LMFDB - Embedded newform 220.2.t.a.9.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(9,220)] 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("220.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.t (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.4
Character	$\chi$	$=$	220.9
Dual form			220.2.t.a.49.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.447653 + 0.616141i) q^{3} +(1.93649 + 1.11803i) q^{5} +(-2.82695 + 3.89096i) q^{7} +(0.747814 - 2.30153i) q^{9} +(2.43653 + 2.25018i) q^{11} +(-2.78175 - 0.903845i) q^{13} +(0.178012 + 1.69364i) q^{15} +(1.74715 - 0.567683i) q^{17} +(3.50701 - 2.54799i) q^{19} -3.66287 q^{21} +0.109291i q^{23} +(2.50001 + 4.33012i) q^{25} +(3.92578 - 1.27556i) q^{27} +(-4.23641 - 3.07793i) q^{29} +(-0.360697 + 1.11011i) q^{31} +(-0.295707 + 2.50855i) q^{33} +(-9.82457 + 4.37420i) q^{35} +(5.24594 - 7.22042i) q^{37} +(-0.688361 - 2.11856i) q^{39} +(-3.43687 + 2.49703i) q^{41} -6.85873i q^{43} +(4.02132 - 3.62083i) q^{45} +(-5.68182 - 7.82036i) q^{47} +(-4.98480 - 15.3416i) q^{49} +(1.13189 + 0.822365i) q^{51} +(-1.03268 - 0.335537i) q^{53} +(2.20256 + 7.08158i) q^{55} +(3.13985 + 1.02020i) q^{57} +(-5.60263 - 4.07055i) q^{59} +(1.90966 + 5.87734i) q^{61} +(6.84114 + 9.41602i) q^{63} +(-4.37631 - 4.86037i) q^{65} +15.0780i q^{67} +(-0.0673388 + 0.0489245i) q^{69} +(-1.20178 - 3.69871i) q^{71} +(8.51324 - 11.7175i) q^{73} +(-1.54883 + 3.47875i) q^{75} +(-15.6433 + 3.11931i) q^{77} +(-1.67784 + 5.16385i) q^{79} +(-3.33009 - 2.41945i) q^{81} +(-8.31420 + 2.70145i) q^{83} +(4.01803 + 0.854052i) q^{85} -3.98807i q^{87} +12.6602 q^{89} +(11.3807 - 8.26854i) q^{91} +(-0.845453 + 0.274704i) q^{93} +(9.64003 - 1.01322i) q^{95} +(-2.20222 - 0.715544i) q^{97} +(7.00094 - 3.92505i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{5} + 14 q^{9} - 2 q^{11} - q^{15} + 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} - 26 q^{31} + 17 q^{35} + 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} - 12 q^{51} - 33 q^{55} - 48 q^{59} - 10 q^{61}+ \cdots + 156 q^{99}+O(q^{100}) $ 24 * q + q^5 + 14 * q^9 - 2 * q^11 - q^15 + 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 - 26 * q^31 + 17 * q^35 + 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 - 12 * q^51 - 33 * q^55 - 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 + 42 * q^71 - 17 * q^75 - 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 + 10 * q^91 + 67 * q^95 + 156 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.447653	+	0.616141i	0.258452	+	0.355729i	0.918449	−	0.395539i	$-0.129442\pi$
$3$	0.447653	+	0.616141i	0.258452	+	0.355729i	−0.659997	+	0.751269i	$0.729442\pi$
$4$		0			0
$5$	1.93649	+	1.11803i	0.866026	+	0.499999i
$5$	1.93649	+	1.11803i	0.866026	+	0.499999i
$6$		0			0
$7$	−2.82695	+	3.89096i	−1.06848	+	1.47064i	−0.196884	+	0.980427i	$0.563082\pi$
$7$	−2.82695	+	3.89096i	−1.06848	+	1.47064i	−0.871601	+	0.490216i	$0.836918\pi$
$8$		0			0
$9$	0.747814	−	2.30153i	0.249271	−	0.767178i
$10$		0			0
$11$	2.43653	+	2.25018i	0.734643	+	0.678454i
$11$	2.43653	+	2.25018i	0.734643	+	0.678454i
$12$		0			0
$13$	−2.78175	−	0.903845i	−0.771518	−	0.250681i	−0.103303	−	0.994650i	$-0.532941\pi$
$13$	−2.78175	−	0.903845i	−0.771518	−	0.250681i	−0.668215	+	0.743969i	$0.732941\pi$
$14$		0			0
$15$	0.178012	+	1.69364i	0.0459624	+	0.437297i
$16$		0			0
$17$	1.74715	−	0.567683i	0.423746	−	0.137683i	−0.0893784	−	0.995998i	$-0.528488\pi$
$17$	1.74715	−	0.567683i	0.423746	−	0.137683i	0.513124	+	0.858314i	$0.328488\pi$
$18$		0			0
$19$	3.50701	−	2.54799i	0.804563	−	0.584549i	−0.107686	−	0.994185i	$-0.534344\pi$
$19$	3.50701	−	2.54799i	0.804563	−	0.584549i	0.912249	+	0.409636i	$0.134344\pi$
$20$		0			0
$21$	−3.66287			−0.799303
$22$		0			0
$23$			0.109291i			0.0227888i	0.999935	+	0.0113944i	$0.00362703\pi$
$23$			0.109291i			0.0227888i	−0.999935	+	0.0113944i	$0.996373\pi$
$24$		0			0
$25$	2.50001	+	4.33012i	0.500003	+	0.866024i
$26$		0			0
$27$	3.92578	−	1.27556i	0.755518	−	0.245483i
$28$		0			0
$29$	−4.23641	−	3.07793i	−0.786681	−	0.571557i	0.120295	−	0.992738i	$-0.461616\pi$
$29$	−4.23641	−	3.07793i	−0.786681	−	0.571557i	−0.906977	+	0.421181i	$0.861616\pi$
$30$		0			0
$31$	−0.360697	+	1.11011i	−0.0647831	+	0.199382i	−0.978209	−	0.207624i	$-0.933427\pi$
$31$	−0.360697	+	1.11011i	−0.0647831	+	0.199382i	0.913426	+	0.407006i	$0.133427\pi$
$32$		0			0
$33$	−0.295707	+	2.50855i	−0.0514759	+	0.436682i
$34$		0			0
$35$	−9.82457	+	4.37420i	−1.66066	+	0.739374i
$36$		0			0
$37$	5.24594	−	7.22042i	0.862427	−	1.18703i	−0.118558	−	0.992947i	$-0.537827\pi$
$37$	5.24594	−	7.22042i	0.862427	−	1.18703i	0.980985	−	0.194082i	$-0.0621728\pi$
$38$		0			0
$39$	−0.688361	−	2.11856i	−0.110226	−	0.339241i
$40$		0			0
$41$	−3.43687	+	2.49703i	−0.536749	+	0.389971i	−0.822876	−	0.568220i	$-0.807632\pi$
$41$	−3.43687	+	2.49703i	−0.536749	+	0.389971i	0.286127	+	0.958192i	$0.407632\pi$
$42$		0			0
$43$		−	6.85873i		−	1.04595i	−0.852349	−	0.522973i	$-0.824823\pi$
$43$		−	6.85873i		−	1.04595i	0.852349	−	0.522973i	$-0.175177\pi$
$44$		0			0
$45$	4.02132	−	3.62083i	0.599464	−	0.539761i
$46$		0			0
$47$	−5.68182	−	7.82036i	−0.828779	−	1.14072i	−0.988149	−	0.153498i	$-0.950946\pi$
$47$	−5.68182	−	7.82036i	−0.828779	−	1.14072i	0.159370	−	0.987219i	$-0.449054\pi$
$48$		0			0
$49$	−4.98480	−	15.3416i	−0.712115	−	2.19166i
$50$		0			0
$51$	1.13189	+	0.822365i	0.158496	+	0.115154i
$52$		0			0
$53$	−1.03268	−	0.335537i	−0.141849	−	0.0460896i	0.237232	−	0.971453i	$-0.423760\pi$
$53$	−1.03268	−	0.335537i	−0.141849	−	0.0460896i	−0.379081	+	0.925363i	$0.623760\pi$
$54$		0			0
$55$	2.20256	+	7.08158i	0.296993	+	0.954880i
$56$		0			0
$57$	3.13985	+	1.02020i	0.415883	+	0.135128i
$58$		0			0
$59$	−5.60263	−	4.07055i	−0.729400	−	0.529940i	0.159974	−	0.987121i	$-0.448859\pi$
$59$	−5.60263	−	4.07055i	−0.729400	−	0.529940i	−0.889374	+	0.457181i	$0.848859\pi$
$60$		0			0
$61$	1.90966	+	5.87734i	0.244507	+	0.752516i	0.995717	+	0.0924528i	$0.0294707\pi$
$61$	1.90966	+	5.87734i	0.244507	+	0.752516i	−0.751210	+	0.660064i	$0.770529\pi$
$62$		0			0
$63$	6.84114	+	9.41602i	0.861903	+	1.18631i
$64$		0			0
$65$	−4.37631	−	4.86037i	−0.542814	−	0.602855i
$66$		0			0
$67$			15.0780i			1.84207i	0.389478	+	0.921036i	$0.372656\pi$
$67$			15.0780i			1.84207i	−0.389478	+	0.921036i	$0.627344\pi$
$68$		0			0
$69$	−0.0673388	+	0.0489245i	−0.00810664	+	0.00588982i
$70$		0			0
$71$	−1.20178	−	3.69871i	−0.142626	−	0.438956i	0.854072	−	0.520154i	$-0.174125\pi$
$71$	−1.20178	−	3.69871i	−0.142626	−	0.438956i	−0.996698	+	0.0811977i	$0.974125\pi$
$72$		0			0
$73$	8.51324	−	11.7175i	0.996399	−	1.37143i	0.0688900	−	0.997624i	$-0.478054\pi$
$73$	8.51324	−	11.7175i	0.996399	−	1.37143i	0.927509	−	0.373801i	$-0.121946\pi$
$74$		0			0
$75$	−1.54883	+	3.47875i	−0.178843	+	0.401692i
