LMFDB - Embedded newform 756.2.bb.a.611.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.4
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35995 - 0.387995i) q^{2} +(1.69892 + 1.05531i) q^{4} +(-3.19234 + 1.84310i) q^{5} +(-2.29354 + 1.31898i) q^{7} +(-1.90099 - 2.09434i) q^{8} +O(q^{10})$	\(q+(-1.35995 - 0.387995i) q^{2} +(1.69892 + 1.05531i) q^{4} +(-3.19234 + 1.84310i) q^{5} +(-2.29354 + 1.31898i) q^{7} +(-1.90099 - 2.09434i) q^{8} +(5.05653 - 1.26790i) q^{10} +(-1.79831 + 3.11476i) q^{11} +(-0.565220 + 0.978990i) q^{13} +(3.63085 - 0.903857i) q^{14} +(1.77265 + 3.58576i) q^{16} +(5.61029 - 3.23910i) q^{17} +(-4.20169 - 2.42585i) q^{19} +(-7.36856 - 0.237626i) q^{20} +(3.65412 - 3.53818i) q^{22} +(-0.522364 - 0.904760i) q^{23} +(4.29402 - 7.43745i) q^{25} +(1.14851 - 1.11207i) q^{26} +(-5.28846 - 0.179553i) q^{28} +(-1.32443 + 0.764659i) q^{29} -3.45679i q^{31} +(-1.01945 - 5.56424i) q^{32} +(-8.88646 + 2.22824i) q^{34} +(4.89074 - 8.43782i) q^{35} +(1.02611 - 1.77727i) q^{37} +(4.77286 + 4.92926i) q^{38} +(9.92866 + 3.18213i) q^{40} +(0.782771 + 0.451933i) q^{41} +(5.77771 - 3.33576i) q^{43} +(-6.34221 + 3.39396i) q^{44} +(0.359345 + 1.43310i) q^{46} +3.71500 q^{47} +(3.52061 - 6.05023i) q^{49} +(-8.72534 + 8.44849i) q^{50} +(-1.99340 + 1.06674i) q^{52} +(-0.975539 + 0.563227i) q^{53} -13.2578i q^{55} +(7.12236 + 2.29608i) q^{56} +(2.09784 - 0.526025i) q^{58} +0.835539 q^{59} -13.5427 q^{61} +(-1.34122 + 4.70106i) q^{62} +(-0.772494 + 7.96262i) q^{64} -4.16702i q^{65} +3.46796i q^{67} +(12.9497 + 0.417609i) q^{68} +(-9.92499 + 9.57742i) q^{70} +2.47422 q^{71} +(3.43894 + 5.95641i) q^{73} +(-2.08503 + 2.01887i) q^{74} +(-4.57832 - 8.55540i) q^{76} +(0.0161899 - 9.51574i) q^{77} -6.62099i q^{79} +(-12.2678 - 8.17980i) q^{80} +(-0.889180 - 0.918317i) q^{82} +(-5.37860 - 9.31600i) q^{83} +(-11.9400 + 20.6806i) q^{85} +(-9.15165 + 2.29474i) q^{86} +(9.94192 - 2.15486i) q^{88} +(-15.6235 - 9.02024i) q^{89} +(0.00508858 - 2.99086i) q^{91} +(0.0673471 - 2.08837i) q^{92} +(-5.05221 - 1.44140i) q^{94} +17.8843 q^{95} +(-5.46022 - 9.45739i) q^{97} +(-7.13531 + 6.86202i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.35995	−	0.387995i	−0.961629	−	0.274354i
$2$	−1.35995	−	0.387995i	−0.961629	−	0.274354i
$3$		0			0
$3$		0			0
$4$	1.69892	+	1.05531i	0.849459	+	0.527654i
$5$	−3.19234	+	1.84310i	−1.42766	+	0.824258i	−0.996936	−	0.0782267i	$-0.975074\pi$
$5$	−3.19234	+	1.84310i	−1.42766	+	0.824258i	−0.430722	+	0.902485i	$0.641741\pi$
$6$		0			0
$7$	−2.29354	+	1.31898i	−0.866875	+	0.498526i
$7$	−2.29354	+	1.31898i	−0.866875	+	0.498526i
$8$	−1.90099	−	2.09434i	−0.672101	−	0.740460i
$9$		0			0
$10$	5.05653	−	1.26790i	1.59901	−	0.400947i
$11$	−1.79831	+	3.11476i	−0.542210	+	0.939136i	0.456566	+	0.889689i	$0.349079\pi$
$11$	−1.79831	+	3.11476i	−0.542210	+	0.939136i	−0.998777	+	0.0494465i	$0.984254\pi$
$12$		0			0
$13$	−0.565220	+	0.978990i	−0.156764	+	0.271523i	−0.933700	−	0.358057i	$-0.883440\pi$
$13$	−0.565220	+	0.978990i	−0.156764	+	0.271523i	0.776936	+	0.629580i	$0.216773\pi$
$14$	3.63085	−	0.903857i	0.970384	−	0.241566i
$15$		0			0
$16$	1.77265	+	3.58576i	0.443163	+	0.896441i
$17$	5.61029	−	3.23910i	1.36069	−	0.785597i	0.370978	−	0.928642i	$-0.379022\pi$
$17$	5.61029	−	3.23910i	1.36069	−	0.785597i	0.989716	+	0.143044i	$0.0456892\pi$
$18$		0			0
$19$	−4.20169	−	2.42585i	−0.963934	−	0.556528i	−0.0665524	−	0.997783i	$-0.521200\pi$
$19$	−4.20169	−	2.42585i	−0.963934	−	0.556528i	−0.897382	+	0.441255i	$0.854533\pi$
$20$	−7.36856	−	0.237626i	−1.64766	−	0.0531348i
$21$		0			0
$22$	3.65412	−	3.53818i	0.779061	−	0.754342i
$23$	−0.522364	−	0.904760i	−0.108920	−	0.188656i	0.806413	−	0.591353i	$-0.201406\pi$
$23$	−0.522364	−	0.904760i	−0.108920	−	0.188656i	−0.915333	+	0.402697i	$0.868073\pi$
$24$		0			0
$25$	4.29402	−	7.43745i	0.858803	−	1.48749i
$26$	1.14851	−	1.11207i	0.225242	−	0.218096i
$27$		0			0
$28$	−5.28846	−	0.179553i	−0.999424	−	0.0339323i
$29$	−1.32443	+	0.764659i	−0.245940	+	0.141994i	−0.617904	−	0.786254i	$-0.712018\pi$
$29$	−1.32443	+	0.764659i	−0.245940	+	0.141994i	0.371964	+	0.928247i	$0.378685\pi$
$30$		0			0
$31$		−	3.45679i		−	0.620859i	−0.950596	−	0.310429i	$-0.899527\pi$
$31$		−	3.45679i		−	0.620859i	0.950596	−	0.310429i	$-0.100473\pi$
$32$	−1.01945	−	5.56424i	−0.180216	−	0.983627i
$33$		0			0
$34$	−8.88646	+	2.22824i	−1.52401	+	0.382141i
$35$	4.89074	−	8.43782i	0.826686	−	1.42625i
$36$		0			0
$37$	1.02611	−	1.77727i	0.168691	−	0.292182i	−0.769269	−	0.638925i	$-0.779379\pi$
$37$	1.02611	−	1.77727i	0.168691	−	0.292182i	0.937960	+	0.346744i	$0.112713\pi$
$38$	4.77286	+	4.92926i	0.774261	+	0.799632i
$39$		0			0
$40$	9.92866	+	3.18213i	1.56986	+	0.503138i
$41$	0.782771	+	0.451933i	0.122248	+	0.0705801i	0.559877	−	0.828576i	$-0.310848\pi$
$41$	0.782771	+	0.451933i	0.122248	+	0.0705801i	−0.437629	+	0.899156i	$0.644182\pi$
$42$		0			0
$43$	5.77771	−	3.33576i	0.881093	−	0.508699i	0.0100740	−	0.999949i	$-0.496793\pi$
$43$	5.77771	−	3.33576i	0.881093	−	0.508699i	0.871018	+	0.491250i	$0.163460\pi$
$44$	−6.34221	+	3.39396i	−0.956124	+	0.511658i
$45$		0			0
$46$	0.359345	+	1.43310i	0.0529825	+	0.211299i
$47$	3.71500			0.541889			0.270944	−	0.962595i	$-0.412664\pi$
$47$	3.71500			0.541889			0.270944	+	0.962595i	$0.412664\pi$
$48$		0			0
$49$	3.52061	−	6.05023i	0.502944	−	0.864319i
$50$	−8.72534	+	8.44849i	−1.23395	+	1.19480i
$51$		0			0
$52$	−1.99340	+	1.06674i	−0.276435	+	0.147931i
$53$	−0.975539	+	0.563227i	−0.134001	+	0.0773652i	−0.565502	−	0.824747i	$-0.691317\pi$
$53$	−0.975539	+	0.563227i	−0.134001	+	0.0773652i	0.431501	+	0.902112i	$0.357984\pi$
$54$		0			0
$55$		−	13.2578i		−	1.78769i
$56$	7.12236	+	2.29608i	0.951765	+	0.306827i
$57$		0			0
$58$	2.09784	−	0.526025i	0.275460	−	0.0690704i
$59$	0.835539			0.108778			0.0543890	−	0.998520i	$-0.482679\pi$
$59$	0.835539			0.108778			0.0543890	+	0.998520i	$0.482679\pi$
$60$		0			0
$61$	−13.5427			−1.73397			−0.866983	−	0.498339i	$-0.833944\pi$
$61$	−13.5427			−1.73397			−0.866983	+	0.498339i	$0.833944\pi$
$62$	−1.34122	+	4.70106i	−0.170335	+	0.597036i
$63$		0			0
$64$	−0.772494	+	7.96262i	−0.0965617	+	0.995327i
$65$		−	4.16702i		−	0.516856i
$66$		0			0
$67$			3.46796i			0.423679i	0.977304	+	0.211839i	$0.0679454\pi$
$67$			3.46796i			0.423679i	−0.977304	+	0.211839i	$0.932055\pi$
$68$	12.9497	+	0.417609i	1.57038	+	0.0506425i
$69$		0			0
$70$	−9.92499	+	9.57742i	−1.18626	+	1.14472i
$71$	2.47422			0.293636			0.146818	−	0.989164i	$-0.453097\pi$
$71$	2.47422			0.293636			0.146818	+	0.989164i	$0.453097\pi$
$72$		0			0
$73$	3.43894	+	5.95641i	0.402497	+	0.697145i	0.994027	−	0.109138i	$-0.0348090\pi$
$73$	3.43894	+	5.95641i	0.402497	+	0.697145i	−0.591530	+	0.806283i	$0.701476\pi$
$74$	−2.08503	+	2.01887i	−0.242380	+	0.234689i
$75$		0			0
$76$	−4.57832	−	8.55540i	−0.525169	−	0.981371i
$77$	0.0161899	−	9.51574i	0.00184501	−	1.08442i
$78$		0			0
$79$		−	6.62099i		−	0.744919i	−0.928048	−	0.372460i	$-0.878514\pi$
$79$		−	6.62099i		−	0.744919i	0.928048	−	0.372460i	$-0.121486\pi$
$80$	−12.2678	−	8.17980i	−1.37158	−	0.914530i
$81$		0			0
$82$	−0.889180	−	0.918317i	−0.0981935	−	0.101411i
$83$	−5.37860	−	9.31600i	−0.590378	−	1.02256i	−0.994181	−	0.107718i	$-0.965645\pi$
$83$	−5.37860	−	9.31600i	−0.590378	−	1.02256i	0.403804	−	0.914846i	$-0.367688\pi$
$84$		0			0
$85$	−11.9400	+	20.6806i	−1.29507	+	2.24313i
