LMFDB - Embedded newform 810.3.j.h.539.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.5
Character	$\chi$	$=$	810.539
Dual form			810.3.j.h.269.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-4.91871 - 0.897918i) q^{5} +(8.15650 - 4.70916i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-4.91871 - 0.897918i) q^{5} +(8.15650 - 4.70916i) q^{7} +2.82843 q^{8} +(2.37833 + 6.65909i) q^{10} +(2.03913 - 1.17729i) q^{11} +(1.33223 + 0.769165i) q^{13} +(-11.5350 - 6.65975i) q^{14} +(-2.00000 - 3.46410i) q^{16} -11.0873 q^{17} +7.09220 q^{19} +(6.47395 - 7.62154i) q^{20} +(-2.88377 - 1.66494i) q^{22} +(-4.09795 + 7.09786i) q^{23} +(23.3875 + 8.83321i) q^{25} -2.17553i q^{26} +18.8366i q^{28} +(15.5447 - 8.97476i) q^{29} +(29.3583 - 50.8500i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(7.83988 + 13.5791i) q^{34} +(-44.3479 + 15.8391i) q^{35} +20.7943i q^{37} +(-5.01495 - 8.68614i) q^{38} +(-13.9122 - 2.53970i) q^{40} +(42.3552 + 24.4538i) q^{41} +(3.07880 - 1.77754i) q^{43} +4.70917i q^{44} +11.5908 q^{46} +(-34.8853 - 60.4231i) q^{47} +(19.8523 - 34.3852i) q^{49} +(-5.71902 - 34.8897i) q^{50} +(-2.66447 + 1.53833i) q^{52} -69.0100 q^{53} +(-11.0870 + 3.95979i) q^{55} +(23.0701 - 13.3195i) q^{56} +(-21.9836 - 12.6922i) q^{58} +(-34.0732 - 19.6721i) q^{59} +(-57.8340 - 100.172i) q^{61} -83.0377 q^{62} +8.00000 q^{64} +(-5.86222 - 4.97954i) q^{65} +(-88.8111 - 51.2751i) q^{67} +(11.0873 - 19.2037i) q^{68} +(50.7576 + 43.1149i) q^{70} -102.667i q^{71} +120.613i q^{73} +(25.4677 - 14.7038i) q^{74} +(-7.09220 + 12.2841i) q^{76} +(11.0881 - 19.2052i) q^{77} +(9.13011 + 15.8138i) q^{79} +(6.72695 + 18.8348i) q^{80} -69.1657i q^{82} +(-80.9703 - 140.245i) q^{83} +(54.5351 + 9.95546i) q^{85} +(-4.35408 - 2.51383i) q^{86} +(5.76753 - 3.32989i) q^{88} -88.2337i q^{89} +14.4885 q^{91} +(-8.19590 - 14.1957i) q^{92} +(-49.3353 + 85.4512i) q^{94} +(-34.8845 - 6.36822i) q^{95} +(121.781 - 70.3100i) q^{97} -56.1508 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 24 q^{7}+O(q^{10}) $ 24 * q - 24 * q^4 + 24 * q^7	$ 24 q - 24 q^{4} + 24 q^{7} - 12 q^{10} + 48 q^{13} - 48 q^{16} - 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{40} - 24 q^{43} - 36 q^{49} - 96 q^{52} + 216 q^{55} + 396 q^{58} - 60 q^{61} + 192 q^{64} - 1032 q^{67} + 288 q^{70} - 240 q^{79} - 48 q^{85} + 240 q^{88} + 48 q^{91} - 48 q^{94} - 1440 q^{97}+O(q^{100}) $ 24 * q - 24 * q^4 + 24 * q^7 - 12 * q^10 + 48 * q^13 - 48 * q^16 - 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^40 - 24 * q^43 - 36 * q^49 - 96 * q^52 + 216 * q^55 + 396 * q^58 - 60 * q^61 + 192 * q^64 - 1032 * q^67 + 288 * q^70 - 240 * q^79 - 48 * q^85 + 240 * q^88 + 48 * q^91 - 48 * q^94 - 1440 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−4.91871	−	0.897918i	−0.983743	−	0.179584i
$5$	−4.91871	−	0.897918i	−0.983743	−	0.179584i
$6$		0			0
$7$	8.15650	−	4.70916i	1.16521	−	0.672737i	0.212666	−	0.977125i	$-0.431785\pi$
$7$	8.15650	−	4.70916i	1.16521	−	0.672737i	0.952548	+	0.304388i	$0.0984520\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	2.37833	+	6.65909i	0.237833	+	0.665909i
$11$	2.03913	−	1.17729i	0.185375	−	0.107027i	−0.404440	−	0.914564i	$-0.632534\pi$
$11$	2.03913	−	1.17729i	0.185375	−	0.107027i	0.589816	+	0.807538i	$0.299200\pi$
$12$		0			0
$13$	1.33223	+	0.769165i	0.102479	+	0.0591665i	0.550364	−	0.834925i	$-0.314489\pi$
$13$	1.33223	+	0.769165i	0.102479	+	0.0591665i	−0.447884	+	0.894092i	$0.647822\pi$
$14$	−11.5350	−	6.65975i	−0.823931	−	0.475697i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−11.0873			−0.652192			−0.326096	−	0.945337i	$-0.605733\pi$
$17$	−11.0873			−0.652192			−0.326096	+	0.945337i	$0.605733\pi$
$18$		0			0
$19$	7.09220			0.373274			0.186637	−	0.982429i	$-0.440241\pi$
$19$	7.09220			0.373274			0.186637	+	0.982429i	$0.440241\pi$
$20$	6.47395	−	7.62154i	0.323698	−	0.381077i
$21$		0			0
$22$	−2.88377	−	1.66494i	−0.131080	−	0.0756792i
$23$	−4.09795	+	7.09786i	−0.178172	+	0.308603i	−0.941254	−	0.337698i	$-0.890352\pi$
$23$	−4.09795	+	7.09786i	−0.178172	+	0.308603i	0.763083	+	0.646301i	$0.223685\pi$
$24$		0			0
$25$	23.3875	+	8.83321i	0.935499	+	0.353328i
$26$		−	2.17553i		−	0.0836741i
$27$		0			0
$28$			18.8366i			0.672737i
$29$	15.5447	−	8.97476i	0.536025	−	0.309474i	−0.207441	−	0.978247i	$-0.566514\pi$
$29$	15.5447	−	8.97476i	0.536025	−	0.309474i	0.743467	+	0.668773i	$0.233180\pi$
$30$		0			0
$31$	29.3583	−	50.8500i	0.947041	−	1.64032i	0.195428	−	0.980718i	$-0.437390\pi$
$31$	29.3583	−	50.8500i	0.947041	−	1.64032i	0.751613	−	0.659605i	$-0.229276\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$	7.83988	+	13.5791i	0.230585	+	0.399384i
$35$	−44.3479	+	15.8391i	−1.26708	+	0.452546i
$36$		0			0
$37$			20.7943i			0.562007i	0.959707	+	0.281004i	$0.0906673\pi$
$37$			20.7943i			0.562007i	−0.959707	+	0.281004i	$0.909333\pi$
$38$	−5.01495	−	8.68614i	−0.131972	−	0.228583i
$39$		0			0
$40$	−13.9122	−	2.53970i	−0.347806	−	0.0634924i
$41$	42.3552	+	24.4538i	1.03305	+	0.596433i	0.917858	−	0.396909i	$-0.129917\pi$
$41$	42.3552	+	24.4538i	1.03305	+	0.596433i	0.115195	+	0.993343i	$0.463251\pi$
$42$		0			0
$43$	3.07880	−	1.77754i	0.0715999	−	0.0413382i	−0.463773	−	0.885954i	$-0.653505\pi$
$43$	3.07880	−	1.77754i	0.0715999	−	0.0413382i	0.535373	+	0.844616i	$0.320171\pi$
$44$			4.70917i			0.107027i
$45$		0			0
$46$	11.5908			0.251973
$47$	−34.8853	−	60.4231i	−0.742241	−	1.28560i	−0.951473	−	0.307733i	$-0.900430\pi$
$47$	−34.8853	−	60.4231i	−0.742241	−	1.28560i	0.209232	−	0.977866i	$-0.432904\pi$
$48$		0			0
$49$	19.8523	−	34.3852i	0.405149	−	0.701739i
$50$	−5.71902	−	34.8897i	−0.114380	−	0.697794i
$51$		0			0
$52$	−2.66447	+	1.53833i	−0.0512397	+	0.0295833i
$53$	−69.0100			−1.30208			−0.651038	−	0.759045i	$-0.725666\pi$
$53$	−69.0100			−1.30208			−0.651038	+	0.759045i	$0.725666\pi$
$54$		0			0
$55$	−11.0870	+	3.95979i	−0.201582	+	0.0719962i
$56$	23.0701	−	13.3195i	0.411965	−	0.237848i
$57$		0			0
$58$	−21.9836	−	12.6922i	−0.379027	−	0.218831i
$59$	−34.0732	−	19.6721i	−0.577511	−	0.333426i	0.182633	−	0.983181i	$-0.441538\pi$
$59$	−34.0732	−	19.6721i	−0.577511	−	0.333426i	−0.760144	+	0.649755i	$0.774871\pi$
$60$		0			0
$61$	−57.8340	−	100.172i	−0.948099	−	1.64216i	−0.749424	−	0.662091i	$-0.769669\pi$
$61$	−57.8340	−	100.172i	−0.948099	−	1.64216i	−0.198675	−	0.980065i	$-0.563664\pi$
$62$	−83.0377			−1.33932
$63$		0			0
$64$	8.00000			0.125000
$65$	−5.86222	−	4.97954i	−0.0901881	−	0.0766083i
$66$		0			0
$67$	−88.8111	−	51.2751i	−1.32554	−	0.765300i	−0.340933	−	0.940088i	$-0.610743\pi$
$67$	−88.8111	−	51.2751i	−1.32554	−	0.765300i	−0.984606	+	0.174788i	$0.944076\pi$
$68$	11.0873	−	19.2037i	0.163048	−	0.282407i
$69$		0			0
$70$	50.7576	+	43.1149i	0.725109	+	0.615928i
$71$		−	102.667i		−	1.44601i	−0.690842	−	0.723006i	$-0.742760\pi$
$71$		−	102.667i		−	1.44601i	0.690842	−	0.723006i	$-0.257240\pi$
$72$		0			0
$73$			120.613i			1.65223i	0.563503	+	0.826114i	$0.309453\pi$
$73$			120.613i			1.65223i	−0.563503	+	0.826114i	$0.690547\pi$
$74$	25.4677	−	14.7038i	0.344158	−	0.198700i
$75$		0			0
$76$	−7.09220	+	12.2841i	−0.0933185	+	0.161632i
$77$	11.0881	−	19.2052i	0.144001	−	0.249418i
$78$		0			0
$79$	9.13011	+	15.8138i	0.115571	+	0.200175i	0.918008	−	0.396562i	$-0.129797\pi$
