LMFDB - Embedded newform 693.2.m.i.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.3
Root			$0.435488 - 1.34029i$ of defining polynomial
Character	$\chi$	$=$	693.64
Dual form			693.2.m.i.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.435488 - 1.34029i) q^{2} +(0.0112975 + 0.00820814i) q^{4} +(0.565930 + 1.74175i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(2.29616 - 1.66826i) q^{8} +O(q^{10})$	\(q+(0.435488 - 1.34029i) q^{2} +(0.0112975 + 0.00820814i) q^{4} +(0.565930 + 1.74175i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(2.29616 - 1.66826i) q^{8} +2.58091 q^{10} +(2.26009 - 2.42734i) q^{11} +(-1.43602 + 4.41961i) q^{13} +(-1.14012 + 0.828347i) q^{14} +(-1.22738 - 3.77748i) q^{16} +(1.69039 + 5.20248i) q^{17} +(4.69325 - 3.40985i) q^{19} +(-0.00790293 + 0.0243227i) q^{20} +(-2.26911 - 4.08626i) q^{22} +0.719682 q^{23} +(1.33166 - 0.967509i) q^{25} +(5.29821 + 3.84937i) q^{26} +(-0.00431527 - 0.0132810i) q^{28} +(-0.948551 - 0.689163i) q^{29} +(-0.404153 + 1.24385i) q^{31} +0.0789938 q^{32} +7.70900 q^{34} +(0.565930 - 1.74175i) q^{35} +(-1.69468 - 1.23126i) q^{37} +(-2.52634 - 7.77528i) q^{38} +(4.20516 + 3.05523i) q^{40} +(-0.741582 + 0.538791i) q^{41} +8.02379 q^{43} +(0.0454574 - 0.00887181i) q^{44} +(0.313413 - 0.964586i) q^{46} +(4.83455 - 3.51251i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-0.716823 - 2.20615i) q^{50} +(-0.0525003 + 0.0381437i) q^{52} +(-3.13496 + 9.64840i) q^{53} +(5.50688 + 2.56282i) q^{55} -2.83822 q^{56} +(-1.33676 + 0.971215i) q^{58} +(-6.21390 - 4.51466i) q^{59} +(-1.93943 - 5.96895i) q^{61} +(1.49113 + 1.08337i) q^{62} +(2.48916 - 7.66083i) q^{64} -8.51056 q^{65} -15.4673 q^{67} +(-0.0236055 + 0.0726501i) q^{68} +(-2.08800 - 1.51702i) q^{70} +(-4.29593 - 13.2215i) q^{71} +(-4.86593 - 3.53531i) q^{73} +(-2.38826 + 1.73517i) q^{74} +0.0810106 q^{76} +(-3.25521 + 0.635311i) q^{77} +(-4.83332 + 14.8754i) q^{79} +(5.88482 - 4.27557i) q^{80} +(0.399188 + 1.22857i) q^{82} +(1.35217 + 4.16157i) q^{83} +(-8.10479 + 5.88848i) q^{85} +(3.49426 - 10.7542i) q^{86} +(1.14011 - 9.34400i) q^{88} -15.3437 q^{89} +(3.75955 - 2.73147i) q^{91} +(0.00813063 + 0.00590725i) q^{92} +(-2.60240 - 8.00937i) q^{94} +(8.59515 + 6.24474i) q^{95} +(0.745114 - 2.29323i) q^{97} +1.40927 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	$ 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.435488	−	1.34029i	0.307936	−	0.947730i	−0.670629	−	0.741793i	$-0.733976\pi$
$2$	0.435488	−	1.34029i	0.307936	−	0.947730i	0.978565	−	0.205937i	$-0.0660243\pi$
$3$		0			0
$3$		0			0
$4$	0.0112975	+	0.00820814i	0.00564876	+	0.00410407i
$5$	0.565930	+	1.74175i	0.253091	+	0.778935i	0.994200	+	0.107550i	$0.0343005\pi$
$5$	0.565930	+	1.74175i	0.253091	+	0.778935i	−0.741108	+	0.671385i	$0.765700\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	2.29616	−	1.66826i	0.811817	−	0.589819i
$9$		0			0
$10$	2.58091			0.816157
$11$	2.26009	−	2.42734i	0.681444	−	0.731871i
$11$	2.26009	−	2.42734i	0.681444	−	0.731871i
$12$		0			0
$13$	−1.43602	+	4.41961i	−0.398280	+	1.22578i	0.528097	+	0.849184i	$0.322906\pi$
$13$	−1.43602	+	4.41961i	−0.398280	+	1.22578i	−0.926377	+	0.376596i	$0.877094\pi$
$14$	−1.14012	+	0.828347i	−0.304710	+	0.221385i
$15$		0			0
$16$	−1.22738	−	3.77748i	−0.306844	−	0.944370i
$17$	1.69039	+	5.20248i	0.409980	+	1.26179i	0.916665	+	0.399656i	$0.130871\pi$
$17$	1.69039	+	5.20248i	0.409980	+	1.26179i	−0.506685	+	0.862131i	$0.669129\pi$
$18$		0			0
$19$	4.69325	−	3.40985i	1.07671	−	0.782272i	0.0995999	−	0.995028i	$-0.468244\pi$
$19$	4.69325	−	3.40985i	1.07671	−	0.782272i	0.977106	+	0.212755i	$0.0682437\pi$
$20$	−0.00790293	+	0.0243227i	−0.00176715	+	0.00543873i
$21$		0			0
$22$	−2.26911	−	4.08626i	−0.483775	−	0.871194i
$23$	0.719682			0.150064			0.0750321	−	0.997181i	$-0.476094\pi$
$23$	0.719682			0.150064			0.0750321	+	0.997181i	$0.476094\pi$
$24$		0			0
$25$	1.33166	−	0.967509i	0.266332	−	0.193502i
$26$	5.29821	+	3.84937i	1.03906	+	0.754924i
$27$		0			0
$28$	−0.00431527	−	0.0132810i	−0.000815510	−	0.00250988i
$29$	−0.948551	−	0.689163i	−0.176142	−	0.127974i	0.496221	−	0.868196i	$-0.334720\pi$
$29$	−0.948551	−	0.689163i	−0.176142	−	0.127974i	−0.672363	+	0.740222i	$0.734720\pi$
$30$		0			0
$31$	−0.404153	+	1.24385i	−0.0725879	+	0.223403i	−0.980768	−	0.195177i	$-0.937472\pi$
$31$	−0.404153	+	1.24385i	−0.0725879	+	0.223403i	0.908180	+	0.418580i	$0.137472\pi$
$32$	0.0789938			0.0139643
$33$		0			0
$34$	7.70900			1.32208
$35$	0.565930	−	1.74175i	0.0956595	−	0.294410i
$36$		0			0
$37$	−1.69468	−	1.23126i	−0.278604	−	0.202417i	0.439705	−	0.898142i	$-0.355083\pi$
$37$	−1.69468	−	1.23126i	−0.278604	−	0.202417i	−0.718308	+	0.695725i	$0.755083\pi$
$38$	−2.52634	−	7.77528i	−0.409827	−	1.26132i
$39$		0			0
$40$	4.20516	+	3.05523i	0.664895	+	0.483074i
$41$	−0.741582	+	0.538791i	−0.115816	+	0.0841449i	−0.644185	−	0.764869i	$-0.722803\pi$
$41$	−0.741582	+	0.538791i	−0.115816	+	0.0841449i	0.528370	+	0.849014i	$0.322803\pi$
$42$		0			0
$43$	8.02379			1.22362			0.611808	−	0.791006i	$-0.290442\pi$
$43$	8.02379			1.22362			0.611808	+	0.791006i	$0.290442\pi$
$44$	0.0454574	−	0.00887181i	0.00685296	−	0.00133748i
$45$		0			0
$46$	0.313413	−	0.964586i	0.0462102	−	0.142220i
$47$	4.83455	−	3.51251i	0.705192	−	0.512352i	−0.176427	−	0.984314i	$-0.556454\pi$
$47$	4.83455	−	3.51251i	0.705192	−	0.512352i	0.881619	+	0.471962i	$0.156454\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.716823	−	2.20615i	−0.101374	−	0.311997i
$51$		0			0
$52$	−0.0525003	+	0.0381437i	−0.00728048	+	0.00528958i
$53$	−3.13496	+	9.64840i	−0.430619	+	1.32531i	0.466890	+	0.884315i	$0.345374\pi$
$53$	−3.13496	+	9.64840i	−0.430619	+	1.32531i	−0.897510	+	0.440995i	$0.854626\pi$
$54$		0			0
$55$	5.50688	+	2.56282i	0.742547	+	0.345570i
$56$	−2.83822			−0.379272
$57$		0			0
$58$	−1.33676	+	0.971215i	−0.175526	+	0.127527i
$59$	−6.21390	−	4.51466i	−0.808981	−	0.587759i	0.104554	−	0.994519i	$-0.466659\pi$
$59$	−6.21390	−	4.51466i	−0.808981	−	0.587759i	−0.913535	+	0.406760i	$0.866659\pi$
$60$		0			0
$61$	−1.93943	−	5.96895i	−0.248318	−	0.764246i	−0.995073	−	0.0991458i	$-0.968389\pi$
$61$	−1.93943	−	5.96895i	−0.248318	−	0.764246i	0.746754	−	0.665100i	$-0.231611\pi$
$62$	1.49113	+	1.08337i	0.189373	+	0.137588i
$63$		0			0
$64$	2.48916	−	7.66083i	0.311144	−	0.957604i
$65$	−8.51056			−1.05560
$66$		0			0
$67$	−15.4673			−1.88963			−0.944814	−	0.327608i	$-0.893758\pi$
$67$	−15.4673			−1.88963			−0.944814	+	0.327608i	$0.893758\pi$
$68$	−0.0236055	+	0.0726501i	−0.00286258	+	0.00881012i
$69$		0			0
$70$	−2.08800	−	1.51702i	−0.249564	−	0.181319i
$71$	−4.29593	−	13.2215i	−0.509833	−	1.56910i	−0.792491	−	0.609883i	$-0.791216\pi$
$71$	−4.29593	−	13.2215i	−0.509833	−	1.56910i	0.282659	−	0.959221i	$-0.408784\pi$
$72$		0			0
$73$	−4.86593	−	3.53531i	−0.569514	−	0.413776i	0.265414	−	0.964134i	$-0.414491\pi$
$73$	−4.86593	−	3.53531i	−0.569514	−	0.413776i	−0.834929	+	0.550358i	$0.814491\pi$
$74$	−2.38826	+	1.73517i	−0.277629	+	0.201709i
$75$		0			0
$76$	0.0810106			0.00929255
$77$	−3.25521	+	0.635311i	−0.370965	+	0.0724004i
$78$		0			0
$79$	−4.83332	+	14.8754i	−0.543791	+	1.67362i	0.180058	+	0.983656i	$0.442372\pi$
$79$	−4.83332	+	14.8754i	−0.543791	+	1.67362i	−0.723848	+	0.689959i	$0.757628\pi$
$80$	5.88482	−	4.27557i	0.657943	−	0.478024i
$81$		0			0
$82$	0.399188	+	1.22857i	0.0440829	+	0.135673i
$83$	1.35217	+	4.16157i	0.148420	+	0.456791i	0.997435	−	0.0715783i	$-0.0228036\pi$
$83$	1.35217	+	4.16157i	0.148420	+	0.456791i	−0.849015	+	0.528370i	$0.822804\pi$
$84$		0			0
$85$	−8.10479	+	5.88848i	−0.879088	+	0.638695i
$86$	3.49426	−	10.7542i	0.376796	−	1.15966i
$87$		0			0
$88$	1.14011	−	9.34400i	0.121536	−	0.996073i
