LMFDB - Embedded newform 405.3.n.a.179.6

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			179.6
Character	$\chi$	$=$	405.179
Dual form			405.3.n.a.224.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.82399 - 1.02785i) q^{2} +(3.85425 + 3.23410i) q^{4} +(-4.01334 - 2.98213i) q^{5} +(-7.59850 - 9.05554i) q^{7} +(-1.54973 - 2.68422i) q^{8} +(8.26843 + 12.5466i) q^{10} +(-11.5608 + 2.03849i) q^{11} +(-4.88572 - 13.4234i) q^{13} +(12.1503 + 33.3828i) q^{14} +(-1.87729 - 10.6466i) q^{16} +(5.22423 - 9.04864i) q^{17} +(7.65850 + 13.2649i) q^{19} +(-5.82387 - 24.4734i) q^{20} +(34.7429 + 6.12611i) q^{22} +(-18.2900 - 15.3471i) q^{23} +(7.21374 + 23.9366i) q^{25} +42.9293i q^{26} -59.4766i q^{28} +(6.33581 - 17.4075i) q^{29} +(-22.3385 - 18.7442i) q^{31} +(-7.79453 + 44.2050i) q^{32} +(-24.0538 + 20.1835i) q^{34} +(3.49050 + 59.0027i) q^{35} +(-3.15030 - 1.81883i) q^{37} +(-7.99320 - 45.3317i) q^{38} +(-1.78509 + 15.3942i) q^{40} +(8.41546 + 23.1213i) q^{41} +(-14.5661 + 2.56840i) q^{43} +(-51.1509 - 29.5320i) q^{44} +(35.8762 + 62.1393i) q^{46} +(-33.0925 + 27.7679i) q^{47} +(-15.7569 + 89.3615i) q^{49} +(4.23167 - 75.0113i) q^{50} +(24.5818 - 67.5380i) q^{52} +84.2928 q^{53} +(52.4766 + 26.2948i) q^{55} +(-12.5314 + 34.4297i) q^{56} +(-35.7844 + 42.6462i) q^{58} +(80.2108 + 14.1433i) q^{59} +(51.0771 - 42.8588i) q^{61} +(43.8174 + 75.8940i) q^{62} +(45.8258 - 79.3727i) q^{64} +(-20.4224 + 68.4425i) q^{65} +(38.8900 + 106.849i) q^{67} +(49.3996 - 17.9800i) q^{68} +(50.7886 - 170.210i) q^{70} +(-5.55345 - 3.20629i) q^{71} +(-64.9541 + 37.5013i) q^{73} +(7.02693 + 8.37437i) q^{74} +(-13.3823 + 75.8946i) q^{76} +(106.305 + 89.2002i) q^{77} +(84.6709 + 30.8177i) q^{79} +(-24.2155 + 48.3268i) q^{80} -73.9440i q^{82} +(-49.9577 - 18.1831i) q^{83} +(-47.9509 + 20.7359i) q^{85} +(43.7744 + 7.71861i) q^{86} +(23.3879 + 27.8727i) q^{88} +(20.0986 - 11.6039i) q^{89} +(-84.4321 + 146.241i) q^{91} +(-20.8600 - 118.303i) q^{92} +(121.994 - 44.4022i) q^{94} +(8.82162 - 76.0753i) q^{95} +(-17.5234 + 3.08985i) q^{97} +(136.347 - 236.160i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.480279	−	0.877116i	$-0.659464\pi$
$2$	−2.82399	−	1.02785i	−1.41199	−	0.513923i	−0.931714	+	0.363193i	$0.881687\pi$
$3$		0			0
$3$		0			0
$4$	3.85425	+	3.23410i	0.963561	+	0.808524i
$5$	−4.01334	−	2.98213i	−0.802667	−	0.596427i
$5$	−4.01334	−	2.98213i	−0.802667	−	0.596427i
$6$		0			0
$7$	−7.59850	−	9.05554i	−1.08550	−	1.29365i	−0.953167	−	0.302444i	$-0.902198\pi$
$7$	−7.59850	−	9.05554i	−1.08550	−	1.29365i	−0.132333	−	0.991205i	$-0.542247\pi$
$8$	−1.54973	−	2.68422i	−0.193717	−	0.335527i
$9$		0			0
$10$	8.26843	+	12.5466i	0.826843	+	1.25466i
$11$	−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	$-0.925960\pi$
$13$	−4.88572	−	13.4234i	−0.375825	−	1.03257i	0.597245	−	0.802059i	$-0.296262\pi$
$14$	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	−0.670465	−	0.741941i	$-0.733905\pi$
$17$	5.22423	−	9.04864i	0.307308	−	0.532273i	0.977772	+	0.209669i	$0.0672386\pi$
$18$		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	$0.701273\pi$
$20$	−5.82387	−	24.4734i	−0.291194	−	1.22367i
$21$		0			0
$22$	34.7429	+	6.12611i	1.57922	+	0.278459i
$23$	−18.2900	−	15.3471i	−0.795217	−	0.667266i	0.151814	−	0.988409i	$-0.451488\pi$
$23$	−18.2900	−	15.3471i	−0.795217	−	0.667266i	−0.947031	+	0.321143i	$0.895933\pi$
$24$		0			0
$25$	7.21374	+	23.9366i	0.288550	+	0.957465i
$26$			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
$35$	3.49050	+	59.0027i	0.0997286	+	1.68579i
$36$		0			0
$37$	−3.15030	−	1.81883i	−0.0851433	−	0.0491575i	0.456824	−	0.889557i	$-0.348987\pi$
$37$	−3.15030	−	1.81883i	−0.0851433	−	0.0491575i	−0.541967	+	0.840400i	$0.682320\pi$
$38$	−7.99320	−	45.3317i	−0.210347	−	1.19294i
$39$		0			0
$40$	−1.78509	+	15.3942i	−0.0446274	+	0.384854i
$41$	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	−0.340434	−	0.940268i	$-0.610574\pi$
$43$	−14.5661	+	2.56840i	−0.338747	+	0.0597302i	0.00168729	+	0.999999i	$0.499463\pi$
$44$	−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	−0.922936	−	0.384954i	$-0.874217\pi$
$47$	−33.0925	+	27.7679i	−0.704097	+	0.590807i	0.218839	+	0.975761i	$0.429773\pi$
$48$		0			0
$49$	−15.7569	+	89.3615i	−0.321568	+	1.82371i
$50$	4.23167	−	75.0113i	0.0846333	−	1.50023i
$51$		0			0
