LMFDB - Embedded newform 288.2.w.a.179.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(35,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("288.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			179.4
Character	$\chi$	$=$	288.179
Dual form			288.2.w.a.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.337906 - 1.37325i) q^{2} +(-1.77164 + 0.928061i) q^{4} +(1.32268 + 3.19322i) q^{5} +(-2.32913 - 2.32913i) q^{7} +(1.87311 + 2.11931i) q^{8} +O(q^{10})$	\(q+(-0.337906 - 1.37325i) q^{2} +(-1.77164 + 0.928061i) q^{4} +(1.32268 + 3.19322i) q^{5} +(-2.32913 - 2.32913i) q^{7} +(1.87311 + 2.11931i) q^{8} +(3.93816 - 2.89538i) q^{10} +(1.47061 + 3.55036i) q^{11} +(4.49745 + 1.86291i) q^{13} +(-2.41145 + 3.98551i) q^{14} +(2.27741 - 3.28838i) q^{16} +4.93452 q^{17} +(-1.98599 + 4.79460i) q^{19} +(-5.30681 - 4.42971i) q^{20} +(4.37861 - 3.21920i) q^{22} +(1.08935 + 1.08935i) q^{23} +(-4.91167 + 4.91167i) q^{25} +(1.03852 - 6.80562i) q^{26} +(6.28795 + 1.96480i) q^{28} +(-3.43073 - 1.42105i) q^{29} -8.82364i q^{31} +(-5.28532 - 2.01629i) q^{32} +(-1.66741 - 6.77634i) q^{34} +(4.35675 - 10.5181i) q^{35} +(1.94208 - 0.804437i) q^{37} +(7.25526 + 1.10713i) q^{38} +(-4.28990 + 8.78441i) q^{40} +(-5.87486 + 5.87486i) q^{41} +(-2.44320 + 1.01201i) q^{43} +(-5.90033 - 4.92514i) q^{44} +(1.12785 - 1.86404i) q^{46} +1.61865i q^{47} +3.84969i q^{49} +(8.40464 + 5.08527i) q^{50} +(-9.69675 + 0.873514i) q^{52} +(-5.62320 + 2.32921i) q^{53} +(-9.39195 + 9.39195i) q^{55} +(0.573428 - 9.29886i) q^{56} +(-0.792199 + 5.19143i) q^{58} +(7.67495 - 3.17907i) q^{59} +(3.16892 - 7.65045i) q^{61} +(-12.1171 + 2.98157i) q^{62} +(-0.982926 + 7.93939i) q^{64} +16.8254i q^{65} +(3.31324 + 1.37239i) q^{67} +(-8.74219 + 4.57954i) q^{68} +(-15.9162 - 2.42877i) q^{70} +(2.13686 - 2.13686i) q^{71} +(-1.81541 - 1.81541i) q^{73} +(-1.76094 - 2.39514i) q^{74} +(-0.931227 - 10.3374i) q^{76} +(4.84401 - 11.6945i) q^{77} +1.42339 q^{79} +(13.5128 + 2.92281i) q^{80} +(10.0528 + 6.08250i) q^{82} +(1.04174 + 0.431504i) q^{83} +(6.52678 + 15.7570i) q^{85} +(2.21532 + 3.01317i) q^{86} +(-4.76969 + 9.76688i) q^{88} +(-0.708782 - 0.708782i) q^{89} +(-6.13620 - 14.8141i) q^{91} +(-2.94090 - 0.918947i) q^{92} +(2.22282 - 0.546953i) q^{94} -17.9370 q^{95} +12.2142 q^{97} +(5.28660 - 1.30084i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) $ 32 * q - 4 * q^2 - 4 * q^8	$ 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) $ 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.337906	−	1.37325i	−0.238936	−	0.971035i
$2$	−0.337906	−	1.37325i	−0.238936	−	0.971035i
$3$		0			0
$3$		0			0
$4$	−1.77164	+	0.928061i	−0.885819	+	0.464030i
$5$	1.32268	+	3.19322i	0.591519	+	1.42805i	0.882035	+	0.471183i	$0.156173\pi$
$5$	1.32268	+	3.19322i	0.591519	+	1.42805i	−0.290517	+	0.956870i	$0.593827\pi$
$6$		0			0
$7$	−2.32913	−	2.32913i	−0.880328	−	0.880328i	0.113239	−	0.993568i	$-0.463877\pi$
$7$	−2.32913	−	2.32913i	−0.880328	−	0.880328i	−0.993568	+	0.113239i	$0.963877\pi$
$8$	1.87311	+	2.11931i	0.662244	+	0.749288i
$9$		0			0
$10$	3.93816	−	2.89538i	1.24535	−	0.915599i
$11$	1.47061	+	3.55036i	0.443405	+	1.07047i	0.974746	+	0.223316i	$0.0716881\pi$
$11$	1.47061	+	3.55036i	0.443405	+	1.07047i	−0.531341	+	0.847158i	$0.678312\pi$
$12$		0			0
$13$	4.49745	+	1.86291i	1.24737	+	0.516677i	0.906010	−	0.423256i	$-0.139113\pi$
$13$	4.49745	+	1.86291i	1.24737	+	0.516677i	0.341358	+	0.939933i	$0.389113\pi$
$14$	−2.41145	+	3.98551i	−0.644488	+	1.06517i
$15$		0			0
$16$	2.27741	−	3.28838i	0.569351	−	0.822094i
$17$	4.93452			1.19680			0.598399	−	0.801199i	$-0.295804\pi$
$17$	4.93452			1.19680			0.598399	+	0.801199i	$0.295804\pi$
$18$		0			0
$19$	−1.98599	+	4.79460i	−0.455617	+	1.09996i	0.514538	+	0.857468i	$0.327964\pi$
$19$	−1.98599	+	4.79460i	−0.455617	+	1.09996i	−0.970154	+	0.242488i	$0.922036\pi$
$20$	−5.30681	−	4.42971i	−1.18664	−	0.990514i
$21$		0			0
$22$	4.37861	−	3.21920i	0.933522	−	0.686336i
$23$	1.08935	+	1.08935i	0.227144	+	0.227144i	0.811499	−	0.584354i	$-0.198652\pi$
$23$	1.08935	+	1.08935i	0.227144	+	0.227144i	−0.584354	+	0.811499i	$0.698652\pi$
$24$		0			0
$25$	−4.91167	+	4.91167i	−0.982334	+	0.982334i
$26$	1.03852	−	6.80562i	0.203670	−	1.33469i
$27$		0			0
$28$	6.28795	+	1.96480i	1.18831	+	0.371313i
$29$	−3.43073	−	1.42105i	−0.637070	−	0.263883i	0.0406838	−	0.999172i	$-0.487046\pi$
$29$	−3.43073	−	1.42105i	−0.637070	−	0.263883i	−0.677754	+	0.735289i	$0.737046\pi$
$30$		0			0
$31$		−	8.82364i		−	1.58477i	−0.610019	−	0.792387i	$-0.708838\pi$
$31$		−	8.82364i		−	1.58477i	0.610019	−	0.792387i	$-0.291162\pi$
$32$	−5.28532	−	2.01629i	−0.934321	−	0.356433i
$33$		0			0
$34$	−1.66741	−	6.77634i	−0.285958	−	1.16213i
$35$	4.35675	−	10.5181i	0.736425	−	1.77789i
$36$		0			0
$37$	1.94208	−	0.804437i	0.319276	−	0.132249i	−0.217289	−	0.976107i	$-0.569721\pi$
$37$	1.94208	−	0.804437i	0.319276	−	0.132249i	0.536565	+	0.843859i	$0.319721\pi$
$38$	7.25526	+	1.10713i	1.17696	+	0.179601i
$39$		0			0
$40$	−4.28990	+	8.78441i	−0.678293	+	1.38894i
$41$	−5.87486	+	5.87486i	−0.917498	+	0.917498i	−0.996847	−	0.0793485i	$-0.974716\pi$
$41$	−5.87486	+	5.87486i	−0.917498	+	0.917498i	0.0793485	+	0.996847i	$0.474716\pi$
$42$		0			0
$43$	−2.44320	+	1.01201i	−0.372585	+	0.154330i	−0.561115	−	0.827738i	$-0.689628\pi$
$43$	−2.44320	+	1.01201i	−0.372585	+	0.154330i	0.188530	+	0.982067i	$0.439628\pi$
$44$	−5.90033	−	4.92514i	−0.889509	−	0.742493i
$45$		0			0
$46$	1.12785	−	1.86404i	0.166292	−	0.274838i
$47$			1.61865i			0.236105i	0.993007	+	0.118052i	$0.0376651\pi$
$47$			1.61865i			0.236105i	−0.993007	+	0.118052i	$0.962335\pi$
$48$		0			0
$49$			3.84969i			0.549956i
$50$	8.40464	+	5.08527i	1.18860	+	0.719166i
$51$		0			0
$52$	−9.69675	+	0.873514i	−1.34470	+	0.121135i
$53$	−5.62320	+	2.32921i	−0.772407	+	0.319941i	−0.733847	−	0.679315i	$-0.762277\pi$
$53$	−5.62320	+	2.32921i	−0.772407	+	0.319941i	−0.0385598	+	0.999256i	$0.512277\pi$
$54$		0			0
$55$	−9.39195	+	9.39195i	−1.26641	+	1.26641i
$56$	0.573428	−	9.29886i	0.0766275	−	1.24261i
$57$		0			0
$58$	−0.792199	+	5.19143i	−0.104021	+	0.681668i
$59$	7.67495	−	3.17907i	0.999193	−	0.413879i	0.177692	−	0.984086i	$-0.443137\pi$
$59$	7.67495	−	3.17907i	0.999193	−	0.413879i	0.821501	+	0.570207i	$0.193137\pi$
$60$		0			0
$61$	3.16892	−	7.65045i	0.405738	−	0.979539i	−0.580508	−	0.814255i	$-0.697146\pi$
$61$	3.16892	−	7.65045i	0.405738	−	0.979539i	0.986246	−	0.165284i	$-0.0528542\pi$
$62$	−12.1171	+	2.98157i	−1.53887	+	0.378659i
$63$		0			0
$64$	−0.982926	+	7.93939i	−0.122866	+	0.992423i
$65$			16.8254i			2.08693i
$66$		0			0
$67$	3.31324	+	1.37239i	0.404777	+	0.167664i	0.575777	−	0.817607i	$-0.304700\pi$
$67$	3.31324	+	1.37239i	0.404777	+	0.167664i	−0.171000	+	0.985271i	$0.554700\pi$
$68$	−8.74219	+	4.57954i	−1.06015	+	0.555350i
$69$		0			0
$70$	−15.9162	−	2.42877i	−1.90235	−	0.290293i
$71$	2.13686	−	2.13686i	0.253599	−	0.253599i	−0.568846	−	0.822444i	$-0.692610\pi$
$71$	2.13686	−	2.13686i	0.253599	−	0.253599i	0.822444	+	0.568846i	$0.192610\pi$
$72$		0			0
$73$	−1.81541	−	1.81541i	−0.212478	−	0.212478i	0.592841	−	0.805319i	$-0.298006\pi$
$73$	−1.81541	−	1.81541i	−0.212478	−	0.212478i	−0.805319	+	0.592841i	$0.798006\pi$
$74$	−1.76094	−	2.39514i	−0.204705	−	0.278430i
$75$		0			0
$76$	−0.931227	−	10.3374i	−0.106819	−	1.18578i
$77$	4.84401	−	11.6945i	0.552027	−	1.33271i
$78$		0			0
$79$	1.42339			0.160144			0.0800721	−	0.996789i	$-0.474485\pi$
