LMFDB - Embedded newform 351.3.n.a.116.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,3,Mod(116,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("351.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	351.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.56405727905$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.15
Character	$\chi$	$=$	351.116
Dual form			351.3.n.a.233.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.245962 - 0.426018i) q^{2} +(1.87901 + 3.25453i) q^{4} +(-1.35391 - 2.34503i) q^{5} +(-8.51494 - 4.91611i) q^{7} +3.81635 q^{8} -1.33204 q^{10} +(7.77093 - 13.4596i) q^{11} +(-12.6433 + 3.02429i) q^{13} +(-4.18870 + 2.41835i) q^{14} +(-6.57735 + 11.3923i) q^{16} -22.4699i q^{17} -10.5454i q^{19} +(5.08800 - 8.81267i) q^{20} +(-3.82270 - 6.62112i) q^{22} +(-2.18641 + 1.26233i) q^{23} +(8.83387 - 15.3007i) q^{25} +(-1.82137 + 6.13015i) q^{26} -36.9496i q^{28} +(-2.12707 - 1.22806i) q^{29} +(32.9508 - 19.0241i) q^{31} +(10.8683 + 18.8244i) q^{32} +(-9.57260 - 5.52674i) q^{34} +26.6238i q^{35} +10.3786i q^{37} +(-4.49252 - 2.59376i) q^{38} +(-5.16698 - 8.94947i) q^{40} +(-36.5879 - 63.3720i) q^{41} +(-22.9633 + 39.7736i) q^{43} +58.4065 q^{44} +1.24194i q^{46} +(-13.6798 + 23.6942i) q^{47} +(23.8362 + 41.2855i) q^{49} +(-4.34559 - 7.52679i) q^{50} +(-33.5995 - 35.4655i) q^{52} +0.0370030i q^{53} -42.0844 q^{55} +(-32.4960 - 18.7616i) q^{56} +(-1.04636 + 0.604114i) q^{58} +(-32.9332 - 57.0420i) q^{59} +(40.6820 - 70.4633i) q^{61} -18.7168i q^{62} -41.9261 q^{64} +(24.2099 + 25.5544i) q^{65} +(-56.2009 + 32.4476i) q^{67} +(73.1291 - 42.2211i) q^{68} +(11.3422 + 6.54843i) q^{70} +29.5878 q^{71} +28.3208i q^{73} +(4.42149 + 2.55275i) q^{74} +(34.3203 - 19.8148i) q^{76} +(-132.338 + 76.4054i) q^{77} +(-36.3943 + 63.0368i) q^{79} +35.6204 q^{80} -35.9969 q^{82} +(-71.9367 + 124.598i) q^{83} +(-52.6927 + 30.4222i) q^{85} +(11.2962 + 19.5656i) q^{86} +(29.6566 - 51.3667i) q^{88} +80.5846 q^{89} +(122.525 + 36.4043i) q^{91} +(-8.21657 - 4.74384i) q^{92} +(6.72944 + 11.6557i) q^{94} +(-24.7293 + 14.2775i) q^{95} +(97.7027 + 56.4087i) q^{97} +23.4512 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 50 q^{4} + 8 q^{10} - 6 q^{13} + 6 q^{14} - 90 q^{16} + 14 q^{22} - 138 q^{23} - 92 q^{25} - 48 q^{29} - 324 q^{38} - 68 q^{40} + 62 q^{43} + 70 q^{49} - 4 q^{52} + 92 q^{55} + 276 q^{56} + 12 q^{61}+ \cdots - 504 q^{95}+O(q^{100}) $ 52 * q - 50 * q^4 + 8 * q^10 - 6 * q^13 + 6 * q^14 - 90 * q^16 + 14 * q^22 - 138 * q^23 - 92 * q^25 - 48 * q^29 - 324 * q^38 - 68 * q^40 + 62 * q^43 + 70 * q^49 - 4 * q^52 + 92 * q^55 + 276 * q^56 + 12 * q^61 + 12 * q^64 + 588 * q^65 + 144 * q^68 - 342 * q^74 + 510 * q^77 - 24 * q^79 - 292 * q^82 - 62 * q^88 + 264 * q^91 + 396 * q^92 - 160 * q^94 - 504 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.245962	−	0.426018i	0.122981	−	0.213009i	−0.797961	−	0.602709i	$-0.794088\pi$
$2$	0.245962	−	0.426018i	0.122981	−	0.213009i	0.920942	+	0.389700i	$0.127421\pi$
$3$		0			0
$3$		0			0
$4$	1.87901	+	3.25453i	0.469751	+	0.813633i
$5$	−1.35391	−	2.34503i	−0.270781	−	0.469007i	0.698281	−	0.715824i	$-0.253949\pi$
$5$	−1.35391	−	2.34503i	−0.270781	−	0.469007i	−0.969062	+	0.246817i	$0.920615\pi$
$6$		0			0
$7$	−8.51494	−	4.91611i	−1.21642	−	0.702301i	−0.252270	−	0.967657i	$-0.581177\pi$
$7$	−8.51494	−	4.91611i	−1.21642	−	0.702301i	−0.964150	+	0.265356i	$0.914510\pi$
$8$	3.81635			0.477044
$9$		0			0
$10$	−1.33204			−0.133204
$11$	7.77093	−	13.4596i	0.706448	−	1.22360i	−0.259718	−	0.965684i	$-0.583630\pi$
$11$	7.77093	−	13.4596i	0.706448	−	1.22360i	0.966166	−	0.257920i	$-0.0830370\pi$
$12$		0			0
$13$	−12.6433	+	3.02429i	−0.972564	+	0.232637i
$13$	−12.6433	+	3.02429i	−0.972564	+	0.232637i
$14$	−4.18870	+	2.41835i	−0.299193	+	0.172739i
$15$		0			0
$16$	−6.57735	+	11.3923i	−0.411084	+	0.712019i
$17$		−	22.4699i		−	1.32176i	−0.750492	−	0.660880i	$-0.770183\pi$
$17$		−	22.4699i		−	1.32176i	0.750492	−	0.660880i	$-0.229817\pi$
$18$		0			0
$19$		−	10.5454i		−	0.555020i	−0.960723	−	0.277510i	$-0.910491\pi$
$19$		−	10.5454i		−	0.555020i	0.960723	−	0.277510i	$-0.0895091\pi$
$20$	5.08800	−	8.81267i	0.254400	−	0.440633i
$21$		0			0
$22$	−3.82270	−	6.62112i	−0.173759	−	0.300960i
$23$	−2.18641	+	1.26233i	−0.0950615	+	0.0548838i	−0.546777	−	0.837278i	$-0.684146\pi$
$23$	−2.18641	+	1.26233i	−0.0950615	+	0.0548838i	0.451716	+	0.892162i	$0.350812\pi$
$24$		0			0
$25$	8.83387	−	15.3007i	0.353355	−	0.612029i
$26$	−1.82137	+	6.13015i	−0.0700528	+	0.235775i
$27$		0			0
$28$		−	36.9496i		−	1.31963i
$29$	−2.12707	−	1.22806i	−0.0733472	−	0.0423470i	0.462878	−	0.886422i	$-0.346817\pi$
$29$	−2.12707	−	1.22806i	−0.0733472	−	0.0423470i	−0.536225	+	0.844075i	$0.680150\pi$
$30$		0			0
$31$	32.9508	−	19.0241i	1.06293	−	0.613682i	0.136687	−	0.990614i	$-0.456354\pi$
$31$	32.9508	−	19.0241i	1.06293	−	0.613682i	0.926241	+	0.376933i	$0.123021\pi$
$32$	10.8683	+	18.8244i	0.339633	+	0.588261i
$33$		0			0
$34$	−9.57260	−	5.52674i	−0.281547	−	0.162551i
$35$			26.6238i			0.760680i
$36$		0			0
$37$			10.3786i			0.280504i	0.990116	+	0.140252i	$0.0447912\pi$
$37$			10.3786i			0.280504i	−0.990116	+	0.140252i	$0.955209\pi$
$38$	−4.49252	−	2.59376i	−0.118224	−	0.0682568i
$39$		0			0
$40$	−5.16698	−	8.94947i	−0.129174	−	0.223737i
$41$	−36.5879	−	63.3720i	−0.892387	−	1.54566i	−0.837006	−	0.547194i	$-0.815696\pi$
$41$	−36.5879	−	63.3720i	−0.892387	−	1.54566i	−0.0553805	−	0.998465i	$-0.517637\pi$
$42$		0			0
$43$	−22.9633	+	39.7736i	−0.534030	+	0.924967i	0.465180	+	0.885216i	$0.345990\pi$
$43$	−22.9633	+	39.7736i	−0.534030	+	0.924967i	−0.999210	+	0.0397508i	$0.987344\pi$
$44$	58.4065			1.32742
$45$		0			0
$46$			1.24194i			0.0269986i
$47$	−13.6798	+	23.6942i	−0.291060	+	0.504132i	−0.974061	−	0.226287i	$-0.927341\pi$
$47$	−13.6798	+	23.6942i	−0.291060	+	0.504132i	0.683000	+	0.730418i	$0.260675\pi$
$48$		0			0
$49$	23.8362	+	41.2855i	0.486453	+	0.842561i
$50$	−4.34559	−	7.52679i	−0.0869118	−	0.150536i
$51$		0			0
$52$	−33.5995	−	35.4655i	−0.646145	−	0.682028i
$53$			0.0370030i			0.000698170i	1.00000		0.000349085i	$0.000111117\pi$
$53$			0.0370030i			0.000698170i	−1.00000		0.000349085i	$0.999889\pi$
$54$		0			0
$55$	−42.0844			−0.765172
$56$	−32.4960	−	18.7616i	−0.580286	−	0.335028i
$57$		0			0
$58$	−1.04636	+	0.604114i	−0.0180406	+	0.0104158i
$59$	−32.9332	−	57.0420i	−0.558190	−	0.966814i	−0.997648	−	0.0685502i	$-0.978163\pi$
$59$	−32.9332	−	57.0420i	−0.558190	−	0.966814i	0.439458	−	0.898263i	$-0.355171\pi$
$60$		0			0
$61$	40.6820	−	70.4633i	0.666918	−	1.15514i	−0.311843	−	0.950134i	$-0.600946\pi$
$61$	40.6820	−	70.4633i	0.666918	−	1.15514i	0.978761	−	0.205003i	$-0.0657204\pi$
$62$		−	18.7168i		−	0.301885i
$63$		0			0
$64$	−41.9261			−0.655095
$65$	24.2099	+	25.5544i	0.372461	+	0.393145i
$66$		0			0
$67$	−56.2009	+	32.4476i	−0.838819	+	0.484293i	−0.856863	−	0.515545i	$-0.827590\pi$
$67$	−56.2009	+	32.4476i	−0.838819	+	0.484293i	0.0180434	+	0.999837i	$0.494256\pi$
$68$	73.1291	−	42.2211i	1.07543	−	0.620899i
$69$		0			0
$70$	11.3422	+	6.54843i	0.162032	+	0.0935491i
$71$	29.5878			0.416730			0.208365	−	0.978051i	$-0.433186\pi$
