LMFDB - Embedded newform 675.2.u.b.124.4

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			124.4
Character	$\chi$	$=$	675.124
Dual form			675.2.u.b.49.4

$q$-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} +(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} + 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}+ \cdots + 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

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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	−0.0271067	−	0.999633i	$-0.508629\pi$
$2$	1.36054	−	1.62143i	0.962046	−	1.14652i	0.989153	−	0.146889i	$-0.0469262\pi$
$3$	−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	0.351653	−	0.936130i	$-0.385620\pi$
$7$	0.957561	+	0.168844i	0.361924	+	0.0638170i	0.0102706	+	0.999947i	$0.496731\pi$
$8$	−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	−0.296736	−	0.954960i	$-0.595898\pi$
$11$	0.297791	−	0.108387i	0.0897872	−	0.0326799i	0.386523	+	0.922280i	$0.373676\pi$
$12$	3.02185	+	3.05303i	0.872332	+	0.881335i
$13$	0.973200	+	1.15981i	0.269917	+	0.321675i	0.883928	−	0.467623i	$-0.154889\pi$
$13$	0.973200	+	1.15981i	0.269917	+	0.321675i	−0.614011	+	0.789297i	$0.710445\pi$
$14$	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	−0.371534	−	0.928419i	$-0.621168\pi$
$17$	1.01731	−	0.587342i	0.246733	−	0.142451i	0.618267	+	0.785968i	$0.287835\pi$
$18$	−3.11830	−	5.53146i	−0.734991	−	1.30378i
$19$	3.11040	−	5.38737i	0.713575	−	1.23595i	−0.249931	−	0.968264i	$-0.580408\pi$
$19$	3.11040	−	5.38737i	0.713575	−	1.23595i	0.963507	−	0.267685i	$-0.0862586\pi$
$20$		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	0.0528796	−	0.998601i	$-0.483160\pi$
$23$	2.12988	−	0.375556i	0.444112	−	0.0783089i	0.391232	+	0.920292i	$0.372049\pi$
$24$	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	0.899871	−	0.436156i	$-0.143660\pi$
$29$	3.37436	+	2.83142i	0.626602	+	0.525782i	−0.273269	+	0.961938i	$0.588105\pi$
$30$		0			0
$31$	−1.50609	−	8.54146i	−0.270502	−	1.53409i	−0.752897	−	0.658138i	$-0.771344\pi$
$31$	−1.50609	−	8.54146i	−0.270502	−	1.53409i	0.482395	−	0.875954i	$-0.339767\pi$
$32$	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	−0.783046	−	0.621964i	$-0.786335\pi$
$37$	−3.86823	+	2.23332i	−0.635933	+	0.367156i	0.147113	+	0.989120i	$0.453002\pi$
$38$	−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	−0.222278	−	0.974983i	$-0.571349\pi$
$41$	4.47767	−	3.75721i	0.699295	−	0.586778i	0.921573	+	0.388205i	$0.126905\pi$
$42$	−0.940269	+	3.43842i	−0.145087	+	0.530560i
$43$	1.91223	+	5.25381i	0.291613	+	0.801199i	0.995831	+	0.0912158i	$0.0290753\pi$
$43$	1.91223	+	5.25381i	0.291613	+	0.801199i	−0.704219	+	0.709983i	$0.748702\pi$
$44$	−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	−0.00704911	−	0.999975i	$-0.502244\pi$
$47$	−2.43845	−	0.429965i	−0.355685	−	0.0627168i	−0.348636	+	0.937258i	$0.613355\pi$
$48$	−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	$0.269016\pi$
$53$			10.8920i			1.49613i	−0.663628	+	0.748063i	$0.730984\pi$
$54$	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	0.234391	−	0.972142i	$-0.424690\pi$
$59$	−1.62023	−	0.589715i	−0.210936	−	0.0767743i	−0.445327	+	0.895368i	$0.646913\pi$
$60$		0			0
$61$	0.176214	−	0.999361i	0.0225619	−	0.127955i	−0.971446	−	0.237259i	$-0.923751\pi$
$61$	0.176214	−	0.999361i	0.0225619	−	0.127955i	0.994008	+	0.109304i	$0.0348621\pi$
$62$	−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	0.798627	−	0.601826i	$-0.205560\pi$
$67$	0.550580	+	0.656156i	0.0672641	+	0.0801622i	−0.731363	+	0.681988i	$0.761116\pi$
$68$	−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	0.996625	+	0.0820894i	$0.0261593\pi$
$71$	4.79788	+	8.31018i	0.569404	+	0.986237i	−0.427221	+	0.904147i	$0.640507\pi$
$72$	−2.35530	+	1.93547i	−0.277574	+	0.228097i
$73$	−13.1998	−	7.62091i	−1.54492	−	0.891960i	−0.998517	−	0.0544385i	$-0.982663\pi$
$73$	−13.1998	−	7.62091i	−1.54492	−	0.891960i	−0.546404	−	0.837522i	$-0.684004\pi$
$74$	−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	0.981995	−	0.188908i	$-0.0604949\pi$
$79$	8.59024	+	7.20807i	0.966478	+	0.810971i	−0.0155168	+	0.999880i	$0.504939\pi$
$80$		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	−0.575017	−	0.818141i	$-0.695005\pi$
$83$	3.01141	−	3.58886i	0.330546	−	0.393929i	0.905563	+	0.424212i	$0.139449\pi$
$84$	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	0.0831130	+	0.996540i	$0.473514\pi$
$89$	−7.74976	+	13.4230i	−0.821473	+	1.42283i	−0.904586	+	0.426292i	$0.859820\pi$
$90$		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	0.997987	−	0.0634241i	$-0.0202021\pi$
$97$	1.89804	+	5.21481i	0.192716	+	0.529484i	−0.805270	+	0.592908i	$0.797980\pi$
$98$	−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	0.762737	+	0.646709i	$0.223855\pi$
$101$	−1.76063	+	9.98501i	−0.175189	+	0.993546i	−0.937926	+	0.346836i	$0.887256\pi$
