LMFDB - Embedded newform 297.2.f.a.190.1

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			190.1
Root			$-1.43906 - 1.04554i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.a.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24808 + 1.63332i) q^{2} +(1.76807 - 5.44156i) q^{4} +(-0.818541 - 0.594705i) q^{5} +(-0.587909 + 1.80940i) q^{7} +(3.19570 + 9.83534i) q^{8} +O(q^{10})$	\(q+(-2.24808 + 1.63332i) q^{2} +(1.76807 - 5.44156i) q^{4} +(-0.818541 - 0.594705i) q^{5} +(-0.587909 + 1.80940i) q^{7} +(3.19570 + 9.83534i) q^{8} +2.81149 q^{10} +(0.135769 - 3.31384i) q^{11} +(-3.79677 + 2.75851i) q^{13} +(-1.63367 - 5.02791i) q^{14} +(-13.9907 - 10.1649i) q^{16} +(-2.68981 - 1.95426i) q^{17} +(-0.965525 - 2.97158i) q^{19} +(-4.68336 + 3.40266i) q^{20} +(5.10736 + 7.67153i) q^{22} -2.89287 q^{23} +(-1.22875 - 3.78170i) q^{25} +(4.02988 - 12.4027i) q^{26} +(8.80648 + 6.39829i) q^{28} +(-0.0896641 + 0.275958i) q^{29} +(-2.22471 + 1.61634i) q^{31} +27.3718 q^{32} +9.23884 q^{34} +(1.55728 - 1.13143i) q^{35} +(1.67679 - 5.16064i) q^{37} +(7.02413 + 5.10333i) q^{38} +(3.23332 - 9.95112i) q^{40} +(-1.59222 - 4.90035i) q^{41} -5.61199 q^{43} +(-17.7924 - 6.59791i) q^{44} +(6.50340 - 4.72500i) q^{46} +(-2.36297 - 7.27246i) q^{47} +(2.73484 + 1.98698i) q^{49} +(8.93907 + 6.49461i) q^{50} +(8.29767 + 25.5376i) q^{52} +(-7.56640 + 5.49731i) q^{53} +(-2.08189 + 2.63177i) q^{55} -19.6748 q^{56} +(-0.249156 - 0.766824i) q^{58} +(-1.51350 + 4.65807i) q^{59} +(-0.747856 - 0.543349i) q^{61} +(2.36130 - 7.26733i) q^{62} +(-33.5524 + 24.3772i) q^{64} +4.74831 q^{65} -6.67334 q^{67} +(-15.3900 + 11.1815i) q^{68} +(-1.65290 + 5.08710i) q^{70} +(4.40059 + 3.19721i) q^{71} +(4.49398 - 13.8311i) q^{73} +(4.65944 + 14.3403i) q^{74} -17.8772 q^{76} +(5.91624 + 2.19390i) q^{77} +(-8.23017 + 5.97957i) q^{79} +(5.40689 + 16.6407i) q^{80} +(11.5833 + 8.41575i) q^{82} +(-5.04876 - 3.66814i) q^{83} +(1.03951 + 3.19929i) q^{85} +(12.6162 - 9.16619i) q^{86} +(33.0267 - 9.25471i) q^{88} +9.83568 q^{89} +(-2.75909 - 8.49161i) q^{91} +(-5.11481 + 15.7418i) q^{92} +(17.1904 + 12.4896i) q^{94} +(-0.976891 + 3.00656i) q^{95} +(7.16712 - 5.20722i) q^{97} -9.39350 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.740270\pi$
$2$	−2.24808	+	1.63332i	−1.58963	+	1.15493i	−0.904466	+	0.426546i	$0.859730\pi$
$3$		0			0
$3$		0			0
$4$	1.76807	−	5.44156i	0.884036	−	2.72078i
$5$	−0.818541	−	0.594705i	−0.366063	−	0.265960i	0.389514	−	0.921021i	$-0.372643\pi$
$5$	−0.818541	−	0.594705i	−0.366063	−	0.265960i	−0.755576	+	0.655061i	$0.772643\pi$
$6$		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	0.211705	−	0.977334i	$-0.432099\pi$
$17$	−2.68981	−	1.95426i	−0.652375	−	0.473978i	−0.864079	+	0.503356i	$0.832099\pi$
$18$		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	$-0.597522\pi$
$23$	−2.89287			−0.603206			−0.301603	+	0.953434i	$0.597522\pi$
$24$		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	−0.959036	−	0.283283i	$-0.908576\pi$
$29$	−0.0896641	+	0.275958i	−0.0166502	+	0.0512440i	0.942386	+	0.334527i	$0.108576\pi$
$30$		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	$-0.968195\pi$
$41$	−1.59222	−	4.90035i	−0.248663	−	0.765306i	0.746349	−	0.665554i	$-0.231805\pi$
$42$		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	$-0.911686\pi$
$47$	−2.36297	−	7.27246i	−0.344674	−	1.06080i	0.617084	−	0.786897i	$-0.288314\pi$
$48$		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	−0.970154	−	0.242491i	$-0.922036\pi$
