LMFDB - Embedded newform 27.5.d.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,5,Mod(8,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("27.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	27.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79098900326$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.39400128.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 $ x^6 - x^5 + 11x^4 + 14x^3 + 98x^2 + 20x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Root			$1.89154 - 3.27625i$ of defining polynomial
Character	$\chi$	$=$	27.17
Dual form			27.5.d.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.67463 - 3.27625i) q^{2} +(13.4676 - 23.3266i) q^{4} +(-10.2044 - 5.89150i) q^{5} +(26.6364 + 46.1356i) q^{7} -71.6534i q^{8} +O(q^{10})$	\(q+(5.67463 - 3.27625i) q^{2} +(13.4676 - 23.3266i) q^{4} +(-10.2044 - 5.89150i) q^{5} +(26.6364 + 46.1356i) q^{7} -71.6534i q^{8} -77.2081 q^{10} +(-108.228 + 62.4856i) q^{11} +(37.3052 - 64.6145i) q^{13} +(302.304 + 174.535i) q^{14} +(-19.2722 - 33.3805i) q^{16} +7.70989i q^{17} -54.1307 q^{19} +(-274.858 + 158.689i) q^{20} +(-409.437 + 709.166i) q^{22} +(-346.370 - 199.977i) q^{23} +(-243.080 - 421.028i) q^{25} -488.885i q^{26} +1434.92 q^{28} +(468.219 - 270.326i) q^{29} +(766.083 - 1326.89i) q^{31} +(774.133 + 446.946i) q^{32} +(25.2595 + 43.7508i) q^{34} -627.714i q^{35} -1719.10 q^{37} +(-307.172 + 177.346i) q^{38} +(-422.146 + 731.178i) q^{40} +(-1090.87 - 629.816i) q^{41} +(1303.89 + 2258.41i) q^{43} +3366.13i q^{44} -2620.70 q^{46} +(692.850 - 400.017i) q^{47} +(-218.498 + 378.449i) q^{49} +(-2758.78 - 1592.79i) q^{50} +(-1004.83 - 1740.41i) q^{52} +4229.81i q^{53} +1472.54 q^{55} +(3305.77 - 1908.59i) q^{56} +(1771.31 - 3068.01i) q^{58} +(2886.63 + 1666.60i) q^{59} +(7.50843 + 13.0050i) q^{61} -10039.5i q^{62} +6473.94 q^{64} +(-761.353 + 439.567i) q^{65} +(-2591.20 + 4488.08i) q^{67} +(179.846 + 103.834i) q^{68} +(-2056.55 - 3562.05i) q^{70} +1924.16i q^{71} +949.554 q^{73} +(-9755.28 + 5632.21i) q^{74} +(-729.012 + 1262.69i) q^{76} +(-5765.63 - 3328.79i) q^{77} +(118.990 + 206.097i) q^{79} +454.169i q^{80} -8253.75 q^{82} +(11402.0 - 6582.95i) q^{83} +(45.4228 - 78.6746i) q^{85} +(14798.2 + 8543.77i) q^{86} +(4477.31 + 7754.92i) q^{88} +575.925i q^{89} +3974.71 q^{91} +(-9329.58 + 5386.44i) q^{92} +(2621.11 - 4539.90i) q^{94} +(552.370 + 318.911i) q^{95} +(-7561.70 - 13097.3i) q^{97} +2863.41i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7	$ 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7} - 36 q^{10} - 483 q^{11} - 6 q^{13} + 1146 q^{14} + 15 q^{16} - 258 q^{19} - 1614 q^{20} - 369 q^{22} + 282 q^{23} - 273 q^{25} + 1308 q^{28} + 1056 q^{29} + 1290 q^{31} + 1161 q^{32} + 513 q^{34} + 12 q^{37} + 789 q^{38} - 1314 q^{40} - 7629 q^{41} - 285 q^{43} - 5760 q^{46} + 9642 q^{47} - 1863 q^{49} - 3027 q^{50} - 240 q^{52} + 2016 q^{55} + 462 q^{56} + 6462 q^{58} - 6225 q^{59} + 3630 q^{61} + 15450 q^{64} + 7158 q^{65} - 5055 q^{67} + 10503 q^{68} - 9684 q^{70} - 14622 q^{73} - 26454 q^{74} - 4047 q^{76} - 2580 q^{77} + 4764 q^{79} - 9702 q^{82} + 1866 q^{83} + 12366 q^{85} + 37731 q^{86} + 14787 q^{88} + 34836 q^{91} - 33636 q^{92} - 12708 q^{94} + 13362 q^{95} - 28959 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7 - 36 * q^10 - 483 * q^11 - 6 * q^13 + 1146 * q^14 + 15 * q^16 - 258 * q^19 - 1614 * q^20 - 369 * q^22 + 282 * q^23 - 273 * q^25 + 1308 * q^28 + 1056 * q^29 + 1290 * q^31 + 1161 * q^32 + 513 * q^34 + 12 * q^37 + 789 * q^38 - 1314 * q^40 - 7629 * q^41 - 285 * q^43 - 5760 * q^46 + 9642 * q^47 - 1863 * q^49 - 3027 * q^50 - 240 * q^52 + 2016 * q^55 + 462 * q^56 + 6462 * q^58 - 6225 * q^59 + 3630 * q^61 + 15450 * q^64 + 7158 * q^65 - 5055 * q^67 + 10503 * q^68 - 9684 * q^70 - 14622 * q^73 - 26454 * q^74 - 4047 * q^76 - 2580 * q^77 + 4764 * q^79 - 9702 * q^82 + 1866 * q^83 + 12366 * q^85 + 37731 * q^86 + 14787 * q^88 + 34836 * q^91 - 33636 * q^92 - 12708 * q^94 + 13362 * q^95 - 28959 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	5.67463	−	3.27625i	1.41866	−	0.819063i	0.422477	−	0.906374i	$-0.361161\pi$
$2$	5.67463	−	3.27625i	1.41866	−	0.819063i	0.996181	+	0.0873110i	$0.0278274\pi$
$3$		0			0
$3$		0			0
$4$	13.4676	−	23.3266i	0.841727	−	1.45791i
$5$	−10.2044	−	5.89150i	−0.408175	−	0.235660i	0.281830	−	0.959464i	$-0.409058\pi$
$5$	−10.2044	−	5.89150i	−0.408175	−	0.235660i	−0.690005	+	0.723804i	$0.742392\pi$
$6$		0			0
$7$	26.6364	+	46.1356i	0.543600	+	0.941544i	0.998694	+	0.0510997i	$0.0162726\pi$
$7$	26.6364	+	46.1356i	0.543600	+	0.941544i	−0.455093	+	0.890444i	$0.650394\pi$
$8$		−	71.6534i		−	1.11958i
$9$		0			0
$10$	−77.2081			−0.772081
$11$	−108.228	+	62.4856i	−0.894449	+	0.516410i	−0.875395	−	0.483408i	$-0.839399\pi$
$11$	−108.228	+	62.4856i	−0.894449	+	0.516410i	−0.0190536	+	0.999818i	$0.506065\pi$
$12$		0			0
$13$	37.3052	−	64.6145i	0.220741	−	0.382334i	−0.734292	−	0.678833i	$-0.762486\pi$
$13$	37.3052	−	64.6145i	0.220741	−	0.382334i	0.955033	+	0.296499i	$0.0958192\pi$
$14$	302.304	+	174.535i	1.54237	+	0.890486i
$15$		0			0
$16$	−19.2722	−	33.3805i	−0.0752822	−	0.130393i
$17$			7.70989i			0.0266778i	0.999911	+	0.0133389i	$0.00424603\pi$
$17$			7.70989i			0.0266778i	−0.999911	+	0.0133389i	$0.995754\pi$
$18$		0			0
$19$	−54.1307			−0.149946			−0.0749732	−	0.997186i	$-0.523887\pi$
$19$	−54.1307			−0.149946			−0.0749732	+	0.997186i	$0.523887\pi$
$20$	−274.858	+	158.689i	−0.687144	+	0.396723i
$21$		0			0
$22$	−409.437	+	709.166i	−0.845944	+	1.46522i
$23$	−346.370	−	199.977i	−0.654765	−	0.378029i	0.135515	−	0.990775i	$-0.456731\pi$
$23$	−346.370	−	199.977i	−0.654765	−	0.378029i	−0.790279	+	0.612747i	$0.790065\pi$
$24$		0			0
$25$	−243.080	−	421.028i	−0.388929	−	0.673644i
$26$		−	488.885i		−	0.723202i
$27$		0			0
$28$	1434.92			1.83025
$29$	468.219	−	270.326i	0.556741	−	0.321435i	−0.195095	−	0.980784i	$-0.562502\pi$
$29$	468.219	−	270.326i	0.556741	−	0.321435i	0.751836	+	0.659350i	$0.229168\pi$
$30$		0			0
$31$	766.083	−	1326.89i	0.797173	−	1.38074i	−0.124278	−	0.992247i	$-0.539661\pi$
$31$	766.083	−	1326.89i	0.797173	−	1.38074i	0.921450	−	0.388496i	$-0.127005\pi$
$32$	774.133	+	446.946i	0.755989	+	0.436470i
$33$		0			0
$34$	25.2595	+	43.7508i	0.0218508	+	0.0378467i
$35$		−	627.714i		−	0.512419i
$36$		0			0
$37$	−1719.10			−1.25574			−0.627868	−	0.778320i	$-0.716072\pi$
$37$	−1719.10			−1.25574			−0.627868	+	0.778320i	$0.716072\pi$
$38$	−307.172	+	177.346i	−0.212723	+	0.122816i
$39$		0			0
$40$	−422.146	+	731.178i	−0.263841	+	0.456986i
$41$	−1090.87	−	629.816i	−0.648944	−	0.374668i	0.139108	−	0.990277i	$-0.455577\pi$
$41$	−1090.87	−	629.816i	−0.648944	−	0.374668i	−0.788051	+	0.615610i	$0.788910\pi$
$42$		0			0
$43$	1303.89	+	2258.41i	0.705189	+	1.22142i	0.966623	+	0.256202i	$0.0824711\pi$
$43$	1303.89	+	2258.41i	0.705189	+	1.22142i	−0.261434	+	0.965221i	$0.584196\pi$
$44$			3366.13i			1.73871i
$45$		0			0
$46$	−2620.70			−1.23852
$47$	692.850	−	400.017i	0.313649	−	0.181085i	−0.334909	−	0.942250i	$-0.608706\pi$
$47$	692.850	−	400.017i	0.313649	−	0.181085i	0.648558	+	0.761165i	$0.275372\pi$
$48$		0			0
$49$	−218.498	+	378.449i	−0.0910029	+	0.157622i
$50$	−2758.78	−	1592.79i	−1.10351	−	0.637114i
$51$		0			0
$52$	−1004.83	−	1740.41i	−0.371607	−	0.643643i
$53$			4229.81i			1.50581i	0.658131	+	0.752904i	$0.271347\pi$
$53$			4229.81i			1.50581i	−0.658131	+	0.752904i	$0.728653\pi$
$54$		0			0
