LMFDB - Embedded newform 756.2.o.a.359.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(179,756)]

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, 4]))

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

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

chi := DirichletCharacter("756.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.o (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			359.1
Character	$\chi$	$=$	756.359
Dual form			756.2.o.a.179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41419 + 0.00770275i) q^{2} +(1.99988 - 0.0217863i) q^{4} +2.17323i q^{5} +(-0.191082 - 2.63884i) q^{7} +(-2.82805 + 0.0462147i) q^{8} +O(q^{10})$	\(q+(-1.41419 + 0.00770275i) q^{2} +(1.99988 - 0.0217863i) q^{4} +2.17323i q^{5} +(-0.191082 - 2.63884i) q^{7} +(-2.82805 + 0.0462147i) q^{8} +(-0.0167398 - 3.07336i) q^{10} -1.58540 q^{11} +(1.44655 + 2.50550i) q^{13} +(0.290553 + 3.73036i) q^{14} +(3.99905 - 0.0871402i) q^{16} +(2.58107 - 1.49018i) q^{17} +(1.40642 + 0.811997i) q^{19} +(0.0473467 + 4.34619i) q^{20} +(2.24206 - 0.0122119i) q^{22} +5.43086 q^{23} +0.277087 q^{25} +(-2.06500 - 3.53211i) q^{26} +(-0.439632 - 5.27321i) q^{28} +(3.61383 + 2.08645i) q^{29} +(-2.97782 - 1.71924i) q^{31} +(-5.65476 + 0.154037i) q^{32} +(-3.63866 + 2.12729i) q^{34} +(5.73480 - 0.415265i) q^{35} +(-4.84724 + 8.39566i) q^{37} +(-1.99520 - 1.13749i) q^{38} +(-0.100435 - 6.14599i) q^{40} +(-8.56561 + 4.94536i) q^{41} +(8.83531 + 5.10107i) q^{43} +(-3.17061 + 0.0345401i) q^{44} +(-7.68028 + 0.0418325i) q^{46} +(0.953235 + 1.65105i) q^{47} +(-6.92698 + 1.00847i) q^{49} +(-0.391855 + 0.00213433i) q^{50} +(2.94751 + 4.97918i) q^{52} +(9.44107 - 5.45080i) q^{53} -3.44543i q^{55} +(0.662343 + 7.45395i) q^{56} +(-5.12673 - 2.92280i) q^{58} +(5.27736 - 9.14066i) q^{59} +(5.68603 + 9.84849i) q^{61} +(4.22445 + 2.40840i) q^{62} +(7.99573 - 0.261395i) q^{64} +(-5.44501 + 3.14368i) q^{65} +(5.00642 + 2.89046i) q^{67} +(5.12938 - 3.03642i) q^{68} +(-8.10691 + 0.631438i) q^{70} +2.73233 q^{71} +(2.24800 + 3.89365i) q^{73} +(6.79026 - 11.9104i) q^{74} +(2.83036 + 1.59326i) q^{76} +(0.302942 + 4.18362i) q^{77} +(5.14844 - 2.97245i) q^{79} +(0.189375 + 8.69084i) q^{80} +(12.0753 - 7.05966i) q^{82} +(-5.68306 + 9.84336i) q^{83} +(3.23851 + 5.60926i) q^{85} +(-12.5341 - 7.14584i) q^{86} +(4.48359 - 0.0732687i) q^{88} +(4.12683 + 2.38263i) q^{89} +(6.33520 - 4.29597i) q^{91} +(10.8611 - 0.118319i) q^{92} +(-1.36078 - 2.32756i) q^{94} +(-1.76465 + 3.05647i) q^{95} +(4.73593 - 8.20287i) q^{97} +(9.78831 - 1.47953i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 3 q^{2} + q^{4}+O(q^{10}) $ 88 * q + 3 * q^2 + q^4	$ 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) $ 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.41419	+	0.00770275i	−0.999985	+	0.00544667i
$2$	−1.41419	+	0.00770275i	−0.999985	+	0.00544667i
$3$		0			0
$3$		0			0
$4$	1.99988	−	0.0217863i	0.999941	−	0.0108932i
$5$			2.17323i			0.971896i	0.873988	+	0.485948i	$0.161526\pi$
$5$			2.17323i			0.971896i	−0.873988	+	0.485948i	$0.838474\pi$
$6$		0			0
$7$	−0.191082	−	2.63884i	−0.0722223	−	0.997389i
$7$	−0.191082	−	2.63884i	−0.0722223	−	0.997389i
$8$	−2.82805	+	0.0462147i	−0.999867	+	0.0163394i
$9$		0			0
$10$	−0.0167398	−	3.07336i	−0.00529360	−	0.971882i
$11$	−1.58540			−0.478016			−0.239008	−	0.971018i	$-0.576822\pi$
$11$	−1.58540			−0.478016			−0.239008	+	0.971018i	$0.576822\pi$
$12$		0			0
$13$	1.44655	+	2.50550i	0.401201	+	0.694900i	0.993871	−	0.110545i	$-0.0352597\pi$
$13$	1.44655	+	2.50550i	0.401201	+	0.694900i	−0.592671	+	0.805445i	$0.701926\pi$
$14$	0.290553	+	3.73036i	0.0776536	+	0.996980i
$15$		0			0
$16$	3.99905	−	0.0871402i	0.999763	−	0.0217850i
$17$	2.58107	−	1.49018i	0.626002	−	0.361423i	−0.153200	−	0.988195i	$-0.548958\pi$
$17$	2.58107	−	1.49018i	0.626002	−	0.361423i	0.779202	+	0.626773i	$0.215624\pi$
$18$		0			0
$19$	1.40642	+	0.811997i	0.322655	+	0.186285i	0.652575	−	0.757724i	$-0.273689\pi$
$19$	1.40642	+	0.811997i	0.322655	+	0.186285i	−0.329920	+	0.944009i	$0.607022\pi$
$20$	0.0473467	+	4.34619i	0.0105870	+	0.971839i
$21$		0			0
$22$	2.24206	−	0.0122119i	0.478009	−	0.00260359i
$23$	5.43086			1.13241			0.566206	−	0.824264i	$-0.308411\pi$
$23$	5.43086			1.13241			0.566206	+	0.824264i	$0.308411\pi$
$24$		0			0
$25$	0.277087			0.0554174
$26$	−2.06500	−	3.53211i	−0.404980	−	0.692704i
$27$		0			0
$28$	−0.439632	−	5.27321i	−0.0830827	−	0.996543i
$29$	3.61383	+	2.08645i	0.671072	+	0.387443i	0.796483	−	0.604661i	$-0.206692\pi$
$29$	3.61383	+	2.08645i	0.671072	+	0.387443i	−0.125411	+	0.992105i	$0.540025\pi$
$30$		0			0
$31$	−2.97782	−	1.71924i	−0.534832	−	0.308785i	0.208150	−	0.978097i	$-0.433256\pi$
$31$	−2.97782	−	1.71924i	−0.534832	−	0.308785i	−0.742982	+	0.669312i	$0.766589\pi$
$32$	−5.65476	+	0.154037i	−0.999629	+	0.0272301i
$33$		0			0
$34$	−3.63866	+	2.12729i	−0.624025	+	0.364827i
$35$	5.73480	−	0.415265i	0.969358	−	0.0701926i
$36$		0			0
$37$	−4.84724	+	8.39566i	−0.796881	+	1.38024i	0.124756	+	0.992187i	$0.460185\pi$
$37$	−4.84724	+	8.39566i	−0.796881	+	1.38024i	−0.921638	+	0.388051i	$0.873148\pi$
$38$	−1.99520	−	1.13749i	−0.323665	−	0.184525i
$39$		0			0
$40$	−0.100435	−	6.14599i	−0.0158802	−	0.971767i
$41$	−8.56561	+	4.94536i	−1.33772	+	0.772335i	−0.986469	−	0.163945i	$-0.947578\pi$
$41$	−8.56561	+	4.94536i	−1.33772	+	0.772335i	−0.351254	+	0.936280i	$0.614245\pi$
$42$		0			0
$43$	8.83531	+	5.10107i	1.34737	+	0.777906i	0.987877	−	0.155241i	$-0.0496154\pi$
$43$	8.83531	+	5.10107i	1.34737	+	0.777906i	0.359496	+	0.933147i	$0.382949\pi$
$44$	−3.17061	+	0.0345401i	−0.477987	+	0.00520711i
$45$		0			0
$46$	−7.68028	+	0.0418325i	−1.13240	+	0.00616787i
$47$	0.953235	+	1.65105i	0.139044	+	0.240831i	0.927135	−	0.374728i	$-0.122264\pi$
$47$	0.953235	+	1.65105i	0.139044	+	0.240831i	−0.788091	+	0.615558i	$0.788931\pi$
$48$		0			0
$49$	−6.92698	+	1.00847i	−0.989568	+	0.144067i
$50$	−0.391855	+	0.00213433i	−0.0554166	+	0.000301840i
$51$		0			0
$52$	2.94751	+	4.97918i	0.408746	+	0.690488i
$53$	9.44107	−	5.45080i	1.29683	−	0.748725i	0.316975	−	0.948434i	$-0.397333\pi$
$53$	9.44107	−	5.45080i	1.29683	−	0.748725i	0.979855	+	0.199709i	$0.0639996\pi$
$54$		0			0
$55$		−	3.44543i		−	0.464582i
$56$	0.662343	+	7.45395i	0.0885093	+	0.996075i
$57$		0			0
$58$	−5.12673	−	2.92280i	−0.673172	−	0.383783i
$59$	5.27736	−	9.14066i	0.687054	−	1.19001i	−0.285733	−	0.958309i	$-0.592237\pi$
$59$	5.27736	−	9.14066i	0.687054	−	1.19001i	0.972787	−	0.231703i	$-0.0744298\pi$
$60$		0			0
$61$	5.68603	+	9.84849i	0.728021	+	1.26097i	0.957718	+	0.287707i	$0.0928930\pi$
$61$	5.68603	+	9.84849i	0.728021	+	1.26097i	−0.229697	+	0.973262i	$0.573774\pi$
$62$	4.22445	+	2.40840i	0.536505	+	0.305868i
$63$		0			0
$64$	7.99573	−	0.261395i	0.999466	−	0.0326743i
$65$	−5.44501	+	3.14368i	−0.675371	+	0.389925i
$66$		0			0
$67$	5.00642	+	2.89046i	0.611632	+	0.353126i	0.773604	−	0.633670i	$-0.218452\pi$
$67$	5.00642	+	2.89046i	0.611632	+	0.353126i	−0.161972	+	0.986795i	$0.551785\pi$
$68$	5.12938	−	3.03642i	0.622028	−	0.368220i
$69$		0			0
$70$	−8.10691	+	0.631438i	−0.968962	+	0.0754713i
$71$	2.73233			0.324268			0.162134	−	0.986769i	$-0.448162\pi$
$71$	2.73233			0.324268			0.162134	+	0.986769i	$0.448162\pi$
$72$		0			0
$73$	2.24800	+	3.89365i	0.263109	+	0.455718i	0.967066	−	0.254524i	$-0.0819189\pi$
$73$	2.24800	+	3.89365i	0.263109	+	0.455718i	−0.703958	+	0.710242i	$0.748586\pi$
$74$	6.79026	−	11.9104i	0.789352	−	1.38456i
$75$		0			0
$76$	2.83036	+	1.59326i	0.324665	+	0.182759i
$77$	0.302942	+	4.18362i	0.0345234	+	0.476768i
$78$		0			0