$53$	−7.56640	+	5.49731i	−1.03933	+	0.755114i	−0.0691716	+	0.997605i	$0.522036\pi$
$54$		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	$0.203286\pi$
$59$	−1.51350	+	4.65807i	−0.197041	+	0.606430i	−0.999947	+	0.0103237i	$0.996714\pi$
$60$		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	0.817452	−	0.575997i	$-0.195386\pi$
$71$	4.40059	+	3.19721i	0.522253	+	0.379439i	−0.295199	+	0.955436i	$0.595386\pi$
$72$		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	0.275149	−	0.961402i	$-0.411273\pi$
$83$	−5.04876	−	3.66814i	−0.554173	−	0.402630i	−0.829322	+	0.558771i	$0.811273\pi$
$84$		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	$-0.325451\pi$
$89$	9.83568			1.04258			0.521290	+	0.853380i	$0.325451\pi$
$90$		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	−0.571877	−	0.820339i	$-0.693785\pi$
$101$	0.317491	−	0.230671i	0.0315915	−	0.0229526i	0.603469	+	0.797386i	$0.293785\pi$
$102$		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	$0.0625929\pi$
$107$	3.12538	+	9.61893i	0.302142	+	0.929897i	−0.678586	+	0.734521i	$0.737407\pi$
$108$		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	$0.0105733\pi$
$113$	2.23657	+	6.88344i	0.210398	+	0.647540i	−0.789050	+	0.614329i	$0.789427\pi$
$114$		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	$-0.540865\pi$
$131$	−2.93074			−0.256060			−0.128030	+	0.991770i	$0.540865\pi$
$132$		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	0.852809	−	0.522223i	$-0.174897\pi$
$137$	7.25315	+	5.26972i	0.619678	+	0.450223i	−0.233131	+	0.972445i	$0.574897\pi$
$138$		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	0.752778	−	0.658274i	$-0.228713\pi$
$149$	4.38635	+	3.18687i	0.359344	+	0.261079i	−0.393434	+	0.919353i	$0.628713\pi$
$150$		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	−0.304977	−	0.952360i	$-0.598649\pi$
$167$	6.54578	−	4.75579i	0.506528	−	0.368014i	0.811505	+	0.584346i	$0.198649\pi$
$168$		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	$-0.867636\pi$
$173$	−5.42093	−	16.6839i	−0.412146	−	1.26845i	0.502634	−	0.864500i	$-0.332364\pi$
$174$		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	$-0.969678\pi$
$179$	−3.29158	−	10.1304i	−0.246024	−	0.757185i	0.749442	−	0.662070i	$-0.230322\pi$
$180$		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	$0.212354\pi$
$191$	−2.95265	+	9.08734i	−0.213647	+	0.657537i	−0.999247	+	0.0388023i	$0.987646\pi$
$192$		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	$-0.533121\pi$
$197$	−2.91565			−0.207732			−0.103866	+	0.994591i	$0.533121\pi$
$198$		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	−0.962683	−	0.270633i	$-0.912767\pi$
$227$	−0.373378	+	1.14914i	−0.0247820	+	0.0762711i	0.937901	+	0.346904i	$0.112767\pi$
$228$		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	−0.944101	−	0.329657i	$-0.893067\pi$
$233$	−14.0786	+	10.2287i	−0.922321	+	0.670106i	0.0217795	+	0.999763i	$0.493067\pi$
$234$		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	0.995127	−	0.0985980i	$-0.0314358\pi$
$239$	2.04219	+	6.28520i	0.132098	+	0.406556i	−0.863029	+	0.505154i	$0.831436\pi$
$240$		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	−0.758665	−	0.651481i	$-0.774148\pi$
$251$	−5.91751	+	4.29933i	−0.373510	+	0.271371i	0.385155	+	0.922852i	$0.374148\pi$
$252$		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	$-0.713766\pi$
$257$	5.47170	−	16.8402i	0.341315	−	1.05046i	0.963527	−	0.267611i	$-0.0862342\pi$
