LMFDB - Embedded newform 460.2.e.b.91.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(91,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("460.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.e (of order $2$, degree $1$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.7
Character	$\chi$	$=$	460.91
Dual form			460.2.e.b.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05127 + 0.945957i) q^{2} +1.57817i q^{3} +(0.210332 - 1.98891i) q^{4} -1.00000i q^{5} +(-1.49288 - 1.65908i) q^{6} -1.14830 q^{7} +(1.66031 + 2.28984i) q^{8} +0.509388 q^{9} +O(q^{10})$	\(q+(-1.05127 + 0.945957i) q^{2} +1.57817i q^{3} +(0.210332 - 1.98891i) q^{4} -1.00000i q^{5} +(-1.49288 - 1.65908i) q^{6} -1.14830 q^{7} +(1.66031 + 2.28984i) q^{8} +0.509388 q^{9} +(0.945957 + 1.05127i) q^{10} -5.86684 q^{11} +(3.13883 + 0.331939i) q^{12} -2.69569 q^{13} +(1.20717 - 1.08624i) q^{14} +1.57817 q^{15} +(-3.91152 - 0.836662i) q^{16} -0.337371i q^{17} +(-0.535504 + 0.481859i) q^{18} -4.49236 q^{19} +(-1.98891 - 0.210332i) q^{20} -1.81221i q^{21} +(6.16763 - 5.54978i) q^{22} +(-2.43592 + 4.13114i) q^{23} +(-3.61376 + 2.62024i) q^{24} -1.00000 q^{25} +(2.83389 - 2.55000i) q^{26} +5.53840i q^{27} +(-0.241524 + 2.28387i) q^{28} -9.68157 q^{29} +(-1.65908 + 1.49288i) q^{30} -4.80948i q^{31} +(4.90351 - 2.82057i) q^{32} -9.25886i q^{33} +(0.319138 + 0.354668i) q^{34} +1.14830i q^{35} +(0.107141 - 1.01313i) q^{36} -3.78190i q^{37} +(4.72267 - 4.24958i) q^{38} -4.25424i q^{39} +(2.28984 - 1.66031i) q^{40} +7.24551 q^{41} +(1.71427 + 1.90512i) q^{42} +11.1493 q^{43} +(-1.23398 + 11.6686i) q^{44} -0.509388i q^{45} +(-1.34708 - 6.64721i) q^{46} -2.80145i q^{47} +(1.32039 - 6.17303i) q^{48} -5.68141 q^{49} +(1.05127 - 0.945957i) q^{50} +0.532428 q^{51} +(-0.566989 + 5.36148i) q^{52} +7.11746i q^{53} +(-5.23909 - 5.82235i) q^{54} +5.86684i q^{55} +(-1.90653 - 2.62943i) q^{56} -7.08969i q^{57} +(10.1779 - 9.15835i) q^{58} +1.70388i q^{59} +(0.331939 - 3.13883i) q^{60} -13.9664i q^{61} +(4.54956 + 5.05606i) q^{62} -0.584931 q^{63} +(-2.48676 + 7.60368i) q^{64} +2.69569i q^{65} +(8.75848 + 9.73355i) q^{66} -6.00623 q^{67} +(-0.671000 - 0.0709599i) q^{68} +(-6.51963 - 3.84428i) q^{69} +(-1.08624 - 1.20717i) q^{70} +3.87736i q^{71} +(0.845741 + 1.16642i) q^{72} -1.87205 q^{73} +(3.57751 + 3.97579i) q^{74} -1.57817i q^{75} +(-0.944886 + 8.93489i) q^{76} +6.73690 q^{77} +(4.02433 + 4.47235i) q^{78} +5.07701 q^{79} +(-0.836662 + 3.91152i) q^{80} -7.21236 q^{81} +(-7.61698 + 6.85394i) q^{82} -15.7178 q^{83} +(-3.60432 - 0.381166i) q^{84} -0.337371 q^{85} +(-11.7209 + 10.5468i) q^{86} -15.2791i q^{87} +(-9.74076 - 13.4341i) q^{88} +18.1716i q^{89} +(0.481859 + 0.535504i) q^{90} +3.09546 q^{91} +(7.70411 + 5.71373i) q^{92} +7.59017 q^{93} +(2.65005 + 2.94508i) q^{94} +4.49236i q^{95} +(4.45134 + 7.73855i) q^{96} +14.5800i q^{97} +(5.97268 - 5.37436i) q^{98} -2.98850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9	$ 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.05127	+	0.945957i	−0.743359	+	0.668892i
$2$	−1.05127	+	0.945957i	−0.743359	+	0.668892i
$3$			1.57817i			0.911155i	0.890196	+	0.455578i	$0.150567\pi$
$3$			1.57817i			0.911155i	−0.890196	+	0.455578i	$0.849433\pi$
$4$	0.210332	−	1.98891i	0.105166	−	0.994455i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.49288	−	1.65908i	−0.609465	−	0.677316i
$7$	−1.14830			−0.434017			−0.217008	−	0.976170i	$-0.569630\pi$
$7$	−1.14830			−0.434017			−0.217008	+	0.976170i	$0.569630\pi$
$8$	1.66031	+	2.28984i	0.587007	+	0.809582i
$9$	0.509388			0.169796
$10$	0.945957	+	1.05127i	0.299138	+	0.332440i
$11$	−5.86684			−1.76892			−0.884460	−	0.466617i	$-0.845473\pi$
$11$	−5.86684			−1.76892			−0.884460	+	0.466617i	$0.845473\pi$
$12$	3.13883	+	0.331939i	0.906103	+	0.0958225i
$13$	−2.69569			−0.747649			−0.373824	−	0.927499i	$-0.621954\pi$
$13$	−2.69569			−0.747649			−0.373824	+	0.927499i	$0.621954\pi$
$14$	1.20717	−	1.08624i	0.322630	−	0.290311i
$15$	1.57817			0.407481
$16$	−3.91152	−	0.836662i	−0.977880	−	0.209165i
$17$		−	0.337371i		−	0.0818245i	−0.999163	−	0.0409122i	$-0.986974\pi$
$17$		−	0.337371i		−	0.0818245i	0.999163	−	0.0409122i	$-0.0130264\pi$
$18$	−0.535504	+	0.481859i	−0.126219	+	0.113575i
$19$	−4.49236			−1.03062			−0.515309	−	0.857005i	$-0.672323\pi$
$19$	−4.49236			−1.03062			−0.515309	+	0.857005i	$0.672323\pi$
$20$	−1.98891	−	0.210332i	−0.444734	−	0.0470316i
$21$		−	1.81221i		−	0.395457i
$22$	6.16763	−	5.54978i	1.31494	−	1.18322i
$23$	−2.43592	+	4.13114i	−0.507924	+	0.861402i
$23$	−2.43592	+	4.13114i	−0.507924	+	0.861402i
$24$	−3.61376	+	2.62024i	−0.737655	+	0.534855i
$25$	−1.00000			−0.200000
$26$	2.83389	−	2.55000i	0.555772	−	0.500097i
$27$			5.53840i			1.06587i
$28$	−0.241524	+	2.28387i	−0.0456438	+	0.431610i
$29$	−9.68157			−1.79782			−0.898911	−	0.438131i	$-0.855641\pi$
$29$	−9.68157			−1.79782			−0.898911	+	0.438131i	$0.855641\pi$
$30$	−1.65908	+	1.49288i	−0.302905	+	0.272561i
$31$		−	4.80948i		−	0.863809i	−0.901919	−	0.431904i	$-0.857842\pi$
$31$		−	4.80948i		−	0.863809i	0.901919	−	0.431904i	$-0.142158\pi$
$32$	4.90351	−	2.82057i	0.866826	−	0.498612i
$33$		−	9.25886i		−	1.61176i
$34$	0.319138	+	0.354668i	0.0547318	+	0.0608250i
$35$			1.14830i			0.194098i
$36$	0.107141	−	1.01313i	0.0178568	−	0.168854i
$37$		−	3.78190i		−	0.621740i	−0.950452	−	0.310870i	$-0.899380\pi$
$37$		−	3.78190i		−	0.621740i	0.950452	−	0.310870i	$-0.100620\pi$
$38$	4.72267	−	4.24958i	0.766119	−	0.689372i
$39$		−	4.25424i		−	0.681224i
$40$	2.28984	−	1.66031i	0.362056	−	0.262518i
$41$	7.24551			1.13156			0.565779	−	0.824557i	$-0.308575\pi$
$41$	7.24551			1.13156			0.565779	+	0.824557i	$0.308575\pi$
$42$	1.71427	+	1.90512i	0.264518	+	0.293966i
$43$	11.1493			1.70026			0.850129	−	0.526575i	$-0.176524\pi$
$43$	11.1493			1.70026			0.850129	+	0.526575i	$0.176524\pi$
$44$	−1.23398	+	11.6686i	−0.186030	+	1.75911i
$45$		−	0.509388i		−	0.0759351i
$46$	−1.34708	−	6.64721i	−0.198616	−	0.980077i
$47$		−	2.80145i		−	0.408633i	−0.978905	−	0.204317i	$-0.934503\pi$
$47$		−	2.80145i		−	0.408633i	0.978905	−	0.204317i	$-0.0654972\pi$
$48$	1.32039	−	6.17303i	0.190582	−	0.891001i
$49$	−5.68141			−0.811629
$50$	1.05127	−	0.945957i	0.148672	−	0.133778i
$51$	0.532428			0.0745548
$52$	−0.566989	+	5.36148i	−0.0786272	+	0.743503i
$53$			7.11746i			0.977659i	0.872379	+	0.488829i	$0.162576\pi$
$53$			7.11746i			0.977659i	−0.872379	+	0.488829i	$0.837424\pi$
$54$	−5.23909	−	5.82235i	−0.712950	−	0.792321i
$55$			5.86684i			0.791085i
$56$	−1.90653	−	2.62943i	−0.254771	−	0.351372i
$57$		−	7.08969i		−	0.939052i
$58$	10.1779	−	9.15835i	1.33643	−	1.20255i
$59$			1.70388i			0.221826i	0.993830	+	0.110913i	$0.0353775\pi$
$59$			1.70388i			0.221826i	−0.993830	+	0.110913i	$0.964622\pi$
$60$	0.331939	−	3.13883i	0.0428531	−	0.405221i
$61$		−	13.9664i		−	1.78821i	−0.447854	−	0.894107i	$-0.647812\pi$
$61$		−	13.9664i		−	1.78821i	0.447854	−	0.894107i	$-0.352188\pi$
$62$	4.54956	+	5.05606i	0.577795	+	0.642120i
$63$	−0.584931			−0.0736944
$64$	−2.48676	+	7.60368i	−0.310845	+	0.950461i
$65$			2.69569i			0.334359i
$66$	8.75848	+	9.73355i	1.07809	+	1.19812i
$67$	−6.00623			−0.733778			−0.366889	−	0.930265i	$-0.619577\pi$
$67$	−6.00623			−0.733778			−0.366889	+	0.930265i	$0.619577\pi$
$68$	−0.671000	−	0.0709599i	−0.0813707	−	0.00860515i
$69$	−6.51963	−	3.84428i	−0.784871	−	0.462797i
$70$	−1.08624	−	1.20717i	−0.129831	−	0.144285i
$71$			3.87736i			0.460158i	0.973172	+	0.230079i	$0.0738985\pi$
$71$			3.87736i			0.460158i	−0.973172	+	0.230079i	$0.926102\pi$
$72$	0.845741	+	1.16642i	0.0996715	+	0.137464i
$73$	−1.87205			−0.219106			−0.109553	−	0.993981i	$-0.534942\pi$
$73$	−1.87205			−0.219106			−0.109553	+	0.993981i	$0.534942\pi$
$74$	3.57751	+	3.97579i	0.415877	+	0.462176i
$75$		−	1.57817i		−	0.182231i
