LMFDB - Embedded newform 441.2.u.d.127.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			127.6
Character	$\chi$	$=$	441.127
Dual form			441.2.u.d.316.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37817 + 1.14527i) q^{2} +(3.09710 + 3.88364i) q^{4} +(0.398449 + 1.74572i) q^{5} +(0.566955 - 2.58429i) q^{7} +(1.74291 + 7.63618i) q^{8} +O(q^{10})$	\(q+(2.37817 + 1.14527i) q^{2} +(3.09710 + 3.88364i) q^{4} +(0.398449 + 1.74572i) q^{5} +(0.566955 - 2.58429i) q^{7} +(1.74291 + 7.63618i) q^{8} +(-1.05174 + 4.60796i) q^{10} +(-1.38032 - 0.664728i) q^{11} +(-4.78678 - 2.30519i) q^{13} +(4.30803 - 5.49658i) q^{14} +(-2.38986 + 10.4706i) q^{16} +(3.34085 - 4.18930i) q^{17} -2.34574 q^{19} +(-5.54571 + 6.95409i) q^{20} +(-2.52136 - 3.16168i) q^{22} +(2.25032 + 2.82181i) q^{23} +(1.61607 - 0.778257i) q^{25} +(-8.74374 - 10.9643i) q^{26} +(11.7924 - 5.80195i) q^{28} +(-4.39760 + 5.51442i) q^{29} -1.98138 q^{31} +(-7.90815 + 9.91651i) q^{32} +(12.7430 - 6.13671i) q^{34} +(4.73735 - 0.0399647i) q^{35} +(7.41784 - 9.30168i) q^{37} +(-5.57859 - 2.68651i) q^{38} +(-12.6362 + 6.08526i) q^{40} +(0.667868 + 2.92612i) q^{41} +(-2.38427 + 10.4462i) q^{43} +(-1.69343 - 7.41940i) q^{44} +(2.11992 + 9.28798i) q^{46} +(-7.07508 - 3.40718i) q^{47} +(-6.35712 - 2.93035i) q^{49} +4.73460 q^{50} +(-5.87260 - 25.7295i) q^{52} +(0.538950 + 0.675822i) q^{53} +(0.610441 - 2.67452i) q^{55} +(20.7223 - 0.174815i) q^{56} +(-16.7738 + 8.07782i) q^{58} +(-1.13862 + 4.98863i) q^{59} +(4.29940 - 5.39128i) q^{61} +(-4.71207 - 2.26921i) q^{62} +(-10.8114 + 5.20648i) q^{64} +(2.11693 - 9.27489i) q^{65} +8.90123 q^{67} +26.6167 q^{68} +(11.3120 + 5.33050i) q^{70} +(-5.10139 - 6.39694i) q^{71} +(5.23694 - 2.52198i) q^{73} +(28.2938 - 13.6256i) q^{74} +(-7.26499 - 9.11001i) q^{76} +(-2.50043 + 3.19028i) q^{77} -3.91143 q^{79} -19.2310 q^{80} +(-1.76289 + 7.72372i) q^{82} +(2.93149 - 1.41173i) q^{83} +(8.64450 + 4.16297i) q^{85} +(-17.6339 + 22.1122i) q^{86} +(2.67021 - 11.6989i) q^{88} +(-7.35043 + 3.53978i) q^{89} +(-8.67118 + 11.0635i) q^{91} +(-3.98943 + 17.4788i) q^{92} +(-12.9237 - 16.2057i) q^{94} +(-0.934659 - 4.09501i) q^{95} -3.04941 q^{97} +(-11.7623 - 14.2495i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	2.37817	+	1.14527i	1.68162	+	0.809827i	0.996697	+	0.0812156i	$0.0258802\pi$
$2$	2.37817	+	1.14527i	1.68162	+	0.809827i	0.684927	+	0.728612i	$0.259834\pi$
$3$		0			0
$3$		0			0
$4$	3.09710	+	3.88364i	1.54855	+	1.94182i
$5$	0.398449	+	1.74572i	0.178192	+	0.780710i	0.982465	+	0.186449i	$0.0596980\pi$
$5$	0.398449	+	1.74572i	0.178192	+	0.780710i	−0.804273	+	0.594260i	$0.797445\pi$
$6$		0			0
$7$	0.566955	−	2.58429i	0.214289	−	0.976770i
$7$	0.566955	−	2.58429i	0.214289	−	0.976770i
$8$	1.74291	+	7.63618i	0.616211	+	2.69980i
$9$		0			0
$10$	−1.05174	+	4.60796i	−0.332588	+	1.45716i
$11$	−1.38032	−	0.664728i	−0.416183	−	0.200423i	0.214061	−	0.976820i	$-0.431331\pi$
$11$	−1.38032	−	0.664728i	−0.416183	−	0.200423i	−0.630244	+	0.776397i	$0.717045\pi$
$12$		0			0
$13$	−4.78678	−	2.30519i	−1.32761	−	0.639346i	−0.370440	−	0.928856i	$-0.620793\pi$
$13$	−4.78678	−	2.30519i	−1.32761	−	0.639346i	−0.957175	+	0.289511i	$0.906507\pi$
$14$	4.30803	−	5.49658i	1.15137	−	1.46902i
$15$		0			0
$16$	−2.38986	+	10.4706i	−0.597464	+	2.61766i
$17$	3.34085	−	4.18930i	0.810276	−	1.01605i	−0.189142	−	0.981950i	$-0.560571\pi$
$17$	3.34085	−	4.18930i	0.810276	−	1.01605i	0.999418	−	0.0341044i	$-0.0108579\pi$
$18$		0			0
$19$	−2.34574			−0.538150			−0.269075	−	0.963119i	$-0.586718\pi$
$19$	−2.34574			−0.538150			−0.269075	+	0.963119i	$0.586718\pi$
$20$	−5.54571	+	6.95409i	−1.24006	+	1.55498i
$21$		0			0
$22$	−2.52136	−	3.16168i	−0.537555	−	0.674072i
$23$	2.25032	+	2.82181i	0.469224	+	0.588388i	0.958981	−	0.283471i	$-0.0914859\pi$
$23$	2.25032	+	2.82181i	0.469224	+	0.588388i	−0.489757	+	0.871859i	$0.662914\pi$
$24$		0			0
$25$	1.61607	−	0.778257i	0.323213	−	0.155651i
$26$	−8.74374	−	10.9643i	−1.71479	−	2.15028i
$27$		0			0
$28$	11.7924	−	5.80195i	2.22855	−	1.09647i
$29$	−4.39760	+	5.51442i	−0.816614	+	1.02400i	0.182553	+	0.983196i	$0.441564\pi$
$29$	−4.39760	+	5.51442i	−0.816614	+	1.02400i	−0.999167	+	0.0408060i	$0.987007\pi$
$30$		0			0
$31$	−1.98138			−0.355866			−0.177933	−	0.984043i	$-0.556941\pi$
$31$	−1.98138			−0.355866			−0.177933	+	0.984043i	$0.556941\pi$
$32$	−7.90815	+	9.91651i	−1.39798	+	1.75301i
$33$		0			0
$34$	12.7430	−	6.13671i	2.18541	−	1.05244i
$35$	4.73735	−	0.0399647i	0.800759	−	0.00675527i
$36$		0			0
$37$	7.41784	−	9.30168i	1.21949	−	1.52919i	0.446470	−	0.894799i	$-0.352681\pi$
$37$	7.41784	−	9.30168i	1.21949	−	1.52919i	0.773015	−	0.634388i	$-0.218748\pi$
$38$	−5.57859	−	2.68651i	−0.904966	−	0.435809i
$39$		0			0
$40$	−12.6362	+	6.08526i	−1.99795	+	0.962164i
$41$	0.667868	+	2.92612i	0.104303	+	0.456983i	0.999926	+	0.0121684i	$0.00387341\pi$
$41$	0.667868	+	2.92612i	0.104303	+	0.456983i	−0.895623	+	0.444815i	$0.853269\pi$
$42$		0			0
$43$	−2.38427	+	10.4462i	−0.363598	+	1.59303i	0.380385	+	0.924828i	$0.375791\pi$
$43$	−2.38427	+	10.4462i	−0.363598	+	1.59303i	−0.743983	+	0.668199i	$0.767066\pi$
$44$	−1.69343	−	7.41940i	−0.255294	−	1.11852i
$45$		0			0
$46$	2.11992	+	9.28798i	0.312565	+	1.36944i
$47$	−7.07508	−	3.40718i	−1.03201	−	0.496988i	−0.160327	−	0.987064i	$-0.551255\pi$
$47$	−7.07508	−	3.40718i	−1.03201	−	0.496988i	−0.871680	+	0.490075i	$0.836969\pi$
$48$		0			0
$49$	−6.35712	−	2.93035i	−0.908161	−	0.418622i
$50$	4.73460			0.669574
$51$		0			0
$52$	−5.87260	−	25.7295i	−0.814383	−	3.56804i
$53$	0.538950	+	0.675822i	0.0740304	+	0.0928312i	0.817468	−	0.575974i	$-0.195377\pi$
$53$	0.538950	+	0.675822i	0.0740304	+	0.0928312i	−0.743437	+	0.668806i	$0.766806\pi$
$54$		0			0
$55$	0.610441	−	2.67452i	0.0823119	−	0.360632i
$56$	20.7223	−	0.174815i	2.76913	−	0.0233606i
$57$		0			0
$58$	−16.7738	+	8.07782i	−2.20250	+	1.06067i
$59$	−1.13862	+	4.98863i	−0.148236	+	0.649464i	0.845139	+	0.534546i	$0.179517\pi$
$59$	−1.13862	+	4.98863i	−0.148236	+	0.649464i	−0.993375	+	0.114917i	$0.963340\pi$
$60$		0			0
$61$	4.29940	−	5.39128i	0.550482	−	0.690283i	−0.426284	−	0.904589i	$-0.640178\pi$
$61$	4.29940	−	5.39128i	0.550482	−	0.690283i	0.976766	+	0.214306i	$0.0687491\pi$
$62$	−4.71207	−	2.26921i	−0.598433	−	0.288190i
$63$		0			0
$64$	−10.8114	+	5.20648i	−1.35142	+	0.650811i
$65$	2.11693	−	9.27489i	0.262573	−	1.15041i
$66$		0			0
$67$	8.90123			1.08746			0.543729	−	0.839261i	$-0.317012\pi$
$67$	8.90123			1.08746			0.543729	+	0.839261i	$0.317012\pi$
$68$	26.6167			3.22774
$69$		0			0
$70$	11.3120	+	5.33050i	1.35205	+	0.637116i
$71$	−5.10139	−	6.39694i	−0.605423	−	0.759177i	0.380789	−	0.924662i	$-0.375652\pi$
$71$	−5.10139	−	6.39694i	−0.605423	−	0.759177i	−0.986212	+	0.165485i	$0.947081\pi$
$72$		0			0
$73$	5.23694	−	2.52198i	0.612937	−	0.295175i	−0.101543	−	0.994831i	$-0.532378\pi$
$73$	5.23694	−	2.52198i	0.612937	−	0.295175i	0.714480	+	0.699656i	$0.246664\pi$
$74$	28.2938	−	13.6256i	3.28909	−	1.58394i
$75$		0			0
$76$	−7.26499	−	9.11001i	−0.833351	−	1.04499i
$77$	−2.50043	+	3.19028i	−0.284951	+	0.363567i
$78$		0			0
$79$	−3.91143			−0.440070			−0.220035	−	0.975492i	$-0.570617\pi$
$79$	−3.91143			−0.440070			−0.220035	+	0.975492i	$0.570617\pi$
$80$	−19.2310			−2.15010
$81$		0			0
$82$	−1.76289	+	7.72372i	−0.194678	+	0.852942i
