LMFDB - Embedded newform 99.2.f.a.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.f (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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	99.82
Dual form			99.2.f.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 2.48990i) q^{2} +(-3.92705 + 2.85317i) q^{4} +(0.190983 - 0.587785i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-6.04508 - 4.39201i) q^{8} +O(q^{10})$	\(q+(0.809017 + 2.48990i) q^{2} +(-3.92705 + 2.85317i) q^{4} +(0.190983 - 0.587785i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-6.04508 - 4.39201i) q^{8} +1.61803 q^{10} +(3.30902 - 0.224514i) q^{11} +(0.0729490 + 0.224514i) q^{13} +(2.11803 + 1.53884i) q^{14} +(3.04508 - 9.37181i) q^{16} +(0.354102 - 1.08981i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(0.927051 + 2.85317i) q^{20} +(3.23607 + 8.05748i) q^{22} -0.236068 q^{23} +(3.73607 + 2.71441i) q^{25} +(-0.500000 + 0.363271i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(-4.85410 + 3.52671i) q^{29} +(-1.88197 - 5.79210i) q^{31} +10.8541 q^{32} +3.00000 q^{34} +(-0.190983 - 0.587785i) q^{35} +(5.04508 - 3.66547i) q^{37} +(4.73607 - 14.5761i) q^{38} +(-3.73607 + 2.71441i) q^{40} +(0.190983 + 0.138757i) q^{41} -6.70820 q^{43} +(-12.3541 + 10.3229i) q^{44} +(-0.190983 - 0.587785i) q^{46} +(-8.16312 - 5.93085i) q^{47} +(-1.85410 + 5.70634i) q^{49} +(-3.73607 + 11.4984i) q^{50} +(-0.927051 - 0.673542i) q^{52} +(0.118034 + 0.363271i) q^{53} +(0.500000 - 1.98787i) q^{55} -7.47214 q^{56} +(-12.7082 - 9.23305i) q^{58} +(5.97214 - 4.33901i) q^{59} +(-3.57295 + 10.9964i) q^{61} +(12.8992 - 9.37181i) q^{62} +(2.69098 + 8.28199i) q^{64} +0.145898 q^{65} +1.85410 q^{67} +(1.71885 + 5.29007i) q^{68} +(1.30902 - 0.951057i) q^{70} +(-3.19098 + 9.82084i) q^{71} +(4.61803 - 3.35520i) q^{73} +(13.2082 + 9.59632i) q^{74} +28.4164 q^{76} +(2.54508 - 2.12663i) q^{77} +(3.39919 + 10.4616i) q^{79} +(-4.92705 - 3.57971i) q^{80} +(-0.190983 + 0.587785i) q^{82} +(-0.454915 + 1.40008i) q^{83} +(-0.572949 - 0.416272i) q^{85} +(-5.42705 - 16.7027i) q^{86} +(-20.9894 - 13.1760i) q^{88} +8.23607 q^{89} +(0.190983 + 0.138757i) q^{91} +(0.927051 - 0.673542i) q^{92} +(8.16312 - 25.1235i) q^{94} +(-2.92705 + 2.12663i) q^{95} +(2.42705 + 7.46969i) q^{97} -15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 9 q^{4} + 3 q^{5} + q^{7} - 13 q^{8}+O(q^{10}) $ 4 * q + q^2 - 9 * q^4 + 3 * q^5 + q^7 - 13 * q^8	$ 4 q + q^{2} - 9 q^{4} + 3 q^{5} + q^{7} - 13 q^{8} + 2 q^{10} + 11 q^{11} + 7 q^{13} + 4 q^{14} + q^{16} - 12 q^{17} - 10 q^{19} - 3 q^{20} + 4 q^{22} + 8 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 6 q^{29} - 12 q^{31} + 30 q^{32} + 12 q^{34} - 3 q^{35} + 9 q^{37} + 10 q^{38} - 6 q^{40} + 3 q^{41} - 36 q^{44} - 3 q^{46} - 17 q^{47} + 6 q^{49} - 6 q^{50} + 3 q^{52} - 4 q^{53} + 2 q^{55} - 12 q^{56} - 24 q^{58} + 6 q^{59} - 21 q^{61} + 27 q^{62} + 13 q^{64} + 14 q^{65} - 6 q^{67} + 27 q^{68} + 3 q^{70} - 15 q^{71} + 14 q^{73} + 26 q^{74} + 60 q^{76} - q^{77} - 11 q^{79} - 13 q^{80} - 3 q^{82} - 13 q^{83} - 9 q^{85} - 15 q^{86} - 37 q^{88} + 24 q^{89} + 3 q^{91} - 3 q^{92} + 17 q^{94} - 5 q^{95} + 3 q^{97} - 36 q^{98}+O(q^{100}) $ 4 * q + q^2 - 9 * q^4 + 3 * q^5 + q^7 - 13 * q^8 + 2 * q^10 + 11 * q^11 + 7 * q^13 + 4 * q^14 + q^16 - 12 * q^17 - 10 * q^19 - 3 * q^20 + 4 * q^22 + 8 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 6 * q^29 - 12 * q^31 + 30 * q^32 + 12 * q^34 - 3 * q^35 + 9 * q^37 + 10 * q^38 - 6 * q^40 + 3 * q^41 - 36 * q^44 - 3 * q^46 - 17 * q^47 + 6 * q^49 - 6 * q^50 + 3 * q^52 - 4 * q^53 + 2 * q^55 - 12 * q^56 - 24 * q^58 + 6 * q^59 - 21 * q^61 + 27 * q^62 + 13 * q^64 + 14 * q^65 - 6 * q^67 + 27 * q^68 + 3 * q^70 - 15 * q^71 + 14 * q^73 + 26 * q^74 + 60 * q^76 - q^77 - 11 * q^79 - 13 * q^80 - 3 * q^82 - 13 * q^83 - 9 * q^85 - 15 * q^86 - 37 * q^88 + 24 * q^89 + 3 * q^91 - 3 * q^92 + 17 * q^94 - 5 * q^95 + 3 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.809017	+	2.48990i	0.572061	+	1.76062i	0.645974	+	0.763359i	$0.276451\pi$
$2$	0.809017	+	2.48990i	0.572061	+	1.76062i	−0.0739128	+	0.997265i	$0.523549\pi$
$3$		0			0
$3$		0			0
$4$	−3.92705	+	2.85317i	−1.96353	+	1.42658i
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	−0.899226	−	0.437485i	$-0.855869\pi$
$5$	0.190983	−	0.587785i	0.0854102	−	0.262866i	0.984636	+	0.174619i	$0.0558694\pi$
$6$		0			0
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i	−0.424304	−	0.905520i	$-0.639481\pi$
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i	0.730084	+	0.683358i	$0.239481\pi$
$8$	−6.04508	−	4.39201i	−2.13726	−	1.55281i
$9$		0			0
$10$	1.61803			0.511667
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$11$	3.30902	−	0.224514i	0.997706	−	0.0676935i
$12$		0			0
$13$	0.0729490	+	0.224514i	0.0202324	+	0.0622690i	0.960663	−	0.277717i	$-0.0895777\pi$
$13$	0.0729490	+	0.224514i	0.0202324	+	0.0622690i	−0.940431	+	0.339986i	$0.889578\pi$
$14$	2.11803	+	1.53884i	0.566068	+	0.411273i
$15$		0			0
$16$	3.04508	−	9.37181i	0.761271	−	2.34295i
$17$	0.354102	−	1.08981i	0.0858823	−	0.264319i	−0.898888	−	0.438178i	$-0.855624\pi$
$17$	0.354102	−	1.08981i	0.0858823	−	0.264319i	0.984770	+	0.173860i	$0.0556239\pi$
$18$		0			0
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.107719	−	0.994181i	$-0.534355\pi$
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.978810	+	0.204772i	$0.934355\pi$
$20$	0.927051	+	2.85317i	0.207295	+	0.637988i
$21$		0			0
$22$	3.23607	+	8.05748i	0.689932	+	1.71786i
$23$	−0.236068			−0.0492236			−0.0246118	−	0.999697i	$-0.507835\pi$
$23$	−0.236068			−0.0492236			−0.0246118	+	0.999697i	$0.507835\pi$
$24$		0			0
$25$	3.73607	+	2.71441i	0.747214	+	0.542882i
$26$	−0.500000	+	0.363271i	−0.0980581	+	0.0712434i
$27$		0			0
$28$	−1.50000	+	4.61653i	−0.283473	+	0.872441i
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	−0.938821	−	0.344405i	$-0.888081\pi$
$29$	−4.85410	+	3.52671i	−0.901384	+	0.654894i	0.0374370	+	0.999299i	$0.488081\pi$
$30$		0			0
$31$	−1.88197	−	5.79210i	−0.338011	−	1.04029i	−0.965220	−	0.261440i	$-0.915803\pi$
$31$	−1.88197	−	5.79210i	−0.338011	−	1.04029i	0.627209	−	0.778851i	$-0.284197\pi$
$32$	10.8541			1.91875
$33$		0			0
$34$	3.00000			0.514496
$35$	−0.190983	−	0.587785i	−0.0322820	−	0.0993538i
$36$		0			0
$37$	5.04508	−	3.66547i	0.829407	−	0.602599i	−0.0899846	−	0.995943i	$-0.528682\pi$
$37$	5.04508	−	3.66547i	0.829407	−	0.602599i	0.919391	+	0.393344i	$0.128682\pi$
$38$	4.73607	−	14.5761i	0.768292	−	2.36456i
$39$		0			0
$40$	−3.73607	+	2.71441i	−0.590724	+	0.429186i
$41$	0.190983	+	0.138757i	0.0298265	+	0.0216702i	0.602599	−	0.798044i	$-0.294132\pi$
$41$	0.190983	+	0.138757i	0.0298265	+	0.0216702i	−0.572772	+	0.819715i	$0.694132\pi$
$42$		0			0
$43$	−6.70820			−1.02299			−0.511496	−	0.859286i	$-0.670908\pi$
$43$	−6.70820			−1.02299			−0.511496	+	0.859286i	$0.670908\pi$
$44$	−12.3541	+	10.3229i	−1.86245	+	1.55623i
$45$		0			0
$46$	−0.190983	−	0.587785i	−0.0281589	−	0.0866642i
$47$	−8.16312	−	5.93085i	−1.19071	−	0.865104i	−0.197374	−	0.980328i	$-0.563241\pi$
$47$	−8.16312	−	5.93085i	−1.19071	−	0.865104i	−0.993339	+	0.115224i	$0.963241\pi$
$48$		0			0
$49$	−1.85410	+	5.70634i	−0.264872	+	0.815191i
$50$	−3.73607	+	11.4984i	−0.528360	+	1.62612i
$51$		0			0
$52$	−0.927051	−	0.673542i	−0.128559	−	0.0934035i
$53$	0.118034	+	0.363271i	0.0162132	+	0.0498991i	0.958836	−	0.283961i	$-0.0916486\pi$
$53$	0.118034	+	0.363271i	0.0162132	+	0.0498991i	−0.942623	+	0.333860i	$0.891649\pi$
$54$		0			0
$55$	0.500000	−	1.98787i	0.0674200	−	0.268044i
$56$	−7.47214			−0.998506
$57$		0			0
$58$	−12.7082	−	9.23305i	−1.66867	−	1.21236i
$59$	5.97214	−	4.33901i	0.777506	−	0.564891i	−0.126724	−	0.991938i	$-0.540446\pi$
$59$	5.97214	−	4.33901i	0.777506	−	0.564891i	0.904229	+	0.427047i	$0.140446\pi$
$60$		0			0
$61$	−3.57295	+	10.9964i	−0.457469	+	1.40795i	0.410742	+	0.911751i	$0.365270\pi$
