LMFDB - Embedded newform 1100.2.q.b.441.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(221,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			441.1
Character	$\chi$	$=$	1100.441
Dual form			1100.2.q.b.661.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.994170 - 3.05974i) q^{3} +(0.246812 - 2.22240i) q^{5} +3.71818 q^{7} +(-5.94659 + 4.32045i) q^{9} +(0.809017 + 0.587785i) q^{11} +(4.28842 - 3.11572i) q^{13} +(-7.04536 + 1.45427i) q^{15} +(1.97041 - 6.06429i) q^{17} +(0.930947 - 2.86516i) q^{19} +(-3.69650 - 11.3767i) q^{21} +(-3.48288 - 2.53046i) q^{23} +(-4.87817 - 1.09703i) q^{25} +(11.3231 + 8.22668i) q^{27} +(2.45046 + 7.54173i) q^{29} +(1.25238 - 3.85444i) q^{31} +(0.994170 - 3.05974i) q^{33} +(0.917693 - 8.26330i) q^{35} +(3.83144 - 2.78371i) q^{37} +(-13.7967 - 10.0239i) q^{39} +(-4.61092 + 3.35003i) q^{41} -6.06383 q^{43} +(8.13410 + 14.2821i) q^{45} +(2.92003 + 8.98693i) q^{47} +6.82487 q^{49} -20.5141 q^{51} +(4.42752 + 13.6265i) q^{53} +(1.50597 - 1.65289i) q^{55} -9.69216 q^{57} +(-8.86637 + 6.44179i) q^{59} +(8.31256 + 6.03943i) q^{61} +(-22.1105 + 16.0642i) q^{63} +(-5.86595 - 10.2996i) q^{65} +(1.52762 - 4.70152i) q^{67} +(-4.27997 + 13.1724i) q^{69} +(1.01480 + 3.12325i) q^{71} +(3.37402 + 2.45137i) q^{73} +(1.49309 + 16.0166i) q^{75} +(3.00807 + 2.18549i) q^{77} +(-0.287925 - 0.886141i) q^{79} +(7.10029 - 21.8524i) q^{81} +(-0.0152076 + 0.0468041i) q^{83} +(-12.9910 - 5.87578i) q^{85} +(20.6396 - 14.9955i) q^{87} +(-8.33891 - 6.05857i) q^{89} +(15.9451 - 11.5848i) q^{91} -13.0387 q^{93} +(-6.13778 - 2.77610i) q^{95} +(3.88576 + 11.9591i) q^{97} -7.35039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.994170	−	3.05974i	−0.573984	−	1.76654i	−0.639612	−	0.768698i	$-0.720905\pi$
$3$	−0.994170	−	3.05974i	−0.573984	−	1.76654i	0.0656278	−	0.997844i	$-0.479095\pi$
$4$		0			0
$5$	0.246812	−	2.22240i	0.110378	−	0.993890i
$5$	0.246812	−	2.22240i	0.110378	−	0.993890i
$6$		0			0
$7$	3.71818			1.40534			0.702670	−	0.711516i	$-0.251991\pi$
$7$	3.71818			1.40534			0.702670	+	0.711516i	$0.251991\pi$
$8$		0			0
$9$	−5.94659	+	4.32045i	−1.98220	+	1.44015i
$10$		0			0
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$11$	0.809017	+	0.587785i	0.243928	+	0.177224i
$12$		0			0
$13$	4.28842	−	3.11572i	1.18939	−	0.864145i	0.196193	−	0.980565i	$-0.437142\pi$
$13$	4.28842	−	3.11572i	1.18939	−	0.864145i	0.993200	+	0.116420i	$0.0371419\pi$
$14$		0			0
$15$	−7.04536	+	1.45427i	−1.81910	+	0.375490i
$16$		0			0
$17$	1.97041	−	6.06429i	0.477894	−	1.47081i	−0.364121	−	0.931351i	$-0.618631\pi$
$17$	1.97041	−	6.06429i	0.477894	−	1.47081i	0.842015	−	0.539454i	$-0.181369\pi$
$18$		0			0
$19$	0.930947	−	2.86516i	0.213574	−	0.657313i	−0.785678	−	0.618636i	$-0.787686\pi$
$19$	0.930947	−	2.86516i	0.213574	−	0.657313i	0.999252	−	0.0386769i	$-0.0123143\pi$
$20$		0			0
$21$	−3.69650	−	11.3767i	−0.806643	−	2.48259i
$22$		0			0
$23$	−3.48288	−	2.53046i	−0.726230	−	0.527637i	0.162139	−	0.986768i	$-0.448161\pi$
$23$	−3.48288	−	2.53046i	−0.726230	−	0.527637i	−0.888369	+	0.459131i	$0.848161\pi$
$24$		0			0
$25$	−4.87817	−	1.09703i	−0.975633	−	0.219407i
$26$		0			0
$27$	11.3231	+	8.22668i	2.17912	+	1.58323i
$28$		0			0
$29$	2.45046	+	7.54173i	0.455039	+	1.40046i	0.871090	+	0.491123i	$0.163414\pi$
$29$	2.45046	+	7.54173i	0.455039	+	1.40046i	−0.416051	+	0.909341i	$0.636586\pi$
$30$		0			0
$31$	1.25238	−	3.85444i	0.224935	−	0.692278i	−0.773364	−	0.633963i	$-0.781427\pi$
$31$	1.25238	−	3.85444i	0.224935	−	0.692278i	0.998298	−	0.0583150i	$-0.0185728\pi$
$32$		0			0
$33$	0.994170	−	3.05974i	0.173063	−	0.532632i
$34$		0			0
$35$	0.917693	−	8.26330i	0.155118	−	1.39675i
$36$		0			0
$37$	3.83144	−	2.78371i	0.629885	−	0.457639i	−0.226475	−	0.974017i	$-0.572720\pi$
$37$	3.83144	−	2.78371i	0.629885	−	0.457639i	0.856361	+	0.516378i	$0.172720\pi$
$38$		0			0
$39$	−13.7967	−	10.0239i	−2.20924	−	1.60511i
$40$		0			0
$41$	−4.61092	+	3.35003i	−0.720105	+	0.523187i	−0.886418	−	0.462886i	$-0.846814\pi$
$41$	−4.61092	+	3.35003i	−0.720105	+	0.523187i	0.166313	+	0.986073i	$0.446814\pi$
$42$		0			0
$43$	−6.06383			−0.924725			−0.462362	−	0.886691i	$-0.652998\pi$
$43$	−6.06383			−0.924725			−0.462362	+	0.886691i	$0.652998\pi$
$44$		0			0
$45$	8.13410	+	14.2821i	1.21256	+	2.12904i
$46$		0			0
$47$	2.92003	+	8.98693i	0.425930	+	1.31088i	0.902101	+	0.431526i	$0.142025\pi$
$47$	2.92003	+	8.98693i	0.425930	+	1.31088i	−0.476170	+	0.879353i	$0.657975\pi$
$48$		0			0
$49$	6.82487			0.974982
$50$		0			0
$51$	−20.5141			−2.87254
$52$		0			0
$53$	4.42752	+	13.6265i	0.608167	+	1.87175i	0.473347	+	0.880876i	$0.343046\pi$
$53$	4.42752	+	13.6265i	0.608167	+	1.87175i	0.134820	+	0.990870i	$0.456954\pi$
$54$		0			0
$55$	1.50597	−	1.65289i	0.203065	−	0.222876i
$56$		0			0
$57$	−9.69216			−1.28376
$58$		0			0
$59$	−8.86637	+	6.44179i	−1.15430	+	0.838650i	−0.989047	−	0.147601i	$-0.952845\pi$
$59$	−8.86637	+	6.44179i	−1.15430	+	0.838650i	−0.165256	+	0.986251i	$0.552845\pi$
$60$		0			0
$61$	8.31256	+	6.03943i	1.06431	+	0.773270i	0.974882	−	0.222723i	$-0.0714947\pi$
$61$	8.31256	+	6.03943i	1.06431	+	0.773270i	0.0894325	+	0.995993i	$0.471495\pi$
$62$		0			0
$63$	−22.1105	+	16.0642i	−2.78566	+	2.02390i
$64$		0			0
$65$	−5.86595	−	10.2996i	−0.727582	−	1.27751i
$66$		0			0
$67$	1.52762	−	4.70152i	0.186628	−	0.574382i	−0.813345	−	0.581782i	$-0.802356\pi$
$67$	1.52762	−	4.70152i	0.186628	−	0.574382i	0.999973	+	0.00740032i	$0.00235562\pi$
$68$		0			0
$69$	−4.27997	+	13.1724i	−0.515248	+	1.58577i
$70$		0			0
$71$	1.01480	+	3.12325i	0.120435	+	0.370661i	0.993042	−	0.117762i	$-0.0375721\pi$
$71$	1.01480	+	3.12325i	0.120435	+	0.370661i	−0.872607	+	0.488424i	$0.837572\pi$
$72$		0			0
$73$	3.37402	+	2.45137i	0.394900	+	0.286911i	0.767460	−	0.641096i	$-0.221520\pi$
$73$	3.37402	+	2.45137i	0.394900	+	0.286911i	−0.372561	+	0.928008i	$0.621520\pi$
$74$		0			0
$75$	1.49309	+	16.0166i	0.172407	+	1.84943i
$76$		0			0
$77$	3.00807	+	2.18549i	0.342802	+	0.249060i
$78$		0			0
$79$	−0.287925	−	0.886141i	−0.0323941	−	0.0996987i	0.933552	−	0.358442i	$-0.116692\pi$
$79$	−0.287925	−	0.886141i	−0.0323941	−	0.0996987i	−0.965946	+	0.258743i	$0.916692\pi$
$80$		0			0
$81$	7.10029	−	21.8524i	0.788921	−	2.42805i
$82$		0			0
$83$	−0.0152076	+	0.0468041i	−0.00166925	+	0.00513742i	−0.951888	−	0.306447i	$-0.900860\pi$
$83$	−0.0152076	+	0.0468041i	−0.00166925	+	0.00513742i	0.950218	+	0.311585i	$0.100860\pi$