$83$	2.93149	−	1.41173i	0.321773	−	0.154958i	−0.266023	−	0.963967i	$-0.585710\pi$
$83$	2.93149	−	1.41173i	0.321773	−	0.154958i	0.587797	+	0.809009i	$0.299996\pi$
$84$		0			0
$85$	8.64450	+	4.16297i	0.937628	+	0.451538i
$86$	−17.6339	+	22.1122i	−1.90151	+	2.38442i
$87$		0			0
$88$	2.67021	−	11.6989i	0.284645	−	1.24711i
$89$	−7.35043	+	3.53978i	−0.779144	+	0.375216i	−0.780799	−	0.624783i	$-0.785188\pi$
$89$	−7.35043	+	3.53978i	−0.779144	+	0.375216i	0.00165489	+	0.999999i	$0.499473\pi$
$90$		0			0
$91$	−8.67118	+	11.0635i	−0.908987	+	1.15977i
$92$	−3.98943	+	17.4788i	−0.415927	+	1.82229i
$93$		0			0
$94$	−12.9237	−	16.2057i	−1.33297	−	1.67150i
$95$	−0.934659	−	4.09501i	−0.0958940	−	0.420139i
$96$		0			0
$97$	−3.04941			−0.309620			−0.154810	−	0.987944i	$-0.549477\pi$
$97$	−3.04941			−0.309620			−0.154810	+	0.987944i	$0.549477\pi$
$98$	−11.7623	−	14.2495i	−1.18817	−	1.43942i
$99$		0			0
$100$	8.02758	+	3.86588i	0.802758	+	0.386588i
$101$	0.0204095	+	0.0894199i	0.00203082	+	0.00889762i	0.975933	−	0.218070i	$-0.0699760\pi$
$101$	0.0204095	+	0.0894199i	0.00203082	+	0.00889762i	−0.973902	+	0.226967i	$0.927119\pi$
$102$		0			0
$103$	1.33053	+	5.82945i	0.131101	+	0.574393i	0.997217	+	0.0745497i	$0.0237519\pi$
$103$	1.33053	+	5.82945i	0.131101	+	0.574393i	−0.866116	+	0.499843i	$0.833391\pi$
$104$	9.25995	−	40.5705i	0.908013	−	3.97826i
$105$		0			0
$106$	0.507719	+	2.22446i	0.0493141	+	0.216059i
$107$	−14.8991	+	7.17503i	−1.44035	+	0.693637i	−0.980890	−	0.194561i	$-0.937672\pi$
$107$	−14.8991	+	7.17503i	−1.44035	+	0.693637i	−0.459461	+	0.888198i	$0.651957\pi$
$108$		0			0
$109$	−1.55180	−	0.747307i	−0.148635	−	0.0715790i	0.358087	−	0.933688i	$-0.383429\pi$
$109$	−1.55180	−	0.747307i	−0.148635	−	0.0715790i	−0.506723	+	0.862109i	$0.669143\pi$
$110$	4.51478	−	5.66135i	0.430467	−	0.539789i
$111$		0			0
$112$	25.7042	+	12.1125i	2.42882	+	1.14452i
$113$	3.19410	−	1.53820i	0.300476	−	0.144702i	−0.277571	−	0.960705i	$-0.589529\pi$
$113$	3.19410	−	1.53820i	0.300476	−	0.144702i	0.578047	+	0.816004i	$0.303815\pi$
$114$		0			0
$115$	−4.02945	+	5.05278i	−0.375749	+	0.471174i
$116$	−35.0358			−3.25299
$117$		0			0
$118$	−8.42116	+	10.5598i	−0.775230	+	0.972108i
$119$	−8.93226	−	11.0089i	−0.818818	−	1.00918i
$120$		0			0
$121$	−5.39496	−	6.76507i	−0.490451	−	0.615006i
$122$	16.3992	−	7.89744i	1.48471	−	0.715000i
$123$		0			0
$124$	−6.13652	−	7.69496i	−0.551076	−	0.691027i
$125$	7.58469	+	9.51090i	0.678395	+	0.850681i
$126$		0			0
$127$	−4.67554	+	5.86295i	−0.414887	+	0.520252i	−0.944733	−	0.327842i	$-0.893679\pi$
$127$	−4.67554	+	5.86295i	−0.414887	+	0.520252i	0.529845	+	0.848094i	$0.322250\pi$
$128$	−6.30679			−0.557447
$129$		0			0
$130$	15.6567	−	19.6328i	1.37318	−	1.72191i
$131$	−3.75761	+	16.4632i	−0.328304	+	1.43839i	0.494058	+	0.869429i	$0.335513\pi$
$131$	−3.75761	+	16.4632i	−0.328304	+	1.43839i	−0.822362	+	0.568964i	$0.807344\pi$
$132$		0			0
$133$	−1.32993	+	6.06208i	−0.115320	+	0.525649i
$134$	21.1687	+	10.1943i	1.82870	+	0.880653i
$135$		0			0
$136$	37.8130	+	18.2098i	3.24244	+	1.56148i
$137$	−1.17701	+	5.15682i	−0.100559	+	0.440577i	0.899435	+	0.437055i	$0.143978\pi$
$137$	−1.17701	+	5.15682i	−0.100559	+	0.440577i	−0.999994	+	0.00352252i	$0.998879\pi$
$138$		0			0
$139$	0.790609	+	3.46389i	0.0670586	+	0.293803i	0.997326	−	0.0730788i	$-0.0232825\pi$
$139$	0.790609	+	3.46389i	0.0670586	+	0.293803i	−0.930268	+	0.366882i	$0.880425\pi$
$140$	14.8272	+	18.2744i	1.25313	+	1.54447i
$141$		0			0
$142$	−4.80578	−	21.0555i	−0.403292	−	1.76694i
$143$	5.07498	+	6.36382i	0.424391	+	0.532169i
$144$		0			0
$145$	−11.3789	−	5.47977i	−0.944963	−	0.455070i
$146$	15.3427			1.26977
$147$		0			0
$148$	59.0981			4.85783
$149$	−2.07490	−	0.999220i	−0.169983	−	0.0818593i	0.346958	−	0.937881i	$-0.387215\pi$
$149$	−2.07490	−	0.999220i	−0.169983	−	0.0818593i	−0.516940	+	0.856021i	$0.672929\pi$
$150$		0			0
$151$	0.301576	+	0.378164i	0.0245419	+	0.0307746i	0.793951	−	0.607982i	$-0.208021\pi$
$151$	0.301576	+	0.378164i	0.0245419	+	0.0307746i	−0.769409	+	0.638756i	$0.779449\pi$
$152$	−4.08841	−	17.9125i	−0.331614	−	1.45290i
$153$		0			0
$154$	−9.60020	+	4.72339i	−0.773606	+	0.380621i
$155$	−0.789479	−	3.45893i	−0.0634125	−	0.277828i
$156$		0			0
$157$	−3.60217	+	15.7822i	−0.287485	+	1.25955i	0.600479	+	0.799640i	$0.294976\pi$
$157$	−3.60217	+	15.7822i	−0.287485	+	1.25955i	−0.887964	+	0.459913i	$0.847881\pi$
$158$	−9.30205	−	4.47963i	−0.740032	−	0.356380i
$159$		0			0
$160$	−20.4624	−	9.85419i	−1.61770	−	0.779043i
$161$	8.56821	−	4.21564i	0.675269	−	0.332239i
$162$		0			0
$163$	1.17964	−	5.16835i	0.0923967	−	0.404817i	−0.907487	−	0.420081i	$-0.862002\pi$
$163$	1.17964	−	5.16835i	0.0923967	−	0.404817i	0.999883	+	0.0152641i	$0.00485891\pi$
$164$	−9.29554	+	11.6562i	−0.725859	+	0.910199i
$165$		0			0
$166$	8.58842			0.666591
$167$	2.61864	−	3.28367i	0.202636	−	0.254098i	−0.670121	−	0.742251i	$-0.733758\pi$
$167$	2.61864	−	3.28367i	0.202636	−	0.254098i	0.872758	+	0.488154i	$0.162329\pi$
$168$		0			0
$169$	9.49401	+	11.9051i	0.730309	+	0.915778i
$170$	15.7904	+	19.8006i	1.21107	+	1.51863i
$171$		0			0
$172$	−47.9535	+	23.0932i	−3.65642	+	1.76084i
$173$	11.0839	+	13.8988i	0.842696	+	1.05671i	0.997632	+	0.0687833i	$0.0219117\pi$
$173$	11.0839	+	13.8988i	0.842696	+	1.05671i	−0.154935	+	0.987925i	$0.549517\pi$
$174$		0			0
$175$	−1.09501	−	4.61762i	−0.0827746	−	0.349060i
$176$	10.2589	−	12.8643i	0.773294	−	0.969680i
$177$		0			0
$178$	−21.5346			−1.61409
$179$	7.04916	−	8.83937i	0.526879	−	0.660685i	−0.445175	−	0.895444i	$-0.646858\pi$
$179$	7.04916	−	8.83937i	0.526879	−	0.660685i	0.972054	+	0.234758i	$0.0754299\pi$
$180$		0			0
$181$	21.0553	−	10.1397i	1.56503	−	0.753676i	0.567459	−	0.823402i	$-0.307927\pi$
$181$	21.0553	−	10.1397i	1.56503	−	0.753676i	0.997566	+	0.0697253i	$0.0222123\pi$
$182$	−33.2923	+	16.3801i	−2.46779	+	1.21417i
$183$		0			0
$184$	−17.6258	+	22.1020i	−1.29939	+	1.62938i
$185$	19.1938	+	9.24323i	1.41115	+	0.679576i
$186$		0			0
$187$	−7.39620	+	3.56182i	−0.540864	+	0.260466i
$188$	−8.67997	−	38.0294i	−0.633052	−	2.77358i
$189$		0			0
$190$	2.46710	−	10.8091i	0.178982	−	0.784174i
$191$	−5.19931	−	22.7797i	−0.376209	−	1.64828i	−0.708948	−	0.705261i	$-0.750830\pi$
$191$	−5.19931	−	22.7797i	−0.376209	−	1.64828i	0.332739	−	0.943019i	$-0.392027\pi$
$192$		0			0
$193$	1.06198	+	4.65286i	0.0764433	+	0.334920i	0.998660	−	0.0517538i	$-0.0164811\pi$
$193$	1.06198	+	4.65286i	0.0764433	+	0.334920i	−0.922217	+	0.386674i	$0.873624\pi$
$194$	−7.25202	−	3.49239i	−0.520665	−	0.250739i
$195$		0			0
$196$	−8.30820	−	33.7643i	−0.593443	−	2.41174i
$197$	−4.37045			−0.311382			−0.155691	−	0.987806i	$-0.549760\pi$
$197$	−4.37045			−0.311382			−0.155691	+	0.987806i	$0.549760\pi$
$198$		0			0
$199$	2.20081	+	9.64238i	0.156011	+	0.683530i	0.991067	+	0.133365i	$0.0425782\pi$
$199$	2.20081	+	9.64238i	0.156011	+	0.683530i	−0.835056	+	0.550165i	$0.814565\pi$
$200$	8.75956	+	10.9841i	0.619395	+	0.776696i
$201$		0			0
$202$	−0.0538725	+	0.236031i	−0.00379045	+	0.0166071i
$203$	11.7576	+	14.4911i	0.825224	+	1.01708i
$204$		0			0
$205$	−4.84208	+	2.33182i	−0.338185	+	0.162861i
$206$	−3.51205	+	15.3873i	−0.244696	+	1.07208i
$207$		0			0
$208$	35.5766	−	44.6116i	2.46679	−	3.09326i
$209$	3.23788	+	1.55928i	0.223969	+	0.107858i
$210$		0			0
$211$	−8.21209	+	3.95473i	−0.565343	+	0.272255i	−0.694648	−	0.719350i	$-0.744440\pi$