$79$	1.42339			0.160144			0.0800721	+	0.996789i	$0.474485\pi$
$80$	13.5128	+	2.92281i	1.51078	+	0.326780i
$81$		0			0
$82$	10.0528	+	6.08250i	1.11015	+	0.671700i
$83$	1.04174	+	0.431504i	0.114346	+	0.0473637i	0.439123	−	0.898427i	$-0.355289\pi$
$83$	1.04174	+	0.431504i	0.114346	+	0.0473637i	−0.324777	+	0.945791i	$0.605289\pi$
$84$		0			0
$85$	6.52678	+	15.7570i	0.707928	+	1.70909i
$86$	2.21532	+	3.01317i	0.238884	+	0.324918i
$87$		0			0
$88$	−4.76969	+	9.76688i	−0.508451	+	1.04115i
$89$	−0.708782	−	0.708782i	−0.0751308	−	0.0751308i	0.668543	−	0.743674i	$-0.266918\pi$
$89$	−0.708782	−	0.708782i	−0.0751308	−	0.0751308i	−0.743674	+	0.668543i	$0.766918\pi$
$90$		0			0
$91$	−6.13620	−	14.8141i	−0.643248	−	1.55294i
$92$	−2.94090	−	0.918947i	−0.306611	−	0.0958069i
$93$		0			0
$94$	2.22282	−	0.546953i	0.229266	−	0.0564139i
$95$	−17.9370			−1.84030
$96$		0			0
$97$	12.2142			1.24016			0.620082	−	0.784537i	$-0.287099\pi$
$97$	12.2142			1.24016			0.620082	+	0.784537i	$0.287099\pi$
$98$	5.28660	−	1.30084i	0.534027	−	0.131404i
$99$		0			0
$100$	4.14337	−	13.2600i	0.414337	−	1.32600i
$101$	−6.13564	−	14.8127i	−0.610519	−	1.47392i	−0.862432	−	0.506173i	$-0.831060\pi$
$101$	−6.13564	−	14.8127i	−0.610519	−	1.47392i	0.251913	−	0.967750i	$-0.418940\pi$
$102$		0			0
$103$	−9.45184	−	9.45184i	−0.931318	−	0.931318i	0.0664707	−	0.997788i	$-0.478826\pi$
$103$	−9.45184	−	9.45184i	−0.931318	−	0.931318i	−0.997788	+	0.0664707i	$0.978826\pi$
$104$	4.47615	+	13.0209i	0.438922	+	1.27680i
$105$		0			0
$106$	5.09870	+	6.93502i	0.495230	+	0.673589i
$107$	−3.93527	−	9.50057i	−0.380436	−	0.918455i	−0.991881	−	0.127168i	$-0.959411\pi$
$107$	−3.93527	−	9.50057i	−0.380436	−	0.918455i	0.611445	−	0.791287i	$-0.290589\pi$
$108$		0			0
$109$	−10.8399	−	4.49003i	−1.03827	−	0.430067i	−0.202582	−	0.979265i	$-0.564933\pi$
$109$	−10.8399	−	4.49003i	−1.03827	−	0.430067i	−0.835692	+	0.549198i	$0.814933\pi$
$110$	16.0711	+	9.72391i	1.53232	+	0.927139i
$111$		0			0
$112$	−12.9634	+	2.35468i	−1.22493	+	0.222497i
$113$	9.42620			0.886742			0.443371	−	0.896338i	$-0.353782\pi$
$113$	9.42620			0.886742			0.443371	+	0.896338i	$0.353782\pi$
$114$		0			0
$115$	−2.03767	+	4.91937i	−0.190014	+	0.458734i
$116$	7.39683	−	0.666330i	0.686778	−	0.0618672i
$117$		0			0
$118$	−6.95907	−	9.46540i	−0.640634	−	0.871361i
$119$	−11.4931	−	11.4931i	−1.05357	−	1.05357i
$120$		0			0
$121$	−2.66419	+	2.66419i	−0.242199	+	0.242199i
$122$	−11.5768	−	1.76659i	−1.04811	−	0.159939i
$123$		0			0
$124$	8.18888	+	15.6323i	0.735383	+	1.40382i
$125$	−6.21449	−	2.57413i	−0.555841	−	0.230237i
$126$		0			0
$127$			6.69360i			0.593961i	0.954884	+	0.296980i	$0.0959796\pi$
$127$			6.69360i			0.593961i	−0.954884	+	0.296980i	$0.904020\pi$
$128$	11.2349	−	1.33297i	0.993035	−	0.117819i
$129$		0			0
$130$	23.1055	−	5.68541i	2.02649	−	0.498643i
$131$	−5.25325	+	12.6825i	−0.458979	+	1.10807i	0.509833	+	0.860273i	$0.329707\pi$
$131$	−5.25325	+	12.6825i	−0.458979	+	1.10807i	−0.968811	+	0.247799i	$0.920293\pi$
$132$		0			0
$133$	15.7929	−	6.54162i	1.36941	−	0.567230i
$134$	0.765070	−	5.01365i	0.0660920	−	0.433114i
$135$		0			0
$136$	9.24290	+	10.4578i	0.792572	+	0.896746i
$137$	3.46480	−	3.46480i	0.296018	−	0.296018i	−0.543434	−	0.839452i	$-0.682876\pi$
$137$	3.46480	−	3.46480i	0.296018	−	0.296018i	0.839452	+	0.543434i	$0.182876\pi$
$138$		0			0
$139$	15.2400	−	6.31262i	1.29264	−	0.535429i	0.372869	−	0.927884i	$-0.378374\pi$
$139$	15.2400	−	6.31262i	1.29264	−	0.535429i	0.919771	+	0.392455i	$0.128374\pi$
$140$	2.04287	+	22.6776i	0.172654	+	1.91661i
$141$		0			0
$142$	−3.65650	−	2.21239i	−0.306847	−	0.185659i
$143$			18.7072i			1.56437i
$144$		0			0
$145$		−	12.8347i		−	1.06586i
$146$	−1.87958	+	3.10645i	−0.155555	+	0.257092i
$147$		0			0
$148$	−2.69410	+	3.22754i	−0.221454	+	0.265302i
$149$	−8.66511	+	3.58921i	−0.709873	+	0.294039i	−0.708252	−	0.705959i	$-0.750516\pi$
$149$	−8.66511	+	3.58921i	−0.709873	+	0.294039i	−0.00162119	+	0.999999i	$0.500516\pi$
$150$		0			0
$151$	16.6619	−	16.6619i	1.35592	−	1.35592i	0.477045	−	0.878879i	$-0.341708\pi$
$151$	16.6619	−	16.6619i	1.35592	−	1.35592i	0.878879	−	0.477045i	$-0.158292\pi$
$152$	−13.8812	+	4.77189i	−1.12591	+	0.387051i
$153$		0			0
$154$	−17.6963	−	2.70041i	−1.42601	−	0.217605i
$155$	28.1759	−	11.6708i	2.26314	−	0.937423i
$156$		0			0
$157$	3.37611	−	8.15066i	0.269443	−	0.650493i	−0.730014	−	0.683432i	$-0.760487\pi$
$157$	3.37611	−	8.15066i	0.269443	−	0.650493i	0.999457	+	0.0329386i	$0.0104866\pi$
$158$	−0.480974	−	1.95468i	−0.0382642	−	0.155506i
$159$		0			0
$160$	−0.552311	−	19.5441i	−0.0436641	−	1.54510i
$161$		−	5.07445i		−	0.399923i
$162$		0			0
$163$	14.2435	+	5.89984i	1.11564	+	0.462112i	0.862875	−	0.505417i	$-0.168661\pi$
$163$	14.2435	+	5.89984i	1.11564	+	0.462112i	0.252761	+	0.967529i	$0.418661\pi$
$164$	4.95590	−	15.8603i	0.386991	−	1.23849i
$165$		0			0
$166$	0.240552	−	1.57638i	0.0186704	−	0.122351i
$167$	−10.0550	+	10.0550i	−0.778080	+	0.778080i	−0.979504	−	0.201424i	$-0.935443\pi$
$167$	−10.0550	+	10.0550i	−0.778080	+	0.778080i	0.201424	+	0.979504i	$0.435443\pi$
$168$		0			0
$169$	7.56426	+	7.56426i	0.581866	+	0.581866i
$170$	19.4329	−	14.2873i	1.49044	−	1.09579i
$171$		0			0
$172$	3.38927	−	4.06035i	0.258429	−	0.309599i
$173$	3.57483	−	8.63040i	0.271789	−	0.656157i	−0.727771	−	0.685820i	$-0.759444\pi$
$173$	3.57483	−	8.63040i	0.271789	−	0.656157i	0.999560	+	0.0296634i	$0.00944353\pi$
$174$		0			0
$175$	22.8798			1.72955
$176$	15.0241	+	3.24970i	1.13248	+	0.244955i
$177$		0			0
$178$	−0.733834	+	1.21284i	−0.0550032	+	0.0909061i
$179$	−6.36855	−	2.63794i	−0.476008	−	0.197169i	0.131763	−	0.991281i	$-0.457936\pi$
$179$	−6.36855	−	2.63794i	−0.476008	−	0.197169i	−0.607771	+	0.794112i	$0.707936\pi$
$180$		0			0
$181$	−2.04004	−	4.92510i	−0.151635	−	0.366080i	0.829748	−	0.558138i	$-0.188484\pi$
$181$	−2.04004	−	4.92510i	−0.151635	−	0.366080i	−0.981384	+	0.192058i	$0.938484\pi$
$182$	−18.2700	+	13.4323i	−1.35426	+	0.995670i
$183$		0			0
$184$	−0.268195	+	4.34912i	−0.0197716	+	0.320621i
$185$	5.13749	+	5.13749i	0.377716	+	0.377716i
$186$		0			0
$187$	7.25674	+	17.5193i	0.530665	+	1.28114i
$188$	−1.50221	−	2.86767i	−0.109560	−	0.209146i
$189$		0			0
$190$	6.06104	+	24.6321i	0.439714	+	1.78700i
$191$	9.91926			0.717732			0.358866	−	0.933389i	$-0.383163\pi$
$191$	9.91926			0.717732			0.358866	+	0.933389i	$0.383163\pi$
$192$		0			0
$193$	−20.8089			−1.49785			−0.748927	−	0.662653i	$-0.769431\pi$
$193$	−20.8089			−1.49785			−0.748927	+	0.662653i	$0.769431\pi$
$194$	−4.12726	−	16.7732i	−0.296320	−	1.20424i
$195$		0			0
$196$	−3.57275	−	6.82026i	−0.255196	−	0.487162i
$197$	2.99573	+	7.23234i	0.213437	+	0.515283i	0.993947	−	0.109861i	$-0.0350405\pi$
$197$	2.99573	+	7.23234i	0.213437	+	0.515283i	−0.780510	+	0.625143i	$0.785040\pi$
$198$		0			0
$199$	−16.3928	−	16.3928i	−1.16205	−	1.16205i	−0.984026	−	0.178027i	$-0.943029\pi$
$199$	−16.3928	−	16.3928i	−1.16205	−	1.16205i	−0.178027	−	0.984026i	$-0.556971\pi$
$200$	−19.6094	−	1.20924i	−1.38660	−	0.0855065i
$201$		0			0
$202$	−18.2683	+	13.4311i	−1.28536	+	0.945009i
$203$	4.68079	+	11.3004i	0.328527	+	0.793134i
$204$		0			0
$205$	−26.5303	−	10.9892i	−1.85295	−	0.767519i
$206$	−9.78592	+	16.1736i	−0.681817	+	1.12687i
$207$		0			0
$208$	16.3685	−	10.5467i	1.13495	−	0.731284i
$209$	−19.9431			−1.37950
$210$		0			0
$211$	−9.39938	+	22.6921i	−0.647080	+	1.56219i	0.169861	+	0.985468i	$0.445668\pi$
$211$	−9.39938	+	22.6921i	−0.647080	+	1.56219i	−0.816941	+	0.576721i	$0.804332\pi$
