LMFDB - Embedded newform 1152.2.i.f.769.1

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			769.1
Root			$1.06839 + 1.36328i$ of defining polynomial
Character	$\chi$	$=$	1152.769
Dual form			1152.2.i.f.385.1

$q$-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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

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

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	−0.393605	−	0.919279i	$-0.628772\pi$
$5$	1.34011	−	2.32114i	0.599317	−	1.03805i	0.992922	−	0.118767i	$-0.0378943\pi$
$6$		0			0
$7$	2.48656	+	4.30684i	0.939830	+	1.62783i	0.765786	+	0.643095i	$0.222350\pi$
$7$	2.48656	+	4.30684i	0.939830	+	1.62783i	0.174043	+	0.984738i	$0.444317\pi$
$8$		0			0
$9$	2.88131	+	0.835506i	0.960436	+	0.278502i
$10$		0			0
$11$	1.26947	+	2.19879i	0.382760	+	0.662960i	0.991456	−	0.130444i	$-0.0416402\pi$
$11$	1.26947	+	2.19879i	0.382760	+	0.662960i	−0.608696	+	0.793404i	$0.708307\pi$
$12$		0			0
$13$	−2.21483	+	3.83620i	−0.614284	+	1.06397i	0.376225	+	0.926528i	$0.377222\pi$
$13$	−2.21483	+	3.83620i	−0.614284	+	1.06397i	−0.990510	+	0.137443i	$0.956111\pi$
$14$		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	$-0.871298\pi$
$23$	−0.570641	+	0.988379i	−0.118987	+	0.206091i	0.800380	+	0.599494i	$0.204631\pi$
$24$		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	−0.997672	−	0.0681908i	$-0.978277\pi$
$29$	−3.00434	−	5.20366i	−0.557891	−	0.966296i	0.439781	−	0.898105i	$-0.355056\pi$
$30$		0			0
$31$	−2.65303	+	4.59518i	−0.476498	+	0.825319i	−0.999637	−	0.0269282i	$-0.991427\pi$
$31$	−2.65303	+	4.59518i	−0.476498	+	0.825319i	0.523139	+	0.852247i	$0.324761\pi$
$32$		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	$-0.506321\pi$
$37$	−0.241556			−0.0397115			−0.0198558	+	0.999803i	$0.506321\pi$
$38$		0			0
$39$	4.73261	−	6.03889i	0.757825	−	0.966997i
$40$		0			0
$41$	−3.21105	+	5.56170i	−0.501482	+	0.868592i	0.498517	+	0.866880i	$0.333878\pi$
$41$	−3.21105	+	5.56170i	−0.501482	+	0.868592i	−0.999999	+	0.00171211i	$0.999455\pi$
$42$		0			0
$43$	5.57273	+	9.65224i	0.849833	+	1.47195i	0.881357	+	0.472451i	$0.156630\pi$
$43$	5.57273	+	9.65224i	0.849833	+	1.47195i	−0.0315245	+	0.999503i	$0.510036\pi$
$44$		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	$-0.279385\pi$
$47$	−2.37728	−	4.11757i	−0.346762	−	0.600609i	−0.985672	+	0.168672i	$0.946052\pi$
$48$		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	$-0.277083\pi$
$53$	9.38345			1.28892			0.644458	+	0.764640i	$0.277083\pi$
$54$		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	0.262781	+	0.964856i	$0.415360\pi$
$59$	−5.40906	+	9.36876i	−0.704199	+	1.21971i	−0.966980	+	0.254853i	$0.917973\pi$
$60$		0			0
$61$	−4.16044	−	7.20610i	−0.532690	−	0.922646i	−0.999271	−	0.0381677i	$-0.987848\pi$
$61$	−4.16044	−	7.20610i	−0.532690	−	0.922646i	0.466581	−	0.884478i	$-0.345485\pi$
$62$		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	−0.788503	−	0.615030i	$-0.789144\pi$
$67$	1.13269	−	1.96188i	0.138380	−	0.239682i	0.926884	+	0.375349i	$0.122477\pi$
$68$		0			0
$69$	1.21933	−	1.55589i	0.146791	−	0.187307i
$70$		0			0
$71$	−4.52639			−0.537183			−0.268592	−	0.963254i	$-0.586558\pi$
$71$	−4.52639			−0.537183			−0.268592	+	0.963254i	$0.586558\pi$
$72$		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	$-0.281660\pi$
