LMFDB - Embedded newform 441.3.l.b.391.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(97,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("441.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.l (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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			391.5
Character	$\chi$	$=$	441.391
Dual form			441.3.l.b.97.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.840995 - 1.45665i) q^{2} +(-2.99659 - 0.143035i) q^{3} +(0.585454 - 1.01404i) q^{4} +(-2.03050 - 1.17231i) q^{5} +(2.31176 + 4.48526i) q^{6} -8.69742 q^{8} +(8.95908 + 0.857237i) q^{9} +O(q^{10})$	\(q+(-0.840995 - 1.45665i) q^{2} +(-2.99659 - 0.143035i) q^{3} +(0.585454 - 1.01404i) q^{4} +(-2.03050 - 1.17231i) q^{5} +(2.31176 + 4.48526i) q^{6} -8.69742 q^{8} +(8.95908 + 0.857237i) q^{9} +3.94363i q^{10} +(3.10369 + 5.37574i) q^{11} +(-1.89941 + 2.95491i) q^{12} +(-21.3461 - 12.3242i) q^{13} +(5.91690 + 3.80337i) q^{15} +(4.97267 + 8.61292i) q^{16} +22.5368i q^{17} +(-6.28585 - 13.7711i) q^{18} +10.7958i q^{19} +(-2.37753 + 1.37267i) q^{20} +(5.22037 - 9.04195i) q^{22} +(4.27197 - 7.39927i) q^{23} +(26.0626 + 1.24404i) q^{24} +(-9.75137 - 16.8899i) q^{25} +41.4583i q^{26} +(-26.7241 - 3.85025i) q^{27} +(16.1494 + 27.9715i) q^{29} +(0.564079 - 11.8174i) q^{30} +(1.44290 + 0.833060i) q^{31} +(-9.03085 + 15.6419i) q^{32} +(-8.53154 - 16.5528i) q^{33} +(32.8282 - 18.9534i) q^{34} +(6.11440 - 8.58296i) q^{36} +39.5686 q^{37} +(15.7256 - 9.07919i) q^{38} +(62.2027 + 39.9837i) q^{39} +(17.6601 + 10.1961i) q^{40} +(27.9638 + 16.1449i) q^{41} +(-2.15380 - 3.73049i) q^{43} +7.26826 q^{44} +(-17.1865 - 12.2435i) q^{45} -14.3708 q^{46} +(42.0916 - 24.3016i) q^{47} +(-13.6691 - 26.5206i) q^{48} +(-16.4017 + 28.4086i) q^{50} +(3.22356 - 67.5336i) q^{51} +(-24.9943 + 14.4305i) q^{52} +2.09872 q^{53} +(16.8664 + 42.1656i) q^{54} -14.5539i q^{55} +(1.54418 - 32.3505i) q^{57} +(27.1631 - 47.0478i) q^{58} +(91.7236 + 52.9566i) q^{59} +(7.32082 - 3.77325i) q^{60} +(-20.0381 + 11.5690i) q^{61} -2.80240i q^{62} +70.1610 q^{64} +(28.8955 + 50.0485i) q^{65} +(-16.9366 + 26.3483i) q^{66} +(1.29860 - 2.24925i) q^{67} +(22.8531 + 13.1943i) q^{68} +(-13.8597 + 21.5615i) q^{69} -66.6892 q^{71} +(-77.9209 - 7.45575i) q^{72} +21.3604i q^{73} +(-33.2770 - 57.6375i) q^{74} +(26.8050 + 52.0068i) q^{75} +(10.9473 + 6.32042i) q^{76} +(5.93001 - 124.233i) q^{78} +(51.5954 + 89.3659i) q^{79} -23.3181i q^{80} +(79.5303 + 15.3601i) q^{81} -54.3111i q^{82} +(10.0537 - 5.80449i) q^{83} +(26.4202 - 45.7611i) q^{85} +(-3.62267 + 6.27465i) q^{86} +(-44.3920 - 86.1290i) q^{87} +(-26.9940 - 46.7551i) q^{88} +13.8710i q^{89} +(-3.38063 + 35.3313i) q^{90} +(-5.00208 - 8.66386i) q^{92} +(-4.20463 - 2.70272i) q^{93} +(-70.7976 - 40.8750i) q^{94} +(12.6560 - 21.9208i) q^{95} +(29.2991 - 45.5806i) q^{96} +(13.0649 - 7.54303i) q^{97} +(23.1979 + 50.8223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9	$ 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9} + 7 q^{11} + 27 q^{12} - 15 q^{13} - 18 q^{15} - 27 q^{16} + 9 q^{18} - 108 q^{20} - 10 q^{22} + 34 q^{23} + 120 q^{24} + 31 q^{25} + 81 q^{27} + 70 q^{29} + 33 q^{30} + 45 q^{31} + 153 q^{32} - 111 q^{33} - 12 q^{34} - 174 q^{36} - 18 q^{37} - 87 q^{38} - 9 q^{39} + 102 q^{40} + 234 q^{41} + 30 q^{43} - 102 q^{44} + 3 q^{45} + 44 q^{46} - 111 q^{47} - 147 q^{48} + 241 q^{50} - 6 q^{51} + 219 q^{52} - 296 q^{53} + 207 q^{54} + 189 q^{57} + 17 q^{58} + 42 q^{59} - 489 q^{60} + 120 q^{61} - 48 q^{64} + 114 q^{65} - 705 q^{66} - 34 q^{67} + 18 q^{68} - 78 q^{69} - 350 q^{71} + 177 q^{72} + 359 q^{74} + 387 q^{75} - 72 q^{76} - 375 q^{78} - 82 q^{79} + 438 q^{81} - 738 q^{83} + 3 q^{85} + 17 q^{86} + 564 q^{87} + 25 q^{88} + 543 q^{90} + 288 q^{92} - 30 q^{93} - 3 q^{94} + 507 q^{95} - 813 q^{96} + 57 q^{97} - 162 q^{99}+O(q^{100}) $ 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9 + 7 * q^11 + 27 * q^12 - 15 * q^13 - 18 * q^15 - 27 * q^16 + 9 * q^18 - 108 * q^20 - 10 * q^22 + 34 * q^23 + 120 * q^24 + 31 * q^25 + 81 * q^27 + 70 * q^29 + 33 * q^30 + 45 * q^31 + 153 * q^32 - 111 * q^33 - 12 * q^34 - 174 * q^36 - 18 * q^37 - 87 * q^38 - 9 * q^39 + 102 * q^40 + 234 * q^41 + 30 * q^43 - 102 * q^44 + 3 * q^45 + 44 * q^46 - 111 * q^47 - 147 * q^48 + 241 * q^50 - 6 * q^51 + 219 * q^52 - 296 * q^53 + 207 * q^54 + 189 * q^57 + 17 * q^58 + 42 * q^59 - 489 * q^60 + 120 * q^61 - 48 * q^64 + 114 * q^65 - 705 * q^66 - 34 * q^67 + 18 * q^68 - 78 * q^69 - 350 * q^71 + 177 * q^72 + 359 * q^74 + 387 * q^75 - 72 * q^76 - 375 * q^78 - 82 * q^79 + 438 * q^81 - 738 * q^83 + 3 * q^85 + 17 * q^86 + 564 * q^87 + 25 * q^88 + 543 * q^90 + 288 * q^92 - 30 * q^93 - 3 * q^94 + 507 * q^95 - 813 * q^96 + 57 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.840995	−	1.45665i	−0.420498	−	0.728323i	0.575490	−	0.817808i	$-0.304811\pi$
$2$	−0.840995	−	1.45665i	−0.420498	−	0.728323i	−0.995988	+	0.0894852i	$0.971478\pi$
$3$	−2.99659	−	0.143035i	−0.998863	−	0.0476785i
$3$	−2.99659	−	0.143035i	−0.998863	−	0.0476785i
$4$	0.585454	−	1.01404i	0.146363	−	0.253509i
$5$	−2.03050	−	1.17231i	−0.406100	−	0.234462i	0.283012	−	0.959116i	$-0.408666\pi$
$5$	−2.03050	−	1.17231i	−0.406100	−	0.234462i	−0.689113	+	0.724654i	$0.742000\pi$
$6$	2.31176	+	4.48526i	0.385294	+	0.747544i
$7$		0			0
$7$		0			0
$8$	−8.69742			−1.08718
$9$	8.95908	+	0.857237i	0.995454	+	0.0952486i
$10$			3.94363i			0.394363i
$11$	3.10369	+	5.37574i	0.282153	+	0.488704i	0.971915	−	0.235333i	$-0.0756180\pi$
$11$	3.10369	+	5.37574i	0.282153	+	0.488704i	−0.689762	+	0.724037i	$0.742285\pi$
$12$	−1.89941	+	2.95491i	−0.158284	+	0.246242i
$13$	−21.3461	−	12.3242i	−1.64201	−	0.948013i	−0.980119	−	0.198411i	$-0.936422\pi$
$13$	−21.3461	−	12.3242i	−1.64201	−	0.948013i	−0.661889	−	0.749602i	$-0.730245\pi$
$14$		0			0
$15$	5.91690	+	3.80337i	0.394460	+	0.253558i
$16$	4.97267	+	8.61292i	0.310792	+	0.538308i
$17$			22.5368i			1.32569i	0.748754	+	0.662847i	$0.230652\pi$
$17$			22.5368i			1.32569i	−0.748754	+	0.662847i	$0.769348\pi$
$18$	−6.28585	−	13.7711i	−0.349214	−	0.765064i
$19$			10.7958i			0.568198i	0.958795	+	0.284099i	$0.0916945\pi$
$19$			10.7958i			0.568198i	−0.958795	+	0.284099i	$0.908306\pi$
$20$	−2.37753	+	1.37267i	−0.118877	+	0.0686334i
$21$		0			0
$22$	5.22037	−	9.04195i	0.237290	−	0.410998i
$23$	4.27197	−	7.39927i	0.185738	−	0.321707i	−0.758087	−	0.652153i	$-0.773866\pi$
$23$	4.27197	−	7.39927i	0.185738	−	0.321707i	0.943825	+	0.330446i	$0.107199\pi$
$24$	26.0626	+	1.24404i	1.08594	+	0.0518350i
$25$	−9.75137	−	16.8899i	−0.390055	−	0.675595i
$26$			41.4583i			1.59455i
