LMFDB - Embedded newform 675.2.u.b.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	675.49
Dual form			675.2.u.b.124.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36054 + 1.62143i) q^{2} +(-1.42389 - 0.986166i) q^{3} +(-0.430663 + 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(0.957561 - 0.168844i) q^{7} +(-0.880031 + 0.508086i) q^{8} +(1.05495 + 2.80839i) q^{9} +O(q^{10})$	\(q+(1.36054 + 1.62143i) q^{2} +(-1.42389 - 0.986166i) q^{3} +(-0.430663 + 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(0.957561 - 0.168844i) q^{7} +(-0.880031 + 0.508086i) q^{8} +(1.05495 + 2.80839i) q^{9} +(0.297791 + 0.108387i) q^{11} +(3.02185 - 3.05303i) q^{12} +(0.973200 - 1.15981i) q^{13} +(1.57657 + 1.32290i) q^{14} +(2.63991 + 0.960847i) q^{16} +(1.01731 + 0.587342i) q^{17} +(-3.11830 + 5.53146i) q^{18} +(3.11040 + 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(0.229414 + 0.630310i) q^{22} +(2.12988 + 0.375556i) q^{23} +(1.75413 + 0.144396i) q^{24} +3.20463 q^{26} +(1.26740 - 5.03922i) q^{27} +2.41147i q^{28} +(3.37436 - 2.83142i) q^{29} +(-1.50609 + 8.54146i) q^{31} +(2.72885 + 7.49746i) q^{32} +(-0.317135 - 0.448003i) q^{33} +(0.431752 + 2.44859i) q^{34} +(-7.31359 + 1.36716i) q^{36} +(-3.86823 - 2.23332i) q^{37} +(-4.50341 + 12.3730i) q^{38} +(-2.52950 + 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(-0.940269 - 3.43842i) q^{42} +(1.91223 - 5.25381i) q^{43} +(-0.392973 + 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(-2.43845 + 0.429965i) q^{47} +(-2.81139 - 3.97153i) q^{48} +(-5.68943 + 2.07078i) q^{49} +(-0.869320 - 1.83955i) q^{51} +(2.41362 + 2.87645i) q^{52} -10.8920i q^{53} +(9.89507 - 4.80105i) q^{54} +(-0.756896 + 0.635111i) q^{56} +(0.883963 - 10.7384i) q^{57} +(9.18189 + 1.61901i) q^{58} +(-1.62023 + 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(-15.8985 + 9.17898i) q^{62} +(1.48436 + 2.51109i) q^{63} +(-5.63455 + 9.75933i) q^{64} +(0.294929 - 1.12374i) q^{66} +(0.550580 - 0.656156i) q^{67} +(-1.87265 + 2.23174i) q^{68} +(-2.66237 - 2.63517i) q^{69} +(4.79788 - 8.31018i) q^{71} +(-2.35530 - 1.93547i) q^{72} +(-13.1998 + 7.62091i) q^{73} +(-1.64171 - 9.31057i) q^{74} +(-14.4977 + 5.27674i) q^{76} +(0.303453 + 0.0535070i) q^{77} +(-4.56306 - 3.16030i) q^{78} +(8.59024 - 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} +12.3721i q^{82} +(3.01141 + 3.58886i) q^{83} +(2.37811 - 3.43369i) q^{84} +(11.1203 - 4.04747i) q^{86} +(-7.59698 + 0.703969i) q^{87} +(-0.317135 + 0.0559194i) q^{88} +(-7.74976 - 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(-1.83453 + 5.04032i) q^{92} +(10.5678 - 10.6769i) q^{93} +(-4.01476 - 3.36879i) q^{94} +(3.50815 - 13.3667i) q^{96} +(1.89804 - 5.21481i) q^{97} +(-11.0983 - 6.40762i) q^{98} +(0.00976156 + 0.950656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4}+O(q^{10}) $ 24 * q + 12 * q^4	$ 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	1.36054	+	1.62143i	0.962046	+	1.14652i	0.989153	+	0.146889i	$0.0469262\pi$
$2$	1.36054	+	1.62143i	0.962046	+	1.14652i	−0.0271067	+	0.999633i	$0.508629\pi$
$3$	−1.42389	−	0.986166i	−0.822086	−	0.569363i
$3$	−1.42389	−	0.986166i	−0.822086	−	0.569363i
$4$	−0.430663	+	2.44241i	−0.215332	+	1.22121i
$5$		0			0
$5$		0			0
$6$	−0.338267	−	3.65046i	−0.138097	−	1.49029i
$7$	0.957561	−	0.168844i	0.361924	−	0.0638170i	0.0102706	−	0.999947i	$-0.496731\pi$
$7$	0.957561	−	0.168844i	0.361924	−	0.0638170i	0.351653	+	0.936130i	$0.385620\pi$
$8$	−0.880031	+	0.508086i	−0.311138	+	0.179636i
$9$	1.05495	+	2.80839i	0.351651	+	0.936131i
$10$		0			0
$11$	0.297791	+	0.108387i	0.0897872	+	0.0326799i	0.386523	−	0.922280i	$-0.373676\pi$
$11$	0.297791	+	0.108387i	0.0897872	+	0.0326799i	−0.296736	+	0.954960i	$0.595898\pi$
$12$	3.02185	−	3.05303i	0.872332	−	0.881335i
$13$	0.973200	−	1.15981i	0.269917	−	0.321675i	−0.614011	−	0.789297i	$-0.710445\pi$
$13$	0.973200	−	1.15981i	0.269917	−	0.321675i	0.883928	+	0.467623i	$0.154889\pi$
$14$	1.57657	+	1.32290i	0.421355	+	0.353559i
$15$		0			0
$16$	2.63991	+	0.960847i	0.659977	+	0.240212i
$17$	1.01731	+	0.587342i	0.246733	+	0.142451i	0.618267	−	0.785968i	$-0.287835\pi$
$17$	1.01731	+	0.587342i	0.246733	+	0.142451i	−0.371534	+	0.928419i	$0.621168\pi$
$18$	−3.11830	+	5.53146i	−0.734991	+	1.30378i
$19$	3.11040	+	5.38737i	0.713575	+	1.23595i	0.963507	+	0.267685i	$0.0862586\pi$
$19$	3.11040	+	5.38737i	0.713575	+	1.23595i	−0.249931	+	0.968264i	$0.580408\pi$
$20$		0			0
$21$	−1.52997	−	0.703898i	−0.333868	−	0.153603i
$22$	0.229414	+	0.630310i	0.0489113	+	0.134383i
$23$	2.12988	+	0.375556i	0.444112	+	0.0783089i	0.391232	−	0.920292i	$-0.372049\pi$
$23$	2.12988	+	0.375556i	0.444112	+	0.0783089i	0.0528796	+	0.998601i	$0.483160\pi$
$24$	1.75413	+	0.144396i	0.358060	+	0.0294747i
$25$		0			0
$26$	3.20463			0.628480
$27$	1.26740	−	5.03922i	0.243912	−	0.969797i
$28$			2.41147i			0.455726i
$29$	3.37436	−	2.83142i	0.626602	−	0.525782i	−0.273269	−	0.961938i	$-0.588105\pi$
$29$	3.37436	−	2.83142i	0.626602	−	0.525782i	0.899871	+	0.436156i	$0.143660\pi$
$30$		0			0
$31$	−1.50609	+	8.54146i	−0.270502	+	1.53409i	0.482395	+	0.875954i	$0.339767\pi$
$31$	−1.50609	+	8.54146i	−0.270502	+	1.53409i	−0.752897	+	0.658138i	$0.771344\pi$
$32$	2.72885	+	7.49746i	0.482398	+	1.32538i
$33$	−0.317135	−	0.448003i	−0.0552061	−	0.0779872i
$34$	0.431752	+	2.44859i	0.0740449	+	0.419930i
$35$		0			0
$36$	−7.31359	+	1.36716i	−1.21893	+	0.227859i
$37$	−3.86823	−	2.23332i	−0.635933	−	0.367156i	0.147113	−	0.989120i	$-0.453002\pi$
$37$	−3.86823	−	2.23332i	−0.635933	−	0.367156i	−0.783046	+	0.621964i	$0.786335\pi$
$38$	−4.50341	+	12.3730i	−0.730550	+	2.00717i
$39$	−2.52950	+	0.691717i	−0.405045	+	0.110763i
$40$		0			0
$41$	4.47767	+	3.75721i	0.699295	+	0.586778i	0.921573	−	0.388205i	$-0.126905\pi$
$41$	4.47767	+	3.75721i	0.699295	+	0.586778i	−0.222278	+	0.974983i	$0.571349\pi$
$42$	−0.940269	−	3.43842i	−0.145087	−	0.530560i
$43$	1.91223	−	5.25381i	0.291613	−	0.801199i	−0.704219	−	0.709983i	$-0.748702\pi$
$43$	1.91223	−	5.25381i	0.291613	−	0.801199i	0.995831	−	0.0912158i	$-0.0290753\pi$
$44$	−0.392973	+	0.680649i	−0.0592429	+	0.102612i
$45$		0			0
$46$	2.28885	+	3.96441i	0.337473	+	0.584521i
$47$	−2.43845	+	0.429965i	−0.355685	+	0.0627168i	−0.348636	−	0.937258i	$-0.613355\pi$
$47$	−2.43845	+	0.429965i	−0.355685	+	0.0627168i	−0.00704911	+	0.999975i	$0.502244\pi$
$48$	−2.81139	−	3.97153i	−0.405790	−	0.573241i
$49$	−5.68943	+	2.07078i	−0.812776	+	0.295826i
$50$		0			0
$51$	−0.869320	−	1.83955i	−0.121729	−	0.257588i
$52$	2.41362	+	2.87645i	0.334710	+	0.398891i
$53$		−	10.8920i		−	1.49613i	−0.663628	−	0.748063i	$-0.730984\pi$
