LMFDB - Embedded newform 432.3.bc.a.257.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			257.3
Character	$\chi$	$=$	432.257
Dual form			432.3.bc.a.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10490 + 2.78912i) q^{3} +(-3.46013 + 4.12362i) q^{5} +(-9.89907 - 3.60297i) q^{7} +(-6.55839 - 6.16340i) q^{9} +O(q^{10})$	\(q+(-1.10490 + 2.78912i) q^{3} +(-3.46013 + 4.12362i) q^{5} +(-9.89907 - 3.60297i) q^{7} +(-6.55839 - 6.16340i) q^{9} +(7.54888 + 8.99640i) q^{11} +(1.95057 - 11.0622i) q^{13} +(-7.67818 - 14.2069i) q^{15} +(2.73630 + 1.57980i) q^{17} +(-2.26051 - 3.91532i) q^{19} +(20.9866 - 23.6288i) q^{21} +(-6.80880 - 18.7070i) q^{23} +(-0.690550 - 3.91630i) q^{25} +(24.4368 - 11.4822i) q^{27} +(24.9744 - 4.40366i) q^{29} +(20.7874 - 7.56598i) q^{31} +(-33.4328 + 11.1146i) q^{33} +(49.1093 - 28.3533i) q^{35} +(-8.82807 + 15.2907i) q^{37} +(28.6987 + 17.6630i) q^{39} +(-12.2557 - 2.16101i) q^{41} +(-27.9211 + 23.4286i) q^{43} +(48.1084 - 5.71818i) q^{45} +(4.24091 - 11.6518i) q^{47} +(47.4740 + 39.8354i) q^{49} +(-7.42960 + 5.88634i) q^{51} -84.6210i q^{53} -63.2178 q^{55} +(13.4179 - 1.97880i) q^{57} +(43.8854 - 52.3006i) q^{59} +(-73.3637 - 26.7022i) q^{61} +(42.7155 + 84.6415i) q^{63} +(38.8672 + 46.3201i) q^{65} +(16.8654 - 95.6483i) q^{67} +(59.6992 + 1.67882i) q^{69} +(-105.364 - 60.8322i) q^{71} +(-45.5705 - 78.9304i) q^{73} +(11.6860 + 2.40109i) q^{75} +(-42.3131 - 116.254i) q^{77} +(3.54032 + 20.0781i) q^{79} +(5.02506 + 80.8440i) q^{81} +(-31.1219 + 5.48763i) q^{83} +(-15.9824 + 5.81713i) q^{85} +(-15.3119 + 74.5223i) q^{87} +(59.7756 - 34.5114i) q^{89} +(-59.1656 + 102.478i) q^{91} +(-1.86551 + 66.3381i) q^{93} +(23.9669 + 4.22602i) q^{95} +(-61.1335 + 51.2971i) q^{97} +(5.93989 - 105.529i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7}+O(q^{10}) $ 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7	$ 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37} - 15 q^{39} + 228 q^{41} + 96 q^{43} + 477 q^{45} - 399 q^{47} - 78 q^{49} - 36 q^{51} + 12 q^{55} - 192 q^{57} + 474 q^{59} + 138 q^{61} + 585 q^{63} - 411 q^{65} - 354 q^{67} + 99 q^{69} - 315 q^{71} - 66 q^{73} - 255 q^{75} + 201 q^{77} - 30 q^{79} + 36 q^{81} + 33 q^{83} - 261 q^{85} + 279 q^{87} + 72 q^{89} - 96 q^{91} + 591 q^{93} - 681 q^{95} - 582 q^{97} - 513 q^{99}+O(q^{100}) $ 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{18}\right)$

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			0
$2$		0			0
$3$	−1.10490	+	2.78912i	−0.368300	+	0.929707i
$3$	−1.10490	+	2.78912i	−0.368300	+	0.929707i
$4$		0			0
$5$	−3.46013	+	4.12362i	−0.692026	+	0.824724i	−0.991599	−	0.129349i	$-0.958711\pi$
$5$	−3.46013	+	4.12362i	−0.692026	+	0.824724i	0.299574	+	0.954073i	$0.403156\pi$
$6$		0			0
$7$	−9.89907	−	3.60297i	−1.41415	−	0.514709i	−0.481807	−	0.876278i	$-0.660019\pi$
$7$	−9.89907	−	3.60297i	−1.41415	−	0.514709i	−0.932346	+	0.361568i	$0.882241\pi$
$8$		0			0
$9$	−6.55839	−	6.16340i	−0.728710	−	0.684822i
$10$		0			0
$11$	7.54888	+	8.99640i	0.686262	+	0.817855i	0.990898	−	0.134614i	$-0.0429794\pi$
$11$	7.54888	+	8.99640i	0.686262	+	0.817855i	−0.304636	+	0.952469i	$0.598535\pi$
$12$		0			0
$13$	1.95057	−	11.0622i	0.150044	−	0.850940i	−0.813134	−	0.582076i	$-0.802241\pi$
$13$	1.95057	−	11.0622i	0.150044	−	0.850940i	0.963178	−	0.268864i	$-0.0866482\pi$
$14$		0			0
$15$	−7.67818	−	14.2069i	−0.511879	−	0.947127i
$16$		0			0
$17$	2.73630	+	1.57980i	0.160959	+	0.0929296i	0.578316	−	0.815813i	$-0.303710\pi$
$17$	2.73630	+	1.57980i	0.160959	+	0.0929296i	−0.417357	+	0.908743i	$0.637044\pi$
$18$		0			0
$19$	−2.26051	−	3.91532i	−0.118974	−	0.206069i	0.800387	−	0.599483i	$-0.204627\pi$
$19$	−2.26051	−	3.91532i	−0.118974	−	0.206069i	−0.919361	+	0.393414i	$0.871294\pi$
$20$		0			0
$21$	20.9866	−	23.6288i	0.999361	−	1.12518i
$22$		0			0
$23$	−6.80880	−	18.7070i	−0.296035	−	0.813349i	−0.995153	−	0.0983427i	$-0.968646\pi$
$23$	−6.80880	−	18.7070i	−0.296035	−	0.813349i	0.699118	−	0.715007i	$-0.253576\pi$
$24$		0			0
$25$	−0.690550	−	3.91630i	−0.0276220	−	0.156652i
$26$		0			0
$27$	24.4368	−	11.4822i	0.905068	−	0.425267i
$28$		0			0
$29$	24.9744	−	4.40366i	0.861187	−	0.151851i	0.274424	−	0.961609i	$-0.411513\pi$
$29$	24.9744	−	4.40366i	0.861187	−	0.151851i	0.586763	+	0.809758i	$0.300402\pi$
$30$		0			0
$31$	20.7874	−	7.56598i	0.670560	−	0.244064i	0.0157712	−	0.999876i	$-0.494980\pi$
$31$	20.7874	−	7.56598i	0.670560	−	0.244064i	0.654789	+	0.755812i	$0.272757\pi$
$32$		0			0
$33$	−33.4328	+	11.1146i	−1.01312	+	0.336807i
$34$		0			0
$35$	49.1093	−	28.3533i	1.40312	−	0.810093i
$36$		0			0
$37$	−8.82807	+	15.2907i	−0.238596	+	0.413261i	−0.960312	−	0.278929i	$-0.910021\pi$
$37$	−8.82807	+	15.2907i	−0.238596	+	0.413261i	0.721715	+	0.692190i	$0.243354\pi$
$38$		0			0
$39$	28.6987	+	17.6630i	0.735864	+	0.452898i
$40$		0			0
$41$	−12.2557	−	2.16101i	−0.298920	−	0.0527076i	0.0221770	−	0.999754i	$-0.492940\pi$
$41$	−12.2557	−	2.16101i	−0.298920	−	0.0527076i	−0.321096	+	0.947046i	$0.604051\pi$
$42$		0			0
$43$	−27.9211	+	23.4286i	−0.649329	+	0.544851i	−0.906867	−	0.421417i	$-0.861533\pi$
$43$	−27.9211	+	23.4286i	−0.649329	+	0.544851i	0.257539	+	0.966268i	$0.417089\pi$
$44$		0			0
$45$	48.1084	−	5.71818i	1.06908	−	0.127071i
$46$		0			0
$47$	4.24091	−	11.6518i	0.0902320	−	0.247910i	−0.886365	−	0.462987i	$-0.846778\pi$
$47$	4.24091	−	11.6518i	0.0902320	−	0.247910i	0.976597	+	0.215076i	$0.0690000\pi$
$48$		0			0
$49$	47.4740	+	39.8354i	0.968857	+	0.812967i
$50$		0			0
$51$	−7.42960	+	5.88634i	−0.145678	+	0.115419i
$52$		0			0
$53$		−	84.6210i		−	1.59662i	−0.602245	−	0.798311i	$-0.705727\pi$
$53$		−	84.6210i		−	1.59662i	0.602245	−	0.798311i	$-0.294273\pi$
$54$		0			0
$55$	−63.2178			−1.14942
$56$		0			0
$57$	13.4179	−	1.97880i	0.235402	−	0.0347158i
$58$		0			0
$59$	43.8854	−	52.3006i	0.743820	−	0.886451i	−0.252890	−	0.967495i	$-0.581381\pi$
$59$	43.8854	−	52.3006i	0.743820	−	0.886451i	0.996711	+	0.0810443i	$0.0258255\pi$
$60$		0			0
$61$	−73.3637	−	26.7022i	−1.20268	−	0.437741i	−0.338523	−	0.940958i	$-0.609927\pi$
$61$	−73.3637	−	26.7022i	−1.20268	−	0.437741i	−0.864160	+	0.503217i	$0.832150\pi$
$62$		0			0
$63$	42.7155	+	84.6415i	0.678023	+	1.34352i
$64$		0			0
$65$	38.8672	+	46.3201i	0.597956	+	0.712617i
$66$		0			0
$67$	16.8654	−	95.6483i	0.251722	−	1.42759i	−0.552627	−	0.833429i	$-0.686375\pi$
$67$	16.8654	−	95.6483i	0.251722	−	1.42759i	0.804349	−	0.594157i	$-0.202514\pi$
$68$		0			0
$69$	59.6992	+	1.67882i	0.865206	+	0.0243307i
$70$		0			0
$71$	−105.364	−	60.8322i	−1.48401	−	0.856791i	−0.484171	−	0.874973i	$-0.660879\pi$
$71$	−105.364	−	60.8322i	−1.48401	−	0.856791i	−0.999835	+	0.0181820i	$0.994212\pi$
$72$		0			0
$73$	−45.5705	−	78.9304i	−0.624254	−	1.08124i	−0.988685	−	0.150009i	$-0.952070\pi$
$73$	−45.5705	−	78.9304i	−0.624254	−	1.08124i	0.364431	−	0.931230i	$-0.381263\pi$
$74$		0			0
$75$	11.6860	+	2.40109i	0.155814	+	0.0320146i
