LMFDB - Embedded newform 297.2.e.e.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(100,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("297.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			199.4
Root			$-0.734668 - 0.348716i$ of defining polynomial
Character	$\chi$	$=$	297.199
Dual form			297.2.e.e.100.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23467 + 2.13851i) q^{2} +(-2.04881 + 3.54864i) q^{4} +(-1.21814 + 2.10988i) q^{5} +(-1.16933 - 2.02534i) q^{7} -5.17972 q^{8} +O(q^{10})$	\(q+(1.23467 + 2.13851i) q^{2} +(-2.04881 + 3.54864i) q^{4} +(-1.21814 + 2.10988i) q^{5} +(-1.16933 - 2.02534i) q^{7} -5.17972 q^{8} -6.01598 q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.35519 + 4.07931i) q^{13} +(2.88747 - 5.00124i) q^{14} +(-2.29761 - 3.97958i) q^{16} +3.20799 q^{17} +7.77494 q^{19} +(-4.99146 - 8.64547i) q^{20} +(-1.23467 + 2.13851i) q^{22} +(1.37948 - 2.38932i) q^{23} +(-0.467722 - 0.810117i) q^{25} -11.6315 q^{26} +9.58293 q^{28} +(-1.18586 - 2.05397i) q^{29} +(0.685860 - 1.18794i) q^{31} +(0.493856 - 0.855383i) q^{32} +(3.96080 + 6.86030i) q^{34} +5.69762 q^{35} -8.47256 q^{37} +(9.59946 + 16.6268i) q^{38} +(6.30961 - 10.9286i) q^{40} +(1.77332 - 3.07149i) q^{41} +(3.73467 + 6.46863i) q^{43} -4.09762 q^{44} +6.81278 q^{46} +(0.103993 + 0.180122i) q^{47} +(0.765332 - 1.32559i) q^{49} +(1.15496 - 2.00045i) q^{50} +(-9.65066 - 16.7154i) q^{52} +9.11360 q^{53} -2.43628 q^{55} +(6.05680 + 10.4907i) q^{56} +(2.92829 - 5.07194i) q^{58} +(-0.120523 + 0.208751i) q^{59} +(-0.830670 - 1.43876i) q^{61} +3.38724 q^{62} -6.75145 q^{64} +(-5.73789 - 9.93832i) q^{65} +(3.84027 - 6.65155i) q^{67} +(-6.57255 + 11.3840i) q^{68} +(7.03467 + 12.1844i) q^{70} -1.07731 q^{71} -2.37495 q^{73} +(-10.4608 - 18.1186i) q^{74} +(-15.9294 + 27.5904i) q^{76} +(1.16933 - 2.02534i) q^{77} +(-6.35680 - 11.0103i) q^{79} +11.1952 q^{80} +8.75786 q^{82} +(5.25042 + 9.09399i) q^{83} +(-3.90777 + 6.76846i) q^{85} +(-9.22215 + 15.9732i) q^{86} +(-2.58986 - 4.48577i) q^{88} +14.2933 q^{89} +11.0160 q^{91} +(5.65257 + 9.79053i) q^{92} +(-0.256795 + 0.444781i) q^{94} +(-9.47095 + 16.4042i) q^{95} +(-4.46694 - 7.73697i) q^{97} +3.77972 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7}+O(q^{10}) $ 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7	$ 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7} + 2 q^{10} + 4 q^{11} - 7 q^{13} + q^{14} - 17 q^{16} + 10 q^{17} + 18 q^{19} - 10 q^{20} - q^{22} + 14 q^{23} - 14 q^{25} - 44 q^{26} - 2 q^{28} - 6 q^{29} + 2 q^{31} - 34 q^{32} - 16 q^{34} + 16 q^{35} + 6 q^{37} + 3 q^{38} - 12 q^{40} - 2 q^{41} + 21 q^{43} - 22 q^{44} + 4 q^{46} - 7 q^{47} + 15 q^{49} + 23 q^{50} + 10 q^{52} + 12 q^{53} + 8 q^{55} + 18 q^{56} + 21 q^{58} + 2 q^{59} - 15 q^{61} + 40 q^{62} + 32 q^{64} + 19 q^{65} - 14 q^{67} - 7 q^{68} + 38 q^{70} + 6 q^{71} + 44 q^{73} - 36 q^{74} - 42 q^{76} + q^{77} - 11 q^{79} + 68 q^{80} - 34 q^{82} + 18 q^{83} - 13 q^{85} - 24 q^{86} + 12 q^{89} + 38 q^{91} + 67 q^{92} + 19 q^{94} - 30 q^{95} - 26 q^{97} - 30 q^{98}+O(q^{100}) $ 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7 + 2 * q^10 + 4 * q^11 - 7 * q^13 + q^14 - 17 * q^16 + 10 * q^17 + 18 * q^19 - 10 * q^20 - q^22 + 14 * q^23 - 14 * q^25 - 44 * q^26 - 2 * q^28 - 6 * q^29 + 2 * q^31 - 34 * q^32 - 16 * q^34 + 16 * q^35 + 6 * q^37 + 3 * q^38 - 12 * q^40 - 2 * q^41 + 21 * q^43 - 22 * q^44 + 4 * q^46 - 7 * q^47 + 15 * q^49 + 23 * q^50 + 10 * q^52 + 12 * q^53 + 8 * q^55 + 18 * q^56 + 21 * q^58 + 2 * q^59 - 15 * q^61 + 40 * q^62 + 32 * q^64 + 19 * q^65 - 14 * q^67 - 7 * q^68 + 38 * q^70 + 6 * q^71 + 44 * q^73 - 36 * q^74 - 42 * q^76 + q^77 - 11 * q^79 + 68 * q^80 - 34 * q^82 + 18 * q^83 - 13 * q^85 - 24 * q^86 + 12 * q^89 + 38 * q^91 + 67 * q^92 + 19 * q^94 - 30 * q^95 - 26 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.23467	+	2.13851i	0.873042	+	1.51215i	0.858834	+	0.512254i	$0.171189\pi$
$2$	1.23467	+	2.13851i	0.873042	+	1.51215i	0.0142076	+	0.999899i	$0.495477\pi$
$3$		0			0
$3$		0			0
$4$	−2.04881	+	3.54864i	−1.02440	+	1.77432i
$5$	−1.21814	+	2.10988i	−0.544768	+	0.943566i	0.453853	+	0.891076i	$0.350049\pi$
$5$	−1.21814	+	2.10988i	−0.544768	+	0.943566i	−0.998621	+	0.0524895i	$0.983284\pi$
$6$		0			0
$7$	−1.16933	−	2.02534i	−0.441965	−	0.765506i	0.555870	−	0.831269i	$-0.312385\pi$
$7$	−1.16933	−	2.02534i	−0.441965	−	0.765506i	−0.997835	+	0.0657628i	$0.979052\pi$
$8$	−5.17972			−1.83131
$9$		0			0
$10$	−6.01598			−1.90242
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−2.35519	+	4.07931i	−0.653212	+	1.13140i	0.329127	+	0.944286i	$0.393246\pi$
$13$	−2.35519	+	4.07931i	−0.653212	+	1.13140i	−0.982339	+	0.187111i	$0.940088\pi$
$14$	2.88747	−	5.00124i	0.771708	−	1.33664i
$15$		0			0
$16$	−2.29761	−	3.97958i	−0.574403	−	0.994895i
$17$	3.20799			0.778051			0.389026	−	0.921227i	$-0.372812\pi$
$17$	3.20799			0.778051			0.389026	+	0.921227i	$0.372812\pi$
$18$		0			0
$19$	7.77494			1.78369			0.891846	−	0.452338i	$-0.149410\pi$
$19$	7.77494			1.78369			0.891846	+	0.452338i	$0.149410\pi$
$20$	−4.99146	−	8.64547i	−1.11612	−	1.93318i
$21$		0			0
$22$	−1.23467	+	2.13851i	−0.263232	+	0.455931i
$23$	1.37948	−	2.38932i	0.287641	−	0.498209i	−0.685605	−	0.727973i	$-0.740462\pi$
$23$	1.37948	−	2.38932i	0.287641	−	0.498209i	0.973246	+	0.229765i	$0.0737957\pi$
$24$		0			0
$25$	−0.467722	−	0.810117i	−0.0935443	−	0.162023i
$26$	−11.6315			−2.28113
$27$		0			0
$28$	9.58293			1.81100
$29$	−1.18586	−	2.05397i	−0.220209	−	0.381413i	0.734663	−	0.678433i	$-0.237340\pi$
$29$	−1.18586	−	2.05397i	−0.220209	−	0.381413i	−0.954871	+	0.297020i	$0.904007\pi$
$30$		0			0
$31$	0.685860	−	1.18794i	0.123184	−	0.213361i	−0.797838	−	0.602872i	$-0.794023\pi$
$31$	0.685860	−	1.18794i	0.123184	−	0.213361i	0.921022	+	0.389511i	$0.127356\pi$
$32$	0.493856	−	0.855383i	0.0873022	−	0.151212i
$33$		0			0
$34$	3.96080	+	6.86030i	0.679271	+	1.17653i
$35$	5.69762			0.963074
$36$		0			0
$37$	−8.47256			−1.39288			−0.696440	−	0.717615i	$-0.745234\pi$
$37$	−8.47256			−1.39288			−0.696440	+	0.717615i	$0.745234\pi$
$38$	9.59946	+	16.6268i	1.55724	+	2.69722i
$39$		0			0
$40$	6.30961	−	10.9286i	0.997637	−	1.72796i
$41$	1.77332	−	3.07149i	0.276947	−	0.479686i	−0.693678	−	0.720285i	$-0.744011\pi$
$41$	1.77332	−	3.07149i	0.276947	−	0.479686i	0.970624	+	0.240600i	$0.0773441\pi$
$42$		0			0
$43$	3.73467	+	6.46863i	0.569531	+	0.986457i	0.996612	+	0.0822439i	$0.0262087\pi$
$43$	3.73467	+	6.46863i	0.569531	+	0.986457i	−0.427081	+	0.904213i	$0.640458\pi$
$44$	−4.09762			−0.617739
$45$		0			0
$46$	6.81278			1.00449
$47$	0.103993	+	0.180122i	0.0151690	+	0.0262735i	0.873510	−	0.486806i	$-0.161838\pi$
$47$	0.103993	+	0.180122i	0.0151690	+	0.0262735i	−0.858341	+	0.513079i	$0.828505\pi$
$48$		0			0
$49$	0.765332	−	1.32559i	0.109333	−	0.189371i
$50$	1.15496	−	2.00045i	0.163336	−	0.282907i
$51$		0			0
$52$	−9.65066	−	16.7154i	−1.33831	−	2.31801i
$53$	9.11360			1.25185			0.625925	−	0.779884i	$-0.284722\pi$
$53$	9.11360			1.25185			0.625925	+	0.779884i	$0.284722\pi$
$54$		0			0
$55$	−2.43628			−0.328507
$56$	6.05680	+	10.4907i	0.809374	+	1.40188i
$57$		0			0
$58$	2.92829	−	5.07194i	0.384503	−	0.665978i
$59$	−0.120523	+	0.208751i	−0.0156907	+	0.0271771i	−0.873764	−	0.486350i	$-0.838328\pi$
