LMFDB - Embedded newform 1148.2.n.e.57.6

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			57.6
Character	$\chi$	$=$	1148.57
Dual form			1148.2.n.e.141.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.93296 q^{3} +(3.52188 + 2.55880i) q^{5} +(-0.309017 - 0.951057i) q^{7} +5.60225 q^{9} +O(q^{10})$	\(q+2.93296 q^{3} +(3.52188 + 2.55880i) q^{5} +(-0.309017 - 0.951057i) q^{7} +5.60225 q^{9} +(-4.11268 + 2.98804i) q^{11} +(1.16062 - 3.57203i) q^{13} +(10.3295 + 7.50485i) q^{15} +(-1.33944 + 0.973161i) q^{17} +(-1.59938 - 4.92239i) q^{19} +(-0.906334 - 2.78941i) q^{21} +(2.15126 - 6.62091i) q^{23} +(4.31112 + 13.2683i) q^{25} +7.63231 q^{27} +(0.108230 + 0.0786337i) q^{29} +(-6.41341 + 4.65961i) q^{31} +(-12.0623 + 8.76379i) q^{33} +(1.34524 - 4.14022i) q^{35} +(5.41110 + 3.93140i) q^{37} +(3.40406 - 10.4766i) q^{39} +(-1.55578 - 6.21124i) q^{41} +(-0.807217 + 2.48436i) q^{43} +(19.7305 + 14.3350i) q^{45} +(1.57886 - 4.85923i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-3.92853 + 2.85424i) q^{51} +(-8.18456 - 5.94643i) q^{53} -22.1302 q^{55} +(-4.69092 - 14.4372i) q^{57} +(-1.35454 + 4.16884i) q^{59} +(4.32512 + 13.3113i) q^{61} +(-1.73119 - 5.32806i) q^{63} +(13.2277 - 9.61046i) q^{65} +(-4.88998 - 3.55278i) q^{67} +(6.30957 - 19.4189i) q^{69} +(-10.3009 + 7.48408i) q^{71} -4.07576 q^{73} +(12.6444 + 38.9153i) q^{75} +(4.11268 + 2.98804i) q^{77} -6.74845 q^{79} +5.57849 q^{81} +8.24641 q^{83} -7.20747 q^{85} +(0.317434 + 0.230629i) q^{87} +(0.538266 + 1.65661i) q^{89} -3.75585 q^{91} +(-18.8103 + 13.6665i) q^{93} +(6.96256 - 21.4286i) q^{95} +(-6.04918 - 4.39499i) q^{97} +(-23.0403 + 16.7397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	$ 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) $ 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	2.93296			1.69335			0.846673	−	0.532114i	$-0.178602\pi$
$3$	2.93296			1.69335			0.846673	+	0.532114i	$0.178602\pi$
$4$		0			0
$5$	3.52188	+	2.55880i	1.57503	+	1.14433i	0.922125	+	0.386892i	$0.126451\pi$
$5$	3.52188	+	2.55880i	1.57503	+	1.14433i	0.652908	+	0.757437i	$0.273549\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$		0			0
$9$	5.60225			1.86742
$10$		0			0
$11$	−4.11268	+	2.98804i	−1.24002	+	0.900927i	−0.997600	−	0.0692445i	$-0.977941\pi$
$11$	−4.11268	+	2.98804i	−1.24002	+	0.900927i	−0.242420	+	0.970171i	$0.577941\pi$
$12$		0			0
$13$	1.16062	−	3.57203i	0.321899	−	0.990702i	−0.650922	−	0.759144i	$-0.725618\pi$
$13$	1.16062	−	3.57203i	0.321899	−	0.990702i	0.972821	−	0.231558i	$-0.0743823\pi$
$14$		0			0
$15$	10.3295	+	7.50485i	2.66708	+	1.93774i
$16$		0			0
$17$	−1.33944	+	0.973161i	−0.324862	+	0.236026i	−0.738247	−	0.674530i	$-0.764346\pi$
$17$	−1.33944	+	0.973161i	−0.324862	+	0.236026i	0.413385	+	0.910556i	$0.364346\pi$
$18$		0			0
$19$	−1.59938	−	4.92239i	−0.366923	−	1.12927i	−0.948768	−	0.315974i	$-0.897669\pi$
$19$	−1.59938	−	4.92239i	−0.366923	−	1.12927i	0.581845	−	0.813300i	$-0.302331\pi$
$20$		0			0
$21$	−0.906334	−	2.78941i	−0.197778	−	0.608699i
$22$		0			0
$23$	2.15126	−	6.62091i	0.448569	−	1.38055i	−0.429952	−	0.902852i	$-0.641470\pi$
$23$	2.15126	−	6.62091i	0.448569	−	1.38055i	0.878522	−	0.477703i	$-0.158530\pi$
$24$		0			0
$25$	4.31112	+	13.2683i	0.862225	+	2.65366i
$26$		0			0
$27$	7.63231			1.46884
$28$		0			0
$29$	0.108230	+	0.0786337i	0.0200978	+	0.0146019i	0.597789	−	0.801654i	$-0.296046\pi$
$29$	0.108230	+	0.0786337i	0.0200978	+	0.0146019i	−0.577691	+	0.816256i	$0.696046\pi$
$30$		0			0
$31$	−6.41341	+	4.65961i	−1.15188	+	0.836891i	−0.988730	−	0.149710i	$-0.952166\pi$
$31$	−6.41341	+	4.65961i	−1.15188	+	0.836891i	−0.163152	+	0.986601i	$0.552166\pi$
$32$		0			0
$33$	−12.0623	+	8.76379i	−2.09978	+	1.52558i
$34$		0			0
$35$	1.34524	−	4.14022i	0.227387	−	0.699825i
$36$		0			0
$37$	5.41110	+	3.93140i	0.889580	+	0.646318i	0.935768	−	0.352615i	$-0.114707\pi$
$37$	5.41110	+	3.93140i	0.889580	+	0.646318i	−0.0461885	+	0.998933i	$0.514707\pi$
$38$		0			0
$39$	3.40406	−	10.4766i	0.545086	−	1.67760i
$40$		0			0
$41$	−1.55578	−	6.21124i	−0.242972	−	0.970033i
$41$	−1.55578	−	6.21124i	−0.242972	−	0.970033i
$42$		0			0
$43$	−0.807217	+	2.48436i	−0.123099	+	0.378861i	−0.993550	−	0.113395i	$-0.963828\pi$
$43$	−0.807217	+	2.48436i	−0.123099	+	0.378861i	0.870451	+	0.492256i	$0.163828\pi$
$44$		0			0
$45$	19.7305	+	14.3350i	2.94125	+	2.13694i
$46$		0			0
$47$	1.57886	−	4.85923i	0.230300	−	0.708791i	−0.767410	−	0.641157i	$-0.778455\pi$
$47$	1.57886	−	4.85923i	0.230300	−	0.708791i	0.997710	−	0.0676345i	$-0.0215452\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$		0			0
$51$	−3.92853	+	2.85424i	−0.550104	+	0.399674i
$52$		0			0
$53$	−8.18456	−	5.94643i	−1.12424	−	0.816805i	−0.139390	−	0.990238i	$-0.544514\pi$
$53$	−8.18456	−	5.94643i	−1.12424	−	0.816805i	−0.984846	+	0.173433i	$0.944514\pi$
$54$		0			0
$55$	−22.1302			−2.98403
$56$		0			0
$57$	−4.69092	−	14.4372i	−0.621328	−	1.91225i
$58$		0			0
$59$	−1.35454	+	4.16884i	−0.176346	+	0.542736i	−0.999692	−	0.0248024i	$-0.992104\pi$
$59$	−1.35454	+	4.16884i	−0.176346	+	0.542736i	0.823347	+	0.567539i	$0.192104\pi$
$60$		0			0
$61$	4.32512	+	13.3113i	0.553774	+	1.70434i	0.699159	+	0.714967i	$0.253558\pi$
$61$	4.32512	+	13.3113i	0.553774	+	1.70434i	−0.145384	+	0.989375i	$0.546442\pi$
$62$		0			0
$63$	−1.73119	−	5.32806i	−0.218110	−	0.671273i
$64$		0			0
$65$	13.2277	−	9.61046i	1.64069	−	1.19203i
$66$		0			0
$67$	−4.88998	−	3.55278i	−0.597406	−	0.434041i	0.247551	−	0.968875i	$-0.420374\pi$
$67$	−4.88998	−	3.55278i	−0.597406	−	0.434041i	−0.844957	+	0.534834i	$0.820374\pi$
$68$		0			0
$69$	6.30957	−	19.4189i	0.759583	−	2.33775i
$70$		0			0
$71$	−10.3009	+	7.48408i	−1.22250	+	0.888196i	−0.996305	−	0.0858863i	$-0.972628\pi$
$71$	−10.3009	+	7.48408i	−1.22250	+	0.888196i	−0.226192	+	0.974083i	$0.572628\pi$
$72$		0			0
$73$	−4.07576			−0.477032			−0.238516	−	0.971139i	$-0.576661\pi$
$73$	−4.07576			−0.477032			−0.238516	+	0.971139i	$0.576661\pi$
$74$		0			0
$75$	12.6444	+	38.9153i	1.46004	+	4.49355i
$76$		0			0
$77$	4.11268	+	2.98804i	0.468683	+	0.340518i
$78$		0			0
$79$	−6.74845			−0.759260			−0.379630	−	0.925138i	$-0.623949\pi$
$79$	−6.74845			−0.759260			−0.379630	+	0.925138i	$0.623949\pi$
$80$		0			0
$81$	5.57849			0.619832
$82$		0			0
$83$	8.24641			0.905161			0.452580	−	0.891724i	$-0.350504\pi$
$83$	8.24641			0.905161			0.452580	+	0.891724i	$0.350504\pi$
$84$		0			0
$85$	−7.20747			−0.781760
$86$		0			0
$87$	0.317434	+	0.230629i	0.0340325	+	0.0247261i
$88$		0			0