$211$	−8.21209	+	3.95473i	−0.565343	+	0.272255i	0.129304	+	0.991605i	$0.458726\pi$
$212$	−0.955466	+	4.18617i	−0.0656217	+	0.287507i
$213$		0			0
$214$	−43.6500			−2.98386
$215$	−19.1861			−1.30848
$216$		0			0
$217$	−1.12335	+	5.12046i	−0.0762581	+	0.347600i
$218$	−2.83458	−	3.55445i	−0.191982	−	0.240738i
$219$		0			0
$220$	12.2774	−	5.91251i	0.827745	−	0.398621i
$221$	−25.6491	+	12.3519i	−1.72534	+	0.830882i
$222$		0			0
$223$	−7.02894	−	8.81401i	−0.470693	−	0.590230i	0.488648	−	0.872481i	$-0.337490\pi$
$223$	−7.02894	−	8.81401i	−0.470693	−	0.590230i	−0.959341	+	0.282251i	$0.908919\pi$
$224$	21.1436	+	26.0592i	1.41272	+	1.74115i
$225$		0			0
$226$	9.35778			0.622470
$227$	−13.1283			−0.871356			−0.435678	−	0.900102i	$-0.643491\pi$
$227$	−13.1283			−0.871356			−0.435678	+	0.900102i	$0.643491\pi$
$228$		0			0
$229$	−3.22059	+	14.1103i	−0.212822	+	0.932435i	0.749816	+	0.661646i	$0.230142\pi$
$229$	−3.22059	+	14.1103i	−0.212822	+	0.932435i	−0.962639	+	0.270789i	$0.912715\pi$
$230$	−15.3695	+	7.40158i	−1.01344	+	0.488045i
$231$		0			0
$232$	−49.7737	−	23.9698i	−3.26781	−	1.57369i
$233$	2.14189	−	2.68584i	0.140320	−	0.175955i	−0.706706	−	0.707507i	$-0.749820\pi$
$233$	2.14189	−	2.68584i	0.140320	−	0.175955i	0.847026	+	0.531552i	$0.178391\pi$
$234$		0			0
$235$	3.12892	−	13.7087i	0.204108	−	0.894258i
$236$	−22.9004	+	11.0283i	−1.49069	+	0.717879i
$237$		0			0
$238$	−8.63434	−	36.4109i	−0.559681	−	2.36017i
$239$	1.81753	−	7.96314i	0.117567	−	0.515093i	−0.881512	−	0.472162i	$-0.843474\pi$
$239$	1.81753	−	7.96314i	0.117567	−	0.515093i	0.999078	−	0.0429301i	$-0.0136693\pi$
$240$		0			0
$241$	13.9683	+	17.5158i	0.899780	+	1.12829i	0.991186	+	0.132475i	$0.0422925\pi$
$241$	13.9683	+	17.5158i	0.899780	+	1.12829i	−0.0914060	+	0.995814i	$0.529136\pi$
$242$	−5.08234	−	22.2672i	−0.326705	−	1.43139i
$243$		0			0
$244$	34.2534			2.19285
$245$	2.58258	−	12.2654i	0.164995	−	0.783605i
$246$		0			0
$247$	11.2286	+	5.40739i	0.714456	+	0.344064i
$248$	−3.45336	−	15.1302i	−0.219289	−	0.960767i
$249$		0			0
$250$	7.14518	+	31.3051i	0.451901	+	1.97991i
$251$	2.22318	−	9.74038i	0.140326	−	0.614807i	−0.855033	−	0.518574i	$-0.826463\pi$
$251$	2.22318	−	9.74038i	0.140326	−	0.614807i	0.995359	−	0.0962337i	$-0.0306796\pi$
$252$		0			0
$253$	−1.23043	−	5.39086i	−0.0773564	−	0.338920i
$254$	−17.8339	+	8.58836i	−1.11900	+	0.538881i
$255$		0			0
$256$	6.62411	+	3.19000i	0.414007	+	0.199375i
$257$	8.02047	−	10.0573i	0.500303	−	0.627360i	−0.465995	−	0.884788i	$-0.654303\pi$
$257$	8.02047	−	10.0573i	0.500303	−	0.627360i	0.966298	+	0.257428i	$0.0828749\pi$
$258$		0			0
$259$	−19.8327	−	24.4435i	−1.23234	−	1.51884i
$260$	42.5766	−	20.5038i	2.64049	−	1.27159i
$261$		0			0
$262$	−27.7910	+	34.8488i	−1.71693	+	2.15297i
$263$	10.2760			0.633648			0.316824	−	0.948484i	$-0.397384\pi$
$263$	10.2760			0.633648			0.316824	+	0.948484i	$0.397384\pi$
$264$		0			0
$265$	−0.965051	+	1.21014i	−0.0592826	+	0.0743381i
$266$	−10.1055	+	12.8936i	−0.619609	+	0.790555i
$267$		0			0
$268$	27.5680	+	34.5691i	1.68398	+	2.11165i
$269$	−18.3625	+	8.84293i	−1.11958	+	0.539163i	−0.899764	−	0.436377i	$-0.856261\pi$
$269$	−18.3625	+	8.84293i	−1.11958	+	0.539163i	−0.219820	+	0.975540i	$0.570547\pi$
$270$		0			0
$271$	−5.33220	−	6.68637i	−0.323908	−	0.406168i	0.593041	−	0.805172i	$-0.297927\pi$
$271$	−5.33220	−	6.68637i	−0.323908	−	0.406168i	−0.916949	+	0.399004i	$0.869356\pi$
$272$	35.8805	+	44.9927i	2.17557	+	2.72808i
$273$		0			0
$274$	−8.70509	+	10.9158i	−0.525894	+	0.659450i
$275$	−2.74802			−0.165712
$276$		0			0
$277$	10.0253	−	12.5713i	0.602362	−	0.755339i	−0.383382	−	0.923590i	$-0.625241\pi$
$277$	10.0253	−	12.5713i	0.602362	−	0.755339i	0.985744	+	0.168251i	$0.0538120\pi$
$278$	−2.08687	+	9.14319i	−0.125162	+	0.548372i
$279$		0			0
$280$	8.56195	+	36.1056i	0.511674	+	2.15772i
$281$	13.7664	+	6.62954i	0.821233	+	0.395485i	0.796820	−	0.604217i	$-0.206514\pi$
$281$	13.7664	+	6.62954i	0.821233	+	0.395485i	0.0244131	+	0.999702i	$0.492228\pi$
$282$		0			0
$283$	−7.83964	−	3.77537i	−0.466018	−	0.224423i	0.186113	−	0.982528i	$-0.440411\pi$
$283$	−7.83964	−	3.77537i	−0.466018	−	0.224423i	−0.652132	+	0.758106i	$0.726125\pi$
$284$	9.04389	−	39.6239i	0.536656	−	2.35124i
$285$		0			0
$286$	4.78090	+	20.9465i	0.282701	+	1.23859i
$287$	7.94060	−	0.0669876i	0.468719	−	0.00395415i
$288$		0			0
$289$	−2.60606	−	11.4179i	−0.153298	−	0.671641i
$290$	−20.7851	−	26.0637i	−1.22054	−	1.53051i
$291$		0			0
$292$	26.0137	+	12.5276i	1.52234	+	0.733119i
$293$	2.71829			0.158804			0.0794020	−	0.996843i	$-0.474699\pi$
$293$	2.71829			0.158804			0.0794020	+	0.996843i	$0.474699\pi$
$294$		0			0
$295$	−9.16243			−0.533457
$296$	83.9579	+	40.4320i	4.87995	+	2.35006i
$297$		0			0
$298$	−3.79011	−	4.75264i	−0.219555	−	0.275313i
$299$	−4.26697	−	18.6948i	−0.246765	−	1.08115i
$300$		0			0
$301$	25.6442	+	12.0842i	1.47811	+	0.696519i
$302$	0.284101	+	1.24473i	0.0163482	+	0.0716260i
$303$		0			0
$304$	5.60599	−	24.5614i	0.321525	−	1.40869i
$305$	11.1248	+	5.35740i	0.637002	+	0.306764i
$306$		0			0
$307$	13.0455	+	6.28238i	0.744546	+	0.358555i	0.767387	−	0.641184i	$-0.221557\pi$
$307$	13.0455	+	6.28238i	0.744546	+	0.358555i	−0.0228404	+	0.999739i	$0.507271\pi$
$308$	−20.1340	+	0.169852i	−1.14724	+	0.00967822i
$309$		0			0
$310$	2.08389	−	9.13012i	0.118357	−	0.518556i
$311$	−12.9246	+	16.2070i	−0.732888	+	0.919013i	−0.998990	−	0.0449322i	$-0.985693\pi$
$311$	−12.9246	+	16.2070i	−0.732888	+	0.919013i	0.266102	+	0.963945i	$0.414264\pi$
$312$		0			0
$313$	−1.33532			−0.0754765			−0.0377383	−	0.999288i	$-0.512015\pi$
$313$	−1.33532			−0.0754765			−0.0377383	+	0.999288i	$0.512015\pi$
$314$	−26.6414	+	33.4073i	−1.50346	+	1.88528i
$315$		0			0
$316$	−12.1141	−	15.1905i	−0.681469	−	0.854535i
$317$	−8.90936	−	11.1720i	−0.500399	−	0.627481i	0.465920	−	0.884827i	$-0.345723\pi$
$317$	−8.90936	−	11.1720i	−0.500399	−	0.627481i	−0.966319	+	0.257346i	$0.917152\pi$
$318$		0			0
$319$	9.73570	−	4.68847i	0.545095	−	0.262504i
$320$	−13.3969	−	16.7991i	−0.748907	−	0.939099i
$321$		0			0
$322$	25.2047	−	0.212629i	1.40461	−	0.0118494i
$323$	−7.83678	+	9.82702i	−0.436050	+	0.546790i
$324$		0			0
$325$	−9.52979			−0.528618
$326$	8.72455	−	10.9402i	0.483208	−	0.605924i
$327$		0			0
$328$	−21.1804	+	10.1999i	−1.16949	+	0.563196i
$329$	−12.8164	+	16.3524i	−0.706591	+	0.901535i
$330$		0			0
$331$	8.78177	−	11.0120i	0.482690	−	0.605274i	−0.479538	−	0.877521i	$-0.659196\pi$
$331$	8.78177	−	11.0120i	0.482690	−	0.605274i	0.962227	+	0.272248i	$0.0877670\pi$
$332$	14.5618	+	7.01258i	0.799181	+	0.384865i
$333$		0			0
$334$	9.98826	−	4.81009i	0.546533	−	0.263197i
$335$	3.54669	+	15.5391i	0.193776	+	0.848989i
$336$		0			0
$337$	−0.952328	+	4.17242i	−0.0518766	+	0.227286i	−0.994220	−	0.107361i	$-0.965760\pi$
$337$	−0.952328	+	4.17242i	−0.0518766	+	0.227286i	0.942343	+	0.334647i	$0.108617\pi$
$338$	8.94387	+	39.1856i	0.486482	+	2.13142i
$339$		0			0
$340$	10.6054	+	46.4652i	0.575158	+	2.51993i
$341$	2.73494	+	1.31708i	0.148105	+	0.0713238i
$342$		0			0
$343$	−11.1771	+	14.7673i	−0.603506	+	0.797359i
$344$	−83.9244			−4.52490
$345$		0			0
$346$	10.4417	+	45.7479i	0.561347	+	2.45942i
$347$	13.2491	+	16.6139i	0.711250	+	0.891879i	0.997807	−	0.0661839i	$-0.0210824\pi$
$347$	13.2491	+	16.6139i	0.711250	+	0.891879i	−0.286558	+	0.958063i	$0.592511\pi$