$59$	−0.120523	+	0.208751i	−0.0156907	+	0.0271771i	0.858073	+	0.513527i	$0.171661\pi$
$60$		0			0
$61$	−0.830670	−	1.43876i	−0.106356	−	0.184215i	0.807935	−	0.589271i	$-0.200585\pi$
$61$	−0.830670	−	1.43876i	−0.106356	−	0.184215i	−0.914292	+	0.405057i	$0.867252\pi$
$62$	3.38724			0.430179
$63$		0			0
$64$	−6.75145			−0.843932
$65$	−5.73789	−	9.93832i	−0.711698	−	1.23270i
$66$		0			0
$67$	3.84027	−	6.65155i	0.469164	−	0.812616i	−0.530214	−	0.847864i	$-0.677889\pi$
$67$	3.84027	−	6.65155i	0.469164	−	0.812616i	0.999379	+	0.0352474i	$0.0112219\pi$
$68$	−6.57255	+	11.3840i	−0.797039	+	1.38051i
$69$		0			0
$70$	7.03467	+	12.1844i	0.840804	+	1.45632i
$71$	−1.07731			−0.127854			−0.0639268	−	0.997955i	$-0.520362\pi$
$71$	−1.07731			−0.127854			−0.0639268	+	0.997955i	$0.520362\pi$
$72$		0			0
$73$	−2.37495			−0.277966			−0.138983	−	0.990295i	$-0.544383\pi$
$73$	−2.37495			−0.277966			−0.138983	+	0.990295i	$0.544383\pi$
$74$	−10.4608	−	18.1186i	−1.21604	−	2.10625i
$75$		0			0
$76$	−15.9294	+	27.5904i	−1.82722	+	3.16484i
$77$	1.16933	−	2.02534i	0.133258	−	0.230809i
$78$		0			0
$79$	−6.35680	−	11.0103i	−0.715196	−	1.23876i	−0.962884	−	0.269916i	$-0.913004\pi$
$79$	−6.35680	−	11.0103i	−0.715196	−	1.23876i	0.247687	−	0.968840i	$-0.420329\pi$
$80$	11.1952			1.25166
$81$		0			0
$82$	8.75786			0.967144
$83$	5.25042	+	9.09399i	0.576308	+	0.998195i	0.995898	+	0.0904812i	$0.0288405\pi$
$83$	5.25042	+	9.09399i	0.576308	+	0.998195i	−0.419590	+	0.907714i	$0.637826\pi$
$84$		0			0
$85$	−3.90777	+	6.76846i	−0.423857	+	0.734142i
$86$	−9.22215	+	15.9732i	−0.994450	+	1.72244i
$87$		0			0
$88$	−2.58986	−	4.48577i	−0.276080	−	0.478184i
$89$	14.2933			1.51509			0.757544	−	0.652784i	$-0.226399\pi$
$89$	14.2933			1.51509			0.757544	+	0.652784i	$0.226399\pi$
$90$		0			0
$91$	11.0160			1.15479
$92$	5.65257	+	9.79053i	0.589321	+	1.02073i
$93$		0			0
$94$	−0.256795	+	0.444781i	−0.0264863	+	0.0458757i
$95$	−9.47095	+	16.4042i	−0.971699	+	1.68303i
$96$		0			0
$97$	−4.46694	−	7.73697i	−0.453549	−	0.785570i	0.545054	−	0.838401i	$-0.316509\pi$
$97$	−4.46694	−	7.73697i	−0.453549	−	0.785570i	−0.998603	+	0.0528305i	$0.983176\pi$
$98$	3.77972			0.381810
$99$		0			0
$100$	3.83309			0.383309
$101$	−2.43844	−	4.22350i	−0.242633	−	0.420254i	0.718830	−	0.695186i	$-0.244678\pi$
$101$	−2.43844	−	4.22350i	−0.242633	−	0.420254i	−0.961464	+	0.274932i	$0.911345\pi$
$102$		0			0
$103$	5.08509	−	8.80764i	0.501049	−	0.867843i	−0.498950	−	0.866631i	$-0.666281\pi$
$103$	5.08509	−	8.80764i	0.501049	−	0.867843i	0.999999	−	0.00121186i	$-0.000385748\pi$
$104$	12.1992	−	21.1297i	1.19623	−	2.07193i
$105$		0			0
$106$	11.2523	+	19.4895i	1.09292	+	1.89299i
$107$	−9.59845			−0.927917			−0.463959	−	0.885857i	$-0.653571\pi$
$107$	−9.59845			−0.927917			−0.463959	+	0.885857i	$0.653571\pi$
$108$		0			0
$109$	−1.95143			−0.186913			−0.0934564	−	0.995623i	$-0.529792\pi$
$109$	−1.95143			−0.186913			−0.0934564	+	0.995623i	$0.529792\pi$
$110$	−3.00799	−	5.20999i	−0.286801	−	0.496753i
$111$		0			0
$112$	−5.37333	+	9.30689i	−0.507732	+	0.879418i
$113$	−3.95281	+	6.84646i	−0.371849	+	0.644061i	−0.989850	−	0.142116i	$-0.954609\pi$
$113$	−3.95281	+	6.84646i	−0.371849	+	0.644061i	0.618001	+	0.786177i	$0.287943\pi$
$114$		0			0
$115$	3.36079	+	5.82106i	0.313395	+	0.542816i
$116$	9.71839			0.902330
$117$		0			0
$118$	−0.595222			−0.0547946
$119$	−3.75120	−	6.49726i	−0.343872	−	0.595603i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	2.05120	−	3.55278i	0.185707	−	0.321654i
$123$		0			0
$124$	2.81039	+	4.86774i	0.252380	+	0.437136i
$125$	−9.90238			−0.885696
$126$		0			0
$127$	−0.943412			−0.0837142			−0.0418571	−	0.999124i	$-0.513327\pi$
$127$	−0.943412			−0.0837142			−0.0418571	+	0.999124i	$0.513327\pi$
$128$	−9.32351	−	16.1488i	−0.824090	−	1.42737i
$129$		0			0
$130$	14.1688	−	24.5411i	1.24268	−	2.15239i
$131$	−1.53066	+	2.65119i	−0.133735	+	0.231636i	−0.925113	−	0.379691i	$-0.876030\pi$
$131$	−1.53066	+	2.65119i	−0.133735	+	0.231636i	0.791379	+	0.611326i	$0.209364\pi$
$132$		0			0
$133$	−9.09147	−	15.7469i	−0.788331	−	1.36543i
$134$	18.9658			1.63840
$135$		0			0
$136$	−16.6165			−1.42485
$137$	−10.2280	−	17.7154i	−0.873835	−	1.51353i	−0.857999	−	0.513652i	$-0.828292\pi$
$137$	−10.2280	−	17.7154i	−0.873835	−	1.51353i	−0.0158365	−	0.999875i	$-0.505041\pi$
$138$		0			0
$139$	−6.45442	+	11.1794i	−0.547457	+	0.948223i	0.450991	+	0.892528i	$0.351071\pi$
$139$	−6.45442	+	11.1794i	−0.547457	+	0.948223i	−0.998448	+	0.0556944i	$0.982263\pi$
$140$	−11.6733	+	20.2188i	−0.986577	+	1.70880i
$141$		0			0
$142$	−1.33012	−	2.30384i	−0.111621	−	0.193334i
$143$	−4.71038			−0.393902
$144$		0			0
$145$	5.77816			0.479850
$146$	−2.93227	−	5.07884i	−0.242676	−	0.420328i
$147$		0			0
$148$	17.3587	−	30.0661i	1.42687	−	2.47142i
$149$	5.04027	−	8.73000i	0.412915	−	0.715190i	−0.582292	−	0.812980i	$-0.697844\pi$
$149$	5.04027	−	8.73000i	0.412915	−	0.715190i	0.995207	+	0.0977899i	$0.0311773\pi$
$150$		0			0
$151$	−2.36295	−	4.09275i	−0.192294	−	0.333063i	0.753716	−	0.657200i	$-0.228259\pi$
$151$	−2.36295	−	4.09275i	−0.192294	−	0.333063i	−0.946010	+	0.324137i	$0.894926\pi$
$152$	−40.2720			−3.26649
$153$		0			0
$154$	5.77494			0.465358
$155$	1.67094	+	2.89416i	0.134213	+	0.232465i
$156$		0			0
$157$	2.47733	−	4.29086i	0.197712	−	0.342448i	−0.750074	−	0.661354i	$-0.769982\pi$
$157$	2.47733	−	4.29086i	0.197712	−	0.342448i	0.947786	+	0.318906i	$0.103316\pi$
$158$	15.6971	−	27.1881i	1.24879	−	2.16297i
$159$		0			0
$160$	1.20317	+	2.08395i	0.0951189	+	0.164751i
$161$	−6.45226			−0.508509
$162$		0			0
$163$	−8.60277			−0.673821			−0.336910	−	0.941537i	$-0.609382\pi$
$163$	−8.60277			−0.673821			−0.336910	+	0.941537i	$0.609382\pi$
$164$	7.26640	+	12.5858i	0.567410	+	0.982784i
$165$		0			0
$166$	−12.9650	+	22.4561i	−1.00628	+	1.74293i
$167$	3.58908	−	6.21646i	0.277731	−	0.481044i	−0.693089	−	0.720852i	$-0.743751\pi$
$167$	3.58908	−	6.21646i	0.277731	−	0.481044i	0.970821	+	0.239807i	$0.0770842\pi$
$168$		0			0
$169$	−4.59384	−	7.95677i	−0.353372	−	0.612059i
$170$	−19.2992			−1.48018
$171$		0			0
$172$	−30.6065			−2.33372
$173$	3.62591	+	6.28026i	0.275673	+	0.477479i	0.970305	−	0.241886i	$-0.0777660\pi$
$173$	3.62591	+	6.28026i	0.275673	+	0.477479i	−0.694632	+	0.719365i	$0.744433\pi$
$174$		0			0
$175$	−1.09384	+	1.89459i	−0.0826867	+	0.143218i
$176$	2.29761	−	3.97958i	0.173189	−	0.299972i
$177$		0			0
$178$	17.6475	+	30.5663i	1.32274	+	2.29104i
$179$	7.29009			0.544887			0.272443	−	0.962172i	$-0.412168\pi$
$179$	7.29009			0.544887			0.272443	+	0.962172i	$0.412168\pi$
$180$		0			0
$181$	13.4235			0.997762			0.498881	−	0.866670i	$-0.333744\pi$
$181$	13.4235			0.997762			0.498881	+	0.866670i	$0.333744\pi$
$182$	13.6011	+	23.5578i	1.00818	+	1.74622i
$183$		0			0
$184$	−7.14530	+	12.3760i	−0.526758	+	0.912372i
$185$	10.3208	−	17.8761i	0.758797	−	1.31427i
$186$		0			0
$187$	1.60399	+	2.77820i	0.117296	+	0.203162i
$188$	−0.852250			−0.0621567
$189$		0			0
$190$	−46.7739			−3.39333
$191$	−1.15041	−	1.99256i	−0.0832406	−	0.144177i	0.821400	−	0.570353i	$-0.193194\pi$
$191$	−1.15041	−	1.99256i	−0.0832406	−	0.144177i	−0.904640	+	0.426176i	$0.859860\pi$
$192$		0			0
$193$	−7.04904	+	12.2093i	−0.507401	+	0.878844i	0.492562	+	0.870277i	$0.336060\pi$
$193$	−7.04904	+	12.2093i	−0.507401	+	0.878844i	−0.999963	+	0.00856725i	$0.997273\pi$
