LMFDB - Embedded newform 308.2.q.a.285.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,2,Mod(241,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("308.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	308.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45939238226$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 17x^{12} - 343x^{10} + 490x^{8} - 16807x^{6} - 40817x^{4} + 235298x^{2} + 5764801 $ x^16 + 2x^14 - 17x^12 - 343x^10 + 490x^8 - 16807x^6 - 40817x^4 + 235298*x^2 + 5764801
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			285.8
Root			$-2.64407 + 0.0942693i$ of defining polynomial
Character	$\chi$	$=$	308.285
Dual form			308.2.q.a.241.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37157 - 1.36923i) q^{3} +(0.316246 + 0.182585i) q^{5} +(2.64407 + 0.0942693i) q^{7} +(2.24957 - 3.89637i) q^{9} +O(q^{10})$	\(q+(2.37157 - 1.36923i) q^{3} +(0.316246 + 0.182585i) q^{5} +(2.64407 + 0.0942693i) q^{7} +(2.24957 - 3.89637i) q^{9} +(-2.70717 + 1.91604i) q^{11} -4.51413 q^{13} +1.00000 q^{15} +(1.66183 + 2.87837i) q^{17} +(1.66183 - 2.87837i) q^{19} +(6.39968 - 3.39677i) q^{21} +(-2.55533 + 4.42596i) q^{23} +(-2.43333 - 4.21464i) q^{25} -4.10534i q^{27} -5.32202i q^{29} +(-4.37714 + 2.52714i) q^{31} +(-3.79676 + 8.25077i) q^{33} +(0.818964 + 0.512579i) q^{35} +(-0.305755 + 0.529584i) q^{37} +(-10.7056 + 6.18087i) q^{39} +4.51413 q^{41} -7.03973i q^{43} +(1.42284 - 0.821474i) q^{45} +(0.505569 + 0.291890i) q^{47} +(6.98223 + 0.498510i) q^{49} +(7.88229 + 4.55084i) q^{51} +(6.87072 + 11.9004i) q^{53} +(-1.20597 + 0.111652i) q^{55} -9.10169i q^{57} +(-2.95431 + 1.70567i) q^{59} +(-5.72010 + 9.90750i) q^{61} +(6.31534 - 10.0902i) q^{63} +(-1.42757 - 0.824210i) q^{65} +(-5.43739 - 9.41784i) q^{67} +13.9953i q^{69} -9.37564 q^{71} +(1.56695 + 2.71404i) q^{73} +(-11.5416 - 6.66356i) q^{75} +(-7.33858 + 4.81095i) q^{77} +(10.3291 + 5.96351i) q^{79} +(1.12757 + 1.95301i) q^{81} -14.7639 q^{83} +1.21370i q^{85} +(-7.28705 - 12.6215i) q^{87} +(7.38527 + 4.26389i) q^{89} +(-11.9357 - 0.425544i) q^{91} +(-6.92047 + 11.9866i) q^{93} +(1.05109 - 0.606848i) q^{95} -9.15963i q^{97} +(1.37564 + 14.8584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{5} + 4 q^{9}+O(q^{10}) $ 16 * q + 6 * q^5 + 4 * q^9	$ 16 q + 6 q^{5} + 4 q^{9} - q^{11} + 16 q^{15} - 2 q^{23} - 6 q^{25} - 12 q^{31} + 21 q^{33} + 2 q^{37} - 18 q^{45} - 12 q^{47} - 4 q^{49} + 8 q^{53} - 30 q^{59} - 18 q^{67} - 76 q^{71} + 6 q^{75} - 25 q^{77} - 8 q^{81} - 12 q^{89} + 6 q^{91} + 10 q^{93} - 52 q^{99}+O(q^{100}) $ 16 * q + 6 * q^5 + 4 * q^9 - q^11 + 16 * q^15 - 2 * q^23 - 6 * q^25 - 12 * q^31 + 21 * q^33 + 2 * q^37 - 18 * q^45 - 12 * q^47 - 4 * q^49 + 8 * q^53 - 30 * q^59 - 18 * q^67 - 76 * q^71 + 6 * q^75 - 25 * q^77 - 8 * q^81 - 12 * q^89 + 6 * q^91 + 10 * q^93 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.37157	−	1.36923i	1.36923	−	0.790524i	0.378399	−	0.925643i	$-0.376475\pi$
$3$	2.37157	−	1.36923i	1.36923	−	0.790524i	0.990829	+	0.135118i	$0.0431415\pi$
$4$		0			0
$5$	0.316246	+	0.182585i	0.141429	+	0.0816543i	0.569045	−	0.822306i	$-0.307313\pi$
$5$	0.316246	+	0.182585i	0.141429	+	0.0816543i	−0.427616	+	0.903961i	$0.640646\pi$
$6$		0			0
$7$	2.64407	+	0.0942693i	0.999365	+	0.0356305i
$7$	2.64407	+	0.0942693i	0.999365	+	0.0356305i
$8$		0			0
$9$	2.24957	−	3.89637i	0.749857	−	1.29879i
$10$		0			0
$11$	−2.70717	+	1.91604i	−0.816243	+	0.577709i
$11$	−2.70717	+	1.91604i	−0.816243	+	0.577709i
$12$		0			0
$13$	−4.51413			−1.25199			−0.625997	−	0.779826i	$-0.715308\pi$
$13$	−4.51413			−1.25199			−0.625997	+	0.779826i	$0.715308\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	1.66183	+	2.87837i	0.403052	+	0.698107i	0.994093	−	0.108535i	$-0.0346159\pi$
$17$	1.66183	+	2.87837i	0.403052	+	0.698107i	−0.591040	+	0.806642i	$0.701283\pi$
$18$		0			0
$19$	1.66183	−	2.87837i	0.381249	−	0.660343i	−0.609992	−	0.792408i	$-0.708827\pi$
$19$	1.66183	−	2.87837i	0.381249	−	0.660343i	0.991241	+	0.132064i	$0.0421606\pi$
$20$		0			0
$21$	6.39968	−	3.39677i	1.39653	−	0.741236i
$22$		0			0
$23$	−2.55533	+	4.42596i	−0.532822	+	0.922876i	0.466443	+	0.884551i	$0.345535\pi$
$23$	−2.55533	+	4.42596i	−0.532822	+	0.922876i	−0.999265	+	0.0383243i	$0.987798\pi$
$24$		0			0
$25$	−2.43333	−	4.21464i	−0.486665	−	0.842929i
$26$		0			0
$27$		−	4.10534i		−	0.790073i
$28$		0			0
$29$		−	5.32202i		−	0.988274i	−0.869384	−	0.494137i	$-0.835484\pi$
$29$		−	5.32202i		−	0.988274i	0.869384	−	0.494137i	$-0.164516\pi$
$30$		0			0
$31$	−4.37714	+	2.52714i	−0.786158	+	0.453888i	−0.838608	−	0.544735i	$-0.816630\pi$
$31$	−4.37714	+	2.52714i	−0.786158	+	0.453888i	0.0524503	+	0.998624i	$0.483297\pi$
$32$		0			0
$33$	−3.79676	+	8.25077i	−0.660930	+	1.43627i
$34$		0			0
$35$	0.818964	+	0.512579i	0.138430	+	0.0866417i
$36$		0			0
$37$	−0.305755	+	0.529584i	−0.0502659	+	0.0870630i	−0.890064	−	0.455836i	$-0.849340\pi$
$37$	−0.305755	+	0.529584i	−0.0502659	+	0.0870630i	0.839798	+	0.542899i	$0.182674\pi$
$38$		0			0
$39$	−10.7056	+	6.18087i	−1.71427	+	0.989731i
$40$		0			0
$41$	4.51413			0.704988			0.352494	−	0.935814i	$-0.385334\pi$
$41$	4.51413			0.704988			0.352494	+	0.935814i	$0.385334\pi$
$42$		0			0
$43$		−	7.03973i		−	1.07355i	−0.843726	−	0.536774i	$-0.819643\pi$
$43$		−	7.03973i		−	1.07355i	0.843726	−	0.536774i	$-0.180357\pi$
$44$		0			0
$45$	1.42284	−	0.821474i	0.212104	−	0.122458i
$46$		0			0
$47$	0.505569	+	0.291890i	0.0737448	+	0.0425766i	0.536419	−	0.843952i	$-0.319777\pi$
$47$	0.505569	+	0.291890i	0.0737448	+	0.0425766i	−0.462674	+	0.886528i	$0.653110\pi$
$48$		0			0
$49$	6.98223	+	0.498510i	0.997461	+	0.0712157i
$50$		0			0
$51$	7.88229	+	4.55084i	1.10374	+	0.637245i
$52$		0			0
$53$	6.87072	+	11.9004i	0.943765	+	1.63465i	0.758204	+	0.652017i	$0.226077\pi$
$53$	6.87072	+	11.9004i	0.943765	+	1.63465i	0.185561	+	0.982633i	$0.440590\pi$
$54$		0			0
$55$	−1.20597	+	0.111652i	−0.162613	+	0.0150552i
$56$		0			0
$57$		−	9.10169i		−	1.20555i
$58$		0			0
$59$	−2.95431	+	1.70567i	−0.384618	+	0.222059i	−0.679826	−	0.733374i	$-0.737945\pi$
$59$	−2.95431	+	1.70567i	−0.384618	+	0.222059i	0.295208	+	0.955433i	$0.404611\pi$
$60$		0			0
$61$	−5.72010	+	9.90750i	−0.732384	+	1.26853i	0.223478	+	0.974709i	$0.428259\pi$
$61$	−5.72010	+	9.90750i	−0.732384	+	1.26853i	−0.955862	+	0.293817i	$0.905074\pi$
$62$		0			0
$63$	6.31534	−	10.0902i	0.795658	−	1.27125i
$64$		0			0
$65$	−1.42757	−	0.824210i	−0.177069	−	0.102231i
$66$		0			0
$67$	−5.43739	−	9.41784i	−0.664283	−	1.15057i	−0.979479	−	0.201545i	$-0.935404\pi$
$67$	−5.43739	−	9.41784i	−0.664283	−	1.15057i	0.315196	−	0.949027i	$-0.397930\pi$
$68$		0			0
$69$			13.9953i			1.68484i
$70$		0			0
