LMFDB - Embedded newform 975.2.n.r.824.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(749,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.749"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,12,16,0,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			824.12
Character	$\chi$	$=$	975.824
Dual form			975.2.n.r.749.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.455718 - 0.455718i) q^{2} +(1.67352 + 0.446465i) q^{3} +1.58464i q^{4} +(0.966114 - 0.559191i) q^{6} +(2.89711 - 2.89711i) q^{7} +(1.63358 + 1.63358i) q^{8} +(2.60134 + 1.49434i) q^{9} +(2.45902 - 2.45902i) q^{11} +(-0.707488 + 2.65193i) q^{12} +(-1.09825 - 3.43422i) q^{13} -2.64053i q^{14} -1.68038 q^{16} -6.48865i q^{17} +(1.86647 - 0.504480i) q^{18} +(-3.48002 + 3.48002i) q^{19} +(6.14183 - 3.55491i) q^{21} -2.24123i q^{22} +2.39321i q^{23} +(2.00450 + 3.46318i) q^{24} +(-2.06553 - 1.06454i) q^{26} +(3.68622 + 3.66221i) q^{27} +(4.59088 + 4.59088i) q^{28} -0.0728607i q^{29} +(-3.16484 + 3.16484i) q^{31} +(-4.03295 + 4.03295i) q^{32} +(5.21308 - 3.01735i) q^{33} +(-2.95699 - 2.95699i) q^{34} +(-2.36799 + 4.12219i) q^{36} +(-6.34157 + 6.34157i) q^{37} +3.17182i q^{38} +(-0.304692 - 6.23756i) q^{39} +(-2.12973 - 2.12973i) q^{41} +(1.17890 - 4.41897i) q^{42} -3.53474 q^{43} +(3.89666 + 3.89666i) q^{44} +(1.09063 + 1.09063i) q^{46} +(8.05214 + 8.05214i) q^{47} +(-2.81215 - 0.750230i) q^{48} -9.78648i q^{49} +(2.89695 - 10.8589i) q^{51} +(5.44201 - 1.74034i) q^{52} +9.32683 q^{53} +(3.34881 - 0.0109441i) q^{54} +9.46535 q^{56} +(-7.37760 + 4.27018i) q^{57} +(-0.0332039 - 0.0332039i) q^{58} +(-3.31055 + 3.31055i) q^{59} -1.29568 q^{61} +2.88455i q^{62} +(11.8656 - 3.20711i) q^{63} +0.315013i q^{64} +(1.00063 - 3.75075i) q^{66} +(0.922676 + 0.922676i) q^{67} +10.2822 q^{68} +(-1.06849 + 4.00509i) q^{69} +(-2.96569 - 2.96569i) q^{71} +(1.80838 + 6.69063i) q^{72} +(-5.91079 + 5.91079i) q^{73} +5.77993i q^{74} +(-5.51460 - 5.51460i) q^{76} -14.2481i q^{77} +(-2.98142 - 2.70371i) q^{78} -9.54897 q^{79} +(4.53392 + 7.77455i) q^{81} -1.94111 q^{82} +(-2.62525 + 2.62525i) q^{83} +(5.63327 + 9.73260i) q^{84} +(-1.61084 + 1.61084i) q^{86} +(0.0325297 - 0.121934i) q^{87} +8.03402 q^{88} +(-7.03107 + 7.03107i) q^{89} +(-13.1311 - 6.76754i) q^{91} -3.79239 q^{92} +(-6.70942 + 3.88344i) q^{93} +7.33901 q^{94} +(-8.54979 + 4.94865i) q^{96} +(6.77490 + 6.77490i) q^{97} +(-4.45987 - 4.45987i) q^{98} +(10.0713 - 2.72214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{6} + 16 q^{7} + 24 q^{12} - 24 q^{13} - 64 q^{16} - 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} - 32 q^{28} + 32 q^{31} - 4 q^{33} + 16 q^{34} - 32 q^{37} + 8 q^{39} + 32 q^{43} - 40 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) $ 40 * q + 12 * q^6 + 16 * q^7 + 24 * q^12 - 24 * q^13 - 64 * q^16 - 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 - 32 * q^28 + 32 * q^31 - 4 * q^33 + 16 * q^34 - 32 * q^37 + 8 * q^39 + 32 * q^43 - 40 * q^46 + 8 * q^52 + 32 * q^54 - 36 * q^57 - 24 * q^58 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 - 132 * q^72 - 64 * q^73 + 16 * q^76 + 108 * q^78 - 40 * q^79 + 72 * q^81 + 128 * q^82 - 124 * q^84 + 80 * q^88 + 8 * q^91 + 108 * q^93 + 32 * q^94 - 76 * q^96 + 24 * q^97 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	0.455718	−	0.455718i	0.322241	−	0.322241i	−0.527385	−	0.849626i	$-0.676828\pi$
$2$	0.455718	−	0.455718i	0.322241	−	0.322241i	0.849626	+	0.527385i	$0.176828\pi$
$3$	1.67352	+	0.446465i	0.966207	+	0.257767i
$3$	1.67352	+	0.446465i	0.966207	+	0.257767i
$4$			1.58464i			0.792321i
$5$		0			0
$5$		0			0
$6$	0.966114	−	0.559191i	0.394415	−	0.228289i
$7$	2.89711	−	2.89711i	1.09500	−	1.09500i	0.100019	−	0.994986i	$-0.468110\pi$
$7$	2.89711	−	2.89711i	1.09500	−	1.09500i	0.994986	−	0.100019i	$-0.0318902\pi$
$8$	1.63358	+	1.63358i	0.577559	+	0.577559i
$9$	2.60134	+	1.49434i	0.867113	+	0.498112i
$10$		0			0
$11$	2.45902	−	2.45902i	0.741421	−	0.741421i	−0.231430	−	0.972851i	$-0.574341\pi$
$11$	2.45902	−	2.45902i	0.741421	−	0.741421i	0.972851	+	0.231430i	$0.0743406\pi$
$12$	−0.707488	+	2.65193i	−0.204234	+	0.765547i
$13$	−1.09825	−	3.43422i	−0.304601	−	0.952480i
$13$	−1.09825	−	3.43422i	−0.304601	−	0.952480i
$14$		−	2.64053i		−	0.705711i
$15$		0			0
$16$	−1.68038			−0.420095
$17$		−	6.48865i		−	1.57373i	−0.617126	−	0.786864i	$-0.711703\pi$
$17$		−	6.48865i		−	1.57373i	0.617126	−	0.786864i	$-0.288297\pi$
$18$	1.86647	−	0.504480i	0.439931	−	0.118907i
$19$	−3.48002	+	3.48002i	−0.798372	+	0.798372i	−0.982839	−	0.184466i	$-0.940944\pi$
$19$	−3.48002	+	3.48002i	−0.798372	+	0.798372i	0.184466	+	0.982839i	$0.440944\pi$
$20$		0			0
$21$	6.14183	−	3.55491i	1.34026	−	0.775745i
$22$		−	2.24123i		−	0.477833i
$23$			2.39321i			0.499020i	0.968372	+	0.249510i	$0.0802695\pi$
$23$			2.39321i			0.499020i	−0.968372	+	0.249510i	$0.919730\pi$
$24$	2.00450	+	3.46318i	0.409167	+	0.706918i
$25$		0			0
$26$	−2.06553	−	1.06454i	−0.405083	−	0.208773i
$27$	3.68622	+	3.66221i	0.709414	+	0.704792i
$28$	4.59088	+	4.59088i	0.867595	+	0.867595i
$29$		−	0.0728607i		−	0.0135299i	−0.999977	−	0.00676494i	$-0.997847\pi$
$29$		−	0.0728607i		−	0.0135299i	0.999977	−	0.00676494i	$-0.00215336\pi$
$30$		0			0
$31$	−3.16484	+	3.16484i	−0.568423	+	0.568423i	−0.931686	−	0.363264i	$-0.881662\pi$
$31$	−3.16484	+	3.16484i	−0.568423	+	0.568423i	0.363264	+	0.931686i	$0.381662\pi$
$32$	−4.03295	+	4.03295i	−0.712931	+	0.712931i
$33$	5.21308	−	3.01735i	0.907480	−	0.525253i
$34$	−2.95699	−	2.95699i	−0.507120	−	0.507120i
$35$		0			0
$36$	−2.36799	+	4.12219i	−0.394665	+	0.687032i
$37$	−6.34157	+	6.34157i	−1.04255	+	1.04255i	−0.0434947	+	0.999054i	$0.513849\pi$
$37$	−6.34157	+	6.34157i	−1.04255	+	1.04255i	−0.999054	+	0.0434947i	$0.986151\pi$
$38$			3.17182i			0.514537i
$39$	−0.304692	−	6.23756i	−0.0487897	−	0.998809i
$40$		0			0
$41$	−2.12973	−	2.12973i	−0.332607	−	0.332607i	0.520968	−	0.853576i	$-0.325571\pi$
$41$	−2.12973	−	2.12973i	−0.332607	−	0.332607i	−0.853576	+	0.520968i	$0.825571\pi$
$42$	1.17890	−	4.41897i	0.181909	−	0.681863i
$43$	−3.53474			−0.539043			−0.269522	−	0.962994i	$-0.586866\pi$
$43$	−3.53474			−0.539043			−0.269522	+	0.962994i	$0.586866\pi$
$44$	3.89666	+	3.89666i	0.587444	+	0.587444i
$45$		0			0
$46$	1.09063	+	1.09063i	0.160805	+	0.160805i
$47$	8.05214	+	8.05214i	1.17453	+	1.17453i	0.981119	+	0.193407i	$0.0619538\pi$
$47$	8.05214	+	8.05214i	1.17453	+	1.17453i	0.193407	+	0.981119i	$0.438046\pi$
$48$	−2.81215	−	0.750230i	−0.405899	−	0.108286i
$49$		−	9.78648i		−	1.39807i
$50$		0			0
$51$	2.89695	−	10.8589i	0.405655	−	1.52055i
$52$	5.44201	−	1.74034i	0.754670	−	0.241342i
$53$	9.32683			1.28114			0.640569	−	0.767901i	$-0.278699\pi$
$53$	9.32683			1.28114			0.640569	+	0.767901i	$0.278699\pi$
$54$	3.34881	−	0.0109441i	0.455715	−	0.00148931i
$55$		0			0
$56$	9.46535			1.26486
$57$	−7.37760	+	4.27018i	−0.977187	+	0.565599i
$58$	−0.0332039	−	0.0332039i	−0.00435988	−	0.00435988i
$59$	−3.31055	+	3.31055i	−0.430996	+	0.430996i	−0.888967	−	0.457971i	$-0.848576\pi$
$59$	−3.31055	+	3.31055i	−0.430996	+	0.430996i	0.457971	+	0.888967i	$0.348576\pi$
$60$		0			0
$61$	−1.29568			−0.165895			−0.0829473	−	0.996554i	$-0.526433\pi$
$61$	−1.29568			−0.165895			−0.0829473	+	0.996554i	$0.526433\pi$
$62$			2.88455i			0.366338i
$63$	11.8656	−	3.20711i	1.49493	−	0.404057i
$64$			0.315013i			0.0393766i
$65$		0			0
$66$	1.00063	−	3.75075i	0.123169	−	0.461685i
$67$	0.922676	+	0.922676i	0.112723	+	0.112723i	0.761218	−	0.648496i	$-0.224601\pi$
$67$	0.922676	+	0.922676i	0.112723	+	0.112723i	−0.648496	+	0.761218i	$0.724601\pi$
$68$	10.2822			1.24690
$69$	−1.06849	+	4.00509i	−0.128631	+	0.482156i
$70$		0			0
$71$	−2.96569	−	2.96569i	−0.351963	−	0.351963i	0.508877	−	0.860839i	$-0.330061\pi$
