LMFDB - Embedded newform 549.2.s.j.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [549,2,Mod(109,549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(549, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("549.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 549 = 3^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	549.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.38378707097$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.542936601.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 2x^{6} - 4x^{5} + x^{4} - 8x^{3} + 8x^{2} - 8x + 16 $ x^8 - x^7 + 2x^6 - 4x^5 + x^4 - 8x^3 + 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 61)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.1
Root			$1.41379 + 0.0347146i$ of defining polynomial
Character	$\chi$	$=$	549.109
Dual form			549.2.s.j.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.15074 - 1.24173i) q^{2} +(2.08380 + 3.60925i) q^{4} +(-1.17683 + 2.03833i) q^{5} +(-2.32076 - 1.33989i) q^{7} -5.38317i q^{8} +O(q^{10})$	\(q+(-2.15074 - 1.24173i) q^{2} +(2.08380 + 3.60925i) q^{4} +(-1.17683 + 2.03833i) q^{5} +(-2.32076 - 1.33989i) q^{7} -5.38317i q^{8} +(5.06212 - 2.92262i) q^{10} +0.681986i q^{11} +(-2.09062 + 3.62106i) q^{13} +(3.32757 + 5.76353i) q^{14} +(-2.51686 + 4.35933i) q^{16} +(0.990775 - 0.572024i) q^{17} +(-1.14393 - 1.98134i) q^{19} -9.80912 q^{20} +(0.846845 - 1.46678i) q^{22} -6.21331i q^{23} +(-0.269858 - 0.467407i) q^{25} +(8.99277 - 5.19198i) q^{26} -11.1683i q^{28} +(2.79112 - 1.61146i) q^{29} +(7.38288 - 4.26251i) q^{31} +(1.50232 - 0.867363i) q^{32} -2.84120 q^{34} +(5.46228 - 3.15365i) q^{35} -9.43622i q^{37} +5.68182i q^{38} +(10.9727 + 6.33508i) q^{40} +0.405830 q^{41} +(-1.28023 - 0.739138i) q^{43} +(-2.46146 + 1.42112i) q^{44} +(-7.71528 + 13.3633i) q^{46} +(-4.73455 - 8.20048i) q^{47} +(0.0906174 + 0.156954i) q^{49} +1.34036i q^{50} -17.4257 q^{52} +5.68277i q^{53} +(-1.39011 - 0.802582i) q^{55} +(-7.21287 + 12.4931i) q^{56} -8.00399 q^{58} +(-1.80117 - 1.03990i) q^{59} +(-7.68238 - 1.40751i) q^{61} -21.1716 q^{62} +5.75930 q^{64} +(-4.92060 - 8.52273i) q^{65} +(-7.07217 - 4.08312i) q^{67} +(4.12916 + 2.38397i) q^{68} -15.6640 q^{70} +(2.40133 - 1.38641i) q^{71} +(2.94187 + 5.09546i) q^{73} +(-11.7173 + 20.2949i) q^{74} +(4.76745 - 8.25746i) q^{76} +(0.913787 - 1.58273i) q^{77} +(8.50114 + 4.90814i) q^{79} +(-5.92383 - 10.2604i) q^{80} +(-0.872837 - 0.503933i) q^{82} +(5.67683 - 9.83256i) q^{83} +2.69270i q^{85} +(1.83563 + 3.17940i) q^{86} +3.67125 q^{88} -5.38412i q^{89} +(9.70364 - 5.60240i) q^{91} +(22.4254 - 12.9473i) q^{92} +23.5162i q^{94} +5.38484 q^{95} +(-3.93505 - 6.81571i) q^{97} -0.450091i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 6 q^{5} - 3 q^{7}+O(q^{10}) $ 8 * q + 8 * q^4 - 6 * q^5 - 3 * q^7	$ 8 q + 8 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{10} - 3 q^{13} + 6 q^{14} - 20 q^{16} - 6 q^{17} + 3 q^{19} - 30 q^{20} + 5 q^{22} - 4 q^{25} + 15 q^{26} - 3 q^{31} - 48 q^{32} + 8 q^{34} - 3 q^{35} + 21 q^{40} + 24 q^{41} + 18 q^{44} - 17 q^{46} - 12 q^{47} - 13 q^{49} - 12 q^{52} - 6 q^{55} + 6 q^{56} + 22 q^{58} + 3 q^{59} - 8 q^{61} - 66 q^{62} - 98 q^{64} - 24 q^{65} - 15 q^{67} + 57 q^{68} - 36 q^{70} - 15 q^{71} - 16 q^{73} - 6 q^{74} + 21 q^{76} - 3 q^{77} + 42 q^{79} - 42 q^{80} + 60 q^{82} + 42 q^{83} + 42 q^{86} + 84 q^{88} + 69 q^{92} - 54 q^{95} + 3 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^10 - 3 * q^13 + 6 * q^14 - 20 * q^16 - 6 * q^17 + 3 * q^19 - 30 * q^20 + 5 * q^22 - 4 * q^25 + 15 * q^26 - 3 * q^31 - 48 * q^32 + 8 * q^34 - 3 * q^35 + 21 * q^40 + 24 * q^41 + 18 * q^44 - 17 * q^46 - 12 * q^47 - 13 * q^49 - 12 * q^52 - 6 * q^55 + 6 * q^56 + 22 * q^58 + 3 * q^59 - 8 * q^61 - 66 * q^62 - 98 * q^64 - 24 * q^65 - 15 * q^67 + 57 * q^68 - 36 * q^70 - 15 * q^71 - 16 * q^73 - 6 * q^74 + 21 * q^76 - 3 * q^77 + 42 * q^79 - 42 * q^80 + 60 * q^82 + 42 * q^83 + 42 * q^86 + 84 * q^88 + 69 * q^92 - 54 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/549\mathbb{Z}\right)^\times$.

$n$	$245$	$307$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.15074	−	1.24173i	−1.52081	−	0.878038i	−0.999699	−	0.0245469i	$-0.992186\pi$
$2$	−2.15074	−	1.24173i	−1.52081	−	0.878038i	−0.521108	−	0.853491i	$-0.674481\pi$
$3$		0			0
$3$		0			0
$4$	2.08380	+	3.60925i	1.04190	+	1.80463i
$5$	−1.17683	+	2.03833i	−0.526294	+	0.911569i	0.473236	+	0.880936i	$0.343086\pi$
$5$	−1.17683	+	2.03833i	−0.526294	+	0.911569i	−0.999531	+	0.0306331i	$0.990248\pi$
$6$		0			0
$7$	−2.32076	−	1.33989i	−0.877165	−	0.506431i	−0.00744223	−	0.999972i	$-0.502369\pi$
$7$	−2.32076	−	1.33989i	−0.877165	−	0.506431i	−0.869723	+	0.493541i	$0.835702\pi$
$8$		−	5.38317i		−	1.90324i
$9$		0			0
$10$	5.06212	−	2.92262i	1.60078	−	0.924213i
$11$			0.681986i			0.205627i	0.994701	+	0.102813i	$0.0327844\pi$
$11$			0.681986i			0.205627i	−0.994701	+	0.102813i	$0.967216\pi$
$12$		0			0
$13$	−2.09062	+	3.62106i	−0.579833	+	1.00430i	0.415665	+	0.909518i	$0.363549\pi$
$13$	−2.09062	+	3.62106i	−0.579833	+	1.00430i	−0.995498	+	0.0947824i	$0.969784\pi$
$14$	3.32757	+	5.76353i	0.889332	+	1.54037i
$15$		0			0
$16$	−2.51686	+	4.35933i	−0.629215	+	1.08983i
$17$	0.990775	−	0.572024i	0.240298	−	0.138736i	−0.375016	−	0.927019i	$-0.622363\pi$
$17$	0.990775	−	0.572024i	0.240298	−	0.138736i	0.615314	+	0.788282i	$0.289029\pi$
$18$		0			0
$19$	−1.14393	−	1.98134i	−0.262436	−	0.454552i	0.704453	−	0.709751i	$-0.251192\pi$
$19$	−1.14393	−	1.98134i	−0.262436	−	0.454552i	−0.966889	+	0.255199i	$0.917859\pi$
$20$	−9.80912			−2.19339
$21$		0			0
$22$	0.846845	−	1.46678i	0.180548	−	0.312718i
$23$		−	6.21331i		−	1.29557i	−0.761825	−	0.647783i	$-0.775696\pi$
$23$		−	6.21331i		−	1.29557i	0.761825	−	0.647783i	$-0.224304\pi$
$24$		0			0
$25$	−0.269858	−	0.467407i	−0.0539715	−	0.0934814i
$26$	8.99277	−	5.19198i	1.76363	−	1.01823i
$27$		0			0
$28$		−	11.1683i		−	2.11061i
$29$	2.79112	−	1.61146i	0.518298	−	0.299240i	−0.217940	−	0.975962i	$-0.569934\pi$
$29$	2.79112	−	1.61146i	0.518298	−	0.299240i	0.736238	+	0.676722i	$0.236600\pi$
$30$		0			0
$31$	7.38288	−	4.26251i	1.32600	−	0.765569i	0.341326	−	0.939945i	$-0.389124\pi$
$31$	7.38288	−	4.26251i	1.32600	−	0.765569i	0.984679	+	0.174376i	$0.0557908\pi$
$32$	1.50232	−	0.867363i	0.265575	−	0.153330i
$33$		0			0
$34$	−2.84120			−0.487263
$35$	5.46228	−	3.15365i	0.923294	−	0.533064i
$36$		0			0
$37$		−	9.43622i		−	1.55131i	−0.631160	−	0.775653i	$-0.717421\pi$
$37$		−	9.43622i		−	1.55131i	0.631160	−	0.775653i	$-0.282579\pi$
$38$			5.68182i			0.921713i
$39$		0			0
$40$	10.9727	+	6.33508i	1.73493	+	1.00166i
$41$	0.405830			0.0633800			0.0316900	−	0.999498i	$-0.489911\pi$
$41$	0.405830			0.0633800			0.0316900	+	0.999498i	$0.489911\pi$
$42$		0			0
$43$	−1.28023	−	0.739138i	−0.195232	−	0.112718i	0.399197	−	0.916865i	$-0.369289\pi$
$43$	−1.28023	−	0.739138i	−0.195232	−	0.112718i	−0.594430	+	0.804148i	$0.702622\pi$
$44$	−2.46146	+	1.42112i	−0.371079	+	0.214243i
$45$		0			0
$46$	−7.71528	+	13.3633i	−1.13756	+	1.97030i
$47$	−4.73455	−	8.20048i	−0.690605	−	1.19616i	−0.971640	−	0.236465i	$-0.924011\pi$
$47$	−4.73455	−	8.20048i	−0.690605	−	1.19616i	0.281035	−	0.959697i	$-0.409322\pi$
$48$		0			0
$49$	0.0906174	+	0.156954i	0.0129453	+	0.0224220i
$50$			1.34036i			0.189556i
$51$		0			0
$52$	−17.4257			−2.41651
