LMFDB - Embedded newform 405.3.n.a.179.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(44,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("405.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.n (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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.29
Character	$\chi$	$=$	405.179
Dual form			405.3.n.a.224.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82399 + 1.02785i) q^{2} +(3.85425 + 3.23410i) q^{4} +(-4.79125 + 1.42965i) q^{5} +(7.59850 + 9.05554i) q^{7} +(1.54973 + 2.68422i) q^{8} +(-14.9999 - 0.887368i) q^{10} +(-11.5608 + 2.03849i) q^{11} +(4.88572 + 13.4234i) q^{13} +(12.1503 + 33.3828i) q^{14} +(-1.87729 - 10.6466i) q^{16} +(-5.22423 + 9.04864i) q^{17} +(7.65850 + 13.2649i) q^{19} +(-23.0903 - 9.98516i) q^{20} +(-34.7429 - 6.12611i) q^{22} +(18.2900 + 15.3471i) q^{23} +(20.9122 - 13.6996i) q^{25} +42.9293i q^{26} +59.4766i q^{28} +(6.33581 - 17.4075i) q^{29} +(-22.3385 - 18.7442i) q^{31} +(7.79453 - 44.2050i) q^{32} +(-24.0538 + 20.1835i) q^{34} +(-49.3526 - 32.5242i) q^{35} +(3.15030 + 1.81883i) q^{37} +(7.99320 + 45.3317i) q^{38} +(-11.2626 - 10.6452i) q^{40} +(8.41546 + 23.1213i) q^{41} +(14.5661 - 2.56840i) q^{43} +(-51.1509 - 29.5320i) q^{44} +(35.8762 + 62.1393i) q^{46} +(33.0925 - 27.7679i) q^{47} +(-15.7569 + 89.3615i) q^{49} +(73.1369 - 17.1930i) q^{50} +(-24.5818 + 67.5380i) q^{52} -84.2928 q^{53} +(52.4766 - 26.2948i) q^{55} +(-12.5314 + 34.4297i) q^{56} +(35.7844 - 42.6462i) q^{58} +(80.2108 + 14.1433i) q^{59} +(51.0771 - 42.8588i) q^{61} +(-43.8174 - 75.8940i) q^{62} +(45.8258 - 79.3727i) q^{64} +(-42.5995 - 57.3301i) q^{65} +(-38.8900 - 106.849i) q^{67} +(-49.3996 + 17.9800i) q^{68} +(-105.941 - 142.575i) q^{70} +(-5.55345 - 3.20629i) q^{71} +(64.9541 - 37.5013i) q^{73} +(7.02693 + 8.37437i) q^{74} +(-13.3823 + 75.8946i) q^{76} +(-106.305 - 89.2002i) q^{77} +(84.6709 + 30.8177i) q^{79} +(24.2155 + 48.3268i) q^{80} +73.9440i q^{82} +(49.9577 + 18.1831i) q^{83} +(12.0943 - 50.8231i) q^{85} +(43.7744 + 7.71861i) q^{86} +(-23.3879 - 27.8727i) q^{88} +(20.0986 - 11.6039i) q^{89} +(-84.4321 + 146.241i) q^{91} +(20.8600 + 118.303i) q^{92} +(121.994 - 44.4022i) q^{94} +(-55.6580 - 52.6066i) q^{95} +(17.5234 - 3.08985i) q^{97} +(-136.347 + 236.160i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) $ 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	2.82399	+	1.02785i	1.41199	+	0.513923i	0.931714	−	0.363193i	$-0.118313\pi$
$2$	2.82399	+	1.02785i	1.41199	+	0.513923i	0.480279	+	0.877116i	$0.340536\pi$
$3$		0			0
$3$		0			0
$4$	3.85425	+	3.23410i	0.963561	+	0.808524i
$5$	−4.79125	+	1.42965i	−0.958251	+	0.285930i
$5$	−4.79125	+	1.42965i	−0.958251	+	0.285930i
$6$		0			0
$7$	7.59850	+	9.05554i	1.08550	+	1.29365i	0.953167	+	0.302444i	$0.0978024\pi$
$7$	7.59850	+	9.05554i	1.08550	+	1.29365i	0.132333	+	0.991205i	$0.457753\pi$
$8$	1.54973	+	2.68422i	0.193717	+	0.335527i
$9$		0			0
$10$	−14.9999	−	0.887368i	−1.49999	−	0.0887368i
$11$	−11.5608	+	2.03849i	−1.05098	+	0.185317i	−0.672353	−	0.740230i	$-0.734716\pi$
$11$	−11.5608	+	2.03849i	−1.05098	+	0.185317i	−0.378632	+	0.925547i	$0.623605\pi$
$12$		0			0
$13$	4.88572	+	13.4234i	0.375825	+	1.03257i	0.973070	+	0.230511i	$0.0740398\pi$
$13$	4.88572	+	13.4234i	0.375825	+	1.03257i	−0.597245	+	0.802059i	$0.703738\pi$
$14$	12.1503	+	33.3828i	0.867882	+	2.38449i
$15$		0			0
$16$	−1.87729	−	10.6466i	−0.117330	−	0.665413i
$17$	−5.22423	+	9.04864i	−0.307308	+	0.532273i	−0.977772	−	0.209669i	$-0.932761\pi$
$17$	−5.22423	+	9.04864i	−0.307308	+	0.532273i	0.670465	+	0.741941i	$0.266095\pi$
$18$		0			0
$19$	7.65850	+	13.2649i	0.403079	+	0.698154i	0.994096	−	0.108506i	$-0.0346066\pi$
$19$	7.65850	+	13.2649i	0.403079	+	0.698154i	−0.591017	+	0.806659i	$0.701273\pi$
$20$	−23.0903	−	9.98516i	−1.15451	−	0.499258i
$21$		0			0
$22$	−34.7429	−	6.12611i	−1.57922	−	0.278459i
$23$	18.2900	+	15.3471i	0.795217	+	0.667266i	0.947031	−	0.321143i	$-0.104067\pi$
$23$	18.2900	+	15.3471i	0.795217	+	0.667266i	−0.151814	+	0.988409i	$0.548512\pi$
$24$		0			0
$25$	20.9122	−	13.6996i	0.836489	−	0.547984i
$26$			42.9293i			1.65113i
$27$		0			0
$28$			59.4766i			2.12416i
$29$	6.33581	−	17.4075i	0.218476	−	0.600258i	−0.781236	−	0.624235i	$-0.785411\pi$
$29$	6.33581	−	17.4075i	0.218476	−	0.600258i	0.999713	+	0.0239772i	$0.00763290\pi$
$30$		0			0
$31$	−22.3385	−	18.7442i	−0.720597	−	0.604653i	0.206953	−	0.978351i	$-0.433645\pi$
$31$	−22.3385	−	18.7442i	−0.720597	−	0.604653i	−0.927550	+	0.373698i	$0.878090\pi$
$32$	7.79453	−	44.2050i	0.243579	−	1.38140i
$33$		0			0
$34$	−24.0538	+	20.1835i	−0.707464	+	0.593632i
$35$	−49.3526	−	32.5242i	−1.41007	−	0.929263i
$36$		0			0
$37$	3.15030	+	1.81883i	0.0851433	+	0.0491575i	0.541967	−	0.840400i	$-0.317680\pi$
$37$	3.15030	+	1.81883i	0.0851433	+	0.0491575i	−0.456824	+	0.889557i	$0.651013\pi$
$38$	7.99320	+	45.3317i	0.210347	+	1.19294i
$39$		0			0
$40$	−11.2626	−	10.6452i	−0.281566	−	0.266130i
$41$	8.41546	+	23.1213i	0.205255	+	0.563934i	0.999019	−	0.0442926i	$-0.0141034\pi$
$41$	8.41546	+	23.1213i	0.205255	+	0.563934i	−0.793763	+	0.608227i	$0.791881\pi$
$42$		0			0
$43$	14.5661	−	2.56840i	0.338747	−	0.0597302i	−0.00168729	−	0.999999i	$-0.500537\pi$
$43$	14.5661	−	2.56840i	0.338747	−	0.0597302i	0.340434	+	0.940268i	$0.389426\pi$
$44$	−51.1509	−	29.5320i	−1.16252	−	0.671182i
$45$		0			0
$46$	35.8762	+	62.1393i	0.779916	+	1.35085i
$47$	33.0925	−	27.7679i	0.704097	−	0.590807i	−0.218839	−	0.975761i	$-0.570227\pi$
$47$	33.0925	−	27.7679i	0.704097	−	0.590807i	0.922936	+	0.384954i	$0.125783\pi$
$48$		0			0
$49$	−15.7569	+	89.3615i	−0.321568	+	1.82371i
$50$	73.1369	−	17.1930i	1.46274	−	0.343859i
$51$		0			0
$52$	−24.5818	+	67.5380i	−0.472727	+	1.29881i
$53$	−84.2928			−1.59043			−0.795215	−	0.606327i	$-0.792642\pi$
$53$	−84.2928			−1.59043			−0.795215	+	0.606327i	$0.792642\pi$
$54$		0			0
$55$	52.4766	−	26.2948i	0.954119	−	0.478088i
$56$	−12.5314	+	34.4297i	−0.223775	+	0.614816i
$57$		0			0
$58$	35.7844	−	42.6462i	0.616973	−	0.735280i
$59$	80.2108	+	14.1433i	1.35950	+	0.239717i	0.805401	−	0.592731i	$-0.201950\pi$
$59$	80.2108	+	14.1433i	1.35950	+	0.239717i	0.554103	+	0.832448i	$0.313061\pi$
$60$		0			0
$61$	51.0771	−	42.8588i	0.837330	−	0.702603i	−0.119631	−	0.992818i	$-0.538171\pi$
$61$	51.0771	−	42.8588i	0.837330	−	0.702603i	0.956962	+	0.290215i	$0.0937268\pi$
$62$	−43.8174	−	75.8940i	−0.706732	−	1.22410i
$63$		0			0
$64$	45.8258	−	79.3727i	0.716028	−	1.24020i
$65$	−42.5995	−	57.3301i	−0.655377	−	0.882001i
$66$		0			0
$67$	−38.8900	−	106.849i	−0.580447	−	1.59477i	−0.787419	−	0.616418i	$-0.788583\pi$
$67$	−38.8900	−	106.849i	−0.580447	−	1.59477i	0.206972	−	0.978347i	$-0.433639\pi$
$68$	−49.3996	+	17.9800i	−0.726465	+	0.264412i
$69$		0			0
$70$	−105.941	−	142.575i	−1.51344	−	2.03678i
$71$	−5.55345	−	3.20629i	−0.0782176	−	0.0451590i	0.460381	−	0.887721i	$-0.347713\pi$
$71$	−5.55345	−	3.20629i	−0.0782176	−	0.0451590i	−0.538599	+	0.842562i	$0.681046\pi$
$72$		0			0
$73$	64.9541	−	37.5013i	0.889782	−	0.513716i	0.0159111	−	0.999873i	$-0.494935\pi$
$73$	64.9541	−	37.5013i	0.889782	−	0.513716i	0.873871	+	0.486157i	$0.161602\pi$
$74$	7.02693	+	8.37437i	0.0949585	+	0.113167i
$75$		0			0
$76$	−13.3823	+	75.8946i	−0.176082	+	0.998613i
$77$	−106.305	−	89.2002i	−1.38058	−	1.15844i
$78$		0			0
$79$	84.6709	+	30.8177i	1.07178	+	0.390097i	0.816844	−	0.576859i	$-0.195722\pi$
$79$	84.6709	+	30.8177i	1.07178	+	0.390097i	0.254940	+	0.966957i	$0.417944\pi$