$79$	−3.14159	−	5.44139i	−0.353457	−	0.612205i	−0.986853	+	0.161623i	$0.948327\pi$
$80$		0			0
$81$	7.60386	+	4.81470i	0.844873	+	0.534966i
$82$		0			0
$83$	0.738248	+	1.27868i	0.0810332	+	0.140354i	0.903694	−	0.428179i	$-0.140845\pi$
$83$	0.738248	+	1.27868i	0.0810332	+	0.140354i	−0.822661	+	0.568533i	$0.807511\pi$
$84$		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	0.992978	+	0.118296i	$0.0377432\pi$
$97$	5.89884	+	10.2171i	0.598937	+	1.03739i	−0.394042	+	0.919093i	$0.628923\pi$
$98$		0			0
$99$	1.82064	+	7.39604i	0.182981	+	0.743330i
$100$		0			0
$101$	5.81211	+	10.0669i	0.578326	+	1.00169i	0.995671	+	0.0929424i	$0.0296272\pi$
$101$	5.81211	+	10.0669i	0.578326	+	1.00169i	−0.417345	+	0.908748i	$0.637039\pi$
$102$		0			0
$103$	9.54962	−	16.5404i	0.940952	−	1.62978i	0.177292	−	0.984158i	$-0.443266\pi$
$103$	9.54962	−	16.5404i	0.940952	−	1.62978i	0.763660	−	0.645618i	$-0.223400\pi$
$104$		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	$-0.467061\pi$
$109$	2.15690			0.206594			0.103297	+	0.994651i	$0.467061\pi$
$110$		0			0
$111$	0.414228	+	0.0588457i	0.0393168	+	0.00558539i
$112$		0			0
$113$	10.2451	−	17.7451i	0.963782	−	1.66932i	0.250929	−	0.968005i	$-0.419264\pi$
$113$	10.2451	−	17.7451i	0.963782	−	1.66932i	0.712853	−	0.701314i	$-0.247403\pi$
$114$		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	$-0.358092\pi$
$127$	9.71867			0.862392			0.431196	+	0.902258i	$0.358092\pi$
$128$		0			0
$129$	−7.20490	−	17.9096i	−0.634356	−	1.57685i
$130$		0			0
$131$	−3.49219	+	6.04865i	−0.305114	+	0.528473i	−0.977287	−	0.211921i	$-0.932028\pi$
$131$	−3.49219	+	6.04865i	−0.305114	+	0.528473i	0.672173	+	0.740394i	$0.265361\pi$
$132$		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	0.728558	+	0.684984i	$0.240191\pi$
$137$	11.2072	+	19.4114i	0.957493	+	1.65843i	0.228935	+	0.973442i	$0.426476\pi$
$138$		0			0
$139$	−2.56822	+	4.44830i	−0.217834	+	0.377299i	−0.954146	−	0.299343i	$-0.903232\pi$
$139$	−2.56822	+	4.44830i	−0.217834	+	0.377299i	0.736312	+	0.676643i	$0.236566\pi$
$140$		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	$-0.804986\pi$
$149$	1.08562	−	1.88034i	0.0889372	−	0.154044i	0.907062	+	0.420997i	$0.138320\pi$
$150$		0			0
$151$	−3.10508	−	5.37816i	−0.252688	−	0.437669i	0.711577	−	0.702608i	$-0.247981\pi$
$151$	−3.10508	−	5.37816i	−0.252688	−	0.437669i	−0.964265	+	0.264940i	$0.914648\pi$
$152$		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	0.349651	+	0.936880i	$0.386300\pi$
$157$	−7.97578	+	13.8144i	−0.636536	+	1.10251i	−0.986187	+	0.165633i	$0.947033\pi$
$158$		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	$-0.804077\pi$
$167$	1.18611	−	2.05440i	0.0917836	−	0.158974i	0.908262	+	0.418403i	$0.137410\pi$
$168$		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	$-0.195633\pi$
$173$	−1.19528	−	2.07028i	−0.0908752	−	0.157400i	−0.907880	+	0.419231i	$0.862300\pi$
$174$		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	$-0.561590\pi$
$181$	−5.17390			−0.384573			−0.192287	+	0.981339i	$0.561590\pi$
$182$		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	$-0.151581\pi$
$191$	0.654726	+	1.13402i	0.0473743	+	0.0820548i	−0.841366	+	0.540466i	$0.818248\pi$
$192$		0			0
$193$	10.0726	−	17.4463i	0.725043	−	1.25581i	−0.233913	−	0.972257i	$-0.575153\pi$