$53$			5.68277i			0.780588i	0.920690	+	0.390294i	$0.127627\pi$
$53$			5.68277i			0.780588i	−0.920690	+	0.390294i	$0.872373\pi$
$54$		0			0
$55$	−1.39011	−	0.802582i	−0.187443	−	0.108220i
$56$	−7.21287	+	12.4931i	−0.963860	+	1.66945i
$57$		0			0
$58$	−8.00399			−1.05098
$59$	−1.80117	−	1.03990i	−0.234492	−	0.135384i	0.378151	−	0.925744i	$-0.376560\pi$
$59$	−1.80117	−	1.03990i	−0.234492	−	0.135384i	−0.612643	+	0.790360i	$0.709893\pi$
$60$		0			0
$61$	−7.68238	−	1.40751i	−0.983628	−	0.180213i
$61$	−7.68238	−	1.40751i	−0.983628	−	0.180213i
$62$	−21.1716			−2.68880
$63$		0			0
$64$	5.75930			0.719913
$65$	−4.92060	−	8.52273i	−0.610326	−	1.05711i
$66$		0			0
$67$	−7.07217	−	4.08312i	−0.864003	−	0.498832i	0.00134794	−	0.999999i	$-0.499571\pi$
$67$	−7.07217	−	4.08312i	−0.864003	−	0.498832i	−0.865351	+	0.501167i	$0.832904\pi$
$68$	4.12916	+	2.38397i	0.500734	+	0.289099i
$69$		0			0
$70$	−15.6640			−1.87220
$71$	2.40133	−	1.38641i	0.284986	−	0.164537i	−0.350693	−	0.936491i	$-0.614054\pi$
$71$	2.40133	−	1.38641i	0.284986	−	0.164537i	0.635678	+	0.771954i	$0.280720\pi$
$72$		0			0
$73$	2.94187	+	5.09546i	0.344320	+	0.596379i	0.985230	−	0.171237i	$-0.0547763\pi$
$73$	2.94187	+	5.09546i	0.344320	+	0.596379i	−0.640910	+	0.767616i	$0.721443\pi$
$74$	−11.7173	+	20.2949i	−1.36211	+	2.35924i
$75$		0			0
$76$	4.76745	−	8.25746i	0.546864	−	0.947196i
$77$	0.913787	−	1.58273i	0.104136	−	0.180368i
$78$		0			0
$79$	8.50114	+	4.90814i	0.956453	+	0.552209i	0.895080	−	0.445906i	$-0.147119\pi$
$79$	8.50114	+	4.90814i	0.956453	+	0.552209i	0.0613736	+	0.998115i	$0.480452\pi$
$80$	−5.92383	−	10.2604i	−0.662305	−	1.14715i
$81$		0			0
$82$	−0.872837	−	0.503933i	−0.0963887	−	0.0556501i
$83$	5.67683	−	9.83256i	0.623113	−	1.07926i	−0.365789	−	0.930698i	$-0.619201\pi$
$83$	5.67683	−	9.83256i	0.623113	−	1.07926i	0.988903	−	0.148566i	$-0.0474657\pi$
$84$		0			0
$85$			2.69270i			0.292064i
$86$	1.83563	+	3.17940i	0.197941	+	0.342843i
$87$		0			0
$88$	3.67125			0.391357
$89$		−	5.38412i		−	0.570716i	−0.958421	−	0.285358i	$-0.907888\pi$
$89$		−	5.38412i		−	0.570716i	0.958421	−	0.285358i	$-0.0921124\pi$
$90$		0			0
$91$	9.70364	−	5.60240i	1.01722	−	0.587291i
$92$	22.4254	−	12.9473i	2.33801	−	1.34985i
$93$		0			0
$94$			23.5162i			2.42551i
$95$	5.38484			0.552473
$96$		0			0
$97$	−3.93505	−	6.81571i	−0.399544	−	0.692031i	0.594126	−	0.804372i	$-0.297498\pi$
$97$	−3.93505	−	6.81571i	−0.399544	−	0.692031i	−0.993670	+	0.112342i	$0.964165\pi$
$98$		−	0.450091i		−	0.0454660i
$99$		0			0
$100$	1.12466	−	1.94797i	0.112466	−	0.194797i
$101$	−7.76177	−	4.48126i	−0.772325	−	0.445902i	0.0613781	−	0.998115i	$-0.480450\pi$
$101$	−7.76177	−	4.48126i	−0.772325	−	0.445902i	−0.833704	+	0.552212i	$0.813784\pi$
$102$		0			0
$103$	−7.38855	−	12.7974i	−0.728016	−	1.26096i	−0.957721	−	0.287700i	$-0.907109\pi$
$103$	−7.38855	−	12.7974i	−0.728016	−	1.26096i	0.229705	−	0.973260i	$-0.426224\pi$
$104$	19.4928	+	11.2542i	1.91142	+	1.10356i
$105$		0			0
$106$	7.05648	−	12.2222i	0.685386	−	1.18712i
$107$	−7.99036	+	13.8397i	−0.772457	+	1.33794i	0.163755	+	0.986501i	$0.447639\pi$
$107$	−7.99036	+	13.8397i	−0.772457	+	1.33794i	−0.936213	+	0.351434i	$0.885694\pi$
$108$		0			0
$109$	−3.92060	+	6.79068i	−0.375526	+	0.650429i	−0.990406	−	0.138191i	$-0.955871\pi$
$109$	−3.92060	+	6.79068i	−0.375526	+	0.650429i	0.614880	+	0.788621i	$0.289204\pi$
$110$	1.99318	+	3.45230i	0.190043	+	0.329164i
$111$		0			0
$112$	11.6821	−	6.74464i	1.10385	−	0.637308i
$113$	12.5982			1.18514			0.592568	−	0.805521i	$-0.298114\pi$
$113$	12.5982			1.18514			0.592568	+	0.805521i	$0.298114\pi$
$114$		0			0
$115$	12.6648	+	7.31201i	1.18100	+	0.681849i
$116$	11.6323	+	6.71591i	1.08003	+	0.623556i
$117$		0			0
$118$	2.58257	+	4.47314i	0.237745	+	0.411786i
$119$	−3.06580			−0.281041
$120$		0			0
$121$	10.5349			0.957718
$122$	14.7751	+	12.5667i	1.33767	+	1.13773i
$123$		0			0
$124$	30.7689	+	17.7645i	2.76313	+	1.59529i
$125$	−10.4980			−0.938969
$126$		0			0
$127$	1.56013	−	2.70222i	0.138439	−	0.239783i	−0.788467	−	0.615077i	$-0.789125\pi$
$127$	1.56013	−	2.70222i	0.138439	−	0.239783i	0.926906	+	0.375294i	$0.122458\pi$
$128$	−15.3914	−	8.88625i	−1.36042	−	0.785441i
$129$		0			0
$130$			24.4403i			2.14356i
$131$	10.6078			0.926808			0.463404	−	0.886147i	$-0.346628\pi$
$131$	10.6078			0.926808			0.463404	+	0.886147i	$0.346628\pi$
$132$		0			0
$133$			6.13097i			0.531622i
$134$	10.1403	+	17.5635i	0.875987	+	1.51725i
$135$		0			0
$136$	−3.07930	−	5.33351i	−0.264048	−	0.457345i
$137$	3.80390	−	6.58855i	0.324989	−	0.562898i	−0.656521	−	0.754308i	$-0.727973\pi$
$137$	3.80390	−	6.58855i	0.324989	−	0.562898i	0.981510	+	0.191410i	$0.0613060\pi$
$138$		0			0
$139$	−12.7839	+	7.38080i	−1.08432	+	0.626031i	−0.932058	−	0.362309i	$-0.881989\pi$
$139$	−12.7839	+	7.38080i	−1.08432	+	0.626031i	−0.152260	+	0.988340i	$0.548655\pi$
$140$	22.7646	+	13.1432i	1.92396	+	1.11080i
$141$		0			0
$142$	−6.88620			−0.577877
$143$	−2.46951	−	1.42577i	−0.206511	−	0.119229i
$144$		0			0
$145$			7.58564i			0.629953i
$146$		−	14.6121i		−	1.20930i
$147$		0			0
$148$	34.0577	−	19.6632i	2.79953	−	1.61631i
$149$	2.93420			0.240379			0.120190	−	0.992751i	$-0.461650\pi$
$149$	2.93420			0.240379			0.120190	+	0.992751i	$0.461650\pi$
$150$		0			0
$151$	11.2313	−	6.48440i	0.913992	−	0.527693i	0.0322783	−	0.999479i	$-0.489724\pi$
$151$	11.2313	−	6.48440i	0.913992	−	0.527693i	0.881713	+	0.471786i	$0.156390\pi$
$152$	−10.6659	+	6.15797i	−0.865120	+	0.499478i
$153$		0			0
$154$	−3.93065	+	2.26936i	−0.316741	+	0.182870i
$155$			20.0650i			1.61166i
$156$		0			0
$157$	15.9321	−	9.19843i	1.27152	−	0.734114i	0.296249	−	0.955111i	$-0.404264\pi$
$157$	15.9321	−	9.19843i	1.27152	−	0.734114i	0.975275	+	0.220996i	$0.0709309\pi$
$158$	−12.1892	−	21.1123i	−0.969720	−	1.67960i
$159$		0			0
$160$			4.08296i			0.322786i
$161$	−8.32516	+	14.4196i	−0.656115	+	1.13642i
$162$		0			0
$163$	−6.08817			−0.476863			−0.238431	−	0.971159i	$-0.576633\pi$
$163$	−6.08817			−0.476863			−0.238431	+	0.971159i	$0.576633\pi$
$164$	0.845670	+	1.46474i	0.0660357	+	0.114377i
$165$		0			0
$166$	−24.4188	+	14.0982i	−1.89527	+	1.09423i
$167$	7.15274	−	12.3889i	0.553496	−	0.958683i	−0.444523	−	0.895767i	$-0.646627\pi$
$167$	7.15274	−	12.3889i	0.553496	−	0.958683i	0.998019	−	0.0629152i	$-0.0200398\pi$
$168$		0			0
$169$	−2.24136	−	3.88215i	−0.172412	−	0.298627i
$170$	3.34362	−	5.79131i	0.256444	−	0.444173i
$171$		0			0
$172$		−	6.16087i		−	0.469762i
$173$	−3.95027	+	2.28069i	−0.300334	+	0.173398i	−0.642593	−	0.766208i	$-0.722141\pi$
$173$	−3.95027	+	2.28069i	−0.300334	+	0.173398i	0.342259	+	0.939606i	$0.388808\pi$
$174$		0			0
$175$			1.44632i			0.109331i
$176$	−2.97300	−	1.71646i	−0.224098	−	0.129383i
$177$		0			0
$178$	−6.68564	+	11.5799i	−0.501110	+	0.867948i
$179$	9.86247	+	17.0823i	0.737156	+	1.27679i	0.953771	+	0.300534i	$0.0971649\pi$
$179$	9.86247	+	17.0823i	0.737156	+	1.27679i	−0.216616	+	0.976257i	$0.569502\pi$
$180$		0			0
$181$	−8.52159	−	4.91994i	−0.633405	−	0.365696i	0.148665	−	0.988888i	$-0.452502\pi$
$181$	−8.52159	−	4.91994i	−0.633405	−	0.365696i	−0.782069	+	0.623191i	$0.785836\pi$
$182$	−27.8267			−2.06266
$183$		0			0
$184$	−33.4473			−2.46577
$185$	19.2341	+	11.1048i	1.41412	+	0.816443i
$186$		0			0
$187$	0.390113	+	0.675695i	0.0285279	+	0.0494117i
$188$	19.7317	−	34.1763i	1.43908	−	2.49257i
$189$		0			0
$190$	−11.5814	−	6.68654i	−0.840205	−	0.485093i
