LMFDB - Embedded newform 441.3.r.g.50.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,3,Mod(50,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.50"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,6,11] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			50.11
Character	$\chi$	$=$	441.50
Dual form			441.3.r.g.344.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.19625 - 1.84536i) q^{2} +(-1.88682 - 2.33236i) q^{3} +(4.81069 - 8.33236i) q^{4} +(-5.05096 - 2.91617i) q^{5} +(-10.3348 - 3.97296i) q^{6} -20.7469i q^{8} +(-1.87982 + 8.80149i) q^{9} -21.5255 q^{10} +(-2.91374 + 1.68225i) q^{11} +(-28.5110 + 4.50140i) q^{12} +(0.158134 - 0.273895i) q^{13} +(2.72868 + 17.2829i) q^{15} +(-19.0428 - 32.9830i) q^{16} -3.46309i q^{17} +(10.2335 + 31.6007i) q^{18} +24.0674 q^{19} +(-48.5972 + 28.0576i) q^{20} +(-6.20870 + 10.7538i) q^{22} +(-29.4672 - 17.0129i) q^{23} +(-48.3893 + 39.1457i) q^{24} +(4.50810 + 7.80826i) q^{25} -1.16725i q^{26} +(24.0751 - 12.2224i) q^{27} +(31.6161 - 18.2536i) q^{29} +(40.6148 + 50.2053i) q^{30} +(-12.0916 + 20.9433i) q^{31} +(-49.8615 - 28.7875i) q^{32} +(9.42131 + 3.62179i) q^{33} +(-6.39064 - 11.0689i) q^{34} +(64.2940 + 58.0046i) q^{36} -8.46807 q^{37} +(76.9256 - 44.4130i) q^{38} +(-0.937193 + 0.147967i) q^{39} +(-60.5016 + 104.792i) q^{40} +(-39.9308 - 23.0541i) q^{41} +(-26.4994 - 45.8984i) q^{43} +32.3711i q^{44} +(35.1615 - 38.9741i) q^{45} -125.579 q^{46} +(17.2703 - 9.97104i) q^{47} +(-40.9981 + 106.648i) q^{48} +(28.8181 + 16.6381i) q^{50} +(-8.07717 + 6.53422i) q^{51} +(-1.52146 - 2.63525i) q^{52} +33.8223i q^{53} +(54.3955 - 83.4932i) q^{54} +19.6229 q^{55} +(-45.4109 - 56.1339i) q^{57} +(67.3688 - 116.686i) q^{58} +(-31.5660 - 18.2246i) q^{59} +(157.135 + 60.4066i) q^{60} +(-6.02138 - 10.4293i) q^{61} +89.2535i q^{62} -60.1511 q^{64} +(-1.59745 + 0.922289i) q^{65} +(36.7964 - 5.80952i) q^{66} +(17.4628 - 30.2465i) q^{67} +(-28.8557 - 16.6599i) q^{68} +(15.9191 + 100.828i) q^{69} -85.7413i q^{71} +(182.604 + 39.0005i) q^{72} +70.7566 q^{73} +(-27.0661 + 15.6266i) q^{74} +(9.70571 - 25.2473i) q^{75} +(115.781 - 200.539i) q^{76} +(-2.72245 + 2.20240i) q^{78} +(50.7030 + 87.8201i) q^{79} +222.128i q^{80} +(-73.9326 - 33.0904i) q^{81} -170.172 q^{82} +(26.0171 - 15.0210i) q^{83} +(-10.0990 + 17.4919i) q^{85} +(-169.398 - 97.8019i) q^{86} +(-102.228 - 39.2990i) q^{87} +(34.9015 + 60.4511i) q^{88} -53.7441i q^{89} +(40.4641 - 189.457i) q^{90} +(-283.515 + 163.688i) q^{92} +(71.6621 - 11.3142i) q^{93} +(36.8003 - 63.7400i) q^{94} +(-121.563 - 70.1847i) q^{95} +(26.9367 + 170.612i) q^{96} +(-3.60974 - 6.25225i) q^{97} +(-9.32899 - 28.8076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{2} + 11 q^{3} + 12 q^{4} - 12 q^{5} - 8 q^{6} + 17 q^{9} - 50 q^{10} - 24 q^{11} - 20 q^{12} - 18 q^{13} + 53 q^{15} + 12 q^{16} + 16 q^{18} - 6 q^{19} - 39 q^{20} - 59 q^{22} - 81 q^{23} - 141 q^{24}+ \cdots - 103 q^{99}+O(q^{100}) $ 22 * q + 6 * q^2 + 11 * q^3 + 12 * q^4 - 12 * q^5 - 8 * q^6 + 17 * q^9 - 50 * q^10 - 24 * q^11 - 20 * q^12 - 18 * q^13 + 53 * q^15 + 12 * q^16 + 16 * q^18 - 6 * q^19 - 39 * q^20 - 59 * q^22 - 81 * q^23 - 141 * q^24 + 57 * q^25 - 97 * q^27 - 63 * q^29 + 58 * q^30 - 29 * q^31 - 246 * q^32 - 73 * q^33 - 99 * q^34 + 76 * q^36 + 40 * q^37 + 48 * q^38 - 124 * q^39 - 105 * q^40 - 51 * q^41 + 65 * q^43 + 143 * q^45 - 150 * q^46 - 261 * q^47 - 113 * q^48 + 63 * q^50 - 63 * q^51 - 46 * q^52 + 52 * q^54 - 100 * q^55 + 224 * q^57 + 40 * q^58 + 102 * q^59 + 379 * q^60 + 78 * q^61 + 106 * q^64 + 225 * q^65 + 340 * q^66 - 132 * q^67 - 27 * q^68 - 297 * q^69 + 288 * q^72 - 2 * q^73 - 342 * q^74 + 541 * q^75 + 233 * q^76 - 440 * q^78 + 140 * q^79 + 65 * q^81 + 314 * q^82 + 255 * q^83 + 102 * q^85 - 504 * q^86 - 568 * q^87 + 408 * q^88 + 418 * q^90 - 1239 * q^92 - 174 * q^93 + 261 * q^94 - 642 * q^95 - 142 * q^96 + 178 * q^97 - 103 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	3.19625	−	1.84536i	1.59813	−	0.922679i	0.606279	−	0.795252i	$-0.292661\pi$
$2$	3.19625	−	1.84536i	1.59813	−	0.922679i	0.991848	−	0.127427i	$-0.0406718\pi$
$3$	−1.88682	−	2.33236i	−0.628940	−	0.777454i
$3$	−1.88682	−	2.33236i	−0.628940	−	0.777454i
$4$	4.81069	−	8.33236i	1.20267	−	2.08309i
$5$	−5.05096	−	2.91617i	−1.01019	−	0.583234i	−0.0989435	−	0.995093i	$-0.531546\pi$
$5$	−5.05096	−	2.91617i	−1.01019	−	0.583234i	−0.911248	+	0.411859i	$0.864880\pi$
$6$	−10.3348	−	3.97296i	−1.72247	−	0.662160i
$7$		0			0
$7$		0			0
$8$		−	20.7469i		−	2.59337i
$9$	−1.87982	+	8.80149i	−0.208869	+	0.977944i
$10$	−21.5255			−2.15255
$11$	−2.91374	+	1.68225i	−0.264885	+	0.152932i	−0.626561	−	0.779372i	$-0.715538\pi$
$11$	−2.91374	+	1.68225i	−0.264885	+	0.152932i	0.361676	+	0.932304i	$0.382205\pi$
$12$	−28.5110	+	4.50140i	−2.37592	+	0.375117i
$13$	0.158134	−	0.273895i	0.0121641	−	0.0210689i	−0.859879	−	0.510497i	$-0.829461\pi$
$13$	0.158134	−	0.273895i	0.0121641	−	0.0210689i	0.872043	+	0.489429i	$0.162795\pi$
$14$		0			0
$15$	2.72868	+	17.2829i	0.181912	+	1.15220i
$16$	−19.0428	−	32.9830i	−1.19017	−	2.06144i
$17$		−	3.46309i		−	0.203711i	−0.994799	−	0.101856i	$-0.967522\pi$
$17$		−	3.46309i		−	0.203711i	0.994799	−	0.101856i	$-0.0324779\pi$
$18$	10.2335	+	31.6007i	0.568529	+	1.75560i
$19$	24.0674			1.26671			0.633353	−	0.773863i	$-0.281678\pi$
$19$	24.0674			1.26671			0.633353	+	0.773863i	$0.281678\pi$
$20$	−48.5972	+	28.0576i	−2.42986	+	1.40288i
$21$		0			0
$22$	−6.20870	+	10.7538i	−0.282214	+	0.488808i
$23$	−29.4672	−	17.0129i	−1.28118	−	0.739691i	−0.304117	−	0.952635i	$-0.598362\pi$
$23$	−29.4672	−	17.0129i	−1.28118	−	0.739691i	−0.977064	+	0.212944i	$0.931695\pi$
$24$	−48.3893	+	39.1457i	−2.01622	+	1.63107i
$25$	4.50810	+	7.80826i	0.180324	+	0.312331i
$26$		−	1.16725i		−	0.0448943i
$27$	24.0751	−	12.2224i	0.891672	−	0.452682i
$28$		0			0
$29$	31.6161	−	18.2536i	1.09021	−	0.629434i	0.156579	−	0.987665i	$-0.449953\pi$
$29$	31.6161	−	18.2536i	1.09021	−	0.629434i	0.933633	+	0.358231i	$0.116620\pi$
$30$	40.6148	+	50.2053i	1.35383	+	1.67351i
$31$	−12.0916	+	20.9433i	−0.390052	+	0.675591i	−0.992456	−	0.122601i	$-0.960876\pi$
$31$	−12.0916	+	20.9433i	−0.390052	+	0.675591i	0.602404	+	0.798192i	$0.294210\pi$
$32$	−49.8615	−	28.7875i	−1.55817	−	0.899610i
$33$	9.42131	+	3.62179i	0.285494	+	0.109751i
$34$	−6.39064	−	11.0689i	−0.187960	−	0.325556i
$35$		0			0
$36$	64.2940	+	58.0046i	1.78594	+	1.61124i
$37$	−8.46807			−0.228867			−0.114433	−	0.993431i	$-0.536505\pi$
$37$	−8.46807			−0.228867			−0.114433	+	0.993431i	$0.536505\pi$
$38$	76.9256	−	44.4130i	2.02436	−	1.16876i
$39$	−0.937193	+	0.147967i	−0.0240306	+	0.00379402i
$40$	−60.5016	+	104.792i	−1.51254	+	2.61980i
$41$	−39.9308	−	23.0541i	−0.973922	−	0.562294i	−0.0734924	−	0.997296i	$-0.523414\pi$
$41$	−39.9308	−	23.0541i	−0.973922	−	0.562294i	−0.900430	+	0.435002i	$0.856748\pi$
$42$		0			0
$43$	−26.4994	−	45.8984i	−0.616266	−	1.06740i	−0.990161	−	0.139933i	$-0.955311\pi$
$43$	−26.4994	−	45.8984i	−0.616266	−	1.06740i	0.373895	−	0.927471i	$-0.378022\pi$
$44$			32.3711i			0.735707i
$45$	35.1615	−	38.9741i	0.781368	−	0.866091i
$46$	−125.579			−2.72999
$47$	17.2703	−	9.97104i	0.367454	−	0.212150i	−0.304891	−	0.952387i	$-0.598620\pi$
$47$	17.2703	−	9.97104i	0.367454	−	0.212150i	0.672346	+	0.740237i	$0.265287\pi$
$48$	−40.9981	+	106.648i	−0.854126	+	2.22182i
$49$		0			0
$50$	28.8181	+	16.6381i	0.576362	+	0.332763i
$51$	−8.07717	+	6.53422i	−0.158376	+	0.128122i
$52$	−1.52146	−	2.63525i	−0.0292589	−	0.0506779i
$53$			33.8223i			0.638156i	0.947728	+	0.319078i	$0.103373\pi$
$53$			33.8223i			0.638156i	−0.947728	+	0.319078i	$0.896627\pi$
$54$	54.3955	−	83.4932i	1.00732	−	1.54617i
$55$	19.6229			0.356780
$56$		0			0
$57$	−45.4109	−	56.1339i	−0.796682	−	0.984806i
$58$	67.3688	−	116.686i	1.16153	−	2.01183i
$59$	−31.5660	−	18.2246i	−0.535017	−	0.308892i	0.208040	−	0.978120i	$-0.433292\pi$
$59$	−31.5660	−	18.2246i	−0.535017	−	0.308892i	−0.743057	+	0.669228i	$0.766625\pi$
$60$	157.135	+	60.4066i	2.61891	+	1.00678i
$61$	−6.02138	−	10.4293i	−0.0987111	−	0.170973i	0.812440	−	0.583044i	$-0.198139\pi$
$61$	−6.02138	−	10.4293i	−0.0987111	−	0.170973i	−0.911151	+	0.412072i	$0.864805\pi$
$62$			89.2535i			1.43957i
$63$		0			0
$64$	−60.1511			−0.939861
$65$	−1.59745	+	0.922289i	−0.0245762	+	0.0141891i
$66$	36.7964	−	5.80952i	0.557521	−	0.0880231i