$71$	−2.96569	−	2.96569i	−0.351963	−	0.351963i	−0.860839	+	0.508877i	$0.830061\pi$
$72$	1.80838	+	6.69063i	0.213120	+	0.788498i
$73$	−5.91079	+	5.91079i	−0.691805	+	0.691805i	−0.962629	−	0.270824i	$-0.912704\pi$
$73$	−5.91079	+	5.91079i	−0.691805	+	0.691805i	0.270824	+	0.962629i	$0.412704\pi$
$74$			5.77993i			0.671904i
$75$		0			0
$76$	−5.51460	−	5.51460i	−0.632568	−	0.632568i
$77$		−	14.2481i		−	1.62372i
$78$	−2.98142	−	2.70371i	−0.337579	−	0.306135i
$79$	−9.54897			−1.07434			−0.537171	−	0.843473i	$-0.680507\pi$
$79$	−9.54897			−1.07434			−0.537171	+	0.843473i	$0.680507\pi$
$80$		0			0
$81$	4.53392	+	7.77455i	0.503769	+	0.863838i
$82$	−1.94111			−0.214360
$83$	−2.62525	+	2.62525i	−0.288158	+	0.288158i	−0.836352	−	0.548193i	$-0.815316\pi$
$83$	−2.62525	+	2.62525i	−0.288158	+	0.288158i	0.548193	+	0.836352i	$0.315316\pi$
$84$	5.63327	+	9.73260i	0.614640	+	1.06191i
$85$		0			0
$86$	−1.61084	+	1.61084i	−0.173702	+	0.173702i
$87$	0.0325297	−	0.121934i	0.00348755	−	0.0130727i
$88$	8.03402			0.856429
$89$	−7.03107	+	7.03107i	−0.745292	+	0.745292i	−0.973591	−	0.228299i	$-0.926683\pi$
$89$	−7.03107	+	7.03107i	−0.745292	+	0.745292i	0.228299	+	0.973591i	$0.426683\pi$
$90$		0			0
$91$	−13.1311	−	6.76754i	−1.37651	−	0.709431i
$92$	−3.79239			−0.395384
$93$	−6.70942	+	3.88344i	−0.695735	+	0.402694i
$94$	7.33901			0.756961
$95$		0			0
$96$	−8.54979	+	4.94865i	−0.872609	+	0.505069i
$97$	6.77490	+	6.77490i	0.687887	+	0.687887i	0.961765	−	0.273878i	$-0.0883063\pi$
$97$	6.77490	+	6.77490i	0.687887	+	0.687887i	−0.273878	+	0.961765i	$0.588306\pi$
$98$	−4.45987	−	4.45987i	−0.450515	−	0.450515i
$99$	10.0713	−	2.72214i	1.01221	−	0.273585i
$100$		0			0
$101$	3.16651			0.315080			0.157540	−	0.987513i	$-0.449644\pi$
$101$	3.16651			0.315080			0.157540	+	0.987513i	$0.449644\pi$
$102$	−3.62839	−	6.26878i	−0.359264	−	0.620702i
$103$	−13.7432			−1.35416			−0.677080	−	0.735910i	$-0.736755\pi$
$103$	−13.7432			−1.35416			−0.677080	+	0.735910i	$0.736755\pi$
$104$	3.81599	−	7.40417i	0.374189	−	0.726039i
$105$		0			0
$106$	4.25040	−	4.25040i	0.412835	−	0.412835i
$107$	9.01108			0.871134			0.435567	−	0.900156i	$-0.356548\pi$
$107$	9.01108			0.871134			0.435567	+	0.900156i	$0.356548\pi$
$108$	−5.80329	+	5.84135i	−0.558422	+	0.562084i
$109$	5.87504	−	5.87504i	0.562727	−	0.562727i	−0.367354	−	0.930081i	$-0.619736\pi$
$109$	5.87504	−	5.87504i	0.562727	−	0.562727i	0.930081	+	0.367354i	$0.119736\pi$
$110$		0			0
$111$	−13.4440	+	7.78146i	−1.27605	+	0.738584i
$112$	−4.86824	+	4.86824i	−0.460006	+	0.460006i
$113$	0.651432			0.0612816			0.0306408	−	0.999530i	$-0.490245\pi$
$113$	0.651432			0.0612816			0.0306408	+	0.999530i	$0.490245\pi$
$114$	−1.41611	+	5.30810i	−0.132630	+	0.497149i
$115$		0			0
$116$	0.115458			0.0107200
$117$	2.27494	−	10.5747i	0.210319	−	0.977633i
$118$			3.01735i			0.277769i
$119$	−18.7983	−	18.7983i	−1.72324	−	1.72324i
$120$		0			0
$121$		−	1.09351i		−	0.0994103i
$122$	−0.590464	+	0.590464i	−0.0534581	+	0.0534581i
$123$	−2.61329	−	4.51499i	−0.235633	−	0.407103i
$124$	−5.01515	−	5.01515i	−0.450374	−	0.450374i
$125$		0			0
$126$	3.94583	−	6.86890i	0.351523	−	0.611931i
$127$	3.65542			0.324366			0.162183	−	0.986761i	$-0.448147\pi$
$127$	3.65542			0.324366			0.162183	+	0.986761i	$0.448147\pi$
$128$	−7.92234	−	7.92234i	−0.700242	−	0.700242i
$129$	−5.91546	−	1.57814i	−0.520827	−	0.138947i
$130$		0			0
$131$		−	10.5741i		−	0.923863i	−0.886916	−	0.461932i	$-0.847157\pi$
$131$		−	10.5741i		−	0.923863i	0.886916	−	0.461932i	$-0.152843\pi$
$132$	4.78142	+	8.26086i	0.416169	+	0.719016i
$133$			20.1640i			1.74844i
$134$	0.840960			0.0726479
$135$		0			0
$136$	10.5998	−	10.5998i	0.908922	−	0.908922i
$137$	4.62847	+	4.62847i	0.395437	+	0.395437i	0.876620	−	0.481183i	$-0.159793\pi$
$137$	4.62847	+	4.62847i	0.395437	+	0.395437i	−0.481183	+	0.876620i	$0.659793\pi$
$138$	1.33826	+	2.31212i	0.113921	+	0.196821i
$139$	−8.02113			−0.680343			−0.340172	−	0.940363i	$-0.610485\pi$
$139$	−8.02113			−0.680343			−0.340172	+	0.940363i	$0.610485\pi$
$140$		0			0
$141$	9.88042	+	17.0704i	0.832082	+	1.43759i
$142$	−2.70304			−0.226834
$143$	−11.1454	−	5.74417i	−0.932026	−	0.480351i
$144$	−4.37123	−	2.51105i	−0.364270	−	0.209254i
$145$		0			0
$146$			5.38730i			0.445856i
$147$	4.36932	−	16.3779i	0.360375	−	1.35082i
$148$	−10.0491	−	10.0491i	−0.826033	−	0.826033i
$149$	−1.16217	−	1.16217i	−0.0952087	−	0.0952087i	0.657898	−	0.753107i	$-0.271446\pi$
$149$	−1.16217	−	1.16217i	−0.0952087	−	0.0952087i	−0.753107	+	0.657898i	$0.771446\pi$
$150$		0			0
$151$	5.51342	+	5.51342i	0.448675	+	0.448675i	0.894914	−	0.446239i	$-0.147237\pi$
$151$	5.51342	+	5.51342i	0.448675	+	0.448675i	−0.446239	+	0.894914i	$0.647237\pi$
$152$	−11.3698			−0.922215
$153$	9.69622	−	16.8792i	0.783893	−	1.36460i
$154$	−6.49310	−	6.49310i	−0.523229	−	0.523229i
$155$		0			0
$156$	9.88431	−	0.482828i	0.791378	−	0.0386571i
$157$		−	20.7693i		−	1.65757i	−0.559567	−	0.828785i	$-0.689032\pi$
$157$		−	20.7693i		−	1.65757i	0.559567	−	0.828785i	$-0.310968\pi$
$158$	−4.35163	+	4.35163i	−0.346197	+	0.346197i
$159$	15.6086	+	4.16410i	1.23784	+	0.330235i
$160$		0			0
$161$	6.93340	+	6.93340i	0.546429	+	0.546429i
$162$	5.60918	+	1.47681i	0.440699	+	0.116029i
$163$	−1.79004	+	1.79004i	−0.140207	+	0.140207i	−0.773726	−	0.633520i	$-0.781610\pi$
$163$	−1.79004	+	1.79004i	−0.140207	+	0.140207i	0.633520	+	0.773726i	$0.281610\pi$
$164$	3.37486	−	3.37486i	0.263532	−	0.263532i
$165$		0			0
$166$			2.39274i			0.185713i
$167$	−7.06139	−	7.06139i	−0.546427	−	0.546427i	0.378979	−	0.925405i	$-0.376275\pi$
$167$	−7.06139	−	7.06139i	−0.546427	−	0.546427i	−0.925405	+	0.378979i	$0.876275\pi$
$168$	15.8404	+	4.22595i	1.22212	+	0.326039i
$169$	−10.5877	+	7.54328i	−0.814437	+	0.580252i
$170$		0			0
$171$	−14.2530	+	3.85239i	−1.08996	+	0.294600i
$172$		−	5.60130i		−	0.427095i
$173$		−	22.6054i		−	1.71866i	−0.511423	−	0.859329i	$-0.670881\pi$
$173$		−	22.6054i		−	1.71866i	0.511423	−	0.859329i	$-0.329119\pi$
$174$	−0.0407430	−	0.0703917i	−0.00308872	−	0.00533638i
$175$		0			0
$176$	−4.13208	+	4.13208i	−0.311467	+	0.311467i
$177$	−7.01831	+	4.06222i	−0.527528	+	0.305335i
$178$			6.40836i			0.480327i
$179$	14.3368			1.07158			0.535790	−	0.844351i	$-0.320014\pi$
$179$	14.3368			1.07158			0.535790	+	0.844351i	$0.320014\pi$
$180$		0			0
$181$			14.9736i			1.11298i	0.830856	+	0.556488i	$0.187852\pi$
$181$			14.9736i			1.11298i	−0.830856	+	0.556488i	$0.812148\pi$
$182$	−9.06814	+	2.89997i	−0.672175	+	0.214960i
$183$	−2.16834	−	0.578475i	−0.160289	−	0.0427621i
$184$	−3.90952	+	3.90952i	−0.288214	+	0.288214i
$185$		0			0
$186$	−1.28785	+	4.82735i	−0.0944298	+	0.353959i
$187$	−15.9557	−	15.9557i	−1.16680	−	1.16680i
$188$	−12.7598	+	12.7598i	−0.930602	+	0.930602i
$189$	21.2892	−	0.0695745i	1.54856	−	0.00506080i
$190$		0			0
$191$			13.0774i			0.946247i	0.880996	+	0.473124i	$0.156874\pi$
$191$			13.0774i			0.946247i	−0.880996	+	0.473124i	$0.843126\pi$
$192$	−0.140642	+	0.527180i	−0.0101500	+	0.0380459i
$193$	8.44842	−	8.44842i	0.608130	−	0.608130i	−0.334327	−	0.942457i	$-0.608509\pi$
$193$	8.44842	−	8.44842i	0.608130	−	0.608130i	0.942457	+	0.334327i	$0.108509\pi$
$194$	6.17488			0.443331
$195$		0			0
$196$	15.5081			1.10772
$197$	−6.31663	+	6.31663i	−0.450041	+	0.450041i	−0.895368	−	0.445327i	$-0.853088\pi$
$197$	−6.31663	+	6.31663i	−0.450041	+	0.450041i	0.445327	+	0.895368i	$0.353088\pi$
$198$	3.34916	−	5.83021i	0.238014	−	0.414335i
$199$		−	21.9442i		−	1.55558i	−0.628523	−	0.777791i	$-0.716340\pi$
$199$		−	21.9442i		−	1.55558i	0.628523	−	0.777791i	$-0.283660\pi$
$200$		0			0
$201$	1.13217	+	1.95606i	0.0798575	+	0.137970i
$202$	1.44304	−	1.44304i	0.101532	−	0.101532i
$203$	−0.211085	−	0.211085i	−0.0148153	−	0.0148153i
$204$	17.2075	+	4.59064i	1.20476	+	0.321409i