$191$		−	12.0748i		−	0.873699i	−0.899535	−	0.436849i	$-0.856094\pi$
$191$		−	12.0748i		−	0.873699i	0.899535	−	0.436849i	$-0.143906\pi$
$192$		0			0
$193$	−4.82913	+	2.78810i	−0.347609	+	0.200692i	−0.663631	−	0.748060i	$-0.730986\pi$
$193$	−4.82913	+	2.78810i	−0.347609	+	0.200692i	0.316023	+	0.948752i	$0.397652\pi$
$194$			19.5451i			1.40326i
$195$		0			0
$196$	−0.377658	+	0.654122i	−0.0269755	+	0.0467230i
$197$	−7.79908	−	13.5084i	−0.555661	−	0.962434i	−0.997852	−	0.0655126i	$-0.979132\pi$
$197$	−7.79908	−	13.5084i	−0.555661	−	0.962434i	0.442190	−	0.896921i	$-0.354202\pi$
$198$		0			0
$199$	6.07217	−	10.5173i	0.430444	−	0.745552i	−0.566467	−	0.824084i	$-0.691690\pi$
$199$	6.07217	−	10.5173i	0.430444	−	0.745552i	0.996912	+	0.0785327i	$0.0250235\pi$
$200$	−2.51613	+	1.45269i	−0.177917	+	0.102721i
$201$		0			0
$202$	11.1291	+	19.2761i	0.783038	+	1.35626i
$203$	−8.63670			−0.606177
$204$		0			0
$205$	−0.477593	+	0.827215i	−0.0333565	+	0.0577752i
$206$			36.6985i			2.55690i
$207$		0			0
$208$	−10.5236	−	18.2274i	−0.729679	−	1.26384i
$209$	1.35125	−	0.780144i	0.0934679	−	0.0539637i
$210$		0			0
$211$			1.79046i			0.123260i	0.998099	+	0.0616300i	$0.0196299\pi$
$211$			1.79046i			0.123260i	−0.998099	+	0.0616300i	$0.980370\pi$
$212$	−20.5105	+	11.8418i	−1.40867	+	0.813296i
$213$		0			0
$214$	34.3704	−	19.8438i	2.34952	−	1.35649i
$215$	3.01321	−	1.73968i	0.205500	−	0.118645i
$216$		0			0
$217$	−22.8452			−1.55083
$218$	16.8644	−	9.73668i	1.14220	−	0.659451i
$219$		0			0
$220$		−	6.68969i		−	0.451019i
$221$			4.78353i			0.321775i
$222$		0			0
$223$	13.4238	+	7.75022i	0.898922	+	0.518993i	0.876850	−	0.480763i	$-0.159640\pi$
$223$	13.4238	+	7.75022i	0.898922	+	0.518993i	0.0220719	+	0.999756i	$0.492974\pi$
$224$	−4.64869			−0.310604
$225$		0			0
$226$	−27.0954	−	15.6436i	−1.80236	−	1.04059i
$227$	−10.6755	+	6.16348i	−0.708556	+	0.409085i	−0.810526	−	0.585703i	$-0.800819\pi$
$227$	−10.6755	+	6.16348i	−0.708556	+	0.409085i	0.101970	+	0.994787i	$0.467485\pi$
$228$		0			0
$229$	−1.98282	+	3.43434i	−0.131028	+	0.226948i	−0.924073	−	0.382216i	$-0.875161\pi$
$229$	−1.98282	+	3.43434i	−0.131028	+	0.226948i	0.793045	+	0.609163i	$0.208495\pi$
$230$	−18.1591	−	31.4526i	−1.19738	−	2.07392i
$231$		0			0
$232$	−8.67474	−	15.0251i	−0.569525	−	0.986446i
$233$			20.5351i			1.34530i	0.739962	+	0.672649i	$0.234843\pi$
$233$			20.5351i			1.34530i	−0.739962	+	0.672649i	$0.765157\pi$
$234$		0			0
$235$	22.2870			1.45385
$236$		−	8.66782i		−	0.564227i
$237$		0			0
$238$	6.59375	+	3.80691i	0.427410	+	0.246765i
$239$	−3.64478	+	6.31295i	−0.235761	+	0.408351i	−0.959494	−	0.281730i	$-0.909092\pi$
$239$	−3.64478	+	6.31295i	−0.235761	+	0.408351i	0.723732	+	0.690081i	$0.242425\pi$
$240$		0			0
$241$	−21.6158			−1.39239			−0.696197	−	0.717850i	$-0.745126\pi$
$241$	−21.6158			−1.39239			−0.696197	+	0.717850i	$0.745126\pi$
$242$	−22.6579	−	13.0815i	−1.45650	−	0.840912i
$243$		0			0
$244$	−10.9285	−	30.6606i	−0.699626	−	1.96284i
$245$	−0.426565			−0.0272522
$246$		0			0
$247$	9.56608			0.608675
$248$	−22.9458	−	39.7433i	−1.45706	−	2.52370i
$249$		0			0
$250$	22.5785	+	13.0357i	1.42799	+	0.824450i
$251$	−6.74221	−	3.89262i	−0.425565	−	0.245700i	0.271891	−	0.962328i	$-0.412351\pi$
$251$	−6.74221	−	3.89262i	−0.425565	−	0.245700i	−0.697455	+	0.716628i	$0.745684\pi$
$252$		0			0
$253$	4.23739			0.266403
$254$	−6.71087	+	3.87452i	−0.421078	+	0.243109i
$255$		0			0
$256$	16.3094	+	28.2487i	1.01934	+	1.76554i
$257$	−7.87166	+	13.6341i	−0.491021	+	0.850473i	−0.999947	−	0.0103375i	$-0.996709\pi$
$257$	−7.87166	+	13.6341i	−0.491021	+	0.850473i	0.508926	+	0.860810i	$0.330043\pi$
$258$		0			0
$259$	−12.6435	+	21.8992i	−0.785630	+	1.36075i
$260$	20.5071	−	35.5194i	1.27180	−	2.20282i
$261$		0			0
$262$	−22.8147	−	13.1721i	−1.40950	−	0.813772i
$263$	−1.75864	−	3.04605i	−0.108442	−	0.187827i	0.806697	−	0.590965i	$-0.201253\pi$
$263$	−1.75864	−	3.04605i	−0.108442	−	0.187827i	−0.915139	+	0.403138i	$0.867920\pi$
$264$		0			0
$265$	−11.5834	−	6.68765i	−0.711560	−	0.410819i
$266$	7.61302	−	13.1861i	0.466784	−	0.808494i
$267$		0			0
$268$		−	34.0336i		−	2.07894i
$269$	−8.57657	−	14.8551i	−0.522923	−	0.905729i	−0.999644	−	0.0266744i	$-0.991508\pi$
$269$	−8.57657	−	14.8551i	−0.522923	−	0.905729i	0.476721	−	0.879054i	$-0.341825\pi$
$270$		0			0
$271$	−13.8020			−0.838413			−0.419206	−	0.907891i	$-0.637692\pi$
$271$	−13.8020			−0.838413			−0.419206	+	0.907891i	$0.637692\pi$
$272$			5.75882i			0.349180i
$273$		0			0
$274$	−16.3624	+	9.44686i	−0.988491	+	0.570706i
$275$	0.318765	−	0.184039i	0.0192223	−	0.0110980i
$276$		0			0
$277$			31.8003i			1.91070i	0.295481	+	0.955349i	$0.404520\pi$
$277$			31.8003i			1.91070i	−0.295481	+	0.955349i	$0.595480\pi$
$278$	36.6599			2.19872
$279$		0			0
$280$	−16.9766	−	29.4044i	−1.01455	−	1.75725i
$281$		−	12.5688i		−	0.749790i	−0.927067	−	0.374895i	$-0.877679\pi$
$281$		−	12.5688i		−	0.749790i	0.927067	−	0.374895i	$-0.122321\pi$
$282$		0			0
$283$	0.478735	−	0.829194i	0.0284579	−	0.0492905i	−0.851446	−	0.524443i	$-0.824274\pi$
$283$	0.478735	−	0.829194i	0.0284579	−	0.0492905i	0.879904	+	0.475152i	$0.157607\pi$
$284$	10.0078	+	5.77801i	0.593854	+	0.342862i
$285$		0			0
$286$	3.54086	+	6.13294i	0.209375	+	0.362649i
$287$	−0.941834	−	0.543768i	−0.0555947	−	0.0320976i
$288$		0			0
$289$	−7.84558	+	13.5889i	−0.461505	+	0.799349i
$290$	9.41933	−	16.3148i	0.553122	−	0.958036i
$291$		0			0
$292$	−12.2605	+	21.2359i	−0.717494	+	1.24274i
$293$	1.12551	+	1.94944i	0.0657531	+	0.113888i	0.897028	−	0.441974i	$-0.145722\pi$
$293$	1.12551	+	1.94944i	0.0657531	+	0.113888i	−0.831275	+	0.555862i	$0.812388\pi$
$294$		0			0
$295$	4.23933	−	2.44758i	0.246824	−	0.142504i
$296$	−50.7968			−2.95251
$297$		0			0
$298$	−6.31072	−	3.64349i	−0.365570	−	0.211062i
$299$	22.4988	+	12.9897i	1.30114	+	0.751212i
$300$		0			0
$301$	1.98073	+	3.43072i	0.114167	+	0.197744i
$302$	−32.2076			−1.85334
$303$		0			0
$304$	11.5164			0.660513
$305$	11.9098	−	14.0028i	0.681954	−	0.801799i
$306$		0			0
$307$	5.74189	+	3.31508i	0.327707	+	0.189202i	0.654823	−	0.755783i	$-0.272743\pi$
$307$	5.74189	+	3.31508i	0.327707	+	0.189202i	−0.327116	+	0.944984i	$0.606077\pi$
$308$	7.61661			0.433997
$309$		0			0
$310$	24.9154	−	43.1547i	1.41510	−	2.45102i
$311$	−13.4637	−	7.77330i	−0.763459	−	0.440783i	0.0670773	−	0.997748i	$-0.478633\pi$
$311$	−13.4637	−	7.77330i	−0.763459	−	0.440783i	−0.830536	+	0.556965i	$0.811966\pi$
$312$		0			0
$313$		−	10.4570i		−	0.591065i	−0.955333	−	0.295532i	$-0.904503\pi$
$313$		−	10.4570i		−	0.591065i	0.955333	−	0.295532i	$-0.0954971\pi$
$314$	−45.6880			−2.57832
$315$		0			0
$316$			40.9103i			2.30139i
$317$	−14.9086	−	25.8224i	−0.837348	−	1.45033i	−0.892105	−	0.451829i	$-0.850772\pi$
$317$	−14.9086	−	25.8224i	−0.837348	−	1.45033i	0.0547569	−	0.998500i	$-0.482562\pi$
$318$		0			0
$319$	1.09899	+	1.90351i	0.0615316	+	0.106576i
$320$	−6.77772	+	11.7394i	−0.378886	+	0.656250i
$321$		0			0
$322$	35.8106	−	20.6753i	1.99565	−	1.15219i
$323$	−2.26675	−	1.30871i	−0.126126	−	0.0728186i
$324$		0			0
$325$	2.25668			0.125178
$326$	13.0941	+	7.55989i	0.725216	+	0.418703i
$327$		0			0
$328$		−	2.18465i		−	0.120627i
$329$			25.3751i			1.39898i
$330$		0			0
$331$	9.62919	−	5.55942i	0.529268	−	0.305573i	−0.211450	−	0.977389i	$-0.567819\pi$
$331$	9.62919	−	5.55942i	0.529268	−	0.305573i	0.740718	+	0.671816i	$0.234485\pi$