$67$	17.4628	−	30.2465i	0.260639	−	0.451440i	−0.705773	−	0.708438i	$-0.749400\pi$
$67$	17.4628	−	30.2465i	0.260639	−	0.451440i	0.966412	+	0.256998i	$0.0827334\pi$
$68$	−28.8557	−	16.6599i	−0.424349	−	0.244998i
$69$	15.9191	+	100.828i	0.230711	+	1.46128i
$70$		0			0
$71$		−	85.7413i		−	1.20762i	−0.797127	−	0.603812i	$-0.793648\pi$
$71$		−	85.7413i		−	1.20762i	0.797127	−	0.603812i	$-0.206352\pi$
$72$	182.604	+	39.0005i	2.53617	+	0.541673i
$73$	70.7566			0.969268			0.484634	−	0.874717i	$-0.338953\pi$
$73$	70.7566			0.969268			0.484634	+	0.874717i	$0.338953\pi$
$74$	−27.0661	+	15.6266i	−0.365758	+	0.211170i
$75$	9.70571	−	25.2473i	0.129410	−	0.336631i
$76$	115.781	−	200.539i	1.52343	−	2.63866i
$77$		0			0
$78$	−2.72245	+	2.20240i	−0.0349033	+	0.0282358i
$79$	50.7030	+	87.8201i	0.641810	+	1.11165i	0.985029	+	0.172392i	$0.0551494\pi$
$79$	50.7030	+	87.8201i	0.641810	+	1.11165i	−0.343219	+	0.939255i	$0.611517\pi$
$80$			222.128i			2.77660i
$81$	−73.9326	−	33.0904i	−0.912748	−	0.408524i
$82$	−170.172			−2.07527
$83$	26.0171	−	15.0210i	0.313459	−	0.180976i	−0.335014	−	0.942213i	$-0.608741\pi$
$83$	26.0171	−	15.0210i	0.313459	−	0.180976i	0.648473	+	0.761237i	$0.275408\pi$
$84$		0			0
$85$	−10.0990	+	17.4919i	−0.118811	+	0.205787i
$86$	−169.398	−	97.8019i	−1.96974	−	1.13723i
$87$	−102.228	−	39.2990i	−1.17503	−	0.451713i
$88$	34.9015	+	60.4511i	0.396608	+	0.686945i
$89$		−	53.7441i		−	0.603866i	−0.953329	−	0.301933i	$-0.902368\pi$
$89$		−	53.7441i		−	0.603866i	0.953329	−	0.301933i	$-0.0976320\pi$
$90$	40.4641	−	189.457i	0.449601	−	2.10507i
$91$		0			0
$92$	−283.515	+	163.688i	−3.08169	+	1.77921i
$93$	71.6621	−	11.3142i	0.770560	−	0.121658i
$94$	36.8003	−	63.7400i	0.391492	−	0.678085i
$95$	−121.563	−	70.1847i	−1.27962	−	0.738786i
$96$	26.9367	+	170.612i	0.280591	+	1.77721i
$97$	−3.60974	−	6.25225i	−0.0372138	−	0.0644561i	0.846819	−	0.531882i	$-0.178515\pi$
$97$	−3.60974	−	6.25225i	−0.0372138	−	0.0644561i	−0.884032	+	0.467426i	$0.845182\pi$
$98$		0			0
$99$	−9.32899	−	28.8076i	−0.0942322	−	0.290986i
$100$	86.7484			0.867484
$101$	52.3908	−	30.2479i	0.518721	−	0.299484i	−0.217690	−	0.976018i	$-0.569852\pi$
$101$	52.3908	−	30.2479i	0.518721	−	0.299484i	0.736411	+	0.676534i	$0.236519\pi$
$102$	−13.7587	+	35.7903i	−0.134889	+	0.350885i
$103$	81.6220	−	141.373i	0.792447	−	1.37256i	−0.132001	−	0.991250i	$-0.542140\pi$
$103$	81.6220	−	141.373i	0.792447	−	1.37256i	0.924448	−	0.381308i	$-0.124526\pi$
$104$	−5.68249	−	3.28079i	−0.0546393	−	0.0315460i
$105$		0			0
$106$	62.4142	+	108.105i	0.588813	+	1.01985i
$107$			112.941i			1.05552i	0.849392	+	0.527762i	$0.176969\pi$
$107$			112.941i			1.05552i	−0.849392	+	0.527762i	$0.823031\pi$
$108$	13.9765	−	259.401i	0.129412	−	2.40186i
$109$	125.264			1.14921			0.574607	−	0.818430i	$-0.305155\pi$
$109$	125.264			1.14921			0.574607	+	0.818430i	$0.305155\pi$
$110$	62.7197	−	36.2112i	0.570179	−	0.329193i
$111$	15.9777	+	19.7506i	0.143943	+	0.177933i
$112$		0			0
$113$	−29.6935	−	17.1435i	−0.262774	−	0.151713i	0.362825	−	0.931857i	$-0.381812\pi$
$113$	−29.6935	−	17.1435i	−0.262774	−	0.151713i	−0.625599	+	0.780144i	$0.715146\pi$
$114$	−248.732	−	95.6189i	−2.18186	−	0.838762i
$115$	99.2250	+	171.863i	0.862826	+	1.49446i
$116$		−	351.250i		−	3.02801i
$117$	2.11343	+	1.90669i	0.0180635	+	0.0162965i
$118$	−134.524			−1.14003
$119$		0			0
$120$	358.568	−	56.6118i	2.98807	−	0.471765i
$121$	−54.8401	+	94.9858i	−0.453224	+	0.785007i
$122$	−38.4917	−	22.2232i	−0.315506	−	0.182157i
$123$	21.5719	+	136.632i	0.175381	+	1.11083i
$124$	116.338	+	201.504i	0.938211	+	1.62503i
$125$			93.2229i			0.745784i
$126$		0			0
$127$	216.982			1.70852			0.854259	−	0.519847i	$-0.174011\pi$
$127$	216.982			1.70852			0.854259	+	0.519847i	$0.174011\pi$
$128$	7.18756	−	4.14974i	0.0561528	−	0.0324199i
$129$	−57.0519	+	148.408i	−0.442263	+	1.15045i
$130$	−3.40391	+	5.89574i	−0.0261839	+	0.0453519i
$131$	107.699	+	62.1798i	0.822126	+	0.474655i	0.851149	−	0.524924i	$-0.175906\pi$
$131$	107.699	+	62.1798i	0.822126	+	0.474655i	−0.0290229	+	0.999579i	$0.509240\pi$
$132$	75.5011	−	61.0784i	0.571978	−	0.462716i
$133$		0			0
$134$		−	128.901i		−	0.961944i
$135$	−157.245	−	8.47232i	−1.16478	−	0.0627580i
$136$	−71.8485			−0.528298
$137$	5.77715	−	3.33544i	0.0421690	−	0.0243463i	−0.478767	−	0.877942i	$-0.658916\pi$
$137$	5.77715	−	3.33544i	0.0421690	−	0.0243463i	0.520936	+	0.853596i	$0.325583\pi$
$138$	236.946	+	292.897i	1.71700	+	2.12244i
$139$	−8.80202	+	15.2455i	−0.0633239	+	0.109680i	−0.895949	−	0.444156i	$-0.853503\pi$
$139$	−8.80202	+	15.2455i	−0.0633239	+	0.109680i	0.832625	+	0.553837i	$0.186837\pi$
$140$		0			0
$141$	−55.8421	−	21.4671i	−0.396043	−	0.152249i
$142$	−158.223	−	274.051i	−1.11425	−	1.92994i
$143$			1.06408i			0.00744111i
$144$	326.097	−	105.603i	2.26456	−	0.733351i
$145$	−212.922			−1.46843
$146$	226.156	−	130.571i	1.54901	−	0.894323i
$147$		0			0
$148$	−40.7373	+	70.5590i	−0.275252	+	0.476750i
$149$	25.7165	+	14.8474i	0.172594	+	0.0996472i	0.583808	−	0.811891i	$-0.301562\pi$
$149$	25.7165	+	14.8474i	0.172594	+	0.0996472i	−0.411214	+	0.911539i	$0.634895\pi$
$150$	−15.5684	−	98.6074i	−0.103789	−	0.657382i
$151$	34.9796	+	60.5864i	0.231653	+	0.401234i	0.958295	−	0.285782i	$-0.0922534\pi$
$151$	34.9796	+	60.5864i	0.231653	+	0.401234i	−0.726642	+	0.687016i	$0.758920\pi$
$152$		−	499.325i		−	3.28503i
$153$	30.4803	+	6.50998i	0.199218	+	0.0425489i
$154$		0			0
$155$	122.149	−	70.5225i	0.788055	−	0.454984i
$156$	−3.27563	+	8.52085i	−0.0209977	+	0.0546209i
$157$	98.3195	−	170.294i	0.626239	−	1.08468i	−0.362061	−	0.932155i	$-0.617927\pi$
$157$	98.3195	−	170.294i	0.626239	−	1.08468i	0.988300	−	0.152523i	$-0.0487400\pi$
$158$	324.119	+	187.130i	2.05139	+	1.18437i
$159$	78.8857	−	63.8165i	0.496137	−	0.401362i
$160$	167.899	+	290.809i	1.04937	+	1.81756i
$161$		0			0
$162$	−297.371	+	30.6667i	−1.83562	+	0.189300i
$163$	9.28348			0.0569539			0.0284769	−	0.999594i	$-0.490934\pi$
$163$	9.28348			0.0569539			0.0284769	+	0.999594i	$0.490934\pi$
$164$	−384.190	+	221.812i	−2.34262	+	1.35251i
$165$	−37.0249	−	45.7677i	−0.224393	−	0.277380i
$166$	55.4382	−	96.0219i	0.333965	−	0.578445i
$167$	−91.5268	−	52.8430i	−0.548065	−	0.316425i	0.200276	−	0.979739i	$-0.435816\pi$
$167$	−91.5268	−	52.8430i	−0.548065	−	0.316425i	−0.748341	+	0.663314i	$0.769149\pi$
$168$		0			0
$169$	84.4500	+	146.272i	0.499704	+	0.865513i
$170$			74.5448i			0.438499i
$171$	−45.2424	+	211.829i	−0.264575	+	1.23877i
$172$	−509.922			−2.96466
$173$	−166.778	+	96.2891i	−0.964033	+	0.556585i	−0.897412	−	0.441194i	$-0.854555\pi$
$173$	−166.778	+	96.2891i	−0.964033	+	0.556585i	−0.0666210	+	0.997778i	$0.521222\pi$
$174$	−399.267	+	63.0375i	−2.29464	+	0.362284i
$175$		0			0
$176$	110.971	+	64.0692i	0.630518	+	0.364030i
$177$	17.0529	+	108.010i	0.0963443	+	0.610226i
$178$	−99.1771	−	171.780i	−0.557175	−	0.965055i
$179$		−	53.5738i		−	0.299295i	−0.988739	−	0.149648i	$-0.952186\pi$
$179$		−	53.5738i		−	0.299295i	0.988739	−	0.149648i	$-0.0478139\pi$
$180$	−155.595	−	480.471i	−0.864416	−	2.66928i
$181$	−113.509			−0.627124			−0.313562	−	0.949568i	$-0.601522\pi$
$181$	−113.509			−0.627124			−0.313562	+	0.949568i	$0.601522\pi$
$182$		0			0
$183$	−12.9637	+	33.7223i	−0.0708400	+	0.184275i
$184$	−352.965	+	611.354i	−1.91829	+	3.32257i
$185$	42.7718	+	24.6943i	0.231199	+	0.133483i
$186$	208.171	−	168.405i	1.11920	−	0.905405i
$187$	5.82577	+	10.0905i	0.0311539	+	0.0539601i
$188$		−	191.870i		−	1.02059i
$189$		0			0
$190$	−518.064			−2.72665
$191$	149.464	−	86.2931i	0.782535	−	0.451797i	−0.0547932	−	0.998498i	$-0.517450\pi$
$191$	149.464	−	86.2931i	0.782535	−	0.451797i	0.837328	+	0.546701i	$0.184117\pi$
$192$	113.494	+	140.294i	0.591116	+	0.730699i
$193$	−95.1620	+	164.825i	−0.493068	+	0.854018i	−0.999968	−	0.00798645i	$-0.997458\pi$
$193$	−95.1620	+	164.825i	−0.493068	+	0.854018i	0.506901	+	0.862005i	$0.330791\pi$
$194$	−23.0753	−	13.3225i	−0.118945	−	0.0686727i
$195$	5.16522	+	1.98564i	0.0264883	+	0.0101828i
$196$		0			0
$197$		−	98.0156i		−	0.497541i	−0.968562	−	0.248770i	$-0.919974\pi$
$197$		−	98.0156i		−	0.497541i	0.968562	−	0.248770i	$-0.0800265\pi$
$198$	−82.9781	−	74.8610i	−0.419081	−	0.378086i
$199$	−256.298			−1.28793			−0.643965	−	0.765055i	$-0.722712\pi$
$199$	−256.298			−1.28793			−0.643965	+	0.765055i	$0.722712\pi$