$53$		−	10.8920i		−	1.49613i	0.663628	−	0.748063i	$-0.269016\pi$
$54$	9.89507	−	4.80105i	1.34655	−	0.653340i
$55$		0			0
$56$	−0.756896	+	0.635111i	−0.101145	+	0.0848703i
$57$	0.883963	−	10.7384i	0.117084	−	1.42234i
$58$	9.18189	+	1.61901i	1.20564	+	0.212587i
$59$	−1.62023	+	0.589715i	−0.210936	+	0.0767743i	−0.445327	−	0.895368i	$-0.646913\pi$
$59$	−1.62023	+	0.589715i	−0.210936	+	0.0767743i	0.234391	+	0.972142i	$0.424690\pi$
$60$		0			0
$61$	0.176214	+	0.999361i	0.0225619	+	0.127955i	0.994008	−	0.109304i	$-0.0348621\pi$
$61$	0.176214	+	0.999361i	0.0225619	+	0.127955i	−0.971446	+	0.237259i	$0.923751\pi$
$62$	−15.8985	+	9.17898i	−2.01911	+	1.16573i
$63$	1.48436	+	2.51109i	0.187012	+	0.316367i
$64$	−5.63455	+	9.75933i	−0.704319	+	1.21992i
$65$		0			0
$66$	0.294929	−	1.12374i	0.0363033	−	0.138322i
$67$	0.550580	−	0.656156i	0.0672641	−	0.0801622i	−0.731363	−	0.681988i	$-0.761116\pi$
$67$	0.550580	−	0.656156i	0.0672641	−	0.0801622i	0.798627	+	0.601826i	$0.205560\pi$
$68$	−1.87265	+	2.23174i	−0.227092	+	0.270638i
$69$	−2.66237	−	2.63517i	−0.320512	−	0.317238i
$70$		0			0
$71$	4.79788	−	8.31018i	0.569404	−	0.986237i	−0.427221	−	0.904147i	$-0.640507\pi$
$71$	4.79788	−	8.31018i	0.569404	−	0.986237i	0.996625	−	0.0820894i	$-0.0261593\pi$
$72$	−2.35530	−	1.93547i	−0.277574	−	0.228097i
$73$	−13.1998	+	7.62091i	−1.54492	+	0.891960i	−0.546404	+	0.837522i	$0.684004\pi$
$73$	−13.1998	+	7.62091i	−1.54492	+	0.891960i	−0.998517	+	0.0544385i	$0.982663\pi$
$74$	−1.64171	−	9.31057i	−0.190844	−	1.08233i
$75$		0			0
$76$	−14.4977	+	5.27674i	−1.66300	+	0.605284i
$77$	0.303453	+	0.0535070i	0.0345817	+	0.00609768i
$78$	−4.56306	−	3.16030i	−0.516664	−	0.357833i
$79$	8.59024	−	7.20807i	0.966478	−	0.810971i	−0.0155168	−	0.999880i	$-0.504939\pi$
$79$	8.59024	−	7.20807i	0.966478	−	0.810971i	0.981995	+	0.188908i	$0.0604949\pi$
$80$		0			0
$81$	−6.77415	+	5.92544i	−0.752684	+	0.658382i
$82$			12.3721i			1.36626i
$83$	3.01141	+	3.58886i	0.330546	+	0.393929i	0.905563	−	0.424212i	$-0.139449\pi$
$83$	3.01141	+	3.58886i	0.330546	+	0.393929i	−0.575017	+	0.818141i	$0.695005\pi$
$84$	2.37811	−	3.43369i	0.259474	−	0.374646i
$85$		0			0
$86$	11.1203	−	4.04747i	1.19914	−	0.436450i
$87$	−7.59698	+	0.703969i	−0.814482	+	0.0754734i
$88$	−0.317135	+	0.0559194i	−0.0338067	+	0.00596103i
$89$	−7.74976	−	13.4230i	−0.821473	−	1.42283i	−0.904586	−	0.426292i	$-0.859820\pi$
$89$	−7.74976	−	13.4230i	−0.821473	−	1.42283i	0.0831130	−	0.996540i	$-0.473514\pi$
$90$		0			0
$91$	0.736071	−	1.27491i	0.0771612	−	0.133647i
$92$	−1.83453	+	5.04032i	−0.191263	+	0.525490i
$93$	10.5678	−	10.6769i	1.09583	−	1.10714i
$94$	−4.01476	−	3.36879i	−0.414091	−	0.347464i
$95$		0			0
$96$	3.50815	−	13.3667i	0.358049	−	1.36423i
$97$	1.89804	−	5.21481i	0.192716	−	0.529484i	−0.805270	−	0.592908i	$-0.797980\pi$
$97$	1.89804	−	5.21481i	0.192716	−	0.529484i	0.997987	+	0.0634241i	$0.0202021\pi$
$98$	−11.0983	−	6.40762i	−1.12110	−	0.647267i
$99$	0.00976156	+	0.950656i	0.000981074	+	0.0955445i
$100$		0			0
$101$	−1.76063	−	9.98501i	−0.175189	−	0.993546i	−0.937926	−	0.346836i	$-0.887256\pi$
$101$	−1.76063	−	9.98501i	−0.175189	−	0.993546i	0.762737	−	0.646709i	$-0.223855\pi$
$102$	1.79995	−	3.91231i	0.178221	−	0.387377i
$103$	3.37002	+	9.25906i	0.332058	+	0.912323i	0.987576	+	0.157143i	$0.0502283\pi$
$103$	3.37002	+	9.25906i	0.332058	+	0.912323i	−0.655518	+	0.755180i	$0.727549\pi$
$104$	−0.267160	+	1.51514i	−0.0261972	+	0.148572i
$105$		0			0
$106$	17.6605	−	14.8189i	1.71534	−	1.43934i
$107$		−	5.17080i		−	0.499880i	−0.968261	−	0.249940i	$-0.919589\pi$
$107$		−	5.17080i		−	0.499880i	0.968261	−	0.249940i	$-0.0804109\pi$
$108$	11.7620	+	5.26573i	1.13180	+	0.506695i
$109$	7.31065			0.700234			0.350117	−	0.936706i	$-0.386142\pi$
$109$	7.31065			0.700234			0.350117	+	0.936706i	$0.386142\pi$
$110$		0			0
$111$	3.30552	+	6.99473i	0.313746	+	0.663911i
$112$	2.69010	+	0.474338i	0.254191	+	0.0448207i
$113$	−3.54868	−	9.74991i	−0.333832	−	0.917195i	−0.987105	−	0.160073i	$-0.948827\pi$
$113$	−3.54868	−	9.74991i	−0.333832	−	0.917195i	0.653274	−	0.757122i	$-0.273395\pi$
$114$	18.6142	−	13.1768i	1.74338	−	1.23412i
$115$		0			0
$116$	5.46229	+	9.46096i	0.507161	+	0.878428i
$117$	4.28390	+	1.50958i	0.396046	+	0.139561i
$118$	−3.16056	−	1.82475i	−0.290953	−	0.167982i
$119$	1.07330	+	0.390650i	0.0983894	+	0.0358108i
$120$		0			0
$121$	−8.34956	−	7.00611i	−0.759051	−	0.636919i
$122$	−1.38064	+	1.64539i	−0.124998	+	0.148966i
$123$	−2.67050	−	9.76560i	−0.240790	−	0.880535i
$124$	−20.2132	−	7.35699i	−1.81520	−	0.660677i
$125$		0			0
$126$	−2.05201	+	5.82321i	−0.182808	+	0.518773i
$127$	−4.52709	+	2.61372i	−0.401714	+	0.231930i	−0.687223	−	0.726446i	$-0.741171\pi$
$127$	−4.52709	+	2.61372i	−0.401714	+	0.231930i	0.285509	+	0.958376i	$0.407837\pi$
$128$	−7.77522	+	1.37098i	−0.687239	+	0.121179i
$129$	−7.90395	+	5.59510i	−0.695904	+	0.492621i
$130$		0			0
$131$	−1.25622	+	7.12440i	−0.109757	+	0.622461i	0.879457	+	0.475979i	$0.157906\pi$
$131$	−1.25622	+	7.12440i	−0.109757	+	0.622461i	−0.989213	+	0.146482i	$0.953205\pi$
$132$	1.23079	−	0.581636i	0.107126	−	0.0506249i
$133$	3.88802	+	4.63357i	0.337134	+	0.401781i
$134$	1.81300			0.156619
$135$		0			0
$136$	−1.19368			−0.102357
$137$	−7.23092	−	8.61748i	−0.617779	−	0.736241i	0.362907	−	0.931825i	$-0.381784\pi$
$137$	−7.23092	−	8.61748i	−0.617779	−	0.736241i	−0.980687	+	0.195584i	$0.937340\pi$
$138$	0.650482	−	7.90210i	0.0553727	−	0.672671i
$139$	−1.62885	+	9.23766i	−0.138157	+	0.783528i	0.834452	+	0.551081i	$0.185784\pi$
$139$	−1.62885	+	9.23766i	−0.138157	+	0.783528i	−0.972609	+	0.232447i	$0.925327\pi$
$140$		0			0
$141$	3.89612	+	1.79249i	0.328112	+	0.150955i
$142$	20.0021	−	3.52690i	1.67854	−	0.295971i
$143$	0.415518	−	0.239900i	0.0347474	−	0.0200614i
$144$	0.0865360	+	8.42754i	0.00721133	+	0.702295i
$145$		0			0
$146$	−30.3156	−	11.0340i	−2.50894	−	0.913179i
$147$	10.1433	+	2.66215i	0.836605	+	0.219570i
$148$	7.12060	−	8.48600i	0.585310	−	0.697545i
$149$	−14.5941	−	12.2459i	−1.19560	−	1.00322i	−0.999745	−	0.0225899i	$-0.992809\pi$
$149$	−14.5941	−	12.2459i	−1.19560	−	1.00322i	−0.195851	−	0.980634i	$-0.562747\pi$
$150$		0			0
$151$	−3.77193	−	1.37287i	−0.306955	−	0.111723i	0.183950	−	0.982936i	$-0.441112\pi$
$151$	−3.77193	−	1.37287i	−0.306955	−	0.111723i	−0.490905	+	0.871213i	$0.663334\pi$
$152$	−5.47450	−	3.16070i	−0.444041	−	0.256367i
$153$	−0.576279	+	3.47661i	−0.0465894	+	0.281068i
$154$	0.326102	+	0.564825i	0.0262780	+	0.0455149i
$155$		0			0
$156$	−0.600093	−	6.47599i	−0.0480459	−	0.518494i
