LMFDB - Embedded newform 171.5.p.a.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,5,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("171.46");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, degree $2$, 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:	$17.6762636873$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 $ x^10 + 109x^8 + 4107x^6 + 61507x^4 + 300520x^2 + 108300
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			46.3
Root			$0.625165i$ of defining polynomial
Character	$\chi$	$=$	171.46
Dual form			171.5.p.a.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.541408 + 0.312582i) q^{2} +(-7.80458 - 13.5179i) q^{4} +(-4.61985 + 8.00181i) q^{5} +0.274467 q^{7} -19.7609i q^{8} +O(q^{10})$	\(q+(0.541408 + 0.312582i) q^{2} +(-7.80458 - 13.5179i) q^{4} +(-4.61985 + 8.00181i) q^{5} +0.274467 q^{7} -19.7609i q^{8} +(-5.00245 + 2.88816i) q^{10} -45.5269 q^{11} +(111.271 - 64.2421i) q^{13} +(0.148599 + 0.0857934i) q^{14} +(-118.696 + 205.588i) q^{16} +(-212.040 + 367.264i) q^{17} +(-280.252 - 227.552i) q^{19} +144.224 q^{20} +(-24.6486 - 14.2309i) q^{22} +(286.876 + 496.884i) q^{23} +(269.814 + 467.332i) q^{25} +80.3238 q^{26} +(-2.14210 - 3.71022i) q^{28} +(-763.678 + 440.909i) q^{29} +1531.33i q^{31} +(-402.342 + 232.292i) q^{32} +(-229.600 + 132.560i) q^{34} +(-1.26799 + 2.19623i) q^{35} -71.9344i q^{37} +(-80.6022 - 210.800i) q^{38} +(158.123 + 91.2925i) q^{40} +(-1112.58 - 642.350i) q^{41} +(603.976 - 1046.12i) q^{43} +(355.318 + 615.429i) q^{44} +358.690i q^{46} +(1347.59 + 2334.09i) q^{47} -2400.92 q^{49} +337.356i q^{50} +(-1736.84 - 1002.77i) q^{52} +(-1834.78 + 1059.31i) q^{53} +(210.327 - 364.297i) q^{55} -5.42372i q^{56} -551.282 q^{58} +(-4850.33 - 2800.34i) q^{59} +(1240.48 + 2148.57i) q^{61} +(-478.666 + 829.075i) q^{62} +3507.84 q^{64} +1187.16i q^{65} +(-656.457 + 379.006i) q^{67} +6619.53 q^{68} +(-1.37300 + 0.792705i) q^{70} +(5268.29 + 3041.65i) q^{71} +(3512.83 - 6084.39i) q^{73} +(22.4854 - 38.9459i) q^{74} +(-888.778 + 5564.38i) q^{76} -12.4956 q^{77} +(-2796.99 - 1614.84i) q^{79} +(-1096.72 - 1899.57i) q^{80} +(-401.574 - 695.547i) q^{82} -5586.78 q^{83} +(-1959.18 - 3393.40i) q^{85} +(653.995 - 377.584i) q^{86} +899.653i q^{88} +(4918.49 - 2839.69i) q^{89} +(30.5401 - 17.6323i) q^{91} +(4477.90 - 7755.95i) q^{92} +1684.93i q^{94} +(3115.55 - 1191.27i) q^{95} +(10277.2 + 5933.52i) q^{97} +(-1299.88 - 750.487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} + 29 q^{4} - 8 q^{5} - 24 q^{7}+O(q^{10}) $ 10 * q + 3 * q^2 + 29 * q^4 - 8 * q^5 - 24 * q^7	$ 10 q + 3 q^{2} + 29 q^{4} - 8 q^{5} - 24 q^{7} + 144 q^{10} - 50 q^{11} - 624 q^{13} + 474 q^{14} + 285 q^{16} + 292 q^{17} + 305 q^{19} + 652 q^{20} + 1629 q^{22} - 98 q^{23} - 681 q^{25} - 1524 q^{26} - 1472 q^{28} - 2598 q^{29} + 2745 q^{32} + 486 q^{34} - 694 q^{35} + 342 q^{38} + 8784 q^{40} + 1407 q^{41} + 5424 q^{43} - 4151 q^{44} + 2416 q^{47} - 17826 q^{49} - 19962 q^{52} - 1122 q^{53} + 11424 q^{55} - 20236 q^{58} - 15387 q^{59} + 860 q^{61} - 21636 q^{62} + 19710 q^{64} + 14763 q^{67} + 48844 q^{68} - 20334 q^{70} + 27264 q^{71} + 1561 q^{73} - 17094 q^{74} + 1955 q^{76} + 18392 q^{77} + 24750 q^{79} + 2002 q^{80} + 14479 q^{82} - 6002 q^{83} - 14944 q^{85} - 59946 q^{86} + 22566 q^{89} + 8724 q^{91} - 9572 q^{92} + 7312 q^{95} + 46287 q^{97} - 25515 q^{98}+O(q^{100}) $ 10 * q + 3 * q^2 + 29 * q^4 - 8 * q^5 - 24 * q^7 + 144 * q^10 - 50 * q^11 - 624 * q^13 + 474 * q^14 + 285 * q^16 + 292 * q^17 + 305 * q^19 + 652 * q^20 + 1629 * q^22 - 98 * q^23 - 681 * q^25 - 1524 * q^26 - 1472 * q^28 - 2598 * q^29 + 2745 * q^32 + 486 * q^34 - 694 * q^35 + 342 * q^38 + 8784 * q^40 + 1407 * q^41 + 5424 * q^43 - 4151 * q^44 + 2416 * q^47 - 17826 * q^49 - 19962 * q^52 - 1122 * q^53 + 11424 * q^55 - 20236 * q^58 - 15387 * q^59 + 860 * q^61 - 21636 * q^62 + 19710 * q^64 + 14763 * q^67 + 48844 * q^68 - 20334 * q^70 + 27264 * q^71 + 1561 * q^73 - 17094 * q^74 + 1955 * q^76 + 18392 * q^77 + 24750 * q^79 + 2002 * q^80 + 14479 * q^82 - 6002 * q^83 - 14944 * q^85 - 59946 * q^86 + 22566 * q^89 + 8724 * q^91 - 9572 * q^92 + 7312 * q^95 + 46287 * q^97 - 25515 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.541408	+	0.312582i	0.135352	+	0.0781456i	0.566147	−	0.824304i	$-0.308433\pi$
$2$	0.541408	+	0.312582i	0.135352	+	0.0781456i	−0.430795	+	0.902450i	$0.641767\pi$
$3$		0			0
$3$		0			0
$4$	−7.80458	−	13.5179i	−0.487787	−	0.844871i
$5$	−4.61985	+	8.00181i	−0.184794	+	0.320072i	−0.943507	−	0.331353i	$-0.892495\pi$
$5$	−4.61985	+	8.00181i	−0.184794	+	0.320072i	0.758713	+	0.651425i	$0.225828\pi$
$6$		0			0
$7$	0.274467			0.00560136			0.00280068	−	0.999996i	$-0.499109\pi$
$7$	0.274467			0.00560136			0.00280068	+	0.999996i	$0.499109\pi$
$8$		−	19.7609i		−	0.308765i
$9$		0			0
$10$	−5.00245	+	2.88816i	−0.0500245	+	0.0288816i
$11$	−45.5269			−0.376255			−0.188128	−	0.982145i	$-0.560242\pi$
$11$	−45.5269			−0.376255			−0.188128	+	0.982145i	$0.560242\pi$
$12$		0			0
$13$	111.271	−	64.2421i	0.658406	−	0.380131i	−0.133263	−	0.991081i	$-0.542546\pi$
$13$	111.271	−	64.2421i	0.658406	−	0.380131i	0.791669	+	0.610950i	$0.209212\pi$
$14$	0.148599	+	0.0857934i	0.000758156	+	0.000437722i
$15$		0			0
$16$	−118.696	+	205.588i	−0.463658	+	0.803079i
$17$	−212.040	+	367.264i	−0.733702	+	1.27081i	0.221589	+	0.975140i	$0.428876\pi$
$17$	−212.040	+	367.264i	−0.733702	+	1.27081i	−0.955291	+	0.295669i	$0.904458\pi$
$18$		0			0
$19$	−280.252	−	227.552i	−0.776322	−	0.630337i
$19$	−280.252	−	227.552i	−0.776322	−	0.630337i
$20$	144.224			0.360560
$21$		0			0
$22$	−24.6486	−	14.2309i	−0.0509269	−	0.0294027i
$23$	286.876	+	496.884i	0.542299	+	0.939289i	0.998772	+	0.0495518i	$0.0157793\pi$
$23$	286.876	+	496.884i	0.542299	+	0.939289i	−0.456473	+	0.889737i	$0.650887\pi$
$24$		0			0
$25$	269.814	+	467.332i	0.431702	+	0.747731i
$26$	80.3238			0.118822
$27$		0			0
$28$	−2.14210	−	3.71022i	−0.00273227	−	0.00473243i
$29$	−763.678	+	440.909i	−0.908059	+	0.524268i	−0.879806	−	0.475333i	$-0.842328\pi$
$29$	−763.678	+	440.909i	−0.908059	+	0.524268i	−0.0282529	+	0.999601i	$0.508994\pi$
$30$		0			0
$31$			1531.33i			1.59348i	0.604326	+	0.796738i	$0.293443\pi$
$31$			1531.33i			1.59348i	−0.604326	+	0.796738i	$0.706557\pi$
$32$	−402.342	+	232.292i	−0.392912	+	0.226848i
$33$		0			0
$34$	−229.600	+	132.560i	−0.198616	+	0.114671i
$35$	−1.26799	+	2.19623i	−0.00103510	+	0.00179284i
$36$		0			0
$37$		−	71.9344i		−	0.0525452i	−0.999655	−	0.0262726i	$-0.991636\pi$
$37$		−	71.9344i		−	0.0525452i	0.999655	−	0.0262726i	$-0.00836380\pi$
$38$	−80.6022	−	210.800i	−0.0558187	−	0.145984i
$39$		0			0
$40$	158.123	+	91.2925i	0.0988270	+	0.0570578i
$41$	−1112.58	−	642.350i	−0.661857	−	0.382123i	0.131127	−	0.991366i	$-0.458140\pi$
$41$	−1112.58	−	642.350i	−0.661857	−	0.382123i	−0.792984	+	0.609242i	$0.791474\pi$
$42$		0			0
$43$	603.976	−	1046.12i	0.326650	−	0.565775i	−0.655195	−	0.755460i	$-0.727413\pi$
$43$	603.976	−	1046.12i	0.326650	−	0.565775i	0.981845	+	0.189685i	$0.0607468\pi$
$44$	355.318	+	615.429i	0.183532	+	0.317887i
$45$		0			0
$46$			358.690i			0.169513i
$47$	1347.59	+	2334.09i	0.610045	+	1.05663i	0.991232	+	0.132131i	$0.0421819\pi$
$47$	1347.59	+	2334.09i	0.610045	+	1.05663i	−0.381187	+	0.924498i	$0.624485\pi$
$48$		0			0
$49$	−2400.92			−0.999969
$50$			337.356i			0.134943i
$51$		0			0
$52$	−1736.84	−	1002.77i	−0.642323	−	0.370846i
$53$	−1834.78	+	1059.31i	−0.653177	+	0.377112i	−0.789673	−	0.613529i	$-0.789750\pi$