$27$	−26.7241	−	3.85025i	−0.989780	−	0.142602i
$28$		0			0
$29$	16.1494	+	27.9715i	0.556874	+	0.964535i	0.997755	+	0.0669689i	$0.0213328\pi$
$29$	16.1494	+	27.9715i	0.556874	+	0.964535i	−0.440881	+	0.897566i	$0.645334\pi$
$30$	0.564079	−	11.8174i	0.0188026	−	0.393915i
$31$	1.44290	+	0.833060i	0.0465452	+	0.0268729i	0.523092	−	0.852276i	$-0.324778\pi$
$31$	1.44290	+	0.833060i	0.0465452	+	0.0268729i	−0.476547	+	0.879149i	$0.658112\pi$
$32$	−9.03085	+	15.6419i	−0.282214	+	0.488809i
$33$	−8.53154	−	16.5528i	−0.258532	−	0.501601i
$34$	32.8282	−	18.9534i	0.965535	−	0.557452i
$35$		0			0
$36$	6.11440	−	8.58296i	0.169844	−	0.238415i
$37$	39.5686			1.06942			0.534711	−	0.845035i	$-0.320421\pi$
$37$	39.5686			1.06942			0.534711	+	0.845035i	$0.320421\pi$
$38$	15.7256	−	9.07919i	0.413832	−	0.238926i
$39$	62.2027	+	39.9837i	1.59494	+	1.02522i
$40$	17.6601	+	10.1961i	0.441503	+	0.254902i
$41$	27.9638	+	16.1449i	0.682044	+	0.393778i	0.800625	−	0.599166i	$-0.204501\pi$
$41$	27.9638	+	16.1449i	0.682044	+	0.393778i	−0.118581	+	0.992944i	$0.537835\pi$
$42$		0			0
$43$	−2.15380	−	3.73049i	−0.0500884	−	0.0867556i	0.839894	−	0.542750i	$-0.182617\pi$
$43$	−2.15380	−	3.73049i	−0.0500884	−	0.0867556i	−0.889983	+	0.455995i	$0.849284\pi$
$44$	7.26826			0.165188
$45$	−17.1865	−	12.2435i	−0.381922	−	0.272077i
$46$	−14.3708			−0.312409
$47$	42.0916	−	24.3016i	0.895565	−	0.517055i	0.0198064	−	0.999804i	$-0.493695\pi$
$47$	42.0916	−	24.3016i	0.895565	−	0.517055i	0.875759	+	0.482749i	$0.160362\pi$
$48$	−13.6691	−	26.5206i	−0.284773	−	0.552514i
$49$		0			0
$50$	−16.4017	+	28.4086i	−0.328034	+	0.568172i
$51$	3.22356	−	67.5336i	0.0632071	−	1.32419i
$52$	−24.9943	+	14.4305i	−0.480660	+	0.277509i
$53$	2.09872			0.0395984			0.0197992	−	0.999804i	$-0.493697\pi$
$53$	2.09872			0.0395984			0.0197992	+	0.999804i	$0.493697\pi$
$54$	16.8664	+	42.1656i	0.312340	+	0.780844i
$55$		−	14.5539i		−	0.264617i
$56$		0			0
$57$	1.54418	−	32.3505i	0.0270908	−	0.567552i
$58$	27.1631	−	47.0478i	0.468329	−	0.811169i
$59$	91.7236	+	52.9566i	1.55464	+	0.897570i	0.997754	+	0.0669793i	$0.0213361\pi$
$59$	91.7236	+	52.9566i	1.55464	+	0.897570i	0.556883	+	0.830591i	$0.311997\pi$
$60$	7.32082	−	3.77325i	0.122014	−	0.0628875i
$61$	−20.0381	+	11.5690i	−0.328493	+	0.189656i	−0.655172	−	0.755480i	$-0.727404\pi$
$61$	−20.0381	+	11.5690i	−0.328493	+	0.189656i	0.326679	+	0.945135i	$0.394070\pi$
$62$		−	2.80240i		−	0.0452000i
$63$		0			0
$64$	70.1610			1.09627
$65$	28.8955	+	50.0485i	0.444547	+	0.769977i
$66$	−16.9366	+	26.3483i	−0.256615	+	0.399216i
$67$	1.29860	−	2.24925i	0.0193822	−	0.0335709i	−0.856172	−	0.516692i	$-0.827163\pi$
$67$	1.29860	−	2.24925i	0.0193822	−	0.0335709i	0.875554	+	0.483121i	$0.160497\pi$
$68$	22.8531	+	13.1943i	0.336075	+	0.194033i
$69$	−13.8597	+	21.5615i	−0.200865	+	0.312486i
$70$		0			0
$71$	−66.6892			−0.939285			−0.469642	−	0.882857i	$-0.655617\pi$
$71$	−66.6892			−0.939285			−0.469642	+	0.882857i	$0.655617\pi$
$72$	−77.9209	−	7.45575i	−1.08223	−	0.103552i
$73$			21.3604i			0.292608i	0.989240	+	0.146304i	$0.0467378\pi$
$73$			21.3604i			0.292608i	−0.989240	+	0.146304i	$0.953262\pi$
$74$	−33.2770	−	57.6375i	−0.449689	−	0.778885i
$75$	26.8050	+	52.0068i	0.357400	+	0.693424i
$76$	10.9473	+	6.32042i	0.144043	+	0.0831634i
$77$		0			0
$78$	5.93001	−	124.233i	0.0760257	−	1.59274i
$79$	51.5954	+	89.3659i	0.653107	+	1.13121i	0.982365	+	0.186974i	$0.0598680\pi$
$79$	51.5954	+	89.3659i	0.653107	+	1.13121i	−0.329258	+	0.944240i	$0.606799\pi$
$80$		−	23.3181i		−	0.291476i
$81$	79.5303	+	15.3601i	0.981855	+	0.189631i
$82$		−	54.3111i		−	0.662331i
$83$	10.0537	−	5.80449i	0.121129	−	0.0699337i	−0.438211	−	0.898872i	$-0.644388\pi$
$83$	10.0537	−	5.80449i	0.121129	−	0.0699337i	0.559340	+	0.828938i	$0.311055\pi$
$84$		0			0
$85$	26.4202	−	45.7611i	0.310825	−	0.538365i
$86$	−3.62267	+	6.27465i	−0.0421241	+	0.0729611i
$87$	−44.3920	−	86.1290i	−0.510253	−	0.989989i
$88$	−26.9940	−	46.7551i	−0.306751	−	0.531308i
$89$			13.8710i			0.155854i	0.996959	+	0.0779270i	$0.0248301\pi$
$89$			13.8710i			0.155854i	−0.996959	+	0.0779270i	$0.975170\pi$
$90$	−3.38063	+	35.3313i	−0.0375625	+	0.392570i
$91$		0			0
$92$	−5.00208	−	8.66386i	−0.0543704	−	0.0941723i
$93$	−4.20463	−	2.70272i	−0.0452110	−	0.0290615i
$94$	−70.7976	−	40.8750i	−0.753166	−	0.434841i
$95$	12.6560	−	21.9208i	0.133221	−	0.230746i
$96$	29.2991	−	45.5806i	0.305199	−	0.474797i
$97$	13.0649	−	7.54303i	0.134690	−	0.0777632i	−0.431141	−	0.902285i	$-0.641889\pi$
$97$	13.0649	−	7.54303i	0.134690	−	0.0777632i	0.565831	+	0.824521i	$0.308556\pi$
$98$		0			0
$99$	23.1979	+	50.8223i	0.234322	+	0.513356i
$100$	−22.8359			−0.228359
$101$	−86.1345	+	49.7297i	−0.852816	+	0.492374i	−0.861600	−	0.507588i	$-0.830537\pi$
$101$	−86.1345	+	49.7297i	−0.852816	+	0.492374i	0.00878376	+	0.999961i	$0.497204\pi$
$102$	−101.084	+	52.0998i	−0.991015	+	0.510782i
$103$	−18.1666	−	10.4885i	−0.176374	−	0.101830i	0.409214	−	0.912439i	$-0.365803\pi$
$103$	−18.1666	−	10.4885i	−0.176374	−	0.101830i	−0.585588	+	0.810609i	$0.699136\pi$
$104$	185.656	+	107.189i	1.78515	+	1.03066i
$105$		0			0
$106$	−1.76501	−	3.05709i	−0.0166510	−	0.0288404i
$107$	−125.432			−1.17226			−0.586130	−	0.810217i	$-0.699349\pi$
$107$	−125.432			−1.17226			−0.586130	+	0.810217i	$0.699349\pi$
$108$	−19.5500	+	24.8450i	−0.181018	+	0.230046i
$109$	−103.333			−0.948011			−0.474005	−	0.880522i	$-0.657192\pi$
$109$	−103.333			−0.948011			−0.474005	+	0.880522i	$0.657192\pi$
$110$	−21.1999	+	12.2398i	−0.192727	+	0.111271i
$111$	−118.571	−	5.65971i	−1.06821	−	0.0509884i
$112$		0			0
$113$	−95.5545	+	165.505i	−0.845615	+	1.46465i	0.0394714	+	0.999221i	$0.487433\pi$
$113$	−95.5545	+	165.505i	−0.845615	+	1.46465i	−0.885086	+	0.465427i	$0.845901\pi$
$114$	−48.4218	+	24.9573i	−0.424753	+	0.218923i
$115$	−17.3485	+	10.0162i	−0.150856	+	0.0870970i
$116$	37.8188			0.326024
$117$	−180.677	−	128.712i	−1.54425	−	1.10010i
$118$		−	178.145i		−	1.50970i
$119$		0			0
$120$	−51.4617	−	33.0795i	−0.428848	−	0.275662i
$121$	41.2343	−	71.4199i	0.340779	−	0.590247i
$122$	33.7039	+	19.4589i	0.276261	+	0.159499i
$123$	−81.4867	−	52.3794i	−0.662493	−	0.425849i
$124$	1.68950	−	0.975436i	0.0136250	−	0.00786642i
$125$			104.342i			0.834737i
$126$		0			0
$127$	45.5817			0.358911			0.179456	−	0.983766i	$-0.442566\pi$
$127$	45.5817			0.358911			0.179456	+	0.983766i	$0.442566\pi$
$128$	−22.8817	−	39.6322i	−0.178763	−	0.309627i
$129$	5.92046	+	11.4868i	0.0458950	+	0.0890451i
$130$	48.6020	−	84.1812i	0.373862	−	0.647547i
$131$	−83.9828	−	48.4875i	−0.641090	−	0.370134i	0.143944	−	0.989586i	$-0.454021\pi$
$131$	−83.9828	−	48.4875i	−0.641090	−	0.370134i	−0.785034	+	0.619452i	$0.787355\pi$
