LMFDB - Embedded newform 1148.2.n.d.141.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(57,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1148.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.n (of order $5$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Character	$\chi$	$=$	1148.141
Dual form			1148.2.n.d.57.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.15594 q^{3} +(1.01403 - 0.736733i) q^{5} +(0.309017 - 0.951057i) q^{7} +6.95994 q^{9} +O(q^{10})$	\(q-3.15594 q^{3} +(1.01403 - 0.736733i) q^{5} +(0.309017 - 0.951057i) q^{7} +6.95994 q^{9} +(3.45379 + 2.50933i) q^{11} +(-1.21867 - 3.75068i) q^{13} +(-3.20020 + 2.32508i) q^{15} +(-4.64208 - 3.37267i) q^{17} +(-1.20120 + 3.69691i) q^{19} +(-0.975238 + 3.00147i) q^{21} +(1.39102 + 4.28111i) q^{23} +(-1.05961 + 3.26115i) q^{25} -12.4973 q^{27} +(5.73934 - 4.16987i) q^{29} +(7.70828 + 5.60039i) q^{31} +(-10.8999 - 7.91928i) q^{33} +(-0.387324 - 1.19206i) q^{35} +(-3.60250 + 2.61737i) q^{37} +(3.84604 + 11.8369i) q^{39} +(4.01533 - 4.98770i) q^{41} +(-3.40218 - 10.4708i) q^{43} +(7.05756 - 5.12762i) q^{45} +(-0.993775 - 3.05853i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(14.6501 + 10.6439i) q^{51} +(1.84803 - 1.34267i) q^{53} +5.35094 q^{55} +(3.79090 - 11.6672i) q^{57} +(-0.664850 - 2.04620i) q^{59} +(3.86793 - 11.9043i) q^{61} +(2.15074 - 6.61929i) q^{63} +(-3.99901 - 2.90545i) q^{65} +(7.13959 - 5.18722i) q^{67} +(-4.38996 - 13.5109i) q^{69} +(-10.5922 - 7.69567i) q^{71} +12.7893 q^{73} +(3.34407 - 10.2920i) q^{75} +(3.45379 - 2.50933i) q^{77} +16.3615 q^{79} +18.5609 q^{81} +4.27741 q^{83} -7.19195 q^{85} +(-18.1130 + 13.1599i) q^{87} +(-0.204910 + 0.630649i) q^{89} -3.94370 q^{91} +(-24.3268 - 17.6745i) q^{93} +(1.50559 + 4.63372i) q^{95} +(5.16775 - 3.75459i) q^{97} +(24.0382 + 17.4648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	$ 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) $ 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−3.15594			−1.82208			−0.911040	−	0.412317i	$-0.864720\pi$
$3$	−3.15594			−1.82208			−0.911040	+	0.412317i	$0.864720\pi$
$4$		0			0
$5$	1.01403	−	0.736733i	0.453486	−	0.329477i	−0.337484	−	0.941331i	$-0.609576\pi$
$5$	1.01403	−	0.736733i	0.453486	−	0.329477i	0.790971	+	0.611854i	$0.209576\pi$
$6$		0			0
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$		0			0
$9$	6.95994			2.31998
$10$		0			0
$11$	3.45379	+	2.50933i	1.04136	+	0.756591i	0.970550	−	0.240899i	$-0.0774424\pi$
$11$	3.45379	+	2.50933i	1.04136	+	0.756591i	0.0708075	+	0.997490i	$0.477442\pi$
$12$		0			0
$13$	−1.21867	−	3.75068i	−0.337998	−	1.04025i	−0.965226	−	0.261416i	$-0.915811\pi$
$13$	−1.21867	−	3.75068i	−0.337998	−	1.04025i	0.627228	−	0.778835i	$-0.284189\pi$
$14$		0			0
$15$	−3.20020	+	2.32508i	−0.826289	+	0.600334i
$16$		0			0
$17$	−4.64208	−	3.37267i	−1.12587	−	0.817992i	−0.140781	−	0.990041i	$-0.544961\pi$
$17$	−4.64208	−	3.37267i	−1.12587	−	0.817992i	−0.985088	+	0.172049i	$0.944961\pi$
$18$		0			0
$19$	−1.20120	+	3.69691i	−0.275574	+	0.848128i	0.713494	+	0.700662i	$0.247112\pi$
$19$	−1.20120	+	3.69691i	−0.275574	+	0.848128i	−0.989067	+	0.147466i	$0.952888\pi$
$20$		0			0
$21$	−0.975238	+	3.00147i	−0.212814	+	0.654975i
$22$		0			0
$23$	1.39102	+	4.28111i	0.290047	+	0.892673i	0.984840	+	0.173463i	$0.0554958\pi$
$23$	1.39102	+	4.28111i	0.290047	+	0.892673i	−0.694793	+	0.719209i	$0.744504\pi$
$24$		0			0
$25$	−1.05961	+	3.26115i	−0.211922	+	0.652230i
$26$		0			0
$27$	−12.4973			−2.40511
$28$		0			0
$29$	5.73934	−	4.16987i	1.06577	−	0.774326i	0.0906214	−	0.995885i	$-0.471115\pi$
$29$	5.73934	−	4.16987i	1.06577	−	0.774326i	0.975147	+	0.221559i	$0.0711147\pi$
$30$		0			0
$31$	7.70828	+	5.60039i	1.38445	+	1.00586i	0.996449	+	0.0842000i	$0.0268335\pi$
$31$	7.70828	+	5.60039i	1.38445	+	1.00586i	0.387999	+	0.921660i	$0.373167\pi$
$32$		0			0
$33$	−10.8999	−	7.91928i	−1.89744	−	1.37857i
$34$		0			0
$35$	−0.387324	−	1.19206i	−0.0654697	−	0.201495i
$36$		0			0
$37$	−3.60250	+	2.61737i	−0.592248	+	0.430293i	−0.843119	−	0.537727i	$-0.819283\pi$
$37$	−3.60250	+	2.61737i	−0.592248	+	0.430293i	0.250871	+	0.968021i	$0.419283\pi$
$38$		0			0
$39$	3.84604	+	11.8369i	0.615860	+	1.89542i
$40$		0			0
$41$	4.01533	−	4.98770i	0.627089	−	0.778948i
$41$	4.01533	−	4.98770i	0.627089	−	0.778948i
$42$		0			0
$43$	−3.40218	−	10.4708i	−0.518827	−	1.59678i	−0.776209	−	0.630475i	$-0.782860\pi$
$43$	−3.40218	−	10.4708i	−0.518827	−	1.59678i	0.257383	−	0.966310i	$-0.417140\pi$
$44$		0			0
$45$	7.05756	−	5.12762i	1.05208	−	0.764380i
$46$		0			0
$47$	−0.993775	−	3.05853i	−0.144957	−	0.446132i	0.852048	−	0.523463i	$-0.175360\pi$
$47$	−0.993775	−	3.05853i	−0.144957	−	0.446132i	−0.997005	+	0.0773311i	$0.975360\pi$
$48$		0			0
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$		0			0
$51$	14.6501	+	10.6439i	2.05143	+	1.49045i
$52$		0			0
$53$	1.84803	−	1.34267i	0.253846	−	0.184430i	−0.453584	−	0.891214i	$-0.649855\pi$
$53$	1.84803	−	1.34267i	0.253846	−	0.184430i	0.707430	+	0.706784i	$0.249855\pi$
$54$		0			0
$55$	5.35094			0.721521
$56$		0			0
$57$	3.79090	−	11.6672i	0.502117	−	1.54536i
$58$		0			0
$59$	−0.664850	−	2.04620i	−0.0865561	−	0.266392i	0.898405	−	0.439168i	$-0.144727\pi$
$59$	−0.664850	−	2.04620i	−0.0865561	−	0.266392i	−0.984961	+	0.172775i	$0.944727\pi$
$60$		0			0
$61$	3.86793	−	11.9043i	0.495238	−	1.52419i	−0.321348	−	0.946961i	$-0.604136\pi$
$61$	3.86793	−	11.9043i	0.495238	−	1.52419i	0.816586	−	0.577224i	$-0.195864\pi$
$62$		0			0
$63$	2.15074	−	6.61929i	0.270968	−	0.833952i
$64$		0			0
$65$	−3.99901	−	2.90545i	−0.496017	−	0.360377i
$66$		0			0
$67$	7.13959	−	5.18722i	0.872240	−	0.633719i	−0.0589471	−	0.998261i	$-0.518774\pi$
$67$	7.13959	−	5.18722i	0.872240	−	0.633719i	0.931187	+	0.364542i	$0.118774\pi$
$68$		0			0
$69$	−4.38996	−	13.5109i	−0.528489	−	1.62652i
$70$		0			0
$71$	−10.5922	−	7.69567i	−1.25706	−	0.913308i	−0.258451	−	0.966024i	$-0.583212\pi$
$71$	−10.5922	−	7.69567i	−1.25706	−	0.913308i	−0.998610	+	0.0527165i	$0.983212\pi$
$72$		0			0
$73$	12.7893			1.49688			0.748438	−	0.663205i	$-0.230804\pi$
$73$	12.7893			1.49688			0.748438	+	0.663205i	$0.230804\pi$
$74$		0			0
$75$	3.34407	−	10.2920i	0.386139	−	1.18842i
$76$		0			0
$77$	3.45379	−	2.50933i	0.393596	−	0.285964i
$78$		0			0
$79$	16.3615			1.84081			0.920407	−	0.390962i	$-0.127858\pi$
$79$	16.3615			1.84081			0.920407	+	0.390962i	$0.127858\pi$
$80$		0			0
$81$	18.5609			2.06232
$82$		0			0
$83$	4.27741			0.469507			0.234754	−	0.972055i	$-0.424572\pi$
$83$	4.27741			0.469507			0.234754	+	0.972055i	$0.424572\pi$