$61$	−3.57295	+	10.9964i	−0.457469	+	1.40795i	−0.868212	+	0.496194i	$0.834730\pi$
$62$	12.8992	−	9.37181i	1.63820	−	1.19022i
$63$		0			0
$64$	2.69098	+	8.28199i	0.336373	+	1.03525i
$65$	0.145898			0.0180964
$66$		0			0
$67$	1.85410			0.226515			0.113257	−	0.993566i	$-0.463872\pi$
$67$	1.85410			0.226515			0.113257	+	0.993566i	$0.463872\pi$
$68$	1.71885	+	5.29007i	0.208441	+	0.641515i
$69$		0			0
$70$	1.30902	−	0.951057i	0.156457	−	0.113673i
$71$	−3.19098	+	9.82084i	−0.378700	+	1.16552i	0.562248	+	0.826968i	$0.309937\pi$
$71$	−3.19098	+	9.82084i	−0.378700	+	1.16552i	−0.940948	+	0.338550i	$0.890063\pi$
$72$		0			0
$73$	4.61803	−	3.35520i	0.540500	−	0.392696i	−0.283771	−	0.958892i	$-0.591585\pi$
$73$	4.61803	−	3.35520i	0.540500	−	0.392696i	0.824271	+	0.566196i	$0.191585\pi$
$74$	13.2082	+	9.59632i	1.53542	+	1.11555i
$75$		0			0
$76$	28.4164			3.25959
$77$	2.54508	−	2.12663i	0.290039	−	0.242352i
$78$		0			0
$79$	3.39919	+	10.4616i	0.382438	+	1.17702i	0.938322	+	0.345764i	$0.112380\pi$
$79$	3.39919	+	10.4616i	0.382438	+	1.17702i	−0.555883	+	0.831260i	$0.687620\pi$
$80$	−4.92705	−	3.57971i	−0.550861	−	0.400224i
$81$		0			0
$82$	−0.190983	+	0.587785i	−0.0210905	+	0.0649100i
$83$	−0.454915	+	1.40008i	−0.0499334	+	0.153679i	−0.972914	−	0.231167i	$-0.925746\pi$
$83$	−0.454915	+	1.40008i	−0.0499334	+	0.153679i	0.922981	+	0.384846i	$0.125746\pi$
$84$		0			0
$85$	−0.572949	−	0.416272i	−0.0621450	−	0.0451510i
$86$	−5.42705	−	16.7027i	−0.585214	−	1.80110i
$87$		0			0
$88$	−20.9894	−	13.1760i	−2.23747	−	1.40457i
$89$	8.23607			0.873021			0.436511	−	0.899699i	$-0.356214\pi$
$89$	8.23607			0.873021			0.436511	+	0.899699i	$0.356214\pi$
$90$		0			0
$91$	0.190983	+	0.138757i	0.0200205	+	0.0145457i
$92$	0.927051	−	0.673542i	0.0966517	−	0.0702216i
$93$		0			0
$94$	8.16312	−	25.1235i	0.841961	−	2.59129i
$95$	−2.92705	+	2.12663i	−0.300309	+	0.218187i
$96$		0			0
$97$	2.42705	+	7.46969i	0.246430	+	0.758433i	0.995398	+	0.0958268i	$0.0305495\pi$
$97$	2.42705	+	7.46969i	0.246430	+	0.758433i	−0.748968	+	0.662606i	$0.769451\pi$
$98$	−15.7082			−1.58677
$99$		0			0
$100$	−22.4164			−2.24164
$101$	3.16312	+	9.73508i	0.314742	+	0.968677i	0.975860	+	0.218395i	$0.0700821\pi$
$101$	3.16312	+	9.73508i	0.314742	+	0.968677i	−0.661118	+	0.750282i	$0.729918\pi$
$102$		0			0
$103$	8.85410	−	6.43288i	0.872421	−	0.633851i	−0.0588148	−	0.998269i	$-0.518732\pi$
$103$	8.85410	−	6.43288i	0.872421	−	0.633851i	0.931235	+	0.364418i	$0.118732\pi$
$104$	0.545085	−	1.67760i	0.0534500	−	0.164502i
$105$		0			0
$106$	−0.809017	+	0.587785i	−0.0785787	+	0.0570908i
$107$	−9.28115	−	6.74315i	−0.897243	−	0.651885i	0.0405134	−	0.999179i	$-0.487101\pi$
$107$	−9.28115	−	6.74315i	−0.897243	−	0.651885i	−0.937756	+	0.347294i	$0.887101\pi$
$108$		0			0
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$	5.35410	−	0.363271i	0.510494	−	0.0346366i
$111$		0			0
$112$	−3.04508	−	9.37181i	−0.287733	−	0.885553i
$113$	10.8992	+	7.91872i	1.02531	+	0.744931i	0.967364	−	0.253389i	$-0.0815453\pi$
$113$	10.8992	+	7.91872i	1.02531	+	0.744931i	0.0579448	+	0.998320i	$0.481545\pi$
$114$		0			0
$115$	−0.0450850	+	0.138757i	−0.00420420	+	0.0129392i
$116$	9.00000	−	27.6992i	0.835629	−	2.57180i
$117$		0			0
$118$	15.6353	+	11.3597i	1.43934	+	1.04574i
$119$	−0.354102	−	1.08981i	−0.0324605	−	0.0999031i
$120$		0			0
$121$	10.8992	−	1.48584i	0.990835	−	0.135076i
$122$	−30.2705			−2.74056
$123$		0			0
$124$	23.9164	+	17.3763i	2.14776	+	1.56044i
$125$	4.80902	−	3.49396i	0.430132	−	0.312509i
$126$		0			0
$127$	2.38197	−	7.33094i	0.211365	−	0.650516i	−0.788026	−	0.615641i	$-0.788897\pi$
$127$	2.38197	−	7.33094i	0.211365	−	0.650516i	0.999392	−	0.0348741i	$-0.0111030\pi$
$128$	−0.881966	+	0.640786i	−0.0779555	+	0.0566380i
$129$		0			0
$130$	0.118034	+	0.363271i	0.0103523	+	0.0318610i
$131$	11.7984			1.03083			0.515414	−	0.856941i	$-0.327638\pi$
$131$	11.7984			1.03083			0.515414	+	0.856941i	$0.327638\pi$
$132$		0			0
$133$	−5.85410			−0.507615
$134$	1.50000	+	4.61653i	0.129580	+	0.398807i
$135$		0			0
$136$	−6.92705	+	5.03280i	−0.593990	+	0.431559i
$137$	−3.01722	+	9.28605i	−0.257779	+	0.793361i	0.735491	+	0.677535i	$0.236952\pi$
$137$	−3.01722	+	9.28605i	−0.257779	+	0.793361i	−0.993269	+	0.115826i	$0.963048\pi$
$138$		0			0
$139$	−11.7812	+	8.55951i	−0.999264	+	0.726008i	−0.961930	−	0.273295i	$-0.911887\pi$
$139$	−11.7812	+	8.55951i	−0.999264	+	0.726008i	−0.0373340	+	0.999303i	$0.511887\pi$
$140$	2.42705	+	1.76336i	0.205123	+	0.149031i
$141$		0			0
$142$	−27.0344			−2.26868
$143$	0.291796	+	0.726543i	0.0244012	+	0.0607565i
$144$		0			0
$145$	1.14590	+	3.52671i	0.0951617	+	0.292877i
$146$	12.0902	+	8.78402i	1.00059	+	0.726971i
$147$		0			0
$148$	−9.35410	+	28.7890i	−0.768902	+	2.36644i
$149$	1.30902	−	4.02874i	0.107239	−	0.330047i	−0.883011	−	0.469353i	$-0.844487\pi$
$149$	1.30902	−	4.02874i	0.107239	−	0.330047i	0.990249	+	0.139306i	$0.0444871\pi$
$150$		0			0
$151$	−0.854102	−	0.620541i	−0.0695058	−	0.0504989i	0.552490	−	0.833520i	$-0.313678\pi$
$151$	−0.854102	−	0.620541i	−0.0695058	−	0.0504989i	−0.621996	+	0.783021i	$0.713678\pi$
$152$	13.5172	+	41.6017i	1.09639	+	3.37435i
$153$		0			0
$154$	7.35410	+	4.61653i	0.592610	+	0.372010i
$155$	−3.76393			−0.302326
$156$		0			0
$157$	−12.7082	−	9.23305i	−1.01423	−	0.736878i	−0.0491340	−	0.998792i	$-0.515646\pi$
$157$	−12.7082	−	9.23305i	−1.01423	−	0.736878i	−0.965091	+	0.261915i	$0.915646\pi$
$158$	−23.2984	+	16.9273i	−1.85352	+	1.34666i
$159$		0			0
$160$	2.07295	−	6.37988i	0.163881	−	0.504374i
$161$	−0.190983	+	0.138757i	−0.0150516	+	0.0109356i
$162$		0			0
$163$	−1.59017	−	4.89404i	−0.124552	−	0.383331i	0.869267	−	0.494342i	$-0.164591\pi$
$163$	−1.59017	−	4.89404i	−0.124552	−	0.383331i	−0.993819	+	0.111011i	$0.964591\pi$
$164$	−1.14590			−0.0894796
$165$		0			0
$166$	−3.85410			−0.299136
$167$	−3.71885	−	11.4454i	−0.287773	−	0.885674i	−0.985554	−	0.169363i	$-0.945829\pi$
$167$	−3.71885	−	11.4454i	−0.287773	−	0.885674i	0.697781	−	0.716311i	$-0.254171\pi$
$168$		0			0
$169$	10.4721	−	7.60845i	0.805549	−	0.585266i
$170$	0.572949	−	1.76336i	0.0439432	−	0.135243i
$171$		0			0
$172$	26.3435	−	19.1396i	2.00867	−	1.45938i
$173$	−14.5902	−	10.6004i	−1.10927	−	0.805932i	−0.126722	−	0.991938i	$-0.540445\pi$
$173$	−14.5902	−	10.6004i	−1.10927	−	0.805932i	−0.982549	+	0.186006i	$0.940445\pi$
$174$		0			0
$175$	4.61803			0.349091
$176$	7.97214	−	31.6951i	0.600922	−	2.38911i
$177$		0			0
$178$	6.66312	+	20.5070i	0.499422	+	1.53706i
$179$	−6.89919	−	5.01255i	−0.515669	−	0.374656i	0.299301	−	0.954159i	$-0.403247\pi$
$179$	−6.89919	−	5.01255i	−0.515669	−	0.374656i	−0.814970	+	0.579503i	$0.803247\pi$
$180$		0			0
$181$	0.781153	−	2.40414i	0.0580626	−	0.178698i	−0.917819	−	0.396999i	$-0.870051\pi$
$181$	0.781153	−	2.40414i	0.0580626	−	0.178698i	0.975881	+	0.218301i	$0.0700515\pi$
$182$	−0.190983	+	0.587785i	−0.0141566	+	0.0435695i
$183$		0			0
$184$	1.42705	+	1.03681i	0.105204	+	0.0764349i
$185$	−1.19098	−	3.66547i	−0.0875628	−	0.269491i
$186$		0			0
$187$	0.927051	−	3.68571i	0.0677927	−	0.269526i
$188$	48.9787			3.57214
$189$		0			0
$190$	−7.66312	−	5.56758i	−0.555941	−	0.403915i
$191$	−0.663119	+	0.481784i	−0.0479816	+	0.0348607i	−0.611518	−	0.791231i	$-0.709441\pi$
$191$	−0.663119	+	0.481784i	−0.0479816	+	0.0348607i	0.563536	+	0.826092i	$0.309441\pi$
$192$		0			0
$193$	−0.972136	+	2.99193i	−0.0699759	+	0.215364i	−0.979929	−	0.199348i	$-0.936118\pi$
$193$	−0.972136	+	2.99193i	−0.0699759	+	0.215364i	0.909953	+	0.414712i	$0.136118\pi$
$194$	−16.6353	+	12.0862i	−1.19434	+	0.867740i
$195$		0			0
$196$	−9.00000	−	27.6992i	−0.642857	−	1.97851i
$197$	−13.0344			−0.928666			−0.464333	−	0.885661i	$-0.653706\pi$
$197$	−13.0344			−0.928666			−0.464333	+	0.885661i	$0.653706\pi$
$198$		0			0
$199$	6.70820			0.475532			0.237766	−	0.971322i	$-0.423585\pi$
$199$	6.70820			0.475532			0.237766	+	0.971322i	$0.423585\pi$
