LMFDB - Embedded newform 552.2.n.a.91.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(91,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("552.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.13
Character	$\chi$	$=$	552.91
Dual form			552.2.n.a.91.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0902148 - 1.41133i) q^{2} +1.00000 q^{3} +(-1.98372 - 0.254646i) q^{4} -3.06098 q^{5} +(0.0902148 - 1.41133i) q^{6} -0.892124 q^{7} +(-0.538352 + 2.77672i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.0902148 - 1.41133i) q^{2} +1.00000 q^{3} +(-1.98372 - 0.254646i) q^{4} -3.06098 q^{5} +(0.0902148 - 1.41133i) q^{6} -0.892124 q^{7} +(-0.538352 + 2.77672i) q^{8} +1.00000 q^{9} +(-0.276146 + 4.32007i) q^{10} +3.95311i q^{11} +(-1.98372 - 0.254646i) q^{12} +4.14787i q^{13} +(-0.0804827 + 1.25908i) q^{14} -3.06098 q^{15} +(3.87031 + 1.01029i) q^{16} +1.01396i q^{17} +(0.0902148 - 1.41133i) q^{18} -0.195663i q^{19} +(6.07214 + 0.779468i) q^{20} -0.892124 q^{21} +(5.57915 + 0.356629i) q^{22} +(-4.42425 - 1.85094i) q^{23} +(-0.538352 + 2.77672i) q^{24} +4.36961 q^{25} +(5.85403 + 0.374200i) q^{26} +1.00000 q^{27} +(1.76973 + 0.227176i) q^{28} +3.05624i q^{29} +(-0.276146 + 4.32007i) q^{30} -2.58909i q^{31} +(1.77502 - 5.37115i) q^{32} +3.95311i q^{33} +(1.43104 + 0.0914745i) q^{34} +2.73077 q^{35} +(-1.98372 - 0.254646i) q^{36} +6.01692 q^{37} +(-0.276146 - 0.0176517i) q^{38} +4.14787i q^{39} +(1.64789 - 8.49949i) q^{40} -10.2344 q^{41} +(-0.0804827 + 1.25908i) q^{42} +10.0034i q^{43} +(1.00664 - 7.84187i) q^{44} -3.06098 q^{45} +(-3.01142 + 6.07712i) q^{46} +7.33196i q^{47} +(3.87031 + 1.01029i) q^{48} -6.20412 q^{49} +(0.394204 - 6.16698i) q^{50} +1.01396i q^{51} +(1.05624 - 8.22823i) q^{52} -11.2321 q^{53} +(0.0902148 - 1.41133i) q^{54} -12.1004i q^{55} +(0.480276 - 2.47718i) q^{56} -0.195663i q^{57} +(4.31337 + 0.275718i) q^{58} -4.35054 q^{59} +(6.07214 + 0.779468i) q^{60} +7.63888 q^{61} +(-3.65407 - 0.233574i) q^{62} -0.892124 q^{63} +(-7.42035 - 2.98971i) q^{64} -12.6966i q^{65} +(5.57915 + 0.356629i) q^{66} -3.60187i q^{67} +(0.258202 - 2.01142i) q^{68} +(-4.42425 - 1.85094i) q^{69} +(0.246356 - 3.85403i) q^{70} +10.5891i q^{71} +(-0.538352 + 2.77672i) q^{72} +3.24682 q^{73} +(0.542815 - 8.49188i) q^{74} +4.36961 q^{75} +(-0.0498249 + 0.388141i) q^{76} -3.52666i q^{77} +(5.85403 + 0.374200i) q^{78} +1.85136 q^{79} +(-11.8470 - 3.09250i) q^{80} +1.00000 q^{81} +(-0.923296 + 14.4442i) q^{82} -3.79082i q^{83} +(1.76973 + 0.227176i) q^{84} -3.10373i q^{85} +(14.1181 + 0.902455i) q^{86} +3.05624i q^{87} +(-10.9767 - 2.12816i) q^{88} -10.7963i q^{89} +(-0.276146 + 4.32007i) q^{90} -3.70042i q^{91} +(8.30516 + 4.79837i) q^{92} -2.58909i q^{93} +(10.3478 + 0.661451i) q^{94} +0.598921i q^{95} +(1.77502 - 5.37115i) q^{96} -2.49750i q^{97} +(-0.559703 + 8.75607i) q^{98} +3.95311i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9	$ 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) $ 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 4 * q^24 + 24 * q^25 + 24 * q^27 - 4 * q^32 + 4 * q^36 + 4 * q^46 + 4 * q^48 - 8 * q^49 - 44 * q^50 - 4 * q^54 + 48 * q^58 - 40 * q^62 + 4 * q^64 - 4 * q^72 - 32 * q^73 + 24 * q^75 + 24 * q^81 - 40 * q^82 - 52 * q^92 + 40 * q^94 - 4 * q^96 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	0.0902148	−	1.41133i	0.0637915	−	0.997963i
$2$	0.0902148	−	1.41133i	0.0637915	−	0.997963i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.98372	−	0.254646i	−0.991861	−	0.127323i
$5$	−3.06098			−1.36891			−0.684457	−	0.729054i	$-0.739960\pi$
$5$	−3.06098			−1.36891			−0.684457	+	0.729054i	$0.739960\pi$
$6$	0.0902148	−	1.41133i	0.0368300	−	0.576174i
$7$	−0.892124			−0.337191			−0.168596	−	0.985685i	$-0.553923\pi$
$7$	−0.892124			−0.337191			−0.168596	+	0.985685i	$0.553923\pi$
$8$	−0.538352	+	2.77672i	−0.190336	+	0.981719i
$9$	1.00000			0.333333
$10$	−0.276146	+	4.32007i	−0.0873250	+	1.36612i
$11$			3.95311i			1.19191i	0.803019	+	0.595953i	$0.203226\pi$
$11$			3.95311i			1.19191i	−0.803019	+	0.595953i	$0.796774\pi$
$12$	−1.98372	−	0.254646i	−0.572651	−	0.0735100i
$13$			4.14787i			1.15041i	0.818008	+	0.575207i	$0.195078\pi$
$13$			4.14787i			1.15041i	−0.818008	+	0.575207i	$0.804922\pi$
$14$	−0.0804827	+	1.25908i	−0.0215099	+	0.336504i
$15$	−3.06098			−0.790342
$16$	3.87031	+	1.01029i	0.967578	+	0.252574i
$17$			1.01396i			0.245922i	0.992411	+	0.122961i	$0.0392391\pi$
$17$			1.01396i			0.245922i	−0.992411	+	0.122961i	$0.960761\pi$
$18$	0.0902148	−	1.41133i	0.0212638	−	0.332654i
$19$		−	0.195663i		−	0.0448882i	−0.999748	−	0.0224441i	$-0.992855\pi$
$19$		−	0.195663i		−	0.0448882i	0.999748	−	0.0224441i	$-0.00714478\pi$
$20$	6.07214	+	0.779468i	1.35777	+	0.174294i
$21$	−0.892124			−0.194677
$22$	5.57915	+	0.356629i	1.18948	+	0.0760335i
$23$	−4.42425	−	1.85094i	−0.922521	−	0.385947i
$23$	−4.42425	−	1.85094i	−0.922521	−	0.385947i
$24$	−0.538352	+	2.77672i	−0.109891	+	0.566796i
$25$	4.36961			0.873923
$26$	5.85403	+	0.374200i	1.14807	+	0.0733866i
$27$	1.00000			0.192450
$28$	1.76973	+	0.227176i	0.334447	+	0.0429322i
$29$			3.05624i			0.567530i	0.958894	+	0.283765i	$0.0915835\pi$
$29$			3.05624i			0.567530i	−0.958894	+	0.283765i	$0.908416\pi$
$30$	−0.276146	+	4.32007i	−0.0504171	+	0.788733i
$31$		−	2.58909i		−	0.465015i	−0.972595	−	0.232507i	$-0.925307\pi$
$31$		−	2.58909i		−	0.465015i	0.972595	−	0.232507i	$-0.0746930\pi$
$32$	1.77502	−	5.37115i	0.313783	−	0.949495i
$33$			3.95311i			0.688147i
$34$	1.43104	+	0.0914745i	0.245421	+	0.0156878i
$35$	2.73077			0.461585
$36$	−1.98372	−	0.254646i	−0.330620	−	0.0424410i
$37$	6.01692			0.989176			0.494588	−	0.869128i	$-0.335319\pi$
$37$	6.01692			0.989176			0.494588	+	0.869128i	$0.335319\pi$
$38$	−0.276146	−	0.0176517i	−0.0447968	−	0.00286349i
$39$			4.14787i			0.664192i
$40$	1.64789	−	8.49949i	0.260554	−	1.34389i
$41$	−10.2344			−1.59835			−0.799174	−	0.601099i	$-0.794730\pi$
$41$	−10.2344			−1.59835			−0.799174	+	0.601099i	$0.794730\pi$
$42$	−0.0804827	+	1.25908i	−0.0124188	+	0.194281i
$43$			10.0034i			1.52550i	0.646691	+	0.762752i	$0.276153\pi$
$43$			10.0034i			1.52550i	−0.646691	+	0.762752i	$0.723847\pi$
$44$	1.00664	−	7.84187i	0.151757	−	1.18221i
$45$	−3.06098			−0.456304
$46$	−3.01142	+	6.07712i	−0.444010	+	0.896022i
$47$			7.33196i			1.06948i	0.845018	+	0.534738i	$0.179590\pi$
$47$			7.33196i			1.06948i	−0.845018	+	0.534738i	$0.820410\pi$
$48$	3.87031	+	1.01029i	0.558631	+	0.145824i
$49$	−6.20412			−0.886302
$50$	0.394204	−	6.16698i	0.0557488	−	0.872143i
$51$			1.01396i			0.141983i
$52$	1.05624	−	8.22823i	0.146474	−	1.14105i
$53$	−11.2321			−1.54285			−0.771425	−	0.636320i	$-0.780456\pi$
$53$	−11.2321			−1.54285			−0.771425	+	0.636320i	$0.780456\pi$
$54$	0.0902148	−	1.41133i	0.0122767	−	0.192058i
$55$		−	12.1004i		−	1.63162i
$56$	0.480276	−	2.47718i	0.0641796	−	0.331027i
$57$		−	0.195663i		−	0.0259162i
$58$	4.31337	+	0.275718i	0.566374	+	0.0362036i
$59$	−4.35054			−0.566393			−0.283196	−	0.959062i	$-0.591395\pi$
$59$	−4.35054			−0.566393			−0.283196	+	0.959062i	$0.591395\pi$
$60$	6.07214	+	0.779468i	0.783910	+	0.100629i
$61$	7.63888			0.978059			0.489029	−	0.872267i	$-0.337351\pi$
$61$	7.63888			0.978059			0.489029	+	0.872267i	$0.337351\pi$
$62$	−3.65407	−	0.233574i	−0.464068	−	0.0296640i
$63$	−0.892124			−0.112397
$64$	−7.42035	−	2.98971i	−0.927544	−	0.373713i
$65$		−	12.6966i		−	1.57482i
$66$	5.57915	+	0.356629i	0.686746	+	0.0438980i
$67$		−	3.60187i		−	0.440039i	−0.975496	−	0.220019i	$-0.929388\pi$
$67$		−	3.60187i		−	0.440039i	0.975496	−	0.220019i	$-0.0706120\pi$
$68$	0.258202	−	2.01142i	0.0313116	−	0.243921i
$69$	−4.42425	−	1.85094i	−0.532618	−	0.222827i
$70$	0.246356	−	3.85403i	0.0294452	−	0.460645i
$71$			10.5891i			1.25669i	0.777933	+	0.628347i	$0.216268\pi$
$71$			10.5891i			1.25669i	−0.777933	+	0.628347i	$0.783732\pi$
