LMFDB - Embedded newform 672.2.bb.a.271.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,2,Mod(271,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.271"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.9
Character	$\chi$	$=$	672.271
Dual form			672.2.bb.a.367.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{3} +(-1.61398 + 2.79550i) q^{5} +(1.82725 + 1.91341i) q^{7} +(0.500000 - 0.866025i) q^{9} +(1.10660 + 1.91668i) q^{11} -5.08369 q^{13} +3.22796i q^{15} +(-2.73597 + 1.57961i) q^{17} +(-2.93566 - 1.69490i) q^{19} +(2.53915 + 0.743436i) q^{21} +(2.65351 + 1.53200i) q^{23} +(-2.70987 - 4.69363i) q^{25} -1.00000i q^{27} +9.88340i q^{29} +(-1.01402 - 1.75634i) q^{31} +(1.91668 + 1.10660i) q^{33} +(-8.29809 + 2.01987i) q^{35} +(0.798374 + 0.460941i) q^{37} +(-4.40261 + 2.54185i) q^{39} +5.96303i q^{41} +6.68790 q^{43} +(1.61398 + 2.79550i) q^{45} +(1.06113 - 1.83793i) q^{47} +(-0.322287 + 6.99258i) q^{49} +(-1.57961 + 2.73597i) q^{51} +(3.12560 - 1.80457i) q^{53} -7.14411 q^{55} -3.38981 q^{57} +(10.6351 - 6.14015i) q^{59} +(6.34115 - 10.9832i) q^{61} +(2.57069 - 0.625743i) q^{63} +(8.20498 - 14.2114i) q^{65} +(4.40720 + 7.63350i) q^{67} +3.06401 q^{69} +11.7036i q^{71} +(7.82068 - 4.51527i) q^{73} +(-4.69363 - 2.70987i) q^{75} +(-1.64537 + 5.61964i) q^{77} +(-9.60105 - 5.54317i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.57322i q^{83} -10.1979i q^{85} +(4.94170 + 8.55928i) q^{87} +(-6.32253 - 3.65032i) q^{89} +(-9.28920 - 9.72719i) q^{91} +(-1.75634 - 1.01402i) q^{93} +(9.47619 - 5.47108i) q^{95} +15.2238i q^{97} +2.21319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) $ 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	−1.61398	+	2.79550i	−0.721794	+	1.25018i	0.238486	+	0.971146i	$0.423349\pi$
$5$	−1.61398	+	2.79550i	−0.721794	+	1.25018i	−0.960280	+	0.279038i	$0.909984\pi$
$6$		0			0
$7$	1.82725	+	1.91341i	0.690637	+	0.723202i
$7$	1.82725	+	1.91341i	0.690637	+	0.723202i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.10660	+	1.91668i	0.333652	+	0.577902i	0.983225	−	0.182397i	$-0.0583857\pi$
$11$	1.10660	+	1.91668i	0.333652	+	0.577902i	−0.649573	+	0.760299i	$0.725052\pi$
$12$		0			0
$13$	−5.08369			−1.40996			−0.704981	−	0.709226i	$-0.749045\pi$
$13$	−5.08369			−1.40996			−0.704981	+	0.709226i	$0.749045\pi$
$14$		0			0
$15$			3.22796i			0.833456i
$16$		0			0
$17$	−2.73597	+	1.57961i	−0.663571	+	0.383113i	−0.793636	−	0.608393i	$-0.791815\pi$
$17$	−2.73597	+	1.57961i	−0.663571	+	0.383113i	0.130065	+	0.991505i	$0.458481\pi$
$18$		0			0
$19$	−2.93566	−	1.69490i	−0.673486	−	0.388838i	0.123910	−	0.992293i	$-0.460457\pi$
$19$	−2.93566	−	1.69490i	−0.673486	−	0.388838i	−0.797396	+	0.603456i	$0.793790\pi$
$20$		0			0
$21$	2.53915	+	0.743436i	0.554089	+	0.162231i
$22$		0			0
$23$	2.65351	+	1.53200i	0.553294	+	0.319445i	0.750450	−	0.660928i	$-0.229837\pi$
$23$	2.65351	+	1.53200i	0.553294	+	0.319445i	−0.197155	+	0.980372i	$0.563170\pi$
$24$		0			0
$25$	−2.70987	−	4.69363i	−0.541974	−	0.938726i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			9.88340i			1.83530i	0.397387	+	0.917651i	$0.369917\pi$
$29$			9.88340i			1.83530i	−0.397387	+	0.917651i	$0.630083\pi$
$30$		0			0
$31$	−1.01402	−	1.75634i	−0.182124	−	0.315448i	0.760480	−	0.649362i	$-0.224964\pi$
$31$	−1.01402	−	1.75634i	−0.182124	−	0.315448i	−0.942604	+	0.333914i	$0.891631\pi$
$32$		0			0
$33$	1.91668	+	1.10660i	0.333652	+	0.192634i
$34$		0			0
$35$	−8.29809	+	2.01987i	−1.40263	+	0.341421i
$36$		0			0
$37$	0.798374	+	0.460941i	0.131252	+	0.0757783i	0.564188	−	0.825646i	$-0.309189\pi$
$37$	0.798374	+	0.460941i	0.131252	+	0.0757783i	−0.432936	+	0.901424i	$0.642523\pi$
$38$		0			0
$39$	−4.40261	+	2.54185i	−0.704981	+	0.407021i
$40$		0			0
$41$			5.96303i			0.931269i	0.884977	+	0.465635i	$0.154174\pi$
$41$			5.96303i			0.931269i	−0.884977	+	0.465635i	$0.845826\pi$
$42$		0			0
$43$	6.68790			1.01990			0.509948	−	0.860205i	$-0.329665\pi$
$43$	6.68790			1.01990			0.509948	+	0.860205i	$0.329665\pi$
$44$		0			0
$45$	1.61398	+	2.79550i	0.240598	+	0.416728i
$46$		0			0
$47$	1.06113	−	1.83793i	0.154782	−	0.268090i	−0.778198	−	0.628019i	$-0.783866\pi$
$47$	1.06113	−	1.83793i	0.154782	−	0.268090i	0.932980	+	0.359929i	$0.117199\pi$
$48$		0			0
$49$	−0.322287	+	6.99258i	−0.0460410	+	0.998940i
$50$		0			0
$51$	−1.57961	+	2.73597i	−0.221190	+	0.383113i
$52$		0			0
$53$	3.12560	−	1.80457i	0.429334	−	0.247876i	−0.269729	−	0.962936i	$-0.586934\pi$
$53$	3.12560	−	1.80457i	0.429334	−	0.247876i	0.699063	+	0.715060i	$0.253601\pi$
$54$		0			0
$55$	−7.14411			−0.963311
$56$		0			0
$57$	−3.38981			−0.448991
$58$		0			0
$59$	10.6351	−	6.14015i	1.38457	−	0.799379i	0.391869	−	0.920021i	$-0.371828\pi$
$59$	10.6351	−	6.14015i	1.38457	−	0.799379i	0.992696	+	0.120642i	$0.0384952\pi$
$60$		0			0
$61$	6.34115	−	10.9832i	0.811901	−	1.40625i	−0.0996301	−	0.995025i	$-0.531766\pi$
$61$	6.34115	−	10.9832i	0.811901	−	1.40625i	0.911532	−	0.411230i	$-0.134901\pi$
$62$		0			0
$63$	2.57069	−	0.625743i	0.323876	−	0.0788361i
$64$		0			0
$65$	8.20498	−	14.2114i	1.01770	−	1.76271i
$66$		0			0
$67$	4.40720	+	7.63350i	0.538425	+	0.932580i	0.998989	+	0.0449534i	$0.0143139\pi$
$67$	4.40720	+	7.63350i	0.538425	+	0.932580i	−0.460564	+	0.887627i	$0.652353\pi$
$68$		0			0
$69$	3.06401			0.368863
$70$		0			0
$71$			11.7036i			1.38896i	0.719512	+	0.694480i	$0.244366\pi$
$71$			11.7036i			1.38896i	−0.719512	+	0.694480i	$0.755634\pi$
$72$		0			0
$73$	7.82068	−	4.51527i	0.915342	−	0.528473i	0.0331957	−	0.999449i	$-0.489432\pi$
$73$	7.82068	−	4.51527i	0.915342	−	0.528473i	0.882146	+	0.470976i	$0.156098\pi$
$74$		0			0
$75$	−4.69363	−	2.70987i	−0.541974	−	0.312909i
$76$		0			0
$77$	−1.64537	+	5.61964i	−0.187507	+	0.640418i
$78$		0			0
$79$	−9.60105	−	5.54317i	−1.08020	−	0.623655i	−0.149252	−	0.988799i	$-0.547687\pi$
$79$	−9.60105	−	5.54317i	−1.08020	−	0.623655i	−0.930951	+	0.365144i	$0.881020\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	3.57322i		−	0.392212i	−0.980583	−	0.196106i	$-0.937170\pi$
$83$		−	3.57322i		−	0.392212i	0.980583	−	0.196106i	$-0.0628297\pi$
$84$		0			0
$85$		−	10.1979i		−	1.10611i
$86$		0			0
$87$	4.94170	+	8.55928i	0.529806	+	0.917651i
$88$		0			0
$89$	−6.32253	−	3.65032i	−0.670187	−	0.386933i	0.125960	−	0.992035i	$-0.459799\pi$
$89$	−6.32253	−	3.65032i	−0.670187	−	0.386933i	−0.796147	+	0.605103i	$0.793132\pi$
$90$		0			0
$91$	−9.28920	−	9.72719i	−0.973772	−	1.01969i
$92$		0			0
