−0.140168			−0.0700839	−	0.997541i	$-0.522327\pi$
$307$	−2.45594			−0.140168			−0.0700839	+	0.997541i	$0.522327\pi$
$308$		0			0
$309$	20.4054	+	26.0377i	1.16083	+	1.48123i
$310$		0			0
$311$	−2.06337	−	3.57386i	−0.117003	−	0.202655i	0.801576	−	0.597893i	$-0.203995\pi$
$311$	−2.06337	−	3.57386i	−0.117003	−	0.202655i	−0.918579	+	0.395238i	$0.870662\pi$
$312$		0			0
$313$	2.66061	−	4.60831i	0.150386	−	0.260477i	−0.780983	−	0.624552i	$-0.785282\pi$
$313$	2.66061	−	4.60831i	0.150386	−	0.260477i	0.931370	+	0.364075i	$0.118615\pi$
$314$		0			0
$315$	38.4051	−	11.1365i	2.16388	−	0.627471i
$316$		0			0
$317$	10.1291	−	17.5440i	0.568904	−	0.985371i	−0.427770	−	0.903887i	$-0.640701\pi$
$317$	10.1291	−	17.5440i	0.568904	−	0.985371i	0.996675	−	0.0814836i	$-0.0259658\pi$
$318$		0			0
$319$	−7.62784	−	13.2118i	−0.427077	−	0.739719i
$320$		0			0
$321$	8.56892	−	1.21731i	0.478270	−	0.0679437i
$322$		0			0
$323$	10.1836			0.566631
$324$		0			0
$325$	−9.67266			−0.536543
$326$		0			0
$327$	3.69873	−	0.525446i	0.204540	−	0.0290572i
$328$		0			0
$329$	11.8225	+	20.4771i	0.651794	+	1.12894i
$330$		0			0
$331$	4.88990	−	8.46955i	0.268773	−	0.465529i	−0.699772	−	0.714366i	$-0.746715\pi$
$331$	4.88990	−	8.46955i	0.268773	−	0.465529i	0.968545	+	0.248837i	$0.0800485\pi$
$332$		0			0
$333$	0.695996	−	0.201821i	0.0381404	−	0.0110597i
$334$		0			0
$335$	3.03587	−	5.25828i	0.165867	−	0.287290i
$336$		0			0
$337$	−7.61501	−	13.1896i	−0.414816	−	0.718482i	0.580593	−	0.814194i	$-0.302821\pi$
$337$	−7.61501	−	13.1896i	−0.414816	−	0.718482i	−0.995409	+	0.0957115i	$0.969487\pi$
$338$		0			0
$339$	−21.8916	−	27.9341i	−1.18899	−	1.51717i
$340$		0			0
$341$	13.4718			0.729538
$342$		0			0
$343$	53.3706			2.88174
$344$		0			0
$345$	−1.97740	+	4.91532i	−0.106460	+	0.264632i
$346$		0			0
$347$	−3.12881	−	5.41925i	−0.167963	−	0.290921i	0.769741	−	0.638357i	$-0.220386\pi$
$347$	−3.12881	−	5.41925i	−0.167963	−	0.290921i	−0.937704	+	0.347436i	$0.887052\pi$
$348$		0			0
$349$	−10.0277	+	17.3685i	−0.536772	+	0.929716i	0.462304	+	0.886722i	$0.347023\pi$
$349$	−10.0277	+	17.3685i	−0.536772	+	0.929716i	−0.999075	+	0.0429941i	$0.986310\pi$
$350$		0			0
$351$	−18.6816	−	13.4458i	−0.997152	−	0.717682i
$352$		0			0
$353$	−9.26961	+	16.0554i	−0.493372	+	0.854545i	−0.999971	−	0.00763681i	$-0.997569\pi$
$353$	−9.26961	+	16.0554i	−0.493372	+	0.854545i	0.506599	+	0.862182i	$0.330902\pi$
$354$		0			0
$355$	−6.06587	−	10.5064i	−0.321943	−	0.557621i
$356$		0			0
$357$	−7.82545	+	19.4521i	−0.414166	+	1.02951i
$358$		0			0
$359$	25.2838			1.33443			0.667213	−	0.744867i	$-0.267487\pi$
$359$	25.2838			1.33443			0.667213	+	0.744867i	$0.267487\pi$
$360$		0			0
$361$	−1.49741			−0.0788112
$362$		0			0
$363$	−4.86520	−	6.20808i	−0.255357	−	0.325839i
$364$		0			0
$365$	4.48573	+	7.76951i	0.234794	+	0.406675i
$366$		0			0
$367$	−6.32458	+	10.9545i	−0.330141	+	0.571820i	−0.982539	−	0.186056i	$-0.940429\pi$
$367$	−6.32458	+	10.9545i	−0.330141	+	0.571820i	0.652399	+	0.757876i	$0.273763\pi$
$368$		0			0
$369$	−13.8989	−	13.3421i	−0.723546	−	0.694563i
$370$		0			0
$371$	23.3325	−	40.4130i	1.21136	−	2.09814i
$372$		0			0
$373$	−9.39906	−	16.2796i	−0.486665	−	0.842928i	0.513218	−	0.858258i	$-0.328453\pi$
$373$	−9.39906	−	16.2796i	−0.486665	−	0.842928i	−0.999882	+	0.0153303i	$0.995120\pi$
$374$		0			0
$375$	12.9445	−	1.83892i	0.668452	−	0.0949612i
$376$		0			0
$377$	26.6164			1.37081
$378$		0			0
$379$	2.15057			0.110467			0.0552337	−	0.998473i	$-0.482410\pi$
$379$	2.15057			0.110467			0.0552337	+	0.998473i	$0.482410\pi$
$380$		0			0
$381$	16.6659	−	2.36758i	0.853820	−	0.121295i
$382$		0			0
$383$	−16.2847	−	28.2060i	−0.832111	−	1.44126i	−0.896361	−	0.443324i	$-0.853799\pi$
$383$	−16.2847	−	28.2060i	−0.832111	−	1.44126i	0.0642505	−	0.997934i	$-0.479534\pi$
$384$		0			0
$385$	16.9209	−	29.3078i	0.862367	−	1.49366i
$386$		0			0
$387$	7.99223	−	32.4671i	0.406268	−	1.65040i
$388$		0			0
$389$	11.9569	−	20.7100i	0.606241	−	1.05004i	−0.385613	−	0.922661i	$-0.626010\pi$
$389$	11.9569	−	20.7100i	0.606241	−	1.05004i	0.991854	−	0.127380i	$-0.0406567\pi$
$390$		0			0
$391$	−1.38904	−	2.40588i	−0.0702466	−	0.121671i
$392$		0			0
$393$	7.46205	+	9.52169i	0.376410	+	0.480306i
$394$		0			0
$395$	−16.8403			−0.847329
$396$		0			0
$397$	4.42557			0.222113			0.111056	−	0.993814i	$-0.464577\pi$
$397$	4.42557			0.222113			0.111056	+	0.993814i	$0.464577\pi$
$398$		0			0
$399$	−13.4496	+	33.4323i	−0.673323	+	1.67371i
