LMFDB - Embedded newform 1100.2.q.b.221.12

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			221.12
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.51887 + 1.83006i) q^{3} +(1.68514 + 1.46980i) q^{5} +1.24095 q^{7} +(2.06850 + 6.36620i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(-1.66241 - 5.11638i) q^{13} +(1.55483 + 6.78613i) q^{15} +(0.211678 - 0.153793i) q^{17} +(4.53677 - 3.29616i) q^{19} +(3.12580 + 2.27102i) q^{21} +(0.370857 - 1.14138i) q^{23} +(0.679401 + 4.95363i) q^{25} +(-3.55390 + 10.9378i) q^{27} +(0.930471 + 0.676027i) q^{29} +(-6.17760 + 4.48829i) q^{31} +(-2.51887 + 1.83006i) q^{33} +(2.09118 + 1.82395i) q^{35} +(-2.82189 - 8.68487i) q^{37} +(5.17590 - 15.9298i) q^{39} +(0.996569 + 3.06712i) q^{41} -9.25739 q^{43} +(-5.87129 + 13.7682i) q^{45} +(1.07023 + 0.777570i) q^{47} -5.46003 q^{49} +0.814638 q^{51} +(-2.04784 - 1.48785i) q^{53} +(-1.91860 + 1.14847i) q^{55} +17.4597 q^{57} +(-2.54009 - 7.81760i) q^{59} +(3.06011 - 9.41804i) q^{61} +(2.56692 + 7.90016i) q^{63} +(4.71863 - 11.0652i) q^{65} +(4.97493 - 3.61450i) q^{67} +(3.02294 - 2.19630i) q^{69} +(1.10442 + 0.802409i) q^{71} +(-2.22196 + 6.83850i) q^{73} +(-7.35413 + 13.7209i) q^{75} +(-0.383476 + 1.18022i) q^{77} +(-3.80976 - 2.76796i) q^{79} +(-12.7224 + 9.24334i) q^{81} +(0.143927 - 0.104569i) q^{83} +(0.582750 + 0.0519603i) q^{85} +(1.10656 + 3.40564i) q^{87} +(-3.99906 + 12.3078i) q^{89} +(-2.06298 - 6.34919i) q^{91} -23.7744 q^{93} +(12.4898 + 1.11364i) q^{95} +(2.67517 + 1.94362i) q^{97} -6.69381 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	2.51887	+	1.83006i	1.45427	+	1.05659i	0.984811	+	0.173632i	$0.0555504\pi$
$3$	2.51887	+	1.83006i	1.45427	+	1.05659i	0.469457	+	0.882955i	$0.344450\pi$
$4$		0			0
$5$	1.68514	+	1.46980i	0.753618	+	0.657313i
$5$	1.68514	+	1.46980i	0.753618	+	0.657313i
$6$		0			0
$7$	1.24095			0.469037			0.234518	−	0.972112i	$-0.424649\pi$
$7$	1.24095			0.469037			0.234518	+	0.972112i	$0.424649\pi$
$8$		0			0
$9$	2.06850	+	6.36620i	0.689501	+	2.12207i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	−1.66241	−	5.11638i	−0.461070	−	1.41903i	−0.863858	−	0.503735i	$-0.831959\pi$
$13$	−1.66241	−	5.11638i	−0.461070	−	1.41903i	0.402788	−	0.915293i	$-0.368041\pi$
$14$		0			0
$15$	1.55483	+	6.78613i	0.401454	+	1.75217i
$16$		0			0
$17$	0.211678	−	0.153793i	0.0513393	−	0.0373002i	−0.561820	−	0.827260i	$-0.689899\pi$
$17$	0.211678	−	0.153793i	0.0513393	−	0.0373002i	0.613159	+	0.789960i	$0.289899\pi$
$18$		0			0
$19$	4.53677	−	3.29616i	1.04081	−	0.756190i	0.0703640	−	0.997521i	$-0.477584\pi$
$19$	4.53677	−	3.29616i	1.04081	−	0.756190i	0.970443	+	0.241331i	$0.0775839\pi$
$20$		0			0
$21$	3.12580	+	2.27102i	0.682105	+	0.495578i
$22$		0			0
$23$	0.370857	−	1.14138i	0.0773291	−	0.237995i	−0.904918	−	0.425586i	$-0.860068\pi$
$23$	0.370857	−	1.14138i	0.0773291	−	0.237995i	0.982247	+	0.187591i	$0.0600680\pi$
$24$		0			0
$25$	0.679401	+	4.95363i	0.135880	+	0.990725i
$26$		0			0
$27$	−3.55390	+	10.9378i	−0.683948	+	2.10497i
$28$		0			0
$29$	0.930471	+	0.676027i	0.172784	+	0.125535i	0.670816	−	0.741624i	$-0.265944\pi$
$29$	0.930471	+	0.676027i	0.172784	+	0.125535i	−0.498032	+	0.867159i	$0.665944\pi$
$30$		0			0
$31$	−6.17760	+	4.48829i	−1.10953	+	0.806120i	−0.982589	−	0.185790i	$-0.940515\pi$
$31$	−6.17760	+	4.48829i	−1.10953	+	0.806120i	−0.126940	+	0.991910i	$0.540515\pi$
$32$		0			0
$33$	−2.51887	+	1.83006i	−0.438478	+	0.318573i
$34$		0			0
$35$	2.09118	+	1.82395i	0.353474	+	0.308304i
$36$		0			0
$37$	−2.82189	−	8.68487i	−0.463915	−	1.42778i	−0.860342	−	0.509718i	$-0.829750\pi$
$37$	−2.82189	−	8.68487i	−0.463915	−	1.42778i	0.396427	−	0.918066i	$-0.370250\pi$
$38$		0			0
$39$	5.17590	−	15.9298i	0.828807	−	2.55081i
$40$		0			0
$41$	0.996569	+	3.06712i	0.155638	+	0.479004i	0.998225	−	0.0595559i	$-0.0189684\pi$
$41$	0.996569	+	3.06712i	0.155638	+	0.479004i	−0.842587	+	0.538560i	$0.818968\pi$
$42$		0			0
$43$	−9.25739			−1.41174			−0.705869	−	0.708342i	$-0.749443\pi$
$43$	−9.25739			−1.41174			−0.705869	+	0.708342i	$0.749443\pi$
$44$		0			0
$45$	−5.87129	+	13.7682i	−0.875240	+	2.05244i
$46$		0			0
$47$	1.07023	+	0.777570i	0.156110	+	0.113420i	0.663098	−	0.748533i	$-0.269241\pi$
$47$	1.07023	+	0.777570i	0.156110	+	0.113420i	−0.506988	+	0.861953i	$0.669241\pi$
$48$		0			0
$49$	−5.46003			−0.780005
$50$		0			0
$51$	0.814638			0.114072
$52$		0			0
$53$	−2.04784	−	1.48785i	−0.281293	−	0.204371i	0.438188	−	0.898883i	$-0.355620\pi$
$53$	−2.04784	−	1.48785i	−0.281293	−	0.204371i	−0.719481	+	0.694512i	$0.755620\pi$
$54$		0			0
$55$	−1.91860	+	1.14847i	−0.258703	+	0.154860i
$56$		0			0
$57$	17.4597			2.31259
$58$		0			0
$59$	−2.54009	−	7.81760i	−0.330692	−	1.01776i	−0.968805	−	0.247823i	$-0.920285\pi$
$59$	−2.54009	−	7.81760i	−0.330692	−	1.01776i	0.638114	−	0.769942i	$-0.279715\pi$
$60$		0			0
$61$	3.06011	−	9.41804i	0.391807	−	1.20586i	−0.539614	−	0.841913i	$-0.681430\pi$
$61$	3.06011	−	9.41804i	0.391807	−	1.20586i	0.931421	−	0.363944i	$-0.118570\pi$
$62$		0			0
$63$	2.56692	+	7.90016i	0.323401	+	0.995326i
$64$		0			0
$65$	4.71863	−	11.0652i	0.585274	−	1.37247i
$66$		0			0
$67$	4.97493	−	3.61450i	0.607784	−	0.441581i	−0.240849	−	0.970563i	$-0.577426\pi$
$67$	4.97493	−	3.61450i	0.607784	−	0.441581i	0.848633	+	0.528982i	$0.177426\pi$
$68$		0			0
$69$	3.02294	−	2.19630i	0.363919	−	0.264403i
$70$		0			0
$71$	1.10442	+	0.802409i	0.131071	+	0.0952284i	0.651389	−	0.758744i	$-0.274187\pi$
$71$	1.10442	+	0.802409i	0.131071	+	0.0952284i	−0.520318	+	0.853972i	$0.674187\pi$
$72$		0			0
$73$	−2.22196	+	6.83850i	−0.260061	+	0.800386i	0.732729	+	0.680521i	$0.238246\pi$
$73$	−2.22196	+	6.83850i	−0.260061	+	0.800386i	−0.992790	+	0.119866i	$0.961754\pi$
$74$		0			0
$75$	−7.35413	+	13.7209i	−0.849182	+	1.58435i
$76$		0			0
$77$	−0.383476	+	1.18022i	−0.0437011	+	0.134498i
$78$		0			0
$79$	−3.80976	−	2.76796i	−0.428632	−	0.311419i	0.352470	−	0.935823i	$-0.385342\pi$
$79$	−3.80976	−	2.76796i	−0.428632	−	0.311419i	−0.781102	+	0.624404i	$0.785342\pi$
$80$		0			0
$81$	−12.7224	+	9.24334i	−1.41360	+	1.02704i
$82$		0			0
$83$	0.143927	−	0.104569i	0.0157980	−	0.0114779i	−0.579858	−	0.814717i	$-0.696892\pi$
$83$	0.143927	−	0.104569i	0.0157980	−	0.0114779i	0.595656	+	0.803239i	$0.296892\pi$
$84$		0			0
$85$	0.582750	+	0.0519603i	0.0632082	+	0.00563588i
$86$		0			0
$87$	1.10656	+	3.40564i	0.118636	+	0.365123i
$88$		0			0