$332$	47.3176			2.59689
$333$		0			0
$334$	−30.7674	+	17.7636i	−1.68352	+	0.971980i
$335$	16.6455	−	9.61027i	0.909440	−	0.525065i
$336$		0			0
$337$	22.6659	−	13.0862i	1.23469	−	0.712849i	0.266687	−	0.963783i	$-0.414071\pi$
$337$	22.6659	−	13.0862i	1.23469	−	0.712849i	0.968004	+	0.250934i	$0.0807376\pi$
$338$			11.1327i			0.605539i
$339$		0			0
$340$	−9.71863	+	5.61106i	−0.527067	+	0.304302i
$341$	2.90697	+	5.03502i	0.157421	+	0.272662i
$342$		0			0
$343$			18.2728i			0.986639i
$344$	−3.97891	+	6.89167i	−0.214528	+	0.371574i
$345$		0			0
$346$	11.3280			0.608999
$347$	8.14866	+	14.1139i	0.437443	+	0.757673i	0.997491	−	0.0707865i	$-0.0225509\pi$
$347$	8.14866	+	14.1139i	0.437443	+	0.757673i	−0.560049	+	0.828460i	$0.689218\pi$
$348$		0			0
$349$	0.111915	−	0.0646141i	0.00599067	−	0.00345871i	−0.497002	−	0.867750i	$-0.665566\pi$
$349$	0.111915	−	0.0646141i	0.00599067	−	0.00345871i	0.502992	+	0.864291i	$0.332232\pi$
$350$	1.79594	−	3.11066i	0.0959972	−	0.166272i
$351$		0			0
$352$	0.591530	+	1.02456i	0.0315286	+	0.0546092i
$353$	−0.0108972	+	0.0188745i	−0.000579999	+	0.00100459i	−0.866315	−	0.499498i	$-0.833518\pi$
$353$	−0.0108972	+	0.0188745i	−0.000579999	+	0.00100459i	0.865735	+	0.500502i	$0.166851\pi$
$354$		0			0
$355$			6.52628i			0.346379i
$356$	19.4326	−	11.2194i	1.02993	−	0.594629i
$357$		0			0
$358$		−	48.9862i		−	2.58900i
$359$	7.48187	+	4.31966i	0.394878	+	0.227983i	0.684272	−	0.729227i	$-0.260120\pi$
$359$	7.48187	+	4.31966i	0.394878	+	0.227983i	−0.289394	+	0.957210i	$0.593454\pi$
$360$		0			0
$361$	6.88285	−	11.9214i	0.362255	−	0.627444i
$362$	12.2185	+	21.1631i	0.642190	+	1.11231i
$363$		0			0
$364$	40.4409	+	23.3486i	2.11968	+	1.22380i
$365$	−13.8483			−0.724854
$366$		0			0
$367$	−4.38175			−0.228726			−0.114363	−	0.993439i	$-0.536483\pi$
$367$	−4.38175			−0.228726			−0.114363	+	0.993439i	$0.536483\pi$
$368$	27.0859	+	15.6380i	1.41195	+	0.815189i
$369$		0			0
$370$	−27.5785	−	47.7673i	−1.43374	−	2.48330i
$371$	7.61429	−	13.1883i	0.395314	−	0.684705i
$372$		0			0
$373$	−24.4188	−	14.0982i	−1.26436	−	0.729978i	−0.290444	−	0.956892i	$-0.593803\pi$
$373$	−24.4188	−	14.0982i	−1.26436	−	0.729978i	−0.973915	+	0.226914i	$0.927136\pi$
$374$		−	1.93766i		−	0.100194i
$375$		0			0
$376$	−44.1446	+	25.4869i	−2.27658	+	1.31439i
$377$			13.4757i			0.694036i
$378$		0			0
$379$	−10.2537	+	17.7600i	−0.526698	+	0.912268i	0.472818	+	0.881160i	$0.343237\pi$
$379$	−10.2537	+	17.7600i	−0.526698	+	0.912268i	−0.999516	+	0.0311081i	$0.990096\pi$
$380$	11.2210	+	19.4353i	0.575623	+	0.997008i
$381$		0			0
$382$	−14.9936	+	25.9697i	−0.767140	+	1.32873i
$383$	−8.23103	+	4.75219i	−0.420586	+	0.242825i	−0.695328	−	0.718693i	$-0.744741\pi$
$383$	−8.23103	+	4.75219i	−0.420586	+	0.242825i	0.274742	+	0.961518i	$0.411408\pi$
$384$		0			0
$385$	2.15074	+	3.72520i	0.109612	+	0.189854i
$386$	13.8483			0.704860
$387$		0			0
$388$	16.3997	−	28.4052i	0.832571	−	1.44205i
$389$		−	15.4097i		−	0.781305i	−0.920538	−	0.390652i	$-0.872249\pi$
$389$		−	15.4097i		−	0.781305i	0.920538	−	0.390652i	$-0.127751\pi$
$390$		0			0
$391$	−3.55416	−	6.15599i	−0.179742	−	0.311322i
$392$	0.844910	−	0.487809i	0.0426744	−	0.0246381i
$393$		0			0
$394$			38.7375i			1.95157i
$395$	−20.0088	+	11.5521i	−1.00675	+	0.581248i
$396$		0			0
$397$	1.99110	−	1.14956i	0.0999303	−	0.0576948i	−0.449202	−	0.893430i	$-0.648292\pi$
$397$	1.99110	−	1.14956i	0.0999303	−	0.0576948i	0.549132	+	0.835735i	$0.314958\pi$
$398$	−26.1194	+	15.0800i	−1.30925	+	0.755893i
$399$		0			0
$400$	2.71677			0.135839
$401$	2.12114	−	1.22464i	0.105925	−	0.0611556i	−0.446102	−	0.894982i	$-0.647188\pi$
$401$	2.12114	−	1.22464i	0.105925	−	0.0611556i	0.552026	+	0.833827i	$0.313855\pi$
$402$		0			0
$403$			35.6451i			1.77561i
$404$		−	37.3523i		−	1.85834i
$405$		0			0
$406$	18.5753	+	10.7245i	0.921878	+	0.532247i
$407$	6.43537			0.318990
$408$		0			0
$409$	−9.64433	−	5.56816i	−0.476882	−	0.275328i	0.242234	−	0.970218i	$-0.422120\pi$
$409$	−9.64433	−	5.56816i	−0.476882	−	0.275328i	−0.719116	+	0.694890i	$0.755453\pi$
$410$	2.05436	−	1.18609i	0.101458	−	0.0585766i
$411$		0			0
$412$	30.7926	−	53.3343i	1.51704	−	2.62759i
$413$	2.78672	+	4.82674i	0.137125	+	0.237508i
$414$		0			0
$415$	13.3613	+	23.1425i	0.655882	+	1.13602i
$416$			7.25330i			0.355622i
$417$		0			0
$418$	−3.87492			−0.189529
$419$		−	34.9761i		−	1.70870i	−0.519701	−	0.854348i	$-0.673957\pi$
$419$		−	34.9761i		−	1.70870i	0.519701	−	0.854348i	$-0.326043\pi$
$420$		0			0
$421$	3.80755	+	2.19829i	0.185568	+	0.107138i	0.589906	−	0.807472i	$-0.299165\pi$
$421$	3.80755	+	2.19829i	0.185568	+	0.107138i	−0.404338	+	0.914610i	$0.632498\pi$
$422$	2.22327	−	3.85081i	0.108227	−	0.187455i
$423$		0			0
$424$	30.5913			1.48565
$425$	−0.534736	−	0.308730i	−0.0259385	−	0.0149756i
$426$		0			0
$427$	15.9430	+	13.5600i	0.771538	+	0.656216i
$428$	−66.6013			−3.21930
$429$		0			0
$430$	−8.64087			−0.416700
$431$	0.234547	+	0.406248i	0.0112977	+	0.0195683i	0.871619	−	0.490184i	$-0.163070\pi$
$431$	0.234547	+	0.406248i	0.0112977	+	0.0195683i	−0.860321	+	0.509752i	$0.829737\pi$
$432$		0			0
$433$	−11.3432	−	6.54902i	−0.545121	−	0.314726i	0.202031	−	0.979379i	$-0.435246\pi$
$433$	−11.3432	−	6.54902i	−0.545121	−	0.314726i	−0.747152	+	0.664653i	$0.768579\pi$
$434$	49.1342	+	28.3676i	2.35852	+	1.36169i
$435$		0			0
$436$	−32.6790			−1.56504
$437$	−12.3107	+	7.10759i	−0.588901	+	0.340002i
$438$		0			0
$439$	−12.5822	−	21.7931i	−0.600518	−	1.04013i	−0.992743	−	0.120258i	$-0.961628\pi$
$439$	−12.5822	−	21.7931i	−0.600518	−	1.04013i	0.392225	−	0.919869i	$-0.371705\pi$
$440$	−4.32044	+	7.48322i	−0.205969	+	0.356748i
$441$		0			0
$442$	5.93987	−	10.2882i	0.282531	−	0.489358i
$443$	2.28032	−	3.94963i	0.108341	−	0.187652i	−0.806757	−	0.590883i	$-0.798779\pi$
$443$	2.28032	−	3.94963i	0.108341	−	0.187652i	0.915098	+	0.403231i	$0.132113\pi$
$444$		0			0
$445$	10.9746	+	6.33619i	0.520246	+	0.300364i
$446$	−19.2474	−	33.3375i	−0.911391	−	1.57858i
$447$		0			0
$448$	−13.3660	−	7.71684i	−0.631482	−	0.364587i
$449$	−4.17318	+	7.22817i	−0.196945	+	0.341118i	−0.947536	−	0.319648i	$-0.896435\pi$
$449$	−4.17318	+	7.22817i	−0.196945	+	0.341118i	0.750592	+	0.660766i	$0.229769\pi$
$450$		0			0
$451$			0.276771i			0.0130326i
$452$	26.2521	+	45.4699i	1.23479	+	2.13873i
$453$		0			0
$454$	30.6136			1.43677
$455$			26.3723i			1.23635i
$456$		0			0
$457$	10.6692	−	6.15986i	0.499084	−	0.288146i	−0.229251	−	0.973367i	$-0.573628\pi$
$457$	10.6692	−	6.15986i	0.499084	−	0.288146i	0.728335	+	0.685221i	$0.240294\pi$
$458$	8.52907	−	4.92426i	0.398537	−	0.230096i
$459$		0			0
$460$			60.9472i			2.84168i
$461$	−34.2684			−1.59604			−0.798019	−	0.602632i	$-0.794119\pi$
$461$	−34.2684			−1.59604			−0.798019	+	0.602632i	$0.794119\pi$
$462$		0			0
$463$	−8.14425	−	14.1063i	−0.378496	−	0.655573i	0.612348	−	0.790588i	$-0.290225\pi$
$463$	−8.14425	−	14.1063i	−0.378496	−	0.655573i	−0.990844	+	0.135015i	$0.956892\pi$
$464$			16.2232i			0.753144i
$465$		0			0
$466$	25.4991	−	44.1657i	1.18122	−	2.04594i
$467$	31.3972	+	18.1272i	1.45289	+	0.838826i	0.998644	−	0.0520507i	$-0.0165758\pi$
$467$	31.3972	+	18.1272i	1.45289	+	0.838826i	0.454245	+	0.890877i	$0.349909\pi$
$468$		0			0
$469$	10.9419	+	18.9519i	0.505248	+	0.875116i
$470$	−47.9337	−	27.6745i	−2.21102	−	1.27653i
$471$		0			0
$472$	−5.59798	+	9.69599i	−0.257668	+	0.446294i