$200$	161.998	−	93.5293i	0.809988	−	0.467647i
$201$	−103.495	+	16.3401i	−0.514900	+	0.0812939i
$202$	111.636	−	193.360i	0.552655	−	0.957226i
$203$		0			0
$204$	15.5887	+	98.7361i	0.0764154	+	0.484000i
$205$	134.459	+	232.890i	0.655898	+	1.13605i
$206$		−	602.487i		−	2.92470i
$207$	205.132	−	227.374i	0.990975	−	1.09843i
$208$	−12.0452			−0.0579096
$209$	−70.1262	+	40.4874i	−0.335532	+	0.193719i
$210$		0			0
$211$	−130.914	+	226.750i	−0.620447	+	1.07465i	0.368955	+	0.929447i	$0.379716\pi$
$211$	−130.914	+	226.750i	−0.620447	+	1.07465i	−0.989402	+	0.145199i	$0.953618\pi$
$212$	281.819	+	162.708i	1.32934	+	0.767493i
$213$	−199.980	+	161.778i	−0.938872	+	0.759523i
$214$	208.417	+	360.989i	0.973911	+	1.68686i
$215$			309.107i			1.43771i
$216$	−253.578	−	499.485i	−1.17397	−	2.31243i
$217$		0			0
$218$	400.377	−	231.157i	1.83659	−	1.06036i
$219$	−133.505	−	165.030i	−0.609611	−	0.753561i
$220$	94.3997	−	163.505i	0.429089	−	0.743205i
$221$	−0.948524	−	0.547631i	−0.00429196	−	0.00247797i
$222$	87.5157	+	33.6433i	0.394215	+	0.151546i
$223$	179.709	+	311.266i	0.805872	+	1.39581i	0.915701	+	0.401860i	$0.131636\pi$
$223$	179.709	+	311.266i	0.805872	+	1.39581i	−0.109829	+	0.993950i	$0.535030\pi$
$224$		0			0
$225$	−77.1988	+	24.9999i	−0.343106	+	0.111111i
$226$	−126.544			−0.559929
$227$	353.118	−	203.873i	1.55559	−	0.898118i	0.557916	−	0.829897i	$-0.311601\pi$
$227$	353.118	−	203.873i	1.55559	−	0.898118i	0.997670	−	0.0682208i	$-0.0217322\pi$
$228$	−686.186	+	108.337i	−3.00959	+	0.475163i
$229$	−38.7964	+	67.1973i	−0.169417	+	0.293438i	−0.938215	−	0.346053i	$-0.887522\pi$
$229$	−38.7964	+	67.1973i	−0.169417	+	0.293438i	0.768798	+	0.639491i	$0.220855\pi$
$230$	634.296	+	366.211i	2.75781	+	1.59222i
$231$		0			0
$232$	−378.706	−	655.938i	−1.63235	−	2.82732i
$233$		−	454.356i		−	1.95003i	−0.222148	−	0.975013i	$-0.571307\pi$
$233$		−	454.356i		−	1.95003i	0.222148	−	0.975013i	$-0.428693\pi$
$234$	10.2736	+	2.19422i	0.0439041	+	0.00937702i
$235$	−116.309			−0.494932
$236$	−303.709	+	175.346i	−1.28690	+	0.742993i
$237$	109.161	−	283.958i	0.460594	−	1.19814i
$238$		0			0
$239$	−44.0684	−	25.4429i	−0.184387	−	0.106456i	0.404965	−	0.914332i	$-0.367284\pi$
$239$	−44.0684	−	25.4429i	−0.184387	−	0.106456i	−0.589352	+	0.807876i	$0.700617\pi$
$240$	518.082	−	419.115i	2.15867	−	1.74631i
$241$	95.7821	+	165.900i	0.397436	+	0.688380i	0.993409	−	0.114625i	$-0.0365666\pi$
$241$	95.7821	+	165.900i	0.397436	+	0.688380i	−0.595973	+	0.803005i	$0.703233\pi$
$242$			404.798i			1.67272i
$243$	62.3186	+	234.873i	0.256455	+	0.966556i
$244$	−115.868			−0.474869
$245$		0			0
$246$	321.084	+	396.903i	1.30522	+	1.61342i
$247$	3.80587	−	6.59196i	0.0154084	−	0.0266881i
$248$	434.509	+	250.864i	1.75205	+	1.01155i
$249$	−84.1241	−	32.3394i	−0.337848	−	0.129877i
$250$	172.030	+	297.964i	0.688119	+	1.19186i
$251$			262.216i			1.04469i	0.852735	+	0.522343i	$0.174942\pi$
$251$			262.216i			1.04469i	−0.852735	+	0.522343i	$0.825058\pi$
$252$		0			0
$253$	114.480			0.452488
$254$	693.529	−	400.409i	2.73043	−	1.57641i
$255$	59.8524	−	9.44967i	0.234715	−	0.0370575i
$256$	135.618	−	234.897i	0.529757	−	0.917566i
$257$	−122.518	−	70.7359i	−0.476724	−	0.275237i	0.242326	−	0.970195i	$-0.422090\pi$
$257$	−122.518	−	70.7359i	−0.476724	−	0.275237i	−0.719050	+	0.694958i	$0.755423\pi$
$258$	91.5139	+	579.631i	0.354705	+	2.24663i
$259$		0			0
$260$			17.7474i			0.0682592i
$261$	101.226	+	312.583i	0.387840	+	1.19763i
$262$	458.976			1.75182
$263$	382.349	−	220.750i	1.45380	−	0.839352i	0.455106	−	0.890437i	$-0.349601\pi$
$263$	382.349	−	220.750i	1.45380	−	0.839352i	0.998694	+	0.0510853i	$0.0162680\pi$
$264$	75.1411	−	195.463i	0.284625	−	0.740391i
$265$	98.6315	−	170.835i	0.372194	−	0.644659i
$266$		0			0
$267$	−125.351	+	101.405i	−0.469478	+	0.379796i
$268$	−168.016	−	291.013i	−0.626927	−	1.08587i
$269$			102.334i			0.380424i	0.981743	+	0.190212i	$0.0609176\pi$
$269$			102.334i			0.380424i	−0.981743	+	0.190212i	$0.939082\pi$
$270$	−518.230	+	263.094i	−1.91937	+	0.974422i
$271$	320.806			1.18379			0.591893	−	0.806016i	$-0.298381\pi$
$271$	320.806			1.18379			0.591893	+	0.806016i	$0.298381\pi$
$272$	−114.223	+	65.9467i	−0.419938	+	0.242451i
$273$		0			0
$274$	12.3102	−	21.3218i	0.0449276	−	0.0778168i
$275$	−26.2709	−	15.1675i	−0.0955304	−	0.0551545i
$276$	916.720	+	352.411i	3.32145	+	1.27685i
$277$	−102.207	−	177.028i	−0.368979	−	0.639091i	0.620427	−	0.784264i	$-0.286959\pi$
$277$	−102.207	−	177.028i	−0.368979	−	0.639091i	−0.989406	+	0.145173i	$0.953626\pi$
$278$			64.9715i			0.233710i
$279$	−161.602	−	145.794i	−0.579220	−	0.522559i
$280$		0			0
$281$	−10.0933	+	5.82736i	−0.0359191	+	0.0207379i	−0.517852	−	0.855470i	$-0.673268\pi$
$281$	−10.0933	+	5.82736i	−0.0359191	+	0.0207379i	0.481933	+	0.876208i	$0.339935\pi$
$282$	−218.100	+	34.4343i	−0.773405	+	0.122107i
$283$	−173.123	+	299.857i	−0.611740	+	1.05957i	0.379207	+	0.925312i	$0.376197\pi$
$283$	−173.123	+	299.857i	−0.611740	+	1.05957i	−0.990947	+	0.134254i	$0.957136\pi$
$284$	−714.428	−	412.475i	−2.51559	−	1.45238i
$285$	65.6723	+	415.956i	0.230429	+	1.45949i
$286$	1.96361	+	3.40107i	0.00686576	+	0.0118918i
$287$		0			0
$288$	347.104	−	384.740i	1.20522	−	1.33590i
$289$	277.007			0.958502
$290$	−680.554	+	392.918i	−2.34674	+	1.35489i
$291$	−7.77157	+	20.2161i	−0.0267064	+	0.0694710i
$292$	340.388	−	589.569i	1.16571	−	2.01907i
$293$	−81.5708	−	47.0949i	−0.278399	−	0.160734i	0.354300	−	0.935132i	$-0.384719\pi$
$293$	−81.5708	−	47.0949i	−0.278399	−	0.160734i	−0.632698	+	0.774398i	$0.718053\pi$
$294$		0			0
$295$	106.292	+	184.104i	0.360313	+	0.624081i
$296$			175.686i			0.593535i
$297$	−49.5875	+	76.1133i	−0.166961	+	0.256274i
$298$	109.595			0.367769
$299$	−9.31950	+	5.38062i	−0.0311689	+	0.0179954i
$300$	−163.679	−	202.329i	−0.545595	−	0.674429i
$301$		0			0
$302$	223.607	+	129.100i	0.740421	+	0.427482i
$303$	−169.401	−	65.1221i	−0.559079	−	0.214924i
$304$	−458.310	−	793.816i	−1.50760	−	2.61124i
$305$			70.2375i			0.230287i
$306$	109.436	−	35.4396i	0.357635	−	0.115816i
$307$	−503.730			−1.64081			−0.820407	−	0.571781i	$-0.806253\pi$
$307$	−503.730			−1.64081			−0.820407	+	0.571781i	$0.806253\pi$
$308$		0			0
$309$	−483.740	+	76.3743i	−1.56550	+	0.247166i
$310$	260.278	−	450.816i	0.839608	−	1.45424i
$311$	238.993	+	137.983i	0.768467	+	0.443675i	0.832328	−	0.554284i	$-0.187008\pi$
$311$	238.993	+	137.983i	0.768467	+	0.443675i	−0.0638603	+	0.997959i	$0.520341\pi$
$312$	3.06986	+	19.4439i	0.00983928	+	0.0623201i
$313$	−190.541	−	330.028i	−0.608759	−	1.05440i	−0.991445	−	0.130523i	$-0.958334\pi$
$313$	−190.541	−	330.028i	−0.608759	−	1.05440i	0.382687	−	0.923878i	$-0.374999\pi$
$314$		−	725.739i		−	2.31127i
$315$		0			0
$316$	975.665			3.08755
$317$	−527.735	+	304.688i	−1.66478	+	0.961160i	−0.694394	+	0.719595i	$0.744328\pi$
$317$	−527.735	+	304.688i	−1.66478	+	0.961160i	−0.970384	+	0.241566i	$0.922339\pi$
$318$	134.374	−	349.546i	0.422561	−	1.09920i
$319$	−61.4141	+	106.372i	−0.192521	+	0.333456i
$320$	303.821	+	175.411i	0.949440	+	0.548159i
$321$	263.420	−	213.100i	0.820622	−	0.663862i
$322$		0			0
$323$		−	83.3476i		−	0.258042i
$324$	−631.388	+	456.845i	−1.94873	+	1.41002i
$325$	2.85153			0.00877394
$326$	29.6724	−	17.1313i	0.0910195	−	0.0525501i
$327$	−236.351	−	292.162i	−0.722787	−	0.893461i
$328$	−478.301	+	828.442i	−1.45824	+	2.52574i
$329$		0			0
$330$	−202.799	−	77.9609i	−0.614541	−	0.236245i
$331$	255.442	+	442.438i	0.771727	+	1.33667i	0.936616	+	0.350358i	$0.113940\pi$
$331$	255.442	+	442.438i	0.771727	+	1.33667i	−0.164889	+	0.986312i	$0.552727\pi$
$332$		−	289.046i		−	0.870619i
$333$	15.9184	−	74.5316i	0.0478031	−	0.223819i
$334$	−390.057			−1.16784
$335$	−176.408	+	101.849i	−0.526590	+	0.304027i
$336$		0			0
$337$	−72.9765	+	126.399i	−0.216547	+	0.375071i	−0.953750	−	0.300600i	$-0.902813\pi$
$337$	−72.9765	+	126.399i	−0.216547	+	0.375071i	0.737203	+	0.675672i	$0.236146\pi$
$338$	539.847	+	311.681i	1.59718	+	0.922133i
$339$	16.0413	+	101.603i	0.0473196	+	0.299713i
$340$	97.1659	+	168.296i	0.285782	+	0.494989i
$341$		−	81.3644i		−	0.238605i
$342$	246.295	+	760.548i	0.720160	+	2.22383i
$343$		0			0
$344$	−952.250	+	549.782i	−2.76817	+	1.59820i
$345$	213.626	−	555.702i	0.619206	−	1.61073i
$346$	−355.376	+	615.529i	−1.02710	+	1.77899i