$76$		0			0
$77$	−15.6433	+	3.11931i	−1.78272	+	0.355479i
$78$		0			0
$79$	−1.67784	+	5.16385i	−0.188772	+	0.580979i	−0.999993	−	0.00376007i	$-0.998803\pi$
$79$	−1.67784	+	5.16385i	−0.188772	+	0.580979i	0.811221	+	0.584739i	$0.198803\pi$
$80$		0			0
$81$	−3.33009	−	2.41945i	−0.370010	−	0.268828i
$82$		0			0
$83$	−8.31420	+	2.70145i	−0.912602	+	0.296522i	−0.727428	−	0.686184i	$-0.759285\pi$
$83$	−8.31420	+	2.70145i	−0.912602	+	0.296522i	−0.185173	+	0.982706i	$0.559285\pi$
$84$		0			0
$85$	4.01803	+	0.854052i	0.435816	+	0.0926349i
$86$		0			0
$87$		−	3.98807i		−	0.427566i
$88$		0			0
$89$	12.6602			1.34198			0.670988	−	0.741468i	$-0.265870\pi$
$89$	12.6602			1.34198			0.670988	+	0.741468i	$0.265870\pi$
$90$		0			0
$91$	11.3807	−	8.26854i	1.19302	−	0.866778i
$92$		0			0
$93$	−0.845453	+	0.274704i	−0.0876694	+	0.0284855i
$94$		0			0
$95$	9.64003	−	1.01322i	0.989047	−	0.103954i
$96$		0			0
$97$	−2.20222	−	0.715544i	−0.223601	−	0.0726525i	0.195074	−	0.980789i	$-0.437505\pi$
$97$	−2.20222	−	0.715544i	−0.223601	−	0.0726525i	−0.418675	+	0.908136i	$0.637505\pi$
$98$		0			0
$99$	7.00094	−	3.92505i	0.703621	−	0.394483i
$100$		0			0
$101$	−4.43335	+	13.6444i	−0.441135	+	1.35767i	0.445533	+	0.895266i	$0.353014\pi$
$101$	−4.43335	+	13.6444i	−0.441135	+	1.35767i	−0.886667	+	0.462408i	$0.846986\pi$
$102$		0			0
$103$	−0.437619	+	0.602330i	−0.0431198	+	0.0593494i	−0.830033	−	0.557715i	$-0.811678\pi$
$103$	−0.437619	+	0.602330i	−0.0431198	+	0.0593494i	0.786913	+	0.617064i	$0.211678\pi$
$104$		0			0
$105$	−7.09312	−	4.09520i	−0.692218	−	0.399651i
$106$		0			0
$107$	3.69610	+	5.08724i	0.357315	+	0.491802i	0.949398	−	0.314075i	$-0.101694\pi$
$107$	3.69610	+	5.08724i	0.357315	+	0.491802i	−0.592083	+	0.805877i	$0.701694\pi$
$108$		0			0
$109$	2.75501			0.263882			0.131941	−	0.991258i	$-0.457879\pi$
$109$	2.75501			0.263882			0.131941	+	0.991258i	$0.457879\pi$
$110$		0			0
$111$	6.79716			0.645158
$112$		0			0
$113$	8.19794	+	11.2835i	0.771197	+	1.06146i	0.996199	+	0.0871038i	$0.0277612\pi$
$113$	8.19794	+	11.2835i	0.771197	+	1.06146i	−0.225002	+	0.974358i	$0.572239\pi$
$114$		0			0
$115$	−0.122191	+	0.211642i	−0.0113944	+	0.0197357i
$116$		0			0
$117$	−4.16046	+	5.72638i	−0.384635	+	0.529404i
$118$		0			0
$119$	−2.73026	+	8.40288i	−0.250283	+	0.770291i
$120$		0			0
$121$	0.873392	+	10.9653i	0.0793993	+	0.996843i
$122$		0			0
$123$	−3.07705	−	0.999795i	−0.277448	−	0.0901485i
$124$		0			0
$125$	5.00640e−5		11.1803i	4.47786e−6		1.00000i
$126$		0			0
$127$	6.29139	−	2.04419i	0.558270	−	0.181393i	−0.0162725	−	0.999868i	$-0.505180\pi$
$127$	6.29139	−	2.04419i	0.558270	−	0.181393i	0.574543	+	0.818475i	$0.305180\pi$
$128$		0			0
$129$	4.22595	−	3.07033i	0.372074	−	0.270327i
$130$		0			0
$131$	−14.5964			−1.27529			−0.637645	−	0.770330i	$-0.720091\pi$
$131$	−14.5964			−1.27529			−0.637645	+	0.770330i	$0.720091\pi$
$132$		0			0
$133$			20.8486i			1.80781i
$134$		0			0
$135$	9.02838	+	1.91903i	0.777039	+	0.165163i
$136$		0			0
$137$	11.4325	−	3.71466i	0.976748	−	0.317365i	0.223211	−	0.974770i	$-0.428346\pi$
$137$	11.4325	−	3.71466i	0.976748	−	0.317365i	0.753537	+	0.657405i	$0.228346\pi$
$138$		0			0
$139$	−5.38545	−	3.91276i	−0.456788	−	0.331876i	0.335482	−	0.942047i	$-0.391101\pi$
$139$	−5.38545	−	3.91276i	−0.456788	−	0.331876i	−0.792270	+	0.610171i	$0.791101\pi$
$140$		0			0
$141$	2.27496	−	7.00161i	0.191586	−	0.589642i
$142$		0			0
$143$	−4.74401	−	8.46168i	−0.396714	−	0.707601i
$144$		0			0
$145$	−4.76255	−	10.6968i	−0.395509	−	0.888323i
$146$		0			0
$147$	7.22116	−	9.93907i	0.595591	−	0.819761i
$148$		0			0
$149$	4.64359	+	14.2915i	0.380418	+	1.17081i	0.939750	+	0.341862i	$0.111057\pi$
$149$	4.64359	+	14.2915i	0.380418	+	1.17081i	−0.559333	+	0.828943i	$0.688943\pi$
$150$		0			0
$151$	16.4236	−	11.9324i	1.33653	−	0.971047i	0.336968	−	0.941516i	$-0.390599\pi$
$151$	16.4236	−	11.9324i	1.33653	−	0.971047i	0.999564	−	0.0295311i	$-0.00940141\pi$
$152$		0			0
$153$		−	4.44564i		−	0.359409i
$154$		0			0
$155$	−1.93963	+	1.74645i	−0.155795	+	0.140279i
$156$		0			0
$157$	0.784796	+	1.08018i	0.0626336	+	0.0862077i	0.839185	−	0.543847i	$-0.183033\pi$
$157$	0.784796	+	1.08018i	0.0626336	+	0.0862077i	−0.776551	+	0.630054i	$0.783033\pi$
$158$		0			0
$159$	−0.255542	−	0.786479i	−0.0202658	−	0.0623718i
$160$		0			0
$161$	−0.425247	−	0.308960i	−0.0335142	−	0.0243495i
$162$		0			0
$163$	−11.8169	−	3.83955i	−0.925572	−	0.300737i	−0.192821	−	0.981234i	$-0.561764\pi$
$163$	−11.8169	−	3.83955i	−0.925572	−	0.300737i	−0.732751	+	0.680497i	$0.761764\pi$
$164$		0			0
$165$	−3.37727	+	4.52718i	−0.262920	+	0.352440i
$166$		0			0
$167$	−7.69770	−	2.50113i	−0.595666	−	0.193544i	−0.00435939	−	0.999990i	$-0.501388\pi$
$167$	−7.69770	−	2.50113i	−0.595666	−	0.193544i	−0.591306	+	0.806447i	$0.701388\pi$
$168$		0			0
$169$	−3.59604	−	2.61267i	−0.276618	−	0.200975i
$170$		0			0
$171$	−3.24170	−	9.97693i	−0.247899	−	0.762955i
$172$		0			0
$173$	−12.3822	−	17.0426i	−0.941399	−	1.29572i	−0.955244	−	0.295820i	$-0.904407\pi$
$173$	−12.3822	−	17.0426i	−0.941399	−	1.29572i	0.0138445	−	0.999904i	$-0.495593\pi$
$174$		0			0
$175$	−23.9157	−	2.51357i	−1.80786	−	0.190008i
$176$		0			0
$177$		−	5.27420i		−	0.396433i
$178$		0			0
$179$	−17.9839	+	13.0661i	−1.34418	+	0.976603i	−0.344900	+	0.938639i	$0.612087\pi$
$179$	−17.9839	+	13.0661i	−1.34418	+	0.976603i	−0.999279	+	0.0379638i	$0.987913\pi$
$180$		0			0
$181$	1.51674	+	4.66803i	0.112738	+	0.346972i	0.991469	−	0.130346i	$-0.0416089\pi$
$181$	1.51674	+	4.66803i	0.112738	+	0.346972i	−0.878730	+	0.477318i	$0.841609\pi$
$182$		0			0
$183$	−2.76641	+	3.80763i	−0.204499	+	0.281468i
$184$		0			0
$185$	18.2314	−	8.11716i	1.34040	−	0.596786i
$186$		0			0
$187$	5.53437	+	2.54822i	0.404713	+	0.186344i
$188$		0			0
$189$	−6.13481	+	18.8810i	−0.446242	+	1.37339i
$190$		0			0
$191$	−8.63441	−	6.27326i	−0.624764	−	0.453917i	0.229819	−	0.973234i	$-0.426187\pi$
$191$	−8.63441	−	6.27326i	−0.624764	−	0.453917i	−0.854582	+	0.519316i	$0.826187\pi$
$192$		0			0
$193$	5.20904	−	1.69252i	0.374955	−	0.121830i	−0.115476	−	0.993310i	$-0.536839\pi$
$193$	5.20904	−	1.69252i	0.374955	−	0.121830i	0.490431	+	0.871480i	$0.336839\pi$
$194$		0			0
$195$	1.03561	−	4.87218i	0.0741613	−	0.348904i
$196$		0			0
$197$			2.94305i			0.209684i	0.994489	+	0.104842i	$0.0334337\pi$
$197$			2.94305i			0.209684i	−0.994489	+	0.104842i	$0.966566\pi$
$198$		0			0
$199$	−2.97074			−0.210590			−0.105295	−	0.994441i	$-0.533579\pi$
$199$	−2.97074			−0.210590			−0.105295	+	0.994441i	$0.533579\pi$
$200$		0			0
$201$	−9.29018	+	6.74971i	−0.655279	+	0.476088i
$202$		0			0
$203$	23.9522	−	7.78254i	1.68111	−	0.546227i
$204$		0			0
$205$	−9.44725	+	0.992960i	−0.659824	+	0.0693513i
$206$		0			0
$207$	0.251537	+	0.0817294i	0.0174831	+	0.00568059i
$208$		0			0