$258$		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	$-0.589029\pi$
$263$	−8.95390			−0.552121			−0.276061	+	0.961140i	$0.589029\pi$
$264$		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	−0.290075	−	0.957004i	$-0.593680\pi$
$269$	−21.1556	−	15.3704i	−1.28988	−	0.937151i	−0.999803	+	0.0198527i	$0.993680\pi$
$270$		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	$-0.835923\pi$
$281$	−26.9507	−	19.5808i	−1.60774	−	1.16809i	−0.737677	−	0.675154i	$-0.764077\pi$
$282$		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	−0.933242	−	0.359249i	$-0.883033\pi$
$293$	0.563633	−	1.73468i	0.0329278	−	0.101341i	0.966170	+	0.257907i	$0.0830330\pi$
$294$		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	$-0.776631\pi$
$311$	−9.26374	−	28.5109i	−0.525299	−	1.61670i	0.238426	−	0.971161i	$-0.423369\pi$
$312$		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	0.100066	−	0.994981i	$-0.468095\pi$
$317$	19.1803	−	13.9353i	1.07727	−	0.782683i	0.977205	+	0.212297i	$0.0680945\pi$
$318$		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	−0.0891857	−	0.996015i	$-0.528426\pi$
$347$	−19.8203	−	14.4003i	−1.06401	−	0.773050i	−0.974826	+	0.222965i	$0.928426\pi$
$348$		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	$-0.409615\pi$
$353$	10.5272			0.560307			0.280153	+	0.959955i	$0.409615\pi$
$354$		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	$-0.753264\pi$
$359$	5.20899	−	16.0316i	0.274920	−	0.846117i	0.989241	−	0.146298i	$-0.0467360\pi$
$360$		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	−0.998918	−	0.0465043i	$-0.985192\pi$
$383$	−24.7247	+	17.9635i	−1.26337	+	0.917894i	−0.264454	+	0.964398i	$0.585192\pi$
$384$		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	−0.997894	−	0.0648591i	$-0.979340\pi$
$389$	−3.00693	+	9.25439i	−0.152458	+	0.469216i	0.845437	+	0.534075i	$0.179340\pi$
$390$		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	0.870177	−	0.492739i	$-0.164004\pi$
$401$	13.4258	+	9.75443i	0.670453	+	0.487113i	−0.199723	+	0.979852i	$0.564004\pi$
$402$		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	$-0.495733\pi$
$419$	0.548783			0.0268098			0.0134049	+	0.999910i	$0.495733\pi$
$420$		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	$-0.278116\pi$
$431$	32.5848	−	23.6742i	1.56955	−	1.14035i	0.927582	−	0.373620i	$-0.121884\pi$
$432$		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	$0.153049\pi$
$443$	9.28582	+	28.5788i	0.441183	+	1.35782i	−0.445434	+	0.895315i	$0.646951\pi$
$444$		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	−0.999992	−	0.00406952i	$-0.998705\pi$
$449$	−27.6553	+	20.0928i	−1.30514	+	0.948237i	−0.305144	+	0.952306i	$0.598705\pi$
$450$		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	$-0.198208\pi$
$461$	34.8822			1.62463			0.812313	+	0.583222i	$0.198208\pi$
$462$		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	0.499541	−	0.866290i	$-0.333502\pi$
$467$	−3.67335	−	2.66885i	−0.169982	−	0.123499i	−0.669524	+	0.742791i	$0.733502\pi$
$468$		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	0.190987	−	0.981592i	$-0.438831\pi$
$479$	−14.9601	−	10.8691i	−0.683544	−	0.496624i	−0.874532	+	0.484969i	$0.838831\pi$
$480$		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	−0.825769	−	0.564009i	$-0.809258\pi$
$491$	3.85133	−	11.8532i	0.173808	−	0.534927i	0.999577	+	0.0290819i	$0.00925837\pi$
$492$		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	$0.262765\pi$
$503$	12.5927	+	38.7562i	0.561479	+	1.72805i	−0.116710	+	0.993166i	$0.537235\pi$