$79$	5.14844	−	2.97245i	0.579245	−	0.334427i	−0.181588	−	0.983375i	$-0.558124\pi$
$79$	5.14844	−	2.97245i	0.579245	−	0.334427i	0.760833	+	0.648948i	$0.224791\pi$
$80$	0.189375	+	8.69084i	0.0211728	+	0.971666i
$81$		0			0
$82$	12.0753	−	7.05966i	1.33350	−	0.779610i
$83$	−5.68306	+	9.84336i	−0.623797	+	1.08045i	0.364975	+	0.931017i	$0.381078\pi$
$83$	−5.68306	+	9.84336i	−0.623797	+	1.08045i	−0.988772	+	0.149431i	$0.952256\pi$
$84$		0			0
$85$	3.23851	+	5.60926i	0.351265	+	0.608409i
$86$	−12.5341	−	7.14584i	−1.35159	−	0.770555i
$87$		0			0
$88$	4.48359	−	0.0732687i	0.477952	−	0.00781047i
$89$	4.12683	+	2.38263i	0.437443	+	0.252558i	0.702512	−	0.711672i	$-0.252062\pi$
$89$	4.12683	+	2.38263i	0.437443	+	0.252558i	−0.265069	+	0.964229i	$0.585395\pi$
$90$		0			0
$91$	6.33520	−	4.29597i	0.664109	−	0.450340i
$92$	10.8611	−	0.118319i	1.13234	−	0.0123356i
$93$		0			0
$94$	−1.36078	−	2.32756i	−0.140353	−	0.240070i
$95$	−1.76465	+	3.05647i	−0.181050	+	0.313587i
$96$		0			0
$97$	4.73593	−	8.20287i	0.480861	−	0.832875i	−0.518898	−	0.854836i	$-0.673658\pi$
$97$	4.73593	−	8.20287i	0.480861	−	0.832875i	0.999759	+	0.0219611i	$0.00699099\pi$
$98$	9.78831	−	1.47953i	0.988769	−	0.149455i
$99$		0			0
$100$	0.554141	−	0.00603671i	0.0554141	−	0.000603671i
$101$			2.24516i			0.223402i	0.993742	+	0.111701i	$0.0356298\pi$
$101$			2.24516i			0.223402i	−0.993742	+	0.111701i	$0.964370\pi$
$102$		0			0
$103$			14.4813i			1.42688i	0.700715	+	0.713441i	$0.252864\pi$
$103$			14.4813i			1.42688i	−0.700715	+	0.713441i	$0.747136\pi$
$104$	−4.20670	−	7.01882i	−0.412501	−	0.688252i
$105$		0			0
$106$	−13.3095	+	7.78121i	−1.29273	+	0.755778i
$107$	−0.546040	+	0.945769i	−0.0527877	+	0.0914309i	−0.891212	−	0.453587i	$-0.850144\pi$
$107$	−0.546040	+	0.945769i	−0.0527877	+	0.0914309i	0.838424	+	0.545018i	$0.183477\pi$
$108$		0			0
$109$	−8.41858	−	14.5814i	−0.806354	−	1.39665i	−0.915373	−	0.402607i	$-0.868104\pi$
$109$	−8.41858	−	14.5814i	−0.806354	−	1.39665i	0.109019	−	0.994040i	$-0.465229\pi$
$110$	0.0265393	+	4.87250i	0.00253042	+	0.464575i
$111$		0			0
$112$	−0.994096	−	10.5362i	−0.0939333	−	0.995578i
$113$	13.5485	−	7.82226i	1.27454	−	0.735856i	0.298701	−	0.954347i	$-0.403447\pi$
$113$	13.5485	−	7.82226i	1.27454	−	0.735856i	0.975839	+	0.218491i	$0.0701134\pi$
$114$		0			0
$115$			11.8025i			1.10059i
$116$	7.27269	+	4.09391i	0.675252	+	0.380110i
$117$		0			0
$118$	−7.39280	+	12.9673i	−0.680562	+	1.19374i
$119$	−4.42556	−	6.52630i	−0.405690	−	0.598265i
$120$		0			0
$121$	−8.48651			−0.771501
$122$	−8.11700	−	13.8839i	−0.734878	−	1.25699i
$123$		0			0
$124$	−5.99273	−	3.37341i	−0.538163	−	0.302941i
$125$			11.4683i			1.02576i
$126$		0			0
$127$		−	3.32444i		−	0.294996i	−0.989062	−	0.147498i	$-0.952878\pi$
$127$		−	3.32444i		−	0.294996i	0.989062	−	0.147498i	$-0.0471220\pi$
$128$	−11.3055	+	0.431252i	−0.999273	+	0.0381176i
$129$		0			0
$130$	7.67608	−	4.48771i	0.673237	−	0.393598i
$131$	−14.4289			−1.26066			−0.630330	−	0.776327i	$-0.717081\pi$
$131$	−14.4289			−1.26066			−0.630330	+	0.776327i	$0.717081\pi$
$132$		0			0
$133$	1.87399	−	3.86648i	0.162496	−	0.335266i
$134$	−7.10231	−	4.04910i	−0.613546	−	0.349789i
$135$		0			0
$136$	−7.23054	+	4.33360i	−0.620013	+	0.371603i
$137$			15.1112i			1.29104i	0.763744	+	0.645520i	$0.223359\pi$
$137$			15.1112i			1.29104i	−0.763744	+	0.645520i	$0.776641\pi$
$138$		0			0
$139$	−9.08290	+	5.24401i	−0.770401	+	0.444791i	−0.833018	−	0.553246i	$-0.813389\pi$
$139$	−9.08290	+	5.24401i	−0.770401	+	0.444791i	0.0626166	+	0.998038i	$0.480055\pi$
$140$	11.4599	−	0.955421i	0.968536	−	0.0807478i
$141$		0			0
$142$	−3.86404	+	0.0210465i	−0.324263	+	0.00176618i
$143$	−2.29336	−	3.97221i	−0.191780	−	0.332173i
$144$		0			0
$145$	−4.53432	+	7.85368i	−0.376555	+	0.652212i
$146$	−3.20910	−	5.48906i	−0.265587	−	0.454278i
$147$		0			0
$148$	−9.51099	+	16.8959i	−0.781799	+	1.38884i
$149$			3.09954i			0.253924i	0.991908	+	0.126962i	$0.0405226\pi$
$149$			3.09954i			0.253924i	−0.991908	+	0.126962i	$0.959477\pi$
$150$		0			0
$151$		−	19.3647i		−	1.57588i	−0.615754	−	0.787938i	$-0.711149\pi$
$151$		−	19.3647i		−	1.57588i	0.615754	−	0.787938i	$-0.288851\pi$
$152$	−4.01495	−	2.23137i	−0.325656	−	0.180988i
$153$		0			0
$154$	−0.460643	−	5.91411i	−0.0371197	−	0.476572i
$155$	3.73630	−	6.47147i	0.300107	−	0.519801i
$156$		0			0
$157$	3.43313	−	5.94635i	0.273994	−	0.474571i	−0.695887	−	0.718151i	$-0.744989\pi$
$157$	3.43313	−	5.94635i	0.273994	−	0.474571i	0.969881	+	0.243580i	$0.0783220\pi$
$158$	−7.25799	+	4.24328i	−0.577415	+	0.337577i
$159$		0			0
$160$	−0.334757	−	12.2891i	−0.0264648	−	0.971536i
$161$	−1.03774	−	14.3312i	−0.0817854	−	1.12945i
$162$		0			0
$163$	−15.3848	−	8.88239i	−1.20503	−	0.695723i	−0.243358	−	0.969936i	$-0.578249\pi$
$163$	−15.3848	−	8.88239i	−1.20503	−	0.695723i	−0.961669	+	0.274214i	$0.911582\pi$
$164$	−17.0225	+	10.0767i	−1.32923	+	0.786861i
$165$		0			0
$166$	7.96113	−	13.9642i	0.617903	−	1.08383i
$167$	−0.187956	−	0.325549i	−0.0145445	−	0.0251917i	0.858662	−	0.512543i	$-0.171296\pi$
$167$	−0.187956	−	0.325549i	−0.0145445	−	0.0251917i	−0.873206	+	0.487351i	$0.837963\pi$
$168$		0			0
$169$	2.31499	−	4.00968i	0.178076	−	0.308437i
$170$	−4.62308	−	7.90763i	−0.354574	−	0.606487i
$171$		0			0
$172$	17.7807	+	10.0090i	1.35577	+	0.763182i
$173$	17.4175	−	10.0560i	1.32423	−	0.764544i	0.339829	−	0.940487i	$-0.389631\pi$
$173$	17.4175	−	10.0560i	1.32423	−	0.764544i	0.984400	+	0.175943i	$0.0562974\pi$
$174$		0			0
$175$	−0.0529464	−	0.731189i	−0.00400237	−	0.0552727i
$176$	−6.34009	+	0.138152i	−0.477902	+	0.0104136i
$177$		0			0
$178$	−5.85448	−	3.33770i	−0.438812	−	0.250171i
$179$	−8.38933	−	14.5307i	−0.627048	−	1.08608i	−0.988141	−	0.153549i	$-0.950930\pi$
$179$	−8.38933	−	14.5307i	−0.627048	−	1.08608i	0.361093	−	0.932530i	$-0.382404\pi$
$180$		0			0
$181$	12.5809			0.935134			0.467567	−	0.883958i	$-0.345131\pi$
$181$	12.5809			0.935134			0.467567	+	0.883958i	$0.345131\pi$
$182$	−8.92610	+	6.12413i	−0.661647	+	0.453951i
$183$		0			0
$184$	−15.3587	+	0.250985i	−1.13226	+	0.0185029i
$185$	−18.2457	−	10.5341i	−1.34145	−	0.774486i
$186$		0			0
$187$	−4.09203	+	2.36254i	−0.299239	+	0.172766i
$188$	1.94233	+	3.28114i	0.141659	+	0.239302i
$189$		0			0
$190$	2.47202	−	4.33603i	0.179339	−	0.314569i
$191$	−4.42371	−	7.66209i	−0.320089	−	0.554410i	0.660417	−	0.750899i	$-0.270379\pi$
$191$	−4.42371	−	7.66209i	−0.320089	−	0.554410i	−0.980506	+	0.196489i	$0.937046\pi$
$192$		0			0
$193$	1.67484	−	2.90091i	0.120558	−	0.208812i	−0.799430	−	0.600759i	$-0.794865\pi$
$193$	1.67484	−	2.90091i	0.120558	−	0.208812i	0.919988	+	0.391947i	$0.128198\pi$
$194$	−6.63433	+	11.6369i	−0.476317	+	0.835482i
$195$		0			0
$196$	−13.8312	+	2.16774i	−0.987940	+	0.154838i
$197$			2.41234i			0.171872i	0.996301	+	0.0859361i	$0.0273881\pi$
$197$			2.41234i			0.171872i	−0.996301	+	0.0859361i	$0.972612\pi$
$198$		0			0
$199$	5.45281	−	3.14818i	0.386539	−	0.223169i	−0.294120	−	0.955768i	$-0.595027\pi$
$199$	5.45281	−	3.14818i	0.386539	−	0.223169i	0.680660	+	0.732600i	$0.261693\pi$
$200$	−0.783616	+	0.0128055i	−0.0554100	+	0.000905485i
$201$		0			0
$202$	−0.0172939	−	3.17509i	−0.00121679	−	0.223398i
$203$	4.81527	−	9.93502i	0.337965	−	0.697301i
$204$		0			0
$205$	−10.7474	−	18.6150i	−0.750629	−	1.30013i
$206$	−0.111546	−	20.4793i	−0.00777175	−	1.42686i
$207$		0			0
$208$	6.00315	+	9.89356i	0.416244	+	0.685995i
$209$	−2.22974	−	1.28734i	−0.154234	−	0.0890472i
$210$		0			0
$211$	−11.3936	+	6.57810i	−0.784368	+	0.452855i	−0.837976	−	0.545707i	$-0.816261\pi$
$211$	−11.3936	+	6.57810i	−0.784368	+	0.452855i	0.0536080	+	0.998562i	$0.482928\pi$