$72$	−0.538352	+	2.77672i	−0.0634454	+	0.327240i
$73$	3.24682			0.380011			0.190006	−	0.981783i	$-0.439149\pi$
$73$	3.24682			0.380011			0.190006	+	0.981783i	$0.439149\pi$
$74$	0.542815	−	8.49188i	0.0631010	−	0.987161i
$75$	4.36961			0.504560
$76$	−0.0498249	+	0.388141i	−0.00571531	+	0.0445229i
$77$		−	3.52666i		−	0.401900i
$78$	5.85403	+	0.374200i	0.662839	+	0.0423698i
$79$	1.85136			0.208294			0.104147	−	0.994562i	$-0.466789\pi$
$79$	1.85136			0.208294			0.104147	+	0.994562i	$0.466789\pi$
$80$	−11.8470	−	3.09250i	−1.32453	−	0.345751i
$81$	1.00000			0.111111
$82$	−0.923296	+	14.4442i	−0.101961	+	1.59509i
$83$		−	3.79082i		−	0.416097i	−0.978119	−	0.208048i	$-0.933289\pi$
$83$		−	3.79082i		−	0.416097i	0.978119	−	0.208048i	$-0.0667111\pi$
$84$	1.76973	+	0.227176i	0.193093	+	0.0247869i
$85$		−	3.10373i		−	0.336646i
$86$	14.1181	+	0.902455i	1.52240	+	0.0973142i
$87$			3.05624i			0.327663i
$88$	−10.9767	−	2.12816i	−1.17012	−	0.226863i
$89$		−	10.7963i		−	1.14440i	−0.820113	−	0.572202i	$-0.806089\pi$
$89$		−	10.7963i		−	1.14440i	0.820113	−	0.572202i	$-0.193911\pi$
$90$	−0.276146	+	4.32007i	−0.0291083	+	0.455375i
$91$		−	3.70042i		−	0.387909i
$92$	8.30516	+	4.79837i	0.865873	+	0.500264i
$93$		−	2.58909i		−	0.268476i
$94$	10.3478	+	0.661451i	1.06730	+	0.0682235i
$95$			0.598921i			0.0614480i
$96$	1.77502	−	5.37115i	0.181162	−	0.548191i
$97$		−	2.49750i		−	0.253583i	−0.991929	−	0.126792i	$-0.959532\pi$
$97$		−	2.49750i		−	0.253583i	0.991929	−	0.126792i	$-0.0404679\pi$
$98$	−0.559703	+	8.75607i	−0.0565385	+	0.884497i
$99$			3.95311i			0.397302i
$100$	−8.66810	−	1.11271i	−0.866810	−	0.111271i
$101$		−	3.30462i		−	0.328822i	−0.986392	−	0.164411i	$-0.947428\pi$
$101$		−	3.30462i		−	0.328822i	0.986392	−	0.164411i	$-0.0525723\pi$
$102$	1.43104	+	0.0914745i	0.141694	+	0.00905733i
$103$	10.3779			1.02257			0.511284	−	0.859412i	$-0.329170\pi$
$103$	10.3779			1.02257			0.511284	+	0.859412i	$0.329170\pi$
$104$	−11.5175	−	2.23302i	−1.12938	−	0.218965i
$105$	2.73077			0.266496
$106$	−1.01330	+	15.8523i	−0.0984207	+	1.53971i
$107$			18.3222i			1.77127i	0.464381	+	0.885635i	$0.346277\pi$
$107$			18.3222i			1.77127i	−0.464381	+	0.885635i	$0.653723\pi$
$108$	−1.98372	−	0.254646i	−0.190884	−	0.0245033i
$109$	−12.4462			−1.19213			−0.596064	−	0.802937i	$-0.703269\pi$
$109$	−12.4462			−1.19213			−0.596064	+	0.802937i	$0.703269\pi$
$110$	−17.0777	−	1.09163i	−1.62829	−	0.104083i
$111$	6.01692			0.571101
$112$	−3.45280	−	0.901308i	−0.326259	−	0.0851656i
$113$		−	16.0203i		−	1.50707i	−0.657410	−	0.753533i	$-0.728348\pi$
$113$		−	16.0203i		−	1.50707i	0.657410	−	0.753533i	$-0.271652\pi$
$114$	−0.276146	−	0.0176517i	−0.0258634	−	0.00165323i
$115$	13.5426	+	5.66569i	1.26285	+	0.528328i
$116$	0.778260	−	6.06273i	0.0722596	−	0.562911i
$117$			4.14787i			0.383471i
$118$	−0.392483	+	6.14007i	−0.0361310	+	0.565239i
$119$		−	0.904581i		−	0.0829228i
$120$	1.64789	−	8.49949i	0.150431	−	0.775894i
$121$	−4.62705			−0.420641
$122$	0.689140	−	10.7810i	0.0623918	−	0.976067i
$123$	−10.2344			−0.922807
$124$	−0.659303	+	5.13604i	−0.0592071	+	0.461230i
$125$	1.92960			0.172589
$126$	−0.0804827	+	1.25908i	−0.00716997	+	0.112168i
$127$			0.281251i			0.0249569i	0.999922	+	0.0124785i	$0.00397212\pi$
$127$			0.281251i			0.0249569i	−0.999922	+	0.0124785i	$0.996028\pi$
$128$	−4.88890	+	10.2029i	−0.432121	+	0.901815i
$129$			10.0034i			0.880751i
$130$	−17.9191	−	1.14542i	−1.57161	−	0.100460i
$131$	21.7964			1.90436			0.952179	−	0.305542i	$-0.0988377\pi$
$131$	21.7964			1.90436			0.952179	+	0.305542i	$0.0988377\pi$
$132$	1.00664	−	7.84187i	0.0876171	−	0.682547i
$133$			0.174556i			0.0151359i
$134$	−5.08344	−	0.324942i	−0.439142	−	0.0280707i
$135$	−3.06098			−0.263447
$136$	−2.81549	−	0.545869i	−0.241427	−	0.0468079i
$137$		−	19.1551i		−	1.63653i	−0.574839	−	0.818267i	$-0.694935\pi$
$137$		−	19.1551i		−	1.63653i	0.574839	−	0.818267i	$-0.305065\pi$
$138$	−3.01142	+	6.07712i	−0.256349	+	0.517318i
$139$	−13.3472			−1.13210			−0.566048	−	0.824373i	$-0.691528\pi$
$139$	−13.3472			−1.13210			−0.566048	+	0.824373i	$0.691528\pi$
$140$	−5.41710	−	0.695382i	−0.457828	−	0.0587705i
$141$			7.33196i			0.617462i
$142$	14.9447	+	0.955293i	1.25413	+	0.0801664i
$143$	−16.3970			−1.37119
$144$	3.87031	+	1.01029i	0.322526	+	0.0841912i
$145$		−	9.35510i		−	0.776899i
$146$	0.292911	−	4.58234i	0.0242415	−	0.379237i
$147$	−6.20412			−0.511707
$148$	−11.9359	−	1.53219i	−0.981125	−	0.125945i
$149$	−1.91404			−0.156804			−0.0784020	−	0.996922i	$-0.524982\pi$
$149$	−1.91404			−0.156804			−0.0784020	+	0.996922i	$0.524982\pi$
$150$	0.394204	−	6.16698i	0.0321866	−	0.503532i
$151$			15.4992i			1.26131i	0.776064	+	0.630654i	$0.217213\pi$
$151$			15.4992i			1.26131i	−0.776064	+	0.630654i	$0.782787\pi$
$152$	0.543302	+	0.105336i	0.0440676	+	0.00854385i
$153$			1.01396i			0.0819741i
$154$	−4.97729	−	0.318157i	−0.401082	−	0.0256378i
$155$			7.92517i			0.636565i
$156$	1.05624	−	8.22823i	0.0845669	−	0.658786i
$157$	11.0597			0.882663			0.441331	−	0.897344i	$-0.354506\pi$
$157$	11.0597			0.882663			0.441331	+	0.897344i	$0.354506\pi$
$158$	0.167020	−	2.61288i	0.0132874	−	0.207870i
$159$	−11.2321			−0.890765
$160$	−5.43331	+	16.4410i	−0.429541	+	1.29978i
$161$	3.94698	+	1.65126i	0.311066	+	0.130138i
$162$	0.0902148	−	1.41133i	0.00708794	−	0.110885i
$163$	10.0689			0.788659			0.394330	−	0.918969i	$-0.370977\pi$
$163$	10.0689			0.788659			0.394330	+	0.918969i	$0.370977\pi$
$164$	20.3023	+	2.60616i	1.58534	+	0.203507i
$165$		−	12.1004i		−	0.942014i
$166$	−5.35011	−	0.341988i	−0.415249	−	0.0265434i
$167$		−	11.5383i		−	0.892858i	−0.894819	−	0.446429i	$-0.852696\pi$
$167$		−	11.5383i		−	0.892858i	0.894819	−	0.446429i	$-0.147304\pi$
$168$	0.480276	−	2.47718i	0.0370541	−	0.191118i
$169$	−4.20486			−0.323451
$170$	−4.38039	−	0.280002i	−0.335961	−	0.0214752i
$171$		−	0.195663i		−	0.0149627i
$172$	2.54733	−	19.8440i	0.194232	−	1.51309i
$173$		−	6.42949i		−	0.488825i	−0.969671	−	0.244413i	$-0.921405\pi$
$173$		−	6.42949i		−	0.488825i	0.969671	−	0.244413i	$-0.0785951\pi$
$174$	4.31337	+	0.275718i	0.326996	+	0.0209021i
$175$	−3.89824			−0.294679
$176$	−3.99380	+	15.2997i	−0.301044	+	1.15326i
$177$	−4.35054			−0.327007
$178$	−15.2371	−	0.973984i	−1.14207	−	0.0730032i
$179$	−0.681542			−0.0509408			−0.0254704	−	0.999676i	$-0.508108\pi$
$179$	−0.681542			−0.0509408			−0.0254704	+	0.999676i	$0.508108\pi$
$180$	6.07214	+	0.779468i	0.452591	+	0.0580981i
$181$	−8.75811			−0.650985			−0.325492	−	0.945545i	$-0.605530\pi$
$181$	−8.75811			−0.650985			−0.325492	+	0.945545i	$0.605530\pi$
$182$	−5.22252	−	0.333832i	−0.387119	−	0.0247453i
$183$	7.63888			0.564682
$184$	7.52134	−	11.2885i	0.554481	−	0.832197i
$185$	−18.4177			−1.35410
$186$	−3.65407	−	0.233574i	−0.267930	−	0.0171265i
$187$	−4.00831			−0.293116
$188$	1.86706	−	14.5446i	0.136169	−	1.06077i
$189$	−0.892124			−0.0648924
$190$	0.845278	+	0.0540316i	0.0613229	+	0.00391986i
$191$	7.03883			0.509312			0.254656	−	0.967032i	$-0.418038\pi$
$191$	7.03883			0.509312			0.254656	+	0.967032i	$0.418038\pi$
$192$	−7.42035	−	2.98971i	−0.535518	−	0.215763i
$193$	−21.4049			−1.54076			−0.770379	−	0.637586i	$-0.779933\pi$
$193$	−21.4049			−1.54076			−0.770379	+	0.637586i	$0.779933\pi$
$194$	−3.52481	−	0.225312i	−0.253067	−	0.0161764i
$195$		−	12.6966i		−	0.909220i
$196$	12.3072	+	1.57985i	0.879089	+	0.112847i
$197$			16.5652i			1.18022i	0.807323	+	0.590109i	$0.200915\pi$
$197$			16.5652i			1.18022i	−0.807323	+	0.590109i	$0.799085\pi$
$198$	5.57915	+	0.356629i	0.396493	+	0.0253445i
$199$	18.7514			1.32925			0.664627	−	0.747175i	$-0.268591\pi$
$199$	18.7514			1.32925			0.664627	+	0.747175i	$0.268591\pi$
$200$	−2.35239	+	12.1332i	−0.166339	+	0.857947i
$201$		−	3.60187i		−	0.254056i
$202$	−4.66392	−	0.298125i	−0.328152	−	0.0209760i
$203$		−	2.72654i		−	0.191366i
$204$	0.258202	−	2.01142i	0.0180778	−	0.140828i
$205$	31.3274			2.18800
