LMFDB - Embedded newform 468.2.cg.a.281.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,2,Mod(5,468)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(468, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 9]))

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

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

chi := DirichletCharacter("468.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.cg (of order $12$, 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:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			281.6
Character	$\chi$	$=$	468.281
Dual form			468.2.cg.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.763329 + 1.55478i) q^{3} +(0.391929 + 0.105017i) q^{5} +(-1.14793 - 4.28414i) q^{7} +(-1.83466 - 2.37361i) q^{9} +O(q^{10})$	\(q+(-0.763329 + 1.55478i) q^{3} +(0.391929 + 0.105017i) q^{5} +(-1.14793 - 4.28414i) q^{7} +(-1.83466 - 2.37361i) q^{9} +(-5.35589 + 1.43511i) q^{11} +(-1.41280 + 3.31723i) q^{13} +(-0.462449 + 0.529200i) q^{15} -2.10279 q^{17} +(-2.08178 - 2.08178i) q^{19} +(7.53713 + 1.48543i) q^{21} +(-1.61975 - 2.80548i) q^{23} +(-4.18755 - 2.41768i) q^{25} +(5.09088 - 1.04063i) q^{27} +(1.51221 + 0.873077i) q^{29} +(1.59885 - 5.96700i) q^{31} +(1.85704 - 9.42267i) q^{33} -1.79963i q^{35} +(0.419848 - 0.419848i) q^{37} +(-4.07911 - 4.72872i) q^{39} +(7.47510 + 2.00295i) q^{41} +(-5.17242 - 2.98630i) q^{43} +(-0.469786 - 1.12296i) q^{45} +(1.59728 - 0.427989i) q^{47} +(-10.9739 + 6.33580i) q^{49} +(1.60512 - 3.26937i) q^{51} +10.2290i q^{53} -2.24984 q^{55} +(4.82579 - 1.64762i) q^{57} +(-3.92005 + 14.6298i) q^{59} +(0.552523 - 0.956999i) q^{61} +(-8.06282 + 10.5847i) q^{63} +(-0.902083 + 1.15175i) q^{65} +(1.45577 - 5.43302i) q^{67} +(5.59829 - 0.376835i) q^{69} +(-0.450191 + 0.450191i) q^{71} +(4.21227 - 4.21227i) q^{73} +(6.95543 - 4.66521i) q^{75} +(12.2964 + 21.2980i) q^{77} +(-2.65252 + 4.59429i) q^{79} +(-2.26807 + 8.70953i) q^{81} +(-2.68228 - 10.0104i) q^{83} +(-0.824145 - 0.220829i) q^{85} +(-2.51176 + 1.68471i) q^{87} +(-9.01543 - 9.01543i) q^{89} +(15.8333 + 2.24468i) q^{91} +(8.05689 + 7.04064i) q^{93} +(-0.597288 - 1.03453i) q^{95} +(10.3378 - 2.77000i) q^{97} +(13.2326 + 10.0799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{7}+O(q^{10}) $ 56 * q - 2 * q^7	$ 56 q - 2 q^{7} - 12 q^{11} - 12 q^{15} + 4 q^{19} - 12 q^{21} + 36 q^{27} - 4 q^{31} + 12 q^{33} - 4 q^{37} + 24 q^{41} + 6 q^{45} + 66 q^{47} - 48 q^{57} - 30 q^{63} - 78 q^{65} - 14 q^{67} + 28 q^{73} - 24 q^{79} - 78 q^{83} + 36 q^{85} - 8 q^{91} + 6 q^{93} + 26 q^{97} + 54 q^{99}+O(q^{100}) $ 56 * q - 2 * q^7 - 12 * q^11 - 12 * q^15 + 4 * q^19 - 12 * q^21 + 36 * q^27 - 4 * q^31 + 12 * q^33 - 4 * q^37 + 24 * q^41 + 6 * q^45 + 66 * q^47 - 48 * q^57 - 30 * q^63 - 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 - 78 * q^83 + 36 * q^85 - 8 * q^91 + 6 * q^93 + 26 * q^97 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.763329	+	1.55478i	−0.440708	+	0.897650i
$3$	−0.763329	+	1.55478i	−0.440708	+	0.897650i
$4$		0			0
$5$	0.391929	+	0.105017i	0.175276	+	0.0469651i	0.345390	−	0.938459i	$-0.387747\pi$
$5$	0.391929	+	0.105017i	0.175276	+	0.0469651i	−0.170114	+	0.985424i	$0.554413\pi$
$6$		0			0
$7$	−1.14793	−	4.28414i	−0.433877	−	1.61925i	−0.743739	−	0.668471i	$-0.766949\pi$
$7$	−1.14793	−	4.28414i	−0.433877	−	1.61925i	0.309861	−	0.950782i	$-0.399717\pi$
$8$		0			0
$9$	−1.83466	−	2.37361i	−0.611552	−	0.791204i
$10$		0			0
$11$	−5.35589	+	1.43511i	−1.61486	+	0.432701i	−0.949487	−	0.313807i	$-0.898395\pi$
$11$	−5.35589	+	1.43511i	−1.61486	+	0.432701i	−0.665376	+	0.746508i	$0.731729\pi$
$12$		0			0
$13$	−1.41280	+	3.31723i	−0.391840	+	0.920033i
$13$	−1.41280	+	3.31723i	−0.391840	+	0.920033i
$14$		0			0
$15$	−0.462449	+	0.529200i	−0.119404	+	0.136639i
$16$		0			0
$17$	−2.10279			−0.510001			−0.255001	−	0.966941i	$-0.582076\pi$
$17$	−2.10279			−0.510001			−0.255001	+	0.966941i	$0.582076\pi$
$18$		0			0
$19$	−2.08178	−	2.08178i	−0.477593	−	0.477593i	0.426768	−	0.904361i	$-0.359652\pi$
$19$	−2.08178	−	2.08178i	−0.477593	−	0.477593i	−0.904361	+	0.426768i	$0.859652\pi$
$20$		0			0
$21$	7.53713	+	1.48543i	1.64474	+	0.324148i
$22$		0			0
$23$	−1.61975	−	2.80548i	−0.337740	−	0.584983i	0.646267	−	0.763111i	$-0.276329\pi$
$23$	−1.61975	−	2.80548i	−0.337740	−	0.584983i	−0.984007	+	0.178128i	$0.942996\pi$
$24$		0			0
$25$	−4.18755	−	2.41768i	−0.837509	−	0.483536i
$26$		0			0
$27$	5.09088	−	1.04063i	0.979741	−	0.200270i
$28$		0			0
$29$	1.51221	+	0.873077i	0.280811	+	0.162126i	0.633791	−	0.773505i	$-0.281498\pi$
$29$	1.51221	+	0.873077i	0.280811	+	0.162126i	−0.352980	+	0.935631i	$0.614831\pi$
$30$		0			0
$31$	1.59885	−	5.96700i	0.287162	−	1.07170i	−0.660083	−	0.751193i	$-0.729479\pi$
$31$	1.59885	−	5.96700i	0.287162	−	1.07170i	0.947245	−	0.320511i	$-0.103855\pi$
$32$		0			0
$33$	1.85704	−	9.42267i	0.323269	−	1.64028i
$34$		0			0
$35$		−	1.79963i		−	0.304193i
$36$		0			0
$37$	0.419848	−	0.419848i	0.0690225	−	0.0690225i	−0.671753	−	0.740775i	$-0.734458\pi$
$37$	0.419848	−	0.419848i	0.0690225	−	0.0690225i	0.740775	+	0.671753i	$0.234458\pi$
$38$		0			0
$39$	−4.07911	−	4.72872i	−0.653181	−	0.757202i
$40$		0			0
$41$	7.47510	+	2.00295i	1.16741	+	0.312808i	0.789924	−	0.613205i	$-0.210120\pi$
$41$	7.47510	+	2.00295i	1.16741	+	0.312808i	0.377491	+	0.926013i	$0.376787\pi$
$42$		0			0
$43$	−5.17242	−	2.98630i	−0.788786	−	0.455406i	0.0507489	−	0.998711i	$-0.483839\pi$
$43$	−5.17242	−	2.98630i	−0.788786	−	0.455406i	−0.839535	+	0.543306i	$0.817173\pi$
$44$		0			0
$45$	−0.469786	−	1.12296i	−0.0700315	−	0.167401i
$46$		0			0
$47$	1.59728	−	0.427989i	0.232987	−	0.0624286i	−0.140437	−	0.990090i	$-0.544851\pi$
$47$	1.59728	−	0.427989i	0.232987	−	0.0624286i	0.373423	+	0.927661i	$0.378184\pi$
$48$		0			0
$49$	−10.9739	+	6.33580i	−1.56770	+	0.905114i
$50$		0			0
$51$	1.60512	−	3.26937i	0.224762	−	0.457803i
$52$		0			0
$53$			10.2290i			1.40507i	0.711651	+	0.702533i	$0.247948\pi$
$53$			10.2290i			1.40507i	−0.711651	+	0.702533i	$0.752052\pi$
$54$		0			0
$55$	−2.24984			−0.303369
$56$		0			0
$57$	4.82579	−	1.64762i	0.639191	−	0.218232i
$58$		0			0
$59$	−3.92005	+	14.6298i	−0.510347	+	1.90464i	−0.0936260	+	0.995607i	$0.529846\pi$
$59$	−3.92005	+	14.6298i	−0.510347	+	1.90464i	−0.416721	+	0.909034i	$0.636821\pi$
$60$		0			0
$61$	0.552523	−	0.956999i	0.0707434	−	0.122531i	−0.828484	−	0.560013i	$-0.810796\pi$
$61$	0.552523	−	0.956999i	0.0707434	−	0.122531i	0.899227	+	0.437482i	$0.144130\pi$
$62$		0			0
$63$	−8.06282	+	10.5847i	−1.01582	+	1.33354i
$64$		0			0
$65$	−0.902083	+	1.15175i	−0.111890	+	0.142857i
$66$		0			0
$67$	1.45577	−	5.43302i	0.177851	−	0.663749i	−0.818197	−	0.574937i	$-0.805026\pi$
$67$	1.45577	−	5.43302i	0.177851	−	0.663749i	0.996048	−	0.0888117i	$-0.0283070\pi$
$68$		0			0
$69$	5.59829	−	0.376835i	0.673955	−	0.0453656i
$70$		0			0