$212$	18.7623	−	11.1066i	1.28860	−	0.762807i
$213$		0			0
$214$	0.764920	−	1.34170i	0.0522889	−	0.0917171i
$215$	−11.0858	+	19.2011i	−0.756044	+	1.30951i
$216$		0			0
$217$	−3.96780	+	8.18650i	−0.269352	+	0.555736i
$218$	12.0178	+	20.5561i	0.813949	+	1.39223i
$219$		0			0
$220$	−0.0750633	−	6.89045i	−0.00506077	−	0.464554i
$221$	7.46730	+	4.31125i	0.502305	+	0.290006i
$222$		0			0
$223$	−14.1567	−	8.17335i	−0.948000	−	0.547328i	−0.0555409	−	0.998456i	$-0.517688\pi$
$223$	−14.1567	−	8.17335i	−0.948000	−	0.547328i	−0.892459	+	0.451128i	$0.851022\pi$
$224$	1.48700	+	14.8926i	0.0993545	+	0.995052i
$225$		0			0
$226$	−19.1000	+	11.1665i	−1.27051	+	0.742787i
$227$	11.6501			0.773247			0.386623	−	0.922238i	$-0.373641\pi$
$227$	11.6501			0.773247			0.386623	+	0.922238i	$0.373641\pi$
$228$		0			0
$229$	17.5349			1.15874			0.579371	−	0.815064i	$-0.303298\pi$
$229$	17.5349			1.15874			0.579371	+	0.815064i	$0.303298\pi$
$230$	−0.0909116	−	16.6910i	−0.00599453	−	1.10057i
$231$		0			0
$232$	−10.3165	−	5.73356i	−0.677313	−	0.376427i
$233$	−19.4054	−	11.2037i	−1.27129	−	0.733981i	−0.296061	−	0.955169i	$-0.595673\pi$
$233$	−19.4054	−	11.2037i	−1.27129	−	0.733981i	−0.975231	+	0.221188i	$0.929007\pi$
$234$		0			0
$235$	−3.58811	+	2.07160i	−0.234062	+	0.135136i
$236$	10.3550	−	18.3952i	0.674050	−	1.19743i
$237$		0			0
$238$	6.30886	+	9.19536i	0.408943	+	0.596046i
$239$	1.51180	+	2.61852i	0.0977902	+	0.169378i	0.910770	−	0.412915i	$-0.135489\pi$
$239$	1.51180	+	2.61852i	0.0977902	+	0.169378i	−0.812979	+	0.582292i	$0.802156\pi$
$240$		0			0
$241$	−6.94821			−0.447574			−0.223787	−	0.974638i	$-0.571842\pi$
$241$	−6.94821			−0.447574			−0.223787	+	0.974638i	$0.571842\pi$
$242$	12.0016	−	0.0653695i	0.771489	−	0.00420211i
$243$		0			0
$244$	11.5859	+	19.5719i	0.741714	+	1.25296i
$245$	−2.19164	−	15.0539i	−0.140019	−	0.961757i
$246$		0			0
$247$			4.69838i			0.298951i
$248$	8.50087	+	4.72449i	0.539805	+	0.300005i
$249$		0			0
$250$	−0.0883375	−	16.2184i	−0.00558695	−	1.02574i
$251$	−1.22641			−0.0774106			−0.0387053	−	0.999251i	$-0.512323\pi$
$251$	−1.22641			−0.0774106			−0.0387053	+	0.999251i	$0.512323\pi$
$252$		0			0
$253$	−8.61008			−0.541311
$254$	0.0256073	+	4.70140i	0.00160675	+	0.294992i
$255$		0			0
$256$	15.9848	−	0.696956i	0.999051	−	0.0435598i
$257$		−	11.8135i		−	0.736904i	−0.929647	−	0.368452i	$-0.879888\pi$
$257$		−	11.8135i		−	0.736904i	0.929647	−	0.368452i	$-0.120112\pi$
$258$		0			0
$259$	23.0811	+	11.1868i	1.43419	+	0.695116i
$260$	−10.8209	+	6.40561i	−0.671083	+	0.397259i
$261$		0			0
$262$	20.4053	−	0.111142i	1.26064	−	0.00686640i
$263$	8.68662			0.535640			0.267820	−	0.963469i	$-0.413697\pi$
$263$	8.68662			0.535640			0.267820	+	0.963469i	$0.413697\pi$
$264$		0			0
$265$	11.8458	+	20.5176i	0.727683	+	1.26038i
$266$	−2.62040	+	5.48238i	−0.160667	+	0.336146i
$267$		0			0
$268$	10.0752	+	5.67150i	0.615442	+	0.346442i
$269$	7.04068	−	4.06494i	0.429278	−	0.247844i	−0.269761	−	0.962927i	$-0.586945\pi$
$269$	7.04068	−	4.06494i	0.429278	−	0.247844i	0.699039	+	0.715084i	$0.253611\pi$
$270$		0			0
$271$	−21.2148	−	12.2484i	−1.28871	−	0.744036i	−0.310284	−	0.950644i	$-0.600424\pi$
$271$	−21.2148	−	12.2484i	−1.28871	−	0.744036i	−0.978424	+	0.206608i	$0.933757\pi$
$272$	10.1920	−	6.18424i	0.617980	−	0.374974i
$273$		0			0
$274$	−0.116398	−	21.3702i	−0.00703186	−	1.29102i
$275$	−0.439294			−0.0264904
$276$		0			0
$277$	−15.7691			−0.947473			−0.473736	−	0.880667i	$-0.657095\pi$
$277$	−15.7691			−0.947473			−0.473736	+	0.880667i	$0.657095\pi$
$278$	12.8046	−	7.48601i	0.767967	−	0.448981i
$279$		0			0
$280$	−16.1991	+	1.43942i	−0.968082	+	0.0860219i
$281$	−14.6020	−	8.43048i	−0.871084	−	0.502921i	−0.00337562	−	0.999994i	$-0.501074\pi$
$281$	−14.6020	−	8.43048i	−0.871084	−	0.502921i	−0.867708	+	0.497074i	$0.834408\pi$
$282$		0			0
$283$	−18.2106	−	10.5139i	−1.08251	−	0.624986i	−0.150935	−	0.988544i	$-0.548228\pi$
$283$	−18.2106	−	10.5139i	−1.08251	−	0.624986i	−0.931572	+	0.363558i	$0.881562\pi$
$284$	5.46434	−	0.0595275i	0.324249	−	0.00353231i
$285$		0			0
$286$	3.27385	+	5.59981i	0.193587	+	0.331124i
$287$	14.6867	+	21.6583i	0.866931	+	1.27845i
$288$		0			0
$289$	−4.05870	+	7.02988i	−0.238747	+	0.413522i
$290$	6.35191	−	11.1415i	0.372997	−	0.654254i
$291$		0			0
$292$	4.58057	+	7.73787i	0.268057	+	0.452825i
$293$	−3.61477	+	2.08699i	−0.211177	+	0.121923i	−0.601858	−	0.798603i	$-0.705573\pi$
$293$	−3.61477	+	2.08699i	−0.211177	+	0.121923i	0.390681	+	0.920526i	$0.372239\pi$
$294$		0			0
$295$	19.8647	+	11.4689i	1.15657	+	0.667745i
$296$	13.3202	−	23.9674i	0.774223	−	1.39308i
$297$		0			0
$298$	−0.0238750	−	4.38334i	−0.00138304	−	0.253920i
$299$	7.85600	+	13.6070i	0.454324	+	0.786913i
$300$		0			0
$301$	11.7726	−	24.2897i	0.678564	−	1.40004i
$302$	0.149161	+	27.3854i	0.00858327	+	1.57585i
$303$		0			0
$304$	5.69510	+	3.12466i	0.326637	+	0.179212i
$305$	−21.4030	+	12.3570i	−1.22553	+	0.707561i
$306$		0			0
$307$		−	2.95195i		−	0.168477i	−0.996446	−	0.0842384i	$-0.973154\pi$
$307$		−	2.95195i		−	0.168477i	0.996446	−	0.0842384i	$-0.0268457\pi$
$308$	0.696993	+	8.36014i	0.0397149	+	0.476363i
$309$		0			0
$310$	−5.23401	+	9.18068i	−0.297272	+	0.521428i
$311$	−16.5988	+	28.7500i	−0.941232	+	1.63026i	−0.178106	+	0.984011i	$0.556997\pi$
$311$	−16.5988	+	28.7500i	−0.941232	+	1.63026i	−0.763126	+	0.646250i	$0.776336\pi$
$312$		0			0
$313$	−2.72052	−	4.71208i	−0.153773	−	0.266342i	0.778839	−	0.627224i	$-0.215809\pi$
$313$	−2.72052	−	4.71208i	−0.153773	−	0.266342i	−0.932612	+	0.360882i	$0.882476\pi$
$314$	−4.80930	+	8.43573i	−0.271405	+	0.476056i
$315$		0			0
$316$	10.2315	−	6.05672i	0.575567	−	0.340717i
$317$	−2.89818	+	1.67326i	−0.162778	+	0.0939799i	−0.579176	−	0.815203i	$-0.696626\pi$
$317$	−2.89818	+	1.67326i	−0.162778	+	0.0939799i	0.416398	+	0.909182i	$0.363292\pi$
$318$		0			0
$319$	−5.72937	−	3.30785i	−0.320783	−	0.185204i
$320$	0.568070	+	17.3765i	0.0317561	+	0.971377i
$321$		0			0
$322$	1.57795	+	20.2590i	0.0879359	+	1.12899i
$323$	4.84010			0.269310
$324$		0			0
$325$	0.400820	+	0.694241i	0.0222335	+	0.0385096i
$326$	21.8254	+	12.4429i	1.20880	+	0.689149i
$327$		0			0
$328$	23.9954	−	14.3816i	1.32493	−	0.794089i
$329$	4.17472	−	2.83092i	0.230160	−	0.156074i
$330$		0			0
$331$	2.51447	−	1.45173i	0.138208	−	0.0797943i	−0.429302	−	0.903161i	$-0.641240\pi$
$331$	2.51447	−	1.45173i	0.138208	−	0.0797943i	0.567510	+	0.823367i	$0.307907\pi$
$332$	−11.1510	+	19.8094i	−0.611991	+	1.08718i
$333$		0			0
$334$	0.268313	+	0.458941i	0.0146815	+	0.0251122i
$335$	−6.28162	+	10.8801i	−0.343202	+	0.594443i
$336$		0			0
$337$	4.51173	+	7.81454i	0.245769	+	0.425685i	0.962348	−	0.271822i	$-0.0876260\pi$
$337$	4.51173	+	7.81454i	0.245769	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$338$	−3.24296	+	5.68829i	−0.176394	+	0.309402i
$339$		0			0
$340$	6.59883	+	11.1473i	0.357872	+	0.604547i
$341$	4.72103	+	2.72569i	0.255658	+	0.147604i
$342$		0			0
$343$	3.98482	+	18.0865i	0.215160	+	0.976579i
$344$	−25.2224	−	14.0178i	−1.35990	−	0.755787i
$345$		0			0
$346$	−24.5543	+	14.3553i	−1.32005	+	0.771746i
$347$	−5.15674	+	8.93174i	−0.276829	+	0.479481i	−0.970595	−	0.240719i	$-0.922617\pi$
$347$	−5.15674	+	8.93174i	−0.276829	+	0.479481i	0.693766	+	0.720200i	$0.255950\pi$
$348$		0			0
$349$	−1.36318	+	2.36109i	−0.0729692	+	0.126386i	−0.900201	−	0.435474i	$-0.856581\pi$
$349$	−1.36318	+	2.36109i	−0.0729692	+	0.126386i	0.827232	+	0.561860i	$0.189914\pi$
$350$	0.0805086	+	1.03363i	0.00430336	+	0.0552501i
$351$		0			0
$352$	8.96505	−	0.244210i	0.477839	−	0.0130164i
$353$			14.5433i			0.774059i	0.922067	+	0.387030i	$0.126499\pi$
