LMFDB - Embedded newform 693.2.m.j.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.4
Root			$0.648215 + 1.99500i$ of defining polynomial
Character	$\chi$	$=$	693.64
Dual form			693.2.m.j.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.648215 - 1.99500i) q^{2} +(-1.94181 - 1.41081i) q^{4} +(-0.976330 - 3.00483i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-0.679172 + 0.493447i) q^{8} +O(q^{10})$	\(q+(0.648215 - 1.99500i) q^{2} +(-1.94181 - 1.41081i) q^{4} +(-0.976330 - 3.00483i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-0.679172 + 0.493447i) q^{8} -6.62751 q^{10} +(0.965987 - 3.17283i) q^{11} +(0.657781 - 2.02444i) q^{13} +(1.69705 - 1.23298i) q^{14} +(-0.939232 - 2.89066i) q^{16} +(1.48152 + 4.55965i) q^{17} +(-1.24465 + 0.904290i) q^{19} +(-2.34339 + 7.21222i) q^{20} +(-5.70363 - 3.98382i) q^{22} -5.11509 q^{23} +(-4.03072 + 2.92849i) q^{25} +(-3.61238 - 2.62455i) q^{26} +(-0.741705 - 2.28273i) q^{28} +(-0.775237 - 0.563243i) q^{29} +(-2.23122 + 6.86698i) q^{31} -8.05469 q^{32} +10.0569 q^{34} +(0.976330 - 3.00483i) q^{35} +(-1.94084 - 1.41010i) q^{37} +(0.997259 + 3.06925i) q^{38} +(2.14582 + 1.55903i) q^{40} +(0.215938 - 0.156888i) q^{41} +9.28678 q^{43} +(-6.35202 + 4.79821i) q^{44} +(-3.31568 + 10.2046i) q^{46} +(8.35271 - 6.06860i) q^{47} +(0.309017 + 0.951057i) q^{49} +(3.22956 + 9.93958i) q^{50} +(-4.13338 + 3.00308i) q^{52} +(0.292206 - 0.899319i) q^{53} +(-10.4770 + 0.195099i) q^{55} -0.839503 q^{56} +(-1.62619 + 1.18150i) q^{58} +(-7.72673 - 5.61380i) q^{59} +(2.64443 + 8.13872i) q^{61} +(12.2533 + 8.90256i) q^{62} +(-3.34271 + 10.2878i) q^{64} -6.72532 q^{65} +13.2710 q^{67} +(3.55596 - 10.9441i) q^{68} +(-5.36177 - 3.89556i) q^{70} +(-4.37458 - 13.4636i) q^{71} +(-6.24721 - 4.53887i) q^{73} +(-4.07123 + 2.95792i) q^{74} +3.69265 q^{76} +(2.64644 - 1.99908i) q^{77} +(2.87765 - 8.85649i) q^{79} +(-7.76895 + 5.64447i) q^{80} +(-0.173018 - 0.532493i) q^{82} +(5.20805 + 16.0287i) q^{83} +(12.2545 - 8.90345i) q^{85} +(6.01983 - 18.5271i) q^{86} +(0.909554 + 2.63156i) q^{88} +11.2670 q^{89} +(1.72209 - 1.25117i) q^{91} +(9.93253 + 7.21641i) q^{92} +(-6.69251 - 20.5974i) q^{94} +(3.93243 + 2.85708i) q^{95} +(2.19028 - 6.74098i) q^{97} +2.09767 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.648215	−	1.99500i	0.458357	−	1.41068i	−0.408791	−	0.912628i	$-0.634050\pi$
$2$	0.648215	−	1.99500i	0.458357	−	1.41068i	0.867148	−	0.498050i	$-0.165950\pi$
$3$		0			0
$3$		0			0
$4$	−1.94181	−	1.41081i	−0.970904	−	0.705403i
$5$	−0.976330	−	3.00483i	−0.436628	−	1.34380i	−0.891409	−	0.453199i	$-0.850283\pi$
$5$	−0.976330	−	3.00483i	−0.436628	−	1.34380i	0.454781	−	0.890603i	$-0.349717\pi$
$6$		0			0
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	−0.679172	+	0.493447i	−0.240124	+	0.174460i
$9$		0			0
$10$	−6.62751			−2.09580
$11$	0.965987	−	3.17283i	0.291256	−	0.956645i
$11$	0.965987	−	3.17283i	0.291256	−	0.956645i
$12$		0			0
$13$	0.657781	−	2.02444i	0.182436	−	0.561479i	−0.817459	−	0.575986i	$-0.804618\pi$
$13$	0.657781	−	2.02444i	0.182436	−	0.561479i	0.999895	+	0.0145076i	$0.00461808\pi$
$14$	1.69705	−	1.23298i	0.453555	−	0.329527i
$15$		0			0
$16$	−0.939232	−	2.89066i	−0.234808	−	0.722665i
$17$	1.48152	+	4.55965i	0.359322	+	1.10588i	0.953461	+	0.301516i	$0.0974928\pi$
$17$	1.48152	+	4.55965i	0.359322	+	1.10588i	−0.594139	+	0.804362i	$0.702507\pi$
$18$		0			0
$19$	−1.24465	+	0.904290i	−0.285542	+	0.207458i	−0.721331	−	0.692590i	$-0.756469\pi$
$19$	−1.24465	+	0.904290i	−0.285542	+	0.207458i	0.435789	+	0.900049i	$0.356469\pi$
$20$	−2.34339	+	7.21222i	−0.523999	+	1.61270i
$21$		0			0
$22$	−5.70363	−	3.98382i	−1.21602	−	0.849354i
$23$	−5.11509			−1.06657			−0.533285	−	0.845935i	$-0.679043\pi$
$23$	−5.11509			−1.06657			−0.533285	+	0.845935i	$0.679043\pi$
$24$		0			0
$25$	−4.03072	+	2.92849i	−0.806144	+	0.585698i
$26$	−3.61238	−	2.62455i	−0.708445	−	0.514716i
$27$		0			0
$28$	−0.741705	−	2.28273i	−0.140169	−	0.431396i
$29$	−0.775237	−	0.563243i	−0.143958	−	0.104592i	0.513475	−	0.858104i	$-0.328358\pi$
$29$	−0.775237	−	0.563243i	−0.143958	−	0.104592i	−0.657433	+	0.753513i	$0.728358\pi$
$30$		0			0
$31$	−2.23122	+	6.86698i	−0.400739	+	1.23335i	0.523663	+	0.851926i	$0.324565\pi$
$31$	−2.23122	+	6.86698i	−0.400739	+	1.23335i	−0.924401	+	0.381421i	$0.875435\pi$
$32$	−8.05469			−1.42388
$33$		0			0
$34$	10.0569			1.72474
$35$	0.976330	−	3.00483i	0.165030	−	0.507910i
$36$		0			0
$37$	−1.94084	−	1.41010i	−0.319072	−	0.231819i	0.416707	−	0.909041i	$-0.363184\pi$
$37$	−1.94084	−	1.41010i	−0.319072	−	0.231819i	−0.735779	+	0.677221i	$0.763184\pi$
$38$	0.997259	+	3.06925i	0.161777	+	0.497898i
$39$		0			0
$40$	2.14582	+	1.55903i	0.339284	+	0.246504i
$41$	0.215938	−	0.156888i	0.0337238	−	0.0245018i	−0.570796	−	0.821092i	$-0.693365\pi$
$41$	0.215938	−	0.156888i	0.0337238	−	0.0245018i	0.604519	+	0.796590i	$0.293365\pi$
$42$		0			0
$43$	9.28678			1.41622			0.708110	−	0.706102i	$-0.249548\pi$
$43$	9.28678			1.41622			0.708110	+	0.706102i	$0.249548\pi$
$44$	−6.35202	+	4.79821i	−0.957603	+	0.723358i
$45$		0			0
$46$	−3.31568	+	10.2046i	−0.488870	+	1.50459i
$47$	8.35271	−	6.06860i	1.21837	−	0.885196i	0.222404	−	0.974954i	$-0.428609\pi$
$47$	8.35271	−	6.06860i	1.21837	−	0.885196i	0.995964	+	0.0897583i	$0.0286095\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	3.22956	+	9.93958i	0.456729	+	1.40567i
$51$		0			0
$52$	−4.13338	+	3.00308i	−0.573197	+	0.416452i
$53$	0.292206	−	0.899319i	0.0401376	−	0.123531i	−0.928980	−	0.370130i	$-0.879313\pi$
$53$	0.292206	−	0.899319i	0.0401376	−	0.123531i	0.969118	+	0.246599i	$0.0793131\pi$
$54$		0			0
$55$	−10.4770	+	0.195099i	−1.41271	+	0.0263071i
$56$	−0.839503			−0.112183
$57$		0			0
$58$	−1.62619	+	1.18150i	−0.213529	+	0.155138i
$59$	−7.72673	−	5.61380i	−1.00593	−	0.730855i	−0.0425824	−	0.999093i	$-0.513558\pi$
$59$	−7.72673	−	5.61380i	−1.00593	−	0.730855i	−0.963353	+	0.268238i	$0.913558\pi$
$60$		0			0
$61$	2.64443	+	8.13872i	0.338585	+	1.04206i	0.964929	+	0.262510i	$0.0845503\pi$
$61$	2.64443	+	8.13872i	0.338585	+	1.04206i	−0.626345	+	0.779546i	$0.715450\pi$
$62$	12.2533	+	8.90256i	1.55617	+	1.13063i
$63$		0			0
$64$	−3.34271	+	10.2878i	−0.417838	+	1.28597i
$65$	−6.72532			−0.834173
$66$		0			0
$67$	13.2710			1.62131			0.810657	−	0.585521i	$-0.199110\pi$
$67$	13.2710			1.62131			0.810657	+	0.585521i	$0.199110\pi$
$68$	3.55596	−	10.9441i	0.431223	−	1.32717i
$69$		0			0
$70$	−5.36177	−	3.89556i	−0.640854	−	0.465608i
$71$	−4.37458	−	13.4636i	−0.519167	−	1.59783i	−0.775570	−	0.631262i	$-0.782537\pi$
$71$	−4.37458	−	13.4636i	−0.519167	−	1.59783i	0.256402	−	0.966570i	$-0.417463\pi$
$72$		0			0
$73$	−6.24721	−	4.53887i	−0.731181	−	0.531234i	0.158756	−	0.987318i	$-0.449252\pi$
$73$	−6.24721	−	4.53887i	−0.731181	−	0.531234i	−0.889937	+	0.456084i	$0.849252\pi$
$74$	−4.07123	+	2.95792i	−0.473271	+	0.343852i
$75$		0			0
$76$	3.69265			0.423576
$77$	2.64644	−	1.99908i	0.301590	−	0.227817i
$78$		0			0
$79$	2.87765	−	8.85649i	0.323761	−	0.996432i	−0.648236	−	0.761439i	$-0.724493\pi$
$79$	2.87765	−	8.85649i	0.323761	−	0.996432i	0.971997	−	0.234993i	$-0.0755068\pi$
$80$	−7.76895	+	5.64447i	−0.868595	+	0.631071i
$81$		0			0
$82$	−0.173018	−	0.532493i	−0.0191066	−	0.0588040i