$55$	1472.54			0.486789
$56$	3305.77	−	1908.59i	1.05414	−	0.608606i
$57$		0			0
$58$	1771.31	−	3068.01i	0.526550	−	0.912011i
$59$	2886.63	+	1666.60i	0.829253	+	0.478769i	0.853597	−	0.520934i	$-0.174416\pi$
$59$	2886.63	+	1666.60i	0.829253	+	0.478769i	−0.0243441	+	0.999704i	$0.507750\pi$
$60$		0			0
$61$	7.50843	+	13.0050i	0.00201785	+	0.00349502i	0.867033	−	0.498251i	$-0.166024\pi$
$61$	7.50843	+	13.0050i	0.00201785	+	0.00349502i	−0.865015	+	0.501746i	$0.832691\pi$
$62$		−	10039.5i		−	2.61174i
$63$		0			0
$64$	6473.94			1.58055
$65$	−761.353	+	439.567i	−0.180202	+	0.104040i
$66$		0			0
$67$	−2591.20	+	4488.08i	−0.577233	+	0.999796i	0.418563	+	0.908188i	$0.362534\pi$
$67$	−2591.20	+	4488.08i	−0.577233	+	0.999796i	−0.995795	+	0.0916081i	$0.970799\pi$
$68$	179.846	+	103.834i	0.0388940	+	0.0224554i
$69$		0			0
$70$	−2056.55	−	3562.05i	−0.419704	−	0.726948i
$71$			1924.16i			0.381701i	0.981619	+	0.190851i	$0.0611246\pi$
$71$			1924.16i			0.381701i	−0.981619	+	0.190851i	$0.938875\pi$
$72$		0			0
$73$	949.554			0.178186			0.0890931	−	0.996023i	$-0.471603\pi$
$73$	949.554			0.178186			0.0890931	+	0.996023i	$0.471603\pi$
$74$	−9755.28	+	5632.21i	−1.78146	+	1.02853i
$75$		0			0
$76$	−729.012	+	1262.69i	−0.126214	+	0.218609i
$77$	−5765.63	−	3328.79i	−0.972445	−	0.561442i
$78$		0			0
$79$	118.990	+	206.097i	0.0190659	+	0.0330231i	0.875401	−	0.483398i	$-0.160597\pi$
$79$	118.990	+	206.097i	0.0190659	+	0.0330231i	−0.856335	+	0.516421i	$0.827264\pi$
$80$			454.169i			0.0709640i
$81$		0			0
$82$	−8253.75			−1.22751
$83$	11402.0	−	6582.95i	1.65510	−	0.955574i	0.680177	−	0.733048i	$-0.261903\pi$
$83$	11402.0	−	6582.95i	1.65510	−	0.955574i	0.974927	−	0.222526i	$-0.0714304\pi$
$84$		0			0
$85$	45.4228	−	78.6746i	0.00628689	−	0.0108892i
$86$	14798.2	+	8543.77i	2.00084	+	1.15519i
$87$		0			0
$88$	4477.31	+	7754.92i	0.578164	+	1.00141i
$89$			575.925i			0.0727086i	0.999339	+	0.0363543i	$0.0115745\pi$
$89$			575.925i			0.0727086i	−0.999339	+	0.0363543i	$0.988426\pi$
$90$		0			0
$91$	3974.71			0.479979
$92$	−9329.58	+	5386.44i	−1.10227	+	0.636394i
$93$		0			0
$94$	2621.11	−	4539.90i	0.296640	−	0.513796i
$95$	552.370	+	318.911i	0.0612044	+	0.0353364i
$96$		0			0
$97$	−7561.70	−	13097.3i	−0.803667	−	1.39199i	−0.917187	−	0.398456i	$-0.869546\pi$
$97$	−7561.70	−	13097.3i	−0.803667	−	1.39199i	0.113520	−	0.993536i	$-0.463787\pi$
$98$			2863.41i			0.298148i
$99$		0			0
$100$	−13094.9			−1.30949
$101$	−9578.90	+	5530.38i	−0.939016	+	0.542141i	−0.889652	−	0.456640i	$-0.849053\pi$
$101$	−9578.90	+	5530.38i	−0.939016	+	0.542141i	−0.0493643	+	0.998781i	$0.515720\pi$
$102$		0			0
$103$	1781.46	−	3085.58i	0.167920	−	0.290846i	−0.769769	−	0.638323i	$-0.779628\pi$
$103$	1781.46	−	3085.58i	0.167920	−	0.290846i	0.937688	+	0.347478i	$0.112962\pi$
$104$	−4629.85	−	2673.04i	−0.428055	−	0.247138i
$105$		0			0
$106$	13857.9	+	24002.6i	1.23335	+	2.13623i
$107$		−	11432.7i		−	0.998576i	−0.866436	−	0.499288i	$-0.833595\pi$
$107$		−	11432.7i		−	0.998576i	0.866436	−	0.499288i	$-0.166405\pi$
$108$		0			0
$109$	−4780.43			−0.402359			−0.201180	−	0.979554i	$-0.564478\pi$
$109$	−4780.43			−0.402359			−0.201180	+	0.979554i	$0.564478\pi$
$110$	8356.10	−	4824.40i	0.690587	−	0.398710i
$111$		0			0
$112$	1026.69	−	1778.27i	0.0818468	−	0.141763i
$113$	−3889.66	−	2245.69i	−0.304617	−	0.175871i	0.339898	−	0.940462i	$-0.389607\pi$
$113$	−3889.66	−	2245.69i	−0.304617	−	0.175871i	−0.644515	+	0.764592i	$0.722941\pi$
$114$		0			0
$115$	2356.33	+	4081.28i	0.178172	+	0.308604i
$116$		−	14562.6i		−	1.08224i
$117$		0			0
$118$	21840.7			1.56857
$119$	−355.701	+	205.364i	−0.0251183	+	0.0145021i
$120$		0			0
$121$	488.406	−	845.944i	0.0333588	−	0.0577791i
$122$	85.2151	+	49.1990i	0.00572528	+	0.00330549i
$123$		0			0
$124$	−20634.7	−	35740.3i	−1.34200	−	2.32442i
$125$			13092.8i			0.837940i
$126$		0			0
$127$	13521.3			0.838322			0.419161	−	0.907912i	$-0.362324\pi$
$127$	13521.3			0.838322			0.419161	+	0.907912i	$0.362324\pi$
$128$	24351.1	−	14059.1i	1.48627	−	0.858100i
$129$		0			0
$130$	−2880.26	+	4988.76i	−0.170430	+	0.295193i
$131$	−2941.86	−	1698.48i	−0.171427	−	0.0989735i	0.411831	−	0.911260i	$-0.364889\pi$
$131$	−2941.86	−	1698.48i	−0.171427	−	0.0989735i	−0.583259	+	0.812287i	$0.698223\pi$
$132$		0			0
$133$	−1441.85	−	2497.35i	−0.0815110	−	0.141181i
$134$			33957.6i			1.89116i
$135$		0			0
$136$	552.439			0.0298680
$137$	−3310.98	+	1911.60i	−0.176407	+	0.101849i	−0.585603	−	0.810598i	$-0.699142\pi$
$137$	−3310.98	+	1911.60i	−0.176407	+	0.101849i	0.409197	+	0.912446i	$0.365809\pi$
$138$		0			0
$139$	−1738.31	+	3010.85i	−0.0899702	+	0.155833i	−0.907498	−	0.420056i	$-0.862010\pi$
$139$	−1738.31	+	3010.85i	−0.0899702	+	0.155833i	0.817528	+	0.575889i	$0.195344\pi$
$140$	−14642.4	−	8453.82i	−0.747064	−	0.431317i
$141$		0			0
$142$	6304.02	+	10918.9i	0.312637	+	0.541504i
$143$			9324.16i			0.455971i
$144$		0			0
$145$	−6370.51			−0.302997
$146$	5388.37	−	3110.98i	0.252785	−	0.145946i
$147$		0			0
$148$	−23152.3	+	40100.9i	−1.05699	+	1.83076i
$149$	−7717.10	−	4455.47i	−0.347602	−	0.200688i	0.316027	−	0.948750i	$-0.397651\pi$
$149$	−7717.10	−	4455.47i	−0.347602	−	0.200688i	−0.663628	+	0.748062i	$0.730984\pi$
$150$		0			0
$151$	4957.66	+	8586.92i	0.217432	+	0.376603i	0.954022	−	0.299736i	$-0.0968987\pi$
$151$	4957.66	+	8586.92i	0.217432	+	0.376603i	−0.736590	+	0.676339i	$0.763565\pi$
$152$			3878.65i			0.167878i
$153$		0			0
$154$	−43623.8			−1.83942
$155$	−15634.8	+	9026.75i	−0.650772	+	0.375723i
$156$		0			0
$157$	−2823.47	+	4890.39i	−0.114547	+	0.198401i	−0.917599	−	0.397508i	$-0.869875\pi$
$157$	−2823.47	+	4890.39i	−0.114547	+	0.198401i	0.803052	+	0.595909i	$0.203208\pi$
$158$	1350.45	+	779.684i	0.0540960	+	0.0312323i
$159$		0			0
$160$	−5266.36	−	9121.60i	−0.205717	−	0.356313i
$161$		−	21306.7i		−	0.821986i
$162$		0			0
$163$	−2153.55			−0.0810552			−0.0405276	−	0.999178i	$-0.512904\pi$
$163$	−2153.55			−0.0810552			−0.0405276	+	0.999178i	$0.512904\pi$
$164$	−29383.0	+	16964.3i	−1.09247	+	0.630736i
$165$		0			0
$166$	43134.8	−	74711.7i	1.56535	−	2.71127i
$167$	32060.4	+	18510.1i	1.14957	+	0.663706i	0.948783	−	0.315929i	$-0.102316\pi$
$167$	32060.4	+	18510.1i	1.14957	+	0.663706i	0.200789	+	0.979635i	$0.435649\pi$
$168$		0			0
$169$	11497.1	+	19913.6i	0.402547	+	0.697232i
$170$		−	595.266i		−	0.0205974i
$171$		0			0
$172$	70241.5			2.37431
$173$	42076.2	−	24292.7i	1.40587	−	0.811678i	0.410882	−	0.911689i	$-0.365221\pi$
$173$	42076.2	−	24292.7i	1.40587	−	0.811678i	0.994986	+	0.100010i	$0.0318876\pi$
$174$		0			0
$175$	12949.6	−	22429.3i	0.422844	−	0.732387i
$176$	4171.60	+	2408.48i	0.134672	+	0.0777530i
$177$		0			0
$178$	1886.87	+	3268.16i	0.0595529	+	0.103149i
$179$		−	47717.9i		−	1.48928i	−0.667468	−	0.744639i	$-0.732622\pi$
$179$		−	47717.9i		−	1.48928i	0.667468	−	0.744639i	$-0.267378\pi$
$180$		0			0
$181$	−45767.2			−1.39700			−0.698502	−	0.715608i	$-0.746150\pi$
$181$	−45767.2			−1.39700			−0.698502	+	0.715608i	$0.746150\pi$
$182$	22555.0	−	13022.1i	0.680927	−	0.393133i
$183$		0			0
$184$	−14329.0	+	24818.6i	−0.423235	+	0.733064i
$185$	17542.4	+	10128.1i	0.512560	+	0.295927i
$186$		0			0
$187$	−481.757	−	834.428i	−0.0137767	−	0.0238619i
$188$		−	21549.1i		−	0.609697i
$189$		0			0
$190$	4179.33			0.115771
$191$	−40460.3	+	23359.7i	−1.10908	+	0.640326i	−0.938590	−	0.345034i	$-0.887867\pi$
$191$	−40460.3	+	23359.7i	−1.10908	+	0.640326i	−0.170487	+	0.985360i	$0.554534\pi$