$79$	9.13011	+	15.8138i	0.115571	+	0.200175i	−0.802437	+	0.596737i	$0.796464\pi$
$80$	6.72695	+	18.8348i	0.0840868	+	0.235435i
$81$		0			0
$82$		−	69.1657i		−	0.843484i
$83$	−80.9703	−	140.245i	−0.975546	−	1.68970i	−0.678120	−	0.734951i	$-0.737205\pi$
$83$	−80.9703	−	140.245i	−0.975546	−	1.68970i	−0.297426	−	0.954745i	$-0.596128\pi$
$84$		0			0
$85$	54.5351	+	9.95546i	0.641589	+	0.117123i
$86$	−4.35408	−	2.51383i	−0.0506288	−	0.0292305i
$87$		0			0
$88$	5.76753	−	3.32989i	0.0655401	−	0.0378396i
$89$		−	88.2337i		−	0.991390i	−0.868497	−	0.495695i	$-0.834913\pi$
$89$		−	88.2337i		−	0.991390i	0.868497	−	0.495695i	$-0.165087\pi$
$90$		0			0
$91$	14.4885			0.159214
$92$	−8.19590	−	14.1957i	−0.0890859	−	0.154301i
$93$		0			0
$94$	−49.3353	+	85.4512i	−0.524844	+	0.909056i
$95$	−34.8845	−	6.36822i	−0.367205	−	0.0670339i
$96$		0			0
$97$	121.781	−	70.3100i	1.25547	−	0.724846i	0.283279	−	0.959037i	$-0.408578\pi$
$97$	121.781	−	70.3100i	1.25547	−	0.724846i	0.972190	+	0.234192i	$0.0752444\pi$
$98$	−56.1508			−0.572968
$99$		0			0
$100$	−38.6870	+	31.6751i	−0.386870	+	0.316751i
$101$	47.6060	−	27.4854i	0.471347	−	0.272132i	−0.245456	−	0.969408i	$-0.578938\pi$
$101$	47.6060	−	27.4854i	0.471347	−	0.272132i	0.716803	+	0.697275i	$0.245604\pi$
$102$		0			0
$103$	12.3470	+	7.12857i	0.119874	+	0.0692094i	0.558738	−	0.829344i	$-0.311286\pi$
$103$	12.3470	+	7.12857i	0.119874	+	0.0692094i	−0.438864	+	0.898554i	$0.644619\pi$
$104$	3.76812	+	2.17553i	0.0362320	+	0.0209185i
$105$		0			0
$106$	48.7974	+	84.5196i	0.460353	+	0.797355i
$107$	81.9655			0.766033			0.383017	−	0.923741i	$-0.374885\pi$
$107$	81.9655			0.766033			0.383017	+	0.923741i	$0.374885\pi$
$108$		0			0
$109$	−112.498			−1.03209			−0.516044	−	0.856562i	$-0.672596\pi$
$109$	−112.498			−1.03209			−0.516044	+	0.856562i	$0.672596\pi$
$110$	12.6894	+	10.7788i	0.115358	+	0.0979887i
$111$		0			0
$112$	−32.6260	−	18.8366i	−0.291304	−	0.168184i
$113$	−44.9017	+	77.7720i	−0.397360	+	0.688248i	−0.993399	−	0.114707i	$-0.963407\pi$
$113$	−44.9017	+	77.7720i	−0.397360	+	0.688248i	0.596039	+	0.802955i	$0.296740\pi$
$114$		0			0
$115$	26.5299	−	31.2327i	0.230695	−	0.271589i
$116$			35.8990i			0.309474i
$117$		0			0
$118$			55.6412i			0.471536i
$119$	−90.4332	+	52.2116i	−0.759943	+	0.438753i
$120$		0			0
$121$	−57.7280	+	99.9878i	−0.477091	+	0.826345i
$122$	−81.7897	+	141.664i	−0.670407	+	1.16118i
$123$		0			0
$124$	58.7165	+	101.700i	0.473520	+	0.820161i
$125$	−107.105	−	64.4481i	−0.856839	−	0.515585i
$126$		0			0
$127$		−	88.3594i		−	0.695743i	−0.937542	−	0.347872i	$-0.886905\pi$
$127$		−	88.3594i		−	0.695743i	0.937542	−	0.347872i	$-0.113095\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.95345	+	10.7008i	−0.0150265	+	0.0823138i
$131$	150.462	+	86.8691i	1.14856	+	0.663123i	0.948537	−	0.316667i	$-0.102564\pi$
$131$	150.462	+	86.8691i	1.14856	+	0.663123i	0.200026	+	0.979791i	$0.435897\pi$
$132$		0			0
$133$	57.8475	−	33.3983i	0.434944	−	0.251115i
$134$			145.028i			1.08230i
$135$		0			0
$136$	−31.3595			−0.230585
$137$	−54.4790	−	94.3604i	−0.397657	−	0.688762i	0.595779	−	0.803148i	$-0.296843\pi$
$137$	−54.4790	−	94.3604i	−0.397657	−	0.688762i	−0.993436	+	0.114386i	$0.963510\pi$
$138$		0			0
$139$	66.6557	−	115.451i	0.479537	−	0.830583i	−0.520187	−	0.854052i	$-0.674138\pi$
$139$	66.6557	−	115.451i	0.479537	−	0.830583i	0.999725	+	0.0234692i	$0.00747116\pi$
$140$	16.9138	−	92.6520i	0.120813	−	0.661800i
$141$		0			0
$142$	−125.741	+	72.5964i	−0.885498	+	0.511242i
$143$	3.62213			0.0253296
$144$		0			0
$145$	−84.5187	+	30.1864i	−0.582888	+	0.208182i
$146$	147.720	−	85.2860i	1.01178	−	0.584151i
$147$		0			0
$148$	−36.0167	−	20.7943i	−0.243356	−	0.140502i
$149$	107.431	+	62.0253i	0.721013	+	0.416277i	0.815125	−	0.579285i	$-0.196668\pi$
$149$	107.431	+	62.0253i	0.721013	+	0.416277i	−0.0941124	+	0.995562i	$0.530001\pi$
$150$		0			0
$151$	−6.81915	−	11.8111i	−0.0451600	−	0.0782193i	0.842562	−	0.538600i	$-0.181046\pi$
$151$	−6.81915	−	11.8111i	−0.0451600	−	0.0782193i	−0.887722	+	0.460380i	$0.847713\pi$
$152$	20.0598			0.131972
$153$		0			0
$154$	−31.3619			−0.203649
$155$	−190.064	+	223.755i	−1.22622	+	1.44358i
$156$		0			0
$157$	−213.175	−	123.077i	−1.35780	−	0.783929i	−0.368476	−	0.929637i	$-0.620120\pi$
$157$	−213.175	−	123.077i	−1.35780	−	0.783929i	−0.989328	+	0.145709i	$0.953454\pi$
$158$	12.9119	−	22.3641i	0.0817210	−	0.141545i
$159$		0			0
$160$	18.3111	−	21.5570i	0.114444	−	0.134731i
$161$			77.1916i			0.479451i
$162$		0			0
$163$		−	56.4039i		−	0.346036i	−0.984919	−	0.173018i	$-0.944648\pi$
$163$		−	56.4039i		−	0.346036i	0.984919	−	0.173018i	$-0.0553519\pi$
$164$	−84.7103	+	48.9075i	−0.516527	+	0.298217i
$165$		0			0
$166$	−114.509	+	198.336i	−0.689815	+	1.19480i
$167$	−49.6876	+	86.0614i	−0.297530	+	0.515338i	−0.975570	−	0.219687i	$-0.929496\pi$
$167$	−49.6876	+	86.0614i	−0.297530	+	0.515338i	0.678040	+	0.735025i	$0.262830\pi$
$168$		0			0
$169$	−83.3168	−	144.309i	−0.492999	−	0.853899i
$170$	−26.3692	−	73.8311i	−0.155113	−	0.434301i
$171$		0			0
$172$			7.11018i			0.0413382i
$173$	142.790	+	247.320i	0.825378	+	1.42960i	0.901630	+	0.432508i	$0.142371\pi$
$173$	142.790	+	247.320i	0.825378	+	1.42960i	−0.0762517	+	0.997089i	$0.524295\pi$
$174$		0			0
$175$	232.357	−	38.0873i	1.32775	−	0.217642i
$176$	−8.15652	−	4.70917i	−0.0463439	−	0.0267566i
$177$		0			0
$178$	−108.064	+	62.3907i	−0.607100	+	0.350509i
$179$		−	180.570i		−	1.00877i	−0.863479	−	0.504385i	$-0.831719\pi$
$179$		−	180.570i		−	1.00877i	0.863479	−	0.504385i	$-0.168281\pi$
$180$		0			0
$181$	87.7217			0.484650			0.242325	−	0.970195i	$-0.422090\pi$
$181$	87.7217			0.484650			0.242325	+	0.970195i	$0.422090\pi$
$182$	−10.2449	−	17.7447i	−0.0562907	−	0.0974983i
$183$		0			0
$184$	−11.5908	+	20.0758i	−0.0629932	+	0.109107i
$185$	18.6716	−	102.281i	0.100927	−	0.552870i
$186$		0			0
$187$	−22.6084	+	13.0529i	−0.120900	+	0.0698018i
$188$	139.541			0.742241
$189$		0			0
$190$	16.8676	+	47.2276i	0.0887770	+	0.248567i
$191$	53.6132	−	30.9536i	0.280698	−	0.162061i	−0.353042	−	0.935608i	$-0.614853\pi$
$191$	53.6132	−	30.9536i	0.280698	−	0.162061i	0.633739	+	0.773547i	$0.281519\pi$
$192$		0			0
$193$	194.664	+	112.389i	1.00862	+	0.582329i	0.910788	−	0.412874i	$-0.135475\pi$
$193$	194.664	+	112.389i	1.00862	+	0.582329i	0.0978350	+	0.995203i	$0.468808\pi$
$194$	−172.224	−	99.4334i	−0.887751	−	0.512543i
$195$		0			0
$196$	39.7046	+	68.7704i	0.202575	+	0.350870i
$197$	260.281			1.32122			0.660612	−	0.750728i	$-0.270297\pi$
$197$	260.281			1.32122			0.660612	+	0.750728i	$0.270297\pi$
$198$		0			0
$199$	−27.2102			−0.136735			−0.0683673	−	0.997660i	$-0.521779\pi$
$199$	−27.2102			−0.136735			−0.0683673	+	0.997660i	$0.521779\pi$
$200$	66.1498	+	24.9841i	0.330749	+	0.124920i
$201$		0			0
$202$	−67.3251	−	38.8702i	−0.333293	−	0.192427i
$203$	84.5271	−	146.405i	0.416390	−	0.721208i
$204$		0			0
$205$	−186.375	−	158.313i	−0.909149	−	0.772257i
$206$		−	20.1626i		−	0.0978769i
$207$		0			0
$208$		−	6.15332i		−	0.0295833i
$209$	14.4619	−	8.34960i	0.0691958	−	0.0399502i
$210$		0			0
$211$	−61.2522	+	106.092i	−0.290295	+	0.502805i	−0.973879	−	0.227066i	$-0.927087\pi$
$211$	−61.2522	+	106.092i	−0.290295	+	0.502805i	0.683585	+	0.729871i	$0.260420\pi$