$206$	0.936243	−	14.6467i	0.0652311	−	1.02049i
$207$	−4.42425	−	1.85094i	−0.307507	−	0.128649i
$208$	−4.19058	+	16.0536i	−0.290564	+	1.11311i
$209$	0.773477			0.0535025
$210$	0.246356	−	3.85403i	0.0170002	−	0.265954i
$211$	−4.73983			−0.326303			−0.163152	−	0.986601i	$-0.552166\pi$
$211$	−4.73983			−0.326303			−0.163152	+	0.986601i	$0.552166\pi$
$212$	22.2814	+	2.86022i	1.53029	+	0.196441i
$213$			10.5891i			0.725553i
$214$	25.8587	+	1.65293i	1.76766	+	0.112992i
$215$		−	30.6202i		−	2.08828i
$216$	−0.538352	+	2.77672i	−0.0366302	+	0.188932i
$217$			2.30979i			0.156799i
$218$	−1.12283	+	17.5657i	−0.0760476	+	1.18970i
$219$	3.24682			0.219400
$220$	−3.08132	+	24.0038i	−0.207742	+	1.61834i
$221$	−4.20580			−0.282912
$222$	0.542815	−	8.49188i	0.0364314	−	0.569938i
$223$		−	8.79654i		−	0.589060i	−0.955642	−	0.294530i	$-0.904837\pi$
$223$		−	8.79654i		−	0.589060i	0.955642	−	0.294530i	$-0.0951631\pi$
$224$	−1.58354	+	4.79173i	−0.105805	+	0.320161i
$225$	4.36961			0.291308
$226$	−22.6100	−	1.44527i	−1.50400	−	0.0961380i
$227$			23.9345i			1.58859i	0.607534	+	0.794294i	$0.292159\pi$
$227$			23.9345i			1.58859i	−0.607534	+	0.794294i	$0.707841\pi$
$228$	−0.0498249	+	0.388141i	−0.00329973	+	0.0257053i
$229$	−8.58118			−0.567060			−0.283530	−	0.958963i	$-0.591506\pi$
$229$	−8.58118			−0.567060			−0.283530	+	0.958963i	$0.591506\pi$
$230$	9.21791	−	18.6019i	0.607811	−	1.22658i
$231$		−	3.52666i		−	0.232037i
$232$	−8.48633	−	1.64533i	−0.557155	−	0.108021i
$233$	6.59907			0.432319			0.216160	−	0.976358i	$-0.430647\pi$
$233$	6.59907			0.432319			0.216160	+	0.976358i	$0.430647\pi$
$234$	5.85403	+	0.374200i	0.382690	+	0.0244622i
$235$		−	22.4430i		−	1.46402i
$236$	8.63027	+	1.10785i	0.561783	+	0.0721149i
$237$	1.85136			0.120258
$238$	−1.27667	−	0.0816066i	−0.0827539	−	0.00528977i
$239$			14.2318i			0.920576i	0.887770	+	0.460288i	$0.152254\pi$
$239$			14.2318i			0.920576i	−0.887770	+	0.460288i	$0.847746\pi$
$240$	−11.8470	−	3.09250i	−0.764718	−	0.199620i
$241$			18.9358i			1.21976i	0.792492	+	0.609882i	$0.208783\pi$
$241$			18.9358i			1.21976i	−0.792492	+	0.609882i	$0.791217\pi$
$242$	−0.417428	+	6.53031i	−0.0268333	+	0.419784i
$243$	1.00000			0.0641500
$244$	−15.1534	−	1.94521i	−0.970099	−	0.124529i
$245$	18.9907			1.21327
$246$	−0.923296	+	14.4442i	−0.0588672	+	0.920927i
$247$	0.811586			0.0516400
$248$	7.18918	+	1.39384i	0.456514	+	0.0885091i
$249$		−	3.79082i		−	0.240233i
$250$	0.174078	−	2.72331i	0.0110097	−	0.172237i
$251$			16.7334i			1.05620i	0.849182	+	0.528100i	$0.177096\pi$
$251$			16.7334i			1.05620i	−0.849182	+	0.528100i	$0.822904\pi$
$252$	1.76973	+	0.227176i	0.111482	+	0.0143107i
$253$	7.31695	−	17.4895i	0.460013	−	1.09956i
$254$	0.396938	+	0.0253730i	0.0249061	+	0.00159204i
$255$		−	3.10373i		−	0.194363i
$256$	13.9586	+	7.82031i	0.872413	+	0.488769i
$257$	10.9984			0.686064			0.343032	−	0.939324i	$-0.388546\pi$
$257$	10.9984			0.686064			0.343032	+	0.939324i	$0.388546\pi$
$258$	14.1181	+	0.902455i	0.878957	+	0.0561844i
$259$	−5.36784			−0.333541
$260$	−3.23313	+	25.1865i	−0.200510	+	1.56200i
$261$			3.05624i			0.189177i
$262$	1.96635	−	30.7619i	0.121482	−	1.90048i
$263$	32.1667			1.98348			0.991742	−	0.128249i	$-0.0409357\pi$
$263$	32.1667			1.98348			0.991742	+	0.128249i	$0.0409357\pi$
$264$	−10.9767	−	2.12816i	−0.675567	−	0.130979i
$265$	34.3813			2.11203
$266$	0.246356	+	0.0157475i	0.0151051	+	0.000965542i
$267$		−	10.7963i		−	0.660721i
$268$	−0.917203	+	7.14511i	−0.0560271	+	0.436457i
$269$			21.2979i			1.29856i	0.760550	+	0.649279i	$0.224929\pi$
$269$			21.2979i			1.29856i	−0.760550	+	0.649279i	$0.775071\pi$
$270$	−0.276146	+	4.32007i	−0.0168057	+	0.262911i
$271$		−	2.36324i		−	0.143556i	−0.997421	−	0.0717782i	$-0.977133\pi$
$271$		−	2.36324i		−	0.143556i	0.997421	−	0.0717782i	$-0.0228674\pi$
$272$	−1.02440	+	3.92436i	−0.0621135	+	0.237949i
$273$		−	3.70042i		−	0.223959i
$274$	−27.0343	−	1.72808i	−1.63320	−	0.104397i
$275$			17.2736i			1.04163i
$276$	8.30516	+	4.79837i	0.499912	+	0.288828i
$277$		−	9.50918i		−	0.571351i	−0.958326	−	0.285676i	$-0.907782\pi$
$277$		−	9.50918i		−	0.571351i	0.958326	−	0.285676i	$-0.0922180\pi$
$278$	−1.20412	+	18.8374i	−0.0722180	+	1.12979i
$279$		−	2.58909i		−	0.155005i
$280$	−1.47012	+	7.58260i	−0.0878563	+	0.453147i
$281$			22.7904i			1.35956i	0.733416	+	0.679780i	$0.237925\pi$
$281$			22.7904i			1.35956i	−0.733416	+	0.679780i	$0.762075\pi$
$282$	10.3478	+	0.661451i	0.616205	+	0.0393888i
$283$			17.0253i			1.01205i	0.862519	+	0.506025i	$0.168886\pi$
$283$			17.0253i			1.01205i	−0.862519	+	0.506025i	$0.831114\pi$
$284$	2.69647	−	21.0058i	0.160006	−	1.24647i
$285$			0.598921i			0.0354770i
$286$	−1.47925	+	23.1416i	−0.0874699	+	1.36839i
$287$	9.13037			0.538949
$288$	1.77502	−	5.37115i	0.104594	−	0.316498i
$289$	15.9719			0.939522
$290$	−13.2032	−	0.843968i	−0.775316	−	0.0495595i
$291$		−	2.49750i		−	0.146406i
$292$	−6.44079	−	0.826790i	−0.376918	−	0.0483842i
$293$	13.2959			0.776757			0.388378	−	0.921500i	$-0.373035\pi$
$293$	13.2959			0.776757			0.388378	+	0.921500i	$0.373035\pi$
$294$	−0.559703	+	8.75607i	−0.0326425	+	0.510665i
$295$	13.3169			0.775342
$296$	−3.23922	+	16.7073i	−0.188276	+	0.971093i
$297$			3.95311i			0.229382i
$298$	−0.172674	+	2.70134i	−0.0100028	+	0.156485i
$299$	7.67746	−	18.3513i	0.443999	−	1.06128i
$300$	−8.66810	−	1.11271i	−0.500453	−	0.0642421i
$301$		−	8.92427i		−	0.514387i
$302$	21.8745	+	1.39826i	1.25874	+	0.0804607i
$303$		−	3.30462i		−	0.189845i
$304$	0.197677	−	0.757277i	0.0113376	−	0.0434328i
$305$	−23.3825			−1.33888
$306$	1.43104	+	0.0914745i	0.0818072	+	0.00522925i
$307$	−6.89668			−0.393614			−0.196807	−	0.980442i	$-0.563057\pi$
$307$	−6.89668			−0.393614			−0.196807	+	0.980442i	$0.563057\pi$
$308$	−0.898051	+	6.99591i	−0.0511712	+	0.398629i
$309$	10.3779			0.590380
$310$	11.1850	+	0.714967i	0.635268	+	0.0406074i
$311$		−	20.2868i		−	1.15036i	−0.818026	−	0.575181i	$-0.804932\pi$
$311$		−	20.2868i		−	1.15036i	0.818026	−	0.575181i	$-0.195068\pi$
$312$	−11.5175	−	2.23302i	−0.652049	−	0.126420i
$313$			28.1949i			1.59367i	0.604198	+	0.796835i	$0.293494\pi$
$313$			28.1949i			1.59367i	−0.604198	+	0.796835i	$0.706506\pi$
$314$	0.997751	−	15.6090i	0.0563064	−	0.880865i
$315$	2.73077			0.153862
$316$	−3.67258	−	0.471441i	−0.206599	−	0.0265206i
$317$		−	8.49011i		−	0.476852i	−0.971161	−	0.238426i	$-0.923369\pi$
$317$		−	8.49011i		−	0.476852i	0.971161	−	0.238426i	$-0.0766315\pi$
$318$	−1.01330	+	15.8523i	−0.0568232	+	0.888951i
$319$	−12.0816			−0.676442
$320$	22.7136	+	9.15144i	1.26973	+	0.511581i
$321$			18.3222i			1.02264i
$322$	2.68656	−	5.42154i	0.149716	−	0.302131i
$323$	0.198395			0.0110390
$324$	−1.98372	−	0.254646i	−0.110207	−	0.0141470i
$325$			18.1246i			1.00537i
$326$	0.908366	−	14.2106i	0.0503097	−	0.787053i
$327$	−12.4462			−0.688275
$328$	5.50972	−	28.4181i	0.304223	−	1.56913i
$329$		−	6.54101i		−	0.360618i
$330$	−17.0777	−	1.09163i	−0.940095	−	0.0600925i
$331$	−14.3840			−0.790619			−0.395309	−	0.918548i	$-0.629363\pi$
$331$	−14.3840			−0.790619			−0.395309	+	0.918548i	$0.629363\pi$
$332$	−0.965318	+	7.51994i	−0.0529787	+	0.412710i
$333$	6.01692			0.329725
$334$	−16.2843	−	1.04092i	−0.891040	−	0.0569567i
$335$			11.0253i			0.602375i
$336$	−3.45280	−	0.901308i	−0.188365	−	0.0491704i
$337$		−	29.2613i		−	1.59396i	−0.604003	−	0.796982i	$-0.706429\pi$
$337$		−	29.2613i		−	1.59396i	0.604003	−	0.796982i	$-0.293571\pi$
$338$	−0.379341	+	5.93447i	−0.0206334	+	0.322792i
$339$		−	16.0203i		−	0.870105i
$340$	−0.790352	+	6.15693i	−0.0428629	+	0.333906i
$341$	10.2350			0.554254
$342$	−0.276146	−	0.0176517i	−0.0149323	−	0.000954495i
$343$	11.7797			0.636044
$344$	−27.7767	−	5.38535i	−1.49762	−	0.290359i
$345$	13.5426	+	5.66569i	0.729107	+	0.305030i
$346$	−9.07416	−	0.580035i	−0.487830	−	0.0311829i
$347$	2.16372			0.116155			0.0580774	−	0.998312i	$-0.481503\pi$