$132$	−21.7800	−	1.03962i	−0.165000	−	0.00787590i
$133$		0			0
$134$	−4.36848			−0.0326006
$135$	49.7496	+	39.1469i	0.368515	+	0.289977i
$136$		−	196.012i		−	1.44127i
$137$	93.1817	+	161.395i	0.680158	+	1.17807i	0.974932	+	0.222502i	$0.0714224\pi$
$137$	93.1817	+	161.395i	0.680158	+	1.17807i	−0.294774	+	0.955567i	$0.595244\pi$
$138$	43.0634	+	2.05554i	0.312054	+	0.0148952i
$139$	−144.973	−	83.7005i	−1.04297	−	0.602162i	−0.122300	−	0.992493i	$-0.539027\pi$
$139$	−144.973	−	83.7005i	−1.04297	−	0.602162i	−0.920674	+	0.390331i	$0.872360\pi$
$140$		0			0
$141$	−129.607	+	66.8012i	−0.919199	+	0.473768i
$142$	56.0853	+	97.1426i	0.394967	+	0.684103i
$143$		−	153.001i		−	1.06994i
$144$	37.1673	+	81.4266i	0.258106	+	0.565463i
$145$		−	75.7283i		−	0.522264i
$146$	31.1146	−	17.9640i	0.213114	−	0.123041i
$147$		0			0
$148$	23.1656	−	40.1240i	0.156524	−	0.271108i
$149$	−126.319	+	218.791i	−0.847779	+	1.46840i	0.0354077	+	0.999373i	$0.488727\pi$
$149$	−126.319	+	218.791i	−0.847779	+	1.46840i	−0.883186	+	0.469023i	$0.844606\pi$
$150$	53.2126	−	82.7829i	0.354751	−	0.551886i
$151$	42.5237	+	73.6531i	0.281614	+	0.487769i	0.971782	−	0.235879i	$-0.0757970\pi$
$151$	42.5237	+	73.6531i	0.281614	+	0.487769i	−0.690169	+	0.723648i	$0.742464\pi$
$152$		−	93.8953i		−	0.617732i
$153$	−19.3194	+	201.909i	−0.126271	+	1.31967i
$154$		0			0
$155$	−1.95321	−	3.38306i	−0.0126014	−	0.0218262i
$156$	76.9617	−	39.6671i	0.493344	−	0.254276i
$157$	215.937	+	124.671i	1.37539	+	0.794083i	0.991601	−	0.129336i	$-0.0412846\pi$
$157$	215.937	+	124.671i	1.37539	+	0.794083i	0.383792	+	0.923420i	$0.374618\pi$
$158$	86.7830	−	150.313i	0.549260	−	0.951346i
$159$	−6.28899	−	0.300191i	−0.0395534	−	0.00188799i
$160$	36.6743	−	21.1739i	0.229214	−	0.132337i
$161$		0			0
$162$	−44.5103	−	128.765i	−0.274755	−	0.794848i
$163$	−176.577			−1.08329			−0.541646	−	0.840607i	$-0.682199\pi$
$163$	−176.577			−1.08329			−0.541646	+	0.840607i	$0.682199\pi$
$164$	32.7430	−	18.9042i	0.199652	−	0.115269i
$165$	−2.08173	+	43.6122i	−0.0126165	+	0.264316i
$166$	−16.9102	−	9.76310i	−0.101869	−	0.0588139i
$167$	−48.6253	−	28.0738i	−0.291169	−	0.168107i	0.347300	−	0.937754i	$-0.387099\pi$
$167$	−48.6253	−	28.0738i	−0.291169	−	0.168107i	−0.638469	+	0.769647i	$0.720432\pi$
$168$		0			0
$169$	219.271	+	379.788i	1.29746	+	2.24726i
$170$	−88.8769			−0.522805
$171$	−9.25453	+	96.7201i	−0.0541201	+	0.565615i
$172$	−5.04380			−0.0293244
$173$	5.15846	−	2.97824i	0.0298177	−	0.0172152i	−0.485017	−	0.874505i	$-0.661187\pi$
$173$	5.15846	−	2.97824i	0.0298177	−	0.0172152i	0.514835	+	0.857289i	$0.327853\pi$
$174$	−88.1260	+	137.098i	−0.506471	+	0.787917i
$175$		0			0
$176$	−30.8672	+	53.4636i	−0.175382	+	0.303770i
$177$	−267.283	−	171.809i	−1.51007	−	0.970672i
$178$	20.2052	−	11.6654i	0.113512	−	0.0655362i
$179$	−256.849			−1.43491			−0.717454	−	0.696606i	$-0.754693\pi$
$179$	−256.849			−1.43491			−0.717454	+	0.696606i	$0.754693\pi$
$180$	−22.4772	+	10.2597i	−0.124873	+	0.0569985i
$181$			102.528i			0.566453i	0.959053	+	0.283226i	$0.0914048\pi$
$181$			102.528i			0.566453i	−0.959053	+	0.283226i	$0.908595\pi$
$182$		0			0
$183$	61.7006	−	31.8013i	0.337162	−	0.173778i
$184$	−37.1551	+	64.3545i	−0.201930	+	0.349753i
$185$	−80.3441	−	46.3867i	−0.434293	−	0.250739i
$186$	−0.400842	+	8.39763i	−0.00215507	+	0.0451486i
$187$	−121.152	+	69.9472i	−0.647872	+	0.374049i
$188$		−	56.9098i		−	0.302712i
$189$		0			0
$190$	−42.5745			−0.224076
$191$	60.5381	+	104.855i	0.316953	+	0.548979i	0.979851	−	0.199731i	$-0.0640068\pi$
$191$	60.5381	+	104.855i	0.316953	+	0.548979i	−0.662898	+	0.748710i	$0.730674\pi$
$192$	−210.244	−	10.0355i	−1.09502	−	0.0522683i
$193$	−135.025	+	233.870i	−0.699610	+	1.21176i	0.268992	+	0.963142i	$0.413309\pi$
$193$	−135.025	+	233.870i	−0.699610	+	1.21176i	−0.968602	+	0.248617i	$0.920024\pi$
$194$	−21.9750	−	12.6873i	−0.113273	−	0.0653985i
$195$	−79.4293	−	154.108i	−0.407330	−	0.790297i
$196$		0			0
$197$	−11.6897			−0.0593383			−0.0296692	−	0.999560i	$-0.509445\pi$
$197$	−11.6897			−0.0593383			−0.0296692	+	0.999560i	$0.509445\pi$
$198$	54.5208	−	76.5324i	0.275358	−	0.386527i
$199$		−	264.578i		−	1.32954i	−0.747050	−	0.664768i	$-0.768530\pi$
$199$		−	264.578i		−	1.32954i	0.747050	−	0.664768i	$-0.231470\pi$
$200$	84.8118	+	146.898i	0.424059	+	0.734491i
$201$	−4.21310	+	6.55433i	−0.0209607	+	0.0326086i
$202$	144.877	+	83.6450i	0.717215	+	0.414084i
$203$		0			0
$204$	−66.5942	−	42.8066i	−0.326442	−	0.209836i
$205$	−37.8537	−	65.5645i	−0.184652	−	0.319827i
$206$			35.2830i			0.171277i
$207$	44.6158	−	62.6285i	0.215535	−	0.302553i
$208$		−	245.136i		−	1.17854i
$209$	−58.0352	+	33.5067i	−0.277681	+	0.160319i
$210$		0			0
$211$	−60.7117	+	105.156i	−0.287733	+	0.498369i	−0.973268	−	0.229671i	$-0.926235\pi$
$211$	−60.7117	+	105.156i	−0.287733	+	0.498369i	0.685535	+	0.728040i	$0.259568\pi$
$212$	1.22870	−	2.12817i	0.00579576	−	0.0100385i
$213$	199.840	+	9.53892i	0.938216	+	0.0447837i
$214$	105.488	+	182.710i	0.492933	+	0.853785i
$215$			10.0997i			0.0469753i
$216$	232.430	+	33.4873i	1.07607	+	0.155034i
$217$		0			0
$218$	86.9027	+	150.520i	0.398636	+	0.690459i
$219$	3.05530	−	64.0084i	0.0139511	−	0.292276i
$220$	−14.7582	−	8.52066i	−0.0670828	−	0.0387303i
$221$	277.748	−	481.073i	1.25678	−	2.17680i
$222$	91.4733	+	177.476i	0.412042	+	0.799439i
$223$	262.513	−	151.562i	1.17719	−	0.679651i	0.221828	−	0.975086i	$-0.428798\pi$
$223$	262.513	−	151.562i	1.17719	−	0.679651i	0.955363	+	0.295435i	$0.0954644\pi$
$224$		0			0
$225$	−72.8847	−	159.677i	−0.323932	−	0.709676i
$226$	321.443			1.42232
$227$	−154.342	+	89.1093i	−0.679920	+	0.392552i	−0.799825	−	0.600233i	$-0.795074\pi$
$227$	−154.342	+	89.1093i	−0.679920	+	0.392552i	0.119905	+	0.992785i	$0.461741\pi$
$228$	−31.9005	−	20.5055i	−0.139914	−	0.0899366i
$229$	245.158	+	141.542i	1.07056	+	0.618088i	0.928334	−	0.371746i	$-0.121241\pi$
$229$	245.158	+	141.542i	1.07056	+	0.618088i	0.142225	+	0.989834i	$0.454574\pi$
$230$	29.1800	+	16.8471i	0.126870	+	0.0732481i
$231$		0			0
$232$	−140.458	−	243.280i	−0.605421	−	1.04862i
$233$	239.439			1.02763			0.513817	−	0.857900i	$-0.328231\pi$
$233$	239.439			1.02763			0.513817	+	0.857900i	$0.328231\pi$
$234$	−35.5396	+	371.428i	−0.151879	+	1.58730i
$235$	−113.956			−0.484919
$236$	107.400	−	62.0073i	0.455084	−	0.262743i
$237$	−141.828	−	275.173i	−0.598429	−	1.16107i
$238$		0			0
$239$	219.092	−	379.478i	0.916702	−	1.58777i	0.112311	−	0.993673i	$-0.464175\pi$
$239$	219.092	−	379.478i	0.916702	−	1.58777i	0.804391	−	0.594101i	$-0.202492\pi$
$240$	−3.33531	+	69.8747i	−0.0138971	+	0.291144i