$76$		0			0
$77$	−42.3131	−	116.254i	−0.549521	−	1.50980i
$78$		0			0
$79$	3.54032	+	20.0781i	0.0448142	+	0.254154i	0.998982	−	0.0451196i	$-0.0143669\pi$
$79$	3.54032	+	20.0781i	0.0448142	+	0.254154i	−0.954167	+	0.299273i	$0.903256\pi$
$80$		0			0
$81$	5.02506	+	80.8440i	0.0620378	+	0.998074i
$82$		0			0
$83$	−31.1219	+	5.48763i	−0.374963	+	0.0661161i	−0.357954	−	0.933739i	$-0.616526\pi$
$83$	−31.1219	+	5.48763i	−0.374963	+	0.0661161i	−0.0170090	+	0.999855i	$0.505414\pi$
$84$		0			0
$85$	−15.9824	+	5.81713i	−0.188029	+	0.0684369i
$86$		0			0
$87$	−15.3119	+	74.5223i	−0.175999	+	0.856578i
$88$		0			0
$89$	59.7756	−	34.5114i	0.671636	−	0.387769i	−0.125060	−	0.992149i	$-0.539912\pi$
$89$	59.7756	−	34.5114i	0.671636	−	0.387769i	0.796696	+	0.604380i	$0.206579\pi$
$90$		0			0
$91$	−59.1656	+	102.478i	−0.650171	+	1.12613i
$92$		0			0
$93$	−1.86551	+	66.3381i	−0.0200592	+	0.713313i
$94$		0			0
$95$	23.9669	+	4.22602i	0.252283	+	0.0444844i
$96$		0			0
$97$	−61.1335	+	51.2971i	−0.630243	+	0.528836i	−0.901004	−	0.433810i	$-0.857169\pi$
$97$	−61.1335	+	51.2971i	−0.630243	+	0.528836i	0.270762	+	0.962646i	$0.412724\pi$
$98$		0			0
$99$	5.93989	−	105.529i	0.0599989	−	1.06595i
$100$		0			0
$101$	−1.63372	+	4.48862i	−0.0161755	+	0.0444417i	−0.947518	−	0.319704i	$-0.896417\pi$
$101$	−1.63372	+	4.48862i	−0.0161755	+	0.0444417i	0.931342	+	0.364145i	$0.118639\pi$
$102$		0			0
$103$	55.3795	+	46.4689i	0.537665	+	0.451154i	0.870738	−	0.491746i	$-0.163641\pi$
$103$	55.3795	+	46.4689i	0.537665	+	0.451154i	−0.333074	+	0.942901i	$0.608086\pi$
$104$		0			0
$105$	24.8199	+	168.299i	0.236380	+	1.60285i
$106$		0			0
$107$			158.133i			1.47788i	0.673773	+	0.738938i	$0.264672\pi$
$107$			158.133i			1.47788i	−0.673773	+	0.738938i	$0.735328\pi$
$108$		0			0
$109$	−18.5788			−0.170448			−0.0852240	−	0.996362i	$-0.527161\pi$
$109$	−18.5788			−0.170448			−0.0852240	+	0.996362i	$0.527161\pi$
$110$		0			0
$111$	−32.8934	−	41.5172i	−0.296337	−	0.374029i
$112$		0			0
$113$	−11.5806	+	13.8012i	−0.102483	+	0.122134i	−0.814848	−	0.579675i	$-0.803180\pi$
$113$	−11.5806	+	13.8012i	−0.102483	+	0.122134i	0.712365	+	0.701809i	$0.247624\pi$
$114$		0			0
$115$	100.700	+	36.6518i	0.875652	+	0.318711i
$116$		0			0
$117$	−80.9734	+	60.5283i	−0.692081	+	0.517336i
$118$		0			0
$119$	−21.3948	−	25.4974i	−0.179788	−	0.214264i
$120$		0			0
$121$	−2.93828	+	16.6638i	−0.0242833	+	0.137717i
$122$		0			0
$123$	19.5686	−	31.7949i	0.159095	−	0.258495i
$124$		0			0
$125$	−98.0067	−	56.5842i	−0.784054	−	0.452674i
$126$		0			0
$127$	−78.1067	−	135.285i	−0.615013	−	1.06523i	−0.990382	−	0.138359i	$-0.955817\pi$
$127$	−78.1067	−	135.285i	−0.615013	−	1.06523i	0.375369	−	0.926876i	$-0.377516\pi$
$128$		0			0
$129$	−34.4952	−	103.762i	−0.267405	−	0.804354i
$130$		0			0
$131$	−33.6955	−	92.5776i	−0.257217	−	0.706699i	−0.999336	−	0.0364307i	$-0.988401\pi$
$131$	−33.6955	−	92.5776i	−0.257217	−	0.706699i	0.742119	−	0.670268i	$-0.233821\pi$
$132$		0			0
$133$	8.27018	+	46.9025i	0.0621818	+	0.352651i
$134$		0			0
$135$	−37.2062	+	140.498i	−0.275602	+	1.04073i
$136$		0			0
$137$	−64.6590	+	11.4011i	−0.471963	+	0.0832199i	−0.404571	−	0.914507i	$-0.632579\pi$
$137$	−64.6590	+	11.4011i	−0.471963	+	0.0832199i	−0.0673925	+	0.997727i	$0.521468\pi$
$138$		0			0
$139$	−117.744	+	42.8553i	−0.847080	+	0.308312i	−0.728849	−	0.684674i	$-0.759944\pi$
$139$	−117.744	+	42.8553i	−0.847080	+	0.308312i	−0.118231	+	0.992986i	$0.537722\pi$
$140$		0			0
$141$	27.8125	+	24.7025i	0.197252	+	0.175195i
$142$		0			0
$143$	114.245	−	65.9593i	0.798915	−	0.461254i
$144$		0			0
$145$	−68.2557	+	118.222i	−0.470729	+	0.815326i
$146$		0			0
$147$	−163.560	+	88.3966i	−1.11265	+	0.601337i
$148$		0			0
$149$	198.691	+	35.0346i	1.33350	+	0.235132i	0.794546	−	0.607204i	$-0.207709\pi$
$149$	198.691	+	35.0346i	1.33350	+	0.235132i	0.538953	+	0.842336i	$0.318820\pi$
$150$		0			0
$151$	−98.1613	+	82.3671i	−0.650075	+	0.545478i	−0.907094	−	0.420929i	$-0.861704\pi$
$151$	−98.1613	+	82.3671i	−0.650075	+	0.545478i	0.257019	+	0.966406i	$0.417260\pi$
$152$		0			0
$153$	−8.20877	−	27.2259i	−0.0536521	−	0.177947i
$154$		0			0
$155$	−40.7277	+	111.898i	−0.262759	+	0.721926i
$156$		0			0
$157$	−106.439	−	89.3129i	−0.677955	−	0.568872i	0.237453	−	0.971399i	$-0.423687\pi$
$157$	−106.439	−	89.3129i	−0.677955	−	0.568872i	−0.915408	+	0.402527i	$0.868132\pi$
$158$		0			0
$159$	236.018	+	93.4977i	1.48439	+	0.588036i
$160$		0			0
$161$			209.714i			1.30257i
$162$		0			0
$163$	−39.8569			−0.244521			−0.122261	−	0.992498i	$-0.539014\pi$
$163$	−39.8569			−0.244521			−0.122261	+	0.992498i	$0.539014\pi$
$164$		0			0
$165$	69.8494	−	176.322i	0.423329	−	1.06862i
$166$		0			0
$167$	106.672	−	127.127i	0.638757	−	0.761241i	−0.345416	−	0.938450i	$-0.612262\pi$
$167$	106.672	−	127.127i	0.638757	−	0.761241i	0.984173	+	0.177208i	$0.0567067\pi$
$168$		0			0
$169$	40.2401	+	14.6462i	0.238107	+	0.0866639i
$170$		0			0
$171$	−9.30634	+	39.6106i	−0.0544231	+	0.231641i
$172$		0			0
$173$	−7.00006	−	8.34234i	−0.0404628	−	0.0482216i	0.745434	−	0.666580i	$-0.232243\pi$
$173$	−7.00006	−	8.34234i	−0.0404628	−	0.0482216i	−0.785896	+	0.618358i	$0.787798\pi$
$174$		0			0
$175$	−7.27451	+	41.2558i	−0.0415686	+	0.235747i
$176$		0			0
$177$	97.3837	+	180.189i	0.550191	+	1.01801i
$178$		0			0
$179$	244.720	+	141.289i	1.36715	+	0.789326i	0.990564	−	0.137054i	$-0.0437633\pi$
$179$	244.720	+	141.289i	1.36715	+	0.789326i	0.376590	+	0.926380i	$0.377097\pi$
$180$		0			0
$181$	54.3996	+	94.2228i	0.300550	+	0.520568i	0.976261	−	0.216599i	$-0.0694964\pi$
$181$	54.3996	+	94.2228i	0.300550	+	0.520568i	−0.675711	+	0.737167i	$0.736163\pi$
$182$		0			0
$183$	155.535	−	175.117i	0.849919	−	0.956923i
$184$		0			0
$185$	−32.5066	−	89.3112i	−0.175711	−	0.482763i
$186$		0			0
$187$	6.44344	+	36.5426i	0.0344569	+	0.195415i
$188$		0			0
$189$	−283.272	+	25.6182i	−1.49879	+	0.135546i
$190$		0			0
$191$	−106.979	+	18.8633i	−0.560100	+	0.0987607i	−0.446529	−	0.894769i	$-0.647340\pi$
$191$	−106.979	+	18.8633i	−0.560100	+	0.0987607i	−0.113571	+	0.993530i	$0.536229\pi$
$192$		0			0
$193$	−188.040	+	68.4410i	−0.974301	+	0.354617i	−0.779622	−	0.626250i	$-0.784589\pi$
$193$	−188.040	+	68.4410i	−0.974301	+	0.354617i	−0.194679	+	0.980867i	$0.562367\pi$
$194$		0			0
$195$	−172.137	+	57.2262i	−0.882752	+	0.293468i
$196$		0			0
$197$	253.494	−	146.355i	1.28677	−	0.742918i	0.308694	−	0.951161i	$-0.400108\pi$
$197$	253.494	−	146.355i	1.28677	−	0.742918i	0.978077	+	0.208243i	$0.0667746\pi$
$198$		0			0
$199$	−41.1548	+	71.2822i	−0.206808	+	0.358202i	−0.950707	−	0.310090i	$-0.899641\pi$
$199$	−41.1548	+	71.2822i	−0.206808	+	0.358202i	0.743899	+	0.668292i	$0.232974\pi$
$200$		0			0
$201$	248.140	+	152.721i	1.23453	+	0.759807i
$202$		0			0
$203$	−263.090	−	46.3898i	−1.29601	−	0.228521i
$204$		0			0
$205$	51.3175	−	43.0605i	0.250329	−	0.210051i
$206$		0			0
$207$	−70.6441	+	164.653i	−0.341276	+	0.795427i