$80$	24.2155	+	48.3268i	0.302693	+	0.604085i
$81$		0			0
$82$			73.9440i			0.901756i
$83$	49.9577	+	18.1831i	0.601900	+	0.219074i	0.624955	−	0.780661i	$-0.285117\pi$
$83$	49.9577	+	18.1831i	0.601900	+	0.219074i	−0.0230554	+	0.999734i	$0.507339\pi$
$84$		0			0
$85$	12.0943	−	50.8231i	0.142285	−	0.597919i
$86$	43.7744	+	7.71861i	0.509005	+	0.0897513i
$87$		0			0
$88$	−23.3879	−	27.8727i	−0.265772	−	0.316735i
$89$	20.0986	−	11.6039i	0.225827	−	0.130381i	−0.382819	−	0.923824i	$-0.625047\pi$
$89$	20.0986	−	11.6039i	0.225827	−	0.130381i	0.608645	+	0.793442i	$0.291713\pi$
$90$		0			0
$91$	−84.4321	+	146.241i	−0.927825	+	1.60704i
$92$	20.8600	+	118.303i	0.226739	+	1.28590i
$93$		0			0
$94$	121.994	−	44.4022i	1.29781	−	0.472364i
$95$	−55.6580	−	52.6066i	−0.585874	−	0.553754i
$96$		0			0
$97$	17.5234	−	3.08985i	0.180654	−	0.0318542i	−0.0825892	−	0.996584i	$-0.526319\pi$
$97$	17.5234	−	3.08985i	0.180654	−	0.0318542i	0.263243	+	0.964730i	$0.415208\pi$
$98$	−136.347	+	236.160i	−1.39130	+	2.40980i
$99$		0			0
$100$	124.907	+	14.8304i	1.24907	+	0.148304i
$101$	−40.9814	−	48.8397i	−0.405756	−	0.483561i	0.524010	−	0.851712i	$-0.324435\pi$
$101$	−40.9814	−	48.8397i	−0.405756	−	0.483561i	−0.929766	+	0.368151i	$0.879991\pi$
$102$		0			0
$103$	−8.64884	−	1.52502i	−0.0839694	−	0.0148061i	0.131506	−	0.991315i	$-0.458019\pi$
$103$	−8.64884	−	1.52502i	−0.0839694	−	0.0148061i	−0.215475	+	0.976509i	$0.569130\pi$
$104$	−28.4598	+	33.9170i	−0.273652	+	0.326125i
$105$		0			0
$106$	−238.042	−	86.6401i	−2.24568	−	0.817359i
$107$	211.857			1.97997			0.989984	−	0.141177i	$-0.0450887\pi$
$107$	211.857			1.97997			0.989984	+	0.141177i	$0.0450887\pi$
$108$		0			0
$109$	−100.928			−0.925947			−0.462973	−	0.886372i	$-0.653217\pi$
$109$	−100.928			−0.925947			−0.462973	+	0.886372i	$0.653217\pi$
$110$	175.220	−	20.3184i	1.59291	−	0.184712i
$111$		0			0
$112$	82.1463	−	97.8982i	0.733449	−	0.874091i
$113$	−2.67270	+	15.1576i	−0.0236522	+	0.134138i	−0.994347	−	0.106176i	$-0.966139\pi$
$113$	−2.67270	+	15.1576i	−0.0236522	+	0.134138i	0.970695	+	0.240314i	$0.0772505\pi$
$114$		0			0
$115$	−109.573	−	47.3837i	−0.952808	−	0.412032i
$116$	80.7172	−	46.6021i	0.695838	−	0.401742i
$117$		0			0
$118$	211.977	+	122.385i	1.79641	+	1.03716i
$119$	−121.637	+	21.4478i	−1.02216	+	0.180234i
$120$		0			0
$121$	15.7946	−	5.74877i	0.130534	−	0.0475105i
$122$	188.293	−	68.5332i	1.54339	−	0.561747i
$123$		0			0
$124$	−25.4774	−	144.490i	−0.205463	−	1.16524i
$125$	−80.6101	+	95.5354i	−0.644881	+	0.764283i
$126$		0			0
$127$	−179.281	+	103.508i	−1.41166	+	0.815023i	−0.995545	−	0.0942888i	$-0.969942\pi$
$127$	−179.281	+	103.508i	−1.41166	+	0.815023i	−0.416116	+	0.909312i	$0.636609\pi$
$128$	73.4529	−	61.6343i	0.573851	−	0.481518i
$129$		0			0
$130$	−61.3738	−	205.685i	−0.472106	−	1.58219i
$131$	52.2452	−	62.2635i	0.398819	−	0.475294i	−0.528841	−	0.848721i	$-0.677373\pi$
$131$	52.2452	−	62.2635i	0.398819	−	0.475294i	0.927659	+	0.373428i	$0.121818\pi$
$132$		0			0
$133$	−61.9279	+	170.145i	−0.465623	+	1.27929i
$134$		−	341.714i		−	2.55010i
$135$		0			0
$136$	−32.3847			−0.238122
$137$	29.1079	+	10.5944i	0.212467	+	0.0773315i	0.446061	−	0.895003i	$-0.352826\pi$
$137$	29.1079	+	10.5944i	0.212467	+	0.0773315i	−0.233594	+	0.972334i	$0.575049\pi$
$138$		0			0
$139$	−128.959	−	108.209i	−0.927760	−	0.778483i	0.0476535	−	0.998864i	$-0.484826\pi$
$139$	−128.959	−	108.209i	−0.927760	−	0.778483i	−0.975414	+	0.220380i	$0.929270\pi$
$140$	−85.0306	−	284.967i	−0.607361	−	2.03548i
$141$		0			0
$142$	−12.3873	−	14.7626i	−0.0872344	−	0.103962i
$143$	−83.8465	−	145.226i	−0.586339	−	1.01557i
$144$		0			0
$145$	−5.46988	+	92.4616i	−0.0377233	+	0.637666i
$146$	221.975	−	39.1402i	1.52038	−	0.268083i
$147$		0			0
$148$	6.25977	+	17.1986i	0.0422958	+	0.116207i
$149$	22.0664	+	60.6271i	0.148097	+	0.406893i	0.991453	−	0.130462i	$-0.0416459\pi$
$149$	22.0664	+	60.6271i	0.148097	+	0.406893i	−0.843356	+	0.537355i	$0.819424\pi$
$150$		0			0
$151$	33.6453	+	190.812i	0.222817	+	1.26366i	0.866815	+	0.498629i	$0.166163\pi$
$151$	33.6453	+	190.812i	0.222817	+	1.26366i	−0.643999	+	0.765026i	$0.722726\pi$
$152$	−23.7373	+	41.1142i	−0.156166	+	0.270488i
$153$		0			0
$154$	−208.519	−	361.165i	−1.35402	−	2.34523i
$155$	133.827	+	57.8722i	0.863401	+	0.373369i
$156$		0			0
$157$	150.983	+	26.6225i	0.961678	+	0.169570i	0.632382	−	0.774657i	$-0.282077\pi$
$157$	150.983	+	26.6225i	0.961678	+	0.169570i	0.329296	+	0.944227i	$0.393188\pi$
$158$	207.434	+	174.057i	1.31287	+	1.10163i
$159$		0			0
$160$	25.8520	+	222.941i	0.161575	+	1.39338i
$161$			282.241i			1.75305i
$162$		0			0
$163$			37.9711i			0.232951i	0.993194	+	0.116476i	$0.0371597\pi$
$163$			37.9711i			0.232951i	−0.993194	+	0.116476i	$0.962840\pi$
$164$	−42.3412	+	116.332i	−0.258178	+	0.709339i
$165$		0			0
$166$	122.390	+	102.698i	0.737291	+	0.618661i
$167$	−6.11658	+	34.6889i	−0.0366263	+	0.207718i	−0.997629	−	0.0688209i	$-0.978076\pi$
$167$	−6.11658	+	34.6889i	−0.0366263	+	0.207718i	0.961003	+	0.276539i	$0.0891874\pi$
$168$		0			0
$169$	−26.8561	+	22.5350i	−0.158912	+	0.133343i
$170$	86.3924	−	131.093i	0.508190	−	0.771133i
$171$		0			0
$172$	64.4478	+	37.2090i	0.374697	+	0.216331i
$173$	6.67558	+	37.8591i	0.0385872	+	0.218839i	0.998004	−	0.0631536i	$-0.0201158\pi$
$173$	6.67558	+	37.8591i	0.0385872	+	0.218839i	−0.959417	+	0.281992i	$0.909005\pi$
$174$		0			0
$175$	282.959	+	85.2749i	1.61691	+	0.487285i
$176$	43.4060	+	119.257i	0.246625	+	0.677596i
$177$		0			0
$178$	68.6852	−	12.1110i	0.385872	−	0.0680396i
$179$	−196.409	−	113.397i	−1.09726	−	0.633502i	−0.161759	−	0.986830i	$-0.551717\pi$
$179$	−196.409	−	113.397i	−1.09726	−	0.633502i	−0.935500	+	0.353328i	$0.885050\pi$
$180$		0			0
$181$	−32.1294	−	55.6497i	−0.177510	−	0.307457i	0.763517	−	0.645788i	$-0.223471\pi$
$181$	−32.1294	−	55.6497i	−0.177510	−	0.307457i	−0.941027	+	0.338331i	$0.890138\pi$
$182$	−388.748	+	326.198i	−2.13598	+	1.79230i
$183$		0			0
$184$	−12.8504	+	72.8782i	−0.0698391	+	0.396077i
$185$	−17.6942	−	4.21064i	−0.0956442	−	0.0227602i
$186$		0			0
$187$	41.9510	−	115.259i	0.224337	−	0.616360i
$188$	217.351			1.15612
$189$		0			0
$190$	−103.106	−	205.768i	−0.542662	−	1.08299i
$191$	−100.954	+	277.368i	−0.528552	+	1.45219i	0.332223	+	0.943201i	$0.392201\pi$
$191$	−100.954	+	277.368i	−0.528552	+	1.45219i	−0.860775	+	0.508985i	$0.830021\pi$
$192$		0			0
$193$	−136.412	+	162.569i	−0.706796	+	0.842327i	−0.993277	−	0.115759i	$-0.963070\pi$
$193$	−136.412	+	162.569i	−0.706796	+	0.842327i	0.286481	+	0.958086i	$0.407514\pi$
$194$	52.6618	+	9.28570i	0.271453	+	0.0478644i
$195$		0			0
$196$	−349.735	+	293.462i	−1.78436	+	1.49726i
$197$	−3.49781	−	6.05838i	−0.0177554	−	0.0307532i	0.857011	−	0.515298i	$-0.172319\pi$
$197$	−3.49781	−	6.05838i	−0.0177554	−	0.0307532i	−0.874767	+	0.484545i	$0.838985\pi$
$198$		0			0
$199$	53.2212	−	92.1818i	0.267443	−	0.463225i	−0.700758	−	0.713399i	$-0.747155\pi$
$199$	53.2212	−	92.1818i	0.267443	−	0.463225i	0.968201	+	0.250174i	$0.0804879\pi$
$200$	69.1811	+	34.9022i	0.345905	+	0.174511i
$201$		0			0
$202$	−65.5311	−	180.045i	−0.324411	−	0.891313i
$203$	205.777	−	74.8967i	1.01368	−	0.368949i
$204$		0			0
$205$	−73.3759	−	98.7488i	−0.357931	−	0.481702i
$206$	−22.8567	−	13.1963i	−0.110955	−	0.0640599i
$207$		0			0
$208$	133.742	−	77.2160i	0.642990	−	0.371231i
$209$	−115.579	−	137.742i	−0.553010	−	0.659051i
$210$		0			0