$52$	24.5818	−	67.5380i	0.472727	−	1.29881i
$53$	84.2928			1.59043			0.795215	−	0.606327i	$-0.207358\pi$
$53$	84.2928			1.59043			0.795215	+	0.606327i	$0.207358\pi$
$54$		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
$65$	−20.4224	+	68.4425i	−0.314190	+	1.05296i
$66$		0			0
$67$	38.8900	+	106.849i	0.580447	+	1.59477i	0.787419	+	0.616418i	$0.211417\pi$
$67$	38.8900	+	106.849i	0.580447	+	1.59477i	−0.206972	+	0.978347i	$0.566361\pi$
$68$	49.3996	−	17.9800i	0.726465	−	0.264412i
$69$		0			0
$70$	50.7886	−	170.210i	0.725551	−	2.43158i
$71$	−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	−0.873871	−	0.486157i	$-0.838398\pi$
$73$	−64.9541	+	37.5013i	−0.889782	+	0.513716i	−0.0159111	+	0.999873i	$0.505065\pi$
$74$	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	0.0230554	−	0.999734i	$-0.492661\pi$
$83$	−49.9577	−	18.1831i	−0.601900	−	0.219074i	−0.624955	+	0.780661i	$0.714883\pi$
$84$		0			0
$85$	−47.9509	+	20.7359i	−0.564128	+	0.243951i
$86$	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
$95$	8.82162	−	76.0753i	0.0928591	−	0.800792i
$96$		0			0
$97$	−17.5234	+	3.08985i	−0.180654	+	0.0318542i	−0.263243	−	0.964730i	$-0.584792\pi$
$97$	−17.5234	+	3.08985i	−0.180654	+	0.0318542i	0.0825892	+	0.996584i	$0.473681\pi$
$98$	136.347	−	236.160i	1.39130	−	2.40980i
$99$		0			0
$100$	−49.6098	+	115.588i	−0.496098	+	1.15588i
$101$	−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	0.215475	−	0.976509i	$-0.430870\pi$
$103$	8.64884	+	1.52502i	0.0839694	+	0.0148061i	−0.131506	+	0.991315i	$0.541981\pi$
$104$	−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	$-0.954911\pi$
$107$	−211.857			−1.97997			−0.989984	+	0.141177i	$0.954911\pi$
$108$		0			0
$109$	−100.928			−0.925947			−0.462973	−	0.886372i	$-0.653217\pi$
$109$	−100.928			−0.925947			−0.462973	+	0.886372i	$0.653217\pi$
$110$	−121.166	−	128.194i	−1.10151	−	1.16540i
$111$		0			0
$112$	−82.1463	+	97.8982i	−0.733449	+	0.874091i
$113$	2.67270	−	15.1576i	0.0236522	−	0.134138i	−0.970695	−	0.240314i	$-0.922750\pi$
$113$	2.67270	−	15.1576i	0.0236522	−	0.134138i	0.994347	+	0.106176i	$0.0338606\pi$
$114$		0			0
$115$	27.6367	+	116.136i	0.240319	+	1.00988i
$116$	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
$125$	42.4310	−	117.578i	0.339448	−	0.940625i
$126$		0			0
$127$	179.281	−	103.508i	1.41166	−	0.815023i	0.416116	−	0.909312i	$-0.363391\pi$
$127$	179.281	−	103.508i	1.41166	−	0.815023i	0.995545	+	0.0942888i	$0.0300577\pi$
$128$	−73.4529	+	61.6343i	−0.573851	+	0.481518i
$129$		0			0
$130$	128.021	−	172.290i	0.984776	−	1.32531i
$131$	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	0.233594	−	0.972334i	$-0.424951\pi$
$137$	−29.1079	−	10.5944i	−0.212467	−	0.0773315i	−0.446061	+	0.895003i	$0.647174\pi$
$138$		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	$0.929270\pi$
$140$	−177.367	+	238.699i	−1.26691	+	1.70500i
$141$		0			0
$142$	12.3873	+	14.7626i	0.0872344	+	0.103962i
$143$	83.8465	+	145.226i	0.586339	+	1.01557i
$144$		0			0
$145$	−77.3392	+	50.9679i	−0.533374	+	0.351503i
$146$	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
$155$	33.7541	+	141.843i	0.217769	+	0.915118i
$156$		0			0
$157$	−150.983	−	26.6225i	−0.961678	−	0.169570i	−0.329296	−	0.944227i	$-0.606812\pi$
$157$	−150.983	−	26.6225i	−0.961678	−	0.169570i	−0.632382	+	0.774657i	$0.717923\pi$
$158$	−207.434	−	174.057i	−1.31287	−	1.10163i
$159$		0			0
$160$	163.107	−	154.165i	1.01942	−	0.963532i
$161$			282.241i			1.75305i
$162$		0			0
$163$		−	37.9711i		−	0.232951i	−0.993194	−	0.116476i	$-0.962840\pi$
$163$		−	37.9711i		−	0.232951i	0.993194	−	0.116476i	$-0.0371597\pi$
$164$	−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	−0.961003	−	0.276539i	$-0.910813\pi$
$167$	6.11658	−	34.6889i	0.0366263	−	0.207718i	0.997629	+	0.0688209i	$0.0219237\pi$
$168$		0			0
$169$	−26.8561	+	22.5350i	−0.158912	+	0.133343i
$170$	156.726	−	9.27163i	0.921916	−	0.0545390i
$171$		0			0
$172$	−64.4478	−	37.2090i	−0.374697	−	0.216331i
$173$	−6.67558	−	37.8591i	−0.0385872	−	0.218839i	0.959417	−	0.281992i	$-0.0909953\pi$
$173$	−6.67558	−	37.8591i	−0.0385872	−	0.218839i	−0.998004	+	0.0631536i	$0.979884\pi$
$174$		0			0
$175$	161.945	−	247.207i	0.925403	−	1.41261i
$176$	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
$185$	7.21923	+	16.6942i	0.0390229	+	0.0902389i