$71$	−9.37564			−1.11268			−0.556342	−	0.830954i	$-0.687795\pi$
$71$	−9.37564			−1.11268			−0.556342	+	0.830954i	$0.687795\pi$
$72$		0			0
$73$	1.56695	+	2.71404i	0.183398	+	0.317655i	0.943036	−	0.332692i	$-0.107957\pi$
$73$	1.56695	+	2.71404i	0.183398	+	0.317655i	−0.759637	+	0.650347i	$0.774624\pi$
$74$		0			0
$75$	−11.5416	−	6.66356i	−1.33271	−	0.769441i
$76$		0			0
$77$	−7.33858	+	4.81095i	−0.836309	+	0.548259i
$78$		0			0
$79$	10.3291	+	5.96351i	1.16211	+	0.670947i	0.951810	−	0.306689i	$-0.0992210\pi$
$79$	10.3291	+	5.96351i	1.16211	+	0.670947i	0.210305	+	0.977636i	$0.432554\pi$
$80$		0			0
$81$	1.12757	+	1.95301i	0.125286	+	0.217001i
$82$		0			0
$83$	−14.7639			−1.62054			−0.810272	−	0.586054i	$-0.800681\pi$
$83$	−14.7639			−1.62054			−0.810272	+	0.586054i	$0.800681\pi$
$84$		0			0
$85$			1.21370i			0.131644i
$86$		0			0
$87$	−7.28705	−	12.6215i	−0.781254	−	1.35317i
$88$		0			0
$89$	7.38527	+	4.26389i	0.782837	+	0.451971i	0.837435	−	0.546537i	$-0.184054\pi$
$89$	7.38527	+	4.26389i	0.782837	+	0.451971i	−0.0545977	+	0.998508i	$0.517388\pi$
$90$		0			0
$91$	−11.9357	−	0.425544i	−1.25120	−	0.0446091i
$92$		0			0
$93$	−6.92047	+	11.9866i	−0.717620	+	1.24295i
$94$		0			0
$95$	1.05109	−	0.606848i	0.107840	−	0.0622613i
$96$		0			0
$97$		−	9.15963i		−	0.930019i	−0.885306	−	0.465010i	$-0.846051\pi$
$97$		−	9.15963i		−	0.930019i	0.885306	−	0.465010i	$-0.153949\pi$
$98$		0			0
$99$	1.37564	+	14.8584i	0.138257	+	1.49333i
$100$		0			0
$101$	−6.69182	−	11.5906i	−0.665861	−	1.15330i	−0.979051	−	0.203614i	$-0.934731\pi$
$101$	−6.69182	−	11.5906i	−0.665861	−	1.15330i	0.313190	−	0.949690i	$-0.398602\pi$
$102$		0			0
$103$	−5.92284	−	3.41955i	−0.583594	−	0.336938i	0.178966	−	0.983855i	$-0.442725\pi$
$103$	−5.92284	−	3.41955i	−0.583594	−	0.336938i	−0.762561	+	0.646917i	$0.776058\pi$
$104$		0			0
$105$	2.64407	+	0.0942693i	0.258035	+	0.00919974i
$106$		0			0
$107$	9.65449	+	5.57402i	0.933335	+	0.538861i	0.887865	−	0.460105i	$-0.152188\pi$
$107$	9.65449	+	5.57402i	0.933335	+	0.538861i	0.0454701	+	0.998966i	$0.485521\pi$
$108$		0			0
$109$	9.65449	−	5.57402i	0.924732	−	0.533895i	0.0395907	−	0.999216i	$-0.487395\pi$
$109$	9.65449	−	5.57402i	0.924732	−	0.533895i	0.885142	+	0.465321i	$0.154061\pi$
$110$		0			0
$111$			1.67460i			0.158946i
$112$		0			0
$113$	8.84567			0.832131			0.416065	−	0.909335i	$-0.363409\pi$
$113$	8.84567			0.832131			0.416065	+	0.909335i	$0.363409\pi$
$114$		0			0
$115$	−1.61622	+	0.933127i	−0.150714	+	0.0870145i
$116$		0			0
$117$	−10.1549	+	17.5887i	−0.938817	+	1.62608i
$118$		0			0
$119$	4.12265	+	7.76727i	0.377923	+	0.712025i
$120$		0			0
$121$	3.65756	−	10.3741i	0.332506	−	0.943101i
$122$		0			0
$123$	10.7056	−	6.18087i	0.965290	−	0.557310i
$124$		0			0
$125$		−	3.60300i		−	0.322262i
$126$		0			0
$127$			7.03973i			0.624675i	0.949971	+	0.312337i	$0.101112\pi$
$127$			7.03973i			0.624675i	−0.949971	+	0.312337i	$0.898888\pi$
$128$		0			0
$129$	−9.63899	−	16.6952i	−0.848666	−	1.46993i
$130$		0			0
$131$	4.43475	−	7.68122i	0.387466	−	0.671111i	−0.604642	−	0.796498i	$-0.706684\pi$
$131$	4.43475	−	7.68122i	0.387466	−	0.671111i	0.992108	+	0.125386i	$0.0400170\pi$
$132$		0			0
$133$	4.66533	−	7.45396i	0.404536	−	0.646340i
$134$		0			0
$135$	0.749572	−	1.29830i	0.0645128	−	0.111740i
$136$		0			0
$137$	−4.28798	−	7.42700i	−0.366347	−	0.634532i	0.622644	−	0.782505i	$-0.286058\pi$
$137$	−4.28798	−	7.42700i	−0.366347	−	0.634532i	−0.988991	+	0.147973i	$0.952725\pi$
$138$		0			0
$139$	−12.8204			−1.08741			−0.543707	−	0.839275i	$-0.682980\pi$
$139$	−12.8204			−1.08741			−0.543707	+	0.839275i	$0.682980\pi$
$140$		0			0
$141$	1.59866			0.134631
$142$		0			0
$143$	12.2205	−	8.64926i	1.02193	−	0.723288i
$144$		0			0
$145$	0.971718	−	1.68307i	0.0806968	−	0.139771i
$146$		0			0
$147$	17.2414	−	8.37801i	1.42205	−	0.691007i
$148$		0			0
$149$	18.5879	+	10.7317i	1.52278	+	0.879176i	0.999637	+	0.0269298i	$0.00857307\pi$
$149$	18.5879	+	10.7317i	1.52278	+	0.879176i	0.523141	+	0.852246i	$0.324760\pi$
$150$		0			0
$151$	−1.05109	+	0.606848i	−0.0855367	+	0.0493846i	−0.542158	−	0.840276i	$-0.682393\pi$
$151$	−1.05109	+	0.606848i	−0.0855367	+	0.0493846i	0.456622	+	0.889661i	$0.349059\pi$
$152$		0			0
$153$	14.9536			1.20893
$154$		0			0
$155$	−1.84567			−0.148248
$156$		0			0
$157$	13.8949	−	8.02223i	1.10893	−	0.640243i	0.170381	−	0.985378i	$-0.445500\pi$
$157$	13.8949	−	8.02223i	1.10893	−	0.640243i	0.938553	+	0.345135i	$0.112167\pi$
$158$		0			0
$159$	32.5888	+	18.8152i	2.58446	+	1.49214i
$160$		0			0
$161$	−7.17370	+	11.4617i	−0.565367	+	0.903305i
$162$		0			0
$163$	9.61878	−	16.6602i	0.753401	−	1.30493i	−0.192764	−	0.981245i	$-0.561745\pi$
$163$	9.61878	−	16.6602i	0.753401	−	1.30493i	0.946165	−	0.323684i	$-0.104921\pi$
$164$		0			0
$165$	−2.70717	+	1.91604i	−0.210753	+	0.149164i
$166$		0			0
$167$	0.189746			0.0146830			0.00734151	−	0.999973i	$-0.497663\pi$
$167$	0.189746			0.0146830			0.00734151	+	0.999973i	$0.497663\pi$
$168$		0			0
$169$	7.37735			0.567489
$170$		0			0
$171$	−7.47680	−	12.9502i	−0.571765	−	0.990326i
$172$		0			0
$173$	−11.3008	+	19.5736i	−0.859185	+	1.48815i	0.0135217	+	0.999909i	$0.495696\pi$
$173$	−11.3008	+	19.5736i	−0.859185	+	1.48815i	−0.872707	+	0.488244i	$0.837638\pi$
$174$		0			0
$175$	−6.03658	−	11.3732i	−0.456322	−	0.859734i
$176$		0			0
$177$	−4.67090	+	8.09024i	−0.351086	+	0.608100i
$178$		0			0
$179$	3.44231	+	5.96226i	0.257290	+	0.445640i	0.965515	−	0.260347i	$-0.0838370\pi$
$179$	3.44231	+	5.96226i	0.257290	+	0.445640i	−0.708225	+	0.705987i	$0.750504\pi$
$180$		0			0
$181$		−	20.3397i		−	1.51184i	−0.654664	−	0.755920i	$-0.727190\pi$
$181$		−	20.3397i		−	1.51184i	0.654664	−	0.755920i	$-0.272810\pi$
$182$		0			0
$183$			31.3285i			2.31587i
$184$		0			0
$185$	−0.193388	+	0.111652i	−0.0142181	+	0.00820885i
$186$		0			0
$187$	−10.0139	−	4.60811i	−0.732291	−	0.336978i
$188$		0			0
$189$	0.387007	−	10.8548i	0.0281506	−	0.789571i
$190$		0			0
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$		0			0
$193$	22.4623	−	12.9686i	1.61687	−	0.933500i	0.629145	−	0.777288i	$-0.283405\pi$
$193$	22.4623	−	12.9686i	1.61687	−	0.933500i	0.987724	−	0.156212i	$-0.0499282\pi$
$194$		0			0
$195$	−4.51413			−0.323263
$196$		0			0
$197$		−	15.7067i		−	1.11906i	−0.828812	−	0.559528i	$-0.810983\pi$
$197$		−	15.7067i		−	1.11906i	0.828812	−	0.559528i	$-0.189017\pi$
$198$		0			0
$199$	−1.63099	+	0.941651i	−0.115618	+	0.0667519i	−0.556694	−	0.830718i	$-0.687930\pi$
$199$	−1.63099	+	0.941651i	−0.115618	+	0.0667519i	0.441076	+	0.897470i	$0.354597\pi$
$200$		0			0
$201$	−25.7903	−	14.8901i	−1.81911	−	1.05026i
$202$		0			0
$203$	0.501703	−	14.0718i	0.0352126	−	0.987646i