$212$	7.80064	−	9.34519i	0.535750	−	0.641830i
$213$		0			0
$214$	−11.7169	+	8.61441i	−0.800952	+	0.588869i
$215$	−6.46314	−	6.46314i	−0.440782	−	0.440782i
$216$		0			0
$217$	−20.5514	+	20.5514i	−1.39512	+	1.39512i
$218$	−2.50307	+	16.4031i	−0.169529	+	1.11096i
$219$		0			0
$220$	7.92284	−	25.3555i	0.534158	−	1.70946i
$221$	22.1928	+	9.19255i	1.49285	+	0.618358i
$222$		0			0
$223$			13.0361i			0.872961i	0.899714	+	0.436480i	$0.143775\pi$
$223$			13.0361i			0.872961i	−0.899714	+	0.436480i	$0.856225\pi$
$224$	7.61400	+	17.0064i	0.508732	+	1.13629i
$225$		0			0
$226$	−3.18517	−	12.9445i	−0.211875	−	0.861058i
$227$	−0.970105	+	2.34204i	−0.0643882	+	0.155447i	−0.952798	−	0.303603i	$-0.901810\pi$
$227$	−0.970105	+	2.34204i	−0.0643882	+	0.155447i	0.888410	+	0.459050i	$0.151810\pi$
$228$		0			0
$229$	10.5855	−	4.38467i	0.699512	−	0.289747i	−0.00444500	−	0.999990i	$-0.501415\pi$
$229$	10.5855	−	4.38467i	0.699512	−	0.289747i	0.703957	+	0.710243i	$0.251415\pi$
$230$	7.44408	+	1.13595i	0.490848	+	0.0749021i
$231$		0			0
$232$	−3.41447	−	9.93255i	−0.224171	−	0.652104i
$233$	15.0433	−	15.0433i	0.985522	−	0.985522i	−0.0143751	−	0.999897i	$-0.504576\pi$
$233$	15.0433	−	15.0433i	0.985522	−	0.985522i	0.999897	+	0.0143751i	$0.00457589\pi$
$234$		0			0
$235$	−5.16872	+	2.14095i	−0.337170	+	0.139660i
$236$	−10.6469	+	12.7550i	−0.693052	+	0.830278i
$237$		0			0
$238$	−11.8994	+	19.6666i	−0.771321	+	1.27479i
$239$			10.1723i			0.657989i	0.944332	+	0.328995i	$0.106710\pi$
$239$			10.1723i			0.657989i	−0.944332	+	0.328995i	$0.893290\pi$
$240$		0			0
$241$		−	20.6542i		−	1.33045i	−0.746642	−	0.665227i	$-0.768335\pi$
$241$		−	20.6542i		−	1.33045i	0.746642	−	0.665227i	$-0.231665\pi$
$242$	4.55885	+	2.75836i	0.293054	+	0.177314i
$243$		0			0
$244$	1.48590	+	16.4948i	0.0951251	+	1.05597i
$245$	−12.2929	+	5.09190i	−0.785366	+	0.325309i
$246$		0			0
$247$	−17.8638	+	17.8638i	−1.13664	+	1.13664i
$248$	18.7000	−	16.5276i	1.18745	−	1.04951i
$249$		0			0
$250$	−1.43501	+	9.40387i	−0.0907577	+	0.594753i
$251$	−18.5479	+	7.68280i	−1.17073	+	0.484934i	−0.881435	−	0.472304i	$-0.843422\pi$
$251$	−18.5479	+	7.68280i	−1.17073	+	0.484934i	−0.289299	+	0.957239i	$0.593422\pi$
$252$		0			0
$253$	−2.26557	+	5.46957i	−0.142435	+	0.343869i
$254$	9.19199	−	2.26181i	0.576757	−	0.141919i
$255$		0			0
$256$	−5.62685	−	14.9779i	−0.351678	−	0.936121i
$257$			7.80823i			0.487064i	0.969893	+	0.243532i	$0.0783061\pi$
$257$			7.80823i			0.487064i	−0.969893	+	0.243532i	$0.921694\pi$
$258$		0			0
$259$	−6.39700	−	2.64972i	−0.397490	−	0.164646i
$260$	−15.6150	−	29.8085i	−0.968400	−	1.84864i
$261$		0			0
$262$	19.1913	+	2.92855i	1.18564	+	0.180926i
$263$	19.5761	−	19.5761i	1.20711	−	1.20711i	0.235158	−	0.971957i	$-0.424439\pi$
$263$	19.5761	−	19.5761i	1.20711	−	1.20711i	0.971957	−	0.235158i	$-0.0755606\pi$
$264$		0			0
$265$	−14.8754	−	14.8754i	−0.913786	−	0.913786i
$266$	−14.3198	−	19.4771i	−0.878003	−	1.19422i
$267$		0			0
$268$	−7.14353	+	0.643512i	−0.436360	+	0.0393088i
$269$	−1.69145	+	4.08353i	−0.103130	+	0.248977i	−0.967019	−	0.254705i	$-0.918022\pi$
$269$	−1.69145	+	4.08353i	−0.103130	+	0.248977i	0.863889	+	0.503682i	$0.168022\pi$
$270$		0			0
$271$	6.31185			0.383418			0.191709	−	0.981452i	$-0.438597\pi$
$271$	6.31185			0.383418			0.191709	+	0.981452i	$0.438597\pi$
$272$	11.2379	−	16.2266i	0.681398	−	0.983880i
$273$		0			0
$274$	−5.92883	−	3.58727i	−0.358173	−	0.216715i
$275$	−24.6613	−	10.2151i	−1.48713	−	0.615991i
$276$		0			0
$277$	7.53180	+	18.1834i	0.452542	+	1.09253i	0.971352	+	0.237644i	$0.0763751\pi$
$277$	7.53180	+	18.1834i	0.452542	+	1.09253i	−0.518810	+	0.854889i	$0.673625\pi$
$278$	−13.8185	−	18.7953i	−0.828779	−	1.12727i
$279$		0			0
$280$	30.4518	−	10.4683i	1.81984	−	0.625600i
$281$	−16.2957	−	16.2957i	−0.972118	−	0.972118i	0.0275040	−	0.999622i	$-0.491244\pi$
$281$	−16.2957	−	16.2957i	−0.972118	−	0.972118i	−0.999622	+	0.0275040i	$0.991244\pi$
$282$		0			0
$283$	−3.93995	−	9.51187i	−0.234206	−	0.565422i	0.762458	−	0.647037i	$-0.223992\pi$
$283$	−3.93995	−	9.51187i	−0.234206	−	0.565422i	−0.996664	+	0.0816150i	$0.973992\pi$
$284$	−1.80261	+	5.76888i	−0.106965	+	0.342320i
$285$		0			0
$286$	25.6896	−	6.32127i	1.51906	−	0.373785i
$287$	27.3666			1.61540
$288$		0			0
$289$	7.34950			0.432324
$290$	−17.6252	+	4.33692i	−1.03499	+	0.254673i
$291$		0			0
$292$	4.90106	+	1.53144i	0.286813	+	0.0896207i
$293$	−5.02532	−	12.1322i	−0.293582	−	0.708770i	−1.00000		0.000974464i	$-0.999690\pi$
$293$	−5.02532	−	12.1322i	−0.293582	−	0.708770i	0.706417	−	0.707795i	$-0.250310\pi$
$294$		0			0
$295$	20.3029	+	20.3029i	1.18208	+	1.18208i
$296$	5.34258	+	2.60907i	0.310531	+	0.151649i
$297$		0			0
$298$	7.85688	+	10.6866i	0.455137	+	0.619056i
$299$	2.86993	+	6.92862i	0.165972	+	0.400693i
$300$		0			0
$301$	8.04764	+	3.33344i	0.463858	+	0.192136i
$302$	−28.5111	−	17.2508i	−1.64063	−	0.992671i
$303$		0			0
$304$	11.2435	+	17.4499i	0.644861	+	1.00082i
$305$	28.6210			1.63884
$306$		0			0
$307$	−5.19514	+	12.5422i	−0.296502	+	0.715820i	0.703485	+	0.710710i	$0.251626\pi$
$307$	−5.19514	+	12.5422i	−0.296502	+	0.715820i	−0.999987	+	0.00510930i	$0.998374\pi$
$308$	2.27135	+	25.2139i	0.129422	+	1.43670i
$309$		0			0
$310$	−25.5478	−	34.7489i	−1.45102	−	1.97360i
$311$	5.27753	+	5.27753i	0.299261	+	0.299261i	0.840725	−	0.541463i	$-0.182129\pi$
$311$	5.27753	+	5.27753i	0.299261	+	0.299261i	−0.541463	+	0.840725i	$0.682129\pi$
$312$		0			0
$313$	−18.5402	+	18.5402i	−1.04795	+	1.04795i	−0.0491617	+	0.998791i	$0.515655\pi$
$313$	−18.5402	+	18.5402i	−1.04795	+	1.04795i	−0.998791	+	0.0491617i	$0.984345\pi$
$314$	−12.3337	−	1.88209i	−0.696032	−	0.106213i
$315$		0			0
$316$	−2.52174	+	1.32100i	−0.141859	+	0.0743118i
$317$	11.2977	+	4.67965i	0.634540	+	0.262835i	0.676681	−	0.736276i	$-0.263418\pi$
$317$	11.2977	+	4.67965i	0.634540	+	0.262835i	−0.0421404	+	0.999112i	$0.513418\pi$
$318$		0			0
$319$		−	14.2701i		−	0.798973i
$320$	−26.6523	+	7.36254i	−1.48991	+	0.411578i
$321$		0			0
$322$	−6.96850	+	1.71469i	−0.388339	+	0.0955560i
$323$	−9.79989	+	23.6590i	−0.545281	+	1.31642i
$324$		0			0
$325$	−31.2400	+	12.9400i	−1.73288	+	0.717783i
$326$	3.28900	−	21.5535i	0.182161	−	1.19374i
$327$		0			0
$328$	−23.4549	−	1.44638i	−1.29508	−	0.0798629i
$329$	3.77005	−	3.77005i	0.207850	−	0.207850i
$330$		0			0
$331$	26.3575	−	10.9176i	1.44874	−	0.600087i	0.486839	−	0.873492i	$-0.338150\pi$
$331$	26.3575	−	10.9176i	1.44874	−	0.600087i	0.961899	+	0.273405i	$0.0881498\pi$
$332$	−2.24605	+	0.202332i	−0.123268	+	0.0111044i
$333$		0			0
$334$	17.2057	+	10.4104i	0.941455	+	0.569632i
$335$			12.3952i			0.677219i
$336$		0			0
$337$		−	8.96574i		−	0.488395i	−0.969726	−	0.244197i	$-0.921475\pi$
$337$		−	8.96574i		−	0.488395i	0.969726	−	0.244197i	$-0.0785245\pi$
$338$	7.83162	−	12.9436i	0.425984	−	0.704041i
$339$		0			0
$340$	−26.1866	−	21.8585i	−1.42017	−	1.18544i
$341$	31.3271	−	12.9761i	1.69646	−	0.702696i
$342$		0			0
$343$	−7.33747	+	7.33747i	−0.396186	+	0.396186i
$344$	−6.72114	−	3.28230i	−0.362380	−	0.176970i
$345$		0			0
$346$	−13.0597	−	1.99287i	−0.702092	−	0.107137i
$347$	−0.0344829	+	0.0142833i	−0.00185114	+	0.000766767i	−0.383609	−	0.923496i	$-0.625319\pi$
$347$	−0.0344829	+	0.0142833i	−0.00185114	+	0.000766767i	0.381758	+	0.924262i	$0.375319\pi$
$348$		0			0
$349$	−1.36920	+	3.30553i	−0.0732914	+	0.176941i	−0.956280	−	0.292454i	$-0.905528\pi$
