LMFDB - Embedded newform 164.2.o.b.111.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,2,Mod(7,164)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([20, 39]))

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

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

chi := DirichletCharacter("164.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	164.o (of order $40$, degree $16$, 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:	$1.30954659315$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			111.16
Character	$\chi$	$=$	164.111
Dual form			164.2.o.b.99.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32047 - 0.506330i) q^{2} +(0.323235 + 0.133889i) q^{3} +(1.48726 - 1.33718i) q^{4} +(-0.705993 + 0.359722i) q^{5} +(0.494613 + 0.0131313i) q^{6} +(2.28906 + 3.73541i) q^{7} +(1.28682 - 2.51875i) q^{8} +(-2.03477 - 2.03477i) q^{9} +O(q^{10})$	\(q+(1.32047 - 0.506330i) q^{2} +(0.323235 + 0.133889i) q^{3} +(1.48726 - 1.33718i) q^{4} +(-0.705993 + 0.359722i) q^{5} +(0.494613 + 0.0131313i) q^{6} +(2.28906 + 3.73541i) q^{7} +(1.28682 - 2.51875i) q^{8} +(-2.03477 - 2.03477i) q^{9} +(-0.750102 + 0.832466i) q^{10} +(-2.94031 - 0.231408i) q^{11} +(0.659768 - 0.233098i) q^{12} +(-1.05491 - 4.39401i) q^{13} +(4.91398 + 3.77346i) q^{14} +(-0.276365 + 0.0217504i) q^{15} +(0.423882 - 3.97748i) q^{16} +(-2.76691 + 2.36316i) q^{17} +(-3.71710 - 1.65657i) q^{18} +(4.50401 + 1.08132i) q^{19} +(-0.568982 + 1.47904i) q^{20} +(0.239778 + 1.51390i) q^{21} +(-3.99975 + 1.18320i) q^{22} +(-6.50021 + 4.72268i) q^{23} +(0.753177 - 0.641859i) q^{24} +(-2.56990 + 3.53716i) q^{25} +(-3.61779 - 5.26801i) q^{26} +(-0.786942 - 1.89985i) q^{27} +(8.39936 + 2.49463i) q^{28} +(5.31907 + 4.54292i) q^{29} +(-0.353917 + 0.168652i) q^{30} +(0.131241 + 0.403918i) q^{31} +(-1.45419 - 5.46675i) q^{32} +(-0.919431 - 0.468474i) q^{33} +(-2.45707 + 4.52145i) q^{34} +(-2.95977 - 1.81375i) q^{35} +(-5.74708 - 0.305370i) q^{36} +(2.21897 - 6.82927i) q^{37} +(6.49489 - 0.852674i) q^{38} +(0.247324 - 1.56154i) q^{39} +(-0.00243738 + 2.24112i) q^{40} +(1.56856 - 6.20803i) q^{41} +(1.08315 + 1.87764i) q^{42} +(-3.65616 - 0.579078i) q^{43} +(-4.68245 + 3.58758i) q^{44} +(2.16848 + 0.704582i) q^{45} +(-6.19207 + 9.52739i) q^{46} +(4.08444 - 6.66520i) q^{47} +(0.669552 - 1.22891i) q^{48} +(-5.53555 + 10.8641i) q^{49} +(-1.60249 + 5.97192i) q^{50} +(-1.21076 + 0.393401i) q^{51} +(-7.44452 - 5.12443i) q^{52} +(-1.61175 + 1.88712i) q^{53} +(-2.00108 - 2.11023i) q^{54} +(2.15908 - 0.894322i) q^{55} +(12.3542 - 0.958776i) q^{56} +(1.31108 + 0.952555i) q^{57} +(9.32387 + 3.30556i) q^{58} +(2.29771 + 3.16253i) q^{59} +(-0.381942 + 0.401899i) q^{60} +(12.3904 - 1.96244i) q^{61} +(0.377815 + 0.466908i) q^{62} +(2.94298 - 12.2584i) q^{63} +(-4.68819 - 6.48235i) q^{64} +(2.32538 + 2.72267i) q^{65} +(-1.45128 - 0.153068i) q^{66} +(0.516254 + 6.55963i) q^{67} +(-0.955130 + 7.21451i) q^{68} +(-2.73341 + 0.656234i) q^{69} +(-4.82663 - 0.896373i) q^{70} +(0.111273 - 1.41386i) q^{71} +(-7.74344 + 2.50669i) q^{72} +(2.08819 - 2.08819i) q^{73} +(-0.527799 - 10.1414i) q^{74} +(-1.30427 + 0.799256i) q^{75} +(8.14455 - 4.41449i) q^{76} +(-5.86616 - 11.5130i) q^{77} +(-0.464072 - 2.18719i) q^{78} +(3.24666 - 7.83812i) q^{79} +(1.13153 + 2.96055i) q^{80} +7.91332i q^{81} +(-1.07208 - 8.99170i) q^{82} +5.01948i q^{83} +(2.38097 + 1.93093i) q^{84} +(1.10334 - 2.66370i) q^{85} +(-5.12103 + 1.08657i) q^{86} +(1.11107 + 2.18059i) q^{87} +(-4.36651 + 7.10813i) q^{88} +(-5.31834 + 3.25908i) q^{89} +(3.22015 - 0.167591i) q^{90} +(13.9987 - 13.9987i) q^{91} +(-3.35241 + 15.7158i) q^{92} +(-0.0116583 + 0.148132i) q^{93} +(2.01857 - 10.8692i) q^{94} +(-3.56877 + 0.856786i) q^{95} +(0.261887 - 1.96175i) q^{96} +(0.157358 + 1.99942i) q^{97} +(-1.80867 + 17.1485i) q^{98} +(5.51199 + 6.45371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$e\left(\frac{7}{40}\right)$

Coefficient data

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

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

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

$2$	1.32047	−	0.506330i	0.933710	−	0.358029i
$2$	1.32047	−	0.506330i	0.933710	−	0.358029i
$3$	0.323235	+	0.133889i	0.186620	+	0.0773006i	0.474037	−	0.880505i	$-0.342796\pi$
$3$	0.323235	+	0.133889i	0.186620	+	0.0773006i	−0.287417	+	0.957806i	$0.592796\pi$
$4$	1.48726	−	1.33718i	0.743630	−	0.668592i
$5$	−0.705993	+	0.359722i	−0.315730	+	0.160872i	−0.604673	−	0.796474i	$-0.706696\pi$
$5$	−0.705993	+	0.359722i	−0.315730	+	0.160872i	0.288943	+	0.957346i	$0.406696\pi$
$6$	0.494613	+	0.0131313i	0.201925	+	0.00536085i
$7$	2.28906	+	3.73541i	0.865184	+	1.41185i	0.910780	+	0.412892i	$0.135481\pi$
$7$	2.28906	+	3.73541i	0.865184	+	1.41185i	−0.0455958	+	0.998960i	$0.514519\pi$
$8$	1.28682	−	2.51875i	0.454959	−	0.890512i
$9$	−2.03477	−	2.03477i	−0.678255	−	0.678255i
$10$	−0.750102	+	0.832466i	−0.237203	+	0.263249i
$11$	−2.94031	−	0.231408i	−0.886538	−	0.0697721i	−0.372993	−	0.927834i	$-0.621668\pi$
$11$	−2.94031	−	0.231408i	−0.886538	−	0.0697721i	−0.513546	+	0.858062i	$0.671668\pi$
$12$	0.659768	−	0.233098i	0.190459	−	0.0672896i
$13$	−1.05491	−	4.39401i	−0.292579	−	1.21868i	−0.904055	−	0.427416i	$-0.859424\pi$
$13$	−1.05491	−	4.39401i	−0.292579	−	1.21868i	0.611476	−	0.791263i	$-0.290576\pi$
$14$	4.91398	+	3.77346i	1.31332	+	1.00850i
$15$	−0.276365	+	0.0217504i	−0.0713570	+	0.00561592i
$16$	0.423882	−	3.97748i	0.105971	−	0.994369i
$17$	−2.76691	+	2.36316i	−0.671074	+	0.573152i	−0.918338	−	0.395797i	$-0.870469\pi$
$17$	−2.76691	+	2.36316i	−0.671074	+	0.573152i	0.247264	+	0.968948i	$0.420469\pi$
$18$	−3.71710	−	1.65657i	−0.876129	−	0.390458i
$19$	4.50401	+	1.08132i	1.03329	+	0.248071i	0.714413	−	0.699725i	$-0.246694\pi$
$19$	4.50401	+	1.08132i	1.03329	+	0.248071i	0.318878	+	0.947796i	$0.396694\pi$
$20$	−0.568982	+	1.47904i	−0.127228	+	0.330724i
$21$	0.239778	+	1.51390i	0.0523238	+	0.330359i
$22$	−3.99975	+	1.18320i	−0.852750	+	0.252260i
$23$	−6.50021	+	4.72268i	−1.35539	+	0.984747i	−0.356665	+	0.934232i	$0.616086\pi$
$23$	−6.50021	+	4.72268i	−1.35539	+	0.984747i	−0.998723	+	0.0505147i	$0.983914\pi$
$24$	0.753177	−	0.641859i	0.153742	−	0.131019i
$25$	−2.56990	+	3.53716i	−0.513980	+	0.707433i
$26$	−3.61779	−	5.26801i	−0.709507	−	1.03314i
$27$	−0.786942	−	1.89985i	−0.151447	−	0.365626i
$28$	8.39936	+	2.49463i	1.58733	+	0.471440i
$29$	5.31907	+	4.54292i	0.987727	+	0.843598i	0.987694	−	0.156402i	$-0.0499894\pi$
$29$	5.31907	+	4.54292i	0.987727	+	0.843598i	3.32856e−5		1.00000i	$0.499989\pi$
$30$	−0.353917	+	0.168652i	−0.0646161	+	0.0307916i
$31$	0.131241	+	0.403918i	0.0235715	+	0.0725458i	0.962150	−	0.272519i	$-0.0878569\pi$
$31$	0.131241	+	0.403918i	0.0235715	+	0.0725458i	−0.938579	+	0.345065i	$0.887857\pi$
$32$	−1.45419	−	5.46675i	−0.257068	−	0.966393i
$33$	−0.919431	−	0.468474i	−0.160052	−	0.0815508i
$34$	−2.45707	+	4.52145i	−0.421384	+	0.775422i
$35$	−2.95977	−	1.81375i	−0.500292	−	0.306580i
$36$	−5.74708	−	0.305370i	−0.957846	−	0.0508950i
$37$	2.21897	−	6.82927i	0.364796	−	1.12273i	−0.585313	−	0.810807i	$-0.699028\pi$
$37$	2.21897	−	6.82927i	0.364796	−	1.12273i	0.950109	−	0.311918i	$-0.100972\pi$
$38$	6.49489	−	0.852674i	1.05361	−	0.138322i
$39$	0.247324	−	1.56154i	0.0396035	−	0.250046i
$40$	−0.00243738	+	2.24112i	−0.000385384	+	0.354352i
$41$	1.56856	−	6.20803i	0.244968	−	0.969531i
$41$	1.56856	−	6.20803i	0.244968	−	0.969531i
$42$	1.08315	+	1.87764i	0.167134	+	0.289726i
$43$	−3.65616	−	0.579078i	−0.557559	−	0.0883086i	−0.128705	−	0.991683i	$-0.541082\pi$
$43$	−3.65616	−	0.579078i	−0.557559	−	0.0883086i	−0.428853	+	0.903374i	$0.641082\pi$
$44$	−4.68245	+	3.58758i	−0.705905	+	0.540847i
$45$	2.16848	+	0.704582i	0.323258	+	0.105033i
$46$	−6.19207	+	9.52739i	−0.912971	+	1.40474i
$47$	4.08444	−	6.66520i	0.595777	−	0.972219i	−0.402606	−	0.915373i	$-0.631896\pi$
$47$	4.08444	−	6.66520i	0.595777	−	0.972219i	0.998383	−	0.0568459i	$-0.0181044\pi$
$48$	0.669552	−	1.22891i	0.0966415	−	0.177378i
$49$	−5.53555	+	10.8641i	−0.790792	+	1.55202i
$50$	−1.60249	+	5.97192i	−0.226627	+	0.844557i
$51$	−1.21076	+	0.393401i	−0.169541	+	0.0550872i
$52$	−7.44452	−	5.12443i	−1.03237	−	0.710630i
$53$	−1.61175	+	1.88712i	−0.221391	+	0.259216i	−0.859975	−	0.510337i	$-0.829521\pi$
$53$	−1.61175	+	1.88712i	−0.221391	+	0.259216i	0.638583	+	0.769553i	$0.279521\pi$
$54$	−2.00108	−	2.11023i	−0.272312	−	0.287166i
$55$	2.15908	−	0.894322i	0.291131	−	0.120590i
$56$	12.3542	−	0.958776i	1.65090	−	0.128122i
$57$	1.31108	+	0.952555i	0.173657	+	0.126169i
$58$	9.32387	+	3.30556i	1.22428	+	0.434041i
$59$	2.29771	+	3.16253i	0.299136	+	0.411726i	0.931955	−	0.362574i	$-0.118102\pi$
$59$	2.29771	+	3.16253i	0.299136	+	0.411726i	−0.632819	+	0.774300i	$0.718102\pi$
$60$	−0.381942	+	0.401899i	−0.0493085	+	0.0518849i
$61$	12.3904	−	1.96244i	1.58643	−	0.251265i	0.700002	−	0.714141i	$-0.253182\pi$
$61$	12.3904	−	1.96244i	1.58643	−	0.251265i	0.886423	+	0.462875i	$0.153182\pi$
$62$	0.377815	+	0.466908i	0.0479825	+	0.0592974i
$63$	2.94298	−	12.2584i	0.370780	−	1.54441i
$64$	−4.68819	−	6.48235i	−0.586024	−	0.810294i
$65$	2.32538	+	2.72267i	0.288428	+	0.337705i
$66$	−1.45128	−	0.153068i	−0.178640	−	0.0188413i
$67$	0.516254	+	6.55963i	0.0630705	+	0.801386i	0.944382	+	0.328851i	$0.106661\pi$
$67$	0.516254	+	6.55963i	0.0630705	+	0.801386i	−0.881311	+	0.472536i	$0.843339\pi$
$68$	−0.955130	+	7.21451i	−0.115826	+	0.874887i