$71$	29.5878			0.416730			0.208365	+	0.978051i	$0.433186\pi$
$72$		0			0
$73$			28.3208i			0.387956i	0.981006	+	0.193978i	$0.0621390\pi$
$73$			28.3208i			0.387956i	−0.981006	+	0.193978i	$0.937861\pi$
$74$	4.42149	+	2.55275i	0.0597498	+	0.0344966i
$75$		0			0
$76$	34.3203	−	19.8148i	0.451583	−	0.260721i
$77$	−132.338	+	76.4054i	−1.71868	+	0.992278i
$78$		0			0
$79$	−36.3943	+	63.0368i	−0.460688	+	0.797935i	−0.998995	−	0.0448138i	$-0.985731\pi$
$79$	−36.3943	+	63.0368i	−0.460688	+	0.797935i	0.538308	+	0.842748i	$0.319064\pi$
$80$	35.6204			0.445256
$81$		0			0
$82$	−35.9969			−0.438986
$83$	−71.9367	+	124.598i	−0.866708	+	1.50118i	−0.00136586	+	0.999999i	$0.500435\pi$
$83$	−71.9367	+	124.598i	−0.866708	+	1.50118i	−0.865342	+	0.501182i	$0.832899\pi$
$84$		0			0
$85$	−52.6927	+	30.4222i	−0.619915	+	0.357908i
$86$	11.2962	+	19.5656i	0.131351	+	0.227507i
$87$		0			0
$88$	29.6566	−	51.3667i	0.337007	−	0.583713i
$89$	80.5846			0.905445			0.452722	−	0.891652i	$-0.350453\pi$
$89$	80.5846			0.905445			0.452722	+	0.891652i	$0.350453\pi$
$90$		0			0
$91$	122.525	+	36.4043i	1.34643	+	0.400047i
$92$	−8.21657	−	4.74384i	−0.0893105	−	0.0515635i
$93$		0			0
$94$	6.72944	+	11.6557i	0.0715898	+	0.123997i
$95$	−24.7293	+	14.2775i	−0.260308	+	0.150289i
$96$		0			0
$97$	97.7027	+	56.4087i	1.00724	+	0.581533i	0.910384	−	0.413765i	$-0.135787\pi$
$97$	97.7027	+	56.4087i	1.00724	+	0.581533i	0.0968606	+	0.995298i	$0.469120\pi$
$98$	23.4512			0.239298
$99$		0			0
$100$	66.3956			0.663956
$101$	171.233	+	98.8613i	1.69538	+	0.978825i	0.950036	+	0.312139i	$0.101046\pi$
$101$	171.233	+	98.8613i	1.69538	+	0.978825i	0.745339	+	0.666686i	$0.232288\pi$
$102$		0			0
$103$	10.9095	+	18.8959i	0.105918	+	0.183455i	0.914113	−	0.405460i	$-0.132889\pi$
$103$	10.9095	+	18.8959i	0.105918	+	0.183455i	−0.808195	+	0.588915i	$0.799555\pi$
$104$	−48.2513	+	11.5417i	−0.463955	+	0.110978i
$105$		0			0
$106$	0.0157640	+	0.00910133i	0.000148717	+	8.58616e-5i
$107$		−	180.007i		−	1.68231i	−0.540796	−	0.841154i	$-0.681877\pi$
$107$		−	180.007i		−	1.68231i	0.540796	−	0.841154i	$-0.318123\pi$
$108$		0			0
$109$			117.078i			1.07411i	0.843548	+	0.537055i	$0.180463\pi$
$109$			117.078i			1.07411i	−0.843548	+	0.537055i	$0.819537\pi$
$110$	−10.3512	+	17.9287i	−0.0941015	+	0.162989i
$111$		0			0
$112$	112.011	−	64.6699i	1.00010	−	0.577409i
$113$	59.6664	−	34.4484i	0.528021	−	0.304853i	−0.212189	−	0.977229i	$-0.568059\pi$
$113$	59.6664	−	34.4484i	0.528021	−	0.304853i	0.740210	+	0.672375i	$0.234726\pi$
$114$		0			0
$115$	5.92040	+	3.41815i	0.0514818	+	0.0297230i
$116$		−	9.23016i		−	0.0795703i
$117$		0			0
$118$	−32.4013			−0.274587
$119$	−110.464	+	191.330i	−0.928273	+	1.60782i
$120$		0			0
$121$	−60.2747	−	104.399i	−0.498138	−	0.862801i
$122$	−20.0124	−	34.6626i	−0.164036	−	0.284119i
$123$		0			0
$124$	123.829	+	71.4929i	0.998624	+	0.576556i
$125$	−115.536			−0.924290
$126$		0			0
$127$	70.8862			0.558159			0.279080	−	0.960268i	$-0.409971\pi$
$127$	70.8862			0.558159			0.279080	+	0.960268i	$0.409971\pi$
$128$	−53.7852	+	93.1587i	−0.420197	+	0.727803i
$129$		0			0
$130$	16.8414	−	4.02846i	0.129549	−	0.0309882i
$131$	127.088	−	73.3745i	0.970140	−	0.560111i	0.0708610	−	0.997486i	$-0.477425\pi$
$131$	127.088	−	73.3745i	0.970140	−	0.560111i	0.899279	+	0.437376i	$0.144092\pi$
$132$		0			0
$133$	−51.8422	+	89.7933i	−0.389791	+	0.675137i
$134$			31.9235i			0.238235i
$135$		0			0
$136$		−	85.7531i		−	0.630537i
$137$	−34.9983	+	60.6188i	−0.255462	+	0.442473i	−0.965021	−	0.262173i	$-0.915561\pi$
$137$	−34.9983	+	60.6188i	−0.255462	+	0.442473i	0.709559	+	0.704646i	$0.248894\pi$
$138$		0			0
$139$	−76.5741	−	132.630i	−0.550892	−	0.954174i	−0.998210	−	0.0597988i	$-0.980954\pi$
$139$	−76.5741	−	132.630i	−0.550892	−	0.954174i	0.447318	−	0.894375i	$-0.352379\pi$
$140$	−86.6480	+	50.0262i	−0.618914	+	0.357330i
$141$		0			0
$142$	7.27747	−	12.6049i	0.0512498	−	0.0887672i
$143$	−57.5446	+	193.676i	−0.402410	+	1.35438i
$144$		0			0
$145$			6.65074i			0.0458672i
$146$	12.0652	+	6.96583i	0.0826382	+	0.0477112i
$147$		0			0
$148$	−33.7776	+	19.5015i	−0.228227	+	0.131767i
$149$	−16.2539	−	28.1526i	−0.109087	−	0.188944i	0.806314	−	0.591488i	$-0.201459\pi$
$149$	−16.2539	−	28.1526i	−0.109087	−	0.188944i	−0.915400	+	0.402544i	$0.868126\pi$
$150$		0			0
$151$	−29.5608	−	17.0670i	−0.195767	−	0.113026i	0.398912	−	0.916989i	$-0.369388\pi$
$151$	−29.5608	−	17.0670i	−0.195767	−	0.113026i	−0.594680	+	0.803963i	$0.702721\pi$
$152$		−	40.2448i		−	0.264769i
$153$		0			0
$154$			75.1713i			0.488125i
$155$	−89.2245	−	51.5138i	−0.575642	−	0.332347i
$156$		0			0
$157$	110.354	+	191.138i	0.702889	+	1.21744i	0.967448	+	0.253070i	$0.0814401\pi$
$157$	110.354	+	191.138i	0.702889	+	1.21744i	−0.264559	+	0.964369i	$0.585227\pi$
$158$	17.9032	+	31.0093i	0.113312	+	0.196261i
$159$		0			0
$160$	29.4292	−	50.9728i	0.183932	−	0.318580i
$161$	24.8229			0.154180
$162$		0			0
$163$		−	42.5714i		−	0.261174i	−0.991437	−	0.130587i	$-0.958314\pi$
$163$		−	42.5714i		−	0.261174i	0.991437	−	0.130587i	$-0.0416862\pi$
$164$	137.498	−	238.153i	0.838400	−	1.45215i
$165$		0			0
$166$	35.3874	+	61.2927i	0.213177	+	0.369233i
$167$	−103.978	−	180.096i	−0.622624	−	1.07842i	−0.988995	−	0.147948i	$-0.952733\pi$
$167$	−103.978	−	180.096i	−0.622624	−	1.07842i	0.366371	−	0.930469i	$-0.380600\pi$
$168$		0			0
$169$	150.707	−	76.4741i	0.891760	−	0.452509i
$170$			29.9308i			0.176063i
$171$		0			0
$172$	−172.593			−1.00345
$173$	−47.0331	−	27.1546i	−0.271867	−	0.156963i	0.357869	−	0.933772i	$-0.383504\pi$
$173$	−47.0331	−	27.1546i	−0.271867	−	0.156963i	−0.629736	+	0.776809i	$0.716837\pi$
$174$		0			0
$175$	−150.440	+	86.8565i	−0.859657	+	0.496323i
$176$	102.224	+	177.058i	0.580819	+	1.00601i
$177$		0			0
$178$	19.8207	−	34.3305i	0.111352	−	0.192868i
$179$			82.5470i			0.461156i	0.973054	+	0.230578i	$0.0740617\pi$
$179$			82.5470i			0.461156i	−0.973054	+	0.230578i	$0.925938\pi$
$180$		0			0
$181$	166.981			0.922544			0.461272	−	0.887259i	$-0.347393\pi$
$181$	166.981			0.922544			0.461272	+	0.887259i	$0.347393\pi$
$182$	45.6453	−	43.2438i	0.250799	−	0.237603i
$183$		0			0
$184$	−8.34412	+	4.81748i	−0.0453485	+	0.0261820i
$185$	24.3383	−	14.0517i	0.131558	−	0.0759551i
$186$		0			0
$187$	−302.437	−	174.612i	−1.61731	−	0.933755i
$188$	−102.818			−0.546904
$189$		0			0
$190$			14.0468i			0.0739307i
$191$	−61.1253	−	35.2907i	−0.320028	−	0.184768i	0.331377	−	0.943498i	$-0.392487\pi$
$191$	−61.1253	−	35.2907i	−0.320028	−	0.184768i	−0.651405	+	0.758730i	$0.725820\pi$
$192$		0			0
$193$	40.4093	−	23.3303i	0.209375	−	0.120883i	−0.391646	−	0.920116i	$-0.628094\pi$
$193$	40.4093	−	23.3303i	0.209375	−	0.120883i	0.601021	+	0.799233i	$0.294761\pi$
$194$	48.0623	−	27.7488i	0.247744	−	0.143035i
$195$		0			0
$196$	−89.5766	+	155.151i	−0.457024	+	0.791588i
$197$	194.423			0.986919			0.493460	−	0.869769i	$-0.335732\pi$
$197$	194.423			0.986919			0.493460	+	0.869769i	$0.335732\pi$
$198$		0			0
$199$	−22.2689			−0.111904			−0.0559520	−	0.998433i	$-0.517819\pi$
$199$	−22.2689			−0.111904			−0.0559520	+	0.998433i	$0.517819\pi$
$200$	33.7131	−	58.3929i	0.168566	−	0.291964i
$201$		0			0
$202$	84.2335	−	48.6322i	0.416998	−	0.240754i