$89$	−15.3437			−1.62643			−0.813215	−	0.581963i	$-0.802285\pi$
$89$	−15.3437			−1.62643			−0.813215	+	0.581963i	$0.802285\pi$
$90$		0			0
$91$	3.75955	−	2.73147i	0.394108	−	0.286336i
$92$	0.00813063	+	0.00590725i	0.000847677	+	0.000615873i
$93$		0			0
$94$	−2.60240	−	8.00937i	−0.268417	−	0.826104i
$95$	8.59515	+	6.24474i	0.881844	+	0.640697i
$96$		0			0
$97$	0.745114	−	2.29323i	0.0756549	−	0.232842i	−0.906077	−	0.423114i	$-0.860937\pi$
$97$	0.745114	−	2.29323i	0.0756549	−	0.232842i	0.981731	+	0.190272i	$0.0609370\pi$
$98$	1.40927			0.142358
$99$		0			0
$100$	0.0229859			0.00229859
$101$	−3.67603	+	11.3136i	−0.365778	+	1.12575i	0.583714	+	0.811959i	$0.301599\pi$
$101$	−3.67603	+	11.3136i	−0.365778	+	1.12575i	−0.949492	+	0.313790i	$0.898401\pi$
$102$		0			0
$103$	−0.320625	−	0.232947i	−0.0315921	−	0.0229530i	0.571877	−	0.820339i	$-0.306215\pi$
$103$	−0.320625	−	0.232947i	−0.0315921	−	0.0229530i	−0.603469	+	0.797386i	$0.706215\pi$
$104$	4.07573	+	12.5438i	0.399658	+	1.23002i
$105$		0			0
$106$	11.5665	+	8.40352i	1.12343	+	0.816222i
$107$	−2.64496	+	1.92168i	−0.255698	+	0.185776i	−0.708248	−	0.705963i	$-0.750514\pi$
$107$	−2.64496	+	1.92168i	−0.255698	+	0.185776i	0.452550	+	0.891739i	$0.350514\pi$
$108$		0			0
$109$	−2.84638			−0.272634			−0.136317	−	0.990665i	$-0.543527\pi$
$109$	−2.84638			−0.272634			−0.136317	+	0.990665i	$0.543527\pi$
$110$	5.83310	−	6.26476i	0.556165	−	0.597321i
$111$		0			0
$112$	−1.22738	+	3.77748i	−0.115976	+	0.356938i
$113$	11.7668	−	8.54906i	1.10692	−	0.804228i	0.124748	−	0.992188i	$-0.460188\pi$
$113$	11.7668	−	8.54906i	1.10692	−	0.804228i	0.982177	+	0.187961i	$0.0601878\pi$
$114$		0			0
$115$	0.407290	+	1.25351i	0.0379799	+	0.116890i
$116$	−0.00505954	−	0.0155717i	−0.000469767	−	0.00144579i
$117$		0			0
$118$	−8.75705	+	6.36237i	−0.806152	+	0.585704i
$119$	1.69039	−	5.20248i	0.154958	−	0.476911i
$120$		0			0
$121$	−0.783964	−	10.9720i	−0.0712695	−	0.997457i
$122$	−8.84474			−0.800765
$123$		0			0
$124$	−0.0147756	+	0.0107351i	−0.00132689	+	0.000964044i
$125$	9.84690	+	7.15419i	0.880734	+	0.639890i
$126$		0			0
$127$	1.55524	+	4.78655i	0.138006	+	0.424737i	0.996045	−	0.0888458i	$-0.0283178\pi$
$127$	1.55524	+	4.78655i	0.138006	+	0.424737i	−0.858040	+	0.513583i	$0.828318\pi$
$128$	−9.05595	−	6.57953i	−0.800440	−	0.581554i
$129$		0			0
$130$	−3.70624	+	11.4066i	−0.325059	+	1.00043i
$131$	0.180053			0.0157313			0.00786565	−	0.999969i	$-0.497496\pi$
$131$	0.180053			0.0157313			0.00786565	+	0.999969i	$0.497496\pi$
$132$		0			0
$133$	−5.80118			−0.503026
$134$	−6.73581	+	20.7307i	−0.581885	+	1.79086i
$135$		0			0
$136$	12.5605	+	9.12574i	1.07705	+	0.782526i
$137$	−2.57224	−	7.91655i	−0.219762	−	0.676357i	−0.998781	−	0.0493570i	$-0.984283\pi$
$137$	−2.57224	−	7.91655i	−0.219762	−	0.676357i	0.779020	−	0.627000i	$-0.215717\pi$
$138$		0			0
$139$	5.63172	+	4.09169i	0.477677	+	0.347052i	0.800425	−	0.599432i	$-0.204607\pi$
$139$	5.63172	+	4.09169i	0.477677	+	0.347052i	−0.322749	+	0.946485i	$0.604607\pi$
$140$	0.0206901	−	0.0150323i	0.00174864	−	0.00127046i
$141$		0			0
$142$	−19.5915			−1.64408
$143$	7.48237	+	13.4744i	0.625707	+	1.12679i
$144$		0			0
$145$	0.663538	−	2.04216i	0.0551038	−	0.169592i
$146$	−6.85740	+	4.98219i	−0.567523	+	0.412329i
$147$		0			0
$148$	−0.00903937	−	0.0278203i	−0.000743031	−	0.00228682i
$149$	0.993277	+	3.05699i	0.0813724	+	0.250439i	0.983463	−	0.181108i	$-0.0579682\pi$
$149$	0.993277	+	3.05699i	0.0813724	+	0.250439i	−0.902091	+	0.431546i	$0.857968\pi$
$150$		0			0
$151$	−18.0144	+	13.0882i	−1.46599	+	1.06510i	−0.484239	+	0.874936i	$0.660903\pi$
$151$	−18.0144	+	13.0882i	−1.46599	+	1.06510i	−0.981752	+	0.190168i	$0.939097\pi$
$152$	5.08796	−	15.6591i	0.412688	−	1.27012i
$153$		0			0
$154$	−0.566100	+	4.63960i	−0.0456177	+	0.373870i
$155$	−2.39521			−0.192388
$156$		0			0
$157$	−10.7233	+	7.79096i	−0.855816	+	0.621786i	−0.926743	−	0.375695i	$-0.877404\pi$
$157$	−10.7233	+	7.79096i	−0.855816	+	0.621786i	0.0709277	+	0.997481i	$0.477404\pi$
$158$	17.8326	+	12.9561i	1.41868	+	1.03073i
$159$		0			0
$160$	0.0447049	+	0.137588i	0.00353423	+	0.0108773i
$161$	−0.582235	−	0.423019i	−0.0458866	−	0.0333385i
$162$		0			0
$163$	4.23920	−	13.0469i	0.332040	−	1.02191i	−0.636122	−	0.771589i	$-0.719462\pi$
$163$	4.23920	−	13.0469i	0.332040	−	1.02191i	0.968162	−	0.250325i	$-0.0805375\pi$
$164$	−0.0128005			−0.000999552
$165$		0			0
$166$	6.16657			0.478619
$167$	−2.87651	+	8.85300i	−0.222591	+	0.685066i	0.775936	+	0.630812i	$0.217278\pi$
$167$	−2.87651	+	8.85300i	−0.222591	+	0.685066i	−0.998527	+	0.0542539i	$0.982722\pi$
$168$		0			0
$169$	−6.95361	−	5.05209i	−0.534893	−	0.388623i
$170$	4.36275	+	13.4272i	0.334608	+	1.02982i
$171$		0			0
$172$	0.0906490	+	0.0658604i	0.00691192	+	0.00502181i
$173$	8.49927	−	6.17508i	0.646188	−	0.469483i	−0.215783	−	0.976441i	$-0.569230\pi$
$173$	8.49927	−	6.17508i	0.646188	−	0.469483i	0.861970	+	0.506959i	$0.169230\pi$
$174$		0			0
$175$	−1.64602			−0.124428
$176$	−11.9432	−	5.55819i	−0.900254	−	0.418964i
$177$		0			0
$178$	−6.68200	+	20.5651i	−0.500837	+	1.54142i
$179$	−6.73370	+	4.89232i	−0.503300	+	0.365669i	−0.810276	−	0.586048i	$-0.800683\pi$
$179$	−6.73370	+	4.89232i	−0.503300	+	0.365669i	0.306976	+	0.951717i	$0.400683\pi$
$180$		0			0
$181$	−4.57437	−	14.0785i	−0.340010	−	1.04644i	−0.964201	−	0.265172i	$-0.914571\pi$
$181$	−4.57437	−	14.0785i	−0.340010	−	1.04644i	0.624191	−	0.781272i	$-0.285429\pi$
$182$	−2.02374	−	6.22842i	−0.150009	−	0.461681i
$183$		0			0
$184$	1.65251	−	1.20062i	0.121825	−	0.0885107i
$185$	1.18547	−	3.64852i	0.0871578	−	0.268244i
$186$		0			0
$187$	16.4486	+	7.65494i	1.20284	+	0.559785i
$188$	0.0834496			0.00608619
$189$		0			0
$190$	12.1129	−	8.80052i	0.878760	−	0.638457i
$191$	−7.77203	−	5.64671i	−0.562364	−	0.408582i	0.269959	−	0.962872i	$-0.412990\pi$
$191$	−7.77203	−	5.64671i	−0.562364	−	0.408582i	−0.832324	+	0.554290i	$0.812990\pi$
$192$		0			0
$193$	−0.459758	−	1.41499i	−0.0330941	−	0.101853i	0.933145	−	0.359500i	$-0.117053\pi$
$193$	−0.459758	−	1.41499i	−0.0330941	−	0.101853i	−0.966239	+	0.257647i	$0.917053\pi$
$194$	−2.74911	−	1.99734i	−0.197374	−	0.143401i
$195$		0			0
$196$	−0.00431527	+	0.0132810i	−0.000308234	+	0.000948646i
$197$	14.0434			1.00055			0.500274	−	0.865867i	$-0.333233\pi$
$197$	14.0434			1.00055			0.500274	+	0.865867i	$0.333233\pi$
$198$		0			0
$199$	−4.28729			−0.303918			−0.151959	−	0.988387i	$-0.548558\pi$
$199$	−4.28729			−0.303918			−0.151959	+	0.988387i	$0.548558\pi$
$200$	1.44366	−	4.44312i	0.102082	−	0.314176i
$201$		0			0
$202$	13.5627	+	9.85391i	0.954271	+	0.693318i
$203$	0.362314	+	1.11509i	0.0254295	+	0.0782639i
$204$		0			0
$205$	−1.35812	−	0.986734i	−0.0948554	−	0.0689165i
$206$	−0.451846	+	0.328285i	−0.0314816	+	0.0228727i
$207$		0			0
$208$	18.4575			1.27980
$209$	2.33032	−	19.0987i	0.161192	−	1.32108i
$210$		0			0
$211$	−0.449704	+	1.38405i	−0.0309589	+	0.0952816i	−0.965342	−	0.260988i	$-0.915952\pi$
$211$	−0.449704	+	1.38405i	−0.0309589	+	0.0952816i	0.934383	+	0.356270i	$0.115952\pi$
$212$	−0.114613	+	0.0832710i	−0.00787163	+	0.00571907i
$213$		0			0
$214$	1.42376	+	4.38189i	0.0973264	+	0.299540i
$215$	4.54090	+	13.9755i	0.309687	+	0.953118i
$216$		0			0
$217$	1.05809	−	0.768744i	0.0718275	−	0.0521857i
$218$	−1.23957	+	3.81499i	−0.0839540	+	0.258384i
$219$		0			0
$220$	0.0411782	+	0.0741547i	0.00277623	+	0.00499951i
$221$	−25.4204			−1.70996
$222$		0			0
$223$	3.92893	−	2.85453i	0.263101	−	0.191154i	−0.448412	−	0.893827i	$-0.648010\pi$
$223$	3.92893	−	2.85453i	0.263101	−	0.191154i	0.711513	+	0.702673i	$0.248010\pi$
$224$	−0.0639073	−	0.0464314i	−0.00426999	−	0.00310233i
$225$		0			0
$226$	−6.33396	−	19.4939i	−0.421329	−	1.29672i