$69$	−2.73341	+	0.656234i	−0.329064	+	0.0790013i
$70$	−4.82663	−	0.896373i	−0.576893	−	0.107137i
$71$	0.111273	−	1.41386i	0.0132057	−	0.167794i	−0.986778	−	0.162078i	$-0.948180\pi$
$71$	0.111273	−	1.41386i	0.0132057	−	0.167794i	0.999984	−	0.00571647i	$-0.00181962\pi$
$72$	−7.74344	+	2.50669i	−0.912573	+	0.295416i
$73$	2.08819	−	2.08819i	0.244404	−	0.244404i	−0.574265	−	0.818669i	$-0.694712\pi$
$73$	2.08819	−	2.08819i	0.244404	−	0.244404i	0.818669	+	0.574265i	$0.194712\pi$
$74$	−0.527799	−	10.1414i	−0.0613554	−	1.17891i
$75$	−1.30427	+	0.799256i	−0.150604	+	0.0922902i
$76$	8.14455	−	4.41449i	0.934244	−	0.506376i
$77$	−5.86616	−	11.5130i	−0.668511	−	1.31203i
$78$	−0.464072	−	2.18719i	−0.0525458	−	0.247650i
$79$	3.24666	−	7.83812i	0.365277	−	0.881858i	−0.629233	−	0.777217i	$-0.716631\pi$
$79$	3.24666	−	7.83812i	0.365277	−	0.881858i	0.994510	−	0.104641i	$-0.0333693\pi$
$80$	1.13153	+	2.96055i	0.126508	+	0.331000i
$81$			7.91332i			0.879258i
$82$	−1.07208	−	8.99170i	−0.118391	−	0.992967i
$83$			5.01948i			0.550959i	0.961307	+	0.275480i	$0.0888366\pi$
$83$			5.01948i			0.550959i	−0.961307	+	0.275480i	$0.911163\pi$
$84$	2.38097	+	1.93093i	0.259785	+	0.210682i
$85$	1.10334	−	2.66370i	0.119674	−	0.288918i
$86$	−5.12103	+	1.08657i	−0.552215	+	0.117168i
$87$	1.11107	+	2.18059i	0.119119	+	0.233784i
$88$	−4.36651	+	7.10813i	−0.465472	+	0.757730i
$89$	−5.31834	+	3.25908i	−0.563743	+	0.345462i	−0.774993	−	0.631970i	$-0.782247\pi$
$89$	−5.31834	+	3.25908i	−0.563743	+	0.345462i	0.211250	+	0.977432i	$0.432247\pi$
$90$	3.22015	−	0.167591i	0.339434	−	0.0176656i
$91$	13.9987	−	13.9987i	1.46746	−	1.46746i
$92$	−3.35241	+	15.7158i	−0.349513	+	1.63849i
$93$	−0.0116583	+	0.148132i	−0.00120890	+	0.0153606i
$94$	2.01857	−	10.8692i	0.208200	−	1.12108i
$95$	−3.56877	+	0.856786i	−0.366148	+	0.0879044i
$96$	0.261887	−	1.96175i	0.0267288	−	0.200220i
$97$	0.157358	+	1.99942i	0.0159772	+	0.203010i	0.999725	+	0.0234538i	$0.00746625\pi$
$97$	0.157358	+	1.99942i	0.0159772	+	0.203010i	−0.983748	+	0.179556i	$0.942534\pi$
$98$	−1.80867	+	17.1485i	−0.182703	+	1.73226i
$99$	5.51199	+	6.45371i	0.553976	+	0.648622i
$100$	0.907728	+	8.69711i	0.0907728	+	0.869711i
$101$	3.78349	−	15.7593i	0.376471	−	1.56811i	−0.386880	−	0.922130i	$-0.626447\pi$
$101$	3.78349	−	15.7593i	0.376471	−	1.56811i	0.763351	−	0.645984i	$-0.223553\pi$
$102$	−1.39958	+	1.13252i	−0.138579	+	0.112136i
$103$	1.52470	−	0.241489i	0.150233	−	0.0237946i	−0.0808647	−	0.996725i	$-0.525768\pi$
$103$	1.52470	−	0.241489i	0.150233	−	0.0237946i	0.231098	+	0.972930i	$0.425768\pi$
$104$	−12.4249	−	2.99725i	−1.21836	−	0.293904i
$105$	−0.713862	−	0.982547i	−0.0696658	−	0.0958868i
$106$	−1.17276	+	3.30796i	−0.113908	+	0.321297i
$107$	0.703145	+	0.510864i	0.0679755	+	0.0493871i	0.621254	−	0.783609i	$-0.286623\pi$
$107$	0.703145	+	0.510864i	0.0679755	+	0.0493871i	−0.553279	+	0.832996i	$0.686623\pi$
$108$	−3.71083	−	1.77328i	−0.357075	−	0.170634i
$109$	10.4947	−	4.34703i	1.00521	−	0.416370i	0.181502	−	0.983391i	$-0.441904\pi$
$109$	10.4947	−	4.34703i	1.00521	−	0.416370i	0.823704	+	0.567021i	$0.191904\pi$
$110$	2.39817	−	2.27413i	0.228657	−	0.216830i
$111$	1.63161	−	1.91037i	0.154866	−	0.181324i
$112$	15.8278	−	7.52132i	1.49559	−	0.710698i
$113$	1.51165	−	0.491163i	0.142204	−	0.0462048i	−0.237050	−	0.971497i	$-0.576181\pi$
$113$	1.51165	−	0.491163i	0.142204	−	0.0462048i	0.379254	+	0.925293i	$0.376181\pi$
$114$	2.21354	+	0.593977i	0.207317	+	0.0556311i
$115$	2.89026	−	5.67245i	0.269518	−	0.528958i
$116$	13.9856	−	0.356078i	1.29853	−	0.0330610i
$117$	−6.79429	+	11.0873i	−0.628132	+	1.02502i
$118$	4.63533	+	3.01261i	0.426717	+	0.277333i
$119$	−15.1610	−	4.92611i	−1.38981	−	0.451576i
$120$	−0.300848	+	0.724082i	−0.0274635	+	0.0660993i
$121$	−2.27267	−	0.359956i	−0.206607	−	0.0327233i
$122$	15.3674	−	8.86496i	1.39130	−	0.802596i
$123$	1.33820	−	1.79664i	0.120661	−	0.161998i
$124$	0.735301	+	0.425237i	0.0660320	+	0.0381875i
$125$	1.16170	−	7.33466i	0.103905	−	0.656032i
$126$	−2.32069	−	17.6769i	−0.206743	−	1.57478i
$127$	−5.39088	+	16.5914i	−0.478364	+	1.47225i	0.363004	+	0.931788i	$0.381751\pi$
$127$	−5.39088	+	16.5914i	−0.478364	+	1.47225i	−0.841367	+	0.540464i	$0.818249\pi$
$128$	−9.47281	−	6.18595i	−0.837286	−	0.546766i
$129$	−1.10427	−	0.676696i	−0.0972253	−	0.0595797i
$130$	4.44915	+	2.41778i	0.390216	+	0.212053i
$131$	−7.43509	−	3.78837i	−0.649607	−	0.330991i	0.0979479	−	0.995192i	$-0.468772\pi$
$131$	−7.43509	−	3.78837i	−0.649607	−	0.330991i	−0.747555	+	0.664200i	$0.768772\pi$
$132$	−1.99387	+	0.532706i	−0.173544	+	0.0463661i
$133$	6.27079	+	19.2995i	0.543747	+	1.67348i
$134$	4.00303	+	8.40037i	0.345809	+	0.725682i
$135$	1.23899	+	1.05820i	0.106635	+	0.0910752i
$136$	2.39171	+	10.0101i	0.205087	+	0.858361i
$137$	4.55146	+	10.9882i	0.388858	+	0.938785i	0.990183	+	0.139781i	$0.0446397\pi$
$137$	4.55146	+	10.9882i	0.388858	+	0.938785i	−0.601325	+	0.799005i	$0.705360\pi$
$138$	−3.27711	+	2.25054i	−0.278966	+	0.191579i
$139$	−6.04258	+	8.31690i	−0.512525	+	0.705430i	−0.984343	−	0.176266i	$-0.943598\pi$
$139$	−6.04258	+	8.31690i	−0.512525	+	0.705430i	0.471818	+	0.881696i	$0.343598\pi$
$140$	−6.82726	+	1.26024i	−0.577009	+	0.106510i
$141$	2.21263	−	1.60757i	0.186337	−	0.135382i
$142$	−0.568948	−	1.92330i	−0.0477451	−	0.161399i
$143$	2.08495	+	13.1639i	0.174353	+	1.10082i
$144$	−8.95573	+	7.23073i	−0.746311	+	0.602561i
$145$	−5.38941	−	1.29388i	−0.447566	−	0.107451i
$146$	1.70007	−	3.81469i	0.140699	−	0.315706i
$147$	−3.24387	+	2.77052i	−0.267550	+	0.228509i
$148$	−5.83181	−	13.1241i	−0.479372	−	1.07879i
$149$	−7.30837	+	0.575181i	−0.598725	+	0.0471207i	−0.374201	−	0.927348i	$-0.622083\pi$
$149$	−7.30837	+	0.575181i	−0.598725	+	0.0471207i	−0.224524	+	0.974468i	$0.572083\pi$
$150$	−1.31755	+	1.71578i	−0.107578	+	0.140093i
$151$	3.19774	+	13.3195i	0.260228	+	1.08393i	0.937442	+	0.348142i	$0.113187\pi$
$151$	3.19774	+	13.3195i	0.260228	+	1.08393i	−0.677213	+	0.735787i	$0.736813\pi$
$152$	8.51941	−	9.95301i	0.691015	−	0.807296i
$153$	10.4385	+	0.821528i	0.843903	+	0.0664166i
$154$	−13.5754	−	12.2323i	−1.09394	−	0.985706i
$155$	−0.237953	−	0.237953i	−0.0191128	−	0.0191128i
$156$	−1.72023	−	2.65313i	−0.137729	−	0.212421i
$157$	−3.07843	−	5.02354i	−0.245686	−	0.400922i	0.705898	−	0.708314i	$-0.250544\pi$
$157$	−3.07843	−	5.02354i	−0.245686	−	0.400922i	−0.951583	+	0.307391i	$0.900544\pi$
$158$	0.318421	−	11.9939i	0.0253322	−	0.954180i
$159$	−0.773640	+	0.394189i	−0.0613536	+	0.0312612i
$160$	2.99316	+	3.33638i	0.236630	+	0.263764i
$161$	−32.5205	−	13.4704i	−2.56298	−	1.06162i
$162$	4.00675	+	10.4493i	0.314800	+	0.820972i
$163$	−13.4559			−1.05395			−0.526973	−	0.849882i	$-0.676673\pi$
$163$	−13.4559			−1.05395			−0.526973	+	0.849882i	$0.676673\pi$
$164$	−5.96841	−	11.3304i	−0.466054	−	0.884756i
$165$	0.817632			0.0636526
$166$	2.54151	+	6.62805i	0.197260	+	0.514436i
$167$	−0.0425390	−	0.0176203i	−0.00329177	−	0.00136350i	0.381037	−	0.924560i	$-0.375567\pi$
$167$	−0.0425390	−	0.0176203i	−0.00329177	−	0.00136350i	−0.384329	+	0.923196i	$0.625567\pi$
$168$	4.12167	+	1.34417i	0.317994	+	0.103705i
$169$	−6.61140	+	3.36868i	−0.508569	+	0.259129i
$170$	0.108212	−	4.07597i	0.00829946	−	0.312613i
$171$	−6.96437	−	11.3648i	−0.532579	−	0.869090i
$172$	−6.21199	+	4.02771i	−0.473660	+	0.307110i
$173$	1.82188	+	1.82188i	0.138515	+	0.138515i	0.772964	−	0.634450i	$-0.218773\pi$
$173$	1.82188	+	1.82188i	0.138515	+	0.138515i	−0.634450	+	0.772964i	$0.718773\pi$
$174$	2.57123	+	2.31683i	0.194924	+	0.175639i
$175$	−19.0954	−	1.50284i	−1.44348	−	0.113604i
$176$	−2.16677	+	11.5969i	−0.163326	+	0.874153i
$177$	0.319275	+	1.32988i	0.0239982	+	0.0999597i
$178$	−5.37251	+	6.99634i	−0.402687	+	0.524398i
$179$	−4.95719	+	0.390139i	−0.370518	+	0.0291604i	−0.262351	−	0.964972i	$-0.584498\pi$
$179$	−4.95719	+	0.390139i	−0.370518	+	0.0291604i	−0.108166	+	0.994133i	$0.534498\pi$
$180$	4.16725	−	1.85176i	0.310608	−	0.138022i
$181$	−1.52780	+	1.30487i	−0.113561	+	0.0969899i	−0.704415	−	0.709788i	$-0.748791\pi$
$181$	−1.52780	+	1.30487i	−0.113561	+	0.0969899i	0.590855	+	0.806778i	$0.298791\pi$
$182$	11.3968	−	25.5727i	0.844788	−	1.89558i
$183$	4.26776	+	1.02460i	0.315482	+	0.0757405i
$184$	3.53065	+	22.4496i	0.260283	+	1.65501i
$185$	0.890062	+	5.61963i	0.0654387	+	0.413164i
$186$	0.0596095	+	0.201506i	0.00437078	+	0.0147752i
$187$	8.68244	−	6.30816i	0.634923	−	0.461299i
$188$	−2.83797	−	15.3745i	−0.206980	−	1.12130i
$189$	5.29535	−	7.28842i	0.385180	−	0.530154i
$190$	−4.27863	+	2.93833i	−0.310404	+	0.213169i
$191$	−3.03196	−	7.31979i	−0.219385	−	0.529642i	0.775420	−	0.631446i	$-0.217538\pi$
$191$	−3.03196	−	7.31979i	−0.219385	−	0.529642i	−0.994804	+	0.101805i	$0.967538\pi$
$192$	−0.647478	−	2.72302i	−0.0467277	−	0.196517i
$193$	−6.27221	−	5.35697i	−0.451484	−	0.385603i	0.394428	−	0.918927i	$-0.370943\pi$
$193$	−6.27221	−	5.35697i	−0.451484	−	0.385603i	−0.845911	+	0.533324i	$0.820943\pi$
$194$	1.22015	+	2.56049i	0.0876018	+	0.183832i
$195$	0.387111	+	1.19140i	0.0277216	+	0.0853182i
$196$	6.29453	+	23.5598i	0.449609	+	1.68284i
$197$	−5.64488	−	2.87621i	−0.402181	−	0.204922i	0.241187	−	0.970479i	$-0.422463\pi$
$197$	−5.64488	−	2.87621i	−0.402181	−	0.204922i	−0.643368	+	0.765557i	$0.722463\pi$
$198$	10.5461	+	5.73102i	0.749479	+	0.407286i
$199$	14.7707	+	9.05148i	1.04706	+	0.641642i	0.935938	−	0.352164i	$-0.114554\pi$
$199$	14.7707	+	9.05148i	1.04706	+	0.641642i	0.111126	+	0.993806i	$0.464554\pi$