$84$		0			0
$85$	−12.9910	−	5.87578i	−1.40907	−	0.637318i
$86$		0			0
$87$	20.6396	−	14.9955i	2.21279	−	1.60769i
$88$		0			0
$89$	−8.33891	−	6.05857i	−0.883923	−	0.642207i	0.0503636	−	0.998731i	$-0.483962\pi$
$89$	−8.33891	−	6.05857i	−0.883923	−	0.642207i	−0.934286	+	0.356524i	$0.883962\pi$
$90$		0			0
$91$	15.9451	−	11.5848i	1.67150	−	1.21442i
$92$		0			0
$93$	−13.0387			−1.35205
$94$		0			0
$95$	−6.13778	−	2.77610i	−0.629722	−	0.284822i
$96$		0			0
$97$	3.88576	+	11.9591i	0.394539	+	1.21427i	0.929320	+	0.369276i	$0.120394\pi$
$97$	3.88576	+	11.9591i	0.394539	+	1.21427i	−0.534781	+	0.844991i	$0.679606\pi$
$98$		0			0
$99$	−7.35039			−0.738742
$100$		0			0
$101$	11.8986			1.18396			0.591978	−	0.805954i	$-0.298347\pi$
$101$	11.8986			1.18396			0.591978	+	0.805954i	$0.298347\pi$
$102$		0			0
$103$	−3.68467	−	11.3403i	−0.363062	−	1.11739i	−0.951186	−	0.308618i	$-0.900133\pi$
$103$	−3.68467	−	11.3403i	−0.363062	−	1.11739i	0.588124	−	0.808770i	$-0.299867\pi$
$104$		0			0
$105$	−26.1959	+	5.40723i	−2.55646	+	0.527691i
$106$		0			0
$107$	−10.7914			−1.04325			−0.521624	−	0.853176i	$-0.674673\pi$
$107$	−10.7914			−1.04325			−0.521624	+	0.853176i	$0.674673\pi$
$108$		0			0
$109$	6.75935	−	4.91095i	0.647428	−	0.470384i	−0.214966	−	0.976622i	$-0.568964\pi$
$109$	6.75935	−	4.91095i	0.647428	−	0.470384i	0.862394	+	0.506237i	$0.168964\pi$
$110$		0			0
$111$	−12.3265	−	8.95575i	−1.16998	−	0.850042i
$112$		0			0
$113$	−9.39054	+	6.82263i	−0.883388	+	0.641819i	−0.934146	−	0.356892i	$-0.883836\pi$
$113$	−9.39054	+	6.82263i	−0.883388	+	0.641819i	0.0507578	+	0.998711i	$0.483836\pi$
$114$		0			0
$115$	−6.48332	+	7.11581i	−0.604573	+	0.663553i
$116$		0			0
$117$	−12.0402	+	37.0558i	−1.11311	+	3.42581i
$118$		0			0
$119$	7.32633	−	22.5481i	0.671603	−	2.06698i
$120$		0			0
$121$	0.309017	+	0.951057i	0.0280925	+	0.0864597i
$122$		0			0
$123$	14.8343	+	10.7777i	1.33756	+	0.971795i
$124$		0			0
$125$	−3.64205	+	10.5705i	−0.325754	+	0.945454i
$126$		0			0
$127$	−6.22216	−	4.52067i	−0.552128	−	0.401144i	0.276442	−	0.961031i	$-0.410845\pi$
$127$	−6.22216	−	4.52067i	−0.552128	−	0.401144i	−0.828569	+	0.559886i	$0.810845\pi$
$128$		0			0
$129$	6.02847	+	18.5537i	0.530778	+	1.63357i
$130$		0			0
$131$	1.97025	−	6.06382i	0.172142	−	0.529798i	−0.827349	−	0.561688i	$-0.810152\pi$
$131$	1.97025	−	6.06382i	0.172142	−	0.529798i	0.999491	+	0.0318891i	$0.0101523\pi$
$132$		0			0
$133$	3.46143	−	10.6532i	0.300144	−	0.923748i
$134$		0			0
$135$	21.0777	−	23.1340i	1.81408	−	1.99106i
$136$		0			0
$137$	9.37429	−	6.81082i	0.800899	−	0.581887i	−0.110279	−	0.993901i	$-0.535174\pi$
$137$	9.37429	−	6.81082i	0.800899	−	0.581887i	0.911178	+	0.412013i	$0.135174\pi$
$138$		0			0
$139$	−8.41594	−	6.11454i	−0.713831	−	0.518628i	0.170576	−	0.985344i	$-0.445437\pi$
$139$	−8.41594	−	6.11454i	−0.713831	−	0.518628i	−0.884407	+	0.466716i	$0.845437\pi$
$140$		0			0
$141$	24.5947	−	17.8691i	2.07125	−	1.50485i
$142$		0			0
$143$	5.30078			0.443273
$144$		0			0
$145$	17.3656	−	3.58452i	1.44213	−	0.297678i
$146$		0			0
$147$	−6.78508	−	20.8823i	−0.559624	−	1.72235i
$148$		0			0
$149$	3.77702			0.309425			0.154713	−	0.987960i	$-0.450555\pi$
$149$	3.77702			0.309425			0.154713	+	0.987960i	$0.450555\pi$
$150$		0			0
$151$	16.4622			1.33968			0.669839	−	0.742506i	$-0.266363\pi$
$151$	16.4622			1.33968			0.669839	+	0.742506i	$0.266363\pi$
$152$		0			0
$153$	14.4832	+	44.5748i	1.17090	+	3.60366i
$154$		0			0
$155$	−8.25702	−	3.73463i	−0.663220	−	0.299972i
$156$		0			0
$157$	−18.0578			−1.44117			−0.720585	−	0.693367i	$-0.756126\pi$
$157$	−18.0578			−1.44117			−0.720585	+	0.693367i	$0.756126\pi$
$158$		0			0
$159$	37.2919	−	27.0941i	2.95744	−	2.14871i
$160$		0			0
$161$	−12.9500	−	9.40870i	−1.02060	−	0.741509i
$162$		0			0
$163$	−7.21135	+	5.23935i	−0.564836	+	0.410378i	−0.833226	−	0.552933i	$-0.813509\pi$
$163$	−7.21135	+	5.23935i	−0.564836	+	0.410378i	0.268390	+	0.963310i	$0.413509\pi$
$164$		0			0
$165$	−6.55461	−	2.96463i	−0.510276	−	0.230796i
$166$		0			0
$167$	1.01765	−	3.13200i	0.0787480	−	0.242361i	−0.903931	−	0.427679i	$-0.859331\pi$
$167$	1.01765	−	3.13200i	0.0787480	−	0.242361i	0.982679	+	0.185318i	$0.0593314\pi$
$168$		0			0
$169$	4.66561	−	14.3593i	0.358893	−	1.10456i
$170$		0			0
$171$	6.84282	+	21.0600i	0.523283	+	1.61050i
$172$		0			0
$173$	6.29010	+	4.57002i	0.478227	+	0.347453i	0.800639	−	0.599147i	$-0.204494\pi$
$173$	6.29010	+	4.57002i	0.478227	+	0.347453i	−0.322412	+	0.946600i	$0.604494\pi$
$174$		0			0
$175$	−18.1379	−	4.07897i	−1.37110	−	0.308341i
$176$		0			0
$177$	28.5249	+	20.7245i	2.14406	+	1.55775i
$178$		0			0
$179$	1.88690	+	5.80727i	0.141033	+	0.434056i	0.996480	−	0.0838356i	$-0.0267170\pi$
$179$	1.88690	+	5.80727i	0.141033	+	0.434056i	−0.855446	+	0.517892i	$0.826717\pi$
$180$		0			0
$181$	−2.87031	+	8.83392i	−0.213349	+	0.656620i	0.785918	+	0.618331i	$0.212191\pi$
$181$	−2.87031	+	8.83392i	−0.213349	+	0.656620i	−0.999267	+	0.0382891i	$0.987809\pi$
$182$		0			0
$183$	10.2150	−	31.4385i	0.755114	−	2.32400i
$184$		0			0
$185$	−5.24088	−	9.20207i	−0.385317	−	0.676550i
$186$		0			0
$187$	5.15859	−	3.74793i	0.377233	−	0.274076i
$188$		0			0
$189$	42.1012	+	30.5883i	3.06241	+	2.22497i
$190$		0			0
$191$	−8.84700	+	6.42772i	−0.640147	+	0.465094i	−0.859901	−	0.510462i	$-0.829475\pi$
$191$	−8.84700	+	6.42772i	−0.640147	+	0.465094i	0.219754	+	0.975555i	$0.429475\pi$
$192$		0			0
$193$	−9.47584			−0.682086			−0.341043	−	0.940048i	$-0.610780\pi$
$193$	−9.47584			−0.682086			−0.341043	+	0.940048i	$0.610780\pi$
$194$		0			0
$195$	−25.6824	+	28.1879i	−1.83915	+	2.01857i
$196$		0			0
$197$	3.25113	+	10.0060i	0.231634	+	0.712895i	0.997550	+	0.0699550i	$0.0222856\pi$
$197$	3.25113	+	10.0060i	0.231634	+	0.712895i	−0.765917	+	0.642940i	$0.777714\pi$
$198$		0			0
$199$	−1.76349			−0.125010			−0.0625051	−	0.998045i	$-0.519909\pi$
$199$	−1.76349			−0.125010			−0.0625051	+	0.998045i	$0.519909\pi$
$200$		0			0
$201$	−15.9041			−1.12179
$202$		0			0
$203$	9.11124	+	28.0415i	0.639484	+	1.96813i
$204$		0			0
$205$	6.30709	+	11.0742i	0.440507	+	0.773453i
$206$		0			0
$207$	31.6439			2.19941
$208$		0			0
$209$	2.43725	−	1.77077i	0.168588	−	0.122486i
$210$		0			0
$211$	−2.28222	−	1.65813i	−0.157115	−	0.114150i	0.506450	−	0.862269i	$-0.330957\pi$
$211$	−2.28222	−	1.65813i	−0.157115	−	0.114150i	−0.663565	+	0.748119i	$0.730957\pi$
$212$		0			0
$213$	8.54744	−	6.21008i	0.585661	−	0.425508i
