LMFDB - Embedded newform 675.2.r.a.46.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.18
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.293899 + 0.326408i) q^{2} +(0.188891 - 1.79718i) q^{4} +(-2.06853 + 0.849220i) q^{5} +(-0.888066 + 1.53818i) q^{7} +(1.35281 - 0.982874i) q^{8} +O(q^{10})$	\(q+(0.293899 + 0.326408i) q^{2} +(0.188891 - 1.79718i) q^{4} +(-2.06853 + 0.849220i) q^{5} +(-0.888066 + 1.53818i) q^{7} +(1.35281 - 0.982874i) q^{8} +(-0.885131 - 0.425600i) q^{10} +(2.88123 + 3.19993i) q^{11} +(4.29288 - 4.76773i) q^{13} +(-0.763074 + 0.162196i) q^{14} +(-2.81678 - 0.598725i) q^{16} +(-0.162997 + 0.118424i) q^{17} +(4.79916 - 3.48679i) q^{19} +(1.13548 + 3.87794i) q^{20} +(-0.197692 + 1.88091i) q^{22} +(2.67917 - 0.569475i) q^{23} +(3.55765 - 3.51328i) q^{25} +2.81790 q^{26} +(2.59663 + 1.88657i) q^{28} +(0.675896 - 0.300928i) q^{29} +(2.52989 + 1.12638i) q^{31} +(-2.30458 - 3.99166i) q^{32} +(-0.0865590 - 0.0183987i) q^{34} +(0.530743 - 3.93593i) q^{35} +(-1.36941 - 4.21461i) q^{37} +(2.54858 + 0.541718i) q^{38} +(-1.96365 + 3.18194i) q^{40} +(8.41459 - 9.34535i) q^{41} +(-3.91700 + 6.78444i) q^{43} +(6.29511 - 4.57366i) q^{44} +(0.973285 + 0.707133i) q^{46} +(-0.452987 + 0.201683i) q^{47} +(1.92268 + 3.33017i) q^{49} +(2.19235 + 0.128696i) q^{50} +(-7.75759 - 8.61567i) q^{52} +(-5.99398 - 4.35488i) q^{53} +(-8.67738 - 4.17236i) q^{55} +(0.310448 + 2.95372i) q^{56} +(0.296870 + 0.132175i) q^{58} +(-6.51328 + 7.23373i) q^{59} +(6.51135 + 7.23158i) q^{61} +(0.375873 + 1.15682i) q^{62} +(-1.15416 + 3.55215i) q^{64} +(-4.83111 + 13.5078i) q^{65} +(0.130253 + 0.0579926i) q^{67} +(0.182041 + 0.315304i) q^{68} +(1.44070 - 0.983526i) q^{70} +(-1.95406 - 1.41971i) q^{71} +(-0.860848 + 2.64942i) q^{73} +(0.973212 - 1.68565i) q^{74} +(-5.35988 - 9.28359i) q^{76} +(-7.48079 + 1.59009i) q^{77} +(11.7563 - 5.23422i) q^{79} +(6.33505 - 1.15358i) q^{80} +5.52343 q^{82} +(0.359051 + 3.41614i) q^{83} +(0.236596 - 0.383384i) q^{85} +(-3.36569 + 0.715400i) q^{86} +(7.04289 + 1.49701i) q^{88} +(-3.29985 + 10.1559i) q^{89} +(3.52124 + 10.8373i) q^{91} +(-0.517378 - 4.92252i) q^{92} +(-0.198963 - 0.0885841i) q^{94} +(-6.96616 + 11.2881i) q^{95} +(-14.4851 + 6.44917i) q^{97} +(-0.521922 + 1.60631i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.293899	+	0.326408i	0.207818	+	0.230805i	0.838039	−	0.545611i	$-0.183702\pi$
$2$	0.293899	+	0.326408i	0.207818	+	0.230805i	−0.630221	+	0.776416i	$0.717036\pi$
$3$		0			0
$3$		0			0
$4$	0.188891	−	1.79718i	0.0944457	−	0.898591i
$5$	−2.06853	+	0.849220i	−0.925076	+	0.379783i
$5$	−2.06853	+	0.849220i	−0.925076	+	0.379783i
$6$		0			0
$7$	−0.888066	+	1.53818i	−0.335657	+	0.581376i	−0.983611	−	0.180304i	$-0.942292\pi$
$7$	−0.888066	+	1.53818i	−0.335657	+	0.581376i	0.647953	+	0.761680i	$0.275625\pi$
$8$	1.35281	−	0.982874i	0.478290	−	0.347498i
$9$		0			0
$10$	−0.885131	−	0.425600i	−0.279903	−	0.134587i
$11$	2.88123	+	3.19993i	0.868725	+	0.964817i	0.999647	−	0.0265760i	$-0.00846040\pi$
$11$	2.88123	+	3.19993i	0.868725	+	0.964817i	−0.130922	+	0.991393i	$0.541794\pi$
$12$		0			0
$13$	4.29288	−	4.76773i	1.19063	−	1.32233i	0.256014	−	0.966673i	$-0.417591\pi$
$13$	4.29288	−	4.76773i	1.19063	−	1.32233i	0.934617	−	0.355657i	$-0.115743\pi$
$14$	−0.763074	+	0.162196i	−0.203940	+	0.0433488i
$15$		0			0
$16$	−2.81678	−	0.598725i	−0.704195	−	0.149681i
$17$	−0.162997	+	0.118424i	−0.0395325	+	0.0287220i	−0.607376	−	0.794414i	$-0.707778\pi$
$17$	−0.162997	+	0.118424i	−0.0395325	+	0.0287220i	0.567844	+	0.823137i	$0.307778\pi$
$18$		0			0
$19$	4.79916	−	3.48679i	1.10100	−	0.799925i	0.119779	−	0.992801i	$-0.461781\pi$
$19$	4.79916	−	3.48679i	1.10100	−	0.799925i	0.981223	+	0.192875i	$0.0617813\pi$
$20$	1.13548	+	3.87794i	0.253900	+	0.867134i
$21$		0			0
$22$	−0.197692	+	1.88091i	−0.0421481	+	0.401012i
$23$	2.67917	−	0.569475i	0.558645	−	0.118744i	0.0800683	−	0.996789i	$-0.474486\pi$
$23$	2.67917	−	0.569475i	0.558645	−	0.118744i	0.478577	+	0.878046i	$0.341153\pi$
$24$		0			0
$25$	3.55765	−	3.51328i	0.711530	−	0.702656i
$26$	2.81790			0.552635
$27$		0			0
$28$	2.59663	+	1.88657i	0.490718	+	0.356527i
$29$	0.675896	−	0.300928i	0.125511	−	0.0558809i	−0.343020	−	0.939328i	$-0.611450\pi$
$29$	0.675896	−	0.300928i	0.125511	−	0.0558809i	0.468531	+	0.883447i	$0.344783\pi$
$30$		0			0
$31$	2.52989	+	1.12638i	0.454382	+	0.202304i	0.621149	−	0.783693i	$-0.286666\pi$
$31$	2.52989	+	1.12638i	0.454382	+	0.202304i	−0.166767	+	0.985996i	$0.553333\pi$
$32$	−2.30458	−	3.99166i	−0.407397	−	0.705632i
$33$		0			0
$34$	−0.0865590	−	0.0183987i	−0.0148448	−	0.00315535i
$35$	0.530743	−	3.93593i	0.0897120	−	0.665294i
$36$		0			0
$37$	−1.36941	−	4.21461i	−0.225129	−	0.692877i	−0.998278	−	0.0586526i	$-0.981320\pi$
$37$	−1.36941	−	4.21461i	−0.225129	−	0.692877i	0.773149	−	0.634224i	$-0.218680\pi$
$38$	2.54858	+	0.541718i	0.413435	+	0.0878783i
$39$		0			0
$40$	−1.96365	+	3.18194i	−0.310481	+	0.503109i
$41$	8.41459	−	9.34535i	1.31414	−	1.45950i	0.516607	−	0.856223i	$-0.327195\pi$
$41$	8.41459	−	9.34535i	1.31414	−	1.45950i	0.797532	−	0.603276i	$-0.206138\pi$
$42$		0			0
$43$	−3.91700	+	6.78444i	−0.597336	+	1.03462i	0.395876	+	0.918304i	$0.370441\pi$
$43$	−3.91700	+	6.78444i	−0.597336	+	1.03462i	−0.993213	+	0.116313i	$0.962892\pi$
$44$	6.29511	−	4.57366i	0.949023	−	0.689506i
$45$		0			0
$46$	0.973285	+	0.707133i	0.143503	+	0.104261i
$47$	−0.452987	+	0.201683i	−0.0660749	+	0.0294185i	−0.439508	−	0.898239i	$-0.644847\pi$
$47$	−0.452987	+	0.201683i	−0.0660749	+	0.0294185i	0.373433	+	0.927657i	$0.378181\pi$
$48$		0			0
$49$	1.92268	+	3.33017i	0.274668	+	0.475739i
$50$	2.19235	+	0.128696i	0.310045	+	0.0182003i
$51$		0			0
$52$	−7.75759	−	8.61567i	−1.07578	−	1.19478i
$53$	−5.99398	−	4.35488i	−0.823336	−	0.598189i	0.0943302	−	0.995541i	$-0.469929\pi$
$53$	−5.99398	−	4.35488i	−0.823336	−	0.598189i	−0.917666	+	0.397352i	$0.869929\pi$
$54$		0			0
$55$	−8.67738	−	4.17236i	−1.17006	−	0.562602i
$56$	0.310448	+	2.95372i	0.0414854	+	0.394707i
$57$		0			0
$58$	0.296870	+	0.132175i	0.0389810	+	0.0173554i
$59$	−6.51328	+	7.23373i	−0.847957	+	0.941751i	−0.998905	−	0.0467905i	$-0.985101\pi$
$59$	−6.51328	+	7.23373i	−0.847957	+	0.941751i	0.150948	+	0.988542i	$0.451767\pi$
$60$		0			0
$61$	6.51135	+	7.23158i	0.833692	+	0.925909i	0.998170	−	0.0604716i	$-0.0192605\pi$
$61$	6.51135	+	7.23158i	0.833692	+	0.925909i	−0.164477	+	0.986381i	$0.552594\pi$
$62$	0.375873	+	1.15682i	0.0477359	+	0.146916i
$63$		0			0
$64$	−1.15416	+	3.55215i	−0.144270	+	0.444019i
$65$	−4.83111	+	13.5078i	−0.599226	+	1.67544i
$66$		0			0
$67$	0.130253	+	0.0579926i	0.0159130	+	0.00708492i	0.414678	−	0.909968i	$-0.363894\pi$
$67$	0.130253	+	0.0579926i	0.0159130	+	0.00708492i	−0.398765	+	0.917053i	$0.630561\pi$
$68$	0.182041	+	0.315304i	0.0220757	+	0.0382362i
$69$		0			0
$70$	1.44070	−	0.983526i	0.172197	−	0.117554i
$71$	−1.95406	−	1.41971i	−0.231905	−	0.168489i	0.465764	−	0.884909i	$-0.345779\pi$
$71$	−1.95406	−	1.41971i	−0.231905	−	0.168489i	−0.697669	+	0.716420i	$0.745779\pi$
$72$		0			0
$73$	−0.860848	+	2.64942i	−0.100755	+	0.310091i	−0.988711	−	0.149837i	$-0.952125\pi$
$73$	−0.860848	+	2.64942i	−0.100755	+	0.310091i	0.887956	+	0.459928i	$0.152125\pi$
$74$	0.973212	−	1.68565i	0.113134	−	0.195953i
$75$		0			0
$76$	−5.35988	−	9.28359i	−0.614821	−	1.06490i
$77$	−7.48079	+	1.59009i	−0.852515	+	0.181208i
$78$		0			0
$79$	11.7563	−	5.23422i	1.32268	−	0.588896i	0.380744	−	0.924681i	$-0.375668\pi$
$79$	11.7563	−	5.23422i	1.32268	−	0.588896i	0.941939	+	0.335784i	$0.109001\pi$
$80$	6.33505	−	1.15358i	0.708280	−	0.128975i
$81$		0			0
$82$	5.52343			0.609961