$200$	5.60223	+	11.0246i	0.396137	+	0.779558i
$201$	−0.711387	+	2.18943i	−0.0501774	+	0.154430i
$202$	−2.98347	−	22.7254i	−0.209916	−	1.59895i
$203$	−4.79397	+	30.2679i	−0.336471	+	2.12439i
$204$	−1.27467	+	2.20410i	−0.0892448	+	0.154318i
$205$	1.12577	+	4.94707i	0.0786269	+	0.345518i
$206$	1.89104	−	1.09088i	0.131755	−	0.0760053i
$207$	22.8360	+	3.61686i	1.58721	+	0.251389i
$208$	−17.9242	+	2.33333i	−1.24282	+	0.161787i
$209$	−12.9930	−	4.22167i	−0.898743	−	0.292019i
$210$	−1.44012	−	0.935970i	−0.0993780	−	0.0645881i
$211$	11.6615	−	19.0298i	0.802807	−	1.31006i	−0.144425	−	0.989516i	$-0.546133\pi$
$211$	11.6615	−	19.0298i	0.802807	−	1.31006i	0.947233	−	0.320547i	$-0.103867\pi$
$212$	0.126331	+	4.96185i	0.00867642	+	0.340781i
$213$	0.225267	−	0.442112i	0.0154351	−	0.0302930i
$214$	1.18714	+	0.318556i	0.0811515	+	0.0217760i
$215$	2.78953	−	0.906373i	0.190244	−	0.0618141i
$216$	−5.79789	−	0.462649i	−0.394496	−	0.0314793i
$217$	−1.20838	+	1.41483i	−0.0820302	+	0.0960450i
$218$	11.6568	−	11.0539i	0.789498	−	0.748662i
$219$	0.954561	−	0.395392i	0.0645033	−	0.0267181i
$220$	2.01525	−	4.21718i	0.135868	−	0.284322i
$221$	13.3026	+	9.66491i	0.894830	+	0.650132i
$222$	1.18721	−	3.34871i	0.0796801	−	0.224751i
$223$	7.80365	+	10.7408i	0.522571	+	0.719257i	0.985976	−	0.166890i	$-0.0533724\pi$
$223$	7.80365	+	10.7408i	0.522571	+	0.719257i	−0.463405	+	0.886147i	$0.653372\pi$
$224$	17.0918	−	17.9457i	1.14199	−	1.19905i
$225$	12.4264	−	1.96815i	0.828429	−	0.131210i
$226$	1.74739	−	1.41396i	0.116234	−	0.0940550i
$227$	−0.891771	+	3.71449i	−0.0591889	+	0.246540i	−0.994119	−	0.108292i	$-0.965462\pi$
$227$	−0.891771	+	3.71449i	−0.0591889	+	0.246540i	0.934930	+	0.354832i	$0.115462\pi$
$228$	3.22366	−	0.336457i	0.213492	−	0.0222824i
$229$	−5.77472	−	6.76133i	−0.381604	−	0.446801i	0.536047	−	0.844188i	$-0.319917\pi$
$229$	−5.77472	−	6.76133i	−0.381604	−	0.446801i	−0.917651	+	0.397387i	$0.869917\pi$
$230$	0.944353	−	8.95370i	0.0622688	−	0.590389i
$231$	−0.354694	−	4.50682i	−0.0233372	−	0.296527i
$232$	18.2871	−	7.55149i	1.20061	−	0.495780i
$233$	14.3261	−	3.43938i	0.938531	−	0.225321i	0.264805	−	0.964302i	$-0.414693\pi$
$233$	14.3261	−	3.43938i	0.938531	−	0.225321i	0.673727	+	0.738981i	$0.264693\pi$
$234$	−3.35780	+	18.0805i	−0.219507	+	1.18196i
$235$	−0.485971	+	6.17485i	−0.0317012	+	0.402803i
$236$	7.64617	+	1.63104i	0.497723	+	0.106172i
$237$	2.09887	−	2.09887i	0.136336	−	0.136336i
$238$	−22.5138	+	1.17172i	−1.45936	+	0.0759511i
$239$	−24.5473	+	15.0426i	−1.58784	+	0.973027i	−0.603367	+	0.797464i	$0.706175\pi$
$239$	−24.5473	+	15.0426i	−1.58784	+	0.973027i	−0.984468	+	0.175563i	$0.943825\pi$
$240$	−0.0306344	+	1.10845i	−0.00197744	+	0.0715504i
$241$	7.01085	+	13.7596i	0.451608	+	0.886331i	0.998783	+	0.0493130i	$0.0157032\pi$
$241$	7.01085	+	13.7596i	0.451608	+	0.886331i	−0.547175	+	0.837018i	$0.684297\pi$
$242$	−3.18324	+	0.675413i	−0.204627	+	0.0434172i
$243$	−3.42033	+	8.25740i	−0.219414	+	0.529713i
$244$	15.8036	−	19.4869i	1.01172	−	1.24752i
$245$		−	9.66125i		−	0.617235i
$246$	0.857352	−	3.04997i	0.0546628	−	0.194459i
$247$		−	20.9313i		−	1.33183i
$248$	1.18625	+	0.189206i	0.0753270	+	0.0120146i
$249$	−0.672050	+	1.62247i	−0.0425894	+	0.102820i
$250$	−2.17978	−	10.2734i	−0.137861	−	0.649745i
$251$	−11.8937	−	23.3427i	−0.750724	−	1.47338i	−0.876542	−	0.481325i	$-0.840156\pi$
$251$	−11.8937	−	23.3427i	−0.750724	−	1.47338i	0.125818	−	0.992053i	$-0.459844\pi$
$252$	−12.0147	−	22.1667i	−0.756857	−	1.39637i
$253$	20.2055	−	12.3820i	1.27031	−	0.778448i
$254$	1.28227	+	24.6380i	0.0804565	+	1.54592i
$255$	0.713276	−	0.713276i	0.0446671	−	0.0446671i
$256$	−15.6406	−	3.37196i	−0.977541	−	0.210748i
$257$	−0.256622	+	3.26070i	−0.0160077	+	0.203397i	0.983713	+	0.179748i	$0.0575283\pi$
$257$	−0.256622	+	3.26070i	−0.0160077	+	0.203397i	−0.999720	+	0.0236486i	$0.992472\pi$
$258$	−1.80078	−	0.334430i	−0.112112	−	0.0208207i
$259$	30.5895	−	7.34389i	1.90074	−	0.456327i
$260$	7.09915	+	0.939857i	0.440270	+	0.0582875i
$261$	−1.57929	−	20.0668i	−0.0977558	−	1.24211i
$262$	−11.7359	−	1.23780i	−0.725049	−	0.0764715i
$263$	0.939777	+	1.10034i	0.0579491	+	0.0678497i	0.788623	−	0.614877i	$-0.210794\pi$
$263$	0.939777	+	1.10034i	0.0579491	+	0.0678497i	−0.730674	+	0.682726i	$0.760794\pi$
$264$	−2.36311	+	1.71298i	−0.145439	+	0.105426i
$265$	0.459049	−	1.91208i	0.0281992	−	0.117458i
$266$	18.0523	+	22.3093i	1.10686	+	1.36787i
$267$	−2.15543	+	0.341386i	−0.131910	+	0.0208925i
$268$	9.53923	+	9.06555i	0.582701	+	0.553766i
$269$	5.24896	+	7.22457i	0.320035	+	0.440490i	0.938478	−	0.345340i	$-0.112236\pi$
$269$	5.24896	+	7.22457i	0.320035	+	0.440490i	−0.618443	+	0.785830i	$0.712236\pi$
$270$	2.17184	+	0.769976i	0.132174	+	0.0468593i
$271$	−8.83318	−	6.41768i	−0.536577	−	0.389846i	0.286235	−	0.958159i	$-0.407596\pi$
$271$	−8.83318	−	6.41768i	−0.536577	−	0.389846i	−0.822812	+	0.568313i	$0.807596\pi$
$272$	8.22659	+	12.0070i	0.498810	+	0.728033i
$273$	6.39913	−	2.65061i	0.387293	−	0.160422i
$274$	11.5737	+	12.2050i	0.699193	+	0.737331i
$275$	8.37484	−	9.80568i	0.505022	−	0.591305i
$276$	−3.18779	+	4.63106i	−0.191882	+	0.278757i
$277$	−30.2769	+	9.83757i	−1.81916	+	0.591082i	−0.819321	+	0.573335i	$0.805650\pi$
$277$	−30.2769	+	9.83757i	−1.81916	+	0.591082i	−0.999843	+	0.0177475i	$0.994350\pi$
$278$	−3.76792	+	14.0417i	−0.225985	+	0.842166i
$279$	0.554833	−	1.08892i	0.0332170	−	0.0651921i
$280$	−8.37707	+	5.12095i	−0.500626	+	0.306035i
$281$	4.01399	−	6.55023i	0.239454	−	0.390754i	−0.710226	−	0.703973i	$-0.751407\pi$
$281$	4.01399	−	6.55023i	0.239454	−	0.390754i	0.949681	+	0.313219i	$0.101407\pi$
$282$	2.10774	−	3.24306i	0.125514	−	0.193121i
$283$	−6.99558	−	2.27300i	−0.415844	−	0.135116i	0.0936196	−	0.995608i	$-0.470156\pi$
$283$	−6.99558	−	2.27300i	−0.415844	−	0.135116i	−0.509464	+	0.860492i	$0.670156\pi$
$284$	−1.72510	−	2.25157i	−0.102366	−	0.133606i
$285$	−1.26827	−	0.200874i	−0.0751257	−	0.0118987i
$286$	9.41838	+	16.3268i	0.556921	+	0.965423i
$287$	26.7801	−	8.35133i	1.58078	−	0.492964i
$288$	−8.16460	+	14.0825i	−0.481104	+	0.829819i
$289$	−0.588140	+	3.71337i	−0.0345965	+	0.218434i
$290$	−7.77167	+	1.02029i	−0.456368	+	0.0599137i
$291$	−0.216836	+	0.667351i	−0.0127111	+	0.0391208i
$292$	0.313388	−	5.89797i	0.0183396	−	0.345153i
$293$	17.4618	+	10.7006i	1.02013	+	0.625136i	0.928760	−	0.370682i	$-0.120876\pi$
$293$	17.4618	+	10.7006i	1.02013	+	0.625136i	0.0913686	+	0.995817i	$0.470876\pi$
$294$	−2.88061	+	5.30085i	−0.168001	+	0.309152i
$295$	−2.75980	−	1.40619i	−0.160682	−	0.0818713i
$296$	−14.3458	−	14.3771i	−0.833834	−	0.835650i
$297$	1.87422	+	5.76825i	0.108753	+	0.334708i
$298$	−9.35922	+	4.45996i	−0.542165	+	0.258358i
$299$	27.6086	+	23.5800i	1.59665	+	1.36367i
$300$	−0.871033	+	2.93275i	−0.0502891	+	0.169322i
$301$	−6.20607	−	14.9828i	−0.357712	−	0.863593i
$302$	10.9666	+	15.9689i	0.631057	+	0.918906i
$303$	3.33295	−	4.58742i	0.191473	−	0.263540i
$304$	6.21008	−	17.4562i	0.356173	−	1.00118i
$305$	−8.04159	+	5.84256i	−0.460460	+	0.334544i
$306$	14.1996	−	4.20053i	0.811740	−	0.240128i
$307$	−4.80089	−	30.3116i	−0.274001	−	1.72998i	−0.613786	−	0.789472i	$-0.710354\pi$
$307$	−4.80089	−	30.3116i	−0.274001	−	1.72998i	0.339785	−	0.940503i	$-0.389646\pi$
$308$	−24.1195	−	9.27867i	−1.37433	−	0.528701i
$309$	0.525171	+	0.126082i	0.0298759	+	0.00717257i
$310$	−0.434692	−	0.193726i	−0.0246888	−	0.0110029i
$311$	6.63079	−	5.66323i	0.375998	−	0.321132i	−0.441287	−	0.897366i	$-0.645478\pi$
$311$	6.63079	−	5.66323i	0.375998	−	0.321132i	0.817285	+	0.576233i	$0.195478\pi$
$312$	−3.61487	−	2.63236i	−0.204651	−	0.149028i
$313$	−27.2026	+	2.14089i	−1.53758	+	0.121010i	−0.818741	−	0.574163i	$-0.805327\pi$
$313$	−27.2026	+	2.14089i	−1.53758	+	0.121010i	−0.718842	+	0.695174i	$0.755327\pi$
$314$	−6.60854	−	5.07472i	−0.372941	−	0.286383i
$315$	2.33188	+	9.71299i	0.131387	+	0.547265i
$316$	−5.65239	−	15.9987i	−0.317972	−	0.899997i
$317$	−5.74002	−	0.451749i	−0.322392	−	0.0253728i	−0.0837692	−	0.996485i	$-0.526696\pi$
$317$	−5.74002	−	0.451749i	−0.322392	−	0.0253728i	−0.238623	+	0.971112i	$0.576696\pi$
$318$	−0.821975	+	0.912231i	−0.0460941	+	0.0511554i
$319$	−14.5885	−	14.5885i	−0.816798	−	0.816798i
$320$	5.64167	+	2.89005i	0.315379	+	0.161559i
$321$	0.158882	+	0.259272i	0.00886795	+	0.0144712i
$322$	−49.7628	−	1.32114i	−2.77317	−	0.0736241i
$323$	−15.0175	+	7.65181i	−0.835597	+	0.425758i
$324$	10.5816	+	11.7692i	0.587864	+	0.653842i
$325$	18.2533	+	7.56078i	1.01251	+	0.419397i
$326$	−17.7680	+	6.81312i	−0.984081	+	0.377344i
$327$	3.97426			0.219777
$328$	−13.6180	−	11.9394i	−0.751929	−	0.659245i
$329$	34.2468			1.88809
$330$	1.07966	−	0.413992i	0.0594331	−	0.0227895i
$331$	−20.2682	−	8.39535i	−1.11404	−	0.461450i	−0.251712	−	0.967802i	$-0.580994\pi$
$331$	−20.2682	−	8.39535i	−1.11404	−	0.461450i	−0.862327	+	0.506352i	$0.830994\pi$
$332$	6.71196	+	7.46526i	0.368367	+	0.409710i
$333$	−18.4110	+	9.38090i	−1.00892	+	0.514070i
$334$	−0.0650930	−	0.00172814i	−0.00356173	−	9.45593e-5i
$335$	−2.72411	−	4.44535i	−0.148834	−	0.242875i
$336$	6.12312	−	0.311996i	0.334044	−	0.0170208i
$337$	13.5042	+	13.5042i	0.735622	+	0.735622i	0.971727	−	0.236106i	$-0.0758711\pi$
$337$	13.5042	+	13.5042i	0.735622	+	0.735622i	−0.236106	+	0.971727i	$0.575871\pi$
$338$	−7.02446	+	7.79577i	−0.382080	+	0.424034i
$339$	0.554379	+	0.0436305i	0.0301097	+	0.00236969i
$340$	−1.92090	−	5.43697i	−0.104175	−	0.294861i
$341$	−0.292420	−	1.21802i	−0.0158354	−	0.0659592i