$76$	−0.944886	+	8.93489i	−0.108386	+	1.02490i
$77$	6.73690			0.767741
$78$	4.02433	+	4.47235i	0.455666	+	0.506394i
$79$	5.07701			0.571209			0.285604	−	0.958348i	$-0.407806\pi$
$79$	5.07701			0.571209			0.285604	+	0.958348i	$0.407806\pi$
$80$	−0.836662	+	3.91152i	−0.0935416	+	0.437321i
$81$	−7.21236			−0.801373
$82$	−7.61698	+	6.85394i	−0.841155	+	0.756891i
$83$	−15.7178			−1.72525			−0.862625	−	0.505844i	$-0.831181\pi$
$83$	−15.7178			−1.72525			−0.862625	+	0.505844i	$0.831181\pi$
$84$	−3.60432	−	0.381166i	−0.393264	−	0.0415886i
$85$	−0.337371			−0.0365930
$86$	−11.7209	+	10.5468i	−1.26390	+	1.13729i
$87$		−	15.2791i		−	1.63810i
$88$	−9.74076	−	13.4341i	−1.03837	−	1.43208i
$89$			18.1716i			1.92618i	0.269177	+	0.963091i	$0.413248\pi$
$89$			18.1716i			1.92618i	−0.269177	+	0.963091i	$0.586752\pi$
$90$	0.481859	+	0.535504i	0.0507924	+	0.0564471i
$91$	3.09546			0.324492
$92$	7.70411	+	5.71373i	0.803209	+	0.595697i
$93$	7.59017			0.787064
$94$	2.65005	+	2.94508i	0.273332	+	0.303761i
$95$			4.49236i			0.460906i
$96$	4.45134	+	7.73855i	0.454313	+	0.789813i
$97$			14.5800i			1.48037i	0.672401	+	0.740187i	$0.265263\pi$
$97$			14.5800i			1.48037i	−0.672401	+	0.740187i	$0.734737\pi$
$98$	5.97268	−	5.37436i	0.603332	−	0.542893i
$99$	−2.98850			−0.300356
$100$	−0.210332	+	1.98891i	−0.0210332	+	0.198891i
$101$	10.0447			0.999484			0.499742	−	0.866174i	$-0.333428\pi$
$101$	10.0447			0.999484			0.499742	+	0.866174i	$0.333428\pi$
$102$	−0.559725	+	0.503654i	−0.0554210	+	0.0498691i
$103$	−4.24087			−0.417866			−0.208933	−	0.977930i	$-0.566999\pi$
$103$	−4.24087			−0.417866			−0.208933	+	0.977930i	$0.566999\pi$
$104$	−4.47567	−	6.17270i	−0.438875	−	0.605283i
$105$	−1.81221			−0.176854
$106$	−6.73281	−	7.48237i	−0.653948	−	0.726752i
$107$	−0.286082			−0.0276566			−0.0138283	−	0.999904i	$-0.504402\pi$
$107$	−0.286082			−0.0276566			−0.0138283	+	0.999904i	$0.504402\pi$
$108$	11.0154	+	1.16490i	1.05996	+	0.112093i
$109$		−	3.95997i		−	0.379296i	−0.981852	−	0.189648i	$-0.939265\pi$
$109$		−	3.95997i		−	0.379296i	0.981852	−	0.189648i	$-0.0607347\pi$
$110$	−5.54978	−	6.16763i	−0.529151	−	0.588060i
$111$	5.96847			0.566502
$112$	4.49160	+	0.960739i	0.424417	+	0.0907813i
$113$			12.7684i			1.20115i	0.799568	+	0.600575i	$0.205062\pi$
$113$			12.7684i			1.20115i	−0.799568	+	0.600575i	$0.794938\pi$
$114$	6.70654	+	7.45317i	0.628125	+	0.698053i
$115$	4.13114	+	2.43592i	0.385231	+	0.227150i
$116$	−2.03634	+	19.2558i	−0.189070	+	1.78785i
$117$	−1.37315			−0.126948
$118$	−1.61180	−	1.79123i	−0.148378	−	0.164896i
$119$			0.387403i			0.0355132i
$120$	2.62024	+	3.61376i	0.239194	+	0.329889i
$121$	23.4198			2.12908
$122$	13.2116	+	14.6824i	1.19612	+	1.32928i
$123$			11.4346i			1.03103i
$124$	−9.56563	−	1.01159i	−0.859018	−	0.0908432i
$125$			1.00000i			0.0894427i
$126$	0.614919	−	0.553319i	0.0547814	−	0.0492936i
$127$			4.67666i			0.414986i	0.978236	+	0.207493i	$0.0665305\pi$
$127$			4.67666i			0.414986i	−0.978236	+	0.207493i	$0.933470\pi$
$128$	−4.57850	−	10.3459i	−0.404686	−	0.914456i
$129$			17.5955i			1.54920i
$130$	−2.55000	−	2.83389i	−0.223650	−	0.248549i
$131$			6.59198i			0.575944i	0.957639	+	0.287972i	$0.0929810\pi$
$131$			6.59198i			0.575944i	−0.957639	+	0.287972i	$0.907019\pi$
$132$	−18.4150	−	1.94743i	−1.60282	−	0.169502i
$133$	5.15858			0.447305
$134$	6.31416	−	5.68163i	0.545460	−	0.490818i
$135$	5.53840			0.476670
$136$	0.772527	−	0.560139i	0.0662436	−	0.0480316i
$137$		−	14.5643i		−	1.24431i	−0.782892	−	0.622157i	$-0.786256\pi$
$137$		−	14.5643i		−	1.24431i	0.782892	−	0.622157i	$-0.213744\pi$
$138$	10.4904	−	2.12591i	0.893003	−	0.180970i
$139$		−	11.4233i		−	0.968913i	−0.874815	−	0.484457i	$-0.839017\pi$
$139$		−	11.4233i		−	0.968913i	0.874815	−	0.484457i	$-0.160983\pi$
$140$	2.28387	+	0.241524i	0.193022	+	0.0204125i
$141$	4.42115			0.372328
$142$	−3.66781	−	4.07615i	−0.307796	−	0.342063i
$143$	15.8152			1.32253
$144$	−1.99248	−	0.426186i	−0.166040	−	0.0355155i
$145$			9.68157i			0.804011i
$146$	1.96802	−	1.77087i	0.162875	−	0.146559i
$147$		−	8.96621i		−	0.739520i
$148$	−7.52185	−	0.795454i	−0.618293	−	0.0653859i
$149$		−	0.711718i		−	0.0583062i	−0.999575	−	0.0291531i	$-0.990719\pi$
$149$		−	0.711718i		−	0.0583062i	0.999575	−	0.0291531i	$-0.00928103\pi$
$150$	1.49288	+	1.65908i	0.121893	+	0.135463i
$151$		−	15.5590i		−	1.26617i	−0.774080	−	0.633087i	$-0.781787\pi$
$151$		−	15.5590i		−	1.26617i	0.774080	−	0.633087i	$-0.218213\pi$
$152$	−7.45869	−	10.2868i	−0.604980	−	0.834369i
$153$		−	0.171853i		−	0.0138935i
$154$	−7.08229	+	6.37281i	−0.570707	+	0.513536i
$155$	−4.80948			−0.386307
$156$	−8.46131	−	0.894803i	−0.677447	−	0.0716416i
$157$			10.2830i			0.820671i	0.911935	+	0.410335i	$0.134588\pi$
$157$			10.2830i			0.820671i	−0.911935	+	0.410335i	$0.865412\pi$
$158$	−5.33730	+	4.80263i	−0.424613	+	0.382077i
$159$	−11.2325			−0.890799
$160$	−2.82057	−	4.90351i	−0.222986	−	0.387656i
$161$	2.79716	−	4.74379i	0.220447	−	0.373863i
$162$	7.58213	−	6.82258i	0.595708	−	0.536032i
$163$			1.47445i			0.115488i	0.998331	+	0.0577441i	$0.0183908\pi$
$163$			1.47445i			0.115488i	−0.998331	+	0.0577441i	$0.981609\pi$
$164$	1.52396	−	14.4107i	0.119001	−	1.12528i
$165$	−9.25886			−0.720801
$166$	16.5236	−	14.8683i	1.28248	−	1.15401i
$167$		−	5.14954i		−	0.398484i	−0.979950	−	0.199242i	$-0.936152\pi$
$167$		−	5.14954i		−	0.398484i	0.979950	−	0.199242i	$-0.0638479\pi$
$168$	4.14968	−	3.00883i	0.320155	−	0.232136i
$169$	−5.73327			−0.441021
$170$	0.354668	−	0.319138i	0.0272018	−	0.0244768i
$171$	−2.28835			−0.174995
$172$	2.34506	−	22.1750i	0.178809	−	1.69083i
$173$	−5.92631			−0.450569			−0.225285	−	0.974293i	$-0.572331\pi$
$173$	−5.92631			−0.450569			−0.225285	+	0.974293i	$0.572331\pi$
$174$	14.4534	+	16.0625i	1.09571	+	1.21769i
$175$	1.14830			0.0868034
$176$	22.9483	+	4.90856i	1.72979	+	0.369997i
$177$	−2.68901			−0.202118
$178$	−17.1895	−	19.1032i	−1.28841	−	1.43184i
$179$			14.4540i			1.08034i	0.841556	+	0.540170i	$0.181640\pi$
$179$			14.4540i			1.08034i	−0.841556	+	0.540170i	$0.818360\pi$
$180$	−1.01313	−	0.107141i	−0.0755140	−	0.00798578i
$181$			15.1528i			1.12630i	0.826354	+	0.563151i	$0.190411\pi$
$181$			15.1528i			1.12630i	−0.826354	+	0.563151i	$0.809589\pi$
$182$	−3.25416	+	2.92817i	−0.241214	+	0.217050i
$183$	22.0413			1.62934
$184$	−13.5040	+	1.28109i	−0.995530	+	0.0944434i
$185$	−3.78190			−0.278051
$186$	−7.97931	+	7.17997i	−0.585071	+	0.526461i
$187$			1.97930i			0.144741i
$188$	−5.57183	−	0.589234i	−0.406367	−	0.0429743i
$189$		−	6.35975i		−	0.462604i
$190$	−4.24958	−	4.72267i	−0.308297	−	0.342619i
$191$	−8.58891			−0.621472			−0.310736	−	0.950496i	$-0.600575\pi$
$191$	−8.58891			−0.621472			−0.310736	+	0.950496i	$0.600575\pi$
$192$	−11.9999	−	3.92453i	−0.866017	−	0.283228i
$193$	−19.5535			−1.40749			−0.703744	−	0.710453i	$-0.748490\pi$
$193$	−19.5535			−1.40749			−0.703744	+	0.710453i	$0.748490\pi$
$194$	−13.7920	−	15.3275i	−0.990211	−	1.10045i
$195$	−4.25424			−0.304653
$196$	−1.19498	+	11.2998i	−0.0853557	+	0.807129i
$197$	9.69326			0.690616			0.345308	−	0.938489i	$-0.387774\pi$
$197$	9.69326			0.690616			0.345308	+	0.938489i	$0.387774\pi$
$198$	3.14172	−	2.82699i	0.223272	−	0.200906i
$199$	14.5777			1.03339			0.516694	−	0.856170i	$-0.327162\pi$
$199$	14.5777			1.03339			0.516694	+	0.856170i	$0.327162\pi$
$200$	−1.66031	−	2.28984i	−0.117401	−	0.161916i
$201$		−	9.47883i		−	0.668585i
$202$	−10.5597	+	9.50184i	−0.742976	+	0.668547i
$203$	11.1174			0.780285
$204$	0.111987	−	1.05895i	0.00784062	−	0.0741414i
$205$		−	7.24551i		−	0.506049i
$206$	4.45830	−	4.01168i	0.310624	−	0.279507i
$207$	−1.24083	+	2.10435i	−0.0862434	+	0.146263i
$208$	10.5442	+	2.25538i	0.731111	+	0.156382i
$209$	26.3559			1.82308
$210$	1.90512	−	1.71427i	0.131466	−	0.118296i