$347$	−238.896	−	137.927i	−0.688461	−	0.397483i	0.114574	−	0.993415i	$-0.463450\pi$
$347$	−238.896	−	137.927i	−0.688461	−	0.397483i	−0.803035	+	0.595931i	$0.796783\pi$
$348$	−819.241	+	662.745i	−2.35414	+	1.90444i
$349$	119.986	+	207.822i	0.343800	+	0.595480i	0.985135	−	0.171782i	$-0.0549523\pi$
$349$	119.986	+	207.822i	0.343800	+	0.595480i	−0.641335	+	0.767261i	$0.721619\pi$
$350$		0			0
$351$	0.459424	−	8.52685i	0.00130890	−	0.0242930i
$352$	193.711			0.550315
$353$	−469.244	+	270.918i	−1.32930	+	0.767474i	−0.985192	−	0.171455i	$-0.945153\pi$
$353$	−469.244	+	270.918i	−1.32930	+	0.767474i	−0.344112	+	0.938929i	$0.611820\pi$
$354$	253.823	+	313.759i	0.717013	+	0.886324i
$355$	−250.036	+	433.076i	−0.704328	+	1.21993i
$356$	−447.815	−	258.546i	−1.25791	−	0.726254i
$357$		0			0
$358$	−98.8629	−	171.236i	−0.276153	−	0.478312i
$359$		−	442.377i		−	1.23225i	−0.787649	−	0.616124i	$-0.788702\pi$
$359$		−	442.377i		−	1.23225i	0.787649	−	0.616124i	$-0.211298\pi$
$360$	−808.593	−	729.494i	−2.24609	−	2.02637i
$361$	218.241			0.604545
$362$	−362.805	+	209.466i	−1.00222	+	0.578634i
$363$	325.015	−	51.3143i	0.895357	−	0.141362i
$364$		0			0
$365$	−357.388	−	206.338i	−0.979146	−	0.565310i
$366$	20.7944	+	131.708i	0.0568153	+	0.359857i
$367$	153.095	+	265.167i	0.417151	+	0.722527i	0.995652	−	0.0931549i	$-0.0296952\pi$
$367$	153.095	+	265.167i	0.417151	+	0.722527i	−0.578500	+	0.815682i	$0.696362\pi$
$368$			1295.89i			3.52144i
$369$	277.973	−	308.113i	0.753314	−	0.834995i
$370$	182.279			0.492647
$371$		0			0
$372$	250.470	−	651.544i	0.673307	−	1.75146i
$373$	−109.315	+	189.339i	−0.293069	+	0.507610i	−0.974534	−	0.224241i	$-0.928010\pi$
$373$	−109.315	+	189.339i	−0.293069	+	0.507610i	0.681465	+	0.731851i	$0.261343\pi$
$374$	37.2413	+	21.5013i	0.0995756	+	0.0574900i
$375$	217.430	−	175.895i	0.579812	−	0.469053i
$376$	−206.869	−	358.307i	−0.550182	−	0.952944i
$377$		−	11.5460i		−	0.0306261i
$378$		0			0
$379$	254.498			0.671500			0.335750	−	0.941951i	$-0.391010\pi$
$379$	254.498			0.671500			0.335750	+	0.941951i	$0.391010\pi$
$380$	−1169.61	+	675.274i	−3.07792	+	1.77704i
$381$	−409.406	−	506.080i	−1.07456	−	1.32829i
$382$	318.483	−	551.630i	0.833726	−	1.44406i
$383$	491.482	+	283.757i	1.28324	+	0.740881i	0.977440	−	0.211214i	$-0.0677417\pi$
$383$	491.482	+	283.757i	1.28324	+	0.740881i	0.305803	+	0.952095i	$0.401075\pi$
$384$	−23.2403	−	8.93418i	−0.0605217	−	0.0232661i
$385$		0			0
$386$			702.432i			1.81977i
$387$	453.788	−	146.954i	1.17258	−	0.379726i
$388$	−69.4613			−0.179024
$389$	−251.771	+	145.360i	−0.647226	+	0.373676i	−0.787393	−	0.616452i	$-0.788570\pi$
$389$	−251.771	+	145.360i	−0.647226	+	0.373676i	0.140166	+	0.990128i	$0.455236\pi$
$390$	20.1736	−	3.18506i	0.0517271	−	0.00816682i
$391$	−58.9171	+	102.047i	−0.150683	+	0.260991i
$392$		0			0
$393$	−58.1821	−	368.514i	−0.148046	−	0.937695i
$394$	−180.874	−	313.283i	−0.459071	−	0.795134i
$395$		−	591.434i		−	1.49730i
$396$	−284.914	−	60.8518i	−0.719480	−	0.153666i
$397$	−459.086			−1.15639			−0.578194	−	0.815899i	$-0.696242\pi$
$397$	−459.086			−1.15639			−0.578194	+	0.815899i	$0.696242\pi$
$398$	−819.194	+	472.962i	−2.05828	+	1.18835i
$399$		0			0
$400$	171.693	−	297.382i	0.429234	−	0.743454i
$401$	−398.361	−	229.994i	−0.993418	−	0.573550i	−0.0871241	−	0.996197i	$-0.527768\pi$
$401$	−398.361	−	229.994i	−0.993418	−	0.573550i	−0.906294	+	0.422647i	$0.861101\pi$
$402$	−300.643	+	243.212i	−0.747867	+	0.605005i
$403$	3.82418	+	6.62368i	0.00948929	+	0.0164359i
$404$		−	582.052i		−	1.44072i
$405$	276.933	+	382.738i	0.683785	+	0.945033i
$406$		0			0
$407$	24.6737	−	14.2454i	0.0606234	−	0.0350009i
$408$	135.565	+	167.577i	0.332267	+	0.410727i
$409$	291.920	−	505.621i	0.713741	−	1.23624i	−0.249702	−	0.968323i	$-0.580333\pi$
$409$	291.920	−	505.621i	0.713741	−	1.23624i	0.963443	−	0.267913i	$-0.0863340\pi$
$410$	859.531	+	496.251i	2.09642	+	1.21037i
$411$	−18.6799	−	7.18102i	−0.0454498	−	0.0174721i
$412$	−785.317	−	1360.21i	−1.90611	−	3.30148i
$413$		0			0
$414$	236.067	−	1105.29i	0.570209	−	2.66977i
$415$	−175.215			−0.422205
$416$	−15.7695	+	9.10455i	−0.0379076	+	0.0218859i
$417$	52.1659	−	8.23611i	0.125098	−	0.0197509i
$418$	−149.427	+	258.816i	−0.357482	+	0.619176i
$419$	125.878	+	72.6756i	0.300424	+	0.173450i	0.642634	−	0.766174i	$-0.277842\pi$
$419$	125.878	+	72.6756i	0.300424	+	0.173450i	−0.342209	+	0.939624i	$0.611175\pi$
$420$		0			0
$421$	23.2429	+	40.2578i	0.0552087	+	0.0956243i	0.892309	−	0.451425i	$-0.149084\pi$
$421$	23.2429	+	40.2578i	0.0552087	+	0.0956243i	−0.837100	+	0.547050i	$0.815751\pi$
$422$			966.336i			2.28990i
$423$	55.2949	+	170.749i	0.130721	+	0.403661i
$424$	701.708			1.65497
$425$	27.0407	−	15.6120i	0.0636252	−	0.0367340i
$426$	−340.647	+	886.119i	−0.799640	+	2.08009i
$427$		0			0
$428$	941.067	+	543.325i	2.19875	+	1.26945i
$429$	2.48182	−	2.00773i	0.00578512	−	0.00468002i
$430$	570.414	+	987.986i	1.32654	+	2.29764i
$431$		−	250.930i		−	0.582205i	−0.956692	−	0.291103i	$-0.905978\pi$
$431$		−	250.930i		−	0.582205i	0.956692	−	0.291103i	$-0.0940221\pi$
$432$	−861.589	−	561.322i	−1.99442	−	1.29936i
$433$	158.357			0.365720			0.182860	−	0.983139i	$-0.441464\pi$
$433$	158.357			0.365720			0.182860	+	0.983139i	$0.441464\pi$
$434$		0			0
$435$	401.746	+	496.612i	0.923554	+	1.14164i
$436$	602.608	−	1043.75i	1.38213	−	2.39392i
$437$	−709.199	−	409.456i	−1.62288	−	0.936971i
$438$	−731.255	−	281.113i	−1.66953	−	0.641810i
$439$	−167.384	−	289.917i	−0.381284	−	0.660403i	0.609962	−	0.792431i	$-0.291185\pi$
$439$	−167.384	−	289.917i	−0.381284	−	0.660403i	−0.991246	+	0.132027i	$0.957851\pi$
$440$		−	407.115i		−	0.925261i
$441$		0			0
$442$	−4.04230			−0.00914547
$443$	−18.5652	+	10.7187i	−0.0419080	+	0.0241956i	−0.520808	−	0.853674i	$-0.674369\pi$
$443$	−18.5652	+	10.7187i	−0.0419080	+	0.0241956i	0.478900	+	0.877870i	$0.341036\pi$
$444$	241.433	−	38.1181i	0.543768	−	0.0858517i
$445$	−156.727	+	271.459i	−0.352196	+	0.610021i
$446$	1148.79	+	663.256i	2.57577	+	1.48712i
$447$	−13.8928	−	87.9946i	−0.0310802	−	0.196856i
$448$		0			0
$449$		−	113.632i		−	0.253078i	−0.991962	−	0.126539i	$-0.959613\pi$
$449$		−	113.632i		−	0.253078i	0.991962	−	0.126539i	$-0.0403868\pi$
$450$	−200.613	+	222.366i	−0.445807	+	0.494146i
$451$	155.131			0.343970
$452$	−285.692	+	164.945i	−0.632063	+	0.364922i
$453$	75.3092	−	195.901i	0.166245	−	0.432452i
$454$	752.437	−	1303.26i	1.65735	−	2.87061i
$455$		0			0
$456$	−1164.61	+	942.137i	−2.55396	+	2.06609i
$457$	−55.7498	−	96.5615i	−0.121991	−	0.211294i	0.798562	−	0.601913i	$-0.205595\pi$
$457$	−55.7498	−	96.5615i	−0.121991	−	0.211294i	−0.920553	+	0.390618i	$0.872261\pi$
$458$			286.373i			0.625268i
$459$	−42.3273	−	83.3743i	−0.0922164	−	0.181643i
$460$	1909.36			4.15079
$461$	−143.867	+	83.0619i	−0.312077	+	0.180178i	−0.647855	−	0.761763i	$-0.724334\pi$
$461$	−143.867	+	83.0619i	−0.312077	+	0.180178i	0.335779	+	0.941941i	$0.391001\pi$
$462$		0			0
$463$	121.635	−	210.678i	0.262711	−	0.455028i	−0.704251	−	0.709951i	$-0.748717\pi$
$463$	121.635	−	210.678i	0.262711	−	0.455028i	0.966961	+	0.254923i	$0.0820502\pi$
$464$	−1204.12	−	695.197i	−2.59508	−	1.49827i
$465$	−394.956	−	151.831i	−0.849368	−	0.326519i
$466$	−838.450	−	1452.24i	−1.79925	−	3.11639i
$467$			346.467i			0.741900i	0.928653	+	0.370950i	$0.120968\pi$
$467$			346.467i			0.741900i	−0.928653	+	0.370950i	$0.879032\pi$
$468$	26.0542	−	8.43736i	0.0556715	−	0.0180285i
$469$		0			0
$470$	−371.753	+	214.632i	−0.790964	+	0.456663i
$471$	−582.699	+	91.9983i	−1.23715	+	0.195325i
$472$	−378.106	+	654.898i	−0.801071	+	1.38750i
$473$	154.425	+	89.1572i	0.326479	+	0.188493i
$474$	−175.099	−	1109.04i	−0.369407	−	2.33976i
$475$	108.498	+	187.925i	0.228418	+	0.395631i
$476$		0			0
$477$	−297.686	−	63.5797i	−0.624080	−	0.133291i
$478$	−187.805			−0.392898
$479$	482.865	−	278.782i	1.00807	−	0.582009i	0.0974437	−	0.995241i	$-0.468933\pi$
$479$	482.865	−	278.782i	1.00807	−	0.582009i	0.910626	+	0.413232i	$0.135600\pi$
$480$	361.477	−	940.305i	0.753077	−	1.95897i
$481$	−1.33909	+	2.31936i	−0.00278396	+	0.00482196i
$482$	612.288	+	353.505i	1.27031	+	0.733412i
$483$		0			0
$484$	527.638	+	913.895i	1.09016	+	1.88821i
$485$			42.1064i			0.0868174i
$486$	632.611	+	635.714i	1.30167	+	1.30805i
$487$	381.980			0.784353			0.392176	−	0.919890i	$-0.371722\pi$
$487$	381.980			0.784353			0.392176	+	0.919890i	$0.371722\pi$