$93$	−1.75634	−	1.01402i	−0.182124	−	0.105149i
$94$		0			0
$95$	9.47619	−	5.47108i	0.972237	−	0.561321i
$96$		0			0
$97$			15.2238i			1.54574i	0.634566	+	0.772869i	$0.281179\pi$
$97$			15.2238i			1.54574i	−0.634566	+	0.772869i	$0.718821\pi$
$98$		0			0
$99$	2.21319			0.222434
$100$		0			0
$101$	−4.92124	−	8.52383i	−0.489681	−	0.848153i	0.510248	−	0.860027i	$-0.329554\pi$
$101$	−4.92124	−	8.52383i	−0.489681	−	0.848153i	−0.999929	+	0.0118744i	$0.996220\pi$
$102$		0			0
$103$	0.992258	−	1.71864i	0.0977701	−	0.169343i	−0.812991	−	0.582276i	$-0.802162\pi$
$103$	0.992258	−	1.71864i	0.0977701	−	0.169343i	0.910761	+	0.412933i	$0.135496\pi$
$104$		0			0
$105$	−6.17642	+	5.89831i	−0.602757	+	0.575616i
$106$		0			0
$107$	−1.61805	+	2.80255i	−0.156423	+	0.270933i	−0.933576	−	0.358379i	$-0.883330\pi$
$107$	−1.61805	+	2.80255i	−0.156423	+	0.270933i	0.777153	+	0.629311i	$0.216663\pi$
$108$		0			0
$109$	−3.62997	+	2.09576i	−0.347688	+	0.200738i	−0.663666	−	0.748029i	$-0.731001\pi$
$109$	−3.62997	+	2.09576i	−0.347688	+	0.200738i	0.315979	+	0.948766i	$0.397667\pi$
$110$		0			0
$111$	0.921883			0.0875012
$112$		0			0
$113$	−2.84651			−0.267777			−0.133889	−	0.990996i	$-0.542746\pi$
$113$	−2.84651			−0.267777			−0.133889	+	0.990996i	$0.542746\pi$
$114$		0			0
$115$	−8.56542	+	4.94525i	−0.798729	+	0.461147i
$116$		0			0
$117$	−2.54185	+	4.40261i	−0.234994	+	0.407021i
$118$		0			0
$119$	−8.02177	−	2.34868i	−0.735354	−	0.215304i
$120$		0			0
$121$	3.05088	−	5.28429i	0.277353	−	0.480390i
$122$		0			0
$123$	2.98152	+	5.16414i	0.268834	+	0.465635i
$124$		0			0
$125$	1.35490			0.121186
$126$		0			0
$127$		−	21.0058i		−	1.86396i	−0.362506	−	0.931981i	$-0.618079\pi$
$127$		−	21.0058i		−	1.86396i	0.362506	−	0.931981i	$-0.381921\pi$
$128$		0			0
$129$	5.79189	−	3.34395i	0.509948	−	0.294418i
$130$		0			0
$131$	0.494446	+	0.285468i	0.0431999	+	0.0249415i	0.521444	−	0.853285i	$-0.325393\pi$
$131$	0.494446	+	0.285468i	0.0431999	+	0.0249415i	−0.478245	+	0.878227i	$0.658727\pi$
$132$		0			0
$133$	−2.12115	−	8.71414i	−0.183927	−	0.755612i
$134$		0			0
$135$	2.79550	+	1.61398i	0.240598	+	0.138909i
$136$		0			0
$137$	6.57813	+	11.3937i	0.562008	+	0.973426i	0.997321	+	0.0731470i	$0.0233042\pi$
$137$	6.57813	+	11.3937i	0.562008	+	0.973426i	−0.435313	+	0.900279i	$0.643362\pi$
$138$		0			0
$139$			9.54821i			0.809869i	0.914346	+	0.404934i	$0.132706\pi$
$139$			9.54821i			0.809869i	−0.914346	+	0.404934i	$0.867294\pi$
$140$		0			0
$141$		−	2.12226i		−	0.178727i
$142$		0			0
$143$	−5.62560	−	9.74383i	−0.470436	−	0.814820i
$144$		0			0
$145$	−27.6290	−	15.9516i	−2.29447	−	1.32471i
$146$		0			0
$147$	3.21718	+	6.21689i	0.265349	+	0.512761i
$148$		0			0
$149$	9.17651	+	5.29806i	0.751769	+	0.434034i	0.826333	−	0.563182i	$-0.190423\pi$
$149$	9.17651	+	5.29806i	0.751769	+	0.434034i	−0.0745636	+	0.997216i	$0.523756\pi$
$150$		0			0
$151$	−1.05318	+	0.608052i	−0.0857063	+	0.0494826i	−0.542241	−	0.840223i	$-0.682424\pi$
$151$	−1.05318	+	0.608052i	−0.0857063	+	0.0494826i	0.456534	+	0.889706i	$0.349091\pi$
$152$		0			0
$153$			3.15923i			0.255409i
$154$		0			0
$155$	6.54645			0.525824
$156$		0			0
$157$	−1.81252	−	3.13938i	−0.144655	−	0.250550i	0.784589	−	0.620016i	$-0.212874\pi$
$157$	−1.81252	−	3.13938i	−0.144655	−	0.250550i	−0.929244	+	0.369466i	$0.879541\pi$
$158$		0			0
$159$	1.80457	−	3.12560i	0.143111	−	0.247876i
$160$		0			0
$161$	1.91728	+	7.87661i	0.151103	+	0.620764i
$162$		0			0
$163$	9.91572	−	17.1745i	0.776659	−	1.34521i	−0.157198	−	0.987567i	$-0.550246\pi$
$163$	9.91572	−	17.1745i	0.776659	−	1.34521i	0.933857	−	0.357646i	$-0.116420\pi$
$164$		0			0
$165$	−6.18698	+	3.57205i	−0.481656	+	0.278084i
$166$		0			0
$167$	12.3971			0.959317			0.479659	−	0.877455i	$-0.340760\pi$
$167$	12.3971			0.959317			0.479659	+	0.877455i	$0.340760\pi$
$168$		0			0
$169$	12.8439			0.987994
$170$		0			0
$171$	−2.93566	+	1.69490i	−0.224495	+	0.129613i
$172$		0			0
$173$	0.519326	−	0.899499i	0.0394836	−	0.0683876i	−0.845608	−	0.533804i	$-0.820762\pi$
$173$	0.519326	−	0.899499i	0.0394836	−	0.0683876i	0.885092	+	0.465416i	$0.154095\pi$
$174$		0			0
$175$	4.02923	−	13.7615i	0.304581	−	1.04028i
$176$		0			0
$177$	6.14015	−	10.6351i	0.461522	−	0.799379i
$178$		0			0
$179$	−1.26304	−	2.18764i	−0.0944038	−	0.163512i	0.814956	−	0.579523i	$-0.196761\pi$
$179$	−1.26304	−	2.18764i	−0.0944038	−	0.163512i	−0.909360	+	0.416011i	$0.863428\pi$
$180$		0			0
$181$	8.29867			0.616835			0.308418	−	0.951251i	$-0.400201\pi$
$181$	8.29867			0.616835			0.308418	+	0.951251i	$0.400201\pi$
$182$		0			0
$183$		−	12.6823i		−	0.937503i
$184$		0			0
$185$	−2.57712	+	1.48790i	−0.189474	+	0.109393i
$186$		0			0
$187$	−6.05524	−	3.49599i	−0.442803	−	0.255652i
$188$		0			0
$189$	1.91341	−	1.82725i	0.139180	−	0.132913i
$190$		0			0
$191$	5.26146	+	3.03771i	0.380706	+	0.219801i	0.678125	−	0.734946i	$-0.262793\pi$
$191$	5.26146	+	3.03771i	0.380706	+	0.219801i	−0.297419	+	0.954747i	$0.596126\pi$
$192$		0			0
$193$	4.59340	+	7.95599i	0.330640	+	0.572685i	0.982637	−	0.185536i	$-0.0594021\pi$
$193$	4.59340	+	7.95599i	0.330640	+	0.572685i	−0.651998	+	0.758221i	$0.726069\pi$
$194$		0			0
$195$		−	16.4100i		−	1.17514i
$196$		0			0
$197$		−	20.2764i		−	1.44463i	−0.691563	−	0.722316i	$-0.743078\pi$
$197$		−	20.2764i		−	1.44463i	0.691563	−	0.722316i	$-0.256922\pi$
$198$		0			0
$199$	−1.64355	−	2.84672i	−0.116508	−	0.201799i	0.801873	−	0.597494i	$-0.203837\pi$
$199$	−1.64355	−	2.84672i	−0.116508	−	0.201799i	−0.918382	+	0.395696i	$0.870504\pi$
$200$		0			0
$201$	7.63350	+	4.40720i	0.538425	+	0.310860i
$202$		0			0
$203$	−18.9110	+	18.0595i	−1.32729	+	1.26753i
$204$		0			0
$205$	−16.6696	−	9.62422i	−1.16426	−	0.672185i
$206$		0			0
$207$	2.65351	−	1.53200i	0.184431	−	0.106482i
$208$		0			0
$209$		−	7.50230i		−	0.518945i
$210$		0			0
$211$	21.6901			1.49320			0.746602	−	0.665271i	$-0.231684\pi$
$211$	21.6901			1.49320			0.746602	+	0.665271i	$0.231684\pi$
$212$		0			0
$213$	5.85179	+	10.1356i	0.400958	+	0.694480i
$214$		0			0
$215$	−10.7941	+	18.6960i	−0.736154	+	1.27506i
$216$		0			0
$217$	1.50772	−	5.14952i	0.102351	−	0.349572i
$218$		0			0
$219$	4.51527	−	7.82068i	0.305114	−	0.528473i
$220$		0			0
$221$	13.9088	−	8.03027i	0.935610	−	0.540175i
$222$		0			0
$223$	19.3266			1.29420			0.647102	−	0.762404i	$-0.275981\pi$
$223$	19.3266			1.29420			0.647102	+	0.762404i	$0.275981\pi$
$224$		0			0
$225$	−5.41974			−0.361316
$226$		0			0
$227$	0.466841	−	0.269531i	0.0309853	−	0.0178894i	−0.484427	−	0.874832i	$-0.660972\pi$