$83$	0.359051	+	3.41614i	0.0394109	+	0.374970i	0.996395	+	0.0848308i	$0.0270350\pi$
$83$	0.359051	+	3.41614i	0.0394109	+	0.374970i	−0.956984	+	0.290139i	$0.906298\pi$
$84$		0			0
$85$	0.236596	−	0.383384i	0.0256624	−	0.0415838i
$86$	−3.36569	+	0.715400i	−0.362932	+	0.0771436i
$87$		0			0
$88$	7.04289	+	1.49701i	0.750775	+	0.159582i
$89$	−3.29985	+	10.1559i	−0.349784	+	1.07652i	0.609189	+	0.793025i	$0.291495\pi$
$89$	−3.29985	+	10.1559i	−0.349784	+	1.07652i	−0.958973	+	0.283499i	$0.908505\pi$
$90$		0			0
$91$	3.52124	+	10.8373i	0.369126	+	1.13605i
$92$	−0.517378	−	4.92252i	−0.0539404	−	0.513208i
$93$		0			0
$94$	−0.198963	−	0.0885841i	−0.0205215	−	0.00913675i
$95$	−6.96616	+	11.2881i	−0.714713	+	1.15813i
$96$		0			0
$97$	−14.4851	+	6.44917i	−1.47074	+	0.654814i	−0.976697	−	0.214625i	$-0.931147\pi$
$97$	−14.4851	+	6.44917i	−1.47074	+	0.654814i	−0.494040	+	0.869439i	$0.664480\pi$
$98$	−0.521922	+	1.60631i	−0.0527221	+	0.162262i
$99$		0			0
$100$	−5.64199	−	7.05737i	−0.564199	−	0.705737i
$101$	5.03293	−	8.71729i	0.500795	−	0.867403i	−0.499204	−	0.866484i	$-0.666374\pi$
$101$	5.03293	−	8.71729i	0.500795	−	0.867403i	1.00000		0.000918779i	$-0.000292456\pi$
$102$		0			0
$103$	−0.521550	+	4.96221i	−0.0513898	+	0.488942i	0.938311	+	0.345792i	$0.112390\pi$
$103$	−0.521550	+	4.96221i	−0.0513898	+	0.488942i	−0.989701	+	0.143150i	$0.954277\pi$
$104$	1.12138	−	10.6692i	0.109960	−	1.04620i
$105$		0			0
$106$	−0.340157	−	3.23637i	−0.0330389	−	0.314344i
$107$	7.10081			0.686461			0.343230	−	0.939251i	$-0.388479\pi$
$107$	7.10081			0.686461			0.343230	+	0.939251i	$0.388479\pi$
$108$		0			0
$109$	0.177831	+	0.547308i	0.0170331	+	0.0524226i	0.959212	−	0.282688i	$-0.0912262\pi$
$109$	0.177831	+	0.547308i	0.0170331	+	0.0524226i	−0.942179	+	0.335111i	$0.891226\pi$
$110$	−1.18838	−	4.05861i	−0.113307	−	0.386974i
$111$		0			0
$112$	3.42243	−	3.80099i	0.323389	−	0.359160i
$113$	0.183560	−	0.203864i	0.0172679	−	0.0191779i	−0.734449	−	0.678664i	$-0.762559\pi$
$113$	0.183560	−	0.203864i	0.0172679	−	0.0191779i	0.751717	+	0.659486i	$0.229226\pi$
$114$		0			0
$115$	−5.05833	+	3.45318i	−0.471692	+	0.322011i
$116$	−0.413152	−	1.27155i	−0.0383602	−	0.118060i
$117$		0			0
$118$	−4.27539			−0.393581
$119$	−0.0374051	−	0.355886i	−0.00342892	−	0.0326240i
$120$		0			0
$121$	−0.788259	+	7.49978i	−0.0716599	+	0.681799i
$122$	−0.446767	+	4.25071i	−0.0404484	+	0.384841i
$123$		0			0
$124$	2.50218	−	4.33391i	0.224703	−	0.389196i
$125$	−4.37556	+	10.2886i	−0.391362	+	0.920237i
$126$		0			0
$127$	0.765000	−	2.35443i	0.0678828	−	0.208922i	−0.911361	−	0.411608i	$-0.864967\pi$
$127$	0.765000	−	2.35443i	0.0678828	−	0.208922i	0.979244	+	0.202687i	$0.0649672\pi$
$128$	−9.92003	+	4.41668i	−0.876815	+	0.390383i
$129$		0			0
$130$	−5.82891	+	2.39301i	−0.511229	+	0.209881i
$131$	−1.05560	−	0.469984i	−0.0922283	−	0.0410627i	0.360104	−	0.932912i	$-0.382741\pi$
$131$	−1.05560	−	0.469984i	−0.0922283	−	0.0410627i	−0.452332	+	0.891849i	$0.649408\pi$
$132$		0			0
$133$	1.10133	+	10.4785i	0.0954974	+	0.908597i
$134$	0.0193521	+	0.0595597i	0.00167177	+	0.00514517i
$135$		0			0
$136$	−0.104108	+	0.320410i	−0.00892716	+	0.0274750i
$137$	−8.25584	−	1.75483i	−0.705344	−	0.149925i	−0.158744	−	0.987320i	$-0.550745\pi$
$137$	−8.25584	−	1.75483i	−0.705344	−	0.149925i	−0.546599	+	0.837394i	$0.684078\pi$
$138$		0			0
$139$	−3.40960	+	0.724732i	−0.289198	+	0.0614710i	−0.350226	−	0.936665i	$-0.613895\pi$
$139$	−3.40960	+	0.724732i	−0.289198	+	0.0614710i	0.0610282	+	0.998136i	$0.480562\pi$
$140$	−6.97333	−	1.69731i	−0.589354	−	0.143449i
$141$		0			0
$142$	−0.110893	−	1.05507i	−0.00930590	−	0.0885398i
$143$	27.6252			2.31014
$144$		0			0
$145$	−1.14256	+	1.19646i	−0.0948842	+	0.0993609i
$146$	−1.11779	+	0.497673i	−0.0925092	+	0.0411878i
$147$		0			0
$148$	−7.83308	+	1.66497i	−0.643876	+	0.136860i
$149$	−6.94885	−	12.0358i	−0.569272	−	0.986008i	−0.996638	−	0.0819294i	$-0.973892\pi$
$149$	−6.94885	−	12.0358i	−0.569272	−	0.986008i	0.427366	−	0.904079i	$-0.359442\pi$
$150$		0			0
$151$	2.35078	−	4.07166i	0.191303	−	0.331347i	−0.754379	−	0.656439i	$-0.772062\pi$
$151$	2.35078	−	4.07166i	0.191303	−	0.331347i	0.945682	+	0.325092i	$0.105395\pi$
$152$	3.06527	−	9.43393i	0.248626	−	0.765193i
$153$		0			0
$154$	−2.71761	−	1.97446i	−0.218991	−	0.159107i
$155$	−6.18970	−	0.181518i	−0.497169	−	0.0145799i
$156$		0			0
$157$	−4.75661	−	8.23869i	−0.379619	−	0.657519i	0.611388	−	0.791331i	$-0.290611\pi$
$157$	−4.75661	−	8.23869i	−0.379619	−	0.657519i	−0.991007	+	0.133812i	$0.957278\pi$
$158$	5.16364	+	2.29900i	0.410797	+	0.182899i
$159$		0			0
$160$	8.15690	+	6.29977i	0.644860	+	0.498041i
$161$	−1.50333	+	4.62676i	−0.118479	+	0.364640i
$162$		0			0
$163$	2.56478	+	7.89358i	0.200889	+	0.618273i	0.999857	+	0.0168995i	$0.00537954\pi$
$163$	2.56478	+	7.89358i	0.200889	+	0.618273i	−0.798968	+	0.601373i	$0.794620\pi$
$164$	−15.2059	−	16.8878i	−1.18738	−	1.31872i
$165$		0			0
$166$	−1.00953	+	1.12120i	−0.0783547	+	0.0870217i
$167$	−13.0313	−	5.80192i	−1.00840	−	0.448966i	−0.165019	−	0.986290i	$-0.552769\pi$
$167$	−13.0313	−	5.80192i	−1.00840	−	0.448966i	−0.843376	+	0.537324i	$0.819435\pi$
$168$		0			0
$169$	−2.94353	−	28.0058i	−0.226425	−	2.15429i
$170$	0.194675	−	0.0354494i	0.0149309	−	0.00271885i
$171$		0			0
$172$	11.4530	+	8.32108i	0.873282	+	0.634476i
$173$	14.4518	+	16.0504i	1.09875	+	1.22029i	0.973627	+	0.228146i	$0.0732664\pi$
$173$	14.4518	+	16.0504i	1.09875	+	1.22029i	0.125125	+	0.992141i	$0.460067\pi$
$174$		0			0
$175$	2.24461	+	8.59232i	0.169677	+	0.649518i
$176$	−6.19992	−	10.7386i	−0.467336	−	0.809450i
$177$		0			0
$178$	−4.28479	+	1.90771i	−0.321159	+	0.142989i
$179$	−15.0286	−	10.9189i	−1.12329	−	0.816116i	−0.138583	−	0.990351i	$-0.544255\pi$
$179$	−15.0286	−	10.9189i	−1.12329	−	0.816116i	−0.984704	+	0.174235i	$0.944255\pi$
$180$		0			0
$181$	1.04274	−	0.757596i	0.0775063	−	0.0563116i	−0.548357	−	0.836244i	$-0.684747\pi$
$181$	1.04274	−	0.757596i	0.0775063	−	0.0563116i	0.625864	+	0.779932i	$0.284747\pi$
$182$	−2.50248	+	4.33442i	−0.185496	+	0.321288i
$183$		0			0
$184$	3.06468	−	3.40367i	0.225931	−	0.250922i
$185$	6.41179	+	7.55512i	0.471405	+	0.555463i
$186$		0			0
$187$	−0.848581	−	0.180371i	−0.0620544	−	0.0131901i
$188$	0.276895	+	0.852196i	0.0201947	+	0.0621528i
$189$		0			0
$190$	−5.73186	+	1.04375i	−0.415833	+	0.0757214i
$191$	−1.51610	−	0.322257i	−0.109701	−	0.0233177i	0.152734	−	0.988267i	$-0.451192\pi$
$191$	−1.51610	−	0.322257i	−0.109701	−	0.0233177i	−0.262435	+	0.964950i	$0.584526\pi$
$192$		0			0
$193$	−5.73764	−	9.93788i	−0.413004	−	0.715344i	0.582212	−	0.813037i	$-0.302187\pi$
$193$	−5.73764	−	9.93788i	−0.413004	−	0.715344i	−0.995217	+	0.0976925i	$0.968854\pi$
$194$	−6.36220	−	2.83264i	−0.456780	−	0.203371i
$195$		0			0
$196$	6.34811	−	2.82636i	0.453436	−	0.201883i
$197$	−18.5783	−	13.4979i	−1.32365	−	0.961687i	−0.999879	−	0.0155518i	$-0.995050\pi$
$197$	−18.5783	−	13.4979i	−1.32365	−	0.961687i	−0.323770	−	0.946136i	$-0.604950\pi$
$198$		0			0
$199$	−4.17299			−0.295816			−0.147908	−	0.989001i	$-0.547254\pi$
$199$	−4.17299			−0.295816			−0.147908	+	0.989001i	$0.547254\pi$
$200$	1.35971	−	8.24952i	0.0961462	−	0.583329i
$201$		0			0
$202$	4.32456	−	0.919215i	0.304275	−	0.0646757i
$203$	−0.137360	+	1.30689i	−0.00964076	+	0.0917257i
$204$		0			0
$205$	−9.46959	+	26.4770i	−0.661385	+	1.84923i
$206$	−1.77299	+	1.28815i	−0.123530	+	0.0897497i
$207$		0			0
$208$	−14.9466	+	10.8594i	−1.03636	+	0.752962i
$209$	24.9850	+	5.31073i	1.72825	+	0.367351i
$210$		0			0
$211$	−2.77190	+	0.589186i	−0.190826	+	0.0405612i	−0.302333	−	0.953202i	$-0.597765\pi$
$211$	−2.77190	+	0.589186i	−0.190826	+	0.0405612i	0.111507	+	0.993764i	$0.464432\pi$
