LMFDB - Embedded newform 1100.2.q.b.221.2

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			221.2
Character	$\chi$	$=$	1100.221
Dual form			1100.2.q.b.881.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98827 - 1.44456i) q^{3} +(1.83057 + 1.28413i) q^{5} +0.715669 q^{7} +(0.939404 + 2.89119i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.954784 + 2.93852i) q^{13} +(-1.78467 - 5.19758i) q^{15} +(-5.47348 + 3.97672i) q^{17} +(-2.57392 + 1.87006i) q^{19} +(-1.42294 - 1.03383i) q^{21} +(2.53525 - 7.80270i) q^{23} +(1.70201 + 4.70140i) q^{25} +(0.0303586 - 0.0934342i) q^{27} +(-3.40696 - 2.47530i) q^{29} +(-7.37566 + 5.35873i) q^{31} +(1.98827 - 1.44456i) q^{33} +(1.31009 + 0.919014i) q^{35} +(-1.53622 - 4.72801i) q^{37} +(2.34651 - 7.22182i) q^{39} +(3.82940 + 11.7857i) q^{41} +1.10672 q^{43} +(-1.99302 + 6.49885i) q^{45} +(-7.74451 - 5.62672i) q^{47} -6.48782 q^{49} +16.6274 q^{51} +(5.29564 + 3.84751i) q^{53} +(-1.78696 + 1.34416i) q^{55} +7.81906 q^{57} +(3.23428 + 9.95409i) q^{59} +(-3.28831 + 10.1204i) q^{61} +(0.672302 + 2.06913i) q^{63} +(-2.02565 + 6.60526i) q^{65} +(6.40912 - 4.65650i) q^{67} +(-16.3122 + 11.8515i) q^{69} +(6.13072 + 4.45423i) q^{71} +(-0.786184 + 2.41963i) q^{73} +(3.40742 - 11.8063i) q^{75} +(-0.221154 + 0.680642i) q^{77} +(11.6906 + 8.49372i) q^{79} +(7.18284 - 5.21864i) q^{81} +(-1.79508 + 1.30420i) q^{83} +(-15.1263 + 0.251003i) q^{85} +(3.19823 + 9.84314i) q^{87} +(-1.91900 + 5.90606i) q^{89} +(0.683310 + 2.10301i) q^{91} +22.4058 q^{93} +(-7.11315 + 0.118034i) q^{95} +(-4.09703 - 2.97667i) q^{97} -3.03997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.98827	−	1.44456i	−1.14793	−	0.834018i	−0.159724	−	0.987162i	$-0.551060\pi$
$3$	−1.98827	−	1.44456i	−1.14793	−	0.834018i	−0.988204	+	0.153143i	$0.951060\pi$
$4$		0			0
$5$	1.83057	+	1.28413i	0.818658	+	0.574281i
$5$	1.83057	+	1.28413i	0.818658	+	0.574281i
$6$		0			0
$7$	0.715669			0.270497			0.135249	−	0.990812i	$-0.456817\pi$
$7$	0.715669			0.270497			0.135249	+	0.990812i	$0.456817\pi$
$8$		0			0
$9$	0.939404	+	2.89119i	0.313135	+	0.963729i
$10$		0			0
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$11$	−0.309017	+	0.951057i	−0.0931721	+	0.286754i
$12$		0			0
$13$	0.954784	+	2.93852i	0.264809	+	0.815000i	0.991737	+	0.128286i	$0.0409475\pi$
$13$	0.954784	+	2.93852i	0.264809	+	0.815000i	−0.726928	+	0.686714i	$0.759053\pi$
$14$		0			0
$15$	−1.78467	−	5.19758i	−0.460799	−	1.34201i
$16$		0			0
$17$	−5.47348	+	3.97672i	−1.32752	+	0.964496i	−0.327709	+	0.944779i	$0.606277\pi$
$17$	−5.47348	+	3.97672i	−1.32752	+	0.964496i	−0.999806	+	0.0197175i	$0.993723\pi$
$18$		0			0
$19$	−2.57392	+	1.87006i	−0.590497	+	0.429021i	−0.842493	−	0.538707i	$-0.818913\pi$
$19$	−2.57392	+	1.87006i	−0.590497	+	0.429021i	0.251996	+	0.967728i	$0.418913\pi$
$20$		0			0
$21$	−1.42294	−	1.03383i	−0.310512	−	0.225600i
$22$		0			0
$23$	2.53525	−	7.80270i	0.528636	−	1.62698i	−0.228375	−	0.973573i	$-0.573341\pi$
$23$	2.53525	−	7.80270i	0.528636	−	1.62698i	0.757011	−	0.653402i	$-0.226659\pi$
$24$		0			0
$25$	1.70201	+	4.70140i	0.340402	+	0.940280i
$26$		0			0
$27$	0.0303586	−	0.0934342i	0.00584252	−	0.0179814i
$28$		0			0
$29$	−3.40696	−	2.47530i	−0.632657	−	0.459652i	0.224662	−	0.974437i	$-0.427872\pi$
$29$	−3.40696	−	2.47530i	−0.632657	−	0.459652i	−0.857320	+	0.514784i	$0.827872\pi$
$30$		0			0
$31$	−7.37566	+	5.35873i	−1.32471	+	0.962456i	−0.324846	+	0.945767i	$0.605313\pi$
$31$	−7.37566	+	5.35873i	−1.32471	+	0.962456i	−0.999861	+	0.0166893i	$0.994687\pi$
$32$		0			0
$33$	1.98827	−	1.44456i	0.346113	−	0.251466i
$34$		0			0
$35$	1.31009	+	0.919014i	0.221445	+	0.155342i
$36$		0			0
$37$	−1.53622	−	4.72801i	−0.252554	−	0.777280i	−0.994302	−	0.106602i	$-0.966003\pi$
$37$	−1.53622	−	4.72801i	−0.252554	−	0.777280i	0.741748	−	0.670678i	$-0.233997\pi$
$38$		0			0
$39$	2.34651	−	7.22182i	0.375743	−	1.15642i
$40$		0			0
$41$	3.82940	+	11.7857i	0.598051	+	1.84061i	0.538911	+	0.842363i	$0.318836\pi$
$41$	3.82940	+	11.7857i	0.598051	+	1.84061i	0.0591408	+	0.998250i	$0.481164\pi$
$42$		0			0
$43$	1.10672			0.168773			0.0843866	−	0.996433i	$-0.473107\pi$
$43$	1.10672			0.168773			0.0843866	+	0.996433i	$0.473107\pi$
$44$		0			0
$45$	−1.99302	+	6.49885i	−0.297102	+	0.968792i
$46$		0			0
$47$	−7.74451	−	5.62672i	−1.12965	−	0.820741i	−0.144009	−	0.989576i	$-0.545999\pi$
$47$	−7.74451	−	5.62672i	−1.12965	−	0.820741i	−0.985644	+	0.168835i	$0.945999\pi$
$48$		0			0
$49$	−6.48782			−0.926831
$50$		0			0
$51$	16.6274			2.32830
$52$		0			0
$53$	5.29564	+	3.84751i	0.727412	+	0.528496i	0.888744	−	0.458405i	$-0.151579\pi$
$53$	5.29564	+	3.84751i	0.727412	+	0.528496i	−0.161332	+	0.986900i	$0.551579\pi$
$54$		0			0
$55$	−1.78696	+	1.34416i	−0.240954	+	0.181247i
$56$		0			0
$57$	7.81906			1.03566
$58$		0			0
$59$	3.23428	+	9.95409i	0.421067	+	1.29591i	0.906710	+	0.421754i	$0.138586\pi$
$59$	3.23428	+	9.95409i	0.421067	+	1.29591i	−0.485643	+	0.874157i	$0.661414\pi$
$60$		0			0
$61$	−3.28831	+	10.1204i	−0.421025	+	1.29578i	0.485725	+	0.874111i	$0.338556\pi$
$61$	−3.28831	+	10.1204i	−0.421025	+	1.29578i	−0.906750	+	0.421669i	$0.861444\pi$
$62$		0			0
$63$	0.672302	+	2.06913i	0.0847021	+	0.260686i
$64$		0			0
$65$	−2.02565	+	6.60526i	−0.251251	+	0.819281i
$66$		0			0
$67$	6.40912	−	4.65650i	0.782999	−	0.568882i	−0.122878	−	0.992422i	$-0.539213\pi$
$67$	6.40912	−	4.65650i	0.782999	−	0.568882i	0.905878	+	0.423540i	$0.139213\pi$
$68$		0			0
$69$	−16.3122	+	11.8515i	−1.96376	+	1.42676i
$70$		0			0
$71$	6.13072	+	4.45423i	0.727582	+	0.528620i	0.888798	−	0.458300i	$-0.151541\pi$
$71$	6.13072	+	4.45423i	0.727582	+	0.528620i	−0.161215	+	0.986919i	$0.551541\pi$
$72$		0			0
$73$	−0.786184	+	2.41963i	−0.0920159	+	0.283196i	−0.986465	−	0.163975i	$-0.947568\pi$
$73$	−0.786184	+	2.41963i	−0.0920159	+	0.283196i	0.894449	+	0.447171i	$0.147568\pi$
$74$		0			0
$75$	3.40742	−	11.8063i	0.393455	−	1.36327i
$76$		0			0
$77$	−0.221154	+	0.680642i	−0.0252028	+	0.0775663i
$78$		0			0
$79$	11.6906	+	8.49372i	1.31530	+	0.955618i	0.999978	+	0.00663174i	$0.00211096\pi$
$79$	11.6906	+	8.49372i	1.31530	+	0.955618i	0.315317	+	0.948986i	$0.397889\pi$
$80$		0			0
$81$	7.18284	−	5.21864i	0.798093	−	0.579849i
$82$		0			0
$83$	−1.79508	+	1.30420i	−0.197035	+	0.143154i	−0.681928	−	0.731419i	$-0.738858\pi$
$83$	−1.79508	+	1.30420i	−0.197035	+	0.143154i	0.484893	+	0.874573i	$0.338858\pi$
$84$		0			0
$85$	−15.1263	+	0.251003i	−1.64067	+	0.0272251i