$200$	−10.6631	−	32.8177i	−0.753996	−	2.32056i
$201$		0			0
$202$	−21.6803	+	15.7517i	−1.52542	+	1.10828i
$203$	−1.85410	+	5.70634i	−0.130132	+	0.400506i
$204$		0			0
$205$	0.118034	−	0.0857567i	0.00824385	−	0.00598951i
$206$	23.1803	+	16.8415i	1.61505	+	1.17340i
$207$		0			0
$208$	2.32624			0.161296
$209$	−16.4443	−	10.3229i	−1.13747	−	0.714047i
$210$		0			0
$211$	1.11803	+	3.44095i	0.0769686	+	0.236885i	0.982137	−	0.188169i	$-0.0602552\pi$
$211$	1.11803	+	3.44095i	0.0769686	+	0.236885i	−0.905168	+	0.425054i	$0.860255\pi$
$212$	−1.50000	−	1.08981i	−0.103020	−	0.0748487i
$213$		0			0
$214$	9.28115	−	28.5645i	0.634447	−	1.95263i
$215$	−1.28115	+	3.94298i	−0.0873739	+	0.268909i
$216$		0			0
$217$	−4.92705	−	3.57971i	−0.334470	−	0.243007i
$218$	−9.70820	−	29.8788i	−0.657523	−	2.02365i
$219$		0			0
$220$	3.70820	+	9.23305i	0.250007	+	0.622492i
$221$	0.270510			0.0181965
$222$		0			0
$223$	−5.80902	−	4.22050i	−0.389001	−	0.282625i	0.376045	−	0.926601i	$-0.377284\pi$
$223$	−5.80902	−	4.22050i	−0.389001	−	0.282625i	−0.765046	+	0.643976i	$0.777284\pi$
$224$	8.78115	−	6.37988i	0.586715	−	0.426274i
$225$		0			0
$226$	−10.8992	+	33.5442i	−0.725003	+	2.23133i
$227$	10.6631	−	7.74721i	0.707736	−	0.514200i	−0.174706	−	0.984621i	$-0.555898\pi$
$227$	10.6631	−	7.74721i	0.707736	−	0.514200i	0.882443	+	0.470420i	$0.155898\pi$
$228$		0			0
$229$	0.145898	+	0.449028i	0.00964121	+	0.0296726i	0.955761	−	0.294143i	$-0.0950342\pi$
$229$	0.145898	+	0.449028i	0.00964121	+	0.0296726i	−0.946120	+	0.323816i	$0.895034\pi$
$230$	−0.381966			−0.0251861
$231$		0			0
$232$	44.8328			2.94342
$233$	1.28115	+	3.94298i	0.0839311	+	0.258313i	0.984211	−	0.176997i	$-0.0566384\pi$
$233$	1.28115	+	3.94298i	0.0839311	+	0.258313i	−0.900280	+	0.435311i	$0.856638\pi$
$234$		0			0
$235$	−5.04508	+	3.66547i	−0.329105	+	0.239109i
$236$	−11.0729	+	34.0790i	−0.720788	+	2.21836i
$237$		0			0
$238$	2.42705	−	1.76336i	0.157322	−	0.114301i
$239$	0.309017	+	0.224514i	0.0199886	+	0.0145226i	0.597735	−	0.801694i	$-0.296068\pi$
$239$	0.309017	+	0.224514i	0.0199886	+	0.0145226i	−0.577746	+	0.816217i	$0.696068\pi$
$240$		0			0
$241$	8.29180			0.534122			0.267061	−	0.963680i	$-0.413948\pi$
$241$	8.29180			0.534122			0.267061	+	0.963680i	$0.413948\pi$
$242$	12.5172	+	25.9358i	0.804637	+	1.66722i
$243$		0			0
$244$	−17.3435	−	53.3777i	−1.11030	−	3.41716i
$245$	3.00000	+	2.17963i	0.191663	+	0.139251i
$246$		0			0
$247$	0.427051	−	1.31433i	0.0271726	−	0.0836287i
$248$	−14.0623	+	43.2793i	−0.892957	+	2.74824i
$249$		0			0
$250$	12.5902	+	9.14729i	0.796272	+	0.578526i
$251$	6.79180	+	20.9030i	0.428694	+	1.31939i	0.899412	+	0.437102i	$0.143995\pi$
$251$	6.79180	+	20.9030i	0.428694	+	1.31939i	−0.470718	+	0.882284i	$0.656005\pi$
$252$		0			0
$253$	−0.781153	+	0.0530006i	−0.0491107	+	0.00333212i
$254$	20.1803			1.26623
$255$		0			0
$256$	11.7812	+	8.55951i	0.736322	+	0.534969i
$257$	24.0623	−	17.4823i	1.50097	−	1.09052i	0.530970	−	0.847390i	$-0.321828\pi$
$257$	24.0623	−	17.4823i	1.50097	−	1.09052i	0.969995	−	0.243125i	$-0.0781725\pi$
$258$		0			0
$259$	1.92705	−	5.93085i	0.119741	−	0.368525i
$260$	−0.572949	+	0.416272i	−0.0355328	+	0.0258161i
$261$		0			0
$262$	9.54508	+	29.3768i	0.589697	+	1.81490i
$263$	15.2705			0.941620			0.470810	−	0.882235i	$-0.343962\pi$
$263$	15.2705			0.941620			0.470810	+	0.882235i	$0.343962\pi$
$264$		0			0
$265$	0.236068			0.0145015
$266$	−4.73607	−	14.5761i	−0.290387	−	0.893719i
$267$		0			0
$268$	−7.28115	+	5.29007i	−0.444767	+	0.323142i
$269$	7.85410	−	24.1724i	0.478873	−	1.47382i	−0.361789	−	0.932260i	$-0.617834\pi$
$269$	7.85410	−	24.1724i	0.478873	−	1.47382i	0.840662	−	0.541560i	$-0.182166\pi$
$270$		0			0
$271$	−15.0623	+	10.9434i	−0.914970	+	0.664765i	−0.942267	−	0.334863i	$-0.891310\pi$
$271$	−15.0623	+	10.9434i	−0.914970	+	0.664765i	0.0272970	+	0.999627i	$0.491310\pi$
$272$	−9.13525	−	6.63715i	−0.553906	−	0.402436i
$273$		0			0
$274$	−25.5623			−1.54428
$275$	12.9721	+	8.14324i	0.782249	+	0.491056i
$276$		0			0
$277$	−9.02786	−	27.7849i	−0.542432	−	1.66943i	−0.727019	−	0.686617i	$-0.759095\pi$
$277$	−9.02786	−	27.7849i	−0.542432	−	1.66943i	0.184587	−	0.982816i	$-0.440905\pi$
$278$	−30.8435	−	22.4091i	−1.84987	−	1.34401i
$279$		0			0
$280$	−1.42705	+	4.39201i	−0.0852826	+	0.262473i
$281$	−7.65248	+	23.5519i	−0.456508	+	1.40499i	0.412847	+	0.910801i	$0.364535\pi$
$281$	−7.65248	+	23.5519i	−0.456508	+	1.40499i	−0.869355	+	0.494188i	$0.835465\pi$
$282$		0			0
$283$	4.61803	+	3.35520i	0.274514	+	0.199446i	0.716521	−	0.697566i	$-0.245733\pi$
$283$	4.61803	+	3.35520i	0.274514	+	0.199446i	−0.442007	+	0.897011i	$0.645733\pi$
$284$	−15.4894	−	47.6713i	−0.919124	−	2.82877i
$285$		0			0
$286$	−1.57295	+	1.31433i	−0.0930104	+	0.0777178i
$287$	0.236068			0.0139347
$288$		0			0
$289$	12.6910	+	9.22054i	0.746528	+	0.542385i
$290$	−7.85410	+	5.70634i	−0.461209	+	0.335088i
$291$		0			0
$292$	−8.56231	+	26.3521i	−0.501071	+	1.54214i
$293$	−17.5172	+	12.7270i	−1.02337	+	0.743520i	−0.966970	−	0.254889i	$-0.917961\pi$
$293$	−17.5172	+	12.7270i	−1.02337	+	0.743520i	−0.0563966	+	0.998408i	$0.517961\pi$
$294$		0			0
$295$	−1.40983	−	4.33901i	−0.0820835	−	0.252627i
$296$	−46.5967			−2.70838
$297$		0			0
$298$	11.0902			0.642436
$299$	−0.0172209	−	0.0530006i	−0.000995912	−	0.00306510i
$300$		0			0
$301$	−5.42705	+	3.94298i	−0.312810	+	0.227270i
$302$	0.854102	−	2.62866i	0.0491480	−	0.151262i
$303$		0			0
$304$	−46.6697	+	33.9075i	−2.67669	+	1.94473i
$305$	5.78115	+	4.20025i	0.331028	+	0.240506i
$306$		0			0
$307$	27.9787			1.59683			0.798415	−	0.602108i	$-0.205672\pi$
$307$	27.9787			1.59683			0.798415	+	0.602108i	$0.205672\pi$
$308$	−3.92705	+	15.6129i	−0.223764	+	0.889629i
$309$		0			0
$310$	−3.04508	−	9.37181i	−0.172949	−	0.532283i
$311$	9.42705	+	6.84915i	0.534559	+	0.388380i	0.822060	−	0.569400i	$-0.192825\pi$
$311$	9.42705	+	6.84915i	0.534559	+	0.388380i	−0.287501	+	0.957780i	$0.592825\pi$
$312$		0			0
$313$	−0.781153	+	2.40414i	−0.0441534	+	0.135890i	−0.970703	−	0.240282i	$-0.922760\pi$
$313$	−0.781153	+	2.40414i	−0.0441534	+	0.135890i	0.926550	+	0.376172i	$0.122760\pi$
$314$	12.7082	−	39.1118i	0.717165	−	2.20721i
$315$		0			0
$316$	−43.1976	−	31.3849i	−2.43005	−	1.76554i
$317$	2.10739	+	6.48588i	0.118363	+	0.364283i	0.992634	−	0.121155i	$-0.0386599\pi$
$317$	2.10739	+	6.48588i	0.118363	+	0.364283i	−0.874271	+	0.485439i	$0.838660\pi$
$318$		0			0
$319$	−15.2705	+	12.7598i	−0.854984	+	0.714410i
$320$	5.38197			0.300861
$321$		0			0
$322$	−0.500000	−	0.363271i	−0.0278639	−	0.0202443i
$323$	−5.42705	+	3.94298i	−0.301969	+	0.219393i
$324$		0			0
$325$	−0.336881	+	1.03681i	−0.0186868	+	0.0575121i
$326$	10.8992	−	7.91872i	0.603650	−	0.438577i
$327$		0			0
$328$	−0.545085	−	1.67760i	−0.0300973	−	0.0926299i
$329$	−10.0902			−0.556289
$330$		0			0
$331$	16.7082			0.918366			0.459183	−	0.888342i	$-0.348142\pi$
$331$	16.7082			0.918366			0.459183	+	0.888342i	$0.348142\pi$
$332$	−2.20820	−	6.79615i	−0.121191	−	0.372987i
$333$		0			0
$334$	25.4894	−	18.5191i	1.39472	−	1.01332i
$335$	0.354102	−	1.08981i	0.0193467	−	0.0595429i
$336$		0			0
$337$	14.7082	−	10.6861i	0.801207	−	0.582111i	−0.110061	−	0.993925i	$-0.535105\pi$
$337$	14.7082	−	10.6861i	0.801207	−	0.582111i	0.911268	+	0.411814i	$0.135105\pi$
$338$	27.4164	+	19.9192i	1.49126	+	1.08346i
$339$		0			0
$340$	3.43769			0.186435
$341$	−7.52786	−	18.7436i	−0.407657	−	1.01502i
$342$		0			0
$343$	4.01722	+	12.3637i	0.216910	+	0.667579i
$344$	40.5517	+	29.4625i	2.18640	+	1.58851i
$345$		0			0
$346$	14.5902	−	44.9039i	0.784372	−	2.41405i
$347$	0.472136	−	1.45309i	0.0253456	−	0.0780057i	−0.937584	−	0.347760i	$-0.886942\pi$
$347$	0.472136	−	1.45309i	0.0253456	−	0.0780057i	0.962929	+	0.269754i	$0.0869424\pi$
$348$		0			0
$349$	−10.2812	−	7.46969i	−0.550337	−	0.399844i	0.277572	−	0.960705i	$-0.410470\pi$
$349$	−10.2812	−	7.46969i	−0.550337	−	0.399844i	−0.827910	+	0.560861i	$0.810470\pi$