$347$	2.16372			0.116155			0.0580774	+	0.998312i	$0.481503\pi$
$348$	0.778260	−	6.06273i	0.0417191	−	0.324997i
$349$		−	23.8000i		−	1.27399i	−0.770869	−	0.636993i	$-0.780178\pi$
$349$		−	23.8000i		−	1.27399i	0.770869	−	0.636993i	$-0.219822\pi$
$350$	−0.351679	+	5.50171i	−0.0187980	+	0.294079i
$351$			4.14787i			0.221397i
$352$	21.2327	+	7.01685i	1.13171	+	0.373999i
$353$	20.3453			1.08287			0.541436	−	0.840742i	$-0.317881\pi$
$353$	20.3453			1.08287			0.541436	+	0.840742i	$0.317881\pi$
$354$	−0.392483	+	6.14007i	−0.0208603	+	0.326341i
$355$		−	32.4130i		−	1.72030i
$356$	−2.74923	+	21.4168i	−0.145709	+	1.13509i
$357$		−	0.904581i		−	0.0478755i
$358$	−0.0614852	+	0.961883i	−0.00324959	+	0.0508371i
$359$	−11.3988			−0.601608			−0.300804	−	0.953686i	$-0.597255\pi$
$359$	−11.3988			−0.601608			−0.300804	+	0.953686i	$0.597255\pi$
$360$	1.64789	−	8.49949i	0.0868512	−	0.447963i
$361$	18.9617			0.997985
$362$	−0.790111	+	12.3606i	−0.0415273	+	0.649659i
$363$	−4.62705			−0.242857
$364$	−0.942297	+	7.34060i	−0.0493898	+	0.384752i
$365$	−9.93845			−0.520202
$366$	0.689140	−	10.7810i	0.0360219	−	0.563532i
$367$	−1.55485			−0.0811626			−0.0405813	−	0.999176i	$-0.512921\pi$
$367$	−1.55485			−0.0811626			−0.0405813	+	0.999176i	$0.512921\pi$
$368$	−15.2532	−	11.6335i	−0.795131	−	0.606438i
$369$	−10.2344			−0.532783
$370$	−1.66155	+	25.9935i	−0.0863798	+	1.35134i
$371$	10.0204			0.520235
$372$	−0.659303	+	5.13604i	−0.0341832	+	0.266291i
$373$	9.25006			0.478950			0.239475	−	0.970903i	$-0.423025\pi$
$373$	9.25006			0.478950			0.239475	+	0.970903i	$0.423025\pi$
$374$	−0.361609	+	5.65706i	−0.0186983	+	0.292519i
$375$	1.92960			0.0996441
$376$	−20.3588	−	3.94717i	−1.04993	−	0.203560i
$377$	−12.6769			−0.652894
$378$	−0.0804827	+	1.25908i	−0.00413959	+	0.0647603i
$379$		−	23.7934i		−	1.22219i	−0.791559	−	0.611093i	$-0.790730\pi$
$379$		−	23.7934i		−	1.22219i	0.791559	−	0.611093i	$-0.209270\pi$
$380$	0.152513	−	1.18809i	0.00782376	−	0.0609479i
$381$			0.281251i			0.0144089i
$382$	0.635007	−	9.93414i	0.0324898	−	0.508275i
$383$	−13.8513			−0.707766			−0.353883	−	0.935290i	$-0.615139\pi$
$383$	−13.8513			−0.707766			−0.353883	+	0.935290i	$0.615139\pi$
$384$	−4.88890	+	10.2029i	−0.249485	+	0.520663i
$385$			10.7950i			0.550166i
$386$	−1.93104	+	30.2094i	−0.0982872	+	1.53762i
$387$			10.0034i			0.508502i
$388$	−0.635980	+	4.95436i	−0.0322870	+	0.251519i
$389$	−25.1821			−1.27678			−0.638392	−	0.769711i	$-0.720400\pi$
$389$	−25.1821			−1.27678			−0.638392	+	0.769711i	$0.720400\pi$
$390$	−17.9191	−	1.14542i	−0.907369	−	0.0580005i
$391$	1.87678	−	4.48603i	0.0949130	−	0.226869i
$392$	3.34000	−	17.2271i	0.168695	−	0.870100i
$393$	21.7964			1.09948
$394$	23.3790	+	1.49442i	1.17782	+	0.0752879i
$395$	−5.66697			−0.285136
$396$	1.00664	−	7.84187i	0.0505857	−	0.394069i
$397$		−	34.8682i		−	1.74998i	−0.484137	−	0.874992i	$-0.660866\pi$
$397$		−	34.8682i		−	1.74998i	0.484137	−	0.874992i	$-0.339134\pi$
$398$	1.69166	−	26.4645i	0.0847951	−	1.32655i
$399$			0.174556i			0.00873872i
$400$	16.9118	+	4.41460i	0.845588	+	0.220730i
$401$			26.5370i			1.32520i	0.748976	+	0.662598i	$0.230546\pi$
$401$			26.5370i			1.32520i	−0.748976	+	0.662598i	$0.769454\pi$
$402$	−5.08344	−	0.324942i	−0.253539	−	0.0162066i
$403$	10.7392			0.534959
$404$	−0.841509	+	6.55545i	−0.0418666	+	0.326146i
$405$	−3.06098			−0.152101
$406$	−3.84806	−	0.245975i	−0.190976	−	0.0122075i
$407$			23.7855i			1.17900i
$408$	−2.81549	−	0.545869i	−0.139388	−	0.0270246i
$409$	−24.6444			−1.21859			−0.609294	−	0.792944i	$-0.708547\pi$
$409$	−24.6444			−1.21859			−0.609294	+	0.792944i	$0.708547\pi$
$410$	2.82619	−	44.2134i	0.139576	−	2.18354i
$411$		−	19.1551i		−	0.944853i
$412$	−20.5869	−	2.64270i	−1.01425	−	0.130197i
$413$	3.88122			0.190982
$414$	−3.01142	+	6.07712i	−0.148003	+	0.298674i
$415$			11.6036i			0.569600i
$416$	22.2789	+	7.36257i	1.09231	+	0.360980i
$417$	−13.3472			−0.653616
$418$	0.0697791	−	1.09163i	0.00341301	−	0.0533936i
$419$			12.6674i			0.618843i	0.950925	+	0.309421i	$0.100135\pi$
$419$			12.6674i			0.618843i	−0.950925	+	0.309421i	$0.899865\pi$
$420$	−5.41710	−	0.695382i	−0.264327	−	0.0339311i
$421$	−28.7090			−1.39919			−0.699594	−	0.714540i	$-0.746636\pi$
$421$	−28.7090			−1.39919			−0.699594	+	0.714540i	$0.746636\pi$
$422$	−0.427603	+	6.68948i	−0.0208154	+	0.325639i
$423$			7.33196i			0.356492i
$424$	6.04683	−	31.1885i	0.293660	−	1.51465i
$425$			4.43063i			0.214917i
$426$	14.9447	+	0.955293i	0.724075	+	0.0462841i
$427$	−6.81483			−0.329793
$428$	4.66567	−	36.3461i	0.225524	−	1.75685i
$429$	−16.3970			−0.791654
$430$	−43.2154	−	2.76240i	−2.08403	−	0.133215i
$431$	−22.9516			−1.10554			−0.552770	−	0.833334i	$-0.686429\pi$
$431$	−22.9516			−1.10554			−0.552770	+	0.833334i	$0.686429\pi$
$432$	3.87031	+	1.01029i	0.186210	+	0.0486078i
$433$			15.0677i			0.724106i	0.932157	+	0.362053i	$0.117924\pi$
$433$			15.0677i			0.724106i	−0.932157	+	0.362053i	$0.882076\pi$
$434$	3.25988	+	0.208377i	0.156479	+	0.0100024i
$435$		−	9.35510i		−	0.448543i
$436$	24.6898	+	3.16937i	1.18243	+	0.151785i
$437$	−0.362160	+	0.865664i	−0.0173245	+	0.0414103i
$438$	0.292911	−	4.58234i	0.0139958	−	0.218953i
$439$			22.4462i			1.07130i	0.844441	+	0.535649i	$0.179933\pi$
$439$			22.4462i			1.07130i	−0.844441	+	0.535649i	$0.820067\pi$
$440$	33.5994	+	6.51427i	1.60179	+	0.310555i
$441$	−6.20412			−0.295434
$442$	−0.379425	+	5.93578i	−0.0180474	+	0.282336i
$443$	−28.7923			−1.36796			−0.683981	−	0.729500i	$-0.739753\pi$
$443$	−28.7923			−1.36796			−0.683981	+	0.729500i	$0.739753\pi$
$444$	−11.9359	−	1.53219i	−0.566453	−	0.0727144i
$445$			33.0472i			1.56659i
$446$	−12.4149	−	0.793578i	−0.587860	−	0.0375770i
$447$	−1.91404			−0.0905308
$448$	6.61987	+	2.66719i	0.312760	+	0.126013i
$449$	10.0261			0.473160			0.236580	−	0.971612i	$-0.423973\pi$
$449$	10.0261			0.473160			0.236580	+	0.971612i	$0.423973\pi$
$450$	0.394204	−	6.16698i	0.0185829	−	0.290714i
$451$		−	40.4578i		−	1.90508i
$452$	−4.07952	+	31.7799i	−0.191884	+	1.49480i
$453$			15.4992i			0.728216i
$454$	33.7795	+	2.15924i	1.58535	+	0.101338i
$455$			11.3269i			0.531014i
$456$	0.543302	+	0.105336i	0.0254424	+	0.00493279i
$457$		−	8.91212i		−	0.416891i	−0.978034	−	0.208446i	$-0.933160\pi$
$457$		−	8.91212i		−	0.416891i	0.978034	−	0.208446i	$-0.0668404\pi$
$458$	−0.774149	+	12.1109i	−0.0361736	+	0.565905i
$459$			1.01396i			0.0473278i
$460$	−25.4220	−	14.6877i	−1.18530	−	0.684818i
$461$		−	36.2700i		−	1.68926i	−0.535349	−	0.844631i	$-0.679820\pi$
$461$		−	36.2700i		−	1.68926i	0.535349	−	0.844631i	$-0.320180\pi$
$462$	−4.97729	−	0.318157i	−0.231565	−	0.0148020i
$463$			29.5920i			1.37525i	0.726064	+	0.687627i	$0.241348\pi$
$463$			29.5920i			1.37525i	−0.726064	+	0.687627i	$0.758652\pi$
$464$	−3.08770	+	11.8286i	−0.143343	+	0.549129i
$465$			7.92517i			0.367521i
$466$	0.595334	−	9.31348i	0.0275783	−	0.431439i
$467$		−	0.403565i		−	0.0186747i	−0.999956	−	0.00933737i	$-0.997028\pi$
$467$		−	0.403565i		−	0.0186747i	0.999956	−	0.00933737i	$-0.00297222\pi$
$468$	1.05624	−	8.22823i	0.0488247	−	0.380350i
$469$			3.21331i			0.148377i
$470$	−31.6745	−	2.02469i	−1.46104	−	0.0933920i
$471$	11.0597			0.509606
$472$	2.34212	−	12.0802i	0.107805	−	0.556038i
$473$	−39.5445			−1.81826
$474$	0.167020	−	2.61288i	0.00767147	−	0.120014i
$475$		−	0.854973i		−	0.0392288i
$476$	−0.230348	+	1.79444i	−0.0105580	+	0.0822479i
$477$	−11.2321			−0.514284
$478$	20.0858	+	1.28391i	0.918701	+	0.0587249i
$479$	−9.40765			−0.429846			−0.214923	−	0.976631i	$-0.568950\pi$
$479$	−9.40765			−0.429846			−0.214923	+	0.976631i	$0.568950\pi$
$480$	−5.43331	+	16.4410i	−0.247996	+	0.750426i
$481$			24.9574i			1.13796i
$482$	26.7248	+	1.70829i	1.21728	+	0.0778105i
$483$	3.94698	+	1.65126i	0.179594	+	0.0751352i
$484$	9.17878	+	1.17826i	0.417217	+	0.0535573i
$485$			7.64482i			0.347133i
$486$	0.0902148	−	1.41133i	0.00409223	−	0.0640194i