$214$		0			0
$215$	−1.49663	+	13.4763i	−0.102069	+	0.919075i
$216$		0			0
$217$	4.65659	−	14.3315i	0.316110	−	0.972886i
$218$		0			0
$219$	4.14621	−	12.7607i	0.280175	−	0.862290i
$220$		0			0
$221$	−10.4447	−	32.1454i	−0.702585	−	2.16234i
$222$		0			0
$223$	3.10581	+	2.25650i	0.207980	+	0.151107i	0.686899	−	0.726753i	$-0.258971\pi$
$223$	3.10581	+	2.25650i	0.207980	+	0.151107i	−0.478919	+	0.877859i	$0.658971\pi$
$224$		0			0
$225$	33.7481	−	14.5523i	2.24988	−	0.970151i
$226$		0			0
$227$	4.57523	+	3.32410i	0.303669	+	0.220628i	0.729175	−	0.684327i	$-0.239904\pi$
$227$	4.57523	+	3.32410i	0.303669	+	0.220628i	−0.425506	+	0.904955i	$0.639904\pi$
$228$		0			0
$229$	−1.29729	−	3.99264i	−0.0857271	−	0.263841i	0.898999	−	0.437950i	$-0.144295\pi$
$229$	−1.29729	−	3.99264i	−0.0857271	−	0.263841i	−0.984726	+	0.174109i	$0.944295\pi$
$230$		0			0
$231$	3.69650	−	11.3767i	0.243212	−	0.748530i
$232$		0			0
$233$	2.28962	−	7.04672i	0.149998	−	0.461646i	−0.847622	−	0.530601i	$-0.821966\pi$
$233$	2.28962	−	7.04672i	0.149998	−	0.461646i	0.997620	+	0.0689546i	$0.0219664\pi$
$234$		0			0
$235$	20.6933	−	4.27141i	1.34988	−	0.278636i
$236$		0			0
$237$	−2.42512	+	1.76195i	−0.157528	+	0.114451i
$238$		0			0
$239$	2.81918	+	2.04825i	0.182357	+	0.132490i	0.675219	−	0.737617i	$-0.264049\pi$
$239$	2.81918	+	2.04825i	0.182357	+	0.132490i	−0.492862	+	0.870108i	$0.664049\pi$
$240$		0			0
$241$	−20.0026	+	14.5328i	−1.28848	+	0.936138i	−0.999774	−	0.0212788i	$-0.993226\pi$
$241$	−20.0026	+	14.5328i	−1.28848	+	0.936138i	−0.288710	+	0.957417i	$0.593226\pi$
$242$		0			0
$243$	−31.9335			−2.04853
$244$		0			0
$245$	1.68446	−	15.1676i	0.107616	−	0.969024i
$246$		0			0
$247$	−4.93474	−	15.1876i	−0.313990	−	0.966362i
$248$		0			0
$249$	0.158327			0.0100336
$250$		0			0
$251$	−9.84212			−0.621229			−0.310614	−	0.950536i	$-0.600535\pi$
$251$	−9.84212			−0.621229			−0.310614	+	0.950536i	$0.600535\pi$
$252$		0			0
$253$	−1.33034	−	4.09437i	−0.0836378	−	0.257411i
$254$		0			0
$255$	−5.06312	+	45.5905i	−0.317065	+	2.85499i
$256$		0			0
$257$	19.6576			1.22621			0.613103	−	0.790003i	$-0.289921\pi$
$257$	19.6576			1.22621			0.613103	+	0.790003i	$0.289921\pi$
$258$		0			0
$259$	14.2460	−	10.3503i	0.885203	−	0.643138i
$260$		0			0
$261$	−47.1555	−	34.2605i	−2.91885	−	2.12067i
$262$		0			0
$263$	−5.25486	+	3.81788i	−0.324029	+	0.235421i	−0.737893	−	0.674918i	$-0.764179\pi$
$263$	−5.25486	+	3.81788i	−0.324029	+	0.235421i	0.413864	+	0.910339i	$0.364179\pi$
$264$		0			0
$265$	31.3764	−	6.47656i	1.92744	−	0.397852i
$266$		0			0
$267$	−10.2474	+	31.5382i	−0.627129	+	1.93010i
$268$		0			0
$269$	8.83947	−	27.2051i	0.538952	−	1.65872i	−0.195999	−	0.980604i	$-0.562795\pi$
$269$	8.83947	−	27.2051i	0.538952	−	1.65872i	0.734951	−	0.678120i	$-0.237205\pi$
$270$		0			0
$271$	1.77165	+	5.45257i	0.107620	+	0.331220i	0.990336	−	0.138686i	$-0.0442878\pi$
$271$	1.77165	+	5.45257i	0.107620	+	0.331220i	−0.882716	+	0.469906i	$0.844288\pi$
$272$		0			0
$273$	−51.2987	−	37.2707i	−3.10474	−	2.25572i
$274$		0			0
$275$	−3.30170	−	3.75483i	−0.199100	−	0.226425i
$276$		0			0
$277$	5.74721	+	4.17560i	0.345317	+	0.250887i	0.746902	−	0.664935i	$-0.231541\pi$
$277$	5.74721	+	4.17560i	0.345317	+	0.250887i	−0.401585	+	0.915822i	$0.631541\pi$
$278$		0			0
$279$	9.20550	+	28.3316i	0.551119	+	1.69617i
$280$		0			0
$281$	−1.42886	+	4.39757i	−0.0852385	+	0.262337i	−0.984587	−	0.174895i	$-0.944041\pi$
$281$	−1.42886	+	4.39757i	−0.0852385	+	0.262337i	0.899349	+	0.437232i	$0.144041\pi$
$282$		0			0
$283$	5.02107	−	15.4533i	0.298472	−	0.918602i	−0.683561	−	0.729893i	$-0.739570\pi$
$283$	5.02107	−	15.4533i	0.298472	−	0.918602i	0.982033	−	0.188709i	$-0.0604302\pi$
$284$		0			0
$285$	−2.39215	+	21.5399i	−0.141698	+	1.27591i
$286$		0			0
$287$	−17.1442	+	12.4560i	−1.01199	+	0.735256i
$288$		0			0
$289$	−19.1398	−	13.9059i	−1.12587	−	0.817992i
$290$		0			0
$291$	32.7287	−	23.7788i	1.91859	−	1.39394i
$292$		0			0
$293$	15.6306			0.913152			0.456576	−	0.889684i	$-0.349076\pi$
$293$	15.6306			0.913152			0.456576	+	0.889684i	$0.349076\pi$
$294$		0			0
$295$	12.1279	+	21.2946i	0.706116	+	1.23982i
$296$		0			0
$297$	4.32502	+	13.3111i	0.250963	+	0.772386i
$298$		0			0
$299$	−22.8202			−1.31973
$300$		0			0
$301$	−22.5464			−1.29955
$302$		0			0
$303$	−11.8292	−	36.4067i	−0.679572	−	2.09151i
$304$		0			0
$305$	15.4737	−	16.9833i	0.886021	−	0.972459i
$306$		0			0
$307$	16.5989			0.947349			0.473675	−	0.880700i	$-0.342927\pi$
$307$	16.5989			0.947349			0.473675	+	0.880700i	$0.342927\pi$
$308$		0			0
$309$	−31.0351	+	22.5483i	−1.76552	+	1.28273i
$310$		0			0
$311$	−4.18645	−	3.04163i	−0.237392	−	0.172475i	0.462729	−	0.886500i	$-0.346870\pi$
$311$	−4.18645	−	3.04163i	−0.237392	−	0.172475i	−0.700120	+	0.714025i	$0.746870\pi$
$312$		0			0
$313$	21.3432	−	15.5067i	1.20639	−	0.876491i	0.211489	−	0.977380i	$-0.432169\pi$
$313$	21.3432	−	15.5067i	1.20639	−	0.876491i	0.994898	+	0.100889i	$0.0321687\pi$
$314$		0			0
$315$	30.2440	+	53.1033i	1.70406	+	2.99203i
$316$		0			0
$317$	−0.398261	+	1.22572i	−0.0223686	+	0.0688433i	−0.961618	−	0.274393i	$-0.911523\pi$
$317$	−0.398261	+	1.22572i	−0.0223686	+	0.0688433i	0.939249	+	0.343236i	$0.111523\pi$
$318$		0			0
$319$	−2.45046	+	7.54173i	−0.137199	+	0.422256i
$320$		0			0
$321$	10.7285	+	33.0190i	0.598807	+	1.84294i
$322$		0			0
$323$	−15.5408	−	11.2911i	−0.864713	−	0.628251i
$324$		0			0
$325$	−24.3377	+	10.4945i	−1.35001	+	0.582128i
$326$		0			0
$327$	−21.7462	−	15.7995i	−1.20257	−	0.873716i
$328$		0			0
$329$	10.8572	+	33.4150i	0.598577	+	1.84223i
$330$		0			0
$331$	−2.78600	+	8.57444i	−0.153133	+	0.471294i	−0.997967	−	0.0637343i	$-0.979699\pi$
$331$	−2.78600	+	8.57444i	−0.153133	+	0.471294i	0.844834	+	0.535028i	$0.179699\pi$
$332$		0			0
$333$	−10.7572	+	33.1071i	−0.589488	+	1.81426i
$334$		0			0
$335$	−10.0716	−	4.55537i	−0.550273	−	0.248887i
$336$		0			0
$337$	17.0409	−	12.3809i	0.928276	−	0.674432i	−0.0172942	−	0.999850i	$-0.505505\pi$
$337$	17.0409	−	12.3809i	0.928276	−	0.674432i	0.945570	+	0.325419i	$0.105505\pi$
$338$		0			0
$339$	30.2113	+	21.9498i	1.64085	+	1.19215i
$340$		0			0
$341$	3.27878	−	2.38217i	0.177556	−	0.129002i
$342$		0			0
$343$	−0.651161			−0.0351594
$344$		0			0
$345$	28.2181	+	12.7629i	1.51921	+	0.687134i
$346$		0			0
$347$	−2.89573	−	8.91215i	−0.155451	−	0.478429i	0.842755	−	0.538297i	$-0.180932\pi$
$347$	−2.89573	−	8.91215i	−0.155451	−	0.478429i	−0.998206	+	0.0598677i	$0.980932\pi$