$342$	−14.9506	−	11.4806i	−0.808434	−	0.620799i
$343$	−22.6808	+	1.78501i	−1.22465	+	0.0963817i
$344$	−6.16336	+	8.46377i	−0.332306	+	0.456336i
$345$	1.69371	−	1.44656i	0.0911862	−	0.0778804i
$346$	3.32820	+	1.48326i	0.178925	+	0.0797403i
$347$	11.3378	+	2.72196i	0.608643	+	0.146122i	0.526039	−	0.850460i	$-0.323676\pi$
$347$	11.3378	+	2.72196i	0.608643	+	0.146122i	0.0826037	+	0.996582i	$0.473676\pi$
$348$	4.56830	+	1.75741i	0.244887	+	0.0942069i
$349$	1.55129	+	9.79445i	0.0830386	+	0.524285i	0.993785	+	0.111318i	$0.0355074\pi$
$349$	1.55129	+	9.79445i	0.0830386	+	0.524285i	−0.910746	+	0.412967i	$0.864493\pi$
$350$	−25.9758	+	7.68413i	−1.38846	+	0.410734i
$351$	−7.51779	+	5.46199i	−0.401270	+	0.291540i
$352$	3.01074	+	16.4105i	0.160473	+	0.874681i
$353$	−11.3727	+	15.6532i	−0.605309	+	0.833136i	−0.996181	−	0.0873089i	$-0.972173\pi$
$353$	−11.3727	+	15.6532i	−0.605309	+	0.833136i	0.390873	+	0.920445i	$0.372173\pi$
$354$	1.09495	+	1.59440i	0.0581959	+	0.0847413i
$355$	0.430038	+	1.03820i	0.0228241	+	0.0551021i
$356$	−3.55176	+	11.9587i	−0.188243	+	0.633809i
$357$	−4.24103	−	3.62218i	−0.224459	−	0.191706i
$358$	−6.34826	+	3.02514i	−0.335516	+	0.159884i
$359$	−9.08716	−	27.9674i	−0.479602	−	1.47606i	−0.839650	−	0.543128i	$-0.817240\pi$
$359$	−9.08716	−	27.9674i	−0.479602	−	1.47606i	0.360048	−	0.932934i	$-0.382760\pi$
$360$	4.56511	−	4.55519i	0.240602	−	0.240079i
$361$	2.18772	+	1.11470i	0.115143	+	0.0586684i
$362$	−1.35672	+	2.49660i	−0.0713074	+	0.131219i
$363$	−0.686414	−	0.420635i	−0.0360274	−	0.0220776i
$364$	2.10087	−	39.5385i	0.110115	−	2.07238i
$365$	−0.723081	+	2.22541i	−0.0378478	+	0.116483i
$366$	6.15421	−	0.807948i	0.321686	−	0.0422321i
$367$	−3.53600	+	22.3254i	−0.184578	+	1.16538i	0.705209	+	0.709000i	$0.250853\pi$
$367$	−3.53600	+	22.3254i	−0.184578	+	1.16538i	−0.889786	+	0.456377i	$0.849147\pi$
$368$	16.0290	+	27.8563i	0.835571	+	1.45211i
$369$	−15.8235	+	9.44022i	−0.823740	+	0.491438i
$370$	4.02069	+	6.96987i	0.209025	+	0.362346i
$371$	−10.7386	−	1.70082i	−0.557519	−	0.0883024i
$372$	0.180741	+	0.235900i	0.00937098	+	0.0122309i
$373$	16.5106	+	5.36463i	0.854888	+	0.277770i	0.703492	−	0.710703i	$-0.251623\pi$
$373$	16.5106	+	5.36463i	0.854888	+	0.277770i	0.151396	+	0.988473i	$0.451623\pi$
$374$	8.27085	−	12.7259i	0.427676	−	0.658040i
$375$	1.35753	−	2.21528i	0.0701024	−	0.114397i
$376$	−11.5320	−	18.8646i	−0.594719	−	0.972867i
$377$	14.3505	−	28.1644i	0.739087	−	1.45054i
$378$	3.30198	−	12.3053i	0.169835	−	0.632916i
$379$	−26.3680	+	8.56749i	−1.35443	+	0.440082i	−0.894181	−	0.447705i	$-0.852241\pi$
$379$	−26.3680	+	8.56749i	−1.35443	+	0.440082i	−0.460253	+	0.887788i	$0.652241\pi$
$380$	−4.16201	+	6.04637i	−0.213507	+	0.310172i
$381$	−3.96393	+	4.64116i	−0.203078	+	0.237774i
$382$	−7.70983	−	8.13036i	−0.394469	−	0.415986i
$383$	24.0206	−	9.94967i	1.22740	−	0.508405i	0.327643	−	0.944802i	$-0.393746\pi$
$383$	24.0206	−	9.94967i	1.22740	−	0.508405i	0.899754	+	0.436397i	$0.143746\pi$
$384$	−2.23372	−	3.26782i	−0.113989	−	0.166760i
$385$	8.28294	+	6.01791i	0.422138	+	0.306701i
$386$	−10.9946	−	3.89789i	−0.559612	−	0.198397i
$387$	6.26113	+	8.61771i	0.318271	+	0.438063i
$388$	2.90762	+	2.76324i	0.147612	+	0.140282i
$389$	−6.51857	+	1.03244i	−0.330504	+	0.0523468i	−0.319482	−	0.947592i	$-0.603509\pi$
$389$	−6.51857	+	1.03244i	−0.330504	+	0.0523468i	−0.0110228	+	0.999939i	$0.503509\pi$
$390$	1.11441	+	1.37720i	0.0564303	+	0.0697374i
$391$	6.82503	−	28.4283i	0.345157	−	1.43768i
$392$	20.2408	+	27.9228i	1.02231	+	1.41032i
$393$	−1.89607	−	2.22001i	−0.0956439	−	0.111985i
$394$	−8.91019	−	0.939764i	−0.448889	−	0.0473446i
$395$	0.527424	+	6.70156i	0.0265376	+	0.337192i
$396$	16.8276	+	2.22780i	0.845616	+	0.111951i
$397$	11.8694	−	2.84959i	0.595709	−	0.143017i	0.0756310	−	0.997136i	$-0.475903\pi$
$397$	11.8694	−	2.84959i	0.595709	−	0.143017i	0.520078	+	0.854119i	$0.325903\pi$
$398$	24.0872	+	4.47333i	1.20738	+	0.224228i
$399$	−0.557041	+	7.07788i	−0.0278869	+	0.354337i
$400$	12.9797	+	11.7211i	0.648983	+	0.586053i
$401$	9.57283	−	9.57283i	0.478044	−	0.478044i	−0.426461	−	0.904506i	$-0.640240\pi$
$401$	9.57283	−	9.57283i	0.478044	−	0.478044i	0.904506	+	0.426461i	$0.140240\pi$
$402$	0.169209	+	3.25126i	0.00843939	+	0.162158i
$403$	1.63637	−	1.00277i	0.0815134	−	0.0499515i
$404$	−15.4461	−	28.4975i	−0.768473	−	1.41780i
$405$	−2.84659	−	5.58675i	−0.141448	−	0.277608i
$406$	8.99529	+	42.3951i	0.446429	+	2.10403i
$407$	−8.10480	+	19.5667i	−0.401740	+	0.969887i
$408$	−0.567156	+	3.55585i	−0.0280784	+	0.176041i
$409$		−	39.9052i		−	1.97318i	−0.163208	−	0.986592i	$-0.552184\pi$
$409$		−	39.9052i		−	1.97318i	0.163208	−	0.986592i	$-0.447816\pi$
$410$	3.99139	+	5.96243i	0.197121	+	0.294463i
$411$			4.16116i			0.205255i
$412$	1.94471	−	2.39796i	0.0958092	−	0.118139i
$413$	−6.55373	+	15.8221i	−0.322488	+	0.778555i
$414$	31.9854	−	6.78659i	1.57200	−	0.333543i
$415$	−1.80561	−	3.54372i	−0.0886341	−	0.173954i
$416$	−22.4869	+	12.1567i	−1.10251	+	0.596029i
$417$	−3.06671	+	1.87928i	−0.150178	+	0.0920289i
$418$	−19.2943	+	1.00416i	−0.943717	+	0.0491151i
$419$	12.8287	−	12.8287i	0.626725	−	0.626725i	−0.320518	−	0.947243i	$-0.603857\pi$
$419$	12.8287	−	12.8287i	0.626725	−	0.626725i	0.947243	+	0.320518i	$0.103857\pi$
$420$	−2.37554	−	0.506738i	−0.115915	−	0.0247263i
$421$	−1.61823	+	20.5616i	−0.0788677	+	1.00211i	0.822418	+	0.568884i	$0.192625\pi$
$421$	−1.61823	+	20.5616i	−0.0788677	+	1.00211i	−0.901286	+	0.433226i	$0.857375\pi$
$422$	5.76321	−	31.0327i	0.280548	−	1.51065i
$423$	−21.8730	+	5.25124i	−1.06350	+	0.255324i
$424$	2.67915	+	6.48799i	0.130111	+	0.315085i
$425$	−1.24822	−	15.8601i	−0.0605474	−	0.769328i
$426$	0.0736031	−	0.697853i	0.00356608	−	0.0338111i
$427$	35.6929	+	41.7910i	1.72730	+	2.02241i
$428$	1.72888	−	0.180445i	0.0835685	−	0.00872214i
$429$	−1.08856	+	4.53418i	−0.0525562	+	0.218913i
$430$	3.22455	−	2.60926i	0.155502	−	0.125830i
$431$	5.90755	−	0.935665i	0.284557	−	0.0450694i	−0.0125245	−	0.999922i	$-0.503987\pi$
$431$	5.90755	−	0.935665i	0.284557	−	0.0450694i	0.297081	+	0.954852i	$0.403987\pi$
$432$	−7.89017	+	2.32473i	−0.379616	+	0.111849i
$433$	−23.4383	−	32.2600i	−1.12637	−	1.55032i	−0.794782	−	0.606895i	$-0.792415\pi$
$433$	−23.4383	−	32.2600i	−1.12637	−	1.55032i	−0.331591	−	0.943423i	$-0.607585\pi$
$434$	−0.879253	+	2.48007i	−0.0422055	+	0.119047i
$435$	−1.56881	−	1.13981i	−0.0752188	−	0.0546497i
$436$	9.79550	−	20.4984i	0.469120	−	0.981697i
$437$	−34.3837	+	14.2422i	−1.64480	+	0.681297i
$438$	1.06027	−	1.00542i	0.0506615	−	0.0480411i
$439$	11.2823	−	13.2099i	0.538475	−	0.630473i	−0.422747	−	0.906248i	$-0.638934\pi$
$439$	11.2823	−	13.2099i	0.538475	−	0.630473i	0.961222	+	0.275774i	$0.0889343\pi$
$440$	0.525778	−	6.58902i	0.0250655	−	0.314119i
$441$	33.3695	−	10.8424i	1.58902	−	0.516305i
$442$	22.4593	+	6.02667i	1.06828	+	0.286659i
$443$	15.8069	−	31.0228i	0.751009	−	1.47394i	−0.125265	−	0.992123i	$-0.539978\pi$
$443$	15.8069	−	31.0228i	0.751009	−	1.47394i	0.876274	−	0.481814i	$-0.160022\pi$
$444$	−0.127887	−	5.02298i	−0.00606925	−	0.238380i
$445$	2.58235	−	4.21401i	0.122415	−	0.199763i
$446$	15.7428	+	10.2316i	0.745445	+	0.484482i
$447$	−2.43933	−	0.792588i	−0.115377	−	0.0374881i
$448$	13.4827	−	32.3508i	0.636996	−	1.52843i
$449$	16.4974	+	2.61294i	0.778562	+	0.123312i	0.533053	−	0.846082i	$-0.321045\pi$
$449$	16.4974	+	2.61294i	0.778562	+	0.123312i	0.245510	+	0.969394i	$0.421045\pi$
$450$	15.4122	−	8.89076i	0.726536	−	0.419114i
$451$	−6.04866	+	17.8906i	−0.284820	+	0.842434i
$452$	1.59143	−	2.75183i	0.0748548	−	0.129435i
$453$	−0.749711	+	4.73349i	−0.0352245	+	0.222399i
$454$	0.703207	+	5.35639i	0.0330031	+	0.251388i
$455$	−4.84734	+	14.9186i	−0.227247	+	0.699394i
$456$	4.08637	−	2.07651i	0.191362	−	0.0972417i
$457$	−7.93267	−	4.86114i	−0.371074	−	0.227395i	0.324441	−	0.945906i	$-0.394824\pi$
$457$	−7.93267	−	4.86114i	−0.371074	−	0.227395i	−0.695515	+	0.718511i	$0.744824\pi$
$458$	−11.0488	−	6.00419i	−0.516276	−	0.280557i
$459$	6.66705	+	3.39703i	0.311191	+	0.158560i
$460$	−3.28654	−	12.3012i	−0.153236	−	0.573547i
$461$	3.33116	+	10.2523i	0.155148	+	0.477495i	0.998176	−	0.0603741i	$-0.0192294\pi$
$461$	3.33116	+	10.2523i	0.155148	+	0.477495i	−0.843028	+	0.537869i	$0.819229\pi$
$462$	−2.75030	−	5.77150i	−0.127955	−	0.268515i
$463$	4.09007	+	3.49325i	0.190082	+	0.162345i	0.739396	−	0.673271i	$-0.235111\pi$
$463$	4.09007	+	3.49325i	0.190082	+	0.162345i	−0.549315	+	0.835616i	$0.685111\pi$
$464$	20.3240	−	19.2308i	0.943518	−	0.892769i
$465$	−0.0450557	−	0.108774i	−0.00208941	−	0.00504428i
$466$	17.1756	−	11.7953i	0.795645	−	0.546407i
$467$	−9.33868	+	12.8536i	−0.432142	+	0.594793i	−0.968443	−	0.249234i	$-0.919821\pi$
$467$	−9.33868	+	12.8536i	−0.432142	+	0.594793i	0.536301	+	0.844027i	$0.319821\pi$
$468$	4.72084	+	25.5749i	0.218221	+	1.18220i
$469$	−23.3212	+	16.9438i	−1.07687	+	0.782393i
$470$	2.48480	+	8.39973i	0.114615	+	0.387451i
$471$	−0.322463	−	2.03595i	−0.0148583	−	0.0938118i
$472$	10.9223	−	1.71775i	0.502742	−	0.0790661i
$473$	10.6162	+	2.54873i	0.488135	+	0.117191i
$474$	1.70876	−	3.83421i	0.0784861	−	0.176111i
$475$	−15.3996	+	13.1525i	−0.706584	+	0.603480i
$476$	−29.1355	+	12.9466i	−1.33542	+	0.593409i
$477$	7.11939	−	0.560308i	0.325975	−	0.0256548i
$478$	−24.7974	+	32.2923i	−1.13421	+	1.47702i
$479$	9.27763	+	38.6441i	0.423906	+	1.76569i	0.619487	+	0.785007i	$0.287341\pi$
$479$	9.27763	+	38.6441i	0.423906	+	1.76569i	−0.195581	+	0.980687i	$0.562659\pi$