$487$			28.2242i			1.27896i	0.768808	+	0.639480i	$0.220850\pi$
$487$			28.2242i			1.27896i	−0.768808	+	0.639480i	$0.779150\pi$
$488$	−4.11241	+	21.2110i	−0.186160	+	0.960179i
$489$	10.0689			0.455333
$490$	1.71324	−	26.8022i	0.0773963	−	1.21080i
$491$	22.7769			1.02791			0.513953	−	0.857818i	$-0.328180\pi$
$491$	22.7769			1.02791			0.513953	+	0.857818i	$0.328180\pi$
$492$	20.3023	+	2.60616i	0.915297	+	0.117495i
$493$	−3.09892			−0.139568
$494$	0.0732171	−	1.14542i	0.00329419	−	0.0515348i
$495$		−	12.1004i		−	0.543872i
$496$	2.61575	−	10.0206i	0.117450	−	0.449938i
$497$		−	9.44678i		−	0.423746i
$498$	−5.35011	−	0.341988i	−0.239744	−	0.0153248i
$499$	−17.9463			−0.803386			−0.401693	−	0.915774i	$-0.631578\pi$
$499$	−17.9463			−0.803386			−0.401693	+	0.915774i	$0.631578\pi$
$500$	−3.82779	−	0.491365i	−0.171184	−	0.0219745i
$501$		−	11.5383i		−	0.515492i
$502$	23.6164	+	1.50960i	1.05405	+	0.0673766i
$503$	19.7331			0.879856			0.439928	−	0.898033i	$-0.355004\pi$
$503$	19.7331			0.879856			0.439928	+	0.898033i	$0.355004\pi$
$504$	0.480276	−	2.47718i	0.0213932	−	0.110342i
$505$			10.1154i			0.450128i
$506$	−24.0235	−	11.9045i	−1.06797	−	0.529218i
$507$	−4.20486			−0.186745
$508$	0.0716194	−	0.557923i	0.00317760	−	0.0247538i
$509$			18.5397i			0.821756i	0.911690	+	0.410878i	$0.134778\pi$
$509$			18.5397i			0.821756i	−0.911690	+	0.410878i	$0.865222\pi$
$510$	−4.38039	−	0.280002i	−0.193967	−	0.0123987i
$511$	−2.89656			−0.128136
$512$	12.2963	−	18.9947i	0.543426	−	0.839457i
$513$		−	0.195663i		−	0.00863874i
$514$	0.992222	−	15.5225i	0.0437650	−	0.684666i
$515$	−31.7667			−1.39981
$516$	2.54733	−	19.8440i	0.112140	−	0.873583i
$517$	−28.9840			−1.27472
$518$	−0.484258	+	7.57581i	−0.0212771	+	0.332862i
$519$		−	6.42949i		−	0.282223i
$520$	35.2548	+	6.83522i	1.54603	+	0.299744i
$521$		−	17.7765i		−	0.778803i	−0.921068	−	0.389401i	$-0.872682\pi$
$521$		−	17.7765i		−	0.778803i	0.921068	−	0.389401i	$-0.127318\pi$
$522$	4.31337	+	0.275718i	0.188791	+	0.0120679i
$523$		−	23.3129i		−	1.01940i	−0.860352	−	0.509701i	$-0.829756\pi$
$523$		−	23.3129i		−	1.01940i	0.860352	−	0.509701i	$-0.170244\pi$
$524$	−43.2379	−	5.55036i	−1.88886	−	0.242469i
$525$	−3.89824			−0.170133
$526$	2.90191	−	45.3979i	0.126529	−	1.97944i
$527$	2.62525			0.114358
$528$	−3.99380	+	15.2997i	−0.173808	+	0.665836i
$529$	16.1481	+	16.3780i	0.702090	+	0.712089i
$530$	3.10170	−	48.5235i	0.134729	−	2.10773i
$531$	−4.35054			−0.188798
$532$	0.0444500	−	0.346270i	0.00192715	−	0.0150127i
$533$		−	42.4511i		−	1.83876i
$534$	−15.2371	−	0.973984i	−0.659376	−	0.0421484i
$535$		−	56.0838i		−	2.42472i
$536$	10.0014	+	1.93907i	0.431994	+	0.0837552i
$537$	−0.681542			−0.0294107
$538$	30.0585	+	1.92139i	1.29591	+	0.0828370i
$539$		−	24.5255i		−	1.05639i
$540$	6.07214	+	0.779468i	0.261303	+	0.0335429i
$541$			34.5138i			1.48386i	0.670475	+	0.741932i	$0.266090\pi$
$541$			34.5138i			1.48386i	−0.670475	+	0.741932i	$0.733910\pi$
$542$	−3.33531	−	0.213199i	−0.143264	−	0.00915767i
$543$	−8.75811			−0.375846
$544$	5.44616	+	1.79981i	0.233502	+	0.0771661i
$545$	38.0975			1.63192
$546$	−5.22252	−	0.333832i	−0.223503	−	0.0142867i
$547$	7.58510			0.324315			0.162158	−	0.986765i	$-0.448155\pi$
$547$	7.58510			0.324315			0.162158	+	0.986765i	$0.448155\pi$
$548$	−4.87778	+	37.9985i	−0.208369	+	1.62321i
$549$	7.63888			0.326020
$550$	24.3787	+	1.55833i	1.03951	+	0.0664474i
$551$	0.597994			0.0254754
$552$	7.52134	−	11.2885i	0.320130	−	0.480469i
$553$	−1.65164			−0.0702348
$554$	−13.4206	−	0.857869i	−0.570188	−	0.0364474i
$555$	−18.4177			−0.781788
$556$	26.4772	+	3.39882i	1.12288	+	0.144142i
$557$	−23.6692			−1.00290			−0.501448	−	0.865188i	$-0.667199\pi$
$557$	−23.6692			−1.00290			−0.501448	+	0.865188i	$0.667199\pi$
$558$	−3.65407	−	0.233574i	−0.154689	−	0.00988799i
$559$	−41.4929			−1.75496
$560$	10.5689	+	2.75889i	0.446620	+	0.116584i
$561$	−4.00831			−0.169231
$562$	32.1648	+	2.05603i	1.35679	+	0.0867284i
$563$		−	14.4822i		−	0.610351i	−0.952296	−	0.305176i	$-0.901285\pi$
$563$		−	14.4822i		−	0.610351i	0.952296	−	0.305176i	$-0.0987152\pi$
$564$	1.86706	−	14.5446i	0.0786172	−	0.612437i
$565$			49.0379i			2.06304i
$566$	24.0284	+	1.53593i	1.00999	+	0.0645601i
$567$	−0.892124			−0.0374657
$568$	−29.4029	−	5.70066i	−1.23372	−	0.239194i
$569$			11.4721i			0.480935i	0.970657	+	0.240467i	$0.0773007\pi$
$569$			11.4721i			0.480935i	−0.970657	+	0.240467i	$0.922699\pi$
$570$	0.845278	+	0.0540316i	0.0354048	+	0.00226313i
$571$			29.6426i			1.24051i	0.784402	+	0.620253i	$0.212970\pi$
$571$			29.6426i			1.24051i	−0.784402	+	0.620253i	$0.787030\pi$
$572$	32.5271	+	4.17543i	1.36003	+	0.174584i
$573$	7.03883			0.294052
$574$	0.823695	−	12.8860i	0.0343803	−	0.537851i
$575$	−19.3323	−	8.08788i	−0.806212	−	0.337288i
$576$	−7.42035	−	2.98971i	−0.309181	−	0.124571i
$577$	−4.38359			−0.182491			−0.0912456	−	0.995828i	$-0.529085\pi$
$577$	−4.38359			−0.182491			−0.0912456	+	0.995828i	$0.529085\pi$
$578$	1.44090	−	22.5416i	0.0599335	−	0.937609i
$579$	−21.4049			−0.889557
$580$	−2.38224	+	18.5579i	−0.0989172	+	0.770576i
$581$			3.38188i			0.140304i
$582$	−3.52481	−	0.225312i	−0.146108	−	0.00933948i
$583$		−	44.4018i		−	1.83893i
$584$	−1.74793	+	9.01551i	−0.0723299	+	0.373064i
$585$		−	12.6966i		−	0.524939i
$586$	1.19949	−	18.7650i	0.0495505	−	0.775175i
$587$	44.8384			1.85068			0.925339	−	0.379140i	$-0.123780\pi$
$587$	44.8384			1.85068			0.925339	+	0.379140i	$0.123780\pi$
$588$	12.3072	+	1.57985i	0.507542	+	0.0651521i
$589$	−0.506590			−0.0208737
$590$	1.20138	−	18.7946i	0.0494602	−	0.773763i
$591$			16.5652i			0.681400i
$592$	23.2874	+	6.07887i	0.957104	+	0.249840i
$593$	36.8434			1.51298			0.756489	−	0.654006i	$-0.226913\pi$
$593$	36.8434			1.51298			0.756489	+	0.654006i	$0.226913\pi$
$594$	5.57915	+	0.356629i	0.228915	+	0.0146327i
$595$			2.76891i			0.113514i
$596$	3.79692	+	0.487402i	0.155528	+	0.0199648i
$597$	18.7514			0.767445
$598$	−25.2071	−	12.4910i	−1.03080	−	0.510795i
$599$		−	0.536356i		−	0.0219149i	−0.999940	−	0.0109575i	$-0.996512\pi$
$599$		−	0.536356i		−	0.0219149i	0.999940	−	0.0109575i	$-0.00348794\pi$
$600$	−2.35239	+	12.1332i	−0.0960359	+	0.495336i
$601$	2.32091			0.0946721			0.0473360	−	0.998879i	$-0.484927\pi$
$601$	2.32091			0.0946721			0.0473360	+	0.998879i	$0.484927\pi$
$602$	−12.5951	−	0.805101i	−0.513339	−	0.0328135i
$603$		−	3.60187i		−	0.146680i
$604$	3.94681	−	30.7461i	0.160594	−	1.25104i
$605$	14.1633			0.575821
$606$	−4.66392	−	0.298125i	−0.189459	−	0.0121105i
$607$			4.31945i			0.175321i	0.996150	+	0.0876605i	$0.0279391\pi$
$607$			4.31945i			0.175321i	−0.996150	+	0.0876605i	$0.972061\pi$
$608$	−1.05094	−	0.347306i	−0.0426211	−	0.0140851i
$609$		−	2.72654i		−	0.110485i
$610$	−2.10945	+	33.0005i	−0.0854090	+	1.33615i
$611$	−30.4120			−1.23034
$612$	0.258202	−	2.01142i	0.0104372	−	0.0813070i
$613$	4.29197			0.173351			0.0866756	−	0.996237i	$-0.472376\pi$
$613$	4.29197			0.173351			0.0866756	+	0.996237i	$0.472376\pi$
$614$	−0.622182	+	9.73351i	−0.0251092	+	0.392813i
$615$	31.3274			1.26324
$616$	9.79255	+	1.89858i	0.394553	+	0.0764961i
$617$			36.9423i			1.48724i	0.668602	+	0.743621i	$0.266893\pi$
$617$			36.9423i			1.48724i	−0.668602	+	0.743621i	$0.733107\pi$
$618$	0.936243	−	14.6467i	0.0376612	−	0.589178i
$619$			2.34420i			0.0942215i	0.998890	+	0.0471108i	$0.0150014\pi$
$619$			2.34420i			0.0942215i	−0.998890	+	0.0471108i	$0.984999\pi$
$620$	2.01811	−	15.7213i	0.0810494	−	0.631384i
$621$	−4.42425	−	1.85094i	−0.177539	−	0.0742756i
$622$	−28.6315	−	1.83017i	−1.14802	−	0.0733833i
$623$			9.63161i			0.385882i
$624$	−4.19058	+	16.0536i	−0.167757	+	0.642657i
$625$	−27.7545			−1.11018
$626$	39.7924	+	2.54360i	1.59042	+	0.101663i
$627$	0.773477			0.0308897
$628$	−21.9394	−	2.81632i	−0.875479	−	0.112383i
$629$			6.10094i			0.243260i
$630$	0.246356	−	3.85403i	0.00981507	−	0.153548i