$53$	−1834.78	+	1059.31i	−0.653177	+	0.377112i	0.136495	+	0.990641i	$0.456416\pi$
$54$		0			0
$55$	210.327	−	364.297i	0.0695296	−	0.120429i
$56$		−	5.42372i		−	0.00172950i
$57$		0			0
$58$	−551.282			−0.163877
$59$	−4850.33	−	2800.34i	−1.39337	−	0.804465i	−0.399686	−	0.916652i	$-0.630881\pi$
$59$	−4850.33	−	2800.34i	−1.39337	−	0.804465i	−0.993687	+	0.112187i	$0.964214\pi$
$60$		0			0
$61$	1240.48	+	2148.57i	0.333372	+	0.577417i	0.983171	−	0.182689i	$-0.0584803\pi$
$61$	1240.48	+	2148.57i	0.333372	+	0.577417i	−0.649799	+	0.760106i	$0.725147\pi$
$62$	−478.666	+	829.075i	−0.124523	+	0.215680i
$63$		0			0
$64$	3507.84			0.856407
$65$			1187.16i			0.280983i
$66$		0			0
$67$	−656.457	+	379.006i	−0.146237	+	0.0844298i	−0.571333	−	0.820718i	$-0.693574\pi$
$67$	−656.457	+	379.006i	−0.146237	+	0.0844298i	0.425096	+	0.905148i	$0.360240\pi$
$68$	6619.53			1.43156
$69$		0			0
$70$	−1.37300	+	0.792705i	−0.000280205	+	0.000161776i
$71$	5268.29	+	3041.65i	1.04509	+	0.603381i	0.921270	−	0.388924i	$-0.127153\pi$
$71$	5268.29	+	3041.65i	1.04509	+	0.603381i	0.123817	+	0.992305i	$0.460486\pi$
$72$		0			0
$73$	3512.83	−	6084.39i	0.659191	−	1.14175i	−0.321635	−	0.946864i	$-0.604232\pi$
$73$	3512.83	−	6084.39i	0.659191	−	1.14175i	0.980826	−	0.194888i	$-0.0624343\pi$
$74$	22.4854	−	38.9459i	0.00410618	−	0.00711211i
$75$		0			0
$76$	−888.778	+	5564.38i	−0.153874	+	0.963362i
$77$	−12.4956			−0.00210754
$78$		0			0
$79$	−2796.99	−	1614.84i	−0.448164	−	0.258747i	0.258891	−	0.965907i	$-0.416643\pi$
$79$	−2796.99	−	1614.84i	−0.448164	−	0.258747i	−0.707054	+	0.707159i	$0.749976\pi$
$80$	−1096.72	−	1899.57i	−0.171362	−	0.296808i
$81$		0			0
$82$	−401.574	−	695.547i	−0.0597225	−	0.103442i
$83$	−5586.78			−0.810971			−0.405485	−	0.914102i	$-0.632897\pi$
$83$	−5586.78			−0.810971			−0.405485	+	0.914102i	$0.632897\pi$
$84$		0			0
$85$	−1959.18	−	3393.40i	−0.271167	−	0.469675i
$86$	653.995	−	377.584i	0.0884256	−	0.0510525i
$87$		0			0
$88$			899.653i			0.116174i
$89$	4918.49	−	2839.69i	0.620943	−	0.358502i	−0.156293	−	0.987711i	$-0.549954\pi$
$89$	4918.49	−	2839.69i	0.620943	−	0.358502i	0.777236	+	0.629209i	$0.216621\pi$
$90$		0			0
$91$	30.5401	−	17.6323i	0.00368797	−	0.00212925i
$92$	4477.90	−	7755.95i	0.529052	−	0.916345i
$93$		0			0
$94$			1684.93i			0.190689i
$95$	3115.55	−	1191.27i	0.345213	−	0.131997i
$96$		0			0
$97$	10277.2	+	5933.52i	1.09227	+	0.630622i	0.934180	−	0.356803i	$-0.116133\pi$
$97$	10277.2	+	5933.52i	1.09227	+	0.630622i	0.158089	+	0.987425i	$0.449467\pi$
$98$	−1299.88	−	750.487i	−0.135348	−	0.0781431i
$99$		0			0
$100$	4211.57	−	7294.66i	0.421157	−	0.729466i
$101$	−7781.01	−	13477.1i	−0.762769	−	1.32116i	−0.941418	−	0.337242i	$-0.890506\pi$
$101$	−7781.01	−	13477.1i	−0.762769	−	1.32116i	0.178649	−	0.983913i	$-0.442827\pi$
$102$		0			0
$103$			1961.40i			0.184881i	0.995718	+	0.0924403i	$0.0294667\pi$
$103$			1961.40i			0.184881i	−0.995718	+	0.0924403i	$0.970533\pi$
$104$	−1269.48	−	2198.81i	−0.117371	−	0.203293i
$105$		0			0
$106$	−1324.48			−0.117879
$107$		−	18401.5i		−	1.60726i	−0.595128	−	0.803631i	$-0.702898\pi$
$107$		−	18401.5i		−	1.60726i	0.595128	−	0.803631i	$-0.297102\pi$
$108$		0			0
$109$	−6715.47	−	3877.18i	−0.565228	−	0.326334i	0.190013	−	0.981782i	$-0.439147\pi$
$109$	−6715.47	−	3877.18i	−0.565228	−	0.326334i	−0.755241	+	0.655447i	$0.772480\pi$
$110$	227.746	−	131.489i	0.0188220	−	0.0108669i
$111$		0			0
$112$	−32.5782	+	56.4271i	−0.00259712	+	0.00449834i
$113$			4465.17i			0.349688i	0.984596	+	0.174844i	$0.0559421\pi$
$113$			4465.17i			0.349688i	−0.984596	+	0.174844i	$0.944058\pi$
$114$		0			0
$115$	−5301.29			−0.400854
$116$	11920.4	+	6882.23i	0.885878	+	0.511462i
$117$		0			0
$118$	−1750.67	−	3032.26i	−0.125731	−	0.217772i
$119$	−58.1979	+	100.802i	−0.00410973	+	0.00711826i
$120$		0			0
$121$	−12568.3			−0.858432
$122$			1551.00i			0.104206i
$123$		0			0
$124$	20700.4	−	11951.4i	1.34628	−	0.777276i
$125$	−10760.8			−0.688691
$126$		0			0
$127$	−355.004	+	204.962i	−0.0220103	+	0.0127076i	−0.510965	−	0.859602i	$-0.670712\pi$
$127$	−355.004	+	204.962i	−0.0220103	+	0.0127076i	0.488954	+	0.872309i	$0.337378\pi$
$128$	8336.65	+	4813.17i	0.508829	+	0.293772i
$129$		0			0
$130$	−371.084	+	642.736i	−0.0219576	+	0.0380317i
$131$	1477.71	−	2559.46i	0.0861084	−	0.149144i	−0.819755	−	0.572715i	$-0.805890\pi$
$131$	1477.71	−	2559.46i	0.0861084	−	0.149144i	0.905863	+	0.423571i	$0.139224\pi$
$132$		0			0
$133$	−76.9199	−	62.4554i	−0.00434846	−	0.00353075i
$134$	−473.882			−0.0263913
$135$		0			0
$136$	7257.48	+	4190.11i	0.392381	+	0.226541i
$137$	13132.3	+	22745.8i	0.699679	+	1.21188i	0.968578	+	0.248711i	$0.0800070\pi$
$137$	13132.3	+	22745.8i	0.699679	+	1.21188i	−0.268899	+	0.963168i	$0.586660\pi$
$138$		0			0
$139$	−2168.28	−	3755.57i	−0.112224	−	0.194378i	0.804443	−	0.594030i	$-0.202464\pi$
$139$	−2168.28	−	3755.57i	−0.112224	−	0.194378i	−0.916667	+	0.399653i	$0.869131\pi$
$140$	39.5847			0.00201963
$141$		0			0
$142$	1901.53	+	3293.55i	0.0943032	+	0.163338i
$143$	−5065.80	+	2924.74i	−0.247729	+	0.143026i
$144$		0			0
$145$		−	8147.73i		−	0.387526i
$146$	3803.75	−	2196.09i	0.178446	−	0.103026i
$147$		0			0
$148$	−972.405	+	561.418i	−0.0443939	+	0.0256309i
$149$	1635.85	−	2833.37i	0.0736835	−	0.127623i	−0.826830	−	0.562453i	$-0.809858\pi$
$149$	1635.85	−	2833.37i	0.0736835	−	0.127623i	0.900513	+	0.434829i	$0.143191\pi$
$150$		0			0
$151$		−	3278.86i		−	0.143803i	−0.997412	−	0.0719016i	$-0.977093\pi$
$151$		−	3278.86i		−	0.143803i	0.997412	−	0.0719016i	$-0.0229068\pi$
$152$	−4496.63	+	5538.04i	−0.194626	+	0.239701i
$153$		0			0
$154$	−6.76523	−	3.90591i	−0.000285260	−	0.000164695i
$155$	−12253.4	−	7074.51i	−0.510027	−	0.294464i
$156$		0			0
$157$	−15632.5	+	27076.3i	−0.634204	+	1.09847i	0.352479	+	0.935820i	$0.385339\pi$
$157$	−15632.5	+	27076.3i	−0.634204	+	1.09847i	−0.986683	+	0.162654i	$0.947995\pi$
$158$	−1009.54	−	1748.58i	−0.0404399	−	0.0700440i
$159$		0			0
$160$		−	4292.62i		−	0.167680i
$161$	78.7379	+	136.378i	0.00303761	+	0.00526130i
$162$		0			0
$163$	32759.0			1.23298			0.616489	−	0.787363i	$-0.288554\pi$
$163$	32759.0			1.23298			0.616489	+	0.787363i	$0.288554\pi$
$164$			20053.1i			0.745579i
$165$		0			0
$166$	−3024.73	−	1746.33i	−0.109767	−	0.0633738i
$167$	−22419.2	+	12943.7i	−0.803872	+	0.464116i	−0.844823	−	0.535045i	$-0.820295\pi$
$167$	−22419.2	+	12943.7i	−0.803872	+	0.464116i	0.0409511	+	0.999161i	$0.486961\pi$
$168$		0			0
$169$	−6026.39	+	10438.0i	−0.211001	+	0.365464i
$170$		−	2449.62i		−	0.0847621i
$171$		0			0
$172$	−18855.1			−0.637342
$173$	3010.79	+	1738.28i	0.100598	+	0.0580802i	0.549455	−	0.835523i	$-0.314835\pi$
$173$	3010.79	+	1738.28i	0.100598	+	0.0580802i	−0.448857	+	0.893604i	$0.648169\pi$
$174$		0			0
$175$	74.0550	+	128.267i	0.00241812	+	0.00418831i
$176$	5403.88	−	9359.79i	0.174454	−	0.302163i
$177$		0			0
$178$	3550.55			0.112061
$179$			40116.5i			1.25204i	0.779809	+	0.626018i	$0.215316\pi$
$179$			40116.5i			1.25204i	−0.779809	+	0.626018i	$0.784684\pi$
$180$		0			0
$181$	−43406.5	+	25060.8i	−1.32494	+	0.764957i	−0.984513	−	0.175313i	$-0.943906\pi$
$181$	−43406.5	+	25060.8i	−1.32494	+	0.764957i	−0.340431	+	0.940269i	$0.610573\pi$
$182$	22.0462			0.000665566
$183$		0			0
$184$	9818.89	−	5668.94i	0.290019	−	0.167443i
$185$	575.605	+	332.326i	0.0168183	+	0.00971003i
$186$		0			0
$187$	9653.51	−	16720.4i	0.276059	−	0.478148i
$188$	21034.7	−	36433.2i	0.595143	−	1.03082i
$189$		0			0
$190$	2059.15	+	328.901i	0.0570402	+	0.00911083i