$89$	−3.99906	+	12.3078i	−0.423900	+	1.30463i	0.480144	+	0.877190i	$0.340584\pi$
$89$	−3.99906	+	12.3078i	−0.423900	+	1.30463i	−0.904044	+	0.427440i	$0.859416\pi$
$90$		0			0
$91$	−2.06298	−	6.34919i	−0.216259	−	0.665576i
$92$		0			0
$93$	−23.7744			−2.46529
$94$		0			0
$95$	12.4898	+	1.11364i	1.28142	+	0.114257i
$96$		0			0
$97$	2.67517	+	1.94362i	0.271622	+	0.197345i	0.715255	−	0.698864i	$-0.246311\pi$
$97$	2.67517	+	1.94362i	0.271622	+	0.197345i	−0.443633	+	0.896209i	$0.646311\pi$
$98$		0			0
$99$	−6.69381			−0.672754
$100$		0			0
$101$	−16.8548			−1.67712			−0.838559	−	0.544811i	$-0.816601\pi$
$101$	−16.8548			−1.67712			−0.838559	+	0.544811i	$0.816601\pi$
$102$		0			0
$103$	5.69324	+	4.13638i	0.560971	+	0.407570i	0.831814	−	0.555054i	$-0.187302\pi$
$103$	5.69324	+	4.13638i	0.560971	+	0.407570i	−0.270843	+	0.962624i	$0.587302\pi$
$104$		0			0
$105$	1.92947	+	8.42128i	0.188297	+	0.821833i
$106$		0			0
$107$	18.6643			1.80435			0.902174	−	0.431372i	$-0.141970\pi$
$107$	18.6643			1.80435			0.902174	+	0.431372i	$0.141970\pi$
$108$		0			0
$109$	−1.47808	−	4.54906i	−0.141574	−	0.435721i	0.854980	−	0.518661i	$-0.173569\pi$
$109$	−1.47808	−	4.54906i	−0.141574	−	0.435721i	−0.996555	+	0.0829395i	$0.973569\pi$
$110$		0			0
$111$	8.78591	−	27.0403i	0.833922	−	2.56655i
$112$		0			0
$113$	−5.68964	−	17.5109i	−0.535236	−	1.64729i	−0.743138	−	0.669138i	$-0.766664\pi$
$113$	−5.68964	−	17.5109i	−0.535236	−	1.64729i	0.207902	−	0.978150i	$-0.433336\pi$
$114$		0			0
$115$	2.30255	−	1.37830i	0.214713	−	0.128528i
$116$		0			0
$117$	29.1332	−	21.1665i	2.69336	−	1.95684i
$118$		0			0
$119$	0.262682	−	0.190850i	0.0240800	−	0.0174952i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	−3.10281	+	9.54946i	−0.279771	+	0.861046i
$124$		0			0
$125$	−6.13593	+	9.34614i	−0.548814	+	0.835944i
$126$		0			0
$127$	−4.78914	+	14.7395i	−0.424968	+	1.30792i	0.478058	+	0.878328i	$0.341341\pi$
$127$	−4.78914	+	14.7395i	−0.424968	+	1.30792i	−0.903025	+	0.429587i	$0.858659\pi$
$128$		0			0
$129$	−23.3181	−	16.9416i	−2.05305	−	1.49163i
$130$		0			0
$131$	−1.02096	+	0.741773i	−0.0892020	+	0.0648090i	−0.631492	−	0.775382i	$-0.717557\pi$
$131$	−1.02096	+	0.741773i	−0.0892020	+	0.0648090i	0.542290	+	0.840191i	$0.317557\pi$
$132$		0			0
$133$	5.62993	−	4.09038i	0.488177	−	0.354681i
$134$		0			0
$135$	−22.0651	+	13.2082i	−1.89906	+	1.13678i
$136$		0			0
$137$	6.42680	+	19.7797i	0.549079	+	1.68989i	0.711089	+	0.703102i	$0.248202\pi$
$137$	6.42680	+	19.7797i	0.549079	+	1.68989i	−0.162010	+	0.986789i	$0.551798\pi$
$138$		0			0
$139$	0.497916	−	1.53243i	0.0422327	−	0.129979i	−0.927717	−	0.373284i	$-0.878232\pi$
$139$	0.497916	−	1.53243i	0.0422327	−	0.129979i	0.969950	+	0.243305i	$0.0782317\pi$
$140$		0			0
$141$	1.27277	+	3.91719i	0.107187	+	0.329887i
$142$		0			0
$143$	5.37968			0.449871
$144$		0			0
$145$	0.574354	+	2.50680i	0.0476975	+	0.208179i
$146$		0			0
$147$	−13.7531	−	9.99220i	−1.13434	−	0.824143i
$148$		0			0
$149$	0.565134			0.0462976			0.0231488	−	0.999732i	$-0.492631\pi$
$149$	0.565134			0.0462976			0.0231488	+	0.999732i	$0.492631\pi$
$150$		0			0
$151$	16.1189			1.31174			0.655869	−	0.754875i	$-0.272303\pi$
$151$	16.1189			1.31174			0.655869	+	0.754875i	$0.272303\pi$
$152$		0			0
$153$	1.41693	+	1.02946i	0.114552	+	0.0832269i
$154$		0			0
$155$	−17.0070	−	1.51641i	−1.36603	−	0.121801i
$156$		0			0
$157$	21.2358			1.69480			0.847400	−	0.530954i	$-0.178166\pi$
$157$	21.2358			1.69480			0.847400	+	0.530954i	$0.178166\pi$
$158$		0			0
$159$	−2.43539	−	7.49537i	−0.193139	−	0.594421i
$160$		0			0
$161$	0.460217	−	1.41640i	0.0362702	−	0.111628i
$162$		0			0
$163$	−0.581591	−	1.78995i	−0.0455537	−	0.140200i	0.925693	−	0.378276i	$-0.123483\pi$
$163$	−0.581591	−	1.78995i	−0.0455537	−	0.140200i	−0.971246	+	0.238076i	$0.923483\pi$
$164$		0			0
$165$	−6.93446	−	0.618304i	−0.539847	−	0.0481349i
$166$		0			0
$167$	4.75022	−	3.45124i	0.367583	−	0.267065i	−0.388625	−	0.921396i	$-0.627050\pi$
$167$	4.75022	−	3.45124i	0.367583	−	0.267065i	0.756208	+	0.654331i	$0.227050\pi$
$168$		0			0
$169$	−12.8965	+	9.36985i	−0.992037	+	0.720757i
$170$		0			0
$171$	30.3683	+	22.0639i	2.32232	+	1.68727i
$172$		0			0
$173$	0.333804	−	1.02734i	0.0253786	−	0.0781075i	−0.937565	−	0.347810i	$-0.886925\pi$
$173$	0.333804	−	1.02734i	0.0253786	−	0.0781075i	0.962944	+	0.269703i	$0.0869254\pi$
$174$		0			0
$175$	0.843106	+	6.14722i	0.0637328	+	0.464686i
$176$		0			0
$177$	7.90855	−	24.3400i	0.594443	−	1.82951i
$178$		0			0
$179$	17.6065	+	12.7919i	1.31598	+	0.956112i	0.999973	+	0.00735353i	$0.00234072\pi$
$179$	17.6065	+	12.7919i	1.31598	+	0.956112i	0.316002	+	0.948758i	$0.397659\pi$
$180$		0			0
$181$	−4.24116	+	3.08138i	−0.315243	+	0.229037i	−0.734143	−	0.678995i	$-0.762416\pi$
$181$	−4.24116	+	3.08138i	−0.315243	+	0.229037i	0.418900	+	0.908032i	$0.362416\pi$
$182$		0			0
$183$	24.9436	−	18.1226i	1.84389	−	1.33966i
$184$		0			0
$185$	8.00971	−	18.7828i	0.588886	−	1.38094i
$186$		0			0
$187$	0.0808536	+	0.248842i	0.00591260	+	0.0181971i
$188$		0			0
$189$	−4.41022	+	13.5733i	−0.320797	+	0.987310i
$190$		0			0
$191$	−4.54787	−	13.9969i	−0.329072	−	1.01278i	−0.969569	−	0.244819i	$-0.921271\pi$
$191$	−4.54787	−	13.9969i	−0.329072	−	1.01278i	0.640496	−	0.767961i	$-0.278729\pi$
$192$		0			0
$193$	−21.6039			−1.55508			−0.777540	−	0.628833i	$-0.783533\pi$
$193$	−21.6039			−1.55508			−0.777540	+	0.628833i	$0.783533\pi$
$194$		0			0
$195$	32.1357	−	19.2364i	2.30128	−	1.37755i
$196$		0			0
$197$	5.86993	+	4.26475i	0.418215	+	0.303851i	0.776919	−	0.629600i	$-0.216781\pi$
$197$	5.86993	+	4.26475i	0.418215	+	0.303851i	−0.358704	+	0.933451i	$0.616781\pi$
$198$		0			0
$199$	2.77724			0.196873			0.0984366	−	0.995143i	$-0.468616\pi$
$199$	2.77724			0.196873			0.0984366	+	0.995143i	$0.468616\pi$
$200$		0			0
$201$	19.1459			1.35045
$202$		0			0
$203$	1.15467	+	0.838918i	0.0810421	+	0.0588805i
$204$		0			0
$205$	−2.82869	+	6.63329i	−0.197564	+	0.463289i
$206$		0			0
$207$	8.03338			0.558359
$208$		0			0
$209$	1.73289	+	5.33330i	0.119867	+	0.368912i
$210$		0			0
$211$	−3.67292	+	11.3041i	−0.252854	+	0.778206i	0.741391	+	0.671074i	$0.234167\pi$
$211$	−3.67292	+	11.3041i	−0.252854	+	0.778206i	−0.994245	+	0.107132i	$0.965833\pi$
$212$		0			0
$213$	1.31343	+	4.04232i	0.0899947	+	0.276975i
$214$		0			0
$215$	−15.6000	−	13.6065i	−1.06391	−	0.927954i
$216$		0			0
$217$	−7.66612	+	5.56976i	−0.520410	+	0.378100i
$218$		0			0
$219$	−18.1117	+	13.1589i	−1.22388	+	0.889199i