$186$		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	−0.286481	−	0.958086i	$-0.592486\pi$
$193$	136.412	−	162.569i	0.706796	−	0.842327i	0.993277	+	0.115759i	$0.0369300\pi$
$194$	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	0.874767	−	0.484545i	$-0.161015\pi$
$197$	3.49781	+	6.05838i	0.0177554	+	0.0307532i	−0.857011	+	0.515298i	$0.827681\pi$
$198$		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	$0.0804879\pi$
$200$	53.0717	−	56.4586i	0.265358	−	0.282293i
$201$		0			0
$202$	65.5311	+	180.045i	0.324411	+	0.891313i
$203$	−205.777	+	74.8967i	−1.01368	+	0.368949i
$204$		0			0
$205$	35.1767	−	117.890i	0.171594	−	0.575071i
$206$	−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
$220$	117.218	+	271.061i	0.532807	+	1.23210i
$221$	−146.988	−	25.9179i	−0.665103	−	0.117276i
$222$		0			0
$223$	50.8002	+	60.5414i	0.227804	+	0.271486i	0.867824	−	0.496872i	$-0.165518\pi$
$223$	50.8002	+	60.5414i	0.227804	+	0.271486i	−0.640020	+	0.768358i	$0.721074\pi$
$224$	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	0.963694	−	0.267009i	$-0.0860352\pi$
$227$	−7.53741	−	42.7468i	−0.0332045	−	0.188312i	−0.996899	+	0.0786968i	$0.974924\pi$
$228$		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	$0.637309\pi$
$230$	41.3247	−	356.374i	0.179673	−	1.54945i
$231$		0			0
$232$	−56.5443	+	9.97028i	−0.243725	+	0.0429753i
$233$	82.0547	−	142.123i	0.352166	−	0.609970i	−0.634463	−	0.772954i	$-0.718779\pi$
$233$	82.0547	−	142.123i	0.352166	−	0.609970i	0.986629	+	0.162984i	$0.0521119\pi$
$234$		0			0
$235$	215.619	−	12.7557i	0.917529	−	0.0542795i
$236$	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
$245$	329.726	−	311.649i	1.34582	−	1.27204i
$246$		0			0
$247$	140.643	−	167.612i	0.569405	−	0.678591i
$248$	−15.6949	+	89.0099i	−0.0632857	+	0.358911i
$249$		0			0
$250$	−240.677	+	288.426i	−0.962707	+	1.15370i
$251$	−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	−0.542253	−	0.840216i	$-0.682428\pi$
$257$	−107.313	+	39.0589i	−0.417562	+	0.151980i	0.124691	+	0.992196i	$0.460206\pi$
$258$		0			0
$259$	7.46711	+	42.3481i	0.0288305	+	0.163506i
$260$	−300.063	+	197.746i	−1.15409	+	0.760563i
$261$		0			0
$262$	−211.537	+	122.131i	−0.807393	+	0.466149i
$263$	−213.136	+	178.843i	−0.810405	+	0.680010i	−0.950704	−	0.310099i	$-0.899638\pi$
$263$	−213.136	+	178.843i	−0.810405	+	0.680010i	0.140300	+	0.990109i	$0.455193\pi$
$264$		0			0
$265$	−338.296	−	251.373i	−1.27659	−	0.948576i
$266$	−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
$275$	−132.191	−	262.022i	−0.480696	−	0.952808i
$276$		0			0
$277$	−15.0444	−	17.9292i	−0.0543120	−	0.0647265i	0.738205	−	0.674577i	$-0.235674\pi$
$277$	−15.0444	−	17.9292i	−0.0543120	−	0.0647265i	−0.792517	+	0.609850i	$0.791229\pi$
$278$	252.955	+	438.131i	0.909910	+	1.57601i
$279$		0			0
$280$	152.967	−	100.808i	0.546309	−	0.360027i
$281$	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	0.906931	−	0.421279i	$-0.138419\pi$
$283$	−16.5869	−	45.5722i	−0.0586110	−	0.161032i	−0.965542	+	0.260246i	$0.916196\pi$
$284$	−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
$290$	270.792	−	64.4397i	0.933765	−	0.222206i
$291$		0			0
$292$	−371.632	−	65.5287i	−1.27271	−	0.224413i
$293$	94.0109	+	78.8845i	0.320856	+	0.269230i	0.788962	−	0.614442i	$-0.210619\pi$
$293$	94.0109	+	78.8845i	0.320856	+	0.269230i	−0.468106	+	0.883673i	$0.655063\pi$
$294$		0			0
$295$	−279.735	−	295.961i	−0.948256	−	1.00326i
$296$			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
$305$	−332.801	+	19.6879i	−1.09115	+	0.0645506i
$306$		0			0
$307$	255.991	+	147.796i	0.833847	+	0.481422i	0.855168	−	0.518351i	$-0.173454\pi$
$307$	255.991	+	147.796i	0.833847	+	0.481422i	−0.0213210	+	0.999773i	$0.506787\pi$
$308$	121.242	+	687.599i	0.393643	+	2.23246i
$309$		0			0
$310$	50.4721	−	435.258i	0.162813	−	1.40406i
$311$	−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	−0.221837	−	0.975084i	$-0.571205\pi$
$313$	−30.2976	+	5.34228i	−0.0967974	+	0.0170680i	0.125040	+	0.992152i	$0.460094\pi$
$314$	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	−0.999233	−	0.0391564i	$-0.987533\pi$
$317$	−359.537	+	301.687i	−1.13419	+	0.951696i	−0.134953	+	0.990852i	$0.543088\pi$
$318$		0			0
$319$	−37.7623	+	214.160i	−0.118377	+	0.671349i
$320$	−420.614	+	181.890i	−1.31442	+	0.568408i
$321$		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