$350$	3.73607	+	11.4984i	0.199701	+	0.614617i
$351$		0			0
$352$	35.9164	−	2.43690i	1.91435	−	0.129887i
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$		0			0
$355$	5.16312	+	3.75123i	0.274030	+	0.199094i
$356$	−32.3435	+	23.4989i	−1.71420	+	1.24544i
$357$		0			0
$358$	6.89919	−	21.2335i	0.364633	−	1.12223i
$359$	−7.85410	+	5.70634i	−0.414524	+	0.301169i	−0.775431	−	0.631433i	$-0.782467\pi$
$359$	−7.85410	+	5.70634i	−0.414524	+	0.301169i	0.360907	+	0.932602i	$0.382467\pi$
$360$		0			0
$361$	4.71885	+	14.5231i	0.248360	+	0.764375i
$362$	6.61803			0.347836
$363$		0			0
$364$	−1.14590			−0.0600614
$365$	−1.09017	−	3.35520i	−0.0570621	−	0.175619i
$366$		0			0
$367$	−17.9164	+	13.0170i	−0.935229	+	0.679484i	−0.947267	−	0.320444i	$-0.896168\pi$
$367$	−17.9164	+	13.0170i	−0.935229	+	0.679484i	0.0120386	+	0.999928i	$0.496168\pi$
$368$	−0.718847	+	2.21238i	−0.0374725	+	0.115328i
$369$		0			0
$370$	8.16312	−	5.93085i	0.424380	−	0.308330i
$371$	0.309017	+	0.224514i	0.0160434	+	0.0116562i
$372$		0			0
$373$	0.888544			0.0460071			0.0230035	−	0.999735i	$-0.492677\pi$
$373$	0.888544			0.0460071			0.0230035	+	0.999735i	$0.492677\pi$
$374$	9.92705	−	0.673542i	0.513316	−	0.0348280i
$375$		0			0
$376$	23.2984	+	71.7050i	1.20152	+	3.69790i
$377$	−1.14590	−	0.832544i	−0.0590168	−	0.0428782i
$378$		0			0
$379$	−7.69098	+	23.6704i	−0.395059	+	1.21587i	0.533856	+	0.845575i	$0.320742\pi$
$379$	−7.69098	+	23.6704i	−0.395059	+	1.21587i	−0.928915	+	0.370292i	$0.879258\pi$
$380$	5.42705	−	16.7027i	0.278402	−	0.856833i
$381$		0			0
$382$	−1.73607	−	1.26133i	−0.0888250	−	0.0645351i
$383$	3.92705	+	12.0862i	0.200663	+	0.617577i	0.999864	+	0.0165128i	$0.00525642\pi$
$383$	3.92705	+	12.0862i	0.200663	+	0.617577i	−0.799201	+	0.601064i	$0.794744\pi$
$384$		0			0
$385$	−0.763932	−	1.90211i	−0.0389336	−	0.0969407i
$386$	−8.23607			−0.419205
$387$		0			0
$388$	−30.8435	−	22.4091i	−1.56584	−	1.13765i
$389$	−29.7254	+	21.5968i	−1.50714	+	1.09500i	−0.539712	+	0.841850i	$0.681467\pi$
$389$	−29.7254	+	21.5968i	−1.50714	+	1.09500i	−0.967427	+	0.253151i	$0.918533\pi$
$390$		0			0
$391$	−0.0835921	+	0.257270i	−0.00422744	+	0.0130107i
$392$	36.2705	−	26.3521i	1.83194	−	1.33098i
$393$		0			0
$394$	−10.5451	−	32.4544i	−0.531254	−	1.63503i
$395$	6.79837			0.342063
$396$		0			0
$397$	−18.7082			−0.938938			−0.469469	−	0.882949i	$-0.655555\pi$
$397$	−18.7082			−0.938938			−0.469469	+	0.882949i	$0.655555\pi$
$398$	5.42705	+	16.7027i	0.272033	+	0.837233i
$399$		0			0
$400$	36.8156	−	26.7481i	1.84078	−	1.33740i
$401$	9.79180	−	30.1360i	0.488979	−	1.50492i	−0.337155	−	0.941449i	$-0.609465\pi$
$401$	9.79180	−	30.1360i	0.488979	−	1.50492i	0.826134	−	0.563473i	$-0.190535\pi$
$402$		0			0
$403$	1.16312	−	0.845055i	0.0579391	−	0.0420952i
$404$	−40.1976	−	29.2052i	−1.99990	−	1.45301i
$405$		0			0
$406$	−15.7082			−0.779585
$407$	15.8713	−	13.2618i	0.786712	−	0.657363i
$408$		0			0
$409$	−2.00000	−	6.15537i	−0.0988936	−	0.304363i	0.889355	−	0.457217i	$-0.151154\pi$
$409$	−2.00000	−	6.15537i	−0.0988936	−	0.304363i	−0.988249	+	0.152854i	$0.951154\pi$
$410$	0.309017	+	0.224514i	0.0152613	+	0.0110880i
$411$		0			0
$412$	−16.4164	+	50.5245i	−0.808778	+	2.48916i
$413$	2.28115	−	7.02067i	0.112248	−	0.345464i
$414$		0			0
$415$	0.736068	+	0.534785i	0.0361322	+	0.0262515i
$416$	0.791796	+	2.43690i	0.0388210	+	0.119479i
$417$		0			0
$418$	12.3992	−	49.2959i	0.606464	−	2.41114i
$419$	−31.4508			−1.53647			−0.768237	−	0.640165i	$-0.778866\pi$
$419$	−31.4508			−1.53647			−0.768237	+	0.640165i	$0.778866\pi$
$420$		0			0
$421$	−8.50000	−	6.17561i	−0.414265	−	0.300981i	0.361061	−	0.932542i	$-0.382414\pi$
$421$	−8.50000	−	6.17561i	−0.414265	−	0.300981i	−0.775326	+	0.631561i	$0.782414\pi$
$422$	−7.66312	+	5.56758i	−0.373035	+	0.271026i
$423$		0			0
$424$	0.881966	−	2.71441i	0.0428321	−	0.131824i
$425$	4.28115	−	3.11044i	0.207666	−	0.150878i
$426$		0			0
$427$	3.57295	+	10.9964i	0.172907	+	0.532153i
$428$	55.6869			2.69173
$429$		0			0
$430$	−10.8541			−0.523431
$431$	1.82624	+	5.62058i	0.0879668	+	0.270734i	0.985357	−	0.170504i	$-0.0545395\pi$
$431$	1.82624	+	5.62058i	0.0879668	+	0.270734i	−0.897390	+	0.441238i	$0.854540\pi$
$432$		0			0
$433$	−28.5623	+	20.7517i	−1.37262	+	0.997264i	−0.375089	+	0.926989i	$0.622388\pi$
$433$	−28.5623	+	20.7517i	−1.37262	+	0.997264i	−0.997528	+	0.0702758i	$0.977612\pi$
$434$	4.92705	−	15.1639i	0.236506	−	0.727891i
$435$		0			0
$436$	47.1246	−	34.2380i	2.25686	−	1.63970i
$437$	1.11803	+	0.812299i	0.0534828	+	0.0388575i
$438$		0			0
$439$	23.2918			1.11166			0.555828	−	0.831297i	$-0.312401\pi$
$439$	23.2918			1.11166			0.555828	+	0.831297i	$0.312401\pi$
$440$	−11.7533	+	9.82084i	−0.560316	+	0.468190i
$441$		0			0
$442$	0.218847	+	0.673542i	0.0104095	+	0.0320371i
$443$	−25.5623	−	18.5721i	−1.21450	−	0.882387i	−0.218870	−	0.975754i	$-0.570237\pi$
$443$	−25.5623	−	18.5721i	−1.21450	−	0.882387i	−0.995632	+	0.0933668i	$0.970237\pi$
$444$		0			0
$445$	1.57295	−	4.84104i	0.0745649	−	0.229487i
$446$	5.80902	−	17.8783i	0.275065	−	0.846563i
$447$		0			0
$448$	7.04508	+	5.11855i	0.332849	+	0.241829i
$449$	2.79837	+	8.61251i	0.132063	+	0.406449i	0.995122	−	0.0986549i	$-0.0314540\pi$
$449$	2.79837	+	8.61251i	0.132063	+	0.406449i	−0.863058	+	0.505104i	$0.831454\pi$
$450$		0			0
$451$	0.663119	+	0.416272i	0.0312251	+	0.0196015i
$452$	−65.3951			−3.07593
$453$		0			0
$454$	27.9164	+	20.2825i	1.31018	+	0.951903i
$455$	0.118034	−	0.0857567i	0.00553352	−	0.00402034i
$456$		0			0
$457$	7.40983	−	22.8051i	0.346617	−	1.06678i	−0.614095	−	0.789232i	$-0.710479\pi$
$457$	7.40983	−	22.8051i	0.346617	−	1.06678i	0.960712	−	0.277546i	$-0.0895211\pi$
$458$	−1.00000	+	0.726543i	−0.0467269	+	0.0339491i
$459$		0			0
$460$	−0.218847	−	0.673542i	−0.0102038	−	0.0314041i
$461$	−9.27051			−0.431771			−0.215885	−	0.976419i	$-0.569264\pi$
$461$	−9.27051			−0.431771			−0.215885	+	0.976419i	$0.569264\pi$
$462$		0			0
$463$	1.72949			0.0803762			0.0401881	−	0.999192i	$-0.487204\pi$
$463$	1.72949			0.0803762			0.0401881	+	0.999192i	$0.487204\pi$
$464$	18.2705	+	56.2308i	0.848187	+	2.61045i
$465$		0			0
$466$	−8.78115	+	6.37988i	−0.406779	+	0.295542i
$467$	−6.45492	+	19.8662i	−0.298698	+	0.919297i	0.683256	+	0.730179i	$0.260563\pi$
$467$	−6.45492	+	19.8662i	−0.298698	+	0.919297i	−0.981954	+	0.189119i	$0.939437\pi$
$468$		0			0
$469$	1.50000	−	1.08981i	0.0692636	−	0.0503229i
$470$	−13.2082	−	9.59632i	−0.609249	−	0.442645i
$471$		0			0
$472$	−55.1591			−2.53890
$473$	−22.1976	+	1.50609i	−1.02064	+	0.0692499i
$474$		0			0
$475$	−8.35410	−	25.7113i	−0.383312	−	1.17971i
$476$	4.50000	+	3.26944i	0.206257	+	0.149855i
$477$		0			0
$478$	−0.309017	+	0.951057i	−0.0141341	+	0.0435003i
$479$	8.77051	−	26.9929i	0.400735	−	1.23333i	−0.523670	−	0.851921i	$-0.675437\pi$
$479$	8.77051	−	26.9929i	0.400735	−	1.23333i	0.924405	−	0.381414i	$-0.124563\pi$
$480$		0			0
$481$	1.19098	+	0.865300i	0.0543042	+	0.0394543i
$482$	6.70820	+	20.6457i	0.305550	+	0.940387i
$483$		0			0
$484$	−38.5623	+	36.9322i	−1.75283	+	1.67874i
$485$	4.85410			0.220413
$486$		0			0
$487$	10.2812	+	7.46969i	0.465884	+	0.338484i	0.795835	−	0.605514i	$-0.207032\pi$
$487$	10.2812	+	7.46969i	0.465884	+	0.338484i	−0.329951	+	0.943998i	$0.607032\pi$
$488$	69.8951	−	50.7818i	3.16400	−	2.29878i
$489$		0			0
$490$	−3.00000	+	9.23305i	−0.135526	+	0.417107i
$491$	−14.4894	+	10.5271i	−0.653896	+	0.475083i	−0.864596	−	0.502468i	$-0.832426\pi$
$491$	−14.4894	+	10.5271i	−0.653896	+	0.475083i	0.210700	+	0.977551i	$0.432426\pi$
$492$		0			0
$493$	2.12461	+	6.53888i	0.0956877	+	0.294496i
$494$	3.61803			0.162783
$495$		0			0
$496$	−60.0132			−2.69467
$497$	3.19098	+	9.82084i	0.143135	+	0.440525i
$498$		0			0
$499$	14.6803	−	10.6659i	0.657182	−	0.477471i	−0.208528	−	0.978016i	$-0.566867\pi$
$499$	14.6803	−	10.6659i	0.657182	−	0.477471i	0.865710	+	0.500546i	$0.166867\pi$