$84$		0			0
$85$	−7.19195			−0.780076
$86$		0			0
$87$	−18.1130	+	13.1599i	−1.94192	+	1.41088i
$88$		0			0
$89$	−0.204910	+	0.630649i	−0.0217205	+	0.0668487i	−0.961329	−	0.275402i	$-0.911189\pi$
$89$	−0.204910	+	0.630649i	−0.0217205	+	0.0668487i	0.939609	+	0.342250i	$0.111189\pi$
$90$		0			0
$91$	−3.94370			−0.413412
$92$		0			0
$93$	−24.3268	−	17.6745i	−2.52258	−	1.83276i
$94$		0			0
$95$	1.50559	+	4.63372i	0.154470	+	0.475410i
$96$		0			0
$97$	5.16775	−	3.75459i	0.524706	−	0.381221i	−0.293668	−	0.955908i	$-0.594876\pi$
$97$	5.16775	−	3.75459i	0.524706	−	0.381221i	0.818374	+	0.574686i	$0.194876\pi$
$98$		0			0
$99$	24.0382	+	17.4648i	2.41593	+	1.75527i
$100$		0			0
$101$	−1.31051	+	4.03333i	−0.130400	+	0.401331i	−0.994846	−	0.101395i	$-0.967669\pi$
$101$	−1.31051	+	4.03333i	−0.130400	+	0.401331i	0.864446	+	0.502726i	$0.167669\pi$
$102$		0			0
$103$	−2.60205	+	8.00830i	−0.256388	+	0.789081i	0.737165	+	0.675713i	$0.236164\pi$
$103$	−2.60205	+	8.00830i	−0.256388	+	0.789081i	−0.993553	+	0.113368i	$0.963836\pi$
$104$		0			0
$105$	1.22237	+	3.76206i	0.119291	+	0.367140i
$106$		0			0
$107$	1.73550	−	5.34131i	0.167777	−	0.516364i	−0.831453	−	0.555595i	$-0.812491\pi$
$107$	1.73550	−	5.34131i	0.167777	−	0.516364i	0.999230	+	0.0392306i	$0.0124907\pi$
$108$		0			0
$109$	−5.64781			−0.540962			−0.270481	−	0.962725i	$-0.587183\pi$
$109$	−5.64781			−0.540962			−0.270481	+	0.962725i	$0.587183\pi$
$110$		0			0
$111$	11.3693	−	8.26026i	1.07912	−	0.784029i
$112$		0			0
$113$	11.0992	+	8.06402i	1.04412	+	0.758599i	0.971086	−	0.238730i	$-0.0767311\pi$
$113$	11.0992	+	8.06402i	1.04412	+	0.758599i	0.0730363	+	0.997329i	$0.476731\pi$
$114$		0			0
$115$	4.56456	+	3.31635i	0.425648	+	0.309251i
$116$		0			0
$117$	−8.48186	−	26.1045i	−0.784148	−	2.41336i
$118$		0			0
$119$	−4.64208	+	3.37267i	−0.425539	+	0.309172i
$120$		0			0
$121$	2.23277	+	6.87177i	0.202979	+	0.624706i
$122$		0			0
$123$	−12.6721	+	15.7409i	−1.14261	+	1.41931i
$124$		0			0
$125$	3.26474	+	10.0478i	0.292007	+	0.898706i
$126$		0			0
$127$	−9.57363	+	6.95565i	−0.849522	+	0.617214i	−0.925014	−	0.379932i	$-0.875947\pi$
$127$	−9.57363	+	6.95565i	−0.849522	+	0.617214i	0.0754920	+	0.997146i	$0.475947\pi$
$128$		0			0
$129$	10.7370	+	33.0452i	0.945344	+	2.90947i
$130$		0			0
$131$	−14.1541	−	10.2836i	−1.23665	−	0.898481i	−0.239283	−	0.970950i	$-0.576912\pi$
$131$	−14.1541	−	10.2836i	−1.23665	−	0.898481i	−0.997371	+	0.0724687i	$0.976912\pi$
$132$		0			0
$133$	3.14478	+	2.28481i	0.272687	+	0.198118i
$134$		0			0
$135$	−12.6726	+	9.20718i	−1.09068	+	0.792428i
$136$		0			0
$137$	7.20159			0.615273			0.307637	−	0.951504i	$-0.400462\pi$
$137$	7.20159			0.615273			0.307637	+	0.951504i	$0.400462\pi$
$138$		0			0
$139$	1.91396	−	5.89055i	0.162340	−	0.499630i	−0.836491	−	0.547981i	$-0.815397\pi$
$139$	1.91396	−	5.89055i	0.162340	−	0.499630i	0.998830	+	0.0483511i	$0.0153966\pi$
$140$		0			0
$141$	3.13629	+	9.65251i	0.264123	+	0.812888i
$142$		0			0
$143$	5.20265	−	16.0121i	0.435067	−	1.33900i
$144$		0			0
$145$	2.74776	−	8.45672i	0.228189	−	0.702293i
$146$		0			0
$147$	2.55321	+	1.85501i	0.210585	+	0.152999i
$148$		0			0
$149$	−3.84729	+	2.79522i	−0.315182	+	0.228993i	−0.734117	−	0.679023i	$-0.762404\pi$
$149$	−3.84729	+	2.79522i	−0.315182	+	0.228993i	0.418935	+	0.908016i	$0.362404\pi$
$150$		0			0
$151$	−7.23704	−	22.2733i	−0.588942	−	1.81258i	−0.582826	−	0.812597i	$-0.698053\pi$
$151$	−7.23704	−	22.2733i	−0.588942	−	1.81258i	−0.00611625	−	0.999981i	$-0.501947\pi$
$152$		0			0
$153$	−32.3086	−	23.4736i	−2.61199	−	1.89772i
$154$		0			0
$155$	11.9424			0.959236
$156$		0			0
$157$	3.54746	−	10.9180i	0.283118	−	0.871348i	−0.703838	−	0.710360i	$-0.748532\pi$
$157$	3.54746	−	10.9180i	0.283118	−	0.871348i	0.986956	−	0.160988i	$-0.0514680\pi$
$158$		0			0
$159$	−5.83226	+	4.23738i	−0.462528	+	0.336046i
$160$		0			0
$161$	4.50142			0.354762
$162$		0			0
$163$	−7.36249			−0.576675			−0.288337	−	0.957529i	$-0.593102\pi$
$163$	−7.36249			−0.576675			−0.288337	+	0.957529i	$0.593102\pi$
$164$		0			0
$165$	−16.8872			−1.31467
$166$		0			0
$167$	−3.27528			−0.253449			−0.126724	−	0.991938i	$-0.540446\pi$
$167$	−3.27528			−0.253449			−0.126724	+	0.991938i	$0.540446\pi$
$168$		0			0
$169$	−2.06521	+	1.50046i	−0.158862	+	0.115420i
$170$		0			0
$171$	−8.36026	+	25.7302i	−0.639325	+	1.96764i
$172$		0			0
$173$	16.8284			1.27944			0.639720	−	0.768608i	$-0.279050\pi$
$173$	16.8284			1.27944			0.639720	+	0.768608i	$0.279050\pi$
$174$		0			0
$175$	2.77410	+	2.01550i	0.209702	+	0.152358i
$176$		0			0
$177$	2.09823	+	6.45767i	0.157712	+	0.485389i
$178$		0			0
$179$	9.26947	−	6.73467i	0.692833	−	0.503373i	−0.184757	−	0.982784i	$-0.559150\pi$
$179$	9.26947	−	6.73467i	0.692833	−	0.503373i	0.877590	+	0.479412i	$0.159150\pi$
$180$		0			0
$181$	−0.342373	−	0.248748i	−0.0254484	−	0.0184893i	0.574988	−	0.818162i	$-0.305007\pi$
$181$	−0.342373	−	0.248748i	−0.0254484	−	0.0184893i	−0.600437	+	0.799672i	$0.705007\pi$
$182$		0			0
$183$	−12.2069	+	37.5691i	−0.902363	+	2.77719i
$184$		0			0
$185$	−1.72473	+	5.30817i	−0.126805	+	0.390265i
$186$		0			0
$187$	−7.56965	−	23.2970i	−0.553548	−	1.70364i
$188$		0			0
$189$	−3.86188	+	11.8856i	−0.280910	+	0.864554i
$190$		0			0
$191$	−0.115828			−0.00838106			−0.00419053	−	0.999991i	$-0.501334\pi$
$191$	−0.115828			−0.00838106			−0.00419053	+	0.999991i	$0.501334\pi$
$192$		0			0
$193$	14.5964	−	10.6049i	1.05067	−	0.763359i	0.0783335	−	0.996927i	$-0.475040\pi$
$193$	14.5964	−	10.6049i	1.05067	−	0.763359i	0.972341	+	0.233568i	$0.0750401\pi$
$194$		0			0
$195$	12.6206	+	9.16943i	0.903782	+	0.656636i
$196$		0			0
$197$	−3.79423	−	2.75667i	−0.270327	−	0.196404i	0.444360	−	0.895848i	$-0.353431\pi$
$197$	−3.79423	−	2.75667i	−0.270327	−	0.196404i	−0.714688	+	0.699444i	$0.753431\pi$
$198$		0			0
$199$	0.486159	+	1.49624i	0.0344629	+	0.106066i	0.966808	−	0.255503i	$-0.0822411\pi$
$199$	0.486159	+	1.49624i	0.0344629	+	0.106066i	−0.932345	+	0.361569i	$0.882241\pi$
$200$		0			0
$201$	−22.5321	+	16.3705i	−1.58929	+	1.15469i
$202$		0			0
$203$	−2.19223	−	6.74700i	−0.153865	−	0.473546i
$204$		0			0
$205$	0.397042	−	8.01589i	0.0277306	−	0.559854i
$206$		0			0
$207$	9.68138	+	29.7962i	0.672903	+	2.07098i
$208$		0			0
$209$	−13.4254	+	9.75415i	−0.928656	+	0.674708i
$210$		0			0
$211$	−8.79499	−	27.0682i	−0.605472	−	1.86345i	−0.493512	−	0.869739i	$-0.664287\pi$
$211$	−8.79499	−	27.0682i	−0.605472	−	1.86345i	−0.111961	−	0.993713i	$-0.535713\pi$
$212$		0			0
$213$	33.4282	+	24.2870i	2.29047	+	1.66412i
$214$		0			0
$215$	−11.1641	−	8.11119i	−0.761385	−	0.553179i