$208$		0			0
$209$	18.1595	−	49.8927i	0.0868874	−	0.238721i
$210$		0			0
$211$	−88.7425	−	74.4638i	−0.420581	−	0.352909i	0.407803	−	0.913070i	$-0.366295\pi$
$211$	−88.7425	−	74.4638i	−0.420581	−	0.352909i	−0.828384	+	0.560161i	$0.810739\pi$
$212$		0			0
$213$	286.085	−	226.661i	1.34312	−	1.06413i
$214$		0			0
$215$		−	196.202i		−	0.912568i
$216$		0			0
$217$	−233.036			−1.07390
$218$		0			0
$219$	270.497	−	39.8915i	1.23515	−	0.182153i
$220$		0			0
$221$	22.8135	−	27.1880i	0.103228	−	0.123023i
$222$		0			0
$223$	−186.281	−	67.8007i	−0.835341	−	0.304039i	−0.111292	−	0.993788i	$-0.535499\pi$
$223$	−186.281	−	67.8007i	−0.835341	−	0.304039i	−0.724049	+	0.689749i	$0.757721\pi$
$224$		0			0
$225$	−19.6088	+	29.9408i	−0.0871504	+	0.133070i
$226$		0			0
$227$	3.31155	+	3.94655i	0.0145883	+	0.0173857i	0.773289	−	0.634053i	$-0.218610\pi$
$227$	3.31155	+	3.94655i	0.0145883	+	0.0173857i	−0.758701	+	0.651439i	$0.774166\pi$
$228$		0			0
$229$	61.3581	−	347.979i	0.267939	−	1.51956i	−0.492594	−	0.870259i	$-0.663951\pi$
$229$	61.3581	−	347.979i	0.267939	−	1.51956i	0.760533	−	0.649299i	$-0.224938\pi$
$230$		0			0
$231$	370.999	+	10.4330i	1.60606	+	0.0451643i
$232$		0			0
$233$	121.729	+	70.2803i	0.522442	+	0.301632i	0.737933	−	0.674874i	$-0.235802\pi$
$233$	121.729	+	70.2803i	0.522442	+	0.301632i	−0.215491	+	0.976506i	$0.569135\pi$
$234$		0			0
$235$	33.3735	+	57.8046i	0.142015	+	0.245977i
$236$		0			0
$237$	−59.9121	−	12.3100i	−0.252794	−	0.0519407i
$238$		0			0
$239$	50.5074	+	138.768i	0.211328	+	0.580619i	0.999388	−	0.0349794i	$-0.0111366\pi$
$239$	50.5074	+	138.768i	0.211328	+	0.580619i	−0.788060	+	0.615598i	$0.788914\pi$
$240$		0			0
$241$	52.8609	+	299.789i	0.219340	+	1.24394i	0.873215	+	0.487335i	$0.162031\pi$
$241$	52.8609	+	299.789i	0.219340	+	1.24394i	−0.653875	+	0.756602i	$0.726858\pi$
$242$		0			0
$243$	−231.036	−	75.3090i	−0.950765	−	0.309913i
$244$		0			0
$245$	−328.532	+	57.9291i	−1.34095	+	0.236445i
$246$		0			0
$247$	−47.7214	+	17.3692i	−0.193204	+	0.0703205i
$248$		0			0
$249$	19.0809	−	92.8661i	0.0766302	−	0.372956i
$250$		0			0
$251$	108.072	−	62.3955i	0.430567	−	0.248588i	−0.269021	−	0.963134i	$-0.586700\pi$
$251$	108.072	−	62.3955i	0.430567	−	0.248588i	0.699588	+	0.714546i	$0.253367\pi$
$252$		0			0
$253$	116.897	−	202.472i	0.462044	−	0.800284i
$254$		0			0
$255$	1.43430	−	51.0043i	0.00562472	−	0.200017i
$256$		0			0
$257$	−450.088	−	79.3627i	−1.75132	−	0.308804i	−0.796199	−	0.605035i	$-0.793159\pi$
$257$	−450.088	−	79.3627i	−1.75132	−	0.308804i	−0.955116	+	0.296231i	$0.904270\pi$
$258$		0			0
$259$	142.481	−	119.556i	0.550121	−	0.461606i
$260$		0			0
$261$	−190.934	−	125.046i	−0.731547	−	0.479105i
$262$		0			0
$263$	160.047	−	439.726i	0.608545	−	1.67196i	−0.124863	−	0.992174i	$-0.539849\pi$
$263$	160.047	−	439.726i	0.608545	−	1.67196i	0.733408	−	0.679789i	$-0.237929\pi$
$264$		0			0
$265$	348.945	+	292.799i	1.31677	+	1.10490i
$266$		0			0
$267$	30.2106	+	204.853i	0.113148	+	0.767240i
$268$		0			0
$269$			317.049i			1.17862i	0.807907	+	0.589310i	$0.200601\pi$
$269$			317.049i			1.17862i	−0.807907	+	0.589310i	$0.799399\pi$
$270$		0			0
$271$	−115.698			−0.426931			−0.213465	−	0.976951i	$-0.568475\pi$
$271$	−115.698			−0.426931			−0.213465	+	0.976951i	$0.568475\pi$
$272$		0			0
$273$	−220.451	−	278.248i	−0.807513	−	1.01922i
$274$		0			0
$275$	30.0198	−	35.7762i	0.109163	−	0.130095i
$276$		0			0
$277$	108.352	+	39.4370i	0.391163	+	0.142372i	0.530112	−	0.847928i	$-0.322150\pi$
$277$	108.352	+	39.4370i	0.391163	+	0.142372i	−0.138949	+	0.990300i	$0.544372\pi$
$278$		0			0
$279$	−182.964	−	78.5001i	−0.655785	−	0.281362i
$280$		0			0
$281$	−52.4463	−	62.5031i	−0.186642	−	0.222431i	0.664607	−	0.747193i	$-0.268599\pi$
$281$	−52.4463	−	62.5031i	−0.186642	−	0.222431i	−0.851249	+	0.524762i	$0.824154\pi$
$282$		0			0
$283$	72.4355	−	410.802i	0.255956	−	1.45160i	−0.537652	−	0.843167i	$-0.680689\pi$
$283$	72.4355	−	410.802i	0.255956	−	1.45160i	0.793608	−	0.608430i	$-0.208200\pi$
$284$		0			0
$285$	−38.2679	+	62.1773i	−0.134273	+	0.218166i
$286$		0			0
$287$	113.534	+	65.5489i	0.395589	+	0.228393i
$288$		0			0
$289$	−139.508	−	241.636i	−0.482728	−	0.836110i
$290$		0			0
$291$	−75.5275	−	227.187i	−0.259545	−	0.780712i
$292$		0			0
$293$	−118.282	−	324.977i	−0.403693	−	1.10914i	−0.960448	−	0.278460i	$-0.910176\pi$
$293$	−118.282	−	324.977i	−0.403693	−	1.10914i	0.556755	−	0.830676i	$-0.312046\pi$
$294$		0			0
$295$	63.8186	+	361.933i	0.216334	+	1.22689i
$296$		0			0
$297$	287.769	+	133.166i	0.968920	+	0.448369i
$298$		0			0
$299$	−220.222	+	38.8311i	−0.736529	+	0.129870i
$300$		0			0
$301$	360.806	−	131.323i	1.19869	−	0.436287i
$302$		0			0
$303$	−10.7142	−	9.51612i	−0.0353604	−	0.0314063i
$304$		0			0
$305$	363.957	−	210.131i	1.19330	−	0.688954i
$306$		0			0
$307$	288.668	−	499.988i	0.940286	−	1.62862i	0.175362	−	0.984504i	$-0.443890\pi$
$307$	288.668	−	499.988i	0.940286	−	1.62862i	0.764925	−	0.644120i	$-0.222776\pi$
$308$		0			0
$309$	−190.796	+	103.117i	−0.617463	+	0.333711i
$310$		0			0
$311$	−442.280	−	77.9859i	−1.42212	−	0.250759i	−0.590921	−	0.806730i	$-0.701235\pi$
$311$	−442.280	−	77.9859i	−1.42212	−	0.250759i	−0.831202	+	0.555971i	$0.812347\pi$
$312$		0			0
$313$	8.30206	−	6.96625i	0.0265241	−	0.0222564i	−0.629429	−	0.777058i	$-0.716711\pi$
$313$	8.30206	−	6.96625i	0.0265241	−	0.0222564i	0.655953	+	0.754801i	$0.272267\pi$
$314$		0			0
$315$	−496.830	−	116.728i	−1.57724	−	0.370566i
$316$		0			0
$317$	−74.6402	+	205.072i	−0.235458	+	0.646916i	0.764539	+	0.644577i	$0.222967\pi$
$317$	−74.6402	+	205.072i	−0.235458	+	0.646916i	−0.999997	+	0.00233841i	$0.999256\pi$
$318$		0			0
$319$	228.146	+	191.437i	0.715191	+	0.600117i
$320$		0			0
$321$	−441.051	−	174.721i	−1.37399	−	0.544302i
$322$		0			0
$323$		−	14.2846i		−	0.0442249i
$324$		0			0
$325$	−44.6700			−0.137446
$326$		0			0
$327$	20.5277	−	51.8186i	0.0627760	−	0.158467i
$328$		0			0
$329$	−83.9620	+	100.062i	−0.255204	+	0.304140i
$330$		0			0
$331$	564.453	+	205.444i	1.70530	+	0.620677i	0.996411	−	0.0846470i	$-0.0269763\pi$
$331$	564.453	+	205.444i	1.70530	+	0.620677i	0.708885	+	0.705324i	$0.249198\pi$
$332$		0			0
$333$	152.140	−	45.8713i	0.456878	−	0.137752i
$334$		0			0
$335$	336.061	+	400.502i	1.00317	+	1.19553i
$336$		0			0
$337$	78.0147	−	442.443i	0.231498	−	1.31289i	−0.618368	−	0.785889i	$-0.712206\pi$
$337$	78.0147	−	442.443i	0.231498	−	1.31289i	0.849865	−	0.527000i	$-0.176683\pi$
$338$		0			0
$339$	−25.6978	−	47.5485i	−0.0758047	−	0.140261i
$340$		0			0
$341$	224.988	+	129.897i	0.659789	+	0.380929i
$342$		0			0
$343$	−68.3305	−	118.352i	−0.199214	−	0.345049i
$344$		0			0
$345$	−213.490	+	240.368i	−0.618811	+	0.696719i
$346$		0			0
$347$	80.7717	+	221.918i	0.232771	+	0.639534i	0.999998	−	0.00184170i	$-0.000586231\pi$
$347$	80.7717	+	221.918i	0.232771	+	0.639534i	−0.767227	+	0.641376i	$0.778364\pi$
$348$		0			0