$220$		0			0
$221$	−1.13876	−	0.827355i	−0.0766011	−	0.0556539i
$222$		0			0
$223$	5.11056	−	15.7287i	0.342228	−	1.05327i	−0.620822	−	0.783951i	$-0.713201\pi$
$223$	5.11056	−	15.7287i	0.342228	−	1.05327i	0.963051	−	0.269320i	$-0.0867988\pi$
$224$		0			0
$225$	−30.1304	+	14.5718i	−2.00869	+	0.971452i
$226$		0			0
$227$	8.09915	−	24.9266i	0.537560	−	1.65444i	−0.200493	−	0.979695i	$-0.564254\pi$
$227$	8.09915	−	24.9266i	0.537560	−	1.65444i	0.738052	−	0.674743i	$-0.235746\pi$
$228$		0			0
$229$	12.5389	+	9.11006i	0.828595	+	0.602010i	0.919162	−	0.393881i	$-0.128868\pi$
$229$	12.5389	+	9.11006i	0.828595	+	0.602010i	−0.0905663	+	0.995890i	$0.528868\pi$
$230$		0			0
$231$	−3.12580	+	2.27102i	−0.205662	+	0.149422i
$232$		0			0
$233$	1.00208	−	0.728054i	0.0656485	−	0.0476964i	−0.554477	−	0.832199i	$-0.687082\pi$
$233$	1.00208	−	0.728054i	0.0656485	−	0.0476964i	0.620125	+	0.784503i	$0.287082\pi$
$234$		0			0
$235$	0.660625	+	2.88334i	0.0430944	+	0.188088i
$236$		0			0
$237$	−4.53075	−	13.9442i	−0.294304	−	0.905774i
$238$		0			0
$239$	8.71113	−	26.8101i	0.563476	−	1.73420i	−0.108961	−	0.994046i	$-0.534752\pi$
$239$	8.71113	−	26.8101i	0.563476	−	1.73420i	0.672437	−	0.740155i	$-0.265248\pi$
$240$		0			0
$241$	6.31640	+	19.4399i	0.406875	+	1.25223i	0.919319	+	0.393512i	$0.128740\pi$
$241$	6.31640	+	19.4399i	0.406875	+	1.25223i	−0.512444	+	0.858721i	$0.671260\pi$
$242$		0			0
$243$	−14.4599			−0.927601
$244$		0			0
$245$	−9.20093	−	8.02513i	−0.587826	−	0.512707i
$246$		0			0
$247$	−24.4064	−	17.7323i	−1.55294	−	1.12828i
$248$		0			0
$249$	0.553901			0.0351020
$250$		0			0
$251$	14.0074			0.884137			0.442068	−	0.896981i	$-0.354245\pi$
$251$	14.0074			0.884137			0.442068	+	0.896981i	$0.354245\pi$
$252$		0			0
$253$	0.970918	+	0.705413i	0.0610411	+	0.0443489i
$254$		0			0
$255$	1.37278	+	1.19735i	0.0859668	+	0.0749810i
$256$		0			0
$257$	−0.236800			−0.0147712			−0.00738558	−	0.999973i	$-0.502351\pi$
$257$	−0.236800			−0.0147712			−0.00738558	+	0.999973i	$0.502351\pi$
$258$		0			0
$259$	−3.50183	−	10.7775i	−0.217593	−	0.669683i
$260$		0			0
$261$	−2.37904	+	7.32192i	−0.147259	+	0.453216i
$262$		0			0
$263$	−6.36683	−	19.5951i	−0.392596	−	1.20829i	−0.930818	−	0.365483i	$-0.880904\pi$
$263$	−6.36683	−	19.5951i	−0.392596	−	1.20829i	0.538222	−	0.842803i	$-0.319096\pi$
$264$		0			0
$265$	−1.26408	−	5.51714i	−0.0776516	−	0.338915i
$266$		0			0
$267$	−32.5972	+	23.6833i	−1.99492	+	1.44939i
$268$		0			0
$269$	3.62524	−	2.63389i	0.221035	−	0.160591i	−0.471757	−	0.881728i	$-0.656380\pi$
$269$	3.62524	−	2.63389i	0.221035	−	0.160591i	0.692792	+	0.721137i	$0.256380\pi$
$270$		0			0
$271$	−15.7858	−	11.4691i	−0.958921	−	0.696697i	−0.00602109	−	0.999982i	$-0.501917\pi$
$271$	−15.7858	−	11.4691i	−0.958921	−	0.696697i	−0.952900	+	0.303285i	$0.901917\pi$
$272$		0			0
$273$	6.42306	−	19.7681i	0.388741	−	1.19642i
$274$		0			0
$275$	−4.92113	−	0.884606i	−0.296755	−	0.0533437i
$276$		0			0
$277$	−9.05408	+	27.8656i	−0.544007	+	1.67428i	0.179333	+	0.983788i	$0.442606\pi$
$277$	−9.05408	+	27.8656i	−0.544007	+	1.67428i	−0.723340	+	0.690492i	$0.757394\pi$
$278$		0			0
$279$	−41.3517	−	30.0438i	−2.47566	−	1.79867i
$280$		0			0
$281$	−17.6511	+	12.8243i	−1.05298	+	0.765034i	−0.972777	−	0.231745i	$-0.925557\pi$
$281$	−17.6511	+	12.8243i	−1.05298	+	0.765034i	−0.0802020	+	0.996779i	$0.525557\pi$
$282$		0			0
$283$	15.1606	−	11.0148i	0.901204	−	0.654763i	−0.0375707	−	0.999294i	$-0.511962\pi$
$283$	15.1606	−	11.0148i	0.901204	−	0.654763i	0.938775	+	0.344531i	$0.111962\pi$
$284$		0			0
$285$	29.4220	+	25.6622i	1.74281	+	1.52010i
$286$		0			0
$287$	1.23670	+	3.80616i	0.0729999	+	0.224671i
$288$		0			0
$289$	−5.23213	+	16.1029i	−0.307773	+	0.947227i
$290$		0			0
$291$	3.18143	+	9.79144i	0.186499	+	0.573985i
$292$		0			0
$293$	14.2511			0.832559			0.416280	−	0.909237i	$-0.363334\pi$
$293$	14.2511			0.832559			0.416280	+	0.909237i	$0.363334\pi$
$294$		0			0
$295$	7.20986	−	16.9072i	0.419774	−	0.984374i
$296$		0			0
$297$	−9.30422	−	6.75991i	−0.539886	−	0.392250i
$298$		0			0
$299$	−6.45626			−0.373375
$300$		0			0
$301$	−11.4880			−0.662157
$302$		0			0
$303$	−42.4550	−	30.8454i	−2.43898	−	1.77202i
$304$		0			0
$305$	18.9993	−	11.3730i	1.08790	−	0.651216i
$306$		0			0
$307$	−30.5540			−1.74381			−0.871904	−	0.489677i	$-0.837115\pi$
$307$	−30.5540			−1.74381			−0.871904	+	0.489677i	$0.837115\pi$
$308$		0			0
$309$	6.77067	+	20.8380i	0.385170	+	1.18543i
$310$		0			0
$311$	7.32474	−	22.5432i	0.415348	−	1.27831i	−0.496592	−	0.867984i	$-0.665415\pi$
$311$	7.32474	−	22.5432i	0.415348	−	1.27831i	0.911940	−	0.410325i	$-0.134585\pi$
$312$		0			0
$313$	−6.26458	−	19.2804i	−0.354095	−	1.08979i	−0.956533	−	0.291626i	$-0.905804\pi$
$313$	−6.26458	−	19.2804i	−0.354095	−	1.08979i	0.602438	−	0.798166i	$-0.294196\pi$
$314$		0			0
$315$	−7.28600	+	17.0857i	−0.410520	+	0.962671i
$316$		0			0
$317$	−13.4822	+	9.79536i	−0.757234	+	0.550162i	−0.898061	−	0.439872i	$-0.855024\pi$
$317$	−13.4822	+	9.79536i	−0.757234	+	0.550162i	0.140827	+	0.990034i	$0.455024\pi$
$318$		0			0
$319$	−0.930471	+	0.676027i	−0.0520964	+	0.0378502i
$320$		0			0
$321$	47.0129	+	34.1569i	2.62401	+	1.90645i
$322$		0			0
$323$	0.453408	−	1.39544i	0.0252283	−	0.0776446i
$324$		0			0
$325$	24.2152	−	11.7110i	1.34322	−	0.649612i
$326$		0			0
$327$	4.60199	−	14.1635i	0.254490	−	0.783241i
$328$		0			0
$329$	1.32811	+	0.964929i	0.0732211	+	0.0531983i
$330$		0			0
$331$	−23.6515	+	17.1838i	−1.30000	+	0.944507i	−0.999956	−	0.00941805i	$-0.997002\pi$
$331$	−23.6515	+	17.1838i	−1.30000	+	0.944507i	−0.300046	+	0.953925i	$0.597002\pi$
$332$		0			0
$333$	49.4525	−	35.9294i	2.70998	−	1.96892i
$334$		0			0
$335$	13.6960	+	1.22119i	0.748294	+	0.0667208i
$336$		0			0
$337$	−7.72236	−	23.7670i	−0.420664	−	1.29467i	−0.907086	−	0.420946i	$-0.861698\pi$
$337$	−7.72236	−	23.7670i	−0.420664	−	1.29467i	0.486422	−	0.873724i	$-0.338302\pi$
$338$		0			0
$339$	17.7146	−	54.5200i	0.962126	−	2.96112i
$340$		0			0
$341$	−2.35963	−	7.26220i	−0.127781	−	0.393270i
$342$		0			0
$343$	−15.4623			−0.834887
$344$		0			0
$345$	8.32219	+	0.742039i	0.448052	+	0.0399500i
$346$		0			0
$347$	18.5149	+	13.4519i	0.993933	+	0.722135i	0.960779	−	0.277315i	$-0.0894447\pi$
$347$	18.5149	+	13.4519i	0.993933	+	0.722135i	0.0331543	+	0.999450i	$0.489445\pi$
$348$		0			0
$349$	−17.1243			−0.916641			−0.458321	−	0.888787i	$-0.651549\pi$