$89$	0.538266	+	1.65661i	0.0570560	+	0.175600i	0.975523	−	0.219897i	$-0.0705722\pi$
$89$	0.538266	+	1.65661i	0.0570560	+	0.175600i	−0.918467	+	0.395498i	$0.870572\pi$
$90$		0			0
$91$	−3.75585			−0.393720
$92$		0			0
$93$	−18.8103	+	13.6665i	−1.95053	+	1.41715i
$94$		0			0
$95$	6.96256	−	21.4286i	0.714344	−	2.19852i
$96$		0			0
$97$	−6.04918	−	4.39499i	−0.614202	−	0.446244i	0.236690	−	0.971585i	$-0.423937\pi$
$97$	−6.04918	−	4.39499i	−0.614202	−	0.446244i	−0.850891	+	0.525342i	$0.823937\pi$
$98$		0			0
$99$	−23.0403	+	16.7397i	−2.31564	+	1.68241i
$100$		0			0
$101$	−3.25811	−	10.0274i	−0.324195	−	0.997768i	−0.971803	−	0.235795i	$-0.924231\pi$
$101$	−3.25811	−	10.0274i	−0.324195	−	0.997768i	0.647608	−	0.761973i	$-0.275769\pi$
$102$		0			0
$103$	2.70845	+	8.33575i	0.266871	+	0.821346i	0.991256	+	0.131950i	$0.0421238\pi$
$103$	2.70845	+	8.33575i	0.266871	+	0.821346i	−0.724385	+	0.689396i	$0.757876\pi$
$104$		0			0
$105$	3.94553	−	12.1431i	0.385045	−	1.18505i
$106$		0			0
$107$	−5.31650	−	16.3625i	−0.513966	−	1.58182i	−0.785156	−	0.619298i	$-0.787417\pi$
$107$	−5.31650	−	16.3625i	−0.513966	−	1.58182i	0.271190	−	0.962526i	$-0.412583\pi$
$108$		0			0
$109$	6.90818			0.661683			0.330842	−	0.943686i	$-0.392667\pi$
$109$	6.90818			0.661683			0.330842	+	0.943686i	$0.392667\pi$
$110$		0			0
$111$	15.8706	+	11.5306i	1.50637	+	1.09444i
$112$		0			0
$113$	10.7204	−	7.78883i	1.00849	−	0.732711i	0.0445985	−	0.999005i	$-0.485799\pi$
$113$	10.7204	−	7.78883i	1.00849	−	0.732711i	0.963892	+	0.266294i	$0.0857992\pi$
$114$		0			0
$115$	24.5180	−	17.8134i	2.28632	−	1.66111i
$116$		0			0
$117$	6.50210	−	20.0114i	0.601119	−	1.85006i
$118$		0			0
$119$	1.33944	+	0.973161i	0.122786	+	0.0892095i
$120$		0			0
$121$	4.58658	−	14.1161i	0.416962	−	1.28328i
$122$		0			0
$123$	−4.56303	−	18.2173i	−0.411435	−	1.64260i
$124$		0			0
$125$	−12.0414	+	37.0595i	−1.07701	+	3.31470i
$126$		0			0
$127$	7.24862	+	5.26643i	0.643211	+	0.467320i	0.860952	−	0.508686i	$-0.169869\pi$
$127$	7.24862	+	5.26643i	0.643211	+	0.467320i	−0.217741	+	0.976007i	$0.569869\pi$
$128$		0			0
$129$	−2.36753	+	7.28652i	−0.208450	+	0.641542i
$130$		0			0
$131$	4.83502	−	3.51285i	0.422437	−	0.306919i	−0.356180	−	0.934417i	$-0.615921\pi$
$131$	4.83502	−	3.51285i	0.422437	−	0.306919i	0.778618	+	0.627498i	$0.215921\pi$
$132$		0			0
$133$	−4.18724	+	3.04220i	−0.363079	+	0.263793i
$134$		0			0
$135$	26.8801	+	19.5295i	2.31347	+	1.68083i
$136$		0			0
$137$	16.4460			1.40508			0.702540	−	0.711644i	$-0.252049\pi$
$137$	16.4460			1.40508			0.702540	+	0.711644i	$0.252049\pi$
$138$		0			0
$139$	−0.761317	−	2.34309i	−0.0645740	−	0.198738i	0.913564	−	0.406695i	$-0.133319\pi$
$139$	−0.761317	−	2.34309i	−0.0645740	−	0.198738i	−0.978138	+	0.207956i	$0.933319\pi$
$140$		0			0
$141$	4.63073	−	14.2519i	0.389978	−	1.20023i
$142$		0			0
$143$	5.90008	+	18.1586i	0.493390	+	1.51850i
$144$		0			0
$145$	0.179966	+	0.553877i	0.0149453	+	0.0459970i
$146$		0			0
$147$	−2.37281	+	1.72395i	−0.195706	+	0.142189i
$148$		0			0
$149$	−2.25669	−	1.63958i	−0.184876	−	0.134320i	0.491498	−	0.870879i	$-0.336450\pi$
$149$	−2.25669	−	1.63958i	−0.184876	−	0.134320i	−0.676374	+	0.736559i	$0.736450\pi$
$150$		0			0
$151$	−0.240872	+	0.741327i	−0.0196019	+	0.0603283i	−0.960379	−	0.278697i	$-0.910097\pi$
$151$	−0.240872	+	0.741327i	−0.0196019	+	0.0603283i	0.940777	+	0.339026i	$0.110097\pi$
$152$		0			0
$153$	−7.50389	+	5.45189i	−0.606654	+	0.440760i
$154$		0			0
$155$	−34.5103			−2.77193
$156$		0			0
$157$	−2.53605	−	7.80515i	−0.202398	−	0.622918i	−0.999810	−	0.0194828i	$-0.993798\pi$
$157$	−2.53605	−	7.80515i	−0.202398	−	0.622918i	0.797412	−	0.603436i	$-0.206202\pi$
$158$		0			0
$159$	−24.0050	−	17.4406i	−1.90372	−	1.38313i
$160$		0			0
$161$	−6.96163			−0.548653
$162$		0			0
$163$	13.9523			1.09283			0.546415	−	0.837514i	$-0.315992\pi$
$163$	13.9523			1.09283			0.546415	+	0.837514i	$0.315992\pi$
$164$		0			0
$165$	−64.9068			−5.05299
$166$		0			0
$167$	12.3530			0.955902			0.477951	−	0.878386i	$-0.341380\pi$
$167$	12.3530			0.955902			0.477951	+	0.878386i	$0.341380\pi$
$168$		0			0
$169$	−0.895115	−	0.650339i	−0.0688550	−	0.0500261i
$170$		0			0
$171$	−8.96014	−	27.5765i	−0.685199	−	2.10883i
$172$		0			0
$173$	6.68228			0.508044			0.254022	−	0.967198i	$-0.418246\pi$
$173$	6.68228			0.508044			0.254022	+	0.967198i	$0.418246\pi$
$174$		0			0
$175$	11.2867	−	8.20025i	0.853192	−	0.619880i
$176$		0			0
$177$	−3.97280	+	12.2270i	−0.298614	+	0.919040i
$178$		0			0
$179$	15.0629	+	10.9439i	1.12586	+	0.817983i	0.985087	−	0.172059i	$-0.0550420\pi$
$179$	15.0629	+	10.9439i	1.12586	+	0.817983i	0.140771	+	0.990042i	$0.455042\pi$
$180$		0			0
$181$	−9.19534	+	6.68080i	−0.683484	+	0.496580i	−0.874512	−	0.485004i	$-0.838818\pi$
$181$	−9.19534	+	6.68080i	−0.683484	+	0.496580i	0.191028	+	0.981585i	$0.438818\pi$
$182$		0			0
$183$	12.6854	+	39.0416i	0.937731	+	2.88604i
$184$		0			0
$185$	8.99762	+	27.6918i	0.661518	+	2.03594i
$186$		0			0
$187$	2.60085	−	8.00460i	0.190193	−	0.585354i
$188$		0			0
$189$	−2.35851	−	7.25876i	−0.171557	−	0.527997i
$190$		0			0
$191$	−20.2547			−1.46558			−0.732788	−	0.680457i	$-0.761781\pi$
$191$	−20.2547			−1.46558			−0.732788	+	0.680457i	$0.761781\pi$
$192$		0			0
$193$	5.41130	+	3.93154i	0.389514	+	0.282999i	0.765256	−	0.643726i	$-0.222612\pi$
$193$	5.41130	+	3.93154i	0.389514	+	0.282999i	−0.375742	+	0.926724i	$0.622612\pi$
$194$		0			0
$195$	38.7962	−	28.1871i	2.77825	−	2.01852i
$196$		0			0
$197$	6.47377	−	4.70347i	0.461237	−	0.335108i	−0.332779	−	0.943005i	$-0.607986\pi$
$197$	6.47377	−	4.70347i	0.461237	−	0.335108i	0.794016	+	0.607897i	$0.207986\pi$
$198$		0			0
$199$	−1.98618	+	6.11282i	−0.140796	+	0.433326i	−0.996446	−	0.0842282i	$-0.973158\pi$
$199$	−1.98618	+	6.11282i	−0.140796	+	0.433326i	0.855650	+	0.517555i	$0.173158\pi$
$200$		0			0
$201$	−14.3421	−	10.4202i	−1.01162	−	0.734982i
$202$		0			0
$203$	0.0413402	−	0.127232i	0.00290151	−	0.00892994i
$204$		0			0
$205$	10.4140	−	25.8562i	0.727349	−	1.80587i
$206$		0			0
$207$	12.0519	−	37.0920i	0.837666	−	2.57807i
$208$		0			0
$209$	21.2860	+	15.4652i	1.47239	+	1.06975i
$210$		0			0
$211$	−1.74685	+	5.37626i	−0.120258	+	0.370117i	−0.993007	−	0.118052i	$-0.962335\pi$
$211$	−1.74685	+	5.37626i	−0.120258	+	0.370117i	0.872749	+	0.488169i	$0.162335\pi$
$212$		0			0
$213$	−30.2123	+	21.9505i	−2.07011	+	1.50402i
$214$		0			0
$215$	−9.19989	+	6.68411i	−0.627427	+	0.455853i
$216$		0			0
$217$	6.41341	+	4.65961i	0.435370	+	0.316315i
$218$		0			0
$219$	−11.9541			−0.807780
$220$		0			0