$335$	162.560	−	544.797i	0.485255	−	1.62626i
$336$		0			0
$337$	79.0320	+	217.139i	0.234516	+	0.644328i	1.00000		0.000872393i	$0.000277691\pi$
$337$	79.0320	+	217.139i	0.234516	+	0.644328i	−0.765483	+	0.643456i	$0.777500\pi$
$338$	99.0039	−	36.0345i	0.292911	−	0.106611i
$339$		0			0
$340$	−251.876	−	75.1566i	−0.740812	−	0.221049i
$341$	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	0.935581	−	0.353113i	$-0.114877\pi$
$347$	260.352	+	218.461i	0.750293	+	0.629571i	−0.185287	+	0.982684i	$0.559321\pi$
$348$		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	0.161749	−	0.986832i	$-0.448287\pi$
$353$	−123.080	−	44.7973i	−0.348667	−	0.126905i	−0.510416	+	0.859927i	$0.670509\pi$
$354$		0			0
$355$	12.7263	+	29.4290i	0.0358487	+	0.0828987i
$356$	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
$365$	372.517	+	43.1967i	1.02059	+	0.118347i
$366$		0			0
$367$	−344.630	+	60.7675i	−0.939046	+	0.165579i	−0.622165	−	0.782886i	$-0.713747\pi$
$367$	−344.630	+	60.7675i	−0.939046	+	0.165579i	−0.316881	+	0.948465i	$0.602636\pi$
$368$	−129.059	+	223.537i	−0.350705	+	0.607438i
$369$		0			0
$370$	−3.22794	−	54.5644i	−0.00872416	−	0.147471i
$371$	−640.499	−	763.317i	−1.72641	−	2.05746i
$372$		0			0
$373$	336.395	+	59.3155i	0.901863	+	0.159023i	0.605306	−	0.795993i	$-0.293051\pi$
$373$	336.395	+	59.3155i	0.901863	+	0.159023i	0.296556	+	0.955015i	$0.404162\pi$
$374$	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	$0.708846\pi$
$380$	280.035	−	264.683i	0.736935	−	0.696534i
$381$		0			0
$382$	570.182	−	679.517i	1.49262	−	1.77884i
$383$	27.6776	−	156.967i	0.0722652	−	0.409837i	−0.927120	−	0.374766i	$-0.877723\pi$
$383$	27.6776	−	156.967i	0.0722652	−	0.409837i	0.999385	−	0.0350709i	$-0.0111657\pi$
$384$		0			0
$385$	−160.629	−	675.005i	−0.417219	−	1.75326i
$386$	−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
$395$	−247.910	−	376.182i	−0.627621	−	0.952359i
$396$		0			0
$397$	−351.860	+	203.147i	−0.886297	+	0.511704i	−0.872730	−	0.488204i	$-0.837652\pi$
$397$	−351.860	+	203.147i	−0.886297	+	0.511704i	−0.0135678	+	0.999908i	$0.504319\pi$
$398$	−245.045	+	205.617i	−0.615690	+	0.516625i
$399$		0			0
$400$	241.302	−	121.738i	0.603254	−	0.304345i
$401$	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	$0.797358\pi$
$410$	−220.511	+	296.762i	−0.537832	+	0.723810i
$411$		0			0
$412$	28.4027	+	33.8490i	0.0689386	+	0.0821578i
$413$	−481.406	−	833.820i	−1.16563	−	2.01893i
$414$		0			0
$415$	146.273	+	221.955i	0.352464	+	0.534833i
$416$	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
$425$	254.280	+	59.7759i	0.598306	+	0.140649i
$426$		0			0
$427$	−776.220	−	136.868i	−1.81784	−	0.320535i
$428$	−816.548	−	685.165i	−1.90782	−	1.60085i
$429$		0			0
$430$	−152.664	−	161.519i	−0.355031	−	0.375625i
$431$			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	$-0.845613\pi$
$433$		−	403.752i		−	0.932453i	0.884665	−	0.466226i	$-0.154387\pi$
$434$	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	$0.176544\pi$
$440$	−10.7436	−	181.608i	−0.0244174	−	0.412746i
$441$		0			0
$442$	388.451	+	224.273i	0.878849	+	0.507404i
$443$	144.009	+	816.715i	0.325076	+	1.84360i	0.509138	+	0.860685i	$0.329964\pi$
$443$	144.009	+	816.715i	0.325076	+	1.84360i	−0.184062	+	0.982915i	$0.558925\pi$
$444$		0			0
$445$	−115.267	−	13.3662i	−0.259027	−	0.0300365i
$446$	−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
$455$	774.964	−	335.125i	1.70322	−	0.736539i
$456$		0			0
$457$	−191.174	+	525.245i	−0.418323	+	1.14933i	0.534330	+	0.845276i	$0.320564\pi$
$457$	−191.174	+	525.245i	−0.418323	+	1.14933i	−0.952654	+	0.304058i	$0.901658\pi$
$458$	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	−0.995118	−	0.0986910i	$-0.968534\pi$
$463$	−335.733	+	400.111i	−0.725126	+	0.864172i	0.269992	+	0.962863i	$0.412979\pi$
$464$	−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	$0.0275163\pi$
$467$	267.546	+	463.403i	0.572903	+	0.992297i	−0.423363	+	0.905960i	$0.639150\pi$
$468$		0			0
$469$	672.073	−	1164.06i	1.43299	−	2.48201i
$470$	−622.016	−	185.602i	−1.32344	−	0.394897i
$471$		0			0
$472$	−86.3415	−	237.221i	−0.182927	−	0.502588i
$473$	163.161	−	59.3857i	0.344949	−	0.125551i
$474$		0			0
$475$	−262.271	+	279.008i	−0.552149	+	0.587386i
$476$	−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	$0.227834\pi$