$211$	41.8113	−	237.123i	0.198158	−	1.12381i	−0.709692	−	0.704512i	$-0.751166\pi$
$211$	41.8113	−	237.123i	0.198158	−	1.12381i	0.907850	−	0.419296i	$-0.137723\pi$
$212$	−324.885	−	272.611i	−1.53248	−	1.28590i
$213$		0			0
$214$	598.280	+	217.756i	2.79570	+	1.01755i
$215$	−66.1180	+	33.1303i	−0.307526	+	0.154094i
$216$		0			0
$217$		−	344.715i		−	1.58855i
$218$	−285.020	−	103.739i	−1.30743	−	0.475866i
$219$		0			0
$220$	287.298	+	68.3675i	1.30590	+	0.310761i
$221$	−146.988	−	25.9179i	−0.665103	−	0.117276i
$222$		0			0
$223$	−50.8002	−	60.5414i	−0.227804	−	0.271486i	0.640020	−	0.768358i	$-0.278926\pi$
$223$	−50.8002	−	60.5414i	−0.227804	−	0.271486i	−0.867824	+	0.496872i	$0.834482\pi$
$224$	459.527	−	265.308i	2.05146	−	1.18441i
$225$		0			0
$226$	−23.1274	+	40.0578i	−0.102334	+	0.177247i
$227$	7.53741	+	42.7468i	0.0332045	+	0.188312i	0.996899	−	0.0786968i	$-0.0250759\pi$
$227$	7.53741	+	42.7468i	0.0332045	+	0.188312i	−0.963694	+	0.267009i	$0.913965\pi$
$228$		0			0
$229$	−302.810	+	110.214i	−1.32231	+	0.481283i	−0.904199	−	0.427111i	$-0.859531\pi$
$229$	−302.810	+	110.214i	−1.32231	+	0.481283i	−0.418115	+	0.908394i	$0.637309\pi$
$230$	−260.729	−	246.435i	−1.13360	−	1.07146i
$231$		0			0
$232$	56.5443	−	9.97028i	0.243725	−	0.0429753i
$233$	−82.0547	+	142.123i	−0.352166	+	0.609970i	−0.986629	−	0.162984i	$-0.947888\pi$
$233$	−82.0547	+	142.123i	−0.352166	+	0.609970i	0.634463	+	0.772954i	$0.281221\pi$
$234$		0			0
$235$	−118.856	+	180.354i	−0.505772	+	0.767463i
$236$	263.411	+	313.921i	1.11615	+	1.33017i
$237$		0			0
$238$	−365.545	−	64.4555i	−1.53590	−	0.270821i
$239$	25.3352	−	30.1933i	0.106005	−	0.126332i	−0.710433	−	0.703765i	$-0.751501\pi$
$239$	25.3352	−	30.1933i	0.106005	−	0.126332i	0.816438	+	0.577433i	$0.195945\pi$
$240$		0			0
$241$	420.528	+	153.060i	1.74493	+	0.635102i	0.999504	−	0.0314879i	$-0.0100246\pi$
$241$	420.528	+	153.060i	1.74493	+	0.635102i	0.745425	+	0.666590i	$0.232247\pi$
$242$	50.5126			0.208730
$243$		0			0
$244$	335.473			1.37489
$245$	−52.2605	−	450.681i	−0.213308	−	1.83951i
$246$		0			0
$247$	−140.643	+	167.612i	−0.569405	+	0.678591i
$248$	15.6949	−	89.0099i	0.0632857	−	0.358911i
$249$		0			0
$250$	−325.837	+	186.936i	−1.30335	+	0.747743i
$251$	−11.9298	+	6.88767i	−0.0475290	+	0.0274409i	−0.523576	−	0.851979i	$-0.675402\pi$
$251$	−11.9298	+	6.88767i	−0.0475290	+	0.0274409i	0.476047	+	0.879420i	$0.342069\pi$
$252$		0			0
$253$	−242.732	−	140.142i	−0.959416	−	0.553919i
$254$	−612.677	+	108.031i	−2.41211	+	0.425321i
$255$		0			0
$256$	−73.7169	+	26.8308i	−0.287957	+	0.104808i
$257$	107.313	−	39.0589i	0.417562	−	0.151980i	−0.124691	−	0.992196i	$-0.539794\pi$
$257$	107.313	−	39.0589i	0.417562	−	0.151980i	0.542253	+	0.840216i	$0.317572\pi$
$258$		0			0
$259$	7.46711	+	42.3481i	0.0288305	+	0.163506i
$260$	21.2222	−	358.735i	0.0816237	−	1.37975i
$261$		0			0
$262$	211.537	−	122.131i	0.807393	−	0.466149i
$263$	213.136	−	178.843i	0.810405	−	0.680010i	−0.140300	−	0.990109i	$-0.544807\pi$
$263$	213.136	−	178.843i	0.810405	−	0.680010i	0.950704	+	0.310099i	$0.100362\pi$
$264$		0			0
$265$	403.868	−	120.509i	1.52403	−	0.454751i
$266$	−349.767	+	416.836i	−1.31491	+	1.56705i
$267$		0			0
$268$	195.669	−	537.597i	0.730109	−	2.00596i
$269$			91.5594i			0.340369i	0.985412	+	0.170185i	$0.0544364\pi$
$269$			91.5594i			0.340369i	−0.985412	+	0.170185i	$0.945564\pi$
$270$		0			0
$271$	−330.566			−1.21980			−0.609900	−	0.792478i	$-0.708790\pi$
$271$	−330.566			−1.21980			−0.609900	+	0.792478i	$0.708790\pi$
$272$	106.145	+	38.6335i	0.390238	+	0.142035i
$273$		0			0
$274$	71.3109	+	59.8370i	0.260259	+	0.218383i
$275$	−213.836	+	201.008i	−0.777586	+	0.730939i
$276$		0			0
$277$	15.0444	+	17.9292i	0.0543120	+	0.0647265i	0.792517	−	0.609850i	$-0.208771\pi$
$277$	15.0444	+	17.9292i	0.0543120	+	0.0647265i	−0.738205	+	0.674577i	$0.764326\pi$
$278$	−252.955	−	438.131i	−0.909910	−	1.57601i
$279$		0			0
$280$	10.8187	−	182.877i	0.0386382	−	0.653132i
$281$	353.029	−	62.2485i	1.25633	−	0.221525i	0.494429	−	0.869218i	$-0.335377\pi$
$281$	353.029	−	62.2485i	1.25633	−	0.221525i	0.761901	+	0.647693i	$0.224266\pi$
$282$		0			0
$283$	16.5869	+	45.5722i	0.0586110	+	0.161032i	0.965542	−	0.260246i	$-0.0838037\pi$
$283$	16.5869	+	45.5722i	0.0586110	+	0.161032i	−0.906931	+	0.421279i	$0.861581\pi$
$284$	−11.0349	−	30.3182i	−0.0388554	−	0.106754i
$285$		0			0
$286$	−87.5108	−	496.298i	−0.305982	−	1.73531i
$287$	−145.431	+	251.894i	−0.506728	+	0.877679i
$288$		0			0
$289$	89.9148	+	155.737i	0.311124	+	0.538882i
$290$	−110.483	+	255.488i	−0.380977	+	0.880993i
$291$		0			0
$292$	371.632	+	65.5287i	1.27271	+	0.224413i
$293$	−94.0109	−	78.8845i	−0.320856	−	0.269230i	0.468106	−	0.883673i	$-0.344937\pi$
$293$	−94.0109	−	78.8845i	−0.320856	−	0.269230i	−0.788962	+	0.614442i	$0.789381\pi$
$294$		0			0
$295$	−404.530	+	46.9089i	−1.37129	+	0.159013i
$296$			11.2748i			0.0380905i
$297$		0			0
$298$			193.891i			0.650640i
$299$	−116.651	+	320.496i	−0.390137	+	1.07189i
$300$		0			0
$301$	133.939	+	112.388i	0.444980	+	0.373382i
$302$	−101.112	+	573.432i	−0.334807	+	1.89878i
$303$		0			0
$304$	126.849	−	106.439i	0.417267	−	0.350129i
$305$	−183.451	+	278.370i	−0.601477	+	0.912688i
$306$		0			0
$307$	−255.991	−	147.796i	−0.833847	−	0.481422i	0.0213210	−	0.999773i	$-0.493213\pi$
$307$	−255.991	−	147.796i	−0.833847	−	0.481422i	−0.855168	+	0.518351i	$0.826546\pi$
$308$	−121.242	−	687.599i	−0.393643	−	2.23246i
$309$		0			0
$310$	318.442	+	300.984i	1.02723	+	0.970916i
$311$	−109.714	−	301.436i	−0.352777	−	0.969247i	−0.981474	−	0.191596i	$-0.938634\pi$
$311$	−109.714	−	301.436i	−0.352777	−	0.969247i	0.628697	−	0.777651i	$-0.283589\pi$
$312$		0			0
$313$	30.2976	−	5.34228i	0.0967974	−	0.0170680i	−0.125040	−	0.992152i	$-0.539906\pi$
$313$	30.2976	−	5.34228i	0.0967974	−	0.0170680i	0.221837	+	0.975084i	$0.428795\pi$
$314$	399.011	+	230.369i	1.27074	+	0.733660i
$315$		0			0
$316$	226.675	+	392.613i	0.717326	+	1.24245i
$317$	359.537	−	301.687i	1.13419	−	0.951696i	0.134953	−	0.990852i	$-0.456912\pi$
$317$	359.537	−	301.687i	1.13419	−	0.951696i	0.999233	+	0.0391564i	$0.0124671\pi$
$318$		0			0
$319$	−37.7623	+	214.160i	−0.118377	+	0.671349i
$320$	−106.088	+	445.809i	−0.331525	+	1.39315i
$321$		0			0
$322$	−290.100	+	797.044i	−0.900932	+	2.47529i
$323$	−160.039			−0.495477
$324$		0			0
$325$	286.067	+	213.781i	0.880205	+	0.657787i
$326$	−39.0285	+	107.230i	−0.119719	+	0.328926i
$327$		0			0
$328$	−49.0208	+	58.4208i	−0.149454	+	0.178112i
$329$	502.907	+	88.6762i	1.52859	+	0.269532i
$330$		0			0
$331$	−301.261	+	252.788i	−0.910155	+	0.763711i	−0.972148	−	0.234366i	$-0.924699\pi$
$331$	−301.261	+	252.788i	−0.910155	+	0.763711i	0.0619937	+	0.998077i	$0.480254\pi$
$332$	133.743	+	231.650i	0.402841	+	0.697741i
$333$		0			0
$334$	−52.9280	+	91.6739i	−0.158467	+	0.274473i
$335$	339.088	+	456.343i	1.01220	+	1.36222i
$336$		0			0
$337$	−79.0320	−	217.139i	−0.234516	−	0.644328i	−1.00000		0.000872393i	$-0.999722\pi$
$337$	−79.0320	−	217.139i	−0.234516	−	0.644328i	0.765483	−	0.643456i	$-0.222500\pi$
$338$	−99.0039	+	36.0345i	−0.292911	+	0.106611i
$339$		0			0
$340$	210.981	−	156.771i	0.620533	−	0.461091i
$341$	296.462	+	171.162i	0.869389	+	0.501942i
$342$		0			0
$343$	−427.311	+	246.708i	−1.24581	+	0.719266i
$344$	29.4677	+	35.1183i	0.0856620	+	0.102088i
$345$		0			0
$346$	−20.0616	+	113.775i	−0.0579815	+	0.328830i
$347$	−260.352	−	218.461i	−0.750293	−	0.629571i	0.185287	−	0.982684i	$-0.440679\pi$