$191$	−65019.2			−1.78227			−0.891137	−	0.453734i	$-0.850092\pi$
$191$	−65019.2			−1.78227			−0.891137	+	0.453734i	$0.850092\pi$
$192$		0			0
$193$	−57399.9	−	33139.8i	−1.54098	−	0.889684i	−0.998777	−	0.0494353i	$-0.984258\pi$
$193$	−57399.9	−	33139.8i	−1.54098	−	0.889684i	−0.542201	−	0.840249i	$-0.682409\pi$
$194$	3709.43	+	6424.91i	0.0985606	+	0.170712i
$195$		0			0
$196$	18738.2	+	32455.5i	0.487771	+	0.844845i
$197$	−44015.7			−1.13416			−0.567081	−	0.823662i	$-0.691927\pi$
$197$	−44015.7			−1.13416			−0.567081	+	0.823662i	$0.691927\pi$
$198$		0			0
$199$	35353.3	+	61233.7i	0.892738	+	1.54627i	0.836580	+	0.547845i	$0.184552\pi$
$199$	35353.3	+	61233.7i	0.892738	+	1.54627i	0.0561582	+	0.998422i	$0.482115\pi$
$200$	9234.91	−	5331.78i	0.230873	−	0.133294i
$201$		0			0
$202$		−	9728.82i		−	0.238428i
$203$	−209.604	+	121.015i	−0.00508637	+	0.00293661i
$204$		0			0
$205$	10279.9	−	5935.11i	0.244614	−	0.141228i
$206$	−613.098	+	1061.92i	−0.0144476	+	0.0250240i
$207$		0			0
$208$			30501.3i			0.705003i
$209$	12759.0	+	10359.7i	0.292095	+	0.237168i
$210$		0			0
$211$	−15047.0	−	8687.41i	−0.337976	−	0.195131i	0.321400	−	0.946943i	$-0.395846\pi$
$211$	−15047.0	−	8687.41i	−0.337976	−	0.195131i	−0.659377	+	0.751813i	$0.729180\pi$
$212$	28639.3	+	16534.9i	0.637222	+	0.367900i
$213$		0			0
$214$	5752.00	−	9962.75i	0.125600	−	0.217546i
$215$	5580.55	+	9665.80i	0.120726	+	0.209103i
$216$		0			0
$217$			420.299i			0.00892563i
$218$	−2423.88	−	4198.27i	−0.0510032	−	0.0883401i
$219$		0			0
$220$	−6566.06			−0.135662
$221$			54487.6i			1.11561i
$222$		0			0
$223$	21863.6	+	12622.9i	0.439654	+	0.253835i	0.703451	−	0.710744i	$-0.251641\pi$
$223$	21863.6	+	12622.9i	0.439654	+	0.253835i	−0.263797	+	0.964578i	$0.584975\pi$
$224$	−110.429	+	63.7565i	−0.00220084	+	0.00127066i
$225$		0			0
$226$	−1395.73	+	2417.48i	−0.0273266	+	0.0473310i
$227$		−	916.210i		−	0.0177805i	−0.999960	−	0.00889024i	$-0.997170\pi$
$227$		−	916.210i		−	0.0177805i	0.999960	−	0.00889024i	$-0.00282989\pi$
$228$		0			0
$229$	−4664.33			−0.0889443			−0.0444721	−	0.999011i	$-0.514161\pi$
$229$	−4664.33			−0.0889443			−0.0444721	+	0.999011i	$0.514161\pi$
$230$	−2870.16	−	1657.09i	−0.0542564	−	0.0313250i
$231$		0			0
$232$	8712.78	+	15091.0i	0.161875	+	0.280376i
$233$	33186.8	−	57481.2i	0.611299	−	1.05880i	−0.379723	−	0.925100i	$-0.623981\pi$
$233$	33186.8	−	57481.2i	0.611299	−	1.05880i	0.991022	−	0.133701i	$-0.0426860\pi$
$234$		0			0
$235$	−24902.6			−0.450930
$236$			87422.0i			1.56963i
$237$		0			0
$238$	−63.0176	+	36.3833i	−0.00111252	+	0.000642314i
$239$	−32277.5			−0.565073			−0.282537	−	0.959257i	$-0.591176\pi$
$239$	−32277.5			−0.565073			−0.282537	+	0.959257i	$0.591176\pi$
$240$		0			0
$241$	71795.8	−	41451.3i	1.23613	−	0.713681i	0.267830	−	0.963466i	$-0.413693\pi$
$241$	71795.8	−	41451.3i	1.23613	−	0.713681i	0.968301	+	0.249785i	$0.0803600\pi$
$242$	−6804.59	−	3928.63i	−0.116191	−	0.0670827i
$243$		0			0
$244$	19362.8	−	33537.3i	0.325228	−	0.563312i
$245$	11091.9	−	19211.7i	0.184788	−	0.320062i
$246$		0			0
$247$	−45802.2	−	7315.83i	−0.750746	−	0.119914i
$248$	30260.5			0.492009
$249$		0			0
$250$	−5825.99	−	3363.64i	−0.0932158	−	0.0538182i
$251$	32836.9	+	56875.1i	0.521212	+	0.902766i	0.999696	+	0.0246692i	$0.00785326\pi$
$251$	32836.9	+	56875.1i	0.521212	+	0.902766i	−0.478484	+	0.878096i	$0.658813\pi$
$252$		0			0
$253$	−13060.6	−	22621.6i	−0.204043	−	0.353412i
$254$	−256.270			−0.00397219
$255$		0			0
$256$	−25053.7	−	43394.3i	−0.382290	−	0.662145i
$257$	7843.69	−	4528.55i	0.118756	−	0.0685635i	−0.439446	−	0.898269i	$-0.644825\pi$
$257$	7843.69	−	4528.55i	0.118756	−	0.0685635i	0.558201	+	0.829706i	$0.311492\pi$
$258$		0			0
$259$		−	19.7436i		−	0.000294325i
$260$	16047.9	−	9265.25i	0.237395	−	0.137060i
$261$		0			0
$262$	1600.08	−	923.809i	0.0233099	−	0.0134580i
$263$	46299.9	−	80193.7i	0.669373	−	1.15939i	−0.308707	−	0.951157i	$-0.599896\pi$
$263$	46299.9	−	80193.7i	0.669373	−	1.15939i	0.978080	−	0.208231i	$-0.0667705\pi$
$264$		0			0
$265$		−	19575.4i		−	0.278752i
$266$	−22.1226	−	57.8576i	−0.000312661	−	0.000817707i
$267$		0			0
$268$	10246.7	+	5915.96i	0.142665	+	0.0823675i
$269$	−43611.5	−	25179.1i	−0.602693	−	0.347965i	0.167407	−	0.985888i	$-0.446460\pi$
$269$	−43611.5	−	25179.1i	−0.602693	−	0.347965i	−0.770100	+	0.637923i	$0.779794\pi$
$270$		0			0
$271$	−3028.20	+	5245.00i	−0.0412331	+	0.0714179i	−0.885905	−	0.463866i	$-0.846462\pi$
$271$	−3028.20	+	5245.00i	−0.0412331	+	0.0714179i	0.844672	+	0.535284i	$0.179795\pi$
$272$	−50336.8	−	87185.8i	−0.680373	−	1.17844i
$273$		0			0
$274$			16419.7i			0.218707i
$275$	−12283.8	−	21276.1i	−0.162430	−	0.281337i
$276$		0			0
$277$	94487.4			1.23144			0.615721	−	0.787964i	$-0.288865\pi$
$277$	94487.4			1.23144			0.615721	+	0.787964i	$0.288865\pi$
$278$		−	2711.06i		−	0.0350792i
$279$		0			0
$280$	43.3995	+	25.0567i	0.000553566	+	0.000319601i
$281$	−25206.5	+	14553.0i	−0.319227	+	0.184306i	−0.651048	−	0.759036i	$-0.725670\pi$
$281$	−25206.5	+	14553.0i	−0.319227	+	0.184306i	0.331821	+	0.943342i	$0.392337\pi$
$282$		0			0
$283$	−34326.4	+	59455.1i	−0.428603	+	0.742363i	−0.996749	−	0.0805650i	$-0.974328\pi$
$283$	−34326.4	+	59455.1i	−0.428603	+	0.742363i	0.568146	+	0.822928i	$0.307661\pi$
$284$		−	94955.1i		−	1.17729i
$285$		0			0
$286$	−3656.89			−0.0447075
$287$	−305.367	−	176.304i	−0.00370730	−	0.00214041i
$288$		0			0
$289$	−48161.3	−	83417.8i	−0.576637	−	0.998765i
$290$	2546.84	−	4411.25i	0.0302834	−	0.0524525i
$291$		0			0
$292$	−109665.			−1.28618
$293$		−	155003.i		−	1.80553i	−0.430132	−	0.902766i	$-0.641533\pi$
$293$		−	155003.i		−	1.80553i	0.430132	−	0.902766i	$-0.358467\pi$
$294$		0			0
$295$	44815.6	−	25874.3i	0.514974	−	0.297320i
$296$	−1421.49			−0.0162241
$297$		0			0
$298$	1771.32	−	1022.67i	0.0199464	−	0.0115161i
$299$	63841.8	+	36859.1i	0.714106	+	0.412289i
$300$		0			0
$301$	165.771	−	287.124i	0.00182969	−	0.00316911i
$302$	1024.91	−	1775.20i	0.0112376	−	0.0194641i
$303$		0			0
$304$	80046.9	−	30607.0i	0.866158	−	0.331187i
$305$	−22923.2			−0.246420
$306$		0			0
$307$	86829.3	+	50130.9i	0.921275	+	0.531899i	0.884042	−	0.467408i	$-0.154812\pi$
$307$	86829.3	+	50130.9i	0.921275	+	0.531899i	0.0372337	+	0.999307i	$0.488145\pi$
$308$	97.5230	+	168.915i	0.00102803	+	0.00178060i
$309$		0			0
$310$	−4422.73	−	7660.39i	−0.0460222	−	0.0797127i
$311$	43558.3			0.450350			0.225175	−	0.974318i	$-0.427705\pi$
$311$	43558.3			0.450350			0.225175	+	0.974318i	$0.427705\pi$
$312$		0			0
$313$	−33606.5	−	58208.2i	−0.343032	−	0.594149i	0.641962	−	0.766736i	$-0.278121\pi$
$313$	−33606.5	−	58208.2i	−0.343032	−	0.594149i	−0.984994	+	0.172587i	$0.944787\pi$
$314$	−16927.1	+	9772.88i	−0.171682	+	0.0991205i
$315$		0			0
$316$			50412.7i			0.504854i
$317$	20383.1	−	11768.2i	0.202839	−	0.117109i	−0.395140	−	0.918621i	$-0.629304\pi$
$317$	20383.1	−	11768.2i	0.202839	−	0.117109i	0.597979	+	0.801512i	$0.295971\pi$
$318$		0			0
$319$	34767.8	−	20073.2i	0.341662	−	0.197259i
$320$	−16205.7	+	28069.1i	−0.158259	+	0.274112i
$321$		0			0
$322$			98.4483i			0.000949504i
$323$	142996.	−	54676.4i	1.37063	−	0.524077i
$324$		0			0
$325$	60044.8	+	34666.9i	0.568471	+	0.328207i
$326$	17736.0	+	10239.9i	0.166886	+	0.0963518i
$327$		0			0
$328$	−12693.4	+	21985.7i	−0.117986	+	0.204358i
$329$	369.868	+	640.631i	0.00341708	+	0.00591856i
$330$		0			0
$331$		−	23677.2i		−	0.216110i	−0.994145	−	0.108055i	$-0.965538\pi$
$331$		−	23677.2i		−	0.216110i	0.994145	−	0.108055i	$-0.0344622\pi$
$332$	43602.5	+	75521.7i	0.395581	+	0.685166i