$349$	41.6381	+	236.141i	0.119307	+	0.676622i	0.984527	+	0.175231i	$0.0560672\pi$
$349$	41.6381	+	236.141i	0.119307	+	0.676622i	−0.865221	+	0.501391i	$0.832822\pi$
$350$		0			0
$351$	−79.3531	−	292.722i	−0.226077	−	0.833967i
$352$		0			0
$353$	25.2020	−	4.44379i	0.0713937	−	0.0125886i	−0.137837	−	0.990455i	$-0.544015\pi$
$353$	25.2020	−	4.44379i	0.0713937	−	0.0125886i	0.209231	+	0.977866i	$0.432904\pi$
$354$		0			0
$355$	615.423	−	223.996i	1.73359	−	0.630974i
$356$		0			0
$357$	94.7544	−	31.5007i	0.265418	−	0.0882374i
$358$		0			0
$359$	−16.7796	+	9.68773i	−0.0467399	+	0.0269853i	−0.523188	−	0.852217i	$-0.675257\pi$
$359$	−16.7796	+	9.68773i	−0.0467399	+	0.0269853i	0.476448	+	0.879203i	$0.341924\pi$
$360$		0			0
$361$	170.280	−	294.934i	0.471690	−	0.816992i
$362$		0			0
$363$	−43.2308	−	26.6070i	−0.119093	−	0.0732976i
$364$		0			0
$365$	483.159	+	85.1939i	1.32372	+	0.233408i
$366$		0			0
$367$	−299.305	+	251.147i	−0.815545	+	0.684324i	−0.951924	−	0.306333i	$-0.900898\pi$
$367$	−299.305	+	251.147i	−0.815545	+	0.684324i	0.136379	+	0.990657i	$0.456453\pi$
$368$		0			0
$369$	67.0585	+	89.7095i	0.181730	+	0.243115i
$370$		0			0
$371$	−304.886	+	837.669i	−0.821796	+	2.25787i
$372$		0			0
$373$	−136.986	−	114.945i	−0.367255	−	0.308164i	0.440419	−	0.897792i	$-0.354830\pi$
$373$	−136.986	−	114.945i	−0.367255	−	0.308164i	−0.807675	+	0.589628i	$0.799274\pi$
$374$		0			0
$375$	266.108	−	210.833i	0.709621	−	0.562221i
$376$		0			0
$377$		−	284.862i		−	0.755603i
$378$		0			0
$379$	−3.48118			−0.00918518			−0.00459259	−	0.999989i	$-0.501462\pi$
$379$	−3.48118			−0.00918518			−0.00459259	+	0.999989i	$0.501462\pi$
$380$		0			0
$381$	463.626	−	68.3730i	1.21687	−	0.179457i
$382$		0			0
$383$	−11.0730	+	13.1963i	−0.0289112	+	0.0344550i	−0.780306	−	0.625398i	$-0.784937\pi$
$383$	−11.0730	+	13.1963i	−0.0289112	+	0.0344550i	0.751395	+	0.659853i	$0.229381\pi$
$384$		0			0
$385$	625.797	+	227.772i	1.62545	+	0.591615i
$386$		0			0
$387$	327.518	+	18.4350i	0.846299	+	0.0476356i
$388$		0			0
$389$	203.618	+	242.662i	0.523439	+	0.623810i	0.961390	−	0.275189i	$-0.0887403\pi$
$389$	203.618	+	242.662i	0.523439	+	0.623810i	−0.437952	+	0.898999i	$0.644296\pi$
$390$		0			0
$391$	10.9225	−	61.9446i	0.0279348	−	0.158426i
$392$		0			0
$393$	295.440	+	8.30814i	0.751756	+	0.0211403i
$394$		0			0
$395$	−95.0446	−	54.8740i	−0.240619	−	0.138922i
$396$		0			0
$397$	−134.041	−	232.165i	−0.337634	−	0.584800i	0.646353	−	0.763039i	$-0.276293\pi$
$397$	−134.041	−	232.165i	−0.337634	−	0.584800i	−0.983987	+	0.178239i	$0.942960\pi$
$398$		0			0
$399$	−139.955	−	28.7560i	−0.350763	−	0.0720703i
$400$		0			0
$401$	33.3356	+	91.5887i	0.0831311	+	0.228401i	0.974293	−	0.225285i	$-0.0723312\pi$
$401$	33.3356	+	91.5887i	0.0831311	+	0.228401i	−0.891162	+	0.453685i	$0.850109\pi$
$402$		0			0
$403$	−43.1494	−	244.712i	−0.107070	−	0.607227i
$404$		0			0
$405$	−350.757	−	259.009i	−0.866067	−	0.639528i
$406$		0			0
$407$	−204.203	+	36.0065i	−0.501727	+	0.0884680i
$408$		0			0
$409$	380.898	−	138.636i	0.931292	−	0.338962i	0.168570	−	0.985690i	$-0.446085\pi$
$409$	380.898	−	138.636i	0.931292	−	0.338962i	0.762721	+	0.646727i	$0.223863\pi$
$410$		0			0
$411$	39.6426	−	192.939i	0.0964539	−	0.469437i
$412$		0			0
$413$	−622.862	+	359.609i	−1.50814	+	0.870725i
$414$		0			0
$415$	85.0569	−	147.323i	0.204956	−	0.354995i
$416$		0			0
$417$	10.5666	−	375.753i	0.0253397	−	0.901087i
$418$		0			0
$419$	−115.552	−	20.3750i	−0.275781	−	0.0486277i	0.0340470	−	0.999420i	$-0.489160\pi$
$419$	−115.552	−	20.3750i	−0.275781	−	0.0486277i	−0.309828	+	0.950793i	$0.600272\pi$
$420$		0			0
$421$	−399.365	+	335.107i	−0.948610	+	0.795979i	−0.979063	−	0.203558i	$-0.934750\pi$
$421$	−399.365	+	335.107i	−0.948610	+	0.795979i	0.0304527	+	0.999536i	$0.490305\pi$
$422$		0			0
$423$	−99.6282	+	50.2787i	−0.235528	+	0.118862i
$424$		0			0
$425$	4.29744	−	11.8071i	0.0101116	−	0.0277814i
$426$		0			0
$427$	630.025	+	528.654i	1.47547	+	1.23806i
$428$		0			0
$429$	57.7393	+	391.521i	0.134591	+	0.912636i
$430$		0			0
$431$		−	263.580i		−	0.611555i	−0.952103	−	0.305777i	$-0.901084\pi$
$431$		−	263.580i		−	0.611555i	0.952103	−	0.305777i	$-0.0989163\pi$
$432$		0			0
$433$	−702.013			−1.62128			−0.810639	−	0.585547i	$-0.800880\pi$
$433$	−702.013			−1.62128			−0.810639	+	0.585547i	$0.800880\pi$
$434$		0			0
$435$	−254.321	−	320.997i	−0.584645	−	0.737924i
$436$		0			0
$437$	−57.8526	+	68.9461i	−0.132386	+	0.157771i
$438$		0			0
$439$	−416.204	−	151.486i	−0.948073	−	0.345070i	−0.178724	−	0.983899i	$-0.557197\pi$
$439$	−416.204	−	151.486i	−0.948073	−	0.345070i	−0.769349	+	0.638829i	$0.779419\pi$
$440$		0			0
$441$	−65.8317	−	553.857i	−0.149278	−	1.25591i
$442$		0			0
$443$	390.071	+	464.868i	0.880520	+	1.04936i	0.998412	+	0.0563369i	$0.0179421\pi$
$443$	390.071	+	464.868i	0.880520	+	1.04936i	−0.117891	+	0.993026i	$0.537613\pi$
$444$		0			0
$445$	−64.5191	+	365.906i	−0.144987	+	0.822260i
$446$		0			0
$447$	−317.250	+	515.464i	−0.709731	+	1.15316i
$448$		0			0
$449$	347.745	+	200.771i	0.774488	+	0.447151i	0.834473	−	0.551048i	$-0.185772\pi$
$449$	347.745	+	200.771i	0.774488	+	0.447151i	−0.0599853	+	0.998199i	$0.519105\pi$
$450$		0			0
$451$	−73.0755	−	126.570i	−0.162030	−	0.280644i
$452$		0			0
$453$	−121.274	−	364.791i	−0.267712	−	0.805279i
$454$		0			0
$455$	−217.859	−	598.563i	−0.478811	−	1.31552i
$456$		0			0
$457$	−25.5458	−	144.878i	−0.0558990	−	0.317019i	0.944018	−	0.329894i	$-0.107013\pi$
$457$	−25.5458	−	144.878i	−0.0558990	−	0.317019i	−0.999917	+	0.0128747i	$0.995902\pi$
$458$		0			0
$459$	85.0061	+	7.18658i	0.185198	+	0.0156570i
$460$		0			0
$461$	−773.480	+	136.385i	−1.67783	+	0.295847i	−0.929868	−	0.367893i	$-0.880079\pi$
$461$	−773.480	+	136.385i	−1.67783	+	0.295847i	−0.747963	+	0.663740i	$0.768968\pi$
$462$		0			0
$463$	−336.835	+	122.598i	−0.727506	+	0.264791i	−0.679109	−	0.734037i	$-0.737634\pi$
$463$	−336.835	+	122.598i	−0.727506	+	0.264791i	−0.0483975	+	0.998828i	$0.515411\pi$
$464$		0			0
$465$	−267.098	−	237.231i	−0.574405	−	0.510174i
$466$		0			0
$467$	88.2727	−	50.9643i	0.189021	−	0.109131i	−0.402503	−	0.915419i	$-0.631860\pi$
$467$	88.2727	−	50.9643i	0.189021	−	0.109131i	0.591524	+	0.806287i	$0.298526\pi$
$468$		0			0
$469$	−511.569	+	886.063i	−1.09077	+	1.88926i
$470$		0			0
$471$	366.709	−	198.189i	0.778575	−	0.420784i
$472$		0			0
$473$	−421.547	−	74.3300i	−0.891219	−	0.157146i
$474$		0			0
$475$	−13.7726	+	11.5566i	−0.0289949	+	0.0243296i
$476$		0			0
$477$	−521.553	+	554.978i	−1.09340	+	1.16348i
$478$		0			0
$479$	−43.2210	+	118.749i	−0.0902318	+	0.247910i	−0.976597	−	0.215077i	$-0.931000\pi$
$479$	−43.2210	+	118.749i	−0.0902318	+	0.247910i	0.886365	+	0.462986i	$0.153222\pi$
$480$		0			0
$481$	151.929	+	127.483i	0.315860	+	0.265038i
$482$		0			0
$483$	−584.918	−	231.713i	−1.21101	−	0.479737i
$484$		0			0
$485$		−	429.586i		−	0.885745i
$486$		0			0
$487$	−454.010			−0.932258			−0.466129	−	0.884717i	$-0.654352\pi$