$157$	2.48851	+	6.83713i	0.198605	+	0.545662i	0.998516	−	0.0544560i	$-0.0173425\pi$
$157$	2.48851	+	6.83713i	0.198605	+	0.545662i	−0.799911	+	0.600118i	$0.795120\pi$
$158$	23.3747	+	4.12159i	1.85959	+	0.327896i
$159$	−10.7413	+	15.5090i	−0.851839	+	1.22994i
$160$		0			0
$161$	2.10290			0.165732
$162$	−18.8242	−	2.92200i	−1.47897	−	0.229574i
$163$			12.4492i			0.975094i	0.873097	+	0.487547i	$0.162108\pi$
$163$			12.4492i			0.975094i	−0.873097	+	0.487547i	$0.837892\pi$
$164$	−11.1050	+	9.31823i	−0.867157	+	0.727632i
$165$		0			0
$166$	−1.72194	+	9.76558i	−0.133648	+	0.757956i
$167$	−0.797553	−	2.19126i	−0.0617165	−	0.169565i	0.905002	−	0.425408i	$-0.139869\pi$
$167$	−0.797553	−	2.19126i	−0.0617165	−	0.169565i	−0.966718	+	0.255843i	$0.917647\pi$
$168$	1.70407	−	0.157906i	0.131472	−	0.0121827i
$169$	1.85937	+	10.5450i	0.143029	+	0.811157i
$170$		0			0
$171$	−11.8485	+	14.4187i	−0.906081	+	1.10262i
$172$	12.0085	+	6.93308i	0.915636	+	0.528643i
$173$	−1.22521	+	3.36623i	−0.0931509	+	0.255930i	−0.977514	−	0.210869i	$-0.932371\pi$
$173$	−1.22521	+	3.36623i	−0.0931509	+	0.255930i	0.884363	+	0.466799i	$0.154593\pi$
$174$	−11.4774	−	11.3602i	−0.870101	−	0.861213i
$175$		0			0
$176$	0.681996	+	0.572262i	0.0514074	+	0.0431359i
$177$	2.88859	+	0.758123i	0.217120	+	0.0569840i
$178$	11.2205	−	30.8281i	0.841014	−	2.31067i
$179$	−9.99785	+	17.3168i	−0.747275	+	1.29432i	0.201850	+	0.979416i	$0.435305\pi$
$179$	−9.99785	+	17.3168i	−0.747275	+	1.29432i	−0.949124	+	0.314901i	$0.898029\pi$
$180$		0			0
$181$	−4.86616	−	8.42844i	−0.361699	−	0.626481i	0.626542	−	0.779388i	$-0.284470\pi$
$181$	−4.86616	−	8.42844i	−0.361699	−	0.626481i	−0.988241	+	0.152907i	$0.951136\pi$
$182$	3.06863	−	0.541082i	0.227462	−	0.0401077i
$183$	0.734626	−	1.59676i	0.0543051	−	0.118036i
$184$	−2.06518	+	0.751664i	−0.152247	+	0.0554134i
$185$		0			0
$186$	31.6897	+	2.60862i	2.32360	+	0.191274i
$187$	0.239284	+	0.285168i	0.0174982	+	0.0208535i
$188$		−	6.14088i		−	0.447869i
$189$	0.362776	−	5.03935i	0.0263881	−	0.366559i
$190$		0			0
$191$	−13.6023	+	11.4137i	−0.984227	+	0.825864i	−0.984722	−	0.174135i	$-0.944287\pi$
$191$	−13.6023	+	11.4137i	−0.984227	+	0.825864i	0.000494763		1.00000i	$0.499843\pi$
$192$	17.6473	−	8.33965i	1.27359	−	0.601862i
$193$	10.4235	+	1.83795i	0.750303	+	0.132299i	0.535706	−	0.844404i	$-0.320045\pi$
$193$	10.4235	+	1.83795i	0.750303	+	0.132299i	0.214596	+	0.976703i	$0.431156\pi$
$194$	11.0378	−	4.01743i	0.792467	−	0.288434i
$195$		0			0
$196$	−2.60748	−	14.7878i	−0.186249	−	1.05627i
$197$	−12.2620	+	7.07945i	−0.873628	+	0.504390i	−0.868552	−	0.495597i	$-0.834949\pi$
$197$	−12.2620	+	7.07945i	−0.873628	+	0.504390i	−0.00507615	+	0.999987i	$0.501616\pi$
$198$	−1.52814	+	1.30923i	−0.108600	+	0.0930431i
$199$	3.77010	−	6.53000i	0.267255	−	0.462899i	−0.700897	−	0.713263i	$-0.747217\pi$
$199$	3.77010	−	6.53000i	0.267255	−	0.462899i	0.968152	+	0.250363i	$0.0805501\pi$
$200$		0			0
$201$	−1.43105	+	0.391333i	−0.100938	+	0.0276025i
$202$	13.7946	−	16.4397i	0.970582	−	1.15669i
$203$	2.75308	−	3.28100i	0.193229	−	0.230281i
$204$	4.86732	−	1.33101i	0.340780	−	0.0931896i
$205$		0			0
$206$	−10.4278	+	18.0616i	−0.726543	+	1.25841i
$207$	1.19222	+	6.37775i	0.0828648	+	0.443284i
$208$	3.68356	−	2.12670i	0.255409	−	0.147460i
$209$	0.342328	+	1.94144i	0.0236793	+	0.134292i
$210$		0			0
$211$	−4.89922	+	1.78317i	−0.337276	+	0.122758i	−0.505106	−	0.863058i	$-0.668546\pi$
$211$	−4.89922	+	1.78317i	−0.337276	+	0.122758i	0.167829	+	0.985816i	$0.446324\pi$
$212$	26.6027	+	4.69077i	1.82708	+	0.322163i
$213$	−15.0269	+	7.10131i	−1.02963	+	0.486573i
$214$	8.38408	−	7.03508i	0.573124	−	0.480908i
$215$		0			0
$216$	1.44500	+	5.07862i	0.0983199	+	0.345556i
$217$			8.43326i			0.572487i
$218$	9.94643	+	11.8537i	0.673657	+	0.802833i
$219$	26.3106	+	2.16583i	1.77791	+	0.146353i
$220$		0			0
$221$	1.67125	−	0.608285i	0.112420	−	0.0409177i
$222$	−6.84416	+	14.8763i	−0.459350	+	0.998430i
$223$	−17.4250	+	3.07250i	−1.16686	+	0.205750i	−0.723326	−	0.690506i	$-0.757388\pi$
$223$	−17.4250	+	3.07250i	−1.16686	+	0.205750i	−0.443537	+	0.896256i	$0.646277\pi$
$224$	3.87894	+	6.71853i	0.259173	+	0.448901i
$225$		0			0
$226$	10.9807	−	19.0191i	0.730423	−	1.26513i
$227$	5.39434	−	14.8208i	0.358035	−	0.983692i	−0.621676	−	0.783275i	$-0.713548\pi$
$227$	5.39434	−	14.8208i	0.358035	−	0.983692i	0.979711	−	0.200418i	$-0.0642299\pi$
$228$	25.8470	+	6.78365i	1.71176	+	0.449258i
$229$	1.35350	+	1.13572i	0.0894415	+	0.0750504i	0.686412	−	0.727213i	$-0.259185\pi$
$229$	1.35350	+	1.13572i	0.0894415	+	0.0750504i	−0.596971	+	0.802263i	$0.703629\pi$
$230$		0			0
$231$	−0.379318	−	0.375443i	−0.0249573	−	0.0247024i
$232$	−1.53093	+	4.20620i	−0.100511	+	0.276151i
$233$	12.0364	+	6.94920i	0.788529	+	0.455257i	0.839444	−	0.543446i	$-0.182881\pi$
$233$	12.0364	+	6.94920i	0.788529	+	0.455257i	−0.0509157	+	0.998703i	$0.516214\pi$
$234$	3.38073	+	8.99987i	0.221005	+	0.588340i
$235$		0			0
$236$	−0.742554	−	4.21123i	−0.0483362	−	0.274128i
$237$	−19.3400	+	1.79212i	−1.25627	+	0.116411i
$238$	0.826858	+	2.27177i	0.0535973	+	0.147257i
$239$	3.44391	−	19.5314i	0.222768	−	1.26338i	−0.644138	−	0.764909i	$-0.722784\pi$
$239$	3.44391	−	19.5314i	0.222768	−	1.26338i	0.866906	−	0.498471i	$-0.166105\pi$
$240$		0			0
$241$	14.8419	−	12.4538i	0.956050	−	0.802221i	−0.0242563	−	0.999706i	$-0.507722\pi$
$241$	14.8419	−	12.4538i	0.956050	−	0.802221i	0.980306	+	0.197485i	$0.0632773\pi$
$242$		−	23.0703i		−	1.48301i
$243$	15.4892	−	1.75676i	0.993629	−	0.112696i
$244$	−2.51674			−0.161118
$245$		0			0
$246$	12.2009	−	17.6165i	0.777901	−	1.12319i
$247$	9.27540	+	1.63550i	0.590179	+	0.104065i
$248$	−3.01439	−	8.28198i	−0.191414	−	0.525906i
$249$	−0.748720	−	8.07992i	−0.0474482	−	0.512044i
$250$		0			0
$251$	2.73786	+	4.74212i	0.172812	+	0.299320i	0.939402	−	0.342818i	$-0.111381\pi$
$251$	2.73786	+	4.74212i	0.172812	+	0.299320i	−0.766590	+	0.642137i	$0.778048\pi$
$252$	−6.77237	+	2.54399i	−0.426619	+	0.160256i
$253$	0.593554	+	0.342689i	0.0373164	+	0.0215447i
$254$	−10.3972	−	3.78428i	−0.652380	−	0.237447i
$255$		0			0
$256$	4.46383	+	3.74560i	0.278989	+	0.234100i
$257$	−7.43395	+	8.85943i	−0.463717	+	0.552636i	−0.946332	−	0.323196i	$-0.895243\pi$
$257$	−7.43395	+	8.85943i	−0.463717	+	0.552636i	0.482615	+	0.875833i	$0.339687\pi$
$258$	−19.8257	−	5.20333i	−1.23429	−	0.323945i
$259$	−4.08115	−	1.48542i	−0.253590	−	0.0922993i
$260$		0			0
$261$	11.5115	+	6.48951i	0.712546	+	0.401691i
$262$	−13.2608	+	7.65614i	−0.819257	+	0.472998i
$263$	−6.37952	+	1.12488i	−0.393378	+	0.0693632i	−0.366839	−	0.930285i	$-0.619560\pi$