$347$	−260.352	−	218.461i	−0.750293	−	0.629571i	−0.935581	+	0.353113i	$0.885123\pi$
$348$		0			0
$349$	271.947	+	98.9805i	0.779217	+	0.283612i	0.700846	−	0.713313i	$-0.252806\pi$
$349$	271.947	+	98.9805i	0.779217	+	0.283612i	0.0783708	+	0.996924i	$0.475028\pi$
$350$	711.422	+	531.653i	2.03263	+	1.51901i
$351$		0			0
$352$			526.935i			1.49697i
$353$	123.080	+	44.7973i	0.348667	+	0.126905i	0.510416	−	0.859927i	$-0.329491\pi$
$353$	123.080	+	44.7973i	0.348667	+	0.126905i	−0.161749	+	0.986832i	$0.551713\pi$
$354$		0			0
$355$	31.1918	+	7.42265i	0.0878643	+	0.0209089i
$356$	114.993	+	20.2764i	0.323014	+	0.0569561i
$357$		0			0
$358$	−438.102	−	522.110i	−1.22375	−	1.45841i
$359$	−451.001	+	260.385i	−1.25627	+	0.725307i	−0.972347	−	0.233540i	$-0.924969\pi$
$359$	−451.001	+	260.385i	−1.25627	+	0.725307i	−0.283922	+	0.958847i	$0.591636\pi$
$360$		0			0
$361$	63.1946	−	109.456i	0.175054	−	0.303203i
$362$	−33.5335	−	190.178i	−0.0926340	−	0.525354i
$363$		0			0
$364$	−798.378	+	290.586i	−2.19335	+	0.798313i
$365$	−257.598	+	272.540i	−0.705748	+	0.746684i
$366$		0			0
$367$	344.630	−	60.7675i	0.939046	−	0.165579i	0.316881	−	0.948465i	$-0.397364\pi$
$367$	344.630	−	60.7675i	0.939046	−	0.165579i	0.622165	+	0.782886i	$0.286253\pi$
$368$	129.059	−	223.537i	0.350705	−	0.607438i
$369$		0			0
$370$	−45.6402	−	30.0777i	−0.123352	−	0.0812910i
$371$	−640.499	−	763.317i	−1.72641	−	2.05746i
$372$		0			0
$373$	−336.395	−	59.3155i	−0.901863	−	0.159023i	−0.296556	−	0.955015i	$-0.595838\pi$
$373$	−336.395	−	59.3155i	−0.901863	−	0.159023i	−0.605306	+	0.795993i	$0.706949\pi$
$374$	236.938	−	282.371i	0.633523	−	0.755004i
$375$		0			0
$376$	125.820	+	45.7946i	0.334627	+	0.121794i
$377$	264.623			0.701917
$378$		0			0
$379$	−462.410			−1.22008			−0.610039	−	0.792371i	$-0.708846\pi$
$379$	−462.410			−1.22008			−0.610039	+	0.792371i	$0.708846\pi$
$380$	−44.3847	−	382.762i	−0.116802	−	1.00727i
$381$		0			0
$382$	−570.182	+	679.517i	−1.49262	+	1.77884i
$383$	−27.6776	+	156.967i	−0.0722652	+	0.409837i	0.927120	+	0.374766i	$0.122277\pi$
$383$	−27.6776	+	156.967i	−0.0722652	+	0.409837i	−0.999385	+	0.0350709i	$0.988834\pi$
$384$		0			0
$385$	636.857	+	275.402i	1.65417	+	0.715331i
$386$	−552.321	+	318.882i	−1.43088	+	0.826120i
$387$		0			0
$388$	77.5325	+	44.7634i	0.199826	+	0.115370i
$389$	−233.949	+	41.2515i	−0.601411	+	0.106045i	−0.466061	−	0.884753i	$-0.654327\pi$
$389$	−233.949	+	41.2515i	−0.601411	+	0.106045i	−0.135351	+	0.990798i	$0.543216\pi$
$390$		0			0
$391$	−234.422	+	85.3225i	−0.599544	+	0.218216i
$392$	−264.285	+	96.1917i	−0.674195	+	0.245387i
$393$		0			0
$394$	−3.65067	−	20.7040i	−0.00926566	−	0.0525482i
$395$	−449.738	−	26.6058i	−1.13858	−	0.0673564i
$396$		0			0
$397$	351.860	−	203.147i	0.886297	−	0.511704i	0.0135678	−	0.999908i	$-0.495681\pi$
$397$	351.860	−	203.147i	0.886297	−	0.511704i	0.872730	+	0.488204i	$0.162348\pi$
$398$	245.045	−	205.617i	0.615690	−	0.516625i
$399$		0			0
$400$	−185.113	−	196.926i	−0.462782	−	0.492316i
$401$	356.231	−	424.540i	0.888358	−	1.05870i	−0.109546	−	0.993982i	$-0.534940\pi$
$401$	356.231	−	424.540i	0.888358	−	1.05870i	0.997903	−	0.0647217i	$-0.0206160\pi$
$402$		0			0
$403$	142.472	−	391.438i	0.353528	−	0.971310i
$404$		−	320.778i		−	0.794005i
$405$		0			0
$406$	658.093			1.62092
$407$	−40.1278	−	14.6053i	−0.0985940	−	0.0358853i
$408$		0			0
$409$	−146.542	−	122.963i	−0.358293	−	0.300644i	0.445817	−	0.895124i	$-0.352913\pi$
$409$	−146.542	−	122.963i	−0.358293	−	0.300644i	−0.804110	+	0.594480i	$0.797358\pi$
$410$	−105.714	−	354.284i	−0.257839	−	0.864108i
$411$		0			0
$412$	−28.4027	−	33.8490i	−0.0689386	−	0.0821578i
$413$	481.406	+	833.820i	1.16563	+	2.01893i
$414$		0			0
$415$	−265.355	−	15.6980i	−0.639411	−	0.0378265i
$416$	631.463	−	111.344i	1.51794	−	0.267654i
$417$		0			0
$418$	−184.816	−	507.778i	−0.442144	−	1.21478i
$419$	282.003	+	774.798i	0.673039	+	1.84916i	0.504373	+	0.863486i	$0.331723\pi$
$419$	282.003	+	774.798i	0.673039	+	1.84916i	0.168665	+	0.985673i	$0.446054\pi$
$420$		0			0
$421$	−106.950	−	606.542i	−0.254037	−	1.44072i	−0.798532	−	0.601953i	$-0.794390\pi$
$421$	−106.950	−	606.542i	−0.254037	−	1.44072i	0.544494	−	0.838765i	$-0.316722\pi$
$422$	361.801	−	626.657i	0.857348	−	1.48497i
$423$		0			0
$424$	−130.631	−	226.260i	−0.308093	−	0.533632i
$425$	14.7125	+	260.797i	0.0346177	+	0.613640i
$426$		0			0
$427$	776.220	+	136.868i	1.81784	+	0.320535i
$428$	816.548	+	685.165i	1.90782	+	1.60085i
$429$		0			0
$430$	−220.769	+	25.6002i	−0.513417	+	0.0595353i
$431$			119.081i			0.276291i	0.990412	+	0.138145i	$0.0441141\pi$
$431$			119.081i			0.276291i	−0.990412	+	0.138145i	$0.955886\pi$
$432$		0			0
$433$			403.752i			0.932453i	0.884665	+	0.466226i	$0.154387\pi$
$433$			403.752i			0.932453i	−0.884665	+	0.466226i	$0.845613\pi$
$434$	354.315	−	973.471i	0.816393	−	2.24302i
$435$		0			0
$436$	−389.002	−	326.411i	−0.892207	−	0.748650i
$437$	−63.5044	+	360.151i	−0.145319	+	0.824144i
$438$		0			0
$439$	210.318	−	176.478i	0.479084	−	0.401999i	−0.371011	−	0.928628i	$-0.620989\pi$
$439$	210.318	−	176.478i	0.479084	−	0.401999i	0.850095	+	0.526629i	$0.176544\pi$
$440$	151.906	+	100.108i	0.345240	+	0.227519i
$441$		0			0
$442$	−388.451	−	224.273i	−0.878849	−	0.507404i
$443$	−144.009	−	816.715i	−0.325076	−	1.84360i	−0.509138	−	0.860685i	$-0.670036\pi$
$443$	−144.009	−	816.715i	−0.325076	−	1.84360i	0.184062	−	0.982915i	$-0.441075\pi$
$444$		0			0
$445$	−79.7079	+	84.3312i	−0.179119	+	0.189508i
$446$	−81.2319	−	223.183i	−0.182134	−	0.500410i
$447$		0			0
$448$	1066.97	−	188.136i	2.38163	−	0.419946i
$449$	173.559	+	100.204i	0.386546	+	0.223172i	0.680662	−	0.732597i	$-0.261692\pi$
$449$	173.559	+	100.204i	0.386546	+	0.223172i	−0.294117	+	0.955770i	$0.595025\pi$
$450$		0			0
$451$	−144.422	−	250.147i	−0.320227	−	0.554649i
$452$	−59.3225	+	49.7775i	−0.131244	+	0.110127i
$453$		0			0
$454$	−22.6516	+	128.464i	−0.0498934	+	0.282959i
$455$	195.463	−	821.384i	0.429589	−	1.80524i
$456$		0			0
$457$	191.174	−	525.245i	0.418323	−	1.14933i	−0.534330	−	0.845276i	$-0.679436\pi$
$457$	191.174	−	525.245i	0.418323	−	1.14933i	0.952654	−	0.304058i	$-0.0983416\pi$
$458$	−968.413			−2.11444
$459$		0			0
$460$	−269.077	−	536.998i	−0.584951	−	1.16739i
$461$	58.5842	−	160.959i	0.127081	−	0.349151i	−0.859794	−	0.510642i	$-0.829408\pi$
$461$	58.5842	−	160.959i	0.127081	−	0.349151i	0.986874	+	0.161490i	$0.0516301\pi$
$462$		0			0
$463$	335.733	−	400.111i	0.725126	−	0.864172i	−0.269992	−	0.962863i	$-0.587021\pi$
$463$	335.733	−	400.111i	0.725126	−	0.864172i	0.995118	+	0.0986910i	$0.0314655\pi$
$464$	−197.225	−	34.7761i	−0.425054	−	0.0749484i
$465$		0			0
$466$	−377.802	+	317.013i	−0.810734	+	0.680286i
$467$	−267.546	−	463.403i	−0.572903	−	0.992297i	−0.996266	−	0.0863372i	$-0.972484\pi$
$467$	−267.546	−	463.403i	−0.572903	−	0.992297i	0.423363	−	0.905960i	$-0.360850\pi$
$468$		0			0
$469$	672.073	−	1164.06i	1.43299	−	2.48201i
$470$	−521.025	+	387.151i	−1.10856	+	0.823725i
$471$		0			0
$472$	86.3415	+	237.221i	0.182927	+	0.502588i
$473$	−163.161	+	59.3857i	−0.344949	+	0.125551i
$474$		0			0
$475$	341.880	+	172.480i	0.719748	+	0.363116i
$476$	−538.182	−	310.719i	−1.13063	−	0.652772i
$477$		0			0
$478$	102.580	−	59.2248i	0.214603	−	0.123901i
$479$	338.977	+	403.978i	0.707677	+	0.843377i	0.993372	−	0.114944i	$-0.0366688\pi$
$479$	338.977	+	403.978i	0.707677	+	0.843377i	−0.285695	+	0.958321i	$0.592224\pi$
$480$		0			0
$481$	−9.02337	+	51.1741i	−0.0187596	+	0.106391i