$192$		0			0
$193$	13603.9	−	23562.6i	0.365215	−	0.632571i	−0.623596	−	0.781747i	$-0.714329\pi$
$193$	13603.9	−	23562.6i	0.365215	−	0.632571i	0.988811	+	0.149176i	$0.0476621\pi$
$194$	−85819.8	−	49548.1i	−2.28026	−	1.31651i
$195$		0			0
$196$	5885.30	+	10193.6i	0.153199	+	0.265349i
$197$			64665.2i			1.66624i	0.553090	+	0.833122i	$0.313449\pi$
$197$			64665.2i			1.66624i	−0.553090	+	0.833122i	$0.686551\pi$
$198$		0			0
$199$	−25841.3			−0.652542			−0.326271	−	0.945276i	$-0.605792\pi$
$199$	−25841.3			−0.652542			−0.326271	+	0.945276i	$0.605792\pi$
$200$	−30168.1	+	17417.5i	−0.754201	+	0.435438i
$201$		0			0
$202$	−36237.8	+	62765.8i	−0.888095	+	1.53823i
$203$	24943.4	+	14401.1i	0.605289	+	0.349464i
$204$		0			0
$205$	7421.13	+	12853.8i	0.176588	+	0.305860i
$206$		−	23346.0i		−	0.550147i
$207$		0			0
$208$	−2875.82			−0.0664714
$209$	5858.47	−	3382.39i	0.134119	−	0.0774339i
$210$		0			0
$211$	−23029.3	+	39888.0i	−0.517269	+	0.895936i	0.482530	+	0.875879i	$0.339718\pi$
$211$	−23029.3	+	39888.0i	−0.517269	+	0.895936i	−0.999799	+	0.0200565i	$0.993615\pi$
$212$	98667.3	+	56965.6i	2.19534	+	1.26748i
$213$		0			0
$214$	−37456.4	−	64876.4i	−0.817896	−	1.41664i
$215$		−	30727.6i		−	0.664739i
$216$		0			0
$217$	81622.8			1.73337
$218$	−27127.2	+	15661.9i	−0.570810	+	0.329558i
$219$		0			0
$220$	19831.6	−	34349.3i	0.409743	−	0.709696i
$221$	498.171	+	287.619i	0.0101998	+	0.00588888i
$222$		0			0
$223$	−10955.5	−	18975.6i	−0.220305	−	0.381579i	0.734596	−	0.678505i	$-0.237372\pi$
$223$	−10955.5	−	18975.6i	−0.220305	−	0.381579i	−0.954901	+	0.296926i	$0.904039\pi$
$224$			47620.1i			0.949062i
$225$		0			0
$226$	−29429.8			−0.576197
$227$	−43115.6	+	24892.8i	−0.836726	+	0.483084i	−0.856150	−	0.516727i	$-0.827150\pi$
$227$	−43115.6	+	24892.8i	−0.836726	+	0.483084i	0.0194241	+	0.999811i	$0.493817\pi$
$228$		0			0
$229$	−14260.5	+	24699.9i	−0.271934	+	0.471003i	−0.969357	−	0.245656i	$-0.920996\pi$
$229$	−14260.5	+	24699.9i	−0.271934	+	0.471003i	0.697423	+	0.716660i	$0.254330\pi$
$230$	26742.6	+	15439.9i	0.505531	+	0.291869i
$231$		0			0
$232$	−19369.8	−	33549.5i	−0.359873	−	0.623318i
$233$		−	44050.2i		−	0.811403i	−0.914006	−	0.405701i	$-0.867027\pi$
$233$		−	44050.2i		−	0.811403i	0.914006	−	0.405701i	$-0.132973\pi$
$234$		0			0
$235$	−9426.80			−0.170698
$236$	77752.1	−	44890.2i	1.39601	−	0.805986i
$237$		0			0
$238$	−1345.65	+	2330.73i	−0.0237562	+	0.0411470i
$239$	−17818.6	−	10287.6i	−0.311945	−	0.180102i	0.335851	−	0.941915i	$-0.390976\pi$
$239$	−17818.6	−	10287.6i	−0.311945	−	0.180102i	−0.647797	+	0.761813i	$0.724309\pi$
$240$		0			0
$241$	28958.8	+	50158.0i	0.498593	+	0.863588i	0.999999	−	0.00162435i	$-0.000517045\pi$
$241$	28958.8	+	50158.0i	0.498593	+	0.863588i	−0.501406	+	0.865212i	$0.667184\pi$
$242$		−	6400.56i		−	0.109292i
$243$		0			0
$244$	404.483			0.00679392
$245$	4459.27	−	2574.56i	0.0742902	−	0.0428915i
$246$		0			0
$247$	−2019.36	+	3497.63i	−0.0330993	+	0.0573297i
$248$	−95076.5	−	54892.4i	−1.54586	−	0.892502i
$249$		0			0
$250$	42895.3	+	74296.9i	0.686325	+	1.18875i
$251$			54140.4i			0.859357i	0.902982	+	0.429679i	$0.141373\pi$
$251$			54140.4i			0.859357i	−0.902982	+	0.429679i	$0.858627\pi$
$252$		0			0
$253$	49982.8			0.780871
$254$	76728.4	−	44299.2i	1.18929	−	0.686639i
$255$		0			0
$256$	40330.8	−	69855.0i	0.615399	−	1.06590i
$257$	−98522.7	−	56882.1i	−1.49166	−	0.861211i	−0.491706	−	0.870761i	$-0.663627\pi$
$257$	−98522.7	−	56882.1i	−1.49166	−	0.861211i	−0.999954	+	0.00955057i	$0.996960\pi$
$258$		0			0
$259$	−45790.8	−	79311.9i	−0.682619	−	1.18233i
$260$			23679.7i			0.350292i
$261$		0			0
$262$	−22258.6			−0.324262
$263$	−38420.1	+	22181.8i	−0.555452	+	0.320691i	−0.751318	−	0.659940i	$-0.770582\pi$
$263$	−38420.1	+	22181.8i	−0.555452	+	0.320691i	0.195866	+	0.980631i	$0.437248\pi$
$264$		0			0
$265$	24919.9	−	43162.6i	0.354859	−	0.614633i
$266$	−16363.9	−	9447.71i	−0.231272	−	0.133525i
$267$		0			0
$268$	69794.6	+	120888.i	0.971745	+	1.68311i
$269$			4429.77i			0.0612176i	0.999531	+	0.0306088i	$0.00974461\pi$
$269$			4429.77i			0.0612176i	−0.999531	+	0.0306088i	$0.990255\pi$
$270$		0			0
$271$	−86111.9			−1.17253			−0.586266	−	0.810119i	$-0.699403\pi$
$271$	−86111.9			−1.17253			−0.586266	+	0.810119i	$0.699403\pi$
$272$	257.360	−	148.587i	0.00347859	−	0.00200836i
$273$		0			0
$274$	−12525.7	+	21695.2i	−0.166841	+	0.288977i
$275$	52616.4	+	30378.1i	0.695754	+	0.401693i
$276$		0			0
$277$	−35306.7	−	61153.0i	−0.460148	−	0.797000i	0.538820	−	0.842421i	$-0.318870\pi$
$277$	−35306.7	−	61153.0i	−0.460148	−	0.797000i	−0.998968	+	0.0454210i	$0.985537\pi$
$278$			22780.6i			0.294765i
$279$		0			0
$280$	−44977.8			−0.573697
$281$	129258.	−	74627.2i	1.63699	−	0.945114i	0.655123	−	0.755522i	$-0.272617\pi$
$281$	129258.	−	74627.2i	1.63699	−	0.945114i	0.981863	−	0.189592i	$-0.0607166\pi$
$282$		0			0
$283$	41963.4	−	72682.7i	0.523959	−	0.907524i	−0.475652	−	0.879634i	$-0.657788\pi$
$283$	41963.4	−	72682.7i	0.523959	−	0.907524i	0.999611	−	0.0278902i	$-0.00887887\pi$
$284$	44884.1	+	25913.8i	0.556488	+	0.321288i
$285$		0			0
$286$	30548.3	+	52911.2i	0.373469	+	0.646867i
$287$		−	67104.2i		−	0.814678i
$288$		0			0
$289$	83461.6			0.999288
$290$	−36150.3	+	20871.4i	−0.429849	+	0.248174i
$291$		0			0
$292$	12788.2	−	22149.9i	0.149984	−	0.259780i
$293$	31092.9	+	17951.5i	0.362182	+	0.209106i	0.670037	−	0.742327i	$-0.266278\pi$
$293$	31092.9	+	17951.5i	0.362182	+	0.209106i	−0.307856	+	0.951433i	$0.599611\pi$
$294$		0			0
$295$	−19637.5	−	34013.1i	−0.225653	−	0.390843i
$296$			123180.i			1.40590i
$297$		0			0
$298$	−58389.0			−0.657504
$299$	−25842.8	+	14920.4i	−0.289067	+	0.166893i
$300$		0			0
$301$	−69462.2	+	120312.i	−0.766682	+	1.32793i
$302$	56265.8	+	32485.1i	0.616923	+	0.356181i
$303$		0			0
$304$	1043.22	+	1806.91i	0.0112883	+	0.0195519i
$305$		−	176.944i		−	0.00190211i
$306$		0			0
$307$	7054.30			0.0748475			0.0374238	−	0.999299i	$-0.488085\pi$
$307$	7054.30			0.0748475			0.0374238	+	0.999299i	$0.488085\pi$
$308$	−155299.	+	89661.8i	−1.63707	+	0.945161i
$309$		0			0
$310$	−59147.8	+	102447.i	−0.615482	+	1.06605i
$311$	−74184.9	−	42830.7i	−0.766999	−	0.442827i	0.0648038	−	0.997898i	$-0.479358\pi$
$311$	−74184.9	−	42830.7i	−0.766999	−	0.442827i	−0.831803	+	0.555071i	$0.812691\pi$
$312$		0			0
$313$	−36721.2	−	63603.1i	−0.374825	−	0.649216i	0.615476	−	0.788156i	$-0.288964\pi$
$313$	−36721.2	−	63603.1i	−0.374825	−	0.649216i	−0.990301	+	0.138940i	$0.955631\pi$
$314$			37001.5i			0.375284i
$315$		0			0
$316$	6410.07			0.0641931
$317$	−42642.8	+	24619.8i	−0.424353	+	0.245000i	−0.696938	−	0.717132i	$-0.745455\pi$
$317$	−42642.8	+	24619.8i	−0.424353	+	0.245000i	0.272585	+	0.962132i	$0.412121\pi$
$318$		0			0
$319$	−33783.0	+	58513.9i	−0.331984	+	0.575013i
$320$	−66062.5	−	38141.2i	−0.645141	−	0.372473i
$321$		0			0
$322$	−69806.1	−	120908.i	−0.673258	−	1.16612i
$323$		−	417.341i		−	0.00400024i
$324$		0			0
$325$	−36272.7			−0.343410
$326$	−12220.6	+	7055.58i	−0.114990	+	0.0663893i
$327$		0			0
$328$	−45128.5	+	78164.8i	−0.419472	+	0.726547i
$329$	36910.1	+	21310.0i	0.340999	+	0.196876i
$330$		0			0
$331$	41005.6	+	71023.7i	0.374271	+	0.648257i	0.990218	−	0.139531i	$-0.0445595\pi$
$331$	41005.6	+	71023.7i	0.374271	+	0.648257i	−0.615946	+	0.787788i	$0.711226\pi$
$332$		−	354627.i		−	3.21733i
$333$		0			0
$334$	242575.			2.17447
$335$	52883.1	−	30532.1i	0.471224	−	0.272061i