$227$	0.321296	+	0.233435i	0.0213252	+	0.0154936i	0.598397	−	0.801200i	$-0.295805\pi$
$227$	0.321296	+	0.233435i	0.0213252	+	0.0154936i	−0.577072	+	0.816694i	$0.695805\pi$
$228$		0			0
$229$	0.676634	−	2.08246i	0.0447132	−	0.137613i	−0.926208	−	0.377014i	$-0.876951\pi$
$229$	0.676634	−	2.08246i	0.0447132	−	0.137613i	0.970921	+	0.239401i	$0.0769509\pi$
$230$	1.85744			0.122476
$231$		0			0
$232$	−3.32773			−0.218476
$233$	0.389410	−	1.19848i	0.0255111	−	0.0785150i	−0.937490	−	0.348011i	$-0.886857\pi$
$233$	0.389410	−	1.19848i	0.0255111	−	0.0785150i	0.963001	+	0.269496i	$0.0868571\pi$
$234$		0			0
$235$	8.85393	+	6.43276i	0.577567	+	0.419627i
$236$	−0.0331448	−	0.102009i	−0.00215754	−	0.00664023i
$237$		0			0
$238$	−6.23671	−	4.53123i	−0.404266	−	0.293716i
$239$	−9.02997	+	6.56066i	−0.584100	+	0.424374i	−0.840200	−	0.542277i	$-0.817562\pi$
$239$	−9.02997	+	6.56066i	−0.584100	+	0.424374i	0.256100	+	0.966650i	$0.417562\pi$
$240$		0			0
$241$	−21.4843			−1.38392			−0.691962	−	0.721934i	$-0.743254\pi$
$241$	−21.4843			−1.38392			−0.691962	+	0.721934i	$0.743254\pi$
$242$	−15.0471	−	3.72744i	−0.967267	−	0.239609i
$243$		0			0
$244$	0.0270832	−	0.0833535i	0.00173382	−	0.00533616i
$245$	−1.48162	+	1.07646i	−0.0946574	+	0.0687726i
$246$		0			0
$247$	8.33060	+	25.6390i	0.530063	+	1.63137i
$248$	1.14707	+	3.53032i	0.0728391	+	0.224176i
$249$		0			0
$250$	13.8769	−	10.0822i	0.877653	−	0.637652i
$251$	0.130968	−	0.403077i	0.00826660	−	0.0254420i	−0.946838	−	0.321710i	$-0.895742\pi$
$251$	0.130968	−	0.403077i	0.00826660	−	0.0254420i	0.955105	+	0.296268i	$0.0957423\pi$
$252$		0			0
$253$	1.62655	−	1.74691i	0.102260	−	0.109828i
$254$	7.09267			0.445033
$255$		0			0
$256$	0.271127	−	0.196986i	0.0169455	−	0.0123116i
$257$	14.1093	+	10.2510i	0.880115	+	0.639441i	0.933282	−	0.359145i	$-0.116932\pi$
$257$	14.1093	+	10.2510i	0.880115	+	0.639441i	−0.0531672	+	0.998586i	$0.516932\pi$
$258$		0			0
$259$	0.647310	+	1.99221i	0.0402219	+	0.123790i
$260$	−0.0961483	−	0.0698558i	−0.00596286	−	0.00433227i
$261$		0			0
$262$	0.0784109	−	0.241324i	0.00484424	−	0.0149090i
$263$	−1.51519			−0.0934307			−0.0467153	−	0.998908i	$-0.514875\pi$
$263$	−1.51519			−0.0934307			−0.0467153	+	0.998908i	$0.514875\pi$
$264$		0			0
$265$	−18.5793			−1.14132
$266$	−2.52634	+	7.77528i	−0.154900	+	0.476733i
$267$		0			0
$268$	−0.174742	−	0.126957i	−0.0106741	−	0.00775516i
$269$	0.627622	+	1.93162i	0.0382668	+	0.117773i	0.968365	−	0.249538i	$-0.0802786\pi$
$269$	0.627622	+	1.93162i	0.0382668	+	0.117773i	−0.930098	+	0.367311i	$0.880279\pi$
$270$		0			0
$271$	−6.15212	−	4.46978i	−0.373715	−	0.271520i	0.385035	−	0.922902i	$-0.374189\pi$
$271$	−6.15212	−	4.46978i	−0.373715	−	0.271520i	−0.758750	+	0.651382i	$0.774189\pi$
$272$	17.5775	−	12.7708i	1.06579	−	0.774344i
$273$		0			0
$274$	−11.7307			−0.708676
$275$	0.661205	−	5.41905i	0.0398722	−	0.326781i
$276$		0			0
$277$	4.45813	−	13.7207i	0.267863	−	0.824398i	−0.723157	−	0.690684i	$-0.757310\pi$
$277$	4.45813	−	13.7207i	0.267863	−	0.824398i	0.991020	−	0.133714i	$-0.0426903\pi$
$278$	7.93661	−	5.76628i	0.476006	−	0.345839i
$279$		0			0
$280$	−1.60623	−	4.94347i	−0.0959906	−	0.295429i
$281$	−5.48494	−	16.8809i	−0.327204	−	1.00703i	−0.970436	−	0.241359i	$-0.922407\pi$
$281$	−5.48494	−	16.8809i	−0.327204	−	1.00703i	0.643232	−	0.765672i	$-0.277593\pi$
$282$		0			0
$283$	25.1897	−	18.3014i	1.49737	−	1.08790i	0.525956	−	0.850512i	$-0.323708\pi$
$283$	25.1897	−	18.3014i	1.49737	−	1.08790i	0.971414	−	0.237392i	$-0.0762924\pi$
$284$	0.0599905	−	0.184632i	0.00355978	−	0.0109559i
$285$		0			0
$286$	21.3182	−	4.16062i	1.26057	−	0.246022i
$287$	0.916645			0.0541079
$288$		0			0
$289$	−10.4551	+	7.59609i	−0.615007	+	0.446829i
$290$	−2.44813	−	1.77867i	−0.143759	−	0.104447i
$291$		0			0
$292$	−0.0259547	−	0.0798805i	−0.00151889	−	0.00467465i
$293$	−19.4409	−	14.1247i	−1.13575	−	0.825171i	−0.149229	−	0.988803i	$-0.547679\pi$
$293$	−19.4409	−	14.1247i	−1.13575	−	0.825171i	−0.986522	+	0.163632i	$0.947679\pi$
$294$		0			0
$295$	4.34679	−	13.3781i	0.253080	−	0.778901i
$296$	−5.94532			−0.345565
$297$		0			0
$298$	4.52983			0.262406
$299$	−1.03348	+	3.18072i	−0.0597676	+	0.183946i
$300$		0			0
$301$	−6.49138	−	4.71627i	−0.374157	−	0.271841i
$302$	9.69701	+	29.8443i	0.558000	+	1.71735i
$303$		0			0
$304$	−18.6410	−	13.5435i	−1.06914	−	0.776772i
$305$	9.29885	−	6.75601i	0.532450	−	0.386848i
$306$		0			0
$307$	−5.46298			−0.311789			−0.155894	−	0.987774i	$-0.549826\pi$
$307$	−5.46298			−0.311789			−0.155894	+	0.987774i	$0.549826\pi$
$308$	−0.0419905	−	0.0195417i	−0.00239263	−	0.00111349i
$309$		0			0
$310$	−1.04308	+	3.21028i	−0.0592431	+	0.182332i
$311$	11.2360	−	8.16342i	0.637134	−	0.462905i	−0.221730	−	0.975108i	$-0.571170\pi$
$311$	11.2360	−	8.16342i	0.637134	−	0.462905i	0.858864	+	0.512203i	$0.171170\pi$
$312$		0			0
$313$	8.48207	+	26.1051i	0.479435	+	1.47555i	0.839882	+	0.542770i	$0.182624\pi$
$313$	8.48207	+	26.1051i	0.479435	+	1.47555i	−0.360447	+	0.932780i	$0.617376\pi$
$314$	5.77229	+	17.7653i	0.325749	+	1.00255i
$315$		0			0
$316$	−0.176704	+	0.128383i	−0.00994038	+	0.00722211i
$317$	−2.41828	+	7.44269i	−0.135824	+	0.418023i	−0.995717	−	0.0924507i	$-0.970530\pi$
$317$	−2.41828	+	7.44269i	−0.135824	+	0.418023i	0.859893	+	0.510474i	$0.170530\pi$
$318$		0			0
$319$	−3.81665	+	0.744885i	−0.213691	+	0.0417056i
$320$	14.7520			0.824659
$321$		0			0
$322$	−0.820525	+	0.596147i	−0.0457261	+	0.0332220i
$323$	25.6731	+	18.6526i	1.42849	+	1.03786i
$324$		0			0
$325$	2.36372	+	7.27479i	0.131116	+	0.403533i
$326$	−15.6406	−	11.3635i	−0.866252	−	0.629369i
$327$		0			0
$328$	−0.803950	+	2.47430i	−0.0443907	+	0.136621i
$329$	−5.97584			−0.329458
$330$		0			0
$331$	−28.1462			−1.54705			−0.773527	−	0.633764i	$-0.781509\pi$
$331$	−28.1462			−1.54705			−0.773527	+	0.633764i	$0.781509\pi$
$332$	−0.0188825	+	0.0581143i	−0.00103631	+	0.00318943i
$333$		0			0
$334$	10.6129	+	7.71075i	0.580714	+	0.421913i
$335$	−8.75338	−	26.9401i	−0.478248	−	1.47190i
$336$		0			0
$337$	20.2084	+	14.6823i	1.10082	+	0.799793i	0.981194	−	0.193025i	$-0.0618300\pi$
$337$	20.2084	+	14.6823i	1.10082	+	0.799793i	0.119628	+	0.992819i	$0.461830\pi$
$338$	−9.79950	+	7.11975i	−0.533022	+	0.387263i
$339$		0			0
$340$	−0.139898			−0.00758701
$341$	2.10583	+	3.79224i	0.114037	+	0.205361i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	18.4239	−	13.3858i	0.993352	−	0.721713i
$345$		0			0
$346$	−4.57509	−	14.0807i	−0.245959	−	0.756983i
$347$	−6.38096	−	19.6386i	−0.342548	−	1.05425i	−0.962883	−	0.269918i	$-0.913003\pi$
$347$	−6.38096	−	19.6386i	−0.342548	−	1.05425i	0.620335	−	0.784337i	$-0.286997\pi$
$348$		0			0
$349$	4.85185	−	3.52507i	0.259713	−	0.188693i	−0.450307	−	0.892874i	$-0.648686\pi$
$349$	4.85185	−	3.52507i	0.259713	−	0.188693i	0.710021	+	0.704181i	$0.248686\pi$
$350$	−0.716823	+	2.20615i	−0.0383158	+	0.117924i
$351$		0			0
$352$	0.178533	−	0.191745i	0.00951585	−	0.0102200i
$353$	−24.0382			−1.27942			−0.639712	−	0.768615i	$-0.720946\pi$
$353$	−24.0382			−1.27942			−0.639712	+	0.768615i	$0.720946\pi$
$354$		0			0
$355$	20.5974	−	14.9649i	1.09320	−	0.794253i
$356$	−0.173346	−	0.125943i	−0.00918732	−	0.00667498i
$357$		0			0
$358$	3.62470	+	11.1557i	0.191571	+	0.589596i
$359$	−8.85883	−	6.43632i	−0.467551	−	0.339696i	0.328935	−	0.944353i	$-0.393310\pi$
$359$	−8.85883	−	6.43632i	−0.467551	−	0.339696i	−0.796486	+	0.604657i	$0.793310\pi$
$360$		0			0
$361$	4.52822	−	13.9364i	0.238328	−	0.733497i
$362$	−20.8613			−1.09645
$363$		0			0
$364$	0.0648939			0.00340136
$365$	3.40385	−	10.4760i	0.178166	−	0.548338i
$366$		0			0
$367$	−8.58995	−	6.24096i	−0.448392	−	0.325776i	0.340569	−	0.940220i	$-0.389380\pi$
$367$	−8.58995	−	6.24096i	−0.448392	−	0.325776i	−0.788960	+	0.614444i	$0.789380\pi$