$212$	−8.95872	+	9.94967i	−0.615287	+	0.683346i
$213$		0			0
$214$	2.08692	+	2.31776i	0.142659	+	0.158439i
$215$	2.34095	−	17.3602i	0.159652	−	1.18396i
$216$		0			0
$217$	−3.97928	+	2.89112i	−0.270131	+	0.196262i
$218$	−0.126381	+	0.218899i	−0.00855962	+	0.0148257i
$219$		0			0
$220$	−9.13758	+	14.8067i	−0.616056	+	0.998268i
$221$	−0.135112	+	1.28550i	−0.00908861	+	0.0864724i
$222$		0			0
$223$	−13.8777	−	15.4127i	−0.929317	−	1.03211i	−0.999402	−	0.0345702i	$-0.988994\pi$
$223$	−13.8777	−	15.4127i	−0.929317	−	1.03211i	0.0700852	−	0.997541i	$-0.477673\pi$
$224$	8.18649			0.546983
$225$		0			0
$226$	0.120491			0.00801494
$227$	0.902845	+	1.00271i	0.0599239	+	0.0665522i	0.772361	−	0.635183i	$-0.219075\pi$
$227$	0.902845	+	1.00271i	0.0599239	+	0.0665522i	−0.712437	+	0.701736i	$0.752409\pi$
$228$		0			0
$229$	−2.68476	+	25.5438i	−0.177414	+	1.68798i	0.437366	+	0.899284i	$0.355911\pi$
$229$	−2.68476	+	25.5438i	−0.177414	+	1.68798i	−0.614780	+	0.788698i	$0.710755\pi$
$230$	−2.61378	−	0.636194i	−0.172348	−	0.0419494i
$231$		0			0
$232$	0.618584	−	1.07142i	0.0406120	−	0.0703421i
$233$	−12.2726	+	8.91660i	−0.804008	+	0.584146i	−0.912087	−	0.409996i	$-0.865530\pi$
$233$	−12.2726	+	8.91660i	−0.804008	+	0.584146i	0.108079	+	0.994142i	$0.465530\pi$
$234$		0			0
$235$	0.765745	−	0.801873i	0.0499517	−	0.0523084i
$236$	11.7700	+	13.0719i	0.766163	+	0.850911i
$237$		0			0
$238$	0.105171	−	0.116804i	0.00681720	−	0.00757126i
$239$	13.7038	−	2.91284i	0.886427	−	0.188416i	0.257870	−	0.966180i	$-0.416979\pi$
$239$	13.7038	−	2.91284i	0.886427	−	0.188416i	0.628557	+	0.777764i	$0.283646\pi$
$240$		0			0
$241$	22.0088	+	4.67811i	1.41771	+	0.301344i	0.852122	−	0.523343i	$-0.175315\pi$
$241$	22.0088	+	4.67811i	1.41771	+	0.301344i	0.565589	+	0.824687i	$0.308649\pi$
$242$	−2.67966	+	1.94688i	−0.172255	+	0.125150i
$243$		0			0
$244$	14.2264	−	10.3361i	0.910752	−	0.661700i
$245$	−6.80517	−	5.25579i	−0.434766	−	0.335780i
$246$		0			0
$247$	3.97814	−	37.8495i	0.253123	−	2.40830i
$248$	4.52955	−	0.962785i	0.287627	−	0.0611369i
$249$		0			0
$250$	−4.64424	+	1.59558i	−0.293727	+	0.100913i
$251$	−0.464195			−0.0292997			−0.0146499	−	0.999893i	$-0.504663\pi$
$251$	−0.464195			−0.0292997			−0.0146499	+	0.999893i	$0.504663\pi$
$252$		0			0
$253$	9.54159	+	6.93237i	0.599875	+	0.435834i
$254$	0.993336	−	0.442262i	0.0623274	−	0.0277500i
$255$		0			0
$256$	2.46697	+	1.09837i	0.154186	+	0.0686480i
$257$	13.5014	+	23.3852i	0.842197	+	1.45873i	0.888034	+	0.459779i	$0.152071\pi$
$257$	13.5014	+	23.3852i	0.842197	+	1.45873i	−0.0458368	+	0.998949i	$0.514595\pi$
$258$		0			0
$259$	7.69893	+	1.63646i	0.478388	+	0.101685i
$260$	23.3634	+	11.2339i	1.44894	+	0.696696i
$261$		0			0
$262$	−0.156834	−	0.482684i	−0.00968921	−	0.0298203i
$263$	−8.34826	−	1.77448i	−0.514776	−	0.109419i	−0.0568033	−	0.998385i	$-0.518091\pi$
$263$	−8.34826	−	1.77448i	−0.514776	−	0.109419i	−0.457972	+	0.888966i	$0.651424\pi$
$264$		0			0
$265$	16.0970	+	3.91800i	0.988830	+	0.240681i
$266$	−3.09657	+	3.43909i	−0.189863	+	0.210864i
$267$		0			0
$268$	0.128827	−	0.223135i	0.00786936	−	0.0136301i
$269$	−0.950788	+	0.690788i	−0.0579706	+	0.0421181i	−0.616393	−	0.787439i	$-0.711407\pi$
$269$	−0.950788	+	0.690788i	−0.0579706	+	0.0421181i	0.558423	+	0.829557i	$0.311407\pi$
$270$		0			0
$271$	6.66331	+	4.84118i	0.404767	+	0.294081i	0.771480	−	0.636254i	$-0.219517\pi$
$271$	6.66331	+	4.84118i	0.404767	+	0.294081i	−0.366713	+	0.930334i	$0.619517\pi$
$272$	0.530029	−	0.235984i	0.0321377	−	0.0143086i
$273$		0			0
$274$	−1.85359	−	3.21051i	−0.111979	−	0.193954i
$275$	21.4927	+	1.26167i	1.29606	+	0.0760813i
$276$		0			0
$277$	−6.30699	−	7.00462i	−0.378950	−	0.420867i	0.523254	−	0.852177i	$-0.324718\pi$
$277$	−6.30699	−	7.00462i	−0.378950	−	0.420867i	−0.902204	+	0.431310i	$0.858051\pi$
$278$	−1.23863	−	0.899921i	−0.0742884	−	0.0539737i
$279$		0			0
$280$	−3.15053	−	5.84622i	−0.188280	−	0.349378i
$281$	−1.57750	−	15.0089i	−0.0941057	−	0.895356i	−0.935117	−	0.354339i	$-0.884706\pi$
$281$	−1.57750	−	15.0089i	−0.0941057	−	0.895356i	0.841011	−	0.541017i	$-0.181961\pi$
$282$		0			0
$283$	21.3125	+	9.48893i	1.26690	+	0.564058i	0.926525	−	0.376233i	$-0.122781\pi$
$283$	21.3125	+	9.48893i	1.26690	+	0.564058i	0.340370	+	0.940291i	$0.389448\pi$
$284$	−2.92059	+	3.24364i	−0.173305	+	0.192475i
$285$		0			0
$286$	8.11902	+	9.01708i	0.480088	+	0.533191i
$287$	6.90208	+	21.2424i	0.407417	+	1.25390i
$288$		0			0
$289$	−5.24075	+	16.1294i	−0.308279	+	0.948786i
$290$	−0.726331	−	0.0213003i	−0.0426516	−	0.00125079i
$291$		0			0
$292$	4.59888	+	2.04755i	0.269129	+	0.119824i
$293$	−4.27487	−	7.40429i	−0.249740	−	0.432563i	0.713713	−	0.700438i	$-0.247012\pi$
$293$	−4.27487	−	7.40429i	−0.249740	−	0.432563i	−0.963454	+	0.267875i	$0.913679\pi$
$294$		0			0
$295$	7.32989	−	20.4944i	0.426763	−	1.19323i
$296$	−5.99498	−	4.35560i	−0.348451	−	0.253164i
$297$		0			0
$298$	1.88631	−	5.80545i	0.109271	−	0.336301i
$299$	8.78625	−	15.2182i	0.508122	−	0.880093i
$300$		0			0
$301$	−6.95711	−	12.0501i	−0.401001	−	0.694554i
$302$	2.01991	−	0.429346i	0.116233	−	0.0247061i
$303$		0			0
$304$	−15.6058	+	6.94815i	−0.895054	+	0.398504i
$305$	−19.6101	−	9.42919i	−1.12287	−	0.539914i
$306$		0			0
$307$	20.4968			1.16981			0.584907	−	0.811101i	$-0.301131\pi$
$307$	20.4968			1.16981			0.584907	+	0.811101i	$0.301131\pi$
$308$	1.44463	+	13.7447i	0.0823152	+	0.783177i
$309$		0			0
$310$	−1.75990	−	2.07371i	−0.0999554	−	0.117779i
$311$	1.15735	−	0.246002i	0.0656273	−	0.0139495i	−0.174981	−	0.984572i	$-0.555986\pi$
$311$	1.15735	−	0.246002i	0.0656273	−	0.0139495i	0.240608	+	0.970622i	$0.422653\pi$
$312$		0			0
$313$	−14.5216	−	3.08667i	−0.820811	−	0.174469i	−0.221679	−	0.975120i	$-0.571154\pi$
$313$	−14.5216	−	3.08667i	−0.820811	−	0.174469i	−0.599131	+	0.800651i	$0.704487\pi$
$314$	1.29121	−	3.97393i	0.0728672	−	0.224262i
$315$		0			0
$316$	−7.18620	−	22.1168i	−0.404255	−	1.24417i
$317$	−0.0365481	−	0.347732i	−0.00205275	−	0.0195306i	0.993448	−	0.114289i	$-0.0364589\pi$
$317$	−0.0365481	−	0.347732i	−0.00205275	−	0.0195306i	−0.995500	+	0.0947581i	$0.969792\pi$
$318$		0			0
$319$	2.91036	+	1.29578i	0.162949	+	0.0725496i
$320$	−0.629134	−	8.32788i	−0.0351697	−	0.465542i
$321$		0			0
$322$	−1.95204	+	0.869103i	−0.108783	+	0.0484332i
$323$	−0.369327	+	1.13667i	−0.0205499	+	0.0632461i
$324$		0			0
$325$	−1.47779	−	32.0440i	−0.0819731	−	1.77748i
$326$	−1.82274	+	3.15708i	−0.100952	+	0.174854i
$327$		0			0
$328$	2.19804	−	20.9130i	0.121367	−	1.15473i
$329$	0.0920588	−	0.875881i	0.00507537	−	0.0482889i
$330$		0			0
$331$	1.62915	+	15.5003i	0.0895462	+	0.851975i	0.943443	+	0.331534i	$0.107566\pi$
$331$	1.62915	+	15.5003i	0.0895462	+	0.851975i	−0.853897	+	0.520442i	$0.825767\pi$
$332$	6.20725			0.340667
$333$		0			0
$334$	−1.93610	−	5.95871i	−0.105939	−	0.326046i
$335$	−0.318682	−	0.00934561i	−0.0174115	−	0.000510605i
$336$		0			0
$337$	−14.0544	+	15.6089i	−0.765589	+	0.850273i	−0.992322	−	0.123684i	$-0.960529\pi$
$337$	−14.0544	+	15.6089i	−0.765589	+	0.850273i	0.226732	+	0.973957i	$0.427196\pi$
$338$	8.27621	−	9.19166i	0.450166	−	0.499960i
$339$		0			0
$340$	−0.644320	−	0.497624i	−0.0349432	−	0.0269874i
$341$	3.68486	+	11.3408i	0.199547	+	0.614141i
$342$		0			0
$343$	−19.2628			−1.04009
$344$	1.36929	+	13.0280i	0.0738274	+	0.702421i
$345$		0			0
$346$	−0.991592	+	9.43437i	−0.0533083	+	0.507195i
$347$	0.418011	−	3.97711i	0.0224400	−	0.213502i	−0.977556	−	0.210676i	$-0.932434\pi$
$347$	0.418011	−	3.97711i	0.0224400	−	0.213502i	0.999996	−	0.00282668i	$-0.000899761\pi$
$348$		0			0
$349$	−1.07056	+	1.85427i	−0.0573059	+	0.0992567i	−0.893255	−	0.449550i	$-0.851584\pi$