$211$		−	13.5180i		−	0.930616i	−0.885149	−	0.465308i	$-0.845943\pi$
$211$		−	13.5180i		−	0.930616i	0.885149	−	0.465308i	$-0.154057\pi$
$212$	14.1560	+	1.49703i	0.972237	+	0.102816i
$213$	−6.11912			−0.419275
$214$	0.300749	−	0.270621i	0.0205588	−	0.0184993i
$215$		−	11.1493i		−	0.760378i
$216$	−12.6821	+	9.19545i	−0.862906	+	0.625671i
$217$			5.52273i			0.374908i
$218$	3.74596	+	4.16299i	0.253708	+	0.281953i
$219$		−	2.95440i		−	0.199640i
$220$	11.6686	+	1.23398i	0.786698	+	0.0831951i
$221$			0.909447i			0.0611760i
$222$	−6.27446	+	5.64591i	−0.421114	+	0.378929i
$223$		−	7.21182i		−	0.482939i	−0.970408	−	0.241469i	$-0.922371\pi$
$223$		−	7.21182i		−	0.482939i	0.970408	−	0.241469i	$-0.0776294\pi$
$224$	−5.63070	+	3.23887i	−0.376217	+	0.216406i
$225$	−0.509388			−0.0339592
$226$	−12.0784	−	13.4230i	−0.803440	−	0.892886i
$227$	16.4000			1.08851			0.544254	−	0.838921i	$-0.316813\pi$
$227$	16.4000			1.08851			0.544254	+	0.838921i	$0.316813\pi$
$228$	−14.1008	−	1.49119i	−0.933845	−	0.0987563i
$229$		−	1.03931i		−	0.0686794i	−0.999410	−	0.0343397i	$-0.989067\pi$
$229$		−	1.03931i		−	0.0686794i	0.999410	−	0.0343397i	$-0.0109328\pi$
$230$	−6.64721	+	1.34708i	−0.438304	+	0.0888236i
$231$			10.6320i			0.699531i
$232$	−16.0744	−	22.1693i	−1.05533	−	1.45548i
$233$	−10.7887			−0.706793			−0.353396	−	0.935474i	$-0.614973\pi$
$233$	−10.7887			−0.706793			−0.353396	+	0.935474i	$0.614973\pi$
$234$	1.44355	−	1.29894i	0.0943679	−	0.0849145i
$235$	−2.80145			−0.182746
$236$	3.38886	+	0.358380i	0.220596	+	0.0233285i
$237$			8.01237i			0.520460i
$238$	−0.366467	−	0.407265i	−0.0237545	−	0.0263991i
$239$			6.39755i			0.413823i	0.978360	+	0.206912i	$0.0663413\pi$
$239$			6.39755i			0.413823i	−0.978360	+	0.206912i	$0.933659\pi$
$240$	−6.17303	−	1.32039i	−0.398468	−	0.0852310i
$241$		−	6.97534i		−	0.449321i	−0.974437	−	0.224660i	$-0.927873\pi$
$241$		−	6.97534i		−	0.449321i	0.974437	−	0.224660i	$-0.0721273\pi$
$242$	−24.6205	+	22.1541i	−1.58267	+	1.42412i
$243$			5.23290i			0.335690i
$244$	−27.7779	−	2.93758i	−1.77830	−	0.188059i
$245$			5.68141i			0.362972i
$246$	−10.8167	−	12.0209i	−0.689645	−	0.766423i
$247$	12.1100			0.770540
$248$	11.0130	−	7.98522i	0.699324	−	0.507062i
$249$		−	24.8053i		−	1.57197i
$250$	−0.945957	−	1.05127i	−0.0598276	−	0.0664881i
$251$	0.980458			0.0618860			0.0309430	−	0.999521i	$-0.490149\pi$
$251$	0.980458			0.0618860			0.0309430	+	0.999521i	$0.490149\pi$
$252$	−0.123030	+	1.16337i	−0.00775013	+	0.0732857i
$253$	14.2911	−	24.2367i	0.898476	−	1.52375i
$254$	−4.42392	−	4.91642i	−0.277581	−	0.308484i
$255$		−	0.532428i		−	0.0333419i
$256$	14.6000	+	6.54524i	0.912500	+	0.409078i
$257$	10.2797			0.641231			0.320615	−	0.947209i	$-0.396110\pi$
$257$	10.2797			0.641231			0.320615	+	0.947209i	$0.396110\pi$
$258$	−16.6446	−	18.4976i	−1.03625	−	1.15161i
$259$			4.34276i			0.269846i
$260$	5.36148	+	0.566989i	0.332505	+	0.0351631i
$261$	−4.93168			−0.305263
$262$	−6.23573	−	6.92994i	−0.385244	−	0.428133i
$263$	6.93989			0.427932			0.213966	−	0.976841i	$-0.431362\pi$
$263$	6.93989			0.427932			0.213966	+	0.976841i	$0.431362\pi$
$264$	21.2013	−	15.3725i	1.30485	−	0.946115i
$265$	7.11746			0.437222
$266$	−5.42305	+	4.87979i	−0.332509	+	0.299199i
$267$	−28.6778			−1.75505
$268$	−1.26330	+	11.9458i	−0.0771684	+	0.729709i
$269$	−14.1252			−0.861231			−0.430615	−	0.902536i	$-0.641703\pi$
$269$	−14.1252			−0.861231			−0.430615	+	0.902536i	$0.641703\pi$
$270$	−5.82235	+	5.23909i	−0.354337	+	0.318841i
$271$		−	13.9803i		−	0.849245i	−0.905370	−	0.424623i	$-0.860407\pi$
$271$		−	13.9803i		−	0.849245i	0.905370	−	0.424623i	$-0.139593\pi$
$272$	−0.282265	+	1.31963i	−0.0171149	+	0.0800146i
$273$			4.88515i			0.295663i
$274$	13.7772	+	15.3110i	0.832313	+	0.924973i
$275$	5.86684			0.353784
$276$	−9.01722	+	12.1584i	−0.542773	+	0.731848i
$277$	−12.1270			−0.728642			−0.364321	−	0.931273i	$-0.618699\pi$
$277$	−12.1270			−0.728642			−0.364321	+	0.931273i	$0.618699\pi$
$278$	10.8060	+	12.0090i	0.648099	+	0.720250i
$279$		−	2.44989i		−	0.146671i
$280$	−2.62943	+	1.90653i	−0.157138	+	0.113937i
$281$			2.06076i			0.122935i	0.998109	+	0.0614673i	$0.0195780\pi$
$281$			2.06076i			0.122935i	−0.998109	+	0.0614673i	$0.980422\pi$
$282$	−4.64782	+	4.18222i	−0.276774	+	0.249048i
$283$	−14.8377			−0.882009			−0.441004	−	0.897505i	$-0.645378\pi$
$283$	−14.8377			−0.882009			−0.441004	+	0.897505i	$0.645378\pi$
$284$	7.71172	+	0.815532i	0.457606	+	0.0483929i
$285$	−7.08969			−0.419957
$286$	−16.6260	+	14.9605i	−0.983115	+	0.884631i
$287$	−8.32003			−0.491116
$288$	2.49779	−	1.43677i	0.147184	−	0.0846623i
$289$	16.8862			0.993305
$290$	−9.15835	−	10.1779i	−0.537797	−	0.597669i
$291$	−23.0097			−1.34885
$292$	−0.393751	+	3.72333i	−0.0230425	+	0.217891i
$293$			2.87892i			0.168189i	0.996458	+	0.0840943i	$0.0267997\pi$
$293$			2.87892i			0.168189i	−0.996458	+	0.0840943i	$0.973200\pi$
$294$	8.48164	+	9.42589i	0.494660	+	0.549729i
$295$	1.70388			0.0992037
$296$	8.65995	−	6.27911i	0.503350	−	0.364966i
$297$		−	32.4929i		−	1.88543i
$298$	0.673254	+	0.748207i	0.0390006	+	0.0433424i
$299$	6.56647	−	11.1363i	0.379749	−	0.644026i
$300$	−3.13883	−	0.331939i	−0.181221	−	0.0191645i
$301$	−12.8028			−0.737940
$302$	14.7182	+	16.3567i	0.846935	+	0.941223i
$303$			15.8522i			0.910685i
$304$	17.5719	+	3.75858i	1.00782	+	0.215570i
$305$	−13.9664			−0.799713
$306$	0.162565	+	0.180663i	0.00929324	+	0.0103278i
$307$			13.6048i			0.776465i	0.921562	+	0.388232i	$0.126914\pi$
$307$			13.6048i			0.776465i	−0.921562	+	0.388232i	$0.873086\pi$
$308$	1.41698	−	13.3991i	0.0807402	−	0.763483i
$309$		−	6.69281i		−	0.380741i
$310$	5.05606	−	4.54956i	0.287165	−	0.258398i
$311$		−	34.4429i		−	1.95307i	−0.215348	−	0.976537i	$-0.569088\pi$
$311$		−	34.4429i		−	1.95307i	0.215348	−	0.976537i	$-0.430912\pi$
$312$	9.74155	−	7.06335i	0.551507	−	0.399884i
$313$			12.8201i			0.724633i	0.932055	+	0.362316i	$0.118014\pi$
$313$			12.8201i			0.724633i	−0.932055	+	0.362316i	$0.881986\pi$
$314$	−9.72725	−	10.8102i	−0.548940	−	0.610053i
$315$			0.584931i			0.0329571i
$316$	1.06786	−	10.0977i	0.0600717	−	0.568041i
$317$	−18.6402			−1.04694			−0.523470	−	0.852044i	$-0.675363\pi$
$317$	−18.6402			−1.04694			−0.523470	+	0.852044i	$0.675363\pi$
$318$	11.8084	−	10.6255i	0.662184	−	0.595849i
$319$	56.8002			3.18020
$320$	7.60368	+	2.48676i	0.425059	+	0.139014i
$321$		−	0.451485i		−	0.0251994i
$322$	1.54685	+	7.63300i	0.0862025	+	0.425370i
$323$			1.51559i			0.0843297i
$324$	−1.51699	+	14.3447i	−0.0842771	+	0.796929i
$325$	2.69569			0.149530
$326$	−1.39477	−	1.55005i	−0.0772492	−	0.0858492i
$327$	6.24949			0.345598
$328$	12.0298	+	16.5911i	0.664233	+	0.916089i
$329$			3.21691i			0.177354i
$330$	9.73355	−	8.75848i	0.535814	−	0.482138i
$331$			4.03755i			0.221924i	0.993825	+	0.110962i	$0.0353931\pi$
$331$			4.03755i			0.221924i	−0.993825	+	0.110962i	$0.964607\pi$
$332$	−3.30595	+	31.2612i	−0.181437	+	1.71568i
$333$		−	1.92645i		−	0.105569i
$334$	4.87124	+	5.41355i	0.266543	+	0.296216i
$335$			6.00623i			0.328155i
$336$	−1.51621	+	7.08850i	−0.0827159	+	0.386709i
$337$			16.2100i			0.883014i	0.897258	+	0.441507i	$0.145556\pi$
$337$			16.2100i			0.883014i	−0.897258	+	0.441507i	$0.854444\pi$
$338$	6.02721	−	5.42343i	0.327837	−	0.294996i
$339$	−20.1507			−1.09443
$340$	−0.0709599	+	0.671000i	−0.00384834	+	0.0363901i
$341$			28.2165i			1.52801i
$342$	2.40567	−	2.16468i	0.130084	−	0.117053i
$343$	14.5621			0.786278
$344$	18.5113	+	25.5302i	0.998063	+	1.37650i
$345$	−3.84428	+	6.51963i	−0.206969	+	0.351005i
$346$	6.23015	−	5.60604i	0.334935	−	0.301382i
$347$		−	26.2792i		−	1.41074i	−0.708839	−	0.705371i	$-0.750781\pi$
$347$		−	26.2792i		−	1.41074i	0.708839	−	0.705371i	$-0.249219\pi$
$348$	−30.3888	−	3.21369i	−1.62901	−	0.172272i