$86$	−9.15165	+	2.29474i	−0.986848	+	0.247448i
$87$		0			0
$88$	9.94192	−	2.15486i	1.05981	−	0.229709i
$89$	−15.6235	−	9.02024i	−1.65609	−	0.956144i	−0.974494	−	0.224415i	$-0.927953\pi$
$89$	−15.6235	−	9.02024i	−1.65609	−	0.956144i	−0.681596	−	0.731729i	$-0.738714\pi$
$90$		0			0
$91$	0.00508858	−	2.99086i	0.000533428	−	0.313527i
$92$	0.0673471	−	2.08837i	0.00702142	−	0.217728i
$93$		0			0
$94$	−5.05221	−	1.44140i	−0.521096	−	0.148670i
$95$	17.8843			1.83489
$96$		0			0
$97$	−5.46022	−	9.45739i	−0.554402	−	0.960252i	−0.997950	−	0.0640014i	$-0.979614\pi$
$97$	−5.46022	−	9.45739i	−0.554402	−	0.960252i	0.443548	−	0.896251i	$-0.353720\pi$
$98$	−7.13531	+	6.86202i	−0.720775	+	0.693169i
$99$		0			0
$100$	15.1440	−	8.10412i	1.51440	−	0.810412i
$101$	−6.36259	−	3.67344i	−0.633101	−	0.365521i	0.148851	−	0.988860i	$-0.452443\pi$
$101$	−6.36259	−	3.67344i	−0.633101	−	0.365521i	−0.781952	+	0.623339i	$0.785776\pi$
$102$		0			0
$103$	1.01104	−	0.583722i	0.0996204	−	0.0575158i	−0.449362	−	0.893350i	$-0.648349\pi$
$103$	1.01104	−	0.583722i	0.0996204	−	0.0575158i	0.548982	+	0.835834i	$0.315015\pi$
$104$	3.12481	−	0.677287i	0.306413	−	0.0664134i
$105$		0			0
$106$	1.54521	−	0.387456i	0.150084	−	0.0376330i
$107$	7.59837	−	13.1608i	0.734562	−	1.27230i	−0.220353	−	0.975420i	$-0.570721\pi$
$107$	7.59837	−	13.1608i	0.734562	−	1.27230i	0.954915	−	0.296878i	$-0.0959456\pi$
$108$		0			0
$109$	6.64628	+	11.5117i	0.636598	+	1.10262i	0.986174	+	0.165712i	$0.0529923\pi$
$109$	6.64628	+	11.5117i	0.636598	+	1.10262i	−0.349576	+	0.936908i	$0.613674\pi$
$110$	−5.14398	+	18.0300i	−0.490459	+	1.71909i
$111$		0			0
$112$	−8.79517	−	5.88599i	−0.831066	−	0.556174i
$113$	0.272599	+	0.157385i	0.0256440	+	0.0148055i	0.512767	−	0.858528i	$-0.328620\pi$
$113$	0.272599	+	0.157385i	0.0256440	+	0.0148055i	−0.487123	+	0.873333i	$0.661954\pi$
$114$		0			0
$115$	3.33512	+	1.92553i	0.311002	+	0.179557i
$116$	−3.05705	−	0.0985856i	−0.283840	−	0.00915344i
$117$		0			0
$118$	−1.13629	−	0.324185i	−0.104604	−	0.0298437i
$119$	−8.59510	+	14.8288i	−0.787911	+	1.35936i
$120$		0			0
$121$	−0.967824	−	1.67632i	−0.0879840	−	0.152393i
$122$	18.4174	+	5.25451i	1.66743	+	0.475721i
$123$		0			0
$124$	3.64798	−	5.87281i	0.327598	−	0.527394i
$125$			13.2262i			1.18299i
$126$		0			0
$127$			7.20459i			0.639304i	0.947535	+	0.319652i	$0.103566\pi$
$127$			7.20459i			0.639304i	−0.947535	+	0.319652i	$0.896434\pi$
$128$	4.14001	−	10.5290i	0.365929	−	0.930643i
$129$		0			0
$130$	−1.61679	+	5.66694i	−0.141802	+	0.497023i
$131$	−7.01097	−	12.1434i	−0.612551	−	1.06097i	−0.990809	−	0.135270i	$-0.956810\pi$
$131$	−7.01097	−	12.1434i	−0.612551	−	1.06097i	0.378257	−	0.925700i	$-0.376523\pi$
$132$		0			0
$133$	12.8364	+	0.0218395i	1.11305	+	0.00189372i
$134$	1.34555	−	4.71625i	0.116238	−	0.407422i
$135$		0			0
$136$	−17.4489	−	5.59234i	−1.49623	−	0.479539i
$137$	16.1736	+	9.33782i	1.38180	+	0.797784i	0.992373	−	0.123273i	$-0.0393391\pi$
$137$	16.1736	+	9.33782i	1.38180	+	0.797784i	0.389429	+	0.921057i	$0.372672\pi$
$138$		0			0
$139$	0.265228	+	0.153129i	0.0224963	+	0.0129883i	0.511206	−	0.859458i	$-0.329199\pi$
$139$	0.265228	+	0.153129i	0.0224963	+	0.0129883i	−0.488710	+	0.872446i	$0.662532\pi$
$140$	17.2135	−	9.17394i	1.45480	−	0.775340i
$141$		0			0
$142$	−3.36481	−	0.959985i	−0.282368	−	0.0805602i
$143$	−2.03288	−	3.52105i	−0.169998	−	0.294445i
$144$		0			0
$145$	2.81868	−	4.88210i	0.234079	−	0.405437i
$146$	−2.36571	−	9.43471i	−0.195788	−	0.780822i
$147$		0			0
$148$	3.61885	−	1.93658i	0.297467	−	0.159186i
$149$	8.46904	−	4.88960i	0.693810	−	0.400572i	−0.111228	−	0.993795i	$-0.535478\pi$
$149$	8.46904	−	4.88960i	0.693810	−	0.400572i	0.805038	+	0.593223i	$0.202145\pi$
$150$		0			0
$151$	−20.1095	−	11.6102i	−1.63649	−	0.944829i	−0.982028	−	0.188735i	$-0.939561\pi$
$151$	−20.1095	−	11.6102i	−1.63649	−	0.944829i	−0.654463	−	0.756094i	$-0.727105\pi$
$152$	2.90682	+	13.4113i	0.235774	+	1.08780i
$153$		0			0
$154$	−3.71408	+	12.9346i	−0.299289	+	1.04230i
$155$	6.37121	+	11.0353i	0.511748	+	0.886373i
$156$		0			0
$157$	−6.42697			−0.512928			−0.256464	−	0.966554i	$-0.582557\pi$
$157$	−6.42697			−0.512928			−0.256464	+	0.966554i	$0.582557\pi$
$158$	−2.56891	+	9.00420i	−0.204372	+	0.716336i
$159$		0			0
$160$	13.5099	+	15.8840i	1.06805	+	1.25574i
$161$	2.39142	+	1.38612i	0.188470	+	0.109241i
$162$		0			0
$163$	6.27359	+	3.62206i	0.491386	+	0.283702i	0.725149	−	0.688592i	$-0.241771\pi$
$163$	6.27359	+	3.62206i	0.491386	+	0.283702i	−0.233763	+	0.972294i	$0.575104\pi$
$164$	0.852936	+	1.59386i	0.0666031	+	0.124460i
$165$		0			0
$166$	3.70005	+	14.7562i	0.287179	+	1.14530i
$167$	−8.90378	+	15.4218i	−0.688995	+	1.19337i	0.283168	+	0.959070i	$0.408614\pi$
$167$	−8.90378	+	15.4218i	−0.688995	+	1.19337i	−0.972163	+	0.234304i	$0.924719\pi$
$168$		0			0
$169$	5.86105	+	10.1516i	0.450850	+	0.780895i
$170$	24.2617	−	23.4919i	1.86079	−	1.80175i
$171$		0			0
$172$	13.3361	+	0.430072i	1.01687	+	0.0327926i
$173$			8.82819i			0.671195i	0.942006	+	0.335597i	$0.108938\pi$
$173$			8.82819i			0.671195i	−0.942006	+	0.335597i	$0.891062\pi$
$174$		0			0
$175$	−0.0386583	+	22.7218i	−0.00292229	+	1.71760i
$176$	−14.3566	−	0.926924i	−1.08217	−	0.0698695i
$177$		0			0
$178$	17.7474	+	18.3289i	1.33022	+	1.37381i
$179$	6.44399	+	11.1613i	0.481646	+	0.834236i	0.999778	−	0.0210647i	$-0.00670560\pi$
$179$	6.44399	+	11.1613i	0.481646	+	0.834236i	−0.518132	+	0.855301i	$0.673372\pi$
$180$		0			0
$181$	−9.19667			−0.683583			−0.341792	−	0.939776i	$-0.611034\pi$
$181$	−9.19667			−0.683583			−0.341792	+	0.939776i	$0.611034\pi$
$182$	−1.16736	+	4.06544i	−0.0865305	+	0.301351i
$183$		0			0
$184$	−0.901866	+	2.81394i	−0.0664865	+	0.207447i
$185$			7.56487i			0.556181i
$186$		0			0
$187$			23.2996i			1.70384i
$188$	6.31149	+	3.92047i	0.460313	+	0.285930i
$189$		0			0
$190$	−24.3217	−	6.93902i	−1.76448	−	0.503410i
$191$	−9.10663			−0.658932			−0.329466	−	0.944167i	$-0.606869\pi$
$191$	−9.10663			−0.658932			−0.329466	+	0.944167i	$0.606869\pi$
$192$		0			0
$193$	−11.5357			−0.830356			−0.415178	−	0.909740i	$-0.636281\pi$
$193$	−11.5357			−0.830356			−0.415178	+	0.909740i	$0.636281\pi$
$194$	3.75620	+	14.9801i	0.269679	+	1.07551i
$195$		0			0
$196$	12.3661	−	6.56353i	0.883292	−	0.468824i
$197$			12.9243i			0.920815i	0.887708	+	0.460408i	$0.152297\pi$
$197$			12.9243i			0.920815i	−0.887708	+	0.460408i	$0.847703\pi$
$198$		0			0
$199$	9.22615	−	5.32672i	0.654024	−	0.377601i	−0.135972	−	0.990713i	$-0.543416\pi$
$199$	9.22615	−	5.32672i	0.654024	−	0.377601i	0.789996	+	0.613112i	$0.210082\pi$
$200$	−23.7394	+	5.14539i	−1.67863	+	0.363834i
$201$		0			0
$202$	7.22751	+	7.46435i	0.508526	+	0.525189i
$203$	2.02906	−	3.50066i	0.142412	−	0.245698i
$204$		0			0
$205$	−3.33183			−0.232705
$206$	−1.60144	+	0.401554i	−0.111578	+	0.0279776i
$207$		0			0
$208$	−4.51237	−	0.291338i	−0.312876	−	0.0202007i
$209$	15.1119	−	8.72484i	1.04531	−	0.603510i
$210$		0			0
$211$	0.485988	+	0.280585i	0.0334568	+	0.0193163i	0.516635	−	0.856206i	$-0.327184\pi$
$211$	0.485988	+	0.280585i	0.0334568	+	0.0193163i	−0.483178	+	0.875522i	$0.660518\pi$
$212$	−2.25174	−	0.0726155i	−0.154650	−	0.00498725i
$213$		0			0
$214$	−15.4397	+	14.9498i	−1.05544	+	1.02195i
$215$	−12.2963	+	21.2978i	−0.838599	+	1.45250i
$216$		0			0
$217$	4.55943	+	7.92828i	0.309514	+	0.538207i
$218$	−4.57211	−	18.2340i	−0.309662	−	1.23496i