$194$	11.0304	−	19.1052i	0.791935	−	1.37167i
$195$		0			0
$196$	3.13604	+	5.43178i	0.224003	+	0.387984i
$197$	−1.31362			−0.0935913			−0.0467957	−	0.998904i	$-0.514901\pi$
$197$	−1.31362			−0.0935913			−0.0467957	+	0.998904i	$0.514901\pi$
$198$		0			0
$199$	15.8491			1.12351			0.561755	−	0.827303i	$-0.310126\pi$
$199$	15.8491			1.12351			0.561755	+	0.827303i	$0.310126\pi$
$200$	2.42266	+	4.19618i	0.171308	+	0.296715i
$201$		0			0
$202$	6.02132	−	10.4292i	0.423658	−	0.733798i
$203$	−2.77332	+	4.80354i	−0.194649	+	0.337142i
$204$		0			0
$205$	4.32031	+	7.48299i	0.301743	+	0.522635i
$206$	25.1136			1.74975
$207$		0			0
$208$	21.6452			1.50083
$209$	3.88747	+	6.73329i	0.268902	+	0.465752i
$210$		0			0
$211$	4.29225	−	7.43439i	0.295490	−	0.511804i	−0.679608	−	0.733575i	$-0.737850\pi$
$211$	4.29225	−	7.43439i	0.295490	−	0.511804i	0.975099	+	0.221771i	$0.0711836\pi$
$212$	−18.6720	+	32.3409i	−1.28240	+	2.22118i
$213$		0			0
$214$	−11.8509	−	20.5263i	−0.810110	−	1.40315i
$215$	−18.1974			−1.24105
$216$		0			0
$217$	−3.20799			−0.217772
$218$	−2.40936	−	4.17314i	−0.163183	−	0.282641i
$219$		0			0
$220$	4.99146	−	8.64547i	0.336524	−	0.582877i
$221$	−7.55542	+	13.0864i	−0.508233	+	0.880285i
$222$		0			0
$223$	13.2592	+	22.9656i	0.887901	+	1.53789i	0.842352	+	0.538927i	$0.181170\pi$
$223$	13.2592	+	22.9656i	0.887901	+	1.53789i	0.0455487	+	0.998962i	$0.485496\pi$
$224$	−2.30992			−0.154338
$225$		0			0
$226$	−19.5216			−1.29856
$227$	11.8427	+	20.5121i	0.786025	+	1.36144i	0.928385	+	0.371621i	$0.121198\pi$
$227$	11.8427	+	20.5121i	0.786025	+	1.36144i	−0.142359	+	0.989815i	$0.545469\pi$
$228$		0			0
$229$	5.99547	−	10.3845i	0.396192	−	0.686224i	−0.597061	−	0.802196i	$-0.703665\pi$
$229$	5.99547	−	10.3845i	0.396192	−	0.686224i	0.993253	+	0.115972i	$0.0369982\pi$
$230$	−8.29891	+	14.3741i	−0.547214	+	0.947803i
$231$		0			0
$232$	6.14242	+	10.6390i	0.403269	+	0.698483i
$233$	−18.9188			−1.23941			−0.619707	−	0.784833i	$-0.712749\pi$
$233$	−18.9188			−1.23941			−0.619707	+	0.784833i	$0.712749\pi$
$234$		0			0
$235$	−0.506713			−0.0330543
$236$	−0.493856	−	0.855383i	−0.0321473	−	0.0556807i
$237$		0			0
$238$	9.26296	−	16.0439i	0.600429	−	1.03997i
$239$	−8.28293	+	14.3465i	−0.535778	+	0.927995i	0.463347	+	0.886177i	$0.346648\pi$
$239$	−8.28293	+	14.3465i	−0.535778	+	0.927995i	−0.999125	+	0.0418181i	$0.986685\pi$
$240$		0			0
$241$	8.14450	+	14.1067i	0.524633	+	0.908691i	0.999589	+	0.0286815i	$0.00913084\pi$
$241$	8.14450	+	14.1067i	0.524633	+	0.908691i	−0.474955	+	0.880010i	$0.657536\pi$
$242$	−2.46934			−0.158735
$243$		0			0
$244$	6.80753			0.435807
$245$	1.86456	+	3.22952i	0.119122	+	0.206326i
$246$		0			0
$247$	−18.3115	+	31.7164i	−1.16513	+	2.01806i
$248$	−3.55256	+	6.15321i	−0.225588	+	0.390729i
$249$		0			0
$250$	−12.2262	−	21.1763i	−0.773250	−	1.33931i
$251$	15.1248			0.954671			0.477336	−	0.878721i	$-0.341603\pi$
$251$	15.1248			0.954671			0.477336	+	0.878721i	$0.341603\pi$
$252$		0			0
$253$	2.75895			0.173454
$254$	−1.16480	−	2.01749i	−0.0730860	−	0.126589i
$255$		0			0
$256$	16.2714	−	28.1829i	1.01696	−	1.76143i
$257$	9.75281	−	16.8924i	0.608364	−	1.05372i	−0.383147	−	0.923688i	$-0.625160\pi$
$257$	9.75281	−	16.8924i	0.608364	−	1.05372i	0.991510	−	0.130029i	$-0.0415071\pi$
$258$		0			0
$259$	9.90723	+	17.1598i	0.615605	+	1.06626i
$260$	47.0234			2.91627
$261$		0			0
$262$	−7.55945			−0.467024
$263$	4.71975	+	8.17485i	0.291032	+	0.504083i	0.974054	−	0.226315i	$-0.0726679\pi$
$263$	4.71975	+	8.17485i	0.291032	+	0.504083i	−0.683022	+	0.730398i	$0.739335\pi$
$264$		0			0
$265$	−11.1016	+	19.2286i	−0.681967	+	1.18120i
$266$	22.4499	−	38.8843i	1.37649	−	2.38415i
$267$		0			0
$268$	15.7360	+	27.2555i	0.961227	+	1.66489i
$269$	−7.33069			−0.446960			−0.223480	−	0.974708i	$-0.571742\pi$
$269$	−7.33069			−0.446960			−0.223480	+	0.974708i	$0.571742\pi$
$270$		0			0
$271$	−2.50286			−0.152038			−0.0760190	−	0.997106i	$-0.524221\pi$
$271$	−2.50286			−0.152038			−0.0760190	+	0.997106i	$0.524221\pi$
$272$	−7.37071	−	12.7664i	−0.446915	−	0.774079i
$273$		0			0
$274$	25.2563	−	43.7452i	1.52579	−	2.64274i
$275$	0.467722	−	0.810117i	0.0282047	−	0.0488519i
$276$		0			0
$277$	−10.9945	−	19.0430i	−0.660593	−	1.14418i	−0.980460	−	0.196718i	$-0.936972\pi$
$277$	−10.9945	−	19.0430i	−0.660593	−	1.14418i	0.319867	−	0.947462i	$-0.396362\pi$
$278$	−31.8762			−1.91181
$279$		0			0
$280$	−29.5121			−1.76368
$281$	−8.49685	−	14.7170i	−0.506880	−	0.877941i	−0.999968	−	0.00796209i	$-0.997466\pi$
$281$	−8.49685	−	14.7170i	−0.506880	−	0.877941i	0.493089	−	0.869979i	$-0.335868\pi$
$282$		0			0
$283$	−1.88908	+	3.27199i	−0.112294	+	0.194499i	−0.916695	−	0.399588i	$-0.869153\pi$
$283$	−1.88908	+	3.27199i	−0.112294	+	0.194499i	0.804401	+	0.594087i	$0.202487\pi$
$284$	2.20721	−	3.82299i	0.130974	−	0.226853i
$285$		0			0
$286$	−5.81575	−	10.0732i	−0.343893	−	0.595640i
$287$	−8.29441			−0.489603
$288$		0			0
$289$	−6.70882			−0.394636
$290$	7.13411	+	12.3566i	0.418929	+	0.725607i
$291$		0			0
$292$	4.86581	−	8.42783i	0.284750	−	0.493201i
$293$	−11.6877	+	20.2437i	−0.682803	+	1.18265i	0.291319	+	0.956626i	$0.405906\pi$
$293$	−11.6877	+	20.2437i	−0.682803	+	1.18265i	−0.974122	+	0.226024i	$0.927427\pi$
$294$		0			0
$295$	−0.293627	−	0.508576i	−0.0170956	−	0.0296105i
$296$	43.8855			2.55079
$297$		0			0
$298$	24.8922			1.44197
$299$	6.49786	+	11.2546i	0.375781	+	0.650872i
$300$		0			0
$301$	8.73412	−	15.1279i	0.503426	−	0.871960i
$302$	5.83491	−	10.1064i	0.335761	−	0.581556i
$303$		0			0
$304$	−17.8638	−	30.9410i	−1.02456	−	1.77459i
$305$	4.04748			0.231758
$306$		0			0
$307$	15.5574			0.887909			0.443954	−	0.896049i	$-0.353575\pi$
$307$	15.5574			0.887909			0.443954	+	0.896049i	$0.353575\pi$
$308$	4.79147	+	8.29906i	0.273019	+	0.472883i
$309$		0			0
$310$	−4.12612	+	7.14665i	−0.234348	+	0.405902i
$311$	12.1419	−	21.0304i	0.688504	−	1.19252i	−0.283818	−	0.958878i	$-0.591601\pi$
$311$	12.1419	−	21.0304i	0.688504	−	1.19252i	0.972322	−	0.233645i	$-0.0750654\pi$
$312$		0			0
$313$	−3.90184	−	6.75818i	−0.220545	−	0.381995i	0.734429	−	0.678686i	$-0.237450\pi$
$313$	−3.90184	−	6.75818i	−0.220545	−	0.381995i	−0.954974	+	0.296691i	$0.904117\pi$
$314$	12.2347			0.690444
$315$		0			0
$316$	52.0955			2.93060
$317$	6.78748	+	11.7563i	0.381223	+	0.660298i	0.991237	−	0.132093i	$-0.0421697\pi$
$317$	6.78748	+	11.7563i	0.381223	+	0.660298i	−0.610014	+	0.792390i	$0.708836\pi$
$318$		0			0
$319$	1.18586	−	2.05397i	0.0663954	−	0.115000i
$320$	8.22420	−	14.2447i	0.459747	−	0.796305i
$321$		0			0
$322$	−7.96640	−	13.7982i	−0.443950	−	0.768944i
$323$	24.9419			1.38780
$324$		0			0
$325$	4.40629			0.244417
$326$	−10.6216	−	18.3971i	−0.588274	−	1.01892i
$327$		0			0
$328$	−9.18531	+	15.9094i	−0.507174	+	0.878451i
$329$	0.243205	−	0.421244i	0.0134083	−	0.0232239i
$330$		0			0
$331$	−10.3955	−	18.0055i	−0.571387	−	0.989672i	−0.996424	−	0.0844958i	$-0.973072\pi$
$331$	−10.3955	−	18.0055i	−0.571387	−	0.989672i	0.425036	−	0.905176i	$-0.360261\pi$
$332$	−43.0284			−2.36149
$333$		0			0
$334$	17.7253			0.969884
$335$	9.35597	+	16.2050i	0.511171	+	0.885375i
$336$		0			0
$337$	−3.33252	+	5.77209i	−0.181534	+	0.314426i	−0.942403	−	0.334480i	$-0.891439\pi$
$337$	−3.33252	+	5.77209i	−0.181534	+	0.314426i	0.760869	+	0.648905i	$0.224773\pi$