$193$	10.0726	−	17.4463i	0.725043	−	1.25581i	0.958956	−	0.283554i	$-0.0915135\pi$
$194$		0			0
$195$	−7.67490	−	19.0779i	−0.549611	−	1.36619i
$196$		0			0
$197$	7.46023			0.531520			0.265760	−	0.964039i	$-0.414377\pi$
$197$	7.46023			0.531520			0.265760	+	0.964039i	$0.414377\pi$
$198$		0			0
$199$	−3.47361			−0.246238			−0.123119	−	0.992392i	$-0.539290\pi$
$199$	−3.47361			−0.246238			−0.123119	+	0.992392i	$0.539290\pi$
$200$		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	−0.976620	−	0.214975i	$-0.931033\pi$
$211$	−4.38878	+	7.60159i	−0.302136	+	0.523315i	0.674483	+	0.738290i	$0.264366\pi$
$212$		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	$-0.00104469\pi$
$223$	7.42411	+	12.8589i	0.497155	+	0.861098i	−0.502840	+	0.864380i	$0.667711\pi$
$224$		0			0
$225$	−1.56583	−	6.36094i	−0.104389	−	0.424062i
$226$		0			0
$227$	−9.49314	−	16.4426i	−0.630082	−	1.09133i	−0.987535	−	0.157403i	$-0.949688\pi$
$227$	−9.49314	−	16.4426i	−0.630082	−	1.09133i	0.357453	−	0.933931i	$-0.383645\pi$
$228$		0			0
$229$	1.17194	−	2.02986i	0.0774441	−	0.134137i	−0.824702	−	0.565567i	$-0.808657\pi$
$229$	1.17194	−	2.02986i	0.0774441	−	0.134137i	0.902147	+	0.431430i	$0.141991\pi$
$230$		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	$-0.671073\pi$
$239$	7.54375	−	13.0662i	0.487965	−	0.845180i	0.999904	+	0.0138417i	$0.00440610\pi$
$240$		0			0
$241$	1.01095	+	1.75101i	0.0651208	+	0.112793i	0.896748	−	0.442542i	$-0.145923\pi$
$241$	1.01095	+	1.75101i	0.0651208	+	0.112793i	−0.831627	+	0.555335i	$0.812590\pi$
$242$		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	0.244642	+	0.969613i	$0.421329\pi$
$257$	−11.5006	+	19.9197i	−0.717389	+	1.24255i	−0.962031	+	0.272940i	$0.912004\pi$
$258$		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	−0.992376	−	0.123245i	$-0.960670\pi$
$263$	−9.77774	−	16.9356i	−0.602922	−	1.04429i	0.389455	−	0.921046i	$-0.372663\pi$
$264$		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	$-0.368060\pi$
$269$	13.2107			0.805468			0.402734	+	0.915317i	$0.368060\pi$
$270$		0			0
$271$	−8.63055			−0.524268			−0.262134	−	0.965031i	$-0.584426\pi$
$271$	−8.63055			−0.524268			−0.262134	+	0.965031i	$0.584426\pi$
$272$		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	$-0.143380\pi$
$277$	1.21650	+	2.10705i	0.0730927	+	0.126600i	−0.827163	+	0.561963i	$0.810046\pi$
$278$		0			0
$279$	−11.4835	+	11.0235i	−0.687499	+	0.659960i
$280$		0			0
$281$	−4.75715	−	8.23962i	−0.283787	−	0.491534i	0.688527	−	0.725211i	$-0.258258\pi$
$281$	−4.75715	−	8.23962i	−0.283787	−	0.491534i	−0.972314	+	0.233676i	$0.924924\pi$
$282$		0			0
$283$	5.27042	−	9.12864i	0.313294	−	0.542641i	−0.665779	−	0.746149i	$-0.731901\pi$
$283$	5.27042	−	9.12864i	0.313294	−	0.542641i	0.979073	+	0.203507i	$0.0652341\pi$
$284$		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	$-0.891468\pi$
$293$	−3.10888	+	5.38474i	−0.181623	+	0.314580i	0.760811	+	0.648974i	$0.224802\pi$
$294$		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	$-0.796005\pi$
$311$	2.06337	−	3.57386i	0.117003	−	0.202655i	0.918579	+	0.395238i	$0.129338\pi$
$312$		0			0
$313$	2.66061	+	4.60831i	0.150386	+	0.260477i	0.931370	−	0.364075i	$-0.118615\pi$
$313$	2.66061	+	4.60831i	0.150386	+	0.260477i	−0.780983	+	0.624552i	$0.785282\pi$
$314$		0			0