$209$	14.2784	+	1.68313i	0.987656	+	0.116425i
$210$		0			0
$211$	4.14795	−	12.7661i	0.285556	−	0.878852i	−0.700675	−	0.713481i	$-0.747118\pi$
$211$	4.14795	−	12.7661i	0.285556	−	0.878852i	0.986231	−	0.165372i	$-0.0528823\pi$
$212$		0			0
$213$	1.74095	−	2.39621i	0.119288	−	0.164185i
$214$		0			0
$215$	7.66827	−	13.2819i	0.522972	−	0.905817i
$216$		0			0
$217$	−3.29973	−	4.54168i	−0.224000	−	0.308309i
$218$		0			0
$219$	11.0306			0.745378
$220$		0			0
$221$	−5.37322			−0.361442
$222$		0			0
$223$	−0.593077	−	0.816301i	−0.0397154	−	0.0546635i	0.788697	−	0.614781i	$-0.210756\pi$
$223$	−0.593077	−	0.816301i	−0.0397154	−	0.0546635i	−0.828413	+	0.560118i	$0.810756\pi$
$224$		0			0
$225$	11.8355	−	2.51574i	0.789031	−	0.167716i
$226$		0			0
$227$	3.29250	−	4.53173i	0.218531	−	0.300782i	−0.685650	−	0.727931i	$-0.740482\pi$
$227$	3.29250	−	4.53173i	0.218531	−	0.300782i	0.904181	+	0.427149i	$0.140482\pi$
$228$		0			0
$229$	−6.22567	+	19.1606i	−0.411404	+	1.26617i	0.504024	+	0.863689i	$0.331852\pi$
$229$	−6.22567	+	19.1606i	−0.411404	+	1.26617i	−0.915428	+	0.402481i	$0.868148\pi$
$230$		0			0
$231$	−8.92470	−	8.24211i	−0.587202	−	0.542291i
$232$		0			0
$233$	−9.59168	−	3.11652i	−0.628372	−	0.204170i	−0.0225180	−	0.999746i	$-0.507168\pi$
$233$	−9.59168	−	3.11652i	−0.628372	−	0.204170i	−0.605854	+	0.795576i	$0.707168\pi$
$234$		0			0
$235$	−2.25941	−	21.4965i	−0.147388	−	1.40228i
$236$		0			0
$237$	−3.93275	+	1.27783i	−0.255460	+	0.0830039i
$238$		0			0
$239$	−1.33100	+	0.967028i	−0.0860952	+	0.0625518i	−0.630000	−	0.776595i	$-0.716945\pi$
$239$	−1.33100	+	0.967028i	−0.0860952	+	0.0625518i	0.543905	+	0.839147i	$0.316945\pi$
$240$		0			0
$241$	2.47074			0.159154			0.0795770	−	0.996829i	$-0.474643\pi$
$241$	2.47074			0.159154			0.0795770	+	0.996829i	$0.474643\pi$
$242$		0			0
$243$		−	15.5183i		−	0.995501i
$244$		0			0
$245$	7.49940	−	35.2822i	0.479119	−	2.25409i
$246$		0			0
$247$	−12.0586	+	3.91808i	−0.767270	+	0.249301i
$248$		0			0
$249$	−5.38635	−	3.91341i	−0.341346	−	0.248002i
$250$		0			0
$251$	−0.462829	+	1.42444i	−0.0292135	+	0.0899099i	−0.964600	−	0.263717i	$-0.915052\pi$
$251$	−0.462829	+	1.42444i	−0.0292135	+	0.0899099i	0.935387	+	0.353627i	$0.115052\pi$
$252$		0			0
$253$	−0.245925	+	0.266292i	−0.0154611	+	0.0167416i
$254$		0			0
$255$	1.27246	+	2.85799i	0.0796848	+	0.178974i
$256$		0			0
$257$	−18.1780	+	25.0199i	−1.13392	+	1.56070i	−0.353505	+	0.935433i	$0.615010\pi$
$257$	−18.1780	+	25.0199i	−1.13392	+	1.56070i	−0.780410	+	0.625268i	$0.784990\pi$
$258$		0			0
$259$	13.2643	+	40.8234i	0.824206	+	2.53665i
$260$		0			0
$261$	−10.2520	+	7.44852i	−0.634583	+	0.461052i
$262$		0			0
$263$			9.45633i			0.583103i	0.956555	+	0.291551i	$0.0941714\pi$
$263$			9.45633i			0.583103i	−0.956555	+	0.291551i	$0.905829\pi$
$264$		0			0
$265$	−1.62463	−	1.80433i	−0.0998003	−	0.110839i
$266$		0			0
$267$	5.66737	+	7.80046i	0.346837	+	0.477380i
$268$		0			0
$269$	−5.43094	−	16.7147i	−0.331131	−	1.01911i	−0.968597	−	0.248637i	$-0.920017\pi$
$269$	−5.43094	−	16.7147i	−0.331131	−	1.01911i	0.637466	−	0.770478i	$-0.279983\pi$
$270$		0			0
$271$	5.95324	+	4.32528i	0.361633	+	0.262742i	0.753733	−	0.657181i	$-0.228251\pi$
$271$	5.95324	+	4.32528i	0.361633	+	0.262742i	−0.392100	+	0.919923i	$0.628251\pi$
$272$		0			0
$273$	10.1892	+	3.31066i	0.616677	+	0.200370i
$274$		0			0
$275$	−3.65218	+	16.1760i	−0.220235	+	0.975447i
$276$		0			0
$277$	−11.0843	−	3.60149i	−0.665988	−	0.216393i	−0.0435375	−	0.999052i	$-0.513863\pi$
$277$	−11.0843	−	3.60149i	−0.665988	−	0.216393i	−0.622451	+	0.782659i	$0.713863\pi$
$278$		0			0
$279$	2.28523	+	1.66031i	0.136813	+	0.0994004i
$280$		0			0
$281$	−8.84788	−	27.2310i	−0.527820	−	1.62446i	−0.758671	−	0.651475i	$-0.774151\pi$
$281$	−8.84788	−	27.2310i	−0.527820	−	1.62446i	0.230850	−	0.972989i	$-0.425849\pi$
$282$		0			0
$283$	14.0912	+	19.3949i	0.837637	+	1.15291i	0.986453	+	0.164043i	$0.0524537\pi$
$283$	14.0912	+	19.3949i	0.837637	+	1.15291i	−0.148816	+	0.988865i	$0.547546\pi$
$284$		0			0
$285$	4.93968	+	5.48605i	0.292601	+	0.324966i
$286$		0			0
$287$		−	20.4317i		−	1.20605i
$288$		0			0
$289$	−11.0230	+	8.00870i	−0.648413	+	0.471100i
$290$		0			0
$291$	−0.544953	−	1.67719i	−0.0319457	−	0.0983188i
$292$		0			0
$293$	−5.13518	+	7.06797i	−0.300000	+	0.412915i	−0.932230	−	0.361866i	$-0.882140\pi$
$293$	−5.13518	+	7.06797i	−0.300000	+	0.412915i	0.632230	+	0.774781i	$0.282140\pi$
$294$		0			0
$295$	−6.29845	−	14.1465i	−0.366710	−	0.823641i
$296$		0			0
$297$	12.4356	+	5.72576i	0.721584	+	0.332242i
$298$		0			0
$299$	0.0987822	−	0.304020i	0.00571272	−	0.0175820i
$300$		0			0
$301$	26.6870	+	19.3893i	1.53821	+	1.11758i
$302$		0			0
$303$	−10.3915	+	3.37641i	−0.596977	+	0.193969i
$304$		0			0
$305$	−2.87300	+	13.5165i	−0.164507	+	0.773952i
$306$		0			0
$307$		−	6.87006i		−	0.392095i	−0.980594	−	0.196047i	$-0.937189\pi$
$307$		−	6.87006i		−	0.392095i	0.980594	−	0.196047i	$-0.0628106\pi$
$308$		0			0
$309$	−0.567022			−0.0322567
$310$		0			0
$311$	11.7118	−	8.50914i	0.664117	−	0.482509i	−0.203934	−	0.978985i	$-0.565373\pi$
$311$	11.7118	−	8.50914i	0.664117	−	0.482509i	0.868051	+	0.496476i	$0.165373\pi$
$312$		0			0
$313$	−25.6856	+	8.34576i	−1.45184	+	0.471730i	−0.925566	−	0.378587i	$-0.876410\pi$
$313$	−25.6856	+	8.34576i	−1.45184	+	0.471730i	−0.526270	+	0.850317i	$0.676410\pi$
$314$		0			0
$315$	2.72042	+	25.8827i	0.153278	+	1.45832i
$316$		0			0
$317$	27.9475	+	9.08070i	1.56969	+	0.510023i	0.959374	−	0.282136i	$-0.0910431\pi$
$317$	27.9475	+	9.08070i	1.56969	+	0.510023i	0.610315	+	0.792159i	$0.291043\pi$
$318$		0			0
$319$	−3.39626	−	17.0322i	−0.190154	−	0.953618i
$320$		0			0
$321$	−1.47989	+	4.55463i	−0.0825994	+	0.254215i
$322$		0			0
$323$	4.68081	−	6.44259i	0.260447	−	0.358475i
$324$		0			0
$325$	−3.04065	−	14.3049i	−0.168665	−	0.793494i
$326$		0			0
$327$	1.23329	+	1.69747i	0.0682009	+	0.0938706i
$328$		0			0
$329$	46.4909			2.56313
$330$		0			0
$331$	19.6296			1.07894			0.539470	−	0.842005i	$-0.318625\pi$
$331$	19.6296			1.07894			0.539470	+	0.842005i	$0.318625\pi$
$332$		0			0
$333$	−12.6951	−	17.4732i	−0.695685	−	0.957528i
$334$		0			0
$335$	−16.8577	+	29.1985i	−0.921033	+	1.59528i
$336$		0			0
$337$	16.9635	−	23.3482i	0.924060	−	1.27186i	−0.0380714	−	0.999275i	$-0.512121\pi$
$337$	16.9635	−	23.3482i	0.924060	−	1.27186i	0.962132	−	0.272585i	$-0.0878786\pi$
$338$		0			0
$339$	−3.28240	+	10.1022i	−0.178275	+	0.548675i
$340$		0			0
$341$	−3.37680	+	1.89319i	−0.182864	+	0.102522i
$342$		0			0
$343$	41.7668	+	13.5708i	2.25519	+	0.732757i
$344$		0			0
$345$	−0.185100	+	0.0194551i	−0.00996546	+	0.00104743i
$346$		0			0
$347$	−9.51578	+	3.09187i	−0.510834	+	0.165980i	−0.553082	−	0.833127i	$-0.686548\pi$
$347$	−9.51578	+	3.09187i	−0.510834	+	0.165980i	0.0422475	+	0.999107i	$0.486548\pi$
