LMFDB - Embedded newform 576.2.bd.a.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(37,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 9, 0]))

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

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

chi := DirichletCharacter("576.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			181.1
Character	$\chi$	$=$	576.181
Dual form			576.2.bd.a.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28112 + 0.598933i) q^{2} +(1.28256 - 1.53462i) q^{4} +(-0.884671 - 1.32400i) q^{5} +(-2.40727 - 0.997123i) q^{7} +(-0.723982 + 2.73420i) q^{8} +O(q^{10})$	\(q+(-1.28112 + 0.598933i) q^{2} +(1.28256 - 1.53462i) q^{4} +(-0.884671 - 1.32400i) q^{5} +(-2.40727 - 0.997123i) q^{7} +(-0.723982 + 2.73420i) q^{8} +(1.92636 + 1.16635i) q^{10} +(0.432397 - 2.17381i) q^{11} +(-2.18211 + 3.26576i) q^{13} +(3.68122 - 0.164355i) q^{14} +(-0.710093 - 3.93647i) q^{16} +(-4.38547 + 4.38547i) q^{17} +(2.64242 + 1.76561i) q^{19} +(-3.16648 - 0.340480i) q^{20} +(0.748011 + 3.04389i) q^{22} +(2.12144 + 5.12160i) q^{23} +(0.943074 - 2.27678i) q^{25} +(0.839581 - 5.49078i) q^{26} +(-4.61766 + 2.41536i) q^{28} +(0.836699 + 4.20637i) q^{29} +8.37185i q^{31} +(3.26740 + 4.61780i) q^{32} +(2.99173 - 8.24494i) q^{34} +(0.809445 + 4.06936i) q^{35} +(-5.42017 + 3.62164i) q^{37} +(-4.44275 - 0.679329i) q^{38} +(4.26058 - 1.46031i) q^{40} +(-3.00227 - 7.24812i) q^{41} +(8.60595 + 1.71183i) q^{43} +(-2.78138 - 3.45159i) q^{44} +(-5.78532 - 5.29081i) q^{46} +(-0.0771294 + 0.0771294i) q^{47} +(-0.149067 - 0.149067i) q^{49} +(0.155446 + 3.48168i) q^{50} +(2.21300 + 7.53722i) q^{52} +(-0.846775 + 4.25703i) q^{53} +(-3.26066 + 1.35061i) q^{55} +(4.46915 - 5.86005i) q^{56} +(-3.59125 - 4.88776i) q^{58} +(0.657977 + 0.984732i) q^{59} +(-9.90754 + 1.97073i) q^{61} +(-5.01418 - 10.7254i) q^{62} +(-6.95170 - 3.95902i) q^{64} +6.25433 q^{65} +(-9.06082 + 1.80231i) q^{67} +(1.10540 + 12.3546i) q^{68} +(-3.47427 - 4.72855i) q^{70} +(-9.94840 - 4.12076i) q^{71} +(-10.8278 + 4.48502i) q^{73} +(4.77479 - 7.88609i) q^{74} +(6.09858 - 1.79060i) q^{76} +(-3.20845 + 4.80178i) q^{77} +(-0.842912 - 0.842912i) q^{79} +(-4.58370 + 4.42264i) q^{80} +(8.18742 + 7.48758i) q^{82} +(-0.766957 - 0.512464i) q^{83} +(9.68608 + 1.92668i) q^{85} +(-12.0506 + 2.96132i) q^{86} +(5.63057 + 2.75606i) q^{88} +(-2.03287 + 4.90777i) q^{89} +(8.50928 - 5.68572i) q^{91} +(10.5806 + 3.31316i) q^{92} +(0.0526169 - 0.145008i) q^{94} -5.06055i q^{95} -5.90730i q^{97} +(0.280255 + 0.101692i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	$ 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) $ 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	−1.28112	+	0.598933i	−0.905891	+	0.423510i
$2$	−1.28112	+	0.598933i	−0.905891	+	0.423510i
$3$		0			0
$3$		0			0
$4$	1.28256	−	1.53462i	0.641279	−	0.767308i
$5$	−0.884671	−	1.32400i	−0.395637	−	0.592113i	0.579158	−	0.815215i	$-0.303381\pi$
$5$	−0.884671	−	1.32400i	−0.395637	−	0.592113i	−0.974795	+	0.223103i	$0.928381\pi$
$6$		0			0
$7$	−2.40727	−	0.997123i	−0.909861	−	0.376877i	−0.121858	−	0.992548i	$-0.538885\pi$
$7$	−2.40727	−	0.997123i	−0.909861	−	0.376877i	−0.788004	+	0.615671i	$0.788885\pi$
$8$	−0.723982	+	2.73420i	−0.255966	+	0.966686i
$9$		0			0
$10$	1.92636	+	1.16635i	0.609170	+	0.368834i
$11$	0.432397	−	2.17381i	0.130373	−	0.655427i	−0.859229	−	0.511591i	$-0.829056\pi$
$11$	0.432397	−	2.17381i	0.130373	−	0.655427i	0.989602	−	0.143836i	$-0.0459438\pi$
$12$		0			0
$13$	−2.18211	+	3.26576i	−0.605208	+	0.905758i	−0.999915	−	0.0130490i	$-0.995846\pi$
$13$	−2.18211	+	3.26576i	−0.605208	+	0.905758i	0.394707	+	0.918807i	$0.370846\pi$
$14$	3.68122	−	0.164355i	0.983847	−	0.0439257i
$15$		0			0
$16$	−0.710093	−	3.93647i	−0.177523	−	0.984117i
$17$	−4.38547	+	4.38547i	−1.06363	+	1.06363i	−0.0658001	+	0.997833i	$0.520960\pi$
$17$	−4.38547	+	4.38547i	−1.06363	+	1.06363i	−0.997833	+	0.0658001i	$0.979040\pi$
$18$		0			0
$19$	2.64242	+	1.76561i	0.606212	+	0.405058i	0.820446	−	0.571724i	$-0.193725\pi$
$19$	2.64242	+	1.76561i	0.606212	+	0.405058i	−0.214234	+	0.976782i	$0.568725\pi$
$20$	−3.16648	−	0.340480i	−0.708046	−	0.0761337i
$21$		0			0
$22$	0.748011	+	3.04389i	0.159477	+	0.648960i
$23$	2.12144	+	5.12160i	0.442350	+	1.06793i	0.975122	+	0.221669i	$0.0711505\pi$
$23$	2.12144	+	5.12160i	0.442350	+	1.06793i	−0.532772	+	0.846259i	$0.678850\pi$
$24$		0			0
$25$	0.943074	−	2.27678i	0.188615	−	0.455356i
$26$	0.839581	−	5.49078i	0.164655	−	1.07683i
$27$		0			0
$28$	−4.61766	+	2.41536i	−0.872655	+	0.456461i
$29$	0.836699	+	4.20637i	0.155371	+	0.781104i	0.977357	+	0.211596i	$0.0678661\pi$
$29$	0.836699	+	4.20637i	0.155371	+	0.781104i	−0.821986	+	0.569508i	$0.807134\pi$
$30$		0			0
$31$			8.37185i			1.50363i	0.659375	+	0.751815i	$0.270821\pi$
$31$			8.37185i			1.50363i	−0.659375	+	0.751815i	$0.729179\pi$
$32$	3.26740	+	4.61780i	0.577600	+	0.816320i
$33$		0			0
$34$	2.99173	−	8.24494i	0.513077	−	1.41400i
$35$	0.809445	+	4.06936i	0.136821	+	0.687847i
$36$		0			0
$37$	−5.42017	+	3.62164i	−0.891070	+	0.595394i	−0.914614	−	0.404329i	$-0.867505\pi$
$37$	−5.42017	+	3.62164i	−0.891070	+	0.595394i	0.0235436	+	0.999723i	$0.492505\pi$
$38$	−4.44275	−	0.679329i	−0.720708	−	0.110202i
$39$		0			0
$40$	4.26058	−	1.46031i	0.673656	−	0.230896i
$41$	−3.00227	−	7.24812i	−0.468876	−	1.13197i	−0.964655	−	0.263517i	$-0.915117\pi$
$41$	−3.00227	−	7.24812i	−0.468876	−	1.13197i	0.495779	−	0.868449i	$-0.334883\pi$
$42$		0			0
$43$	8.60595	+	1.71183i	1.31239	+	0.261052i	0.801191	−	0.598408i	$-0.204200\pi$
$43$	8.60595	+	1.71183i	1.31239	+	0.261052i	0.511203	+	0.859460i	$0.329200\pi$
$44$	−2.78138	−	3.45159i	−0.419309	−	0.520347i
$45$		0			0
$46$	−5.78532	−	5.29081i	−0.852999	−	0.780087i
$47$	−0.0771294	+	0.0771294i	−0.0112505	+	0.0112505i	−0.712710	−	0.701459i	$-0.752532\pi$
$47$	−0.0771294	+	0.0771294i	−0.0112505	+	0.0112505i	0.701459	+	0.712710i	$0.252532\pi$
$48$		0			0
$49$	−0.149067	−	0.149067i	−0.0212953	−	0.0212953i
$50$	0.155446	+	3.48168i	0.0219834	+	0.492384i
$51$		0			0
$52$	2.21300	+	7.53722i	0.306888	+	1.04522i
$53$	−0.846775	+	4.25703i	−0.116314	+	0.584748i	0.878036	+	0.478594i	$0.158853\pi$
$53$	−0.846775	+	4.25703i	−0.116314	+	0.584748i	−0.994350	+	0.106153i	$0.966147\pi$
$54$		0			0
$55$	−3.26066	+	1.35061i	−0.439667	+	0.182116i
$56$	4.46915	−	5.86005i	0.597215	−	0.783082i
$57$		0			0
$58$	−3.59125	−	4.88776i	−0.471555	−	0.641794i
$59$	0.657977	+	0.984732i	0.0856613	+	0.128201i	0.871826	−	0.489816i	$-0.162936\pi$
$59$	0.657977	+	0.984732i	0.0856613	+	0.128201i	−0.786164	+	0.618017i	$0.787936\pi$
$60$		0			0
$61$	−9.90754	+	1.97073i	−1.26853	+	0.252327i	−0.783071	−	0.621932i	$-0.786348\pi$
$61$	−9.90754	+	1.97073i	−1.26853	+	0.252327i	−0.485460	+	0.874259i	$0.661348\pi$
$62$	−5.01418	−	10.7254i	−0.636802	−	1.36212i
$63$		0			0
$64$	−6.95170	−	3.95902i	−0.868962	−	0.494878i
$65$	6.25433			0.775754
$66$		0			0
$67$	−9.06082	+	1.80231i	−1.10696	+	0.220187i	−0.714536	−	0.699599i	$-0.753362\pi$
$67$	−9.06082	+	1.80231i	−1.10696	+	0.220187i	−0.392420	+	0.919786i	$0.628362\pi$
$68$	1.10540	+	12.3546i	0.134049	+	1.49822i
$69$		0			0
$70$	−3.47427	−	4.72855i	−0.415255	−	0.565169i
$71$	−9.94840	−	4.12076i	−1.18066	−	0.489044i	−0.295956	−	0.955202i	$-0.595638\pi$
$71$	−9.94840	−	4.12076i	−1.18066	−	0.489044i	−0.884702	+	0.466157i	$0.845638\pi$
$72$		0			0
$73$	−10.8278	+	4.48502i	−1.26730	+	0.524931i	−0.912141	−	0.409876i	$-0.865572\pi$
$73$	−10.8278	+	4.48502i	−1.26730	+	0.524931i	−0.355155	+	0.934807i	$0.615572\pi$
$74$	4.77479	−	7.88609i	0.555058	−	0.916739i
$75$		0			0
$76$	6.09858	−	1.79060i	0.699555	−	0.205396i
$77$	−3.20845	+	4.80178i	−0.365636	+	0.547214i
$78$		0			0
$79$	−0.842912	−	0.842912i	−0.0948351	−	0.0948351i	0.658098	−	0.752933i	$-0.271361\pi$