$349$	−17.1243			−0.916641			−0.458321	+	0.888787i	$0.651549\pi$
$350$		0			0
$351$	61.8698			3.30237
$352$		0			0
$353$	12.7463	+	9.26076i	0.678420	+	0.492901i	0.872833	−	0.488019i	$-0.162280\pi$
$353$	12.7463	+	9.26076i	0.678420	+	0.492901i	−0.194413	+	0.980920i	$0.562280\pi$
$354$		0			0
$355$	0.681728	+	2.97544i	0.0361824	+	0.157920i
$356$		0			0
$357$	1.01093			0.0535040
$358$		0			0
$359$	8.08436	+	24.8811i	0.426676	+	1.31317i	0.901380	+	0.433029i	$0.142555\pi$
$359$	8.08436	+	24.8811i	0.426676	+	1.31317i	−0.474704	+	0.880145i	$0.657445\pi$
$360$		0			0
$361$	3.84632	−	11.8378i	0.202438	−	0.623040i
$362$		0			0
$363$	−0.962121	−	2.96110i	−0.0504983	−	0.155418i
$364$		0			0
$365$	−13.7955	+	8.25801i	−0.722091	+	0.432244i
$366$		0			0
$367$	10.1083	−	7.34410i	0.527648	−	0.383359i	−0.291829	−	0.956470i	$-0.594264\pi$
$367$	10.1083	−	7.34410i	0.527648	−	0.383359i	0.819477	+	0.573112i	$0.194264\pi$
$368$		0			0
$369$	−17.4645	+	12.6887i	−0.909166	+	0.660548i
$370$		0			0
$371$	−2.54128	−	1.84635i	−0.131937	−	0.0958576i
$372$		0			0
$373$	4.85418	−	14.9396i	0.251340	−	0.773545i	−0.743189	−	0.669082i	$-0.766688\pi$
$373$	4.85418	−	14.9396i	0.251340	−	0.773545i	0.994529	−	0.104463i	$-0.0333124\pi$
$374$		0			0
$375$	−32.5596	+	12.3125i	−1.68137	+	0.635816i
$376$		0			0
$377$	1.91198	−	5.88447i	0.0984721	−	0.303066i
$378$		0			0
$379$	−11.2930	−	8.20484i	−0.580082	−	0.421454i	0.258672	−	0.965965i	$-0.416715\pi$
$379$	−11.2930	−	8.20484i	−0.580082	−	0.421454i	−0.838754	+	0.544511i	$0.816715\pi$
$380$		0			0
$381$	−39.0373	+	28.3623i	−1.99994	+	1.45304i
$382$		0			0
$383$	5.31079	−	3.85851i	0.271369	−	0.197161i	−0.443775	−	0.896138i	$-0.646361\pi$
$383$	5.31079	−	3.85851i	0.271369	−	0.197161i	0.715144	+	0.698977i	$0.246361\pi$
$384$		0			0
$385$	−2.38089	+	1.42520i	−0.121341	+	0.0726350i
$386$		0			0
$387$	−19.1489	−	58.9344i	−0.973395	−	2.99580i
$388$		0			0
$389$	−9.27892	+	28.5576i	−0.470460	+	1.44793i	0.381524	+	0.924359i	$0.375399\pi$
$389$	−9.27892	+	28.5576i	−0.470460	+	1.44793i	−0.851984	+	0.523568i	$0.824601\pi$
$390$		0			0
$391$	−0.0970340	−	0.298640i	−0.00490722	−	0.0151029i
$392$		0			0
$393$	−3.92916			−0.198200
$394$		0			0
$395$	−2.35166	−	10.2640i	−0.118325	−	0.516436i
$396$		0			0
$397$	18.7750	+	13.6408i	0.942291	+	0.684614i	0.948971	−	0.315363i	$-0.102126\pi$
$397$	18.7750	+	13.6408i	0.942291	+	0.684614i	−0.00668031	+	0.999978i	$0.502126\pi$
$398$		0			0
$399$	21.6667			1.08469
$400$		0			0
$401$	2.90231			0.144934			0.0724672	−	0.997371i	$-0.476913\pi$
$401$	2.90231			0.144934			0.0724672	+	0.997371i	$0.476913\pi$
$402$		0			0
$403$	33.2335	+	24.1455i	1.65548	+	1.20277i
$404$		0			0
$405$	−35.0248	−	3.12295i	−1.74040	−	0.155180i
$406$		0			0
$407$	9.13181			0.452647
$408$		0			0
$409$	−7.14970	−	22.0045i	−0.353530	−	1.08805i	−0.956857	−	0.290559i	$-0.906159\pi$
$409$	−7.14970	−	22.0045i	−0.353530	−	1.08805i	0.603327	−	0.797494i	$-0.293841\pi$
$410$		0			0
$411$	−20.0098	+	61.5838i	−0.987010	+	3.03770i
$412$		0			0
$413$	−3.15214	−	9.70128i	−0.155107	−	0.477369i
$414$		0			0
$415$	0.396232	+	0.0353296i	0.0194503	+	0.00173426i
$416$		0			0
$417$	4.05862	−	2.94876i	0.198752	−	0.144401i
$418$		0			0
$419$	−30.4854	+	22.1490i	−1.48931	+	1.08205i	−0.514905	+	0.857247i	$0.672173\pi$
$419$	−30.4854	+	22.1490i	−1.48931	+	1.08205i	−0.974405	+	0.224800i	$0.927827\pi$
$420$		0			0
$421$	1.74657	+	1.26896i	0.0851225	+	0.0618451i	0.629533	−	0.776974i	$-0.283246\pi$
$421$	1.74657	+	1.26896i	0.0851225	+	0.0618451i	−0.544410	+	0.838819i	$0.683246\pi$
$422$		0			0
$423$	−2.73638	+	8.42172i	−0.133048	+	0.409478i
$424$		0			0
$425$	0.905646	+	0.944084i	0.0439303	+	0.0457948i
$426$		0			0
$427$	3.79745	−	11.6874i	0.183772	−	0.565591i
$428$		0			0
$429$	13.5507	+	9.84515i	0.654233	+	0.475328i
$430$		0			0
$431$	31.5806	−	22.9446i	1.52118	−	1.10520i	0.560286	−	0.828299i	$-0.310691\pi$
$431$	31.5806	−	22.9446i	1.52118	−	1.10520i	0.960897	−	0.276905i	$-0.0893087\pi$
$432$		0			0
$433$	−27.3208	+	19.8497i	−1.31296	+	0.953918i	−0.312964	+	0.949765i	$0.601322\pi$
$433$	−27.3208	+	19.8497i	−1.31296	+	0.953918i	−0.999991	+	0.00415267i	$0.998678\pi$
$434$		0			0
$435$	−3.14089	+	7.36540i	−0.150594	+	0.353144i
$436$		0			0
$437$	−2.07968	−	6.40059i	−0.0994846	−	0.306182i
$438$		0			0
$439$	−2.37156	+	7.29892i	−0.113188	+	0.348358i	−0.991565	−	0.129611i	$-0.958627\pi$
$439$	−2.37156	+	7.29892i	−0.113188	+	0.348358i	0.878376	+	0.477969i	$0.158627\pi$
$440$		0			0
$441$	−11.2941	−	34.7596i	−0.537814	−	1.65522i
$442$		0			0
$443$	−19.4593			−0.924541			−0.462270	−	0.886739i	$-0.652965\pi$
$443$	−19.4593			−0.924541			−0.462270	+	0.886739i	$0.652965\pi$
$444$		0			0
$445$	−24.8290	+	14.8627i	−1.17701	+	0.704557i
$446$		0			0
$447$	1.42350	+	1.03423i	0.0673291	+	0.0489175i
$448$		0			0
$449$	−28.3678			−1.33876			−0.669380	−	0.742920i	$-0.733440\pi$
$449$	−28.3678			−1.33876			−0.669380	+	0.742920i	$0.733440\pi$
$450$		0			0
$451$	−3.22497			−0.151858
$452$		0			0
$453$	40.6013	+	29.4986i	1.90762	+	1.38596i
$454$		0			0
$455$	5.85561	−	13.7314i	0.274515	−	0.643740i
$456$		0			0
$457$	−30.3952			−1.42183			−0.710914	−	0.703279i	$-0.751719\pi$
$457$	−30.3952			−1.42183			−0.710914	+	0.703279i	$0.751719\pi$
$458$		0			0
$459$	0.929869	+	2.86184i	0.0434026	+	0.133579i
$460$		0			0
$461$	4.76525	−	14.6659i	0.221940	−	0.683061i	−0.776648	−	0.629935i	$-0.783082\pi$
$461$	4.76525	−	14.6659i	0.221940	−	0.683061i	0.998588	−	0.0531257i	$-0.0169184\pi$
$462$		0			0
$463$	3.98323	+	12.2591i	0.185116	+	0.569729i	0.999950	−	0.00996505i	$-0.00317203\pi$
$463$	3.98323	+	12.2591i	0.185116	+	0.569729i	−0.814834	+	0.579694i	$0.803172\pi$
$464$		0			0
$465$	−40.0632	−	34.9435i	−1.85789	−	1.62047i
$466$		0			0
$467$	12.8842	−	9.36090i	0.596209	−	0.433171i	−0.248322	−	0.968677i	$-0.579879\pi$
$467$	12.8842	−	9.36090i	0.596209	−	0.433171i	0.844531	+	0.535506i	$0.179879\pi$
$468$		0			0
$469$	6.17366	−	4.48542i	0.285073	−	0.207118i
$470$		0			0
$471$	53.4901	+	38.8628i	2.46469	+	1.79071i
$472$		0			0
$473$	2.86069	−	8.80430i	0.131535	−	0.404822i
$474$		0			0
$475$	19.4102	+	20.2341i	0.890602	+	0.928402i
$476$		0			0
$477$	5.23595	−	16.1146i	0.239738	−	0.737836i
$478$		0			0
$479$	−10.0642	−	7.31210i	−0.459847	−	0.334098i	0.333624	−	0.942706i	$-0.391728\pi$
$479$	−10.0642	−	7.31210i	−0.459847	−	0.334098i	−0.793471	+	0.608608i	$0.791728\pi$
$480$		0			0
$481$	−39.7439	+	28.8757i	−1.81217	+	1.31662i