$205$		0			0
$206$	−6.26302	+	6.26302i	−0.436366	+	0.436366i
$207$	−3.57627	+	6.22556i	−0.248568	+	0.432706i
$208$	1.84548	+	5.77079i	0.127961	+	0.400132i
$209$			17.1149i			1.18386i
$210$		0			0
$211$	0.438580			0.0301931			0.0150966	−	0.999886i	$-0.495194\pi$
$211$	0.438580			0.0301931			0.0150966	+	0.999886i	$0.495194\pi$
$212$			14.7797i			1.01507i
$213$	−3.63907	−	6.28722i	−0.249345	−	0.430793i
$214$	4.10651	−	4.10651i	0.280715	−	0.280715i
$215$		0			0
$216$	0.0392308	+	12.0043i	0.00266932	+	0.816788i
$217$			18.3378i			1.24485i
$218$		−	5.35472i		−	0.362667i
$219$	−12.5308	+	7.25286i	−0.846752	+	0.490103i
$220$		0			0
$221$	−22.2834	+	7.12618i	−1.49895	+	0.479359i
$222$	−2.58054	+	9.67283i	−0.173194	+	0.649198i
$223$	1.59677	+	1.59677i	0.106927	+	0.106927i	0.758546	−	0.651619i	$-0.225910\pi$
$223$	1.59677	+	1.59677i	0.106927	+	0.106927i	−0.651619	+	0.758546i	$0.725910\pi$
$224$			23.3678i			1.56133i
$225$		0			0
$226$	0.296869	−	0.296869i	0.0197474	−	0.0197474i
$227$	13.0961	−	13.0961i	0.869216	−	0.869216i	−0.123169	−	0.992386i	$-0.539306\pi$
$227$	13.0961	−	13.0961i	0.869216	−	0.869216i	0.992386	+	0.123169i	$0.0393058\pi$
$228$	−6.76671	−	11.6909i	−0.448137	−	0.774246i
$229$	2.58892	+	2.58892i	0.171080	+	0.171080i	0.787454	−	0.616373i	$-0.211399\pi$
$229$	2.58892	+	2.58892i	0.171080	+	0.171080i	−0.616373	+	0.787454i	$0.711399\pi$
$230$		0			0
$231$	6.36126	−	23.8444i	0.418540	−	1.56885i
$232$	0.119024	−	0.119024i	0.00781431	−	0.00781431i
$233$			6.66598i			0.436703i	0.975870	+	0.218351i	$0.0700679\pi$
$233$			6.66598i			0.436703i	−0.975870	+	0.218351i	$0.929932\pi$
$234$	−3.78235	−	5.85582i	−0.247260	−	0.382807i
$235$		0			0
$236$	−5.24603	−	5.24603i	−0.341488	−	0.341488i
$237$	−15.9804	−	4.26328i	−1.03804	−	0.276930i
$238$	−17.1335			−1.11060
$239$	−1.15681	−	1.15681i	−0.0748278	−	0.0748278i	0.668702	−	0.743530i	$-0.266850\pi$
$239$	−1.15681	−	1.15681i	−0.0748278	−	0.0748278i	−0.743530	+	0.668702i	$0.766850\pi$
$240$		0			0
$241$	3.93884	+	3.93884i	0.253723	+	0.253723i	0.822495	−	0.568772i	$-0.192581\pi$
$241$	3.93884	+	3.93884i	0.253723	+	0.253723i	−0.568772	+	0.822495i	$0.692581\pi$
$242$	−0.498333	−	0.498333i	−0.0320341	−	0.0320341i
$243$	4.11654	+	15.0351i	0.264076	+	0.964502i
$244$		−	2.05319i		−	0.131442i
$245$		0			0
$246$	−3.24848	−	0.866637i	−0.207116	−	0.0552547i
$247$	15.7731	+	8.12921i	1.00362	+	0.517249i
$248$	−10.3401			−0.656596
$249$	−5.56549	+	3.22132i	−0.352698	+	0.204143i
$250$		0			0
$251$	17.0218			1.07441			0.537205	−	0.843452i	$-0.319480\pi$
$251$	17.0218			1.07441			0.537205	+	0.843452i	$0.319480\pi$
$252$	5.08212	+	18.8028i	0.320143	+	1.18446i
$253$	5.88495	+	5.88495i	0.369984	+	0.369984i
$254$	1.66584	−	1.66584i	0.104524	−	0.104524i
$255$		0			0
$256$	−7.85072			−0.490670
$257$		−	15.7772i		−	0.984152i	−0.870552	−	0.492076i	$-0.836238\pi$
$257$		−	15.7772i		−	0.984152i	0.870552	−	0.492076i	$-0.163762\pi$
$258$	−3.41496	+	1.97659i	−0.212606	+	0.123057i
$259$			36.7445i			2.28319i
$260$		0			0
$261$	0.108878	−	0.189535i	0.00673940	−	0.0117319i
$262$	−4.81880	−	4.81880i	−0.297707	−	0.297707i
$263$	5.23074			0.322541			0.161271	−	0.986910i	$-0.448441\pi$
$263$	5.23074			0.322541			0.161271	+	0.986910i	$0.448441\pi$
$264$	13.4451	+	3.58691i	0.827488	+	0.220759i
$265$		0			0
$266$	9.18910	+	9.18910i	0.563420	+	0.563420i
$267$	−14.9058	+	8.62751i	−0.912217	+	0.527995i
$268$	−1.46211	+	1.46211i	−0.0893127	+	0.0893127i
$269$		−	24.7143i		−	1.50686i	−0.657529	−	0.753429i	$-0.728398\pi$
$269$		−	24.7143i		−	1.50686i	0.657529	−	0.753429i	$-0.271602\pi$
$270$		0			0
$271$	−13.3905	−	13.3905i	−0.813413	−	0.813413i	0.171730	−	0.985144i	$-0.445064\pi$
$271$	−13.3905	−	13.3905i	−0.813413	−	0.813413i	−0.985144	+	0.171730i	$0.945064\pi$
$272$			10.9034i			0.661115i
$273$	−18.9536	−	17.1882i	−1.14713	−	1.04028i
$274$	4.21855			0.254852
$275$		0			0
$276$	−6.34664	−	1.69317i	−0.382023	−	0.101917i
$277$	5.07891			0.305162			0.152581	−	0.988291i	$-0.451241\pi$
$277$	5.07891			0.305162			0.152581	+	0.988291i	$0.451241\pi$
$278$	−3.65537	+	3.65537i	−0.219234	+	0.219234i
$279$	−12.9622	+	3.50349i	−0.776025	+	0.209748i
$280$		0			0
$281$	1.89588	−	1.89588i	0.113098	−	0.113098i	−0.648293	−	0.761391i	$-0.724517\pi$
$281$	1.89588	−	1.89588i	0.113098	−	0.113098i	0.761391	+	0.648293i	$0.224517\pi$
$282$	12.2820	+	3.27661i	0.731381	+	0.195119i
$283$	12.6318			0.750881			0.375440	−	0.926847i	$-0.377491\pi$
$283$	12.6318			0.750881			0.375440	+	0.926847i	$0.377491\pi$
$284$	4.69956	−	4.69956i	0.278868	−	0.278868i
$285$		0			0
$286$	−7.69688	+	2.46144i	−0.455126	+	0.145548i
$287$	−12.3401			−0.728413
$288$	−16.5176	+	4.46448i	−0.973311	+	0.263072i
$289$	−25.1026			−1.47662
$290$		0			0
$291$	8.31317	+	14.3627i	0.487327	+	0.841956i
$292$	−9.36649	−	9.36649i	−0.548132	−	0.548132i
$293$	−19.7059	−	19.7059i	−1.15123	−	1.15123i	−0.986306	−	0.164928i	$-0.947261\pi$
$293$	−19.7059	−	19.7059i	−1.15123	−	1.15123i	−0.164928	−	0.986306i	$-0.552739\pi$
$294$	−5.47251	−	9.45486i	−0.319163	−	0.551419i
$295$		0			0
$296$	−20.7190			−1.20427
$297$	18.0699	−	0.0590536i	1.04852	−	0.00342664i
$298$	−1.05924			−0.0613603
$299$	8.21882	−	2.62836i	0.475306	−	0.152002i
$300$		0			0
$301$	−10.2405	+	10.2405i	−0.590254	+	0.590254i
$302$	5.02512			0.289163
$303$	5.29922	+	1.41374i	0.304432	+	0.0812171i
$304$	5.84776	−	5.84776i	0.335392	−	0.335392i
$305$		0			0
$306$	−3.27340	−	12.1109i	−0.187128	−	0.692333i
$307$	−8.41607	+	8.41607i	−0.480330	+	0.480330i	−0.905237	−	0.424907i	$-0.860307\pi$
$307$	−8.41607	+	8.41607i	−0.480330	+	0.480330i	0.424907	+	0.905237i	$0.360307\pi$
$308$	22.5781			1.28651
$309$	−22.9995	−	6.13586i	−1.30840	−	0.349057i
$310$		0			0
$311$	−24.9831			−1.41666			−0.708330	−	0.705881i	$-0.750551\pi$
$311$	−24.9831			−1.41666			−0.708330	+	0.705881i	$0.750551\pi$
$312$	9.69184	−	10.6873i	0.548693	−	0.605051i
$313$			8.22919i			0.465141i	0.972579	+	0.232571i	$0.0747137\pi$
$313$			8.22919i			0.465141i	−0.972579	+	0.232571i	$0.925286\pi$
$314$	−9.46493	−	9.46493i	−0.534137	−	0.534137i
$315$		0			0
$316$		−	15.1317i		−	0.851225i
$317$	5.60105	−	5.60105i	0.314586	−	0.314586i	−0.532097	−	0.846683i	$-0.678596\pi$
$317$	5.60105	−	5.60105i	0.314586	−	0.314586i	0.846683	+	0.532097i	$0.178596\pi$
$318$	9.01078	−	5.21547i	0.505300	−	0.292469i
$319$	−0.179165	−	0.179165i	−0.0100313	−	0.0100313i
$320$		0			0
$321$	15.0802	+	4.02313i	0.841696	+	0.224549i
$322$	6.31935			0.352163
$323$	22.5807	+	22.5807i	1.25642	+	1.25642i
$324$	−12.3199	+	7.18464i	−0.684438	+	0.399147i
$325$		0			0
$326$			1.63150i			0.0903607i
$327$	12.4550	−	7.20900i	0.688763	−	0.398658i
$328$		−	6.95818i		−	0.384201i
$329$	46.6559			2.57222
$330$		0			0
$331$	0.890691	−	0.890691i	0.0489568	−	0.0489568i	−0.682205	−	0.731161i	$-0.738979\pi$
$331$	0.890691	−	0.890691i	0.0489568	−	0.0489568i	0.731161	+	0.682205i	$0.238979\pi$
$332$	−4.16008	−	4.16008i	−0.228314	−	0.228314i
$333$	−25.9730	+	7.02014i	−1.42331	+	0.384701i
$334$	−6.43600			−0.352162
$335$		0			0
$336$	−10.3206	+	5.97360i	−0.563035	+	0.325887i
$337$	0.362018			0.0197204			0.00986020	−	0.999951i	$-0.496861\pi$
$337$	0.362018			0.0197204			0.00986020	+	0.999951i	$0.496861\pi$
$338$	−1.38739	+	8.26260i	−0.0754639	+	0.449426i
$339$	1.09018	+	0.290842i	0.0592107	+	0.0157964i
$340$		0			0
$341$			15.5648i			0.842881i
$342$	−4.73976	+	8.25097i	−0.256297	+	0.446161i
$343$	−8.07273	−	8.07273i	−0.435887	−	0.435887i
$344$	−5.77430	−	5.77430i	−0.311329	−	0.311329i
$345$		0			0
$346$	−10.3017	−	10.3017i	−0.553822	−	0.553822i
$347$	5.96761			0.320358			0.160179	−	0.987088i	$-0.448793\pi$
$347$	5.96761			0.320358			0.160179	+	0.987088i	$0.448793\pi$
$348$	0.193221	+	0.0515480i	0.0103578	+	0.00276326i