$349$	−1.07056	+	1.85427i	−0.0573059	+	0.0992567i	0.835949	+	0.548807i	$0.184918\pi$
$350$	−2.14491	+	3.25793i	−0.114650	+	0.174144i
$351$		0			0
$352$	6.13300	−	18.8754i	0.326890	−	1.00606i
$353$	−10.3585	+	4.61188i	−0.551325	+	0.245466i	−0.663440	−	0.748229i	$-0.730904\pi$
$353$	−10.3585	+	4.61188i	−0.551325	+	0.245466i	0.112115	+	0.993695i	$0.464238\pi$
$354$		0			0
$355$	5.24769	+	1.27729i	0.278519	+	0.0677913i
$356$	17.6287	+	7.84880i	0.934319	+	0.415986i
$357$		0			0
$358$	−0.852867	−	8.11448i	−0.0450754	−	0.428864i
$359$	7.26044	+	22.3453i	0.383191	+	1.17934i	0.937784	+	0.347219i	$0.112874\pi$
$359$	7.26044	+	22.3453i	0.383191	+	1.17934i	−0.554593	+	0.832122i	$0.687126\pi$
$360$		0			0
$361$	5.00287	−	15.3973i	0.263309	−	0.810382i
$362$	0.553745	+	0.117702i	0.0291042	+	0.00618629i
$363$		0			0
$364$	20.1417	−	4.28124i	1.05571	−	0.224398i
$365$	−0.469248	−	6.21146i	−0.0245616	−	0.325123i
$366$		0			0
$367$	2.13043	+	20.2697i	0.111207	+	1.05807i	0.897742	+	0.440522i	$0.145207\pi$
$367$	2.13043	+	20.2697i	0.111207	+	1.05807i	−0.786534	+	0.617546i	$0.788127\pi$
$368$	−7.88758			−0.411168
$369$		0			0
$370$	−0.581630	+	4.31330i	−0.0302375	+	0.224238i
$371$	12.0216	−	5.35237i	0.624131	−	0.277881i
$372$		0			0
$373$	30.1757	−	6.41404i	1.56244	−	0.332106i	0.656104	−	0.754670i	$-0.272203\pi$
$373$	30.1757	−	6.41404i	1.56244	−	0.332106i	0.906333	+	0.422564i	$0.138870\pi$
$374$	−0.190522	−	0.329994i	−0.00985167	−	0.0170636i
$375$		0			0
$376$	−0.414576	+	0.718068i	−0.0213801	+	0.0370315i
$377$	1.46680	−	4.51433i	0.0755439	−	0.232500i
$378$		0			0
$379$	−26.1852	−	19.0246i	−1.34504	−	0.977230i	−0.999242	−	0.0389217i	$-0.987608\pi$
$379$	−26.1852	−	19.0246i	−1.34504	−	0.977230i	−0.345800	−	0.938308i	$-0.612392\pi$
$380$	18.9709	+	14.6517i	0.973187	+	0.751615i
$381$		0			0
$382$	−0.340393	−	0.589578i	−0.0174160	−	0.0301654i
$383$	31.3522	+	13.9589i	1.60202	+	0.713266i	0.996581	−	0.0826230i	$-0.0263297\pi$
$383$	31.3522	+	13.9589i	1.60202	+	0.713266i	0.605442	+	0.795890i	$0.292996\pi$
$384$		0			0
$385$	14.1239	−	9.64199i	0.719821	−	0.491401i
$386$	1.55752	−	4.79354i	0.0792754	−	0.243985i
$387$		0			0
$388$	8.85423	+	27.2505i	0.449505	+	1.38344i
$389$	−2.75983	−	3.06510i	−0.139929	−	0.155407i	0.669107	−	0.743166i	$-0.266677\pi$
$389$	−2.75983	−	3.06510i	−0.139929	−	0.155407i	−0.809036	+	0.587759i	$0.800010\pi$
$390$		0			0
$391$	−0.369256	+	0.410100i	−0.0186741	+	0.0207397i
$392$	5.87416	+	2.61534i	0.296690	+	0.132095i
$393$		0			0
$394$	−1.05431	−	10.0311i	−0.0531156	−	0.505361i
$395$	−19.8732	+	20.8108i	−0.999929	+	1.04711i
$396$		0			0
$397$	−15.7730	−	11.4597i	−0.791622	−	0.575147i	0.116822	−	0.993153i	$-0.462729\pi$
$397$	−15.7730	−	11.4597i	−0.791622	−	0.575147i	−0.908444	+	0.418006i	$0.862729\pi$
$398$	−1.22644	−	1.36210i	−0.0614757	−	0.0682757i
$399$		0			0
$400$	−12.1246	+	7.76608i	−0.606230	+	0.388304i
$401$	10.5037	+	18.1930i	0.524530	+	0.908513i	0.999592	+	0.0285608i	$0.00909243\pi$
$401$	10.5037	+	18.1930i	0.524530	+	0.908513i	−0.475062	+	0.879953i	$0.657574\pi$
$402$		0			0
$403$	16.2308	−	7.22641i	0.808513	−	0.359973i
$404$	−14.7159	−	10.6917i	−0.732143	−	0.531933i
$405$		0			0
$406$	−0.466949	+	0.339258i	−0.0231743	+	0.0168371i
$407$	9.54088	−	16.5253i	0.472924	−	0.819128i
$408$		0			0
$409$	−4.54343	+	5.04599i	−0.224658	+	0.249508i	−0.844928	−	0.534881i	$-0.820357\pi$
$409$	−4.54343	+	5.04599i	−0.224658	+	0.249508i	0.620270	+	0.784389i	$0.287023\pi$
$410$	−11.4254	+	4.69061i	−0.564260	+	0.231653i
$411$		0			0
$412$	8.81949	+	1.87464i	0.434505	+	0.0923569i
$413$	−5.34252	−	16.4426i	−0.262888	−	0.809087i
$414$		0			0
$415$	−3.64376	−	6.76148i	−0.178865	−	0.331908i
$416$	−28.9244	−	6.14808i	−1.41814	−	0.301434i
$417$		0			0
$418$	5.60960	+	9.71612i	0.274375	+	0.475231i
$419$	30.6449	+	13.6440i	1.49710	+	0.666552i	0.981707	−	0.190400i	$-0.0609786\pi$
$419$	30.6449	+	13.6440i	1.49710	+	0.666552i	0.515395	+	0.856953i	$0.327645\pi$
$420$		0			0
$421$	−21.0420	+	9.36850i	−1.02552	+	0.456593i	−0.849386	−	0.527773i	$-0.823027\pi$
$421$	−21.0420	+	9.36850i	−1.02552	+	0.456593i	−0.176138	+	0.984365i	$0.556361\pi$
$422$	−1.00697	−	0.731609i	−0.0490187	−	0.0356142i
$423$		0			0
$424$	−12.3890			−0.601663
$425$	−0.163828	+	0.993964i	−0.00794685	+	0.0482143i
$426$		0			0
$427$	−16.9060	+	3.59347i	−0.818136	+	0.173900i
$428$	1.34128	−	12.7614i	0.0648333	−	0.616848i
$429$		0			0
$430$	6.35451	−	4.33804i	0.306442	−	0.209199i
$431$	15.8922	−	11.5463i	0.765498	−	0.556167i	−0.135094	−	0.990833i	$-0.543134\pi$
$431$	15.8922	−	11.5463i	0.765498	−	0.556167i	0.900592	+	0.434666i	$0.143134\pi$
$432$		0			0
$433$	−1.24749	+	0.906354i	−0.0599505	+	0.0435566i	−0.617357	−	0.786683i	$-0.711797\pi$
$433$	−1.24749	+	0.906354i	−0.0599505	+	0.0435566i	0.557406	+	0.830240i	$0.311797\pi$
$434$	−2.11319	−	0.449172i	−0.101436	−	0.0215609i
$435$		0			0
$436$	1.01720	−	0.216213i	0.0487152	−	0.0103547i
$437$	10.8721	−	12.0747i	0.520084	−	0.577611i
$438$		0			0
$439$	2.31295	+	2.56879i	0.110391	+	0.122602i	0.795808	−	0.605549i	$-0.207047\pi$
$439$	2.31295	+	2.56879i	0.110391	+	0.122602i	−0.685417	+	0.728151i	$0.740380\pi$
$440$	−15.8397	+	2.88435i	−0.755130	+	0.137506i
$441$		0			0
$442$	−0.459308	+	0.333707i	−0.0218470	+	0.0158728i
$443$	11.4007	−	19.7467i	0.541666	−	0.938193i	−0.457143	−	0.889393i	$-0.651127\pi$
$443$	11.4007	−	19.7467i	0.541666	−	0.938193i	0.998809	−	0.0487993i	$-0.0155395\pi$
$444$		0			0
$445$	−1.79875	−	23.8101i	−0.0852689	−	1.12871i
$446$	0.952197	−	9.05955i	0.0450878	−	0.428982i
$447$		0			0
$448$	−4.43886	−	4.92985i	−0.209716	−	0.232914i
$449$	−19.8521			−0.936876			−0.468438	−	0.883496i	$-0.655183\pi$
$449$	−19.8521			−0.936876			−0.468438	+	0.883496i	$0.655183\pi$
$450$		0			0
$451$	54.1489			2.54977
$452$	−0.331708	−	0.368399i	−0.0156022	−	0.0173280i
$453$		0			0
$454$	−0.0619475	+	0.589391i	−0.00290734	+	0.0276615i
$455$	−16.4870	−	19.4269i	−0.772924	−	0.910748i
$456$		0			0
$457$	−3.84410	+	6.65818i	−0.179820	+	0.311457i	−0.941819	−	0.336122i	$-0.890885\pi$
$457$	−3.84410	+	6.65818i	−0.179820	+	0.311457i	0.761999	+	0.647578i	$0.224218\pi$
$458$	−9.12674	+	6.63097i	−0.426465	+	0.309845i
$459$		0			0
$460$	5.25052	+	9.74302i	0.244807	+	0.454271i
$461$	−3.64123	−	4.04400i	−0.169589	−	0.188348i	0.652359	−	0.757910i	$-0.273779\pi$
$461$	−3.64123	−	4.04400i	−0.169589	−	0.188348i	−0.821948	+	0.569562i	$0.807113\pi$
$462$		0			0
$463$	3.95193	−	4.38906i	0.183662	−	0.203977i	−0.644282	−	0.764788i	$-0.722844\pi$
$463$	3.95193	−	4.38906i	0.183662	−	0.203977i	0.827944	+	0.560811i	$0.189511\pi$
$464$	−2.08402	+	0.442972i	−0.0967483	+	0.0205645i
$465$		0			0
$466$	−6.51736	−	1.38531i	−0.301911	−	0.0641732i
$467$	−19.9403	+	14.4875i	−0.922727	+	0.670400i	−0.944201	−	0.329369i	$-0.893164\pi$
$467$	−19.9403	+	14.4875i	−0.922727	+	0.670400i	0.0214742	+	0.999769i	$0.493164\pi$
$468$		0			0
$469$	−0.204876	+	0.148851i	−0.00946032	+	0.00687332i
$470$	0.486789	+	0.0142755i	0.0224539	+	0.000658479i
$471$		0			0
$472$	−1.70138	+	16.1876i	−0.0783126	+	0.745094i
$473$	−32.9955	+	7.01342i	−1.51714	+	0.322477i
$474$		0			0
$475$	4.82365	−	29.2656i	0.221324	−	1.34280i
$476$	−0.646657			−0.0296395
$477$		0			0
$478$	4.97831	+	3.61696i	0.227703	+	0.165436i
$479$	−14.5472	+	6.47682i	−0.664677	+	0.295933i	−0.711206	−	0.702984i	$-0.751851\pi$
$479$	−14.5472	+	6.47682i	−0.664677	+	0.295933i	0.0465289	+	0.998917i	$0.485184\pi$
$480$		0			0
$481$	−25.9728	−	11.5638i	−1.18426	−	0.527266i
$482$	4.94139	+	8.55873i	0.225074	+	0.389840i
$483$		0			0
$484$	13.3296	+	2.83329i	0.605890	+	0.128786i
$485$	24.4861	−	25.6413i	1.11186	−	1.16431i