$353$			14.5433i			0.774059i	−0.922067	+	0.387030i	$0.873501\pi$
$354$		0			0
$355$			5.93797i			0.315155i
$356$	8.30508	+	4.67506i	0.440168	+	0.247778i
$357$		0			0
$358$	11.9761	+	20.4846i	0.632954	+	1.08265i
$359$	7.76006	−	13.4408i	0.409560	−	0.709379i	−0.585280	−	0.810831i	$-0.699016\pi$
$359$	7.76006	−	13.4408i	0.409560	−	0.709379i	0.994840	+	0.101452i	$0.0323489\pi$
$360$		0			0
$361$	−8.18132	−	14.1705i	−0.430596	−	0.745814i
$362$	−17.7919	+	0.0969078i	−0.935120	+	0.00509336i
$363$		0			0
$364$	12.5761	−	8.72945i	0.659164	−	0.457548i
$365$	−8.46179	+	4.88542i	−0.442910	+	0.255714i
$366$		0			0
$367$			23.4154i			1.22227i	0.791525	+	0.611136i	$0.209287\pi$
$367$			23.4154i			1.22227i	−0.791525	+	0.611136i	$0.790713\pi$
$368$	21.7183	−	0.473246i	1.13214	−	0.0246697i
$369$		0			0
$370$	25.8840	+	14.7568i	1.34565	+	0.767168i
$371$	−16.1878	−	23.8719i	−0.840430	−	1.23937i
$372$		0			0
$373$	19.3695			1.00291			0.501457	−	0.865183i	$-0.332798\pi$
$373$	19.3695			1.00291			0.501457	+	0.865183i	$0.332798\pi$
$374$	5.76872	−	3.37260i	0.298294	−	0.174393i
$375$		0			0
$376$	−2.77210	−	4.62520i	−0.142960	−	0.238527i
$377$			12.0726i			0.621770i
$378$		0			0
$379$			5.17988i			0.266072i	0.991111	+	0.133036i	$0.0424726\pi$
$379$			5.17988i			0.266072i	−0.991111	+	0.133036i	$0.957527\pi$
$380$	−3.46251	+	6.15102i	−0.177623	+	0.315541i
$381$		0			0
$382$	6.31500	+	10.8016i	0.323104	+	0.552658i
$383$	26.8251			1.37070			0.685350	−	0.728214i	$-0.259649\pi$
$383$	26.8251			1.37070			0.685350	+	0.728214i	$0.259649\pi$
$384$		0			0
$385$	−9.09195	+	0.658360i	−0.463369	+	0.0335532i
$386$	−2.34621	+	4.11535i	−0.119419	+	0.209466i
$387$		0			0
$388$	9.29258	−	16.5079i	0.471759	−	0.838064i
$389$		−	3.47355i		−	0.176116i	−0.996115	−	0.0880579i	$-0.971934\pi$
$389$		−	3.47355i		−	0.176116i	0.996115	−	0.0880579i	$-0.0280661\pi$
$390$		0			0
$391$	14.0174	−	8.09298i	0.708893	−	0.409279i
$392$	19.5432	−	3.17213i	0.987082	−	0.160217i
$393$		0			0
$394$	−0.0185817	−	3.41152i	−0.000936131	−	0.171870i
$395$	6.45981	+	11.1887i	0.325028	+	0.562966i
$396$		0			0
$397$	16.3980	−	28.4022i	0.822993	−	1.42547i	−0.0804507	−	0.996759i	$-0.525636\pi$
$397$	16.3980	−	28.4022i	0.822993	−	1.42547i	0.903444	−	0.428707i	$-0.141031\pi$
$398$	−7.68707	+	4.49413i	−0.385318	+	0.225271i
$399$		0			0
$400$	1.10809	−	0.0241454i	0.0554043	−	0.00120727i
$401$		−	12.0250i		−	0.600501i	−0.953860	−	0.300250i	$-0.902930\pi$
$401$		−	12.0250i		−	0.600501i	0.953860	−	0.300250i	$-0.0970702\pi$
$402$		0			0
$403$		−	9.94788i		−	0.495539i
$404$	0.0489138	+	4.49005i	0.00243355	+	0.223388i
$405$		0			0
$406$	−6.73319	+	14.0871i	−0.334162	+	0.699132i
$407$	7.68481	−	13.3105i	0.380922	−	0.659776i
$408$		0			0
$409$	−0.333132	+	0.577002i	−0.0164723	+	0.0285309i	−0.874144	−	0.485667i	$-0.838577\pi$
$409$	−0.333132	+	0.577002i	−0.0164723	+	0.0285309i	0.857672	+	0.514198i	$0.171910\pi$
$410$	15.3422	+	26.2424i	0.757700	+	1.29602i
$411$		0			0
$412$	0.315494	+	28.9608i	0.0155433	+	1.42680i
$413$	−25.1292	−	12.1795i	−1.23653	−	0.599314i
$414$		0			0
$415$	−21.3918	−	12.3506i	−1.05008	−	0.606266i
$416$	−8.56582	−	13.9452i	−0.419974	−	0.683717i
$417$		0			0
$418$	3.16320	+	1.80337i	0.154717	+	0.0882058i
$419$	−11.8411	−	20.5094i	−0.578476	−	1.00195i	−0.995654	−	0.0931254i	$-0.970314\pi$
$419$	−11.8411	−	20.5094i	−0.578476	−	1.00195i	0.417178	−	0.908825i	$-0.363019\pi$
$420$		0			0
$421$	11.3611	−	19.6780i	0.553707	−	0.959049i	−0.444295	−	0.895880i	$-0.646546\pi$
$421$	11.3611	−	19.6780i	0.553707	−	0.959049i	0.998003	−	0.0631691i	$-0.0201207\pi$
$422$	16.0621	−	9.39046i	0.781890	−	0.457121i
$423$		0			0
$424$	−26.4479	+	15.8515i	−1.28442	+	0.769815i
$425$	0.715182	−	0.412911i	0.0346914	−	0.0200291i
$426$		0			0
$427$	24.9021	−	16.8864i	1.20510	−	0.817190i
$428$	−1.07141	+	1.90332i	−0.0517885	+	0.0920005i
$429$		0			0
$430$	15.5295	−	27.2395i	0.748900	−	1.31360i
$431$	−11.4017	−	19.7483i	−0.549199	−	0.951240i	−0.998330	−	0.0577744i	$-0.981600\pi$
$431$	−11.4017	−	19.7483i	−0.549199	−	0.951240i	0.449131	−	0.893466i	$-0.351734\pi$
$432$		0			0
$433$	−9.81871			−0.471857			−0.235929	−	0.971770i	$-0.575813\pi$
$433$	−9.81871			−0.471857			−0.235929	+	0.971770i	$0.575813\pi$
$434$	5.54818	−	11.6079i	0.266321	−	0.557195i
$435$		0			0
$436$	−17.1538	−	28.9777i	−0.821520	−	1.38778i
$437$	7.63807	+	4.40984i	0.365378	+	0.210951i
$438$		0			0
$439$	−3.49352	+	2.01698i	−0.166736	+	0.0962653i	−0.581046	−	0.813871i	$-0.697356\pi$
$439$	−3.49352	+	2.01698i	−0.166736	+	0.0962653i	0.414310	+	0.910136i	$0.364023\pi$
$440$	0.159229	+	9.74385i	0.00759097	+	0.464520i
$441$		0			0
$442$	−10.5934	−	6.03942i	−0.503877	−	0.287266i
$443$	17.4609	+	30.2432i	0.829595	+	1.43690i	0.898357	+	0.439267i	$0.144762\pi$
$443$	17.4609	+	30.2432i	0.829595	+	1.43690i	−0.0687620	+	0.997633i	$0.521905\pi$
$444$		0			0
$445$	−5.17799	+	8.96853i	−0.245460	+	0.425149i
$446$	20.0832	+	11.4496i	0.950967	+	0.542156i
$447$		0			0
$448$	−2.21762	−	21.0495i	−0.104773	−	0.994496i
$449$			8.15081i			0.384661i	0.981330	+	0.192330i	$0.0616045\pi$
$449$			8.15081i			0.384661i	−0.981330	+	0.192330i	$0.938395\pi$
$450$		0			0
$451$	13.5799	−	7.84036i	0.639453	−	0.369188i
$452$	26.9251	−	15.9388i	1.26645	−	0.749696i
$453$		0			0
$454$	−16.4755	+	0.0897381i	−0.773235	+	0.00421162i
$455$	9.33612	+	13.7678i	0.437684	+	0.645446i
$456$		0			0
$457$	10.3772	+	17.9738i	0.485424	+	0.840780i	0.999860	−	0.0167495i	$-0.00533178\pi$
$457$	10.3772	+	17.9738i	0.485424	+	0.840780i	−0.514435	+	0.857529i	$0.671998\pi$
$458$	−24.7978	+	0.135067i	−1.15872	+	0.00631128i
$459$		0			0
$460$	0.257133	+	23.6036i	0.0119889	+	1.10052i
$461$	13.1398	+	7.58629i	0.611983	+	0.353329i	0.773741	−	0.633502i	$-0.218383\pi$
$461$	13.1398	+	7.58629i	0.611983	+	0.353329i	−0.161758	+	0.986830i	$0.551716\pi$
$462$		0			0
$463$	18.2308	−	10.5256i	0.847257	−	0.489164i	−0.0124676	−	0.999922i	$-0.503969\pi$
$463$	18.2308	−	10.5256i	0.847257	−	0.489164i	0.859724	+	0.510758i	$0.170635\pi$
$464$	14.6337	+	8.02890i	0.679353	+	0.372732i
$465$		0			0
$466$	27.5293	+	15.6948i	1.27527	+	0.727046i
$467$	−0.273182	+	0.473166i	−0.0126414	+	0.0218955i	−0.872277	−	0.489012i	$-0.837357\pi$
$467$	−0.273182	+	0.473166i	−0.0126414	+	0.0218955i	0.859636	+	0.510908i	$0.170691\pi$
$468$		0			0
$469$	6.67082	−	13.7635i	0.308030	−	0.635538i
$470$	5.05832	−	2.95727i	0.233323	−	0.136409i
$471$		0			0
$472$	−14.5022	+	26.0941i	−0.667518	+	1.20108i
$473$	−14.0075	−	8.08723i	−0.644065	−	0.371851i
$474$		0			0
$475$	0.389701	+	0.224994i	0.0178807	+	0.0103234i
$476$	−8.99277	−	12.9554i	−0.412183	−	0.593810i
$477$		0			0
$478$	−2.15815	−	3.69144i	−0.0987113	−	0.168843i
$479$	−6.55728			−0.299610			−0.149805	−	0.988716i	$-0.547865\pi$
$479$	−6.55728			−0.299610			−0.149805	+	0.988716i	$0.547865\pi$
$480$		0			0
$481$	−28.0471			−1.27884
$482$	9.82611	−	0.0535203i	0.447567	−	0.00243778i
$483$		0			0
$484$	−16.9720	+	0.184890i	−0.771455	+	0.00840409i
$485$	17.8267	+	10.2922i	0.809468	+	0.467347i
$486$		0			0
$487$	27.4457	−	15.8458i	1.24368	−	0.718040i	0.273840	−	0.961775i	$-0.411706\pi$
$487$	27.4457	−	15.8458i	1.24368	−	0.718040i	0.969842	+	0.243735i	$0.0783727\pi$
$488$	−16.5355	−	27.5892i	−0.748527	−	1.24891i
$489$		0			0
$490$	3.21535	+	21.2722i	0.145255	+	0.960981i
$491$	0.843433	+	1.46087i	0.0380636	+	0.0659281i	0.884430	−	0.466674i	$-0.154548\pi$
$491$	0.843433	+	1.46087i	0.0380636	+	0.0659281i	−0.846366	+	0.532602i	$0.821214\pi$
$492$		0			0
$493$	12.4368			0.560123
$494$	−0.0361904	−	6.64441i	−0.00162828	−	0.298946i
$495$		0			0