$349$	13.7435	+	13.7435i	0.735673	+	0.735673i	0.971737	−	0.236064i	$-0.0758575\pi$
$349$	13.7435	+	13.7435i	0.735673	+	0.735673i	−0.236064	+	0.971737i	$0.575858\pi$
$350$		0			0
$351$	8.52841	−	16.6813i	0.455213	−	0.890383i
$352$			19.8342i			1.05716i
$353$	−13.8222	+	13.8222i	−0.735682	+	0.735682i	−0.971739	−	0.236057i	$-0.924145\pi$
$353$	−13.8222	+	13.8222i	−0.735682	+	0.735682i	0.236057	+	0.971739i	$0.424145\pi$
$354$	−1.34714	+	5.04959i	−0.0715997	+	0.268383i
$355$		0			0
$356$	−11.1417	−	11.1417i	−0.590511	−	0.590511i
$357$	−23.0666	−	39.8522i	−1.22081	−	2.10920i
$358$	6.53352	−	6.53352i	0.345307	−	0.345307i
$359$	−1.19127	+	1.19127i	−0.0628729	+	0.0628729i	−0.737844	−	0.674971i	$-0.764156\pi$
$359$	−1.19127	+	1.19127i	−0.0628729	+	0.0628729i	0.674971	+	0.737844i	$0.264156\pi$
$360$		0			0
$361$		−	5.22115i		−	0.274797i
$362$	6.82372	+	6.82372i	0.358647	+	0.358647i
$363$	0.488215	−	1.83002i	0.0256247	−	0.0960509i
$364$	10.7241	−	20.8080i	0.562097	−	1.09064i
$365$		0			0
$366$	−1.25177	+	0.724531i	−0.0654313	+	0.0378719i
$367$			23.7852i			1.24158i	0.783977	+	0.620790i	$0.213188\pi$
$367$			23.7852i			1.24158i	−0.783977	+	0.620790i	$0.786812\pi$
$368$		−	4.02151i		−	0.209636i
$369$	−2.35761	−	8.72267i	−0.122732	−	0.454084i
$370$		0			0
$371$	27.0208	−	27.0208i	1.40285	−	1.40285i
$372$	−6.15386	−	10.6320i	−0.319063	−	0.551246i
$373$		−	27.0932i		−	1.40283i	−0.712752	−	0.701416i	$-0.752552\pi$
$373$		−	27.0932i		−	1.40283i	0.712752	−	0.701416i	$-0.247448\pi$
$374$	−14.5426			−0.751979
$375$		0			0
$376$			26.3077i			1.35672i
$377$	−0.250219	+	0.0800195i	−0.0128869	+	0.00412121i
$378$	9.67016	−	9.73357i	0.497379	−	0.500641i
$379$	9.55318	−	9.55318i	0.490714	−	0.490714i	−0.417817	−	0.908531i	$-0.637205\pi$
$379$	9.55318	−	9.55318i	0.490714	−	0.490714i	0.908531	+	0.417817i	$0.137205\pi$
$380$		0			0
$381$	6.11741	+	1.63201i	0.313404	+	0.0836107i
$382$	5.95960	+	5.95960i	0.304920	+	0.304920i
$383$	19.9744	−	19.9744i	1.02064	−	1.02064i	0.0208607	−	0.999782i	$-0.493359\pi$
$383$	19.9744	−	19.9744i	1.02064	−	1.02064i	0.999782	−	0.0208607i	$-0.00664064\pi$
$384$	−9.72115	−	16.7952i	−0.496080	−	0.857079i
$385$		0			0
$386$		−	7.70018i		−	0.391929i
$387$	−9.19506	−	5.28209i	−0.467411	−	0.268504i
$388$	−10.7358	+	10.7358i	−0.545028	+	0.545028i
$389$	−35.1328			−1.78130			−0.890651	−	0.454688i	$-0.849751\pi$
$389$	−35.1328			−1.78130			−0.890651	+	0.454688i	$0.849751\pi$
$390$		0			0
$391$	15.5287			0.785322
$392$	15.9870	−	15.9870i	0.807468	−	0.807468i
$393$	4.72096	−	17.6960i	0.238141	−	0.892643i
$394$			5.75720i			0.290044i
$395$		0			0
$396$	4.31361	+	15.9595i	0.216767	+	0.801993i
$397$	13.0793	−	13.0793i	0.656433	−	0.656433i	−0.298101	−	0.954534i	$-0.596353\pi$
$397$	13.0793	−	13.0793i	0.656433	−	0.656433i	0.954534	+	0.298101i	$0.0963532\pi$
$398$	−10.0004	−	10.0004i	−0.501272	−	0.501272i
$399$	−9.00253	+	33.7449i	−0.450690	+	1.68936i
$400$		0			0
$401$	1.57949	−	1.57949i	0.0788759	−	0.0788759i	−0.666568	−	0.745444i	$-0.732237\pi$
$401$	1.57949	−	1.57949i	0.0788759	−	0.0788759i	0.745444	+	0.666568i	$0.232237\pi$
$402$	1.40736	+	0.375459i	0.0701929	+	0.0187262i
$403$	14.3446	+	7.39296i	0.714553	+	0.368270i
$404$			5.01779i			0.249644i
$405$		0			0
$406$	−0.192391			−0.00954818
$407$			31.1881i			1.54593i
$408$	22.4713	−	13.0065i	1.11250	−	0.643917i
$409$	9.54482	−	9.54482i	0.471961	−	0.471961i	−0.430588	−	0.902549i	$-0.641694\pi$
$409$	9.54482	−	9.54482i	0.471961	−	0.471961i	0.902549	+	0.430588i	$0.141694\pi$
$410$		0			0
$411$	5.67939	+	9.81229i	0.280144	+	0.484005i
$412$		−	21.7781i		−	1.07293i
$413$			19.1820i			0.943885i
$414$	1.20733	+	4.46687i	0.0593370	+	0.219534i
$415$		0			0
$416$	18.2792	+	9.42082i	0.896212	+	0.461894i
$417$	−13.4235	−	3.58115i	−0.657353	−	0.175370i
$418$	7.79955	+	7.79955i	0.381488	+	0.381488i
$419$			36.4123i			1.77886i	0.457074	+	0.889428i	$0.348897\pi$
$419$			36.4123i			1.77886i	−0.457074	+	0.889428i	$0.651103\pi$
$420$		0			0
$421$	−4.66950	+	4.66950i	−0.227578	+	0.227578i	−0.811680	−	0.584102i	$-0.801447\pi$
$421$	−4.66950	+	4.66950i	−0.227578	+	0.227578i	0.584102	+	0.811680i	$0.301447\pi$
$422$	0.199869	−	0.199869i	0.00972946	−	0.00972946i
$423$	8.91374	+	32.9790i	0.433401	+	1.60349i
$424$	15.2362	+	15.2362i	0.739933	+	0.739933i
$425$		0			0
$426$	−4.52359	−	1.20681i	−0.219168	−	0.0584702i
$427$	−3.75372	+	3.75372i	−0.181655	+	0.181655i
$428$			14.2794i			0.690218i
$429$	−16.0875	−	14.5890i	−0.776712	−	0.704364i
$430$		0			0
$431$	3.48824	+	3.48824i	0.168023	+	0.168023i	0.786110	−	0.618087i	$-0.212092\pi$
$431$	3.48824	+	3.48824i	0.168023	+	0.168023i	−0.618087	+	0.786110i	$0.712092\pi$
$432$	−6.19425	−	6.15390i	−0.298021	−	0.296080i
$433$	0.0657330			0.00315893			0.00157946	−	0.999999i	$-0.499497\pi$
$433$	0.0657330			0.00315893			0.00157946	+	0.999999i	$0.499497\pi$
$434$	8.35686	+	8.35686i	0.401142	+	0.401142i
$435$		0			0
$436$	9.30984	+	9.30984i	0.445860	+	0.445860i
$437$	−8.32845	−	8.32845i	−0.398404	−	0.398404i
$438$	−2.40524	+	9.01575i	−0.114927	+	0.430789i
$439$			9.56530i			0.456527i	0.973599	+	0.228264i	$0.0733048\pi$
$439$			9.56530i			0.456527i	−0.973599	+	0.228264i	$0.926695\pi$
$440$		0			0
$441$	14.6243	−	25.4579i	0.696395	−	1.21228i
$442$	−6.90742	+	13.4025i	−0.328553	+	0.637491i
$443$	35.0176			1.66374			0.831868	−	0.554973i	$-0.187272\pi$
$443$	35.0176			1.66374			0.831868	+	0.554973i	$0.187272\pi$
$444$	−12.3308	−	21.3040i	−0.585196	−	1.01104i
$445$		0			0
$446$	1.45535			0.0689128
$447$	−1.42605	−	2.46378i	−0.0674497	−	0.116533i
$448$	0.912626	+	0.912626i	0.0431175	+	0.0431175i
$449$	23.2242	−	23.2242i	1.09602	−	1.09602i	0.101149	−	0.994871i	$-0.467748\pi$
$449$	23.2242	−	23.2242i	1.09602	−	1.09602i	0.994871	−	0.101149i	$-0.0322517\pi$
$450$		0			0
$451$	−10.4741			−0.493204
$452$			1.03229i			0.0485547i
$453$	6.76526	+	11.6884i	0.317860	+	0.549167i
$454$		−	11.9362i		−	0.560194i
$455$		0			0
$456$	−19.0276	−	5.07623i	−0.891051	−	0.237716i
$457$	5.85273	+	5.85273i	0.273779	+	0.273779i	0.830620	−	0.556840i	$-0.187986\pi$
$457$	5.85273	+	5.85273i	0.273779	+	0.273779i	−0.556840	+	0.830620i	$0.687986\pi$
$458$	2.35963			0.110258
$459$	23.7628	−	23.9186i	1.10915	−	1.11643i
$460$		0			0
$461$	−24.2884	−	24.2884i	−1.13122	−	1.13122i	−0.989974	−	0.141250i	$-0.954888\pi$
$461$	−24.2884	−	24.2884i	−1.13122	−	1.13122i	−0.141250	−	0.989974i	$-0.545112\pi$
$462$	−7.96739	−	13.7653i	−0.370676	−	0.640418i
$463$	11.4811	−	11.4811i	0.533570	−	0.533570i	−0.388063	−	0.921633i	$-0.626856\pi$
$463$	11.4811	−	11.4811i	0.533570	−	0.533570i	0.921633	+	0.388063i	$0.126856\pi$
$464$			0.122434i			0.00568383i
$465$		0			0
$466$	3.03780	+	3.03780i	0.140724	+	0.140724i
$467$			21.9057i			1.01367i	0.862042	+	0.506837i	$0.169185\pi$
$467$			21.9057i			1.01367i	−0.862042	+	0.506837i	$0.830815\pi$
$468$	16.7571	+	3.60497i	0.774600	+	0.166640i
$469$	5.34619			0.246864
$470$		0			0
$471$	9.27276	−	34.7578i	0.427266	−	1.60156i
$472$	−10.8161			−0.497852
$473$	−8.69198	+	8.69198i	−0.399658	+	0.399658i
$474$	−9.22539	+	5.33969i	−0.423736	+	0.245260i
$475$		0			0
$476$	29.7886	−	29.7886i	1.36536	−	1.36536i
$477$	24.2622	+	13.9374i	1.11089	+	0.638150i
$478$	−1.05436			−0.0482251
$479$	−19.9645	+	19.9645i	−0.912201	+	0.912201i	−0.996445	−	0.0842446i	$-0.973152\pi$
$479$	−19.9645	+	19.9645i	−0.912201	+	0.912201i	0.0842446	+	0.996445i	$0.473152\pi$
$480$		0			0
$481$	28.7430	+	14.8137i	1.31057	+	0.675446i
$482$	3.59000			0.163520
$483$	8.50767	+	14.6987i	0.387112	+	0.668814i
$484$	1.73283			0.0787649
$485$		0			0
$486$	8.72774	+	4.97578i	0.395898	+	0.225706i
$487$	12.2103	+	12.2103i	0.553302	+	0.553302i	0.927392	−	0.374091i	$-0.122045\pi$
$487$	12.2103	+	12.2103i	0.553302	+	0.553302i	−0.374091	+	0.927392i	$0.622045\pi$
$488$	−2.11660	−	2.11660i	−0.0958140	−	0.0958140i