$349$	29.5366			1.58106			0.790530	−	0.612423i	$-0.209805\pi$
$349$	29.5366			1.58106			0.790530	+	0.612423i	$0.209805\pi$
$350$	−1.20717	+	1.08624i	−0.0645261	+	0.0580621i
$351$		−	14.9298i		−	0.796893i
$352$	−28.7681	+	16.5479i	−1.53334	+	0.882004i
$353$	1.05126			0.0559531			0.0279766	−	0.999609i	$-0.491094\pi$
$353$	1.05126			0.0559531			0.0279766	+	0.999609i	$0.491094\pi$
$354$	2.82687	−	2.54368i	0.150246	−	0.135195i
$355$	3.87736			0.205789
$356$	36.1416	+	3.82206i	1.91550	+	0.202569i
$357$	−0.611387			−0.0323580
$358$	−13.6728	−	15.1950i	−0.722632	−	0.803081i
$359$	−5.35785			−0.282776			−0.141388	−	0.989954i	$-0.545157\pi$
$359$	−5.35785			−0.282776			−0.141388	+	0.989954i	$0.545157\pi$
$360$	1.16642	−	0.845741i	0.0614757	−	0.0445744i
$361$	1.18127			0.0621722
$362$	−14.3339	−	15.9297i	−0.753375	−	0.837247i
$363$			36.9604i			1.93992i
$364$	0.651073	−	6.15659i	0.0341255	−	0.322693i
$365$			1.87205i			0.0979873i
$366$	−23.1713	+	20.8501i	−1.21118	+	1.08985i
$367$	13.8808			0.724570			0.362285	−	0.932067i	$-0.381997\pi$
$367$	13.8808			0.724570			0.362285	+	0.932067i	$0.381997\pi$
$368$	12.9845	−	14.1210i	0.676864	−	0.736108i
$369$	3.69078			0.192134
$370$	3.97579	−	3.57751i	0.206692	−	0.185986i
$371$		−	8.17299i		−	0.424320i
$372$	1.59645	−	15.0962i	0.0827723	−	0.782699i
$373$			33.2992i			1.72417i	0.506766	+	0.862084i	$0.330841\pi$
$373$			33.2992i			1.72417i	−0.506766	+	0.862084i	$0.669159\pi$
$374$	−1.87233	−	2.08078i	−0.0968161	−	0.107594i
$375$	−1.57817			−0.0814962
$376$	6.41488	−	4.65127i	0.330822	−	0.239871i
$377$	26.0985			1.34414
$378$	6.01605	+	6.68581i	0.309432	+	0.343881i
$379$	−30.2336			−1.55300			−0.776498	−	0.630120i	$-0.783006\pi$
$379$	−30.2336			−1.55300			−0.776498	+	0.630120i	$0.783006\pi$
$380$	8.93489	+	0.944886i	0.458350	+	0.0484716i
$381$	−7.38055			−0.378117
$382$	9.02925	−	8.12474i	0.461977	−	0.415698i
$383$	−27.0139			−1.38035			−0.690173	−	0.723645i	$-0.742466\pi$
$383$	−27.0139			−1.38035			−0.690173	+	0.723645i	$0.742466\pi$
$384$	16.3275	−	7.22564i	0.833211	−	0.368732i
$385$		−	6.73690i		−	0.343344i
$386$	20.5559	−	18.4967i	1.04627	−	0.941459i
$387$	5.67934			0.288697
$388$	28.9983	+	3.06664i	1.47216	+	0.155685i
$389$		−	26.5759i		−	1.34745i	−0.738982	−	0.673726i	$-0.764693\pi$
$389$		−	26.5759i		−	1.34745i	0.738982	−	0.673726i	$-0.235307\pi$
$390$	4.47235	−	4.02433i	0.226466	−	0.203780i
$391$	1.39373	+	0.821808i	0.0704838	+	0.0415606i
$392$	−9.43288	−	13.0095i	−0.476432	−	0.657080i
$393$	−10.4032			−0.524774
$394$	−10.1902	+	9.16940i	−0.513376	+	0.461948i
$395$		−	5.07701i		−	0.255452i
$396$	−0.628577	+	5.94385i	−0.0315872	+	0.298690i
$397$	−0.161514			−0.00810615			−0.00405307	−	0.999992i	$-0.501290\pi$
$397$	−0.161514			−0.00810615			−0.00405307	+	0.999992i	$0.501290\pi$
$398$	−15.3251	+	13.7899i	−0.768179	+	0.691226i
$399$			8.14110i			0.407565i
$400$	3.91152	+	0.836662i	0.195576	+	0.0418331i
$401$		−	28.4480i		−	1.42063i	−0.703886	−	0.710313i	$-0.748553\pi$
$401$		−	28.4480i		−	1.42063i	0.703886	−	0.710313i	$-0.251447\pi$
$402$	8.96657	+	9.96480i	0.447212	+	0.496999i
$403$			12.9649i			0.645826i
$404$	2.11272	−	19.9780i	0.105112	−	0.993942i
$405$			7.21236i			0.358385i
$406$	−11.6873	+	10.5165i	−0.580032	+	0.521927i
$407$			22.1878i			1.09981i
$408$	0.883994	+	1.21918i	0.0437642	+	0.0603582i
$409$	−11.3916			−0.563278			−0.281639	−	0.959520i	$-0.590878\pi$
$409$	−11.3916			−0.563278			−0.281639	+	0.959520i	$0.590878\pi$
$410$	6.85394	+	7.61698i	0.338492	+	0.376176i
$411$	22.9849			1.13376
$412$	−0.891991	+	8.43471i	−0.0439452	+	0.415549i
$413$		−	1.95657i		−	0.0962763i
$414$	−0.686185	−	3.38601i	−0.0337241	−	0.166413i
$415$			15.7178i			0.771555i
$416$	−13.2183	+	7.60338i	−0.648081	+	0.372786i
$417$	18.0279			0.882830
$418$	−27.7072	+	24.9316i	−1.35520	+	1.21944i
$419$	−16.7783			−0.819672			−0.409836	−	0.912159i	$-0.634414\pi$
$419$	−16.7783			−0.819672			−0.409836	+	0.912159i	$0.634414\pi$
$420$	−0.381166	+	3.60432i	−0.0185990	+	0.175873i
$421$		−	2.44644i		−	0.119232i	−0.998221	−	0.0596161i	$-0.981012\pi$
$421$		−	2.44644i		−	0.119232i	0.998221	−	0.0596161i	$-0.0189876\pi$
$422$	12.7874	+	14.2110i	0.622482	+	0.691782i
$423$		−	1.42702i		−	0.0693843i
$424$	−16.2979	+	11.8172i	−0.791495	+	0.573893i
$425$			0.337371i			0.0163649i
$426$	6.43284	−	5.78842i	0.311672	−	0.280450i
$427$			16.0376i			0.776115i
$428$	−0.0601721	+	0.568991i	−0.00290853	+	0.0275032i
$429$			24.9590i			1.20503i
$430$	10.5468	+	11.7209i	0.508611	+	0.565234i
$431$	−14.5579			−0.701231			−0.350615	−	0.936520i	$-0.614028\pi$
$431$	−14.5579			−0.701231			−0.350615	+	0.936520i	$0.614028\pi$
$432$	4.63377	−	21.6636i	0.222942	−	1.04229i
$433$			32.9891i			1.58535i	0.609642	+	0.792676i	$0.291313\pi$
$433$			32.9891i			1.58535i	−0.609642	+	0.792676i	$0.708687\pi$
$434$	−5.22427	−	5.80588i	−0.250773	−	0.278691i
$435$	−15.2791			−0.732579
$436$	−7.87602	−	0.832907i	−0.377193	−	0.0398890i
$437$	10.9430	−	18.5586i	0.523475	−	0.887776i
$438$	2.79474	+	3.10587i	0.133538	+	0.148404i
$439$			37.4011i			1.78506i	0.450992	+	0.892528i	$0.351070\pi$
$439$			37.4011i			1.78506i	−0.450992	+	0.892528i	$0.648930\pi$
$440$	−13.4341	+	9.74076i	−0.640448	+	0.464372i
$441$	−2.89404			−0.137811
$442$	−0.860297	−	0.956073i	−0.0409202	−	0.0454757i
$443$			15.9532i			0.757961i	0.925405	+	0.378981i	$0.123725\pi$
$443$			15.9532i			0.757961i	−0.925405	+	0.378981i	$0.876275\pi$
$444$	1.25536	−	11.8707i	0.0595767	−	0.563360i
$445$	18.1716			0.861415
$446$	6.82207	+	7.58156i	0.323034	+	0.358997i
$447$	1.12321			0.0531260
$448$	2.85555	−	8.73132i	0.134912	−	0.412516i
$449$	9.04758			0.426982			0.213491	−	0.976945i	$-0.431517\pi$
$449$	9.04758			0.426982			0.213491	+	0.976945i	$0.431517\pi$
$450$	0.535504	−	0.481859i	0.0252439	−	0.0227151i
$451$	−42.5083			−2.00164
$452$	25.3952	+	2.68560i	1.19449	+	0.126320i
$453$	24.5547			1.15368
$454$	−17.2408	+	15.5137i	−0.809152	+	0.728095i
$455$		−	3.09546i		−	0.145117i
$456$	16.2343	−	11.7711i	0.760240	−	0.551231i
$457$		−	13.2620i		−	0.620368i	−0.950676	−	0.310184i	$-0.899609\pi$
$457$		−	13.2620i		−	0.620368i	0.950676	−	0.310184i	$-0.100391\pi$
$458$	0.983140	+	1.09259i	0.0459391	+	0.0510535i
$459$	1.86850			0.0872139
$460$	5.71373	−	7.70411i	0.266404	−	0.359206i
$461$	−33.8884			−1.57834			−0.789170	−	0.614175i	$-0.789489\pi$
$461$	−33.8884			−1.57834			−0.789170	+	0.614175i	$0.789489\pi$
$462$	−10.0574	−	11.1770i	−0.467911	−	0.520003i
$463$		−	18.5528i		−	0.862220i	−0.902299	−	0.431110i	$-0.858122\pi$
$463$		−	18.5528i		−	0.862220i	0.902299	−	0.431110i	$-0.141878\pi$
$464$	37.8697	+	8.10020i	1.75806	+	0.376042i
$465$		−	7.59017i		−	0.351986i
$466$	11.3419	−	10.2057i	0.525401	−	0.472768i
$467$	−36.4158			−1.68512			−0.842561	−	0.538600i	$-0.818953\pi$
$467$	−36.4158			−1.68512			−0.842561	+	0.538600i	$0.818953\pi$
$468$	−0.288817	+	2.73107i	−0.0133506	+	0.126244i
$469$	6.89696			0.318472
$470$	2.94508	−	2.65005i	0.135846	−	0.122238i
$471$	−16.2283			−0.747758
$472$	−3.90161	+	2.82896i	−0.179586	+	0.130214i
$473$	−65.4114			−3.00762
$474$	−7.57936	−	8.42316i	−0.348132	−	0.386888i
$475$	4.49236			0.206123
$476$	0.770510	+	0.0814833i	0.0353163	+	0.00373478i
$477$			3.62555i			0.166003i
$478$	−6.05181	−	6.72555i	−0.276803	−	0.307619i
$479$	−17.9165			−0.818624			−0.409312	−	0.912394i	$-0.634231\pi$
$479$	−17.9165			−0.818624			−0.409312	+	0.912394i	$0.634231\pi$
$480$	7.73855	−	4.45134i	0.353215	−	0.203175i
$481$			10.1948i			0.464843i
$482$	6.59837	+	7.33295i	0.300547	+	0.334007i
$483$	7.48649	+	4.41439i	0.340647	+	0.200862i
$484$	4.92593	−	46.5799i	0.223906	−	2.11727i
$485$	14.5800			0.662043
$486$	−4.95009	−	5.50118i	−0.224541	−	0.249539i
$487$		−	34.9503i		−	1.58375i	−0.610682	−	0.791876i	$-0.709105\pi$
$487$		−	34.9503i		−	1.58375i	0.610682	−	0.791876i	$-0.290895\pi$