$241$	−4.96577	+	2.86699i	−0.0206048	+	0.0118962i	−0.510267	−	0.860016i	$-0.670453\pi$
$241$	−4.96577	+	2.86699i	−0.0206048	+	0.0118962i	0.489662	+	0.871912i	$0.337120\pi$
$242$	−138.711			−0.573187
$243$	−236.122	−	57.4036i	−0.971697	−	0.236229i
$244$			27.0924i			0.111035i
$245$		0			0
$246$	−7.76842	+	162.748i	−0.0315789	+	0.661578i
$247$	133.049	−	230.447i	0.538659	−	0.932986i
$248$	−12.5495	−	7.24547i	−0.0506029	−	0.0292156i
$249$	−30.9570	+	15.9556i	−0.124325	+	0.0640789i
$250$	151.990	−	87.7512i	0.607958	−	0.351005i
$251$			3.69228i			0.0147103i	0.999973	+	0.00735514i	$0.00234124\pi$
$251$			3.69228i			0.0147103i	−0.999973	+	0.00735514i	$0.997659\pi$
$252$		0			0
$253$	53.0354			0.209626
$254$	−38.3340	−	66.3965i	−0.150921	−	0.261403i
$255$	−85.7158	+	133.348i	−0.336140	+	0.522933i
$256$	101.835	−	176.384i	0.397794	−	0.688999i
$257$	178.998	+	103.344i	0.696489	+	0.402118i	0.806038	−	0.591863i	$-0.201608\pi$
$257$	178.998	+	103.344i	0.696489	+	0.402118i	−0.109550	+	0.993981i	$0.534941\pi$
$258$	11.7532	−	18.2844i	0.0455549	−	0.0708697i
$259$		0			0
$260$	67.6680			0.260262
$261$	120.705	+	264.443i	0.462472	+	1.01319i
$262$			163.111i			0.622561i
$263$	−63.1809	−	109.433i	−0.240232	−	0.416094i	0.720548	−	0.693405i	$-0.243890\pi$
$263$	−63.1809	−	109.433i	−0.240232	−	0.416094i	−0.960780	+	0.277311i	$0.910557\pi$
$264$	74.2024	+	143.967i	0.281070	+	0.545329i
$265$	−4.26145	−	2.46035i	−0.0160809	−	0.00928433i
$266$		0			0
$267$	1.98405	−	41.5657i	0.00743088	−	0.155677i
$268$	−1.52055	−	2.63366i	−0.00567368	−	0.00982710i
$269$		−	246.229i		−	0.915351i	−0.889119	−	0.457676i	$-0.848682\pi$
$269$		−	246.229i		−	0.915351i	0.889119	−	0.457676i	$-0.151318\pi$
$270$	15.1840	−	105.390i	0.0562370	−	0.390333i
$271$			238.276i			0.879247i	0.898182	+	0.439623i	$0.144888\pi$
$271$			238.276i			0.879247i	−0.898182	+	0.439623i	$0.855112\pi$
$272$	−194.108	+	112.068i	−0.713632	+	0.412015i
$273$		0			0
$274$	156.731	−	271.466i	0.572010	−	0.990751i
$275$	60.5304	−	104.842i	0.220110	−	0.381243i
$276$	13.7499	+	26.6775i	0.0498186	+	0.0966575i
$277$	−84.9697	−	147.172i	−0.306750	−	0.531306i	0.670900	−	0.741548i	$-0.265908\pi$
$277$	−84.9697	−	147.172i	−0.306750	−	0.531306i	−0.977649	+	0.210242i	$0.932575\pi$
$278$			281.567i			1.01283i
$279$	12.2129	+	8.70036i	0.0437740	+	0.0311841i
$280$		0			0
$281$	−113.910	−	197.298i	−0.405374	−	0.702128i	0.588991	−	0.808140i	$-0.299525\pi$
$281$	−113.910	−	197.298i	−0.405374	−	0.702128i	−0.994365	+	0.106011i	$0.966192\pi$
$282$	206.305	+	132.612i	0.731577	+	0.470256i
$283$	112.569	+	64.9915i	0.397769	+	0.229652i	0.685521	−	0.728053i	$-0.259575\pi$
$283$	112.569	+	64.9915i	0.397769	+	0.229652i	−0.287752	+	0.957705i	$0.592908\pi$
$284$	−39.0434	+	67.6252i	−0.137477	+	0.238117i
$285$	−41.0603	+	63.8774i	−0.144071	+	0.224131i
$286$	−222.869	+	128.673i	−0.779262	+	0.449907i
$287$		0			0
$288$	−94.3169	+	132.395i	−0.327489	+	0.459706i
$289$	−218.908			−0.757467
$290$	−110.309	+	63.6871i	−0.380377	+	0.219611i
$291$	−40.2291	+	20.7346i	−0.138244	+	0.0712529i
$292$	21.6602	+	12.5055i	0.0741788	+	0.0428272i
$293$	129.475	+	74.7526i	0.441895	+	0.255128i	0.704401	−	0.709802i	$-0.251216\pi$
$293$	129.475	+	74.7526i	0.441895	+	0.255128i	−0.262506	+	0.964930i	$0.584549\pi$
$294$		0			0
$295$	−124.163	−	215.057i	−0.420893	−	0.729007i
$296$	−344.145			−1.16265
$297$	−62.2451	−	155.612i	−0.209580	−	0.523945i
$298$	424.935			1.42596
$299$	−182.380	+	105.297i	−0.609966	+	0.352164i
$300$	68.4298	+	3.26635i	0.228099	+	0.0108878i
$301$		0			0
$302$	71.5244	−	123.884i	0.236836	−	0.410211i
$303$	265.223	−	136.699i	0.875322	−	0.451153i
$304$	−92.9831	+	53.6838i	−0.305865	+	0.176591i
$305$	54.2498			0.177868
$306$	310.358	−	141.663i	1.01424	−	0.462951i
$307$		−	10.5618i		−	0.0344031i	−0.999852	−	0.0172016i	$-0.994524\pi$
$307$		−	10.5618i		−	0.0344031i	0.999852	−	0.0172016i	$-0.00547570\pi$
$308$		0			0
$309$	52.9375	+	34.0281i	0.171319	+	0.110123i
$310$	−3.28528	+	5.69028i	−0.0105977	+	0.0183557i
$311$	391.106	+	225.805i	1.25757	+	0.726061i	0.972602	−	0.232475i	$-0.0746823\pi$
$311$	391.106	+	225.805i	1.25757	+	0.726061i	0.284972	+	0.958536i	$0.408016\pi$
$312$	−541.003	−	347.755i	−1.73398	−	1.11460i
$313$	−146.790	+	84.7492i	−0.468977	+	0.270764i	−0.715812	−	0.698293i	$-0.753943\pi$
$313$	−146.790	+	84.7492i	−0.468977	+	0.270764i	0.246834	+	0.969058i	$0.420610\pi$
$314$		−	419.391i		−	1.33564i
$315$		0			0
$316$	120.827			0.382364
$317$	83.0363	+	143.823i	0.261944	+	0.453701i	0.966759	−	0.255691i	$-0.0823030\pi$
$317$	83.0363	+	143.823i	0.261944	+	0.453701i	−0.704814	+	0.709392i	$0.748970\pi$
$318$	4.85174	+	9.41329i	0.0152570	+	0.0296015i
$319$	−100.245	+	173.629i	−0.314248	+	0.544293i
$320$	−142.462	−	82.2505i	−0.445194	−	0.257033i
$321$	375.868	+	17.9412i	1.17093	+	0.0558916i
$322$		0			0
$323$	−243.302			−0.753257
$324$	62.1370	−	71.6539i	0.191781	−	0.221154i
$325$			480.711i			1.47911i
$326$	148.500	+	257.210i	0.455522	+	0.788987i
$327$	309.647	+	14.7803i	0.946933	+	0.0451997i
$328$	−243.213	−	140.419i	−0.741502	−	0.428107i
$329$		0			0
$330$	65.2782	−	33.6453i	0.197813	−	0.101955i
$331$	−43.0182	−	74.5096i	−0.129964	−	0.225105i	0.793698	−	0.608312i	$-0.208153\pi$
$331$	−43.0182	−	74.5096i	−0.129964	−	0.225105i	−0.923662	+	0.383207i	$0.874820\pi$
$332$		−	13.5931i		−	0.0409429i
$333$	354.498	+	33.9197i	1.06456	+	0.101861i
$334$			94.4398i			0.282754i
$335$	−5.27364	+	3.04474i	−0.0157422	+	0.00908876i
$336$		0			0
$337$	−274.510	+	475.466i	−0.814570	+	1.41088i	0.0950656	+	0.995471i	$0.469694\pi$
$337$	−274.510	+	475.466i	−0.814570	+	1.41088i	−0.909636	+	0.415406i	$0.863639\pi$
$338$	368.811	−	638.799i	1.09116	−	1.88994i
$339$	310.011	−	482.283i	0.914485	−	1.42266i
$340$	−30.9356	−	53.5820i	−0.0909869	−	0.157594i
$341$			10.3422i			0.0303291i
$342$	148.670	−	67.8606i	0.434708	−	0.198423i
$343$		0			0
$344$	18.7325	+	32.4456i	0.0544549	+	0.0943187i
$345$	53.4189	−	27.5328i	0.154837	−	0.0798053i
$346$	−8.67647	−	5.00936i	−0.0250765	−	0.0144779i
$347$	−207.465	+	359.340i	−0.597882	+	1.03556i	0.395251	+	0.918573i	$0.370658\pi$
$347$	−207.465	+	359.340i	−0.597882	+	1.03556i	−0.993133	+	0.116990i	$0.962676\pi$
$348$	−113.327	−	5.40943i	−0.325653	−	0.0155443i
$349$	−307.486	+	177.527i	−0.881050	+	0.508674i	−0.871004	−	0.491275i	$-0.836531\pi$
$349$	−307.486	+	177.527i	−0.881050	+	0.508674i	−0.0100455	+	0.999950i	$0.503198\pi$
$350$		0			0
$351$	523.003	+	411.540i	1.49004	+	1.17248i
$352$	−112.116			−0.318510
$353$	−411.949	+	237.839i	−1.16699	+	0.673764i	−0.952970	−	0.303064i	$-0.901990\pi$
$353$	−411.949	+	237.839i	−1.16699	+	0.673764i	−0.214024	+	0.976828i	$0.568657\pi$