$227$	0.466841	−	0.269531i	0.0309853	−	0.0178894i	0.515413	+	0.856942i	$0.327639\pi$
$228$		0			0
$229$	−11.4311	+	19.7993i	−0.755392	+	1.30838i	0.189788	+	0.981825i	$0.439220\pi$
$229$	−11.4311	+	19.7993i	−0.755392	+	1.30838i	−0.945179	+	0.326551i	$0.894113\pi$
$230$		0			0
$231$	1.38489	+	5.68944i	0.0911191	+	0.374337i
$232$		0			0
$233$	1.50245	−	2.60232i	0.0984287	−	0.170484i	−0.812606	−	0.582814i	$-0.801952\pi$
$233$	1.50245	−	2.60232i	0.0984287	−	0.170484i	0.911034	+	0.412330i	$0.135285\pi$
$234$		0			0
$235$	3.42529	+	5.93277i	0.223441	+	0.387011i
$236$		0			0
$237$	−11.0863			−0.720135
$238$		0			0
$239$		−	11.2699i		−	0.728988i	−0.931206	−	0.364494i	$-0.881242\pi$
$239$		−	11.2699i		−	0.728988i	0.931206	−	0.364494i	$-0.118758\pi$
$240$		0			0
$241$	9.76276	−	5.63653i	0.628875	−	0.363081i	−0.151441	−	0.988466i	$-0.548392\pi$
$241$	9.76276	−	5.63653i	0.628875	−	0.363081i	0.780316	+	0.625385i	$0.215058\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−19.0276	−	12.1868i	−1.21563	−	0.778588i
$246$		0			0
$247$	14.9240	+	8.61637i	0.949590	+	0.548246i
$248$		0			0
$249$	−1.78661	−	3.09450i	−0.113222	−	0.196106i
$250$		0			0
$251$			3.26625i			0.206164i	0.994673	+	0.103082i	$0.0328704\pi$
$251$			3.26625i			0.206164i	−0.994673	+	0.103082i	$0.967130\pi$
$252$		0			0
$253$			6.78124i			0.426333i
$254$		0			0
$255$	−5.09893	−	8.83161i	−0.319308	−	0.553057i
$256$		0			0
$257$	−10.4533	−	6.03522i	−0.652059	−	0.376467i	0.137185	−	0.990545i	$-0.456194\pi$
$257$	−10.4533	−	6.03522i	−0.652059	−	0.376467i	−0.789245	+	0.614079i	$0.789528\pi$
$258$		0			0
$259$	0.576861	+	2.36987i	0.0358444	+	0.147257i
$260$		0			0
$261$	8.55928	+	4.94170i	0.529806	+	0.305884i
$262$		0			0
$263$	−14.1861	+	8.19034i	−0.874752	+	0.505038i	−0.868924	−	0.494945i	$-0.835188\pi$
$263$	−14.1861	+	8.19034i	−0.874752	+	0.505038i	−0.00582745	+	0.999983i	$0.501855\pi$
$264$		0			0
$265$			11.6501i			0.715663i
$266$		0			0
$267$	−7.30063			−0.446791
$268$		0			0
$269$	3.73572	+	6.47046i	0.227771	+	0.394511i	0.957147	−	0.289602i	$-0.0935229\pi$
$269$	3.73572	+	6.47046i	0.227771	+	0.394511i	−0.729376	+	0.684113i	$0.760190\pi$
$270$		0			0
$271$	4.48617	−	7.77027i	0.272515	−	0.472011i	−0.696990	−	0.717081i	$-0.745478\pi$
$271$	4.48617	−	7.77027i	0.272515	−	0.472011i	0.969505	+	0.245070i	$0.0788111\pi$
$272$		0			0
$273$	−12.9083	−	3.77940i	−0.781244	−	0.228740i
$274$		0			0
$275$	5.99747	−	10.3879i	0.361661	−	0.626415i
$276$		0			0
$277$	−5.31638	+	3.06942i	−0.319430	+	0.184423i	−0.651139	−	0.758959i	$-0.725708\pi$
$277$	−5.31638	+	3.06942i	−0.319430	+	0.184423i	0.331708	+	0.943382i	$0.392375\pi$
$278$		0			0
$279$	−2.02805			−0.121416
$280$		0			0
$281$	−19.2936			−1.15096			−0.575480	−	0.817816i	$-0.695185\pi$
$281$	−19.2936			−1.15096			−0.575480	+	0.817816i	$0.695185\pi$
$282$		0			0
$283$	−19.3500	+	11.1718i	−1.15024	+	0.664092i	−0.948946	−	0.315439i	$-0.897848\pi$
$283$	−19.3500	+	11.1718i	−1.15024	+	0.664092i	−0.201295	+	0.979531i	$0.564515\pi$
$284$		0			0
$285$	5.47108	−	9.47619i	0.324079	−	0.561321i
$286$		0			0
$287$	−11.4097	+	10.8960i	−0.673495	+	0.643169i
$288$		0			0
$289$	−3.50964	+	6.07887i	−0.206449	+	0.357581i
$290$		0			0
$291$	7.61188	+	13.1842i	0.446216	+	0.772869i
$292$		0			0
$293$	14.0707			0.822018			0.411009	−	0.911631i	$-0.365176\pi$
$293$	14.0707			0.822018			0.411009	+	0.911631i	$0.365176\pi$
$294$		0			0
$295$			39.6403i			2.30795i
$296$		0			0
$297$	1.91668	−	1.10660i	0.111217	−	0.0642113i
$298$		0			0
$299$	−13.4896	−	7.78823i	−0.780124	−	0.450405i
$300$		0			0
$301$	12.2205	+	12.7967i	0.704377	+	0.737590i
$302$		0			0
$303$	−8.52383	−	4.92124i	−0.489681	−	0.282718i
$304$		0			0
$305$	20.4690	+	35.4533i	1.17205	+	2.03005i
$306$		0			0
$307$			9.61787i			0.548921i	0.961598	+	0.274460i	$0.0884992\pi$
$307$			9.61787i			0.548921i	−0.961598	+	0.274460i	$0.911501\pi$
$308$		0			0
$309$		−	1.98452i		−	0.112895i
$310$		0			0
$311$	10.8485	+	18.7902i	0.615162	+	1.06549i	0.990356	+	0.138546i	$0.0442428\pi$
$311$	10.8485	+	18.7902i	0.615162	+	1.06549i	−0.375194	+	0.926946i	$0.622424\pi$
$312$		0			0
$313$	−9.46514	−	5.46470i	−0.535001	−	0.308883i	0.208049	−	0.978118i	$-0.433289\pi$
$313$	−9.46514	−	5.46470i	−0.535001	−	0.308883i	−0.743051	+	0.669235i	$0.766622\pi$
$314$		0			0
$315$	−2.39978	+	8.19629i	−0.135212	+	0.461809i
$316$		0			0
$317$	6.14253	+	3.54639i	0.344999	+	0.199185i	0.662480	−	0.749079i	$-0.269504\pi$
$317$	6.14253	+	3.54639i	0.344999	+	0.199185i	−0.317482	+	0.948264i	$0.602837\pi$
$318$		0			0
$319$	−18.9433	+	10.9369i	−1.06062	+	0.612352i
$320$		0			0
$321$			3.23611i			0.180622i
$322$		0			0
$323$	10.7092			0.595874
$324$		0			0
$325$	13.7761	+	23.8610i	0.764163	+	1.32357i
$326$		0			0
$327$	−2.09576	+	3.62997i	−0.115896	+	0.200738i
$328$		0			0
$329$	5.45567	−	1.32799i	0.300781	−	0.0732144i
$330$		0			0
$331$	5.86202	−	10.1533i	0.322206	−	0.558077i	−0.658737	−	0.752373i	$-0.728909\pi$
$331$	5.86202	−	10.1533i	0.322206	−	0.558077i	0.980943	+	0.194297i	$0.0622424\pi$
$332$		0			0
$333$	0.798374	−	0.460941i	0.0437506	−	0.0252594i
$334$		0			0
$335$	−28.4526			−1.55453
$336$		0			0
$337$	23.5287			1.28169			0.640846	−	0.767670i	$-0.278584\pi$
$337$	23.5287			1.28169			0.640846	+	0.767670i	$0.278584\pi$
$338$		0			0
$339$	−2.46515	+	1.42326i	−0.133889	+	0.0773007i
$340$		0			0
$341$	2.24423	−	3.88712i	0.121532	−	0.210499i
$342$		0			0
$343$	−13.9686	+	12.1605i	−0.754232	+	0.656608i
$344$		0			0
$345$	−4.94525	+	8.56542i	−0.266243	+	0.461147i
$346$		0			0
$347$	−5.17132	−	8.95699i	−0.277611	−	0.480837i	0.693179	−	0.720765i	$-0.256209\pi$
$347$	−5.17132	−	8.95699i	−0.277611	−	0.480837i	−0.970791	+	0.239928i	$0.922876\pi$
$348$		0			0
$349$	−0.830301			−0.0444450			−0.0222225	−	0.999753i	$-0.507074\pi$
$349$	−0.830301			−0.0444450			−0.0222225	+	0.999753i	$0.507074\pi$
$350$		0			0
$351$			5.08369i			0.271347i
$352$		0			0
$353$	−4.21179	+	2.43168i	−0.224171	+	0.129425i	−0.607880	−	0.794029i	$-0.707980\pi$
$353$	−4.21179	+	2.43168i	−0.224171	+	0.129425i	0.383709	+	0.923454i	$0.374647\pi$
$354$		0			0
$355$	−32.7173	−	18.8894i	−1.73646	−	1.00254i
$356$		0			0
$357$	−8.12140	+	1.97686i	−0.429830	+	0.104627i
$358$		0			0
$359$	−16.3080	−	9.41543i	−0.860704	−	0.496928i	0.00354407	−	0.999994i	$-0.498872\pi$
$359$	−16.3080	−	9.41543i	−0.860704	−	0.496928i	−0.864248	+	0.503066i	$0.832205\pi$
$360$		0			0
$361$	−3.75460	−	6.50317i	−0.197611	−	0.342272i