$349$	−1.36920	+	3.30553i	−0.0732914	+	0.176941i	0.882988	+	0.469395i	$0.155528\pi$
$350$	−7.73124	−	31.4198i	−0.413252	−	1.67946i
$351$		0			0
$352$	−0.614083	−	21.7299i	−0.0327307	−	1.15821i
$353$			10.2214i			0.544031i	0.962293	+	0.272016i	$0.0876902\pi$
$353$			10.2214i			0.544031i	−0.962293	+	0.272016i	$0.912310\pi$
$354$		0			0
$355$	9.64984	+	3.99710i	0.512161	+	0.212144i
$356$	1.91350	+	0.597913i	0.101415	+	0.0316893i
$357$		0			0
$358$	−1.47058	+	9.63700i	−0.0777226	+	0.509331i
$359$	−21.7022	+	21.7022i	−1.14540	+	1.14540i	−0.157953	+	0.987447i	$0.550489\pi$
$359$	−21.7022	+	21.7022i	−1.14540	+	1.14540i	−0.987447	+	0.157953i	$0.949511\pi$
$360$		0			0
$361$	−5.60898	−	5.60898i	−0.295210	−	0.295210i
$362$	−6.07406	+	4.46572i	−0.319245	+	0.234713i
$363$		0			0
$364$	24.6195	+	20.5505i	1.29041	+	1.07714i
$365$	3.39581	−	8.19821i	0.177745	−	0.429114i
$366$		0			0
$367$	−2.68336			−0.140070			−0.0700350	−	0.997545i	$-0.522311\pi$
$367$	−2.68336			−0.140070			−0.0700350	+	0.997545i	$0.522311\pi$
$368$	6.06306	−	1.10130i	0.316059	−	0.0574091i
$369$		0			0
$370$	5.31908	−	8.79106i	0.276526	−	0.457026i
$371$	18.5222	+	7.67215i	0.961625	+	0.398318i
$372$		0			0
$373$	−3.60763	−	8.70959i	−0.186796	−	0.450965i	0.802543	−	0.596594i	$-0.203480\pi$
$373$	−3.60763	−	8.70959i	−0.186796	−	0.450965i	−0.989339	+	0.145628i	$0.953480\pi$
$374$	21.6063	−	15.8852i	1.11724	−	0.821405i
$375$		0			0
$376$	−3.43042	+	3.03191i	−0.176911	+	0.156359i
$377$	−12.7822	−	12.7822i	−0.658318	−	0.658318i
$378$		0			0
$379$	−7.30210	−	17.6288i	−0.375083	−	0.905532i	−0.992872	−	0.119187i	$-0.961971\pi$
$379$	−7.30210	−	17.6288i	−0.375083	−	0.905532i	0.617788	−	0.786344i	$-0.288029\pi$
$380$	31.7779	−	16.6467i	1.63017	−	0.853956i
$381$		0			0
$382$	−3.35178	−	13.6216i	−0.171492	−	0.696943i
$383$	−17.7992			−0.909497			−0.454748	−	0.890620i	$-0.650271\pi$
$383$	−17.7992			−0.909497			−0.454748	+	0.890620i	$0.650271\pi$
$384$		0			0
$385$	43.7502			2.22971
$386$	7.03145	+	28.5758i	0.357891	+	1.45447i
$387$		0			0
$388$	−21.6391	+	11.3355i	−1.09856	+	0.575474i
$389$	10.4216	+	25.1599i	0.528396	+	1.27566i	0.932574	+	0.360979i	$0.117558\pi$
$389$	10.4216	+	25.1599i	0.528396	+	1.27566i	−0.404178	+	0.914680i	$0.632442\pi$
$390$		0			0
$391$	5.37540	+	5.37540i	0.271846	+	0.271846i
$392$	−8.15868	+	7.21089i	−0.412076	+	0.364205i
$393$		0			0
$394$	8.91954	−	6.55775i	0.449360	−	0.330375i
$395$	1.88269	+	4.54521i	0.0947284	+	0.228695i
$396$		0			0
$397$	−6.35478	−	2.63224i	−0.318938	−	0.132108i	0.217471	−	0.976067i	$-0.430219\pi$
$397$	−6.35478	−	2.63224i	−0.318938	−	0.132108i	−0.536408	+	0.843959i	$0.680219\pi$
$398$	−16.9722	+	28.0506i	−0.850738	+	1.40605i
$399$		0			0
$400$	4.96556	+	27.3373i	0.248278	+	1.36686i
$401$	14.1764			0.707935			0.353968	−	0.935258i	$-0.384832\pi$
$401$	14.1764			0.707935			0.353968	+	0.935258i	$0.384832\pi$
$402$		0			0
$403$	16.4376	−	39.6839i	0.818816	−	1.97680i
$404$	24.6173	+	20.5486i	1.22475	+	1.02233i
$405$		0			0
$406$	13.9367	−	10.2464i	0.691664	−	0.508520i
$407$	5.71208	+	5.71208i	0.283137	+	0.283137i
$408$		0			0
$409$	23.0001	−	23.0001i	1.13728	−	1.13728i	0.148347	−	0.988935i	$-0.452605\pi$
$409$	23.0001	−	23.0001i	1.13728	−	1.13728i	0.988935	−	0.148347i	$-0.0473951\pi$
$410$	−6.12618	+	40.1460i	−0.302550	+	1.98267i
$411$		0			0
$412$	25.5171	+	7.97336i	1.25714	+	0.392819i
$413$	−25.2804	−	10.4715i	−1.24397	−	0.515268i
$414$		0			0
$415$			3.89725i			0.191309i
$416$	−20.0143	−	18.9142i	−0.981282	−	0.927345i
$417$		0			0
$418$	6.73892	+	27.3870i	0.329611	+	1.33954i
$419$	3.33096	−	8.04166i	0.162728	−	0.392861i	−0.821392	−	0.570364i	$-0.806802\pi$
$419$	3.33096	−	8.04166i	0.162728	−	0.392861i	0.984120	+	0.177503i	$0.0568021\pi$
$420$		0			0
$421$	−6.91049	+	2.86242i	−0.336797	+	0.139506i	−0.544671	−	0.838650i	$-0.683346\pi$
$421$	−6.91049	+	2.86242i	−0.336797	+	0.139506i	0.207874	+	0.978156i	$0.433346\pi$
$422$	34.3381	+	5.23990i	1.67155	+	0.255074i
$423$		0			0
$424$	−15.4692	−	7.55444i	−0.751250	−	0.366876i
$425$	−24.2367	+	24.2367i	−1.17565	+	1.17565i
$426$		0			0
$427$	−25.1997	+	10.4381i	−1.21950	+	0.505133i
$428$	15.7890	+	13.1794i	0.763189	+	0.637051i
$429$		0			0
$430$	−6.69157	+	11.0594i	−0.322696	+	0.533334i
$431$		−	18.8488i		−	0.907917i	−0.891023	−	0.453958i	$-0.850011\pi$
$431$		−	18.8488i		−	0.907917i	0.891023	−	0.453958i	$-0.149989\pi$
$432$		0			0
$433$			32.1408i			1.54459i	0.635264	+	0.772295i	$0.280891\pi$
$433$			32.1408i			1.54459i	−0.635264	+	0.772295i	$0.719109\pi$
$434$	35.1667	+	21.2778i	1.68806	+	1.02137i
$435$		0			0
$436$	23.3714	−	2.10537i	1.11929	−	0.100829i
$437$	−7.38640	+	3.05955i	−0.353339	+	0.146358i
$438$		0			0
$439$	−19.4979	+	19.4979i	−0.930584	+	0.930584i	−0.997742	−	0.0671583i	$-0.978607\pi$
$439$	−19.4979	+	19.4979i	−0.930584	+	0.930584i	0.0671583	+	0.997742i	$0.478607\pi$
$440$	−37.4966	−	2.31228i	−1.78758	−	0.110234i
$441$		0			0
$442$	5.12460	−	33.5825i	0.243752	−	1.59736i
$443$	−12.4270	+	5.14742i	−0.590424	+	0.244561i	−0.657833	−	0.753164i	$-0.728527\pi$
$443$	−12.4270	+	5.14742i	−0.590424	+	0.244561i	0.0674092	+	0.997725i	$0.478527\pi$
$444$		0			0
$445$	1.32581	−	3.20079i	0.0628494	−	0.151732i
$446$	17.9018	−	4.40498i	0.847676	−	0.208582i
$447$		0			0
$448$	20.7812	−	16.2025i	0.981821	−	0.765496i
$449$		−	16.8751i		−	0.796387i	−0.917301	−	0.398194i	$-0.869637\pi$
$449$		−	16.8751i		−	0.796387i	0.917301	−	0.398194i	$-0.130363\pi$
$450$		0			0
$451$	−29.4975	−	12.2182i	−1.38898	−	0.575335i
$452$	−16.6998	+	8.74809i	−0.785493	+	0.411475i
$453$		0			0
$454$	3.54402	+	0.540808i	0.166329	+	0.0253814i
$455$	39.1885	−	39.1885i	1.83719	−	1.83719i
$456$		0			0
$457$	19.1686	+	19.1686i	0.896670	+	0.896670i	0.995140	−	0.0984696i	$-0.0313947\pi$
$457$	19.1686	+	19.1686i	0.896670	+	0.896670i	−0.0984696	+	0.995140i	$0.531395\pi$
$458$	−9.59818	−	13.0550i	−0.448493	−	0.610020i
$459$		0			0
$460$	−0.955462	−	10.6064i	−0.0445486	−	0.494528i
$461$	−6.32718	+	15.2752i	−0.294686	+	0.711436i	0.705311	+	0.708898i	$0.250808\pi$
$461$	−6.32718	+	15.2752i	−0.294686	+	0.711436i	−0.999997	+	0.00253708i	$0.999192\pi$
$462$		0			0
$463$	32.5710			1.51370			0.756852	−	0.653587i	$-0.226737\pi$
$463$	32.5710			1.51370			0.756852	+	0.653587i	$0.226737\pi$
$464$	−12.4861	+	8.04520i	−0.579653	+	0.373489i
$465$		0			0
$466$	−25.7415	−	15.5750i	−1.19245	−	0.721500i
$467$	−5.84384	−	2.42060i	−0.270420	−	0.112012i	0.243353	−	0.969938i	$-0.421753\pi$
$467$	−5.84384	−	2.42060i	−0.270420	−	0.112012i	−0.513773	+	0.857926i	$0.671753\pi$
$468$		0			0
$469$	−4.52050	−	10.9134i	−0.208737	−	0.503936i
$470$	4.68661	+	6.37451i	0.216177	+	0.294034i
$471$		0			0
$472$	21.1134	+	10.3108i	0.971824	+	0.474594i
$473$	−7.18598	−	7.18598i	−0.330412	−	0.330412i
$474$		0			0
$475$	−13.7950	−	33.3040i	−0.632956	−	1.52809i
$476$	31.0280	+	9.69536i	1.42217	+	0.444386i
$477$		0			0
$478$	13.9691	−	3.43728i	0.638931	−	0.157217i
$479$	−7.92963			−0.362314			−0.181157	−	0.983454i	$-0.557984\pi$
$479$	−7.92963			−0.362314			−0.181157	+	0.983454i	$0.557984\pi$
$480$		0			0
$481$	10.2330			0.466585
$482$	−28.3634	+	6.97918i	−1.29192	+	0.317893i
$483$		0			0
$484$	2.24745	−	7.19251i	0.102157	−	0.326932i
$485$	16.1554	+	39.0027i	0.733581	+	1.77102i
$486$		0			0
$487$	10.7904	+	10.7904i	0.488961	+	0.488961i	0.907978	−	0.419017i	$-0.137625\pi$
$487$	10.7904	+	10.7904i	0.488961	+	0.488961i	−0.419017	+	0.907978i	$0.637625\pi$
$488$	22.1494	−	7.61421i	1.00266	−	0.344679i