$348$		0			0
$349$	22.0088			1.17810			0.589052	−	0.808095i	$-0.299501\pi$
$349$	22.0088			1.17810			0.589052	+	0.808095i	$0.299501\pi$
$350$		0			0
$351$	74.1900			3.95997
$352$		0			0
$353$	−7.68439	−	23.6501i	−0.408999	−	1.25877i	−0.917510	−	0.397714i	$-0.869804\pi$
$353$	−7.68439	−	23.6501i	−0.408999	−	1.25877i	0.508510	−	0.861056i	$-0.330196\pi$
$354$		0			0
$355$	7.19159	−	1.48445i	0.381690	−	0.0787865i
$356$		0			0
$357$	−76.2750			−4.03690
$358$		0			0
$359$	3.30963	−	2.40459i	0.174676	−	0.126909i	−0.497012	−	0.867743i	$-0.665570\pi$
$359$	3.30963	−	2.40459i	0.174676	−	0.126909i	0.671688	+	0.740834i	$0.265570\pi$
$360$		0			0
$361$	8.02885	+	5.83330i	0.422571	+	0.307016i
$362$		0			0
$363$	2.60277	−	1.89102i	0.136610	−	0.0992530i
$364$		0			0
$365$	6.28069	−	6.89342i	0.328747	−	0.360818i
$366$		0			0
$367$	−9.56795	+	29.4471i	−0.499443	+	1.53713i	0.310474	+	0.950582i	$0.399512\pi$
$367$	−9.56795	+	29.4471i	−0.499443	+	1.53713i	−0.809917	+	0.586545i	$0.800488\pi$
$368$		0			0
$369$	12.9456	−	39.8425i	0.673922	−	2.07412i
$370$		0			0
$371$	16.4623	+	50.6659i	0.854682	+	2.63044i
$372$		0			0
$373$	17.9151	+	13.0161i	0.927607	+	0.673946i	0.945406	−	0.325895i	$-0.105666\pi$
$373$	17.9151	+	13.0161i	0.927607	+	0.673946i	−0.0177984	+	0.999842i	$0.505666\pi$
$374$		0			0
$375$	35.9638	+	0.634838i	1.85716	+	0.0327829i
$376$		0			0
$377$	34.0065	+	24.7072i	1.75142	+	1.27248i
$378$		0			0
$379$	4.88063	+	15.0210i	0.250701	+	0.771579i	0.994646	+	0.103338i	$0.0329525\pi$
$379$	4.88063	+	15.0210i	0.250701	+	0.771579i	−0.743945	+	0.668241i	$0.767048\pi$
$380$		0			0
$381$	−7.64618	+	23.5325i	−0.391726	+	1.20561i
$382$		0			0
$383$	5.39746	−	16.6117i	0.275797	−	0.848817i	−0.713210	−	0.700950i	$-0.752759\pi$
$383$	5.39746	−	16.6117i	0.275797	−	0.848817i	0.989007	−	0.147867i	$-0.0472406\pi$
$384$		0			0
$385$	5.59948	−	6.14575i	0.285376	−	0.313216i
$386$		0			0
$387$	36.0591	−	26.1985i	1.83299	−	1.33174i
$388$		0			0
$389$	0.870599	+	0.632527i	0.0441411	+	0.0320704i	0.609637	−	0.792681i	$-0.291315\pi$
$389$	0.870599	+	0.632527i	0.0441411	+	0.0320704i	−0.565496	+	0.824751i	$0.691315\pi$
$390$		0			0
$391$	−22.2081	+	16.1351i	−1.12311	+	0.815988i
$392$		0			0
$393$	−20.5125			−1.03472
$394$		0			0
$395$	−2.04043	+	0.421175i	−0.102665	+	0.0211916i
$396$		0			0
$397$	6.46998	+	19.9126i	0.324719	+	0.999382i	0.971567	+	0.236764i	$0.0760867\pi$
$397$	6.46998	+	19.9126i	0.324719	+	0.999382i	−0.646848	+	0.762619i	$0.723913\pi$
$398$		0			0
$399$	−36.0372			−1.80412
$400$		0			0
$401$	−9.24122			−0.461485			−0.230742	−	0.973015i	$-0.574115\pi$
$401$	−9.24122			−0.461485			−0.230742	+	0.973015i	$0.574115\pi$
$402$		0			0
$403$	−6.63861	−	20.4315i	−0.330693	−	1.01777i
$404$		0			0
$405$	−46.8125	−	21.1732i	−2.32613	−	1.05210i
$406$		0			0
$407$	4.73592			0.234751
$408$		0			0
$409$	13.1492	−	9.55344i	0.650186	−	0.472387i	−0.213149	−	0.977020i	$-0.568372\pi$
$409$	13.1492	−	9.55344i	0.650186	−	0.472387i	0.863334	+	0.504632i	$0.168372\pi$
$410$		0			0
$411$	−30.1590	−	21.9118i	−1.48763	−	1.08083i
$412$		0			0
$413$	−32.9668	+	23.9517i	−1.62219	+	1.17859i
$414$		0			0
$415$	0.100264	+	0.0453492i	0.00492178	+	0.00222611i
$416$		0			0
$417$	−10.3420	+	31.8295i	−0.506451	+	1.55870i
$418$		0			0
$419$	2.96105	−	9.11319i	0.144657	−	0.445208i	−0.852310	−	0.523037i	$-0.824799\pi$
$419$	2.96105	−	9.11319i	0.144657	−	0.445208i	0.996967	+	0.0778291i	$0.0247988\pi$
$420$		0			0
$421$	−6.74467	−	20.7579i	−0.328715	−	1.01168i	−0.969736	−	0.244157i	$-0.921489\pi$
$421$	−6.74467	−	20.7579i	−0.328715	−	1.01168i	0.641021	−	0.767523i	$-0.278511\pi$
$422$		0			0
$423$	−56.1918	−	40.8257i	−2.73214	−	1.98502i
$424$		0			0
$425$	−16.2647	+	27.4210i	−0.788954	+	1.33011i
$426$		0			0
$427$	30.9076	+	22.4557i	1.49572	+	1.08671i
$428$		0			0
$429$	−5.26987	−	16.2190i	−0.254432	−	0.783061i
$430$		0			0
$431$	−3.52610	+	10.8522i	−0.169846	+	0.522733i	−0.999361	−	0.0357524i	$-0.988617\pi$
$431$	−3.52610	+	10.8522i	−0.169846	+	0.522733i	0.829515	+	0.558485i	$0.188617\pi$
$432$		0			0
$433$	−6.23270	+	19.1823i	−0.299524	+	0.921841i	0.682140	+	0.731222i	$0.261050\pi$
$433$	−6.23270	+	19.1823i	−0.299524	+	0.921841i	−0.981664	+	0.190619i	$0.938950\pi$
$434$		0			0
$435$	−28.2320	−	49.5706i	−1.35362	−	2.37673i
$436$		0			0
$437$	−10.4925	+	7.62327i	−0.501926	+	0.364671i
$438$		0			0
$439$	−18.7487	−	13.6217i	−0.894826	−	0.650129i	0.0423059	−	0.999105i	$-0.486530\pi$
$439$	−18.7487	−	13.6217i	−0.894826	−	0.650129i	−0.937132	+	0.348976i	$0.886530\pi$
$440$		0			0
$441$	−40.5847	+	29.4865i	−1.93260	+	1.40412i
$442$		0			0
$443$	−5.64478			−0.268191			−0.134096	−	0.990968i	$-0.542813\pi$
$443$	−5.64478			−0.268191			−0.134096	+	0.990968i	$0.542813\pi$
$444$		0			0
$445$	−15.5227	+	17.0371i	−0.735849	+	0.807636i
$446$		0			0
$447$	−3.75500	−	11.5567i	−0.177605	−	0.546613i
$448$		0			0
$449$	−24.5065			−1.15653			−0.578265	−	0.815849i	$-0.696270\pi$
$449$	−24.5065			−1.15653			−0.578265	+	0.815849i	$0.696270\pi$
$450$		0			0
$451$	−5.69941			−0.268375
$452$		0			0
$453$	−16.3663	−	50.3702i	−0.768954	−	2.36660i
$454$		0			0
$455$	−21.8107	−	38.2958i	−1.02250	−	1.79533i
$456$		0			0
$457$	−2.88430			−0.134922			−0.0674610	−	0.997722i	$-0.521490\pi$
$457$	−2.88430			−0.134922			−0.0674610	+	0.997722i	$0.521490\pi$
$458$		0			0
$459$	72.2000	−	52.4564i	3.37001	−	2.44845i
$460$		0			0
$461$	23.8252	+	17.3100i	1.10965	+	0.806207i	0.982608	−	0.185691i	$-0.0594522\pi$
$461$	23.8252	+	17.3100i	1.10965	+	0.806207i	0.127040	+	0.991898i	$0.459452\pi$
$462$		0			0
$463$	31.6859	−	23.0212i	1.47257	−	1.06988i	0.492711	−	0.870193i	$-0.336006\pi$
$463$	31.6859	−	23.0212i	1.47257	−	1.06988i	0.979859	−	0.199691i	$-0.0639939\pi$
$464$		0			0
$465$	−3.21810	+	28.9772i	−0.149236	+	1.34379i
$466$		0			0
$467$	3.52392	−	10.8455i	0.163068	−	0.501871i	−0.835821	−	0.549002i	$-0.815008\pi$
$467$	3.52392	−	10.8455i	0.163068	−	0.501871i	0.998889	+	0.0471312i	$0.0150079\pi$
$468$		0			0
$469$	5.67995	−	17.4811i	0.262276	−	0.807202i
$470$		0			0
$471$	17.9525	+	55.2522i	0.827208	+	2.54589i
$472$		0			0
$473$	−4.90574	−	3.56423i	−0.225566	−	0.163883i
$474$		0			0
$475$	−7.68449	+	12.9554i	−0.352589	+	0.594437i
$476$		0			0
$477$	−85.2013	−	61.9024i	−3.90110	−	2.83432i
$478$		0			0
$479$	−7.18276	−	22.1062i	−0.328188	−	1.01006i	−0.969981	−	0.243182i	$-0.921809\pi$