$204$		0			0
$205$	1.42757	+	0.824210i	0.0997061	+	0.0575653i
$206$		0			0
$207$	11.4968	+	19.9130i	0.799082	+	1.38405i
$208$		0			0
$209$	1.01623	+	10.9764i	0.0702938	+	0.759252i
$210$		0			0
$211$		−	11.5135i		−	0.792621i	−0.918117	−	0.396310i	$-0.870290\pi$
$211$		−	11.5135i		−	0.792621i	0.918117	−	0.396310i	$-0.129710\pi$
$212$		0			0
$213$	−22.2350	+	12.8374i	−1.52352	+	0.879603i
$214$		0			0
$215$	1.28535	−	2.22628i	0.0876598	−	0.151831i
$216$		0			0
$217$	−11.8117	+	6.26932i	−0.801831	+	0.425589i
$218$		0			0
$219$	7.43229	+	4.29104i	0.502228	+	0.289961i
$220$		0			0
$221$	−7.50170	−	12.9933i	−0.504619	−	0.874026i
$222$		0			0
$223$			0.120749i			0.00808595i	0.999992	+	0.00404298i	$0.00128692\pi$
$223$			0.120749i			0.00808595i	−0.999992	+	0.00404298i	$0.998713\pi$
$224$		0			0
$225$	−21.8958			−1.45972
$226$		0			0
$227$	−0.595236	−	1.03098i	−0.0395072	−	0.0684285i	0.845596	−	0.533824i	$-0.179245\pi$
$227$	−0.595236	−	1.03098i	−0.0395072	−	0.0684285i	−0.885103	+	0.465395i	$0.845912\pi$
$228$		0			0
$229$	−13.8401	−	7.99058i	−0.914579	−	0.528032i	−0.0326773	−	0.999466i	$-0.510403\pi$
$229$	−13.8401	−	7.99058i	−0.914579	−	0.528032i	−0.881902	+	0.471434i	$0.843737\pi$
$230$		0			0
$231$	−10.8167	+	21.4577i	−0.711686	+	1.41181i
$232$		0			0
$233$	−7.14767	−	4.12671i	−0.468260	−	0.270350i	0.247251	−	0.968951i	$-0.420473\pi$
$233$	−7.14767	−	4.12671i	−0.468260	−	0.270350i	−0.715511	+	0.698602i	$0.753806\pi$
$234$		0			0
$235$	0.106589	+	0.184618i	0.00695313	+	0.0120432i
$236$		0			0
$237$	32.6616			2.12160
$238$		0			0
$239$			2.89462i			0.187238i	0.995608	+	0.0936188i	$0.0298435\pi$
$239$			2.89462i			0.187238i	−0.995608	+	0.0936188i	$0.970157\pi$
$240$		0			0
$241$	−0.376482	−	0.652086i	−0.0242513	−	0.0420045i	0.853645	−	0.520855i	$-0.174387\pi$
$241$	−0.376482	−	0.652086i	−0.0242513	−	0.0420045i	−0.877896	+	0.478851i	$0.841054\pi$
$242$		0			0
$243$	16.0142	+	9.24581i	1.02731	+	0.593119i
$244$		0			0
$245$	2.11708	+	1.43250i	0.135255	+	0.0915190i
$246$		0			0
$247$	−7.50170	+	12.9933i	−0.477322	+	0.826746i
$248$		0			0
$249$	−35.0136	+	20.2151i	−2.21889	+	1.28108i
$250$		0			0
$251$			3.66515i			0.231342i	0.993288	+	0.115671i	$0.0369018\pi$
$251$			3.66515i			0.231342i	−0.993288	+	0.115671i	$0.963098\pi$
$252$		0			0
$253$	−1.56261	−	16.8779i	−0.0982404	−	1.06111i
$254$		0			0
$255$	1.66183	+	2.87837i	0.104068	+	0.180251i
$256$		0			0
$257$	−3.51220	−	2.02777i	−0.219085	−	0.126489i	0.386441	−	0.922314i	$-0.373704\pi$
$257$	−3.51220	−	2.02777i	−0.219085	−	0.126489i	−0.605527	+	0.795825i	$0.707037\pi$
$258$		0			0
$259$	−0.858363	+	1.37143i	−0.0533361	+	0.0852168i
$260$		0			0
$261$	−20.7366	−	11.9723i	−1.28356	−	0.741064i
$262$		0			0
$263$	7.88229	−	4.55084i	0.486043	−	0.280617i	−0.236888	−	0.971537i	$-0.576128\pi$
$263$	7.88229	−	4.55084i	0.486043	−	0.280617i	0.722931	+	0.690920i	$0.242794\pi$
$264$		0			0
$265$			5.01795i			0.308250i
$266$		0			0
$267$	23.3529			1.42918
$268$		0			0
$269$	5.64213	−	3.25748i	0.344006	−	0.198612i	−0.318036	−	0.948079i	$-0.603023\pi$
$269$	5.64213	−	3.25748i	0.344006	−	0.198612i	0.662042	+	0.749466i	$0.269690\pi$
$270$		0			0
$271$	−4.01376	+	6.95204i	−0.243819	+	0.422307i	−0.961799	−	0.273757i	$-0.911734\pi$
$271$	−4.01376	+	6.95204i	−0.243819	+	0.422307i	0.717980	+	0.696064i	$0.245067\pi$
$272$		0			0
$273$	−28.8890	+	15.3335i	−1.74844	+	0.928023i
$274$		0			0
$275$	14.6629	+	6.74741i	0.884204	+	0.406884i
$276$		0			0
$277$	1.84572	−	1.06562i	0.110898	−	0.0640272i	−0.443525	−	0.896262i	$-0.646272\pi$
$277$	1.84572	−	1.06562i	0.110898	−	0.0640272i	0.554423	+	0.832235i	$0.312939\pi$
$278$		0			0
$279$			22.7400i			1.36141i
$280$		0			0
$281$		−	4.54304i		−	0.271015i	−0.990776	−	0.135508i	$-0.956733\pi$
$281$		−	4.54304i		−	0.271015i	0.990776	−	0.135508i	$-0.0432665\pi$
$282$		0			0
$283$	15.9098	+	27.5566i	0.945741	+	1.63807i	0.754261	+	0.656574i	$0.227995\pi$
$283$	15.9098	+	27.5566i	0.945741	+	1.63807i	0.191479	+	0.981497i	$0.438672\pi$
$284$		0			0
$285$	1.66183	−	2.87837i	0.0984382	−	0.170500i
$286$		0			0
$287$	11.9357	+	0.425544i	0.704541	+	0.0251191i
$288$		0			0
$289$	2.97666	−	5.15572i	0.175097	−	0.303278i
$290$		0			0
$291$	−12.5416	−	21.7227i	−0.735203	−	1.27341i
$292$		0			0
$293$	−14.3263			−0.836954			−0.418477	−	0.908227i	$-0.637436\pi$
$293$	−14.3263			−0.836954			−0.418477	+	0.908227i	$0.637436\pi$
$294$		0			0
$295$	−1.24572			−0.0725284
$296$		0			0
$297$	7.86600	+	11.1139i	0.456432	+	0.644891i
$298$		0			0
$299$	11.5351	−	19.9793i	0.667090	−	1.15543i
$300$		0			0
$301$	0.663630	−	18.6135i	0.0382510	−	1.07287i
$302$		0			0
$303$	−31.7403	−	18.3253i	−1.82343	−	1.05276i
$304$		0			0
$305$	−3.61792	+	2.08880i	−0.207161	+	0.119605i
$306$		0			0
$307$	−25.9253			−1.47963			−0.739817	−	0.672808i	$-0.765088\pi$
$307$	−25.9253			−1.47963			−0.739817	+	0.672808i	$0.765088\pi$
$308$		0			0
$309$	−18.7286			−1.06543
$310$		0			0
$311$	−20.9162	+	12.0760i	−1.18605	+	0.684766i	−0.957406	−	0.288745i	$-0.906762\pi$
$311$	−20.9162	+	12.0760i	−1.18605	+	0.684766i	−0.228643	+	0.973510i	$0.573429\pi$
$312$		0			0
$313$	23.8345	+	13.7609i	1.34721	+	0.777810i	0.987853	−	0.155391i	$-0.0496638\pi$
$313$	23.8345	+	13.7609i	1.34721	+	0.777810i	0.359354	+	0.933201i	$0.382997\pi$
$314$		0			0
$315$	3.83952	−	2.03791i	0.216332	−	0.114823i
$316$		0			0
$317$	7.28798	−	12.6232i	0.409334	−	0.708987i	−0.585481	−	0.810686i	$-0.699094\pi$
$317$	7.28798	−	12.6232i	0.409334	−	0.708987i	0.994815	+	0.101699i	$0.0324278\pi$
$318$		0			0
$319$	10.1972	+	14.4076i	0.570934	+	0.806672i
$320$		0			0
$321$	30.5284			1.70393
$322$		0			0
$323$	11.0467			0.614654
$324$		0			0
$325$	10.9843	+	19.0254i	0.609302	+	1.05534i
$326$		0			0
$327$	15.2642	−	26.4384i	0.844113	−	1.46205i
$328$		0			0
$329$	1.30924	+	0.819439i	0.0721810	+	0.0451771i
$330$		0			0
$331$	−12.2414	+	21.2028i	−0.672850	+	1.16541i	0.304242	+	0.952595i	$0.401597\pi$
$331$	−12.2414	+	21.2028i	−0.672850	+	1.16541i	−0.977092	+	0.212816i	$0.931737\pi$
$332$		0			0
$333$	1.37564	+	2.38267i	0.0753845	+	0.130570i
$334$		0			0
$335$		−	3.97114i		−	0.216966i
$336$		0			0
$337$			4.14510i			0.225798i	0.993606	+	0.112899i	$0.0360137\pi$
$337$			4.14510i			0.225798i	−0.993606	+	0.112899i	$0.963986\pi$
$338$		0			0
$339$	20.9782	−	12.1117i	1.13938	−	0.657819i
$340$		0			0
$341$	7.00756	−	15.2282i	0.379481	−	0.824653i
$342$		0			0
$343$	18.4145	+	1.97630i	0.994290	+	0.106710i
$344$		0			0
$345$	−2.55533	+	4.42596i	−0.137574	+	0.238285i
$346$		0			0
$347$	−14.6535	+	8.46019i	−0.786640	+	0.454167i	−0.838778	−	0.544473i	$-0.816730\pi$
$347$	−14.6535	+	8.46019i	−0.786640	+	0.454167i	0.0521382	+	0.998640i	$0.483396\pi$