$221$	1.92157	+	5.91399i	0.129259	+	0.397818i
$222$		0			0
$223$	0.804246	−	2.47522i	0.0538563	−	0.165753i	−0.920511	−	0.390718i	$-0.872227\pi$
$223$	0.804246	−	2.47522i	0.0538563	−	0.165753i	0.974367	+	0.224965i	$0.0722268\pi$
$224$		0			0
$225$	24.1520	+	74.3323i	1.61013	+	4.95548i
$226$		0			0
$227$	−2.77971	−	8.55508i	−0.184496	−	0.567821i	0.815443	−	0.578837i	$-0.196493\pi$
$227$	−2.77971	−	8.55508i	−0.184496	−	0.567821i	−0.999939	+	0.0110165i	$0.996493\pi$
$228$		0			0
$229$	−6.66965	+	4.84578i	−0.440743	+	0.320218i	−0.785930	−	0.618315i	$-0.787815\pi$
$229$	−6.66965	+	4.84578i	−0.440743	+	0.320218i	0.345187	+	0.938534i	$0.387815\pi$
$230$		0			0
$231$	12.0623	+	8.76379i	0.793643	+	0.576615i
$232$		0			0
$233$	7.43526	−	22.8834i	0.487100	−	1.49914i	−0.341816	−	0.939767i	$-0.611042\pi$
$233$	7.43526	−	22.8834i	0.487100	−	1.49914i	0.828916	−	0.559373i	$-0.188958\pi$
$234$		0			0
$235$	17.9943	−	13.0736i	1.17382	−	0.852831i
$236$		0			0
$237$	−19.7929			−1.28569
$238$		0			0
$239$	−4.13231	−	12.7179i	−0.267297	−	0.822655i	−0.991155	−	0.132707i	$-0.957633\pi$
$239$	−4.13231	−	12.7179i	−0.267297	−	0.822655i	0.723859	−	0.689948i	$-0.242367\pi$
$240$		0			0
$241$	−4.48141	−	3.25594i	−0.288673	−	0.209733i	0.434018	−	0.900904i	$-0.357095\pi$
$241$	−4.48141	−	3.25594i	−0.288673	−	0.209733i	−0.722692	+	0.691171i	$0.757095\pi$
$242$		0			0
$243$	−6.53543			−0.419248
$244$		0			0
$245$	−4.35329			−0.278121
$246$		0			0
$247$	−19.4392			−1.23689
$248$		0			0
$249$	24.1864			1.53275
$250$		0			0
$251$	−15.7570	−	11.4482i	−0.994575	−	0.722601i	−0.0336567	−	0.999433i	$-0.510715\pi$
$251$	−15.7570	−	11.4482i	−0.994575	−	0.722601i	−0.960918	+	0.276833i	$0.910715\pi$
$252$		0			0
$253$	10.9361	+	33.6577i	0.687544	+	2.11604i
$254$		0			0
$255$	−21.1392			−1.32379
$256$		0			0
$257$	1.86027	−	1.35156i	0.116040	−	0.0843081i	−0.528252	−	0.849088i	$-0.677152\pi$
$257$	1.86027	−	1.35156i	0.116040	−	0.0843081i	0.644292	+	0.764780i	$0.277152\pi$
$258$		0			0
$259$	2.06686	−	6.36113i	0.128428	−	0.395262i
$260$		0			0
$261$	0.606332	+	0.440526i	0.0375310	+	0.0272679i
$262$		0			0
$263$	−1.09899	+	0.798466i	−0.0677669	+	0.0492355i	−0.621153	−	0.783689i	$-0.713335\pi$
$263$	−1.09899	+	0.798466i	−0.0677669	+	0.0492355i	0.553386	+	0.832925i	$0.313335\pi$
$264$		0			0
$265$	−13.6093	−	41.8852i	−0.836015	−	2.57299i
$266$		0			0
$267$	1.57871	+	4.85877i	0.0966156	+	0.297352i
$268$		0			0
$269$	3.01150	−	9.26845i	0.183614	−	0.565107i	−0.816307	−	0.577618i	$-0.803982\pi$
$269$	3.01150	−	9.26845i	0.183614	−	0.565107i	0.999922	+	0.0125106i	$0.00398236\pi$
$270$		0			0
$271$	7.45500	+	22.9441i	0.452859	+	1.39376i	0.873631	+	0.486590i	$0.161759\pi$
$271$	7.45500	+	22.9441i	0.452859	+	1.39376i	−0.420772	+	0.907167i	$0.638241\pi$
$272$		0			0
$273$	−11.0158			−0.666704
$274$		0			0
$275$	−57.3764	−	41.6864i	−3.45993	−	2.51378i
$276$		0			0
$277$	1.82751	−	1.32776i	0.109804	−	0.0797774i	−0.531528	−	0.847041i	$-0.678382\pi$
$277$	1.82751	−	1.32776i	0.109804	−	0.0797774i	0.641332	+	0.767263i	$0.278382\pi$
$278$		0			0
$279$	−35.9295	+	26.1043i	−2.15105	+	1.56283i
$280$		0			0
$281$	−4.98324	+	15.3368i	−0.297275	+	0.914918i	0.685173	+	0.728381i	$0.259727\pi$
$281$	−4.98324	+	15.3368i	−0.297275	+	0.914918i	−0.982448	+	0.186538i	$0.940273\pi$
$282$		0			0
$283$	−19.4798	−	14.1529i	−1.15795	−	0.841301i	−0.168434	−	0.985713i	$-0.553871\pi$
$283$	−19.4798	−	14.1529i	−1.15795	−	0.841301i	−0.989518	+	0.144412i	$0.953871\pi$
$284$		0			0
$285$	20.4209	−	62.8491i	1.20963	−	3.72286i
$286$		0			0
$287$	−5.42648	+	3.39901i	−0.320315	+	0.200637i
$288$		0			0
$289$	−4.40623	+	13.5610i	−0.259190	+	0.797705i
$290$		0			0
$291$	−17.7420	−	12.8903i	−1.04006	−	0.755644i
$292$		0			0
$293$	−9.25600	+	28.4870i	−0.540741	+	1.66423i	0.190164	+	0.981752i	$0.439098\pi$
$293$	−9.25600	+	28.4870i	−0.540741	+	1.66423i	−0.730905	+	0.682479i	$0.760902\pi$
$294$		0			0
$295$	−15.4377	+	11.2162i	−0.898819	+	0.653031i
$296$		0			0
$297$	−31.3892	+	22.8056i	−1.82139	+	1.32332i
$298$		0			0
$299$	−21.1533	−	15.3687i	−1.22332	−	0.888797i
$300$		0			0
$301$	2.61221			0.150565
$302$		0			0
$303$	−9.55592	−	29.4101i	−0.548973	−	1.68957i
$304$		0			0
$305$	−18.8285	+	57.9480i	−1.07811	+	3.31810i
$306$		0			0
$307$	−6.44908	−	19.8482i	−0.368069	−	1.13280i	−0.948037	−	0.318160i	$-0.896935\pi$
$307$	−6.44908	−	19.8482i	−0.368069	−	1.13280i	0.579968	−	0.814639i	$-0.303065\pi$
$308$		0			0
$309$	7.94377	+	24.4484i	0.451905	+	1.39082i
$310$		0			0
$311$	−1.71143	+	1.24343i	−0.0970463	+	0.0705082i	−0.635250	−	0.772306i	$-0.719103\pi$
$311$	−1.71143	+	1.24343i	−0.0970463	+	0.0705082i	0.538204	+	0.842815i	$0.319103\pi$
$312$		0			0
$313$	10.4136	+	7.56589i	0.588609	+	0.427650i	0.841818	−	0.539762i	$-0.181486\pi$
$313$	10.4136	+	7.56589i	0.588609	+	0.427650i	−0.253208	+	0.967412i	$0.581486\pi$
$314$		0			0
$315$	7.53637	−	23.1946i	0.424626	−	1.30687i
$316$		0			0
$317$	−5.78478	+	4.20289i	−0.324906	+	0.236058i	−0.738266	−	0.674510i	$-0.764355\pi$
$317$	−5.78478	+	4.20289i	−0.324906	+	0.236058i	0.413360	+	0.910568i	$0.364355\pi$
$318$		0			0
$319$	−0.680076			−0.0380769
$320$		0			0
$321$	−15.5931	−	47.9906i	−0.870322	−	2.67857i
$322$		0			0
$323$	6.93256	+	5.03680i	0.385738	+	0.280255i
$324$		0			0
$325$	52.3982			2.90653
$326$		0			0
$327$	20.2614			1.12046
$328$		0			0
$329$	−5.10929			−0.281685
$330$		0			0
$331$	13.9045			0.764260			0.382130	−	0.924109i	$-0.375191\pi$
$331$	13.9045			0.764260			0.382130	+	0.924109i	$0.375191\pi$
$332$		0			0
$333$	30.3144	+	22.0247i	1.66122	+	1.20695i
$334$		0			0
$335$	−8.13110	−	25.0249i	−0.444249	−	1.36726i
$336$		0			0
$337$	9.67213			0.526874			0.263437	−	0.964677i	$-0.415144\pi$
$337$	9.67213			0.526874			0.263437	+	0.964677i	$0.415144\pi$
$338$		0			0
$339$	31.4425	−	22.8443i	1.70772	−	1.24073i
$340$		0			0
$341$	12.4532	−	38.3270i	0.674378	−	2.07552i
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$		0			0
$345$	71.9104	−	52.2460i	3.87153	−	2.81283i
$346$		0			0
$347$	−2.66432	−	8.19994i	−0.143028	−	0.440196i	0.853724	−	0.520726i	$-0.174339\pi$
$347$	−2.66432	−	8.19994i	−0.143028	−	0.440196i	−0.996752	+	0.0805302i	$0.974339\pi$
$348$		0			0
$349$	9.08477	+	27.9601i	0.486297	+	1.49667i	0.830094	+	0.557624i	$0.188287\pi$
$349$	9.08477	+	27.9601i	0.486297	+	1.49667i	−0.343797	+	0.939044i	$0.611713\pi$
$350$		0			0
$351$	8.85822	−	27.2628i	0.472817	−	1.45518i
$352$		0			0
$353$	−5.41899	−	16.6779i	−0.288424	−	0.887676i	−0.985352	−	0.170535i	$-0.945450\pi$