$71$	−0.450191	+	0.450191i	−0.0534279	+	0.0534279i	−0.733316	−	0.679888i	$-0.762028\pi$
$71$	−0.450191	+	0.450191i	−0.0534279	+	0.0534279i	0.679888	+	0.733316i	$0.262028\pi$
$72$		0			0
$73$	4.21227	−	4.21227i	0.493009	−	0.493009i	−0.416244	−	0.909253i	$-0.636654\pi$
$73$	4.21227	−	4.21227i	0.493009	−	0.493009i	0.909253	+	0.416244i	$0.136654\pi$
$74$		0			0
$75$	6.95543	−	4.66521i	0.803144	−	0.538692i
$76$		0			0
$77$	12.2964	+	21.2980i	1.40130	+	2.42713i
$78$		0			0
$79$	−2.65252	+	4.59429i	−0.298431	+	0.516898i	−0.975777	−	0.218766i	$-0.929797\pi$
$79$	−2.65252	+	4.59429i	−0.298431	+	0.516898i	0.677346	+	0.735665i	$0.263130\pi$
$80$		0			0
$81$	−2.26807	+	8.70953i	−0.252008	+	0.967725i
$82$		0			0
$83$	−2.68228	−	10.0104i	−0.294418	−	1.09878i	−0.941678	−	0.336514i	$-0.890752\pi$
$83$	−2.68228	−	10.0104i	−0.294418	−	1.09878i	0.647260	−	0.762269i	$-0.275915\pi$
$84$		0			0
$85$	−0.824145	−	0.220829i	−0.0893911	−	0.0239523i
$86$		0			0
$87$	−2.51176	+	1.68471i	−0.269289	+	0.180620i
$88$		0			0
$89$	−9.01543	−	9.01543i	−0.955634	−	0.955634i	0.0434230	−	0.999057i	$-0.486174\pi$
$89$	−9.01543	−	9.01543i	−0.955634	−	0.955634i	−0.999057	+	0.0434230i	$0.986174\pi$
$90$		0			0
$91$	15.8333	+	2.24468i	1.65978	+	0.235306i
$92$		0			0
$93$	8.05689	+	7.04064i	0.835461	+	0.730080i
$94$		0			0
$95$	−0.597288	−	1.03453i	−0.0612805	−	0.106141i
$96$		0			0
$97$	10.3378	−	2.77000i	1.04964	−	0.281251i	0.307538	−	0.951536i	$-0.400495\pi$
$97$	10.3378	−	2.77000i	1.04964	−	0.281251i	0.742104	+	0.670285i	$0.233828\pi$
$98$		0			0
$99$	13.2326	+	10.0799i	1.32993	+	1.01307i
$100$		0			0
$101$	−2.67367	+	4.63093i	−0.266040	+	0.460794i	−0.967836	−	0.251584i	$-0.919049\pi$
$101$	−2.67367	+	4.63093i	−0.266040	+	0.460794i	0.701796	+	0.712378i	$0.252382\pi$
$102$		0			0
$103$	−10.4205	+	6.01629i	−1.02676	+	0.592803i	−0.916056	−	0.401050i	$-0.868645\pi$
$103$	−10.4205	+	6.01629i	−1.02676	+	0.592803i	−0.110708	+	0.993853i	$0.535312\pi$
$104$		0			0
$105$	2.79802	+	1.37371i	0.273059	+	0.134061i
$106$		0			0
$107$		−	8.36405i		−	0.808583i	−0.914630	−	0.404292i	$-0.867518\pi$
$107$		−	8.36405i		−	0.808583i	0.914630	−	0.404292i	$-0.132482\pi$
$108$		0			0
$109$	−11.2997	−	11.2997i	−1.08231	−	1.08231i	−0.996294	−	0.0860169i	$-0.972586\pi$
$109$	−11.2997	−	11.2997i	−1.08231	−	1.08231i	−0.0860169	−	0.996294i	$-0.527414\pi$
$110$		0			0
$111$	0.332287	+	0.973251i	0.0315393	+	0.0923769i
$112$		0			0
$113$	−8.32100	+	4.80413i	−0.782774	+	0.451935i	−0.837412	−	0.546571i	$-0.815933\pi$
$113$	−8.32100	+	4.80413i	−0.782774	+	0.451935i	0.0546385	+	0.998506i	$0.482599\pi$
$114$		0			0
$115$	−0.340202	−	1.26965i	−0.0317240	−	0.118396i
$116$		0			0
$117$	10.4658	−	2.73254i	0.967565	−	0.252623i
$118$		0			0
$119$	2.41386	+	9.00864i	0.221278	+	0.825821i
$120$		0			0
$121$	17.0998	−	9.87256i	1.55453	−	0.897506i
$122$		0			0
$123$	−8.82010	+	10.0932i	−0.795281	+	0.910073i
$124$		0			0
$125$	−2.82189	−	2.82189i	−0.252397	−	0.252397i
$126$		0			0
$127$			11.1563i			0.989959i	0.868905	+	0.494980i	$0.164825\pi$
$127$			11.1563i			0.989959i	−0.868905	+	0.494980i	$0.835175\pi$
$128$		0			0
$129$	8.59128	−	5.76242i	0.756420	−	0.507353i
$130$		0			0
$131$	−15.8493	+	9.15060i	−1.38476	+	0.799492i	−0.992719	−	0.120456i	$-0.961564\pi$
$131$	−15.8493	+	9.15060i	−1.38476	+	0.799492i	−0.392042	+	0.919947i	$0.628231\pi$
$132$		0			0
$133$	−6.52890	+	11.3084i	−0.566127	+	0.980561i
$134$		0			0
$135$	2.10455	+	0.126776i	0.181131	+	0.0109111i
$136$		0			0
$137$	17.7113	−	4.74572i	1.51318	−	0.405454i	0.595687	−	0.803217i	$-0.296880\pi$
$137$	17.7113	−	4.74572i	1.51318	−	0.405454i	0.917488	+	0.397763i	$0.130213\pi$
$138$		0			0
$139$	6.58884	+	11.4122i	0.558858	+	0.967971i	0.997592	+	0.0693537i	$0.0220937\pi$
$139$	6.58884	+	11.4122i	0.558858	+	0.967971i	−0.438734	+	0.898617i	$0.644573\pi$
$140$		0			0
$141$	−0.553821	+	2.81010i	−0.0466401	+	0.236653i
$142$		0			0
$143$	2.80622	−	19.7942i	0.234668	−	1.65528i
$144$		0			0
$145$	0.500993	+	0.500993i	0.0416052	+	0.0416052i
$146$		0			0
$147$	−1.47403	−	21.8983i	−0.121576	−	1.80614i
$148$		0			0
$149$	9.04349	+	2.42320i	0.740872	+	0.198516i	0.609466	−	0.792813i	$-0.291384\pi$
$149$	9.04349	+	2.42320i	0.740872	+	0.198516i	0.131406	+	0.991329i	$0.458051\pi$
$150$		0			0
$151$	−0.348550	−	1.30081i	−0.0283646	−	0.105858i	0.950292	−	0.311359i	$-0.100784\pi$
$151$	−0.348550	−	1.30081i	−0.0283646	−	0.105858i	−0.978657	+	0.205501i	$0.934118\pi$
$152$		0			0
$153$	3.85790	+	4.99121i	0.311892	+	0.403515i
$154$		0			0
$155$	1.25327	−	2.17073i	0.100665	−	0.174358i
$156$		0			0
$157$	−10.9253	−	18.9232i	−0.871936	−	1.51024i	−0.859991	−	0.510310i	$-0.829531\pi$
$157$	−10.9253	−	18.9232i	−0.871936	−	1.51024i	−0.0119456	−	0.999929i	$-0.503802\pi$
$158$		0			0
$159$	−15.9039	−	7.80813i	−1.26126	−	0.619225i
$160$		0			0
$161$	−10.1597	+	10.1597i	−0.800698	+	0.800698i
$162$		0			0
$163$	−2.48610	+	2.48610i	−0.194726	+	0.194726i	−0.797735	−	0.603009i	$-0.793968\pi$
$163$	−2.48610	+	2.48610i	−0.194726	+	0.194726i	0.603009	+	0.797735i	$0.293968\pi$
$164$		0			0
$165$	1.71737	−	3.49800i	0.133697	−	0.272319i
$166$		0			0
$167$	−0.659859	+	2.46263i	−0.0510615	+	0.190564i	−0.986746	−	0.162275i	$-0.948117\pi$
$167$	−0.659859	+	2.46263i	−0.0510615	+	0.190564i	0.935684	+	0.352839i	$0.114784\pi$
$168$		0			0
$169$	−9.00800	−	9.37315i	−0.692923	−	0.721012i
$170$		0			0
$171$	−1.12199	+	8.76070i	−0.0858006	+	0.669947i
$172$		0			0
$173$	12.2720	−	21.2556i	0.933019	−	1.61604i	0.154891	−	0.987932i	$-0.450497\pi$
$173$	12.2720	−	21.2556i	0.933019	−	1.61604i	0.778128	−	0.628105i	$-0.216169\pi$
$174$		0			0
$175$	−5.55067	+	20.7154i	−0.419591	+	1.56593i
$176$		0			0
$177$	−19.7538	−	17.2622i	−1.48479	−	1.29750i
$178$		0			0
$179$	9.78923			0.731681			0.365841	−	0.930677i	$-0.380781\pi$
$179$	9.78923			0.731681			0.365841	+	0.930677i	$0.380781\pi$
$180$		0			0
$181$			7.06580i			0.525197i	0.964905	+	0.262598i	$0.0845795\pi$
$181$			7.06580i			0.525197i	−0.964905	+	0.262598i	$0.915421\pi$
$182$		0			0
$183$	1.06616	+	1.58956i	0.0788129	+	0.117503i
$184$		0			0
$185$	0.208642	−	0.120459i	0.0153397	−	0.00885635i
$186$		0			0
$187$	11.2623	−	3.01773i	0.823582	−	0.220678i
$188$		0			0
$189$	−10.3022	−	20.6155i	−0.749375	−	1.49956i
$190$		0			0
$191$	19.7368	+	11.3950i	1.42810	+	0.824515i	0.996971	−	0.0777744i	$-0.0247814\pi$
$191$	19.7368	+	11.3950i	1.42810	+	0.824515i	0.431131	+	0.902289i	$0.358115\pi$
$192$		0			0
$193$	12.7404	+	3.41378i	0.917073	+	0.245729i	0.686334	−	0.727287i	$-0.259219\pi$
$193$	12.7404	+	3.41378i	0.917073	+	0.245729i	0.230739	+	0.973016i	$0.425886\pi$
$194$		0			0
$195$	−1.10213	−	2.28170i	−0.0789250	−	0.163396i
$196$		0			0
$197$	−14.5291	+	14.5291i	−1.03515	+	1.03515i	−0.0357936	+	0.999359i	$0.511396\pi$
$197$	−14.5291	+	14.5291i	−1.03515	+	1.03515i	−0.999359	+	0.0357936i	$0.988604\pi$
$198$		0			0