$400$		0			0
$401$	−3.04462	−	5.27344i	−0.152041	−	0.263343i	0.779936	−	0.625859i	$-0.215251\pi$
$401$	−3.04462	−	5.27344i	−0.152041	−	0.263343i	−0.931978	+	0.362515i	$0.881918\pi$
$402$		0			0
$403$	−11.7520	+	20.3551i	−0.585411	+	1.01396i
$404$		0			0
$405$	−21.3656	−	11.1974i	−1.06167	−	0.556404i
$406$		0			0
$407$	0.306648	−	0.531130i	0.0152000	−	0.0263272i
$408$		0			0
$409$	−1.23061	−	2.13148i	−0.0608497	−	0.105395i	0.833996	−	0.551771i	$-0.186048\pi$
$409$	−1.23061	−	2.13148i	−0.0608497	−	0.105395i	−0.894845	+	0.446376i	$0.852714\pi$
$410$		0			0
$411$	−14.4896	+	36.0175i	−0.714719	+	1.77661i
$412$		0			0
$413$	53.7997			2.64731
$414$		0			0
$415$	−3.95734			−0.194258
$416$		0			0
$417$	5.48773	+	7.00244i	0.268735	+	0.342911i
$418$		0			0
$419$	−9.75667	−	16.8991i	−0.476645	−	0.825573i	0.522997	−	0.852334i	$-0.324814\pi$
$419$	−9.75667	−	16.8991i	−0.476645	−	0.825573i	−0.999642	+	0.0267617i	$0.991480\pi$
$420$		0			0
$421$	9.52846	−	16.5038i	0.464389	−	0.804345i	−0.534785	−	0.844988i	$-0.679607\pi$
$421$	9.52846	−	16.5038i	0.464389	−	0.804345i	0.999174	+	0.0406435i	$0.0129408\pi$
$422$		0			0
$423$	3.40942	−	13.8502i	0.165772	−	0.673420i
$424$		0			0
$425$	2.65764	−	4.60316i	0.128914	−	0.223286i
$426$		0			0
$427$	20.6903	+	35.8367i	1.00128	+	1.73426i
$428$		0			0
$429$	−19.2862	+	2.73982i	−0.931145	+	0.132280i
$430$		0			0
$431$	−23.6111			−1.13731			−0.568654	−	0.822577i	$-0.692536\pi$
$431$	−23.6111			−1.13731			−0.568654	+	0.822577i	$0.692536\pi$
$432$		0			0
$433$	−2.09660			−0.100756			−0.0503780	−	0.998730i	$-0.516043\pi$
$433$	−2.09660			−0.100756			−0.0503780	+	0.998730i	$0.516043\pi$
$434$		0			0
$435$	27.6167	−	3.92326i	1.32412	−	0.188106i
$436$		0			0
$437$	−2.38734	−	4.13499i	−0.114202	−	0.197804i
$438$		0			0
$439$	−4.38026	+	7.58684i	−0.209059	+	0.362100i	−0.951418	−	0.307901i	$-0.900373\pi$
$439$	−4.38026	+	7.58684i	−0.209059	+	0.362100i	0.742360	+	0.670002i	$0.233707\pi$
$440$		0			0
$441$	−38.3757	−	36.8385i	−1.82741	−	1.75421i
$442$		0			0
$443$	4.51251	−	7.81590i	0.214396	−	0.371345i	−0.738690	−	0.674046i	$-0.764555\pi$
$443$	4.51251	−	7.81590i	0.214396	−	0.371345i	0.953086	+	0.302701i	$0.0978884\pi$
$444$		0			0
$445$	−19.9440	−	34.5440i	−0.945437	−	1.63754i
$446$		0			0
$447$	2.31972	+	2.96001i	0.109719	+	0.140003i
$448$		0			0
$449$	−2.54295			−0.120009			−0.0600047	−	0.998198i	$-0.519112\pi$
$449$	−2.54295			−0.120009			−0.0600047	+	0.998198i	$0.519112\pi$
$450$		0			0
$451$	−16.3054			−0.767789
$452$		0			0
$453$	−4.01452	+	9.97908i	−0.188619	+	0.468858i
$454$		0			0
$455$	29.5216	+	51.1330i	1.38400	+	2.39715i
$456$		0			0
$457$	12.9090	−	22.3590i	0.603855	−	1.04591i	−0.388376	−	0.921501i	$-0.626964\pi$
$457$	12.9090	−	22.3590i	0.603855	−	1.04591i	0.992231	−	0.124407i	$-0.0397029\pi$
$458$		0			0
$459$	11.5317	−	5.19615i	0.538253	−	0.242536i
$460$		0			0
$461$	−12.4517	+	21.5669i	−0.579932	+	1.00447i	0.415554	+	0.909568i	$0.363588\pi$
$461$	−12.4517	+	21.5669i	−0.579932	+	1.00447i	−0.995486	+	0.0949039i	$0.969746\pi$
$462$		0			0
$463$	−11.0655	−	19.1660i	−0.514258	−	0.890721i	−0.999863	−	0.0165428i	$-0.994734\pi$
$463$	−11.0655	−	19.1660i	−0.514258	−	0.890721i	0.485605	−	0.874178i	$-0.338599\pi$
$464$		0			0
$465$	−9.19335	+	22.8524i	−0.426331	+	1.05975i
$466$		0			0
$467$	−24.7135			−1.14361			−0.571803	−	0.820391i	$-0.693756\pi$
$467$	−24.7135			−1.14361			−0.571803	+	0.820391i	$0.693756\pi$
$468$		0			0
$469$	−11.2660			−0.520215
$470$		0			0
$471$	−17.0425	−	21.7465i	−0.785276	−	1.00203i
$472$		0			0
$473$	−14.1488	−	24.5065i	−0.650564	−	1.12681i
$474$		0			0
$475$	4.56768	−	7.91146i	0.209580	−	0.363003i
$476$		0			0
$477$	−27.0366	+	7.83993i	−1.23792	+	0.358966i
$478$		0			0
$479$	−19.6023	+	33.9522i	−0.895653	+	1.55132i	−0.0626578	+	0.998035i	$0.519958\pi$
$479$	−19.6023	+	33.9522i	−0.895653	+	1.55132i	−0.832995	+	0.553281i	$0.813376\pi$
$480$		0			0
$481$	0.535006	+	0.926657i	0.0243942	+	0.0422519i
$482$		0			0
$483$	9.73292	−	1.38267i	0.442863	−	0.0629137i
$484$		0			0
$485$	−31.6204			−1.43581
$486$		0			0
$487$	−29.3140			−1.32835			−0.664173	−	0.747579i	$-0.731216\pi$
$487$	−29.3140			−1.32835			−0.664173	+	0.747579i	$0.731216\pi$
$488$		0			0
$489$	−8.11100	+	1.15226i	−0.366792	+	0.0521069i
$490$		0			0
$491$	2.57211	+	4.45503i	0.116078	+	0.201052i	0.918210	−	0.396094i	$-0.129635\pi$
$491$	2.57211	+	4.45503i	0.116078	+	0.201052i	−0.802132	+	0.597146i	$0.796301\pi$