$83$	5.20805	+	16.0287i	0.571658	+	1.75938i	0.647288	+	0.762245i	$0.275903\pi$
$83$	5.20805	+	16.0287i	0.571658	+	1.75938i	−0.0756307	+	0.997136i	$0.524097\pi$
$84$		0			0
$85$	12.2545	−	8.90345i	1.32919	−	0.965715i
$86$	6.01983	−	18.5271i	0.649135	−	1.99783i
$87$		0			0
$88$	0.909554	+	2.63156i	0.0969588	+	0.280526i
$89$	11.2670			1.19430			0.597150	−	0.802130i	$-0.296300\pi$
$89$	11.2670			1.19430			0.597150	+	0.802130i	$0.296300\pi$
$90$		0			0
$91$	1.72209	−	1.25117i	0.180524	−	0.131159i
$92$	9.93253	+	7.21641i	1.03554	+	0.752363i
$93$		0			0
$94$	−6.69251	−	20.5974i	−0.690279	−	2.12446i
$95$	3.93243	+	2.85708i	0.403459	+	0.293130i
$96$		0			0
$97$	2.19028	−	6.74098i	0.222389	−	0.684443i	−0.776157	−	0.630540i	$-0.782834\pi$
$97$	2.19028	−	6.74098i	0.222389	−	0.684443i	0.998546	−	0.0539036i	$-0.0171664\pi$
$98$	2.09767			0.211896
$99$		0			0
$100$	11.9584			1.19584
$101$	−2.57908	+	7.93761i	−0.256629	+	0.789821i	0.736876	+	0.676028i	$0.236300\pi$
$101$	−2.57908	+	7.93761i	−0.256629	+	0.789821i	−0.993504	+	0.113793i	$0.963700\pi$
$102$		0			0
$103$	6.09639	+	4.42929i	0.600695	+	0.436431i	0.846126	−	0.532984i	$-0.178929\pi$
$103$	6.09639	+	4.42929i	0.600695	+	0.436431i	−0.245430	+	0.969414i	$0.578929\pi$
$104$	0.552209	+	1.69952i	0.0541485	+	0.166652i
$105$		0			0
$106$	−1.60473	−	1.16590i	−0.155865	−	0.113243i
$107$	12.4497	−	9.04525i	1.20356	−	0.874437i	0.208930	−	0.977931i	$-0.433002\pi$
$107$	12.4497	−	9.04525i	1.20356	−	0.874437i	0.994630	+	0.103493i	$0.0330020\pi$
$108$		0			0
$109$	20.2581			1.94038			0.970188	−	0.242353i	$-0.0779192\pi$
$109$	20.2581			1.94038			0.970188	+	0.242353i	$0.0779192\pi$
$110$	−6.40210	+	21.0280i	−0.610416	+	2.00494i
$111$		0			0
$112$	0.939232	−	2.89066i	0.0887491	−	0.273142i
$113$	−14.6447	+	10.6400i	−1.37766	+	1.00093i	−0.380564	+	0.924755i	$0.624270\pi$
$113$	−14.6447	+	10.6400i	−1.37766	+	1.00093i	−0.997095	+	0.0761731i	$0.975730\pi$
$114$		0			0
$115$	4.99402	+	15.3700i	0.465694	+	1.43326i
$116$	0.710736	+	2.18742i	0.0659902	+	0.203097i
$117$		0			0
$118$	−16.2081	+	11.7759i	−1.49208	+	1.08406i
$119$	−1.48152	+	4.55965i	−0.135811	+	0.417983i
$120$		0			0
$121$	−9.13374	−	6.12983i	−0.830340	−	0.557258i
$122$	17.9509			1.62520
$123$		0			0
$124$	14.0206	−	10.1866i	1.25909	−	0.914779i
$125$	−0.0453845	−	0.0329738i	−0.00405932	−	0.00294927i
$126$		0			0
$127$	−4.74993	−	14.6188i	−0.421488	−	1.29721i	−0.906318	−	0.422597i	$-0.861118\pi$
$127$	−4.74993	−	14.6188i	−0.421488	−	1.29721i	0.484830	−	0.874608i	$-0.338882\pi$
$128$	5.32459	+	3.86854i	0.470632	+	0.341934i
$129$		0			0
$130$	−4.35945	+	13.4170i	−0.382349	+	1.17675i
$131$	10.7418			0.938516			0.469258	−	0.883061i	$-0.344522\pi$
$131$	10.7418			0.938516			0.469258	+	0.883061i	$0.344522\pi$
$132$		0			0
$133$	−1.53847			−0.133402
$134$	8.60248	−	26.4757i	0.743141	−	2.28715i
$135$		0			0
$136$	−3.25616	−	2.36574i	−0.279213	−	0.202860i
$137$	1.36775	+	4.20949i	0.116855	+	0.359641i	0.992329	−	0.123623i	$-0.0394512\pi$
$137$	1.36775	+	4.20949i	0.116855	+	0.359641i	−0.875475	+	0.483264i	$0.839451\pi$
$138$		0			0
$139$	−3.66084	−	2.65976i	−0.310509	−	0.225598i	0.421606	−	0.906779i	$-0.361467\pi$
$139$	−3.66084	−	2.65976i	−0.310509	−	0.225598i	−0.732115	+	0.681181i	$0.761467\pi$
$140$	−6.13508	+	4.45740i	−0.518509	+	0.376719i
$141$		0			0
$142$	−29.6955			−2.49199
$143$	−5.78780	−	4.04261i	−0.484001	−	0.338060i
$144$		0			0
$145$	−0.935564	+	2.87937i	−0.0776944	+	0.239119i
$146$	−13.1046	+	9.52103i	−1.08454	+	0.787966i
$147$		0			0
$148$	1.77936	+	5.47629i	0.146262	+	0.450149i
$149$	−0.925416	−	2.84814i	−0.0758130	−	0.233329i	0.905967	−	0.423347i	$-0.139145\pi$
$149$	−0.925416	−	2.84814i	−0.0758130	−	0.233329i	−0.981780	+	0.190019i	$0.939145\pi$
$150$		0			0
$151$	−7.12954	+	5.17991i	−0.580194	+	0.421535i	−0.838794	−	0.544449i	$-0.816739\pi$
$151$	−7.12954	+	5.17991i	−0.580194	+	0.421535i	0.258600	+	0.965984i	$0.416739\pi$
$152$	0.399111	−	1.22834i	0.0323722	−	0.0996313i
$153$		0			0
$154$	−2.27271	−	6.57549i	−0.183140	−	0.529868i
$155$	22.8125			1.83235
$156$		0			0
$157$	−1.26737	+	0.920796i	−0.101147	+	0.0734875i	−0.637209	−	0.770691i	$-0.719911\pi$
$157$	−1.26737	+	0.920796i	−0.101147	+	0.0734875i	0.536062	+	0.844178i	$0.319911\pi$
$158$	−15.8034	−	11.4818i	−1.25725	−	0.913444i
$159$		0			0
$160$	7.86404	+	24.2030i	0.621707	+	1.91342i
$161$	−4.13820	−	3.00658i	−0.326136	−	0.236951i
$162$		0			0
$163$	−2.10307	+	6.47258i	−0.164725	+	0.506972i	−0.999016	−	0.0443528i	$-0.985877\pi$
$163$	−2.10307	+	6.47258i	−0.164725	+	0.506972i	0.834291	+	0.551325i	$0.185877\pi$
$164$	−0.640649			−0.0500263
$165$		0			0
$166$	35.3532			2.74394
$167$	3.78538	−	11.6502i	0.292921	−	0.901519i	−0.690990	−	0.722864i	$-0.742825\pi$
$167$	3.78538	−	11.6502i	0.292921	−	0.901519i	0.983912	−	0.178655i	$-0.0571746\pi$
$168$		0			0
$169$	6.85154	+	4.97793i	0.527041	+	0.382918i
$170$	−9.81881	−	30.2192i	−0.753068	−	2.31771i
$171$		0			0
$172$	−18.0331	−	13.1018i	−1.37501	−	0.999007i
$173$	−16.0590	+	11.6675i	−1.22094	+	0.887066i	−0.996178	−	0.0873476i	$-0.972161\pi$
$173$	−16.0590	+	11.6675i	−1.22094	+	0.887066i	−0.224763	+	0.974413i	$0.572161\pi$
$174$		0			0
$175$	−4.98224			−0.376622
$176$	−10.0789	+	0.187686i	−0.759723	+	0.0141473i
$177$		0			0
$178$	7.30344	−	22.4777i	0.547416	−	1.68477i
$179$	6.65199	−	4.83295i	0.497193	−	0.361232i	−0.310751	−	0.950491i	$-0.600580\pi$
$179$	6.65199	−	4.83295i	0.497193	−	0.361232i	0.807944	+	0.589260i	$0.200580\pi$
$180$		0			0
$181$	3.22357	+	9.92113i	0.239606	+	0.737432i	0.996477	+	0.0838672i	$0.0267271\pi$
$181$	3.22357	+	9.92113i	0.239606	+	0.737432i	−0.756871	+	0.653564i	$0.773273\pi$
$182$	−1.37981	−	4.24660i	−0.102278	−	0.314779i
$183$		0			0
$184$	3.47403	−	2.52403i	0.256109	−	0.186074i
$185$	−2.34222	+	7.20862i	−0.172204	+	0.529988i
$186$		0			0
$187$	15.8982	−	0.296051i	1.16259	−	0.0216494i
$188$	−24.7810			−1.80734
$189$		0			0
$190$	8.24893	−	5.99320i	0.598440	−	0.434792i
$191$	11.5012	+	8.35609i	0.832195	+	0.604625i	0.920180	−	0.391497i	$-0.128043\pi$
$191$	11.5012	+	8.35609i	0.832195	+	0.604625i	−0.0879842	+	0.996122i	$0.528043\pi$
$192$		0			0
$193$	−2.16817	−	6.67293i	−0.156068	−	0.480328i	0.842200	−	0.539166i	$-0.181260\pi$
$193$	−2.16817	−	6.67293i	−0.156068	−	0.480328i	−0.998268	+	0.0588382i	$0.981260\pi$
$194$	−12.0285	−	8.73921i	−0.863595	−	0.627439i
$195$		0			0
$196$	0.741705	−	2.28273i	0.0529789	−	0.163052i
$197$	3.60302			0.256705			0.128352	−	0.991729i	$-0.459031\pi$
$197$	3.60302			0.256705			0.128352	+	0.991729i	$0.459031\pi$
$198$		0			0
$199$	−3.85136			−0.273015			−0.136508	−	0.990639i	$-0.543588\pi$
$199$	−3.85136			−0.273015			−0.136508	+	0.990639i	$0.543588\pi$
$200$	1.29250	−	3.97790i	0.0913933	−	0.281280i
$201$		0			0
$202$	14.1637	+	10.2905i	0.996556	+	0.724041i
$203$	−0.296114	−	0.911346i	−0.0207831	−	0.0639640i
$204$		0			0
$205$	−0.682249	−	0.495683i	−0.0476503	−	0.0346200i
$206$	12.7882	−	9.29117i	0.890996	−	0.647347i
$207$		0			0
$208$	−6.46978			−0.448598
$209$	1.66685	+	4.82259i	0.115298	+	0.333586i
$210$		0			0
$211$	3.44012	−	10.5876i	0.236828	−	0.728881i	−0.760046	−	0.649870i	$-0.774824\pi$
$211$	3.44012	−	10.5876i	0.236828	−	0.728881i	0.996874	−	0.0790118i	$-0.0251765\pi$