$362$		0			0
$363$		−	6.10177i		−	0.320260i
$364$		0			0
$365$			29.1503i			1.52579i
$366$		0			0
$367$	10.7270	+	18.5796i	0.559943	+	0.969850i	0.997501	+	0.0706593i	$0.0225103\pi$
$367$	10.7270	+	18.5796i	0.559943	+	0.969850i	−0.437557	+	0.899190i	$0.644156\pi$
$368$		0			0
$369$	5.16414	+	2.98152i	0.268834	+	0.155212i
$370$		0			0
$371$	9.16414	+	2.68316i	0.475779	+	0.139303i
$372$		0			0
$373$	14.1525	+	8.17098i	0.732791	+	0.423077i	0.819442	−	0.573162i	$-0.194283\pi$
$373$	14.1525	+	8.17098i	0.732791	+	0.423077i	−0.0866513	+	0.996239i	$0.527617\pi$
$374$		0			0
$375$	1.17337	−	0.677448i	0.0605928	−	0.0349832i
$376$		0			0
$377$		−	50.2442i		−	2.58771i
$378$		0			0
$379$	4.31636			0.221717			0.110858	−	0.993836i	$-0.464640\pi$
$379$	4.31636			0.221717			0.110858	+	0.993836i	$0.464640\pi$
$380$		0			0
$381$	−10.5029	−	18.1916i	−0.538080	−	0.931981i
$382$		0			0
$383$	10.0948	−	17.4848i	0.515823	−	0.893431i	−0.484009	−	0.875063i	$-0.660820\pi$
$383$	10.0948	−	17.4848i	0.515823	−	0.893431i	0.999831	−	0.0183677i	$-0.00584695\pi$
$384$		0			0
$385$	−13.0541	−	13.6696i	−0.665298	−	0.696668i
$386$		0			0
$387$	3.34395	−	5.79189i	0.169983	−	0.294418i
$388$		0			0
$389$	−29.2383	+	16.8807i	−1.48244	+	0.855886i	−0.999801	−	0.0199339i	$-0.993654\pi$
$389$	−29.2383	+	16.8807i	−1.48244	+	0.855886i	−0.482637	+	0.875820i	$0.660321\pi$
$390$		0			0
$391$	−9.67989			−0.489533
$392$		0			0
$393$	0.570937			0.0287999
$394$		0			0
$395$	30.9918	−	17.8931i	1.55937	−	0.900302i
$396$		0			0
$397$	−0.0441158	+	0.0764109i	−0.00221411	+	0.00383495i	−0.867130	−	0.498081i	$-0.834038\pi$
$397$	−0.0441158	+	0.0764109i	−0.00221411	+	0.00383495i	0.864916	+	0.501916i	$0.167371\pi$
$398$		0			0
$399$	−6.19404	−	6.48610i	−0.310090	−	0.324711i
$400$		0			0
$401$	12.6037	−	21.8303i	0.629400	−	1.09015i	−0.358272	−	0.933617i	$-0.616634\pi$
$401$	12.6037	−	21.8303i	0.629400	−	1.09015i	0.987672	−	0.156536i	$-0.0500327\pi$
$402$		0			0
$403$	5.15498	+	8.92869i	0.256788	+	0.444770i
$404$		0			0
$405$	3.22796			0.160399
$406$		0			0
$407$			2.04031i			0.101134i
$408$		0			0
$409$	−26.9181	+	15.5412i	−1.33102	+	0.768462i	−0.985455	−	0.169935i	$-0.945644\pi$
$409$	−26.9181	+	15.5412i	−1.33102	+	0.768462i	−0.345560	+	0.938397i	$0.612311\pi$
$410$		0			0
$411$	11.3937	+	6.57813i	0.562008	+	0.324475i
$412$		0			0
$413$	31.1816	+	9.12962i	1.53434	+	0.449239i
$414$		0			0
$415$	9.98894	+	5.76712i	0.490338	+	0.283097i
$416$		0			0
$417$	4.77411	+	8.26899i	0.233789	+	0.404934i
$418$		0			0
$419$			22.7655i			1.11217i	0.831126	+	0.556085i	$0.187697\pi$
$419$			22.7655i			1.11217i	−0.831126	+	0.556085i	$0.812303\pi$
$420$		0			0
$421$			24.0207i			1.17070i	0.810781	+	0.585349i	$0.199042\pi$
$421$			24.0207i			1.17070i	−0.810781	+	0.585349i	$0.800958\pi$
$422$		0			0
$423$	−1.06113	−	1.83793i	−0.0515939	−	0.0893633i
$424$		0			0
$425$	14.8283	+	8.56109i	0.719276	+	0.415274i
$426$		0			0
$427$	32.6023	−	7.93586i	1.57773	−	0.384043i
$428$		0			0
$429$	−9.74383	−	5.62560i	−0.470436	−	0.271607i
$430$		0			0
$431$	28.2391	−	16.3039i	1.36023	−	0.785330i	0.370577	−	0.928802i	$-0.379160\pi$
$431$	28.2391	−	16.3039i	1.36023	−	0.785330i	0.989654	+	0.143471i	$0.0458265\pi$
$432$		0			0
$433$			18.4752i			0.887861i	0.896061	+	0.443931i	$0.146416\pi$
$433$			18.4752i			0.887861i	−0.896061	+	0.443931i	$0.853584\pi$
$434$		0			0
$435$	−31.9032			−1.52964
$436$		0			0
$437$	−5.19319	−	8.99487i	−0.248424	−	0.430283i
$438$		0			0
$439$	−11.2138	+	19.4229i	−0.535206	+	0.927004i	0.463947	+	0.885863i	$0.346433\pi$
$439$	−11.2138	+	19.4229i	−0.535206	+	0.927004i	−0.999153	+	0.0411413i	$0.986901\pi$
$440$		0			0
$441$	5.89461	+	3.77540i	0.280696	+	0.179781i
$442$		0			0
$443$	4.52168	−	7.83178i	0.214832	−	0.372099i	−0.738389	−	0.674375i	$-0.764413\pi$
$443$	4.52168	−	7.83178i	0.214832	−	0.372099i	0.953220	+	0.302276i	$0.0977464\pi$
$444$		0			0
$445$	20.4089	−	11.7831i	0.967474	−	0.558571i
$446$		0			0
$447$	10.5961			0.501179
$448$		0			0
$449$	5.65664			0.266954			0.133477	−	0.991052i	$-0.457386\pi$
$449$	5.65664			0.266954			0.133477	+	0.991052i	$0.457386\pi$
$450$		0			0
$451$	−11.4292	+	6.59867i	−0.538182	+	0.310719i
$452$		0			0
$453$	−0.608052	+	1.05318i	−0.0285688	+	0.0494826i
$454$		0			0
$455$	42.1849	−	10.2684i	1.97766	−	0.481391i
$456$		0			0
$457$	−4.68971	+	8.12282i	−0.219376	+	0.379970i	−0.954617	−	0.297835i	$-0.903735\pi$
$457$	−4.68971	+	8.12282i	−0.219376	+	0.379970i	0.735242	+	0.677805i	$0.237069\pi$
$458$		0			0
$459$	1.57961	+	2.73597i	0.0737301	+	0.127704i
$460$		0			0
$461$	−31.7960			−1.48089			−0.740444	−	0.672118i	$-0.765385\pi$
$461$	−31.7960			−1.48089			−0.740444	+	0.672118i	$0.765385\pi$
$462$		0			0
$463$			8.87505i			0.412458i	0.978504	+	0.206229i	$0.0661193\pi$
$463$			8.87505i			0.412458i	−0.978504	+	0.206229i	$0.933881\pi$
$464$		0			0
$465$	5.66939	−	3.27323i	0.262912	−	0.151792i
$466$		0			0
$467$	−2.70998	−	1.56461i	−0.125403	−	0.0724015i	0.435986	−	0.899953i	$-0.356400\pi$
$467$	−2.70998	−	1.56461i	−0.125403	−	0.0724015i	−0.561389	+	0.827552i	$0.689733\pi$
$468$		0			0
$469$	−6.55294	+	22.3811i	−0.302587	+	1.03346i
$470$		0			0
$471$	−3.13938	−	1.81252i	−0.144655	−	0.0835165i
$472$		0			0
$473$	7.40081	+	12.8186i	0.340290	+	0.589399i
$474$		0			0
$475$			18.3719i			0.842959i
$476$		0			0
$477$		−	3.60913i		−	0.165251i
$478$		0			0
$479$	−8.19517	−	14.1945i	−0.374447	−	0.648561i	0.615797	−	0.787905i	$-0.288834\pi$
$479$	−8.19517	−	14.1945i	−0.374447	−	0.648561i	−0.990244	+	0.139344i	$0.955501\pi$
$480$		0			0
$481$	−4.05869	−	2.34328i	−0.185060	−	0.106845i
$482$		0			0
$483$	5.59872	+	5.86270i	0.254750	+	0.266762i
$484$		0			0
$485$	−42.5580	−	24.5708i	−1.93246	−	1.11570i
$486$		0			0
$487$	25.4297	−	14.6819i	1.15233	−	0.665299i	0.202877	−	0.979204i	$-0.434971\pi$
$487$	25.4297	−	14.6819i	1.15233	−	0.665299i	0.949454	+	0.313905i	$0.101637\pi$
$488$		0			0
$489$		−	19.8314i		−	0.896808i
$490$		0			0
$491$	−33.8967			−1.52974			−0.764869	−	0.644186i	$-0.777196\pi$
$491$	−33.8967			−1.52974			−0.764869	+	0.644186i	$0.777196\pi$
$492$		0			0
$493$	−15.6120	−	27.0407i	−0.703128	−	1.21785i
$494$		0			0
$495$	−3.57205	+	6.18698i	−0.160552	+	0.278084i
$496$		0			0
$497$	−22.3938	+	21.3854i	−1.00450	+	0.959267i
$498$		0			0
$499$	−4.44527	+	7.69943i	−0.198997	+	0.344674i	−0.948204	−	0.317663i	$-0.897102\pi$
$499$	−4.44527	+	7.69943i	−0.198997	+	0.344674i	0.749206	+	0.662337i	$0.230435\pi$