$486$		0			0
$487$	9.80003	+	30.1614i	0.444082	+	1.36674i	0.883488	+	0.468454i	$0.155189\pi$
$487$	9.80003	+	30.1614i	0.444082	+	1.36674i	−0.439406	+	0.898289i	$0.644811\pi$
$488$	15.9163	+	3.38312i	0.720499	+	0.153147i
$489$		0			0
$490$	−0.284499	−	3.76593i	−0.0128524	−	0.170127i
$491$	15.1147	−	16.7866i	0.682117	−	0.757567i	−0.298306	−	0.954470i	$-0.596422\pi$
$491$	15.1147	−	16.7866i	0.682117	−	0.757567i	0.980423	+	0.196903i	$0.0630883\pi$
$492$		0			0
$493$	−0.0745316	+	0.129093i	−0.00335674	+	0.00581404i
$494$	13.5235	−	9.82542i	0.608452	−	0.442066i
$495$		0			0
$496$	−6.45175	−	4.68747i	−0.289692	−	0.210474i
$497$	3.91910	−	1.74490i	0.175796	−	0.0782694i
$498$		0			0
$499$	9.74420	+	16.8775i	0.436210	+	0.755539i	0.997394	−	0.0721531i	$-0.0229870\pi$
$499$	9.74420	+	16.8775i	0.436210	+	0.755539i	−0.561183	+	0.827692i	$0.689654\pi$
$500$	17.6639	+	9.80711i	0.789954	+	0.438587i
$501$		0			0
$502$	−0.136426	−	0.151517i	−0.00608901	−	0.00676253i
$503$	14.7866	+	10.7431i	0.659301	+	0.479010i	0.866427	−	0.499304i	$-0.166411\pi$
$503$	14.7866	+	10.7431i	0.659301	+	0.479010i	−0.207126	+	0.978314i	$0.566411\pi$
$504$		0			0
$505$	−3.00788	+	22.3061i	−0.133849	+	0.992607i
$506$	0.541483	+	5.15186i	0.0240718	+	0.229028i
$507$		0			0
$508$	−4.08683	−	1.81958i	−0.181324	−	0.0807306i
$509$	−15.0769	+	16.7446i	−0.668274	+	0.742193i	−0.977994	−	0.208635i	$-0.933098\pi$
$509$	−15.0769	+	16.7446i	−0.668274	+	0.742193i	0.309720	+	0.950828i	$0.399765\pi$
$510$		0			0
$511$	−3.31078	−	3.67700i	−0.146460	−	0.162661i
$512$	7.07765	+	21.7828i	0.312791	+	0.962671i
$513$		0			0
$514$	−3.66505	+	11.2799i	−0.161658	+	0.497533i
$515$	−3.13517	−	10.7074i	−0.138152	−	0.471825i
$516$		0			0
$517$	−1.95053	−	0.868433i	−0.0857844	−	0.0381937i
$518$	1.72855	+	2.99394i	0.0759483	+	0.131546i
$519$		0			0
$520$	6.74089	+	23.0219i	0.295608	+	1.00958i
$521$	4.02702	+	2.92580i	0.176427	+	0.128182i	0.672494	−	0.740103i	$-0.265223\pi$
$521$	4.02702	+	2.92580i	0.176427	+	0.128182i	−0.496067	+	0.868284i	$0.665223\pi$
$522$		0			0
$523$	−0.936421	+	2.88201i	−0.0409468	+	0.126021i	−0.969440	−	0.245327i	$-0.921105\pi$
$523$	−0.936421	+	2.88201i	−0.0409468	+	0.126021i	0.928493	+	0.371349i	$0.121105\pi$
$524$	−1.04404	+	1.80833i	−0.0456091	+	0.0789973i
$525$		0			0
$526$	−1.87434	−	3.24645i	−0.0817251	−	0.141552i
$527$	−0.545754	+	0.116004i	−0.0237734	+	0.00505320i
$528$		0			0
$529$	−14.1579	+	6.30351i	−0.615561	+	0.274066i
$530$	3.45202	+	6.40567i	0.149946	+	0.278245i
$531$		0			0
$532$	19.0397			0.825477
$533$	−8.43325	−	80.2370i	−0.365284	−	3.47545i
$534$		0			0
$535$	−14.6882	+	6.03015i	−0.635028	+	0.260706i
$536$	0.233208	−	0.0495698i	0.0100730	−	0.00214109i
$537$		0			0
$538$	−0.504914	−	0.107323i	−0.0217684	−	0.00462702i
$539$	−5.11666	+	15.7475i	−0.220390	+	0.678291i
$540$		0			0
$541$	−4.84376	−	14.9075i	−0.208249	−	0.640925i	−0.999564	−	0.0295168i	$-0.990603\pi$
$541$	−4.84376	−	14.9075i	−0.208249	−	0.640925i	0.791315	−	0.611409i	$-0.209397\pi$
$542$	0.378141	+	3.59777i	0.0162426	+	0.154538i
$543$		0			0
$544$	0.848348	+	0.377709i	0.0363726	+	0.0161941i
$545$	−0.832635	−	0.981107i	−0.0356662	−	0.0420260i
$546$		0			0
$547$	−6.97246	+	3.10434i	−0.298121	+	0.132732i	−0.550346	−	0.834937i	$-0.685504\pi$
$547$	−6.97246	+	3.10434i	−0.298121	+	0.132732i	0.252225	+	0.967669i	$0.418838\pi$
$548$	−4.71321	+	14.5058i	−0.201338	+	0.619656i
$549$		0			0
$550$	5.90486	+	7.38618i	0.251784	+	0.314948i
$551$	2.19446	−	3.80091i	0.0934870	−	0.161924i
$552$		0			0
$553$	−2.38918	+	22.7315i	−0.101598	+	0.966643i
$554$	0.432745	−	4.11730i	0.0183856	−	0.174927i
$555$		0			0
$556$	0.658432	+	6.26456i	0.0279237	+	0.265677i
$557$	−17.3196			−0.733856			−0.366928	−	0.930249i	$-0.619590\pi$
$557$	−17.3196			−0.733856			−0.366928	+	0.930249i	$0.619590\pi$
$558$		0			0
$559$	15.5311	+	47.8000i	0.656898	+	2.02172i
$560$	−3.85152	+	10.7689i	−0.162757	+	0.455068i
$561$		0			0
$562$	4.43540	−	4.92601i	0.187096	−	0.207791i
$563$	−17.2901	+	19.2026i	−0.728690	+	0.809292i	−0.987663	−	0.156593i	$-0.949949\pi$
$563$	−17.2901	+	19.2026i	−0.728690	+	0.809292i	0.258974	+	0.965884i	$0.416616\pi$
$564$		0			0
$565$	−0.206574	+	0.577582i	−0.00869065	+	0.0242991i
$566$	3.16645	+	9.74534i	0.133096	+	0.409627i
$567$		0			0
$568$	−4.03887			−0.169467
$569$	−0.0181346	−	0.172539i	−0.000760241	−	0.00723321i	0.994135	−	0.108144i	$-0.0344909\pi$
$569$	−0.0181346	−	0.172539i	−0.000760241	−	0.00723321i	−0.994895	+	0.100911i	$0.967824\pi$
$570$		0			0
$571$	2.57200	−	24.4709i	0.107635	−	1.02408i	−0.798762	−	0.601648i	$-0.794511\pi$
$571$	2.57200	−	24.4709i	0.107635	−	1.02408i	0.906396	−	0.422428i	$-0.138822\pi$
$572$	5.21817	−	49.6475i	0.218183	−	2.07587i
$573$		0			0
$574$	−4.90518	+	8.49601i	−0.204738	+	0.354617i
$575$	7.53082	−	11.4387i	0.314057	−	0.477025i
$576$		0			0
$577$	−8.78272	+	27.0304i	−0.365629	+	1.12529i	0.583957	+	0.811785i	$0.301504\pi$
$577$	−8.78272	+	27.0304i	−0.365629	+	1.12529i	−0.949586	+	0.313506i	$0.898496\pi$
$578$	−6.80499	+	3.02978i	−0.283050	+	0.126022i
$579$		0			0
$580$	1.93444	+	2.27939i	0.0803234	+	0.0946463i
$581$	−5.57348	−	2.48147i	−0.231227	−	0.102949i
$582$		0			0
$583$	−3.33472	−	31.7278i	−0.138110	−	1.31403i
$584$	1.43948	+	4.43027i	0.0595661	+	0.183326i
$585$		0			0
$586$	1.16044	−	3.57146i	0.0479373	−	0.147536i
$587$	−12.6109	−	2.68054i	−0.520509	−	0.110638i	−0.0598372	−	0.998208i	$-0.519058\pi$
$587$	−12.6109	−	2.68054i	−0.520509	−	0.110638i	−0.460672	+	0.887571i	$0.652392\pi$
$588$		0			0
$589$	16.0688	−	3.41553i	0.662103	−	0.140734i
$590$	8.84378	−	3.63075i	0.364093	−	0.149476i
$591$		0			0
$592$	1.33393	+	12.6915i	0.0548242	+	0.521618i
$593$	−27.5686			−1.13211			−0.566053	−	0.824369i	$-0.691530\pi$
$593$	−27.5686			−1.13211			−0.566053	+	0.824369i	$0.691530\pi$
$594$		0			0
$595$	0.379599	+	0.704396i	0.0155621	+	0.0288774i
$596$	−22.9430	+	10.2149i	−0.939783	+	0.418419i
$597$		0			0
$598$	7.54961	−	1.60472i	0.308727	−	0.0656219i
$599$	23.0932	+	39.9986i	0.943563	+	1.63430i	0.758604	+	0.651552i	$0.225882\pi$
$599$	23.0932	+	39.9986i	0.943563	+	1.63430i	0.184958	+	0.982746i	$0.440785\pi$
$600$		0			0
$601$	−20.7102	+	35.8711i	−0.844787	+	1.46321i	0.0410187	+	0.999158i	$0.486940\pi$
$601$	−20.7102	+	35.8711i	−0.844787	+	1.46321i	−0.885806	+	0.464056i	$0.846394\pi$
$602$	1.88855	−	5.81235i	0.0769714	−	0.236894i
$603$		0			0
$604$	−6.87348	−	4.99388i	−0.279678	−	0.203198i
$605$	−4.73843	−	16.1829i	−0.192645	−	0.657930i
$606$		0			0
$607$	−8.40346	−	14.5552i	−0.341086	−	0.590778i	0.643549	−	0.765405i	$-0.277461\pi$
$607$	−8.40346	−	14.5552i	−0.341086	−	0.590778i	−0.984635	+	0.174627i	$0.944128\pi$
$608$	−24.9781	−	11.1210i	−1.01300	−	0.451016i
$609$		0			0
$610$	−2.68563	−	9.17213i	−0.108738	−	0.371369i
$611$	−0.983051	+	3.02552i	−0.0397700	+	0.122399i
$612$		0			0
$613$	−6.05434	−	18.6333i	−0.244532	−	0.752593i	−0.995713	−	0.0924965i	$-0.970515\pi$
$613$	−6.05434	−	18.6333i	−0.244532	−	0.752593i	0.751181	−	0.660097i	$-0.229485\pi$
$614$	6.02398	+	6.69031i	0.243108	+	0.269999i
$615$		0			0
$616$	−8.55723	+	9.50376i	−0.344780	+	0.382918i
$617$	5.95230	+	2.65013i	0.239631	+	0.106690i	0.523039	−	0.852309i	$-0.324798\pi$
$617$	5.95230	+	2.65013i	0.239631	+	0.106690i	−0.283408	+	0.958999i	$0.591465\pi$
$618$		0			0
$619$	−3.90571	−	37.1603i	−0.156984	−	1.49360i	−0.735275	−	0.677769i	$-0.762947\pi$
$619$	−3.90571	−	37.1603i	−0.156984	−	1.49360i	0.578291	−	0.815831i	$-0.303720\pi$
$620$	−1.49540	+	11.0897i	−0.0600568	+	0.445374i
$621$		0			0
$622$	0.420441	+	0.305468i	0.0168581	+	0.0122482i
$623$	−12.6911	−	14.0949i	−0.508457	−	0.564699i