$492$		0			0
$493$	−7.31306	+	12.6666i	−0.329364	+	0.570474i
$494$		0			0
$495$	−19.6071	+	5.68557i	−0.881275	+	0.255547i
$496$		0			0
$497$	−11.2551	+	19.4944i	−0.504861	+	0.874445i
$498$		0			0
$499$	17.5877	+	30.4627i	0.787332	+	1.36370i	0.927596	+	0.373585i	$0.121872\pi$
$499$	17.5877	+	30.4627i	0.787332	+	1.36370i	−0.140263	+	0.990114i	$0.544795\pi$
$500$		0			0
$501$	2.53445	+	3.23400i	0.113231	+	0.144484i
$502$		0			0
$503$	13.2366			0.590192			0.295096	−	0.955468i	$-0.404648\pi$
$503$	13.2366			0.590192			0.295096	+	0.955468i	$0.404648\pi$
$504$		0			0
$505$	31.1555			1.38640
$506$		0			0
$507$	4.28071	−	10.6408i	0.190113	−	0.472573i
$508$		0			0
$509$	−15.8738	−	27.4942i	−0.703593	−	1.21866i	−0.967197	−	0.254028i	$-0.918245\pi$
$509$	−15.8738	−	27.4942i	−0.703593	−	1.21866i	0.263604	−	0.964631i	$-0.415089\pi$
$510$		0			0
$511$	8.32319	−	14.4162i	0.368196	−	0.637735i
$512$		0			0
$513$	19.8195	−	8.93064i	0.875053	−	0.394297i
$514$		0			0
$515$	−25.5951	+	44.3321i	−1.12786	+	1.95350i
$516$		0			0
$517$	−6.03578	−	10.4543i	−0.265453	−	0.459778i
$518$		0			0
$519$	−1.54536	+	3.84137i	−0.0678336	+	0.168617i
$520$		0			0
$521$	−2.83339			−0.124133			−0.0620666	−	0.998072i	$-0.519769\pi$
$521$	−2.83339			−0.124133			−0.0620666	+	0.998072i	$0.519769\pi$
$522$		0			0
$523$	32.0242			1.40032			0.700160	−	0.713986i	$-0.253112\pi$
$523$	32.0242			1.40032			0.700160	+	0.713986i	$0.253112\pi$
$524$		0			0
$525$	11.6020	+	14.8044i	0.506353	+	0.646115i
$526$		0			0
$527$	−6.45792	−	11.1854i	−0.281311	−	0.487246i
$528$		0			0
$529$	10.8487	−	18.7906i	0.471684	−	0.816981i
$530$		0			0
$531$	−23.4128	−	22.4750i	−1.01603	−	0.975331i
$532$		0			0
$533$	14.2239	−	24.6365i	0.616105	−	1.06713i
$534$		0			0
$535$	6.69646	+	11.5986i	0.289513	+	0.501452i
$536$		0			0
$537$	−2.05038	+	0.291280i	−0.0884805	+	0.0125697i
$538$		0			0
$539$	−45.0201			−1.93915
$540$		0			0
$541$	−3.84546			−0.165329			−0.0826646	−	0.996577i	$-0.526343\pi$
$541$	−3.84546			−0.165329			−0.0826646	+	0.996577i	$0.526343\pi$
$542$		0			0
$543$	−8.87238	+	1.26042i	−0.380750	+	0.0540899i
$544$		0			0
$545$	2.89049	+	5.00648i	0.123815	+	0.214454i
$546$		0			0
$547$	22.4749	−	38.9277i	0.960958	−	1.66443i	0.240856	−	0.970561i	$-0.422572\pi$
$547$	22.4749	−	38.9277i	0.960958	−	1.66443i	0.720102	−	0.693868i	$-0.244095\pi$
$548$		0			0
$549$	5.96677	−	24.2390i	0.254656	−	1.03450i
$550$		0			0
$551$	−12.5690	+	21.7701i	−0.535456	+	0.927437i
$552$		0			0
$553$	15.6235	+	27.0607i	0.664378	+	1.15074i
$554$		0			0
$555$	0.691702	+	0.882622i	0.0293611	+	0.0374652i
$556$		0			0
$557$	35.8629			1.51956			0.759780	−	0.650180i	$-0.225307\pi$
$557$	35.8629			1.51956			0.759780	+	0.650180i	$0.225307\pi$
$558$		0			0
$559$	49.3706			2.08816
$560$		0			0
$561$	3.99516	−	9.93096i	0.168676	−	0.419285i
$562$		0			0
$563$	5.11092	+	8.85237i	0.215400	+	0.373083i	0.953396	−	0.301721i	$-0.0975613\pi$
$563$	5.11092	+	8.85237i	0.215400	+	0.373083i	−0.737997	+	0.674805i	$0.764228\pi$
$564$		0			0
$565$	27.4593	−	47.5609i	1.15522	−	2.00090i
$566$		0			0
$567$	1.82872	+	44.7206i	0.0767989	+	1.87809i
$568$		0			0
$569$	11.4319	−	19.8006i	0.479250	−	0.830085i	−0.520467	−	0.853882i	$-0.674242\pi$
$569$	11.4319	−	19.8006i	0.479250	−	0.830085i	0.999717	+	0.0237967i	$0.00757544\pi$
$570$		0			0
$571$	−1.63442	−	2.83091i	−0.0683985	−	0.118470i	0.829798	−	0.558064i	$-0.188456\pi$
$571$	−1.63442	−	2.83091i	−0.0683985	−	0.118470i	−0.898197	+	0.439594i	$0.855122\pi$
$572$		0			0
$573$	0.846487	−	2.10415i	0.0353625	−	0.0879023i
$574$		0			0
$575$	−2.49211			−0.103928
$576$		0			0
$577$	−40.2432			−1.67535			−0.837673	−	0.546172i	$-0.816084\pi$
$577$	−40.2432			−1.67535			−0.837673	+	0.546172i	$0.816084\pi$
$578$		0			0
$579$	−21.5230	−	27.4637i	−0.894465	−	1.14135i
$580$		0			0
$581$	3.67139	+	6.35903i	0.152315	+	0.263817i
$582$		0			0
$583$	−11.9120	+	20.6322i	−0.493346	+	0.854500i
$584$		0			0
$585$	8.51359	−	34.5851i	0.351993	−	1.42992i
$586$		0			0
$587$	13.3312	−	23.0903i	0.550236	−	0.953037i	−0.448021	−	0.894023i	$-0.647871\pi$
$587$	13.3312	−	23.0903i	0.550236	−	0.953037i	0.998257	−	0.0590141i	$-0.0187957\pi$
$588$		0			0
$589$	−11.0992	−	19.2244i	−0.457336	−	0.792129i
$590$		0			0
$591$	12.7931	−	1.81740i	0.526236	−	0.0747578i
$592$		0			0
$593$	36.4349			1.49620			0.748101	−	0.663585i	$-0.230966\pi$
$593$	36.4349			1.49620			0.748101	+	0.663585i	$0.230966\pi$
$594$		0			0
$595$	−32.4452			−1.33012