$199$		−	9.73887i		−	0.690370i	−0.938535	−	0.345185i	$-0.887816\pi$
$199$		−	9.73887i		−	0.690370i	0.938535	−	0.345185i	$-0.112184\pi$
$200$		0			0
$201$	7.33590	+	6.41059i	0.517434	+	0.452168i
$202$		0			0
$203$	2.00447	−	7.48077i	0.140686	−	0.525047i
$204$		0			0
$205$	2.71937	+	1.57003i	0.189929	+	0.109655i
$206$		0			0
$207$	−3.68745	+	8.99174i	−0.256295	+	0.624969i
$208$		0			0
$209$	14.1374	+	8.16222i	0.977903	+	0.564593i
$210$		0			0
$211$	−3.17035	−	5.49121i	−0.218256	−	0.378031i	0.736019	−	0.676961i	$-0.236703\pi$
$211$	−3.17035	−	5.49121i	−0.218256	−	0.378031i	−0.954275	+	0.298930i	$0.903370\pi$
$212$		0			0
$213$	−0.356302	−	1.04359i	−0.0244134	−	0.0715056i
$214$		0			0
$215$	−1.71361	−	1.71361i	−0.116867	−	0.116867i
$216$		0			0
$217$	−27.3988			−1.85995
$218$		0			0
$219$	3.33379	+	9.76449i	0.225277	+	0.659823i
$220$		0			0
$221$	2.97082	−	6.97543i	0.199839	−	0.469218i
$222$		0			0
$223$	13.5444	−	3.62920i	0.906999	−	0.243030i	0.224979	−	0.974364i	$-0.427769\pi$
$223$	13.5444	−	3.62920i	0.906999	−	0.243030i	0.682019	+	0.731334i	$0.261102\pi$
$224$		0			0
$225$	1.94407	+	14.3752i	0.129605	+	0.958349i
$226$		0			0
$227$	−7.04300	−	26.2848i	−0.467460	−	1.74458i	−0.648602	−	0.761128i	$-0.724646\pi$
$227$	−7.04300	−	26.2848i	−0.467460	−	1.74458i	0.181142	−	0.983457i	$-0.442021\pi$
$228$		0			0
$229$	−2.19791	−	0.588928i	−0.145242	−	0.0389174i	0.185466	−	0.982651i	$-0.440621\pi$
$229$	−2.19791	−	0.588928i	−0.145242	−	0.0389174i	−0.330707	+	0.943733i	$0.607287\pi$
$230$		0			0
$231$	−42.4998	+	2.86077i	−2.79628	+	0.188225i
$232$		0			0
$233$	−18.9902			−1.24409			−0.622045	−	0.782981i	$-0.713698\pi$
$233$	−18.9902			−1.24409			−0.622045	+	0.782981i	$0.713698\pi$
$234$		0			0
$235$	0.670965			0.0437689
$236$		0			0
$237$	−5.11835	−	7.63103i	−0.332473	−	0.495688i
$238$		0			0
$239$	−6.68343	−	1.79082i	−0.432315	−	0.115839i	0.0360975	−	0.999348i	$-0.488507\pi$
$239$	−6.68343	−	1.79082i	−0.432315	−	0.115839i	−0.468413	+	0.883510i	$0.655174\pi$
$240$		0			0
$241$	2.73843	+	10.2200i	0.176398	+	0.658327i	0.996309	+	0.0858359i	$0.0273561\pi$
$241$	2.73843	+	10.2200i	0.176398	+	0.658327i	−0.819911	+	0.572491i	$0.805977\pi$
$242$		0			0
$243$	−11.8101	−	10.1746i	−0.757617	−	0.652700i
$244$		0			0
$245$	−4.96637	+	1.33073i	−0.317290	+	0.0850175i
$246$		0			0
$247$	9.84688	−	3.96460i	0.626542	−	0.252262i
$248$		0			0
$249$	17.6114	+	3.47089i	1.11608	+	0.219959i
$250$		0			0
$251$	−15.2350			−0.961622			−0.480811	−	0.876824i	$-0.659658\pi$
$251$	−15.2350			−0.961622			−0.480811	+	0.876824i	$0.659658\pi$
$252$		0			0
$253$	12.7013	+	12.7013i	0.798527	+	0.798527i
$254$		0			0
$255$	0.972433	−	1.11280i	0.0608961	−	0.0696859i
$256$		0			0
$257$	−7.45431	−	12.9112i	−0.464987	−	0.805381i	0.534214	−	0.845349i	$-0.320608\pi$
$257$	−7.45431	−	12.9112i	−0.464987	−	0.805381i	−0.999201	+	0.0399681i	$0.987274\pi$
$258$		0			0
$259$	−2.28064	−	1.31673i	−0.141712	−	0.0818176i
$260$		0			0
$261$	−0.702047	−	5.19120i	−0.0434556	−	0.321328i
$262$		0			0
$263$	−21.1298	−	12.1993i	−1.30292	−	0.752242i	−0.322017	−	0.946734i	$-0.604361\pi$
$263$	−21.1298	−	12.1993i	−1.30292	−	0.752242i	−0.980904	+	0.194492i	$0.937694\pi$
$264$		0			0
$265$	−1.07422	+	4.00906i	−0.0659891	+	0.246275i
$266$		0			0
$267$	20.8987	−	7.13523i	1.27898	−	0.436669i
$268$		0			0
$269$			1.89602i			0.115603i	0.998328	+	0.0578013i	$0.0184090\pi$
$269$			1.89602i			0.115603i	−0.998328	+	0.0578013i	$0.981591\pi$
$270$		0			0
$271$	−7.94297	+	7.94297i	−0.482501	+	0.482501i	−0.905930	−	0.423429i	$-0.860826\pi$
$271$	−7.94297	+	7.94297i	−0.482501	+	0.482501i	0.423429	+	0.905930i	$0.360826\pi$
$272$		0			0
$273$	−15.5760	+	22.9037i	−0.942700	+	1.38620i
$274$		0			0
$275$	25.8977	+	6.93926i	1.56169	+	0.418453i
$276$		0			0
$277$	−2.46433	−	1.42278i	−0.148068	−	0.0854868i	0.424136	−	0.905599i	$-0.360578\pi$
$277$	−2.46433	−	1.42278i	−0.148068	−	0.0854868i	−0.572203	+	0.820112i	$0.693911\pi$
$278$		0			0
$279$	−17.0967	+	7.15233i	−1.02355	+	0.428199i
$280$		0			0
$281$	−6.20037	+	1.66138i	−0.369883	+	0.0991098i	−0.438972	−	0.898501i	$-0.644657\pi$
$281$	−6.20037	+	1.66138i	−0.369883	+	0.0991098i	0.0690892	+	0.997610i	$0.477991\pi$
$282$		0			0
$283$	17.4050	−	10.0488i	1.03462	−	0.597337i	0.116314	−	0.993213i	$-0.462892\pi$
$283$	17.4050	−	10.0488i	1.03462	−	0.597337i	0.918304	+	0.395876i	$0.129559\pi$
$284$		0			0
$285$	2.06440	−	0.138960i	0.122284	−	0.00823126i
$286$		0			0
$287$		−	34.3236i		−	2.02606i
$288$		0			0
$289$	−12.5783			−0.739899
$290$		0			0
$291$	−3.58440	+	18.1873i	−0.210121	+	1.06616i
$292$		0			0
$293$	7.00311	−	26.1360i	0.409126	−	1.52688i	−0.387190	−	0.922000i	$-0.626554\pi$
$293$	7.00311	−	26.1360i	0.409126	−	1.52688i	0.796317	−	0.604880i	$-0.206779\pi$
$294$		0			0
$295$	−3.07277	+	5.32219i	−0.178903	+	0.309870i
$296$		0			0
$297$	−25.7728	+	12.8795i	−1.49549	+	0.747343i
$298$		0			0
$299$	11.5948	−	1.40948i	0.670544	−	0.0815125i
$300$		0			0
$301$	−6.85613	+	25.5874i	−0.395181	+	1.47483i
$302$		0			0
$303$	−5.15916	−	7.69187i	−0.296386	−	0.441887i
$304$		0			0
$305$	0.317051	−	0.317051i	0.0181543	−	0.0181543i
$306$		0			0
$307$	23.6643	−	23.6643i	1.35059	−	1.35059i	0.465594	−	0.884998i	$-0.345841\pi$
$307$	23.6643	−	23.6643i	1.35059	−	1.35059i	0.884998	−	0.465594i	$-0.154159\pi$
$308$		0			0
$309$	−1.39969	−	20.7940i	−0.0796258	−	1.18293i
$310$		0			0
$311$	−4.82212	−	8.35216i	−0.273437	−	0.473607i	0.696302	−	0.717749i	$-0.254827\pi$
$311$	−4.82212	−	8.35216i	−0.273437	−	0.473607i	−0.969740	+	0.244141i	$0.921494\pi$
$312$		0			0
$313$	−8.33294	+	14.4331i	−0.471006	+	0.815806i	−0.999450	−	0.0331624i	$-0.989442\pi$
$313$	−8.33294	+	14.4331i	−0.471006	+	0.815806i	0.528444	+	0.848968i	$0.322775\pi$
$314$		0			0
$315$	−4.27163	+	3.30171i	−0.240679	+	0.186030i
$316$		0			0
$317$	−4.59720	−	17.1570i	−0.258204	−	0.963632i	−0.966280	−	0.257495i	$-0.917103\pi$
$317$	−4.59720	−	17.1570i	−0.258204	−	0.963632i	0.708075	−	0.706137i	$-0.249564\pi$
$318$		0			0
$319$	−9.35221	−	2.50592i	−0.523623	−	0.140304i
$320$		0			0
$321$	13.0042	+	6.38453i	0.725825	+	0.356349i
$322$		0			0
$323$	4.37755	+	4.37755i	0.243573	+	0.243573i
$324$		0			0
$325$	13.9362	−	10.4753i	0.773039	−	0.581068i
$326$		0			0
$327$	26.1938	−	8.94307i	1.44852	−	0.494553i
$328$		0			0
$329$	−3.66713	−	6.35165i	−0.202175	−	0.350178i
$330$		0			0
$331$	23.1595	−	6.20558i	1.27296	−	0.341089i	0.441797	−	0.897115i	$-0.354341\pi$
$331$	23.1595	−	6.20558i	1.27296	−	0.341089i	0.831165	+	0.556025i	$0.187674\pi$
$332$		0			0
$333$	−1.76683	−	0.226279i	−0.0968218	−	0.0124000i
$334$		0			0
$335$	1.14112	−	1.97648i	0.0623461	−	0.107987i
$336$		0			0
$337$	24.5119	−	14.1519i	1.33525	−	0.770904i	0.349147	−	0.937068i	$-0.386471\pi$
$337$	24.5119	−	14.1519i	1.33525	−	0.770904i	0.986098	+	0.166163i	$0.0531379\pi$
$338$		0			0
$339$	−1.11768	−	16.6044i	−0.0607043	−	0.901829i
$340$		0			0