$488$	31.9808	−	23.1885i	1.44770	−	1.04969i
$489$	−2.32694			−0.105228
$490$	−5.37436	−	5.97268i	−0.242789	−	0.269818i
$491$			24.9004i			1.12374i	0.827226	+	0.561869i	$0.189918\pi$
$491$			24.9004i			1.12374i	−0.827226	+	0.561869i	$0.810082\pi$
$492$	22.7424	+	2.40507i	1.02531	+	0.108429i
$493$			3.26628i			0.147106i
$494$	−12.7309	+	11.4555i	−0.572788	+	0.515408i
$495$			2.98850i			0.134323i
$496$	−4.02391	+	18.8124i	−0.180679	+	0.844701i
$497$		−	4.45238i		−	0.199716i
$498$	23.4647	+	26.0770i	1.05148	+	1.16854i
$499$		−	29.8277i		−	1.33527i	−0.744488	−	0.667636i	$-0.767306\pi$
$499$		−	29.8277i		−	1.33527i	0.744488	−	0.667636i	$-0.232694\pi$
$500$	1.98891	+	0.210332i	0.0889467	+	0.00940632i
$501$	8.12684			0.363080
$502$	−1.03072	+	0.927471i	−0.0460035	+	0.0413951i
$503$	−3.77428			−0.168287			−0.0841434	−	0.996454i	$-0.526815\pi$
$503$	−3.77428			−0.168287			−0.0841434	+	0.996454i	$0.526815\pi$
$504$	−0.971165	−	1.33940i	−0.0432591	−	0.0596616i
$505$		−	10.0447i		−	0.446983i
$506$	7.90308	+	38.9981i	0.351335	+	1.73368i
$507$		−	9.04806i		−	0.401839i
$508$	9.30145	+	0.983650i	0.412685	+	0.0436424i
$509$	13.2522			0.587392			0.293696	−	0.955899i	$-0.405115\pi$
$509$	13.2522			0.587392			0.293696	+	0.955899i	$0.405115\pi$
$510$	0.503654	+	0.559725i	0.0223022	+	0.0247850i
$511$	2.14967			0.0950959
$512$	−21.5400	+	6.93016i	−0.951944	+	0.306273i
$513$		−	24.8805i		−	1.09850i
$514$	−10.8067	+	9.72416i	−0.476665	+	0.428914i
$515$			4.24087i			0.186875i
$516$	34.9959	+	3.70090i	1.54061	+	0.162923i
$517$			16.4357i			0.722839i
$518$	−4.10806	−	4.56540i	−0.180498	−	0.200592i
$519$		−	9.35272i		−	0.410539i
$520$	−6.17270	+	4.47567i	−0.270691	+	0.196271i
$521$			20.1710i			0.883708i	0.897087	+	0.441854i	$0.145679\pi$
$521$			20.1710i			0.883708i	−0.897087	+	0.441854i	$0.854321\pi$
$522$	5.18452	−	4.66515i	0.226920	−	0.204188i
$523$	26.3693			1.15305			0.576524	−	0.817080i	$-0.304409\pi$
$523$	26.3693			1.15305			0.576524	+	0.817080i	$0.304409\pi$
$524$	13.1108	+	1.38650i	0.572750	+	0.0605696i
$525$			1.81221i			0.0790914i
$526$	−7.29568	+	6.56483i	−0.318107	+	0.286240i
$527$	−1.62258			−0.0706807
$528$	−7.74653	+	36.2162i	−0.337125	+	1.57611i
$529$	−11.1326	−	20.1262i	−0.484027	−	0.875053i
$530$	−7.48237	+	6.73281i	−0.325013	+	0.292455i
$531$			0.867936i			0.0376652i
$532$	1.08501	−	10.2599i	0.0470413	−	0.444825i
$533$	−19.5316			−0.846009
$534$	30.1480	−	27.1279i	1.30463	−	1.17394i
$535$			0.286082i			0.0123684i
$536$	−9.97218	−	13.7533i	−0.430733	−	0.594053i
$537$	−22.8108			−0.984358
$538$	14.8494	−	13.3619i	0.640204	−	0.576071i
$539$	33.3319			1.43571
$540$	1.16490	−	11.0154i	0.0501294	−	0.474026i
$541$	10.3731			0.445973			0.222987	−	0.974822i	$-0.428419\pi$
$541$	10.3731			0.445973			0.222987	+	0.974822i	$0.428419\pi$
$542$	13.2248	+	14.6971i	0.568054	+	0.631294i
$543$	−23.9137			−1.02624
$544$	−0.951580	−	1.65430i	−0.0407986	−	0.0709276i
$545$	−3.95997			−0.169626
$546$	−4.62114	−	5.13561i	−0.197767	−	0.219784i
$547$			16.8233i			0.719313i	0.933085	+	0.359657i	$0.117106\pi$
$547$			16.8233i			0.719313i	−0.933085	+	0.359657i	$0.882894\pi$
$548$	−28.9671	−	3.06334i	−1.23741	−	0.130859i
$549$		−	7.11431i		−	0.303632i
$550$	−6.16763	+	5.54978i	−0.262988	+	0.236643i
$551$	43.4931			1.85287
$552$	−2.02178	−	21.3116i	−0.0860526	−	0.907083i
$553$	−5.82994			−0.247914
$554$	12.7488	−	11.4716i	0.541643	−	0.487383i
$555$		−	5.96847i		−	0.253347i
$556$	−22.7199	−	2.40269i	−0.963540	−	0.101897i
$557$		−	11.0734i		−	0.469196i	−0.972092	−	0.234598i	$-0.924623\pi$
$557$		−	11.0734i		−	0.469196i	0.972092	−	0.234598i	$-0.0753774\pi$
$558$	2.31749	+	2.57550i	0.0981073	+	0.109029i
$559$	−30.0551			−1.27120
$560$	0.960739	−	4.49160i	0.0405986	−	0.189805i
$561$	−3.12367			−0.131881
$562$	−1.94939	−	2.16641i	−0.0822301	−	0.0913846i
$563$	3.00895			0.126812			0.0634060	−	0.997988i	$-0.479804\pi$
$563$	3.00895			0.126812			0.0634060	+	0.997988i	$0.479804\pi$
$564$	0.929909	−	8.79328i	0.0391563	−	0.370264i
$565$	12.7684			0.537171
$566$	15.5984	−	14.0358i	0.655649	−	0.589969i
$567$	8.28196			0.347810
$568$	−8.87854	+	6.43761i	−0.372535	+	0.270116i
$569$		−	37.3566i		−	1.56607i	−0.621977	−	0.783035i	$-0.713670\pi$
$569$		−	37.3566i		−	1.56607i	0.621977	−	0.783035i	$-0.286330\pi$
$570$	7.45317	−	6.70654i	0.312179	−	0.280906i
$571$	10.7952			0.451765			0.225883	−	0.974155i	$-0.427473\pi$
$571$	10.7952			0.451765			0.225883	+	0.974155i	$0.427473\pi$
$572$	3.32643	−	31.4549i	0.139085	−	1.31520i
$573$		−	13.5547i		−	0.566257i
$574$	8.74658	−	7.87039i	0.365075	−	0.328504i
$575$	2.43592	−	4.13114i	0.101585	−	0.172280i
$576$	−1.26673	+	3.87323i	−0.0527803	+	0.161384i
$577$	−31.0255			−1.29161			−0.645805	−	0.763503i	$-0.723478\pi$
$577$	−31.0255			−1.29161			−0.645805	+	0.763503i	$0.723478\pi$
$578$	−17.7519	+	15.9736i	−0.738382	+	0.664414i
$579$		−	30.8586i		−	1.28244i
$580$	19.2558	+	2.03634i	0.799552	+	0.0845545i
$581$	18.0487			0.748787
$582$	24.1893	−	21.7661i	1.00268	−	0.902236i
$583$		−	41.7570i		−	1.72940i
$584$	−3.10817	−	4.28669i	−0.128617	−	0.177385i
$585$			1.37315i			0.0567728i
$586$	−2.72334	−	3.02652i	−0.112500	−	0.125024i
$587$			28.8629i			1.19130i	0.803245	+	0.595649i	$0.203105\pi$
$587$			28.8629i			1.19130i	−0.803245	+	0.595649i	$0.796895\pi$
$588$	−17.8330	−	1.88588i	−0.735419	−	0.0777723i
$589$			21.6059i			0.890256i
$590$	−1.79123	+	1.61180i	−0.0737440	+	0.0663566i
$591$			15.2976i			0.629259i
$592$	−3.16417	+	14.7930i	−0.130047	+	0.607988i
$593$	24.4483			1.00397			0.501986	−	0.864876i	$-0.332603\pi$
$593$	24.4483			1.00397			0.501986	+	0.864876i	$0.332603\pi$
$594$	30.7369	+	34.1588i	1.26115	+	1.40155i
$595$	0.387403			0.0158820
$596$	−1.41554	−	0.149697i	−0.0579829	−	0.00613182i
$597$			23.0061i			0.941577i
$598$	3.63130	+	17.9188i	0.148495	+	0.732754i
$599$			1.87197i			0.0764868i	0.999268	+	0.0382434i	$0.0121762\pi$
$599$			1.87197i			0.0764868i	−0.999268	+	0.0382434i	$0.987824\pi$
$600$	3.61376	−	2.62024i	0.147531	−	0.106971i
$601$	−3.78423			−0.154362			−0.0771809	−	0.997017i	$-0.524592\pi$
$601$	−3.78423			−0.154362			−0.0771809	+	0.997017i	$0.524592\pi$
$602$	13.4592	−	12.1109i	0.548555	−	0.493603i
$603$	−3.05950			−0.124593
$604$	−30.9455	−	3.27256i	−1.25915	−	0.133158i
$605$		−	23.4198i		−	0.952151i
$606$	−14.9955	−	16.6649i	−0.609150	−	0.676966i
$607$		−	3.61540i		−	0.146745i	−0.997305	−	0.0733723i	$-0.976624\pi$
$607$		−	3.61540i		−	0.146745i	0.997305	−	0.0733723i	$-0.0233762\pi$
$608$	−22.0283	+	12.6710i	−0.893365	+	0.513878i
$609$			17.5450i			0.710961i
$610$	14.6824	−	13.2116i	0.594474	−	0.534922i
$611$			7.55183i			0.305514i
$612$	−0.341800	−	0.0361461i	−0.0138164	−	0.00146112i
$613$		−	38.0798i		−	1.53803i	−0.639232	−	0.769014i	$-0.720748\pi$
$613$		−	38.0798i		−	1.53803i	0.639232	−	0.769014i	$-0.279252\pi$
$614$	−12.8695	−	14.3023i	−0.519371	−	0.577192i
$615$	11.4346			0.461089
$616$	11.1853	+	15.4264i	0.450669	+	0.621549i
$617$			18.4344i			0.742143i	0.928604	+	0.371071i	$0.121009\pi$
$617$			18.4344i			0.742143i	−0.928604	+	0.371071i	$0.878991\pi$
$618$	6.33111	+	7.03594i	0.254674	+	0.283027i
$619$	−19.6955			−0.791629			−0.395815	−	0.918330i	$-0.629538\pi$
$619$	−19.6955			−0.791629			−0.395815	+	0.918330i	$0.629538\pi$
$620$	−1.01159	+	9.56563i	−0.0406263	+	0.384165i
$621$	−22.8799	−	13.4911i	−0.918139	−	0.541378i
$622$	32.5814	+	36.2087i	1.30640	+	1.45184i
$623$		−	20.8664i		−	0.835995i
$624$	−3.55936	+	16.6406i	−0.142489	+	0.666156i
$625$	1.00000			0.0400000
$626$	−12.1272	−	13.4773i	−0.484701	−	0.538662i
$627$			41.5941i			1.66111i
$628$	20.4519	+	2.16284i	0.816120	+	0.0863066i
$629$	−1.27590			−0.0508736
$630$	−0.553319	−	0.614919i	−0.0220448	−	0.0244990i
$631$	22.8886			0.911179			0.455590	−	0.890190i	$-0.349428\pi$