$219$		0			0
$220$	13.9911	−	22.5240i	0.943279	−	1.51857i
$221$			7.32322i			0.492613i
$222$		0			0
$223$	13.4947	−	7.79117i	0.903672	−	0.521735i	0.0252823	−	0.999680i	$-0.491952\pi$
$223$	13.4947	−	7.79117i	0.903672	−	0.521735i	0.878390	+	0.477945i	$0.158618\pi$
$224$	9.67724	+	11.4171i	0.646588	+	0.762839i
$225$		0			0
$226$	−0.309656	−	0.319803i	−0.0205980	−	0.0212730i
$227$	9.96283	−	17.2561i	0.661256	−	1.14533i	−0.319029	−	0.947745i	$-0.603357\pi$
$227$	9.96283	−	17.2561i	0.661256	−	1.14533i	0.980286	−	0.197585i	$-0.0633098\pi$
$228$		0			0
$229$	−5.23823	−	9.07287i	−0.346152	−	0.599552i	0.639411	−	0.768865i	$-0.279178\pi$
$229$	−5.23823	−	9.07287i	−0.346152	−	0.599552i	−0.985562	+	0.169313i	$0.945845\pi$
$230$	−3.78850	−	3.91264i	−0.249806	−	0.257992i
$231$		0			0
$232$	4.11918	+	1.32019i	0.270437	+	0.0866749i
$233$	−20.8229	−	12.0221i	−1.36415	−	0.787595i	−0.373981	−	0.927436i	$-0.622007\pi$
$233$	−20.8229	−	12.0221i	−1.36415	−	0.787595i	−0.990174	+	0.139841i	$0.955341\pi$
$234$		0			0
$235$	−11.8595	+	6.84711i	−0.773632	+	0.446656i
$236$	1.41951	+	0.881751i	0.0924024	+	0.0573971i
$237$		0			0
$238$	17.4424	−	16.8316i	1.13062	−	1.09103i
$239$	6.39090	−	11.0694i	0.413393	−	0.716017i	−0.581865	−	0.813285i	$-0.697677\pi$
$239$	6.39090	−	11.0694i	0.413393	−	0.716017i	0.995258	+	0.0972677i	$0.0310103\pi$
$240$		0			0
$241$	7.41032	−	12.8351i	0.477341	−	0.826778i	−0.522322	−	0.852748i	$-0.674934\pi$
$241$	7.41032	−	12.8351i	0.477341	−	0.826778i	0.999663	+	0.0259699i	$0.00826741\pi$
$242$	0.665786	+	2.65522i	0.0427983	+	0.170684i
$243$		0			0
$244$	−23.0080	−	14.2917i	−1.47293	−	0.914933i
$245$	−0.0878022	+	25.8032i	−0.00560948	+	1.64851i
$246$		0			0
$247$	4.74976	−	2.74228i	0.302220	−	0.174487i
$248$	−7.23969	+	6.57132i	−0.459721	+	0.417279i
$249$		0			0
$250$	5.13170	−	17.9869i	0.324557	−	1.13759i
$251$	−11.5264			−0.727542			−0.363771	−	0.931488i	$-0.618511\pi$
$251$	−11.5264			−0.727542			−0.363771	+	0.931488i	$0.618511\pi$
$252$		0			0
$253$	3.75748			0.236231
$254$	2.79535	−	9.79787i	0.175396	−	0.614773i
$255$		0			0
$256$	−9.71541	+	12.7126i	−0.607213	+	0.794539i
$257$	15.0476	−	8.68772i	0.938642	−	0.541925i	0.0491076	−	0.998793i	$-0.484362\pi$
$257$	15.0476	−	8.68772i	0.938642	−	0.541925i	0.889534	+	0.456868i	$0.151029\pi$
$258$		0			0
$259$	−0.00923788	+	5.42965i	−0.000574014	+	0.337382i
$260$	4.39749	−	7.07944i	0.272721	−	0.439048i
$261$		0			0
$262$	4.82299	+	19.2346i	0.297965	+	1.18832i
$263$	5.80575	−	10.0558i	0.357998	−	0.620070i	−0.629629	−	0.776896i	$-0.716793\pi$
$263$	5.80575	−	10.0558i	0.357998	−	0.620070i	0.987626	+	0.156826i	$0.0501262\pi$
$264$		0			0
$265$	2.07617	−	3.59603i	0.127538	−	0.220902i
$266$	−17.4483	−	5.01015i	−1.06982	−	0.307192i
$267$		0			0
$268$	−3.65977	+	5.89179i	−0.223556	+	0.359898i
$269$	−14.3096	+	8.26163i	−0.872469	+	0.503720i	−0.868168	−	0.496271i	$-0.834702\pi$
$269$	−14.3096	+	8.26163i	−0.872469	+	0.503720i	−0.00430110	+	0.999991i	$0.501369\pi$
$270$		0			0
$271$	7.51182	+	4.33695i	0.456310	+	0.263451i	0.710492	−	0.703706i	$-0.248473\pi$
$271$	7.51182	+	4.33695i	0.456310	+	0.263451i	−0.254181	+	0.967157i	$0.581806\pi$
$272$	21.5597	+	14.3754i	1.30725	+	0.871635i
$273$		0			0
$274$	−18.3722	−	18.9742i	−1.10990	−	1.14627i
$275$	15.4439	+	26.7497i	0.931304	+	1.61307i
$276$		0			0
$277$	9.02246	−	15.6274i	0.542107	−	0.938957i	−0.456676	−	0.889633i	$-0.650960\pi$
$277$	9.02246	−	15.6274i	0.542107	−	0.938957i	0.998783	−	0.0493237i	$-0.0157066\pi$
$278$	−0.301283	−	0.311155i	−0.0180697	−	0.0186619i
$279$		0			0
$280$	−26.9689	+	5.79734i	−1.61170	+	0.346457i
$281$	−20.2561	+	11.6949i	−1.20838	+	0.697658i	−0.962405	−	0.271619i	$-0.912441\pi$
$281$	−20.2561	+	11.6949i	−1.20838	+	0.697658i	−0.245974	+	0.969276i	$0.579108\pi$
$282$		0			0
$283$		−	12.4850i		−	0.742157i	−0.928602	−	0.371078i	$-0.878988\pi$
$283$		−	12.4850i		−	0.742157i	0.928602	−	0.371078i	$-0.121012\pi$
$284$	4.20350	+	2.61106i	0.249432	+	0.154938i
$285$		0			0
$286$	1.39846	+	5.57720i	0.0826927	+	0.329787i
$287$	−2.39140	−	0.00406867i	−0.141160	−	0.000240166i
$288$		0			0
$289$	12.4835	−	21.6221i	0.734326	−	1.27189i
$290$	−5.72750	+	5.54577i	−0.336330	+	0.325659i
$291$		0			0
$292$	−0.443374	+	13.7486i	−0.0259465	+	0.804576i
$293$	3.37934	+	1.95106i	0.197423	+	0.113982i	0.595453	−	0.803390i	$-0.296973\pi$
$293$	3.37934	+	1.95106i	0.197423	+	0.113982i	−0.398030	+	0.917373i	$0.630306\pi$
$294$		0			0
$295$	−2.66732	+	1.53998i	−0.155298	+	0.0896611i
$296$	−5.67283	+	1.22956i	−0.329726	+	0.0714665i
$297$		0			0
$298$	−13.4146	+	3.36366i	−0.777087	+	0.194851i
$299$	1.18100			0.0682991
$300$		0			0
$301$	−8.85159	+	15.2713i	−0.510197	+	0.880226i
$302$	22.8432	+	23.5917i	1.31448	+	1.35755i
$303$		0			0
$304$	1.25038	−	19.3665i	0.0717144	−	1.11074i
$305$	43.2329	−	24.9605i	2.47551	−	1.42923i
$306$		0			0
$307$		−	5.13048i		−	0.292812i	−0.989225	−	0.146406i	$-0.953229\pi$
$307$		−	5.13048i		−	0.292812i	0.989225	−	0.146406i	$-0.0467706\pi$
$308$	10.0695	−	16.1494i	0.573765	−	0.920196i
$309$		0			0
$310$	−4.38289	−	17.4794i	−0.248931	−	0.992762i
$311$	−5.75440			−0.326302			−0.163151	−	0.986601i	$-0.552166\pi$
$311$	−5.75440			−0.326302			−0.163151	+	0.986601i	$0.552166\pi$
$312$		0			0
$313$	2.38124			0.134596			0.0672978	−	0.997733i	$-0.478562\pi$
$313$	2.38124			0.134596			0.0672978	+	0.997733i	$0.478562\pi$
$314$	8.74034	+	2.49363i	0.493246	+	0.140724i
$315$		0			0
$316$	6.98718	−	11.2485i	0.393060	−	0.632779i
$317$		−	11.0574i		−	0.621046i	−0.950566	−	0.310523i	$-0.899496\pi$
$317$		−	11.0574i		−	0.621046i	0.950566	−	0.310523i	$-0.100504\pi$
$318$		0			0
$319$		−	5.50037i		−	0.307962i
$320$	−12.2098	−	26.8431i	−0.682549	−	1.50058i
$321$		0			0
$322$	−2.71440	−	2.81290i	−0.151267	−	0.156757i
$323$	−31.4303			−1.74883
$324$		0			0
$325$	4.85413	+	8.40760i	0.269259	+	0.466370i
$326$	−7.12642	−	7.35994i	−0.394696	−	0.407629i
$327$		0			0
$328$	−0.541538	−	2.49850i	−0.0299014	−	0.137957i
$329$	−8.52049	+	4.90000i	−0.469750	+	0.270146i
$330$		0			0
$331$			9.44833i			0.519327i	0.965699	+	0.259664i	$0.0836117\pi$
$331$			9.44833i			0.519327i	−0.965699	+	0.259664i	$0.916388\pi$
$332$	0.693449	−	21.5032i	0.0380580	−	1.18014i
$333$		0			0
$334$	18.0923	−	17.5182i	0.989965	−	0.958554i
$335$	−6.39179	−	11.0709i	−0.349221	−	0.604868i
$336$		0			0
$337$	9.17654	−	15.8942i	0.499878	−	0.865814i	−0.500122	−	0.865955i	$-0.666712\pi$
$337$	9.17654	−	15.8942i	0.499878	−	0.865814i	1.00000		0.000141125i	$4.49213e-5\pi$
$338$	−4.03194	−	16.0798i	−0.219308	−	0.874624i
$339$		0			0
$340$	−42.1094	+	22.5344i	−2.28370	+	1.22210i
$341$	10.7671	+	6.21638i	0.583071	+	0.336636i
$342$		0			0
$343$	−0.0945293	+	18.5200i	−0.00510410	+	0.999987i
$344$	−17.9696	−	5.75923i	−0.968854	−	0.310517i
$345$		0			0
$346$	3.42530	−	12.0059i	0.184145	−	0.645440i
$347$	−33.8066			−1.81483			−0.907416	−	0.420233i	$-0.861948\pi$
$347$	−33.8066			−1.81483			−0.907416	+	0.420233i	$0.861948\pi$
$348$		0			0
$349$	−7.41378	−	12.8410i	−0.396851	−	0.687365i	0.596485	−	0.802624i	$-0.296564\pi$
$349$	−7.41378	−	12.8410i	−0.396851	−	0.687365i	−0.993335	+	0.115259i	$0.963230\pi$
$350$	8.86852	−	30.8854i	0.474042	−	1.65090i
$351$		0			0
$352$	19.1646	+	6.83085i	1.02147	+	0.364086i
$353$	−22.0009	−	12.7022i	−1.17099	−	0.676071i	−0.217077	−	0.976155i	$-0.569652\pi$