$263$	−6.37952	+	1.12488i	−0.393378	+	0.0693632i	−0.0265395	+	0.999648i	$0.508449\pi$
$264$	0.506712	+	0.233124i	0.0311860	+	0.0143478i
$265$		0			0
$266$	−2.22318	+	12.6083i	−0.136312	+	0.773064i
$267$	−2.20245	+	26.7554i	−0.134788	+	1.63741i
$268$	1.36549	+	1.62733i	0.0834106	+	0.0994048i
$269$	13.8387			0.843758			0.421879	−	0.906652i	$-0.361371\pi$
$269$	13.8387			0.843758			0.421879	+	0.906652i	$0.361371\pi$
$270$		0			0
$271$	1.94536			0.118172			0.0590860	−	0.998253i	$-0.481181\pi$
$271$	1.94536			0.118172			0.0590860	+	0.998253i	$0.481181\pi$
$272$	2.12125	+	2.52800i	0.128619	+	0.153283i
$273$	−2.30536	+	1.08945i	−0.139527	+	0.0659366i
$274$	4.13466	−	23.4488i	0.249784	−	1.41660i
$275$		0			0
$276$	7.58277	−	5.36774i	0.456429	−	0.323100i
$277$	12.2832	−	2.16586i	0.738026	−	0.130134i	0.208016	−	0.978125i	$-0.433299\pi$
$277$	12.2832	−	2.16586i	0.738026	−	0.130134i	0.530010	+	0.847991i	$0.322188\pi$
$278$	−17.1943	+	9.92713i	−1.03125	+	0.595390i
$279$	−25.5766	+	4.78114i	−1.53123	+	0.286239i
$280$		0			0
$281$	−9.16752	−	3.33670i	−0.546888	−	0.199051i	0.0537751	−	0.998553i	$-0.482875\pi$
$281$	−9.16752	−	3.33670i	−0.546888	−	0.199051i	−0.600663	+	0.799502i	$0.705097\pi$
$282$	2.39442	+	8.75602i	0.142585	+	0.521414i
$283$	−17.0797	+	20.3547i	−1.01528	+	1.20996i	−0.0377246	+	0.999288i	$0.512011\pi$
$283$	−17.0797	+	20.3547i	−1.01528	+	1.20996i	−0.977556	+	0.210676i	$0.932433\pi$
$284$	18.2306	+	15.2973i	1.08179	+	0.907728i
$285$		0			0
$286$	0.954309	+	0.347340i	0.0564295	+	0.0205386i
$287$	4.92202	+	2.84173i	0.290538	+	0.167742i
$288$	−18.1770	+	15.5732i	−1.07109	+	0.917657i
$289$	−7.81006	−	13.5274i	−0.459415	−	0.795730i
$290$		0			0
$291$	−7.84527	+	5.55356i	−0.459898	+	0.325556i
$292$	−12.9287	−	35.5214i	−0.756598	−	2.07873i
$293$	12.0712	+	2.12849i	0.705210	+	0.124347i	0.514741	−	0.857346i	$-0.327888\pi$
$293$	12.0712	+	2.12849i	0.705210	+	0.124347i	0.190469	+	0.981693i	$0.438999\pi$
$294$	9.48386	+	20.0686i	0.553110	+	1.17042i
$295$		0			0
$296$	4.53888			0.263817
$297$	0.923606	−	1.36326i	0.0535930	−	0.0791044i
$298$		−	40.3243i		−	2.33592i
$299$	2.50838	−	2.10478i	0.145063	−	0.121723i
$300$		0			0
$301$	0.944004	−	5.35371i	0.0544115	−	0.308583i
$302$	−2.90585	−	7.98375i	−0.167213	−	0.459413i
$303$	−7.33993	+	15.9539i	−0.421668	+	0.916526i
$304$	3.03473	+	17.2108i	0.174053	+	0.987106i
$305$		0			0
$306$	−6.42113	+	3.79567i	−0.367071	+	0.216984i
$307$	−22.9271	−	13.2370i	−1.30852	−	0.755475i	−0.326671	−	0.945138i	$-0.605927\pi$
$307$	−22.9271	−	13.2370i	−1.30852	−	0.755475i	−0.981849	+	0.189663i	$0.939260\pi$
$308$	−0.261372	+	0.718114i	−0.0148931	+	0.0409184i
$309$	4.33242	−	16.5073i	0.246463	−	0.939070i
$310$		0			0
$311$	−13.5280	−	11.3513i	−0.767100	−	0.643673i	0.172865	−	0.984946i	$-0.444698\pi$
$311$	−13.5280	−	11.3513i	−0.767100	−	0.643673i	−0.939964	+	0.341272i	$0.889142\pi$
$312$	1.87459	−	1.89394i	0.106128	−	0.107223i
$313$	3.29954	−	9.06541i	0.186501	−	0.512407i	−0.810841	−	0.585266i	$-0.800990\pi$
$313$	3.29954	−	9.06541i	0.186501	−	0.512407i	0.997342	+	0.0728589i	$0.0232123\pi$
$314$	−7.70019	+	13.3371i	−0.434547	+	0.752657i
$315$		0			0
$316$	13.9056	+	24.0852i	0.782250	+	1.35490i
$317$	−3.65412	+	0.644320i	−0.205236	+	0.0361886i	−0.275321	−	0.961352i	$-0.588784\pi$
$317$	−3.65412	+	0.644320i	−0.205236	+	0.0361886i	0.0700850	+	0.997541i	$0.477673\pi$
$318$	−39.7606	+	3.68439i	−2.22967	+	0.206610i
$319$	1.31174	−	0.477435i	0.0734434	−	0.0267312i
$320$		0			0
$321$	−5.09927	+	7.36268i	−0.284614	+	0.410945i
$322$	2.86108	+	3.40971i	0.159442	+	0.190016i
$323$			7.30748i			0.406599i
$324$	−11.5550	−	19.0972i	−0.641944	−	1.06095i
$325$		0			0
$326$	−20.1854	+	16.9376i	−1.11797	+	0.938085i
$327$	−10.4096	−	7.20952i	−0.575652	−	0.398687i
$328$	−5.84948	−	1.03142i	−0.322983	−	0.0569507i
$329$	−2.26237	+	0.823435i	−0.124728	+	0.0453974i
$330$		0			0
$331$	−0.245329	−	1.39133i	−0.0134845	−	0.0764745i	0.977323	−	0.211755i	$-0.0679177\pi$
$331$	−0.245329	−	1.39133i	−0.0134845	−	0.0764745i	−0.990807	+	0.135280i	$0.956807\pi$
$332$	−10.0624	+	5.80953i	−0.552246	+	0.318839i
$333$	2.19126	−	13.2196i	0.120080	−	0.724427i
$334$	2.46786	−	4.27446i	0.135035	−	0.233888i
$335$		0			0
$336$	−3.36265	−	3.32830i	−0.183447	−	0.181573i
$337$	−8.34986	+	9.95097i	−0.454846	+	0.542064i	−0.943918	−	0.330179i	$-0.892891\pi$
$337$	−8.34986	+	9.95097i	−0.454846	+	0.542064i	0.489073	+	0.872243i	$0.337335\pi$
$338$	−14.5683	+	17.3618i	−0.792409	+	0.944356i
$339$	−4.56209	+	17.3824i	−0.247779	+	0.944084i
$340$		0			0
$341$	−1.37428	+	2.38033i	−0.0744215	+	0.128902i
$342$	−39.4992	+	0.405587i	−2.13587	+	0.0219316i
$343$	−10.9928	+	6.34669i	−0.593555	+	0.342689i
$344$	0.986567	+	5.59510i	0.0531921	+	0.301667i
$345$		0			0
$346$	−7.12504	+	2.59330i	−0.383045	+	0.139417i
$347$	4.72753	+	0.833591i	0.253787	+	0.0447495i	0.299094	−	0.954224i	$-0.403316\pi$
$347$	4.72753	+	0.833591i	0.253787	+	0.0447495i	−0.0453070	+	0.998973i	$0.514427\pi$
$348$	1.55236	−	18.8581i	0.0832152	−	1.01090i
$349$	17.2954	−	14.5126i	0.925803	−	0.776841i	−0.0492565	−	0.998786i	$-0.515685\pi$
$349$	17.2954	−	14.5126i	0.925803	−	0.776841i	0.975059	+	0.221946i	$0.0712407\pi$
$350$		0			0
$351$	−4.61112	−	6.37412i	−0.246123	−	0.340225i
$352$			2.52845i			0.134767i
$353$	−19.0950	−	22.7565i	−1.01632	−	1.21121i	−0.977276	−	0.211972i	$-0.932012\pi$
$353$	−19.0950	−	22.7565i	−1.01632	−	1.21121i	−0.0390490	−	0.999237i	$-0.512433\pi$
$354$	2.70080	+	5.71509i	0.143546	+	0.303754i
$355$		0			0
$356$	36.1220	−	13.1473i	1.91446	−	0.696807i
$357$	−1.14302	−	1.61470i	−0.0604952	−	0.0854589i
$358$	−41.6804	+	7.34937i	−2.20288	+	0.388427i
$359$	6.70991	+	11.6219i	0.354136	+	0.613381i	0.986970	−	0.160906i	$-0.0514418\pi$
$359$	6.70991	+	11.6219i	0.354136	+	0.613381i	−0.632834	+	0.774288i	$0.718108\pi$
$360$		0			0
$361$	−9.84920	+	17.0593i	−0.518379	+	0.897858i
$362$	7.04550	−	19.3573i	0.370303	−	1.01740i
$363$	4.97970	+	18.2100i	0.261366	+	0.955778i
$364$	2.79686	+	2.34685i	0.146595	+	0.123008i
$365$		0			0
$366$	3.58852	−	0.981314i	0.187575	−	0.0512941i
$367$	2.71905	−	7.47054i	0.141933	−	0.389959i	−0.848275	−	0.529556i	$-0.822359\pi$
$367$	2.71905	−	7.47054i	0.141933	−	0.389959i	0.990208	+	0.139597i	$0.0445808\pi$
$368$	5.26184	+	3.03793i	0.274293	+	0.158363i
$369$	−5.82801	+	16.5387i	−0.303394	+	0.860973i
$370$		0			0
$371$	−1.83904	−	10.4297i	−0.0954782	−	0.541484i
$372$	21.5262	+	30.4091i	1.11608	+	1.57664i
$373$	3.90604	+	10.7318i	0.202247	+	0.555670i	0.998804	−	0.0488939i	$-0.0155696\pi$
$373$	3.90604	+	10.7318i	0.202247	+	0.555670i	−0.796557	+	0.604564i	$0.793347\pi$