$203$	12.0746	+	20.9138i	0.0594807	+	0.103024i
$204$		0			0
$205$	−99.0731	+	171.600i	−0.483283	+	0.837071i
$206$	10.7333			0.0521034
$207$		0			0
$208$	48.7059	−	163.928i	0.234163	−	0.788117i
$209$	−141.937	−	81.9474i	−0.679125	−	0.392093i
$210$		0			0
$211$	−96.7627	−	167.598i	−0.458591	−	0.794303i	0.540296	−	0.841475i	$-0.318312\pi$
$211$	−96.7627	−	167.598i	−0.458591	−	0.794303i	−0.998887	+	0.0471724i	$0.984979\pi$
$212$	−0.120428	+	0.0695289i	−0.000568054	+	0.000327966i
$213$		0			0
$214$	−76.6863	−	44.2748i	−0.358347	−	0.206892i
$215$	124.361			0.578421
$216$		0			0
$217$	−374.099			−1.72396
$218$	49.8773	+	28.7967i	0.228795	+	0.132095i
$219$		0			0
$220$	−79.0769	−	136.965i	−0.359441	−	0.622569i
$221$	67.9555	+	284.095i	0.307491	+	1.28550i
$222$		0			0
$223$	198.753	+	114.750i	0.891271	+	0.514575i	0.874358	−	0.485282i	$-0.161283\pi$
$223$	198.753	+	114.750i	0.891271	+	0.514575i	0.0169128	+	0.999857i	$0.494616\pi$
$224$		−	213.718i		−	0.954097i
$225$		0			0
$226$		−	33.8920i		−	0.149964i
$227$	124.606	−	215.824i	0.548925	−	0.950766i	−0.449423	−	0.893319i	$-0.648371\pi$
$227$	124.606	−	215.824i	0.548925	−	0.950766i	0.998349	−	0.0574473i	$-0.0182961\pi$
$228$		0			0
$229$	−46.3299	+	26.7486i	−0.202314	+	0.116806i	−0.597734	−	0.801694i	$-0.703932\pi$
$229$	−46.3299	+	26.7486i	−0.202314	+	0.116806i	0.395420	+	0.918500i	$0.370599\pi$
$230$	2.91239	−	1.68147i	0.0126625	−	0.00731072i
$231$		0			0
$232$	−8.11764	−	4.68672i	−0.0349898	−	0.0202014i
$233$			111.432i			0.478248i	0.970989	+	0.239124i	$0.0768602\pi$
$233$			111.432i			0.478248i	−0.970989	+	0.239124i	$0.923140\pi$
$234$		0			0
$235$	74.0849			0.315255
$236$	123.763	−	214.364i	0.524421	−	0.908324i
$237$		0			0
$238$	54.3401	+	94.1198i	0.228320	+	0.395461i
$239$	−117.640	−	203.758i	−0.492217	−	0.852545i	0.507743	−	0.861509i	$-0.330480\pi$
$239$	−117.640	−	203.758i	−0.492217	−	0.852545i	−0.999960	+	0.00896368i	$0.997147\pi$
$240$		0			0
$241$	−220.705	−	127.424i	−0.915787	−	0.528730i	−0.0334983	−	0.999439i	$-0.510665\pi$
$241$	−220.705	−	127.424i	−0.915787	−	0.528730i	−0.882289	+	0.470709i	$0.843998\pi$
$242$	−59.3011			−0.245046
$243$		0			0
$244$	305.767			1.25314
$245$	64.5439	−	111.793i	0.263445	−	0.456299i
$246$		0			0
$247$	31.8922	+	133.329i	0.129118	+	0.539792i
$248$	125.752	−	72.6027i	0.507063	−	0.292753i
$249$		0			0
$250$	−28.4175	+	49.2206i	−0.113670	+	0.196882i
$251$		−	222.888i		−	0.888002i	−0.896026	−	0.444001i	$-0.853559\pi$
$251$		−	222.888i		−	0.888002i	0.896026	−	0.444001i	$-0.146441\pi$
$252$		0			0
$253$			39.2378i			0.155090i
$254$	17.4353	−	30.1988i	0.0686429	−	0.118893i
$255$		0			0
$256$	−57.3939	−	99.4092i	−0.224195	−	0.388317i
$257$	−203.969	+	117.762i	−0.793654	+	0.458217i	−0.841247	−	0.540650i	$-0.818178\pi$
$257$	−203.969	+	117.762i	−0.793654	+	0.458217i	0.0475931	+	0.998867i	$0.484845\pi$
$258$		0			0
$259$	51.0224	−	88.3735i	0.196998	−	0.341210i
$260$	−37.6771	+	126.809i	−0.144912	+	0.487727i
$261$		0			0
$262$		−	72.1893i		−	0.275532i
$263$	45.2489	+	26.1244i	0.172049	+	0.0993325i	0.583552	−	0.812076i	$-0.301663\pi$
$263$	45.2489	+	26.1244i	0.172049	+	0.0993325i	−0.411503	+	0.911409i	$0.634996\pi$
$264$		0			0
$265$	0.0867734	−	0.0500986i	0.000327447	−	0.000189051i
$266$	25.5024	+	44.1714i	0.0958737	+	0.166058i
$267$		0			0
$268$	−211.204	−	121.938i	−0.788073	−	0.454994i
$269$		−	435.342i		−	1.61837i	−0.587553	−	0.809186i	$-0.699909\pi$
$269$		−	435.342i		−	1.61837i	0.587553	−	0.809186i	$-0.300091\pi$
$270$		0			0
$271$		−	535.820i		−	1.97720i	−0.150574	−	0.988599i	$-0.548112\pi$
$271$		−	535.820i		−	1.97720i	0.150574	−	0.988599i	$-0.451888\pi$
$272$	255.984	+	147.792i	0.941118	+	0.543355i
$273$		0			0
$274$	17.2165	+	29.8198i	0.0628339	+	0.108832i
$275$	−137.295	−	237.802i	−0.499254	−	0.864733i
$276$		0			0
$277$	13.4558	−	23.3061i	0.0485769	−	0.0841376i	−0.840715	−	0.541479i	$-0.817865\pi$
$277$	13.4558	−	23.3061i	0.0485769	−	0.0841376i	0.889291	+	0.457341i	$0.151198\pi$
$278$	−75.3372			−0.270997
$279$		0			0
$280$			101.606i			0.362877i
$281$	−36.6045	+	63.4009i	−0.130265	+	0.225626i	−0.923779	−	0.382927i	$-0.874916\pi$
$281$	−36.6045	+	63.4009i	−0.130265	+	0.225626i	0.793514	+	0.608553i	$0.208250\pi$
$282$		0			0
$283$	127.130	+	220.196i	0.449223	+	0.778077i	0.998336	−	0.0576712i	$-0.0183675\pi$
$283$	127.130	+	220.196i	0.449223	+	0.778077i	−0.549113	+	0.835748i	$0.685034\pi$
$284$	55.5957	+	96.2945i	0.195759	+	0.339065i
$285$		0			0
$286$	68.3559	+	72.1520i	0.239006	+	0.252280i
$287$			719.479i			2.50690i
$288$		0			0
$289$	−215.897			−0.747049
$290$	2.83334	+	1.63583i	0.00977012	+	0.00564078i
$291$		0			0
$292$	−92.1709	+	53.2149i	−0.315654	+	0.182243i
$293$	21.1134	+	36.5695i	0.0720594	+	0.124810i	0.899804	−	0.436295i	$-0.143710\pi$
$293$	21.1134	+	36.5695i	0.0720594	+	0.124810i	−0.827744	+	0.561105i	$0.810376\pi$
$294$		0			0
$295$	−89.1770	+	154.459i	−0.302295	+	0.523590i
$296$			39.6085i			0.133812i
$297$		0			0
$298$	−15.9914			−0.0536623
$299$	23.8259	−	22.5724i	0.0796853	−	0.0754928i
$300$		0			0
$301$	391.062	−	225.780i	1.29921	−	0.750099i
$302$	−14.5417	+	8.39564i	−0.0481512	+	0.0278001i
$303$		0			0
$304$	120.136	+	69.3606i	0.395184	+	0.228160i
$305$	−220.319			−0.722356
$306$		0			0
$307$			136.458i			0.444490i	0.974991	+	0.222245i	$0.0713385\pi$
$307$			136.458i			0.444490i	−0.974991	+	0.222245i	$0.928662\pi$
$308$	−497.328	−	287.132i	−1.61470	−	0.932248i
$309$		0			0
$310$	−43.8916	+	25.3409i	−0.141586	+	0.0817447i
$311$	−272.833	+	157.520i	−0.877277	+	0.506496i	−0.869759	−	0.493476i	$-0.835726\pi$
$311$	−272.833	+	157.520i	−0.877277	+	0.506496i	−0.00751707	+	0.999972i	$0.502393\pi$
$312$		0			0
$313$	261.082	−	452.207i	0.834127	−	1.44475i	−0.0606123	−	0.998161i	$-0.519305\pi$
$313$	261.082	−	452.207i	0.834127	−	1.44475i	0.894739	−	0.446589i	$-0.147361\pi$
$314$	108.571			0.345768
$315$		0			0
$316$	−273.541			−0.865635
$317$	41.1674	−	71.3040i	0.129866	−	0.224934i	−0.793759	−	0.608233i	$-0.791879\pi$
$317$	41.1674	−	71.3040i	0.129866	−	0.224934i	0.923624	+	0.383299i	$0.125212\pi$
$318$		0			0
$319$	−33.0586	+	19.0864i	−0.103632	+	0.0598320i
$320$	56.7640	+	98.3181i	0.177387	+	0.307244i
$321$		0			0
$322$	6.10549	−	10.5750i	0.0189612	−	0.0328417i
$323$	−236.954			−0.733603
$324$		0			0
$325$	−65.4158	+	220.168i	−0.201279	+	0.677440i
$326$	−18.1362	−	10.4709i	−0.0556325	−	0.0321194i
$327$		0			0
$328$	−139.632	−	241.850i	−0.425707	−	0.737347i
$329$	232.966	−	134.503i	0.708104	−	0.408824i
$330$		0			0
$331$	−130.559	−	75.3781i	−0.394437	−	0.227728i	0.289644	−	0.957135i	$-0.406463\pi$
$331$	−130.559	−	75.3781i	−0.394437	−	0.227728i	−0.684081	+	0.729406i	$0.739797\pi$
$332$	−540.678			−1.62855
$333$		0			0
$334$	−102.299			−0.306283
$335$	152.182	+	87.8620i	0.454273	+	0.262275i
$336$		0			0
$337$	120.680	+	209.024i	0.358100	+	0.620248i	0.987643	−	0.156718i	$-0.0500912\pi$
$337$	120.680	+	209.024i	0.358100	+	0.620248i	−0.629543	+	0.776966i	$0.716758\pi$
$338$	4.48889	−	83.0138i	0.0132807	−	0.245603i
$339$		0			0
$340$	−198.020	−	114.327i	−0.582411	−	0.336255i
$341$		−	591.341i		−	1.73414i
$342$		0			0
$343$			13.0537i			0.0380573i