$488$	−216.377	+	124.925i	−0.443395	+	0.255994i
$489$	−17.5163	−	21.6524i	−0.0358206	−	0.0442790i
$490$		0			0
$491$	448.359	+	258.860i	0.913155	+	0.527210i	0.881445	−	0.472287i	$-0.156571\pi$
$491$	448.359	+	258.860i	0.913155	+	0.527210i	0.0317099	+	0.999497i	$0.489905\pi$
$492$	1242.24	+	477.550i	2.52488	+	0.970629i
$493$	−63.2138	−	109.489i	−0.128223	−	0.222088i
$494$		−	28.0928i		−	0.0568679i
$495$	−36.8875	+	172.711i	−0.0745201	+	0.348910i
$496$	921.031			1.85692
$497$		0			0
$498$	−328.560	+	51.8740i	−0.659758	+	0.104165i
$499$	31.1288	−	53.9167i	0.0623824	−	0.108049i	−0.833147	−	0.553051i	$-0.813463\pi$
$499$	31.1288	−	53.9167i	0.0623824	−	0.108049i	0.895530	+	0.445001i	$0.146797\pi$
$500$	776.767	+	448.467i	1.55353	+	0.896934i
$501$	49.4456	+	313.179i	0.0986938	+	0.625108i
$502$	483.883	+	838.110i	0.963911	+	1.66954i
$503$		−	608.089i		−	1.20892i	−0.796634	−	0.604462i	$-0.793388\pi$
$503$		−	608.089i		−	1.20892i	0.796634	−	0.604462i	$-0.206612\pi$
$504$		0			0
$505$	−352.832			−0.698677
$506$	365.906	−	211.256i	0.723134	−	0.417501i
$507$	181.816	−	472.956i	0.358612	−	0.932853i
$508$	1043.83	−	1807.97i	2.05479	−	3.55900i
$509$	−335.722	−	193.829i	−0.659572	−	0.380804i	0.132542	−	0.991177i	$-0.457686\pi$
$509$	−335.722	−	193.829i	−0.659572	−	0.380804i	−0.792114	+	0.610373i	$0.791019\pi$
$510$	173.865	−	140.653i	0.340912	−	0.275789i
$511$		0			0
$512$		−	967.855i		−	1.89034i
$513$	579.427	−	294.162i	1.12949	−	0.573415i
$514$	−522.132			−1.01582
$515$	−824.538	+	476.047i	−1.60105	+	0.924364i
$516$	962.132	+	1189.32i	1.86460	+	2.30489i
$517$	−33.5475	+	58.1060i	−0.0648888	+	0.112391i
$518$		0			0
$519$	539.261	+	207.306i	1.03904	+	0.399433i
$520$	19.1347	+	33.1422i	0.0367974	+	0.0637351i
$521$			528.324i			1.01406i	0.861929	+	0.507029i	$0.169256\pi$
$521$			528.324i			1.01406i	−0.861929	+	0.507029i	$0.830744\pi$
$522$	900.372	+	812.295i	1.72485	+	1.55612i
$523$	359.674			0.687713			0.343856	−	0.939022i	$-0.388267\pi$
$523$	359.674			0.687713			0.343856	+	0.939022i	$0.388267\pi$
$524$	1036.21	−	598.256i	1.97750	−	1.14171i
$525$		0			0
$526$	814.724	−	1411.14i	1.54890	−	2.68278i
$527$	72.5285	+	41.8744i	0.137625	+	0.0794580i
$528$	−59.9501	−	379.712i	−0.113542	−	0.719152i
$529$	314.377	+	544.516i	0.594285	+	1.02933i
$530$		−	728.042i		−	1.37366i
$531$	219.742	−	243.569i	0.413828	−	0.458699i
$532$		0			0
$533$	−12.6288	+	7.29124i	−0.0236938	+	0.0136796i
$534$	−213.523	+	555.435i	−0.399856	+	1.04014i
$535$	329.356	−	570.461i	0.615618	−	1.06628i
$536$	−627.522	−	362.300i	−1.17075	−	0.675932i
$537$	−124.954	+	101.084i	−0.232688	+	0.188239i
$538$	188.843	+	327.086i	0.351009	+	0.607966i
$539$		0			0
$540$	−827.052	+	1269.47i	−1.53158	+	2.35086i
$541$	−71.0694			−0.131367			−0.0656834	−	0.997841i	$-0.520923\pi$
$541$	−71.0694			−0.131367			−0.0656834	+	0.997841i	$0.520923\pi$
$542$	1025.38	−	592.002i	1.89184	−	1.09225i
$543$	214.172	+	264.745i	0.394424	+	0.487560i
$544$	−99.6937	+	172.675i	−0.183261	+	0.317417i
$545$	−632.705	−	365.292i	−1.16093	−	0.670261i
$546$		0			0
$547$	−180.236	−	312.177i	−0.329498	−	0.570708i	0.652914	−	0.757432i	$-0.273546\pi$
$547$	−180.236	−	312.177i	−0.329498	−	0.570708i	−0.982412	+	0.186724i	$0.940213\pi$
$548$		−	64.1831i		−	0.117122i
$549$	103.113	−	33.3919i	0.187819	−	0.0608231i
$550$	−111.958			−0.203560
$551$	760.919	−	439.317i	1.38098	−	0.797308i
$552$	2091.88	−	330.272i	3.78964	−	0.598319i
$553$		0			0
$554$	−653.361	−	377.218i	−1.17935	−	0.680899i
$555$	−23.1067	−	146.353i	−0.0416336	−	0.263699i
$556$	84.6876	+	146.683i	0.152316	+	0.263819i
$557$			154.238i			0.276908i	0.990369	+	0.138454i	$0.0442132\pi$
$557$			154.238i			0.276908i	−0.990369	+	0.138454i	$0.955787\pi$
$558$	−785.564	−	167.780i	−1.40782	−	0.300682i
$559$	−16.7618			−0.0299853
$560$		0			0
$561$	12.5426	−	32.6268i	0.0223575	−	0.0581583i
$562$	−21.5071	+	37.2514i	−0.0382689	+	0.0662837i
$563$	686.120	+	396.131i	1.21869	+	0.703608i	0.964637	−	0.263583i	$-0.0849044\pi$
$563$	686.120	+	396.131i	1.21869	+	0.703608i	0.254049	+	0.967191i	$0.418238\pi$
$564$	−447.511	+	362.025i	−0.793460	+	0.641888i
$565$	99.9870	+	173.183i	0.176968	+	0.306518i
$566$			1277.89i			2.25776i
$567$		0			0
$568$	−1778.87			−3.13181
$569$	−223.053	+	128.780i	−0.392009	+	0.226327i	−0.683030	−	0.730390i	$-0.739338\pi$
$569$	−223.053	+	128.780i	−0.392009	+	0.226327i	0.291021	+	0.956717i	$0.406005\pi$
$570$	977.493	+	1208.31i	1.71490	+	2.11984i
$571$	−336.677	+	583.142i	−0.589627	+	1.02126i	0.404654	+	0.914470i	$0.367392\pi$
$571$	−336.677	+	583.142i	−0.589627	+	1.02126i	−0.994281	+	0.106794i	$0.965941\pi$
$572$	8.86630	+	5.11896i	0.0155005	+	0.00894923i
$573$	−483.279	−	185.785i	−0.843418	−	0.324232i
$574$		0			0
$575$		−	306.783i		−	0.533536i
$576$	113.073	−	529.420i	0.196308	−	0.919131i
$577$	−849.888			−1.47294			−0.736472	−	0.676468i	$-0.763510\pi$
$577$	−849.888			−1.47294			−0.736472	+	0.676468i	$0.763510\pi$
$578$	885.385	−	511.177i	1.53181	−	0.884389i
$579$	563.986	−	89.0438i	0.974070	−	0.153789i
$580$	−1024.30	+	1774.15i	−1.76604	+	3.05887i
$581$		0			0
$582$	12.4660	+	78.9570i	0.0214192	+	0.135665i
$583$	−56.8974	−	98.5492i	−0.0975942	−	0.169038i
$584$		−	1467.98i		−	2.51367i
$585$	−5.11460	−	15.7937i	−0.00874291	−	0.0269978i
$586$	−347.628			−0.593222
$587$	181.073	−	104.543i	0.308472	−	0.178097i	−0.337770	−	0.941229i	$-0.609673\pi$
$587$	181.073	−	104.543i	0.308472	−	0.178097i	0.646243	+	0.763132i	$0.276339\pi$
$588$		0			0
$589$	−291.014	+	504.051i	−0.494082	+	0.855775i
$590$	679.475	+	392.295i	1.15165	+	0.664907i
$591$	−228.608	+	184.938i	−0.386815	+	0.312923i
$592$	161.255	+	279.302i	0.272391	+	0.471794i
$593$		−	143.049i		−	0.241230i	−0.992699	−	0.120615i	$-0.961513\pi$
$593$		−	143.049i		−	0.241230i	0.992699	−	0.120615i	$-0.0384866\pi$
$594$	−18.0381	+	334.784i	−0.0303671	+	0.563610i
$595$		0			0
$596$	247.428	−	142.853i	0.415148	−	0.239686i
$597$	483.588	+	597.780i	0.810031	+	1.00131i
$598$	−19.8583	+	34.3956i	−0.0332079	+	0.0575178i
$599$	−567.489	−	327.640i	−0.947394	−	0.546978i	−0.0551235	−	0.998480i	$-0.517555\pi$
$599$	−567.489	−	327.640i	−0.947394	−	0.546978i	−0.892270	+	0.451501i	$0.850889\pi$
$600$	−523.804	−	201.364i	−0.873007	−	0.335606i
$601$	−403.102	−	698.192i	−0.670718	−	1.16172i	−0.977701	−	0.210003i	$-0.932653\pi$
$601$	−403.102	−	698.192i	−0.670718	−	1.16172i	0.306983	−	0.951715i	$-0.400681\pi$
$602$		0			0
$603$	233.387	+	210.557i	0.387044	+	0.349182i
$604$	673.104			1.11441
$605$	553.990	−	319.846i	0.915685	−	0.528671i
$606$	−661.622	+	104.459i	−1.09179	+	0.172374i
$607$	593.332	−	1027.68i	0.977483	−	1.69305i	0.305996	−	0.952033i	$-0.401010\pi$
$607$	593.332	−	1027.68i	0.977483	−	1.69305i	0.671486	−	0.741017i	$-0.265656\pi$
$608$	−1200.04	−	692.841i	−1.97374	−	1.13954i
$609$		0			0
$610$	129.613	+	224.497i	0.212481	+	0.368028i
$611$		−	6.30703i		−	0.0103225i
$612$	200.875	−	222.656i	0.328227	−	0.363817i
$613$	350.738			0.572166			0.286083	−	0.958205i	$-0.407647\pi$
$613$	350.738			0.572166			0.286083	+	0.958205i	$0.407647\pi$
$614$	−1610.05	+	929.562i	−2.62223	+	1.51394i
$615$	289.484	−	753.029i	0.470705	−	1.22444i
$616$		0			0
$617$	−161.583	−	93.2899i	−0.261885	−	0.151199i	0.363309	−	0.931669i	$-0.381647\pi$
$617$	−161.583	−	93.2899i	−0.261885	−	0.151199i	−0.625194	+	0.780469i	$0.714980\pi$
$618$	−1405.22	+	1136.79i	−2.27382	+	1.83946i
$619$	−271.539	−	470.319i	−0.438673	−	0.759804i	0.558915	−	0.829225i	$-0.311218\pi$
$619$	−271.539	−	470.319i	−0.438673	−	0.759804i	−0.997587	+	0.0694215i	$0.977885\pi$
$620$		−	1357.05i		−	2.18879i
$621$	−917.365	−	49.4274i	−1.47724	−	0.0795932i
$622$	1018.51			1.63748
$623$		0			0
$624$	22.7271	+	28.0937i	0.0364217	+	0.0450220i
$625$	384.557	−	666.072i	0.615291	−	1.06571i
$626$	−1218.04	−	703.235i	−1.94575	−	1.12338i
$627$	226.747	+	87.1672i	0.361637	+	0.139023i
$628$	−945.970	−	1638.47i	−1.50632	−	2.60903i
$629$			29.3257i			0.0466227i
$630$		0			0
$631$	−181.605			−0.287805			−0.143902	−	0.989592i	$-0.545965\pi$
$631$	−181.605			−0.287805			−0.143902	+	0.989592i	$0.545965\pi$
$632$	1822.00	−	1051.93i	2.88291	−	1.66445i
$633$	775.876	−	122.498i	1.22571	−	0.193519i
$634$	−1124.52	+	1947.72i	−1.77369	+	3.07211i
$635$	−1095.97	−	632.756i	−1.72593	−	0.996466i
$636$	−152.247	−	964.306i	−0.239383	−	1.51620i