$479$	−7.18276	−	22.1062i	−0.328188	−	1.01006i	0.641792	−	0.766879i	$-0.278191\pi$
$480$		0			0
$481$	7.75759	−	23.8754i	0.353716	−	1.08862i
$482$		0			0
$483$	−15.9137	+	48.9774i	−0.724099	+	2.22855i
$484$		0			0
$485$	27.5371	−	5.68407i	1.25040	−	0.258100i
$486$		0			0
$487$	5.23312	−	3.80208i	0.237135	−	0.172289i	−0.462871	−	0.886426i	$-0.653181\pi$
$487$	5.23312	−	3.80208i	0.237135	−	0.172289i	0.700006	+	0.714137i	$0.253181\pi$
$488$		0			0
$489$	23.2004	+	16.8560i	1.04916	+	0.762257i
$490$		0			0
$491$	−22.0060	+	15.9883i	−0.993118	+	0.721542i	−0.960602	−	0.277929i	$-0.910352\pi$
$491$	−22.0060	+	15.9883i	−0.993118	+	0.721542i	−0.0325161	+	0.999471i	$0.510352\pi$
$492$		0			0
$493$	50.5636			2.27727
$494$		0			0
$495$	−1.81417	+	16.3355i	−0.0815407	+	0.734228i
$496$		0			0
$497$	3.77323	+	11.6128i	0.169252	+	0.520905i
$498$		0			0
$499$	19.6609			0.880142			0.440071	−	0.897963i	$-0.354953\pi$
$499$	19.6609			0.880142			0.440071	+	0.897963i	$0.354953\pi$
$500$		0			0
$501$	−10.5948			−0.473342
$502$		0			0
$503$	−13.1346	−	40.4240i	−0.585641	−	1.80242i	−0.596679	−	0.802480i	$-0.703513\pi$
$503$	−13.1346	−	40.4240i	−0.585641	−	1.80242i	0.0110376	−	0.999939i	$-0.496487\pi$
$504$		0			0
$505$	2.93672	−	26.4435i	0.130682	−	1.17672i
$506$		0			0
$507$	−48.5741			−2.15725
$508$		0			0
$509$	9.42281	−	6.84607i	0.417659	−	0.303447i	−0.359037	−	0.933324i	$-0.616895\pi$
$509$	9.42281	−	6.84607i	0.417659	−	0.303447i	0.776695	+	0.629877i	$0.216895\pi$
$510$		0			0
$511$	12.5452	+	9.11465i	0.554969	+	0.403208i
$512$		0			0
$513$	34.1119	−	24.7838i	1.50608	−	1.09423i
$514$		0			0
$515$	−26.1121	+	5.38992i	−1.15064	+	0.237508i
$516$		0			0
$517$	−2.92003	+	8.98693i	−0.128423	+	0.395245i
$518$		0			0
$519$	7.72966	−	23.7895i	0.339294	−	1.04424i
$520$		0			0
$521$	−10.5452	−	32.4548i	−0.461993	−	1.42187i	−0.862725	−	0.505674i	$-0.831244\pi$
$521$	−10.5452	−	32.4548i	−0.461993	−	1.42187i	0.400732	−	0.916196i	$-0.368756\pi$
$522$		0			0
$523$	30.9093	+	22.4569i	1.35157	+	0.981974i	0.998932	+	0.0462146i	$0.0147158\pi$
$523$	30.9093	+	22.4569i	1.35157	+	0.981974i	0.352639	+	0.935759i	$0.385284\pi$
$524$		0			0
$525$	5.55157	+	59.5525i	0.242291	+	2.59908i
$526$		0			0
$527$	−20.9067	−	15.1896i	−0.910711	−	0.661670i
$528$		0			0
$529$	−1.38018	−	4.24776i	−0.0600079	−	0.184685i
$530$		0			0
$531$	24.8932	−	76.6134i	1.08027	−	3.32474i
$532$		0			0
$533$	−9.33581	+	28.7327i	−0.404379	+	1.24455i
$534$		0			0
$535$	−2.66346	+	23.9829i	−0.115151	+	1.03687i
$536$		0			0
$537$	15.8929	−	11.5468i	0.685827	−	0.498283i
$538$		0			0
$539$	5.52144	+	4.01156i	0.237825	+	0.172790i
$540$		0			0
$541$	−19.7634	+	14.3590i	−0.849695	+	0.617340i	−0.925062	−	0.379816i	$-0.875987\pi$
$541$	−19.7634	+	14.3590i	−0.849695	+	0.617340i	0.0753666	+	0.997156i	$0.475987\pi$
$542$		0			0
$543$	29.8831			1.28241
$544$		0			0
$545$	−9.24584	−	16.2341i	−0.396048	−	0.695392i
$546$		0			0
$547$	0.291181	+	0.896163i	0.0124500	+	0.0383171i	0.957089	−	0.289796i	$-0.0935874\pi$
$547$	0.291181	+	0.896163i	0.0124500	+	0.0383171i	−0.944639	+	0.328113i	$0.893587\pi$
$548$		0			0
$549$	−75.5244			−3.22330
$550$		0			0
$551$	23.8895			1.01773
$552$		0			0
$553$	−1.07056	−	3.29483i	−0.0455247	−	0.140111i
$554$		0			0
$555$	−22.9456	+	25.1841i	−0.973988	+	1.06901i
$556$		0			0
$557$	−6.63108			−0.280968			−0.140484	−	0.990083i	$-0.544866\pi$
$557$	−6.63108			−0.280968			−0.140484	+	0.990083i	$0.544866\pi$
$558$		0			0
$559$	−26.0042	+	18.8932i	−1.09986	+	0.799096i
$560$		0			0
$561$	−16.5962	−	12.0579i	−0.700693	−	0.509083i
$562$		0			0
$563$	15.0030	−	10.9003i	0.632303	−	0.459395i	−0.224894	−	0.974383i	$-0.572204\pi$
$563$	15.0030	−	10.9003i	0.632303	−	0.459395i	0.857197	+	0.514988i	$0.172204\pi$
$564$		0			0
$565$	12.8449	+	22.5535i	0.540391	+	0.948833i
$566$		0			0
$567$	26.4002	−	81.2513i	1.10870	−	3.41224i
$568$		0			0
$569$	−0.349559	+	1.07583i	−0.0146543	+	0.0451012i	−0.958116	−	0.286380i	$-0.907548\pi$
$569$	−0.349559	+	1.07583i	−0.0146543	+	0.0451012i	0.943462	+	0.331481i	$0.107548\pi$
$570$		0			0
$571$	4.49662	+	13.8392i	0.188178	+	0.579151i	0.999989	−	0.00476914i	$-0.00151807\pi$
$571$	4.49662	+	13.8392i	0.188178	+	0.579151i	−0.811811	+	0.583920i	$0.801518\pi$
$572$		0			0
$573$	28.4626	+	20.6793i	1.18904	+	0.863890i
$574$		0			0
$575$	14.2141	+	16.1648i	0.592767	+	0.674120i
$576$		0			0
$577$	12.7349	+	9.25246i	0.530161	+	0.385185i	0.820418	−	0.571764i	$-0.193741\pi$
$577$	12.7349	+	9.25246i	0.530161	+	0.385185i	−0.290257	+	0.956949i	$0.593741\pi$
$578$		0			0
$579$	9.42059	+	28.9936i	0.391506	+	1.20493i
$580$		0			0
$581$	−0.0565445	+	0.174026i	−0.00234586	+	0.00721982i
$582$		0			0
$583$	−4.42752	+	13.6265i	−0.183369	+	0.564353i
$584$		0			0
$585$	79.3813	+	35.9039i	3.28201	+	1.48444i
$586$		0			0
$587$	11.1215	−	8.08026i	0.459035	−	0.333508i	−0.334118	−	0.942531i	$-0.608438\pi$
$587$	11.1215	−	8.08026i	0.459035	−	0.333508i	0.793152	+	0.609023i	$0.208438\pi$
$588$		0			0
$589$	−9.87768	−	7.17656i	−0.407003	−	0.295705i
$590$		0			0
$591$	27.3835	−	19.8952i	1.12640	−	0.818381i
$592$		0			0
$593$	−33.4386			−1.37316			−0.686579	−	0.727056i	$-0.740888\pi$
$593$	−33.4386			−1.37316			−0.686579	+	0.727056i	$0.740888\pi$
$594$		0			0
$595$	−48.3028	−	21.8472i	−1.98022	−	0.895649i
$596$		0			0
$597$	1.75321	+	5.39581i	0.0717539	+	0.220836i
$598$		0			0
$599$	−30.2632			−1.23652			−0.618261	−	0.785973i	$-0.712163\pi$
$599$	−30.2632			−1.23652			−0.618261	+	0.785973i	$0.712163\pi$
$600$		0			0
$601$	−0.603355			−0.0246114			−0.0123057	−	0.999924i	$-0.503917\pi$
$601$	−0.603355			−0.0246114			−0.0123057	+	0.999924i	$0.503917\pi$
$602$		0			0
$603$	11.2286	+	34.5580i	0.457263	+	1.40731i
$604$		0			0
$605$	2.18990	−	0.452028i	0.0890322	−	0.0183776i
$606$		0			0
$607$	−32.5021			−1.31922			−0.659609	−	0.751609i	$-0.729278\pi$
$607$	−32.5021			−1.31922			−0.659609	+	0.751609i	$0.729278\pi$
$608$		0			0
$609$	76.7417	−	55.7561i	3.10973	−	2.25935i
$610$		0			0
$611$	40.5231	+	29.4417i	1.63939	+	1.19109i
$612$		0			0
$613$	−3.48071	+	2.52889i	−0.140585	+	0.102141i	−0.655855	−	0.754887i	$-0.727692\pi$
$613$	−3.48071	+	2.52889i	−0.140585	+	0.102141i	0.515270	+	0.857028i	$0.327692\pi$
$614$		0			0
$615$	27.6138	−	30.3077i	1.11349	−	1.22212i
$616$		0			0
$617$	0.596063	−	1.83449i	0.0239966	−	0.0738540i	−0.938341	−	0.345711i	$-0.887638\pi$
$617$	0.596063	−	1.83449i	0.0239966	−	0.0738540i	0.962338	+	0.271857i	$0.0876378\pi$