$102$	1.79995	+	3.91231i	0.178221	+	0.387377i
$103$	3.37002	−	9.25906i	0.332058	−	0.912323i	−0.655518	−	0.755180i	$-0.727549\pi$
$103$	3.37002	−	9.25906i	0.332058	−	0.912323i	0.987576	−	0.157143i	$-0.0502283\pi$
$104$	−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	$0.0804109\pi$
$107$			5.17080i			0.499880i	−0.968261	+	0.249940i	$0.919589\pi$
$108$	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	0.653274	+	0.757122i	$0.273395\pi$
$113$	−3.54868	+	9.74991i	−0.333832	+	0.917195i	−0.987105	+	0.160073i	$0.948827\pi$
$114$	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	0.285509	−	0.958376i	$-0.407837\pi$
$127$	−4.52709	−	2.61372i	−0.401714	−	0.231930i	−0.687223	+	0.726446i	$0.741171\pi$
$128$	−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	−0.989213	−	0.146482i	$-0.953205\pi$
$131$	−1.25622	−	7.12440i	−0.109757	−	0.622461i	0.879457	−	0.475979i	$-0.157906\pi$
$132$	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	−0.980687	−	0.195584i	$-0.937340\pi$
$137$	−7.23092	+	8.61748i	−0.617779	+	0.736241i	0.362907	+	0.931825i	$0.381784\pi$
$138$	0.650482	+	7.90210i	0.0553727	+	0.672671i
$139$	−1.62885	−	9.23766i	−0.138157	−	0.783528i	−0.972609	−	0.232447i	$-0.925327\pi$
$139$	−1.62885	−	9.23766i	−0.138157	−	0.783528i	0.834452	−	0.551081i	$-0.185784\pi$
$140$		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	−0.195851	+	0.980634i	$0.562747\pi$
$149$	−14.5941	+	12.2459i	−1.19560	+	1.00322i	−0.999745	+	0.0225899i	$0.992809\pi$
$150$		0			0
$151$	−3.77193	+	1.37287i	−0.306955	+	0.111723i	−0.490905	−	0.871213i	$-0.663334\pi$
$151$	−3.77193	+	1.37287i	−0.306955	+	0.111723i	0.183950	+	0.982936i	$0.441112\pi$
$152$	−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	−0.799911	−	0.600118i	$-0.795120\pi$
$157$	2.48851	−	6.83713i	0.198605	−	0.545662i	0.998516	+	0.0544560i	$0.0173425\pi$
$158$	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	$-0.837892\pi$
$163$		−	12.4492i		−	0.975094i	0.873097	−	0.487547i	$-0.162108\pi$
$164$	−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	−0.966718	−	0.255843i	$-0.917647\pi$
$167$	−0.797553	+	2.19126i	−0.0617165	+	0.169565i	0.905002	+	0.425408i	$0.139869\pi$
$168$	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	0.884363	−	0.466799i	$-0.154593\pi$
$173$	−1.22521	−	3.36623i	−0.0931509	−	0.255930i	−0.977514	+	0.210869i	$0.932371\pi$
$174$	−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	−0.949124	−	0.314901i	$-0.898029\pi$
$179$	−9.99785	−	17.3168i	−0.747275	−	1.29432i	0.201850	−	0.979416i	$-0.435305\pi$
$180$		0			0
$181$	−4.86616	+	8.42844i	−0.361699	+	0.626481i	−0.988241	−	0.152907i	$-0.951136\pi$
$181$	−4.86616	+	8.42844i	−0.361699	+	0.626481i	0.626542	+	0.779388i	$0.284470\pi$
$182$	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	0.000494763	−	1.00000i	$-0.499843\pi$
$191$	−13.6023	−	11.4137i	−0.984227	−	0.825864i	−0.984722	+	0.174135i	$0.944287\pi$
$192$	17.6473	+	8.33965i	1.27359	+	0.601862i
$193$	10.4235	−	1.83795i	0.750303	−	0.132299i	0.214596	−	0.976703i	$-0.431156\pi$
$193$	10.4235	−	1.83795i	0.750303	−	0.132299i	0.535706	+	0.844404i	$0.320045\pi$
$194$	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	−0.00507615	−	0.999987i	$-0.501616\pi$
$197$	−12.2620	−	7.07945i	−0.873628	−	0.504390i	−0.868552	+	0.495597i	$0.834949\pi$
$198$	−1.52814	−	1.30923i	−0.108600	−	0.0930431i
$199$	3.77010	+	6.53000i	0.267255	+	0.462899i	0.968152	−	0.250363i	$-0.0805501\pi$
$199$	3.77010	+	6.53000i	0.267255	+	0.462899i	−0.700897	+	0.713263i	$0.747217\pi$
$200$		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	0.167829	−	0.985816i	$-0.446324\pi$
$211$	−4.89922	−	1.78317i	−0.337276	−	0.122758i	−0.505106	+	0.863058i	$0.668546\pi$
$212$	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	−0.443537	−	0.896256i	$-0.646277\pi$
$223$	−17.4250	−	3.07250i	−1.16686	−	0.205750i	−0.723326	+	0.690506i	$0.757388\pi$
$224$	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	0.979711	+	0.200418i	$0.0642299\pi$
$227$	5.39434	+	14.8208i	0.358035	+	0.983692i	−0.621676	+	0.783275i	$0.713548\pi$
$228$	25.8470	−	6.78365i	1.71176	−	0.449258i
$229$	1.35350	−	1.13572i	0.0894415	−	0.0750504i	−0.596971	−	0.802263i	$-0.703629\pi$
$229$	1.35350	−	1.13572i	0.0894415	−	0.0750504i	0.686412	+	0.727213i	$0.259185\pi$
$230$		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	−0.0509157	−	0.998703i	$-0.516214\pi$
$233$	12.0364	−	6.94920i	0.788529	−	0.455257i	0.839444	+	0.543446i	$0.182881\pi$
$234$	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	0.866906	+	0.498471i	$0.166105\pi$
$239$	3.44391	+	19.5314i	0.222768	+	1.26338i	−0.644138	+	0.764909i	$0.722784\pi$
$240$		0			0
$241$	14.8419	+	12.4538i	0.956050	+	0.802221i	0.980306	−	0.197485i	$-0.0632773\pi$
$241$	14.8419	+	12.4538i	0.956050	+	0.802221i	−0.0242563	+	0.999706i	$0.507722\pi$