$348$		0			0
$349$	−19.0882			−1.02177			−0.510885	−	0.859649i	$-0.670682\pi$
$349$	−19.0882			−1.02177			−0.510885	+	0.859649i	$0.670682\pi$
$350$		0			0
$351$			18.5320i			0.989166i
$352$		0			0
$353$	−19.5015	+	11.2592i	−1.03796	+	0.599266i	−0.919255	−	0.393663i	$-0.871208\pi$
$353$	−19.5015	+	11.2592i	−1.03796	+	0.599266i	−0.118705	+	0.992930i	$0.537874\pi$
$354$		0			0
$355$	−2.96501	−	1.71185i	−0.157366	−	0.0908554i
$356$		0			0
$357$	20.4123	+	12.7758i	1.08034	+	0.676168i
$358$		0			0
$359$	−21.4247	−	12.3695i	−1.13075	−	0.652839i	−0.186627	−	0.982431i	$-0.559756\pi$
$359$	−21.4247	−	12.3695i	−1.13075	−	0.652839i	−0.944124	+	0.329591i	$0.893089\pi$
$360$		0			0
$361$	3.97666	+	6.88777i	0.209298	+	0.362514i
$362$		0			0
$363$	−5.53035	−	29.6110i	−0.290268	−	1.55417i
$364$		0			0
$365$			1.14441i			0.0599010i
$366$		0			0
$367$	6.50706	−	3.75685i	0.339666	−	0.196106i	−0.320458	−	0.947263i	$-0.603837\pi$
$367$	6.50706	−	3.75685i	0.339666	−	0.196106i	0.660124	+	0.751156i	$0.270504\pi$
$368$		0			0
$369$	10.1549	−	17.5887i	0.528641	−	0.915632i
$370$		0			0
$371$	17.0448	+	32.1133i	0.884923	+	1.66724i
$372$		0			0
$373$	−4.29253	−	2.47829i	−0.222259	−	0.128321i	0.384737	−	0.923026i	$-0.374292\pi$
$373$	−4.29253	−	2.47829i	−0.222259	−	0.128321i	−0.606996	+	0.794705i	$0.707625\pi$
$374$		0			0
$375$	−4.93333	−	8.54477i	−0.254756	−	0.441250i
$376$		0			0
$377$			24.0243i			1.23731i
$378$		0			0
$379$	−31.3080			−1.60818			−0.804091	−	0.594506i	$-0.797348\pi$
$379$	−31.3080			−1.60818			−0.804091	+	0.594506i	$0.797348\pi$
$380$		0			0
$381$	9.63899	+	16.6952i	0.493820	+	0.855322i
$382$		0			0
$383$	−14.1421	−	8.16495i	−0.722628	−	0.417210i	0.0930910	−	0.995658i	$-0.470325\pi$
$383$	−14.1421	−	8.16495i	−0.722628	−	0.417210i	−0.815719	+	0.578448i	$0.803659\pi$
$384$		0			0
$385$	−3.19920	+	0.181531i	−0.163046	+	0.00925167i
$386$		0			0
$387$	−27.4294	−	15.8364i	−1.39431	−	0.805008i
$388$		0			0
$389$	−8.74465	−	15.1462i	−0.443371	−	0.767942i	0.554566	−	0.832140i	$-0.312884\pi$
$389$	−8.74465	−	15.1462i	−0.443371	−	0.767942i	−0.997937	+	0.0641981i	$0.979551\pi$
$390$		0			0
$391$	−16.9861			−0.859022
$392$		0			0
$393$		−	24.2888i		−	1.22521i
$394$		0			0
$395$	2.17769	+	3.77187i	0.109571	+	0.189783i
$396$		0			0
$397$	19.3203	+	11.1546i	0.969658	+	0.559832i	0.899132	−	0.437678i	$-0.144199\pi$
$397$	19.3203	+	11.1546i	0.969658	+	0.559832i	0.0705261	+	0.997510i	$0.477532\pi$
$398$		0			0
$399$	0.858010	−	24.0655i	0.0429542	−	1.20478i
$400$		0			0
$401$	−15.4179	+	26.7046i	−0.769933	+	1.33356i	0.167665	+	0.985844i	$0.446377\pi$
$401$	−15.4179	+	26.7046i	−0.769933	+	1.33356i	−0.937599	+	0.347720i	$0.886956\pi$
$402$		0			0
$403$	19.7590	−	11.4079i	0.984265	−	0.568266i
$404$		0			0
$405$			0.823508i			0.0409204i
$406$		0			0
$407$	−0.186973	−	2.01951i	−0.00926789	−	0.100104i
$408$		0			0
$409$	14.6845	+	25.4343i	0.726101	+	1.25764i	0.958519	+	0.285028i	$0.0920028\pi$
$409$	14.6845	+	25.4343i	0.726101	+	1.25764i	−0.232418	+	0.972616i	$0.574664\pi$
$410$		0			0
$411$	−20.3385	−	11.7425i	−1.00323	−	0.579212i
$412$		0			0
$413$	−7.97219	+	4.23141i	−0.392286	+	0.208214i
$414$		0			0
$415$	−4.66901	−	2.69565i	−0.229193	−	0.132324i
$416$		0			0
$417$	−30.4046	+	17.5541i	−1.48892	+	0.859627i
$418$		0			0
$419$		−	35.2447i		−	1.72181i	−0.508762	−	0.860907i	$-0.669897\pi$
$419$		−	35.2447i		−	1.72181i	0.508762	−	0.860907i	$-0.330103\pi$
$420$		0			0
$421$	−9.47173			−0.461624			−0.230812	−	0.972998i	$-0.574138\pi$
$421$	−9.47173			−0.461624			−0.230812	+	0.972998i	$0.574138\pi$
$422$		0			0
$423$	2.27463	−	1.31326i	0.110596	−	0.0638527i
$424$		0			0
$425$	8.08754	−	14.0080i	0.392303	−	0.679489i
$426$		0			0
$427$	−16.0583	+	25.6569i	−0.777117	+	1.24163i
$428$		0			0
$429$	17.1390	−	37.2450i	0.827481	−	1.79821i
$430$		0			0
$431$	−22.9123	+	13.2284i	−1.10364	+	0.637189i	−0.937176	−	0.348857i	$-0.886570\pi$
$431$	−22.9123	+	13.2284i	−1.10364	+	0.637189i	−0.166469	+	0.986047i	$0.553236\pi$
$432$		0			0
$433$			23.5184i			1.13022i	0.825015	+	0.565110i	$0.191166\pi$
$433$			23.5184i			1.13022i	−0.825015	+	0.565110i	$0.808834\pi$
$434$		0			0
$435$		−	5.32202i		−	0.255171i
$436$		0			0
$437$	8.49303	+	14.7104i	0.406277	+	0.703692i
$438$		0			0
$439$	12.5862	−	21.7999i	0.600705	−	1.04045i	−0.392010	−	0.919961i	$-0.628220\pi$
$439$	12.5862	−	21.7999i	0.600705	−	1.04045i	0.992715	−	0.120490i	$-0.0384466\pi$
$440$		0			0
$441$	17.6494	−	26.0839i	0.840447	−	1.24209i
$442$		0			0
$443$	12.2936	−	21.2931i	0.584084	−	1.01166i	−0.410905	−	0.911678i	$-0.634787\pi$
$443$	12.2936	−	21.2931i	0.584084	−	1.01166i	0.994989	−	0.0999853i	$-0.0318796\pi$
$444$		0			0
$445$	1.55704	+	2.69687i	0.0738108	+	0.127844i
$446$		0			0
$447$	58.7767			2.78004
$448$		0			0
$449$	18.8474			0.889462			0.444731	−	0.895664i	$-0.353299\pi$
$449$	18.8474			0.889462			0.444731	+	0.895664i	$0.353299\pi$
$450$		0			0
$451$	−12.2205	+	8.64926i	−0.575442	+	0.407278i
$452$		0			0
$453$	−1.66183	+	2.87837i	−0.0780795	+	0.135238i
$454$		0			0
$455$	−3.69691	−	2.31385i	−0.173314	−	0.108475i
$456$		0			0
$457$	0.661101	+	0.381687i	0.0309250	+	0.0178546i	0.515383	−	0.856960i	$-0.327650\pi$
$457$	0.661101	+	0.381687i	0.0309250	+	0.0178546i	−0.484458	+	0.874815i	$0.660983\pi$
$458$		0			0
$459$	11.8167	−	6.82236i	0.551555	−	0.318441i
$460$		0			0
$461$	12.0034			0.559055			0.279527	−	0.960138i	$-0.409822\pi$
$461$	12.0034			0.559055			0.279527	+	0.960138i	$0.409822\pi$
$462$		0			0
$463$	22.8940			1.06398			0.531988	−	0.846752i	$-0.321445\pi$
$463$	22.8940			1.06398			0.531988	+	0.846752i	$0.321445\pi$
$464$		0			0
$465$	−4.37714	+	2.52714i	−0.202985	+	0.117193i
$466$		0			0
$467$	31.7736	+	18.3445i	1.47031	+	0.848883i	0.999445	−	0.0333234i	$-0.0106091\pi$
$467$	31.7736	+	18.3445i	1.47031	+	0.848883i	0.470863	+	0.882206i	$0.343942\pi$
$468$		0			0
$469$	−13.4890	−	25.4140i	−0.622866	−	1.17351i
$470$		0			0
$471$	21.9685	−	38.0506i	1.01226	−	1.75328i
$472$		0			0
$473$	13.4884	+	19.0578i	0.620198	+	0.876276i
$474$		0			0
$475$	−16.1751			−0.742163
$476$		0			0
$477$	61.8247			2.83076
$478$		0			0
$479$	6.72668	+	11.6510i	0.307350	+	0.532346i	0.977782	−	0.209625i	$-0.0672244\pi$
$479$	6.72668	+	11.6510i	0.307350	+	0.532346i	−0.670432	+	0.741971i	$0.733891\pi$
$480$		0			0
$481$	1.38022	−	2.39061i	0.0629326	−	0.109002i
$482$		0			0
$483$	−1.31933	+	37.0046i	−0.0600315	+	1.68377i
$484$		0			0
$485$	1.67241	−	2.89669i	0.0759401	−	0.131532i
$486$		0			0
$487$	15.2863	+	26.4766i	0.692687	+	1.19977i	0.970954	+	0.239265i	$0.0769066\pi$
$487$	15.2863	+	26.4766i	0.692687	+	1.19977i	−0.278267	+	0.960504i	$0.589760\pi$
$488$		0			0