$596$		0			0
$597$	−5.95667	+	0.846212i	−0.243790	+	0.0346331i
$598$		0			0
$599$	−6.51357	−	11.2818i	−0.266137	−	0.460963i	0.701724	−	0.712449i	$-0.252414\pi$
$599$	−6.51357	−	11.2818i	−0.266137	−	0.460963i	−0.967861	+	0.251486i	$0.919081\pi$
$600$		0			0
$601$	−23.1094	+	40.0267i	−0.942653	+	1.63272i	−0.182268	+	0.983249i	$0.558344\pi$
$601$	−23.1094	+	40.0267i	−0.942653	+	1.63272i	−0.760384	+	0.649473i	$0.774989\pi$
$602$		0			0
$603$	4.90279	+	4.70640i	0.199657	+	0.191660i
$604$		0			0
$605$	6.10256	−	10.5699i	0.248104	−	0.429729i
$606$		0			0
$607$	6.32515	+	10.9555i	0.256730	+	0.444669i	0.965364	−	0.260907i	$-0.0840215\pi$
$607$	6.32515	+	10.9555i	0.256730	+	0.444669i	−0.708634	+	0.705576i	$0.750688\pi$
$608$		0			0
$609$	−31.9254	−	40.7374i	−1.29368	−	1.65076i
$610$		0			0
$611$	21.0611			0.852041
$612$		0			0
$613$	−16.2013			−0.654365			−0.327182	−	0.944961i	$-0.606099\pi$
$613$	−16.2013			−0.654365			−0.327182	+	0.944961i	$0.606099\pi$
$614$		0			0
$615$	11.1270	−	27.6590i	0.448685	−	1.11532i
$616$		0			0
$617$	−2.54706	−	4.41164i	−0.102541	−	0.177606i	0.810190	−	0.586167i	$-0.199364\pi$
$617$	−2.54706	−	4.41164i	−0.102541	−	0.177606i	−0.912731	+	0.408561i	$0.866031\pi$
$618$		0			0
$619$	12.5926	−	21.8111i	0.506140	−	0.876660i	−0.493835	−	0.869556i	$-0.664405\pi$
$619$	12.5926	−	21.8111i	0.506140	−	0.876660i	0.999975	−	0.00710457i	$-0.00226147\pi$
$620$		0			0
$621$	−4.81323	−	3.46424i	−0.193148	−	0.139015i
$622$		0			0
$623$	−37.0058	+	64.0959i	−1.48260	+	2.56795i
$624$		0			0
$625$	15.5749	+	26.9766i	0.622998	+	1.07906i
$626$		0			0
$627$	6.86648	−	17.0684i	0.274221	−	0.681644i
$628$		0			0
$629$	−0.587987			−0.0234446
$630$		0			0
$631$	18.4509			0.734518			0.367259	−	0.930119i	$-0.380296\pi$
$631$	18.4509			0.734518			0.367259	+	0.930119i	$0.380296\pi$
$632$		0			0
$633$	9.37786	+	11.9663i	0.372737	+	0.475618i
$634$		0			0
$635$	13.0241	+	22.5584i	0.516846	+	0.895204i
$636$		0			0
$637$	39.2731	−	68.0230i	1.55606	−	2.69517i
$638$		0			0
$639$	13.0419	−	3.78182i	0.515930	−	0.149607i
$640$		0			0
$641$	−17.2431	+	29.8659i	−0.681062	+	1.17963i	0.293595	+	0.955930i	$0.405148\pi$
$641$	−17.2431	+	29.8659i	−0.681062	+	1.17963i	−0.974657	+	0.223704i	$0.928185\pi$
$642$		0			0
$643$	5.28665	+	9.15675i	0.208485	+	0.361107i	0.951238	−	0.308459i	$-0.0998133\pi$
$643$	5.28665	+	9.15675i	0.208485	+	0.361107i	−0.742752	+	0.669566i	$0.766480\pi$
$644$		0			0
$645$	51.2261	−	7.27724i	2.01702	−	0.286541i
$646$		0			0
$647$	−14.5011			−0.570098			−0.285049	−	0.958513i	$-0.592010\pi$
$647$	−14.5011			−0.570098			−0.285049	+	0.958513i	$0.592010\pi$
$648$		0			0
$649$	−27.4666			−1.07816
$650$		0			0
$651$	45.2504	−	6.42833i	1.77350	−	0.251946i
$652$		0			0
$653$	−3.29761	−	5.71162i	−0.129045	−	0.223513i	0.794262	−	0.607576i	$-0.207858\pi$
$653$	−3.29761	−	5.71162i	−0.129045	−	0.223513i	−0.923307	+	0.384063i	$0.874525\pi$
$654$		0			0
$655$	−9.35986	+	16.2117i	−0.365720	+	0.633445i
$656$		0			0
$657$	−9.64454	+	2.79667i	−0.376269	+	0.109109i
$658$		0			0
$659$	−15.5531	+	26.9387i	−0.605861	+	1.04938i	0.386053	+	0.922476i	$0.373838\pi$
$659$	−15.5531	+	26.9387i	−0.605861	+	1.04938i	−0.991915	+	0.126906i	$0.959495\pi$
$660$		0			0
$661$	17.1695	+	29.7384i	0.667816	+	1.15669i	0.978514	+	0.206182i	$0.0661040\pi$
$661$	17.1695	+	29.7384i	0.667816	+	1.15669i	−0.310698	+	0.950509i	$0.600563\pi$
$662$		0			0
$663$	11.5200	+	14.6997i	0.447399	+	0.570888i
$664$		0			0
$665$	−55.7636			−2.16242
$666$		0			0
$667$	6.85759			0.265527
$668$		0			0
$669$	9.59853	−	23.8595i	0.371100	−	0.922462i
$670$		0			0
$671$	−10.5631	−	18.2959i	−0.407785	−	0.706304i
$672$		0			0
$673$	6.32809	−	10.9606i	0.243930	−	0.422499i	−0.717900	−	0.696146i	$-0.754897\pi$
$673$	6.32809	−	10.9606i	0.243930	−	0.422499i	0.961830	+	0.273647i	$0.0882299\pi$
$674$		0			0
$675$	1.13554	−	11.2894i	0.0437071	−	0.434529i
$676$		0			0
$677$	6.78910	−	11.7591i	0.260926	−	0.451938i	−0.705562	−	0.708648i	$-0.749305\pi$
$677$	6.78910	−	11.7591i	0.260926	−	0.451938i	0.966488	+	0.256710i	$0.0826387\pi$
$678$		0			0
$679$	29.3356	+	50.8107i	1.12580	+	1.94994i
$680$		0			0
$681$	12.2736	−	30.5090i	0.470324	−	1.16911i
$682$		0			0
$683$	3.85174			0.147383			0.0736914	−	0.997281i	$-0.476522\pi$
$683$	3.85174			0.147383			0.0736914	+	0.997281i	$0.476522\pi$
$684$		0			0
$685$	−60.0755			−2.29537
$686$		0			0
$687$	2.50418	+	3.19538i	0.0955406	+	0.121911i
$688$		0			0