$500$		0			0
$501$	10.7362	−	6.19856i	0.479659	−	0.276931i
$502$		0			0
$503$	1.51626			0.0676065			0.0338032	−	0.999429i	$-0.489238\pi$
$503$	1.51626			0.0676065			0.0338032	+	0.999429i	$0.489238\pi$
$504$		0			0
$505$	31.7711			1.41380
$506$		0			0
$507$	11.1232	−	6.42196i	0.493997	−	0.285209i
$508$		0			0
$509$	3.71720	−	6.43837i	0.164762	−	0.285376i	−0.771809	−	0.635855i	$-0.780648\pi$
$509$	3.71720	−	6.43837i	0.164762	−	0.285376i	0.936571	+	0.350479i	$0.113981\pi$
$510$		0			0
$511$	22.9299	+	6.71363i	1.01436	+	0.296994i
$512$		0			0
$513$	−1.69490	+	2.93566i	−0.0748318	+	0.129613i
$514$		0			0
$515$	3.20297	+	5.54771i	0.141140	+	0.244461i
$516$		0			0
$517$	4.69698			0.206573
$518$		0			0
$519$		−	1.03865i		−	0.0455917i
$520$		0			0
$521$	−11.7724	+	6.79678i	−0.515757	+	0.297772i	−0.735197	−	0.677854i	$-0.762910\pi$
$521$	−11.7724	+	6.79678i	−0.515757	+	0.297772i	0.219440	+	0.975626i	$0.429577\pi$
$522$		0			0
$523$	−3.38679	−	1.95536i	−0.148094	−	0.0855020i	0.424122	−	0.905605i	$-0.360583\pi$
$523$	−3.38679	−	1.95536i	−0.148094	−	0.0855020i	−0.572216	+	0.820103i	$0.693916\pi$
$524$		0			0
$525$	−3.39136	−	13.9325i	−0.148011	−	0.608063i
$526$		0			0
$527$	5.54868	+	3.20353i	0.241704	+	0.139548i
$528$		0			0
$529$	−6.80594	−	11.7882i	−0.295910	−	0.512532i
$530$		0			0
$531$		−	12.2803i		−	0.532920i
$532$		0			0
$533$		−	30.3142i		−	1.31305i
$534$		0			0
$535$	−5.22301	−	9.04652i	−0.225811	−	0.391115i
$536$		0			0
$537$	−2.18764	−	1.26304i	−0.0944038	−	0.0545041i
$538$		0			0
$539$	−13.7592	+	7.12025i	−0.592650	+	0.306691i
$540$		0			0
$541$	29.3866	+	16.9663i	1.26343	+	0.729440i	0.973736	−	0.227680i	$-0.0731140\pi$
$541$	29.3866	+	16.9663i	1.26343	+	0.729440i	0.289691	+	0.957120i	$0.406447\pi$
$542$		0			0
$543$	7.18686	−	4.14933i	0.308418	−	0.178065i
$544$		0			0
$545$		−	13.5301i		−	0.579565i
$546$		0			0
$547$	−19.9416			−0.852640			−0.426320	−	0.904572i	$-0.640190\pi$
$547$	−19.9416			−0.852640			−0.426320	+	0.904572i	$0.640190\pi$
$548$		0			0
$549$	−6.34115	−	10.9832i	−0.270634	−	0.468752i
$550$		0			0
$551$	16.7514	−	29.0143i	0.713634	−	1.23605i
$552$		0			0
$553$	−6.93720	−	28.4995i	−0.295000	−	1.21192i
$554$		0			0
$555$	−1.48790	+	2.57712i	−0.0631579	+	0.109393i
$556$		0			0
$557$	−29.5999	+	17.0895i	−1.25419	+	0.724107i	−0.971939	−	0.235234i	$-0.924414\pi$
$557$	−29.5999	+	17.0895i	−1.25419	+	0.724107i	−0.282251	+	0.959341i	$0.591081\pi$
$558$		0			0
$559$	−33.9992			−1.43801
$560$		0			0
$561$	−6.99199			−0.295202
$562$		0			0
$563$	−1.95583	+	1.12920i	−0.0824283	+	0.0475900i	−0.540648	−	0.841249i	$-0.681821\pi$
$563$	−1.95583	+	1.12920i	−0.0824283	+	0.0475900i	0.458219	+	0.888839i	$0.348487\pi$
$564$		0			0
$565$	4.59422	−	7.95742i	0.193280	−	0.334771i
$566$		0			0
$567$	0.743436	−	2.53915i	0.0312214	−	0.106634i
$568$		0			0
$569$	−14.5803	+	25.2538i	−0.611236	+	1.05869i	0.379796	+	0.925070i	$0.375994\pi$
$569$	−14.5803	+	25.2538i	−0.611236	+	1.05869i	−0.991032	+	0.133622i	$0.957339\pi$
$570$		0			0
$571$	−13.1289	−	22.7399i	−0.549427	−	0.951636i	−0.998314	−	0.0580474i	$-0.981513\pi$
$571$	−13.1289	−	22.7399i	−0.549427	−	0.951636i	0.448886	−	0.893589i	$-0.351821\pi$
$572$		0			0
$573$	6.07541			0.253804
$574$		0			0
$575$		−	16.6061i		−	0.692522i
$576$		0			0
$577$	0.0467698	−	0.0270026i	0.00194705	−	0.00112413i	−0.499026	−	0.866587i	$-0.666309\pi$
$577$	0.0467698	−	0.0270026i	0.00194705	−	0.00112413i	0.500973	+	0.865463i	$0.332976\pi$
$578$		0			0
$579$	7.95599	+	4.59340i	0.330640	+	0.190895i
$580$		0			0
$581$	6.83705	−	6.52919i	0.283649	−	0.270876i
$582$		0			0
$583$	6.91756	+	3.99386i	0.286496	+	0.165409i
$584$		0			0
$585$	−8.20498	−	14.2114i	−0.339234	−	0.587571i
$586$		0			0
$587$			4.75946i			0.196444i	0.995165	+	0.0982219i	$0.0313155\pi$
$587$			4.75946i			0.196444i	−0.995165	+	0.0982219i	$0.968685\pi$
$588$		0			0
$589$			6.87468i			0.283266i
$590$		0			0
$591$	−10.1382	−	17.5599i	−0.417029	−	0.722316i
$592$		0			0
$593$	−10.2802	−	5.93527i	−0.422157	−	0.243732i	0.273843	−	0.961774i	$-0.411705\pi$
$593$	−10.2802	−	5.93527i	−0.422157	−	0.243732i	−0.696000	+	0.718042i	$0.745038\pi$
$594$		0			0
$595$	19.5127	−	18.6341i	0.799944	−	0.763923i
$596$		0			0
$597$	−2.84672	−	1.64355i	−0.116508	−	0.0672662i
$598$		0			0
$599$	−25.6580	+	14.8136i	−1.04836	+	0.605269i	−0.922189	−	0.386740i	$-0.873601\pi$
$599$	−25.6580	+	14.8136i	−1.04836	+	0.605269i	−0.126167	+	0.992009i	$0.540268\pi$
$600$		0			0
$601$			26.4608i			1.07936i	0.841870	+	0.539680i	$0.181455\pi$
$601$			26.4608i			1.07936i	−0.841870	+	0.539680i	$0.818545\pi$
$602$		0			0
$603$	8.81440			0.358950
$604$		0			0
$605$	9.84814	+	17.0575i	0.400384	+	0.693485i
$606$		0			0
$607$	7.69208	−	13.3231i	0.312212	−	0.540767i	−0.666629	−	0.745390i	$-0.732263\pi$
$607$	7.69208	−	13.3231i	0.312212	−	0.540767i	0.978841	+	0.204623i	$0.0655967\pi$
$608$		0			0
$609$	−7.34768	+	25.0955i	−0.297743	+	1.01692i
$610$		0			0
$611$	−5.39446	+	9.34348i	−0.218237	+	0.377997i
$612$		0			0
$613$	16.8302	−	9.71692i	0.679765	−	0.392463i	−0.120001	−	0.992774i	$-0.538290\pi$
$613$	16.8302	−	9.71692i	0.679765	−	0.392463i	0.799767	+	0.600311i	$0.204957\pi$
$614$		0			0
$615$	−19.2484			−0.776172
$616$		0			0
$617$	−0.173969			−0.00700371			−0.00350186	−	0.999994i	$-0.501115\pi$
$617$	−0.173969			−0.00700371			−0.00350186	+	0.999994i	$0.501115\pi$
$618$		0			0
$619$	32.8798	−	18.9832i	1.32155	−	0.762998i	0.337575	−	0.941299i	$-0.390393\pi$
$619$	32.8798	−	18.9832i	1.32155	−	0.762998i	0.983976	+	0.178300i	$0.0570599\pi$
$620$		0			0
$621$	1.53200	−	2.65351i	0.0614771	−	0.106482i
$622$		0			0
$623$	−4.56831	−	18.7677i	−0.183026	−	0.751910i
$624$		0			0
$625$	11.3626	−	19.6805i	0.454503	−	0.787222i
$626$		0			0
$627$	−3.75115	−	6.49718i	−0.149807	−	0.259473i
$628$		0			0
$629$	−2.91244			−0.116127
$630$		0			0
$631$		−	26.0140i		−	1.03560i	−0.855501	−	0.517801i	$-0.826751\pi$
$631$		−	26.0140i		−	1.03560i	0.855501	−	0.517801i	$-0.173249\pi$
$632$		0			0
$633$	18.7841	−	10.8450i	0.746602	−	0.431051i
$634$		0			0
$635$	58.7216	+	33.9030i	2.33030	+	1.34540i
$636$		0			0
$637$	1.63841	−	35.5481i	0.0649161	−	1.40847i
$638$		0			0
$639$	10.1356	+	5.85179i	0.400958	+	0.231493i
$640$		0			0
$641$	−12.4573	−	21.5767i	−0.492035	−	0.852230i	0.507923	−	0.861403i	$-0.330413\pi$
$641$	−12.4573	−	21.5767i	−0.492035	−	0.852230i	−0.999958	+	0.00917289i	$0.997080\pi$
$642$		0			0