$353$	−5.41899	−	16.6779i	−0.288424	−	0.887676i	0.696928	−	0.717141i	$-0.254550\pi$
$354$		0			0
$355$	−55.4289			−2.94186
$356$		0			0
$357$	3.92853	+	2.85424i	0.207920	+	0.151063i
$358$		0			0
$359$	2.62166	−	1.90475i	0.138366	−	0.100529i	−0.516449	−	0.856318i	$-0.672747\pi$
$359$	2.62166	−	1.90475i	0.138366	−	0.100529i	0.654815	+	0.755789i	$0.272747\pi$
$360$		0			0
$361$	−6.30058	+	4.57764i	−0.331610	+	0.240928i
$362$		0			0
$363$	13.4523	−	41.4018i	0.706061	−	2.17303i
$364$		0			0
$365$	−14.3544	−	10.4290i	−0.751341	−	0.545881i
$366$		0			0
$367$	−3.71501	+	11.4336i	−0.193922	+	0.596830i	0.806066	+	0.591826i	$0.201593\pi$
$367$	−3.71501	+	11.4336i	−0.193922	+	0.596830i	−0.999987	+	0.00500402i	$0.998407\pi$
$368$		0			0
$369$	−8.71586	−	34.7970i	−0.453729	−	1.81146i
$370$		0			0
$371$	−3.12622	+	9.62152i	−0.162305	+	0.499525i
$372$		0			0
$373$	−3.46230	−	2.51551i	−0.179271	−	0.130248i	0.494531	−	0.869160i	$-0.335340\pi$
$373$	−3.46230	−	2.51551i	−0.179271	−	0.130248i	−0.673802	+	0.738912i	$0.735340\pi$
$374$		0			0
$375$	−35.3168	+	108.694i	−1.82375	+	5.61293i
$376$		0			0
$377$	0.406496	−	0.295337i	0.0209356	−	0.0152106i
$378$		0			0
$379$	6.22365	−	4.52175i	0.319688	−	0.232267i	−0.416355	−	0.909202i	$-0.636692\pi$
$379$	6.22365	−	4.52175i	0.319688	−	0.232267i	0.736042	+	0.676936i	$0.236692\pi$
$380$		0			0
$381$	21.2599	+	15.4462i	1.08918	+	0.791334i
$382$		0			0
$383$	25.0685			1.28094			0.640471	−	0.767983i	$-0.278739\pi$
$383$	25.0685			1.28094			0.640471	+	0.767983i	$0.278739\pi$
$384$		0			0
$385$	6.83859	+	21.0470i	0.348527	+	1.07266i
$386$		0			0
$387$	−4.52223	+	13.9180i	−0.229878	+	0.707492i
$388$		0			0
$389$	−4.69941	−	14.4633i	−0.238270	−	0.733319i	−0.996671	−	0.0815308i	$-0.974019\pi$
$389$	−4.69941	−	14.4633i	−0.238270	−	0.733319i	0.758401	−	0.651788i	$-0.225981\pi$
$390$		0			0
$391$	3.56172	+	10.9618i	0.180124	+	0.554364i
$392$		0			0
$393$	14.1809	−	10.3030i	0.715332	−	0.519719i
$394$		0			0
$395$	−23.7672	−	17.2679i	−1.19586	−	0.868843i
$396$		0			0
$397$	−1.87980	+	5.78542i	−0.0943443	+	0.290362i	−0.987082	−	0.160214i	$-0.948781\pi$
$397$	−1.87980	+	5.78542i	−0.0943443	+	0.290362i	0.892738	+	0.450576i	$0.148781\pi$
$398$		0			0
$399$	−12.2810	+	8.92266i	−0.614819	+	0.446692i
$400$		0			0
$401$	−6.40643			−0.319922			−0.159961	−	0.987123i	$-0.551137\pi$
$401$	−6.40643			−0.319922			−0.159961	+	0.987123i	$0.551137\pi$
$402$		0			0
$403$	9.20072	+	28.3169i	0.458321	+	1.41057i
$404$		0			0
$405$	19.6468	+	14.2742i	0.976257	+	0.709292i
$406$		0			0
$407$	−34.0013			−1.68538
$408$		0			0
$409$	−21.8453			−1.08018			−0.540091	−	0.841607i	$-0.681610\pi$
$409$	−21.8453			−1.08018			−0.540091	+	0.841607i	$0.681610\pi$
$410$		0			0
$411$	48.2356			2.37929
$412$		0			0
$413$	4.38338			0.215692
$414$		0			0
$415$	29.0429	+	21.1009i	1.42566	+	1.03580i
$416$		0			0
$417$	−2.23291	−	6.87220i	−0.109346	−	0.336533i
$418$		0			0
$419$	20.6188			1.00729			0.503646	−	0.863910i	$-0.331992\pi$
$419$	20.6188			1.00729			0.503646	+	0.863910i	$0.331992\pi$
$420$		0			0
$421$	−9.96468	+	7.23976i	−0.485649	+	0.352844i	−0.803508	−	0.595293i	$-0.797036\pi$
$421$	−9.96468	+	7.23976i	−0.485649	+	0.352844i	0.317860	+	0.948138i	$0.397036\pi$
$422$		0			0
$423$	8.84517	−	27.2226i	0.430067	−	1.32361i
$424$		0			0
$425$	−18.6867	−	13.5767i	−0.906436	−	0.658565i
$426$		0			0
$427$	11.3233	−	8.22686i	0.547973	−	0.398126i
$428$		0			0
$429$	17.3047	+	53.2584i	0.835479	+	2.57134i
$430$		0			0
$431$	0.983452	+	3.02675i	0.0473712	+	0.145794i	0.971944	−	0.235211i	$-0.0755782\pi$
$431$	0.983452	+	3.02675i	0.0473712	+	0.145794i	−0.924573	+	0.381005i	$0.875578\pi$
$432$		0			0
$433$	−2.66965	+	8.21633i	−0.128295	+	0.394852i	−0.994487	−	0.104860i	$-0.966561\pi$
$433$	−2.66965	+	8.21633i	−0.128295	+	0.394852i	0.866192	+	0.499711i	$0.166561\pi$
$434$		0			0
$435$	0.527832	+	1.62450i	0.0253076	+	0.0778888i
$436$		0			0
$437$	−36.0314			−1.72361
$438$		0			0
$439$	6.70426	+	4.87093i	0.319977	+	0.232477i	0.736166	−	0.676801i	$-0.236634\pi$
$439$	6.70426	+	4.87093i	0.319977	+	0.232477i	−0.416189	+	0.909278i	$0.636634\pi$
$440$		0			0
$441$	−4.53232	+	3.29292i	−0.215825	+	0.156806i
$442$		0			0
$443$	−2.56268	+	1.86190i	−0.121757	+	0.0884615i	−0.646997	−	0.762492i	$-0.723975\pi$
$443$	−2.56268	+	1.86190i	−0.121757	+	0.0884615i	0.525240	+	0.850954i	$0.323975\pi$
$444$		0			0
$445$	−2.34322	+	7.21170i	−0.111079	+	0.341867i
$446$		0			0
$447$	−6.61879	−	4.80884i	−0.313058	−	0.227450i
$448$		0			0
$449$	−6.50329	+	20.0151i	−0.306909	+	0.944569i	0.672049	+	0.740507i	$0.265415\pi$
$449$	−6.50329	+	20.0151i	−0.306909	+	0.944569i	−0.978958	+	0.204062i	$0.934585\pi$
$450$		0			0
$451$	24.9578	+	20.8961i	1.17522	+	0.983961i
$452$		0			0
$453$	−0.706467	+	2.17428i	−0.0331927	+	0.102157i
$454$		0			0
$455$	−13.2277	−	9.61046i	−0.620123	−	0.450545i
$456$		0			0
$457$	−7.07313	+	21.7689i	−0.330867	+	1.01830i	0.637855	+	0.770156i	$0.279822\pi$
$457$	−7.07313	+	21.7689i	−0.330867	+	1.01830i	−0.968722	+	0.248148i	$0.920178\pi$
$458$		0			0
$459$	−10.2230	+	7.42746i	−0.477170	+	0.346684i
$460$		0			0
$461$	−4.78876	+	3.47924i	−0.223035	+	0.162044i	−0.693692	−	0.720272i	$-0.744017\pi$
$461$	−4.78876	+	3.47924i	−0.223035	+	0.162044i	0.470657	+	0.882316i	$0.344017\pi$
$462$		0			0
$463$	16.3986	+	11.9143i	0.762110	+	0.553705i	0.899557	−	0.436804i	$-0.143890\pi$
$463$	16.3986	+	11.9143i	0.762110	+	0.553705i	−0.137447	+	0.990509i	$0.543890\pi$
$464$		0			0
$465$	−101.217			−4.69384
$466$		0			0
$467$	−0.959856	−	2.95413i	−0.0444168	−	0.136701i	0.926389	−	0.376568i	$-0.122896\pi$
$467$	−0.959856	−	2.95413i	−0.0444168	−	0.136701i	−0.970806	+	0.239867i	$0.922896\pi$
$468$		0			0
$469$	−1.86781	+	5.74852i	−0.0862473	+	0.265442i
$470$		0			0
$471$	−7.43812	−	22.8922i	−0.342731	−	1.05482i
$472$		0			0
$473$	−4.10353	−	12.6294i	−0.188680	−	0.580699i
$474$		0			0
$475$	58.4165	−	42.4421i	2.68033	−	1.94738i
$476$		0			0
$477$	−45.8520	−	33.3134i	−2.09942	−	1.52532i
$478$		0			0
$479$	−4.05255	+	12.4725i	−0.185166	+	0.569882i	−0.999951	−	0.00988087i	$-0.996855\pi$
$479$	−4.05255	+	12.4725i	−0.185166	+	0.569882i	0.814785	+	0.579763i	$0.196855\pi$
$480$		0			0
$481$	20.3233	−	14.7657i	0.926663	−	0.673260i
$482$		0			0
$483$	−20.4182			−0.929060
$484$		0			0
$485$	−10.0586	−	30.9573i	−0.456739	−	1.40570i
$486$		0			0
$487$	−13.8933	−	10.0941i	−0.629566	−	0.457407i	0.226684	−	0.973968i	$-0.427212\pi$
$487$	−13.8933	−	10.0941i	−0.629566	−	0.457407i	−0.856250	+	0.516562i	$0.827212\pi$
$488$		0			0