$216$		0			0
$217$	7.70828	−	5.60039i	0.523272	−	0.380179i
$218$		0			0
$219$	−40.3623			−2.72743
$220$		0			0
$221$	−6.99263	+	21.5211i	−0.470375	+	1.44767i
$222$		0			0
$223$	2.81394	+	8.66042i	0.188435	+	0.579945i	0.999991	−	0.00433112i	$-0.00137864\pi$
$223$	2.81394	+	8.66042i	0.188435	+	0.579945i	−0.811555	+	0.584276i	$0.801379\pi$
$224$		0			0
$225$	−7.37483	+	22.6974i	−0.491655	+	1.51316i
$226$		0			0
$227$	−5.42725	+	16.7034i	−0.360219	+	1.10864i	0.592701	+	0.805422i	$0.298061\pi$
$227$	−5.42725	+	16.7034i	−0.360219	+	1.10864i	−0.952921	+	0.303219i	$0.901939\pi$
$228$		0			0
$229$	−10.8187	−	7.86025i	−0.714920	−	0.519420i	0.169837	−	0.985472i	$-0.445676\pi$
$229$	−10.8187	−	7.86025i	−0.714920	−	0.519420i	−0.884757	+	0.466052i	$0.845676\pi$
$230$		0			0
$231$	−10.8999	+	7.91928i	−0.717164	+	0.521050i
$232$		0			0
$233$	6.03862	+	18.5850i	0.395603	+	1.21754i	0.928491	+	0.371356i	$0.121107\pi$
$233$	6.03862	+	18.5850i	0.395603	+	1.21754i	−0.532887	+	0.846186i	$0.678893\pi$
$234$		0			0
$235$	−3.26103	−	2.36928i	−0.212726	−	0.154555i
$236$		0			0
$237$	−51.6359			−3.35411
$238$		0			0
$239$	−2.16553	+	6.66482i	−0.140076	+	0.431111i	−0.996345	−	0.0854198i	$-0.972777\pi$
$239$	−2.16553	+	6.66482i	−0.140076	+	0.431111i	0.856269	+	0.516531i	$0.172777\pi$
$240$		0			0
$241$	21.2762	−	15.4580i	1.37052	−	0.995740i	0.372821	−	0.927903i	$-0.378390\pi$
$241$	21.2762	−	15.4580i	1.37052	−	0.995740i	0.997696	−	0.0678364i	$-0.0216096\pi$
$242$		0			0
$243$	−21.0851			−1.35261
$244$		0			0
$245$	−1.25341			−0.0800772
$246$		0			0
$247$	15.3298			0.975410
$248$		0			0
$249$	−13.4992			−0.855480
$250$		0			0
$251$	−14.9309	+	10.8479i	−0.942428	+	0.684714i	−0.949004	−	0.315265i	$-0.897907\pi$
$251$	−14.9309	+	10.8479i	−0.942428	+	0.684714i	0.00657615	+	0.999978i	$0.497907\pi$
$252$		0			0
$253$	−5.93842	+	18.2766i	−0.373345	+	1.14904i
$254$		0			0
$255$	22.6973			1.42136
$256$		0			0
$257$	−12.7564	−	9.26806i	−0.795722	−	0.578126i	0.113934	−	0.993488i	$-0.463655\pi$
$257$	−12.7564	−	9.26806i	−0.795722	−	0.578126i	−0.909656	+	0.415362i	$0.863655\pi$
$258$		0			0
$259$	1.37603	+	4.23500i	0.0855026	+	0.263150i
$260$		0			0
$261$	39.9454	−	29.0220i	2.47256	−	1.79642i
$262$		0			0
$263$	19.3718	+	14.0744i	1.19452	+	0.867866i	0.993734	−	0.111770i	$-0.0356519\pi$
$263$	19.3718	+	14.0744i	1.19452	+	0.867866i	0.200781	+	0.979636i	$0.435652\pi$
$264$		0			0
$265$	0.884759	−	2.72301i	0.0543503	−	0.167273i
$266$		0			0
$267$	0.646684	−	1.99029i	0.0395764	−	0.121804i
$268$		0			0
$269$	4.15058	+	12.7742i	0.253065	+	0.778855i	0.994205	+	0.107504i	$0.0342857\pi$
$269$	4.15058	+	12.7742i	0.253065	+	0.778855i	−0.741139	+	0.671351i	$0.765714\pi$
$270$		0			0
$271$	−3.14388	+	9.67586i	−0.190977	+	0.587767i	−1.00000		1.02693e-5i	$-0.999997\pi$
$271$	−3.14388	+	9.67586i	−0.190977	+	0.587767i	0.809023	+	0.587777i	$0.199997\pi$
$272$		0			0
$273$	12.4461			0.753270
$274$		0			0
$275$	−11.8430	+	8.60442i	−0.714158	+	0.518866i
$276$		0			0
$277$	−16.1314	−	11.7202i	−0.969242	−	0.704196i	−0.0139634	−	0.999903i	$-0.504445\pi$
$277$	−16.1314	−	11.7202i	−0.969242	−	0.704196i	−0.955279	+	0.295707i	$0.904445\pi$
$278$		0			0
$279$	53.6491	+	38.9784i	3.21189	+	2.33357i
$280$		0			0
$281$	−0.538471	−	1.65724i	−0.0321225	−	0.0988628i	0.933710	−	0.358031i	$-0.116552\pi$
$281$	−0.538471	−	1.65724i	−0.0321225	−	0.0988628i	−0.965832	+	0.259168i	$0.916552\pi$
$282$		0			0
$283$	−6.25174	+	4.54216i	−0.371628	+	0.270003i	−0.757886	−	0.652388i	$-0.773767\pi$
$283$	−6.25174	+	4.54216i	−0.371628	+	0.270003i	0.386258	+	0.922391i	$0.373767\pi$
$284$		0			0
$285$	−4.75154	−	14.6237i	−0.281457	−	0.866235i
$286$		0			0
$287$	−3.50278	−	5.36009i	−0.206763	−	0.316396i
$288$		0			0
$289$	4.92072	+	15.1444i	0.289454	+	0.890849i
$290$		0			0
$291$	−16.3091	+	11.8493i	−0.956057	+	0.694616i
$292$		0			0
$293$	2.57054	+	7.91132i	0.150173	+	0.462184i	0.997640	−	0.0686637i	$-0.0218736\pi$
$293$	2.57054	+	7.91132i	0.150173	+	0.462184i	−0.847467	+	0.530848i	$0.821874\pi$
$294$		0			0
$295$	−2.18168	−	1.58508i	−0.127022	−	0.0922871i
$296$		0			0
$297$	−43.1631	−	31.3598i	−2.50458	−	1.81968i
$298$		0			0
$299$	14.3619	−	10.4345i	0.830568	−	0.603443i
$300$		0			0
$301$	−11.0097			−0.634587
$302$		0			0
$303$	4.13588	−	12.7289i	0.237600	−	0.731258i
$304$		0			0
$305$	−4.84809	−	14.9209i	−0.277601	−	0.854367i
$306$		0			0
$307$	3.46507	−	10.6644i	0.197762	−	0.608649i	−0.802171	−	0.597094i	$-0.796322\pi$
$307$	3.46507	−	10.6644i	0.197762	−	0.608649i	0.999933	−	0.0115549i	$-0.00367813\pi$
$308$		0			0
$309$	8.21192	−	25.2737i	0.467160	−	1.43777i
$310$		0			0
$311$	−18.8796	−	13.7168i	−1.07056	−	0.777808i	−0.0945484	−	0.995520i	$-0.530141\pi$
$311$	−18.8796	−	13.7168i	−1.07056	−	0.777808i	−0.976013	+	0.217712i	$0.930141\pi$
$312$		0			0
$313$	−13.9312	+	10.1216i	−0.787439	+	0.572108i	−0.907202	−	0.420694i	$-0.861787\pi$
$313$	−13.9312	+	10.1216i	−0.787439	+	0.572108i	0.119763	+	0.992803i	$0.461787\pi$
$314$		0			0
$315$	−2.69575	−	8.29666i	−0.151888	−	0.467464i
$316$		0			0
$317$	−11.6582	−	8.47017i	−0.654789	−	0.475732i	0.210110	−	0.977678i	$-0.432618\pi$
$317$	−11.6582	−	8.47017i	−0.654789	−	0.475732i	−0.864899	+	0.501946i	$0.832618\pi$
$318$		0			0
$319$	30.2861			1.69569
$320$		0			0
$321$	−5.47712	+	16.8568i	−0.305703	+	0.940857i
$322$		0			0
$323$	18.0445	−	13.1101i	1.00402	−	0.729465i
$324$		0			0
$325$	13.5228			0.750112
$326$		0			0
$327$	17.8241			0.985677
$328$		0			0
$329$	−3.21592			−0.177300
$330$		0			0
$331$	15.7925			0.868036			0.434018	−	0.900904i	$-0.357095\pi$
$331$	15.7925			0.868036			0.434018	+	0.900904i	$0.357095\pi$
$332$		0			0
$333$	−25.0732	+	18.2167i	−1.37400	+	0.998272i
$334$		0			0
$335$	3.41814	−	10.5200i	0.186753	−	0.574766i
$336$		0			0
$337$	33.0218			1.79881			0.899406	−	0.437114i	$-0.143999\pi$
$337$	33.0218			1.79881			0.899406	+	0.437114i	$0.143999\pi$
$338$		0			0
$339$	−35.0283	−	25.4495i	−1.90248	−	1.38223i
$340$		0			0
$341$	12.5696	+	38.6852i	0.680681	+	2.09492i
$342$		0			0
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$		0			0
$345$	−14.4055	−	10.4662i	−0.775564	−	0.563480i
$346$		0			0
$347$	3.23879	−	9.96798i	0.173867	−	0.535109i	−0.825712	−	0.564091i	$-0.809227\pi$
$347$	3.23879	−	9.96798i	0.173867	−	0.535109i	0.999580	+	0.0289822i	$0.00922662\pi$
$348$		0			0
$349$	2.98288	−	9.18036i	0.159670	−	0.491414i	−0.838934	−	0.544233i	$-0.816821\pi$
$349$	2.98288	−	9.18036i	0.159670	−	0.491414i	0.998604	+	0.0528194i	$0.0168208\pi$
$350$		0			0
$351$	15.2301	+	46.8734i	0.812922	+	2.50192i