$689$	−20.7828	−	35.9968i	−0.791761	−	1.37137i
$690$		0			0
$691$	20.3658	−	35.2746i	0.774752	−	1.34191i	−0.160182	−	0.987087i	$-0.551208\pi$
$691$	20.3658	−	35.2746i	0.774752	−	1.34191i	0.934934	−	0.354822i	$-0.115458\pi$
$692$		0			0
$693$	27.3264	+	26.2319i	1.03805	+	0.996466i
$694$		0			0
$695$	−6.88342	+	11.9224i	−0.261103	+	0.452244i
$696$		0			0
$697$	7.81624	+	13.5381i	0.296061	+	0.512793i
$698$		0			0
$699$	−20.7344	+	2.94555i	−0.784246	+	0.111411i
$700$		0			0
$701$	−17.5260			−0.661948			−0.330974	−	0.943640i	$-0.607377\pi$
$701$	−17.5260			−0.661948			−0.330974	+	0.943640i	$0.607377\pi$
$702$		0			0
$703$	−1.01057			−0.0381146
$704$		0			0
$705$	21.8526	−	3.10441i	0.823017	−	0.116919i
$706$		0			0
$707$	−28.9043	−	50.0636i	−1.08706	−	1.88284i
$708$		0			0
$709$	−11.5020	+	19.9220i	−0.431965	+	0.748185i	−0.997042	−	0.0768527i	$-0.975513\pi$
$709$	−11.5020	+	19.9220i	−0.431965	+	0.748185i	0.565078	+	0.825038i	$0.308846\pi$
$710$		0			0
$711$	4.50557	−	18.3031i	0.168972	−	0.686421i
$712$		0			0
$713$	−3.02786	+	5.24440i	−0.113394	+	0.196404i
$714$		0			0
$715$	−15.0718	−	26.1051i	−0.563654	−	0.976277i
$716$		0			0
$717$	16.1193	+	20.5685i	0.601988	+	0.768147i
$718$		0			0
$719$	−11.6172			−0.433250			−0.216625	−	0.976255i	$-0.569505\pi$
$719$	−11.6172			−0.433250			−0.216625	+	0.976255i	$0.569505\pi$
$720$		0			0
$721$	94.9826			3.53734
$722$		0			0
$723$	−1.30704	+	3.24897i	−0.0486093	+	0.120831i
$724$		0			0
$725$	6.56030	+	11.3628i	0.243643	+	0.422003i
$726$		0			0
$727$	23.5416	−	40.7752i	0.873109	−	1.51227i	0.0143459	−	0.999897i	$-0.495433\pi$
$727$	23.5416	−	40.7752i	0.873109	−	1.51227i	0.858763	−	0.512373i	$-0.171233\pi$
$728$		0			0
$729$	17.8863	−	20.2257i	0.662457	−	0.749100i
$730$		0			0
$731$	−13.5650	+	23.4952i	−0.501718	+	0.869001i
$732$		0			0
$733$	12.5946	+	21.8145i	0.465193	+	0.805737i	0.999210	−	0.0397362i	$-0.0126518\pi$
$733$	12.5946	+	21.8145i	0.465193	+	0.805737i	−0.534018	+	0.845473i	$0.679318\pi$
$734$		0			0
$735$	30.7224	−	76.3682i	1.13321	−	2.81688i
$736$		0			0
$737$	5.75168			0.211866
$738$		0			0
$739$	−9.73735			−0.358194			−0.179097	−	0.983831i	$-0.557318\pi$
$739$	−9.73735			−0.358194			−0.179097	+	0.983831i	$0.557318\pi$
$740$		0			0
$741$	19.7994	+	25.2644i	0.727349	+	0.928110i
$742$		0			0
$743$	18.0084	+	31.1915i	0.660666	+	1.14431i	0.980441	+	0.196813i	$0.0630592\pi$
$743$	18.0084	+	31.1915i	0.660666	+	1.14431i	−0.319775	+	0.947493i	$0.603607\pi$
$744$		0			0
$745$	−2.90970	+	5.03974i	−0.106603	+	0.184642i
$746$		0			0
$747$	1.05877	−	4.30109i	0.0387384	−	0.157369i
$748$		0			0
$749$	12.4252	−	21.5210i	0.454006	−	0.786361i
$750$		0			0
$751$	14.3734	+	24.8954i	0.524493	+	0.908448i	0.999593	+	0.0285164i	$0.00907828\pi$
$751$	14.3734	+	24.8954i	0.524493	+	0.908448i	−0.475101	+	0.879931i	$0.657588\pi$
$752$		0			0
$753$	−32.2039	+	4.57493i	−1.17358	+	0.166720i
$754$		0			0
$755$	−16.6446			−0.605761
$756$		0			0
$757$	−53.3478			−1.93896			−0.969479	−	0.245174i	$-0.921155\pi$
$757$	−53.3478			−1.93896			−0.969479	+	0.245174i	$0.921155\pi$
$758$		0			0
$759$	−4.96899	+	0.705901i	−0.180363	+	0.0256226i
$760$		0			0
$761$	13.4580	+	23.3100i	0.487853	+	0.844986i	0.999902	−	0.0139702i	$-0.00444701\pi$
$761$	13.4580	+	23.3100i	0.487853	+	0.844986i	−0.512050	+	0.858956i	$0.671114\pi$
$762$		0			0
$763$	5.36326	−	9.28943i	0.194163	−	0.336300i
$764$		0			0
$765$	14.1196	+	13.5541i	0.510497	+	0.490048i
$766$		0			0
$767$	23.9603	−	41.5005i	0.865157	−	1.49850i
$768$		0			0
$769$	−4.56541	−	7.90752i	−0.164633	−	0.285152i	0.771892	−	0.635754i	$-0.219311\pi$
$769$	−4.56541	−	7.90752i	−0.164633	−	0.285152i	−0.936525	+	0.350601i	$0.885977\pi$
$770$		0			0
$771$	24.5743	+	31.3572i	0.885022	+	1.12930i
$772$		0			0
$773$	−20.5628			−0.739591			−0.369796	−	0.929113i	$-0.620572\pi$
$773$	−20.5628			−0.739591			−0.369796	+	0.929113i	$0.620572\pi$
$774$		0			0
$775$	−11.5864			−0.416194
$776$		0			0
$777$	0.776562	−	1.93034i	0.0278590	−	0.0692505i
$778$		0			0
$779$	13.4338	+	23.2680i	0.481315	+	0.833663i
$780$		0			0
$781$	5.74612	−	9.95257i	0.205612	−	0.356131i
$782$		0			0
$783$	−3.12469	+	31.0652i	−0.111667	+	1.11018i
$784$		0			0
$785$	21.3769	−	37.0258i	0.762974	−	1.32151i
$786$		0			0
$787$	−3.17998	−	5.50789i	−0.113354	−	0.196335i	0.803767	−	0.594945i	$-0.202826\pi$
$787$	−3.17998	−	5.50789i	−0.113354	−	0.196335i	−0.917121	+	0.398610i	$0.869493\pi$
$788$		0			0
$789$	−12.6415	+	31.4236i	−0.450050	+	1.11871i