$631$	22.8886			0.911179			0.455590	+	0.890190i	$0.349428\pi$
$632$	8.42940	+	11.6256i	0.335303	+	0.462440i
$633$	21.3336			0.847936
$634$	19.5959	−	17.6328i	0.778252	−	0.700290i
$635$	4.67666			0.185588
$636$	−2.36256	+	22.3405i	−0.0936817	+	0.885859i
$637$	15.3153			0.606814
$638$	−59.7123	+	53.7306i	−2.36403	+	2.12721i
$639$			1.97508i			0.0781330i
$640$	−10.3459	+	4.57850i	−0.408957	+	0.180981i
$641$		−	46.4771i		−	1.83574i	−0.396885	−	0.917868i	$-0.629909\pi$
$641$		−	46.4771i		−	1.83574i	0.396885	−	0.917868i	$-0.370091\pi$
$642$	0.427085	+	0.474632i	0.0168557	+	0.0187322i
$643$	−20.6356			−0.813791			−0.406895	−	0.913475i	$-0.633389\pi$
$643$	−20.6356			−0.813791			−0.406895	+	0.913475i	$0.633389\pi$
$644$	−8.84664	−	6.56108i	−0.348606	−	0.258543i
$645$	17.5955			0.692823
$646$	−1.43368	−	1.59329i	−0.0564075	−	0.0626873i
$647$			12.8995i			0.507133i	0.967318	+	0.253566i	$0.0816037\pi$
$647$			12.8995i			0.507133i	−0.967318	+	0.253566i	$0.918396\pi$
$648$	−11.9747	−	16.5152i	−0.470412	−	0.648777i
$649$		−	9.99639i		−	0.392392i
$650$	−2.83389	+	2.55000i	−0.111154	+	0.100019i
$651$	−8.71580			−0.341599
$652$	2.93256	+	0.310125i	0.114848	+	0.0121454i
$653$	−42.5451			−1.66492			−0.832460	−	0.554086i	$-0.813068\pi$
$653$	−42.5451			−1.66492			−0.832460	+	0.554086i	$0.813068\pi$
$654$	−6.56990	+	5.91175i	−0.256903	+	0.231168i
$655$	6.59198			0.257570
$656$	−28.3410	−	6.06204i	−1.10653	−	0.236683i
$657$	−0.953598			−0.0372034
$658$	−3.04305	−	3.38183i	−0.118631	−	0.131838i
$659$	2.95845			0.115245			0.0576224	−	0.998338i	$-0.481648\pi$
$659$	2.95845			0.115245			0.0576224	+	0.998338i	$0.481648\pi$
$660$	−1.94743	+	18.4150i	−0.0758037	+	0.716804i
$661$			6.49895i			0.252780i	0.991981	+	0.126390i	$0.0403390\pi$
$661$			6.49895i			0.252780i	−0.991981	+	0.126390i	$0.959661\pi$
$662$	−3.81934	−	4.24455i	−0.148443	−	0.164969i
$663$	−1.43526			−0.0557408
$664$	−26.0963	−	35.9912i	−1.01273	−	1.39673i
$665$		−	5.15858i		−	0.200041i
$666$	1.82234	+	2.02522i	0.0706143	+	0.0784757i
$667$	23.5835	−	39.9959i	0.913157	−	1.54865i
$668$	−10.2420	−	1.08311i	−0.396274	−	0.0419069i
$669$	11.3815			0.440032
$670$	−5.68163	−	6.31416i	−0.219501	−	0.243937i
$671$			81.9386i			3.16320i
$672$	−5.11147	−	8.88619i	−0.197179	−	0.342792i
$673$	−24.0548			−0.927245			−0.463623	−	0.886033i	$-0.653451\pi$
$673$	−24.0548			−0.927245			−0.463623	+	0.886033i	$0.653451\pi$
$674$	−15.3339	−	17.0411i	−0.590642	−	0.656397i
$675$		−	5.53840i		−	0.213173i
$676$	−1.20589	+	11.4030i	−0.0463804	+	0.438575i
$677$		−	42.9245i		−	1.64972i	−0.565336	−	0.824861i	$-0.691253\pi$
$677$		−	42.9245i		−	1.64972i	0.565336	−	0.824861i	$-0.308747\pi$
$678$	21.1838	−	19.0617i	0.813558	−	0.732059i
$679$		−	16.7422i		−	0.642507i
$680$	−0.560139	−	0.772527i	−0.0214804	−	0.0296250i
$681$			25.8820i			0.991800i
$682$	−26.6916	−	29.6631i	−1.02207	−	1.13586i
$683$		−	42.6624i		−	1.63243i	−0.577747	−	0.816216i	$-0.696068\pi$
$683$		−	42.6624i		−	1.63243i	0.577747	−	0.816216i	$-0.303932\pi$
$684$	−0.481314	+	4.55133i	−0.0184035	+	0.174024i
$685$	−14.5643			−0.556474
$686$	−15.3086	+	13.7751i	−0.584487	+	0.525935i
$687$	1.64020			0.0625776
$688$	−43.6108	−	9.32822i	−1.66265	−	0.355635i
$689$		−	19.1864i		−	0.730945i
$690$	−2.12591	−	10.4904i	−0.0809321	−	0.399363i
$691$			23.5330i			0.895237i	0.894225	+	0.447619i	$0.147728\pi$
$691$			23.5330i			0.895237i	−0.894225	+	0.447619i	$0.852272\pi$
$692$	−1.24649	+	11.7869i	−0.0473845	+	0.448071i
$693$	3.43170			0.130359
$694$	24.8590	+	27.6265i	0.943634	+	1.04869i
$695$	−11.4233			−0.433311
$696$	34.9868	−	25.3681i	1.32617	−	0.961574i
$697$		−	2.44443i		−	0.0925892i
$698$	−31.0510	+	27.9404i	−1.17530	+	1.05756i
$699$		−	17.0264i		−	0.643998i
$700$	0.241524	−	2.28387i	0.00912876	−	0.0863220i
$701$			23.7221i			0.895971i	0.894041	+	0.447985i	$0.147858\pi$
$701$			23.7221i			0.895971i	−0.894041	+	0.447985i	$0.852142\pi$
$702$	14.1229	+	15.6952i	0.533036	+	0.592378i
$703$			16.9896i			0.640776i
$704$	14.5894	−	44.6096i	0.549860	−	1.68129i
$705$		−	4.42115i		−	0.166510i
$706$	−1.10516	+	0.994450i	−0.0415933	+	0.0374266i
$707$	−11.5343			−0.433793
$708$	−0.565583	+	5.34819i	−0.0212559	+	0.200997i
$709$			42.8775i			1.61030i	0.593072	+	0.805150i	$0.297915\pi$
$709$			42.8775i			1.61030i	−0.593072	+	0.805150i	$0.702085\pi$
$710$	−4.07615	+	3.66781i	−0.152975	+	0.137651i
$711$	2.58617			0.0969890
$712$	−41.6100	+	30.1704i	−1.55940	+	1.13068i
$713$	19.8686	+	11.7155i	0.744087	+	0.438749i
$714$	0.642732	−	0.578346i	0.0240537	−	0.0216441i
$715$		−	15.8152i		−	0.591454i
$716$	28.7476	+	3.04013i	1.07435	+	0.113615i
$717$	−10.0964			−0.377057
$718$	5.63254	−	5.06829i	0.210204	−	0.189147i
$719$		−	3.31292i		−	0.123551i	−0.998090	−	0.0617755i	$-0.980324\pi$
$719$		−	3.31292i		−	0.123551i	0.998090	−	0.0617755i	$-0.0196763\pi$
$720$	−0.426186	+	1.99248i	−0.0158830	+	0.0742554i
$721$	4.86980			0.181361
$722$	−1.24183	+	1.11743i	−0.0462163	+	0.0415865i
$723$	11.0082			0.409401
$724$	30.1376	+	3.18713i	1.12006	+	0.118449i
$725$	9.68157			0.359564
$726$	−34.9629	−	38.8553i	−1.29760	−	1.44206i
$727$	1.18980			0.0441272			0.0220636	−	0.999757i	$-0.492976\pi$
$727$	1.18980			0.0441272			0.0220636	+	0.999757i	$0.492976\pi$
$728$	5.13941	+	7.08812i	0.190479	+	0.262703i
$729$	−29.8955			−1.10724
$730$	−1.77087	−	1.96802i	−0.0655430	−	0.0728398i
$731$		−	3.76146i		−	0.139123i
$732$	4.63599	−	43.8381i	0.171351	−	1.62030i
$733$		−	15.0297i		−	0.555133i	−0.960706	−	0.277567i	$-0.910472\pi$
$733$		−	15.0297i		−	0.555133i	0.960706	−	0.277567i	$-0.0895279\pi$
$734$	−14.5924	+	13.1306i	−0.538616	+	0.484659i
$735$	−8.96621			−0.330724
$736$	−0.292349	+	27.1277i	−0.0107761	+	0.999942i
$737$	35.2376			1.29799
$738$	−3.88000	+	3.49132i	−0.142825	+	0.128517i
$739$			27.5735i			1.01431i	0.861856	+	0.507154i	$0.169302\pi$
$739$			27.5735i			1.01431i	−0.861856	+	0.507154i	$0.830698\pi$
$740$	−0.795454	+	7.52185i	−0.0292415	+	0.276509i
$741$			19.1116i			0.702082i
$742$	7.73129	+	8.59201i	0.283825	+	0.315422i
$743$	−27.4567			−1.00729			−0.503644	−	0.863911i	$-0.668008\pi$
$743$	−27.4567			−1.00729			−0.503644	+	0.863911i	$0.668008\pi$
$744$	12.6020	+	17.3803i	0.462012	+	0.637192i
$745$	−0.711718			−0.0260753
$746$	−31.4996	−	35.0064i	−1.15328	−	1.28168i
$747$	−8.00645			−0.292941
$748$	3.93665	+	0.416310i	0.143938	+	0.0152218i
$749$	0.328508			0.0120034
$750$	1.65908	−	1.49288i	0.0605810	−	0.0545122i
$751$	10.1529			0.370485			0.185242	−	0.982693i	$-0.440693\pi$
$751$	10.1529			0.370485			0.185242	+	0.982693i	$0.440693\pi$
$752$	−2.34387	+	10.9579i	−0.0854720	+	0.399594i
$753$			1.54733i			0.0563877i
$754$	−27.4365	+	24.6880i	−0.999179	+	0.899085i
$755$	−15.5590			−0.566251
$756$	−12.6490	−	1.33766i	−0.460039	−	0.0486501i
$757$			19.3939i			0.704884i	0.935834	+	0.352442i	$0.114649\pi$
$757$			19.3939i			0.704884i	−0.935834	+	0.352442i	$0.885351\pi$
$758$	31.7836	−	28.5997i	1.15443	−	1.03879i
$759$	38.2496	+	22.5538i	1.38837	+	0.818651i
$760$	−10.2868	+	7.45869i	−0.373141	+	0.270555i
$761$	−20.9777			−0.760442			−0.380221	−	0.924896i	$-0.624152\pi$
$761$	−20.9777			−0.760442			−0.380221	+	0.924896i	$0.624152\pi$
$762$	7.75894	−	6.98168i	0.281077	−	0.252920i
$763$			4.54723i			0.164621i
$764$	−1.80652	+	17.0826i	−0.0653576	+	0.618026i
$765$	−0.171853			−0.00621335
$766$	28.3989	−	25.5540i	1.02609	−	0.923303i
$767$		−	4.59312i		−	0.165848i
$768$	−10.3295	+	23.0412i	−0.372733	+	0.831429i
$769$			25.4748i			0.918646i	0.888269	+	0.459323i	$0.151908\pi$
$769$			25.4748i			0.918646i	−0.888269	+	0.459323i	$0.848092\pi$
$770$	6.37281	+	7.08229i	0.229660	+	0.255228i
$771$			16.2231i			0.584261i
$772$	−4.11271	+	38.8901i	−0.148020	+	1.39968i
$773$		−	13.7357i		−	0.494037i	−0.969011	−	0.247019i	$-0.920549\pi$