$504$		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	0.996456	−	0.0841165i	$-0.0268068\pi$
$509$	3.17803	+	9.78097i	0.140864	+	0.433534i	−0.855592	+	0.517650i	$0.826807\pi$
$510$		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	$-0.531554\pi$
$521$	12.9191	−	39.7610i	0.565998	−	1.74196i	0.664967	−	0.746873i	$-0.268446\pi$
$522$		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	$-0.629438\pi$
$557$	10.9582	−	33.7259i	0.464315	−	1.42901i	0.859842	−	0.510559i	$-0.170562\pi$
$558$		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	−0.453858	−	0.891074i	$-0.649953\pi$
$563$	6.01147	−	4.36759i	0.253353	−	0.184072i	0.707212	+	0.707002i	$0.249953\pi$
$564$		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	$0.143056\pi$
$569$	10.1946	+	31.3757i	0.427379	+	1.31534i	−0.473319	+	0.880891i	$0.656944\pi$
$570$		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	$0.494563\pi$
$587$	−14.1598	+	43.5794i	−0.584437	+	1.79871i	−0.601518	+	0.798859i	$0.705437\pi$
$588$		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	$-0.692921\pi$
$593$	−27.7437			−1.13930			−0.569649	+	0.821888i	$0.692921\pi$
$594$		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	0.122650	−	0.992450i	$-0.460861\pi$
$599$	−19.1715	−	13.9289i	−0.783325	−	0.569119i	−0.905975	+	0.423331i	$0.860861\pi$
$600$		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	$-0.419928\pi$
$617$	12.3655			0.497816			0.248908	+	0.968527i	$0.419928\pi$
$618$		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	0.988124	−	0.153660i	$-0.0491060\pi$
$641$	2.49118	+	7.66708i	0.0983959	+	0.302831i	−0.889728	+	0.456491i	$0.849106\pi$
$642$		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	−0.763603	−	0.645685i	$-0.776572\pi$
$647$	−9.80531	+	7.12397i	−0.385487	+	0.280072i	0.378117	+	0.925758i	$0.376572\pi$
$648$		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	$0.466829\pi$
$653$	−14.4310	+	44.4142i	−0.564730	+	1.73806i	−0.668752	+	0.743485i	$0.733171\pi$
$654$		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	$-0.321087\pi$
$659$	27.3622			1.06588			0.532940	+	0.846153i	$0.321087\pi$
$660$		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	−0.153954	−	0.988078i	$-0.549201\pi$
$677$	−29.6943	−	21.5742i	−1.14125	−	0.829164i	−0.987292	+	0.158914i	$0.949201\pi$
$678$		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	$-0.335123\pi$
$683$	25.8794			0.990246			0.495123	+	0.868823i	$0.335123\pi$
$684$		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	0.872124	−	0.489286i	$-0.162742\pi$
$701$	−3.20455	−	9.86258i	−0.121034	−	0.372505i	−0.993158	+	0.116781i	$0.962742\pi$
$702$		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	−0.836107	−	0.548567i	$-0.815174\pi$
$719$	4.36421	−	13.4316i	0.162757	−	0.500916i	0.998864	+	0.0476511i	$0.0151736\pi$
$720$		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	0.615029	−	0.788504i	$-0.289144\pi$
$743$	1.50387	+	1.09263i	0.0551717	+	0.0400846i	−0.559858	+	0.828589i	$0.689144\pi$
$744$		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	$-0.338828\pi$
$761$	40.4571	−	29.3938i	1.46657	−	1.06552i	0.981591	−	0.190997i	$-0.0611720\pi$
$762$		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	$-0.906966\pi$
$773$	−9.79338	−	30.1409i	−0.352243	−	1.08409i	0.605347	−	0.795962i	$-0.293034\pi$
$774$		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	0.548271	−	0.836301i	$-0.315286\pi$