$212$	−1.83617	+	1.33406i	−0.126109	+	0.0916235i
$213$		0			0
$214$	−9.97518	−	30.7005i	−0.681890	−	2.09864i
$215$	−9.06696	−	27.9052i	−0.618361	−	1.90312i
$216$		0			0
$217$	−5.84141	+	4.24403i	−0.396540	+	0.288103i
$218$	13.1316	−	40.4150i	0.889385	−	2.73725i
$219$		0			0
$220$	20.6195	+	14.4021i	1.39017	+	0.970990i
$221$	10.2053			0.686481
$222$		0			0
$223$	4.26448	−	3.09833i	0.285571	−	0.207479i	−0.435773	−	0.900057i	$-0.643525\pi$
$223$	4.26448	−	3.09833i	0.285571	−	0.207479i	0.721344	+	0.692577i	$0.243525\pi$
$224$	−6.51638	−	4.73443i	−0.435394	−	0.316332i
$225$		0			0
$226$	11.7339	+	36.1132i	0.780527	+	2.40222i
$227$	−11.9899	−	8.71118i	−0.795799	−	0.578182i	0.113880	−	0.993495i	$-0.463672\pi$
$227$	−11.9899	−	8.71118i	−0.795799	−	0.578182i	−0.909679	+	0.415313i	$0.863672\pi$
$228$		0			0
$229$	2.35001	−	7.23258i	0.155293	−	0.477942i	−0.842898	−	0.538074i	$-0.819152\pi$
$229$	2.35001	−	7.23258i	0.155293	−	0.477942i	0.998190	+	0.0601317i	$0.0191521\pi$
$230$	33.9004			2.23532
$231$		0			0
$232$	0.804450			0.0528147
$233$	0.465207	−	1.43176i	0.0304767	−	0.0937978i	−0.934661	−	0.355540i	$-0.884297\pi$
$233$	0.465207	−	1.43176i	0.0304767	−	0.0937978i	0.965138	+	0.261742i	$0.0842970\pi$
$234$		0			0
$235$	−26.3901	−	19.1736i	−1.72150	−	1.25074i
$236$	7.08385	+	21.8019i	0.461119	+	1.41918i
$237$		0			0
$238$	8.13617	+	5.91127i	0.527389	+	0.383171i
$239$	−4.06399	+	2.95266i	−0.262877	+	0.190992i	−0.711415	−	0.702773i	$-0.751945\pi$
$239$	−4.06399	+	2.95266i	−0.262877	+	0.190992i	0.448537	+	0.893764i	$0.351945\pi$
$240$		0			0
$241$	16.1502			1.04033			0.520164	−	0.854066i	$-0.325871\pi$
$241$	16.1502			1.04033			0.520164	+	0.854066i	$0.325871\pi$
$242$	−18.1496	+	14.2484i	−1.16670	+	0.915919i
$243$		0			0
$244$	6.34718	−	19.5346i	0.406337	−	1.25058i
$245$	2.55606	−	1.85709i	0.163301	−	0.118645i
$246$		0			0
$247$	1.01198	+	3.11454i	0.0643905	+	0.198174i
$248$	−1.87311	−	5.76485i	−0.118943	−	0.366068i
$249$		0			0
$250$	−0.0952016	+	0.0691680i	−0.00602108	+	0.00437457i
$251$	−7.96538	+	24.5149i	−0.502770	+	1.54737i	0.301716	+	0.953398i	$0.402440\pi$
$251$	−7.96538	+	24.5149i	−0.502770	+	1.54737i	−0.804487	+	0.593971i	$0.797560\pi$
$252$		0			0
$253$	−4.94112	+	16.2293i	−0.310645	+	1.02033i
$254$	−32.2434			−2.02313
$255$		0			0
$256$	−6.33342	+	4.60150i	−0.395839	+	0.287594i
$257$	14.2935	+	10.3848i	0.891605	+	0.647789i	0.936296	−	0.351212i	$-0.114230\pi$
$257$	14.2935	+	10.3848i	0.891605	+	0.647789i	−0.0446908	+	0.999001i	$0.514230\pi$
$258$		0			0
$259$	−0.741334	−	2.28159i	−0.0460643	−	0.141771i
$260$	13.0593	+	9.48812i	0.809902	+	0.588429i
$261$		0			0
$262$	6.96300	−	21.4299i	0.430175	−	1.32394i
$263$	−18.6325			−1.14893			−0.574465	−	0.818529i	$-0.694790\pi$
$263$	−18.6325			−1.14893			−0.574465	+	0.818529i	$0.694790\pi$
$264$		0			0
$265$	−2.98759			−0.183526
$266$	−0.997259	+	3.06925i	−0.0611459	+	0.188188i
$267$		0			0
$268$	−25.7698	−	18.7229i	−1.57414	−	1.14368i
$269$	6.40055	+	19.6989i	0.390248	+	1.20106i	0.932601	+	0.360910i	$0.117534\pi$
$269$	6.40055	+	19.6989i	0.390248	+	1.20106i	−0.542352	+	0.840151i	$0.682466\pi$
$270$		0			0
$271$	−12.0088	−	8.72494i	−0.729486	−	0.530002i	0.159915	−	0.987131i	$-0.448878\pi$
$271$	−12.0088	−	8.72494i	−0.729486	−	0.530002i	−0.889401	+	0.457128i	$0.848878\pi$
$272$	11.7889	−	8.56515i	0.714808	−	0.519338i
$273$		0			0
$274$	9.28453			0.560899
$275$	5.39798	+	15.6177i	0.325511	+	0.941782i
$276$		0			0
$277$	−0.949638	+	2.92268i	−0.0570582	+	0.175607i	−0.975524	−	0.219894i	$-0.929429\pi$
$277$	−0.949638	+	2.92268i	−0.0570582	+	0.175607i	0.918466	+	0.395501i	$0.129429\pi$
$278$	−7.67923	+	5.57929i	−0.460570	+	0.334624i
$279$		0			0
$280$	0.819631	+	2.52257i	0.0489823	+	0.150752i
$281$	−1.26604	−	3.89646i	−0.0755254	−	0.232443i	0.906166	−	0.422923i	$-0.138996\pi$
$281$	−1.26604	−	3.89646i	−0.0755254	−	0.232443i	−0.981691	+	0.190479i	$0.938996\pi$
$282$		0			0
$283$	5.98511	−	4.34844i	0.355778	−	0.258488i	−0.395511	−	0.918461i	$-0.629432\pi$
$283$	5.98511	−	4.34844i	0.355778	−	0.258488i	0.751289	+	0.659973i	$0.229432\pi$
$284$	−10.4999	+	32.3154i	−0.623055	+	1.91756i
$285$		0			0
$286$	−11.8168	+	8.92619i	−0.698739	+	0.527817i
$287$	0.266914			0.0157554
$288$		0			0
$289$	−4.84225	+	3.51810i	−0.284839	+	0.206947i
$290$	5.13790	+	3.73290i	0.301708	+	0.219203i
$291$		0			0
$292$	5.72743	+	17.6272i	0.335172	+	1.03155i
$293$	−8.53424	−	6.20049i	−0.498576	−	0.362236i	0.309897	−	0.950770i	$-0.399705\pi$
$293$	−8.53424	−	6.20049i	−0.498576	−	0.362236i	−0.808473	+	0.588534i	$0.799705\pi$
$294$		0			0
$295$	−9.32470	+	28.6985i	−0.542905	+	1.67089i
$296$	2.01397			0.117060
$297$		0			0
$298$	−6.28190			−0.363901
$299$	−3.36461	+	10.3552i	−0.194580	+	0.598857i
$300$		0			0
$301$	7.51316	+	5.45863i	0.433051	+	0.314630i
$302$	5.71246	+	17.5811i	0.328715	+	1.01168i
$303$		0			0
$304$	3.78301	+	2.74852i	0.216970	+	0.157638i
$305$	21.8737	−	15.8921i	1.25248	−	0.909982i
$306$		0			0
$307$	1.74955			0.0998522			0.0499261	−	0.998753i	$-0.484101\pi$
$307$	1.74955			0.0998522			0.0499261	+	0.998753i	$0.484101\pi$
$308$	−7.95921	+	0.148214i	−0.453518	+	0.00844529i
$309$		0			0
$310$	14.7874	−	45.5110i	0.839870	−	2.58485i
$311$	−18.6134	+	13.5235i	−1.05547	+	0.766845i	−0.973245	−	0.229769i	$-0.926203\pi$
$311$	−18.6134	+	13.5235i	−1.05547	+	0.766845i	−0.0822263	+	0.996614i	$0.526203\pi$
$312$		0			0
$313$	5.64166	+	17.3632i	0.318885	+	0.981428i	0.974126	+	0.226007i	$0.0725674\pi$
$313$	5.64166	+	17.3632i	0.318885	+	0.981428i	−0.655240	+	0.755421i	$0.727433\pi$
$314$	1.01546	+	3.12527i	0.0573058	+	0.176369i
$315$		0			0
$316$	−18.0826	+	13.1378i	−1.01723	+	0.739059i
$317$	−10.0803	+	31.0241i	−0.566168	+	1.74249i	0.0982886	+	0.995158i	$0.468663\pi$
$317$	−10.0803	+	31.0241i	−0.566168	+	1.74249i	−0.664456	+	0.747327i	$0.731337\pi$
$318$		0			0
$319$	−2.53594	+	1.91561i	−0.141986	+	0.107254i
$320$	34.1767			1.91054
$321$		0			0
$322$	−8.68056	+	6.30680i	−0.483749	+	0.351464i
$323$	−5.96722	−	4.33544i	−0.332025	−	0.241230i
$324$		0			0
$325$	3.27722	+	10.0863i	0.181788	+	0.559485i
$326$	11.5496	+	8.39125i	0.639671	+	0.464748i
$327$		0			0
$328$	−0.0692430	+	0.213108i	−0.00382330	+	0.0117669i
$329$	10.3245			0.569209
$330$		0			0
$331$	6.80537			0.374057			0.187029	−	0.982354i	$-0.440114\pi$
$331$	6.80537			0.374057			0.187029	+	0.982354i	$0.440114\pi$
$332$	12.5004	−	38.4723i	0.686048	−	2.11144i
$333$		0			0
$334$	−20.7884	−	15.1037i	−1.13749	−	0.826435i
$335$	−12.9569	−	39.8772i	−0.707911	−	2.17873i
$336$		0			0
$337$	−0.300988	−	0.218680i	−0.0163958	−	0.0119123i	0.579557	−	0.814932i	$-0.303226\pi$
$337$	−0.300988	−	0.218680i	−0.0163958	−	0.0119123i	−0.595953	+	0.803019i	$0.703226\pi$
$338$	14.3722	−	10.4420i	0.781747	−	0.567972i
$339$		0			0
$340$	−36.3570			−1.97174
$341$	19.6325	+	13.7127i	1.06316	+	0.742584i
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−6.30732	+	4.58254i	−0.340068	+	0.247074i
$345$		0			0
$346$	12.8671	+	39.6007i	0.691737	+	2.12895i
$347$	−1.77708	−	5.46929i	−0.0953986	−	0.293607i	0.891959	−	0.452117i	$-0.149331\pi$
$347$	−1.77708	−	5.46929i	−0.0953986	−	0.293607i	−0.987357	+	0.158510i	$0.949331\pi$
$348$		0			0
$349$	0.523048	−	0.380017i	0.0279981	−	0.0203418i	−0.573698	−	0.819067i	$-0.694492\pi$