$86$		0			0
$87$	3.19823	+	9.84314i	0.342886	+	1.05530i
$88$		0			0
$89$	−1.91900	+	5.90606i	−0.203413	+	0.626041i	0.796362	+	0.604821i	$0.206755\pi$
$89$	−1.91900	+	5.90606i	−0.203413	+	0.626041i	−0.999775	+	0.0212207i	$0.993245\pi$
$90$		0			0
$91$	0.683310	+	2.10301i	0.0716303	+	0.220455i
$92$		0			0
$93$	22.4058			2.32337
$94$		0			0
$95$	−7.11315	+	0.118034i	−0.729794	+	0.0121101i
$96$		0			0
$97$	−4.09703	−	2.97667i	−0.415990	−	0.302235i	0.360032	−	0.932940i	$-0.382766\pi$
$97$	−4.09703	−	2.97667i	−0.415990	−	0.302235i	−0.776023	+	0.630705i	$0.782766\pi$
$98$		0			0
$99$	−3.03997			−0.305529
$100$		0			0
$101$	15.5198			1.54428			0.772141	−	0.635452i	$-0.219186\pi$
$101$	15.5198			1.54428			0.772141	+	0.635452i	$0.219186\pi$
$102$		0			0
$103$	−8.27062	−	6.00895i	−0.814928	−	0.592080i	0.100327	−	0.994955i	$-0.468011\pi$
$103$	−8.27062	−	6.00895i	−0.814928	−	0.592080i	−0.915255	+	0.402875i	$0.868011\pi$
$104$		0			0
$105$	−1.27723	−	3.71975i	−0.124645	−	0.363010i
$106$		0			0
$107$	−9.88850			−0.955958			−0.477979	−	0.878371i	$-0.658630\pi$
$107$	−9.88850			−0.955958			−0.477979	+	0.878371i	$0.658630\pi$
$108$		0			0
$109$	−2.96850	−	9.13610i	−0.284331	−	0.875080i	−0.986598	−	0.163167i	$-0.947829\pi$
$109$	−2.96850	−	9.13610i	−0.284331	−	0.875080i	0.702268	−	0.711913i	$-0.252171\pi$
$110$		0			0
$111$	−3.77548	+	11.6197i	−0.358353	+	1.10290i
$112$		0			0
$113$	4.19234	+	12.9027i	0.394382	+	1.21378i	0.929441	+	0.368970i	$0.120289\pi$
$113$	4.19234	+	12.9027i	0.394382	+	1.21378i	−0.535059	+	0.844815i	$0.679711\pi$
$114$		0			0
$115$	14.6607	−	11.0278i	1.36711	−	1.02835i
$116$		0			0
$117$	−7.59889	+	5.52092i	−0.702518	+	0.510409i
$118$		0			0
$119$	−3.91720	+	2.84602i	−0.359089	+	0.260894i
$120$		0			0
$121$	−0.809017	−	0.587785i	−0.0735470	−	0.0534350i
$122$		0			0
$123$	9.41126	−	28.9649i	0.848585	−	2.61168i
$124$		0			0
$125$	−2.92157	+	10.7919i	−0.261313	+	0.965254i
$126$		0			0
$127$	−1.96781	+	6.05631i	−0.174615	+	0.537411i	−0.999616	−	0.0277215i	$-0.991175\pi$
$127$	−1.96781	+	6.05631i	−0.174615	+	0.537411i	0.825000	+	0.565132i	$0.191175\pi$
$128$		0			0
$129$	−2.20046	−	1.59873i	−0.193740	−	0.140760i
$130$		0			0
$131$	9.33776	−	6.78428i	0.815844	−	0.592746i	−0.0996749	−	0.995020i	$-0.531780\pi$
$131$	9.33776	−	6.78428i	0.815844	−	0.592746i	0.915519	+	0.402275i	$0.131780\pi$
$132$		0			0
$133$	−1.84207	+	1.33834i	−0.159728	+	0.116049i
$134$		0			0
$135$	0.175556	−	0.132054i	0.0151094	−	0.0113654i
$136$		0			0
$137$	1.17175	+	3.60629i	0.100110	+	0.308106i	0.988552	−	0.150883i	$-0.0482117\pi$
$137$	1.17175	+	3.60629i	0.100110	+	0.308106i	−0.888442	+	0.458989i	$0.848212\pi$
$138$		0			0
$139$	−3.32662	+	10.2383i	−0.282161	+	0.868401i	0.705075	+	0.709133i	$0.250913\pi$
$139$	−3.32662	+	10.2383i	−0.282161	+	0.868401i	−0.987235	+	0.159268i	$0.949087\pi$
$140$		0			0
$141$	7.27003	+	22.3749i	0.612247	+	1.88430i
$142$		0			0
$143$	−3.08975			−0.258378
$144$		0			0
$145$	−3.05808	−	8.90622i	−0.253960	−	0.739621i
$146$		0			0
$147$	12.8995	+	9.37206i	1.06394	+	0.772994i
$148$		0			0
$149$	−14.7879			−1.21147			−0.605734	−	0.795667i	$-0.707121\pi$
$149$	−14.7879			−1.21147			−0.605734	+	0.795667i	$0.707121\pi$
$150$		0			0
$151$	−12.5874			−1.02435			−0.512174	−	0.858881i	$-0.671160\pi$
$151$	−12.5874			−1.02435			−0.512174	+	0.858881i	$0.671160\pi$
$152$		0			0
$153$	−16.6393	−	12.0891i	−1.34520	−	0.977348i
$154$		0			0
$155$	−20.3830	+	0.338232i	−1.63720	+	0.0271675i
$156$		0			0
$157$	15.2347			1.21586			0.607929	−	0.793991i	$-0.292000\pi$
$157$	15.2347			1.21586			0.607929	+	0.793991i	$0.292000\pi$
$158$		0			0
$159$	−4.97119	−	15.2998i	−0.394241	−	1.21335i
$160$		0			0
$161$	1.81440	−	5.58415i	0.142995	−	0.440093i
$162$		0			0
$163$	−1.43102	−	4.40423i	−0.112086	−	0.344966i	0.879242	−	0.476376i	$-0.158050\pi$
$163$	−1.43102	−	4.40423i	−0.112086	−	0.344966i	−0.991328	+	0.131409i	$0.958050\pi$
$164$		0			0
$165$	5.49468	−	0.0911779i	0.427761	−	0.00709819i
$166$		0			0
$167$	18.0692	−	13.1280i	1.39823	−	1.01588i	0.403330	−	0.915054i	$-0.367853\pi$
$167$	18.0692	−	13.1280i	1.39823	−	1.01588i	0.994904	−	0.100823i	$-0.0321475\pi$
$168$		0			0
$169$	2.79391	−	2.02990i	0.214916	−	0.156146i
$170$		0			0
$171$	−7.82464	−	5.68493i	−0.598365	−	0.434738i
$172$		0			0
$173$	6.69772	−	20.6135i	0.509218	−	1.56721i	−0.284343	−	0.958723i	$-0.591775\pi$
$173$	6.69772	−	20.6135i	0.509218	−	1.56721i	0.793561	−	0.608491i	$-0.208225\pi$
$174$		0			0
$175$	1.21807	+	3.36465i	0.0920778	+	0.254343i
$176$		0			0
$177$	7.94868	−	24.4635i	0.597459	−	1.83879i
$178$		0			0
$179$	−16.4940	−	11.9836i	−1.23282	−	0.895695i	−0.235721	−	0.971821i	$-0.575745\pi$
$179$	−16.4940	−	11.9836i	−1.23282	−	0.895695i	−0.997098	+	0.0761256i	$0.975745\pi$
$180$		0			0
$181$	10.1734	−	7.39142i	0.756184	−	0.549400i	−0.141554	−	0.989931i	$-0.545210\pi$
$181$	10.1734	−	7.39142i	0.756184	−	0.549400i	0.897738	+	0.440531i	$0.145210\pi$
$182$		0			0
$183$	21.1575	−	15.3719i	1.56401	−	1.13632i
$184$		0			0
$185$	3.25922	−	10.6277i	0.239623	−	0.781363i
$186$		0			0
$187$	−2.09069	−	6.43447i	−0.152886	−	0.470535i
$188$		0			0
$189$	0.0217267	−	0.0668680i	0.00158039	−	0.00486393i
$190$		0			0
$191$	0.107336	+	0.330348i	0.00776659	+	0.0239031i	0.954865	−	0.297041i	$-0.0959998\pi$
$191$	0.107336	+	0.330348i	0.00776659	+	0.0239031i	−0.947098	+	0.320944i	$0.896000\pi$
$192$		0			0
$193$	−21.1996			−1.52598			−0.762992	−	0.646408i	$-0.776270\pi$
$193$	−21.1996			−1.52598			−0.762992	+	0.646408i	$0.776270\pi$
$194$		0			0
$195$	13.5692	−	10.2069i	0.971713	−	0.730928i
$196$		0			0
$197$	−3.74970	−	2.72432i	−0.267155	−	0.194100i	0.446140	−	0.894963i	$-0.352798\pi$
$197$	−3.74970	−	2.72432i	−0.267155	−	0.194100i	−0.713295	+	0.700863i	$0.752798\pi$
$198$		0			0
$199$	−18.2489			−1.29363			−0.646815	−	0.762647i	$-0.723899\pi$
$199$	−18.2489			−1.29363			−0.646815	+	0.762647i	$0.723899\pi$
$200$		0			0
$201$	−19.4697			−1.37328
$202$		0			0
$203$	−2.43826	−	1.77150i	−0.171132	−	0.124335i
$204$		0			0
$205$	−8.12437	+	26.4920i	−0.567430	+	1.85028i
$206$		0			0
$207$	24.9407			1.73350
$208$		0			0
$209$	−0.983149	−	3.02582i	−0.0680058	−	0.209300i
$210$		0			0
$211$	−0.724670	+	2.23030i	−0.0498883	+	0.153541i	−0.972897	−	0.231238i	$-0.925722\pi$
$211$	−0.724670	+	2.23030i	−0.0498883	+	0.153541i	0.923009	+	0.384779i	$0.125722\pi$
$212$		0			0
$213$	−5.75511	−	17.7124i	−0.394334	−	1.21363i
$214$		0			0