$489$		−	52.6812i		−	2.38233i
$490$		0			0
$491$		−	40.4514i		−	1.82554i	−0.408469	−	0.912772i	$-0.633937\pi$
$491$		−	40.4514i		−	1.82554i	0.408469	−	0.912772i	$-0.366063\pi$
$492$		0			0
$493$	15.3187	−	8.84427i	0.689921	−	0.398326i
$494$		0			0
$495$	−2.27788	+	4.95009i	−0.102383	+	0.222490i
$496$		0			0
$497$	−24.7899	−	0.883835i	−1.11198	−	0.0396454i
$498$		0			0
$499$	−8.03061	+	13.9094i	−0.359500	+	0.622672i	−0.987877	−	0.155237i	$-0.950386\pi$
$499$	−8.03061	+	13.9094i	−0.359500	+	0.622672i	0.628378	+	0.777908i	$0.283719\pi$
$500$		0			0
$501$	0.449997	−	0.259806i	0.0201044	−	0.0116073i
$502$		0			0
$503$	22.2531			0.992219			0.496109	−	0.868260i	$-0.334762\pi$
$503$	22.2531			0.992219			0.496109	+	0.868260i	$0.334762\pi$
$504$		0			0
$505$		−	4.88729i		−	0.217482i
$506$		0			0
$507$	17.4959	−	10.1013i	0.777021	−	0.448613i
$508$		0			0
$509$	−22.4284	−	12.9490i	−0.994121	−	0.573956i	−0.0876175	−	0.996154i	$-0.527925\pi$
$509$	−22.4284	−	12.9490i	−0.994121	−	0.573956i	−0.906504	+	0.422198i	$0.861259\pi$
$510$		0			0
$511$	3.88729	+	7.32384i	0.171964	+	0.323988i
$512$		0			0
$513$	−11.8167	−	6.82236i	−0.521719	−	0.301215i
$514$		0			0
$515$	−1.24871	−	2.16284i	−0.0550249	−	0.0953060i
$516$		0			0
$517$	−1.92794	+	0.178494i	−0.0847906	+	0.00785016i
$518$		0			0
$519$			61.8936i			2.71683i
$520$		0			0
$521$	19.9066	−	11.4931i	0.872122	−	0.503520i	0.00406920	−	0.999992i	$-0.498705\pi$
$521$	19.9066	−	11.4931i	0.872122	−	0.503520i	0.868053	+	0.496472i	$0.165371\pi$
$522$		0			0
$523$	−9.49961	+	16.4538i	−0.415389	+	0.719475i	−0.995469	−	0.0950845i	$-0.969688\pi$
$523$	−9.49961	+	16.4538i	−0.415389	+	0.719475i	0.580080	+	0.814559i	$0.303021\pi$
$524$		0			0
$525$	−29.8887	−	18.7069i	−1.30445	−	0.816438i
$526$		0			0
$527$	−14.5481	−	8.39936i	−0.633726	−	0.365882i
$528$		0			0
$529$	−1.55939	−	2.70095i	−0.0677996	−	0.117432i
$530$		0			0
$531$			15.3481i			0.666051i
$532$		0			0
$533$	−20.3774			−0.882641
$534$		0			0
$535$	2.03546	+	3.52552i	0.0880007	+	0.152422i
$536$		0			0
$537$	16.3274	+	9.42662i	0.704579	+	0.406789i
$538$		0			0
$539$	−19.8573	+	12.0287i	−0.855313	+	0.518112i
$540$		0			0
$541$	−0.358135	−	0.206769i	−0.0153974	−	0.00888970i	0.492282	−	0.870436i	$-0.336163\pi$
$541$	−0.358135	−	0.206769i	−0.0153974	−	0.00888970i	−0.507679	+	0.861546i	$0.669496\pi$
$542$		0			0
$543$	−27.8497	−	48.2371i	−1.19515	−	2.07005i
$544$		0			0
$545$	4.07092			0.174379
$546$		0			0
$547$		−	1.64842i		−	0.0704814i	−0.999379	−	0.0352407i	$-0.988780\pi$
$547$		−	1.64842i		−	0.0704814i	0.999379	−	0.0352407i	$-0.0112198\pi$
$548$		0			0
$549$	25.7355	+	44.5753i	1.09837	+	1.90243i
$550$		0			0
$551$	−15.3187	−	8.84427i	−0.652600	−	0.376779i
$552$		0			0
$553$	26.7487	+	16.7417i	1.13747	+	0.711928i
$554$		0			0
$555$	−0.305755	+	0.529584i	−0.0129786	+	0.0224796i
$556$		0			0
$557$	28.0905	−	16.2181i	1.19023	−	0.687181i	0.231873	−	0.972746i	$-0.425515\pi$
$557$	28.0905	−	16.2181i	1.19023	−	0.687181i	0.958359	+	0.285565i	$0.0921812\pi$
$558$		0			0
$559$			31.7782i			1.34408i
$560$		0			0
$561$	−30.0583	+	2.78289i	−1.26906	+	0.117494i
$562$		0			0
$563$	−12.9781	−	22.4788i	−0.546964	−	0.947369i	−0.998480	−	0.0551062i	$-0.982450\pi$
$563$	−12.9781	−	22.4788i	−0.546964	−	0.947369i	0.451517	−	0.892263i	$-0.350883\pi$
$564$		0			0
$565$	2.79741	+	1.61508i	0.117688	+	0.0679471i
$566$		0			0
$567$	2.79727	+	5.27019i	0.117474	+	0.221327i
$568$		0			0
$569$	30.0464	+	17.3473i	1.25961	+	0.727237i	0.972999	−	0.230810i	$-0.0741374\pi$
$569$	30.0464	+	17.3473i	1.25961	+	0.727237i	0.286613	+	0.958047i	$0.407471\pi$
$570$		0			0
$571$	29.9681	−	17.3021i	1.25412	−	0.724069i	0.282199	−	0.959356i	$-0.408936\pi$
$571$	29.9681	−	17.3021i	1.25412	−	0.724069i	0.971926	+	0.235287i	$0.0756030\pi$
$572$		0			0
$573$			8.21537i			0.343202i
$574$		0			0
$575$	24.8718			1.03722
$576$		0			0
$577$	0.406054	−	0.234435i	0.0169042	−	0.00975966i	−0.491524	−	0.870864i	$-0.663560\pi$
$577$	0.406054	−	0.234435i	0.0169042	−	0.00975966i	0.508428	+	0.861104i	$0.330227\pi$
$578$		0			0
$579$	35.5139	−	61.5119i	1.47591	−	2.55635i
$580$		0			0
$581$	−39.0367	−	1.39178i	−1.61951	−	0.0577407i
$582$		0			0
$583$	−41.4019	−	19.0519i	−1.71469	−	0.789050i
$584$		0			0
$585$	−6.42286	+	3.70824i	−0.265553	+	0.153317i
$586$		0			0
$587$			44.9718i			1.85618i	0.372352	+	0.928091i	$0.378551\pi$
$587$			44.9718i			1.85618i	−0.372352	+	0.928091i	$0.621449\pi$
$588$		0			0
$589$			16.7987i			0.692179i
$590$		0			0
$591$	−21.5060	−	37.2496i	−0.884640	−	1.53224i
$592$		0			0
$593$	−7.75841	+	13.4380i	−0.318600	+	0.551831i	−0.980196	−	0.198029i	$-0.936546\pi$
$593$	−7.75841	+	13.4380i	−0.318600	+	0.551831i	0.661596	+	0.749860i	$0.269879\pi$
$594$		0			0
$595$	−0.114414	+	3.20910i	−0.00469053	+	0.131560i
$596$		0			0
$597$	−2.57867	+	4.46639i	−0.105538	+	0.182797i
$598$		0			0
$599$	−4.44231	−	7.69431i	−0.181508	−	0.314381i	0.760886	−	0.648885i	$-0.224764\pi$
$599$	−4.44231	−	7.69431i	−0.181508	−	0.314381i	−0.942394	+	0.334504i	$0.891431\pi$
$600$		0			0
$601$	10.2497			0.418095			0.209048	−	0.977905i	$-0.432964\pi$
$601$	10.2497			0.418095			0.209048	+	0.977905i	$0.432964\pi$
$602$		0			0
$603$	−48.9272			−1.99247
$604$		0			0
$605$	3.05084	−	2.61296i	0.124034	−	0.106232i
$606$		0			0
$607$	−21.5505	+	37.3266i	−0.874710	+	1.51504i	−0.0176380	+	0.999844i	$0.505615\pi$
$607$	−21.5505	+	37.3266i	−0.874710	+	1.51504i	−0.857072	+	0.515197i	$0.827719\pi$
$608$		0			0
$609$	−18.0777	−	34.0592i	−0.732544	−	1.38015i
$610$		0			0
$611$	−2.28220	−	1.31763i	−0.0923281	−	0.0533056i
$612$		0			0
$613$	12.0830	−	6.97610i	0.488026	−	0.281762i	−0.235729	−	0.971819i	$-0.575748\pi$
$613$	12.0830	−	6.97610i	0.488026	−	0.281762i	0.723755	+	0.690057i	$0.242415\pi$
$614$		0			0
$615$	4.51413			0.182027
$616$		0			0
$617$	−13.7915			−0.555226			−0.277613	−	0.960693i	$-0.589543\pi$
$617$	−13.7915			−0.555226			−0.277613	+	0.960693i	$0.589543\pi$
$618$		0			0
$619$	−30.0553	+	17.3524i	−1.20803	+	0.697454i	−0.962328	−	0.271893i	$-0.912350\pi$
$619$	−30.0553	+	17.3524i	−1.20803	+	0.697454i	−0.245698	+	0.969347i	$0.579017\pi$
$620$		0			0
$621$	18.1700	+	10.4905i	0.729139	+	0.420968i
$622$		0			0
$623$	19.1252	+	11.9702i	0.766236	+	0.479577i
$624$		0			0
$625$	−11.5088	+	19.9338i	−0.460351	+	0.797351i
$626$		0			0
$627$	17.4392	+	24.6398i	0.696455	+	0.984020i
$628$		0			0
$629$	−2.03245			−0.0810391
$630$		0			0
$631$	−10.9790			−0.437067			−0.218533	−	0.975829i	$-0.570127\pi$
$631$	−10.9790			−0.437067			−0.218533	+	0.975829i	$0.570127\pi$
$632$		0			0
$633$	−15.7646	−	27.3051i	−0.626586	−	1.08528i
$634$		0			0
$635$	−1.28535	+	2.22628i	−0.0510074	+	0.0883474i