$348$		0			0
$349$	−2.65310	+	11.6240i	−0.142017	+	0.622217i	0.852948	+	0.521996i	$0.174812\pi$
$349$	−2.65310	+	11.6240i	−0.142017	+	0.622217i	−0.994965	+	0.100222i	$0.968045\pi$
$350$	2.68431	−	12.2356i	0.143482	−	0.654020i
$351$		0			0
$352$	17.5076	−	8.43121i	0.933157	−	0.449385i
$353$	7.24421	−	31.7390i	0.385571	−	1.68929i	−0.294098	−	0.955775i	$-0.595019\pi$
$353$	7.24421	−	31.7390i	0.385571	−	1.68929i	0.679668	−	0.733520i	$-0.262124\pi$
$354$		0			0
$355$	9.13462	−	11.4545i	0.484815	−	0.607939i
$356$	−36.5122	−	17.5833i	−1.93514	−	0.931915i
$357$		0			0
$358$	26.8876	−	12.9484i	1.42105	−	0.684343i
$359$	7.81583	−	34.2434i	0.412504	−	1.80730i	−0.159677	−	0.987169i	$-0.551045\pi$
$359$	7.81583	−	34.2434i	0.412504	−	1.80730i	0.572181	−	0.820128i	$-0.306098\pi$
$360$		0			0
$361$	−13.4975			−0.710394
$362$	61.6857			3.24213
$363$		0			0
$364$	−69.8221	+	0.589025i	−3.65967	+	0.0308733i
$365$	6.48932	+	8.13735i	0.339666	+	0.425928i
$366$		0			0
$367$	18.4150	−	8.86821i	0.961256	−	0.462917i	0.113637	−	0.993522i	$-0.463750\pi$
$367$	18.4150	−	8.86821i	0.961256	−	0.462917i	0.847619	+	0.530606i	$0.178036\pi$
$368$	−34.9241	+	16.8186i	−1.82054	+	0.876728i
$369$		0			0
$370$	35.0601	+	43.9640i	1.82269	+	2.28558i
$371$	2.05208	−	1.00964i	0.106539	−	0.0524181i
$372$		0			0
$373$	−23.6582			−1.22497			−0.612487	−	0.790481i	$-0.709831\pi$
$373$	−23.6582			−1.22497			−0.612487	+	0.790481i	$0.709831\pi$
$374$	−21.6687			−1.12046
$375$		0			0
$376$	13.6866	−	59.9650i	0.705834	−	3.09246i
$377$	33.7622	−	16.2590i	1.73884	−	0.837382i
$378$		0			0
$379$	−8.31500	−	4.00429i	−0.427113	−	0.205687i	0.207963	−	0.978137i	$-0.433317\pi$
$379$	−8.31500	−	4.00429i	−0.427113	−	0.205687i	−0.635076	+	0.772450i	$0.719031\pi$
$380$	13.0088	−	16.3125i	0.667337	−	0.836814i
$381$		0			0
$382$	13.7240	−	60.1287i	0.702180	−	3.07645i
$383$	2.36925	−	1.14097i	0.121063	−	0.0583009i	−0.372372	−	0.928084i	$-0.621455\pi$
$383$	2.36925	−	1.14097i	0.121063	−	0.0583009i	0.493435	+	0.869783i	$0.335741\pi$
$384$		0			0
$385$	−6.56564	−	3.09389i	−0.334616	−	0.157679i
$386$	−2.80319	+	12.2816i	−0.142678	+	0.625115i
$387$		0			0
$388$	−9.44430	−	11.8428i	−0.479462	−	0.601226i
$389$	−0.709059	−	3.10659i	−0.0359507	−	0.157510i	0.953766	−	0.300549i	$-0.0971699\pi$
$389$	−0.709059	−	3.10659i	−0.0359507	−	0.157510i	−0.989717	+	0.143039i	$0.954313\pi$
$390$		0			0
$391$	19.3394			0.978035
$392$	11.2968	−	53.6515i	0.570575	−	2.70981i
$393$		0			0
$394$	−10.3937	−	5.00534i	−0.523627	−	0.252166i
$395$	−1.55850	−	6.82825i	−0.0784169	−	0.343567i
$396$		0			0
$397$	−6.07957	−	26.6363i	−0.305125	−	1.33684i	−0.862280	−	0.506431i	$-0.830964\pi$
$397$	−6.07957	−	26.6363i	−0.305125	−	1.33684i	0.557156	−	0.830408i	$-0.311893\pi$
$398$	−5.80920	+	25.4518i	−0.291189	+	1.27578i
$399$		0			0
$400$	4.28668	+	18.7812i	0.214334	+	0.939059i
$401$	27.3826	−	13.1867i	1.36742	−	0.658515i	0.401142	−	0.916016i	$-0.368613\pi$
$401$	27.3826	−	13.1867i	1.36742	−	0.658515i	0.966278	+	0.257501i	$0.0828992\pi$
$402$		0			0
$403$	9.48444	+	4.56746i	0.472453	+	0.227522i
$404$	−0.284064	+	0.356205i	−0.0141327	+	0.0177219i
$405$		0			0
$406$	11.3655	+	47.9280i	0.564059	+	2.37863i
$407$	−16.4221	+	7.90846i	−0.814013	+	0.392008i
$408$		0			0
$409$	21.4490	−	26.8962i	1.06059	−	1.32993i	0.119101	−	0.992882i	$-0.461999\pi$
$409$	21.4490	−	26.8962i	1.06059	−	1.32993i	0.941486	−	0.337051i	$-0.109430\pi$
$410$	−14.1859			−0.700590
$411$		0			0
$412$	−18.5187	+	23.2217i	−0.912350	+	1.14405i
$413$	12.2465	+	5.77085i	0.602612	+	0.283965i
$414$		0			0
$415$	3.63254	+	4.55506i	0.178314	+	0.223599i
$416$	60.7141	−	29.2384i	2.97675	−	1.43353i
$417$		0			0
$418$	5.91445	+	7.41649i	0.289285	+	0.362752i
$419$	6.86103	+	8.60346i	0.335183	+	0.420307i	0.920649	−	0.390390i	$-0.127660\pi$
$419$	6.86103	+	8.60346i	0.335183	+	0.420307i	−0.585466	+	0.810697i	$0.699089\pi$
$420$		0			0
$421$	21.2007	−	26.5848i	1.03326	−	1.29567i	0.0789392	−	0.996879i	$-0.474847\pi$
$421$	21.2007	−	26.5848i	1.03326	−	1.29567i	0.954320	−	0.298787i	$-0.0965819\pi$
$422$	−24.0590			−1.17117
$423$		0			0
$424$	−4.22136	+	5.29341i	−0.205007	+	0.257071i
$425$	2.13869	−	9.37023i	0.103742	−	0.454523i
$426$		0			0
$427$	−11.4951	−	14.1675i	−0.556286	−	0.685614i
$428$	−74.0092	−	35.6410i	−3.57737	−	1.72277i
$429$		0			0
$430$	−45.6279	−	21.9733i	−2.20037	−	1.05964i
$431$	−6.35134	+	27.8270i	−0.305933	+	1.34038i	0.555079	+	0.831798i	$0.312688\pi$
$431$	−6.35134	+	27.8270i	−0.305933	+	1.34038i	−0.861012	+	0.508584i	$0.830169\pi$
$432$		0			0
$433$	1.57050	+	6.88082i	0.0754735	+	0.330671i	0.998543	−	0.0539622i	$-0.0171850\pi$
$433$	1.57050	+	6.88082i	0.0754735	+	0.330671i	−0.923069	+	0.384633i	$0.874328\pi$
$434$	−8.53583	+	10.8908i	−0.409733	+	0.522776i
$435$		0			0
$436$	−1.90380	−	8.34110i	−0.0911756	−	0.399466i
$437$	−5.27867	−	6.61924i	−0.252513	−	0.316641i
$438$		0			0
$439$	−9.22824	−	4.44409i	−0.440440	−	0.212105i	0.200503	−	0.979693i	$-0.435742\pi$
$439$	−9.22824	−	4.44409i	−0.440440	−	0.212105i	−0.640943	+	0.767588i	$0.721457\pi$
$440$	21.4870			1.02435
$441$		0			0
$442$	−75.1443			−3.57425
$443$	4.57159	+	2.20156i	0.217203	+	0.104599i	0.539322	−	0.842100i	$-0.318681\pi$
$443$	4.57159	+	2.20156i	0.217203	+	0.104599i	−0.322119	+	0.946699i	$0.604395\pi$
$444$		0			0
$445$	−9.10824	−	11.4214i	−0.431772	−	0.541425i
$446$	−6.62164	−	29.0113i	−0.313544	−	1.37372i
$447$		0			0
$448$	7.32551	+	30.8916i	0.346098	+	1.45949i
$449$	2.92148	+	12.7998i	0.137873	+	0.604062i	0.995900	+	0.0904577i	$0.0288330\pi$
$449$	2.92148	+	12.7998i	0.137873	+	0.604062i	−0.858027	+	0.513604i	$0.828310\pi$
$450$		0			0
$451$	1.02320	−	4.48294i	0.0481807	−	0.211093i
$452$	15.8662	+	7.64078i	0.746285	+	0.359392i
$453$		0			0
$454$	−31.2214	−	15.0354i	−1.46529	−	0.705648i
$455$	−22.7688	−	10.7292i	−1.06742	−	0.502993i
$456$		0			0
$457$	0.0106933	−	0.0468503i	0.000500211	−	0.00219157i	−0.974677	−	0.223617i	$-0.928214\pi$
$457$	0.0106933	−	0.0468503i	0.000500211	−	0.00219157i	0.975177	+	0.221425i	$0.0710708\pi$
$458$	−23.8192	+	29.8683i	−1.11300	+	1.39566i
$459$		0			0
$460$	−32.1027			−1.49680
$461$	20.3947	−	25.5742i	0.949876	−	1.19111i	−0.0315958	−	0.999501i	$-0.510059\pi$
$461$	20.3947	−	25.5742i	0.949876	−	1.19111i	0.981472	−	0.191606i	$-0.0613696\pi$
$462$		0			0
$463$	−0.560737	−	0.703142i	−0.0260597	−	0.0326778i	0.768631	−	0.639693i	$-0.220938\pi$
$463$	−0.560737	−	0.703142i	−0.0260597	−	0.0326778i	−0.794691	+	0.607015i	$0.792367\pi$
$464$	−47.2299	−	59.2244i	−2.19259	−	2.74942i
$465$		0			0
$466$	8.16980	−	3.93437i	0.378459	−	0.182256i
$467$	−23.5198	−	29.4929i	−1.08837	−	1.36477i	−0.925775	−	0.378074i	$-0.876586\pi$
$467$	−23.5198	−	29.4929i	−1.08837	−	1.36477i	−0.162591	−	0.986694i	$-0.551985\pi$
$468$		0			0
$469$	5.04659	−	23.0034i	0.233030	−	1.06220i
$470$	23.1413	−	29.0182i	1.06743	−	1.33851i
$471$		0			0
$472$	−40.0786			−1.84477
$473$	10.2349	−	12.8342i	0.470603	−	0.590117i
$474$		0			0
$475$	−3.79088	+	1.82559i	−0.173937	+	0.0837638i
$476$	15.0904	−	68.7852i	0.691669	−	3.15276i
$477$		0			0
$478$	13.4423	−	16.8562i	0.614839	−	0.770983i
$479$	15.9852	+	7.69808i	0.730384	+	0.351734i	0.761835	−	0.647771i	$-0.224299\pi$
$479$	15.9852	+	7.69808i	0.730384	+	0.351734i	−0.0314514	+	0.999505i	$0.510013\pi$
$480$		0			0
$481$	−56.9498	+	27.4256i	−2.59669	+	1.25050i