$352$		0			0
$353$	−7.02245	+	21.6129i	−0.373767	+	1.15034i	0.570539	+	0.821271i	$0.306734\pi$
$353$	−7.02245	+	21.6129i	−0.373767	+	1.15034i	−0.944306	+	0.329067i	$0.893266\pi$
$354$		0			0
$355$	−16.4104			−0.870974
$356$		0			0
$357$	14.6501	−	10.6439i	0.775366	−	0.563336i
$358$		0			0
$359$	10.7688	+	7.82403i	0.568358	+	0.412936i	0.834508	−	0.550995i	$-0.185752\pi$
$359$	10.7688	+	7.82403i	0.568358	+	0.412936i	−0.266150	+	0.963932i	$0.585752\pi$
$360$		0			0
$361$	3.14709	+	2.28649i	0.165636	+	0.120342i
$362$		0			0
$363$	−7.04649	−	21.6869i	−0.369845	−	1.13827i
$364$		0			0
$365$	12.9687	−	9.42232i	0.678813	−	0.493187i
$366$		0			0
$367$	5.37959	+	16.5567i	0.280813	+	0.864252i	0.987623	+	0.156849i	$0.0501335\pi$
$367$	5.37959	+	16.5567i	0.280813	+	0.864252i	−0.706810	+	0.707403i	$0.749866\pi$
$368$		0			0
$369$	27.9464	−	34.7141i	1.45483	−	1.80714i
$370$		0			0
$371$	−0.705884	−	2.17249i	−0.0366477	−	0.112790i
$372$		0			0
$373$	1.77691	−	1.29100i	0.0920051	−	0.0668456i	−0.540832	−	0.841131i	$-0.681890\pi$
$373$	1.77691	−	1.29100i	0.0920051	−	0.0668456i	0.632837	+	0.774285i	$0.281890\pi$
$374$		0			0
$375$	−10.3033	−	31.7103i	−0.532061	−	1.63752i
$376$		0			0
$377$	−22.6342	−	16.4447i	−1.16572	−	0.846946i
$378$		0			0
$379$	23.0535	+	16.7493i	1.18418	+	0.860355i	0.992637	−	0.121130i	$-0.0386518\pi$
$379$	23.0535	+	16.7493i	1.18418	+	0.860355i	0.191540	+	0.981485i	$0.438652\pi$
$380$		0			0
$381$	30.2138	−	21.9516i	1.54790	−	1.12461i
$382$		0			0
$383$	20.1177			1.02796			0.513982	−	0.857801i	$-0.328170\pi$
$383$	20.1177			1.02796			0.513982	+	0.857801i	$0.328170\pi$
$384$		0			0
$385$	1.65353	−	5.08905i	0.0842718	−	0.259362i
$386$		0			0
$387$	−23.6789	−	72.8762i	−1.20367	−	3.70451i
$388$		0			0
$389$	−5.54872	+	17.0772i	−0.281331	+	0.865848i	0.706143	+	0.708069i	$0.250433\pi$
$389$	−5.54872	+	17.0772i	−0.281331	+	0.865848i	−0.987474	+	0.157779i	$0.949567\pi$
$390$		0			0
$391$	7.98155	−	24.5647i	0.403644	−	1.24229i
$392$		0			0
$393$	44.6696	+	32.4544i	2.25328	+	1.63711i
$394$		0			0
$395$	16.5910	−	12.0541i	0.834784	−	0.606506i
$396$		0			0
$397$	−2.36080	−	7.26580i	−0.118485	−	0.364660i	0.874173	−	0.485615i	$-0.161404\pi$
$397$	−2.36080	−	7.26580i	−0.118485	−	0.364660i	−0.992658	+	0.120955i	$0.961404\pi$
$398$		0			0
$399$	−9.92471	−	7.21073i	−0.496857	−	0.360988i
$400$		0			0
$401$	11.1470			0.556655			0.278327	−	0.960486i	$-0.410220\pi$
$401$	11.1470			0.556655			0.278327	+	0.960486i	$0.410220\pi$
$402$		0			0
$403$	11.6114	−	35.7363i	0.578406	−	1.78015i
$404$		0			0
$405$	18.8212	−	13.6744i	0.935235	−	0.679488i
$406$		0			0
$407$	−19.0101			−0.942298
$408$		0			0
$409$	−20.6247			−1.01982			−0.509912	−	0.860226i	$-0.670322\pi$
$409$	−20.6247			−1.01982			−0.509912	+	0.860226i	$0.670322\pi$
$410$		0			0
$411$	−22.7278			−1.12108
$412$		0			0
$413$	−2.15150			−0.105868
$414$		0			0
$415$	4.33741	−	3.15131i	0.212915	−	0.154692i
$416$		0			0
$417$	−6.04032	+	18.5902i	−0.295796	+	0.910366i
$418$		0			0
$419$	−10.7005			−0.522754			−0.261377	−	0.965237i	$-0.584177\pi$
$419$	−10.7005			−0.522754			−0.261377	+	0.965237i	$0.584177\pi$
$420$		0			0
$421$	16.2365	+	11.7965i	0.791320	+	0.574927i	0.908355	−	0.418200i	$-0.137339\pi$
$421$	16.2365	+	11.7965i	0.791320	+	0.574927i	−0.117035	+	0.993128i	$0.537339\pi$
$422$		0			0
$423$	−6.91661	−	21.2871i	−0.336297	−	1.03502i
$424$		0			0
$425$	15.9176	−	11.5648i	0.772116	−	0.560975i
$426$		0			0
$427$	−10.1264	−	7.35724i	−0.490050	−	0.356042i
$428$		0			0
$429$	−16.4192	+	50.5332i	−0.792728	+	2.43977i
$430$		0			0
$431$	−11.1462	+	34.3045i	−0.536894	+	1.65239i	0.202628	+	0.979256i	$0.435052\pi$
$431$	−11.1462	+	34.3045i	−0.536894	+	1.65239i	−0.739521	+	0.673133i	$0.764948\pi$
$432$		0			0
$433$	−4.13561	−	12.7281i	−0.198745	−	0.611673i	−0.999912	−	0.0132333i	$-0.995788\pi$
$433$	−4.13561	−	12.7281i	−0.198745	−	0.611673i	0.801168	−	0.598440i	$-0.204212\pi$
$434$		0			0
$435$	−8.67174	+	26.6889i	−0.415778	+	1.27963i
$436$		0			0
$437$	−17.4977			−0.837030
$438$		0			0
$439$	11.5283	−	8.37577i	0.550214	−	0.399754i	−0.277651	−	0.960682i	$-0.589556\pi$
$439$	11.5283	−	8.37577i	0.550214	−	0.399754i	0.827864	+	0.560928i	$0.189556\pi$
$440$		0			0
$441$	−5.63071	−	4.09095i	−0.268129	−	0.194807i
$442$		0			0
$443$	−8.93886	−	6.49446i	−0.424698	−	0.308561i	0.354827	−	0.934932i	$-0.384540\pi$
$443$	−8.93886	−	6.49446i	−0.424698	−	0.308561i	−0.779525	+	0.626371i	$0.784540\pi$
$444$		0			0
$445$	0.256836	+	0.790459i	0.0121752	+	0.0374714i
$446$		0			0
$447$	12.1418	−	8.82154i	0.574288	−	0.417244i
$448$		0			0
$449$	5.84981	+	18.0039i	0.276070	+	0.849656i	0.988934	+	0.148354i	$0.0473974\pi$
$449$	5.84981	+	18.0039i	0.276070	+	0.849656i	−0.712865	+	0.701302i	$0.752603\pi$
$450$		0			0
$451$	26.3839	−	7.15071i	1.24237	−	0.336714i
$452$		0			0
$453$	22.8397	+	70.2932i	1.07310	+	3.30266i
$454$		0			0
$455$	−3.99901	+	2.90545i	−0.187477	+	0.136210i
$456$		0			0
$457$	2.79119	+	8.59039i	0.130566	+	0.401841i	0.994874	−	0.101122i	$-0.0322432\pi$
$457$	2.79119	+	8.59039i	0.130566	+	0.401841i	−0.864308	+	0.502963i	$0.832243\pi$
$458$		0			0
$459$	58.0135	+	42.1493i	2.70784	+	1.96736i
$460$		0			0
$461$	−24.4117	−	17.7361i	−1.13697	−	0.826055i	−0.150273	−	0.988645i	$-0.548015\pi$
$461$	−24.4117	−	17.7361i	−1.13697	−	0.826055i	−0.986694	+	0.162590i	$0.948015\pi$
$462$		0			0
$463$	−2.61139	+	1.89729i	−0.121362	+	0.0881744i	−0.646810	−	0.762651i	$-0.723897\pi$
$463$	−2.61139	+	1.89729i	−0.121362	+	0.0881744i	0.525449	+	0.850825i	$0.323897\pi$
$464$		0			0
$465$	−37.6894			−1.74781
$466$		0			0
$467$	−1.63165	+	5.02171i	−0.0755038	+	0.232377i	−0.981685	−	0.190514i	$-0.938985\pi$
$467$	−1.63165	+	5.02171i	−0.0755038	+	0.232377i	0.906181	+	0.422891i	$0.138985\pi$
$468$		0			0
$469$	−2.72708	−	8.39309i	−0.125925	−	0.387557i
$470$		0			0
$471$	−11.1956	+	34.4564i	−0.515864	+	1.58767i
$472$		0			0
$473$	14.5243	−	44.7012i	0.667828	−	2.05536i
$474$		0			0
$475$	−10.7834	−	7.83456i	−0.494774	−	0.359474i
$476$		0			0
$477$	12.8622	−	9.34490i	0.588918	−	0.427874i
$478$		0			0
$479$	6.47986	+	19.9430i	0.296072	+	0.911217i	0.982859	+	0.184358i	$0.0590207\pi$
$479$	6.47986	+	19.9430i	0.296072	+	0.911217i	−0.686787	+	0.726859i	$0.740979\pi$
$480$		0			0
$481$	14.2072	+	10.3221i	0.647792	+	0.470648i
$482$		0			0
$483$	−14.2062			−0.646405
$484$		0			0
$485$	2.47411	−	7.61451i	0.112343	−	0.345757i
$486$		0			0
$487$	−22.8425	+	16.5960i	−1.03509	+	0.752038i	−0.969321	−	0.245797i	$-0.920950\pi$
$487$	−22.8425	+	16.5960i	−1.03509	+	0.752038i	−0.0657703	+	0.997835i	$0.520950\pi$