$353$	−22.0009	−	12.7022i	−1.17099	−	0.676071i	−0.953913	+	0.300083i	$0.902986\pi$
$354$		0			0
$355$	−7.89854	+	4.56022i	−0.419211	+	0.242032i
$356$	−17.0240	−	31.8123i	−0.902268	−	1.68605i
$357$		0			0
$358$	−4.43295	−	17.6791i	−0.234289	−	0.934367i
$359$	7.27219	−	12.5958i	0.383811	−	0.664781i	−0.607792	−	0.794096i	$-0.707945\pi$
$359$	7.27219	−	12.5958i	0.383811	−	0.664781i	0.991604	+	0.129315i	$0.0412780\pi$
$360$		0			0
$361$	2.26947	+	3.93084i	0.119446	+	0.206886i
$362$	12.5070	+	3.56827i	0.657353	+	0.187544i
$363$		0			0
$364$	3.16492	−	5.07586i	0.165887	−	0.266047i
$365$	−21.9565	−	12.6766i	−1.14926	−	0.663523i
$366$		0			0
$367$	−12.4958	−	7.21446i	−0.652276	−	0.376592i	0.137052	−	0.990564i	$-0.456237\pi$
$367$	−12.4958	−	7.21446i	−0.652276	−	0.376592i	−0.789328	+	0.613972i	$0.789571\pi$
$368$	2.31829	−	3.47690i	0.120849	−	0.181246i
$369$		0			0
$370$	2.93514	−	10.2878i	0.152591	−	0.534839i
$371$	1.49455	−	2.57849i	0.0775931	−	0.133869i
$372$		0			0
$373$	−0.658883	−	1.14122i	−0.0341157	−	0.0590901i	0.848463	−	0.529254i	$-0.177528\pi$
$373$	−0.658883	−	1.14122i	−0.0341157	−	0.0590901i	−0.882579	+	0.470164i	$0.844195\pi$
$374$	9.04014	−	31.6863i	0.467455	−	1.63846i
$375$		0			0
$376$	−7.06217	−	7.78047i	−0.364204	−	0.401247i
$377$		−	1.72880i		−	0.0890379i
$378$		0			0
$379$			19.4758i			1.00041i	0.865908	+	0.500203i	$0.166741\pi$
$379$			19.4758i			1.00041i	−0.865908	+	0.500203i	$0.833259\pi$
$380$	30.3840	+	18.8734i	1.55866	+	0.968187i
$381$		0			0
$382$	12.3845	+	3.53333i	0.633648	+	0.180781i
$383$	−1.15780	−	2.00538i	−0.0591611	−	0.102470i	0.834928	−	0.550359i	$-0.185509\pi$
$383$	−1.15780	−	2.00538i	−0.0591611	−	0.102470i	−0.894089	+	0.447889i	$0.852176\pi$
$384$		0			0
$385$	17.4867	+	30.4073i	0.891207	+	1.54970i
$386$	15.6879	+	4.47579i	0.798494	+	0.227812i
$387$		0			0
$388$	0.703973	−	21.8295i	0.0357388	−	1.10823i
$389$	0.391507	+	0.226037i	0.0198502	+	0.0114605i	0.509892	−	0.860238i	$-0.329685\pi$
$389$	0.391507	+	0.226037i	0.0198502	+	0.0114605i	−0.490042	+	0.871699i	$0.663019\pi$
$390$		0			0
$391$	−5.86122	−	3.38398i	−0.296415	−	0.171135i
$392$	−19.3639	+	4.12808i	−0.978022	+	0.208499i
$393$		0			0
$394$	5.01455	−	17.5763i	0.252630	−	0.885482i
$395$	12.2031	+	21.1364i	0.614006	+	1.06349i
$396$		0			0
$397$	−14.3892	+	24.9228i	−0.722174	+	1.25084i	0.237953	+	0.971277i	$0.423524\pi$
$397$	−14.3892	+	24.9228i	−0.722174	+	1.25084i	−0.960127	+	0.279565i	$0.909810\pi$
$398$	−14.6138	+	3.66436i	−0.732525	+	0.183678i
$399$		0			0
$400$	34.2808	+	2.21332i	1.71404	+	0.110666i
$401$	−10.2380	+	5.91088i	−0.511259	+	0.295176i	−0.733351	−	0.679850i	$-0.762045\pi$
$401$	−10.2380	+	5.91088i	−0.511259	+	0.295176i	0.222092	+	0.975026i	$0.428711\pi$
$402$		0			0
$403$	3.38417	+	1.95385i	0.168577	+	0.0973282i
$404$	−6.93291	−	12.9554i	−0.344925	−	0.644554i
$405$		0			0
$406$	−4.11765	+	3.97345i	−0.204356	+	0.197199i
$407$	3.69052	+	6.39217i	0.182932	+	0.316848i
$408$		0			0
$409$	−35.8514			−1.77274			−0.886369	−	0.462979i	$-0.846780\pi$
$409$	−35.8514			−1.77274			−0.886369	+	0.462979i	$0.846780\pi$
$410$	4.53111	+	1.29273i	0.223776	+	0.0638436i
$411$		0			0
$412$	2.33368	+	0.0752578i	0.114972	+	0.00370769i
$413$	−1.91634	+	1.10206i	−0.0942968	+	0.0542286i
$414$		0			0
$415$	34.3406	+	19.8266i	1.68571	+	0.973247i
$416$	6.02355	+	2.14698i	0.295329	+	0.105265i
$417$		0			0
$418$	−23.9366	+	6.00200i	−1.17078	+	0.293567i
$419$	−12.3927	+	21.4647i	−0.605421	+	1.04862i	0.386564	+	0.922263i	$0.373662\pi$
$419$	−12.3927	+	21.4647i	−0.605421	+	1.04862i	−0.991985	+	0.126357i	$0.959671\pi$
$420$		0			0
$421$	−12.5570	−	21.7493i	−0.611990	−	1.06000i	−0.990905	−	0.134566i	$-0.957036\pi$
$421$	−12.5570	−	21.7493i	−0.611990	−	1.06000i	0.378914	−	0.925432i	$-0.376297\pi$
$422$	−0.552053	−	0.570143i	−0.0268735	−	0.0277541i
$423$		0			0
$424$	3.03407	+	0.972418i	0.147348	+	0.0472248i
$425$		−	55.6350i		−	2.69869i
$426$		0			0
$427$	31.0607	−	17.8625i	1.50313	−	0.864426i
$428$	26.7977	−	14.3404i	1.29531	−	0.693172i
$429$		0			0
$430$	24.9857	−	24.1930i	1.20492	−	1.16669i
$431$	−3.15851	−	5.47070i	−0.152140	−	0.263514i	0.779874	−	0.625937i	$-0.215283\pi$
$431$	−3.15851	−	5.47070i	−0.152140	−	0.263514i	−0.932014	+	0.362422i	$0.881950\pi$
$432$		0			0
$433$	27.4268			1.31805			0.659024	−	0.752122i	$-0.270969\pi$
$433$	27.4268			1.31805			0.659024	+	0.752122i	$0.270969\pi$
$434$	−3.12445	−	12.5511i	−0.149978	−	0.602472i
$435$		0			0
$436$	−0.856888	+	26.5713i	−0.0410375	+	1.27253i
$437$			5.06870i			0.242469i
$438$		0			0
$439$		−	5.09892i		−	0.243358i	−0.992569	−	0.121679i	$-0.961172\pi$
$439$		−	5.09892i		−	0.243358i	0.992569	−	0.121679i	$-0.0388279\pi$
$440$	−27.7664	+	25.2030i	−1.32371	+	1.20150i
$441$		0			0
$442$	2.84138	−	9.95920i	0.135151	−	0.473711i
$443$	3.95739			0.188021			0.0940106	−	0.995571i	$-0.470031\pi$
$443$	3.95739			0.188021			0.0940106	+	0.995571i	$0.470031\pi$
$444$		0			0
$445$	66.5007			3.15244
$446$	−21.3750	+	5.35970i	−1.01214	+	0.253789i
$447$		0			0
$448$	−8.73075	−	19.2814i	−0.412489	−	0.910962i
$449$			5.92979i			0.279844i	0.990163	+	0.139922i	$0.0446852\pi$
$449$			5.92979i			0.279844i	−0.990163	+	0.139922i	$0.955315\pi$
$450$		0			0
$451$	−2.81533	+	1.62543i	−0.132569	+	0.0765385i
$452$	0.297034	+	0.555060i	0.0139713	+	0.0261078i
$453$		0			0
$454$	−20.2442	+	19.6019i	−0.950109	+	0.919963i
$455$	5.49620	+	9.55722i	0.257666	+	0.448049i
$456$		0			0
$457$	−30.7269			−1.43734			−0.718671	−	0.695350i	$-0.755249\pi$
$457$	−30.7269			−1.43734			−0.718671	+	0.695350i	$0.755249\pi$
$458$	3.60348	+	14.3710i	0.168380	+	0.671515i
$459$		0			0
$460$	3.63407	+	6.79091i	0.169440	+	0.316628i
$461$	9.98931	−	5.76733i	0.465248	−	0.268611i	−0.249000	−	0.968503i	$-0.580102\pi$
$461$	9.98931	−	5.76733i	0.465248	−	0.268611i	0.714249	+	0.699892i	$0.246769\pi$
$462$		0			0
$463$	−33.1945	−	19.1649i	−1.54268	−	0.890667i	−0.998668	−	0.0515888i	$-0.983571\pi$
$463$	−33.1945	−	19.1649i	−1.54268	−	0.890667i	−0.544011	−	0.839078i	$-0.683095\pi$
$464$	−5.08964	−	3.39362i	−0.236281	−	0.157545i
$465$		0			0
$466$	23.6536	+	24.4287i	1.09573	+	1.13164i
$467$	−1.92182	+	3.32869i	−0.0889313	+	0.154033i	−0.907060	−	0.421002i	$-0.861678\pi$
$467$	−1.92182	+	3.32869i	−0.0889313	+	0.154033i	0.818128	+	0.575036i	$0.195012\pi$
$468$		0			0
$469$	−4.57416	−	7.95389i	−0.211215	−	0.367277i
$470$	18.7850	−	4.71027i	0.866488	−	0.217268i
$471$		0			0
$472$	−1.58835	−	1.74990i	−0.0731097	−	0.0805457i
$473$			23.9949i			1.10329i
$474$		0			0
$475$	−36.0843	+	20.8333i	−1.65566	+	0.955895i
$476$	−30.2513	+	16.1225i	−1.38657	+	0.738973i
$477$		0			0
$478$	−12.9862	+	12.5741i	−0.593973	+	0.575127i
$479$	−15.7732	+	27.3199i	−0.720695	+	1.24828i	0.240027	+	0.970766i	$0.422844\pi$
$479$	−15.7732	+	27.3199i	−0.720695	+	1.24828i	−0.960722	+	0.277514i	$0.910490\pi$
$480$		0			0
$481$	1.15996	+	2.00910i	0.0528894	+	0.0916071i
$482$	−15.0576	+	14.5798i	−0.685855	+	0.664093i
$483$		0			0
$484$	0.124779	−	3.86928i	0.00567178	−	0.175877i
$485$	34.8618	+	20.1274i	1.58299	+	0.913940i
$486$		0			0
$487$	0.788735	−	0.455376i	0.0357410	−	0.0206351i	−0.482023	−	0.876159i	$-0.660098\pi$
$487$	0.788735	−	0.455376i	0.0357410	−	0.0206351i	0.517764	+	0.855523i	$0.326765\pi$
$488$	25.7445	+	28.3630i	1.16540	+	1.28393i
$489$		0			0
$490$	10.1309	−	35.0570i	0.457669	−	1.58371i
$491$	5.42838	−	9.40224i	0.244980	−	0.424317i	−0.717146	−	0.696923i	$-0.754552\pi$