$496$	−12.0583	−	6.61585i	−0.541432	−	0.297061i
$497$	−0.522100	−	7.21019i	−0.0234194	−	0.323421i
$498$		0			0
$499$			12.7363i			0.570154i	0.958505	+	0.285077i	$0.0920192\pi$
$499$			12.7363i			0.570154i	−0.958505	+	0.285077i	$0.907981\pi$
$500$	0.249852	+	22.9352i	0.0111737	+	1.02570i
$501$		0			0
$502$	1.73439	−	0.00944677i	0.0774095	−	0.000421630i
$503$	−26.0911			−1.16334			−0.581671	−	0.813424i	$-0.697601\pi$
$503$	−26.0911			−1.16334			−0.581671	+	0.813424i	$0.697601\pi$
$504$		0			0
$505$	−4.87924			−0.217123
$506$	12.1763	−	0.0663213i	0.541303	−	0.00294834i
$507$		0			0
$508$	−0.0724273	−	6.64848i	−0.00321344	−	0.294979i
$509$			14.2125i			0.629959i	0.949098	+	0.314980i	$0.101998\pi$
$509$			14.2125i			0.629959i	−0.949098	+	0.314980i	$0.898002\pi$
$510$		0			0
$511$	9.84518	−	6.67613i	0.435525	−	0.295335i
$512$	−22.6002	+	1.10876i	−0.998799	+	0.0490006i
$513$		0			0
$514$	0.0909962	+	16.7065i	0.00401367	+	0.736893i
$515$	−31.4711			−1.38678
$516$		0			0
$517$	−1.51126	−	2.61758i	−0.0664650	−	0.115121i
$518$	−32.7272	−	15.6426i	−1.43795	−	0.687294i
$519$		0			0
$520$	15.2535	−	9.14212i	0.668909	−	0.400908i
$521$	−22.1514	+	12.7891i	−0.970470	+	0.560301i	−0.899380	−	0.437169i	$-0.855981\pi$
$521$	−22.1514	+	12.7891i	−0.970470	+	0.560301i	−0.0710907	+	0.997470i	$0.522648\pi$
$522$		0			0
$523$	−18.0150	−	10.4009i	−0.787739	−	0.454801i	0.0514271	−	0.998677i	$-0.483623\pi$
$523$	−18.0150	−	10.4009i	−0.787739	−	0.454801i	−0.839166	+	0.543876i	$0.816956\pi$
$524$	−28.8561	+	0.314353i	−1.26059	+	0.0137326i
$525$		0			0
$526$	−12.2846	+	0.0669109i	−0.535632	+	0.00291745i
$527$	−10.2480			−0.446408
$528$		0			0
$529$	6.49422			0.282357
$530$	−16.9103	−	28.9246i	−0.734537	−	1.25640i
$531$		0			0
$532$	3.66352	−	7.77333i	0.158834	−	0.337017i
$533$	−24.7811	−	14.3074i	−1.07339	−	0.619722i
$534$		0			0
$535$	−2.05537	−	1.18667i	−0.0888614	−	0.0513041i
$536$	−14.2920	−	7.94299i	−0.617320	−	0.343085i
$537$		0			0
$538$	−9.92557	+	5.80284i	−0.427922	+	0.250178i
$539$	10.9820	−	1.59883i	0.473029	−	0.0688665i
$540$		0			0
$541$	8.29333	−	14.3645i	0.356558	−	0.617577i	−0.630825	−	0.775925i	$-0.717284\pi$
$541$	8.29333	−	14.3645i	0.356558	−	0.617577i	0.987383	+	0.158348i	$0.0506168\pi$
$542$	30.0962	+	17.1581i	1.29274	+	0.737005i
$543$		0			0
$544$	−14.3658	+	8.82421i	−0.615929	+	0.378335i
$545$	31.6887	−	18.2955i	1.35740	−	0.783693i
$546$		0			0
$547$	−24.0183	−	13.8669i	−1.02695	−	0.592908i	−0.110838	−	0.993838i	$-0.535353\pi$
$547$	−24.0183	−	13.8669i	−1.02695	−	0.592908i	−0.916108	+	0.400931i	$0.868687\pi$
$548$	0.329218	+	30.2207i	0.0140635	+	1.29096i
$549$		0			0
$550$	0.621246	−	0.00338377i	0.0264900	−	0.000144284i
$551$	3.38838	+	5.86884i	0.144350	+	0.250021i
$552$		0			0
$553$	−8.82761	−	13.0179i	−0.375388	−	0.553579i
$554$	22.3005	−	0.121465i	0.947459	−	0.00516057i
$555$		0			0
$556$	−18.0505	+	10.6853i	−0.765510	+	0.453157i
$557$	20.0598	−	11.5815i	0.849961	−	0.490725i	−0.0106766	−	0.999943i	$-0.503399\pi$
$557$	20.0598	−	11.5815i	0.849961	−	0.490725i	0.860638	+	0.509218i	$0.170065\pi$
$558$		0			0
$559$			29.5158i			1.24838i
$560$	22.8976	−	2.16040i	0.967599	−	0.0912934i
$561$		0			0
$562$	20.7150	+	11.8099i	0.873810	+	0.498169i
$563$	0.369977	−	0.640819i	0.0155927	−	0.0270073i	−0.858124	−	0.513443i	$-0.828370\pi$
$563$	0.369977	−	0.640819i	0.0155927	−	0.0270073i	0.873716	+	0.486436i	$0.161703\pi$
$564$		0			0
$565$	16.9995	+	29.4441i	0.715176	+	1.23872i
$566$	25.8343	+	14.7284i	1.08589	+	0.619080i
$567$		0			0
$568$	−7.72717	+	0.126274i	−0.324225	+	0.00529833i
$569$	15.1901	−	8.77001i	0.636802	−	0.367658i	−0.146579	−	0.989199i	$-0.546826\pi$
$569$	15.1901	−	8.77001i	0.636802	−	0.367658i	0.783382	+	0.621541i	$0.213493\pi$
$570$		0			0
$571$	−13.8570	−	8.00033i	−0.579897	−	0.334803i	0.181196	−	0.983447i	$-0.442003\pi$
$571$	−13.8570	−	8.00033i	−0.579897	−	0.334803i	−0.761092	+	0.648644i	$0.775337\pi$
$572$	−4.67298	−	7.89399i	−0.195387	−	0.330064i
$573$		0			0
$574$	−20.9367	−	30.5159i	−0.873882	−	1.27371i
$575$	1.50482			0.0627554
$576$		0			0
$577$	15.8382	+	27.4326i	0.659353	+	1.14203i	0.980783	+	0.195099i	$0.0625029\pi$
$577$	15.8382	+	27.4326i	0.659353	+	1.14203i	−0.321431	+	0.946933i	$0.604164\pi$
$578$	5.68564	−	9.97287i	0.236491	−	0.414817i
$579$		0			0
$580$	−8.89700	+	15.8052i	−0.369428	+	0.656275i
$581$	27.0610	+	13.1158i	1.12268	+	0.544136i
$582$		0			0
$583$	−14.9679	+	8.64170i	−0.619905	+	0.357903i
$584$	−6.53740	−	10.9076i	−0.270520	−	0.451358i
$585$		0			0
$586$	5.09590	−	2.97925i	0.210510	−	0.123072i
$587$	−9.32266	+	16.1473i	−0.384787	+	0.666471i	−0.991740	−	0.128267i	$-0.959059\pi$
$587$	−9.32266	+	16.1473i	−0.384787	+	0.666471i	0.606952	+	0.794738i	$0.292392\pi$
$588$		0			0
$589$	−2.79204	−	4.83596i	−0.115044	−	0.199262i
$590$	−28.1809	−	16.0662i	−1.16019	−	0.661436i
$591$		0			0
$592$	−18.6528	+	33.9971i	−0.766624	+	1.39727i
$593$	3.94872	+	2.27980i	0.162155	+	0.0936200i	0.578881	−	0.815412i	$-0.303489\pi$
$593$	3.94872	+	2.27980i	0.162155	+	0.0936200i	−0.416727	+	0.909032i	$0.636823\pi$
$594$		0			0
$595$	14.1831	−	9.61774i	0.581451	−	0.394289i
$596$	0.0675276	+	6.19871i	0.00276604	+	0.253909i
$597$		0			0
$598$	−11.2147	−	19.1824i	−0.458604	−	0.784427i
$599$	1.90003	−	3.29095i	0.0776331	−	0.134464i	−0.824595	−	0.565723i	$-0.808597\pi$
$599$	1.90003	−	3.29095i	0.0776331	−	0.134464i	0.902228	+	0.431259i	$0.141930\pi$
$600$		0			0
$601$	−19.9890	+	34.6219i	−0.815368	+	1.41226i	0.0936959	+	0.995601i	$0.470132\pi$
$601$	−19.9890	+	34.6219i	−0.815368	+	1.41226i	−0.909064	+	0.416657i	$0.863201\pi$
$602$	−16.4617	+	34.4410i	−0.670928	+	1.40371i
$603$		0			0
$604$	−0.421886	−	38.7271i	−0.0171663	−	1.57578i
$605$		−	18.4431i		−	0.749819i
$606$		0			0
$607$			28.2208i			1.14545i	0.819748	+	0.572724i	$0.194113\pi$
$607$			28.2208i			1.14545i	−0.819748	+	0.572724i	$0.805887\pi$
$608$	−8.07804	−	4.37501i	−0.327608	−	0.177430i
$609$		0			0
$610$	30.1728	−	17.6401i	1.22166	−	0.714226i
$611$	−2.75780	+	4.77665i	−0.111569	+	0.193243i
$612$		0			0
$613$	−0.844751	−	1.46315i	−0.0341192	−	0.0590961i	0.848462	−	0.529257i	$-0.177529\pi$
$613$	−0.844751	−	1.46315i	−0.0341192	−	0.0590961i	−0.882581	+	0.470161i	$0.844196\pi$
$614$	0.0227381	+	4.17463i	0.000917637	+	0.168474i
$615$		0			0
$616$	−1.05008	−	11.8175i	−0.0423089	−	0.476140i
$617$	−20.9691	+	12.1065i	−0.844186	+	0.487391i	−0.858685	−	0.512504i	$-0.828718\pi$
$617$	−20.9691	+	12.1065i	−0.844186	+	0.487391i	0.0144988	+	0.999895i	$0.495385\pi$
$618$		0			0
$619$			3.12947i			0.125784i	0.998020	+	0.0628921i	$0.0200324\pi$
$619$			3.12947i			0.125784i	−0.998020	+	0.0628921i	$0.979968\pi$
$620$	7.33118	−	13.0236i	0.294427	−	0.523039i
$621$		0			0
$622$	23.2525	−	40.7859i	0.932338	−	1.63536i
$623$	5.49881	−	11.3453i	0.220305	−	0.454541i
$624$		0			0
$625$	−23.5378			−0.941511
$626$	3.88363	+	6.64283i	0.155221	+	0.265501i
$627$		0			0
$628$	6.73630	−	11.9668i	0.268808	−	0.477527i
$629$			28.8931i			1.15204i
$630$		0			0
$631$			21.9280i			0.872940i	0.899719	+	0.436470i	$0.143771\pi$
$631$			21.9280i			0.872940i	−0.899719	+	0.436470i	$0.856229\pi$
$632$	−14.4227	+	8.64418i	−0.573703	+	0.343847i
$633$		0			0
$634$	4.08570	−	2.38864i	0.162264	−	0.0948651i
$635$	7.22476			0.286706
$636$		0			0
$637$	−12.5469	−	15.8967i	−0.497128	−	0.629851i
$638$	8.12791	+	4.63381i	0.321787	+	0.183454i
$639$		0			0
$640$	−0.937207	−	24.5694i	−0.0370464	−	0.971190i
$641$			12.7873i			0.505066i	0.967588	+	0.252533i	$0.0812637\pi$
$641$			12.7873i			0.505066i	−0.967588	+	0.252533i	$0.918736\pi$
$642$		0			0