$482$		0			0
$483$	3.75133	−	2.72550i	0.170692	−	0.124015i
$484$		0			0
$485$	1.65131	+	7.20722i	0.0749819	+	0.327263i
$486$		0			0
$487$	8.62090	+	26.5324i	0.390650	+	1.20230i	0.932298	+	0.361692i	$0.117801\pi$
$487$	8.62090	+	26.5324i	0.390650	+	1.20230i	−0.541647	+	0.840606i	$0.682199\pi$
$488$		0			0
$489$	1.81078	−	5.57300i	0.0818862	−	0.252020i
$490$		0			0
$491$	2.36963	+	7.29296i	0.106940	+	0.329127i	0.990181	−	0.139792i	$-0.0446435\pi$
$491$	2.36963	+	7.29296i	0.106940	+	0.329127i	−0.883241	+	0.468919i	$0.844644\pi$
$492$		0			0
$493$	0.300928			0.0135531
$494$		0			0
$495$	−11.2800	−	9.83854i	−0.506999	−	0.442209i
$496$		0			0
$497$	1.37054	+	0.995752i	0.0614769	+	0.0446656i
$498$		0			0
$499$	−16.9627			−0.759356			−0.379678	−	0.925119i	$-0.623965\pi$
$499$	−16.9627			−0.759356			−0.379678	+	0.925119i	$0.623965\pi$
$500$		0			0
$501$	18.2812			0.816742
$502$		0			0
$503$	3.74051	+	2.71764i	0.166781	+	0.121174i	0.668045	−	0.744121i	$-0.267131\pi$
$503$	3.74051	+	2.71764i	0.166781	+	0.121174i	−0.501264	+	0.865295i	$0.667131\pi$
$504$		0			0
$505$	−28.4027	−	24.7731i	−1.26391	−	1.10239i
$506$		0			0
$507$	−49.6319			−2.20423
$508$		0			0
$509$	11.8695	+	36.5306i	0.526107	+	1.61919i	0.762117	+	0.647439i	$0.224160\pi$
$509$	11.8695	+	36.5306i	0.526107	+	1.61919i	−0.236011	+	0.971750i	$0.575840\pi$
$510$		0			0
$511$	−2.75736	+	8.48627i	−0.121978	+	0.375411i
$512$		0			0
$513$	19.9294	+	61.3364i	0.879904	+	2.70807i
$514$		0			0
$515$	3.51428	+	15.3383i	0.154858	+	0.675885i
$516$		0			0
$517$	−1.07023	+	0.777570i	−0.0470688	+	0.0341975i
$518$		0			0
$519$	2.72091	−	1.97686i	0.119435	−	0.0867744i
$520$		0			0
$521$	−2.41915	−	1.75761i	−0.105985	−	0.0770024i	0.533531	−	0.845781i	$-0.320865\pi$
$521$	−2.41915	−	1.75761i	−0.105985	−	0.0770024i	−0.639515	+	0.768778i	$0.720865\pi$
$522$		0			0
$523$	2.51432	−	7.73827i	0.109943	−	0.338371i	−0.880916	−	0.473274i	$-0.843072\pi$
$523$	2.51432	−	7.73827i	0.109943	−	0.338371i	0.990859	+	0.134903i	$0.0430722\pi$
$524$		0			0
$525$	−9.12614	+	17.0270i	−0.398297	+	0.743118i
$526$		0			0
$527$	−0.617393	+	1.90014i	−0.0268940	+	0.0827713i
$528$		0			0
$529$	17.4422	+	12.6725i	0.758355	+	0.550977i
$530$		0			0
$531$	44.5142	−	32.3414i	1.93175	−	1.40350i
$532$		0			0
$533$	14.0359	−	10.1976i	0.607961	−	0.441709i
$534$		0			0
$535$	31.4520	+	27.4327i	1.35979	+	1.18602i
$536$		0			0
$537$	20.9385	+	64.4422i	0.903564	+	2.78089i
$538$		0			0
$539$	1.68724	−	5.19280i	0.0726747	−	0.223670i
$540$		0			0
$541$	−10.3097	−	31.7299i	−0.443247	−	1.36418i	−0.884394	−	0.466740i	$-0.845428\pi$
$541$	−10.3097	−	31.7299i	−0.443247	−	1.36418i	0.441147	−	0.897435i	$-0.354572\pi$
$542$		0			0
$543$	−16.3220			−0.700445
$544$		0			0
$545$	4.19542	−	9.83829i	0.179712	−	0.421426i
$546$		0			0
$547$	34.1621	+	24.8202i	1.46067	+	1.06124i	0.983189	+	0.182593i	$0.0584489\pi$
$547$	34.1621	+	24.8202i	1.46067	+	1.06124i	0.477478	+	0.878644i	$0.341551\pi$
$548$		0			0
$549$	66.2870			2.82906
$550$		0			0
$551$	6.44962			0.274763
$552$		0			0
$553$	−4.72774	−	3.43491i	−0.201044	−	0.146067i
$554$		0			0
$555$	54.5491	−	32.6531i	2.31548	−	1.38605i
$556$		0			0
$557$	19.3696			0.820718			0.410359	−	0.911924i	$-0.365403\pi$
$557$	19.3696			0.820718			0.410359	+	0.911924i	$0.365403\pi$
$558$		0			0
$559$	15.3896	+	47.3643i	0.650910	+	2.00330i
$560$		0			0
$561$	−0.251737	+	0.774766i	−0.0106283	+	0.0327107i
$562$		0			0
$563$	5.16835	+	15.9065i	0.217820	+	0.670380i	0.998941	+	0.0460014i	$0.0146479\pi$
$563$	5.16835	+	15.9065i	0.217820	+	0.670380i	−0.781122	+	0.624379i	$0.785352\pi$
$564$		0			0
$565$	16.1496	−	37.8710i	0.679419	−	1.59324i
$566$		0			0
$567$	−15.7879	+	11.4706i	−0.663028	+	0.481718i
$568$		0			0
$569$	−16.7198	+	12.1476i	−0.700930	+	0.509255i	−0.880235	−	0.474538i	$-0.842615\pi$
$569$	−16.7198	+	12.1476i	−0.700930	+	0.509255i	0.179305	+	0.983793i	$0.442615\pi$
$570$		0			0
$571$	22.3682	+	16.2515i	0.936081	+	0.680103i	0.947474	−	0.319832i	$-0.103627\pi$
$571$	22.3682	+	16.2515i	0.936081	+	0.680103i	−0.0113931	+	0.999935i	$0.503627\pi$
$572$		0			0
$573$	14.1597	−	43.5792i	0.591532	−	1.82055i
$574$		0			0
$575$	5.90594	+	1.06163i	0.246295	+	0.0442732i
$576$		0			0
$577$	−10.2093	+	31.4211i	−0.425021	+	1.30808i	0.477954	+	0.878385i	$0.341379\pi$
$577$	−10.2093	+	31.4211i	−0.425021	+	1.30808i	−0.902975	+	0.429694i	$0.858621\pi$
$578$		0			0
$579$	−54.4173	−	39.5365i	−2.26150	−	1.64308i
$580$		0			0
$581$	0.178607	−	0.129765i	0.00740986	−	0.00538358i
$582$		0			0
$583$	2.04784	−	1.48785i	0.0848130	−	0.0616203i
$584$		0			0
$585$	80.2039	+	7.15129i	3.31602	+	0.295669i
$586$		0			0
$587$	−0.825165	−	2.53960i	−0.0340582	−	0.104820i	0.932582	−	0.360958i	$-0.117550\pi$
$587$	−0.825165	−	2.53960i	−0.0340582	−	0.104820i	−0.966640	+	0.256137i	$0.917550\pi$
$588$		0			0
$589$	−13.2322	+	40.7247i	−0.545225	+	1.67803i
$590$		0			0
$591$	6.98080	+	21.4847i	0.287152	+	0.883762i
$592$		0			0
$593$	12.9033			0.529877			0.264938	−	0.964265i	$-0.414648\pi$
$593$	12.9033			0.529877			0.264938	+	0.964265i	$0.414648\pi$
$594$		0			0
$595$	0.723167	+	0.0644803i	0.0296469	+	0.00264344i
$596$		0			0
$597$	6.99549	+	5.08252i	0.286306	+	0.208014i
$598$		0			0
$599$	−24.8502			−1.01535			−0.507676	−	0.861548i	$-0.669495\pi$
$599$	−24.8502			−1.01535			−0.507676	+	0.861548i	$0.669495\pi$
$600$		0			0
$601$	−8.42933			−0.343840			−0.171920	−	0.985111i	$-0.554997\pi$
$601$	−8.42933			−0.343840			−0.171920	+	0.985111i	$0.554997\pi$
$602$		0			0
$603$	33.3012	+	24.1948i	1.35613	+	0.985287i
$604$		0			0
$605$	−0.499384	−	2.17959i	−0.0203028	−	0.0886130i
$606$		0			0
$607$	6.98135			0.283364			0.141682	−	0.989912i	$-0.454749\pi$
$607$	6.98135			0.283364			0.141682	+	0.989912i	$0.454749\pi$
$608$		0			0
$609$	1.37319	+	4.22624i	0.0556445	+	0.171256i
$610$		0			0
$611$	2.19917	−	6.76836i	0.0889690	−	0.273819i
$612$		0			0
$613$	1.21750	+	3.74707i	0.0491743	+	0.151343i	0.972628	−	0.232366i	$-0.0746467\pi$
$613$	1.21750	+	3.74707i	0.0491743	+	0.151343i	−0.923454	+	0.383709i	$0.874647\pi$
$614$		0			0
$615$	−19.2644	+	11.5317i	−0.776816	+	0.465003i
$616$		0			0
$617$	19.2796	−	14.0075i	0.776168	−	0.563919i	−0.127658	−	0.991818i	$-0.540746\pi$
$617$	19.2796	−	14.0075i	0.776168	−	0.563919i	0.903827	+	0.427899i	$0.140746\pi$
$618$		0			0
$619$	−21.6163	+	15.7052i	−0.868832	+	0.631244i	−0.930273	−	0.366867i	$-0.880430\pi$