$480$	0.520792	+	1.47919i	0.0237708	+	0.0675153i
$481$	−32.3487	−	2.54590i	−1.47497	−	0.116083i
$482$	16.2245	+	14.6192i	0.739004	+	0.665887i
$483$	−8.70825	−	8.70825i	−0.396239	−	0.396239i
$484$	−3.86138	+	2.50363i	−0.175517	+	0.113801i
$485$	−0.830327	−	1.35497i	−0.0377032	−	0.0615261i
$486$	−0.335454	+	12.6354i	−0.0152165	+	0.573155i
$487$	−17.8399	+	9.08986i	−0.808401	+	0.411901i	−0.808789	−	0.588099i	$-0.799876\pi$
$487$	−17.8399	+	9.08986i	−0.808401	+	0.411901i	0.000388037		1.00000i	$0.499876\pi$
$488$	11.0013	−	33.7336i	0.498004	−	1.52705i
$489$	−4.34942	−	1.80159i	−0.196688	−	0.0814707i
$490$	−4.89178	−	12.7574i	−0.220988	−	0.576319i
$491$	−21.4025			−0.965880			−0.482940	−	0.875653i	$-0.660431\pi$
$491$	−21.4025			−0.965880			−0.482940	+	0.875653i	$0.660431\pi$
$492$	−0.412191	−	4.46149i	−0.0185830	−	0.201140i
$493$	−25.4531			−1.14635
$494$	−10.5982	−	27.6391i	−0.476834	−	1.24354i
$495$	−6.21297	−	2.57349i	−0.279252	−	0.115670i
$496$	1.66220	−	0.350794i	0.0746352	−	0.0157511i
$497$	5.53606	−	2.82076i	0.248326	−	0.126529i
$498$	−0.0659124	+	2.48270i	−0.00295361	+	0.111252i
$499$	5.03879	+	8.22256i	0.225567	+	0.368092i	0.945323	−	0.326135i	$-0.105746\pi$
$499$	5.03879	+	8.22256i	0.225567	+	0.368092i	−0.719756	+	0.694227i	$0.755746\pi$
$500$	−8.08004	−	12.4619i	−0.361350	−	0.557315i
$501$	−0.0113910	−	0.0113910i	−0.000508911	−	0.000508911i
$502$	−27.5243	−	24.8011i	−1.22847	−	1.10693i
$503$	43.5925	+	3.43081i	1.94370	+	0.152972i	0.989332	−	0.145676i	$-0.0465358\pi$
$503$	43.5925	+	3.43081i	1.94370	+	0.152972i	0.954363	+	0.298649i	$0.0965358\pi$
$504$	−27.0887	−	23.1869i	−1.20663	−	1.03283i
$505$	2.99786	+	12.4870i	0.133403	+	0.555664i
$506$	20.4114	−	26.5806i	0.907395	−	1.18165i
$507$	−2.58807	+	0.203685i	−0.114940	+	0.00904598i
$508$	14.1681	+	31.8844i	0.628610	+	1.41464i
$509$	23.4359	−	20.0161i	1.03878	−	0.887199i	0.0450444	−	0.998985i	$-0.485657\pi$
$509$	23.4359	−	20.0161i	1.03878	−	0.887199i	0.993732	+	0.111786i	$0.0356571\pi$
$510$	0.580704	−	1.30301i	0.0257140	−	0.0576983i
$511$	12.5802	+	3.02025i	0.556517	+	0.133608i
$512$	−22.3603	+	3.46677i	−0.988193	+	0.153211i
$513$	−1.49006	−	9.40786i	−0.0657877	−	0.415367i
$514$	1.31213	+	4.43557i	0.0578755	+	0.195645i
$515$	−0.989561	+	0.718958i	−0.0436053	+	0.0316811i
$516$	−2.54720	+	0.470185i	−0.112134	+	0.0206988i
$517$	−13.5519	+	18.6526i	−0.596013	+	0.820341i
$518$	36.6739	−	25.1857i	1.61136	−	1.10660i
$519$	0.344967	+	0.832824i	0.0151424	+	0.0365569i
$520$	9.85006	−	2.35346i	0.431954	−	0.103206i
$521$	12.3344	+	10.5346i	0.540381	+	0.461529i	0.877258	−	0.480020i	$-0.159371\pi$
$521$	12.3344	+	10.5346i	0.540381	+	0.461529i	−0.336877	+	0.941549i	$0.609371\pi$
$522$	−12.2458	−	25.6979i	−0.535986	−	1.12477i
$523$	−4.94887	−	15.2311i	−0.216399	−	0.666008i	−0.999051	−	0.0435487i	$-0.986134\pi$
$523$	−4.94887	−	15.2311i	−0.216399	−	0.666008i	0.782652	−	0.622459i	$-0.213866\pi$
$524$	−16.1236	+	4.30779i	−0.704365	+	0.188187i
$525$	−5.97110	−	3.04243i	−0.260600	−	0.132782i
$526$	1.79808	+	0.977121i	0.0783999	+	0.0426045i
$527$	−1.31766	−	0.807460i	−0.0573980	−	0.0351735i
$528$	−2.25307	+	3.45844i	−0.0980524	+	0.150509i
$529$	12.8417	−	39.5226i	0.558333	−	1.71837i
$530$	−0.361984	−	2.75726i	−0.0157236	−	0.119768i
$531$	1.75970	−	11.1103i	0.0763644	−	0.482146i
$532$	35.1333	+	20.3182i	1.52322	+	0.880905i
$533$	−28.9328	−	0.343382i	−1.25322	−	0.0148735i
$534$	−2.67332	+	1.54215i	−0.115686	+	0.0667353i
$535$	−0.680184	−	0.107731i	−0.0294069	−	0.00465760i
$536$	17.1864	+	7.14074i	0.742339	+	0.308433i
$537$	−1.65457	−	0.537604i	−0.0714002	−	0.0231993i
$538$	10.5891	+	6.88209i	0.456528	+	0.296708i
$539$	18.7903	−	30.6630i	0.809355	−	1.32075i
$540$	3.25771	−	0.0829425i	0.140189	−	0.00356928i
$541$	6.52465	−	12.8054i	0.280517	−	0.550545i	−0.707160	−	0.707054i	$-0.750024\pi$
$541$	6.52465	−	12.8054i	0.280517	−	0.550545i	0.987677	+	0.156509i	$0.0500239\pi$
$542$	−14.9134	−	4.00182i	−0.640584	−	0.171893i
$543$	−0.668546	+	0.217224i	−0.0286901	+	0.00932197i
$544$	16.9424	+	11.6895i	0.726402	+	0.501183i
$545$	−5.84544	+	6.84413i	−0.250391	+	0.293170i
$546$	7.10775	−	6.74011i	0.304184	−	0.288450i
$547$	−14.4186	+	5.97236i	−0.616493	+	0.255360i	−0.669002	−	0.743261i	$-0.733278\pi$
$547$	−14.4186	+	5.97236i	−0.616493	+	0.255360i	0.0525089	+	0.998620i	$0.483278\pi$
$548$	21.4624	+	10.2562i	0.916830	+	0.438122i
$549$	−29.2046	−	21.2184i	−1.24642	−	0.905579i
$550$	6.09378	−	17.1885i	0.259840	−	0.732920i
$551$	19.0448	+	26.2129i	0.811336	+	1.11671i
$552$	−1.86452	+	7.72923i	−0.0793591	+	0.328978i
$553$	36.7104	−	5.81436i	1.56109	−	0.247252i
$554$	−34.9986	+	28.3203i	−1.48695	+	1.20321i
$555$	−0.464704	+	1.93563i	−0.0197256	+	0.0821631i
$556$	2.13433	+	20.4494i	0.0905158	+	0.867248i
$557$	−6.66607	−	7.80497i	−0.282451	−	0.330707i	0.600985	−	0.799261i	$-0.294775\pi$
$557$	−6.66607	−	7.80497i	−0.282451	−	0.330707i	−0.883435	+	0.468554i	$0.844775\pi$
$558$	0.181285	−	1.71881i	0.00767439	−	0.0727632i
$559$	1.31243	+	16.6761i	0.0555100	+	0.705322i
$560$	−8.46874	+	11.0036i	−0.357870	+	0.464987i
$561$	3.65106	−	0.876543i	0.154148	−	0.0370077i
$562$	1.98375	−	10.6818i	0.0836795	−	0.450583i
$563$	−1.29198	+	16.4162i	−0.0544506	+	0.691861i	0.907749	+	0.419515i	$0.137800\pi$
$563$	−1.29198	+	16.4162i	−0.0544506	+	0.691861i	−0.962199	+	0.272346i	$0.912200\pi$
$564$	1.14114	−	5.34956i	0.0480506	−	0.225257i
$565$	−0.890530	+	0.890530i	−0.0374649	+	0.0374649i
$566$	−10.3883	+	0.540652i	−0.436654	+	0.0227253i
$567$	−29.5595	+	18.1141i	−1.24138	+	0.760720i
$568$	−3.41797	−	2.09965i	−0.143415	−	0.0880995i
$569$	10.9819	+	21.5532i	0.460385	+	0.903556i	0.998170	+	0.0604738i	$0.0192611\pi$
$569$	10.9819	+	21.5532i	0.460385	+	0.903556i	−0.537785	+	0.843082i	$0.680739\pi$
$570$	−1.77641	+	0.376915i	−0.0744057	+	0.0157872i
$571$	−5.91140	+	14.2714i	−0.247384	+	0.597239i	−0.997980	−	0.0635226i	$-0.979767\pi$
$571$	−5.91140	+	14.2714i	−0.247384	+	0.597239i	0.750596	+	0.660761i	$0.229767\pi$
$572$	20.7034	+	16.7901i	0.865652	+	0.702031i
$573$		−	2.77196i		−	0.115800i
$574$	31.1336	−	24.5872i	1.29949	−	1.02625i
$575$		−	35.1291i		−	1.46499i
$576$	−3.65069	+	22.7294i	−0.152112	+	0.947060i
$577$	−12.8937	+	31.1282i	−0.536773	+	1.29588i	0.390191	+	0.920734i	$0.372409\pi$
$577$	−12.8937	+	31.1282i	−0.536773	+	1.29588i	−0.926964	+	0.375151i	$0.877591\pi$
$578$	1.10357	+	5.20117i	0.0459026	+	0.216340i
$579$	−1.31016	−	2.57134i	−0.0544485	−	0.106861i
$580$	−9.74562	+	5.28229i	−0.404665	+	0.219335i
$581$	−18.7498	+	11.4899i	−0.777873	+	0.476681i
$582$	0.0515761	+	0.991005i	0.00213790	+	0.0410785i
$583$	5.17576	−	5.17576i	0.214358	−	0.214358i
$584$	−2.57250	−	7.94674i	−0.106451	−	0.328839i
$585$	0.808391	−	10.2716i	0.0334229	−	0.424678i
$586$	28.4757	+	5.28834i	1.17632	+	0.218459i
$587$	−2.73564	+	0.656768i	−0.112912	+	0.0271077i	−0.289507	−	0.957176i	$-0.593492\pi$
$587$	−2.73564	+	0.656768i	−0.112912	+	0.0271077i	0.176596	+	0.984283i	$0.443492\pi$
$588$	−1.11977	+	8.45813i	−0.0461787	+	0.348807i
$589$	0.154347	+	1.96116i	0.00635975	+	0.0808083i
$590$	−4.35621	−	0.459453i	−0.179342	−	0.0189154i
$591$	−1.43953	−	1.68548i	−0.0592145	−	0.0693313i
$592$	−26.2227	−	11.7207i	−1.07775	−	0.481717i
$593$	−9.04729	+	37.6847i	−0.371528	+	1.54752i	0.403129	+	0.915143i	$0.367923\pi$
$593$	−9.04729	+	37.6847i	−0.371528	+	1.54752i	−0.774657	+	0.632382i	$0.782077\pi$
$594$	5.39548	+	6.66780i	0.221379	+	0.273583i
$595$	12.4756	−	1.97594i	0.511450	−	0.0810057i
$596$	−10.1003	+	10.6281i	−0.413725	+	0.435343i
$597$	3.56251	+	4.90338i	0.145804	+	0.200682i
$598$	48.3955	+	17.1575i	1.97904	+	0.701622i
$599$	0.135318	+	0.0983142i	0.00552894	+	0.00401701i	0.590546	−	0.807004i	$-0.298912\pi$
$599$	0.135318	+	0.0983142i	0.00552894	+	0.00401701i	−0.585017	+	0.811021i	$0.698912\pi$
$600$	0.334769	+	4.31362i	0.0136669	+	0.176103i
$601$	21.1471	−	8.75944i	0.862610	−	0.357305i	0.0928824	−	0.995677i	$-0.470392\pi$
$601$	21.1471	−	8.75944i	0.862610	−	0.357305i	0.769728	+	0.638372i	$0.220392\pi$
$602$	−15.7811	−	16.6419i	−0.643191	−	0.678275i
$603$	12.2969	−	14.3978i	0.500766	−	0.586322i
$604$	22.5665	+	15.5337i	0.918220	+	0.632056i
$605$	1.73398	−	0.563403i	0.0704961	−	0.0229056i
$606$	2.07830	−	7.74510i	0.0844253	−	0.314623i
$607$	−4.16571	+	8.17566i	−0.169081	+	0.331840i	−0.959962	−	0.280130i	$-0.909622\pi$
$607$	−4.16571	+	8.17566i	−0.169081	+	0.331840i	0.790881	+	0.611969i	$0.209622\pi$
$608$	−0.638421	−	26.1947i	−0.0258914	−	1.06234i
$609$	−5.60211	+	9.14181i	−0.227009	+	0.370445i
$610$	−7.66038	+	11.7866i	−0.310160	+	0.477225i
$611$	−33.5957	−	10.9159i	−1.35913	−	0.441610i
$612$	16.6233	−	12.7364i	0.671957	−	0.514837i
$613$	−2.70083	−	0.427770i	−0.109086	−	0.0172774i	0.101653	−	0.994820i	$-0.467587\pi$
$613$	−2.70083	−	0.427770i	−0.109086	−	0.0172774i	−0.210739	+	0.977542i	$0.567587\pi$
$614$	−21.6871	−	37.5946i	−0.875220	−	1.51720i
$615$	−0.298469	+	1.74980i	−0.0120354	+	0.0705586i
$616$	−36.5470	−	0.0397476i	−1.47252	−	0.00160148i
$617$	3.72748	−	23.5344i	0.150063	−	0.947459i	−0.791634	−	0.610996i	$-0.790769\pi$
$617$	3.72748	−	23.5344i	0.150063	−	0.947459i	0.941697	−	0.336463i	$-0.109231\pi$
$618$	0.757309	−	0.0994224i	0.0304634	−	0.00399935i
$619$	1.33096	−	4.09627i	0.0534957	−	0.164643i	−0.920739	−	0.390179i	$-0.872413\pi$
$619$	1.33096	−	4.09627i	0.0534957	−	0.164643i	0.974235	+	0.225536i	$0.0724132\pi$
$620$	−0.672085	−	0.0357111i	−0.0269916	−	0.00143419i