$212$	69.0100	−	119.529i	0.325519	−	0.563815i
$213$		0			0
$214$	−57.9584	−	100.387i	−0.270834	−	0.469098i
$215$	−16.7398	+	5.97872i	−0.0778596	+	0.0278080i
$216$		0			0
$217$		−	553.011i		−	2.54844i
$218$	79.5479	+	137.781i	0.364899	+	0.632023i
$219$		0			0
$220$	4.22845	−	23.1631i	0.0192202	−	0.105287i
$221$	−14.7708	−	8.52793i	−0.0668363	−	0.0385879i
$222$		0			0
$223$	−239.237	+	138.123i	−1.07281	+	0.619388i	−0.928948	−	0.370210i	$-0.879286\pi$
$223$	−239.237	+	138.123i	−1.07281	+	0.619388i	−0.143863	+	0.989598i	$0.545952\pi$
$224$			53.2780i			0.237848i
$225$		0			0
$226$	127.001			0.561952
$227$	1.35387	+	2.34497i	0.00596417	+	0.0103302i	0.868992	−	0.494826i	$-0.164768\pi$
$227$	1.35387	+	2.34497i	0.00596417	+	0.0103302i	−0.863028	+	0.505156i	$0.831435\pi$
$228$		0			0
$229$	104.818	−	181.550i	0.457720	−	0.792795i	−0.541120	−	0.840946i	$-0.681999\pi$
$229$	104.818	−	181.550i	0.457720	−	0.792795i	0.998840	+	0.0481507i	$0.0153328\pi$
$230$	−57.0116	−	10.4076i	−0.247877	−	0.0452502i
$231$		0			0
$232$	43.9671	−	25.3844i	0.189514	−	0.109416i
$233$	183.458			0.787375			0.393688	−	0.919244i	$-0.371199\pi$
$233$	183.458			0.787375			0.393688	+	0.919244i	$0.371199\pi$
$234$		0			0
$235$	117.336	+	328.528i	0.499301	+	1.39799i
$236$	68.1463	−	39.3443i	0.288756	−	0.166713i
$237$		0			0
$238$	127.892	+	73.8384i	0.537361	+	0.310245i
$239$	50.2172	+	28.9929i	0.210114	+	0.121309i	0.601364	−	0.798975i	$-0.294624\pi$
$239$	50.2172	+	28.9929i	0.210114	+	0.121309i	−0.391251	+	0.920284i	$0.627957\pi$
$240$		0			0
$241$	−78.5200	−	136.001i	−0.325809	−	0.564318i	0.655867	−	0.754877i	$-0.272303\pi$
$241$	−78.5200	−	136.001i	−0.325809	−	0.564318i	−0.981676	+	0.190559i	$0.938970\pi$
$242$	163.279			0.674708
$243$		0			0
$244$	231.336			0.948099
$245$	−128.523	+	151.305i	−0.524584	+	0.617573i
$246$		0			0
$247$	9.44847	+	5.45508i	0.0382529	+	0.0220853i
$248$	83.0377	−	143.826i	0.334829	−	0.579942i
$249$		0			0
$250$	−3.19789	+	176.748i	−0.0127915	+	0.706991i
$251$			254.026i			1.01206i	0.862517	+	0.506029i	$0.168887\pi$
$251$			254.026i			1.01206i	−0.862517	+	0.506029i	$0.831113\pi$
$252$		0			0
$253$			19.2979i			0.0762764i
$254$	−108.218	+	62.4795i	−0.426054	+	0.245982i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−132.376	+	229.281i	−0.515080	+	0.892145i	0.484767	+	0.874644i	$0.338905\pi$
$257$	−132.376	+	229.281i	−0.515080	+	0.892145i	−0.999847	+	0.0175016i	$0.994429\pi$
$258$		0			0
$259$	97.9235	+	169.608i	0.378083	+	0.654859i
$260$	14.4870	−	5.17413i	0.0557194	−	0.0199005i
$261$		0			0
$262$		−	245.703i		−	0.937798i
$263$	89.1350	+	154.386i	0.338916	+	0.587021i	0.984229	−	0.176898i	$-0.0566063\pi$
$263$	89.1350	+	154.386i	0.338916	+	0.587021i	−0.645313	+	0.763919i	$0.723273\pi$
$264$		0			0
$265$	339.440	+	61.9653i	1.28091	+	0.233831i
$266$	−81.8088	−	47.2323i	−0.307552	−	0.177565i
$267$		0			0
$268$	177.622	−	102.550i	0.662769	−	0.382650i
$269$			270.345i			1.00500i	0.864577	+	0.502501i	$0.167587\pi$
$269$			270.345i			1.00500i	−0.864577	+	0.502501i	$0.832413\pi$
$270$		0			0
$271$	389.617			1.43770			0.718850	−	0.695165i	$-0.244669\pi$
$271$	389.617			1.43770			0.718850	+	0.695165i	$0.244669\pi$
$272$	22.1745	+	38.4074i	0.0815240	+	0.141204i
$273$		0			0
$274$	−77.0450	+	133.446i	−0.281186	+	0.487028i
$275$	58.0894	−	9.52185i	0.211234	−	0.0346249i
$276$		0			0
$277$	−418.704	+	241.739i	−1.51156	+	0.872702i	−0.511656	+	0.859190i	$0.670968\pi$
$277$	−418.704	+	241.739i	−1.51156	+	0.872702i	−0.999909	+	0.0135122i	$0.995699\pi$
$278$	−188.531			−0.678168
$279$		0			0
$280$	−125.435	+	44.7998i	−0.447982	+	0.159999i
$281$	238.029	−	137.426i	0.847078	−	0.489061i	−0.0125860	−	0.999921i	$-0.504006\pi$
$281$	238.029	−	137.426i	0.847078	−	0.489061i	0.859664	+	0.510860i	$0.170673\pi$
$282$		0			0
$283$	400.583	+	231.277i	1.41549	+	0.817233i	0.995898	−	0.0904802i	$-0.0288402\pi$
$283$	400.583	+	231.277i	1.41549	+	0.817233i	0.419591	+	0.907713i	$0.362174\pi$
$284$	177.824	+	102.667i	0.626141	+	0.361503i
$285$		0			0
$286$	−2.56123	−	4.43618i	−0.00895535	−	0.0155111i
$287$	460.627			1.60497
$288$		0			0
$289$	−166.073			−0.574646
$290$	96.7343	+	82.1689i	0.333567	+	0.283341i
$291$		0			0
$292$	−208.907	−	120.613i	−0.715435	−	0.413057i
$293$	30.5190	−	52.8605i	0.104160	−	0.180411i	−0.809234	−	0.587486i	$-0.800118\pi$
$293$	30.5190	−	52.8605i	0.104160	−	0.180411i	0.913395	+	0.407075i	$0.133451\pi$
$294$		0			0
$295$	149.932	+	127.357i	0.508244	+	0.431717i
$296$			58.8151i			0.198700i
$297$		0			0
$298$		−	175.434i		−	0.588705i
$299$	−10.9189	+	6.30400i	−0.0365179	+	0.0210836i
$300$		0			0
$301$	16.7415	−	28.9971i	0.0556195	−	0.0963358i
$302$	−9.64374	+	16.7034i	−0.0319329	+	0.0553094i
$303$		0			0
$304$	−14.1844	−	24.5681i	−0.0466592	−	0.0808162i
$305$	194.523	+	544.645i	0.637781	+	1.78572i
$306$		0			0
$307$		−	108.831i		−	0.354498i	−0.984166	−	0.177249i	$-0.943280\pi$
$307$		−	108.831i		−	0.354498i	0.984166	−	0.177249i	$-0.0567198\pi$
$308$	22.1762	+	38.4103i	0.0720007	+	0.124709i
$309$		0			0
$310$	408.439	+	74.5611i	1.31754	+	0.240520i
$311$	218.945	+	126.408i	0.704004	+	0.406457i	0.808837	−	0.588033i	$-0.200097\pi$
$311$	218.945	+	126.408i	0.704004	+	0.406457i	−0.104833	+	0.994490i	$0.533431\pi$
$312$		0			0
$313$	381.600	−	220.317i	1.21917	−	0.703888i	0.254430	−	0.967091i	$-0.418112\pi$
$313$	381.600	−	220.317i	1.21917	−	0.703888i	0.964740	+	0.263203i	$0.0847789\pi$
$314$			348.114i			1.10864i
$315$		0			0
$316$	−36.5204			−0.115571
$317$	−94.1053	−	162.995i	−0.296862	−	0.514181i	0.678554	−	0.734550i	$-0.262607\pi$
$317$	−94.1053	−	162.995i	−0.296862	−	0.514181i	−0.975416	+	0.220370i	$0.929274\pi$
$318$		0			0
$319$	21.1318	−	36.6014i	0.0662440	−	0.114738i
$320$	−39.3497	−	7.18335i	−0.122968	−	0.0224480i
$321$		0			0
$322$	94.5400	−	54.5827i	0.293602	−	0.169511i
$323$	−78.6331			−0.243446
$324$		0			0
$325$	24.3634	+	29.7567i	0.0749643	+	0.0915592i
$326$	−69.0804	+	39.8836i	−0.211903	+	0.122342i
$327$		0			0
$328$	119.799	+	69.1657i	0.365239	+	0.210871i
$329$	−569.084	−	328.561i	−1.72974	−	0.998665i
$330$		0			0
$331$	−81.2810	−	140.783i	−0.245562	−	0.425326i	0.716727	−	0.697353i	$-0.245639\pi$
$331$	−81.2810	−	140.783i	−0.245562	−	0.425326i	−0.962289	+	0.272027i	$0.912306\pi$
$332$	323.881			0.975546
$333$		0			0
$334$	140.538			0.420771
$335$	390.795	+	331.953i	1.16655	+	0.990904i
$336$		0			0
$337$	−199.576	−	115.225i	−0.592213	−	0.341915i	0.173759	−	0.984788i	$-0.444409\pi$
$337$	−199.576	−	115.225i	−0.592213	−	0.341915i	−0.765972	+	0.642874i	$0.777742\pi$
$338$	−117.828	+	204.084i	−0.348603	+	0.603798i
$339$		0			0
$340$	−71.7784	+	84.5020i	−0.211113	+	0.248535i
$341$		−	138.253i		−	0.405434i
$342$		0			0
$343$			87.5467i			0.255238i
$344$	8.70815	−	5.02765i	0.0253144	−	0.0146153i
$345$		0			0
$346$	201.936	−	349.764i	0.583631	−	1.01088i
$347$	−287.428	+	497.840i	−0.828322	+	1.43470i	0.0710309	+	0.997474i	$0.477371\pi$
$347$	−287.428	+	497.840i	−0.828322	+	1.43470i	−0.899353	+	0.437222i	$0.855962\pi$
$348$		0			0
$349$	24.7392	+	42.8496i	0.0708860	+	0.122778i	0.899290	−	0.437353i	$-0.144084\pi$
$349$	24.7392	+	42.8496i	0.0708860	+	0.122778i	−0.828404	+	0.560131i	$0.810751\pi$