$773$		−	13.7357i		−	0.494037i	0.969011	−	0.247019i	$-0.0794509\pi$
$774$	−5.97051	+	5.37241i	−0.214606	+	0.193107i
$775$			4.80948i			0.172762i
$776$	−33.3859	+	24.2073i	−1.19848	+	0.868990i
$777$	−6.85360			−0.245871
$778$	25.1396	+	27.9384i	0.901300	+	1.00164i
$779$	−32.5494			−1.16620
$780$	−0.894803	+	8.46131i	−0.0320391	+	0.302963i
$781$		−	22.7479i		−	0.813982i
$782$	−2.24258	+	0.454464i	−0.0801943	+	0.0162516i
$783$		−	53.6204i		−	1.91624i
$784$	22.2229	+	4.75341i	0.793676	+	0.169765i
$785$	10.2830			0.367015
$786$	10.9366	−	9.84102i	0.390096	−	0.351017i
$787$	24.3399			0.867625			0.433813	−	0.901003i	$-0.357168\pi$
$787$	24.3399			0.867625			0.433813	+	0.901003i	$0.357168\pi$
$788$	2.03880	−	19.2790i	0.0726293	−	0.686786i
$789$			10.9523i			0.389912i
$790$	4.80263	+	5.33730i	0.170870	+	0.189893i
$791$		−	14.6620i		−	0.521320i
$792$	−4.96183	−	6.84319i	−0.176311	−	0.243162i
$793$			37.6490i			1.33696i
$794$	0.169794	−	0.152785i	0.00602578	−	0.00542214i
$795$			11.2325i			0.398377i
$796$	3.06616	−	28.9938i	0.108677	−	1.02766i
$797$		−	8.57495i		−	0.303740i	−0.988400	−	0.151870i	$-0.951470\pi$
$797$		−	8.57495i		−	0.303740i	0.988400	−	0.151870i	$-0.0485295\pi$
$798$	−7.70113	−	8.55848i	−0.272617	−	0.302967i
$799$	−0.945128			−0.0334362
$800$	−4.90351	+	2.82057i	−0.173365	+	0.0997223i
$801$			9.25638i			0.327058i
$802$	26.9106	+	29.9065i	0.950247	+	1.05604i
$803$	10.9830			0.387581
$804$	−18.8525	−	1.99370i	−0.664878	−	0.0703124i
$805$	−4.74379	−	2.79716i	−0.167197	−	0.0985871i
$806$	−12.2642	−	13.6295i	−0.431988	−	0.480080i
$807$		−	22.2920i		−	0.784715i
$808$	16.6773	+	23.0008i	0.586704	+	0.809164i
$809$	−24.7677			−0.870786			−0.435393	−	0.900241i	$-0.643390\pi$
$809$	−24.7677			−0.870786			−0.435393	+	0.900241i	$0.643390\pi$
$810$	−6.82258	−	7.58213i	−0.239721	−	0.266409i
$811$		−	32.7032i		−	1.14837i	−0.818727	−	0.574183i	$-0.805320\pi$
$811$		−	32.7032i		−	1.14837i	0.818727	−	0.574183i	$-0.194680\pi$
$812$	2.33833	−	22.1114i	0.0820594	−	0.775958i
$813$	22.0633			0.773794
$814$	−20.9887	−	23.3253i	−0.735653	−	0.817553i
$815$	1.47445			0.0516479
$816$	−2.08260	−	0.445462i	−0.0729057	−	0.0155943i
$817$	−50.0868			−1.75231
$818$	11.9756	−	10.7760i	0.418718	−	0.376772i
$819$	1.57679			0.0550975
$820$	−14.4107	−	1.52396i	−0.503242	−	0.0532191i
$821$	−36.3720			−1.26939			−0.634695	−	0.772763i	$-0.718874\pi$
$821$	−36.3720			−1.26939			−0.634695	+	0.772763i	$0.718874\pi$
$822$	−24.1634	+	21.7428i	−0.842794	+	0.758366i
$823$		−	31.8719i		−	1.11099i	−0.831522	−	0.555493i	$-0.812530\pi$
$823$		−	31.8719i		−	1.11099i	0.831522	−	0.555493i	$-0.187470\pi$
$824$	−7.04115	−	9.71094i	−0.245290	−	0.338296i
$825$			9.25886i			0.322352i
$826$	1.85083	+	2.05688i	0.0643985	+	0.0715679i
$827$	29.1203			1.01261			0.506306	−	0.862354i	$-0.331011\pi$
$827$	29.1203			1.01261			0.506306	+	0.862354i	$0.331011\pi$
$828$	3.92438	+	2.91050i	0.136382	+	0.101147i
$829$	31.1522			1.08196			0.540981	−	0.841035i	$-0.318053\pi$
$829$	31.1522			1.08196			0.540981	+	0.841035i	$0.318053\pi$
$830$	−14.8683	−	16.5236i	−0.516087	−	0.573543i
$831$		−	19.1385i		−	0.663906i
$832$	6.70353	−	20.4972i	0.232403	−	0.710611i
$833$			1.91674i			0.0664112i
$834$	−18.9522	+	17.0536i	−0.656260	+	0.590518i
$835$	−5.14954			−0.178207
$836$	5.54349	−	52.4196i	0.191726	−	1.81297i
$837$	26.6368			0.920704
$838$	17.6385	−	15.8715i	0.609311	−	0.548273i
$839$	46.6020			1.60888			0.804440	−	0.594034i	$-0.202465\pi$
$839$	46.6020			1.60888			0.804440	+	0.594034i	$0.202465\pi$
$840$	−3.00883	−	4.14968i	−0.103814	−	0.143177i
$841$	64.7328			2.23217
$842$	2.31423	+	2.57187i	0.0797535	+	0.0886323i
$843$	−3.25223			−0.112013
$844$	−26.8860	−	2.84326i	−0.925456	−	0.0978691i
$845$			5.73327i			0.197231i
$846$	1.34990	+	1.50019i	0.0464106	+	0.0515775i
$847$	−26.8930			−0.924055
$848$	5.95491	−	27.8401i	0.204492	−	0.956033i
$849$		−	23.4163i		−	0.803647i
$850$	−0.319138	−	0.354668i	−0.0109464	−	0.0121650i
$851$	15.6235	+	9.21239i	0.535568	+	0.315797i
$852$	−1.28705	+	12.1704i	−0.0440935	+	0.416950i
$853$	31.9161			1.09279			0.546393	−	0.837529i	$-0.316000\pi$
$853$	31.9161			1.09279			0.546393	+	0.837529i	$0.316000\pi$
$854$	−15.1709	−	16.8598i	−0.519137	−	0.576932i
$855$			2.28835i			0.0782600i
$856$	−0.474984	−	0.655082i	−0.0162346	−	0.0223903i
$857$	3.36985			0.115112			0.0575560	−	0.998342i	$-0.481669\pi$
$857$	3.36985			0.115112			0.0575560	+	0.998342i	$0.481669\pi$
$858$	−23.6101	−	26.2386i	−0.806036	−	0.895771i
$859$			5.06773i			0.172909i	0.996256	+	0.0864543i	$0.0275537\pi$
$859$			5.06773i			0.172909i	−0.996256	+	0.0864543i	$0.972446\pi$
$860$	−22.1750	−	2.34506i	−0.756162	−	0.0799659i
$861$		−	13.1304i		−	0.447483i
$862$	15.3043	−	13.7712i	0.521266	−	0.469048i
$863$		−	14.7315i		−	0.501467i	−0.968056	−	0.250733i	$-0.919328\pi$
$863$		−	14.7315i		−	0.501467i	0.968056	−	0.250733i	$-0.0806717\pi$
$864$	15.6215	+	27.1576i	0.531453	+	0.923920i
$865$			5.92631i			0.201501i
$866$	−31.2062	−	34.6804i	−1.06043	−	1.17849i
$867$			26.6492i			0.905055i
$868$	10.9842	+	1.16161i	0.372829	+	0.0394275i
$869$	−29.7860			−1.01042
$870$	16.0625	−	14.4534i	0.544569	−	0.490016i
$871$	16.1909			0.548608
$872$	9.06771	−	6.57476i	0.307071	−	0.222650i
$873$			7.42688i			0.251362i
$874$	6.05155	+	29.8616i	0.204697	+	1.01008i
$875$		−	1.14830i		−	0.0388197i
$876$	−5.87604	−	0.621405i	−0.198533	−	0.0209953i
$877$	−38.2958			−1.29316			−0.646579	−	0.762847i	$-0.723801\pi$
$877$	−38.2958			−1.29316			−0.646579	+	0.762847i	$0.723801\pi$
$878$	−35.3798	−	39.3186i	−1.19401	−	1.32694i
$879$	−4.54342			−0.153246
$880$	4.90856	−	22.9483i	0.165468	−	0.773586i
$881$			24.7855i			0.835046i	0.908666	+	0.417523i	$0.137102\pi$
$881$			24.7855i			0.835046i	−0.908666	+	0.417523i	$0.862898\pi$
$882$	3.04241	−	2.73764i	0.102443	−	0.0921810i
$883$			29.7961i			1.00272i	0.865239	+	0.501359i	$0.167166\pi$
$883$			29.7961i			1.00272i	−0.865239	+	0.501359i	$0.832834\pi$
$884$	1.80881	+	0.191286i	0.0608368	+	0.00643363i
$885$			2.68901i			0.0903899i
$886$	−15.0911	−	16.7711i	−0.506994	−	0.563437i
$887$		−	4.35497i		−	0.146225i	−0.997324	−	0.0731127i	$-0.976707\pi$
$887$		−	4.35497i		−	0.146225i	0.997324	−	0.0731127i	$-0.0232933\pi$
$888$	9.90949	+	13.6669i	0.332541	+	0.458630i
$889$		−	5.37021i		−	0.180111i
$890$	−19.1032	+	17.1895i	−0.640340	+	0.576194i
$891$	42.3138			1.41756
$892$	−14.3437	−	1.51687i	−0.480261	−	0.0507887i
$893$			12.5851i			0.421145i
$894$	−1.18080	+	1.06251i	−0.0394917	+	0.0355356i
$895$	14.4540			0.483143
$896$	5.25750	+	11.8802i	0.175641	+	0.396889i
$897$	17.5749	+	10.3630i	0.586808	+	0.346010i
$898$	−9.51144	+	8.55862i	−0.317401	+	0.285605i
$899$			46.5633i			1.55297i
$900$	−0.107141	+	1.01313i	−0.00357135	+	0.0337709i
$901$	2.40123			0.0799964
$902$	44.6876	−	40.2110i	1.48793	−	1.33888i
$903$		−	20.2049i		−	0.672378i
$904$	−29.2376	+	21.1995i	−0.972429	+	0.705084i
$905$	15.1528			0.503698
$906$	−25.8136	+	23.2277i	−0.857600	+	0.771689i
$907$	31.0041			1.02948			0.514738	−	0.857348i	$-0.327889\pi$
$907$	31.0041			1.02948			0.514738	+	0.857348i	$0.327889\pi$
$908$	3.44945	−	32.6182i	0.114474	−	1.08247i
$909$	5.11665			0.169708
$910$	2.92817	+	3.25416i	0.0970679	+	0.107874i
$911$	−7.92111			−0.262438			−0.131219	−	0.991353i	$-0.541889\pi$
$911$	−7.92111			−0.262438			−0.131219	+	0.991353i	$0.541889\pi$
$912$	−5.93167	+	27.7315i	−0.196417	+	0.918281i
$913$	92.2137			3.05183
$914$	12.5452	+	13.9419i	0.414960	+	0.461157i
$915$		−	22.0413i		−	0.728663i
$916$	−2.06709	−	0.218599i	−0.0682985	−	0.00722273i
$917$		−	7.56957i		−	0.249969i
$918$	−1.96429	+	1.76752i	−0.0648313	+	0.0583367i
$919$	9.16166			0.302215			0.151108	−	0.988517i	$-0.451716\pi$
$919$	9.16166			0.302215			0.151108	+	0.988517i	$0.451716\pi$