$500$	−8.91641	+	27.4419i	−0.398754	+	1.22724i
$501$		0			0
$502$	−46.5517	+	33.8218i	−2.07770	+	1.50954i
$503$	7.00000	+	5.08580i	0.312115	+	0.226765i	0.732803	−	0.680441i	$-0.238212\pi$
$503$	7.00000	+	5.08580i	0.312115	+	0.226765i	−0.420689	+	0.907205i	$0.638212\pi$
$504$		0			0
$505$	6.32624			0.281514
$506$	−0.763932	−	1.90211i	−0.0339609	−	0.0845592i
$507$		0			0
$508$	11.5623	+	35.5851i	0.512994	+	1.57883i
$509$	31.3435	+	22.7724i	1.38927	+	1.00937i	0.995945	+	0.0899695i	$0.0286770\pi$
$509$	31.3435	+	22.7724i	1.38927	+	1.00937i	0.393330	+	0.919397i	$0.371323\pi$
$510$		0			0
$511$	1.76393	−	5.42882i	0.0780318	−	0.240157i
$512$	−12.4549	+	38.3323i	−0.550435	+	1.69406i
$513$		0			0
$514$	62.9959	+	45.7692i	2.77863	+	2.01879i
$515$	−2.09017	−	6.43288i	−0.0921039	−	0.283467i
$516$		0			0
$517$	−28.3435	−	17.7926i	−1.24654	−	0.782516i
$518$	16.3262			0.717334
$519$		0			0
$520$	−0.881966	−	0.640786i	−0.0386768	−	0.0281003i
$521$	7.23607	−	5.25731i	0.317018	−	0.230327i	−0.417884	−	0.908500i	$-0.637228\pi$
$521$	7.23607	−	5.25731i	0.317018	−	0.230327i	0.734902	+	0.678173i	$0.237228\pi$
$522$		0			0
$523$	5.64590	−	17.3763i	0.246878	−	0.759812i	−0.748444	−	0.663198i	$-0.769199\pi$
$523$	5.64590	−	17.3763i	0.246878	−	0.759812i	0.995322	−	0.0966140i	$-0.0308013\pi$
$524$	−46.3328	+	33.6628i	−2.02406	+	1.47056i
$525$		0			0
$526$	12.3541	+	38.0220i	0.538664	+	1.65784i
$527$	−6.97871			−0.303998
$528$		0			0
$529$	−22.9443			−0.997577
$530$	0.190983	+	0.587785i	0.00829577	+	0.0255318i
$531$		0			0
$532$	22.9894	−	16.7027i	0.996715	−	0.724156i
$533$	−0.0172209	+	0.0530006i	−0.000745921	+	0.00229571i
$534$		0			0
$535$	−5.73607	+	4.16750i	−0.247992	+	0.180177i
$536$	−11.2082	−	8.14324i	−0.484121	−	0.351734i
$537$		0			0
$538$	66.5410			2.86879
$539$	−4.85410	+	19.2986i	−0.209081	+	0.831251i
$540$		0			0
$541$	−2.31559	−	7.12667i	−0.0995552	−	0.306399i	0.888859	−	0.458181i	$-0.151499\pi$
$541$	−2.31559	−	7.12667i	−0.0995552	−	0.306399i	−0.988414	+	0.151782i	$0.951499\pi$
$542$	−39.4336	−	28.6502i	−1.69382	−	1.23063i
$543$		0			0
$544$	3.84346	−	11.8290i	0.164787	−	0.507162i
$545$	−2.29180	+	7.05342i	−0.0981698	+	0.302135i
$546$		0			0
$547$	24.8713	+	18.0701i	1.06342	+	0.772621i	0.974718	−	0.223438i	$-0.0717279\pi$
$547$	24.8713	+	18.0701i	1.06342	+	0.772621i	0.0887027	+	0.996058i	$0.471728\pi$
$548$	−14.6459	−	45.0754i	−0.625642	−	1.92553i
$549$		0			0
$550$	−9.78115	+	38.8873i	−0.417070	+	1.65816i
$551$	35.1246			1.49636
$552$		0			0
$553$	8.89919	+	6.46564i	0.378432	+	0.274947i
$554$	61.8779	−	44.9569i	2.62894	−	1.91004i
$555$		0			0
$556$	21.8435	−	67.2273i	0.926369	−	2.85107i
$557$	30.4443	−	22.1191i	1.28997	−	0.937215i	0.290161	−	0.956978i	$-0.406291\pi$
$557$	30.4443	−	22.1191i	1.28997	−	0.937215i	0.999805	+	0.0197634i	$0.00629130\pi$
$558$		0			0
$559$	−0.489357	−	1.50609i	−0.0206976	−	0.0637006i
$560$	−6.09017			−0.257357
$561$		0			0
$562$	−64.8328			−2.73481
$563$	−12.5451	−	38.6098i	−0.528712	−	1.62721i	−0.756856	−	0.653582i	$-0.773266\pi$
$563$	−12.5451	−	38.6098i	−0.528712	−	1.62721i	0.228144	−	0.973627i	$-0.426734\pi$
$564$		0			0
$565$	6.73607	−	4.89404i	0.283389	−	0.205894i
$566$	−4.61803	+	14.2128i	−0.194110	+	0.597411i
$567$		0			0
$568$	62.4230	−	45.3530i	2.61921	−	1.90297i
$569$	27.6525	+	20.0907i	1.15925	+	0.842246i	0.989683	−	0.143272i	$-0.0457625\pi$
$569$	27.6525	+	20.0907i	1.15925	+	0.842246i	0.169569	+	0.985518i	$0.445763\pi$
$570$		0			0
$571$	−9.09017			−0.380412			−0.190206	−	0.981744i	$-0.560916\pi$
$571$	−9.09017			−0.380412			−0.190206	+	0.981744i	$0.560916\pi$
$572$	−3.21885	−	2.02063i	−0.134587	−	0.0844866i
$573$		0			0
$574$	0.190983	+	0.587785i	0.00797148	+	0.0245337i
$575$	−0.881966	−	0.640786i	−0.0367805	−	0.0267226i
$576$		0			0
$577$	9.79837	−	30.1563i	0.407912	−	1.25542i	−0.510528	−	0.859861i	$-0.670550\pi$
$577$	9.79837	−	30.1563i	0.407912	−	1.25542i	0.918439	−	0.395562i	$-0.129450\pi$
$578$	−12.6910	+	39.0588i	−0.527875	+	1.62463i
$579$		0			0
$580$	−14.5623	−	10.5801i	−0.604667	−	0.439316i
$581$	0.454915	+	1.40008i	0.0188731	+	0.0580853i
$582$		0			0
$583$	0.472136	+	1.17557i	0.0195539	+	0.0486872i
$584$	−42.6525			−1.76497
$585$		0			0
$586$	−45.8607	−	33.3197i	−1.89449	−	1.37643i
$587$	−1.71885	+	1.24882i	−0.0709444	+	0.0515441i	−0.622692	−	0.782467i	$-0.713961\pi$
$587$	−1.71885	+	1.24882i	−0.0709444	+	0.0515441i	0.551748	+	0.834011i	$0.313961\pi$
$588$		0			0
$589$	−11.0172	+	33.9075i	−0.453957	+	1.39714i
$590$	9.66312	−	7.02067i	0.397824	−	0.289036i
$591$		0			0
$592$	−18.9894	−	58.4432i	−0.780458	−	2.40200i
$593$	14.0344			0.576325			0.288163	−	0.957581i	$-0.406956\pi$
$593$	14.0344			0.576325			0.288163	+	0.957581i	$0.406956\pi$
$594$		0			0
$595$	−0.708204			−0.0290335
$596$	6.35410	+	19.5559i	0.260274	+	0.801041i
$597$		0			0
$598$	0.118034	−	0.0857567i	0.00482677	−	0.00350685i
$599$	−3.90983	+	12.0332i	−0.159751	+	0.491664i	−0.998611	−	0.0526833i	$-0.983223\pi$
$599$	−3.90983	+	12.0332i	−0.159751	+	0.491664i	0.838860	+	0.544347i	$0.183223\pi$
$600$		0			0
$601$	5.57295	−	4.04898i	0.227325	−	0.165162i	−0.468293	−	0.883573i	$-0.655131\pi$
$601$	5.57295	−	4.04898i	0.227325	−	0.165162i	0.695618	+	0.718412i	$0.255131\pi$
$602$	−14.2082	−	10.3229i	−0.579083	−	0.420729i
$603$		0			0
$604$	5.12461			0.208517
$605$	1.20820	−	6.69015i	0.0491205	−	0.271993i
$606$		0			0
$607$	−5.11803	−	15.7517i	−0.207735	−	0.639341i	−0.999590	−	0.0286327i	$-0.990885\pi$
$607$	−5.11803	−	15.7517i	−0.207735	−	0.639341i	0.791855	−	0.610709i	$-0.209115\pi$
$608$	−51.4058	−	37.3485i	−2.08478	−	1.51468i
$609$		0			0
$610$	−5.78115	+	17.7926i	−0.234072	+	0.720400i
$611$	0.736068	−	2.26538i	0.0297781	−	0.0916476i
$612$		0			0
$613$	11.5623	+	8.40051i	0.466997	+	0.339293i	0.796270	−	0.604942i	$-0.206804\pi$
$613$	11.5623	+	8.40051i	0.466997	+	0.339293i	−0.329273	+	0.944235i	$0.606804\pi$
$614$	22.6353	+	69.6642i	0.913485	+	2.81142i
$615$		0			0
$616$	−24.7254	+	1.67760i	−0.996216	+	0.0675924i
$617$	−11.1803			−0.450104			−0.225052	−	0.974347i	$-0.572255\pi$
$617$	−11.1803			−0.450104			−0.225052	+	0.974347i	$0.572255\pi$
$618$		0			0
$619$	−19.5172	−	14.1801i	−0.784463	−	0.569946i	0.121852	−	0.992548i	$-0.461117\pi$
$619$	−19.5172	−	14.1801i	−0.784463	−	0.569946i	−0.906315	+	0.422602i	$0.861117\pi$
$620$	14.7812	−	10.7391i	0.593625	−	0.431294i
$621$		0			0
$622$	−9.42705	+	29.0135i	−0.377990	+	1.16333i
$623$	6.66312	−	4.84104i	0.266952	−	0.193952i
$624$		0			0
$625$	6.00000	+	18.4661i	0.240000	+	0.738644i
$626$	−6.61803			−0.264510
$627$		0			0
$628$	76.2492			3.04268
$629$	−2.20820	−	6.79615i	−0.0880469	−	0.270980i
$630$		0			0
$631$	−15.5451	+	11.2942i	−0.618840	+	0.449614i	−0.852516	−	0.522701i	$-0.824924\pi$
$631$	−15.5451	+	11.2942i	−0.618840	+	0.449614i	0.233676	+	0.972314i	$0.424924\pi$
$632$	25.3992	−	78.1707i	1.01033	−	3.10946i
$633$		0			0
$634$	−14.4443	+	10.4944i	−0.573655	+	0.416785i
$635$	−3.85410	−	2.80017i	−0.152945	−	0.111121i
$636$		0			0
$637$	−1.41641			−0.0561201
$638$	−44.1246	−	27.6992i	−1.74691	−	1.09662i
$639$		0			0
$640$	0.208204	+	0.640786i	0.00822998	+	0.0253293i
$641$	−20.2984	−	14.7476i	−0.801738	−	0.582496i	0.109686	−	0.993966i	$-0.465016\pi$
$641$	−20.2984	−	14.7476i	−0.801738	−	0.582496i	−0.911423	+	0.411470i	$0.865016\pi$
$642$		0			0
$643$	6.44427	−	19.8334i	0.254137	−	0.782154i	−0.739861	−	0.672760i	$-0.765109\pi$
$643$	6.44427	−	19.8334i	0.254137	−	0.782154i	0.993998	−	0.109394i	$-0.0348912\pi$
$644$	0.354102	−	1.08981i	0.0139536	−	0.0429447i
$645$		0			0
$646$	−14.2082	−	10.3229i	−0.559014	−	0.406148i
$647$	−13.9164	−	42.8303i	−0.547110	−	1.68383i	−0.715918	−	0.698184i	$-0.753992\pi$
$647$	−13.9164	−	42.8303i	−0.547110	−	1.68383i	0.168808	−	0.985649i	$-0.446008\pi$
$648$		0			0
$649$	18.7877	−	15.6987i	0.737483	−	0.616227i
$650$	−2.85410			−0.111947
$651$		0			0