$489$	−3.79486	+	2.19648i	−0.171609	+	0.0993281i
$490$		0			0
$491$	23.7653			1.07251			0.536257	−	0.844054i	$-0.319838\pi$
$491$	23.7653			1.07251			0.536257	+	0.844054i	$0.319838\pi$
$492$	7.15464	−	4.14113i	0.322556	−	0.186697i
$493$	−0.472767			−0.0212924
$494$	10.8927	−	3.48346i	0.490086	−	0.156728i
$495$		0			0
$496$	5.31814	−	5.31814i	0.238791	−	0.238791i
$497$	−17.1839			−0.770802
$498$	−1.06828	+	4.00430i	−0.0478706	+	0.179437i
$499$	−13.6731	+	13.6731i	−0.612092	+	0.612092i	−0.943491	−	0.331399i	$-0.892480\pi$
$499$	−13.6731	+	13.6731i	−0.612092	+	0.612092i	0.331399	+	0.943491i	$0.392480\pi$
$500$		0			0
$501$	−8.66471	−	14.9700i	−0.387111	−	0.668812i
$502$	7.75715	−	7.75715i	0.346219	−	0.346219i
$503$	17.6986			0.789140			0.394570	−	0.918866i	$-0.370894\pi$
$503$	17.6986			0.789140			0.394570	+	0.918866i	$0.370894\pi$
$504$	24.6226	+	14.1444i	1.09678	+	0.630042i
$505$		0			0
$506$	5.36375			0.238448
$507$	−21.0865	+	7.89680i	−0.936484	+	0.350709i
$508$			5.79253i			0.257002i
$509$	−23.6849	−	23.6849i	−1.04982	−	1.04982i	−0.998692	−	0.0511241i	$-0.983720\pi$
$509$	−23.6849	−	23.6849i	−1.04982	−	1.04982i	−0.0511241	−	0.998692i	$-0.516280\pi$
$510$		0			0
$511$			34.2484i			1.51506i
$512$	12.2670	−	12.2670i	0.542128	−	0.542128i
$513$	−25.5727	+	0.0835734i	−1.12906	+	0.00368985i
$514$	−7.18993	−	7.18993i	−0.317134	−	0.317134i
$515$		0			0
$516$	2.50079	−	9.37389i	0.110091	−	0.412663i
$517$	39.6007			1.74164
$518$	16.7451	+	16.7451i	0.735737	+	0.735737i
$519$	10.0925	−	37.8306i	0.443013	−	1.66058i
$520$		0			0
$521$			12.3852i			0.542605i	0.962494	+	0.271302i	$0.0874544\pi$
$521$			12.3852i			0.542605i	−0.962494	+	0.271302i	$0.912546\pi$
$522$	−0.0367568	−	0.135992i	−0.00160880	−	0.00595222i
$523$		−	41.8255i		−	1.82890i	−0.404699	−	0.914450i	$-0.632624\pi$
$523$		−	41.8255i		−	1.82890i	0.404699	−	0.914450i	$-0.367376\pi$
$524$	16.7562			0.731997
$525$		0			0
$526$	2.38374	−	2.38374i	0.103936	−	0.103936i
$527$	20.5356	+	20.5356i	0.894543	+	0.894543i
$528$	−8.75994	+	5.07029i	−0.381228	+	0.220656i
$529$	17.2725			0.750979
$530$		0			0
$531$	−13.5589	+	3.66478i	−0.588407	+	0.159038i
$532$	−31.9528			−1.38533
$533$	−4.97496	+	9.65292i	−0.215490	+	0.418114i
$534$	−2.86111	+	10.7245i	−0.123812	+	0.464095i
$535$		0			0
$536$			3.01454i			0.130208i
$537$	23.9929	+	6.40087i	1.03537	+	0.276218i
$538$	−11.2627	−	11.2627i	−0.485571	−	0.485571i
$539$	−24.0651	−	24.0651i	−1.03656	−	1.03656i
$540$		0			0
$541$	−22.6303	−	22.6303i	−0.972954	−	0.972954i	0.0266894	−	0.999644i	$-0.491504\pi$
$541$	−22.6303	−	22.6303i	−0.972954	−	0.972954i	−0.999644	+	0.0266894i	$0.991504\pi$
$542$	−12.2046			−0.524230
$543$	−6.68517	+	25.0586i	−0.286888	+	1.07537i
$544$	26.1684	+	26.1684i	1.12196	+	1.12196i
$545$		0			0
$546$	−16.4704	+	0.804547i	−0.704870	+	0.0344314i
$547$		−	38.6695i		−	1.65339i	−0.562652	−	0.826694i	$-0.690219\pi$
$547$		−	38.6695i		−	1.65339i	0.562652	−	0.826694i	$-0.309781\pi$
$548$	−7.33448	+	7.33448i	−0.313313	+	0.313313i
$549$	−3.37050	−	1.93618i	−0.143849	−	0.0826341i
$550$		0			0
$551$	0.253557	+	0.253557i	0.0108019	+	0.0108019i
$552$	−8.28812	+	4.79720i	−0.352766	+	0.204182i
$553$	−27.6644	+	27.6644i	−1.17641	+	1.17641i
$554$	2.31455	−	2.31455i	0.0983358	−	0.0983358i
$555$		0			0
$556$		−	12.7106i		−	0.539051i
$557$	7.82191	+	7.82191i	0.331425	+	0.331425i	0.853128	−	0.521702i	$-0.174703\pi$
$557$	7.82191	+	7.82191i	0.331425	+	0.331425i	−0.521702	+	0.853128i	$0.674703\pi$
$558$	−4.31049	+	7.50369i	−0.182477	+	0.317657i
$559$	3.88204	+	12.1391i	0.164193	+	0.513428i
$560$		0			0
$561$	−19.5785	−	33.8258i	−0.826605	−	1.42813i
$562$		−	1.72797i		−	0.0728899i
$563$		−	37.4306i		−	1.57751i	−0.614708	−	0.788755i	$-0.710726\pi$
$563$		−	37.4306i		−	1.57751i	0.614708	−	0.788755i	$-0.289274\pi$
$564$	−27.0505	+	15.6569i	−1.13903	+	0.659276i
$565$		0			0
$566$	5.75652	−	5.75652i	0.241965	−	0.241965i
$567$	35.6590	+	9.38845i	1.49754	+	0.394278i
$568$		−	9.68942i		−	0.406559i
$569$	2.32113			0.0973066			0.0486533	−	0.998816i	$-0.484507\pi$
$569$	2.32113			0.0973066			0.0486533	+	0.998816i	$0.484507\pi$
$570$		0			0
$571$		−	12.7963i		−	0.535507i	−0.963487	−	0.267753i	$-0.913719\pi$
$571$		−	12.7963i		−	0.535507i	0.963487	−	0.267753i	$-0.0862812\pi$
$572$	9.10246	−	17.6615i	0.380593	−	0.738464i
$573$	−5.83860	+	21.8853i	−0.243911	+	0.914271i
$574$	−5.62360	+	5.62360i	−0.234725	+	0.234725i
$575$		0			0
$576$	−0.470735	+	0.819454i	−0.0196139	+	0.0341439i
$577$	−0.396526	−	0.396526i	−0.0165076	−	0.0165076i	0.698805	−	0.715312i	$-0.253716\pi$
$577$	−0.396526	−	0.396526i	−0.0165076	−	0.0165076i	−0.715312	+	0.698805i	$0.753716\pi$
$578$	−11.4397	+	11.4397i	−0.475828	+	0.475828i
$579$	17.9105	−	10.3667i	0.744336	−	0.430824i
$580$		0			0
$581$			15.2113i			0.631069i
$582$	10.3338	+	2.75687i	0.428349	+	0.114276i
$583$	22.9348	−	22.9348i	0.949863	−	0.949863i
$584$	−19.3115			−0.799117
$585$		0			0
$586$	−17.9607			−0.741949
$587$	−4.38510	+	4.38510i	−0.180992	+	0.180992i	−0.791788	−	0.610796i	$-0.790850\pi$
$587$	−4.38510	+	4.38510i	−0.180992	+	0.180992i	0.610796	+	0.791788i	$0.290850\pi$
$588$	25.9531	+	6.92381i	1.07029	+	0.285533i
$589$		−	22.0275i		−	0.907626i
$590$		0			0
$591$	−13.3912	+	7.75086i	−0.550839	+	0.318828i
$592$	10.6562	−	10.6562i	0.437969	−	0.437969i
$593$	−4.95766	−	4.95766i	−0.203587	−	0.203587i	0.597948	−	0.801535i	$-0.295983\pi$
$593$	−4.95766	−	4.95766i	−0.203587	−	0.203587i	−0.801535	+	0.597948i	$0.795983\pi$
$594$	8.20786	−	8.26168i	0.336773	−	0.338981i
$595$		0			0
$596$	1.84162	−	1.84162i	0.0754359	−	0.0754359i
$597$	9.79731	−	36.7240i	0.400977	−	1.50302i
$598$	2.54767	−	4.94325i	0.104182	−	0.202144i
$599$			5.16408i			0.210998i	0.994419	+	0.105499i	$0.0336441\pi$
$599$			5.16408i			0.210998i	−0.994419	+	0.105499i	$0.966356\pi$
$600$		0			0
$601$	28.3815			1.15770			0.578852	−	0.815432i	$-0.303501\pi$
$601$	28.3815			1.15770			0.578852	+	0.815432i	$0.303501\pi$
$602$			9.33358i			0.380408i
$603$	1.02140	+	3.77898i	0.0415948	+	0.153892i
$604$	−8.73679	+	8.73679i	−0.355495	+	0.355495i
$605$		0			0
$606$	3.05921	−	1.77068i	0.124272	−	0.0719291i
$607$		−	35.8341i		−	1.45446i	−0.686394	−	0.727230i	$-0.740808\pi$
$607$		−	35.8341i		−	1.45446i	0.686394	−	0.727230i	$-0.259192\pi$
$608$		−	28.0695i		−	1.13837i
$609$	−0.259013	−	0.447498i	−0.0104957	−	0.0181335i
$610$		0			0
$611$	18.8095	−	36.4961i	0.760951	−	1.47647i
$612$	26.7475	+	15.3651i	1.08120	+	0.621095i
$613$	−5.88345	−	5.88345i	−0.237630	−	0.237630i	0.578238	−	0.815868i	$-0.303741\pi$
$613$	−5.88345	−	5.88345i	−0.237630	−	0.237630i	−0.815868	+	0.578238i	$0.803741\pi$
$614$			7.67070i			0.309564i
$615$		0			0
$616$	23.2754	−	23.2754i	0.937794	−	0.937794i
$617$	−30.1305	+	30.1305i	−1.21301	+	1.21301i	−0.242977	+	0.970032i	$0.578124\pi$
$617$	−30.1305	+	30.1305i	−1.21301	+	1.21301i	−0.970032	+	0.242977i	$0.921876\pi$
$618$	−13.2775	+	7.68508i	−0.534100	+	0.309139i
$619$	8.02687	+	8.02687i	0.322627	+	0.322627i	0.849774	−	0.527147i	$-0.176738\pi$
$619$	8.02687	+	8.02687i	0.322627	+	0.322627i	−0.527147	+	0.849774i	$0.676738\pi$
$620$		0			0
$621$	−8.76445	+	8.82192i	−0.351705	+	0.354012i
$622$	−11.3852	+	11.3852i	−0.456506	+	0.456506i
$623$			40.7395i			1.63219i
$624$	0.511998	+	10.4815i	0.0204963	+	0.419594i
$625$		0			0
$626$	3.75019	+	3.75019i	0.149888	+	0.149888i
$627$	−7.64119	+	28.6421i	−0.305160	+	1.14385i
$628$	32.9119			1.31333
$629$	41.1483	+	41.1483i	1.64069	+	1.64069i
$630$		0			0
$631$	−14.4365	−	14.4365i	−0.574709	−	0.574709i	0.358732	−	0.933441i	$-0.383209\pi$
$631$	−14.4365	−	14.4365i	−0.574709	−	0.574709i	−0.933441	+	0.358732i	$0.883209\pi$
$632$	−15.5990	−	15.5990i	−0.620497	−	0.620497i
$633$	0.733973	+	0.195811i	0.0291728	+	0.00778278i