$624$		0			0
$625$	0.313739	−	24.9980i	0.0125496	−	0.999921i
$626$	−3.26038	−	5.64714i	−0.130311	−	0.225705i
$627$		0			0
$628$	−15.7049	+	6.99227i	−0.626694	+	0.279022i
$629$	0.722320	+	0.524796i	0.0288008	+	0.0209250i
$630$		0			0
$631$	10.2656	−	7.45836i	0.408665	−	0.296913i	−0.364396	−	0.931244i	$-0.618725\pi$
$631$	10.2656	−	7.45836i	0.408665	−	0.296913i	0.773061	+	0.634331i	$0.218725\pi$
$632$	10.7594	−	18.6358i	0.427986	−	0.741294i
$633$		0			0
$634$	0.102761	−	0.114128i	0.00408116	−	0.00453259i
$635$	0.417001	+	5.51986i	0.0165482	+	0.219049i
$636$		0			0
$637$	24.1312	+	5.12924i	0.956112	+	0.203228i
$638$	0.432401	+	1.33079i	0.0171189	+	0.0526866i
$639$		0			0
$640$	16.7692	−	17.5603i	0.662859	−	0.694133i
$641$	8.36417	+	1.77786i	0.330365	+	0.0702213i	0.370108	−	0.928989i	$-0.379321\pi$
$641$	8.36417	+	1.77786i	0.330365	+	0.0702213i	−0.0397431	+	0.999210i	$0.512654\pi$
$642$		0			0
$643$	4.36268	+	7.55638i	0.172047	+	0.297994i	0.939135	−	0.343547i	$-0.111629\pi$
$643$	4.36268	+	7.55638i	0.172047	+	0.297994i	−0.767088	+	0.641542i	$0.778295\pi$
$644$	8.03117	+	3.57571i	0.316472	+	0.140903i
$645$		0			0
$646$	−0.479563	+	0.213515i	−0.0188682	+	0.00840064i
$647$	0.0235532	+	0.0171124i	0.000925971	+	0.000672757i	0.588248	−	0.808680i	$-0.299818\pi$
$647$	0.0235532	+	0.0171124i	0.000925971	+	0.000672757i	−0.587322	+	0.809353i	$0.699818\pi$
$648$		0			0
$649$	−41.9137			−1.64526
$650$	10.0251	−	9.90005i	0.393216	−	0.388312i
$651$		0			0
$652$	14.6707	−	3.11835i	0.574548	−	0.122124i
$653$	1.80357	−	17.1598i	0.0705791	−	0.671515i	−0.900841	−	0.434149i	$-0.857049\pi$
$653$	1.80357	−	17.1598i	0.0705791	−	0.671515i	0.971420	−	0.237366i	$-0.0762841\pi$
$654$		0			0
$655$	2.58266	+	0.0757388i	0.100913	+	0.00295936i
$656$	−29.2973	+	21.2858i	−1.14387	+	0.831069i
$657$		0			0
$658$	0.312950	−	0.227372i	0.0122001	−	0.00886387i
$659$	−36.7429	−	7.80994i	−1.43130	−	0.304232i	−0.573918	−	0.818913i	$-0.694577\pi$
$659$	−36.7429	−	7.80994i	−1.43130	−	0.304232i	−0.857382	+	0.514681i	$0.827910\pi$
$660$		0			0
$661$	−49.0303	+	10.4217i	−1.90706	+	0.405358i	−0.999882	−	0.0153926i	$-0.995100\pi$
$661$	−49.0303	+	10.4217i	−1.90706	+	0.405358i	−0.907176	+	0.420750i	$0.861767\pi$
$662$	−4.58062	+	5.08730i	−0.178031	+	0.197723i
$663$		0			0
$664$	3.84336	+	4.26849i	0.149151	+	0.165649i
$665$	−11.1767	−	20.7397i	−0.433412	−	0.804253i
$666$		0			0
$667$	1.63947	−	1.19114i	0.0634804	−	0.0461212i
$668$	−12.8886	+	22.3237i	−0.498676	+	0.863732i
$669$		0			0
$670$	−0.0906098	−	0.106767i	−0.00350056	−	0.00412476i
$671$	−4.37988	+	41.6718i	−0.169083	+	1.60872i
$672$		0			0
$673$	−3.20020	−	3.55418i	−0.123359	−	0.137004i	0.678302	−	0.734784i	$-0.262716\pi$
$673$	−3.20020	−	3.55418i	−0.123359	−	0.137004i	−0.801660	+	0.597780i	$0.796050\pi$
$674$	−9.22544			−0.355351
$675$		0			0
$676$	−50.8875			−1.95721
$677$	18.2605	+	20.2804i	0.701809	+	0.779438i	0.983663	−	0.180019i	$-0.0576160\pi$
$677$	18.2605	+	20.2804i	0.701809	+	0.779438i	−0.281854	+	0.959457i	$0.590949\pi$
$678$		0			0
$679$	2.94375	−	28.0079i	0.112971	−	1.07484i
$680$	−0.0567490	−	0.751189i	−0.00217623	−	0.0288068i
$681$		0			0
$682$	−2.61876	+	4.53583i	−0.100278	+	0.173686i
$683$	3.32056	−	2.41252i	0.127058	−	0.0923127i	−0.522441	−	0.852675i	$-0.674979\pi$
$683$	3.32056	−	2.41252i	0.127058	−	0.0923127i	0.649499	+	0.760362i	$0.274979\pi$
$684$		0			0
$685$	18.5677	−	3.38110i	0.709435	−	0.129185i
$686$	−5.66131	−	6.28752i	−0.216150	−	0.240059i
$687$		0			0
$688$	15.0953	−	16.7651i	0.575504	−	0.639162i
$689$	−46.4943	+	9.88267i	−1.77129	+	0.376500i
$690$		0			0
$691$	−18.3696	−	3.90457i	−0.698811	−	0.148537i	−0.155211	−	0.987881i	$-0.549606\pi$
$691$	−18.3696	−	3.90457i	−0.698811	−	0.148537i	−0.543600	+	0.839344i	$0.682939\pi$
$692$	31.5753	−	22.9408i	1.20031	−	0.872077i
$693$		0			0
$694$	1.42101	−	1.03243i	0.0539409	−	0.0391903i
$695$	6.43740	−	4.39463i	0.244185	−	0.166698i
$696$		0			0
$697$	−0.264837	+	2.51975i	−0.0100314	+	0.0954424i
$698$	−0.919885	+	0.195528i	−0.0348181	+	0.00740083i
$699$		0			0
$700$	15.8659	−	2.41096i	0.599676	−	0.0911258i
$701$	−22.5412			−0.851368			−0.425684	−	0.904872i	$-0.639967\pi$
$701$	−22.5412			−0.851368			−0.425684	+	0.904872i	$0.639967\pi$
$702$		0			0
$703$	−21.2675	−	15.4517i	−0.802118	−	0.582773i
$704$	−14.6921	+	6.54133i	−0.553728	+	0.246536i
$705$		0			0
$706$	−4.54969	−	2.02565i	−0.171230	−	0.0762365i
$707$	8.93915	+	15.4831i	0.336192	+	0.582301i
$708$		0			0
$709$	14.5880	+	3.10077i	0.547862	+	0.116452i	0.473523	−	0.880781i	$-0.342982\pi$
$709$	14.5880	+	3.10077i	0.547862	+	0.116452i	0.0743389	+	0.997233i	$0.476315\pi$
$710$	1.12537	+	2.08828i	0.0422346	+	0.0783718i
$711$		0			0
$712$	5.51790	+	16.9823i	0.206792	+	0.636440i
$713$	7.41944	+	1.57705i	0.277860	+	0.0590610i
$714$		0			0
$715$	−57.1436	+	23.4599i	−2.13705	+	0.877350i
$716$	−22.4620	+	24.9466i	−0.839444	+	0.932297i
$717$		0			0
$718$	−5.15985	+	8.93713i	−0.192564	+	0.333531i
$719$	35.1450	−	25.5343i	1.31069	−	0.952270i	0.310689	−	0.950512i	$-0.399440\pi$
$719$	35.1450	−	25.5343i	1.31069	−	0.952270i	0.999998	−	0.00175887i	$-0.000559868\pi$
$720$		0			0
$721$	−7.16959	−	5.20901i	−0.267009	−	0.193994i
$722$	6.49612	−	2.89226i	0.241761	−	0.107639i
$723$		0			0
$724$	−1.16457	−	2.01710i	−0.0432810	−	0.0749649i
$725$	1.34736	−	3.44521i	0.0500395	−	0.127952i
$726$		0			0
$727$	−10.6471	−	11.8248i	−0.394879	−	0.438557i	0.512618	−	0.858617i	$-0.328676\pi$
$727$	−10.6471	−	11.8248i	−0.394879	−	0.438557i	−0.907496	+	0.420060i	$0.862009\pi$
$728$	15.4152	+	11.1998i	0.571326	+	0.415093i
$729$		0			0
$730$	1.88956	−	1.97871i	0.0699356	−	0.0732352i
$731$	−0.164983	−	1.56971i	−0.00610211	−	0.0580577i
$732$		0			0
$733$	−14.3020	−	6.36765i	−0.528255	−	0.235194i	0.125238	−	0.992127i	$-0.460031\pi$
$733$	−14.3020	−	6.36765i	−0.528255	−	0.235194i	−0.653493	+	0.756932i	$0.726697\pi$
$734$	−5.99005	+	6.65262i	−0.221097	+	0.245553i
$735$		0			0
$736$	−8.44751	−	9.38192i	−0.311380	−	0.345822i
$737$	0.189718	+	0.583893i	0.00698836	+	0.0215080i
$738$		0			0
$739$	−11.5329	+	35.4945i	−0.424243	+	1.30569i	0.479473	+	0.877556i	$0.340828\pi$
$739$	−11.5329	+	35.4945i	−0.424243	+	1.30569i	−0.903717	+	0.428131i	$0.859172\pi$
$740$	14.7891	−	10.0961i	0.543657	−	0.371139i
$741$		0			0
$742$	5.28019	+	2.35089i	0.193842	+	0.0863040i
$743$	−5.72347	−	9.91334i	−0.209974	−	0.363685i	0.741732	−	0.670696i	$-0.234005\pi$
$743$	−5.72347	−	9.91334i	−0.209974	−	0.363685i	−0.951706	+	0.307011i	$0.900671\pi$
$744$		0			0
$745$	24.5949	+	18.9953i	0.901089	+	0.695932i
$746$	10.9622	+	7.96449i	0.401354	+	0.291601i
$747$		0			0
$748$	−0.484450	+	1.49098i	−0.0177132	+	0.0545158i
$749$	−6.30599	+	10.9223i	−0.230416	+	0.399092i
$750$		0			0
$751$	12.6924	+	21.9839i	0.463152	+	0.802203i	0.999116	−	0.0420379i	$-0.0133850\pi$
$751$	12.6924	+	21.9839i	0.463152	+	0.802203i	−0.535964	+	0.844241i	$0.680052\pi$
$752$	1.39672	−	0.296881i	0.0509330	−	0.0108261i
$753$		0			0
$754$	1.90460	−	0.847984i	0.0693616	−	0.0308818i
$755$	−1.40492	+	10.4187i	−0.0511301	+	0.379175i
$756$		0			0
$757$	−15.8030			−0.574370			−0.287185	−	0.957875i	$-0.592719\pi$
$757$	−15.8030			−0.574370			−0.287185	+	0.957875i	$0.592719\pi$
$758$	−1.48600	−	14.1384i	−0.0539740	−	0.513528i
$759$		0			0
$760$	1.67088	+	22.1175i	0.0606091	+	0.802286i
$761$	−40.6361	+	8.63747i	−1.47306	+	0.313108i	−0.873343	−	0.487105i	$-0.838053\pi$
$761$	−40.6361	+	8.63747i	−1.47306	+	0.313108i	−0.599715	+	0.800214i	$0.704719\pi$
$762$		0			0
$763$	−0.999782	−	0.212510i	−0.0361945	−	0.00769339i
$764$	−0.865533	+	2.66384i	−0.0313139	+	0.0963742i
$765$		0			0
$766$	4.65808	+	14.3361i	0.168303	+	0.517984i