$619$	−21.6163	+	15.7052i	−0.868832	+	0.631244i	0.0614410	+	0.998111i	$0.480430\pi$
$620$		0			0
$621$	11.1662	+	8.11271i	0.448083	+	0.325552i
$622$		0			0
$623$	−4.96265	+	15.2735i	−0.198825	+	0.611919i
$624$		0			0
$625$	−24.0768	+	6.73100i	−0.963073	+	0.269240i
$626$		0			0
$627$	−5.39534	+	16.6052i	−0.215469	+	0.663146i
$628$		0			0
$629$	−1.93300	−	1.40441i	−0.0770738	−	0.0559974i
$630$		0			0
$631$	−14.2660	+	10.3649i	−0.567921	+	0.412619i	−0.834349	−	0.551236i	$-0.814156\pi$
$631$	−14.2660	+	10.3649i	−0.567921	+	0.412619i	0.266428	+	0.963855i	$0.414156\pi$
$632$		0			0
$633$	−29.9388	+	21.7518i	−1.18996	+	0.864557i
$634$		0			0
$635$	−29.7344	+	17.7990i	−1.17997	+	0.706332i
$636$		0			0
$637$	9.07682	+	27.9356i	0.359637	+	1.10685i
$638$		0			0
$639$	−2.82379	+	8.69074i	−0.111708	+	0.343800i
$640$		0			0
$641$	−4.63574	−	14.2673i	−0.183101	−	0.563526i	0.816810	−	0.576907i	$-0.195741\pi$
$641$	−4.63574	−	14.2673i	−0.183101	−	0.563526i	−0.999910	+	0.0133810i	$0.995741\pi$
$642$		0			0
$643$	4.96220			0.195690			0.0978451	−	0.995202i	$-0.468805\pi$
$643$	4.96220			0.195690			0.0978451	+	0.995202i	$0.468805\pi$
$644$		0			0
$645$	−14.3936	−	62.8219i	−0.566748	−	2.47361i
$646$		0			0
$647$	9.43245	+	6.85308i	0.370828	+	0.269422i	0.757554	−	0.652772i	$-0.226394\pi$
$647$	9.43245	+	6.85308i	0.370828	+	0.269422i	−0.386726	+	0.922195i	$0.626394\pi$
$648$		0			0
$649$	8.21991			0.322660
$650$		0			0
$651$	−29.5029			−1.15631
$652$		0			0
$653$	1.09495	+	0.795531i	0.0428489	+	0.0311315i	0.609004	−	0.793167i	$-0.291570\pi$
$653$	1.09495	+	0.795531i	0.0428489	+	0.0311315i	−0.566155	+	0.824299i	$0.691570\pi$
$654$		0			0
$655$	−2.81072	−	0.250615i	−0.109824	−	0.00979233i
$656$		0			0
$657$	−48.1314			−1.87778
$658$		0			0
$659$	5.84167	+	17.9788i	0.227559	+	0.700356i	0.998022	+	0.0628701i	$0.0200254\pi$
$659$	5.84167	+	17.9788i	0.227559	+	0.700356i	−0.770462	+	0.637485i	$0.779975\pi$
$660$		0			0
$661$	−10.8537	+	33.4042i	−0.422160	+	1.29927i	0.483528	+	0.875329i	$0.339355\pi$
$661$	−10.8537	+	33.4042i	−0.422160	+	1.29927i	−0.905688	+	0.423945i	$0.860645\pi$
$662$		0			0
$663$	−1.35426	−	4.16799i	−0.0525952	−	0.161871i
$664$		0			0
$665$	15.4992	+	1.38197i	0.601035	+	0.0535906i
$666$		0			0
$667$	1.11668	−	0.811313i	0.0432379	−	0.0314142i
$668$		0			0
$669$	41.6573	−	30.2658i	1.61056	−	1.17014i
$670$		0			0
$671$	8.01147	+	5.82067i	0.309279	+	0.224705i
$672$		0			0
$673$	5.33590	−	16.4222i	0.205684	−	0.633029i	−0.794001	−	0.607917i	$-0.792005\pi$
$673$	5.33590	−	16.4222i	0.205684	−	0.633029i	0.999685	−	0.0251128i	$-0.00799451\pi$
$674$		0			0
$675$	−56.5961	−	10.1735i	−2.17839	−	0.391580i
$676$		0			0
$677$	12.4495	−	38.3156i	0.478473	−	1.47259i	−0.362744	−	0.931889i	$-0.618160\pi$
$677$	12.4495	−	38.3156i	0.478473	−	1.47259i	0.841216	−	0.540699i	$-0.181840\pi$
$678$		0			0
$679$	3.31976	+	2.41195i	0.127401	+	0.0925620i
$680$		0			0
$681$	66.0180	−	47.9649i	2.52981	−	1.83802i
$682$		0			0
$683$	36.3996	−	26.4459i	1.39279	−	1.01192i	0.397240	−	0.917715i	$-0.369968\pi$
$683$	36.3996	−	26.4459i	1.39279	−	1.01192i	0.995552	−	0.0942085i	$-0.0300320\pi$
$684$		0			0
$685$	−18.2420	+	42.7776i	−0.696991	+	1.63445i
$686$		0			0
$687$	14.9119	+	45.8940i	0.568924	+	1.75097i
$688$		0			0
$689$	−4.20802	+	12.9510i	−0.160313	+	0.493392i
$690$		0			0
$691$	0.174727	+	0.537755i	0.00664694	+	0.0204572i	0.954325	−	0.298771i	$-0.0965765\pi$
$691$	0.174727	+	0.537755i	0.00664694	+	0.0204572i	−0.947678	+	0.319228i	$0.896577\pi$
$692$		0			0
$693$	−8.30672			−0.315546
$694$		0			0
$695$	3.09141	−	1.85052i	0.117264	−	0.0701943i
$696$		0			0
$697$	0.682653	+	0.495976i	0.0258573	+	0.0187864i
$698$		0			0
$699$	3.85649			0.145866
$700$		0			0
$701$	−44.3282			−1.67425			−0.837127	−	0.547009i	$-0.815766\pi$
$701$	−44.3282			−1.67425			−0.837127	+	0.547009i	$0.815766\pi$
$702$		0			0
$703$	−41.4290	−	30.0999i	−1.56252	−	1.13524i
$704$		0			0
$705$	−3.61267	+	8.47173i	−0.136061	+	0.319064i
$706$		0			0
$707$	−20.9161			−0.786629
$708$		0			0
$709$	−4.58141	−	14.1001i	−0.172058	−	0.529542i	0.827428	−	0.561571i	$-0.189803\pi$
$709$	−4.58141	−	14.1001i	−0.172058	−	0.529542i	−0.999487	+	0.0320296i	$0.989803\pi$
$710$		0			0
$711$	9.74084	−	29.9792i	0.365310	−	1.12431i
$712$		0			0
$713$	2.83184	+	8.71551i	0.106053	+	0.326399i
$714$		0			0
$715$	9.06552	+	7.90703i	0.339031	+	0.295706i
$716$		0			0
$717$	71.0063	−	51.5891i	2.65178	−	1.92663i
$718$		0			0
$719$	−1.56717	+	1.13861i	−0.0584455	+	0.0424631i	−0.616624	−	0.787257i	$-0.711500\pi$
$719$	−1.56717	+	1.13861i	−0.0584455	+	0.0424631i	0.558179	+	0.829721i	$0.311500\pi$
$720$		0			0
$721$	7.06505	+	5.13306i	0.263116	+	0.191165i
$722$		0			0
$723$	−19.6660	+	60.5259i	−0.731388	+	2.25098i
$724$		0			0
$725$	−2.71662	+	5.06850i	−0.100893	+	0.188239i
$726$		0			0
$727$	0.924321	−	2.84477i	0.0342812	−	0.105507i	−0.932452	−	0.361295i	$-0.882335\pi$
$727$	0.924321	−	2.84477i	0.0342812	−	0.105507i	0.966733	+	0.255788i	$0.0823349\pi$
$728$		0			0
$729$	1.74464	+	1.26755i	0.0646162	+	0.0469464i
$730$		0			0
$731$	−1.95958	+	1.42372i	−0.0724777	+	0.0526582i
$732$		0			0
$733$	−36.2485	+	26.3361i	−1.33887	+	0.972745i	−0.339384	+	0.940648i	$0.610218\pi$
$733$	−36.2485	+	26.3361i	−1.33887	+	0.972745i	−0.999485	+	0.0320967i	$0.989782\pi$
$734$		0			0
$735$	−8.48940	−	37.0525i	−0.313136	−	1.36670i
$736$		0			0
$737$	1.90025	+	5.84838i	0.0699967	+	0.215428i
$738$		0			0
$739$	1.98683	−	6.11484i	0.0730868	−	0.224938i	−0.907840	−	0.419318i	$-0.862269\pi$
$739$	1.98683	−	6.11484i	0.0730868	−	0.224938i	0.980926	+	0.194380i	$0.0622693\pi$
$740$		0			0
$741$	−29.0252	−	89.3304i	−1.06627	−	3.28163i
$742$		0			0
$743$	−24.7462			−0.907850			−0.453925	−	0.891040i	$-0.649977\pi$
$743$	−24.7462			−0.907850			−0.453925	+	0.891040i	$0.649977\pi$
$744$		0			0
$745$	0.952331	+	0.830632i	0.0348907	+	0.0304320i
$746$		0			0
$747$	0.963421	+	0.699966i	0.0352497	+	0.0256104i
$748$		0			0
$749$	23.1616			0.846305
$750$		0			0
$751$	23.6539			0.863142			0.431571	−	0.902079i	$-0.357959\pi$
$751$	23.6539			0.863142			0.431571	+	0.902079i	$0.357959\pi$
$752$		0			0
$753$	35.2827	+	25.6344i	1.28577	+	0.934168i
$754$		0			0
$755$	27.1626	+	23.6915i	0.988549	+	0.862221i
$756$		0			0
$757$	10.3542			0.376329			0.188165	−	0.982138i	$-0.439746\pi$
$757$	10.3542			0.376329			0.188165	+	0.982138i	$0.439746\pi$
$758$		0			0
$759$	1.15466	+	3.55368i	0.0419115	+	0.128990i