$488$		0			0
$489$	23.2356			1.05075
$490$		0			0
$491$	−31.2287			−1.40933			−0.704665	−	0.709540i	$-0.748903\pi$
$491$	−31.2287			−1.40933			−0.704665	+	0.709540i	$0.748903\pi$
$492$		0			0
$493$	−40.7061			−1.83331
$494$		0			0
$495$	37.2422			1.67391
$496$		0			0
$497$	−10.5922	+	7.69567i	−0.475124	+	0.345198i
$498$		0			0
$499$	−1.41863	+	4.36609i	−0.0635066	+	0.195453i	−0.977776	−	0.209655i	$-0.932766\pi$
$499$	−1.41863	+	4.36609i	−0.0635066	+	0.195453i	0.914269	+	0.405108i	$0.132766\pi$
$500$		0			0
$501$	10.3366			0.461804
$502$		0			0
$503$	−21.7226	−	15.7824i	−0.968563	−	0.703702i	−0.0134395	−	0.999910i	$-0.504278\pi$
$503$	−21.7226	−	15.7824i	−0.968563	−	0.703702i	−0.955124	+	0.296207i	$0.904278\pi$
$504$		0			0
$505$	1.64260	+	5.05539i	0.0730946	+	0.224962i
$506$		0			0
$507$	6.51768	−	4.73537i	0.289460	−	0.210305i
$508$		0			0
$509$	11.2782	+	8.19409i	0.499897	+	0.363197i	0.808978	−	0.587839i	$-0.200021\pi$
$509$	11.2782	+	8.19409i	0.499897	+	0.363197i	−0.309080	+	0.951036i	$0.600021\pi$
$510$		0			0
$511$	3.95212	−	12.1634i	0.174831	−	0.538076i
$512$		0			0
$513$	15.0117	−	46.2014i	0.662784	−	2.03984i
$514$		0			0
$515$	3.26143	+	10.0376i	0.143716	+	0.442312i
$516$		0			0
$517$	4.24255	−	13.0572i	0.186587	−	0.574256i
$518$		0			0
$519$	−53.1094			−2.33124
$520$		0			0
$521$	−14.8024	+	10.7546i	−0.648507	+	0.471168i	−0.862762	−	0.505610i	$-0.831267\pi$
$521$	−14.8024	+	10.7546i	−0.648507	+	0.471168i	0.214256	+	0.976778i	$0.431267\pi$
$522$		0			0
$523$	16.3298	+	11.8643i	0.714054	+	0.518791i	0.884479	−	0.466580i	$-0.154514\pi$
$523$	16.3298	+	11.8643i	0.714054	+	0.518791i	−0.170425	+	0.985371i	$0.554514\pi$
$524$		0			0
$525$	−8.75488	−	6.36079i	−0.382094	−	0.277608i
$526$		0			0
$527$	−16.8942	−	51.9949i	−0.735922	−	2.26493i
$528$		0			0
$529$	2.21444	−	1.60888i	0.0962799	−	0.0699514i
$530$		0			0
$531$	−4.62732	−	14.2414i	−0.200808	−	0.618025i
$532$		0			0
$533$	−23.6006	−	8.98184i	−1.02226	−	0.389047i
$534$		0			0
$535$	−2.17528	−	6.69483i	−0.0940456	−	0.289443i
$536$		0			0
$537$	−29.2539	+	21.2542i	−1.26240	+	0.917185i
$538$		0			0
$539$	−1.31923	−	4.06018i	−0.0568233	−	0.174884i
$540$		0			0
$541$	17.4266	+	12.6611i	0.749226	+	0.544345i	0.895587	−	0.444887i	$-0.146756\pi$
$541$	17.4266	+	12.6611i	0.749226	+	0.544345i	−0.146361	+	0.989231i	$0.546756\pi$
$542$		0			0
$543$	1.08051	+	0.785034i	0.0463690	+	0.0336890i
$544$		0			0
$545$	−5.72703	+	4.16093i	−0.245319	+	0.178235i
$546$		0			0
$547$	28.3546			1.21236			0.606178	−	0.795329i	$-0.292702\pi$
$547$	28.3546			1.21236			0.606178	+	0.795329i	$0.292702\pi$
$548$		0			0
$549$	26.9205	−	82.8529i	1.14894	−	3.53608i
$550$		0			0
$551$	8.52155	+	26.2266i	0.363030	+	1.11729i
$552$		0			0
$553$	5.05599	−	15.5607i	0.215002	−	0.661709i
$554$		0			0
$555$	5.44314	−	16.7523i	0.231048	−	0.711094i
$556$		0			0
$557$	−8.04817	−	5.84733i	−0.341012	−	0.247760i	0.404077	−	0.914725i	$-0.367593\pi$
$557$	−8.04817	−	5.84733i	−0.341012	−	0.247760i	−0.745089	+	0.666966i	$0.767593\pi$
$558$		0			0
$559$	−35.1265	+	25.5209i	−1.48569	+	1.07942i
$560$		0			0
$561$	23.8893	+	73.5238i	1.00861	+	3.10418i
$562$		0			0
$563$	35.7511	+	25.9747i	1.50673	+	1.09470i	0.967603	+	0.252476i	$0.0812448\pi$
$563$	35.7511	+	25.9747i	1.50673	+	1.09470i	0.539125	+	0.842226i	$0.318755\pi$
$564$		0			0
$565$	17.1959			0.723436
$566$		0			0
$567$	5.73563	−	17.6525i	0.240874	−	0.741334i
$568$		0			0
$569$	−5.25165	+	3.81555i	−0.220161	+	0.159956i	−0.692399	−	0.721515i	$-0.743446\pi$
$569$	−5.25165	+	3.81555i	−0.220161	+	0.159956i	0.472238	+	0.881471i	$0.343446\pi$
$570$		0			0
$571$	−16.4108			−0.686772			−0.343386	−	0.939194i	$-0.611574\pi$
$571$	−16.4108			−0.686772			−0.343386	+	0.939194i	$0.611574\pi$
$572$		0			0
$573$	0.365547			0.0152710
$574$		0			0
$575$	−15.4353			−0.643695
$576$		0			0
$577$	−9.91315			−0.412690			−0.206345	−	0.978479i	$-0.566157\pi$
$577$	−9.91315			−0.412690			−0.206345	+	0.978479i	$0.566157\pi$
$578$		0			0
$579$	−46.0654	+	33.4685i	−1.91441	+	1.39090i
$580$		0			0
$581$	1.32179	−	4.06806i	0.0548372	−	0.168772i
$582$		0			0
$583$	9.75190			0.403883
$584$		0			0
$585$	−27.8329	−	20.2218i	−1.15075	−	0.836067i
$586$		0			0
$587$	10.7516	+	33.0901i	0.443767	+	1.36577i	0.883830	+	0.467807i	$0.154956\pi$
$587$	10.7516	+	33.0901i	0.443767	+	1.36577i	−0.440064	+	0.897967i	$0.645044\pi$
$588$		0			0
$589$	−29.9633	+	21.7696i	−1.23462	+	0.897001i
$590$		0			0
$591$	11.9743	+	8.69987i	0.492559	+	0.357865i
$592$		0			0
$593$	−0.358209	+	1.10246i	−0.0147099	+	0.0452724i	−0.958142	−	0.286293i	$-0.907577\pi$
$593$	−0.358209	+	1.10246i	−0.0147099	+	0.0452724i	0.943432	+	0.331566i	$0.107577\pi$
$594$		0			0
$595$	−2.22243	+	6.83995i	−0.0911109	+	0.280411i
$596$		0			0
$597$	−1.53429	−	4.72205i	−0.0627942	−	0.193261i
$598$		0			0
$599$	9.75854	−	30.0337i	0.398723	−	1.22714i	−0.527301	−	0.849679i	$-0.676796\pi$
$599$	9.75854	−	30.0337i	0.398723	−	1.22714i	0.926024	−	0.377465i	$-0.123204\pi$
$600$		0			0
$601$	−7.43552			−0.303301			−0.151651	−	0.988434i	$-0.548459\pi$
$601$	−7.43552			−0.303301			−0.151651	+	0.988434i	$0.548459\pi$
$602$		0			0
$603$	49.6911	−	36.1027i	2.02358	−	1.47022i
$604$		0			0
$605$	7.32675	+	5.32320i	0.297875	+	0.216419i
$606$		0			0
$607$	−8.60764	−	6.25382i	−0.349374	−	0.253835i	0.399233	−	0.916850i	$-0.369277\pi$
$607$	−8.60764	−	6.25382i	−0.349374	−	0.253835i	−0.748606	+	0.663015i	$0.769277\pi$
$608$		0			0
$609$	6.91855	+	21.2931i	0.280354	+	0.862840i
$610$		0			0
$611$	−10.2605	+	7.45466i	−0.415094	+	0.301583i
$612$		0			0
$613$	3.46086	+	10.6514i	0.139783	+	0.430207i	0.996303	−	0.0859058i	$-0.0273784\pi$
$613$	3.46086	+	10.6514i	0.139783	+	0.430207i	−0.856520	+	0.516113i	$0.827378\pi$
$614$		0			0
$615$	−1.25304	+	25.2976i	−0.0505275	+	1.02010i
$616$		0			0
$617$	−9.53414	−	29.3431i	−0.383830	−	1.18131i	−0.937326	−	0.348455i	$-0.886706\pi$
$617$	−9.53414	−	29.3431i	−0.383830	−	1.18131i	0.553496	−	0.832852i	$-0.313294\pi$
$618$		0			0
$619$	12.8947	−	9.36857i	0.518283	−	0.376555i	−0.297674	−	0.954668i	$-0.596211\pi$
$619$	12.8947	−	9.36857i	0.518283	−	0.376555i	0.815957	+	0.578113i	$0.196211\pi$
$620$		0			0
$621$	−17.3840	−	53.5023i	−0.697594	−	2.14697i
$622$		0			0
$623$	0.536462	+	0.389763i	0.0214929	+	0.0156155i
$624$		0			0
$625$	−3.15738	−	2.29397i	−0.126295	−	0.0917588i
$626$		0			0
$627$	42.3698	−	30.7835i	1.69209	−	1.22937i
$628$		0			0
$629$	25.5506			1.01877
$630$		0			0
$631$	14.2326	−	43.8033i	0.566589	−	1.74378i	−0.0965917	−	0.995324i	$-0.530794\pi$
