LMFDB - Embedded newform 297.2.f.d.190.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 8 x^{14} - 22 x^{13} + 62 x^{12} - 24 x^{11} + 152 x^{10} - 161 x^{9} + 552 x^{8} + \cdots + 25 $ x^16 - 2x^15 + 8x^14 - 22x^13 + 62x^12 - 24x^11 + 152x^10 - 161x^9 + 552x^8 - 609x^7 + 1150x^6 - 862x^5 + 1346x^4 - 235x^3 + 340x^2 + 150*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.4
Root			$-1.43906 - 1.04554i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.d.136.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24808 - 1.63332i) q^{2} +(1.76807 - 5.44156i) q^{4} +(0.818541 + 0.594705i) q^{5} +(-0.587909 + 1.80940i) q^{7} +(-3.19570 - 9.83534i) q^{8} +O(q^{10})$	\(q+(2.24808 - 1.63332i) q^{2} +(1.76807 - 5.44156i) q^{4} +(0.818541 + 0.594705i) q^{5} +(-0.587909 + 1.80940i) q^{7} +(-3.19570 - 9.83534i) q^{8} +2.81149 q^{10} +(-0.135769 + 3.31384i) q^{11} +(-3.79677 + 2.75851i) q^{13} +(1.63367 + 5.02791i) q^{14} +(-13.9907 - 10.1649i) q^{16} +(2.68981 + 1.95426i) q^{17} +(-0.965525 - 2.97158i) q^{19} +(4.68336 - 3.40266i) q^{20} +(5.10736 + 7.67153i) q^{22} +2.89287 q^{23} +(-1.22875 - 3.78170i) q^{25} +(-4.02988 + 12.4027i) q^{26} +(8.80648 + 6.39829i) q^{28} +(0.0896641 - 0.275958i) q^{29} +(-2.22471 + 1.61634i) q^{31} -27.3718 q^{32} +9.23884 q^{34} +(-1.55728 + 1.13143i) q^{35} +(1.67679 - 5.16064i) q^{37} +(-7.02413 - 5.10333i) q^{38} +(3.23332 - 9.95112i) q^{40} +(1.59222 + 4.90035i) q^{41} -5.61199 q^{43} +(17.7924 + 6.59791i) q^{44} +(6.50340 - 4.72500i) q^{46} +(2.36297 + 7.27246i) q^{47} +(2.73484 + 1.98698i) q^{49} +(-8.93907 - 6.49461i) q^{50} +(8.29767 + 25.5376i) q^{52} +(7.56640 - 5.49731i) q^{53} +(-2.08189 + 2.63177i) q^{55} +19.6748 q^{56} +(-0.249156 - 0.766824i) q^{58} +(1.51350 - 4.65807i) q^{59} +(-0.747856 - 0.543349i) q^{61} +(-2.36130 + 7.26733i) q^{62} +(-33.5524 + 24.3772i) q^{64} -4.74831 q^{65} -6.67334 q^{67} +(15.3900 - 11.1815i) q^{68} +(-1.65290 + 5.08710i) q^{70} +(-4.40059 - 3.19721i) q^{71} +(4.49398 - 13.8311i) q^{73} +(-4.65944 - 14.3403i) q^{74} -17.8772 q^{76} +(-5.91624 - 2.19390i) q^{77} +(-8.23017 + 5.97957i) q^{79} +(-5.40689 - 16.6407i) q^{80} +(11.5833 + 8.41575i) q^{82} +(5.04876 + 3.66814i) q^{83} +(1.03951 + 3.19929i) q^{85} +(-12.6162 + 9.16619i) q^{86} +(33.0267 - 9.25471i) q^{88} -9.83568 q^{89} +(-2.75909 - 8.49161i) q^{91} +(5.11481 - 15.7418i) q^{92} +(17.1904 + 12.4896i) q^{94} +(0.976891 - 3.00656i) q^{95} +(7.16712 - 5.20722i) q^{97} +9.39350 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7}+O(q^{10}) $ 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7	$ 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7} + 6 q^{10} + 13 q^{11} - 2 q^{13} - 22 q^{14} - 24 q^{16} - 2 q^{17} - 2 q^{19} + 15 q^{22} + 14 q^{23} - 19 q^{25} + 21 q^{26} + 15 q^{28} + q^{29} + 14 q^{31} - 48 q^{32} + 10 q^{34} - 18 q^{35} + 9 q^{37} + 11 q^{38} + 33 q^{40} + 25 q^{41} + 14 q^{43} + 14 q^{44} + 4 q^{46} - 28 q^{47} - 4 q^{49} - 63 q^{50} + 10 q^{52} + q^{53} - 40 q^{55} + 96 q^{56} - 20 q^{58} + 41 q^{59} - 5 q^{62} - 92 q^{64} - 60 q^{65} - 48 q^{67} + 25 q^{68} - 31 q^{70} + 3 q^{71} - 13 q^{73} + 29 q^{74} - 58 q^{76} - 2 q^{77} - 83 q^{80} + 41 q^{82} - 14 q^{83} - 10 q^{85} - 56 q^{86} + 86 q^{88} + 82 q^{89} + 14 q^{91} + 74 q^{92} - 2 q^{94} - 56 q^{95} + 12 q^{97} + 26 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7 + 6 * q^10 + 13 * q^11 - 2 * q^13 - 22 * q^14 - 24 * q^16 - 2 * q^17 - 2 * q^19 + 15 * q^22 + 14 * q^23 - 19 * q^25 + 21 * q^26 + 15 * q^28 + q^29 + 14 * q^31 - 48 * q^32 + 10 * q^34 - 18 * q^35 + 9 * q^37 + 11 * q^38 + 33 * q^40 + 25 * q^41 + 14 * q^43 + 14 * q^44 + 4 * q^46 - 28 * q^47 - 4 * q^49 - 63 * q^50 + 10 * q^52 + q^53 - 40 * q^55 + 96 * q^56 - 20 * q^58 + 41 * q^59 - 5 * q^62 - 92 * q^64 - 60 * q^65 - 48 * q^67 + 25 * q^68 - 31 * q^70 + 3 * q^71 - 13 * q^73 + 29 * q^74 - 58 * q^76 - 2 * q^77 - 83 * q^80 + 41 * q^82 - 14 * q^83 - 10 * q^85 - 56 * q^86 + 86 * q^88 + 82 * q^89 + 14 * q^91 + 74 * q^92 - 2 * q^94 - 56 * q^95 + 12 * q^97 + 26 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	2.24808	−	1.63332i	1.58963	−	1.15493i	0.685165	−	0.728388i	$-0.259730\pi$
$2$	2.24808	−	1.63332i	1.58963	−	1.15493i	0.904466	−	0.426546i	$-0.140270\pi$
$3$		0			0
$3$		0			0
$4$	1.76807	−	5.44156i	0.884036	−	2.72078i
$5$	0.818541	+	0.594705i	0.366063	+	0.265960i	0.755576	−	0.655061i	$-0.227357\pi$
$5$	0.818541	+	0.594705i	0.366063	+	0.265960i	−0.389514	+	0.921021i	$0.627357\pi$
$6$		0			0
$7$	−0.587909	+	1.80940i	−0.222209	+	0.683888i	0.776354	+	0.630297i	$0.217067\pi$
$7$	−0.587909	+	1.80940i	−0.222209	+	0.683888i	−0.998563	+	0.0535911i	$0.982933\pi$
$8$	−3.19570	−	9.83534i	−1.12985	−	3.47732i
$9$		0			0
$10$	2.81149			0.889071
$11$	−0.135769	+	3.31384i	−0.0409358	+	0.999162i
$11$	−0.135769	+	3.31384i	−0.0409358	+	0.999162i
$12$		0			0
$13$	−3.79677	+	2.75851i	−1.05303	+	0.765074i	−0.972787	−	0.231701i	$-0.925571\pi$
$13$	−3.79677	+	2.75851i	−1.05303	+	0.765074i	−0.0802465	+	0.996775i	$0.525571\pi$
$14$	1.63367	+	5.02791i	0.436616	+	1.34377i
$15$		0			0
$16$	−13.9907	−	10.1649i	−3.49768	−	2.54121i
$17$	2.68981	+	1.95426i	0.652375	+	0.473978i	0.864079	−	0.503356i	$-0.167901\pi$
$17$	2.68981	+	1.95426i	0.652375	+	0.473978i	−0.211705	+	0.977334i	$0.567901\pi$
$18$		0			0
$19$	−0.965525	−	2.97158i	−0.221507	−	0.681727i	−0.998627	−	0.0523758i	$-0.983321\pi$
$19$	−0.965525	−	2.97158i	−0.221507	−	0.681727i	0.777121	−	0.629351i	$-0.216679\pi$
$20$	4.68336	−	3.40266i	1.04723	−	0.760858i
$21$		0			0
$22$	5.10736	+	7.67153i	1.08889	+	1.63558i
$23$	2.89287			0.603206			0.301603	−	0.953434i	$-0.402478\pi$
$23$	2.89287			0.603206			0.301603	+	0.953434i	$0.402478\pi$
$24$		0			0
$25$	−1.22875	−	3.78170i	−0.245750	−	0.756340i
$26$	−4.02988	+	12.4027i	−0.790325	+	2.43237i
$27$		0			0
$28$	8.80648	+	6.39829i	1.66427	+	1.20916i
$29$	0.0896641	−	0.275958i	0.0166502	−	0.0512440i	−0.942386	−	0.334527i	$-0.891424\pi$
$29$	0.0896641	−	0.275958i	0.0166502	−	0.0512440i	0.959036	+	0.283283i	$0.0914235\pi$
$30$		0			0
$31$	−2.22471	+	1.61634i	−0.399569	+	0.290304i	−0.769365	−	0.638809i	$-0.779427\pi$
$31$	−2.22471	+	1.61634i	−0.399569	+	0.290304i	0.369796	+	0.929113i	$0.379427\pi$
$32$	−27.3718			−4.83869
$33$		0			0
$34$	9.23884			1.58445
$35$	−1.55728	+	1.13143i	−0.263229	+	0.191247i
$36$		0			0
$37$	1.67679	−	5.16064i	0.275663	−	0.848404i	−0.713380	−	0.700777i	$-0.752837\pi$
$37$	1.67679	−	5.16064i	0.275663	−	0.848404i	0.989043	−	0.147627i	$-0.0471634\pi$
$38$	−7.02413	−	5.10333i	−1.13946	−	0.827869i
$39$		0			0
$40$	3.23332	−	9.95112i	0.511232	−	1.57341i
$41$	1.59222	+	4.90035i	0.248663	+	0.765306i	0.995012	+	0.0997515i	$0.0318048\pi$
$41$	1.59222	+	4.90035i	0.248663	+	0.765306i	−0.746349	+	0.665554i	$0.768195\pi$
$42$		0			0
$43$	−5.61199			−0.855820			−0.427910	−	0.903821i	$-0.640750\pi$
$43$	−5.61199			−0.855820			−0.427910	+	0.903821i	$0.640750\pi$
$44$	17.7924	+	6.59791i	2.68231	+	0.994672i
$45$		0			0
$46$	6.50340	−	4.72500i	0.958875	−	0.696663i
$47$	2.36297	+	7.27246i	0.344674	+	1.06080i	0.961758	+	0.273900i	$0.0883138\pi$
$47$	2.36297	+	7.27246i	0.344674	+	1.06080i	−0.617084	+	0.786897i	$0.711686\pi$
$48$		0			0
$49$	2.73484	+	1.98698i	0.390691	+	0.283854i
$50$	−8.93907	−	6.49461i	−1.26418	−	0.918477i
$51$		0			0
$52$	8.29767	+	25.5376i	1.15068	+	3.54143i
$53$	7.56640	−	5.49731i	1.03933	−	0.755114i	0.0691716	−	0.997605i	$-0.477964\pi$
$53$	7.56640	−	5.49731i	1.03933	−	0.755114i	0.970154	+	0.242491i	$0.0779644\pi$
$54$		0			0
$55$	−2.08189	+	2.63177i	−0.280722	+	0.354868i
$56$	19.6748			2.62916
$57$		0			0
$58$	−0.249156	−	0.766824i	−0.0327158	−	0.100689i
$59$	1.51350	−	4.65807i	0.197041	−	0.606430i	−0.802906	−	0.596106i	$-0.796714\pi$