$215$	2.02593	+	1.42118i	0.138168	+	0.0969234i
$216$		0			0
$217$	−5.27853	+	3.83508i	−0.358330	+	0.260342i
$218$		0			0
$219$	5.05845	−	3.67518i	0.341818	−	0.248345i
$220$		0			0
$221$	−16.9117	−	12.2871i	−1.13760	−	0.826517i
$222$		0			0
$223$	−4.74252	+	14.5960i	−0.317582	+	0.977418i	0.657096	+	0.753807i	$0.271785\pi$
$223$	−4.74252	+	14.5960i	−0.317582	+	0.977418i	−0.974678	+	0.223611i	$0.928215\pi$
$224$		0			0
$225$	−11.9938	+	9.33734i	−0.799584	+	0.622489i
$226$		0			0
$227$	1.63768	−	5.04025i	0.108696	−	0.334533i	−0.881884	−	0.471467i	$-0.843725\pi$
$227$	1.63768	−	5.04025i	0.108696	−	0.334533i	0.990580	+	0.136934i	$0.0437247\pi$
$228$		0			0
$229$	−6.80267	−	4.94243i	−0.449533	−	0.326605i	0.339878	−	0.940469i	$-0.389614\pi$
$229$	−6.80267	−	4.94243i	−0.449533	−	0.326605i	−0.789412	+	0.613864i	$0.789614\pi$
$230$		0			0
$231$	1.42294	−	1.03383i	0.0936228	−	0.0680209i
$232$		0			0
$233$	−11.2474	+	8.17169i	−0.736839	+	0.535345i	−0.891720	−	0.452588i	$-0.850501\pi$
$233$	−11.2474	+	8.17169i	−0.736839	+	0.535345i	0.154880	+	0.987933i	$0.450501\pi$
$234$		0			0
$235$	−6.95146	−	20.2451i	−0.453463	−	1.32064i
$236$		0			0
$237$	−10.9744	−	33.7756i	−0.712861	−	2.19396i
$238$		0			0
$239$	−0.488284	+	1.50278i	−0.0315845	+	0.0972070i	−0.965606	−	0.260010i	$-0.916274\pi$
$239$	−0.488284	+	1.50278i	−0.0315845	+	0.0972070i	0.934022	+	0.357217i	$0.116274\pi$
$240$		0			0
$241$	3.65077	+	11.2359i	0.235167	+	0.723769i	0.997099	+	0.0761127i	$0.0242509\pi$
$241$	3.65077	+	11.2359i	0.235167	+	0.723769i	−0.761932	+	0.647657i	$0.775749\pi$
$242$		0			0
$243$	−22.1148			−1.41866
$244$		0			0
$245$	−11.8764	−	8.33122i	−0.758758	−	0.532262i
$246$		0			0
$247$	−7.95275	−	5.77801i	−0.506021	−	0.367646i
$248$		0			0
$249$	5.45309			0.345576
$250$		0			0
$251$	9.63078			0.607889			0.303945	−	0.952690i	$-0.401696\pi$
$251$	9.63078			0.607889			0.303945	+	0.952690i	$0.401696\pi$
$252$		0			0
$253$	6.63737	+	4.82233i	0.417288	+	0.303178i
$254$		0			0
$255$	30.4377	+	21.3518i	1.90608	+	1.33710i
$256$		0			0
$257$	−1.91026			−0.119159			−0.0595793	−	0.998224i	$-0.518976\pi$
$257$	−1.91026			−0.119159			−0.0595793	+	0.998224i	$0.518976\pi$
$258$		0			0
$259$	−1.09943	−	3.38369i	−0.0683151	−	0.210252i
$260$		0			0
$261$	3.95605	−	12.1755i	0.244874	−	0.753643i
$262$		0			0
$263$	6.95205	+	21.3962i	0.428682	+	1.31935i	0.899424	+	0.437076i	$0.143986\pi$
$263$	6.95205	+	21.3962i	0.428682	+	1.31935i	−0.470743	+	0.882271i	$0.656014\pi$
$264$		0			0
$265$	4.75335	+	13.8434i	0.291996	+	0.850396i
$266$		0			0
$267$	12.3472	−	8.97074i	0.755634	−	0.549000i
$268$		0			0
$269$	18.3000	−	13.2957i	1.11577	−	0.810655i	0.132209	−	0.991222i	$-0.457793\pi$
$269$	18.3000	−	13.2957i	1.11577	−	0.810655i	0.983563	+	0.180566i	$0.0577931\pi$
$270$		0			0
$271$	−13.2104	−	9.59795i	−0.802478	−	0.583034i	0.109162	−	0.994024i	$-0.465183\pi$
$271$	−13.2104	−	9.59795i	−0.802478	−	0.583034i	−0.911640	+	0.410990i	$0.865183\pi$
$272$		0			0
$273$	1.67933	−	5.16843i	0.101637	−	0.312808i
$274$		0			0
$275$	−4.99725	+	0.165893i	−0.301345	+	0.0100037i
$276$		0			0
$277$	−4.11865	+	12.6759i	−0.247466	+	0.761621i	0.747755	+	0.663974i	$0.231132\pi$
$277$	−4.11865	+	12.6759i	−0.247466	+	0.761621i	−0.995221	+	0.0976468i	$0.968868\pi$
$278$		0			0
$279$	−22.4218	−	16.2904i	−1.34236	−	0.975281i
$280$		0			0
$281$	22.1676	−	16.1057i	1.32241	−	0.960787i	0.322512	−	0.946566i	$-0.395473\pi$
$281$	22.1676	−	16.1057i	1.32241	−	0.960787i	0.999899	−	0.0142220i	$-0.00452714\pi$
$282$		0			0
$283$	5.10643	−	3.71004i	0.303546	−	0.220539i	−0.425576	−	0.904923i	$-0.639929\pi$
$283$	5.10643	−	3.71004i	0.303546	−	0.220539i	0.729122	+	0.684384i	$0.239929\pi$
$284$		0			0
$285$	14.3134	+	10.0407i	0.847851	+	0.594760i
$286$		0			0
$287$	2.74058	+	8.43464i	0.161771	+	0.497881i
$288$		0			0
$289$	8.89145	−	27.3651i	0.523026	−	1.60971i
$290$		0			0
$291$	3.84602	+	11.8368i	0.225458	+	0.693887i
$292$		0			0
$293$	16.7886			0.980799			0.490399	−	0.871498i	$-0.336851\pi$
$293$	16.7886			0.980799			0.490399	+	0.871498i	$0.336851\pi$
$294$		0			0
$295$	−6.86178	+	22.3749i	−0.399508	+	1.30272i
$296$		0			0
$297$	0.0794799	+	0.0577455i	0.00461189	+	0.00335073i
$298$		0			0
$299$	25.3490			1.46597
$300$		0			0
$301$	0.792045			0.0456527
$302$		0			0
$303$	−30.8576	−	22.4194i	−1.77272	−	1.28796i
$304$		0			0
$305$	−19.0154	+	14.3035i	−1.08882	+	0.819014i
$306$		0			0
$307$	10.9550			0.625235			0.312617	−	0.949879i	$-0.398794\pi$
$307$	10.9550			0.625235			0.312617	+	0.949879i	$0.398794\pi$
$308$		0			0
$309$	7.76390	+	23.8948i	0.441673	+	1.35933i
$310$		0			0
$311$	−6.59408	+	20.2945i	−0.373916	+	1.15080i	0.570291	+	0.821443i	$0.306830\pi$
$311$	−6.59408	+	20.2945i	−0.373916	+	1.15080i	−0.944207	+	0.329352i	$0.893170\pi$
$312$		0			0
$313$	−0.905505	−	2.78686i	−0.0511822	−	0.157523i	0.922199	−	0.386717i	$-0.126391\pi$
$313$	−0.905505	−	2.78686i	−0.0511822	−	0.157523i	−0.973381	+	0.229194i	$0.926391\pi$
$314$		0			0
$315$	−1.42634	+	4.65103i	−0.0803653	+	0.262056i
$316$		0			0
$317$	23.0447	−	16.7430i	1.29432	−	0.940379i	0.294438	−	0.955671i	$-0.404868\pi$
$317$	23.0447	−	16.7430i	1.29432	−	0.940379i	0.999883	+	0.0152915i	$0.00486764\pi$
$318$		0			0
$319$	3.40696	−	2.47530i	0.190753	−	0.138590i
$320$		0			0
$321$	19.6610	+	14.2846i	1.09737	+	0.797286i
$322$		0			0
$323$	6.65159	−	20.4715i	0.370104	−	1.13906i
$324$		0			0
$325$	−12.1901	+	9.49021i	−0.676187	+	0.526422i
$326$		0			0
$327$	−7.29549	+	22.4532i	−0.403442	+	1.24167i
$328$		0			0
$329$	−5.54251	−	4.02687i	−0.305568	−	0.222008i
$330$		0			0
$331$	−1.85725	+	1.34937i	−0.102084	+	0.0741683i	−0.637656	−	0.770321i	$-0.720096\pi$
$331$	−1.85725	+	1.34937i	−0.102084	+	0.0741683i	0.535572	+	0.844489i	$0.320096\pi$
$332$		0			0
$333$	12.2264	−	8.88302i	0.670004	−	0.486786i
$334$		0			0
$335$	17.7119	−	0.293909i	0.967707	−	0.0160580i
$336$		0			0
$337$	1.96657	+	6.05249i	0.107126	+	0.329700i	0.990224	−	0.139489i	$-0.0445461\pi$
$337$	1.96657	+	6.05249i	0.107126	+	0.329700i	−0.883098	+	0.469189i	$0.844546\pi$
$338$		0			0
$339$	10.3033	−	31.7102i	0.559596	−	1.72226i
$340$		0			0
$341$	−2.81725	−	8.67060i	−0.152563	−	0.469540i
$342$		0			0
$343$	−9.65281			−0.521203
$344$		0			0
$345$	−45.0797	+	0.748046i	−2.42701	+	0.0402734i
$346$		0			0
$347$	21.4203	+	15.5627i	1.14990	+	0.835452i	0.988468	−	0.151432i	$-0.0483884\pi$
$347$	21.4203	+	15.5627i	1.14990	+	0.835452i	0.161433	+	0.986884i	$0.448388\pi$