$631$	14.2326	−	43.8033i	0.566589	−	1.74378i	0.663181	−	0.748459i	$-0.269206\pi$
$632$		0			0
$633$	27.7564	+	85.4255i	1.10322	+	3.39536i
$634$		0			0
$635$	−4.58346	+	14.1064i	−0.181889	+	0.559796i
$636$		0			0
$637$	−1.21867	+	3.75068i	−0.0482854	+	0.148607i
$638$		0			0
$639$	−73.7209	−	53.5614i	−2.91635	−	2.11885i
$640$		0			0
$641$	−24.7826	+	18.0056i	−0.978852	+	0.711178i	−0.957452	−	0.288593i	$-0.906813\pi$
$641$	−24.7826	+	18.0056i	−0.978852	+	0.711178i	−0.0214006	+	0.999771i	$0.506813\pi$
$642$		0			0
$643$	14.4701	+	44.5344i	0.570645	+	1.75626i	0.650552	+	0.759461i	$0.274537\pi$
$643$	14.4701	+	44.5344i	0.570645	+	1.75626i	−0.0799079	+	0.996802i	$0.525463\pi$
$644$		0			0
$645$	35.2332	+	25.5984i	1.38731	+	1.00794i
$646$		0			0
$647$	20.2921			0.797766			0.398883	−	0.917002i	$-0.369398\pi$
$647$	20.2921			0.797766			0.398883	+	0.917002i	$0.369398\pi$
$648$		0			0
$649$	2.83833	−	8.73547i	0.111414	−	0.342897i
$650$		0			0
$651$	−24.3268	+	17.6745i	−0.953444	+	0.692717i
$652$		0			0
$653$	−9.59929			−0.375649			−0.187825	−	0.982203i	$-0.560144\pi$
$653$	−9.59929			−0.375649			−0.187825	+	0.982203i	$0.560144\pi$
$654$		0			0
$655$	−21.9289			−0.856835
$656$		0			0
$657$	89.0128			3.47272
$658$		0			0
$659$	−45.3125			−1.76512			−0.882561	−	0.470197i	$-0.844183\pi$
$659$	−45.3125			−1.76512			−0.882561	+	0.470197i	$0.844183\pi$
$660$		0			0
$661$	−14.6319	+	10.6307i	−0.569116	+	0.413487i	−0.834784	−	0.550577i	$-0.814408\pi$
$661$	−14.6319	+	10.6307i	−0.569116	+	0.413487i	0.265668	+	0.964065i	$0.414408\pi$
$662$		0			0
$663$	22.0683	−	67.9193i	0.857062	−	2.63777i
$664$		0			0
$665$	4.87218			0.188935
$666$		0			0
$667$	25.8352	+	18.7704i	1.00034	+	0.726791i
$668$		0			0
$669$	−8.88062	−	27.3317i	−0.343345	−	1.05671i
$670$		0			0
$671$	43.2307	−	31.4090i	1.66890	−	1.21253i
$672$		0			0
$673$	3.15809	+	2.29449i	0.121735	+	0.0884459i	0.646987	−	0.762501i	$-0.276029\pi$
$673$	3.15809	+	2.29449i	0.121735	+	0.0884459i	−0.525252	+	0.850947i	$0.676029\pi$
$674$		0			0
$675$	13.2423	−	40.7556i	0.509696	−	1.56868i
$676$		0			0
$677$	1.22645	−	3.77461i	0.0471361	−	0.145070i	−0.924718	−	0.380652i	$-0.875700\pi$
$677$	1.22645	−	3.77461i	0.0471361	−	0.145070i	0.971854	+	0.235582i	$0.0756996\pi$
$678$		0			0
$679$	−1.97391	−	6.07506i	−0.0757516	−	0.233139i
$680$		0			0
$681$	17.1281	−	52.7148i	0.656349	−	2.02003i
$682$		0			0
$683$	−35.3123			−1.35119			−0.675594	−	0.737273i	$-0.736113\pi$
$683$	−35.3123			−1.35119			−0.675594	+	0.737273i	$0.736113\pi$
$684$		0			0
$685$	7.30260	−	5.30565i	0.279018	−	0.202718i
$686$		0			0
$687$	34.1432	+	24.8065i	1.30264	+	0.946425i
$688$		0			0
$689$	−7.28806	−	5.29509i	−0.277653	−	0.201727i
$690$		0			0
$691$	5.78326	+	17.7990i	0.220006	+	0.677108i	0.998760	+	0.0497790i	$0.0158517\pi$
$691$	5.78326	+	17.7990i	0.220006	+	0.677108i	−0.778755	+	0.627329i	$0.784148\pi$
$692$		0			0
$693$	24.0382	−	17.4648i	0.913135	−	0.663431i
$694$		0			0
$695$	−2.39896	−	7.38325i	−0.0909978	−	0.280063i
$696$		0			0
$697$	−35.4613	+	9.61094i	−1.34319	+	0.364040i
$698$		0			0
$699$	−19.0575	−	58.6530i	−0.720821	−	2.21846i
$700$		0			0
$701$	9.81990	−	7.13457i	0.370892	−	0.269469i	−0.386689	−	0.922210i	$-0.626381\pi$
$701$	9.81990	−	7.13457i	0.370892	−	0.269469i	0.757581	+	0.652741i	$0.226381\pi$
$702$		0			0
$703$	−5.34886	−	16.4621i	−0.201736	−	0.620880i
$704$		0			0
$705$	10.2916	+	7.47729i	0.387605	+	0.281611i
$706$		0			0
$707$	3.43095	+	2.49273i	0.129034	+	0.0937489i
$708$		0			0
$709$	−4.08504	+	2.96795i	−0.153417	+	0.111464i	−0.661846	−	0.749640i	$-0.730227\pi$
$709$	−4.08504	+	2.96795i	−0.153417	+	0.111464i	0.508429	+	0.861104i	$0.330227\pi$
$710$		0			0
$711$	113.875			4.27065
$712$		0			0
$713$	−13.2535	+	40.7902i	−0.496349	+	1.52760i
$714$		0			0
$715$	−6.52103	−	20.0697i	−0.243873	−	0.750563i
$716$		0			0
$717$	6.83427	−	21.0337i	0.255231	−	0.785519i
$718$		0			0
$719$	−11.8523	+	36.4776i	−0.442015	+	1.36038i	0.443709	+	0.896171i	$0.353663\pi$
$719$	−11.8523	+	36.4776i	−0.442015	+	1.36038i	−0.885724	+	0.464212i	$0.846337\pi$
$720$		0			0
$721$	6.81226	+	4.94940i	0.253702	+	0.184325i
$722$		0			0
$723$	−67.1462	+	48.7846i	−2.49719	+	1.81432i
$724$		0			0
$725$	7.51711	+	23.1353i	0.279178	+	0.859223i
$726$		0			0
$727$	18.9155	+	13.7429i	0.701537	+	0.509697i	0.880433	−	0.474171i	$-0.157252\pi$
$727$	18.9155	+	13.7429i	0.701537	+	0.509697i	−0.178895	+	0.983868i	$0.557252\pi$
$728$		0			0
$729$	10.8606			0.402243
$730$		0			0
$731$	−19.5214	+	60.0808i	−0.722026	+	2.22217i
$732$		0			0
$733$	1.76394	−	1.28158i	0.0651526	−	0.0473361i	−0.554732	−	0.832029i	$-0.687179\pi$
$733$	1.76394	−	1.28158i	0.0651526	−	0.0473361i	0.619885	+	0.784693i	$0.287179\pi$
$734$		0			0
$735$	3.95567			0.145907
$736$		0			0
$737$	37.6751			1.38778
$738$		0			0
$739$	38.0739			1.40057			0.700285	−	0.713864i	$-0.253056\pi$
$739$	38.0739			1.40057			0.700285	+	0.713864i	$0.253056\pi$
$740$		0			0
$741$	−48.3798			−1.77728
$742$		0			0
$743$	−34.3086	+	24.9266i	−1.25866	+	0.914470i	−0.998691	−	0.0511471i	$-0.983712\pi$
$743$	−34.3086	+	24.9266i	−1.25866	+	0.914470i	−0.259969	+	0.965617i	$0.583712\pi$
$744$		0			0
$745$	−1.84192	+	5.66885i	−0.0674828	+	0.207691i
$746$		0			0
$747$	29.7705			1.08925
$748$		0			0
$749$	−4.54359	−	3.30111i	−0.166019	−	0.120620i
$750$		0			0
$751$	−0.103612	−	0.318885i	−0.00378086	−	0.0116363i	0.949148	−	0.314829i	$-0.101947\pi$
$751$	−0.103612	−	0.318885i	−0.00378086	−	0.0116363i	−0.952929	+	0.303193i	$0.901947\pi$
$752$		0			0
$753$	47.1209	−	34.2353i	1.71718	−	1.24760i
$754$		0			0
$755$	−23.7481	−	17.2540i	−0.864281	−	0.627937i
$756$		0			0
$757$	3.72787	−	11.4732i	0.135492	−	0.417000i	−0.860175	−	0.510000i	$-0.829645\pi$
$757$	3.72787	−	11.4732i	0.135492	−	0.417000i	0.995666	+	0.0929995i	$0.0296455\pi$
$758$		0			0
$759$	18.7413	−	57.6797i	0.680265	−	2.09364i
$760$		0			0
$761$	2.34379	+	7.21344i	0.0849623	+	0.261487i	0.984508	−	0.175340i	$-0.0561023\pi$
$761$	2.34379	+	7.21344i	0.0849623	+	0.261487i	−0.899546	+	0.436827i	$0.856102\pi$
$762$		0			0
$763$	−1.74527	+	5.37139i	−0.0631830	+	0.194457i
$764$		0			0
$765$	−50.0555			−1.80976
$766$		0			0
$767$	−6.86440	+	4.98728i	−0.247859	+	0.180080i
$768$		0			0
$769$	8.25907	+	6.00057i	0.297830	+	0.216386i	0.726657	−	0.687001i	$-0.241073\pi$
$769$	8.25907	+	6.00057i	0.297830	+	0.216386i	−0.428827	+	0.903387i	$0.641073\pi$
$770$		0			0
$771$	40.2584	+	29.2494i	1.44987	+	1.05339i
$772$		0			0
$773$	−2.77789	−	8.54947i	−0.0999138	−	0.307503i	0.888589	−	0.458704i	$-0.151686\pi$