$79$	−0.842912	−	0.842912i	−0.0948351	−	0.0948351i	−0.752933	+	0.658098i	$0.771361\pi$
$80$	−4.58370	+	4.42264i	−0.512473	+	0.494467i
$81$		0			0
$82$	8.18742	+	7.48758i	0.904149	+	0.826865i
$83$	−0.766957	−	0.512464i	−0.0841845	−	0.0562503i	0.512766	−	0.858529i	$-0.328621\pi$
$83$	−0.766957	−	0.512464i	−0.0841845	−	0.0562503i	−0.596950	+	0.802278i	$0.703621\pi$
$84$		0			0
$85$	9.68608	+	1.92668i	1.05060	+	0.208978i
$86$	−12.0506	+	2.96132i	−1.29944	+	0.319328i
$87$		0			0
$88$	5.63057	+	2.75606i	0.600221	+	0.293797i
$89$	−2.03287	+	4.90777i	−0.215483	+	0.520223i	−0.994249	−	0.107092i	$-0.965846\pi$
$89$	−2.03287	+	4.90777i	−0.215483	+	0.520223i	0.778766	+	0.627315i	$0.215846\pi$
$90$		0			0
$91$	8.50928	−	5.68572i	0.892015	−	0.596025i
$92$	10.5806	+	3.31316i	1.10310	+	0.345421i
$93$		0			0
$94$	0.0526169	−	0.145008i	0.00542702	−	0.0149564i
$95$		−	5.06055i		−	0.519202i
$96$		0			0
$97$		−	5.90730i		−	0.599796i	−0.953971	−	0.299898i	$-0.903047\pi$
$97$		−	5.90730i		−	0.599796i	0.953971	−	0.299898i	$-0.0969526\pi$
$98$	0.280255	+	0.101692i	0.0283100	+	0.0102725i
$99$		0			0
$100$	−2.28444	−	4.36736i	−0.228444	−	0.436736i
$101$	0.429855	−	0.287220i	0.0427722	−	0.0285794i	−0.534000	−	0.845484i	$-0.679312\pi$
$101$	0.429855	−	0.287220i	0.0427722	−	0.0285794i	0.576773	+	0.816905i	$0.304312\pi$
$102$		0			0
$103$	3.33979	−	8.06296i	0.329079	−	0.794467i	−0.669582	−	0.742738i	$-0.733527\pi$
$103$	3.33979	−	8.06296i	0.329079	−	0.794467i	0.998661	−	0.0517290i	$-0.0164732\pi$
$104$	−7.34943	−	8.33067i	−0.720671	−	0.816890i
$105$		0			0
$106$	−1.46485	−	5.96094i	−0.142279	−	0.578978i
$107$	18.7622	+	3.73203i	1.81381	+	0.360789i	0.981188	−	0.193054i	$-0.0618392\pi$
$107$	18.7622	+	3.73203i	1.81381	+	0.360789i	0.832621	+	0.553843i	$0.186839\pi$
$108$		0			0
$109$	10.6124	+	7.09099i	1.01648	+	0.679193i	0.947938	−	0.318455i	$-0.103164\pi$
$109$	10.6124	+	7.09099i	1.01648	+	0.679193i	0.0685465	+	0.997648i	$0.478164\pi$
$110$	3.36838	−	3.68321i	0.321163	−	0.351181i
$111$		0			0
$112$	−2.21576	+	10.1842i	−0.209369	+	0.962314i
$113$	−11.6172	−	11.6172i	−1.09285	−	1.09285i	−0.995223	−	0.0976320i	$-0.968873\pi$
$113$	−11.6172	−	11.6172i	−1.09285	−	1.09285i	−0.0976320	−	0.995223i	$-0.531127\pi$
$114$		0			0
$115$	4.90425	−	7.33973i	0.457323	−	0.684433i
$116$	7.52828	+	4.11090i	0.698983	+	0.381688i
$117$		0			0
$118$	−1.43274	−	0.867479i	−0.131894	−	0.0798579i
$119$	14.9299	−	6.18415i	1.36862	−	0.566900i
$120$		0			0
$121$	5.62421	+	2.32962i	0.511292	+	0.211784i
$122$	11.5125	−	8.45871i	1.04229	−	0.765816i
$123$		0			0
$124$	12.8476	+	10.7374i	1.15375	+	0.964245i
$125$	−11.6576	+	2.31885i	−1.04269	+	0.207404i
$126$		0			0
$127$	2.24655			0.199349			0.0996747	−	0.995020i	$-0.468220\pi$
$127$	2.24655			0.199349			0.0996747	+	0.995020i	$0.468220\pi$
$128$	11.2772	+	0.908394i	0.996771	+	0.0802915i
$129$		0			0
$130$	−8.01257	+	3.74592i	−0.702749	+	0.328539i
$131$	5.29169	−	1.05258i	0.462338	−	0.0919646i	0.0415748	−	0.999135i	$-0.486763\pi$
$131$	5.29169	−	1.05258i	0.462338	−	0.0919646i	0.420763	+	0.907171i	$0.361763\pi$
$132$		0			0
$133$	−4.60048	−	6.88510i	−0.398912	−	0.597014i
$134$	10.5286	−	7.73581i	0.909530	−	0.668272i
$135$		0			0
$136$	−8.81575	−	15.1658i	−0.755945	−	1.30045i
$137$	−6.00408	+	2.48697i	−0.512963	+	0.212476i	−0.624123	−	0.781326i	$-0.714543\pi$
$137$	−6.00408	+	2.48697i	−0.512963	+	0.212476i	0.111160	+	0.993803i	$0.464543\pi$
$138$		0			0
$139$	−0.350641	+	1.76279i	−0.0297410	+	0.149518i	−0.992802	−	0.119764i	$-0.961786\pi$
$139$	−0.350641	+	1.76279i	−0.0297410	+	0.149518i	0.963061	+	0.269282i	$0.0867863\pi$
$140$	7.28306	+	3.97700i	0.615531	+	0.336117i
$141$		0			0
$142$	15.2132	−	0.679222i	1.27666	−	0.0569991i
$143$	6.15559	+	6.15559i	0.514756	+	0.514756i
$144$		0			0
$145$	4.82905	−	4.82905i	0.401031	−	0.401031i
$146$	11.1855	−	12.2310i	0.925719	−	1.01224i
$147$		0			0
$148$	−1.39385	+	12.9628i	−0.114574	+	1.06554i
$149$	3.29611	+	0.655636i	0.270028	+	0.0537118i	0.328247	−	0.944592i	$-0.393542\pi$
$149$	3.29611	+	0.655636i	0.270028	+	0.0537118i	−0.0582192	+	0.998304i	$0.518542\pi$
$150$		0			0
$151$	−1.32342	−	3.19501i	−0.107698	−	0.260007i	0.860838	−	0.508879i	$-0.169940\pi$
$151$	−1.32342	−	3.19501i	−0.107698	−	0.260007i	−0.968536	+	0.248873i	$0.919940\pi$
$152$	−6.74059	+	5.94663i	−0.546734	+	0.482335i
$153$		0			0
$154$	1.23447	−	8.07332i	0.0994765	−	0.650567i
$155$	11.0844	−	7.40634i	0.890318	−	0.594891i
$156$		0			0
$157$	−0.605421	−	3.04366i	−0.0483178	−	0.242910i	0.949077	−	0.315044i	$-0.102019\pi$
$157$	−0.605421	−	3.04366i	−0.0483178	−	0.242910i	−0.997395	+	0.0721336i	$0.977019\pi$
$158$	1.58472	+	0.575027i	0.126074	+	0.0457467i
$159$		0			0
$160$	3.22342	−	8.41129i	0.254833	−	0.664971i
$161$		−	14.4444i		−	1.13838i
$162$		0			0
$163$	0.0943209	+	0.474183i	0.00738778	+	0.0371409i	0.984303	−	0.176485i	$-0.0564727\pi$
$163$	0.0943209	+	0.474183i	0.00738778	+	0.0371409i	−0.976916	+	0.213626i	$0.931473\pi$
$164$	−14.9737	−	4.68880i	−1.16925	−	0.366133i
$165$		0			0
$166$	1.28950	+	0.197174i	0.100085	+	0.0153037i
$167$	3.40598	−	8.22277i	0.263563	−	0.636297i	−0.735591	−	0.677426i	$-0.763095\pi$
$167$	3.40598	−	8.22277i	0.263563	−	0.636297i	0.999154	+	0.0411288i	$0.0130954\pi$
$168$		0			0
$169$	−0.928687	−	2.24205i	−0.0714375	−	0.172465i
$170$	−13.5630	+	3.33300i	−1.04024	+	0.255629i
$171$		0			0
$172$	13.6646	−	11.0113i	1.04192	−	0.839604i
$173$	−10.7422	−	7.17768i	−0.816711	−	0.545709i	0.0755956	−	0.997139i	$-0.475914\pi$
$173$	−10.7422	−	7.17768i	−0.816711	−	0.545709i	−0.892307	+	0.451430i	$0.850914\pi$
$174$		0			0
$175$	−4.54046	+	4.54046i	−0.343227	+	0.343227i
$176$	−8.86416	−	0.158511i	−0.668161	−	0.0119482i
$177$		0			0
$178$	−0.335076	−	7.50502i	−0.0251150	−	0.562525i
$179$	−8.89422	+	13.3111i	−0.664785	+	0.994921i	0.333847	+	0.942627i	$0.391653\pi$
$179$	−8.89422	+	13.3111i	−0.664785	+	0.994921i	−0.998632	+	0.0522939i	$0.983347\pi$
$180$		0			0
$181$	−0.271646	+	1.36566i	−0.0201913	+	0.101508i	−0.989567	−	0.144075i	$-0.953979\pi$
$181$	−0.271646	+	1.36566i	−0.0201913	+	0.101508i	0.969376	+	0.245583i	$0.0789794\pi$
$182$	−7.49608	+	12.3806i	−0.555646	+	0.917712i
$183$		0			0
$184$	−15.5394	+	2.09249i	−1.14558	+	0.154260i
$185$	9.59013	+	3.97236i	0.705081	+	0.292054i
$186$		0			0
$187$	7.63690	+	11.4294i	0.558465	+	0.835803i
$188$	0.0194411	+	0.217287i	0.00141789	+	0.0158473i
$189$		0			0
$190$	3.03093	+	6.48319i	0.219887	+	0.470340i
$191$	3.56574			0.258008			0.129004	−	0.991644i	$-0.458822\pi$
$191$	3.56574			0.258008			0.129004	+	0.991644i	$0.458822\pi$
$192$		0			0
$193$	−3.86751			−0.278389			−0.139195	−	0.990265i	$-0.544451\pi$
$193$	−3.86751			−0.278389			−0.139195	+	0.990265i	$0.544451\pi$
$194$	3.53808	+	7.56799i	0.254019	+	0.543350i
$195$		0			0
$196$	−0.419948	+	0.0375737i	−0.0299963	+	0.00268384i
$197$	10.0325	+	15.0147i	0.714788	+	1.06976i	0.993984	+	0.109522i	$0.0349320\pi$
$197$	10.0325	+	15.0147i	0.714788	+	1.06976i	−0.279196	+	0.960234i	$0.590068\pi$
$198$		0			0
$199$	−12.9440	−	5.36160i	−0.917579	−	0.380074i	−0.126626	−	0.991951i	$-0.540415\pi$
$199$	−12.9440	−	5.36160i	−0.917579	−	0.380074i	−0.790953	+	0.611877i	$0.790415\pi$
$200$	5.54241	+	4.22690i	0.391907	+	0.298887i
$201$		0			0
$202$	−0.378672	+	0.625419i	−0.0266433	+	0.0440043i
$203$	2.18011	−	10.9602i	0.153014	−	0.769252i
$204$		0			0
$205$	−6.94051	+	10.3872i	−0.484747	+	0.725474i
$206$	0.550495	+	12.3300i	0.0383548	+	0.859069i
$207$		0			0
$208$	14.4050	+	6.27081i	0.998810	+	0.434802i
$209$	4.98066	−	4.98066i	0.344519	−	0.344519i
$210$		0			0
$211$	15.7003	+	10.4906i	1.08085	+	0.722204i	0.962640	−	0.270784i	$-0.0872829\pi$
$211$	15.7003	+	10.4906i	1.08085	+	0.722204i	0.118215	+	0.992988i	$0.462283\pi$
$212$	5.44686	+	6.75936i	0.374092	+	0.464234i
$213$		0			0