$348$		0			0
$349$	11.3557			0.607859			0.303930	−	0.952694i	$-0.401701\pi$
$349$	11.3557			0.607859			0.303930	+	0.952694i	$0.401701\pi$
$350$		0			0
$351$	0.303545			0.0162020
$352$		0			0
$353$	22.8343	+	16.5901i	1.21535	+	0.883002i	0.995705	−	0.0925787i	$-0.0295110\pi$
$353$	22.8343	+	16.5901i	1.21535	+	0.883002i	0.219642	+	0.975580i	$0.429511\pi$
$354$		0			0
$355$	5.50292	+	16.0265i	0.292065	+	0.850596i
$356$		0			0
$357$	11.8997			0.629799
$358$		0			0
$359$	5.97803	+	18.3985i	0.315509	+	0.971035i	0.975545	+	0.219801i	$0.0705410\pi$
$359$	5.97803	+	18.3985i	0.315509	+	0.971035i	−0.660036	+	0.751234i	$0.729459\pi$
$360$		0			0
$361$	−2.74340	+	8.44332i	−0.144389	+	0.444385i
$362$		0			0
$363$	0.759451	+	2.33735i	0.0398609	+	0.122679i
$364$		0			0
$365$	−4.54629	+	3.41974i	−0.237964	+	0.178998i
$366$		0			0
$367$	−14.9590	+	10.8683i	−0.780853	+	0.567323i	−0.905235	−	0.424911i	$-0.860305\pi$
$367$	−14.9590	+	10.8683i	−0.780853	+	0.567323i	0.124382	+	0.992234i	$0.460305\pi$
$368$		0			0
$369$	−30.4772	+	22.1430i	−1.58658	+	1.15272i
$370$		0			0
$371$	3.78992	+	2.75354i	0.196763	+	0.142957i
$372$		0			0
$373$	2.27743	−	7.00921i	0.117921	−	0.362923i	−0.874624	−	0.484802i	$-0.838892\pi$
$373$	2.27743	−	7.00921i	0.117921	−	0.362923i	0.992545	+	0.121878i	$0.0388918\pi$
$374$		0			0
$375$	21.3984	−	17.2368i	1.10501	−	0.890102i
$376$		0			0
$377$	4.02082	−	12.3748i	0.207083	−	0.637336i
$378$		0			0
$379$	−12.9117	−	9.38087i	−0.663227	−	0.481863i	0.204524	−	0.978862i	$-0.434435\pi$
$379$	−12.9117	−	9.38087i	−0.663227	−	0.481863i	−0.867751	+	0.496999i	$0.834435\pi$
$380$		0			0
$381$	12.6613	−	9.19895i	0.648656	−	0.471276i
$382$		0			0
$383$	−16.4952	+	11.9845i	−0.842867	+	0.612379i	−0.923170	−	0.384392i	$-0.874411\pi$
$383$	−16.4952	+	11.9845i	−0.842867	+	0.612379i	0.0803032	+	0.996770i	$0.474411\pi$
$384$		0			0
$385$	−1.27887	+	0.961975i	−0.0651774	+	0.0490268i
$386$		0			0
$387$	1.03966	+	3.19974i	0.0528487	+	0.162652i
$388$		0			0
$389$	−2.81270	+	8.65661i	−0.142610	+	0.438907i	−0.996696	−	0.0812240i	$-0.974117\pi$
$389$	−2.81270	+	8.65661i	−0.142610	+	0.438907i	0.854086	+	0.520132i	$0.174117\pi$
$390$		0			0
$391$	17.1525	+	52.7899i	0.867439	+	2.66970i
$392$		0			0
$393$	−28.3663			−1.43089
$394$		0			0
$395$	10.4935	+	30.5607i	0.527983	+	1.53767i
$396$		0			0
$397$	−14.7531	−	10.7188i	−0.740437	−	0.537959i	0.152411	−	0.988317i	$-0.451296\pi$
$397$	−14.7531	−	10.7188i	−0.740437	−	0.537959i	−0.892848	+	0.450358i	$0.851296\pi$
$398$		0			0
$399$	5.59586			0.280143
$400$		0			0
$401$	−13.8647			−0.692371			−0.346186	−	0.938166i	$-0.612523\pi$
$401$	−13.8647			−0.692371			−0.346186	+	0.938166i	$0.612523\pi$
$402$		0			0
$403$	−22.7889	−	16.5571i	−1.13520	−	0.824769i
$404$		0			0
$405$	19.8501	−	0.329390i	0.986362	−	0.0163675i
$406$		0			0
$407$	4.97132			0.246419
$408$		0			0
$409$	−1.58196	−	4.86878i	−0.0782229	−	0.240745i	0.904297	−	0.426905i	$-0.140396\pi$
$409$	−1.58196	−	4.86878i	−0.0782229	−	0.240745i	−0.982520	+	0.186159i	$0.940396\pi$
$410$		0			0
$411$	2.87974	−	8.86294i	0.142047	−	0.437176i
$412$		0			0
$413$	2.31467	+	7.12383i	0.113898	+	0.350541i
$414$		0			0
$415$	−4.96078	+	0.0823185i	−0.243515	+	0.00404085i
$416$		0			0
$417$	21.4041	−	15.5510i	1.04816	−	0.761535i
$418$		0			0
$419$	15.6808	−	11.3927i	0.766056	−	0.556572i	−0.134706	−	0.990886i	$-0.543009\pi$
$419$	15.6808	−	11.3927i	0.766056	−	0.556572i	0.900762	+	0.434314i	$0.143009\pi$
$420$		0			0
$421$	−11.6425	−	8.45876i	−0.567420	−	0.412255i	0.266747	−	0.963767i	$-0.414051\pi$
$421$	−11.6425	−	8.45876i	−0.567420	−	0.412255i	−0.834167	+	0.551512i	$0.814051\pi$
$422$		0			0
$423$	8.99267	−	27.6766i	0.437239	−	1.34568i
$424$		0			0
$425$	−28.0121	−	18.9646i	−1.35878	−	0.919920i
$426$		0			0
$427$	−2.35334	+	7.24283i	−0.113886	+	0.350505i
$428$		0			0
$429$	6.14325	+	4.46333i	0.296599	+	0.215492i
$430$		0			0
$431$	26.9286	−	19.5647i	1.29710	−	0.942401i	0.297180	−	0.954821i	$-0.403954\pi$
$431$	26.9286	−	19.5647i	1.29710	−	0.942401i	0.999923	+	0.0124206i	$0.00395371\pi$
$432$		0			0
$433$	−11.3756	+	8.26485i	−0.546676	+	0.397183i	−0.826558	−	0.562851i	$-0.809704\pi$
$433$	−11.3756	+	8.26485i	−0.546676	+	0.397183i	0.279883	+	0.960034i	$0.409704\pi$
$434$		0			0
$435$	−6.78530	+	22.1256i	−0.325330	+	1.06084i
$436$		0			0
$437$	8.06599	+	24.8246i	0.385849	+	1.18752i
$438$		0			0
$439$	−0.558426	+	1.71866i	−0.0266522	+	0.0820270i	−0.963498	−	0.267716i	$-0.913731\pi$
$439$	−0.558426	+	1.71866i	−0.0266522	+	0.0820270i	0.936846	+	0.349743i	$0.113731\pi$
$440$		0			0
$441$	−6.09468	−	18.7575i	−0.290223	−	0.893214i
$442$		0			0
$443$	6.11601			0.290580			0.145290	−	0.989389i	$-0.453588\pi$
$443$	6.11601			0.290580			0.145290	+	0.989389i	$0.453588\pi$
$444$		0			0
$445$	−11.0970	+	8.34725i	−0.526050	+	0.395697i
$446$		0			0
$447$	29.4023	+	21.3620i	1.39068	+	1.01039i
$448$		0			0
$449$	30.0931			1.42018			0.710090	−	0.704111i	$-0.248654\pi$
$449$	30.0931			1.42018			0.710090	+	0.704111i	$0.248654\pi$
$450$		0			0
$451$	−12.3922			−0.583525
$452$		0			0
$453$	25.0272	+	18.1833i	1.17588	+	0.854326i
$454$		0			0
$455$	−1.44969	+	4.72718i	−0.0679627	+	0.221614i
$456$		0			0
$457$	−24.9412			−1.16670			−0.583351	−	0.812220i	$-0.698259\pi$
$457$	−24.9412			−1.16670			−0.583351	+	0.812220i	$0.698259\pi$
$458$		0			0
$459$	0.205394	+	0.632138i	0.00958698	+	0.0295057i
$460$		0			0
$461$	−1.69482	+	5.21612i	−0.0789356	+	0.242939i	−0.982735	−	0.185017i	$-0.940766\pi$
$461$	−1.69482	+	5.21612i	−0.0789356	+	0.242939i	0.903800	+	0.427956i	$0.140766\pi$
$462$		0			0
$463$	1.26548	+	3.89475i	0.0588118	+	0.181004i	0.976147	−	0.217113i	$-0.0696639\pi$
$463$	1.26548	+	3.89475i	0.0588118	+	0.181004i	−0.917335	+	0.398117i	$0.869664\pi$
$464$		0			0
$465$	41.0155	+	28.7720i	1.90205	+	1.33427i
$466$		0			0
$467$	−2.80250	+	2.03613i	−0.129684	+	0.0942210i	−0.650736	−	0.759304i	$-0.725540\pi$
$467$	−2.80250	+	2.03613i	−0.129684	+	0.0942210i	0.521052	+	0.853525i	$0.325540\pi$
$468$		0			0
$469$	4.58681	−	3.33251i	0.211799	−	0.153881i
$470$		0			0
$471$	−30.2906	−	22.0074i	−1.39572	−	1.01405i
$472$		0			0
$473$	−0.341995	+	1.05255i	−0.0157250	+	0.0483965i
$474$		0			0
$475$	−13.1727	−	8.91816i	−0.604406	−	0.409193i
$476$		0			0
$477$	−6.14912	+	18.9250i	−0.281549	+	0.866518i
$478$		0			0
$479$	−27.8338	−	20.2224i	−1.27176	−	0.923986i	−0.272487	−	0.962160i	$-0.587846\pi$
$479$	−27.8338	−	20.2224i	−1.27176	−	0.923986i	−0.999271	+	0.0381733i	$0.987846\pi$