$487$			639.130i			1.31238i	−0.754595	+	0.656191i	$0.772166\pi$
$488$	−194.198	−	70.6824i	−0.397947	−	0.144841i
$489$		0			0
$490$	−1251.47	+	541.184i	−2.55402	+	1.10446i
$491$	−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	$0.499328\pi$
$500$	543.798	−	315.949i	1.08760	−	0.631897i
$501$		0			0
$502$	40.7690	−	7.18868i	0.0812132	−	0.0143201i
$503$	−215.970	+	374.071i	−0.429364	+	0.743680i	−0.996817	−	0.0797255i	$-0.974596\pi$
$503$	−215.970	+	374.071i	−0.429364	+	0.743680i	0.567453	+	0.823406i	$0.307929\pi$
$504$		0			0
$505$	18.8255	+	318.222i	0.0372782	+	0.630143i
$506$	−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
$515$	−30.1629	−	31.9125i	−0.0585687	−	0.0619659i
$516$		0			0
$517$	325.973	−	388.479i	0.630508	−	0.751410i
$518$	22.4403	−	127.265i	0.0433211	−	0.245686i
$519$		0			0
$520$	215.364	−	51.2496i	0.414161	−	0.0985569i
$521$	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	0.283898	−	0.958855i	$-0.408372\pi$
$523$	−211.577	−	122.154i	−0.404546	−	0.233564i	−0.688443	+	0.725290i	$0.741706\pi$
$524$	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
$530$	696.969	+	1057.59i	1.31504	+	1.99545i
$531$		0			0
$532$	788.952	−	455.502i	1.48299	−	0.856206i
$533$	269.251	−	225.928i	0.505161	−	0.423881i
$534$		0			0
$535$	850.252	+	631.785i	1.58926	+	1.18091i
$536$	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
$545$	405.059	+	300.982i	0.743227	+	0.552260i
$546$		0			0
$547$	657.900	+	784.054i	1.20274	+	1.43337i	0.871899	+	0.489686i	$0.162888\pi$
$547$	657.900	+	784.054i	1.20274	+	1.43337i	0.330843	+	0.943686i	$0.392667\pi$
$548$	−77.9257	−	134.971i	−0.142200	−	0.246298i
$549$		0			0
$550$	103.988	+	875.819i	0.189069	+	1.59240i
$551$	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	$0.404011\pi$
$557$	−377.892	+	654.528i	−0.678442	+	1.17510i	−0.975450	+	0.220221i	$0.929322\pi$
$558$		0			0
$559$	105.643	+	182.978i	0.188985	+	0.327332i
$560$	621.626	−	147.927i	1.11005	−	0.264155i
$561$		0			0
$562$	−1060.93	−	187.070i	−1.88777	−	0.332866i
$563$	281.344	+	236.076i	0.499723	+	0.419317i	0.857495	−	0.514491i	$-0.172019\pi$
$563$	281.344	+	236.076i	0.499723	+	0.419317i	−0.357773	+	0.933809i	$0.616464\pi$
$564$		0			0
$565$	−55.9286	+	52.8623i	−0.0989886	+	0.0935617i
$566$			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
$575$	235.419	−	548.511i	0.409424	−	0.953931i
$576$		0			0
$577$	−396.854	−	229.124i	−0.687789	−	0.397095i	0.114994	−	0.993366i	$-0.463315\pi$
$577$	−396.854	−	229.124i	−0.687789	−	0.397095i	−0.802783	+	0.596271i	$0.796648\pi$
$578$	−93.8443	−	532.218i	−0.162360	−	0.920792i
$579$		0			0
$580$	−462.919	−	53.6797i	−0.798137	−	0.0925512i
$581$	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	−0.906968	−	0.421200i	$-0.861609\pi$
$587$	−381.350	+	319.991i	−0.649660	+	0.545129i	0.257308	+	0.966329i	$0.417165\pi$
$588$		0			0
$589$	77.5612	−	439.871i	0.131683	−	0.746810i
$590$	485.766	+	1123.32i	0.823332	+	1.90392i
$591$		0			0
$592$	−13.4503	+	36.9545i	−0.0227202	+	0.0624232i
$593$	379.139			0.639357			0.319679	−	0.947526i	$-0.396425\pi$
$593$	379.139			0.639357			0.319679	+	0.947526i	$0.396425\pi$
$594$		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
$605$	−80.5327	−	24.0299i	−0.133112	−	0.0397189i
$606$		0			0
$607$	−130.172	−	357.645i	−0.214451	−	0.589200i	0.785093	−	0.619378i	$-0.212615\pi$
$607$	−130.172	−	357.645i	−0.214451	−	0.589200i	−0.999545	+	0.0301773i	$0.990393\pi$
$608$	−646.070	+	235.150i	−1.06261	+	0.386760i
$609$		0			0
$610$	960.060	+	286.469i	1.57387	+	0.469622i
$611$	534.421	+	308.548i	0.874667	+	0.504989i
$612$		0			0
$613$	210.200	−	121.359i	0.342903	−	0.197975i	−0.318652	−	0.947872i	$-0.603230\pi$
$613$	210.200	−	121.359i	0.342903	−	0.197975i	0.661555	+	0.749896i	$0.269897\pi$
$614$	−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	0.755467	−	0.655187i	$-0.227410\pi$
$617$	148.955	+	124.988i	0.241419	+	0.202574i	−0.514048	+	0.857761i	$0.671855\pi$
$618$		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
$625$	−520.924	+	345.345i	−0.833478	+	0.552553i
$626$	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
$635$	−1028.19	−	119.228i	−1.61920	−	0.187760i
$636$		0			0
$637$	1276.52	−	225.085i	2.00396	−	0.353352i
$638$	326.764	−	565.972i	0.512170	−	0.887104i
$639$		0			0
$640$	478.593	−	28.3128i	0.747802	−	0.0442387i