$348$		0			0
$349$	−13.2827	+	9.65042i	−0.711005	+	0.516575i	−0.883498	−	0.468435i	$-0.844818\pi$
$349$	−13.2827	+	9.65042i	−0.711005	+	0.516575i	0.172493	+	0.985011i	$0.444818\pi$
$350$		0			0
$351$	−12.0735			−0.644433
$352$		0			0
$353$			21.2166i			1.12924i	0.825350	+	0.564622i	$0.190978\pi$
$353$			21.2166i			1.12924i	−0.825350	+	0.564622i	$0.809022\pi$
$354$		0			0
$355$	1.80803	−	8.50616i	0.0959601	−	0.451460i
$356$		0			0
$357$	−6.39957	+	2.07935i	−0.338701	+	0.110051i
$358$		0			0
$359$	12.2286	+	8.88461i	0.645402	+	0.468912i	0.861702	−	0.507415i	$-0.169399\pi$
$359$	12.2286	+	8.88461i	0.645402	+	0.468912i	−0.216300	+	0.976327i	$0.569399\pi$
$360$		0			0
$361$	−0.0644696	+	0.198417i	−0.00339314	+	0.0104430i
$362$		0			0
$363$	−6.36518	+	5.44677i	−0.334085	+	0.285881i
$364$		0			0
$365$	29.5863	−	13.1727i	1.54862	−	0.689492i
$366$		0			0
$367$	−8.65332	+	11.9103i	−0.451700	+	0.621711i	−0.972762	−	0.231807i	$-0.925536\pi$
$367$	−8.65332	+	11.9103i	−0.451700	+	0.621711i	0.521062	+	0.853519i	$0.325536\pi$
$368$		0			0
$369$	3.17687	+	9.77740i	0.165381	+	0.508991i
$370$		0			0
$371$	4.22488	−	3.06956i	0.219345	−	0.159363i
$372$		0			0
$373$			4.29655i			0.222467i	0.993794	+	0.111233i	$0.0354801\pi$
$373$			4.29655i			0.222467i	−0.993794	+	0.111233i	$0.964520\pi$
$374$		0			0
$375$	−6.88865	+	5.00494i	−0.355728	+	0.258454i
$376$		0			0
$377$	9.00265	+	12.3911i	0.463660	+	0.638173i
$378$		0			0
$379$	−2.56446	−	7.89260i	−0.131728	−	0.405416i	0.863339	−	0.504624i	$-0.168369\pi$
$379$	−2.56446	−	7.89260i	−0.131728	−	0.405416i	−0.995067	+	0.0992085i	$0.968369\pi$
$380$		0			0
$381$	4.07587	+	2.96129i	0.208813	+	0.151712i
$382$		0			0
$383$	−10.5498	−	3.42785i	−0.539072	−	0.175155i	0.0268113	−	0.999641i	$-0.491465\pi$
$383$	−10.5498	−	3.42785i	−0.539072	−	0.175155i	−0.565883	+	0.824485i	$0.691465\pi$
$384$		0			0
$385$	−33.7806	−	11.4492i	−1.72162	−	0.583503i
$386$		0			0
$387$	−15.7856	−	5.12905i	−0.802427	−	0.260724i
$388$		0			0
$389$	−3.41745	−	2.48292i	−0.173271	−	0.125889i	0.497769	−	0.867309i	$-0.334153\pi$
$389$	−3.41745	−	2.48292i	−0.173271	−	0.125889i	−0.671041	+	0.741420i	$0.734153\pi$
$390$		0			0
$391$	0.0620427	+	0.190948i	0.00313763	+	0.00965665i
$392$		0			0
$393$	−6.53410	−	8.99342i	−0.329602	−	0.453658i
$394$		0			0
$395$	−9.02247	+	8.12390i	−0.453970	+	0.408758i
$396$		0			0
$397$		−	11.5205i		−	0.578195i	−0.957300	−	0.289098i	$-0.906645\pi$
$397$		−	11.5205i		−	0.578195i	0.957300	−	0.289098i	$-0.0933552\pi$
$398$		0			0
$399$	−12.8457	+	9.33296i	−0.643090	+	0.467232i
$400$		0			0
$401$	1.25283	+	3.85583i	0.0625636	+	0.192551i	0.977453	−	0.211154i	$-0.0677222\pi$
$401$	1.25283	+	3.85583i	0.0625636	+	0.192551i	−0.914889	+	0.403705i	$0.867722\pi$
$402$		0			0
$403$	2.00674	−	2.76204i	0.0999627	−	0.137587i
$404$		0			0
$405$	−3.74368	−	8.40840i	−0.186025	−	0.417817i
$406$		0			0
$407$	29.0291	−	5.78849i	1.43892	−	0.286925i
$408$		0			0
$409$	6.71259	−	20.6592i	0.331916	−	1.02153i	−0.636305	−	0.771438i	$-0.719538\pi$
$409$	6.71259	−	20.6592i	0.331916	−	1.02153i	0.968221	−	0.250096i	$-0.0804620\pi$
$410$		0			0
$411$	7.40656	+	5.38118i	0.365339	+	0.265434i
$412$		0			0
$413$	31.6766	−	10.2924i	1.55871	−	0.506454i
$414$		0			0
$415$	−19.1207	−	4.06420i	−0.938598	−	0.199504i
$416$		0			0
$417$		−	5.06976i		−	0.248267i
$418$		0			0
$419$	−24.0859			−1.17667			−0.588337	−	0.808616i	$-0.700217\pi$
$419$	−24.0859			−1.17667			−0.588337	+	0.808616i	$0.700217\pi$
$420$		0			0
$421$	4.42530	−	3.21517i	0.215676	−	0.156698i	−0.474702	−	0.880147i	$-0.657444\pi$
$421$	4.42530	−	3.21517i	0.215676	−	0.156698i	0.690378	+	0.723449i	$0.257444\pi$
$422$		0			0
$423$	−22.2478	+	7.22874i	−1.08172	+	0.351473i
$424$		0			0
$425$	6.82603	+	6.14615i	0.331111	+	0.298132i
$426$		0			0
$427$	−28.2670	−	9.18450i	−1.36794	−	0.444469i
$428$		0			0
$429$	3.08992	−	6.71087i	0.149183	−	0.324004i
$430$		0			0
$431$	3.79917	−	11.6926i	0.182999	−	0.563214i	−0.816909	−	0.576767i	$-0.804314\pi$
$431$	3.79917	−	11.6926i	0.182999	−	0.563214i	0.999908	+	0.0135526i	$0.00431405\pi$
$432$		0			0
$433$	0.257579	−	0.354527i	0.0123785	−	0.0170375i	−0.802783	−	0.596271i	$-0.796648\pi$
$433$	0.257579	−	0.354527i	0.0123785	−	0.0170375i	0.815161	+	0.579234i	$0.196648\pi$
$434$		0			0
$435$	4.45879	−	7.72287i	0.213782	−	0.370283i
$436$		0			0
$437$	0.278473	+	0.383285i	0.0133212	+	0.0183350i
$438$		0			0
$439$	28.9786			1.38307			0.691537	−	0.722341i	$-0.256934\pi$
$439$	28.9786			1.38307			0.691537	+	0.722341i	$0.256934\pi$
$440$		0			0
$441$	−39.0370			−1.85891
$442$		0			0
$443$	3.05825	+	4.20932i	0.145302	+	0.199991i	0.875464	−	0.483283i	$-0.160556\pi$
$443$	3.05825	+	4.20932i	0.145302	+	0.199991i	−0.730162	+	0.683274i	$0.760556\pi$
$444$		0			0
$445$	24.5164	+	14.1545i	1.16219	+	0.670987i
$446$		0			0
$447$	−6.72687	+	9.25874i	−0.318170	+	0.437923i
$448$		0			0
$449$	7.62962	−	23.4815i	0.360064	−	1.10816i	−0.592951	−	0.805239i	$-0.702037\pi$
$449$	7.62962	−	23.4815i	0.360064	−	1.10816i	0.953015	−	0.302924i	$-0.0979628\pi$
$450$		0			0
$451$	−13.9928	−	1.64947i	−0.658897	−	0.0776705i
$452$		0			0
$453$	14.7041	+	4.77766i	0.690860	+	0.224474i
$454$		0			0
$455$	31.2831	−	3.28803i	1.46657	−	0.154145i
$456$		0			0
$457$	−21.4460	+	6.96822i	−1.00320	+	0.325960i	−0.764144	−	0.645046i	$-0.776838\pi$
$457$	−21.4460	+	6.96822i	−1.00320	+	0.325960i	−0.239057	+	0.971006i	$0.576838\pi$
$458$		0			0
$459$	6.13481	−	4.45720i	0.286348	−	0.208044i
$460$		0			0
$461$	−2.01614			−0.0939009			−0.0469504	−	0.998897i	$-0.514950\pi$
$461$	−2.01614			−0.0939009			−0.0469504	+	0.998897i	$0.514950\pi$
$462$		0			0
$463$		−	25.7780i		−	1.19800i	−0.800747	−	0.599002i	$-0.795564\pi$
$463$		−	25.7780i		−	1.19800i	0.800747	−	0.599002i	$-0.204436\pi$
$464$		0			0
$465$	−1.94434	−	0.413280i	−0.0901667	−	0.0191654i
$466$		0			0
$467$	−15.2156	+	4.94384i	−0.704092	+	0.228773i	−0.639113	−	0.769113i	$-0.720698\pi$
$467$	−15.2156	+	4.94384i	−0.704092	+	0.228773i	−0.0649797	+	0.997887i	$0.520698\pi$
$468$		0			0
$469$	−58.6679	−	42.6247i	−2.70903	−	1.96823i
$470$		0			0
$471$	−0.314227	+	0.967091i	−0.0144788	+	0.0445612i
$472$		0			0
$473$	15.4334	−	16.7115i	0.709627	−	0.768397i
$474$		0			0
$475$	19.8007	+	8.81576i	0.908517	+	0.404495i
$476$		0			0
$477$	−1.54450	+	2.12582i	−0.0707178	+	0.0973347i
$478$		0			0
$479$	−2.00010	−	6.15568i	−0.0913869	−	0.281260i	0.894908	−	0.446250i	$-0.147241\pi$
$479$	−2.00010	−	6.15568i	−0.0913869	−	0.281260i	−0.986295	+	0.164990i	$0.947241\pi$
$480$		0			0
$481$	−21.1190	+	15.3439i	−0.962944	+	0.699620i
$482$		0			0
$483$		−	0.400319i		−	0.0182152i
$484$		0			0
$485$	−3.46458	−	3.84780i	−0.157319	−	0.174719i
$486$		0			0
$487$	17.6556	+	24.3008i	0.800050	+	1.10117i	0.992783	+	0.119923i	$0.0382646\pi$