$480$		0			0
$481$	12.4266	−	9.02846i	0.566604	−	0.411662i
$482$		0			0
$483$	−11.6742	+	8.48178i	−0.531193	+	0.385934i
$484$		0			0
$485$	−3.67749	−	10.7101i	−0.166986	−	0.486322i
$486$		0			0
$487$	−8.91955	−	27.4515i	−0.404183	−	1.24395i	−0.921575	−	0.388200i	$-0.873097\pi$
$487$	−8.91955	−	27.4515i	−0.404183	−	1.24395i	0.517392	−	0.855749i	$-0.326903\pi$
$488$		0			0
$489$	−3.51693	+	10.8240i	−0.159041	+	0.489478i
$490$		0			0
$491$	−0.224666	−	0.691452i	−0.0101391	−	0.0312048i	0.945859	−	0.324578i	$-0.105222\pi$
$491$	−0.224666	−	0.691452i	−0.0101391	−	0.0312048i	−0.955998	+	0.293373i	$0.905222\pi$
$492$		0			0
$493$	28.4916			1.28320
$494$		0			0
$495$	−5.56490	−	3.90373i	−0.250124	−	0.175460i
$496$		0			0
$497$	4.38757	+	3.18775i	0.196809	+	0.142990i
$498$		0			0
$499$	6.93923			0.310642			0.155321	−	0.987864i	$-0.450359\pi$
$499$	6.93923			0.310642			0.155321	+	0.987864i	$0.450359\pi$
$500$		0			0
$501$	−54.8906			−2.45233
$502$		0			0
$503$	−29.2396	−	21.2438i	−1.30373	−	0.947216i	−0.303746	−	0.952753i	$-0.598237\pi$
$503$	−29.2396	−	21.2438i	−1.30373	−	0.947216i	−0.999985	+	0.00553740i	$0.998237\pi$
$504$		0			0
$505$	28.4102	+	19.9295i	1.26424	+	0.886852i
$506$		0			0
$507$	−8.48736			−0.376937
$508$		0			0
$509$	−9.15286	−	28.1696i	−0.405693	−	1.24860i	−0.920315	−	0.391178i	$-0.872068\pi$
$509$	−9.15286	−	28.1696i	−0.405693	−	1.24860i	0.514621	−	0.857417i	$-0.327932\pi$
$510$		0			0
$511$	−0.562648	+	1.73165i	−0.0248901	+	0.0766038i
$512$		0			0
$513$	0.0965870	+	0.297264i	0.00426442	+	0.0131245i
$514$		0			0
$515$	−7.42369	−	21.6204i	−0.327127	−	0.952709i
$516$		0			0
$517$	7.74451	−	5.62672i	0.340603	−	0.247463i
$518$		0			0
$519$	−43.0943	+	31.3099i	−1.89163	+	1.37435i
$520$		0			0
$521$	−14.9084	−	10.8316i	−0.653147	−	0.474539i	0.211194	−	0.977444i	$-0.432265\pi$
$521$	−14.9084	−	10.8316i	−0.653147	−	0.474539i	−0.864342	+	0.502905i	$0.832265\pi$
$522$		0			0
$523$	−2.17653	+	6.69868i	−0.0951732	+	0.292913i	−0.987299	−	0.158874i	$-0.949213\pi$
$523$	−2.17653	+	6.69868i	−0.0951732	+	0.292913i	0.892126	+	0.451788i	$0.149213\pi$
$524$		0			0
$525$	2.43858	−	8.44941i	0.106428	−	0.368762i
$526$		0			0
$527$	19.0604	−	58.6618i	0.830283	−	2.55535i
$528$		0			0
$529$	−35.8472	−	26.0445i	−1.55858	−	1.13237i
$530$		0			0
$531$	−25.7408	+	18.7018i	−1.11706	+	0.811590i
$532$		0			0
$533$	−30.9762	+	22.5055i	−1.34173	+	0.974823i
$534$		0			0
$535$	−18.1016	−	12.6981i	−0.782602	−	0.548989i
$536$		0			0
$537$	15.4835	+	47.6532i	0.668161	+	2.05639i
$538$		0			0
$539$	2.00485	−	6.17028i	0.0863548	−	0.265773i
$540$		0			0
$541$	−2.91688	−	8.97723i	−0.125406	−	0.385961i	0.868568	−	0.495569i	$-0.165040\pi$
$541$	−2.91688	−	8.97723i	−0.125406	−	0.385961i	−0.993975	+	0.109608i	$0.965040\pi$
$542$		0			0
$543$	−30.9049			−1.32625
$544$		0			0
$545$	6.29791	−	20.5363i	0.269773	−	0.879677i
$546$		0			0
$547$	25.1386	+	18.2643i	1.07485	+	0.780925i	0.976778	−	0.214254i	$-0.0687321\pi$
$547$	25.1386	+	18.2643i	1.07485	+	0.780925i	0.0980731	+	0.995179i	$0.468732\pi$
$548$		0			0
$549$	−32.3489			−1.38062
$550$		0			0
$551$	13.3982			0.570783
$552$		0			0
$553$	8.36660	+	6.07869i	0.355784	+	0.258492i
$554$		0			0
$555$	−21.8326	+	16.4226i	−0.926741	+	0.697099i
$556$		0			0
$557$	1.56735			0.0664105			0.0332053	−	0.999449i	$-0.489428\pi$
$557$	1.56735			0.0664105			0.0332053	+	0.999449i	$0.489428\pi$
$558$		0			0
$559$	1.05668	+	3.25212i	0.0446928	+	0.137550i
$560$		0			0
$561$	−5.13814	+	15.8136i	−0.216933	+	0.667650i
$562$		0			0
$563$	−0.509474	−	1.56800i	−0.0214718	−	0.0660833i	0.939746	−	0.341872i	$-0.111061\pi$
$563$	−0.509474	−	1.56800i	−0.0214718	−	0.0660833i	−0.961218	+	0.275789i	$0.911061\pi$
$564$		0			0
$565$	−8.89439	+	29.0029i	−0.374190	+	1.22016i
$566$		0			0
$567$	5.14054	−	3.73482i	0.215882	−	0.156848i
$568$		0			0
$569$	10.0445	−	7.29774i	0.421086	−	0.305937i	−0.356988	−	0.934109i	$-0.616196\pi$
$569$	10.0445	−	7.29774i	0.421086	−	0.305937i	0.778075	+	0.628172i	$0.216196\pi$
$570$		0			0
$571$	28.7895	+	20.9168i	1.20480	+	0.875342i	0.994749	−	0.102348i	$-0.0326354\pi$
$571$	28.7895	+	20.9168i	1.20480	+	0.875342i	0.210056	+	0.977689i	$0.432635\pi$
$572$		0			0
$573$	0.263794	−	0.811874i	0.0110202	−	0.0339165i
$574$		0			0
$575$	40.9986	−	1.36102i	1.70976	−	0.0567586i
$576$		0			0
$577$	−4.17874	+	12.8608i	−0.173963	+	0.535404i	−0.999585	−	0.0288207i	$-0.990825\pi$
$577$	−4.17874	+	12.8608i	−0.173963	+	0.535404i	0.825621	+	0.564225i	$0.190825\pi$
$578$		0			0
$579$	42.1506	+	30.6242i	1.75172	+	1.27270i
$580$		0			0
$581$	−1.28468	+	0.933375i	−0.0532975	+	0.0387229i
$582$		0			0
$583$	−5.29564	+	3.84751i	−0.219323	+	0.159347i
$584$		0			0
$585$	−20.9999	+	0.348470i	−0.868241	+	0.0144074i
$586$		0			0
$587$	−1.92344	−	5.91975i	−0.0793891	−	0.244334i	0.903483	−	0.428624i	$-0.141002\pi$
$587$	−1.92344	−	5.91975i	−0.0793891	−	0.244334i	−0.982872	+	0.184290i	$0.941002\pi$
$588$		0			0
$589$	8.96318	−	27.5858i	0.369322	−	1.13665i
$590$		0			0
$591$	3.51997	+	10.8333i	0.144792	+	0.445624i
$592$		0			0
$593$	−2.63619			−0.108255			−0.0541277	−	0.998534i	$-0.517238\pi$
$593$	−2.63619			−0.108255			−0.0541277	+	0.998534i	$0.517238\pi$
$594$		0			0
$595$	−10.8254	+	0.179635i	−0.443798	+	0.00736431i
$596$		0			0
$597$	36.2837	+	26.3617i	1.48499	+	1.07891i
$598$		0			0
$599$	−2.78637			−0.113848			−0.0569240	−	0.998379i	$-0.518129\pi$
$599$	−2.78637			−0.113848			−0.0569240	+	0.998379i	$0.518129\pi$
$600$		0			0
$601$	35.6674			1.45490			0.727451	−	0.686160i	$-0.240705\pi$
$601$	35.6674			1.45490			0.727451	+	0.686160i	$0.240705\pi$
$602$		0			0
$603$	19.4836	+	14.1556i	0.793432	+	0.576462i
$604$		0			0
$605$	−0.726172	−	2.11487i	−0.0295231	−	0.0859817i
$606$		0			0
$607$	−16.1679			−0.656236			−0.328118	−	0.944637i	$-0.606414\pi$
$607$	−16.1679			−0.656236			−0.328118	+	0.944637i	$0.606414\pi$
$608$		0			0
$609$	2.28887	+	7.04443i	0.0927499	+	0.285455i
$610$		0			0
$611$	9.13990	−	28.1297i	0.369761	−	1.13801i
$612$		0			0
$613$	12.5099	+	38.5015i	0.505270	+	1.55506i	0.800316	+	0.599579i	$0.204665\pi$
$613$	12.5099	+	38.5015i	0.505270	+	1.55506i	−0.295046	+	0.955483i	$0.595335\pi$
$614$		0			0
$615$	54.4228	−	40.9371i	2.19454	−	1.65074i
$616$		0			0
$617$	1.65346	−	1.20131i	0.0665657	−	0.0483628i	−0.554005	−	0.832513i	$-0.686901\pi$
$617$	1.65346	−	1.20131i	0.0665657	−	0.0483628i	0.620570	+	0.784151i	$0.286901\pi$
$618$		0			0