$641$	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	0.149983	−	0.988689i	$-0.452078\pi$
$643$	−30.3696	−	5.35498i	−0.0472311	−	0.00832812i	−0.197214	+	0.980361i	$0.563189\pi$
$644$	−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	$-0.402680\pi$
$647$	389.494			0.602000			0.301000	+	0.953624i	$0.402680\pi$
$648$		0			0
$649$	−956.134			−1.47324
$650$	−1027.58	+	309.681i	−1.58090	+	0.476432i
$651$		0			0
$652$	122.802	−	146.350i	0.188347	−	0.224463i
$653$	173.274	−	982.684i	0.265350	−	1.50488i	−0.502686	−	0.864469i	$-0.667655\pi$
$653$	173.274	−	982.684i	0.265350	−	1.50488i	0.768036	−	0.640407i	$-0.221234\pi$
$654$		0			0
$655$	−395.356	+	94.0819i	−0.603597	+	0.143636i
$656$	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
$665$	−755.934	+	498.174i	−1.13674	+	0.749133i
$666$		0			0
$667$	−383.036	+	221.146i	−0.574268	+	0.331554i
$668$	135.762	−	113.918i	0.203236	−	0.170536i
$669$		0			0
$670$	−1019.04	+	1371.41i	−1.52095	+	2.04688i
$671$	−503.127	+	599.604i	−0.749817	+	0.893597i
$672$		0			0
$673$	−117.908	+	323.950i	−0.175198	+	0.481352i	−0.995948	−	0.0899359i	$-0.971334\pi$
$673$	−117.908	+	323.950i	−0.175198	+	0.481352i	0.820750	+	0.571288i	$0.193556\pi$
$674$		−	694.429i		−	1.03031i
$675$		0			0
$676$	−176.390			−0.260933
$677$	−690.627	−	251.368i	−1.02013	−	0.371297i	−0.222815	−	0.974861i	$-0.571524\pi$
$677$	−690.627	−	251.368i	−1.02013	−	0.371297i	−0.797314	+	0.603564i	$0.793747\pi$
$678$		0			0
$679$	161.132	+	135.206i	0.237308	+	0.199125i
$680$	129.971	+	96.5754i	0.191133	+	0.142023i
$681$		0			0
$682$	−661.275	−	788.076i	−0.969611	−	1.15554i
$683$	−233.214	−	403.938i	−0.341455	−	0.591418i	0.643248	−	0.765658i	$-0.277586\pi$
$683$	−233.214	−	403.938i	−0.341455	−	0.591418i	−0.984703	+	0.174240i	$0.944253\pi$
$684$		0			0
$685$	85.2259	+	129.323i	0.124417	+	0.188792i
$686$	−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
$695$	194.860	+	818.852i	0.280375	+	1.17820i
$696$		0			0
$697$	253.181	+	44.6426i	0.363243	+	0.0640496i
$698$	−666.237	−	559.039i	−0.954494	−	0.800915i
$699$		0			0
$700$	1423.67	−	429.049i	2.03381	−	0.612927i
$701$		−	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	$0.896859\pi$
$710$	−5.69031	−	96.1878i	−0.00801452	−	0.135476i
$711$		0			0
$712$	−62.2949	−	35.9660i	−0.0874928	−	0.0505140i
$713$	120.901	+	685.663i	0.169567	+	0.961660i
$714$		0			0
$715$	96.5804	−	832.884i	0.135077	−	1.16487i
$716$	−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
$725$	462.381	+	26.0847i	0.637767	+	0.0359788i
$726$		0			0
$727$	248.711	−	683.327i	0.342105	−	0.939927i	−0.642678	−	0.766137i	$-0.722176\pi$
$727$	248.711	−	683.327i	0.342105	−	0.939927i	0.984783	−	0.173790i	$-0.0556013\pi$
$728$	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	−0.936170	−	0.351547i	$-0.885656\pi$
$733$	−313.284	+	373.357i	−0.427400	+	0.509355i	0.508770	+	0.860902i	$0.330100\pi$
$734$	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	$0.938561\pi$
$740$	−26.1659	+	87.6912i	−0.0353594	+	0.118502i
$741$		0			0
$742$	1024.19	+	2813.93i	1.38031	+	3.79236i
$743$	−46.3654	+	16.8756i	−0.0624030	+	0.0227128i	−0.373033	−	0.927818i	$-0.621682\pi$
$743$	−46.3654	+	16.8756i	−0.0624030	+	0.0227128i	0.310630	+	0.950531i	$0.399460\pi$
$744$		0			0
$745$	92.2380	−	309.122i	0.123809	−	0.414929i
$746$	−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	$-0.858015\pi$
$757$		−	653.161i		−	0.862828i	0.902154	−	0.431414i	$-0.141985\pi$
$758$	1305.84	+	475.286i	1.72274	+	0.627026i
$759$		0			0
$760$	−217.874	+	94.2172i	−0.286676	+	0.123970i
$761$	−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	$0.0887996\pi$
$770$	−240.187	+	2071.31i	−0.311931	+	2.69001i
$771$		0			0
$772$	1051.53	−	185.413i	1.36208	−	0.240172i
$773$	535.789	−	928.014i	0.693130	−	1.20054i	−0.277677	−	0.960674i	$-0.589565\pi$
$773$	535.789	−	928.014i	0.693130	−	1.20054i	0.970807	−	0.239862i	$-0.0771021\pi$
$774$		0			0
$775$	287.529	−	669.924i	0.371006	−	0.864419i
$776$	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
$785$	526.556	+	557.098i	0.670772	+	0.709679i
$786$		0			0
$787$	259.579	−	309.354i	0.329833	−	0.393080i	−0.575486	−	0.817812i	$-0.695187\pi$
$787$	259.579	−	309.354i	0.329833	−	0.393080i	0.905319	+	0.424732i	$0.139632\pi$
$788$	−6.11197	+	34.6627i	−0.00775631	+	0.0439882i
$789$		0			0