$333$		0			0
$334$	−16183.9			−0.145074
$335$		−	7003.79i		−	0.0624085i
$336$		0			0
$337$	−135878.	−	78449.2i	−1.19644	−	0.690763i	−0.236677	−	0.971588i	$-0.576058\pi$
$337$	−135878.	−	78449.2i	−1.19644	−	0.690763i	−0.959759	+	0.280825i	$0.909392\pi$
$338$	−6525.48	+	3767.49i	−0.0571188	+	0.0329776i
$339$		0			0
$340$	−30581.2	+	52968.2i	−0.264543	+	0.458203i
$341$		−	69716.6i		−	0.599553i
$342$		0			0
$343$	−1317.97			−0.0112025
$344$	−20672.3	−	11935.1i	−0.174691	−	0.100858i
$345$		0			0
$346$	1086.71	+	1882.24i	0.00907742	+	0.0157225i
$347$	−102854.	+	178148.i	−0.854204	+	1.47953i	0.0231772	+	0.999731i	$0.492622\pi$
$347$	−102854.	+	178148.i	−0.854204	+	1.47953i	−0.877381	+	0.479794i	$0.840712\pi$
$348$		0			0
$349$	147121.			1.20788			0.603939	−	0.797031i	$-0.293597\pi$
$349$	147121.			1.20788			0.603939	+	0.797031i	$0.293597\pi$
$350$			92.5931i			0.000755862i
$351$		0			0
$352$	18317.4	−	10575.5i	0.147835	−	0.0853527i
$353$	75142.1			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$353$	75142.1			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$354$		0			0
$355$	−48677.3	+	28103.9i	−0.386251	+	0.223002i
$356$	−76773.5	−	44325.2i	−0.605775	−	0.349745i
$357$		0			0
$358$	−12539.7	+	21719.4i	−0.0978410	+	0.169466i
$359$	−9387.33	+	16259.3i	−0.0728372	+	0.126158i	−0.900144	−	0.435593i	$-0.856539\pi$
$359$	−9387.33	+	16259.3i	−0.0728372	+	0.126158i	0.827307	+	0.561751i	$0.189872\pi$
$360$		0			0
$361$	26761.5	+	127544.i	0.205350	+	0.978688i
$362$	−31334.2			−0.239112
$363$		0			0
$364$	−476.705	−	275.226i	−0.00359789	−	0.00207724i
$365$	32457.4	+	56217.9i	0.243629	+	0.421977i
$366$		0			0
$367$	22404.8	+	38806.3i	0.166345	+	0.288118i	0.937132	−	0.348975i	$-0.113470\pi$
$367$	22404.8	+	38806.3i	0.166345	+	0.288118i	−0.770787	+	0.637093i	$0.780137\pi$
$368$	−136205.			−1.00576
$369$		0			0
$370$	207.758	+	359.848i	0.00151759	+	0.00262855i
$371$	−503.585	+	290.745i	−0.00365868	+	0.00211234i
$372$		0			0
$373$			163639.i			1.17617i	0.808799	+	0.588085i	$0.200118\pi$
$373$			163639.i			1.17617i	−0.808799	+	0.588085i	$0.799882\pi$
$374$	10453.0	−	6035.03i	0.0747304	−	0.0431456i
$375$		0			0
$376$	46123.8	−	26629.6i	0.326249	−	0.188360i
$377$	−56649.9	+	98120.6i	−0.398581	+	0.690363i
$378$		0			0
$379$		−	132155.i		−	0.920039i	−0.887909	−	0.460019i	$-0.847842\pi$
$379$		−	132155.i		−	0.920039i	0.887909	−	0.460019i	$-0.152158\pi$
$380$	−40419.1	−	32818.4i	−0.279910	−	0.227274i
$381$		0			0
$382$	−35201.9	−	20323.8i	−0.241235	−	0.139277i
$383$	200322.	+	115656.i	1.36562	+	0.788442i	0.990365	−	0.138479i	$-0.0442214\pi$
$383$	200322.	+	115656.i	1.36562	+	0.788442i	0.375256	+	0.926921i	$0.377555\pi$
$384$		0			0
$385$	57.7278	−	99.9875i	0.000389461	−	0.000674565i
$386$	−20717.9	−	35884.4i	−0.139050	−	0.240841i
$387$		0			0
$388$		−	185235.i		−	1.23043i
$389$	826.840	+	1432.13i	0.00546414	+	0.00946418i	0.868745	−	0.495260i	$-0.164927\pi$
$389$	826.840	+	1432.13i	0.00546414	+	0.00946418i	−0.863280	+	0.504725i	$0.831594\pi$
$390$		0			0
$391$	−243317.			−1.59154
$392$			47444.5i			0.308755i
$393$		0			0
$394$	−23830.5	−	13758.5i	−0.153511	−	0.0886297i
$395$	25843.3	−	14920.6i	0.165636	−	0.0956299i
$396$		0			0
$397$	102128.	−	176890.i	0.647981	−	1.12234i	−0.335623	−	0.941996i	$-0.608947\pi$
$397$	102128.	−	176890.i	0.647981	−	1.12234i	0.983604	−	0.180340i	$-0.0577198\pi$
$398$			44203.3i			0.279054i
$399$		0			0
$400$	−128104.			−0.800649
$401$	−56182.7	−	32437.1i	−0.349393	−	0.201722i	0.315025	−	0.949083i	$-0.397987\pi$
$401$	−56182.7	−	32437.1i	−0.349393	−	0.201722i	−0.664418	+	0.747361i	$0.731320\pi$
$402$		0			0
$403$	98375.9	+	170392.i	0.605729	+	1.04915i
$404$	−121455.	+	210366.i	−0.744137	+	1.28888i
$405$		0			0
$406$	−151.309			−0.000917934
$407$			3274.95i			0.0197704i
$408$		0			0
$409$	−219413.	+	126678.i	−1.31164	+	0.757276i	−0.982368	−	0.186958i	$-0.940137\pi$
$409$	−219413.	+	126678.i	−1.31164	+	0.757276i	−0.329273	+	0.944235i	$0.606804\pi$
$410$	7420.84			0.0441454
$411$		0			0
$412$	26514.1	−	15307.9i	0.156200	−	0.0901823i
$413$	−1331.25	−	768.600i	−0.00780479	−	0.00450610i
$414$		0			0
$415$	25810.0	−	44704.3i	0.149862	−	0.259569i
$416$	−29845.9	+	51694.6i	−0.172464	+	0.298716i
$417$		0			0
$418$	3669.57	+	9597.07i	0.0210021	+	0.0549271i
$419$	46712.5			0.266076			0.133038	−	0.991111i	$-0.457527\pi$
$419$	46712.5			0.266076			0.133038	+	0.991111i	$0.457527\pi$
$420$		0			0
$421$	19528.3	+	11274.7i	0.110179	+	0.0636121i	0.554077	−	0.832465i	$-0.313071\pi$
$421$	19528.3	+	11274.7i	0.110179	+	0.0636121i	−0.443898	+	0.896078i	$0.646405\pi$
$422$	−5431.06	−	9406.88i	−0.0304972	−	0.0528227i
$423$		0			0
$424$	20932.9	+	36256.9i	0.116439	+	0.201678i
$425$	−228845.			−1.26696
$426$		0			0
$427$	340.469	+	589.710i	0.00186733	+	0.00323432i
$428$	−248751.	+	143616.i	−1.35793	+	0.784001i
$429$		0			0
$430$			6977.53i			0.0377368i
$431$	215793.	−	124588.i	1.16167	−	0.670690i	0.209966	−	0.977709i	$-0.432665\pi$
$431$	215793.	−	124588.i	1.16167	−	0.670690i	0.951704	+	0.307018i	$0.0993313\pi$
$432$		0			0
$433$	38427.2	−	22186.0i	0.204957	−	0.118332i	−0.394008	−	0.919107i	$-0.628912\pi$
$433$	38427.2	−	22186.0i	0.204957	−	0.118332i	0.598966	+	0.800775i	$0.295579\pi$
$434$	−131.378	+	227.553i	−0.000697498	+	0.00120810i
$435$		0			0
$436$			121039.i			0.636726i
$437$	32669.1	−	204532.i	0.171070	−	1.07102i
$438$		0			0
$439$	211594.	+	122164.i	1.09793	+	0.633888i	0.935676	−	0.352861i	$-0.114791\pi$
$439$	211594.	+	122164.i	1.09793	+	0.633888i	0.162251	+	0.986749i	$0.448125\pi$
$440$	−7198.85	−	4156.26i	−0.0371842	−	0.0214683i
$441$		0			0
$442$	−17031.9	+	29500.0i	−0.0871801	+	0.151000i
$443$	29784.6	+	51588.5i	0.151770	+	0.262873i	0.931878	−	0.362772i	$-0.118169\pi$
$443$	29784.6	+	51588.5i	0.151770	+	0.262873i	−0.780108	+	0.625644i	$0.784836\pi$
$444$		0			0
$445$			52475.7i			0.264996i
$446$	7891.41	+	13668.3i	0.0396721	+	0.0687141i
$447$		0			0
$448$	962.786			0.00479705
$449$			181264.i			0.899122i	0.893250	+	0.449561i	$0.148420\pi$
$449$			181264.i			0.899122i	−0.893250	+	0.449561i	$0.851580\pi$
$450$		0			0
$451$	50652.4	+	29244.2i	0.249027	+	0.143776i
$452$	60359.9	−	34848.8i	0.295441	−	0.170573i
$453$		0			0
$454$	286.391	−	496.044i	0.00138947	−	0.00240662i
$455$			325.835i			0.00157389i
$456$		0			0
$457$	−51325.5			−0.245754			−0.122877	−	0.992422i	$-0.539212\pi$
$457$	−51325.5			−0.245754			−0.122877	+	0.992422i	$0.539212\pi$
$458$	−2525.31	−	1457.99i	−0.0120388	−	0.00695060i
$459$		0			0
$460$	41374.4	+	71662.6i	0.195531	+	0.338670i
$461$	66811.0	−	115720.i	0.314373	−	0.544511i	−0.664931	−	0.746905i	$-0.731539\pi$
$461$	66811.0	−	115720.i	0.314373	−	0.544511i	0.979304	+	0.202394i	$0.0648723\pi$
$462$		0			0
$463$	−171665.			−0.800792			−0.400396	−	0.916342i	$-0.631127\pi$
$463$	−171665.			−0.800792			−0.400396	+	0.916342i	$0.631127\pi$
$464$		−	209338.i		−	0.972324i
$465$		0			0
$466$	35935.2	−	20747.2i	0.165481	−	0.0955406i
$467$	−143069.			−0.656012			−0.328006	−	0.944676i	$-0.606377\pi$
$467$	−143069.			−0.656012			−0.328006	+	0.944676i	$0.606377\pi$
$468$		0			0
$469$	−180.176	+	104.024i	−0.000819125	+	0.000472922i
$470$	−13482.5	−	7784.12i	−0.0610343	−	0.0352382i
$471$		0			0
$472$	−55337.4	+	95847.1i	−0.248390	+	0.430224i
$473$	−27497.1	+	47626.4i	−0.122904	+	0.212876i
$474$		0			0
$475$	30726.1	−	192367.i	0.136182	−	0.852598i
$476$	1816.84			0.00801868
$477$		0			0
$478$	−17475.3	−	10089.4i	−0.0764838	−	0.0441580i