$643$	−22.4590	+	12.9667i	−0.885696	+	0.511357i	−0.872532	−	0.488556i	$-0.837524\pi$
$643$	−22.4590	+	12.9667i	−0.885696	+	0.511357i	−0.0131640	+	0.999913i	$0.504190\pi$
$644$	−2.38758	−	28.6380i	−0.0940839	−	1.12850i
$645$		0			0
$646$	−6.84483	+	0.0372821i	−0.269306	+	0.00146684i
$647$	−0.517794	−	0.896845i	−0.0203566	−	0.0352586i	0.855668	−	0.517526i	$-0.173147\pi$
$647$	−0.517794	−	0.896845i	−0.0203566	−	0.0352586i	−0.876024	+	0.482267i	$0.839813\pi$
$648$		0			0
$649$	−8.36673	+	14.4916i	−0.328423	+	0.568845i
$650$	−0.572184	−	0.978703i	−0.0224429	−	0.0383879i
$651$		0			0
$652$	−30.9612	−	17.4286i	−1.21253	−	0.682555i
$653$		−	15.6174i		−	0.611156i	−0.952167	−	0.305578i	$-0.901150\pi$
$653$		−	15.6174i		−	0.611156i	0.952167	−	0.305578i	$-0.0988497\pi$
$654$		0			0
$655$		−	31.3573i		−	1.22523i
$656$	−33.8234	+	20.5231i	−1.32058	+	0.801294i
$657$		0			0
$658$	−5.88205	+	4.03563i	−0.229306	+	0.157325i
$659$	7.88212	−	13.6522i	0.307044	−	0.531816i	−0.670670	−	0.741756i	$-0.733993\pi$
$659$	7.88212	−	13.6522i	0.307044	−	0.531816i	0.977714	+	0.209940i	$0.0673268\pi$
$660$		0			0
$661$	−3.39515	+	5.88057i	−0.132056	+	0.228728i	−0.924469	−	0.381257i	$-0.875491\pi$
$661$	−3.39515	+	5.88057i	−0.132056	+	0.228728i	0.792413	+	0.609985i	$0.208825\pi$
$662$	−3.54476	+	2.07239i	−0.137771	+	0.0805458i
$663$		0			0
$664$	15.6171	−	28.1001i	0.606060	−	1.09050i
$665$	8.40274	+	4.07261i	0.325844	+	0.157929i
$666$		0			0
$667$	19.6262	+	11.3312i	0.759930	+	0.438746i
$668$	−0.382982	−	0.646965i	−0.0148180	−	0.0250318i
$669$		0			0
$670$	8.79961	−	15.4349i	0.339959	−	0.596303i
$671$	−9.01462	−	15.6138i	−0.348006	−	0.602763i
$672$		0			0
$673$	20.3296	−	35.2118i	0.783647	−	1.35732i	−0.146157	−	0.989261i	$-0.546690\pi$
$673$	20.3296	−	35.2118i	0.783647	−	1.35732i	0.929804	−	0.368055i	$-0.119976\pi$
$674$	−6.44065	−	11.0165i	−0.248084	−	0.424340i
$675$		0			0
$676$	4.54235	−	8.06932i	0.174706	−	0.310359i
$677$	−21.1501	+	12.2110i	−0.812864	+	0.469307i	−0.847950	−	0.530077i	$-0.822163\pi$
$677$	−21.1501	+	12.2110i	−0.812864	+	0.469307i	0.0350854	+	0.999384i	$0.488830\pi$
$678$		0			0
$679$	−22.5510	−	10.9299i	−0.865429	−	0.419453i
$680$	−9.41789	−	15.7136i	−0.361160	−	0.602589i
$681$		0			0
$682$	−6.69744	−	3.81828i	−0.256458	−	0.146210i
$683$	−16.3081	−	28.2464i	−0.624011	−	1.08082i	−0.988731	−	0.149701i	$-0.952169\pi$
$683$	−16.3081	−	28.2464i	−0.624011	−	1.08082i	0.364721	−	0.931117i	$-0.381164\pi$
$684$		0			0
$685$	−32.8401			−1.25476
$686$	−5.77462	−	25.5471i	−0.220476	−	0.975392i
$687$		0			0
$688$	35.7774	+	19.6295i	1.36400	+	0.748369i
$689$	27.3139	+	15.7697i	1.04058	+	0.600778i
$690$		0			0
$691$	21.7218	−	12.5411i	0.826335	−	0.477085i	−0.0262613	−	0.999655i	$-0.508360\pi$
$691$	21.7218	−	12.5411i	0.826335	−	0.477085i	0.852596	+	0.522571i	$0.175027\pi$
$692$	34.6139	−	20.4903i	1.31582	−	0.778924i
$693$		0			0
$694$	7.22383	−	12.6709i	0.274213	−	0.480982i
$695$	−11.3964	−	19.7392i	−0.432291	−	0.748750i
$696$		0			0
$697$	−14.7390	+	25.5287i	−0.558279	+	0.966967i
$698$	1.90961	−	3.34954i	0.0722798	−	0.126782i
$699$		0			0
$700$	−0.121816	−	1.46114i	−0.00460423	−	0.0552258i
$701$		−	26.2055i		−	0.989769i	−0.868959	−	0.494885i	$-0.835210\pi$
$701$		−	26.2055i		−	0.989769i	0.868959	−	0.494885i	$-0.164790\pi$
$702$		0			0
$703$	−13.6345	+	7.87189i	−0.514235	+	0.296894i
$704$	−12.6764	+	0.414415i	−0.477761	+	0.0156189i
$705$		0			0
$706$	−0.112023	−	20.5670i	−0.00421604	−	0.774048i
$707$	5.92462	−	0.429010i	0.222818	−	0.0161346i
$708$		0			0
$709$	18.3224	+	31.7354i	0.688113	+	1.19185i	0.972447	+	0.233122i	$0.0748941\pi$
$709$	18.3224	+	31.7354i	0.688113	+	1.19185i	−0.284334	+	0.958725i	$0.591773\pi$
$710$	−0.0457387	−	8.39744i	−0.00171654	−	0.315150i
$711$		0			0
$712$	−11.7810	−	6.54746i	−0.441511	−	0.245377i
$713$	−16.1721	−	9.33696i	−0.605650	−	0.349672i
$714$		0			0
$715$	8.63252	−	4.98399i	0.322838	−	0.186391i
$716$	−17.0942	−	28.8770i	−0.638841	−	1.07918i
$717$		0			0
$718$	−10.8707	+	19.0677i	−0.405690	+	0.711599i
$719$	−13.3024	+	23.0404i	−0.496095	+	0.859263i	−0.999990	−	0.00450268i	$-0.998567\pi$
$719$	−13.3024	+	23.0404i	−0.496095	+	0.859263i	0.503894	+	0.863765i	$0.331900\pi$
$720$		0			0
$721$	38.2138	−	2.76711i	1.42316	−	0.103053i
$722$	11.6791	+	19.9767i	0.434652	+	0.743457i
$723$		0			0
$724$	25.1604	−	0.274093i	0.935079	−	0.0101866i
$725$	1.00135	+	0.578128i	0.0371891	+	0.0214711i
$726$		0			0
$727$	−21.4647	−	12.3927i	−0.796082	−	0.459618i	0.0460172	−	0.998941i	$-0.485347\pi$
$727$	−21.4647	−	12.3927i	−0.796082	−	0.459618i	−0.842099	+	0.539322i	$0.818680\pi$
$728$	−17.7177	+	12.4420i	−0.656663	+	0.461131i
$729$		0			0
$730$	11.9290	−	6.97410i	0.441511	−	0.258123i
$731$	30.4061			1.12461
$732$		0			0
$733$	−43.3563			−1.60140			−0.800701	−	0.599064i	$-0.795540\pi$
$733$	−43.3563			−1.60140			−0.800701	+	0.599064i	$0.795540\pi$
$734$	−0.180363	−	33.1138i	−0.00665731	−	1.22225i
$735$		0			0
$736$	−30.7102	+	0.836551i	−1.13199	+	0.0308357i
$737$	−7.93717	−	4.58253i	−0.292370	−	0.168800i
$738$		0			0
$739$	0.367189	−	0.211997i	0.0135073	−	0.00779842i	−0.493231	−	0.869898i	$-0.664184\pi$
$739$	0.367189	−	0.211997i	0.0135073	−	0.00779842i	0.506738	+	0.862100i	$0.330851\pi$
$740$	−36.7187	−	20.6695i	−1.34981	−	0.759827i
$741$		0			0
$742$	23.0766	+	33.6348i	0.847168	+	1.23477i
$743$	−5.74814	−	9.95606i	−0.210879	−	0.365253i	0.741111	−	0.671382i	$-0.234299\pi$
$743$	−5.74814	−	9.95606i	−0.210879	−	0.365253i	−0.951990	+	0.306130i	$0.900966\pi$
$744$		0			0
$745$	−6.73600			−0.246788
$746$	−27.3922	+	0.149198i	−1.00290	+	0.00546254i
$747$		0			0
$748$	−8.13211	+	4.81394i	−0.297339	+	0.176015i
$749$	2.60007	+	1.26019i	0.0950046	+	0.0460465i
$750$		0			0
$751$			2.98424i			0.108896i	0.998517	+	0.0544482i	$0.0173400\pi$
$751$			2.98424i			0.108896i	−0.998517	+	0.0544482i	$0.982660\pi$
$752$	3.95591	+	6.51957i	0.144257	+	0.237744i
$753$		0			0
$754$	−0.0929922	−	17.0730i	−0.00338657	−	0.621761i
$755$	42.0839			1.53159
$756$		0			0
$757$	4.04059			0.146858			0.0734289	−	0.997300i	$-0.476606\pi$
$757$	4.04059			0.146858			0.0734289	+	0.997300i	$0.476606\pi$
$758$	−0.0398993	−	7.32534i	−0.00144921	−	0.266068i
$759$		0			0
$760$	4.84928	−	8.72540i	0.175902	−	0.316504i
$761$			31.1701i			1.12992i	0.825120	+	0.564958i	$0.191108\pi$
$761$			31.1701i			1.12992i	−0.825120	+	0.564958i	$0.808892\pi$
$762$		0			0
$763$	−36.8694	+	25.0016i	−1.33476	+	0.905117i
$764$	−9.01383	−	15.2269i	−0.326109	−	0.550890i
$765$		0			0
$766$	−37.9359	+	0.206627i	−1.37068	+	0.00746574i
$767$	30.5359			1.10259
$768$		0			0
$769$	−2.61705	−	4.53286i	−0.0943731	−	0.163459i	0.814974	−	0.579498i	$-0.196751\pi$
$769$	−2.61705	−	4.53286i	−0.0943731	−	0.163459i	−0.909347	+	0.416039i	$0.863418\pi$
$770$	12.8527	−	1.00108i	0.463179	−	0.0360765i
$771$		0			0
$772$	3.28629	−	5.83797i	0.118276	−	0.210113i
$773$	44.3921	−	25.6298i	1.59667	−	0.921839i	0.604549	−	0.796568i	$-0.293353\pi$
$773$	44.3921	−	25.6298i	1.59667	−	0.921839i	0.992123	−	0.125271i	$-0.0399799\pi$
$774$		0			0
$775$	−0.825114	−	0.476380i	−0.0296390	−	0.0171121i
$776$	−13.0143	+	23.4170i	−0.467188	+	0.840621i
$777$		0			0
$778$	0.0267559	+	4.91227i	0.000959245	+	0.176113i
$779$	−16.0625			−0.575497
$780$		0			0
$781$	−4.33184			−0.155005
$782$	−19.7610	+	11.5530i	−0.706653	+	0.413134i
$783$		0			0
$784$	−27.6134	+	4.63655i	−0.986195	+	0.165591i
$785$	12.9228	+	7.46097i	0.461234	+	0.266293i
$786$		0			0
$787$	34.5147	+	19.9271i	1.23032	+	0.710323i	0.967096	−	0.254413i	$-0.0818822\pi$
$787$	34.5147	+	19.9271i	1.23032	+	0.710323i	0.263220	+	0.964736i	$0.415216\pi$