$790$	313.438	+	1317.15i	0.396757	+	1.66727i
$791$	−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	−0.482758	−	0.875754i	$-0.660365\pi$
$797$	−230.850	+	84.0224i	−0.289648	+	0.105423i	0.193110	+	0.981177i	$0.438143\pi$
$798$		0			0
$799$	78.3788	+	444.508i	0.0980962	+	0.556331i
$800$	−1114.35	+	132.309i	−1.39293	+	0.165386i
$801$		0			0
$802$	−1442.35	+	832.744i	−1.79845	+	1.03833i
$803$	674.478	−	565.954i	0.839947	−	0.704800i
$804$		0			0
$805$	841.680	−	1132.73i	1.04557	−	1.40711i
$806$	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
$815$	−113.235	+	152.391i	−0.138939	+	0.186983i
$816$		0			0
$817$	−145.624	−	173.548i	−0.178243	−	0.212421i
$818$	287.445	+	497.869i	0.351400	+	0.608642i
$819$		0			0
$820$	516.846	−	340.611i	0.630300	−	0.415379i
$821$	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	0.926799	−	0.375557i	$-0.122549\pi$
$823$	−20.2243	−	55.5657i	−0.0245738	−	0.0675160i	−0.951373	+	0.308041i	$0.900326\pi$
$824$	−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	−0.649591	−	0.760284i	$-0.725060\pi$
$827$	275.911	−	477.893i	0.333629	−	0.577863i	0.983221	+	0.182421i	$0.0583933\pi$
$828$		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	$0.585142\pi$
$830$	−184.935	−	777.145i	−0.222814	−	0.936319i
$831$		0			0
$832$	−1289.34	−	227.346i	−1.54969	−	0.273253i
$833$	726.283	+	609.423i	0.871888	+	0.731601i
$834$		0			0
$835$	−127.995	+	120.978i	−0.153287	+	0.144883i
$836$		−	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
$845$	174.985	−	10.3518i	0.207083	−	0.0122507i
$846$		0			0
$847$	−172.074	−	99.3468i	−0.203157	−	0.117293i
$848$	−158.242	−	897.433i	−0.186606	−	1.05829i
$849$		0			0
$850$	−656.643	−	430.167i	−0.772521	−	0.506079i
$851$	29.7052	+	81.6144i	0.0349062	+	0.0959041i
$852$		0			0
$853$	−538.725	+	94.9917i	−0.631565	+	0.111362i	−0.480261	−	0.877125i	$-0.659458\pi$
$853$	−538.725	+	94.9917i	−0.631565	+	0.111362i	−0.151303	+	0.988487i	$0.548347\pi$
$854$	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	$-0.423325\pi$
$857$	1059.56	−	889.075i	1.23636	−	1.03743i	0.997800	−	0.0662989i	$-0.0211191\pi$
$858$		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	$0.0697760\pi$
$860$	147.689	+	341.524i	0.171731	+	0.397121i
$861$		0			0
$862$	122.397	−	336.284i	0.141992	−	0.390121i
$863$	85.6487			0.0992453			0.0496226	−	0.998768i	$-0.484198\pi$
$863$	85.6487			0.0992453			0.0496226	+	0.998768i	$0.484198\pi$
$864$		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
$875$	−1387.15	+	509.181i	−1.58531	+	0.581921i
$876$		0			0
$877$	373.044	+	1024.93i	0.425363	+	1.16868i	0.948597	+	0.316487i	$0.102503\pi$
$877$	373.044	+	1024.93i	0.425363	+	1.16868i	−0.523234	+	0.852189i	$0.675275\pi$
$878$	−775.326	+	282.196i	−0.883059	+	0.321407i
$879$		0			0
$880$	181.437	−	608.061i	0.206179	−	0.690978i
$881$	−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	−0.346754	−	0.937956i	$-0.612716\pi$
$883$	257.980	−	148.945i	0.292163	−	0.168680i	0.638917	+	0.769276i	$0.279383\pi$
$884$	−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	0.997631	−	0.0687965i	$-0.0219159\pi$
$887$	978.464	+	821.029i	1.10312	+	0.925624i	0.105485	+	0.994421i	$0.466360\pi$
$888$		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
$895$	450.091	+	1040.82i	0.502896	+	1.16293i
$896$	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
$905$	−37.0089	+	319.155i	−0.0408939	+	0.352658i
$906$		0			0
$907$	−1520.14	+	268.041i	−1.67601	+	0.295525i	−0.929216	−	0.369536i	$-0.879517\pi$
$907$	−1520.14	+	268.041i	−1.67601	+	0.295525i	−0.746789	+	0.665061i	$0.768406\pi$
$908$	109.196	−	189.133i	0.120260	−	0.208297i
$909$		0			0
$910$	−2532.94	+	149.845i	−2.78345	+	0.164665i
$911$	−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	$0.544859\pi$
$920$	268.906	−	254.163i	0.292289	−	0.276264i
$921$		0			0
$922$	−330.882	+	394.329i	−0.358874	+	0.427689i
$923$	−15.9067	+	90.2112i	−0.0172337	+	0.0977370i
$924$		0			0
$925$	20.8111	−	88.5281i	0.0224985	−	0.0957061i
$926$	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
$935$	512.082	−	337.471i	0.547681	−	0.360932i
$936$		0			0
$937$	1193.28	−	688.938i	1.27351	−	0.735259i	0.297860	−	0.954610i	$-0.403727\pi$
$937$	1193.28	−	688.938i	1.27351	−	0.735259i	0.975646	+	0.219351i	$0.0703938\pi$
$938$	−3094.40	+	2596.51i	−3.29894	+	2.76814i
$939$		0			0