$482$	13.1589	+	57.6530i	0.599373	+	2.62602i
$483$		0			0
$484$	9.56434	−	41.9041i	0.434743	−	1.90473i
$485$	−1.21503	−	5.32341i	−0.0551718	−	0.241724i
$486$		0			0
$487$	−1.95538	−	8.56710i	−0.0886069	−	0.388212i	0.911106	−	0.412172i	$-0.135230\pi$
$487$	−1.95538	−	8.56710i	−0.0886069	−	0.388212i	−0.999713	+	0.0239598i	$0.992373\pi$
$488$	48.6623	+	23.4345i	2.20284	+	1.06083i
$489$		0			0
$490$	20.1890	−	26.2114i	0.912045	−	1.18411i
$491$	5.48916			0.247722			0.123861	−	0.992300i	$-0.460472\pi$
$491$	5.48916			0.247722			0.123861	+	0.992300i	$0.460472\pi$
$492$		0			0
$493$	8.40980	+	36.8457i	0.378758	+	1.65945i
$494$	20.5106	+	25.7194i	0.922814	+	1.15717i
$495$		0			0
$496$	4.73521	−	20.7463i	0.212617	−	0.931537i
$497$	−19.4238	+	9.55670i	−0.871277	+	0.428677i
$498$		0			0
$499$	5.95033	−	2.86553i	0.266373	−	0.128279i	−0.295930	−	0.955210i	$-0.595630\pi$
$499$	5.95033	−	2.86553i	0.266373	−	0.128279i	0.562303	+	0.826931i	$0.309915\pi$
$500$	−13.4464	+	58.9123i	−0.601339	+	2.63464i
$501$		0			0
$502$	16.4425	−	20.6182i	0.733863	−	0.920235i
$503$	−25.8228	−	12.4356i	−1.15138	−	0.554477i	−0.241934	−	0.970293i	$-0.577782\pi$
$503$	−25.8228	−	12.4356i	−1.15138	−	0.554477i	−0.909449	+	0.415816i	$0.863496\pi$
$504$		0			0
$505$	−0.147970	+	0.0712586i	−0.00658458	+	0.00317097i
$506$	3.24781	−	14.2296i	0.144383	−	0.632582i
$507$		0			0
$508$	−37.2501			−1.65271
$509$	10.5248			0.466504			0.233252	−	0.972416i	$-0.425063\pi$
$509$	10.5248			0.466504			0.233252	+	0.972416i	$0.425063\pi$
$510$		0			0
$511$	−3.54841	−	14.9636i	−0.156973	−	0.661951i
$512$	19.9643	+	25.0345i	0.882306	+	1.10638i
$513$		0			0
$514$	30.5924	−	14.7325i	1.34937	−	0.649824i
$515$	−9.64644	+	4.64548i	−0.425073	+	0.204704i
$516$		0			0
$517$	7.50105	+	9.40602i	0.329896	+	0.413676i
$518$	−19.1712	−	80.8446i	−0.842333	−	3.55211i
$519$		0			0
$520$	74.5143			3.26767
$521$	33.3040			1.45907			0.729537	−	0.683941i	$-0.239735\pi$
$521$	33.3040			1.45907			0.729537	+	0.683941i	$0.239735\pi$
$522$		0			0
$523$	−1.33205	+	5.83608i	−0.0582464	+	0.255194i	−0.995665	−	0.0930099i	$-0.970351\pi$
$523$	−1.33205	+	5.83608i	−0.0582464	+	0.255194i	0.937419	+	0.348204i	$0.113208\pi$
$524$	−75.5746	+	36.3948i	−3.30149	+	1.58991i
$525$		0			0
$526$	24.4382	+	11.7688i	1.06556	+	0.513146i
$527$	−6.61950	+	8.30059i	−0.288350	+	0.361579i
$528$		0			0
$529$	2.21930	−	9.72340i	0.0964914	−	0.422756i
$530$	−3.68099	+	1.77267i	−0.159892	+	0.0770000i
$531$		0			0
$532$	−27.6618	+	13.6099i	−1.19929	+	0.590063i
$533$	3.54834	−	15.5463i	0.153695	−	0.673384i
$534$		0			0
$535$	−18.4621	−	23.1508i	−0.798188	−	1.00090i
$536$	15.5140	+	67.9714i	0.670104	+	2.93592i
$537$		0			0
$538$	−53.7969			−2.31935
$539$	6.82699	+	8.27059i	0.294059	+	0.356240i
$540$		0			0
$541$	33.8112	+	16.2826i	1.45366	+	0.700044i	0.983226	−	0.182393i	$-0.0583845\pi$
$541$	33.8112	+	16.2826i	1.45366	+	0.700044i	0.470430	+	0.882437i	$0.344099\pi$
$542$	−5.02322	−	22.0082i	−0.215766	−	0.945332i
$543$		0			0
$544$	15.1232	+	66.2592i	0.648403	+	2.84084i
$545$	0.686276	−	3.00677i	0.0293968	−	0.128796i
$546$		0			0
$547$	8.93834	+	39.1614i	0.382176	+	1.67442i	0.690650	+	0.723189i	$0.257324\pi$
$547$	8.93834	+	39.1614i	0.382176	+	1.67442i	−0.308474	+	0.951233i	$0.599818\pi$
$548$	−23.6725	+	11.4001i	−1.01124	+	0.486988i
$549$		0			0
$550$	−6.53528	−	3.14722i	−0.278665	−	0.134198i
$551$	10.3156	−	12.9354i	0.439461	−	0.551067i
$552$		0			0
$553$	−2.21760	+	10.1083i	−0.0943020	+	0.429847i
$554$	38.2395	−	18.4152i	1.62464	−	0.782386i
$555$		0			0
$556$	−11.0039	+	13.7984i	−0.466668	+	0.585184i
$557$	−4.25487			−0.180285			−0.0901424	−	0.995929i	$-0.528732\pi$
$557$	−4.25487			−0.180285			−0.0901424	+	0.995929i	$0.528732\pi$
$558$		0			0
$559$	35.4934	−	44.5074i	1.50121	−	1.88246i
$560$	−10.9031	+	49.6986i	−0.460741	+	2.10015i
$561$		0			0
$562$	25.1462	+	31.5324i	1.06073	+	1.33011i
$563$	−36.4588	+	17.5576i	−1.53656	+	0.739966i	−0.994922	−	0.100649i	$-0.967908\pi$
$563$	−36.4588	+	17.5576i	−1.53656	+	0.739966i	−0.541633	+	0.840615i	$0.682194\pi$
$564$		0			0
$565$	3.95795	+	4.96311i	0.166512	+	0.208800i
$566$	−14.3202	−	17.9570i	−0.601924	−	0.754789i
$567$		0			0
$568$	39.9569	−	50.1044i	1.67656	−	2.10233i
$569$	−6.50763			−0.272814			−0.136407	−	0.990653i	$-0.543555\pi$
$569$	−6.50763			−0.272814			−0.136407	+	0.990653i	$0.543555\pi$
$570$		0			0
$571$	−22.1244	+	27.7431i	−0.925876	+	1.16101i	0.0607737	+	0.998152i	$0.480643\pi$
$571$	−22.1244	+	27.7431i	−0.925876	+	1.16101i	−0.986649	+	0.162860i	$0.947928\pi$
$572$	−8.99707	+	39.4187i	−0.376186	+	1.64818i
$573$		0			0
$574$	18.9609	+	8.93481i	0.791411	+	0.372932i
$575$	5.83276	+	2.80891i	0.243243	+	0.117140i
$576$		0			0
$577$	4.22495	+	2.03463i	0.175887	+	0.0847028i	0.519755	−	0.854315i	$-0.326023\pi$
$577$	4.22495	+	2.03463i	0.175887	+	0.0847028i	−0.343868	+	0.939018i	$0.611737\pi$
$578$	6.87889	−	30.1384i	0.286124	−	1.25359i
$579$		0			0
$580$	−13.9600	−	61.1627i	−0.579657	−	2.53964i
$581$	−1.98631	−	8.37622i	−0.0824058	−	0.347504i
$582$		0			0
$583$	−0.294687	−	1.29111i	−0.0122047	−	0.0534722i
$584$	28.3858	+	35.5946i	1.17461	+	1.47292i
$585$		0			0
$586$	6.46456	+	3.11317i	0.267049	+	0.128604i
$587$	−14.3998			−0.594345			−0.297172	−	0.954824i	$-0.596044\pi$
$587$	−14.3998			−0.594345			−0.297172	+	0.954824i	$0.596044\pi$
$588$		0			0
$589$	4.64781			0.191510
$590$	−21.7899	−	10.4934i	−0.897074	−	0.432008i
$591$		0			0
$592$	79.6670	+	99.8992i	3.27429	+	4.10583i
$593$	8.92181	+	39.0890i	0.366375	+	1.60519i	0.736652	+	0.676272i	$0.236406\pi$
$593$	8.92181	+	39.0890i	0.366375	+	1.60519i	−0.370277	+	0.928921i	$0.620737\pi$
$594$		0			0
$595$	15.6594	−	19.9797i	0.641972	−	0.819088i
$596$	−2.54556	−	11.1528i	−0.104270	−	0.456838i
$597$		0			0
$598$	11.2630	−	49.3464i	0.460578	−	2.01792i
$599$	−0.366701	−	0.176594i	−0.0149830	−	0.00721543i	0.426377	−	0.904545i	$-0.359790\pi$
$599$	−0.366701	−	0.176594i	−0.0149830	−	0.00721543i	−0.441360	+	0.897330i	$0.645504\pi$
$600$		0			0
$601$	26.8731	+	12.9414i	1.09618	+	0.527892i	0.892455	−	0.451137i	$-0.148981\pi$
$601$	26.8731	+	12.9414i	1.09618	+	0.527892i	0.203724	+	0.979028i	$0.434696\pi$
$602$	47.1468	+	58.1077i	1.92156	+	2.36829i
$603$		0			0
$604$	−0.534643	+	2.34242i	−0.0217543	+	0.0953118i
$605$	9.66030	−	12.1136i	0.392747	−	0.492489i
$606$		0			0
$607$	10.5466			0.428073			0.214037	−	0.976826i	$-0.431339\pi$
$607$	10.5466			0.428073			0.214037	+	0.976826i	$0.431339\pi$
$608$	18.5505	−	23.2616i	0.752322	−	0.943381i
$609$		0			0
$610$	20.3210	+	25.4817i	0.822772	+	1.03172i
$611$	26.0127	+	32.6189i	1.05236	+	1.31962i
$612$		0			0
$613$	37.1141	−	17.8732i	1.49903	−	0.721892i	0.508737	−	0.860922i	$-0.330113\pi$
$613$	37.1141	−	17.8732i	1.49903	−	0.721892i	0.990288	+	0.139030i	$0.0443983\pi$
$614$	23.8295	+	29.8812i	0.961679	+	1.20591i
$615$		0			0
$616$	−28.7196	−	13.5334i	−1.15715	−	0.545275i
$617$	−1.32165	+	1.65730i	−0.0532078	+	0.0667204i	−0.807723	−	0.589562i	$-0.799300\pi$
$617$	−1.32165	+	1.65730i	−0.0532078	+	0.0667204i	0.754516	+	0.656282i	$0.227872\pi$
$618$		0			0
$619$	37.8076			1.51961			0.759807	−	0.650148i	$-0.225293\pi$
$619$	37.8076			1.51961			0.759807	+	0.650148i	$0.225293\pi$
$620$	10.9881	−	13.7787i	0.441295	−	0.553366i
$621$		0			0
$622$	−49.2983	+	23.7408i	−1.97668	+	0.951921i
$623$	4.98046	+	21.0025i	0.199538	+	0.841449i