$368$	−0.883322	−	2.71859i	−0.0460463	−	0.141716i
$369$		0			0
$370$	−4.37382	−	3.17777i	−0.227384	−	0.165204i
$371$	8.20742	−	5.96304i	0.426108	−	0.309586i
$372$		0			0
$373$	36.6036			1.89526			0.947631	−	0.319367i	$-0.103470\pi$
$373$	36.6036			1.89526			0.947631	+	0.319367i	$0.103470\pi$
$374$	17.4230	−	18.7124i	0.900924	−	0.967593i
$375$		0			0
$376$	5.24115	−	16.1306i	0.270292	−	0.831872i
$377$	4.40797	−	3.20258i	0.227022	−	0.164941i
$378$		0			0
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	−0.999856	−	0.0169501i	$-0.994604\pi$
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	0.798938	−	0.601414i	$-0.205396\pi$
$380$	0.0458463	+	0.141100i	0.00235187	+	0.00723830i
$381$		0			0
$382$	−10.9529	+	7.95773i	−0.560398	+	0.407153i
$383$	4.77984	−	14.7108i	0.244238	−	0.751688i	−0.751522	−	0.659708i	$-0.770680\pi$
$383$	4.77984	−	14.7108i	0.244238	−	0.751688i	0.995761	−	0.0919809i	$-0.0293199\pi$
$384$		0			0
$385$	−2.94877	−	5.31022i	−0.150283	−	0.270634i
$386$	−2.09672			−0.106720
$387$		0			0
$388$	0.0272411	−	0.0197918i	0.00138296	−	0.00100478i
$389$	−10.2850	−	7.47249i	−0.521470	−	0.378870i	0.295687	−	0.955285i	$-0.404451\pi$
$389$	−10.2850	−	7.47249i	−0.521470	−	0.378870i	−0.817157	+	0.576415i	$0.804451\pi$
$390$		0			0
$391$	1.21654	+	3.74414i	0.0615232	+	0.189349i
$392$	2.29616	+	1.66826i	0.115974	+	0.0842599i
$393$		0			0
$394$	6.11571	−	18.8222i	0.308105	−	0.948250i
$395$	−28.6446			−1.44127
$396$		0			0
$397$	−18.9574			−0.951445			−0.475722	−	0.879596i	$-0.657813\pi$
$397$	−18.9574			−0.951445			−0.475722	+	0.879596i	$0.657813\pi$
$398$	−1.86706	+	5.74622i	−0.0935873	+	0.288032i
$399$		0			0
$400$	−5.28919	−	3.84282i	−0.264460	−	0.192141i
$401$	2.68291	+	8.25715i	0.133978	+	0.412343i	0.995430	−	0.0954974i	$-0.0304442\pi$
$401$	2.68291	+	8.25715i	0.133978	+	0.412343i	−0.861451	+	0.507840i	$0.830444\pi$
$402$		0			0
$403$	−4.91698	−	3.57240i	−0.244932	−	0.177954i
$404$	−0.134394	+	0.0976429i	−0.00668635	+	0.00485792i
$405$		0			0
$406$	1.65233			0.0820037
$407$	−6.81881	+	1.33081i	−0.337996	+	0.0659658i
$408$		0			0
$409$	1.76574	−	5.43440i	0.0873104	−	0.268714i	−0.897863	−	0.440275i	$-0.854881\pi$
$409$	1.76574	−	5.43440i	0.0873104	−	0.268714i	0.985173	+	0.171561i	$0.0548811\pi$
$410$	−1.91396	+	1.39057i	−0.0945237	+	0.0686755i
$411$		0			0
$412$	−0.00171020	−	0.00526346i	−8.42556e−5	−	0.000259312i
$413$	2.37350	+	7.30488i	0.116792	+	0.359450i
$414$		0			0
$415$	−6.48318	+	4.71031i	−0.318247	+	0.231220i
$416$	−0.113437	+	0.349122i	−0.00556169	+	0.0171171i
$417$		0			0
$418$	−24.5830	−	11.4406i	−1.20239	−	0.559576i
$419$	27.1909			1.32836			0.664181	−	0.747571i	$-0.268780\pi$
$419$	27.1909			1.32836			0.664181	+	0.747571i	$0.268780\pi$
$420$		0			0
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	−0.00467947	−	0.999989i	$-0.501490\pi$
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	0.949600	+	0.313464i	$0.101490\pi$
$422$	1.65919	+	1.20547i	0.0807679	+	0.0586813i
$423$		0			0
$424$	8.89768	+	27.3842i	0.432110	+	1.32990i
$425$	7.28447	+	5.29248i	0.353349	+	0.256723i
$426$		0			0
$427$	−1.93943	+	5.96895i	−0.0938555	+	0.288858i
$428$	−0.0456549			−0.00220681
$429$		0			0
$430$	20.7087			0.998663
$431$	−5.09049	+	15.6669i	−0.245200	+	0.754649i	0.750403	+	0.660980i	$0.229859\pi$
$431$	−5.09049	+	15.6669i	−0.245200	+	0.754649i	−0.995603	+	0.0936683i	$0.970141\pi$
$432$		0			0
$433$	−16.2539	−	11.8092i	−0.781113	−	0.567512i	0.124200	−	0.992257i	$-0.460364\pi$
$433$	−16.2539	−	11.8092i	−0.781113	−	0.567512i	−0.905313	+	0.424745i	$0.860364\pi$
$434$	−0.569559	−	1.75292i	−0.0273397	−	0.0841430i
$435$		0			0
$436$	−0.0321571	−	0.0233635i	−0.00154005	−	0.00111891i
$437$	3.37765	−	2.45401i	0.161575	−	0.117391i
$438$		0			0
$439$	26.7682			1.27758			0.638788	−	0.769383i	$-0.279436\pi$
$439$	26.7682			1.27758			0.638788	+	0.769383i	$0.279436\pi$
$440$	16.9201	−	3.30226i	0.806636	−	0.157429i
$441$		0			0
$442$	−11.0703	+	34.0708i	−0.526559	+	1.62058i
$443$	21.2086	−	15.4090i	1.00765	−	0.732103i	0.0439378	−	0.999034i	$-0.486010\pi$
$443$	21.2086	−	15.4090i	1.00765	−	0.732103i	0.963716	+	0.266931i	$0.0860097\pi$
$444$		0			0
$445$	−8.68346	−	26.7249i	−0.411635	−	1.26688i
$446$	−2.11491	−	6.50903i	−0.100144	−	0.308212i
$447$		0			0
$448$	−6.51669	+	4.73465i	−0.307885	+	0.223691i
$449$	−3.01211	+	9.27033i	−0.142150	+	0.437494i	−0.996634	−	0.0819851i	$-0.973874\pi$
$449$	−3.01211	+	9.27033i	−0.142150	+	0.437494i	0.854483	+	0.519479i	$0.173874\pi$
$450$		0			0
$451$	−0.368215	+	3.01779i	−0.0173386	+	0.142102i
$452$	0.203107			0.00955336
$453$		0			0
$454$	0.452792	−	0.328973i	0.0212506	−	0.0154395i
$455$	6.88518	+	5.00238i	0.322782	+	0.234515i
$456$		0			0
$457$	3.67276	+	11.3036i	0.171805	+	0.528760i	0.999473	−	0.0324572i	$-0.0103333\pi$
$457$	3.67276	+	11.3036i	0.171805	+	0.528760i	−0.827669	+	0.561217i	$0.810333\pi$
$458$	−2.49645	−	1.81378i	−0.116651	−	0.0847522i
$459$		0			0
$460$	−0.00568760	+	0.0175046i	−0.000265186	+	0.000816158i
$461$	−9.14737			−0.426035			−0.213018	−	0.977048i	$-0.568329\pi$
$461$	−9.14737			−0.426035			−0.213018	+	0.977048i	$0.568329\pi$
$462$		0			0
$463$	38.9342			1.80943			0.904713	−	0.426021i	$-0.140085\pi$
$463$	38.9342			1.80943			0.904713	+	0.426021i	$0.140085\pi$
$464$	−1.43907	+	4.42899i	−0.0668070	+	0.205611i
$465$		0			0
$466$	−1.43673	−	1.04385i	−0.0665553	−	0.0483552i
$467$	6.42243	+	19.7662i	0.297195	+	0.914671i	0.982475	+	0.186392i	$0.0596795\pi$
$467$	6.42243	+	19.7662i	0.297195	+	0.914671i	−0.685281	+	0.728279i	$0.740320\pi$
$468$		0			0
$469$	12.5133	+	9.09143i	0.577810	+	0.419803i
$470$	12.4776	−	9.06548i	0.575547	−	0.418159i
$471$		0			0
$472$	−21.7998			−1.00342
$473$	18.1345	−	19.4765i	0.833826	−	0.895529i
$474$		0			0
$475$	2.95076	−	9.08152i	0.135390	−	0.416689i
$476$	0.0617999	−	0.0449003i	0.00283259	−	0.00205800i
$477$		0			0
$478$	4.86076	+	14.9599i	0.222326	+	0.684249i
$479$	7.58214	+	23.3354i	0.346437	+	1.06622i	0.960810	+	0.277207i	$0.0894088\pi$
$479$	7.58214	+	23.3354i	0.346437	+	1.06622i	−0.614374	+	0.789015i	$0.710591\pi$
$480$		0			0
$481$	7.87527	−	5.72172i	0.359081	−	0.260888i
$482$	−9.35614	+	28.7952i	−0.426161	+	1.31159i
$483$		0			0
$484$	0.0812030	−	0.130392i	0.00369105	−	0.00592690i
$485$	4.41591			0.200516
$486$		0			0
$487$	10.0086	−	7.27168i	0.453533	−	0.329511i	−0.337456	−	0.941341i	$-0.609566\pi$
$487$	10.0086	−	7.27168i	0.453533	−	0.329511i	0.790989	+	0.611830i	$0.209566\pi$
$488$	−14.4110	−	10.4702i	−0.652356	−	0.473964i
$489$		0			0
$490$	0.797546	+	2.45459i	0.0360295	+	0.110887i
$491$	13.3691	+	9.71320i	0.603338	+	0.438350i	0.847062	−	0.531494i	$-0.178369\pi$
$491$	13.3691	+	9.71320i	0.603338	+	0.438350i	−0.243724	+	0.969845i	$0.578369\pi$
$492$		0			0
$493$	1.98194	−	6.09977i	0.0892620	−	0.274720i
$494$	37.9916			1.70932
$495$		0			0
$496$	5.19468			0.233248
$497$	−4.29593	+	13.2215i	−0.192699	+	0.593065i
$498$		0			0
$499$	11.1167	+	8.07673i	0.497650	+	0.361564i	0.808119	−	0.589020i	$-0.200486\pi$
$499$	11.1167	+	8.07673i	0.497650	+	0.361564i	−0.310469	+	0.950584i	$0.600486\pi$
$500$	0.0525231	+	0.161649i	0.00234890	+	0.00722918i
$501$		0			0
$502$	−0.483206	−	0.351070i	−0.0215665	−	0.0156690i
$503$	−18.2812	+	13.2820i	−0.815117	+	0.592217i	−0.915310	−	0.402751i	$-0.868054\pi$
$503$	−18.2812	+	13.2820i	−0.815117	+	0.592217i	0.100193	+	0.994968i	$0.468054\pi$
$504$		0			0
$505$	−21.7859			−0.969461
$506$	−1.63304	−	2.94081i	−0.0725973	−	0.130735i
$507$		0			0
$508$	−0.0217182	+	0.0668418i	−0.000963590	+	0.00296563i
$509$	−17.3644	+	12.6160i	−0.769664	+	0.559194i	−0.901859	−	0.432030i	$-0.857798\pi$
$509$	−17.3644	+	12.6160i	−0.769664	+	0.559194i	0.132195	+	0.991224i	$0.457798\pi$