$773$	−2.77789	−	8.54947i	−0.0999138	−	0.307503i	−0.988503	+	0.151201i	$0.951686\pi$
$774$		0			0
$775$	−26.4315	+	19.2036i	−0.949447	+	0.689814i
$776$		0			0
$777$	−4.34268	−	13.3654i	−0.155793	−	0.479481i
$778$		0			0
$779$	13.6159	+	20.8355i	0.487839	+	0.746509i
$780$		0			0
$781$	−17.2722	−	53.1585i	−0.618049	−	1.90216i
$782$		0			0
$783$	−71.7263	+	52.1122i	−2.56329	+	1.86234i
$784$		0			0
$785$	−4.44641	−	13.6846i	−0.158699	−	0.488425i
$786$		0			0
$787$	−3.82743	−	2.78079i	−0.136433	−	0.0991245i	0.517475	−	0.855698i	$-0.326872\pi$
$787$	−3.82743	−	2.78079i	−0.136433	−	0.0991245i	−0.653909	+	0.756574i	$0.726872\pi$
$788$		0			0
$789$	−61.1361	−	44.4180i	−2.17650	−	1.58132i
$790$		0			0
$791$	11.0992	−	8.06402i	0.394641	−	0.286724i
$792$		0			0
$793$	−49.3628			−1.75292
$794$		0			0
$795$	−2.79224	+	8.59364i	−0.0990306	+	0.304785i
$796$		0			0
$797$	−5.14868	−	15.8460i	−0.182376	−	0.561295i	0.817518	−	0.575904i	$-0.195350\pi$
$797$	−5.14868	−	15.8460i	−0.182376	−	0.561295i	−0.999893	+	0.0146089i	$0.995350\pi$
$798$		0			0
$799$	−5.70221	+	17.5496i	−0.201730	+	0.620860i
$800$		0			0
$801$	−1.42616	+	4.38928i	−0.0503910	+	0.155088i
$802$		0			0
$803$	44.1716	+	32.0926i	1.55878	+	1.13252i
$804$		0			0
$805$	4.56456	−	3.31635i	0.160880	−	0.116886i
$806$		0			0
$807$	−13.0990	−	40.3145i	−0.461105	−	1.41914i
$808$		0			0
$809$	−33.9364	−	24.6562i	−1.19314	−	0.866867i	−0.199547	−	0.979888i	$-0.563947\pi$
$809$	−33.9364	−	24.6562i	−1.19314	−	0.866867i	−0.993593	+	0.113022i	$0.963947\pi$
$810$		0			0
$811$	15.4768			0.543466			0.271733	−	0.962373i	$-0.412403\pi$
$811$	15.4768			0.543466			0.271733	+	0.962373i	$0.412403\pi$
$812$		0			0
$813$	9.92188	−	30.5364i	0.347975	−	1.07096i
$814$		0			0
$815$	−7.46576	+	5.42419i	−0.261514	+	0.190001i
$816$		0			0
$817$	42.7963			1.49725
$818$		0			0
$819$	−27.4479			−0.959106
$820$		0			0
$821$	24.0868			0.840636			0.420318	−	0.907377i	$-0.361919\pi$
$821$	24.0868			0.840636			0.420318	+	0.907377i	$0.361919\pi$
$822$		0			0
$823$	−26.9985			−0.941109			−0.470555	−	0.882371i	$-0.655946\pi$
$823$	−26.9985			−0.941109			−0.470555	+	0.882371i	$0.655946\pi$
$824$		0			0
$825$	37.3756	−	27.1550i	1.30125	−	0.945416i
$826$		0			0
$827$	10.1841	−	31.3435i	0.354137	−	1.08992i	−0.602372	−	0.798216i	$-0.705777\pi$
$827$	10.1841	−	31.3435i	0.354137	−	1.08992i	0.956508	−	0.291705i	$-0.0942225\pi$
$828$		0			0
$829$	35.0194			1.21627			0.608137	−	0.793832i	$-0.291917\pi$
$829$	35.0194			1.21627			0.608137	+	0.793832i	$0.291917\pi$
$830$		0			0
$831$	50.9097	+	36.9881i	1.76604	+	1.28310i
$832$		0			0
$833$	1.77312	+	5.45709i	0.0614349	+	0.189077i
$834$		0			0
$835$	−3.32122	+	2.41301i	−0.114936	+	0.0835056i
$836$		0			0
$837$	−96.3327	−	69.9898i	−3.32975	−	2.41920i
$838$		0			0
$839$	2.22305	−	6.84185i	0.0767483	−	0.236207i	−0.905321	−	0.424729i	$-0.860370\pi$
$839$	2.22305	−	6.84185i	0.0767483	−	0.236207i	0.982069	+	0.188522i	$0.0603695\pi$
$840$		0			0
$841$	6.59066	−	20.2840i	0.227264	−	0.699448i
$842$		0			0
$843$	1.69938	+	5.23015i	0.0585298	+	0.180136i
$844$		0			0
$845$	−0.988738	+	3.04302i	−0.0340136	+	0.104683i
$846$		0			0
$847$	7.22540			0.248268
$848$		0			0
$849$	19.7301	−	14.3348i	0.677135	−	0.491968i
$850$		0			0
$851$	−16.2164	−	11.7819i	−0.555891	−	0.403878i
$852$		0			0
$853$	15.2568	+	11.0847i	0.522382	+	0.379532i	0.817500	−	0.575928i	$-0.195359\pi$
$853$	15.2568	+	11.0847i	0.522382	+	0.379532i	−0.295119	+	0.955461i	$0.595359\pi$
$854$		0			0
$855$	10.4788	+	32.2504i	0.358367	+	1.10294i
$856$		0			0
$857$	−30.5545	+	22.1992i	−1.04372	+	0.758310i	−0.971009	−	0.239043i	$-0.923166\pi$
$857$	−30.5545	+	22.1992i	−1.04372	+	0.758310i	−0.0727146	+	0.997353i	$0.523166\pi$
$858$		0			0
$859$	−7.38427	−	22.7265i	−0.251948	−	0.775417i	−0.994416	−	0.105535i	$-0.966345\pi$
$859$	−7.38427	−	22.7265i	−0.251948	−	0.775417i	0.742468	−	0.669882i	$-0.233655\pi$
$860$		0			0
$861$	11.0546	+	16.9161i	0.376738	+	0.576499i
$862$		0			0
$863$	−1.04880	−	3.22788i	−0.0357017	−	0.109878i	0.931618	−	0.363440i	$-0.118398\pi$
$863$	−1.04880	−	3.22788i	−0.0357017	−	0.109878i	−0.967319	+	0.253562i	$0.918398\pi$
$864$		0			0
$865$	17.0645	−	12.3980i	0.580209	−	0.421546i
$866$		0			0
$867$	−15.5295	−	47.7949i	−0.527409	−	1.62320i
$868$		0			0
$869$	56.5093	+	41.0564i	1.91695	+	1.39274i
$870$		0			0
$871$	−28.1564	−	20.4568i	−0.954043	−	0.693153i
$872$		0			0
$873$	35.9672	−	26.1317i	1.21731	−	0.884425i
$874$		0			0
$875$	10.5649			0.357160
$876$		0			0
$877$	11.7764	−	36.2441i	0.397661	−	1.22388i	−0.529208	−	0.848492i	$-0.677511\pi$
$877$	11.7764	−	36.2441i	0.397661	−	1.22388i	0.926869	−	0.375384i	$-0.122489\pi$
$878$		0			0
$879$	−8.11247	−	24.9676i	−0.273627	−	0.842137i
$880$		0			0
$881$	0.473874	−	1.45844i	0.0159652	−	0.0491359i	−0.942757	−	0.333482i	$-0.891776\pi$
$881$	0.473874	−	1.45844i	0.0159652	−	0.0491359i	0.958722	+	0.284346i	$0.0917764\pi$
$882$		0			0
$883$	4.11917	−	12.6775i	0.138621	−	0.426632i	−0.857515	−	0.514460i	$-0.827993\pi$
$883$	4.11917	−	12.6775i	0.138621	−	0.426632i	0.996136	+	0.0878277i	$0.0279925\pi$
$884$		0			0
$885$	6.88524	+	5.00242i	0.231445	+	0.168155i
$886$		0			0
$887$	−15.5796	+	11.3192i	−0.523112	+	0.380063i	−0.817775	−	0.575538i	$-0.804793\pi$
$887$	−15.5796	+	11.3192i	−0.523112	+	0.380063i	0.294663	+	0.955601i	$0.404793\pi$
$888$		0			0
$889$	3.65680	+	11.2545i	0.122645	+	0.377463i
$890$		0			0
$891$	64.1055	+	46.5754i	2.14762	+	1.56033i
$892$		0			0
$893$	12.5008			0.418323
$894$		0			0
$895$	4.43784	−	13.6583i	0.148341	−	0.456545i
$896$		0			0
$897$	−45.3251	+	32.9306i	−1.51336	+	1.09952i
$898$		0			0
$899$	67.5933			2.25436
$900$		0			0
$901$	−13.1071			−0.436660
$902$		0			0
$903$	34.7458			1.15627
$904$		0			0
$905$	−0.530436			−0.0176323
$906$		0			0
$907$	−35.5563	+	25.8332i	−1.18063	+	0.857776i	−0.992242	−	0.124319i	$-0.960325\pi$
$907$	−35.5563	+	25.8332i	−1.18063	+	0.857776i	−0.188385	+	0.982095i	$0.560325\pi$
$908$		0			0
$909$	−9.12105	+	28.0717i	−0.302526	+	0.931079i
$910$		0			0
$911$	−10.5889			−0.350827			−0.175413	−	0.984495i	$-0.556126\pi$
$911$	−10.5889			−0.350827			−0.175413	+	0.984495i	$0.556126\pi$
$912$		0			0
$913$	14.7733	+	10.7334i	0.488925	+	0.355225i
$914$		0			0
$915$	15.3003	+	47.0893i	0.505811	+	1.55673i
$916$		0			0
$917$	−14.1541	+	10.2836i	−0.467411	+	0.339594i
$918$		0			0
$919$	−28.0842	−	20.4043i	−0.926411	−	0.673077i	0.0187005	−	0.999825i	$-0.494047\pi$
$919$	−28.0842	−	20.4043i	−0.926411	−	0.673077i	−0.945111	+	0.326748i	$0.894047\pi$
$920$		0			0
$921$	−10.9355	+	33.6561i	−0.360338	+	1.10901i
$922$		0			0