$767$	6.52772	+	62.1071i	0.235702	+	2.24256i
$768$		0			0
$769$	22.4840	+	10.0105i	0.810795	+	0.360989i	0.769892	−	0.638174i	$-0.220310\pi$
$769$	22.4840	+	10.0105i	0.810795	+	0.360989i	0.0409029	+	0.999163i	$0.486977\pi$
$770$	7.29822	+	1.77638i	0.263010	+	0.0640164i
$771$		0			0
$772$	−18.9440	+	8.43440i	−0.681808	+	0.303561i
$773$	17.0063	−	52.3400i	0.611674	−	1.88254i	0.169747	−	0.985488i	$-0.445705\pi$
$773$	17.0063	−	52.3400i	0.611674	−	1.88254i	0.441927	−	0.897051i	$-0.354295\pi$
$774$		0			0
$775$	12.9577	−	4.88094i	0.465456	−	0.175329i
$776$	−13.2568	+	22.9615i	−0.475892	+	0.824270i
$777$		0			0
$778$	0.189362	−	1.80166i	0.00678895	−	0.0645925i
$779$	7.79766	−	74.1898i	0.279380	−	2.65812i
$780$		0			0
$781$	−1.08714	−	10.3434i	−0.0389008	−	0.370116i
$782$	−0.242384			−0.00866763
$783$		0			0
$784$	−3.42190	−	10.5315i	−0.122211	−	0.376126i
$785$	16.8357	+	13.0026i	0.600890	+	0.464082i
$786$		0			0
$787$	23.8278	−	26.4635i	0.849370	−	0.943321i	−0.149597	−	0.988747i	$-0.547798\pi$
$787$	23.8278	−	26.4635i	0.849370	−	0.943321i	0.998968	+	0.0454257i	$0.0144644\pi$
$788$	−27.7675	+	30.8390i	−0.989177	+	1.09859i
$789$		0			0
$790$	−12.6335	−	0.370488i	−0.449480	−	0.0131814i
$791$	0.150565	+	0.463393i	0.00535349	+	0.0164763i
$792$		0			0
$793$	62.4306			2.21698
$794$	−0.895111	−	8.51641i	−0.0317663	−	0.302236i
$795$		0			0
$796$	−0.788242	+	7.49963i	−0.0279385	+	0.265817i
$797$	2.25837	−	21.4870i	0.0799957	−	0.761109i	−0.878834	−	0.477127i	$-0.841678\pi$
$797$	2.25837	−	21.4870i	0.0799957	−	0.761109i	0.958830	−	0.283981i	$-0.0916553\pi$
$798$		0			0
$799$	0.0499513	−	0.0865182i	0.00176715	−	0.00306079i
$800$	−22.2227	−	6.10427i	−0.785691	−	0.215818i
$801$		0			0
$802$	−2.85129	+	8.77538i	−0.100683	+	0.309870i
$803$	−10.9583	+	4.87894i	−0.386709	+	0.172174i
$804$		0			0
$805$	−0.819462	−	10.8473i	−0.0288823	−	0.382316i
$806$	7.12896	+	3.17402i	0.251107	+	0.111800i
$807$		0			0
$808$	−1.75940	−	16.7396i	−0.0618955	−	0.588896i
$809$	5.39556	+	16.6058i	0.189698	+	0.583830i	0.999998	−	0.00218564i	$-0.000695713\pi$
$809$	5.39556	+	16.6058i	0.189698	+	0.583830i	−0.810300	+	0.586016i	$0.800696\pi$
$810$		0			0
$811$	6.07813	−	18.7066i	0.213432	−	0.656876i	−0.785829	−	0.618444i	$-0.787764\pi$
$811$	6.07813	−	18.7066i	0.213432	−	0.656876i	0.999261	−	0.0384326i	$-0.0122365\pi$
$812$	2.32277	+	0.493721i	0.0815134	+	0.0173262i
$813$		0			0
$814$	8.19803	−	1.74255i	0.287341	−	0.0610762i
$815$	−12.0087	−	14.1501i	−0.420647	−	0.495655i
$816$		0			0
$817$	4.85764	+	46.2173i	0.169947	+	1.61694i
$818$	−2.98236			−0.104276
$819$		0			0
$820$	45.7953	+	22.0199i	1.59924	+	0.768967i
$821$	28.8086	−	12.8264i	1.00543	−	0.447645i	0.163100	−	0.986610i	$-0.447851\pi$
$821$	28.8086	−	12.8264i	1.00543	−	0.447645i	0.842329	+	0.538964i	$0.181184\pi$
$822$		0			0
$823$	−23.9485	+	5.09041i	−0.834791	+	0.177440i	−0.605428	−	0.795900i	$-0.706998\pi$
$823$	−23.9485	+	5.09041i	−0.834791	+	0.177440i	−0.229364	+	0.973341i	$0.573665\pi$
$824$	4.17167	+	7.22555i	0.145327	+	0.251714i
$825$		0			0
$826$	3.79683	−	6.57630i	0.132109	−	0.228819i
$827$	14.6947	−	45.2257i	0.510985	−	1.57265i	−0.279484	−	0.960150i	$-0.590164\pi$
$827$	14.6947	−	45.2257i	0.510985	−	1.57265i	0.790470	−	0.612501i	$-0.209836\pi$
$828$		0			0
$829$	−26.8175	−	19.4840i	−0.931409	−	0.676708i	0.0149285	−	0.999889i	$-0.495248\pi$
$829$	−26.8175	−	19.4840i	−0.931409	−	0.676708i	−0.946337	+	0.323180i	$0.895248\pi$
$830$	1.13610	−	3.17654i	0.0394347	−	0.110259i
$831$		0			0
$832$	11.9810	+	20.7517i	0.415366	+	0.719436i
$833$	−0.707763	−	0.315116i	−0.0245225	−	0.0109181i
$834$		0			0
$835$	31.8828	+	0.934991i	1.10335	+	0.0323567i
$836$	14.2638	−	43.8995i	0.493324	−	1.51829i
$837$		0			0
$838$	4.55300	+	14.0127i	0.157281	+	0.484060i
$839$	36.9376	+	41.0234i	1.27523	+	1.41629i	0.862999	+	0.505205i	$0.168583\pi$
$839$	36.9376	+	41.0234i	1.27523	+	1.41629i	0.412230	+	0.911080i	$0.364750\pi$
$840$		0			0
$841$	−19.0385	+	21.1444i	−0.656500	+	0.729118i
$842$	−9.24217	−	4.11488i	−0.318506	−	0.141808i
$843$		0			0
$844$	0.535286	+	5.09291i	0.0184253	+	0.175305i
$845$	29.8719	+	55.4312i	1.02762	+	1.90689i
$846$		0			0
$847$	−10.8360	−	7.87279i	−0.372328	−	0.270512i
$848$	14.2763	+	15.8555i	0.490251	+	0.544479i
$849$		0			0
$850$	−0.372587	+	0.238650i	−0.0127796	+	0.00818563i
$851$	−6.06899	−	10.5118i	−0.208042	−	0.360340i
$852$		0			0
$853$	14.3972	−	6.41003i	0.492949	−	0.219475i	−0.145179	−	0.989405i	$-0.546376\pi$
$853$	14.3972	−	6.41003i	0.492949	−	0.219475i	0.638128	+	0.769930i	$0.279709\pi$
$854$	−6.14158	−	4.46212i	−0.210160	−	0.152690i
$855$		0			0
$856$	9.60604	−	6.97920i	0.328328	−	0.238544i
$857$	14.8902	−	25.7906i	0.508640	−	0.880990i	−0.491310	−	0.870985i	$-0.663482\pi$
$857$	14.8902	−	25.7906i	0.508640	−	0.880990i	0.999950	−	0.0100052i	$-0.00318481\pi$
$858$		0			0
$859$	−1.04331	+	1.15871i	−0.0355972	+	0.0395347i	−0.760680	−	0.649127i	$-0.775135\pi$
$859$	−1.04331	+	1.15871i	−0.0355972	+	0.0395347i	0.725083	+	0.688661i	$0.241801\pi$
$860$	−30.7573	−	7.48631i	−1.04882	−	0.255281i
$861$		0			0
$862$	8.43949	+	1.79387i	0.287450	+	0.0610995i
$863$	2.62898	+	8.09117i	0.0894915	+	0.275427i	0.985779	−	0.168047i	$-0.0537460\pi$
$863$	2.62898	+	8.09117i	0.0894915	+	0.275427i	−0.896287	+	0.443474i	$0.853746\pi$
$864$		0			0
$865$	−43.5244	−	20.9279i	−1.47987	−	0.711571i
$866$	−0.662476	−	0.140814i	−0.0225119	−	0.00478504i
$867$		0			0
$868$	4.44421	+	7.69760i	0.150846	+	0.261273i
$869$	50.6217	+	22.5382i	1.71722	+	0.764558i
$870$		0			0
$871$	0.835655	−	0.372058i	0.0283151	−	0.0126067i
$872$	0.778507	+	0.565618i	0.0263636	+	0.0191543i
$873$		0			0
$874$	7.13657			0.241398
$875$	−11.9398	−	15.8673i	−0.403640	−	0.536413i
$876$		0			0
$877$	−12.4505	+	2.64642i	−0.420422	+	0.0893634i	−0.413265	−	0.910611i	$-0.635612\pi$
$877$	−12.4505	+	2.64642i	−0.420422	+	0.0893634i	−0.00715720	+	0.999974i	$0.502278\pi$
$878$	−0.158700	+	1.50993i	−0.00535587	+	0.0509577i
$879$		0			0
$880$	21.9441	+	16.9480i	0.739737	+	0.571316i
$881$	−3.42753	+	2.49025i	−0.115477	+	0.0838986i	−0.644025	−	0.765005i	$-0.722737\pi$
$881$	−3.42753	+	2.49025i	−0.115477	+	0.0838986i	0.528548	+	0.848903i	$0.322737\pi$
$882$		0			0
$883$	27.7814	−	20.1844i	0.934919	−	0.679258i	−0.0122733	−	0.999925i	$-0.503907\pi$
$883$	27.7814	−	20.1844i	0.934919	−	0.679258i	0.947192	+	0.320666i	$0.103907\pi$
$884$	2.28476	+	0.485641i	0.0768449	+	0.0163339i
$885$		0			0
$886$	9.79613	−	2.08223i	0.329107	−	0.0699539i
$887$	18.8062	−	20.8864i	0.631451	−	0.701297i	−0.339492	−	0.940609i	$-0.610255\pi$
$887$	18.8062	−	20.8864i	0.631451	−	0.701297i	0.970943	+	0.239312i	$0.0769218\pi$
$888$		0			0
$889$	2.94215	+	3.26759i	0.0986766	+	0.109592i
$890$	7.24316	−	7.58489i	0.242791	−	0.254246i
$891$		0			0
$892$	−30.3208	+	22.0294i	−1.01522	+	0.737598i
$893$	−1.47073	+	2.54738i	−0.0492161	+	0.0852448i
$894$		0			0
$895$	40.3596	+	9.82351i	1.34907	+	0.328364i
$896$	2.01601	−	19.1810i	0.0673502	−	0.640794i
$897$		0			0
$898$	−5.83449	−	6.47986i	−0.194700	−	0.216236i
$899$	2.04890			0.0683347
$900$		0			0
$901$	1.49272			0.0497297
$902$	15.9143	+	17.6746i	0.529889	+	0.588501i
$903$		0			0
$904$	0.0479492	−	0.456206i	0.00159477	−	0.0151732i
$905$	−1.51358	+	2.45263i	−0.0503130	+	0.0815281i
$906$		0			0
$907$	20.9176	−	36.2304i	0.694558	−	1.20301i	−0.275771	−	0.961223i	$-0.588933\pi$
$907$	20.9176	−	36.2304i	0.694558	−	1.20301i	0.970329	−	0.241787i	$-0.0777334\pi$
$908$	1.97259	−	1.43317i	0.0654628	−	0.0475615i
$909$		0			0
$910$	1.49558	−	11.0910i	0.0495780	−	0.367664i
$911$	−9.08784	−	10.0931i	−0.301094	−	0.334398i	0.573545	−	0.819174i	$-0.305568\pi$