$242$			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	−0.766590	−	0.642137i	$-0.778048\pi$
$251$	2.73786	−	4.74212i	0.172812	−	0.299320i	0.939402	+	0.342818i	$0.111381\pi$
$252$	−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	0.482615	−	0.875833i	$-0.339687\pi$
$257$	−7.43395	−	8.85943i	−0.463717	−	0.552636i	−0.946332	+	0.323196i	$0.895243\pi$
$258$	−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	−0.0265395	−	0.999648i	$-0.508449\pi$
$263$	−6.37952	−	1.12488i	−0.393378	−	0.0693632i	−0.366839	+	0.930285i	$0.619560\pi$
$264$	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	0.530010	−	0.847991i	$-0.322188\pi$
$277$	12.2832	+	2.16586i	0.738026	+	0.130134i	0.208016	+	0.978125i	$0.433299\pi$
$278$	−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	−0.600663	−	0.799502i	$-0.705097\pi$
$281$	−9.16752	+	3.33670i	−0.546888	+	0.199051i	0.0537751	+	0.998553i	$0.482875\pi$
$282$	2.39442	−	8.75602i	0.142585	−	0.521414i
$283$	−17.0797	−	20.3547i	−1.01528	−	1.20996i	−0.977556	−	0.210676i	$-0.932433\pi$
$283$	−17.0797	−	20.3547i	−1.01528	−	1.20996i	−0.0377246	−	0.999288i	$-0.512011\pi$
$284$	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	0.190469	−	0.981693i	$-0.438999\pi$
$293$	12.0712	−	2.12849i	0.705210	−	0.124347i	0.514741	+	0.857346i	$0.327888\pi$
$294$	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	−0.981849	−	0.189663i	$-0.939260\pi$
$307$	−22.9271	+	13.2370i	−1.30852	+	0.755475i	−0.326671	+	0.945138i	$0.605927\pi$
$308$	−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	−0.939964	−	0.341272i	$-0.889142\pi$
$311$	−13.5280	+	11.3513i	−0.767100	+	0.643673i	0.172865	+	0.984946i	$0.444698\pi$
$312$	1.87459	+	1.89394i	0.106128	+	0.107223i
$313$	3.29954	+	9.06541i	0.186501	+	0.512407i	0.997342	−	0.0728589i	$-0.0232123\pi$
$313$	3.29954	+	9.06541i	0.186501	+	0.512407i	−0.810841	+	0.585266i	$0.800990\pi$
$314$	−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	0.0700850	−	0.997541i	$-0.477673\pi$
$317$	−3.65412	−	0.644320i	−0.205236	−	0.0361886i	−0.275321	+	0.961352i	$0.588784\pi$
$318$	−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	−0.990807	−	0.135280i	$-0.956807\pi$
$331$	−0.245329	+	1.39133i	−0.0134845	+	0.0764745i	0.977323	+	0.211755i	$0.0679177\pi$
$332$	−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	0.489073	−	0.872243i	$-0.337335\pi$
$337$	−8.34986	−	9.95097i	−0.454846	−	0.542064i	−0.943918	+	0.330179i	$0.892891\pi$
$338$	−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	−0.0453070	−	0.998973i	$-0.514427\pi$
$347$	4.72753	−	0.833591i	0.253787	−	0.0447495i	0.299094	+	0.954224i	$0.403316\pi$
$348$	1.55236	+	18.8581i	0.0832152	+	1.01090i
$349$	17.2954	+	14.5126i	0.925803	+	0.776841i	0.975059	−	0.221946i	$-0.0712407\pi$
$349$	17.2954	+	14.5126i	0.925803	+	0.776841i	−0.0492565	+	0.998786i	$0.515685\pi$
$350$		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	−0.0390490	+	0.999237i	$0.512433\pi$
$353$	−19.0950	+	22.7565i	−1.01632	+	1.21121i	−0.977276	+	0.211972i	$0.932012\pi$
$354$	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	−0.632834	−	0.774288i	$-0.718108\pi$
$359$	6.70991	−	11.6219i	0.354136	−	0.613381i	0.986970	+	0.160906i	$0.0514418\pi$
$360$		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	0.990208	−	0.139597i	$-0.0445808\pi$
$367$	2.71905	+	7.47054i	0.141933	+	0.389959i	−0.848275	+	0.529556i	$0.822359\pi$
$368$	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	−0.796557	−	0.604564i	$-0.793347\pi$
$373$	3.90604	−	10.7318i	0.202247	−	0.555670i	0.998804	+	0.0488939i	$0.0155696\pi$
$374$	−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	−0.994451	−	0.105202i	$-0.966451\pi$
$383$	−3.22979	+	8.87378i	−0.165035	+	0.453429i	0.829416	+	0.558631i	$0.188673\pi$
$384$	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	−0.401998	−	0.915641i	$-0.631684\pi$
$389$	−2.39406	+	0.871367i	−0.121384	+	0.0441801i	0.280614	+	0.959821i	$0.409462\pi$
$390$		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	0.417999	−	0.908447i	$-0.362731\pi$
$397$	−3.18279	−	1.83759i	−0.159740	−	0.0922258i	−0.577739	+	0.816222i	$0.696065\pi$
$398$	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	0.971220	+	0.238182i	$0.0765516\pi$
$401$	2.80420	+	15.9034i	0.140035	+	0.794177i	−0.831186	+	0.555995i	$0.812337\pi$
$402$	−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	−0.998517	−	0.0544462i	$-0.982661\pi$
$409$	−1.59443	−	9.04248i	−0.0788396	−	0.447122i	0.919677	−	0.392676i	$-0.128450\pi$
$410$		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	−0.502791	−	0.864408i	$-0.667694\pi$
$419$	5.34613	−	4.48594i	0.261176	−	0.219152i	0.763967	+	0.645256i	$0.223249\pi$
$420$		0			0
$421$	−28.9525	+	10.5379i	−1.41106	+	0.513584i	−0.931441	−	0.363894i	$-0.881447\pi$
$421$	−28.9525	+	10.5379i	−1.41106	+	0.513584i	−0.479619	+	0.877477i	$0.659225\pi$