$338$	11.3437	−	19.6479i	0.617018	−	1.06871i
$339$		0			0
$340$	−16.0125	−	27.7345i	−0.868402	−	1.50412i
$341$	1.37172			0.0742828
$342$		0			0
$343$	−19.9503			−1.07722
$344$	−19.3445	−	33.5057i	−1.04299	−	1.80651i
$345$		0			0
$346$	−8.95359	+	15.5081i	−0.481348	+	0.833719i
$347$	−3.45734	+	5.98828i	−0.185600	+	0.321468i	−0.943778	−	0.330579i	$-0.892756\pi$
$347$	−3.45734	+	5.98828i	−0.185600	+	0.321468i	0.758179	+	0.652047i	$0.226089\pi$
$348$		0			0
$349$	−2.83783	−	4.91526i	−0.151905	−	0.263108i	0.780022	−	0.625751i	$-0.215208\pi$
$349$	−2.83783	−	4.91526i	−0.151905	−	0.263108i	−0.931928	+	0.362644i	$0.881874\pi$
$350$	−5.40213			−0.288756
$351$		0			0
$352$	0.987711			0.0526452
$353$	−3.78324	−	6.55277i	−0.201362	−	0.348769i	0.747606	−	0.664143i	$-0.231203\pi$
$353$	−3.78324	−	6.55277i	−0.201362	−	0.348769i	−0.948967	+	0.315374i	$0.897870\pi$
$354$		0			0
$355$	1.31232	−	2.27300i	0.0696505	−	0.120638i
$356$	−29.2843	+	50.7218i	−1.55206	+	2.68825i
$357$		0			0
$358$	9.00083	+	15.5899i	0.475709	+	0.823952i
$359$	−29.1504			−1.53850			−0.769248	−	0.638950i	$-0.779369\pi$
$359$	−29.1504			−1.53850			−0.769248	+	0.638950i	$0.779369\pi$
$360$		0			0
$361$	41.4497			2.18156
$362$	16.5736	+	28.7063i	0.871088	+	1.50877i
$363$		0			0
$364$	−22.5696	+	39.0917i	−1.18297	+	2.04896i
$365$	2.89301	−	5.01085i	0.151427	−	0.262280i
$366$		0			0
$367$	17.2272	+	29.8384i	0.899254	+	1.55755i	0.828450	+	0.560063i	$0.189223\pi$
$367$	17.2272	+	29.8384i	0.899254	+	1.55755i	0.0708032	+	0.997490i	$0.477444\pi$
$368$	−12.6780			−0.660887
$369$		0			0
$370$	50.9708			2.64985
$371$	−10.6568	−	18.4581i	−0.553274	−	0.958299i
$372$		0			0
$373$	−1.95278	+	3.38232i	−0.101111	+	0.175130i	−0.912143	−	0.409873i	$-0.865573\pi$
$373$	−1.95278	+	3.38232i	−0.101111	+	0.175130i	0.811031	+	0.585002i	$0.198906\pi$
$374$	−3.96080	+	6.86030i	−0.204808	+	0.354738i
$375$		0			0
$376$	−0.538656	−	0.932980i	−0.0277791	−	0.0481148i
$377$	11.1717			0.575372
$378$		0			0
$379$	−10.2129			−0.524600			−0.262300	−	0.964986i	$-0.584481\pi$
$379$	−10.2129			−0.524600			−0.262300	+	0.964986i	$0.584481\pi$
$380$	−38.8083	−	67.2180i	−1.99082	−	3.44821i
$381$		0			0
$382$	2.84074	−	4.92031i	0.145345	−	0.251745i
$383$	7.06195	−	12.2317i	0.360849	−	0.625009i	−0.627252	−	0.778816i	$-0.715820\pi$
$383$	7.06195	−	12.2317i	0.360849	−	0.625009i	0.988101	+	0.153808i	$0.0491537\pi$
$384$		0			0
$385$	2.84881	+	4.93429i	0.145189	+	0.251475i
$386$	−34.8129			−1.77193
$387$		0			0
$388$	36.6076			1.85847
$389$	7.11383	+	12.3215i	0.360686	+	0.624726i	0.988074	−	0.153981i	$-0.0492094\pi$
$389$	7.11383	+	12.3215i	0.360686	+	0.624726i	−0.627388	+	0.778707i	$0.715876\pi$
$390$		0			0
$391$	4.42535	−	7.66492i	0.223799	−	0.387632i
$392$	−3.96420	+	6.86620i	−0.200223	+	0.346796i
$393$		0			0
$394$	−1.62188	−	2.80918i	−0.0817091	−	0.141524i
$395$	30.9739			1.55846
$396$		0			0
$397$	−23.5328			−1.18108			−0.590539	−	0.807009i	$-0.701085\pi$
$397$	−23.5328			−1.18108			−0.590539	+	0.807009i	$0.701085\pi$
$398$	19.5683	+	33.8933i	0.980872	+	1.69892i
$399$		0			0
$400$	−2.14928	+	3.72267i	−0.107464	+	0.186133i
$401$	−18.2654	+	31.6366i	−0.912131	+	1.57986i	−0.101083	+	0.994878i	$0.532231\pi$
$401$	−18.2654	+	31.6366i	−0.912131	+	1.57986i	−0.811048	+	0.584979i	$0.801103\pi$
$402$		0			0
$403$	3.23066	+	5.59567i	0.160931	+	0.278740i
$404$	19.9835			0.994219
$405$		0			0
$406$	−13.6965			−0.679747
$407$	−4.23628	−	7.33745i	−0.209985	−	0.363704i
$408$		0			0
$409$	−8.39364	+	14.5382i	−0.415039	+	0.718868i	−0.995433	−	0.0954680i	$-0.969565\pi$
$409$	−8.39364	+	14.5382i	−0.415039	+	0.718868i	0.580394	+	0.814336i	$0.302899\pi$
$410$	−10.6683	+	18.4780i	−0.526869	+	0.912564i
$411$		0			0
$412$	20.8368	+	36.0903i	1.02655	+	1.77804i
$413$	0.563724			0.0277390
$414$		0			0
$415$	−25.5829			−1.25582
$416$	2.32625	+	4.02918i	0.114054	+	0.197547i
$417$		0			0
$418$	−9.59946	+	16.6268i	−0.469525	+	0.813241i
$419$	4.33728	−	7.51239i	0.211890	−	0.367004i	−0.740416	−	0.672149i	$-0.765371\pi$
$419$	4.33728	−	7.51239i	0.211890	−	0.367004i	0.952306	+	0.305145i	$0.0987048\pi$
$420$		0			0
$421$	−10.1827	−	17.6370i	−0.496275	−	0.859573i	0.503716	−	0.863869i	$-0.331966\pi$
$421$	−10.1827	−	17.6370i	−0.496275	−	0.859573i	−0.999991	+	0.00429609i	$0.998633\pi$
$422$	21.1980			1.03190
$423$		0			0
$424$	−47.2058			−2.29252
$425$	−1.50044	−	2.59885i	−0.0727822	−	0.126063i
$426$		0			0
$427$	−1.94265	+	3.36478i	−0.0940116	+	0.162833i
$428$	19.6654	−	34.0614i	0.950562	−	1.64642i
$429$		0			0
$430$	−22.4677	−	38.9152i	−1.08349	−	1.87666i
$431$	30.7365			1.48053			0.740263	−	0.672318i	$-0.234701\pi$
$431$	30.7365			1.48053			0.740263	+	0.672318i	$0.234701\pi$
$432$		0			0
$433$	−35.7978			−1.72033			−0.860167	−	0.510012i	$-0.829641\pi$
$433$	−35.7978			−1.72033			−0.860167	+	0.510012i	$0.829641\pi$
$434$	−3.96080	−	6.86030i	−0.190124	−	0.329305i
$435$		0			0
$436$	3.99810	−	6.92491i	0.191474	−	0.331643i
$437$	10.7253	−	18.5769i	0.513063	−	0.888651i
$438$		0			0
$439$	9.15420	+	15.8555i	0.436906	+	0.756744i	0.997449	−	0.0713815i	$-0.0227408\pi$
$439$	9.15420	+	15.8555i	0.436906	+	0.756744i	−0.560543	+	0.828125i	$0.689407\pi$
$440$	12.6192			0.601598
$441$		0			0
$442$	−37.3137			−1.77483
$443$	0.526658	+	0.912198i	0.0250223	+	0.0433398i	0.878265	−	0.478174i	$-0.158701\pi$
$443$	0.526658	+	0.912198i	0.0250223	+	0.0433398i	−0.853243	+	0.521513i	$0.825368\pi$
$444$		0			0
$445$	−17.4112	+	30.1571i	−0.825372	+	1.42959i
$446$	−32.7414	+	56.7097i	−1.55035	+	2.68528i
$447$		0			0
$448$	7.89468	+	13.6740i	0.372989	+	0.646035i
$449$	−29.3702			−1.38607			−0.693033	−	0.720906i	$-0.743726\pi$
$449$	−29.3702			−1.38607			−0.693033	+	0.720906i	$0.743726\pi$
$450$		0			0
$451$	3.54665			0.167005
$452$	−16.1971	−	28.0542i	−0.761846	−	1.31956i
$453$		0			0
$454$	−29.2435	+	50.6513i	−1.37247	+	2.37718i
$455$	−13.4190	+	23.2424i	−0.629092	+	1.08962i
$456$		0			0
$457$	−2.65837	−	4.60443i	−0.124353	−	0.215386i	0.797127	−	0.603812i	$-0.206352\pi$
$457$	−2.65837	−	4.60443i	−0.124353	−	0.215386i	−0.921480	+	0.388426i	$0.873019\pi$
$458$	29.6096			1.38357
$459$		0			0
$460$	−27.5424			−1.28417
$461$	−3.43008	−	5.94107i	−0.159755	−	0.276703i	0.775025	−	0.631930i	$-0.217737\pi$
$461$	−3.43008	−	5.94107i	−0.159755	−	0.276703i	−0.934780	+	0.355227i	$0.884404\pi$
$462$		0			0
$463$	12.6530	−	21.9157i	0.588036	−	1.01851i	−0.406453	−	0.913672i	$-0.633235\pi$
$463$	12.6530	−	21.9157i	0.588036	−	1.01851i	0.994489	−	0.104837i	$-0.0334322\pi$
$464$	−5.44929	+	9.43844i	−0.252977	+	0.438169i
$465$		0			0
$466$	−23.3585	−	40.4581i	−1.08206	−	1.87418i
$467$	−40.1018			−1.85569			−0.927844	−	0.372967i	$-0.878340\pi$
$467$	−40.1018			−1.85569			−0.927844	+	0.372967i	$0.878340\pi$
$468$		0			0
$469$	−17.9622			−0.829417
$470$	−0.625623	−	1.08361i	−0.0288578	−	0.0499832i
$471$		0			0
$472$	0.624273	−	1.08127i	0.0287345	−	0.0497696i
$473$	−3.73467	+	6.46863i	−0.171720	+	0.297428i
$474$		0			0
$475$	−3.63651	−	6.29861i	−0.166854	−	0.289000i
$476$	30.7419			1.40905
$477$		0			0
$478$	−40.9067			−1.87103
$479$	−8.18768	−	14.1815i	−0.374105	−	0.647969i	0.616088	−	0.787678i	$-0.288717\pi$
$479$	−8.18768	−	14.1815i	−0.374105	−	0.647969i	−0.990193	+	0.139709i	$0.955383\pi$
$480$		0			0