$59$	1.51350	−	4.65807i	0.197041	−	0.606430i	0.999947	−	0.0103237i	$-0.00328618\pi$
$60$		0			0
$61$	−0.747856	−	0.543349i	−0.0957532	−	0.0695688i	0.538878	−	0.842384i	$-0.318848\pi$
$61$	−0.747856	−	0.543349i	−0.0957532	−	0.0695688i	−0.634632	+	0.772815i	$0.718848\pi$
$62$	−2.36130	+	7.26733i	−0.299885	+	0.922952i
$63$		0			0
$64$	−33.5524	+	24.3772i	−4.19405	+	3.04715i
$65$	−4.74831			−0.588955
$66$		0			0
$67$	−6.67334			−0.815278			−0.407639	−	0.913143i	$-0.633648\pi$
$67$	−6.67334			−0.815278			−0.407639	+	0.913143i	$0.633648\pi$
$68$	15.3900	−	11.1815i	1.86631	−	1.35596i
$69$		0			0
$70$	−1.65290	+	5.08710i	−0.197559	+	0.608025i
$71$	−4.40059	−	3.19721i	−0.522253	−	0.379439i	0.295199	−	0.955436i	$-0.404614\pi$
$71$	−4.40059	−	3.19721i	−0.522253	−	0.379439i	−0.817452	+	0.575997i	$0.804614\pi$
$72$		0			0
$73$	4.49398	−	13.8311i	0.525981	−	1.61880i	−0.236387	−	0.971659i	$-0.575963\pi$
$73$	4.49398	−	13.8311i	0.525981	−	1.61880i	0.762368	−	0.647144i	$-0.224037\pi$
$74$	−4.65944	−	14.3403i	−0.541648	−	1.66702i
$75$		0			0
$76$	−17.8772			−2.05065
$77$	−5.91624	−	2.19390i	−0.674218	−	0.250018i
$78$		0			0
$79$	−8.23017	+	5.97957i	−0.925967	+	0.672754i	−0.945002	−	0.327065i	$-0.893941\pi$
$79$	−8.23017	+	5.97957i	−0.925967	+	0.672754i	0.0190353	+	0.999819i	$0.493941\pi$
$80$	−5.40689	−	16.6407i	−0.604509	−	1.86049i
$81$		0			0
$82$	11.5833	+	8.41575i	1.27916	+	0.929364i
$83$	5.04876	+	3.66814i	0.554173	+	0.402630i	0.829322	−	0.558771i	$-0.188727\pi$
$83$	5.04876	+	3.66814i	0.554173	+	0.402630i	−0.275149	+	0.961402i	$0.588727\pi$
$84$		0			0
$85$	1.03951	+	3.19929i	0.112751	+	0.347011i
$86$	−12.6162	+	9.16619i	−1.36044	+	0.988416i
$87$		0			0
$88$	33.0267	−	9.25471i	3.52065	−	0.986555i
$89$	−9.83568			−1.04258			−0.521290	−	0.853380i	$-0.674549\pi$
$89$	−9.83568			−1.04258			−0.521290	+	0.853380i	$0.674549\pi$
$90$		0			0
$91$	−2.75909	−	8.49161i	−0.289231	−	0.890163i
$92$	5.11481	−	15.7418i	0.533255	−	1.64119i
$93$		0			0
$94$	17.1904	+	12.4896i	1.77306	+	1.28820i
$95$	0.976891	−	3.00656i	0.100227	−	0.308467i
$96$		0			0
$97$	7.16712	−	5.20722i	0.727710	−	0.528713i	−0.161128	−	0.986934i	$-0.551513\pi$
$97$	7.16712	−	5.20722i	0.727710	−	0.528713i	0.888838	+	0.458221i	$0.151513\pi$
$98$	9.39350			0.948887
$99$		0			0
$100$	−22.7509			−2.27509
$101$	−0.317491	+	0.230671i	−0.0315915	+	0.0229526i	−0.603469	−	0.797386i	$-0.706215\pi$
$101$	−0.317491	+	0.230671i	−0.0315915	+	0.0229526i	0.571877	+	0.820339i	$0.306215\pi$
$102$		0			0
$103$	−3.72580	+	11.4668i	−0.367114	+	1.12986i	0.581533	+	0.813523i	$0.302453\pi$
$103$	−3.72580	+	11.4668i	−0.367114	+	1.12986i	−0.948647	+	0.316337i	$0.897547\pi$
$104$	39.2642	+	28.5271i	3.85017	+	2.79731i
$105$		0			0
$106$	8.03097	−	24.7168i	0.780036	−	2.40070i
$107$	−3.12538	−	9.61893i	−0.302142	−	0.929897i	−0.980728	−	0.195376i	$-0.937407\pi$
$107$	−3.12538	−	9.61893i	−0.302142	−	0.929897i	0.678586	−	0.734521i	$-0.262593\pi$
$108$		0			0
$109$	−4.00524			−0.383633			−0.191816	−	0.981431i	$-0.561438\pi$
$109$	−4.00524			−0.383633			−0.191816	+	0.981431i	$0.561438\pi$
$110$	−0.381712	+	9.31684i	−0.0363948	+	0.888325i
$111$		0			0
$112$	26.6175	−	19.3388i	2.51512	−	1.82734i
$113$	−2.23657	−	6.88344i	−0.210398	−	0.647540i	−0.999448	−	0.0332107i	$-0.989427\pi$
$113$	−2.23657	−	6.88344i	−0.210398	−	0.647540i	0.789050	−	0.614329i	$-0.210573\pi$
$114$		0			0
$115$	2.36794	+	1.72041i	0.220811	+	0.160429i
$116$	−1.34311	−	0.975825i	−0.124704	−	0.0906031i
$117$		0			0
$118$	−4.20568	−	12.9437i	−0.387164	−	1.19157i
$119$	−5.11740	+	3.71801i	−0.469111	+	0.340829i
$120$		0			0
$121$	−10.9631	−	0.899832i	−0.996649	−	0.0818029i
$122$	−2.56870			−0.232560
$123$		0			0
$124$	4.86200	+	14.9637i	0.436620	+	1.34378i
$125$	2.80649	−	8.63748i	0.251020	−	0.772560i
$126$		0			0
$127$	11.1015	+	8.06569i	0.985097	+	0.715715i	0.958842	−	0.283941i	$-0.0916419\pi$
$127$	11.1015	+	8.06569i	0.985097	+	0.715715i	0.0262548	+	0.999655i	$0.491642\pi$
$128$	−18.6958	+	57.5396i	−1.65249	+	5.08583i
$129$		0			0
$130$	−10.6746	+	7.75552i	−0.936221	+	0.680205i
$131$	2.93074			0.256060			0.128030	−	0.991770i	$-0.459135\pi$
$131$	2.93074			0.256060			0.128030	+	0.991770i	$0.459135\pi$
$132$		0			0
$133$	5.94441			0.515446
$134$	−15.0022	+	10.8997i	−1.29599	+	0.941593i
$135$		0			0
$136$	10.6250	−	32.7004i	0.911087	−	2.80404i
$137$	−7.25315	−	5.26972i	−0.619678	−	0.450223i	0.233131	−	0.972445i	$-0.425103\pi$
$137$	−7.25315	−	5.26972i	−0.619678	−	0.450223i	−0.852809	+	0.522223i	$0.825103\pi$
$138$		0			0
$139$	−0.697264	+	2.14596i	−0.0591412	+	0.182018i	−0.976263	−	0.216590i	$-0.930507\pi$
$139$	−0.697264	+	2.14596i	−0.0591412	+	0.182018i	0.917121	+	0.398608i	$0.130507\pi$
$140$	3.40338	+	10.4745i	0.287638	+	0.885258i
$141$		0			0
$142$	−15.1149			−1.26842
$143$	−8.62580	−	12.9564i	−0.721326	−	1.08347i
$144$		0			0
$145$	0.237507	−	0.172559i	0.0197239	−	0.0143302i
$146$	−12.4878	−	38.4334i	−1.03350	−	3.18077i
$147$		0			0
$148$	−25.1173	−	18.2488i	−2.06463	−	1.50004i
$149$	−4.38635	−	3.18687i	−0.359344	−	0.261079i	0.393434	−	0.919353i	$-0.371287\pi$
$149$	−4.38635	−	3.18687i	−0.359344	−	0.261079i	−0.752778	+	0.658274i	$0.771287\pi$
$150$		0			0
$151$	5.06189	+	15.5789i	0.411931	+	1.26779i	0.914967	+	0.403528i	$0.132216\pi$
$151$	5.06189	+	15.5789i	0.411931	+	1.26779i	−0.503036	+	0.864265i	$0.667784\pi$
$152$	−26.1410	+	18.9925i	−2.12031	+	1.54050i
$153$		0			0
$154$	−16.8835	+	4.73109i	−1.36051	+	0.381242i
$155$	−2.78226			−0.223476
$156$		0			0
$157$	−5.16242	−	15.8883i	−0.412006	−	1.26802i	−0.914902	−	0.403676i	$-0.867732\pi$
$157$	−5.16242	−	15.8883i	−0.412006	−	1.26802i	0.502896	−	0.864347i	$-0.332268\pi$
$158$	−8.73549	+	26.8851i	−0.694958	+	2.13886i
$159$		0			0
$160$	−22.4049	−	16.2781i	−1.77126	−	1.28690i
$161$	−1.70075	+	5.23436i	−0.134038	+	0.412525i
$162$		0			0
$163$	1.91381	−	1.39046i	0.149901	−	0.108910i	−0.510307	−	0.859992i	$-0.670468\pi$
$163$	1.91381	−	1.39046i	0.149901	−	0.108910i	0.660208	+	0.751083i	$0.270468\pi$
$164$	29.4807			2.30206
$165$		0			0
$166$	17.3413			1.34594
$167$	−6.54578	+	4.75579i	−0.506528	+	0.368014i	−0.811505	−	0.584346i	$-0.801351\pi$
$167$	−6.54578	+	4.75579i	−0.506528	+	0.368014i	0.304977	+	0.952360i	$0.401351\pi$
$168$		0			0
$169$	2.78882	−	8.58312i	0.214525	−	0.660240i
$170$	7.56237	+	5.49438i	0.580007	+	0.421400i
$171$		0			0
$172$	−9.92239	+	30.5380i	−0.756575	+	2.32850i
$173$	5.42093	+	16.6839i	0.412146	+	1.26845i	0.914779	+	0.403954i	$0.132364\pi$
$173$	5.42093	+	16.6839i	0.412146	+	1.26845i	−0.502634	+	0.864500i	$0.667636\pi$
$174$		0			0
$175$	7.56499			0.571860
$176$	35.5843	−	44.9830i	2.68226	−	3.39072i
$177$		0			0
$178$	−22.1114	+	16.0648i	−1.65732	+	1.20411i
$179$	3.29158	+	10.1304i	0.246024	+	0.757185i	0.995466	+	0.0951152i	$0.0303219\pi$
$179$	3.29158	+	10.1304i	0.246024	+	0.757185i	−0.749442	+	0.662070i	$0.769678\pi$
$180$		0			0
$181$	3.38753	+	2.46118i	0.251793	+	0.182938i	0.706521	−	0.707692i	$-0.250264\pi$
$181$	3.38753	+	2.46118i	0.251793	+	0.182938i	−0.454728	+	0.890630i	$0.650264\pi$
$182$	−20.0722	−	14.5833i	−1.48785	−	1.08099i
$183$		0			0
$184$	−9.24475	−	28.4524i	−0.681532	−	2.09754i
$185$	4.44158	−	3.22700i	0.326552	−	0.237254i
$186$		0			0
$187$	−6.84131	+	8.64828i	−0.500286	+	0.632425i
$188$	43.7515			3.19090
$189$		0			0
$190$	−2.71456	−	8.35456i	−0.196935	−	0.606104i
$191$	2.95265	−	9.08734i	0.213647	−	0.657537i	−0.785600	−	0.618734i	$-0.787646\pi$
$191$	2.95265	−	9.08734i	0.213647	−	0.657537i	0.999247	−	0.0388023i	$-0.0123542\pi$
$192$		0			0
$193$	11.9549	+	8.68574i	0.860532	+	0.625213i	0.928030	−	0.372506i	$-0.121501\pi$