$491$	5.42838	−	9.40224i	0.244980	−	0.424317i	0.962126	+	0.272606i	$0.0878854\pi$
$492$		0			0
$493$	−4.95362	+	8.57992i	−0.223100	+	0.386420i
$494$	−7.52342	+	1.88647i	−0.338495	+	0.0848762i
$495$		0			0
$496$	12.3953	−	6.12769i	0.556563	−	0.275142i
$497$	−5.67471	+	3.26343i	−0.254545	+	0.146385i
$498$		0			0
$499$	−8.57499	+	4.95078i	−0.383869	+	0.221627i	−0.679500	−	0.733675i	$-0.737803\pi$
$499$	−8.57499	+	4.95078i	−0.383869	+	0.221627i	0.295631	+	0.955302i	$0.404470\pi$
$500$	−13.9577	+	22.4702i	−0.624207	+	1.00490i
$501$		0			0
$502$	15.6753	+	4.47220i	0.699625	+	0.199604i
$503$	−7.43095			−0.331330			−0.165665	−	0.986182i	$-0.552977\pi$
$503$	−7.43095			−0.331330			−0.165665	+	0.986182i	$0.552977\pi$
$504$		0			0
$505$	27.0820			1.20513
$506$	−5.10998	−	1.45789i	−0.227166	−	0.0648110i
$507$		0			0
$508$	−7.60306	+	12.2400i	−0.337331	+	0.543063i
$509$	27.9418	−	16.1322i	1.23850	−	0.715048i	0.269712	−	0.962941i	$-0.413071\pi$
$509$	27.9418	−	16.1322i	1.23850	−	0.715048i	0.968788	+	0.247893i	$0.0797380\pi$
$510$		0			0
$511$	−15.7437	−	9.12537i	−0.696460	−	0.403683i
$512$	18.1449	−	13.5190i	0.801899	−	0.597460i
$513$		0			0
$514$	−23.8347	+	5.97646i	−1.05130	+	0.263610i
$515$	−2.15171	+	3.72688i	−0.0948158	+	0.164226i
$516$		0			0
$517$	−6.68072	+	11.5713i	−0.293818	+	0.508907i
$518$	2.11924	−	7.38046i	0.0931142	−	0.324279i
$519$		0			0
$520$	−8.72715	+	7.92146i	−0.382711	+	0.347379i
$521$	−2.39057	+	1.38020i	−0.104733	+	0.0604675i	−0.551452	−	0.834207i	$-0.685926\pi$
$521$	−2.39057	+	1.38020i	−0.104733	+	0.0604675i	0.446719	+	0.894674i	$0.352592\pi$
$522$		0			0
$523$	−30.8196	−	17.7937i	−1.34765	−	0.778065i	−0.359732	−	0.933056i	$-0.617132\pi$
$523$	−30.8196	−	17.7937i	−1.34765	−	0.778065i	−0.987916	+	0.154991i	$0.950465\pi$
$524$	0.903907	−	28.0293i	0.0394874	−	1.22447i
$525$		0			0
$526$	−11.7971	+	11.4228i	−0.514380	+	0.498059i
$527$	−11.1969	−	19.3936i	−0.487745	−	0.844799i
$528$		0			0
$529$	10.9543	−	18.9734i	0.476273	−	0.824929i
$530$	−4.21872	+	4.08487i	−0.183250	+	0.177435i
$531$		0			0
$532$	21.7849	+	13.5834i	0.944495	+	0.588916i
$533$	−0.884876	+	0.510883i	−0.0383282	+	0.0221288i
$534$		0			0
$535$			56.0181i			2.42187i
$536$	7.26308	−	6.59255i	0.313717	−	0.284755i
$537$		0			0
$538$	22.6657	−	5.68334i	0.977189	−	0.245026i
$539$	12.5139	+	21.8460i	0.539012	+	0.940975i
$540$		0			0
$541$	−8.40724	+	14.5618i	−0.361455	+	0.626059i	−0.988201	−	0.153165i	$-0.951053\pi$
$541$	−8.40724	+	14.5618i	−0.361455	+	0.626059i	0.626745	+	0.779224i	$0.284387\pi$
$542$	−8.53297	−	8.81258i	−0.366522	−	0.378533i
$543$		0			0
$544$	−23.7425	−	27.9148i	−1.01795	−	1.19684i
$545$	−42.4343	−	24.4995i	−1.81769	−	1.04944i
$546$		0			0
$547$	24.7313	−	14.2786i	1.05743	−	0.610509i	0.132712	−	0.991155i	$-0.457631\pi$
$547$	24.7313	−	14.2786i	1.05743	−	0.610509i	0.924721	+	0.380645i	$0.124298\pi$
$548$	17.6233	+	32.9323i	0.752831	+	1.40680i
$549$		0			0
$550$	−10.6242	−	42.3703i	−0.453017	−	1.80668i
$551$	7.41979			0.316094
$552$		0			0
$553$	8.73292	+	15.1855i	0.371362	+	0.645752i
$554$	−18.3334	+	17.7517i	−0.778912	+	0.754199i
$555$		0			0
$556$	0.289002	+	0.540052i	0.0122564	+	0.0229033i
$557$	25.4527	−	14.6951i	1.07847	−	0.622652i	0.147983	−	0.988990i	$-0.452722\pi$
$557$	25.4527	−	14.6951i	1.07847	−	0.622652i	0.930482	+	0.366338i	$0.119388\pi$
$558$		0			0
$559$			7.54176i			0.318983i
$560$	38.9256	+	2.57972i	1.64491	+	0.109013i
$561$		0			0
$562$	32.0848	−	8.04515i	1.35342	−	0.339364i
$563$	−17.2010			−0.724937			−0.362469	−	0.931996i	$-0.618066\pi$
$563$	−17.2010			−0.724937			−0.362469	+	0.931996i	$0.618066\pi$
$564$		0			0
$565$	−1.16030			−0.0488144
$566$	−4.84413	+	16.9790i	−0.203614	+	0.713679i
$567$		0			0
$568$	−4.70346	−	5.18185i	−0.197353	−	0.217425i
$569$			0.765439i			0.0320889i	0.999871	+	0.0160444i	$0.00510732\pi$
$569$			0.765439i			0.0320889i	−0.999871	+	0.0160444i	$0.994893\pi$
$570$		0			0
$571$		−	1.65866i		−	0.0694127i	−0.999398	−	0.0347064i	$-0.988950\pi$
$571$		−	1.65866i		−	0.0694127i	0.999398	−	0.0347064i	$-0.0110496\pi$
$572$	0.262094	−	8.12730i	0.0109587	−	0.339819i
$573$		0			0
$574$	3.25060	+	0.933386i	0.135678	+	0.0389588i
$575$	−8.97215			−0.374165
$576$		0			0
$577$	−5.33017	−	9.23213i	−0.221898	−	0.384339i	0.733486	−	0.679704i	$-0.237892\pi$
$577$	−5.33017	−	9.23213i	−0.221898	−	0.384339i	−0.955384	+	0.295366i	$0.904559\pi$
$578$	−25.3663	+	24.5614i	−1.05510	+	1.02162i
$579$		0			0
$580$	9.94083	−	5.31972i	0.412771	−	0.220889i
$581$	24.6236	+	14.2723i	1.02156	+	0.592117i
$582$		0			0
$583$		−	4.05143i		−	0.167793i
$584$	5.93736	−	18.5254i	0.245690	−	0.766585i
$585$		0			0
$586$	−3.83873	−	3.96452i	−0.158576	−	0.163773i
$587$	−17.4777	−	30.2723i	−0.721383	−	1.24947i	−0.960445	−	0.278468i	$-0.910173\pi$
$587$	−17.4777	−	30.2723i	−0.721383	−	1.24947i	0.239062	−	0.971004i	$-0.423160\pi$
$588$		0			0
$589$	−8.38566	+	14.5244i	−0.345525	+	0.598467i
$590$	4.22493	−	1.05938i	0.173938	−	0.0436141i
$591$		0			0
$592$	8.19181	+	0.528900i	0.336682	+	0.0217376i
$593$	−10.4609	−	6.03961i	−0.429578	−	0.248017i	0.269589	−	0.962976i	$-0.413112\pi$
$593$	−10.4609	−	6.03961i	−0.429578	−	0.248017i	−0.699167	+	0.714958i	$0.746446\pi$
$594$		0			0
$595$	0.107493	−	63.1802i	0.00440680	−	2.59014i
$596$	19.5482	+	0.630404i	0.800727	+	0.0258224i
$597$		0			0
$598$	−1.60610	−	0.458224i	−0.0656784	−	0.0187382i
$599$	26.2805			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$599$	26.2805			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$600$		0			0
$601$	4.09157	+	7.08681i	0.166899	+	0.289077i	0.937328	−	0.348449i	$-0.113291\pi$
$601$	4.09157	+	7.08681i	0.166899	+	0.289077i	−0.770429	+	0.637525i	$0.779958\pi$
$602$	17.9629	−	17.3339i	0.732114	−	0.706476i
$603$		0			0
$604$	−21.9121	−	40.9466i	−0.891591	−	1.66609i
$605$	6.17924	+	3.56759i	0.251222	+	0.145043i
$606$		0			0
$607$	36.8640	−	21.2834i	1.49626	−	0.863869i	0.496273	−	0.868166i	$-0.334701\pi$
$607$	36.8640	−	21.2834i	1.49626	−	0.863869i	0.999991	+	0.00429768i	$0.00136800\pi$
$608$	−9.21456	+	25.8522i	−0.373700	+	1.04845i
$609$		0			0
$610$	−68.4791	+	17.1708i	−2.77264	+	0.695227i
$611$	−2.09980	+	3.63695i	−0.0849486	+	0.147135i
$612$		0			0
$613$	−23.0509	−	39.9254i	−0.931018	−	1.61257i	−0.781585	−	0.623799i	$-0.785588\pi$
$613$	−23.0509	−	39.9254i	−0.931018	−	1.61257i	−0.149433	−	0.988772i	$-0.547745\pi$
$614$	−1.99061	+	6.97719i	−0.0803343	+	0.281577i
$615$		0			0
$616$	−19.9599	+	18.0554i	−0.804209	+	0.727472i
$617$	19.9837	+	11.5376i	0.804515	+	0.464487i	0.845047	−	0.534691i	$-0.179572\pi$
$617$	19.9837	+	11.5376i	0.804515	+	0.464487i	−0.0405327	+	0.999178i	$0.512905\pi$
$618$		0			0
$619$	19.1629	+	11.0637i	0.770222	+	0.444688i	0.832954	−	0.553343i	$-0.186648\pi$
$619$	19.1629	+	11.0637i	0.770222	+	0.444688i	−0.0627318	+	0.998030i	$0.519981\pi$
$620$	−0.821424	+	25.4716i	−0.0329892	+	1.02296i
$621$		0			0
$622$	7.82568	+	2.23268i	0.313781	+	0.0895223i
$623$	47.7306	+	0.0812077i	1.91228	+	0.00325352i
$624$		0			0
$625$	−2.90707	−	5.03519i	−0.116283	−	0.201407i
$626$	−3.23836	−	0.923909i	−0.129431	−	0.0369268i
$627$		0			0
$628$	−10.9189	−	6.78243i	−0.435711	−	0.270648i
$629$		−	13.2947i		−	0.530094i
$630$		0			0
$631$		−	45.8081i		−	1.82359i	−0.410642	−	0.911797i	$-0.634695\pi$
$631$		−	45.8081i		−	1.82359i	0.410642	−	0.911797i	$-0.365305\pi$