$481$	19.9545	−	34.5622i	0.909847	−	1.57590i
$482$	−20.1115	+	34.8341i	−0.916053	+	1.58665i
$483$		0			0
$484$	−2.04881	−	3.54864i	−0.0931276	−	0.161302i
$485$	21.7654			0.988316
$486$		0			0
$487$	14.9456			0.677249			0.338625	−	0.940922i	$-0.390038\pi$
$487$	14.9456			0.677249			0.338625	+	0.940922i	$0.390038\pi$
$488$	4.30263	+	7.45238i	0.194771	+	0.337353i
$489$		0			0
$490$	−4.60423	+	7.97476i	−0.207998	+	0.360263i
$491$	13.9341	−	24.1346i	0.628839	−	1.08918i	−0.358946	−	0.933358i	$-0.616864\pi$
$491$	13.9341	−	24.1346i	0.628839	−	1.08918i	0.987785	−	0.155823i	$-0.0498028\pi$
$492$		0			0
$493$	−3.80422	−	6.58911i	−0.171334	−	0.296758i
$494$	−90.4342			−4.06883
$495$		0			0
$496$	−6.30336			−0.283029
$497$	1.25973	+	2.18192i	0.0565068	+	0.0978727i
$498$		0			0
$499$	16.5776	−	28.7133i	0.742116	−	1.28538i	−0.209414	−	0.977827i	$-0.567156\pi$
$499$	16.5776	−	28.7133i	0.742116	−	1.28538i	0.951530	−	0.307556i	$-0.0995111\pi$
$500$	20.2881	−	35.1400i	0.907311	−	1.57151i
$501$		0			0
$502$	18.6741	+	32.3446i	0.833468	+	1.44361i
$503$	−8.90129			−0.396889			−0.198444	−	0.980112i	$-0.563589\pi$
$503$	−8.90129			−0.396889			−0.198444	+	0.980112i	$0.563589\pi$
$504$		0			0
$505$	11.8814			0.528716
$506$	3.40639	+	5.90004i	0.151433	+	0.262289i
$507$		0			0
$508$	1.93287	−	3.34783i	0.0857572	−	0.148536i
$509$	20.3942	−	35.3237i	0.903955	−	1.56570i	0.0816414	−	0.996662i	$-0.473984\pi$
$509$	20.3942	−	35.3237i	0.903955	−	1.56570i	0.822314	−	0.569034i	$-0.192683\pi$
$510$		0			0
$511$	2.77710	+	4.81007i	0.122852	+	0.212785i
$512$	43.0651			1.90323
$513$		0			0
$514$	48.1659			2.12451
$515$	12.3887	+	21.4578i	0.545911	+	0.945546i
$516$		0			0
$517$	−0.103993	+	0.180122i	−0.00457363	+	0.00792175i
$518$	−24.4643	+	42.3733i	−1.07490	+	1.86178i
$519$		0			0
$520$	29.7207	+	51.4777i	1.30334	+	2.25745i
$521$	8.54191			0.374228			0.187114	−	0.982338i	$-0.440087\pi$
$521$	8.54191			0.374228			0.187114	+	0.982338i	$0.440087\pi$
$522$		0			0
$523$	26.9328			1.17769			0.588845	−	0.808246i	$-0.299583\pi$
$523$	26.9328			1.17769			0.588845	+	0.808246i	$0.299583\pi$
$524$	−6.27208	−	10.8636i	−0.273997	−	0.474577i
$525$		0			0
$526$	−11.6546	+	20.1864i	−0.508167	+	0.880171i
$527$	2.20023	−	3.81091i	0.0958435	−	0.166006i
$528$		0			0
$529$	7.69408	+	13.3265i	0.334525	+	0.579415i
$530$	−54.8273			−2.38154
$531$		0			0
$532$	74.5067			3.23028
$533$	8.35303	+	14.4679i	0.361810	+	0.626673i
$534$		0			0
$535$	11.6922	−	20.2515i	0.505500	−	0.875551i
$536$	−19.8915	+	34.4531i	−0.859183	+	1.48815i
$537$		0			0
$538$	−9.05097	−	15.6767i	−0.390215	−	0.675872i
$539$	1.53066			0.0659304
$540$		0			0
$541$	44.5039			1.91337			0.956686	−	0.291121i	$-0.0940284\pi$
$541$	44.5039			1.91337			0.956686	+	0.291121i	$0.0940284\pi$
$542$	−3.09020	−	5.35239i	−0.132736	−	0.229905i
$543$		0			0
$544$	1.58428	−	2.74406i	0.0679256	−	0.117651i
$545$	2.37711	−	4.11727i	0.101824	−	0.176364i
$546$		0			0
$547$	−4.84725	−	8.39569i	−0.207254	−	0.358974i	0.743595	−	0.668630i	$-0.233119\pi$
$547$	−4.84725	−	8.39569i	−0.207254	−	0.358974i	−0.950848	+	0.309657i	$0.899786\pi$
$548$	83.8206			3.58064
$549$		0			0
$550$	2.30992			0.0984954
$551$	−9.21999	−	15.9695i	−0.392785	−	0.680323i
$552$		0			0
$553$	−14.8664	+	25.7494i	−0.632184	+	1.09497i
$554$	27.1490	−	47.0234i	1.15345	−	1.99783i
$555$		0			0
$556$	−26.4477	−	45.8088i	−1.12163	−	1.94273i
$557$	−44.5990			−1.88972			−0.944861	−	0.327473i	$-0.893803\pi$
$557$	−44.5990			−1.88972			−0.944861	+	0.327473i	$0.893803\pi$
$558$		0			0
$559$	−35.1834			−1.48810
$560$	−13.0909	−	22.6741i	−0.553193	−	0.958158i
$561$		0			0
$562$	20.9816	−	36.3411i	0.885054	−	1.53296i
$563$	−13.9051	+	24.0843i	−0.586029	+	1.01503i	0.408718	+	0.912661i	$0.365976\pi$
$563$	−13.9051	+	24.0843i	−0.586029	+	1.01503i	−0.994746	+	0.102370i	$0.967357\pi$
$564$		0			0
$565$	−9.63013	−	16.6799i	−0.405143	−	0.701727i
$566$	−9.32955			−0.392150
$567$		0			0
$568$	5.58017			0.234139
$569$	18.5056	+	32.0527i	0.775796	+	1.34372i	0.934346	+	0.356367i	$0.115985\pi$
$569$	18.5056	+	32.0527i	0.775796	+	1.34372i	−0.158550	+	0.987351i	$0.550682\pi$
$570$		0			0
$571$	13.9640	−	24.1863i	0.584374	−	1.01217i	−0.410579	−	0.911825i	$-0.634673\pi$
$571$	13.9640	−	24.1863i	0.584374	−	1.01217i	0.994953	−	0.100340i	$-0.0319932\pi$
$572$	9.65066	−	16.7154i	0.403515	−	0.698908i
$573$		0			0
$574$	−10.2408	−	17.7376i	−0.427444	−	0.740355i
$575$	−2.58084			−0.107629
$576$		0			0
$577$	24.6587			1.02656			0.513278	−	0.858222i	$-0.328431\pi$
$577$	24.6587			1.02656			0.513278	+	0.858222i	$0.328431\pi$
$578$	−8.28316	−	14.3469i	−0.344534	−	0.596751i
$579$		0			0
$580$	−11.8383	+	20.5046i	−0.491561	+	0.851408i
$581$	12.2789	−	21.2678i	0.509416	−	0.882335i
$582$		0			0
$583$	4.55680	+	7.89261i	0.188723	+	0.326878i
$584$	12.3015			0.509042
$585$		0			0
$586$	−57.7217			−2.38446
$587$	−13.1231	−	22.7300i	−0.541650	−	0.938166i	−0.998809	−	0.0487810i	$-0.984466\pi$
$587$	−13.1231	−	22.7300i	−0.541650	−	0.938166i	0.457159	−	0.889385i	$-0.348867\pi$
$588$		0			0
$589$	5.33252	−	9.23619i	0.219723	−	0.380571i
$590$	0.725063	−	1.25585i	0.0298504	−	0.0517023i
$591$		0			0
$592$	19.4667	+	33.7172i	0.800074	+	1.38577i
$593$	−11.8551			−0.486829			−0.243414	−	0.969922i	$-0.578267\pi$
$593$	−11.8551			−0.486829			−0.243414	+	0.969922i	$0.578267\pi$
$594$		0			0
$595$	18.2779			0.749321
$596$	20.6531	+	35.7722i	0.845983	+	1.46529i
$597$		0			0
$598$	−16.0454	+	27.7914i	−0.656145	+	1.13648i
$599$	15.2879	−	26.4795i	0.624648	−	1.08192i	−0.363961	−	0.931414i	$-0.618576\pi$
$599$	15.2879	−	26.4795i	0.624648	−	1.08192i	0.988609	−	0.150508i	$-0.0480908\pi$
$600$		0			0
$601$	−13.9118	−	24.0959i	−0.567472	−	0.982891i	−0.996815	−	0.0797492i	$-0.974588\pi$
$601$	−13.9118	−	24.0959i	−0.567472	−	0.982891i	0.429343	−	0.903142i	$-0.358745\pi$
$602$	43.1349			1.75805
$603$		0			0
$604$	19.3649			0.787947
$605$	−1.21814	−	2.10988i	−0.0495244	−	0.0857787i
$606$		0			0
$607$	4.59543	−	7.95952i	0.186523	−	0.323067i	−0.757566	−	0.652759i	$-0.773611\pi$
$607$	4.59543	−	7.95952i	0.186523	−	0.323067i	0.944089	+	0.329692i	$0.106945\pi$
$608$	3.83970	−	6.65055i	0.155720	−	0.269715i
$609$		0			0
$610$	4.99729	+	8.65557i	0.202335	+	0.350454i
$611$	−0.979697			−0.0396343
$612$		0			0
$613$	−12.7376			−0.514467			−0.257234	−	0.966349i	$-0.582811\pi$
$613$	−12.7376			−0.514467			−0.257234	+	0.966349i	$0.582811\pi$
$614$	19.2082	+	33.2697i	0.775182	+	1.34265i
$615$		0			0
$616$	−6.05680	+	10.4907i	−0.244035	+	0.422682i
$617$	6.91123	−	11.9706i	0.278236	−	0.481918i	−0.692711	−	0.721216i	$-0.743584\pi$
$617$	6.91123	−	11.9706i	0.278236	−	0.481918i	0.970946	+	0.239297i	$0.0769170\pi$
$618$		0			0
$619$	−22.6728	−	39.2705i	−0.911297	−	1.57841i	−0.812234	−	0.583332i	$-0.801749\pi$
$619$	−22.6728	−	39.2705i	−0.911297	−	1.57841i	−0.0990636	−	0.995081i	$-0.531585\pi$
$620$	−13.6938			−0.549955
$621$		0			0
$622$	59.9648			2.40437
$623$	−16.7136	−	28.9488i	−0.669617	−	1.15981i
$624$		0			0
$625$	14.4011	−	24.9434i	0.576043	−	0.997736i
$626$	9.63495	−	16.6882i	0.385090	−	0.666995i
$627$		0			0
$628$	10.1511	+	17.5823i	0.405074	+	0.701609i
$629$	−27.1799			−1.08373
$630$		0			0
$631$	−48.0257			−1.91187			−0.955936	−	0.293576i	$-0.905155\pi$
$631$	−48.0257			−1.91187			−0.955936	+	0.293576i	$0.905155\pi$