$624$		0			0
$625$	−7.98949	+	10.0185i	−0.319580	+	0.400740i
$626$	−3.17561	−	1.52930i	−0.126923	−	0.0611229i
$627$		0			0
$628$	−72.4484	+	34.8893i	−2.89101	+	1.39224i
$629$	−14.1856	−	62.1511i	−0.565616	−	2.47813i
$630$		0			0
$631$	1.66288	−	7.28554i	0.0661981	−	0.290033i	−0.930983	−	0.365062i	$-0.881048\pi$
$631$	1.66288	−	7.28554i	0.0661981	−	0.290033i	0.997181	+	0.0750291i	$0.0239050\pi$
$632$	−6.81726	−	29.8683i	−0.271176	−	1.18810i
$633$		0			0
$634$	−8.39309	−	36.7725i	−0.333332	−	1.46042i
$635$	−12.0980	−	5.82610i	−0.480096	−	0.231202i
$636$		0			0
$637$	23.6752	+	28.6814i	0.938044	+	1.13640i
$638$	28.5228			1.12923
$639$		0			0
$640$	−2.51294	−	11.0099i	−0.0993325	−	0.435204i
$641$	−22.2314	−	27.8773i	−0.878088	−	1.10109i	−0.994167	−	0.107848i	$-0.965604\pi$
$641$	−22.2314	−	27.8773i	−0.878088	−	1.10109i	0.116079	−	0.993240i	$-0.462967\pi$
$642$		0			0
$643$	−7.38477	+	32.3548i	−0.291227	+	1.27595i	0.591593	+	0.806237i	$0.298499\pi$
$643$	−7.38477	+	32.3548i	−0.291227	+	1.27595i	−0.882820	+	0.469712i	$0.844358\pi$
$644$	42.9086	+	20.2196i	1.69083	+	0.796762i
$645$		0			0
$646$	−29.8918	+	14.3951i	−1.17608	+	0.566369i
$647$	6.04643	−	26.4912i	0.237710	−	1.04147i	−0.705352	−	0.708857i	$-0.749211\pi$
$647$	6.04643	−	26.4912i	0.237710	−	1.04147i	0.943062	−	0.332617i	$-0.107932\pi$
$648$		0			0
$649$	4.88774	−	6.12904i	0.191861	−	0.240586i
$650$	−22.6635	−	10.9142i	−0.888936	−	0.428089i
$651$		0			0
$652$	23.7255	−	11.4256i	0.929161	−	0.447460i
$653$	2.93715	−	12.8685i	0.114940	−	0.503584i	−0.884382	−	0.466763i	$-0.845420\pi$
$653$	2.93715	−	12.8685i	0.114940	−	0.503584i	0.999322	−	0.0368202i	$-0.0117229\pi$
$654$		0			0
$655$	−30.2373			−1.18147
$656$	−32.2345			−1.25854
$657$		0			0
$658$	−49.2075	+	24.2106i	−1.91831	+	0.943826i
$659$	−12.3068	−	15.4322i	−0.479405	−	0.601155i	0.482041	−	0.876149i	$-0.339896\pi$
$659$	−12.3068	−	15.4322i	−0.479405	−	0.601155i	−0.961446	+	0.274994i	$0.911324\pi$
$660$		0			0
$661$	−29.4936	+	14.2034i	−1.14717	+	0.552448i	−0.908182	−	0.418575i	$-0.862530\pi$
$661$	−29.4936	+	14.2034i	−1.14717	+	0.552448i	−0.238987	+	0.971023i	$0.576815\pi$
$662$	33.4963	−	16.1310i	1.30187	−	0.626947i
$663$		0			0
$664$	15.8896	+	19.9249i	0.616635	+	0.773236i
$665$	−11.1126	+	0.0937470i	−0.430929	+	0.00363535i
$666$		0			0
$667$	−25.4567			−0.985686
$668$	20.8627			0.807204
$669$		0			0
$670$	−9.36175	+	41.0165i	−0.361676	+	1.58461i
$671$	−9.51830	+	4.58377i	−0.367450	+	0.176955i
$672$		0			0
$673$	−19.4386	−	9.36115i	−0.749304	−	0.360846i	0.0199397	−	0.999801i	$-0.493653\pi$
$673$	−19.4386	−	9.36115i	−0.749304	−	0.360846i	−0.769244	+	0.638955i	$0.779367\pi$
$674$	−7.04335	+	8.83208i	−0.271300	+	0.340199i
$675$		0			0
$676$	−16.8313	+	73.7426i	−0.647356	+	2.83625i
$677$	−34.7563	+	16.7377i	−1.33579	+	0.643283i	−0.959103	−	0.283057i	$-0.908652\pi$
$677$	−34.7563	+	16.7377i	−1.33579	+	0.643283i	−0.376689	+	0.926340i	$0.622937\pi$
$678$		0			0
$679$	−1.72887	+	7.88055i	−0.0663481	+	0.302428i
$680$	−16.7226	+	73.2667i	−0.641284	+	2.80965i
$681$		0			0
$682$	4.99576	+	6.26449i	0.191298	+	0.239880i
$683$	4.00457	+	17.5452i	0.153231	+	0.671348i	0.991934	+	0.126759i	$0.0404574\pi$
$683$	4.00457	+	17.5452i	0.153231	+	0.671348i	−0.838703	+	0.544589i	$0.816686\pi$
$684$		0			0
$685$	−9.47135			−0.361882
$686$	−43.4936	+	22.3184i	−1.66059	+	0.852121i
$687$		0			0
$688$	−103.680	−	49.9297i	−3.95277	−	1.90355i
$689$	−1.02194	−	4.47740i	−0.0389327	−	0.170575i
$690$		0			0
$691$	5.17014	+	22.6518i	0.196681	+	0.861717i	0.972895	+	0.231247i	$0.0742805\pi$
$691$	5.17014	+	22.6518i	0.196681	+	0.861717i	−0.776214	+	0.630470i	$0.782862\pi$
$692$	−19.6499	+	86.0920i	−0.746978	+	3.27273i
$693$		0			0
$694$	12.4814	+	54.6845i	0.473787	+	2.07579i
$695$	−5.73196	+	2.76037i	−0.217426	+	0.104707i
$696$		0			0
$697$	14.4896	+	6.97784i	0.548834	+	0.264305i
$698$	−19.6221	+	24.6054i	−0.742708	+	0.931326i
$699$		0			0
$700$	14.5418	−	18.5538i	0.549630	−	0.701269i
$701$	3.36892	−	1.62239i	0.127243	−	0.0612768i	−0.369179	−	0.929358i	$-0.620361\pi$
$701$	3.36892	−	1.62239i	0.127243	−	0.0612768i	0.496422	+	0.868081i	$0.334647\pi$
$702$		0			0
$703$	−17.4003	+	21.8193i	−0.656266	+	0.822932i
$704$	18.3841			0.692876
$705$		0			0
$706$	53.5776	−	67.1842i	2.01642	−	2.52851i
$707$	0.242658	−	0.00204709i	0.00912611	−	7.69887e-5i
$708$		0			0
$709$	−26.9325	−	33.7723i	−1.01147	−	1.26835i	−0.962994	−	0.269522i	$-0.913134\pi$
$709$	−26.9325	−	33.7723i	−1.01147	−	1.26835i	−0.0484785	−	0.998824i	$-0.515437\pi$
$710$	34.8422	−	16.7791i	1.30760	−	0.629708i
$711$		0			0
$712$	−39.8415	−	49.9597i	−1.49312	−	1.87232i
$713$	−4.45874	−	5.59108i	−0.166981	−	0.209387i
$714$		0			0
$715$	−9.08733	+	11.3951i	−0.339847	+	0.426154i
$716$	56.1608			2.09883
$717$		0			0
$718$	57.8053	−	72.4855i	2.15727	−	2.70514i
$719$	7.92776	−	34.7338i	0.295655	−	1.29535i	−0.580870	−	0.813996i	$-0.697288\pi$
$719$	7.92776	−	34.7338i	0.295655	−	1.29535i	0.876526	−	0.481355i	$-0.159855\pi$
$720$		0			0
$721$	15.8194	−	0.133454i	0.589144	−	0.00497007i
$722$	−32.0994	−	15.4583i	−1.19462	−	0.575297i
$723$		0			0
$724$	104.589	+	50.3674i	3.88702	+	1.87189i
$725$	−2.81519	+	12.3341i	−0.104553	+	0.458078i
$726$		0			0
$727$	−6.96096	−	30.4980i	−0.258168	−	1.13111i	−0.923208	−	0.384300i	$-0.874443\pi$
$727$	−6.96096	−	30.4980i	−0.258168	−	1.13111i	0.665041	−	0.746807i	$-0.268414\pi$
$728$	−99.5960	−	46.9320i	−3.69127	−	1.73942i
$729$		0			0
$730$	6.11328	+	26.7840i	0.226263	+	0.991322i
$731$	35.7966	+	44.8876i	1.32399	+	1.66023i
$732$		0			0
$733$	12.7882	+	6.15846i	0.472342	+	0.227468i	0.654883	−	0.755730i	$-0.272718\pi$
$733$	12.7882	+	6.15846i	0.472342	+	0.227468i	−0.182541	+	0.983198i	$0.558432\pi$
$734$	53.9506			1.99135
$735$		0			0
$736$	−45.7784			−1.68741
$737$	−12.2866	−	5.91690i	−0.452581	−	0.217952i
$738$		0			0
$739$	22.3928	+	28.0797i	0.823733	+	1.03293i	0.998829	+	0.0483769i	$0.0154049\pi$
$739$	22.3928	+	28.0797i	0.823733	+	1.03293i	−0.175096	+	0.984551i	$0.556024\pi$
$740$	23.5476	+	103.169i	0.865626	+	3.79256i
$741$		0			0
$742$	6.03652	−	0.0509246i	0.221608	−	0.00186950i
$743$	10.1054	+	44.2746i	0.370731	+	1.62428i	0.724731	+	0.689032i	$0.241964\pi$
$743$	10.1054	+	44.2746i	0.370731	+	1.62428i	−0.354000	+	0.935245i	$0.615179\pi$
$744$		0			0
$745$	0.917616	−	4.02034i	0.0336188	−	0.147294i
$746$	−56.2633	−	27.0950i	−2.05995	−	0.992017i
$747$		0			0
$748$	−36.7396	−	17.6928i	−1.34333	−	0.646914i
$749$	10.0953	+	42.5716i	0.368873	+	1.55553i
$750$		0			0
$751$	4.08632	−	17.9033i	0.149112	−	0.653302i	−0.844021	−	0.536310i	$-0.819818\pi$
$751$	4.08632	−	17.9033i	0.149112	−	0.653302i	0.993133	−	0.116992i	$-0.0373250\pi$
$752$	52.5838	−	65.9380i	1.91753	−	2.40451i
$753$		0			0
$754$	98.9133			3.60221
$755$	−0.540006	+	0.677147i	−0.0196528	+	0.0246439i
$756$		0			0
$757$	−13.0046	−	16.3073i	−0.472662	−	0.592699i	0.487159	−	0.873313i	$-0.338033\pi$
$757$	−13.0046	−	16.3073i	−0.472662	−	0.592699i	−0.959821	+	0.280614i	$0.909462\pi$
$758$	−15.1885	−	19.0458i	−0.551672	−	0.691775i
$759$		0			0
$760$	29.6412	−	14.2745i	1.07520	−	0.517789i
$761$	−9.16903	−	11.4976i	−0.332377	−	0.416788i	0.587358	−	0.809327i	$-0.300168\pi$
$761$	−9.16903	−	11.4976i	−0.332377	−	0.416788i	−0.919735	+	0.392539i	$0.871597\pi$
$762$		0			0
$763$	−2.81106	+	3.58661i	−0.101767	+	0.129844i