$632$	−13.8666	+	12.5864i	−0.551583	+	0.500661i
$633$		0			0
$634$	−4.29022	+	15.0375i	−0.170387	+	0.597216i
$635$	−13.2788	−	22.9995i	−0.526951	−	0.912706i
$636$		0			0
$637$	3.93320	+	6.86636i	0.155839	+	0.272055i
$638$	−2.13412	+	7.48022i	−0.0844906	+	0.296145i
$639$		0			0
$640$	6.18970	+	41.2426i	0.244669	+	1.63026i
$641$	−1.63602	−	0.944559i	−0.0646191	−	0.0373078i	0.467342	−	0.884076i	$-0.345212\pi$
$641$	−1.63602	−	0.944559i	−0.0646191	−	0.0373078i	−0.531961	+	0.846769i	$0.678545\pi$
$642$		0			0
$643$	13.3963	+	7.73434i	0.528297	+	0.305013i	0.740323	−	0.672251i	$-0.234673\pi$
$643$	13.3963	+	7.73434i	0.528297	+	0.305013i	−0.212025	+	0.977264i	$0.568006\pi$
$644$	2.60004	+	4.87858i	0.102456	+	0.192243i
$645$		0			0
$646$	42.7435	+	12.1948i	1.68172	+	0.479798i
$647$	−3.68660	−	6.38537i	−0.144935	−	0.251035i	0.784414	−	0.620238i	$-0.212964\pi$
$647$	−3.68660	−	6.38537i	−0.144935	−	0.251035i	−0.929349	+	0.369203i	$0.879631\pi$
$648$		0			0
$649$	−1.50256	+	2.60250i	−0.0589805	+	0.102157i
$650$	−3.33926	−	13.3173i	−0.130976	−	0.522347i
$651$		0			0
$652$	6.83594	+	12.7742i	0.267716	+	0.500275i
$653$	−43.2008	+	24.9420i	−1.69058	+	0.976055i	−0.736528	+	0.676407i	$0.763536\pi$
$653$	−43.2008	+	24.9420i	−1.69058	+	0.976055i	−0.954050	+	0.299648i	$0.903131\pi$
$654$		0			0
$655$	44.7628	+	25.8438i	1.74903	+	1.00980i
$656$	−0.232945	+	3.60795i	−0.00909499	+	0.140867i
$657$		0			0
$658$	13.4886	−	3.35783i	0.525841	−	0.130902i
$659$	10.8898	+	18.8616i	0.424205	+	0.734745i	0.996346	−	0.0854106i	$-0.0272202\pi$
$659$	10.8898	+	18.8616i	0.424205	+	0.734745i	−0.572141	+	0.820155i	$0.693887\pi$
$660$		0			0
$661$	−7.83210			−0.304634			−0.152317	−	0.988332i	$-0.548673\pi$
$661$	−7.83210			−0.304634			−0.152317	+	0.988332i	$0.548673\pi$
$662$	3.66591	−	12.8492i	0.142480	−	0.499400i
$663$		0			0
$664$	−9.28620	+	28.9742i	−0.360375	+	1.12442i
$665$	−41.0183	+	23.5889i	−1.59062	+	0.914740i
$666$		0			0
$667$	1.38367	+	0.798860i	0.0535758	+	0.0309320i
$668$	−31.4015	+	16.8042i	−1.21496	+	0.650172i
$669$		0			0
$670$	4.39704	+	17.5358i	0.169873	+	0.677469i
$671$	24.3539	−	42.1823i	0.940174	−	1.62843i
$672$		0			0
$673$	14.7309	+	25.5146i	0.567833	+	0.983516i	0.996780	+	0.0801864i	$0.0255515\pi$
$673$	14.7309	+	25.5146i	0.567833	+	0.983516i	−0.428947	+	0.903330i	$0.641115\pi$
$674$	−18.6465	+	18.0549i	−0.718236	+	0.695448i
$675$		0			0
$676$	−0.755651	+	23.4320i	−0.0290635	+	0.901232i
$677$			23.3331i			0.896764i	0.893842	+	0.448382i	$0.148000\pi$
$677$			23.3331i			0.896764i	−0.893842	+	0.448382i	$0.852000\pi$
$678$		0			0
$679$	24.9973	+	14.4889i	0.959307	+	0.556035i
$680$	66.0099	−	14.3073i	2.53136	−	0.548660i
$681$		0			0
$682$	−12.2308	−	12.6315i	−0.468340	−	0.483687i
$683$	−5.29091	−	9.16412i	−0.202451	−	0.350655i	0.746867	−	0.664974i	$-0.231557\pi$
$683$	−5.29091	−	9.16412i	−0.202451	−	0.350655i	−0.949318	+	0.314319i	$0.898224\pi$
$684$		0			0
$685$	−68.8420			−2.63032
$686$	7.31424	−	25.1496i	0.279259	−	0.960216i
$687$		0			0
$688$	22.2031	+	14.8044i	0.846486	+	0.564411i
$689$		−	1.27339i		−	0.0485123i
$690$		0			0
$691$			12.3492i			0.469786i	0.972021	+	0.234893i	$0.0754740\pi$
$691$			12.3492i			0.469786i	−0.972021	+	0.234893i	$0.924526\pi$
$692$	−9.31646	+	14.9984i	−0.354159	+	0.570153i
$693$		0			0
$694$	45.9752	+	13.1168i	1.74520	+	0.497907i
$695$	−1.12893			−0.0428227
$696$		0			0
$697$	5.85543			0.221790
$698$	5.10009	+	20.3397i	0.193041	+	0.769868i
$699$		0			0
$700$	−24.0441	+	38.5616i	−0.908783	+	1.45749i
$701$			8.26934i			0.312329i	0.987731	+	0.156164i	$0.0499130\pi$
$701$			8.26934i			0.312329i	−0.987731	+	0.156164i	$0.950087\pi$
$702$		0			0
$703$	−8.62279	+	4.97837i	−0.325215	+	0.187763i
$704$	−23.4125	−	16.7254i	−0.882390	−	0.630361i
$705$		0			0
$706$	24.9917	+	25.8106i	0.940574	+	0.971396i
$707$	19.4380	+	0.0330714i	0.731041	+	0.00124378i
$708$		0			0
$709$	5.36467			0.201475			0.100737	−	0.994913i	$-0.467880\pi$
$709$	5.36467			0.201475			0.100737	+	0.994913i	$0.467880\pi$
$710$	12.5110	−	3.13707i	0.469528	−	0.117732i
$711$		0			0
$712$	10.8087	+	49.8683i	0.405073	+	1.86889i
$713$	−3.12757	+	1.80570i	−0.117128	+	0.0676242i
$714$		0			0
$715$	12.9793	+	7.49359i	0.485398	+	0.280245i
$716$	−0.830808	+	25.7626i	−0.0310487	+	0.962792i
$717$		0			0
$718$	−14.7769	+	14.3081i	−0.551469	+	0.533972i
$719$	3.38933	−	5.87049i	0.126401	−	0.218932i	−0.795879	−	0.605456i	$-0.792991\pi$
$719$	3.38933	−	5.87049i	0.126401	−	0.218932i	0.922280	+	0.386524i	$0.126324\pi$
$720$		0			0
$721$	−1.54893	+	2.67232i	−0.0576853	+	0.0995224i
$722$	−1.56122	−	6.22628i	−0.0581024	−	0.231718i
$723$		0			0
$724$	−15.6244	−	9.70532i	−0.580676	−	0.360695i
$725$			13.1338i			0.487778i
$726$		0			0
$727$	−3.83172	+	2.21224i	−0.142110	+	0.0820475i	−0.569369	−	0.822082i	$-0.692813\pi$
$727$	−3.83172	+	2.21224i	−0.142110	+	0.0820475i	0.427259	+	0.904129i	$0.359479\pi$
$728$	−6.27354	+	5.67493i	−0.232513	+	0.210327i
$729$		0			0
$730$	24.9412	+	25.7585i	0.923117	+	0.953366i
$731$	21.6097	−	37.4292i	0.799265	−	1.38437i
$732$		0			0
$733$	−20.7029	−	35.8585i	−0.764679	−	1.32446i	−0.940416	−	0.340025i	$-0.889564\pi$
$733$	−20.7029	−	35.8585i	−0.764679	−	1.32446i	0.175738	−	0.984437i	$-0.443769\pi$
$734$	14.1945	+	14.6596i	0.523928	+	0.541096i
$735$		0			0
$736$	−4.50177	+	3.82892i	−0.165938	+	0.141136i
$737$	−10.8019	−	6.23646i	−0.397892	−	0.229723i
$738$		0			0
$739$	−12.0981	+	6.98485i	−0.445037	+	0.256942i	−0.705732	−	0.708479i	$-0.749382\pi$
$739$	−12.0981	+	6.98485i	−0.445037	+	0.256942i	0.260695	+	0.965421i	$0.416048\pi$
$740$	−7.98327	+	12.8521i	−0.293471	+	0.472453i
$741$		0			0
$742$	−3.03295	+	2.92674i	−0.111343	+	0.107444i
$743$	8.17429	−	14.1583i	0.299886	−	0.519417i	−0.676224	−	0.736696i	$-0.736385\pi$
$743$	8.17429	−	14.1583i	0.299886	−	0.519417i	0.976110	+	0.217279i	$0.0697181\pi$
$744$		0			0
$745$	−18.0240	+	31.2185i	−0.660349	+	1.14376i
$746$	0.453259	+	1.80764i	0.0165950	+	0.0661825i
$747$		0			0
$748$	−24.5882	+	39.5841i	−0.899035	+	1.44734i
$749$	−0.0684068	+	40.2067i	−0.00249953	+	1.46912i
$750$		0			0
$751$	−40.1194	+	23.1629i	−1.46398	+	0.845227i	−0.999192	−	0.0401971i	$-0.987201\pi$
$751$	−40.1194	+	23.1629i	−1.46398	+	0.845227i	−0.464784	+	0.885424i	$0.653868\pi$
$752$	6.58541	+	13.3211i	0.240145	+	0.485771i
$753$		0			0
$754$	−0.670768	+	2.35108i	−0.0244279	+	0.0856214i
$755$	85.5953			3.11513
$756$		0			0
$757$	18.2447			0.663115			0.331558	−	0.943435i	$-0.392426\pi$
$757$	18.2447			0.663115			0.331558	+	0.943435i	$0.392426\pi$
$758$	7.55654	−	26.4861i	0.274466	−	0.962020i
$759$		0			0
$760$	−33.9978	−	37.4557i	−1.23323	−	1.35866i
$761$	−13.2289	+	7.63773i	−0.479548	+	0.276867i	−0.720228	−	0.693737i	$-0.755963\pi$
$761$	−13.2289	+	7.63773i	−0.479548	+	0.276867i	0.240680	+	0.970605i	$0.422630\pi$
$762$		0			0
$763$	−30.4271	−	17.6362i	−1.10154	−	0.638473i
$764$	−15.4714	−	9.61029i	−0.559736	−	0.347688i
$765$		0			0
$766$	0.796478	+	3.17643i	0.0287779	+	0.114769i
$767$	−0.472264	+	0.817985i	−0.0170525	+	0.0295357i
$768$		0			0
$769$	20.8322	−	36.0824i	0.751227	−	1.30116i	−0.196001	−	0.980604i	$-0.562795\pi$
$769$	20.8322	−	36.0824i	0.751227	−	1.30116i	0.947228	−	0.320560i	$-0.103871\pi$
$770$	−11.9832	−	48.1371i	−0.431844	−	1.73474i
$771$		0			0
$772$	−19.5982	−	12.1737i	−0.705354	−	0.438140i
$773$	1.49050	−	0.860538i	0.0536094	−	0.0309514i	−0.472956	−	0.881086i	$-0.656813\pi$