$636$		0			0
$637$	−31.5187	−	2.25034i	−1.24881	−	0.0891616i
$638$		0			0
$639$	−21.0912	+	36.5310i	−0.834354	+	1.44514i
$640$		0			0
$641$	−6.85401	−	11.8715i	−0.270717	−	0.468896i	0.698329	−	0.715777i	$-0.253927\pi$
$641$	−6.85401	−	11.8715i	−0.270717	−	0.468896i	−0.969046	+	0.246882i	$0.920594\pi$
$642$		0			0
$643$		−	10.7909i		−	0.425553i	−0.977101	−	0.212777i	$-0.931749\pi$
$643$		−	10.7909i		−	0.425553i	0.977101	−	0.212777i	$-0.0682507\pi$
$644$		0			0
$645$		−	7.03973i		−	0.277189i
$646$		0			0
$647$	0.193388	−	0.111652i	0.00760286	−	0.00438951i	−0.496194	−	0.868212i	$-0.665269\pi$
$647$	0.193388	−	0.111652i	0.00760286	−	0.00438951i	0.503797	+	0.863822i	$0.331936\pi$
$648$		0			0
$649$	4.72968	−	10.2781i	0.185656	−	0.403451i
$650$		0			0
$651$	−19.4282	+	31.0411i	−0.761451	+	1.21660i
$652$		0			0
$653$	−11.8497	+	20.5243i	−0.463716	+	0.803180i	−0.999143	−	0.0414022i	$-0.986818\pi$
$653$	−11.8497	+	20.5243i	−0.463716	+	0.803180i	0.535427	+	0.844582i	$0.320151\pi$
$654$		0			0
$655$	2.80494	−	1.61944i	0.109598	−	0.0632766i
$656$		0			0
$657$	14.0999			0.550090
$658$		0			0
$659$			32.3521i			1.26026i	0.776490	+	0.630130i	$0.216998\pi$
$659$			32.3521i			1.26026i	−0.776490	+	0.630130i	$0.783002\pi$
$660$		0			0
$661$	−35.9690	+	20.7667i	−1.39903	+	0.807732i	−0.994291	−	0.106699i	$-0.965972\pi$
$661$	−35.9690	+	20.7667i	−1.39903	+	0.807732i	−0.404742	+	0.914431i	$0.632639\pi$
$662$		0			0
$663$	−35.5817	−	20.5431i	−1.38188	−	0.797827i
$664$		0			0
$665$	2.83637	−	1.50546i	0.109990	−	0.0583794i
$666$		0			0
$667$	23.5550	+	13.5995i	0.912054	+	0.526574i
$668$		0			0
$669$	0.165333	+	0.286365i	0.00639214	+	0.0110715i
$670$		0			0
$671$	−3.49790	−	37.7813i	−0.135035	−	1.45853i
$672$		0			0
$673$			24.8621i			0.958362i	0.877716	+	0.479181i	$0.159066\pi$
$673$			24.8621i			0.958362i	−0.877716	+	0.479181i	$0.840934\pi$
$674$		0			0
$675$	−17.3025	+	9.98962i	−0.665975	+	0.384501i
$676$		0			0
$677$	12.6335	−	21.8819i	0.485546	−	0.840990i	−0.514316	−	0.857601i	$-0.671954\pi$
$677$	12.6335	−	21.8819i	0.485546	−	0.840990i	0.999862	+	0.0166108i	$0.00528763\pi$
$678$		0			0
$679$	0.863472	−	24.2187i	0.0331370	−	0.929429i
$680$		0			0
$681$	−2.82329	−	1.63003i	−0.108189	−	0.0624628i
$682$		0			0
$683$	4.64769	+	8.05004i	0.177839	+	0.308026i	0.941140	−	0.338017i	$-0.109756\pi$
$683$	4.64769	+	8.05004i	0.177839	+	0.308026i	−0.763301	+	0.646043i	$0.776423\pi$
$684$		0			0
$685$		−	3.13168i		−	0.119655i
$686$		0			0
$687$	−43.7637			−1.66969
$688$		0			0
$689$	−31.0153	−	53.7201i	−1.18159	−	2.04657i
$690$		0			0
$691$	14.1609	+	8.17577i	0.538704	+	0.311021i	0.744554	−	0.667563i	$-0.232662\pi$
$691$	14.1609	+	8.17577i	0.538704	+	0.311021i	−0.205849	+	0.978584i	$0.565996\pi$
$692$		0			0
$693$	2.23659	+	39.4164i	0.0849610	+	1.49731i
$694$		0			0
$695$	−4.05440	−	2.34081i	−0.153792	−	0.0887920i
$696$		0			0
$697$	7.50170	+	12.9933i	0.284147	+	0.492157i
$698$		0			0
$699$	−22.6016			−0.854872
$700$		0			0
$701$			42.9480i			1.62213i	0.584959	+	0.811063i	$0.301110\pi$
$701$			42.9480i			1.62213i	−0.584959	+	0.811063i	$0.698890\pi$
$702$		0			0
$703$	1.01623	+	1.76015i	0.0383277	+	0.0663855i
$704$		0			0
$705$	0.505569	+	0.291890i	0.0190408	+	0.0109932i
$706$		0			0
$707$	−16.6010	−	31.2771i	−0.624345	−	1.17630i
$708$		0			0
$709$	−2.39812	+	4.15367i	−0.0900634	+	0.155994i	−0.907538	−	0.419971i	$-0.862040\pi$
$709$	−2.39812	+	4.15367i	−0.0900634	+	0.155994i	0.817474	+	0.575965i	$0.195374\pi$
$710$		0			0
$711$	46.4721	−	26.8307i	1.74284	−	1.00623i
$712$		0			0
$713$		−	25.8307i		−	0.967368i
$714$		0			0
$715$	5.44391	−	0.504013i	0.203591	−	0.0188490i
$716$		0			0
$717$	3.96340	+	6.86481i	0.148016	+	0.256371i
$718$		0			0
$719$	2.29184	+	1.32319i	0.0854711	+	0.0493468i	0.542126	−	0.840297i	$-0.317619\pi$
$719$	2.29184	+	1.32319i	0.0854711	+	0.0493468i	−0.456655	+	0.889644i	$0.650953\pi$
$720$		0			0
$721$	−15.3380	−	9.59988i	−0.571218	−	0.357518i
$722$		0			0
$723$	−1.78571	−	1.03098i	−0.0664112	−	0.0383425i
$724$		0			0
$725$	−22.4304	+	12.9502i	−0.833044	+	0.480958i
$726$		0			0
$727$			17.1118i			0.634642i	0.948318	+	0.317321i	$0.102783\pi$
$727$			17.1118i			0.634642i	−0.948318	+	0.317321i	$0.897217\pi$
$728$		0			0
$729$	43.8731			1.62493
$730$		0			0
$731$	20.2629	−	11.6988i	0.749452	−	0.432696i
$732$		0			0
$733$	6.17596	−	10.6971i	0.228114	−	0.395105i	−0.729135	−	0.684370i	$-0.760077\pi$
$733$	6.17596	−	10.6971i	0.228114	−	0.395105i	0.957249	+	0.289265i	$0.0934107\pi$
$734$		0			0
$735$	6.98223	+	0.498510i	0.257543	+	0.0183878i
$736$		0			0
$737$	32.7649	+	15.0774i	1.20691	+	0.555384i
$738$		0			0
$739$	17.4903	−	10.0980i	0.643390	−	0.371462i	−0.142529	−	0.989791i	$-0.545523\pi$
$739$	17.4903	−	10.0980i	0.643390	−	0.371462i	0.785919	+	0.618329i	$0.212190\pi$
$740$		0			0
$741$			41.0862i			1.50934i
$742$		0			0
$743$			9.44593i			0.346538i	0.984875	+	0.173269i	$0.0554330\pi$
$743$			9.44593i			0.346538i	−0.984875	+	0.173269i	$0.944567\pi$
$744$		0			0
$745$	3.91889	+	6.78772i	0.143577	+	0.248683i
$746$		0			0
$747$	−33.2123	+	57.5255i	−1.21518	+	2.10475i
$748$		0			0
$749$	25.0017	+	15.6482i	0.913542	+	0.571774i
$750$		0			0
$751$	0.592367	−	1.02601i	0.0216158	−	0.0374397i	−0.855015	−	0.518603i	$-0.826452\pi$
$751$	0.592367	−	1.02601i	0.0216158	−	0.0374397i	0.876631	+	0.481163i	$0.159786\pi$
$752$		0			0
$753$	5.01842	+	8.69216i	0.182881	+	0.316760i
$754$		0			0
$755$	−0.443205			−0.0161299
$756$		0			0
$757$	39.1275			1.42211			0.711057	−	0.703134i	$-0.248217\pi$
$757$	39.1275			1.42211			0.711057	+	0.703134i	$0.248217\pi$
$758$		0			0
$759$	−26.8156	−	37.8877i	−0.973344	−	1.37524i
$760$		0			0
$761$	−2.17769	+	3.77187i	−0.0789412	+	0.136730i	−0.902793	−	0.430075i	$-0.858487\pi$
$761$	−2.17769	+	3.77187i	−0.0789412	+	0.136730i	0.823852	+	0.566805i	$0.191821\pi$
$762$		0			0
$763$	26.0526	−	13.8280i	0.943168	−	0.500607i
$764$		0			0
$765$	4.72901	+	2.73030i	0.170978	+	0.0987141i
$766$		0			0
$767$	13.3361	−	7.69961i	0.481539	−	0.278017i
$768$		0			0
$769$	−21.5312			−0.776434			−0.388217	−	0.921568i	$-0.626909\pi$
$769$	−21.5312			−0.776434			−0.388217	+	0.921568i	$0.626909\pi$
$770$		0			0
$771$	−11.1059			−0.399970
$772$		0			0
$773$	7.31569	−	4.22372i	0.263127	−	0.151917i	−0.362633	−	0.931932i	$-0.618122\pi$
$773$	7.31569	−	4.22372i	0.263127	−	0.151917i	0.625760	+	0.780015i	$0.284789\pi$
$774$		0			0
$775$	21.3020	+	12.2987i	0.765191	+	0.441783i
$776$		0			0
$777$	−0.157863	+	4.42775i	−0.00566330	+	0.158845i
$778$		0			0
$779$	7.50170	−	12.9933i	0.268776	−	0.465534i
$780$		0			0
$781$	25.3815	−	17.9641i	0.908220	−	0.642807i
$782$		0			0
$783$	−21.8487			−0.780808