$788$	0.0525561	+	4.82440i	0.00187223	+	0.171862i
$789$		0			0
$790$	−9.22160	−	15.7733i	−0.328090	−	0.561187i
$791$	−23.2306	−	34.2578i	−0.825984	−	1.21807i
$792$		0			0
$793$	−16.4502	+	28.4926i	−0.584165	+	1.01180i
$794$	−22.9712	+	40.2925i	−0.815217	+	1.42993i
$795$		0			0
$796$	10.8364	−	6.41478i	0.384085	−	0.227366i
$797$	18.6851	−	10.7879i	0.661861	−	0.382126i	−0.131125	−	0.991366i	$-0.541859\pi$
$797$	18.6851	−	10.7879i	0.661861	−	0.382126i	0.792986	+	0.609240i	$0.208525\pi$
$798$		0			0
$799$	4.92074	+	2.84099i	0.174083	+	0.100507i
$800$	−1.56686	+	0.0426816i	−0.0553969	+	0.00150902i
$801$		0			0
$802$	0.0926257	+	17.0057i	0.00327073	+	0.600492i
$803$	−3.56398	−	6.17300i	−0.125770	−	0.217840i
$804$		0			0
$805$	31.1449	−	2.25524i	1.09771	−	0.0794869i
$806$	0.0766260	+	14.0682i	0.00269904	+	0.495532i
$807$		0			0
$808$	−0.103759	−	6.34942i	−0.00365024	−	0.223372i
$809$	−16.1063	+	9.29896i	−0.566266	+	0.326934i	−0.755657	−	0.654968i	$-0.772682\pi$
$809$	−16.1063	+	9.29896i	−0.566266	+	0.326934i	0.189390	+	0.981902i	$0.439349\pi$
$810$		0			0
$811$			5.79262i			0.203406i	0.994815	+	0.101703i	$0.0324292\pi$
$811$			5.79262i			0.203406i	−0.994815	+	0.101703i	$0.967571\pi$
$812$	9.41351	−	19.9738i	0.330349	−	0.700942i
$813$		0			0
$814$	−10.7653	+	18.8828i	−0.377323	+	0.661841i
$815$	19.3035	−	33.4346i	0.676170	−	1.17116i
$816$		0			0
$817$	8.28411	+	14.3485i	0.289824	+	0.501990i
$818$	0.466669	−	0.818558i	0.0163167	−	0.0286202i
$819$		0			0
$820$	−21.8990	−	36.9937i	−0.764747	−	1.29187i
$821$	23.7800	−	13.7294i	0.829926	−	0.479158i	−0.0239013	−	0.999714i	$-0.507609\pi$
$821$	23.7800	−	13.7294i	0.829926	−	0.479158i	0.853827	+	0.520556i	$0.174275\pi$
$822$		0			0
$823$	3.30590	+	1.90866i	0.115237	+	0.0665318i	0.556510	−	0.830841i	$-0.312140\pi$
$823$	3.30590	+	1.90866i	0.115237	+	0.0665318i	−0.441274	+	0.897372i	$0.645473\pi$
$824$	−0.669247	−	40.9537i	−0.0233143	−	1.42669i
$825$		0			0
$826$	35.6313	+	17.0306i	1.23977	+	0.592571i
$827$	35.4266			1.23190			0.615951	−	0.787784i	$-0.288772\pi$
$827$	35.4266			1.23190			0.615951	+	0.787784i	$0.288772\pi$
$828$		0			0
$829$	3.21958	+	5.57647i	0.111821	+	0.193679i	0.916504	−	0.400025i	$-0.130998\pi$
$829$	3.21958	+	5.57647i	0.111821	+	0.193679i	−0.804684	+	0.593704i	$0.797665\pi$
$830$	30.3473	+	17.3013i	1.05337	+	0.600538i
$831$		0			0
$832$	12.2211	+	19.6552i	0.423692	+	0.681420i
$833$	−16.3762	+	12.9254i	−0.567403	+	0.447839i
$834$		0			0
$835$	0.707492	−	0.408471i	0.0244838	−	0.0141357i
$836$	−4.48726	−	2.52595i	−0.155195	−	0.0873618i
$837$		0			0
$838$	16.9036	+	28.9130i	0.583925	+	0.998785i
$839$	11.5771	−	20.0521i	0.399686	−	0.692276i	−0.594001	−	0.804464i	$-0.702453\pi$
$839$	11.5771	−	20.0521i	0.399686	−	0.692276i	0.993687	+	0.112188i	$0.0357859\pi$
$840$		0			0
$841$	−5.79348	−	10.0346i	−0.199775	−	0.346021i
$842$	−15.9152	+	27.9161i	−0.548476	+	0.962051i
$843$		0			0
$844$	−22.6425	+	13.4036i	−0.779389	+	0.461373i
$845$	8.71394	+	5.03100i	0.299769	+	0.173072i
$846$		0			0
$847$	1.62162	+	22.3946i	0.0557195	+	0.769486i
$848$	37.2803	−	22.6207i	1.28021	−	0.776799i
$849$		0			0
$850$	−1.00822	+	0.589444i	−0.0345818	+	0.0202178i
$851$	−26.3247	+	45.5957i	−0.902398	+	1.56300i
$852$		0			0
$853$	10.7558	−	18.6296i	0.368272	−	0.637865i	−0.621024	−	0.783792i	$-0.713283\pi$
$853$	10.7558	−	18.6296i	0.368272	−	0.637865i	0.989295	+	0.145927i	$0.0466163\pi$
$854$	−35.0863	+	24.0724i	−1.20063	+	0.823742i
$855$		0			0
$856$	1.50052	−	2.69992i	0.0512867	−	0.0922812i
$857$			7.71222i			0.263444i	0.991287	+	0.131722i	$0.0420507\pi$
$857$			7.71222i			0.263444i	−0.991287	+	0.131722i	$0.957949\pi$
$858$		0			0
$859$		−	12.7145i		−	0.433813i	−0.976192	−	0.216907i	$-0.930403\pi$
$859$		−	12.7145i		−	0.433813i	0.976192	−	0.216907i	$-0.0695967\pi$
$860$	−21.7519	+	38.6415i	−0.741734	+	1.31766i
$861$		0			0
$862$	16.2763	+	27.8400i	0.554372	+	0.948235i
$863$	−8.09063	+	14.0134i	−0.275408	+	0.477021i	−0.970238	−	0.242153i	$-0.922146\pi$
$863$	−8.09063	+	14.0134i	−0.275408	+	0.477021i	0.694830	+	0.719174i	$0.255480\pi$
$864$		0			0
$865$	21.8540	+	37.8522i	0.743058	+	1.28701i
$866$	13.8855	−	0.0756311i	0.471850	−	0.00257005i
$867$		0			0
$868$	−7.75678	+	16.4585i	−0.263282	+	0.558637i
$869$	−8.16233	+	4.71252i	−0.276888	+	0.159861i
$870$		0			0
$871$			16.7248i			0.566697i
$872$	24.4820	+	40.8479i	0.829067	+	1.38328i
$873$		0			0
$874$	−10.8357	−	6.17753i	−0.366522	−	0.208958i
$875$	30.2630	−	2.19139i	1.02308	−	0.0740825i
$876$		0			0
$877$	22.6743			0.765657			0.382829	−	0.923819i	$-0.374950\pi$
$877$	22.6743			0.765657			0.382829	+	0.923819i	$0.374950\pi$
$878$	4.92497	−	2.87931i	0.166210	−	0.0971721i
$879$		0			0
$880$	−0.300236	−	13.7785i	−0.0101209	−	0.464472i
$881$		−	32.4526i		−	1.09336i	−0.837343	−	0.546678i	$-0.815892\pi$
$881$		−	32.4526i		−	1.09336i	0.837343	−	0.546678i	$-0.184108\pi$
$882$		0			0
$883$			17.1370i			0.576708i	0.957524	+	0.288354i	$0.0931079\pi$
$883$			17.1370i			0.576708i	−0.957524	+	0.288354i	$0.906892\pi$
$884$	15.0276	+	8.45930i	0.505434	+	0.284517i
$885$		0			0
$886$	−24.9261	−	42.6353i	−0.837409	−	1.43236i
$887$	16.1179			0.541188			0.270594	−	0.962694i	$-0.412780\pi$
$887$	16.1179			0.541188			0.270594	+	0.962694i	$0.412780\pi$
$888$		0			0
$889$	−8.77267	+	0.635241i	−0.294226	+	0.0213053i
$890$	7.25359	−	12.7231i	0.243141	−	0.426480i
$891$		0			0
$892$	−28.4897	−	16.0373i	−0.953906	−	0.536969i
$893$			3.09610i			0.103607i
$894$		0			0
$895$	31.5786	−	18.2319i	1.05556	−	0.609425i
$896$	3.29828	+	29.7510i	0.110188	+	0.993911i
$897$		0			0
$898$	−0.0627837	−	11.5268i	−0.00209512	−	0.384655i
$899$	−7.17422	−	12.4261i	−0.239274	−	0.414434i
$900$		0			0
$901$	16.2454	−	28.1378i	0.541213	−	0.937408i
$902$	−19.1442	+	11.1924i	−0.637433	+	0.372666i
$903$		0			0
$904$	−37.9544	+	22.7479i	−1.26235	+	0.756583i
$905$			27.3412i			0.908853i
$906$		0			0
$907$		−	22.5781i		−	0.749692i	−0.927087	−	0.374846i	$-0.877696\pi$
$907$		−	22.5781i		−	0.749692i	0.927087	−	0.374846i	$-0.122304\pi$
$908$	23.2989	−	0.253814i	0.773201	−	0.00842311i
$909$		0			0
$910$	−13.3091	−	19.3984i	−0.441193	−	0.643052i
$911$	1.81686	−	3.14689i	0.0601951	−	0.104261i	−0.834357	−	0.551224i	$-0.814161\pi$
$911$	1.81686	−	3.14689i	0.0601951	−	0.104261i	0.894553	+	0.446963i	$0.147494\pi$
$912$		0			0
$913$	9.00993	−	15.6056i	0.298185	−	0.516472i
$914$	−14.8138	−	25.3385i	−0.489997	−	0.838123i
$915$		0			0
$916$	35.0678	−	0.382022i	1.15867	−	0.0126224i
$917$	2.75711	+	38.0756i	0.0910478	+	1.25737i
$918$		0			0
$919$	43.8787	+	25.3334i	1.44742	+	0.835671i	0.998327	−	0.0578124i	$-0.0184125\pi$
$919$	43.8787	+	25.3334i	1.44742	+	0.835671i	0.449097	+	0.893483i	$0.351746\pi$
$920$	−0.545448	−	33.3780i	−0.0179829	−	1.10044i
$921$		0			0
$922$	−18.6407	−	10.6273i	−0.613899	−	0.349990i
$923$	3.95245	+	6.84585i	0.130097	+	0.225334i
$924$		0			0
$925$	−1.34311	+	2.32633i	−0.0441611	+	0.0764893i
$926$	−25.7008	+	15.0256i	−0.844580	+	0.493771i
$927$		0			0
$928$	−20.7567	−	11.2417i	−0.681373	−	0.369026i
$929$	26.6636	−	15.3942i	0.874804	−	0.505068i	0.00586201	−	0.999983i	$-0.498134\pi$
$929$	26.6636	−	15.3942i	0.874804	−	0.505068i	0.868942	+	0.494915i	$0.164801\pi$
$930$		0			0
$931$	−10.5611	−	4.20635i	−0.346127	−	0.137858i
$932$	−39.0527	−	21.9834i	−1.27921	−	0.720089i
$933$		0			0
$934$	0.382688	−	0.671252i	0.0125219	−	0.0219640i
$935$	−5.13433	−	8.89291i	−0.167910	−	0.290829i
$936$		0			0
$937$	8.42154			0.275120			0.137560	−	0.990493i	$-0.456074\pi$
$937$	8.42154			0.275120			0.137560	+	0.990493i	$0.456074\pi$
$938$	−9.32781	+	19.5156i	−0.304564	+	0.637206i