$344$	−87.6359	+	151.790i	−0.254756	+	0.441250i
$345$		0			0
$346$	−23.1367	+	13.3580i	−0.0668690	+	0.0386068i
$347$	449.622	−	259.590i	1.29574	−	0.748097i	0.316076	−	0.948734i	$-0.397634\pi$
$347$	449.622	−	259.590i	1.29574	−	0.748097i	0.979666	+	0.200637i	$0.0643011\pi$
$348$		0			0
$349$	313.905	+	181.233i	0.899442	+	0.519293i	0.877019	−	0.480456i	$-0.159529\pi$
$349$	313.905	+	181.233i	0.899442	+	0.519293i	0.0224227	+	0.999749i	$0.492862\pi$
$350$			85.4535i			0.244153i
$351$		0			0
$352$	337.826			0.959732
$353$	−31.9628	+	55.3612i	−0.0905462	+	0.156831i	−0.907741	−	0.419531i	$-0.862195\pi$
$353$	−31.9628	+	55.3612i	−0.0905462	+	0.156831i	0.817195	+	0.576361i	$0.195528\pi$
$354$		0			0
$355$	−40.0591	−	69.3844i	−0.112843	−	0.195449i
$356$	151.419	+	262.265i	0.425334	+	0.736700i
$357$		0			0
$358$	35.1665	+	20.3034i	0.0982305	+	0.0567134i
$359$	359.930			1.00259			0.501295	−	0.865276i	$-0.332857\pi$
$359$	359.930			1.00259			0.501295	+	0.865276i	$0.332857\pi$
$360$		0			0
$361$	249.795			0.691953
$362$	41.0708	−	71.1368i	0.113455	−	0.196510i
$363$		0			0
$364$	111.746	+	467.165i	0.306995	+	1.28342i
$365$	66.4132	−	38.3437i	0.181954	−	0.105051i
$366$		0			0
$367$	73.7089	−	127.668i	0.200842	−	0.347868i	−0.747958	−	0.663746i	$-0.768966\pi$
$367$	73.7089	−	127.668i	0.200842	−	0.347868i	0.948800	+	0.315878i	$0.102299\pi$
$368$		−	33.2110i		−	0.0902474i
$369$		0			0
$370$		−	13.8247i		−	0.0373641i
$371$	0.181911	−	0.315079i	0.000490325	−	0.000849268i
$372$		0			0
$373$	−285.025	−	493.678i	−0.764143	−	1.32353i	−0.940699	−	0.339243i	$-0.889829\pi$
$373$	−285.025	−	493.678i	−0.764143	−	1.32353i	0.176556	−	0.984291i	$-0.443504\pi$
$374$	−148.776	+	85.8959i	−0.397797	+	0.229668i
$375$		0			0
$376$	−52.2071	+	90.4253i	−0.138849	+	0.240493i
$377$	30.6073	+	9.09395i	0.0811864	+	0.0241219i
$378$		0			0
$379$			333.547i			0.880071i	0.897980	+	0.440036i	$0.145034\pi$
$379$			333.547i			0.880071i	−0.897980	+	0.440036i	$0.854966\pi$
$380$	−92.9329	−	53.6548i	−0.244560	−	0.141197i
$381$		0			0
$382$	−30.0690	+	17.3603i	−0.0787146	+	0.0454459i
$383$	226.922	+	393.041i	0.592486	+	1.02622i	0.993896	+	0.110318i	$0.0351868\pi$
$383$	226.922	+	393.041i	0.592486	+	1.02622i	−0.401410	+	0.915898i	$0.631480\pi$
$384$		0			0
$385$	358.347	+	206.892i	0.930771	+	0.537381i
$386$		−	22.9535i		−	0.0594650i
$387$		0			0
$388$			423.969i			1.09270i
$389$	331.803	+	191.567i	0.852965	+	0.492460i	0.861650	−	0.507503i	$-0.169431\pi$
$389$	331.803	+	191.567i	0.852965	+	0.492460i	−0.00868524	+	0.999962i	$0.502765\pi$
$390$		0			0
$391$	28.3644	+	49.1286i	0.0725432	+	0.125648i
$392$	90.9672	+	157.560i	0.232059	+	0.401938i
$393$		0			0
$394$	47.8206	−	82.8278i	0.121372	−	0.210223i
$395$	197.098			0.498983
$396$		0			0
$397$		−	114.607i		−	0.288682i	−0.989528	−	0.144341i	$-0.953894\pi$
$397$		−	114.607i		−	0.288682i	0.989528	−	0.144341i	$-0.0461062\pi$
$398$	−5.47730	+	9.48696i	−0.0137621	+	0.0238366i
$399$		0			0
$400$	116.207	+	201.276i	0.290517	+	0.503191i
$401$	168.468	+	291.795i	0.420119	+	0.727667i	0.995951	−	0.0899009i	$-0.0286550\pi$
$401$	168.468	+	291.795i	0.420119	+	0.727667i	−0.575832	+	0.817568i	$0.695322\pi$
$402$		0			0
$403$	−359.073	+	340.181i	−0.891000	+	0.844121i
$404$			743.044i			1.83922i
$405$		0			0
$406$	11.8795			0.0292600
$407$	139.693	+	80.6516i	0.343225	+	0.198161i
$408$		0			0
$409$	537.500	−	310.326i	1.31418	−	0.758742i	0.331395	−	0.943492i	$-0.392481\pi$
$409$	537.500	−	310.326i	1.31418	−	0.758742i	0.982786	+	0.184750i	$0.0591475\pi$
$410$	48.7364	+	84.4139i	0.118869	+	0.205888i
$411$		0			0
$412$	−40.9981	+	71.0108i	−0.0995100	+	0.172356i
$413$			647.613i			1.56807i
$414$		0			0
$415$	389.582			0.938753
$416$	−194.341	−	205.134i	−0.467166	−	0.493110i
$417$		0			0
$418$	−69.8222	+	40.3119i	−0.167039	+	0.0964398i
$419$	−217.694	+	125.686i	−0.519557	+	0.299966i	−0.736753	−	0.676162i	$-0.763642\pi$
$419$	−217.694	+	125.686i	−0.519557	+	0.299966i	0.217196	+	0.976128i	$0.430309\pi$
$420$		0			0
$421$	643.709	+	371.645i	1.52900	+	0.882768i	0.999404	+	0.0345179i	$0.0109896\pi$
$421$	643.709	+	371.645i	1.52900	+	0.882768i	0.529595	+	0.848250i	$0.322344\pi$
$422$	−95.1997			−0.225592
$423$		0			0
$424$			0.141216i			0.000333058i
$425$	−343.806	−	198.496i	−0.808955	−	0.467050i
$426$		0			0
$427$	−692.810	+	399.994i	−1.62251	+	0.936755i
$428$	585.839	−	338.234i	1.36878	−	0.790267i
$429$		0			0
$430$	30.5880	−	52.9799i	0.0711348	−	0.123209i
$431$	−649.249			−1.50638			−0.753189	−	0.657804i	$-0.771485\pi$
$431$	−649.249			−1.50638			−0.753189	+	0.657804i	$0.771485\pi$
$432$		0			0
$433$	245.607			0.567222			0.283611	−	0.958939i	$-0.408468\pi$
$433$	245.607			0.567222			0.283611	+	0.958939i	$0.408468\pi$
$434$	−92.0140	+	159.373i	−0.212014	+	0.367219i
$435$		0			0
$436$	−381.034	+	219.990i	−0.873931	+	0.504564i
$437$	13.3117	+	23.0566i	0.0304616	+	0.0527610i
$438$		0			0
$439$	15.0625	−	26.0889i	0.0343108	−	0.0594281i	−0.848360	−	0.529420i	$-0.822410\pi$
$439$	15.0625	−	26.0889i	0.0343108	−	0.0594281i	0.882671	+	0.469992i	$0.155743\pi$
$440$	−160.609			−0.365020
$441$		0			0
$442$	137.744	+	40.9261i	0.311638	+	0.0925930i
$443$	−152.079	−	87.8030i	−0.343294	−	0.198201i	0.318434	−	0.947945i	$-0.396843\pi$
$443$	−152.079	−	87.8030i	−0.343294	−	0.198201i	−0.661728	+	0.749744i	$0.730176\pi$
$444$		0			0
$445$	−109.104	−	188.974i	−0.245178	−	0.424660i
$446$	97.7715	−	56.4484i	0.219219	−	0.126566i
$447$		0			0
$448$	356.998	+	206.113i	0.796871	+	0.460074i
$449$	126.404			0.281523			0.140762	−	0.990044i	$-0.455045\pi$
$449$	126.404			0.281523			0.140762	+	0.990044i	$0.455045\pi$
$450$		0			0
$451$	−1137.29			−2.52170
$452$	224.227	+	129.458i	0.496077	+	0.286410i
$453$		0			0
$454$	−61.2966	−	106.169i	−0.135015	−	0.233852i
$455$	−80.5180	−	336.613i	−0.176963	−	0.739809i
$456$		0			0
$457$	−574.817	−	331.871i	−1.25781	−	0.726194i	−0.285158	−	0.958481i	$-0.592046\pi$
$457$	−574.817	−	331.871i	−1.25781	−	0.726194i	−0.972647	+	0.232286i	$0.925379\pi$
$458$			26.3165i			0.0574597i
$459$		0			0
$460$			25.6909i			0.0558497i
$461$	−15.6227	+	27.0593i	−0.0338887	+	0.0586969i	−0.882472	−	0.470364i	$-0.844123\pi$
$461$	−15.6227	+	27.0593i	−0.0338887	+	0.0586969i	0.848584	+	0.529061i	$0.177456\pi$
$462$		0			0
$463$	558.193	−	322.273i	1.20560	−	0.696053i	0.243805	−	0.969824i	$-0.421604\pi$
$463$	558.193	−	322.273i	1.20560	−	0.696053i	0.961795	+	0.273771i	$0.0882710\pi$
$464$	27.9810	−	16.1548i	0.0603038	−	0.0348164i
$465$		0			0
$466$	47.4720	+	27.4080i	0.101871	+	0.0588154i
$467$		−	594.979i		−	1.27405i	−0.770845	−	0.637023i	$-0.780166\pi$
$467$		−	594.979i		−	1.27405i	0.770845	−	0.637023i	$-0.219834\pi$
$468$		0			0
$469$	638.063			1.36048
$470$	18.2221	−	31.5615i	0.0387703	−	0.0671522i
$471$		0			0
$472$	−125.685	−	217.692i	−0.266281	−	0.461212i
$473$	356.892	+	618.156i	0.754529	+	1.30688i
$474$		0			0
$475$	−161.352	−	93.1565i	−0.339688	−	0.196119i
$476$	−830.254			−1.74423
$477$		0			0
$478$	−115.740			−0.242133
$479$	−31.4715	+	54.5102i	−0.0657025	+	0.113800i	−0.897005	−	0.442020i	$-0.854262\pi$
$479$	−31.4715	+	54.5102i	−0.0657025	+	0.113800i	0.831303	+	0.555820i	$0.187595\pi$
$480$		0			0