$354$	−25.4811	+	533.828i	−0.0719805	+	1.50799i
$355$	135.413	+	78.1805i	0.381444	+	0.220227i
$356$	14.0657	+	8.12083i	0.0395104	+	0.0228113i
$357$		0			0
$358$	216.008	+	374.138i	0.603375	+	1.04508i
$359$	219.114			0.610346			0.305173	−	0.952297i	$-0.401286\pi$
$359$	219.114			0.610346			0.305173	+	0.952297i	$0.401286\pi$
$360$	149.478	+	106.486i	0.415217	+	0.295796i
$361$	244.451			0.677151
$362$	149.347	−	86.2256i	0.412561	−	0.238192i
$363$	−133.778	+	208.118i	−0.368534	+	0.573328i
$364$		0			0
$365$	25.0410	−	43.3724i	0.0686056	−	0.118828i
$366$	−98.2132	−	63.1312i	−0.268342	−	0.172490i
$367$	181.195	−	104.613i	0.493720	−	0.285049i	−0.232396	−	0.972621i	$-0.574657\pi$
$367$	181.195	−	104.613i	0.493720	−	0.285049i	0.726116	+	0.687572i	$0.241323\pi$
$368$	84.9724			0.230903
$369$	236.690	+	168.615i	0.641436	+	0.456951i
$370$			156.044i			0.421741i
$371$		0			0
$372$	−5.20227	+	2.68132i	−0.0139846	+	0.00720785i
$373$	−127.379	+	220.626i	−0.341498	+	0.591492i	−0.984711	−	0.174196i	$-0.944268\pi$
$373$	−127.379	+	220.626i	−0.341498	+	0.591492i	0.643213	+	0.765687i	$0.277601\pi$
$374$	203.777	+	117.650i	0.544857	+	0.314574i
$375$	14.9246	−	312.670i	0.0397990	−	0.833788i
$376$	−366.088	+	211.361i	−0.973638	+	0.562130i
$377$		−	796.110i		−	2.11170i
$378$		0			0
$379$	−437.733			−1.15497			−0.577484	−	0.816402i	$-0.695965\pi$
$379$	−437.733			−1.15497			−0.577484	+	0.816402i	$0.695965\pi$
$380$	−14.8190	−	25.6673i	−0.0389974	−	0.0675454i
$381$	−136.590	−	6.51980i	−0.358503	−	0.0171123i
$382$	101.824	−	176.365i	0.266556	−	0.461689i
$383$	−239.024	−	138.001i	−0.624084	−	0.360315i	0.154373	−	0.988013i	$-0.450664\pi$
$383$	−239.024	−	138.001i	−0.624084	−	0.360315i	−0.778457	+	0.627697i	$0.783998\pi$
$384$	62.8981	+	122.034i	0.163797	+	0.317798i
$385$		0			0
$386$	454.220			1.17674
$387$	−16.0982	−	35.2681i	−0.0415973	−	0.0911320i
$388$		−	17.6644i		−	0.0455267i
$389$	31.9090	+	55.2681i	0.0820284	+	0.142077i	0.904121	−	0.427276i	$-0.140527\pi$
$389$	31.9090	+	55.2681i	0.0820284	+	0.142077i	−0.822093	+	0.569354i	$0.807194\pi$
$390$	−157.681	+	245.304i	−0.404311	+	0.628986i
$391$	166.756	+	96.2766i	0.426486	+	0.246232i
$392$		0			0
$393$	244.727	+	157.310i	0.622714	+	0.400279i
$394$	9.83094	+	17.0277i	0.0249516	+	0.0432175i
$395$		−	241.944i		−	0.612515i
$396$	65.1169	+	6.23062i	0.164437	+	0.0157339i
$397$		−	128.830i		−	0.324509i	−0.986749	−	0.162254i	$-0.948123\pi$
$397$		−	128.830i		−	0.324509i	0.986749	−	0.162254i	$-0.0518765\pi$
$398$	−385.396	+	222.509i	−0.968332	+	0.559067i
$399$		0			0
$400$	96.9808	−	167.976i	0.242452	−	0.419939i
$401$	179.729	−	311.299i	0.448201	−	0.776307i	−0.550068	−	0.835120i	$-0.685398\pi$
$401$	179.729	−	311.299i	0.448201	−	0.776307i	0.998269	+	0.0588127i	$0.0187315\pi$
$402$	13.0905	+	0.624848i	0.0325635	+	0.00155435i
$403$	−20.5336	−	35.5652i	−0.0509517	−	0.0882510i
$404$			116.458i			0.288262i
$405$	−143.480	−	124.423i	−0.354271	−	0.307217i
$406$		0			0
$407$	122.808	+	212.711i	0.301741	+	0.522630i
$408$	−28.0367	+	587.368i	−0.0687174	+	1.43963i
$409$	−24.8046	−	14.3210i	−0.0606470	−	0.0350146i	0.469370	−	0.883002i	$-0.344481\pi$
$409$	−24.8046	−	14.3210i	−0.0606470	−	0.0350146i	−0.530017	+	0.847987i	$0.677814\pi$
$410$	−63.6696	+	110.279i	−0.155292	+	0.268973i
$411$	−256.142	−	496.964i	−0.623216	−	1.20916i
$412$	−21.2714	+	12.2810i	−0.0516295	+	0.0298083i
$413$		0			0
$414$	−128.749	−	12.3192i	−0.310989	−	0.0297565i
$415$	−27.2187			−0.0655872
$416$	385.547	−	222.595i	0.926795	−	0.535085i
$417$	422.454	+	271.552i	1.01308	+	0.651204i
$418$	97.6147	+	56.3579i	0.233528	+	0.134827i
$419$	−174.539	−	100.770i	−0.416560	−	0.240501i	0.277044	−	0.960857i	$-0.410645\pi$
$419$	−174.539	−	100.770i	−0.416560	−	0.240501i	−0.693604	+	0.720356i	$0.743978\pi$
$420$		0			0
$421$	−324.035	−	561.245i	−0.769680	−	1.33312i	−0.937737	−	0.347347i	$-0.887083\pi$
$421$	−324.035	−	561.245i	−0.769680	−	1.33312i	0.168057	−	0.985777i	$-0.446251\pi$
$422$	204.233			0.483965
$423$	397.934	−	181.637i	0.940742	−	0.429403i
$424$	−18.2534			−0.0430505
$425$	380.644	−	219.765i	0.895633	−	0.517094i
$426$	−154.170	−	299.119i	−0.361901	−	0.702156i
$427$		0			0
$428$	−73.4346	+	127.192i	−0.171576	+	0.297178i
$429$	−21.8846	+	458.482i	−0.0510131	+	1.06872i
$430$	14.7117	−	8.49380i	0.0342132	−	0.0197530i
$431$	−477.826			−1.10864			−0.554322	−	0.832302i	$-0.687023\pi$
$431$	−477.826			−1.10864			−0.554322	+	0.832302i	$0.687023\pi$
$432$	−99.7281	−	249.318i	−0.230852	−	0.577126i
$433$			760.468i			1.75628i	0.478406	+	0.878139i	$0.341215\pi$
$433$			760.468i			1.75628i	−0.478406	+	0.878139i	$0.658785\pi$
$434$		0			0
$435$	−10.8318	+	226.926i	−0.0249008	+	0.521670i
$436$	−60.4968	+	104.784i	−0.138754	+	0.240329i
$437$	79.8807	+	46.1192i	0.182793	+	0.105536i
$438$	−95.8070	+	49.3802i	−0.218738	+	0.112740i
$439$	299.570	−	172.957i	0.682391	−	0.393979i	−0.118364	−	0.992970i	$-0.537765\pi$
$439$	299.570	−	172.957i	0.682391	−	0.393979i	0.800755	+	0.598992i	$0.204432\pi$
$440$			126.582i			0.287686i
$441$		0			0
$442$	−934.338			−2.11389
$443$	26.1810	+	45.3468i	0.0590993	+	0.102363i	0.894061	−	0.447945i	$-0.147844\pi$
$443$	26.1810	+	45.3468i	0.0590993	+	0.102363i	−0.834962	+	0.550308i	$0.814510\pi$
$444$	−75.1569	+	116.922i	−0.169272	+	0.263337i
$445$	16.2611	−	28.1651i	0.0365419	−	0.0632924i
$446$	−441.545	−	254.926i	−0.990012	−	0.571584i
$447$	409.821	−	637.558i	0.916825	−	1.42630i
$448$		0			0
$449$	29.7022			0.0661518			0.0330759	−	0.999453i	$-0.489470\pi$
$449$	29.7022			0.0661518			0.0330759	+	0.999453i	$0.489470\pi$
$450$	−171.297	+	240.455i	−0.380661	+	0.534344i
$451$			200.435i			0.444423i
$452$	111.885	+	193.791i	0.247534	+	0.428742i
$453$	−116.891	−	226.790i	−0.258037	−	0.500641i
$454$	259.602	+	149.881i	0.571810	+	0.330134i
$455$		0			0
$456$	−13.4304	+	281.365i	−0.0294525	+	0.617030i
$457$	−59.4080	−	102.898i	−0.129996	−	0.225159i	0.793679	−	0.608337i	$-0.208163\pi$
$457$	−59.4080	−	102.898i	−0.129996	−	0.225159i	−0.923675	+	0.383178i	$0.874830\pi$
$458$		−	476.145i		−	1.03962i
$459$	86.7724	−	602.275i	0.189047	−	1.31215i
$460$			23.4560i			0.0509912i
$461$	−657.900	+	379.839i	−1.42711	+	0.823945i	−0.996892	−	0.0787777i	$-0.974898\pi$
$461$	−657.900	+	379.839i	−1.42711	+	0.823945i	−0.430223	+	0.902723i	$0.641565\pi$
$462$		0			0
$463$	59.1866	−	102.514i	0.127833	−	0.221413i	−0.795004	−	0.606604i	$-0.792531\pi$
$463$	59.1866	−	102.514i	0.127833	−	0.221413i	0.922837	+	0.385191i	$0.125865\pi$
$464$	−160.611	+	278.186i	−0.346144	+	0.599539i
$465$	5.36907	+	10.4170i	0.0115464	+	0.0224022i
$466$	−201.367	−	348.778i	−0.432118	−	0.748450i