$214$	−26.2719	+	6.45611i	−1.79591	+	0.441330i
$215$	−5.34696	−	12.9087i	−0.364660	−	0.880367i
$216$		0			0
$217$	8.34776	−	20.1533i	0.566683	−	1.36809i
$218$	−17.8428	−	2.72830i	−1.20847	−	0.184784i
$219$		0			0
$220$	−2.10931	+	6.73609i	−0.142210	+	0.454147i
$221$	−4.75231	−	23.8915i	−0.319675	−	1.60711i
$222$		0			0
$223$		−	25.9711i		−	1.73915i	−0.493797	−	0.869577i	$-0.664391\pi$
$223$		−	25.9711i		−	1.73915i	0.493797	−	0.869577i	$-0.335609\pi$
$224$	−3.26099	−	14.3743i	−0.217884	−	0.960422i
$225$		0			0
$226$	21.8410	+	7.92515i	1.45284	+	0.527173i
$227$	0.214031	+	1.07600i	0.0142057	+	0.0714169i	0.987238	−	0.159253i	$-0.0509084\pi$
$227$	0.214031	+	1.07600i	0.0142057	+	0.0714169i	−0.973032	+	0.230669i	$0.925908\pi$
$228$		0			0
$229$	−13.0798	+	8.73965i	−0.864338	+	0.577532i	−0.906798	−	0.421566i	$-0.861481\pi$
$229$	−13.0798	+	8.73965i	−0.864338	+	0.577532i	0.0424596	+	0.999098i	$0.486481\pi$
$230$	−1.88694	+	12.3404i	−0.124421	+	0.813703i
$231$		0			0
$232$	−12.1068	−	0.757634i	−0.794851	−	0.0497411i
$233$	7.41658	+	17.9052i	0.485876	+	1.17301i	0.956777	+	0.290823i	$0.0939291\pi$
$233$	7.41658	+	17.9052i	0.485876	+	1.17301i	−0.470900	+	0.882186i	$0.656071\pi$
$234$		0			0
$235$	0.170354	+	0.0338855i	0.0111127	+	0.00221044i
$236$	2.35508	+	0.253233i	0.153303	+	0.0164841i
$237$		0			0
$238$	−15.4231	+	16.8646i	−0.999731	+	1.09317i
$239$	−7.81165	+	7.81165i	−0.505293	+	0.505293i	−0.913078	−	0.407785i	$-0.866301\pi$
$239$	−7.81165	+	7.81165i	−0.505293	+	0.505293i	0.407785	+	0.913078i	$0.366301\pi$
$240$		0			0
$241$	−6.52981	−	6.52981i	−0.420622	−	0.420622i	0.464796	−	0.885418i	$-0.346128\pi$
$241$	−6.52981	−	6.52981i	−0.420622	−	0.420622i	−0.885418	+	0.464796i	$0.846128\pi$
$242$	−8.60060	+	0.383990i	−0.552867	+	0.0246838i
$243$		0			0
$244$	−9.68268	+	17.7319i	−0.619870	+	1.13517i
$245$	−0.0654901	+	0.329241i	−0.00418401	+	0.0210344i
$246$		0			0
$247$	−11.5321	+	4.77675i	−0.733769	+	0.303937i
$248$	−22.8903	−	6.06107i	−1.45354	−	0.384878i
$249$		0			0
$250$	13.5460	−	9.95287i	0.856726	−	0.629475i
$251$	4.91732	+	7.35930i	0.310379	+	0.464515i	0.953562	−	0.301198i	$-0.0973865\pi$
$251$	4.91732	+	7.35930i	0.310379	+	0.464515i	−0.643183	+	0.765713i	$0.722386\pi$
$252$		0			0
$253$	12.0507	−	2.39703i	0.757619	−	0.150700i
$254$	−2.87811	+	1.34554i	−0.180589	+	0.0844265i
$255$		0			0
$256$	−14.9915	+	5.59052i	−0.936971	+	0.349407i
$257$	−4.85309			−0.302727			−0.151364	−	0.988478i	$-0.548366\pi$
$257$	−4.85309			−0.302727			−0.151364	+	0.988478i	$0.548366\pi$
$258$		0			0
$259$	16.6590	−	3.31368i	1.03514	−	0.205902i
$260$	8.02153	−	9.59799i	0.497474	−	0.595242i
$261$		0			0
$262$	−6.14889	+	4.51786i	−0.379880	+	0.279115i
$263$	−15.7364	−	6.51821i	−0.970346	−	0.401930i	−0.159505	−	0.987197i	$-0.550990\pi$
$263$	−15.7364	−	6.51821i	−0.970346	−	0.401930i	−0.810841	+	0.585267i	$0.800990\pi$
$264$		0			0
$265$	6.38544	−	2.64493i	0.392254	−	0.162477i
$266$	10.0175	+	6.06529i	0.614212	+	0.371887i
$267$		0			0
$268$	−8.85517	+	16.2164i	−0.540915	+	0.990577i
$269$	−1.78214	+	2.66716i	−0.108659	+	0.162620i	−0.881814	−	0.471598i	$-0.843678\pi$
$269$	−1.78214	+	2.66716i	−0.108659	+	0.162620i	0.773155	+	0.634217i	$0.218678\pi$
$270$		0			0
$271$	−4.32788	−	4.32788i	−0.262900	−	0.262900i	0.563331	−	0.826231i	$-0.309520\pi$
$271$	−4.32788	−	4.32788i	−0.262900	−	0.262900i	−0.826231	+	0.563331i	$0.809520\pi$
$272$	20.3774	+	14.1492i	1.23556	+	0.857919i
$273$		0			0
$274$	6.20244	−	6.78216i	0.374703	−	0.409725i
$275$	−4.54150	−	3.03453i	−0.273863	−	0.182989i
$276$		0			0
$277$	3.82789	+	0.761415i	0.229996	+	0.0457490i	0.308742	−	0.951146i	$-0.400092\pi$
$277$	3.82789	+	0.761415i	0.229996	+	0.0457490i	−0.0787468	+	0.996895i	$0.525092\pi$
$278$	−0.606580	−	2.46836i	−0.0363802	−	0.148043i
$279$		0			0
$280$	−11.7125	−	0.732956i	−0.699953	−	0.0438025i
$281$	−2.18086	+	5.26507i	−0.130099	+	0.314088i	−0.975484	−	0.220070i	$-0.929371\pi$
$281$	−2.18086	+	5.26507i	−0.130099	+	0.314088i	0.845385	+	0.534158i	$0.179371\pi$
$282$		0			0
$283$	−18.8263	+	12.5793i	−1.11911	+	0.747764i	−0.970492	−	0.241131i	$-0.922482\pi$
$283$	−18.8263	+	12.5793i	−1.11911	+	0.747764i	−0.148615	+	0.988895i	$0.547482\pi$
$284$	−19.0832	+	9.98186i	−1.13238	+	0.592314i
$285$		0			0
$286$	−11.5729	−	4.19928i	−0.684317	−	0.248309i
$287$			20.4418i			1.20664i
$288$		0			0
$289$		−	21.4647i		−	1.26263i
$290$	−3.29433	+	9.07889i	−0.193450	+	0.533131i
$291$		0			0
$292$	−7.00448	+	22.3688i	−0.409906	+	1.30903i
$293$	5.52242	−	3.68996i	0.322623	−	0.215570i	−0.383703	−	0.923457i	$-0.625351\pi$
$293$	5.52242	−	3.68996i	0.322623	−	0.215570i	0.706326	+	0.707887i	$0.250351\pi$
$294$		0			0
$295$	0.721696	−	1.74233i	0.0420187	−	0.101442i
$296$	−5.97818	−	17.4418i	−0.347475	−	1.01379i
$297$		0			0
$298$	−4.61540	+	1.13420i	−0.267363	+	0.0657023i
$299$	−21.3551	−	4.24780i	−1.23500	−	0.245657i
$300$		0			0
$301$	−19.0099	−	12.7020i	−1.09571	−	0.732132i
$302$	3.60906	+	3.30057i	0.207678	+	0.189926i
$303$		0			0
$304$	5.07389	−	11.6555i	0.291008	−	0.668491i
$305$	11.3742	+	11.3742i	0.651283	+	0.651283i
$306$		0			0
$307$	1.13328	−	1.69608i	0.0646798	−	0.0968002i	−0.797720	−	0.603028i	$-0.793961\pi$
$307$	1.13328	−	1.69608i	0.0646798	−	0.0968002i	0.862400	+	0.506228i	$0.168961\pi$
$308$	3.25387	+	11.0823i	0.185407	+	0.631472i
$309$		0			0
$310$	−9.76454	+	16.1272i	−0.554589	+	0.915965i
$311$	−24.3362	+	10.0804i	−1.37998	+	0.571607i	−0.944476	−	0.328580i	$-0.893430\pi$
$311$	−24.3362	+	10.0804i	−1.37998	+	0.571607i	−0.435505	+	0.900186i	$0.643430\pi$
$312$		0			0
$313$	10.8933	+	4.51214i	0.615725	+	0.255041i	0.668674	−	0.743556i	$-0.266862\pi$
$313$	10.8933	+	4.51214i	0.615725	+	0.255041i	−0.0529494	+	0.998597i	$0.516862\pi$
$314$	2.59857	+	3.53669i	0.146646	+	0.199587i
$315$		0			0
$316$	−2.37463	+	0.212463i	−0.133583	+	0.0119520i
$317$	−13.7108	+	2.72726i	−0.770078	+	0.153178i	−0.564467	−	0.825456i	$-0.690918\pi$
$317$	−13.7108	+	2.72726i	−0.770078	+	0.153178i	−0.205611	+	0.978634i	$0.565918\pi$
$318$		0			0
$319$	9.50562			0.532213
$320$	0.908205	+	12.7065i	0.0507702	+	0.710316i
$321$		0			0
$322$	8.65123	+	18.5051i	0.482114	+	1.03125i
$323$	−19.3313	+	3.84523i	−1.07562	+	0.213954i
$324$		0			0
$325$	5.37753	+	8.04804i	0.298292	+	0.446425i
$326$	−0.404841	−	0.550996i	−0.0224221	−	0.0305168i
$327$		0			0
$328$	21.9914	−	2.96130i	1.21427	−	0.163510i
$329$	0.262578	−	0.108764i	0.0144764	−	0.00599633i
$330$		0			0
$331$	6.48019	−	32.5781i	0.356184	−	1.79066i	−0.222318	−	0.974974i	$-0.571362\pi$
$331$	6.48019	−	32.5781i	0.356184	−	1.79066i	0.578501	−	0.815682i	$-0.303638\pi$
$332$	−1.77010	+	0.519720i	−0.0971470	+	0.0285233i
$333$		0			0
$334$	0.561406	+	12.5743i	0.0307188	+	0.688038i
$335$	10.4021	+	10.4021i	0.568328	+	0.568328i
$336$		0			0
$337$	4.67117	−	4.67117i	0.254455	−	0.254455i	−0.568339	−	0.822794i	$-0.692414\pi$
$337$	4.67117	−	4.67117i	0.254455	−	0.254455i	0.822794	+	0.568339i	$0.192414\pi$
$338$	2.53260	+	2.31612i	0.137755	+	0.125980i
$339$		0			0
$340$	15.3797	−	12.3933i	0.834080	−	0.672123i
$341$	18.1988	+	3.61996i	0.985520	+	0.196032i
$342$		0			0
$343$	7.19006	+	17.3584i	0.388227	+	0.937263i
$344$	−10.9110	+	22.2910i	−0.588284	+	1.20185i
$345$		0			0
$346$	18.0610	+	2.76166i	0.970965	+	0.148468i
$347$	11.6056	−	7.75460i	0.623020	−	0.416289i	−0.203596	−	0.979055i	$-0.565263\pi$
$347$	11.6056	−	7.75460i	0.623020	−	0.416289i	0.826616	+	0.562766i	$0.190263\pi$
$348$		0			0
$349$	3.22983	+	16.2374i	0.172889	+	0.869170i	0.965692	+	0.259692i	$0.0836210\pi$
$349$	3.22983	+	16.2374i	0.172889	+	0.869170i	−0.792803	+	0.609478i	$0.791379\pi$
$350$	3.09746	−	8.53633i	0.165566	−	0.456286i
$351$		0			0
$352$	11.4510	−	5.10597i	0.610342	−	0.272149i
$353$		−	29.4440i		−	1.56715i	−0.621299	−	0.783573i	$-0.713395\pi$