$374$	−0.136823	+	0.775963i	−0.00707496	+	0.0401241i
$375$		0			0
$376$	1.92745	−	1.61733i	0.0994009	−	0.0834072i
$377$		−	6.66917i		−	0.343480i
$378$	8.66451	−	6.26801i	0.445654	−	0.322392i
$379$	24.1705			1.24155			0.620777	−	0.783987i	$-0.286817\pi$
$379$	24.1705			1.24155			0.620777	+	0.783987i	$0.286817\pi$
$380$		0			0
$381$	9.02366	+	0.742807i	0.462296	+	0.0380551i
$382$	−37.0129	−	6.52637i	−1.89374	−	0.333918i
$383$	−3.22979	−	8.87378i	−0.165035	−	0.453429i	0.829416	−	0.558631i	$-0.188673\pi$
$383$	−3.22979	−	8.87378i	−0.165035	−	0.453429i	−0.994451	+	0.105202i	$0.966451\pi$
$384$	12.4231	+	5.71553i	0.633964	+	0.291669i
$385$		0			0
$386$	11.2015	+	19.4016i	0.570143	+	0.987516i
$387$	16.7721	−	0.172220i	0.852573	−	0.00875442i
$388$	11.9193	+	6.88162i	0.605111	+	0.349361i
$389$	−2.39406	−	0.871367i	−0.121384	−	0.0441801i	0.280614	−	0.959821i	$-0.409462\pi$
$389$	−2.39406	−	0.871367i	−0.121384	−	0.0441801i	−0.401998	+	0.915641i	$0.631684\pi$
$390$		0			0
$391$	1.94617	+	1.63303i	0.0984218	+	0.0825857i
$392$	3.95474	−	4.71308i	0.199745	−	0.238046i
$393$	8.81457	−	8.90554i	0.444636	−	0.449225i
$394$	−28.1617	−	10.2500i	−1.41876	−	0.516388i
$395$		0			0
$396$	−2.32610	−	0.385571i	−0.116891	−	0.0193757i
$397$	−3.18279	+	1.83759i	−0.159740	+	0.0922258i	−0.577739	−	0.816222i	$-0.696065\pi$
$397$	−3.18279	+	1.83759i	−0.159740	+	0.0922258i	0.417999	+	0.908447i	$0.362731\pi$
$398$	15.7173	−	2.77138i	0.787836	−	0.138917i
$399$	−0.966669	−	10.4319i	−0.0483940	−	0.522251i
$400$		0			0
$401$	2.80420	−	15.9034i	0.140035	−	0.794177i	−0.831186	−	0.555995i	$-0.812337\pi$
$401$	2.80420	−	15.9034i	0.140035	−	0.794177i	0.971220	−	0.238182i	$-0.0765516\pi$
$402$	−2.58151	−	1.78791i	−0.128754	−	0.0891731i
$403$	8.44078	+	10.0593i	0.420465	+	0.501091i
$404$	25.1458			1.25105
$405$		0			0
$406$	9.06558			0.449917
$407$	−0.909859	−	1.08433i	−0.0451000	−	0.0537481i
$408$	1.69968	+	1.17717i	0.0841465	+	0.0582785i
$409$	−1.59443	+	9.04248i	−0.0788396	+	0.447122i	0.919677	+	0.392676i	$0.128450\pi$
$409$	−1.59443	+	9.04248i	−0.0788396	+	0.447122i	−0.998517	+	0.0544462i	$0.982661\pi$
$410$		0			0
$411$	1.79780	+	19.4013i	0.0886792	+	0.956994i
$412$	−24.0658	+	4.24345i	−1.18564	+	0.209060i
$413$	−1.45190	+	0.838253i	−0.0714432	+	0.0412477i
$414$	−8.71900	+	10.6103i	−0.428515	+	0.521466i
$415$		0			0
$416$	11.3514	+	4.13157i	0.556548	+	0.202567i
$417$	11.4292	−	11.5471i	0.559689	−	0.565466i
$418$	−2.68215	+	3.19646i	−0.131188	+	0.156344i
$419$	5.34613	+	4.48594i	0.261176	+	0.219152i	0.763967	−	0.645256i	$-0.223249\pi$
$419$	5.34613	+	4.48594i	0.261176	+	0.219152i	−0.502791	+	0.864408i	$0.667694\pi$
$420$		0			0
$421$	−28.9525	−	10.5379i	−1.41106	−	0.513584i	−0.479619	−	0.877477i	$-0.659225\pi$
$421$	−28.9525	−	10.5379i	−1.41106	−	0.513584i	−0.931441	+	0.363894i	$0.881447\pi$
$422$	−9.55686	−	5.51765i	−0.465221	−	0.268595i
$423$	−3.77996	−	6.39454i	−0.183788	−	0.310913i
$424$	5.53405	+	9.58526i	0.268757	+	0.465502i
$425$		0			0
$426$	−31.9589	−	14.7034i	−1.54842	−	0.712383i
$427$	0.337472	+	0.927196i	0.0163314	+	0.0448702i
$428$	12.6292	+	2.22687i	0.610457	+	0.107640i
$429$	−0.828236	−	0.0681784i	−0.0399876	−	0.00329169i
$430$		0			0
$431$	27.8971			1.34376			0.671879	−	0.740661i	$-0.265487\pi$
$431$	27.8971			1.34376			0.671879	+	0.740661i	$0.265487\pi$
$432$	8.18774	−	12.0853i	0.393933	−	0.581453i
$433$			19.1706i			0.921278i	0.887588	+	0.460639i	$0.152380\pi$
$433$			19.1706i			0.921278i	−0.887588	+	0.460639i	$0.847620\pi$
$434$	−13.6739	+	11.4738i	−0.656369	+	0.550759i
$435$		0			0
$436$	−3.14843	+	17.8556i	−0.150782	+	0.855130i
$437$	4.60154	+	12.6426i	0.220121	+	0.604778i
$438$	32.2849	+	45.6075i	1.54263	+	2.17921i
$439$	4.12397	+	23.3882i	0.196826	+	1.11626i	0.909794	+	0.415060i	$0.136239\pi$
$439$	4.12397	+	23.3882i	0.196826	+	1.11626i	−0.712968	+	0.701197i	$0.752649\pi$
$440$		0			0
$441$	−11.8177	−	13.7936i	−0.562746	−	0.656838i
$442$	3.26009	+	1.88221i	0.155067	+	0.0895278i
$443$	7.98900	−	21.9496i	0.379569	−	1.04286i	−0.591967	−	0.805962i	$-0.701648\pi$
$443$	7.98900	−	21.9496i	0.379569	−	1.04286i	0.971536	−	0.236894i	$-0.0761294\pi$
$444$	−18.5076	+	5.06108i	−0.878332	+	0.240188i
$445$		0			0
$446$	−28.6892	−	24.0731i	−1.35847	−	1.13989i
$447$	8.70396	+	31.8291i	0.411683	+	1.50546i
$448$	−3.74762	+	10.2965i	−0.177059	+	0.486464i
$449$	2.40953	−	4.17343i	0.113713	−	0.196956i	−0.803552	−	0.595235i	$-0.797059\pi$
$449$	2.40953	−	4.17343i	0.113713	−	0.196956i	0.917264	+	0.398279i	$0.130392\pi$
$450$		0			0
$451$	0.926176	+	1.60418i	0.0436119	+	0.0755380i
$452$	25.3416	−	4.46841i	1.19197	−	0.210176i
$453$	4.01695	+	5.67457i	0.188733	+	0.266615i
$454$	31.3701	−	11.4178i	1.47227	−	0.535863i
$455$		0			0
$456$	4.67813	+	9.89928i	0.219074	+	0.463576i
$457$	3.14555	+	3.74872i	0.147142	+	0.175358i	0.834581	−	0.550885i	$-0.185710\pi$
$457$	3.14555	+	3.74872i	0.147142	+	0.175358i	−0.687439	+	0.726242i	$0.741265\pi$
$458$			3.73978i			0.174749i
$459$	4.24908	−	4.38203i	0.198330	−	0.204535i
$460$		0			0
$461$	21.4419	−	17.9919i	0.998650	−	0.837967i	0.0118535	−	0.999930i	$-0.496227\pi$
$461$	21.4419	−	17.9919i	0.998650	−	0.837967i	0.986797	+	0.161963i	$0.0517824\pi$
$462$	0.0926768	−	1.12584i	0.00431171	−	0.0523789i
$463$	−27.0579	−	4.77104i	−1.25749	−	0.221729i	−0.495093	−	0.868840i	$-0.664866\pi$
$463$	−27.0579	−	4.77104i	−1.25749	−	0.221729i	−0.762396	+	0.647111i	$0.775977\pi$
$464$	11.6285	−	4.23245i	0.539842	−	0.196486i
$465$		0			0
$466$	5.10832	+	28.9707i	0.236639	+	1.34204i
$467$	18.4000	−	10.6232i	0.851450	−	0.491585i	−0.00968963	−	0.999953i	$-0.503084\pi$
$467$	18.4000	−	10.6232i	0.851450	−	0.491585i	0.861140	+	0.508368i	$0.169751\pi$
$468$	−5.53194	+	9.81292i	−0.255714	+	0.453602i
$469$	0.416426	−	0.721272i	0.0192288	−	0.0333052i
$470$		0			0
$471$	3.19917	−	12.1894i	0.147410	−	0.561659i
$472$	1.12623	−	1.34218i	0.0518387	−	0.0617790i
$473$	1.13889	−	1.35728i	0.0523662	−	0.0624076i
$474$	−29.2186	−	28.9201i	−1.34205	−	1.32834i
$475$		0			0
$476$	−1.41636	+	2.45321i	−0.0649188	+	0.112443i
$477$	30.5889	−	11.4905i	1.40057	−	0.526113i
$478$	36.3543	−	20.9892i	1.66281	−	0.960022i
$479$	7.23745	+	41.0456i	0.330688	+	1.87542i	0.466248	+	0.884654i	$0.345606\pi$
$479$	7.23745	+	41.0456i	0.330688	+	1.87542i	−0.135560	+	0.990769i	$0.543283\pi$
$480$		0			0
$481$	−6.35480	+	2.31296i	−0.289754	+	0.105462i
$482$	40.3859	+	7.12113i	1.83953	+	0.324358i
$483$	−2.99431	−	2.07381i	−0.136246	−	0.0943618i
$484$	20.7077	−	17.3758i	0.941258	−	0.789809i
$485$		0			0
$486$	23.9220	+	22.7244i	1.08513	+	1.03080i