$643$			4.80941i			0.189665i	0.995493	+	0.0948323i	$0.0302315\pi$
$643$			4.80941i			0.189665i	−0.995493	+	0.0948323i	$0.969769\pi$
$644$		0			0
$645$			21.5883i			0.850038i
$646$		0			0
$647$	−4.27034	−	7.39644i	−0.167884	−	0.290784i	0.769792	−	0.638295i	$-0.220360\pi$
$647$	−4.27034	−	7.39644i	−0.167884	−	0.290784i	−0.937676	+	0.347511i	$0.887027\pi$
$648$		0			0
$649$	23.5374	+	13.5893i	0.923925	+	0.533428i
$650$		0			0
$651$	−1.26903	−	5.21348i	−0.0497374	−	0.204332i
$652$		0			0
$653$	24.1955	+	13.9693i	0.946845	+	0.546661i	0.892099	−	0.451839i	$-0.149232\pi$
$653$	24.1955	+	13.9693i	0.946845	+	0.546661i	0.0547454	+	0.998500i	$0.482565\pi$
$654$		0			0
$655$	−1.59605	+	0.921481i	−0.0623629	+	0.0360052i
$656$		0			0
$657$		−	9.03055i		−	0.352315i
$658$		0			0
$659$	−28.0553			−1.09288			−0.546439	−	0.837499i	$-0.684017\pi$
$659$	−28.0553			−1.09288			−0.546439	+	0.837499i	$0.684017\pi$
$660$		0			0
$661$	4.47127	+	7.74447i	0.173912	+	0.301225i	0.939784	−	0.341768i	$-0.111026\pi$
$661$	4.47127	+	7.74447i	0.173912	+	0.301225i	−0.765872	+	0.642993i	$0.777692\pi$
$662$		0			0
$663$	8.03027	−	13.9088i	0.311870	−	0.540175i
$664$		0			0
$665$	27.7838	+	8.13480i	1.07741	+	0.315454i
$666$		0			0
$667$	−15.1414	+	26.2257i	−0.586277	+	1.01546i
$668$		0			0
$669$	16.7373	−	9.66329i	0.647102	−	0.373604i
$670$		0			0
$671$	28.0684			1.08357
$672$		0			0
$673$	45.4881			1.75344			0.876720	−	0.481002i	$-0.159727\pi$
$673$	45.4881			1.75344			0.876720	+	0.481002i	$0.159727\pi$
$674$		0			0
$675$	−4.69363	+	2.70987i	−0.180658	+	0.104303i
$676$		0			0
$677$	5.48447	−	9.49939i	0.210785	−	0.365091i	−0.741175	−	0.671312i	$-0.765731\pi$
$677$	5.48447	−	9.49939i	0.210785	−	0.365091i	0.951961	+	0.306221i	$0.0990645\pi$
$678$		0			0
$679$	−29.1293	+	27.8177i	−1.11788	+	1.06754i
$680$		0			0
$681$	0.269531	−	0.466841i	0.0103284	−	0.0178894i
$682$		0			0
$683$	−14.1037	−	24.4283i	−0.539663	−	0.934723i	−0.998922	−	0.0464211i	$-0.985218\pi$
$683$	−14.1037	−	24.4283i	−0.539663	−	0.934723i	0.459259	−	0.888302i	$-0.348115\pi$
$684$		0			0
$685$	−42.4679			−1.62262
$686$		0			0
$687$			22.8623i			0.872251i
$688$		0			0
$689$	−15.8896	+	9.17386i	−0.605345	+	0.349496i
$690$		0			0
$691$	−8.22050	−	4.74611i	−0.312723	−	0.180550i	0.335422	−	0.942068i	$-0.391121\pi$
$691$	−8.22050	−	4.74611i	−0.312723	−	0.180550i	−0.648144	+	0.761518i	$0.724455\pi$
$692$		0			0
$693$	4.04407	+	4.23475i	0.153621	+	0.160865i
$694$		0			0
$695$	−26.6920	−	15.4106i	−1.01249	−	0.584559i
$696$		0			0
$697$	−9.41929	−	16.3147i	−0.356781	−	0.617963i
$698$		0			0
$699$		−	3.00490i		−	0.113656i
$700$		0			0
$701$		−	14.3589i		−	0.542328i	−0.962533	−	0.271164i	$-0.912591\pi$
$701$		−	14.3589i		−	0.542328i	0.962533	−	0.271164i	$-0.0874085\pi$
$702$		0			0
$703$	−1.56250	−	2.70633i	−0.0589309	−	0.102071i
$704$		0			0
$705$	5.93277	+	3.42529i	0.223441	+	0.129004i
$706$		0			0
$707$	7.31725	−	24.9915i	0.275193	−	0.939904i
$708$		0			0
$709$	−8.90161	−	5.13935i	−0.334307	−	0.193012i	0.323445	−	0.946247i	$-0.395159\pi$
$709$	−8.90161	−	5.13935i	−0.334307	−	0.193012i	−0.657752	+	0.753235i	$0.728492\pi$
$710$		0			0
$711$	−9.60105	+	5.54317i	−0.360068	+	0.207885i
$712$		0			0
$713$		−	6.21394i		−	0.232714i
$714$		0			0
$715$	36.3184			1.35823
$716$		0			0
$717$	−5.63494	−	9.76000i	−0.210441	−	0.364494i
$718$		0			0
$719$	−7.39467	+	12.8079i	−0.275775	+	0.477656i	−0.970330	−	0.241783i	$-0.922268\pi$
$719$	−7.39467	+	12.8079i	−0.275775	+	0.477656i	0.694556	+	0.719439i	$0.255601\pi$
$720$		0			0
$721$	5.10158	−	1.24180i	0.189993	−	0.0462469i
$722$		0			0
$723$	5.63653	−	9.76276i	0.209625	−	0.363081i
$724$		0			0
$725$	46.3890	−	26.7827i	1.72285	−	0.994685i
$726$		0			0
$727$	43.5679			1.61585			0.807923	−	0.589289i	$-0.200592\pi$
$727$	43.5679			1.61585			0.807923	+	0.589289i	$0.200592\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−18.2979	+	10.5643i	−0.676773	+	0.390735i
$732$		0			0
$733$	11.3412	−	19.6435i	0.418896	−	0.725549i	−0.576933	−	0.816792i	$-0.695750\pi$
$733$	11.3412	−	19.6435i	0.418896	−	0.725549i	0.995829	+	0.0912424i	$0.0290838\pi$
$734$		0			0
$735$	−22.5718	−	1.04033i	−0.832572	−	0.0383731i
$736$		0			0
$737$	−9.75399	+	16.8944i	−0.359293	+	0.622314i
$738$		0			0
$739$	2.32595	+	4.02866i	0.0855615	+	0.148197i	0.905630	−	0.424068i	$-0.139398\pi$
$739$	2.32595	+	4.02866i	0.0855615	+	0.148197i	−0.820069	+	0.572265i	$0.806065\pi$
$740$		0			0
$741$	17.2327			0.633060
$742$		0			0
$743$		−	28.3209i		−	1.03899i	−0.854473	−	0.519496i	$-0.826120\pi$
$743$		−	28.3209i		−	1.03899i	0.854473	−	0.519496i	$-0.173880\pi$
$744$		0			0
$745$	−29.6214	+	17.1019i	−1.08525	+	0.626567i
$746$		0			0
$747$	−3.09450	−	1.78661i	−0.113222	−	0.0653687i
$748$		0			0
$749$	−8.31902	+	2.02497i	−0.303971	+	0.0739908i
$750$		0			0
$751$	−28.5823	−	16.5020i	−1.04298	−	0.602166i	−0.122306	−	0.992492i	$-0.539029\pi$
$751$	−28.5823	−	16.5020i	−1.04298	−	0.602166i	−0.920677	+	0.390326i	$0.872362\pi$
$752$		0			0
$753$	1.63312	+	2.82866i	0.0595144	+	0.103082i
$754$		0			0
$755$		−	3.92554i		−	0.142865i
$756$		0			0
$757$		−	19.0350i		−	0.691838i	−0.938264	−	0.345919i	$-0.887567\pi$
$757$		−	19.0350i		−	0.691838i	0.938264	−	0.345919i	$-0.112433\pi$
$758$		0			0
$759$	3.39062	+	5.87273i	0.123072	+	0.213166i
$760$		0			0
$761$	43.2756	+	24.9852i	1.56874	+	0.905712i	0.996316	+	0.0857544i	$0.0273301\pi$
$761$	43.2756	+	24.9852i	1.56874	+	0.905712i	0.572424	+	0.819958i	$0.306003\pi$
$762$		0			0
$763$	−10.6429	−	3.11613i	−0.385300	−	0.112811i
$764$		0			0
$765$	−8.83161	−	5.09893i	−0.319308	−	0.184352i
$766$		0			0
$767$	−54.0653	+	31.2146i	−1.95219	+	1.12709i
$768$		0			0
$769$		−	24.2908i		−	0.875949i	−0.898987	−	0.437974i	$-0.855696\pi$
$769$		−	24.2908i		−	0.875949i	0.898987	−	0.437974i	$-0.144304\pi$
$770$		0			0
$771$	−12.0704			−0.434706
$772$		0			0
$773$	8.01612	+	13.8843i	0.288320	+	0.499385i	0.973409	−	0.229075i	$-0.0735700\pi$
$773$	8.01612	+	13.8843i	0.288320	+	0.499385i	−0.685089	+	0.728459i	$0.740237\pi$
$774$		0			0
$775$	−5.49574	+	9.51890i	−0.197413	+	0.341929i
$776$		0			0
$777$	1.68451	+	1.76394i	0.0604316	+	0.0632810i
$778$		0			0
$779$	10.1068	−	17.5054i	0.362112	−	0.627197i
$780$		0			0
$781$	−22.4321	+	12.9512i	−0.802682	+	0.463429i
$782$		0			0
$783$	9.88340			0.353204
$784$		0			0
$785$	11.7015			0.417644
$786$		0			0
$787$	8.71618	−	5.03229i	0.310698	−	0.179382i	−0.336541	−	0.941669i	$-0.609257\pi$
$787$	8.71618	−	5.03229i	0.310698	−	0.179382i	0.647239	+	0.762287i	$0.275924\pi$