$487$	17.6556	+	24.3008i	0.800050	+	1.10117i	−0.192734	+	0.981251i	$0.561735\pi$
$488$		0			0
$489$	−2.92417	−	8.99967i	−0.132236	−	0.406979i
$490$		0			0
$491$	−6.75443	−	4.90738i	−0.304823	−	0.221467i	0.424849	−	0.905264i	$-0.360327\pi$
$491$	−6.75443	−	4.90738i	−0.304823	−	0.221467i	−0.729672	+	0.683797i	$0.760327\pi$
$492$		0			0
$493$	−9.14892	−	2.97266i	−0.412047	−	0.133882i
$494$		0			0
$495$	17.9456	+	0.226430i	0.806595	+	0.0101773i
$496$		0			0
$497$	17.7889	+	5.77996i	0.797941	+	0.259267i
$498$		0			0
$499$	−22.9808	−	16.6965i	−1.02876	−	0.747439i	−0.0607010	−	0.998156i	$-0.519334\pi$
$499$	−22.9808	−	16.6965i	−1.02876	−	0.747439i	−0.968060	+	0.250717i	$0.919334\pi$
$500$		0			0
$501$	−1.90485	−	5.86251i	−0.0851022	−	0.261918i
$502$		0			0
$503$	−9.16716	−	12.6175i	−0.408743	−	0.562587i	0.554168	−	0.832405i	$-0.313036\pi$
$503$	−9.16716	−	12.6175i	−0.408743	−	0.562587i	−0.962911	+	0.269818i	$0.913036\pi$
$504$		0			0
$505$	−23.8401	+	21.4658i	−1.06087	+	0.955214i
$506$		0			0
$507$		−	3.38524i		−	0.150344i
$508$		0			0
$509$	−27.9625	+	20.3160i	−1.23942	+	0.900490i	−0.997559	−	0.0698215i	$-0.977757\pi$
$509$	−27.9625	+	20.3160i	−1.23942	+	0.900490i	−0.241859	+	0.970311i	$0.577757\pi$
$510$		0			0
$511$	21.5257	+	66.2493i	0.952240	+	2.93069i
$512$		0			0
$513$	10.5176	−	14.4763i	0.464365	−	0.639143i
$514$		0			0
$515$	−1.52087	+	0.677137i	−0.0670175	+	0.0298382i
$516$		0			0
$517$	3.75325	−	31.8397i	0.165068	−	1.40031i
$518$		0			0
$519$	4.95773	−	15.2583i	0.217620	−	0.669766i
$520$		0			0
$521$	5.06120	+	3.67718i	0.221735	+	0.161100i	0.693107	−	0.720834i	$-0.256241\pi$
$521$	5.06120	+	3.67718i	0.221735	+	0.161100i	−0.471372	+	0.881934i	$0.656241\pi$
$522$		0			0
$523$	−33.3151	+	10.8247i	−1.45677	+	0.473332i	−0.927080	−	0.374862i	$-0.877690\pi$
$523$	−33.3151	+	10.8247i	−1.45677	+	0.473332i	−0.529685	+	0.848194i	$0.677690\pi$
$524$		0			0
$525$	−9.15722	−	15.8607i	−0.399654	−	0.692216i
$526$		0			0
$527$			2.14429i			0.0934068i
$528$		0			0
$529$	22.9881			0.999481
$530$		0			0
$531$	−13.5582	+	9.85063i	−0.588377	+	0.427481i
$532$		0			0
$533$	11.8174	−	3.83972i	0.511870	−	0.166317i
$534$		0			0
$535$	1.46977	+	13.9838i	0.0635438	+	0.604570i
$536$		0			0
$537$	−16.1011	−	5.23156i	−0.694813	−	0.225758i
$538$		0			0
$539$	22.3758	−	48.5971i	0.963794	−	2.09323i
$540$		0			0
$541$	9.09994	−	28.0067i	0.391237	−	1.20410i	−0.540617	−	0.841269i	$-0.681809\pi$
$541$	9.09994	−	28.0067i	0.391237	−	1.20410i	0.931854	−	0.362834i	$-0.118191\pi$
$542$		0			0
$543$	−2.19720	+	3.02418i	−0.0942908	+	0.129780i
$544$		0			0
$545$	5.33506	+	3.08019i	0.228529	+	0.131941i
$546$		0			0
$547$	−2.48910	−	3.42595i	−0.106426	−	0.146483i	0.752482	−	0.658613i	$-0.228857\pi$
$547$	−2.48910	−	3.42595i	−0.106426	−	0.146483i	−0.858908	+	0.512130i	$0.828857\pi$
$548$		0			0
$549$	14.9550			0.638263
$550$		0			0
$551$	−22.6997			−0.967038
$552$		0			0
$553$	−15.3492	−	21.1263i	−0.652713	−	0.898383i
$554$		0			0
$555$	13.1626	+	7.59943i	0.558723	+	0.322578i
$556$		0			0
$557$	3.08098	−	4.24061i	0.130545	−	0.179680i	−0.738740	−	0.673990i	$-0.764579\pi$
$557$	3.08098	−	4.24061i	0.130545	−	0.179680i	0.869286	+	0.494310i	$0.164579\pi$
$558$		0			0
$559$	−6.19923	+	19.0793i	−0.262199	+	0.806967i
$560$		0			0
$561$	0.907416	+	4.55067i	0.0383111	+	0.192130i
$562$		0			0
$563$	−12.2182	−	3.96993i	−0.514935	−	0.167312i	0.0400105	−	0.999199i	$-0.487261\pi$
$563$	−12.2182	−	3.96993i	−0.514935	−	0.167312i	−0.554945	+	0.831887i	$0.687261\pi$
$564$		0			0
$565$	3.25996	+	31.0160i	0.137147	+	1.30485i
$566$		0			0
$567$	18.8280	−	6.11758i	0.790700	−	0.256914i
$568$		0			0
$569$	1.14709	−	0.833412i	0.0480886	−	0.0349384i	−0.563481	−	0.826129i	$-0.690538\pi$
$569$	1.14709	−	0.833412i	0.0480886	−	0.0349384i	0.611570	+	0.791190i	$0.290538\pi$
$570$		0			0
$571$	31.9080			1.33531			0.667653	−	0.744472i	$-0.267299\pi$
$571$	31.9080			1.33531			0.667653	+	0.744472i	$0.267299\pi$
$572$		0			0
$573$		−	8.12826i		−	0.339563i
$574$		0			0
$575$	−0.473244	+	0.273229i	−0.0197356	+	0.0113944i
$576$		0			0
$577$	9.75941	−	3.17103i	0.406290	−	0.132011i	−0.0987405	−	0.995113i	$-0.531481\pi$
$577$	9.75941	−	3.17103i	0.406290	−	0.132011i	0.505030	+	0.863102i	$0.331481\pi$
$578$		0			0
$579$	3.37468	+	2.45185i	0.140247	+	0.101895i
$580$		0			0
$581$	12.9926	−	39.9870i	0.539023	−	1.65894i
$582$		0			0
$583$	−1.76113	−	3.14125i	−0.0729387	−	0.130097i
$584$		0			0
$585$	−14.4590	+	6.43758i	−0.597805	+	0.266161i
$586$		0			0
$587$	1.59687	−	2.19791i	0.0659100	−	0.0907173i	−0.774789	−	0.632219i	$-0.782144\pi$
$587$	1.59687	−	2.19791i	0.0659100	−	0.0907173i	0.840699	+	0.541502i	$0.182144\pi$
$588$		0			0
$589$	1.56359	+	4.81223i	0.0644265	+	0.198284i
$590$		0			0
$591$	−1.81334	+	1.31747i	−0.0745907	+	0.0541933i
$592$		0			0
$593$			41.5417i			1.70591i	0.521983	+	0.852956i	$0.325192\pi$
$593$			41.5417i			1.70591i	−0.521983	+	0.852956i	$0.674808\pi$
$594$		0			0
$595$	−14.6818	+	13.2196i	−0.601896	+	0.541951i
$596$		0			0
$597$	−1.32986	−	1.83040i	−0.0544276	−	0.0749131i
$598$		0			0
$599$	−10.2599	−	31.5767i	−0.419208	−	1.29019i	−0.908432	−	0.418032i	$-0.862720\pi$
$599$	−10.2599	−	31.5767i	−0.419208	−	1.29019i	0.489224	−	0.872158i	$-0.337280\pi$
$600$		0			0
$601$	25.0930	+	18.2312i	1.02357	+	0.743664i	0.967011	−	0.254735i	$-0.0819883\pi$
$601$	25.0930	+	18.2312i	1.02357	+	0.743664i	0.0565554	+	0.998399i	$0.481988\pi$
$602$		0			0
$603$	34.7026	+	11.2755i	1.41320	+	0.459176i
$604$		0			0
$605$	−10.5682	+	22.2107i	−0.429658	+	0.902992i
$606$		0			0
$607$	31.2702	+	10.1603i	1.26922	+	0.412395i	0.864771	−	0.502166i	$-0.167463\pi$
$607$	31.2702	+	10.1603i	1.26922	+	0.412395i	0.404449	+	0.914561i	$0.367463\pi$
$608$		0			0
$609$	15.5174	+	11.2741i	0.628797	+	0.456848i
$610$		0			0
$611$	8.73701	+	26.8898i	0.353462	+	1.08784i
$612$		0			0
$613$	4.31112	+	5.93375i	0.174125	+	0.239662i	0.887155	−	0.461471i	$-0.152678\pi$
$613$	4.31112	+	5.93375i	0.174125	+	0.239662i	−0.713031	+	0.701133i	$0.752678\pi$
$614$		0			0
$615$	−4.84089	−	5.37634i	−0.195204	−	0.216795i
$616$		0			0
$617$		−	12.5755i		−	0.506269i	−0.967431	−	0.253135i	$-0.918538\pi$
$617$		−	12.5755i		−	0.506269i	0.967431	−	0.253135i	$-0.0814615\pi$
$618$		0			0
$619$	−9.56190	+	6.94713i	−0.384325	+	0.279229i	−0.763126	−	0.646250i	$-0.776337\pi$
$619$	−9.56190	+	6.94713i	−0.384325	+	0.279229i	0.378801	+	0.925478i	$0.376337\pi$
$620$		0			0
$621$	0.139408	+	0.429053i	0.00559425	+	0.0172173i
$622$		0			0
$623$	−35.7896	+	49.2602i	−1.43388	+	1.97357i
$624$		0			0
$625$	−12.4999	+	21.6507i	−0.499995	+	0.866028i
$626$		0			0
$627$	5.35471	+	9.55096i	0.213847	+	0.381429i
$628$		0			0
$629$	5.06653	−	15.5932i	0.202016	−	0.621740i
$630$		0			0
$631$	−19.5463	−	14.2012i	−0.778127	−	0.565343i	0.126289	−	0.991993i	$-0.459693\pi$