$315$	38.4051	+	11.1365i	2.16388	+	0.627471i
$316$		0			0
$317$	−10.1291	−	17.5440i	−0.568904	−	0.985371i	−0.996675	−	0.0814836i	$-0.974034\pi$
$317$	−10.1291	−	17.5440i	−0.568904	−	0.985371i	0.427770	−	0.903887i	$-0.359299\pi$
$318$		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	0.968545	−	0.248837i	$-0.0800485\pi$
$331$	4.88990	+	8.46955i	0.268773	+	0.465529i	−0.699772	+	0.714366i	$0.746715\pi$
$332$		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	−0.995409	−	0.0957115i	$-0.969487\pi$
$337$	−7.61501	+	13.1896i	−0.414816	+	0.718482i	0.580593	+	0.814194i	$0.302821\pi$
$338$		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	−0.937704	−	0.347436i	$-0.887052\pi$
$347$	−3.12881	+	5.41925i	−0.167963	+	0.290921i	0.769741	+	0.638357i	$0.220386\pi$
$348$		0			0
$349$	10.0277	+	17.3685i	0.536772	+	0.929716i	0.999075	+	0.0429941i	$0.0136897\pi$
$349$	10.0277	+	17.3685i	0.536772	+	0.929716i	−0.462304	+	0.886722i	$0.652977\pi$
$350$		0			0
$351$	18.6816	−	13.4458i	0.997152	−	0.717682i
$352$		0			0
$353$	−9.26961	−	16.0554i	−0.493372	−	0.854545i	0.506599	−	0.862182i	$-0.330902\pi$
$353$	−9.26961	−	16.0554i	−0.493372	−	0.854545i	−0.999971	+	0.00763681i	$0.997569\pi$
$354$		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	$-0.732513\pi$
$359$	−25.2838			−1.33443			−0.667213	+	0.744867i	$0.732513\pi$
$360$		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	$-0.0595705\pi$
$367$	6.32458	+	10.9545i	0.330141	+	0.571820i	−0.652399	+	0.757876i	$0.726237\pi$
$368$		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	$-0.671547\pi$
$373$	9.39906	−	16.2796i	0.486665	−	0.842928i	0.999882	+	0.0153303i	$0.00487998\pi$
$374$		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	−0.0642505	−	0.997934i	$-0.520466\pi$
$383$	16.2847	−	28.2060i	0.832111	−	1.44126i	0.896361	−	0.443324i	$-0.146201\pi$
$384$		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	−0.991854	−	0.127380i	$-0.959343\pi$
$389$	−11.9569	−	20.7100i	−0.606241	−	1.05004i	0.385613	−	0.922661i	$-0.373990\pi$
$390$		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	$-0.535423\pi$
$397$	−4.42557			−0.222113			−0.111056	+	0.993814i	$0.535423\pi$
$398$		0			0
$399$	13.4496	+	33.4323i	0.673323	+	1.67371i
$400$		0			0
$401$	−3.04462	+	5.27344i	−0.152041	+	0.263343i	−0.931978	−	0.362515i	$-0.881918\pi$
$401$	−3.04462	+	5.27344i	−0.152041	+	0.263343i	0.779936	+	0.625859i	$0.215251\pi$
$402$		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	−0.894845	−	0.446376i	$-0.852714\pi$
$409$	−1.23061	+	2.13148i	−0.0608497	+	0.105395i	0.833996	+	0.551771i	$0.186048\pi$
$410$		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	−0.999642	−	0.0267617i	$-0.991480\pi$
$419$	−9.75667	+	16.8991i	−0.476645	+	0.825573i	0.522997	+	0.852334i	$0.324814\pi$
$420$		0			0
$421$	−9.52846	−	16.5038i	−0.464389	−	0.804345i	0.534785	−	0.844988i	$-0.320393\pi$
$421$	−9.52846	−	16.5038i	−0.464389	−	0.804345i	−0.999174	+	0.0406435i	$0.987059\pi$
$422$		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	$-0.307464\pi$
$431$	23.6111			1.13731			0.568654	+	0.822577i	$0.307464\pi$
$432$		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	$-0.0996267\pi$
$439$	4.38026	+	7.58684i	0.209059	+	0.362100i	−0.742360	+	0.670002i	$0.766293\pi$
$440$		0			0
$441$	−38.3757	+	36.8385i	−1.82741	+	1.75421i