$634$		−	5.10500i		−	0.202745i
$635$		0			0
$636$	−6.59861	+	24.7341i	−0.261652	+	0.980771i
$637$	−33.6089	+	10.7480i	−1.33163	+	0.425853i
$638$	−0.163298			−0.00646502
$639$	−3.28303	−	12.1465i	−0.129875	−	0.480508i
$640$		0			0
$641$	−13.1832			−0.520706			−0.260353	−	0.965513i	$-0.583839\pi$
$641$	−13.1832			−0.520706			−0.260353	+	0.965513i	$0.583839\pi$
$642$	8.70574	−	5.03891i	0.343588	−	0.198870i
$643$	26.1092	+	26.1092i	1.02964	+	1.02964i	0.999547	+	0.0300976i	$0.00958181\pi$
$643$	26.1092	+	26.1092i	1.02964	+	1.02964i	0.0300976	+	0.999547i	$0.490418\pi$
$644$	−10.9870	+	10.9870i	−0.432947	+	0.432947i
$645$		0			0
$646$	20.5808			0.809741
$647$		−	24.4734i		−	0.962150i	−0.876679	−	0.481075i	$-0.840246\pi$
$647$		−	24.4734i		−	0.962150i	0.876679	−	0.481075i	$-0.159754\pi$
$648$	−5.29384	+	20.1069i	−0.207962	+	0.789875i
$649$			16.2814i			0.639099i
$650$		0			0
$651$	−8.18718	+	30.6887i	−0.320881	+	1.20278i
$652$	−2.83657	−	2.83657i	−0.111089	−	0.111089i
$653$	27.4272			1.07331			0.536655	−	0.843802i	$-0.319688\pi$
$653$	27.4272			1.07331			0.536655	+	0.843802i	$0.319688\pi$
$654$	2.39069	−	8.96123i	0.0934835	−	0.350412i
$655$		0			0
$656$	3.57875	+	3.57875i	0.139727	+	0.139727i
$657$	−24.2087	+	6.54325i	−0.944470	+	0.255277i
$658$	21.2619	−	21.2619i	0.828875	−	0.828875i
$659$			28.8992i			1.12575i	0.826541	+	0.562877i	$0.190305\pi$
$659$			28.8992i			1.12575i	−0.826541	+	0.562877i	$0.809695\pi$
$660$		0			0
$661$	2.27091	+	2.27091i	0.0883282	+	0.0883282i	0.749890	−	0.661562i	$-0.230106\pi$
$661$	2.27091	+	2.27091i	0.0883282	+	0.0883282i	−0.661562	+	0.749890i	$0.730106\pi$
$662$		−	0.811807i		−	0.0315518i
$663$	−40.4733	+	1.97704i	−1.57185	+	0.0767818i
$664$	−8.57713			−0.332857
$665$		0			0
$666$	−8.63716	+	15.0356i	−0.334683	+	0.582616i
$667$	0.174371			0.00675168
$668$	11.1898	−	11.1898i	0.432946	−	0.432946i
$669$	1.95932	+	3.38512i	0.0757517	+	0.130876i
$670$		0			0
$671$	−3.18609	+	3.18609i	−0.122998	+	0.122998i
$672$	−10.4329	+	39.1064i	−0.402458	+	1.50856i
$673$	−35.6852			−1.37556			−0.687782	−	0.725918i	$-0.741415\pi$
$673$	−35.6852			−1.37556			−0.687782	+	0.725918i	$0.741415\pi$
$674$	0.164978	−	0.164978i	0.00635472	−	0.00635472i
$675$		0			0
$676$	−11.9534	−	16.7777i	−0.459746	−	0.645296i
$677$	−2.22785			−0.0856231			−0.0428116	−	0.999083i	$-0.513632\pi$
$677$	−2.22785			−0.0856231			−0.0428116	+	0.999083i	$0.513632\pi$
$678$	0.629358	−	0.364275i	0.0241704	−	0.0139899i
$679$	39.2552			1.50648
$680$		0			0
$681$	27.7635	−	16.0696i	1.06390	−	0.615788i
$682$	7.09315	+	7.09315i	0.271611	+	0.271611i
$683$	−5.68940	−	5.68940i	−0.217699	−	0.217699i	0.589829	−	0.807528i	$-0.299195\pi$
$683$	−5.68940	−	5.68940i	−0.217699	−	0.217699i	−0.807528	+	0.589829i	$0.799195\pi$
$684$	−6.10467	−	22.5860i	−0.233418	−	0.863597i
$685$		0			0
$686$	−7.35777			−0.280921
$687$	3.17674	+	5.48847i	0.121200	+	0.209398i
$688$	5.93971			0.226449
$689$	−10.2432	−	32.0303i	−0.390236	−	1.22026i
$690$		0			0
$691$	10.3521	−	10.3521i	0.393813	−	0.393813i	−0.482231	−	0.876044i	$-0.660174\pi$
$691$	10.3521	−	10.3521i	0.393813	−	0.393813i	0.876044	+	0.482231i	$0.160174\pi$
$692$	35.8215			1.36173
$693$	21.2914	−	37.0640i	0.808794	−	1.40795i
$694$	2.71954	−	2.71954i	0.103232	−	0.103232i
$695$		0			0
$696$	0.252329	−	0.146049i	0.00956451	−	0.00553598i
$697$	−13.8191	+	13.8191i	−0.523434	+	0.523434i
$698$	12.5263			0.474128
$699$	−2.97613	+	11.1557i	−0.112567	+	0.421946i
$700$		0			0
$701$	−12.8424			−0.485052			−0.242526	−	0.970145i	$-0.577976\pi$
$701$	−12.8424			−0.485052			−0.242526	+	0.970145i	$0.577976\pi$
$702$	−3.71542	−	11.4885i	−0.140230	−	0.433606i
$703$		−	44.1377i		−	1.66468i
$704$	0.774621	+	0.774621i	0.0291946	+	0.0291946i
$705$		0			0
$706$			12.5980i			0.474134i
$707$	9.17373	−	9.17373i	0.345014	−	0.345014i
$708$	−6.43717	−	11.1215i	−0.241924	−	0.417972i
$709$	4.43471	+	4.43471i	0.166549	+	0.166549i	0.785461	−	0.618912i	$-0.212426\pi$
$709$	4.43471	+	4.43471i	0.166549	+	0.166549i	−0.618912	+	0.785461i	$0.712426\pi$
$710$		0			0
$711$	−24.8401	−	14.2694i	−0.931576	−	0.535143i
$712$	−22.9717			−0.860900
$713$	−7.57415	−	7.57415i	−0.283654	−	0.283654i
$714$	−28.6732	−	7.64949i	−1.07307	−	0.286275i
$715$		0			0
$716$			22.7187i			0.849036i
$717$	−1.41947	−	2.45242i	−0.0530110	−	0.0915872i
$718$			1.08577i			0.0405204i
$719$	−47.3354			−1.76531			−0.882656	−	0.470019i	$-0.844247\pi$
$719$	−47.3354			−1.76531			−0.882656	+	0.470019i	$0.844247\pi$
$720$		0			0
$721$	−39.8156	+	39.8156i	−1.48281	+	1.48281i
$722$	−2.37937	−	2.37937i	−0.0885509	−	0.0885509i
$723$	4.83317	+	8.35028i	0.179748	+	0.310550i
$724$	−23.7278			−0.881835
$725$		0			0
$726$	−0.611482	−	1.05646i	−0.0226942	−	0.0392089i
$727$	−12.6597			−0.469523			−0.234762	−	0.972053i	$-0.575431\pi$
$727$	−12.6597			−0.469523			−0.234762	+	0.972053i	$0.575431\pi$
$728$	−10.3953	−	32.5060i	−0.385277	−	1.20475i
$729$	0.176474	+	26.9994i	0.00653606	+	0.999979i
$730$		0			0
$731$			22.9357i			0.848308i
$732$	0.916677	−	3.43605i	0.0338813	−	0.127000i
$733$	34.2421	+	34.2421i	1.26476	+	1.26476i	0.948758	+	0.316003i	$0.102341\pi$
$733$	34.2421	+	34.2421i	1.26476	+	1.26476i	0.316003	+	0.948758i	$0.397659\pi$
$734$	10.8394	+	10.8394i	0.400088	+	0.400088i
$735$		0			0
$736$	−9.65171	−	9.65171i	−0.355767	−	0.355767i
$737$	4.53775			0.167150
$738$	−5.04948	−	2.90067i	−0.185874	−	0.106775i
$739$	−0.527783	−	0.527783i	−0.0194148	−	0.0194148i	0.697333	−	0.716748i	$-0.254370\pi$
$739$	−0.527783	−	0.527783i	−0.0194148	−	0.0194148i	−0.716748	+	0.697333i	$0.754370\pi$
$740$		0			0
$741$	22.7672	+	20.6465i	0.836374	+	0.758469i
$742$		−	24.6277i		−	0.904113i
$743$	−15.9143	+	15.9143i	−0.583840	+	0.583840i	−0.935956	−	0.352116i	$-0.885462\pi$
$743$	−15.9143	+	15.9143i	−0.583840	+	0.583840i	0.352116	+	0.935956i	$0.385462\pi$
$744$	−17.3043	−	4.61648i	−0.634408	−	0.169249i
$745$		0			0
$746$	−12.3468	−	12.3468i	−0.452050	−	0.452050i
$747$	−10.7522	+	2.90616i	−0.393401	+	0.106331i
$748$	25.2841	−	25.2841i	0.924477	−	0.924477i
$749$	26.1061	−	26.1061i	0.953896	−	0.953896i
$750$		0			0
$751$			44.2811i			1.61584i	0.589292	+	0.807920i	$0.299407\pi$
$751$			44.2811i			1.61584i	−0.589292	+	0.807920i	$0.700593\pi$
$752$	−13.5307	−	13.5307i	−0.493412	−	0.493412i
$753$	28.4864	+	7.59966i	1.03810	+	0.276947i
$754$	−0.0775630	+	0.150496i	−0.00282468	+	0.00548073i
$755$		0			0
$756$	0.110251	+	33.7358i	0.00400978	+	1.22696i
$757$			22.8856i			0.831790i	0.909413	+	0.415895i	$0.136532\pi$
$757$			22.8856i			0.831790i	−0.909413	+	0.415895i	$0.863468\pi$
$758$		−	8.70710i		−	0.316256i
$759$	7.22116	+	12.4760i	0.262111	+	0.452850i
$760$		0			0
$761$	−7.52971	+	7.52971i	−0.272952	+	0.272952i	−0.830287	−	0.557336i	$-0.811824\pi$
$761$	−7.52971	+	7.52971i	−0.272952	+	0.272952i	0.557336	+	0.830287i	$0.311824\pi$
$762$	3.53155	−	2.04407i	0.127935	−	0.0740490i
$763$		−	34.0413i		−	1.23238i
$764$	−20.7230			−0.749732
$765$		0			0
$766$		−	18.2054i		−	0.657786i
$767$	15.0049	+	7.73331i	0.541797	+	0.279234i
$768$	−13.1383	−	3.50507i	−0.474089	−	0.126478i
$769$	−36.8433	+	36.8433i	−1.32860	+	1.32860i	−0.422015	+	0.906589i	$0.638677\pi$
$769$	−36.8433	+	36.8433i	−1.32860	+	1.32860i	−0.906589	+	0.422015i	$0.861323\pi$
$770$		0			0
$771$	7.04394	−	26.4034i	0.253681	−	0.950894i
$772$	13.3877	+	13.3877i	0.481835	+	0.481835i
$773$	10.1075	−	10.1075i	0.363542	−	0.363542i	−0.501573	−	0.865115i	$-0.667245\pi$
$773$	10.1075	−	10.1075i	0.363542	−	0.363542i	0.865115	+	0.501573i	$0.167245\pi$
$774$	−6.59749	+	1.78321i	−0.237142	+	0.0640961i
$775$		0			0
$776$			22.1347i			0.794591i
$777$	−16.4051	+	61.4926i	−0.588530	+	2.20603i
$778$	−16.0106	+	16.0106i	−0.574008	+	0.574008i
$779$	14.8230			0.531089
$780$		0			0
$781$	−14.5854			−0.521905