$790$		0			0
$791$	−101.900			−3.62316
$792$		0			0
$793$	36.8587			1.30889
$794$		0			0
$795$	−26.8698	−	34.2863i	−0.952973	−	1.21601i
$796$		0			0
$797$	−10.3241	−	17.8819i	−0.365699	−	0.633409i	0.623189	−	0.782071i	$-0.285837\pi$
$797$	−10.3241	−	17.8819i	−0.365699	−	0.633409i	−0.988888	+	0.148662i	$0.952503\pi$
$798$		0			0
$799$	−5.78670	+	10.0229i	−0.204719	+	0.354583i
$800$		0			0
$801$	42.8806	−	12.4343i	1.51511	−	0.439344i
$802$		0			0
$803$	−4.24928	+	7.35996i	−0.149954	+	0.259727i
$804$		0			0
$805$	7.60611	+	13.1742i	0.268080	+	0.464328i
$806$		0			0
$807$	22.6541	−	3.21827i	0.797461	−	0.113288i
$808$		0			0
$809$	−45.2805			−1.59198			−0.795989	−	0.605311i	$-0.793049\pi$
$809$	−45.2805			−1.59198			−0.795989	+	0.605311i	$0.793049\pi$
$810$		0			0
$811$	4.29363			0.150770			0.0753848	−	0.997155i	$-0.475981\pi$
$811$	4.29363			0.150770			0.0753848	+	0.997155i	$0.475981\pi$
$812$		0			0
$813$	−14.7999	+	2.10250i	−0.519057	+	0.0737379i
$814$		0			0
$815$	−6.33861	−	10.9788i	−0.222032	−	0.384570i
$816$		0			0
$817$	−23.3141	+	40.3812i	−0.815657	+	1.41276i
$818$		0			0
$819$	−63.4730	+	18.4055i	−2.21792	+	0.643142i
$820$		0			0
$821$	−8.49228	+	14.7091i	−0.296383	+	0.513350i	−0.975306	−	0.220860i	$-0.929114\pi$
$821$	−8.49228	+	14.7091i	−0.296383	+	0.513350i	0.678923	+	0.734210i	$0.262447\pi$
$822$		0			0
$823$	−2.98907	−	5.17721i	−0.104192	−	0.180466i	0.809216	−	0.587512i	$-0.199892\pi$
$823$	−2.98907	−	5.17721i	−0.104192	−	0.180466i	−0.913408	+	0.407045i	$0.866559\pi$
$824$		0			0
$825$	−5.92322	−	7.55813i	−0.206220	−	0.263140i
$826$		0			0
$827$	−11.4590			−0.398469			−0.199234	−	0.979952i	$-0.563845\pi$
$827$	−11.4590			−0.398469			−0.199234	+	0.979952i	$0.563845\pi$
$828$		0			0
$829$	−34.5859			−1.20122			−0.600609	−	0.799543i	$-0.705075\pi$
$829$	−34.5859			−1.20122			−0.600609	+	0.799543i	$0.705075\pi$
$830$		0			0
$831$	1.57280	−	3.90959i	0.0545599	−	0.135622i
$832$		0			0
$833$	21.5811	+	37.3796i	0.747742	+	1.29513i
$834$		0			0
$835$	−3.17903	+	5.50625i	−0.110015	+	0.190551i
$836$		0			0
$837$	−22.3777	−	16.1060i	−0.773488	−	0.556704i
$838$		0			0
$839$	12.1093	−	20.9740i	0.418060	−	0.724102i	−0.577684	−	0.816261i	$-0.696043\pi$
$839$	12.1093	−	20.9740i	0.418060	−	0.724102i	0.995744	+	0.0921587i	$0.0293767\pi$
$840$		0			0
$841$	−3.55207	−	6.15236i	−0.122485	−	0.212150i
$842$		0			0
$843$	6.15045	−	15.2885i	0.211833	−	0.526563i
$844$		0			0
$845$	17.7483			0.610561
$846$		0			0
$847$	−22.6464			−0.778139
$848$		0			0
$849$	−11.2617	−	14.3702i	−0.386502	−	0.493183i
$850$		0			0
$851$	0.137842	+	0.238749i	0.00472515	+	0.00818420i
$852$		0			0
$853$	−26.7241	+	46.2875i	−0.915016	+	1.58485i	−0.108138	+	0.994136i	$0.534489\pi$
$853$	−26.7241	+	46.2875i	−0.915016	+	1.58485i	−0.806878	+	0.590719i	$0.798844\pi$
$854$		0			0
$855$	24.2675	+	23.2954i	0.829930	+	0.796686i
$856$		0			0
$857$	1.79836	−	3.11486i	0.0614310	−	0.106402i	−0.833674	−	0.552256i	$-0.813767\pi$
$857$	1.79836	−	3.11486i	0.0614310	−	0.106402i	0.895105	+	0.445855i	$0.147100\pi$
$858$		0			0
$859$	15.9691	+	27.6594i	0.544860	+	0.943726i	0.998616	+	0.0525994i	$0.0167506\pi$
$859$	15.9691	+	27.6594i	0.544860	+	0.943726i	−0.453755	+	0.891126i	$0.649916\pi$
$860$		0			0
$861$	−54.7681	+	7.78042i	−1.86649	+	0.265156i
$862$		0			0
$863$	−2.20625			−0.0751016			−0.0375508	−	0.999295i	$-0.511956\pi$
$863$	−2.20625			−0.0751016			−0.0375508	+	0.999295i	$0.511956\pi$
$864$		0			0
$865$	−6.40722			−0.217852
$866$		0			0
$867$	18.9915	−	2.69795i	0.644984	−	0.0916273i
$868$		0			0
$869$	−7.97632	−	13.8154i	−0.270578	−	0.468655i
$870$		0			0
$871$	−5.01744	+	8.69047i	−0.170010	+	0.294465i
$872$		0			0
$873$	8.45993	−	34.3671i	0.286325	−	1.16315i
$874$		0			0
$875$	18.7699	−	32.5105i	0.634539	−	1.09905i
$876$		0			0
$877$	3.07129	+	5.31962i	0.103710	+	0.179631i	0.913210	−	0.407488i	$-0.133595\pi$
$877$	3.07129	+	5.31962i	0.103710	+	0.179631i	−0.809500	+	0.587119i	$0.800262\pi$
$878$		0			0
$879$	−6.64299	−	8.47657i	−0.224063	−	0.285907i
$880$		0			0
$881$	−38.6422			−1.30189			−0.650945	−	0.759125i	$-0.725627\pi$
$881$	−38.6422			−1.30189			−0.650945	+	0.759125i	$0.725627\pi$
$882$		0			0
$883$	38.4651			1.29446			0.647228	−	0.762297i	$-0.275928\pi$
$883$	38.4651			1.29446			0.647228	+	0.762297i	$0.275928\pi$
$884$		0			0
$885$	18.7436	−	46.5919i	0.630059	−	1.56617i
$886$		0			0
$887$	−25.1015	−	43.4770i	−0.842825	−	1.45982i	−0.887497	−	0.460814i	$-0.847557\pi$