$652$	20.2082	+	14.6821i	0.791414	+	0.574996i
$653$	−4.54508	+	3.30220i	−0.177863	+	0.129225i	−0.673155	−	0.739502i	$-0.735061\pi$
$653$	−4.54508	+	3.30220i	−0.177863	+	0.129225i	0.495292	+	0.868727i	$0.335061\pi$
$654$		0			0
$655$	2.25329	−	6.93491i	0.0880433	−	0.270969i
$656$	1.88197	−	1.36733i	0.0734784	−	0.0533852i
$657$		0			0
$658$	−8.16312	−	25.1235i	−0.318232	−	0.979416i
$659$	41.1246			1.60199			0.800994	−	0.598673i	$-0.204305\pi$
$659$	41.1246			1.60199			0.800994	+	0.598673i	$0.204305\pi$
$660$		0			0
$661$	36.5623			1.42211			0.711054	−	0.703137i	$-0.248218\pi$
$661$	36.5623			1.42211			0.711054	+	0.703137i	$0.248218\pi$
$662$	13.5172	+	41.6017i	0.525362	+	1.61690i
$663$		0			0
$664$	8.89919	−	6.46564i	0.345355	−	0.250915i
$665$	−1.11803	+	3.44095i	−0.0433555	+	0.133435i
$666$		0			0
$667$	1.14590	−	0.832544i	0.0443693	−	0.0322362i
$668$	47.2599	+	34.3363i	1.82854	+	1.32851i
$669$		0			0
$670$	3.00000			0.115900
$671$	−9.35410	+	37.1895i	−0.361111	+	1.43568i
$672$		0			0
$673$	11.0729	+	34.0790i	0.426831	+	1.31365i	0.901230	+	0.433340i	$0.142665\pi$
$673$	11.0729	+	34.0790i	0.426831	+	1.31365i	−0.474399	+	0.880310i	$0.657335\pi$
$674$	38.5066	+	27.9767i	1.48322	+	1.07762i
$675$		0			0
$676$	−19.4164	+	59.7576i	−0.746785	+	2.29837i
$677$	−4.18034	+	12.8658i	−0.160664	+	0.494471i	−0.998691	−	0.0511572i	$-0.983709\pi$
$677$	−4.18034	+	12.8658i	−0.160664	+	0.494471i	0.838027	+	0.545629i	$0.183709\pi$
$678$		0			0
$679$	6.35410	+	4.61653i	0.243848	+	0.177166i
$680$	1.63525	+	5.03280i	0.0627092	+	0.192999i
$681$		0			0
$682$	40.5795	−	33.9075i	1.55387	−	1.29839i
$683$	−9.06888			−0.347011			−0.173506	−	0.984833i	$-0.555509\pi$
$683$	−9.06888			−0.347011			−0.173506	+	0.984833i	$0.555509\pi$
$684$		0			0
$685$	4.88197	+	3.54696i	0.186530	+	0.135522i
$686$	−27.5344	+	20.0049i	−1.05127	+	0.763792i
$687$		0			0
$688$	−20.4271	+	62.8680i	−0.778774	+	2.39682i
$689$	−0.0729490	+	0.0530006i	−0.00277914	+	0.00201916i
$690$		0			0
$691$	0.416408	+	1.28157i	0.0158409	+	0.0487533i	0.958665	−	0.284539i	$-0.0918405\pi$
$691$	0.416408	+	1.28157i	0.0158409	+	0.0487533i	−0.942824	+	0.333292i	$0.891840\pi$
$692$	87.5410			3.32781
$693$		0			0
$694$	4.00000			0.151838
$695$	2.78115	+	8.55951i	0.105495	+	0.324681i
$696$		0			0
$697$	0.218847	−	0.159002i	0.00828942	−	0.00602262i
$698$	10.2812	−	31.6421i	0.389147	−	1.19767i
$699$		0			0
$700$	−18.1353	+	13.1760i	−0.685448	+	0.498007i
$701$	−28.1525	−	20.4540i	−1.06330	−	0.772536i	−0.0886075	−	0.996067i	$-0.528242\pi$
$701$	−28.1525	−	20.4540i	−1.06330	−	0.772536i	−0.974697	+	0.223531i	$0.928242\pi$
$702$		0			0
$703$	−36.5066			−1.37687
$704$	10.7639	+	26.8011i	0.405681	+	1.01010i
$705$		0			0
$706$	9.70820	+	29.8788i	0.365373	+	1.12450i
$707$	8.28115	+	6.01661i	0.311445	+	0.226278i
$708$		0			0
$709$	3.46556	−	10.6659i	0.130152	−	0.400566i	−0.864653	−	0.502370i	$-0.832462\pi$
$709$	3.46556	−	10.6659i	0.130152	−	0.400566i	0.994804	+	0.101804i	$0.0324615\pi$
$710$	−5.16312	+	15.8904i	−0.193768	+	0.596358i
$711$		0			0
$712$	−49.7877	−	36.1729i	−1.86587	−	1.35564i
$713$	0.444272	+	1.36733i	0.0166381	+	0.0512068i
$714$		0			0
$715$	0.482779	−	0.0327561i	0.0180549	−	0.00122501i
$716$	41.3951			1.54701
$717$		0			0
$718$	−20.5623	−	14.9394i	−0.767378	−	0.557533i
$719$	−31.1353	+	22.6211i	−1.16115	+	0.843624i	−0.989923	−	0.141608i	$-0.954773\pi$
$719$	−31.1353	+	22.6211i	−1.16115	+	0.843624i	−0.171226	+	0.985232i	$0.554773\pi$
$720$		0			0
$721$	3.38197	−	10.4086i	0.125951	−	0.387637i
$722$	−32.3435	+	23.4989i	−1.20370	+	0.874538i
$723$		0			0
$724$	3.79180	+	11.6699i	0.140921	+	0.433710i
$725$	−27.7082			−1.02906
$726$		0			0
$727$	−9.14590			−0.339203			−0.169601	−	0.985513i	$-0.554248\pi$
$727$	−9.14590			−0.339203			−0.169601	+	0.985513i	$0.554248\pi$
$728$	−0.545085	−	1.67760i	−0.0202022	−	0.0621760i
$729$		0			0
$730$	7.47214	−	5.42882i	0.276556	−	0.200930i
$731$	−2.37539	+	7.31069i	−0.0878569	+	0.270396i
$732$		0			0
$733$	0.326238	−	0.237026i	0.0120499	−	0.00875474i	−0.581744	−	0.813372i	$-0.697629\pi$
$733$	0.326238	−	0.237026i	0.0120499	−	0.00875474i	0.593794	+	0.804617i	$0.297629\pi$
$734$	−46.9058	−	34.0790i	−1.73132	−	1.25788i
$735$		0			0
$736$	−2.56231			−0.0944478
$737$	6.13525	−	0.416272i	0.225995	−	0.0153336i
$738$		0			0
$739$	0.927051	+	2.85317i	0.0341021	+	0.104956i	0.966659	−	0.256068i	$-0.0824272\pi$
$739$	0.927051	+	2.85317i	0.0341021	+	0.104956i	−0.932557	+	0.361024i	$0.882427\pi$
$740$	15.1353	+	10.9964i	0.556383	+	0.404236i
$741$		0			0
$742$	−0.309017	+	0.951057i	−0.0113444	+	0.0349144i
$743$	13.2533	−	40.7894i	0.486216	−	1.49642i	−0.343996	−	0.938971i	$-0.611781\pi$
$743$	13.2533	−	40.7894i	0.486216	−	1.49642i	0.830212	−	0.557448i	$-0.188219\pi$
$744$		0			0
$745$	−2.11803	−	1.53884i	−0.0775988	−	0.0563788i
$746$	0.718847	+	2.21238i	0.0263189	+	0.0810011i
$747$		0			0
$748$	6.87539	+	17.1190i	0.251389	+	0.625933i
$749$	−11.4721			−0.419183
$750$		0			0
$751$	−13.0623	−	9.49032i	−0.476650	−	0.346307i	0.323377	−	0.946270i	$-0.395182\pi$
$751$	−13.0623	−	9.49032i	−0.476650	−	0.346307i	−0.800027	+	0.599963i	$0.795182\pi$
$752$	−80.4402	+	58.4432i	−2.93335	+	2.13121i
$753$		0			0
$754$	1.14590	−	3.52671i	0.0417311	−	0.128435i
$755$	−0.527864	+	0.383516i	−0.0192109	+	0.0139576i
$756$		0			0
$757$	1.54508	+	4.75528i	0.0561571	+	0.172834i	0.975201	−	0.221322i	$-0.0710371\pi$
$757$	1.54508	+	4.75528i	0.0561571	+	0.172834i	−0.919044	+	0.394156i	$0.871037\pi$
$758$	−65.1591			−2.36668
$759$		0			0
$760$	27.0344			0.980642
$761$	−9.05166	−	27.8582i	−0.328123	−	1.00986i	−0.970011	−	0.243060i	$-0.921849\pi$
$761$	−9.05166	−	27.8582i	−0.328123	−	1.00986i	0.641889	−	0.766798i	$-0.278151\pi$
$762$		0			0
$763$	−9.70820	+	7.05342i	−0.351461	+	0.255351i
$764$	1.22949	−	3.78398i	0.0444814	−	0.136900i
$765$		0			0
$766$	−26.9164	+	19.5559i	−0.972529	+	0.706584i
$767$	1.40983	+	1.02430i	0.0509060	+	0.0369854i
$768$		0			0
$769$	−34.5066			−1.24434			−0.622170	−	0.782883i	$-0.713749\pi$
$769$	−34.5066			−1.24434			−0.622170	+	0.782883i	$0.713749\pi$
$770$	4.11803	−	3.44095i	0.148404	−	0.124003i
$771$		0			0
$772$	−4.71885	−	14.5231i	−0.169835	−	0.522698i
$773$	21.9894	+	15.9762i	0.790902	+	0.574624i	0.908231	−	0.418469i	$-0.137433\pi$
$773$	21.9894	+	15.9762i	0.790902	+	0.574624i	−0.117329	+	0.993093i	$0.537433\pi$
$774$		0			0
$775$	8.69098	−	26.7481i	0.312189	−	0.960820i
$776$	18.1353	−	55.8146i	0.651018	−	2.00363i
$777$		0			0
$778$	−77.8222	−	56.5411i	−2.79006	−	2.02710i
$779$	−0.427051	−	1.31433i	−0.0153007	−	0.0470907i
$780$		0			0
$781$	−8.35410	+	33.2137i	−0.298933	+	1.18848i
$782$	−0.708204			−0.0253253
$783$		0			0
$784$	47.8328	+	34.7526i	1.70831	+	1.24116i
$785$	−7.85410	+	5.70634i	−0.280325	+	0.203668i
$786$		0			0
$787$	−3.00000	+	9.23305i	−0.106938	+	0.329123i	−0.990181	−	0.139795i	$-0.955356\pi$
$787$	−3.00000	+	9.23305i	−0.106938	+	0.329123i	0.883242	+	0.468917i	$0.155356\pi$
$788$	51.1869	−	37.1895i	1.82346	−	1.32482i
$789$		0			0
$790$	5.50000	+	16.9273i	0.195681	+	0.602245i
$791$	13.4721			0.479014
$792$		0			0
$793$	−2.72949			−0.0969270
$794$	−15.1353	−	46.5815i	−0.537130	−	1.65312i
$795$		0			0
$796$	−26.3435	+	19.1396i	−0.933719	+	0.678387i
$797$	−5.72949	+	17.6336i	−0.202949	+	0.624613i	0.796842	+	0.604187i	$0.206502\pi$
$797$	−5.72949	+	17.6336i	−0.202949	+	0.624613i	−0.999791	+	0.0204255i	$0.993498\pi$
$798$		0			0
$799$	−9.35410	+	6.79615i	−0.330924	+	0.240431i
$800$	40.5517	+	29.4625i	1.43372	+	1.04166i
$801$		0			0
$802$	82.9574			2.92933
$803$	14.5279	−	12.1392i	0.512677	−	0.428384i
$804$		0			0
$805$	0.0450850	+	0.138757i	0.00158904	+	0.00489055i
$806$	3.04508	+	2.21238i	0.107259	+	0.0779279i
$807$		0			0
$808$	23.6353	−	72.7418i	0.831485	−	2.55905i
$809$	−8.37132	+	25.7643i	−0.294320	+	0.905824i	0.689129	+	0.724639i	$0.257993\pi$
$809$	−8.37132	+	25.7643i	−0.294320	+	0.905824i	−0.983449	+	0.181185i	$0.942007\pi$