$422$	−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	$-0.847620\pi$
$433$		−	19.1706i		−	0.921278i	0.887588	−	0.460639i	$-0.152380\pi$
$434$	−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	−0.712968	−	0.701197i	$-0.752649\pi$
$439$	4.12397	−	23.3882i	0.196826	−	1.11626i	0.909794	−	0.415060i	$-0.136239\pi$
$440$		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	0.971536	+	0.236894i	$0.0761294\pi$
$443$	7.98900	+	21.9496i	0.379569	+	1.04286i	−0.591967	+	0.805962i	$0.701648\pi$
$444$	−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	0.917264	−	0.398279i	$-0.130392\pi$
$449$	2.40953	+	4.17343i	0.113713	+	0.196956i	−0.803552	+	0.595235i	$0.797059\pi$
$450$		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	−0.687439	−	0.726242i	$-0.741265\pi$
$457$	3.14555	−	3.74872i	0.147142	−	0.175358i	0.834581	+	0.550885i	$0.185710\pi$
$458$		−	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	0.986797	−	0.161963i	$-0.0517824\pi$
$461$	21.4419	+	17.9919i	0.998650	+	0.837967i	0.0118535	+	0.999930i	$0.496227\pi$
$462$	0.0926768	+	1.12584i	0.00431171	+	0.0523789i
$463$	−27.0579	+	4.77104i	−1.25749	+	0.221729i	−0.762396	−	0.647111i	$-0.775977\pi$
$463$	−27.0579	+	4.77104i	−1.25749	+	0.221729i	−0.495093	+	0.868840i	$0.664866\pi$
$464$	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	0.861140	−	0.508368i	$-0.169751\pi$
$467$	18.4000	+	10.6232i	0.851450	+	0.491585i	−0.00968963	+	0.999953i	$0.503084\pi$
$468$	−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	−0.135560	−	0.990769i	$-0.543283\pi$
$479$	7.23745	−	41.0456i	0.330688	−	1.87542i	0.466248	−	0.884654i	$-0.345606\pi$
$480$		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	$0.0290905\pi$
$487$			4.02801i			0.182527i	−0.995827	+	0.0912634i	$0.970909\pi$
$488$	−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	0.986660	−	0.162793i	$-0.0520504\pi$
$491$	36.2922	+	13.2093i	1.63784	+	0.596126i	0.651184	+	0.758920i	$0.274273\pi$
$492$	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	−0.570295	−	0.821440i	$-0.693171\pi$
$499$	3.11922	−	2.61734i	0.139636	−	0.117168i	0.709930	+	0.704272i	$0.248726\pi$
$500$		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	−0.432395	−	0.901684i	$-0.642331\pi$
$503$	2.96695	−	1.71297i	0.132290	−	0.0763775i	0.564684	+	0.825307i	$0.308998\pi$
$504$	−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	0.994933	+	0.100542i	$0.0320578\pi$
$509$	2.12952	+	12.0771i	0.0943893	+	0.535308i	−0.900543	+	0.434766i	$0.856831\pi$
$510$		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	−0.978030	−	0.208465i	$-0.933153\pi$
$521$	−7.04117	+	12.1957i	−0.308479	+	0.534302i	0.669551	+	0.742766i	$0.266487\pi$
$522$	5.13962	−	27.4943i	0.224955	−	1.20339i
$523$	−8.46897	+	4.88956i	−0.370322	+	0.213806i	−0.673599	−	0.739097i	$-0.735253\pi$
$523$	−8.46897	+	4.88956i	−0.370322	+	0.213806i	0.303277	+	0.952902i	$0.401919\pi$
$524$	−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	0.196975	−	0.980409i	$-0.436888\pi$
$547$	1.09341	+	0.192798i	0.0467508	+	0.00824343i	−0.150224	+	0.988652i	$0.547999\pi$
$548$	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	0.307890	−	0.951422i	$-0.400377\pi$
$557$	30.3458	−	17.5201i	1.28579	−	0.742352i	0.977901	+	0.209070i	$0.0670437\pi$
$558$	−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	−0.904724	−	0.425998i	$-0.859923\pi$
$563$	−38.1822	+	6.73255i	−1.60919	+	0.283743i	−0.704463	+	0.709741i	$0.748812\pi$
$564$	−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	0.996777	−	0.0802169i	$-0.0255613\pi$
$569$	26.0213	+	21.8344i	1.09087	+	0.915347i	0.0940904	+	0.995564i	$0.470006\pi$
$570$		0			0
$571$	1.75191	+	9.93559i	0.0733153	+	0.415792i	0.999272	+	0.0381610i	$0.0121500\pi$
$571$	1.75191	+	9.93559i	0.0733153	+	0.415792i	−0.925956	+	0.377631i	$0.876739\pi$
$572$	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	−0.702497	−	0.711687i	$-0.747932\pi$
$577$	−10.5069	+	6.06615i	−0.437407	+	0.252537i	0.265090	+	0.964224i	$0.414598\pi$
$578$	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	0.776442	−	0.630189i	$-0.217023\pi$
$587$	31.2669	+	5.51319i	1.29052	+	0.227554i	0.514079	+	0.857743i	$0.328134\pi$
$588$	−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	$-0.910661\pi$
$593$		−	13.4906i		−	0.553993i	0.960871	−	0.276996i	$-0.0893390\pi$
$594$	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	−0.644020	−	0.765009i	$-0.722735\pi$
$599$	−39.8715	−	14.5120i	−1.62911	−	0.592946i	−0.985086	+	0.172063i	$0.944957\pi$
$600$		0			0
$601$	−3.43906	+	19.5039i	−0.140282	+	0.795579i	0.830753	+	0.556641i	$0.187910\pi$
$601$	−3.43906	+	19.5039i	−0.140282	+	0.795579i	−0.971035	+	0.238938i	$0.923201\pi$
$602$	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	−0.992684	−	0.120741i	$-0.961473\pi$