$341$			34.2531i			1.85491i
$342$		0			0
$343$	17.7873	+	17.7873i	0.960424	+	0.960424i
$344$		0			0
$345$	2.23371	+	0.440224i	0.120259	+	0.0237009i
$346$		0			0
$347$	8.97732	−	5.18306i	0.481928	−	0.278241i	−0.239292	−	0.970948i	$-0.576915\pi$
$347$	8.97732	−	5.18306i	0.481928	−	0.278241i	0.721220	+	0.692707i	$0.243582\pi$
$348$		0			0
$349$	3.51515	+	13.1187i	0.188162	+	0.702230i	0.993932	+	0.110001i	$0.0350853\pi$
$349$	3.51515	+	13.1187i	0.188162	+	0.702230i	−0.805770	+	0.592229i	$0.798248\pi$
$350$		0			0
$351$	−3.74038	+	18.3578i	−0.199647	+	0.979868i
$352$		0			0
$353$	−3.05941	−	11.4179i	−0.162836	−	0.607712i	−0.998306	−	0.0581765i	$-0.981471\pi$
$353$	−3.05941	−	11.4179i	−0.162836	−	0.607712i	0.835470	−	0.549536i	$-0.185195\pi$
$354$		0			0
$355$	−0.223721	+	0.129165i	−0.0118739	+	0.00685538i
$356$		0			0
$357$	−15.8490	−	3.12355i	−0.838818	−	0.165316i
$358$		0			0
$359$	−1.42804	−	1.42804i	−0.0753689	−	0.0753689i	0.668417	−	0.743786i	$-0.266972\pi$
$359$	−1.42804	−	1.42804i	−0.0753689	−	0.0753689i	−0.743786	+	0.668417i	$0.766972\pi$
$360$		0			0
$361$		−	10.3324i		−	0.543809i
$362$		0			0
$363$	2.29686	+	34.1224i	0.120554	+	1.79096i
$364$		0			0
$365$	2.09327	−	1.20855i	0.109567	−	0.0632585i
$366$		0			0
$367$	−4.24794	+	7.35764i	−0.221740	+	0.384066i	−0.955337	−	0.295520i	$-0.904507\pi$
$367$	−4.24794	+	7.35764i	−0.221740	+	0.384066i	0.733596	+	0.679586i	$0.237840\pi$
$368$		0			0
$369$	−8.96002	−	21.4177i	−0.466440	−	1.11496i
$370$		0			0
$371$	43.8226	−	11.7422i	2.27516	−	0.609627i
$372$		0			0
$373$	−14.9146	−	25.8329i	−0.772251	−	1.33758i	−0.936327	−	0.351130i	$-0.885797\pi$
$373$	−14.9146	−	25.8329i	−0.772251	−	1.33758i	0.164075	−	0.986448i	$-0.447536\pi$
$374$		0			0
$375$	6.54143	−	2.23337i	0.337798	−	0.115331i
$376$		0			0
$377$	−5.03265	+	3.78287i	−0.259195	+	0.194828i
$378$		0			0
$379$	11.6310	+	11.6310i	0.597444	+	0.597444i	0.939632	−	0.342188i	$-0.111168\pi$
$379$	11.6310	+	11.6310i	0.597444	+	0.597444i	−0.342188	+	0.939632i	$0.611168\pi$
$380$		0			0
$381$	−17.3455	−	8.51591i	−0.888637	−	0.436283i
$382$		0			0
$383$	−13.1603	−	3.52629i	−0.672460	−	0.180185i	−0.0935975	−	0.995610i	$-0.529837\pi$
$383$	−13.1603	−	3.52629i	−0.672460	−	0.180185i	−0.578863	+	0.815425i	$0.696503\pi$
$384$		0			0
$385$	2.58267	+	9.63864i	0.131625	+	0.491230i
$386$		0			0
$387$	2.40130	+	17.7561i	0.122065	+	0.902595i
$388$		0			0
$389$	−10.7454	+	18.6115i	−0.544812	+	0.943642i	0.453807	+	0.891100i	$0.350066\pi$
$389$	−10.7454	+	18.6115i	−0.544812	+	0.943642i	−0.998619	+	0.0525417i	$0.983268\pi$
$390$		0			0
$391$	3.40598	+	5.89934i	0.172248	+	0.298342i
$392$		0			0
$393$	−2.12889	−	31.6270i	−0.107389	−	1.59537i
$394$		0			0
$395$	−1.52208	+	1.52208i	−0.0765841	+	0.0765841i
$396$		0			0
$397$	−15.2775	+	15.2775i	−0.766756	+	0.766756i	−0.977534	−	0.210778i	$-0.932400\pi$
$397$	−15.2775	+	15.2775i	−0.766756	+	0.766756i	0.210778	+	0.977534i	$0.432400\pi$
$398$		0			0
$399$	−12.5983	−	18.7830i	−0.630704	−	0.940326i
$400$		0			0
$401$	−3.94101	+	14.7080i	−0.196804	+	0.734484i	0.794988	+	0.606625i	$0.207477\pi$
$401$	−3.94101	+	14.7080i	−0.196804	+	0.734484i	−0.991792	+	0.127859i	$0.959190\pi$
$402$		0			0
$403$	17.5350	+	13.7339i	0.873482	+	0.684135i
$404$		0			0
$405$	−1.80357	+	3.17533i	−0.0896203	+	0.157784i
$406$		0			0
$407$	−1.64613	+	2.85119i	−0.0815958	+	0.141328i
$408$		0			0
$409$	3.22377	−	12.0313i	0.159405	−	0.594908i	−0.839283	−	0.543695i	$-0.817025\pi$
$409$	3.22377	−	12.0313i	0.159405	−	0.594908i	0.998688	−	0.0512125i	$-0.0163086\pi$
$410$		0			0
$411$	−6.14100	+	31.1596i	−0.302913	+	1.53699i
$412$		0			0
$413$	67.1762			3.30552
$414$		0			0
$415$		−	4.20505i		−	0.206418i
$416$		0			0
$417$	−22.7729	+	1.53290i	−1.11519	+	0.0750664i
$418$		0			0
$419$	−19.9329	+	11.5083i	−0.973785	+	0.562215i	−0.900388	−	0.435088i	$-0.856717\pi$
$419$	−19.9329	+	11.5083i	−0.973785	+	0.562215i	−0.0733971	+	0.997303i	$0.523384\pi$
$420$		0			0
$421$	−21.6709	+	5.80671i	−1.05618	+	0.283002i	−0.744802	−	0.667286i	$-0.767456\pi$
$421$	−21.6709	+	5.80671i	−1.05618	+	0.283002i	−0.311375	+	0.950287i	$0.600789\pi$
$422$		0			0
$423$	−3.94633	−	3.00610i	−0.191877	−	0.146162i
$424$		0			0
$425$	8.80553	+	5.08388i	0.427131	+	0.246604i
$426$		0			0
$427$	−4.73417	−	1.26852i	−0.229103	−	0.0613879i
$428$		0			0
$429$	28.6335	+	19.4726i	1.38244	+	0.940145i
$430$		0			0
$431$	−14.1858	+	14.1858i	−0.683306	+	0.683306i	−0.960744	−	0.277438i	$-0.910515\pi$
$431$	−14.1858	+	14.1858i	−0.683306	+	0.683306i	0.277438	+	0.960744i	$0.410515\pi$
$432$		0			0
$433$			17.5195i			0.841934i	0.907076	+	0.420967i	$0.138309\pi$
$433$			17.5195i			0.841934i	−0.907076	+	0.420967i	$0.861691\pi$
$434$		0			0
$435$	−1.16135	+	0.396509i	−0.0556827	+	0.0190112i
$436$		0			0
$437$	−2.46844	+	9.21235i	−0.118082	+	0.440687i
$438$		0			0
$439$	27.4263	+	15.8346i	1.30899	+	0.755743i	0.981927	−	0.189261i	$-0.0606093\pi$
$439$	27.4263	+	15.8346i	1.30899	+	0.755743i	0.327058	+	0.945004i	$0.393943\pi$
$440$		0			0
$441$	35.1721	+	14.4238i	1.67486	+	0.686849i
$442$		0			0
$443$	24.1512	+	13.9437i	1.14746	+	0.662486i	0.948267	−	0.317475i	$-0.102835\pi$
$443$	24.1512	+	13.9437i	1.14746	+	0.662486i	0.199192	+	0.979960i	$0.436168\pi$
$444$		0			0
$445$	−2.58664	−	4.48019i	−0.122618	−	0.212381i
$446$		0			0
$447$	−10.6707	+	12.2109i	−0.504706	+	0.577556i
$448$		0			0
$449$	−3.58832	−	3.58832i	−0.169343	−	0.169343i	0.617347	−	0.786691i	$-0.288207\pi$
$449$	−3.58832	−	3.58832i	−0.169343	−	0.169343i	−0.786691	+	0.617347i	$0.788207\pi$
$450$		0			0
$451$	−42.9103			−2.02057
$452$		0			0
$453$	2.28852	+	0.451027i	0.107524	+	0.0211911i
$454$		0			0
$455$	5.96979	+	2.54252i	0.279868	+	0.119195i
$456$		0			0
$457$	1.29241	−	0.346300i	0.0604563	−	0.0161992i	−0.228464	−	0.973552i	$-0.573370\pi$
$457$	1.29241	−	0.346300i	0.0604563	−	0.0161992i	0.288920	+	0.957353i	$0.406704\pi$
$458$		0			0
$459$	−10.7051	+	2.18823i	−0.499669	+	0.102138i
$460$		0			0
$461$	−4.61145	−	17.2102i	−0.214777	−	0.801557i	−0.986245	−	0.165290i	$-0.947144\pi$
$461$	−4.61145	−	17.2102i	−0.214777	−	0.801557i	0.771468	−	0.636268i	$-0.219523\pi$
$462$		0			0
$463$	16.1139	+	4.31772i	0.748879	+	0.200661i	0.613021	−	0.790067i	$-0.289954\pi$
$463$	16.1139	+	4.31772i	0.748879	+	0.200661i	0.135858	+	0.990728i	$0.456621\pi$
$464$		0			0
$465$	2.41834	+	3.60554i	0.112148	+	0.167203i
$466$		0			0
$467$	−33.3328			−1.54246			−0.771230	−	0.636556i	$-0.780358\pi$
$467$	−33.3328			−1.54246			−0.771230	+	0.636556i	$0.780358\pi$
$468$		0			0
$469$	−24.9469			−1.15194
$470$		0			0
$471$	37.7610	−	2.54179i	1.73994	−	0.117119i
$472$		0			0
$473$	31.9886	+	8.57131i	1.47084	+	0.394109i
$474$		0			0
$475$	3.68447	+	13.7506i	0.169055	+	0.630923i
$476$		0			0
$477$	24.2798	−	18.7668i	1.11169	−	0.859271i
$478$		0			0
$479$	−22.8819	+	6.13117i	−1.04550	+	0.280141i	−0.740390	−	0.672177i	$-0.765359\pi$