$487$	−454.010			−0.932258			−0.466129	+	0.884717i	$0.654352\pi$
$488$		0			0
$489$	44.0379	−	111.166i	0.0900571	−	0.227333i
$490$		0			0
$491$	−203.177	+	242.137i	−0.413803	+	0.493151i	−0.932177	−	0.362003i	$-0.882093\pi$
$491$	−203.177	+	242.137i	−0.413803	+	0.493151i	0.518374	+	0.855154i	$0.326537\pi$
$492$		0			0
$493$	75.2944	+	27.4049i	0.152727	+	0.0555881i
$494$		0			0
$495$	414.607	+	389.637i	0.837591	+	0.787145i
$496$		0			0
$497$	823.833	+	981.806i	1.65761	+	1.97547i
$498$		0			0
$499$	−21.2323	+	120.414i	−0.0425497	+	0.241312i	−0.998663	−	0.0516842i	$-0.983541\pi$
$499$	−21.2323	+	120.414i	−0.0425497	+	0.241312i	0.956114	+	0.292996i	$0.0946522\pi$
$500$		0			0
$501$	236.711	+	437.985i	0.472477	+	0.874222i
$502$		0			0
$503$	391.041	+	225.768i	0.777418	+	0.448843i	0.835515	−	0.549468i	$-0.185170\pi$
$503$	391.041	+	225.768i	0.777418	+	0.448843i	−0.0580963	+	0.998311i	$0.518503\pi$
$504$		0			0
$505$	−12.8565	−	22.2680i	−0.0254583	−	0.0440951i
$506$		0			0
$507$	−85.3113	+	96.0519i	−0.168267	+	0.189452i
$508$		0			0
$509$	−170.911	−	469.573i	−0.335778	−	0.922541i	−0.986578	−	0.163292i	$-0.947789\pi$
$509$	−170.911	−	469.573i	−0.335778	−	0.922541i	0.650800	−	0.759249i	$-0.274434\pi$
$510$		0			0
$511$	166.722	+	945.527i	0.326266	+	1.85035i
$512$		0			0
$513$	−100.196	−	69.7223i	−0.195314	−	0.135911i
$514$		0			0
$515$	−383.240	+	67.5756i	−0.744156	+	0.131215i
$516$		0			0
$517$	136.838	−	49.8051i	0.264678	−	0.0963348i
$518$		0			0
$519$	31.0022	−	10.3066i	0.0597344	−	0.0198585i
$520$		0			0
$521$	−595.632	+	343.888i	−1.14325	+	0.660054i	−0.947233	−	0.320546i	$-0.896133\pi$
$521$	−595.632	+	343.888i	−1.14325	+	0.660054i	−0.196015	+	0.980601i	$0.562800\pi$
$522$		0			0
$523$	−260.218	+	450.711i	−0.497549	+	0.861780i	−0.999996	−	0.00282784i	$-0.999100\pi$
$523$	−260.218	+	450.711i	−0.497549	+	0.861780i	0.502447	+	0.864608i	$0.332433\pi$
$524$		0			0
$525$	−107.030	−	65.8730i	−0.203866	−	0.125472i
$526$		0			0
$527$	68.8332	+	12.1372i	0.130613	+	0.0230306i
$528$		0			0
$529$	101.644	−	85.2896i	0.192144	−	0.161228i
$530$		0			0
$531$	−610.167	+	72.5247i	−1.14909	+	0.136581i
$532$		0			0
$533$	−47.8111	+	131.360i	−0.0897020	+	0.246454i
$534$		0			0
$535$	−652.079	−	547.160i	−1.21884	−	1.02273i
$536$		0			0
$537$	−664.465	+	526.444i	−1.23736	+	0.980343i
$538$		0			0
$539$			727.808i			1.35029i
$540$		0			0
$541$	803.120			1.48451			0.742255	−	0.670117i	$-0.233756\pi$
$541$	803.120			1.48451			0.742255	+	0.670117i	$0.233756\pi$
$542$		0			0
$543$	−322.905	+	47.6203i	−0.594668	+	0.0876984i
$544$		0			0
$545$	64.2851	−	76.6120i	0.117954	−	0.140572i
$546$		0			0
$547$	−64.5461	−	23.4929i	−0.118000	−	0.0429486i	0.282345	−	0.959313i	$-0.408888\pi$
$547$	−64.5461	−	23.4929i	−0.118000	−	0.0429486i	−0.400345	+	0.916364i	$0.631110\pi$
$548$		0			0
$549$	316.572	+	627.293i	0.576633	+	1.14261i
$550$		0			0
$551$	−73.6967	−	87.8283i	−0.133751	−	0.159398i
$552$		0			0
$553$	37.2950	−	211.511i	0.0674412	−	0.382478i
$554$		0			0
$555$	285.016	+	8.01501i	0.513543	+	0.0144415i
$556$		0			0
$557$	575.120	+	332.045i	1.03253	+	0.596132i	0.917709	−	0.397254i	$-0.130037\pi$
$557$	575.120	+	332.045i	1.03253	+	0.596132i	0.114822	+	0.993386i	$0.463370\pi$
$558$		0			0
$559$	204.710	+	354.569i	0.366208	+	0.634291i
$560$		0			0
$561$	−109.041	−	22.4043i	−0.194369	−	0.0399364i
$562$		0			0
$563$	118.905	+	326.689i	0.211199	+	0.580264i	0.999381	−	0.0351778i	$-0.0111997\pi$
$563$	118.905	+	326.689i	0.211199	+	0.580264i	−0.788182	+	0.615442i	$0.788978\pi$
$564$		0			0
$565$	−16.8406	−	95.5076i	−0.0298063	−	0.169040i
$566$		0			0
$567$	241.535	−	818.385i	0.425987	−	1.44336i
$568$		0			0
$569$	−385.078	+	67.8997i	−0.676763	+	0.119332i	−0.501457	−	0.865182i	$-0.667203\pi$
$569$	−385.078	+	67.8997i	−0.676763	+	0.119332i	−0.175306	+	0.984514i	$0.556091\pi$
$570$		0			0
$571$	804.118	−	292.675i	1.40826	−	0.512566i	0.477644	−	0.878554i	$-0.341491\pi$
$571$	804.118	−	292.675i	1.40826	−	0.512566i	0.930620	+	0.365988i	$0.119269\pi$
$572$		0			0
$573$	65.5891	−	319.219i	0.114466	−	0.557102i
$574$		0			0
$575$	−68.5606	+	39.5835i	−0.119236	+	0.0688408i
$576$		0			0
$577$	313.746	−	543.423i	0.543753	−	0.941808i	−0.454931	−	0.890527i	$-0.650336\pi$
$577$	313.746	−	543.423i	0.543753	−	0.941808i	0.998684	−	0.0512815i	$-0.0163306\pi$
$578$		0			0
$579$	16.8752	−	600.087i	0.0291454	−	1.03642i
$580$		0			0
$581$	327.850	+	57.8088i	0.564285	+	0.0994987i
$582$		0			0
$583$	761.285	−	638.794i	1.30581	−	1.09570i
$584$		0			0
$585$	30.5829	−	543.339i	0.0522785	−	0.928785i
$586$		0			0
$587$	254.654	−	699.655i	0.433822	−	1.19192i	−0.509626	−	0.860396i	$-0.670216\pi$
$587$	254.654	−	699.655i	0.433822	−	1.19192i	0.943448	−	0.331520i	$-0.107561\pi$
$588$		0			0
$589$	−76.6133	−	64.2862i	−0.130073	−	0.109145i
$590$		0			0
$591$	128.116	+	868.733i	0.216778	+	1.46994i
$592$		0			0
$593$		−	625.722i		−	1.05518i	−0.849499	−	0.527591i	$-0.823096\pi$
$593$		−	625.722i		−	1.05518i	0.849499	−	0.527591i	$-0.176904\pi$
$594$		0			0
$595$	179.170			0.301126
$596$		0			0
$597$	−153.343	−	193.546i	−0.256856	−	0.324197i
$598$		0			0
$599$	368.344	−	438.975i	0.614932	−	0.732847i	−0.365258	−	0.930906i	$-0.619019\pi$
$599$	368.344	−	438.975i	0.614932	−	0.732847i	0.980190	+	0.198059i	$0.0634638\pi$
$600$		0			0
$601$	−1063.24	−	386.989i	−1.76912	−	0.643908i	−0.999988	−	0.00482034i	$-0.998466\pi$
$601$	−1063.24	−	386.989i	−1.76912	−	0.643908i	−0.769134	−	0.639088i	$-0.779312\pi$
$602$		0			0
$603$	−700.128	+	523.351i	−1.16107	+	0.867912i
$604$		0			0
$605$	−58.5483	−	69.7752i	−0.0967741	−	0.115331i
$606$		0			0
$607$	40.3687	−	228.942i	0.0665052	−	0.377170i	−0.933330	−	0.359019i	$-0.883111\pi$
$607$	40.3687	−	228.942i	0.0665052	−	0.377170i	0.999835	−	0.0181503i	$-0.00577772\pi$
$608$		0			0
$609$	420.075	−	682.533i	0.689778	−	1.12074i
$610$		0			0
$611$	−120.623	−	69.6414i	−0.197418	−	0.113979i
$612$		0			0
$613$	533.889	+	924.724i	0.870945	+	1.50852i	0.861020	+	0.508571i	$0.169826\pi$
$613$	533.889	+	924.724i	0.870945	+	1.50852i	0.00992514	+	0.999951i	$0.496841\pi$
$614$		0			0
$615$	63.4002	+	190.708i	0.103090	+	0.310095i
$616$		0			0
$617$	144.247	+	396.317i	0.233788	+	0.642328i	1.00000		0.000260046i	$-8.27751e-5\pi$
$617$	144.247	+	396.317i	0.233788	+	0.642328i	−0.766212	+	0.642588i	$0.777861\pi$
$618$		0			0
$619$	−104.335	−	591.711i	−0.168554	−	0.955915i	−0.945324	−	0.326131i	$-0.894255\pi$
$619$	−104.335	−	591.711i	−0.168554	−	0.955915i	0.776771	−	0.629783i	$-0.216856\pi$
$620$		0			0
$621$	−381.184	−	378.960i	−0.613823	−	0.610242i
$622$		0			0
$623$	−716.066	+	126.262i	−1.14938	+	0.202667i
$624$		0			0
$625$	665.870	−	242.357i	1.06539	−	0.387771i
$626$		0			0
$627$	119.092	+	105.775i	0.189940	+	0.168701i
$628$		0			0
$629$	−48.3124	+	27.8932i	−0.0768083	+	0.0443453i
$630$		0			0
$631$	−554.621	+	960.632i	−0.878956	+	1.52240i	−0.0264679	+	0.999650i	$0.508426\pi$