$473$	0.504082	−	0.873096i	0.0231777	−	0.0401450i
$474$		0			0
$475$	−0.617396	+	1.06936i	−0.0283281	+	0.0490657i
$476$	−6.38852	−	11.0652i	−0.292817	−	0.507175i
$477$		0			0
$478$	15.6780	−	9.05169i	0.717095	−	0.414015i
$479$	22.7691			1.04035			0.520174	−	0.854061i	$-0.325867\pi$
$479$	22.7691			1.04035			0.520174	+	0.854061i	$0.325867\pi$
$480$		0			0
$481$	34.1691	+	19.7275i	1.55798	+	0.899498i
$482$	46.4900	+	26.8410i	2.11756	+	1.22258i
$483$		0			0
$484$	21.9526	+	38.0231i	0.997847	+	1.72832i
$485$	18.5235			0.841111
$486$		0			0
$487$	−26.0425			−1.18010			−0.590050	−	0.807367i	$-0.700892\pi$
$487$	−26.0425			−1.18010			−0.590050	+	0.807367i	$0.700892\pi$
$488$	−7.57687	+	41.3556i	−0.342989	+	1.87208i
$489$		0			0
$490$	0.917433	+	0.529680i	0.0414454	+	0.0239285i
$491$	24.0079			1.08346			0.541731	−	0.840552i	$-0.317769\pi$
$491$	24.0079			1.08346			0.541731	+	0.840552i	$0.317769\pi$
$492$		0			0
$493$	1.84358	−	3.19318i	0.0830308	−	0.143814i
$494$	−20.5742	−	11.8785i	−0.925677	−	0.534440i
$495$		0			0
$496$			42.9125i			1.92683i
$497$	−7.43055			−0.333306
$498$		0			0
$499$		−	18.1931i		−	0.814437i	−0.913331	−	0.407218i	$-0.866499\pi$
$499$		−	18.1931i		−	0.814437i	0.913331	−	0.407218i	$-0.133501\pi$
$500$	−21.8757	−	37.8899i	−0.978313	−	1.69449i
$501$		0			0
$502$	9.66719	+	16.7441i	0.431468	+	0.747324i
$503$	2.94942	−	5.10855i	0.131508	−	0.227779i	−0.792750	−	0.609547i	$-0.791351\pi$
$503$	2.94942	−	5.10855i	0.131508	−	0.227779i	0.924258	+	0.381768i	$0.124685\pi$
$504$		0			0
$505$	18.2686	−	10.5474i	0.812941	−	0.469352i
$506$	−9.11355	−	5.26171i	−0.405147	−	0.233912i
$507$		0			0
$508$	13.0040			0.576959
$509$	−31.3246	−	18.0853i	−1.38844	−	0.801616i	−0.395301	−	0.918552i	$-0.629360\pi$
$509$	−31.3246	−	18.0853i	−1.38844	−	0.801616i	−0.993140	+	0.116935i	$0.962693\pi$
$510$		0			0
$511$		−	15.7671i		−	0.697497i
$512$		−	45.4626i		−	2.00918i
$513$		0			0
$514$	33.8599	−	19.5490i	1.49350	−	0.862270i
$515$	34.7803			1.53260
$516$		0			0
$517$	5.59261	−	3.22890i	0.245963	−	0.142007i
$518$	54.3859	−	31.3997i	2.38958	−	1.37963i
$519$		0			0
$520$	−45.8794	+	26.4885i	−2.01194	+	1.16160i
$521$			38.1443i			1.67113i	0.549389	+	0.835566i	$0.314860\pi$
$521$			38.1443i			1.67113i	−0.549389	+	0.835566i	$0.685140\pi$
$522$		0			0
$523$	27.7465	−	16.0194i	1.21327	−	0.700481i	0.249798	−	0.968298i	$-0.419636\pi$
$523$	27.7465	−	16.0194i	1.21327	−	0.700481i	0.963470	+	0.267817i	$0.0863023\pi$
$524$	22.1046	+	38.2862i	0.965642	+	1.67254i
$525$		0			0
$526$			8.73503i			0.380866i
$527$	4.87652	−	8.44637i	0.212424	−	0.367930i
$528$		0			0
$529$	−15.6053			−0.678490
$530$	16.6086	+	28.7669i	0.721430	+	1.24955i
$531$		0			0
$532$	−22.1282	+	12.7757i	−0.959379	+	0.553898i
$533$	−0.848436	+	1.46953i	−0.0367498	+	0.0636526i
$534$		0			0
$535$	−18.8066	−	32.5740i	−0.813080	−	1.40830i
$536$	−21.9801	+	38.0707i	−0.949397	+	1.64440i
$537$		0			0
$538$			42.5993i			1.83658i
$539$	−0.107040	+	0.0617998i	−0.00461056	+	0.00266191i
$540$		0			0
$541$		−	31.8649i		−	1.36998i	−0.728554	−	0.684989i	$-0.759807\pi$
$541$		−	31.8649i		−	1.36998i	0.728554	−	0.684989i	$-0.240193\pi$
$542$	29.6846	+	17.1384i	1.27506	+	0.736158i
$543$		0			0
$544$	0.992305	−	1.71872i	0.0425447	−	0.0736897i
$545$	−9.22777	−	15.9830i	−0.395274	−	0.684635i
$546$		0			0
$547$	−22.4895	−	12.9843i	−0.961581	−	0.555169i	−0.0649220	−	0.997890i	$-0.520680\pi$
$547$	−22.4895	−	12.9843i	−0.961581	−	0.555169i	−0.896659	+	0.442721i	$0.854013\pi$
$548$	31.7063			1.35443
$549$		0			0
$550$	−0.914110			−0.0389778
$551$	−6.38570	−	3.68678i	−0.272040	−	0.157062i
$552$		0			0
$553$	−13.1527	−	22.7812i	−0.559311	−	0.968756i
$554$	39.4875	−	68.3944i	1.67766	−	2.90580i
$555$		0			0
$556$	−53.2783	−	30.7603i	−2.25951	−	1.30453i
$557$		−	1.06265i		−	0.0450258i	−0.999747	−	0.0225129i	$-0.992833\pi$
$557$		−	1.06265i		−	0.0450258i	0.999747	−	0.0225129i	$-0.00716669\pi$
$558$		0			0
$559$	5.35292	−	3.09051i	0.226404	−	0.130715i
$560$			31.7492i			1.34165i
$561$		0			0
$562$	−15.6071	+	27.0322i	−0.658344	+	1.14029i
$563$	−14.8769	−	25.7676i	−0.626987	−	1.08597i	−0.988153	−	0.153472i	$-0.950954\pi$
$563$	−14.8769	−	25.7676i	−0.626987	−	1.08597i	0.361166	−	0.932502i	$-0.382379\pi$
$564$		0			0
$565$	−14.8259	+	25.6792i	−0.623730	+	1.08033i
$566$	−2.05928	+	1.18892i	−0.0865578	+	0.0499742i
$567$		0			0
$568$	−7.46328	−	12.9268i	−0.313152	−	0.542396i
$569$	−11.4274			−0.479060			−0.239530	−	0.970889i	$-0.576993\pi$
$569$	−11.4274			−0.479060			−0.239530	+	0.970889i	$0.576993\pi$
$570$		0			0
$571$	0.609035	−	1.05488i	0.0254873	−	0.0441453i	−0.853000	−	0.521910i	$-0.825220\pi$
$571$	0.609035	−	1.05488i	0.0254873	−	0.0441453i	0.878488	+	0.477765i	$0.158553\pi$
$572$		−	11.8841i		−	0.496900i
$573$		0			0
$574$	1.35043	+	2.33901i	0.0563659	+	0.0976285i
$575$	−2.90415	+	1.67671i	−0.121111	+	0.0699236i
$576$		0			0
$577$			12.0167i			0.500261i	0.968212	+	0.250131i	$0.0804735\pi$
$577$			12.0167i			0.500261i	−0.968212	+	0.250131i	$0.919526\pi$
$578$	33.7477	−	19.4842i	1.40372	−	0.810437i
$579$		0			0
$580$	−27.3785	+	15.8070i	−1.13683	+	0.656348i
$581$	−26.3491	+	15.2127i	−1.09315	+	0.631128i
$582$		0			0
$583$	−3.87557			−0.160510
$584$	27.4298	−	15.8366i	1.13505	−	0.655322i
$585$		0			0
$586$		−	5.59034i		−	0.230935i
$587$			29.9327i			1.23546i	0.786392	+	0.617728i	$0.211947\pi$
$587$			29.9327i			1.23546i	−0.786392	+	0.617728i	$0.788053\pi$
$588$		0			0
$589$	−16.8910	−	9.75202i	−0.695981	−	0.401825i
$590$	−12.1570			−0.500495
$591$		0			0
$592$	41.1356	+	23.7497i	1.69066	+	0.976105i
$593$	−38.1190	+	22.0080i	−1.56536	+	0.903760i	−0.568660	+	0.822573i	$0.692538\pi$
$593$	−38.1190	+	22.0080i	−1.56536	+	0.903760i	−0.996699	+	0.0811875i	$0.974129\pi$
$594$		0			0
$595$	3.60793	−	6.24911i	0.147911	−	0.256189i
$596$	6.11429	+	10.5903i	0.250451	+	0.433794i
$597$		0			0
$598$	−32.2594	−	55.8749i	−1.31918	−	2.28489i
$599$			13.9494i			0.569959i	0.958534	+	0.284979i	$0.0919868\pi$
$599$			13.9494i			0.569959i	−0.958534	+	0.284979i	$0.908013\pi$
$600$		0			0
$601$	−37.0471			−1.51118			−0.755591	−	0.655043i	$-0.772650\pi$
$601$	−37.0471			−1.51118			−0.755591	+	0.655043i	$0.772650\pi$
$602$		−	9.83815i		−	0.400973i
$603$		0			0
$604$	46.8077	+	27.0244i	1.90458	+	1.09961i
$605$	−12.3978	+	21.4736i	−0.504041	+	0.873025i
$606$		0			0
$607$	40.0752			1.62660			0.813302	−	0.581842i	$-0.197668\pi$
$607$	40.0752			1.62660			0.813302	+	0.581842i	$0.197668\pi$
$608$	−3.43709	−	1.98441i	−0.139392	−	0.0804783i
$609$		0			0
$610$	−43.0027	+	15.3277i	−1.74113	+	0.620599i
$611$	39.5925			1.60174
$612$		0			0
$613$	−30.0296			−1.21288			−0.606442	−	0.795128i	$-0.707404\pi$
$613$	−30.0296			−1.21288			−0.606442	+	0.795128i	$0.707404\pi$
$614$	−8.23290	−	14.2598i	−0.332253	−	0.575478i
$615$		0			0
$616$	−8.52009	−	4.91908i	−0.343284	−	0.198195i
$617$	−23.5748	−	13.6109i	−0.949085	−	0.547954i	−0.0562882	−	0.998415i	$-0.517927\pi$
$617$	−23.5748	−	13.6109i	−0.949085	−	0.547954i	−0.892796	+	0.450460i	$0.851260\pi$
$618$		0			0
$619$	−17.4050			−0.699566			−0.349783	−	0.936831i	$-0.613745\pi$
$619$	−17.4050			−0.699566			−0.349783	+	0.936831i	$0.613745\pi$
$620$	−72.4196	+	41.8115i	−2.90844	+	1.67919i
$621$		0			0
$622$	19.3047	+	33.4368i	0.774049	+	1.34069i
$623$	−7.21413	+	12.4952i	−0.289028	+	0.500612i
$624$		0			0
$625$	13.7036	−	23.7354i	0.548146	−	0.949416i