$631$	−19.5463	−	14.2012i	−0.778127	−	0.565343i	−0.904416	+	0.426651i	$0.859693\pi$
$632$		0			0
$633$	9.72254	−	3.15904i	0.386436	−	0.125561i
$634$		0			0
$635$	14.4687	+	3.07539i	0.574173	+	0.122043i
$636$		0			0
$637$			47.1821i			1.86942i
$638$		0			0
$639$	−9.41142			−0.372310
$640$		0			0
$641$	7.93668	−	5.76633i	0.313480	−	0.227757i	−0.419908	−	0.907567i	$-0.637938\pi$
$641$	7.93668	−	5.76633i	0.313480	−	0.227757i	0.733388	+	0.679810i	$0.237938\pi$
$642$		0			0
$643$	−12.9114	+	4.19515i	−0.509174	+	0.165441i	−0.552327	−	0.833628i	$-0.686260\pi$
$643$	−12.9114	+	4.19515i	−0.509174	+	0.165441i	0.0431525	+	0.999068i	$0.486260\pi$
$644$		0			0
$645$	11.6162	−	1.22093i	0.457389	−	0.0480742i
$646$		0			0
$647$	17.5900	+	5.71535i	0.691535	+	0.224693i	0.633639	−	0.773629i	$-0.281561\pi$
$647$	17.5900	+	5.71535i	0.691535	+	0.224693i	0.0578966	+	0.998323i	$0.481561\pi$
$648$		0			0
$649$	−4.49153	−	22.5249i	−0.176308	−	0.884181i
$650$		0			0
$651$	1.32119	−	4.06619i	0.0517814	−	0.159367i
$652$		0			0
$653$	−10.0391	+	13.8176i	−0.392860	+	0.540726i	−0.958934	−	0.283629i	$-0.908462\pi$
$653$	−10.0391	+	13.8176i	−0.392860	+	0.540726i	0.566074	+	0.824354i	$0.308462\pi$
$654$		0			0
$655$	−28.2658	−	16.3192i	−1.10443	−	0.637643i
$656$		0			0
$657$	−20.6018	−	28.3560i	−0.803754	−	1.10627i
$658$		0			0
$659$	44.5096			1.73385			0.866924	−	0.498441i	$-0.166094\pi$
$659$	44.5096			1.73385			0.866924	+	0.498441i	$0.166094\pi$
$660$		0			0
$661$	27.5948			1.07331			0.536656	−	0.843801i	$-0.319687\pi$
$661$	27.5948			1.07331			0.536656	+	0.843801i	$0.319687\pi$
$662$		0			0
$663$	−2.40534	−	3.31066i	−0.0934156	−	0.128576i
$664$		0			0
$665$	−23.3094	+	40.3733i	−0.903901	+	1.56561i
$666$		0			0
$667$	0.336391	−	0.463002i	0.0130251	−	0.0179275i
$668$		0			0
$669$	0.237464	−	0.730839i	0.00918089	−	0.0282559i
$670$		0			0
$671$	−8.57211	+	18.6174i	−0.330923	+	0.718718i
$672$		0			0
$673$	1.57477	+	0.511675i	0.0607031	+	0.0197236i	0.339211	−	0.940710i	$-0.389840\pi$
$673$	1.57477	+	0.511675i	0.0607031	+	0.0197236i	−0.278508	+	0.960434i	$0.589840\pi$
$674$		0			0
$675$	15.3379	+	13.8102i	0.590354	+	0.531554i
$676$		0			0
$677$	9.21996	−	2.99575i	0.354352	−	0.115136i	−0.126431	−	0.991975i	$-0.540352\pi$
$677$	9.21996	−	2.99575i	0.354352	−	0.115136i	0.480783	+	0.876839i	$0.340352\pi$
$678$		0			0
$679$	9.00970	−	6.54593i	0.345761	−	0.251210i
$680$		0			0
$681$	4.26608			0.163477
$682$		0			0
$683$		−	21.7907i		−	0.833796i	−0.908953	−	0.416898i	$-0.863117\pi$
$683$		−	21.7907i		−	0.833796i	0.908953	−	0.416898i	$-0.136883\pi$
$684$		0			0
$685$	26.2921	+	5.58853i	1.00457	+	0.213527i
$686$		0			0
$687$	−14.5926	+	4.74142i	−0.556742	+	0.180897i
$688$		0			0
$689$	2.56937	+	1.86676i	0.0978853	+	0.0711178i
$690$		0			0
$691$	−11.8700	+	36.5320i	−0.451554	+	1.38974i	0.423579	+	0.905859i	$0.360774\pi$
$691$	−11.8700	+	36.5320i	−0.451554	+	1.38974i	−0.875133	+	0.483882i	$0.839226\pi$
$692$		0			0
$693$	−4.51906	+	38.3362i	−0.171665	+	1.45627i
$694$		0			0
$695$	−6.05430	−	13.5981i	−0.229653	−	0.515807i
$696$		0			0
$697$	−4.58720	+	6.31374i	−0.173753	+	0.239150i
$698$		0			0
$699$	−2.37352	−	7.30495i	−0.0897748	−	0.276299i
$700$		0			0
$701$	−7.14600	+	5.19187i	−0.269901	+	0.196094i	−0.714500	−	0.699635i	$-0.753346\pi$
$701$	−7.14600	+	5.19187i	−0.269901	+	0.196094i	0.444600	+	0.895729i	$0.353346\pi$
$702$		0			0
$703$		−	38.6887i		−	1.45917i
$704$		0			0
$705$	12.2335	−	11.0151i	0.460739	−	0.414853i
$706$		0			0
$707$	−40.5571	−	55.8221i	−1.52531	−	2.09941i
$708$		0			0
$709$	−1.42580	−	4.38818i	−0.0535472	−	0.164801i	0.920707	−	0.390256i	$-0.127613\pi$
$709$	−1.42580	−	4.38818i	−0.0535472	−	0.164801i	−0.974254	+	0.225454i	$0.927613\pi$
$710$		0			0
$711$	10.6301	+	7.72321i	0.398659	+	0.289643i
$712$		0			0
$713$	−0.121325	−	0.0394210i	−0.00454367	−	0.00147633i
$714$		0			0
$715$	0.273675	−	21.6899i	0.0102348	−	0.811157i
$716$		0			0
$717$	−1.19165	−	0.387191i	−0.0445030	−	0.0144599i
$718$		0			0
$719$	−0.974716	−	0.708173i	−0.0363508	−	0.0264104i	0.569462	−	0.822018i	$-0.307152\pi$
$719$	−0.974716	−	0.708173i	−0.0363508	−	0.0264104i	−0.605812	+	0.795608i	$0.707152\pi$
$720$		0			0
$721$	−1.10652	−	3.40551i	−0.0412089	−	0.126828i
$722$		0			0
$723$	1.10603	+	1.52232i	0.0411338	+	0.0566158i
$724$		0			0
$725$	2.73673	−	26.0390i	0.101640	−	0.967065i
$726$		0			0
$727$			9.92301i			0.368024i	0.982924	+	0.184012i	$0.0589085\pi$
$727$			9.92301i			0.368024i	−0.982924	+	0.184012i	$0.941091\pi$
$728$		0			0
$729$	−0.428794	+	0.311537i	−0.0158813	+	0.0115384i
$730$		0			0
$731$	−3.89358	−	11.9832i	−0.144009	−	0.443215i
$732$		0			0
$733$	17.1392	−	23.5900i	0.633049	−	0.871318i	−0.365172	−	0.930940i	$-0.618990\pi$
$733$	17.1392	−	23.5900i	0.633049	−	0.871318i	0.998221	+	0.0596224i	$0.0189897\pi$
$734$		0			0
$735$	25.0959	−	11.1735i	0.925677	−	0.412140i
$736$		0			0
$737$	−33.9282	+	36.7381i	−1.24976	+	1.35326i
$738$		0			0
$739$	−0.418431	+	1.28780i	−0.0153922	+	0.0473724i	−0.958458	−	0.285235i	$-0.907928\pi$
$739$	−0.418431	+	1.28780i	−0.0153922	+	0.0473724i	0.943065	+	0.332607i	$0.107928\pi$
$740$		0			0
$741$	−7.81216	−	5.67586i	−0.286987	−	0.208508i
$742$		0			0
$743$	33.9985	−	11.0468i	1.24728	−	0.405267i	0.390337	−	0.920672i	$-0.372359\pi$
$743$	33.9985	−	11.0468i	1.24728	−	0.405267i	0.856947	+	0.515405i	$0.172359\pi$
$744$		0			0
$745$	−6.98606	+	32.8671i	−0.255949	+	1.20416i
$746$		0			0
$747$			21.1556i			0.774043i
$748$		0			0
$749$	−30.2429			−1.10505
$750$		0			0
$751$	36.2063	−	26.3054i	1.32119	−	0.959899i	0.321271	−	0.946987i	$-0.395890\pi$
$751$	36.2063	−	26.3054i	1.32119	−	0.959899i	0.999917	−	0.0129112i	$-0.00410989\pi$
$752$		0			0
$753$	−1.08484	+	0.352487i	−0.0395339	+	0.0128453i
$754$		0			0
$755$	45.1450	−	4.74500i	1.64299	−	0.172688i
$756$		0			0
$757$	29.6866	+	9.64576i	1.07898	+	0.350581i	0.793978	−	0.607947i	$-0.208007\pi$
$757$	29.6866	+	9.64576i	1.07898	+	0.350581i	0.284999	+	0.958528i	$0.408007\pi$
$758$		0			0
$759$	−0.274162	−	0.0323181i	−0.00995145	−	0.00117307i
$760$		0			0
$761$	−10.4937	+	32.2961i	−0.380395	+	1.17073i	0.559372	+	0.828917i	$0.311042\pi$
$761$	−10.4937	+	32.2961i	−0.380395	+	1.17073i	−0.939766	+	0.341817i	$0.888958\pi$
$762$		0			0
$763$	−7.78826	+	10.7196i	−0.281954	+	0.388076i
$764$		0			0
$765$	4.97037	−	8.60896i	0.179704	−	0.311258i
$766$		0			0
$767$	11.9059	+	16.3871i	0.429899	+	0.591705i
$768$		0			0
$769$	13.4436			0.484787			0.242393	−	0.970178i	$-0.422068\pi$
$769$	13.4436			0.484787			0.242393	+	0.970178i	$0.422068\pi$
$770$		0			0
$771$	−23.5533			−0.848250
$772$		0			0
$773$	16.4009	+	22.5740i	0.589901	+	0.811929i	0.994737	−	0.102461i	$-0.0326715\pi$
$773$	16.4009	+	22.5740i	0.589901	+	0.811929i	−0.404836	+	0.914389i	$0.632672\pi$
$774$		0			0