$760$		0			0
$761$	−7.83822	+	24.1236i	−0.284135	+	0.874478i	0.702521	+	0.711663i	$0.252058\pi$
$761$	−7.83822	+	24.1236i	−0.284135	+	0.874478i	−0.986657	+	0.162815i	$0.947942\pi$
$762$		0			0
$763$	−1.83423	−	5.64518i	−0.0664036	−	0.204369i
$764$		0			0
$765$	0.874631	+	3.81738i	0.0316224	+	0.138018i
$766$		0			0
$767$	−35.7751	+	25.9921i	−1.29176	+	0.938522i
$768$		0			0
$769$	−15.9736	+	11.6055i	−0.576021	+	0.418504i	−0.837288	−	0.546763i	$-0.815860\pi$
$769$	−15.9736	+	11.6055i	−0.576021	+	0.418504i	0.261266	+	0.965267i	$0.415860\pi$
$770$		0			0
$771$	−0.596467	−	0.433358i	−0.0214812	−	0.0156070i
$772$		0			0
$773$	−3.46457	+	10.6629i	−0.124612	+	0.383517i	−0.993830	−	0.110912i	$-0.964623\pi$
$773$	−3.46457	+	10.6629i	−0.124612	+	0.383517i	0.869218	+	0.494429i	$0.164623\pi$
$774$		0			0
$775$	−26.4304	−	27.5522i	−0.949407	−	0.989703i
$776$		0			0
$777$	10.9029	−	33.5557i	0.391140	−	1.20380i
$778$		0			0
$779$	14.6309	+	10.6300i	0.524208	+	0.380859i
$780$		0			0
$781$	−1.10442	+	0.802409i	−0.0395193	+	0.0287124i
$782$		0			0
$783$	−10.7010	+	7.77475i	−0.382423	+	0.277847i
$784$		0			0
$785$	35.7853	+	31.2123i	1.27723	+	1.11401i
$786$		0			0
$787$	−3.58737	−	11.0408i	−0.127876	−	0.393562i	0.866538	−	0.499111i	$-0.166340\pi$
$787$	−3.58737	−	11.0408i	−0.127876	−	0.393562i	−0.994414	+	0.105549i	$0.966340\pi$
$788$		0			0
$789$	19.8231	−	61.0091i	0.705720	−	2.17198i
$790$		0			0
$791$	−7.06058	−	21.7302i	−0.251045	−	0.772638i
$792$		0			0
$793$	−53.2734			−1.89180
$794$		0			0
$795$	6.91268	−	16.2103i	0.245167	−	0.574919i
$796$		0			0
$797$	−30.1188	−	21.8826i	−1.06686	−	0.775122i	−0.0915176	−	0.995803i	$-0.529172\pi$
$797$	−30.1188	−	21.8826i	−1.06686	−	0.775122i	−0.975346	+	0.220682i	$0.929172\pi$
$798$		0			0
$799$	0.346129			0.0122452
$800$		0			0
$801$	−86.6262			−3.06079
$802$		0			0
$803$	−5.81718	−	4.22643i	−0.205284	−	0.149147i
$804$		0			0
$805$	2.85735	−	1.71041i	0.100708	−	0.0602842i
$806$		0			0
$807$	13.9517			0.491123
$808$		0			0
$809$	−2.37380	−	7.30581i	−0.0834584	−	0.256859i	0.900616	−	0.434616i	$-0.143116\pi$
$809$	−2.37380	−	7.30581i	−0.0834584	−	0.256859i	−0.984074	+	0.177757i	$0.943116\pi$
$810$		0			0
$811$	−10.8819	+	33.4911i	−0.382116	+	1.17603i	0.556436	+	0.830891i	$0.312169\pi$
$811$	−10.8819	+	33.4911i	−0.382116	+	1.17603i	−0.938551	+	0.345140i	$0.887831\pi$
$812$		0			0
$813$	−18.7733	−	57.7781i	−0.658407	−	2.02637i
$814$		0			0
$815$	1.65080	−	3.87114i	0.0578251	−	0.135600i
$816$		0			0
$817$	−41.9987	+	30.5138i	−1.46935	+	1.06754i
$818$		0			0
$819$	36.1529	−	26.2666i	1.26329	−	0.917830i
$820$		0			0
$821$	20.8823	+	15.1719i	0.728797	+	0.529502i	0.889183	−	0.457552i	$-0.151274\pi$
$821$	20.8823	+	15.1719i	0.728797	+	0.529502i	−0.160386	+	0.987054i	$0.551274\pi$
$822$		0			0
$823$	2.36153	−	7.26803i	0.0823176	−	0.253348i	−0.901424	−	0.432937i	$-0.857477\pi$
$823$	2.36153	−	7.26803i	0.0823176	−	0.253348i	0.983742	+	0.179590i	$0.0574771\pi$
$824$		0			0
$825$	−10.7768	−	11.2342i	−0.375199	−	0.391124i
$826$		0			0
$827$	9.38646	−	28.8885i	0.326399	−	1.00455i	−0.644406	−	0.764683i	$-0.722895\pi$
$827$	9.38646	−	28.8885i	0.326399	−	1.00455i	0.970805	−	0.239870i	$-0.0771047\pi$
$828$		0			0
$829$	−2.41142	−	1.75200i	−0.0837519	−	0.0608494i	0.545121	−	0.838357i	$-0.316484\pi$
$829$	−2.41142	−	1.75200i	−0.0837519	−	0.0608494i	−0.628873	+	0.777508i	$0.716484\pi$
$830$		0			0
$831$	−73.8018	+	53.6201i	−2.56016	+	1.86006i
$832$		0			0
$833$	−1.15577	+	0.839713i	−0.0400449	+	0.0290943i
$834$		0			0
$835$	13.0774	+	1.16603i	0.452562	+	0.0403522i
$836$		0			0
$837$	−27.1373	−	83.5200i	−0.938002	−	2.88687i
$838$		0			0
$839$	11.3440	−	34.9133i	0.391639	−	1.20534i	−0.539910	−	0.841723i	$-0.681542\pi$
$839$	11.3440	−	34.9133i	0.391639	−	1.20534i	0.931549	−	0.363617i	$-0.118458\pi$
$840$		0			0
$841$	−8.55273	−	26.3226i	−0.294922	−	0.907676i
$842$		0			0
$843$	−67.9301			−2.33964
$844$		0			0
$845$	−35.5042	−	3.16569i	−1.22138	−	0.108903i
$846$		0			0
$847$	−1.00395	−	0.729415i	−0.0344962	−	0.0250630i
$848$		0			0
$849$	58.3453			2.00241
$850$		0			0
$851$	−10.9593			−0.375679
$852$		0			0
$853$	−16.9624	−	12.3239i	−0.580781	−	0.421962i	0.258224	−	0.966085i	$-0.416863\pi$
$853$	−16.9624	−	12.3239i	−0.580781	−	0.421962i	−0.839006	+	0.544123i	$0.816863\pi$
$854$		0			0
$855$	18.7455	+	81.8159i	0.641083	+	2.79805i
$856$		0			0
$857$	−7.59222			−0.259345			−0.129673	−	0.991557i	$-0.541393\pi$
$857$	−7.59222			−0.259345			−0.129673	+	0.991557i	$0.541393\pi$
$858$		0			0
$859$	−14.7739	−	45.4694i	−0.504079	−	1.55140i	−0.802313	−	0.596903i	$-0.796398\pi$
$859$	−14.7739	−	45.4694i	−0.504079	−	1.55140i	0.298234	−	0.954493i	$-0.403602\pi$
$860$		0			0
$861$	−3.85044	+	11.8504i	−0.131223	+	0.403862i
$862$		0			0
$863$	6.57250	+	20.2281i	0.223731	+	0.688572i	0.998418	+	0.0562275i	$0.0179072\pi$
$863$	6.57250	+	20.2281i	0.223731	+	0.688572i	−0.774687	+	0.632344i	$0.782093\pi$
$864$		0			0
$865$	2.07249	−	1.24059i	0.0704668	−	0.0421815i
$866$		0			0
$867$	−42.6483	+	30.9858i	−1.44841	+	1.05233i
$868$		0			0
$869$	3.80976	−	2.76796i	0.129237	−	0.0938965i
$870$		0			0
$871$	−26.7635	−	19.4448i	−0.906847	−	0.658863i
$872$		0			0
$873$	−6.83989	+	21.0510i	−0.231495	+	0.712469i
$874$		0			0
$875$	−7.61441	+	11.5981i	−0.257414	+	0.392088i
$876$		0			0
$877$	12.8426	−	39.5254i	0.433663	−	1.33468i	−0.460787	−	0.887511i	$-0.652433\pi$
$877$	12.8426	−	39.5254i	0.433663	−	1.33468i	0.894450	−	0.447167i	$-0.147567\pi$
$878$		0			0
$879$	35.8967	+	26.0804i	1.21076	+	0.879672i
$880$		0			0
$881$	13.5835	−	9.86896i	0.457639	−	0.332494i	−0.334966	−	0.942230i	$-0.608725\pi$
$881$	13.5835	−	9.86896i	0.457639	−	0.332494i	0.792604	+	0.609736i	$0.208725\pi$
$882$		0			0
$883$	8.28568	−	6.01990i	0.278835	−	0.202586i	−0.439574	−	0.898206i	$-0.644871\pi$
$883$	8.28568	−	6.01990i	0.278835	−	0.202586i	0.718409	+	0.695621i	$0.244871\pi$
$884$		0			0
$885$	49.1019	−	29.3924i	1.65054	−	0.988015i
$886$		0			0
$887$	15.8282	+	48.7141i	0.531458	+	1.63566i	0.751181	+	0.660097i	$0.229485\pi$
$887$	15.8282	+	48.7141i	0.531458	+	1.63566i	−0.219723	+	0.975562i	$0.570515\pi$
$888$		0			0
$889$	−5.94311	+	18.2910i	−0.199325	+	0.613460i
$890$		0			0
$891$	−4.85951	−	14.9560i	−0.162800	−	0.501046i
$892$		0			0
$893$	7.41840			0.248247
$894$		0			0
$895$	10.8680	+	47.4342i	0.363278	+	1.58555i
$896$		0			0
$897$	−16.2624	−	11.8154i	−0.542987	−	0.394503i