$607$	−23.1397	−	27.5769i	−0.939213	−	1.11931i	0.0534715	−	0.998569i	$-0.482971\pi$
$608$	−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	0.885426	−	0.464780i	$-0.153867\pi$
$613$	22.9175	+	13.2314i	0.925627	+	0.534411i	0.0402013	+	0.999192i	$0.487200\pi$
$614$	−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	−0.947611	+	0.319425i	$0.896510\pi$
$617$	−48.3705	+	8.52903i	−1.94732	+	0.343366i	−0.999713	+	0.0239406i	$0.992379\pi$
$618$	32.6599	+	15.4342i	1.31377	+	0.620853i
$619$	18.5430	+	15.5595i	0.745307	+	0.625387i	0.934257	−	0.356600i	$-0.116064\pi$
$619$	18.5430	+	15.5595i	0.745307	+	0.625387i	−0.188950	+	0.981987i	$0.560508\pi$
$620$		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	0.634393	−	0.773010i	$-0.281250\pi$
$631$	−8.84842	−	15.3259i	−0.352250	−	0.610115i	−0.986643	+	0.162895i	$0.947917\pi$
$632$	−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	−0.519278	−	0.854605i	$-0.673799\pi$
$641$	6.60738	−	37.4723i	0.260976	−	1.48007i	0.780254	−	0.625463i	$-0.215090\pi$
$642$	−18.8758	−	1.74911i	−0.744968	−	0.0690319i
$643$	−16.0553	+	44.1115i	−0.633158	+	1.73959i	0.0390615	+	0.999237i	$0.487563\pi$
$643$	−16.0553	+	44.1115i	−0.633158	+	1.73959i	−0.672220	+	0.740352i	$0.734659\pi$
$644$	−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	$-0.812725\pi$
$647$		−	28.2333i		−	1.10997i	0.831862	−	0.554983i	$-0.187275\pi$
$648$	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	0.443125	+	0.896460i	$0.353870\pi$
$653$	−12.0758	+	33.1779i	−0.472562	+	1.29835i	−0.915687	+	0.401893i	$0.868353\pi$
$654$	−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	0.563519	−	0.826103i	$-0.309447\pi$
$659$	39.1793	−	14.2601i	1.52621	−	0.555494i	0.962689	+	0.270609i	$0.0872250\pi$
$660$		0			0
$661$	0.975874	−	0.818856i	0.0379571	−	0.0318498i	−0.623612	−	0.781734i	$-0.714335\pi$
$661$	0.975874	−	0.818856i	0.0379571	−	0.0318498i	0.661569	+	0.749884i	$0.269891\pi$
$662$	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	−0.115370	−	0.993323i	$-0.536805\pi$
$673$	22.9043	−	27.2963i	0.882896	−	1.05219i	0.998266	−	0.0588715i	$-0.0187502\pi$
$674$	−27.4951			−1.05907
$675$		0			0
$676$	−26.5561			−1.02139
$677$	−11.5714	+	13.7902i	−0.444725	+	0.530002i	−0.941110	−	0.338100i	$-0.890216\pi$
$677$	−11.5714	+	13.7902i	−0.444725	+	0.530002i	0.496386	+	0.868102i	$0.334660\pi$
$678$	−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	0.983341	−	0.181768i	$-0.0581820\pi$
$683$	34.4344	+	19.8807i	1.31760	+	0.760715i	0.334255	+	0.942483i	$0.391515\pi$
$684$	−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	−0.0229909	−	0.999736i	$-0.507319\pi$
$691$	15.8251	−	5.75986i	0.602015	−	0.219115i	0.625006	+	0.780620i	$0.285097\pi$
$692$	−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	0.866747	+	0.498748i	$0.166207\pi$
$709$	−3.15026	+	17.8660i	−0.118311	+	0.670973i	−0.985058	+	0.172225i	$0.944904\pi$
$710$		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	0.994401	+	0.105675i	$0.0337004\pi$
$719$	15.7860	+	27.3421i	0.588718	+	1.01969i	−0.405683	+	0.914014i	$0.632966\pi$
$720$		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	0.0798662	+	0.996806i	$0.474551\pi$
$727$	−24.6890	+	29.4232i	−0.915664	+	1.09125i	−0.995530	+	0.0944407i	$0.969894\pi$
$728$		−	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	−0.695478	−	0.718547i	$-0.744807\pi$
$733$	−29.8695	+	5.26680i	−1.10326	+	0.194534i	−0.407778	+	0.913081i	$0.633696\pi$
$734$	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	0.943230	−	0.332139i	$-0.107770\pi$
$739$	5.00127	+	8.66245i	0.183975	+	0.318653i	−0.759256	+	0.650792i	$0.774437\pi$
$740$		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	−0.999554	−	0.0298642i	$-0.990493\pi$
$743$	−23.3163	−	27.7873i	−0.855394	−	1.01942i	0.144160	−	0.989554i	$-0.453952\pi$
$744$	−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	0.579274	−	0.815133i	$-0.303336\pi$
$751$	13.6766	+	4.97788i	0.499067	+	0.181646i	−0.0802073	+	0.996778i	$0.525558\pi$
$752$	−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	$-0.689347\pi$
$757$		−	45.5754i		−	1.65646i	0.560385	−	0.828232i	$-0.310653\pi$
$758$	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	−0.0658978	−	0.997826i	$-0.520991\pi$
$761$	−20.9040	−	7.60843i	−0.757769	−	0.275805i	−0.691871	+	0.722021i	$0.743213\pi$
$762$	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	−0.811714	−	0.584056i	$-0.801465\pi$
$769$	−10.4679	+	8.78365i	−0.377484	+	0.316747i	0.434230	+	0.900802i	$0.357021\pi$
$770$		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	−0.142557	−	0.989787i	$-0.545532\pi$
$773$	17.8869	−	10.3270i	0.643345	−	0.371436i	0.785902	+	0.618351i	$0.212199\pi$
$774$	23.0983	−	26.9604i	0.830252	−	0.969072i
$775$		0			0
$776$	0.979243	−	5.55356i	0.0351528	−	0.199361i
$777$	4.34626	−	6.13977i	0.155921	−	0.220263i
$778$	−1.84436	+	5.06732i	−0.0661233	+	0.181672i