$631$	−42.3515			−1.68599			−0.842993	−	0.537925i	$-0.819209\pi$
$631$	−42.3515			−1.68599			−0.842993	+	0.537925i	$0.819209\pi$
$632$	−0.996681	+	5.14070i	−0.0396458	+	0.204486i
$633$	−4.73983			−0.188391
$634$	−11.9824	−	0.765934i	−0.475881	−	0.0304191i
$635$		−	0.860903i		−	0.0341639i
$636$	22.2814	+	2.86022i	0.883516	+	0.113415i
$637$		−	25.7339i		−	1.01961i
$638$	−1.08994	+	17.0512i	−0.0431513	+	0.675064i
$639$			10.5891i			0.418898i
$640$	14.9648	−	31.2308i	0.591537	−	1.23451i
$641$		−	35.6357i		−	1.40753i	−0.710435	−	0.703763i	$-0.751502\pi$
$641$		−	35.6357i		−	1.40753i	0.710435	−	0.703763i	$-0.248498\pi$
$642$	25.8587	+	1.65293i	1.02056	+	0.0652360i
$643$			17.2554i			0.680486i	0.940338	+	0.340243i	$0.110509\pi$
$643$			17.2554i			0.680486i	−0.940338	+	0.340243i	$0.889491\pi$
$644$	−7.40923	−	4.28074i	−0.291965	−	0.168685i
$645$		−	30.6202i		−	1.20567i
$646$	0.0178982	−	0.280002i	0.000704195	−	0.0110165i
$647$		−	20.7332i		−	0.815107i	−0.913181	−	0.407553i	$-0.866382\pi$
$647$		−	20.7332i		−	0.815107i	0.913181	−	0.407553i	$-0.133618\pi$
$648$	−0.538352	+	2.77672i	−0.0211485	+	0.109080i
$649$		−	17.1982i		−	0.675087i
$650$	25.5799	+	1.63511i	1.00332	+	0.0641342i
$651$			2.30979i			0.0905278i
$652$	−19.9740	−	2.56401i	−0.782240	−	0.100415i
$653$			41.9915i			1.64325i	0.570026	+	0.821626i	$0.306933\pi$
$653$			41.9915i			1.64325i	−0.570026	+	0.821626i	$0.693067\pi$
$654$	−1.12283	+	17.5657i	−0.0439061	+	0.686873i
$655$	−66.7183			−2.60690
$656$	−39.6104	−	10.3398i	−1.54653	−	0.403701i
$657$	3.24682			0.126670
$658$	−9.23155	−	0.590096i	−0.359883	−	0.0230043i
$659$			5.13261i			0.199938i	0.994991	+	0.0999690i	$0.0318744\pi$
$659$			5.13261i			0.199938i	−0.994991	+	0.0999690i	$0.968126\pi$
$660$	−3.08132	+	24.0038i	−0.119940	+	0.934347i
$661$	−6.38665			−0.248412			−0.124206	−	0.992256i	$-0.539638\pi$
$661$	−6.38665			−0.248412			−0.124206	+	0.992256i	$0.539638\pi$
$662$	−1.29765	+	20.3007i	−0.0504347	+	0.789008i
$663$	−4.20580			−0.163340
$664$	10.5260	+	2.04079i	0.408490	+	0.0791982i
$665$		−	0.534312i		−	0.0207197i
$666$	0.542815	−	8.49188i	0.0210337	−	0.329054i
$667$	5.65691	−	13.5216i	0.219036	−	0.523558i
$668$	−2.93818	+	22.8887i	−0.113681	+	0.885591i
$669$		−	8.79654i		−	0.340094i
$670$	15.5603	+	0.994642i	0.601148	+	0.0384264i
$671$			30.1973i			1.16575i
$672$	−1.58354	+	4.79173i	−0.0610863	+	0.184845i
$673$	6.07738			0.234266			0.117133	−	0.993116i	$-0.462630\pi$
$673$	6.07738			0.234266			0.117133	+	0.993116i	$0.462630\pi$
$674$	−41.2974	−	2.63980i	−1.59072	−	0.101681i
$675$	4.36961			0.168187
$676$	8.34129	+	1.07075i	0.320819	+	0.0411828i
$677$	−7.89600			−0.303468			−0.151734	−	0.988421i	$-0.548486\pi$
$677$	−7.89600			−0.303468			−0.151734	+	0.988421i	$0.548486\pi$
$678$	−22.6100	−	1.44527i	−0.868333	−	0.0555053i
$679$			2.22808i			0.0855060i
$680$	8.61818	+	1.67090i	0.330492	+	0.0640760i
$681$			23.9345i			0.917172i
$682$	0.923344	−	14.4449i	0.0353567	−	0.553125i
$683$	43.6655			1.67082			0.835408	−	0.549631i	$-0.185232\pi$
$683$	43.6655			1.67082			0.835408	+	0.549631i	$0.185232\pi$
$684$	−0.0498249	+	0.388141i	−0.00190510	+	0.0148410i
$685$			58.6335i			2.24027i
$686$	1.06270	−	16.6251i	0.0405742	−	0.634749i
$687$	−8.58118			−0.327392
$688$	−10.1064	+	38.7163i	−0.385302	+	1.47604i
$689$		−	46.5894i		−	1.77492i
$690$	9.21791	−	18.6019i	0.350920	−	0.708164i
$691$	−15.7471			−0.599049			−0.299525	−	0.954089i	$-0.596828\pi$
$691$	−15.7471			−0.599049			−0.299525	+	0.954089i	$0.596828\pi$
$692$	−1.63725	+	12.7543i	−0.0622388	+	0.484847i
$693$		−	3.52666i		−	0.133967i
$694$	0.195200	−	3.05373i	0.00740968	−	0.115918i
$695$	40.8556			1.54974
$696$	−8.48633	−	1.64533i	−0.321673	−	0.0623662i
$697$		−	10.3773i		−	0.393070i
$698$	−33.5898	−	2.14712i	−1.27139	−	0.0812695i
$699$	6.59907			0.249600
$700$	7.73302	+	0.992671i	0.292281	+	0.0375194i
$701$	35.7030			1.34849			0.674243	−	0.738510i	$-0.264470\pi$
$701$	35.7030			1.34849			0.674243	+	0.738510i	$0.264470\pi$
$702$	5.85403	+	0.374200i	0.220946	+	0.0141233i
$703$		−	1.17729i		−	0.0444023i
$704$	11.8186	−	29.3335i	0.445431	−	1.10555i
$705$		−	22.4430i		−	0.845252i
$706$	1.83545	−	28.7140i	0.0690780	−	1.08067i
$707$			2.94813i			0.110876i
$708$	8.63027	+	1.10785i	0.324345	+	0.0416355i
$709$	−25.5486			−0.959499			−0.479749	−	0.877406i	$-0.659272\pi$
$709$	−25.5486			−0.959499			−0.479749	+	0.877406i	$0.659272\pi$
$710$	−45.7456	−	2.92413i	−1.71680	−	0.109741i
$711$	1.85136			0.0694313
$712$	29.9782	+	5.81220i	1.12348	+	0.217821i
$713$	−4.79225	+	11.4548i	−0.179471	+	0.428986i
$714$	−1.27667	−	0.0816066i	−0.0477780	−	0.00305405i
$715$	50.1909			1.87703
$716$	1.35199	+	0.173552i	0.0505262	+	0.00648595i
$717$			14.2318i			0.531495i
$718$	−1.02834	+	16.0876i	−0.0383774	+	0.600382i
$719$		−	12.9790i		−	0.484036i	−0.970272	−	0.242018i	$-0.922191\pi$
$719$		−	12.9790i		−	0.484036i	0.970272	−	0.242018i	$-0.0778094\pi$
$720$	−11.8470	−	3.09250i	−0.441510	−	0.115250i
$721$	−9.25840			−0.344801
$722$	1.71063	−	26.7613i	0.0636630	−	0.995952i
$723$			18.9358i			0.704231i
$724$	17.3737	+	2.23022i	0.645687	+	0.0828854i
$725$			13.3546i			0.495977i
$726$	−0.417428	+	6.53031i	−0.0154922	+	0.242362i
$727$	25.5652			0.948160			0.474080	−	0.880482i	$-0.342781\pi$
$727$	25.5652			0.948160			0.474080	+	0.880482i	$0.342781\pi$
$728$	10.2750	+	1.99213i	0.380818	+	0.0738331i
$729$	1.00000			0.0370370
$730$	−0.896595	+	14.0265i	−0.0331845	+	0.519143i
$731$	−10.1431			−0.375156
$732$	−15.1534	−	1.94521i	−0.560087	−	0.0718971i
$733$	35.4883			1.31079			0.655395	−	0.755286i	$-0.272502\pi$
$733$	35.4883			1.31079			0.655395	+	0.755286i	$0.272502\pi$
$734$	−0.140271	+	2.19442i	−0.00517749	+	0.0809973i
$735$	18.9907			0.700482
$736$	−17.7948	+	20.4779i	−0.655926	+	0.754825i
$737$	14.2386			0.524485
$738$	−0.923296	+	14.4442i	−0.0339870	+	0.531698i
$739$	−41.9864			−1.54449			−0.772247	−	0.635322i	$-0.780867\pi$
$739$	−41.9864			−1.54449			−0.772247	+	0.635322i	$0.780867\pi$
$740$	36.5356	+	4.69000i	1.34308	+	0.172408i
$741$	0.811586			0.0298144
$742$	0.903992	−	14.1422i	0.0331866	−	0.519176i
$743$	22.8728			0.839123			0.419561	−	0.907727i	$-0.362184\pi$
$743$	22.8728			0.839123			0.419561	+	0.907727i	$0.362184\pi$
$744$	7.18918	+	1.39384i	0.263568	+	0.0511007i
$745$	5.85883			0.214651
$746$	0.834492	−	13.0549i	0.0305529	−	0.477974i
$747$		−	3.79082i		−	0.138699i
$748$	7.95137	+	1.02070i	0.290731	+	0.0373205i
$749$		−	16.3456i		−	0.597257i
$750$	0.174078	−	2.72331i	0.00635644	−	0.0994411i
$751$	−18.3558			−0.669812			−0.334906	−	0.942251i	$-0.608705\pi$
$751$	−18.3558			−0.669812			−0.334906	+	0.942251i	$0.608705\pi$
$752$	−7.40744	+	28.3770i	−0.270122	+	1.03480i
$753$			16.7334i			0.609798i
$754$	−1.14364	+	17.8913i	−0.0416491	+	0.651564i
$755$		−	47.4428i		−	1.72662i
$756$	1.76973	+	0.227176i	0.0643643	+	0.00826231i
$757$	−13.2658			−0.482155			−0.241078	−	0.970506i	$-0.577501\pi$
$757$	−13.2658			−0.482155			−0.241078	+	0.970506i	$0.577501\pi$
$758$	−33.5805	−	2.14652i	−1.21970	−	0.0779651i
$759$	7.31695	−	17.4895i	0.265589	−	0.634830i
$760$	−1.66304	−	0.322430i	−0.0603247	−	0.0116958i
$761$	24.5251			0.889034			0.444517	−	0.895770i	$-0.353375\pi$
$761$	24.5251			0.889034			0.444517	+	0.895770i	$0.353375\pi$
$762$	0.396938	+	0.0253730i	0.0143796	+	0.000919165i
$763$	11.1035			0.401975
$764$	−13.9631	−	1.79241i	−0.505167	−	0.0648472i
$765$		−	3.10373i		−	0.112215i
$766$	−1.24959	+	19.5487i	−0.0451494	+	0.706324i
$767$		−	18.0455i		−	0.651586i
$768$	13.9586	+	7.82031i	0.503688	+	0.282191i
$769$			3.94832i			0.142380i	0.997463	+	0.0711901i	$0.0226797\pi$
$769$			3.94832i			0.142380i	−0.997463	+	0.0711901i	$0.977320\pi$
$770$	15.2354	+	0.973873i	0.549046	+	0.0350959i
$771$	10.9984			0.396099
$772$	42.4614	+	5.45068i	1.52822	+	0.196174i
$773$	16.8096			0.604599			0.302300	−	0.953213i	$-0.402246\pi$