$510$		0			0
$511$	1.85862	+	5.72025i	0.0822206	+	0.253049i
$512$	−7.06408	−	21.7410i	−0.312191	−	0.960825i
$513$		0			0
$514$	19.8838	−	14.4464i	0.877037	−	0.637204i
$515$	0.224286	−	0.690280i	0.00988321	−	0.0304174i
$516$		0			0
$517$	2.40048	−	19.6737i	0.105573	−	0.865248i
$518$	2.95205			0.129706
$519$		0			0
$520$	−19.5416	+	14.1978i	−0.856957	+	0.622616i
$521$	28.0822	+	20.4029i	1.23031	+	0.893869i	0.996913	−	0.0785132i	$-0.0250173\pi$
$521$	28.0822	+	20.4029i	1.23031	+	0.893869i	0.233393	+	0.972383i	$0.425017\pi$
$522$		0			0
$523$	6.09633	+	18.7626i	0.266574	+	0.820430i	0.991327	+	0.131421i	$0.0419540\pi$
$523$	6.09633	+	18.7626i	0.266574	+	0.820430i	−0.724753	+	0.689009i	$0.758046\pi$
$524$	0.00203415	+	0.00147790i	8.88624e−5	+	6.45623e-5i
$525$		0			0
$526$	−0.659847	+	2.03080i	−0.0287707	+	0.0885471i
$527$	−7.15430			−0.311646
$528$		0			0
$529$	−22.4821			−0.977481
$530$	−8.09105	+	24.9017i	−0.351453	+	1.08166i
$531$		0			0
$532$	−0.0655390	−	0.0476168i	−0.00284147	−	0.00206445i
$533$	−1.31632	−	4.05122i	−0.0570162	−	0.175478i
$534$		0			0
$535$	−4.84395	−	3.51933i	−0.209422	−	0.152154i
$536$	−35.5154	+	25.8034i	−1.53403	+	1.11454i
$537$		0			0
$538$	2.86226			0.123401
$539$	3.00695	+	1.39939i	0.129518	+	0.0602758i
$540$		0			0
$541$	−1.71487	+	5.27782i	−0.0737279	+	0.226911i	−0.981129	−	0.193355i	$-0.938063\pi$
$541$	−1.71487	+	5.27782i	−0.0737279	+	0.226911i	0.907401	+	0.420266i	$0.138063\pi$
$542$	−8.66998	+	6.29911i	−0.372408	+	0.270570i
$543$		0			0
$544$	0.133530	+	0.410964i	0.00572506	+	0.0176199i
$545$	−1.61085	−	4.95770i	−0.0690014	−	0.212364i
$546$		0			0
$547$	6.83353	−	4.96485i	0.292181	−	0.212282i	−0.432032	−	0.901858i	$-0.642203\pi$
$547$	6.83353	−	4.96485i	0.292181	−	0.212282i	0.724213	+	0.689576i	$0.242203\pi$
$548$	0.0359201	−	0.110551i	0.00153443	−	0.00472250i
$549$		0			0
$550$	−6.97518	−	3.24614i	−0.297422	−	0.138416i
$551$	−6.80173			−0.289763
$552$		0			0
$553$	12.6538	−	9.19351i	0.538094	−	0.390948i
$554$	−16.4483	−	11.9504i	−0.698822	−	0.507724i
$555$		0			0
$556$	0.0300394	+	0.0924519i	0.00127396	+	0.00392083i
$557$	−9.85665	−	7.16128i	−0.417640	−	0.303433i	0.359048	−	0.933319i	$-0.383102\pi$
$557$	−9.85665	−	7.16128i	−0.417640	−	0.303433i	−0.776687	+	0.629886i	$0.783102\pi$
$558$		0			0
$559$	−11.5223	+	35.4620i	−0.487342	+	1.49988i
$560$	−7.27404			−0.307384
$561$		0			0
$562$	−25.0140			−1.05515
$563$	8.45270	−	26.0147i	0.356239	−	1.09639i	−0.599049	−	0.800713i	$-0.704454\pi$
$563$	8.45270	−	26.0147i	0.356239	−	1.09639i	0.955288	−	0.295678i	$-0.0955456\pi$
$564$		0			0
$565$	21.5495	+	15.6566i	0.906594	+	0.658679i
$566$	−13.5594	−	41.7316i	−0.569944	−	1.75411i
$567$		0			0
$568$	−31.9211	−	23.1920i	−1.33938	−	0.973115i
$569$	5.77253	−	4.19399i	0.241997	−	0.175821i	−0.460176	−	0.887828i	$-0.652214\pi$
$569$	5.77253	−	4.19399i	0.241997	−	0.175821i	0.702173	+	0.712007i	$0.252214\pi$
$570$		0			0
$571$	32.4839			1.35941			0.679705	−	0.733486i	$-0.262108\pi$
$571$	32.4839			1.35941			0.679705	+	0.733486i	$0.262108\pi$
$572$	−0.0260678	+	0.213644i	−0.00108995	+	0.00893291i
$573$		0			0
$574$	0.399188	−	1.22857i	0.0166618	−	0.0512797i
$575$	0.958373	−	0.696299i	0.0399669	−	0.0290377i
$576$		0			0
$577$	10.7482	+	33.0795i	0.447453	+	1.37712i	0.879771	+	0.475398i	$0.157696\pi$
$577$	10.7482	+	33.0795i	0.447453	+	1.37712i	−0.432317	+	0.901721i	$0.642304\pi$
$578$	5.62791	+	17.3209i	0.234090	+	0.720456i
$579$		0			0
$580$	0.0242587	−	0.0176249i	0.00100729	−	0.000731836i
$581$	1.35217	−	4.16157i	0.0560977	−	0.172651i
$582$		0			0
$583$	16.3347	+	29.4159i	0.676513	+	1.21828i
$584$	−17.0708			−0.706395
$585$		0			0
$586$	−27.3975	+	19.9054i	−1.13178	+	0.822285i
$587$	−11.7105	−	8.50816i	−0.483343	−	0.351169i	0.319276	−	0.947662i	$-0.396560\pi$
$587$	−11.7105	−	8.50816i	−0.483343	−	0.351169i	−0.802618	+	0.596493i	$0.796560\pi$
$588$		0			0
$589$	2.34456	+	7.21581i	0.0966059	+	0.297322i
$590$	−16.0375	−	11.6520i	−0.660255	−	0.479704i
$591$		0			0
$592$	−2.57103	+	7.91283i	−0.105669	+	0.325215i
$593$	15.0291			0.617169			0.308585	−	0.951197i	$-0.400145\pi$
$593$	15.0291			0.617169			0.308585	+	0.951197i	$0.400145\pi$
$594$		0			0
$595$	10.0181			0.410701
$596$	−0.0138706	+	0.0426894i	−0.000568163	+	0.00174863i
$597$		0			0
$598$	3.81303	+	2.77033i	0.155926	+	0.113287i
$599$	−0.544010	−	1.67429i	−0.0222276	−	0.0684097i	0.939327	−	0.343022i	$-0.111451\pi$
$599$	−0.544010	−	1.67429i	−0.0222276	−	0.0684097i	−0.961555	+	0.274612i	$0.911451\pi$
$600$		0			0
$601$	−18.9605	−	13.7756i	−0.773415	−	0.561919i	0.129581	−	0.991569i	$-0.458637\pi$
$601$	−18.9605	−	13.7756i	−0.773415	−	0.561919i	−0.902995	+	0.429650i	$0.858637\pi$
$602$	−9.14810	+	6.64648i	−0.372849	+	0.270890i
$603$		0			0
$604$	−0.310948			−0.0126523
$605$	18.6669	−	7.57487i	0.758917	−	0.307962i
$606$		0			0
$607$	−7.81149	+	24.0413i	−0.317059	+	0.975806i	0.657840	+	0.753158i	$0.271470\pi$
$607$	−7.81149	+	24.0413i	−0.317059	+	0.975806i	−0.974899	+	0.222649i	$0.928530\pi$
$608$	0.370738	−	0.269357i	0.0150354	−	0.0109239i
$609$		0			0
$610$	−5.00550	−	15.4053i	−0.202667	−	0.623744i
$611$	8.58142	+	26.4109i	0.347167	+	1.06847i
$612$		0			0
$613$	−0.939222	+	0.682385i	−0.0379348	+	0.0275613i	−0.606591	−	0.795014i	$-0.707463\pi$
$613$	−0.939222	+	0.682385i	−0.0379348	+	0.0275613i	0.568656	+	0.822575i	$0.307463\pi$
$614$	−2.37906	+	7.32199i	−0.0960110	+	0.295492i
$615$		0			0
$616$	−6.41463	+	6.88931i	−0.258453	+	0.277578i
$617$	−12.9711			−0.522197			−0.261098	−	0.965312i	$-0.584085\pi$
$617$	−12.9711			−0.522197			−0.261098	+	0.965312i	$0.584085\pi$
$618$		0			0
$619$	−37.0465	+	26.9158i	−1.48902	+	1.08184i	−0.514517	+	0.857480i	$0.672029\pi$
$619$	−37.0465	+	26.9158i	−1.48902	+	1.08184i	−0.974507	+	0.224358i	$0.927971\pi$
$620$	−0.0270599	−	0.0196602i	−0.00108675	−	0.000789572i
$621$		0			0
$622$	−6.04824	−	18.6146i	−0.242512	−	0.746377i
$623$	12.4133	+	9.01881i	0.497329	+	0.361331i
$624$		0			0
$625$	−4.34493	+	13.3723i	−0.173797	+	0.534893i
$626$	38.6824			1.54606
$627$		0			0
$628$	−0.185097			−0.00738615
$629$	3.54092	−	10.8978i	0.141186	−	0.434525i
$630$		0			0
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	0.772170	−	0.635416i	$-0.219171\pi$
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	−0.365703	+	0.930732i	$0.619171\pi$
$632$	13.7180	+	42.2196i	0.545672	+	1.67941i
$633$		0			0
$634$	8.92225	+	6.48240i	0.354348	+	0.257449i
$635$	−7.45682	+	5.41770i	−0.295915	+	0.214995i
$636$		0			0
$637$	−4.64706			−0.184123
$638$	−0.663738	+	5.43981i	−0.0262776	+	0.215364i
$639$		0			0
$640$	6.33488	−	19.4968i	0.250408	−	0.770678i
$641$	22.6175	−	16.4326i	0.893336	−	0.649047i	−0.0434095	−	0.999057i	$-0.513822\pi$
$641$	22.6175	−	16.4326i	0.893336	−	0.649047i	0.936746	+	0.350011i	$0.113822\pi$
$642$		0			0
$643$	−15.3575	−	47.2657i	−0.605642	−	1.86398i	−0.492313	−	0.870418i	$-0.663848\pi$
$643$	−15.3575	−	47.2657i	−0.605642	−	1.86398i	−0.113330	−	0.993557i	$-0.536152\pi$
$644$	−0.00310563	−	0.00955813i	−0.000122379	−	0.000376643i
$645$		0			0
$646$	36.1802	−	26.2865i	1.42349	−	1.03423i
$647$	3.40125	−	10.4680i	0.133717	−	0.411539i	−0.861671	−	0.507467i	$-0.830582\pi$
$647$	3.40125	−	10.4680i	0.133717	−	0.411539i	0.995388	+	0.0959281i	$0.0305819\pi$
$648$		0			0
$649$	−25.0026	+	4.87970i	−0.981439	+	0.191545i
$650$	10.7797			0.422816
$651$		0			0
$652$	0.154983	−	0.112602i	0.00606962	−	0.00440984i
$653$	23.4100	+	17.0084i	0.916106	+	0.665590i	0.942552	−	0.334060i	$-0.108419\pi$
$653$	23.4100	+	17.0084i	0.916106	+	0.665590i	−0.0264458	+	0.999650i	$0.508419\pi$
$654$		0			0
$655$	0.101897	+	0.313608i	0.00398146	+	0.0122537i
$656$	2.94547	+	2.14001i	0.115001	+	0.0835533i