$637$		0			0
$638$			453.324i			0.710539i
$639$	754.652	+	161.178i	1.18099	+	0.252235i
$640$	−48.4054			−0.0756335
$641$	286.732	−	165.545i	0.447320	−	0.258260i	−0.259378	−	0.965776i	$-0.583517\pi$
$641$	286.732	−	165.545i	0.447320	−	0.258260i	0.706698	+	0.707516i	$0.250184\pi$
$642$	448.711	−	1167.22i	0.698926	−	1.81811i
$643$	457.251	−	791.983i	0.711122	−	1.23170i	−0.253314	−	0.967384i	$-0.581521\pi$
$643$	457.251	−	791.983i	0.711122	−	1.23170i	0.964436	−	0.264315i	$-0.0851459\pi$
$644$		0			0
$645$	720.950	−	583.230i	1.11775	−	0.904233i
$646$	−153.806	−	266.400i	−0.238090	−	0.412384i
$647$			421.160i			0.650943i	0.945552	+	0.325472i	$0.105523\pi$
$647$			421.160i			0.650943i	−0.945552	+	0.325472i	$0.894477\pi$
$648$	−686.525	+	1533.87i	−1.05945	+	2.36709i
$649$	122.633			0.188958
$650$	9.11422	−	5.26209i	0.0140219	−	0.00809553i
$651$		0			0
$652$	44.6600	−	77.3533i	0.0684969	−	0.118640i
$653$	245.370	+	141.664i	0.375758	+	0.216944i	0.675971	−	0.736928i	$-0.263724\pi$
$653$	245.370	+	141.664i	0.375758	+	0.216944i	−0.300213	+	0.953872i	$0.597058\pi$
$654$	−1294.58	−	497.670i	−1.97948	−	0.760963i
$655$	−362.654	−	628.135i	−0.553670	−	0.958984i
$656$			1756.05i			2.67691i
$657$	−133.009	+	622.763i	−0.202450	+	0.947889i
$658$		0			0
$659$	98.1069	−	56.6421i	0.148872	−	0.0859515i	−0.423713	−	0.905796i	$-0.639274\pi$
$659$	98.1069	−	56.6421i	0.148872	−	0.0859515i	0.572586	+	0.819845i	$0.305940\pi$
$660$	−559.468	+	88.3304i	−0.847679	+	0.133834i
$661$	534.002	−	924.918i	0.807869	−	1.39927i	−0.106468	−	0.994316i	$-0.533954\pi$
$661$	534.002	−	924.918i	0.807869	−	1.39927i	0.914337	−	0.404954i	$-0.132713\pi$
$662$	1632.91	+	942.762i	2.46664	+	1.42411i
$663$	0.512422	+	3.24558i	0.000772884	+	0.00489530i
$664$	−311.640	−	539.776i	−0.469337	−	0.812915i
$665$		0			0
$666$	−86.6582	−	267.597i	−0.130117	−	0.401798i
$667$	−1242.18			−1.86235
$668$	−880.615	+	508.423i	−1.31829	+	0.761112i
$669$	386.905	−	1006.45i	0.578333	−	1.50441i
$670$	−375.896	+	651.071i	−0.561039	+	0.971748i
$671$	35.0894	+	20.2589i	0.0522943	+	0.0301921i
$672$		0			0
$673$	−438.286	−	759.133i	−0.651242	−	1.12798i	−0.982822	−	0.184557i	$-0.940915\pi$
$673$	−438.286	−	759.133i	−0.651242	−	1.12798i	0.331580	−	0.943427i	$-0.392418\pi$
$674$			538.671i			0.799215i
$675$	203.969	+	132.885i	0.302176	+	0.196867i
$676$	1625.05			2.40392
$677$	1029.66	−	594.477i	1.52092	−	0.878104i	0.521226	−	0.853419i	$-0.325475\pi$
$677$	1029.66	−	594.477i	1.52092	−	0.878104i	0.999695	−	0.0246857i	$-0.00785851\pi$
$678$	238.766	+	295.146i	0.352162	+	0.435319i
$679$		0			0
$680$	362.903	+	209.522i	0.533681	+	0.308121i
$681$	−1141.78	−	438.928i	−1.67662	−	0.644534i
$682$	−150.146	−	260.061i	−0.220156	−	0.381322i
$683$			697.998i			1.02196i	0.859593	+	0.510980i	$0.170717\pi$
$683$			697.998i			1.02196i	−0.859593	+	0.510980i	$0.829283\pi$
$684$	1547.39	+	1396.02i	2.26227	+	2.04097i
$685$	−38.9068			−0.0567983
$686$		0			0
$687$	229.930	−	36.3021i	0.334687	−	0.0528414i
$688$	−1009.24	+	1748.06i	−1.46692	+	2.54079i
$689$	9.26376	+	5.34844i	0.0134452	+	0.00776261i
$690$	−342.666	−	2170.38i	−0.496618	−	3.14548i
$691$	506.608	+	877.470i	0.733151	+	1.26986i	0.955530	+	0.294895i	$0.0952846\pi$
$691$	506.608	+	877.470i	0.733151	+	1.26986i	−0.222378	+	0.974960i	$0.571382\pi$
$692$			1852.87i			2.67756i
$693$		0			0
$694$	−1018.10			−1.46700
$695$	88.9172	−	51.3364i	0.127938	−	0.0738653i
$696$	−815.334	+	2120.92i	−1.17146	+	3.04729i
$697$	−79.8382	+	138.284i	−0.114546	+	0.198399i
$698$	767.013	+	442.835i	1.09887	+	0.634435i
$699$	−1059.72	+	857.288i	−1.51606	+	1.22645i
$700$		0			0
$701$			910.897i			1.29942i	0.760180	+	0.649712i	$0.225111\pi$
$701$			910.897i			1.29942i	−0.760180	+	0.649712i	$0.774889\pi$
$702$	−14.2666	−	28.1018i	−0.0203229	−	0.0400310i
$703$	−203.804			−0.289907
$704$	175.265	−	101.189i	0.248955	−	0.143734i
$705$	219.454	+	271.275i	0.311283	+	0.384787i
$706$	−999.883	+	1731.85i	−1.41626	+	2.45304i
$707$		0			0
$708$	982.015	+	377.512i	1.38703	+	0.533208i
$709$	469.175	+	812.635i	0.661742	+	1.14617i	0.980158	+	0.198219i	$0.0635159\pi$
$709$	469.175	+	812.635i	0.661742	+	1.14617i	−0.318416	+	0.947951i	$0.603151\pi$
$710$			1845.63i			2.59947i
$711$	−868.261	+	281.176i	−1.22118	+	0.395465i
$712$	−1115.03			−1.56605
$713$	712.612	−	411.427i	0.999456	−	0.577036i
$714$		0			0
$715$	3.10304	−	5.37462i	0.00433991	−	0.00751695i
$716$	−446.397	−	257.727i	−0.623459	−	0.359954i
$717$	23.8071	+	150.790i	0.0332038	+	0.210306i
$718$	−816.344	−	1413.95i	−1.13697	−	1.96929i
$719$			309.993i			0.431145i	0.976488	+	0.215572i	$0.0691617\pi$
$719$			309.993i			0.431145i	−0.976488	+	0.215572i	$0.930838\pi$
$720$	−1955.06	−	417.560i	−2.71535	−	0.579944i
$721$		0			0
$722$	697.553	−	402.732i	0.966140	−	0.557801i
$723$	206.214	−	536.421i	0.285220	−	0.741938i
$724$	−546.059	+	945.802i	−0.754225	+	1.30636i
$725$	285.058	+	164.578i	0.393183	+	0.227004i
$726$	944.136	−	763.782i	1.30046	−	1.05204i
$727$	712.724	+	1234.47i	0.980363	+	1.69804i	0.660963	+	0.750418i	$0.270148\pi$
$727$	712.724	+	1234.47i	0.980363	+	1.69804i	0.319400	+	0.947620i	$0.396519\pi$
$728$		0			0
$729$	430.225	−	588.513i	0.590158	−	0.807288i
$730$	−1523.07			−2.08640
$731$	−158.950	+	91.7699i	−0.217442	+	0.125540i
$732$	218.622	+	270.246i	0.298664	+	0.369189i
$733$	470.224	−	814.451i	0.641506	−	1.11112i	−0.343591	−	0.939119i	$-0.611643\pi$
$733$	470.224	−	814.451i	0.641506	−	1.11112i	0.985097	−	0.172001i	$-0.0550232\pi$
$734$	978.658	+	565.028i	1.33332	+	0.769793i
$735$		0			0
$736$	979.518	+	1696.57i	1.33087	+	2.30513i
$737$			117.507i			0.159440i
$738$	319.892	−	1497.77i	0.433459	−	2.02950i
$739$	−977.531			−1.32277			−0.661387	−	0.750045i	$-0.730032\pi$
$739$	−977.531			−1.32277			−0.661387	+	0.750045i	$0.730032\pi$
$740$	411.524	−	237.594i	0.556114	−	0.321072i
$741$	−22.5558	+	3.56118i	−0.0304397	+	0.00480591i
$742$		0			0
$743$	626.132	+	361.497i	0.842707	+	0.486537i	0.858184	−	0.513343i	$-0.171593\pi$
$743$	626.132	+	361.497i	0.842707	+	0.486537i	−0.0154762	+	0.999880i	$0.504926\pi$
$744$	−234.735	−	1486.77i	−0.315505	−	1.99834i
$745$	−86.5953	−	149.987i	−0.116235	−	0.201325i
$746$			806.899i			1.08163i
$747$	83.2997	+	257.226i	0.111512	+	0.344346i
$748$	112.104			0.149872
$749$		0			0
$750$	370.371	−	963.440i	0.493828	−	1.28459i
$751$	115.796	−	200.565i	0.154189	−	0.267064i	−0.778574	−	0.627553i	$-0.784057\pi$
$751$	115.796	−	200.565i	0.154189	−	0.267064i	0.932764	+	0.360489i	$0.117390\pi$
$752$	−657.750	−	379.752i	−0.874668	−	0.504990i
$753$	611.583	−	494.755i	0.812196	−	0.657045i
$754$	−21.3065	−	36.9040i	−0.0282580	−	0.0489443i
$755$		−	408.026i		−	0.540431i
$756$		0			0
$757$	1088.59			1.43804			0.719018	−	0.694992i	$-0.244592\pi$
$757$	1088.59			1.43804			0.719018	+	0.694992i	$0.244592\pi$
$758$	813.442	−	469.641i	1.07314	−	0.619579i
$759$	−216.002	−	267.008i	−0.284588	−	0.351789i
$760$	−1456.12	+	2522.07i	−1.91594	+	3.31851i
$761$	117.838	+	68.0337i	0.154846	+	0.0894004i	0.575421	−	0.817857i	$-0.304838\pi$
$761$	117.838	+	68.0337i	0.154846	+	0.0894004i	−0.420575	+	0.907258i	$0.638172\pi$
$762$	−2242.46	−	862.060i	−2.94287	−	1.13131i
$763$		0			0
$764$		−	1660.52i		−	2.17345i
$765$	−134.971	−	121.768i	−0.176432	−	0.159173i
$766$	2094.54			2.73438
$767$	−9.98330	+	5.76386i	−0.0130160	+	0.00751481i
$768$	−803.751	+	126.899i	−1.04655	+	0.165232i
$769$	−402.392	+	696.964i	−0.523267	+	0.906325i	0.476367	+	0.879247i	$0.341954\pi$
$769$	−402.392	+	696.964i	−0.523267	+	0.906325i	−0.999633	+	0.0270779i	$0.991380\pi$
$770$		0			0
$771$	66.1881	+	419.222i	0.0858470	+	0.543739i
$772$	915.591	+	1585.85i	1.18600	+	2.05421i
$773$		−	345.902i		−	0.447480i	−0.974649	−	0.223740i	$-0.928173\pi$
$773$		−	345.902i		−	0.447480i	0.974649	−	0.223740i	$-0.0718266\pi$
$774$	1179.24	−	1307.10i	1.52357	−	1.68876i
$775$	−218.041			−0.281343
$776$	−129.715	+	74.8910i	−0.167158	+	0.0965090i
$777$		0			0
$778$	−536.483	+	929.215i	−0.689566	+	1.19436i
$779$	−961.031	−	554.852i	−1.23367	−	0.712262i
$780$	41.3933	−	33.4862i	0.0530684	−	0.0429310i
$781$	144.238	+	249.828i	0.184684	+	0.319882i
$782$			434.893i			0.556129i
$783$	538.060	−	825.883i	0.687178	−	1.05477i
$784$		0			0
$785$	−993.215	+	573.433i	−1.26524	+	0.730488i
$786$	−866.005	−	1070.50i	−1.10179	−	1.36196i