$479$	−22.8819	+	6.13117i	−1.04550	+	0.280141i	−0.305108	+	0.952318i	$0.598693\pi$
$480$		0			0
$481$	0.799570	+	1.98589i	0.0364572	+	0.0905488i
$482$		0			0
$483$	−8.04087	−	23.5513i	−0.365872	−	1.07162i
$484$		0			0
$485$	4.34257			0.197186
$486$		0			0
$487$	18.2840	+	18.2840i	0.828525	+	0.828525i	0.987313	−	0.158788i	$-0.0507586\pi$
$487$	18.2840	+	18.2840i	0.828525	+	0.828525i	−0.158788	+	0.987313i	$0.550759\pi$
$488$		0			0
$489$	−1.96761	−	5.76303i	−0.0889785	−	0.260613i
$490$		0			0
$491$	−7.54168	−	13.0626i	−0.340351	−	0.589506i	0.644147	−	0.764902i	$-0.277213\pi$
$491$	−7.54168	−	13.0626i	−0.340351	−	0.589506i	−0.984498	+	0.175396i	$0.943879\pi$
$492$		0			0
$493$	−3.17987	−	1.83590i	−0.143214	−	0.0826846i
$494$		0			0
$495$	4.12769	+	5.34025i	0.185526	+	0.240027i
$496$		0			0
$497$	2.44547	+	1.41189i	0.109694	+	0.0633320i
$498$		0			0
$499$	−7.64139	+	28.5180i	−0.342076	+	1.27664i	0.553916	+	0.832572i	$0.313133\pi$
$499$	−7.64139	+	28.5180i	−0.342076	+	1.27664i	−0.895992	+	0.444071i	$0.853534\pi$
$500$		0			0
$501$	−3.32515	−	2.90573i	−0.148557	−	0.129818i
$502$		0			0
$503$		−	0.405291i		−	0.0180710i	−0.999959	−	0.00903551i	$-0.997124\pi$
$503$		−	0.405291i		−	0.0180710i	0.999959	−	0.00903551i	$-0.00287613\pi$
$504$		0			0
$505$	−1.53421	+	1.53421i	−0.0682717	+	0.0682717i
$506$		0			0
$507$	21.4492	−	6.85061i	0.952593	−	0.304246i
$508$		0			0
$509$	5.44273	+	1.45837i	0.241245	+	0.0646413i	0.377415	−	0.926044i	$-0.376813\pi$
$509$	5.44273	+	1.45837i	0.241245	+	0.0646413i	−0.136171	+	0.990685i	$0.543480\pi$
$510$		0			0
$511$	−22.8814	−	13.2106i	−1.01221	−	0.584401i
$512$		0			0
$513$	−12.7645	−	8.43174i	−0.563565	−	0.372270i
$514$		0			0
$515$	−4.71592	+	1.26363i	−0.207808	+	0.0556821i
$516$		0			0
$517$	−7.94063	+	4.58452i	−0.349228	+	0.201627i
$518$		0			0
$519$	23.6802	+	35.3052i	1.03945	+	1.54973i
$520$		0			0
$521$		−	6.28532i		−	0.275365i	−0.990476	−	0.137682i	$-0.956035\pi$
$521$		−	6.28532i		−	0.275365i	0.990476	−	0.137682i	$-0.0439654\pi$
$522$		0			0
$523$	1.24475			0.0544292			0.0272146	−	0.999630i	$-0.491336\pi$
$523$	1.24475			0.0544292			0.0272146	+	0.999630i	$0.491336\pi$
$524$		0			0
$525$	−27.9708	−	24.4427i	−1.22074	−	1.06677i
$526$		0			0
$527$	−3.36205	+	12.5473i	−0.146453	+	0.546571i
$528$		0			0
$529$	6.25285	−	10.8303i	0.271863	−	0.470881i
$530$		0			0
$531$	41.9175	−	17.5360i	1.81906	−	0.760999i
$532$		0			0
$533$	−17.2050	+	21.9668i	−0.745233	+	0.951490i
$534$		0			0
$535$	0.878369	−	3.27812i	0.0379752	−	0.141725i
$536$		0			0
$537$	−7.47241	+	15.2201i	−0.322458	+	0.656794i
$538$		0			0
$539$	49.6826	−	49.6826i	2.13998	−	2.13998i
$540$		0			0
$541$	8.55853	−	8.55853i	0.367960	−	0.367960i	−0.498773	−	0.866733i	$-0.666216\pi$
$541$	8.55853	−	8.55853i	0.367960	−	0.367960i	0.866733	+	0.498773i	$0.166216\pi$
$542$		0			0
$543$	−10.9857	−	5.39353i	−0.471443	−	0.231459i
$544$		0			0
$545$	−3.24201	−	5.61532i	−0.138872	−	0.240534i
$546$		0			0
$547$	3.06558	−	5.30973i	0.131075	−	0.227028i	−0.793017	−	0.609200i	$-0.791491\pi$
$547$	3.06558	−	5.30973i	0.131075	−	0.227028i	0.924091	+	0.382172i	$0.124824\pi$
$548$		0			0
$549$	−3.28523	+	0.444287i	−0.140210	+	0.0189617i
$550$		0			0
$551$	−1.33054	−	4.96565i	−0.0566830	−	0.211544i
$552$		0			0
$553$	22.7275	+	6.08981i	0.966471	+	0.258965i
$554$		0			0
$555$	0.0280250	+	0.416341i	0.00118959	+	0.0176727i
$556$		0			0
$557$	6.11659	+	6.11659i	0.259168	+	0.259168i	0.824716	−	0.565547i	$-0.191335\pi$
$557$	6.11659	+	6.11659i	0.259168	+	0.259168i	−0.565547	+	0.824716i	$0.691335\pi$
$558$		0			0
$559$	17.2138	−	12.9390i	0.728067	−	0.547263i
$560$		0			0
$561$	−3.90497	+	19.8139i	−0.164868	+	0.836544i
$562$		0			0
$563$	1.44515	+	2.50307i	0.0609057	+	0.105492i	0.894870	−	0.446326i	$-0.147268\pi$
$563$	1.44515	+	2.50307i	0.0609057	+	0.105492i	−0.833965	+	0.551818i	$0.813934\pi$
$564$		0			0
$565$	−3.76576	+	1.00903i	−0.158427	+	0.0424503i
$566$		0			0
$567$	39.9164	−	0.281212i	1.67633	−	0.0118098i
$568$		0			0
$569$	−1.30194	+	2.25502i	−0.0545800	+	0.0945354i	−0.892025	−	0.451987i	$-0.850715\pi$
$569$	−1.30194	+	2.25502i	−0.0545800	+	0.0945354i	0.837444	+	0.546522i	$0.184049\pi$
$570$		0			0
$571$	16.5573	−	9.55937i	0.692902	−	0.400047i	−0.111796	−	0.993731i	$-0.535660\pi$
$571$	16.5573	−	9.55937i	0.692902	−	0.400047i	0.804698	+	0.593684i	$0.202327\pi$
$572$		0			0
$573$	−32.7824	+	21.9881i	−1.36950	+	0.918565i
$574$		0			0
$575$			15.6641i			0.653239i
$576$		0			0
$577$	−6.04143	−	6.04143i	−0.251508	−	0.251508i	0.570081	−	0.821589i	$-0.306912\pi$
$577$	−6.04143	−	6.04143i	−0.251508	−	0.251508i	−0.821589	+	0.570081i	$0.806912\pi$
$578$		0			0
$579$	−15.0328	+	17.2026i	−0.624741	+	0.714916i
$580$		0			0
$581$	−39.8069	+	22.9825i	−1.65147	+	0.953475i
$582$		0			0
$583$	−14.6798	−	54.7856i	−0.607974	−	2.26899i
$584$		0			0
$585$	4.38882	+	0.0281290i	0.181455	+	0.00116299i
$586$		0			0
$587$	−1.96452	−	7.33169i	−0.0810844	−	0.302611i	0.913460	−	0.406930i	$-0.133401\pi$
$587$	−1.96452	−	7.33169i	−0.0810844	−	0.302611i	−0.994544	+	0.104318i	$0.966734\pi$
$588$		0			0
$589$	−15.7504	+	9.09352i	−0.648986	+	0.374692i
$590$		0			0
$591$	−11.4990	−	33.6799i	−0.473005	−	1.38541i
$592$		0			0
$593$	−32.5715	−	32.5715i	−1.33755	−	1.33755i	−0.898424	−	0.439129i	$-0.855287\pi$
$593$	−32.5715	−	32.5715i	−1.33755	−	1.33755i	−0.439129	−	0.898424i	$-0.644713\pi$
$594$		0			0
$595$			3.78425i			0.155139i
$596$		0			0
$597$	15.1418	+	7.43396i	0.619711	+	0.304252i
$598$		0			0
$599$	−12.5652	+	7.25452i	−0.513400	+	0.296412i	−0.734230	−	0.678900i	$-0.762457\pi$
$599$	−12.5652	+	7.25452i	−0.513400	+	0.296412i	0.220830	+	0.975312i	$0.429123\pi$
$600$		0			0
$601$	5.39354	−	9.34188i	0.220007	−	0.381063i	−0.734803	−	0.678281i	$-0.762725\pi$
$601$	5.39354	−	9.34188i	0.220007	−	0.381063i	0.954810	+	0.297218i	$0.0960587\pi$
$602$		0			0
$603$	−15.5667	+	6.51229i	−0.633926	+	0.265201i
$604$		0			0
$605$	7.73869	−	2.07358i	0.314623	−	0.0843029i
$606$		0			0
$607$	−2.32578	−	4.02837i	−0.0944005	−	0.163506i	0.814958	−	0.579520i	$-0.196760\pi$
$607$	−2.32578	−	4.02837i	−0.0944005	−	0.163506i	−0.909358	+	0.416014i	$0.863427\pi$
$608$		0			0
$609$	10.1008	+	8.82678i	0.409307	+	0.357679i
$610$		0			0
$611$	−0.836894	+	5.90319i	−0.0338571	+	0.238817i
$612$		0			0
$613$	1.73826	+	1.73826i	0.0702077	+	0.0702077i	0.741339	−	0.671131i	$-0.234191\pi$
$613$	1.73826	+	1.73826i	0.0702077	+	0.0702077i	−0.671131	+	0.741339i	$0.734191\pi$
$614$		0			0
$615$	−4.51681	+	3.02956i	−0.182136	+	0.122164i
$616$		0			0
$617$	−0.976480	−	0.261647i	−0.0393116	−	0.0105335i	0.239110	−	0.970993i	$-0.423144\pi$
$617$	−0.976480	−	0.261647i	−0.0393116	−	0.0105335i	−0.278421	+	0.960459i	$0.589811\pi$
$618$		0			0
$619$	−10.3162	−	38.5007i	−0.414645	−	1.54747i	−0.785547	−	0.618803i	$-0.787618\pi$
$619$	−10.3162	−	38.5007i	−0.414645	−	1.54747i	0.370902	−	0.928672i	$-0.379049\pi$