$764$	72.3652	−	90.7431i	2.61808	−	3.28297i
$765$		0			0
$766$	6.94121			0.250796
$767$	16.9501	−	21.2547i	0.612032	−	0.767464i
$768$		0			0
$769$	−14.0175	+	6.75046i	−0.505483	+	0.243428i	−0.669204	−	0.743079i	$-0.733365\pi$
$769$	−14.0175	+	6.75046i	−0.505483	+	0.243428i	0.163721	+	0.986507i	$0.447650\pi$
$770$	−12.0709	−	14.8772i	−0.435005	−	0.536138i
$771$		0			0
$772$	−14.7809	+	18.5347i	−0.531977	+	0.667078i
$773$	2.92554	+	1.40886i	0.105224	+	0.0506733i	0.485755	−	0.874095i	$-0.338545\pi$
$773$	2.92554	+	1.40886i	0.105224	+	0.0506733i	−0.380531	+	0.924768i	$0.624259\pi$
$774$		0			0
$775$	−3.20204	+	1.54202i	−0.115021	+	0.0553911i
$776$	−5.31483	−	23.2858i	−0.190791	−	0.835912i
$777$		0			0
$778$	1.87161	−	8.20008i	0.0671006	−	0.293987i
$779$	−1.56665	−	6.86393i	−0.0561309	−	0.245926i
$780$		0			0
$781$	2.78933	+	12.2209i	0.0998103	+	0.437297i
$782$	45.9925	+	22.1488i	1.64469	+	0.792039i
$783$		0			0
$784$	45.8753	−	59.5601i	1.63840	−	2.12714i
$785$	−28.9865			−1.03457
$786$		0			0
$787$	−0.865094	−	3.79023i	−0.0308373	−	0.135107i	0.957166	−	0.289540i	$-0.0935022\pi$
$787$	−0.865094	−	3.79023i	−0.0308373	−	0.135107i	−0.988003	+	0.154433i	$0.950645\pi$
$788$	−13.5357	−	16.9732i	−0.482190	−	0.604647i
$789$		0			0
$790$	4.11379	−	18.0237i	0.146362	−	0.641254i
$791$	−2.16424	−	9.12658i	−0.0769516	−	0.324504i
$792$		0			0
$793$	−33.0083	+	15.8959i	−1.17216	+	0.564481i
$794$	16.0475	−	70.3086i	0.569504	−	2.49516i
$795$		0			0
$796$	−30.6314	+	38.4105i	−1.08570	+	1.36142i
$797$	25.9510	+	12.4973i	0.919232	+	0.442679i	0.832797	−	0.553579i	$-0.186738\pi$
$797$	25.9510	+	12.4973i	0.919232	+	0.442679i	0.0864349	+	0.996257i	$0.472453\pi$
$798$		0			0
$799$	−37.9105	+	18.2567i	−1.34118	+	0.645877i
$800$	−5.06251	+	22.1803i	−0.178987	+	0.784192i
$801$		0			0
$802$	80.2229			2.83277
$803$	−8.90509			−0.314254
$804$		0			0
$805$	10.7733	+	13.2780i	0.379710	+	0.467987i
$806$	17.3247	+	21.7245i	0.610236	+	0.765211i
$807$		0			0
$808$	−0.647255	+	0.311702i	−0.0227703	+	0.0109656i
$809$	−21.6736	+	10.4374i	−0.762002	+	0.366961i	−0.774180	−	0.632965i	$-0.781838\pi$
$809$	−21.6736	+	10.4374i	−0.762002	+	0.366961i	0.0121785	+	0.999926i	$0.496123\pi$
$810$		0			0
$811$	−24.8093	−	31.1099i	−0.871172	−	1.09242i	−0.994976	−	0.100109i	$-0.968081\pi$
$811$	−24.8093	−	31.1099i	−0.871172	−	1.09242i	0.123804	−	0.992307i	$-0.460491\pi$
$812$	−19.8637	+	90.5427i	−0.697080	+	3.17743i
$813$		0			0
$814$	−48.1119			−1.68632
$815$	9.49252			0.332509
$816$		0			0
$817$	5.59289	−	24.5040i	0.195670	−	0.857288i
$818$	81.8130	−	39.3991i	2.86052	−	1.37756i
$819$		0			0
$820$	−24.0523	−	11.5830i	−0.839943	−	0.404495i
$821$	−20.0111	+	25.0931i	−0.698392	+	0.875756i	−0.996902	−	0.0786508i	$-0.974939\pi$
$821$	−20.0111	+	25.0931i	−0.698392	+	0.875756i	0.298510	+	0.954406i	$0.403510\pi$
$822$		0			0
$823$	−1.70609	+	7.47486i	−0.0594705	+	0.260557i	−0.995919	−	0.0902466i	$-0.971234\pi$
$823$	−1.70609	+	7.47486i	−0.0594705	+	0.260557i	0.936449	+	0.350804i	$0.114092\pi$
$824$	−42.1958	+	20.3204i	−1.46996	+	0.707895i
$825$		0			0
$826$	22.5152	+	27.7497i	0.783403	+	0.965534i
$827$	−6.19704	+	27.1510i	−0.215492	+	0.944133i	0.745271	+	0.666762i	$0.232320\pi$
$827$	−6.19704	+	27.1510i	−0.215492	+	0.944133i	−0.960763	+	0.277371i	$0.910537\pi$
$828$		0			0
$829$	−13.2092	−	16.5638i	−0.458773	−	0.575284i	0.497609	−	0.867401i	$-0.334211\pi$
$829$	−13.2092	−	16.5638i	−0.458773	−	0.575284i	−0.956382	+	0.292118i	$0.905640\pi$
$830$	3.42205	+	14.9930i	0.118781	+	0.520414i
$831$		0			0
$832$	63.7537			2.21026
$833$	−33.5143	+	16.8420i	−1.16120	+	0.583541i
$834$		0			0
$835$	6.77576	+	3.26303i	0.234485	+	0.112922i
$836$	3.97235	+	17.4040i	0.137387	+	0.601930i
$837$		0			0
$838$	6.46346	+	28.3183i	0.223276	+	0.978238i
$839$	−6.50588	+	28.5041i	−0.224608	+	0.984072i	0.729352	+	0.684138i	$0.239822\pi$
$839$	−6.50588	+	28.5041i	−0.224608	+	0.984072i	−0.953960	+	0.299933i	$0.903036\pi$
$840$		0			0
$841$	−4.61681	−	20.2276i	−0.159200	−	0.697502i
$842$	80.8658	−	38.9429i	2.78682	−	1.34206i
$843$		0			0
$844$	−40.7924	−	19.6446i	−1.40413	−	0.676194i
$845$	−17.0001	+	21.3175i	−0.584822	+	0.733343i
$846$		0			0
$847$	−20.5416	+	10.1067i	−0.705818	+	0.347269i
$848$	−8.36430	+	4.02803i	−0.287231	+	0.138323i
$849$		0			0
$850$	15.8176	−	19.8347i	0.542540	−	0.680323i
$851$	42.9401			1.47197
$852$		0			0
$853$	−17.5428	+	21.9980i	−0.600655	+	0.753198i	−0.985480	−	0.169792i	$-0.945690\pi$
$853$	−17.5428	+	21.9980i	−0.600655	+	0.753198i	0.384825	+	0.922990i	$0.374262\pi$
$854$	−11.1117	−	46.8578i	−0.380234	−	1.60344i
$855$		0			0
$856$	−80.7576	−	101.267i	−2.76024	−	3.46123i
$857$	20.7934	−	10.0136i	0.710289	−	0.342057i	−0.0436090	−	0.999049i	$-0.513886\pi$
$857$	20.7934	−	10.0136i	0.710289	−	0.342057i	0.753898	+	0.656992i	$0.228171\pi$
$858$		0			0
$859$	−5.74935	−	7.20945i	−0.196165	−	0.245983i	0.674014	−	0.738718i	$-0.264569\pi$
$859$	−5.74935	−	7.20945i	−0.196165	−	0.245983i	−0.870179	+	0.492735i	$0.835997\pi$
$860$	−59.4212	−	74.5119i	−2.02625	−	2.54083i
$861$		0			0
$862$	−46.9740	+	58.9036i	−1.59994	+	2.00626i
$863$	−28.7289			−0.977944			−0.488972	−	0.872299i	$-0.662628\pi$
$863$	−28.7289			−0.977944			−0.488972	+	0.872299i	$0.662628\pi$
$864$		0			0
$865$	−19.8471	+	24.8874i	−0.674821	+	0.846198i
$866$	−4.14546	+	18.1624i	−0.140868	+	0.617185i
$867$		0			0
$868$	−23.3651	+	11.4959i	−0.793064	+	0.390195i
$869$	5.39903	+	2.60003i	0.183149	+	0.0882001i
$870$		0			0
$871$	−42.6083	−	20.5191i	−1.44373	−	0.695262i
$872$	3.00193	−	13.1523i	0.101658	−	0.445393i
$873$		0			0
$874$	−4.97279	−	21.7872i	−0.168207	−	0.736963i
$875$	28.8791	−	14.2088i	0.976292	−	0.480345i
$876$		0			0
$877$	−0.846002	−	3.70658i	−0.0285675	−	0.125162i	0.958634	−	0.284643i	$-0.0918751\pi$
$877$	−0.846002	−	3.70658i	−0.0285675	−	0.125162i	−0.987201	+	0.159481i	$0.949018\pi$
$878$	−16.8567	−	21.1376i	−0.568886	−	0.713360i
$879$		0			0
$880$	26.5450	+	12.7834i	0.894833	+	0.430929i
$881$	−50.3402			−1.69600			−0.848002	−	0.529993i	$-0.822194\pi$
$881$	−50.3402			−1.69600			−0.848002	+	0.529993i	$0.822194\pi$
$882$		0			0
$883$	30.3903			1.02271			0.511357	−	0.859368i	$-0.329143\pi$
$883$	30.3903			1.02271			0.511357	+	0.859368i	$0.329143\pi$
$884$	−127.408	−	61.3565i	−4.28520	−	2.06364i
$885$		0			0
$886$	8.35067	+	10.4714i	0.280546	+	0.351794i
$887$	−5.23407	−	22.9320i	−0.175743	−	0.769980i	−0.983565	−	0.180554i	$-0.942211\pi$
$887$	−5.23407	−	22.9320i	−0.175743	−	0.769980i	0.807822	−	0.589426i	$-0.200646\pi$
$888$		0			0
$889$	12.5007	+	15.4070i	0.419261	+	0.516734i
$890$	−8.58045	−	37.5934i	−0.287617	−	1.26013i
$891$		0			0
$892$	12.4611	−	54.5957i	0.417229	−	1.82800i
$893$	16.5963	+	7.99237i	0.555375	+	0.267454i
$894$		0			0
$895$	18.2398	+	8.78382i	0.609689	+	0.293611i
$896$	−3.57566	+	16.2986i	−0.119455	+	0.544497i
$897$		0			0
$898$	−7.71147	+	33.7862i	−0.257335	+	1.12746i
$899$	8.71332	−	10.9262i	0.290606	−	0.364408i
$900$		0			0
$901$	4.63177			0.154307
$902$	7.56752	−	9.48938i	0.251971	−	0.315962i
$903$		0			0
$904$	17.3130	+	21.7098i	0.575821	+	0.722057i
$905$	26.0905	+	32.7164i	0.867277	+	1.08753i
$906$		0			0
$907$	−42.3907	+	20.4143i	−1.40756	+	0.677846i	−0.974680	−	0.223605i	$-0.928218\pi$
$907$	−42.3907	+	20.4143i	−1.40756	+	0.677846i	−0.432882	+	0.901451i	$0.642503\pi$