$442$		0			0
$443$	4.51251	+	7.81590i	0.214396	+	0.371345i	0.953086	−	0.302701i	$-0.0978884\pi$
$443$	4.51251	+	7.81590i	0.214396	+	0.371345i	−0.738690	+	0.674046i	$0.764555\pi$
$444$		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	0.992231	+	0.124407i	$0.0397029\pi$
$457$	12.9090	+	22.3590i	0.603855	+	1.04591i	−0.388376	+	0.921501i	$0.626964\pi$
$458$		0			0
$459$	11.5317	+	5.19615i	0.538253	+	0.242536i
$460$		0			0
$461$	12.4517	+	21.5669i	0.579932	+	1.00447i	0.995486	+	0.0949039i	$0.0302544\pi$
$461$	12.4517	+	21.5669i	0.579932	+	1.00447i	−0.415554	+	0.909568i	$0.636412\pi$
$462$		0			0
$463$	11.0655	−	19.1660i	0.514258	−	0.890721i	−0.485605	−	0.874178i	$-0.661401\pi$
$463$	11.0655	−	19.1660i	0.514258	−	0.890721i	0.999863	−	0.0165428i	$-0.00526597\pi$
$464$		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	0.832995	+	0.553281i	$0.186624\pi$
$479$	19.6023	+	33.9522i	0.895653	+	1.55132i	0.0626578	+	0.998035i	$0.480042\pi$
$480$		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	$-0.268784\pi$
$487$	29.3140			1.32835			0.664173	+	0.747579i	$0.268784\pi$
$488$		0			0
$489$	−8.11100	−	1.15226i	−0.366792	−	0.0521069i
$490$		0			0
$491$	2.57211	−	4.45503i	0.116078	−	0.201052i	−0.802132	−	0.597146i	$-0.796301\pi$
$491$	2.57211	−	4.45503i	0.116078	−	0.201052i	0.918210	+	0.396094i	$0.129635\pi$
$492$		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	−0.140263	−	0.990114i	$-0.544795\pi$
$499$	17.5877	−	30.4627i	0.787332	−	1.36370i	0.927596	−	0.373585i	$-0.121872\pi$
$500$		0			0
$501$	−2.53445	+	3.23400i	−0.113231	+	0.144484i
$502$		0			0
$503$	−13.2366			−0.590192			−0.295096	−	0.955468i	$-0.595352\pi$
$503$	−13.2366			−0.590192			−0.295096	+	0.955468i	$0.595352\pi$
$504$		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	−0.263604	−	0.964631i	$-0.584911\pi$
$509$	15.8738	−	27.4942i	0.703593	−	1.21866i	0.967197	−	0.254028i	$-0.0817554\pi$
$510$		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	$-0.473657\pi$
$541$	3.84546			0.165329			0.0826646	+	0.996577i	$0.473657\pi$
$542$		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	0.720102	+	0.693868i	$0.244095\pi$
$547$	22.4749	+	38.9277i	0.960958	+	1.66443i	0.240856	+	0.970561i	$0.422572\pi$
$548$		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	$-0.774693\pi$
$557$	−35.8629			−1.51956			−0.759780	+	0.650180i	$0.774693\pi$
$558$		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	−0.737997	−	0.674805i	$-0.764228\pi$
$563$	5.11092	−	8.85237i	0.215400	−	0.373083i	0.953396	+	0.301721i	$0.0975613\pi$
$564$		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	0.999717	−	0.0237967i	$-0.00757544\pi$
$569$	11.4319	+	19.8006i	0.479250	+	0.830085i	−0.520467	+	0.853882i	$0.674242\pi$
$570$		0			0
$571$	−1.63442	+	2.83091i	−0.0683985	+	0.118470i	−0.898197	−	0.439594i	$-0.855122\pi$
$571$	−1.63442	+	2.83091i	−0.0683985	+	0.118470i	0.829798	+	0.558064i	$0.188456\pi$
$572$		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	0.998257	+	0.0590141i	$0.0187957\pi$
$587$	13.3312	+	23.0903i	0.550236	+	0.953037i	−0.448021	+	0.894023i	$0.647871\pi$
$588$		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	$-0.747586\pi$
$599$	6.51357	−	11.2818i	0.266137	−	0.460963i	0.967861	+	0.251486i	$0.0809193\pi$
$600$		0			0