$779$	−6.31415	−	35.8093i	−0.226228	−	1.28300i
$780$		0			0
$781$	2.32948	+	1.95466i	0.0833553	+	0.0699434i
$782$		−	5.37736i		−	0.192294i
$783$	−9.99147	+	20.5927i	−0.357066	+	0.735922i
$784$	−17.0093			−0.607474
$785$		0			0
$786$	26.4323	−	2.17584i	0.942807	−	0.0776097i
$787$	24.3281	−	4.28970i	0.867202	−	0.152911i	0.277690	−	0.960671i	$-0.410431\pi$
$787$	24.3281	−	4.28970i	0.867202	−	0.152911i	0.589512	+	0.807759i	$0.299320\pi$
$788$	−12.0102	+	32.9976i	−0.427844	+	1.17549i
$789$	10.1931	−	4.68956i	0.362884	−	0.166953i
$790$		0			0
$791$	−5.04429	+	8.73696i	−0.179354	+	0.310651i
$792$	−0.491606	+	0.831647i	−0.0174685	+	0.0295513i
$793$	1.33057	−	0.768202i	0.0472498	−	0.0272797i
$794$	−7.30983	+	2.66056i	−0.259416	+	0.0944197i
$795$		0			0
$796$	14.3253	−	12.0204i	0.507747	−	0.426051i
$797$	−19.6473	−	23.4148i	−0.695943	−	0.829393i	0.296117	−	0.955152i	$-0.404308\pi$
$797$	−19.6473	−	23.4148i	−0.695943	−	0.829393i	−0.992061	+	0.125758i	$0.959864\pi$
$798$	15.5995	+	15.7605i	0.552215	+	0.557914i
$799$	−2.73319	+	0.994799i	−0.0966933	+	0.0351935i
$800$		0			0
$801$	29.5214	+	35.9250i	1.04309	+	1.26935i
$802$	29.6014	+	17.0904i	1.04526	+	0.603482i
$803$	−4.75679	−	0.838750i	−0.167863	−	0.0295988i
$804$	−0.339498	+	3.66374i	−0.0119732	+	0.129210i
$805$		0			0
$806$	−4.82646	−	27.3722i	−0.170005	−	0.964146i
$807$	−19.7048	+	13.6472i	−0.693642	+	0.480405i
$808$	6.62265	−	7.89257i	0.232984	−	0.277660i
$809$	−46.8599			−1.64751			−0.823753	−	0.566949i	$-0.808124\pi$
$809$	−46.8599			−1.64751			−0.823753	+	0.566949i	$0.808124\pi$
$810$		0			0
$811$	10.9984			0.386206			0.193103	−	0.981178i	$-0.438145\pi$
$811$	10.9984			0.386206			0.193103	+	0.981178i	$0.438145\pi$
$812$	6.82790	−	8.13717i	0.239612	−	0.285559i
$813$	−2.76999	+	1.91845i	−0.0971476	+	0.0672829i
$814$	0.520260	+	2.95054i	0.0182351	+	0.103416i
$815$		0			0
$816$	−0.527400	+	5.69151i	−0.0184627	+	0.199243i
$817$	34.2521	+	6.03956i	1.19833	+	0.211298i
$818$	−16.8310	−	9.71738i	−0.588482	−	0.339760i
$819$	4.35697	−	0.722206i	0.152245	−	0.0252359i
$820$		0			0
$821$	33.8133	−	12.3070i	1.18009	−	0.429518i	0.323857	−	0.946106i	$-0.395020\pi$
$821$	33.8133	−	12.3070i	1.18009	−	0.429518i	0.856234	+	0.516588i	$0.172798\pi$
$822$	−29.0118	−	29.3112i	−1.01190	−	1.02235i
$823$	31.4880	+	37.5259i	1.09760	+	1.30807i	0.947626	+	0.319383i	$0.103476\pi$
$823$	31.4880	+	37.5259i	1.09760	+	1.30807i	0.149977	+	0.988689i	$0.452080\pi$
$824$	−7.67013	+	6.43600i	−0.267202	+	0.224209i
$825$		0			0
$826$	−3.33453	+	1.21367i	−0.116023	+	0.0422290i
$827$	−13.5192	+	7.80533i	−0.470109	+	0.271418i	−0.716286	−	0.697807i	$-0.754159\pi$
$827$	−13.5192	+	7.80533i	−0.470109	+	0.271418i	0.246176	+	0.969225i	$0.420826\pi$
$828$	−16.0905	−	0.165222i	−0.559185	−	0.00574184i
$829$	5.73541	−	9.93401i	0.199199	−	0.345023i	−0.749070	−	0.662491i	$-0.769499\pi$
$829$	5.73541	−	9.93401i	0.199199	−	0.345023i	0.948269	+	0.317468i	$0.102833\pi$
$830$		0			0
$831$	−19.6259	+	9.02932i	−0.680814	+	0.313224i
$832$	5.83547	−	16.0328i	0.202308	−	0.555838i
$833$	−7.00416	+	1.23502i	−0.242680	+	0.0427910i
$834$	34.2727	−	2.82125i	1.18677	−	0.0976918i
$835$		0			0
$836$	−4.88922			−0.169097
$837$	41.1334	−	18.4150i	1.42178	−	0.636515i
$838$		−	14.7716i		−	0.510278i
$839$	0.517329	+	0.434090i	0.0178602	+	0.0149865i	0.651674	−	0.758499i	$-0.274067\pi$
$839$	0.517329	+	0.434090i	0.0178602	+	0.0149865i	−0.633814	+	0.773486i	$0.718511\pi$
$840$		0			0
$841$	−1.66646	−	9.45097i	−0.0574642	−	0.325895i
$842$	−22.3047	+	61.2815i	−0.768669	+	2.11190i
$843$	9.76304	−	13.7918i	0.336257	−	0.475015i
$844$	−2.24532	+	12.7339i	−0.0772872	+	0.438318i
$845$		0			0
$846$	5.22550	+	14.8290i	0.179656	+	0.509830i
$847$	−9.17815	+	5.29901i	−0.315365	+	0.182076i
$848$	10.4655	+	28.7537i	0.359387	+	0.987408i
$849$	44.3928	+	12.1396i	1.52356	+	0.416631i
$850$		0			0
$851$	−7.40014	+	6.20946i	−0.253674	+	0.212857i
$852$	−10.8728	+	39.7602i	−0.372496	+	1.36216i
$853$	13.4605	+	36.9823i	0.460877	+	1.26625i	0.924827	+	0.380388i	$0.124210\pi$
$853$	13.4605	+	36.9823i	0.460877	+	1.26625i	−0.463949	+	0.885862i	$0.653568\pi$
$854$	−1.04424	−	1.80867i	−0.0357331	−	0.0618915i
$855$		0			0
$856$	2.62721	−	4.55047i	0.0897963	−	0.155532i
$857$	32.1659	+	5.67172i	1.09877	+	0.193742i	0.693500	−	0.720457i	$-0.256068\pi$
$857$	32.1659	+	5.67172i	1.09877	+	0.193742i	0.405266	+	0.914199i	$0.367179\pi$
$858$	−1.01630	+	1.43568i	−0.0346959	+	0.0490134i
$859$	−31.1946	−	11.3539i	−1.06435	−	0.387391i	−0.250287	−	0.968172i	$-0.580525\pi$
$859$	−31.1946	−	11.3539i	−1.06435	−	0.387391i	−0.814060	+	0.580781i	$0.802747\pi$
$860$		0			0
$861$	−4.20602	+	8.90026i	−0.143341	+	0.303320i
$862$	37.9551	−	45.2332i	1.29276	−	1.54065i
$863$		−	22.6796i		−	0.772024i	−0.922494	−	0.386012i	$-0.873852\pi$
$863$		−	22.6796i		−	0.772024i	0.922494	−	0.386012i	$-0.126148\pi$