$657$		0			0
$658$	−2.60240	+	8.00937i	−0.101452	+	0.312238i
$659$	−10.8405			−0.422288			−0.211144	−	0.977455i	$-0.567719\pi$
$659$	−10.8405			−0.422288			−0.211144	+	0.977455i	$0.567719\pi$
$660$		0			0
$661$	20.3444			0.791305			0.395652	−	0.918400i	$-0.370519\pi$
$661$	20.3444			0.791305			0.395652	+	0.918400i	$0.370519\pi$
$662$	−12.2573	+	37.7241i	−0.476394	+	1.46619i
$663$		0			0
$664$	10.0474	+	7.29986i	0.389915	+	0.283289i
$665$	−3.28306	−	10.1042i	−0.127311	−	0.391824i
$666$		0			0
$667$	−0.682656	−	0.495978i	−0.0264325	−	0.0192044i
$668$	−0.105164	+	0.0764062i	−0.00406892	+	0.00295625i
$669$		0			0
$670$	−39.9197			−1.54223
$671$	−18.8720	−	8.78272i	−0.728544	−	0.339053i
$672$		0			0
$673$	−3.73255	+	11.4876i	−0.143879	+	0.442815i	−0.996865	−	0.0791188i	$-0.974789\pi$
$673$	−3.73255	+	11.4876i	−0.143879	+	0.442815i	0.852986	+	0.521934i	$0.174789\pi$
$674$	28.4790	−	20.6912i	1.09697	−	0.796996i
$675$		0			0
$676$	−0.0370903	−	0.114152i	−0.00142655	−	0.00439047i
$677$	−1.04951	−	3.23007i	−0.0403361	−	0.124142i	0.928861	−	0.370429i	$-0.120789\pi$
$677$	−1.04951	−	3.23007i	−0.0403361	−	0.124142i	−0.969197	+	0.246287i	$0.920789\pi$
$678$		0			0
$679$	−1.95073	+	1.41729i	−0.0748623	+	0.0543906i
$680$	−8.78642	+	27.0418i	−0.336944	+	1.03701i
$681$		0			0
$682$	5.99978	−	1.17096i	0.229743	−	0.0448384i
$683$	4.75643			0.182000			0.0909999	−	0.995851i	$-0.470994\pi$
$683$	4.75643			0.182000			0.0909999	+	0.995851i	$0.470994\pi$
$684$		0			0
$685$	12.3330	−	8.96042i	0.471218	−	0.342360i
$686$	−1.14012	−	0.828347i	−0.0435300	−	0.0316264i
$687$		0			0
$688$	−9.84822	−	30.3097i	−0.375460	−	1.15555i
$689$	−38.1404	−	27.7106i	−1.45303	−	1.05569i
$690$		0			0
$691$	2.04998	−	6.30920i	0.0779850	−	0.240013i	−0.904462	−	0.426554i	$-0.859728\pi$
$691$	2.04998	−	6.30920i	0.0779850	−	0.240013i	0.982447	+	0.186540i	$0.0597275\pi$
$692$	0.146707			0.00557695
$693$		0			0
$694$	−29.1003			−1.10463
$695$	−3.93955	+	12.1247i	−0.149435	+	0.459915i
$696$		0			0
$697$	−4.05661	−	2.94730i	−0.153655	−	0.111637i
$698$	−2.61171	−	8.03802i	−0.0988547	−	0.304244i
$699$		0			0
$700$	−0.0185960	−	0.0135108i	−0.000702863	−	0.000510660i
$701$	2.45134	−	1.78101i	0.0925860	−	0.0672677i	−0.540529	−	0.841325i	$-0.681776\pi$
$701$	2.45134	−	1.78101i	0.0925860	−	0.0672677i	0.633115	+	0.774058i	$0.281776\pi$
$702$		0			0
$703$	−12.1519			−0.458319
$704$	−12.9697	−	23.3562i	−0.488815	−	0.880270i
$705$		0			0
$706$	−10.4683	+	32.2182i	−0.393981	+	1.21255i
$707$	9.62396	−	6.99222i	0.361946	−	0.262969i
$708$		0			0
$709$	−4.22026	−	12.9886i	−0.158495	−	0.487798i	0.840003	−	0.542582i	$-0.182553\pi$
$709$	−4.22026	−	12.9886i	−0.158495	−	0.487798i	−0.998498	+	0.0547836i	$0.982553\pi$
$710$	−11.0874	−	34.1236i	−0.416103	−	1.28063i
$711$		0			0
$712$	−35.2317	+	25.5973i	−1.32036	+	0.959300i
$713$	−0.290862	+	0.895180i	−0.0108928	+	0.0335247i
$714$		0			0
$715$	−19.2346	+	20.6580i	−0.719335	+	0.772566i
$716$	−0.116231			−0.00434376
$717$		0			0
$718$	−12.4845	+	9.07050i	−0.465916	+	0.338508i
$719$	−1.53737	−	1.11696i	−0.0573341	−	0.0416557i	0.558749	−	0.829337i	$-0.311281\pi$
$719$	−1.53737	−	1.11696i	−0.0573341	−	0.0416557i	−0.616083	+	0.787681i	$0.711281\pi$
$720$		0			0
$721$	0.122468	+	0.376917i	0.00456094	+	0.0140371i
$722$	−16.7069	−	12.1383i	−0.621768	−	0.451741i
$723$		0			0
$724$	0.0638788	−	0.196599i	0.00237404	−	0.00730654i
$725$	−1.92992			−0.0716754
$726$		0			0
$727$	−13.8211			−0.512595			−0.256298	−	0.966598i	$-0.582503\pi$
$727$	−13.8211			−0.512595			−0.256298	+	0.966598i	$0.582503\pi$
$728$	4.07573	−	12.5438i	0.151057	−	0.464905i
$729$		0			0
$730$	−12.5586	−	9.12432i	−0.464813	−	0.337706i
$731$	13.5633	+	41.7436i	0.501658	+	1.54394i
$732$		0			0
$733$	−39.1357	−	28.4337i	−1.44551	−	1.05022i	−0.986855	−	0.161610i	$-0.948331\pi$
$733$	−39.1357	−	28.4337i	−1.44551	−	1.05022i	−0.458655	−	0.888615i	$-0.651669\pi$
$734$	−12.1055	+	8.79519i	−0.446824	+	0.324636i
$735$		0			0
$736$	0.0568504			0.00209553
$737$	−34.9575	+	37.5443i	−1.28767	+	1.38296i
$738$		0			0
$739$	7.17170	−	22.0722i	0.263815	−	0.811939i	−0.728149	−	0.685419i	$-0.759619\pi$
$739$	7.17170	−	22.0722i	0.263815	−	0.811939i	0.991964	−	0.126520i	$-0.0403809\pi$
$740$	0.0433404	−	0.0314887i	0.00159323	−	0.00115755i
$741$		0			0
$742$	−4.41799	−	13.5972i	−0.162190	−	0.499168i
$743$	13.8536	+	42.6369i	0.508238	+	1.56420i	0.795257	+	0.606272i	$0.207336\pi$
$743$	13.8536	+	42.6369i	0.508238	+	1.56420i	−0.287019	+	0.957925i	$0.592664\pi$
$744$		0			0
$745$	−4.76240	+	3.46009i	−0.174481	+	0.126768i
$746$	15.9404	−	49.0596i	0.583620	−	1.79620i
$747$		0			0
$748$	0.122996	+	0.221495i	0.00449718	+	0.00809864i
$749$	3.26935			0.119460
$750$		0			0
$751$	33.3199	−	24.2083i	1.21586	−	0.883373i	0.220109	−	0.975475i	$-0.429359\pi$
$751$	33.3199	−	24.2083i	1.21586	−	0.883373i	0.995750	+	0.0921022i	$0.0293587\pi$
$752$	−19.2022	−	13.9512i	−0.700234	−	0.508750i
$753$		0			0
$754$	−2.37278	−	7.30266i	−0.0864115	−	0.265947i
$755$	−32.9913	−	23.9696i	−1.20068	−	0.872343i
$756$		0			0
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	0.749655	+	0.661829i	$0.230219\pi$
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	−0.995497	+	0.0947948i	$0.969781\pi$
$758$	−17.8382			−0.647912
$759$		0			0
$760$	30.1537			1.09379
$761$	11.0367	−	33.9673i	0.400078	−	1.23131i	−0.524857	−	0.851190i	$-0.675881\pi$
$761$	11.0367	−	33.9673i	0.400078	−	1.23131i	0.924935	−	0.380124i	$-0.124119\pi$
$762$		0			0
$763$	2.30277	+	1.67306i	0.0833660	+	0.0605690i
$764$	−0.0414558	−	0.127588i	−0.00149982	−	0.00461596i
$765$		0			0
$766$	−17.6353	−	12.8128i	−0.637188	−	0.462944i
$767$	28.8764	−	20.9799i	1.04266	−	0.757540i
$768$		0			0
$769$	5.30246			0.191212			0.0956058	−	0.995419i	$-0.469521\pi$
$769$	5.30246			0.191212			0.0956058	+	0.995419i	$0.469521\pi$
$770$	−8.40141	+	1.63968i	−0.302766	+	0.0590900i
$771$		0			0
$772$	0.00642030	−	0.0197596i	0.000231072	−	0.000711165i
$773$	−40.3628	+	29.3253i	−1.45175	+	1.05476i	−0.466332	+	0.884610i	$0.654425\pi$
$773$	−40.3628	+	29.3253i	−1.45175	+	1.05476i	−0.985418	+	0.170149i	$0.945575\pi$
$774$		0			0
$775$	0.665245	+	2.04741i	0.0238963	+	0.0735452i
$776$	−2.11479	−	6.50867i	−0.0759167	−	0.233648i
$777$		0			0
$778$	−14.4943	+	10.5307i	−0.519646	+	0.377545i
$779$	−1.64324	+	5.05736i	−0.0588750	+	0.181199i
$780$		0			0
$781$	−41.8023	−	19.4541i	−1.49580	−	0.696124i
$782$	5.54803			0.198397
$783$		0			0
$784$	3.21332	−	2.33461i	0.114761	−	0.0833789i
$785$	−19.6386	−	14.2683i	−0.700931	−	0.509256i
$786$		0			0
$787$	11.0804	+	34.1020i	0.394974	+	1.21560i	0.928982	+	0.370125i	$0.120685\pi$
$787$	11.0804	+	34.1020i	0.394974	+	1.21560i	−0.534008	+	0.845479i	$0.679315\pi$
$788$	0.158655	+	0.115270i	0.00565186	+	0.00410632i
$789$		0			0
$790$	−12.4744	+	38.3922i	−0.443818	+	1.36593i
$791$	−14.5445			−0.517144
$792$		0			0
$793$	29.1655			1.03570
$794$	−8.25571	+	25.4085i	−0.292984	+	0.901713i
$795$		0			0
$796$	−0.0484357	−	0.0351906i	−0.00171676	−	0.00124730i
$797$	−4.55530	−	14.0198i	−0.161357	−	0.496606i	0.837392	−	0.546602i	$-0.184079\pi$
$797$	−4.55530	−	14.0198i	−0.161357	−	0.496606i	−0.998749	+	0.0499962i	$0.984079\pi$
$798$		0			0
$799$	26.4460	+	19.2142i	0.935593	+	0.679748i
$800$	0.105193	−	0.0764272i	0.00371913	−	0.00270211i
$801$		0			0
$802$	12.2354			0.432046
$803$	−19.5789	+	3.82116i	−0.690923	+	0.134846i
$804$		0			0
$805$	0.407290	−	1.25351i	0.0143551	−	0.0441804i
$806$	−6.92934	+	5.03446i	−0.244076	+	0.177331i
$807$		0			0
$808$	10.4334	+	32.1106i	0.367044	+	1.12965i
$809$	8.33599	+	25.6556i	0.293078	+	0.902001i	0.983860	+	0.178938i	$0.0572663\pi$
$809$	8.33599	+	25.6556i	0.293078	+	0.902001i	−0.690782	+	0.723063i	$0.742734\pi$