$353$		−	29.4440i		−	1.56715i	0.621299	−	0.783573i	$-0.286605\pi$
$354$		0			0
$355$	3.34516	+	16.8172i	0.177542	+	0.892566i
$356$	4.92428	+	9.41417i	0.260986	+	0.498950i
$357$		0			0
$358$	3.42211	−	22.3803i	0.180864	−	1.18283i
$359$	6.81567	−	16.4545i	0.359717	−	0.868435i	−0.635622	−	0.772001i	$-0.719256\pi$
$359$	6.81567	−	16.4545i	0.359717	−	0.868435i	0.995339	−	0.0964342i	$-0.0307437\pi$
$360$		0			0
$361$	−3.40598	−	8.22277i	−0.179262	−	0.432777i
$362$	−0.469925	−	1.91227i	−0.0246987	−	0.100507i
$363$		0			0
$364$	2.18824	−	20.3507i	0.114695	−	1.06667i
$365$	15.5172	+	10.3683i	0.812208	+	0.542700i
$366$		0			0
$367$	−21.7396	+	21.7396i	−1.13480	+	1.13480i	−0.145427	+	0.989369i	$0.546455\pi$
$367$	−21.7396	+	21.7396i	−1.13480	+	1.13480i	−0.989369	+	0.145427i	$0.953545\pi$
$368$	18.6546	−	11.9878i	0.972438	−	0.624906i
$369$		0			0
$370$	−14.6653	+	0.654762i	−0.762414	+	0.0340394i
$371$	6.28319	−	9.40346i	0.326207	−	0.488203i
$372$		0			0
$373$	−2.98424	+	15.0028i	−0.154518	+	0.776816i	0.823340	+	0.567548i	$0.192108\pi$
$373$	−2.98424	+	15.0028i	−0.154518	+	0.776816i	−0.977858	+	0.209268i	$0.932892\pi$
$374$	−16.6293	−	10.0685i	−0.859880	−	0.520631i
$375$		0			0
$376$	−0.155047	−	0.266728i	−0.00799593	−	0.0137554i
$377$	−15.5628	−	6.44631i	−0.801523	−	0.332002i
$378$		0			0
$379$	−9.23758	−	13.8250i	−0.474503	−	0.710143i	0.514590	−	0.857436i	$-0.327944\pi$
$379$	−9.23758	−	13.8250i	−0.474503	−	0.710143i	−0.989093	+	0.147293i	$0.952944\pi$
$380$	−7.76601	−	6.49045i	−0.398388	−	0.332953i
$381$		0			0
$382$	−4.56816	+	2.13564i	−0.233727	+	0.109269i
$383$	10.4632			0.534645			0.267322	−	0.963607i	$-0.413861\pi$
$383$	10.4632			0.534645			0.267322	+	0.963607i	$0.413861\pi$
$384$		0			0
$385$	9.19599			0.468671
$386$	4.95476	−	2.31638i	0.252190	−	0.117901i
$387$		0			0
$388$	−9.06544	−	7.57645i	−0.460228	−	0.384636i
$389$	−5.64815	−	8.45306i	−0.286373	−	0.428587i	0.660194	−	0.751095i	$-0.270474\pi$
$389$	−5.64815	−	8.45306i	−0.286373	−	0.428587i	−0.946567	+	0.322508i	$0.895474\pi$
$390$		0			0
$391$	−31.7641	−	13.1571i	−1.60638	−	0.665385i
$392$	0.515502	−	0.299658i	0.0260368	−	0.0151350i
$393$		0			0
$394$	−21.8457	−	13.2269i	−1.10057	−	0.666363i
$395$	−0.370319	+	1.86172i	−0.0186328	+	0.0936733i
$396$		0			0
$397$	−1.45561	+	2.17847i	−0.0730549	+	0.109334i	−0.866198	−	0.499701i	$-0.833443\pi$
$397$	−1.45561	+	2.17847i	−0.0730549	+	0.109334i	0.793143	+	0.609035i	$0.208443\pi$
$398$	19.7942	−	0.883749i	0.992192	−	0.0442983i
$399$		0			0
$400$	−9.63214	−	2.09565i	−0.481607	−	0.104783i
$401$	14.8490	−	14.8490i	0.741524	−	0.741524i	−0.231347	−	0.972871i	$-0.574313\pi$
$401$	14.8490	−	14.8490i	0.741524	−	0.741524i	0.972871	+	0.231347i	$0.0743134\pi$
$402$		0			0
$403$	−27.3404	−	18.2683i	−1.36192	−	0.910009i
$404$	0.110541	−	1.02804i	0.00549964	−	0.0511468i
$405$		0			0
$406$	3.77141	+	15.3471i	0.187172	+	0.761661i
$407$	5.52908	+	13.3484i	0.274066	+	0.661655i
$408$		0			0
$409$	−8.95302	+	21.6145i	−0.442698	+	1.06877i	0.532300	+	0.846556i	$0.321328\pi$
$409$	−8.95302	+	21.6145i	−0.442698	+	1.06877i	−0.974998	+	0.222212i	$0.928672\pi$
$410$	2.67041	−	17.4642i	0.131882	−	0.862496i
$411$		0			0
$412$	−8.09008	−	15.4665i	−0.398570	−	0.761980i
$413$	−0.602027	−	3.02660i	−0.0296238	−	0.148929i
$414$		0			0
$415$			1.46882i			0.0721014i
$416$	−22.2104	+	0.593981i	−1.08896	+	0.0291223i
$417$		0			0
$418$	−3.39776	+	9.36393i	−0.166190	+	0.458005i
$419$	2.28680	+	11.4965i	0.111718	+	0.561643i	0.995582	+	0.0938989i	$0.0299331\pi$
$419$	2.28680	+	11.4965i	0.111718	+	0.561643i	−0.883864	+	0.467744i	$0.845067\pi$
$420$		0			0
$421$	27.2435	−	18.2035i	1.32777	−	0.887185i	0.329392	−	0.944193i	$-0.393156\pi$
$421$	27.2435	−	18.2035i	1.32777	−	0.887185i	0.998374	+	0.0570087i	$0.0181563\pi$
$422$	−26.3972	−	4.03634i	−1.28500	−	0.196486i
$423$		0			0
$424$	−11.0265	−	5.39726i	−0.535495	−	0.262114i
$425$	5.84894	+	14.1206i	0.283715	+	0.684949i
$426$		0			0
$427$	25.8152	+	5.13496i	1.24928	+	0.248498i
$428$	29.7908	−	24.0062i	1.43999	−	1.16038i
$429$		0			0
$430$	14.5816	+	13.3352i	0.703186	+	0.643080i
$431$	−11.1659	+	11.1659i	−0.537842	+	0.537842i	−0.922895	−	0.385053i	$-0.874183\pi$
$431$	−11.1659	+	11.1659i	−0.537842	+	0.537842i	0.385053	+	0.922895i	$0.374183\pi$
$432$		0			0
$433$	15.3110	+	15.3110i	0.735802	+	0.735802i	0.971763	−	0.235961i	$-0.0758237\pi$
$433$	15.3110	+	15.3110i	0.735802	+	0.735802i	−0.235961	+	0.971763i	$0.575824\pi$
$434$	1.37596	+	30.8186i	0.0660480	+	1.47934i
$435$		0			0
$436$	24.4930	−	7.19138i	1.17300	−	0.344405i
$437$	−3.43701	+	17.2790i	−0.164415	+	0.826568i
$438$		0			0
$439$	37.8088	−	15.6609i	1.80452	−	0.747455i	0.819951	−	0.572434i	$-0.194001\pi$
$439$	37.8088	−	15.6609i	1.80452	−	0.747455i	0.984565	−	0.175021i	$-0.0559995\pi$
$440$	−1.33218	−	9.89310i	−0.0635090	−	0.471635i
$441$		0			0
$442$	20.3977	+	27.7616i	0.970219	+	1.32049i
$443$	−18.8638	−	28.2317i	−0.896247	−	1.34133i	−0.939602	−	0.342269i	$-0.888805\pi$
$443$	−18.8638	−	28.2317i	−0.896247	−	1.34133i	0.0433550	−	0.999060i	$-0.486195\pi$
$444$		0			0
$445$	8.29633	−	1.65024i	0.393284	−	0.0782290i
$446$	15.5550	+	33.2722i	0.736549	+	1.57549i
$447$		0			0
$448$	12.7870	+	16.4621i	0.604127	+	0.777762i
$449$	2.12507			0.100288			0.0501442	−	0.998742i	$-0.484032\pi$
$449$	2.12507			0.100288			0.0501442	+	0.998742i	$0.484032\pi$
$450$		0			0
$451$	−17.0542	+	3.39229i	−0.803050	+	0.159737i
$452$	−32.7277	+	2.92822i	−1.53938	+	0.137732i
$453$		0			0
$454$	−0.918655	−	1.25031i	−0.0431146	−	0.0586797i
$455$	−15.0558	−	6.23633i	−0.705828	−	0.292364i
$456$		0			0
$457$	−32.1519	+	13.3177i	−1.50400	+	0.622978i	−0.974310	−	0.225213i	$-0.927692\pi$
$457$	−32.1519	+	13.3177i	−1.50400	+	0.622978i	−0.529691	+	0.848190i	$0.677692\pi$
$458$	11.5224	−	19.0305i	0.538406	−	0.889237i
$459$		0			0
$460$	−4.97368	−	16.9398i	−0.231899	−	0.789820i
$461$	−7.57489	+	11.3366i	−0.352798	+	0.528000i	−0.964844	−	0.262822i	$-0.915347\pi$
$461$	−7.57489	+	11.3366i	−0.352798	+	0.528000i	0.612046	+	0.790822i	$0.290347\pi$
$462$		0			0
$463$	16.2876	+	16.2876i	0.756949	+	0.756949i	0.975766	−	0.218817i	$-0.0702197\pi$
$463$	16.2876	+	16.2876i	0.756949	+	0.756949i	−0.218817	+	0.975766i	$0.570220\pi$
$464$	15.9641	−	6.28055i	0.741115	−	0.291567i
$465$		0			0
$466$	−20.2256	−	18.4968i	−0.936932	−	0.856846i
$467$	13.6451	+	9.11734i	0.631418	+	0.421900i	0.829672	−	0.558250i	$-0.188527\pi$
$467$	13.6451	+	9.11734i	0.631418	+	0.421900i	−0.198254	+	0.980151i	$0.563527\pi$
$468$		0			0
$469$	23.6089	+	4.69611i	1.09016	+	0.216846i
$470$	−0.238539	+	0.0586191i	−0.0110030	+	0.00270390i
$471$		0			0
$472$	−3.16882	+	1.08611i	−0.145857	+	0.0499924i
$473$	7.44237	−	17.9675i	0.342201	−	0.826145i
$474$		0			0
$475$	6.51190	−	4.35111i	0.298786	−	0.199643i
$476$	9.65810	−	30.8431i	0.442678	−	1.41369i
$477$		0			0
$478$	5.32903	−	14.6863i	0.243744	−	0.671738i
$479$		−	4.14550i		−	0.189413i	−0.995505	−	0.0947064i	$-0.969809\pi$
$479$		−	4.14550i		−	0.189413i	0.995505	−	0.0947064i	$-0.0301912\pi$
$480$		0			0
$481$		−	25.6038i		−	1.16743i
$482$	12.2764	+	4.45457i	0.559175	+	0.202900i
$483$		0			0
$484$	10.7884	−	5.64312i	0.490384	−	0.256506i
$485$	−7.82129	+	5.22602i	−0.355146	+	0.237301i
$486$		0			0
$487$	0.228313	−	0.551195i	0.0103458	−	0.0249770i	−0.918622	−	0.395137i	$-0.870697\pi$
$487$	0.228313	−	0.551195i	0.0103458	−	0.0249770i	0.928968	+	0.370160i	$0.120697\pi$
$488$	1.78451	−	28.5160i	0.0807808	−	1.29086i
$489$		0			0
$490$	−0.113293	−	0.461023i	−0.00511804	−	0.0208269i
$491$	31.2490	+	6.21581i	1.41025	+	0.280516i	0.840726	−	0.541461i	$-0.182129\pi$
$491$	31.2490	+	6.21581i	1.41025	+	0.280516i	0.569521	+	0.821977i	$0.307129\pi$
$492$		0			0
$493$	−22.1162	−	14.7776i	−0.996065	−	0.665550i
$494$	11.9131	−	13.0266i	0.535995	−	0.586093i
$495$		0			0