$940$	872.302	+	648.170i	0.927981	+	0.689542i
$941$	−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	0.408164	−	0.912909i	$-0.366169\pi$
$947$	126.925	+	46.1971i	0.134029	+	0.0487826i	−0.274135	+	0.961691i	$0.588391\pi$
$948$		0			0
$949$	820.743	+	688.685i	0.864850	+	0.725695i
$950$	1027.43	−	518.342i	1.08150	−	0.545623i
$951$		0			0
$952$	246.075	+	293.261i	0.258482	+	0.308047i
$953$	629.190	+	1089.79i	0.660220	+	1.14353i	0.980558	+	0.196231i	$0.0628704\pi$
$953$	629.190	+	1089.79i	0.660220	+	1.14353i	−0.320337	+	0.947303i	$0.603796\pi$
$954$		0			0
$955$	1232.31	−	812.112i	1.29037	−	0.850379i
$956$	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
$965$	−1032.27	+	245.647i	−1.06971	+	0.254556i
$966$		0			0
$967$	−599.358	−	105.683i	−0.619812	−	0.109290i	−0.145080	−	0.989420i	$-0.546344\pi$
$967$	−599.358	−	105.683i	−0.619812	−	0.109290i	−0.474732	+	0.880130i	$0.657455\pi$
$968$	−39.9084	−	33.4871i	−0.0412277	−	0.0345941i
$969$		0			0
$970$	−183.658	−	194.311i	−0.189339	−	0.200321i
$971$		−	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	$-0.810680\pi$
$977$	138.429	−	785.069i	0.141688	−	0.803551i	0.969967	−	0.243236i	$-0.0782088\pi$
$978$		0			0
$979$	−208.702	+	175.122i	−0.213179	+	0.178878i
$980$	2278.75	−	134.807i	2.32525	−	0.137558i
$981$		0			0
$982$	905.538	+	522.812i	0.922136	+	0.532396i
$983$	−81.4145	−	461.724i	−0.0828225	−	0.469710i	−0.997805	−	0.0662167i	$-0.978907\pi$
$983$	−81.4145	−	461.724i	−0.0828225	−	0.469710i	0.914983	−	0.403493i	$-0.132204\pi$
$984$		0			0
$985$	4.02903	−	34.7452i	0.00409038	−	0.0352744i
$986$	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
$995$	−488.493	+	211.244i	−0.490948	+	0.212305i
$996$		0			0
$997$	−248.507	+	682.768i	−0.249255	+	0.684822i	0.750459	+	0.660917i	$0.229832\pi$
$997$	−248.507	+	682.768i	−0.249255	+	0.684822i	−0.999714	+	0.0239057i	$0.992390\pi$
$998$	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.179.6		204
3.2	odd	2		135.3.n.a.104.29	yes	204
5.4	even	2	inner	405.3.n.a.179.29		204
15.14	odd	2		135.3.n.a.104.6	yes	204
27.7	even	9		135.3.n.a.74.6	✓	204
27.20	odd	18	inner	405.3.n.a.224.29		204
135.34	even	18		135.3.n.a.74.29	yes	204
135.74	odd	18	inner	405.3.n.a.224.6		204

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

\(f(q)\)	\(=\)	\(q+(-2.82399 - 1.02785i) q^{2} +(3.85425 + 3.23410i) q^{4} +(-4.01334 - 2.98213i) q^{5} +(-7.59850 - 9.05554i) q^{7} +(-1.54973 - 2.68422i) q^{8} +(8.26843 + 12.5466i) q^{10} +(-11.5608 + 2.03849i) q^{11} +(-4.88572 - 13.4234i) q^{13} +(12.1503 + 33.3828i) q^{14} +(-1.87729 - 10.6466i) q^{16} +(5.22423 - 9.04864i) q^{17} +(7.65850 + 13.2649i) q^{19} +(-5.82387 - 24.4734i) q^{20} +(34.7429 + 6.12611i) q^{22} +(-18.2900 - 15.3471i) q^{23} +(7.21374 + 23.9366i) q^{25} +42.9293i q^{26} -59.4766i q^{28} +(6.33581 - 17.4075i) q^{29} +(-22.3385 - 18.7442i) q^{31} +(-7.79453 + 44.2050i) q^{32} +(-24.0538 + 20.1835i) q^{34} +(3.49050 + 59.0027i) q^{35} +(-3.15030 - 1.81883i) q^{37} +(-7.99320 - 45.3317i) q^{38} +(-1.78509 + 15.3942i) q^{40} +(8.41546 + 23.1213i) q^{41} +(-14.5661 + 2.56840i) q^{43} +(-51.1509 - 29.5320i) q^{44} +(35.8762 + 62.1393i) q^{46} +(-33.0925 + 27.7679i) q^{47} +(-15.7569 + 89.3615i) q^{49} +(4.23167 - 75.0113i) q^{50} +(24.5818 - 67.5380i) q^{52} +84.2928 q^{53} +(52.4766 + 26.2948i) q^{55} +(-12.5314 + 34.4297i) q^{56} +(-35.7844 + 42.6462i) q^{58} +(80.2108 + 14.1433i) q^{59} +(51.0771 - 42.8588i) q^{61} +(43.8174 + 75.8940i) q^{62} +(45.8258 - 79.3727i) q^{64} +(-20.4224 + 68.4425i) q^{65} +(38.8900 + 106.849i) q^{67} +(49.3996 - 17.9800i) q^{68} +(50.7886 - 170.210i) q^{70} +(-5.55345 - 3.20629i) q^{71} +(-64.9541 + 37.5013i) q^{73} +(7.02693 + 8.37437i) q^{74} +(-13.3823 + 75.8946i) q^{76} +(106.305 + 89.2002i) q^{77} +(84.6709 + 30.8177i) q^{79} +(-24.2155 + 48.3268i) q^{80} -73.9440i q^{82} +(-49.9577 - 18.1831i) q^{83} +(-47.9509 + 20.7359i) q^{85} +(43.7744 + 7.71861i) q^{86} +(23.3879 + 27.8727i) q^{88} +(20.0986 - 11.6039i) q^{89} +(-84.4321 + 146.241i) q^{91} +(-20.8600 - 118.303i) q^{92} +(121.994 - 44.4022i) q^{94} +(8.82162 - 76.0753i) q^{95} +(-17.5234 + 3.08985i) q^{97} +(136.347 - 236.160i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) \) 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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