$350$	−210.948	−	257.646i	−0.602710	−	0.736132i
$351$		0			0
$352$			13.3195i			0.0378396i
$353$	201.200	+	348.488i	0.569971	+	0.987219i	0.996568	+	0.0827770i	$0.0263789\pi$
$353$	201.200	+	348.488i	0.569971	+	0.987219i	−0.426597	+	0.904442i	$0.640288\pi$
$354$		0			0
$355$	−92.1864	+	504.989i	−0.259680	+	1.42250i
$356$	152.825	+	88.2337i	0.429285	+	0.247848i
$357$		0			0
$358$	−221.152	+	127.682i	−0.617743	+	0.356654i
$359$		−	562.625i		−	1.56720i	−0.621266	−	0.783600i	$-0.713381\pi$
$359$		−	562.625i		−	1.56720i	0.621266	−	0.783600i	$-0.286619\pi$
$360$		0			0
$361$	−310.701			−0.860667
$362$	−62.0286	−	107.437i	−0.171350	−	0.296786i
$363$		0			0
$364$	−14.4885	+	25.0948i	−0.0398035	+	0.0689417i
$365$	108.300	−	593.259i	0.296713	−	1.62537i
$366$		0			0
$367$	−162.226	+	93.6613i	−0.442033	+	0.255208i	−0.704460	−	0.709744i	$-0.748811\pi$
$367$	−162.226	+	93.6613i	−0.442033	+	0.255208i	0.262427	+	0.964952i	$0.415477\pi$
$368$	32.7836			0.0890859
$369$		0			0
$370$	−138.471	+	49.4557i	−0.374246	+	0.133664i
$371$	−562.880	+	324.979i	−1.51720	+	0.875954i
$372$		0			0
$373$	−478.852	−	276.465i	−1.28378	−	0.741193i	−0.306246	−	0.951952i	$-0.599073\pi$
$373$	−478.852	−	276.465i	−1.28378	−	0.741193i	−0.977538	+	0.210759i	$0.932406\pi$
$374$	31.9731	+	18.4597i	0.0854895	+	0.0493574i
$375$		0			0
$376$	−98.6706	−	170.902i	−0.262422	−	0.454528i
$377$	27.6123			0.0732421
$378$		0			0
$379$	447.398			1.18047			0.590235	−	0.807232i	$-0.299035\pi$
$379$	447.398			1.18047			0.590235	+	0.807232i	$0.299035\pi$
$380$	45.9146	−	54.0535i	0.120828	−	0.142246i
$381$		0			0
$382$	−75.8206	−	43.7750i	−0.198483	−	0.114594i
$383$	280.756	−	486.284i	0.733045	−	1.26967i	−0.222531	−	0.974926i	$-0.571432\pi$
$383$	280.756	−	486.284i	0.733045	−	1.26967i	0.955576	−	0.294746i	$-0.0952349\pi$
$384$		0			0
$385$	−71.7839	+	84.5085i	−0.186452	+	0.219503i
$386$		−	317.885i		−	0.823537i
$387$		0			0
$388$			281.240i			0.724846i
$389$	373.187	−	215.460i	0.959350	−	0.553881i	0.0633770	−	0.997990i	$-0.479813\pi$
$389$	373.187	−	215.460i	0.959350	−	0.553881i	0.895973	+	0.444109i	$0.146480\pi$
$390$		0			0
$391$	45.4350	−	78.6958i	0.116202	−	0.201268i
$392$	56.1508	−	97.2561i	0.143242	−	0.248102i
$393$		0			0
$394$	−184.046	−	318.778i	−0.467123	−	0.809081i
$395$	−30.7089	−	85.9817i	−0.0777440	−	0.217675i
$396$		0			0
$397$		−	656.459i		−	1.65355i	−0.562533	−	0.826775i	$-0.690173\pi$
$397$		−	656.459i		−	1.65355i	0.562533	−	0.826775i	$-0.309827\pi$
$398$	19.2405	+	33.3255i	0.0483430	+	0.0837325i
$399$		0			0
$400$	−16.1758	−	98.6830i	−0.0404396	−	0.246708i
$401$	−232.242	−	134.085i	−0.579157	−	0.334376i	0.181642	−	0.983365i	$-0.441859\pi$
$401$	−232.242	−	134.085i	−0.579157	−	0.334376i	−0.760798	+	0.648989i	$0.775192\pi$
$402$		0			0
$403$	78.2241	−	45.1627i	0.194104	−	0.112066i
$404$			109.941i			0.272132i
$405$		0			0
$406$	−239.079			−0.588864
$407$	24.4809	+	42.4022i	0.0601497	+	0.104182i
$408$		0			0
$409$	−153.664	+	266.154i	−0.375706	+	0.650742i	−0.990432	−	0.137998i	$-0.955933\pi$
$409$	−153.664	+	266.154i	−0.375706	+	0.650742i	0.614726	+	0.788741i	$0.289266\pi$
$410$	−62.1052	+	340.206i	−0.151476	+	0.829771i
$411$		0			0
$412$	−24.6941	+	14.2571i	−0.0599371	+	0.0346047i
$413$	−370.557			−0.897232
$414$		0			0
$415$	272.342	+	762.529i	0.656245	+	1.83742i
$416$	−7.53625	+	4.35105i	−0.0181160	+	0.0104593i
$417$		0			0
$418$	−20.4522	−	11.8081i	−0.0489288	−	0.0282491i
$419$	278.539	+	160.815i	0.664772	+	0.383806i	0.794093	−	0.607797i	$-0.207946\pi$
$419$	278.539	+	160.815i	0.664772	+	0.383806i	−0.129321	+	0.991603i	$0.541280\pi$
$420$		0			0
$421$	−160.887	−	278.664i	−0.382154	−	0.661909i	0.609216	−	0.793004i	$-0.291484\pi$
$421$	−160.887	−	278.664i	−0.382154	−	0.661909i	−0.991370	+	0.131095i	$0.958151\pi$
$422$	173.247			0.410539
$423$		0			0
$424$	−195.190			−0.460353
$425$	−259.303	−	97.9361i	−0.610125	−	0.230438i
$426$		0			0
$427$	−943.447	−	544.699i	−2.20948	−	1.27564i
$428$	−81.9655	+	141.968i	−0.191508	+	0.331702i
$429$		0			0
$430$	19.1592	+	16.2744i	0.0445564	+	0.0378474i
$431$		−	90.0447i		−	0.208920i	−0.994529	−	0.104460i	$-0.966689\pi$
$431$		−	90.0447i		−	0.208920i	0.994529	−	0.104460i	$-0.0333115\pi$
$432$		0			0
$433$		−	22.6191i		−	0.0522382i	−0.999659	−	0.0261191i	$-0.991685\pi$
$433$		−	22.6191i		−	0.0522382i	0.999659	−	0.0261191i	$-0.00831491\pi$
$434$	−677.297	+	391.038i	−1.56059	+	0.901008i
$435$		0			0
$436$	112.498	−	194.852i	0.258022	−	0.446908i
$437$	−29.0635	+	50.3395i	−0.0665069	+	0.115193i
$438$		0			0
$439$	319.657	+	553.663i	0.728149	+	1.26119i	0.957665	+	0.287886i	$0.0929525\pi$
$439$	319.657	+	553.663i	0.728149	+	1.26119i	−0.229516	+	0.973305i	$0.573714\pi$
$440$	−31.3588	+	11.2000i	−0.0712700	+	0.0254545i
$441$		0			0
$442$			24.1206i			0.0545716i
$443$	−220.042	−	381.124i	−0.496709	−	0.860325i	0.503284	−	0.864121i	$-0.332125\pi$
$443$	−220.042	−	381.124i	−0.496709	−	0.860325i	−0.999993	+	0.00379617i	$0.998792\pi$
$444$		0			0
$445$	−79.2267	+	433.996i	−0.178037	+	0.975273i
$446$	338.332	+	195.336i	0.758592	+	0.437973i
$447$		0			0
$448$	65.2520	−	37.6733i	0.145652	−	0.0840921i
$449$		−	281.927i		−	0.627899i	−0.949440	−	0.313949i	$-0.898348\pi$
$449$		−	281.927i		−	0.627899i	0.949440	−	0.313949i	$-0.101652\pi$
$450$		0			0
$451$	115.157			0.255337
$452$	−89.8034	−	155.544i	−0.198680	−	0.344124i
$453$		0			0
$454$	1.91466	−	3.31628i	0.00421731	−	0.00730459i
$455$	−71.2647	−	13.0095i	−0.156626	−	0.0285922i
$456$		0			0
$457$	321.896	−	185.847i	0.704367	−	0.406667i	−0.104605	−	0.994514i	$-0.533358\pi$
$457$	321.896	−	185.847i	0.704367	−	0.406667i	0.808972	+	0.587847i	$0.200024\pi$
$458$	−296.470			−0.647314
$459$		0			0
$460$	27.5667	+	77.1839i	0.0599276	+	0.167791i
$461$	−192.177	+	110.954i	−0.416870	+	0.240680i	−0.693737	−	0.720228i	$-0.744037\pi$
$461$	−192.177	+	110.954i	−0.416870	+	0.240680i	0.276867	+	0.960908i	$0.410704\pi$
$462$		0			0
$463$	309.991	+	178.973i	0.669526	+	0.386551i	0.795897	−	0.605432i	$-0.207000\pi$
$463$	309.991	+	178.973i	0.669526	+	0.386551i	−0.126371	+	0.991983i	$0.540333\pi$
$464$	−62.1789	−	35.8990i	−0.134006	−	0.0773686i
$465$		0			0
$466$	−129.725	−	224.690i	−0.278379	−	0.482167i
$467$	−392.199			−0.839826			−0.419913	−	0.907564i	$-0.637939\pi$
$467$	−392.199			−0.839826			−0.419913	+	0.907564i	$0.637939\pi$
$468$		0			0
$469$	−965.850			−2.05938
$470$	319.394	−	376.011i	0.679563	−	0.800024i
$471$		0			0
$472$	−96.3734	−	55.6412i	−0.204181	−	0.117884i
$473$	4.18538	−	7.24929i	0.00884858	−	0.0153262i
$474$		0			0
$475$	165.869	+	62.6469i	0.349197	+	0.131888i
$476$		−	208.847i		−	0.438753i
$477$		0			0
$478$		−	82.0043i		−	0.171557i
$479$	697.138	−	402.493i	1.45540	−	0.840278i	0.456624	−	0.889660i	$-0.349059\pi$
$479$	697.138	−	402.493i	1.45540	−	0.840278i	0.998780	+	0.0493823i	$0.0157253\pi$
$480$		0			0
$481$	−15.9942	+	27.7028i	−0.0332520	+	0.0575942i
$482$	−111.044	+	192.334i	−0.230382	+	0.399033i
$483$		0			0
$484$	−115.456	−	199.976i	−0.238545	−	0.413173i
$485$	−662.136	+	236.486i	−1.36523	+	0.487600i
$486$		0			0
$487$		−	477.427i		−	0.980342i	−0.871626	−	0.490171i	$-0.836934\pi$
$487$		−	477.427i		−	0.980342i	0.871626	−	0.490171i	$-0.163066\pi$