$618$		0			0
$619$	2.27854	−	7.01264i	0.0915824	−	0.281862i	−0.894766	−	0.446536i	$-0.852657\pi$
$619$	2.27854	−	7.01264i	0.0915824	−	0.281862i	0.986348	+	0.164675i	$0.0526574\pi$
$620$		0			0
$621$	−18.6195	−	57.3050i	−0.747176	−	2.29957i
$622$		0			0
$623$	−31.0056	−	22.5269i	−1.24221	−	0.902520i
$624$		0			0
$625$	22.5930	+	10.7030i	0.903721	+	0.428121i
$626$		0			0
$627$	−7.84112	−	5.69691i	−0.313144	−	0.227513i
$628$		0			0
$629$	−9.33169	−	28.7200i	−0.372079	−	1.14514i
$630$		0			0
$631$	0.918705	−	2.82748i	0.0365731	−	0.112560i	−0.931103	−	0.364756i	$-0.881153\pi$
$631$	0.918705	−	2.82748i	0.0365731	−	0.112560i	0.967676	+	0.252195i	$0.0811525\pi$
$632$		0			0
$633$	−2.80454	+	8.63147i	−0.111470	+	0.343070i
$634$		0			0
$635$	−11.5825	+	12.7124i	−0.459636	+	0.504477i
$636$		0			0
$637$	29.2679	−	21.2644i	1.15964	−	0.842525i
$638$		0			0
$639$	−19.5285	−	14.1883i	−0.772534	−	0.561279i
$640$		0			0
$641$	21.5917	−	15.6873i	0.852823	−	0.619612i	−0.0731002	−	0.997325i	$-0.523289\pi$
$641$	21.5917	−	15.6873i	0.852823	−	0.619612i	0.925923	+	0.377713i	$0.123289\pi$
$642$		0			0
$643$	18.4589			0.727949			0.363974	−	0.931409i	$-0.381420\pi$
$643$	18.4589			0.727949			0.363974	+	0.931409i	$0.381420\pi$
$644$		0			0
$645$	42.7218	−	8.81842i	1.68217	−	0.347225i
$646$		0			0
$647$	8.60400	+	26.4804i	0.338258	+	1.04105i	0.965095	+	0.261901i	$0.0843494\pi$
$647$	8.60400	+	26.4804i	0.338258	+	1.04105i	−0.626836	+	0.779151i	$0.715651\pi$
$648$		0			0
$649$	−10.9594			−0.430195
$650$		0			0
$651$	−48.4801			−1.90009
$652$		0			0
$653$	−0.287129	−	0.883691i	−0.0112362	−	0.0345815i	0.945281	−	0.326257i	$-0.105787\pi$
$653$	−0.287129	−	0.883691i	−0.0112362	−	0.0345815i	−0.956517	+	0.291675i	$0.905787\pi$
$654$		0			0
$655$	−12.9900	−	5.87533i	−0.507561	−	0.229568i
$656$		0			0
$657$	−30.6550			−1.19596
$658$		0			0
$659$	−30.6607	+	22.2763i	−1.19437	+	0.867763i	−0.993720	−	0.111900i	$-0.964306\pi$
$659$	−30.6607	+	22.2763i	−1.19437	+	0.867763i	−0.200653	+	0.979662i	$0.564306\pi$
$660$		0			0
$661$	15.1522	+	11.0087i	0.589353	+	0.428190i	0.842084	−	0.539346i	$-0.181329\pi$
$661$	15.1522	+	11.0087i	0.589353	+	0.428190i	−0.252731	+	0.967537i	$0.581329\pi$
$662$		0			0
$663$	−87.9729	+	63.9160i	−3.41658	+	2.48229i
$664$		0			0
$665$	−22.8214	−	10.3220i	−0.884974	−	0.400271i
$666$		0			0
$667$	10.5494	−	32.4677i	0.408474	−	1.25715i
$668$		0			0
$669$	3.81661	−	11.7463i	0.147559	−	0.454139i
$670$		0			0
$671$	3.17512	+	9.77200i	0.122574	+	0.377244i
$672$		0			0
$673$	7.25486	+	5.27096i	0.279654	+	0.203181i	0.718767	−	0.695251i	$-0.244707\pi$
$673$	7.25486	+	5.27096i	0.279654	+	0.203181i	−0.439112	+	0.898432i	$0.644707\pi$
$674$		0			0
$675$	−46.2108	−	52.5529i	−1.77866	−	2.02276i
$676$		0			0
$677$	0.0417597	+	0.0303402i	0.00160496	+	0.00116607i	0.588587	−	0.808434i	$-0.299684\pi$
$677$	0.0417597	+	0.0303402i	0.00160496	+	0.00116607i	−0.586982	+	0.809600i	$0.699684\pi$
$678$		0			0
$679$	14.4480	+	44.4662i	0.554462	+	1.70646i
$680$		0			0
$681$	5.62232	−	17.3037i	0.215448	−	0.663080i
$682$		0			0
$683$	5.62967	−	17.3263i	0.215413	−	0.662974i	−0.783711	−	0.621126i	$-0.786676\pi$
$683$	5.62967	−	17.3263i	0.215413	−	0.662974i	0.999124	−	0.0418479i	$-0.0133245\pi$
$684$		0			0
$685$	−12.8227	−	22.5145i	−0.489930	−	0.860233i
$686$		0			0
$687$	−10.9267	+	7.93872i	−0.416880	+	0.302881i
$688$		0			0
$689$	61.4435	+	44.6413i	2.34081	+	1.70070i
$690$		0			0
$691$	−5.81655	+	4.22597i	−0.221272	+	0.160763i	−0.692899	−	0.721035i	$-0.743667\pi$
$691$	−5.81655	+	4.22597i	−0.221272	+	0.160763i	0.471627	+	0.881798i	$0.343667\pi$
$692$		0			0
$693$	−27.3301			−1.03818
$694$		0			0
$695$	−15.6661	+	17.1945i	−0.594251	+	0.652224i
$696$		0			0
$697$	11.2302	+	34.5629i	0.425373	+	1.30916i
$698$		0			0
$699$	−23.8374			−0.901614
$700$		0			0
$701$	−23.6591			−0.893592			−0.446796	−	0.894636i	$-0.647435\pi$
$701$	−23.6591			−0.893592			−0.446796	+	0.894636i	$0.647435\pi$
$702$		0			0
$703$	−4.40889	−	13.5692i	−0.166285	−	0.511771i
$704$		0			0
$705$	−33.6421	−	59.0696i	−1.26703	−	2.22469i
$706$		0			0
$707$	44.2412			1.66386
$708$		0			0
$709$	14.0389	−	10.1998i	0.527240	−	0.383062i	−0.292084	−	0.956393i	$-0.594349\pi$
$709$	14.0389	−	10.1998i	0.527240	−	0.383062i	0.819324	+	0.573330i	$0.194349\pi$
$710$		0			0
$711$	5.54070	+	4.02555i	0.207792	+	0.150970i
$712$		0			0
$713$	−14.1154	+	10.2554i	−0.528626	+	0.384069i
$714$		0			0
$715$	1.30830	−	11.7805i	0.0489275	−	0.440565i
$716$		0			0
$717$	3.46438	−	10.6623i	0.129380	−	0.398189i
$718$		0			0
$719$	−9.07401	+	27.9269i	−0.338404	+	1.04150i	0.626618	+	0.779327i	$0.284439\pi$
$719$	−9.07401	+	27.9269i	−0.338404	+	1.04150i	−0.965021	+	0.262172i	$0.915561\pi$
$720$		0			0
$721$	−13.7003	−	42.1651i	−0.510225	−	1.57031i
$722$		0			0
$723$	64.3525	+	46.7548i	2.39330	+	1.73883i
$724$		0			0
$725$	−3.68021	−	39.4781i	−0.136679	−	1.46618i
$726$		0			0
$727$	−30.5312	−	22.1822i	−1.13234	−	0.822693i	−0.146306	−	0.989239i	$-0.546739\pi$
$727$	−30.5312	−	22.1822i	−1.13234	−	0.822693i	−0.986034	+	0.166546i	$0.946739\pi$
$728$		0			0
$729$	10.4464	+	32.1509i	0.386905	+	1.19077i
$730$		0			0
$731$	−11.9482	+	36.7728i	−0.441920	+	1.36009i
$732$		0			0
$733$	14.4350	−	44.4265i	0.533171	−	1.64093i	−0.214398	−	0.976746i	$-0.568779\pi$
$733$	14.4350	−	44.4265i	0.533171	−	1.64093i	0.747569	−	0.664184i	$-0.231221\pi$
$734$		0			0
$735$	−48.0836	+	9.92518i	−1.77359	+	0.366096i
$736$		0			0
$737$	3.99935	−	2.90570i	0.147318	−	0.107033i
$738$		0			0
$739$	5.32107	+	3.86598i	0.195739	+	0.142212i	0.681338	−	0.731969i	$-0.261399\pi$
$739$	5.32107	+	3.86598i	0.195739	+	0.142212i	−0.485599	+	0.874182i	$0.661399\pi$
$740$		0			0
$741$	−41.5641	+	30.1981i	−1.52689	+	1.10935i
$742$		0			0
$743$	−3.86186			−0.141678			−0.0708390	−	0.997488i	$-0.522568\pi$
$743$	−3.86186			−0.141678			−0.0708390	+	0.997488i	$0.522568\pi$
$744$		0			0
$745$	0.932214	−	8.39406i	0.0341537	−	0.307534i
$746$		0			0
$747$	−0.111782	−	0.344028i	−0.00408987	−	0.0125873i
$748$		0			0
$749$	−40.1245			−1.46612
$750$		0			0
$751$	10.1520			0.370453			0.185226	−	0.982696i	$-0.440698\pi$
$751$	10.1520			0.370453			0.185226	+	0.982696i	$0.440698\pi$
$752$		0			0
$753$	9.78474	+	30.1143i	0.356576	+	1.09743i
$754$		0			0
$755$	4.06308	−	36.5858i	0.147871	−	1.33149i
$756$		0			0
$757$	−32.8152			−1.19269			−0.596345	−	0.802728i	$-0.703381\pi$