$489$		0			0
$490$	11.1463	+	15.1607i	0.503539	+	0.684890i
$491$	−1.68219	−	4.06116i	−0.0759160	−	0.183277i	0.881366	−	0.472435i	$-0.156625\pi$
$491$	−1.68219	−	4.06116i	−0.0759160	−	0.183277i	−0.957282	+	0.289158i	$0.906625\pi$
$492$		0			0
$493$	−16.9290	−	7.01222i	−0.762443	−	0.315814i
$494$	30.5677	+	18.4951i	1.37531	+	0.832136i
$495$		0			0
$496$	−29.0155	−	20.0950i	−1.30283	−	0.902293i
$497$	−9.95405			−0.446500
$498$		0			0
$499$	−15.0645	+	36.3690i	−0.674380	+	1.62810i	0.0997053	+	0.995017i	$0.468210\pi$
$499$	−15.0645	+	36.3690i	−0.674380	+	1.62810i	−0.774086	+	0.633081i	$0.781790\pi$
$500$	13.3988	−	1.20700i	0.599211	−	0.0539789i
$501$		0			0
$502$	16.8179	+	22.8749i	0.750619	+	1.02096i
$503$	8.41533	+	8.41533i	0.375221	+	0.375221i	0.869375	−	0.494153i	$-0.164522\pi$
$503$	8.41533	+	8.41533i	0.375221	+	0.375221i	−0.494153	+	0.869375i	$0.664522\pi$
$504$		0			0
$505$	39.1849	−	39.1849i	1.74371	−	1.74371i
$506$	8.27664	+	1.26299i	0.367941	+	0.0561469i
$507$		0			0
$508$	−6.21206	−	11.8586i	−0.275616	−	0.526142i
$509$	16.2989	+	6.75122i	0.722436	+	0.299243i	0.713440	−	0.700717i	$-0.247136\pi$
$509$	16.2989	+	6.75122i	0.722436	+	0.299243i	0.00899639	+	0.999960i	$0.497136\pi$
$510$		0			0
$511$			8.45666i			0.374100i
$512$	−18.6671	+	12.7882i	−0.824978	+	0.565165i
$513$		0			0
$514$	10.7227	−	2.63845i	0.472957	−	0.116377i
$515$	17.6801	−	42.6836i	0.779079	−	1.88086i
$516$		0			0
$517$	−5.74680	+	2.38040i	−0.252744	+	0.104690i
$518$	−1.47715	+	9.68005i	−0.0649022	+	0.425317i
$519$		0			0
$520$	−35.6582	+	31.5158i	−1.56371	+	1.38206i
$521$	−17.7934	+	17.7934i	−0.779542	+	0.779542i	−0.979753	−	0.200211i	$-0.935837\pi$
$521$	−17.7934	+	17.7934i	−0.779542	+	0.779542i	0.200211	+	0.979753i	$0.435837\pi$
$522$		0			0
$523$	10.5763	−	4.38083i	0.462468	−	0.191560i	−0.139270	−	0.990254i	$-0.544475\pi$
$523$	10.5763	−	4.38083i	0.462468	−	0.191560i	0.601737	+	0.798694i	$0.294475\pi$
$524$	−2.46324	−	27.3441i	−0.107607	−	1.19453i
$525$		0			0
$526$	−33.4978	−	20.2680i	−1.46057	−	0.883728i
$527$		−	43.5405i		−	1.89665i
$528$		0			0
$529$		−	20.6267i		−	0.896811i
$530$	−15.4011	+	25.4541i	−0.668982	+	1.10565i
$531$		0			0
$532$	−21.9082	+	26.2461i	−0.949842	+	1.13791i
$533$	−37.3662	+	15.4776i	−1.61851	+	0.670408i
$534$		0			0
$535$	25.1324	−	25.1324i	1.08657	−	1.08657i
$536$	3.29755	+	9.59241i	0.142432	+	0.414329i
$537$		0			0
$538$	6.17926	+	0.942939i	0.266407	+	0.0406530i
$539$	−13.6678	+	5.66139i	−0.588714	+	0.243853i
$540$		0			0
$541$	−0.161261	+	0.389318i	−0.00693315	+	0.0167381i	−0.927308	−	0.374299i	$-0.877883\pi$
$541$	−0.161261	+	0.389318i	−0.00693315	+	0.0167381i	0.920375	+	0.391037i	$0.127883\pi$
$542$	−2.13281	−	8.66776i	−0.0916122	−	0.372312i
$543$		0			0
$544$	−26.0805	−	9.94941i	−1.11819	−	0.426577i
$545$		−	40.5531i		−	1.73710i
$546$		0			0
$547$	2.37145	+	0.982285i	0.101396	+	0.0419995i	0.432805	−	0.901488i	$-0.357524\pi$
$547$	2.37145	+	0.982285i	0.101396	+	0.0419995i	−0.331409	+	0.943487i	$0.607524\pi$
$548$	−2.92283	+	9.35393i	−0.124857	+	0.399580i
$549$		0			0
$550$	−5.69462	+	37.3179i	−0.242819	+	1.59124i
$551$	13.6268	−	13.6268i	0.580519	−	0.580519i
$552$		0			0
$553$	−3.31527	−	3.31527i	−0.140980	−	0.140980i
$554$	22.4253	−	16.4873i	0.952760	−	0.700480i
$555$		0			0
$556$	−21.1413	+	25.3273i	−0.896590	+	1.07412i
$557$	−0.975580	+	2.35526i	−0.0413366	+	0.0997955i	−0.943199	−	0.332227i	$-0.892200\pi$
$557$	−0.975580	+	2.35526i	−0.0413366	+	0.0997955i	0.901863	+	0.432023i	$0.142200\pi$
$558$		0			0
$559$	−12.8735			−0.544489
$560$	−24.6655	−	38.2806i	−1.04231	−	1.61765i
$561$		0			0
$562$	−16.8716	+	27.8844i	−0.711687	+	1.17623i
$563$	−9.62858	−	3.98829i	−0.405796	−	0.168086i	0.170443	−	0.985368i	$-0.445480\pi$
$563$	−9.62858	−	3.98829i	−0.405796	−	0.168086i	−0.576239	+	0.817281i	$0.695480\pi$
$564$		0			0
$565$	12.4678	+	30.1000i	0.524525	+	1.26631i
$566$	−11.7309	+	8.62466i	−0.493085	+	0.362522i
$567$		0			0
$568$	8.53123	+	0.526091i	0.357963	+	0.0220743i
$569$	−18.8578	−	18.8578i	−0.790559	−	0.790559i	0.191026	−	0.981585i	$-0.438819\pi$
$569$	−18.8578	−	18.8578i	−0.790559	−	0.790559i	−0.981585	+	0.191026i	$0.938819\pi$
$570$		0			0
$571$	2.27949	+	5.50317i	0.0953936	+	0.230300i	0.964372	−	0.264549i	$-0.0852231\pi$
$571$	2.27949	+	5.50317i	0.0953936	+	0.230300i	−0.868979	+	0.494850i	$0.835223\pi$
$572$	−17.3614	−	33.1423i	−0.725916	−	1.38575i
$573$		0			0
$574$	−9.24735	−	37.5812i	−0.385977	−	1.56861i
$575$	−10.7010			−0.446263
$576$		0			0
$577$	−2.80878			−0.116931			−0.0584655	−	0.998289i	$-0.518621\pi$
$577$	−2.80878			−0.116931			−0.0584655	+	0.998289i	$0.518621\pi$
$578$	−2.48344	−	10.0927i	−0.103298	−	0.419801i
$579$		0			0
$580$	11.9114	+	22.7384i	0.494592	+	0.944160i
$581$	−1.42132	−	3.43138i	−0.0589665	−	0.142358i
$582$		0			0
$583$	−16.5390	−	16.5390i	−0.684977	−	0.684977i
$584$	0.446951	−	7.24788i	0.0184950	−	0.299919i
$585$		0			0
$586$	−14.9625	+	11.0006i	−0.618093	+	0.454429i
$587$	10.2932	+	24.8501i	0.424848	+	1.02567i	0.980898	+	0.194524i	$0.0623162\pi$
$587$	10.2932	+	24.8501i	0.424848	+	1.02567i	−0.556050	+	0.831149i	$0.687684\pi$
$588$		0			0
$589$	42.3058	+	17.5236i	1.74318	+	0.722049i
$590$	21.0205	−	34.7415i	0.865402	−	1.43029i
$591$		0			0
$592$	1.77762	−	8.21833i	0.0730597	−	0.337771i
$593$	−40.3079			−1.65525			−0.827624	−	0.561283i	$-0.810308\pi$
$593$	−40.3079			−1.65525			−0.827624	+	0.561283i	$0.810308\pi$
$594$		0			0
$595$	21.4985	−	51.9019i	0.881351	−	2.12777i
$596$	12.0204	−	14.4005i	0.492376	−	0.589868i
$597$		0			0
$598$	8.54497	−	6.28236i	0.349430	−	0.256905i
$599$	−12.4557	−	12.4557i	−0.508926	−	0.508926i	0.405271	−	0.914197i	$-0.367177\pi$
$599$	−12.4557	−	12.4557i	−0.508926	−	0.508926i	−0.914197	+	0.405271i	$0.867177\pi$
$600$		0			0
$601$	6.85263	−	6.85263i	0.279525	−	0.279525i	−0.553395	−	0.832919i	$-0.686668\pi$
$601$	6.85263	−	6.85263i	0.279525	−	0.279525i	0.832919	+	0.553395i	$0.186668\pi$
$602$	1.85830	−	12.1778i	0.0757388	−	0.496331i
$603$		0			0
$604$	−14.0556	+	44.9820i	−0.571913	+	1.83029i
$605$	−12.0312	−	4.98349i	−0.489139	−	0.202608i
$606$		0			0
$607$		−	5.54311i		−	0.224988i	−0.993652	−	0.112494i	$-0.964116\pi$
$607$		−	5.54311i		−	0.224988i	0.993652	−	0.112494i	$-0.0358839\pi$
$608$	20.1639	−	21.3366i	0.817752	−	0.865315i
$609$		0			0
$610$	−9.67123	−	39.3039i	−0.391577	−	1.59137i
$611$	−3.01540	+	7.27981i	−0.121990	+	0.294510i
$612$		0			0
$613$	1.34403	−	0.556714i	0.0542847	−	0.0224855i	−0.355376	−	0.934723i	$-0.615647\pi$
$613$	1.34403	−	0.556714i	0.0542847	−	0.0224855i	0.409661	+	0.912238i	$0.365647\pi$
$614$	18.9790	+	2.89615i	0.765931	+	0.116879i
$615$		0			0
$616$	33.8576	−	11.6391i	1.36416	−	0.468952i
$617$	27.3420	−	27.3420i	1.10075	−	1.10075i	0.106429	−	0.994320i	$-0.466058\pi$
$617$	27.3420	−	27.3420i	1.10075	−	1.10075i	0.994320	−	0.106429i	$-0.0339417\pi$
$618$		0			0
$619$	−27.2304	+	11.2792i	−1.09448	+	0.453350i	−0.855568	−	0.517690i	$-0.826792\pi$
$619$	−27.2304	+	11.2792i	−1.09448	+	0.453350i	−0.238916	+	0.971040i	$0.576792\pi$
$620$	−39.0862	+	46.8254i	−1.56974	+	1.88055i
$621$		0			0
$622$	5.46407	−	9.03069i	0.219089	−	0.362098i
$623$			3.30169i			0.132280i
$624$		0			0
$625$			11.4818i			0.459270i
$626$	31.7252	+	19.1955i	1.26799	+	0.767205i
$627$		0			0
$628$	1.58306	+	17.5733i	0.0631708	+	0.701249i
$629$	9.58325	−	3.96951i	0.382109	−	0.158275i
$630$		0			0
$631$	−6.25063	+	6.25063i	−0.248834	+	0.248834i	−0.820492	−	0.571658i	$-0.806300\pi$