$488$	−163.579	−	283.328i	−0.335204	−	0.580590i
$489$		0			0
$490$	276.190	+	50.4189i	0.563653	+	0.102896i
$491$	311.235	+	179.691i	0.633879	+	0.365970i	0.782253	−	0.622961i	$-0.214070\pi$
$491$	311.235	+	179.691i	0.633879	+	0.365970i	−0.148374	+	0.988931i	$0.547404\pi$
$492$		0			0
$493$	−172.349	+	99.5055i	−0.349591	+	0.201837i
$494$		−	15.4293i		−	0.0312334i
$495$		0			0
$496$	−234.866			−0.473520
$497$	−483.474	−	837.402i	−0.972785	−	1.68491i
$498$		0			0
$499$	−194.053	+	336.109i	−0.388883	+	0.673565i	−0.992300	−	0.123861i	$-0.960472\pi$
$499$	−194.053	+	336.109i	−0.388883	+	0.673565i	0.603417	+	0.797426i	$0.293806\pi$
$500$	218.732	−	121.063i	0.437464	−	0.242126i
$501$		0			0
$502$	311.118	−	179.624i	0.619756	−	0.357816i
$503$	−23.5000			−0.0467197			−0.0233598	−	0.999727i	$-0.507436\pi$
$503$	−23.5000			−0.0467197			−0.0233598	+	0.999727i	$0.507436\pi$
$504$		0			0
$505$	−258.840	+	92.4463i	−0.512555	+	0.183062i
$506$	23.6351	−	13.6457i	0.0467096	−	0.0269678i
$507$		0			0
$508$	153.043	+	88.3594i	0.301266	+	0.173936i
$509$	137.817	+	79.5684i	0.270759	+	0.156323i	0.629233	−	0.777217i	$-0.283369\pi$
$509$	137.817	+	79.5684i	0.270759	+	0.156323i	−0.358473	+	0.933540i	$0.616703\pi$
$510$		0			0
$511$	567.984	+	983.777i	1.11151	+	1.92520i
$512$	22.6274			0.0441942
$513$		0			0
$514$	374.415			0.728434
$515$	−54.3307	−	46.1500i	−0.105496	−	0.0896117i
$516$		0			0
$517$	−142.271	−	82.1404i	−0.275186	−	0.158879i
$518$	138.485	−	239.862i	0.267345	−	0.463055i
$519$		0			0
$520$	−16.5809	−	14.0843i	−0.0318863	−	0.0270851i
$521$			591.045i			1.13444i	0.823565	+	0.567222i	$0.191982\pi$
$521$			591.045i			1.13444i	−0.823565	+	0.567222i	$0.808018\pi$
$522$		0			0
$523$			542.921i			1.03809i	0.854747	+	0.519045i	$0.173712\pi$
$523$			542.921i			1.03809i	−0.854747	+	0.519045i	$0.826288\pi$
$524$	−300.923	+	173.738i	−0.574281	+	0.331562i
$525$		0			0
$526$	126.056	−	218.335i	0.239650	−	0.415086i
$527$	−325.503	+	563.787i	−0.617652	+	1.06980i
$528$		0			0
$529$	230.914	+	399.954i	0.436510	+	0.756057i
$530$	−164.129	−	459.544i	−0.309677	−	0.867064i
$531$		0			0
$532$			133.593i			0.251115i
$533$	37.6180	+	65.1562i	0.0705778	+	0.122244i
$534$		0			0
$535$	−403.165	−	73.5984i	−0.753579	−	0.137567i
$536$	−251.196	−	145.028i	−0.468649	−	0.270574i
$537$		0			0
$538$	331.104	−	191.163i	0.615435	−	0.355322i
$539$		−	93.4879i		−	0.173447i
$540$		0			0
$541$	−744.623			−1.37638			−0.688192	−	0.725529i	$-0.741595\pi$
$541$	−744.623			−1.37638			−0.688192	+	0.725529i	$0.741595\pi$
$542$	−275.501	−	477.181i	−0.508304	−	0.880408i
$543$		0			0
$544$	31.3595	−	54.3163i	0.0576462	−	0.0998461i
$545$	553.344	+	101.014i	1.01531	+	0.185346i
$546$		0			0
$547$	−109.584	+	63.2684i	−0.200337	+	0.115664i	−0.596812	−	0.802381i	$-0.703566\pi$
$547$	−109.584	+	63.2684i	−0.200337	+	0.115664i	0.396476	+	0.918045i	$0.370233\pi$
$548$	217.916			0.397657
$549$		0			0
$550$	−52.7372	−	64.4117i	−0.0958859	−	0.117112i
$551$	110.246	−	63.6508i	0.200084	−	0.115519i
$552$		0			0
$553$	148.939	+	85.9902i	0.269330	+	0.155498i
$554$	592.136	+	341.870i	1.06884	+	0.617094i
$555$		0			0
$556$	133.311	+	230.902i	0.239769	+	0.415292i
$557$	−363.331			−0.652301			−0.326150	−	0.945318i	$-0.605752\pi$
$557$	−363.331			−0.652301			−0.326150	+	0.945318i	$0.605752\pi$
$558$		0			0
$559$	5.46890			0.00978336
$560$	143.564	+	121.947i	0.256365	+	0.217763i
$561$		0			0
$562$	−336.624	−	194.350i	−0.598975	−	0.345818i
$563$	−152.845	+	264.736i	−0.271484	+	0.470223i	−0.969242	−	0.246110i	$-0.920848\pi$
$563$	−152.845	+	264.736i	−0.271484	+	0.470223i	0.697758	+	0.716333i	$0.254181\pi$
$564$		0			0
$565$	290.692	−	342.220i	0.514498	−	0.605700i
$566$		−	654.150i		−	1.15574i
$567$		0			0
$568$		−	290.386i		−	0.511242i
$569$	787.058	−	454.408i	1.38323	−	0.798609i	0.390690	−	0.920522i	$-0.372236\pi$
$569$	787.058	−	454.408i	1.38323	−	0.798609i	0.992541	+	0.121914i	$0.0389031\pi$
$570$		0			0
$571$	−210.253	+	364.168i	−0.368218	+	0.637773i	−0.989287	−	0.145983i	$-0.953365\pi$
$571$	−210.253	+	364.168i	−0.368218	+	0.637773i	0.621069	+	0.783756i	$0.286699\pi$
$572$	−3.62213	+	6.27371i	−0.00633239	+	0.0109680i
$573$		0			0
$574$	−325.712	−	564.150i	−0.567443	−	0.982840i
$575$	−158.538	+	129.803i	−0.275718	+	0.225744i
$576$		0			0
$577$			488.343i			0.846348i	0.906048	+	0.423174i	$0.139084\pi$
$577$			488.343i			0.846348i	−0.906048	+	0.423174i	$0.860916\pi$
$578$	117.431	+	203.397i	0.203168	+	0.351897i
$579$		0			0
$580$	32.2344	−	176.577i	0.0555765	−	0.304443i
$581$	−1320.87	−	762.604i	−2.27344	−	1.31257i
$582$		0			0
$583$	−140.720	+	81.2449i	−0.241373	+	0.139357i
$584$			341.144i			0.584151i
$585$		0			0
$586$	−86.3208			−0.147305
$587$	−344.218	−	596.203i	−0.586402	−	1.01568i	−0.994699	−	0.102828i	$-0.967211\pi$
$587$	−344.218	−	596.203i	−0.586402	−	1.01568i	0.408298	−	0.912849i	$-0.366123\pi$
$588$		0			0
$589$	208.215	−	360.639i	0.353506	−	0.612290i
$590$	49.9613	−	273.683i	0.0846801	−	0.463870i
$591$		0			0
$592$	72.0334	−	41.5885i	0.121678	−	0.0702509i
$593$	−532.286			−0.897616			−0.448808	−	0.893628i	$-0.648151\pi$
$593$	−532.286			−0.897616			−0.448808	+	0.893628i	$0.648151\pi$
$594$		0			0
$595$	491.697	−	175.612i	0.826381	−	0.295147i
$596$	−214.862	+	124.051i	−0.360506	+	0.208139i
$597$		0			0
$598$	15.4416	+	8.91520i	0.0258220	+	0.0149084i
$599$	−120.652	−	69.6587i	−0.201423	−	0.116292i	0.395896	−	0.918295i	$-0.370434\pi$
$599$	−120.652	−	69.6587i	−0.201423	−	0.116292i	−0.597319	+	0.802004i	$0.703767\pi$
$600$		0			0
$601$	6.08331	+	10.5366i	0.0101220	+	0.0175318i	0.871042	−	0.491208i	$-0.163445\pi$
$601$	6.08331	+	10.5366i	0.0101220	+	0.0175318i	−0.860920	+	0.508740i	$0.830111\pi$
$602$	−47.3520			−0.0786579
$603$		0			0
$604$	27.2766			0.0451600
$605$	373.728	−	439.976i	0.617733	−	0.727233i
$606$		0			0
$607$	−321.687	−	185.726i	−0.529962	−	0.305974i	0.211039	−	0.977478i	$-0.432315\pi$
$607$	−321.687	−	185.726i	−0.529962	−	0.305974i	−0.741001	+	0.671504i	$0.765649\pi$
$608$	−20.0598	+	34.7446i	−0.0329931	+	0.0571457i
$609$		0			0
$610$	529.503	−	623.364i	0.868037	−	1.02191i
$611$		−	107.330i		−	0.175663i
$612$		0			0
$613$			656.136i			1.07037i	0.844736	+	0.535184i	$0.179758\pi$
$613$			656.136i			1.07037i	−0.844736	+	0.535184i	$0.820242\pi$
$614$	−133.290	+	76.9551i	−0.217085	+	0.125334i
$615$		0			0
$616$	31.3619	−	54.3204i	0.0509122	−	0.0881825i
$617$	264.682	−	458.443i	0.428982	−	0.743019i	−0.567801	−	0.823166i	$-0.692206\pi$
$617$	264.682	−	458.443i	0.428982	−	0.743019i	0.996783	+	0.0801472i	$0.0255390\pi$
$618$		0			0
$619$	201.069	+	348.262i	0.324829	+	0.562620i	0.981478	−	0.191576i	$-0.0613599\pi$
$619$	201.069	+	348.262i	0.324829	+	0.562620i	−0.656649	+	0.754197i	$0.728027\pi$
$620$	−197.491	−	552.956i	−0.318535	−	0.891864i
$621$		0			0
$622$		−	357.536i		−	0.574817i
$623$	−415.506	−	719.678i	−0.666944	−	1.15518i
$624$		0			0
$625$	468.949	+	413.173i	0.750318	+	0.661077i
$626$	−539.664	−	311.575i	−0.862084	−	0.497724i
$627$		0			0
$628$	426.350	−	246.154i	0.678902	−	0.391964i
$629$		−	230.551i		−	0.366536i
$630$		0			0
$631$	576.351			0.913393			0.456696	−	0.889623i	$-0.349033\pi$
$631$	576.351			0.913393			0.456696	+	0.889623i	$0.349033\pi$
$632$	25.8238	+	44.7282i	0.0408605	+	0.0707725i