$619$	−17.2511	+	12.5337i	−0.693381	+	0.503771i	−0.877770	−	0.479083i	$-0.840969\pi$
$619$	−17.2511	+	12.5337i	−0.693381	+	0.503771i	0.184389	+	0.982853i	$0.440969\pi$
$620$		0			0
$621$	−0.652072	−	0.473758i	−0.0261668	−	0.0190113i
$622$		0			0
$623$	−1.37337	+	4.22679i	−0.0550228	+	0.169343i
$624$		0			0
$625$	−19.2063	+	16.0036i	−0.768254	+	0.640146i
$626$		0			0
$627$	−2.41622	+	7.43637i	−0.0964946	+	0.296980i
$628$		0			0
$629$	27.2105	+	19.7696i	1.08495	+	0.788264i
$630$		0			0
$631$	4.04855	−	2.94145i	0.161170	−	0.117097i	−0.504277	−	0.863542i	$-0.668241\pi$
$631$	4.04855	−	2.94145i	0.161170	−	0.117097i	0.665447	+	0.746445i	$0.268241\pi$
$632$		0			0
$633$	4.66265	−	3.38762i	0.185324	−	0.134646i
$634$		0			0
$635$	−11.3793	+	8.55959i	−0.451575	+	0.339677i
$636$		0			0
$637$	−6.19447	−	19.0646i	−0.245434	−	0.755367i
$638$		0			0
$639$	−7.11879	+	21.9094i	−0.281615	+	0.866721i
$640$		0			0
$641$	−7.68438	−	23.6501i	−0.303515	−	0.934123i	−0.980227	−	0.197875i	$-0.936596\pi$
$641$	−7.68438	−	23.6501i	−0.303515	−	0.934123i	0.676712	−	0.736248i	$-0.263404\pi$
$642$		0			0
$643$	−26.8639			−1.05941			−0.529705	−	0.848182i	$-0.677697\pi$
$643$	−26.8639			−1.05941			−0.529705	+	0.848182i	$0.677697\pi$
$644$		0			0
$645$	−1.97513	−	5.75227i	−0.0777705	−	0.226495i
$646$		0			0
$647$	1.96071	+	1.42454i	0.0770834	+	0.0560044i	0.625660	−	0.780096i	$-0.284830\pi$
$647$	1.96071	+	1.42454i	0.0770834	+	0.0560044i	−0.548576	+	0.836101i	$0.684830\pi$
$648$		0			0
$649$	−10.4663			−0.410840
$650$		0			0
$651$	16.0351			0.628467
$652$		0			0
$653$	1.60325	+	1.16483i	0.0627401	+	0.0455834i	0.618713	−	0.785617i	$-0.287654\pi$
$653$	1.60325	+	1.16483i	0.0627401	+	0.0455834i	−0.555973	+	0.831200i	$0.687654\pi$
$654$		0			0
$655$	25.8054	−	0.428211i	1.00830	−	0.0167316i
$656$		0			0
$657$	−7.73414			−0.301738
$658$		0			0
$659$	3.07272	+	9.45686i	0.119696	+	0.368387i	0.992898	−	0.118973i	$-0.0379601\pi$
$659$	3.07272	+	9.45686i	0.119696	+	0.368387i	−0.873201	+	0.487360i	$0.837960\pi$
$660$		0			0
$661$	2.12394	−	6.53682i	0.0826118	−	0.254253i	−0.901216	−	0.433370i	$-0.857324\pi$
$661$	2.12394	−	6.53682i	0.0826118	−	0.254253i	0.983828	+	0.179117i	$0.0573242\pi$
$662$		0			0
$663$	15.8756	+	48.8599i	0.616556	+	1.89756i
$664$		0			0
$665$	−5.09066	+	0.0844736i	−0.197407	+	0.00327575i
$666$		0			0
$667$	−27.9516	+	20.3080i	−1.08229	+	0.786329i
$668$		0			0
$669$	30.5142	−	22.1698i	1.17975	−	0.857136i
$670$		0			0
$671$	−8.60890	−	6.25473i	−0.332343	−	0.241461i
$672$		0			0
$673$	8.78361	−	27.0332i	0.338583	−	1.04205i	−0.626347	−	0.779544i	$-0.715451\pi$
$673$	8.78361	−	27.0332i	0.338583	−	1.04205i	0.964930	−	0.262507i	$-0.0845494\pi$
$674$		0			0
$675$	0.490942	−	0.0162977i	0.0188964	−	0.000627300i
$676$		0			0
$677$	11.2869	−	34.7375i	0.433791	−	1.33507i	−0.460530	−	0.887644i	$-0.652341\pi$
$677$	11.2869	−	34.7375i	0.433791	−	1.33507i	0.894321	−	0.447426i	$-0.147659\pi$
$678$		0			0
$679$	−2.93212	−	2.13031i	−0.112524	−	0.0817537i
$680$		0			0
$681$	−10.5371	+	7.65565i	−0.403783	+	0.293365i
$682$		0			0
$683$	10.4730	−	7.60910i	0.400739	−	0.291154i	−0.369103	−	0.929389i	$-0.620335\pi$
$683$	10.4730	−	7.60910i	0.400739	−	0.291154i	0.769842	+	0.638234i	$0.220335\pi$
$684$		0			0
$685$	−2.48597	+	8.10626i	−0.0949839	+	0.309724i
$686$		0			0
$687$	6.38590	+	19.6538i	0.243637	+	0.749838i
$688$		0			0
$689$	−6.24980	+	19.2349i	−0.238098	+	0.732791i
$690$		0			0
$691$	−7.34995	−	22.6208i	−0.279605	−	0.860537i	−0.987964	−	0.154684i	$-0.950564\pi$
$691$	−7.34995	−	22.6208i	−0.279605	−	0.860537i	0.708359	−	0.705853i	$-0.249436\pi$
$692$		0			0
$693$	−2.17562			−0.0826448
$694$		0			0
$695$	−19.2370	+	14.4701i	−0.729700	+	0.548884i
$696$		0			0
$697$	−67.8285	−	49.2803i	−2.56919	−	1.86662i
$698$		0			0
$699$	34.1673			1.29233
$700$		0			0
$701$	22.0149			0.831492			0.415746	−	0.909481i	$-0.363520\pi$
$701$	22.0149			0.831492			0.415746	+	0.909481i	$0.363520\pi$
$702$		0			0
$703$	12.7958	+	9.29667i	0.482602	+	0.350631i
$704$		0			0
$705$	−15.4239	+	50.2945i	−0.580899	+	1.89420i
$706$		0			0
$707$	11.1071			0.417724
$708$		0			0
$709$	11.7562	+	36.1820i	0.441515	+	1.35884i	0.886261	+	0.463187i	$0.153294\pi$
$709$	11.7562	+	36.1820i	0.441515	+	1.35884i	−0.444746	+	0.895657i	$0.646706\pi$
$710$		0			0
$711$	−13.5747	+	41.7788i	−0.509092	+	1.56683i
$712$		0			0
$713$	23.1134	+	71.1358i	0.865604	+	2.66406i
$714$		0			0
$715$	−5.65601	−	3.96764i	−0.211523	−	0.148381i
$716$		0			0
$717$	3.14170	−	2.28258i	0.117329	−	0.0852446i
$718$		0			0
$719$	−27.5966	+	20.0501i	−1.02918	+	0.747743i	−0.968144	−	0.250393i	$-0.919440\pi$
$719$	−27.5966	+	20.0501i	−1.02918	+	0.747743i	−0.0610355	+	0.998136i	$0.519440\pi$
$720$		0			0
$721$	−5.91902	−	4.30042i	−0.220436	−	0.160156i
$722$		0			0
$723$	8.97227	−	27.6138i	0.333682	−	1.02697i
$724$		0			0
$725$	5.83872	−	20.2305i	0.216845	−	0.751341i
$726$		0			0
$727$	5.57825	−	17.1681i	0.206886	−	0.636729i	−0.792745	−	0.609554i	$-0.791349\pi$
$727$	5.57825	−	17.1681i	0.206886	−	0.636729i	0.999631	−	0.0271754i	$-0.00865125\pi$
$728$		0			0
$729$	22.4216	+	16.2903i	0.830431	+	0.603344i
$730$		0			0
$731$	−6.05762	+	4.40112i	−0.224049	+	0.162781i
$732$		0			0
$733$	33.8167	−	24.5693i	1.24905	−	0.907486i	0.250881	−	0.968018i	$-0.419280\pi$
$733$	33.8167	−	24.5693i	1.24905	−	0.907486i	0.998166	+	0.0605319i	$0.0192797\pi$
$734$		0			0
$735$	11.5786	+	33.7210i	0.427083	+	1.24382i
$736$		0			0
$737$	2.44807	+	7.53438i	0.0901757	+	0.277532i
$738$		0			0
$739$	−1.42571	+	4.38787i	−0.0524454	+	0.161410i	−0.973849	−	0.227197i	$-0.927044\pi$
$739$	−1.42571	+	4.38787i	−0.0524454	+	0.161410i	0.921403	+	0.388608i	$0.127044\pi$
$740$		0			0
$741$	7.46551	+	22.9765i	0.274252	+	0.844062i
$742$		0			0
$743$	11.4450			0.419876			0.209938	−	0.977715i	$-0.432674\pi$
$743$	11.4450			0.419876			0.209938	+	0.977715i	$0.432674\pi$
$744$		0			0
$745$	−27.0703	−	18.9896i	−0.991779	−	0.695724i
$746$		0			0
$747$	−5.45698	−	3.96473i	−0.199661	−	0.145062i
$748$		0			0
$749$	−7.07689			−0.258584
$750$		0			0
$751$	30.8207			1.12466			0.562331	−	0.826912i	$-0.309905\pi$
$751$	30.8207			1.12466			0.562331	+	0.826912i	$0.309905\pi$
$752$		0			0
$753$	−19.1486	−	13.9123i	−0.697813	−	0.506991i
$754$		0			0
$755$	−23.0422	−	16.1639i	−0.838591	−	0.588265i
$756$		0			0
$757$	−3.80272			−0.138212			−0.0691060	−	0.997609i	$-0.522015\pi$
$757$	−3.80272			−0.138212			−0.0691060	+	0.997609i	$0.522015\pi$