$620$		0			0
$621$	−11.1654	−	12.5968i	−0.448052	−	0.505493i
$622$		0			0
$623$	−28.2743	+	48.9725i	−1.13278	+	1.96204i
$624$		0			0
$625$	11.2788	+	19.5354i	0.451151	+	0.781416i
$626$		0			0
$627$	−23.4819	+	15.7500i	−0.937777	+	0.628994i
$628$		0			0
$629$	−0.882851	+	0.882851i	−0.0352016	+	0.0352016i
$630$		0			0
$631$	4.27409	−	4.27409i	0.170149	−	0.170149i	−0.616896	−	0.787045i	$-0.711610\pi$
$631$	4.27409	−	4.27409i	0.170149	−	0.170149i	0.787045	+	0.616896i	$0.211610\pi$
$632$		0			0
$633$	10.9576	−	0.737585i	0.435527	−	0.0293164i
$634$		0			0
$635$	−1.17160	+	4.37247i	−0.0464935	+	0.173516i
$636$		0			0
$637$	−5.51333	−	45.3542i	−0.218446	−	1.79700i
$638$		0			0
$639$	1.89453	+	0.242633i	0.0749463	+	0.00959842i
$640$		0			0
$641$	−1.45992	+	2.52866i	−0.0576634	+	0.0998759i	−0.893416	−	0.449230i	$-0.851698\pi$
$641$	−1.45992	+	2.52866i	−0.0576634	+	0.0998759i	0.835753	+	0.549106i	$0.185032\pi$
$642$		0			0
$643$	−6.39801	+	23.8777i	−0.252313	+	0.941644i	0.717253	+	0.696813i	$0.245399\pi$
$643$	−6.39801	+	23.8777i	−0.252313	+	0.941644i	−0.969566	+	0.244831i	$0.921267\pi$
$644$		0			0
$645$	3.97233	−	1.35623i	0.156410	−	0.0534015i
$646$		0			0
$647$	−11.3151			−0.444842			−0.222421	−	0.974951i	$-0.571396\pi$
$647$	−11.3151			−0.444842			−0.222421	+	0.974951i	$0.571396\pi$
$648$		0			0
$649$		−	83.9815i		−	3.29656i
$650$		0			0
$651$	20.9143	−	42.5990i	0.819697	−	1.66959i
$652$		0			0
$653$	32.6965	−	18.8773i	1.27951	−	0.738727i	0.302754	−	0.953069i	$-0.402094\pi$
$653$	32.6965	−	18.8773i	1.27951	−	0.738727i	0.976759	+	0.214342i	$0.0687606\pi$
$654$		0			0
$655$	−7.17278	+	1.92194i	−0.280264	+	0.0750964i
$656$		0			0
$657$	−17.7264	−	2.27023i	−0.691572	−	0.0885701i
$658$		0			0
$659$	31.7197	+	18.3134i	1.23562	+	0.713387i	0.968197	−	0.250191i	$-0.0804933\pi$
$659$	31.7197	+	18.3134i	1.23562	+	0.713387i	0.267427	+	0.963578i	$0.413827\pi$
$660$		0			0
$661$	−23.5028	−	6.29756i	−0.914154	−	0.244947i	−0.229069	−	0.973410i	$-0.573568\pi$
$661$	−23.5028	−	6.29756i	−0.914154	−	0.244947i	−0.685085	+	0.728464i	$0.740235\pi$
$662$		0			0
$663$	8.57752	+	9.94351i	0.333123	+	0.386174i
$664$		0			0
$665$	−3.74644	+	3.74644i	−0.145281	+	0.145281i
$666$		0			0
$667$		−	5.65665i		−	0.219026i
$668$		0			0
$669$	−4.69622	+	23.8288i	−0.181566	+	0.921273i
$670$		0			0
$671$	−1.58586	+	5.91851i	−0.0612215	+	0.228482i
$672$		0			0
$673$	0.387376	+	0.223652i	0.0149323	+	0.00862115i	0.507448	−	0.861683i	$-0.330589\pi$
$673$	0.387376	+	0.223652i	0.0149323	+	0.00862115i	−0.492515	+	0.870304i	$0.663922\pi$
$674$		0			0
$675$	−23.8342	−	7.95044i	−0.917380	−	0.306012i
$676$		0			0
$677$	−22.9332	−	13.2405i	−0.881396	−	0.508874i	−0.0102773	−	0.999947i	$-0.503271\pi$
$677$	−22.9332	−	13.2405i	−0.881396	−	0.508874i	−0.871118	+	0.491073i	$0.836605\pi$
$678$		0			0
$679$	−23.7341	−	41.1087i	−0.910832	−	1.57761i
$680$		0			0
$681$	46.2431	+	9.11369i	1.77204	+	0.349237i
$682$		0			0
$683$	9.09951	+	9.09951i	0.348183	+	0.348183i	0.859432	−	0.511249i	$-0.170817\pi$
$683$	9.09951	+	9.09951i	0.348183	+	0.348183i	−0.511249	+	0.859432i	$0.670817\pi$
$684$		0			0
$685$	7.43994			0.284266
$686$		0			0
$687$	2.59338	−	2.96771i	0.0989435	−	0.113225i
$688$		0			0
$689$	−33.9320	−	14.4516i	−1.29271	−	0.550561i
$690$		0			0
$691$	−29.6860	+	7.95435i	−1.12931	+	0.302598i	−0.774646	−	0.632396i	$-0.782072\pi$
$691$	−29.6860	+	7.95435i	−1.12931	+	0.302598i	−0.354665	+	0.934994i	$0.615405\pi$
$692$		0			0
$693$	27.9935	−	68.2614i	1.06338	−	2.59304i
$694$		0			0
$695$	1.38388	+	5.16472i	0.0524936	+	0.195909i
$696$		0			0
$697$	−15.7186	−	4.21178i	−0.595383	−	0.159532i
$698$		0			0
$699$	14.4958	−	29.5255i	0.548281	−	1.11676i
$700$		0			0
$701$	−17.7827			−0.671642			−0.335821	−	0.941926i	$-0.609014\pi$
$701$	−17.7827			−0.671642			−0.335821	+	0.941926i	$0.609014\pi$
$702$		0			0
$703$	−1.74806			−0.0659294
$704$		0			0
$705$	−0.512167	+	1.04320i	−0.0192893	+	0.0392892i
$706$		0			0
$707$	22.9087	+	6.13837i	0.861571	+	0.230857i
$708$		0			0
$709$	2.86776	+	10.7026i	0.107701	+	0.401945i	0.998638	−	0.0521824i	$-0.0166177\pi$
$709$	2.86776	+	10.7026i	0.107701	+	0.401945i	−0.890937	+	0.454127i	$0.849951\pi$
$710$		0			0
$711$	15.7715	−	2.13290i	0.591478	−	0.0799902i
$712$		0			0
$713$	−19.3300	+	5.17947i	−0.723915	+	0.193972i
$714$		0			0
$715$	3.17858	−	7.46324i	0.118872	−	0.279109i
$716$		0			0
$717$	7.88599	−	9.02426i	0.294508	−	0.337017i
$718$		0			0
$719$	28.9556			1.07986			0.539930	−	0.841710i	$-0.318451\pi$
$719$	28.9556			1.07986			0.539930	+	0.841710i	$0.318451\pi$
$720$		0			0
$721$	37.7367	+	37.7367i	1.40539	+	1.40539i
$722$		0			0
$723$	−17.9801	−	3.54356i	−0.668687	−	0.131786i
$724$		0			0
$725$	−4.22164	−	7.31210i	−0.156788	−	0.271565i
$726$		0			0
$727$	−19.5931	−	11.3121i	−0.726669	−	0.419543i	0.0905332	−	0.995893i	$-0.471143\pi$
$727$	−19.5931	−	11.3121i	−0.726669	−	0.419543i	−0.817202	+	0.576351i	$0.804476\pi$
$728$		0			0
$729$	24.8342	−	10.5955i	0.919784	−	0.392425i
$730$		0			0
$731$	10.8765	+	6.27955i	0.402282	+	0.232258i
$732$		0			0
$733$	−1.77587	+	6.62765i	−0.0655934	+	0.244798i	−0.990936	−	0.134334i	$-0.957111\pi$
$733$	−1.77587	+	6.62765i	−0.0655934	+	0.244798i	0.925343	+	0.379132i	$0.123777\pi$
$734$		0			0
$735$	1.72198	−	8.73738i	0.0635162	−	0.322283i
$736$		0			0
$737$			31.1879i			1.14882i
$738$		0			0
$739$	6.95891	−	6.95891i	0.255988	−	0.255988i	−0.567432	−	0.823420i	$-0.692063\pi$
$739$	6.95891	−	6.95891i	0.255988	−	0.255988i	0.823420	+	0.567432i	$0.192063\pi$
$740$		0			0
$741$	−1.35234	+	18.3360i	−0.0496796	+	0.673590i
$742$		0			0
$743$	31.3859	+	8.40983i	1.15144	+	0.308527i	0.783541	−	0.621340i	$-0.213412\pi$
$743$	31.3859	+	8.40983i	1.15144	+	0.308527i	0.367896	+	0.929867i	$0.380078\pi$
$744$		0			0
$745$	3.28993	+	1.89944i	0.120534	+	0.0695902i
$746$		0			0
$747$	−18.8397	+	24.7323i	−0.689310	+	0.904908i
$748$		0			0
$749$	−35.8328	+	9.60136i	−1.30930	+	0.350826i
$750$		0			0
$751$	−32.8514	+	18.9668i	−1.19876	+	0.692107i	−0.960280	−	0.279040i	$-0.909984\pi$
$751$	−32.8514	+	18.9668i	−1.19876	+	0.692107i	−0.238484	+	0.971146i	$0.576651\pi$
$752$		0			0
$753$	11.6293	−	23.6869i	0.423795	−	0.863200i
$754$		0			0
$755$		−	0.546428i		−	0.0198866i
$756$		0			0
$757$	−23.4638			−0.852808			−0.426404	−	0.904533i	$-0.640220\pi$
$757$	−23.4638			−0.852808			−0.426404	+	0.904533i	$0.640220\pi$
$758$		0			0
$759$	−29.4431	+	10.0524i	−1.06872	+	0.364880i
$760$		0			0
$761$	3.37555	−	12.5977i	0.122364	−	0.456668i	−0.877368	−	0.479818i	$-0.840703\pi$
$761$	3.37555	−	12.5977i	0.122364	−	0.456668i	0.999732	+	0.0231499i	$0.00736949\pi$
$762$		0			0
$763$	−35.4381	+	61.3805i	−1.28294	+	2.22212i
$764$		0			0
$765$	0.987860	+	2.36135i	0.0357162	+	0.0853746i
$766$		0			0
$767$	−42.9922	−	33.6727i	−1.55236	−	1.21585i
$768$		0			0