$784$		0			0
$785$	5.85894			0.209115
$786$		0			0
$787$	4.65351	+	8.06011i	0.165880	+	0.287312i	0.936967	−	0.349417i	$-0.113620\pi$
$787$	4.65351	+	8.06011i	0.165880	+	0.287312i	−0.771088	+	0.636729i	$0.780287\pi$
$788$		0			0
$789$	12.4623	−	21.5853i	0.443669	−	0.768457i
$790$		0			0
$791$	23.3886	+	0.833875i	0.831602	+	0.0296492i
$792$		0			0
$793$	25.8213	−	44.7237i	0.916940	−	1.58819i
$794$		0			0
$795$	6.87072	+	11.9004i	0.243679	+	0.422065i
$796$		0			0
$797$		−	13.1607i		−	0.466175i	−0.972456	−	0.233088i	$-0.925117\pi$
$797$		−	13.1607i		−	0.466175i	0.972456	−	0.233088i	$-0.0748829\pi$
$798$		0			0
$799$			1.94029i			0.0686424i
$800$		0			0
$801$	33.2274	−	19.1838i	1.17403	−	0.677828i
$802$		0			0
$803$	−9.44224	−	4.34504i	−0.333209	−	0.153333i
$804$		0			0
$805$	−4.36137	+	2.31489i	−0.153718	+	0.0815893i
$806$		0			0
$807$	8.92047	−	15.4507i	0.314016	−	0.543891i
$808$		0			0
$809$	−29.9081	+	17.2674i	−1.05151	+	0.607090i	−0.923072	−	0.384627i	$-0.874330\pi$
$809$	−29.9081	+	17.2674i	−1.05151	+	0.607090i	−0.128439	+	0.991717i	$0.540997\pi$
$810$		0			0
$811$	−14.6941			−0.515980			−0.257990	−	0.966148i	$-0.583060\pi$
$811$	−14.6941			−0.515980			−0.257990	+	0.966148i	$0.583060\pi$
$812$		0			0
$813$			21.9830i			0.770979i
$814$		0			0
$815$	6.08380	−	3.51248i	0.213106	−	0.123037i
$816$		0			0
$817$	−20.2629	−	11.6988i	−0.708910	−	0.409290i
$818$		0			0
$819$	−28.5082	+	45.5485i	−0.996158	+	1.59160i
$820$		0			0
$821$	−28.2742	−	16.3241i	−0.986777	−	0.569716i	−0.0824677	−	0.996594i	$-0.526280\pi$
$821$	−28.2742	−	16.3241i	−0.986777	−	0.569716i	−0.904309	+	0.426878i	$0.859613\pi$
$822$		0			0
$823$	−8.99507	−	15.5799i	−0.313548	−	0.543082i	0.665580	−	0.746327i	$-0.268184\pi$
$823$	−8.99507	−	15.5799i	−0.313548	−	0.543082i	−0.979128	+	0.203245i	$0.934851\pi$
$824$		0			0
$825$	44.0128	−	4.07484i	1.53233	−	0.141868i
$826$		0			0
$827$		−	46.5793i		−	1.61972i	−0.586623	−	0.809860i	$-0.699543\pi$
$827$		−	46.5793i		−	1.61972i	0.586623	−	0.809860i	$-0.300457\pi$
$828$		0			0
$829$	−22.4802	+	12.9789i	−0.780769	+	0.450777i	−0.836703	−	0.547657i	$-0.815520\pi$
$829$	−22.4802	+	12.9789i	−0.780769	+	0.450777i	0.0559338	+	0.998434i	$0.482186\pi$
$830$		0			0
$831$	2.91817	−	5.05441i	0.101230	−	0.175336i
$832$		0			0
$833$	10.1684	+	20.9259i	0.352313	+	0.725038i
$834$		0			0
$835$	0.0600065	+	0.0346448i	0.00207661	+	0.00119893i
$836$		0			0
$837$	10.3748	+	17.9696i	0.358605	+	0.621122i
$838$		0			0
$839$		−	16.9653i		−	0.585707i	−0.956157	−	0.292854i	$-0.905395\pi$
$839$		−	16.9653i		−	0.585707i	0.956157	−	0.292854i	$-0.0946049\pi$
$840$		0			0
$841$	0.676145			0.0233154
$842$		0			0
$843$	−6.22046	−	10.7742i	−0.214244	−	0.371082i
$844$		0			0
$845$	2.33306	+	1.34699i	0.0802596	+	0.0463379i
$846$		0			0
$847$	10.6488	−	27.0851i	0.365898	−	0.930655i
$848$		0			0
$849$	75.4626	+	43.5683i	2.58987	+	1.49526i
$850$		0			0
$851$	−1.56261	−	2.70652i	−0.0535656	−	0.0927783i
$852$		0			0
$853$	10.5342			0.360684			0.180342	−	0.983604i	$-0.442280\pi$
$853$	10.5342			0.360684			0.180342	+	0.983604i	$0.442280\pi$
$854$		0			0
$855$		−	5.46060i		−	0.186748i
$856$		0			0
$857$	−19.5122	−	33.7962i	−0.666525	−	1.15446i	−0.978869	−	0.204487i	$-0.934448\pi$
$857$	−19.5122	−	33.7962i	−0.666525	−	1.15446i	0.312344	−	0.949969i	$-0.398886\pi$
$858$		0			0
$859$	−7.84673	−	4.53031i	−0.267727	−	0.154572i	0.360127	−	0.932903i	$-0.382733\pi$
$859$	−7.84673	−	4.53031i	−0.267727	−	0.154572i	−0.627854	+	0.778331i	$0.716067\pi$
$860$		0			0
$861$	28.8890	−	15.3335i	0.984534	−	0.522563i
$862$		0			0
$863$	13.4590	−	23.3117i	0.458150	−	0.793540i	−0.540713	−	0.841207i	$-0.681845\pi$
$863$	13.4590	−	23.3117i	0.458150	−	0.793540i	0.998863	+	0.0476675i	$0.0151788\pi$
$864$		0			0
$865$	−7.14767	+	4.12671i	−0.243028	+	0.140312i
$866$		0			0
$867$		−	16.3029i		−	0.553675i
$868$		0			0
$869$	−39.3890	+	3.64675i	−1.33618	+	0.123708i
$870$		0			0
$871$	24.5451	+	42.5133i	0.831678	+	1.44051i
$872$		0			0
$873$	−35.6893	−	20.6052i	−1.20790	−	0.697382i
$874$		0			0
$875$	0.339652	−	9.52658i	0.0114823	−	0.322057i
$876$		0			0
$877$	−16.1411	−	9.31905i	−0.545045	−	0.314682i	0.202076	−	0.979370i	$-0.435231\pi$
$877$	−16.1411	−	9.31905i	−0.545045	−	0.314682i	−0.747121	+	0.664688i	$0.768564\pi$
$878$		0			0
$879$	−33.9760	+	19.6160i	−1.14598	+	0.661633i
$880$		0			0
$881$			17.4946i			0.589408i	0.955589	+	0.294704i	$0.0952211\pi$
$881$			17.4946i			0.589408i	−0.955589	+	0.294704i	$0.904779\pi$
$882$		0			0
$883$	27.8846			0.938392			0.469196	−	0.883094i	$-0.344544\pi$
$883$	27.8846			0.938392			0.469196	+	0.883094i	$0.344544\pi$
$884$		0			0
$885$	−2.95431	+	1.70567i	−0.0993079	+	0.0573355i
$886$		0			0
$887$	−16.3947	+	28.3964i	−0.550480	+	0.953459i	0.447760	+	0.894154i	$0.352222\pi$
$887$	−16.3947	+	28.3964i	−0.550480	+	0.953459i	−0.998240	+	0.0593050i	$0.981112\pi$
$888$		0			0
$889$	−0.663630	+	18.6135i	−0.0222574	+	0.624278i
$890$		0			0
$891$	−6.79458	−	3.12666i	−0.227627	−	0.104747i
$892$		0			0
$893$	1.68034	−	0.970143i	0.0562304	−	0.0324646i
$894$		0			0
$895$			2.51405i			0.0840355i
$896$		0			0
$897$		−	63.1766i		−	2.10940i
$898$		0			0
$899$	13.4495	+	23.2952i	0.448566	+	0.776939i
$900$		0			0
$901$	−22.8359	+	39.5529i	−0.760774	+	1.31770i
$902$		0			0
$903$	−23.9123	−	45.0520i	−0.795753	−	1.49924i
$904$		0			0
$905$	3.71372	−	6.43235i	0.123448	−	0.213819i
$906$		0			0
$907$	−3.27698	−	5.67589i	−0.108810	−	0.188465i	0.806478	−	0.591264i	$-0.201371\pi$
$907$	−3.27698	−	5.67589i	−0.108810	−	0.188465i	−0.915289	+	0.402799i	$0.868037\pi$
$908$		0			0
$909$	−60.2149			−1.99720
$910$		0			0
$911$	−32.4216			−1.07418			−0.537088	−	0.843526i	$-0.680476\pi$
$911$	−32.4216			−1.07418			−0.537088	+	0.843526i	$0.680476\pi$
$912$		0			0
$913$	39.9683	−	28.2882i	1.32276	−	0.936202i
$914$		0			0
$915$	−5.72010	+	9.90750i	−0.189101	+	0.327532i
$916$		0			0
$917$	12.4499	−	19.8916i	0.411132	−	0.656880i
$918$		0			0
$919$	5.04549	+	2.91301i	0.166435	+	0.0960915i	0.580904	−	0.813972i	$-0.302699\pi$
$919$	5.04549	+	2.91301i	0.166435	+	0.0960915i	−0.414469	+	0.910064i	$0.636033\pi$
$920$		0			0
$921$	−61.4837	+	35.4976i	−2.02596	+	1.16969i
$922$		0			0
$923$	42.3228			1.39307
$924$		0			0
$925$	2.97601			0.0978506
$926$		0			0
$927$	−26.6477	+	15.3850i	−0.875225	+	0.505311i
$928$		0			0
$929$	14.6675	+	8.46828i	0.481225	+	0.277835i	0.720927	−	0.693011i	$-0.243716\pi$
$929$	14.6675	+	8.46828i	0.481225	+	0.277835i	−0.239702	+	0.970847i	$0.577050\pi$
$930$		0			0
$931$	13.0382	−	19.2690i	0.427308	−	0.631516i
$932$		0			0
$933$	−33.0695	+	57.2781i	−1.08265	+	1.87520i
$934$		0			0
$935$	−2.32549	−	3.28569i	−0.0760518	−	0.107453i