$467$			100.271i			0.214713i	0.994221	+	0.107356i	$0.0342386\pi$
$467$			100.271i			0.214713i	−0.994221	+	0.107356i	$0.965761\pi$
$468$	−236.296	+	107.858i	−0.504907	+	0.230465i
$469$		0			0
$470$	95.8365	+	165.994i	0.203907	+	0.353178i
$471$	−629.241	−	404.475i	−1.33597	−	0.858757i
$472$	−797.759	−	460.586i	−1.69017	−	0.975818i
$473$	13.3694	−	23.1565i	0.0282652	−	0.0489567i
$474$	−281.553	+	438.012i	−0.593994	+	0.924076i
$475$	182.339	−	105.274i	0.383872	−	0.221628i
$476$		0			0
$477$	18.8026	+	1.79910i	0.0394184	+	0.00377169i
$478$	−737.020			−1.54188
$479$	−561.950	+	324.442i	−1.17317	+	0.677331i	−0.954425	−	0.298450i	$-0.903530\pi$
$479$	−561.950	+	324.442i	−1.17317	+	0.677331i	−0.218747	+	0.975782i	$0.570197\pi$
$480$	−112.926	+	58.2038i	−0.235263	+	0.121258i
$481$	−844.635	−	487.650i	−1.75600	−	1.01383i
$482$	8.35237	+	4.82224i	0.0173286	+	0.0100047i
$483$		0			0
$484$	−48.2815	−	83.6260i	−0.0997552	−	0.172781i
$485$	−35.3711			−0.0729301
$486$	114.961	+	392.223i	0.236546	+	0.807044i
$487$	−630.412			−1.29448			−0.647240	−	0.762286i	$-0.724077\pi$
$487$	−630.412			−1.29448			−0.647240	+	0.762286i	$0.724077\pi$
$488$	174.279	−	100.620i	0.357130	−	0.206189i
$489$	529.127	+	25.2567i	1.08206	+	0.0516497i
$490$		0			0
$491$	392.755	−	680.271i	0.799908	−	1.38548i	−0.119768	−	0.992802i	$-0.538215\pi$
$491$	392.755	−	680.271i	0.799908	−	1.38548i	0.919676	−	0.392679i	$-0.128452\pi$
$492$	−100.821	+	51.9646i	−0.204921	+	0.105619i
$493$	−630.389	+	363.955i	−1.27868	+	0.738245i
$494$	−447.574			−0.906020
$495$	12.4762	−	130.390i	0.0252044	−	0.263414i
$496$			16.5701i			0.0334075i
$497$		0			0
$498$	49.2764	+	31.6748i	0.0989486	+	0.0636039i
$499$	−116.379	+	201.574i	−0.233224	+	0.403956i	−0.958755	−	0.284233i	$-0.908261\pi$
$499$	−116.379	+	201.574i	−0.233224	+	0.403956i	0.725531	+	0.688190i	$0.241594\pi$
$500$	105.807	+	61.0875i	0.211613	+	0.122175i
$501$	141.694	+	91.0808i	0.282823	+	0.181798i
$502$	5.37835	−	3.10519i	0.0107138	−	0.00618564i
$503$		−	47.6335i		−	0.0946989i	−0.998878	−	0.0473494i	$-0.984923\pi$
$503$		−	47.6335i		−	0.0946989i	0.998878	−	0.0473494i	$-0.0150774\pi$
$504$		0			0
$505$	233.195			0.461772
$506$	−44.6025	−	77.2538i	−0.0881472	−	0.152675i
$507$	−602.740	−	1169.43i	−1.18884	−	2.30657i
$508$	26.6860	−	46.2215i	0.0525315	−	0.0909872i
$509$	370.733	+	214.043i	0.728356	+	0.420517i	0.817821	−	0.575473i	$-0.195182\pi$
$509$	370.733	+	214.043i	0.728356	+	0.420517i	−0.0894642	+	0.995990i	$0.528515\pi$
$510$	266.328	+	12.7126i	0.522211	+	0.0249266i
$511$		0			0
$512$	−525.625			−1.02661
$513$	41.5664	−	288.507i	0.0810262	−	0.562391i
$514$		−	347.648i		−	0.676358i
$515$	24.5915	+	42.5937i	0.0477505	+	0.0827062i
$516$	15.1142	+	0.721443i	0.0292911	+	0.00139814i
$517$	261.278	+	150.849i	0.505373	+	0.291777i
$518$		0			0
$519$	−15.8838	+	8.18670i	−0.0306045	+	0.0157740i
$520$	−251.317	−	435.293i	−0.483301	−	0.837102i
$521$			537.389i			1.03146i	0.856752	+	0.515728i	$0.172479\pi$
$521$			537.389i			1.03146i	−0.856752	+	0.515728i	$0.827521\pi$
$522$	283.687	−	398.220i	0.543462	−	0.762873i
$523$			548.211i			1.04820i	0.851655	+	0.524102i	$0.175599\pi$
$523$			548.211i			1.04820i	−0.851655	+	0.524102i	$0.824401\pi$
$524$	−98.3361	+	56.7744i	−0.187664	+	0.108348i
$525$		0			0
$526$	−106.270	+	184.065i	−0.202034	+	0.349933i
$527$	−18.7745	+	32.5184i	−0.0356253	+	0.0617048i
$528$	100.144	−	155.793i	0.189666	−	0.295063i
$529$	228.001	+	394.909i	0.431003	+	0.746519i
$530$			8.27656i			0.0156162i
$531$	776.363	+	553.072i	1.46208	+	1.04157i
$532$		0			0
$533$	−397.945	−	689.261i	−0.746614	−	1.29317i
$534$	−62.2151	+	32.0665i	−0.116508	+	0.0600496i
$535$	254.690	+	147.045i	0.476056	+	0.274851i
$536$	−11.2945	+	19.5627i	−0.0210718	+	0.0364975i
$537$	769.669	+	36.7385i	1.43328	+	0.0684143i
$538$	−358.669	+	207.078i	−0.666672	+	0.384903i
$539$		0			0
$540$	68.8224	−	27.5292i	0.127449	−	0.0509799i
$541$	484.286			0.895168			0.447584	−	0.894242i	$-0.352284\pi$
$541$	484.286			0.895168			0.447584	+	0.894242i	$0.352284\pi$
$542$	347.084	−	200.389i	0.640376	−	0.369721i
$543$	14.6651	−	307.234i	0.0270076	−	0.565809i
$544$	−352.518	−	203.527i	−0.648011	−	0.374130i
$545$	209.818	+	121.139i	0.384988	+	0.222273i
$546$		0			0
$547$	−274.632	−	475.676i	−0.502069	−	0.869610i	−0.999997	−	0.00239116i	$-0.999239\pi$
$547$	−274.632	−	475.676i	−0.502069	−	0.869610i	0.497928	−	0.867219i	$-0.334094\pi$
$548$	218.214			0.398201
$549$	−189.440	+	86.4701i	−0.345064	+	0.157505i
$550$	−203.623			−0.370224
$551$	−301.974	+	174.345i	−0.548047	+	0.316415i
$552$	120.543	−	187.529i	0.218376	−	0.339727i
$553$		0			0
$554$	−142.918	+	247.542i	−0.257975	+	0.446826i
$555$	234.123	+	150.494i	0.421844	+	0.271160i
$556$	−169.751	+	98.0055i	−0.305307	+	0.176269i
$557$	−460.020			−0.825888			−0.412944	−	0.910756i	$-0.635500\pi$
$557$	−460.020			−0.825888			−0.412944	+	0.910756i	$0.635500\pi$
$558$	2.40232	−	25.1069i	0.00430523	−	0.0449945i
$559$			106.175i			0.189938i
$560$		0			0
$561$	373.048	−	192.274i	0.664969	−	0.342734i
$562$	−191.596	+	331.853i	−0.340918	+	0.590487i
$563$	−550.709	−	317.952i	−0.978169	−	0.564746i	−0.0764520	−	0.997073i	$-0.524359\pi$
$563$	−550.709	−	317.952i	−0.978169	−	0.564746i	−0.901717	+	0.432327i	$0.857693\pi$
$564$	−8.14012	+	170.535i	−0.0144328	+	0.302367i
$565$	388.047	−	224.039i	0.686809	−	0.396529i
$566$		−	218.630i		−	0.386272i
$567$		0			0
$568$	580.024			1.02117
$569$	−10.5129	−	18.2089i	−0.0184761	−	0.0320016i	0.856640	−	0.515915i	$-0.172548\pi$
$569$	−10.5129	−	18.2089i	−0.0184761	−	0.0320016i	−0.875116	+	0.483914i	$0.839215\pi$
$570$	127.578	+	6.08967i	0.223822	+	0.0106836i
$571$	224.928	−	389.586i	0.393919	−	0.682287i	−0.599044	−	0.800716i	$-0.704453\pi$
$571$	224.928	−	389.586i	0.393919	−	0.682287i	0.992963	+	0.118429i	$0.0377858\pi$
$572$	−155.149	−	89.5753i	−0.271239	−	0.156600i
$573$	−166.410	−	322.866i	−0.290418	−	0.563467i
$574$		0			0
$575$	−166.630			−0.289792
$576$	628.578	+	60.1446i	1.09128	+	0.104418i
$577$		−	78.5449i		−	0.136126i	−0.997681	−	0.0680631i	$-0.978318\pi$
$577$		−	78.5449i		−	0.136126i	0.997681	−	0.0680631i	$-0.0216819\pi$
$578$	184.101	+	318.872i	0.318513	+	0.551681i
$579$	438.065	−	681.497i	0.756589	−	1.17702i
$580$	−76.7912	−	44.3354i	−0.132399	−	0.0764403i
$581$		0			0
$582$	64.0354	+	41.1618i	0.110027	+	0.0707248i
$583$	6.51375	+	11.2822i	0.0111728	+	0.0193519i
$584$		−	185.780i		−	0.318117i
$585$	215.974	+	473.159i	0.369186	+	0.808819i
$586$		−	251.466i		−	0.429124i
$587$	637.878	−	368.279i	1.08667	−	0.627392i	0.153985	−	0.988073i	$-0.450789\pi$