$775$	−5.70866	+	1.21343i	−0.205061	+	0.0435878i
$776$		0			0
$777$	−19.2152	+	26.4474i	−0.689341	+	0.948797i
$778$		0			0
$779$	−5.69072	+	17.5142i	−0.203891	+	0.627513i
$780$		0			0
$781$	5.39457	−	11.7163i	0.193033	−	0.419241i
$782$		0			0
$783$	−20.5573	−	6.67948i	−0.734659	−	0.238705i
$784$		0			0
$785$	0.312079	+	2.96919i	0.0111386	+	0.105975i
$786$		0			0
$787$	22.7773	−	7.40080i	0.811924	−	0.263810i	0.126512	−	0.991965i	$-0.459622\pi$
$787$	22.7773	−	7.40080i	0.811924	−	0.263810i	0.685412	+	0.728155i	$0.259622\pi$
$788$		0			0
$789$	−5.82644	+	4.23315i	−0.207427	+	0.150704i
$790$		0			0
$791$	−67.0787			−2.38504
$792$		0			0
$793$		−	18.0753i		−	0.641873i
$794$		0			0
$795$	0.384452	−	1.80872i	0.0136351	−	0.0641485i
$796$		0			0
$797$	−20.6195	+	6.69969i	−0.730381	+	0.237315i	−0.650518	−	0.759491i	$-0.725448\pi$
$797$	−20.6195	+	6.69969i	−0.730381	+	0.237315i	−0.0798631	+	0.996806i	$0.525448\pi$
$798$		0			0
$799$	−14.3665	−	10.4379i	−0.508249	−	0.369265i
$800$		0			0
$801$	9.46746	−	29.1378i	0.334516	−	1.02954i
$802$		0			0
$803$	47.1092	−	9.39369i	1.66245	−	0.331496i
$804$		0			0
$805$	−0.478061	−	1.07374i	−0.0168494	−	0.0378443i
$806$		0			0
$807$	7.86746	−	10.8286i	0.276948	−	0.381186i
$808$		0			0
$809$	14.5275	+	44.7109i	0.510759	+	1.57195i	0.790869	+	0.611985i	$0.209629\pi$
$809$	14.5275	+	44.7109i	0.510759	+	1.57195i	−0.280111	+	0.959968i	$0.590371\pi$
$810$		0			0
$811$	−11.5006	+	8.35565i	−0.403839	+	0.293407i	−0.771103	−	0.636710i	$-0.780295\pi$
$811$	−11.5006	+	8.35565i	−0.403839	+	0.293407i	0.367264	+	0.930117i	$0.380295\pi$
$812$		0			0
$813$			5.60426i			0.196550i
$814$		0			0
$815$	−18.5906	−	20.6469i	−0.651202	−	0.723230i
$816$		0			0
$817$	−17.4760	−	24.0536i	−0.611407	−	0.841530i
$818$		0			0
$819$	−10.5197	−	32.3763i	−0.367588	−	1.13132i
$820$		0			0
$821$	23.3555	+	16.9688i	0.815114	+	0.592215i	0.915309	−	0.402753i	$-0.131947\pi$
$821$	23.3555	+	16.9688i	0.815114	+	0.592215i	−0.100195	+	0.994968i	$0.531947\pi$
$822$		0			0
$823$	21.9288	+	7.12510i	0.764390	+	0.248365i	0.665162	−	0.746699i	$-0.268363\pi$
$823$	21.9288	+	7.12510i	0.764390	+	0.248365i	0.0992284	+	0.995065i	$0.468363\pi$
$824$		0			0
$825$	−11.6016	+	4.99096i	−0.403915	+	0.173763i
$826$		0			0
$827$	13.4562	+	4.37218i	0.467918	+	0.152036i	0.533480	−	0.845813i	$-0.320884\pi$
$827$	13.4562	+	4.37218i	0.467918	+	0.152036i	−0.0655620	+	0.997848i	$0.520884\pi$
$828$		0			0
$829$	−12.5848	−	9.14336i	−0.437087	−	0.317562i	0.347390	−	0.937721i	$-0.387068\pi$
$829$	−12.5848	−	9.14336i	−0.437087	−	0.317562i	−0.784476	+	0.620159i	$0.787068\pi$
$830$		0			0
$831$	−2.74287	−	8.44168i	−0.0951491	−	0.292839i
$832$		0			0
$833$	−17.4184	−	23.9743i	−0.603511	−	0.830662i
$834$		0			0
$835$	−12.1102	−	13.4497i	−0.419091	−	0.465446i
$836$		0			0
$837$			4.81815i			0.166540i
$838$		0			0
$839$	−10.5380	+	7.65634i	−0.363814	+	0.264326i	−0.754641	−	0.656138i	$-0.772189\pi$
$839$	−10.5380	+	7.65634i	−0.363814	+	0.264326i	0.390827	+	0.920464i	$0.372189\pi$
$840$		0			0
$841$	−0.487997	−	1.50190i	−0.0168275	−	0.0517896i
$842$		0			0
$843$	12.8173	−	17.6416i	0.441453	−	0.607608i
$844$		0			0
$845$	−4.04265	−	9.07991i	−0.139071	−	0.312358i
$846$		0			0
$847$	−45.1344	−	27.5999i	−1.55084	−	0.948343i
$848$		0			0
$849$	−5.64203	+	17.3644i	−0.193634	+	0.595944i
$850$		0			0
$851$	0.789128	+	0.573335i	0.0270509	+	0.0196537i
$852$		0			0
$853$	−19.8443	+	6.44781i	−0.679456	+	0.220769i	−0.628357	−	0.777925i	$-0.716272\pi$
$853$	−19.8443	+	6.44781i	−0.679456	+	0.220769i	−0.0510990	+	0.998694i	$0.516272\pi$
$854$		0			0
$855$	4.87698	−	22.9446i	0.166789	−	0.784688i
$856$		0			0
$857$		−	43.8589i		−	1.49819i	−0.662463	−	0.749095i	$-0.730489\pi$
$857$		−	43.8589i		−	1.49819i	0.662463	−	0.749095i	$-0.269511\pi$
$858$		0			0
$859$	25.0949			0.856228			0.428114	−	0.903725i	$-0.359178\pi$
$859$	25.0949			0.856228			0.428114	+	0.903725i	$0.359178\pi$
$860$		0			0
$861$	12.5888	−	9.14631i	0.429026	−	0.311705i
$862$		0			0
$863$	21.8390	−	7.09591i	0.743407	−	0.241548i	0.0872654	−	0.996185i	$-0.472187\pi$
$863$	21.8390	−	7.09591i	0.743407	−	0.241548i	0.656142	+	0.754637i	$0.272187\pi$
$864$		0			0
$865$	−4.92384	−	46.8465i	−0.167416	−	1.59283i
$866$		0			0
$867$	−9.86898	−	3.20663i	−0.335168	−	0.108903i
$868$		0			0
$869$	−15.7077	+	8.80647i	−0.532847	+	0.298739i
$870$		0			0
$871$	13.6282	−	41.9432i	0.461773	−	1.42119i
$872$		0			0
$873$	−3.29370	+	4.53339i	−0.111475	+	0.153432i
$874$		0			0
$875$	−43.5024	−	31.6060i	−1.47065	−	1.06848i
$876$		0			0
$877$	−3.29334	−	4.53289i	−0.111208	−	0.153065i	0.749785	−	0.661682i	$-0.230157\pi$
$877$	−3.29334	−	4.53289i	−0.111208	−	0.153065i	−0.860993	+	0.508617i	$0.830157\pi$
$878$		0			0
$879$	−6.65364			−0.224422
$880$		0			0
$881$	−7.93724			−0.267412			−0.133706	−	0.991021i	$-0.542688\pi$
$881$	−7.93724			−0.267412			−0.133706	+	0.991021i	$0.542688\pi$
$882$		0			0
$883$	6.72079	+	9.25037i	0.226172	+	0.311300i	0.906989	−	0.421154i	$-0.138375\pi$
$883$	6.72079	+	9.25037i	0.226172	+	0.311300i	−0.680817	+	0.732454i	$0.738375\pi$
$884$		0			0
$885$	5.89672	−	10.2135i	0.198216	−	0.343321i
$886$		0			0
$887$	−7.83793	+	10.7880i	−0.263172	+	0.362225i	−0.920070	−	0.391754i	$-0.871868\pi$
$887$	−7.83793	+	10.7880i	−0.263172	+	0.362225i	0.656898	+	0.753980i	$0.271868\pi$
$888$		0			0
$889$	−9.83153	+	30.2583i	−0.329739	+	1.01483i
$890$		0			0
$891$	−2.66968	−	13.3884i	−0.0894376	−	0.448528i
$892$		0			0
$893$	−39.8524	−	12.9488i	−1.33361	−	0.433316i
$894$		0			0
$895$	−49.4339	+	5.19579i	−1.65239	+	0.173676i
$896$		0			0
$897$	0.231540	−	0.0752318i	0.00773088	−	0.00251192i
$898$		0			0
$899$	4.94491	−	3.59269i	0.164922	−	0.119823i
$900$		0			0
$901$	−1.99472			−0.0664537
$902$		0			0
$903$			25.1226i			0.836029i
$904$		0			0
$905$	−2.28186	+	10.7354i	−0.0758515	+	0.356856i
$906$		0			0
$907$	37.0248	−	12.0301i	1.22939	−	0.399453i	0.378897	−	0.925439i	$-0.376304\pi$
$907$	37.0248	−	12.0301i	1.22939	−	0.399453i	0.850493	+	0.525986i	$0.176304\pi$
$908$		0			0
$909$	28.0879	+	20.4070i	0.931615	+	0.676858i
$910$		0			0
$911$	−11.4970	+	35.3840i	−0.380912	+	1.17233i	0.558491	+	0.829510i	$0.311380\pi$
$911$	−11.4970	+	35.3840i	−0.380912	+	1.17233i	−0.939403	+	0.342815i	$0.888620\pi$
$912$		0			0
$913$	−26.3366	−	12.1263i	−0.871613	−	0.401321i
$914$		0			0
$915$	−9.61418	+	4.28052i	−0.317835	+	0.141510i
$916$		0			0
$917$	41.2631	−	56.7938i	1.36263	−	1.87550i
$918$		0			0
$919$	6.35621	+	19.5624i	0.209672	+	0.645305i	0.999489	+	0.0319619i	$0.0101755\pi$
$919$	6.35621	+	19.5624i	0.209672	+	0.645305i	−0.789817	+	0.613343i	$0.789824\pi$
$920$		0			0
$921$	4.23292	−	3.07540i	0.139480	−	0.101338i
$922$		0			0
$923$			11.3751i			0.374416i
$924$		0			0
$925$	44.3802	+	4.66441i	1.45921	+	0.153365i
$926$		0			0