$633$		0			0
$634$	−133.085	+	230.510i	−0.209913	+	0.363581i
$635$	−79.3395	+	434.614i	−0.124944	+	0.684432i
$636$		0			0
$637$	52.8958	−	30.5394i	0.0830390	−	0.0479426i
$638$	−59.7698			−0.0936831
$639$		0			0
$640$	19.0267	+	53.2727i	0.0297292	+	0.0832387i
$641$	−165.503	+	95.5530i	−0.258194	+	0.149069i	−0.623511	−	0.781815i	$-0.714294\pi$
$641$	−165.503	+	95.5530i	−0.258194	+	0.149069i	0.365316	+	0.930883i	$0.380961\pi$
$642$		0			0
$643$	−761.768	−	439.807i	−1.18471	−	0.683992i	−0.227610	−	0.973752i	$-0.573091\pi$
$643$	−761.768	−	439.807i	−1.18471	−	0.683992i	−0.957099	+	0.289760i	$0.906424\pi$
$644$	−133.700	−	77.1916i	−0.207608	−	0.119863i
$645$		0			0
$646$	55.6020	+	96.3055i	0.0860712	+	0.149080i
$647$	272.480			0.421144			0.210572	−	0.977578i	$-0.432467\pi$
$647$	272.480			0.421144			0.210572	+	0.977578i	$0.432467\pi$
$648$		0			0
$649$	−92.6395			−0.142742
$650$	19.2169	−	50.8801i	0.0295644	−	0.0782771i
$651$		0			0
$652$	97.6945	+	56.4039i	0.149838	+	0.0865091i
$653$	−177.265	+	307.033i	−0.271463	+	0.470188i	−0.969237	−	0.246130i	$-0.920841\pi$
$653$	−177.265	+	307.033i	−0.271463	+	0.470188i	0.697774	+	0.716318i	$0.254174\pi$
$654$		0			0
$655$	−662.077	−	562.387i	−1.01080	−	0.858606i
$656$		−	195.630i		−	0.298217i
$657$		0			0
$658$			929.311i			1.41233i
$659$	−222.074	+	128.215i	−0.336987	+	0.194559i	−0.658939	−	0.752197i	$-0.728994\pi$
$659$	−222.074	+	128.215i	−0.336987	+	0.194559i	0.321952	+	0.946756i	$0.395661\pi$
$660$		0			0
$661$	−403.282	+	698.505i	−0.610109	+	1.05674i	0.381112	+	0.924529i	$0.375541\pi$
$661$	−403.282	+	698.505i	−0.610109	+	1.05674i	−0.991222	+	0.132212i	$0.957792\pi$
$662$	−114.949	+	199.097i	−0.173639	+	0.300751i
$663$		0			0
$664$	−229.019	−	396.672i	−0.344908	−	0.597398i
$665$	−314.524	+	112.334i	−0.472969	+	0.168924i
$666$		0			0
$667$			147.112i			0.220558i
$668$	−99.3751	−	172.123i	−0.148765	−	0.257669i
$669$		0			0
$670$	130.223	−	713.351i	0.194363	−	1.06470i
$671$	−235.862	−	136.175i	−0.351509	−	0.202944i
$672$		0			0
$673$	239.471	−	138.259i	0.355826	−	0.205436i	−0.311422	−	0.950272i	$-0.600805\pi$
$673$	239.471	−	138.259i	0.355826	−	0.205436i	0.667248	+	0.744835i	$0.267472\pi$
$674$			325.906i			0.483540i
$675$		0			0
$676$	333.267			0.492999
$677$	536.338	+	928.965i	0.792228	+	1.37218i	0.924584	+	0.380977i	$0.124412\pi$
$677$	536.338	+	928.965i	0.792228	+	1.37218i	−0.132356	+	0.991202i	$0.542254\pi$
$678$		0			0
$679$	662.202	−	1146.97i	0.975261	−	1.68920i
$680$	154.248	+	28.1583i	0.226836	+	0.0414092i
$681$		0			0
$682$	−169.325	+	97.7596i	−0.248277	+	0.143343i
$683$	−553.261			−0.810046			−0.405023	−	0.914307i	$-0.632736\pi$
$683$	−553.261			−0.810046			−0.405023	+	0.914307i	$0.632736\pi$
$684$		0			0
$685$	183.239	+	513.050i	0.267502	+	0.748978i
$686$	107.222	−	61.9049i	0.156301	−	0.0902403i
$687$		0			0
$688$	−12.3152	−	7.11018i	−0.0179000	−	0.0103346i
$689$	−91.9374	−	53.0801i	−0.133436	−	0.0770393i
$690$		0			0
$691$	626.305	+	1084.79i	0.906375	+	1.56989i	0.819061	+	0.573707i	$0.194495\pi$
$691$	626.305	+	1084.79i	0.906375	+	1.56989i	0.0873141	+	0.996181i	$0.472172\pi$
$692$	−571.162			−0.825378
$693$		0			0
$694$	812.969			1.17142
$695$	−431.526	+	508.019i	−0.620901	+	0.730963i
$696$		0			0
$697$	−469.603	−	271.125i	−0.673749	−	0.388989i
$698$	34.9865	−	60.5984i	0.0501239	−	0.0868172i
$699$		0			0
$700$	−166.388	+	440.541i	−0.237697	+	0.629345i
$701$			727.608i			1.03796i	0.854787	+	0.518979i	$0.173688\pi$
$701$			727.608i			1.03796i	−0.854787	+	0.518979i	$0.826312\pi$
$702$		0			0
$703$			147.477i			0.209783i
$704$	16.3130	−	9.41834i	0.0231719	−	0.0133783i
$705$		0			0
$706$	284.539	−	492.837i	0.403030	−	0.698069i
$707$	258.866	−	448.369i	0.366147	−	0.634185i
$708$		0			0
$709$	−320.409	−	554.964i	−0.451916	−	0.782742i	0.546589	−	0.837401i	$-0.315926\pi$
$709$	−320.409	−	554.964i	−0.451916	−	0.782742i	−0.998505	+	0.0546592i	$0.982593\pi$
$710$	683.668	−	244.176i	0.962913	−	0.343910i
$711$		0			0
$712$		−	249.563i		−	0.350509i
$713$	240.617	+	416.762i	0.337472	+	0.584518i
$714$		0			0
$715$	−17.8162	−	3.25238i	−0.0249178	−	0.00454878i
$716$	312.756	+	180.570i	0.436810	+	0.252193i
$717$		0			0
$718$	−689.072	+	397.836i	−0.959710	+	0.554089i
$719$		−	738.347i		−	1.02691i	−0.858117	−	0.513454i	$-0.828366\pi$
$719$		−	738.347i		−	1.02691i	0.858117	−	0.513454i	$-0.171634\pi$
$720$		0			0
$721$	134.278			0.186239
$722$	219.699	+	380.529i	0.304292	+	0.527049i
$723$		0			0
$724$	−87.7217	+	151.938i	−0.121163	+	0.209860i
$725$	442.828	−	72.5871i	0.610797	−	0.100120i
$726$		0			0
$727$	593.882	−	342.878i	0.816894	−	0.471634i	−0.0324500	−	0.999473i	$-0.510331\pi$
$727$	593.882	−	342.878i	0.816894	−	0.471634i	0.849344	+	0.527839i	$0.176998\pi$
$728$	40.9796			0.0562907
$729$		0			0
$730$	−803.171	+	286.857i	−1.10023	+	0.392955i
$731$	−34.1354	+	19.7081i	−0.0466969	+	0.0269605i
$732$		0			0
$733$	127.317	+	73.5062i	0.173692	+	0.100281i	0.584326	−	0.811519i	$-0.301359\pi$
$733$	127.317	+	73.5062i	0.173692	+	0.100281i	−0.410633	+	0.911801i	$0.634692\pi$
$734$	229.422	+	132.457i	0.312565	+	0.180459i
$735$		0			0
$736$	−23.1815	−	40.1516i	−0.0314966	−	0.0545537i
$737$	−241.463			−0.327630
$738$		0			0
$739$	34.9060			0.0472341			0.0236171	−	0.999721i	$-0.492482\pi$
$739$	34.9060			0.0472341			0.0236171	+	0.999721i	$0.492482\pi$
$740$	158.484	+	134.621i	0.214168	+	0.181920i
$741$		0			0
$742$	796.032	+	459.590i	1.07282	+	0.619393i
$743$	140.465	−	243.293i	0.189051	−	0.327447i	−0.755883	−	0.654707i	$-0.772792\pi$
$743$	140.465	−	243.293i	0.189051	−	0.327447i	0.944934	+	0.327260i	$0.106125\pi$
$744$		0			0
$745$	−472.728	−	401.549i	−0.634535	−	0.538992i
$746$			781.961i			1.04821i
$747$		0			0
$748$		−	52.2118i		−	0.0698018i
$749$	668.552	−	385.989i	0.892593	−	0.515339i
$750$		0			0
$751$	657.302	−	1138.48i	0.875236	−	1.51595i	0.0187252	−	0.999825i	$-0.494039\pi$
$751$	657.302	−	1138.48i	0.875236	−	1.51595i	0.856511	−	0.516129i	$-0.172627\pi$
$752$	−139.541	+	241.693i	−0.185560	+	0.321400i
$753$		0			0
$754$	−19.5248	−	33.8180i	−0.0258950	−	0.0448515i
$755$	22.9360	+	64.2186i	0.0303789	+	0.0850577i
$756$		0			0
$757$		−	670.545i		−	0.885793i	−0.896573	−	0.442897i	$-0.853951\pi$
$757$		−	670.545i		−	0.885793i	0.896573	−	0.442897i	$-0.146049\pi$
$758$	−316.358	−	547.948i	−0.417359	−	0.722887i
$759$		0			0
$760$	−98.6683	−	18.0120i	−0.129827	−	0.0237001i
$761$	−391.292	−	225.912i	−0.514181	−	0.296863i	0.220370	−	0.975416i	$-0.429274\pi$
$761$	−391.292	−	225.912i	−0.514181	−	0.296863i	−0.734551	+	0.678554i	$0.762607\pi$
$762$		0			0
$763$	−917.587	+	529.769i	−1.20260	+	0.694324i
$764$			123.814i			0.162061i
$765$		0			0
$766$	−794.099			−1.03668
$767$	−30.2623	−	52.4158i	−0.0394553	−	0.0683387i
$768$		0			0
$769$	78.9323	−	136.715i	0.102643	−	0.177783i	−0.810130	−	0.586250i	$-0.800603\pi$
$769$	78.9323	−	136.715i	0.102643	−	0.177783i	0.912773	+	0.408468i	$0.133937\pi$
$770$	154.260	+	28.1604i	0.200338	+	0.0365720i
$771$		0			0
$772$	−389.329	+	224.779i	−0.504312	+	0.291164i
$773$	408.029			0.527852			0.263926	−	0.964543i	$-0.414983\pi$
$773$	408.029			0.527852			0.263926	+	0.964543i	$0.414983\pi$
$774$		0			0
$775$	1135.78	−	929.926i	1.46553	−	1.19990i