$631$	−6.25063	+	6.25063i	−0.248834	+	0.248834i	0.571658	+	0.820492i	$0.306300\pi$
$632$	2.66617	+	3.01661i	0.106055	+	0.119994i
$633$		0			0
$634$	2.60878	−	17.0958i	0.103608	−	0.678962i
$635$	−21.3741	+	8.85346i	−0.848207	+	0.351339i
$636$		0			0
$637$	−7.17161	+	17.3138i	−0.284150	+	0.685998i
$638$	−19.5965	+	4.82196i	−0.775831	+	0.190903i
$639$		0			0
$640$	19.1166	+	34.1125i	0.755650	+	1.34841i
$641$		−	13.6953i		−	0.540934i	−0.962729	−	0.270467i	$-0.912822\pi$
$641$		−	13.6953i		−	0.540934i	0.962729	−	0.270467i	$-0.0871781\pi$
$642$		0			0
$643$	17.4338	+	7.22130i	0.687520	+	0.284780i	0.698967	−	0.715154i	$-0.253644\pi$
$643$	17.4338	+	7.22130i	0.687520	+	0.284780i	−0.0114464	+	0.999934i	$0.503644\pi$
$644$	4.70940	+	8.99010i	0.185576	+	0.354259i
$645$		0			0
$646$	35.8013	+	5.46318i	1.40858	+	0.214946i
$647$	2.78525	−	2.78525i	0.109500	−	0.109500i	−0.650234	−	0.759734i	$-0.725329\pi$
$647$	2.78525	−	2.78525i	0.109500	−	0.109500i	0.759734	+	0.650234i	$0.225329\pi$
$648$		0			0
$649$	22.5737	+	22.5737i	0.886094	+	0.886094i
$650$	28.3261	+	38.5278i	1.11104	+	1.51118i
$651$		0			0
$652$	−30.7097	+	2.76643i	−1.20269	+	0.108342i
$653$	3.42546	−	8.26978i	0.134048	−	0.323622i	−0.842575	−	0.538579i	$-0.818961\pi$
$653$	3.42546	−	8.26978i	0.134048	−	0.323622i	0.976623	+	0.214957i	$0.0689613\pi$
$654$		0			0
$655$	−47.4463			−1.85388
$656$	5.93931	+	32.6982i	0.231891	+	1.27665i
$657$		0			0
$658$	−6.45115	−	3.90330i	−0.251492	−	0.152167i
$659$	−44.7390	−	18.5315i	−1.74278	−	0.721885i	−0.998542	−	0.0539756i	$-0.982811\pi$
$659$	−44.7390	−	18.5315i	−1.74278	−	0.721885i	−0.744243	−	0.667909i	$-0.767189\pi$
$660$		0			0
$661$	−5.04994	−	12.1916i	−0.196420	−	0.474200i	0.794727	−	0.606967i	$-0.207614\pi$
$661$	−5.04994	−	12.1916i	−0.196420	−	0.474200i	−0.991147	+	0.132767i	$0.957614\pi$
$662$	−23.8990	−	32.5063i	−0.928861	−	1.26339i
$663$		0			0
$664$	1.03681	+	3.01602i	0.0402359	+	0.117044i
$665$	41.7777	+	41.7777i	1.62007	+	1.62007i
$666$		0			0
$667$	−2.18923	−	5.28526i	−0.0847672	−	0.204646i
$668$	8.48218	−	27.1455i	0.328186	−	1.05029i
$669$		0			0
$670$	17.0217	−	4.18840i	0.657604	−	0.161812i
$671$	31.8221			1.22848
$672$		0			0
$673$	−38.7728			−1.49458			−0.747291	−	0.664497i	$-0.768646\pi$
$673$	−38.7728			−1.49458			−0.747291	+	0.664497i	$0.768646\pi$
$674$	−12.3122	+	3.02958i	−0.474249	+	0.116695i
$675$		0			0
$676$	−20.4212	−	6.38104i	−0.785432	−	0.245425i
$677$	3.27320	+	7.90221i	0.125799	+	0.303706i	0.974214	−	0.225626i	$-0.0724426\pi$
$677$	3.27320	+	7.90221i	0.125799	+	0.303706i	−0.848415	+	0.529332i	$0.822443\pi$
$678$		0			0
$679$	−28.4485	−	28.4485i	−1.09175	−	1.09175i
$680$	−21.1686	+	43.3469i	−0.811780	+	1.66228i
$681$		0			0
$682$	−28.4051	−	38.6353i	−1.08769	−	1.47942i
$683$	−19.5003	−	47.0778i	−0.746157	−	1.80138i	−0.578769	−	0.815491i	$-0.696467\pi$
$683$	−19.5003	−	47.0778i	−0.746157	−	1.80138i	−0.167388	−	0.985891i	$-0.553533\pi$
$684$		0			0
$685$	15.6467	+	6.48108i	0.597830	+	0.247629i
$686$	12.5556	+	7.59682i	0.479374	+	0.290048i
$687$		0			0
$688$	−2.23630	+	10.3389i	−0.0852582	+	0.394168i
$689$	−29.6292			−1.12878
$690$		0			0
$691$	5.45976	−	13.1810i	0.207699	−	0.501430i	−0.785361	−	0.619038i	$-0.787523\pi$
$691$	5.45976	−	13.1810i	0.207699	−	0.501430i	0.993060	+	0.117608i	$0.0375226\pi$
$692$	1.67623	+	18.6076i	0.0637208	+	0.707355i
$693$		0			0
$694$	0.0312665	+	0.0425273i	0.00118686	+	0.00161431i
$695$	40.3152	+	40.3152i	1.52924	+	1.52924i
$696$		0			0
$697$	−28.9896	+	28.9896i	−1.09806	+	1.09806i
$698$	5.00199	+	0.763290i	0.189328	+	0.0288910i
$699$		0			0
$700$	−40.5348	+	21.2339i	−1.53207	+	0.802565i
$701$	6.06309	+	2.51141i	0.229000	+	0.0948547i	0.494233	−	0.869330i	$-0.335449\pi$
$701$	6.06309	+	2.51141i	0.229000	+	0.0948547i	−0.265233	+	0.964184i	$0.585449\pi$
$702$		0			0
$703$			10.9091i			0.411445i
$704$	−29.6332	+	8.18598i	−1.11684	+	0.308521i
$705$		0			0
$706$	14.0366	−	3.45388i	0.528274	−	0.129989i
$707$	−20.2101	+	48.7915i	−0.760079	+	1.83499i
$708$		0			0
$709$	17.0266	−	7.05266i	0.639448	−	0.264868i	−0.0393132	−	0.999227i	$-0.512517\pi$
$709$	17.0266	−	7.05266i	0.639448	−	0.264868i	0.678762	+	0.734359i	$0.262517\pi$
$710$	2.22827	−	14.6023i	0.0836256	−	0.548015i
$711$		0			0
$712$	0.174501	−	2.82975i	0.00653970	−	0.106050i
$713$	9.61199	−	9.61199i	0.359972	−	0.359972i
$714$		0			0
$715$	−59.7362	+	24.7435i	−2.23401	+	0.925356i
$716$	13.7309	−	1.23693i	0.513150	−	0.0462262i
$717$		0			0
$718$	37.1359	+	22.4693i	1.38590	+	0.838546i
$719$		−	40.0842i		−	1.49489i	−0.664324	−	0.747445i	$-0.731281\pi$
$719$		−	40.0842i		−	1.49489i	0.664324	−	0.747445i	$-0.268719\pi$
$720$		0			0
$721$			44.0291i			1.63973i
$722$	−5.80723	+	9.59785i	−0.216123	+	0.357195i
$723$		0			0
$724$	8.18502	+	6.83222i	0.304194	+	0.253917i
$725$	23.8303	−	9.87085i	0.885036	−	0.366594i
$726$		0			0
$727$	17.6896	−	17.6896i	0.656073	−	0.656073i	−0.298376	−	0.954448i	$-0.596445\pi$
$727$	17.6896	−	17.6896i	0.656073	−	0.656073i	0.954448	+	0.298376i	$0.0964449\pi$
$728$	19.9018	−	40.7529i	0.737612	−	1.51040i
$729$		0			0
$730$	−12.4057	−	1.89307i	−0.459155	−	0.0700658i
$731$	−12.0560	+	4.99378i	−0.445909	+	0.184701i
$732$		0			0
$733$	−2.68410	+	6.47999i	−0.0991395	+	0.239344i	−0.965666	−	0.259787i	$-0.916348\pi$
$733$	−2.68410	+	6.47999i	−0.0991395	+	0.239344i	0.866526	+	0.499131i	$0.166348\pi$
$734$	0.906723	+	3.68492i	0.0334678	+	0.136013i
$735$		0			0
$736$	−3.56110	−	7.95397i	−0.131264	−	0.293187i
$737$			13.7814i			0.507646i
$738$		0			0
$739$	−8.93406	−	3.70061i	−0.328645	−	0.136129i	0.212259	−	0.977213i	$-0.431918\pi$
$739$	−8.93406	−	3.70061i	−0.328645	−	0.136129i	−0.540904	+	0.841084i	$0.681918\pi$
$740$	−13.8697	−	4.33387i	−0.509860	−	0.159316i
$741$		0			0
$742$	4.27702	−	28.0281i	0.157014	−	1.02894i
$743$	−32.3436	+	32.3436i	−1.18657	+	1.18657i	−0.208565	+	0.978009i	$0.566879\pi$
$743$	−32.3436	+	32.3436i	−1.18657	+	1.18657i	−0.978009	+	0.208565i	$0.933121\pi$
$744$		0			0
$745$	−22.9223	−	22.9223i	−0.839807	−	0.839807i
$746$	−10.7414	+	7.89721i	−0.393271	+	0.289137i
$747$		0			0
$748$	−29.1153	−	24.3032i	−1.06456	−	0.888613i
$749$	−12.9623	+	31.2938i	−0.473633	+	1.14345i
$750$		0			0
$751$	−34.4295			−1.25635			−0.628175	−	0.778072i	$-0.716198\pi$
$751$	−34.4295			−1.25635			−0.628175	+	0.778072i	$0.716198\pi$
$752$	5.32274	+	3.68633i	0.194100	+	0.134427i
$753$		0			0
$754$	−13.2340	+	21.8724i	−0.481955	+	0.796546i
$755$	75.2433	+	31.1668i	2.73839	+	1.13428i
$756$		0			0
$757$	2.48272	+	5.99382i	0.0902361	+	0.217849i	0.962554	−	0.271090i	$-0.0873840\pi$
$757$	2.48272	+	5.99382i	0.0902361	+	0.217849i	−0.872318	+	0.488939i	$0.837384\pi$
$758$	−21.7414	+	15.9845i	−0.789682	+	0.580583i
$759$		0			0
$760$	−33.5980	−	38.0141i	−1.21873	−	1.37892i
$761$	4.40886	+	4.40886i	0.159821	+	0.159821i	0.782488	−	0.622666i	$-0.213951\pi$
$761$	4.40886	+	4.40886i	0.159821	+	0.159821i	−0.622666	+	0.782488i	$0.713951\pi$
$762$		0			0
$763$	14.7897	+	35.7054i	0.535422	+	1.29262i
$764$	−17.5733	+	9.20567i	−0.635781	+	0.333050i
$765$		0			0
$766$	6.01446	+	24.4428i	0.217311	+	0.883153i
$767$	40.4400			1.46020
$768$		0			0
$769$	−16.9600			−0.611592			−0.305796	−	0.952097i	$-0.598923\pi$
$769$	−16.9600			−0.611592			−0.305796	+	0.952097i	$0.598923\pi$
$770$	−14.7835	−	60.0800i	−0.532759	−	2.16513i
$771$		0			0
$772$	36.8658	−	19.3119i	1.32683	−	0.695050i
$773$	−12.5028	−	30.1845i	−0.449695	−	1.08566i	−0.972436	−	0.233169i	$-0.925090\pi$