$898$		0			0
$899$	−8.78227			−0.292905
$900$		0			0
$901$	−0.662302			−0.0220645
$902$		0			0
$903$	−28.9367	−	21.0238i	−0.962954	−	0.699627i
$904$		0			0
$905$	−11.6759	−	1.04107i	−0.388122	−	0.0346064i
$906$		0			0
$907$	37.4736			1.24429			0.622145	−	0.782902i	$-0.286261\pi$
$907$	37.4736			1.24429			0.622145	+	0.782902i	$0.286261\pi$
$908$		0			0
$909$	−34.8642	−	107.301i	−1.15637	−	3.55895i
$910$		0			0
$911$	12.6602	−	38.9641i	0.419452	−	1.29094i	−0.488756	−	0.872420i	$-0.662549\pi$
$911$	12.6602	−	38.9641i	0.419452	−	1.29094i	0.908208	−	0.418519i	$-0.137451\pi$
$912$		0			0
$913$	0.0549752	+	0.169196i	0.00181941	+	0.00559958i
$914$		0			0
$915$	68.6700	+	6.12289i	2.27016	+	0.202416i
$916$		0			0
$917$	−1.26697	+	0.920507i	−0.0418390	+	0.0303978i
$918$		0			0
$919$	0.129711	−	0.0942404i	0.00427877	−	0.00310870i	−0.585644	−	0.810569i	$-0.699158\pi$
$919$	0.129711	−	0.0942404i	0.00427877	−	0.00310870i	0.589923	+	0.807460i	$0.299158\pi$
$920$		0			0
$921$	−76.9614	−	55.9157i	−2.53596	−	1.84248i
$922$		0			0
$923$	2.26942	−	6.98457i	0.0746990	−	0.229900i
$924$		0			0
$925$	41.1044	−	19.8791i	1.35150	−	0.653620i
$926$		0			0
$927$	−14.5565	+	44.8004i	−0.478099	+	1.47144i
$928$		0			0
$929$	9.58290	+	6.96239i	0.314405	+	0.228428i	0.733784	−	0.679383i	$-0.237752\pi$
$929$	9.58290	+	6.96239i	0.314405	+	0.228428i	−0.419379	+	0.907811i	$0.637752\pi$
$930$		0			0
$931$	−24.7709	+	17.9971i	−0.811834	+	0.589832i
$932$		0			0
$933$	59.7055	−	43.3786i	1.95467	−	1.42015i
$934$		0			0
$935$	−0.229497	+	0.538172i	−0.00750535	+	0.0176001i
$936$		0			0
$937$	3.44987	+	10.6176i	0.112702	+	0.346863i	0.991461	−	0.130404i	$-0.0416275\pi$
$937$	3.44987	+	10.6176i	0.112702	+	0.346863i	−0.878758	+	0.477267i	$0.841628\pi$
$938$		0			0
$939$	19.5047	−	60.0293i	0.636511	−	1.95898i
$940$		0			0
$941$	−15.9063	−	48.9546i	−0.518531	−	1.59588i	−0.776763	−	0.629793i	$-0.783140\pi$
$941$	−15.9063	−	48.9546i	−0.518531	−	1.59588i	0.258232	−	0.966083i	$-0.416860\pi$
$942$		0			0
$943$	3.87035			0.126036
$944$		0			0
$945$	−27.3818	+	16.3907i	−0.890729	+	0.533191i
$946$		0			0
$947$	6.28026	+	4.56287i	0.204081	+	0.148274i	0.685132	−	0.728419i	$-0.259745\pi$
$947$	6.28026	+	4.56287i	0.204081	+	0.148274i	−0.481051	+	0.876693i	$0.659745\pi$
$948$		0			0
$949$	38.6822			1.25568
$950$		0			0
$951$	−51.8859			−1.68251
$952$		0			0
$953$	10.6356	+	7.72722i	0.344521	+	0.250309i	0.746567	−	0.665310i	$-0.231701\pi$
$953$	10.6356	+	7.72722i	0.344521	+	0.250309i	−0.402046	+	0.915619i	$0.631701\pi$
$954$		0			0
$955$	12.9088	−	30.2712i	0.417719	−	0.979553i
$956$		0			0
$957$	−3.58090			−0.115754
$958$		0			0
$959$	7.97537	+	24.5457i	0.257538	+	0.792621i
$960$		0			0
$961$	8.43846	−	25.9709i	0.272208	−	0.837771i
$962$		0			0
$963$	38.6072	+	118.821i	1.24410	+	3.82894i
$964$		0			0
$965$	−36.4056	−	31.7533i	−1.17194	−	1.02217i
$966$		0			0
$967$	−0.914679	+	0.664553i	−0.0294141	+	0.0213706i	−0.602395	−	0.798198i	$-0.705787\pi$
$967$	−0.914679	+	0.664553i	−0.0294141	+	0.0213706i	0.572981	+	0.819569i	$0.305787\pi$
$968$		0			0
$969$	3.69582	−	2.68517i	0.118727	−	0.0862602i
$970$		0			0
$971$	−11.6354	−	8.45365i	−0.373399	−	0.271290i	0.385220	−	0.922825i	$-0.374126\pi$
$971$	−11.6354	−	8.45365i	−0.373399	−	0.271290i	−0.758619	+	0.651534i	$0.774126\pi$
$972$		0			0
$973$	0.617891	−	1.90167i	0.0198087	−	0.0609648i
$974$		0			0
$975$	82.4267	+	14.8168i	2.63977	+	0.474516i
$976$		0			0
$977$	−4.91619	+	15.1305i	−0.157283	+	0.484066i	−0.998385	−	0.0568096i	$-0.981907\pi$
$977$	−4.91619	+	15.1305i	−0.157283	+	0.484066i	0.841102	+	0.540876i	$0.181907\pi$
$978$		0			0
$979$	−10.4697	−	7.60667i	−0.334612	−	0.243110i
$980$		0			0
$981$	25.9028	−	18.8195i	0.827013	−	0.600860i
$982$		0			0
$983$	−12.2549	+	8.90372i	−0.390871	+	0.283984i	−0.765812	−	0.643064i	$-0.777663\pi$
$983$	−12.2549	+	8.90372i	−0.390871	+	0.283984i	0.374941	+	0.927049i	$0.377663\pi$
$984$		0			0
$985$	3.62334	+	15.8143i	0.115449	+	0.503886i
$986$		0			0
$987$	1.57945	+	4.86105i	0.0502745	+	0.154729i
$988$		0			0
$989$	−3.43317	+	10.5662i	−0.109169	+	0.335986i
$990$		0			0
$991$	1.13595	+	3.49610i	0.0360847	+	0.111057i	0.967476	−	0.252961i	$-0.0814045\pi$
$991$	1.13595	+	3.49610i	0.0360847	+	0.111057i	−0.931392	+	0.364018i	$0.881404\pi$
$992$		0			0
$993$	−91.0223			−2.88850
$994$		0			0
$995$	4.68004	+	4.08197i	0.148367	+	0.129407i
$996$		0			0
$997$	13.0897	+	9.51021i	0.414554	+	0.301191i	0.775443	−	0.631418i	$-0.217527\pi$
$997$	13.0897	+	9.51021i	0.414554	+	0.301191i	−0.360889	+	0.932609i	$0.617527\pi$
$998$		0			0
$999$	105.022			3.32274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.12	✓	52
25.6	even	5	inner	1100.2.q.b.881.12	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.12	✓	52	1.1	even	1	trivial
1100.2.q.b.881.12	yes	52	25.6	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)

\(f(q)\)	\(=\)	\(q+(2.51887 + 1.83006i) q^{3} +(1.68514 + 1.46980i) q^{5} +1.24095 q^{7} +(2.06850 + 6.36620i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(-1.66241 - 5.11638i) q^{13} +(1.55483 + 6.78613i) q^{15} +(0.211678 - 0.153793i) q^{17} +(4.53677 - 3.29616i) q^{19} +(3.12580 + 2.27102i) q^{21} +(0.370857 - 1.14138i) q^{23} +(0.679401 + 4.95363i) q^{25} +(-3.55390 + 10.9378i) q^{27} +(0.930471 + 0.676027i) q^{29} +(-6.17760 + 4.48829i) q^{31} +(-2.51887 + 1.83006i) q^{33} +(2.09118 + 1.82395i) q^{35} +(-2.82189 - 8.68487i) q^{37} +(5.17590 - 15.9298i) q^{39} +(0.996569 + 3.06712i) q^{41} -9.25739 q^{43} +(-5.87129 + 13.7682i) q^{45} +(1.07023 + 0.777570i) q^{47} -5.46003 q^{49} +0.814638 q^{51} +(-2.04784 - 1.48785i) q^{53} +(-1.91860 + 1.14847i) q^{55} +17.4597 q^{57} +(-2.54009 - 7.81760i) q^{59} +(3.06011 - 9.41804i) q^{61} +(2.56692 + 7.90016i) q^{63} +(4.71863 - 11.0652i) q^{65} +(4.97493 - 3.61450i) q^{67} +(3.02294 - 2.19630i) q^{69} +(1.10442 + 0.802409i) q^{71} +(-2.22196 + 6.83850i) q^{73} +(-7.35413 + 13.7209i) q^{75} +(-0.383476 + 1.18022i) q^{77} +(-3.80976 - 2.76796i) q^{79} +(-12.7224 + 9.24334i) q^{81} +(0.143927 - 0.104569i) q^{83} +(0.582750 + 0.0519603i) q^{85} +(1.10656 + 3.40564i) q^{87} +(-3.99906 + 12.3078i) q^{89} +(-2.06298 - 6.34919i) q^{91} -23.7744 q^{93} +(12.4898 + 1.11364i) q^{95} +(2.67517 + 1.94362i) q^{97} -6.69381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 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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