$193$	11.9549	+	8.68574i	0.860532	+	0.625213i	−0.0674975	+	0.997719i	$0.521501\pi$
$194$	7.60716	−	23.4124i	0.546163	−	1.68092i
$195$		0			0
$196$	15.6476	−	11.3687i	1.11769	−	0.812048i
$197$	2.91565			0.207732			0.103866	−	0.994591i	$-0.466879\pi$
$197$	2.91565			0.207732			0.103866	+	0.994591i	$0.466879\pi$
$198$		0			0
$199$	15.2678			1.08230			0.541152	−	0.840925i	$-0.317988\pi$
$199$	15.2678			1.08230			0.541152	+	0.840925i	$0.317988\pi$
$200$	−33.2676	+	24.1703i	−2.35238	+	1.70910i
$201$		0			0
$202$	−0.336984	+	1.03713i	−0.0237101	+	0.0729722i
$203$	0.446603	+	0.324476i	0.0313454	+	0.0227737i
$204$		0			0
$205$	−1.61096	+	4.95804i	−0.112515	+	0.346284i
$206$	10.3532	+	31.8637i	0.721339	+	2.22005i
$207$		0			0
$208$	81.1594			5.62739
$209$	9.97844	−	2.79615i	0.690223	−	0.193414i
$210$		0			0
$211$	−12.1021	+	8.79272i	−0.833145	+	0.605316i	−0.920447	−	0.390866i	$-0.872175\pi$
$211$	−12.1021	+	8.79272i	−0.833145	+	0.605316i	0.0873020	+	0.996182i	$0.472175\pi$
$212$	−16.5360	−	50.8927i	−1.13570	−	3.49532i
$213$		0			0
$214$	−22.7369	−	16.5193i	−1.55426	−	1.12924i
$215$	−4.59364	−	3.33748i	−0.313284	−	0.227614i
$216$		0			0
$217$	−1.61668	−	4.97564i	−0.109748	−	0.337768i
$218$	−9.00409	+	6.54186i	−0.609834	+	0.443070i
$219$		0			0
$220$	10.6400	+	15.9819i	0.717351	+	1.07750i
$221$	−15.6034			−1.04960
$222$		0			0
$223$	−7.80713	−	24.0279i	−0.522804	−	1.60903i	−0.768617	−	0.639709i	$-0.779055\pi$
$223$	−7.80713	−	24.0279i	−0.522804	−	1.60903i	0.245813	−	0.969317i	$-0.420945\pi$
$224$	16.0921	−	49.5264i	1.07520	−	3.30912i
$225$		0			0
$226$	−16.2709	−	11.8215i	−1.08232	−	0.786353i
$227$	0.373378	−	1.14914i	0.0247820	−	0.0762711i	−0.937901	−	0.346904i	$-0.887233\pi$
$227$	0.373378	−	1.14914i	0.0247820	−	0.0762711i	0.962683	+	0.270633i	$0.0872330\pi$
$228$		0			0
$229$	19.4633	−	14.1409i	1.28617	−	0.934458i	0.286451	−	0.958095i	$-0.407525\pi$
$229$	19.4633	−	14.1409i	1.28617	−	0.934458i	0.999721	+	0.0236368i	$0.00752453\pi$
$230$	8.13328			0.536293
$231$		0			0
$232$	−3.00068			−0.197004
$233$	14.0786	−	10.2287i	0.922321	−	0.670106i	−0.0217795	−	0.999763i	$-0.506933\pi$
$233$	14.0786	−	10.2287i	0.922321	−	0.670106i	0.944101	+	0.329657i	$0.106933\pi$
$234$		0			0
$235$	−2.39078	+	7.35807i	−0.155957	+	0.479988i
$236$	−22.6712	−	16.4716i	−1.47577	−	1.07221i
$237$		0			0
$238$	−5.43160	+	16.7167i	−0.352078	+	1.08358i
$239$	−2.04219	−	6.28520i	−0.132098	−	0.406556i	0.863029	−	0.505154i	$-0.168564\pi$
$239$	−2.04219	−	6.28520i	−0.132098	−	0.406556i	−0.995127	+	0.0985980i	$0.968564\pi$
$240$		0			0
$241$	−1.24651			−0.0802947			−0.0401474	−	0.999194i	$-0.512783\pi$
$241$	−1.24651			−0.0802947			−0.0401474	+	0.999194i	$0.512783\pi$
$242$	−26.1157	+	15.8835i	−1.67878	+	1.02103i
$243$		0			0
$244$	−4.27893	+	3.10883i	−0.273931	+	0.199022i
$245$	1.05691	+	3.25284i	0.0675237	+	0.207816i
$246$		0			0
$247$	11.8630	+	8.61898i	0.754825	+	0.548413i
$248$	23.0068	+	16.7154i	1.46093	+	1.06143i
$249$		0			0
$250$	−7.79860	−	24.0016i	−0.493227	−	1.51800i
$251$	5.91751	−	4.29933i	0.373510	−	0.271371i	−0.385155	−	0.922852i	$-0.625852\pi$
$251$	5.91751	−	4.29933i	0.373510	−	0.271371i	0.758665	+	0.651481i	$0.225852\pi$
$252$		0			0
$253$	−0.392761	+	9.58654i	−0.0246927	+	0.602700i
$254$	38.1309			2.39254
$255$		0			0
$256$	26.3196	+	81.0034i	1.64497	+	5.06271i
$257$	−5.47170	+	16.8402i	−0.341315	+	1.05046i	0.622212	+	0.782849i	$0.286234\pi$
$257$	−5.47170	+	16.8402i	−0.341315	+	1.05046i	−0.963527	+	0.267611i	$0.913766\pi$
$258$		0			0
$259$	8.35185	+	6.06797i	0.518959	+	0.377045i
$260$	−8.39535	+	25.8382i	−0.520657	+	1.60242i
$261$		0			0
$262$	6.58852	−	4.78684i	0.407040	−	0.295732i
$263$	8.95390			0.552121			0.276061	−	0.961140i	$-0.410971\pi$
$263$	8.95390			0.552121			0.276061	+	0.961140i	$0.410971\pi$
$264$		0			0
$265$	9.46269			0.581288
$266$	13.3635	−	9.70914i	0.819368	−	0.595306i
$267$		0			0
$268$	−11.7989	+	36.3134i	−0.720735	+	2.21819i
$269$	21.1556	+	15.3704i	1.28988	+	0.937151i	0.999803	−	0.0198527i	$-0.00631974\pi$
$269$	21.1556	+	15.3704i	1.28988	+	0.937151i	0.290075	+	0.957004i	$0.406320\pi$
$270$		0			0
$271$	−5.07295	+	15.6129i	−0.308160	+	0.948419i	0.670319	+	0.742073i	$0.266157\pi$
$271$	−5.07295	+	15.6129i	−0.308160	+	0.948419i	−0.978479	+	0.206346i	$0.933843\pi$
$272$	−17.7676	−	54.6831i	−1.07732	−	3.31565i
$273$		0			0
$274$	−24.9128			−1.50504
$275$	12.6988	−	3.55845i	0.765766	−	0.214583i
$276$		0			0
$277$	8.66190	−	6.29324i	0.520443	−	0.378124i	−0.296328	−	0.955086i	$-0.595762\pi$
$277$	8.66190	−	6.29324i	0.520443	−	0.378124i	0.816771	+	0.576962i	$0.195762\pi$
$278$	1.93754	+	5.96314i	0.116206	+	0.357645i
$279$		0			0
$280$	16.1046	+	11.7007i	0.962436	+	0.699251i
$281$	26.9507	+	19.5808i	1.60774	+	1.16809i	0.870064	+	0.492938i	$0.164077\pi$
$281$	26.9507	+	19.5808i	1.60774	+	1.16809i	0.737677	+	0.675154i	$0.235923\pi$
$282$		0			0
$283$	−2.11891	−	6.52134i	−0.125956	−	0.387653i	0.868118	−	0.496358i	$-0.165330\pi$
$283$	−2.11891	−	6.52134i	−0.125956	−	0.387653i	−0.994074	+	0.108705i	$0.965330\pi$
$284$	−25.1784	+	18.2932i	−1.49406	+	1.08550i
$285$		0			0
$286$	−40.5535	−	15.0383i	−2.39798	−	0.889233i
$287$	−9.80276			−0.578638
$288$		0			0
$289$	−1.83735	−	5.65478i	−0.108079	−	0.332634i
$290$	0.252089	−	0.775852i	0.0148032	−	0.0455596i
$291$		0			0
$292$	−67.3169	−	48.9086i	−3.93942	−	2.86216i
$293$	−0.563633	+	1.73468i	−0.0329278	+	0.101341i	−0.966170	−	0.257907i	$-0.916967\pi$
$293$	−0.563633	+	1.73468i	−0.0329278	+	0.101341i	0.933242	+	0.359249i	$0.116967\pi$
$294$		0			0
$295$	4.00904	−	2.91274i	0.233415	−	0.169586i
$296$	−56.1152			−3.26163
$297$		0			0
$298$	−15.0660			−0.872753
$299$	−10.9836	+	7.98003i	−0.635196	+	0.461497i
$300$		0			0
$301$	3.29934	−	10.1543i	0.190171	−	0.585285i
$302$	36.8249	+	26.7549i	2.11904	+	1.53957i
$303$		0			0
$304$	−16.6973	+	51.3890i	−0.957655	+	2.94736i
$305$	−0.289018	−	0.889507i	−0.0165492	−	0.0509330i
$306$		0			0
$307$	−34.3371			−1.95972			−0.979860	−	0.199687i	$-0.936008\pi$
$307$	−34.3371			−1.95972			−0.979860	+	0.199687i	$0.936008\pi$
$308$	−22.3986	+	28.3146i	−1.27628	+	1.61338i
$309$		0			0
$310$	−6.25473	+	4.54433i	−0.355245	+	0.258101i
$311$	9.26374	+	28.5109i	0.525299	+	1.61670i	0.763725	+	0.645542i	$0.223369\pi$
$311$	9.26374	+	28.5109i	0.525299	+	1.61670i	−0.238426	+	0.971161i	$0.576631\pi$
$312$		0			0
$313$	14.3589	+	10.4324i	0.811614	+	0.589672i	0.914298	−	0.405042i	$-0.132743\pi$
$313$	14.3589	+	10.4324i	0.811614	+	0.589672i	−0.102684	+	0.994714i	$0.532743\pi$
$314$	−37.5562	−	27.2862i	−2.11942	−	1.53985i
$315$		0			0
$316$	17.9867	+	55.3573i	1.01183	+	3.11409i
$317$	−19.1803	+	13.9353i	−1.07727	+	0.782683i	−0.977205	−	0.212297i	$-0.931905\pi$
$317$	−19.1803	+	13.9353i	−1.07727	+	0.782683i	−0.100066	+	0.994981i	$0.531905\pi$
$318$		0			0
$319$	0.902307	+	0.334599i	0.0505195	+	0.0187340i
$320$	−41.9612			−2.34571
$321$		0			0
$322$	4.72599	+	14.5451i	0.263369	+	0.810567i
$323$	3.21017	−	9.87987i	0.178618	−	0.549731i
$324$		0			0
$325$	15.0971	+	10.9687i	0.837439	+	0.608435i
$326$	2.03131	−	6.25174i	0.112504	−	0.346252i
$327$		0			0
$328$	43.1083	−	31.3200i	2.38026	−	1.72936i
$329$	−14.5480			−0.802056
$330$		0			0
$331$	7.09439			0.389943			0.194971	−	0.980809i	$-0.437539\pi$
$331$	7.09439			0.389943			0.194971	+	0.980809i	$0.437539\pi$
$332$	28.8870	−	20.9876i	1.58538	−	1.15184i
$333$		0			0
$334$	−6.94768	+	21.3828i	−0.380160	+	1.17001i
$335$	−5.46240	−	3.96867i	−0.298443	−	0.216831i
$336$		0			0
$337$	10.4824	−	32.2616i	0.571014	−	1.75740i	−0.0783552	−	0.996926i	$-0.524967\pi$
$337$	10.4824	−	32.2616i	0.571014	−	1.75740i	0.649369	−	0.760474i	$-0.275033\pi$
$338$	−7.74952	−	23.8506i	−0.421518	−	1.29730i
$339$		0			0
$340$	19.2470			1.04382