$757$	−32.8152			−1.19269			−0.596345	+	0.802728i	$0.703381\pi$
$758$		0			0
$759$	−11.2051	+	8.14099i	−0.406720	+	0.295499i
$760$		0			0
$761$	−5.12931	−	3.72666i	−0.185937	−	0.135091i	0.490923	−	0.871203i	$-0.336660\pi$
$761$	−5.12931	−	3.72666i	−0.185937	−	0.135091i	−0.676860	+	0.736112i	$0.736660\pi$
$762$		0			0
$763$	25.1325	−	18.2598i	0.909857	−	0.661050i
$764$		0			0
$765$	102.638	−	21.1860i	3.71088	−	0.765982i
$766$		0			0
$767$	−17.9519	+	55.2502i	−0.648205	+	1.99497i
$768$		0			0
$769$	−2.09425	+	6.44544i	−0.0755206	+	0.232428i	−0.981690	−	0.190487i	$-0.938993\pi$
$769$	−2.09425	+	6.44544i	−0.0755206	+	0.232428i	0.906169	+	0.422915i	$0.138993\pi$
$770$		0			0
$771$	−19.5430	−	60.1471i	−0.703823	−	2.16614i
$772$		0			0
$773$	24.7709	+	17.9971i	0.890946	+	0.647310i	0.936124	−	0.351669i	$-0.114386\pi$
$773$	24.7709	+	17.9971i	0.890946	+	0.647310i	−0.0451787	+	0.998979i	$0.514386\pi$
$774$		0			0
$775$	−10.3378	+	17.4287i	−0.371344	+	0.626057i
$776$		0			0
$777$	−45.8323	−	33.2991i	−1.64422	−	1.19460i
$778$		0			0
$779$	5.30585	+	16.3297i	0.190102	+	0.585073i
$780$		0			0
$781$	−1.01480	+	3.12325i	−0.0363126	+	0.111759i
$782$		0			0
$783$	−34.2968	+	105.555i	−1.22567	+	3.77221i
$784$		0			0
$785$	−4.45689	+	40.1317i	−0.159073	+	1.43236i
$786$		0			0
$787$	−8.24910	+	5.99332i	−0.294049	+	0.213639i	−0.725022	−	0.688726i	$-0.758170\pi$
$787$	−8.24910	+	5.99332i	−0.294049	+	0.213639i	0.430973	+	0.902365i	$0.358170\pi$
$788$		0			0
$789$	16.9059	+	12.2829i	0.601868	+	0.437282i
$790$		0			0
$791$	−34.9157	+	25.3678i	−1.24146	+	0.901974i
$792$		0			0
$793$	54.4649			1.93411
$794$		0			0
$795$	−51.0101	−	89.5649i	−1.80914	−	3.17654i
$796$		0			0
$797$	9.91955	+	30.5292i	0.351368	+	1.08140i	0.958085	+	0.286483i	$0.0924862\pi$
$797$	9.91955	+	30.5292i	0.351368	+	1.08140i	−0.606717	+	0.794918i	$0.707514\pi$
$798$		0			0
$799$	60.2530			2.13160
$800$		0			0
$801$	75.7638			2.67698
$802$		0			0
$803$	1.28876	+	3.96640i	0.0454795	+	0.139971i
$804$		0			0
$805$	−24.1062	+	26.4579i	−0.849630	+	0.932518i
$806$		0			0
$807$	−92.0285			−3.23956
$808$		0			0
$809$	−25.5622	+	18.5720i	−0.898720	+	0.652958i	−0.938137	−	0.346265i	$-0.887450\pi$
$809$	−25.5622	+	18.5720i	−0.898720	+	0.652958i	0.0394170	+	0.999223i	$0.487450\pi$
$810$		0			0
$811$	−18.3118	−	13.3043i	−0.643016	−	0.467178i	0.217869	−	0.975978i	$-0.430089\pi$
$811$	−18.3118	−	13.3043i	−0.643016	−	0.467178i	−0.860885	+	0.508800i	$0.830089\pi$
$812$		0			0
$813$	14.9221	−	10.8416i	0.523342	−	0.380230i
$814$		0			0
$815$	9.86411	+	17.3197i	0.345525	+	0.606682i
$816$		0			0
$817$	−5.64510	+	17.3738i	−0.197497	+	0.607833i
$818$		0			0
$819$	−44.7675	+	137.780i	−1.56430	+	4.81443i
$820$		0			0
$821$	10.2771	+	31.6297i	0.358674	+	1.10389i	0.953848	+	0.300289i	$0.0970830\pi$
$821$	10.2771	+	31.6297i	0.358674	+	1.10389i	−0.595174	+	0.803597i	$0.702917\pi$
$822$		0			0
$823$	−2.48404	−	1.80476i	−0.0865881	−	0.0629100i	0.543649	−	0.839313i	$-0.317042\pi$
$823$	−2.48404	−	1.80476i	−0.0865881	−	0.0629100i	−0.630237	+	0.776403i	$0.717042\pi$
$824$		0			0
$825$	−8.20637	+	13.8353i	−0.285709	+	0.481683i
$826$		0			0
$827$	39.5262	+	28.7175i	1.37446	+	0.998604i	0.997374	+	0.0724266i	$0.0230743\pi$
$827$	39.5262	+	28.7175i	1.37446	+	0.998604i	0.377087	+	0.926178i	$0.376926\pi$
$828$		0			0
$829$	−12.9849	−	39.9635i	−0.450985	−	1.38799i	−0.875785	−	0.482702i	$-0.839655\pi$
$829$	−12.9849	−	39.9635i	−0.450985	−	1.38799i	0.424799	−	0.905288i	$-0.360345\pi$
$830$		0			0
$831$	7.06253	−	21.7362i	0.244996	−	0.754022i
$832$		0			0
$833$	13.4478	−	41.3880i	0.465938	−	1.43401i
$834$		0			0
$835$	−6.70941	−	3.03464i	−0.232189	−	0.105018i
$836$		0			0
$837$	45.8901	−	33.3411i	1.58619	−	1.15244i
$838$		0			0
$839$	−22.0209	−	15.9991i	−0.760247	−	0.552352i	0.138739	−	0.990329i	$-0.455695\pi$
$839$	−22.0209	−	15.9991i	−0.760247	−	0.552352i	−0.898986	+	0.437977i	$0.855695\pi$
$840$		0			0
$841$	−27.4115	+	19.9156i	−0.945224	+	0.686745i
$842$		0			0
$843$	14.8760			0.512355
$844$		0			0
$845$	−30.7606	−	13.9129i	−1.05820	−	0.478619i
$846$		0			0
$847$	1.14898	+	3.53620i	0.0394795	+	0.121505i
$848$		0			0
$849$	−52.2748			−1.79407
$850$		0			0
$851$	−20.3885			−0.698909
$852$		0			0
$853$	2.03566	+	6.26510i	0.0696995	+	0.214513i	0.979839	−	0.199789i	$-0.0640257\pi$
$853$	2.03566	+	6.26510i	0.0696995	+	0.214513i	−0.910139	+	0.414302i	$0.864026\pi$
$854$		0			0
$855$	48.4928	−	10.0096i	1.65842	−	0.342322i
$856$		0			0
$857$	21.7827			0.744083			0.372042	−	0.928216i	$-0.378658\pi$
$857$	21.7827			0.744083			0.372042	+	0.928216i	$0.378658\pi$
$858$		0			0
$859$	8.32597	−	6.04917i	0.284078	−	0.206395i	−0.436616	−	0.899648i	$-0.643823\pi$
$859$	8.32597	−	6.04917i	0.284078	−	0.206395i	0.720694	+	0.693253i	$0.243823\pi$
$860$		0			0
$861$	55.1565	+	40.0735i	1.87973	+	1.36570i
$862$		0			0
$863$	−2.62042	+	1.90385i	−0.0892003	+	0.0648078i	−0.631492	−	0.775383i	$-0.717557\pi$
$863$	−2.62042	+	1.90385i	−0.0892003	+	0.0648078i	0.542291	+	0.840191i	$0.317557\pi$
$864$		0			0
$865$	11.7089	−	12.8512i	0.398115	−	0.436954i
$866$		0			0
$867$	−23.5201	+	72.3875i	−0.798786	+	2.45841i
$868$		0			0
$869$	0.287925	−	0.886141i	0.00976718	−	0.0300603i
$870$		0			0
$871$	−8.09755	−	24.9217i	−0.274375	−	0.844440i
$872$		0			0
$873$	−74.7758	−	54.3278i	−2.53078	−	1.83872i
$874$		0			0
$875$	−13.5418	+	39.3030i	−0.457796	+	1.32869i
$876$		0			0
$877$	13.9488	+	10.1344i	0.471019	+	0.342215i	0.797838	−	0.602872i	$-0.205977\pi$
$877$	13.9488	+	10.1344i	0.471019	+	0.342215i	−0.326819	+	0.945087i	$0.605977\pi$
$878$		0			0
$879$	−15.5395	−	47.8257i	−0.524135	−	1.61312i
$880$		0			0
$881$	−12.7416	+	39.2146i	−0.429275	+	1.32117i	0.469565	+	0.882898i	$0.344411\pi$
$881$	−12.7416	+	39.2146i	−0.429275	+	1.32117i	−0.898840	+	0.438276i	$0.855589\pi$
$882$		0			0
$883$	−5.70715	+	17.5648i	−0.192061	+	0.591103i	0.807937	+	0.589268i	$0.200584\pi$
$883$	−5.70715	+	17.5648i	−0.192061	+	0.591103i	−0.999998	+	0.00183450i	$0.999416\pi$
$884$		0			0
$885$	53.0986	−	58.2788i	1.78489	−	1.95902i
$886$		0			0
$887$	28.4978	−	20.7049i	0.956862	−	0.695201i	0.00444237	−	0.999990i	$-0.498586\pi$
$887$	28.4978	−	20.7049i	0.956862	−	0.695201i	0.952420	+	0.304789i	$0.0985859\pi$
$888$		0			0
$889$	−23.1351	−	16.8087i	−0.775927	−	0.563744i
$890$		0			0
$891$	18.5888	−	13.5056i	0.622748	−	0.452453i
$892$		0			0
$893$	28.4674			0.952625