$797$	−2.19279	−	1.59316i	−0.0776726	−	0.0564325i	−0.625944	+	0.779868i	$0.715286\pi$
$798$		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	0.272942	−	0.962030i	$-0.412003\pi$
$809$	−15.8615	−	11.5240i	−0.557659	−	0.405163i	−0.830602	+	0.556867i	$0.812003\pi$
$810$		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	−0.946576	−	0.322481i	$-0.895483\pi$
$821$	0.251287	−	0.773382i	0.00876998	−	0.0269912i	0.955346	+	0.295490i	$0.0954830\pi$
$822$		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	−0.442478	−	0.896779i	$-0.645901\pi$
$827$	7.87026	−	5.71808i	0.273676	−	0.198837i	0.716154	+	0.697942i	$0.245901\pi$
$828$		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	0.922339	−	0.386381i	$-0.126275\pi$
$839$	−1.47602	−	4.54271i	−0.0509577	−	0.156832i	−0.973297	+	0.229549i	$0.926275\pi$
$840$		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	$-0.439388\pi$
$857$	11.0816			0.378541			0.189270	+	0.981925i	$0.439388\pi$
$858$		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	$-0.956276\pi$
$863$	−41.9183	−	30.4554i	−1.42692	−	1.03671i	−0.436335	−	0.899784i	$-0.643724\pi$
$864$		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	$-0.679879\pi$
$881$	−31.7893			−1.07101			−0.535505	+	0.844532i	$0.679879\pi$
$882$		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	$-0.740497\pi$
$887$	8.84224	−	27.2136i	0.296893	−	0.913744i	0.982579	−	0.185846i	$-0.0595026\pi$
$888$		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	−0.452805	−	0.891610i	$-0.649577\pi$
$911$	7.70392	−	5.59722i	0.255242	−	0.185444i	0.708047	+	0.706165i	$0.249577\pi$
$912$		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	0.927500	−	0.373824i	$-0.121954\pi$
$929$	26.1692	+	19.0131i	0.858585	+	0.623799i	−0.0689145	+	0.997623i	$0.521954\pi$
$930$		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	0.192070	−	0.981381i	$-0.438480\pi$
$941$	−20.9186	−	15.1982i	−0.681926	−	0.495448i	−0.873996	+	0.485933i	$0.838480\pi$
$942$		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	$-0.363614\pi$
$947$	25.5713			0.830956			0.415478	+	0.909603i	$0.363614\pi$
$948$		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	$-0.726639\pi$
$953$	9.88494	−	30.4227i	0.320205	−	0.985489i	0.973559	−	0.228436i	$-0.0733613\pi$
$954$		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	$-0.861114\pi$
$971$	−13.1341	−	40.4227i	−0.421494	−	1.29723i	0.484817	−	0.874615i	$-0.338886\pi$
$972$		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	−0.0818930	−	0.996641i	$-0.526097\pi$
$977$	26.2766	−	19.0911i	0.840663	−	0.610777i	0.922556	+	0.385864i	$0.126097\pi$
$978$		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	$0.383482\pi$
$983$	−15.0645	+	46.3639i	−0.480484	+	1.47878i	−0.838416	+	0.545031i	$0.816518\pi$
$984$		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.a.190.1	yes	16
3.2	odd	2		297.2.f.d.190.4	yes	16
9.2	odd	6		891.2.n.f.190.1		32
9.4	even	3		891.2.n.i.784.1		32
9.5	odd	6		891.2.n.f.784.4		32
9.7	even	3		891.2.n.i.190.4		32
11.2	odd	10		3267.2.a.bf.1.1		8
11.4	even	5	inner	297.2.f.a.136.1	✓	16
11.9	even	5		3267.2.a.bm.1.8		8
33.2	even	10		3267.2.a.bl.1.8		8
33.20	odd	10		3267.2.a.be.1.1		8
33.26	odd	10		297.2.f.d.136.4	yes	16
99.4	even	15		891.2.n.i.136.4		32
99.59	odd	30		891.2.n.f.136.1		32
99.70	even	15		891.2.n.i.433.1		32
99.92	odd	30		891.2.n.f.433.4		32

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

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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