$482$	1030.24	+	864.476i	2.13743	+	1.79352i
$483$		0			0
$484$	79.4684	+	28.9241i	0.164191	+	0.0597606i
$485$	−79.5418	+	39.8566i	−0.164004	+	0.0821786i
$486$		0			0
$487$		−	639.130i		−	1.31238i	−0.754595	−	0.656191i	$-0.772166\pi$
$487$		−	639.130i		−	1.31238i	0.754595	−	0.656191i	$-0.227834\pi$
$488$	194.198	+	70.6824i	0.397947	+	0.144841i
$489$		0			0
$490$	315.648	−	1326.43i	0.644179	−	2.70700i
$491$	−342.650	−	60.4184i	−0.697862	−	0.123052i	−0.186548	−	0.982446i	$-0.559730\pi$
$491$	−342.650	−	60.4184i	−0.697862	−	0.123052i	−0.511314	+	0.859394i	$0.670841\pi$
$492$		0			0
$493$	124.414	+	148.271i	0.252362	+	0.300753i
$494$	−569.453	+	328.774i	−1.15274	+	0.665535i
$495$		0			0
$496$	−157.627	+	273.018i	−0.317796	+	0.550439i
$497$	−13.1632	−	74.6525i	−0.0264854	−	0.150206i
$498$		0			0
$499$	−318.889	+	116.066i	−0.639057	+	0.232598i	−0.641168	−	0.767400i	$-0.721550\pi$
$499$	−318.889	+	116.066i	−0.639057	+	0.232598i	0.00211177	+	0.999998i	$0.499328\pi$
$500$	−619.662	+	107.516i	−1.23932	+	0.215032i
$501$		0			0
$502$	−40.7690	+	7.18868i	−0.0812132	+	0.0143201i
$503$	215.970	−	374.071i	0.429364	−	0.743680i	−0.567453	−	0.823406i	$-0.692071\pi$
$503$	215.970	−	374.071i	0.429364	−	0.743680i	0.996817	+	0.0797255i	$0.0254044\pi$
$504$		0			0
$505$	266.176	+	175.414i	0.527081	+	0.347355i
$506$	−541.428	−	645.249i	−1.07002	−	1.27520i
$507$		0			0
$508$	−1025.75	−	180.867i	−2.01919	−	0.356037i
$509$	68.1800	−	81.2537i	0.133949	−	0.159634i	−0.694900	−	0.719106i	$-0.744552\pi$
$509$	68.1800	−	81.2537i	0.133949	−	0.159634i	0.828849	+	0.559472i	$0.188996\pi$
$510$		0			0
$511$	833.148	+	303.241i	1.63043	+	0.593427i
$512$	−619.297			−1.20956
$513$		0			0
$514$	343.198			0.667701
$515$	43.6191	−	5.05802i	0.0846972	−	0.00982141i
$516$		0			0
$517$	−325.973	+	388.479i	−0.630508	+	0.751410i
$518$	−22.4403	+	127.265i	−0.0433211	+	0.245686i
$519$		0			0
$520$	87.8685	−	203.193i	0.168978	−	0.390755i
$521$	609.297	−	351.778i	1.16948	−	0.675197i	0.215919	−	0.976411i	$-0.430725\pi$
$521$	609.297	−	351.778i	1.16948	−	0.675197i	0.953557	+	0.301214i	$0.0973918\pi$
$522$		0			0
$523$	211.577	+	122.154i	0.404546	+	0.233564i	0.688443	−	0.725290i	$-0.258294\pi$
$523$	211.577	+	122.154i	0.404546	+	0.233564i	−0.283898	+	0.958855i	$0.591628\pi$
$524$	402.732	−	71.0125i	0.768572	−	0.135520i
$525$		0			0
$526$	785.717	−	285.978i	1.49376	−	0.543684i
$527$	286.311	−	104.209i	0.543285	−	0.197740i
$528$		0			0
$529$	7.12954	+	40.4337i	0.0134774	+	0.0764341i
$530$	1264.38	+	74.7988i	2.38563	+	0.141130i
$531$		0			0
$532$	−788.952	+	455.502i	−1.48299	+	0.856206i
$533$	−269.251	+	225.928i	−0.505161	+	0.423881i
$534$		0			0
$535$	−1015.06	+	302.880i	−1.89731	+	0.566132i
$536$	226.537	−	269.977i	0.422645	−	0.503688i
$537$		0			0
$538$	−94.1090	+	258.562i	−0.174924	+	0.480599i
$539$		−	1065.21i		−	1.97628i
$540$		0			0
$541$	222.608			0.411474			0.205737	−	0.978607i	$-0.434041\pi$
$541$	222.608			0.411474			0.205737	+	0.978607i	$0.434041\pi$
$542$	−933.513	−	339.771i	−1.72235	−	0.626884i
$543$		0			0
$544$	359.274	+	301.467i	0.660430	+	0.554167i
$545$	483.573	−	144.292i	0.887289	−	0.264756i
$546$		0			0
$547$	−657.900	−	784.054i	−1.20274	−	1.43337i	−0.871899	−	0.489686i	$-0.837112\pi$
$547$	−657.900	−	784.054i	−1.20274	−	1.43337i	−0.330843	−	0.943686i	$-0.607333\pi$
$548$	77.9257	+	134.971i	0.142200	+	0.246298i
$549$		0			0
$550$	−810.476	+	347.853i	−1.47359	+	0.632461i
$551$	279.432	−	49.2713i	0.507135	−	0.0894217i
$552$		0			0
$553$	364.301	+	1000.91i	0.658773	+	1.80996i
$554$	24.0567	+	66.0953i	0.0434237	+	0.119306i
$555$		0			0
$556$	−147.080	−	834.130i	−0.264532	−	1.50023i
$557$	377.892	−	654.528i	0.678442	−	1.17510i	−0.297008	−	0.954875i	$-0.595989\pi$
$557$	377.892	−	654.528i	0.678442	−	1.17510i	0.975450	−	0.220221i	$-0.0706777\pi$
$558$		0			0
$559$	105.643	+	182.978i	0.188985	+	0.327332i
$560$	−253.624	+	586.495i	−0.452900	+	1.04731i
$561$		0			0
$562$	1060.93	+	187.070i	1.88777	+	0.332866i
$563$	−281.344	−	236.076i	−0.499723	−	0.419317i	0.357773	−	0.933809i	$-0.383536\pi$
$563$	−281.344	−	236.076i	−0.499723	−	0.419317i	−0.857495	+	0.514491i	$0.827981\pi$
$564$		0			0
$565$	−8.86450	−	76.4451i	−0.0156894	−	0.135301i
$566$			145.744i			0.257498i
$567$		0			0
$568$		−	19.8755i		−	0.0349922i
$569$	−93.5838	+	257.119i	−0.164471	+	0.451879i	−0.994361	−	0.106047i	$-0.966181\pi$
$569$	−93.5838	+	257.119i	−0.164471	+	0.451879i	0.829891	+	0.557926i	$0.188403\pi$
$570$		0			0
$571$	−300.950	−	252.527i	−0.527058	−	0.442254i	0.340026	−	0.940416i	$-0.389564\pi$
$571$	−300.950	−	252.527i	−0.527058	−	0.442254i	−0.867084	+	0.498162i	$0.834008\pi$
$572$	146.511	−	830.905i	0.256138	−	1.45263i
$573$		0			0
$574$	−669.603	+	561.864i	−1.16656	+	0.978857i
$575$	592.734	+	70.3765i	1.03084	+	0.122394i
$576$		0			0
$577$	396.854	+	229.124i	0.687789	+	0.397095i	0.802783	−	0.596271i	$-0.203352\pi$
$577$	396.854	+	229.124i	0.687789	+	0.397095i	−0.114994	+	0.993366i	$0.536685\pi$
$578$	93.8443	+	532.218i	0.162360	+	0.920792i
$579$		0			0
$580$	−320.112	+	338.680i	−0.551917	+	0.583931i
$581$	214.946	+	590.558i	0.369958	+	1.01645i
$582$		0			0
$583$	974.495	−	171.830i	1.67152	−	0.294734i
$584$	201.323	+	116.234i	0.344731	+	0.199031i
$585$		0			0
$586$	−184.404	−	319.397i	−0.314683	−	0.545047i
$587$	381.350	−	319.991i	0.649660	−	0.545129i	−0.257308	−	0.966329i	$-0.582835\pi$
$587$	381.350	−	319.991i	0.649660	−	0.545129i	0.906968	+	0.421200i	$0.138391\pi$
$588$		0			0
$589$	77.5612	−	439.871i	0.131683	−	0.746810i
$590$	−1190.60	−	283.325i	−2.01797	−	0.480211i
$591$		0			0
$592$	13.4503	−	36.9545i	0.0227202	−	0.0624232i
$593$	−379.139			−0.639357			−0.319679	−	0.947526i	$-0.603575\pi$
$593$	−379.139			−0.639357			−0.319679	+	0.947526i	$0.603575\pi$
$594$		0			0
$595$	552.129	−	276.660i	0.927948	−	0.464974i
$596$	−111.024	+	305.037i	−0.186282	+	0.511806i
$597$		0			0
$598$	−658.841	+	785.176i	−1.10174	+	1.31300i
$599$	−853.195	−	150.441i	−1.42437	−	0.251154i	−0.592249	−	0.805755i	$-0.701760\pi$
$599$	−853.195	−	150.441i	−1.42437	−	0.251154i	−0.832117	+	0.554600i	$0.812871\pi$
$600$		0			0
$601$	292.301	−	245.270i	0.486358	−	0.408102i	−0.366361	−	0.930473i	$-0.619397\pi$
$601$	292.301	−	245.270i	0.486358	−	0.408102i	0.852719	+	0.522370i	$0.174952\pi$
$602$	262.724	+	455.051i	0.436418	+	0.755898i
$603$		0			0
$604$	−487.427	+	844.248i	−0.806998	+	1.39776i
$605$	−67.4573	+	50.1246i	−0.111500	+	0.0828505i
$606$		0			0
$607$	130.172	+	357.645i	0.214451	+	0.589200i	0.999545	−	0.0301773i	$-0.00960718\pi$
$607$	130.172	+	357.645i	0.214451	+	0.589200i	−0.785093	+	0.619378i	$0.787385\pi$
$608$	646.070	−	235.150i	1.06261	−	0.386760i
$609$		0			0
$610$	−804.183	+	597.553i	−1.31833	+	0.979595i
$611$	534.421	+	308.548i	0.874667	+	0.504989i
$612$		0			0
$613$	−210.200	+	121.359i	−0.342903	+	0.197975i	−0.661555	−	0.749896i	$-0.730103\pi$
$613$	−210.200	+	121.359i	−0.342903	+	0.197975i	0.318652	+	0.947872i	$0.396770\pi$
$614$	−571.003	−	680.495i	−0.929972	−	1.10830i
$615$		0			0
$616$	74.6888	−	423.581i	0.121248	−	0.687631i
$617$	−148.955	−	124.988i	−0.241419	−	0.202574i	0.514048	−	0.857761i	$-0.328145\pi$
$617$	−148.955	−	124.988i	−0.241419	−	0.202574i	−0.755467	+	0.655187i	$0.772590\pi$
$618$		0			0
$619$	−759.634	−	276.484i	−1.22720	−	0.446663i	−0.354559	−	0.935034i	$-0.615369\pi$
$619$	−759.634	−	276.484i	−1.22720	−	0.446663i	−0.872636	+	0.488371i	$0.837591\pi$
$620$	328.638	+	655.863i	0.530062	+	1.05784i
$621$		0			0