$481$	−31.3880	−	131.220i	−0.0652556	−	0.272808i
$482$	−108.570	+	62.6828i	−0.225249	+	0.130047i
$483$		0			0
$484$	226.513	−	392.332i	0.468002	−	0.810604i
$485$		−	305.488i		−	0.629873i
$486$		0			0
$487$			143.450i			0.294558i	0.989095	+	0.147279i	$0.0470516\pi$
$487$			143.450i			0.294558i	−0.989095	+	0.147279i	$0.952948\pi$
$488$	155.257	−	268.913i	0.318149	−	0.551051i
$489$		0			0
$490$	−31.7507	−	54.9938i	−0.0647973	−	0.112232i
$491$	−824.274	+	475.895i	−1.67877	+	0.969236i	−0.716316	+	0.697776i	$0.754173\pi$
$491$	−824.274	+	475.895i	−1.67877	+	0.969236i	−0.962450	+	0.271460i	$0.912494\pi$
$492$		0			0
$493$	−27.5945	+	47.7951i	−0.0559726	+	0.0969474i
$494$	64.6447	+	19.2071i	0.130860	+	0.0388807i
$495$		0			0
$496$			500.513i			1.00910i
$497$	−251.939	−	145.457i	−0.506919	−	0.292670i
$498$		0			0
$499$	56.3465	−	32.5317i	0.112919	−	0.0651937i	−0.442477	−	0.896780i	$-0.645900\pi$
$499$	56.3465	−	32.5317i	0.112919	−	0.0651937i	0.555396	+	0.831586i	$0.312567\pi$
$500$	−217.093	−	376.017i	−0.434187	−	0.752033i
$501$		0			0
$502$	−94.9546	−	54.8221i	−0.189153	−	0.109207i
$503$		−	493.047i		−	0.980213i	−0.871662	−	0.490107i	$-0.836958\pi$
$503$		−	493.047i		−	0.980213i	0.871662	−	0.490107i	$-0.163042\pi$
$504$		0			0
$505$		−	535.396i		−	1.06019i
$506$	16.7160	+	9.65101i	0.0330356	+	0.0190731i
$507$		0			0
$508$	133.196	+	230.702i	0.262196	+	0.454137i
$509$	288.131	+	499.058i	0.566073	+	0.980468i	0.996949	+	0.0780566i	$0.0248715\pi$
$509$	288.131	+	499.058i	0.566073	+	0.980468i	−0.430875	+	0.902411i	$0.641795\pi$
$510$		0			0
$511$	139.228	−	241.150i	0.272462	−	0.471918i
$512$	−486.749			−0.950681
$513$		0			0
$514$			115.859i			0.225408i
$515$	29.5410	−	51.1664i	0.0573611	−	0.0993523i
$516$		0			0
$517$	212.610	+	368.252i	0.411238	+	0.712286i
$518$	−25.0991	−	43.4730i	−0.0484540	−	0.0839247i
$519$		0			0
$520$	92.3936	+	97.5246i	0.177680	+	0.187547i
$521$			501.004i			0.961620i	0.876825	+	0.480810i	$0.159657\pi$
$521$			501.004i			0.961620i	−0.876825	+	0.480810i	$0.840343\pi$
$522$		0			0
$523$	−400.933			−0.766602			−0.383301	−	0.923624i	$-0.625213\pi$
$523$	−400.933			−0.766602			−0.383301	+	0.923624i	$0.625213\pi$
$524$	477.599	+	275.742i	0.911449	+	0.526225i
$525$		0			0
$526$	22.2590	−	12.8512i	0.0423175	−	0.0244320i
$527$	−427.471	−	740.401i	−0.811140	−	1.40494i
$528$		0			0
$529$	−261.313	+	452.607i	−0.493976	+	0.855591i
$530$		−	0.0492894i		−	9.29988e-5i
$531$		0			0
$532$	−389.647			−0.732419
$533$	654.247	+	690.581i	1.22748	+	1.29565i
$534$		0			0
$535$	−422.123	+	243.713i	−0.789014	+	0.455538i
$536$	−214.482	+	123.831i	−0.400153	+	0.231029i
$537$		0			0
$538$	−185.464	−	107.077i	−0.344728	−	0.199029i
$539$	740.917			1.37461
$540$		0			0
$541$			73.5254i			0.135906i	0.997689	+	0.0679532i	$0.0216469\pi$
$541$			73.5254i			0.135906i	−0.997689	+	0.0679532i	$0.978353\pi$
$542$	−228.269	−	131.791i	−0.421161	−	0.243158i
$543$		0			0
$544$	422.982	−	244.209i	0.777540	−	0.448913i
$545$	274.552	−	158.513i	0.503765	−	0.290849i
$546$		0			0
$547$	−20.0152	+	34.6674i	−0.0365909	+	0.0633774i	−0.883741	−	0.467976i	$-0.844983\pi$
$547$	−20.0152	+	34.6674i	−0.0365909	+	0.0633774i	0.847150	+	0.531354i	$0.178317\pi$
$548$	−263.048			−0.480015
$549$		0			0
$550$	−135.077			−0.245595
$551$	−12.9504	+	22.4308i	−0.0235034	+	0.0407092i
$552$		0			0
$553$	619.791	−	357.837i	1.12078	−	0.647083i
$554$	−6.61922	−	11.4648i	−0.0119481	−	0.0206946i
$555$		0			0
$556$	287.766	−	498.426i	0.517565	−	0.896449i
$557$	475.662			0.853972			0.426986	−	0.904258i	$-0.359575\pi$
$557$	475.662			0.853972			0.426986	+	0.904258i	$0.359575\pi$
$558$		0			0
$559$	170.046	−	572.318i	0.304196	−	1.02382i
$560$	−303.306	−	175.114i	−0.541618	−	0.312703i
$561$		0			0
$562$	18.0066	+	31.1884i	0.0320403	+	0.0554954i
$563$	−494.852	+	285.703i	−0.878955	+	0.507465i	−0.870314	−	0.492498i	$-0.836084\pi$
$563$	−494.852	+	285.703i	−0.878955	+	0.507465i	−0.00864136	+	0.999963i	$0.502751\pi$
$564$		0			0
$565$	−161.565	−	93.2798i	−0.285957	−	0.165097i
$566$	125.077			0.220983
$567$		0			0
$568$	112.917			0.198798
$569$	334.478	+	193.111i	0.587835	+	0.339387i	0.764241	−	0.644931i	$-0.223114\pi$
$569$	334.478	+	193.111i	0.587835	+	0.339387i	−0.176406	+	0.984318i	$0.556447\pi$
$570$		0			0
$571$	440.436	+	762.858i	0.771342	+	1.33600i	0.936828	+	0.349791i	$0.113748\pi$
$571$	440.436	+	762.858i	0.771342	+	1.33600i	−0.165486	+	0.986212i	$0.552919\pi$
$572$	−738.452	+	176.638i	−1.29100	+	0.308808i
$573$		0			0
$574$	306.511	+	176.964i	0.533992	+	0.308300i
$575$			44.6050i			0.0775738i
$576$		0			0
$577$		−	583.864i		−	1.01190i	−0.862564	−	0.505948i	$-0.831143\pi$
$577$		−	583.864i		−	1.01190i	0.862564	−	0.505948i	$-0.168857\pi$
$578$	−53.1025	+	91.9762i	−0.0918728	+	0.159128i
$579$		0			0
$580$	−21.6450	+	12.4968i	−0.0373190	+	0.0215462i
$581$	1225.07	−	707.297i	2.10856	−	1.21738i
$582$		0			0
$583$	0.498047	+	0.287548i	0.000854284	+	0.000493221i
$584$			108.082i			0.185072i
$585$		0			0
$586$	20.7724			0.0354477
$587$	375.099	−	649.690i	0.639010	−	1.10680i	−0.346640	−	0.937998i	$-0.612678\pi$
$587$	375.099	−	649.690i	0.639010	−	1.10680i	0.985650	−	0.168800i	$-0.0539892\pi$
$588$		0			0
$589$	−200.617	−	347.478i	−0.340605	−	0.589946i
$590$	43.8683	+	75.9821i	0.0743530	+	0.128783i
$591$		0			0
$592$	−118.236	−	68.2639i	−0.199724	−	0.115311i
$593$	1077.16			1.81646			0.908231	−	0.418469i	$-0.137433\pi$
$593$	1077.16			1.81646			0.908231	+	0.418469i	$0.137433\pi$
$594$		0			0
$595$	598.234			1.00544
$596$	61.0823	−	105.798i	0.102487	−	0.177513i
$597$		0			0
$598$	−3.75597	−	15.7022i	−0.00628089	−	0.0262579i
$599$	245.190	−	141.561i	0.409333	−	0.236329i	−0.281170	−	0.959658i	$-0.590723\pi$
$599$	245.190	−	141.561i	0.409333	−	0.236329i	0.690503	+	0.723329i	$0.257389\pi$
$600$		0			0
$601$	66.0237	−	114.356i	0.109856	−	0.190277i	−0.805856	−	0.592112i	$-0.798294\pi$
$601$	66.0237	−	114.356i	0.109856	−	0.190277i	0.915712	+	0.401835i	$0.131628\pi$
$602$		−	222.133i		−	0.368992i
$603$		0			0
$604$		−	128.276i		−	0.212377i
$605$	−163.213	+	282.693i	−0.269773	+	0.467260i
$606$		0			0
$607$	−120.206	−	208.203i	−0.198033	−	0.343003i	0.749858	−	0.661599i	$-0.230122\pi$
$607$	−120.206	−	208.203i	−0.198033	−	0.343003i	−0.947891	+	0.318596i	$0.896789\pi$
$608$	198.510	−	114.610i	0.326497	−	0.188503i
$609$		0			0
$610$	−54.1900	+	93.8598i	−0.0888360	+	0.153868i
$611$	101.301	−	340.945i	0.165795	−	0.558012i
$612$		0			0
$613$		−	822.777i		−	1.34221i	−0.741360	−	0.671107i	$-0.765819\pi$
$613$		−	822.777i		−	1.34221i	0.741360	−	0.671107i	$-0.234181\pi$
$614$	58.1338	+	33.5636i	0.0946804	+	0.0546638i
$615$		0			0
$616$	−505.048	+	291.590i	−0.819884	+	0.473360i
$617$	−275.955	−	477.968i	−0.447253	−	0.774665i	0.550953	−	0.834536i	$-0.314264\pi$
$617$	−275.955	−	477.968i	−0.447253	−	0.774665i	−0.998206	+	0.0598711i	$0.980931\pi$
$618$		0			0
$619$	−350.084	−	202.121i	−0.565564	−	0.326529i	0.189812	−	0.981821i	$-0.439212\pi$
$619$	−350.084	−	202.121i	−0.565564	−	0.326529i	−0.755376	+	0.655292i	$0.772546\pi$
$620$		−	387.179i		−	0.624482i
$621$		0			0
$622$			154.976i			0.249157i
$623$	−686.173	−	396.162i	−1.10140	−	0.635895i