$601$	−23.1094	−	40.0267i	−0.942653	−	1.63272i	−0.760384	−	0.649473i	$-0.774989\pi$
$601$	−23.1094	−	40.0267i	−0.942653	−	1.63272i	−0.182268	−	0.983249i	$-0.558344\pi$
$602$		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	$-0.915978\pi$
$607$	−6.32515	+	10.9555i	−0.256730	+	0.444669i	0.708634	+	0.705576i	$0.249312\pi$
$608$		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	$-0.393901\pi$
$613$	16.2013			0.654365			0.327182	+	0.944961i	$0.393901\pi$
$614$		0			0
$615$	−11.1270	−	27.6590i	−0.448685	−	1.11532i
$616$		0			0
$617$	−2.54706	+	4.41164i	−0.102541	+	0.177606i	−0.912731	−	0.408561i	$-0.866031\pi$
$617$	−2.54706	+	4.41164i	−0.102541	+	0.177606i	0.810190	+	0.586167i	$0.199364\pi$
$618$		0			0
$619$	12.5926	+	21.8111i	0.506140	+	0.876660i	0.999975	+	0.00710457i	$0.00226147\pi$
$619$	12.5926	+	21.8111i	0.506140	+	0.876660i	−0.493835	+	0.869556i	$0.664405\pi$
$620$		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	$-0.619704\pi$
$631$	−18.4509			−0.734518			−0.367259	+	0.930119i	$0.619704\pi$
$632$		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	−0.974657	−	0.223704i	$-0.928185\pi$
$641$	−17.2431	−	29.8659i	−0.681062	−	1.17963i	0.293595	−	0.955930i	$-0.405148\pi$
$642$		0			0
$643$	5.28665	−	9.15675i	0.208485	−	0.361107i	−0.742752	−	0.669566i	$-0.766480\pi$
$643$	5.28665	−	9.15675i	0.208485	−	0.361107i	0.951238	+	0.308459i	$0.0998133\pi$
$644$		0			0
$645$	−51.2261	−	7.27724i	−2.01702	−	0.286541i
$646$		0			0
$647$	14.5011			0.570098			0.285049	−	0.958513i	$-0.407990\pi$
$647$	14.5011			0.570098			0.285049	+	0.958513i	$0.407990\pi$
$648$		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	$-0.792142\pi$
$653$	3.29761	−	5.71162i	0.129045	−	0.223513i	0.923307	+	0.384063i	$0.125475\pi$
$654$		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	−0.991915	−	0.126906i	$-0.959495\pi$
$659$	−15.5531	−	26.9387i	−0.605861	−	1.04938i	0.386053	−	0.922476i	$-0.373838\pi$
$660$		0			0
$661$	−17.1695	+	29.7384i	−0.667816	+	1.15669i	0.310698	+	0.950509i	$0.399437\pi$
$661$	−17.1695	+	29.7384i	−0.667816	+	1.15669i	−0.978514	+	0.206182i	$0.933896\pi$
$662$		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	0.961830	−	0.273647i	$-0.0882299\pi$
$673$	6.32809	+	10.9606i	0.243930	+	0.422499i	−0.717900	+	0.696146i	$0.754897\pi$
$674$		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	$-0.250695\pi$
$677$	−6.78910	−	11.7591i	−0.260926	−	0.451938i	−0.966488	+	0.256710i	$0.917361\pi$
$678$		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	0.934934	+	0.354822i	$0.115458\pi$
$691$	20.3658	+	35.2746i	0.774752	+	1.34191i	−0.160182	+	0.987087i	$0.551208\pi$
$692$		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	$-0.392623\pi$
$701$	17.5260			0.661948			0.330974	+	0.943640i	$0.392623\pi$
$702$		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	$-0.0244871\pi$
$709$	11.5020	+	19.9220i	0.431965	+	0.748185i	−0.565078	+	0.825038i	$0.691154\pi$
$710$		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	$-0.430495\pi$
$719$	11.6172			0.433250			0.216625	+	0.976255i	$0.430495\pi$
$720$		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	−0.858763	−	0.512373i	$-0.828767\pi$
$727$	−23.5416	−	40.7752i	−0.873109	−	1.51227i	−0.0143459	−	0.999897i	$-0.504567\pi$
$728$		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	$-0.987348\pi$