$489$	40.9216			1.85054
$490$		0			0
$491$	0.778970			0.0351544			0.0175772	−	0.999846i	$-0.494405\pi$
$491$	0.778970			0.0351544			0.0175772	+	0.999846i	$0.494405\pi$
$492$		0			0
$493$	−0.221491			−0.00997545
$494$		0			0
$495$	−123.979			−5.57243
$496$		0			0
$497$	10.3009	+	7.48408i	0.462061	+	0.335707i
$498$		0			0
$499$	7.92262	+	24.3833i	0.354665	+	1.09155i	0.956203	+	0.292703i	$0.0945546\pi$
$499$	7.92262	+	24.3833i	0.354665	+	1.09155i	−0.601538	+	0.798844i	$0.705445\pi$
$500$		0			0
$501$	36.2308			1.61867
$502$		0			0
$503$	1.88198	−	1.36734i	0.0839136	−	0.0609668i	−0.545037	−	0.838412i	$-0.683485\pi$
$503$	1.88198	−	1.36734i	0.0839136	−	0.0609668i	0.628951	+	0.777445i	$0.283485\pi$
$504$		0			0
$505$	14.1835	−	43.6523i	0.631158	−	1.94250i
$506$		0			0
$507$	−2.62534	−	1.90742i	−0.116595	−	0.0847114i
$508$		0			0
$509$	−25.5408	+	18.5565i	−1.13207	+	0.822501i	−0.985995	−	0.166772i	$-0.946666\pi$
$509$	−25.5408	+	18.5565i	−1.13207	+	0.822501i	−0.146079	+	0.989273i	$0.546666\pi$
$510$		0			0
$511$	1.25948	+	3.87628i	0.0557161	+	0.171477i
$512$		0			0
$513$	−12.2070	−	37.5692i	−0.538951	−	1.65872i
$514$		0			0
$515$	−11.7906	+	36.2879i	−0.519558	+	1.59904i
$516$		0			0
$517$	8.02621	+	24.7021i	0.352992	+	1.08640i
$518$		0			0
$519$	19.5989			0.860295
$520$		0			0
$521$	19.6066	+	14.2450i	0.858981	+	0.624086i	0.927608	−	0.373556i	$-0.121862\pi$
$521$	19.6066	+	14.2450i	0.858981	+	0.624086i	−0.0686266	+	0.997642i	$0.521862\pi$
$522$		0			0
$523$	13.0554	−	9.48532i	0.570874	−	0.414764i	−0.264549	−	0.964372i	$-0.585223\pi$
$523$	13.0554	−	9.48532i	0.570874	−	0.414764i	0.835423	+	0.549608i	$0.185223\pi$
$524$		0			0
$525$	33.1034	−	24.0510i	1.44475	−	1.04967i
$526$		0			0
$527$	4.05583	−	12.4826i	0.176675	−	0.543749i
$528$		0			0
$529$	−20.6011	−	14.9676i	−0.895699	−	0.650763i
$530$		0			0
$531$	−7.58846	+	23.3549i	−0.329311	+	1.01352i
$532$		0			0
$533$	−23.9924	−	1.65163i	−1.03923	−	0.0715400i
$534$		0			0
$535$	23.1443	−	71.2307i	1.00061	−	3.07957i
$536$		0			0
$537$	44.1790	+	32.0979i	1.90646	+	1.38513i
$538$		0			0
$539$	1.57090	−	4.83475i	0.0676636	−	0.208247i
$540$		0			0
$541$	−15.8377	+	11.5068i	−0.680916	+	0.494714i	−0.873661	−	0.486534i	$-0.838261\pi$
$541$	−15.8377	+	11.5068i	−0.680916	+	0.494714i	0.192745	+	0.981249i	$0.438261\pi$
$542$		0			0
$543$	−26.9696	+	19.5945i	−1.15737	+	0.840882i
$544$		0			0
$545$	24.3298	+	17.6766i	1.04217	+	0.757183i
$546$		0			0
$547$	6.49451			0.277685			0.138843	−	0.990314i	$-0.455662\pi$
$547$	6.49451			0.277685			0.138843	+	0.990314i	$0.455662\pi$
$548$		0			0
$549$	24.2304	+	74.5735i	1.03413	+	3.18272i
$550$		0			0
$551$	0.213965	−	0.658516i	0.00911520	−	0.0280537i
$552$		0			0
$553$	2.08538	+	6.41815i	0.0886796	+	0.272928i
$554$		0			0
$555$	26.3897	+	81.2190i	1.12018	+	3.44756i
$556$		0			0
$557$	−1.78047	+	1.29359i	−0.0754410	+	0.0548111i	−0.624866	−	0.780732i	$-0.714847\pi$
$557$	−1.78047	+	1.29359i	−0.0754410	+	0.0548111i	0.549426	+	0.835543i	$0.314847\pi$
$558$		0			0
$559$	7.93732	+	5.76680i	0.335713	+	0.243910i
$560$		0			0
$561$	7.62819	−	23.4772i	0.322063	−	0.991207i
$562$		0			0
$563$	−16.0736	+	11.6782i	−0.677423	+	0.492177i	−0.872502	−	0.488611i	$-0.837504\pi$
$563$	−16.0736	+	11.6782i	−0.677423	+	0.492177i	0.195079	+	0.980788i	$0.437504\pi$
$564$		0			0
$565$	57.6860			2.42687
$566$		0			0
$567$	−1.72385	−	5.30546i	−0.0723948	−	0.222808i
$568$		0			0
$569$	26.2852	+	19.0973i	1.10193	+	0.800600i	0.981374	−	0.192106i	$-0.0615318\pi$
$569$	26.2852	+	19.0973i	1.10193	+	0.800600i	0.120557	+	0.992706i	$0.461532\pi$
$570$		0			0
$571$	−34.5278			−1.44494			−0.722471	−	0.691401i	$-0.756994\pi$
$571$	−34.5278			−1.44494			−0.722471	+	0.691401i	$0.756994\pi$
$572$		0			0
$573$	−59.4061			−2.48173
$574$		0			0
$575$	97.1224			4.05028
$576$		0			0
$577$	5.02718			0.209284			0.104642	−	0.994510i	$-0.466630\pi$
$577$	5.02718			0.209284			0.104642	+	0.994510i	$0.466630\pi$
$578$		0			0
$579$	15.8711	+	11.5311i	0.659582	+	0.479214i
$580$		0			0
$581$	−2.54828	−	7.84280i	−0.105720	−	0.325374i
$582$		0			0
$583$	51.4286			2.12996
$584$		0			0
$585$	74.1047	−	53.8402i	3.06385	−	2.22602i
$586$		0			0
$587$	−5.50767	+	16.9509i	−0.227326	+	0.699637i	0.770721	+	0.637172i	$0.219896\pi$
$587$	−5.50767	+	16.9509i	−0.227326	+	0.699637i	−0.998047	+	0.0624647i	$0.980104\pi$
$588$		0			0
$589$	33.1939	+	24.1168i	1.36773	+	0.993715i
$590$		0			0
$591$	18.9873	−	13.7951i	0.781033	−	0.567454i
$592$		0			0
$593$	−3.76446	−	11.5858i	−0.154588	−	0.475772i	0.843531	−	0.537080i	$-0.180473\pi$
$593$	−3.76446	−	11.5858i	−0.154588	−	0.475772i	−0.998119	+	0.0613081i	$0.980473\pi$
$594$		0			0
$595$	2.22723	+	6.85472i	0.0913076	+	0.281016i
$596$		0			0
$597$	−5.82537	+	17.9287i	−0.238417	+	0.733771i
$598$		0			0
$599$	8.59404	+	26.4497i	0.351143	+	1.08071i	0.958212	+	0.286058i	$0.0923450\pi$
$599$	8.59404	+	26.4497i	0.351143	+	1.08071i	−0.607069	+	0.794649i	$0.707655\pi$
$600$		0			0
$601$	30.9284			1.26160			0.630798	−	0.775947i	$-0.282728\pi$
$601$	30.9284			1.26160			0.630798	+	0.775947i	$0.282728\pi$
$602$		0			0
$603$	−27.3949	−	19.9036i	−1.11561	−	0.810536i
$604$		0			0
$605$	52.2735	−	37.9789i	2.12522	−	1.54406i
$606$		0			0
$607$	36.5550	−	26.5587i	1.48372	−	1.07799i	0.507385	−	0.861719i	$-0.330612\pi$
$607$	36.5550	−	26.5587i	1.48372	−	1.07799i	0.976334	−	0.216266i	$-0.0693879\pi$
$608$		0			0
$609$	0.121249	−	0.373166i	0.00491326	−	0.0151215i
$610$		0			0
$611$	−15.5248	−	11.2795i	−0.628068	−	0.456318i
$612$		0			0
$613$	−10.6742	+	32.8519i	−0.431128	+	1.32687i	0.465875	+	0.884850i	$0.345739\pi$
$613$	−10.6742	+	32.8519i	−0.431128	+	1.32687i	−0.897003	+	0.442024i	$0.854261\pi$
$614$		0			0
$615$	30.5440	−	75.8352i	1.23165	−	3.05797i
$616$		0			0
$617$	−2.80702	+	8.63912i	−0.113006	+	0.347798i	−0.991526	−	0.129908i	$-0.958532\pi$
$617$	−2.80702	+	8.63912i	−0.113006	+	0.347798i	0.878520	+	0.477706i	$0.158532\pi$
$618$		0			0
$619$	5.33688	+	3.87747i	0.214507	+	0.155849i	0.689851	−	0.723952i	$-0.257676\pi$
$619$	5.33688	+	3.87747i	0.214507	+	0.155849i	−0.475343	+	0.879800i	$0.657676\pi$
$620$		0			0
$621$	16.4191	−	50.5328i	0.658876	−	2.02781i
$622$		0			0
$623$	1.40920	−	1.02384i	0.0564583	−	0.0410194i
$624$		0			0
$625$	−80.8026	+	58.7065i	−3.23210	+	2.34826i
$626$		0			0
$627$	62.4311	+	45.3588i	2.49326	+	1.81146i
$628$		0			0
$629$	−11.0737			−0.441539
$630$		0			0
$631$	4.54033	+	13.9737i	0.180748	+	0.556284i	0.999849	−	0.0173645i	$-0.00552757\pi$