$810$		0			0
$811$	−29.5795	−	21.4908i	−1.03868	−	0.754644i	−0.0686507	−	0.997641i	$-0.521869\pi$
$811$	−29.5795	−	21.4908i	−1.03868	−	0.754644i	−0.970027	+	0.242997i	$0.921869\pi$
$812$	−9.00000	−	27.6992i	−0.315838	−	0.972050i
$813$		0			0
$814$	45.8607	+	28.7890i	1.60742	+	1.00905i
$815$	−3.18034			−0.111402
$816$		0			0
$817$	31.7705	+	23.0826i	1.11151	+	0.807559i
$818$	13.7082	−	9.95959i	0.479296	−	0.348229i
$819$		0			0
$820$	−0.218847	+	0.673542i	−0.00764247	+	0.0235211i
$821$	32.8435	−	23.8622i	1.14624	−	0.832795i	0.158268	−	0.987396i	$-0.449409\pi$
$821$	32.8435	−	23.8622i	1.14624	−	0.832795i	0.987977	+	0.154601i	$0.0494091\pi$
$822$		0			0
$823$	−8.60081	−	26.4706i	−0.299805	−	0.922706i	−0.981565	−	0.191130i	$-0.938785\pi$
$823$	−8.60081	−	26.4706i	−0.299805	−	0.922706i	0.681759	−	0.731577i	$-0.261215\pi$
$824$	−81.7771			−2.84884
$825$		0			0
$826$	19.3262			0.672446
$827$	3.29180	+	10.1311i	0.114467	+	0.352293i	0.991835	−	0.127524i	$-0.0407030\pi$
$827$	3.29180	+	10.1311i	0.114467	+	0.352293i	−0.877369	+	0.479817i	$0.840703\pi$
$828$		0			0
$829$	25.3992	−	18.4536i	0.882150	−	0.640920i	−0.0516692	−	0.998664i	$-0.516454\pi$
$829$	25.3992	−	18.4536i	0.882150	−	0.640920i	0.933819	+	0.357745i	$0.116454\pi$
$830$	−0.736068	+	2.26538i	−0.0255493	+	0.0786326i
$831$		0			0
$832$	−1.66312	+	1.20833i	−0.0576583	+	0.0418912i
$833$	5.56231	+	4.04125i	0.192722	+	0.140021i
$834$		0			0
$835$	−7.43769			−0.257392
$836$	94.0304	−	6.37988i	3.25211	−	0.220653i
$837$		0			0
$838$	−25.4443	−	78.3094i	−0.878958	−	2.70515i
$839$	−14.4271	−	10.4819i	−0.498077	−	0.361874i	0.310205	−	0.950670i	$-0.399602\pi$
$839$	−14.4271	−	10.4819i	−0.498077	−	0.361874i	−0.808282	+	0.588796i	$0.799602\pi$
$840$		0			0
$841$	2.16312	−	6.65740i	0.0745903	−	0.229565i
$842$	8.50000	−	26.1603i	0.292929	−	0.901544i
$843$		0			0
$844$	−14.2082	−	10.3229i	−0.489067	−	0.355328i
$845$	−2.47214	−	7.60845i	−0.0850441	−	0.261739i
$846$		0			0
$847$	7.94427	−	7.60845i	0.272968	−	0.261430i
$848$	3.76393			0.129254
$849$		0			0
$850$	11.2082	+	8.14324i	0.384438	+	0.279311i
$851$	−1.19098	+	0.865300i	−0.0408264	+	0.0296621i
$852$		0			0
$853$	−17.2533	+	53.1002i	−0.590741	+	1.81811i	−0.0158658	+	0.999874i	$0.505050\pi$
$853$	−17.2533	+	53.1002i	−0.590741	+	1.81811i	−0.574876	+	0.818241i	$0.694950\pi$
$854$	−24.4894	+	17.7926i	−0.838009	+	0.608849i
$855$		0			0
$856$	26.4894	+	81.5259i	0.905388	+	2.78650i
$857$	−27.7639			−0.948398			−0.474199	−	0.880418i	$-0.657262\pi$
$857$	−27.7639			−0.948398			−0.474199	+	0.880418i	$0.657262\pi$
$858$		0			0
$859$	−34.4164			−1.17427			−0.587136	−	0.809488i	$-0.699745\pi$
$859$	−34.4164			−1.17427			−0.587136	+	0.809488i	$0.699745\pi$
$860$	−6.21885	−	19.1396i	−0.212061	−	0.652656i
$861$		0			0
$862$	−12.5172	+	9.09429i	−0.426338	+	0.309753i
$863$	−0.0344419	+	0.106001i	−0.00117241	+	0.00360832i	−0.951641	−	0.307212i	$-0.900604\pi$
$863$	−0.0344419	+	0.106001i	−0.00117241	+	0.00360832i	0.950469	+	0.310821i	$0.100604\pi$
$864$		0			0
$865$	−9.01722	+	6.55139i	−0.306595	+	0.222754i
$866$	−74.7771	−	54.3287i	−2.54103	−	1.84617i
$867$		0			0
$868$	29.5623			1.00341
$869$	13.5967	+	33.8545i	0.461238	+	1.14844i
$870$		0			0
$871$	0.135255	+	0.416272i	0.00458294	+	0.0141048i
$872$	72.5410	+	52.7041i	2.45655	+	1.78479i
$873$		0			0
$874$	−1.11803	+	3.44095i	−0.0378181	+	0.116392i
$875$	1.83688	−	5.65334i	0.0620979	−	0.191118i
$876$		0			0
$877$	46.8779	+	34.0588i	1.58295	+	1.15008i	0.913208	+	0.407493i	$0.133597\pi$
$877$	46.8779	+	34.0588i	1.58295	+	1.15008i	0.669746	+	0.742590i	$0.266403\pi$
$878$	18.8435	+	57.9942i	0.635936	+	1.95721i
$879$		0			0
$880$	−17.1074	−	10.7391i	−0.576690	−	0.362016i
$881$	−6.20163			−0.208938			−0.104469	−	0.994528i	$-0.533314\pi$
$881$	−6.20163			−0.208938			−0.104469	+	0.994528i	$0.533314\pi$
$882$		0			0
$883$	−0.854102	−	0.620541i	−0.0287428	−	0.0208829i	0.573321	−	0.819331i	$-0.305655\pi$
$883$	−0.854102	−	0.620541i	−0.0287428	−	0.0208829i	−0.602064	+	0.798448i	$0.705655\pi$
$884$	−1.06231	+	0.771810i	−0.0357292	+	0.0259588i
$885$		0			0
$886$	25.5623	−	78.6727i	0.858782	−	2.64306i
$887$	−44.0795	+	32.0257i	−1.48005	+	1.07532i	−0.502504	+	0.864575i	$0.667588\pi$
$887$	−44.0795	+	32.0257i	−1.48005	+	1.07532i	−0.977542	+	0.210741i	$0.932412\pi$
$888$		0			0
$889$	−2.38197	−	7.33094i	−0.0798886	−	0.245872i
$890$	13.3262			0.446697
$891$		0			0
$892$	34.8541			1.16700
$893$	18.2533	+	56.1778i	0.610823	+	1.87992i
$894$		0			0
$895$	−4.26393	+	3.09793i	−0.142528	+	0.103552i
$896$	−0.336881	+	1.03681i	−0.0112544	+	0.0346375i
$897$		0			0
$898$	−19.1803	+	13.9353i	−0.640056	+	0.465028i
$899$	29.5623	+	21.4783i	0.985958	+	0.716340i
$900$		0			0
$901$	0.437694			0.0145817
$902$	−0.500000	+	1.98787i	−0.0166482	+	0.0661888i
$903$		0			0
$904$	−31.1074	−	95.7387i	−1.03462	−	3.18422i
$905$	−1.26393	−	0.918300i	−0.0420145	−	0.0305253i
$906$		0			0
$907$	−13.1008	+	40.3202i	−0.435005	+	1.33881i	0.458076	+	0.888913i	$0.348539\pi$
$907$	−13.1008	+	40.3202i	−0.435005	+	1.33881i	−0.893081	+	0.449896i	$0.851461\pi$
$908$	−19.7705	+	60.8474i	−0.656107	+	2.01929i
$909$		0			0
$910$	0.309017	+	0.224514i	0.0102438	+	0.00744257i
$911$	−11.9271	−	36.7077i	−0.395161	−	1.21618i	−0.928836	−	0.370491i	$-0.879190\pi$
$911$	−11.9271	−	36.7077i	−0.395161	−	1.21618i	0.533675	−	0.845689i	$-0.320810\pi$
$912$		0			0
$913$	−1.19098	+	4.73504i	−0.0394158	+	0.156707i
$914$	62.7771			2.07648
$915$		0			0
$916$	−1.85410	−	1.34708i	−0.0612613	−	0.0445089i
$917$	9.54508	−	6.93491i	0.315206	−	0.229011i
$918$		0			0
$919$	7.92705	−	24.3970i	0.261489	−	0.804781i	−0.730992	−	0.682386i	$-0.760942\pi$
$919$	7.92705	−	24.3970i	0.261489	−	0.804781i	0.992481	−	0.122395i	$-0.0390576\pi$
$920$	0.881966	−	0.640786i	0.0290776	−	0.0211261i
$921$		0			0
$922$	−7.50000	−	23.0826i	−0.246999	−	0.760186i
$923$	−2.43769			−0.0802377
$924$		0			0
$925$	28.7984			0.946885
$926$	1.39919	+	4.30625i	0.0459801	+	0.141512i
$927$		0			0
$928$	−52.6869	+	38.2793i	−1.72953	+	1.25658i
$929$	3.92705	−	12.0862i	0.128842	−	0.396536i	−0.865739	−	0.500495i	$-0.833151\pi$
$929$	3.92705	−	12.0862i	0.128842	−	0.396536i	0.994582	+	0.103959i	$0.0331512\pi$
$930$		0			0
$931$	28.4164	−	20.6457i	0.931310	−	0.676636i
$932$	−16.2812	−	11.8290i	−0.533307	−	0.387470i
$933$		0			0
$934$	−54.6869			−1.78941
$935$	−1.98936	−	1.24882i	−0.0650589	−	0.0408406i
$936$		0			0
$937$	12.8713	+	39.6139i	0.420488	+	1.29413i	0.907249	+	0.420593i	$0.138178\pi$
$937$	12.8713	+	39.6139i	0.420488	+	1.29413i	−0.486761	+	0.873535i	$0.661822\pi$
$938$	3.92705	+	2.85317i	0.128223	+	0.0931593i
$939$		0			0
$940$	9.35410	−	28.7890i	0.305097	−	0.938993i
$941$	4.46556	−	13.7436i	0.145573	−	0.448028i	−0.851511	−	0.524336i	$-0.824313\pi$
$941$	4.46556	−	13.7436i	0.145573	−	0.448028i	0.997084	+	0.0763087i	$0.0243134\pi$
$942$		0			0
$943$	−0.0450850	−	0.0327561i	−0.00146817	−	0.00106669i
$944$	−22.4787	−	69.1824i	−0.731620	−	2.25169i
$945$		0			0
$946$	−21.7082	−	54.0512i	−0.705795	−	1.75736i
$947$	32.3951			1.05270			0.526350	−	0.850268i	$-0.323560\pi$
$947$	32.3951			1.05270			0.526350	+	0.850268i	$0.323560\pi$
$948$		0			0
$949$	1.09017	+	0.792055i	0.0353884	+	0.0257112i
$950$	57.2599	−	41.6017i	1.85776	−	1.34974i
$951$		0			0
$952$	−2.64590	+	8.14324i	−0.0857540	+	0.263924i
$953$	9.18034	−	6.66991i	0.297380	−	0.216059i	−0.429082	−	0.903265i	$-0.641163\pi$
$953$	9.18034	−	6.66991i	0.297380	−	0.216059i	0.726463	+	0.687206i	$0.241163\pi$
$954$		0			0
$955$	0.156541	+	0.481784i	0.00506555	+	0.0155902i
$956$	−1.85410			−0.0599659
$957$		0			0
$958$	74.3050			2.40068
$959$	3.01722	+	9.28605i	0.0974311	+	0.299862i
$960$		0			0
$961$	−4.92705	+	3.57971i	−0.158937	+	0.115475i
$962$	−1.19098	+	3.66547i	−0.0383988	+	0.118179i
$963$		0			0
$964$	−32.5623	+	23.6579i	−1.04876	+	0.761970i