$622$		−	964.019i		−	1.54987i
$623$	257.799	+	93.8312i	0.413803	+	0.150612i
$624$		0			0
$625$	249.641	−	572.978i	0.399426	−	0.916765i
$626$	91.0510	+	16.0547i	0.145449	+	0.0256466i
$627$		0			0
$628$	495.828	+	590.905i	0.789535	+	0.940931i
$629$	−32.9158	+	19.0040i	−0.0523304	+	0.0302130i
$630$		0			0
$631$	498.492	−	863.413i	0.790003	−	1.36832i	−0.135962	−	0.990714i	$-0.543412\pi$
$631$	498.492	−	863.413i	0.790003	−	1.36832i	0.925964	−	0.377611i	$-0.123254\pi$
$632$	48.4960	+	275.034i	0.0767341	+	0.435181i
$633$		0			0
$634$	1325.42	−	482.412i	2.09056	−	0.760902i
$635$	711.000	−	752.241i	1.11969	−	1.18463i
$636$		0			0
$637$	−1276.52	+	225.085i	−2.00396	+	0.353352i
$638$	−326.764	+	565.972i	−0.512170	+	0.887104i
$639$		0			0
$640$	−263.816	+	400.317i	−0.412213	+	0.625496i
$641$	301.260	+	359.028i	0.469985	+	0.560106i	0.948010	−	0.318240i	$-0.103092\pi$
$641$	301.260	+	359.028i	0.469985	+	0.560106i	−0.478026	+	0.878346i	$0.658647\pi$
$642$		0			0
$643$	30.3696	+	5.35498i	0.0472311	+	0.00832812i	0.197214	−	0.980361i	$-0.436811\pi$
$643$	30.3696	+	5.35498i	0.0472311	+	0.00832812i	−0.149983	+	0.988689i	$0.547922\pi$
$644$	−912.794	+	1087.83i	−1.41738	+	1.68917i
$645$		0			0
$646$	−451.948	−	164.496i	−0.699610	−	0.254637i
$647$	−389.494			−0.602000			−0.301000	−	0.953624i	$-0.597320\pi$
$647$	−389.494			−0.602000			−0.301000	+	0.953624i	$0.597320\pi$
$648$		0			0
$649$	−956.134			−1.47324
$650$	588.114	+	897.746i	0.904791	+	1.38115i
$651$		0			0
$652$	−122.802	+	146.350i	−0.188347	+	0.224463i
$653$	−173.274	+	982.684i	−0.265350	+	1.50488i	0.502686	+	0.864469i	$0.332345\pi$
$653$	−173.274	+	982.684i	−0.265350	+	1.50488i	−0.768036	+	0.640407i	$0.778766\pi$
$654$		0			0
$655$	−161.305	+	373.012i	−0.246268	+	0.569484i
$656$	230.365	−	133.001i	0.351167	−	0.202746i
$657$		0			0
$658$	1329.06	+	767.332i	2.01984	+	1.16616i
$659$	81.2990	−	14.3352i	0.123367	−	0.0217530i	−0.111624	−	0.993751i	$-0.535605\pi$
$659$	81.2990	−	14.3352i	0.123367	−	0.0217530i	0.234991	+	0.971998i	$0.424494\pi$
$660$		0			0
$661$	360.048	−	131.047i	0.544702	−	0.198255i	−0.0549888	−	0.998487i	$-0.517512\pi$
$661$	360.048	−	131.047i	0.544702	−	0.198255i	0.599691	+	0.800232i	$0.295290\pi$
$662$	−1110.58	+	404.220i	−1.67762	+	0.610604i
$663$		0			0
$664$	28.6137	+	162.276i	0.0430929	+	0.244392i
$665$	53.4640	−	903.745i	0.0803970	−	1.35901i
$666$		0			0
$667$	383.036	−	221.146i	0.574268	−	0.331554i
$668$	−135.762	+	113.918i	−0.203236	+	0.170536i
$669$		0			0
$670$	488.530	+	1637.24i	0.729150	+	2.44364i
$671$	−503.127	+	599.604i	−0.749817	+	0.893597i
$672$		0			0
$673$	117.908	−	323.950i	0.175198	−	0.481352i	−0.820750	−	0.571288i	$-0.806444\pi$
$673$	117.908	−	323.950i	0.175198	−	0.481352i	0.995948	+	0.0899359i	$0.0286662\pi$
$674$		−	694.429i		−	1.03031i
$675$		0			0
$676$	−176.390			−0.260933
$677$	690.627	+	251.368i	1.02013	+	0.371297i	0.797314	−	0.603564i	$-0.206253\pi$
$677$	690.627	+	251.368i	1.02013	+	0.371297i	0.222815	+	0.974861i	$0.428476\pi$
$678$		0			0
$679$	161.132	+	135.206i	0.237308	+	0.199125i
$680$	155.163	−	46.2987i	0.228181	−	0.0680863i
$681$		0			0
$682$	661.275	+	788.076i	0.969611	+	1.15554i
$683$	233.214	+	403.938i	0.341455	+	0.591418i	0.984703	−	0.174240i	$-0.0557469\pi$
$683$	233.214	+	403.938i	0.341455	+	0.591418i	−0.643248	+	0.765658i	$0.722414\pi$
$684$		0			0
$685$	−154.610	−	9.14645i	−0.225708	−	0.0133525i
$686$	−1460.30	+	257.490i	−2.12872	+	0.375350i
$687$		0			0
$688$	−54.6895	−	150.258i	−0.0794906	−	0.218399i
$689$	−411.831	−	1131.50i	−0.597723	−	1.64223i
$690$		0			0
$691$	49.3428	+	279.837i	0.0714078	+	0.404974i	0.999470	+	0.0325490i	$0.0103625\pi$
$691$	49.3428	+	279.837i	0.0714078	+	0.404974i	−0.928062	+	0.372425i	$0.878526\pi$
$692$	−96.7107	+	167.508i	−0.139755	+	0.242063i
$693$		0			0
$694$	−510.685	−	884.533i	−0.735858	−	1.27454i
$695$	772.575	+	334.092i	1.11162	+	0.480708i
$696$		0			0
$697$	−253.181	−	44.6426i	−0.363243	−	0.0640496i
$698$	666.237	+	559.039i	0.954494	+	0.800915i
$699$		0			0
$700$	814.806	+	1243.79i	1.16401	+	1.77684i
$701$		−	769.747i		−	1.09807i	−0.835799	−	0.549035i	$-0.814995\pi$
$701$		−	769.747i		−	1.09807i	0.835799	−	0.549035i	$-0.185005\pi$
$702$		0			0
$703$			55.7180i			0.0792575i
$704$	−367.985	+	1011.03i	−0.522705	+	1.43612i
$705$		0			0
$706$	301.530	+	253.014i	0.427097	+	0.358377i
$707$	130.873	−	742.217i	0.185110	−	1.04981i
$708$		0			0
$709$	−1011.12	+	848.431i	−1.42612	+	1.19666i	−0.478161	+	0.878272i	$0.658696\pi$
$709$	−1011.12	+	848.431i	−1.42612	+	1.19666i	−0.947961	+	0.318386i	$0.896859\pi$
$710$	80.4560	+	53.0219i	0.113318	+	0.0746787i
$711$		0			0
$712$	62.2949	+	35.9660i	0.0874928	+	0.0505140i
$713$	−120.901	−	685.663i	−0.169567	−	0.961660i
$714$		0			0
$715$	609.352	+	575.945i	0.852241	+	0.805518i
$716$	−390.273	−	1072.27i	−0.545074	−	1.49758i
$717$		0			0
$718$	−1541.25	+	271.765i	−2.14659	+	0.378503i
$719$	253.774	+	146.516i	0.352954	+	0.203778i	0.665985	−	0.745965i	$-0.268011\pi$
$719$	253.774	+	146.516i	0.352954	+	0.203778i	−0.313032	+	0.949743i	$0.601345\pi$
$720$		0			0
$721$	−51.9083	−	89.9079i	−0.0719949	−	0.124699i
$722$	290.965	−	244.149i	0.402999	−	0.338156i
$723$		0			0
$724$	56.1420	−	318.397i	0.0775442	−	0.439775i
$725$	−105.980	−	450.827i	−0.146179	−	0.621830i
$726$		0			0
$727$	−248.711	+	683.327i	−0.342105	+	0.939927i	0.642678	+	0.766137i	$0.277824\pi$
$727$	−248.711	+	683.327i	−0.342105	+	0.939927i	−0.984783	+	0.173790i	$0.944399\pi$
$728$	−523.389			−0.718941
$729$		0			0
$730$	−1007.58	+	504.877i	−1.38025	+	0.691612i
$731$	−52.8563	+	145.221i	−0.0723068	+	0.198661i
$732$		0			0
$733$	313.284	−	373.357i	0.427400	−	0.509355i	−0.508770	−	0.860902i	$-0.669900\pi$
$733$	313.284	−	373.357i	0.427400	−	0.509355i	0.936170	+	0.351547i	$0.114344\pi$
$734$	1035.69	+	182.620i	1.41102	+	0.248801i
$735$		0			0
$736$	820.980	−	688.884i	1.11546	−	0.935984i
$737$	667.411	+	1155.99i	0.905578	+	1.56851i
$738$		0			0
$739$	−485.402	+	840.741i	−0.656837	+	1.13767i	0.324593	+	0.945854i	$0.394773\pi$
$739$	−485.402	+	840.741i	−0.656837	+	1.13767i	−0.981430	+	0.191821i	$0.938561\pi$
$740$	−54.5801	−	73.4535i	−0.0737569	−	0.0992615i
$741$		0			0
$742$	−1024.19	−	2813.93i	−1.38031	−	3.79236i
$743$	46.3654	−	16.8756i	0.0624030	−	0.0227128i	−0.310630	−	0.950531i	$-0.600540\pi$
$743$	46.3654	−	16.8756i	0.0624030	−	0.0227128i	0.373033	+	0.927818i	$0.378318\pi$
$744$		0			0
$745$	−192.401	−	258.932i	−0.258257	−	0.347560i
$746$	−889.006	−	513.268i	−1.19170	−	0.688027i
$747$		0			0
$748$	534.449	−	308.564i	0.714504	−	0.412519i
$749$	1609.79	+	1918.48i	2.14926	+	2.56138i
$750$		0			0
$751$	−218.951	+	1241.73i	−0.291546	+	1.65344i	0.389371	+	0.921081i	$0.372692\pi$
$751$	−218.951	+	1241.73i	−0.291546	+	1.65344i	−0.680917	+	0.732360i	$0.738419\pi$
$752$	−357.759	−	300.195i	−0.475743	−	0.399196i
$753$		0			0
$754$	747.291	+	271.992i	0.991102	+	0.360732i
$755$	−433.997	−	866.128i	−0.574831	−	1.14719i
$756$		0			0
$757$			653.161i			0.862828i	0.902154	+	0.431414i	$0.141985\pi$
$757$			653.161i			0.862828i	−0.902154	+	0.431414i	$0.858015\pi$
$758$	−1305.84	−	475.286i	−1.72274	−	0.627026i
$759$		0			0
$760$	54.9525	−	230.924i	0.0723059	−	0.303848i
$761$	−744.387	−	131.256i	−0.978170	−	0.172478i	−0.338365	−	0.941015i	$-0.609874\pi$
$761$	−744.387	−	131.256i	−0.978170	−	0.172478i	−0.639805	+	0.768537i	$0.720985\pi$
$762$		0			0
$763$	−766.903	−	913.960i	−1.00512	−	1.19785i
$764$	−1286.13	+	742.549i	−1.68342	+	0.971923i