$479$	202937.	+	351498.i	0.884485	+	1.53197i	0.846302	+	0.532703i	$0.178824\pi$
$479$	202937.	+	351498.i	0.884485	+	1.53197i	0.0381829	+	0.999271i	$0.487843\pi$
$480$		0			0
$481$	−4621.22	−	8004.19i	−0.0199741	−	0.0345961i
$482$	51827.8			0.223084
$483$		0			0
$484$	98090.4	+	169898.i	0.418732	+	0.725264i
$485$	−94957.7	+	54823.9i	−0.403689	+	0.233070i
$486$		0			0
$487$			252587.i			1.06501i	0.846428	+	0.532503i	$0.178749\pi$
$487$			252587.i			1.06501i	−0.846428	+	0.532503i	$0.821251\pi$
$488$	42457.7	−	24513.0i	0.178286	−	0.102933i
$489$		0			0
$490$	12010.5	−	6934.26i	0.0500229	−	0.0288807i
$491$	−82201.6	+	142377.i	−0.340971	+	0.590579i	−0.984613	−	0.174747i	$-0.944089\pi$
$491$	−82201.6	+	142377.i	−0.340971	+	0.590579i	0.643642	+	0.765326i	$0.277422\pi$
$492$		0			0
$493$		−	373962.i		−	1.53863i
$494$	−22510.9	−	18277.8i	−0.0922443	−	0.0748980i
$495$		0			0
$496$	−314823.	−	181763.i	−1.27969	−	0.738827i
$497$	1445.97	+	834.831i	0.00585391	+	0.00337976i
$498$		0			0
$499$	32862.8	−	56920.1i	0.131979	−	0.228594i	−0.792461	−	0.609923i	$-0.791200\pi$
$499$	32862.8	−	56920.1i	0.131979	−	0.228594i	0.924439	+	0.381329i	$0.124534\pi$
$500$	83983.6	+	145464.i	0.335934	+	0.581855i
$501$		0			0
$502$			41056.9i			0.162922i
$503$	92338.3	+	159935.i	0.364961	+	0.632130i	0.988770	−	0.149446i	$-0.0477491\pi$
$503$	92338.3	+	159935.i	0.364961	+	0.632130i	−0.623809	+	0.781577i	$0.714416\pi$
$504$		0			0
$505$	143788.			0.563820
$506$		−	16330.0i		−	0.0637801i
$507$		0			0
$508$	5541.32	+	3199.28i	0.0214726	+	0.0123972i
$509$	395925.	−	228587.i	1.52819	−	0.882301i	0.528752	−	0.848777i	$-0.322660\pi$
$509$	395925.	−	228587.i	1.52819	−	0.882301i	0.999438	−	0.0335240i	$-0.0106730\pi$
$510$		0			0
$511$	964.154	−	1669.96i	0.00369236	−	0.00639536i
$512$		−	185347.i		−	0.707042i
$513$		0			0
$514$	5662.18			0.0214318
$515$	−15694.7	−	9061.36i	−0.0591752	−	0.0341648i
$516$		0			0
$517$	−61351.5	−	106264.i	−0.229532	−	0.397562i
$518$	6.17150	−	10.6894i	2.30002e−5	−	3.98375e-5i
$519$		0			0
$520$	23459.3			0.0867577
$521$		−	301070.i		−	1.10916i	−0.832132	−	0.554578i	$-0.812880\pi$
$521$		−	301070.i		−	1.10916i	0.832132	−	0.554578i	$-0.187120\pi$
$522$		0			0
$523$	142864.	−	82482.4i	0.522298	−	0.301549i	−0.215576	−	0.976487i	$-0.569163\pi$
$523$	142864.	−	82482.4i	0.522298	−	0.301549i	0.737874	+	0.674938i	$0.235830\pi$
$524$	−46131.5			−0.168010
$525$		0			0
$526$	50134.3	−	28945.0i	0.181202	−	0.104617i
$527$	−562402.	−	324703.i	−2.02500	−	1.16914i
$528$		0			0
$529$	−24675.3	+	42738.9i	−0.0881762	+	0.152726i
$530$	6118.91	−	10598.3i	0.0217832	−	0.0377297i
$531$		0			0
$532$	−243.940	+	1527.24i	−0.000861905	+	0.00539614i
$533$	−165064.			−0.581028
$534$		0			0
$535$	147246.	+	85012.3i	0.514440	+	0.297012i
$536$	7489.50	+	12972.2i	0.0260689	+	0.0451527i
$537$		0			0
$538$	−15741.1	−	27264.3i	−0.0543838	−	0.0941955i
$539$	109307.			0.376243
$540$		0			0
$541$	−23100.4	−	40011.0i	−0.0789268	−	0.136705i	0.823860	−	0.566793i	$-0.191816\pi$
$541$	−23100.4	−	40011.0i	−0.0789268	−	0.136705i	−0.902787	+	0.430088i	$0.858483\pi$
$542$	−3278.99	+	1893.13i	−0.0111620	+	0.00644438i
$543$		0			0
$544$		−	197021.i		−	0.665755i
$545$	62048.9	−	35823.9i	0.208901	−	0.120609i
$546$		0			0
$547$	−75590.9	+	43642.4i	−0.252636	+	0.145859i	−0.620971	−	0.783834i	$-0.713261\pi$
$547$	−75590.9	+	43642.4i	−0.252636	+	0.145859i	0.368335	+	0.929693i	$0.379928\pi$
$548$	204984.	−	355043.i	0.682588	−	1.18228i
$549$		0			0
$550$		−	15358.8i		−	0.0507728i
$551$	314352.	+	50210.3i	1.03541	+	0.165383i
$552$		0			0
$553$	−767.681	−	443.221i	−0.00251033	−	0.00144934i
$554$	51156.3	+	29535.1i	0.166678	+	0.0962318i
$555$		0			0
$556$	−33845.0	+	58621.3i	−0.109483	+	0.189630i
$557$	−95840.4	−	166000.i	−0.308914	−	0.535055i	0.669211	−	0.743073i	$-0.266632\pi$
$557$	−95840.4	−	166000.i	−0.308914	−	0.535055i	−0.978125	+	0.208017i	$0.933299\pi$
$558$		0			0
$559$		−	155203.i		−	0.496679i
$560$	−301.013	−	521.369i	−0.000959862	−	0.00166253i
$561$		0			0
$562$	−18196.0			−0.0576108
$563$			488949.i			1.54258i	0.636486	+	0.771288i	$0.280387\pi$
$563$			488949.i			1.54258i	−0.636486	+	0.771288i	$0.719613\pi$
$564$		0			0
$565$	−35729.4	−	20628.4i	−0.111926	−	0.0646202i
$566$	−37169.2	+	21459.7i	−0.116025	+	0.0669869i
$567$		0			0
$568$	60105.8	−	104106.i	0.186303	−	0.322686i
$569$		−	606639.i		−	1.87372i	−0.349699	−	0.936862i	$-0.613716\pi$
$569$		−	606639.i		−	1.87372i	0.349699	−	0.936862i	$-0.386284\pi$
$570$		0			0
$571$	92670.7			0.284230			0.142115	−	0.989850i	$-0.454610\pi$
$571$	92670.7			0.284230			0.142115	+	0.989850i	$0.454610\pi$
$572$	79073.0	+	45652.8i	0.241677	+	0.139533i
$573$		0			0
$574$	−110.219	−	190.904i	−0.000334527	−	0.000579418i
$575$	−154806.	+	268133.i	−0.468224	+	0.810987i
$576$		0			0
$577$	−117869.			−0.354037			−0.177019	−	0.984208i	$-0.556645\pi$
$577$	−117869.			−0.354037			−0.177019	+	0.984208i	$0.556645\pi$
$578$		−	60217.5i		−	0.180247i
$579$		0			0
$580$	−110141.	+	63589.7i	−0.327410	+	0.189030i
$581$	−1533.38			−0.00454254
$582$		0			0
$583$	83531.6	−	48227.0i	0.245761	−	0.141890i
$584$	−120233.	−	69416.7i	−0.352532	−	0.203535i
$585$		0			0
$586$	48451.2	−	83920.0i	0.141094	−	0.244383i
$587$	35695.9	−	61827.1i	0.103596	−	0.179433i	−0.809568	−	0.587026i	$-0.800299\pi$
$587$	35695.9	−	61827.1i	0.103596	−	0.179433i	0.913164	+	0.407593i	$0.133632\pi$
$588$		0			0
$589$	348457.	−	429158.i	1.00443	−	1.23705i
$590$	32351.4			0.0929370
$591$		0			0
$592$	14788.9	+	8538.36i	0.0421980	+	0.0243630i
$593$	−70754.5	−	122550.i	−0.201208	−	0.348502i	0.747710	−	0.664025i	$-0.231153\pi$
$593$	−70754.5	−	122550.i	−0.201208	−	0.348502i	−0.948918	+	0.315523i	$0.897820\pi$
$594$		0			0
$595$	−537.730	−	931.376i	−0.00151891	−	0.00263082i
$596$	−51068.4			−0.143767
$597$		0			0
$598$	23043.0	+	39911.6i	0.0644372	+	0.111608i
$599$	462882.	−	267245.i	1.29008	−	0.744828i	0.311412	−	0.950275i	$-0.399198\pi$
$599$	462882.	−	267245.i	1.29008	−	0.744828i	0.978668	+	0.205447i	$0.0658649\pi$
$600$		0			0
$601$		−	126491.i		−	0.350196i	−0.984551	−	0.175098i	$-0.943976\pi$
$601$		−	126491.i		−	0.350196i	0.984551	−	0.175098i	$-0.0560243\pi$
$602$	179.500	−	103.634i	0.000495304	−	0.000285964i
$603$		0			0
$604$	−44323.4	+	25590.1i	−0.121495	+	0.0701453i
$605$	58063.6	−	100569.i	0.158633	−	0.274760i
$606$		0			0
$607$		−	75673.3i		−	0.205383i	−0.994713	−	0.102692i	$-0.967255\pi$
$607$		−	75673.3i		−	0.205383i	0.994713	−	0.102692i	$-0.0327455\pi$
$608$	165616.	+	26453.2i	0.448017	+	0.0715601i
$609$		0			0
$610$	−12410.8	−	7165.39i	−0.0333535	−	0.0192566i
$611$	299894.	+	173144.i	0.803315	+	0.463794i
$612$		0			0
$613$	−336906.	+	583538.i	−0.896577	+	1.55292i	−0.0647358	+	0.997902i	$0.520620\pi$
$613$	−336906.	+	583538.i	−0.896577	+	1.55292i	−0.831841	+	0.555014i	$0.812713\pi$
$614$	31340.1	+	54282.6i	0.0831310	+	0.143987i
$615$		0			0
$616$			246.925i			0.000650734i
$617$	75123.6	+	130118.i	0.197336	+	0.341796i	0.947664	−	0.319270i	$-0.103438\pi$
$617$	75123.6	+	130118.i	0.197336	+	0.341796i	−0.750328	+	0.661066i	$0.770104\pi$
$618$		0			0
$619$	−98758.2			−0.257746			−0.128873	−	0.991661i	$-0.541136\pi$
$619$	−98758.2			−0.257746			−0.128873	+	0.991661i	$0.541136\pi$
$620$			220854.i			0.574543i
$621$		0			0
$622$	23582.8	+	13615.5i	0.0609558	+	0.0351928i
$623$	1349.96	−	779.401i	0.00347813	−	0.00200810i
$624$		0			0
$625$	−118921.	+	205976.i	−0.304437	+	0.527300i
$626$		−	42019.2i		−	0.107226i
$627$		0			0
$628$	488021.			1.23742
$629$	26418.9	+	15253.0i	0.0667750	+	0.0385525i