$631$	−554.621	+	960.632i	−0.878956	+	1.52240i	−0.852488	+	0.522747i	$0.824907\pi$
$632$		0			0
$633$	305.740	−	165.239i	0.483002	−	0.261040i
$634$		0			0
$635$	828.122	+	146.020i	1.30413	+	0.229953i
$636$		0			0
$637$	533.269	−	447.466i	0.837157	−	0.702458i
$638$		0			0
$639$	316.089	+	1048.36i	0.494661	+	1.64063i
$640$		0			0
$641$	−56.5257	+	155.303i	−0.0881837	+	0.242283i	−0.975943	−	0.218025i	$-0.930039\pi$
$641$	−56.5257	+	155.303i	−0.0881837	+	0.242283i	0.887760	+	0.460308i	$0.152261\pi$
$642$		0			0
$643$	−608.717	−	510.774i	−0.946683	−	0.794361i	0.0320527	−	0.999486i	$-0.489796\pi$
$643$	−608.717	−	510.774i	−0.946683	−	0.794361i	−0.978736	+	0.205125i	$0.934240\pi$
$644$		0			0
$645$	547.231	+	216.784i	0.848421	+	0.336099i
$646$		0			0
$647$			222.504i			0.343900i	0.985106	+	0.171950i	$0.0550068\pi$
$647$			222.504i			0.343900i	−0.985106	+	0.171950i	$0.944993\pi$
$648$		0			0
$649$	801.803			1.23544
$650$		0			0
$651$	257.481	−	649.964i	0.395516	−	0.998409i
$652$		0			0
$653$	−299.851	+	357.348i	−0.459190	+	0.547241i	−0.945106	−	0.326764i	$-0.894042\pi$
$653$	−299.851	+	357.348i	−0.459190	+	0.547241i	0.485916	+	0.874006i	$0.338486\pi$
$654$		0			0
$655$	498.345	+	181.383i	0.760833	+	0.276920i
$656$		0			0
$657$	−187.610	+	798.526i	−0.285556	+	1.21541i
$658$		0			0
$659$	133.876	+	159.547i	0.203150	+	0.242104i	0.857994	−	0.513659i	$-0.171710\pi$
$659$	133.876	+	159.547i	0.203150	+	0.242104i	−0.654845	+	0.755764i	$0.727266\pi$
$660$		0			0
$661$	−110.055	+	624.153i	−0.166498	+	0.944256i	0.781009	+	0.624520i	$0.214705\pi$
$661$	−110.055	+	624.153i	−0.166498	+	0.944256i	−0.947507	+	0.319736i	$0.896406\pi$
$662$		0			0
$663$	50.6241	+	93.6695i	0.0763561	+	0.141281i
$664$		0			0
$665$	−222.024	−	128.186i	−0.333871	−	0.192760i
$666$		0			0
$667$	−252.425	−	437.214i	−0.378449	−	0.655493i
$668$		0			0
$669$	394.926	−	444.647i	0.590323	−	0.664645i
$670$		0			0
$671$	−313.590	−	861.581i	−0.467347	−	1.28403i
$672$		0			0
$673$	19.1049	+	108.349i	0.0283877	+	0.160994i	0.995706	−	0.0925699i	$-0.0295082\pi$
$673$	19.1049	+	108.349i	0.0283877	+	0.160994i	−0.967319	+	0.253564i	$0.918397\pi$
$674$		0			0
$675$	−61.8427	−	87.7730i	−0.0916188	−	0.130034i
$676$		0			0
$677$	−140.866	+	24.8384i	−0.208073	+	0.0366890i	−0.276713	−	0.960953i	$-0.589245\pi$
$677$	−140.866	+	24.8384i	−0.208073	+	0.0366890i	0.0686398	+	0.997642i	$0.478134\pi$
$678$		0			0
$679$	789.987	−	287.532i	1.16346	−	0.423463i
$680$		0			0
$681$	−14.6663	+	4.87577i	−0.0215365	+	0.00715972i
$682$		0			0
$683$	−784.050	+	452.671i	−1.14795	+	0.662769i	−0.948387	−	0.317116i	$-0.897286\pi$
$683$	−784.050	+	452.671i	−1.14795	+	0.662769i	−0.199563	+	0.979885i	$0.563952\pi$
$684$		0			0
$685$	176.714	−	306.078i	0.257977	−	0.446830i
$686$		0			0
$687$	902.761	+	555.617i	1.31406	+	0.808758i
$688$		0			0
$689$	−936.096	−	165.059i	−1.35863	−	0.239563i
$690$		0			0
$691$	−407.543	+	341.969i	−0.589788	+	0.494891i	−0.888145	−	0.459564i	$-0.848006\pi$
$691$	−407.543	+	341.969i	−0.589788	+	0.494891i	0.298357	+	0.954454i	$0.403561\pi$
$692$		0			0
$693$	−439.016	+	1023.23i	−0.633500	+	1.47653i
$694$		0			0
$695$	230.690	−	633.817i	0.331929	−	0.911967i
$696$		0			0
$697$	−30.1213	−	25.2748i	−0.0432156	−	0.0362622i
$698$		0			0
$699$	−330.519	+	261.864i	−0.472845	+	0.374627i
$700$		0			0
$701$			905.026i			1.29105i	0.763739	+	0.645525i	$0.223361\pi$
$701$			905.026i			1.29105i	−0.763739	+	0.645525i	$0.776639\pi$
$702$		0			0
$703$	79.8237			0.113547
$704$		0			0
$705$	−198.098	+	29.2144i	−0.280991	+	0.0414389i
$706$		0			0
$707$	32.3447	−	38.5469i	0.0457492	−	0.0545217i
$708$		0			0
$709$	341.922	+	124.450i	0.482260	+	0.175528i	0.571698	−	0.820464i	$-0.306285\pi$
$709$	341.922	+	124.450i	0.482260	+	0.175528i	−0.0894380	+	0.995992i	$0.528507\pi$
$710$		0			0
$711$	100.531	−	153.501i	0.141393	−	0.215894i
$712$		0			0
$713$	−283.074	−	337.355i	−0.397019	−	0.473148i
$714$		0			0
$715$	−123.311	+	699.329i	−0.172462	+	0.978083i
$716$		0			0
$717$	−442.846	−	12.4534i	−0.617638	−	0.0173687i
$718$		0			0
$719$	389.328	+	224.778i	0.541485	+	0.312626i	0.745680	−	0.666304i	$-0.232125\pi$
$719$	389.328	+	224.778i	0.541485	+	0.312626i	−0.204196	+	0.978930i	$0.565458\pi$
$720$		0			0
$721$	−380.779	−	659.529i	−0.528127	−	0.914742i
$722$		0			0
$723$	−894.553	−	183.801i	−1.23728	−	0.254220i
$724$		0			0
$725$	−34.4922	−	94.7665i	−0.0475754	−	0.130712i
$726$		0			0
$727$	−100.606	−	570.564i	−0.138385	−	0.784820i	−0.972443	−	0.233142i	$-0.925099\pi$
$727$	−100.606	−	570.564i	−0.138385	−	0.784820i	0.834058	−	0.551677i	$-0.186012\pi$
$728$		0			0
$729$	465.317	−	561.178i	0.638295	−	0.769792i
$730$		0			0
$731$	−113.413	+	19.9978i	−0.155148	+	0.0273568i
$732$		0			0
$733$	−879.854	+	320.241i	−1.20035	+	0.436891i	−0.863345	−	0.504613i	$-0.831635\pi$
$733$	−879.854	+	320.241i	−1.20035	+	0.436891i	−0.337002	+	0.941504i	$0.609413\pi$
$734$		0			0
$735$	201.424	−	980.321i	0.274046	−	1.33377i
$736$		0			0
$737$	987.805	−	570.310i	1.34031	−	0.773826i
$738$		0			0
$739$	263.918	−	457.119i	0.357128	−	0.618564i	−0.630352	−	0.776310i	$-0.717089\pi$
$739$	263.918	−	457.119i	0.357128	−	0.618564i	0.987480	+	0.157746i	$0.0504227\pi$
$740$		0			0
$741$	4.28263	−	152.292i	0.00577953	−	0.205522i
$742$		0			0
$743$	36.2725	+	6.39582i	0.0488190	+	0.00860811i	0.198004	−	0.980201i	$-0.436554\pi$
$743$	36.2725	+	6.39582i	0.0488190	+	0.00860811i	−0.149185	+	0.988809i	$0.547665\pi$
$744$		0			0
$745$	−831.967	+	698.103i	−1.11673	+	0.937051i
$746$		0			0
$747$	237.932	+	155.827i	0.318517	+	0.208603i
$748$		0			0
$749$	569.747	−	1565.37i	0.760677	−	2.08994i
$750$		0			0
$751$	−75.4565	−	63.3155i	−0.100475	−	0.0843082i	0.591167	−	0.806550i	$-0.298668\pi$
$751$	−75.4565	−	63.3155i	−0.100475	−	0.0843082i	−0.691641	+	0.722241i	$0.743112\pi$
$752$		0			0
$753$	54.6197	+	370.367i	0.0725362	+	0.491856i
$754$		0			0
$755$		−	689.781i		−	0.913617i
$756$		0			0
$757$	−1385.09			−1.82971			−0.914857	−	0.403779i	$-0.867697\pi$
$757$	−1385.09			−1.82971			−0.914857	+	0.403779i	$0.867697\pi$
$758$		0			0
$759$	435.559	+	549.752i	0.573859	+	0.724310i
$760$		0			0
$761$	935.204	−	1114.53i	1.22891	−	1.46456i	0.389541	−	0.921009i	$-0.372634\pi$
$761$	935.204	−	1114.53i	1.22891	−	1.46456i	0.839374	−	0.543555i	$-0.182922\pi$
$762$		0			0
$763$	183.913	+	66.9389i	0.241039	+	0.0877312i
$764$		0			0
$765$	140.672	+	60.3551i	0.183886	+	0.0788956i
$766$		0			0
$767$	−492.959	−	587.486i	−0.642711	−	0.765953i
$768$		0			0
$769$	−17.3763	+	98.5458i	−0.0225959	+	0.128148i	−0.994019	−	0.109206i	$-0.965169\pi$
$769$	−17.3763	+	98.5458i	−0.0225959	+	0.128148i	0.971423	+	0.237354i	$0.0762802\pi$
$770$		0			0
$771$	718.654	−	1167.66i	0.932106	−	1.51448i
$772$		0			0
$773$	−547.928	−	316.347i	−0.708834	−	0.409245i	0.101795	−	0.994805i	$-0.467541\pi$
$773$	−547.928	−	316.347i	−0.708834	−	0.409245i	−0.810629	+	0.585560i	$0.800875\pi$