$621$	14.0877	+	8.63293i	0.565318	+	0.346428i
$622$	5.88827	−	10.8355i	0.236098	−	0.434463i
$623$	−24.3480	−	12.4059i	−0.975482	−	0.497033i
$624$	−6.10615	−	1.64563i	−0.244442	−	0.0658780i
$625$	−4.93709	−	15.1948i	−0.197484	−	0.607793i
$626$	−34.8361	+	16.6005i	−1.39233	+	0.663489i
$627$	−3.63456	−	3.10420i	−0.145150	−	0.123970i
$628$	−11.2958	−	3.35489i	−0.450753	−	0.133875i
$629$	9.99902	+	24.1398i	0.398687	+	0.962516i
$630$	7.99715	+	11.6450i	0.318614	+	0.463947i
$631$	14.0857	−	19.3873i	0.560743	−	0.771796i	−0.430678	−	0.902506i	$-0.641726\pi$
$631$	14.0857	−	19.3873i	0.560743	−	0.771796i	0.991421	+	0.130710i	$0.0417256\pi$
$632$	−15.5644	−	18.2638i	−0.619119	−	0.726493i
$633$	6.31726	−	4.58976i	0.251089	−	0.182427i
$634$	−7.80824	+	2.30983i	−0.310105	+	0.0917349i
$635$	−2.16237	−	13.6527i	−0.0858110	−	0.541789i
$636$	−0.623500	+	1.62076i	−0.0247234	+	0.0642673i
$637$	53.5765	+	12.8626i	2.12278	+	0.509634i
$638$	−26.6502	−	11.8770i	−1.05509	−	0.470215i
$639$	−3.10329	+	2.65046i	−0.122764	+	0.104851i
$640$	8.91296	+	0.959664i	0.352316	+	0.0379340i
$641$	24.8579	−	1.95636i	0.981829	−	0.0772716i	0.422628	−	0.906303i	$-0.361108\pi$
$641$	24.8579	−	1.95636i	0.981829	−	0.0772716i	0.559201	+	0.829032i	$0.311108\pi$
$642$	0.341076	+	0.261913i	0.0134612	+	0.0103369i
$643$	−3.22559	−	13.4356i	−0.127205	−	0.529846i	−0.999187	−	0.0403092i	$-0.987166\pi$
$643$	−3.22559	−	13.4356i	−0.127205	−	0.529846i	0.871982	−	0.489537i	$-0.162834\pi$
$644$	−66.3789	+	23.4519i	−2.61570	+	0.924133i
$645$	1.02303	+	0.0805140i	0.0402817	+	0.00317024i
$646$	−15.9558	+	17.7078i	−0.627772	+	0.696703i
$647$	12.1590	+	12.1590i	0.478021	+	0.478021i	0.904498	−	0.426478i	$-0.140246\pi$
$647$	12.1590	+	12.1590i	0.478021	+	0.478021i	−0.426478	+	0.904498i	$0.640246\pi$
$648$	19.9317	+	10.1830i	0.782990	+	0.400026i
$649$	−6.02416	−	9.83053i	−0.236469	−	0.385882i
$650$	27.9312	+	0.741536i	1.09555	+	0.0290854i
$651$	−0.580021	+	0.295535i	−0.0227328	+	0.0115829i
$652$	−20.0124	+	17.9930i	−0.783746	+	0.704660i
$653$	−0.343848	−	0.142426i	−0.0134558	−	0.00557357i	0.375945	−	0.926642i	$-0.377318\pi$
$653$	−0.343848	−	0.142426i	−0.0134558	−	0.00557357i	−0.389401	+	0.921068i	$0.627318\pi$
$654$	5.24788	−	2.01229i	0.205208	−	0.0786867i
$655$	6.61188			0.258348
$656$	−24.0274	−	8.87040i	−0.938112	−	0.346331i
$657$	−8.49795			−0.331536
$658$	45.2217	−	17.3402i	1.76293	−	0.675991i
$659$	6.27264	+	2.59821i	0.244347	+	0.101212i	0.501496	−	0.865160i	$-0.332783\pi$
$659$	6.27264	+	2.59821i	0.244347	+	0.101212i	−0.257149	+	0.966372i	$0.582783\pi$
$660$	1.21603	−	1.09332i	0.0473340	−	0.0425576i
$661$	29.8801	−	15.2247i	1.16220	−	0.592171i	0.236949	−	0.971522i	$-0.423853\pi$
$661$	29.8801	−	15.2247i	1.16220	−	0.592171i	0.925253	+	0.379351i	$0.123853\pi$
$662$	−31.0142	−	0.823388i	−1.20540	−	0.0320019i
$663$	3.00585	+	4.90511i	0.116738	+	0.190499i
$664$	12.6428	+	6.45916i	0.490636	+	0.250664i
$665$	−11.3696	−	11.3696i	−0.440894	−	0.440894i
$666$	−19.5613	+	21.7092i	−0.757986	+	0.841215i
$667$	−56.0298	−	4.40964i	−2.16948	−	0.170742i
$668$	−0.0868281	+	0.0306766i	−0.00335948	+	0.00118691i
$669$	1.08435	+	4.51663i	0.0419232	+	0.174623i
$670$	−5.84791	−	4.49063i	−0.225924	−	0.173488i
$671$	−36.8857	+	2.90297i	−1.42396	+	0.112068i
$672$	7.92740	−	3.51230i	0.305806	−	0.135490i
$673$	−14.6744	+	12.5331i	−0.565655	+	0.483115i	−0.885681	−	0.464294i	$-0.846308\pi$
$673$	−14.6744	+	12.5331i	−0.565655	+	0.483115i	0.320026	+	0.947409i	$0.396308\pi$
$674$	24.6695	+	10.9943i	0.950232	+	0.423483i
$675$	8.74243	+	2.09887i	0.336496	+	0.0807856i
$676$	−5.32833	+	13.8507i	−0.204936	+	0.532721i
$677$	0.883366	+	5.57736i	0.0339505	+	0.214355i	0.998831	−	0.0483331i	$-0.0153909\pi$
$677$	0.883366	+	5.57736i	0.0339505	+	0.214355i	−0.964881	+	0.262688i	$0.915391\pi$
$678$	0.754129	−	0.223086i	0.0289622	−	0.00856757i
$679$	−7.10845	+	5.16459i	−0.272797	+	0.198199i
$680$	−5.28938	−	6.20673i	−0.202839	−	0.238017i
$681$	−0.785580	+	1.08126i	−0.0301035	+	0.0414339i
$682$	−1.00285	−	1.46029i	−0.0384010	−	0.0559173i
$683$	−11.3178	−	27.3236i	−0.433064	−	1.04551i	−0.978294	−	0.207222i	$-0.933558\pi$
$683$	−11.3178	−	27.3236i	−0.433064	−	1.04551i	0.545230	−	0.838287i	$-0.316442\pi$
$684$	−25.5547	−	7.58980i	−0.977108	−	0.290203i
$685$	−7.16599	−	6.12034i	−0.273798	−	0.233846i
$686$	−29.0454	+	13.8410i	−1.10896	+	0.528452i
$687$	−0.961330	−	2.95867i	−0.0366770	−	0.112880i
$688$	−3.85305	+	14.2968i	−0.146896	+	0.545061i
$689$	9.99228	+	5.09132i	0.380676	+	0.193964i
$690$	1.50405	−	2.76771i	0.0572580	−	0.105365i
$691$	38.4016	+	23.5325i	1.46087	+	0.895220i	0.999970	+	0.00776607i	$0.00247204\pi$
$691$	38.4016	+	23.5325i	1.46087	+	0.895220i	0.460896	+	0.887454i	$0.347528\pi$
$692$	5.14579	+	0.273421i	0.195614	+	0.0103939i
$693$	−11.4900	+	35.3625i	−0.436468	+	1.34331i
$694$	16.3493	−	2.14640i	0.620612	−	0.0814763i
$695$	1.27425	−	8.04532i	0.0483352	−	0.305176i
$696$	6.92211	+	0.00752832i	0.262382	+	0.000285360i
$697$	10.3305	+	20.8838i	0.391296	+	0.791031i
$698$	7.00765	+	12.1478i	0.265243	+	0.459800i
$699$	5.09118	+	0.806364i	0.192566	+	0.0304995i
$700$	−30.4094	+	23.2989i	−1.14937	+	0.880618i
$701$	−26.6916	−	8.67264i	−1.00813	−	0.327561i	−0.242020	−	0.970271i	$-0.577810\pi$
$701$	−26.6916	−	8.67264i	−1.00813	−	0.327561i	−0.766109	+	0.642710i	$0.777810\pi$
$702$	−7.16141	+	11.0189i	−0.270290	+	0.415880i
$703$	17.3788	−	28.3597i	0.655456	−	1.06961i
$704$	12.2847	+	20.1450i	0.462997	+	0.759244i
$705$	−0.983824	+	1.93086i	−0.0370530	+	0.0727205i
$706$	−7.09159	+	26.4279i	−0.266896	+	0.994626i
$707$	67.5283	−	21.9413i	2.53966	−	0.825186i
$708$	2.25314	+	1.55094i	0.0846780	+	0.0582880i
$709$	−2.43790	+	2.85441i	−0.0915571	+	0.107200i	−0.804293	−	0.594233i	$-0.797456\pi$
$709$	−2.43790	+	2.85441i	−0.0915571	+	0.107200i	0.712736	+	0.701432i	$0.247456\pi$
$710$	1.09352	+	1.15317i	0.0410392	+	0.0432778i
$711$	−22.5549	+	9.34256i	−0.845876	+	0.350373i
$712$	1.36507	+	17.5894i	0.0511581	+	0.659191i
$713$	−2.76067	−	2.00574i	−0.103388	−	0.0751157i
$714$	−7.43415	−	2.63560i	−0.278216	−	0.0986350i
$715$	−6.20730	−	8.54361i	−0.232140	−	0.319513i
$716$	−6.85094	+	7.20891i	−0.256032	+	0.269410i
$717$	−9.94861	+	1.57570i	−0.371537	+	0.0588458i
$718$	−26.1600	−	32.3289i	−0.976283	−	1.20650i
$719$	11.6256	−	48.4243i	0.433563	−	1.80592i	−0.144003	−	0.989577i	$-0.545997\pi$
$719$	11.6256	−	48.4243i	0.433563	−	1.80592i	0.577566	−	0.816344i	$-0.304003\pi$
$720$	3.72164	−	8.32642i	0.138697	−	0.310307i
$721$	4.39220	+	5.14261i	0.163574	+	0.191521i
$722$	3.45322	+	0.364214i	0.128515	+	0.0135546i
$723$	0.423907	+	5.38625i	0.0157653	+	0.200317i
$724$	−0.527393	+	3.98362i	−0.0196004	+	0.148050i
$725$	−29.7385	+	7.13959i	−1.10446	+	0.265158i
$726$	−1.11937	−	0.207882i	−0.0415436	−	0.00771523i
$727$	0.626741	−	7.96350i	0.0232445	−	0.295350i	−0.974297	−	0.225268i	$-0.927674\pi$
$727$	0.626741	−	7.96350i	0.0232445	−	0.295350i	0.997541	−	0.0700815i	$-0.0223259\pi$
$728$	−17.2454	−	53.2729i	−0.639156	−	1.97443i
$729$	14.5755	−	14.5755i	0.539835	−	0.539835i
$730$	0.171991	+	3.30470i	0.00636566	+	0.122312i
$731$	11.4847	−	7.03784i	0.424777	−	0.260304i
$732$	7.71734	−	4.18293i	0.285241	−	0.154606i
$733$	−13.6264	−	26.7432i	−0.503301	−	0.987784i	−0.993246	−	0.116031i	$-0.962983\pi$
$733$	−13.6264	−	26.7432i	−0.503301	−	0.987784i	0.489944	−	0.871754i	$-0.337017\pi$
$734$	6.63487	+	31.2703i	0.244897	+	1.15421i
$735$	1.29353	−	3.12286i	0.0477126	−	0.115188i
$736$	35.2703	+	28.6673i	1.30008	+	1.05669i
$737$		−	19.4068i		−	0.714860i
$738$	−16.1146	+	20.4774i	−0.593186	+	0.753784i
$739$			36.2334i			1.33287i	0.745564	+	0.666434i	$0.232180\pi$
$739$			36.2334i			1.33287i	−0.745564	+	0.666434i	$0.767820\pi$
$740$	8.83823	+	7.16767i	0.324900	+	0.263489i
$741$	2.80247	−	6.76575i	0.102951	−	0.248546i
$742$	−15.0411	+	3.19139i	−0.552176	+	0.117159i
$743$	3.72148	+	7.30381i	0.136528	+	0.267951i	0.949140	−	0.314853i	$-0.101955\pi$
$743$	3.72148	+	7.30381i	0.136528	+	0.267951i	−0.812612	+	0.582804i	$0.801955\pi$
$744$	0.358106	+	0.219984i	0.0131288	+	0.00806499i
$745$	4.95275	−	3.03505i	0.181455	−	0.111196i
$746$	24.5180	−	1.27602i	0.897668	−	0.0467185i
$747$	10.2135	−	10.2135i	0.373691	−	0.373691i
$748$	4.47787	−	20.9919i	0.163727	−	0.767540i
$749$	−0.298746	+	3.79593i	−0.0109160	+	0.138700i
$750$	0.670904	−	3.61256i	0.0244979	−	0.131912i
$751$	−17.4094	+	4.17963i	−0.635278	+	0.152517i	−0.538278	−	0.842768i	$-0.680925\pi$
$751$	−17.4094	+	4.17963i	−0.635278	+	0.152517i	−0.0970005	+	0.995284i	$0.530925\pi$
$752$	−24.7794	−	19.0710i	−0.903610	−	0.695449i
$753$	−0.719146	−	9.13762i	−0.0262072	−	0.332993i
$754$	4.68883	−	44.4562i	0.170757	−	1.61900i
$755$	−7.04891	−	8.25321i	−0.256536	−	0.300365i
$756$	−1.87040	−	17.9206i	−0.0680257	−	0.651766i
$757$	5.31897	−	22.1551i	0.193321	−	0.805240i	−0.788438	−	0.615114i	$-0.789110\pi$
$757$	5.31897	−	22.1551i	0.193321	−	0.805240i	0.981760	−	0.190127i	$-0.0608899\pi$
$758$	−30.4801	+	24.6640i	−1.10709	+	0.895837i
$759$	8.18895	−	1.29700i	0.297240	−	0.0470782i
$760$	−2.43433	+	10.0914i	−0.0883026	+	0.366053i
$761$	17.9378	+	24.6893i	0.650246	+	0.894986i	0.999110	−	0.0421869i	$-0.0134325\pi$
$761$	17.9378	+	24.6893i	0.650246	+	0.894986i	−0.348864	+	0.937173i	$0.613433\pi$
$762$	−2.88427	+	8.13555i	−0.104486	+	0.294720i
$763$	40.2609	+	29.2512i	1.45754	+	1.05897i
$764$	−14.2972	−	6.83215i	−0.517255	−	0.247178i
$765$	−7.66503	+	3.17496i	−0.277130	+	0.114791i