$939$		0			0
$940$	−7.13066	+	4.22112i	−0.232576	+	0.137678i
$941$	−1.21299	−	0.700319i	−0.0395423	−	0.0228298i	0.480099	−	0.877215i	$-0.340601\pi$
$941$	−1.21299	−	0.700319i	−0.0395423	−	0.0228298i	−0.519641	+	0.854385i	$0.673934\pi$
$942$		0			0
$943$	−46.5186	+	26.8575i	−1.51485	+	0.874601i
$944$	20.3079	−	37.0138i	0.660966	−	1.20470i
$945$		0			0
$946$	19.8716	+	11.3290i	0.646081	+	0.368338i
$947$	8.75952	+	15.1719i	0.284646	+	0.493022i	0.972523	−	0.232806i	$-0.0747906\pi$
$947$	8.75952	+	15.1719i	0.284646	+	0.493022i	−0.687877	+	0.725827i	$0.741457\pi$
$948$		0			0
$949$	−6.50369	+	11.2647i	−0.211119	+	0.365668i
$950$	−0.552845	−	0.315183i	−0.0179367	−	0.0102259i
$951$		0			0
$952$	12.8173	+	18.2522i	0.415411	+	0.591556i
$953$		−	18.4588i		−	0.597939i	−0.954263	−	0.298969i	$-0.903357\pi$
$953$		−	18.4588i		−	0.597939i	0.954263	−	0.298969i	$-0.0966428\pi$
$954$		0			0
$955$	16.6515	−	9.61373i	0.538829	−	0.311093i
$956$	3.08047	+	5.20378i	0.0996295	+	0.168302i
$957$		0			0
$958$	9.27326	−	0.0505091i	0.299605	−	0.00163187i
$959$	39.8761	−	2.88749i	1.28767	−	0.0932418i
$960$		0			0
$961$	−9.58841	−	16.6076i	−0.309303	−	0.535729i
$962$	39.6640	−	0.216040i	1.27882	−	0.00696540i
$963$		0			0
$964$	−13.8956	+	0.151376i	−0.447547	+	0.00487550i
$965$	6.30434	+	3.63982i	0.202944	+	0.117170i
$966$		0			0
$967$	29.3155	−	16.9253i	0.942724	−	0.544282i	0.0519110	−	0.998652i	$-0.483469\pi$
$967$	29.3155	−	16.9253i	0.942724	−	0.544282i	0.890813	+	0.454370i	$0.150135\pi$
$968$	24.0003	−	0.392201i	0.771398	−	0.0126058i
$969$		0			0
$970$	−25.2896	−	14.4179i	−0.812002	−	0.462931i
$971$	−24.4382	+	42.3283i	−0.784260	+	1.35838i	0.145180	+	0.989405i	$0.453624\pi$
$971$	−24.4382	+	42.3283i	−0.784260	+	1.35838i	−0.929440	+	0.368973i	$0.879709\pi$
$972$		0			0
$973$	15.5737	+	22.9663i	0.499270	+	0.736265i
$974$	−38.6914	+	22.6204i	−1.23975	+	0.724804i
$975$		0			0
$976$	23.5969	+	38.8891i	0.755319	+	1.24481i
$977$	−42.8709	−	24.7515i	−1.37156	−	0.791871i	−0.380437	−	0.924807i	$-0.624226\pi$
$977$	−42.8709	−	24.7515i	−1.37156	−	0.791871i	−0.991125	+	0.132935i	$0.957560\pi$
$978$		0			0
$979$	−6.54267	−	3.77741i	−0.209105	−	0.120727i
$980$	−4.71098	−	30.0582i	−0.150487	−	0.960175i
$981$		0			0
$982$	−1.20403	−	2.05945i	−0.0384221	−	0.0657198i
$983$	−5.13378			−0.163742			−0.0818710	−	0.996643i	$-0.526090\pi$
$983$	−5.13378			−0.163742			−0.0818710	+	0.996643i	$0.526090\pi$
$984$		0			0
$985$	−5.24256			−0.167042
$986$	−17.5880	+	0.0957972i	−0.560115	+	0.00305081i
$987$		0			0
$988$	0.102360	+	9.39620i	0.00325652	+	0.298933i
$989$	47.9833	+	27.7032i	1.52578	+	0.880910i
$990$		0			0
$991$	−3.52532	+	2.03535i	−0.111986	+	0.0646549i	−0.554947	−	0.831886i	$-0.687261\pi$
$991$	−3.52532	+	2.03535i	−0.111986	+	0.0646549i	0.442961	+	0.896541i	$0.353928\pi$
$992$	17.1037	+	9.26321i	0.543041	+	0.294107i
$993$		0			0
$994$	0.793888	+	10.1926i	0.0251806	+	0.323289i
$995$	6.84171	+	11.8502i	0.216897	+	0.375676i
$996$		0			0
$997$	−41.4157			−1.31165			−0.655824	−	0.754913i	$-0.727679\pi$
$997$	−41.4157			−1.31165			−0.655824	+	0.754913i	$0.727679\pi$
$998$	−0.0981043	−	18.0115i	−0.00310544	−	0.570145i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.o.a.359.1		88
3.2	odd	2		252.2.o.a.191.44	yes	88
4.3	odd	2	inner	756.2.o.a.359.15		88
7.4	even	3		756.2.bb.a.683.30		88
9.4	even	3		252.2.bb.a.23.30	yes	88
9.5	odd	6		756.2.bb.a.611.15		88
12.11	even	2		252.2.o.a.191.30	yes	88
21.11	odd	6		252.2.bb.a.11.15	yes	88
28.11	odd	6		756.2.bb.a.683.15		88
36.23	even	6		756.2.bb.a.611.30		88
36.31	odd	6		252.2.bb.a.23.15	yes	88
63.4	even	3		252.2.o.a.95.30	✓	88
63.32	odd	6	inner	756.2.o.a.179.15		88
84.11	even	6		252.2.bb.a.11.30	yes	88
252.67	odd	6		252.2.o.a.95.44	yes	88
252.95	even	6	inner	756.2.o.a.179.1		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.30	✓	88	63.4	even	3
252.2.o.a.95.44	yes	88	252.67	odd	6
252.2.o.a.191.30	yes	88	12.11	even	2
252.2.o.a.191.44	yes	88	3.2	odd	2
252.2.bb.a.11.15	yes	88	21.11	odd	6
252.2.bb.a.11.30	yes	88	84.11	even	6
252.2.bb.a.23.15	yes	88	36.31	odd	6
252.2.bb.a.23.30	yes	88	9.4	even	3
756.2.o.a.179.1		88	252.95	even	6	inner
756.2.o.a.179.15		88	63.32	odd	6	inner
756.2.o.a.359.1		88	1.1	even	1	trivial
756.2.o.a.359.15		88	4.3	odd	2	inner
756.2.bb.a.611.15		88	9.5	odd	6
756.2.bb.a.611.30		88	36.23	even	6
756.2.bb.a.683.15		88	28.11	odd	6
756.2.bb.a.683.30		88	7.4	even	3

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41419 + 0.00770275i) q^{2} +(1.99988 - 0.0217863i) q^{4} +2.17323i q^{5} +(-0.191082 - 2.63884i) q^{7} +(-2.82805 + 0.0462147i) q^{8} +O(q^{10})\)	\(q+(-1.41419 + 0.00770275i) q^{2} +(1.99988 - 0.0217863i) q^{4} +2.17323i q^{5} +(-0.191082 - 2.63884i) q^{7} +(-2.82805 + 0.0462147i) q^{8} +(-0.0167398 - 3.07336i) q^{10} -1.58540 q^{11} +(1.44655 + 2.50550i) q^{13} +(0.290553 + 3.73036i) q^{14} +(3.99905 - 0.0871402i) q^{16} +(2.58107 - 1.49018i) q^{17} +(1.40642 + 0.811997i) q^{19} +(0.0473467 + 4.34619i) q^{20} +(2.24206 - 0.0122119i) q^{22} +5.43086 q^{23} +0.277087 q^{25} +(-2.06500 - 3.53211i) q^{26} +(-0.439632 - 5.27321i) q^{28} +(3.61383 + 2.08645i) q^{29} +(-2.97782 - 1.71924i) q^{31} +(-5.65476 + 0.154037i) q^{32} +(-3.63866 + 2.12729i) q^{34} +(5.73480 - 0.415265i) q^{35} +(-4.84724 + 8.39566i) q^{37} +(-1.99520 - 1.13749i) q^{38} +(-0.100435 - 6.14599i) q^{40} +(-8.56561 + 4.94536i) q^{41} +(8.83531 + 5.10107i) q^{43} +(-3.17061 + 0.0345401i) q^{44} +(-7.68028 + 0.0418325i) q^{46} +(0.953235 + 1.65105i) q^{47} +(-6.92698 + 1.00847i) q^{49} +(-0.391855 + 0.00213433i) q^{50} +(2.94751 + 4.97918i) q^{52} +(9.44107 - 5.45080i) q^{53} -3.44543i q^{55} +(0.662343 + 7.45395i) q^{56} +(-5.12673 - 2.92280i) q^{58} +(5.27736 - 9.14066i) q^{59} +(5.68603 + 9.84849i) q^{61} +(4.22445 + 2.40840i) q^{62} +(7.99573 - 0.261395i) q^{64} +(-5.44501 + 3.14368i) q^{65} +(5.00642 + 2.89046i) q^{67} +(5.12938 - 3.03642i) q^{68} +(-8.10691 + 0.631438i) q^{70} +2.73233 q^{71} +(2.24800 + 3.89365i) q^{73} +(6.79026 - 11.9104i) q^{74} +(2.83036 + 1.59326i) q^{76} +(0.302942 + 4.18362i) q^{77} +(5.14844 - 2.97245i) q^{79} +(0.189375 + 8.69084i) q^{80} +(12.0753 - 7.05966i) q^{82} +(-5.68306 + 9.84336i) q^{83} +(3.23851 + 5.60926i) q^{85} +(-12.5341 - 7.14584i) q^{86} +(4.48359 - 0.0732687i) q^{88} +(4.12683 + 2.38263i) q^{89} +(6.33520 - 4.29597i) q^{91} +(10.8611 - 0.118319i) q^{92} +(-1.36078 - 2.32756i) q^{94} +(-1.76465 + 3.05647i) q^{95} +(4.73593 - 8.20287i) q^{97} +(9.78831 - 1.47953i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 3 q^{2} + q^{4}+O(q^{10}) \) 88 * q + 3 * q^2 + q^4	\( 88 q + 3 q^{2} + q^{4} + 2 q^{10} - 4 q^{13} + 3 q^{14} + q^{16} + 6 q^{20} - 6 q^{22} - 60 q^{25} + 6 q^{26} + 24 q^{29} - 27 q^{32} - 4 q^{34} - 4 q^{37} + 8 q^{40} + 12 q^{41} + 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} + 14 q^{52} + 66 q^{56} - 10 q^{58} + 2 q^{61} - 8 q^{64} - 18 q^{65} + 30 q^{70} - 4 q^{73} - 6 q^{76} + 30 q^{77} - 87 q^{80} - 4 q^{82} - 14 q^{85} - 18 q^{88} - 60 q^{89} - 24 q^{92} + 9 q^{94} - 4 q^{97} + 57 q^{98}+O(q^{100}) \) 88 * q + 3 * q^2 + q^4 + 2 * q^10 - 4 * q^13 + 3 * q^14 + q^16 + 6 * q^20 - 6 * q^22 - 60 * q^25 + 6 * q^26 + 24 * q^29 - 27 * q^32 - 4 * q^34 - 4 * q^37 + 8 * q^40 + 12 * q^41 + 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 + 14 * q^52 + 66 * q^56 - 10 * q^58 + 2 * q^61 - 8 * q^64 - 18 * q^65 + 30 * q^70 - 4 * q^73 - 6 * q^76 + 30 * q^77 - 87 * q^80 - 4 * q^82 - 14 * q^85 - 18 * q^88 - 60 * q^89 - 24 * q^92 + 9 * q^94 - 4 * q^97 + 57 * q^98

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