$496$	32.9555	−	5.94480i	1.47975	−	0.266929i
$497$	19.8395	+	19.8395i	0.889925	+	0.889925i
$498$		0			0
$499$	4.65337	−	6.96426i	0.208313	−	0.311763i	−0.712570	−	0.701601i	$-0.752469\pi$
$499$	4.65337	−	6.96426i	0.208313	−	0.311763i	0.920884	+	0.389838i	$0.127469\pi$
$500$	−11.3930	+	20.8640i	−0.509512	+	0.933068i
$501$		0			0
$502$	−10.7074	−	6.48302i	−0.477896	−	0.289351i
$503$	−16.9351	+	7.01476i	−0.755100	+	0.312772i	−0.726820	−	0.686828i	$-0.759003\pi$
$503$	−16.9351	+	7.01476i	−0.755100	+	0.312772i	−0.0282792	+	0.999600i	$0.509003\pi$
$504$		0			0
$505$	−0.760560	−	0.315034i	−0.0338445	−	0.0140188i
$506$	−14.0027	+	10.2884i	−0.622498	+	0.457377i
$507$		0			0
$508$	2.88133	−	3.44760i	0.127839	−	0.152962i
$509$	13.8146	−	2.74790i	0.612322	−	0.121798i	0.120819	−	0.992675i	$-0.461448\pi$
$509$	13.8146	−	2.74790i	0.612322	−	0.121798i	0.491503	+	0.870876i	$0.336448\pi$
$510$		0			0
$511$	30.5375			1.35090
$512$	15.8577	−	16.1411i	0.700817	−	0.713342i
$513$		0			0
$514$	6.21741	−	2.90668i	0.274238	−	0.128208i
$515$	−13.6300	+	2.71118i	−0.600610	+	0.119469i
$516$		0			0
$517$	0.134314	+	0.201015i	0.00590712	+	0.00884062i
$518$	−19.3576	+	14.2229i	−0.850523	+	0.624917i
$519$		0			0
$520$	−4.52802	+	17.1006i	−0.198567	+	0.749910i
$521$	−1.55454	+	0.643912i	−0.0681057	+	0.0282103i	−0.416476	−	0.909147i	$-0.636735\pi$
$521$	−1.55454	+	0.643912i	−0.0681057	+	0.0282103i	0.348371	+	0.937357i	$0.386735\pi$
$522$		0			0
$523$	−5.90096	+	29.6661i	−0.258031	+	1.29721i	0.606683	+	0.794944i	$0.292500\pi$
$523$	−5.90096	+	29.6661i	−0.258031	+	1.29721i	−0.864714	+	0.502265i	$0.832500\pi$
$524$	5.17159	−	9.47072i	0.225922	−	0.413730i
$525$		0			0
$526$	24.0642	−	1.07439i	1.04925	−	0.0468458i
$527$	−36.7145	−	36.7145i	−1.59931	−	1.59931i
$528$		0			0
$529$	−5.46686	+	5.46686i	−0.237690	+	0.237690i
$530$	−6.59640	+	7.21294i	−0.286529	+	0.313310i
$531$		0			0
$532$	−16.4664	−	1.77057i	−0.713907	−	0.0767640i
$533$	30.2219	+	6.01150i	1.30905	+	0.260387i
$534$		0			0
$535$	−11.6571	−	28.1428i	−0.503982	−	1.21672i
$536$	1.63200	−	26.0789i	0.0704916	−	1.12644i
$537$		0			0
$538$	0.685690	−	4.48435i	0.0295622	−	0.193334i
$539$	−0.388500	+	0.259587i	−0.0167339	+	0.0111812i
$540$		0			0
$541$	−5.86328	−	29.4767i	−0.252082	−	1.26730i	−0.874657	−	0.484742i	$-0.838913\pi$
$541$	−5.86328	−	29.4767i	−0.252082	−	1.26730i	0.622575	−	0.782560i	$-0.286087\pi$
$542$	8.13667	+	2.95244i	0.349500	+	0.126818i
$543$		0			0
$544$	−34.5803	−	5.92216i	−1.48262	−	0.253910i
$545$		−	20.3241i		−	0.870587i
$546$		0			0
$547$	8.35722	+	42.0146i	0.357329	+	1.79641i	0.572572	+	0.819854i	$0.305946\pi$
$547$	8.35722	+	42.0146i	0.357329	+	1.79641i	−0.215243	+	0.976560i	$0.569054\pi$
$548$	−3.88403	+	12.4036i	−0.165917	+	0.529857i
$549$		0			0
$550$	7.63571	+	1.16756i	0.325588	+	0.0497848i
$551$	−5.21589	+	12.5923i	−0.222204	+	0.536449i
$552$		0			0
$553$	1.18863	+	2.86960i	0.0505456	+	0.122028i
$554$	−5.36004	+	1.31719i	−0.227726	+	0.0559618i
$555$		0			0
$556$	2.25549	+	2.79898i	0.0956540	+	0.118703i
$557$	6.44120	+	4.30387i	0.272923	+	0.182361i	0.684498	−	0.729015i	$-0.260021\pi$
$557$	6.44120	+	4.30387i	0.272923	+	0.182361i	−0.411576	+	0.911376i	$0.635021\pi$
$558$		0			0
$559$	−24.3695	+	24.3695i	−1.03072	+	1.03072i
$560$	15.4441	−	6.07598i	0.652632	−	0.256757i
$561$		0			0
$562$	−0.359470	−	8.05140i	−0.0151633	−	0.339628i
$563$	1.09582	−	1.64001i	0.0461832	−	0.0691181i	−0.807659	−	0.589649i	$-0.799266\pi$
$563$	1.09582	−	1.64001i	0.0461832	−	0.0691181i	0.853843	+	0.520531i	$0.174266\pi$
$564$		0			0
$565$	−5.10382	+	25.6586i	−0.214719	+	1.07947i
$566$	16.5846	−	27.3914i	0.697105	−	1.15135i
$567$		0			0
$568$	18.4695	−	24.2176i	0.774961	−	1.01615i
$569$	35.9156	+	14.8767i	1.50566	+	0.623664i	0.974657	−	0.223706i	$-0.0718156\pi$
$569$	35.9156	+	14.8767i	1.50566	+	0.623664i	0.531002	+	0.847370i	$0.321816\pi$
$570$		0			0
$571$	−7.30296	−	10.9297i	−0.305619	−	0.457392i	0.646590	−	0.762838i	$-0.276194\pi$
$571$	−7.30296	−	10.9297i	−0.305619	−	0.457392i	−0.952209	+	0.305446i	$0.901194\pi$
$572$	17.3414	−	1.55157i	0.725079	−	0.0648744i
$573$		0			0
$574$	−12.2433	−	26.1885i	−0.511024	−	1.09308i
$575$	13.6614			0.569722
$576$		0			0
$577$	3.92683			0.163476			0.0817381	−	0.996654i	$-0.473953\pi$
$577$	3.92683			0.163476			0.0817381	+	0.996654i	$0.473953\pi$
$578$	12.8559	+	27.4990i	0.534736	+	1.14381i
$579$		0			0
$580$	−1.21720	−	13.6043i	−0.0505416	−	0.564886i
$581$	1.33528	+	1.99839i	0.0553968	+	0.0829072i
$582$		0			0
$583$	8.88781	+	3.68145i	0.368095	+	0.152470i
$584$	−4.42381	−	32.8524i	−0.183058	−	1.35944i
$585$		0			0
$586$	−4.86486	+	8.03486i	−0.200966	+	0.331917i
$587$	−7.25567	+	36.4767i	−0.299473	+	1.50555i	0.478965	+	0.877834i	$0.341012\pi$
$587$	−7.25567	+	36.4767i	−0.299473	+	1.50555i	−0.778439	+	0.627721i	$0.783988\pi$
$588$		0			0
$589$	−14.7814	+	22.1219i	−0.609057	+	0.911518i
$590$	0.118957	+	2.66439i	0.00489737	+	0.109691i
$591$		0			0
$592$	18.1053	+	18.7646i	0.744123	+	0.771221i
$593$	−6.42206	+	6.42206i	−0.263723	+	0.263723i	−0.826565	−	0.562842i	$-0.809708\pi$
$593$	−6.42206	+	6.42206i	−0.263723	+	0.263723i	0.562842	+	0.826565i	$0.309708\pi$
$594$		0			0
$595$	−21.3958	−	14.2962i	−0.877144	−	0.586089i
$596$	5.23360	−	4.21737i	0.214376	−	0.172750i
$597$		0			0
$598$	29.9027	−	7.34834i	1.22281	−	0.300496i
$599$	−12.0671	−	29.1324i	−0.493046	−	1.19032i	−0.953162	−	0.302460i	$-0.902192\pi$
$599$	−12.0671	−	29.1324i	−0.493046	−	1.19032i	0.460116	−	0.887859i	$-0.347808\pi$
$600$		0			0
$601$	−13.5123	+	32.6215i	−0.551177	+	1.33066i	0.365419	+	0.930843i	$0.380926\pi$
$601$	−13.5123	+	32.6215i	−0.551177	+	1.33066i	−0.916596	+	0.399815i	$0.869074\pi$
$602$	31.9617	+	4.88718i	1.30266	+	0.199187i
$603$		0			0
$604$	−6.60048	−	2.06685i	−0.268570	−	0.0840989i
$605$	−1.89114	−	9.50742i	−0.0768859	−	0.386532i
$606$		0			0
$607$		−	12.7147i		−	0.516076i	−0.966135	−	0.258038i	$-0.916924\pi$
$607$		−	12.7147i		−	0.516076i	0.966135	−	0.258038i	$-0.0830759\pi$
$608$	0.480607	+	17.9711i	0.0194912	+	0.728825i
$609$		0			0
$610$	−21.3841	−	7.75936i	−0.865817	−	0.314167i
$611$	−0.0835811	−	0.420191i	−0.00338133	−	0.0169991i
$612$		0			0
$613$	−0.425673	+	0.284426i	−0.0171928	+	0.0114878i	−0.564137	−	0.825681i	$-0.690791\pi$
$613$	−0.425673	+	0.284426i	−0.0171928	+	0.0114878i	0.546944	+	0.837169i	$0.315791\pi$
$614$	−0.436038	+	2.85164i	−0.0175971	+	0.115083i
$615$		0			0
$616$	−10.8062	−	12.2489i	−0.435393	−	0.493524i
$617$	−4.10135	−	9.90154i	−0.165114	−	0.398621i	0.819567	−	0.572983i	$-0.194214\pi$
$617$	−4.10135	−	9.90154i	−0.165114	−	0.398621i	−0.984682	+	0.174362i	$0.944214\pi$
$618$		0			0
$619$	27.4882	+	5.46774i	1.10484	+	0.219767i	0.713623	−	0.700530i	$-0.247053\pi$
$619$	27.4882	+	5.46774i	1.10484	+	0.219767i	0.391220	+	0.920297i	$0.372053\pi$
$620$	2.85045	−	26.5093i	0.114477	−	1.06464i
$621$		0			0
$622$	25.1402	−	27.4900i	1.00803	−	1.10225i
$623$	9.78730	−	9.78730i	0.392120	−	0.392120i
$624$		0			0
$625$	4.67046	+	4.67046i	0.186818	+	0.186818i
$626$	−16.6581	+	0.743734i	−0.665792	+	0.0297256i
$627$		0			0
$628$	−5.44733	−	2.97457i	−0.217372	−	0.118698i
$629$	7.88739	−	39.6526i	0.314491	−	1.58105i
$630$		0			0
$631$	−39.9593	+	16.5517i	−1.59075	+	0.658911i	−0.990070	−	0.140576i	$-0.955105\pi$
$631$	−39.9593	+	16.5517i	−1.59075	+	0.658911i	−0.600683	+	0.799487i	$0.705105\pi$
$632$	2.91494	−	1.69444i	0.115950	−	0.0674011i
$633$		0			0
$634$	15.9318	−	11.7058i	0.632735	−	0.464898i
$635$	−1.98746	−	2.97445i	−0.0788700	−	0.118037i
$636$		0			0
$637$	0.812099	−	0.161536i	0.0321765	−	0.00640031i
$638$	−12.1779	+	5.69324i	−0.482127	+	0.225397i
$639$		0			0
$640$	−8.77388	−	15.7347i	−0.346818	−	0.621967i
$641$	−5.29159			−0.209005			−0.104503	−	0.994525i	$-0.533325\pi$
$641$	−5.29159			−0.209005			−0.104503	+	0.994525i	$0.533325\pi$