$766$	26.6806	−	25.3006i	0.964010	−	0.914147i
$767$	11.4723	−	13.4323i	0.414241	−	0.485013i
$768$	−4.60414	−	3.18404i	−0.166138	−	0.114894i
$769$	−1.57203	+	0.510784i	−0.0566889	+	0.0184194i	−0.337224	−	0.941424i	$-0.609488\pi$
$769$	−1.57203	+	0.510784i	−0.0566889	+	0.0184194i	0.280535	+	0.959844i	$0.409488\pi$
$770$	13.9844	+	3.75254i	0.503962	+	0.135232i
$771$	−0.519519	+	1.01961i	−0.0187100	+	0.0367205i
$772$	−16.4917	+	0.419884i	−0.593548	+	0.0151120i
$773$	−23.9501	+	39.0830i	−0.861426	+	1.40572i	0.0519713	+	0.998649i	$0.483450\pi$
$773$	−23.9501	+	39.0830i	−0.861426	+	1.40572i	−0.913397	+	0.407070i	$0.866550\pi$
$774$	12.6310	+	8.20919i	0.454012	+	0.295073i
$775$	−1.76600	−	0.573808i	−0.0634365	−	0.0206118i
$776$	5.23852	+	2.17655i	0.188052	+	0.0781334i
$777$	10.8709	+	1.72178i	0.389990	+	0.0617684i
$778$	−8.08479	+	4.66385i	−0.289854	+	0.167207i
$779$	13.7777	−	26.2649i	0.493636	−	0.941038i
$780$	2.16886	+	1.25429i	0.0776576	+	0.0449108i
$781$	−0.654357	+	4.13145i	−0.0234147	+	0.147835i
$782$	−5.38189	−	40.9943i	−0.192456	−	1.46595i
$783$	4.44504	−	13.6804i	0.158853	−	0.488899i
$784$	40.8654	+	26.6226i	1.45948	+	0.950808i
$785$	3.98043	+	2.43921i	0.142068	+	0.0870591i
$786$	−3.62775	−	1.97141i	−0.129397	−	0.0703178i
$787$	−11.2127	−	5.71314i	−0.399688	−	0.203651i	0.242580	−	0.970131i	$-0.422006\pi$
$787$	−11.2127	−	5.71314i	−0.399688	−	0.203651i	−0.642268	+	0.766480i	$0.722006\pi$
$788$	−12.2414	+	3.27057i	−0.436083	+	0.116509i
$789$	0.156447	+	0.481493i	0.00556965	+	0.0171416i
$790$	4.08964	+	8.58212i	0.145503	+	0.305338i
$791$	5.29495	+	4.52231i	0.188267	+	0.160795i
$792$	23.3482	−	5.57856i	0.829643	−	0.198225i
$793$	−21.6937	−	52.3732i	−0.770366	−	1.85983i
$794$	14.2303	−	9.77263i	0.505015	−	0.346818i
$795$	0.404386	−	0.556590i	0.0143421	−	0.0197402i
$796$	34.0713	−	6.28919i	1.20763	−	0.222915i
$797$	21.1237	−	15.3473i	0.748241	−	0.543629i	−0.147040	−	0.989131i	$-0.546975\pi$
$797$	21.1237	−	15.3473i	0.748241	−	0.543629i	0.895281	+	0.445502i	$0.146975\pi$
$798$	2.84819	+	9.62814i	0.100825	+	0.340832i
$799$	4.44969	+	28.0942i	0.157419	+	0.993902i
$800$	23.0739	+	8.90526i	0.815786	+	0.314849i
$801$	17.4530	+	4.19010i	0.616673	+	0.148050i
$802$	7.79358	−	17.4876i	0.275201	−	0.617509i
$803$	−6.62315	+	5.65671i	−0.233726	+	0.199621i
$804$	1.86965	+	4.20750i	0.0659373	+	0.148387i
$805$	27.8049	−	2.18829i	0.979994	−	0.0771272i
$806$	1.65304	−	2.15267i	0.0582258	−	0.0758244i
$807$	0.729362	+	3.03801i	0.0256748	+	0.106943i
$808$	−34.8252	−	29.8091i	−1.22515	−	1.04868i
$809$	32.6829	+	2.57220i	1.14907	+	0.0904337i	0.638654	−	0.769494i	$-0.279492\pi$
$809$	32.6829	+	2.57220i	1.14907	+	0.0904337i	0.510415	+	0.859928i	$0.329492\pi$
$810$	−6.58757	−	5.93580i	−0.231463	−	0.208563i
$811$	−29.7404	−	29.7404i	−1.04433	−	1.04433i	−0.998971	−	0.0453568i	$-0.985558\pi$
$811$	−29.7404	−	29.7404i	−1.04433	−	1.04433i	−0.0453568	−	0.998971i	$-0.514442\pi$
$812$	33.3439	+	51.4267i	1.17014	+	1.80472i
$813$	−1.99594	−	3.25708i	−0.0700008	−	0.114231i
$814$	−0.794892	+	29.9409i	−0.0278609	+	1.04943i
$815$	9.49977	−	4.84037i	0.332762	−	0.169551i
$816$	1.05152	+	4.98254i	0.0368107	+	0.174424i
$817$	−15.8412	−	6.56164i	−0.554213	−	0.229563i
$818$	−20.2052	−	52.6934i	−0.706458	−	1.84238i
$819$	−56.9680			−1.99062
$820$	8.28945	+	5.85222i	0.289480	+	0.204369i
$821$	3.69779			0.129054			0.0645269	−	0.997916i	$-0.479446\pi$
$821$	3.69779			0.129054			0.0645269	+	0.997916i	$0.479446\pi$
$822$	2.10692	+	5.49467i	0.0734874	+	0.191649i
$823$	26.4320	+	10.9485i	0.921361	+	0.381640i	0.792395	−	0.610009i	$-0.208834\pi$
$823$	26.4320	+	10.9485i	0.921361	+	0.381640i	0.128966	+	0.991649i	$0.458834\pi$
$824$	1.35377	−	4.15110i	0.0471607	−	0.144610i
$825$	4.01991	−	2.04825i	0.139955	−	0.0713108i
$826$	−0.642768	+	24.2109i	−0.0223648	+	0.842405i
$827$	22.2130	+	36.2484i	0.772423	+	1.26048i	0.960487	+	0.278324i	$0.0897788\pi$
$827$	22.2130	+	36.2484i	0.772423	+	1.26048i	−0.188064	+	0.982157i	$0.560221\pi$
$828$	38.7994	−	25.1566i	1.34837	−	0.874254i
$829$	11.3356	+	11.3356i	0.393703	+	0.393703i	0.876005	−	0.482302i	$-0.160199\pi$
$829$	11.3356	+	11.3356i	0.393703	+	0.393703i	−0.482302	+	0.876005i	$0.660199\pi$
$830$	−4.17854	−	3.76512i	−0.145039	−	0.130689i
$831$	−11.1037	−	0.873881i	−0.385183	−	0.0303146i
$832$	−23.5379	+	27.4382i	−0.816029	+	0.951250i
$833$	−10.3573	−	43.1415i	−0.358861	−	1.49476i
$834$	−3.09795	+	4.03430i	−0.107273	+	0.139696i
$835$	0.0363707	−	0.00286243i	0.00125866	−	9.90586e-5i
$836$	−24.9691	+	11.0953i	−0.863574	+	0.383738i
$837$	0.664103	−	0.567197i	0.0229547	−	0.0196052i
$838$	10.4443	−	23.4355i	0.360794	−	0.809566i
$839$	−45.2802	−	10.8708i	−1.56325	−	0.375302i	−0.642757	−	0.766070i	$-0.722209\pi$
$839$	−45.2802	−	10.8708i	−1.56325	−	0.375302i	−0.920489	+	0.390768i	$0.872209\pi$
$840$	−3.39340	+	0.533679i	−0.117083	+	0.0184137i
$841$	3.11784	+	19.6852i	0.107512	+	0.678801i
$842$	8.27412	+	27.9702i	0.285145	+	0.963917i
$843$	2.17446	−	1.57984i	0.0748925	−	0.0544126i
$844$	−8.10267	−	43.8957i	−0.278905	−	1.51095i
$845$	3.45582	−	4.75652i	0.118884	−	0.163629i
$846$	−26.2237	+	18.0090i	−0.901588	+	0.619163i
$847$	−3.85770	−	9.31332i	−0.132552	−	0.320010i
$848$	6.82279	+	7.21063i	0.234296	+	0.247614i
$849$	−1.95689	−	1.67134i	−0.0671603	−	0.0573603i
$850$	−9.67868	−	20.3107i	−0.331976	−	0.696652i
$851$	17.8287	+	54.8712i	0.611161	+	1.88096i
$852$	−0.256154	−	0.958759i	−0.00877568	−	0.0328465i
$853$	40.6461	+	20.7102i	1.39170	+	0.709104i	0.979397	−	0.201945i	$-0.0647261\pi$
$853$	40.6461	+	20.7102i	1.39170	+	0.709104i	0.412298	+	0.911049i	$0.364726\pi$
$854$	68.2913	+	37.1112i	2.33688	+	1.26992i
$855$	9.00497	+	5.51826i	0.307964	+	0.188720i
$856$	2.19156	−	1.11365i	0.0749059	−	0.0380639i
$857$	−2.45010	+	7.54062i	−0.0836937	+	0.257583i	−0.984143	−	0.177379i	$-0.943238\pi$
$857$	−2.45010	+	7.54062i	−0.0836937	+	0.257583i	0.900449	+	0.434962i	$0.143238\pi$
$858$	0.858386	+	6.53841i	0.0293048	+	0.223218i
$859$	−5.08378	+	32.0977i	−0.173456	+	1.09516i	0.735272	+	0.677773i	$0.237055\pi$
$859$	−5.08378	+	32.0977i	−0.173456	+	1.09516i	−0.908728	+	0.417389i	$0.862945\pi$
$860$	2.93677	−	5.07812i	0.100143	−	0.173163i
$861$	9.77441	+	0.886096i	0.333111	+	0.0301981i
$862$	7.32697	−	4.22669i	0.249557	−	0.143961i
$863$	−3.62073	−	0.573467i	−0.123251	−	0.0195210i	0.0945042	−	0.995524i	$-0.469873\pi$
$863$	−3.62073	−	0.573467i	−0.123251	−	0.0195210i	−0.217755	+	0.976003i	$0.569873\pi$
$864$	−9.24161	+	7.06476i	−0.314406	+	0.240348i
$865$	−1.94160	−	0.630865i	−0.0660164	−	0.0214500i
$866$	−47.2837	−	30.7308i	−1.60677	−	1.04427i
$867$	−0.687286	+	1.12155i	−0.0233414	+	0.0380898i
$868$	0.0947138	+	3.72005i	0.00321480	+	0.126267i
$869$	−11.3600	+	22.2952i	−0.385361	+	0.756314i
$870$	−2.64868	−	0.710742i	−0.0897988	−	0.0240964i
$871$	28.2785	−	9.18823i	0.958179	−	0.311331i
$872$	2.55565	−	32.0272i	0.0865452	−	1.08458i
$873$	3.74816	−	4.38853i	0.126856	−	0.148529i
$874$	−38.1913	+	36.2159i	−1.29184	+	1.22502i
$875$	30.0572	−	12.4501i	1.01612	−	0.420890i
$876$	0.890968	−	1.86447i	0.0301030	−	0.0629947i
$877$	24.1992	+	17.5818i	0.817149	+	0.593694i	0.915894	−	0.401419i	$-0.131483\pi$
$877$	24.1992	+	17.5818i	0.817149	+	0.593694i	−0.0987454	+	0.995113i	$0.531483\pi$
$878$	8.20933	−	23.1558i	0.277052	−	0.781469i
$879$	4.21158	+	5.79675i	0.142053	+	0.195519i
$880$	−2.64195	−	8.96680i	−0.0890601	−	0.302271i
$881$	−39.6855	+	6.28556i	−1.33704	+	0.211766i	−0.783673	−	0.621173i	$-0.786656\pi$
$881$	−39.6855	+	6.28556i	−1.33704	+	0.211766i	−0.553364	+	0.832939i	$0.686656\pi$
$882$	38.5734	−	31.2130i	1.29883	−	1.05100i
$883$	2.80040	−	11.6645i	0.0942408	−	0.392541i	−0.905235	−	0.424911i	$-0.860305\pi$
$883$	2.80040	−	11.6645i	0.0942408	−	0.392541i	0.999476	+	0.0323697i	$0.0103054\pi$
$884$	32.7082	−	3.41379i	1.10010	−	0.114818i
$885$	−0.703792	−	0.824034i	−0.0236577	−	0.0276996i
$886$	5.16470	−	48.9680i	0.173511	−	1.64511i
$887$	0.739603	+	9.39754i	0.0248334	+	0.315539i	0.996771	+	0.0802990i	$0.0255875\pi$
$887$	0.739603	+	9.39754i	0.0248334	+	0.315539i	−0.971937	+	0.235240i	$0.924412\pi$
$888$	−2.71215	−	6.56792i	−0.0910140	−	0.220405i
$889$	−74.3159	+	17.8417i	−2.49247	+	0.598390i
$890$	1.27622	−	6.87198i	0.0427791	−	0.230349i
$891$	1.83120	−	23.2676i	0.0613476	−	0.779495i
$892$	25.9685	+	5.53945i	0.869489	+	0.185475i
$893$	25.6035	−	25.6035i	0.856790	−	0.856790i
$894$	−3.62237	+	0.188524i	−0.121150	+	0.00630517i
$895$	3.35940	−	2.05864i	0.112292	−	0.0688129i
$896$	1.42320	−	49.5448i	0.0475458	−	1.65518i
$897$	5.76700	+	11.3184i	0.192554	+	0.377909i
$898$	23.1073	−	4.90286i	0.771101	−	0.163610i
$899$	−1.13689	+	2.74468i	−0.0379172	+	0.0915403i
$900$	15.8496	−	19.5436i	0.528319	−	0.651453i
$901$		−	9.03034i		−	0.300844i
$902$	1.07150	+	26.6865i	0.0356769	+	0.888564i
$903$		−	5.67389i		−	0.188815i
$904$	0.708097	−	4.43949i	0.0235510	−	0.147655i
$905$	0.609229	−	1.47081i	0.0202515	−	0.0488914i
$906$	1.40674	+	6.63001i	0.0467358	+	0.220267i
$907$	6.54641	+	12.8480i	0.217370	+	0.426612i	0.973782	−	0.227483i	$-0.0730496\pi$
$907$	6.54641	+	12.8480i	0.217370	+	0.426612i	−0.756412	+	0.654095i	$0.773050\pi$
$908$	3.64066	+	6.71688i	0.120820	+	0.222907i
$909$	−39.7651	+	24.3681i	−1.31892	+	0.808238i
$910$	1.15298	+	22.1538i	0.0382209	+	0.734393i
$911$	18.4932	−	18.4932i	0.612708	−	0.612708i	−0.330943	−	0.943651i	$-0.607367\pi$
$911$	18.4932	−	18.4932i	0.612708	−	0.612708i	0.943651	+	0.330943i	$0.107367\pi$