$894$		0			0
$895$	13.3718	−	2.76014i	0.446971	−	0.0922614i
$896$		0			0
$897$	22.6872	+	69.8240i	0.757503	+	2.33135i
$898$		0			0
$899$	32.1381			1.07186
$900$		0			0
$901$	91.3591			3.04361
$902$		0			0
$903$	22.4150	+	68.9862i	0.745923	+	2.29572i
$904$		0			0
$905$	18.9241	+	8.55932i	0.629059	+	0.284521i
$906$		0			0
$907$	18.8599			0.626234			0.313117	−	0.949715i	$-0.398627\pi$
$907$	18.8599			0.626234			0.313117	+	0.949715i	$0.398627\pi$
$908$		0			0
$909$	−70.7561	+	51.4073i	−2.34683	+	1.70507i
$910$		0			0
$911$	−26.1055	−	18.9668i	−0.864914	−	0.628396i	0.0643037	−	0.997930i	$-0.479517\pi$
$911$	−26.1055	−	18.9668i	−0.864914	−	0.628396i	−0.929217	+	0.369534i	$0.879517\pi$
$912$		0			0
$913$	−0.0398140	+	0.0289265i	−0.00131765	+	0.000957329i
$914$		0			0
$915$	−67.3479	−	30.4612i	−2.22645	−	1.00702i
$916$		0			0
$917$	7.32576	−	22.5464i	0.241918	−	0.744547i
$918$		0			0
$919$	−10.3650	+	31.9001i	−0.341909	+	1.05229i	0.621308	+	0.783566i	$0.286601\pi$
$919$	−10.3650	+	31.9001i	−0.341909	+	1.05229i	−0.963218	+	0.268722i	$0.913399\pi$
$920$		0			0
$921$	−16.5021	−	50.7883i	−0.543764	−	1.67353i
$922$		0			0
$923$	14.0831	+	10.2320i	0.463550	+	0.336789i
$924$		0			0
$925$	−21.7442	+	9.37616i	−0.714946	+	0.308286i
$926$		0			0
$927$	70.9062	+	51.5164i	2.32887	+	1.69202i
$928$		0			0
$929$	3.84014	+	11.8187i	0.125991	+	0.387760i	0.994080	−	0.108648i	$-0.0346520\pi$
$929$	3.84014	+	11.8187i	0.125991	+	0.387760i	−0.868089	+	0.496408i	$0.834652\pi$
$930$		0			0
$931$	6.35359	−	19.5543i	0.208231	−	0.640868i
$932$		0			0
$933$	−5.14456	+	15.8333i	−0.168425	+	0.518360i
$934$		0			0
$935$	−7.05623	−	12.3895i	−0.230763	−	0.405180i
$936$		0			0
$937$	−39.7010	+	28.8445i	−1.29697	+	0.942307i	−0.999921	−	0.0125536i	$-0.996004\pi$
$937$	−39.7010	+	28.8445i	−1.29697	+	0.942307i	−0.297053	+	0.954861i	$0.596004\pi$
$938$		0			0
$939$	−68.6652	−	49.8882i	−2.24081	−	1.62804i
$940$		0			0
$941$	−0.918522	+	0.667345i	−0.0299429	+	0.0217548i	−0.602656	−	0.798001i	$-0.705891\pi$
$941$	−0.918522	+	0.667345i	−0.0299429	+	0.0217548i	0.572713	+	0.819756i	$0.305891\pi$
$942$		0			0
$943$	24.5364			0.799015
$944$		0			0
$945$	78.3707	−	86.0163i	2.54940	−	2.79811i
$946$		0			0
$947$	−13.8654	−	42.6732i	−0.450564	−	1.38669i	−0.876265	−	0.481829i	$-0.839973\pi$
$947$	−13.8654	−	42.6732i	−0.450564	−	1.38669i	0.425702	−	0.904864i	$-0.360027\pi$
$948$		0			0
$949$	22.1070			0.717624
$950$		0			0
$951$	4.14633			0.134454
$952$		0			0
$953$	−3.55460	−	10.9399i	−0.115145	−	0.354379i	0.876832	−	0.480796i	$-0.159652\pi$
$953$	−3.55460	−	10.9399i	−0.115145	−	0.354379i	−0.991977	+	0.126417i	$0.959652\pi$
$954$		0			0
$955$	12.1015	+	21.2481i	0.391594	+	0.687571i
$956$		0			0
$957$	25.5119			0.824683
$958$		0			0
$959$	34.8553	−	25.3239i	1.12554	−	0.817750i
$960$		0			0
$961$	11.7913	+	8.56687i	0.380364	+	0.276351i
$962$		0			0
$963$	64.1722	−	46.6238i	2.06792	−	1.50243i
$964$		0			0
$965$	−2.33875	+	21.0591i	−0.0752871	+	0.677918i
$966$		0			0
$967$	−10.8529	+	33.4017i	−0.349005	+	1.07413i	0.610399	+	0.792094i	$0.291009\pi$
$967$	−10.8529	+	33.4017i	−0.349005	+	1.07413i	−0.959404	+	0.282034i	$0.908991\pi$
$968$		0			0
$969$	−19.0975	+	58.7761i	−0.613500	+	1.88816i
$970$		0			0
$971$	11.6307	+	35.7955i	0.373246	+	1.14873i	0.944655	+	0.328067i	$0.106397\pi$
$971$	11.6307	+	35.7955i	0.373246	+	1.14873i	−0.571409	+	0.820665i	$0.693603\pi$
$972$		0			0
$973$	−31.2920	−	22.7350i	−1.00318	−	0.728850i
$974$		0			0
$975$	56.3061	+	64.0337i	1.80324	+	2.05072i
$976$		0			0
$977$	33.5087	+	24.3455i	1.07204	+	0.778882i	0.976278	−	0.216522i	$-0.0694714\pi$
$977$	33.5087	+	24.3455i	1.07204	+	0.778882i	0.0957615	+	0.995404i	$0.469471\pi$
$978$		0			0
$979$	−3.18518	−	9.80298i	−0.101799	−	0.313304i
$980$		0			0
$981$	−18.9775	+	58.4068i	−0.605906	+	1.86479i
$982$		0			0
$983$	11.8233	−	36.3884i	0.377105	−	1.16061i	−0.564942	−	0.825130i	$-0.691102\pi$
$983$	11.8233	−	36.3884i	0.377105	−	1.16061i	0.942047	−	0.335480i	$-0.108898\pi$
$984$		0			0
$985$	23.0397	−	4.75574i	0.734106	−	0.151530i
$986$		0			0
$987$	91.4475	−	66.4405i	2.91080	−	2.11482i
$988$		0			0
$989$	21.1196	+	15.3443i	0.671563	+	0.487919i
$990$		0			0
$991$	28.7902	−	20.9173i	0.914550	−	0.664460i	−0.0276114	−	0.999619i	$-0.508790\pi$
$991$	28.7902	−	20.9173i	0.914550	−	0.664460i	0.942162	+	0.335159i	$0.108790\pi$
$992$		0			0
$993$	29.0053			0.920456
$994$		0			0
$995$	−0.435250	+	3.91918i	−0.0137984	+	0.124246i
$996$		0			0
$997$	4.29121	+	13.2070i	0.135904	+	0.418269i	0.995730	−	0.0923187i	$-0.0294278\pi$
$997$	4.29121	+	13.2070i	0.135904	+	0.418269i	−0.859826	+	0.510588i	$0.829428\pi$
$998$		0			0
$999$	66.2843			2.09714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.441.1	✓	52
25.11	even	5	inner	1100.2.q.b.661.1	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.441.1	✓	52	1.1	even	1	trivial
1100.2.q.b.661.1	yes	52	25.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.994170 - 3.05974i) q^{3} +(0.246812 - 2.22240i) q^{5} +3.71818 q^{7} +(-5.94659 + 4.32045i) q^{9} +(0.809017 + 0.587785i) q^{11} +(4.28842 - 3.11572i) q^{13} +(-7.04536 + 1.45427i) q^{15} +(1.97041 - 6.06429i) q^{17} +(0.930947 - 2.86516i) q^{19} +(-3.69650 - 11.3767i) q^{21} +(-3.48288 - 2.53046i) q^{23} +(-4.87817 - 1.09703i) q^{25} +(11.3231 + 8.22668i) q^{27} +(2.45046 + 7.54173i) q^{29} +(1.25238 - 3.85444i) q^{31} +(0.994170 - 3.05974i) q^{33} +(0.917693 - 8.26330i) q^{35} +(3.83144 - 2.78371i) q^{37} +(-13.7967 - 10.0239i) q^{39} +(-4.61092 + 3.35003i) q^{41} -6.06383 q^{43} +(8.13410 + 14.2821i) q^{45} +(2.92003 + 8.98693i) q^{47} +6.82487 q^{49} -20.5141 q^{51} +(4.42752 + 13.6265i) q^{53} +(1.50597 - 1.65289i) q^{55} -9.69216 q^{57} +(-8.86637 + 6.44179i) q^{59} +(8.31256 + 6.03943i) q^{61} +(-22.1105 + 16.0642i) q^{63} +(-5.86595 - 10.2996i) q^{65} +(1.52762 - 4.70152i) q^{67} +(-4.27997 + 13.1724i) q^{69} +(1.01480 + 3.12325i) q^{71} +(3.37402 + 2.45137i) q^{73} +(1.49309 + 16.0166i) q^{75} +(3.00807 + 2.18549i) q^{77} +(-0.287925 - 0.886141i) q^{79} +(7.10029 - 21.8524i) q^{81} +(-0.0152076 + 0.0468041i) q^{83} +(-12.9910 - 5.87578i) q^{85} +(20.6396 - 14.9955i) q^{87} +(-8.33891 - 6.05857i) q^{89} +(15.9451 - 11.5848i) q^{91} -13.0387 q^{93} +(-6.13778 - 2.77610i) q^{95} +(3.88576 + 11.9591i) q^{97} -7.35039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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