$631$	4.54033	+	13.9737i	0.180748	+	0.556284i	−0.819102	+	0.573648i	$0.805528\pi$
$632$		0			0
$633$	−5.12345	+	15.7684i	−0.203639	+	0.626736i
$634$		0			0
$635$	12.0531	+	37.0955i	0.478311	+	1.47209i
$636$		0			0
$637$	1.16062	+	3.57203i	0.0459855	+	0.141529i
$638$		0			0
$639$	−57.7085	+	41.9277i	−2.28291	+	1.65863i
$640$		0			0
$641$	23.3660	+	16.9764i	0.922900	+	0.670526i	0.944244	−	0.329246i	$-0.106795\pi$
$641$	23.3660	+	16.9764i	0.922900	+	0.670526i	−0.0213442	+	0.999772i	$0.506795\pi$
$642$		0			0
$643$	9.18203	−	28.2594i	0.362104	−	1.11444i	−0.589671	−	0.807644i	$-0.700742\pi$
$643$	9.18203	−	28.2594i	0.362104	−	1.11444i	0.951775	−	0.306798i	$-0.0992575\pi$
$644$		0			0
$645$	−26.9829	+	19.6042i	−1.06245	+	0.771916i
$646$		0			0
$647$	24.4529			0.961344			0.480672	−	0.876900i	$-0.340393\pi$
$647$	24.4529			0.961344			0.480672	+	0.876900i	$0.340393\pi$
$648$		0			0
$649$	−6.88586	−	21.1925i	−0.270294	−	0.831879i
$650$		0			0
$651$	18.8103	+	13.6665i	0.737233	+	0.535631i
$652$		0			0
$653$	36.4553			1.42661			0.713304	−	0.700855i	$-0.247198\pi$
$653$	36.4553			1.42661			0.713304	+	0.700855i	$0.247198\pi$
$654$		0			0
$655$	26.0170			1.01657
$656$		0			0
$657$	−22.8335			−0.890818
$658$		0			0
$659$	−43.3632			−1.68919			−0.844594	−	0.535407i	$-0.820158\pi$
$659$	−43.3632			−1.68919			−0.844594	+	0.535407i	$0.820158\pi$
$660$		0			0
$661$	33.2698	+	24.1719i	1.29405	+	0.940179i	0.999879	−	0.0155751i	$-0.00495791\pi$
$661$	33.2698	+	24.1719i	1.29405	+	0.940179i	0.294167	+	0.955754i	$0.404958\pi$
$662$		0			0
$663$	5.63590	+	17.3455i	0.218880	+	0.673644i
$664$		0			0
$665$	−22.5313			−0.873728
$666$		0			0
$667$	0.753457	−	0.547419i	0.0291740	−	0.0211961i
$668$		0			0
$669$	2.35882	−	7.25971i	0.0911973	−	0.280676i
$670$		0			0
$671$	−57.5626	−	41.8217i	−2.22218	−	1.61451i
$672$		0			0
$673$	29.1907	−	21.2083i	1.12522	−	0.817520i	0.140228	−	0.990119i	$-0.455217\pi$
$673$	29.1907	−	21.2083i	1.12522	−	0.817520i	0.984992	+	0.172599i	$0.0552165\pi$
$674$		0			0
$675$	32.9038	+	101.268i	1.26647	+	3.89779i
$676$		0			0
$677$	−4.02019	−	12.3729i	−0.154508	−	0.475528i	0.843602	−	0.536968i	$-0.180431\pi$
$677$	−4.02019	−	12.3729i	−0.154508	−	0.475528i	−0.998111	+	0.0614406i	$0.980431\pi$
$678$		0			0
$679$	−2.31058	+	7.11124i	−0.0886720	+	0.272904i
$680$		0			0
$681$	−8.15279	−	25.0917i	−0.312416	−	0.961516i
$682$		0			0
$683$	26.0596			0.997141			0.498571	−	0.866849i	$-0.333858\pi$
$683$	26.0596			0.997141			0.498571	+	0.866849i	$0.333858\pi$
$684$		0			0
$685$	57.9210	+	42.0821i	2.21305	+	1.60787i
$686$		0			0
$687$	−19.5618	+	14.2125i	−0.746330	+	0.542240i
$688$		0			0
$689$	−30.7400	+	22.3339i	−1.17110	+	0.850854i
$690$		0			0
$691$	12.6368	−	38.8920i	0.480726	−	1.47952i	−0.357350	−	0.933970i	$-0.616320\pi$
$691$	12.6368	−	38.8920i	0.480726	−	1.47952i	0.838077	−	0.545553i	$-0.183680\pi$
$692$		0			0
$693$	23.0403	+	16.7397i	0.875228	+	0.635890i
$694$		0			0
$695$	3.31423	−	10.2001i	0.125716	−	0.386914i
$696$		0			0
$697$	8.12841	+	6.80557i	0.307886	+	0.257780i
$698$		0			0
$699$	21.8073	−	67.1160i	0.824829	−	2.53856i
$700$		0			0
$701$	−20.9474	−	15.2192i	−0.791172	−	0.574820i	0.117139	−	0.993116i	$-0.462628\pi$
$701$	−20.9474	−	15.2192i	−0.791172	−	0.574820i	−0.908311	+	0.418295i	$0.862628\pi$
$702$		0			0
$703$	10.6975	−	32.9234i	0.403462	−	1.24173i
$704$		0			0
$705$	52.7767	−	38.3445i	1.98768	−	1.44414i
$706$		0			0
$707$	−8.52985	+	6.19730i	−0.320798	+	0.233074i
$708$		0			0
$709$	−12.2562	−	8.90466i	−0.460292	−	0.334422i	0.333354	−	0.942802i	$-0.391820\pi$
$709$	−12.2562	−	8.90466i	−0.460292	−	0.334422i	−0.793646	+	0.608380i	$0.791820\pi$
$710$		0			0
$711$	−37.8065			−1.41786
$712$		0			0
$713$	17.0539	+	52.4866i	0.638675	+	1.96564i
$714$		0			0
$715$	−25.6847	+	79.0495i	−0.960555	+	2.95628i
$716$		0			0
$717$	−12.1199	−	37.3012i	−0.452626	−	1.39304i
$718$		0			0
$719$	−3.60348	−	11.0904i	−0.134387	−	0.413601i	0.861107	−	0.508424i	$-0.169772\pi$
$719$	−3.60348	−	11.0904i	−0.134387	−	0.413601i	−0.995494	+	0.0948228i	$0.969772\pi$
$720$		0			0
$721$	7.09081	−	5.15177i	0.264076	−	0.191862i
$722$		0			0
$723$	−13.1438	−	9.54954i	−0.488823	−	0.355151i
$724$		0			0
$725$	−0.576741	+	1.77503i	−0.0214196	+	0.0659228i
$726$		0			0
$727$	26.4075	−	19.1862i	0.979400	−	0.711576i	0.0218255	−	0.999762i	$-0.493052\pi$
$727$	26.4075	−	19.1862i	0.979400	−	0.711576i	0.957574	+	0.288186i	$0.0930522\pi$
$728$		0			0
$729$	−35.9036			−1.32976
$730$		0			0
$731$	−1.33646	−	4.11320i	−0.0494308	−	0.152132i
$732$		0			0
$733$	−26.2864	−	19.0982i	−0.970909	−	0.705406i	−0.0152502	−	0.999884i	$-0.504854\pi$
$733$	−26.2864	−	19.0982i	−0.970909	−	0.705406i	−0.955658	+	0.294477i	$0.904854\pi$
$734$		0			0
$735$	−12.7680			−0.470955
$736$		0			0
$737$	30.7268			1.13184
$738$		0			0
$739$	23.7182			0.872486			0.436243	−	0.899829i	$-0.356309\pi$
$739$	23.7182			0.872486			0.436243	+	0.899829i	$0.356309\pi$
$740$		0			0
$741$	−57.0144			−2.09448
$742$		0			0
$743$	−4.02269	−	2.92265i	−0.147578	−	0.107222i	0.511546	−	0.859256i	$-0.329073\pi$
$743$	−4.02269	−	2.92265i	−0.147578	−	0.107222i	−0.659124	+	0.752034i	$0.729073\pi$
$744$		0			0
$745$	−3.75245	−	11.5488i	−0.137479	−	0.423117i
$746$		0			0
$747$	46.1985			1.69031
$748$		0			0
$749$	−13.9188	+	10.1126i	−0.508581	+	0.369506i
$750$		0			0
$751$	−3.33461	+	10.2629i	−0.121682	+	0.374497i	−0.993282	−	0.115720i	$-0.963083\pi$
$751$	−3.33461	+	10.2629i	−0.121682	+	0.374497i	0.871600	+	0.490217i	$0.163083\pi$
$752$		0			0
$753$	−46.2147	−	33.5770i	−1.68416	−	1.22361i
$754$		0			0
$755$	−2.74523	+	1.99452i	−0.0999090	+	0.0725881i
$756$		0			0
$757$	−7.40038	−	22.7760i	−0.268971	−	0.827809i	−0.990752	−	0.135687i	$-0.956676\pi$
$757$	−7.40038	−	22.7760i	−0.268971	−	0.827809i	0.721780	−	0.692122i	$-0.243324\pi$
$758$		0			0
$759$	32.0750	+	98.7167i	1.16425	+	3.58319i
$760$		0			0
$761$	16.2157	−	49.9068i	0.587818	−	1.80912i	0.000172484	−	1.00000i	$-0.499945\pi$
$761$	16.2157	−	49.9068i	0.587818	−	1.80912i	0.587646	−	0.809118i	$-0.300055\pi$
$762$		0			0
$763$	−2.13474	−	6.57007i	−0.0772829	−	0.237852i
$764$		0			0
$765$	−40.3781			−1.45987
$766$		0			0
$767$	13.3191	+	9.67689i	0.480925	+	0.349412i
$768$		0			0
$769$	−35.7763	+	25.9930i	−1.29013	+	0.937331i	−0.999808	−	0.0195991i	$-0.993761\pi$
$769$	−35.7763	+	25.9930i	−1.29013	+	0.937331i	−0.290318	+	0.956930i	$0.593761\pi$
$770$		0			0
$771$	5.45608	−	3.96408i	0.196496	−	0.142763i
$772$		0			0
$773$	−5.06492	+	15.5882i	−0.182173	+	0.560670i	−0.999888	−	0.0149527i	$-0.995240\pi$