$626$	−12.9848	+	22.4904i	−0.518977	+	0.898895i
$627$		0			0
$628$	66.3989	+	38.3354i	2.64960	+	1.52975i
$629$	−5.39775	−	9.34917i	−0.215222	−	0.372776i
$630$		0			0
$631$	−10.7043	−	6.18010i	−0.426130	−	0.246026i	0.271567	−	0.962420i	$-0.412458\pi$
$631$	−10.7043	−	6.18010i	−0.426130	−	0.246026i	−0.697696	+	0.716394i	$0.745792\pi$
$632$	26.4214	−	45.7631i	1.05098	−	1.82036i
$633$		0			0
$634$			74.0498i			2.94089i
$635$	3.67201	+	6.36011i	0.145719	+	0.252393i
$636$		0			0
$637$	−0.757785			−0.0300245
$638$		−	5.45861i		−	0.216108i
$639$		0			0
$640$	36.2262	−	20.9152i	1.43197	−	0.826746i
$641$	5.54164	−	3.19947i	0.218882	−	0.126371i	−0.386551	−	0.922268i	$-0.626334\pi$
$641$	5.54164	−	3.19947i	0.218882	−	0.126371i	0.605432	+	0.795897i	$0.293000\pi$
$642$		0			0
$643$		−	23.3663i		−	0.921477i	−0.887536	−	0.460738i	$-0.847585\pi$
$643$		−	23.3663i		−	0.921477i	0.887536	−	0.460738i	$-0.152415\pi$
$644$	−69.3920			−2.73443
$645$		0			0
$646$	3.25014	+	5.62941i	0.127875	+	0.221486i
$647$			18.2413i			0.717139i	0.933503	+	0.358570i	$0.116735\pi$
$647$			18.2413i			0.717139i	−0.933503	+	0.358570i	$0.883265\pi$
$648$		0			0
$649$	0.709200	−	1.22837i	0.0278386	−	0.0482178i
$650$	−4.85353	−	2.80219i	−0.190371	−	0.109911i
$651$		0			0
$652$	−12.6866	−	21.9738i	−0.496844	−	0.860559i
$653$	34.9274	+	20.1653i	1.36682	+	0.789131i	0.990520	−	0.137369i	$-0.0438646\pi$
$653$	34.9274	+	20.1653i	1.36682	+	0.789131i	0.376295	+	0.926500i	$0.377198\pi$
$654$		0			0
$655$	−12.4836	+	21.6222i	−0.487774	+	0.844849i
$656$	−1.02142	+	1.76915i	−0.0398797	+	0.0690736i
$657$		0			0
$658$	31.5091	−	54.5754i	1.22835	−	2.12757i
$659$	−16.5192	−	28.6121i	−0.643496	−	1.11457i	−0.984647	−	0.174559i	$-0.944150\pi$
$659$	−16.5192	−	28.6121i	−0.643496	−	1.11457i	0.341151	−	0.940009i	$-0.389183\pi$
$660$		0			0
$661$	21.5963	−	12.4686i	0.839999	−	0.484974i	−0.0172648	−	0.999851i	$-0.505496\pi$
$661$	21.5963	−	12.4686i	0.839999	−	0.484974i	0.857264	+	0.514877i	$0.172162\pi$
$662$	−27.6132			−1.07322
$663$		0			0
$664$	−52.9304	−	30.5594i	−2.05410	−	1.18593i
$665$	−12.4969	−	7.21511i	−0.484610	−	0.279790i
$666$		0			0
$667$	−10.0125	−	17.3421i	−0.387685	−	0.671489i
$668$	59.6196			2.30675
$669$		0			0
$670$	−47.7336			−1.84411
$671$	0.959902	−	5.23928i	0.0370566	−	0.202260i
$672$		0			0
$673$	−16.0908	−	9.29005i	−0.620256	−	0.358105i	0.156713	−	0.987644i	$-0.449910\pi$
$673$	−16.0908	−	9.29005i	−0.620256	−	0.358105i	−0.776969	+	0.629539i	$0.783244\pi$
$674$	−64.9982			−2.50364
$675$		0			0
$676$	9.34111	−	16.1793i	0.359274	−	0.622280i
$677$	−10.9724	−	6.33491i	−0.421703	−	0.243470i	0.274103	−	0.961700i	$-0.411619\pi$
$677$	−10.9724	−	6.33491i	−0.421703	−	0.243470i	−0.695806	+	0.718230i	$0.744953\pi$
$678$		0			0
$679$			21.0902i			0.809366i
$680$	14.4953			0.555868
$681$		0			0
$682$		−	14.4387i		−	0.552888i
$683$	−5.91660	−	10.2479i	−0.226392	−	0.392123i	0.730344	−	0.683080i	$-0.239360\pi$
$683$	−5.91660	−	10.2479i	−0.226392	−	0.392123i	−0.956736	+	0.290956i	$0.906027\pi$
$684$		0			0
$685$	8.95309	+	15.5072i	0.342080	+	0.592500i
$686$	22.6900	−	39.3001i	0.866306	−	1.50049i
$687$		0			0
$688$	6.44429	−	3.72061i	0.245686	−	0.141847i
$689$	−20.5776	−	11.8805i	−0.783945	−	0.452611i
$690$		0			0
$691$	−3.65040			−0.138868			−0.0694338	−	0.997587i	$-0.522119\pi$
$691$	−3.65040			−0.138868			−0.0694338	+	0.997587i	$0.522119\pi$
$692$	−16.4632	−	9.50502i	−0.625836	−	0.361327i
$693$		0			0
$694$		−	40.4738i		−	1.53637i
$695$		−	34.7438i		−	1.31791i
$696$		0			0
$697$	0.402086	−	0.232145i	0.0152301	−	0.00879310i
$698$	−0.320934			−0.0121475
$699$		0			0
$700$	−5.22013	+	3.01384i	−0.197302	+	0.113913i
$701$	17.0204	−	9.82672i	0.642851	−	0.371150i	−0.142861	−	0.989743i	$-0.545630\pi$
$701$	17.0204	−	9.82672i	0.642851	−	0.371150i	0.785712	+	0.618593i	$0.212297\pi$
$702$		0			0
$703$	−18.6964	+	10.7944i	−0.705148	+	0.407118i
$704$			3.92777i			0.148033i
$705$		0			0
$706$	0.0468742	−	0.0270628i	0.00176413	−	0.00101852i
$707$	12.0088	+	20.7999i	0.451638	+	0.782260i
$708$		0			0
$709$			4.40036i			0.165259i	0.996580	+	0.0826294i	$0.0263318\pi$
$709$			4.40036i			0.165259i	−0.996580	+	0.0826294i	$0.973668\pi$
$710$	8.10389	−	14.0364i	0.304134	−	0.526775i
$711$		0			0
$712$	−28.9836			−1.08621
$713$	−26.4843	−	45.8722i	−0.991845	−	1.71793i
$714$		0			0
$715$	5.81239	−	3.35578i	0.217371	−	0.125499i
$716$	−41.1029	+	71.1923i	−1.53609	+	2.66058i
$717$		0			0
$718$	−10.7277	−	18.5810i	−0.400355	−	0.693436i
$719$	−14.7694	+	25.5814i	−0.550806	+	0.954024i	0.447411	+	0.894329i	$0.352346\pi$
$719$	−14.7694	+	25.5814i	−0.550806	+	0.954024i	−0.998217	+	0.0596954i	$0.980987\pi$
$720$		0			0
$721$			39.5994i			1.47476i
$722$	−29.6065	+	17.0933i	−1.10184	+	0.636148i
$723$		0			0
$724$		−	41.0087i		−	1.52408i
$725$	−1.50641	−	0.869727i	−0.0559467	−	0.0323008i
$726$		0			0
$727$	8.79993	−	15.2419i	0.326371	−	0.565292i	−0.655418	−	0.755267i	$-0.727507\pi$
$727$	8.79993	−	15.2419i	0.326371	−	0.565292i	0.981789	+	0.189975i	$0.0608407\pi$
$728$	−30.1587	−	52.2364i	−1.11776	−	1.93601i
$729$		0			0
$730$	29.7842	+	17.1959i	1.10236	+	0.636449i
$731$	−1.69122			−0.0625520
$732$		0			0
$733$	20.2317			0.747276			0.373638	−	0.927575i	$-0.378110\pi$
$733$	20.2317			0.747276			0.373638	+	0.927575i	$0.378110\pi$
$734$	9.42403	+	5.44097i	0.347847	+	0.200830i
$735$		0			0
$736$	−5.38920	−	9.33437i	−0.198649	−	0.344069i
$737$	2.78463	−	4.82312i	0.102573	−	0.177662i
$738$		0			0
$739$	−14.6004	−	8.42953i	−0.537083	−	0.310085i	0.206813	−	0.978381i	$-0.433691\pi$
$739$	−14.6004	−	8.42953i	−0.537083	−	0.310085i	−0.743896	+	0.668295i	$0.767024\pi$
$740$			92.5611i			3.40261i
$741$		0			0
$742$	−32.7528	+	18.9098i	−1.20239	+	0.694202i
$743$		−	33.5417i		−	1.23053i	−0.788322	−	0.615263i	$-0.789050\pi$
$743$		−	33.5417i		−	1.23053i	0.788322	−	0.615263i	$-0.210950\pi$
$744$		0			0
$745$	−3.45305	+	5.98087i	−0.126510	+	0.219122i
$746$	35.0124	+	60.6433i	1.28190	+	2.22031i
$747$		0			0
$748$	−1.62583	+	2.81603i	−0.0594464	+	0.102964i
$749$	37.0874	−	21.4124i	1.35514	−	0.782393i
$750$		0			0
$751$	18.4375	+	31.9346i	0.672792	+	1.16531i	0.977109	+	0.212739i	$0.0682385\pi$
$751$	18.4375	+	31.9346i	0.672792	+	1.16531i	−0.304317	+	0.952571i	$0.598428\pi$
$752$	47.6648			1.73816
$753$		0			0
$754$	16.7333	−	28.9829i	0.609390	−	1.05549i
$755$			30.5242i			1.11089i
$756$		0			0
$757$	17.6419	+	30.5566i	0.641205	+	1.11060i	0.985164	+	0.171615i	$0.0548985\pi$
$757$	17.6419	+	30.5566i	0.641205	+	1.11060i	−0.343959	+	0.938985i	$0.611768\pi$
$758$	44.1063	−	25.4648i	1.60201	−	0.924922i
$759$		0			0
$760$		−	28.9875i		−	1.05149i
$761$	21.0095	−	12.1299i	0.761596	−	0.439707i	−0.0682728	−	0.997667i	$-0.521749\pi$
$761$	21.0095	−	12.1299i	0.761596	−	0.439707i	0.829868	+	0.557959i	$0.188415\pi$
$762$		0			0
$763$	18.1976	−	10.5064i	0.658796	−	0.380356i
$764$	43.5808	−	25.1614i	1.57670	−	0.910308i
$765$		0			0
$766$	23.6038			0.852840
$767$	7.53110	−	4.34808i	0.271932	−	0.157000i
$768$		0			0
$769$		−	7.23081i		−	0.260750i	−0.991465	−	0.130375i	$-0.958382\pi$
$769$		−	7.23081i		−	0.260750i	0.991465	−	0.130375i	$-0.0416181\pi$
$770$		−	10.6826i		−	0.384974i
$771$		0			0
$772$	−20.1259	−	11.6197i	−0.724348	−	0.418202i
$773$	2.94718			0.106003			0.0530014	−	0.998594i	$-0.483121\pi$
$773$	2.94718			0.106003			0.0530014	+	0.998594i	$0.483121\pi$