$788$		0			0
$789$	−8.19034	+	14.1861i	−0.291584	+	0.505038i
$790$		0			0
$791$	−5.20130	−	5.44655i	−0.184937	−	0.193657i
$792$		0			0
$793$	−32.2365	+	55.8352i	−1.14475	+	1.98277i
$794$		0			0
$795$	5.82507	+	10.0893i	0.206594	+	0.357831i
$796$		0			0
$797$	53.0872			1.88045			0.940223	−	0.340560i	$-0.110617\pi$
$797$	53.0872			1.88045			0.940223	+	0.340560i	$0.110617\pi$
$798$		0			0
$799$			6.70471i			0.237196i
$800$		0			0
$801$	−6.32253	+	3.65032i	−0.223396	+	0.128978i
$802$		0			0
$803$	17.3087	+	9.99318i	0.610811	+	0.352652i
$804$		0			0
$805$	−25.1135	−	7.35295i	−0.885134	−	0.259157i
$806$		0			0
$807$	6.47046	+	3.73572i	0.227771	+	0.131504i
$808$		0			0
$809$	−26.9529	−	46.6838i	−0.947614	−	1.64132i	−0.750431	−	0.660949i	$-0.770154\pi$
$809$	−26.9529	−	46.6838i	−0.947614	−	1.64132i	−0.197183	−	0.980367i	$-0.563179\pi$
$810$		0			0
$811$			48.2050i			1.69271i	0.532621	+	0.846354i	$0.321207\pi$
$811$			48.2050i			1.69271i	−0.532621	+	0.846354i	$0.678793\pi$
$812$		0			0
$813$		−	8.97234i		−	0.314674i
$814$		0			0
$815$	32.0076	+	55.4387i	1.12118	+	1.94193i
$816$		0			0
$817$	−19.6334	−	11.3353i	−0.686885	−	0.396574i
$818$		0			0
$819$	−13.0686	+	3.18108i	−0.456654	+	0.111156i
$820$		0			0
$821$	−22.4271	−	12.9483i	−0.782712	−	0.451899i	0.0546787	−	0.998504i	$-0.482587\pi$
$821$	−22.4271	−	12.9483i	−0.782712	−	0.451899i	−0.837390	+	0.546605i	$0.815920\pi$
$822$		0			0
$823$	48.1100	−	27.7763i	1.67701	−	0.968221i	0.713457	−	0.700699i	$-0.247129\pi$
$823$	48.1100	−	27.7763i	1.67701	−	0.968221i	0.963552	−	0.267522i	$-0.0862048\pi$
$824$		0			0
$825$		−	11.9949i		−	0.417610i
$826$		0			0
$827$	−23.2870			−0.809770			−0.404885	−	0.914368i	$-0.632688\pi$
$827$	−23.2870			−0.809770			−0.404885	+	0.914368i	$0.632688\pi$
$828$		0			0
$829$	−2.58838	−	4.48320i	−0.0898980	−	0.155708i	0.817570	−	0.575829i	$-0.195321\pi$
$829$	−2.58838	−	4.48320i	−0.0898980	−	0.155708i	−0.907468	+	0.420122i	$0.861987\pi$
$830$		0			0
$831$	−3.06942	+	5.31638i	−0.106477	+	0.184423i
$832$		0			0
$833$	−10.1638	−	19.6406i	−0.352155	−	0.680506i
$834$		0			0
$835$	−20.0087	+	34.6561i	−0.692430	+	1.19932i
$836$		0			0
$837$	−1.75634	+	1.01402i	−0.0607080	+	0.0350498i
$838$		0			0
$839$	−12.7298			−0.439480			−0.219740	−	0.975558i	$-0.570521\pi$
$839$	−12.7298			−0.439480			−0.219740	+	0.975558i	$0.570521\pi$
$840$		0			0
$841$	−68.6816			−2.36833
$842$		0			0
$843$	−16.7087	+	9.64680i	−0.575480	+	0.332253i
$844$		0			0
$845$	−20.7298	+	35.9052i	−0.713128	+	1.23517i
$846$		0			0
$847$	15.6858	−	3.81814i	0.538969	−	0.131193i
$848$		0			0
$849$	−11.1718	+	19.3500i	−0.383414	+	0.664092i
$850$		0			0
$851$	1.41233	+	2.44622i	0.0484139	+	0.0838554i
$852$		0			0
$853$	47.2928			1.61927			0.809637	−	0.586930i	$-0.199664\pi$
$853$	47.2928			1.61927			0.809637	+	0.586930i	$0.199664\pi$
$854$		0			0
$855$		−	10.9422i		−	0.374214i
$856$		0			0
$857$	45.2524	−	26.1265i	1.54579	−	0.892463i	0.547336	−	0.836913i	$-0.315642\pi$
$857$	45.2524	−	26.1265i	1.54579	−	0.892463i	0.998456	−	0.0555505i	$-0.0176914\pi$
$858$		0			0
$859$	−43.7066	−	25.2340i	−1.49125	−	0.860973i	−0.491299	−	0.870991i	$-0.663478\pi$
$859$	−43.7066	−	25.2340i	−1.49125	−	0.860973i	−0.999950	+	0.0100178i	$0.996811\pi$
$860$		0			0
$861$	−4.43313	+	15.1411i	−0.151081	+	0.516006i
$862$		0			0
$863$	23.1918	+	13.3898i	0.789457	+	0.455793i	0.839771	−	0.542940i	$-0.182689\pi$
$863$	23.1918	+	13.3898i	0.789457	+	0.455793i	−0.0503147	+	0.998733i	$0.516022\pi$
$864$		0			0
$865$	1.67636	+	2.90355i	0.0569981	+	0.0987236i
$866$		0			0
$867$			7.01927i			0.238387i
$868$		0			0
$869$		−	24.5362i		−	0.832335i
$870$		0			0
$871$	−22.4049	−	38.8063i	−0.759160	−	1.31490i
$872$		0			0
$873$	13.1842	+	7.61188i	0.446216	+	0.257623i
$874$		0			0
$875$	2.47574	+	2.59247i	0.0836952	+	0.0876416i
$876$		0			0
$877$	−22.4411	−	12.9564i	−0.757783	−	0.437506i	0.0707159	−	0.997496i	$-0.477472\pi$
$877$	−22.4411	−	12.9564i	−0.757783	−	0.437506i	−0.828499	+	0.559990i	$0.810805\pi$
$878$		0			0
$879$	12.1856	−	7.03534i	0.411009	−	0.237296i
$880$		0			0
$881$			10.0120i			0.337313i	0.985675	+	0.168657i	$0.0539429\pi$
$881$			10.0120i			0.337313i	−0.985675	+	0.168657i	$0.946057\pi$
$882$		0			0
$883$	23.6231			0.794981			0.397491	−	0.917606i	$-0.369881\pi$
$883$	23.6231			0.794981			0.397491	+	0.917606i	$0.369881\pi$
$884$		0			0
$885$	19.8202	+	34.3295i	0.666248	+	1.15397i
$886$		0			0
$887$	−9.08123	+	15.7291i	−0.304918	+	0.528133i	−0.977243	−	0.212123i	$-0.931962\pi$
$887$	−9.08123	+	15.7291i	−0.304918	+	0.528133i	0.672325	+	0.740256i	$0.265296\pi$
$888$		0			0
$889$	40.1927	−	38.3829i	1.34802	−	1.28732i
$890$		0			0
$891$	1.10660	−	1.91668i	0.0370724	−	0.0642113i
$892$		0			0
$893$	−6.23023	+	3.59703i	−0.208487	+	0.120370i
$894$		0			0
$895$	8.15407			0.272560
$896$		0			0
$897$	−15.5765			−0.520083
$898$		0			0
$899$	17.3586	−	10.0220i	0.578942	−	0.334252i
$900$		0			0
$901$	−5.70104	+	9.87449i	−0.189929	+	0.328967i
$902$		0			0
$903$	16.9816	+	4.97203i	0.565113	+	0.165459i
$904$		0			0
$905$	−13.3939	+	23.1989i	−0.445228	+	0.771158i
$906$		0			0
$907$	−27.7185	−	48.0098i	−0.920377	−	1.59414i	−0.798832	−	0.601554i	$-0.794548\pi$
$907$	−27.7185	−	48.0098i	−0.920377	−	1.59414i	−0.121546	−	0.992586i	$-0.538785\pi$
$908$		0			0
$909$	−9.84247			−0.326454
$910$		0			0
$911$			18.4722i			0.612012i	0.952030	+	0.306006i	$0.0989928\pi$
$911$			18.4722i			0.612012i	−0.952030	+	0.306006i	$0.901007\pi$
$912$		0			0
$913$	6.84874	−	3.95412i	0.226660	−	0.130862i
$914$		0			0
$915$	35.4533	+	20.4690i	1.17205	+	0.676684i
$916$		0			0
$917$	0.357259	+	1.46770i	0.0117977	+	0.0484678i
$918$		0			0
$919$	0.144308	+	0.0833164i	0.00476029	+	0.00274835i	0.502378	−	0.864648i	$-0.332459\pi$
$919$	0.144308	+	0.0833164i	0.00476029	+	0.00274835i	−0.497618	+	0.867396i	$0.665792\pi$
$920$		0			0
$921$	4.80893	+	8.32932i	0.158460	+	0.274460i
$922$		0			0
$923$		−	59.4974i		−	1.95838i
$924$		0			0
$925$		−	4.99636i		−	0.164279i
$926$		0			0
$927$	−0.992258	−	1.71864i	−0.0325900	−	0.0564476i
$928$		0			0
$929$	14.0194	+	8.09409i	0.459961	+	0.265559i	0.712028	−	0.702151i	$-0.247777\pi$
$929$	14.0194	+	8.09409i	0.459961	+	0.265559i	−0.252067	+	0.967710i	$0.581110\pi$
$930$		0			0
$931$	12.7979	−	19.9816i	0.419433	−	0.654870i
$932$		0			0
$933$	18.7902	+	10.8485i	0.615162	+	0.355164i
$934$		0			0
$935$	19.5461	−	11.2849i	0.639225	−	0.369057i
$936$		0			0