$630$		0			0
$631$	338314.	+	585977.i	0.849691	+	1.47171i	0.881484	+	0.472214i	$0.156545\pi$
$631$	338314.	+	585977.i	0.849691	+	1.47171i	−0.0317927	+	0.999494i	$0.510122\pi$
$632$	−31910.8	+	55271.1i	−0.0798920	+	0.138377i
$633$		0			0
$634$	14714.1			0.0366063
$635$		−	3787.56i		−	0.00939318i
$636$		0			0
$637$	−267152.	+	154241.i	−0.658386	+	0.380119i
$638$	25098.1			0.0616595
$639$		0			0
$640$	−77028.1	+	44472.2i	−0.188057	+	0.108575i
$641$	−615303.	−	355245.i	−1.49752	−	0.864594i	−0.497524	−	0.867450i	$-0.665757\pi$
$641$	−615303.	−	355245.i	−1.49752	−	0.864594i	−0.999996	+	0.00285662i	$0.999091\pi$
$642$		0			0
$643$	70190.5	−	121574.i	0.169768	−	0.294047i	−0.768570	−	0.639766i	$-0.779031\pi$
$643$	70190.5	−	121574.i	0.169768	−	0.294047i	0.938338	+	0.345718i	$0.112365\pi$
$644$	1229.03	−	2128.75i	0.00296341	−	0.00513278i
$645$		0			0
$646$	94510.2	+	15095.8i	0.226472	+	0.0361735i
$647$	−439296.			−1.04942			−0.524710	−	0.851281i	$-0.675826\pi$
$647$	−439296.			−1.04942			−0.524710	+	0.851281i	$0.675826\pi$
$648$		0			0
$649$	220820.	+	127491.i	0.524264	+	0.302684i
$650$	21672.5	+	37537.9i	0.0512958	+	0.0888470i
$651$		0			0
$652$	−255670.	−	442834.i	−0.601430	−	1.04171i
$653$	−694597.			−1.62894			−0.814472	−	0.580203i	$-0.802973\pi$
$653$	−694597.			−1.62894			−0.814472	+	0.580203i	$0.802973\pi$
$654$		0			0
$655$	13653.5	+	23648.6i	0.0318246	+	0.0551218i
$656$	264119.	−	152489.i	0.613751	−	0.354349i
$657$		0			0
$658$			462.457i			0.00106812i
$659$	544541.	−	314391.i	1.25389	−	0.723935i	0.282012	−	0.959411i	$-0.408998\pi$
$659$	544541.	−	314391.i	1.25389	−	0.723935i	0.971880	+	0.235476i	$0.0756649\pi$
$660$		0			0
$661$	−16257.2	+	9386.09i	−0.0372085	+	0.0214823i	−0.518489	−	0.855084i	$-0.673505\pi$
$661$	−16257.2	+	9386.09i	−0.0372085	+	0.0214823i	0.481280	+	0.876567i	$0.340172\pi$
$662$	7401.07	−	12819.0i	0.0168880	−	0.0292509i
$663$		0			0
$664$			110400.i			0.250399i
$665$	855.114	−	326.964i	0.00193366	−	0.000739361i
$666$		0			0
$667$	−438162.	−	252973.i	−0.984879	−	0.568620i
$668$	349945.	+	202041.i	0.784236	+	0.452779i
$669$		0			0
$670$	2189.26	−	3791.91i	0.00487694	−	0.00844712i
$671$	−56475.0	−	97817.5i	−0.125433	−	0.217256i
$672$		0			0
$673$			39754.5i			0.0877721i	0.999037	+	0.0438861i	$0.0139739\pi$
$673$			39754.5i			0.0877721i	−0.999037	+	0.0438861i	$0.986026\pi$
$674$	−49043.7	−	84946.2i	−0.107960	−	0.186992i
$675$		0			0
$676$	188134.			0.411693
$677$			739937.i			1.61442i	0.590262	+	0.807212i	$0.299025\pi$
$677$			739937.i			1.61442i	−0.590262	+	0.807212i	$0.700975\pi$
$678$		0			0
$679$	2820.74	+	1628.55i	0.00611819	+	0.00353234i
$680$	−67056.8	+	38715.3i	−0.145019	+	0.0837268i
$681$		0			0
$682$	21792.2	−	37745.2i	0.0468524	−	0.0811508i
$683$			244927.i			0.525043i	0.964926	+	0.262522i	$0.0845541\pi$
$683$			244927.i			0.525043i	−0.964926	+	0.262522i	$0.915446\pi$
$684$		0			0
$685$	−242676.			−0.517185
$686$	−713.559	−	411.974i	−0.00151629	−	0.000875429i
$687$		0			0
$688$	143380.	+	248341.i	0.302908	+	0.524652i
$689$	−136104.	+	235740.i	−0.286704	+	0.496586i
$690$		0			0
$691$	−607326.			−1.27194			−0.635969	−	0.771715i	$-0.719399\pi$
$691$	−607326.			−1.27194			−0.635969	+	0.771715i	$0.719399\pi$
$692$		−	54266.3i		−	0.113323i
$693$		0			0
$694$	−111372.	+	64300.6i	−0.231237	+	0.133505i
$695$	40068.5			0.0829532
$696$		0			0
$697$	471823.	−	272407.i	0.971212	−	0.560729i
$698$	79652.4	+	45987.3i	0.163489	+	0.0943903i
$699$		0			0
$700$	1155.94	−	2002.14i	0.00235905	−	0.00408600i
$701$	−88390.8	+	153097.i	−0.179875	+	0.311553i	−0.941838	−	0.336068i	$-0.890903\pi$
$701$	−88390.8	+	153097.i	−0.179875	+	0.311553i	0.761963	+	0.647621i	$0.224236\pi$
$702$		0			0
$703$	−16368.8	+	20159.8i	−0.0331212	+	0.0407920i
$704$	−159701.			−0.322228
$705$		0			0
$706$	40682.5	+	23488.1i	0.0816204	+	0.0471236i
$707$	−2135.63	−	3699.02i	−0.00427255	−	0.00740027i
$708$		0			0
$709$	−312672.	−	541564.i	−0.622009	−	1.07735i	−0.989111	−	0.147171i	$-0.952983\pi$
$709$	−312672.	−	541564.i	−0.622009	−	1.07735i	0.367102	−	0.930181i	$-0.380350\pi$
$710$	−35139.1			−0.0697066
$711$		0			0
$712$	−56115.0	−	97194.0i	−0.110693	−	0.191725i
$713$	−760893.	+	439302.i	−1.49673	+	0.864140i
$714$		0			0
$715$		−	54047.5i		−	0.105721i
$716$	542292.	−	313092.i	1.05781	−	0.610726i
$717$		0			0
$718$	−10164.8	+	5868.62i	−0.0197173	+	0.0113838i
$719$	−47265.5	+	81866.2i	−0.0914295	+	0.158360i	−0.908113	−	0.418726i	$-0.862477\pi$
$719$	−47265.5	+	81866.2i	−0.0914295	+	0.158360i	0.816683	+	0.577086i	$0.195810\pi$
$720$		0			0
$721$			538.339i			0.00103558i
$722$	−25379.0	+	77418.4i	−0.0486856	+	0.148515i
$723$		0			0
$724$	677539.	+	391178.i	1.29258	+	0.746271i
$725$	−412102.	−	237927.i	−0.784023	−	0.452656i
$726$		0			0
$727$	4503.05	−	7799.52i	0.00851997	−	0.0147570i	−0.861734	−	0.507360i	$-0.830621\pi$
$727$	4503.05	−	7799.52i	0.00851997	−	0.0147570i	0.870254	+	0.492603i	$0.163955\pi$
$728$	−348.431	−	603.501i	−0.000657437	−	0.00113871i
$729$		0			0
$730$			40582.5i			0.0761540i
$731$	256134.	+	443637.i	0.479328	+	0.830220i
$732$		0			0
$733$	−234971.			−0.437326			−0.218663	−	0.975800i	$-0.570170\pi$
$733$	−234971.			−0.437326			−0.218663	+	0.975800i	$0.570170\pi$
$734$			28013.4i			0.0519965i
$735$		0			0
$736$	−230845.	−	133278.i	−0.426152	−	0.246039i
$737$	29886.4	−	17254.9i	0.0550223	−	0.0317672i
$738$		0			0
$739$	−156095.	+	270364.i	−0.285825	+	0.495063i	−0.972809	−	0.231609i	$-0.925601\pi$
$739$	−156095.	+	270364.i	−0.285825	+	0.495063i	0.686984	+	0.726673i	$0.258934\pi$
$740$		−	10374.7i		−	0.0189457i
$741$		0			0
$742$	−363.527			−0.000660281
$743$	424908.	+	245321.i	0.769693	+	0.444383i	0.832765	−	0.553626i	$-0.186756\pi$
$743$	424908.	+	245321.i	0.769693	+	0.444383i	−0.0630720	+	0.998009i	$0.520090\pi$
$744$		0			0
$745$	15114.7	+	26179.5i	0.0272325	+	0.0471681i
$746$	−51150.8	+	88595.7i	−0.0919125	+	0.159197i
$747$		0			0
$748$	−301367.			−0.538632
$749$		−	5050.61i		−	0.00900286i
$750$		0			0
$751$	695752.	−	401693.i	1.23360	−	0.712220i	0.265822	−	0.964022i	$-0.414357\pi$
$751$	695752.	−	401693.i	1.23360	−	0.712220i	0.967779	+	0.251802i	$0.0810233\pi$
$752$	−639816.			−1.13141
$753$		0			0
$754$	−61341.5	+	35415.5i	−0.107898	+	0.0622947i
$755$	26236.8	+	15147.8i	0.0460274	+	0.0265739i
$756$		0			0
$757$	37763.2	−	65407.7i	0.0658987	−	0.114140i	−0.831194	−	0.555983i	$-0.812342\pi$
$757$	37763.2	−	65407.7i	0.0658987	−	0.114140i	0.897092	+	0.441843i	$0.145675\pi$
$758$	41309.4	−	71550.0i	0.0718970	−	0.124529i
$759$		0			0
$760$	−23540.6	−	61566.1i	−0.0407559	−	0.106590i
$761$	−854120.			−1.47486			−0.737428	−	0.675426i	$-0.763960\pi$
$761$	−854120.			−1.47486			−0.737428	+	0.675426i	$0.763960\pi$
$762$		0			0
$763$	−1843.17	−	1064.16i	−0.00316604	−	0.00182792i
$764$	507447.	+	878925.i	0.869369	+	1.50579i
$765$		0			0
$766$	72303.9	+	125234.i	0.123226	+	0.213435i
$767$	−719600.			−1.22321
$768$		0			0
$769$	268960.	+	465853.i	0.454816	+	0.787764i	0.998678	−	0.0514105i	$-0.0163717\pi$
$769$	268960.	+	465853.i	0.454816	+	0.787764i	−0.543862	+	0.839175i	$0.683038\pi$
$770$	62.5086	−	36.0894i	0.000105429	−	6.08692e-5i
$771$		0			0
$772$			1.03457e6i			1.73590i
$773$	374936.	−	216469.i	0.627477	−	0.362274i	−0.152297	−	0.988335i	$-0.548667\pi$
$773$	374936.	−	216469.i	0.627477	−	0.362274i	0.779774	+	0.626061i	$0.215334\pi$
$774$		0			0
$775$	−715639.	+	413174.i	−1.19149	+	0.687907i
$776$	117252.	−	203086.i	0.194714	−	0.337254i
$777$		0			0