$810$		0			0
$811$	−1.18472	+	0.860750i	−0.0416012	+	0.0302250i	−0.608392	−	0.793637i	$-0.708185\pi$
$811$	−1.18472	+	0.860750i	−0.0416012	+	0.0302250i	0.566790	+	0.823862i	$0.308185\pi$
$812$	−0.00505954	+	0.0155717i	−0.000177555	+	0.000546459i
$813$		0			0
$814$	−1.18583	+	9.71876i	−0.0415634	+	0.340642i
$815$	25.1236			0.880041
$816$		0			0
$817$	37.6577	−	27.3599i	1.31747	−	0.957201i
$818$	−6.51473	−	4.73323i	−0.227782	−	0.165493i
$819$		0			0
$820$	−0.00724418	−	0.0222953i	−0.000252978	−	0.000778586i
$821$	24.7791	+	18.0031i	0.864797	+	0.628312i	0.929186	−	0.369613i	$-0.120510\pi$
$821$	24.7791	+	18.0031i	0.864797	+	0.628312i	−0.0643886	+	0.997925i	$0.520510\pi$
$822$		0			0
$823$	−7.58137	+	23.3330i	−0.264270	+	0.813339i	0.727591	+	0.686011i	$0.240640\pi$
$823$	−7.58137	+	23.3330i	−0.264270	+	0.813339i	−0.991861	+	0.127328i	$0.959360\pi$
$824$	−1.12482			−0.0391851
$825$		0			0
$826$	10.8243			0.376626
$827$	2.02927	−	6.24545i	0.0705646	−	0.217176i	−0.909555	−	0.415584i	$-0.863577\pi$
$827$	2.02927	−	6.24545i	0.0705646	−	0.217176i	0.980119	+	0.198408i	$0.0635772\pi$
$828$		0			0
$829$	16.0543	+	11.6642i	0.557590	+	0.405113i	0.830576	−	0.556905i	$-0.188011\pi$
$829$	16.0543	+	11.6642i	0.557590	+	0.405113i	−0.272986	+	0.962018i	$0.588011\pi$
$830$	3.48985	+	10.7406i	0.121134	+	0.372813i
$831$		0			0
$832$	30.2834	+	22.0022i	1.04989	+	0.762789i
$833$	−4.42550	+	3.21531i	−0.153334	+	0.111404i
$834$		0			0
$835$	−17.0476			−0.589958
$836$	0.183091	−	0.196640i	0.00633235	−	0.00680095i
$837$		0			0
$838$	11.8413	−	36.4438i	0.409051	−	1.25893i
$839$	−6.44019	+	4.67907i	−0.222340	+	0.161539i	−0.693379	−	0.720573i	$-0.743879\pi$
$839$	−6.44019	+	4.67907i	−0.222340	+	0.161539i	0.471039	+	0.882112i	$0.343879\pi$
$840$		0			0
$841$	−8.53669	−	26.2732i	−0.294369	−	0.905973i
$842$	−10.4365	−	32.1202i	−0.359665	−	1.10694i
$843$		0			0
$844$	−0.0164410	+	0.0119451i	−0.000565922	+	0.000411166i
$845$	4.86424	−	14.9706i	0.167335	−	0.515004i
$846$		0			0
$847$	−5.81496	+	9.33736i	−0.199804	+	0.320835i
$848$	40.2944			1.38372
$849$		0			0
$850$	10.2658	−	7.45852i	0.352113	−	0.255825i
$851$	−1.21963	−	0.886114i	−0.0418084	−	0.0303756i
$852$		0			0
$853$	10.5292	+	32.4055i	0.360513	+	1.10954i	0.952744	+	0.303776i	$0.0982473\pi$
$853$	10.5292	+	32.4055i	0.360513	+	1.10954i	−0.592231	+	0.805768i	$0.701753\pi$
$854$	7.15554	+	5.19881i	0.244858	+	0.177900i
$855$		0			0
$856$	−2.86741	+	8.82497i	−0.0980060	+	0.301631i
$857$	−24.8539			−0.848992			−0.424496	−	0.905430i	$-0.639549\pi$
$857$	−24.8539			−0.848992			−0.424496	+	0.905430i	$0.639549\pi$
$858$		0			0
$859$	2.05654			0.0701683			0.0350841	−	0.999384i	$-0.488830\pi$
$859$	2.05654			0.0701683			0.0350841	+	0.999384i	$0.488830\pi$
$860$	−0.0634115	+	0.195160i	−0.00216231	+	0.00665491i
$861$		0			0
$862$	18.7814	+	13.6455i	0.639697	+	0.464767i
$863$	0.0801824	+	0.246776i	0.00272944	+	0.00840035i	0.952412	−	0.304814i	$-0.0985942\pi$
$863$	0.0801824	+	0.246776i	0.00272944	+	0.00840035i	−0.949683	+	0.313214i	$0.898594\pi$
$864$		0			0
$865$	15.5655	+	11.3090i	0.529241	+	0.384516i
$866$	−22.9061	+	16.6423i	−0.778381	+	0.565527i
$867$		0			0
$868$	0.0182637			0.000619910
$869$	25.1840	+	45.3519i	0.854307	+	1.53846i
$870$		0			0
$871$	22.2113	−	68.3593i	0.752601	−	2.31627i
$872$	−6.53577	+	4.74851i	−0.221329	+	0.160805i
$873$		0			0
$874$	−1.81816	−	5.59573i	−0.0615003	−	0.189278i
$875$	−3.76118	−	11.5757i	−0.127151	−	0.391331i
$876$		0			0
$877$	−15.0420	+	10.9287i	−0.507934	+	0.369035i	−0.812039	−	0.583603i	$-0.801642\pi$
$877$	−15.0420	+	10.9287i	−0.507934	+	0.369035i	0.304106	+	0.952638i	$0.401642\pi$
$878$	11.6572	−	35.8772i	0.393412	−	1.21080i
$879$		0			0
$880$	2.92197	−	23.9477i	0.0984996	−	0.807275i
$881$	−6.45292			−0.217404			−0.108702	−	0.994074i	$-0.534670\pi$
$881$	−6.45292			−0.217404			−0.108702	+	0.994074i	$0.534670\pi$
$882$		0			0
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	−0.583988	−	0.811762i	$-0.698508\pi$
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	0.591570	+	0.806254i	$0.298508\pi$
$884$	−0.287188	−	0.208654i	−0.00965917	−	0.00701779i
$885$		0			0
$886$	−11.4165	−	35.1362i	−0.383543	−	1.18042i
$887$	24.7211	+	17.9609i	0.830054	+	0.603069i	0.919575	−	0.392916i	$-0.128534\pi$
$887$	24.7211	+	17.9609i	0.830054	+	0.603069i	−0.0895209	+	0.995985i	$0.528534\pi$
$888$		0			0
$889$	1.55524	−	4.78655i	0.0521612	−	0.160536i
$890$	−39.6008			−1.32742
$891$		0			0
$892$	0.0678176			0.00227070
$893$	10.7127	−	32.9702i	0.358485	−	1.10330i
$894$		0			0
$895$	−12.3320	−	8.95972i	−0.412213	−	0.299491i
$896$	3.45907	+	10.6459i	0.115559	+	0.355655i
$897$		0			0
$898$	11.1132	+	8.07423i	0.370853	+	0.269441i
$899$	1.24058	−	0.901332i	0.0413756	−	0.0300611i
$900$		0			0
$901$	−55.4949			−1.84880
$902$	3.88437	+	1.80773i	0.129335	+	0.0601907i
$903$		0			0
$904$	12.7564	−	39.2601i	0.424271	−	1.30577i
$905$	21.9324	−	15.9348i	0.729058	−	0.529692i
$906$		0			0
$907$	9.86836	+	30.3717i	0.327674	+	1.00848i	0.970219	+	0.242228i	$0.0778782\pi$
$907$	9.86836	+	30.3717i	0.327674	+	1.00848i	−0.642546	+	0.766247i	$0.722122\pi$
$908$	0.00171378	+	0.00527448i	5.68739e−5	+	0.000175040i
$909$		0			0
$910$	9.70307	−	7.04969i	0.321654	−	0.233695i
$911$	−0.865378	+	2.66336i	−0.0286713	+	0.0882411i	−0.964368	−	0.264564i	$-0.914772\pi$
$911$	−0.865378	+	2.66336i	−0.0286713	+	0.0882411i	0.935697	+	0.352805i	$0.114772\pi$
$912$		0			0
$913$	13.1576	+	6.12334i	0.435452	+	0.202653i
$914$	16.7496			0.554027
$915$		0			0
$916$	0.0247374	−	0.0179728i	0.000817348	−	0.000593838i
$917$	−0.145666	−	0.105832i	−0.00481031	−	0.00349490i
$918$		0			0
$919$	−4.89293	−	15.0589i	−0.161403	−	0.496747i	0.837350	−	0.546667i	$-0.184104\pi$
$919$	−4.89293	−	15.0589i	−0.161403	−	0.496747i	−0.998753	+	0.0499194i	$0.984104\pi$
$920$	3.02638	+	2.19880i	0.0997769	+	0.0724922i
$921$		0			0
$922$	−3.98356	+	12.2602i	−0.131192	+	0.403767i
$923$	64.6030			2.12643
$924$		0			0
$925$	−3.44799			−0.113369
$926$	16.9554	−	52.1833i	0.557188	−	1.71485i
$927$		0			0
$928$	−0.0749296	−	0.0544396i	−0.00245969	−	0.00178707i
$929$	8.49282	+	26.1382i	0.278640	+	0.857567i	0.988233	+	0.152955i	$0.0488790\pi$
$929$	8.49282	+	26.1382i	0.278640	+	0.857567i	−0.709593	+	0.704612i	$0.751121\pi$
$930$		0			0
$931$	4.69325	+	3.40985i	0.153815	+	0.111753i
$932$	0.0142366	−	0.0103435i	0.000466337	−	0.000338814i
$933$		0			0
$934$	29.2894			0.958379
$935$	−4.02424	+	32.9816i	−0.131607	+	1.07861i
$936$		0			0
$937$	−3.80357	+	11.7062i	−0.124257	+	0.382425i	−0.993765	−	0.111495i	$-0.964436\pi$
$937$	−3.80357	+	11.7062i	−0.124257	+	0.382425i	0.869508	+	0.493919i	$0.164436\pi$
$938$	17.6346	−	12.8123i	0.575789	−	0.418335i
$939$		0			0
$940$	0.0472266	+	0.145349i	0.00154036	+	0.00474075i
$941$	−0.451208	−	1.38867i	−0.0147089	−	0.0452695i	0.943433	−	0.331564i	$-0.107576\pi$
$941$	−0.451208	−	1.38867i	−0.0147089	−	0.0452695i	−0.958142	+	0.286295i	$0.907576\pi$
$942$		0			0
$943$	−0.533703	+	0.387758i	−0.0173798	+	0.0126271i
$944$	−9.42725	+	29.0141i	−0.306831	+	0.944328i
$945$		0			0
$946$	−18.2068	−	32.7873i	−0.591955	−	1.06601i
$947$	−11.0714			−0.359771			−0.179885	−	0.983688i	$-0.557573\pi$
$947$	−11.0714			−0.359771			−0.179885	+	0.983688i	$0.557573\pi$
$948$		0			0
$949$	22.6123	−	16.4288i	0.734025	−	0.533301i
$950$	−10.8869	−	7.90978i	−0.353217	−	0.256627i
$951$		0			0
$952$	−4.79769	−	14.7658i	−0.155494	−	0.478561i
$953$	−11.9924	−	8.71296i	−0.388471	−	0.282240i	0.376358	−	0.926474i	$-0.377176\pi$
$953$	−11.9924	−	8.71296i	−0.388471	−	0.282240i	−0.764828	+	0.644234i	$0.777176\pi$
$954$		0			0
$955$	5.43675	−	16.7326i	0.175929	−	0.541454i
$956$	−0.155867			−0.00504110