$587$	637.878	−	368.279i	1.08667	−	0.627392i	0.932689	+	0.360681i	$0.117456\pi$
$588$		0			0
$589$	−8.99352	+	15.5772i	−0.0152691	+	0.0264469i
$590$	−208.842	+	361.724i	−0.353969	+	0.613092i
$591$	35.0291	+	1.67204i	0.0592709	+	0.00282916i
$592$	196.762	+	340.801i	0.332368	+	0.575678i
$593$		−	884.110i		−	1.49091i	−0.666556	−	0.745455i	$-0.732232\pi$
$593$		−	884.110i		−	1.49091i	0.666556	−	0.745455i	$-0.267768\pi$
$594$	−174.323	+	221.538i	−0.293473	+	0.372959i
$595$		0			0
$596$	147.908	+	256.184i	0.248168	+	0.429839i
$597$	−37.8440	+	792.830i	−0.0633903	+	1.32802i
$598$	306.761	+	177.109i	0.512978	+	0.296168i
$599$	365.642	−	633.311i	0.610421	−	1.05728i	−0.380748	−	0.924679i	$-0.624333\pi$
$599$	365.642	−	633.311i	0.610421	−	1.05728i	0.991169	−	0.132602i	$-0.0423332\pi$
$600$	−233.134	−	452.325i	−0.388557	−	0.753875i
$601$	−378.525	+	218.541i	−0.629825	+	0.363630i	−0.780684	−	0.624926i	$-0.785129\pi$
$601$	−378.525	+	218.541i	−0.629825	+	0.363630i	0.150859	+	0.988555i	$0.451796\pi$
$602$		0			0
$603$	13.5624	−	19.0380i	0.0224916	−	0.0315721i
$604$	99.5825			0.164872
$605$	−167.453	+	96.6788i	−0.276781	+	0.159800i
$606$	−422.174	−	271.372i	−0.696656	−	0.447809i
$607$	342.651	+	197.830i	0.564500	+	0.325914i	0.754950	−	0.655783i	$-0.227661\pi$
$607$	342.651	+	197.830i	0.564500	+	0.325914i	−0.190450	+	0.981697i	$0.560995\pi$
$608$	−168.866	−	97.4949i	−0.277740	−	0.160353i
$609$		0			0
$610$	−45.6238	−	79.0228i	−0.0747932	−	0.129546i
$611$	−1197.99			−1.96070
$612$	193.432	+	137.799i	0.316066	+	0.225162i
$613$	322.644			0.526336			0.263168	−	0.964750i	$-0.415233\pi$
$613$	322.644			0.526336			0.263168	+	0.964750i	$0.415233\pi$
$614$	−15.3848	+	8.88240i	−0.0250566	+	0.0144664i
$615$	104.054	+	201.884i	0.169193	+	0.328267i
$616$		0			0
$617$	71.0592	−	123.078i	0.115169	−	0.199478i	−0.802678	−	0.596412i	$-0.796592\pi$
$617$	71.0592	−	123.078i	0.115169	−	0.199478i	0.917847	+	0.396934i	$0.129926\pi$
$618$	5.04672	−	105.729i	0.00816622	−	0.171082i
$619$	751.468	−	433.860i	1.21400	−	0.700905i	0.250374	−	0.968149i	$-0.419446\pi$
$619$	751.468	−	433.860i	1.21400	−	0.700905i	0.963629	+	0.267244i	$0.0861131\pi$
$620$	−4.57406			−0.00737751
$621$	−142.653	+	181.290i	−0.229716	+	0.291933i
$622$		−	759.604i		−	1.22123i
$623$		0			0
$624$	−35.0632	+	734.573i	−0.0561910	+	1.17720i
$625$	−121.463	+	210.380i	−0.194341	+	0.336608i
$626$	246.899	+	142.547i	0.394408	+	0.227711i
$627$	178.700	−	92.1046i	0.285008	−	0.146897i
$628$	252.842	−	145.978i	0.402614	−	0.232450i
$629$			891.750i			1.41773i
$630$		0			0
$631$	−467.813			−0.741383			−0.370691	−	0.928756i	$-0.620879\pi$
$631$	−467.813			−0.741383			−0.370691	+	0.928756i	$0.620879\pi$
$632$	−448.747	−	777.253i	−0.710043	−	1.22983i
$633$	196.969	−	306.425i	0.311167	−	0.484083i
$634$	139.666	−	241.909i	0.220294	−	0.381560i
$635$	−92.5538	−	53.4360i	−0.145754	−	0.0841511i
$636$	−3.98631	+	6.20151i	−0.00626779	+	0.00975080i
$637$		0			0
$638$	337.222			0.528562
$639$	−597.474	−	57.1684i	−0.935014	−	0.0894655i
$640$			107.298i			0.167653i
$641$	335.299	+	580.755i	0.523087	+	0.906014i	0.999639	+	0.0268674i	$0.00855318\pi$
$641$	335.299	+	580.755i	0.523087	+	0.906014i	−0.476552	+	0.879146i	$0.658113\pi$
$642$	−289.969	−	562.595i	−0.451665	−	0.876316i
$643$	−115.738	−	66.8215i	−0.179997	−	0.103921i	0.407294	−	0.913297i	$-0.366472\pi$
$643$	−115.738	−	66.8215i	−0.179997	−	0.103921i	−0.587291	+	0.809376i	$0.699806\pi$
$644$		0			0
$645$	1.44461	−	30.2646i	0.00223971	−	0.0469219i
$646$	204.616	+	354.405i	0.316743	+	0.548615i
$647$		−	320.900i		−	0.495981i	−0.968762	−	0.247991i	$-0.920230\pi$
$647$		−	320.900i		−	0.495981i	0.968762	−	0.247991i	$-0.0797702\pi$
$648$	−691.708	−	133.593i	−1.06745	−	0.206163i
$649$			657.443i			1.01301i
$650$	700.225	−	404.275i	1.07727	−	0.621962i
$651$		0			0
$652$	−103.377	+	179.055i	−0.158554	+	0.274624i
$653$	407.688	−	706.137i	0.624331	−	1.08137i	−0.364339	−	0.931266i	$-0.618705\pi$
$653$	407.688	−	706.137i	0.624331	−	1.08137i	0.988670	−	0.150107i	$-0.0479617\pi$
$654$	−238.882	−	463.476i	−0.365263	−	0.708680i
$655$	113.685	+	196.908i	0.173565	+	0.300623i
$656$			321.133i			0.489532i
$657$	−18.3109	+	191.370i	−0.0278705	+	0.291278i
$658$		0			0
$659$	193.167	+	334.575i	0.293121	+	0.507701i	0.974546	−	0.224187i	$-0.0719727\pi$
$659$	193.167	+	334.575i	0.293121	+	0.507701i	−0.681425	+	0.731888i	$0.738639\pi$
$660$	43.0055	+	27.6438i	0.0651599	+	0.0418846i
$661$	−103.735	−	59.8912i	−0.156936	−	0.0906069i	0.419475	−	0.907767i	$-0.362214\pi$
$661$	−103.735	−	59.8912i	−0.156936	−	0.0906069i	−0.576411	+	0.817160i	$0.695547\pi$
$662$	−72.3561	+	125.324i	−0.109299	+	0.189312i
$663$	−901.106	+	1401.85i	−1.35913	+	2.11440i
$664$	−87.4410	+	50.4841i	−0.131688	+	0.0760303i
$665$		0			0
$666$	−248.722	−	544.905i	−0.373457	−	0.818176i
$667$	275.958			0.413730
$668$	−56.9357	+	32.8719i	−0.0852331	+	0.0492094i
$669$	−808.324	+	416.621i	−1.20826	+	0.622752i
$670$	8.87021	+	5.12122i	0.0132391	+	0.00764361i
$671$	−124.384	−	71.8130i	−0.185371	−	0.107024i
$672$		0			0
$673$	242.303	+	419.682i	0.360035	+	0.623599i	0.987966	−	0.154670i	$-0.0494315\pi$
$673$	242.303	+	419.682i	0.360035	+	0.623599i	−0.627931	+	0.778269i	$0.716098\pi$
$674$	923.447			1.37010
$675$	195.566	+	488.911i	0.289727	+	0.724313i
$676$	513.491			0.759602
$677$	−406.464	+	234.672i	−0.600390	+	0.346635i	−0.769195	−	0.639014i	$-0.779343\pi$
$677$	−406.464	+	234.672i	−0.600390	+	0.346635i	0.168805	+	0.985649i	$0.446009\pi$
$678$	−963.234	−	45.9778i	−1.42070	−	0.0678139i
$679$		0			0
$680$	−229.787	+	398.003i	−0.337922	+	0.585299i
$681$	475.245	−	244.948i	0.697863	−	0.359688i
$682$	15.0650	−	8.69776i	0.0220894	−	0.0127533i
$683$	197.068			0.288533			0.144267	−	0.989539i	$-0.453918\pi$
$683$	197.068			0.288533			0.144267	+	0.989539i	$0.453918\pi$
$684$	92.6596	+	66.0096i	0.135467	+	0.0965052i
$685$		−	436.952i		−	0.637886i
$686$		0			0
$687$	−714.392	−	459.210i	−1.03987	−	0.668428i
$688$	21.4203	−	37.1010i	0.0311341	−	0.0539259i
$689$	−44.7994	−	25.8649i	−0.0650209	−	0.0375398i
$690$	−85.0307	−	54.6575i	−0.123233	−	0.0792138i
$691$	983.708	−	567.944i	1.42360	−	0.821916i	0.426996	−	0.904254i	$-0.359572\pi$
$691$	983.708	−	567.944i	1.42360	−	0.821916i	0.996605	+	0.0823375i	$0.0262386\pi$
$692$		−	6.97448i		−	0.0100787i
$693$		0			0
$694$	697.909			1.00563
$695$	196.246	+	339.908i	0.282368	+	0.489076i
$696$	386.096	+	749.100i	0.554736	+	1.07629i
$697$	−363.855	+	630.215i	−0.522030	+	0.904182i
$698$	517.189	+	298.599i	0.740959	+	0.427793i
$699$	−717.500	−	34.2483i	−1.02647	−	0.0489961i
$700$		0			0
$701$	1125.84			1.60605			0.803023	−	0.595947i	$-0.203223\pi$