$336$		0			0
$337$	23491.4	−	40688.3i	0.206847	−	0.358270i	−0.743873	−	0.668322i	$-0.767013\pi$
$337$	23491.4	−	40688.3i	0.206847	−	0.358270i	0.950720	+	0.310052i	$0.100346\pi$
$338$	130484.	+	75335.0i	1.14215	+	0.659422i
$339$		0			0
$340$	−1223.48	−	2119.12i	−0.0105837	−	0.0183315i
$341$			191477.i			1.64667i
$342$		0			0
$343$	104628.			0.889324
$344$	161823.	−	93428.4i	1.36749	−	0.789518i
$345$		0			0
$346$	159178.	−	275705.i	1.32963	−	2.30299i
$347$	−38382.0	−	22159.8i	−0.318763	−	0.184038i	0.332078	−	0.943252i	$-0.392250\pi$
$347$	−38382.0	−	22159.8i	−0.318763	−	0.184038i	−0.650841	+	0.759214i	$0.725584\pi$
$348$		0			0
$349$	93231.7	+	161482.i	0.765442	+	1.32579i	0.940012	+	0.341140i	$0.110813\pi$
$349$	93231.7	+	161482.i	0.765442	+	1.32579i	−0.174570	+	0.984645i	$0.555853\pi$
$350$		−	169704.i		−	1.38534i
$351$		0			0
$352$	−111711.			−0.901591
$353$	146959.	−	84847.1i	1.17936	−	0.680907i	0.223497	−	0.974705i	$-0.428253\pi$
$353$	146959.	−	84847.1i	1.17936	−	0.680907i	0.955868	+	0.293798i	$0.0949193\pi$
$354$		0			0
$355$	11336.2	−	19634.8i	0.0899517	−	0.155801i
$356$	13434.4	+	7756.35i	0.106003	+	0.0612008i
$357$		0			0
$358$	−156336.	−	270782.i	−1.21981	−	2.11278i
$359$			69656.7i			0.540473i	0.962794	+	0.270236i	$0.0871019\pi$
$359$			69656.7i			0.540473i	−0.962794	+	0.270236i	$0.912898\pi$
$360$		0			0
$361$	−127391.			−0.977516
$362$	−259712.	+	149945.i	−1.98187	+	1.14423i
$363$		0			0
$364$	53529.9	−	92716.6i	0.404012	−	0.699769i
$365$	−9689.60	−	5594.30i	−0.0727311	−	0.0419913i
$366$		0			0
$367$	88084.2	+	152566.i	0.653982	+	1.13273i	0.982148	+	0.188110i	$0.0602361\pi$
$367$	88084.2	+	152566.i	0.653982	+	1.13273i	−0.328166	+	0.944620i	$0.606431\pi$
$368$			15416.0i			0.113835i
$369$		0			0
$370$	132729.			0.969531
$371$	−195145.	+	112667.i	−1.41778	+	0.818558i
$372$		0			0
$373$	−33593.6	+	58185.7i	−0.241456	+	0.418214i	−0.961129	−	0.276099i	$-0.910958\pi$
$373$	−33593.6	+	58185.7i	−0.241456	+	0.418214i	0.719673	+	0.694313i	$0.244292\pi$
$374$	−5467.59	−	3156.71i	−0.0390888	−	0.0225679i
$375$		0			0
$376$	−28662.6	−	49645.0i	−0.202740	−	0.351156i
$377$		−	40338.3i		−	0.283815i
$378$		0			0
$379$	43976.9			0.306158			0.153079	−	0.988214i	$-0.451081\pi$
$379$	43976.9			0.306158			0.153079	+	0.988214i	$0.451081\pi$
$380$	14878.2	−	8589.95i	0.103035	−	0.0594872i
$381$		0			0
$382$	−153065.	+	265116.i	−1.04893	+	1.81681i
$383$	160336.	+	92569.8i	1.09303	+	0.631062i	0.934382	−	0.356273i	$-0.115953\pi$
$383$	160336.	+	92569.8i	1.09303	+	0.631062i	0.158649	+	0.987335i	$0.449286\pi$
$384$		0			0
$385$	39223.1	+	67936.4i	0.264619	+	0.458333i
$386$		−	178279.i		−	1.19654i
$387$		0			0
$388$	−407353.			−2.70587
$389$	26364.0	−	15221.3i	0.174226	−	0.100589i	−0.410351	−	0.911928i	$-0.634594\pi$
$389$	26364.0	−	15221.3i	0.174226	−	0.100589i	0.584577	+	0.811338i	$0.301260\pi$
$390$		0			0
$391$	1541.80	−	2670.48i	0.0100850	−	0.0174677i
$392$	27117.2	+	15656.1i	0.176471	+	0.101885i
$393$		0			0
$394$	211860.	+	366951.i	1.36476	+	2.36383i
$395$		−	2804.12i		−	0.0179723i
$396$		0			0
$397$	−235724.			−1.49563			−0.747813	−	0.663910i	$-0.768896\pi$
$397$	−235724.			−1.49563			−0.747813	+	0.663910i	$0.768896\pi$
$398$	−146640.	+	84662.7i	−0.925734	+	0.534473i
$399$		0			0
$400$	−9369.41	+	16228.3i	−0.0585588	+	0.101427i
$401$	−202830.	−	117104.i	−1.26137	−	0.728254i	−0.288032	−	0.957621i	$-0.593001\pi$
$401$	−202830.	−	117104.i	−1.26137	−	0.728254i	−0.973340	+	0.229367i	$0.926334\pi$
$402$		0			0
$403$	−57157.8	−	99000.1i	−0.351937	−	0.609573i
$404$			297925.i			1.82534i
$405$		0			0
$406$	188726.			1.14493
$407$	186056.	−	107419.i	1.12319	−	0.648475i
$408$		0			0
$409$	148893.	−	257890.i	0.890076	−	1.54166i	0.0502930	−	0.998735i	$-0.483984\pi$
$409$	148893.	−	257890.i	0.890076	−	1.54166i	0.839783	−	0.542922i	$-0.182682\pi$
$410$	84224.3	+	48626.9i	0.501037	+	0.289274i
$411$		0			0
$412$	−47984.1	−	83110.9i	−0.282685	−	0.489625i
$413$			177569.i			1.04104i
$414$		0			0
$415$	−155134.			−0.900763
$416$	57758.3	−	33346.8i	0.333755	−	0.192694i
$417$		0			0
$418$	22163.1	−	38387.6i	0.126846	−	0.219704i
$419$	31934.0	+	18437.1i	0.181897	+	0.105018i	0.588184	−	0.808727i	$-0.299843\pi$
$419$	31934.0	+	18437.1i	0.181897	+	0.105018i	−0.406287	+	0.913746i	$0.633177\pi$
$420$		0			0
$421$	−120305.	−	208374.i	−0.678764	−	1.17565i	−0.975353	−	0.220649i	$-0.929183\pi$
$421$	−120305.	−	208374.i	−0.678764	−	1.17565i	0.296589	−	0.955005i	$-0.404151\pi$
$422$			301799.i			1.69470i
$423$		0			0
$424$	303080.			1.68588
$425$	3246.08	−	1874.12i	0.0179714	−	0.0103758i
$426$		0			0
$427$	−399.995	+	692.812i	−0.00219381	+	0.00379979i
$428$	−266686.	−	153971.i	−1.45584	−	0.840529i
$429$		0			0
$430$	−100671.	−	174368.i	−0.544463	−	0.943038i
$431$		−	162758.i		−	0.876169i	−0.898934	−	0.438084i	$-0.855657\pi$
$431$		−	162758.i		−	0.876169i	0.898934	−	0.438084i	$-0.144343\pi$
$432$		0			0
$433$	266637.			1.42215			0.711073	−	0.703118i	$-0.248209\pi$
$433$	266637.			1.42215			0.711073	+	0.703118i	$0.248209\pi$
$434$	463180.	−	267417.i	2.45906	−	1.41974i
$435$		0			0
$436$	−64381.1	+	111511.i	−0.338677	+	0.586605i
$437$	18749.3	+	10824.9i	0.0981796	+	0.0566840i
$438$		0			0
$439$	18408.7	+	31884.8i	0.0955201	+	0.165446i	0.909826	−	0.414991i	$-0.136215\pi$
$439$	18408.7	+	31884.8i	0.0955201	+	0.165446i	−0.814305	+	0.580437i	$0.802882\pi$
$440$		−	105512.i		−	0.545001i
$441$		0			0
$442$	3769.25			0.0192935
$443$	119117.	−	68772.0i	0.606967	−	0.350432i	−0.164811	−	0.986325i	$-0.552701\pi$
$443$	119117.	−	68772.0i	0.606967	−	0.350432i	0.771777	+	0.635893i	$0.219368\pi$
$444$		0			0
$445$	3393.06	−	5876.95i	0.0171345	−	0.0296778i
$446$	−124337.	−	71786.2i	−0.625075	−	0.360887i
$447$		0			0
$448$	172442.	+	298679.i	0.859188	+	1.48816i
$449$		−	174405.i		−	0.865101i	−0.901610	−	0.432550i	$-0.857614\pi$
$449$		−	174405.i		−	0.865101i	0.901610	−	0.432550i	$-0.142386\pi$
$450$		0			0
$451$	157418.			0.773929
$452$	−104769.	+	60488.4i	−0.512809	+	0.296070i
$453$		0			0
$454$	−163110.	+	282515.i	−0.791352	+	1.37066i
$455$	−40559.4	−	23417.0i	−0.195916	−	0.113112i
$456$		0			0
$457$	−57654.7	−	99860.9i	−0.276059	−	0.478149i	0.694342	−	0.719645i	$-0.255695\pi$
$457$	−57654.7	−	99860.9i	−0.276059	−	0.478149i	−0.970402	+	0.241496i	$0.922362\pi$
$458$			186884.i			0.890923i
$459$		0			0
$460$	126937.			0.599890
$461$	−351141.	+	202731.i	−1.65226	+	0.953936i	−0.676127	+	0.736785i	$0.736343\pi$
$461$	−351141.	+	202731.i	−1.65226	+	0.953936i	−0.976138	+	0.217150i	$0.930324\pi$
$462$		0			0
$463$	−36293.4	+	62861.9i	−0.169303	+	0.293242i	−0.938175	−	0.346161i	$-0.887485\pi$
$463$	−36293.4	+	62861.9i	−0.169303	+	0.293242i	0.768872	+	0.639403i	$0.220818\pi$
$464$	−18047.3	−	10419.6i	−0.0838253	−	0.0483966i
$465$		0			0
$466$	−144320.	−	249969.i	−0.664590	−	1.15110i
$467$		−	358806.i		−	1.64523i	−0.568602	−	0.822613i	$-0.692515\pi$
$467$		−	358806.i		−	1.64523i	0.568602	−	0.822613i	$-0.307485\pi$
$468$		0			0
$469$	−276081.			−1.25514
$470$	−53493.6	+	30884.6i	−0.242162	+	0.139812i
$471$		0			0
$472$	119417.	−	206837.i	0.536022	−	0.928418i
$473$	−282236.	−	162949.i	−1.26151	−	0.728333i
$474$		0			0
$475$	13158.1	+	22790.5i	0.0583185	+	0.101011i
$476$			11063.1i			0.0488271i
$477$		0			0
$478$	−134819.			−0.590058
$479$	22169.8	−	12799.8i	0.0966255	−	0.0557867i	−0.450909	−	0.892570i	$-0.648900\pi$