$624$		0			0
$625$	−64.4216	−	111.581i	−0.103074	−	0.178530i
$626$	−128.432	−	222.451i	−0.205163	−	0.355353i
$627$		0			0
$628$	−414.710	+	718.298i	−0.660366	+	1.14379i
$629$	233.207			0.370758
$630$		0			0
$631$			443.670i			0.703123i	0.936165	+	0.351561i	$0.114349\pi$
$631$			443.670i			0.703123i	−0.936165	+	0.351561i	$0.885651\pi$
$632$	−138.893	+	240.571i	−0.219768	+	0.380650i
$633$		0			0
$634$	−20.2512	−	35.0761i	−0.0319420	−	0.0553251i
$635$	−95.9733	−	166.231i	−0.151139	−	0.261780i
$636$		0			0
$637$	−426.228	−	449.898i	−0.669117	−	0.706277i
$638$			18.7781i			0.0294328i
$639$		0			0
$640$	291.281			0.455126
$641$	−543.758	−	313.939i	−0.848297	−	0.489764i	0.0117791	−	0.999931i	$-0.496251\pi$
$641$	−543.758	−	313.939i	−0.848297	−	0.489764i	−0.860076	+	0.510166i	$0.829584\pi$
$642$		0			0
$643$	−618.928	+	357.338i	−0.962563	+	0.555736i	−0.896961	−	0.442110i	$-0.854230\pi$
$643$	−618.928	+	357.338i	−0.962563	+	0.555736i	−0.0656022	+	0.997846i	$0.520897\pi$
$644$	46.6424	+	80.7870i	0.0724261	+	0.125446i
$645$		0			0
$646$	−58.2816	+	100.947i	−0.0902192	+	0.156264i
$647$			50.9073i			0.0786820i	0.999226	+	0.0393410i	$0.0125259\pi$
$647$			50.9073i			0.0786820i	−0.999226	+	0.0393410i	$0.987474\pi$
$648$		0			0
$649$	−1023.69			−1.57733
$650$	77.7059	+	82.0213i	0.119548	+	0.126187i
$651$		0			0
$652$	138.550	−	79.9918i	0.212500	−	0.122687i
$653$	−370.592	+	213.962i	−0.567523	+	0.327659i	−0.756159	−	0.654388i	$-0.772926\pi$
$653$	−370.592	+	213.962i	−0.567523	+	0.327659i	0.188637	+	0.982047i	$0.439593\pi$
$654$		0			0
$655$	−344.131	−	198.684i	−0.525391	−	0.303335i
$656$	962.604			1.46738
$657$		0			0
$658$		−	132.331i		−	0.201110i
$659$	−472.394	−	272.737i	−0.716835	−	0.413865i	0.0967518	−	0.995309i	$-0.469155\pi$
$659$	−472.394	−	272.737i	−0.716835	−	0.413865i	−0.813587	+	0.581444i	$0.802488\pi$
$660$		0			0
$661$	72.4148	−	41.8087i	0.109553	−	0.0632507i	−0.444222	−	0.895917i	$-0.646520\pi$
$661$	72.4148	−	41.8087i	0.109553	−	0.0632507i	0.553776	+	0.832666i	$0.313187\pi$
$662$	−64.2249	+	37.0803i	−0.0970165	+	0.0560125i
$663$		0			0
$664$	−274.536	+	475.510i	−0.413457	+	0.716129i
$665$	280.758			0.422192
$666$		0			0
$667$	6.20088			0.00929667
$668$	390.751	−	676.801i	0.584957	−	1.01318i
$669$		0			0
$670$	74.8617	−	43.2214i	0.111734	−	0.0645096i
$671$	−632.274	−	1095.13i	−0.942287	−	1.63209i
$672$		0			0
$673$	−65.7751	+	113.926i	−0.0977341	+	0.169280i	−0.910746	−	0.412966i	$-0.864493\pi$
$673$	−65.7751	+	113.926i	−0.0977341	+	0.169280i	0.813012	+	0.582247i	$0.197826\pi$
$674$	118.730			0.176158
$675$		0			0
$676$	532.067	+	346.787i	0.787082	+	0.512998i
$677$	−151.765	−	87.6217i	−0.224173	−	0.129426i	0.383708	−	0.923454i	$-0.374647\pi$
$677$	−151.765	−	87.6217i	−0.224173	−	0.129426i	−0.607881	+	0.794028i	$0.707980\pi$
$678$		0			0
$679$	−554.622	−	960.633i	−0.816822	−	1.41478i
$680$	−201.094	+	116.102i	−0.295726	+	0.170738i
$681$		0			0
$682$	−251.922	−	145.447i	−0.369387	−	0.213266i
$683$	960.521			1.40633			0.703163	−	0.711029i	$-0.251770\pi$
$683$	960.521			1.40633			0.703163	+	0.711029i	$0.251770\pi$
$684$		0			0
$685$	189.538			0.276697
$686$	5.56110	+	3.21070i	0.00810656	+	0.00468032i
$687$		0			0
$688$	−302.075	−	523.209i	−0.439063	−	0.760479i
$689$	−0.111908	−	0.467841i	−0.000162421	−	0.000679015i
$690$		0			0
$691$	−398.707	−	230.194i	−0.577000	−	0.333131i	0.182940	−	0.983124i	$-0.441438\pi$
$691$	−398.707	−	230.194i	−0.577000	−	0.333131i	−0.759940	+	0.649993i	$0.774772\pi$
$692$		−	204.094i		−	0.294934i
$693$		0			0
$694$		−	255.397i		−	0.368007i
$695$	−207.348	+	359.138i	−0.298343	+	0.516745i
$696$		0			0
$697$	−1423.96	+	822.126i	−2.04299	+	1.17952i
$698$	154.417	−	89.1529i	0.221228	−	0.127726i
$699$		0			0
$700$	−565.355	−	326.408i	−0.807650	−	0.466297i
$701$			704.086i			1.00440i	0.864751	+	0.502201i	$0.167476\pi$
$701$			704.086i			1.00440i	−0.864751	+	0.502201i	$0.832524\pi$
$702$		0			0
$703$	109.447			0.155685
$704$	−325.805	+	564.310i	−0.462791	+	0.801577i
$705$		0			0
$706$	15.7233	+	27.2335i	0.0222709	+	0.0385743i
$707$	−972.026	−	1683.60i	−1.37486	−	2.38133i
$708$		0			0
$709$	1153.90	+	666.202i	1.62750	+	0.939636i	0.984837	+	0.173484i	$0.0555026\pi$
$709$	1153.90	+	666.202i	1.62750	+	0.939636i	0.642660	+	0.766151i	$0.277831\pi$
$710$	−39.4121			−0.0555099
$711$		0			0
$712$	307.539			0.431937
$713$	−48.0294	+	83.1893i	−0.0673624	+	0.116675i
$714$		0			0
$715$	532.087	−	127.275i	0.744178	−	0.178008i
$716$	−268.652	+	155.106i	−0.375212	+	0.216629i
$717$		0			0
$718$	88.5290	−	153.337i	0.123299	−	0.213561i
$719$		−	761.577i		−	1.05922i	−0.848242	−	0.529608i	$-0.822339\pi$
$719$		−	761.577i		−	1.05922i	0.848242	−	0.529608i	$-0.177661\pi$
$720$		0			0
$721$		−	214.529i		−	0.297544i
$722$	61.4400	−	106.417i	0.0850970	−	0.147392i
$723$		0			0
$724$	313.757	+	543.444i	0.433367	+	0.750613i
$725$	−37.5805	+	21.6971i	−0.0518352	+	0.0299271i
$726$		0			0
$727$	−482.133	+	835.078i	−0.663181	+	1.14866i	0.316594	+	0.948561i	$0.397461\pi$
$727$	−482.133	+	835.078i	−0.663181	+	1.14866i	−0.979775	+	0.200102i	$0.935873\pi$
$728$	467.598	+	138.931i	0.642305	+	0.190840i
$729$		0			0
$730$		−	37.7243i		−	0.0516772i
$731$	893.709	+	515.983i	1.22258	+	0.705859i
$732$		0			0
$733$	884.929	−	510.914i	1.20727	−	0.697018i	0.245108	−	0.969496i	$-0.421177\pi$
$733$	884.929	−	510.914i	1.20727	−	0.697018i	0.962162	+	0.272478i	$0.0878432\pi$
$734$	−36.2591	−	62.8027i	−0.0493994	−	0.0855622i
$735$		0			0
$736$	−47.5250	−	27.4386i	−0.0645720	−	0.0372807i
$737$			1008.59i			1.36851i
$738$		0			0
$739$			791.607i			1.07119i	0.844476	+	0.535593i	$0.179912\pi$
$739$			791.607i			1.07119i	−0.844476	+	0.535593i	$0.820088\pi$
$740$	91.4634	+	52.8064i	0.123599	+	0.0713600i
$741$		0			0
$742$	−0.0894862	−	0.154995i	−0.000120601	−	0.000208888i
$743$	186.552	+	323.118i	0.251080	+	0.434883i	0.963823	−	0.266542i	$-0.0858809\pi$
$743$	186.552	+	323.118i	0.251080	+	0.434883i	−0.712743	+	0.701425i	$0.752548\pi$
$744$		0			0
$745$	−44.0125	+	76.2319i	−0.0590772	+	0.102325i
$746$	−280.421			−0.375900
$747$		0			0
$748$		−	1312.39i		−	1.75453i
$749$	−884.933	+	1532.75i	−1.18149	+	2.04639i
$750$		0			0
$751$	446.787	+	773.858i	0.594923	+	1.03044i	0.993558	+	0.113327i	$0.0361507\pi$
$751$	446.787	+	773.858i	0.594923	+	1.03044i	−0.398635	+	0.917110i	$0.630516\pi$
$752$	−179.954	−	311.690i	−0.239301	−	0.414481i
$753$		0			0
$754$	11.4024	−	10.8025i	0.0151226	−	0.0143269i
$755$			92.4282i			0.122421i
$756$		0			0
$757$	−121.247			−0.160168			−0.0800839	−	0.996788i	$-0.525519\pi$
$757$	−121.247			−0.160168			−0.0800839	+	0.996788i	$0.525519\pi$
$758$	142.097	+	82.0398i	0.187463	+	0.108232i
$759$		0			0
$760$	−94.3755	+	54.4877i	−0.124178	+	0.0716944i
$761$	342.786	+	593.723i	0.450442	+	0.780189i	0.998413	−	0.0563086i	$-0.0179331\pi$
$761$	342.786	+	593.723i	0.450442	+	0.780189i	−0.547971	+	0.836497i	$0.684600\pi$
$762$		0			0
$763$	575.567	−	996.912i	0.754348	−	1.30657i
$764$		−	265.246i		−	0.347180i
$765$		0			0
$766$	223.257			0.291458
$767$	588.897	+	621.601i	0.767792	+	0.810432i
$768$		0			0
$769$	907.453	−	523.918i	1.18004	−	0.681298i	0.224019	−	0.974585i	$-0.428082\pi$