$937$			19.5153i			0.637538i	0.947832	+	0.318769i	$0.103270\pi$
$937$			19.5153i			0.637538i	−0.947832	+	0.318769i	$0.896730\pi$
$938$		0			0
$939$	−10.9294			−0.356668
$940$		0			0
$941$	12.3201	+	21.3390i	0.401624	+	0.695633i	0.993922	−	0.110086i	$-0.0351126\pi$
$941$	12.3201	+	21.3390i	0.401624	+	0.695633i	−0.592298	+	0.805719i	$0.701779\pi$
$942$		0			0
$943$	−9.13538	+	15.8229i	−0.297489	+	0.515266i
$944$		0			0
$945$	2.01987	+	8.29809i	0.0657065	+	0.269937i
$946$		0			0
$947$	−4.30769	+	7.46115i	−0.139981	+	0.242455i	−0.927489	−	0.373850i	$-0.878038\pi$
$947$	−4.30769	+	7.46115i	−0.139981	+	0.242455i	0.787508	+	0.616304i	$0.211371\pi$
$948$		0			0
$949$	−39.7579	+	22.9543i	−1.29060	+	0.745127i
$950$		0			0
$951$	7.09278			0.229999
$952$		0			0
$953$	−27.4982			−0.890755			−0.445378	−	0.895343i	$-0.646931\pi$
$953$	−27.4982			−0.890755			−0.445378	+	0.895343i	$0.646931\pi$
$954$		0			0
$955$	−16.9838	+	9.80560i	−0.549583	+	0.317302i
$956$		0			0
$957$	−10.9369	+	18.9433i	−0.353541	+	0.612352i
$958$		0			0
$959$	−9.78084	+	33.4058i	−0.315840	+	1.07873i
$960$		0			0
$961$	13.4435	−	23.2849i	0.433662	−	0.751124i
$962$		0			0
$963$	1.61805	+	2.80255i	0.0521410	+	0.0903109i
$964$		0			0
$965$	−29.6546			−0.954616
$966$		0			0
$967$		−	21.2591i		−	0.683647i	−0.939764	−	0.341823i	$-0.888956\pi$
$967$		−	21.2591i		−	0.683647i	0.939764	−	0.341823i	$-0.111044\pi$
$968$		0			0
$969$	9.27442	−	5.35459i	0.297937	−	0.172014i
$970$		0			0
$971$	27.3347	+	15.7817i	0.877213	+	0.506459i	0.869738	−	0.493513i	$-0.164287\pi$
$971$	27.3347	+	15.7817i	0.877213	+	0.506459i	0.00747434	+	0.999972i	$0.497621\pi$
$972$		0			0
$973$	−18.2697	+	17.4470i	−0.585698	+	0.559325i
$974$		0			0
$975$	23.8610	+	13.7761i	0.764163	+	0.441189i
$976$		0			0
$977$	9.75712	+	16.8998i	0.312158	+	0.540673i	0.978829	−	0.204678i	$-0.0656149\pi$
$977$	9.75712	+	16.8998i	0.312158	+	0.540673i	−0.666671	+	0.745352i	$0.732282\pi$
$978$		0			0
$979$		−	16.1577i		−	0.516403i
$980$		0			0
$981$			4.19152i			0.133825i
$982$		0			0
$983$	11.2401	+	19.4684i	0.358503	+	0.620946i	0.987711	−	0.156291i	$-0.0499538\pi$
$983$	11.2401	+	19.4684i	0.358503	+	0.620946i	−0.629208	+	0.777237i	$0.716620\pi$
$984$		0			0
$985$	56.6825	+	32.7257i	1.80606	+	1.04273i
$986$		0			0
$987$	4.06076	−	3.87791i	0.129255	−	0.123435i
$988$		0			0
$989$	17.7464	+	10.2459i	0.564302	+	0.325800i
$990$		0			0
$991$	−38.9073	+	22.4631i	−1.23593	+	0.713565i	−0.968260	−	0.249945i	$-0.919588\pi$
$991$	−38.9073	+	22.4631i	−1.23593	+	0.713565i	−0.267671	+	0.963510i	$0.586254\pi$
$992$		0			0
$993$		−	11.7240i		−	0.372051i
$994$		0			0
$995$	10.6107			0.336381
$996$		0			0
$997$	−14.5890	−	25.2688i	−0.462037	−	0.800272i	0.537025	−	0.843566i	$-0.319548\pi$
$997$	−14.5890	−	25.2688i	−0.462037	−	0.800272i	−0.999062	+	0.0432942i	$0.986215\pi$
$998$		0			0
$999$	0.460941	−	0.798374i	0.0145835	−	0.0252594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bb.a.271.9		32
3.2	odd	2		2016.2.bs.c.271.15		32
4.3	odd	2		168.2.t.a.19.7	yes	32
7.2	even	3		4704.2.p.a.3919.10		32
7.3	odd	6	inner	672.2.bb.a.367.16		32
7.5	odd	6		4704.2.p.a.3919.19		32
8.3	odd	2	inner	672.2.bb.a.271.16		32
8.5	even	2		168.2.t.a.19.5	✓	32
12.11	even	2		504.2.bk.c.19.10		32
21.17	even	6		2016.2.bs.c.1711.2		32
24.5	odd	2		504.2.bk.c.19.12		32
24.11	even	2		2016.2.bs.c.271.2		32
28.3	even	6		168.2.t.a.115.5	yes	32
28.19	even	6		1176.2.p.a.979.29		32
28.23	odd	6		1176.2.p.a.979.30		32
56.3	even	6	inner	672.2.bb.a.367.9		32
56.5	odd	6		1176.2.p.a.979.32		32
56.19	even	6		4704.2.p.a.3919.9		32
56.37	even	6		1176.2.p.a.979.31		32
56.45	odd	6		168.2.t.a.115.7	yes	32
56.51	odd	6		4704.2.p.a.3919.20		32
84.59	odd	6		504.2.bk.c.451.12		32
168.59	odd	6		2016.2.bs.c.1711.15		32
168.101	even	6		504.2.bk.c.451.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.5	✓	32	8.5	even	2
168.2.t.a.19.7	yes	32	4.3	odd	2
168.2.t.a.115.5	yes	32	28.3	even	6
168.2.t.a.115.7	yes	32	56.45	odd	6
504.2.bk.c.19.10		32	12.11	even	2
504.2.bk.c.19.12		32	24.5	odd	2
504.2.bk.c.451.10		32	168.101	even	6
504.2.bk.c.451.12		32	84.59	odd	6
672.2.bb.a.271.9		32	1.1	even	1	trivial
672.2.bb.a.271.16		32	8.3	odd	2	inner
672.2.bb.a.367.9		32	56.3	even	6	inner
672.2.bb.a.367.16		32	7.3	odd	6	inner
1176.2.p.a.979.29		32	28.19	even	6
1176.2.p.a.979.30		32	28.23	odd	6
1176.2.p.a.979.31		32	56.37	even	6
1176.2.p.a.979.32		32	56.5	odd	6
2016.2.bs.c.271.2		32	24.11	even	2
2016.2.bs.c.271.15		32	3.2	odd	2
2016.2.bs.c.1711.2		32	21.17	even	6
2016.2.bs.c.1711.15		32	168.59	odd	6
4704.2.p.a.3919.9		32	56.19	even	6
4704.2.p.a.3919.10		32	7.2	even	3
4704.2.p.a.3919.19		32	7.5	odd	6
4704.2.p.a.3919.20		32	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(-1.61398 + 2.79550i) q^{5} +(1.82725 + 1.91341i) q^{7} +(0.500000 - 0.866025i) q^{9} +(1.10660 + 1.91668i) q^{11} -5.08369 q^{13} +3.22796i q^{15} +(-2.73597 + 1.57961i) q^{17} +(-2.93566 - 1.69490i) q^{19} +(2.53915 + 0.743436i) q^{21} +(2.65351 + 1.53200i) q^{23} +(-2.70987 - 4.69363i) q^{25} -1.00000i q^{27} +9.88340i q^{29} +(-1.01402 - 1.75634i) q^{31} +(1.91668 + 1.10660i) q^{33} +(-8.29809 + 2.01987i) q^{35} +(0.798374 + 0.460941i) q^{37} +(-4.40261 + 2.54185i) q^{39} +5.96303i q^{41} +6.68790 q^{43} +(1.61398 + 2.79550i) q^{45} +(1.06113 - 1.83793i) q^{47} +(-0.322287 + 6.99258i) q^{49} +(-1.57961 + 2.73597i) q^{51} +(3.12560 - 1.80457i) q^{53} -7.14411 q^{55} -3.38981 q^{57} +(10.6351 - 6.14015i) q^{59} +(6.34115 - 10.9832i) q^{61} +(2.57069 - 0.625743i) q^{63} +(8.20498 - 14.2114i) q^{65} +(4.40720 + 7.63350i) q^{67} +3.06401 q^{69} +11.7036i q^{71} +(7.82068 - 4.51527i) q^{73} +(-4.69363 - 2.70987i) q^{75} +(-1.64537 + 5.61964i) q^{77} +(-9.60105 - 5.54317i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.57322i q^{83} -10.1979i q^{85} +(4.94170 + 8.55928i) q^{87} +(-6.32253 - 3.65032i) q^{89} +(-9.28920 - 9.72719i) q^{91} +(-1.75634 - 1.01402i) q^{93} +(9.47619 - 5.47108i) q^{95} +15.2238i q^{97} +2.21319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9} - 8 q^{11} - 16 q^{25} + 24 q^{35} + 16 q^{43} + 8 q^{49} + 16 q^{57} + 96 q^{59} + 32 q^{67} - 24 q^{73} - 16 q^{81} - 56 q^{91} - 16 q^{99}+O(q^{100}) \) 32 * q + 16 * q^9 - 8 * q^11 - 16 * q^25 + 24 * q^35 + 16 * q^43 + 8 * q^49 + 16 * q^57 + 96 * q^59 + 32 * q^67 - 24 * q^73 - 16 * q^81 - 56 * q^91 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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