$479$	22169.8	−	12799.8i	0.0966255	−	0.0557867i	0.547534	+	0.836783i	$0.315567\pi$
$480$		0			0
$481$	−64131.5	+	111079.i	−0.277192	+	0.480111i
$482$	328661.	+	189752.i	1.41466	+	0.816757i
$483$		0			0
$484$	−13155.4	−	22785.7i	−0.0561580	−	0.0972685i
$485$			178199.i			0.757569i
$486$		0			0
$487$	247261.			1.04255			0.521277	−	0.853388i	$-0.325456\pi$
$487$	247261.			1.04255			0.521277	+	0.853388i	$0.325456\pi$
$488$	931.850	−	538.004i	0.00391297	−	0.00225915i
$489$		0			0
$490$	16869.8	−	29219.4i	0.0702616	−	0.121697i
$491$	296403.	+	171128.i	1.22947	+	0.709837i	0.966920	−	0.255081i	$-0.0821020\pi$
$491$	296403.	+	171128.i	1.22947	+	0.709837i	0.262554	+	0.964917i	$0.415435\pi$
$492$		0			0
$493$	2084.19	+	3609.92i	0.00857517	+	0.0148526i
$494$			26463.7i			0.108442i
$495$		0			0
$496$	−59056.5			−0.240052
$497$	−88772.2	+	51252.7i	−0.359389	+	0.207493i
$498$		0			0
$499$	98919.1	−	171333.i	0.397264	−	0.688081i	−0.596124	−	0.802893i	$-0.703293\pi$
$499$	98919.1	−	171333.i	0.397264	−	0.688081i	0.993387	+	0.114812i	$0.0366265\pi$
$500$	305411.	+	176329.i	1.22164	+	0.705317i
$501$		0			0
$502$	177377.	+	307227.i	0.703867	+	1.21913i
$503$			187051.i			0.739305i	0.929170	+	0.369652i	$0.120523\pi$
$503$			187051.i			0.739305i	−0.929170	+	0.369652i	$0.879477\pi$
$504$		0			0
$505$	130329.			0.511044
$506$	283634.	−	163756.i	1.10779	−	0.639582i
$507$		0			0
$508$	182100.	−	315406.i	0.705639	−	1.22220i
$509$	25011.5	+	14440.4i	0.0965393	+	0.0557370i	0.547492	−	0.836811i	$-0.315583\pi$
$509$	25011.5	+	14440.4i	0.0965393	+	0.0557370i	−0.450953	+	0.892548i	$0.648916\pi$
$510$		0			0
$511$	25292.7	+	43808.3i	0.0968620	+	0.167770i
$512$		−	78644.0i		−	0.300003i
$513$		0			0
$514$	−745440.			−2.82154
$515$	−36357.4	+	20990.9i	−0.137081	+	0.0791439i
$516$		0			0
$517$	−49990.6	+	86586.3i	−0.187028	+	0.323943i
$518$	−519692.	−	300044.i	−1.93681	−	1.11822i
$519$		0			0
$520$	31496.5	+	54553.5i	0.116481	+	0.201751i
$521$			269661.i			0.993443i	0.867910	+	0.496721i	$0.165463\pi$
$521$			269661.i			0.993443i	−0.867910	+	0.496721i	$0.834537\pi$
$522$		0			0
$523$	−187282.			−0.684689			−0.342344	−	0.939575i	$-0.611221\pi$
$523$	−187282.			−0.684689			−0.342344	+	0.939575i	$0.611221\pi$
$524$	−79239.8	+	45749.1i	−0.288590	+	0.166617i
$525$		0			0
$526$	−145347.	+	251748.i	−0.525331	+	0.909901i
$527$	10230.2	+	5906.41i	0.0368352	+	0.0212668i
$528$		0			0
$529$	−59938.8	−	103817.i	−0.214189	−	0.370986i
$530$		−	326576.i		−	1.16261i
$531$		0			0
$532$	−77673.1			−0.274440
$533$	−81390.6	+	46990.9i	−0.286497	+	0.165409i
$534$		0			0
$535$	−67355.7	+	116664.i	−0.235324	+	0.407594i
$536$	321586.	+	185668.i	1.11936	+	0.646260i
$537$		0			0
$538$	14513.0	+	25137.3i	0.0501411	+	0.0868469i
$539$		−	54611.9i		−	0.187979i
$540$		0			0
$541$	−25587.9			−0.0874259			−0.0437129	−	0.999044i	$-0.513919\pi$
$541$	−25587.9			−0.0874259			−0.0437129	+	0.999044i	$0.513919\pi$
$542$	−488653.	+	282124.i	−1.66342	+	0.960377i
$543$		0			0
$544$	−3445.90	+	5968.47i	−0.0116441	+	0.0201681i
$545$	48781.3	+	28163.9i	0.164233	+	0.0948200i
$546$		0			0
$547$	138424.	+	239758.i	0.462634	+	0.801306i	0.999091	−	0.0426215i	$-0.0135710\pi$
$547$	138424.	+	239758.i	0.462634	+	0.801306i	−0.536457	+	0.843928i	$0.680238\pi$
$548$			102979.i			0.342915i
$549$		0			0
$550$	398105.			1.31605
$551$	−25345.0	+	14633.0i	−0.0834813	+	0.0481980i
$552$		0			0
$553$	−6338.95	+	10979.4i	−0.0207285	+	0.0359027i
$554$	−400705.	−	231347.i	−1.30559	−	0.753780i
$555$		0			0
$556$	46821.9	+	81098.0i	0.151461	+	0.262338i
$557$		−	461786.i		−	1.48844i	−0.667936	−	0.744219i	$-0.732822\pi$
$557$		−	461786.i		−	1.48844i	0.667936	−	0.744219i	$-0.267178\pi$
$558$		0			0
$559$	194568.			0.622656
$560$	−20953.4	+	12097.4i	−0.0668157	+	0.0385761i
$561$		0			0
$562$	488995.	−	846964.i	1.54822	−	2.68159i
$563$	154104.	+	88972.1i	0.486181	+	0.280697i	0.722989	−	0.690860i	$-0.242768\pi$
$563$	154104.	+	88972.1i	0.486181	+	0.280697i	−0.236808	+	0.971556i	$0.576101\pi$
$564$		0			0
$565$	26461.0	+	45831.8i	0.0828914	+	0.143572i
$566$		−	549930.i		−	1.71662i
$567$		0			0
$568$	137872.			0.427347
$569$	5111.83	−	2951.31i	0.0157889	−	0.00911572i	−0.492085	−	0.870547i	$-0.663765\pi$
$569$	5111.83	−	2951.31i	0.0157889	−	0.00911572i	0.507874	+	0.861432i	$0.330432\pi$
$570$		0			0
$571$	−238346.	+	412828.i	−0.731031	+	1.26618i	0.225411	+	0.974264i	$0.427627\pi$
$571$	−238346.	+	412828.i	−0.731031	+	1.26618i	−0.956443	+	0.291920i	$0.905706\pi$
$572$	217501.	+	125574.i	0.664767	+	0.383803i
$573$		0			0
$574$	−219850.	−	380792.i	−0.667272	−	1.15575i
$575$			194442.i			0.588105i
$576$		0			0
$577$	209901.			0.630468			0.315234	−	0.949014i	$-0.397917\pi$
$577$	209901.			0.630468			0.315234	+	0.949014i	$0.397917\pi$
$578$	473614.	−	273441.i	1.41765	−	0.818480i
$579$		0			0
$580$	−85795.7	+	148603.i	−0.255041	+	0.441744i
$581$	607417.	+	350693.i	1.79943	+	1.03890i
$582$		0			0
$583$	−264302.	−	457785.i	−0.777614	−	1.34687i
$584$		−	68038.7i		−	0.199494i
$585$		0			0
$586$	235255.			0.685083
$587$	156552.	−	90385.1i	0.454340	−	0.262313i	−0.255321	−	0.966856i	$-0.582181\pi$
$587$	156552.	−	90385.1i	0.454340	−	0.262313i	0.709661	+	0.704543i	$0.248848\pi$
$588$		0			0
$589$	−41468.6	+	71825.7i	−0.119533	+	0.207038i
$590$	−222871.	−	128675.i	−0.640250	−	0.369649i
$591$		0			0
$592$	33131.0	+	57384.5i	0.0945346	+	0.163739i
$593$		−	468097.i		−	1.33115i	−0.746332	−	0.665574i	$-0.768187\pi$
$593$		−	468097.i		−	1.33115i	0.746332	−	0.665574i	$-0.231813\pi$
$594$		0			0
$595$	4839.60			0.0136702
$596$	−207862.	+	120009.i	−0.585171	+	0.337849i
$597$		0			0
$598$	−97765.8	+	169335.i	−0.273391	+	0.473527i
$599$	−558557.	−	322483.i	−1.55673	−	0.898780i	−0.997566	−	0.0697251i	$-0.977788\pi$
$599$	−558557.	−	322483.i	−1.55673	−	0.898780i	−0.559167	−	0.829055i	$-0.688879\pi$
$600$		0			0
$601$	−127517.	−	220865.i	−0.353035	−	0.611474i	0.633745	−	0.773542i	$-0.281517\pi$
$601$	−127517.	−	220865.i	−0.353035	−	0.611474i	−0.986780	+	0.162068i	$0.948184\pi$
$602$			910302.i			2.51184i
$603$		0			0
$604$	267072.			0.732073
$605$	−9967.76	+	5754.89i	−0.0272325	+	0.0157227i
$606$		0			0
$607$	176351.	−	305449.i	0.478631	−	0.829013i	−0.521069	−	0.853514i	$-0.674467\pi$
$607$	176351.	−	305449.i	0.478631	−	0.829013i	0.999700	+	0.0245019i	$0.00779999\pi$
$608$	−41904.3	−	24193.5i	−0.113358	−	0.0654472i
$609$		0			0
$610$	−579.711	−	1004.09i	−0.00155795	−	0.00269844i
$611$		−	59690.9i		−	0.159892i
$612$		0			0
$613$	−37013.8			−0.0985015			−0.0492508	−	0.998786i	$-0.515683\pi$
$613$	−37013.8			−0.0985015			−0.0492508	+	0.998786i	$0.515683\pi$
$614$	40030.6	−	23111.7i	0.106183	−	0.0613048i
$615$		0			0
$616$	−238519.	+	413127.i	−0.628581	+	1.08873i
$617$	493797.	+	285094.i	1.29711	+	0.748888i	0.979904	−	0.199467i	$-0.0639212\pi$
$617$	493797.	+	285094.i	1.29711	+	0.748888i	0.317208	+	0.948356i	$0.397255\pi$
$618$		0			0
$619$	220407.	+	381756.i	0.575233	+	0.996333i	0.996016	+	0.0891715i	$0.0284219\pi$
$619$	220407.	+	381756.i	0.575233	+	0.996333i	−0.420783	+	0.907161i	$0.638245\pi$
$620$			486276.i			1.26503i
$621$		0			0
$622$	−561296.			−1.45081
$623$	−26570.7	+	15340.6i	−0.0684583	+	0.0395244i
$624$		0			0
$625$	−74789.0	+	129538.i	−0.191460	+	0.331618i
$626$	−416759.	−	240616.i	−1.06350	−	0.614011i
$627$		0			0
$628$	76050.9	+	131724.i	0.192835	+	0.333999i
$629$		−	13254.1i		−	0.0335003i
$630$		0			0
$631$	−80926.3			−0.203250			−0.101625	−	0.994823i	$-0.532404\pi$