$642$		0			0
$643$	−20.3921	+	4.05624i	−0.804185	+	0.159962i	−0.580034	−	0.814592i	$-0.696961\pi$
$643$	−20.3921	+	4.05624i	−0.804185	+	0.159962i	−0.224151	+	0.974554i	$0.571961\pi$
$644$	−22.1666	−	18.5258i	−0.873487	−	0.730018i
$645$		0			0
$646$	22.4627	−	16.5044i	0.883783	−	0.649355i
$647$	10.8250	+	4.48386i	0.425575	+	0.176279i	0.585182	−	0.810902i	$-0.301023\pi$
$647$	10.8250	+	4.48386i	0.425575	+	0.176279i	−0.159608	+	0.987181i	$0.551023\pi$
$648$		0			0
$649$	2.42512	−	1.00452i	0.0951944	−	0.0394308i
$650$	−11.7095	−	7.08975i	−0.459285	−	0.278083i
$651$		0			0
$652$	0.848661	+	0.463421i	0.0332361	+	0.0181490i
$653$	−20.9476	+	31.3503i	−0.819744	+	1.22683i	0.151431	+	0.988468i	$0.451612\pi$
$653$	−20.9476	+	31.3503i	−0.819744	+	1.22683i	−0.971175	+	0.238366i	$0.923388\pi$
$654$		0			0
$655$	−6.07503	−	6.07503i	−0.237371	−	0.237371i
$656$	−26.4001	+	16.9652i	−1.03075	+	0.662378i
$657$		0			0
$658$	−0.271253	+	0.296607i	−0.0105746	+	0.0115629i
$659$	−29.0678	−	19.4225i	−1.13232	−	0.756594i	−0.159283	−	0.987233i	$-0.550918\pi$
$659$	−29.0678	−	19.4225i	−1.13232	−	0.756594i	−0.973039	+	0.230639i	$0.925918\pi$
$660$		0			0
$661$	43.2043	+	8.59387i	1.68045	+	0.334263i	0.940861	−	0.338793i	$-0.110019\pi$
$661$	43.2043	+	8.59387i	1.68045	+	0.334263i	0.739592	+	0.673056i	$0.235019\pi$
$662$	11.2102	+	45.6178i	0.435697	+	1.77299i
$663$		0			0
$664$	1.95644	−	1.72600i	0.0759247	−	0.0669818i
$665$	−5.04599	+	12.1821i	−0.195675	+	0.472402i
$666$		0			0
$667$	−19.7684	+	13.2088i	−0.765434	+	0.511447i
$668$	−8.25043	−	15.7731i	−0.319219	−	0.610278i
$669$		0			0
$670$	−19.5566	−	7.09622i	−0.755536	−	0.274151i
$671$			22.3892i			0.864326i
$672$		0			0
$673$		−	6.94905i		−	0.267866i	−0.990990	−	0.133933i	$-0.957239\pi$
$673$		−	6.94905i		−	0.267866i	0.990990	−	0.133933i	$-0.0427607\pi$
$674$	−3.18663	+	8.78207i	−0.122744	+	0.338273i
$675$		0			0
$676$	−4.63178	−	1.45038i	−0.178145	−	0.0557838i
$677$	27.1193	−	18.1206i	1.04228	−	0.696430i	0.0882375	−	0.996099i	$-0.471877\pi$
$677$	27.1193	−	18.1206i	1.04228	−	0.696430i	0.954043	+	0.299670i	$0.0968765\pi$
$678$		0			0
$679$	−5.89030	+	14.2204i	−0.226049	+	0.545731i
$680$	−12.2805	+	25.0888i	−0.470935	+	0.962111i
$681$		0			0
$682$	−25.4830	+	6.26224i	−0.975795	+	0.239794i
$683$	11.0672	+	2.20141i	0.423476	+	0.0842347i	0.402228	−	0.915540i	$-0.368236\pi$
$683$	11.0672	+	2.20141i	0.423476	+	0.0842347i	0.0212483	+	0.999774i	$0.493236\pi$
$684$		0			0
$685$	8.60439	+	5.74927i	0.328757	+	0.219668i
$686$	−19.6079	−	17.9318i	−0.748632	−	0.684640i
$687$		0			0
$688$	0.627535	−	35.0926i	0.0239245	−	1.33789i
$689$	−12.0547	−	12.0547i	−0.459246	−	0.459246i
$690$		0			0
$691$	−7.02304	+	10.5107i	−0.267169	+	0.399846i	−0.940661	−	0.339348i	$-0.889794\pi$
$691$	−7.02304	+	10.5107i	−0.267169	+	0.399846i	0.673492	+	0.739194i	$0.264794\pi$
$692$	−24.7924	+	7.27930i	−0.942466	+	0.276717i
$693$		0			0
$694$	−10.2237	+	16.8856i	−0.388086	+	0.640968i
$695$	2.64414	−	1.09524i	0.100298	−	0.0415448i
$696$		0			0
$697$	44.9528	+	18.6200i	1.70271	+	0.705284i
$698$	−13.8630	−	18.8677i	−0.524720	−	0.714154i
$699$		0			0
$700$	1.14446	+	12.7913i	0.0432566	+	0.483464i
$701$	31.1018	−	6.18654i	1.17470	−	0.233662i	0.431111	−	0.902299i	$-0.358122\pi$
$701$	31.1018	−	6.18654i	1.17470	−	0.233662i	0.743589	+	0.668637i	$0.233122\pi$
$702$		0			0
$703$	−20.7167			−0.781347
$704$	−11.6120	+	13.3998i	−0.437645	+	0.505023i
$705$		0			0
$706$	17.6350	+	37.7214i	0.663702	+	1.41966i
$707$	−1.32117	+	0.262797i	−0.0496877	+	0.00988349i
$708$		0			0
$709$	−9.97024	−	14.9215i	−0.374440	−	0.560389i	0.595616	−	0.803269i	$-0.296908\pi$
$709$	−9.97024	−	14.9215i	−0.374440	−	0.560389i	−0.970056	+	0.242880i	$0.921908\pi$
$710$	−14.3580	−	19.5414i	−0.538845	−	0.733377i
$711$		0			0
$712$	−11.9471	−	9.11140i	−0.447736	−	0.341464i
$713$	−42.8773	+	17.7604i	−1.60577	+	0.665131i
$714$		0			0
$715$	2.70435	−	13.5957i	0.101137	−	0.508450i
$716$	9.02014	+	30.7215i	0.337099	+	1.14812i
$717$		0			0
$718$	1.12342	+	25.1624i	0.0419258	+	0.939052i
$719$	30.0253	+	30.0253i	1.11975	+	1.11975i	0.991777	+	0.127978i	$0.0408485\pi$
$719$	30.0253	+	30.0253i	1.11975	+	1.11975i	0.127978	+	0.991777i	$0.459151\pi$
$720$		0			0
$721$	−16.0795	+	16.0795i	−0.598833	+	0.598833i
$722$	9.28838	+	8.49443i	0.345678	+	0.316130i
$723$		0			0
$724$	1.74736	+	2.16840i	0.0649400	+	0.0805881i
$725$	10.3661	+	2.06194i	0.384986	+	0.0765784i
$726$		0			0
$727$	14.5339	+	35.0878i	0.539031	+	1.30134i	0.925400	+	0.378992i	$0.123729\pi$
$727$	14.5339	+	35.0878i	0.539031	+	1.30134i	−0.386369	+	0.922344i	$0.626271\pi$
$728$	9.38533	+	27.3824i	0.347843	+	1.01486i
$729$		0			0
$730$	−26.0894	−	3.98926i	−0.965611	−	0.147649i
$731$	−45.2483	+	30.2340i	−1.67357	+	1.11824i
$732$		0			0
$733$	−7.98081	−	40.1222i	−0.294778	−	1.48195i	−0.789960	−	0.613159i	$-0.789899\pi$
$733$	−7.98081	−	40.1222i	−0.294778	−	1.48195i	0.495182	−	0.868789i	$-0.335101\pi$
$734$	14.8305	−	40.8716i	0.547404	−	1.50860i
$735$		0			0
$736$	−16.7190	+	26.5307i	−0.616269	+	0.977935i
$737$			20.4758i			0.754235i
$738$		0			0
$739$	2.49769	+	12.5568i	0.0918791	+	0.461908i	0.999145	+	0.0413495i	$0.0131657\pi$
$739$	2.49769	+	12.5568i	0.0918791	+	0.461908i	−0.907266	+	0.420558i	$0.861834\pi$
$740$	18.3959	−	9.62239i	0.676248	−	0.353726i
$741$		0			0
$742$	−2.41750	+	15.8102i	−0.0887492	+	0.580411i
$743$	−0.0423479	+	0.102237i	−0.00155359	+	0.00375071i	−0.924654	−	0.380807i	$-0.875646\pi$
$743$	−0.0423479	+	0.102237i	−0.00155359	+	0.00375071i	0.923101	+	0.384558i	$0.125646\pi$
$744$		0			0
$745$	−2.04791	−	4.94408i	−0.0750294	−	0.181137i
$746$	−5.16250	−	21.0078i	−0.189012	−	0.769151i
$747$		0			0
$748$	27.3345	+	2.93919i	0.999450	+	0.107467i
$749$	−41.4443	−	27.6922i	−1.51434	−	1.01185i
$750$		0			0
$751$	1.45742	−	1.45742i	0.0531820	−	0.0531820i	−0.680016	−	0.733198i	$-0.738027\pi$
$751$	1.45742	−	1.45742i	0.0531820	−	0.0531820i	0.733198	+	0.680016i	$0.238027\pi$
$752$	0.358386	+	0.248848i	0.0130690	+	0.00907456i
$753$		0			0
$754$	23.7987	−	1.06254i	0.866699	−	0.0386954i
$755$	−3.05942	+	4.57875i	−0.111344	+	0.166638i
$756$		0			0
$757$	6.72211	−	33.7943i	0.244319	−	1.22828i	−0.642546	−	0.766247i	$-0.722122\pi$
$757$	6.72211	−	33.7943i	0.244319	−	1.22828i	0.886865	−	0.462028i	$-0.152878\pi$
$758$	20.1147	+	12.1789i	0.730601	+	0.442356i
$759$		0			0
$760$	13.8366	+	3.66375i	0.501905	+	0.132898i
$761$	−20.6469	−	8.55221i	−0.748448	−	0.310018i	−0.0243401	−	0.999704i	$-0.507748\pi$
$761$	−20.6469	−	8.55221i	−0.748448	−	0.310018i	−0.724108	+	0.689686i	$0.757748\pi$
$762$		0			0
$763$	−18.4763	−	27.6518i	−0.668888	−	1.00106i
$764$	4.57327	−	5.47204i	0.165455	−	0.197972i
$765$		0			0
$766$	−13.4047	+	6.26676i	−0.484330	+	0.226427i
$767$	−4.65167			−0.167962
$768$		0			0
$769$	−23.8846			−0.861299			−0.430650	−	0.902519i	$-0.641716\pi$
$769$	−23.8846			−0.861299			−0.430650	+	0.902519i	$0.641716\pi$
$770$	−11.7812	+	5.50779i	−0.424565	+	0.198487i
$771$		0			0
$772$	−4.96030	+	5.93514i	−0.178525	+	0.213610i
$773$	−11.9528	−	17.8887i	−0.429914	−	0.643412i	0.551755	−	0.834006i	$-0.313958\pi$
$773$	−11.9528	−	17.8887i	−0.429914	−	0.643412i	−0.981669	+	0.190595i	$0.938958\pi$
$774$		0			0
$775$	19.0609	+	7.89528i	0.684687	+	0.283607i
$776$	16.1517	+	4.27678i	0.579814	+	0.153527i
$777$		0			0
$778$	12.2988	+	7.44655i	0.440933	+	0.266972i
$779$	4.86408	−	24.4534i	0.174274	−	0.876133i
$780$		0			0
$781$	−13.2594	+	19.8441i	−0.474459	+	0.710077i
$782$	48.5741	−	2.16868i	1.73700	−	0.0775519i
$783$		0			0
$784$	−0.480947	+	0.692650i	−0.0171767	+	0.0247375i
$785$	−3.49421	+	3.49421i	−0.124714	+	0.124714i
$786$		0			0
$787$	−16.2057	−	10.8283i	−0.577672	−	0.385988i	0.232136	−	0.972683i	$-0.425429\pi$