$778$			1033.82i			0.00170799i
$779$	165636.	+	433190.i	0.272948	+	0.713844i
$780$		0			0
$781$	−239849.	−	138477.i	−0.393219	−	0.227025i
$782$	−131734.	−	76056.5i	−0.215419	−	0.124372i
$783$		0			0
$784$	284981.	−	493602.i	0.463643	−	0.803054i
$785$	−144439.	−	250176.i	−0.234394	−	0.405982i
$786$		0			0
$787$			451093.i			0.728311i	0.931338	+	0.364155i	$0.118642\pi$
$787$			451093.i			0.728311i	−0.931338	+	0.364155i	$0.881358\pi$
$788$	343524.	+	595001.i	0.553229	+	0.958220i
$789$		0			0
$790$	18655.7			0.0298922
$791$			1225.54i			0.00195873i
$792$		0			0
$793$	276057.	+	159382.i	0.438988	+	0.253450i
$794$	110586.	−	63846.6i	0.175411	−	0.101274i
$795$		0			0
$796$	551836.	−	955808.i	0.870931	−	1.50850i
$797$		−	698630.i		−	1.09984i	−0.835216	−	0.549921i	$-0.814658\pi$
$797$		−	698630.i		−	1.09984i	0.835216	−	0.549921i	$-0.185342\pi$
$798$		0			0
$799$	−1.14297e6			−1.79036
$800$	−217115.	−	125351.i	−0.339242	−	0.195862i
$801$		0			0
$802$	−20278.5	−	35123.4i	−0.0315274	−	0.0546070i
$803$	−159928.	+	277003.i	−0.248024	+	0.429590i
$804$		0			0
$805$	−1455.03			−0.00224533
$806$			123002.i			0.189340i
$807$		0			0
$808$	−266320.	+	153760.i	−0.407926	+	0.235516i
$809$	1.25493e6			1.91744			0.958722	−	0.284345i	$-0.0917763\pi$
$809$	1.25493e6			1.91744			0.958722	+	0.284345i	$0.0917763\pi$
$810$		0			0
$811$	475389.	−	274466.i	0.722782	−	0.417298i	−0.0929939	−	0.995667i	$-0.529644\pi$
$811$	475389.	−	274466.i	0.722782	−	0.417298i	0.815776	+	0.578368i	$0.196310\pi$
$812$	3271.75	+	1888.94i	0.00496212	+	0.00286488i
$813$		0			0
$814$	−1023.69	+	1773.08i	−0.00154497	+	0.00267597i
$815$	−151342.	+	262131.i	−0.227847	+	0.394642i
$816$		0			0
$817$	−407311.	+	155741.i	−0.610214	+	0.233323i
$818$	−158389.			−0.236711
$819$		0			0
$820$	−160461.	−	92642.2i	−0.238639	−	0.137778i
$821$	488125.	+	845457.i	0.724177	+	1.25431i	0.959312	+	0.282348i	$0.0911133\pi$
$821$	488125.	+	845457.i	0.724177	+	1.25431i	−0.235135	+	0.971963i	$0.575553\pi$
$822$		0			0
$823$	404279.	+	700231.i	0.596872	+	1.03381i	0.993280	+	0.115738i	$0.0369233\pi$
$823$	404279.	+	700231.i	0.596872	+	1.03381i	−0.396408	+	0.918074i	$0.629743\pi$
$824$	38759.1			0.0570846
$825$		0			0
$826$	−480.502	−	832.253i	−0.000704263	−	0.00121982i
$827$	−737136.	+	425586.i	−1.07780	+	0.622266i	−0.930301	−	0.366797i	$-0.880454\pi$
$827$	−737136.	+	425586.i	−1.07780	+	0.622266i	−0.147495	+	0.989063i	$0.547121\pi$
$828$		0			0
$829$			305115.i			0.443970i	0.975050	+	0.221985i	$0.0712537\pi$
$829$			305115.i			0.443970i	−0.975050	+	0.221985i	$0.928746\pi$
$830$	27947.5	−	16135.5i	0.0405684	−	0.0234222i
$831$		0			0
$832$	390320.	−	225351.i	0.563864	−	0.325547i
$833$	509092.	−	881773.i	0.733679	−	1.27077i
$834$		0			0
$835$		−	239192.i		−	0.343063i
$836$	40463.3	−	253329.i	0.0578960	−	0.362470i
$837$		0			0
$838$	25290.6	+	14601.5i	0.0360139	+	0.0207927i
$839$	−222988.	−	128742.i	−0.316781	−	0.182893i	0.333176	−	0.942865i	$-0.391880\pi$
$839$	−222988.	−	128742.i	−0.316781	−	0.182893i	−0.649957	+	0.759971i	$0.725213\pi$
$840$		0			0
$841$	35161.8	−	60902.1i	0.0497141	−	0.0861073i
$842$	7048.53	+	12208.4i	0.00994201	+	0.0172201i
$843$		0			0
$844$			271207.i			0.380728i
$845$	−55682.0	−	96444.1i	−0.0779833	−	0.135071i
$846$		0			0
$847$	−3449.58			−0.00480839
$848$		−	502944.i		−	0.699404i
$849$		0			0
$850$	−123899.	−	71533.0i	−0.171486	−	0.0990076i
$851$	35743.1	−	20636.3i	0.0493552	−	0.0284952i
$852$		0			0
$853$	349883.	−	606015.i	0.480866	−	0.832885i	−0.518893	−	0.854839i	$-0.673656\pi$
$853$	349883.	−	606015.i	0.480866	−	0.832885i	0.999759	+	0.0219545i	$0.00698891\pi$
$854$			425.699i			0.000583696i
$855$		0			0
$856$	−363632.			−0.496266
$857$	−402851.	−	232586.i	−0.548508	−	0.316681i	0.200012	−	0.979793i	$-0.435902\pi$
$857$	−402851.	−	232586.i	−0.548508	−	0.316681i	−0.748520	+	0.663112i	$0.769235\pi$
$858$		0			0
$859$	359632.	+	622900.i	0.487384	+	0.844174i	0.999895	−	0.0145066i	$-0.00461777\pi$
$859$	359632.	+	622900.i	0.487384	+	0.844174i	−0.512511	+	0.858681i	$0.671284\pi$
$860$	87107.8	−	150875.i	0.117777	−	0.203996i
$861$		0			0
$862$	155776.			0.209646
$863$		−	380009.i		−	0.510237i	−0.966910	−	0.255118i	$-0.917886\pi$
$863$		−	380009.i		−	0.510237i	0.966910	−	0.255118i	$-0.0821145\pi$
$864$		0			0
$865$	−27818.8	+	16061.2i	−0.0371797	+	0.0214657i
$866$	27739.8			0.0369885
$867$		0			0
$868$	5681.57	−	3280.26i	0.00754101	−	0.00435380i
$869$	127338.	+	73518.7i	0.168624	+	0.0973550i
$870$		0			0
$871$	−48696.3	+	84344.4i	−0.0641888	+	0.111178i
$872$	−76616.7	+	132704.i	−0.100761	+	0.174522i
$873$		0			0
$874$	81620.4	−	100524.i	0.106850	−	0.131597i
$875$	−2953.48			−0.00385761
$876$		0			0
$877$	−7312.18	−	4221.69i	−0.00950710	−	0.00548892i	0.495239	−	0.868757i	$-0.335081\pi$
$877$	−7312.18	−	4221.69i	−0.00950710	−	0.00548892i	−0.504746	+	0.863268i	$0.668414\pi$
$878$	76372.4	+	132281.i	0.0990711	+	0.171596i
$879$		0			0
$880$	49930.2	+	86481.6i	0.0644759	+	0.111676i
$881$	−631669.			−0.813838			−0.406919	−	0.913464i	$-0.633397\pi$
$881$	−631669.			−0.813838			−0.406919	+	0.913464i	$0.633397\pi$
$882$		0			0
$883$	−31430.2	−	54438.8i	−0.0403113	−	0.0698211i	0.845166	−	0.534504i	$-0.179502\pi$
$883$	−31430.2	−	54438.8i	−0.0403113	−	0.0698211i	−0.885477	+	0.464683i	$0.846168\pi$
$884$	736560.	−	425253.i	0.942548	−	0.544180i
$885$		0			0
$886$			37240.6i			0.0474405i
$887$	770362.	−	444769.i	0.979146	−	0.565310i	0.0771338	−	0.997021i	$-0.475423\pi$
$887$	770362.	−	444769.i	0.979146	−	0.565310i	0.902012	+	0.431711i	$0.142090\pi$
$888$		0			0
$889$	−97.4368	+	56.2551i	−0.000123288	+	7.11801e-5i
$890$	−16403.0	+	28410.8i	−0.0207082	+	0.0358677i
$891$		0			0
$892$		−	394067.i		−	0.495268i
$893$	153462.	−	960780.i	0.192441	−	1.20482i
$894$		0			0
$895$	−321004.	−	185332.i	−0.400742	−	0.231368i
$896$	2288.13	+	1321.05i	0.00285013	+	0.00164553i
$897$		0			0
$898$	−56659.9	+	98137.8i	−0.0702624	+	0.121698i
$899$	−675178.	−	1.16944e6i	−0.835408	−	1.44697i
$900$		0			0
$901$		−	898462.i		−	1.10675i
$902$	18282.4	+	31666.1i	0.0224709	+	0.0389207i
$903$		0			0
$904$	88235.9			0.107971
$905$		−	463107.i		−	0.565437i
$906$		0			0
$907$	−408359.	−	235766.i	−0.496396	−	0.286594i	0.230828	−	0.972995i	$-0.425856\pi$
$907$	−408359.	−	235766.i	−0.496396	−	0.286594i	−0.727224	+	0.686400i	$0.759190\pi$
$908$	−12385.3	+	7150.64i	−0.0150222	+	0.00867308i
$909$		0			0
$910$	−101.850	+	176.410i	−0.000122993	+	0.000213029i
$911$		−	227945.i		−	0.274659i	−0.990525	−	0.137329i	$-0.956148\pi$
$911$		−	227945.i		−	0.274659i	0.990525	−	0.137329i	$-0.0438518\pi$
$912$		0			0
$913$	254348.			0.305132
$914$	−27788.1	−	16043.4i	−0.0332633	−	0.0192046i
$915$		0			0
$916$	36403.1	+	63052.1i	0.0433858	+	0.0751464i
$917$	405.581	−	702.487i	0.000482324	−	0.000835410i
$918$		0			0
$919$	1.19281e6			1.41235			0.706173	−	0.708040i	$-0.250420\pi$
$919$	1.19281e6			1.41235			0.706173	+	0.708040i	$0.250420\pi$
$920$			104759.i			0.123770i
$921$		0			0
$922$	72344.0	−	41767.8i	0.0851022	−	0.0491338i
$923$	781607.			0.917456
$924$		0			0
$925$	33617.2	−	19408.9i	0.0392897	−	0.0226839i
$926$	−92940.9	−	53659.4i	−0.108389	−	0.0625784i
$927$		0			0
$928$	204840.	−	354793.i	0.237858	−	0.411983i
$929$	146300.	−	253398.i	0.169516	−	0.293611i	−0.768734	−	0.639569i	$-0.779113\pi$
$929$	146300.	−	253398.i	0.169516	−	0.293611i	0.938250	+	0.345958i	$0.112446\pi$
$930$		0			0
$931$	672864.	+	546334.i	0.776297	+	0.630317i
$932$	−1.03604e6			−1.19273
$933$		0			0
$934$	−77458.8	−	44720.9i	−0.0887926	−	0.0512645i