$349$	0.523048	−	0.380017i	0.0279981	−	0.0203418i	0.601696	+	0.798725i	$0.294492\pi$
$350$	−3.22956	+	9.93958i	−0.172627	+	0.531293i
$351$		0			0
$352$	−7.78073	+	25.5562i	−0.414714	+	1.36215i
$353$	18.3601			0.977209			0.488604	−	0.872505i	$-0.337506\pi$
$353$	18.3601			0.977209			0.488604	+	0.872505i	$0.337506\pi$
$354$		0			0
$355$	−36.1848	+	26.2898i	−1.92049	+	1.39532i
$356$	−21.8784	−	15.8956i	−1.15955	−	0.842463i
$357$		0			0
$358$	−5.32982	−	16.4035i	−0.281690	−	0.866952i
$359$	21.8235	+	15.8557i	1.15180	+	0.836832i	0.988719	−	0.149781i	$-0.0478569\pi$
$359$	21.8235	+	15.8557i	1.15180	+	0.836832i	0.163081	+	0.986613i	$0.447857\pi$
$360$		0			0
$361$	−5.13991	+	15.8190i	−0.270522	+	0.832580i
$362$	21.8822			1.15010
$363$		0			0
$364$	−5.10914			−0.267792
$365$	−7.53920	+	23.2033i	−0.394620	+	1.21451i
$366$		0			0
$367$	−22.9126	−	16.6470i	−1.19603	−	0.868966i	−0.202140	−	0.979357i	$-0.564790\pi$
$367$	−22.9126	−	16.6470i	−1.19603	−	0.868966i	−0.993888	+	0.110391i	$0.964790\pi$
$368$	4.80426	+	14.7860i	0.250439	+	0.770773i
$369$		0			0
$370$	12.8629	+	9.34547i	0.668712	+	0.485848i
$371$	0.765006	−	0.555810i	0.0397171	−	0.0288562i
$372$		0			0
$373$	−12.9215			−0.669050			−0.334525	−	0.942387i	$-0.608576\pi$
$373$	−12.9215			−0.669050			−0.334525	+	0.942387i	$0.608576\pi$
$374$	9.71480	−	31.9087i	0.502340	−	1.64996i
$375$		0			0
$376$	−2.67839	+	8.24324i	−0.138128	+	0.425113i
$377$	−1.65019	+	1.19893i	−0.0849890	+	0.0617481i
$378$		0			0
$379$	6.47330	+	19.9228i	0.332511	+	1.02336i	0.967935	+	0.251200i	$0.0808253\pi$
$379$	6.47330	+	19.9228i	0.332511	+	1.02336i	−0.635424	+	0.772163i	$0.719175\pi$
$380$	−3.60524	−	11.0958i	−0.184945	−	0.569202i
$381$		0			0
$382$	24.1256	−	17.5283i	1.23437	−	0.896825i
$383$	−7.71813	+	23.7540i	−0.394378	+	1.21377i	0.535067	+	0.844810i	$0.320286\pi$
$383$	−7.71813	+	23.7540i	−0.394378	+	1.21377i	−0.929445	+	0.368961i	$0.879714\pi$
$384$		0			0
$385$	−8.59071	−	6.00036i	−0.437823	−	0.305807i
$386$	−14.7179			−0.749123
$387$		0			0
$388$	−13.7633	+	9.99964i	−0.698727	+	0.507655i
$389$	−10.9848	−	7.98093i	−0.556952	−	0.404649i	0.273390	−	0.961903i	$-0.411855\pi$
$389$	−10.9848	−	7.98093i	−0.556952	−	0.404649i	−0.830342	+	0.557254i	$0.811855\pi$
$390$		0			0
$391$	−7.57812	−	23.3231i	−0.383242	−	1.17950i
$392$	−0.679172	−	0.493447i	−0.0343034	−	0.0249229i
$393$		0			0
$394$	2.33553	−	7.18802i	0.117662	−	0.362127i
$395$	−29.4218			−1.48037
$396$		0			0
$397$	−4.26450			−0.214029			−0.107014	−	0.994257i	$-0.534129\pi$
$397$	−4.26450			−0.214029			−0.107014	+	0.994257i	$0.534129\pi$
$398$	−2.49651	+	7.68346i	−0.125139	+	0.385137i
$399$		0			0
$400$	12.2510	+	8.90091i	0.612552	+	0.445045i
$401$	10.0252	+	30.8544i	0.500636	+	1.54080i	0.807986	+	0.589201i	$0.200558\pi$
$401$	10.0252	+	30.8544i	0.500636	+	1.54080i	−0.307351	+	0.951596i	$0.599442\pi$
$402$		0			0
$403$	12.4341	+	9.03394i	0.619389	+	0.450013i
$404$	16.2065	−	11.7747i	0.806304	−	0.585814i
$405$		0			0
$406$	−2.01008			−0.0997587
$407$	−6.34884	+	4.79581i	−0.314700	+	0.237720i
$408$		0			0
$409$	−7.69071	+	23.6696i	−0.380281	+	1.17039i	0.559565	+	0.828787i	$0.310968\pi$
$409$	−7.69071	+	23.6696i	−0.380281	+	1.17039i	−0.939846	+	0.341599i	$0.889032\pi$
$410$	−1.43113	+	1.03978i	−0.0706786	+	0.0513510i
$411$		0			0
$412$	−5.58916	−	17.2017i	−0.275358	−	0.847465i
$413$	−2.95135	−	9.08332i	−0.145226	−	0.446961i
$414$		0			0
$415$	43.0789	−	31.2986i	2.11466	−	1.53639i
$416$	−5.29822	+	16.3063i	−0.259767	+	0.799480i
$417$		0			0
$418$	10.7016	−	0.199281i	0.523430	−	0.00974717i
$419$	−10.5948			−0.517588			−0.258794	−	0.965933i	$-0.583325\pi$
$419$	−10.5948			−0.517588			−0.258794	+	0.965933i	$0.583325\pi$
$420$		0			0
$421$	30.6320	−	22.2554i	1.49291	−	1.08466i	0.519811	−	0.854281i	$-0.326002\pi$
$421$	30.6320	−	22.2554i	1.49291	−	1.08466i	0.973100	−	0.230382i	$-0.0739976\pi$
$422$	−18.8924	−	13.7261i	−0.919665	−	0.668176i
$423$		0			0
$424$	0.245308	+	0.754980i	0.0119132	+	0.0366651i
$425$	−19.3245	−	14.0401i	−0.937376	−	0.681044i
$426$		0			0
$427$	−2.64443	+	8.13872i	−0.127973	+	0.393860i
$428$	−36.9361			−1.78537
$429$		0			0
$430$	−61.5483			−2.96812
$431$	−1.74437	+	5.36860i	−0.0840231	+	0.258597i	−0.984238	−	0.176850i	$-0.943409\pi$
$431$	−1.74437	+	5.36860i	−0.0840231	+	0.258597i	0.900215	+	0.435446i	$0.143409\pi$
$432$		0			0
$433$	2.18053	+	1.58425i	0.104790	+	0.0761341i	0.638946	−	0.769252i	$-0.279371\pi$
$433$	2.18053	+	1.58425i	0.104790	+	0.0761341i	−0.534156	+	0.845386i	$0.679371\pi$
$434$	4.68035	+	14.4046i	0.224664	+	0.691445i
$435$		0			0
$436$	−39.3374	−	28.5803i	−1.88392	−	1.36875i
$437$	6.36649	−	4.62553i	0.304551	−	0.221269i
$438$		0			0
$439$	30.5668			1.45888			0.729438	−	0.684047i	$-0.239782\pi$
$439$	30.5668			1.45888			0.729438	+	0.684047i	$0.239782\pi$
$440$	7.01938	−	5.30233i	0.334636	−	0.252779i
$441$		0			0
$442$	6.61521	−	20.3595i	0.314653	−	0.968403i
$443$	−19.9318	+	14.4813i	−0.946990	+	0.688028i	−0.950093	−	0.311967i	$-0.899012\pi$
$443$	−19.9318	+	14.4813i	−0.946990	+	0.688028i	0.00310332	+	0.999995i	$0.499012\pi$
$444$		0			0
$445$	−11.0003	−	33.8555i	−0.521465	−	1.60490i
$446$	−3.41686	−	10.5160i	−0.161793	−	0.497948i
$447$		0			0
$448$	−8.75132	+	6.35821i	−0.413461	+	0.300397i
$449$	4.75131	−	14.6230i	0.224228	−	0.690103i	−0.774141	−	0.633013i	$-0.781818\pi$
$449$	4.75131	−	14.6230i	0.224228	−	0.690103i	0.998369	−	0.0570896i	$-0.0181821\pi$
$450$		0			0
$451$	−0.289186	−	0.836687i	−0.0136173	−	0.0393980i
$452$	43.4482			2.04363
$453$		0			0
$454$	−25.1509	+	18.2732i	−1.18039	+	0.857602i
$455$	−5.44090	−	3.95304i	−0.255073	−	0.185322i
$456$		0			0
$457$	4.39924	+	13.5395i	0.205788	+	0.633350i	0.999680	+	0.0252913i	$0.00805134\pi$
$457$	4.39924	+	13.5395i	0.205788	+	0.633350i	−0.793892	+	0.608058i	$0.791949\pi$
$458$	−12.9057	−	9.37653i	−0.603043	−	0.438137i
$459$		0			0
$460$	11.9867	−	36.8912i	0.558882	−	1.72006i
$461$	36.7148			1.70998			0.854990	−	0.518645i	$-0.173563\pi$
$461$	36.7148			1.70998			0.854990	+	0.518645i	$0.173563\pi$
$462$		0			0
$463$	−34.7682			−1.61582			−0.807908	−	0.589308i	$-0.799400\pi$
$463$	−34.7682			−1.61582			−0.807908	+	0.589308i	$0.799400\pi$
$464$	−0.900015	+	2.76996i	−0.0417822	+	0.128592i
$465$		0			0
$466$	−2.55481	−	1.85618i	−0.118349	−	0.0859858i
$467$	−4.18828	−	12.8902i	−0.193811	−	0.596488i	−0.999988	−	0.00481441i	$-0.998468\pi$
$467$	−4.18828	−	12.8902i	−0.193811	−	0.596488i	0.806178	−	0.591673i	$-0.201532\pi$
$468$		0			0
$469$	10.7365	+	7.80052i	0.495765	+	0.360194i
$470$	−55.3577	+	40.2197i	−2.55346	+	1.85520i
$471$		0			0
$472$	8.01789			0.369053
$473$	8.97091	−	29.4654i	0.412483	−	1.35482i
$474$		0			0
$475$	2.36863	−	7.28988i	0.108680	−	0.334483i
$476$	9.30962	−	6.76384i	0.426706	−	0.310020i
$477$		0			0
$478$	3.25622	+	10.0216i	0.148936	+	0.458378i
$479$	−8.52803	−	26.2466i	−0.389656	−	1.19924i	−0.933046	−	0.359757i	$-0.882860\pi$
$479$	−8.52803	−	26.2466i	−0.389656	−	1.19924i	0.543390	−	0.839480i	$-0.317140\pi$
$480$		0			0
$481$	−4.13131	+	3.00157i	−0.188372	+	0.136860i
$482$	10.4688	−	32.2197i	0.476842	−	1.46757i
$483$		0			0
$484$	9.08796	+	24.7889i	0.413089	+	1.12677i
$485$	−22.3940			−1.01686
$486$		0			0