$487$		−	4.02801i		−	0.182527i	−0.995827	−	0.0912634i	$-0.970909\pi$
$487$		−	4.02801i		−	0.182527i	0.995827	−	0.0912634i	$-0.0290905\pi$
$488$	−0.662836	−	0.789937i	−0.0300052	−	0.0357588i
$489$	12.2769	−	17.7263i	0.555183	−	0.801611i
$490$		0			0
$491$	36.2922	−	13.2093i	1.63784	−	0.596126i	0.651184	−	0.758920i	$-0.274273\pi$
$491$	36.2922	−	13.2093i	1.63784	−	0.596126i	0.986660	+	0.162793i	$0.0520504\pi$
$492$	25.0017	−	2.31677i	1.12716	−	0.104448i
$493$	5.09577	−	0.898521i	0.229502	−	0.0404674i
$494$	9.96769	+	17.2645i	0.448468	+	0.776769i
$495$		0			0
$496$	−12.1830	+	21.1015i	−0.547032	+	0.947487i
$497$	3.19114	−	8.76759i	0.143142	−	0.393280i
$498$	12.0823	−	12.2070i	0.541423	−	0.547011i
$499$	3.11922	+	2.61734i	0.139636	+	0.117168i	0.709930	−	0.704272i	$-0.248726\pi$
$499$	3.11922	+	2.61734i	0.139636	+	0.117168i	−0.570295	+	0.821440i	$0.693171\pi$
$500$		0			0
$501$	−1.02531	+	3.90664i	−0.0458076	+	0.174536i
$502$	−3.96403	+	10.8911i	−0.176923	+	0.486093i
$503$	2.96695	+	1.71297i	0.132290	+	0.0763775i	0.564684	−	0.825307i	$-0.308998\pi$
$503$	2.96695	+	1.71297i	0.132290	+	0.0763775i	−0.432395	+	0.901684i	$0.642331\pi$
$504$	−2.58213	−	1.45565i	−0.115017	−	0.0648398i
$505$		0			0
$506$	0.251909	+	1.42865i	0.0111987	+	0.0635111i
$507$	7.75161	−	16.8487i	0.344261	−	0.748276i
$508$	−4.43412	−	12.1827i	−0.196732	−	0.540518i
$509$	2.12952	−	12.0771i	0.0943893	−	0.535308i	−0.900543	−	0.434766i	$-0.856831\pi$
$509$	2.12952	−	12.0771i	0.0943893	−	0.535308i	0.994933	−	0.100542i	$-0.0320578\pi$
$510$		0			0
$511$	−11.3529	+	9.52619i	−0.502222	+	0.421414i
$512$			28.1241i			1.24292i
$513$	31.0903	−	8.84601i	1.37267	−	0.390561i
$514$	−24.4791			−1.07973
$515$		0			0
$516$	−10.2616	−	21.7143i	−0.451742	−	0.955920i
$517$	−0.772750	−	0.136257i	−0.0339855	−	0.00599257i
$518$	−3.14407	−	8.63825i	−0.138142	−	0.379543i
$519$	5.06423	−	3.58490i	0.222295	−	0.157360i
$520$		0			0
$521$	−7.04117	−	12.1957i	−0.308479	−	0.534302i	0.669551	−	0.742766i	$-0.266487\pi$
$521$	−7.04117	−	12.1957i	−0.308479	−	0.534302i	−0.978030	+	0.208465i	$0.933153\pi$
$522$	5.13962	+	27.4943i	0.224955	+	1.20339i
$523$	−8.46897	−	4.88956i	−0.370322	−	0.213806i	0.303277	−	0.952902i	$-0.401919\pi$
$523$	−8.46897	−	4.88956i	−0.370322	−	0.213806i	−0.673599	+	0.739097i	$0.735253\pi$
$524$	−16.8597	−	6.13643i	−0.736520	−	0.268071i
$525$		0			0
$526$	−10.5035	−	8.81348i	−0.457974	−	0.384286i
$527$	−6.54892	+	7.80469i	−0.285275	+	0.339978i
$528$	−0.406744	−	1.48740i	−0.0177013	−	0.0647309i
$529$	−17.2176	−	6.26668i	−0.748590	−	0.272464i
$530$		0			0
$531$	−3.36541	−	3.92812i	−0.146047	−	0.170466i
$532$	−12.9915	+	7.50065i	−0.563254	+	0.325195i
$533$	8.71534	−	1.53675i	0.377503	−	0.0665640i
$534$	−46.3785	+	32.8307i	−2.00699	+	1.42072i
$535$		0			0
$536$	−0.151144	+	0.857180i	−0.00652843	+	0.0370245i
$537$	31.3131	−	14.7977i	1.35126	−	0.638569i
$538$	18.8280	+	22.4384i	0.811734	+	0.967387i
$539$	−1.91871			−0.0826445
$540$		0			0
$541$	40.9454			1.76038			0.880189	−	0.474623i	$-0.157416\pi$
$541$	40.9454			1.76038			0.880189	+	0.474623i	$0.157416\pi$
$542$	2.64674	+	3.15426i	0.113687	+	0.135487i
$543$	−1.38294	+	16.8001i	−0.0593477	+	0.720959i
$544$	−1.62750	+	9.22999i	−0.0697783	+	0.395732i
$545$		0			0
$546$	−4.90300	−	2.25573i	−0.209829	−	0.0965365i
$547$	1.09341	−	0.192798i	0.0467508	−	0.00824343i	−0.150224	−	0.988652i	$-0.547999\pi$
$547$	1.09341	−	0.192798i	0.0467508	−	0.00824343i	0.196975	+	0.980409i	$0.436888\pi$
$548$	24.1615	−	13.9497i	1.03213	−	0.595900i
$549$	−2.62070	+	1.54916i	−0.111849	+	0.0661164i
$550$		0			0
$551$	25.7495	+	9.37206i	1.09697	+	0.399263i
$552$	3.68186	+	0.966321i	0.156711	+	0.0411293i
$553$	7.00864	−	8.35257i	0.298038	−	0.355188i
$554$	20.2236	+	16.9696i	0.859216	+	0.720968i
$555$		0			0
$556$	−21.8607	−	7.95664i	−0.927100	−	0.337437i
$557$	30.3458	+	17.5201i	1.28579	+	0.742352i	0.977901	−	0.209070i	$-0.0670437\pi$
$557$	30.3458	+	17.5201i	1.28579	+	0.742352i	0.307890	+	0.951422i	$0.400377\pi$
$558$	−42.5503	−	34.9657i	−1.80130	−	1.48022i
$559$	−4.23247	−	7.33084i	−0.179014	−	0.310062i
$560$		0			0
$561$	−0.0594925	−	0.642022i	−0.00251178	−	0.0271062i
$562$	−7.06254	−	19.4042i	−0.297915	−	0.818516i
$563$	−38.1822	−	6.73255i	−1.60919	−	0.283743i	−0.704463	−	0.709741i	$-0.748812\pi$
$563$	−38.1822	−	6.73255i	−1.60919	−	0.283743i	−0.904724	+	0.425998i	$0.859923\pi$
$564$	−6.05593	+	8.74396i	−0.255001	+	0.368187i
$565$		0			0
$566$	−56.2413			−2.36400
$567$	−5.48619	+	6.81774i	−0.230398	+	0.286318i
$568$			9.75095i			0.409141i
$569$	26.0213	−	21.8344i	1.09087	−	0.915347i	0.0940904	−	0.995564i	$-0.470006\pi$
$569$	26.0213	−	21.8344i	1.09087	−	0.915347i	0.996777	+	0.0802169i	$0.0255613\pi$
$570$		0			0
$571$	1.75191	−	9.93559i	0.0733153	−	0.415792i	−0.925956	−	0.377631i	$-0.876739\pi$
$571$	1.75191	−	9.93559i	0.0733153	−	0.415792i	0.999272	−	0.0381610i	$-0.0121500\pi$
$572$	0.406986	+	1.11818i	0.0170169	+	0.0467536i
$573$	30.6240	−	2.83775i	1.27934	−	0.118549i
$574$	2.08894	+	11.8470i	0.0871908	+	0.494484i
$575$		0			0
$576$	−33.3522	−	5.52842i	−1.38968	−	0.230351i
$577$	−10.5069	−	6.06615i	−0.437407	−	0.252537i	0.265090	−	0.964224i	$-0.414598\pi$
$577$	−10.5069	−	6.06615i	−0.437407	−	0.252537i	−0.702497	+	0.711687i	$0.747932\pi$
$578$	11.3078	−	31.0680i	0.470344	−	1.29226i
$579$	−13.0295	−	12.8964i	−0.541487	−	0.535956i
$580$		0			0
$581$	3.48957	+	2.92810i	0.144772	+	0.121478i
$582$	−19.6785	−	5.16470i	−0.815700	−	0.214084i
$583$	1.18055	−	3.24352i	0.0488932	−	0.134333i
$584$	7.74416	−	13.4133i	0.320456	−	0.555046i
$585$		0			0
$586$	12.9722	+	22.4685i	0.535877	+	0.928167i
$587$	31.2669	−	5.51319i	1.29052	−	0.227554i	0.514079	−	0.857743i	$-0.328134\pi$
$587$	31.2669	−	5.51319i	1.29052	−	0.227554i	0.776442	+	0.630189i	$0.217023\pi$
$588$	−10.8704	+	23.6276i	−0.448288	+	0.974387i
$589$	−50.7006	+	18.4535i	−2.08908	+	0.760363i
$590$		0			0
$591$	24.4412	+	2.01195i	1.00538	+	0.0827605i
$592$	−8.06588	−	9.61254i	−0.331506	−	0.395073i
$593$			13.4906i			0.553993i	0.960871	+	0.276996i	$0.0893390\pi$
$593$			13.4906i			0.553993i	−0.960871	+	0.276996i	$0.910661\pi$
$594$	3.46703	−	0.357210i	0.142254	−	0.0146565i
$595$		0			0
$596$	36.1947	−	30.3710i	1.48259	−	1.24404i
$597$	−11.8079	+	5.58009i	−0.483265	+	0.228378i
$598$	6.82550	+	1.20352i	0.279115	+	0.0492156i
$599$	−39.8715	+	14.5120i	−1.62911	+	0.592946i	−0.985086	−	0.172063i	$-0.944957\pi$
$599$	−39.8715	+	14.5120i	−1.62911	+	0.592946i	−0.644020	+	0.765009i	$0.722735\pi$
$600$		0			0
$601$	−3.43906	−	19.5039i	−0.140282	−	0.795579i	−0.971035	−	0.238938i	$-0.923201\pi$