$773$	−12.5028	−	30.1845i	−0.449695	−	1.08566i	0.522741	−	0.852492i	$-0.324910\pi$
$774$		0			0
$775$	43.3388	+	43.3388i	1.55678	+	1.55678i
$776$	22.8785	+	25.8856i	0.821291	+	0.929240i
$777$		0			0
$778$	31.0294	−	22.8132i	1.11246	−	0.817892i
$779$	−16.5002	−	39.8350i	−0.591180	−	1.42724i
$780$		0			0
$781$	10.7291	+	4.44414i	0.383917	+	0.159024i
$782$	5.56539	−	9.19815i	0.199018	−	0.328925i
$783$		0			0
$784$	12.6592	+	8.76731i	0.452116	+	0.313118i
$785$	30.4924			1.08832
$786$		0			0
$787$	0.0428254	−	0.103390i	0.00152656	−	0.00368545i	−0.923114	−	0.384525i	$-0.874365\pi$
$787$	0.0428254	−	0.103390i	0.00152656	−	0.00368545i	0.924641	+	0.380840i	$0.124365\pi$
$788$	−12.0194	−	10.0329i	−0.428174	−	0.357406i
$789$		0			0
$790$	5.60555	−	4.12126i	0.199436	−	0.146628i
$791$	−21.9548	−	21.9548i	−0.780624	−	0.780624i
$792$		0			0
$793$	28.5041	−	28.5041i	1.01221	−	1.01221i
$794$	−1.46740	+	9.61617i	−0.0520761	+	0.341265i
$795$		0			0
$796$	44.2555	+	13.8286i	1.56860	+	0.490141i
$797$	32.6670	+	13.5311i	1.15712	+	0.479297i	0.876917	−	0.480642i	$-0.159597\pi$
$797$	32.6670	+	13.5311i	1.15712	+	0.479297i	0.280208	+	0.959939i	$0.409597\pi$
$798$		0			0
$799$			7.98728i			0.282569i
$800$	35.8631	−	16.0564i	1.26795	−	0.567679i
$801$		0			0
$802$	−4.79030	−	19.4678i	−0.169151	−	0.687430i
$803$	3.77560	−	9.11512i	0.133238	−	0.321665i
$804$		0			0
$805$	16.2039	−	6.71186i	0.571111	−	0.236562i
$806$	−60.0503	−	9.16352i	−2.11518	−	0.322771i
$807$		0			0
$808$	19.9000	−	40.7492i	0.700081	−	1.43355i
$809$	−22.4803	+	22.4803i	−0.790364	+	0.790364i	−0.981553	−	0.191189i	$-0.938766\pi$
$809$	−22.4803	+	22.4803i	−0.790364	+	0.790364i	0.191189	+	0.981553i	$0.438766\pi$
$810$		0			0
$811$	41.9112	−	17.3602i	1.47170	−	0.609598i	0.504454	−	0.863438i	$-0.331694\pi$
$811$	41.9112	−	17.3602i	1.47170	−	0.609598i	0.967246	+	0.253840i	$0.0816938\pi$
$812$	−18.7801	−	15.6762i	−0.659054	−	0.550127i
$813$		0			0
$814$	5.91397	−	9.77427i	0.207285	−	0.342588i
$815$			53.2862i			1.86653i
$816$		0			0
$817$		−	13.7240i		−	0.480142i
$818$	−39.3568	−	23.8130i	−1.37608	−	0.832603i
$819$		0			0
$820$	57.2007	−	5.15282i	1.99753	−	0.179944i
$821$	2.66376	−	1.10337i	0.0929660	−	0.0385078i	−0.335716	−	0.941963i	$-0.608978\pi$
$821$	2.66376	−	1.10337i	0.0929660	−	0.0385078i	0.428682	+	0.903456i	$0.358978\pi$
$822$		0			0
$823$	27.8538	−	27.8538i	0.970924	−	0.970924i	−0.0286650	−	0.999589i	$-0.509126\pi$
$823$	27.8538	−	27.8538i	0.970924	−	0.970924i	0.999589	+	0.0286650i	$0.00912560\pi$
$824$	2.32703	−	37.7357i	0.0810658	−	1.31458i
$825$		0			0
$826$	−5.83757	+	38.2547i	−0.203115	+	1.33105i
$827$	31.9381	−	13.2292i	1.11060	−	0.460024i	0.249454	−	0.968387i	$-0.419749\pi$
$827$	31.9381	−	13.2292i	1.11060	−	0.460024i	0.861143	+	0.508362i	$0.169749\pi$
$828$		0			0
$829$	4.80176	−	11.5925i	0.166772	−	0.402623i	−0.818294	−	0.574800i	$-0.805080\pi$
$829$	4.80176	−	11.5925i	0.166772	−	0.402623i	0.985066	+	0.172176i	$0.0550799\pi$
$830$	5.35191	−	1.31691i	0.185767	−	0.0457105i
$831$		0			0
$832$	−19.2110	+	33.8759i	−0.666021	+	1.17444i
$833$			18.9964i			0.658186i
$834$		0			0
$835$	−45.4074	−	18.8084i	−1.57139	−	0.650891i
$836$	35.3320	−	18.5085i	1.22198	−	0.640128i
$837$		0			0
$838$	−12.1688	−	1.85692i	−0.420363	−	0.0641463i
$839$	13.8057	−	13.8057i	0.476627	−	0.476627i	−0.427424	−	0.904051i	$-0.640579\pi$
$839$	13.8057	−	13.8057i	0.476627	−	0.476627i	0.904051	+	0.427424i	$0.140579\pi$
$840$		0			0
$841$	−10.7556	−	10.7556i	−0.370883	−	0.370883i
$842$	6.26592	+	8.52261i	0.215938	+	0.293709i
$843$		0			0
$844$	−4.40736	−	48.9254i	−0.151708	−	1.68408i
$845$	−14.1493	+	34.1594i	−0.486751	+	1.17512i
$846$		0			0
$847$	12.4105			0.426430
$848$	−5.14701	+	23.7958i	−0.176749	+	0.817150i
$849$		0			0
$850$	41.4729	+	25.0934i	1.42251	+	0.860696i
$851$	2.99191	+	1.23929i	0.102561	+	0.0424823i
$852$		0			0
$853$	−18.1917	−	43.9187i	−0.622873	−	1.50375i	−0.848315	−	0.529492i	$-0.822383\pi$
$853$	−18.1917	−	43.9187i	−0.622873	−	1.50375i	0.225442	−	0.974257i	$-0.427617\pi$
$854$	22.8492	+	31.0784i	0.781884	+	1.06348i
$855$		0			0
$856$	12.7634	−	26.1356i	0.436246	−	0.893298i
$857$	0.432800	+	0.432800i	0.0147842	+	0.0147842i	0.714460	−	0.699676i	$-0.246672\pi$
$857$	0.432800	+	0.432800i	0.0147842	+	0.0147842i	−0.699676	+	0.714460i	$0.746672\pi$
$858$		0			0
$859$	17.5314	+	42.3246i	0.598164	+	1.44410i	0.875450	+	0.483309i	$0.160565\pi$
$859$	17.5314	+	42.3246i	0.598164	+	1.44410i	−0.277285	+	0.960788i	$0.589435\pi$
$860$	17.4485	+	5.45216i	0.594990	+	0.185917i
$861$		0			0
$862$	−25.8842	+	6.36914i	−0.881619	+	0.216934i
$863$	14.7658			0.502635			0.251318	−	0.967905i	$-0.419136\pi$
$863$	14.7658			0.502635			0.251318	+	0.967905i	$0.419136\pi$
$864$		0			0
$865$	32.2871			1.09780
$866$	44.1374	−	10.8606i	1.49985	−	0.369058i
$867$		0			0
$868$	17.3367	−	55.4826i	0.588446	−	1.88320i
$869$	2.09325	+	5.05356i	0.0710087	+	0.171430i
$870$		0			0
$871$	12.3445	+	12.3445i	0.418278	+	0.418278i
$872$	−10.7886	−	31.3834i	−0.365346	−	1.06278i
$873$		0			0
$874$	6.69744	+	9.10954i	0.226544	+	0.308135i
$875$	8.47888	+	20.4698i	0.286638	+	0.692006i
$876$		0			0
$877$	12.3930	+	5.13334i	0.418481	+	0.173341i	0.581980	−	0.813203i	$-0.302278\pi$
$877$	12.3930	+	5.13334i	0.418481	+	0.173341i	−0.163499	+	0.986544i	$0.552278\pi$
$878$	33.3640	+	20.1871i	1.12598	+	0.681280i
$879$		0			0
$880$	9.49499	+	52.2736i	0.320076	+	1.76214i
$881$	−35.8699			−1.20849			−0.604243	−	0.796800i	$-0.706524\pi$
$881$	−35.8699			−1.20849			−0.604243	+	0.796800i	$0.706524\pi$
$882$		0			0
$883$	−1.07109	+	2.58584i	−0.0360450	+	0.0870203i	−0.940877	−	0.338749i	$-0.889996\pi$
$883$	−1.07109	+	2.58584i	−0.0360450	+	0.0870203i	0.904832	+	0.425769i	$0.139996\pi$
$884$	−47.8488	+	4.31037i	−1.60933	+	0.144974i
$885$		0			0
$886$	11.2679	+	15.3260i	0.378551	+	0.514888i
$887$	−4.02213	−	4.02213i	−0.135050	−	0.135050i	0.636350	−	0.771400i	$-0.280443\pi$
$887$	−4.02213	−	4.02213i	−0.135050	−	0.135050i	−0.771400	+	0.636350i	$0.780443\pi$
$888$		0			0
$889$	15.5903	−	15.5903i	0.522880	−	0.522880i
$890$	−4.84349	−	0.739104i	−0.162354	−	0.0247748i
$891$		0			0
$892$	−12.0983	−	23.0952i	−0.405080	−	0.773286i
$893$	−7.76079	−	3.21462i	−0.259705	−	0.107573i
$894$		0			0
$895$		−	23.8254i		−	0.796394i
$896$	−29.2722	−	23.0629i	−0.977916	−	0.770478i
$897$		0			0
$898$	−23.1738	+	5.70222i	−0.773320	+	0.190286i
$899$	−12.5389	+	30.2715i	−0.418195	+	1.00961i
$900$		0			0
$901$	−27.7478	+	11.4935i	−0.924414	+	0.382905i
$902$	−6.81134	+	44.6360i	−0.226793	+	1.48622i
$903$		0			0
$904$	17.6563	+	19.9770i	0.587240	+	0.664426i
$905$	13.0286	−	13.0286i	0.433086	−	0.433086i
$906$		0			0
$907$	32.7275	−	13.5562i	1.08670	−	0.450125i	0.233843	−	0.972274i	$-0.424870\pi$
$907$	32.7275	−	13.5562i	1.08670	−	0.450125i	0.852854	+	0.522150i	$0.174870\pi$
$908$	−0.454881	−	5.04957i	−0.0150958	−	0.167576i
$909$		0			0
$910$	−67.0577	−	40.5736i	−2.22294	−	1.34500i
$911$		−	0.767731i		−	0.0254361i	−0.999919	−	0.0127180i	$-0.995952\pi$
$911$		−	0.767731i		−	0.0254361i	0.999919	−	0.0127180i	$-0.00404838\pi$
$912$		0			0
$913$			4.33313i			0.143406i
$914$	19.8461	−	32.8005i	0.656452	−	1.08495i
$915$		0			0
$916$	−14.6845	+	17.5921i	−0.485189	+	0.581258i
$917$	41.7746	−	17.3036i	1.37952	−	0.571416i
$918$		0			0
$919$	−1.32571	+	1.32571i	−0.0437311	+	0.0437311i	−0.728634	−	0.684903i	$-0.759845\pi$