$631$	−80926.3			−0.203250			−0.101625	+	0.994823i	$0.532404\pi$
$632$	14767.6	−	8526.05i	0.0369721	−	0.0213459i
$633$		0			0
$634$	−161321.	+	279417.i	−0.401341	+	0.695143i
$635$	−137976.	−	79660.7i	−0.342182	−	0.197559i
$636$		0			0
$637$	16302.2	+	28236.3i	0.0401761	+	0.0695870i
$638$			442727.i			1.08766i
$639$		0			0
$640$	−331317.			−0.808879
$641$	131917.	−	76162.1i	0.321058	−	0.185363i	−0.330806	−	0.943699i	$-0.607321\pi$
$641$	131917.	−	76162.1i	0.321058	−	0.185363i	0.651864	+	0.758336i	$0.273987\pi$
$642$		0			0
$643$	−58437.1	+	101216.i	−0.141340	+	0.244809i	−0.928002	−	0.372576i	$-0.878475\pi$
$643$	−58437.1	+	101216.i	−0.141340	+	0.244809i	0.786661	+	0.617385i	$0.211808\pi$
$644$	−497013.	−	286951.i	−1.19838	−	0.691888i
$645$		0			0
$646$	−1367.31	−	2368.26i	−0.00327645	−	0.00567498i
$647$			481407.i			1.15002i	0.818148	+	0.575008i	$0.195001\pi$
$647$			481407.i			1.15002i	−0.818148	+	0.575008i	$0.804999\pi$
$648$		0			0
$649$	−416553.			−0.988965
$650$	−205834.	+	118838.i	−0.487181	+	0.281274i
$651$		0			0
$652$	−29003.3	+	50235.2i	−0.0682263	+	0.118171i
$653$	−399091.	−	230415.i	−0.935935	−	0.540363i	−0.0472516	−	0.998883i	$-0.515046\pi$
$653$	−399091.	−	230415.i	−0.935935	−	0.540363i	−0.888684	+	0.458520i	$0.848380\pi$
$654$		0			0
$655$	20013.2	+	34663.9i	0.0466482	+	0.0807970i
$656$			48551.9i			0.112823i
$657$		0			0
$658$	279268.			0.645015
$659$	−142960.	+	82538.2i	−0.329189	+	0.190057i	−0.655481	−	0.755212i	$-0.727534\pi$
$659$	−142960.	+	82538.2i	−0.329189	+	0.190057i	0.326292	+	0.945269i	$0.394201\pi$
$660$		0			0
$661$	140878.	−	244008.i	0.322434	−	0.558472i	−0.658556	−	0.752532i	$-0.728832\pi$
$661$	140878.	−	244008.i	0.322434	−	0.558472i	0.980990	+	0.194060i	$0.0621657\pi$
$662$	465383.	+	268689.i	1.06193	+	0.613104i
$663$		0			0
$664$	−471691.	−	816992.i	−1.06985	−	1.85303i
$665$			33978.6i			0.0768355i
$666$		0			0
$667$	−216236.			−0.486046
$668$	863556.	−	498574.i	1.93525	−	1.11732i
$669$		0			0
$670$	200061.	−	346517.i	0.445670	−	0.771924i
$671$	−1625.25	−	938.337i	−0.00360973	−	0.00208408i
$672$		0			0
$673$	378387.	+	655386.i	0.835423	+	1.44699i	0.893686	+	0.448694i	$0.148111\pi$
$673$	378387.	+	655386.i	0.835423	+	1.44699i	−0.0582627	+	0.998301i	$0.518556\pi$
$674$		−	307855.i		−	0.677683i
$675$		0			0
$676$	619357.			1.35534
$677$	59053.2	−	34094.4i	0.128845	−	0.0743885i	−0.434192	−	0.900820i	$-0.642966\pi$
$677$	59053.2	−	34094.4i	0.128845	−	0.0743885i	0.563037	+	0.826432i	$0.309633\pi$
$678$		0			0
$679$	402833.	−	697728.i	0.873747	−	1.51337i
$680$	−5637.30	−	3254.70i	−0.0121914	−	0.00703870i
$681$		0			0
$682$	627326.	+	1.08656e6i	1.34873	+	2.33606i
$683$			31351.1i			0.0672066i	0.999435	+	0.0336033i	$0.0106983\pi$
$683$			31351.1i			0.0672066i	−0.999435	+	0.0336033i	$0.989302\pi$
$684$		0			0
$685$	45048.7			0.0960065
$686$	593726.	−	342788.i	1.26165	−	0.728412i
$687$		0			0
$688$	50257.9	−	87049.3i	0.106176	−	0.183903i
$689$	273307.	+	157794.i	0.575722	+	0.332393i
$690$		0			0
$691$	−187442.	−	324659.i	−0.392565	−	0.679942i	0.600222	−	0.799833i	$-0.295079\pi$
$691$	−187442.	−	324659.i	−0.392565	−	0.679942i	−0.992787	+	0.119891i	$0.961745\pi$
$692$		−	1.30866e6i		−	2.73285i
$693$		0			0
$694$	−290405.			−0.602955
$695$	35476.8	−	20482.5i	0.0734471	−	0.0424047i
$696$		0			0
$697$	4855.81	−	8410.52i	0.00999531	−	0.0173124i
$698$	1.05811e6	+	610901.i	2.17180	+	1.25389i
$699$		0			0
$700$	−348801.	−	604140.i	−0.711838	−	1.23294i
$701$			97448.5i			0.198308i	0.995072	+	0.0991538i	$0.0316136\pi$
$701$			97448.5i			0.198308i	−0.995072	+	0.0991538i	$0.968386\pi$
$702$		0			0
$703$	93056.2			0.188293
$704$	−700663.	+	404528.i	−1.41372	+	0.816212i
$705$		0			0
$706$	555961.	−	962952.i	1.11541	−	1.93195i
$707$	−510295.	−	294619.i	−1.02090	−	0.589416i
$708$		0			0
$709$	146263.	+	253334.i	0.290965	+	0.503967i	0.974038	−	0.226383i	$-0.0726902\pi$
$709$	146263.	+	253334.i	0.290965	+	0.503967i	−0.683073	+	0.730350i	$0.739357\pi$
$710$		−	148561.i		−	0.294704i
$711$		0			0
$712$	41267.0			0.0814034
$713$	−530697.	+	306398.i	−1.04392	+	0.602708i
$714$		0			0
$715$	54933.3	−	95147.2i	0.107454	−	0.186116i
$716$	−1.11310e6	−	642648.i	−2.17124	−	1.25357i
$717$		0			0
$718$	228213.	+	395276.i	0.442681	+	0.766746i
$719$			655579.i			1.26814i	0.773276	+	0.634070i	$0.218617\pi$
$719$			655579.i			1.26814i	−0.773276	+	0.634070i	$0.781383\pi$
$720$		0			0
$721$	189807.			0.365125
$722$	−722896.	+	417364.i	−1.38676	+	0.800647i
$723$		0			0
$724$	−616376.	+	1.06760e6i	−1.17590	+	2.03671i
$725$	−227630.	−	131422.i	−0.433065	−	0.250030i
$726$		0			0
$727$	−129630.	−	224526.i	−0.245266	−	0.424814i	0.716940	−	0.697135i	$-0.245542\pi$
$727$	−129630.	−	224526.i	−0.245266	−	0.424814i	−0.962206	+	0.272321i	$0.912209\pi$
$728$		−	284801.i		−	0.537377i
$729$		0			0
$730$	−73313.3			−0.137574
$731$	−17412.1	+	10052.9i	−0.0325849	+	0.0188129i
$732$		0			0
$733$	−41254.4	+	71454.8i	−0.0767826	+	0.132991i	−0.901860	−	0.432028i	$-0.857798\pi$
$733$	−41254.4	+	71454.8i	−0.0767826	+	0.132991i	0.825077	+	0.565020i	$0.191131\pi$
$734$	999691.	+	577172.i	1.85555	+	1.07130i
$735$		0			0
$736$	−178758.	−	309618.i	−0.329996	−	0.571571i
$737$		−	647650.i		−	1.19235i
$738$		0			0
$739$	−730583.			−1.33777			−0.668884	−	0.743367i	$-0.733228\pi$
$739$	−730583.			−1.33777			−0.668884	+	0.743367i	$0.733228\pi$
$740$	472509.	−	272803.i	0.862872	−	0.498179i
$741$		0			0
$742$	−738251.	+	1.27869e6i	−1.34090	+	2.32251i
$743$	−391257.	−	225892.i	−0.708735	−	0.409189i	0.101857	−	0.994799i	$-0.467521\pi$
$743$	−391257.	−	225892.i	−0.708735	−	0.409189i	−0.810593	+	0.585611i	$0.800855\pi$
$744$		0			0
$745$	52498.8	+	90930.6i	0.0945882	+	0.163832i
$746$			440244.i			0.791071i
$747$		0			0
$748$	−25952.5			−0.0463849
$749$	527455.	−	304526.i	0.940203	−	0.542826i
$750$		0			0
$751$	−290081.	+	502435.i	−0.514327	+	0.890840i	0.485535	+	0.874217i	$0.338625\pi$
$751$	−290081.	+	502435.i	−0.514327	+	0.890840i	−0.999862	+	0.0166228i	$0.994709\pi$
$752$	−26705.5	−	15418.4i	−0.0472243	−	0.0272650i
$753$		0			0
$754$	−132158.	−	228905.i	−0.232462	−	0.402636i
$755$		−	116832.i		−	0.204960i
$756$		0			0
$757$	1.00242e6			1.74928			0.874641	−	0.484771i	$-0.161097\pi$
$757$	1.00242e6			1.74928			0.874641	+	0.484771i	$0.161097\pi$
$758$	249553.	−	144079.i	0.434334	−	0.250763i
$759$		0			0
$760$	22851.0	−	39579.2i	0.0395620	−	0.0685235i
$761$	73367.2	+	42358.6i	0.126687	+	0.0731429i	0.562004	−	0.827134i	$-0.310030\pi$
$761$	73367.2	+	42358.6i	0.126687	+	0.0731429i	−0.435317	+	0.900277i	$0.643364\pi$
$762$		0			0
$763$	−127334.	−	220548.i	−0.218723	−	0.378839i
$764$			1.25840e6i			2.15592i
$765$		0			0
$766$	1.21313e6			2.06752
$767$	215373.	−	124345.i	0.366100	−	0.211368i
$768$		0			0
$769$	341763.	−	591950.i	0.577926	−	1.00100i	−0.417791	−	0.908543i	$-0.637196\pi$
$769$	341763.	−	591950.i	0.577926	−	1.00100i	0.995717	−	0.0924535i	$-0.0294710\pi$
$770$	445153.	+	257009.i	0.750807	+	0.433478i
$771$		0			0
$772$	−366425.	−	634666.i	−0.614823	−	1.06490i
$773$		−	235888.i		−	0.394772i	−0.980326	−	0.197386i	$-0.936755\pi$
$773$		−	235888.i		−	0.394772i	0.980326	−	0.197386i	$-0.0632453\pi$
$774$		0			0
$775$	−744879.			−1.24017
$776$	−938462.	+	541821.i	−1.55845	+	0.899773i
$777$		0			0
$778$	99737.5	−	172750.i	0.164778	−	0.285404i
$779$	59049.7	+	34092.4i	0.0973068	+	0.0561801i
$780$		0			0