$936$		0			0
$937$	8.52101			0.278369			0.139185	−	0.990266i	$-0.455552\pi$
$937$	8.52101			0.278369			0.139185	+	0.990266i	$0.455552\pi$
$938$		0			0
$939$	75.3671			2.45951
$940$		0			0
$941$	−2.94717	−	5.10465i	−0.0960751	−	0.166407i	0.813982	−	0.580891i	$-0.197296\pi$
$941$	−2.94717	−	5.10465i	−0.0960751	−	0.166407i	−0.910057	+	0.414484i	$0.863962\pi$
$942$		0			0
$943$	−11.5351	+	19.9793i	−0.375634	+	0.650617i
$944$		0			0
$945$	2.10431	−	3.36213i	0.0684532	−	0.109370i
$946$		0			0
$947$	−2.16363	+	3.74752i	−0.0703085	+	0.121778i	−0.899037	−	0.437874i	$-0.855732\pi$
$947$	−2.16363	+	3.74752i	−0.0703085	+	0.121778i	0.828728	+	0.559652i	$0.189065\pi$
$948$		0			0
$949$	−7.07343	−	12.2515i	−0.229613	−	0.397702i
$950$		0			0
$951$		−	39.9156i		−	1.29435i
$952$		0			0
$953$		−	42.1267i		−	1.36462i	−0.731064	−	0.682309i	$-0.760976\pi$
$953$		−	42.1267i		−	1.36462i	0.731064	−	0.682309i	$-0.239024\pi$
$954$		0			0
$955$	−0.948737	+	0.547754i	−0.0307004	+	0.0177249i
$956$		0			0
$957$	43.9107	+	20.2064i	1.41943	+	0.653180i
$958$		0			0
$959$	−10.6376	−	20.0417i	−0.343506	−	0.647182i
$960$		0			0
$961$	−2.72709	+	4.72345i	−0.0879705	+	0.152369i
$962$		0			0
$963$	43.4369	−	25.0783i	1.39974	−	0.808138i
$964$		0			0
$965$	9.47146			0.304897
$966$		0			0
$967$		−	3.74288i		−	0.120363i	−0.998187	−	0.0601815i	$-0.980832\pi$
$967$		−	3.74288i		−	0.120363i	0.998187	−	0.0601815i	$-0.0191680\pi$
$968$		0			0
$969$	26.1980	−	15.1254i	0.841602	−	0.485899i
$970$		0			0
$971$	33.7126	+	19.4640i	1.08189	+	0.624630i	0.931406	−	0.363983i	$-0.118583\pi$
$971$	33.7126	+	19.4640i	1.08189	+	0.624630i	0.150485	+	0.988612i	$0.451917\pi$
$972$		0			0
$973$	−33.8981	−	1.20857i	−1.08672	−	0.0387450i
$974$		0			0
$975$	52.1003	+	30.0801i	1.66855	+	0.963336i
$976$		0			0
$977$	−14.2664	−	24.7100i	−0.456421	−	0.790544i	0.542348	−	0.840154i	$-0.317536\pi$
$977$	−14.2664	−	24.7100i	−0.456421	−	0.790544i	−0.998769	+	0.0496097i	$0.984202\pi$
$978$		0			0
$979$	−28.1630	+	2.60741i	−0.900093	+	0.0833333i
$980$		0			0
$981$		−	50.1567i		−	1.60138i
$982$		0			0
$983$	19.0264	−	10.9849i	0.606848	−	0.350364i	−0.164883	−	0.986313i	$-0.552725\pi$
$983$	19.0264	−	10.9849i	0.606848	−	0.350364i	0.771731	+	0.635949i	$0.219391\pi$
$984$		0			0
$985$	2.86780	−	4.96717i	0.0913757	−	0.158267i
$986$		0			0
$987$	4.22697	+	0.150704i	0.134546	+	0.00479698i
$988$		0			0
$989$	31.1575	+	17.9888i	0.990751	+	0.572011i
$990$		0			0
$991$	−13.9739	−	24.2035i	−0.443895	−	0.768849i	0.554079	−	0.832464i	$-0.313070\pi$
$991$	−13.9739	−	24.2035i	−0.443895	−	0.768849i	−0.997975	+	0.0636148i	$0.979737\pi$
$992$		0			0
$993$			67.0453i			2.12762i
$994$		0			0
$995$	−0.687724			−0.0218023
$996$		0			0
$997$	22.7410	+	39.3886i	0.720215	+	1.24745i	0.960913	+	0.276849i	$0.0892903\pi$
$997$	22.7410	+	39.3886i	0.720215	+	1.24745i	−0.240698	+	0.970600i	$0.577376\pi$
$998$		0			0
$999$	2.17412	+	1.25523i	0.0687861	+	0.0397137i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.2.q.a.285.8	yes	16
3.2	odd	2		2772.2.cs.a.901.4		16
4.3	odd	2		1232.2.bn.c.593.1		16
7.2	even	3		2156.2.c.c.1077.15		16
7.3	odd	6	inner	308.2.q.a.241.7	✓	16
7.4	even	3		2156.2.q.c.2089.2		16
7.5	odd	6		2156.2.c.c.1077.1		16
7.6	odd	2		2156.2.q.c.901.1		16
11.10	odd	2	inner	308.2.q.a.285.7	yes	16
21.17	even	6		2772.2.cs.a.2089.3		16
28.3	even	6		1232.2.bn.c.241.2		16
33.32	even	2		2772.2.cs.a.901.3		16
44.43	even	2		1232.2.bn.c.593.2		16
77.10	even	6	inner	308.2.q.a.241.8	yes	16
77.32	odd	6		2156.2.q.c.2089.1		16
77.54	even	6		2156.2.c.c.1077.2		16
77.65	odd	6		2156.2.c.c.1077.16		16
77.76	even	2		2156.2.q.c.901.2		16
231.164	odd	6		2772.2.cs.a.2089.4		16
308.87	odd	6		1232.2.bn.c.241.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.q.a.241.7	✓	16	7.3	odd	6	inner
308.2.q.a.241.8	yes	16	77.10	even	6	inner
308.2.q.a.285.7	yes	16	11.10	odd	2	inner
308.2.q.a.285.8	yes	16	1.1	even	1	trivial
1232.2.bn.c.241.1		16	308.87	odd	6
1232.2.bn.c.241.2		16	28.3	even	6
1232.2.bn.c.593.1		16	4.3	odd	2
1232.2.bn.c.593.2		16	44.43	even	2
2156.2.c.c.1077.1		16	7.5	odd	6
2156.2.c.c.1077.2		16	77.54	even	6
2156.2.c.c.1077.15		16	7.2	even	3
2156.2.c.c.1077.16		16	77.65	odd	6
2156.2.q.c.901.1		16	7.6	odd	2
2156.2.q.c.901.2		16	77.76	even	2
2156.2.q.c.2089.1		16	77.32	odd	6
2156.2.q.c.2089.2		16	7.4	even	3
2772.2.cs.a.901.3		16	33.32	even	2
2772.2.cs.a.901.4		16	3.2	odd	2
2772.2.cs.a.2089.3		16	21.17	even	6
2772.2.cs.a.2089.4		16	231.164	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.37157 - 1.36923i) q^{3} +(0.316246 + 0.182585i) q^{5} +(2.64407 + 0.0942693i) q^{7} +(2.24957 - 3.89637i) q^{9} +O(q^{10})\)	\(q+(2.37157 - 1.36923i) q^{3} +(0.316246 + 0.182585i) q^{5} +(2.64407 + 0.0942693i) q^{7} +(2.24957 - 3.89637i) q^{9} +(-2.70717 + 1.91604i) q^{11} -4.51413 q^{13} +1.00000 q^{15} +(1.66183 + 2.87837i) q^{17} +(1.66183 - 2.87837i) q^{19} +(6.39968 - 3.39677i) q^{21} +(-2.55533 + 4.42596i) q^{23} +(-2.43333 - 4.21464i) q^{25} -4.10534i q^{27} -5.32202i q^{29} +(-4.37714 + 2.52714i) q^{31} +(-3.79676 + 8.25077i) q^{33} +(0.818964 + 0.512579i) q^{35} +(-0.305755 + 0.529584i) q^{37} +(-10.7056 + 6.18087i) q^{39} +4.51413 q^{41} -7.03973i q^{43} +(1.42284 - 0.821474i) q^{45} +(0.505569 + 0.291890i) q^{47} +(6.98223 + 0.498510i) q^{49} +(7.88229 + 4.55084i) q^{51} +(6.87072 + 11.9004i) q^{53} +(-1.20597 + 0.111652i) q^{55} -9.10169i q^{57} +(-2.95431 + 1.70567i) q^{59} +(-5.72010 + 9.90750i) q^{61} +(6.31534 - 10.0902i) q^{63} +(-1.42757 - 0.824210i) q^{65} +(-5.43739 - 9.41784i) q^{67} +13.9953i q^{69} -9.37564 q^{71} +(1.56695 + 2.71404i) q^{73} +(-11.5416 - 6.66356i) q^{75} +(-7.33858 + 4.81095i) q^{77} +(10.3291 + 5.96351i) q^{79} +(1.12757 + 1.95301i) q^{81} -14.7639 q^{83} +1.21370i q^{85} +(-7.28705 - 12.6215i) q^{87} +(7.38527 + 4.26389i) q^{89} +(-11.9357 - 0.425544i) q^{91} +(-6.92047 + 11.9866i) q^{93} +(1.05109 - 0.606848i) q^{95} -9.15963i q^{97} +(1.37564 + 14.8584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{5} + 4 q^{9}+O(q^{10}) \) 16 * q + 6 * q^5 + 4 * q^9	\( 16 q + 6 q^{5} + 4 q^{9} - q^{11} + 16 q^{15} - 2 q^{23} - 6 q^{25} - 12 q^{31} + 21 q^{33} + 2 q^{37} - 18 q^{45} - 12 q^{47} - 4 q^{49} + 8 q^{53} - 30 q^{59} - 18 q^{67} - 76 q^{71} + 6 q^{75} - 25 q^{77} - 8 q^{81} - 12 q^{89} + 6 q^{91} + 10 q^{93} - 52 q^{99}+O(q^{100}) \) 16 * q + 6 * q^5 + 4 * q^9 - q^11 + 16 * q^15 - 2 * q^23 - 6 * q^25 - 12 * q^31 + 21 * q^33 + 2 * q^37 - 18 * q^45 - 12 * q^47 - 4 * q^49 + 8 * q^53 - 30 * q^59 - 18 * q^67 - 76 * q^71 + 6 * q^75 - 25 * q^77 - 8 * q^81 - 12 * q^89 + 6 * q^91 + 10 * q^93 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more