$487$	16.5669	−	12.0365i	0.750716	−	0.545427i	−0.145333	−	0.989383i	$-0.546425\pi$
$487$	16.5669	−	12.0365i	0.750716	−	0.545427i	0.896049	+	0.443956i	$0.146425\pi$
$488$	−5.81205	−	4.22270i	−0.263099	−	0.191153i
$489$		0			0
$490$	−2.04801	−	6.30314i	−0.0925199	−	0.284747i
$491$	23.3534	+	16.9672i	1.05392	+	0.765721i	0.972955	−	0.230996i	$-0.0741983\pi$
$491$	23.3534	+	16.9672i	1.05392	+	0.765721i	0.0809698	+	0.996717i	$0.474198\pi$
$492$		0			0
$493$	1.41966	−	4.36927i	0.0639384	−	0.196782i
$494$	6.86949			0.309073
$495$		0			0
$496$	21.9457			0.985393
$497$	4.37458	−	13.4636i	0.196227	−	0.603924i
$498$		0			0
$499$	17.3890	+	12.6338i	0.778438	+	0.565568i	0.904510	−	0.426453i	$-0.140237\pi$
$499$	17.3890	+	12.6338i	0.778438	+	0.565568i	−0.126072	+	0.992021i	$0.540237\pi$
$500$	0.0416084	+	0.128058i	0.00186079	+	0.00572691i
$501$		0			0
$502$	43.7440	+	31.7819i	1.95239	+	1.41849i
$503$	−6.95915	+	5.05612i	−0.310293	+	0.225441i	−0.732022	−	0.681281i	$-0.761423\pi$
$503$	−6.95915	+	5.05612i	−0.310293	+	0.225441i	0.421729	+	0.906722i	$0.361423\pi$
$504$		0			0
$505$	26.3692			1.17342
$506$	29.1746	+	20.3776i	1.29697	+	0.905896i
$507$		0			0
$508$	−11.4008	+	35.0881i	−0.505829	+	1.55678i
$509$	8.93456	−	6.49134i	0.396017	−	0.287724i	−0.371899	−	0.928273i	$-0.621293\pi$
$509$	8.93456	−	6.49134i	0.396017	−	0.287724i	0.767917	+	0.640550i	$0.221293\pi$
$510$		0			0
$511$	−2.38622	−	7.34404i	−0.105560	−	0.324881i
$512$	9.14220	+	28.1368i	0.404032	+	1.24348i
$513$		0			0
$514$	29.9830	−	21.7840i	1.32250	−	0.960849i
$515$	7.35718	−	22.6431i	0.324196	−	0.997773i
$516$		0			0
$517$	−11.1860	−	32.3639i	−0.491961	−	1.42336i
$518$	−5.03232			−0.221107
$519$		0			0
$520$	4.56765	−	3.31859i	0.200305	−	0.145530i
$521$	−10.2110	−	7.41876i	−0.447354	−	0.325022i	0.341196	−	0.939992i	$-0.389168\pi$
$521$	−10.2110	−	7.41876i	−0.447354	−	0.325022i	−0.788550	+	0.614970i	$0.789168\pi$
$522$		0			0
$523$	−13.5689	−	41.7609i	−0.593328	−	1.82608i	−0.562877	−	0.826541i	$-0.690305\pi$
$523$	−13.5689	−	41.7609i	−0.593328	−	1.82608i	−0.0304515	−	0.999536i	$-0.509695\pi$
$524$	−20.8585	−	15.1546i	−0.911209	−	0.662032i
$525$		0			0
$526$	−12.0779	+	37.1719i	−0.526620	+	1.62077i
$527$	−34.6167			−1.50793
$528$		0			0
$529$	3.16418			0.137573
$530$	−1.93660	+	5.96025i	−0.0841206	+	0.258897i
$531$		0			0
$532$	2.98741	+	2.17048i	0.129521	+	0.0941024i
$533$	−0.175571	−	0.540351i	−0.00760482	−	0.0234052i
$534$		0			0
$535$	−39.3345	−	28.5782i	−1.70058	−	1.23554i
$536$	−9.01331	+	6.54855i	−0.389316	+	0.282854i
$537$		0			0
$538$	43.4482			1.87318
$539$	3.31605	−	0.0617506i	0.142832	−	0.00265979i
$540$		0			0
$541$	−8.44011	+	25.9760i	−0.362869	+	1.11680i	0.588436	+	0.808544i	$0.299744\pi$
$541$	−8.44011	+	25.9760i	−0.362869	+	1.11680i	−0.951305	+	0.308252i	$0.900256\pi$
$542$	−25.1906	+	18.3020i	−1.08203	+	0.786139i
$543$		0			0
$544$	−11.9332	−	36.7266i	−0.511632	−	1.57464i
$545$	−19.7786	−	60.8723i	−0.847222	−	2.60748i
$546$		0			0
$547$	−14.8125	+	10.7619i	−0.633335	+	0.460145i	−0.857554	−	0.514394i	$-0.828017\pi$
$547$	−14.8125	+	10.7619i	−0.633335	+	0.460145i	0.224219	+	0.974539i	$0.428017\pi$
$548$	3.28288	−	10.1037i	0.140238	−	0.431607i
$549$		0			0
$550$	34.6563	−	0.645361i	1.47775	−	0.0275183i
$551$	1.47423			0.0628044
$552$		0			0
$553$	7.53378	−	5.47361i	0.320369	−	0.232762i
$554$	5.21519	+	3.78905i	0.221572	+	0.160981i
$555$		0			0
$556$	3.35625	+	10.3295i	0.142337	+	0.438068i
$557$	−3.09637	−	2.24965i	−0.131198	−	0.0953206i	0.520251	−	0.854013i	$-0.325838\pi$
$557$	−3.09637	−	2.24965i	−0.131198	−	0.0953206i	−0.651449	+	0.758693i	$0.725838\pi$
$558$		0			0
$559$	6.10866	−	18.8005i	0.258369	−	0.795178i
$560$	−9.60295			−0.405799
$561$		0			0
$562$	−8.59411			−0.362520
$563$	11.1700	−	34.3776i	0.470758	−	1.44884i	−0.380836	−	0.924643i	$-0.624364\pi$
$563$	11.1700	−	34.3776i	0.470758	−	1.44884i	0.851594	−	0.524202i	$-0.175636\pi$
$564$		0			0
$565$	46.2695	+	33.6168i	1.94657	+	1.41427i
$566$	−4.79550	−	14.7590i	−0.201570	−	0.620368i
$567$		0			0
$568$	9.61466	+	6.98546i	0.403422	+	0.293103i
$569$	−7.73098	+	5.61689i	−0.324100	+	0.235472i	−0.737923	−	0.674885i	$-0.764193\pi$
$569$	−7.73098	+	5.61689i	−0.324100	+	0.235472i	0.413823	+	0.910357i	$0.364193\pi$
$570$		0			0
$571$	−31.8446			−1.33265			−0.666327	−	0.745659i	$-0.732135\pi$
$571$	−31.8446			−1.33265			−0.666327	+	0.745659i	$0.732135\pi$
$572$	5.53546	+	16.0155i	0.231449	+	0.669640i
$573$		0			0
$574$	0.173018	−	0.532493i	0.00722161	−	0.0222258i
$575$	20.6175	−	14.9795i	0.859810	−	0.624688i
$576$		0			0
$577$	2.67605	+	8.23603i	0.111405	+	0.342870i	0.991180	−	0.132520i	$-0.0423069\pi$
$577$	2.67605	+	8.23603i	0.111405	+	0.342870i	−0.879775	+	0.475390i	$0.842307\pi$
$578$	3.87980	+	11.9408i	0.161378	+	0.496671i
$579$		0			0
$580$	5.87892	−	4.27129i	0.244109	−	0.177355i
$581$	−5.20805	+	16.0287i	−0.216066	+	0.664984i
$582$		0			0
$583$	−2.57112	−	1.79585i	−0.106485	−	0.0743766i
$584$	6.48262			0.268253
$585$		0			0
$586$	−17.9020	+	13.0066i	−0.739525	+	0.537296i
$587$	−4.31139	−	3.13241i	−0.177950	−	0.129288i	0.495245	−	0.868754i	$-0.335078\pi$
$587$	−4.31139	−	3.13241i	−0.177950	−	0.129288i	−0.673195	+	0.739465i	$0.735078\pi$
$588$		0			0
$589$	−3.43266	−	10.5646i	−0.141440	−	0.435309i
$590$	51.2090	+	37.2055i	2.10824	+	1.53173i
$591$		0			0
$592$	−2.25322	+	6.93471i	−0.0926070	+	0.285015i
$593$	−11.0464			−0.453622			−0.226811	−	0.973939i	$-0.572830\pi$
$593$	−11.0464			−0.453622			−0.226811	+	0.973939i	$0.572830\pi$
$594$		0			0
$595$	15.1475			0.620985
$596$	−2.22119	+	6.83612i	−0.0909835	+	0.280018i
$597$		0			0
$598$	18.4776	+	13.4248i	0.755607	+	0.548981i
$599$	−8.12195	−	24.9968i	−0.331854	−	1.02134i	−0.968251	−	0.249980i	$-0.919576\pi$
$599$	−8.12195	−	24.9968i	−0.331854	−	1.02134i	0.636397	−	0.771362i	$-0.280424\pi$
$600$		0			0
$601$	−10.4904	−	7.62173i	−0.427913	−	0.310897i	0.352901	−	0.935661i	$-0.385195\pi$
$601$	−10.4904	−	7.62173i	−0.427913	−	0.310897i	−0.780814	+	0.624764i	$0.785195\pi$
$602$	15.7601	−	11.4504i	0.642334	−	0.466683i
$603$		0			0
$604$	21.1521			0.860665
$605$	−9.50159	+	33.4301i	−0.386295	+	1.35913i
$606$		0			0
$607$	−6.98658	+	21.5025i	−0.283576	+	0.872758i	0.703245	+	0.710947i	$0.251734\pi$
$607$	−6.98658	+	21.5025i	−0.283576	+	0.872758i	−0.986822	+	0.161811i	$0.948266\pi$
$608$	10.0253	−	7.28378i	0.406578	−	0.295396i
$609$		0			0
$610$	−17.5260	−	53.9395i	−0.709607	−	2.18395i
$611$	−6.79127	−	20.9014i	−0.274745	−	0.845579i
$612$		0			0
$613$	17.9126	−	13.0143i	0.723484	−	0.525642i	−0.164011	−	0.986458i	$-0.552443\pi$
$613$	17.9126	−	13.0143i	0.723484	−	0.525642i	0.887495	+	0.460816i	$0.152443\pi$
$614$	1.13408	−	3.49035i	0.0457679	−	0.140859i
$615$		0			0
$616$	−0.810949	+	2.66360i	−0.0326741	+	0.107320i
$617$	20.4747			0.824281			0.412140	−	0.911120i	$-0.364781\pi$
$617$	20.4747			0.824281			0.412140	+	0.911120i	$0.364781\pi$
$618$		0			0
$619$	−32.4426	+	23.5709i	−1.30398	+	0.947396i	−0.999986	−	0.00527850i	$-0.998320\pi$
$619$	−32.4426	+	23.5709i	−1.30398	+	0.947396i	−0.303993	+	0.952674i	$0.598320\pi$
$620$	−44.2976	−	32.1841i	−1.77903	−	1.29254i
$621$		0			0
$622$	14.9138	+	45.8999i	0.597989	+	1.84042i
$623$	9.11520	+	6.62258i	0.365193	+	0.265328i