$776$	344.447	−	198.867i	0.443876	−	0.256272i
$777$		0			0
$778$	−527.766	−	304.706i	−0.678363	−	0.391653i
$779$	300.392	+	173.431i	0.385612	+	0.222633i
$780$		0			0
$781$	−120.869	−	209.351i	−0.154762	−	0.268055i
$782$	−128.510			−0.164335
$783$		0			0
$784$	−158.819			−0.202575
$785$	938.035	+	796.793i	1.19495	+	1.01502i
$786$		0			0
$787$	323.929	+	187.020i	0.411600	+	0.237637i	0.691477	−	0.722399i	$-0.256960\pi$
$787$	323.929	+	187.020i	0.411600	+	0.237637i	−0.279877	+	0.960036i	$0.590294\pi$
$788$	−260.281	+	450.820i	−0.330306	+	0.572106i
$789$		0			0
$790$	−83.5912	+	98.4088i	−0.105812	+	0.124568i
$791$			845.797i			1.06928i
$792$		0			0
$793$		−	177.936i		−	0.224383i
$794$	−803.995	+	464.187i	−1.01259	+	0.584618i
$795$		0			0
$796$	27.2102	−	47.1294i	0.0341837	−	0.0592078i
$797$	269.638	−	467.026i	0.338316	−	0.585980i	−0.645800	−	0.763506i	$-0.723476\pi$
$797$	269.638	−	467.026i	0.338316	−	0.585980i	0.984116	+	0.177526i	$0.0568095\pi$
$798$		0			0
$799$	386.783	+	669.927i	0.484083	+	0.838457i
$800$	−109.423	+	89.5907i	−0.136779	+	0.111988i
$801$		0			0
$802$			379.249i			0.472879i
$803$	141.996	+	245.945i	0.176832	+	0.306282i
$804$		0			0
$805$	69.3117	−	379.683i	0.0861015	−	0.471656i
$806$	−110.626	−	63.8697i	−0.137253	−	0.0792428i
$807$		0			0
$808$	134.650	−	77.7403i	0.166646	−	0.0962133i
$809$		−	220.597i		−	0.272679i	−0.990662	−	0.136339i	$-0.956466\pi$
$809$		−	220.597i		−	0.272679i	0.990662	−	0.136339i	$-0.0435338\pi$
$810$		0			0
$811$	−502.813			−0.619992			−0.309996	−	0.950738i	$-0.600328\pi$
$811$	−502.813			−0.619992			−0.309996	+	0.950738i	$0.600328\pi$
$812$	169.054	+	292.810i	0.208195	+	0.360604i
$813$		0			0
$814$	34.6213	−	59.9658i	0.0425323	−	0.0736680i
$815$	−50.6461	+	277.435i	−0.0621425	+	0.340411i
$816$		0			0
$817$	21.8355	−	12.6067i	0.0267264	−	0.0154305i
$818$	434.627			0.531329
$819$		0			0
$820$	460.581	−	164.499i	0.561684	−	0.200609i
$821$	−485.540	+	280.327i	−0.591401	+	0.341446i	−0.765651	−	0.643256i	$-0.777583\pi$
$821$	−485.540	+	280.327i	−0.591401	+	0.341446i	0.174250	+	0.984701i	$0.444250\pi$
$822$		0			0
$823$	943.551	+	544.759i	1.14648	+	0.661919i	0.948026	−	0.318192i	$-0.103076\pi$
$823$	943.551	+	544.759i	1.14648	+	0.661919i	0.198451	+	0.980111i	$0.436409\pi$
$824$	34.9227	+	20.1626i	0.0423819	+	0.0244692i
$825$		0			0
$826$	262.023	+	453.838i	0.317219	+	0.549440i
$827$	963.697			1.16529			0.582646	−	0.812726i	$-0.302017\pi$
$827$	963.697			1.16529			0.582646	+	0.812726i	$0.302017\pi$
$828$		0			0
$829$	−273.552			−0.329978			−0.164989	−	0.986295i	$-0.552759\pi$
$829$	−273.552			−0.329978			−0.164989	+	0.986295i	$0.552759\pi$
$830$	741.328	−	872.738i	0.893167	−	1.05149i
$831$		0			0
$832$	10.6579	+	6.15332i	0.0128099	+	0.00739582i
$833$	−220.108	+	381.238i	−0.264235	+	0.457669i
$834$		0			0
$835$	321.675	−	378.696i	0.385239	−	0.453528i
$836$			33.3984i			0.0399502i
$837$		0			0
$838$		−	454.853i		−	0.542784i
$839$	483.740	−	279.287i	0.576567	−	0.332881i	−0.183201	−	0.983075i	$-0.558646\pi$
$839$	483.740	−	279.287i	0.576567	−	0.332881i	0.759768	+	0.650194i	$0.225313\pi$
$840$		0			0
$841$	−259.407	+	449.307i	−0.308451	+	0.534253i
$842$	−227.528	+	394.090i	−0.270223	+	0.468041i
$843$		0			0
$844$	−122.504	−	212.184i	−0.145147	−	0.251403i
$845$	280.234	+	784.626i	0.331638	+	0.928551i
$846$		0			0
$847$			1087.40i			1.28383i
$848$	138.020	+	239.058i	0.162759	+	0.281908i
$849$		0			0
$850$	63.4083	+	386.831i	0.0745980	+	0.455096i
$851$	−147.595	−	85.2139i	−0.173437	−	0.100134i
$852$		0			0
$853$	798.259	−	460.875i	0.935825	−	0.540299i	0.0471757	−	0.998887i	$-0.484978\pi$
$853$	798.259	−	460.875i	0.935825	−	0.540299i	0.888649	+	0.458588i	$0.151645\pi$
$854$			1540.64i			1.80403i
$855$		0			0
$856$	231.834			0.270834
$857$	101.333	+	175.514i	0.118241	+	0.204800i	0.919071	−	0.394092i	$-0.128941\pi$
$857$	101.333	+	175.514i	0.118241	+	0.204800i	−0.800829	+	0.598893i	$0.795608\pi$
$858$		0			0
$859$	−663.639	+	1149.46i	−0.772572	+	1.33813i	0.163578	+	0.986530i	$0.447697\pi$
$859$	−663.639	+	1149.46i	−0.772572	+	1.33813i	−0.936149	+	0.351603i	$0.885637\pi$
$860$	6.38436	−	34.9729i	0.00742367	−	0.0406662i
$861$		0			0
$862$	−110.282	+	63.6712i	−0.127937	+	0.0738645i
$863$	983.885			1.14008			0.570038	−	0.821619i	$-0.306929\pi$
$863$	983.885			1.14008			0.570038	+	0.821619i	$0.306929\pi$
$864$		0			0
$865$	−480.272	−	1344.71i	−0.555227	−	1.55458i
$866$	−27.7027	+	15.9941i	−0.0319892	+	0.0184690i
$867$		0			0
$868$	957.843	+	553.011i	1.10351	+	0.637109i
$869$	37.2350	+	21.4976i	0.0428481	+	0.0247383i
$870$		0			0
$871$	−78.8780	−	136.621i	−0.0905603	−	0.156855i
$872$	−318.191			−0.364899
$873$		0			0
$874$	82.2040			0.0940549
$875$	−1177.10	−	21.2971i	−1.34525	−	0.0243396i
$876$		0			0
$877$	1131.82	+	653.455i	1.29056	+	0.745103i	0.978753	−	0.205044i	$-0.0657337\pi$
$877$	1131.82	+	653.455i	1.29056	+	0.745103i	0.311803	+	0.950147i	$0.399067\pi$
$878$	452.064	−	782.998i	0.514879	−	0.891797i
$879$		0			0
$880$	35.8911	+	30.4869i	0.0407854	+	0.0346443i
$881$		−	642.541i		−	0.729331i	−0.931139	−	0.364666i	$-0.881183\pi$
$881$		−	642.541i		−	0.729331i	0.931139	−	0.364666i	$-0.118817\pi$
$882$		0			0
$883$		−	955.440i		−	1.08204i	−0.841010	−	0.541019i	$-0.818039\pi$
$883$		−	955.440i		−	1.08204i	0.841010	−	0.541019i	$-0.181961\pi$
$884$	29.5416	−	17.0559i	0.0334181	−	0.0192940i
$885$		0			0
$886$	−311.186	+	538.991i	−0.351226	+	0.608342i
$887$	432.681	−	749.426i	0.487803	−	0.844900i	−0.512099	−	0.858927i	$-0.671132\pi$
$887$	432.681	−	749.426i	0.487803	−	0.844900i	0.999902	+	0.0140270i	$0.00446508\pi$
$888$		0			0
$889$	−416.098	−	720.703i	−0.468052	−	0.810690i
$890$	587.557	−	209.849i	0.660176	−	0.235786i
$891$		0			0
$892$		−	552.494i		−	0.619388i
$893$	−247.414	−	428.533i	−0.277059	−	0.479880i
$894$		0			0
$895$	−162.137	+	888.172i	−0.181159	+	0.992371i
$896$	−92.2803	−	53.2780i	−0.102991	−	0.0594621i
$897$		0			0
$898$	−345.288	+	199.352i	−0.384508	+	0.221996i
$899$		−	1053.93i		−	1.17234i
$900$		0			0
$901$	765.132			0.849203
$902$	−81.4283	−	141.038i	−0.0902752	−	0.156361i
$903$		0			0
$904$	−127.001	+	219.973i	−0.140488	+	0.243332i
$905$	−431.478	−	78.7669i	−0.476771	−	0.0870353i
$906$		0			0
$907$	−668.018	+	385.680i	−0.736513	+	0.425226i	−0.820800	−	0.571215i	$-0.806472\pi$
$907$	−668.018	+	385.680i	−0.736513	+	0.425226i	0.0842869	+	0.996442i	$0.473139\pi$
$908$	−5.41547			−0.00596417
$909$		0			0
$910$	34.4584	+	96.4801i	0.0378664	+	0.106022i
$911$	−1131.06	+	653.020i	−1.24156	+	0.716817i	−0.969412	−	0.245437i	$-0.921068\pi$
$911$	−1131.06	+	653.020i	−1.24156	+	0.716817i	−0.272151	+	0.962255i	$0.587735\pi$
$912$		0			0
$913$	−330.218	−	190.652i	−0.361685	−	0.208819i
$914$	−455.229	−	262.827i	−0.498063	−	0.287557i
$915$		0			0
$916$	209.636	+	363.100i	0.228860	+	0.396397i
$917$	1636.32			1.78443
$918$		0			0
$919$	1455.53			1.58382			0.791909	−	0.610640i	$-0.209088\pi$
$919$	1455.53			1.58382			0.791909	+	0.610640i	$0.209088\pi$
$920$	75.0380	−	88.3394i	0.0815631	−	0.0960211i
$921$		0			0
$922$	271.780	+	156.912i	0.294772	+	0.170187i
$923$	78.9677	−	136.776i	0.0855555	−	0.148186i
$924$		0			0
$925$	−183.680	+	486.326i	−0.198573	+	0.525757i
$926$		−	506.213i		−	0.546666i