$758$		0			0
$759$	−6.23072	−	19.1762i	−0.226161	−	0.696052i
$760$		0			0
$761$	−7.80757	+	24.0292i	−0.283024	+	0.871059i	0.703960	+	0.710240i	$0.251414\pi$
$761$	−7.80757	+	24.0292i	−0.283024	+	0.871059i	−0.986984	+	0.160819i	$0.948586\pi$
$762$		0			0
$763$	−2.12446	−	6.53843i	−0.0769107	−	0.236707i
$764$		0			0
$765$	−14.9354	−	43.4971i	−0.539989	−	1.57264i
$766$		0			0
$767$	−26.1623	+	19.0080i	−0.944665	+	0.686339i
$768$		0			0
$769$	−17.9892	+	13.0699i	−0.648707	+	0.471313i	−0.862830	−	0.505494i	$-0.831310\pi$
$769$	−17.9892	+	13.0699i	−0.648707	+	0.471313i	0.214124	+	0.976807i	$0.431310\pi$
$770$		0			0
$771$	3.79811	+	2.75949i	0.136785	+	0.0993805i
$772$		0			0
$773$	7.38992	−	22.7438i	0.265797	−	0.818038i	−0.725712	−	0.687999i	$-0.758489\pi$
$773$	7.38992	−	22.7438i	0.265797	−	0.818038i	0.991509	−	0.130040i	$-0.0415105\pi$
$774$		0			0
$775$	−37.7470	−	25.5553i	−1.35591	−	0.917974i
$776$		0			0
$777$	−2.70199	+	8.31588i	−0.0969335	+	0.298330i
$778$		0			0
$779$	−31.8965	−	23.1741i	−1.14281	−	0.830300i
$780$		0			0
$781$	−6.13072	+	4.45423i	−0.219374	+	0.159385i
$782$		0			0
$783$	−0.334709	+	0.243180i	−0.0119615	+	0.00869055i
$784$		0			0
$785$	27.8882	+	19.5633i	0.995372	+	0.698245i
$786$		0			0
$787$	9.26607	+	28.5180i	0.330300	+	1.01656i	0.968991	+	0.247095i	$0.0794761\pi$
$787$	9.26607	+	28.5180i	0.330300	+	1.01656i	−0.638691	+	0.769463i	$0.720524\pi$
$788$		0			0
$789$	17.0856	−	52.5841i	0.608264	−	1.87204i
$790$		0			0
$791$	3.00033	+	9.23407i	0.106679	+	0.328326i
$792$		0			0
$793$	−32.8786			−1.16755
$794$		0			0
$795$	10.5468	−	34.3910i	0.374056	−	1.21972i
$796$		0			0
$797$	10.4564	+	7.59699i	0.370383	+	0.269099i	0.757370	−	0.652986i	$-0.226484\pi$
$797$	10.4564	+	7.59699i	0.370383	+	0.269099i	−0.386987	+	0.922085i	$0.626484\pi$
$798$		0			0
$799$	64.7653			2.29123
$800$		0			0
$801$	−18.8782			−0.667030
$802$		0			0
$803$	−2.05826	−	1.49541i	−0.0726343	−	0.0527719i
$804$		0			0
$805$	10.4922	−	7.89227i	0.369801	−	0.278166i
$806$		0			0
$807$	−55.5919			−1.95693
$808$		0			0
$809$	13.0303	+	40.1031i	0.458120	+	1.40995i	0.867432	+	0.497555i	$0.165769\pi$
$809$	13.0303	+	40.1031i	0.458120	+	1.40995i	−0.409312	+	0.912395i	$0.634231\pi$
$810$		0			0
$811$	−0.914998	+	2.81607i	−0.0321299	+	0.0988857i	−0.965835	−	0.259156i	$-0.916556\pi$
$811$	−0.914998	+	2.81607i	−0.0321299	+	0.0988857i	0.933705	+	0.358042i	$0.116556\pi$
$812$		0			0
$813$	12.4011	+	38.1666i	0.434925	+	1.33856i
$814$		0			0
$815$	3.03603	−	9.89990i	0.106347	−	0.346778i
$816$		0			0
$817$	−2.84861	+	2.06963i	−0.0996601	+	0.0724073i
$818$		0			0
$819$	−5.43829	+	3.95115i	−0.190029	+	0.138064i
$820$		0			0
$821$	31.1997	+	22.6679i	1.08888	+	0.791115i	0.979209	−	0.202854i	$-0.0650215\pi$
$821$	31.1997	+	22.6679i	1.08888	+	0.791115i	0.109667	+	0.993968i	$0.465022\pi$
$822$		0			0
$823$	5.75738	−	17.7194i	0.200690	−	0.617659i	−0.799173	−	0.601101i	$-0.794729\pi$
$823$	5.75738	−	17.7194i	0.200690	−	0.617659i	0.999863	−	0.0165583i	$-0.00527090\pi$
$824$		0			0
$825$	10.1755	+	6.88899i	0.354266	+	0.239844i
$826$		0			0
$827$	−14.8129	+	45.5894i	−0.515095	+	1.58530i	0.268015	+	0.963415i	$0.413632\pi$
$827$	−14.8129	+	45.5894i	−0.515095	+	1.58530i	−0.783110	+	0.621883i	$0.786368\pi$
$828$		0			0
$829$	31.8210	+	23.1193i	1.10519	+	0.802968i	0.981900	−	0.189402i	$-0.0606551\pi$
$829$	31.8210	+	23.1193i	1.10519	+	0.802968i	0.123291	+	0.992371i	$0.460655\pi$
$830$		0			0
$831$	26.5001	−	19.2535i	0.919279	−	0.667895i
$832$		0			0
$833$	35.5110	−	25.8002i	1.23038	−	0.893925i
$834$		0			0
$835$	49.9351	−	0.828615i	1.72808	−	0.0286754i
$836$		0			0
$837$	0.276774	+	0.851822i	0.00956670	+	0.0294433i
$838$		0			0
$839$	5.82709	−	17.9340i	0.201174	−	0.619149i	−0.798675	−	0.601762i	$-0.794465\pi$
$839$	5.82709	−	17.9340i	0.201174	−	0.619149i	0.999849	−	0.0173865i	$-0.00553456\pi$
$840$		0			0
$841$	−3.48122	−	10.7141i	−0.120042	−	0.369452i
$842$		0			0
$843$	−67.3410			−2.31935
$844$		0			0
$845$	7.72112	−	0.128123i	0.265615	−	0.00440757i
$846$		0			0
$847$	−0.578988	−	0.420660i	−0.0198943	−	0.0144540i
$848$		0			0
$849$	−15.5123			−0.532382
$850$		0			0
$851$	−40.7860			−1.39812
$852$		0			0
$853$	−2.83429	−	2.05923i	−0.0970441	−	0.0705067i	0.538205	−	0.842814i	$-0.319103\pi$
$853$	−2.83429	−	2.05923i	−0.0970441	−	0.0705067i	−0.635249	+	0.772307i	$0.719103\pi$
$854$		0			0
$855$	−7.02338	−	20.4546i	−0.240195	−	0.699532i
$856$		0			0
$857$	34.5613			1.18059			0.590296	−	0.807187i	$-0.299011\pi$
$857$	34.5613			1.18059			0.590296	+	0.807187i	$0.299011\pi$
$858$		0			0
$859$	1.33862	+	4.11984i	0.0456731	+	0.140567i	0.971292	−	0.237888i	$-0.0764553\pi$
$859$	1.33862	+	4.11984i	0.0456731	+	0.140567i	−0.925619	+	0.378456i	$0.876455\pi$
$860$		0			0
$861$	6.73535	−	20.7293i	0.229540	−	0.706452i
$862$		0			0
$863$	4.65972	+	14.3411i	0.158619	+	0.488178i	0.998510	−	0.0545774i	$-0.0173812\pi$
$863$	4.65972	+	14.3411i	0.158619	+	0.488178i	−0.839891	+	0.542755i	$0.817381\pi$
$864$		0			0
$865$	38.7311	−	29.1337i	1.31690	−	0.990577i
$866$		0			0
$867$	−57.2091	+	41.5649i	−1.94292	+	1.41162i
$868$		0			0
$869$	−11.6906	+	8.49372i	−0.396576	+	0.288130i
$870$		0			0
$871$	19.8026	+	14.3874i	0.670984	+	0.487499i
$872$		0			0
$873$	4.75734	−	14.6416i	0.161011	−	0.495542i
$874$		0			0
$875$	−2.09088	+	7.72341i	−0.0706845	+	0.261099i
$876$		0			0
$877$	2.97300	−	9.14994i	0.100391	−	0.308972i	−0.888230	−	0.459399i	$-0.848065\pi$
$877$	2.97300	−	9.14994i	0.100391	−	0.308972i	0.988621	+	0.150427i	$0.0480649\pi$
$878$		0			0
$879$	−33.3802	−	24.2521i	−1.12589	−	0.818004i
$880$		0			0
$881$	21.1233	−	15.3470i	0.711662	−	0.517053i	−0.172048	−	0.985089i	$-0.555038\pi$
$881$	21.1233	−	15.3470i	0.711662	−	0.517053i	0.883709	+	0.468036i	$0.155038\pi$
$882$		0			0
$883$	−37.3892	+	27.1648i	−1.25825	+	0.914169i	−0.998670	−	0.0515544i	$-0.983582\pi$
$883$	−37.3892	+	27.1648i	−1.25825	+	0.914169i	−0.259575	+	0.965723i	$0.583582\pi$
$884$		0			0
$885$	45.9651	−	34.5751i	1.54510	−	1.16223i
$886$		0			0
$887$	−9.42969	−	29.0216i	−0.316618	−	0.974450i	−0.975083	−	0.221839i	$-0.928794\pi$
$887$	−9.42969	−	29.0216i	−0.316618	−	0.974450i	0.658465	−	0.752611i	$-0.271206\pi$
$888$		0			0
$889$	−1.40830	+	4.33431i	−0.0472330	+	0.145368i
$890$		0			0
$891$	2.74360	+	8.44394i	0.0919141	+	0.282882i
$892$		0			0
$893$	30.4560			1.01917
$894$		0			0
$895$	−14.8050	−	43.1173i	−0.494876	−	1.44125i
$896$		0			0