$632$	32.9264	+	57.0303i	1.30974	+	2.26854i
$633$		0			0
$634$	−16.7606	+	29.0302i	−0.665647	+	1.15293i
$635$	1.14921	−	1.99048i	0.0456048	−	0.0789899i
$636$		0			0
$637$	3.60501	+	6.24406i	0.142836	+	0.247398i
$638$	5.85657			0.231864
$639$		0			0
$640$	45.4293			1.79575
$641$	−7.37312	−	12.7706i	−0.291221	−	0.504409i	0.682878	−	0.730533i	$-0.260728\pi$
$641$	−7.37312	−	12.7706i	−0.291221	−	0.504409i	−0.974099	+	0.226123i	$0.927395\pi$
$642$		0			0
$643$	22.8328	−	39.5476i	0.900438	−	1.55960i	0.0735112	−	0.997294i	$-0.476580\pi$
$643$	22.8328	−	39.5476i	0.900438	−	1.55960i	0.826927	−	0.562310i	$-0.190087\pi$
$644$	13.2194	−	22.8967i	0.520919	−	0.902258i
$645$		0			0
$646$	30.7950	+	53.3384i	1.21161	+	2.09857i
$647$	−18.8503			−0.741081			−0.370540	−	0.928816i	$-0.620827\pi$
$647$	−18.8503			−0.741081			−0.370540	+	0.928816i	$0.620827\pi$
$648$		0			0
$649$	−0.241045			−0.00946186
$650$	5.44031	+	9.42289i	0.213386	+	0.369596i
$651$		0			0
$652$	17.6254	−	30.5281i	0.690265	−	1.19557i
$653$	−10.0779	+	17.4554i	−0.394378	+	0.683083i	−0.993022	−	0.117933i	$-0.962373\pi$
$653$	−10.0779	+	17.4554i	−0.394378	+	0.683083i	0.598644	+	0.801016i	$0.295707\pi$
$654$		0			0
$655$	−3.72912	−	6.45903i	−0.145709	−	0.252375i
$656$	−16.2976			−0.636316
$657$		0			0
$658$	1.20111			0.0468242
$659$	4.83783	+	8.37936i	0.188455	+	0.326414i	0.944735	−	0.327834i	$-0.106319\pi$
$659$	4.83783	+	8.37936i	0.188455	+	0.326414i	−0.756280	+	0.654248i	$0.772985\pi$
$660$		0			0
$661$	−12.6736	+	21.9513i	−0.492945	+	0.853805i	−0.999967	−	0.00812759i	$-0.997413\pi$
$661$	−12.6736	+	21.9513i	−0.492945	+	0.853805i	0.507022	+	0.861933i	$0.330746\pi$
$662$	25.6699	−	44.4616i	0.997690	−	1.72805i
$663$		0			0
$664$	−27.1957	−	47.1043i	−1.05540	−	1.82800i
$665$	44.2987			1.71783
$666$		0			0
$667$	−6.54347			−0.253364
$668$	14.7067	+	25.4727i	0.569018	+	0.985568i
$669$		0			0
$670$	−23.1030	+	40.0156i	−0.892548	+	1.54594i
$671$	0.830670	−	1.43876i	0.0320676	−	0.0555428i
$672$		0			0
$673$	0.766712	+	1.32798i	0.0295546	+	0.0511900i	0.880424	−	0.474187i	$-0.157258\pi$
$673$	0.766712	+	1.32798i	0.0295546	+	0.0511900i	−0.850870	+	0.525377i	$0.823924\pi$
$674$	−16.4582			−0.633946
$675$		0			0
$676$	37.6476			1.44798
$677$	−2.32984	−	4.03539i	−0.0895429	−	0.155093i	0.817775	−	0.575538i	$-0.195207\pi$
$677$	−2.32984	−	4.03539i	−0.0895429	−	0.155093i	−0.907318	+	0.420445i	$0.861874\pi$
$678$		0			0
$679$	−10.4467	+	18.0941i	−0.400906	+	0.694390i
$680$	20.2411	−	35.0587i	0.776212	−	1.34444i
$681$		0			0
$682$	1.69362	+	2.93343i	0.0648520	+	0.112327i
$683$	25.9322			0.992269			0.496134	−	0.868246i	$-0.334752\pi$
$683$	25.9322			0.992269			0.496134	+	0.868246i	$0.334752\pi$
$684$		0			0
$685$	49.8364			1.90415
$686$	−24.6320	−	42.6639i	−0.940455	−	1.62892i
$687$		0			0
$688$	17.1616	−	29.7248i	0.654281	−	1.13325i
$689$	−21.4643	+	37.1772i	−0.817723	+	1.41634i
$690$		0			0
$691$	13.6320	+	23.6112i	0.518584	+	0.898214i	0.999767	+	0.0215935i	$0.00687394\pi$
$691$	13.6320	+	23.6112i	0.518584	+	0.898214i	−0.481183	+	0.876620i	$0.659793\pi$
$692$	−29.7152			−1.12960
$693$		0			0
$694$	−17.0746			−0.648145
$695$	−15.7247	−	27.2361i	−0.596474	−	1.03312i
$696$		0			0
$697$	5.68880	−	9.85329i	0.215479	−	0.373220i
$698$	7.00755	−	12.1374i	0.265240	−	0.459408i
$699$		0			0
$700$	−4.48214	−	7.76330i	−0.169409	−	0.293425i
$701$	1.77806			0.0671563			0.0335782	−	0.999436i	$-0.489310\pi$
$701$	1.77806			0.0671563			0.0335782	+	0.999436i	$0.489310\pi$
$702$		0			0
$703$	−65.8736			−2.48447
$704$	−3.37573	−	5.84693i	−0.127227	−	0.220364i
$705$		0			0
$706$	9.34209	−	16.1810i	0.351594	−	0.608979i
$707$	−5.70268	+	9.87732i	−0.214471	+	0.371475i
$708$		0			0
$709$	−7.30003	−	12.6440i	−0.274158	−	0.474856i	0.695764	−	0.718270i	$-0.255066\pi$
$709$	−7.30003	−	12.6440i	−0.274158	−	0.474856i	−0.969922	+	0.243414i	$0.921733\pi$
$710$	6.48110			0.243231
$711$		0			0
$712$	−74.0353			−2.77459
$713$	−1.89226	−	3.27748i	−0.0708655	−	0.122743i
$714$		0			0
$715$	5.73789	−	9.93832i	0.214585	−	0.371672i
$716$	−14.9360	+	25.8699i	−0.558184	+	0.966803i
$717$		0			0
$718$	−35.9910	−	62.3382i	−1.34317	−	2.32644i
$719$	−19.7642			−0.737081			−0.368540	−	0.929612i	$-0.620142\pi$
$719$	−19.7642			−0.737081			−0.368540	+	0.929612i	$0.620142\pi$
$720$		0			0
$721$	−23.7846			−0.885785
$722$	51.1765	+	88.6404i	1.90459	+	3.29885i
$723$		0			0
$724$	−27.5022	+	47.6352i	−1.02211	+	1.77035i
$725$	−1.10930	+	1.92137i	−0.0411985	+	0.0713579i
$726$		0			0
$727$	9.40561	+	16.2910i	0.348835	+	0.604200i	0.986043	−	0.166492i	$-0.0532441\pi$
$727$	9.40561	+	16.2910i	0.348835	+	0.604200i	−0.637208	+	0.770692i	$0.719911\pi$
$728$	−57.0597			−2.11477
$729$		0			0
$730$	14.2876			0.528809
$731$	11.9808	+	20.7513i	0.443125	+	0.767514i
$732$		0			0
$733$	−23.3301	+	40.4090i	−0.861719	+	1.49254i	0.00855029	+	0.999963i	$0.497278\pi$
$733$	−23.3301	+	40.4090i	−0.861719	+	1.49254i	−0.870269	+	0.492577i	$0.836055\pi$
$734$	−42.5398	+	73.6811i	−1.57017	+	2.71962i
$735$		0			0
$736$	−1.36253	−	2.35996i	−0.0502234	−	0.0869894i
$737$	7.68055			0.282917
$738$		0			0
$739$	−6.50838			−0.239415			−0.119707	−	0.992809i	$-0.538196\pi$
$739$	−6.50838			−0.239415			−0.119707	+	0.992809i	$0.538196\pi$
$740$	42.2905	+	73.2492i	1.55463	+	2.69270i
$741$		0			0
$742$	26.3152	−	45.5793i	0.966062	−	1.67327i
$743$	−21.8998	+	37.9315i	−0.803425	+	1.39157i	0.113924	+	0.993489i	$0.463658\pi$
$743$	−21.8998	+	37.9315i	−0.803425	+	1.39157i	−0.917349	+	0.398083i	$0.869675\pi$
$744$		0			0
$745$	12.2795	+	21.2687i	0.449886	+	0.779225i
$746$	−9.64415			−0.353097
$747$		0			0
$748$	−13.1451			−0.480632
$749$	11.2238	+	19.4401i	0.410107	+	0.710327i
$750$		0			0
$751$	−9.84965	+	17.0601i	−0.359419	+	0.622531i	−0.987864	−	0.155322i	$-0.950358\pi$
$751$	−9.84965	+	17.0601i	−0.359419	+	0.622531i	0.628445	+	0.777854i	$0.283692\pi$
$752$	0.477873	−	0.827700i	0.0174262	−	0.0301831i
$753$		0			0
$754$	13.7933	+	23.8908i	0.502324	+	0.870050i
$755$	11.5136			0.419022
$756$		0			0
$757$	23.1719			0.842195			0.421098	−	0.907015i	$-0.361645\pi$
$757$	23.1719			0.842195			0.421098	+	0.907015i	$0.361645\pi$
$758$	−12.6095	−	21.8403i	−0.457998	−	0.793276i
$759$		0			0
$760$	49.0568	−	84.9689i	1.77948	−	3.08215i
$761$	6.96855	−	12.0699i	0.252610	−	0.437533i	−0.711634	−	0.702551i	$-0.752044\pi$
$761$	6.96855	−	12.0699i	0.252610	−	0.437533i	0.964244	+	0.265017i	$0.0853777\pi$
$762$		0			0
$763$	2.28186	+	3.95230i	0.0826089	+	0.143083i
$764$	9.42786			0.341088
$765$		0			0
$766$	34.8767			1.26014
$767$	−0.567708	−	0.983299i	−0.0204987	−	0.0355049i
$768$		0			0
$769$	2.54821	−	4.41363i	0.0918907	−	0.159159i	−0.816416	−	0.577464i	$-0.804042\pi$
$769$	2.54821	−	4.41363i	0.0918907	−	0.159159i	0.908307	+	0.418305i	$0.137376\pi$
$770$	−7.03467	+	12.1844i	−0.253512	+	0.439096i
$771$		0			0
$772$	−28.8843	−	50.0290i	−1.03957	−	1.80058i
$773$	20.5798			0.740202			0.370101	−	0.928991i	$-0.379323\pi$
$773$	20.5798			0.740202			0.370101	+	0.928991i	$0.379323\pi$
$774$		0			0
$775$	−1.28317			−0.0460927
$776$	23.1375	+	40.0753i	0.830587	+	1.43862i
$777$		0			0
$778$	−17.5664	+	30.4260i	−0.629787	+	1.09082i
$779$	13.7875	−	23.8806i	0.493988	−	0.855612i
$780$		0			0
$781$	−0.538656	−	0.932980i	−0.0192746	−	0.0333847i