$787$	−18.6416	+	32.2883i	−0.0236870	+	0.0410270i	−0.877626	−	0.479346i	$-0.840874\pi$
$787$	−18.6416	+	32.2883i	−0.0236870	+	0.0410270i	0.853939	+	0.520373i	$0.174207\pi$
$788$	−816.701	−	471.523i	−1.03642	−	0.598379i
$789$	−1236.29	−	475.262i	−1.56691	−	0.602360i
$790$	−1091.41	−	1890.37i	−1.38153	−	2.39288i
$791$		0			0
$792$	−597.669	+	193.548i	−0.754632	+	0.244379i
$793$	−3.80873			−0.00480294
$794$	−1467.36	+	847.178i	−1.84805	+	1.06697i
$795$	−584.548	+	92.2902i	−0.735281	+	0.116088i
$796$	−1232.97	+	2135.57i	−1.54896	+	2.68287i
$797$	−1009.32	−	582.728i	−1.26639	−	0.731152i	−0.292089	−	0.956391i	$-0.594350\pi$
$797$	−1009.32	−	582.728i	−1.26639	−	0.731152i	−0.974304	+	0.225239i	$0.927684\pi$
$798$		0			0
$799$	−34.5306	−	59.8087i	−0.0432173	−	0.0748545i
$800$		−	519.109i		−	0.648886i
$801$	473.028	+	101.029i	0.590547	+	0.126129i
$802$	−1697.68			−2.11681
$803$	−206.166	+	119.030i	−0.256745	+	0.148232i
$804$	−361.731	+	940.964i	−0.449914	+	1.17035i
$805$		0			0
$806$	24.4461	+	14.1140i	0.0303302	+	0.0175111i
$807$	238.680	−	193.086i	0.295762	−	0.239264i
$808$	−627.550	−	1086.95i	−0.776671	−	1.34523i
$809$		−	999.649i		−	1.23566i	−0.786311	−	0.617830i	$-0.788012\pi$
$809$		−	999.649i		−	1.23566i	0.786311	−	0.617830i	$-0.211988\pi$
$810$	1591.44	+	712.288i	1.96474	+	0.879368i
$811$	634.194			0.781990			0.390995	−	0.920393i	$-0.372131\pi$
$811$	634.194			0.781990			0.390995	+	0.920393i	$0.372131\pi$
$812$		0			0
$813$	−605.304	−	748.236i	−0.744531	−	0.920339i
$814$	52.5757	−	91.0637i	0.0645893	−	0.111872i
$815$	−46.8905	−	27.0722i	−0.0575343	−	0.0332174i
$816$	369.330	+	141.980i	0.452610	+	0.173995i
$817$	−637.773	−	1104.66i	−0.780628	−	1.35209i
$818$		−	2154.79i		−	2.63422i
$819$		0			0
$820$	2587.37			3.15532
$821$	−263.766	+	152.285i	−0.321274	+	0.185488i	−0.651960	−	0.758253i	$-0.726053\pi$
$821$	−263.766	+	152.285i	−0.321274	+	0.185488i	0.330686	+	0.943741i	$0.392720\pi$
$822$	−72.9572	+	11.5187i	−0.0887557	+	0.0140130i
$823$	425.387	−	736.793i	0.516874	−	0.895252i	−0.482934	−	0.875657i	$-0.660429\pi$
$823$	425.387	−	736.793i	0.516874	−	0.895252i	0.999808	−	0.0195954i	$-0.00623780\pi$
$824$	−2933.07	−	1693.41i	−3.55955	−	2.05510i
$825$	14.1923	+	89.8915i	0.0172028	+	0.108959i
$826$		0			0
$827$			0.427608i			0.000517059i	1.00000		0.000258530i	$8.22925e-5\pi$
$827$			0.427608i			0.000517059i	−1.00000		0.000258530i	$0.999918\pi$
$828$	−907.738	−	2803.06i	−1.09630	−	3.38534i
$829$	−449.353			−0.542042			−0.271021	−	0.962573i	$-0.587361\pi$
$829$	−449.353			−0.542042			−0.271021	+	0.962573i	$0.587361\pi$
$830$	−560.032	+	323.335i	−0.674738	+	0.389560i
$831$	−220.047	+	572.404i	−0.264798	+	0.688814i
$832$	−9.51191	+	16.4751i	−0.0114326	+	0.0198018i
$833$		0			0
$834$	151.537	−	122.590i	0.181699	−	0.146990i
$835$	308.199	+	533.816i	0.369100	+	0.639300i
$836$			779.089i			0.931925i
$837$	−35.1297	+	652.002i	−0.0419709	+	0.778975i
$838$	536.450			0.640155
$839$	−185.989	+	107.381i	−0.221680	+	0.127987i	−0.606728	−	0.794910i	$-0.707518\pi$
$839$	−185.989	+	107.381i	−0.221680	+	0.127987i	0.385048	+	0.922897i	$0.374185\pi$
$840$		0			0
$841$	245.887	−	425.889i	0.292374	−	0.506407i
$842$	148.580	+	85.7828i	0.176461	+	0.101880i
$843$	32.6357	+	12.5460i	0.0387138	+	0.0148826i
$844$	1259.58	+	2181.65i	1.49239	+	2.58490i
$845$		−	985.082i		−	1.16578i
$846$	491.829	+	443.717i	0.581358	+	0.524488i
$847$		0			0
$848$	1115.56	−	644.069i	1.31552	−	0.759515i
$849$	1026.03	−	161.992i	1.20851	−	0.190803i
$850$	57.6193	−	99.7996i	0.0677874	−	0.117411i
$851$	249.530	+	144.066i	0.293220	+	0.169291i
$852$	385.956	+	2444.57i	0.453000	+	2.86921i
$853$	192.842	+	334.012i	0.226075	+	0.391573i	0.956641	−	0.291269i	$-0.0940773\pi$
$853$	192.842	+	334.012i	0.226075	+	0.391573i	−0.730567	+	0.682841i	$0.760744\pi$
$854$		0			0
$855$	846.248	−	938.006i	0.989763	−	1.09708i
$856$	2343.18			2.73736
$857$	−1130.65	+	652.782i	−1.31931	+	0.761707i	−0.983618	−	0.180264i	$-0.942305\pi$
$857$	−1130.65	+	652.782i	−1.31931	+	0.761707i	−0.335696	+	0.941970i	$0.608972\pi$
$858$	4.22754	−	10.9970i	0.00492721	−	0.0128171i
$859$	−590.609	+	1022.96i	−0.687554	+	1.19088i	0.285073	+	0.958506i	$0.407982\pi$
$859$	−590.609	+	1022.96i	−0.687554	+	1.19088i	−0.972627	+	0.232372i	$0.925351\pi$
$860$	2575.60	+	1487.02i	2.99488	+	1.72909i
$861$		0			0
$862$	−463.056	−	802.037i	−0.537188	−	0.930438i
$863$			903.027i			1.04638i	0.852216	+	0.523191i	$0.175258\pi$
$863$			903.027i			1.04638i	−0.852216	+	0.523191i	$0.824742\pi$
$864$	−1552.27	−	83.6361i	−1.79661	−	0.0968011i
$865$	1123.18			1.29848
$866$	506.148	−	292.225i	0.584467	−	0.337442i
$867$	−522.662	−	646.080i	−0.602840	−	0.745191i
$868$		0			0
$869$	−295.470	−	170.590i	−0.340012	−	0.196306i
$870$	2200.51	+	845.932i	2.52932	+	0.972335i
$871$	−5.52291	−	9.56597i	−0.00634089	−	0.0109827i
$872$		−	2598.85i		−	2.98033i
$873$	61.8147	−	20.0180i	0.0708073	−	0.0229301i
$874$	−3022.37			−3.45809
$875$		0			0
$876$	−2017.34	+	318.504i	−2.30290	+	0.363589i
$877$	277.106	−	479.961i	0.315970	−	0.547276i	−0.663673	−	0.748023i	$-0.731003\pi$
$877$	277.106	−	479.961i	0.315970	−	0.547276i	0.979643	+	0.200747i	$0.0643368\pi$
$878$	−1070.00	−	617.766i	−1.21868	−	0.703606i
$879$	44.0671	+	279.112i	0.0501332	+	0.317534i
$880$	−373.674	−	647.222i	−0.424629	−	0.735479i
$881$			750.603i			0.851990i	0.904726	+	0.425995i	$0.140076\pi$
$881$			750.603i			0.851990i	−0.904726	+	0.425995i	$0.859924\pi$
$882$		0			0
$883$	−1042.83			−1.18101			−0.590504	−	0.807035i	$-0.701071\pi$
$883$	−1042.83			−1.18101			−0.590504	+	0.807035i	$0.701071\pi$
$884$	−9.12611	+	5.26896i	−0.0103237	+	0.00596037i
$885$	228.842	−	595.283i	0.258578	−	0.672636i
$886$	−39.5595	+	68.5191i	−0.0446495	+	0.0773353i
$887$	−73.7419	−	42.5749i	−0.0831363	−	0.0479987i	0.457856	−	0.889027i	$-0.348618\pi$
$887$	−73.7419	−	42.5749i	−0.0831363	−	0.0479987i	−0.540992	+	0.841028i	$0.681951\pi$
$888$	409.764	−	331.489i	0.461446	−	0.373298i
$889$		0			0
$890$			1156.87i			1.29985i
$891$	271.086	−	27.9560i	0.304250	−	0.0313760i
$892$	3458.11			3.87680
$893$	415.653	−	239.977i	0.465457	−	0.268732i
$894$	−206.787	−	255.616i	−0.231305	−	0.285924i
$895$	−156.230	+	270.599i	−0.174559	+	0.302345i
$896$		0			0
$897$	30.1338	+	11.5842i	0.0335939	+	0.0129144i
$898$	−209.691	−	363.196i	−0.233509	−	0.404450i
$899$			882.862i			0.982049i
$900$	−163.071	+	763.515i	−0.181190	+	0.848350i
$901$	117.129			0.129999
$902$	495.837	−	286.271i	0.549708	−	0.317374i
$903$		0			0
$904$	−355.676	+	616.049i	−0.393447	+	0.681470i
$905$	573.331	+	331.013i	0.633515	+	0.365760i
$906$	−120.799	−	765.120i	−0.133333	−	0.844504i
$907$	430.076	+	744.914i	0.474175	+	0.821294i	0.999563	−	0.0295683i	$-0.00941324\pi$
$907$	430.076	+	744.914i	0.474175	+	0.821294i	−0.525388	+	0.850863i	$0.676080\pi$
$908$		−	3923.08i		−	4.32057i
$909$	167.741	+	517.978i	0.184534	+	0.569833i
$910$		0			0
$911$	−1335.63	+	771.127i	−1.46612	+	0.846462i	−0.999282	−	0.0378830i	$-0.987939\pi$
$911$	−1335.63	+	771.127i	−1.46612	+	0.846462i	−0.466833	+	0.884345i	$0.654605\pi$
$912$	−986.717	+	2566.73i	−1.08193	+	2.81440i
$913$	−50.5381	+	87.5345i	−0.0553539	+	0.0958757i
$914$	−356.381	−	205.757i	−0.389914	−	0.225117i
$915$	163.819	−	132.526i	0.179037	−	0.144837i
$916$	373.275	+	646.531i	0.407505	+	0.705820i
$917$		0			0
$918$	−289.144	−	188.376i	−0.314972	−	0.205203i
$919$	−1676.25			−1.82399			−0.911995	−	0.410201i	$-0.865459\pi$
$919$	−1676.25			−1.82399			−0.911995	+	0.410201i	$0.865459\pi$
$920$	3565.62	−	2058.61i	3.87568	−	2.23762i
$921$	950.447	+	1174.88i	1.03197	+	1.27566i
$922$	−306.558	+	530.974i	−0.332492	+	0.575894i
$923$	−23.4842	−	13.5586i	−0.0254433	−	0.0146897i
$924$		0			0
$925$	−38.1749	−	66.1209i	−0.0412702	−	0.0714820i
$926$		−	897.841i		−	0.969590i
$927$	1090.86	+	984.152i	1.17677	+	1.06165i
$928$	−2101.90			−2.26498
$929$	−1270.20	+	733.353i	−1.36728	+	0.789400i	−0.990580	−	0.136935i	$-0.956275\pi$
$929$	−1270.20	+	733.353i	−1.36728	+	0.789400i	−0.376701	+	0.926335i	$0.622942\pi$
$930$	−1542.56	+	243.544i	−1.65867	+	0.261876i
$931$		0			0
$932$	−3785.86	−	2185.77i	−4.06208	−	2.34524i
$933$	−129.112	−	817.768i	−0.138383	−	0.876493i
$934$	639.357	+	1107.40i	0.684536	+	1.18565i
$935$		−	67.9558i		−	0.0726800i
$936$	39.5579	−	43.8471i	0.0422627	−	0.0468452i
$937$	322.074			0.343729			0.171864	−	0.985121i	$-0.445021\pi$