$957$		0			0
$958$	34.5782			1.11717
$959$	−2.57224	+	7.91655i	−0.0830621	+	0.255639i
$960$		0			0
$961$	23.6957	+	17.2159i	0.764377	+	0.555353i
$962$	−4.23920	−	13.0469i	−0.136677	−	0.420649i
$963$		0			0
$964$	−0.242719	−	0.176346i	−0.00781746	−	0.00567972i
$965$	2.20437	−	1.60157i	0.0709612	−	0.0515563i
$966$		0			0
$967$	16.5193			0.531224			0.265612	−	0.964080i	$-0.414426\pi$
$967$	16.5193			0.531224			0.265612	+	0.964080i	$0.414426\pi$
$968$	−20.1043	−	23.8857i	−0.646177	−	0.767716i
$969$		0			0
$970$	1.92308	−	5.91862i	0.0617462	−	0.190035i
$971$	33.0073	−	23.9812i	1.05926	−	0.769595i	0.0853055	−	0.996355i	$-0.472813\pi$
$971$	33.0073	−	23.9812i	1.05926	−	0.769595i	0.973951	+	0.226760i	$0.0728134\pi$
$972$		0			0
$973$	−2.15113	−	6.62049i	−0.0689620	−	0.212243i
$974$	−5.38755	−	16.5812i	−0.172628	−	0.531296i
$975$		0			0
$976$	−20.1672	+	14.6523i	−0.645535	+	0.469009i
$977$	−15.1772	+	46.7107i	−0.485562	+	1.49441i	0.345603	+	0.938381i	$0.387674\pi$
$977$	−15.1772	+	46.7107i	−0.485562	+	1.49441i	−0.831165	+	0.556025i	$0.812326\pi$
$978$		0			0
$979$	−34.6782	+	37.2444i	−1.10832	+	1.19034i
$980$	−0.0255744			−0.000816945
$981$		0			0
$982$	18.8406	−	13.6885i	0.601228	−	0.436817i
$983$	0.895411	+	0.650554i	0.0285592	+	0.0207495i	0.601973	−	0.798516i	$-0.294381\pi$
$983$	0.895411	+	0.650554i	0.0285592	+	0.0207495i	−0.573414	+	0.819266i	$0.694381\pi$
$984$		0			0
$985$	7.94756	+	24.4601i	0.253230	+	0.779362i
$986$	−7.31238	−	5.31275i	−0.232874	−	0.169193i
$987$		0			0
$988$	−0.116333	+	0.358036i	−0.00370104	+	0.0113906i
$989$	5.77458			0.183621
$990$		0			0
$991$	41.7851			1.32735			0.663674	−	0.748022i	$-0.268996\pi$
$991$	41.7851			1.32735			0.663674	+	0.748022i	$0.268996\pi$
$992$	−0.0319255	+	0.0982567i	−0.00101364	+	0.00311965i
$993$		0			0
$994$	15.8499	+	11.5156i	0.502727	+	0.365253i
$995$	−2.42630	−	7.46739i	−0.0769189	−	0.236732i
$996$		0			0
$997$	−35.7541	−	25.9769i	−1.13234	−	0.822695i	−0.146309	−	0.989239i	$-0.546739\pi$
$997$	−35.7541	−	25.9769i	−1.13234	−	0.822695i	−0.986034	+	0.166543i	$0.946739\pi$
$998$	15.6664	−	11.3823i	0.495910	−	0.360300i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.i.64.3		16
3.2	odd	2		77.2.f.b.64.2	✓	16
11.4	even	5		7623.2.a.ct.1.6		8
11.5	even	5	inner	693.2.m.i.379.3		16
11.7	odd	10		7623.2.a.cw.1.3		8
21.2	odd	6		539.2.q.g.361.3		32
21.5	even	6		539.2.q.f.361.3		32
21.11	odd	6		539.2.q.g.471.2		32
21.17	even	6		539.2.q.f.471.2		32
21.20	even	2		539.2.f.e.295.2		16
33.2	even	10		847.2.f.v.729.2		16
33.5	odd	10		77.2.f.b.71.2	yes	16
33.8	even	10		847.2.f.v.323.2		16
33.14	odd	10		847.2.f.w.323.3		16
33.17	even	10		847.2.f.x.148.3		16
33.20	odd	10		847.2.f.w.729.3		16
33.26	odd	10		847.2.a.p.1.3		8
33.29	even	10		847.2.a.o.1.6		8
33.32	even	2		847.2.f.x.372.3		16
231.5	even	30		539.2.q.f.214.2		32
231.38	even	30		539.2.q.f.324.3		32
231.62	odd	10		5929.2.a.bs.1.6		8
231.104	even	10		539.2.f.e.148.2		16
231.125	even	10		5929.2.a.bt.1.3		8
231.137	odd	30		539.2.q.g.324.3		32
231.170	odd	30		539.2.q.g.214.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	3.2	odd	2
77.2.f.b.71.2	yes	16	33.5	odd	10
539.2.f.e.148.2		16	231.104	even	10
539.2.f.e.295.2		16	21.20	even	2
539.2.q.f.214.2		32	231.5	even	30
539.2.q.f.324.3		32	231.38	even	30
539.2.q.f.361.3		32	21.5	even	6
539.2.q.f.471.2		32	21.17	even	6
539.2.q.g.214.2		32	231.170	odd	30
539.2.q.g.324.3		32	231.137	odd	30
539.2.q.g.361.3		32	21.2	odd	6
539.2.q.g.471.2		32	21.11	odd	6
693.2.m.i.64.3		16	1.1	even	1	trivial
693.2.m.i.379.3		16	11.5	even	5	inner
847.2.a.o.1.6		8	33.29	even	10
847.2.a.p.1.3		8	33.26	odd	10
847.2.f.v.323.2		16	33.8	even	10
847.2.f.v.729.2		16	33.2	even	10
847.2.f.w.323.3		16	33.14	odd	10
847.2.f.w.729.3		16	33.20	odd	10
847.2.f.x.148.3		16	33.17	even	10
847.2.f.x.372.3		16	33.32	even	2
5929.2.a.bs.1.6		8	231.62	odd	10
5929.2.a.bt.1.3		8	231.125	even	10
7623.2.a.ct.1.6		8	11.4	even	5
7623.2.a.cw.1.3		8	11.7	odd	10

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.435488 - 1.34029i) q^{2} +(0.0112975 + 0.00820814i) q^{4} +(0.565930 + 1.74175i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(2.29616 - 1.66826i) q^{8} +O(q^{10})\)	\(q+(0.435488 - 1.34029i) q^{2} +(0.0112975 + 0.00820814i) q^{4} +(0.565930 + 1.74175i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(2.29616 - 1.66826i) q^{8} +2.58091 q^{10} +(2.26009 - 2.42734i) q^{11} +(-1.43602 + 4.41961i) q^{13} +(-1.14012 + 0.828347i) q^{14} +(-1.22738 - 3.77748i) q^{16} +(1.69039 + 5.20248i) q^{17} +(4.69325 - 3.40985i) q^{19} +(-0.00790293 + 0.0243227i) q^{20} +(-2.26911 - 4.08626i) q^{22} +0.719682 q^{23} +(1.33166 - 0.967509i) q^{25} +(5.29821 + 3.84937i) q^{26} +(-0.00431527 - 0.0132810i) q^{28} +(-0.948551 - 0.689163i) q^{29} +(-0.404153 + 1.24385i) q^{31} +0.0789938 q^{32} +7.70900 q^{34} +(0.565930 - 1.74175i) q^{35} +(-1.69468 - 1.23126i) q^{37} +(-2.52634 - 7.77528i) q^{38} +(4.20516 + 3.05523i) q^{40} +(-0.741582 + 0.538791i) q^{41} +8.02379 q^{43} +(0.0454574 - 0.00887181i) q^{44} +(0.313413 - 0.964586i) q^{46} +(4.83455 - 3.51251i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-0.716823 - 2.20615i) q^{50} +(-0.0525003 + 0.0381437i) q^{52} +(-3.13496 + 9.64840i) q^{53} +(5.50688 + 2.56282i) q^{55} -2.83822 q^{56} +(-1.33676 + 0.971215i) q^{58} +(-6.21390 - 4.51466i) q^{59} +(-1.93943 - 5.96895i) q^{61} +(1.49113 + 1.08337i) q^{62} +(2.48916 - 7.66083i) q^{64} -8.51056 q^{65} -15.4673 q^{67} +(-0.0236055 + 0.0726501i) q^{68} +(-2.08800 - 1.51702i) q^{70} +(-4.29593 - 13.2215i) q^{71} +(-4.86593 - 3.53531i) q^{73} +(-2.38826 + 1.73517i) q^{74} +0.0810106 q^{76} +(-3.25521 + 0.635311i) q^{77} +(-4.83332 + 14.8754i) q^{79} +(5.88482 - 4.27557i) q^{80} +(0.399188 + 1.22857i) q^{82} +(1.35217 + 4.16157i) q^{83} +(-8.10479 + 5.88848i) q^{85} +(3.49426 - 10.7542i) q^{86} +(1.14011 - 9.34400i) q^{88} -15.3437 q^{89} +(3.75955 - 2.73147i) q^{91} +(0.00813063 + 0.00590725i) q^{92} +(-2.60240 - 8.00937i) q^{94} +(8.59515 + 6.24474i) q^{95} +(0.745114 - 2.29323i) q^{97} +1.40927 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8	\( 16 q + 3 q^{2} - 11 q^{4} + 5 q^{5} - 4 q^{7} + 5 q^{8} + 12 q^{10} + 3 q^{11} - 7 q^{13} - 2 q^{14} + 17 q^{16} + 5 q^{17} + 19 q^{19} - q^{20} - 33 q^{22} - 32 q^{23} + 7 q^{25} + 27 q^{26} + 4 q^{28} - 3 q^{29} - 7 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} + 4 q^{37} + 5 q^{38} - 10 q^{40} + 10 q^{41} - 8 q^{43} + 38 q^{44} - 42 q^{46} + 23 q^{47} - 4 q^{49} - 52 q^{50} + 33 q^{52} - 4 q^{53} - 12 q^{55} + 20 q^{58} - 17 q^{59} - 7 q^{61} - 79 q^{62} + 7 q^{64} + 8 q^{65} - 38 q^{67} + 2 q^{68} - 18 q^{70} + 14 q^{71} - 35 q^{73} + 29 q^{74} + 52 q^{76} + 3 q^{77} + 15 q^{79} + 87 q^{80} + 19 q^{82} - 5 q^{83} + 6 q^{85} + 52 q^{86} + 55 q^{88} - 74 q^{89} + 13 q^{91} + 55 q^{92} - 24 q^{94} - 32 q^{95} + 20 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 11 * q^4 + 5 * q^5 - 4 * q^7 + 5 * q^8 + 12 * q^10 + 3 * q^11 - 7 * q^13 - 2 * q^14 + 17 * q^16 + 5 * q^17 + 19 * q^19 - q^20 - 33 * q^22 - 32 * q^23 + 7 * q^25 + 27 * q^26 + 4 * q^28 - 3 * q^29 - 7 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 + 4 * q^37 + 5 * q^38 - 10 * q^40 + 10 * q^41 - 8 * q^43 + 38 * q^44 - 42 * q^46 + 23 * q^47 - 4 * q^49 - 52 * q^50 + 33 * q^52 - 4 * q^53 - 12 * q^55 + 20 * q^58 - 17 * q^59 - 7 * q^61 - 79 * q^62 + 7 * q^64 + 8 * q^65 - 38 * q^67 + 2 * q^68 - 18 * q^70 + 14 * q^71 - 35 * q^73 + 29 * q^74 + 52 * q^76 + 3 * q^77 + 15 * q^79 + 87 * q^80 + 19 * q^82 - 5 * q^83 + 6 * q^85 + 52 * q^86 + 55 * q^88 - 74 * q^89 + 13 * q^91 + 55 * q^92 - 24 * q^94 - 32 * q^95 + 20 * q^97 - 2 * q^98

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