$769$	2.06684	−	7.71357i	0.0745323	−	0.278158i	−0.918595	−	0.395201i	$-0.870675\pi$
$769$	2.06684	−	7.71357i	0.0745323	−	0.278158i	0.993127	+	0.117043i	$0.0373415\pi$
$770$		0			0
$771$	25.7642	−	1.73425i	0.927874	−	0.0624575i
$772$		0			0
$773$	1.78876	−	1.78876i	0.0643374	−	0.0643374i	−0.674206	−	0.738543i	$-0.735514\pi$
$773$	1.78876	−	1.78876i	0.0643374	−	0.0643374i	0.738543	+	0.674206i	$0.235514\pi$
$774$		0			0
$775$	−21.1216	+	21.1216i	−0.758709	+	0.758709i
$776$		0			0
$777$	3.78810	−	2.54079i	0.135897	−	0.0911503i
$778$		0			0
$779$	−11.3918	−	19.7312i	−0.408155	−	0.706944i
$780$		0			0
$781$	1.76510	−	3.05725i	0.0631604	−	0.109397i
$782$		0			0
$783$	8.60705	+	2.87107i	0.307591	+	0.102604i
$784$		0			0
$785$	−2.29469	−	8.56391i	−0.0819011	−	0.305659i
$786$		0			0
$787$	−22.2235	−	5.95477i	−0.792182	−	0.212264i	−0.160033	−	0.987112i	$-0.551160\pi$
$787$	−22.2235	−	5.95477i	−0.792182	−	0.212264i	−0.632149	+	0.774847i	$0.717827\pi$
$788$		0			0
$789$	35.0962	−	23.5401i	1.24946	−	0.838049i
$790$		0			0
$791$	30.1335	+	30.1335i	1.07142	+	1.07142i
$792$		0			0
$793$	2.39398	+	3.18489i	0.0850126	+	0.113099i
$794$		0			0
$795$	−5.41320	−	4.73041i	−0.191987	−	0.167770i
$796$		0			0
$797$	10.6766	+	18.4924i	0.378184	+	0.655034i	0.990798	−	0.135348i	$-0.0432153\pi$
$797$	10.6766	+	18.4924i	0.378184	+	0.655034i	−0.612614	+	0.790382i	$0.709882\pi$
$798$		0			0
$799$	−3.35873	+	0.899970i	−0.118823	+	0.0318386i
$800$		0			0
$801$	−4.85892	+	37.9394i	−0.171681	+	1.34052i
$802$		0			0
$803$	−16.5154	+	28.6056i	−0.582817	+	1.00947i
$804$		0			0
$805$	−5.04883	+	2.91495i	−0.177948	+	0.102738i
$806$		0			0
$807$	−2.94789	−	1.44729i	−0.103771	−	0.0509470i
$808$		0			0
$809$			1.32749i			0.0466721i	0.999728	+	0.0233361i	$0.00742877\pi$
$809$			1.32749i			0.0466721i	−0.999728	+	0.0233361i	$0.992571\pi$
$810$		0			0
$811$	12.0938	+	12.0938i	0.424670	+	0.424670i	0.886808	−	0.462138i	$-0.152918\pi$
$811$	12.0938	+	12.0938i	0.424670	+	0.424670i	−0.462138	+	0.886808i	$0.652918\pi$
$812$		0			0
$813$	−6.28644	−	18.4126i	−0.220475	−	0.645759i
$814$		0			0
$815$	−1.23546	+	0.713291i	−0.0432761	+	0.0249855i
$816$		0			0
$817$	4.55102	+	16.9847i	0.159220	+	0.594218i
$818$		0			0
$819$	−23.7206	−	41.7002i	−0.828865	−	1.45712i
$820$		0			0
$821$	11.6317	+	43.4100i	0.405948	+	1.51502i	0.802300	+	0.596921i	$0.203610\pi$
$821$	11.6317	+	43.4100i	0.405948	+	1.51502i	−0.396351	+	0.918099i	$0.629724\pi$
$822$		0			0
$823$	−16.9318	+	9.77557i	−0.590205	+	0.340755i	−0.765179	−	0.643818i	$-0.777349\pi$
$823$	−16.9318	+	9.77557i	−0.590205	+	0.340755i	0.174974	+	0.984573i	$0.444016\pi$
$824$		0			0
$825$	−30.5575	+	34.9682i	−1.06387	+	1.21744i
$826$		0			0
$827$	1.57135	+	1.57135i	0.0546411	+	0.0546411i	0.733899	−	0.679258i	$-0.237698\pi$
$827$	1.57135	+	1.57135i	0.0546411	+	0.0546411i	−0.679258	+	0.733899i	$0.737698\pi$
$828$		0			0
$829$			54.6087i			1.89664i	0.317318	+	0.948319i	$0.397218\pi$
$829$			54.6087i			1.89664i	−0.317318	+	0.948319i	$0.602782\pi$
$830$		0			0
$831$	4.09321	−	2.74544i	0.141992	−	0.0952381i
$832$		0			0
$833$	23.0758	−	13.3228i	0.799531	−	0.461609i
$834$		0			0
$835$	−0.517236	+	0.895880i	−0.0178997	+	0.0310032i
$836$		0			0
$837$	1.93012	−	32.0411i	0.0667147	−	1.10750i
$838$		0			0
$839$	−49.8998	+	13.3706i	−1.72273	+	0.461604i	−0.978488	−	0.206304i	$-0.933856\pi$
$839$	−49.8998	+	13.3706i	−1.72273	+	0.461604i	−0.744243	+	0.667909i	$0.767190\pi$
$840$		0			0
$841$	−12.9755	−	22.4742i	−0.447430	−	0.774972i
$842$		0			0
$843$	2.14984	−	10.9084i	0.0740446	−	0.375704i
$844$		0			0
$845$	−2.54616	−	4.61961i	−0.0875904	−	0.158919i
$846$		0			0
$847$	−61.9248	−	61.9248i	−2.12776	−	2.12776i
$848$		0			0
$849$	2.33785	+	34.7313i	0.0802349	+	1.19198i
$850$		0			0
$851$	−1.85792	−	0.497828i	−0.0636887	−	0.0170653i
$852$		0			0
$853$	−11.2882	−	42.1281i	−0.386500	−	1.44244i	−0.835789	−	0.549051i	$-0.814989\pi$
$853$	−11.2882	−	42.1281i	−0.386500	−	1.44244i	0.449289	−	0.893387i	$-0.351678\pi$
$854$		0			0
$855$	−1.35976	+	3.31575i	−0.0465029	+	0.113396i
$856$		0			0
$857$	5.85211	−	10.1361i	0.199904	−	0.346244i	−0.748593	−	0.663030i	$-0.769270\pi$
$857$	5.85211	−	10.1361i	0.199904	−	0.346244i	0.948497	+	0.316786i	$0.102604\pi$
$858$		0			0
$859$	−11.2712	−	19.5222i	−0.384568	−	0.666091i	0.607142	−	0.794594i	$-0.292316\pi$
$859$	−11.2712	−	19.5222i	−0.384568	−	0.666091i	−0.991709	+	0.128503i	$0.958983\pi$
$860$		0			0
$861$	53.3655	+	26.2002i	1.81869	+	0.892901i
$862$		0			0
$863$	0.793544	−	0.793544i	0.0270126	−	0.0270126i	−0.693472	−	0.720484i	$-0.743920\pi$
$863$	0.793544	−	0.793544i	0.0270126	−	0.0270126i	0.720484	+	0.693472i	$0.243920\pi$
$864$		0			0
$865$	7.04194	−	7.04194i	0.239433	−	0.239433i
$866$		0			0
$867$	9.60137	−	19.5564i	0.326080	−	0.664170i
$868$		0			0
$869$	7.61329	−	28.4132i	0.258263	−	0.963851i
$870$		0			0
$871$	15.9659	+	12.5049i	0.540982	+	0.423712i
$872$		0			0
$873$	−25.5412	−	19.4559i	−0.864437	−	0.658481i
$874$		0			0
$875$	−8.85002	+	15.3287i	−0.299185	+	0.518204i
$876$		0			0
$877$	−1.42882	+	5.33244i	−0.0482479	+	0.180064i	−0.985845	−	0.167660i	$-0.946379\pi$
$877$	−1.42882	+	5.33244i	−0.0482479	+	0.180064i	0.937597	+	0.347724i	$0.113045\pi$
$878$		0			0
$879$	35.2899	+	30.8386i	1.19030	+	1.04016i
$880$		0			0
$881$	31.3799			1.05721			0.528607	−	0.848867i	$-0.322715\pi$
$881$	31.3799			1.05721			0.528607	+	0.848867i	$0.322715\pi$
$882$		0			0
$883$		−	24.8209i		−	0.835290i	−0.908610	−	0.417645i	$-0.862856\pi$
$883$		−	24.8209i		−	0.835290i	0.908610	−	0.417645i	$-0.137144\pi$
$884$		0			0
$885$	−5.92928	−	8.84004i	−0.199310	−	0.297155i
$886$		0			0
$887$	−16.4652	+	9.50617i	−0.552846	+	0.319186i	−0.750269	−	0.661132i	$-0.770076\pi$
$887$	−16.4652	+	9.50617i	−0.552846	+	0.319186i	0.197423	+	0.980318i	$0.436743\pi$
$888$		0			0
$889$	47.7950	−	12.8066i	1.60299	−	0.429521i
$890$		0			0
$891$	−0.351562	−	49.9022i	−0.0117778	−	1.67179i
$892$		0			0
$893$	−4.21616	−	2.43420i	−0.141088	−	0.0814574i
$894$		0			0
$895$	3.83669	+	1.02804i	0.128246	+	0.0343635i
$896$		0			0
$897$	−6.65922	+	19.1032i	−0.222345	+	0.637837i
$898$		0			0
$899$	7.62745	−	7.62745i	0.254390	−	0.254390i
$900$		0			0
$901$		−	21.5095i		−	0.716586i
$902$		0			0
$903$	−34.5492	−	30.1914i	−1.14973	−	1.00471i
$904$		0			0
$905$	−0.742030	+	2.76930i	−0.0246659	+	0.0920545i
$906$		0			0
$907$	−24.4984	−	14.1442i	−0.813456	−	0.469649i	0.0346983	−	0.999398i	$-0.488953\pi$
$907$	−24.4984	−	14.1442i	−0.813456	−	0.469649i	−0.848155	+	0.529749i	$0.822286\pi$
$908$		0			0
$909$	15.8973	−	2.14991i	0.527280	−	0.0713081i
$910$		0			0
$911$	41.7482	+	24.1033i	1.38318	+	0.798579i	0.992535	−	0.121962i	$-0.0389185\pi$
$911$	41.7482	+	24.1033i	1.38318	+	0.798579i	0.390645	+	0.920541i	$0.372252\pi$
$912$		0			0
$913$	28.7320	+	49.7653i	0.950890	+	1.64699i
$914$		0			0
$915$	0.250929	+	0.734958i	0.00829546	+	0.0242970i
$916$		0			0