$733$	−12.5946	+	21.8145i	−0.465193	+	0.805737i	0.534018	+	0.845473i	$0.320682\pi$
$734$		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	0.319775	+	0.947493i	$0.396393\pi$
$743$	−18.0084	+	31.1915i	−0.660666	+	1.14431i	−0.980441	+	0.196813i	$0.936941\pi$
$744$		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	0.475101	+	0.879931i	$0.342412\pi$
$751$	−14.3734	+	24.8954i	−0.524493	+	0.908448i	−0.999593	+	0.0285164i	$0.990922\pi$
$752$		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	$-0.0788450\pi$
$757$	53.3478			1.93896			0.969479	+	0.245174i	$0.0788450\pi$
$758$		0			0
$759$	4.96899	+	0.705901i	0.180363	+	0.0256226i
$760$		0			0
$761$	13.4580	−	23.3100i	0.487853	−	0.844986i	−0.512050	−	0.858956i	$-0.671114\pi$
$761$	13.4580	−	23.3100i	0.487853	−	0.844986i	0.999902	+	0.0139702i	$0.00444701\pi$
$762$		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	−0.936525	−	0.350601i	$-0.885977\pi$
$769$	−4.56541	+	7.90752i	−0.164633	+	0.285152i	0.771892	+	0.635754i	$0.219311\pi$
$770$		0			0
$771$	24.5743	−	31.3572i	0.885022	−	1.12930i
$772$		0			0
$773$	20.5628			0.739591			0.369796	−	0.929113i	$-0.379428\pi$
$773$	20.5628			0.739591			0.369796	+	0.929113i	$0.379428\pi$
$774$		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	−0.917121	−	0.398610i	$-0.869493\pi$
$787$	−3.17998	+	5.50789i	−0.113354	+	0.196335i	0.803767	+	0.594945i	$0.202826\pi$
$788$		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	$-0.714163\pi$
$797$	10.3241	−	17.8819i	0.365699	−	0.633409i	0.988888	+	0.148662i	$0.0474967\pi$
$798$		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	$-0.0708863\pi$
$821$	8.49228	+	14.7091i	0.296383	+	0.513350i	−0.678923	+	0.734210i	$0.737553\pi$
$822$		0			0
$823$	2.98907	−	5.17721i	0.104192	−	0.180466i	−0.809216	−	0.587512i	$-0.800108\pi$
$823$	2.98907	−	5.17721i	0.104192	−	0.180466i	0.913408	+	0.407045i	$0.133441\pi$
$824$		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	$-0.294925\pi$
$829$	34.5859			1.20122			0.600609	+	0.799543i	$0.294925\pi$
$830$		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	$-0.303957\pi$
$839$	−12.1093	−	20.9740i	−0.418060	−	0.724102i	−0.995744	+	0.0921587i	$0.970623\pi$
$840$		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	0.806878	+	0.590719i	$0.201156\pi$
$853$	26.7241	+	46.2875i	0.915016	+	1.58485i	0.108138	+	0.994136i	$0.465511\pi$
$854$		0			0
$855$	−24.2675	+	23.2954i	−0.829930	+	0.796686i
$856$		0			0
$857$	1.79836	+	3.11486i	0.0614310	+	0.106402i	0.895105	−	0.445855i	$-0.147100\pi$
$857$	1.79836	+	3.11486i	0.0614310	+	0.106402i	−0.833674	+	0.552256i	$0.813767\pi$
$858$		0			0
$859$	15.9691	−	27.6594i	0.544860	−	0.943726i	−0.453755	−	0.891126i	$-0.649916\pi$
$859$	15.9691	−	27.6594i	0.544860	−	0.943726i	0.998616	−	0.0525994i	$-0.0167506\pi$
$860$		0			0
$861$	54.7681	+	7.78042i	1.86649	+	0.265156i
$862$		0			0
$863$	2.20625			0.0751016			0.0375508	−	0.999295i	$-0.488044\pi$
$863$	2.20625			0.0751016			0.0375508	+	0.999295i	$0.488044\pi$
$864$		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	$-0.866405\pi$
$877$	−3.07129	+	5.31962i	−0.103710	+	0.179631i	0.809500	+	0.587119i	$0.199738\pi$
$878$		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	−0.0446713	−	0.999002i	$-0.514224\pi$