$624$		0			0
$625$	−7.75276	+	23.8605i	−0.310110	+	0.954422i
$626$	38.2967			1.53064
$627$		0			0
$628$	3.76005			0.150042
$629$	3.55418	−	10.9386i	0.141715	−	0.436152i
$630$		0			0
$631$	−23.5482	−	17.1088i	−0.937441	−	0.681091i	0.0103623	−	0.999946i	$-0.496702\pi$
$631$	−23.5482	−	17.1088i	−0.937441	−	0.681091i	−0.947803	+	0.318856i	$0.896702\pi$
$632$	2.41579	+	7.43504i	0.0960950	+	0.295750i
$633$		0			0
$634$	55.3588	+	40.2205i	2.19858	+	1.59736i
$635$	−39.2895	+	28.5455i	−1.55915	+	1.13279i
$636$		0			0
$637$	2.12862			0.0843391
$638$	2.17781	+	6.30094i	0.0862203	+	0.249457i
$639$		0			0
$640$	6.42577	−	19.7765i	0.254001	−	0.781735i
$641$	3.03963	−	2.20842i	0.120058	−	0.0872275i	−0.526136	−	0.850401i	$-0.676360\pi$
$641$	3.03963	−	2.20842i	0.120058	−	0.0872275i	0.646194	+	0.763173i	$0.276360\pi$
$642$		0			0
$643$	−3.07802	−	9.47317i	−0.121385	−	0.373585i	0.871840	−	0.489791i	$-0.162927\pi$
$643$	−3.07802	−	9.47317i	−0.121385	−	0.373585i	−0.993225	+	0.116205i	$0.962927\pi$
$644$	3.79389	+	11.6764i	0.149500	+	0.460114i
$645$		0			0
$646$	−12.5173	+	9.09431i	−0.492485	+	0.357811i
$647$	3.55423	−	10.9388i	0.139731	−	0.430049i	−0.856565	−	0.516040i	$-0.827406\pi$
$647$	3.55423	−	10.9388i	0.139731	−	0.430049i	0.996296	+	0.0859911i	$0.0274057\pi$
$648$		0			0
$649$	−25.2756	+	19.0928i	−0.992153	+	0.749457i
$650$	22.2464			0.872577
$651$		0			0
$652$	13.2153	−	9.60149i	0.517552	−	0.376024i
$653$	−4.11019	−	2.98623i	−0.160844	−	0.116860i	0.504452	−	0.863440i	$-0.331695\pi$
$653$	−4.11019	−	2.98623i	−0.160844	−	0.116860i	−0.665296	+	0.746580i	$0.731695\pi$
$654$		0			0
$655$	−10.4875	−	32.2773i	−0.409782	−	1.26118i
$656$	−0.656326	−	0.476848i	−0.0256252	−	0.0186178i
$657$		0			0
$658$	6.69251	−	20.5974i	0.260901	−	0.802971i
$659$	42.3777			1.65080			0.825401	−	0.564547i	$-0.190949\pi$
$659$	42.3777			1.65080			0.825401	+	0.564547i	$0.190949\pi$
$660$		0			0
$661$	−12.7151			−0.494559			−0.247280	−	0.968944i	$-0.579537\pi$
$661$	−12.7151			−0.494559			−0.247280	+	0.968944i	$0.579537\pi$
$662$	4.41134	−	13.5767i	0.171452	−	0.527674i
$663$		0			0
$664$	−11.4465	−	8.31636i	−0.444210	−	0.322737i
$665$	1.50205	+	4.62285i	0.0582472	+	0.179266i
$666$		0			0
$667$	3.96541	+	2.88104i	0.153541	+	0.111554i
$668$	−23.7866	+	17.2820i	−0.920333	+	0.668661i
$669$		0			0
$670$	−87.9539			−3.39796
$671$	28.3773	−	0.528434i	1.09549	−	0.0204000i
$672$		0			0
$673$	−8.65977	+	26.6520i	−0.333809	+	1.02736i	0.633496	+	0.773746i	$0.281619\pi$
$673$	−8.65977	+	26.6520i	−0.333809	+	1.02736i	−0.967306	+	0.253614i	$0.918381\pi$
$674$	−0.631372	+	0.458719i	−0.0243195	+	0.0176692i
$675$		0			0
$676$	−6.28147	−	19.3324i	−0.241595	−	0.743553i
$677$	−3.81736	−	11.7486i	−0.146713	−	0.451536i	0.850514	−	0.525952i	$-0.176291\pi$
$677$	−3.81736	−	11.7486i	−0.146713	−	0.451536i	−0.997227	+	0.0744157i	$0.976291\pi$
$678$		0			0
$679$	5.73422	−	4.16616i	0.220059	−	0.159882i
$680$	−3.92956	+	12.0939i	−0.150692	+	0.463782i
$681$		0			0
$682$	40.0829	−	30.2780i	1.53485	−	1.15940i
$683$	−4.43874			−0.169844			−0.0849219	−	0.996388i	$-0.527064\pi$
$683$	−4.43874			−0.169844			−0.0849219	+	0.996388i	$0.527064\pi$
$684$		0			0
$685$	11.3135	−	8.21970i	0.432265	−	0.314059i
$686$	1.69705	+	1.23298i	0.0647936	+	0.0470753i
$687$		0			0
$688$	−8.72244	−	26.8449i	−0.332540	−	1.02345i
$689$	−1.62841	−	1.18311i	−0.0620375	−	0.0450729i
$690$		0			0
$691$	10.2415	−	31.5202i	0.389606	−	1.19908i	−0.543478	−	0.839424i	$-0.682893\pi$
$691$	10.2415	−	31.5202i	0.389606	−	1.19908i	0.933084	−	0.359660i	$-0.117107\pi$
$692$	47.6441			1.81116
$693$		0			0
$694$	−12.0632			−0.457911
$695$	−4.41794	+	13.5970i	−0.167582	+	0.515765i
$696$		0			0
$697$	1.03527	+	0.752169i	0.0392137	+	0.0284904i
$698$	−0.419086	−	1.28981i	−0.0158626	−	0.0488201i
$699$		0			0
$700$	9.67457	+	7.02898i	0.365664	+	0.265671i
$701$	3.74246	−	2.71906i	0.141351	−	0.102697i	−0.514863	−	0.857273i	$-0.672157\pi$
$701$	3.74246	−	2.71906i	0.141351	−	0.102697i	0.656213	+	0.754575i	$0.272157\pi$
$702$		0			0
$703$	3.69080			0.139201
$704$	29.4124	+	20.5437i	1.10852	+	0.774271i
$705$		0			0
$706$	11.9013	−	36.6284i	0.447911	−	1.37853i
$707$	−6.75213	+	4.90571i	−0.253940	+	0.184498i
$708$		0			0
$709$	4.60926	+	14.1858i	0.173104	+	0.532761i	0.999542	−	0.0302680i	$-0.00963608\pi$
$709$	4.60926	+	14.1858i	0.173104	+	0.532761i	−0.826437	+	0.563029i	$0.809636\pi$
$710$	28.9926	+	89.2300i	1.08807	+	3.34874i
$711$		0			0
$712$	−7.65223	+	5.55967i	−0.286779	+	0.208357i
$713$	11.4129	−	35.1253i	0.427416	−	1.31545i
$714$		0			0
$715$	−6.49657	+	21.3383i	−0.242958	+	0.798008i
$716$	−19.7352			−0.737541
$717$		0			0
$718$	45.7784	−	33.2600i	1.70844	−	1.24125i
$719$	26.7436	+	19.4304i	0.997369	+	0.724631i	0.961522	−	0.274726i	$-0.0885872\pi$
$719$	26.7436	+	19.4304i	0.997369	+	0.724631i	0.0358465	+	0.999357i	$0.488587\pi$
$720$		0			0
$721$	2.32861	+	7.16674i	0.0867221	+	0.266903i
$722$	28.2272	+	20.5083i	1.05051	+	0.763238i
$723$		0			0
$724$	7.73724	−	23.8128i	0.287552	−	0.884995i
$725$	4.77422			0.177310
$726$		0			0
$727$	6.06384			0.224895			0.112448	−	0.993658i	$-0.464131\pi$
$727$	6.06384			0.224895			0.112448	+	0.993658i	$0.464131\pi$
$728$	−0.552209	+	1.69952i	−0.0204662	+	0.0629885i
$729$		0			0
$730$	41.4035	+	30.0814i	1.53241	+	1.11336i
$731$	13.7586	+	42.3445i	0.508879	+	1.56617i
$732$		0			0
$733$	0.749170	+	0.544304i	0.0276712	+	0.0201043i	0.601535	−	0.798847i	$-0.294556\pi$
$733$	0.749170	+	0.544304i	0.0276712	+	0.0201043i	−0.573864	+	0.818951i	$0.694556\pi$
$734$	−48.0630	+	34.9198i	−1.77404	+	1.28891i
$735$		0			0
$736$	41.2005			1.51867
$737$	12.8196	−	42.1068i	0.472218	−	1.55102i
$738$		0			0
$739$	−9.42384	+	29.0036i	−0.346662	+	1.06691i	0.614027	+	0.789285i	$0.289549\pi$
$739$	−9.42384	+	29.0036i	−0.346662	+	1.06691i	−0.960688	+	0.277629i	$0.910451\pi$
$740$	14.7181	−	10.6933i	0.541049	−	0.393095i
$741$		0			0
$742$	−0.612952	−	1.88647i	−0.0225022	−	0.0692545i
$743$	−5.51656	−	16.9782i	−0.202383	−	0.622871i	−0.999811	−	0.0194563i	$-0.993806\pi$
$743$	−5.51656	−	16.9782i	−0.202383	−	0.622871i	0.797428	−	0.603414i	$-0.206194\pi$
$744$		0			0
$745$	−7.65467	+	5.56144i	−0.280445	+	0.203755i
$746$	−8.37591	+	25.7784i	−0.306664	+	0.943815i
$747$		0			0
$748$	−31.2888	−	21.8543i	−1.14403	−	0.799074i
$749$	15.3887			0.562291
$750$		0			0
$751$	−28.9497	+	21.0332i	−1.05639	+	0.767511i	−0.973417	−	0.229041i	$-0.926441\pi$
$751$	−28.9497	+	21.0332i	−1.05639	+	0.767511i	−0.0829711	+	0.996552i	$0.526441\pi$
$752$	−25.3874	−	18.4450i	−0.925783	−	0.672620i
$753$		0			0
$754$	1.32219	+	4.06929i	0.0481514	+	0.148195i
$755$	22.5256	+	16.3658i	0.819789	+	0.595612i
$756$		0			0
$757$	13.1371	−	40.4318i	0.477475	−	1.46952i	−0.365115	−	0.930963i	$-0.618970\pi$
$757$	13.1371	−	40.4318i	0.477475	−	1.46952i	0.842590	−	0.538556i	$-0.181030\pi$
$758$	43.9420			1.59605
$759$		0			0
$760$	−4.08061			−0.148019
$761$	−2.81382	+	8.66004i	−0.102001	+	0.313926i	−0.989015	−	0.147816i	$-0.952776\pi$
$761$	−2.81382	+	8.66004i	−0.102001	+	0.313926i	0.887014	+	0.461742i	$0.152776\pi$
$762$		0			0
$763$	16.3892	+	11.9074i	0.593328	+	0.431078i
$764$	−10.5442	−	32.4519i	−0.381477	−	1.17407i
$765$		0			0
$766$	42.3862	+	30.7953i	1.53147	+	1.11268i