$917$	57.3964	+	57.3964i	1.89540	+	1.89540i
$918$		0			0
$919$	50.0747			1.65181			0.825906	−	0.563808i	$-0.190664\pi$
$919$	50.0747			1.65181			0.825906	+	0.563808i	$0.190664\pi$
$920$		0			0
$921$	18.7290	+	54.8563i	0.617142	+	1.80758i
$922$		0			0
$923$	−0.857357	−	2.12942i	−0.0282202	−	0.0700906i
$924$		0			0
$925$	−2.77319	+	0.743074i	−0.0911819	+	0.0244321i
$926$		0			0
$927$	33.3984	+	13.6964i	1.09695	+	0.449850i
$928$		0			0
$929$	−7.79987	−	29.1095i	−0.255906	−	0.955053i	−0.967584	−	0.252548i	$-0.918732\pi$
$929$	−7.79987	−	29.1095i	−0.255906	−	0.955053i	0.711679	−	0.702505i	$-0.247935\pi$
$930$		0			0
$931$	36.0351	+	9.65556i	1.18100	+	0.316448i
$932$		0			0
$933$	16.6666	−	1.12187i	0.545640	−	0.0367284i
$934$		0			0
$935$	4.73095			0.154718
$936$		0			0
$937$	46.9496			1.53378			0.766888	−	0.641781i	$-0.221804\pi$
$937$	46.9496			1.53378			0.766888	+	0.641781i	$0.221804\pi$
$938$		0			0
$939$	−16.0794	−	23.9730i	−0.524732	−	0.782331i
$940$		0			0
$941$	24.7775	+	6.63910i	0.807722	+	0.216428i	0.638972	−	0.769230i	$-0.279360\pi$
$941$	24.7775	+	6.63910i	0.807722	+	0.216428i	0.168750	+	0.985659i	$0.446027\pi$
$942$		0			0
$943$	−6.48853	−	24.2155i	−0.211296	−	0.788566i
$944$		0			0
$945$	−1.87275	−	9.16172i	−0.0609207	−	0.298031i
$946$		0			0
$947$	−19.5033	+	5.22590i	−0.633773	+	0.169819i	−0.561381	−	0.827557i	$-0.689730\pi$
$947$	−19.5033	+	5.22590i	−0.633773	+	0.169819i	−0.0723918	+	0.997376i	$0.523063\pi$
$948$		0			0
$949$	8.02197	+	19.9242i	0.260404	+	0.646766i
$950$		0			0
$951$	30.1844	+	5.94881i	0.978797	+	0.192903i
$952$		0			0
$953$	6.16921			0.199840			0.0999202	−	0.994995i	$-0.468141\pi$
$953$	6.16921			0.199840			0.0999202	+	0.994995i	$0.468141\pi$
$954$		0			0
$955$	6.53874	+	6.53874i	0.211589	+	0.211589i
$956$		0			0
$957$	11.0350	−	12.6278i	0.356710	−	0.408197i
$958$		0			0
$959$	−40.6626	−	70.4298i	−1.31307	−	2.27430i
$960$		0			0
$961$	−6.20193	−	3.58068i	−0.200062	−	0.115506i
$962$		0			0
$963$	−19.8530	+	15.3452i	−0.639754	+	0.494491i
$964$		0			0
$965$	4.63483	+	2.67592i	0.149200	+	0.0861409i
$966$		0			0
$967$	9.01547	−	33.6462i	0.289918	−	1.08199i	−0.655252	−	0.755410i	$-0.727438\pi$
$967$	9.01547	−	33.6462i	0.289918	−	1.08199i	0.945170	−	0.326578i	$-0.105896\pi$
$968$		0			0
$969$	−10.1476	+	3.46460i	−0.325988	+	0.111299i
$970$		0			0
$971$			37.3163i			1.19754i	0.800922	+	0.598769i	$0.204343\pi$
$971$			37.3163i			1.19754i	−0.800922	+	0.598769i	$0.795657\pi$
$972$		0			0
$973$	41.3279	−	41.3279i	1.32491	−	1.32491i
$974$		0			0
$975$	5.64894	+	29.6638i	0.180911	+	0.950000i
$976$		0			0
$977$	−36.1460	−	9.68530i	−1.15641	−	0.309860i	−0.370881	−	0.928680i	$-0.620944\pi$
$977$	−36.1460	−	9.68530i	−1.15641	−	0.309860i	−0.785533	+	0.618820i	$0.787611\pi$
$978$		0			0
$979$	61.2238	+	35.3476i	1.95672	+	1.12971i
$980$		0			0
$981$	−6.09001	+	47.5520i	−0.194439	+	1.51822i
$982$		0			0
$983$	11.7964	−	3.16084i	0.376247	−	0.100815i	−0.0657392	−	0.997837i	$-0.520941\pi$
$983$	11.7964	−	3.16084i	0.376247	−	0.100815i	0.441987	+	0.897022i	$0.354274\pi$
$984$		0			0
$985$	−7.22017	+	4.16856i	−0.230054	+	0.132822i
$986$		0			0
$987$	12.6746	−	0.853159i	0.403437	−	0.0271564i
$988$		0			0
$989$			19.3482i			0.615236i
$990$		0			0
$991$	−30.3624			−0.964492			−0.482246	−	0.876036i	$-0.660179\pi$
$991$	−30.3624			−0.964492			−0.482246	+	0.876036i	$0.660179\pi$
$992$		0			0
$993$	−8.03007	+	40.7448i	−0.254826	+	1.29300i
$994$		0			0
$995$	1.02275	−	3.81695i	0.0324233	−	0.121005i
$996$		0			0
$997$	−6.26465	+	10.8507i	−0.198404	+	0.343645i	−0.948011	−	0.318238i	$-0.896909\pi$
$997$	−6.26465	+	10.8507i	−0.198404	+	0.343645i	0.749607	+	0.661883i	$0.230242\pi$
$998$		0			0
$999$	1.70049	−	2.57430i	0.0538011	−	0.0814473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.cg.a.281.6	yes	56
3.2	odd	2		1404.2.cj.a.1061.7		56
9.4	even	3		1404.2.cj.a.125.7		56
9.5	odd	6	inner	468.2.cg.a.437.6	yes	56
13.5	odd	4	inner	468.2.cg.a.317.6	yes	56
39.5	even	4		1404.2.cj.a.629.7		56
117.5	even	12	inner	468.2.cg.a.5.6	✓	56
117.31	odd	12		1404.2.cj.a.1097.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.cg.a.5.6	✓	56	117.5	even	12	inner
468.2.cg.a.281.6	yes	56	1.1	even	1	trivial
468.2.cg.a.317.6	yes	56	13.5	odd	4	inner
468.2.cg.a.437.6	yes	56	9.5	odd	6	inner
1404.2.cj.a.125.7		56	9.4	even	3
1404.2.cj.a.629.7		56	39.5	even	4
1404.2.cj.a.1061.7		56	3.2	odd	2
1404.2.cj.a.1097.7		56	117.31	odd	12

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:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.763329 + 1.55478i) q^{3} +(0.391929 + 0.105017i) q^{5} +(-1.14793 - 4.28414i) q^{7} +(-1.83466 - 2.37361i) q^{9} +O(q^{10})\)	\(q+(-0.763329 + 1.55478i) q^{3} +(0.391929 + 0.105017i) q^{5} +(-1.14793 - 4.28414i) q^{7} +(-1.83466 - 2.37361i) q^{9} +(-5.35589 + 1.43511i) q^{11} +(-1.41280 + 3.31723i) q^{13} +(-0.462449 + 0.529200i) q^{15} -2.10279 q^{17} +(-2.08178 - 2.08178i) q^{19} +(7.53713 + 1.48543i) q^{21} +(-1.61975 - 2.80548i) q^{23} +(-4.18755 - 2.41768i) q^{25} +(5.09088 - 1.04063i) q^{27} +(1.51221 + 0.873077i) q^{29} +(1.59885 - 5.96700i) q^{31} +(1.85704 - 9.42267i) q^{33} -1.79963i q^{35} +(0.419848 - 0.419848i) q^{37} +(-4.07911 - 4.72872i) q^{39} +(7.47510 + 2.00295i) q^{41} +(-5.17242 - 2.98630i) q^{43} +(-0.469786 - 1.12296i) q^{45} +(1.59728 - 0.427989i) q^{47} +(-10.9739 + 6.33580i) q^{49} +(1.60512 - 3.26937i) q^{51} +10.2290i q^{53} -2.24984 q^{55} +(4.82579 - 1.64762i) q^{57} +(-3.92005 + 14.6298i) q^{59} +(0.552523 - 0.956999i) q^{61} +(-8.06282 + 10.5847i) q^{63} +(-0.902083 + 1.15175i) q^{65} +(1.45577 - 5.43302i) q^{67} +(5.59829 - 0.376835i) q^{69} +(-0.450191 + 0.450191i) q^{71} +(4.21227 - 4.21227i) q^{73} +(6.95543 - 4.66521i) q^{75} +(12.2964 + 21.2980i) q^{77} +(-2.65252 + 4.59429i) q^{79} +(-2.26807 + 8.70953i) q^{81} +(-2.68228 - 10.0104i) q^{83} +(-0.824145 - 0.220829i) q^{85} +(-2.51176 + 1.68471i) q^{87} +(-9.01543 - 9.01543i) q^{89} +(15.8333 + 2.24468i) q^{91} +(8.05689 + 7.04064i) q^{93} +(-0.597288 - 1.03453i) q^{95} +(10.3378 - 2.77000i) q^{97} +(13.2326 + 10.0799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{7}+O(q^{10}) \) 56 * q - 2 * q^7	\( 56 q - 2 q^{7} - 12 q^{11} - 12 q^{15} + 4 q^{19} - 12 q^{21} + 36 q^{27} - 4 q^{31} + 12 q^{33} - 4 q^{37} + 24 q^{41} + 6 q^{45} + 66 q^{47} - 48 q^{57} - 30 q^{63} - 78 q^{65} - 14 q^{67} + 28 q^{73} - 24 q^{79} - 78 q^{83} + 36 q^{85} - 8 q^{91} + 6 q^{93} + 26 q^{97} + 54 q^{99}+O(q^{100}) \) 56 * q - 2 * q^7 - 12 * q^11 - 12 * q^15 + 4 * q^19 - 12 * q^21 + 36 * q^27 - 4 * q^31 + 12 * q^33 - 4 * q^37 + 24 * q^41 + 6 * q^45 + 66 * q^47 - 48 * q^57 - 30 * q^63 - 78 * q^65 - 14 * q^67 + 28 * q^73 - 24 * q^79 - 78 * q^83 + 36 * q^85 - 8 * q^91 + 6 * q^93 + 26 * q^97 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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