$601$	−3.43906	−	19.5039i	−0.140282	−	0.795579i	0.830753	−	0.556641i	$-0.187910\pi$
$602$	9.96501	−	5.75330i	0.406144	−	0.234487i
$603$	2.42358	+	0.854034i	0.0986958	+	0.0347789i
$604$	4.97755	−	8.62136i	0.202533	−	0.350798i
$605$		0			0
$606$	−35.8543	+	9.80470i	−1.45648	+	0.398289i
$607$	−23.1397	+	27.5769i	−0.939213	+	1.11931i	0.0534715	+	0.998569i	$0.482971\pi$
$607$	−23.1397	+	27.5769i	−0.939213	+	1.11931i	−0.992684	+	0.120741i	$0.961473\pi$
$608$	−31.9038	+	38.0215i	−1.29387	+	1.54197i
$609$	−7.15571	+	1.95680i	−0.289964	+	0.0792934i
$610$		0			0
$611$	−1.87442	+	3.24659i	−0.0758310	+	0.131343i
$612$	−8.24315	−	2.90476i	−0.333209	−	0.117418i
$613$	22.9175	−	13.2314i	0.925627	−	0.534411i	0.0402013	−	0.999192i	$-0.487200\pi$
$613$	22.9175	−	13.2314i	0.925627	−	0.534411i	0.885426	+	0.464780i	$0.153867\pi$
$614$	−9.73045	−	55.1841i	−0.392689	−	2.22705i
$615$		0			0
$616$	−0.294234	+	0.107093i	−0.0118550	+	0.00431488i
$617$	−48.3705	−	8.52903i	−1.94732	−	0.343366i	−0.999713	−	0.0239406i	$-0.992379\pi$
$617$	−48.3705	−	8.52903i	−1.94732	−	0.343366i	−0.947611	−	0.319425i	$-0.896510\pi$
$618$	32.6599	−	15.4342i	1.31377	−	0.620853i
$619$	18.5430	−	15.5595i	0.745307	−	0.625387i	−0.188950	−	0.981987i	$-0.560508\pi$
$619$	18.5430	−	15.5595i	0.745307	−	0.625387i	0.934257	+	0.356600i	$0.116064\pi$
$620$		0			0
$621$	4.59193	−	10.2570i	0.184268	−	0.411598i
$622$		−	37.3785i		−	1.49874i
$623$	−9.68725	−	11.5448i	−0.388111	−	0.462533i
$624$	−7.34229	−	0.604400i	−0.293927	−	0.0241954i
$625$		0			0
$626$	19.1881	−	6.98388i	0.766909	−	0.279132i
$627$	1.42714	−	3.10199i	0.0569945	−	0.123882i
$628$	−17.7708	+	3.13347i	−0.709132	+	0.125039i
$629$	−2.62345	−	4.54395i	−0.104604	−	0.181179i
$630$		0			0
$631$	−8.84842	+	15.3259i	−0.352250	+	0.610115i	−0.986643	−	0.162895i	$-0.947917\pi$
$631$	−8.84842	+	15.3259i	−0.352250	+	0.610115i	0.634393	+	0.773010i	$0.281250\pi$
$632$	−3.89736	+	10.7079i	−0.155029	+	0.425938i
$633$	8.73447	+	2.29240i	0.347164	+	0.0911147i
$634$	−6.01629	−	5.04827i	−0.238937	−	0.200492i
$635$		0			0
$636$	−33.2535	−	32.9138i	−1.31859	−	1.30512i
$637$	−3.13523	+	8.61398i	−0.124222	+	0.341298i
$638$	2.55880	+	1.47732i	0.101304	+	0.0584878i
$639$	28.3998	+	4.70751i	1.12348	+	0.186226i
$640$		0			0
$641$	6.60738	+	37.4723i	0.260976	+	1.48007i	0.780254	+	0.625463i	$0.215090\pi$
$641$	6.60738	+	37.4723i	0.260976	+	1.48007i	−0.519278	+	0.854605i	$0.673799\pi$
$642$	−18.8758	+	1.74911i	−0.744968	+	0.0690319i
$643$	−16.0553	−	44.1115i	−0.633158	−	1.73959i	−0.672220	−	0.740352i	$-0.734659\pi$
$643$	−16.0553	−	44.1115i	−0.633158	−	1.73959i	0.0390615	−	0.999237i	$-0.487563\pi$
$644$	−0.905644	+	5.13616i	−0.0356874	+	0.202393i
$645$		0			0
$646$	−11.8485	+	9.94211i	−0.466175	+	0.391167i
$647$			28.2333i			1.10997i	0.831862	+	0.554983i	$0.187275\pi$
$647$			28.2333i			1.10997i	−0.831862	+	0.554983i	$0.812725\pi$
$648$	2.95083	−	8.65643i	0.115920	−	0.340057i
$649$	−0.546406			−0.0214483
$650$		0			0
$651$	8.31660	−	12.0081i	0.325953	−	0.470634i
$652$	−30.4060	−	5.36140i	−1.19079	−	0.209969i
$653$	−12.0758	−	33.1779i	−0.472562	−	1.29835i	−0.915687	−	0.401893i	$-0.868353\pi$
$653$	−12.0758	−	33.1779i	−0.472562	−	1.29835i	0.443125	−	0.896460i	$-0.353870\pi$
$654$	−2.47295	−	26.6872i	−0.0967001	−	1.04355i
$655$		0			0
$656$	8.21052	+	14.2210i	0.320567	+	0.555239i
$657$	−35.3277	−	29.0306i	−1.37826	−	1.13259i
$658$	−4.41318	−	2.54795i	−0.172044	−	0.0993295i
$659$	39.1793	+	14.2601i	1.52621	+	0.555494i	0.962689	−	0.270609i	$-0.0872250\pi$
$659$	39.1793	+	14.2601i	1.52621	+	0.555494i	0.563519	+	0.826103i	$0.309447\pi$
$660$		0			0
$661$	0.975874	+	0.818856i	0.0379571	+	0.0318498i	0.661569	−	0.749884i	$-0.269891\pi$
$661$	0.975874	+	0.818856i	0.0379571	+	0.0318498i	−0.623612	+	0.781734i	$0.714335\pi$
$662$	1.92216	−	2.29075i	0.0747070	−	0.0890324i
$663$	−2.97956	−	0.781997i	−0.115716	−	0.0303702i
$664$	−4.47359	−	1.62825i	−0.173609	−	0.0631885i
$665$		0			0
$666$	24.4158	−	14.4328i	0.946095	−	0.559258i
$667$	8.25035	−	4.76334i	0.319455	−	0.184437i
$668$	5.69543	−	1.00426i	0.220363	−	0.0388559i
$669$	27.8413	+	12.8090i	1.07641	+	0.495226i
$670$		0			0
$671$	−0.0558427	+	0.316700i	−0.00215578	+	0.0122261i
$672$	1.10238	−	13.3918i	0.0425252	−	0.516598i
$673$	22.9043	+	27.2963i	0.882896	+	1.05219i	0.998266	+	0.0588715i	$0.0187502\pi$
$673$	22.9043	+	27.2963i	0.882896	+	1.05219i	−0.115370	+	0.993323i	$0.536805\pi$
$674$	−27.4951			−1.05907
$675$		0			0
$676$	−26.5561			−1.02139
$677$	−11.5714	−	13.7902i	−0.444725	−	0.530002i	0.496386	−	0.868102i	$-0.334660\pi$
$677$	−11.5714	−	13.7902i	−0.444725	−	0.530002i	−0.941110	+	0.338100i	$0.890216\pi$
$678$	−34.3913	+	16.2524i	−1.32079	+	0.624169i
$679$	0.936996	−	5.31397i	0.0359586	−	0.203931i
$680$		0			0
$681$	−22.2968	+	15.7836i	−0.854414	+	0.604828i
$682$	−5.72929	+	1.01023i	−0.219386	+	0.0386836i
$683$	34.4344	−	19.8807i	1.31760	−	0.760715i	0.334255	−	0.942483i	$-0.391515\pi$
$683$	34.4344	−	19.8807i	1.31760	−	0.760715i	0.983341	+	0.181768i	$0.0581820\pi$
$684$	−30.1136	−	35.1486i	−1.15142	−	1.34394i
$685$		0			0
$686$	−25.2468	−	9.18909i	−0.963928	−	0.350841i
$687$	−0.807229	−	2.95192i	−0.0307977	−	0.112623i
$688$	10.0962	−	12.0322i	0.384915	−	0.458724i
$689$	−12.6327	−	10.6001i	−0.481266	−	0.403830i
$690$		0			0
$691$	15.8251	+	5.75986i	0.602015	+	0.219115i	0.625006	−	0.780620i	$-0.285097\pi$
$691$	15.8251	+	5.75986i	0.602015	+	0.219115i	−0.0229909	+	0.999736i	$0.507319\pi$
$692$	−7.69408	−	4.44218i	−0.292485	−	0.168866i
$693$	0.169860	+	0.908663i	0.00645244	+	0.0345173i
$694$	5.08038	+	8.79948i	0.192849	+	0.334024i
$695$		0			0
$696$	6.32790	−	4.47944i	0.239859	−	0.169793i
$697$	2.34839	+	6.45216i	0.0889518	+	0.244393i
$698$	47.0622	+	8.29833i	1.78133	+	0.314097i
$699$	−10.2854	−	21.7648i	−0.389031	−	0.823220i
$700$		0			0
$701$	−8.96921			−0.338762			−0.169381	−	0.985551i	$-0.554177\pi$
$701$	−8.96921			−0.338762			−0.169381	+	0.985551i	$0.554177\pi$
$702$	4.06156	−	16.1488i	0.153294	−	0.609498i
$703$		−	27.7861i		−	1.04797i
$704$	−2.73570	+	2.29552i	−0.103106	+	0.0865158i
$705$		0			0
$706$	10.9186	−	61.9223i	0.410926	−	2.33048i
$707$	−3.37181	−	9.26398i	−0.126810	−	0.348408i
$708$	−3.09566	+	6.72864i	−0.116342	+	0.252878i
$709$	−3.15026	−	17.8660i	−0.118311	−	0.670973i	−0.985058	−	0.172225i	$-0.944904\pi$
$709$	−3.15026	−	17.8660i	−0.118311	−	0.670973i	0.866747	−	0.498748i	$-0.166207\pi$
$710$		0			0
$711$	29.3054	+	16.5206i	1.09904	+	0.619572i
$712$	13.6401	+	7.87509i	0.511183	+	0.295131i
$713$	−6.41560	+	17.6267i	−0.240266	+	0.660125i
$714$	1.06299	−	4.05019i	0.0397814	−	0.151574i