$911$	−9.08784	−	10.0931i	−0.301094	−	0.334398i	−0.874638	+	0.484776i	$0.838901\pi$
$912$		0			0
$913$	−9.89691	+	10.9916i	−0.327540	+	0.363770i
$914$	−3.30306	+	0.702087i	−0.109255	+	0.0232230i
$915$		0			0
$916$	45.3997	+	9.65001i	1.50005	+	0.318845i
$917$	1.66036	−	1.20632i	0.0548300	−	0.0398363i
$918$		0			0
$919$	−17.5681	+	12.7639i	−0.579517	+	0.421044i	−0.838550	−	0.544825i	$-0.816596\pi$
$919$	−17.5681	+	12.7639i	−0.579517	+	0.421044i	0.259033	+	0.965868i	$0.416596\pi$
$920$	−3.44892	+	9.64320i	−0.113708	+	0.317927i
$921$		0			0
$922$	0.249838	−	2.37705i	0.00822798	−	0.0782840i
$923$	−15.1574	+	3.22180i	−0.498911	+	0.106047i
$924$		0			0
$925$	−19.6790	−	10.1830i	−0.647040	−	0.334814i
$926$	2.59409			0.0852471
$927$		0			0
$928$	−2.75886	−	2.00443i	−0.0905640	−	0.0657986i
$929$	−11.3040	+	5.03285i	−0.370871	+	0.165123i	−0.583705	−	0.811966i	$-0.698397\pi$
$929$	−11.3040	+	5.03285i	−0.370871	+	0.165123i	0.212834	+	0.977088i	$0.431731\pi$
$930$		0			0
$931$	20.8389	+	9.27806i	0.682966	+	0.304076i
$932$	13.7066	+	23.7404i	0.448973	+	0.777644i
$933$		0			0
$934$	−10.5893	−	2.25082i	−0.346491	−	0.0736489i
$935$	1.90849	−	0.347528i	0.0624144	−	0.0113654i
$936$		0			0
$937$	10.4055	+	32.0249i	0.339934	+	1.04621i	0.964241	+	0.265029i	$0.0853815\pi$
$937$	10.4055	+	32.0249i	0.339934	+	1.04621i	−0.624307	+	0.781179i	$0.714619\pi$
$938$	−0.108799	−	0.0231260i	−0.00355242	−	0.000755090i
$939$		0			0
$940$	−1.29647	−	1.52765i	−0.0422862	−	0.0498265i
$941$	4.48924	−	4.98580i	0.146345	−	0.162533i	−0.665516	−	0.746384i	$-0.731788\pi$
$941$	4.48924	−	4.98580i	0.146345	−	0.162533i	0.811861	+	0.583851i	$0.198455\pi$
$942$		0			0
$943$	17.2222	−	29.8297i	0.560831	−	0.971388i
$944$	22.6775	−	16.4761i	0.738089	−	0.536253i
$945$		0			0
$946$	−11.9866	−	8.70876i	−0.389718	−	0.283146i
$947$	−44.0015	+	19.5907i	−1.42986	+	0.636614i	−0.968139	−	0.250412i	$-0.919434\pi$
$947$	−44.0015	+	19.5907i	−1.42986	+	0.636614i	−0.461719	+	0.887026i	$0.652767\pi$
$948$		0			0
$949$	8.93619	+	15.4779i	0.290081	+	0.502435i
$950$	10.9702	−	7.02664i	0.355919	−	0.227974i
$951$		0			0
$952$	−0.400393	−	0.444682i	−0.0129768	−	0.0144122i
$953$	0.957332	+	0.695542i	0.0310110	+	0.0225308i	0.603183	−	0.797603i	$-0.293899\pi$
$953$	0.957332	+	0.695542i	0.0310110	+	0.0225308i	−0.572172	+	0.820134i	$0.693899\pi$
$954$		0			0
$955$	3.40977	−	0.620904i	0.110338	−	0.0200920i
$956$	−2.64637	−	25.1785i	−0.0855896	−	0.814331i
$957$		0			0
$958$	−6.38948	−	2.84478i	−0.206435	−	0.0919106i
$959$	10.0310	−	11.1405i	0.323917	−	0.359746i
$960$		0			0
$961$	−15.6114	−	17.3383i	−0.503595	−	0.559299i
$962$	−3.85885	−	11.8763i	−0.124414	−	0.382908i
$963$		0			0
$964$	12.5647	−	38.6702i	0.404682	−	1.24548i
$965$	20.3079	+	15.6843i	0.653736	+	0.504896i
$966$		0			0
$967$	−21.0610	−	9.37696i	−0.677276	−	0.301543i	0.0391222	−	0.999234i	$-0.487544\pi$
$967$	−21.0610	−	9.37696i	−0.677276	−	0.301543i	−0.716398	+	0.697692i	$0.754211\pi$
$968$	6.30498	+	10.9205i	0.202650	+	0.350999i
$969$		0			0
$970$	15.5660	+	0.456484i	0.499793	+	0.0146568i
$971$	−5.11486	−	3.71616i	−0.164144	−	0.119257i	0.502681	−	0.864472i	$-0.332347\pi$
$971$	−5.11486	−	3.71616i	−0.164144	−	0.119257i	−0.666825	+	0.745215i	$0.732347\pi$
$972$		0			0
$973$	1.91318	−	5.88817i	0.0613338	−	0.188766i
$974$	−6.96469	+	12.0632i	−0.223163	+	0.386530i
$975$		0			0
$976$	−14.0113	−	24.2683i	−0.448490	−	0.776808i
$977$	33.4625	−	7.11267i	1.07056	−	0.227555i	0.361263	−	0.932464i	$-0.382346\pi$
$977$	33.4625	−	7.11267i	1.07056	−	0.227555i	0.709297	+	0.704909i	$0.249012\pi$
$978$		0			0
$979$	−42.0059	+	18.7022i	−1.34251	+	0.597726i
$980$	−10.7311	+	11.2374i	−0.342791	+	0.358964i
$981$		0			0
$982$	9.92146			0.316606
$983$	5.55563	+	52.8583i	0.177197	+	1.68592i	0.616323	+	0.787493i	$0.288622\pi$
$983$	5.55563	+	52.8583i	0.177197	+	1.68592i	−0.439126	+	0.898426i	$0.644712\pi$
$984$		0			0
$985$	49.8925	+	12.1438i	1.58971	+	0.386934i
$986$	−0.0640416	+	0.0136125i	−0.00203950	+	0.000433509i
$987$		0			0
$988$	−67.2709	−	14.2989i	−2.14017	−	0.454908i
$989$	−6.63073	+	20.4073i	−0.210845	+	0.648914i
$990$		0			0
$991$	−13.5962	−	41.8449i	−0.431899	−	1.32925i	−0.896232	−	0.443586i	$-0.853706\pi$
$991$	−13.5962	−	41.8449i	−0.431899	−	1.32925i	0.464333	−	0.885661i	$-0.346294\pi$
$992$	−1.33422	−	12.6943i	−0.0423616	−	0.403044i
$993$		0			0
$994$	1.72137	+	0.766402i	0.0545985	+	0.0243088i
$995$	8.63197	−	3.54379i	0.273652	−	0.112346i
$996$		0			0
$997$	12.5751	−	5.59878i	0.398256	−	0.177315i	−0.197828	−	0.980237i	$-0.563389\pi$
$997$	12.5751	−	5.59878i	0.398256	−	0.177315i	0.596085	+	0.802922i	$0.296722\pi$
$998$	−2.64512	+	8.14084i	−0.0837298	+	0.257694i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.18		224
3.2	odd	2		225.2.q.a.196.11	yes	224
9.4	even	3	inner	675.2.r.a.496.11		224
9.5	odd	6		225.2.q.a.121.18	yes	224
25.6	even	5	inner	675.2.r.a.181.11		224
75.56	odd	10		225.2.q.a.106.18	yes	224
225.31	even	15	inner	675.2.r.a.631.18		224
225.131	odd	30		225.2.q.a.31.11	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.11	✓	224	225.131	odd	30
225.2.q.a.106.18	yes	224	75.56	odd	10
225.2.q.a.121.18	yes	224	9.5	odd	6
225.2.q.a.196.11	yes	224	3.2	odd	2
675.2.r.a.46.18		224	1.1	even	1	trivial
675.2.r.a.181.11		224	25.6	even	5	inner
675.2.r.a.496.11		224	9.4	even	3	inner
675.2.r.a.631.18		224	225.31	even	15	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.293899 + 0.326408i) q^{2} +(0.188891 - 1.79718i) q^{4} +(-2.06853 + 0.849220i) q^{5} +(-0.888066 + 1.53818i) q^{7} +(1.35281 - 0.982874i) q^{8} +O(q^{10})\)	\(q+(0.293899 + 0.326408i) q^{2} +(0.188891 - 1.79718i) q^{4} +(-2.06853 + 0.849220i) q^{5} +(-0.888066 + 1.53818i) q^{7} +(1.35281 - 0.982874i) q^{8} +(-0.885131 - 0.425600i) q^{10} +(2.88123 + 3.19993i) q^{11} +(4.29288 - 4.76773i) q^{13} +(-0.763074 + 0.162196i) q^{14} +(-2.81678 - 0.598725i) q^{16} +(-0.162997 + 0.118424i) q^{17} +(4.79916 - 3.48679i) q^{19} +(1.13548 + 3.87794i) q^{20} +(-0.197692 + 1.88091i) q^{22} +(2.67917 - 0.569475i) q^{23} +(3.55765 - 3.51328i) q^{25} +2.81790 q^{26} +(2.59663 + 1.88657i) q^{28} +(0.675896 - 0.300928i) q^{29} +(2.52989 + 1.12638i) q^{31} +(-2.30458 - 3.99166i) q^{32} +(-0.0865590 - 0.0183987i) q^{34} +(0.530743 - 3.93593i) q^{35} +(-1.36941 - 4.21461i) q^{37} +(2.54858 + 0.541718i) q^{38} +(-1.96365 + 3.18194i) q^{40} +(8.41459 - 9.34535i) q^{41} +(-3.91700 + 6.78444i) q^{43} +(6.29511 - 4.57366i) q^{44} +(0.973285 + 0.707133i) q^{46} +(-0.452987 + 0.201683i) q^{47} +(1.92268 + 3.33017i) q^{49} +(2.19235 + 0.128696i) q^{50} +(-7.75759 - 8.61567i) q^{52} +(-5.99398 - 4.35488i) q^{53} +(-8.67738 - 4.17236i) q^{55} +(0.310448 + 2.95372i) q^{56} +(0.296870 + 0.132175i) q^{58} +(-6.51328 + 7.23373i) q^{59} +(6.51135 + 7.23158i) q^{61} +(0.375873 + 1.15682i) q^{62} +(-1.15416 + 3.55215i) q^{64} +(-4.83111 + 13.5078i) q^{65} +(0.130253 + 0.0579926i) q^{67} +(0.182041 + 0.315304i) q^{68} +(1.44070 - 0.983526i) q^{70} +(-1.95406 - 1.41971i) q^{71} +(-0.860848 + 2.64942i) q^{73} +(0.973212 - 1.68565i) q^{74} +(-5.35988 - 9.28359i) q^{76} +(-7.48079 + 1.59009i) q^{77} +(11.7563 - 5.23422i) q^{79} +(6.33505 - 1.15358i) q^{80} +5.52343 q^{82} +(0.359051 + 3.41614i) q^{83} +(0.236596 - 0.383384i) q^{85} +(-3.36569 + 0.715400i) q^{86} +(7.04289 + 1.49701i) q^{88} +(-3.29985 + 10.1559i) q^{89} +(3.52124 + 10.8373i) q^{91} +(-0.517378 - 4.92252i) q^{92} +(-0.198963 - 0.0885841i) q^{94} +(-6.96616 + 11.2881i) q^{95} +(-14.4851 + 6.44917i) q^{97} +(-0.521922 + 1.60631i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

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