$773$	16.8096			0.604599			0.302300	+	0.953213i	$0.402246\pi$
$774$	14.1181	+	0.902455i	0.507466	+	0.0324381i
$775$		−	11.3133i		−	0.406387i
$776$	6.93487	+	1.34454i	0.248947	+	0.0482660i
$777$	−5.36784			−0.192570
$778$	−2.27180	+	35.5404i	−0.0814480	+	1.27418i
$779$			2.00250i			0.0717470i
$780$	−3.23313	+	25.1865i	−0.115765	+	0.901821i
$781$	−41.8598			−1.49786
$782$	−6.16198	−	3.05347i	−0.220352	−	0.109192i
$783$			3.05624i			0.109221i
$784$	−24.0119	−	6.26799i	−0.857566	−	0.223857i
$785$	−33.8536			−1.20829
$786$	1.96635	−	30.7619i	0.0701375	−	1.09724i
$787$			41.0427i			1.46302i	0.681833	+	0.731508i	$0.261183\pi$
$787$			41.0427i			1.46302i	−0.681833	+	0.731508i	$0.738817\pi$
$788$	4.21826	−	32.8607i	0.150269	−	1.17061i
$789$	32.1667			1.14516
$790$	−0.511244	+	7.99798i	−0.0181893	+	0.284555i
$791$			14.2921i			0.508169i
$792$	−10.9767	−	2.12816i	−0.390039	−	0.0756209i
$793$			31.6851i			1.12517i
$794$	−49.2106	−	3.14563i	−1.74642	−	0.111634i
$795$	34.3813			1.21938
$796$	−37.1976	−	4.77498i	−1.31844	−	0.169245i
$797$	−34.5930			−1.22535			−0.612674	−	0.790336i	$-0.709906\pi$
$797$	−34.5930			−1.22535			−0.612674	+	0.790336i	$0.709906\pi$
$798$	0.246356	+	0.0157475i	0.00872092	+	0.000557456i
$799$	−7.43434			−0.263008
$800$	7.75616	−	23.4699i	0.274222	−	0.829785i
$801$		−	10.7963i		−	0.381468i
$802$	37.4526	+	2.39403i	1.32250	+	0.0845362i
$803$			12.8350i			0.452938i
$804$	−0.917203	+	7.14511i	−0.0323473	+	0.251989i
$805$	−12.0816	−	5.05449i	−0.425822	−	0.178147i
$806$	0.968837	−	15.1566i	0.0341258	−	0.533870i
$807$			21.2979i			0.749723i
$808$	9.17600	+	1.77905i	0.322811	+	0.0625867i
$809$	−38.0524			−1.33785			−0.668926	−	0.743329i	$-0.733246\pi$
$809$	−38.0524			−1.33785			−0.668926	+	0.743329i	$0.733246\pi$
$810$	−0.276146	+	4.32007i	−0.00970278	+	0.151792i
$811$	−28.4205			−0.997978			−0.498989	−	0.866608i	$-0.666295\pi$
$811$	−28.4205			−0.997978			−0.498989	+	0.866608i	$0.666295\pi$
$812$	−0.694304	+	5.40871i	−0.0243653	+	0.189808i
$813$		−	2.36324i		−	0.0828823i
$814$	33.5693	+	2.14581i	1.17660	+	0.0752105i
$815$	−30.8208			−1.07961
$816$	−1.02440	+	3.92436i	−0.0358613	+	0.137380i
$817$	1.95730			0.0684772
$818$	−2.22329	+	34.7815i	−0.0777356	+	1.21611i
$819$		−	3.70042i		−	0.129303i
$820$	−62.1449	−	7.97740i	−2.17019	−	0.278583i
$821$		−	37.1955i		−	1.29813i	−0.760733	−	0.649065i	$-0.775160\pi$
$821$		−	37.1955i		−	1.29813i	0.760733	−	0.649065i	$-0.224840\pi$
$822$	−27.0343	−	1.72808i	−0.942929	−	0.0602736i
$823$			10.0207i			0.349301i	0.984630	+	0.174651i	$0.0558796\pi$
$823$			10.0207i			0.349301i	−0.984630	+	0.174651i	$0.944120\pi$
$824$	−5.58698	+	28.8166i	−0.194632	+	1.00387i
$825$			17.2736i			0.601388i
$826$	0.350144	−	5.47770i	0.0121831	−	0.190594i
$827$			47.1667i			1.64015i	0.572258	+	0.820073i	$0.306067\pi$
$827$			47.1667i			1.64015i	−0.572258	+	0.820073i	$0.693933\pi$
$828$	8.30516	+	4.79837i	0.288624	+	0.166755i
$829$		−	26.2155i		−	0.910503i	−0.890363	−	0.455252i	$-0.849549\pi$
$829$		−	26.2155i		−	0.910503i	0.890363	−	0.455252i	$-0.150451\pi$
$830$	16.3766	+	1.04682i	0.568440	+	0.0363356i
$831$		−	9.50918i		−	0.329870i
$832$	12.4009	−	30.7787i	0.429925	−	1.06706i
$833$		−	6.29075i		−	0.217962i
$834$	−1.20412	+	18.8374i	−0.0416951	+	0.652284i
$835$			35.3184i			1.22225i
$836$	−1.53436	−	0.196963i	−0.0530671	−	0.00681211i
$837$		−	2.58909i		−	0.0894921i
$838$	17.8779	+	1.14279i	0.617583	+	0.0394769i
$839$	26.6221			0.919097			0.459549	−	0.888153i	$-0.348011\pi$
$839$	26.6221			0.919097			0.459549	+	0.888153i	$0.348011\pi$
$840$	−1.47012	+	7.58260i	−0.0507239	+	0.261625i
$841$	19.6594			0.677910
$842$	−2.58997	+	40.5179i	−0.0892563	+	1.39634i
$843$			22.7904i			0.784942i
$844$	9.40251	+	1.20698i	0.323648	+	0.0415460i
$845$	12.8710			0.442776
$846$	10.3478	+	0.661451i	0.355766	+	0.0227412i
$847$	4.12790			0.141836
$848$	−43.4718	−	11.3478i	−1.49283	−	0.389684i
$849$			17.0253i			0.584307i
$850$	6.25310	+	0.399708i	0.214479	+	0.0137099i
$851$	−26.6204	−	11.1369i	−0.912535	−	0.381770i
$852$	2.69647	−	21.0058i	0.0923796	−	0.719648i
$853$		−	10.7592i		−	0.368388i	−0.982890	−	0.184194i	$-0.941032\pi$
$853$		−	10.7592i		−	0.368388i	0.982890	−	0.184194i	$-0.0589675\pi$
$854$	−0.614798	+	9.61799i	−0.0210380	+	0.329121i
$855$			0.598921i			0.0204827i
$856$	−50.8755	−	9.86377i	−1.73889	−	0.337137i
$857$	−48.2719			−1.64894			−0.824469	−	0.565907i	$-0.808526\pi$
$857$	−48.2719			−1.64894			−0.824469	+	0.565907i	$0.808526\pi$
$858$	−1.47925	+	23.1416i	−0.0505008	+	0.790042i
$859$	41.1208			1.40302			0.701511	−	0.712659i	$-0.252509\pi$
$859$	41.1208			1.40302			0.701511	+	0.712659i	$0.252509\pi$
$860$	−7.79733	+	60.7421i	−0.265887	+	2.07129i
$861$	9.13037			0.311162
$862$	−2.07057	+	32.3924i	−0.0705240	+	1.10329i
$863$		−	26.4666i		−	0.900934i	−0.892793	−	0.450467i	$-0.851257\pi$
$863$		−	26.4666i		−	0.900934i	0.892793	−	0.450467i	$-0.148743\pi$
$864$	1.77502	−	5.37115i	0.0603875	−	0.182730i
$865$			19.6806i			0.669159i
$866$	21.2655	+	1.35933i	0.722632	+	0.0461918i
$867$	15.9719			0.542433
$868$	0.588179	−	4.58198i	0.0199641	−	0.155523i
$869$			7.31861i			0.248267i
$870$	−13.2032	−	0.843968i	−0.447629	−	0.0286132i
$871$	14.9401			0.506226
$872$	6.70042	−	34.5596i	0.226905	−	1.17033i
$873$		−	2.49750i		−	0.0845277i
$874$	1.18907	+	0.589224i	0.0402208	+	0.0199308i
$875$	−1.72144			−0.0581953
$876$	−6.44079	−	0.826790i	−0.217614	−	0.0279346i
$877$			28.8502i			0.974202i	0.873346	+	0.487101i	$0.161946\pi$
$877$			28.8502i			0.974202i	−0.873346	+	0.487101i	$0.838054\pi$
$878$	31.6790	+	2.02498i	1.06912	+	0.0683397i
$879$	13.2959			0.448461
$880$	12.2250	−	46.8323i	0.412103	−	1.57872i
$881$			17.0655i			0.574953i	0.957788	+	0.287476i	$0.0928163\pi$
$881$			17.0655i			0.574953i	−0.957788	+	0.287476i	$0.907184\pi$
$882$	−0.559703	+	8.75607i	−0.0188462	+	0.294832i
$883$	2.35287			0.0791805			0.0395902	−	0.999216i	$-0.487395\pi$
$883$	2.35287			0.0791805			0.0395902	+	0.999216i	$0.487395\pi$
$884$	8.34313	+	1.07099i	0.280610	+	0.0360213i
$885$	13.3169			0.447644
$886$	−2.59749	+	40.6355i	−0.0872644	+	1.36518i
$887$		−	5.60160i		−	0.188083i	−0.995568	−	0.0940417i	$-0.970021\pi$
$887$		−	5.60160i		−	0.188083i	0.995568	−	0.0940417i	$-0.0299787\pi$
$888$	−3.23922	+	16.7073i	−0.108701	+	0.560661i
$889$		−	0.250910i		−	0.00841526i
$890$	46.6406	+	2.98135i	1.56340	+	0.0999350i
$891$			3.95311i			0.132434i
$892$	−2.24001	+	17.4499i	−0.0750010	+	0.584266i
$893$	1.43459			0.0480069
$894$	−0.172674	+	2.70134i	−0.00577509	+	0.0903464i
$895$	2.08619			0.0697336
$896$	4.36150	−	9.10223i	0.145707	−	0.304084i
$897$	7.67746	−	18.3513i	0.256343	−	0.612731i
$898$	0.904500	−	14.1501i	0.0301836	−	0.472196i
$899$	7.91289			0.263910
$900$	−8.66810	−	1.11271i	−0.288937	−	0.0370902i
$901$		−	11.3890i		−	0.379422i
$902$	−57.0994	−	3.64989i	−1.90120	−	0.121528i
$903$		−	8.92427i		−	0.296981i
$904$	44.4840	+	8.62457i	1.47951	+	0.286849i
$905$	26.8084			0.891142
$906$	21.8745	+	1.39826i	0.726733	+	0.0464540i
$907$			53.9169i			1.79028i	0.445783	+	0.895141i	$0.352925\pi$
$907$			53.9169i			1.79028i	−0.445783	+	0.895141i	$0.647075\pi$
$908$	6.09483	−	47.4794i	0.202264	−	1.57566i
$909$		−	3.30462i		−	0.109607i
$910$	15.9860	+	1.02185i	0.529932	+	0.0338742i
$911$	27.6108			0.914785			0.457393	−	0.889265i	$-0.348783\pi$
$911$	27.6108			0.914785			0.457393	+	0.889265i	$0.348783\pi$
$912$	0.197677	−	0.757277i	0.00654576	−	0.0250760i
$913$	14.9855			0.495948
$914$	−12.5780	−	0.804005i	−0.416042	−	0.0265941i
$915$	−23.3825			−0.773001
$916$	17.0227	+	2.18517i	0.562445	+	0.0721999i
$917$	−19.4451			−0.642132
$918$	1.43104	+	0.0914745i	0.0472314	+	0.00301911i
$919$	−19.0333			−0.627850			−0.313925	−	0.949448i	$-0.601644\pi$
$919$	−19.0333			−0.627850			−0.313925	+	0.949448i	$0.601644\pi$
$920$	−23.0227	+	34.5538i	−0.759036	+	1.13920i
$921$	−6.89668			−0.227253