$864$	41.2399	+	4.24897i	1.40301	+	0.144553i
$865$		0			0
$866$	−31.0837	−	26.0823i	−1.05627	−	0.886312i
$867$	−2.21958	−	26.9636i	−0.0753810	−	0.915733i
$868$	−20.5975	+	3.63190i	−0.699125	+	0.123275i
$869$	3.33935	+	1.21543i	0.113280	+	0.0412305i
$870$		0			0
$871$	−0.225195	+	1.27714i	−0.00763043	+	0.0432743i
$872$	−6.43360	−	3.71444i	−0.217869	−	0.125787i
$873$	16.6476	+	0.170941i	0.563435	+	0.00578549i
$874$	−14.2385	−	24.6618i	−0.481625	−	0.834199i
$875$		0			0
$876$	−16.6209	−	63.3287i	−0.561567	−	2.13968i
$877$	5.94178	+	7.08113i	0.200640	+	0.239113i	0.856977	−	0.515354i	$-0.172340\pi$
$877$	5.94178	+	7.08113i	0.200640	+	0.239113i	−0.656338	+	0.754467i	$0.727895\pi$
$878$	−32.3114	−	38.5072i	−1.09046	−	1.29956i
$879$	−15.0891	+	14.9350i	−0.508944	+	0.503745i
$880$		0			0
$881$	−3.89378	−	6.74422i	−0.131185	−	0.227219i	0.792949	−	0.609288i	$-0.208545\pi$
$881$	−3.89378	−	6.74422i	−0.131185	−	0.227219i	−0.924134	+	0.382070i	$0.875211\pi$
$882$	6.28692	+	37.9282i	0.211692	+	1.27711i
$883$	−28.1127	−	16.2309i	−0.946068	−	0.546213i	−0.0542106	−	0.998530i	$-0.517264\pi$
$883$	−28.1127	−	16.2309i	−0.946068	−	0.546213i	−0.891857	+	0.452317i	$0.850598\pi$
$884$	0.765938	−	4.34385i	0.0257613	−	0.146099i
$885$		0			0
$886$	46.4590	+	16.9097i	1.56082	+	0.568092i
$887$	33.3334	−	5.87759i	1.11923	−	0.197350i	0.416726	−	0.909032i	$-0.363177\pi$
$887$	33.3334	−	5.87759i	1.11923	−	0.197350i	0.702502	+	0.711682i	$0.252066\pi$
$888$	−6.46289	+	4.47609i	−0.216880	+	0.150208i
$889$	−3.89365	−	3.26716i	−0.130589	−	0.109577i
$890$		0			0
$891$	−2.65952	−	1.03031i	−0.0890972	−	0.0345167i
$892$			43.8822i			1.46929i
$893$	−9.90095	+	11.7995i	−0.331323	+	0.394855i
$894$	−39.7665	−	57.4176i	−1.32999	−	1.92033i
$895$		0			0
$896$	−7.21376	−	2.62560i	−0.240995	−	0.0877150i
$897$	−5.64733	−	0.523306i	−0.188559	−	0.0174727i
$898$	10.0452	+	1.77124i	0.335212	+	0.0591069i
$899$	19.1024	−	33.0863i	0.637101	−	1.10349i
$900$		0			0
$901$	6.39731	+	11.0805i	0.213125	+	0.369144i
$902$	−1.34097	−	3.68428i	−0.0446494	−	0.122673i
$903$	−6.62382	−	6.69218i	−0.220427	−	0.222702i
$904$	8.07674	−	6.77719i	0.268629	−	0.225406i
$905$		0			0
$906$	−3.73568	−	14.2337i	−0.124110	−	0.472882i
$907$	3.78269	+	10.3929i	0.125602	+	0.345089i	0.986517	−	0.163660i	$-0.0523301\pi$
$907$	3.78269	+	10.3929i	0.125602	+	0.345089i	−0.860915	+	0.508750i	$0.830108\pi$
$908$	33.8754	−	19.5580i	1.12420	−	0.649054i
$909$	26.1845	+	15.4782i	0.868484	+	0.513381i
$910$		0			0
$911$	2.17845	−	12.3546i	0.0721751	−	0.409325i	−0.927219	−	0.374520i	$-0.877808\pi$
$911$	2.17845	−	12.3546i	0.0721751	−	0.409325i	0.999394	−	0.0348058i	$-0.0110813\pi$
$912$	12.6516	+	27.4991i	0.418935	+	0.910586i
$913$	0.507785	−	1.39513i	0.0168052	−	0.0461720i
$914$	−1.79863	−	10.2005i	−0.0594934	−	0.337404i
$915$		0			0
$916$	−3.35679	−	2.81668i	−0.110912	−	0.0930659i
$917$		−	7.03415i		−	0.232288i
$918$	12.8862	−	0.927658i	0.425307	−	0.0306173i
$919$	5.92909			0.195583			0.0977913	−	0.995207i	$-0.468822\pi$
$919$	5.92909			0.195583			0.0977913	+	0.995207i	$0.468822\pi$
$920$		0			0
$921$	19.5920	−	41.4580i	0.645577	−	1.36609i
$922$	58.3452	−	10.2878i	1.92150	−	0.338812i
$923$	−4.96897	+	13.6521i	−0.163555	+	0.449365i
$924$	1.08035	+	0.764763i	0.0355408	+	0.0251588i
$925$		0			0
$926$	−29.0775	+	50.3636i	−0.955545	+	1.65505i
$927$	−22.4479	−	19.2322i	−0.737285	−	0.631669i
$928$	30.4366	−	17.5726i	0.999131	−	0.576848i
$929$	−9.42772	+	3.43141i	−0.309314	+	0.112581i	−0.492013	−	0.870588i	$-0.663739\pi$
$929$	−9.42772	+	3.43141i	−0.309314	+	0.112581i	0.182699	+	0.983169i	$0.441517\pi$
$930$		0			0
$931$	−28.8525	+	24.2101i	−0.945603	+	0.793455i
$932$	−22.1564	−	26.4050i	−0.725758	−	0.864925i
$933$	8.06811	−	29.5039i	0.264138	−	0.965913i
$934$	42.2587	−	15.3809i	1.38275	−	0.503279i
$935$		0			0
$936$	−4.53696	−	0.848110i	−0.148295	−	0.0277214i
$937$	20.3811	+	11.7671i	0.665823	+	0.384413i	0.794492	−	0.607274i	$-0.207737\pi$
$937$	20.3811	+	11.7671i	0.665823	+	0.384413i	−0.128669	+	0.991688i	$0.541070\pi$
$938$	1.73605	+	0.306113i	0.0566841	+	0.00999494i
$939$	−13.6382	−	9.65429i	−0.445066	−	0.315056i
$940$		0			0
$941$	−5.08781	−	28.8544i	−0.165858	−	0.940627i	−0.948175	−	0.317747i	$-0.897074\pi$
$941$	−5.08781	−	28.8544i	−0.165858	−	0.940627i	0.782317	−	0.622880i	$-0.214038\pi$
$942$	24.1169	+	11.3970i	0.785770	+	0.371334i
$943$	8.12588	−	9.68405i	0.264615	−	0.315356i
$944$	−4.84388			−0.157655
$945$		0			0
$946$	3.75023			0.121930
$947$	−34.4932	+	41.1074i	−1.12088	+	1.33581i	−0.185304	+	0.982681i	$0.559327\pi$
$947$	−34.4932	+	41.1074i	−1.12088	+	1.33581i	−0.935574	+	0.353130i	$0.885117\pi$
$948$	3.95191	+	48.0080i	0.128352	+	1.55923i
$949$	−4.00721	−	22.7260i	−0.130079	−	0.737717i
$950$		0			0
$951$	5.83849	−	2.68613i	0.189326	−	0.0871036i
$952$	−1.14302	−	0.201546i	−0.0370456	−	0.00653214i