$782$	21.8553			0.781545
$783$		0			0
$784$	−7.03375			−0.251205
$785$	6.03545	+	10.4537i	0.215415	+	0.373109i
$786$		0			0
$787$	−12.1272	+	21.0049i	−0.432288	+	0.748745i	−0.997070	−	0.0764950i	$-0.975627\pi$
$787$	−12.1272	+	21.0049i	−0.432288	+	0.748745i	0.564782	+	0.825240i	$0.308960\pi$
$788$	2.69135	−	4.66155i	0.0958753	−	0.166061i
$789$		0			0
$790$	38.2424	+	66.2378i	1.36060	+	2.35664i
$791$	18.4885			0.657377
$792$		0			0
$793$	7.82554			0.277893
$794$	−29.0552	−	50.3251i	−1.03113	−	1.78597i
$795$		0			0
$796$	−32.4717	+	56.2426i	−1.15093	+	1.99347i
$797$	19.5678	−	33.8924i	0.693126	−	1.20053i	−0.277682	−	0.960673i	$-0.589566\pi$
$797$	19.5678	−	33.8924i	0.693126	−	1.20053i	0.970808	−	0.239857i	$-0.0771006\pi$
$798$		0			0
$799$	0.333610	+	0.577829i	0.0118023	+	0.0204421i
$800$	−0.923948			−0.0326665
$801$		0			0
$802$	−90.2068			−3.18531
$803$	−1.18747	−	2.05676i	−0.0419050	−	0.0725816i
$804$		0			0
$805$	7.85974	−	13.6135i	0.277020	−	0.479812i
$806$	−7.97758	+	13.8176i	−0.280998	+	0.486703i
$807$		0			0
$808$	12.6304	+	21.8765i	0.444336	+	0.769613i
$809$	32.9926			1.15996			0.579979	−	0.814631i	$-0.303061\pi$
$809$	32.9926			1.15996			0.579979	+	0.814631i	$0.303061\pi$
$810$		0			0
$811$	−32.0811			−1.12652			−0.563259	−	0.826280i	$-0.690453\pi$
$811$	−32.0811			−1.12652			−0.563259	+	0.826280i	$0.690453\pi$
$812$	−11.3640	−	19.6831i	−0.398799	−	0.690740i
$813$		0			0
$814$	10.4608	−	18.1186i	0.366651	−	0.635058i
$815$	10.4794	−	18.1508i	0.367076	−	0.635794i
$816$		0			0
$817$	29.0368	+	50.2932i	1.01587	+	1.75954i
$818$	−41.4534			−1.44938
$819$		0			0
$820$	−35.4059			−1.23643
$821$	21.3784	+	37.0284i	0.746111	+	1.29230i	0.949674	+	0.313240i	$0.101414\pi$
$821$	21.3784	+	37.0284i	0.746111	+	1.29230i	−0.203563	+	0.979062i	$0.565252\pi$
$822$		0			0
$823$	−7.90108	+	13.6851i	−0.275414	+	0.477032i	−0.970240	−	0.242147i	$-0.922148\pi$
$823$	−7.90108	+	13.6851i	−0.275414	+	0.477032i	0.694825	+	0.719179i	$0.255482\pi$
$824$	−26.3393	+	45.6211i	−0.917574	+	1.58929i
$825$		0			0
$826$	0.696011	+	1.20553i	0.0242173	+	0.0419456i
$827$	23.8246			0.828461			0.414230	−	0.910172i	$-0.364051\pi$
$827$	23.8246			0.828461			0.414230	+	0.910172i	$0.364051\pi$
$828$		0			0
$829$	−8.75791			−0.304175			−0.152087	−	0.988367i	$-0.548600\pi$
$829$	−8.75791			−0.304175			−0.152087	+	0.988367i	$0.548600\pi$
$830$	−31.5864	−	54.7093i	−1.09638	−	1.89899i
$831$		0			0
$832$	15.9010	−	27.5413i	0.551266	−	0.954822i
$833$	2.45518	−	4.25249i	0.0850668	−	0.147340i
$834$		0			0
$835$	8.74399	+	15.1450i	0.302598	+	0.524115i
$836$	−31.8587			−1.10186
$837$		0			0
$838$	21.4204			0.739955
$839$	9.74005	+	16.8703i	0.336264	+	0.582426i	0.983727	−	0.179671i	$-0.0575032\pi$
$839$	9.74005	+	16.8703i	0.336264	+	0.582426i	−0.647463	+	0.762097i	$0.724170\pi$
$840$		0			0
$841$	11.6875	−	20.2433i	0.403016	−	0.698045i
$842$	25.1445	−	43.5516i	0.866537	−	1.50089i
$843$		0			0
$844$	17.5880	+	30.4633i	0.605403	+	1.04859i
$845$	22.3837			0.770024
$846$		0			0
$847$	2.33866			0.0803573
$848$	−20.9395	−	36.2683i	−0.719066	−	1.24546i
$849$		0			0
$850$	3.70510	−	6.41742i	0.127084	−	0.220116i
$851$	−11.6877	+	20.2437i	−0.400649	+	0.693945i
$852$		0			0
$853$	−26.1398	−	45.2754i	−0.895008	−	1.55020i	−0.833794	−	0.552075i	$-0.813836\pi$
$853$	−26.1398	−	45.2754i	−0.895008	−	1.55020i	−0.0612137	−	0.998125i	$-0.519497\pi$
$854$	−9.59413			−0.328304
$855$		0			0
$856$	49.7172			1.69930
$857$	−27.4174	−	47.4883i	−0.936560	−	1.62217i	−0.771829	−	0.635831i	$-0.780658\pi$
$857$	−27.4174	−	47.4883i	−0.936560	−	1.62217i	−0.164731	−	0.986339i	$-0.552676\pi$
$858$		0			0
$859$	9.70616	−	16.8116i	0.331170	−	0.573603i	−0.651572	−	0.758587i	$-0.725890\pi$
$859$	9.70616	−	16.8116i	0.331170	−	0.573603i	0.982742	+	0.184984i	$0.0592233\pi$
$860$	37.2829	−	64.5759i	1.27134	−	2.20202i
$861$		0			0
$862$	37.9494	+	65.7302i	1.29256	+	2.23878i
$863$	−2.89484			−0.0985414			−0.0492707	−	0.998785i	$-0.515690\pi$
$863$	−2.89484			−0.0985414			−0.0492707	+	0.998785i	$0.515690\pi$
$864$		0			0
$865$	−17.6674			−0.600711
$866$	−44.1984	−	76.5539i	−1.50192	−	2.60141i
$867$		0			0
$868$	6.57255	−	11.3840i	0.223087	−	0.386398i
$869$	6.35680	−	11.0103i	0.215640	−	0.373499i
$870$		0			0
$871$	18.0892	+	31.3313i	0.612928	+	1.06162i
$872$	10.1078			0.342294
$873$		0			0
$874$	52.9690			1.79170
$875$	11.5792	+	20.0557i	0.391447	+	0.678006i
$876$		0			0
$877$	5.23651	−	9.06991i	0.176825	−	0.306269i	−0.763967	−	0.645256i	$-0.776751\pi$
$877$	5.23651	−	9.06991i	0.176825	−	0.306269i	0.940791	+	0.338987i	$0.110084\pi$
$878$	−22.6048	+	39.1527i	−0.762875	+	1.32134i
$879$		0			0
$880$	5.59762	+	9.69535i	0.188696	+	0.326830i
$881$	−31.5232			−1.06204			−0.531022	−	0.847358i	$-0.678192\pi$
$881$	−31.5232			−1.06204			−0.531022	+	0.847358i	$0.678192\pi$
$882$		0			0
$883$	5.25391			0.176808			0.0884040	−	0.996085i	$-0.471823\pi$
$883$	5.25391			0.176808			0.0884040	+	0.996085i	$0.471823\pi$
$884$	−30.9592	−	53.6229i	−1.04127	−	1.80353i
$885$		0			0
$886$	−1.30049	+	2.25252i	−0.0436910	+	0.0756750i
$887$	10.4309	−	18.0669i	0.350237	−	0.606628i	−0.636054	−	0.771645i	$-0.719434\pi$
$887$	10.4309	−	18.0669i	0.350237	−	0.606628i	0.986291	+	0.165017i	$0.0527678\pi$
$888$		0			0
$889$	1.10316	+	1.91073i	0.0369988	+	0.0640838i
$890$	−85.9883			−2.88234
$891$		0			0
$892$	−108.662			−3.63828
$893$	0.808542	+	1.40044i	0.0270568	+	0.0468638i
$894$		0			0
$895$	−8.88033	+	15.3812i	−0.296837	+	0.514136i
$896$	−21.8045	+	37.7666i	−0.728438	+	1.26169i
$897$		0			0
$898$	−36.2624	−	62.8084i	−1.21009	−	2.09594i
$899$	−3.25333			−0.108505
$900$		0			0
$901$	29.2363			0.974002
$902$	4.37893	+	7.58453i	0.145802	+	0.252537i
$903$		0			0
$904$	20.4744	−	35.4627i	0.680969	−	1.17947i
$905$	−16.3517	+	28.3220i	−0.543549	+	0.941455i
$906$		0			0
$907$	−11.0005	−	19.0534i	−0.365265	−	0.632657i	0.623554	−	0.781780i	$-0.285688\pi$
$907$	−11.0005	−	19.0534i	−0.365265	−	0.632657i	−0.988819	+	0.149124i	$0.952355\pi$
$908$	−97.0534			−3.22083
$909$		0			0
$910$	−66.2720			−2.19689
$911$	2.33067	+	4.03684i	0.0772185	+	0.133746i	0.902049	−	0.431634i	$-0.142063\pi$
$911$	2.33067	+	4.03684i	0.0772185	+	0.133746i	−0.824830	+	0.565380i	$0.808729\pi$
$912$		0			0
$913$	−5.25042	+	9.09399i	−0.173763	+	0.300967i
$914$	6.56440	−	11.3699i	0.217131	−	0.376082i
$915$		0			0
$916$	24.5671	+	42.5515i	0.811721	+	1.40594i
$917$	7.15941			0.236425
$918$		0			0
$919$	−6.91941			−0.228250			−0.114125	−	0.993466i	$-0.536407\pi$
$919$	−6.91941			−0.228250			−0.114125	+	0.993466i	$0.536407\pi$
$920$	−17.4079	−	30.1514i	−0.573922	−	0.994063i
$921$		0			0
$922$	8.47001	−	14.6705i	0.278945	−	0.483147i
$923$	2.53728	−	4.39469i	0.0835155	−	0.144653i
$924$		0			0
$925$	3.96280	+	6.86377i	0.130296	+	0.225679i
$926$	62.4892			2.05352
$927$		0			0
$928$	−2.34257			−0.0768988
$929$	−0.639189	−	1.10711i	−0.0209711	−	0.0363230i	0.855349	−	0.518052i	$-0.173342\pi$
$929$	−0.639189	−	1.10711i	−0.0209711	−	0.0363230i	−0.876321	+	0.481729i	$0.840009\pi$
$930$		0			0
$931$	5.95041	−	10.3064i	0.195017	−	0.337779i
$932$	38.7611	−	67.1361i	1.26966	−	2.19912i
$933$		0			0
$934$	−49.5124	−	85.7579i	−1.62009	−	2.80609i
$935$	−7.81554			−0.255596
$936$		0			0
$937$	−47.7193			−1.55892			−0.779461	−	0.626450i	$-0.784507\pi$