$767$	−16.4473	+	11.9497i	−0.593878	+	0.431477i
$768$		0			0
$769$	−6.93312			−0.250015			−0.125007	−	0.992156i	$-0.539895\pi$
$769$	−6.93312			−0.250015			−0.125007	+	0.992156i	$0.539895\pi$
$770$	−17.5394	+	13.2489i	−0.632074	+	0.477459i
$771$		0			0
$772$	−5.20405	+	16.0164i	−0.187298	+	0.576443i
$773$	−14.7750	+	10.7347i	−0.531421	+	0.386100i	−0.820889	−	0.571088i	$-0.806522\pi$
$773$	−14.7750	+	10.7347i	−0.531421	+	0.386100i	0.289468	+	0.957188i	$0.406522\pi$
$774$		0			0
$775$	−11.1165	−	34.2130i	−0.399316	−	1.22897i
$776$	1.83874	+	5.65907i	0.0660071	+	0.203149i
$777$		0			0
$778$	−23.0425	+	16.7413i	−0.826112	+	0.600206i
$779$	−0.126894	+	0.390541i	−0.00454647	+	0.0139926i
$780$		0			0
$781$	−46.9435	+	0.874168i	−1.67977	+	0.0312802i
$782$	−51.4418			−1.83955
$783$		0			0
$784$	2.45894	−	1.78653i	0.0878193	−	0.0638045i
$785$	4.00421	+	2.90923i	0.142916	+	0.103835i
$786$		0			0
$787$	−3.78765	−	11.6572i	−0.135015	−	0.415534i	0.860577	−	0.509320i	$-0.170103\pi$
$787$	−3.78765	−	11.6572i	−0.135015	−	0.415534i	−0.995592	+	0.0937860i	$0.970103\pi$
$788$	−6.99638	−	5.08316i	−0.249236	−	0.181080i
$789$		0			0
$790$	−19.0716	+	58.6965i	−0.678539	+	2.08833i
$791$	−18.1019			−0.643628
$792$		0			0
$793$	18.2158			0.646862
$794$	−2.76431	+	8.50767i	−0.0981017	+	0.301926i
$795$		0			0
$796$	7.47860	+	5.43352i	0.265072	+	0.192586i
$797$	7.06294	+	21.7375i	0.250182	+	0.769981i	0.994741	+	0.102424i	$0.0326599\pi$
$797$	7.06294	+	21.7375i	0.250182	+	0.769981i	−0.744559	+	0.667557i	$0.767340\pi$
$798$		0			0
$799$	40.0454	+	29.0947i	1.41671	+	1.02930i
$800$	32.4662	−	23.5881i	1.14785	−	0.833965i
$801$		0			0
$802$	68.0531			2.40304
$803$	−20.4358	+	15.4369i	−0.721163	+	0.544755i
$804$		0			0
$805$	−4.99402	+	15.3700i	−0.176016	+	0.541721i
$806$	26.0827	−	18.9502i	0.918724	−	0.667492i
$807$		0			0
$808$	−2.16515	−	6.66364i	−0.0761697	−	0.234426i
$809$	13.4837	+	41.4986i	0.474062	+	1.45901i	0.847219	+	0.531244i	$0.178275\pi$
$809$	13.4837	+	41.4986i	0.474062	+	1.45901i	−0.373157	+	0.927768i	$0.621725\pi$
$810$		0			0
$811$	11.1903	−	8.13021i	0.392944	−	0.285490i	−0.373717	−	0.927543i	$-0.621917\pi$
$811$	11.1903	−	8.13021i	0.392944	−	0.285490i	0.766661	+	0.642052i	$0.221917\pi$
$812$	−0.710736	+	2.18742i	−0.0249419	+	0.0767634i
$813$		0			0
$814$	5.45224	+	15.7747i	0.191101	+	0.552901i
$815$	21.5023			0.753194
$816$		0			0
$817$	−11.5588	+	8.39794i	−0.404390	+	0.293807i
$818$	42.2356	+	30.6859i	1.47673	+	1.07291i
$819$		0			0
$820$	0.625484	+	1.92504i	0.0218429	+	0.0672254i
$821$	−15.8557	−	11.5198i	−0.553368	−	0.402045i	0.275658	−	0.961256i	$-0.411104\pi$
$821$	−15.8557	−	11.5198i	−0.553368	−	0.402045i	−0.829026	+	0.559211i	$0.811104\pi$
$822$		0			0
$823$	11.7569	−	36.1840i	0.409819	−	1.26129i	−0.506985	−	0.861955i	$-0.669240\pi$
$823$	11.7569	−	36.1840i	0.409819	−	1.26129i	0.916804	−	0.399338i	$-0.130760\pi$
$824$	−6.32612			−0.220381
$825$		0			0
$826$	−20.0343			−0.697084
$827$	0.835400	−	2.57110i	0.0290497	−	0.0894058i	−0.935480	−	0.353378i	$-0.885033\pi$
$827$	0.835400	−	2.57110i	0.0290497	−	0.0894058i	0.964530	+	0.263973i	$0.0850328\pi$
$828$		0			0
$829$	14.3125	+	10.3987i	0.497095	+	0.361161i	0.807906	−	0.589311i	$-0.200601\pi$
$829$	14.3125	+	10.3987i	0.497095	+	0.361161i	−0.310811	+	0.950472i	$0.600601\pi$
$830$	−34.5164	−	106.231i	−1.19808	−	3.68732i
$831$		0			0
$832$	18.6283	+	13.5342i	0.645819	+	0.469215i
$833$	−3.87867	+	2.81802i	−0.134388	+	0.0976387i
$834$		0			0
$835$	−38.7027			−1.33936
$836$	3.56705	−	11.7162i	0.123369	−	0.405212i
$837$		0			0
$838$	−6.86768	+	21.1365i	−0.237240	+	0.730150i
$839$	0.136448	−	0.0991353i	0.00471071	−	0.00342253i	−0.585427	−	0.810725i	$-0.699073\pi$
$839$	0.136448	−	0.0991353i	0.00471071	−	0.00342253i	0.590138	+	0.807302i	$0.299073\pi$
$840$		0			0
$841$	−8.67774	−	26.7073i	−0.299233	−	0.920943i
$842$	−24.5435	−	75.5371i	−0.845825	−	2.60318i
$843$		0			0
$844$	−21.6171	+	15.7058i	−0.744093	+	0.540615i
$845$	8.26850	−	25.4478i	0.284445	−	0.875432i
$846$		0			0
$847$	−3.78632	−	10.3278i	−0.130100	−	0.354868i
$848$	−2.87407			−0.0986961
$849$		0			0
$850$	−40.5364	+	29.4514i	−1.39039	+	1.01017i
$851$	9.92757	+	7.21280i	0.340313	+	0.247252i
$852$		0			0
$853$	−13.2806	−	40.8736i	−0.454720	−	1.39948i	−0.871464	−	0.490460i	$-0.836829\pi$
$853$	−13.2806	−	40.8736i	−0.454720	−	1.39948i	0.416743	−	0.909024i	$-0.363171\pi$
$854$	14.5226	+	10.5513i	0.496953	+	0.361057i
$855$		0			0
$856$	−3.99215	+	12.2866i	−0.136449	+	0.419946i
$857$	3.31550			0.113255			0.0566276	−	0.998395i	$-0.481965\pi$
$857$	3.31550			0.113255			0.0566276	+	0.998395i	$0.481965\pi$
$858$		0			0
$859$	12.5924			0.429646			0.214823	−	0.976653i	$-0.431083\pi$
$859$	12.5924			0.429646			0.214823	+	0.976653i	$0.431083\pi$
$860$	−21.7626	+	66.9783i	−0.742098	+	2.28394i
$861$		0			0
$862$	9.57964	+	6.96002i	0.326284	+	0.237059i
$863$	17.2547	+	53.1045i	0.587357	+	1.80770i	0.589593	+	0.807700i	$0.299288\pi$
$863$	17.2547	+	53.1045i	0.587357	+	1.80770i	−0.00223669	+	0.999997i	$0.500712\pi$
$864$		0			0
$865$	50.7378	+	36.8632i	1.72514	+	1.25339i
$866$	4.57403	−	3.32323i	0.155432	−	0.112928i
$867$		0			0
$868$	17.3304			0.588232
$869$	−25.3204	−	17.6855i	−0.858935	−	0.599941i
$870$		0			0
$871$	8.72943	−	26.8664i	0.295785	−	0.910334i
$872$	−13.7587	+	9.99632i	−0.465930	+	0.338518i
$873$		0			0
$874$	−5.10107	−	15.6995i	−0.172546	−	0.531043i
$875$	−0.0173353	−	0.0533527i	−0.000586042	−	0.00180365i
$876$		0			0
$877$	−6.68843	+	4.85943i	−0.225852	+	0.164091i	−0.694957	−	0.719051i	$-0.744577\pi$
$877$	−6.68843	+	4.85943i	−0.225852	+	0.164091i	0.469105	+	0.883143i	$0.344577\pi$
$878$	19.8139	−	60.9809i	0.668686	−	2.05800i
$879$		0			0
$880$	10.4043	+	30.1021i	0.350727	+	1.01474i
$881$	−26.0843			−0.878803			−0.439401	−	0.898291i	$-0.644809\pi$
$881$	−26.0843			−0.878803			−0.439401	+	0.898291i	$0.644809\pi$
$882$		0			0
$883$	−0.740321	+	0.537874i	−0.0249138	+	0.0181009i	−0.600172	−	0.799871i	$-0.704901\pi$
$883$	−0.740321	+	0.537874i	−0.0249138	+	0.0181009i	0.575259	+	0.817972i	$0.304901\pi$
$884$	−19.8167	−	14.3977i	−0.666507	−	0.484246i
$885$		0			0
$886$	15.9701	+	49.1510i	0.536527	+	1.65126i
$887$	−45.3512	−	32.9496i	−1.52274	−	1.10634i	−0.960106	−	0.279635i	$-0.909786\pi$
$887$	−45.3512	−	32.9496i	−1.52274	−	1.10634i	−0.562638	−	0.826703i	$-0.690214\pi$
$888$		0			0
$889$	4.74993	−	14.6188i	0.159307	−	0.490298i
$890$	−74.6722			−2.50302
$891$		0			0
$892$	−12.6520			−0.423619
$893$	−4.90841	+	15.1065i	−0.164254	+	0.505521i
$894$		0			0
$895$	−21.0167	−	15.2696i	−0.702512	−	0.510405i
$896$	2.03381	+	6.25944i	0.0679450	+	0.209113i
$897$		0			0
$898$	−26.0930	−	18.9577i	−0.870736	−	0.632627i
$899$	5.59750	−	4.06682i	0.186687	−	0.135636i
$900$		0			0
$901$	4.53349			0.151033
$902$	−1.85665	+	0.0345739i	−0.0618195	+	0.00115119i
$903$		0			0
$904$	4.69600	−	14.4528i	0.156186	−	0.480693i
$905$	26.6641	−	19.3726i	0.886344	−	0.643966i
$906$		0			0
$907$	2.85729	+	8.79382i	0.0948746	+	0.291994i	0.987221	−	0.159357i	$-0.0509422\pi$
$907$	2.85729	+	8.79382i	0.0948746	+	0.291994i	−0.892346	+	0.451351i	$0.850942\pi$
$908$	10.9923	+	33.8309i	0.364793	+	1.12272i
$909$		0			0
$910$	−11.4132	+	8.29217i	−0.378344	+	0.274883i