$773$	1.49050	−	0.860538i	0.0536094	−	0.0309514i	0.526565	+	0.850135i	$0.323480\pi$
$774$		0			0
$775$	−25.7098	−	14.8435i	−0.923522	−	0.533195i
$776$	−9.42713	+	29.4139i	−0.338414	+	1.05590i
$777$		0			0
$778$	−0.444728	−	0.459301i	−0.0159443	−	0.0164668i
$779$	−2.19264	−	3.79777i	−0.0785595	−	0.136069i
$780$		0			0
$781$	−4.44941	+	7.70660i	−0.159212	+	0.275764i
$782$	6.65799	+	6.87616i	0.238089	+	0.245891i
$783$		0			0
$784$	27.9355	+	1.89912i	0.997697	+	0.0678256i
$785$	20.5171	−	11.8455i	0.732285	−	0.422785i
$786$		0			0
$787$		−	34.6912i		−	1.23661i	−0.785939	−	0.618304i	$-0.787820\pi$
$787$		−	34.6912i		−	1.23661i	0.785939	−	0.618304i	$-0.212180\pi$
$788$	−13.6391	+	21.9573i	−0.485872	+	0.782195i
$789$		0			0
$790$	−8.39478	−	33.4792i	−0.298673	−	1.19114i
$791$	−0.832803	−	0.00141691i	−0.0296110	−	5.03795e-5i
$792$		0			0
$793$	7.65461	−	13.2582i	0.271823	−	0.470812i
$794$	29.2385	−	28.3108i	1.03764	−	1.00471i
$795$		0			0
$796$	21.2958	+	0.686761i	0.754810	+	0.0243416i
$797$	25.7110	+	14.8443i	0.910731	+	0.525811i	0.880666	−	0.473737i	$-0.157095\pi$
$797$	25.7110	+	14.8443i	0.910731	+	0.525811i	0.0300650	+	0.999548i	$0.490429\pi$
$798$		0			0
$799$	20.8422	−	12.0333i	0.737345	−	0.425706i
$800$	−45.7613	−	16.3108i	−1.61791	−	0.576673i
$801$		0			0
$802$	16.2165	−	4.06622i	0.572624	−	0.143583i
$803$	−24.7371			−0.872952
$804$		0			0
$805$	−10.1890	−	0.0173353i	−0.359113	−	0.000610987i
$806$	−3.84421	−	3.97018i	−0.135407	−	0.139844i
$807$		0			0
$808$	4.40177	+	20.3086i	0.154854	+	0.714453i
$809$	−21.1767	+	12.2264i	−0.744534	+	0.429857i	−0.823715	−	0.567004i	$-0.808103\pi$
$809$	−21.1767	+	12.2264i	−0.744534	+	0.429857i	0.0791818	+	0.996860i	$0.474769\pi$
$810$		0			0
$811$			34.3972i			1.20785i	0.797042	+	0.603924i	$0.206397\pi$
$811$			34.3972i			1.20785i	−0.797042	+	0.603924i	$0.793603\pi$
$812$	7.14148	−	3.80606i	0.250617	−	0.133567i
$813$		0			0
$814$	−2.53878	−	10.1249i	−0.0889843	−	0.354878i
$815$	−26.7032			−0.935374
$816$		0			0
$817$	−32.3682			−1.13242
$818$	48.7561	+	13.9102i	1.70472	+	0.486358i
$819$		0			0
$820$	−5.66050	−	3.51610i	−0.197673	−	0.122788i
$821$		−	22.4377i		−	0.783079i	−0.920161	−	0.391540i	$-0.871943\pi$
$821$		−	22.4377i		−	0.783079i	0.920161	−	0.391540i	$-0.128057\pi$
$822$		0			0
$823$		−	25.4294i		−	0.886412i	−0.896420	−	0.443206i	$-0.853841\pi$
$823$		−	25.4294i		−	0.886412i	0.896420	−	0.443206i	$-0.146159\pi$
$824$	−3.14448	−	1.00780i	−0.109543	−	0.0351085i
$825$		0			0
$826$	3.03371	−	0.755208i	0.105556	−	0.0262770i
$827$	51.6448			1.79587			0.897934	−	0.440131i	$-0.145068\pi$
$827$	51.6448			1.79587			0.897934	+	0.440131i	$0.145068\pi$
$828$		0			0
$829$	−6.19638	−	10.7324i	−0.215209	−	0.372753i	0.738128	−	0.674661i	$-0.235710\pi$
$829$	−6.19638	−	10.7324i	−0.215209	−	0.372753i	−0.953337	+	0.301907i	$0.902377\pi$
$830$	−39.0088	−	40.2871i	−1.35402	−	1.39839i
$831$		0			0
$832$	−7.35870	−	5.25690i	−0.255117	−	0.182250i
$833$	0.154306	−	45.3471i	0.00534637	−	1.57119i
$834$		0			0
$835$		−	65.6421i		−	2.27164i
$836$	34.8812	+	1.12487i	1.20639	+	0.0389045i
$837$		0			0
$838$	25.1816	−	24.3826i	0.869883	−	0.842283i
$839$	21.4887	+	37.2196i	0.741873	+	1.28496i	0.951641	+	0.307211i	$0.0993958\pi$
$839$	21.4887	+	37.2196i	0.741873	+	1.28496i	−0.209768	+	0.977751i	$0.567271\pi$
$840$		0			0
$841$	−13.3306	+	23.0893i	−0.459676	+	0.796181i
$842$	8.63821	+	34.4500i	0.297692	+	1.18723i
$843$		0			0
$844$	0.529550	+	0.989558i	0.0182279	+	0.0340620i
$845$	−37.4209	−	21.6050i	−1.28732	−	0.743234i
$846$		0			0
$847$	4.43076	+	2.56816i	0.152243	+	0.0882431i
$848$	−3.74889	−	2.49965i	−0.128737	−	0.0858382i
$849$		0			0
$850$	−21.5861	+	75.6607i	−0.740398	+	2.59514i
$851$	−2.14401			−0.0734957
$852$		0			0
$853$	21.9724	+	38.0573i	0.752320	+	1.30306i	0.946696	+	0.322130i	$0.104399\pi$
$853$	21.9724	+	38.0573i	0.752320	+	1.30306i	−0.194375	+	0.980927i	$0.562268\pi$
$854$	−49.1715	+	12.2407i	−1.68261	+	0.418867i
$855$		0			0
$856$	−42.0075	+	9.10490i	−1.43579	+	0.311199i
$857$	22.1891	+	12.8109i	0.757967	+	0.437612i	0.828565	−	0.559892i	$-0.189158\pi$
$857$	22.1891	+	12.8109i	0.757967	+	0.437612i	−0.0705984	+	0.997505i	$0.522491\pi$
$858$		0			0
$859$	−3.67684	+	2.12282i	−0.125452	+	0.0724298i	−0.561413	−	0.827536i	$-0.689742\pi$
$859$	−3.67684	+	2.12282i	−0.125452	+	0.0724298i	0.435961	+	0.899966i	$0.356409\pi$
$860$	−43.3661	+	23.2068i	−1.47877	+	0.791346i
$861$		0			0
$862$	2.17280	+	8.66536i	0.0740060	+	0.295143i
$863$	−3.42515	+	5.93253i	−0.116593	+	0.201946i	−0.918416	−	0.395617i	$-0.870531\pi$
$863$	−3.42515	+	5.93253i	−0.116593	+	0.201946i	0.801822	+	0.597563i	$0.203864\pi$
$864$		0			0
$865$	−16.2712	−	28.1826i	−0.553238	−	0.958236i
$866$	−37.2990	−	10.6415i	−1.26747	−	0.361612i
$867$		0			0
$868$	−0.620678	+	18.2811i	−0.0210672	+	0.620501i
$869$	20.6228	+	11.9066i	0.699580	+	0.403903i
$870$		0			0
$871$	−3.39510	−	1.96016i	−0.115039	−	0.0664176i
$872$	11.4749	−	35.8031i	0.388588	−	1.21245i
$873$		0			0
$874$	1.96663	−	6.89317i	0.0665223	−	0.233165i
$875$	−17.4450	−	30.3347i	−0.589749	−	1.02550i
$876$		0			0
$877$	18.9329	+	32.7927i	0.639318	+	1.10733i	0.985583	+	0.169195i	$0.0541166\pi$
$877$	18.9329	+	32.7927i	0.639318	+	1.10733i	−0.346265	+	0.938137i	$0.612550\pi$
$878$	−1.97836	+	6.93427i	−0.0667664	+	0.234020i
$879$		0			0
$880$	47.5394	−	23.5015i	1.60255	−	0.792236i
$881$			0.333275i			0.0112283i	0.999984	+	0.00561416i	$0.00178705\pi$
$881$			0.333275i			0.0112283i	−0.999984	+	0.00561416i	$0.998213\pi$
$882$		0			0
$883$			46.2921i			1.55785i	0.627114	+	0.778927i	$0.284236\pi$
$883$			46.2921i			1.55785i	−0.627114	+	0.778927i	$0.715764\pi$
$884$	−7.72825	+	12.4416i	−0.259929	+	0.418455i
$885$		0			0
$886$	−5.38184	−	1.53545i	−0.180807	−	0.0515844i
$887$	21.0495	+	36.4589i	0.706775	+	1.22417i	0.966047	+	0.258366i	$0.0831839\pi$
$887$	21.0495	+	36.4589i	0.706775	+	1.22417i	−0.259273	+	0.965804i	$0.583483\pi$
$888$		0			0
$889$	−9.50267	−	16.5240i	−0.318709	−	0.554196i
$890$	−90.4376	−	25.8020i	−3.03147	−	0.864885i
$891$		0			0
$892$	31.1485	+	1.00450i	1.04293	+	0.0336330i
$893$	−15.6093	−	9.01203i	−0.522345	−	0.301576i
$894$		0			0
$895$	−41.1428	−	23.7538i	−1.37525	−	0.794002i
$896$	4.39226	+	29.6093i	0.146735	+	0.989176i
$897$		0			0
$898$	2.30073	−	8.06421i	0.0767764	−	0.269106i
$899$	2.64327	+	4.57828i	0.0881580	+	0.152694i
$900$		0			0
$901$	−3.64870	+	6.31974i	−0.121556	+	0.210541i
$902$	4.45936	−	1.11817i	0.148480	−	0.0372309i
$903$		0			0
$904$	−0.188590	−	0.870101i	−0.00627241	−	0.0289391i
$905$	29.3589	−	16.9504i	0.975922	−	0.563449i
$906$		0			0
$907$	−12.5719	−	7.25841i	−0.417444	−	0.241011i	0.276539	−	0.961003i	$-0.410812\pi$
$907$	−12.5719	−	7.25841i	−0.417444	−	0.241011i	−0.693983	+	0.719991i	$0.744146\pi$
$908$	35.1366	−	18.8029i	1.16605	−	0.623997i
$909$		0			0
$910$	−3.76639	−	15.1298i	−0.124855	−	0.501549i
$911$	−4.19622	−	7.26807i	−0.139027	−	0.240802i	0.788102	−	0.615545i	$-0.211064\pi$
$911$	−4.19622	−	7.26807i	−0.139027	−	0.240802i	−0.927129	+	0.374743i	$0.877731\pi$
$912$		0			0
$913$	38.6895			1.28044
$914$	41.7869	+	11.9219i	1.38219	+	0.394341i
$915$		0			0
$916$	0.675352	−	20.9420i	0.0223142	−	0.691944i
$917$	32.0967	+	18.6039i	1.05993	+	0.614356i
$918$		0			0
$919$	−49.1071	−	28.3520i	−1.61990	−	0.935247i	−0.986946	−	0.161054i	$-0.948511\pi$