$953$	−4.24055	−	2.44828i	−0.137365	−	0.0793076i	0.429743	−	0.902951i	$-0.358604\pi$
$953$	−4.24055	−	2.44828i	−0.137365	−	0.0793076i	−0.567108	+	0.823644i	$0.691938\pi$
$954$	60.2484	−	33.9644i	1.95061	−	1.09964i
$955$		0			0
$956$	46.2205	−	16.8229i	1.49488	−	0.544092i
$957$	−2.33861	+	0.613778i	−0.0755965	+	0.0198406i
$958$	−56.7057	−	67.5792i	−1.83208	−	2.18338i
$959$	−8.37906	+	7.03086i	−0.270574	+	0.227038i
$960$		0			0
$961$	−41.5578	+	15.1258i	−1.34057	+	0.487929i
$962$	−12.3962	+	7.15698i	−0.399671	+	0.230750i
$963$	14.5216	+	5.45495i	0.467954	+	0.175783i
$964$	24.0255	−	41.6134i	0.773810	−	1.34028i
$965$		0			0
$966$	−0.711343	+	7.67657i	−0.0228871	+	0.246990i
$967$	5.81200	−	15.9683i	0.186901	−	0.513507i	−0.810485	−	0.585759i	$-0.800796\pi$
$967$	5.81200	−	15.9683i	0.186901	−	0.513507i	0.997386	+	0.0722523i	$0.0230187\pi$
$968$	10.9076	−	1.92330i	0.350583	−	0.0618172i
$969$	7.20639	+	10.4051i	0.231503	+	0.334259i
$970$		0			0
$971$	−2.68374			−0.0861253			−0.0430627	−	0.999072i	$-0.513712\pi$
$971$	−2.68374			−0.0861253			−0.0430627	+	0.999072i	$0.513712\pi$
$972$	−2.37987	−	38.5875i	−0.0763345	−	1.23769i
$973$		−	9.12064i		−	0.292394i
$974$	6.53113	+	5.48027i	0.209271	+	0.175599i
$975$		0			0
$976$	−0.495044	−	2.80753i	−0.0158460	−	0.0898670i
$977$	3.75984	−	10.3301i	0.120288	−	0.330488i	−0.864906	−	0.501935i	$-0.832622\pi$
$977$	3.75984	−	10.3301i	0.120288	−	0.330488i	0.985193	+	0.171446i	$0.0548440\pi$
$978$	45.4452	+	4.21114i	1.45318	+	0.134657i
$979$	−0.852930	+	4.83721i	−0.0272598	+	0.154598i
$980$		0			0
$981$	7.71239	−	20.5312i	0.246238	−	0.655511i
$982$	70.7948	−	40.8734i	2.25915	−	1.30432i
$983$	−16.3402	−	44.8944i	−0.521172	−	1.43191i	−0.869217	−	0.494431i	$-0.835376\pi$
$983$	−16.3402	−	44.8944i	−0.521172	−	1.43191i	0.348044	−	0.937478i	$-0.386846\pi$
$984$	7.31189	−	7.23719i	0.233094	−	0.230713i
$985$		0			0
$986$	8.38988	−	7.03994i	0.267188	−	0.224197i
$987$	4.03342	−	1.05859i	0.128385	−	0.0336952i
$988$	−7.98915	−	21.9500i	−0.254169	−	0.698323i
$989$	6.04594	+	10.4719i	0.192250	+	0.332986i
$990$		0			0
$991$	−27.7503	+	48.0649i	−0.881517	+	1.52683i	−0.0318627	+	0.999492i	$0.510144\pi$
$991$	−27.7503	+	48.0649i	−0.881517	+	1.52683i	−0.849654	+	0.527340i	$0.823189\pi$
$992$	−68.1492	−	12.0165i	−2.16374	−	0.381526i
$993$	−1.02276	−	2.22305i	−0.0324564	−	0.0705462i
$994$	18.5577	+	6.75445i	0.588614	+	0.214238i
$995$		0			0
$996$	20.0570	−	1.65104i	0.635529	−	0.0523153i
$997$	28.9555	−	34.5078i	0.917029	−	1.09287i	−0.0783575	−	0.996925i	$-0.524968\pi$
$997$	28.9555	−	34.5078i	0.917029	−	1.09287i	0.995386	−	0.0959472i	$-0.0305880\pi$
$998$		−	8.61859i		−	0.272817i
$999$	−16.1568	−	16.6623i	−0.511179	−	0.527172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.b.124.4		24
5.2	odd	4		675.2.l.c.151.2		12
5.3	odd	4		27.2.e.a.16.1	✓	12
5.4	even	2	inner	675.2.u.b.124.1		24
15.8	even	4		81.2.e.a.46.2		12
20.3	even	4		432.2.u.c.97.2		12
27.22	even	9	inner	675.2.u.b.49.1		24
45.13	odd	12		243.2.e.c.55.2		12
45.23	even	12		243.2.e.b.55.1		12
45.38	even	12		243.2.e.a.217.2		12
45.43	odd	12		243.2.e.d.217.1		12
135.13	odd	36		243.2.e.c.190.2		12
135.22	odd	36		675.2.l.c.76.2		12
135.23	even	36		243.2.e.a.28.2		12
135.38	even	36		729.2.c.b.487.2		12
135.43	odd	36		729.2.c.e.487.5		12
135.49	even	18	inner	675.2.u.b.49.4		24
135.58	odd	36		243.2.e.d.28.1		12
135.68	even	36		243.2.e.b.190.1		12
135.83	even	36		729.2.c.b.244.2		12
135.88	odd	36		729.2.a.a.1.2		6
135.103	odd	36		27.2.e.a.22.1	yes	12
135.113	even	36		81.2.e.a.37.2		12
135.128	even	36		729.2.a.d.1.5		6
135.133	odd	36		729.2.c.e.244.5		12
540.103	even	36		432.2.u.c.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.16.1	✓	12	5.3	odd	4
27.2.e.a.22.1	yes	12	135.103	odd	36
81.2.e.a.37.2		12	135.113	even	36
81.2.e.a.46.2		12	15.8	even	4
243.2.e.a.28.2		12	135.23	even	36
243.2.e.a.217.2		12	45.38	even	12
243.2.e.b.55.1		12	45.23	even	12
243.2.e.b.190.1		12	135.68	even	36
243.2.e.c.55.2		12	45.13	odd	12
243.2.e.c.190.2		12	135.13	odd	36
243.2.e.d.28.1		12	135.58	odd	36
243.2.e.d.217.1		12	45.43	odd	12
432.2.u.c.49.2		12	540.103	even	36
432.2.u.c.97.2		12	20.3	even	4
675.2.l.c.76.2		12	135.22	odd	36
675.2.l.c.151.2		12	5.2	odd	4
675.2.u.b.49.1		24	27.22	even	9	inner
675.2.u.b.49.4		24	135.49	even	18	inner
675.2.u.b.124.1		24	5.4	even	2	inner
675.2.u.b.124.4		24	1.1	even	1	trivial
729.2.a.a.1.2		6	135.88	odd	36
729.2.a.d.1.5		6	135.128	even	36
729.2.c.b.244.2		12	135.83	even	36
729.2.c.b.487.2		12	135.38	even	36
729.2.c.e.244.5		12	135.133	odd	36
729.2.c.e.487.5		12	135.43	odd	36

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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51}+ \cdots + 54 q^{99}+O(q^{100}) \) 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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