$769$	907.453	−	523.918i	1.18004	−	0.681298i	0.956025	+	0.293287i	$0.0947490\pi$
$770$	176.279	−	101.775i	0.228934	−	0.132175i
$771$		0			0
$772$	151.859	+	87.6756i	0.196708	+	0.113569i
$773$	−1233.81			−1.59613			−0.798065	−	0.602571i	$-0.794143\pi$
$773$	−1233.81			−1.59613			−0.798065	+	0.602571i	$0.794143\pi$
$774$		0			0
$775$		−	672.227i		−	0.867390i
$776$	372.868	+	215.275i	0.480499	+	0.277416i
$777$		0			0
$778$	163.222	−	94.2362i	0.209797	−	0.121126i
$779$	−668.282	+	385.833i	−0.857871	+	0.495292i
$780$		0			0
$781$	229.925	−	398.241i	0.294398	−	0.509912i
$782$	27.9062			0.0356857
$783$		0			0
$784$	−627.115			−0.799892
$785$	298.817	−	517.566i	0.380658	−	0.659319i
$786$		0			0
$787$	−519.807	+	300.111i	−0.660492	+	0.381335i	−0.792465	−	0.609918i	$-0.791202\pi$
$787$	−519.807	+	300.111i	−0.660492	+	0.381335i	0.131972	+	0.991253i	$0.457869\pi$
$788$	365.322	+	632.756i	0.463607	+	0.802990i
$789$		0			0
$790$	48.4786	−	83.9674i	0.0613653	−	0.106288i
$791$	−677.408			−0.856394
$792$		0			0
$793$	−301.255	+	1013.92i	−0.379892	+	1.27859i
$794$	−48.8246	−	28.1889i	−0.0614919	−	0.0355024i
$795$		0			0
$796$	−41.8434	−	72.4749i	−0.0525671	−	0.0910488i
$797$	−894.237	+	516.288i	−1.12200	+	0.647789i	−0.941912	−	0.335860i	$-0.890973\pi$
$797$	−894.237	+	516.288i	−1.12200	+	0.647789i	−0.180092	+	0.983650i	$0.557640\pi$
$798$		0			0
$799$	532.406	+	307.385i	0.666341	+	0.384712i
$800$	384.035			0.480044
$801$		0			0
$802$	165.746			0.206666
$803$	381.188	+	220.079i	0.474705	+	0.274071i
$804$		0			0
$805$	−33.6079	−	58.2106i	−0.0417490	−	0.0723113i
$806$	56.6051	+	236.643i	0.0702297	+	0.293602i
$807$		0			0
$808$	653.484	+	377.289i	0.808768	+	0.466942i
$809$		−	1119.42i		−	1.38371i	−0.722036	−	0.691856i	$-0.756793\pi$
$809$		−	1119.42i		−	1.38371i	0.722036	−	0.691856i	$-0.243207\pi$
$810$		0			0
$811$			998.606i			1.23133i	0.788009	+	0.615663i	$0.211112\pi$
$811$			998.606i			1.23133i	−0.788009	+	0.615663i	$0.788888\pi$
$812$	−45.3764	+	78.5943i	−0.0558823	+	0.0967910i
$813$		0			0
$814$	68.7181	−	39.6744i	0.0844203	−	0.0487401i
$815$	−99.8313	+	57.6376i	−0.122492	+	0.0707210i
$816$		0			0
$817$	419.427	+	242.157i	0.513375	+	0.296397i
$818$		−	305.313i		−	0.373243i
$819$		0			0
$820$	−744.635			−0.908092
$821$	−98.4510	+	170.522i	−0.119916	+	0.207701i	−0.919734	−	0.392542i	$-0.871596\pi$
$821$	−98.4510	+	170.522i	−0.119916	+	0.207701i	0.799818	+	0.600242i	$0.204929\pi$
$822$		0			0
$823$	207.026	+	358.580i	0.251551	+	0.435699i	0.963953	−	0.266073i	$-0.0857261\pi$
$823$	207.026	+	358.580i	0.251551	+	0.435699i	−0.712402	+	0.701771i	$0.752393\pi$
$824$	41.6346	+	72.1132i	0.0505274	+	0.0875160i
$825$		0			0
$826$	275.895	+	159.288i	0.334013	+	0.192843i
$827$	519.406			0.628061			0.314030	−	0.949413i	$-0.398321\pi$
$827$	519.406			0.628061			0.314030	+	0.949413i	$0.398321\pi$
$828$		0			0
$829$	−89.7267			−0.108235			−0.0541175	−	0.998535i	$-0.517235\pi$
$829$	−89.7267			−0.108235			−0.0541175	+	0.998535i	$0.517235\pi$
$830$	95.8224	−	165.969i	0.115449	−	0.199963i
$831$		0			0
$832$	530.085	−	126.796i	0.637121	−	0.152400i
$833$	927.681	−	535.597i	1.11366	−	0.642974i
$834$		0			0
$835$	−281.554	+	487.665i	−0.337190	+	0.584030i
$836$		−	615.918i		−	0.736744i
$837$		0			0
$838$			123.656i			0.147561i
$839$	−434.792	+	753.083i	−0.518227	+	0.897596i	0.481549	+	0.876419i	$0.340074\pi$
$839$	−434.792	+	753.083i	−0.518227	+	0.897596i	−0.999776	+	0.0211762i	$0.993259\pi$
$840$		0			0
$841$	−417.484	−	723.103i	−0.496413	−	0.859813i
$842$	316.656	−	182.821i	0.376075	−	0.217127i
$843$		0			0
$844$	363.635	−	629.835i	0.430847	−	0.746250i
$845$	−383.378	−	249.875i	−0.453702	−	0.295710i
$846$		0			0
$847$			1185.27i			1.39937i
$848$	−0.421549	−	0.243382i	−0.000497110	−	0.000287007i
$849$		0			0
$850$	−169.126	+	97.6451i	−0.198972	+	0.114877i
$851$	−13.1012	−	22.6920i	−0.0153951	−	0.0266651i
$852$		0			0
$853$	429.724	+	248.101i	0.503780	+	0.290857i	0.730273	−	0.683155i	$-0.239393\pi$
$853$	429.724	+	248.101i	0.503780	+	0.290857i	−0.226493	+	0.974013i	$0.572726\pi$
$854$			393.533i			0.460812i
$855$		0			0
$856$		−	686.969i		−	0.802534i
$857$	−1249.94	−	721.652i	−1.45850	−	0.842068i	−0.459566	−	0.888144i	$-0.651995\pi$
$857$	−1249.94	−	721.652i	−1.45850	−	0.842068i	−0.998938	+	0.0460758i	$0.985328\pi$
$858$		0			0
$859$	19.8064	+	34.3056i	0.0230575	+	0.0399367i	0.877324	−	0.479899i	$-0.159327\pi$
$859$	19.8064	+	34.3056i	0.0230575	+	0.0399367i	−0.854266	+	0.519835i	$0.825993\pi$
$860$	233.674	+	404.736i	0.271714	+	0.470623i
$861$		0			0
$862$	−159.690	+	276.592i	−0.185256	+	0.320872i
$863$	−661.701			−0.766745			−0.383373	−	0.923594i	$-0.625238\pi$
$863$	−661.701			−0.766745			−0.383373	+	0.923594i	$0.625238\pi$
$864$		0			0
$865$			147.059i			0.170010i
$866$	60.4099	−	104.633i	0.0697574	−	0.120823i
$867$		0			0
$868$	−702.933	−	1217.52i	−0.809831	−	1.40267i
$869$	565.636	+	979.710i	0.650904	+	1.12740i
$870$		0			0
$871$	612.435	−	580.213i	0.703141	−	0.666146i
$872$			446.810i			0.512397i
$873$		0			0
$874$	13.0967			0.0149848
$875$	983.785	+	567.988i	1.12433	+	0.649130i
$876$		0			0
$877$	−469.408	+	271.013i	−0.535243	+	0.309022i	−0.743149	−	0.669126i	$-0.766668\pi$
$877$	−469.408	+	271.013i	−0.535243	+	0.309022i	0.207906	+	0.978149i	$0.433335\pi$
$878$	−7.40958	−	12.8338i	−0.00843915	−	0.0146170i
$879$		0			0
$880$	276.804	−	479.439i	0.314550	−	0.544817i
$881$			923.968i			1.04877i	0.851481	+	0.524386i	$0.175705\pi$
$881$			923.968i			1.04877i	−0.851481	+	0.524386i	$0.824295\pi$
$882$		0			0
$883$	1126.68			1.27597			0.637986	−	0.770048i	$-0.279768\pi$
$883$	1126.68			1.27597			0.637986	+	0.770048i	$0.279768\pi$
$884$	−796.906	+	754.979i	−0.901478	+	0.854048i
$885$		0			0
$886$	−74.8114	+	43.1924i	−0.0844372	+	0.0487498i
$887$	−43.5445	+	25.1404i	−0.0490919	+	0.0283432i	−0.524345	−	0.851506i	$-0.675690\pi$
$887$	−43.5445	+	25.1404i	−0.0490919	+	0.0283432i	0.475253	+	0.879849i	$0.342356\pi$
$888$		0			0
$889$	−603.592	−	348.484i	−0.678956	−	0.391996i
$890$	−107.342			−0.120609
$891$		0			0
$892$			862.466i			0.966890i
$893$	249.864	+	144.259i	0.279803	+	0.161544i
$894$		0			0
$895$	193.576	−	111.761i	0.216286	−	0.124872i
$896$	915.956	−	528.828i	1.02227	−	0.590209i
$897$		0			0
$898$	31.0905	−	53.8504i	0.0346220	−	0.0599670i
$899$	−93.4514			−0.103950
$900$		0			0
$901$	0.831455			0.000922813
$902$	−279.729	+	484.505i	−0.310121	+	0.537145i
$903$		0			0
$904$	227.708	−	131.467i	0.251889	−	0.145428i
$905$	−226.076	−	391.575i	−0.249808	−	0.432680i
$906$		0			0
$907$	−353.741	+	612.697i	−0.390012	+	0.675521i	−0.992451	−	0.122645i	$-0.960862\pi$
$907$	−353.741	+	612.697i	−0.390012	+	0.675521i	0.602439	+	0.798165i	$0.294196\pi$
$908$	936.541			1.03143
$909$		0			0
$910$	−163.208	−	48.4919i	−0.179349	−	0.0532878i
$911$	−528.262	−	304.992i	−0.579870	−	0.334788i	0.181211	−	0.983444i	$-0.441998\pi$
$911$	−528.262	−	304.992i	−0.579870	−	0.334788i	−0.761082	+	0.648656i	$0.775331\pi$
$912$		0			0
$913$	1118.03	+	1936.49i	1.22457	+	2.12101i
$914$	−282.766	+	163.255i	−0.309372	+	0.178616i
$915$		0			0
$916$	−174.108	−	100.522i	−0.190075	−	0.109740i
$917$	−1442.87			−1.57346