$774$		0			0
$775$	−43.9854	−	76.1850i	−0.0567554	−	0.0983032i
$776$		0			0
$777$	176.029	+	529.495i	0.226549	+	0.681461i
$778$		0			0
$779$	19.2431	+	52.8699i	0.0247023	+	0.0678690i
$780$		0			0
$781$	−248.112	−	1407.12i	−0.317686	−	1.80168i
$782$		0			0
$783$	559.732	−	394.373i	0.714856	−	0.503670i
$784$		0			0
$785$	736.585	−	129.880i	0.938325	−	0.165452i
$786$		0			0
$787$	−766.476	+	278.974i	−0.973921	+	0.354478i	−0.779474	−	0.626435i	$-0.784513\pi$
$787$	−766.476	+	278.974i	−0.973921	+	0.354478i	−0.194447	+	0.980913i	$0.562291\pi$
$788$		0			0
$789$	1049.61	+	932.244i	1.33031	+	1.18155i
$790$		0			0
$791$	164.362	−	94.8944i	0.207790	−	0.119968i
$792$		0			0
$793$	−438.486	+	759.481i	−0.552946	+	0.957731i
$794$		0			0
$795$	−1202.20	+	649.735i	−1.51220	+	0.817277i
$796$		0			0
$797$	1233.67	+	217.529i	1.54789	+	0.272934i	0.881323	−	0.472514i	$-0.156653\pi$
$797$	1233.67	+	217.529i	1.54789	+	0.272934i	0.666564	+	0.745448i	$0.267764\pi$
$798$		0			0
$799$	30.0119	−	25.1830i	0.0375618	−	0.0315181i
$800$		0			0
$801$	−604.740	−	142.081i	−0.754981	−	0.177380i
$802$		0			0
$803$	366.084	−	1005.81i	0.455895	−	1.25256i
$804$		0			0
$805$	−864.781	−	725.637i	−1.07426	−	0.901413i
$806$		0			0
$807$	−884.288	−	350.307i	−1.09577	−	0.434086i
$808$		0			0
$809$		−	1021.88i		−	1.26313i	−0.775321	−	0.631567i	$-0.782412\pi$
$809$		−	1021.88i		−	1.26313i	0.775321	−	0.631567i	$-0.217588\pi$
$810$		0			0
$811$	365.788			0.451034			0.225517	−	0.974239i	$-0.427593\pi$
$811$	365.788			0.451034			0.225517	+	0.974239i	$0.427593\pi$
$812$		0			0
$813$	127.835	−	322.696i	0.157239	−	0.396921i
$814$		0			0
$815$	137.910	−	164.355i	0.169215	−	0.201662i
$816$		0			0
$817$	154.846	+	56.3595i	0.189531	+	0.0689835i
$818$		0			0
$819$	1019.64	−	307.429i	1.24498	−	0.375371i
$820$		0			0
$821$	−6.23245	−	7.42755i	−0.00759129	−	0.00904695i	0.762235	−	0.647300i	$-0.224102\pi$
$821$	−6.23245	−	7.42755i	−0.00759129	−	0.00904695i	−0.769827	+	0.638253i	$0.779657\pi$
$822$		0			0
$823$	−0.155222	+	0.880308i	−0.000188605	+	0.00106963i	−0.984902	−	0.173113i	$-0.944617\pi$
$823$	−0.155222	+	0.880308i	−0.000188605	+	0.00106963i	0.984713	+	0.174183i	$0.0557284\pi$
$824$		0			0
$825$	66.6153	+	123.258i	0.0807458	+	0.149403i
$826$		0			0
$827$	583.611	+	336.948i	0.705696	+	0.407434i	0.809465	−	0.587168i	$-0.199757\pi$
$827$	583.611	+	336.948i	0.705696	+	0.407434i	−0.103769	+	0.994601i	$0.533090\pi$
$828$		0			0
$829$	−14.4804	−	25.0808i	−0.0174673	−	0.0302542i	0.857160	−	0.515051i	$-0.172227\pi$
$829$	−14.4804	−	25.0808i	−0.0174673	−	0.0302542i	−0.874627	+	0.484797i	$0.838894\pi$
$830$		0			0
$831$	−229.713	+	258.633i	−0.276429	+	0.311231i
$832$		0			0
$833$	66.9709	+	184.001i	0.0803972	+	0.220890i
$834$		0			0
$835$	155.124	+	879.753i	0.185778	+	1.05360i
$836$		0			0
$837$	421.103	−	423.574i	0.503110	−	0.506062i
$838$		0			0
$839$	−629.012	+	110.912i	−0.749716	+	0.132195i	−0.535434	−	0.844577i	$-0.679852\pi$
$839$	−629.012	+	110.912i	−0.749716	+	0.132195i	−0.214282	+	0.976772i	$0.568741\pi$
$840$		0			0
$841$	−185.952	+	67.6809i	−0.221108	+	0.0804767i
$842$		0			0
$843$	232.277	−	77.2195i	0.275536	−	0.0916008i
$844$		0			0
$845$	−199.631	+	115.257i	−0.236250	+	0.136399i
$846$		0			0
$847$	89.1253	−	154.370i	0.105225	−	0.182254i
$848$		0			0
$849$	1065.74	+	655.926i	1.25529	+	0.772587i
$850$		0			0
$851$	346.151	+	61.0358i	0.406758	+	0.0717225i
$852$		0			0
$853$	595.279	−	499.498i	0.697865	−	0.585578i	−0.223300	−	0.974750i	$-0.571683\pi$
$853$	595.279	−	499.498i	0.697865	−	0.585578i	0.921165	+	0.389171i	$0.127239\pi$
$854$		0			0
$855$	−131.138	−	175.434i	−0.153378	−	0.205185i
$856$		0			0
$857$	368.296	−	1011.88i	0.429750	−	1.18073i	−0.516215	−	0.856459i	$-0.672659\pi$
$857$	368.296	−	1011.88i	0.429750	−	1.18073i	0.945965	−	0.324269i	$-0.105118\pi$
$858$		0			0
$859$	62.0374	+	52.0556i	0.0722205	+	0.0606002i	0.678183	−	0.734893i	$-0.262768\pi$
$859$	62.0374	+	52.0556i	0.0722205	+	0.0606002i	−0.605963	+	0.795493i	$0.707212\pi$
$860$		0			0
$861$	−308.267	+	244.235i	−0.358034	+	0.283664i
$862$		0			0
$863$		−	1599.17i		−	1.85304i	−0.376244	−	0.926520i	$-0.622785\pi$
$863$		−	1599.17i		−	1.85304i	0.376244	−	0.926520i	$-0.377215\pi$
$864$		0			0
$865$	58.6217			0.0677708
$866$		0			0
$867$	828.094	−	122.123i	0.955126	−	0.140857i
$868$		0			0
$869$	−153.906	+	183.418i	−0.177107	+	0.211067i
$870$		0			0
$871$	−1025.19	−	373.137i	−1.17702	−	0.428400i
$872$		0			0
$873$	717.103	+	40.3635i	0.821423	+	0.0462354i
$874$		0			0
$875$	766.304	+	913.245i	0.875776	+	1.04371i
$876$		0			0
$877$	−65.7402	+	372.831i	−0.0749603	+	0.425121i	0.924115	+	0.382116i	$0.124804\pi$
$877$	−65.7402	+	372.831i	−0.0749603	+	0.425121i	−0.999075	+	0.0430055i	$0.986307\pi$
$878$		0			0
$879$	1037.09	+	29.1642i	1.17985	+	0.0331789i
$880$		0			0
$881$	−1046.81	−	604.374i	−1.18820	−	0.686009i	−0.230305	−	0.973119i	$-0.573972\pi$
$881$	−1046.81	−	604.374i	−1.18820	−	0.686009i	−0.957898	+	0.287109i	$0.907306\pi$
$882$		0			0
$883$	−298.144	−	516.401i	−0.337649	−	0.584826i	0.646341	−	0.763049i	$-0.276298\pi$
$883$	−298.144	−	516.401i	−0.337649	−	0.584826i	−0.983990	+	0.178223i	$0.942965\pi$
$884$		0			0
$885$	−1079.99	−	221.902i	−1.22033	−	0.250737i
$886$		0			0
$887$	−34.7360	−	95.4364i	−0.0391612	−	0.107595i	0.918571	−	0.395256i	$-0.129344\pi$
$887$	−34.7360	−	95.4364i	−0.0391612	−	0.107595i	−0.957732	+	0.287662i	$0.907122\pi$
$888$		0			0
$889$	285.757	+	1620.61i	0.321436	+	1.82296i
$890$		0			0
$891$	−689.371	+	655.489i	−0.773705	+	0.735678i
$892$		0			0
$893$	−55.2071	+	9.73450i	−0.0618220	+	0.0109009i
$894$		0			0
$895$	−1429.39	+	520.255i	−1.59708	+	0.581290i
$896$		0			0
$897$	135.019	−	657.131i	0.150523	−	0.732588i
$898$		0			0
$899$	485.835	−	280.497i	0.540417	−	0.312010i
$900$		0			0
$901$	133.684	−	231.548i	0.148373	−	0.256990i
$902$		0			0
$903$	−32.3796	+	1151.43i	−0.0358578	+	1.27511i
$904$		0			0
$905$	−576.769	−	101.700i	−0.637313	−	0.112376i
$906$		0			0
$907$	−1321.91	+	1109.21i	−1.45745	+	1.22295i	−0.530547	+	0.847656i	$0.678013\pi$
$907$	−1321.91	+	1109.21i	−1.45745	+	1.22295i	−0.926906	+	0.375293i	$0.877542\pi$
$908$		0			0
$909$	38.3797	−	19.3688i	0.0422219	−	0.0213078i
$910$		0			0
$911$	−106.953	+	293.850i	−0.117401	+	0.322558i	−0.984450	−	0.175666i	$-0.943792\pi$
$911$	−106.953	+	293.850i	−0.117401	+	0.322558i	0.867048	+	0.498224i	$0.166014\pi$
$912$		0			0
$913$	−284.305	−	238.560i	−0.311396	−	0.261292i
$914$		0			0
$915$	183.944	+	1247.30i	0.201032	+	1.36316i
$916$		0			0
$917$			1037.84i			1.13177i
$918$		0			0
$919$	−198.504			−0.216000			−0.108000	−	0.994151i	$-0.534445\pi$
$919$	−198.504			−0.216000			−0.108000	+	0.994151i	$0.534445\pi$
$920$		0			0
$921$	1075.58	+	1357.57i	1.16784	+	1.47401i
$922$		0			0
$923$	−878.459	+	1046.91i	−0.951743	+	1.13424i
$924$		0			0
$925$	65.9791	+	24.0144i	0.0713287	+	0.0259615i
$926$		0			0