$341$	−5.05427	−	7.59178i	−0.273704	−	0.411118i
$342$		0			0
$343$	−15.9772	+	11.6081i	−0.862689	+	0.626780i
$344$	17.9342	+	55.1958i	0.966948	+	2.97596i
$345$		0			0
$346$	39.4369	+	28.6526i	2.12014	+	1.54037i
$347$	19.8203	+	14.4003i	1.06401	+	0.773050i	0.974826	−	0.222965i	$-0.0715736\pi$
$347$	19.8203	+	14.4003i	1.06401	+	0.773050i	0.0891857	+	0.996015i	$0.471574\pi$
$348$		0			0
$349$	−1.98309	−	6.10332i	−0.106152	−	0.326703i	0.883847	−	0.467776i	$-0.154945\pi$
$349$	−1.98309	−	6.10332i	−0.106152	−	0.326703i	−0.989999	+	0.141073i	$0.954945\pi$
$350$	17.0067	−	12.3561i	0.909046	−	0.660460i
$351$		0			0
$352$	3.71622	−	90.7058i	0.198075	−	4.83463i
$353$	−10.5272			−0.560307			−0.280153	−	0.959955i	$-0.590385\pi$
$353$	−10.5272			−0.560307			−0.280153	+	0.959955i	$0.590385\pi$
$354$		0			0
$355$	−1.70066	−	5.23410i	−0.0902617	−	0.277797i
$356$	−17.3902	+	53.5215i	−0.921677	+	2.83663i
$357$		0			0
$358$	23.9460	+	17.3978i	1.26559	+	0.919503i
$359$	−5.20899	+	16.0316i	−0.274920	+	0.846117i	0.714320	+	0.699819i	$0.246736\pi$
$359$	−5.20899	+	16.0316i	−0.274920	+	0.846117i	−0.989241	+	0.146298i	$0.953264\pi$
$360$		0			0
$361$	7.47327	−	5.42965i	0.393330	−	0.285771i
$362$	11.6353			0.611540
$363$		0			0
$364$	−51.0859			−2.67763
$365$	11.9039	−	8.64869i	0.623079	−	0.452693i
$366$		0			0
$367$	−3.27425	+	10.0771i	−0.170914	+	0.526020i	−0.999423	−	0.0339555i	$-0.989190\pi$
$367$	−3.27425	+	10.0771i	−0.170914	+	0.526020i	0.828509	+	0.559976i	$0.189190\pi$
$368$	−40.4734	−	29.4057i	−2.10982	−	1.53288i
$369$		0			0
$370$	4.71429	−	14.5091i	0.245084	−	0.754291i
$371$	5.49847	+	16.9225i	0.285466	+	0.878575i
$372$		0			0
$373$	11.3447			0.587409			0.293704	−	0.955896i	$-0.405112\pi$
$373$	11.3447			0.587409			0.293704	+	0.955896i	$0.405112\pi$
$374$	−1.25434	+	30.6161i	−0.0648606	+	1.58312i
$375$		0			0
$376$	63.9758	−	46.4812i	3.29930	−	2.39708i
$377$	0.420799	+	1.29509i	0.0216722	+	0.0667003i
$378$		0			0
$379$	8.28638	+	6.02040i	0.425643	+	0.309247i	0.779904	−	0.625899i	$-0.215268\pi$
$379$	8.28638	+	6.02040i	0.425643	+	0.309247i	−0.354262	+	0.935146i	$0.615268\pi$
$380$	−14.6332	−	10.6316i	−0.750666	−	0.545391i
$381$		0			0
$382$	−8.20477	−	25.2517i	−0.419792	−	1.29199i
$383$	24.7247	−	17.9635i	1.26337	−	0.917894i	0.264454	−	0.964398i	$-0.414808\pi$
$383$	24.7247	−	17.9635i	1.26337	−	0.917894i	0.998918	+	0.0465043i	$0.0148081\pi$
$384$		0			0
$385$	−3.53796	−	5.31421i	−0.180311	−	0.270837i
$386$	41.0622			2.09001
$387$		0			0
$388$	−15.6634	−	48.2070i	−0.795190	−	2.44734i
$389$	3.00693	−	9.25439i	0.152458	−	0.469216i	−0.845437	−	0.534075i	$-0.820660\pi$
$389$	3.00693	−	9.25439i	0.152458	−	0.469216i	0.997894	+	0.0648591i	$0.0206598\pi$
$390$		0			0
$391$	7.78128	+	5.65343i	0.393516	+	0.285906i
$392$	10.8029	−	33.2478i	0.545628	−	1.67927i
$393$		0			0
$394$	6.55462	−	4.76221i	0.330217	−	0.239917i
$395$	−10.2928			−0.517887
$396$		0			0
$397$	−1.46894			−0.0737241			−0.0368620	−	0.999320i	$-0.511736\pi$
$397$	−1.46894			−0.0737241			−0.0368620	+	0.999320i	$0.511736\pi$
$398$	34.3231	−	24.9372i	1.72046	−	1.24999i
$399$		0			0
$400$	−21.2494	+	65.3988i	−1.06247	+	3.26994i
$401$	−13.4258	−	9.75443i	−0.670453	−	0.487113i	0.199723	−	0.979852i	$-0.435996\pi$
$401$	−13.4258	−	9.75443i	−0.670453	−	0.487113i	−0.870177	+	0.492739i	$0.835996\pi$
$402$		0			0
$403$	3.98799	−	12.2738i	0.198656	−	0.611399i
$404$	0.693862	+	2.13549i	0.0345209	+	0.106244i
$405$		0			0
$406$	1.53397			0.0761297
$407$	16.8739	+	6.25729i	0.836409	+	0.310162i
$408$		0			0
$409$	−9.72353	+	7.06456i	−0.480798	+	0.349320i	−0.801634	−	0.597815i	$-0.796036\pi$
$409$	−9.72353	+	7.06456i	−0.480798	+	0.349320i	0.320837	+	0.947135i	$0.396036\pi$
$410$	4.47651	+	13.7773i	0.221079	+	0.680411i
$411$		0			0
$412$	55.8100	+	40.5483i	2.74956	+	1.99767i
$413$	7.53851	+	5.47704i	0.370946	+	0.269508i
$414$		0			0
$415$	1.95116	+	6.00504i	0.0957785	+	0.294776i
$416$	103.924	−	75.5053i	5.09530	−	3.70195i
$417$		0			0
$418$	17.8653	−	22.5840i	0.873820	−	1.10462i
$419$	−0.548783			−0.0268098			−0.0134049	−	0.999910i	$-0.504267\pi$
$419$	−0.548783			−0.0268098			−0.0134049	+	0.999910i	$0.504267\pi$
$420$		0			0
$421$	−0.820443	−	2.52506i	−0.0399860	−	0.123064i	0.929071	−	0.369902i	$-0.120609\pi$
$421$	−0.820443	−	2.52506i	−0.0399860	−	0.123064i	−0.969057	+	0.246837i	$0.920609\pi$
$422$	−12.8452	+	39.5334i	−0.625294	+	1.92446i
$423$		0			0
$424$	−78.2479	−	56.8504i	−3.80005	−	2.76090i
$425$	4.08533	−	12.5734i	0.198168	−	0.609897i
$426$		0			0
$427$	1.42281	−	1.03373i	0.0688544	−	0.0500257i
$428$	−57.8679			−2.79715
$429$		0			0
$430$	−15.7780			−0.760885
$431$	−32.5848	+	23.6742i	−1.56955	+	1.14035i	−0.641973	+	0.766728i	$0.721884\pi$
$431$	−32.5848	+	23.6742i	−1.56955	+	1.14035i	−0.927582	+	0.373620i	$0.878116\pi$
$432$		0			0
$433$	−8.82594	+	27.1634i	−0.424147	+	1.30539i	0.479661	+	0.877454i	$0.340760\pi$
$433$	−8.82594	+	27.1634i	−0.424147	+	1.30539i	−0.903808	+	0.427938i	$0.859240\pi$
$434$	−11.7613	−	8.54505i	−0.564558	−	0.410176i
$435$		0			0
$436$	−7.08155	+	21.7948i	−0.339145	+	1.04378i
$437$	−2.79314	−	8.59641i	−0.133614	−	0.411222i
$438$		0			0
$439$	−13.4562			−0.642229			−0.321115	−	0.947040i	$-0.604057\pi$
$439$	−13.4562			−0.642229			−0.321115	+	0.947040i	$0.604057\pi$
$440$	32.5375	+	12.0658i	1.55116	+	0.575212i
$441$		0			0
$442$	−35.0777	+	25.4855i	−1.66848	+	1.21222i
$443$	−9.28582	−	28.5788i	−0.441183	−	1.35782i	−0.886616	−	0.462505i	$-0.846951\pi$
$443$	−9.28582	−	28.5788i	−0.441183	−	1.35782i	0.445434	−	0.895315i	$-0.353049\pi$
$444$		0			0
$445$	−8.05090	−	5.84932i	−0.381649	−	0.277285i
$446$	−56.7964	−	41.2650i	−2.68939	−	1.95395i
$447$		0			0
$448$	−24.3824	−	75.0412i	−1.15196	−	3.54536i
$449$	27.6553	−	20.0928i	1.30514	−	0.948237i	0.305144	−	0.952306i	$-0.401295\pi$
$449$	27.6553	−	20.0928i	1.30514	−	0.948237i	0.999992	+	0.00406952i	$0.00129537\pi$
$450$		0			0
$451$	−16.4552	+	4.61106i	−0.774844	+	0.217126i
$452$	−41.4111			−1.94781
$453$		0			0
$454$	−1.03753	−	3.19320i	−0.0486939	−	0.149864i
$455$	2.79157	−	8.59157i	0.130871	−	0.402779i
$456$		0			0
$457$	−5.82651	−	4.23321i	−0.272553	−	0.198021i	0.443110	−	0.896467i	$-0.353875\pi$
$457$	−5.82651	−	4.23321i	−0.272553	−	0.198021i	−0.715663	+	0.698446i	$0.753875\pi$
$458$	20.6583	−	63.5798i	0.965300	−	2.97089i
$459$		0			0
$460$	13.5484	−	9.84347i	0.631696	−	0.458954i
$461$	−34.8822			−1.62463			−0.812313	−	0.583222i	$-0.801792\pi$
$461$	−34.8822			−1.62463			−0.812313	+	0.583222i	$0.801792\pi$
$462$		0			0
$463$	−7.80157			−0.362570			−0.181285	−	0.983431i	$-0.558026\pi$
$463$	−7.80157			−0.362570			−0.181285	+	0.983431i	$0.558026\pi$
$464$	−4.05953	+	2.94942i	−0.188459	+	0.136924i
$465$		0			0
$466$	14.9430	−	45.9899i	0.692222	−	2.13044i
$467$	3.67335	+	2.66885i	0.169982	+	0.123499i	0.669524	−	0.742791i	$-0.266498\pi$
$467$	3.67335	+	2.66885i	0.169982	+	0.123499i	−0.499541	+	0.866290i	$0.666498\pi$
$468$		0			0
$469$	3.92332	−	12.0747i	0.181162	−	0.557559i
$470$	6.64345	+	20.4464i	0.306440	+	0.943124i
$471$		0			0
$472$	−50.6504			−2.33138
$473$	0.761931	−	18.5973i	0.0350336	−	0.855103i
$474$		0			0
$475$	−10.0512	+	7.30266i	−0.461183	+	0.335069i
$476$	11.1838	+	34.4203i	0.512611	+	1.57765i
$477$		0			0
$478$	−14.8568	−	10.7941i	−0.679532	−	0.493709i
$479$	14.9601	+	10.8691i	0.683544	+	0.496624i	0.874532	−	0.484969i	$-0.161169\pi$
$479$	14.9601	+	10.8691i	0.683544	+	0.496624i	−0.190987	+	0.981592i	$0.561169\pi$
$480$		0			0
$481$	7.86930	+	24.2192i	0.358809	+	1.10430i
$482$	−2.80225	+	2.03595i	−0.127639	+	0.0927351i
$483$		0			0
$484$	−24.2801	+	58.0656i	−1.10364	+	2.63935i
$485$	8.96333			0.407004
$486$		0			0