$887$	−25.1015	−	43.4770i	−0.842825	−	1.45982i	0.0446713	−	0.999002i	$-0.485776\pi$
$888$		0			0
$889$	24.1660	−	41.8568i	0.810502	−	1.40383i
$890$		0			0
$891$	−0.933622	−	22.8314i	−0.0312775	−	0.764881i
$892$		0			0
$893$	−9.94561	+	17.2263i	−0.332817	+	0.576456i
$894$		0			0
$895$	−1.60234	−	2.77533i	−0.0535603	−	0.0927691i
$896$		0			0
$897$	3.26809	−	8.12366i	0.109118	−	0.271241i
$898$		0			0
$899$	31.8824			1.06334
$900$		0			0
$901$	22.8409			0.760941
$902$		0			0
$903$	−59.2183	−	75.5635i	−1.97066	−	2.51460i
$904$		0			0
$905$	−6.93361	−	12.0094i	−0.230481	−	0.399205i
$906$		0			0
$907$	−28.5437	+	49.4391i	−0.947777	+	1.64160i	−0.197684	+	0.980266i	$0.563342\pi$
$907$	−28.5437	+	49.4391i	−0.947777	+	1.64160i	−0.750093	+	0.661332i	$0.769991\pi$
$908$		0			0
$909$	−8.33554	+	33.8618i	−0.276472	+	1.12312i
$910$		0			0
$911$	8.15893	−	14.1317i	0.270317	−	0.468204i	−0.698626	−	0.715487i	$-0.746205\pi$
$911$	8.15893	−	14.1317i	0.270317	−	0.468204i	0.968943	+	0.247284i	$0.0795380\pi$
$912$		0			0
$913$	−1.87437	−	3.24650i	−0.0620326	−	0.107444i
$914$		0			0
$915$	38.2439	−	5.43298i	1.26431	−	0.179609i
$916$		0			0
$917$	34.7341			1.14702
$918$		0			0
$919$	25.5992			0.844441			0.422220	−	0.906493i	$-0.361251\pi$
$919$	25.5992			0.844441			0.422220	+	0.906493i	$0.361251\pi$
$920$		0			0
$921$	4.21153	−	0.598295i	0.138775	−	0.0197145i
$922$		0			0
$923$	10.0252	+	17.3641i	0.329983	+	0.571548i
$924$		0			0
$925$	−0.263732	+	0.456797i	−0.00867145	+	0.0150194i
$926$		0			0
$927$	−41.3350	−	39.6793i	−1.35762	−	1.30324i
$928$		0			0
$929$	−12.3480	+	21.3874i	−0.405126	+	0.701699i	−0.994336	−	0.106281i	$-0.966106\pi$
$929$	−12.3480	+	21.3874i	−0.405126	+	0.701699i	0.589210	+	0.807980i	$0.299439\pi$
$930$		0			0
$931$	37.0915	+	64.2444i	1.21563	+	2.10553i
$932$		0			0
$933$	4.40897	+	5.62592i	0.144343	+	0.184184i
$934$		0			0
$935$	16.5644			0.541713
$936$		0			0
$937$	−27.3574			−0.893728			−0.446864	−	0.894602i	$-0.647459\pi$
$937$	−27.3574			−0.893728			−0.446864	+	0.894602i	$0.647459\pi$
$938$		0			0
$939$	−3.43986	+	8.55063i	−0.112256	+	0.279039i
$940$		0			0
$941$	12.2953	+	21.2962i	0.400817	+	0.694235i	0.993825	−	0.110962i	$-0.0353931\pi$
$941$	12.2953	+	21.2962i	0.400817	+	0.694235i	−0.593008	+	0.805197i	$0.702060\pi$
$942$		0			0
$943$	3.66472	−	6.34747i	0.119340	−	0.206702i
$944$		0			0
$945$	−63.1454	+	28.4532i	−2.05412	+	0.925582i
$946$		0			0
$947$	−10.0107	+	17.3391i	−0.325305	+	0.563445i	−0.981574	−	0.191082i	$-0.938800\pi$
$947$	−10.0107	+	17.3391i	−0.325305	+	0.563445i	0.656269	+	0.754527i	$0.272134\pi$
$948$		0			0
$949$	−7.41366	−	12.8408i	−0.240658	−	0.416831i
$950$		0			0
$951$	−13.0957	+	32.5526i	−0.424657	+	1.05559i
$952$		0			0
$953$	−7.59573			−0.246050			−0.123025	−	0.992404i	$-0.539259\pi$
$953$	−7.59573			−0.246050			−0.123025	+	0.992404i	$0.539259\pi$
$954$		0			0
$955$	3.50963			0.113569
$956$		0			0
$957$	16.2990	+	20.7978i	0.526872	+	0.672298i
$958$		0			0
$959$	55.7345	+	96.5350i	1.79976	+	3.11728i
$960$		0			0
$961$	1.42287	−	2.46448i	0.0458990	−	0.0794994i
$962$		0			0
$963$	−14.3977	+	4.17497i	−0.463960	+	0.134537i
$964$		0			0
$965$	26.9969	−	46.7600i	0.869061	−	1.50526i
$966$		0			0
$967$	−10.2203	−	17.7020i	−0.328662	−	0.569259i	0.653585	−	0.756853i	$-0.273264\pi$
$967$	−10.2203	−	17.7020i	−0.328662	−	0.569259i	−0.982247	+	0.187594i	$0.939931\pi$
$968$		0			0
$969$	−17.4632	+	2.48084i	−0.560999	+	0.0796962i
$970$		0			0
$971$	−47.8189			−1.53458			−0.767290	−	0.641300i	$-0.778395\pi$
$971$	−47.8189			−1.53458			−0.767290	+	0.641300i	$0.778395\pi$
$972$		0			0
$973$	25.5441			0.818907
$974$		0			0
$975$	16.5870	−	2.35637i	0.531209	−	0.0754643i
$976$		0			0
$977$	−5.33054	−	9.23277i	−0.170539	−	0.295382i	0.768069	−	0.640367i	$-0.221218\pi$
$977$	−5.33054	−	9.23277i	−0.170539	−	0.295382i	−0.938608	+	0.344984i	$0.887884\pi$
$978$		0			0
$979$	18.8927	−	32.7231i	0.603813	−	1.04584i
$980$		0			0
$981$	−6.21470	+	1.80210i	−0.198420	+	0.0575367i
$982$		0			0
$983$	11.9147	−	20.6369i	0.380020	−	0.658214i	−0.611045	−	0.791596i	$-0.709250\pi$
$983$	11.9147	−	20.6369i	0.380020	−	0.658214i	0.991065	+	0.133382i	$0.0425837\pi$
$984$		0			0
$985$	9.99755	+	17.3163i	0.318549	+	0.551742i
$986$		0			0
$987$	−25.2620	−	32.2348i	−0.804099	−	1.02604i
$988$		0			0
$989$	12.7201			0.404476
$990$		0			0
$991$	11.3401			0.360231			0.180116	−	0.983645i	$-0.442353\pi$