$781$	−120232.	−	208248.i	−0.197114	−	0.341412i
$782$		−	20205.3i		−	0.0330409i
$783$		0			0
$784$	16843.8			0.0274036
$785$	57623.5	−	33268.9i	0.0935104	−	0.0539883i
$786$		0			0
$787$	228728.	−	396169.i	0.369292	−	0.639633i	−0.620163	−	0.784473i	$-0.712933\pi$
$787$	228728.	−	396169.i	0.369292	−	0.639633i	0.989455	+	0.144840i	$0.0462668\pi$
$788$	1.50842e6	+	870888.i	2.42924	+	1.40252i
$789$		0			0
$790$	−9187.01	−	15912.4i	−0.0147204	−	0.0254965i
$791$		−	239269.i		−	0.382414i
$792$		0			0
$793$	1120.41			0.00178169
$794$	−1.33765e6	+	772291.i	−2.12178	+	1.22501i
$795$		0			0
$796$	−348022.	+	602791.i	−0.549263	+	0.951351i
$797$	148023.	+	85461.0i	0.233030	+	0.134540i	0.611969	−	0.790882i	$-0.290378\pi$
$797$	148023.	+	85461.0i	0.233030	+	0.134540i	−0.378939	+	0.925422i	$0.623711\pi$
$798$		0			0
$799$	3084.09	+	5341.79i	0.00483095	+	0.00836746i
$800$		−	434575.i		−	0.679023i
$801$		0			0
$802$	−1.53465e6			−2.38594
$803$	−102769.	+	59333.5i	−0.159378	+	0.0920171i
$804$		0			0
$805$	−125528.	+	217422.i	−0.193709	+	0.335514i
$806$	−648699.	−	374526.i	−0.998557	−	0.576517i
$807$		0			0
$808$	396271.	+	686361.i	0.606973	+	1.05131i
$809$			252280.i			0.385465i	0.981251	+	0.192733i	$0.0617350\pi$
$809$			252280.i			0.385465i	−0.981251	+	0.192733i	$0.938265\pi$
$810$		0			0
$811$	166784.			0.253579			0.126789	−	0.991930i	$-0.459533\pi$
$811$	166784.			0.253579			0.126789	+	0.991930i	$0.459533\pi$
$812$	671856.	−	387896.i	1.01898	−	0.588307i
$813$		0			0
$814$	703865.	−	1.21913e6i	1.06228	−	1.83993i
$815$	21975.7	+	12687.7i	0.0330847	+	0.0191015i
$816$		0			0
$817$	−70580.7	−	122249.i	−0.105741	−	0.183148i
$818$		−	1.95124e6i		−	2.91611i
$819$		0			0
$820$	399780.			0.594557
$821$	235829.	−	136156.i	0.349873	−	0.201999i	−0.314756	−	0.949173i	$-0.601923\pi$
$821$	235829.	−	136156.i	0.349873	−	0.201999i	0.664629	+	0.747173i	$0.268589\pi$
$822$		0			0
$823$	−482314.	+	835392.i	−0.712082	+	1.23336i	0.251992	+	0.967729i	$0.418914\pi$
$823$	−482314.	+	835392.i	−0.712082	+	1.23336i	−0.964074	+	0.265633i	$0.914419\pi$
$824$	−221092.	−	127648.i	−0.325626	−	0.188000i
$825$		0			0
$826$	581759.	+	1.00764e6i	0.852674	+	1.47687i
$827$			430905.i			0.630043i	0.949085	+	0.315021i	$0.102012\pi$
$827$			430905.i			0.630043i	−0.949085	+	0.315021i	$0.897988\pi$
$828$		0			0
$829$	462870.			0.673520			0.336760	−	0.941591i	$-0.390669\pi$
$829$	462870.			0.673520			0.336760	+	0.941591i	$0.390669\pi$
$830$	−880328.	+	508257.i	−1.27787	+	0.737781i
$831$		0			0
$832$	241511.	−	418310.i	0.348892	−	0.604299i
$833$	−2917.80	−	1684.59i	−0.00420500	−	0.00242776i
$834$		0			0
$835$	−218104.	−	377768.i	−0.312818	−	0.541816i
$836$		−	182211.i		−	0.260713i
$837$		0			0
$838$	241618.			0.344066
$839$	696889.	−	402349.i	0.990010	−	0.571583i	0.0847327	−	0.996404i	$-0.472996\pi$
$839$	696889.	−	402349.i	0.990010	−	0.571583i	0.905277	+	0.424821i	$0.139663\pi$
$840$		0			0
$841$	−207488.	+	359379.i	−0.293360	+	0.508114i
$842$	−1.36537e6	−	788297.i	−1.92587	−	1.11190i
$843$		0			0
$844$	620301.	+	1.07439e6i	0.870799	+	1.50827i
$845$		−	270942.i		−	0.379457i
$846$		0			0
$847$	52037.6			0.0725354
$848$	141193.	−	81518.0i	0.196346	−	0.113360i
$849$		0			0
$850$	12280.2	−	21269.9i	0.0169968	−	0.0294393i
$851$	595447.	+	343781.i	0.822212	+	0.474704i
$852$		0			0
$853$	−105790.	−	183234.i	−0.145394	−	0.251830i	0.784126	−	0.620602i	$-0.213112\pi$
$853$	−105790.	−	183234.i	−0.145394	−	0.251830i	−0.929520	+	0.368772i	$0.879778\pi$
$854$			5241.94i			0.00718747i
$855$		0			0
$856$	−819191.			−1.11799
$857$	245348.	−	141652.i	0.334057	−	0.192868i	−0.323584	−	0.946199i	$-0.604888\pi$
$857$	245348.	−	141652.i	0.334057	−	0.192868i	0.657641	+	0.753332i	$0.271554\pi$
$858$		0			0
$859$	15498.6	−	26844.3i	0.0210042	−	0.0363803i	−0.855332	−	0.518080i	$-0.826647\pi$
$859$	15498.6	−	26844.3i	0.0210042	−	0.0363803i	0.876336	+	0.481700i	$0.159980\pi$
$860$	−716771.	−	413828.i	−0.969133	−	0.559529i
$861$		0			0
$862$	−533236.	−	923592.i	−0.717637	−	1.24298i
$863$			1.35611e6i			1.82085i	0.413677	+	0.910424i	$0.364244\pi$
$863$			1.35611e6i			1.82085i	−0.413677	+	0.910424i	$0.635756\pi$
$864$		0			0
$865$	−572482.			−0.765120
$866$	1.51307e6	−	873569.i	2.01754	−	1.16483i
$867$		0			0
$868$	1.09927e6	−	1.90399e6i	1.45903	−	2.52711i
$869$	−25756.2	−	14870.4i	−0.0341069	−	0.0196916i
$870$		0			0
$871$	193330.	+	334858.i	0.254838	+	0.441392i
$872$			342534.i			0.450475i
$873$		0			0
$874$	141860.			0.185711
$875$	−604045.	+	348746.i	−0.788957	+	0.455504i
$876$		0			0
$877$	226465.	−	392249.i	0.294443	−	0.509991i	−0.680412	−	0.732830i	$-0.738199\pi$
$877$	226465.	−	392249.i	0.294443	−	0.509991i	0.974855	+	0.222839i	$0.0715324\pi$
$878$	208926.	+	120623.i	0.271021	+	0.156474i
$879$		0			0
$880$	−28379.1	−	49154.0i	−0.0366465	−	0.0634736i
$881$			1.13788e6i			1.46603i	0.680211	+	0.733016i	$0.261888\pi$
$881$			1.13788e6i			1.46603i	−0.680211	+	0.733016i	$0.738112\pi$
$882$		0			0
$883$	970367.			1.24456			0.622279	−	0.782796i	$-0.286207\pi$
$883$	970367.			1.24456			0.622279	+	0.782796i	$0.286207\pi$
$884$	13418.4	−	7747.09i	0.0171710	−	0.00991367i
$885$		0			0
$886$	450629.	−	780512.i	0.574052	−	0.994287i
$887$	−1.12349e6	−	648647.i	−1.42798	−	0.824444i	−0.431017	−	0.902344i	$-0.641845\pi$
$887$	−1.12349e6	−	648647.i	−1.42798	−	0.824444i	−0.996961	+	0.0779001i	$0.975178\pi$
$888$		0			0
$889$	360159.	+	623814.i	0.455712	+	0.789317i
$890$		−	44466.1i		−	0.0561369i
$891$		0			0
$892$	−590181.			−0.741747
$893$	−37504.4	+	21653.2i	−0.0470305	+	0.0271531i
$894$		0			0
$895$	−281130.	+	486932.i	−0.350963	+	0.607886i
$896$	1.29725e6	+	748968.i	1.61588	+	0.932927i
$897$		0			0
$898$	−571395.	−	989685.i	−0.708572	−	1.22728i
$899$		−	828370.i		−	1.02496i
$900$		0			0
$901$	−32611.4			−0.0401716
$902$	893289.	−	515740.i	1.09794	−	0.633896i
$903$		0			0
$904$	−160912.	+	278707.i	−0.196902	+	0.341044i
$905$	467026.	+	269638.i	0.570222	+	0.329218i
$906$		0			0
$907$	−76984.1	−	133340.i	−0.0935807	−	0.162087i	0.815435	−	0.578849i	$-0.196498\pi$
$907$	−76984.1	−	133340.i	−0.0935807	−	0.162087i	−0.909015	+	0.416763i	$0.863165\pi$
$908$			1.34099e6i			1.62650i
$909$		0			0
$910$	−306880.			−0.370583
$911$	927466.	−	535473.i	1.11753	−	0.645209i	0.176764	−	0.984253i	$-0.443437\pi$
$911$	927466.	−	535473.i	1.11753	−	0.645209i	0.940770	+	0.339044i	$0.110104\pi$
$912$		0			0
$913$	−822680.	+	1.42492e6i	−0.986937	+	1.70942i
$914$	−654339.	−	377783.i	−0.783268	−	0.452220i
$915$		0			0
$916$	384110.	+	665298.i	0.457788	+	0.792912i
$917$		−	180966.i		−	0.215208i
$918$		0			0
$919$	747688.			0.885298			0.442649	−	0.896695i	$-0.354039\pi$
$919$	747688.			0.885298			0.442649	+	0.896695i	$0.354039\pi$
$920$	292438.	−	168839.i	0.345508	−	0.199479i
$921$		0			0
$922$	−1.32840e6	+	2.30085e6i	−1.56267	+	2.70662i
$923$	124328.	+	71781.1i	0.145938	+	0.0842571i
$924$		0			0
$925$	417881.	+	723790.i	0.488392	+	0.845920i
$926$			475625.i			0.554680i
$927$		0			0
$928$	483285.			0.561187
$929$	−1.28522e6	+	742020.i	−1.48917	+	0.859774i	−0.999923	−	0.0123702i	$-0.996062\pi$
$929$	−1.28522e6	+	742020.i	−1.48917	+	0.859774i	−0.489249	+	0.872144i	$0.662729\pi$
$930$		0			0
$931$	11827.4	−	20485.7i	0.0136456	−	0.0236348i
$932$	−1.02754e6	−	593253.i	−1.18296	−	0.682980i
$933$		0			0
$934$	−1.17554e6	−	2.03609e6i	−1.34754	−	2.33401i
$935$			11353.1i			0.0129865i
$936$		0			0
$937$	−650560.			−0.740983			−0.370491	−	0.928836i	$-0.620811\pi$