$487$	8.31476	+	25.5902i	0.376778	+	1.15960i	0.942272	+	0.334850i	$0.108686\pi$
$487$	8.31476	+	25.5902i	0.376778	+	1.15960i	−0.565494	+	0.824752i	$0.691314\pi$
$488$	−2.95411	+	9.09180i	−0.133726	+	0.411567i
$489$		0			0
$490$	7.68897	+	5.58636i	0.347352	+	0.252366i
$491$	−3.85133	+	11.8532i	−0.173808	+	0.534927i	−0.999577	−	0.0290819i	$-0.990742\pi$
$491$	−3.85133	+	11.8532i	−0.173808	+	0.534927i	0.825769	+	0.564009i	$0.190742\pi$
$492$		0			0
$493$	0.780472	−	0.567046i	0.0351507	−	0.0255385i
$494$	40.7466			1.83327
$495$		0			0
$496$	47.5552			2.13529
$497$	8.37217	−	6.08274i	0.375543	−	0.272848i
$498$		0			0
$499$	8.10757	−	24.9525i	0.362945	−	1.11703i	−0.588314	−	0.808633i	$-0.700208\pi$
$499$	8.10757	−	24.9525i	0.362945	−	1.11703i	0.951258	−	0.308396i	$-0.0997920\pi$
$500$	−42.0393	−	30.5434i	−1.88006	−	1.36594i
$501$		0			0
$502$	6.28084	−	19.3304i	0.280328	−	0.862759i
$503$	−12.5927	−	38.7562i	−0.561479	−	1.72805i	−0.678189	−	0.734888i	$-0.737235\pi$
$503$	−12.5927	−	38.7562i	−0.561479	−	1.72805i	0.116710	−	0.993166i	$-0.462765\pi$
$504$		0			0
$505$	−0.397060			−0.0176689
$506$	14.7750	+	22.1928i	0.656827	+	0.986589i
$507$		0			0
$508$	63.5182	−	46.1487i	2.81816	−	2.04752i
$509$	−3.17803	−	9.78097i	−0.140864	−	0.433534i	0.855592	−	0.517650i	$-0.173193\pi$
$509$	−3.17803	−	9.78097i	−0.140864	−	0.433534i	−0.996456	+	0.0841165i	$0.973193\pi$
$510$		0			0
$511$	22.3838	+	16.2628i	0.990202	+	0.719424i
$512$	93.5809	+	67.9905i	4.13573	+	3.00479i
$513$		0			0
$514$	15.2046	+	46.7950i	0.670647	+	2.06404i
$515$	−9.86909	+	7.17032i	−0.434884	+	0.315962i
$516$		0			0
$517$	−24.4206	+	6.84313i	−1.07402	+	0.300961i
$518$	28.6866			1.26042
$519$		0			0
$520$	15.1741	+	46.7012i	0.665430	+	2.04798i
$521$	−12.9191	+	39.7610i	−0.565998	+	1.74196i	0.0989690	+	0.995091i	$0.468446\pi$
$521$	−12.9191	+	39.7610i	−0.565998	+	1.74196i	−0.664967	+	0.746873i	$0.731554\pi$
$522$		0			0
$523$	−19.2886	−	14.0140i	−0.843431	−	0.612789i	0.0798958	−	0.996803i	$-0.474541\pi$
$523$	−19.2886	−	14.0140i	−0.843431	−	0.612789i	−0.923327	+	0.384015i	$0.874541\pi$
$524$	5.18175	−	15.9478i	0.226366	−	0.696682i
$525$		0			0
$526$	20.1291	−	14.6246i	0.877669	−	0.637663i
$527$	−9.14279			−0.398266
$528$		0			0
$529$	−14.6313			−0.636143
$530$	21.2729	−	15.4556i	0.924034	−	0.671350i
$531$		0			0
$532$	10.5101	−	32.3469i	0.455672	−	1.40241i
$533$	−19.5630	−	14.2133i	−0.847366	−	0.615647i
$534$		0			0
$535$	3.16217	−	9.73216i	0.136713	−	0.420758i
$536$	21.3260	+	65.6346i	0.921141	+	2.83498i
$537$		0			0
$538$	72.6642			3.13278
$539$	−6.95584	+	8.79306i	−0.299609	+	0.378744i
$540$		0			0
$541$	−23.2756	+	16.9107i	−1.00070	+	0.727049i	−0.962238	−	0.272211i	$-0.912245\pi$
$541$	−23.2756	+	16.9107i	−1.00070	+	0.727049i	−0.0384599	+	0.999260i	$0.512245\pi$
$542$	14.0966	+	43.3849i	0.605501	+	1.86354i
$543$		0			0
$544$	−73.6248	−	53.4916i	−3.15664	−	2.29343i
$545$	−3.27845	−	2.38194i	−0.140434	−	0.102031i
$546$		0			0
$547$	−11.7295	−	36.0997i	−0.501518	−	1.54351i	−0.806547	−	0.591170i	$-0.798666\pi$
$547$	−11.7295	−	36.0997i	−0.501518	−	1.54351i	0.305029	−	0.952343i	$-0.401334\pi$
$548$	−41.4996	+	30.1512i	−1.77277	+	1.28800i
$549$		0			0
$550$	22.7358	−	28.7409i	0.969457	−	1.22552i
$551$	−0.906603			−0.0386226
$552$		0			0
$553$	−5.98083	−	18.4071i	−0.254331	−	0.782749i
$554$	9.19373	−	28.2954i	0.390604	−	1.20216i
$555$		0			0
$556$	10.4446	+	7.58841i	0.442948	+	0.321820i
$557$	−10.9582	+	33.7259i	−0.464315	+	1.42901i	0.395528	+	0.918454i	$0.370562\pi$
$557$	−10.9582	+	33.7259i	−0.464315	+	1.42901i	−0.859842	+	0.510559i	$0.829438\pi$
$558$		0			0
$559$	21.3074	−	15.4807i	0.901207	−	0.654765i
$560$	33.2884			1.40669
$561$		0			0
$562$	92.5689			3.90478
$563$	−6.01147	+	4.36759i	−0.253353	+	0.184072i	−0.707212	−	0.707002i	$-0.750047\pi$
$563$	−6.01147	+	4.36759i	−0.253353	+	0.184072i	0.453858	+	0.891074i	$0.350047\pi$
$564$		0			0
$565$	2.26290	−	6.96447i	0.0952007	−	0.292998i
$566$	−15.4149	−	11.1996i	−0.647938	−	0.470754i
$567$		0			0
$568$	−17.3827	+	53.4986i	−0.729364	+	2.24475i
$569$	−10.1946	−	31.3757i	−0.427379	−	1.31534i	−0.900698	−	0.434446i	$-0.856944\pi$
$569$	−10.1946	−	31.3757i	−0.427379	−	1.31534i	0.473319	−	0.880891i	$-0.343056\pi$
$570$		0			0
$571$	13.2029			0.552522			0.276261	−	0.961083i	$-0.410905\pi$
$571$	13.2029			0.552522			0.276261	+	0.961083i	$0.410905\pi$
$572$	−85.7542	+	24.0300i	−3.58556	+	1.00474i
$573$		0			0
$574$	−22.0374	+	16.0111i	−0.919821	+	0.668289i
$575$	−3.55462	−	10.9400i	−0.148238	−	0.456229i
$576$		0			0
$577$	−13.3192	−	9.67697i	−0.554486	−	0.402858i	0.274951	−	0.961458i	$-0.411338\pi$
$577$	−13.3192	−	9.67697i	−0.554486	−	0.402858i	−0.829437	+	0.558601i	$0.811338\pi$
$578$	−13.3666	−	9.71139i	−0.555977	−	0.403941i
$579$		0			0
$580$	−0.519061	−	1.59751i	−0.0215528	−	0.0663328i
$581$	−9.60532	+	6.97868i	−0.398496	+	0.289524i
$582$		0			0
$583$	17.1900	+	25.8202i	0.711936	+	1.06937i
$584$	−150.395			−6.22337
$585$		0			0
$586$	1.56621	+	4.82030i	0.0646995	+	0.199125i
$587$	14.1598	−	43.5794i	0.584437	−	1.79871i	−0.0170805	−	0.999854i	$-0.505437\pi$
$587$	14.1598	−	43.5794i	0.584437	−	1.79871i	0.601518	−	0.798859i	$-0.294563\pi$
$588$		0			0
$589$	6.95110	+	5.05027i	0.286415	+	0.208093i
$590$	4.25519	−	13.0961i	0.175183	−	0.539159i
$591$		0			0
$592$	−75.9168	+	55.1567i	−3.12016	+	2.26693i
$593$	27.7437			1.13930			0.569649	−	0.821888i	$-0.307079\pi$
$593$	27.7437			1.13930			0.569649	+	0.821888i	$0.307079\pi$
$594$		0			0
$595$	−6.39991			−0.262371
$596$	−25.0969	+	18.2340i	−1.02801	+	0.746893i
$597$		0			0
$598$	−11.6579	+	35.8794i	−0.476728	+	1.46722i
$599$	19.1715	+	13.9289i	0.783325	+	0.569119i	0.905975	−	0.423331i	$-0.139139\pi$
$599$	19.1715	+	13.9289i	0.783325	+	0.569119i	−0.122650	+	0.992450i	$0.539139\pi$
$600$		0			0
$601$	−8.33354	+	25.6480i	−0.339932	+	1.04620i	0.624309	+	0.781177i	$0.285381\pi$
$601$	−8.33354	+	25.6480i	−0.339932	+	1.04620i	−0.964241	+	0.265026i	$0.914619\pi$
$602$	−9.16812	−	28.2166i	−0.373665	−	1.15002i
$603$		0			0
$604$	93.7234			3.81355
$605$	−8.43864	−	7.25638i	−0.343079	−	0.295014i
$606$		0			0
$607$	6.35452	−	4.61683i	0.257922	−	0.187391i	−0.451309	−	0.892368i	$-0.649043\pi$
$607$	6.35452	−	4.61683i	0.257922	−	0.187391i	0.709230	+	0.704977i	$0.249043\pi$
$608$	26.4281	+	81.3374i	1.07180	+	3.29867i
$609$		0			0
$610$	−2.10259	−	1.52762i	−0.0851314	−	0.0618516i
$611$	−29.0328	−	21.0936i	−1.17454	−	0.853354i
$612$		0			0
$613$	−4.39908	−	13.5390i	−0.177677	−	0.546834i	0.822069	−	0.569389i	$-0.192820\pi$
$613$	−4.39908	−	13.5390i	−0.177677	−	0.546834i	−0.999746	+	0.0225548i	$0.992820\pi$
$614$	−77.1924	+	56.0835i	−3.11523	+	2.26335i
$615$		0			0
$616$	−2.67122	+	65.1993i	−0.107627	+	2.62695i
$617$	−12.3655			−0.497816			−0.248908	−	0.968527i	$-0.580072\pi$
$617$	−12.3655			−0.497816			−0.248908	+	0.968527i	$0.580072\pi$
$618$		0			0
$619$	−11.0974	−	34.1543i	−0.446042	−	1.37278i	−0.881337	−	0.472488i	$-0.843356\pi$
$619$	−11.0974	−	34.1543i	−0.446042	−	1.37278i	0.435295	−	0.900288i	$-0.356644\pi$
$620$	−4.91923	+	15.1398i	−0.197561	+	0.608031i
$621$		0			0
$622$	67.3931	+	48.9639i	2.70222	+	1.96328i
$623$	5.78248	−	17.7966i	0.231670	−	0.713008i
$624$		0			0
$625$	−8.65056	+	6.28500i	−0.346023	+	0.251400i
$626$	49.3194			1.97120
$627$		0			0
$628$	−95.5846			−3.81424
$629$	14.5955	−	10.6043i	0.581961	−	0.422819i
$630$		0			0
$631$	3.93259	−	12.1033i	0.156554	−	0.481824i	−0.841761	−	0.539850i	$-0.818481\pi$
$631$	3.93259	−	12.1033i	0.156554	−	0.481824i	0.998315	+	0.0580265i	$0.0184808\pi$
$632$	85.1122	+	61.8377i	3.38558	+	2.45977i
$633$		0			0
$634$	−20.3579	+	62.6552i	−0.808516	+	2.48836i
$635$	4.29030	+	13.2042i	0.170256	+	0.523993i
$636$		0			0