$919$	−49.1071	−	28.3520i	−1.61990	−	0.935247i	−0.632949	−	0.774193i	$-0.718156\pi$
$920$	−2.30731	−	10.6453i	−0.0760698	−	0.350965i
$921$		0			0
$922$	−15.8226	+	3.96746i	−0.521091	+	0.130661i
$923$	−1.39848	+	2.42224i	−0.0460315	+	0.0797289i
$924$		0			0
$925$	−8.81226	−	15.2633i	−0.289745	−	0.501853i
$926$	37.7069	+	38.9425i	1.23913	+	1.27973i
$927$		0			0
$928$	5.60494	+	6.58990i	0.183991	+	0.216324i
$929$			18.4293i			0.604646i	0.953206	+	0.302323i	$0.0977621\pi$
$929$			18.4293i			0.604646i	−0.953206	+	0.302323i	$0.902238\pi$
$930$		0			0
$931$	−29.4694	+	16.8808i	−0.965822	+	0.553244i
$932$	−22.6894	−	42.3992i	−0.743217	−	1.38883i
$933$		0			0
$934$	3.90510	−	3.78119i	0.127779	−	0.123724i
$935$	−42.9434	−	74.3802i	−1.40440	−	2.43249i
$936$		0			0
$937$	26.4098			0.862771			0.431386	−	0.902168i	$-0.358025\pi$
$937$	26.4098			0.862771			0.431386	+	0.902168i	$0.358025\pi$
$938$	3.13454	+	12.5916i	0.102346	+	0.411131i
$939$		0			0
$940$	−27.3742	−	0.882781i	−0.892849	−	0.0287931i
$941$		−	42.7788i		−	1.39455i	−0.716804	−	0.697275i	$-0.754396\pi$
$941$		−	42.7788i		−	1.39455i	0.716804	−	0.697275i	$-0.245604\pi$
$942$		0			0
$943$		−	0.944294i		−	0.0307504i
$944$	1.48112	+	2.99605i	0.0482063	+	0.0975130i
$945$		0			0
$946$	9.30992	−	32.6318i	0.302692	−	1.06095i
$947$	6.55037			0.212858			0.106429	−	0.994320i	$-0.466058\pi$
$947$	6.55037			0.212858			0.106429	+	0.994320i	$0.466058\pi$
$948$		0			0
$949$	−7.77503			−0.252388
$950$	57.1559	−	14.3316i	1.85438	−	0.464979i
$951$		0			0
$952$	47.3957	−	10.1884i	1.53610	−	0.330207i
$953$		−	57.3933i		−	1.85915i	−0.368630	−	0.929576i	$-0.620173\pi$
$953$		−	57.3933i		−	1.85915i	0.368630	−	0.929576i	$-0.379827\pi$
$954$		0			0
$955$	29.0714	−	16.7844i	0.940730	−	0.543130i
$956$	22.5392	−	12.0616i	0.728970	−	0.390099i
$957$		0			0
$958$	32.0507	−	31.0338i	1.03551	−	1.00266i
$959$	−49.4110	−	0.0840667i	−1.59556	−	0.00271466i
$960$		0			0
$961$	19.0506			0.614534
$962$	−0.797957	−	3.18233i	−0.0257272	−	0.102602i
$963$		0			0
$964$	26.1345	−	13.9855i	0.841734	−	0.450444i
$965$	36.8258	−	21.2614i	1.18546	−	0.684428i
$966$		0			0
$967$	−21.2476	−	12.2673i	−0.683275	−	0.394489i	0.117813	−	0.993036i	$-0.462412\pi$
$967$	−21.2476	−	12.2673i	−0.683275	−	0.394489i	−0.801088	+	0.598547i	$0.795745\pi$
$968$	−1.67096	+	5.21361i	−0.0537066	+	0.167572i
$969$		0			0
$970$	−39.6008	−	40.8985i	−1.27151	−	1.31317i
$971$	0.228931	−	0.396521i	0.00734676	−	0.0127250i	−0.862329	−	0.506349i	$-0.830995\pi$
$971$	0.228931	−	0.396521i	0.00734676	−	0.0127250i	0.869675	+	0.493624i	$0.164328\pi$
$972$		0			0
$973$	−0.810284	−	0.00137860i	−0.0259765	−	4.41958e-5i
$974$	−1.24932	+	0.313263i	−0.0400309	+	0.0100376i
$975$		0			0
$976$	−24.0065	−	48.5609i	−0.768429	−	1.55440i
$977$			10.8563i			0.347324i	0.984805	+	0.173662i	$0.0555600\pi$
$977$			10.8563i			0.347324i	−0.984805	+	0.173662i	$0.944440\pi$
$978$		0			0
$979$	56.1918	−	32.4423i	1.79590	−	1.03686i
$980$	−27.3795	+	43.7449i	−0.874606	+	1.39738i
$981$		0			0
$982$	−11.0303	+	10.6804i	−0.351993	+	0.340824i
$983$	−17.5837	+	30.4558i	−0.560832	+	0.971390i	0.436592	+	0.899660i	$0.356185\pi$
$983$	−17.5837	+	30.4558i	−0.560832	+	0.971390i	−0.997424	+	0.0717304i	$0.977148\pi$
$984$		0			0
$985$	−23.8207	−	41.2586i	−0.758990	−	1.31461i
$986$	10.0656	−	9.74626i	0.320555	−	0.310384i
$987$		0			0
$988$	10.9634	+	0.353555i	0.348792	+	0.0112481i
$989$	−6.03613	−	3.48496i	−0.191938	−	0.110815i
$990$		0			0
$991$	10.5332	−	6.08134i	0.334598	−	0.193180i	−0.323283	−	0.946302i	$-0.604787\pi$
$991$	10.5332	−	6.08134i	0.334598	−	0.193180i	0.657881	+	0.753122i	$0.271453\pi$
$992$	−19.2344	+	3.52404i	−0.610693	+	0.111888i
$993$		0			0
$994$	8.98350	−	2.23634i	0.284939	−	0.0709324i
$995$	−19.6353	+	34.0094i	−0.622482	+	1.07817i
$996$		0			0
$997$	−16.4463	+	28.4858i	−0.520859	+	0.902155i	0.478847	+	0.877899i	$0.341055\pi$
$997$	−16.4463	+	28.4858i	−0.520859	+	0.902155i	−0.999706	+	0.0242561i	$0.992278\pi$
$998$	13.5824	−	3.40574i	0.429944	−	0.107807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.4		88
3.2	odd	2		252.2.bb.a.23.41	yes	88
4.3	odd	2	inner	756.2.bb.a.611.41		88
7.4	even	3		756.2.o.a.179.32		88
9.2	odd	6		756.2.o.a.359.19		88
9.7	even	3		252.2.o.a.191.26	yes	88
12.11	even	2		252.2.bb.a.23.4	yes	88
21.11	odd	6		252.2.o.a.95.13	✓	88
28.11	odd	6		756.2.o.a.179.19		88
36.7	odd	6		252.2.o.a.191.13	yes	88
36.11	even	6		756.2.o.a.359.32		88
63.11	odd	6	inner	756.2.bb.a.683.41		88
63.25	even	3		252.2.bb.a.11.4	yes	88
84.11	even	6		252.2.o.a.95.26	yes	88
252.11	even	6	inner	756.2.bb.a.683.4		88
252.151	odd	6		252.2.bb.a.11.41	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.13	✓	88	21.11	odd	6
252.2.o.a.95.26	yes	88	84.11	even	6
252.2.o.a.191.13	yes	88	36.7	odd	6
252.2.o.a.191.26	yes	88	9.7	even	3
252.2.bb.a.11.4	yes	88	63.25	even	3
252.2.bb.a.11.41	yes	88	252.151	odd	6
252.2.bb.a.23.4	yes	88	12.11	even	2
252.2.bb.a.23.41	yes	88	3.2	odd	2
756.2.o.a.179.19		88	28.11	odd	6
756.2.o.a.179.32		88	7.4	even	3
756.2.o.a.359.19		88	9.2	odd	6
756.2.o.a.359.32		88	36.11	even	6
756.2.bb.a.611.4		88	1.1	even	1	trivial
756.2.bb.a.611.41		88	4.3	odd	2	inner
756.2.bb.a.683.4		88	252.11	even	6	inner
756.2.bb.a.683.41		88	63.11	odd	6	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.35995 - 0.387995i) q^{2} +(1.69892 + 1.05531i) q^{4} +(-3.19234 + 1.84310i) q^{5} +(-2.29354 + 1.31898i) q^{7} +(-1.90099 - 2.09434i) q^{8} +O(q^{10})\)	\(q+(-1.35995 - 0.387995i) q^{2} +(1.69892 + 1.05531i) q^{4} +(-3.19234 + 1.84310i) q^{5} +(-2.29354 + 1.31898i) q^{7} +(-1.90099 - 2.09434i) q^{8} +(5.05653 - 1.26790i) q^{10} +(-1.79831 + 3.11476i) q^{11} +(-0.565220 + 0.978990i) q^{13} +(3.63085 - 0.903857i) q^{14} +(1.77265 + 3.58576i) q^{16} +(5.61029 - 3.23910i) q^{17} +(-4.20169 - 2.42585i) q^{19} +(-7.36856 - 0.237626i) q^{20} +(3.65412 - 3.53818i) q^{22} +(-0.522364 - 0.904760i) q^{23} +(4.29402 - 7.43745i) q^{25} +(1.14851 - 1.11207i) q^{26} +(-5.28846 - 0.179553i) q^{28} +(-1.32443 + 0.764659i) q^{29} -3.45679i q^{31} +(-1.01945 - 5.56424i) q^{32} +(-8.88646 + 2.22824i) q^{34} +(4.89074 - 8.43782i) q^{35} +(1.02611 - 1.77727i) q^{37} +(4.77286 + 4.92926i) q^{38} +(9.92866 + 3.18213i) q^{40} +(0.782771 + 0.451933i) q^{41} +(5.77771 - 3.33576i) q^{43} +(-6.34221 + 3.39396i) q^{44} +(0.359345 + 1.43310i) q^{46} +3.71500 q^{47} +(3.52061 - 6.05023i) q^{49} +(-8.72534 + 8.44849i) q^{50} +(-1.99340 + 1.06674i) q^{52} +(-0.975539 + 0.563227i) q^{53} -13.2578i q^{55} +(7.12236 + 2.29608i) q^{56} +(2.09784 - 0.526025i) q^{58} +0.835539 q^{59} -13.5427 q^{61} +(-1.34122 + 4.70106i) q^{62} +(-0.772494 + 7.96262i) q^{64} -4.16702i q^{65} +3.46796i q^{67} +(12.9497 + 0.417609i) q^{68} +(-9.92499 + 9.57742i) q^{70} +2.47422 q^{71} +(3.43894 + 5.95641i) q^{73} +(-2.08503 + 2.01887i) q^{74} +(-4.57832 - 8.55540i) q^{76} +(0.0161899 - 9.51574i) q^{77} -6.62099i q^{79} +(-12.2678 - 8.17980i) q^{80} +(-0.889180 - 0.918317i) q^{82} +(-5.37860 - 9.31600i) q^{83} +(-11.9400 + 20.6806i) q^{85} +(-9.15165 + 2.29474i) q^{86} +(9.94192 - 2.15486i) q^{88} +(-15.6235 - 9.02024i) q^{89} +(0.00508858 - 2.99086i) q^{91} +(0.0673471 - 2.08837i) q^{92} +(-5.05221 - 1.44140i) q^{94} +17.8843 q^{95} +(-5.46022 - 9.45739i) q^{97} +(-7.13531 + 6.86202i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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