$937$	−650560.			−0.740983			−0.370491	+	0.928836i	$0.620811\pi$
$938$	−1.56666e6	+	904510.i	−1.78061	+	1.02803i
$939$		0			0
$940$	−126957.	+	219895.i	−0.143681	+	0.248863i
$941$	352436.	+	203479.i	0.398017	+	0.229795i	0.685628	−	0.727952i	$-0.259528\pi$
$941$	352436.	+	203479.i	0.398017	+	0.229795i	−0.287611	+	0.957747i	$0.592861\pi$
$942$		0			0
$943$	251898.	+	436300.i	0.283270	+	0.490638i
$944$		−	128476.i		−	0.144171i
$945$		0			0
$946$	−2.13545e6			−2.38620
$947$	−718809.	+	415005.i	−0.801519	+	0.462757i	−0.844002	−	0.536340i	$-0.819806\pi$
$947$	−718809.	+	415005.i	−0.801519	+	0.462757i	0.0424832	+	0.999097i	$0.486473\pi$
$948$		0			0
$949$	35423.3	−	61355.0i	0.0393330	−	0.0681267i
$950$	149335.	+	86218.5i	0.165468	+	0.0955330i
$951$		0			0
$952$	14715.0	+	25487.1i	0.0162363	+	0.0281221i
$953$		−	927863.i		−	1.02164i	−0.859688	−	0.510820i	$-0.829342\pi$
$953$		−	927863.i		−	1.02164i	0.859688	−	0.510820i	$-0.170658\pi$
$954$		0			0
$955$	550496.			0.603597
$956$	−479949.	+	277099.i	−0.525145	+	0.303193i
$957$		0			0
$958$	83870.5	−	145268.i	0.0913857	−	0.158285i
$959$	−176385.	−	101836.i	−0.191790	−	0.110730i
$960$		0			0
$961$	−712006.	−	1.23323e6i	−0.770968	−	1.33536i
$962$			840444.i			0.908152i
$963$		0			0
$964$	1.56002e6			1.67872
$965$	−277639.	+	160295.i	−0.298143	+	0.172133i
$966$		0			0
$967$	556238.	−	963433.i	0.594851	−	1.03031i	−0.398717	−	0.917074i	$-0.630544\pi$
$967$	556238.	−	963433.i	0.594851	−	1.03031i	0.993568	−	0.113238i	$-0.0361222\pi$
$968$	−60614.8	−	34995.9i	−0.0646886	−	0.0373480i
$969$		0			0
$970$	583825.	+	1.01121e6i	0.620496	+	1.07473i
$971$			68160.6i			0.0722927i	0.999347	+	0.0361464i	$0.0115083\pi$
$971$			68160.6i			0.0722927i	−0.999347	+	0.0361464i	$0.988492\pi$
$972$		0			0
$973$	−185210.			−0.195631
$974$	1.40312e6	−	810090.i	1.47903	−	0.853917i
$975$		0			0
$976$	289.408	−	501.270i	0.000303817	−	0.000526226i
$977$	685124.	+	395556.i	0.717761	+	0.414399i	0.813928	−	0.580966i	$-0.197325\pi$
$977$	685124.	+	395556.i	0.717761	+	0.414399i	−0.0961671	+	0.995365i	$0.530658\pi$
$978$		0			0
$979$	−35987.0	−	62331.4i	−0.0375475	−	0.0650341i
$980$		−	138693.i		−	0.144412i
$981$		0			0
$982$	2.24263e6			2.32560
$983$	948495.	−	547614.i	0.981585	−	0.566718i	0.0788368	−	0.996888i	$-0.474879\pi$
$983$	948495.	−	547614.i	0.981585	−	0.566718i	0.902748	+	0.430169i	$0.141546\pi$
$984$		0			0
$985$	380975.	−	659868.i	0.392667	−	0.680119i
$986$	23654.0	+	13656.6i	0.0243305	+	0.0140472i
$987$		0			0
$988$	54391.9	+	94209.5i	0.0557212	+	0.0965119i
$989$		−	1.04300e6i		−	1.06633i
$990$		0			0
$991$	278492.			0.283573			0.141787	−	0.989897i	$-0.454715\pi$
$991$	278492.			0.283573			0.141787	+	0.989897i	$0.454715\pi$
$992$	1.18610e6	−	684795.i	1.20531	−	0.695884i
$993$		0			0
$994$	−335833.	+	581680.i	−0.339900	+	0.588723i
$995$	263695.	+	152244.i	0.266351	+	0.153778i
$996$		0			0
$997$	−665723.	−	1.15307e6i	−0.669736	−	1.16002i	−0.977978	−	0.208708i	$-0.933074\pi$
$997$	−665723.	−	1.15307e6i	−0.669736	−	1.16002i	0.308242	−	0.951308i	$-0.400259\pi$
$998$		−	1.29633e6i		−	1.30154i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.5.d.a.17.3		6
3.2	odd	2		9.5.d.a.5.1	yes	6
4.3	odd	2		432.5.q.a.17.2		6
9.2	odd	6	inner	27.5.d.a.8.3		6
9.4	even	3		81.5.b.a.80.6		6
9.5	odd	6		81.5.b.a.80.1		6
9.7	even	3		9.5.d.a.2.1	✓	6
12.11	even	2		144.5.q.a.113.2		6
36.7	odd	6		144.5.q.a.65.2		6
36.11	even	6		432.5.q.a.305.2		6
36.23	even	6		1296.5.e.c.161.3		6
36.31	odd	6		1296.5.e.c.161.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.5.d.a.2.1	✓	6	9.7	even	3
9.5.d.a.5.1	yes	6	3.2	odd	2
27.5.d.a.8.3		6	9.2	odd	6	inner
27.5.d.a.17.3		6	1.1	even	1	trivial
81.5.b.a.80.1		6	9.5	odd	6
81.5.b.a.80.6		6	9.4	even	3
144.5.q.a.65.2		6	36.7	odd	6
144.5.q.a.113.2		6	12.11	even	2
432.5.q.a.17.2		6	4.3	odd	2
432.5.q.a.305.2		6	36.11	even	6
1296.5.e.c.161.3		6	36.23	even	6
1296.5.e.c.161.4		6	36.31	odd	6

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.67463 - 3.27625i) q^{2} +(13.4676 - 23.3266i) q^{4} +(-10.2044 - 5.89150i) q^{5} +(26.6364 + 46.1356i) q^{7} -71.6534i q^{8} +O(q^{10})\)	\(q+(5.67463 - 3.27625i) q^{2} +(13.4676 - 23.3266i) q^{4} +(-10.2044 - 5.89150i) q^{5} +(26.6364 + 46.1356i) q^{7} -71.6534i q^{8} -77.2081 q^{10} +(-108.228 + 62.4856i) q^{11} +(37.3052 - 64.6145i) q^{13} +(302.304 + 174.535i) q^{14} +(-19.2722 - 33.3805i) q^{16} +7.70989i q^{17} -54.1307 q^{19} +(-274.858 + 158.689i) q^{20} +(-409.437 + 709.166i) q^{22} +(-346.370 - 199.977i) q^{23} +(-243.080 - 421.028i) q^{25} -488.885i q^{26} +1434.92 q^{28} +(468.219 - 270.326i) q^{29} +(766.083 - 1326.89i) q^{31} +(774.133 + 446.946i) q^{32} +(25.2595 + 43.7508i) q^{34} -627.714i q^{35} -1719.10 q^{37} +(-307.172 + 177.346i) q^{38} +(-422.146 + 731.178i) q^{40} +(-1090.87 - 629.816i) q^{41} +(1303.89 + 2258.41i) q^{43} +3366.13i q^{44} -2620.70 q^{46} +(692.850 - 400.017i) q^{47} +(-218.498 + 378.449i) q^{49} +(-2758.78 - 1592.79i) q^{50} +(-1004.83 - 1740.41i) q^{52} +4229.81i q^{53} +1472.54 q^{55} +(3305.77 - 1908.59i) q^{56} +(1771.31 - 3068.01i) q^{58} +(2886.63 + 1666.60i) q^{59} +(7.50843 + 13.0050i) q^{61} -10039.5i q^{62} +6473.94 q^{64} +(-761.353 + 439.567i) q^{65} +(-2591.20 + 4488.08i) q^{67} +(179.846 + 103.834i) q^{68} +(-2056.55 - 3562.05i) q^{70} +1924.16i q^{71} +949.554 q^{73} +(-9755.28 + 5632.21i) q^{74} +(-729.012 + 1262.69i) q^{76} +(-5765.63 - 3328.79i) q^{77} +(118.990 + 206.097i) q^{79} +454.169i q^{80} -8253.75 q^{82} +(11402.0 - 6582.95i) q^{83} +(45.4228 - 78.6746i) q^{85} +(14798.2 + 8543.77i) q^{86} +(4477.31 + 7754.92i) q^{88} +575.925i q^{89} +3974.71 q^{91} +(-9329.58 + 5386.44i) q^{92} +(2621.11 - 4539.90i) q^{94} +(552.370 + 318.911i) q^{95} +(-7561.70 - 13097.3i) q^{97} +2863.41i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7	\( 6 q + 3 q^{2} + 15 q^{4} + 12 q^{5} + 12 q^{7} - 36 q^{10} - 483 q^{11} - 6 q^{13} + 1146 q^{14} + 15 q^{16} - 258 q^{19} - 1614 q^{20} - 369 q^{22} + 282 q^{23} - 273 q^{25} + 1308 q^{28} + 1056 q^{29} + 1290 q^{31} + 1161 q^{32} + 513 q^{34} + 12 q^{37} + 789 q^{38} - 1314 q^{40} - 7629 q^{41} - 285 q^{43} - 5760 q^{46} + 9642 q^{47} - 1863 q^{49} - 3027 q^{50} - 240 q^{52} + 2016 q^{55} + 462 q^{56} + 6462 q^{58} - 6225 q^{59} + 3630 q^{61} + 15450 q^{64} + 7158 q^{65} - 5055 q^{67} + 10503 q^{68} - 9684 q^{70} - 14622 q^{73} - 26454 q^{74} - 4047 q^{76} - 2580 q^{77} + 4764 q^{79} - 9702 q^{82} + 1866 q^{83} + 12366 q^{85} + 37731 q^{86} + 14787 q^{88} + 34836 q^{91} - 33636 q^{92} - 12708 q^{94} + 13362 q^{95} - 28959 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7 - 36 * q^10 - 483 * q^11 - 6 * q^13 + 1146 * q^14 + 15 * q^16 - 258 * q^19 - 1614 * q^20 - 369 * q^22 + 282 * q^23 - 273 * q^25 + 1308 * q^28 + 1056 * q^29 + 1290 * q^31 + 1161 * q^32 + 513 * q^34 + 12 * q^37 + 789 * q^38 - 1314 * q^40 - 7629 * q^41 - 285 * q^43 - 5760 * q^46 + 9642 * q^47 - 1863 * q^49 - 3027 * q^50 - 240 * q^52 + 2016 * q^55 + 462 * q^56 + 6462 * q^58 - 6225 * q^59 + 3630 * q^61 + 15450 * q^64 + 7158 * q^65 - 5055 * q^67 + 10503 * q^68 - 9684 * q^70 - 14622 * q^73 - 26454 * q^74 - 4047 * q^76 - 2580 * q^77 + 4764 * q^79 - 9702 * q^82 + 1866 * q^83 + 12366 * q^85 + 37731 * q^86 + 14787 * q^88 + 34836 * q^91 - 33636 * q^92 - 12708 * q^94 + 13362 * q^95 - 28959 * q^97

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