$637$	−15.8646			−0.628580
$638$	2.57496	−	0.721555i	0.101944	−	0.0285666i
$639$		0			0
$640$	−49.5223	+	35.9801i	−1.95754	+	1.42224i
$641$	−2.49118	−	7.66708i	−0.0983959	−	0.302831i	0.889728	−	0.456491i	$-0.150894\pi$
$641$	−2.49118	−	7.66708i	−0.0983959	−	0.302831i	−0.988124	+	0.153660i	$0.950894\pi$
$642$		0			0
$643$	−33.5804	−	24.3976i	−1.32428	−	0.962146i	−0.999868	−	0.0162300i	$-0.994834\pi$
$643$	−33.5804	−	24.3976i	−1.32428	−	0.962146i	−0.324412	−	0.945916i	$-0.605166\pi$
$644$	25.4760	+	18.5094i	1.00390	+	0.729374i
$645$		0			0
$646$	−8.92033	−	27.4540i	−0.350966	−	1.08016i
$647$	9.80531	−	7.12397i	0.385487	−	0.280072i	−0.378117	−	0.925758i	$-0.623428\pi$
$647$	9.80531	−	7.12397i	0.385487	−	0.280072i	0.763603	+	0.645685i	$0.223428\pi$
$648$		0			0
$649$	15.2306	+	5.64792i	0.597855	+	0.221700i
$650$	51.8550			2.03392
$651$		0			0
$652$	−4.18255	−	12.8726i	−0.163801	−	0.504128i
$653$	14.4310	−	44.4142i	0.564730	−	1.73806i	−0.104023	−	0.994575i	$-0.533171\pi$
$653$	14.4310	−	44.4142i	0.564730	−	1.73806i	0.668752	−	0.743485i	$-0.266829\pi$
$654$		0			0
$655$	2.39893	+	1.74292i	0.0937338	+	0.0681016i
$656$	27.5350	−	84.7441i	1.07506	−	3.30870i
$657$		0			0
$658$	−32.7050	+	23.7616i	−1.27497	+	0.926322i
$659$	−27.3622			−1.06588			−0.532940	−	0.846153i	$-0.678913\pi$
$659$	−27.3622			−1.06588			−0.532940	+	0.846153i	$0.678913\pi$
$660$		0			0
$661$	−7.52929			−0.292855			−0.146428	−	0.989221i	$-0.546778\pi$
$661$	−7.52929			−0.292855			−0.146428	+	0.989221i	$0.546778\pi$
$662$	15.9487	−	11.5874i	0.619865	−	0.450358i
$663$		0			0
$664$	19.9431	−	61.3785i	0.773942	−	2.38195i
$665$	4.86574	+	3.53517i	0.188685	+	0.137088i
$666$		0			0
$667$	0.259387	−	0.798311i	0.0100435	−	0.0309107i
$668$	14.3055	+	44.0279i	0.553497	+	1.70349i
$669$		0			0
$670$	−18.7620			−0.724840
$671$	1.90211	−	2.40451i	0.0734302	−	0.0928251i
$672$		0			0
$673$	−5.10467	+	3.70876i	−0.196770	+	0.142962i	−0.681808	−	0.731531i	$-0.738806\pi$
$673$	−5.10467	+	3.70876i	−0.196770	+	0.142962i	0.485037	+	0.874493i	$0.338806\pi$
$674$	−29.1283	−	89.6477i	−1.12198	−	3.45310i
$675$		0			0
$676$	−41.7747	−	30.3511i	−1.60672	−	1.16735i
$677$	29.6943	+	21.5742i	1.14125	+	0.829164i	0.987292	−	0.158914i	$-0.0507993\pi$
$677$	29.6943	+	21.5742i	1.14125	+	0.829164i	0.153954	+	0.988078i	$0.450799\pi$
$678$		0			0
$679$	5.20831	+	16.0295i	0.199877	+	0.615157i
$680$	28.1441	−	20.4479i	1.07928	−	0.784141i
$681$		0			0
$682$	−23.7622	−	8.81165i	−0.909902	−	0.337416i
$683$	−25.8794			−0.990246			−0.495123	−	0.868823i	$-0.664877\pi$
$683$	−25.8794			−0.990246			−0.495123	+	0.868823i	$0.664877\pi$
$684$		0			0
$685$	−2.80307	−	8.62696i	−0.107100	−	0.329619i
$686$	−16.9582	+	52.1919i	−0.647467	+	1.99270i
$687$		0			0
$688$	78.5158	+	57.0451i	2.99339	+	2.17482i
$689$	−13.5635	+	41.7440i	−0.516727	+	1.59032i
$690$		0			0
$691$	−19.8993	+	14.4577i	−0.757005	+	0.549997i	−0.897990	−	0.440015i	$-0.854973\pi$
$691$	−19.8993	+	14.4577i	−0.757005	+	0.549997i	0.140985	+	0.990012i	$0.454973\pi$
$692$	100.371			3.81554
$693$		0			0
$694$	68.0781			2.58421
$695$	−1.84695	+	1.34189i	−0.0700588	+	0.0509007i
$696$		0			0
$697$	−5.29379	+	16.2926i	−0.200517	+	0.617127i
$698$	−14.4268	−	10.4817i	−0.546064	−	0.396738i
$699$		0			0
$700$	13.3754	−	41.1654i	0.505544	−	1.55591i
$701$	3.20455	+	9.86258i	0.121034	+	0.372505i	0.993158	−	0.116781i	$-0.0372576\pi$
$701$	3.20455	+	9.86258i	0.121034	+	0.372505i	−0.872124	+	0.489286i	$0.837258\pi$
$702$		0			0
$703$	−16.9542			−0.639441
$704$	−76.2270	−	114.497i	−2.87291	−	4.31527i
$705$		0			0
$706$	−23.6660	+	17.1943i	−0.890681	+	0.647118i
$707$	−0.230719	−	0.710080i	−0.00867708	−	0.0267053i
$708$		0			0
$709$	−17.6194	−	12.8012i	−0.661710	−	0.480760i	0.205530	−	0.978651i	$-0.434108\pi$
$709$	−17.6194	−	12.8012i	−0.661710	−	0.480760i	−0.867240	+	0.497891i	$0.834108\pi$
$710$	−12.3722	−	8.98893i	−0.464320	−	0.337348i
$711$		0			0
$712$	31.4318	+	96.7372i	1.17796	+	3.62538i
$713$	−6.43579	+	4.67588i	−0.241022	+	0.175113i
$714$		0			0
$715$	0.644671	−	15.7352i	0.0241093	−	0.588461i
$716$	60.9452			2.27763
$717$		0			0
$718$	14.4746	+	44.5483i	0.540188	+	1.66253i
$719$	−4.36421	+	13.4316i	−0.162757	+	0.500916i	−0.998864	−	0.0476511i	$-0.984826\pi$
$719$	−4.36421	+	13.4316i	−0.162757	+	0.500916i	0.836107	+	0.548567i	$0.184826\pi$
$720$		0			0
$721$	−18.5576	−	13.4829i	−0.691122	−	0.502129i
$722$	7.93212	−	24.4126i	0.295203	−	0.908541i
$723$		0			0
$724$	19.3821	−	14.0819i	0.720329	−	0.523350i
$725$	−1.15376			−0.0428497
$726$		0			0
$727$	35.1684			1.30432			0.652162	−	0.758079i	$-0.273862\pi$
$727$	35.1684			1.30432			0.652162	+	0.758079i	$0.273862\pi$
$728$	−74.7007	+	54.2732i	−2.76859	+	2.01150i
$729$		0			0
$730$	12.6348	−	38.8858i	0.467634	−	1.43923i
$731$	−15.0952	−	10.9673i	−0.558315	−	0.405640i
$732$		0			0
$733$	−0.250844	+	0.772018i	−0.00926513	+	0.0285151i	−0.955582	−	0.294725i	$-0.904772\pi$
$733$	−0.250844	+	0.772018i	−0.00926513	+	0.0285151i	0.946317	+	0.323240i	$0.104772\pi$
$734$	9.09840	+	28.0020i	0.335828	+	1.03357i
$735$		0			0
$736$	−79.1831			−2.91873
$737$	0.906030	−	22.1144i	0.0333740	−	0.814595i
$738$		0			0
$739$	35.3182	−	25.6601i	1.29920	−	0.943924i	0.299252	−	0.954174i	$-0.403263\pi$
$739$	35.3182	−	25.6601i	1.29920	−	0.943924i	0.999947	+	0.0102505i	$0.00326289\pi$
$740$	−9.70688	−	29.8747i	−0.356832	−	1.09822i
$741$		0			0
$742$	40.0010	+	29.0624i	1.46848	+	1.06691i
$743$	−1.50387	−	1.09263i	−0.0551717	−	0.0400846i	0.559858	−	0.828589i	$-0.310856\pi$
$743$	−1.50387	−	1.09263i	−0.0551717	−	0.0400846i	−0.615029	+	0.788504i	$0.710856\pi$
$744$		0			0
$745$	−1.69516	−	5.21717i	−0.0621059	−	0.191142i
$746$	25.5039	−	18.5296i	0.933763	−	0.678418i
$747$		0			0
$748$	34.9643	+	52.5182i	1.27842	+	1.92026i
$749$	19.2419			0.703084
$750$		0			0
$751$	10.8540	+	33.4053i	0.396069	+	1.21898i	0.928126	+	0.372267i	$0.121419\pi$
$751$	10.8540	+	33.4053i	0.396069	+	1.21898i	−0.532056	+	0.846709i	$0.678581\pi$
$752$	40.8639	−	125.766i	1.49015	−	4.58622i
$753$		0			0
$754$	3.06128	+	2.22415i	0.111485	+	0.0809988i
$755$	−5.12148	+	15.7623i	−0.186390	+	0.573649i
$756$		0			0
$757$	10.1287	−	7.35892i	0.368133	−	0.267464i	−0.388303	−	0.921532i	$-0.626939\pi$
$757$	10.1287	−	7.35892i	0.368133	−	0.267464i	0.756436	+	0.654067i	$0.226939\pi$
$758$	28.4617			1.03377
$759$		0			0
$760$	−32.6924			−1.18588
$761$	−40.4571	+	29.3938i	−1.46657	+	1.06552i	−0.484977	+	0.874527i	$0.661172\pi$
$761$	−40.4571	+	29.3938i	−1.46657	+	1.06552i	−0.981591	+	0.190997i	$0.938828\pi$
$762$		0			0
$763$	2.35472	−	7.24707i	0.0852465	−	0.262362i
$764$	−44.2288	−	32.1341i	−1.60014	−	1.16257i
$765$		0			0
$766$	26.2427	−	80.7668i	0.948189	−	2.91822i
$767$	7.10295	+	21.8606i	0.256473	+	0.789341i
$768$		0			0
$769$	−32.2170			−1.16178			−0.580888	−	0.813983i	$-0.697295\pi$
$769$	−32.2170			−1.16178			−0.580888	+	0.813983i	$0.697295\pi$
$770$	−16.6334	−	6.16812i	−0.599428	−	0.222284i
$771$		0			0
$772$	68.4011	−	49.6963i	2.46181	−	1.78861i
$773$	9.79338	+	30.1409i	0.352243	+	1.08409i	0.957591	+	0.288132i	$0.0930343\pi$
$773$	9.79338	+	30.1409i	0.352243	+	1.08409i	−0.605347	+	0.795962i	$0.706966\pi$
$774$		0			0
$775$	8.84614	+	6.42709i	0.317763	+	0.230868i
$776$	−74.1187	−	53.8504i	−2.66070	−	1.93312i
$777$		0			0
$778$	−8.35560	−	25.7159i	−0.299563	−	0.921959i
$779$	13.0244	−	9.46282i	0.466649	−	0.339041i
$780$		0			0
$781$	11.1925	−	14.1488i	0.400500	−	0.506283i
$782$	26.7268			0.955749
$783$		0			0
$784$	−18.0650	−	55.5985i	−0.645180	−	1.98566i
$785$	5.22319	−	16.0753i	0.186424	−	0.573753i
$786$		0			0
$787$	−16.4620	−	11.9603i	−0.586806	−	0.426340i	0.254365	−	0.967108i	$-0.418134\pi$