$774$		0			0
$775$	−3.98465	−	2.30054i	−0.143133	−	0.0826379i
$776$	−36.6901	+	21.1831i	−1.31710	+	0.760428i
$777$		0			0
$778$	−19.1348	+	33.1424i	−0.686015	+	1.18821i
$779$	−0.464241	−	0.804089i	−0.0166332	−	0.0288095i
$780$		0			0
$781$	0.945512	+	1.63768i	0.0338331	+	0.0586006i
$782$			17.6533i			0.631281i
$783$		0			0
$784$	−0.912285			−0.0325816
$785$			43.2999i			1.54544i
$786$		0			0
$787$	13.1447	+	7.58909i	0.468558	+	0.270522i	0.715636	−	0.698474i	$-0.246137\pi$
$787$	13.1447	+	7.58909i	0.468558	+	0.270522i	−0.247078	+	0.968996i	$0.579470\pi$
$788$	32.5035	−	56.2977i	1.15789	−	2.00552i
$789$		0			0
$790$	57.3784			2.04143
$791$	−29.2373	−	16.8802i	−1.03956	−	0.600190i
$792$		0			0
$793$	21.1576	−	24.8758i	0.751328	−	0.883364i
$794$	−5.70979			−0.202633
$795$		0			0
$796$	50.6128			1.79392
$797$	15.4955	+	26.8390i	0.548880	+	0.950687i	0.998352	+	0.0573930i	$0.0182788\pi$
$797$	15.4955	+	26.8390i	0.548880	+	0.950687i	−0.449472	+	0.893294i	$0.648388\pi$
$798$		0			0
$799$	−9.38174	−	5.41655i	−0.331902	−	0.191624i
$800$	−0.810823	−	0.468129i	−0.0286669	−	0.0165509i
$801$		0			0
$802$	−6.08271			−0.214788
$803$	−3.47504	+	2.00631i	−0.122631	+	0.0708012i
$804$		0			0
$805$	−19.5946	−	33.9389i	−0.690619	−	1.19619i
$806$	44.2617	−	76.6635i	1.55905	−	2.70036i
$807$		0			0
$808$	−24.1234	+	41.7830i	−0.848659	+	1.46992i
$809$	−11.1070	+	19.2379i	−0.390502	+	0.676370i	−0.992516	−	0.122116i	$-0.961032\pi$
$809$	−11.1070	+	19.2379i	−0.390502	+	0.676370i	0.602013	+	0.798486i	$0.294365\pi$
$810$		0			0
$811$	16.8830	+	9.74740i	0.592842	+	0.342277i	0.766220	−	0.642578i	$-0.222135\pi$
$811$	16.8830	+	9.74740i	0.592842	+	0.342277i	−0.173379	+	0.984855i	$0.555468\pi$
$812$	−17.9972	−	31.1720i	−0.631577	−	1.09392i
$813$		0			0
$814$	−13.8408	−	7.99102i	−0.485122	−	0.280085i
$815$	7.16475	−	12.4097i	0.250970	−	0.434693i
$816$		0			0
$817$			3.38209i			0.118324i
$818$	13.8283	+	23.9514i	0.483496	+	0.837440i
$819$		0			0
$820$	−3.98084			−0.139017
$821$			29.0827i			1.01499i	0.861653	+	0.507497i	$0.169429\pi$
$821$			29.0827i			1.01499i	−0.861653	+	0.507497i	$0.830571\pi$
$822$		0			0
$823$	25.2258	−	14.5641i	0.879318	−	0.507674i	0.00888422	−	0.999961i	$-0.497172\pi$
$823$	25.2258	−	14.5641i	0.879318	−	0.507674i	0.870433	+	0.492286i	$0.163839\pi$
$824$	−68.8904	+	39.7739i	−2.39991	+	1.38559i
$825$		0			0
$826$		−	13.8414i		−	0.481605i
$827$	44.1770			1.53619			0.768093	−	0.640338i	$-0.221206\pi$
$827$	44.1770			1.53619			0.768093	+	0.640338i	$0.221206\pi$
$828$		0			0
$829$	6.36561	+	11.0256i	0.221087	+	0.382933i	0.955138	−	0.296160i	$-0.0957063\pi$
$829$	6.36561	+	11.0256i	0.221087	+	0.382933i	−0.734052	+	0.679094i	$0.762373\pi$
$830$		−	66.3648i		−	2.30356i
$831$		0			0
$832$	−12.0405	+	20.8548i	−0.417429	+	0.723009i
$833$	0.179563	+	0.103671i	0.00622148	+	0.00359198i
$834$		0			0
$835$	16.8351	+	29.1593i	0.582603	+	1.00910i
$836$	5.63147	+	3.25133i	0.194769	+	0.112450i
$837$		0			0
$838$	−43.4310	+	75.2248i	−1.50030	+	2.59860i
$839$	16.6475	−	28.8343i	0.574736	−	0.995471i	−0.421335	−	0.906905i	$-0.638438\pi$
$839$	16.6475	−	28.8343i	0.574736	−	0.995471i	0.996070	−	0.0885661i	$-0.0282285\pi$
$840$		0			0
$841$	−9.30642	+	16.1192i	−0.320911	+	0.555834i
$842$	−5.45937	−	9.45591i	−0.188142	−	0.325872i
$843$		0			0
$844$	−6.46220	+	3.73095i	−0.222438	+	0.128425i
$845$	10.5508			0.362959
$846$		0			0
$847$	−24.4490	−	14.1156i	−0.840076	−	0.485018i
$848$	−24.7731	−	14.3027i	−0.850710	−	0.491158i
$849$		0			0
$850$	0.766721	+	1.32800i	0.0262983	+	0.0455500i
$851$	−58.6302			−2.00982
$852$		0			0
$853$	33.4653			1.14583			0.572916	−	0.819614i	$-0.305812\pi$
$853$	33.4653			1.14583			0.572916	+	0.819614i	$0.305812\pi$
$854$	−17.4515	−	48.9612i	−0.597177	−	1.67542i
$855$		0			0
$856$	74.5015	+	43.0135i	2.54641	+	1.47017i
$857$	12.0255			0.410784			0.205392	−	0.978680i	$-0.434153\pi$
$857$	12.0255			0.410784			0.205392	+	0.978680i	$0.434153\pi$
$858$		0			0
$859$	−25.1855	+	43.6226i	−0.859320	+	1.48839i	0.0132590	+	0.999912i	$0.495779\pi$
$859$	−25.1855	+	43.6226i	−0.859320	+	1.48839i	−0.872579	+	0.488473i	$0.837554\pi$
$860$	12.5579	+	7.25030i	0.428220	+	0.247233i
$861$		0			0
$862$		−	1.16498i		−	0.0396794i
$863$	31.6007			1.07570			0.537850	−	0.843041i	$-0.319237\pi$
$863$	31.6007			1.07570			0.537850	+	0.843041i	$0.319237\pi$
$864$		0			0
$865$		−	10.7359i		−	0.365033i
$866$	16.2643	+	28.1705i	0.552682	+	0.957274i
$867$		0			0
$868$	−47.6049	−	82.4541i	−1.61581	−	2.79867i
$869$	−3.34728	+	5.79766i	−0.113549	+	0.196672i
$870$		0			0
$871$	29.5704	−	17.0725i	1.00195	−	0.578479i
$872$	36.5554	+	21.1053i	1.23792	+	0.714715i
$873$		0			0
$874$	35.3029			1.19414
$875$	24.3633	+	14.0662i	0.823631	+	0.475523i
$876$		0			0
$877$			33.6251i			1.13544i	0.823222	+	0.567719i	$0.192174\pi$
$877$			33.6251i			1.13544i	−0.823222	+	0.567719i	$0.807826\pi$
$878$			62.4952i			2.10911i
$879$		0			0
$880$	6.99744	−	4.03997i	0.235884	−	0.136187i
$881$	33.7930			1.13852			0.569258	−	0.822159i	$-0.307231\pi$
$881$	33.7930			1.13852			0.569258	+	0.822159i	$0.307231\pi$
$882$		0			0
$883$	19.7753	−	11.4173i	0.665491	−	0.384221i	−0.128875	−	0.991661i	$-0.541137\pi$
$883$	19.7753	−	11.4173i	0.665491	−	0.384221i	0.794366	+	0.607439i	$0.207803\pi$
$884$	−17.2650	+	9.96794i	−0.580684	+	0.335258i
$885$		0			0
$886$	−9.80876	+	5.66309i	−0.329532	+	0.190255i
$887$		−	19.7835i		−	0.664265i	−0.943233	−	0.332132i	$-0.892232\pi$
$887$		−	19.7835i		−	0.664265i	0.943233	−	0.332132i	$-0.107768\pi$
$888$		0			0
$889$	−7.24136	+	4.18080i	−0.242867	+	0.140220i
$890$	−15.7357	−	27.2551i	−0.527463	−	0.913592i
$891$		0			0
$892$			64.5997i			2.16296i
$893$	−10.8320	+	18.7615i	−0.362478	+	0.627831i
$894$		0			0
$895$	−46.4258			−1.55184
$896$	23.8132	+	41.2457i	0.795543	+	1.37792i
$897$		0			0
$898$	17.9509	−	10.3640i	0.599030	−	0.345850i
$899$	13.7377	−	23.7944i	0.458177	−	0.793587i
$900$		0			0
$901$	3.25068	+	5.63034i	0.108296	+	0.187574i
$902$	0.343675	−	0.595263i	0.0114431	−	0.0198201i
$903$		0			0
$904$		−	67.8181i		−	2.25560i
$905$	20.0569	−	11.5799i	0.666715	−	0.384928i
$906$		0			0
$907$			12.2712i			0.407458i	0.979027	+	0.203729i	$0.0653061\pi$
$907$			12.2712i			0.407458i	−0.979027	+	0.203729i	$0.934694\pi$
$908$	−44.4911	−	25.6870i	−1.47649	−	0.852452i
$909$		0			0
$910$	32.7473	−	56.7201i	1.08556	−	1.88025i
$911$	−9.28633	−	16.0844i	−0.307670	−	0.532900i	0.670182	−	0.742197i	$-0.266216\pi$
$911$	−9.28633	−	16.0844i	−0.307670	−	0.532900i	−0.977852	+	0.209297i	$0.932883\pi$
$912$		0			0
$913$	6.70567	+	3.87152i	0.221925	+	0.128129i
$914$	−30.5956			−1.01201
$915$		0			0
$916$	−16.5272			−0.546074
$917$	−24.6182	−	14.2133i	−0.812963	−	0.469364i
$918$		0			0
$919$	−2.35763	−	4.08353i	−0.0777710	−	0.134703i	0.824517	−	0.565837i	$-0.191447\pi$
$919$	−2.35763	−	4.08353i	−0.0777710	−	0.134703i	−0.902288	+	0.431134i	$0.858114\pi$
$920$	39.3618	−	68.1767i	1.29772	−	2.24772i
$921$		0			0
$922$	73.7026	+	42.5522i	2.42726	+	1.40138i
$923$			11.5938i			0.381615i
$924$		0			0
$925$	−4.41056	+	2.54644i	−0.145018	+	0.0837263i
$926$			40.4520i			1.32933i
$927$		0			0
$928$	2.79543	−	4.84183i	0.0917646	−	0.158941i
$929$	11.0359	+	19.1148i	0.362078	+	0.627137i	0.988303	−	0.152506i	$-0.0487342\pi$
$929$	11.0359	+	19.1148i	0.362078	+	0.627137i	−0.626225	+	0.779642i	$0.715401\pi$
$930$		0			0