$773$	−5.06492	+	15.5882i	−0.182173	+	0.560670i	0.817716	+	0.575623i	$0.195240\pi$
$774$		0			0
$775$	−89.4740	−	65.0067i	−3.21400	−	2.33511i
$776$		0			0
$777$	6.06201	−	18.6570i	0.217473	−	0.669314i
$778$		0			0
$779$	−28.0859	+	17.5923i	−1.00628	+	0.630309i
$780$		0			0
$781$	20.0018	−	61.5592i	0.715721	−	2.20276i
$782$		0			0
$783$	0.826045	+	0.600157i	0.0295204	+	0.0214478i
$784$		0			0
$785$	11.0401	−	33.9780i	0.394039	−	1.21273i
$786$		0			0
$787$	−17.1349	+	12.4492i	−0.610794	+	0.443768i	−0.849694	−	0.527277i	$-0.823213\pi$
$787$	−17.1349	+	12.4492i	−0.610794	+	0.443768i	0.238900	+	0.971044i	$0.423213\pi$
$788$		0			0
$789$	−3.22331	+	2.34187i	−0.114753	+	0.0833727i
$790$		0			0
$791$	−10.7204	−	7.78883i	−0.381174	−	0.276939i
$792$		0			0
$793$	52.5683			1.86675
$794$		0			0
$795$	−39.9156	−	122.848i	−1.41566	−	4.35696i
$796$		0			0
$797$	7.70415	−	23.7109i	0.272895	−	0.839884i	−0.716874	−	0.697203i	$-0.754428\pi$
$797$	7.70415	−	23.7109i	0.272895	−	0.839884i	0.989769	−	0.142681i	$-0.0455724\pi$
$798$		0			0
$799$	2.61402	+	8.04513i	0.0924775	+	0.284616i
$800$		0			0
$801$	3.01550	+	9.28076i	0.106547	+	0.327919i
$802$		0			0
$803$	16.7623	−	12.1785i	0.591529	−	0.429771i
$804$		0			0
$805$	−24.5180	−	17.8134i	−0.864148	−	0.627840i
$806$		0			0
$807$	8.83261	−	27.1840i	0.310923	−	0.956922i
$808$		0			0
$809$	−9.86274	+	7.16570i	−0.346755	+	0.251933i	−0.747507	−	0.664254i	$-0.768749\pi$
$809$	−9.86274	+	7.16570i	−0.346755	+	0.251933i	0.400751	+	0.916187i	$0.368749\pi$
$810$		0			0
$811$	−5.23498			−0.183825			−0.0919124	−	0.995767i	$-0.529298\pi$
$811$	−5.23498			−0.183825			−0.0919124	+	0.995767i	$0.529298\pi$
$812$		0			0
$813$	21.8652	+	67.2942i	0.766847	+	2.36011i
$814$		0			0
$815$	49.1384	+	35.7012i	1.72124	+	1.25056i
$816$		0			0
$817$	13.5200			0.473006
$818$		0			0
$819$	−21.0412			−0.735240
$820$		0			0
$821$	35.3270			1.23292			0.616461	−	0.787386i	$-0.288566\pi$
$821$	35.3270			1.23292			0.616461	+	0.787386i	$0.288566\pi$
$822$		0			0
$823$	−27.8609			−0.971170			−0.485585	−	0.874190i	$-0.661393\pi$
$823$	−27.8609			−0.971170			−0.485585	+	0.874190i	$0.661393\pi$
$824$		0			0
$825$	−168.283	−	122.264i	−5.85885	−	4.25670i
$826$		0			0
$827$	15.3016	+	47.0935i	0.532089	+	1.63760i	0.749856	+	0.661601i	$0.230123\pi$
$827$	15.3016	+	47.0935i	0.532089	+	1.63760i	−0.217767	+	0.976001i	$0.569877\pi$
$828$		0			0
$829$	25.6978			0.892521			0.446261	−	0.894903i	$-0.352755\pi$
$829$	25.6978			0.892521			0.446261	+	0.894903i	$0.352755\pi$
$830$		0			0
$831$	5.36000	−	3.89427i	0.185936	−	0.135091i
$832$		0			0
$833$	0.511621	−	1.57461i	0.0177266	−	0.0545569i
$834$		0			0
$835$	43.5057	+	31.6088i	1.50558	+	1.09387i
$836$		0			0
$837$	−48.9491	+	35.5636i	−1.69193	+	1.22926i
$838$		0			0
$839$	15.9373	+	49.0499i	0.550215	+	1.69339i	0.708255	+	0.705956i	$0.249483\pi$
$839$	15.9373	+	49.0499i	0.550215	+	1.69339i	−0.158040	+	0.987433i	$0.550517\pi$
$840$		0			0
$841$	−8.95596	−	27.5636i	−0.308826	−	0.950470i
$842$		0			0
$843$	−14.6156	+	44.9823i	−0.503389	+	1.54927i
$844$		0			0
$845$	−1.48840	−	4.58083i	−0.0512026	−	0.157585i
$846$		0			0
$847$	−14.8425			−0.509994
$848$		0			0
$849$	−57.1334	−	41.5098i	−1.96081	−	1.42461i
$850$		0			0
$851$	37.6701	−	27.3689i	1.29131	−	0.938195i
$852$		0			0
$853$	−30.5824	+	22.2194i	−1.04712	+	0.760778i	−0.971663	−	0.236371i	$-0.924042\pi$
$853$	−30.5824	+	22.2194i	−1.04712	+	0.760778i	−0.0754584	+	0.997149i	$0.524042\pi$
$854$		0			0
$855$	39.0061	−	120.048i	1.33398	−	4.10556i
$856$		0			0
$857$	−26.7550	−	19.4387i	−0.913934	−	0.664012i	0.0280728	−	0.999606i	$-0.491063\pi$
$857$	−26.7550	−	19.4387i	−0.913934	−	0.664012i	−0.942007	+	0.335594i	$0.891063\pi$
$858$		0			0
$859$	−5.91528	+	18.2054i	−0.201827	+	0.621159i	0.798002	+	0.602655i	$0.205890\pi$
$859$	−5.91528	+	18.2054i	−0.201827	+	0.621159i	−0.999829	+	0.0185042i	$0.994110\pi$
$860$		0			0
$861$	−15.9157	+	9.96917i	−0.542404	+	0.339748i
$862$		0			0
$863$	15.7617	−	48.5096i	0.536535	−	1.65129i	−0.203774	−	0.979018i	$-0.565321\pi$
$863$	15.7617	−	48.5096i	0.536535	−	1.65129i	0.740309	−	0.672267i	$-0.234679\pi$
$864$		0			0
$865$	23.5342	+	17.0986i	0.800187	+	0.581370i
$866$		0			0
$867$	−12.9233	+	39.7738i	−0.438898	+	1.35079i
$868$		0			0
$869$	27.7542	−	20.1646i	0.941497	−	0.684038i
$870$		0			0
$871$	−18.3661	+	13.3437i	−0.622310	+	0.452135i
$872$		0			0
$873$	−33.8891	−	24.6218i	−1.14697	−	0.833323i
$874$		0			0
$875$	38.9667			1.31731
$876$		0			0
$877$	−3.15829	−	9.72023i	−0.106648	−	0.328229i	0.883466	−	0.468496i	$-0.155204\pi$
$877$	−3.15829	−	9.72023i	−0.106648	−	0.328229i	−0.990114	+	0.140267i	$0.955204\pi$
$878$		0			0
$879$	−27.1475	+	83.5514i	−0.915662	+	2.81812i
$880$		0			0
$881$	9.63399	+	29.6504i	0.324578	+	0.998947i	0.971631	+	0.236502i	$0.0760011\pi$
$881$	9.63399	+	29.6504i	0.324578	+	0.998947i	−0.647053	+	0.762445i	$0.723999\pi$
$882$		0			0
$883$	12.0265	+	37.0139i	0.404725	+	1.24562i	0.921125	+	0.389268i	$0.127272\pi$
$883$	12.0265	+	37.0139i	0.404725	+	1.24562i	−0.516399	+	0.856348i	$0.672728\pi$
$884$		0			0
$885$	−45.2782	+	32.8966i	−1.52201	+	1.10581i
$886$		0			0
$887$	−9.87971	−	7.17803i	−0.331728	−	0.241015i	0.409435	−	0.912339i	$-0.365726\pi$
$887$	−9.87971	−	7.17803i	−0.331728	−	0.241015i	−0.741164	+	0.671324i	$0.765726\pi$
$888$		0			0
$889$	2.76873	−	8.52126i	0.0928601	−	0.285794i
$890$		0			0
$891$	−22.9425	+	16.6687i	−0.768604	+	0.558424i
$892$		0			0
$893$	−26.4442			−0.884922
$894$		0			0
$895$	25.0468	+	77.0860i	0.837221	+	2.57670i
$896$		0			0
$897$	−62.0416	−	45.0759i	−2.07151	−	1.50504i
$898$		0			0
$899$	−1.06053			−0.0353705
$900$		0			0
$901$	16.7496			0.558009
$902$		0			0
$903$	7.66150			0.254959
$904$		0			0
$905$	−49.4797			−1.64476
$906$		0			0
$907$	−43.1806	−	31.3726i	−1.43379	−	1.04171i	−0.989295	−	0.145927i	$-0.953383\pi$
$907$	−43.1806	−	31.3726i	−1.43379	−	1.04171i	−0.444494	−	0.895782i	$-0.646617\pi$
$908$		0			0
$909$	−18.2528	−	56.1763i	−0.605407	−	1.86325i
$910$		0			0
$911$	26.6600			0.883284			0.441642	−	0.897191i	$-0.354396\pi$
$911$	26.6600			0.883284			0.441642	+	0.897191i	$0.354396\pi$
$912$		0			0
$913$	−33.9148	+	24.6406i	−1.12242	+	0.815484i
$914$		0			0
$915$	−55.2231	+	169.959i	−1.82562	+	5.61868i
$916$		0			0
$917$	−4.83502	−	3.51285i	−0.159666	−	0.116004i
$918$		0			0
$919$	−40.8950	+	29.7120i	−1.34900	+	0.980107i	−0.349942	+	0.936772i	$0.613799\pi$
$919$	−40.8950	+	29.7120i	−1.34900	+	0.980107i	−0.999061	+	0.0433359i	$0.986201\pi$
$920$		0			0