$787$	−16.4620	−	11.9603i	−0.586806	−	0.426340i	−0.841171	+	0.540768i	$0.818134\pi$
$788$	5.15509	−	15.8657i	0.183642	−	0.565193i
$789$		0			0
$790$	−23.1390	+	16.8115i	−0.823250	+	0.598126i
$791$	13.7698			0.489597
$792$		0			0
$793$	4.33827			0.154057
$794$	−3.30230	+	2.39926i	−0.117194	+	0.0851465i
$795$		0			0
$796$	26.9945	−	83.0805i	0.956795	−	2.94471i
$797$	2.19279	+	1.59316i	0.0776726	+	0.0564325i	0.625944	−	0.779868i	$-0.284714\pi$
$797$	2.19279	+	1.59316i	0.0776726	+	0.0564325i	−0.548271	+	0.836301i	$0.684714\pi$
$798$		0			0
$799$	−7.85636	+	24.1794i	−0.277938	+	0.855405i
$800$	33.6330	+	103.512i	1.18911	+	3.65970i
$801$		0			0
$802$	−46.1144			−1.62836
$803$	45.2238	+	16.7702i	1.59591	+	0.591807i
$804$		0			0
$805$	−4.50503	+	3.27309i	−0.158781	+	0.115361i
$806$	−11.0817	−	34.1060i	−0.390337	−	1.20133i
$807$		0			0
$808$	3.28333	+	2.38548i	0.115507	+	0.0839208i
$809$	15.8615	+	11.5240i	0.557659	+	0.405163i	0.830602	−	0.556867i	$-0.187997\pi$
$809$	15.8615	+	11.5240i	0.557659	+	0.405163i	−0.272942	+	0.962030i	$0.587997\pi$
$810$		0			0
$811$	−1.78087	−	5.48096i	−0.0625348	−	0.192462i	0.914908	−	0.403662i	$-0.132263\pi$
$811$	−1.78087	−	5.48096i	−0.0625348	−	0.192462i	−0.977443	+	0.211200i	$0.932263\pi$
$812$	2.55528	−	1.85652i	0.0896728	−	0.0651511i
$813$		0			0
$814$	48.1540	−	13.4937i	1.68780	−	0.472954i
$815$	2.39345			0.0838388
$816$		0			0
$817$	5.41851	+	16.6765i	0.189570	+	0.583436i
$818$	−10.3205	+	31.7634i	−0.360849	+	1.11058i
$819$		0			0
$820$	24.1312	+	17.5323i	0.842697	+	0.612255i
$821$	−0.251287	+	0.773382i	−0.00876998	+	0.0269912i	−0.955346	−	0.295490i	$-0.904517\pi$
$821$	−0.251287	+	0.773382i	−0.00876998	+	0.0269912i	0.946576	+	0.322481i	$0.104517\pi$
$822$		0			0
$823$	−14.0175	+	10.1843i	−0.488618	+	0.355002i	−0.804652	−	0.593746i	$-0.797648\pi$
$823$	−14.0175	+	10.1843i	−0.488618	+	0.355002i	0.316035	+	0.948748i	$0.397648\pi$
$824$	124.687			4.34367
$825$		0			0
$826$	25.8929			0.900930
$827$	−7.87026	+	5.71808i	−0.273676	+	0.198837i	−0.716154	−	0.697942i	$-0.754099\pi$
$827$	−7.87026	+	5.71808i	−0.273676	+	0.198837i	0.442478	+	0.896779i	$0.354099\pi$
$828$		0			0
$829$	−7.32844	+	22.5546i	−0.254527	+	0.783355i	0.739395	+	0.673272i	$0.235112\pi$
$829$	−7.32844	+	22.5546i	−0.254527	+	0.783355i	−0.993922	+	0.110083i	$0.964888\pi$
$830$	14.1945	+	10.3129i	0.492699	+	0.357967i
$831$		0			0
$832$	60.1457	−	185.109i	2.08518	−	6.41751i
$833$	3.47312	+	10.6892i	0.120337	+	0.370358i
$834$		0			0
$835$	−8.18628			−0.283298
$836$	2.42716	−	59.2421i	0.0839449	−	2.04893i
$837$		0			0
$838$	−1.23371	+	0.896340i	−0.0426177	+	0.0309636i
$839$	1.47602	+	4.54271i	0.0509577	+	0.156832i	0.973297	−	0.229549i	$-0.0737251\pi$
$839$	1.47602	+	4.54271i	0.0509577	+	0.156832i	−0.922339	+	0.386381i	$0.873725\pi$
$840$		0			0
$841$	23.3934	+	16.9963i	0.806668	+	0.586079i
$842$	−5.96867	−	4.33649i	−0.205694	−	0.149445i
$843$		0			0
$844$	26.4487	+	81.4007i	0.910401	+	2.80193i
$845$	7.38719	−	5.36710i	0.254127	−	0.184634i
$846$		0			0
$847$	8.07348	−	19.3076i	0.277408	−	0.663418i
$848$	−161.739			−5.55414
$849$		0			0
$850$	−11.3522	−	34.9386i	−0.389378	−	1.19838i
$851$	4.85075	−	14.9291i	0.166282	−	0.511762i
$852$		0			0
$853$	27.0953	+	19.6859i	0.927726	+	0.674033i	0.945435	−	0.325810i	$-0.105637\pi$
$853$	27.0953	+	19.6859i	0.927726	+	0.674033i	−0.0177086	+	0.999843i	$0.505637\pi$
$854$	1.51016	−	4.64781i	0.0516767	−	0.159045i
$855$		0			0
$856$	−84.6177	+	61.4783i	−2.89217	+	2.10129i
$857$	−11.0816			−0.378541			−0.189270	−	0.981925i	$-0.560612\pi$
$857$	−11.0816			−0.378541			−0.189270	+	0.981925i	$0.560612\pi$
$858$		0			0
$859$	−23.9536			−0.817286			−0.408643	−	0.912694i	$-0.633998\pi$
$859$	−23.9536			−0.817286			−0.408643	+	0.912694i	$0.633998\pi$
$860$	−26.2830	+	19.0957i	−0.896242	+	0.651158i
$861$		0			0
$862$	−34.5854	+	106.443i	−1.17798	+	3.62546i
$863$	41.9183	+	30.4554i	1.42692	+	1.03671i	0.990581	+	0.136930i	$0.0437237\pi$
$863$	41.9183	+	30.4554i	1.42692	+	1.03671i	0.436335	+	0.899784i	$0.356276\pi$
$864$		0			0
$865$	−5.48474	+	16.8803i	−0.186487	+	0.573948i
$866$	24.5253	+	75.4811i	0.833404	+	2.56495i
$867$		0			0
$868$	−29.9337			−1.01601
$869$	−18.6980	−	28.0853i	−0.634285	−	0.952730i
$870$		0			0
$871$	25.3371	−	18.4085i	0.858515	−	0.623748i
$872$	12.7995	+	39.3929i	0.433447	+	1.33401i
$873$		0			0
$874$	−20.3199	−	14.7633i	−0.687331	−	0.499375i
$875$	13.9787	+	10.1561i	0.472566	+	0.343339i
$876$		0			0
$877$	4.84010	+	14.8963i	0.163438	+	0.503012i	0.998918	−	0.0465099i	$-0.0148099\pi$
$877$	4.84010	+	14.8963i	0.163438	+	0.503012i	−0.835479	+	0.549522i	$0.814810\pi$
$878$	−30.2506	+	21.9783i	−1.02091	+	0.741732i
$879$		0			0
$880$	55.8788	−	15.6583i	1.88367	−	0.527842i
$881$	31.7893			1.07101			0.535505	−	0.844532i	$-0.320121\pi$
$881$	31.7893			1.07101			0.535505	+	0.844532i	$0.320121\pi$
$882$		0			0
$883$	−10.8063	−	33.2584i	−0.363661	−	1.11923i	−0.950815	−	0.309759i	$-0.899752\pi$
$883$	−10.8063	−	33.2584i	−0.363661	−	1.11923i	0.587154	−	0.809475i	$-0.300248\pi$
$884$	−27.5880	+	84.9071i	−0.927884	+	2.85573i
$885$		0			0
$886$	−67.5537	−	49.0806i	−2.26951	−	1.64890i
$887$	−8.84224	+	27.2136i	−0.296893	+	0.913744i	0.685685	+	0.727898i	$0.259503\pi$
$887$	−8.84224	+	27.2136i	−0.296893	+	0.913744i	−0.982579	+	0.185846i	$0.940497\pi$
$888$		0			0
$889$	−21.1207	+	15.3451i	−0.708365	+	0.514658i
$890$	−27.6529			−0.926927
$891$		0			0
$892$	−144.553			−4.83999
$893$	19.3292	−	14.0435i	0.646827	−	0.469947i
$894$		0			0
$895$	−3.33033	+	10.2497i	−0.111321	+	0.342610i
$896$	−93.1206	−	67.6561i	−3.11094	−	2.26023i
$897$		0			0
$898$	29.3533	−	90.3402i	0.979533	−	3.01469i
$899$	0.246566	+	0.758852i	0.00822344	+	0.0253091i
$900$		0			0
$901$	31.0954			1.03594
$902$	−29.4611	+	37.2426i	−0.980949	+	1.24004i
$903$		0			0
$904$	−60.5536	+	43.9948i	−2.01398	+	1.46324i
$905$	1.30915	+	4.02916i	0.0435177	+	0.133934i
$906$		0			0
$907$	−4.21846	−	3.06489i	−0.140072	−	0.101768i	0.515543	−	0.856864i	$-0.327590\pi$
$907$	−4.21846	−	3.06489i	−0.140072	−	0.101768i	−0.655614	+	0.755096i	$0.727590\pi$
$908$	−5.59296	−	4.06352i	−0.185609	−	0.134853i
$909$		0			0
$910$	−7.75715	−	23.8741i	−0.257147	−	0.791418i
$911$	−7.70392	+	5.59722i	−0.255242	+	0.185444i	−0.708047	−	0.706165i	$-0.750423\pi$
$911$	−7.70392	+	5.59722i	−0.255242	+	0.185444i	0.452805	+	0.891610i	$0.350423\pi$
$912$		0			0
$913$	−12.8411	+	16.2328i	−0.424978	+	0.537227i
$914$	−20.0126			−0.661959
$915$		0			0
$916$	−42.5362	−	130.913i	−1.40544	−	4.32549i
$917$	−1.72301	+	5.30286i	−0.0568986	+	0.175116i
$918$		0			0
$919$	15.5358	+	11.2874i	0.512479	+	0.372338i	0.813763	−	0.581196i	$-0.197415\pi$
$919$	15.5358	+	11.2874i	0.512479	+	0.372338i	−0.301284	+	0.953534i	$0.597415\pi$
$920$	9.35358	−	28.7873i	0.308378	−	0.949091i
$921$		0			0
$922$	−78.4178	+	56.9739i	−2.58255	+	1.87634i
$923$	25.5275			0.840249
$924$		0			0
$925$	−21.5764			−0.709427
$926$	−17.5385	+	12.7425i	−0.576352	+	0.418744i
$927$		0			0
$928$	−2.45426	+	7.55345i	−0.0805651	+	0.247954i
$929$	−26.1692	−	19.0131i	−0.858585	−	0.623799i	0.0689145	−	0.997623i	$-0.478046\pi$
$929$	−26.1692	−	19.0131i	−0.858585	−	0.623799i	−0.927500	+	0.373824i	$0.878046\pi$
$930$		0			0
$931$	3.26390	−	10.0453i	0.106970	−	0.329220i
$932$	−30.7682	−	94.6948i	−1.00785	−	3.10183i
$933$		0			0
$934$	12.6171			0.412843
$935$	−10.7431	+	3.01041i	−0.351336	+	0.0984511i
$936$		0			0
$937$	39.7056	−	28.8478i	1.29712	−	0.942416i	0.297201	−	0.954815i	$-0.403947\pi$
$937$	39.7056	−	28.8478i	1.29712	−	0.942416i	0.999923	+	0.0123990i	$0.00394683\pi$
$938$	−10.9020	−	33.5530i	−0.355963	−	1.09554i
$939$		0			0
$940$	35.8123	+	26.0192i	1.16807	+	0.848653i
$941$	20.9186	+	15.1982i	0.681926	+	0.495448i	0.873996	−	0.485933i	$-0.161520\pi$