$927$	1.05903	+	1.45763i	0.0347830	+	0.0478747i
$928$		0			0
$929$	5.42422	+	16.6940i	0.177963	+	0.547713i	0.999756	−	0.0220722i	$-0.00702638\pi$
$929$	5.42422	+	16.6940i	0.177963	+	0.547713i	−0.821794	+	0.569785i	$0.807026\pi$
$930$		0			0
$931$	−56.5721	−	41.1020i	−1.85408	−	1.34707i
$932$		0			0
$933$	10.4857	+	3.40700i	0.343285	+	0.111540i
$934$		0			0
$935$	7.86829	+	11.1222i	0.257321	+	0.363735i
$936$		0			0
$937$	50.7254	+	16.4817i	1.65713	+	0.538434i	0.980267	−	0.197677i	$-0.0633398\pi$
$937$	50.7254	+	16.4817i	1.65713	+	0.538434i	0.676861	+	0.736111i	$0.263340\pi$
$938$		0			0
$939$	−16.6404	−	12.0900i	−0.543039	−	0.394541i
$940$		0			0
$941$	−13.7754	−	42.3965i	−0.449067	−	1.38209i	−0.877962	−	0.478731i	$-0.841097\pi$
$941$	−13.7754	−	42.3965i	−0.449067	−	1.38209i	0.428895	−	0.903354i	$-0.358903\pi$
$942$		0			0
$943$	−0.272904	−	0.375620i	−0.00888697	−	0.0122319i
$944$		0			0
$945$	−32.9896	+	29.7040i	−1.07315	+	0.966272i
$946$		0			0
$947$			35.1770i			1.14310i	0.820567	+	0.571550i	$0.193658\pi$
$947$			35.1770i			1.14310i	−0.820567	+	0.571550i	$0.806342\pi$
$948$		0			0
$949$	−34.2724	+	24.9004i	−1.11253	+	0.808301i
$950$		0			0
$951$	6.91579	+	21.2846i	0.224260	+	0.690201i
$952$		0			0
$953$	−35.9080	+	49.4231i	−1.16317	+	1.60097i	−0.464404	+	0.885624i	$0.653731\pi$
$953$	−35.9080	+	49.4231i	−1.16317	+	1.60097i	−0.698770	+	0.715347i	$0.746269\pi$
$954$		0			0
$955$	−9.70677	−	21.8017i	−0.314104	−	0.705485i
$956$		0			0
$957$	8.97387	−	9.71707i	0.290084	−	0.314108i
$958$		0			0
$959$	−17.8656	+	54.9847i	−0.576910	+	1.77555i
$960$		0			0
$961$	23.9773	+	17.4205i	0.773461	+	0.561952i
$962$		0			0
$963$	14.4724	−	4.70238i	0.466368	−	0.151532i
$964$		0			0
$965$	11.9796	+	2.54632i	0.385636	+	0.0819689i
$966$		0			0
$967$		−	18.8968i		−	0.607680i	−0.952723	−	0.303840i	$-0.901731\pi$
$967$		−	18.8968i		−	0.607680i	0.952723	−	0.303840i	$-0.0982688\pi$
$968$		0			0
$969$	6.06492			0.194833
$970$		0			0
$971$	−25.5089	+	18.5333i	−0.818620	+	0.594763i	−0.916317	−	0.400454i	$-0.868853\pi$
$971$	−25.5089	+	18.5333i	−0.818620	+	0.594763i	0.0976966	+	0.995216i	$0.468853\pi$
$972$		0			0
$973$	30.4488	−	9.89340i	0.976142	−	0.317168i
$974$		0			0
$975$	7.45270	−	8.27711i	0.238677	−	0.265080i
$976$		0			0
$977$	−44.0374	−	14.3086i	−1.40888	−	0.457774i	−0.496830	−	0.867848i	$-0.665503\pi$
$977$	−44.0374	−	14.3086i	−1.40888	−	0.457774i	−0.912052	+	0.410074i	$0.865503\pi$
$978$		0			0
$979$	30.8470	+	28.4877i	0.985873	+	0.910470i
$980$		0			0
$981$	2.06023	−	6.34075i	0.0657782	−	0.202445i
$982$		0			0
$983$	10.3360	−	14.2263i	0.329667	−	0.453747i	−0.611721	−	0.791073i	$-0.709523\pi$
$983$	10.3360	−	14.2263i	0.329667	−	0.453747i	0.941388	+	0.337326i	$0.109523\pi$
$984$		0			0
$985$	−3.29043	+	5.69921i	−0.104842	+	0.181592i
$986$		0			0
$987$	20.8118	+	28.6449i	0.662446	+	0.911779i
$988$		0			0
$989$	0.749599			0.0238358
$990$		0			0
$991$	28.9590			0.919912			0.459956	−	0.887942i	$-0.347865\pi$
$991$	28.9590			0.919912			0.459956	+	0.887942i	$0.347865\pi$
$992$		0			0
$993$	8.78725	+	12.0946i	0.278855	+	0.383811i
$994$		0			0
$995$	−5.75282	−	3.32138i	−0.182377	−	0.105295i
$996$		0			0
$997$	5.20788	−	7.16803i	0.164935	−	0.227014i	−0.718547	−	0.695478i	$-0.755193\pi$
$997$	5.20788	−	7.16803i	0.164935	−	0.227014i	0.883482	+	0.468464i	$0.155193\pi$
$998$		0			0
$999$	11.3843	−	35.0373i	0.360184	−	1.10853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.t.a.9.4	yes	24
4.3	odd	2		880.2.cd.d.449.3		24
5.2	odd	4		1100.2.n.f.801.4		24
5.3	odd	4		1100.2.n.f.801.3		24
5.4	even	2	inner	220.2.t.a.9.3	✓	24
11.4	even	5		2420.2.b.i.969.6		12
11.5	even	5	inner	220.2.t.a.49.3	yes	24
11.7	odd	10		2420.2.b.h.969.6		12
20.19	odd	2		880.2.cd.d.449.4		24
44.27	odd	10		880.2.cd.d.49.4		24
55.4	even	10		2420.2.b.i.969.7		12
55.27	odd	20		1100.2.n.f.401.4		24
55.29	odd	10		2420.2.b.h.969.7		12
55.38	odd	20		1100.2.n.f.401.3		24
55.49	even	10	inner	220.2.t.a.49.4	yes	24
220.159	odd	10		880.2.cd.d.49.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.t.a.9.3	✓	24	5.4	even	2	inner
220.2.t.a.9.4	yes	24	1.1	even	1	trivial
220.2.t.a.49.3	yes	24	11.5	even	5	inner
220.2.t.a.49.4	yes	24	55.49	even	10	inner
880.2.cd.d.49.3		24	220.159	odd	10
880.2.cd.d.49.4		24	44.27	odd	10
880.2.cd.d.449.3		24	4.3	odd	2
880.2.cd.d.449.4		24	20.19	odd	2
1100.2.n.f.401.3		24	55.38	odd	20
1100.2.n.f.401.4		24	55.27	odd	20
1100.2.n.f.801.3		24	5.3	odd	4
1100.2.n.f.801.4		24	5.2	odd	4
2420.2.b.h.969.6		12	11.7	odd	10
2420.2.b.h.969.7		12	55.29	odd	10
2420.2.b.i.969.6		12	11.4	even	5
2420.2.b.i.969.7		12	55.4	even	10

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.t (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.447653 + 0.616141i) q^{3} +(1.93649 + 1.11803i) q^{5} +(-2.82695 + 3.89096i) q^{7} +(0.747814 - 2.30153i) q^{9} +(2.43653 + 2.25018i) q^{11} +(-2.78175 - 0.903845i) q^{13} +(0.178012 + 1.69364i) q^{15} +(1.74715 - 0.567683i) q^{17} +(3.50701 - 2.54799i) q^{19} -3.66287 q^{21} +0.109291i q^{23} +(2.50001 + 4.33012i) q^{25} +(3.92578 - 1.27556i) q^{27} +(-4.23641 - 3.07793i) q^{29} +(-0.360697 + 1.11011i) q^{31} +(-0.295707 + 2.50855i) q^{33} +(-9.82457 + 4.37420i) q^{35} +(5.24594 - 7.22042i) q^{37} +(-0.688361 - 2.11856i) q^{39} +(-3.43687 + 2.49703i) q^{41} -6.85873i q^{43} +(4.02132 - 3.62083i) q^{45} +(-5.68182 - 7.82036i) q^{47} +(-4.98480 - 15.3416i) q^{49} +(1.13189 + 0.822365i) q^{51} +(-1.03268 - 0.335537i) q^{53} +(2.20256 + 7.08158i) q^{55} +(3.13985 + 1.02020i) q^{57} +(-5.60263 - 4.07055i) q^{59} +(1.90966 + 5.87734i) q^{61} +(6.84114 + 9.41602i) q^{63} +(-4.37631 - 4.86037i) q^{65} +15.0780i q^{67} +(-0.0673388 + 0.0489245i) q^{69} +(-1.20178 - 3.69871i) q^{71} +(8.51324 - 11.7175i) q^{73} +(-1.54883 + 3.47875i) q^{75} +(-15.6433 + 3.11931i) q^{77} +(-1.67784 + 5.16385i) q^{79} +(-3.33009 - 2.41945i) q^{81} +(-8.31420 + 2.70145i) q^{83} +(4.01803 + 0.854052i) q^{85} -3.98807i q^{87} +12.6602 q^{89} +(11.3807 - 8.26854i) q^{91} +(-0.845453 + 0.274704i) q^{93} +(9.64003 - 1.01322i) q^{95} +(-2.20222 - 0.715544i) q^{97} +(7.00094 - 3.92505i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{5} + 14 q^{9} - 2 q^{11} - q^{15} + 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} - 26 q^{31} + 17 q^{35} + 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} - 12 q^{51} - 33 q^{55} - 48 q^{59} - 10 q^{61}+ \cdots + 156 q^{99}+O(q^{100}) \) 24 * q + q^5 + 14 * q^9 - 2 * q^11 - q^15 + 8 * q^19 - 28 * q^21 + 27 * q^25 - 16 * q^29 - 26 * q^31 + 17 * q^35 + 12 * q^39 + 10 * q^41 - 40 * q^45 - 46 * q^49 - 12 * q^51 - 33 * q^55 - 48 * q^59 - 10 * q^61 - 22 * q^65 - 58 * q^69 + 42 * q^71 - 17 * q^75 - 64 * q^79 + 36 * q^81 - 17 * q^85 + 72 * q^89 + 10 * q^91 + 67 * q^95 + 156 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more