$937$	322.074			0.343729			0.171864	+	0.985121i	$0.445021\pi$
$938$		0			0
$939$	−410.226	+	1067.11i	−0.436875	+	1.13644i
$940$	−559.527	+	969.129i	−0.595241	+	1.03099i
$941$	−324.300	−	187.235i	−0.344633	−	0.198974i	0.317686	−	0.948196i	$-0.397094\pi$
$941$	−324.300	−	187.235i	−0.344633	−	0.198974i	−0.662319	+	0.749222i	$0.730428\pi$
$942$	−1692.69	+	1369.34i	−1.79691	+	1.45365i
$943$	784.432	+	1358.68i	0.831847	+	1.44080i
$944$			1388.19i			1.47054i
$945$		0			0
$946$	658.108			0.695674
$947$	142.844	−	82.4709i	0.150838	−	0.0870865i	−0.422681	−	0.906278i	$-0.638911\pi$
$947$	142.844	−	82.4709i	0.150838	−	0.0870865i	0.573519	+	0.819192i	$0.305578\pi$
$948$	−1840.91	−	2275.60i	−1.94188	−	2.40043i
$949$	11.1890	−	19.3799i	0.0117903	−	0.0204214i
$950$	693.577	+	400.437i	0.730081	+	0.421513i
$951$	1706.38	+	655.977i	1.79430	+	0.689776i
$952$		0			0
$953$			1354.42i			1.42122i	0.703586	+	0.710610i	$0.251581\pi$
$953$			1354.42i			1.42122i	−0.703586	+	0.710610i	$0.748419\pi$
$954$	−1068.81	+	346.121i	−1.12034	+	0.362810i
$955$	−1006.58			−1.05401
$956$	−423.999	+	244.796i	−0.443514	+	0.256063i
$957$	363.976	−	57.4656i	0.380330	−	0.0600477i
$958$	1028.91	−	1782.12i	1.07402	−	1.86025i
$959$		0			0
$960$	−164.133	−	1039.59i	−0.170972	−	1.08290i
$961$	188.085	+	325.773i	0.195718	+	0.338994i
$962$			9.88437i			0.0102748i
$963$	−994.051	−	212.309i	−1.03224	−	0.220466i
$964$	1843.11			1.91194
$965$	961.319	−	555.018i	0.996185	−	0.575148i
$966$		0			0
$967$	−344.963	+	597.493i	−0.356735	+	0.617883i	−0.987413	−	0.158161i	$-0.949443\pi$
$967$	−344.963	+	597.493i	−0.356735	+	0.617883i	0.630678	+	0.776044i	$0.282777\pi$
$968$	1970.66	+	1137.76i	2.03581	+	1.17538i
$969$	−194.397	+	157.262i	−0.200616	+	0.162293i
$970$	77.7014	+	134.583i	0.0801046	+	0.138745i
$971$			768.215i			0.791158i	0.918432	+	0.395579i	$0.129456\pi$
$971$			768.215i			0.791158i	−0.918432	+	0.395579i	$0.870544\pi$
$972$	2256.84	+	610.641i	2.32186	+	0.628231i
$973$		0			0
$974$	1220.90	−	704.889i	1.25350	−	0.723706i
$975$	−5.38033	−	6.65080i	−0.00551828	−	0.00682133i
$976$	−229.327	+	397.207i	−0.234966	+	0.406974i
$977$	−1200.33	−	693.012i	−1.22859	−	0.709326i	−0.261854	−	0.965107i	$-0.584334\pi$
$977$	−1200.33	−	693.012i	−1.22859	−	0.709326i	−0.966735	+	0.255781i	$0.917667\pi$
$978$	−95.9429	−	36.8829i	−0.0981011	−	0.0377126i
$979$	90.4109	+	156.596i	0.0923502	+	0.159955i
$980$		0			0
$981$	−235.474	+	1102.51i	−0.240035	+	1.12387i
$982$	1910.76			1.94578
$983$	−454.966	+	262.675i	−0.462834	+	0.267217i	−0.713235	−	0.700925i	$-0.752771\pi$
$983$	−454.966	+	262.675i	−0.462834	+	0.267217i	0.250401	+	0.968142i	$0.419438\pi$
$984$	2834.69	−	447.550i	2.88079	−	0.454827i
$985$	−285.830	+	495.072i	−0.290183	+	0.502611i
$986$	−404.095	−	233.304i	−0.409832	−	0.236617i
$987$		0			0
$988$	−36.6177	−	63.4238i	−0.0370625	−	0.0641941i
$989$			1803.33i			1.82338i
$990$	200.811	+	620.098i	0.202840	+	0.626361i
$991$	−428.651			−0.432544			−0.216272	−	0.976333i	$-0.569390\pi$
$991$	−428.651			−0.432544			−0.216272	+	0.976333i	$0.569390\pi$
$992$	1205.81	−	696.176i	1.21554	−	0.701790i
$993$	549.953	−	1430.58i	0.553829	−	1.44067i
$994$		0			0
$995$	1294.55	+	747.409i	1.30106	+	0.751165i
$996$	−674.159	+	545.377i	−0.676866	+	0.547567i
$997$	598.383	+	1036.43i	0.600184	+	1.03955i	0.992793	+	0.119843i	$0.0382392\pi$
$997$	598.383	+	1036.43i	0.600184	+	1.03955i	−0.392609	+	0.919705i	$0.628427\pi$
$998$		−	229.775i		−	0.230236i
$999$	−203.870	+	103.500i	−0.204074	+	0.103604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.r.g.50.11		22
7.2	even	3		63.3.n.b.32.1	yes	22
7.3	odd	6		441.3.j.f.275.11		22
7.4	even	3		63.3.j.b.23.11	yes	22
7.5	odd	6		441.3.n.f.410.1		22
7.6	odd	2		441.3.r.f.50.11		22
9.2	odd	6	inner	441.3.r.g.344.11		22
21.2	odd	6		189.3.n.b.179.11		22
21.11	odd	6		189.3.j.b.44.1		22
63.2	odd	6		63.3.j.b.11.1	✓	22
63.11	odd	6		63.3.n.b.2.1	yes	22
63.16	even	3		189.3.j.b.116.11		22
63.20	even	6		441.3.r.f.344.11		22
63.25	even	3		189.3.n.b.170.11		22
63.38	even	6		441.3.n.f.128.1		22
63.47	even	6		441.3.j.f.263.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.1	✓	22	63.2	odd	6
63.3.j.b.23.11	yes	22	7.4	even	3
63.3.n.b.2.1	yes	22	63.11	odd	6
63.3.n.b.32.1	yes	22	7.2	even	3
189.3.j.b.44.1		22	21.11	odd	6
189.3.j.b.116.11		22	63.16	even	3
189.3.n.b.170.11		22	63.25	even	3
189.3.n.b.179.11		22	21.2	odd	6
441.3.j.f.263.1		22	63.47	even	6
441.3.j.f.275.11		22	7.3	odd	6
441.3.n.f.128.1		22	63.38	even	6
441.3.n.f.410.1		22	7.5	odd	6
441.3.r.f.50.11		22	7.6	odd	2
441.3.r.f.344.11		22	63.20	even	6
441.3.r.g.50.11		22	1.1	even	1	trivial
441.3.r.g.344.11		22	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.19625 - 1.84536i) q^{2} +(-1.88682 - 2.33236i) q^{3} +(4.81069 - 8.33236i) q^{4} +(-5.05096 - 2.91617i) q^{5} +(-10.3348 - 3.97296i) q^{6} -20.7469i q^{8} +(-1.87982 + 8.80149i) q^{9} -21.5255 q^{10} +(-2.91374 + 1.68225i) q^{11} +(-28.5110 + 4.50140i) q^{12} +(0.158134 - 0.273895i) q^{13} +(2.72868 + 17.2829i) q^{15} +(-19.0428 - 32.9830i) q^{16} -3.46309i q^{17} +(10.2335 + 31.6007i) q^{18} +24.0674 q^{19} +(-48.5972 + 28.0576i) q^{20} +(-6.20870 + 10.7538i) q^{22} +(-29.4672 - 17.0129i) q^{23} +(-48.3893 + 39.1457i) q^{24} +(4.50810 + 7.80826i) q^{25} -1.16725i q^{26} +(24.0751 - 12.2224i) q^{27} +(31.6161 - 18.2536i) q^{29} +(40.6148 + 50.2053i) q^{30} +(-12.0916 + 20.9433i) q^{31} +(-49.8615 - 28.7875i) q^{32} +(9.42131 + 3.62179i) q^{33} +(-6.39064 - 11.0689i) q^{34} +(64.2940 + 58.0046i) q^{36} -8.46807 q^{37} +(76.9256 - 44.4130i) q^{38} +(-0.937193 + 0.147967i) q^{39} +(-60.5016 + 104.792i) q^{40} +(-39.9308 - 23.0541i) q^{41} +(-26.4994 - 45.8984i) q^{43} +32.3711i q^{44} +(35.1615 - 38.9741i) q^{45} -125.579 q^{46} +(17.2703 - 9.97104i) q^{47} +(-40.9981 + 106.648i) q^{48} +(28.8181 + 16.6381i) q^{50} +(-8.07717 + 6.53422i) q^{51} +(-1.52146 - 2.63525i) q^{52} +33.8223i q^{53} +(54.3955 - 83.4932i) q^{54} +19.6229 q^{55} +(-45.4109 - 56.1339i) q^{57} +(67.3688 - 116.686i) q^{58} +(-31.5660 - 18.2246i) q^{59} +(157.135 + 60.4066i) q^{60} +(-6.02138 - 10.4293i) q^{61} +89.2535i q^{62} -60.1511 q^{64} +(-1.59745 + 0.922289i) q^{65} +(36.7964 - 5.80952i) q^{66} +(17.4628 - 30.2465i) q^{67} +(-28.8557 - 16.6599i) q^{68} +(15.9191 + 100.828i) q^{69} -85.7413i q^{71} +(182.604 + 39.0005i) q^{72} +70.7566 q^{73} +(-27.0661 + 15.6266i) q^{74} +(9.70571 - 25.2473i) q^{75} +(115.781 - 200.539i) q^{76} +(-2.72245 + 2.20240i) q^{78} +(50.7030 + 87.8201i) q^{79} +222.128i q^{80} +(-73.9326 - 33.0904i) q^{81} -170.172 q^{82} +(26.0171 - 15.0210i) q^{83} +(-10.0990 + 17.4919i) q^{85} +(-169.398 - 97.8019i) q^{86} +(-102.228 - 39.2990i) q^{87} +(34.9015 + 60.4511i) q^{88} -53.7441i q^{89} +(40.4641 - 189.457i) q^{90} +(-283.515 + 163.688i) q^{92} +(71.6621 - 11.3142i) q^{93} +(36.8003 - 63.7400i) q^{94} +(-121.563 - 70.1847i) q^{95} +(26.9367 + 170.612i) q^{96} +(-3.60974 - 6.25225i) q^{97} +(-9.32899 - 28.8076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{2} + 11 q^{3} + 12 q^{4} - 12 q^{5} - 8 q^{6} + 17 q^{9} - 50 q^{10} - 24 q^{11} - 20 q^{12} - 18 q^{13} + 53 q^{15} + 12 q^{16} + 16 q^{18} - 6 q^{19} - 39 q^{20} - 59 q^{22} - 81 q^{23} - 141 q^{24}+ \cdots - 103 q^{99}+O(q^{100}) \) 22 * q + 6 * q^2 + 11 * q^3 + 12 * q^4 - 12 * q^5 - 8 * q^6 + 17 * q^9 - 50 * q^10 - 24 * q^11 - 20 * q^12 - 18 * q^13 + 53 * q^15 + 12 * q^16 + 16 * q^18 - 6 * q^19 - 39 * q^20 - 59 * q^22 - 81 * q^23 - 141 * q^24 + 57 * q^25 - 97 * q^27 - 63 * q^29 + 58 * q^30 - 29 * q^31 - 246 * q^32 - 73 * q^33 - 99 * q^34 + 76 * q^36 + 40 * q^37 + 48 * q^38 - 124 * q^39 - 105 * q^40 - 51 * q^41 + 65 * q^43 + 143 * q^45 - 150 * q^46 - 261 * q^47 - 113 * q^48 + 63 * q^50 - 63 * q^51 - 46 * q^52 + 52 * q^54 - 100 * q^55 + 224 * q^57 + 40 * q^58 + 102 * q^59 + 379 * q^60 + 78 * q^61 + 106 * q^64 + 225 * q^65 + 340 * q^66 - 132 * q^67 - 27 * q^68 - 297 * q^69 + 288 * q^72 - 2 * q^73 - 342 * q^74 + 541 * q^75 + 233 * q^76 - 440 * q^78 + 140 * q^79 + 65 * q^81 + 314 * q^82 + 255 * q^83 + 102 * q^85 - 504 * q^86 - 568 * q^87 + 408 * q^88 + 418 * q^90 - 1239 * q^92 - 174 * q^93 + 261 * q^94 - 642 * q^95 - 142 * q^96 + 178 * q^97 - 103 * q^99

Introduction

L-functions

Modular forms

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