$887$	25.1015	−	43.4770i	0.842825	−	1.45982i	0.887497	−	0.460814i	$-0.152443\pi$
$888$		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	−0.750093	−	0.661332i	$-0.769991\pi$
$907$	−28.5437	−	49.4391i	−0.947777	−	1.64160i	−0.197684	−	0.980266i	$-0.563342\pi$
$908$		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	$-0.253795\pi$
$911$	−8.15893	−	14.1317i	−0.270317	−	0.468204i	−0.968943	+	0.247284i	$0.920462\pi$
$912$		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	$-0.638749\pi$
$919$	−25.5992			−0.844441			−0.422220	+	0.906493i	$0.638749\pi$
$920$		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	0.589210	−	0.807980i	$-0.299439\pi$
$929$	−12.3480	−	21.3874i	−0.405126	−	0.701699i	−0.994336	+	0.106281i	$0.966106\pi$
$930$		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	$-0.964607\pi$
$941$	−12.2953	+	21.2962i	−0.400817	+	0.694235i	0.593008	+	0.805197i	$0.297940\pi$
$942$		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	0.656269	−	0.754527i	$-0.272134\pi$
$947$	−10.0107	−	17.3391i	−0.325305	−	0.563445i	−0.981574	+	0.191082i	$0.938800\pi$
$948$		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	$-0.726736\pi$
$967$	10.2203	−	17.7020i	0.328662	−	0.569259i	0.982247	+	0.187594i	$0.0600690\pi$
$968$		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	−0.938608	−	0.344984i	$-0.887884\pi$
$977$	−5.33054	+	9.23277i	−0.170539	+	0.295382i	0.768069	+	0.640367i	$0.221218\pi$
$978$		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	$-0.290750\pi$
$983$	−11.9147	−	20.6369i	−0.380020	−	0.658214i	−0.991065	+	0.133382i	$0.957416\pi$
$984$		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	$-0.557647\pi$
$991$	−11.3401			−0.360231			−0.180116	+	0.983645i	$0.557647\pi$
$992$		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	−0.999955	−	0.00945137i	$-0.996991\pi$
$997$	−16.0454	−	27.7914i	−0.508163	−	0.880164i	0.491793	−	0.870712i	$-0.336342\pi$
$998$		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.f.769.1	yes	10
3.2	odd	2		3456.2.i.g.2305.1		10
4.3	odd	2		1152.2.i.g.769.5	yes	10
8.3	odd	2		1152.2.i.e.769.1	yes	10
8.5	even	2		1152.2.i.h.769.5	yes	10
9.2	odd	6		3456.2.i.g.1153.1		10
9.7	even	3	inner	1152.2.i.f.385.1	yes	10
12.11	even	2		3456.2.i.f.2305.1		10
24.5	odd	2		3456.2.i.h.2305.5		10
24.11	even	2		3456.2.i.e.2305.5		10
36.7	odd	6		1152.2.i.g.385.5	yes	10
36.11	even	6		3456.2.i.f.1153.1		10
72.11	even	6		3456.2.i.e.1153.5		10
72.29	odd	6		3456.2.i.h.1153.5		10
72.43	odd	6		1152.2.i.e.385.1	✓	10
72.61	even	6		1152.2.i.h.385.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.1	✓	10	72.43	odd	6
1152.2.i.e.769.1	yes	10	8.3	odd	2
1152.2.i.f.385.1	yes	10	9.7	even	3	inner
1152.2.i.f.769.1	yes	10	1.1	even	1	trivial
1152.2.i.g.385.5	yes	10	36.7	odd	6
1152.2.i.g.769.5	yes	10	4.3	odd	2
1152.2.i.h.385.5	yes	10	72.61	even	6
1152.2.i.h.769.5	yes	10	8.5	even	2
3456.2.i.e.1153.5		10	72.11	even	6
3456.2.i.e.2305.5		10	24.11	even	2
3456.2.i.f.1153.1		10	36.11	even	6
3456.2.i.f.2305.1		10	12.11	even	2
3456.2.i.g.1153.1		10	9.2	odd	6
3456.2.i.g.2305.1		10	3.2	odd	2
3456.2.i.h.1153.5		10	72.29	odd	6
3456.2.i.h.2305.5		10	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

Varieties

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Database

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