$782$	7.07672	−	7.07672i	0.253063	−	0.253063i
$783$	0.266831	−	0.268581i	0.00953576	−	0.00959829i
$784$			16.4450i			0.587321i
$785$		0			0
$786$	−5.91294	−	10.2158i	−0.210907	−	0.364385i
$787$	−20.3419	+	20.3419i	−0.725112	+	0.725112i	−0.969642	−	0.244530i	$-0.921366\pi$
$787$	−20.3419	+	20.3419i	−0.725112	+	0.725112i	0.244530	+	0.969642i	$0.421366\pi$
$788$	−10.0096	−	10.0096i	−0.356577	−	0.356577i
$789$	8.75375	+	2.33534i	0.311642	+	0.0831404i
$790$		0			0
$791$	1.88727	−	1.88727i	0.0671036	−	0.0671036i
$792$	20.8992	+	12.0055i	0.742621	+	0.426598i
$793$	1.42298	+	4.44964i	0.0505316	+	0.158011i
$794$		−	11.9210i		−	0.423059i
$795$		0			0
$796$	34.7737			1.23252
$797$		−	22.8088i		−	0.807930i	−0.914774	−	0.403965i	$-0.867632\pi$
$797$		−	22.8088i		−	0.807930i	0.914774	−	0.403965i	$-0.132368\pi$
$798$	11.2755	+	19.4808i	0.399149	+	0.689611i
$799$	52.2475	−	52.2475i	1.84838	−	1.84838i
$800$		0			0
$801$	−28.7970	+	7.78341i	−1.01749	+	0.275013i
$802$		−	1.43960i		−	0.0508341i
$803$			29.0694i			1.02584i
$804$	−3.09966	+	1.79409i	−0.109316	+	0.0632728i
$805$		0			0
$806$	9.90617	−	3.16797i	0.348930	−	0.111587i
$807$	11.0341	−	41.3599i	0.388418	−	1.45594i
$808$	5.17277	+	5.17277i	0.181977	+	0.181977i
$809$			2.21292i			0.0778020i	0.999243	+	0.0389010i	$0.0123857\pi$
$809$			2.21292i			0.0778020i	−0.999243	+	0.0389010i	$0.987614\pi$
$810$		0			0
$811$	−10.2655	+	10.2655i	−0.360469	+	0.360469i	−0.863985	−	0.503517i	$-0.832039\pi$
$811$	−10.2655	+	10.2655i	−0.360469	+	0.360469i	0.503517	+	0.863985i	$0.332039\pi$
$812$	0.334495	−	0.334495i	0.0117385	−	0.0117385i
$813$	−16.4309	−	28.3876i	−0.576255	−	0.995597i
$814$	14.2129	+	14.2129i	0.498163	+	0.498163i
$815$		0			0
$816$	−4.86798	+	18.2470i	−0.170413	+	0.638774i
$817$	12.3010	−	12.3010i	0.430357	−	0.430357i
$818$		−	8.69948i		−	0.304170i
$819$	−24.0453	−	37.2269i	−0.840212	−	1.30081i
$820$		0			0
$821$	0.236912	+	0.236912i	0.00826830	+	0.00826830i	0.711229	−	0.702961i	$-0.248139\pi$
$821$	0.236912	+	0.236912i	0.00826830	+	0.00826830i	−0.702961	+	0.711229i	$0.748139\pi$
$822$	7.05983	+	1.88344i	0.246240	+	0.0656924i
$823$	−9.65610			−0.336591			−0.168295	−	0.985737i	$-0.553826\pi$
$823$	−9.65610			−0.336591			−0.168295	+	0.985737i	$0.553826\pi$
$824$	−22.4507	−	22.4507i	−0.782107	−	0.782107i
$825$		0			0
$826$	8.74158	+	8.74158i	0.304159	+	0.304159i
$827$	6.76442	+	6.76442i	0.235222	+	0.235222i	0.814868	−	0.579646i	$-0.196809\pi$
$827$	6.76442	+	6.76442i	0.235222	+	0.235222i	−0.579646	+	0.814868i	$0.696809\pi$
$828$	−9.86529	−	5.66711i	−0.342843	−	0.196946i
$829$		−	10.8499i		−	0.376834i	−0.982089	−	0.188417i	$-0.939664\pi$
$829$		−	10.8499i		−	0.376834i	0.982089	−	0.188417i	$-0.0603356\pi$
$830$		0			0
$831$	8.49966	+	2.26756i	0.294850	+	0.0786607i
$832$	1.08182	−	0.345964i	0.0375054	−	0.0119941i
$833$	−63.5010			−2.20018
$834$	−7.74933	+	4.48534i	−0.268337	+	0.155315i
$835$		0			0
$836$	−27.1210			−0.937998
$837$	−23.2566	+	0.0760042i	−0.803867	+	0.00262709i
$838$	16.5937	+	16.5937i	0.573221	+	0.573221i
$839$	34.4849	−	34.4849i	1.19055	−	1.19055i	0.213640	−	0.976912i	$-0.431468\pi$
$839$	34.4849	−	34.4849i	1.19055	−	1.19055i	0.976912	−	0.213640i	$-0.0685319\pi$
$840$		0			0
$841$	28.9947			0.999817
$842$			4.25595i			0.146670i
$843$	4.01923	−	2.32634i	0.138430	−	0.0801235i
$844$			0.694993i			0.0239227i
$845$		0			0
$846$	19.0912	+	10.9669i	0.656370	+	0.377051i
$847$	−3.16803	−	3.16803i	−0.108855	−	0.108855i
$848$	−15.6726			−0.538199
$849$	21.1395	+	5.63964i	0.725506	+	0.193552i
$850$		0			0
$851$	−15.1767	−	15.1767i	−0.520252	−	0.520252i
$852$	9.96300	−	5.76662i	0.341327	−	0.197561i
$853$	−30.7565	+	30.7565i	−1.05308	+	1.05308i	−0.0545730	+	0.998510i	$0.517380\pi$
$853$	−30.7565	+	30.7565i	−1.05308	+	1.05308i	−0.998510	+	0.0545730i	$0.982620\pi$
$854$			3.42128i			0.117074i
$855$		0			0
$856$	14.7204	+	14.7204i	0.503132	+	0.503132i
$857$		−	38.8679i		−	1.32770i	−0.747864	−	0.663852i	$-0.768921\pi$
$857$		−	38.8679i		−	1.32770i	0.747864	−	0.663852i	$-0.231079\pi$
$858$	−13.9798	+	0.682885i	−0.477263	+	0.0233133i
$859$	3.20072			0.109207			0.0546036	−	0.998508i	$-0.482610\pi$
$859$	3.20072			0.109207			0.0546036	+	0.998508i	$0.482610\pi$
$860$		0			0
$861$	−20.6514	−	5.50942i	−0.703798	−	0.187761i
$862$	3.17930			0.108288
$863$	24.0668	−	24.0668i	0.819244	−	0.819244i	−0.166755	−	0.985998i	$-0.553329\pi$
$863$	24.0668	−	24.0668i	0.819244	−	0.819244i	0.985998	+	0.166755i	$0.0533288\pi$
$864$	−29.6358	+	0.0968519i	−1.00823	+	0.00329497i
$865$		0			0
$866$	0.0299557	−	0.0299557i	0.00101794	−	0.00101794i
$867$	−42.0097	−	11.2074i	−1.42672	−	0.380624i
$868$	−29.0589			−0.986322
$869$	−23.4811	+	23.4811i	−0.796540	+	0.796540i
$870$		0			0
$871$	2.15534	−	4.18200i	0.0730308	−	0.141702i
$872$	19.1948			0.650016
$873$	7.49983	+	27.7478i	0.253831	+	0.939120i
$874$	−7.59084			−0.256764
$875$		0			0
$876$	−11.4932	−	19.8568i	−0.388319	−	0.670899i
$877$	34.6511	+	34.6511i	1.17008	+	1.17008i	0.982189	+	0.187895i	$0.0601664\pi$
$877$	34.6511	+	34.6511i	1.17008	+	1.17008i	0.187895	+	0.982189i	$0.439834\pi$
$878$	4.35908	+	4.35908i	0.147112	+	0.147112i
$879$	−24.1803	−	41.7763i	−0.815580	−	1.40908i
$880$		0			0
$881$	−5.44243			−0.183360			−0.0916800	−	0.995789i	$-0.529224\pi$
$881$	−5.44243			−0.183360			−0.0916800	+	0.995789i	$0.529224\pi$
$882$	−4.93709	−	18.2662i	−0.166240	−	0.615054i
$883$	2.38247			0.0801763			0.0400882	−	0.999196i	$-0.487236\pi$
$883$	2.38247			0.0801763			0.0400882	+	0.999196i	$0.487236\pi$
$884$	−11.2925	−	35.3113i	−0.379806	−	1.18765i
$885$		0			0
$886$	15.9581	−	15.9581i	0.536124	−	0.536124i
$887$	−36.3502			−1.22052			−0.610260	−	0.792201i	$-0.708935\pi$
$887$	−36.3502			−1.22052			−0.610260	+	0.792201i	$0.708935\pi$
$888$	−34.6737	−	9.25031i	−1.16357	−	0.310420i
$889$	10.5901	−	10.5901i	0.355182	−	0.355182i
$890$		0			0
$891$	30.2667	+	7.96875i	1.01397	+	0.266963i
$892$	−2.53030	+	2.53030i	−0.0847209	+	0.0847209i
$893$	−56.0433			−1.87542
$894$	−1.77266	−	0.472915i	−0.0592867	−	0.0158166i
$895$		0			0
$896$	−45.9038			−1.53354
$897$	14.9278	−	0.729193i	0.498425	−	0.0243470i
$898$		−	21.1674i		−	0.706365i
$899$	0.230593	+	0.230593i	0.00769070	+	0.00769070i
$900$		0			0
$901$		−	60.5185i		−	2.01616i
$902$	−4.77321	+	4.77321i	−0.158931	+	0.158931i
$903$	−21.7098	+	12.5657i	−0.722456	+	0.418160i
$904$	1.06417	+	1.06417i	0.0353938	+	0.0353938i
$905$		0			0
$906$	8.40964	+	2.24354i	0.279392	+	0.0745366i
$907$	17.6809			0.587085			0.293542	−	0.955946i	$-0.405166\pi$
$907$	17.6809			0.587085			0.293542	+	0.955946i	$0.405166\pi$
$908$	20.7526	+	20.7526i	0.688699	+	0.688699i
$909$	8.23717	+	4.73183i	0.273210	+	0.156945i
$910$		0			0
$911$		−	5.92923i		−	0.196444i	−0.995165	−	0.0982220i	$-0.968684\pi$
$911$		−	5.92923i		−	0.196444i	0.995165	−	0.0982220i	$-0.0313155\pi$
$912$	12.3972	−	7.17552i	0.410511	−	0.237605i
$913$			12.9111i			0.427293i
$914$	5.33439			0.176446
$915$		0			0
$916$	−4.10251	+	4.10251i	−0.135551	+	0.135551i
$917$	−30.6343	−	30.6343i	−1.01163	−	1.01163i
$918$	−0.0710126	−	21.7292i	−0.00234377	−	0.717172i
$919$	22.9927			0.758459			0.379230	−	0.925303i	$-0.376189\pi$
$919$	22.9927			0.758459			0.379230	+	0.925303i	$0.376189\pi$
$920$		0			0
$921$	−17.8419	+	10.3270i	−0.587912	+	0.340286i
$922$	−22.1373			−0.729054
$923$	−6.92775	+	13.4419i	−0.228030	+	0.442446i
$924$	37.7849	+	10.0803i	1.24303	+	0.331619i
$925$		0			0
$926$		−	10.4642i		−	0.343876i
$927$	−35.7507	−	20.5370i	−1.17421	−	0.674523i
$928$	0.293843	+	0.293843i	0.00964588	+	0.00964588i
$929$	31.4998	+	31.4998i	1.03348	+	1.03348i	0.999420	+	0.0340553i	$0.0108422\pi$
$929$	31.4998	+	31.4998i	1.03348	+	1.03348i	0.0340553	+	0.999420i	$0.489158\pi$
$930$		0			0
$931$	34.0572	+	34.0572i	1.11618	+	1.11618i