$912$	4.34451	−	4.81102i	0.143861	−	0.159309i
$913$	1.16155	−	14.7588i	0.0384415	−	0.488446i
$914$	−12.9362	−	2.40243i	−0.427890	−	0.0794652i
$915$	−3.38158	+	0.811845i	−0.111792	+	0.0268388i
$916$	−17.6296	−	2.33399i	−0.582500	−	0.0771172i
$917$	−2.86828	−	36.4449i	−0.0947188	−	1.20352i
$918$	10.5236	+	1.10994i	0.347331	+	0.0366333i
$919$	−15.0766	−	17.6524i	−0.497330	−	0.582299i	0.453794	−	0.891106i	$-0.350070\pi$
$919$	−15.0766	−	17.6524i	−0.497330	−	0.582299i	−0.951125	+	0.308808i	$0.900070\pi$
$920$	−10.5682	−	14.5792i	−0.348424	−	0.480663i
$921$	2.50656	−	10.4406i	0.0825940	−	0.344029i
$922$	9.58971	+	11.8511i	0.315820	+	0.390295i
$923$	−6.32990	+	1.00256i	−0.208351	+	0.0329996i
$924$	−6.55396	−	6.22851i	−0.215610	−	0.204903i
$925$	18.4537	+	25.3994i	0.606755	+	0.835127i
$926$	7.16953	+	2.54179i	0.235605	+	0.0835284i
$927$	−3.59379	−	2.61104i	−0.118035	−	0.0857578i
$928$	17.1000	−	35.6843i	0.561335	−	1.17139i
$929$	20.7739	−	8.60482i	0.681568	−	0.282315i	−0.0149140	−	0.999889i	$-0.504747\pi$
$929$	20.7739	−	8.60482i	0.681568	−	0.282315i	0.696482	+	0.717574i	$0.254747\pi$
$930$	−0.114570	−	0.120819i	−0.00375690	−	0.00396182i
$931$	−36.6797	+	42.9464i	−1.20213	+	1.40751i
$932$	16.7075	−	24.2718i	0.547272	−	0.795050i
$933$	2.90155	−	0.942770i	0.0949924	−	0.0308649i
$934$	−5.82325	+	21.7012i	−0.190542	+	0.710084i
$935$	−3.86056	+	7.57678i	−0.126254	+	0.247787i
$936$	19.1830	+	31.3804i	0.627017	+	1.02570i
$937$	−9.18474	+	14.9881i	−0.300052	+	0.489641i	−0.966762	−	0.255676i	$-0.917702\pi$
$937$	−9.18474	+	14.9881i	−0.300052	+	0.489641i	0.666710	+	0.745317i	$0.267702\pi$
$938$	−22.2156	+	34.1819i	−0.725366	+	1.11608i
$939$	−9.07949	−	2.95011i	−0.296298	−	0.0962731i
$940$	7.53414	+	9.83343i	0.245736	+	0.320731i
$941$	−52.3912	−	8.29795i	−1.70790	−	0.270505i	−0.775349	−	0.631533i	$-0.782426\pi$
$941$	−52.3912	−	8.29795i	−1.70790	−	0.270505i	−0.932555	+	0.361028i	$0.882426\pi$
$942$	−1.45667	−	2.52513i	−0.0474608	−	0.0822733i
$943$	19.1225	+	47.7613i	0.622716	+	1.55532i
$944$	13.5528	−	7.79855i	0.441107	−	0.253821i
$945$	−1.11668	+	7.05042i	−0.0363255	+	0.229350i
$946$	15.3089	−	2.00981i	0.497735	−	0.0653445i
$947$	−7.94924	+	24.4652i	−0.258316	+	0.795014i	0.734843	+	0.678238i	$0.237256\pi$
$947$	−7.94924	+	24.4652i	−0.258316	+	0.795014i	−0.993158	+	0.116776i	$0.962744\pi$
$948$	0.314991	−	5.92814i	0.0102304	−	0.192537i
$949$	−11.3784	−	6.97267i	−0.369357	−	0.226343i
$950$	−13.6752	+	25.1648i	−0.443681	+	0.816453i
$951$	−1.79489	−	0.914544i	−0.0582034	−	0.0296561i
$952$	−31.9171	+	31.8478i	−1.03444	+	1.03219i
$953$	−9.60517	−	29.5617i	−0.311142	−	0.957596i	−0.977314	−	0.211798i	$-0.932068\pi$
$953$	−9.60517	−	29.5617i	−0.311142	−	0.957596i	0.666172	−	0.745798i	$-0.267932\pi$
$954$	9.11721	−	4.34463i	0.295181	−	0.140663i
$955$	4.77363	+	4.07706i	0.154471	+	0.131931i
$956$	−16.3935	+	55.1966i	−0.530204	+	1.78519i
$957$	−2.76228	−	6.66874i	−0.0892919	−	0.215570i
$958$	31.8175	+	46.3307i	1.02798	+	1.49688i
$959$	−30.6268	+	42.1542i	−0.988992	+	1.36123i
$960$	1.43664	+	1.68952i	0.0463675	+	0.0545291i
$961$	24.9336	−	18.1153i	0.804310	−	0.584365i
$962$	−44.0044	+	13.0173i	−1.41876	+	0.419696i
$963$	−0.391245	−	2.47022i	−0.0126077	−	0.0796018i
$964$	28.8260	+	11.0893i	0.928423	+	0.357161i
$965$	6.35516	+	1.52574i	0.204580	+	0.0491153i
$966$	−15.9082	−	7.08970i	−0.511838	−	0.228107i
$967$	11.0312	−	9.42156i	0.354741	−	0.302977i	−0.454163	−	0.890919i	$-0.650062\pi$
$967$	11.0312	−	9.42156i	0.354741	−	0.302977i	0.808903	+	0.587942i	$0.200062\pi$
$968$	−3.83116	+	5.26109i	−0.123138	+	0.169098i
$969$	−5.87868	+	0.462662i	−0.188851	+	0.0148629i
$970$	−1.78248	−	1.36877i	−0.0572320	−	0.0439487i
$971$	−5.94357	−	24.7568i	−0.190738	−	0.794482i	−0.982895	−	0.184165i	$-0.941042\pi$
$971$	−5.94357	−	24.7568i	−0.190738	−	0.794482i	0.792157	−	0.610317i	$-0.208958\pi$
$972$	5.95475	+	16.8545i	0.190999	+	0.540609i
$973$	−44.8989	−	3.53362i	−1.43939	−	0.113283i
$974$	−18.9544	+	21.0357i	−0.607340	+	0.674027i
$975$	4.88782	+	4.88782i	0.156536	+	0.156536i
$976$	−2.55351	−	50.1143i	−0.0817360	−	1.60412i
$977$	11.5290	+	18.8137i	0.368847	+	0.601903i	0.982185	−	0.187917i	$-0.0601737\pi$
$977$	11.5290	+	18.8137i	0.368847	+	0.601903i	−0.613338	+	0.789820i	$0.710174\pi$
$978$	−6.65546	−	0.176694i	−0.212818	−	0.00565004i
$979$	16.3918	−	8.35202i	0.523883	−	0.266932i
$980$	−12.9189	−	14.3688i	−0.412678	−	0.458994i
$981$	−30.1993	−	12.5090i	−0.964191	−	0.399381i
$982$	−28.2612	+	10.8367i	−0.901852	+	0.345814i
$983$	−9.12057			−0.290901			−0.145450	−	0.989366i	$-0.546463\pi$
$983$	−9.12057			−0.290901			−0.145450	+	0.989366i	$0.546463\pi$
$984$	−2.80327	−	5.68254i	−0.0893650	−	0.181153i
$985$	5.01988			0.159947
$986$	−33.6099	+	12.8876i	−1.07036	+	0.410426i
$987$	11.0698	+	4.58525i	0.352355	+	0.145950i
$988$	−27.9890	−	31.1303i	−0.890450	−	0.990388i
$989$	26.5006	−	13.5027i	0.842670	−	0.429362i
$990$	−9.50705	−	0.252400i	−0.302154	−	0.00802179i
$991$	−28.7489	−	46.9139i	−0.913238	−	1.49027i	−0.871070	−	0.491159i	$-0.836573\pi$
$991$	−28.7489	−	46.9139i	−0.913238	−	1.49027i	−0.0421686	−	0.999111i	$-0.513427\pi$
$992$	2.01727	−	1.30484i	0.0640483	−	0.0414286i
$993$	−5.42735	−	5.42735i	−0.172232	−	0.172232i
$994$	5.88194	−	6.52780i	0.186564	−	0.207049i
$995$	−13.6840	−	1.07695i	−0.433812	−	0.0341417i
$996$	1.17003	+	3.31169i	0.0370738	+	0.104935i
$997$	−2.19554	−	9.14509i	−0.0695335	−	0.289628i	0.926759	−	0.375656i	$-0.122583\pi$
$997$	−2.19554	−	9.14509i	−0.0695335	−	0.289628i	−0.996293	+	0.0860280i	$0.972583\pi$
$998$	10.8169	+	8.30632i	0.342403	+	0.262932i
$999$	−14.7208	+	1.15855i	−0.465745	+	0.0366549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.2.o.b.111.16	yes	288
4.3	odd	2	inner	164.2.o.b.111.4	yes	288
41.17	odd	40	inner	164.2.o.b.99.4	✓	288
164.99	even	40	inner	164.2.o.b.99.16	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.o.b.99.4	✓	288	41.17	odd	40	inner
164.2.o.b.99.16	yes	288	164.99	even	40	inner
164.2.o.b.111.4	yes	288	4.3	odd	2	inner
164.2.o.b.111.16	yes	288	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.o (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32047 - 0.506330i) q^{2} +(0.323235 + 0.133889i) q^{3} +(1.48726 - 1.33718i) q^{4} +(-0.705993 + 0.359722i) q^{5} +(0.494613 + 0.0131313i) q^{6} +(2.28906 + 3.73541i) q^{7} +(1.28682 - 2.51875i) q^{8} +(-2.03477 - 2.03477i) q^{9} +O(q^{10})\)	\(q+(1.32047 - 0.506330i) q^{2} +(0.323235 + 0.133889i) q^{3} +(1.48726 - 1.33718i) q^{4} +(-0.705993 + 0.359722i) q^{5} +(0.494613 + 0.0131313i) q^{6} +(2.28906 + 3.73541i) q^{7} +(1.28682 - 2.51875i) q^{8} +(-2.03477 - 2.03477i) q^{9} +(-0.750102 + 0.832466i) q^{10} +(-2.94031 - 0.231408i) q^{11} +(0.659768 - 0.233098i) q^{12} +(-1.05491 - 4.39401i) q^{13} +(4.91398 + 3.77346i) q^{14} +(-0.276365 + 0.0217504i) q^{15} +(0.423882 - 3.97748i) q^{16} +(-2.76691 + 2.36316i) q^{17} +(-3.71710 - 1.65657i) q^{18} +(4.50401 + 1.08132i) q^{19} +(-0.568982 + 1.47904i) q^{20} +(0.239778 + 1.51390i) q^{21} +(-3.99975 + 1.18320i) q^{22} +(-6.50021 + 4.72268i) q^{23} +(0.753177 - 0.641859i) q^{24} +(-2.56990 + 3.53716i) q^{25} +(-3.61779 - 5.26801i) q^{26} +(-0.786942 - 1.89985i) q^{27} +(8.39936 + 2.49463i) q^{28} +(5.31907 + 4.54292i) q^{29} +(-0.353917 + 0.168652i) q^{30} +(0.131241 + 0.403918i) q^{31} +(-1.45419 - 5.46675i) q^{32} +(-0.919431 - 0.468474i) q^{33} +(-2.45707 + 4.52145i) q^{34} +(-2.95977 - 1.81375i) q^{35} +(-5.74708 - 0.305370i) q^{36} +(2.21897 - 6.82927i) q^{37} +(6.49489 - 0.852674i) q^{38} +(0.247324 - 1.56154i) q^{39} +(-0.00243738 + 2.24112i) q^{40} +(1.56856 - 6.20803i) q^{41} +(1.08315 + 1.87764i) q^{42} +(-3.65616 - 0.579078i) q^{43} +(-4.68245 + 3.58758i) q^{44} +(2.16848 + 0.704582i) q^{45} +(-6.19207 + 9.52739i) q^{46} +(4.08444 - 6.66520i) q^{47} +(0.669552 - 1.22891i) q^{48} +(-5.53555 + 10.8641i) q^{49} +(-1.60249 + 5.97192i) q^{50} +(-1.21076 + 0.393401i) q^{51} +(-7.44452 - 5.12443i) q^{52} +(-1.61175 + 1.88712i) q^{53} +(-2.00108 - 2.11023i) q^{54} +(2.15908 - 0.894322i) q^{55} +(12.3542 - 0.958776i) q^{56} +(1.31108 + 0.952555i) q^{57} +(9.32387 + 3.30556i) q^{58} +(2.29771 + 3.16253i) q^{59} +(-0.381942 + 0.401899i) q^{60} +(12.3904 - 1.96244i) q^{61} +(0.377815 + 0.466908i) q^{62} +(2.94298 - 12.2584i) q^{63} +(-4.68819 - 6.48235i) q^{64} +(2.32538 + 2.72267i) q^{65} +(-1.45128 - 0.153068i) q^{66} +(0.516254 + 6.55963i) q^{67} +(-0.955130 + 7.21451i) q^{68} +(-2.73341 + 0.656234i) q^{69} +(-4.82663 - 0.896373i) q^{70} +(0.111273 - 1.41386i) q^{71} +(-7.74344 + 2.50669i) q^{72} +(2.08819 - 2.08819i) q^{73} +(-0.527799 - 10.1414i) q^{74} +(-1.30427 + 0.799256i) q^{75} +(8.14455 - 4.41449i) q^{76} +(-5.86616 - 11.5130i) q^{77} +(-0.464072 - 2.18719i) q^{78} +(3.24666 - 7.83812i) q^{79} +(1.13153 + 2.96055i) q^{80} +7.91332i q^{81} +(-1.07208 - 8.99170i) q^{82} +5.01948i q^{83} +(2.38097 + 1.93093i) q^{84} +(1.10334 - 2.66370i) q^{85} +(-5.12103 + 1.08657i) q^{86} +(1.11107 + 2.18059i) q^{87} +(-4.36651 + 7.10813i) q^{88} +(-5.31834 + 3.25908i) q^{89} +(3.22015 - 0.167591i) q^{90} +(13.9987 - 13.9987i) q^{91} +(-3.35241 + 15.7158i) q^{92} +(-0.0116583 + 0.148132i) q^{93} +(2.01857 - 10.8692i) q^{94} +(-3.56877 + 0.856786i) q^{95} +(0.261887 - 1.96175i) q^{96} +(0.157358 + 1.99942i) q^{97} +(-1.80867 + 17.1485i) q^{98} +(5.51199 + 6.45371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

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