$787$	−16.2057	−	10.8283i	−0.577672	−	0.385988i	−0.809808	+	0.586695i	$0.800429\pi$
$788$	35.9092	+	3.86119i	1.27921	+	0.137549i
$789$		0			0
$790$	−0.640622	−	2.60689i	−0.0227923	−	0.0927490i
$791$	16.3819	+	39.5495i	0.582474	+	1.40622i
$792$		0			0
$793$	15.1834	−	36.6560i	0.539179	−	1.30169i
$794$	0.560055	−	3.66271i	0.0198756	−	0.129985i
$795$		0			0
$796$	−24.8295	+	12.9876i	−0.880057	+	0.460333i
$797$	−0.0842043	−	0.423324i	−0.00298267	−	0.0149949i	0.979265	−	0.202582i	$-0.0649333\pi$
$797$	−0.0842043	−	0.423324i	−0.00298267	−	0.0149949i	−0.982248	+	0.187587i	$0.939933\pi$
$798$		0			0
$799$		−	0.676497i		−	0.0239328i
$800$	13.5951	−	3.08422i	0.480660	−	0.109044i
$801$		0			0
$802$	−10.1299	+	27.9170i	−0.357697	+	0.985783i
$803$	5.06765	+	25.4768i	0.178834	+	0.899057i
$804$		0			0
$805$	−19.1244	+	12.7785i	−0.674048	+	0.450384i
$806$	45.9680	+	7.02885i	1.61915	+	0.247581i
$807$		0			0
$808$	0.474109	+	1.38325i	0.0166791	+	0.0486626i
$809$	8.87822	+	21.4339i	0.312142	+	0.753576i	0.999625	+	0.0273765i	$0.00871530\pi$
$809$	8.87822	+	21.4339i	0.312142	+	0.753576i	−0.687484	+	0.726200i	$0.741285\pi$
$810$		0			0
$811$	−0.570557	−	0.113491i	−0.0200350	−	0.00398520i	0.185063	−	0.982727i	$-0.440751\pi$
$811$	−0.570557	−	0.113491i	−0.0200350	−	0.00398520i	−0.205098	+	0.978742i	$0.565751\pi$
$812$	−14.0235	−	17.4027i	−0.492129	−	0.610713i
$813$		0			0
$814$	−15.0782	−	13.7894i	−0.528492	−	0.483318i
$815$	0.544377	−	0.544377i	0.0190687	−	0.0190687i
$816$		0			0
$817$	19.7181	+	19.7181i	0.689849	+	0.689849i
$818$	−1.47572	−	33.0531i	−0.0515973	−	1.15567i
$819$		0			0
$820$	7.03878	+	23.9732i	0.245805	+	0.837181i
$821$	−0.267849	+	1.34657i	−0.00934799	+	0.0469955i	−0.985178	−	0.171537i	$-0.945127\pi$
$821$	−0.267849	+	1.34657i	−0.00934799	+	0.0469955i	0.975830	+	0.218532i	$0.0701268\pi$
$822$		0			0
$823$	32.6695	−	13.5321i	1.13879	−	0.471701i	0.268028	−	0.963411i	$-0.413628\pi$
$823$	32.6695	−	13.5321i	1.13879	−	0.471701i	0.870759	+	0.491710i	$0.163628\pi$
$824$	19.6278	+	14.9691i	0.683767	+	0.521473i
$825$		0			0
$826$	2.58400	+	3.51687i	0.0899089	+	0.122368i
$827$	−16.7811	−	25.1146i	−0.583534	−	0.873321i	0.415813	−	0.909450i	$-0.363497\pi$
$827$	−16.7811	−	25.1146i	−0.583534	−	0.873321i	−0.999347	+	0.0361292i	$0.988497\pi$
$828$		0			0
$829$	43.8051	−	8.71338i	1.52142	−	0.302628i	0.637564	−	0.770397i	$-0.279942\pi$
$829$	43.8051	−	8.71338i	1.52142	−	0.302628i	0.883851	+	0.467769i	$0.154942\pi$
$830$	−0.879724	−	1.88174i	−0.0305357	−	0.0653160i
$831$		0			0
$832$	28.0986	−	14.0635i	0.974143	−	0.487566i
$833$	1.30746			0.0453008
$834$		0			0
$835$	−13.9002	+	2.76491i	−0.481035	+	0.0956838i
$836$	−1.25542	−	14.0314i	−0.0434196	−	0.485286i
$837$		0			0
$838$	−9.81534	−	13.3589i	−0.339065	−	0.461474i
$839$	22.5256	+	9.33043i	0.777672	+	0.322122i	0.735976	−	0.677008i	$-0.236724\pi$
$839$	22.5256	+	9.33043i	0.777672	+	0.322122i	0.0416962	+	0.999130i	$0.486724\pi$
$840$		0			0
$841$	9.79901	−	4.05888i	0.337897	−	0.139961i
$842$	−23.9996	+	39.6380i	−0.827080	+	1.36601i
$843$		0			0
$844$	36.2356	−	10.6391i	1.24728	−	0.366214i
$845$	−2.14690	+	3.21306i	−0.0738556	+	0.110533i
$846$		0			0
$847$	−11.2160	−	11.2160i	−0.385388	−	0.385388i
$848$	17.3589	+	0.310417i	0.596108	+	0.0106598i
$849$		0			0
$850$	−15.9505	−	14.5871i	−0.547098	−	0.500333i
$851$	−30.0472	−	20.0769i	−1.03000	−	0.688226i
$852$		0			0
$853$	−30.2500	−	6.01711i	−1.03574	−	0.206022i	−0.352193	−	0.935927i	$-0.614564\pi$
$853$	−30.2500	−	6.01711i	−1.03574	−	0.206022i	−0.683548	+	0.729905i	$0.739564\pi$
$854$	−36.1479	+	8.88305i	−1.23696	+	0.303972i
$855$		0			0
$856$	−23.7876	+	48.5977i	−0.813044	+	1.66103i
$857$	−9.31614	+	22.4912i	−0.318233	+	0.768283i	0.681115	+	0.732177i	$0.261496\pi$
$857$	−9.31614	+	22.4912i	−0.318233	+	0.768283i	−0.999348	+	0.0361064i	$0.988504\pi$
$858$		0			0
$859$	0.219064	−	0.146374i	0.00747437	−	0.00499421i	−0.551827	−	0.833958i	$-0.686069\pi$
$859$	0.219064	−	0.146374i	0.00747437	−	0.00499421i	0.559302	+	0.828964i	$0.311069\pi$
$860$	−26.6677	−	8.35063i	−0.909361	−	0.284754i
$861$		0			0
$862$	7.61726	−	20.9925i	0.259445	−	0.715008i
$863$		−	24.2153i		−	0.824299i	−0.911116	−	0.412150i	$-0.864778\pi$
$863$		−	24.2153i		−	0.824299i	0.911116	−	0.412150i	$-0.135222\pi$
$864$		0			0
$865$			20.5725i			0.699487i
$866$	−28.7856	−	10.4450i	−0.978176	−	0.354937i
$867$		0			0
$868$	−20.2211	−	38.6584i	−0.686348	−	1.31215i
$869$	−2.19680	+	1.46786i	−0.0745214	+	0.0497936i
$870$		0			0
$871$	13.8858	−	33.5233i	0.470502	−	1.13589i
$872$	−27.0714	+	23.8827i	−0.916752	+	0.808770i
$873$		0			0
$874$	−5.94575	−	24.1951i	−0.201118	−	0.818413i
$875$	30.3752	+	6.04200i	1.02687	+	0.204257i
$876$		0			0
$877$	17.9632	+	12.0027i	0.606576	+	0.405301i	0.820580	−	0.571532i	$-0.193651\pi$
$877$	17.9632	+	12.0027i	0.606576	+	0.405301i	−0.214004	+	0.976833i	$0.568651\pi$
$878$	−39.0579	+	42.7085i	−1.31814	+	1.44134i
$879$		0			0
$880$	7.63199	+	11.8764i	0.257274	+	0.400354i
$881$	15.8713	+	15.8713i	0.534718	+	0.534718i	0.921973	−	0.387255i	$-0.126577\pi$
$881$	15.8713	+	15.8713i	0.534718	+	0.534718i	−0.387255	+	0.921973i	$0.626577\pi$
$882$		0			0
$883$	16.2902	−	24.3799i	0.548207	−	0.820450i	−0.449123	−	0.893470i	$-0.648264\pi$
$883$	16.2902	−	24.3799i	0.548207	−	0.820450i	0.997330	+	0.0730197i	$0.0232636\pi$
$884$	−42.7593	−	23.3492i	−1.43815	−	0.785319i
$885$		0			0
$886$	41.0758	+	24.8701i	1.37997	+	0.835529i
$887$	34.2563	−	14.1894i	1.15021	−	0.476435i	0.275609	−	0.961270i	$-0.411120\pi$
$887$	34.2563	−	14.1894i	1.15021	−	0.476435i	0.874606	+	0.484835i	$0.161120\pi$
$888$		0			0
$889$	−5.40805	−	2.24009i	−0.181380	−	0.0751302i
$890$	−9.64024	+	7.08312i	−0.323142	+	0.237427i
$891$		0			0
$892$	−39.8557	−	33.3095i	−1.33447	−	1.11528i
$893$	−0.339988	+	0.0676279i	−0.0113773	+	0.00226308i
$894$		0			0
$895$	25.4925			0.852119
$896$	−26.2414	−	13.4315i	−0.876664	−	0.448714i
$897$		0			0
$898$	−2.72248	+	1.27278i	−0.0908503	+	0.0424731i
$899$	−35.2151	+	7.00472i	−1.17449	+	0.233621i
$900$		0			0
$901$	−14.9556	−	22.3826i	−0.498242	−	0.745672i
$902$	19.8168	−	14.5603i	0.659826	−	0.484803i
$903$		0			0
$904$	40.1744	−	23.3531i	1.33618	−	0.776713i
$905$	2.04845	−	0.848496i	0.0680928	−	0.0282050i
$906$		0			0
$907$	−0.117687	+	0.591654i	−0.00390775	+	0.0196456i	−0.982690	−	0.185258i	$-0.940688\pi$
$907$	−0.117687	+	0.591654i	−0.00390775	+	0.0196456i	0.978782	+	0.204903i	$0.0656880\pi$
$908$	1.92576	+	1.05158i	0.0639086	+	0.0348980i
$909$		0			0
$910$	23.0235	−	1.02793i	0.763223	−	0.0340755i
$911$	25.7854	+	25.7854i	0.854308	+	0.854308i	0.990660	−	0.136352i	$-0.0435379\pi$
$911$	25.7854	+	25.7854i	0.854308	+	0.854308i	−0.136352	+	0.990660i	$0.543538\pi$
$912$		0			0
$913$	−1.44563	+	1.44563i	−0.0478433	+	0.0478433i
$914$	33.2141	−	36.3185i	1.09862	−	1.20131i
$915$		0			0
$916$	−3.36360	+	31.2816i	−0.111136	+	1.03357i
$917$	−13.7881	−	2.74262i	−0.455322	−	0.0905693i
$918$		0			0
$919$	13.0040	+	31.3945i	0.428964	+	1.03561i	0.979617	+	0.200876i	$0.0643788\pi$
$919$	13.0040	+	31.3945i	0.428964	+	1.03561i	−0.550653	+	0.834734i	$0.685621\pi$
$920$	16.5177	+	18.7230i	0.544572	+	0.617280i
$921$		0			0
$922$	2.91449	−	19.0605i	0.0959837	−	0.627724i
$923$	35.1659	−	23.4971i	1.15750	−	0.773417i
$924$		0			0
$925$	3.13407	+	15.7560i	0.103047	+	0.518055i
$926$	−30.6216	−	11.1112i	−1.00629	−	0.365138i
$927$		0			0
$928$	−16.6904	+	17.6076i	−0.547888	+	0.577998i
$929$			9.78678i			0.321094i	0.987028	+	0.160547i	$0.0513258\pi$
$929$			9.78678i			0.321094i	−0.987028	+	0.160547i	$0.948674\pi$
$930$		0			0
$931$	−0.130704	−	0.657092i	−0.00428364	−	0.0215353i
$932$	36.9898	+	11.5829i	1.21164	+	0.379409i
$933$		0			0
$934$	−22.9417	−	3.50796i	−0.750675	−	0.114784i
$935$	8.37646	−	20.2226i	0.273940	−	0.661349i
$936$		0			0