$937$	−47.7193			−1.55892			−0.779461	+	0.626450i	$0.784507\pi$
$938$	−22.1773	−	38.4123i	−0.724116	−	1.25421i
$939$		0			0
$940$	1.03816	−	1.79814i	0.0338610	−	0.0586490i
$941$	−4.06989	+	7.04926i	−0.132675	+	0.229799i	−0.924707	−	0.380680i	$-0.875690\pi$
$941$	−4.06989	+	7.04926i	−0.132675	+	0.229799i	0.792032	+	0.610479i	$0.209023\pi$
$942$		0			0
$943$	−4.89252	−	8.47409i	−0.159322	−	0.275954i
$944$	1.10766			0.0360512
$945$		0			0
$946$	−18.4443			−0.599676
$947$	−13.9845	−	24.2219i	−0.454435	−	0.787105i	0.544220	−	0.838942i	$-0.316826\pi$
$947$	−13.9845	−	24.2219i	−0.454435	−	0.787105i	−0.998656	+	0.0518372i	$0.983492\pi$
$948$		0			0
$949$	5.59345	−	9.68814i	0.181571	−	0.314490i
$950$	8.97975	−	15.5534i	0.291342	−	0.504618i
$951$		0			0
$952$	19.4301	+	33.6540i	0.629734	+	1.09073i
$953$	42.5121			1.37710			0.688551	−	0.725188i	$-0.258247\pi$
$953$	42.5121			1.37710			0.688551	+	0.725188i	$0.258247\pi$
$954$		0			0
$955$	5.60542			0.181387
$956$	−33.9403	−	58.7863i	−1.09771	−	1.90128i
$957$		0			0
$958$	20.2181	−	35.0188i	0.653218	−	1.13141i
$959$	−23.9198	+	41.4303i	−0.772410	+	1.33785i
$960$		0			0
$961$	14.5592	+	25.2173i	0.469651	+	0.813460i
$962$	98.5487			3.17734
$963$		0			0
$964$	−66.7460			−2.14975
$965$	−17.1734	−	29.7452i	−0.552832	−	0.957533i
$966$		0			0
$967$	11.0115	−	19.0724i	0.354104	−	0.613327i	−0.632860	−	0.774266i	$-0.718119\pi$
$967$	11.0115	−	19.0724i	0.354104	−	0.613327i	0.986964	+	0.160940i	$0.0514524\pi$
$968$	2.58986	−	4.48577i	0.0832412	−	0.144178i
$969$		0			0
$970$	26.8730	+	46.5455i	0.862841	+	1.49449i
$971$	29.0719			0.932963			0.466482	−	0.884531i	$-0.345521\pi$
$971$	29.0719			0.932963			0.466482	+	0.884531i	$0.345521\pi$
$972$		0			0
$973$	30.1894			0.967828
$974$	18.4528	+	31.9612i	0.591267	+	1.02410i
$975$		0			0
$976$	−3.81711	+	6.61143i	−0.122183	+	0.211627i
$977$	−21.6241	+	37.4540i	−0.691815	+	1.19826i	0.279428	+	0.960167i	$0.409855\pi$
$977$	−21.6241	+	37.4540i	−0.691815	+	1.19826i	−0.971243	+	0.238092i	$0.923478\pi$
$978$		0			0
$979$	7.14666	+	12.3784i	0.228408	+	0.395615i
$980$	−15.2805			−0.488118
$981$		0			0
$982$	68.8161			2.19601
$983$	−16.1093	−	27.9021i	−0.513807	−	0.889940i	−0.999872	−	0.0160169i	$-0.994901\pi$
$983$	−16.1093	−	27.9021i	−0.513807	−	0.889940i	0.486065	−	0.873923i	$-0.338432\pi$
$984$		0			0
$985$	1.60017	−	2.77157i	0.0509855	−	0.0883096i
$986$	9.39390	−	16.2707i	0.299163	−	0.518165i
$987$		0			0
$988$	−75.0333	−	129.962i	−2.38713	−	4.13463i
$989$	20.6076			0.655282
$990$		0			0
$991$	38.9476			1.23721			0.618605	−	0.785702i	$-0.287698\pi$
$991$	38.9476			1.23721			0.618605	+	0.785702i	$0.287698\pi$
$992$	−0.677432	−	1.17335i	−0.0215085	−	0.0372538i
$993$		0			0
$994$	−3.11071	+	5.38790i	−0.0986656	+	0.170894i
$995$	−19.3064	+	33.4396i	−0.612053	+	1.06011i
$996$		0			0
$997$	18.3566	+	31.7945i	0.581358	+	1.00694i	0.995319	+	0.0966472i	$0.0308119\pi$
$997$	18.3566	+	31.7945i	0.581358	+	1.00694i	−0.413960	+	0.910295i	$0.635855\pi$
$998$	81.8714			2.59159
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.e.e.199.4		8
3.2	odd	2		99.2.e.e.67.1	yes	8
9.2	odd	6		99.2.e.e.34.1	✓	8
9.4	even	3		891.2.a.p.1.1		4
9.5	odd	6		891.2.a.q.1.4		4
9.7	even	3	inner	297.2.e.e.100.4		8
33.32	even	2		1089.2.e.i.364.4		8
99.32	even	6		9801.2.a.bi.1.1		4
99.65	even	6		1089.2.e.i.727.4		8
99.76	odd	6		9801.2.a.bl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.1	✓	8	9.2	odd	6
99.2.e.e.67.1	yes	8	3.2	odd	2
297.2.e.e.100.4		8	9.7	even	3	inner
297.2.e.e.199.4		8	1.1	even	1	trivial
891.2.a.p.1.1		4	9.4	even	3
891.2.a.q.1.4		4	9.5	odd	6
1089.2.e.i.364.4		8	33.32	even	2
1089.2.e.i.727.4		8	99.65	even	6
9801.2.a.bi.1.1		4	99.32	even	6
9801.2.a.bl.1.4		4	99.76	odd	6

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.23467 + 2.13851i) q^{2} +(-2.04881 + 3.54864i) q^{4} +(-1.21814 + 2.10988i) q^{5} +(-1.16933 - 2.02534i) q^{7} -5.17972 q^{8} +O(q^{10})\)	\(q+(1.23467 + 2.13851i) q^{2} +(-2.04881 + 3.54864i) q^{4} +(-1.21814 + 2.10988i) q^{5} +(-1.16933 - 2.02534i) q^{7} -5.17972 q^{8} -6.01598 q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.35519 + 4.07931i) q^{13} +(2.88747 - 5.00124i) q^{14} +(-2.29761 - 3.97958i) q^{16} +3.20799 q^{17} +7.77494 q^{19} +(-4.99146 - 8.64547i) q^{20} +(-1.23467 + 2.13851i) q^{22} +(1.37948 - 2.38932i) q^{23} +(-0.467722 - 0.810117i) q^{25} -11.6315 q^{26} +9.58293 q^{28} +(-1.18586 - 2.05397i) q^{29} +(0.685860 - 1.18794i) q^{31} +(0.493856 - 0.855383i) q^{32} +(3.96080 + 6.86030i) q^{34} +5.69762 q^{35} -8.47256 q^{37} +(9.59946 + 16.6268i) q^{38} +(6.30961 - 10.9286i) q^{40} +(1.77332 - 3.07149i) q^{41} +(3.73467 + 6.46863i) q^{43} -4.09762 q^{44} +6.81278 q^{46} +(0.103993 + 0.180122i) q^{47} +(0.765332 - 1.32559i) q^{49} +(1.15496 - 2.00045i) q^{50} +(-9.65066 - 16.7154i) q^{52} +9.11360 q^{53} -2.43628 q^{55} +(6.05680 + 10.4907i) q^{56} +(2.92829 - 5.07194i) q^{58} +(-0.120523 + 0.208751i) q^{59} +(-0.830670 - 1.43876i) q^{61} +3.38724 q^{62} -6.75145 q^{64} +(-5.73789 - 9.93832i) q^{65} +(3.84027 - 6.65155i) q^{67} +(-6.57255 + 11.3840i) q^{68} +(7.03467 + 12.1844i) q^{70} -1.07731 q^{71} -2.37495 q^{73} +(-10.4608 - 18.1186i) q^{74} +(-15.9294 + 27.5904i) q^{76} +(1.16933 - 2.02534i) q^{77} +(-6.35680 - 11.0103i) q^{79} +11.1952 q^{80} +8.75786 q^{82} +(5.25042 + 9.09399i) q^{83} +(-3.90777 + 6.76846i) q^{85} +(-9.22215 + 15.9732i) q^{86} +(-2.58986 - 4.48577i) q^{88} +14.2933 q^{89} +11.0160 q^{91} +(5.65257 + 9.79053i) q^{92} +(-0.256795 + 0.444781i) q^{94} +(-9.47095 + 16.4042i) q^{95} +(-4.46694 - 7.73697i) q^{97} +3.77972 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7}+O(q^{10}) \) 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7	\( 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7} + 2 q^{10} + 4 q^{11} - 7 q^{13} + q^{14} - 17 q^{16} + 10 q^{17} + 18 q^{19} - 10 q^{20} - q^{22} + 14 q^{23} - 14 q^{25} - 44 q^{26} - 2 q^{28} - 6 q^{29} + 2 q^{31} - 34 q^{32} - 16 q^{34} + 16 q^{35} + 6 q^{37} + 3 q^{38} - 12 q^{40} - 2 q^{41} + 21 q^{43} - 22 q^{44} + 4 q^{46} - 7 q^{47} + 15 q^{49} + 23 q^{50} + 10 q^{52} + 12 q^{53} + 8 q^{55} + 18 q^{56} + 21 q^{58} + 2 q^{59} - 15 q^{61} + 40 q^{62} + 32 q^{64} + 19 q^{65} - 14 q^{67} - 7 q^{68} + 38 q^{70} + 6 q^{71} + 44 q^{73} - 36 q^{74} - 42 q^{76} + q^{77} - 11 q^{79} + 68 q^{80} - 34 q^{82} + 18 q^{83} - 13 q^{85} - 24 q^{86} + 12 q^{89} + 38 q^{91} + 67 q^{92} + 19 q^{94} - 30 q^{95} - 26 q^{97} - 30 q^{98}+O(q^{100}) \) 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7 + 2 * q^10 + 4 * q^11 - 7 * q^13 + q^14 - 17 * q^16 + 10 * q^17 + 18 * q^19 - 10 * q^20 - q^22 + 14 * q^23 - 14 * q^25 - 44 * q^26 - 2 * q^28 - 6 * q^29 + 2 * q^31 - 34 * q^32 - 16 * q^34 + 16 * q^35 + 6 * q^37 + 3 * q^38 - 12 * q^40 - 2 * q^41 + 21 * q^43 - 22 * q^44 + 4 * q^46 - 7 * q^47 + 15 * q^49 + 23 * q^50 + 10 * q^52 + 12 * q^53 + 8 * q^55 + 18 * q^56 + 21 * q^58 + 2 * q^59 - 15 * q^61 + 40 * q^62 + 32 * q^64 + 19 * q^65 - 14 * q^67 - 7 * q^68 + 38 * q^70 + 6 * q^71 + 44 * q^73 - 36 * q^74 - 42 * q^76 + q^77 - 11 * q^79 + 68 * q^80 - 34 * q^82 + 18 * q^83 - 13 * q^85 - 24 * q^86 + 12 * q^89 + 38 * q^91 + 67 * q^92 + 19 * q^94 - 30 * q^95 - 26 * q^97 - 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more