$941$	20.9186	+	15.1982i	0.681926	+	0.495448i	−0.192070	+	0.981381i	$0.561520\pi$
$942$		0			0
$943$	4.60609	+	14.1761i	0.149995	+	0.461637i
$944$	−68.5236	+	49.7853i	−2.23025	+	1.62037i
$945$		0			0
$946$	−28.6625	−	43.0526i	−0.931897	−	1.39976i
$947$	−25.5713			−0.830956			−0.415478	−	0.909603i	$-0.636386\pi$
$947$	−25.5713			−0.830956			−0.415478	+	0.909603i	$0.636386\pi$
$948$		0			0
$949$	21.0905	+	64.9100i	0.684628	+	2.10707i
$950$	−10.6684	+	32.8339i	−0.346128	+	1.06527i
$951$		0			0
$952$	52.9215	+	38.4497i	1.71520	+	1.24616i
$953$	−9.88494	+	30.4227i	−0.320205	+	0.985489i	0.653354	+	0.757052i	$0.273361\pi$
$953$	−9.88494	+	30.4227i	−0.320205	+	0.985489i	−0.973559	+	0.228436i	$0.926639\pi$
$954$		0			0
$955$	7.82115	−	5.68240i	0.253086	−	0.183878i
$956$	−37.8120			−1.22293
$957$		0			0
$958$	51.3843			1.66015
$959$	13.7992	−	10.0257i	0.445600	−	0.323747i
$960$		0			0
$961$	−7.24278	+	22.2910i	−0.233638	+	0.719064i
$962$	57.2486	+	41.5935i	1.84577	+	1.34103i
$963$		0			0
$964$	−2.20392	+	6.78296i	−0.0709834	+	0.218464i
$965$	4.62012	+	14.2193i	0.148727	+	0.457734i
$966$		0			0
$967$	43.4784			1.39817			0.699086	−	0.715038i	$-0.253590\pi$
$967$	43.4784			1.39817			0.699086	+	0.715038i	$0.253590\pi$
$968$	26.1847	+	110.702i	0.841608	+	3.55809i
$969$		0			0
$970$	20.1503	−	14.6400i	0.646986	−	0.470063i
$971$	13.1341	+	40.4227i	0.421494	+	1.29723i	0.906312	+	0.422610i	$0.138886\pi$
$971$	13.1341	+	40.4227i	0.421494	+	1.29723i	−0.484817	+	0.874615i	$0.661114\pi$
$972$		0			0
$973$	−3.47296	−	2.52326i	−0.111338	−	0.0808919i
$974$	60.4893	+	43.9480i	1.93820	+	1.40819i
$975$		0			0
$976$	4.93998	+	15.2037i	0.158125	+	0.486659i
$977$	−26.2766	+	19.0911i	−0.840663	+	0.610777i	−0.922556	−	0.385864i	$-0.873903\pi$
$977$	−26.2766	+	19.0911i	−0.840663	+	0.610777i	0.0818930	+	0.996641i	$0.473903\pi$
$978$		0			0
$979$	1.33538	−	32.5939i	0.0426788	−	1.04171i
$980$	19.5692			0.625116
$981$		0			0
$982$	10.7020	+	32.9374i	0.341514	+	1.05107i
$983$	15.0645	−	46.3639i	0.480484	−	1.47878i	−0.357932	−	0.933748i	$-0.616518\pi$
$983$	15.0645	−	46.3639i	0.480484	−	1.47878i	0.838416	−	0.545031i	$-0.183482\pi$
$984$		0			0
$985$	2.38658	+	1.73395i	0.0760428	+	0.0552484i
$986$	0.828392	−	2.54953i	0.0263814	−	0.0811935i
$987$		0			0
$988$	67.8754	−	49.3144i	2.15940	−	1.56890i
$989$	−16.2348			−0.516236
$990$		0			0
$991$	13.3966			0.425557			0.212778	−	0.977100i	$-0.431749\pi$
$991$	13.3966			0.425557			0.212778	+	0.977100i	$0.431749\pi$
$992$	60.8941	−	44.2422i	1.93339	−	1.40469i
$993$		0			0
$994$	8.88620	−	27.3489i	0.281853	−	0.867455i
$995$	12.4973	+	9.07981i	0.396191	+	0.287849i
$996$		0			0
$997$	−3.75644	+	11.5611i	−0.118968	+	0.366145i	−0.992754	−	0.120165i	$-0.961658\pi$
$997$	−3.75644	+	11.5611i	−0.118968	+	0.366145i	0.873786	+	0.486310i	$0.161658\pi$
$998$	−22.5291	−	69.3375i	−0.713147	−	2.19484i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.d.190.4	yes	16
3.2	odd	2		297.2.f.a.190.1	yes	16
9.2	odd	6		891.2.n.i.190.4		32
9.4	even	3		891.2.n.f.784.4		32
9.5	odd	6		891.2.n.i.784.1		32
9.7	even	3		891.2.n.f.190.1		32
11.2	odd	10		3267.2.a.bl.1.8		8
11.4	even	5	inner	297.2.f.d.136.4	yes	16
11.9	even	5		3267.2.a.be.1.1		8
33.2	even	10		3267.2.a.bf.1.1		8
33.20	odd	10		3267.2.a.bm.1.8		8
33.26	odd	10		297.2.f.a.136.1	✓	16
99.4	even	15		891.2.n.f.136.1		32
99.59	odd	30		891.2.n.i.136.4		32
99.70	even	15		891.2.n.f.433.4		32
99.92	odd	30		891.2.n.i.433.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.136.1	✓	16	33.26	odd	10
297.2.f.a.190.1	yes	16	3.2	odd	2
297.2.f.d.136.4	yes	16	11.4	even	5	inner
297.2.f.d.190.4	yes	16	1.1	even	1	trivial
891.2.n.f.136.1		32	99.4	even	15
891.2.n.f.190.1		32	9.7	even	3
891.2.n.f.433.4		32	99.70	even	15
891.2.n.f.784.4		32	9.4	even	3
891.2.n.i.136.4		32	99.59	odd	30
891.2.n.i.190.4		32	9.2	odd	6
891.2.n.i.433.1		32	99.92	odd	30
891.2.n.i.784.1		32	9.5	odd	6
3267.2.a.be.1.1		8	11.9	even	5
3267.2.a.bf.1.1		8	33.2	even	10
3267.2.a.bl.1.8		8	11.2	odd	10
3267.2.a.bm.1.8		8	33.20	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.24808 - 1.63332i) q^{2} +(1.76807 - 5.44156i) q^{4} +(0.818541 + 0.594705i) q^{5} +(-0.587909 + 1.80940i) q^{7} +(-3.19570 - 9.83534i) q^{8} +O(q^{10})\)	\(q+(2.24808 - 1.63332i) q^{2} +(1.76807 - 5.44156i) q^{4} +(0.818541 + 0.594705i) q^{5} +(-0.587909 + 1.80940i) q^{7} +(-3.19570 - 9.83534i) q^{8} +2.81149 q^{10} +(-0.135769 + 3.31384i) q^{11} +(-3.79677 + 2.75851i) q^{13} +(1.63367 + 5.02791i) q^{14} +(-13.9907 - 10.1649i) q^{16} +(2.68981 + 1.95426i) q^{17} +(-0.965525 - 2.97158i) q^{19} +(4.68336 - 3.40266i) q^{20} +(5.10736 + 7.67153i) q^{22} +2.89287 q^{23} +(-1.22875 - 3.78170i) q^{25} +(-4.02988 + 12.4027i) q^{26} +(8.80648 + 6.39829i) q^{28} +(0.0896641 - 0.275958i) q^{29} +(-2.22471 + 1.61634i) q^{31} -27.3718 q^{32} +9.23884 q^{34} +(-1.55728 + 1.13143i) q^{35} +(1.67679 - 5.16064i) q^{37} +(-7.02413 - 5.10333i) q^{38} +(3.23332 - 9.95112i) q^{40} +(1.59222 + 4.90035i) q^{41} -5.61199 q^{43} +(17.7924 + 6.59791i) q^{44} +(6.50340 - 4.72500i) q^{46} +(2.36297 + 7.27246i) q^{47} +(2.73484 + 1.98698i) q^{49} +(-8.93907 - 6.49461i) q^{50} +(8.29767 + 25.5376i) q^{52} +(7.56640 - 5.49731i) q^{53} +(-2.08189 + 2.63177i) q^{55} +19.6748 q^{56} +(-0.249156 - 0.766824i) q^{58} +(1.51350 - 4.65807i) q^{59} +(-0.747856 - 0.543349i) q^{61} +(-2.36130 + 7.26733i) q^{62} +(-33.5524 + 24.3772i) q^{64} -4.74831 q^{65} -6.67334 q^{67} +(15.3900 - 11.1815i) q^{68} +(-1.65290 + 5.08710i) q^{70} +(-4.40059 - 3.19721i) q^{71} +(4.49398 - 13.8311i) q^{73} +(-4.65944 - 14.3403i) q^{74} -17.8772 q^{76} +(-5.91624 - 2.19390i) q^{77} +(-8.23017 + 5.97957i) q^{79} +(-5.40689 - 16.6407i) q^{80} +(11.5833 + 8.41575i) q^{82} +(5.04876 + 3.66814i) q^{83} +(1.03951 + 3.19929i) q^{85} +(-12.6162 + 9.16619i) q^{86} +(33.0267 - 9.25471i) q^{88} -9.83568 q^{89} +(-2.75909 - 8.49161i) q^{91} +(5.11481 - 15.7418i) q^{92} +(17.1904 + 12.4896i) q^{94} +(0.976891 - 3.00656i) q^{95} +(7.16712 - 5.20722i) q^{97} +9.39350 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7}+O(q^{10}) \) 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7	\( 16 q + 2 q^{2} - 4 q^{4} + q^{5} - 2 q^{7} + 6 q^{10} + 13 q^{11} - 2 q^{13} - 22 q^{14} - 24 q^{16} - 2 q^{17} - 2 q^{19} + 15 q^{22} + 14 q^{23} - 19 q^{25} + 21 q^{26} + 15 q^{28} + q^{29} + 14 q^{31} - 48 q^{32} + 10 q^{34} - 18 q^{35} + 9 q^{37} + 11 q^{38} + 33 q^{40} + 25 q^{41} + 14 q^{43} + 14 q^{44} + 4 q^{46} - 28 q^{47} - 4 q^{49} - 63 q^{50} + 10 q^{52} + q^{53} - 40 q^{55} + 96 q^{56} - 20 q^{58} + 41 q^{59} - 5 q^{62} - 92 q^{64} - 60 q^{65} - 48 q^{67} + 25 q^{68} - 31 q^{70} + 3 q^{71} - 13 q^{73} + 29 q^{74} - 58 q^{76} - 2 q^{77} - 83 q^{80} + 41 q^{82} - 14 q^{83} - 10 q^{85} - 56 q^{86} + 86 q^{88} + 82 q^{89} + 14 q^{91} + 74 q^{92} - 2 q^{94} - 56 q^{95} + 12 q^{97} + 26 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 4 * q^4 + q^5 - 2 * q^7 + 6 * q^10 + 13 * q^11 - 2 * q^13 - 22 * q^14 - 24 * q^16 - 2 * q^17 - 2 * q^19 + 15 * q^22 + 14 * q^23 - 19 * q^25 + 21 * q^26 + 15 * q^28 + q^29 + 14 * q^31 - 48 * q^32 + 10 * q^34 - 18 * q^35 + 9 * q^37 + 11 * q^38 + 33 * q^40 + 25 * q^41 + 14 * q^43 + 14 * q^44 + 4 * q^46 - 28 * q^47 - 4 * q^49 - 63 * q^50 + 10 * q^52 + q^53 - 40 * q^55 + 96 * q^56 - 20 * q^58 + 41 * q^59 - 5 * q^62 - 92 * q^64 - 60 * q^65 - 48 * q^67 + 25 * q^68 - 31 * q^70 + 3 * q^71 - 13 * q^73 + 29 * q^74 - 58 * q^76 - 2 * q^77 - 83 * q^80 + 41 * q^82 - 14 * q^83 - 10 * q^85 - 56 * q^86 + 86 * q^88 + 82 * q^89 + 14 * q^91 + 74 * q^92 - 2 * q^94 - 56 * q^95 + 12 * q^97 + 26 * q^98

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