$919$	−1.32571	+	1.32571i	−0.0437311	+	0.0437311i	0.684903	+	0.728634i	$0.259845\pi$
$920$	−14.2424	+	4.89607i	−0.469560	+	0.161419i
$921$		0			0
$922$	23.1146	+	3.52723i	0.761240	+	0.116163i
$923$	13.5912	−	5.62965i	0.447359	−	0.185302i
$924$		0			0
$925$	−5.58774	+	13.4900i	−0.183724	+	0.443548i
$926$	−11.0060	−	44.7282i	−0.361678	−	1.46986i
$927$		0			0
$928$	15.2672	+	14.4280i	0.501171	+	0.473624i
$929$			33.4339i			1.09693i	0.836173	+	0.548465i	$0.184788\pi$
$929$			33.4339i			1.09693i	−0.836173	+	0.548465i	$0.815212\pi$
$930$		0			0
$931$	−18.4577	−	7.64544i	−0.604927	−	0.250569i
$932$	−12.6902	+	40.6125i	−0.415682	+	1.33031i
$933$		0			0
$934$	−1.34942	+	8.84299i	−0.0441543	+	0.289351i
$935$	−46.3448	+	46.3448i	−1.51564	+	1.51564i
$936$		0			0
$937$	37.9699	+	37.9699i	1.24042	+	1.24042i	0.959826	+	0.280597i	$0.0905324\pi$
$937$	37.9699	+	37.9699i	1.24042	+	1.24042i	0.280597	+	0.959826i	$0.409468\pi$
$938$	−13.4594	+	9.89550i	−0.439465	+	0.323100i
$939$		0			0
$940$	7.17017	−	8.58988i	0.233865	−	0.280171i
$941$	−19.1634	+	46.2645i	−0.624709	+	1.50818i	0.221407	+	0.975181i	$0.428935\pi$
$941$	−19.1634	+	46.2645i	−0.624709	+	1.50818i	−0.846116	+	0.532999i	$0.821065\pi$
$942$		0			0
$943$	−12.7995			−0.416809
$944$	7.02500	−	32.4781i	0.228644	−	1.05707i
$945$		0			0
$946$	−7.43997	+	12.2964i	−0.241894	+	0.399789i
$947$	35.5194	+	14.7126i	1.15422	+	0.478096i	0.875948	−	0.482405i	$-0.160237\pi$
$947$	35.5194	+	14.7126i	1.15422	+	0.478096i	0.278277	+	0.960501i	$0.410237\pi$
$948$		0			0
$949$	−4.78278	−	11.5467i	−0.155256	−	0.374820i
$950$	−41.0733	+	30.1976i	−1.33259	+	0.979739i
$951$		0			0
$952$	2.82959	−	45.8854i	0.0917076	−	1.48715i
$953$	34.4673	+	34.4673i	1.11650	+	1.11650i	0.992250	+	0.124254i	$0.0396538\pi$
$953$	34.4673	+	34.4673i	1.11650	+	1.11650i	0.124254	+	0.992250i	$0.460346\pi$
$954$		0			0
$955$	13.1200	+	31.6744i	0.424552	+	1.02496i
$956$	−9.44049	−	18.0216i	−0.305327	−	0.582860i
$957$		0			0
$958$	2.67947	+	10.8894i	0.0865698	+	0.351820i
$959$	−16.1400			−0.521186
$960$		0			0
$961$	−46.8567			−1.51151
$962$	−3.45780	−	14.0525i	−0.111484	−	0.453071i
$963$		0			0
$964$	19.1683	+	36.5918i	0.617371	+	1.17854i
$965$	−27.5234	−	66.4473i	−0.886009	−	2.13901i
$966$		0			0
$967$	36.1443	+	36.1443i	1.16232	+	1.16232i	0.983966	+	0.178358i	$0.0570786\pi$
$967$	36.1443	+	36.1443i	1.16232	+	1.16232i	0.178358	+	0.983966i	$0.442921\pi$
$968$	−10.6366	−	0.655919i	−0.341872	−	0.0210820i
$969$		0			0
$970$	48.1014	−	35.3647i	1.54444	−	1.13549i
$971$	9.45955	+	22.8374i	0.303571	+	0.732886i	0.999885	+	0.0151489i	$0.00482222\pi$
$971$	9.45955	+	22.8374i	0.303571	+	0.732886i	−0.696314	+	0.717738i	$0.745178\pi$
$972$		0			0
$973$	−50.1989	−	20.7930i	−1.60930	−	0.666594i
$974$	11.1718	−	18.4641i	0.357968	−	0.591629i
$975$		0			0
$976$	−17.9406	−	27.8438i	−0.574266	−	0.891257i
$977$	22.6982			0.726179			0.363090	−	0.931754i	$-0.381722\pi$
$977$	22.6982			0.726179			0.363090	+	0.931754i	$0.381722\pi$
$978$		0			0
$979$	1.47409	−	3.55877i	0.0471122	−	0.113739i
$980$	17.0530	−	20.4296i	0.544739	−	0.652599i
$981$		0			0
$982$	−5.00857	+	3.68236i	−0.159830	+	0.117509i
$983$	−12.1156	−	12.1156i	−0.386428	−	0.386428i	0.486984	−	0.873411i	$-0.338097\pi$
$983$	−12.1156	−	12.1156i	−0.386428	−	0.386428i	−0.873411	+	0.486984i	$0.838097\pi$
$984$		0			0
$985$	−19.1321	+	19.1321i	−0.609599	+	0.609599i
$986$	−3.90912	+	25.6172i	−0.124492	+	0.815819i
$987$		0			0
$988$	15.0695	−	48.2268i	0.479424	−	1.53430i
$989$	−3.76392	−	1.55907i	−0.119686	−	0.0495754i
$990$		0			0
$991$			18.9701i			0.602604i	0.953529	+	0.301302i	$0.0974213\pi$
$991$			18.9701i			0.602604i	−0.953529	+	0.301302i	$0.902579\pi$
$992$	−17.7910	+	46.6358i	−0.564865	+	1.48069i
$993$		0			0
$994$	3.36354	+	13.6694i	0.106685	+	0.433567i
$995$	30.6634	−	74.0281i	0.972096	−	2.34685i
$996$		0			0
$997$	−42.6036	+	17.6470i	−1.34927	+	0.558885i	−0.936089	−	0.351764i	$-0.885582\pi$
$997$	−42.6036	+	17.6470i	−1.34927	+	0.558885i	−0.413179	+	0.910650i	$0.635582\pi$
$998$	55.0341	+	8.39806i	1.74207	+	0.265836i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.a.179.4	✓	32
3.2	odd	2		288.2.w.b.179.5	yes	32
4.3	odd	2		1152.2.w.b.1007.8		32
12.11	even	2		1152.2.w.a.1007.1		32
32.5	even	8		1152.2.w.a.143.1		32
32.27	odd	8		288.2.w.b.251.5	yes	32
96.5	odd	8		1152.2.w.b.143.8		32
96.59	even	8	inner	288.2.w.a.251.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.179.4	✓	32	1.1	even	1	trivial
288.2.w.a.251.4	yes	32	96.59	even	8	inner
288.2.w.b.179.5	yes	32	3.2	odd	2
288.2.w.b.251.5	yes	32	32.27	odd	8
1152.2.w.a.143.1		32	32.5	even	8
1152.2.w.a.1007.1		32	12.11	even	2
1152.2.w.b.143.8		32	96.5	odd	8
1152.2.w.b.1007.8		32	4.3	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.337906 - 1.37325i) q^{2} +(-1.77164 + 0.928061i) q^{4} +(1.32268 + 3.19322i) q^{5} +(-2.32913 - 2.32913i) q^{7} +(1.87311 + 2.11931i) q^{8} +O(q^{10})\)	\(q+(-0.337906 - 1.37325i) q^{2} +(-1.77164 + 0.928061i) q^{4} +(1.32268 + 3.19322i) q^{5} +(-2.32913 - 2.32913i) q^{7} +(1.87311 + 2.11931i) q^{8} +(3.93816 - 2.89538i) q^{10} +(1.47061 + 3.55036i) q^{11} +(4.49745 + 1.86291i) q^{13} +(-2.41145 + 3.98551i) q^{14} +(2.27741 - 3.28838i) q^{16} +4.93452 q^{17} +(-1.98599 + 4.79460i) q^{19} +(-5.30681 - 4.42971i) q^{20} +(4.37861 - 3.21920i) q^{22} +(1.08935 + 1.08935i) q^{23} +(-4.91167 + 4.91167i) q^{25} +(1.03852 - 6.80562i) q^{26} +(6.28795 + 1.96480i) q^{28} +(-3.43073 - 1.42105i) q^{29} -8.82364i q^{31} +(-5.28532 - 2.01629i) q^{32} +(-1.66741 - 6.77634i) q^{34} +(4.35675 - 10.5181i) q^{35} +(1.94208 - 0.804437i) q^{37} +(7.25526 + 1.10713i) q^{38} +(-4.28990 + 8.78441i) q^{40} +(-5.87486 + 5.87486i) q^{41} +(-2.44320 + 1.01201i) q^{43} +(-5.90033 - 4.92514i) q^{44} +(1.12785 - 1.86404i) q^{46} +1.61865i q^{47} +3.84969i q^{49} +(8.40464 + 5.08527i) q^{50} +(-9.69675 + 0.873514i) q^{52} +(-5.62320 + 2.32921i) q^{53} +(-9.39195 + 9.39195i) q^{55} +(0.573428 - 9.29886i) q^{56} +(-0.792199 + 5.19143i) q^{58} +(7.67495 - 3.17907i) q^{59} +(3.16892 - 7.65045i) q^{61} +(-12.1171 + 2.98157i) q^{62} +(-0.982926 + 7.93939i) q^{64} +16.8254i q^{65} +(3.31324 + 1.37239i) q^{67} +(-8.74219 + 4.57954i) q^{68} +(-15.9162 - 2.42877i) q^{70} +(2.13686 - 2.13686i) q^{71} +(-1.81541 - 1.81541i) q^{73} +(-1.76094 - 2.39514i) q^{74} +(-0.931227 - 10.3374i) q^{76} +(4.84401 - 11.6945i) q^{77} +1.42339 q^{79} +(13.5128 + 2.92281i) q^{80} +(10.0528 + 6.08250i) q^{82} +(1.04174 + 0.431504i) q^{83} +(6.52678 + 15.7570i) q^{85} +(2.21532 + 3.01317i) q^{86} +(-4.76969 + 9.76688i) q^{88} +(-0.708782 - 0.708782i) q^{89} +(-6.13620 - 14.8141i) q^{91} +(-2.94090 - 0.918947i) q^{92} +(2.22282 - 0.546953i) q^{94} -17.9370 q^{95} +12.2142 q^{97} +(5.28660 - 1.30084i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 32 * q - 4 * q^2 - 4 * q^8	\( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) 32 * q - 4 * q^2 - 4 * q^8 + 8 * q^10 - 8 * q^11 + 12 * q^14 + 8 * q^16 + 32 * q^20 + 16 * q^22 - 36 * q^26 - 16 * q^29 - 24 * q^32 + 24 * q^35 + 32 * q^38 - 32 * q^40 + 8 * q^44 - 32 * q^46 + 8 * q^50 - 56 * q^52 - 16 * q^53 - 32 * q^55 + 40 * q^56 - 32 * q^58 + 32 * q^59 + 32 * q^61 - 68 * q^62 - 48 * q^64 - 16 * q^67 - 72 * q^68 - 48 * q^70 + 16 * q^71 + 60 * q^74 - 8 * q^76 - 16 * q^77 - 32 * q^79 + 96 * q^80 + 40 * q^82 - 40 * q^83 - 40 * q^86 + 40 * q^88 - 48 * q^91 - 16 * q^92 + 72 * q^94 - 80 * q^95 - 44 * q^98

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