$911$	11.5250	−	35.4704i	0.381841	−	1.17519i	−0.556905	−	0.830576i	$-0.688011\pi$
$911$	11.5250	−	35.4704i	0.381841	−	1.17519i	0.938746	−	0.344609i	$-0.111989\pi$
$912$		0			0
$913$	55.8874	−	1.04072i	1.84960	−	0.0344428i
$914$	29.8629			0.987777
$915$		0			0
$916$	−14.7670	+	10.7289i	−0.487917	+	0.354492i
$917$	8.69030	+	6.31387i	0.286979	+	0.208502i
$918$		0			0
$919$	−4.52355	−	13.9220i	−0.149218	−	0.459246i	0.848311	−	0.529498i	$-0.177620\pi$
$919$	−4.52355	−	13.9220i	−0.149218	−	0.459246i	−0.997529	+	0.0702519i	$0.977620\pi$
$920$	−10.9761	−	7.97459i	−0.361871	−	0.262914i
$921$		0			0
$922$	23.7991	−	73.2461i	0.783781	−	2.41223i
$923$	−30.1337			−0.991864
$924$		0			0
$925$	11.9524			0.392994
$926$	−22.5373	+	69.3626i	−0.740621	+	2.27940i
$927$		0			0
$928$	6.24430	+	4.53675i	0.204979	+	0.148926i
$929$	2.41246	+	7.42479i	0.0791503	+	0.243600i	0.982800	−	0.184673i	$-0.0591225\pi$
$929$	2.41246	+	7.42479i	0.0791503	+	0.243600i	−0.903650	+	0.428272i	$0.859122\pi$
$930$		0			0
$931$	−1.24465	−	0.904290i	−0.0407917	−	0.0296369i
$932$	−2.92328	+	2.12389i	−0.0957553	+	0.0695703i
$933$		0			0
$934$	−28.4309			−0.930287
$935$	−16.4114	−	47.4823i	−0.536711	−	1.55284i
$936$		0			0
$937$	−16.4092	+	50.5023i	−0.536065	+	1.64984i	0.205271	+	0.978705i	$0.434192\pi$
$937$	−16.4092	+	50.5023i	−0.536065	+	1.64984i	−0.741336	+	0.671134i	$0.765808\pi$
$938$	22.5216	−	16.3629i	0.735356	−	0.534267i
$939$		0			0
$940$	24.1944	+	74.4627i	0.789135	+	2.42871i
$941$	4.03537	+	12.4196i	0.131549	+	0.404867i	0.995037	−	0.0995022i	$-0.0317250\pi$
$941$	4.03537	+	12.4196i	0.131549	+	0.404867i	−0.863488	+	0.504369i	$0.831725\pi$
$942$		0			0
$943$	−1.10454	+	0.802497i	−0.0359689	+	0.0261329i
$944$	−8.97039	+	27.6080i	−0.291961	+	0.898564i
$945$		0			0
$946$	−52.9684	−	36.9969i	−1.72215	−	1.20287i
$947$	39.8291			1.29427			0.647136	−	0.762375i	$-0.275967\pi$
$947$	39.8291			1.29427			0.647136	+	0.762375i	$0.275967\pi$
$948$		0			0
$949$	−13.2980	+	9.66153i	−0.431670	+	0.313627i
$950$	−13.0079	−	9.45082i	−0.422033	−	0.306625i
$951$		0			0
$952$	−1.24374	−	3.82784i	−0.0403099	−	0.124061i
$953$	3.06721	+	2.22846i	0.0993567	+	0.0721869i	0.636354	−	0.771397i	$-0.280442\pi$
$953$	3.06721	+	2.22846i	0.0993567	+	0.0721869i	−0.536998	+	0.843584i	$0.680442\pi$
$954$		0			0
$955$	13.8797	−	42.7174i	0.449137	−	1.38230i
$956$	12.0571			0.389955
$957$		0			0
$958$	−57.8899			−1.87034
$959$	−1.36775	+	4.20949i	−0.0441669	+	0.135932i
$960$		0			0
$961$	−17.0976	−	12.4221i	−0.551536	−	0.400714i
$962$	3.31016	+	10.1876i	0.106724	+	0.328463i
$963$		0			0
$964$	−31.3607	−	22.7849i	−1.01006	−	0.733851i
$965$	−17.9342	+	13.0300i	−0.577322	+	0.419449i
$966$		0			0
$967$	5.63563			0.181230			0.0906149	−	0.995886i	$-0.471117\pi$
$967$	5.63563			0.181230			0.0906149	+	0.995886i	$0.471117\pi$
$968$	9.22813	−	0.343806i	0.296603	−	0.0110504i
$969$		0			0
$970$	−14.5161	+	44.6760i	−0.466084	+	1.43446i
$971$	−1.95559	+	1.42082i	−0.0627578	+	0.0455962i	−0.618722	−	0.785610i	$-0.712349\pi$
$971$	−1.95559	+	1.42082i	−0.0627578	+	0.0455962i	0.555964	+	0.831206i	$0.312349\pi$
$972$		0			0
$973$	−1.39832	−	4.30358i	−0.0448280	−	0.137966i
$974$	−13.2740	−	40.8531i	−0.425326	−	1.30902i
$975$		0			0
$976$	21.0425	−	15.2883i	0.673555	−	0.489366i
$977$	−14.4134	+	44.3597i	−0.461124	+	1.41919i	0.402668	+	0.915346i	$0.368083\pi$
$977$	−14.4134	+	44.3597i	−0.461124	+	1.41919i	−0.863792	+	0.503848i	$0.831917\pi$
$978$		0			0
$979$	10.8838	−	35.7483i	0.347847	−	1.14252i
$980$	−7.58338			−0.242242
$981$		0			0
$982$	48.9877	−	35.5916i	1.56326	−	1.13577i
$983$	17.5480	+	12.7494i	0.559695	+	0.406642i	0.831347	−	0.555753i	$-0.187570\pi$
$983$	17.5480	+	12.7494i	0.559695	+	0.406642i	−0.271652	+	0.962395i	$0.587570\pi$
$984$		0			0
$985$	−3.51773	−	10.8265i	−0.112084	−	0.344960i
$986$	−7.79645	−	5.66445i	−0.248290	−	0.180393i
$987$		0			0
$988$	2.42895	−	7.47555i	0.0772753	−	0.237829i
$989$	−47.5027			−1.51050
$990$		0			0
$991$	33.7715			1.07279			0.536394	−	0.843968i	$-0.319786\pi$
$991$	33.7715			1.07279			0.536394	+	0.843968i	$0.319786\pi$
$992$	17.9718	−	55.3114i	0.570605	−	1.75614i
$993$		0			0
$994$	−24.0242	−	17.4546i	−0.762000	−	0.553626i
$995$	3.76019	+	11.5727i	0.119206	+	0.366879i
$996$		0			0
$997$	−0.505573	−	0.367320i	−0.0160117	−	0.0116331i	0.579751	−	0.814794i	$-0.303150\pi$
$997$	−0.505573	−	0.367320i	−0.0160117	−	0.0116331i	−0.595762	+	0.803161i	$0.703150\pi$
$998$	36.4763	−	26.5016i	1.15464	−	0.838893i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.j.64.4		20
3.2	odd	2		231.2.j.g.64.2	✓	20
11.4	even	5		7623.2.a.cx.1.8		10
11.5	even	5	inner	693.2.m.j.379.4		20
11.7	odd	10		7623.2.a.cy.1.3		10
33.5	odd	10		231.2.j.g.148.2	yes	20
33.26	odd	10		2541.2.a.bq.1.3		10
33.29	even	10		2541.2.a.br.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.2	✓	20	3.2	odd	2
231.2.j.g.148.2	yes	20	33.5	odd	10
693.2.m.j.64.4		20	1.1	even	1	trivial
693.2.m.j.379.4		20	11.5	even	5	inner
2541.2.a.bq.1.3		10	33.26	odd	10
2541.2.a.br.1.8		10	33.29	even	10
7623.2.a.cx.1.8		10	11.4	even	5
7623.2.a.cy.1.3		10	11.7	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.648215 - 1.99500i) q^{2} +(-1.94181 - 1.41081i) q^{4} +(-0.976330 - 3.00483i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-0.679172 + 0.493447i) q^{8} +O(q^{10})\)	\(q+(0.648215 - 1.99500i) q^{2} +(-1.94181 - 1.41081i) q^{4} +(-0.976330 - 3.00483i) q^{5} +(0.809017 + 0.587785i) q^{7} +(-0.679172 + 0.493447i) q^{8} -6.62751 q^{10} +(0.965987 - 3.17283i) q^{11} +(0.657781 - 2.02444i) q^{13} +(1.69705 - 1.23298i) q^{14} +(-0.939232 - 2.89066i) q^{16} +(1.48152 + 4.55965i) q^{17} +(-1.24465 + 0.904290i) q^{19} +(-2.34339 + 7.21222i) q^{20} +(-5.70363 - 3.98382i) q^{22} -5.11509 q^{23} +(-4.03072 + 2.92849i) q^{25} +(-3.61238 - 2.62455i) q^{26} +(-0.741705 - 2.28273i) q^{28} +(-0.775237 - 0.563243i) q^{29} +(-2.23122 + 6.86698i) q^{31} -8.05469 q^{32} +10.0569 q^{34} +(0.976330 - 3.00483i) q^{35} +(-1.94084 - 1.41010i) q^{37} +(0.997259 + 3.06925i) q^{38} +(2.14582 + 1.55903i) q^{40} +(0.215938 - 0.156888i) q^{41} +9.28678 q^{43} +(-6.35202 + 4.79821i) q^{44} +(-3.31568 + 10.2046i) q^{46} +(8.35271 - 6.06860i) q^{47} +(0.309017 + 0.951057i) q^{49} +(3.22956 + 9.93958i) q^{50} +(-4.13338 + 3.00308i) q^{52} +(0.292206 - 0.899319i) q^{53} +(-10.4770 + 0.195099i) q^{55} -0.839503 q^{56} +(-1.62619 + 1.18150i) q^{58} +(-7.72673 - 5.61380i) q^{59} +(2.64443 + 8.13872i) q^{61} +(12.2533 + 8.90256i) q^{62} +(-3.34271 + 10.2878i) q^{64} -6.72532 q^{65} +13.2710 q^{67} +(3.55596 - 10.9441i) q^{68} +(-5.36177 - 3.89556i) q^{70} +(-4.37458 - 13.4636i) q^{71} +(-6.24721 - 4.53887i) q^{73} +(-4.07123 + 2.95792i) q^{74} +3.69265 q^{76} +(2.64644 - 1.99908i) q^{77} +(2.87765 - 8.85649i) q^{79} +(-7.76895 + 5.64447i) q^{80} +(-0.173018 - 0.532493i) q^{82} +(5.20805 + 16.0287i) q^{83} +(12.2545 - 8.90345i) q^{85} +(6.01983 - 18.5271i) q^{86} +(0.909554 + 2.63156i) q^{88} +11.2670 q^{89} +(1.72209 - 1.25117i) q^{91} +(9.93253 + 7.21641i) q^{92} +(-6.69251 - 20.5974i) q^{94} +(3.93243 + 2.85708i) q^{95} +(2.19028 - 6.74098i) q^{97} +2.09767 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

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