$765$		0			0
$766$	−239.499	+	414.825i	−0.312663	+	0.541547i
$767$	202.036	+	1145.80i	0.263410	+	1.49387i
$768$		0			0
$769$	1169.47	−	425.651i	1.52076	−	0.553513i	0.559425	−	0.828881i	$-0.311022\pi$
$769$	1169.47	−	425.651i	1.52076	−	0.553513i	0.961339	+	0.275368i	$0.0887996\pi$
$770$	1515.40	+	1432.32i	1.96806	+	1.86016i
$771$		0			0
$772$	−1051.53	+	185.413i	−1.36208	+	0.240172i
$773$	−535.789	+	928.014i	−0.693130	+	1.20054i	0.277677	+	0.960674i	$0.410435\pi$
$773$	−535.789	+	928.014i	−0.693130	+	1.20054i	−0.970807	+	0.239862i	$0.922898\pi$
$774$		0			0
$775$	−723.936	−	85.9545i	−0.934111	−	0.110909i
$776$	35.4505	+	42.2482i	0.0456836	+	0.0544436i
$777$		0			0
$778$	−703.069	−	123.970i	−0.903688	−	0.159344i
$779$	−242.252	+	288.705i	−0.310979	+	0.370610i
$780$		0			0
$781$	70.7385	+	25.7467i	0.0905742	+	0.0329663i
$782$	−749.701			−0.958698
$783$		0			0
$784$	980.978			1.25125
$785$	−761.461	+	88.2983i	−0.970014	+	0.112482i
$786$		0			0
$787$	−259.579	+	309.354i	−0.329833	+	0.393080i	−0.905319	−	0.424732i	$-0.860368\pi$
$787$	−259.579	+	309.354i	−0.329833	+	0.393080i	0.575486	+	0.817812i	$0.304813\pi$
$788$	6.11197	−	34.6627i	0.00775631	−	0.0439882i
$789$		0			0
$790$	−1242.71	−	537.396i	−1.57305	−	0.680248i
$791$	−157.569	+	90.9726i	−0.199202	+	0.115010i
$792$		0			0
$793$	824.860	+	476.233i	1.04018	+	0.600546i
$794$	1202.45	−	212.025i	1.51442	−	0.267033i
$795$		0			0
$796$	503.252	−	183.169i	0.632227	−	0.230112i
$797$	230.850	−	84.0224i	0.289648	−	0.105423i	−0.193110	−	0.981177i	$-0.561857\pi$
$797$	230.850	−	84.0224i	0.289648	−	0.105423i	0.482758	+	0.875754i	$0.339635\pi$
$798$		0			0
$799$	78.3788	+	444.508i	0.0980962	+	0.556331i
$800$	−442.590	−	1031.21i	−0.553237	−	1.28901i
$801$		0			0
$802$	1442.35	−	832.744i	1.79845	−	1.03833i
$803$	−674.478	+	565.954i	−0.839947	+	0.704800i
$804$		0			0
$805$	−403.505	−	1352.29i	−0.501248	−	1.67986i
$806$	804.676	−	958.976i	0.998358	−	1.18980i
$807$		0			0
$808$	67.5861	−	185.691i	0.0836462	−	0.229816i
$809$			1384.62i			1.71153i	0.517368	+	0.855763i	$0.326912\pi$
$809$			1384.62i			1.71153i	−0.517368	+	0.855763i	$0.673088\pi$
$810$		0			0
$811$	−590.867			−0.728566			−0.364283	−	0.931288i	$-0.618686\pi$
$811$	−590.867			−0.728566			−0.364283	+	0.931288i	$0.618686\pi$
$812$	1035.34	+	376.832i	1.27505	+	0.464079i
$813$		0			0
$814$	−98.3082	−	82.4904i	−0.120772	−	0.101340i
$815$	−54.2853	−	181.929i	−0.0666077	−	0.223226i
$816$		0			0
$817$	145.624	+	173.548i	0.178243	+	0.212421i
$818$	−287.445	−	497.869i	−0.351400	−	0.608642i
$819$		0			0
$820$	36.5543	−	617.907i	0.0445785	−	0.753545i
$821$	494.358	−	87.1687i	0.602142	−	0.106174i	0.135737	−	0.990745i	$-0.456660\pi$
$821$	494.358	−	87.1687i	0.602142	−	0.106174i	0.466405	+	0.884571i	$0.345549\pi$
$822$		0			0
$823$	20.2243	+	55.5657i	0.0245738	+	0.0675160i	0.951373	−	0.308041i	$-0.0996735\pi$
$823$	20.2243	+	55.5657i	0.0245738	+	0.0675160i	−0.926799	+	0.375557i	$0.877451\pi$
$824$	−9.30990	−	25.5787i	−0.0112984	−	0.0310422i
$825$		0			0
$826$	502.445	+	2849.51i	0.608287	+	3.44977i
$827$	−275.911	+	477.893i	−0.333629	+	0.577863i	−0.983221	−	0.182421i	$-0.941607\pi$
$827$	−275.911	+	477.893i	−0.333629	+	0.577863i	0.649591	+	0.760284i	$0.274940\pi$
$828$		0			0
$829$	582.852	+	1009.53i	0.703078	+	1.21777i	0.967381	+	0.253327i	$0.0815250\pi$
$829$	582.852	+	1009.53i	0.703078	+	1.21777i	−0.264302	+	0.964440i	$0.585142\pi$
$830$	−733.224	−	317.075i	−0.883403	−	0.382019i
$831$		0			0
$832$	1289.34	+	227.346i	1.54969	+	0.273253i
$833$	−726.283	−	609.423i	−0.871888	−	0.731601i
$834$		0			0
$835$	−20.2868	−	174.948i	−0.0242955	−	0.209518i
$836$		−	904.684i		−	1.08216i
$837$		0			0
$838$			2477.87i			2.95689i
$839$	313.787	−	862.123i	0.374001	−	1.02756i	−0.599798	−	0.800151i	$-0.704753\pi$
$839$	313.787	−	862.123i	0.374001	−	1.02756i	0.973799	−	0.227409i	$-0.0730253\pi$
$840$		0			0
$841$	381.365	+	320.003i	0.453466	+	0.380504i
$842$	321.408	−	1822.79i	0.381719	−	2.16484i
$843$		0			0
$844$	928.031	−	778.710i	1.09956	−	0.922642i
$845$	96.4575	−	146.366i	0.114151	−	0.173214i
$846$		0			0
$847$	172.074	+	99.3468i	0.203157	+	0.117293i
$848$	158.242	+	897.433i	0.186606	+	1.05829i
$849$		0			0
$850$	−226.511	+	751.609i	−0.266484	+	0.884246i
$851$	29.7052	+	81.6144i	0.0349062	+	0.0959041i
$852$		0			0
$853$	538.725	−	94.9917i	0.631565	−	0.111362i	0.151303	−	0.988487i	$-0.451653\pi$
$853$	538.725	−	94.9917i	0.631565	−	0.111362i	0.480261	+	0.877125i	$0.340542\pi$
$854$	2051.35	+	1184.35i	2.40205	+	1.38683i
$855$		0			0
$856$	328.321	+	568.669i	0.383553	+	0.664333i
$857$	−1059.56	+	889.075i	−1.23636	+	1.03743i	−0.238558	+	0.971128i	$0.576675\pi$
$857$	−1059.56	+	889.075i	−1.23636	+	1.03743i	−0.997800	+	0.0662989i	$0.978881\pi$
$858$		0			0
$859$	−13.3234	+	75.5605i	−0.0155103	+	0.0879633i	−0.991580	−	0.129493i	$-0.958665\pi$
$859$	−13.3234	+	75.5605i	−0.0155103	+	0.0879633i	0.976070	+	0.217457i	$0.0697760\pi$
$860$	−361.982	−	86.1399i	−0.420909	−	0.100163i
$861$		0			0
$862$	−122.397	+	336.284i	−0.141992	+	0.390121i
$863$	−85.6487			−0.0992453			−0.0496226	−	0.998768i	$-0.515802\pi$
$863$	−85.6487			−0.0992453			−0.0496226	+	0.998768i	$0.515802\pi$
$864$		0			0
$865$	−86.1096	−	171.849i	−0.0995487	−	0.198669i
$866$	−414.995	+	1140.19i	−0.479209	+	1.31662i
$867$		0			0
$868$	1114.84	−	1328.62i	1.28438	−	1.53067i
$869$	−1041.69	−	183.678i	−1.19872	−	0.211367i
$870$		0			0
$871$	1244.28	−	1044.07i	1.42856	−	1.19870i
$872$	−156.412	−	270.913i	−0.179371	−	0.310680i
$873$		0			0
$874$	−549.515	+	951.789i	−0.628736	+	1.08900i
$875$	−1477.64	−	4.04202i	−1.68873	−	0.00461945i
$876$		0			0
$877$	−373.044	−	1024.93i	−0.425363	−	1.16868i	−0.948597	−	0.316487i	$-0.897497\pi$
$877$	−373.044	−	1024.93i	−0.425363	−	1.16868i	0.523234	−	0.852189i	$-0.324725\pi$
$878$	775.326	−	282.196i	0.883059	−	0.321407i
$879$		0			0
$880$	−378.464	−	509.335i	−0.430073	−	0.578790i
$881$	−768.700	−	443.809i	−0.872531	−	0.503756i	−0.00434241	−	0.999991i	$-0.501382\pi$
$881$	−768.700	−	443.809i	−0.872531	−	0.503756i	−0.868188	+	0.496235i	$0.834716\pi$
$882$		0			0
$883$	−257.980	+	148.945i	−0.292163	+	0.168680i	−0.638917	−	0.769276i	$-0.720617\pi$
$883$	−257.980	+	148.945i	−0.292163	+	0.168680i	0.346754	+	0.937956i	$0.387284\pi$
$884$	−482.706	−	575.266i	−0.546047	−	0.650754i
$885$		0			0
$886$	432.779	−	2454.41i	0.488463	−	2.77021i
$887$	−978.464	−	821.029i	−1.10312	−	0.925624i	−0.105485	−	0.994421i	$-0.533640\pi$
$887$	−978.464	−	821.029i	−1.10312	−	0.925624i	−0.997631	+	0.0687965i	$0.978084\pi$
$888$		0			0
$889$	−2299.59	−	836.981i	−2.58671	−	0.941486i
$890$	−311.773	+	156.223i	−0.350307	+	0.175531i
$891$		0			0
$892$		−	397.634i		−	0.445778i
$893$	621.779	+	226.309i	0.696281	+	0.253425i
$894$		0			0
$895$	1103.16	+	262.517i	1.23259	+	0.293315i
$896$	1116.26	+	196.828i	1.24583	+	0.219674i
$897$		0			0
$898$	387.133	+	461.368i	0.431106	+	0.513772i
$899$	−467.822	+	270.097i	−0.520381	+	0.300442i
$900$		0			0
$901$	440.365	−	762.735i	0.488752	−	0.846543i
$902$	−150.734	−	854.854i	−0.167111	−	0.947732i
$903$		0			0
$904$	−44.8283	+	16.3162i	−0.0495889	+	0.0180489i
$905$	233.500	+	220.698i	0.258011	+	0.243865i
$906$		0			0
$907$	1520.14	−	268.041i	1.67601	−	0.295525i	0.746789	−	0.665061i	$-0.231594\pi$
$907$	1520.14	−	268.041i	1.67601	−	0.295525i	0.929216	+	0.369536i	$0.120483\pi$
$908$	−109.196	+	189.133i	−0.120260	+	0.208297i
$909$		0			0
$910$	1396.24	−	2118.67i	1.53433	−	2.32821i