$923$	−15.9556	+	49.1063i	−0.525185	+	1.61635i
$924$		0			0
$925$	−4.71839	−	14.5217i	−0.155140	−	0.477471i
$926$		0			0
$927$	−18.1101	+	55.7372i	−0.594815	+	1.83065i
$928$		0			0
$929$	−25.4227			−0.834090			−0.417045	−	0.908886i	$-0.636934\pi$
$929$	−25.4227			−0.834090			−0.417045	+	0.908886i	$0.636934\pi$
$930$		0			0
$931$	3.14478	−	2.28481i	0.103066	−	0.0748817i
$932$		0			0
$933$	59.5827	+	43.2894i	1.95065	+	1.41723i
$934$		0			0
$935$	−24.8395	−	18.0470i	−0.812339	−	0.590198i
$936$		0			0
$937$	−1.85865	−	5.72034i	−0.0607195	−	0.186875i	0.916096	−	0.400960i	$-0.131323\pi$
$937$	−1.85865	−	5.72034i	−0.0607195	−	0.186875i	−0.976815	+	0.214084i	$0.931323\pi$
$938$		0			0
$939$	43.9661	−	31.9432i	1.43478	−	1.04243i
$940$		0			0
$941$	18.2109	+	56.0473i	0.593657	+	1.82709i	0.561299	+	0.827613i	$0.310302\pi$
$941$	18.2109	+	56.0473i	0.593657	+	1.82709i	0.0323586	+	0.999476i	$0.489698\pi$
$942$		0			0
$943$	26.9383	+	10.2521i	0.877231	+	0.333853i
$944$		0			0
$945$	4.84050	+	14.8975i	0.157462	+	0.484617i
$946$		0			0
$947$	−1.65803	+	1.20463i	−0.0538787	+	0.0391452i	−0.614399	−	0.788996i	$-0.710601\pi$
$947$	−1.65803	+	1.20463i	−0.0538787	+	0.0391452i	0.560520	+	0.828141i	$0.310601\pi$
$948$		0			0
$949$	−15.5859	−	47.9686i	−0.505941	−	1.55713i
$950$		0			0
$951$	36.7925	+	26.7313i	1.19308	+	0.866823i
$952$		0			0
$953$	9.79766	+	7.11842i	0.317377	+	0.230588i	0.735056	−	0.678007i	$-0.237156\pi$
$953$	9.79766	+	7.11842i	0.317377	+	0.230588i	−0.417678	+	0.908595i	$0.637156\pi$
$954$		0			0
$955$	−0.117453	+	0.0853347i	−0.00380070	+	0.00276137i
$956$		0			0
$957$	−95.5809			−3.08969
$958$		0			0
$959$	2.22541	−	6.84912i	0.0718623	−	0.221169i
$960$		0			0
$961$	18.4736	+	56.8560i	0.595924	+	1.83406i
$962$		0			0
$963$	12.0789	−	37.1752i	0.389239	−	1.19795i
$964$		0			0
$965$	6.98816	−	21.5074i	0.224957	−	0.692346i
$966$		0			0
$967$	−8.35958	−	6.07359i	−0.268826	−	0.195314i	0.445203	−	0.895430i	$-0.353132\pi$
$967$	−8.35958	−	6.07359i	−0.268826	−	0.195314i	−0.714029	+	0.700116i	$0.753132\pi$
$968$		0			0
$969$	−56.9473	+	41.3746i	−1.82941	+	1.32914i
$970$		0			0
$971$	−15.9721	−	49.1571i	−0.512569	−	1.57753i	−0.787661	−	0.616108i	$-0.788708\pi$
$971$	−15.9721	−	49.1571i	−0.512569	−	1.57753i	0.275092	−	0.961418i	$-0.411292\pi$
$972$		0			0
$973$	−5.01080	−	3.64056i	−0.160639	−	0.116711i
$974$		0			0
$975$	−42.6772			−1.36676
$976$		0			0
$977$	−1.86820	+	5.74973i	−0.0597690	+	0.183950i	−0.976483	−	0.215594i	$-0.930831\pi$
$977$	−1.86820	+	5.74973i	−0.0597690	+	0.183950i	0.916714	+	0.399544i	$0.130831\pi$
$978$		0			0
$979$	−2.29022	+	1.66394i	−0.0731958	+	0.0531799i
$980$		0			0
$981$	−39.3084			−1.25502
$982$		0			0
$983$	21.2287			0.677092			0.338546	−	0.940950i	$-0.390065\pi$
$983$	21.2287			0.677092			0.338546	+	0.940950i	$0.390065\pi$
$984$		0			0
$985$	−5.87838			−0.187301
$986$		0			0
$987$	10.1493			0.323054
$988$		0			0
$989$	40.0942	−	29.1302i	1.27492	−	0.926285i
$990$		0			0
$991$	4.03593	−	12.4213i	0.128206	−	0.394577i	−0.866266	−	0.499583i	$-0.833486\pi$
$991$	4.03593	−	12.4213i	0.128206	−	0.394577i	0.994471	+	0.105007i	$0.0334865\pi$
$992$		0			0
$993$	−49.8402			−1.58163
$994$		0			0
$995$	1.59531	+	1.15906i	0.0505748	+	0.0367447i
$996$		0			0
$997$	−0.105570	−	0.324911i	−0.00334344	−	0.0102900i	0.949371	−	0.314157i	$-0.101722\pi$
$997$	−0.105570	−	0.324911i	−0.00334344	−	0.0102900i	−0.952714	+	0.303867i	$0.901722\pi$
$998$		0			0
$999$	45.0216	−	32.7101i	1.42442	−	1.03490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.d.141.1	yes	24
41.16	even	5	inner	1148.2.n.d.57.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.d.57.1	✓	24	41.16	even	5	inner
1148.2.n.d.141.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-3.15594 q^{3} +(1.01403 - 0.736733i) q^{5} +(0.309017 - 0.951057i) q^{7} +6.95994 q^{9} +O(q^{10})\)	\(q-3.15594 q^{3} +(1.01403 - 0.736733i) q^{5} +(0.309017 - 0.951057i) q^{7} +6.95994 q^{9} +(3.45379 + 2.50933i) q^{11} +(-1.21867 - 3.75068i) q^{13} +(-3.20020 + 2.32508i) q^{15} +(-4.64208 - 3.37267i) q^{17} +(-1.20120 + 3.69691i) q^{19} +(-0.975238 + 3.00147i) q^{21} +(1.39102 + 4.28111i) q^{23} +(-1.05961 + 3.26115i) q^{25} -12.4973 q^{27} +(5.73934 - 4.16987i) q^{29} +(7.70828 + 5.60039i) q^{31} +(-10.8999 - 7.91928i) q^{33} +(-0.387324 - 1.19206i) q^{35} +(-3.60250 + 2.61737i) q^{37} +(3.84604 + 11.8369i) q^{39} +(4.01533 - 4.98770i) q^{41} +(-3.40218 - 10.4708i) q^{43} +(7.05756 - 5.12762i) q^{45} +(-0.993775 - 3.05853i) q^{47} +(-0.809017 - 0.587785i) q^{49} +(14.6501 + 10.6439i) q^{51} +(1.84803 - 1.34267i) q^{53} +5.35094 q^{55} +(3.79090 - 11.6672i) q^{57} +(-0.664850 - 2.04620i) q^{59} +(3.86793 - 11.9043i) q^{61} +(2.15074 - 6.61929i) q^{63} +(-3.99901 - 2.90545i) q^{65} +(7.13959 - 5.18722i) q^{67} +(-4.38996 - 13.5109i) q^{69} +(-10.5922 - 7.69567i) q^{71} +12.7893 q^{73} +(3.34407 - 10.2920i) q^{75} +(3.45379 - 2.50933i) q^{77} +16.3615 q^{79} +18.5609 q^{81} +4.27741 q^{83} -7.19195 q^{85} +(-18.1130 + 13.1599i) q^{87} +(-0.204910 + 0.630649i) q^{89} -3.94370 q^{91} +(-24.3268 - 17.6745i) q^{93} +(1.50559 + 4.63372i) q^{95} +(5.16775 - 3.75459i) q^{97} +(24.0382 + 17.4648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9}+O(q^{10}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9	\( 24 q - 10 q^{3} + 4 q^{5} - 6 q^{7} + 38 q^{9} + 11 q^{11} - 4 q^{13} + 10 q^{15} + 9 q^{17} - 23 q^{19} + 5 q^{21} + 28 q^{23} - 10 q^{25} - 76 q^{27} + 28 q^{29} - 18 q^{31} - 27 q^{33} - q^{35} - 29 q^{37} - 6 q^{39} + 65 q^{41} - 15 q^{43} - 20 q^{45} - 11 q^{47} - 6 q^{49} - 18 q^{51} + 8 q^{53} - 50 q^{55} + 8 q^{57} + 55 q^{59} - 10 q^{61} - 2 q^{63} - 11 q^{65} + 65 q^{67} - 2 q^{69} - 14 q^{71} + 48 q^{73} - 77 q^{75} + 11 q^{77} + 22 q^{79} + 80 q^{81} - 22 q^{83} - 78 q^{85} - 4 q^{87} + 16 q^{89} - 4 q^{91} - 60 q^{93} + 56 q^{95} + 15 q^{97} + 80 q^{99}+O(q^{100}) \) 24 * q - 10 * q^3 + 4 * q^5 - 6 * q^7 + 38 * q^9 + 11 * q^11 - 4 * q^13 + 10 * q^15 + 9 * q^17 - 23 * q^19 + 5 * q^21 + 28 * q^23 - 10 * q^25 - 76 * q^27 + 28 * q^29 - 18 * q^31 - 27 * q^33 - q^35 - 29 * q^37 - 6 * q^39 + 65 * q^41 - 15 * q^43 - 20 * q^45 - 11 * q^47 - 6 * q^49 - 18 * q^51 + 8 * q^53 - 50 * q^55 + 8 * q^57 + 55 * q^59 - 10 * q^61 - 2 * q^63 - 11 * q^65 + 65 * q^67 - 2 * q^69 - 14 * q^71 + 48 * q^73 - 77 * q^75 + 11 * q^77 + 22 * q^79 + 80 * q^81 - 22 * q^83 - 78 * q^85 - 4 * q^87 + 16 * q^89 - 4 * q^91 - 60 * q^93 + 56 * q^95 + 15 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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