$921$	−18.9149	−	58.2141i	−0.623267	−	1.91822i
$922$		0			0
$923$	14.7778	+	45.4814i	0.486418	+	1.49704i
$924$		0			0
$925$	−28.8349	+	88.7448i	−0.948086	+	2.91791i
$926$		0			0
$927$	15.1734	+	46.6990i	0.498360	+	1.53380i
$928$		0			0
$929$	−36.9956			−1.21379			−0.606894	−	0.794783i	$-0.707585\pi$
$929$	−36.9956			−1.21379			−0.606894	+	0.794783i	$0.707585\pi$
$930$		0			0
$931$	4.18724	+	3.04220i	0.137231	+	0.0997042i
$932$		0			0
$933$	−5.01955	+	3.64692i	−0.164333	+	0.119395i
$934$		0			0
$935$	29.6420	−	21.5362i	0.969398	−	0.704309i
$936$		0			0
$937$	6.43753	−	19.8127i	0.210305	−	0.647252i	−0.789149	−	0.614202i	$-0.789478\pi$
$937$	6.43753	−	19.8127i	0.210305	−	0.647252i	0.999454	−	0.0330500i	$-0.0105221\pi$
$938$		0			0
$939$	30.5426	+	22.1905i	0.996719	+	0.724158i
$940$		0			0
$941$	7.39498	−	22.7594i	0.241070	−	0.741936i	−0.755189	−	0.655508i	$-0.772455\pi$
$941$	7.39498	−	22.7594i	0.241070	−	0.741936i	0.996258	−	0.0864281i	$-0.0275453\pi$
$942$		0			0
$943$	−44.4709	−	3.06137i	−1.44817	−	0.0996918i
$944$		0			0
$945$	10.2673	−	31.5994i	0.333995	−	1.02793i
$946$		0			0
$947$	9.91587	+	7.20430i	0.322222	+	0.234108i	0.737123	−	0.675758i	$-0.236184\pi$
$947$	9.91587	+	7.20430i	0.322222	+	0.234108i	−0.414901	+	0.909867i	$0.636184\pi$
$948$		0			0
$949$	−4.73042	+	14.5587i	−0.153556	+	0.472597i
$950$		0			0
$951$	−16.9665	+	12.3269i	−0.550178	+	0.399727i
$952$		0			0
$953$	27.0293	−	19.6379i	0.875564	−	0.636135i	−0.0565100	−	0.998402i	$-0.517997\pi$
$953$	27.0293	−	19.6379i	0.875564	−	0.636135i	0.932074	+	0.362267i	$0.117997\pi$
$954$		0			0
$955$	−71.3345	−	51.8276i	−2.30833	−	1.67710i
$956$		0			0
$957$	−1.99463			−0.0644774
$958$		0			0
$959$	−5.08210	−	15.6411i	−0.164110	−	0.505078i
$960$		0			0
$961$	9.84027	−	30.2853i	0.317428	−	0.976944i
$962$		0			0
$963$	−29.7844	−	91.6670i	−0.959789	−	2.95393i
$964$		0			0
$965$	8.99795	+	27.6928i	0.289654	+	0.891464i
$966$		0			0
$967$	−27.6744	+	20.1066i	−0.889948	+	0.646585i	−0.935864	−	0.352360i	$-0.885379\pi$
$967$	−27.6744	+	20.1066i	−0.889948	+	0.646585i	0.0459166	+	0.998945i	$0.485379\pi$
$968$		0			0
$969$	20.3329	+	14.7727i	0.653187	+	0.474568i
$970$		0			0
$971$	7.55402	−	23.2489i	0.242420	−	0.746092i	−0.753630	−	0.657299i	$-0.771699\pi$
$971$	7.55402	−	23.2489i	0.242420	−	0.746092i	0.996050	−	0.0887933i	$-0.0283011\pi$
$972$		0			0
$973$	−1.99315	+	1.44811i	−0.0638976	+	0.0464243i
$974$		0			0
$975$	153.682			4.92176
$976$		0			0
$977$	−3.56351	−	10.9674i	−0.114007	−	0.350877i	0.877732	−	0.479152i	$-0.159056\pi$
$977$	−3.56351	−	10.9674i	−0.114007	−	0.350877i	−0.991739	+	0.128275i	$0.959056\pi$
$978$		0			0
$979$	−7.16373	−	5.20475i	−0.228954	−	0.166345i
$980$		0			0
$981$	38.7014			1.23564
$982$		0			0
$983$	−51.0109			−1.62700			−0.813498	−	0.581568i	$-0.802440\pi$
$983$	−51.0109			−1.62700			−0.813498	+	0.581568i	$0.802440\pi$
$984$		0			0
$985$	34.8351			1.10994
$986$		0			0
$987$	−14.9854			−0.476989
$988$		0			0
$989$	14.7122	+	10.6890i	0.467820	+	0.339891i
$990$		0			0
$991$	−5.85223	−	18.0113i	−0.185902	−	0.572148i	0.814060	−	0.580780i	$-0.197252\pi$
$991$	−5.85223	−	18.0113i	−0.185902	−	0.572148i	−0.999963	+	0.00863179i	$0.997252\pi$
$992$		0			0
$993$	40.7813			1.29416
$994$		0			0
$995$	−22.6365	+	16.4464i	−0.717627	+	0.521386i
$996$		0			0
$997$	−5.05634	+	15.5618i	−0.160136	+	0.492847i	−0.998645	−	0.0520402i	$-0.983428\pi$
$997$	−5.05634	+	15.5618i	−0.160136	+	0.492847i	0.838509	+	0.544887i	$0.183428\pi$
$998$		0			0
$999$	41.2992	+	30.0056i	1.30665	+	0.949336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.n.e.57.6	✓	24
41.18	even	5	inner	1148.2.n.e.141.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.n.e.57.6	✓	24	1.1	even	1	trivial
1148.2.n.e.141.6	yes	24	41.18	even	5	inner

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)

\(f(q)\)	\(=\)	\(q+2.93296 q^{3} +(3.52188 + 2.55880i) q^{5} +(-0.309017 - 0.951057i) q^{7} +5.60225 q^{9} +O(q^{10})\)	\(q+2.93296 q^{3} +(3.52188 + 2.55880i) q^{5} +(-0.309017 - 0.951057i) q^{7} +5.60225 q^{9} +(-4.11268 + 2.98804i) q^{11} +(1.16062 - 3.57203i) q^{13} +(10.3295 + 7.50485i) q^{15} +(-1.33944 + 0.973161i) q^{17} +(-1.59938 - 4.92239i) q^{19} +(-0.906334 - 2.78941i) q^{21} +(2.15126 - 6.62091i) q^{23} +(4.31112 + 13.2683i) q^{25} +7.63231 q^{27} +(0.108230 + 0.0786337i) q^{29} +(-6.41341 + 4.65961i) q^{31} +(-12.0623 + 8.76379i) q^{33} +(1.34524 - 4.14022i) q^{35} +(5.41110 + 3.93140i) q^{37} +(3.40406 - 10.4766i) q^{39} +(-1.55578 - 6.21124i) q^{41} +(-0.807217 + 2.48436i) q^{43} +(19.7305 + 14.3350i) q^{45} +(1.57886 - 4.85923i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-3.92853 + 2.85424i) q^{51} +(-8.18456 - 5.94643i) q^{53} -22.1302 q^{55} +(-4.69092 - 14.4372i) q^{57} +(-1.35454 + 4.16884i) q^{59} +(4.32512 + 13.3113i) q^{61} +(-1.73119 - 5.32806i) q^{63} +(13.2277 - 9.61046i) q^{65} +(-4.88998 - 3.55278i) q^{67} +(6.30957 - 19.4189i) q^{69} +(-10.3009 + 7.48408i) q^{71} -4.07576 q^{73} +(12.6444 + 38.9153i) q^{75} +(4.11268 + 2.98804i) q^{77} -6.74845 q^{79} +5.57849 q^{81} +8.24641 q^{83} -7.20747 q^{85} +(0.317434 + 0.230629i) q^{87} +(0.538266 + 1.65661i) q^{89} -3.75585 q^{91} +(-18.8103 + 13.6665i) q^{93} +(6.96256 - 21.4286i) q^{95} +(-6.04918 - 4.39499i) q^{97} +(-23.0403 + 16.7397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9	\( 24 q + 12 q^{3} + 17 q^{5} + 6 q^{7} + 16 q^{9} - 8 q^{11} + 10 q^{15} + 8 q^{17} - 28 q^{19} + 3 q^{21} - 23 q^{23} + 17 q^{25} + 12 q^{27} - 31 q^{29} + 2 q^{31} + 12 q^{33} + 13 q^{35} + 7 q^{37} - 16 q^{39} - q^{41} - 2 q^{43} + 71 q^{45} + 15 q^{47} - 6 q^{49} + 2 q^{51} + 28 q^{53} - 16 q^{55} - 15 q^{57} + 17 q^{59} + 35 q^{61} - q^{63} + 62 q^{65} - 10 q^{67} - 9 q^{69} - 25 q^{71} - 74 q^{73} + 17 q^{75} + 8 q^{77} + 64 q^{81} + 96 q^{83} - 94 q^{85} - q^{87} - 33 q^{89} - 15 q^{93} - 29 q^{95} - 34 q^{97} - 3 q^{99}+O(q^{100}) \) 24 * q + 12 * q^3 + 17 * q^5 + 6 * q^7 + 16 * q^9 - 8 * q^11 + 10 * q^15 + 8 * q^17 - 28 * q^19 + 3 * q^21 - 23 * q^23 + 17 * q^25 + 12 * q^27 - 31 * q^29 + 2 * q^31 + 12 * q^33 + 13 * q^35 + 7 * q^37 - 16 * q^39 - q^41 - 2 * q^43 + 71 * q^45 + 15 * q^47 - 6 * q^49 + 2 * q^51 + 28 * q^53 - 16 * q^55 - 15 * q^57 + 17 * q^59 + 35 * q^61 - q^63 + 62 * q^65 - 10 * q^67 - 9 * q^69 - 25 * q^71 - 74 * q^73 + 17 * q^75 + 8 * q^77 + 64 * q^81 + 96 * q^83 - 94 * q^85 - q^87 - 33 * q^89 - 15 * q^93 - 29 * q^95 - 34 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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