$932$	−10.5632			−0.346009
$933$	−41.8097	−	11.1541i	−1.36879	−	0.365168i
$934$	9.98280	+	9.98280i	0.326647	+	0.326647i
$935$		0			0
$936$	20.9910	−	13.5584i	0.686113	−	0.443170i
$937$			40.0311i			1.30776i	0.756599	+	0.653879i	$0.226859\pi$
$937$			40.0311i			1.30776i	−0.756599	+	0.653879i	$0.773141\pi$
$938$	2.43635	−	2.43635i	0.0795497	−	0.0795497i
$939$	−3.67405	+	13.7717i	−0.119898	+	0.449423i
$940$		0			0
$941$	41.8084	+	41.8084i	1.36292	+	1.36292i	0.870178	+	0.492738i	$0.164004\pi$
$941$	41.8084	+	41.8084i	1.36292	+	1.36292i	0.492738	+	0.870178i	$0.335996\pi$
$942$	−11.6140	−	20.0655i	−0.378404	−	0.653770i
$943$	5.09689	−	5.09689i	0.165978	−	0.165978i
$944$	5.56297	−	5.56297i	0.181059	−	0.181059i
$945$		0			0
$946$			7.92218i			0.257572i
$947$	−33.2177	−	33.2177i	−1.07943	−	1.07943i	−0.996560	−	0.0828703i	$-0.973591\pi$
$947$	−33.2177	−	33.2177i	−1.07943	−	1.07943i	−0.0828703	−	0.996560i	$-0.526409\pi$
$948$	6.75577	−	25.3232i	0.219417	−	0.822459i
$949$	26.7905	+	13.8074i	0.869655	+	0.448206i
$950$		0			0
$951$	11.8741	−	6.87280i	0.385046	−	0.222866i
$952$		−	61.4173i		−	1.99055i
$953$		−	9.16362i		−	0.296839i	−0.988925	−	0.148419i	$-0.952581\pi$
$953$		−	9.16362i		−	0.296839i	0.988925	−	0.148419i	$-0.0474185\pi$
$954$	17.4082	−	4.70520i	0.563613	−	0.152336i
$955$		0			0
$956$	1.83313	−	1.83313i	0.0592876	−	0.0592876i
$957$	−0.219846	−	0.379828i	−0.00710661	−	0.0122781i
$958$			18.1963i			0.587897i
$959$	26.8184			0.866011
$960$		0			0
$961$			10.9675i			0.353791i
$962$	19.8495	−	6.34783i	0.639975	−	0.204662i
$963$	23.4409	+	13.4656i	0.755372	+	0.433923i
$964$	−6.24165	+	6.24165i	−0.201030	+	0.201030i
$965$		0			0
$966$	10.5756	+	2.82137i	0.340263	+	0.0907760i
$967$	27.6848	+	27.6848i	0.890282	+	0.890282i	0.994549	−	0.104268i	$-0.0332498\pi$
$967$	27.6848	+	27.6848i	0.890282	+	0.890282i	−0.104268	+	0.994549i	$0.533250\pi$
$968$	1.78635	−	1.78635i	0.0574153	−	0.0574153i
$969$	27.7077	+	47.8707i	0.890100	+	1.53783i
$970$		0			0
$971$			22.0979i			0.709156i	0.935026	+	0.354578i	$0.115376\pi$
$971$			22.0979i			0.709156i	−0.935026	+	0.354578i	$0.884624\pi$
$972$	−23.8253	+	6.52325i	−0.764195	+	0.209233i
$973$	−23.2381	+	23.2381i	−0.744979	+	0.744979i
$974$	11.1289			0.356593
$975$		0			0
$976$	2.17723			0.0696915
$977$	−40.2412	+	40.2412i	−1.28743	+	1.28743i	−0.351086	+	0.936343i	$0.614188\pi$
$977$	−40.2412	+	40.2412i	−1.28743	+	1.28743i	−0.936343	+	0.351086i	$0.885812\pi$
$978$	−0.728409	+	2.73036i	−0.0232920	+	0.0873071i
$979$			34.5790i			1.10515i
$980$		0			0
$981$	24.0622	−	6.50368i	0.768248	−	0.207647i
$982$	10.8303	−	10.8303i	0.345608	−	0.345608i
$983$	−10.0169	−	10.0169i	−0.319490	−	0.319490i	0.529081	−	0.848571i	$-0.322537\pi$
$983$	−10.0169	−	10.0169i	−0.319490	−	0.319490i	−0.848571	+	0.529081i	$0.822537\pi$
$984$	3.10658	−	11.6447i	0.0990342	−	0.371218i
$985$		0			0
$986$	−0.215448	+	0.215448i	−0.00686127	+	0.00686127i
$987$	78.0795	+	20.8302i	2.48530	+	0.663033i
$988$	−12.8819	+	24.9947i	−0.409828	+	0.795189i
$989$		−	8.45939i		−	0.268993i
$990$		0			0
$991$	−21.7567			−0.691124			−0.345562	−	0.938396i	$-0.612312\pi$
$991$	−21.7567			−0.691124			−0.345562	+	0.938396i	$0.612312\pi$
$992$		−	25.5273i		−	0.810493i
$993$	1.88825	−	1.09293i	0.0599218	−	0.0346830i
$994$	−7.83099	+	7.83099i	−0.248384	+	0.248384i
$995$		0			0
$996$	−5.10465	−	8.81931i	−0.161747	−	0.279450i
$997$		−	27.2276i		−	0.862308i	−0.902278	−	0.431154i	$-0.858107\pi$
$997$		−	27.2276i		−	0.862308i	0.902278	−	0.431154i	$-0.141893\pi$
$998$			12.4622i			0.394482i
$999$	−46.6006	+	0.152294i	−1.47438	+	0.00481837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.n.r.824.12		40
3.2	odd	2	inner	975.2.n.r.824.9		40
5.2	odd	4		975.2.o.p.551.12		40
5.3	odd	4		195.2.o.a.161.9	yes	40
5.4	even	2		975.2.n.q.824.9		40
13.8	odd	4		975.2.n.q.749.12		40
15.2	even	4		975.2.o.p.551.9		40
15.8	even	4		195.2.o.a.161.12	yes	40
15.14	odd	2		975.2.n.q.824.12		40
39.8	even	4		975.2.n.q.749.9		40
65.8	even	4		195.2.o.a.86.12	yes	40
65.34	odd	4	inner	975.2.n.r.749.9		40
65.47	even	4		975.2.o.p.476.9		40
195.8	odd	4		195.2.o.a.86.9	✓	40
195.47	odd	4		975.2.o.p.476.12		40
195.164	even	4	inner	975.2.n.r.749.12		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.o.a.86.9	✓	40	195.8	odd	4
195.2.o.a.86.12	yes	40	65.8	even	4
195.2.o.a.161.9	yes	40	5.3	odd	4
195.2.o.a.161.12	yes	40	15.8	even	4
975.2.n.q.749.9		40	39.8	even	4
975.2.n.q.749.12		40	13.8	odd	4
975.2.n.q.824.9		40	5.4	even	2
975.2.n.q.824.12		40	15.14	odd	2
975.2.n.r.749.9		40	65.34	odd	4	inner
975.2.n.r.749.12		40	195.164	even	4	inner
975.2.n.r.824.9		40	3.2	odd	2	inner
975.2.n.r.824.12		40	1.1	even	1	trivial
975.2.o.p.476.9		40	65.47	even	4
975.2.o.p.476.12		40	195.47	odd	4
975.2.o.p.551.9		40	15.2	even	4
975.2.o.p.551.12		40	5.2	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.455718 - 0.455718i) q^{2} +(1.67352 + 0.446465i) q^{3} +1.58464i q^{4} +(0.966114 - 0.559191i) q^{6} +(2.89711 - 2.89711i) q^{7} +(1.63358 + 1.63358i) q^{8} +(2.60134 + 1.49434i) q^{9} +(2.45902 - 2.45902i) q^{11} +(-0.707488 + 2.65193i) q^{12} +(-1.09825 - 3.43422i) q^{13} -2.64053i q^{14} -1.68038 q^{16} -6.48865i q^{17} +(1.86647 - 0.504480i) q^{18} +(-3.48002 + 3.48002i) q^{19} +(6.14183 - 3.55491i) q^{21} -2.24123i q^{22} +2.39321i q^{23} +(2.00450 + 3.46318i) q^{24} +(-2.06553 - 1.06454i) q^{26} +(3.68622 + 3.66221i) q^{27} +(4.59088 + 4.59088i) q^{28} -0.0728607i q^{29} +(-3.16484 + 3.16484i) q^{31} +(-4.03295 + 4.03295i) q^{32} +(5.21308 - 3.01735i) q^{33} +(-2.95699 - 2.95699i) q^{34} +(-2.36799 + 4.12219i) q^{36} +(-6.34157 + 6.34157i) q^{37} +3.17182i q^{38} +(-0.304692 - 6.23756i) q^{39} +(-2.12973 - 2.12973i) q^{41} +(1.17890 - 4.41897i) q^{42} -3.53474 q^{43} +(3.89666 + 3.89666i) q^{44} +(1.09063 + 1.09063i) q^{46} +(8.05214 + 8.05214i) q^{47} +(-2.81215 - 0.750230i) q^{48} -9.78648i q^{49} +(2.89695 - 10.8589i) q^{51} +(5.44201 - 1.74034i) q^{52} +9.32683 q^{53} +(3.34881 - 0.0109441i) q^{54} +9.46535 q^{56} +(-7.37760 + 4.27018i) q^{57} +(-0.0332039 - 0.0332039i) q^{58} +(-3.31055 + 3.31055i) q^{59} -1.29568 q^{61} +2.88455i q^{62} +(11.8656 - 3.20711i) q^{63} +0.315013i q^{64} +(1.00063 - 3.75075i) q^{66} +(0.922676 + 0.922676i) q^{67} +10.2822 q^{68} +(-1.06849 + 4.00509i) q^{69} +(-2.96569 - 2.96569i) q^{71} +(1.80838 + 6.69063i) q^{72} +(-5.91079 + 5.91079i) q^{73} +5.77993i q^{74} +(-5.51460 - 5.51460i) q^{76} -14.2481i q^{77} +(-2.98142 - 2.70371i) q^{78} -9.54897 q^{79} +(4.53392 + 7.77455i) q^{81} -1.94111 q^{82} +(-2.62525 + 2.62525i) q^{83} +(5.63327 + 9.73260i) q^{84} +(-1.61084 + 1.61084i) q^{86} +(0.0325297 - 0.121934i) q^{87} +8.03402 q^{88} +(-7.03107 + 7.03107i) q^{89} +(-13.1311 - 6.76754i) q^{91} -3.79239 q^{92} +(-6.70942 + 3.88344i) q^{93} +7.33901 q^{94} +(-8.54979 + 4.94865i) q^{96} +(6.77490 + 6.77490i) q^{97} +(-4.45987 - 4.45987i) q^{98} +(10.0713 - 2.72214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{6} + 16 q^{7} + 24 q^{12} - 24 q^{13} - 64 q^{16} - 4 q^{18} + 16 q^{19} - 12 q^{21} - 8 q^{24} - 32 q^{28} + 32 q^{31} - 4 q^{33} + 16 q^{34} - 32 q^{37} + 8 q^{39} + 32 q^{43} - 40 q^{46}+ \cdots + 20 q^{99}+O(q^{100}) \) 40 * q + 12 * q^6 + 16 * q^7 + 24 * q^12 - 24 * q^13 - 64 * q^16 - 4 * q^18 + 16 * q^19 - 12 * q^21 - 8 * q^24 - 32 * q^28 + 32 * q^31 - 4 * q^33 + 16 * q^34 - 32 * q^37 + 8 * q^39 + 32 * q^43 - 40 * q^46 + 8 * q^52 + 32 * q^54 - 36 * q^57 - 24 * q^58 + 8 * q^61 + 8 * q^63 - 48 * q^66 - 32 * q^67 - 132 * q^72 - 64 * q^73 + 16 * q^76 + 108 * q^78 - 40 * q^79 + 72 * q^81 + 128 * q^82 - 124 * q^84 + 80 * q^88 + 8 * q^91 + 108 * q^93 + 32 * q^94 - 76 * q^96 + 24 * q^97 + 20 * q^99

Introduction

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