$920$	1.28109	+	13.5040i	0.0422364	+	0.445215i
$921$	−21.4706			−0.707480
$922$	35.6258	−	32.0569i	1.17327	−	1.05574i
$923$		−	10.4521i		−	0.344037i
$924$	21.1460	+	2.23624i	0.695652	+	0.0735668i
$925$			3.78190i			0.124348i
$926$	17.5501	+	19.5039i	0.576732	+	0.640939i
$927$	−2.16025			−0.0709520
$928$	−47.4736	+	27.3076i	−1.55840	+	0.896415i
$929$	15.7388			0.516373			0.258186	−	0.966095i	$-0.416875\pi$
$929$	15.7388			0.516373			0.258186	+	0.966095i	$0.416875\pi$
$930$	7.17997	+	7.97931i	0.235440	+	0.261652i
$931$	25.5229			0.836479
$932$	−2.26921	+	21.4578i	−0.0743305	+	0.702874i
$933$	54.3566			1.77955
$934$	38.2828	−	34.4478i	1.25265	−	1.12717i
$935$	1.97930			0.0647301
$936$	−2.27985	−	3.14430i	−0.0745193	−	0.102775i
$937$		−	4.58133i		−	0.149666i	−0.997196	−	0.0748328i	$-0.976158\pi$
$937$		−	4.58133i		−	0.149666i	0.997196	−	0.0748328i	$-0.0238423\pi$
$938$	−7.25055	+	6.52422i	−0.236739	+	0.213023i
$939$	−20.2322			−0.660253
$940$	−0.589234	+	5.57183i	−0.0192187	+	0.181733i
$941$		−	13.5888i		−	0.442981i	−0.975163	−	0.221491i	$-0.928908\pi$
$941$		−	13.5888i		−	0.442981i	0.975163	−	0.221491i	$-0.0710922\pi$
$942$	17.0603	−	15.3512i	0.555853	−	0.500170i
$943$	−17.6495	+	29.9322i	−0.574746	+	0.974727i
$944$	1.42557	−	6.66476i	0.0463984	−	0.216919i
$945$	−6.35975			−0.206883
$946$	68.7649	−	61.8763i	2.23574	−	2.01177i
$947$		−	35.8222i		−	1.16406i	−0.813166	−	0.582032i	$-0.802258\pi$
$947$		−	35.8222i		−	1.16406i	0.813166	−	0.582032i	$-0.197742\pi$
$948$	15.9359	+	1.68526i	0.517574	+	0.0547346i
$949$	5.04645			0.163815
$950$	−4.72267	+	4.24958i	−0.153224	+	0.137874i
$951$		−	29.4174i		−	0.953925i
$952$	−0.887093	+	0.643209i	−0.0287508	+	0.0208465i
$953$		−	34.1621i		−	1.10662i	−0.832975	−	0.553310i	$-0.813364\pi$
$953$		−	34.1621i		−	1.10662i	0.832975	−	0.553310i	$-0.186636\pi$
$954$	−3.42961	−	3.81143i	−0.111038	−	0.123400i
$955$			8.58891i			0.277931i
$956$	12.7242	+	1.34561i	0.411529	+	0.0435201i
$957$			89.6403i			2.89766i
$958$	18.8350	−	16.9482i	0.608532	−	0.547572i
$959$			16.7242i			0.540054i
$960$	−3.92453	+	11.9999i	−0.126664	+	0.387295i
$961$	7.86888			0.253835
$962$	−9.64385	−	10.7175i	−0.310930	−	0.345546i
$963$	−0.145727			−0.00469598
$964$	−13.8733	−	1.46713i	−0.446829	−	0.0472532i
$965$			19.5535i			0.629448i
$966$	−12.0461	+	2.44119i	−0.387578	+	0.0785439i
$967$			36.9685i			1.18883i	0.804160	+	0.594413i	$0.202616\pi$
$967$			36.9685i			1.18883i	−0.804160	+	0.594413i	$0.797384\pi$
$968$	38.8841	+	53.6277i	1.24978	+	1.72366i
$969$	−2.39186			−0.0768375
$970$	−15.3275	+	13.7920i	−0.492136	+	0.442836i
$971$	32.9396			1.05708			0.528541	−	0.848908i	$-0.322739\pi$
$971$	32.9396			1.05708			0.528541	+	0.848908i	$0.322739\pi$
$972$	10.4078	+	1.10064i	0.333829	+	0.0353032i
$973$			13.1174i			0.420525i
$974$	33.0615	+	36.7422i	1.05936	+	1.17730i
$975$			4.25424i			0.136245i
$976$	−11.6851	+	54.6298i	−0.374032	+	1.74866i
$977$			47.6931i			1.52584i	0.646494	+	0.762919i	$0.276234\pi$
$977$			47.6931i			1.52584i	−0.646494	+	0.762919i	$0.723766\pi$
$978$	2.44624	−	2.20118i	0.0782220	−	0.0703860i
$979$		−	106.610i		−	3.40726i
$980$	11.2998	+	1.19498i	0.360959	+	0.0381722i
$981$		−	2.01716i		−	0.0644030i
$982$	−23.5547	−	26.1770i	−0.751660	−	0.835341i
$983$	−20.7502			−0.661827			−0.330914	−	0.943661i	$-0.607357\pi$
$983$	−20.7502			−0.661827			−0.330914	+	0.943661i	$0.607357\pi$
$984$	−26.1835	+	18.9850i	−0.834700	+	0.605220i
$985$		−	9.69326i		−	0.308853i
$986$	−3.08976	−	3.43374i	−0.0983980	−	0.109353i
$987$	−5.07682			−0.161597
$988$	2.54712	−	24.0857i	0.0810345	−	0.766267i
$989$	−27.1588	+	46.0594i	−0.863601	+	1.46461i
$990$	−2.82699	−	3.14172i	−0.0898477	−	0.0998503i
$991$			25.9210i			0.823408i	0.911318	+	0.411704i	$0.135066\pi$
$991$			25.9210i			0.823408i	−0.911318	+	0.411704i	$0.864934\pi$
$992$	−13.5655	−	23.5833i	−0.430705	−	0.748771i
$993$	−6.37192			−0.202207
$994$	4.21175	+	4.68064i	0.133589	+	0.148461i
$995$		−	14.5777i		−	0.462145i
$996$	−49.3354	−	5.21734i	−1.56325	−	0.165318i
$997$	−50.8979			−1.61195			−0.805976	−	0.591948i	$-0.798359\pi$
$997$	−50.8979			−1.61195			−0.805976	+	0.591948i	$0.798359\pi$
$998$	28.2157	+	31.3569i	0.893153	+	0.992586i
$999$	20.9457			0.662692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.b.91.7	yes	32
4.3	odd	2	inner	460.2.e.b.91.5	✓	32
23.22	odd	2	inner	460.2.e.b.91.8	yes	32
92.91	even	2	inner	460.2.e.b.91.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.b.91.5	✓	32	4.3	odd	2	inner
460.2.e.b.91.6	yes	32	92.91	even	2	inner
460.2.e.b.91.7	yes	32	1.1	even	1	trivial
460.2.e.b.91.8	yes	32	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05127 + 0.945957i) q^{2} +1.57817i q^{3} +(0.210332 - 1.98891i) q^{4} -1.00000i q^{5} +(-1.49288 - 1.65908i) q^{6} -1.14830 q^{7} +(1.66031 + 2.28984i) q^{8} +0.509388 q^{9} +O(q^{10})\)	\(q+(-1.05127 + 0.945957i) q^{2} +1.57817i q^{3} +(0.210332 - 1.98891i) q^{4} -1.00000i q^{5} +(-1.49288 - 1.65908i) q^{6} -1.14830 q^{7} +(1.66031 + 2.28984i) q^{8} +0.509388 q^{9} +(0.945957 + 1.05127i) q^{10} -5.86684 q^{11} +(3.13883 + 0.331939i) q^{12} -2.69569 q^{13} +(1.20717 - 1.08624i) q^{14} +1.57817 q^{15} +(-3.91152 - 0.836662i) q^{16} -0.337371i q^{17} +(-0.535504 + 0.481859i) q^{18} -4.49236 q^{19} +(-1.98891 - 0.210332i) q^{20} -1.81221i q^{21} +(6.16763 - 5.54978i) q^{22} +(-2.43592 + 4.13114i) q^{23} +(-3.61376 + 2.62024i) q^{24} -1.00000 q^{25} +(2.83389 - 2.55000i) q^{26} +5.53840i q^{27} +(-0.241524 + 2.28387i) q^{28} -9.68157 q^{29} +(-1.65908 + 1.49288i) q^{30} -4.80948i q^{31} +(4.90351 - 2.82057i) q^{32} -9.25886i q^{33} +(0.319138 + 0.354668i) q^{34} +1.14830i q^{35} +(0.107141 - 1.01313i) q^{36} -3.78190i q^{37} +(4.72267 - 4.24958i) q^{38} -4.25424i q^{39} +(2.28984 - 1.66031i) q^{40} +7.24551 q^{41} +(1.71427 + 1.90512i) q^{42} +11.1493 q^{43} +(-1.23398 + 11.6686i) q^{44} -0.509388i q^{45} +(-1.34708 - 6.64721i) q^{46} -2.80145i q^{47} +(1.32039 - 6.17303i) q^{48} -5.68141 q^{49} +(1.05127 - 0.945957i) q^{50} +0.532428 q^{51} +(-0.566989 + 5.36148i) q^{52} +7.11746i q^{53} +(-5.23909 - 5.82235i) q^{54} +5.86684i q^{55} +(-1.90653 - 2.62943i) q^{56} -7.08969i q^{57} +(10.1779 - 9.15835i) q^{58} +1.70388i q^{59} +(0.331939 - 3.13883i) q^{60} -13.9664i q^{61} +(4.54956 + 5.05606i) q^{62} -0.584931 q^{63} +(-2.48676 + 7.60368i) q^{64} +2.69569i q^{65} +(8.75848 + 9.73355i) q^{66} -6.00623 q^{67} +(-0.671000 - 0.0709599i) q^{68} +(-6.51963 - 3.84428i) q^{69} +(-1.08624 - 1.20717i) q^{70} +3.87736i q^{71} +(0.845741 + 1.16642i) q^{72} -1.87205 q^{73} +(3.57751 + 3.97579i) q^{74} -1.57817i q^{75} +(-0.944886 + 8.93489i) q^{76} +6.73690 q^{77} +(4.02433 + 4.47235i) q^{78} +5.07701 q^{79} +(-0.836662 + 3.91152i) q^{80} -7.21236 q^{81} +(-7.61698 + 6.85394i) q^{82} -15.7178 q^{83} +(-3.60432 - 0.381166i) q^{84} -0.337371 q^{85} +(-11.7209 + 10.5468i) q^{86} -15.2791i q^{87} +(-9.74076 - 13.4341i) q^{88} +18.1716i q^{89} +(0.481859 + 0.535504i) q^{90} +3.09546 q^{91} +(7.70411 + 5.71373i) q^{92} +7.59017 q^{93} +(2.65005 + 2.94508i) q^{94} +4.49236i q^{95} +(4.45134 + 7.73855i) q^{96} +14.5800i q^{97} +(5.97268 - 5.37436i) q^{98} -2.98850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9	\( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 - 4 * q^4 - 16 * q^6 - 2 * q^8 - 52 * q^9 + 24 * q^12 - 4 * q^13 + 20 * q^16 - 56 * q^18 - 6 * q^24 - 32 * q^25 + 68 * q^26 + 8 * q^29 - 16 * q^32 + 8 * q^36 + 44 * q^41 - 4 * q^46 - 4 * q^48 - 12 * q^49 - 4 * q^50 + 16 * q^52 + 42 * q^54 - 10 * q^58 - 36 * q^62 - 22 * q^64 - 44 * q^69 - 42 * q^70 - 32 * q^72 - 8 * q^73 - 72 * q^77 + 122 * q^78 - 32 * q^81 + 20 * q^82 - 44 * q^85 + 64 * q^92 + 40 * q^93 - 26 * q^94 + 16 * q^96 + 62 * q^98

Introduction

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