$908$	−40.6596	−	50.9856i	−1.34934	−	1.69202i
$909$		0			0
$910$	−41.8604	−	51.5923i	−1.38766	−	1.71027i
$911$	−1.43434	+	1.79861i	−0.0475218	+	0.0595904i	−0.805024	−	0.593242i	$-0.797848\pi$
$911$	−1.43434	+	1.79861i	−0.0475218	+	0.0595904i	0.757503	+	0.652832i	$0.226419\pi$
$912$		0			0
$913$	−4.98482			−0.164974
$914$	0.0790867	−	0.0991716i	0.00261596	−	0.00328031i
$915$		0			0
$916$	−64.7738	+	31.1934i	−2.14019	+	1.03066i
$917$	40.4152	+	19.0446i	1.33463	+	0.628909i
$918$		0			0
$919$	16.3488	−	20.5007i	0.539296	−	0.676255i	−0.435285	−	0.900293i	$-0.643352\pi$
$919$	16.3488	−	20.5007i	0.539296	−	0.676255i	0.974581	+	0.224038i	$0.0719238\pi$
$920$	−45.6069	−	21.9631i	−1.50361	−	0.724102i
$921$		0			0
$922$	77.7914	−	37.4624i	2.56192	−	1.23376i
$923$	9.67306	+	42.3805i	0.318393	+	1.39497i
$924$		0			0
$925$	4.74863	−	20.8051i	0.156134	−	0.684068i
$926$	−0.528244	−	2.31439i	−0.0173592	−	0.0760555i
$927$		0			0
$928$	−19.9069	−	87.2177i	−0.653475	−	2.86306i
$929$	42.3617	+	20.4003i	1.38984	+	0.669314i	0.971074	−	0.238779i	$-0.0767471\pi$
$929$	42.3617	+	20.4003i	1.38984	+	0.669314i	0.418770	+	0.908092i	$0.362461\pi$
$930$		0			0
$931$	14.9122	+	6.87385i	0.488727	+	0.225281i
$932$	17.0645			0.558965
$933$		0			0
$934$	−22.1569	−	97.0757i	−0.724996	−	3.17641i
$935$	−9.16496	−	11.4925i	−0.299726	−	0.375845i
$936$		0			0
$937$	−5.87274	+	25.7302i	−0.191854	+	0.840568i	0.783758	+	0.621066i	$0.213300\pi$
$937$	−5.87274	+	25.7302i	−0.191854	+	0.840568i	−0.975612	+	0.219501i	$0.929557\pi$
$938$	38.3467	−	48.9263i	1.25206	−	1.59750i
$939$		0			0
$940$	62.9302	−	30.3056i	2.05256	−	0.988459i
$941$	−4.89461	+	21.4447i	−0.159560	+	0.699076i	0.830334	+	0.557266i	$0.188150\pi$
$941$	−4.89461	+	21.4447i	−0.159560	+	0.699076i	−0.989894	+	0.141811i	$0.954708\pi$
$942$		0			0
$943$	−6.75404	+	8.46930i	−0.219942	+	0.275798i
$944$	−49.5130	−	23.8442i	−1.61151	−	0.776062i
$945$		0			0
$946$	39.0391	−	18.8002i	1.26927	−	0.611248i
$947$	0.776810	−	3.40343i	0.0252429	−	0.110597i	−0.960737	−	0.277461i	$-0.910507\pi$
$947$	0.776810	−	3.40343i	0.0252429	−	0.110597i	0.985980	+	0.166864i	$0.0533642\pi$
$948$		0			0
$949$	−30.8817			−1.00246
$950$	−11.1062			−0.360331
$951$		0			0
$952$	68.4977	−	87.3958i	2.22002	−	2.83251i
$953$	−0.416767	−	0.522609i	−0.0135004	−	0.0169290i	0.775035	−	0.631918i	$-0.217732\pi$
$953$	−0.416767	−	0.522609i	−0.0135004	−	0.0169290i	−0.788536	+	0.614989i	$0.789161\pi$
$954$		0			0
$955$	37.6953	−	18.1531i	1.21979	−	0.587420i
$956$	36.5550	−	17.6040i	1.18227	−	0.569353i
$957$		0			0
$958$	29.1993	+	36.6148i	0.943386	+	1.18297i
$959$	12.6594	+	5.96543i	0.408794	+	0.192634i
$960$		0			0
$961$	−27.0741			−0.873359
$962$	−166.846			−5.37933
$963$		0			0
$964$	−24.7635	+	108.496i	−0.797578	+	3.49442i
$965$	−7.69944	+	3.70785i	−0.247854	+	0.119360i
$966$		0			0
$967$	38.2333	+	18.4122i	1.22950	+	0.592097i	0.931942	−	0.362607i	$-0.118113\pi$
$967$	38.2333	+	18.4122i	1.22950	+	0.592097i	0.297559	+	0.954703i	$0.403827\pi$
$968$	42.2564	−	52.9878i	1.35817	−	1.70309i
$969$		0			0
$970$	3.20717	−	14.0515i	0.102976	−	0.451168i
$971$	−11.5142	+	5.54494i	−0.369508	+	0.177946i	−0.609417	−	0.792850i	$-0.708597\pi$
$971$	−11.5142	+	5.54494i	−0.369508	+	0.177946i	0.239909	+	0.970795i	$0.422882\pi$
$972$		0			0
$973$	9.39993	−	0.0792987i	0.301348	−	0.00254220i
$974$	5.16138	−	22.6135i	0.165381	−	0.724583i
$975$		0			0
$976$	46.1752	+	57.9019i	1.47803	+	1.85339i
$977$	−5.44859	−	23.8718i	−0.174316	−	0.763727i	−0.984189	−	0.177122i	$-0.943321\pi$
$977$	−5.44859	−	23.8718i	−0.174316	−	0.763727i	0.809873	−	0.586605i	$-0.199536\pi$
$978$		0			0
$979$	12.4989			0.399468
$980$	55.6327	−	27.9572i	1.77712	−	0.893059i
$981$		0			0
$982$	13.0542	+	6.28656i	0.416576	+	0.200612i
$983$	−1.76456	−	7.73103i	−0.0562806	−	0.246582i	0.938960	−	0.344025i	$-0.111791\pi$
$983$	−1.76456	−	7.73103i	−0.0562806	−	0.246582i	−0.995241	+	0.0974436i	$0.968933\pi$
$984$		0			0
$985$	−1.74140	−	7.62959i	−0.0554857	−	0.243099i
$986$	−22.1983	+	97.2571i	−0.706938	+	3.09730i
$987$		0			0
$988$	13.7756	+	60.3548i	0.438260	+	1.92014i
$989$	−34.8425	+	16.7793i	−1.10793	+	0.533549i
$990$		0			0
$991$	−6.51600	−	3.13794i	−0.206988	−	0.0996799i	0.327518	−	0.944845i	$-0.393788\pi$
$991$	−6.51600	−	3.13794i	−0.206988	−	0.0996799i	−0.534505	+	0.845165i	$0.679502\pi$
$992$	15.6690	−	19.6484i	0.497493	−	0.623836i
$993$		0			0
$994$	−57.1382	+	0.482023i	−1.81231	+	0.0152888i
$995$	−15.9560	+	7.68400i	−0.505839	+	0.243599i
$996$		0			0
$997$	11.9126	−	14.9379i	0.377276	−	0.473089i	−0.556552	−	0.830813i	$-0.687876\pi$
$997$	11.9126	−	14.9379i	0.377276	−	0.473089i	0.933827	+	0.357724i	$0.116447\pi$
$998$	17.4327			0.551823
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.127.6		36
3.2	odd	2		147.2.i.b.127.1	yes	36
49.22	even	7	inner	441.2.u.d.316.6		36
147.62	even	14		7203.2.a.g.1.18		18
147.71	odd	14		147.2.i.b.22.1	✓	36
147.134	odd	14		7203.2.a.h.1.18		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.22.1	✓	36	147.71	odd	14
147.2.i.b.127.1	yes	36	3.2	odd	2
441.2.u.d.127.6		36	1.1	even	1	trivial
441.2.u.d.316.6		36	49.22	even	7	inner
7203.2.a.g.1.18		18	147.62	even	14
7203.2.a.h.1.18		18	147.134	odd	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.37817 + 1.14527i) q^{2} +(3.09710 + 3.88364i) q^{4} +(0.398449 + 1.74572i) q^{5} +(0.566955 - 2.58429i) q^{7} +(1.74291 + 7.63618i) q^{8} +O(q^{10})\)	\(q+(2.37817 + 1.14527i) q^{2} +(3.09710 + 3.88364i) q^{4} +(0.398449 + 1.74572i) q^{5} +(0.566955 - 2.58429i) q^{7} +(1.74291 + 7.63618i) q^{8} +(-1.05174 + 4.60796i) q^{10} +(-1.38032 - 0.664728i) q^{11} +(-4.78678 - 2.30519i) q^{13} +(4.30803 - 5.49658i) q^{14} +(-2.38986 + 10.4706i) q^{16} +(3.34085 - 4.18930i) q^{17} -2.34574 q^{19} +(-5.54571 + 6.95409i) q^{20} +(-2.52136 - 3.16168i) q^{22} +(2.25032 + 2.82181i) q^{23} +(1.61607 - 0.778257i) q^{25} +(-8.74374 - 10.9643i) q^{26} +(11.7924 - 5.80195i) q^{28} +(-4.39760 + 5.51442i) q^{29} -1.98138 q^{31} +(-7.90815 + 9.91651i) q^{32} +(12.7430 - 6.13671i) q^{34} +(4.73735 - 0.0399647i) q^{35} +(7.41784 - 9.30168i) q^{37} +(-5.57859 - 2.68651i) q^{38} +(-12.6362 + 6.08526i) q^{40} +(0.667868 + 2.92612i) q^{41} +(-2.38427 + 10.4462i) q^{43} +(-1.69343 - 7.41940i) q^{44} +(2.11992 + 9.28798i) q^{46} +(-7.07508 - 3.40718i) q^{47} +(-6.35712 - 2.93035i) q^{49} +4.73460 q^{50} +(-5.87260 - 25.7295i) q^{52} +(0.538950 + 0.675822i) q^{53} +(0.610441 - 2.67452i) q^{55} +(20.7223 - 0.174815i) q^{56} +(-16.7738 + 8.07782i) q^{58} +(-1.13862 + 4.98863i) q^{59} +(4.29940 - 5.39128i) q^{61} +(-4.71207 - 2.26921i) q^{62} +(-10.8114 + 5.20648i) q^{64} +(2.11693 - 9.27489i) q^{65} +8.90123 q^{67} +26.6167 q^{68} +(11.3120 + 5.33050i) q^{70} +(-5.10139 - 6.39694i) q^{71} +(5.23694 - 2.52198i) q^{73} +(28.2938 - 13.6256i) q^{74} +(-7.26499 - 9.11001i) q^{76} +(-2.50043 + 3.19028i) q^{77} -3.91143 q^{79} -19.2310 q^{80} +(-1.76289 + 7.72372i) q^{82} +(2.93149 - 1.41173i) q^{83} +(8.64450 + 4.16297i) q^{85} +(-17.6339 + 22.1122i) q^{86} +(2.67021 - 11.6989i) q^{88} +(-7.35043 + 3.53978i) q^{89} +(-8.67118 + 11.0635i) q^{91} +(-3.98943 + 17.4788i) q^{92} +(-12.9237 - 16.2057i) q^{94} +(-0.934659 - 4.09501i) q^{95} -3.04941 q^{97} +(-11.7623 - 14.2495i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

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