$715$		0			0
$716$	−37.9890	−	31.8766i	−1.41972	−	1.19128i
$717$	−24.1650	+	24.4144i	−0.902457	+	0.911771i
$718$	−9.71498	+	26.6917i	−0.362560	+	0.996125i
$719$	15.7860	−	27.3421i	0.588718	−	1.01969i	−0.405683	−	0.914014i	$-0.632966\pi$
$719$	15.7860	−	27.3421i	0.588718	−	1.01969i	0.994401	−	0.105675i	$-0.0337004\pi$
$720$		0			0
$721$	4.79034	+	8.29711i	0.178402	+	0.309001i
$722$	−41.0606	+	7.24010i	−1.52812	+	0.269449i
$723$	−33.4148	+	3.09636i	−1.24271	+	0.115155i
$724$	22.6814	−	8.25536i	0.842948	−	0.306808i
$725$		0			0
$726$	−22.7511	+	32.8497i	−0.844374	+	1.21916i
$727$	−24.6890	−	29.4232i	−0.915664	−	1.09125i	−0.995530	−	0.0944407i	$-0.969894\pi$
$727$	−24.6890	−	29.4232i	−0.915664	−	1.09125i	0.0798662	−	0.996806i	$-0.474551\pi$
$728$			1.49595i			0.0554436i
$729$	−23.7874	−	12.7734i	−0.881014	−	0.473090i
$730$		0			0
$731$	5.03111	−	4.22160i	0.186082	−	0.156142i
$732$	3.58358	+	2.48193i	0.132453	+	0.0917346i
$733$	−29.8695	−	5.26680i	−1.10326	−	0.194534i	−0.407778	−	0.913081i	$-0.633696\pi$
$733$	−29.8695	−	5.26680i	−1.10326	−	0.194534i	−0.695478	+	0.718547i	$0.744807\pi$
$734$	15.8123	−	5.75521i	0.583643	−	0.212429i
$735$		0			0
$736$	2.99643	+	16.9936i	0.110450	+	0.626391i
$737$	0.235076	−	0.135721i	0.00865915	−	0.00499936i
$738$	−34.7456	+	13.0519i	−1.27900	+	0.480448i
$739$	5.00127	−	8.66245i	0.183975	−	0.318653i	−0.759256	−	0.650792i	$-0.774437\pi$
$739$	5.00127	−	8.66245i	0.183975	−	0.318653i	0.943230	+	0.332139i	$0.107770\pi$
$740$		0			0
$741$	−11.5943	−	11.4759i	−0.425928	−	0.421577i
$742$	14.4089	−	17.1719i	0.528969	−	0.630400i
$743$	−23.3163	+	27.7873i	−0.855394	+	1.01942i	0.144160	+	0.989554i	$0.453952\pi$
$743$	−23.3163	+	27.7873i	−0.855394	+	1.01942i	−0.999554	+	0.0298642i	$0.990493\pi$
$744$	−3.87523	+	14.7654i	−0.142073	+	0.541324i
$745$		0			0
$746$	−12.0865	+	20.9344i	−0.442517	+	0.766461i
$747$	−6.90205	+	12.2433i	−0.252533	+	0.447960i
$748$	−0.799548	+	0.461619i	−0.0292344	+	0.0168785i
$749$	−0.873058	−	4.95136i	−0.0319008	−	0.180919i
$750$		0			0
$751$	13.6766	−	4.97788i	0.499067	−	0.181646i	−0.0802073	−	0.996778i	$-0.525558\pi$
$751$	13.6766	−	4.97788i	0.499067	−	0.181646i	0.579274	+	0.815133i	$0.303336\pi$
$752$	−6.85041	−	1.20791i	−0.249809	−	0.0440480i
$753$	0.778089	−	9.45226i	0.0283551	−	0.344460i
$754$	10.8136	−	9.07366i	0.393807	−	0.330443i
$755$		0			0
$756$	12.1519	+	3.05631i	0.441962	+	0.111157i
$757$			45.5754i			1.65646i	0.560385	+	0.828232i	$0.310653\pi$
$757$			45.5754i			1.65646i	−0.560385	+	0.828232i	$0.689347\pi$
$758$	32.8849	+	39.1907i	1.19443	+	1.42347i
$759$	−0.507211	−	1.07330i	−0.0184106	−	0.0389582i
$760$		0			0
$761$	−20.9040	+	7.60843i	−0.757769	+	0.275805i	−0.691871	−	0.722021i	$-0.743213\pi$
$761$	−20.9040	+	7.60843i	−0.757769	+	0.275805i	−0.0658978	+	0.997826i	$0.520991\pi$
$762$	11.0726	+	15.6418i	0.401119	+	0.566643i
$763$	7.00040	−	1.23436i	0.253431	−	0.0446868i
$764$	−22.0189	−	38.1379i	−0.796616	−	1.37978i
$765$		0			0
$766$	9.99393	−	17.3100i	0.361096	−	0.625436i
$767$	−0.892846	+	2.45307i	−0.0322388	+	0.0885754i
$768$	−2.66224	−	9.73542i	−0.0960654	−	0.351297i
$769$	−10.4679	−	8.78365i	−0.377484	−	0.316747i	0.434230	−	0.900802i	$-0.357021\pi$
$769$	−10.4679	−	8.78365i	−0.377484	−	0.316747i	−0.811714	+	0.584056i	$0.801465\pi$
$770$		0			0
$771$	19.3220	−	5.28379i	0.695866	−	0.190291i
$772$	−8.97807	+	24.6670i	−0.323128	+	0.887786i
$773$	17.8869	+	10.3270i	0.643345	+	0.371436i	0.785902	−	0.618351i	$-0.212199\pi$
$773$	17.8869	+	10.3270i	0.643345	+	0.371436i	−0.142557	+	0.989787i	$0.545532\pi$
$774$	23.0983	+	26.9604i	0.830252	+	0.969072i
$775$		0			0
$776$	0.979243	+	5.55356i	0.0351528	+	0.199361i
$777$	4.34626	+

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36054 + 1.62143i) q^{2} +(-1.42389 - 0.986166i) q^{3} +(-0.430663 + 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(0.957561 - 0.168844i) q^{7} +(-0.880031 + 0.508086i) q^{8} +(1.05495 + 2.80839i) q^{9} +O(q^{10})\)	\(q+(1.36054 + 1.62143i) q^{2} +(-1.42389 - 0.986166i) q^{3} +(-0.430663 + 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(0.957561 - 0.168844i) q^{7} +(-0.880031 + 0.508086i) q^{8} +(1.05495 + 2.80839i) q^{9} +(0.297791 + 0.108387i) q^{11} +(3.02185 - 3.05303i) q^{12} +(0.973200 - 1.15981i) q^{13} +(1.57657 + 1.32290i) q^{14} +(2.63991 + 0.960847i) q^{16} +(1.01731 + 0.587342i) q^{17} +(-3.11830 + 5.53146i) q^{18} +(3.11040 + 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(0.229414 + 0.630310i) q^{22} +(2.12988 + 0.375556i) q^{23} +(1.75413 + 0.144396i) q^{24} +3.20463 q^{26} +(1.26740 - 5.03922i) q^{27} +2.41147i q^{28} +(3.37436 - 2.83142i) q^{29} +(-1.50609 + 8.54146i) q^{31} +(2.72885 + 7.49746i) q^{32} +(-0.317135 - 0.448003i) q^{33} +(0.431752 + 2.44859i) q^{34} +(-7.31359 + 1.36716i) q^{36} +(-3.86823 - 2.23332i) q^{37} +(-4.50341 + 12.3730i) q^{38} +(-2.52950 + 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(-0.940269 - 3.43842i) q^{42} +(1.91223 - 5.25381i) q^{43} +(-0.392973 + 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(-2.43845 + 0.429965i) q^{47} +(-2.81139 - 3.97153i) q^{48} +(-5.68943 + 2.07078i) q^{49} +(-0.869320 - 1.83955i) q^{51} +(2.41362 + 2.87645i) q^{52} -10.8920i q^{53} +(9.89507 - 4.80105i) q^{54} +(-0.756896 + 0.635111i) q^{56} +(0.883963 - 10.7384i) q^{57} +(9.18189 + 1.61901i) q^{58} +(-1.62023 + 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(-15.8985 + 9.17898i) q^{62} +(1.48436 + 2.51109i) q^{63} +(-5.63455 + 9.75933i) q^{64} +(0.294929 - 1.12374i) q^{66} +(0.550580 - 0.656156i) q^{67} +(-1.87265 + 2.23174i) q^{68} +(-2.66237 - 2.63517i) q^{69} +(4.79788 - 8.31018i) q^{71} +(-2.35530 - 1.93547i) q^{72} +(-13.1998 + 7.62091i) q^{73} +(-1.64171 - 9.31057i) q^{74} +(-14.4977 + 5.27674i) q^{76} +(0.303453 + 0.0535070i) q^{77} +(-4.56306 - 3.16030i) q^{78} +(8.59024 - 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} +12.3721i q^{82} +(3.01141 + 3.58886i) q^{83} +(2.37811 - 3.43369i) q^{84} +(11.1203 - 4.04747i) q^{86} +(-7.59698 + 0.703969i) q^{87} +(-0.317135 + 0.0559194i) q^{88} +(-7.74976 - 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(-1.83453 + 5.04032i) q^{92} +(10.5678 - 10.6769i) q^{93} +(-4.01476 - 3.36879i) q^{94} +(3.50815 - 13.3667i) q^{96} +(1.89804 - 5.21481i) q^{97} +(-11.0983 - 6.40762i) q^{98} +(0.00976156 + 0.950656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4}+O(q^{10}) \) 24 * q + 12 * q^4	\( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Introduction

L-functions

Modular forms

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