$927$	−76.7941	−	646.087i	−0.0828416	−	0.696966i
$928$		0			0
$929$	854.746	+	1018.65i	0.920071	+	1.09650i	0.995056	+	0.0993136i	$0.0316647\pi$
$929$	854.746	+	1018.65i	0.920071	+	1.09650i	−0.0749849	+	0.997185i	$0.523891\pi$
$930$		0			0
$931$	48.6528	−	275.924i	0.0522587	−	0.296374i
$932$		0			0
$933$	706.187	−	1147.41i	0.756899	−	1.22980i
$934$		0			0
$935$	−172.983	−	99.8717i	−0.185008	−	0.106815i
$936$		0			0
$937$	−675.671	−	1170.30i	−0.721100	−	1.24898i	−0.960559	−	0.278076i	$-0.910303\pi$
$937$	−675.671	−	1170.30i	−0.721100	−	1.24898i	0.239459	−	0.970906i	$-0.423030\pi$
$938$		0			0
$939$	10.2568	+	30.8524i	0.0109231	+	0.0328567i
$940$		0			0
$941$	265.840	+	730.391i	0.282508	+	0.776186i	0.997062	+	0.0766044i	$0.0244078\pi$
$941$	265.840	+	730.391i	0.282508	+	0.776186i	−0.714553	+	0.699581i	$0.753370\pi$
$942$		0			0
$943$	43.0206	+	243.982i	0.0456210	+	0.258729i
$944$		0			0
$945$	874.517	−	1256.75i	0.925415	−	1.32989i
$946$		0			0
$947$	270.124	−	47.6301i	0.285242	−	0.0502958i	−0.0291967	−	0.999574i	$-0.509295\pi$
$947$	270.124	−	47.6301i	0.285242	−	0.0502958i	0.314438	+	0.949278i	$0.398184\pi$
$948$		0			0
$949$	−962.034	+	350.152i	−1.01373	+	0.368969i
$950$		0			0
$951$	−489.501	−	434.765i	−0.514723	−	0.457166i
$952$		0			0
$953$	858.313	−	495.548i	0.900644	−	0.519987i	0.0232347	−	0.999730i	$-0.492603\pi$
$953$	858.313	−	495.548i	0.900644	−	0.519987i	0.877409	+	0.479743i	$0.159270\pi$
$954$		0			0
$955$	292.376	−	506.410i	0.306153	−	0.530272i
$956$		0			0
$957$	−786.020	+	424.808i	−0.821338	+	0.443896i
$958$		0			0
$959$	681.141	+	120.104i	0.710262	+	0.125238i
$960$		0			0
$961$	−361.298	+	303.165i	−0.375961	+	0.315468i
$962$		0			0
$963$	974.635	−	1037.10i	1.01208	−	1.07694i
$964$		0			0
$965$	368.418	−	1012.22i	0.381780	−	1.04893i
$966$		0			0
$967$	−239.352	−	200.840i	−0.247520	−	0.207694i	0.510583	−	0.859828i	$-0.329429\pi$
$967$	−239.352	−	200.840i	−0.247520	−	0.207694i	−0.758104	+	0.652134i	$0.773874\pi$
$968$		0			0
$969$	39.8416	+	15.7831i	0.0411162	+	0.0162880i
$970$		0			0
$971$			487.838i			0.502407i	0.967934	+	0.251204i	$0.0808264\pi$
$971$			487.838i			0.502407i	−0.967934	+	0.251204i	$0.919174\pi$
$972$		0			0
$973$	1319.96			1.35659
$974$		0			0
$975$	49.3558	−	124.590i	0.0506214	−	0.127785i
$976$		0			0
$977$	−413.839	+	493.194i	−0.423582	+	0.504805i	−0.935059	−	0.354492i	$-0.884654\pi$
$977$	−413.839	+	493.194i	−0.423582	+	0.504805i	0.511478	+	0.859297i	$0.329098\pi$
$978$		0			0
$979$	761.718	+	277.243i	0.778057	+	0.283190i
$980$		0			0
$981$	121.847	+	114.509i	0.124207	+	0.116726i
$982$		0			0
$983$	989.779	+	1179.57i	1.00690	+	1.19997i	0.979726	+	0.200341i	$0.0642051\pi$
$983$	989.779	+	1179.57i	1.00690	+	1.19997i	0.0271699	+	0.999631i	$0.491350\pi$
$984$		0			0
$985$	−273.610	+	1551.72i	−0.277777	+	1.57535i
$986$		0			0
$987$	−186.316	−	344.739i	−0.188770	−	0.349279i
$988$		0			0
$989$	628.389	+	362.801i	0.635378	+	0.366836i
$990$		0			0
$991$	155.571	+	269.456i	0.156984	+	0.271903i	0.933780	−	0.357849i	$-0.116490\pi$
$991$	155.571	+	269.456i	0.156984	+	0.271903i	−0.776796	+	0.629752i	$0.783156\pi$
$992$		0			0
$993$	−1196.67	+	1347.33i	−1.20511	+	1.35683i
$994$		0			0
$995$	−151.540	−	416.352i	−0.152301	−	0.418445i
$996$		0			0
$997$	−8.37502	−	47.4971i	−0.00840022	−	0.0476400i	0.980320	−	0.197417i	$-0.0632554\pi$
$997$	−8.37502	−	47.4971i	−0.00840022	−	0.0476400i	−0.988720	+	0.149777i	$0.952144\pi$
$998$		0			0
$999$	−40.1592	+	475.021i	−0.0401994	+	0.475496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.a.257.3		30
4.3	odd	2		27.3.f.a.14.4	yes	30
12.11	even	2		81.3.f.a.71.2		30
27.2	odd	18	inner	432.3.bc.a.353.3		30
36.7	odd	6		243.3.f.d.134.2		30
36.11	even	6		243.3.f.a.134.4		30
36.23	even	6		243.3.f.b.53.4		30
36.31	odd	6		243.3.f.c.53.2		30
108.7	odd	18		243.3.f.a.107.4		30
108.11	even	18		243.3.f.c.188.2		30
108.43	odd	18		243.3.f.b.188.4		30
108.47	even	18		243.3.f.d.107.2		30
108.59	even	18		729.3.b.a.728.19		30
108.79	odd	18		81.3.f.a.8.2		30
108.83	even	18		27.3.f.a.2.4	✓	30
108.103	odd	18		729.3.b.a.728.12		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.4	✓	30	108.83	even	18
27.3.f.a.14.4	yes	30	4.3	odd	2
81.3.f.a.8.2		30	108.79	odd	18
81.3.f.a.71.2		30	12.11	even	2
243.3.f.a.107.4		30	108.7	odd	18
243.3.f.a.134.4		30	36.11	even	6
243.3.f.b.53.4		30	36.23	even	6
243.3.f.b.188.4		30	108.43	odd	18
243.3.f.c.53.2		30	36.31	odd	6
243.3.f.c.188.2		30	108.11	even	18
243.3.f.d.107.2		30	108.47	even	18
243.3.f.d.134.2		30	36.7	odd	6
432.3.bc.a.257.3		30	1.1	even	1	trivial
432.3.bc.a.353.3		30	27.2	odd	18	inner
729.3.b.a.728.12		30	108.103	odd	18
729.3.b.a.728.19		30	108.59	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.10490 + 2.78912i) q^{3} +(-3.46013 + 4.12362i) q^{5} +(-9.89907 - 3.60297i) q^{7} +(-6.55839 - 6.16340i) q^{9} +O(q^{10})\)	\(q+(-1.10490 + 2.78912i) q^{3} +(-3.46013 + 4.12362i) q^{5} +(-9.89907 - 3.60297i) q^{7} +(-6.55839 - 6.16340i) q^{9} +(7.54888 + 8.99640i) q^{11} +(1.95057 - 11.0622i) q^{13} +(-7.67818 - 14.2069i) q^{15} +(2.73630 + 1.57980i) q^{17} +(-2.26051 - 3.91532i) q^{19} +(20.9866 - 23.6288i) q^{21} +(-6.80880 - 18.7070i) q^{23} +(-0.690550 - 3.91630i) q^{25} +(24.4368 - 11.4822i) q^{27} +(24.9744 - 4.40366i) q^{29} +(20.7874 - 7.56598i) q^{31} +(-33.4328 + 11.1146i) q^{33} +(49.1093 - 28.3533i) q^{35} +(-8.82807 + 15.2907i) q^{37} +(28.6987 + 17.6630i) q^{39} +(-12.2557 - 2.16101i) q^{41} +(-27.9211 + 23.4286i) q^{43} +(48.1084 - 5.71818i) q^{45} +(4.24091 - 11.6518i) q^{47} +(47.4740 + 39.8354i) q^{49} +(-7.42960 + 5.88634i) q^{51} -84.6210i q^{53} -63.2178 q^{55} +(13.4179 - 1.97880i) q^{57} +(43.8854 - 52.3006i) q^{59} +(-73.3637 - 26.7022i) q^{61} +(42.7155 + 84.6415i) q^{63} +(38.8672 + 46.3201i) q^{65} +(16.8654 - 95.6483i) q^{67} +(59.6992 + 1.67882i) q^{69} +(-105.364 - 60.8322i) q^{71} +(-45.5705 - 78.9304i) q^{73} +(11.6860 + 2.40109i) q^{75} +(-42.3131 - 116.254i) q^{77} +(3.54032 + 20.0781i) q^{79} +(5.02506 + 80.8440i) q^{81} +(-31.1219 + 5.48763i) q^{83} +(-15.9824 + 5.81713i) q^{85} +(-15.3119 + 74.5223i) q^{87} +(59.7756 - 34.5114i) q^{89} +(-59.1656 + 102.478i) q^{91} +(-1.86551 + 66.3381i) q^{93} +(23.9669 + 4.22602i) q^{95} +(-61.1335 + 51.2971i) q^{97} +(5.93989 - 105.529i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7}+O(q^{10}) \) 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37} - 15 q^{39} + 228 q^{41} + 96 q^{43} + 477 q^{45} - 399 q^{47} - 78 q^{49} - 36 q^{51} + 12 q^{55} - 192 q^{57} + 474 q^{59} + 138 q^{61} + 585 q^{63} - 411 q^{65} - 354 q^{67} + 99 q^{69} - 315 q^{71} - 66 q^{73} - 255 q^{75} + 201 q^{77} - 30 q^{79} + 36 q^{81} + 33 q^{83} - 261 q^{85} + 279 q^{87} + 72 q^{89} - 96 q^{91} + 591 q^{93} - 681 q^{95} - 582 q^{97} - 513 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Introduction

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