$965$	1.57295	+	1.14281i	0.0506350	+	0.0367885i
$966$		0			0
$967$	43.9230			1.41247			0.706234	−	0.707978i	$-0.250393\pi$
$967$	43.9230			1.41247			0.706234	+	0.707978i	$0.250393\pi$
$968$	−72.4123	−	38.8873i	−2.32742	−	1.24989i
$969$		0			0
$970$	3.92705	+	12.0862i	0.126090	+	0.388065i
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.110957	−	0.993825i	$-0.535392\pi$
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.979472	+	0.201582i	$0.935392\pi$
$972$		0			0
$973$	−4.50000	+	13.8496i	−0.144263	+	0.443997i
$974$	−10.2812	+	31.6421i	−0.329429	+	1.01388i
$975$		0			0
$976$	92.1763	+	66.9700i	2.95049	+	2.14366i
$977$	0.184405	+	0.567541i	0.00589964	+	0.0181572i	0.953963	−	0.299924i	$-0.0969614\pi$
$977$	0.184405	+	0.567541i	0.00589964	+	0.0181572i	−0.948063	+	0.318082i	$0.896961\pi$
$978$		0			0
$979$	27.2533	−	1.84911i	0.871019	−	0.0590979i
$980$	−18.0000			−0.574989
$981$		0			0
$982$	−37.9336	−	27.5604i	−1.21051	−	0.879488i
$983$	−6.56231	+	4.76779i	−0.209305	+	0.152069i	−0.687499	−	0.726185i	$-0.741292\pi$
$983$	−6.56231	+	4.76779i	−0.209305	+	0.152069i	0.478194	+	0.878254i	$0.341292\pi$
$984$		0			0
$985$	−2.48936	+	7.66145i	−0.0793175	+	0.244114i
$986$	−14.5623	+	10.5801i	−0.463758	+	0.336940i
$987$		0			0
$988$	2.07295	+	6.37988i	0.0659493	+	0.202971i
$989$	1.58359			0.0503553
$990$		0			0
$991$	3.74265			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$991$	3.74265			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$992$	−20.4271	−	62.8680i	−0.648560	−	1.99606i
$993$		0			0
$994$	−21.8713	+	15.8904i	−0.693716	+	0.504014i
$995$	1.28115	−	3.94298i	0.0406153	−	0.125001i
$996$		0			0
$997$	17.1525	−	12.4620i	0.543224	−	0.394676i	−0.282057	−	0.959398i	$-0.591017\pi$
$997$	17.1525	−	12.4620i	0.543224	−	0.394676i	0.825281	+	0.564722i	$0.191017\pi$
$998$	38.4336	+	27.9237i	1.21660	+	0.883908i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.f.a.82.1		4
3.2	odd	2		33.2.e.b.16.1	✓	4
9.2	odd	6		891.2.n.c.676.1		8
9.4	even	3		891.2.n.b.379.1		8
9.5	odd	6		891.2.n.c.379.1		8
9.7	even	3		891.2.n.b.676.1		8
11.3	even	5		1089.2.a.t.1.2		2
11.8	odd	10		1089.2.a.l.1.1		2
11.9	even	5	inner	99.2.f.a.64.1		4
12.11	even	2		528.2.y.b.49.1		4
15.2	even	4		825.2.bx.d.49.2		8
15.8	even	4		825.2.bx.d.49.1		8
15.14	odd	2		825.2.n.c.676.1		4
33.2	even	10		363.2.e.f.130.1		4
33.5	odd	10		363.2.e.k.202.1		4
33.8	even	10		363.2.a.i.1.2		2
33.14	odd	10		363.2.a.d.1.1		2
33.17	even	10		363.2.e.b.202.1		4
33.20	odd	10		33.2.e.b.31.1	yes	4
33.26	odd	10		363.2.e.k.124.1		4
33.29	even	10		363.2.e.b.124.1		4
33.32	even	2		363.2.e.f.148.1		4
99.20	odd	30		891.2.n.c.757.1		8
99.31	even	15		891.2.n.b.460.1		8
99.86	odd	30		891.2.n.c.460.1		8
99.97	even	15		891.2.n.b.757.1		8
132.47	even	10		5808.2.a.cj.1.1		2
132.107	odd	10		5808.2.a.ci.1.1		2
132.119	even	10		528.2.y.b.97.1		4
165.14	odd	10		9075.2.a.cb.1.2		2
165.53	even	20		825.2.bx.d.724.2		8
165.74	even	10		9075.2.a.u.1.1		2
165.119	odd	10		825.2.n.c.526.1		4
165.152	even	20		825.2.bx.d.724.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	3.2	odd	2
33.2.e.b.31.1	yes	4	33.20	odd	10
99.2.f.a.64.1		4	11.9	even	5	inner
99.2.f.a.82.1		4	1.1	even	1	trivial
363.2.a.d.1.1		2	33.14	odd	10
363.2.a.i.1.2		2	33.8	even	10
363.2.e.b.124.1		4	33.29	even	10
363.2.e.b.202.1		4	33.17	even	10
363.2.e.f.130.1		4	33.2	even	10
363.2.e.f.148.1		4	33.32	even	2
363.2.e.k.124.1		4	33.26	odd	10
363.2.e.k.202.1		4	33.5	odd	10
528.2.y.b.49.1		4	12.11	even	2
528.2.y.b.97.1		4	132.119	even	10
825.2.n.c.526.1		4	165.119	odd	10
825.2.n.c.676.1		4	15.14	odd	2
825.2.bx.d.49.1		8	15.8	even	4
825.2.bx.d.49.2		8	15.2	even	4
825.2.bx.d.724.1		8	165.152	even	20
825.2.bx.d.724.2		8	165.53	even	20
891.2.n.b.379.1		8	9.4	even	3
891.2.n.b.460.1		8	99.31	even	15
891.2.n.b.676.1		8	9.7	even	3
891.2.n.b.757.1		8	99.97	even	15
891.2.n.c.379.1		8	9.5	odd	6
891.2.n.c.460.1		8	99.86	odd	30
891.2.n.c.676.1		8	9.2	odd	6
891.2.n.c.757.1		8	99.20	odd	30
1089.2.a.l.1.1		2	11.8	odd	10
1089.2.a.t.1.2		2	11.3	even	5
5808.2.a.ci.1.1		2	132.107	odd	10
5808.2.a.cj.1.1		2	132.47	even	10
9075.2.a.u.1.1		2	165.74	even	10
9075.2.a.cb.1.2		2	165.14	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 2.48990i) q^{2} +(-3.92705 + 2.85317i) q^{4} +(0.190983 - 0.587785i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-6.04508 - 4.39201i) q^{8} +O(q^{10})\)	\(q+(0.809017 + 2.48990i) q^{2} +(-3.92705 + 2.85317i) q^{4} +(0.190983 - 0.587785i) q^{5} +(0.809017 - 0.587785i) q^{7} +(-6.04508 - 4.39201i) q^{8} +1.61803 q^{10} +(3.30902 - 0.224514i) q^{11} +(0.0729490 + 0.224514i) q^{13} +(2.11803 + 1.53884i) q^{14} +(3.04508 - 9.37181i) q^{16} +(0.354102 - 1.08981i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(0.927051 + 2.85317i) q^{20} +(3.23607 + 8.05748i) q^{22} -0.236068 q^{23} +(3.73607 + 2.71441i) q^{25} +(-0.500000 + 0.363271i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(-4.85410 + 3.52671i) q^{29} +(-1.88197 - 5.79210i) q^{31} +10.8541 q^{32} +3.00000 q^{34} +(-0.190983 - 0.587785i) q^{35} +(5.04508 - 3.66547i) q^{37} +(4.73607 - 14.5761i) q^{38} +(-3.73607 + 2.71441i) q^{40} +(0.190983 + 0.138757i) q^{41} -6.70820 q^{43} +(-12.3541 + 10.3229i) q^{44} +(-0.190983 - 0.587785i) q^{46} +(-8.16312 - 5.93085i) q^{47} +(-1.85410 + 5.70634i) q^{49} +(-3.73607 + 11.4984i) q^{50} +(-0.927051 - 0.673542i) q^{52} +(0.118034 + 0.363271i) q^{53} +(0.500000 - 1.98787i) q^{55} -7.47214 q^{56} +(-12.7082 - 9.23305i) q^{58} +(5.97214 - 4.33901i) q^{59} +(-3.57295 + 10.9964i) q^{61} +(12.8992 - 9.37181i) q^{62} +(2.69098 + 8.28199i) q^{64} +0.145898 q^{65} +1.85410 q^{67} +(1.71885 + 5.29007i) q^{68} +(1.30902 - 0.951057i) q^{70} +(-3.19098 + 9.82084i) q^{71} +(4.61803 - 3.35520i) q^{73} +(13.2082 + 9.59632i) q^{74} +28.4164 q^{76} +(2.54508 - 2.12663i) q^{77} +(3.39919 + 10.4616i) q^{79} +(-4.92705 - 3.57971i) q^{80} +(-0.190983 + 0.587785i) q^{82} +(-0.454915 + 1.40008i) q^{83} +(-0.572949 - 0.416272i) q^{85} +(-5.42705 - 16.7027i) q^{86} +(-20.9894 - 13.1760i) q^{88} +8.23607 q^{89} +(0.190983 + 0.138757i) q^{91} +(0.927051 - 0.673542i) q^{92} +(8.16312 - 25.1235i) q^{94} +(-2.92705 + 2.12663i) q^{95} +(2.42705 + 7.46969i) q^{97} -15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 9 q^{4} + 3 q^{5} + q^{7} - 13 q^{8}+O(q^{10}) \) 4 * q + q^2 - 9 * q^4 + 3 * q^5 + q^7 - 13 * q^8	\( 4 q + q^{2} - 9 q^{4} + 3 q^{5} + q^{7} - 13 q^{8} + 2 q^{10} + 11 q^{11} + 7 q^{13} + 4 q^{14} + q^{16} - 12 q^{17} - 10 q^{19} - 3 q^{20} + 4 q^{22} + 8 q^{23} + 6 q^{25} - 2 q^{26} - 6 q^{28} - 6 q^{29} - 12 q^{31} + 30 q^{32} + 12 q^{34} - 3 q^{35} + 9 q^{37} + 10 q^{38} - 6 q^{40} + 3 q^{41} - 36 q^{44} - 3 q^{46} - 17 q^{47} + 6 q^{49} - 6 q^{50} + 3 q^{52} - 4 q^{53} + 2 q^{55} - 12 q^{56} - 24 q^{58} + 6 q^{59} - 21 q^{61} + 27 q^{62} + 13 q^{64} + 14 q^{65} - 6 q^{67} + 27 q^{68} + 3 q^{70} - 15 q^{71} + 14 q^{73} + 26 q^{74} + 60 q^{76} - q^{77} - 11 q^{79} - 13 q^{80} - 3 q^{82} - 13 q^{83} - 9 q^{85} - 15 q^{86} - 37 q^{88} + 24 q^{89} + 3 q^{91} - 3 q^{92} + 17 q^{94} - 5 q^{95} + 3 q^{97} - 36 q^{98}+O(q^{100}) \) 4 * q + q^2 - 9 * q^4 + 3 * q^5 + q^7 - 13 * q^8 + 2 * q^10 + 11 * q^11 + 7 * q^13 + 4 * q^14 + q^16 - 12 * q^17 - 10 * q^19 - 3 * q^20 + 4 * q^22 + 8 * q^23 + 6 * q^25 - 2 * q^26 - 6 * q^28 - 6 * q^29 - 12 * q^31 + 30 * q^32 + 12 * q^34 - 3 * q^35 + 9 * q^37 + 10 * q^38 - 6 * q^40 + 3 * q^41 - 36 * q^44 - 3 * q^46 - 17 * q^47 + 6 * q^49 - 6 * q^50 + 3 * q^52 - 4 * q^53 + 2 * q^55 - 12 * q^56 - 24 * q^58 + 6 * q^59 - 21 * q^61 + 27 * q^62 + 13 * q^64 + 14 * q^65 - 6 * q^67 + 27 * q^68 + 3 * q^70 - 15 * q^71 + 14 * q^73 + 26 * q^74 + 60 * q^76 - q^77 - 11 * q^79 - 13 * q^80 - 3 * q^82 - 13 * q^83 - 9 * q^85 - 15 * q^86 - 37 * q^88 + 24 * q^89 + 3 * q^91 - 3 * q^92 + 17 * q^94 - 5 * q^95 + 3 * q^97 - 36 * q^98

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