$922$	−51.1890	−	3.27209i	−1.68582	−	0.107761i
$923$	−43.9222			−1.44572
$924$	−0.898051	+	6.99591i	−0.0295437	+	0.230149i
$925$	26.2916			0.864463
$926$	41.7641	+	2.66963i	1.37245	+	0.0877295i
$927$	10.3779			0.340856
$928$	16.4155	+	5.42489i	0.538866	+	0.178081i
$929$	−21.7196			−0.712596			−0.356298	−	0.934372i	$-0.615961\pi$
$929$	−21.7196			−0.712596			−0.356298	+	0.934372i	$0.615961\pi$
$930$	11.1850	+	0.714967i	0.366772	+	0.0234447i
$931$			1.21392i			0.0397845i
$932$	−13.0907	−	1.68043i	−0.428801	−	0.0550442i
$933$		−	20.2868i		−	0.664161i
$934$	−0.569564	−	0.0364075i	−0.0186367	−	0.00119129i
$935$	12.2694			0.401251
$936$	−11.5175	−	2.23302i	−0.376461	−	0.0729884i
$937$		−	16.7401i		−	0.546875i	−0.961890	−	0.273437i	$-0.911839\pi$
$937$		−	16.7401i		−	0.546875i	0.961890	−	0.273437i	$-0.0881606\pi$
$938$	4.53506	+	0.289888i	0.148075	+	0.00946519i
$939$			28.1949i			0.920105i
$940$	−5.71503	+	44.5207i	−0.186404	+	1.45210i
$941$	−38.9995			−1.27135			−0.635674	−	0.771958i	$-0.719278\pi$
$941$	−38.9995			−1.27135			−0.635674	+	0.771958i	$0.719278\pi$
$942$	0.997751	−	15.6090i	0.0325085	−	0.508568i
$943$	45.2797	+	18.9433i	1.47451	+	0.616878i
$944$	−16.8380	−	4.39533i	−0.548029	−	0.143056i
$945$	2.73077			0.0888321
$946$	−3.56750	+	55.8105i	−0.115989	+	1.81456i
$947$	35.7861			1.16289			0.581446	−	0.813585i	$-0.302487\pi$
$947$	35.7861			1.16289			0.581446	+	0.813585i	$0.302487\pi$
$948$	−3.67258	−	0.471441i	−0.119280	−	0.0153117i
$949$			13.4674i			0.437170i
$950$	−1.20665	−	0.0771312i	−0.0391489	−	0.00250247i
$951$		−	8.49011i		−	0.275311i
$952$	2.51177	+	0.486983i	0.0814069	+	0.0157832i
$953$			4.44958i			0.144136i	0.997400	+	0.0720681i	$0.0229599\pi$
$953$			4.44958i			0.144136i	−0.997400	+	0.0720681i	$0.977040\pi$
$954$	−1.01330	+	15.8523i	−0.0328069	+	0.513236i
$955$	−21.5457			−0.697204
$956$	3.62406	−	28.2319i	0.117211	−	0.913084i
$957$	−12.0816			−0.390544
$958$	−0.848709	+	13.2773i	−0.0274205	+	0.428971i
$959$			17.0887i			0.551824i
$960$	22.7136	+	9.15144i	0.733078	+	0.295361i
$961$	24.2966			0.783761
$962$	35.2233	+	2.25153i	1.13564	+	0.0725922i
$963$			18.3222i			0.590424i
$964$	4.82194	−	37.5634i	0.155304	−	1.20984i
$965$	65.5200			2.10916
$966$	2.68656	−	5.42154i	0.0864387	−	0.174435i
$967$			19.1093i			0.614514i	0.951627	+	0.307257i	$0.0994110\pi$
$967$			19.1093i			0.614514i	−0.951627	+	0.307257i	$0.900589\pi$
$968$	2.49098	−	12.8480i	0.0800631	−	0.412951i
$969$	0.198395			0.00637338
$970$	10.7894	+	0.689676i	0.346426	+	0.0221441i
$971$		−	52.6143i		−	1.68847i	−0.535972	−	0.844236i	$-0.680055\pi$
$971$		−	52.6143i		−	1.68847i	0.535972	−	0.844236i	$-0.319945\pi$
$972$	−1.98372	−	0.254646i	−0.0636279	−	0.00816778i
$973$	11.9074			0.381732
$974$	39.8337	+	2.54624i	1.27635	+	0.0815867i
$975$			18.1246i			0.580452i
$976$	29.5648	+	7.71752i	0.946348	+	0.247032i
$977$			4.07699i			0.130435i	0.997871	+	0.0652173i	$0.0207741\pi$
$977$			4.07699i			0.130435i	−0.997871	+	0.0652173i	$0.979226\pi$
$978$	0.908366	−	14.2106i	0.0290463	−	0.454405i
$979$	42.6788			1.36402
$980$	−37.6723	−	4.83591i	−1.20340	−	0.154477i
$981$	−12.4462			−0.397376
$982$	2.05481	−	32.1458i	0.0655717	−	1.02581i
$983$	3.92937			0.125327			0.0626637	−	0.998035i	$-0.480040\pi$
$983$	3.92937			0.125327			0.0626637	+	0.998035i	$0.480040\pi$
$984$	5.50972	−	28.4181i	0.175643	−	0.905937i
$985$		−	50.7057i		−	1.61562i
$986$	−0.279568	+	4.37361i	−0.00890327	+	0.139284i
$987$		−	6.54101i		−	0.208203i
$988$	−1.60996	−	0.206667i	−0.0512197	−	0.00657497i
$989$	18.5157	−	44.2576i	0.588764	−	1.40731i
$990$	−17.0777	−	1.09163i	−0.542764	−	0.0346944i
$991$			40.8198i			1.29668i	0.761350	+	0.648341i	$0.224537\pi$
$991$			40.8198i			1.29668i	−0.761350	+	0.648341i	$0.775463\pi$
$992$	−13.9064	−	4.59570i	−0.441529	−	0.145913i
$993$	−14.3840			−0.456464
$994$	−13.3326	−	0.852239i	−0.422883	−	0.0270314i
$995$	−57.3978			−1.81963
$996$	−0.965318	+	7.51994i	−0.0305873	+	0.238278i
$997$			16.7467i			0.530374i	0.964197	+	0.265187i	$0.0854337\pi$
$997$			16.7467i			0.530374i	−0.964197	+	0.265187i	$0.914566\pi$
$998$	−1.61902	+	25.3282i	−0.0512492	+	0.801749i
$999$	6.01692			0.190367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.a.91.13	✓	24
4.3	odd	2		2208.2.n.a.367.3		24
8.3	odd	2	inner	552.2.n.a.91.16	yes	24
8.5	even	2		2208.2.n.a.367.21		24
23.22	odd	2	inner	552.2.n.a.91.14	yes	24
92.91	even	2		2208.2.n.a.367.22		24
184.45	odd	2		2208.2.n.a.367.4		24
184.91	even	2	inner	552.2.n.a.91.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.a.91.13	✓	24	1.1	even	1	trivial
552.2.n.a.91.14	yes	24	23.22	odd	2	inner
552.2.n.a.91.15	yes	24	184.91	even	2	inner
552.2.n.a.91.16	yes	24	8.3	odd	2	inner
2208.2.n.a.367.3		24	4.3	odd	2
2208.2.n.a.367.4		24	184.45	odd	2
2208.2.n.a.367.21		24	8.5	even	2
2208.2.n.a.367.22		24	92.91	even	2

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0902148 - 1.41133i) q^{2} +1.00000 q^{3} +(-1.98372 - 0.254646i) q^{4} -3.06098 q^{5} +(0.0902148 - 1.41133i) q^{6} -0.892124 q^{7} +(-0.538352 + 2.77672i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.0902148 - 1.41133i) q^{2} +1.00000 q^{3} +(-1.98372 - 0.254646i) q^{4} -3.06098 q^{5} +(0.0902148 - 1.41133i) q^{6} -0.892124 q^{7} +(-0.538352 + 2.77672i) q^{8} +1.00000 q^{9} +(-0.276146 + 4.32007i) q^{10} +3.95311i q^{11} +(-1.98372 - 0.254646i) q^{12} +4.14787i q^{13} +(-0.0804827 + 1.25908i) q^{14} -3.06098 q^{15} +(3.87031 + 1.01029i) q^{16} +1.01396i q^{17} +(0.0902148 - 1.41133i) q^{18} -0.195663i q^{19} +(6.07214 + 0.779468i) q^{20} -0.892124 q^{21} +(5.57915 + 0.356629i) q^{22} +(-4.42425 - 1.85094i) q^{23} +(-0.538352 + 2.77672i) q^{24} +4.36961 q^{25} +(5.85403 + 0.374200i) q^{26} +1.00000 q^{27} +(1.76973 + 0.227176i) q^{28} +3.05624i q^{29} +(-0.276146 + 4.32007i) q^{30} -2.58909i q^{31} +(1.77502 - 5.37115i) q^{32} +3.95311i q^{33} +(1.43104 + 0.0914745i) q^{34} +2.73077 q^{35} +(-1.98372 - 0.254646i) q^{36} +6.01692 q^{37} +(-0.276146 - 0.0176517i) q^{38} +4.14787i q^{39} +(1.64789 - 8.49949i) q^{40} -10.2344 q^{41} +(-0.0804827 + 1.25908i) q^{42} +10.0034i q^{43} +(1.00664 - 7.84187i) q^{44} -3.06098 q^{45} +(-3.01142 + 6.07712i) q^{46} +7.33196i q^{47} +(3.87031 + 1.01029i) q^{48} -6.20412 q^{49} +(0.394204 - 6.16698i) q^{50} +1.01396i q^{51} +(1.05624 - 8.22823i) q^{52} -11.2321 q^{53} +(0.0902148 - 1.41133i) q^{54} -12.1004i q^{55} +(0.480276 - 2.47718i) q^{56} -0.195663i q^{57} +(4.31337 + 0.275718i) q^{58} -4.35054 q^{59} +(6.07214 + 0.779468i) q^{60} +7.63888 q^{61} +(-3.65407 - 0.233574i) q^{62} -0.892124 q^{63} +(-7.42035 - 2.98971i) q^{64} -12.6966i q^{65} +(5.57915 + 0.356629i) q^{66} -3.60187i q^{67} +(0.258202 - 2.01142i) q^{68} +(-4.42425 - 1.85094i) q^{69} +(0.246356 - 3.85403i) q^{70} +10.5891i q^{71} +(-0.538352 + 2.77672i) q^{72} +3.24682 q^{73} +(0.542815 - 8.49188i) q^{74} +4.36961 q^{75} +(-0.0498249 + 0.388141i) q^{76} -3.52666i q^{77} +(5.85403 + 0.374200i) q^{78} +1.85136 q^{79} +(-11.8470 - 3.09250i) q^{80} +1.00000 q^{81} +(-0.923296 + 14.4442i) q^{82} -3.79082i q^{83} +(1.76973 + 0.227176i) q^{84} -3.10373i q^{85} +(14.1181 + 0.902455i) q^{86} +3.05624i q^{87} +(-10.9767 - 2.12816i) q^{88} -10.7963i q^{89} +(-0.276146 + 4.32007i) q^{90} -3.70042i q^{91} +(8.30516 + 4.79837i) q^{92} -2.58909i q^{93} +(10.3478 + 0.661451i) q^{94} +0.598921i q^{95} +(1.77502 - 5.37115i) q^{96} -2.49750i q^{97} +(-0.559703 + 8.75607i) q^{98} +3.95311i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9	\( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 4 * q^24 + 24 * q^25 + 24 * q^27 - 4 * q^32 + 4 * q^36 + 4 * q^46 + 4 * q^48 - 8 * q^49 - 44 * q^50 - 4 * q^54 + 48 * q^58 - 40 * q^62 + 4 * q^64 - 4 * q^72 - 32 * q^73 + 24 * q^75 + 24 * q^81 - 40 * q^82 - 52 * q^92 + 40 * q^94 - 4 * q^96 - 20 * q^98

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