$897$	−50.4007	−	36.6183i	−1.68283	−	1.22265i
$898$		0			0
$899$	38.3931			1.28048
$900$		0			0
$901$	−44.2860			−1.47538
$902$		0			0
$903$	−1.57480	−	1.14416i	−0.0524060	−	0.0380752i
$904$		0			0
$905$	28.1148	−	0.466532i	0.934566	−	0.0155080i
$906$		0			0
$907$	−23.4425			−0.778395			−0.389198	−	0.921154i	$-0.627248\pi$
$907$	−23.4425			−0.778395			−0.389198	+	0.921154i	$0.627248\pi$
$908$		0			0
$909$	14.5794	+	44.8708i	0.483568	+	1.48827i
$910$		0			0
$911$	−13.8632	+	42.6666i	−0.459309	+	1.41361i	0.406693	+	0.913565i	$0.366682\pi$
$911$	−13.8632	+	42.6666i	−0.459309	+	1.41361i	−0.866001	+	0.500042i	$0.833318\pi$
$912$		0			0
$913$	−0.685658	−	2.11024i	−0.0226920	−	0.0698387i
$914$		0			0
$915$	58.4700	−	0.970241i	1.93296	−	0.0320752i
$916$		0			0
$917$	6.68275	−	4.85530i	0.220684	−	0.160336i
$918$		0			0
$919$	−0.360787	+	0.262127i	−0.0119013	+	0.00864678i	−0.593720	−	0.804672i	$-0.702341\pi$
$919$	−0.360787	+	0.262127i	−0.0119013	+	0.00864678i	0.581819	+	0.813318i	$0.302341\pi$
$920$		0			0
$921$	−21.7815	−	15.8252i	−0.717724	−	0.521457i
$922$		0			0
$923$	−7.23534	+	22.2681i	−0.238154	+	0.732963i
$924$		0			0
$925$	19.6136	−	15.2695i	0.644891	−	0.502058i
$926$		0			0
$927$	9.60357	−	29.5567i	0.315423	−	0.970771i
$928$		0			0
$929$	11.7711	+	8.55217i	0.386196	+	0.280588i	0.763895	−	0.645341i	$-0.223285\pi$
$929$	11.7711	+	8.55217i	0.386196	+	0.280588i	−0.377699	+	0.925928i	$0.623285\pi$
$930$		0			0
$931$	16.6991	−	12.1326i	0.547291	−	0.397630i
$932$		0			0
$933$	42.4275	−	30.8254i	1.38901	−	1.00918i
$934$		0			0
$935$	4.43555	−	14.4635i	0.145058	−	0.473007i
$936$		0			0
$937$	−8.39408	−	25.8343i	−0.274223	−	0.843971i	−0.989424	−	0.145052i	$-0.953665\pi$
$937$	−8.39408	−	25.8343i	−0.274223	−	0.843971i	0.715201	−	0.698919i	$-0.246335\pi$
$938$		0			0
$939$	−2.22540	+	6.84908i	−0.0726233	+	0.223511i
$940$		0			0
$941$	2.14890	+	6.61364i	0.0700522	+	0.215599i	0.979954	−	0.199226i	$-0.0638429\pi$
$941$	2.14890	+	6.61364i	0.0700522	+	0.215599i	−0.909901	+	0.414825i	$0.863843\pi$
$942$		0			0
$943$	101.669			3.31078
$944$		0			0
$945$	0.125640	−	0.0945068i	0.00408706	−	0.00307431i
$946$		0			0
$947$	−21.6795	−	15.7511i	−0.704490	−	0.511842i	0.176901	−	0.984229i	$-0.443393\pi$
$947$	−21.6795	−	15.7511i	−0.704490	−	0.511842i	−0.881392	+	0.472386i	$0.843393\pi$
$948$		0			0
$949$	−7.86077			−0.255171
$950$		0			0
$951$	−70.0054			−2.27008
$952$		0			0
$953$	12.7378	+	9.25453i	0.412617	+	0.299784i	0.774660	−	0.632378i	$-0.217921\pi$
$953$	12.7378	+	9.25453i	0.412617	+	0.299784i	−0.362044	+	0.932161i	$0.617921\pi$
$954$		0			0
$955$	−0.227723	+	0.742560i	−0.00736894	+	0.0240287i
$956$		0			0
$957$	−10.3497			−0.334558
$958$		0			0
$959$	0.838587	+	2.58091i	0.0270794	+	0.0833418i
$960$		0			0
$961$	16.1048	−	49.5655i	0.519510	−	1.59889i
$962$		0			0
$963$	−9.28930	−	28.5895i	−0.299343	−	0.921284i
$964$		0			0
$965$	−38.8075	−	27.2232i	−1.24926	−	0.876344i
$966$		0			0
$967$	−23.7747	+	17.2733i	−0.764544	+	0.555473i	−0.900301	−	0.435269i	$-0.856653\pi$
$967$	−23.7747	+	17.2733i	−0.764544	+	0.555473i	0.135757	+	0.990742i	$0.456653\pi$
$968$		0			0
$969$	−42.7975	+	31.0942i	−1.37485	+	0.998889i
$970$		0			0
$971$	−11.9299	−	8.66760i	−0.382850	−	0.278157i	0.379669	−	0.925122i	$-0.376038\pi$
$971$	−11.9299	−	8.66760i	−0.382850	−	0.278157i	−0.762519	+	0.646966i	$0.776038\pi$
$972$		0			0
$973$	−2.38076	+	7.32723i	−0.0763237	+	0.234900i
$974$		0			0
$975$	37.9465	−	1.25970i	1.21526	−	0.0403427i
$976$		0			0
$977$	11.0200	−	33.9162i	0.352562	−	1.08507i	−0.604847	−	0.796341i	$-0.706766\pi$
$977$	11.0200	−	33.9162i	0.352562	−	1.08507i	0.957410	−	0.288733i	$-0.0932341\pi$
$978$		0			0
$979$	−5.02400	−	3.65015i	−0.160568	−	0.116659i
$980$		0			0
$981$	23.6256	−	17.1650i	0.754306	−	0.548036i
$982$		0			0
$983$	47.4611	−	34.4825i	1.51377	−	1.09982i	0.549304	−	0.835623i	$-0.314893\pi$
$983$	47.4611	−	34.4825i	1.51377	−	1.09982i	0.964469	−	0.264197i	$-0.0851071\pi$
$984$		0			0
$985$	−3.36572	−	9.80218i	−0.107241	−	0.312323i
$986$		0			0
$987$	5.20294	+	16.0130i	0.165611	+	0.509699i
$988$		0			0
$989$	2.80581	−	8.63541i	0.0892197	−	0.274590i
$990$		0			0
$991$	10.3070	+	31.7218i	0.327414	+	1.00768i	0.970339	+	0.241747i	$0.0777205\pi$
$991$	10.3070	+	31.7218i	0.327414	+	1.00768i	−0.642925	+	0.765929i	$0.722279\pi$
$992$		0			0
$993$	5.64198			0.179043
$994$		0			0
$995$	−33.4060	−	23.4340i	−1.05904	−	0.742908i
$996$		0			0
$997$	11.0573	+	8.03358i	0.350188	+	0.254426i	0.748948	−	0.662629i	$-0.230559\pi$
$997$	11.0573	+	8.03358i	0.350188	+	0.254426i	−0.398760	+	0.917055i	$0.630559\pi$
$998$		0			0
$999$	−0.488395			−0.0154521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.221.2	✓	52
25.6	even	5	inner	1100.2.q.b.881.2	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.2	✓	52	1.1	even	1	trivial
1100.2.q.b.881.2	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)

\(f(q)\)	\(=\)	\(q+(-1.98827 - 1.44456i) q^{3} +(1.83057 + 1.28413i) q^{5} +0.715669 q^{7} +(0.939404 + 2.89119i) q^{9} +(-0.309017 + 0.951057i) q^{11} +(0.954784 + 2.93852i) q^{13} +(-1.78467 - 5.19758i) q^{15} +(-5.47348 + 3.97672i) q^{17} +(-2.57392 + 1.87006i) q^{19} +(-1.42294 - 1.03383i) q^{21} +(2.53525 - 7.80270i) q^{23} +(1.70201 + 4.70140i) q^{25} +(0.0303586 - 0.0934342i) q^{27} +(-3.40696 - 2.47530i) q^{29} +(-7.37566 + 5.35873i) q^{31} +(1.98827 - 1.44456i) q^{33} +(1.31009 + 0.919014i) q^{35} +(-1.53622 - 4.72801i) q^{37} +(2.34651 - 7.22182i) q^{39} +(3.82940 + 11.7857i) q^{41} +1.10672 q^{43} +(-1.99302 + 6.49885i) q^{45} +(-7.74451 - 5.62672i) q^{47} -6.48782 q^{49} +16.6274 q^{51} +(5.29564 + 3.84751i) q^{53} +(-1.78696 + 1.34416i) q^{55} +7.81906 q^{57} +(3.23428 + 9.95409i) q^{59} +(-3.28831 + 10.1204i) q^{61} +(0.672302 + 2.06913i) q^{63} +(-2.02565 + 6.60526i) q^{65} +(6.40912 - 4.65650i) q^{67} +(-16.3122 + 11.8515i) q^{69} +(6.13072 + 4.45423i) q^{71} +(-0.786184 + 2.41963i) q^{73} +(3.40742 - 11.8063i) q^{75} +(-0.221154 + 0.680642i) q^{77} +(11.6906 + 8.49372i) q^{79} +(7.18284 - 5.21864i) q^{81} +(-1.79508 + 1.30420i) q^{83} +(-15.1263 + 0.251003i) q^{85} +(3.19823 + 9.84314i) q^{87} +(-1.91900 + 5.90606i) q^{89} +(0.683310 + 2.10301i) q^{91} +22.4058 q^{93} +(-7.11315 + 0.118034i) q^{95} +(-4.09703 - 2.97667i) q^{97} -3.03997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 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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