$937$	9.02858	+	21.7969i	0.294951	+	0.712075i	0.999996	+	0.00291192i	$0.000926893\pi$
$937$	9.02858	+	21.7969i	0.294951	+	0.712075i	−0.705045	+	0.709163i	$0.749073\pi$
$938$	−33.0586	+	8.12388i	−1.07940	+	0.265254i
$939$		0			0
$940$	0.270490	−	0.217968i	0.00882240	−	0.00710932i
$941$	−6.14014	−	4.10271i	−0.200163	−	0.133745i	0.451450	−	0.892297i	$-0.350907\pi$
$941$	−6.14014	−	4.10271i	−0.200163	−	0.133745i	−0.651612	+	0.758552i	$0.725907\pi$
$942$		0			0
$943$	30.7529	−	30.7529i	1.00145	−	1.00145i
$944$	3.40914	−	3.28935i	0.110958	−	0.107059i
$945$		0			0
$946$	1.22672	+	27.4760i	0.0398841	+	0.893323i
$947$	−10.3655	+	15.5130i	−0.336832	+	0.504105i	−0.960762	−	0.277376i	$-0.910535\pi$
$947$	−10.3655	+	15.5130i	−0.336832	+	0.504105i	0.623929	+	0.781481i	$0.285535\pi$
$948$		0			0
$949$	8.98044	−	45.1477i	0.291517	−	1.46556i
$950$	−5.73652	+	9.47450i	−0.186117	+	0.307393i
$951$		0			0
$952$	6.09975	+	45.2984i	0.197694	+	1.46813i
$953$	1.50663	+	0.624068i	0.0488047	+	0.0202156i	0.406952	−	0.913449i	$-0.366592\pi$
$953$	1.50663	+	0.624068i	0.0488047	+	0.0202156i	−0.358148	+	0.933665i	$0.616592\pi$
$954$		0			0
$955$	−3.15451	−	4.72105i	−0.102077	−	0.152770i
$956$	1.96899	+	22.0068i	0.0636818	+	0.711749i
$957$		0			0
$958$	2.48288	+	5.31090i	0.0802182	+	0.171587i
$959$	16.9332			0.546802
$960$		0			0
$961$	−39.0879			−1.26090
$962$	15.3350	+	32.8016i	0.494419	+	1.05757i
$963$		0			0
$964$	−18.3956	+	1.64589i	−0.592482	+	0.0530107i
$965$	3.42147	+	5.12059i	0.110141	+	0.164838i
$966$		0			0
$967$	6.20220	+	2.56904i	0.199449	+	0.0826147i	0.480172	−	0.877174i	$-0.340574\pi$
$967$	6.20220	+	2.56904i	0.199449	+	0.0826147i	−0.280723	+	0.959789i	$0.590574\pi$
$968$	−10.4415	+	13.6911i	−0.335602	+	0.440049i
$969$		0			0
$970$	6.89000	−	11.3796i	0.221225	−	0.365377i
$971$	4.68288	−	23.5424i	0.150281	−	0.755512i	−0.829979	−	0.557795i	$-0.811647\pi$
$971$	4.68288	−	23.5424i	0.150281	−	0.755512i	0.980259	−	0.197716i	$-0.0633525\pi$
$972$		0			0
$973$	2.60180	−	3.89387i	0.0834100	−	0.124832i
$974$	0.0376326	+	0.842894i	0.00120583	+	0.0270081i
$975$		0			0
$976$	14.7930	+	37.6013i	0.473513	+	1.20359i
$977$	24.0769	−	24.0769i	0.770289	−	0.770289i	−0.207868	−	0.978157i	$-0.566652\pi$
$977$	24.0769	−	24.0769i	0.770289	−	0.770289i	0.978157	+	0.207868i	$0.0666524\pi$
$978$		0			0
$979$	9.78954	+	6.54116i	0.312875	+	0.209057i
$980$	0.421264	+	0.522773i	0.0134568	+	0.0166994i
$981$		0			0
$982$	−43.7567	+	10.7528i	−1.39633	+	0.343137i
$983$	−18.5278	−	44.7301i	−0.590946	−	1.42667i	−0.882590	−	0.470143i	$-0.844202\pi$
$983$	−18.5278	−	44.7301i	−0.590946	−	1.42667i	0.291644	−	0.956527i	$-0.405798\pi$
$984$		0			0
$985$	11.0041	−	26.5662i	0.350619	−	0.846470i
$986$	37.1844	+	5.68578i	1.18419	+	0.181072i
$987$		0			0
$988$	−7.46009	+	23.8238i	−0.237337	+	0.757935i
$989$	9.48967	+	47.7078i	0.301754	+	1.51702i
$990$		0			0
$991$			23.7163i			0.753372i	0.926341	+	0.376686i	$0.122936\pi$
$991$			23.7163i			0.753372i	−0.926341	+	0.376686i	$0.877064\pi$
$992$	−38.6596	+	27.3542i	−1.22744	+	0.868496i
$993$		0			0
$994$	−37.2995	−	13.5344i	−1.18307	−	0.429284i
$995$	4.35244	+	21.8812i	0.137982	+	0.693681i
$996$		0			0
$997$	−42.3286	+	28.2831i	−1.34056	+	0.895734i	−0.999026	−	0.0441354i	$-0.985947\pi$
$997$	−42.3286	+	28.2831i	−1.34056	+	0.895734i	−0.341535	+	0.939869i	$0.610947\pi$
$998$	−1.79042	+	11.7091i	−0.0566746	+	0.370646i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.a.181.1		56
3.2	odd	2		64.2.i.a.53.7	yes	56
12.11	even	2		256.2.i.a.49.5		56
24.5	odd	2		512.2.i.b.353.5		56
24.11	even	2		512.2.i.a.353.3		56
64.29	even	16	inner	576.2.bd.a.541.1		56
192.29	odd	16		64.2.i.a.29.7	✓	56
192.35	even	16		256.2.i.a.209.5		56
192.125	odd	16		512.2.i.b.161.5		56
192.131	even	16		512.2.i.a.161.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.7	✓	56	192.29	odd	16
64.2.i.a.53.7	yes	56	3.2	odd	2
256.2.i.a.49.5		56	12.11	even	2
256.2.i.a.209.5		56	192.35	even	16
512.2.i.a.161.3		56	192.131	even	16
512.2.i.a.353.3		56	24.11	even	2
512.2.i.b.161.5		56	192.125	odd	16
512.2.i.b.353.5		56	24.5	odd	2
576.2.bd.a.181.1		56	1.1	even	1	trivial
576.2.bd.a.541.1		56	64.29	even	16	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28112 + 0.598933i) q^{2} +(1.28256 - 1.53462i) q^{4} +(-0.884671 - 1.32400i) q^{5} +(-2.40727 - 0.997123i) q^{7} +(-0.723982 + 2.73420i) q^{8} +O(q^{10})\)	\(q+(-1.28112 + 0.598933i) q^{2} +(1.28256 - 1.53462i) q^{4} +(-0.884671 - 1.32400i) q^{5} +(-2.40727 - 0.997123i) q^{7} +(-0.723982 + 2.73420i) q^{8} +(1.92636 + 1.16635i) q^{10} +(0.432397 - 2.17381i) q^{11} +(-2.18211 + 3.26576i) q^{13} +(3.68122 - 0.164355i) q^{14} +(-0.710093 - 3.93647i) q^{16} +(-4.38547 + 4.38547i) q^{17} +(2.64242 + 1.76561i) q^{19} +(-3.16648 - 0.340480i) q^{20} +(0.748011 + 3.04389i) q^{22} +(2.12144 + 5.12160i) q^{23} +(0.943074 - 2.27678i) q^{25} +(0.839581 - 5.49078i) q^{26} +(-4.61766 + 2.41536i) q^{28} +(0.836699 + 4.20637i) q^{29} +8.37185i q^{31} +(3.26740 + 4.61780i) q^{32} +(2.99173 - 8.24494i) q^{34} +(0.809445 + 4.06936i) q^{35} +(-5.42017 + 3.62164i) q^{37} +(-4.44275 - 0.679329i) q^{38} +(4.26058 - 1.46031i) q^{40} +(-3.00227 - 7.24812i) q^{41} +(8.60595 + 1.71183i) q^{43} +(-2.78138 - 3.45159i) q^{44} +(-5.78532 - 5.29081i) q^{46} +(-0.0771294 + 0.0771294i) q^{47} +(-0.149067 - 0.149067i) q^{49} +(0.155446 + 3.48168i) q^{50} +(2.21300 + 7.53722i) q^{52} +(-0.846775 + 4.25703i) q^{53} +(-3.26066 + 1.35061i) q^{55} +(4.46915 - 5.86005i) q^{56} +(-3.59125 - 4.88776i) q^{58} +(0.657977 + 0.984732i) q^{59} +(-9.90754 + 1.97073i) q^{61} +(-5.01418 - 10.7254i) q^{62} +(-6.95170 - 3.95902i) q^{64} +6.25433 q^{65} +(-9.06082 + 1.80231i) q^{67} +(1.10540 + 12.3546i) q^{68} +(-3.47427 - 4.72855i) q^{70} +(-9.94840 - 4.12076i) q^{71} +(-10.8278 + 4.48502i) q^{73} +(4.77479 - 7.88609i) q^{74} +(6.09858 - 1.79060i) q^{76} +(-3.20845 + 4.80178i) q^{77} +(-0.842912 - 0.842912i) q^{79} +(-4.58370 + 4.42264i) q^{80} +(8.18742 + 7.48758i) q^{82} +(-0.766957 - 0.512464i) q^{83} +(9.68608 + 1.92668i) q^{85} +(-12.0506 + 2.96132i) q^{86} +(5.63057 + 2.75606i) q^{88} +(-2.03287 + 4.90777i) q^{89} +(8.50928 - 5.68572i) q^{91} +(10.5806 + 3.31316i) q^{92} +(0.0526169 - 0.145008i) q^{94} -5.06055i q^{95} -5.90730i q^{97} +(0.280255 + 0.101692i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8}+O(q^{10}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8	\( 56 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} - 32 q^{26} + 32 q^{28} + 8 q^{29} - 32 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} - 32 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} - 8 q^{46} + 8 q^{47} - 8 q^{49} + 32 q^{50} - 56 q^{52} + 8 q^{53} + 56 q^{55} + 64 q^{56} - 80 q^{58} - 56 q^{59} - 8 q^{61} + 40 q^{62} - 104 q^{64} + 16 q^{65} + 72 q^{67} + 56 q^{68} - 104 q^{70} - 56 q^{71} - 8 q^{73} + 64 q^{74} - 72 q^{76} + 8 q^{77} + 24 q^{79} - 32 q^{80} + 72 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} + 72 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} + 88 q^{94} - 128 q^{98}+O(q^{100}) \) 56 * q + 8 * q^2 - 8 * q^4 + 8 * q^5 - 8 * q^7 + 8 * q^8 - 8 * q^10 + 8 * q^11 - 8 * q^13 + 8 * q^14 - 8 * q^16 + 8 * q^17 - 8 * q^19 + 8 * q^20 + 8 * q^23 - 8 * q^25 - 32 * q^26 + 32 * q^28 + 8 * q^29 - 32 * q^32 + 32 * q^34 + 8 * q^35 - 8 * q^37 - 32 * q^38 + 32 * q^40 + 8 * q^41 - 8 * q^43 - 8 * q^46 + 8 * q^47 - 8 * q^49 + 32 * q^50 - 56 * q^52 + 8 * q^53 + 56 * q^55 + 64 * q^56 - 80 * q^58 - 56 * q^59 - 8 * q^61 + 40 * q^62 - 104 * q^64 + 16 * q^65 + 72 * q^67 + 56 * q^68 - 104 * q^70 - 56 * q^71 - 8 * q^73 + 64 * q^74 - 72 * q^76 + 8 * q^77 + 24 * q^79 - 32 * q^80 + 72 * q^82 + 8 * q^83 - 8 * q^85 - 96 * q^86 + 72 * q^88 + 8 * q^89 - 8 * q^91 - 144 * q^92 + 88 * q^94 - 128 * q^98

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