$935$	89195.5	+	154491.i	0.102028	+	0.176718i
$936$		0			0
$937$	−580745.	−	1.00588e6i	−0.661464	−	1.14569i	−0.980231	−	0.197857i	$-0.936602\pi$
$937$	−580745.	−	1.00588e6i	−0.661464	−	1.14569i	0.318767	−	0.947833i	$-0.396731\pi$
$938$	−130.065			−0.000147827
$939$		0			0
$940$	194355.	+	336632.i	0.219958	+	0.380978i
$941$	−494228.	+	285343.i	−0.558147	+	0.322246i	−0.752401	−	0.658705i	$-0.771105\pi$
$941$	−494228.	+	285343.i	−0.558147	+	0.322246i	0.194254	+	0.980951i	$0.437771\pi$
$942$		0			0
$943$		−	737099.i		−	0.828900i
$944$	1.15143e6	−	664781.i	1.29210	−	0.745993i
$945$		0			0
$946$	−29774.4	+	17190.2i	−0.0332706	+	0.0192088i
$947$	−443648.	+	768420.i	−0.494696	+	0.856838i	−0.999981	−	0.00611394i	$-0.998054\pi$
$947$	−443648.	+	768420.i	−0.494696	+	0.856838i	0.505285	+	0.862952i	$0.331387\pi$
$948$		0			0
$949$		−	902686.i		−	1.00232i
$950$	76766.0	−	94544.8i	0.0850593	−	0.104759i
$951$		0			0
$952$	1991.94	+	1150.04i	0.00219787	+	0.00126894i
$953$	323576.	+	186816.i	0.356279	+	0.205698i	0.667447	−	0.744657i	$-0.267387\pi$
$953$	323576.	+	186816.i	0.356279	+	0.205698i	−0.311168	+	0.950355i	$0.600720\pi$
$954$		0			0
$955$	300378.	−	520271.i	0.329353	−	0.570457i
$956$	251913.	+	436326.i	0.275635	+	0.477414i
$957$		0			0
$958$			253738.i			0.276474i
$959$	3604.37	+	6242.96i	0.00391915	+	0.00678818i
$960$		0			0
$961$	−1.42145e6			−1.53916
$962$		−	5778.05i		−	0.00624354i
$963$		0			0
$964$	−1.12067e6	−	647020.i	−1.20594	−	0.696248i
$965$	530357.	−	306202.i	0.569527	−	0.328816i
$966$		0			0
$967$	−426457.	+	738645.i	−0.456060	+	0.789919i	−0.998748	−	0.0500149i	$-0.984073\pi$
$967$	−426457.	+	738645.i	−0.456060	+	0.789919i	0.542688	+	0.839934i	$0.317406\pi$
$968$			248361.i			0.265053i
$969$		0			0
$970$	−68547.9			−0.0728535
$971$	75186.2	+	43408.8i	0.0797443	+	0.0460404i	0.539342	−	0.842087i	$-0.318673\pi$
$971$	75186.2	+	43408.8i	0.0797443	+	0.0460404i	−0.459598	+	0.888127i	$0.652006\pi$
$972$		0			0
$973$	−595.121	−	1030.78i	−0.000628607	−	0.00108878i
$974$	−78954.1	+	136752.i	−0.0832255	+	0.144151i
$975$		0			0
$976$	−588960.			−0.618282
$977$			1.54915e6i			1.62295i	0.584387	+	0.811475i	$0.301335\pi$
$977$			1.54915e6i			1.62295i	−0.584387	+	0.811475i	$0.698665\pi$
$978$		0			0
$979$	−223923.	+	129282.i	−0.233633	+	0.134888i
$980$	−346271.			−0.360548
$981$		0			0
$982$	−89009.3	+	51389.6i	−0.0923023	+	0.0532908i
$983$	420874.	+	242992.i	0.435557	+	0.251469i	0.701711	−	0.712462i	$-0.252420\pi$
$983$	420874.	+	242992.i	0.435557	+	0.251469i	−0.266154	+	0.963930i	$0.585753\pi$
$984$		0			0
$985$	203346.	−	352205.i	0.209586	−	0.363014i
$986$	116894.	−	202466.i	0.120237	−	0.208256i
$987$		0			0
$988$	258573.	+	676249.i	0.264892	+	0.692776i
$989$	693065.			0.708568
$990$		0			0
$991$	664833.	+	383842.i	0.676964	+	0.390845i	0.798710	−	0.601716i	$-0.205516\pi$
$991$	664833.	+	383842.i	0.676964	+	0.390845i	−0.121746	+	0.992561i	$0.538849\pi$
$992$	−355716.	−	616118.i	−0.361477	−	0.626096i
$993$		0			0
$994$	521.906	+	903.969i	0.000528226	+	0.000914915i
$995$	−653307.			−0.659890
$996$		0			0
$997$	−165150.	−	286047.i	−0.166145	−	0.287772i	0.770916	−	0.636936i	$-0.219799\pi$
$997$	−165150.	−	286047.i	−0.166145	−	0.287772i	−0.937061	+	0.349165i	$0.886465\pi$
$998$	35584.4	−	20544.7i	0.0357272	−	0.0206271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.5.p.a.46.3		10
3.2	odd	2		19.5.d.a.8.3	✓	10
12.11	even	2		304.5.r.a.65.5		10
19.12	odd	6	inner	171.5.p.a.145.3		10
57.50	even	6		19.5.d.a.12.3	yes	10
228.107	odd	6		304.5.r.a.145.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.d.a.8.3	✓	10	3.2	odd	2
19.5.d.a.12.3	yes	10	57.50	even	6
171.5.p.a.46.3		10	1.1	even	1	trivial
171.5.p.a.145.3		10	19.12	odd	6	inner
304.5.r.a.65.5		10	12.11	even	2
304.5.r.a.145.5		10	228.107	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.541408 + 0.312582i) q^{2} +(-7.80458 - 13.5179i) q^{4} +(-4.61985 + 8.00181i) q^{5} +0.274467 q^{7} -19.7609i q^{8} +O(q^{10})\)	\(q+(0.541408 + 0.312582i) q^{2} +(-7.80458 - 13.5179i) q^{4} +(-4.61985 + 8.00181i) q^{5} +0.274467 q^{7} -19.7609i q^{8} +(-5.00245 + 2.88816i) q^{10} -45.5269 q^{11} +(111.271 - 64.2421i) q^{13} +(0.148599 + 0.0857934i) q^{14} +(-118.696 + 205.588i) q^{16} +(-212.040 + 367.264i) q^{17} +(-280.252 - 227.552i) q^{19} +144.224 q^{20} +(-24.6486 - 14.2309i) q^{22} +(286.876 + 496.884i) q^{23} +(269.814 + 467.332i) q^{25} +80.3238 q^{26} +(-2.14210 - 3.71022i) q^{28} +(-763.678 + 440.909i) q^{29} +1531.33i q^{31} +(-402.342 + 232.292i) q^{32} +(-229.600 + 132.560i) q^{34} +(-1.26799 + 2.19623i) q^{35} -71.9344i q^{37} +(-80.6022 - 210.800i) q^{38} +(158.123 + 91.2925i) q^{40} +(-1112.58 - 642.350i) q^{41} +(603.976 - 1046.12i) q^{43} +(355.318 + 615.429i) q^{44} +358.690i q^{46} +(1347.59 + 2334.09i) q^{47} -2400.92 q^{49} +337.356i q^{50} +(-1736.84 - 1002.77i) q^{52} +(-1834.78 + 1059.31i) q^{53} +(210.327 - 364.297i) q^{55} -5.42372i q^{56} -551.282 q^{58} +(-4850.33 - 2800.34i) q^{59} +(1240.48 + 2148.57i) q^{61} +(-478.666 + 829.075i) q^{62} +3507.84 q^{64} +1187.16i q^{65} +(-656.457 + 379.006i) q^{67} +6619.53 q^{68} +(-1.37300 + 0.792705i) q^{70} +(5268.29 + 3041.65i) q^{71} +(3512.83 - 6084.39i) q^{73} +(22.4854 - 38.9459i) q^{74} +(-888.778 + 5564.38i) q^{76} -12.4956 q^{77} +(-2796.99 - 1614.84i) q^{79} +(-1096.72 - 1899.57i) q^{80} +(-401.574 - 695.547i) q^{82} -5586.78 q^{83} +(-1959.18 - 3393.40i) q^{85} +(653.995 - 377.584i) q^{86} +899.653i q^{88} +(4918.49 - 2839.69i) q^{89} +(30.5401 - 17.6323i) q^{91} +(4477.90 - 7755.95i) q^{92} +1684.93i q^{94} +(3115.55 - 1191.27i) q^{95} +(10277.2 + 5933.52i) q^{97} +(-1299.88 - 750.487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} + 29 q^{4} - 8 q^{5} - 24 q^{7}+O(q^{10}) \) 10 * q + 3 * q^2 + 29 * q^4 - 8 * q^5 - 24 * q^7	\( 10 q + 3 q^{2} + 29 q^{4} - 8 q^{5} - 24 q^{7} + 144 q^{10} - 50 q^{11} - 624 q^{13} + 474 q^{14} + 285 q^{16} + 292 q^{17} + 305 q^{19} + 652 q^{20} + 1629 q^{22} - 98 q^{23} - 681 q^{25} - 1524 q^{26} - 1472 q^{28} - 2598 q^{29} + 2745 q^{32} + 486 q^{34} - 694 q^{35} + 342 q^{38} + 8784 q^{40} + 1407 q^{41} + 5424 q^{43} - 4151 q^{44} + 2416 q^{47} - 17826 q^{49} - 19962 q^{52} - 1122 q^{53} + 11424 q^{55} - 20236 q^{58} - 15387 q^{59} + 860 q^{61} - 21636 q^{62} + 19710 q^{64} + 14763 q^{67} + 48844 q^{68} - 20334 q^{70} + 27264 q^{71} + 1561 q^{73} - 17094 q^{74} + 1955 q^{76} + 18392 q^{77} + 24750 q^{79} + 2002 q^{80} + 14479 q^{82} - 6002 q^{83} - 14944 q^{85} - 59946 q^{86} + 22566 q^{89} + 8724 q^{91} - 9572 q^{92} + 7312 q^{95} + 46287 q^{97} - 25515 q^{98}+O(q^{100}) \) 10 * q + 3 * q^2 + 29 * q^4 - 8 * q^5 - 24 * q^7 + 144 * q^10 - 50 * q^11 - 624 * q^13 + 474 * q^14 + 285 * q^16 + 292 * q^17 + 305 * q^19 + 652 * q^20 + 1629 * q^22 - 98 * q^23 - 681 * q^25 - 1524 * q^26 - 1472 * q^28 - 2598 * q^29 + 2745 * q^32 + 486 * q^34 - 694 * q^35 + 342 * q^38 + 8784 * q^40 + 1407 * q^41 + 5424 * q^43 - 4151 * q^44 + 2416 * q^47 - 17826 * q^49 - 19962 * q^52 - 1122 * q^53 + 11424 * q^55 - 20236 * q^58 - 15387 * q^59 + 860 * q^61 - 21636 * q^62 + 19710 * q^64 + 14763 * q^67 + 48844 * q^68 - 20334 * q^70 + 27264 * q^71 + 1561 * q^73 - 17094 * q^74 + 1955 * q^76 + 18392 * q^77 + 24750 * q^79 + 2002 * q^80 + 14479 * q^82 - 6002 * q^83 - 14944 * q^85 - 59946 * q^86 + 22566 * q^89 + 8724 * q^91 - 9572 * q^92 + 7312 * q^95 + 46287 * q^97 - 25515 * q^98

Introduction

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