$991$	11.3401			0.360231			0.180116	+	0.983645i	$0.442353\pi$
$992$		0			0
$993$	−6.32208	+	15.7151i	−0.200625	+	0.498704i
$994$		0			0
$995$	−4.65503	−	8.06276i	−0.147575	−	0.255607i
$996$		0			0
$997$	16.0454	−	27.7914i	0.508163	−	0.880164i	−0.491793	−	0.870712i	$-0.663658\pi$
$997$	16.0454	−	27.7914i	0.508163	−	0.880164i	0.999955	−	0.00945137i	$-0.00300851\pi$
$998$		0			0
$999$	−1.14435	+	0.515642i	−0.0362057	+	0.0163142i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.e.385.1	✓	10
3.2	odd	2		3456.2.i.e.1153.5		10
4.3	odd	2		1152.2.i.h.385.5	yes	10
8.3	odd	2		1152.2.i.f.385.1	yes	10
8.5	even	2		1152.2.i.g.385.5	yes	10
9.4	even	3	inner	1152.2.i.e.769.1	yes	10
9.5	odd	6		3456.2.i.e.2305.5		10
12.11	even	2		3456.2.i.h.1153.5		10
24.5	odd	2		3456.2.i.f.1153.1		10
24.11	even	2		3456.2.i.g.1153.1		10
36.23	even	6		3456.2.i.h.2305.5		10
36.31	odd	6		1152.2.i.h.769.5	yes	10
72.5	odd	6		3456.2.i.f.2305.1		10
72.13	even	6		1152.2.i.g.769.5	yes	10
72.59	even	6		3456.2.i.g.2305.1		10
72.67	odd	6		1152.2.i.f.769.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.1	✓	10	1.1	even	1	trivial
1152.2.i.e.769.1	yes	10	9.4	even	3	inner
1152.2.i.f.385.1	yes	10	8.3	odd	2
1152.2.i.f.769.1	yes	10	72.67	odd	6
1152.2.i.g.385.5	yes	10	8.5	even	2
1152.2.i.g.769.5	yes	10	72.13	even	6
1152.2.i.h.385.5	yes	10	4.3	odd	2
1152.2.i.h.769.5	yes	10	36.31	odd	6
3456.2.i.e.1153.5		10	3.2	odd	2
3456.2.i.e.2305.5		10	9.5	odd	6
3456.2.i.f.1153.1		10	24.5	odd	2
3456.2.i.f.2305.1		10	72.5	odd	6
3456.2.i.g.1153.1		10	24.11	even	2
3456.2.i.g.2305.1		10	72.59	even	6
3456.2.i.h.1153.5		10	12.11	even	2
3456.2.i.h.2305.5		10	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71483 + 0.243611i) q^{3} +(-1.34011 - 2.32114i) q^{5} +(-2.48656 + 4.30684i) q^{7} +(2.88131 - 0.835506i) q^{9} +O(q^{10})\)	\(q+(-1.71483 + 0.243611i) q^{3} +(-1.34011 - 2.32114i) q^{5} +(-2.48656 + 4.30684i) q^{7} +(2.88131 - 0.835506i) q^{9} +(1.26947 - 2.19879i) q^{11} +(2.21483 + 3.83620i) q^{13} +(2.86353 + 3.65391i) q^{15} -2.43417 q^{17} -4.18361 q^{19} +(3.21483 - 7.99127i) q^{21} +(0.570641 + 0.988379i) q^{23} +(-1.09180 + 1.89106i) q^{25} +(-4.73742 + 2.13467i) q^{27} +(3.00434 - 5.20366i) q^{29} +(2.65303 + 4.59518i) q^{31} +(-1.64128 + 4.07982i) q^{33} +13.3291 q^{35} +0.241556 q^{37} +(-4.73261 - 6.03889i) q^{39} +(-3.21105 - 5.56170i) q^{41} +(5.57273 - 9.65224i) q^{43} +(-5.80061 - 5.56825i) q^{45} +(2.37728 - 4.11757i) q^{47} +(-8.86592 - 15.3562i) q^{49} +(4.17419 - 0.592991i) q^{51} -9.38345 q^{53} -6.80494 q^{55} +(7.17419 - 1.01917i) q^{57} +(-5.40906 - 9.36876i) q^{59} +(4.16044 - 7.20610i) q^{61} +(-3.56614 + 14.4869i) q^{63} +(5.93625 - 10.2819i) q^{65} +(1.13269 + 1.96188i) q^{67} +(-1.21933 - 1.55589i) q^{69} +4.52639 q^{71} -3.34728 q^{73} +(1.41158 - 3.50883i) q^{75} +(6.31322 + 10.9348i) q^{77} +(3.14159 - 5.44139i) q^{79} +(7.60386 - 4.81470i) q^{81} +(0.738248 - 1.27868i) q^{83} +(3.26206 + 5.65005i) q^{85} +(-3.88426 + 9.65530i) q^{87} +14.8823 q^{89} -22.0292 q^{91} +(-5.66894 - 7.23366i) q^{93} +(5.60651 + 9.71076i) q^{95} +(5.89884 - 10.2171i) q^{97} +(1.82064 - 7.39604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 4 q^{7} - q^{9}+O(q^{10}) \) 10 * q - q^3 - 4 * q^7 - q^9	\( 10 q - q^{3} - 4 q^{7} - q^{9} + q^{11} + 6 q^{13} + 12 q^{15} - 6 q^{17} - 18 q^{19} + 16 q^{21} + 4 q^{23} + q^{25} + 2 q^{27} - 4 q^{29} - 8 q^{31} - 13 q^{33} + 24 q^{35} - 20 q^{37} - 18 q^{39} - 5 q^{41} + 13 q^{43} - 12 q^{45} - 6 q^{47} + 3 q^{49} - 3 q^{51} + 12 q^{55} + 27 q^{57} + 13 q^{59} + 10 q^{61} - 20 q^{63} + 17 q^{67} - 10 q^{69} + 8 q^{71} - 34 q^{73} + 29 q^{75} + 8 q^{77} - 6 q^{79} - q^{81} - 12 q^{83} + 18 q^{85} + 10 q^{87} + 44 q^{89} - 36 q^{91} + 26 q^{93} - 6 q^{95} + 27 q^{97} - 34 q^{99}+O(q^{100}) \) 10 * q - q^3 - 4 * q^7 - q^9 + q^11 + 6 * q^13 + 12 * q^15 - 6 * q^17 - 18 * q^19 + 16 * q^21 + 4 * q^23 + q^25 + 2 * q^27 - 4 * q^29 - 8 * q^31 - 13 * q^33 + 24 * q^35 - 20 * q^37 - 18 * q^39 - 5 * q^41 + 13 * q^43 - 12 * q^45 - 6 * q^47 + 3 * q^49 - 3 * q^51 + 12 * q^55 + 27 * q^57 + 13 * q^59 + 10 * q^61 - 20 * q^63 + 17 * q^67 - 10 * q^69 + 8 * q^71 - 34 * q^73 + 29 * q^75 + 8 * q^77 - 6 * q^79 - q^81 - 12 * q^83 + 18 * q^85 + 10 * q^87 + 44 * q^89 - 36 * q^91 + 26 * q^93 - 6 * q^95 + 27 * q^97 - 34 * q^99

Introduction

L-functions

Modular forms

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Database

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