$927$		0			0
$928$			101.538i			0.109416i
$929$	181.827	−	104.978i	0.195723	−	0.113001i	−0.398936	−	0.916979i	$-0.630620\pi$
$929$	181.827	−	104.978i	0.195723	−	0.113001i	0.594659	+	0.803978i	$0.297287\pi$
$930$		0			0
$931$	140.797	−	243.867i	0.151232	−	0.261941i
$932$	−183.458	+	317.759i	−0.196844	+	0.340944i
$933$		0			0
$934$	277.326	+	480.343i	0.296923	+	0.514286i
$935$	122.925	−	43.9032i	0.131470	−	0.0469553i
$936$		0			0
$937$			890.537i			0.950413i	0.879874	+	0.475206i	$0.157627\pi$
$937$			890.537i			0.950413i	−0.879874	+	0.475206i	$0.842373\pi$
$938$	682.959	+	1182.92i	0.728101	+	1.26111i
$939$		0			0
$940$	−686.364	−	125.297i	−0.730174	−	0.133294i
$941$	936.173	+	540.500i	0.994871	+	0.574389i	0.906727	−	0.421719i	$-0.138573\pi$
$941$	936.173	+	540.500i	0.994871	+	0.574389i	0.0881441	+	0.996108i	$0.471906\pi$
$942$		0			0
$943$	−347.139	+	200.421i	−0.368122	+	0.212535i
$944$			157.377i			0.166713i
$945$		0			0
$946$	−11.8380			−0.0125138
$947$	451.107	+	781.340i	0.476354	+	0.825069i	0.999633	−	0.0270926i	$-0.00862490\pi$
$947$	451.107	+	781.340i	0.476354	+	0.825069i	−0.523279	+	0.852161i	$0.675292\pi$
$948$		0			0
$949$	−92.7710	+	160.684i	−0.0977566	+	0.169319i
$950$	−40.5605	−	247.445i	−0.0426952	−	0.260468i
$951$		0			0
$952$	−255.784	+	147.677i	−0.268680	+	0.155123i
$953$	931.541			0.977483			0.488742	−	0.872429i	$-0.337456\pi$
$953$	931.541			0.977483			0.488742	+	0.872429i	$0.337456\pi$
$954$		0			0
$955$	−291.502	+	104.112i	−0.305238	+	0.109017i
$956$	−100.434	+	57.9858i	−0.105057	+	0.0606546i
$957$		0			0
$958$	−985.902	−	569.211i	−1.02913	−	0.594166i
$959$	−888.716	−	513.101i	−0.926711	−	0.535037i
$960$		0			0
$961$	−1243.32	−	2153.48i	−1.29377	−	2.24088i
$962$	45.2385			0.0470255
$963$		0			0
$964$	314.080			0.325809
$965$	−856.581	−	727.604i	−0.887649	−	0.753994i
$966$		0			0
$967$	1318.94	+	761.492i	1.36395	+	0.787479i	0.990148	−	0.140028i	$-0.0447192\pi$
$967$	1318.94	+	761.492i	1.36395	+	0.787479i	0.373806	+	0.927507i	$0.378052\pi$
$968$	−163.279	+	282.808i	−0.168677	+	0.292157i
$969$		0			0
$970$	757.836	+	643.727i	0.781274	+	0.663636i
$971$		−	11.0650i		−	0.0113955i	−0.999984	−	0.00569775i	$-0.998186\pi$
$971$		−	11.0650i		−	0.0113955i	0.999984	−	0.00569775i	$-0.00181366\pi$
$972$		0			0
$973$		−	1255.57i		−	1.29041i
$974$	−584.726	+	337.592i	−0.600334	+	0.346603i
$975$		0			0
$976$	−231.336	+	400.686i	−0.237025	+	0.410539i
$977$	−273.583	+	473.860i	−0.280024	+	0.485015i	−0.971390	−	0.237489i	$-0.923676\pi$
$977$	−273.583	+	473.860i	−0.280024	+	0.485015i	0.691367	+	0.722504i	$0.257009\pi$
$978$		0			0
$979$	−103.877	−	179.920i	−0.106105	−	0.183779i
$980$	−133.545	−	373.914i	−0.136271	−	0.381545i
$981$		0			0
$982$		−	508.244i		−	0.517560i
$983$	703.023	+	1217.67i	0.715181	+	1.23873i	0.962890	+	0.269895i	$0.0869891\pi$
$983$	703.023	+	1217.67i	0.715181	+	1.23873i	−0.247709	+	0.968835i	$0.579678\pi$
$984$		0			0
$985$	−1280.25	−	233.711i	−1.29974	−	0.237270i
$986$	243.738	+	140.722i	0.247198	+	0.142720i
$987$		0			0
$988$	−18.8969	+	10.9102i	−0.0191265	+	0.0110427i
$989$			29.1372i			0.0294612i
$990$		0			0
$991$	−700.700			−0.707063			−0.353532	−	0.935423i	$-0.615019\pi$
$991$	−700.700			−0.707063			−0.353532	+	0.935423i	$0.615019\pi$
$992$	166.075	+	287.651i	0.167415	+	0.289971i
$993$		0			0
$994$	−683.736	+	1184.26i	−0.687863	+	1.19141i
$995$	133.839	+	24.4325i	0.134512	+	0.0245553i
$996$		0			0
$997$	471.260	−	272.082i	0.472678	−	0.272901i	−0.244682	−	0.969603i	$-0.578684\pi$
$997$	471.260	−	272.082i	0.472678	−	0.272901i	0.717360	+	0.696703i	$0.245350\pi$
$998$	548.864			0.549964
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.h.539.5		24
3.2	odd	2	inner	810.3.j.h.539.10		24
5.4	even	2		810.3.j.g.539.10		24
9.2	odd	6		810.3.j.g.269.10		24
9.4	even	3		810.3.b.c.809.22	yes	24
9.5	odd	6		810.3.b.c.809.3	✓	24
9.7	even	3		810.3.j.g.269.5		24
15.14	odd	2		810.3.j.g.539.5		24
45.4	even	6		810.3.b.c.809.4	yes	24
45.14	odd	6		810.3.b.c.809.21	yes	24
45.29	odd	6	inner	810.3.j.h.269.5		24
45.34	even	6	inner	810.3.j.h.269.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.3.b.c.809.3	✓	24	9.5	odd	6
810.3.b.c.809.4	yes	24	45.4	even	6
810.3.b.c.809.21	yes	24	45.14	odd	6
810.3.b.c.809.22	yes	24	9.4	even	3
810.3.j.g.269.5		24	9.7	even	3
810.3.j.g.269.10		24	9.2	odd	6
810.3.j.g.539.5		24	15.14	odd	2
810.3.j.g.539.10		24	5.4	even	2
810.3.j.h.269.5		24	45.29	odd	6	inner
810.3.j.h.269.10		24	45.34	even	6	inner
810.3.j.h.539.5		24	1.1	even	1	trivial
810.3.j.h.539.10		24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-4.91871 - 0.897918i) q^{5} +(8.15650 - 4.70916i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-4.91871 - 0.897918i) q^{5} +(8.15650 - 4.70916i) q^{7} +2.82843 q^{8} +(2.37833 + 6.65909i) q^{10} +(2.03913 - 1.17729i) q^{11} +(1.33223 + 0.769165i) q^{13} +(-11.5350 - 6.65975i) q^{14} +(-2.00000 - 3.46410i) q^{16} -11.0873 q^{17} +7.09220 q^{19} +(6.47395 - 7.62154i) q^{20} +(-2.88377 - 1.66494i) q^{22} +(-4.09795 + 7.09786i) q^{23} +(23.3875 + 8.83321i) q^{25} -2.17553i q^{26} +18.8366i q^{28} +(15.5447 - 8.97476i) q^{29} +(29.3583 - 50.8500i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(7.83988 + 13.5791i) q^{34} +(-44.3479 + 15.8391i) q^{35} +20.7943i q^{37} +(-5.01495 - 8.68614i) q^{38} +(-13.9122 - 2.53970i) q^{40} +(42.3552 + 24.4538i) q^{41} +(3.07880 - 1.77754i) q^{43} +4.70917i q^{44} +11.5908 q^{46} +(-34.8853 - 60.4231i) q^{47} +(19.8523 - 34.3852i) q^{49} +(-5.71902 - 34.8897i) q^{50} +(-2.66447 + 1.53833i) q^{52} -69.0100 q^{53} +(-11.0870 + 3.95979i) q^{55} +(23.0701 - 13.3195i) q^{56} +(-21.9836 - 12.6922i) q^{58} +(-34.0732 - 19.6721i) q^{59} +(-57.8340 - 100.172i) q^{61} -83.0377 q^{62} +8.00000 q^{64} +(-5.86222 - 4.97954i) q^{65} +(-88.8111 - 51.2751i) q^{67} +(11.0873 - 19.2037i) q^{68} +(50.7576 + 43.1149i) q^{70} -102.667i q^{71} +120.613i q^{73} +(25.4677 - 14.7038i) q^{74} +(-7.09220 + 12.2841i) q^{76} +(11.0881 - 19.2052i) q^{77} +(9.13011 + 15.8138i) q^{79} +(6.72695 + 18.8348i) q^{80} -69.1657i q^{82} +(-80.9703 - 140.245i) q^{83} +(54.5351 + 9.95546i) q^{85} +(-4.35408 - 2.51383i) q^{86} +(5.76753 - 3.32989i) q^{88} -88.2337i q^{89} +14.4885 q^{91} +(-8.19590 - 14.1957i) q^{92} +(-49.3353 + 85.4512i) q^{94} +(-34.8845 - 6.36822i) q^{95} +(121.781 - 70.3100i) q^{97} -56.1508 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 24 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 + 24 * q^7	\( 24 q - 24 q^{4} + 24 q^{7} - 12 q^{10} + 48 q^{13} - 48 q^{16} - 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{40} - 24 q^{43} - 36 q^{49} - 96 q^{52} + 216 q^{55} + 396 q^{58} - 60 q^{61} + 192 q^{64} - 1032 q^{67} + 288 q^{70} - 240 q^{79} - 48 q^{85} + 240 q^{88} + 48 q^{91} - 48 q^{94} - 1440 q^{97}+O(q^{100}) \) 24 * q - 24 * q^4 + 24 * q^7 - 12 * q^10 + 48 * q^13 - 48 * q^16 - 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^40 - 24 * q^43 - 36 * q^49 - 96 * q^52 + 216 * q^55 + 396 * q^58 - 60 * q^61 + 192 * q^64 - 1032 * q^67 + 288 * q^70 - 240 * q^79 - 48 * q^85 + 240 * q^88 + 48 * q^91 - 48 * q^94 - 1440 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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