$911$	−536.186	−	639.001i	−0.588568	−	0.701428i	0.386762	−	0.922180i	$-0.373593\pi$
$911$	−536.186	−	639.001i	−0.588568	−	0.701428i	−0.975330	+	0.220751i	$0.929149\pi$
$912$		0			0
$913$	−614.618	−	108.374i	−0.673186	−	0.118701i
$914$	1079.74	−	1286.79i	1.18134	−	1.40786i
$915$		0			0
$916$	−1523.55	−	554.525i	−1.66326	−	0.605377i
$917$	960.815			1.04778
$918$		0			0
$919$	−258.168			−0.280923			−0.140461	−	0.990086i	$-0.544859\pi$
$919$	−258.168			−0.280923			−0.140461	+	0.990086i	$0.544859\pi$
$920$	−42.6207	−	367.549i	−0.0463268	−	0.399510i
$921$		0			0
$922$	330.882	−	394.329i	0.358874	−	0.427689i
$923$	15.9067	−	90.2112i	0.0172337	−	0.0977370i
$924$		0			0
$925$	90.7970	−	5.12220i	0.0981589	−	0.00553751i
$926$	1359.36	−	784.826i	1.46799	−	0.847545i
$927$		0			0
$928$	−720.112	−	415.757i	−0.775983	−	0.448014i
$929$	−68.6412	+	12.1033i	−0.0738872	+	0.0130283i	−0.210470	−	0.977600i	$-0.567499\pi$
$929$	−68.6412	+	12.1033i	−0.0738872	+	0.0130283i	0.136582	+	0.990629i	$0.456388\pi$
$930$		0			0
$931$	−1306.05	+	475.362i	−1.40284	+	0.510593i
$932$	−775.898	+	282.404i	−0.832509	+	0.303008i
$933$		0			0
$934$	−279.238	−	1583.64i	−0.298970	−	1.69554i
$935$	−36.2174	+	612.212i	−0.0387352	+	0.654772i
$936$		0			0
$937$	−1193.28	+	688.938i	−1.27351	+	0.735259i	−0.975646	−	0.219351i	$-0.929606\pi$
$937$	−1193.28	+	688.938i	−1.27351	+	0.735259i	−0.297860	+	0.954610i	$0.596273\pi$
$938$	3094.40	−	2596.51i	3.29894	−	2.76814i
$939$		0			0
$940$	−1041.38	+	310.735i	−1.10785	+	0.330569i
$941$	−407.413	+	485.535i	−0.432957	+	0.515978i	−0.937773	−	0.347249i	$-0.887116\pi$
$941$	−407.413	+	485.535i	−0.432957	+	0.515978i	0.504816	+	0.863227i	$0.331560\pi$
$942$		0			0
$943$	−200.927	+	552.041i	−0.213072	+	0.585410i
$944$		−	880.524i		−	0.932759i
$945$		0			0
$946$	−521.803			−0.551589
$947$	−126.925	−	46.1971i	−0.134029	−	0.0487826i	0.274135	−	0.961691i	$-0.411609\pi$
$947$	−126.925	−	46.1971i	−0.134029	−	0.0487826i	−0.408164	+	0.912909i	$0.633831\pi$
$948$		0			0
$949$	820.743	+	688.685i	0.864850	+	0.725695i
$950$	788.182	+	838.482i	0.829665	+	0.882613i
$951$		0			0
$952$	−246.075	−	293.261i	−0.258482	−	0.308047i
$953$	−629.190	−	1089.79i	−0.660220	−	1.14353i	−0.980558	−	0.196231i	$-0.937130\pi$
$953$	−629.190	−	1089.79i	−0.660220	−	1.14353i	0.320337	−	0.947303i	$-0.396204\pi$
$954$		0			0
$955$	87.1559	−	1473.27i	0.0912628	−	1.54269i
$956$	195.296	−	34.4360i	0.204285	−	0.0360209i
$957$		0			0
$958$	542.040	+	1489.24i	0.565804	+	1.55453i
$959$	125.238	+	344.090i	0.130593	+	0.358801i
$960$		0			0
$961$	−19.2133	−	108.964i	−0.0199930	−	0.113386i
$962$	−78.0810	+	135.240i	−0.0811652	+	0.140582i
$963$		0			0
$964$	1125.81	+	1949.96i	1.16785	+	2.02278i
$965$	421.166	−	973.930i	0.436442	−	1.00925i
$966$		0			0
$967$	599.358	+	105.683i	0.619812	+	0.109290i	0.474732	−	0.880130i	$-0.342545\pi$
$967$	599.358	+	105.683i	0.619812	+	0.109290i	0.145080	+	0.989420i	$0.453656\pi$
$968$	39.9084	+	33.4871i	0.0412277	+	0.0345941i
$969$		0			0
$970$	−265.591	+	30.7977i	−0.273806	+	0.0317502i
$971$		−	667.066i		−	0.686988i	−0.939155	−	0.343494i	$-0.888389\pi$
$971$		−	667.066i		−	0.686988i	0.939155	−	0.343494i	$-0.111611\pi$
$972$		0			0
$973$		−	1990.02i		−	2.04524i
$974$	656.928	−	1804.89i	0.674464	−	1.85307i
$975$		0			0
$976$	−552.188	−	463.341i	−0.565766	−	0.474734i
$977$	−138.429	+	785.069i	−0.141688	+	0.803551i	0.828280	+	0.560315i	$0.189320\pi$
$977$	−138.429	+	785.069i	−0.141688	+	0.803551i	−0.969967	+	0.243236i	$0.921791\pi$
$978$		0			0
$979$	−208.702	+	175.122i	−0.213179	+	0.178878i
$980$	1256.12	−	1906.05i	1.28175	−	1.94495i
$981$		0			0
$982$	−905.538	−	522.812i	−0.922136	−	0.532396i
$983$	81.4145	+	461.724i	0.0828225	+	0.469710i	0.997805	+	0.0662167i	$0.0210929\pi$
$983$	81.4145	+	461.724i	0.0828225	+	0.469710i	−0.914983	+	0.403493i	$0.867796\pi$
$984$		0			0
$985$	25.4202	+	24.0266i	0.0258073	+	0.0243925i
$986$	198.944	+	546.594i	0.201769	+	0.554355i
$987$		0			0
$988$	−1084.15	+	191.164i	−1.09731	+	0.193486i
$989$	305.831	+	176.572i	0.309233	+	0.178536i
$990$		0			0
$991$	−467.836	−	810.316i	−0.472085	−	0.817675i	0.527405	−	0.849614i	$-0.323165\pi$
$991$	−467.836	−	810.316i	−0.472085	−	0.817675i	−0.999490	+	0.0319388i	$0.989832\pi$
$992$	−1002.71	+	841.370i	−1.01079	+	0.848156i
$993$		0			0
$994$	39.5585	−	224.347i	0.0397973	−	0.225701i
$995$	−123.209	+	517.754i	−0.123828	+	0.520356i
$996$		0			0
$997$	248.507	−	682.768i	0.249255	−	0.684822i	−0.750459	−	0.660917i	$-0.770168\pi$
$997$	248.507	−	682.768i	0.249255	−	0.684822i	0.999714	−	0.0239057i	$-0.00761015\pi$
$998$	−1019.84			−1.02188
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.n.a.179.29		204
3.2	odd	2		135.3.n.a.104.6	yes	204
5.4	even	2	inner	405.3.n.a.179.6		204
15.14	odd	2		135.3.n.a.104.29	yes	204
27.7	even	9		135.3.n.a.74.29	yes	204
27.20	odd	18	inner	405.3.n.a.224.6		204
135.34	even	18		135.3.n.a.74.6	✓	204
135.74	odd	18	inner	405.3.n.a.224.29		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.6	✓	204	135.34	even	18
135.3.n.a.74.29	yes	204	27.7	even	9
135.3.n.a.104.6	yes	204	3.2	odd	2
135.3.n.a.104.29	yes	204	15.14	odd	2
405.3.n.a.179.6		204	5.4	even	2	inner
405.3.n.a.179.29		204	1.1	even	1	trivial
405.3.n.a.224.6		204	27.20	odd	18	inner
405.3.n.a.224.29		204	135.74	odd	18	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.n (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.82399 + 1.02785i) q^{2} +(3.85425 + 3.23410i) q^{4} +(-4.79125 + 1.42965i) q^{5} +(7.59850 + 9.05554i) q^{7} +(1.54973 + 2.68422i) q^{8} +(-14.9999 - 0.887368i) q^{10} +(-11.5608 + 2.03849i) q^{11} +(4.88572 + 13.4234i) q^{13} +(12.1503 + 33.3828i) q^{14} +(-1.87729 - 10.6466i) q^{16} +(-5.22423 + 9.04864i) q^{17} +(7.65850 + 13.2649i) q^{19} +(-23.0903 - 9.98516i) q^{20} +(-34.7429 - 6.12611i) q^{22} +(18.2900 + 15.3471i) q^{23} +(20.9122 - 13.6996i) q^{25} +42.9293i q^{26} +59.4766i q^{28} +(6.33581 - 17.4075i) q^{29} +(-22.3385 - 18.7442i) q^{31} +(7.79453 - 44.2050i) q^{32} +(-24.0538 + 20.1835i) q^{34} +(-49.3526 - 32.5242i) q^{35} +(3.15030 + 1.81883i) q^{37} +(7.99320 + 45.3317i) q^{38} +(-11.2626 - 10.6452i) q^{40} +(8.41546 + 23.1213i) q^{41} +(14.5661 - 2.56840i) q^{43} +(-51.1509 - 29.5320i) q^{44} +(35.8762 + 62.1393i) q^{46} +(33.0925 - 27.7679i) q^{47} +(-15.7569 + 89.3615i) q^{49} +(73.1369 - 17.1930i) q^{50} +(-24.5818 + 67.5380i) q^{52} -84.2928 q^{53} +(52.4766 - 26.2948i) q^{55} +(-12.5314 + 34.4297i) q^{56} +(35.7844 - 42.6462i) q^{58} +(80.2108 + 14.1433i) q^{59} +(51.0771 - 42.8588i) q^{61} +(-43.8174 - 75.8940i) q^{62} +(45.8258 - 79.3727i) q^{64} +(-42.5995 - 57.3301i) q^{65} +(-38.8900 - 106.849i) q^{67} +(-49.3996 + 17.9800i) q^{68} +(-105.941 - 142.575i) q^{70} +(-5.55345 - 3.20629i) q^{71} +(64.9541 - 37.5013i) q^{73} +(7.02693 + 8.37437i) q^{74} +(-13.3823 + 75.8946i) q^{76} +(-106.305 - 89.2002i) q^{77} +(84.6709 + 30.8177i) q^{79} +(24.2155 + 48.3268i) q^{80} +73.9440i q^{82} +(49.9577 + 18.1831i) q^{83} +(12.0943 - 50.8231i) q^{85} +(43.7744 + 7.71861i) q^{86} +(-23.3879 - 27.8727i) q^{88} +(20.0986 - 11.6039i) q^{89} +(-84.4321 + 146.241i) q^{91} +(20.8600 + 118.303i) q^{92} +(121.994 - 44.4022i) q^{94} +(-55.6580 - 52.6066i) q^{95} +(17.5234 - 3.08985i) q^{97} +(-136.347 + 236.160i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) \) 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

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