$918$		0			0
$919$	750.201			0.816323			0.408162	−	0.912910i	$-0.366170\pi$
$919$	750.201			0.816323			0.408162	+	0.912910i	$0.366170\pi$
$920$	22.5943	+	13.0448i	0.0245590	+	0.0141792i
$921$		0			0
$922$	7.68517	+	13.3111i	0.00833532	+	0.0144372i
$923$	−374.088	+	89.4820i	−0.405296	+	0.0969469i
$924$		0			0
$925$	158.801	+	91.6835i	0.171676	+	0.0991173i
$926$		−	317.067i		−	0.342405i
$927$		0			0
$928$		−	53.3876i		−	0.0575298i
$929$	248.612	−	430.609i	0.267613	−	0.463519i	−0.700632	−	0.713523i	$-0.747098\pi$
$929$	248.612	−	430.609i	0.267613	−	0.463519i	0.968245	+	0.250004i	$0.0804318\pi$
$930$		0			0
$931$	435.371	−	251.361i	0.467638	−	0.269991i
$932$	−362.658	+	209.381i	−0.389118	+	0.224658i
$933$		0			0
$934$	−253.472	−	146.342i	−0.271383	−	0.156683i
$935$			945.634i			1.01137i
$936$		0			0
$937$	−549.302			−0.586234			−0.293117	−	0.956077i	$-0.594693\pi$
$937$	−549.302			−0.586234			−0.293117	+	0.956077i	$0.594693\pi$
$938$	156.939	−	271.827i	0.167313	−	0.289794i
$939$		0			0
$940$	139.206	+	241.112i	0.148091	+	0.256502i
$941$	727.049	+	1259.29i	0.772634	+	1.33824i	0.936114	+	0.351695i	$0.114395\pi$
$941$	727.049	+	1259.29i	0.772634	+	1.33824i	−0.163480	+	0.986547i	$0.552272\pi$
$942$		0			0
$943$	159.992	+	92.3717i	0.169663	+	0.0979551i
$944$	866.453			0.917852
$945$		0			0
$946$	351.127			0.371171
$947$	−579.533	+	1003.78i	−0.611968	+	1.05996i	0.378941	+	0.925421i	$0.376288\pi$
$947$	−579.533	+	1003.78i	−0.611968	+	1.05996i	−0.990908	+	0.134538i	$0.957045\pi$
$948$		0			0
$949$	−85.6502	−	358.069i	−0.0902531	−	0.377312i
$950$	−79.3728	+	45.8259i	−0.0835503	+	0.0482378i
$951$		0			0
$952$	−421.571	+	730.182i	−0.442827	+	0.766998i
$953$		−	1594.88i		−	1.67354i	−0.547555	−	0.836770i	$-0.684441\pi$
$953$		−	1594.88i		−	1.67354i	0.547555	−	0.836770i	$-0.315559\pi$
$954$		0			0
$955$			191.121i			0.200127i
$956$	442.092	−	765.726i	0.462439	−	0.800968i
$957$		0			0
$958$	15.4816	+	26.8149i	0.0161603	+	0.0279905i
$959$	596.017	−	344.111i	0.621499	−	0.358822i
$960$		0			0
$961$	243.335	−	421.469i	0.253211	−	0.438574i
$962$	−63.6226	−	18.9034i	−0.0661357	−	0.0196501i
$963$		0			0
$964$		−	957.721i		−	0.993486i
$965$	−109.421	−	63.1741i	−0.113389	−	0.0654654i
$966$		0			0
$967$	−757.971	+	437.615i	−0.783837	+	0.452549i	−0.837789	−	0.545995i	$-0.816152\pi$
$967$	−757.971	+	437.615i	−0.783837	+	0.452549i	0.0539512	+	0.998544i	$0.482818\pi$
$968$	−230.029	−	398.423i	−0.237634	−	0.411594i
$969$		0			0
$970$	−130.144	−	75.1385i	−0.134169	−	0.0774623i
$971$			1712.38i			1.76352i	0.471694	+	0.881762i	$0.343643\pi$
$971$			1712.38i			1.76352i	−0.471694	+	0.881762i	$0.656357\pi$
$972$		0			0
$973$			1505.78i			1.54757i
$974$	61.1123	+	35.2832i	0.0627436	+	0.0362250i
$975$		0			0
$976$	535.160	+	926.923i	0.548319	+	0.949717i
$977$	−545.611	−	945.026i	−0.558455	−	0.967273i	−0.997626	−	0.0688692i	$-0.978061\pi$
$977$	−545.611	−	945.026i	−0.558455	−	0.967273i	0.439170	−	0.898404i	$-0.355272\pi$
$978$		0			0
$979$	626.217	−	1084.64i	0.639650	−	1.10791i
$980$	485.113			0.495014
$981$		0			0
$982$			468.208i			0.476790i
$983$	493.179	−	854.212i	0.501708	−	0.868984i	−0.498290	−	0.867011i	$-0.666038\pi$
$983$	493.179	−	854.212i	0.501708	−	0.868984i	0.999998	−	0.00197385i	$-0.000628296\pi$
$984$		0			0
$985$	−263.231	−	455.929i	−0.267239	−	0.462872i
$986$	13.5744	+	23.5115i	0.0137671	+	0.0238454i
$987$		0			0
$988$	−373.997	+	354.320i	−0.378539	+	0.358623i
$989$		−	115.949i		−	0.117238i
$990$		0			0
$991$	−232.458			−0.234569			−0.117285	−	0.993098i	$-0.537419\pi$
$991$	−232.458			−0.234569			−0.117285	+	0.993098i	$0.537419\pi$
$992$	716.234	+	413.518i	0.722010	+	0.416853i
$993$		0			0
$994$	−123.935	+	71.5536i	−0.124683	+	0.0719855i
$995$	30.1500	+	52.2213i	0.0303015	+	0.0524838i
$996$		0			0
$997$	57.6711	−	99.8893i	0.0578446	−	0.100190i	−0.835653	−	0.549258i	$-0.814911\pi$
$997$	57.6711	−	99.8893i	0.0578446	−	0.100190i	0.893498	+	0.449068i	$0.148244\pi$
$998$		−	32.0062i		−	0.0320703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.3.n.a.116.15		52
3.2	odd	2		117.3.n.a.38.12	✓	52
9.4	even	3		117.3.n.a.77.15	yes	52
9.5	odd	6	inner	351.3.n.a.233.12		52
13.12	even	2	inner	351.3.n.a.116.12		52
39.38	odd	2		117.3.n.a.38.15	yes	52
117.77	odd	6	inner	351.3.n.a.233.15		52
117.103	even	6		117.3.n.a.77.12	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.n.a.38.12	✓	52	3.2	odd	2
117.3.n.a.38.15	yes	52	39.38	odd	2
117.3.n.a.77.12	yes	52	117.103	even	6
117.3.n.a.77.15	yes	52	9.4	even	3
351.3.n.a.116.12		52	13.12	even	2	inner
351.3.n.a.116.15		52	1.1	even	1	trivial
351.3.n.a.233.12		52	9.5	odd	6	inner
351.3.n.a.233.15		52	117.77	odd	6	inner

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	351.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.245962 - 0.426018i) q^{2} +(1.87901 + 3.25453i) q^{4} +(-1.35391 - 2.34503i) q^{5} +(-8.51494 - 4.91611i) q^{7} +3.81635 q^{8} -1.33204 q^{10} +(7.77093 - 13.4596i) q^{11} +(-12.6433 + 3.02429i) q^{13} +(-4.18870 + 2.41835i) q^{14} +(-6.57735 + 11.3923i) q^{16} -22.4699i q^{17} -10.5454i q^{19} +(5.08800 - 8.81267i) q^{20} +(-3.82270 - 6.62112i) q^{22} +(-2.18641 + 1.26233i) q^{23} +(8.83387 - 15.3007i) q^{25} +(-1.82137 + 6.13015i) q^{26} -36.9496i q^{28} +(-2.12707 - 1.22806i) q^{29} +(32.9508 - 19.0241i) q^{31} +(10.8683 + 18.8244i) q^{32} +(-9.57260 - 5.52674i) q^{34} +26.6238i q^{35} +10.3786i q^{37} +(-4.49252 - 2.59376i) q^{38} +(-5.16698 - 8.94947i) q^{40} +(-36.5879 - 63.3720i) q^{41} +(-22.9633 + 39.7736i) q^{43} +58.4065 q^{44} +1.24194i q^{46} +(-13.6798 + 23.6942i) q^{47} +(23.8362 + 41.2855i) q^{49} +(-4.34559 - 7.52679i) q^{50} +(-33.5995 - 35.4655i) q^{52} +0.0370030i q^{53} -42.0844 q^{55} +(-32.4960 - 18.7616i) q^{56} +(-1.04636 + 0.604114i) q^{58} +(-32.9332 - 57.0420i) q^{59} +(40.6820 - 70.4633i) q^{61} -18.7168i q^{62} -41.9261 q^{64} +(24.2099 + 25.5544i) q^{65} +(-56.2009 + 32.4476i) q^{67} +(73.1291 - 42.2211i) q^{68} +(11.3422 + 6.54843i) q^{70} +29.5878 q^{71} +28.3208i q^{73} +(4.42149 + 2.55275i) q^{74} +(34.3203 - 19.8148i) q^{76} +(-132.338 + 76.4054i) q^{77} +(-36.3943 + 63.0368i) q^{79} +35.6204 q^{80} -35.9969 q^{82} +(-71.9367 + 124.598i) q^{83} +(-52.6927 + 30.4222i) q^{85} +(11.2962 + 19.5656i) q^{86} +(29.6566 - 51.3667i) q^{88} +80.5846 q^{89} +(122.525 + 36.4043i) q^{91} +(-8.21657 - 4.74384i) q^{92} +(6.72944 + 11.6557i) q^{94} +(-24.7293 + 14.2775i) q^{95} +(97.7027 + 56.4087i) q^{97} +23.4512 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 50 q^{4} + 8 q^{10} - 6 q^{13} + 6 q^{14} - 90 q^{16} + 14 q^{22} - 138 q^{23} - 92 q^{25} - 48 q^{29} - 324 q^{38} - 68 q^{40} + 62 q^{43} + 70 q^{49} - 4 q^{52} + 92 q^{55} + 276 q^{56} + 12 q^{61}+ \cdots - 504 q^{95}+O(q^{100}) \) 52 * q - 50 * q^4 + 8 * q^10 - 6 * q^13 + 6 * q^14 - 90 * q^16 + 14 * q^22 - 138 * q^23 - 92 * q^25 - 48 * q^29 - 324 * q^38 - 68 * q^40 + 62 * q^43 + 70 * q^49 - 4 * q^52 + 92 * q^55 + 276 * q^56 + 12 * q^61 + 12 * q^64 + 588 * q^65 + 144 * q^68 - 342 * q^74 + 510 * q^77 - 24 * q^79 - 292 * q^82 - 62 * q^88 + 264 * q^91 + 396 * q^92 - 160 * q^94 - 504 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more