$931$	0.207320	−	0.359089i	0.00679464	−	0.0117687i
$932$	−74.1162	+	42.7910i	−2.42776	+	1.40167i
$933$		0			0
$934$	−45.0183	−	77.9739i	−1.47304	−	2.55138i
$935$	−1.83638			−0.0600562
$936$		0			0
$937$	−11.7101	+	20.2825i	−0.382552	+	0.662600i	−0.991426	−	0.130667i	$-0.958288\pi$
$937$	−11.7101	+	20.2825i	−0.382552	+	0.662600i	0.608874	+	0.793267i	$0.291621\pi$
$938$		−	54.3475i		−	1.77451i
$939$		0			0
$940$	46.4418	+	80.4395i	1.51476	+	2.62365i
$941$	−10.8445	+	6.26108i	−0.353521	+	0.204106i	−0.666235	−	0.745742i	$-0.732095\pi$
$941$	−10.8445	+	6.26108i	−0.353521	+	0.204106i	0.312714	+	0.949847i	$0.398762\pi$
$942$		0			0
$943$		−	2.52155i		−	0.0821130i
$944$	9.06657	−	5.23459i	0.295092	−	0.170371i
$945$		0			0
$946$	−2.16830	+	1.25187i	−0.0704977	+	0.0407018i
$947$	−46.5542	+	26.8781i	−1.51281	+	0.873420i	−0.512921	+	0.858436i	$0.671437\pi$
$947$	−46.5542	+	26.8781i	−1.51281	+	0.873420i	−0.999888	+	0.0149844i	$0.995230\pi$
$948$		0			0
$949$	−24.6013			−0.798591
$950$	2.65572	−	1.53328i	0.0861631	−	0.0497463i
$951$		0			0
$952$			16.5037i			0.534889i
$953$		−	19.4789i		−	0.630983i	−0.948928	−	0.315491i	$-0.897831\pi$
$953$		−	19.4789i		−	0.630983i	0.948928	−	0.315491i	$-0.102169\pi$
$954$		0			0
$955$	24.6123	+	14.2099i	0.796436	+	0.459823i
$956$	−30.3800			−0.982560
$957$		0			0
$958$	−48.9705	−	28.2732i	−1.58217	−	0.913464i
$959$	−17.6559	+	10.1936i	−0.570138	+	0.329169i
$960$		0			0
$961$	20.8380	−	36.0924i	0.672192	−	1.16427i
$962$	−48.9927	−	84.8578i	−1.57959	−	2.73592i
$963$		0			0
$964$	−45.0430	−	78.0168i	−1.45074	−	2.51275i
$965$		−	13.1245i		−	0.422492i
$966$		0			0
$967$	−26.8613			−0.863801			−0.431900	−	0.901921i	$-0.642157\pi$
$967$	−26.8613			−0.863801			−0.431900	+	0.901921i	$0.642157\pi$
$968$		−	56.7112i		−	1.82277i
$969$		0			0
$970$	−39.8394	−	23.0013i	−1.27917	−	0.738527i
$971$	25.9704	−	44.9820i	0.833429	−	1.44354i	−0.0618736	−	0.998084i	$-0.519708\pi$
$971$	25.9704	−	44.9820i	0.833429	−	1.44354i	0.895303	−	0.445458i	$-0.146959\pi$
$972$		0			0
$973$	39.5579			1.26817
$974$	56.0108	+	32.3379i	1.79470	+	1.03617i
$975$		0			0
$976$	25.4713	−	29.9475i	0.815315	−	0.958596i
$977$	14.0905			0.450794			0.225397	−	0.974267i	$-0.427632\pi$
$977$	14.0905			0.450794			0.225397	+	0.974267i	$0.427632\pi$
$978$		0			0
$979$	3.67190			0.117354
$980$	−0.888877	−	1.53958i	−0.0283941	−	0.0491801i
$981$		0			0
$982$	−51.6349	−	29.8114i	−1.64774	−	0.951321i
$983$	−34.6070	−	19.9804i	−1.10379	−	0.637275i	−0.166578	−	0.986028i	$-0.553272\pi$
$983$	−34.6070	−	19.9804i	−1.10379	−	0.637275i	−0.937214	+	0.348754i	$0.886605\pi$
$984$		0			0
$985$	36.7128			1.16977
$986$	−7.93015	+	4.57847i	−0.252547	+	0.145808i
$987$		0			0
$988$	19.9338	+	34.5264i	0.634179	+	1.09843i
$989$	−4.59250	+	7.95444i	−0.146033	+	0.252936i
$990$		0			0
$991$	23.6792	−	41.0135i	0.752194	−	1.30284i	−0.194564	−	0.980890i	$-0.562329\pi$
$991$	23.6792	−	41.0135i	0.752194	−	1.30284i	0.946757	−	0.321948i	$-0.104338\pi$
$992$	7.39429	−	12.8073i	0.234769	−	0.406632i
$993$		0			0
$994$	15.9812	+	9.22677i	0.506894	+	0.292655i
$995$	14.2918	+	24.7542i	0.453081	+	0.784759i
$996$		0			0
$997$	−2.74189	−	1.58303i	−0.0868366	−	0.0501351i	0.455953	−	0.890004i	$-0.349299\pi$
$997$	−2.74189	−	1.58303i	−0.0868366	−	0.0501351i	−0.542790	+	0.839869i	$0.682632\pi$
$998$	−22.5910	+	39.1288i	−0.715106	+	1.23860i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	549.2.s.j.109.1		8
3.2	odd	2		61.2.f.b.48.4	yes	8
12.11	even	2		976.2.ba.c.353.4		8
61.14	even	6	inner	549.2.s.j.136.1		8
183.14	odd	6		61.2.f.b.14.4	✓	8
183.101	even	12		3721.2.a.i.1.2		8
183.143	even	12		3721.2.a.i.1.7		8
732.563	even	6		976.2.ba.c.929.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.f.b.14.4	✓	8	183.14	odd	6
61.2.f.b.48.4	yes	8	3.2	odd	2
549.2.s.j.109.1		8	1.1	even	1	trivial
549.2.s.j.136.1		8	61.14	even	6	inner
976.2.ba.c.353.4		8	12.11	even	2
976.2.ba.c.929.4		8	732.563	even	6
3721.2.a.i.1.2		8	183.101	even	12
3721.2.a.i.1.7		8	183.143	even	12

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:	\( N \)	\(=\)	\( 549 = 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	549.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.15074 - 1.24173i) q^{2} +(2.08380 + 3.60925i) q^{4} +(-1.17683 + 2.03833i) q^{5} +(-2.32076 - 1.33989i) q^{7} -5.38317i q^{8} +O(q^{10})\)	\(q+(-2.15074 - 1.24173i) q^{2} +(2.08380 + 3.60925i) q^{4} +(-1.17683 + 2.03833i) q^{5} +(-2.32076 - 1.33989i) q^{7} -5.38317i q^{8} +(5.06212 - 2.92262i) q^{10} +0.681986i q^{11} +(-2.09062 + 3.62106i) q^{13} +(3.32757 + 5.76353i) q^{14} +(-2.51686 + 4.35933i) q^{16} +(0.990775 - 0.572024i) q^{17} +(-1.14393 - 1.98134i) q^{19} -9.80912 q^{20} +(0.846845 - 1.46678i) q^{22} -6.21331i q^{23} +(-0.269858 - 0.467407i) q^{25} +(8.99277 - 5.19198i) q^{26} -11.1683i q^{28} +(2.79112 - 1.61146i) q^{29} +(7.38288 - 4.26251i) q^{31} +(1.50232 - 0.867363i) q^{32} -2.84120 q^{34} +(5.46228 - 3.15365i) q^{35} -9.43622i q^{37} +5.68182i q^{38} +(10.9727 + 6.33508i) q^{40} +0.405830 q^{41} +(-1.28023 - 0.739138i) q^{43} +(-2.46146 + 1.42112i) q^{44} +(-7.71528 + 13.3633i) q^{46} +(-4.73455 - 8.20048i) q^{47} +(0.0906174 + 0.156954i) q^{49} +1.34036i q^{50} -17.4257 q^{52} +5.68277i q^{53} +(-1.39011 - 0.802582i) q^{55} +(-7.21287 + 12.4931i) q^{56} -8.00399 q^{58} +(-1.80117 - 1.03990i) q^{59} +(-7.68238 - 1.40751i) q^{61} -21.1716 q^{62} +5.75930 q^{64} +(-4.92060 - 8.52273i) q^{65} +(-7.07217 - 4.08312i) q^{67} +(4.12916 + 2.38397i) q^{68} -15.6640 q^{70} +(2.40133 - 1.38641i) q^{71} +(2.94187 + 5.09546i) q^{73} +(-11.7173 + 20.2949i) q^{74} +(4.76745 - 8.25746i) q^{76} +(0.913787 - 1.58273i) q^{77} +(8.50114 + 4.90814i) q^{79} +(-5.92383 - 10.2604i) q^{80} +(-0.872837 - 0.503933i) q^{82} +(5.67683 - 9.83256i) q^{83} +2.69270i q^{85} +(1.83563 + 3.17940i) q^{86} +3.67125 q^{88} -5.38412i q^{89} +(9.70364 - 5.60240i) q^{91} +(22.4254 - 12.9473i) q^{92} +23.5162i q^{94} +5.38484 q^{95} +(-3.93505 - 6.81571i) q^{97} -0.450091i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 6 q^{5} - 3 q^{7}+O(q^{10}) \) 8 * q + 8 * q^4 - 6 * q^5 - 3 * q^7	\( 8 q + 8 q^{4} - 6 q^{5} - 3 q^{7} - 6 q^{10} - 3 q^{13} + 6 q^{14} - 20 q^{16} - 6 q^{17} + 3 q^{19} - 30 q^{20} + 5 q^{22} - 4 q^{25} + 15 q^{26} - 3 q^{31} - 48 q^{32} + 8 q^{34} - 3 q^{35} + 21 q^{40} + 24 q^{41} + 18 q^{44} - 17 q^{46} - 12 q^{47} - 13 q^{49} - 12 q^{52} - 6 q^{55} + 6 q^{56} + 22 q^{58} + 3 q^{59} - 8 q^{61} - 66 q^{62} - 98 q^{64} - 24 q^{65} - 15 q^{67} + 57 q^{68} - 36 q^{70} - 15 q^{71} - 16 q^{73} - 6 q^{74} + 21 q^{76} - 3 q^{77} + 42 q^{79} - 42 q^{80} + 60 q^{82} + 42 q^{83} + 42 q^{86} + 84 q^{88} + 69 q^{92} - 54 q^{95} + 3 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 - 6 * q^5 - 3 * q^7 - 6 * q^10 - 3 * q^13 + 6 * q^14 - 20 * q^16 - 6 * q^17 + 3 * q^19 - 30 * q^20 + 5 * q^22 - 4 * q^25 + 15 * q^26 - 3 * q^31 - 48 * q^32 + 8 * q^34 - 3 * q^35 + 21 * q^40 + 24 * q^41 + 18 * q^44 - 17 * q^46 - 12 * q^47 - 13 * q^49 - 12 * q^52 - 6 * q^55 + 6 * q^56 + 22 * q^58 + 3 * q^59 - 8 * q^61 - 66 * q^62 - 98 * q^64 - 24 * q^65 - 15 * q^67 + 57 * q^68 - 36 * q^70 - 15 * q^71 - 16 * q^73 - 6 * q^74 + 21 * q^76 - 3 * q^77 + 42 * q^79 - 42 * q^80 + 60 * q^82 + 42 * q^83 + 42 * q^86 + 84 * q^88 + 69 * q^92 - 54 * q^95 + 3 * q^97

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