$701$	1125.84			1.60605			0.803023	+	0.595947i	$0.203223\pi$
$702$	159.625	−	1107.93i	0.227386	−	1.57825i
$703$			427.173i			0.607643i
$704$	217.758	+	377.167i	0.309315	+	0.535749i
$705$	341.479	+	16.2998i	0.484368	+	0.0231202i
$706$	692.894	+	400.043i	0.981437	+	0.566633i
$707$		0			0
$708$	−330.702	+	170.448i	−0.467094	+	0.240746i
$709$	−322.562	−	558.693i	−0.454953	−	0.788002i	0.543732	−	0.839259i	$-0.317011\pi$
$709$	−322.562	−	558.693i	−0.454953	−	0.788002i	−0.998686	+	0.0512568i	$0.983677\pi$
$710$		−	262.998i		−	0.370419i
$711$	385.640	+	844.866i	0.542391	+	1.18828i
$712$		−	120.642i		−	0.169441i
$713$	12.3281	−	7.11761i	0.0172904	−	0.00998262i
$714$		0			0
$715$	−179.365	+	310.670i	−0.250861	+	0.434503i
$716$	−150.373	+	260.454i	−0.210018	+	0.363762i
$717$	−710.806	+	1105.80i	−0.991362	+	1.54226i
$718$	−184.274	−	319.172i	−0.256649	−	0.444529i
$719$			989.484i			1.37620i	0.725618	+	0.688098i	$0.241554\pi$
$719$			989.484i			1.37620i	−0.725618	+	0.688098i	$0.758446\pi$
$720$	19.9891	−	208.909i	0.0277627	−	0.290151i
$721$		0			0
$722$	−205.583	−	356.079i	−0.284740	−	0.493185i
$723$	15.2904	−	7.88090i	0.0211486	−	0.0109003i
$724$	103.967	+	60.0254i	0.143601	+	0.0829080i
$725$	314.957	−	545.521i	0.434423	−	0.752443i
$726$	415.661	+	19.8406i	0.572535	+	0.0273287i
$727$	691.647	−	399.323i	0.951371	−	0.549274i	0.0578647	−	0.998324i	$-0.481571\pi$
$727$	691.647	−	399.323i	0.951371	−	0.549274i	0.893507	+	0.449050i	$0.148237\pi$
$728$		0			0
$729$	699.351	+	205.789i	0.959329	+	0.282289i
$730$	−84.2376			−0.115394
$731$	84.0734	−	48.5398i	0.115011	−	0.0664019i
$732$	3.87518	−	81.1848i	0.00529396	−	0.110908i
$733$	4.86788	+	2.81047i	0.00664104	+	0.00383421i	0.503317	−	0.864102i	$-0.332113\pi$
$733$	4.86788	+	2.81047i	0.00664104	+	0.00383421i	−0.496676	+	0.867936i	$0.665446\pi$
$734$	−304.769	−	175.958i	−0.415216	−	0.239725i
$735$		0			0
$736$	77.1590	+	133.643i	0.104836	+	0.181581i
$737$	16.1218			0.0218749
$738$	46.5575	−	486.578i	0.0630861	−	0.659320i
$739$	390.819			0.528849			0.264424	−	0.964406i	$-0.414818\pi$
$739$	390.819			0.528849			0.264424	+	0.964406i	$0.414818\pi$
$740$	−94.0755	+	54.3145i	−0.127129	+	0.0733980i
$741$	−431.655	+	671.525i	−0.582530	+	0.906242i
$742$		0			0
$743$	−186.515	+	323.053i	−0.251029	+	0.434795i	−0.963809	−	0.266592i	$-0.914102\pi$
$743$	−186.515	+	323.053i	−0.251029	+	0.434795i	0.712780	+	0.701387i	$0.247436\pi$
$744$	36.5694	+	23.5067i	0.0491524	+	0.0315951i
$745$	512.982	−	296.170i	0.688567	−	0.397544i
$746$	428.499			0.574396
$747$	95.0476	−	43.3846i	0.127239	−	0.0580784i
$748$			163.803i			0.218988i
$749$		0			0
$750$	−468.002	+	241.214i	−0.624002	+	0.321619i
$751$	246.052	−	426.175i	0.327633	−	0.567477i	−0.654409	−	0.756141i	$-0.727082\pi$
$751$	246.052	−	426.175i	0.327633	−	0.567477i	0.982042	+	0.188664i	$0.0604157\pi$
$752$	418.615	+	241.688i	0.556669	+	0.321393i
$753$	0.528127	−	11.0642i	0.000701364	−	0.0146936i
$754$	−1159.65	+	669.525i	−1.53800	+	0.887964i
$755$		−	199.404i		−	0.264111i
$756$		0			0
$757$	591.819			0.781795			0.390898	−	0.920434i	$-0.372165\pi$
$757$	591.819			0.781795			0.390898	+	0.920434i	$0.372165\pi$
$758$	368.131	+	637.622i	0.485661	+	0.841190i
$759$	−158.925	−	7.58594i	−0.209388	−	0.00999465i
$760$	−110.074	+	190.655i	−0.144835	+	0.250861i
$761$	−250.799	−	144.799i	−0.329564	−	0.190274i	0.326083	−	0.945341i	$-0.394271\pi$
$761$	−250.799	−	144.799i	−0.329564	−	0.190274i	−0.655648	+	0.755067i	$0.727604\pi$
$762$	105.374	+	204.446i	0.138286	+	0.268302i
$763$		0			0
$764$	141.769			0.185561
$765$	275.928	−	387.329i	0.360691	−	0.506312i
$766$			464.232i			0.606047i
$767$	−1305.29	−	2260.84i	−1.70182	−	2.94763i
$768$	−330.387	+	513.983i	−0.430192	+	0.669249i
$769$	−388.241	−	224.151i	−0.504865	−	0.291484i	0.225855	−	0.974161i	$-0.427482\pi$
$769$	−388.241	−	224.151i	−0.504865	−	0.291484i	−0.730720	+	0.682677i	$0.760816\pi$
$770$		0			0
$771$	−521.600	−	335.283i	−0.676524	−	0.434868i
$772$	158.101	+	273.840i	0.204795	+	0.354715i
$773$			329.273i			0.425967i	0.977056	+	0.212984i	$0.0683181\pi$
$773$			329.273i			0.425967i	−0.977056	+	0.212984i	$0.931682\pi$
$774$	−37.8347	+	53.1096i	−0.0488820	+	0.0686171i
$775$		−	32.4939i		−	0.0419276i
$776$	−113.631	+	65.6049i	−0.146432	+	0.0845423i
$777$		0			0
$778$	53.6707	−	92.9604i	0.0689855	−	0.119486i
$779$	−174.297	+	301.890i	−0.223744	+	0.387536i
$780$	−202.773	−	9.67892i	−0.259966	−	0.0124089i
$781$	−206.982	−	358.504i	−0.265022	−	0.459032i
$782$		−	323.873i		−	0.414159i
$783$	−323.879	−	809.691i	−0.413639	−	1.03409i
$784$		0			0
$785$	−292.307	−	506.290i	−0.372365	−	0.644955i
$786$	23.3307	−	488.777i	0.0296828	−	0.621853i
$787$	157.300	+	90.8171i	0.199873	+	0.115397i	0.596596	−	0.802542i	$-0.296519\pi$
$787$	157.300	+	90.8171i	0.199873	+	0.115397i	−0.396723	+	0.917938i	$0.629853\pi$
$788$	−6.84375	+	11.8537i	−0.00868496	+	0.0150428i
$789$	173.675	+	336.962i	0.220120	+	0.427074i
$790$	−352.426	+	203.473i	−0.446109	+	0.257561i
$791$		0			0
$792$	−201.762	−	442.023i	−0.254750	−	0.558109i
$793$	570.313			0.719184
$794$	−187.660	+	108.345i	−0.236347	+	0.136455i
$795$	12.4179	+	7.98219i	0.0156200	+	0.0100405i
$796$	−268.291	−	154.898i	−0.337049	−	0.194595i
$797$	−24.1857	−	13.9636i	−0.0303460	−	0.0175202i	0.484750	−	0.874653i	$-0.338910\pi$
$797$	−24.1857	−	13.9636i	−0.0303460	−	0.0175202i	−0.515096	+	0.857132i	$0.672244\pi$
$798$		0			0
$799$	547.680	+	948.610i	0.685457	+	1.18725i
$800$	352.253			0.440316
$801$	−11.8907	+	124.271i	−0.0148449	+	0.155145i
$802$	−604.604			−0.753870
$803$	−114.828	+	66.2960i	−0.142999	+	0.0825604i
$804$	4.17974	+	8.10949i	0.00519868	+	0.0100864i
$805$		0			0
$806$	−34.5372	+	59.8203i	−0.0428502	+	0.0742187i
$807$	−35.2196	+	737.848i	−0.0436426	+	0.914310i
$808$	749.147	−	432.520i	0.927163	−	0.535298i
$809$	493.946			0.610563			0.305282	−	0.952262i	$-0.401249\pi$
$809$	493.946			0.610563			0.305282	+	0.952262i	$0.401249\pi$
$810$	−60.5746	+	313.638i	−0.0747835	+	0.387208i
$811$		−	386.208i		−	0.476212i	−0.971239	−	0.238106i	$-0.923473\pi$
$811$		−	386.208i		−	0.476212i	0.971239	−	0.238106i	$-0.0765266\pi$
$812$		0			0
$813$	34.0819	−	714.015i	0.0419212	−	0.878247i
$814$	206.563	−	357.777i	0.253763	−	0.439530i
$815$	358.539	+	207.003i	0.439925	+	0.253991i
$816$	597.691	−	308.058i	0.732464	−	0.377522i
$817$	40.2735	−	23.2519i	0.0492944	−	0.0284601i
$818$			48.1754i			0.0588942i
$819$		0			0
$820$	−88.6463			−0.108105
$821$	611.025	+	1058.33i	0.744244	+	1.28907i	0.950547	+	0.310581i	$0.100524\pi$
$821$	611.025	+	1058.33i	0.744244	+	1.28907i	−0.206303	+	0.978488i	$0.566143\pi$
$822$	−508.487	+	791.053i	−0.618597	+	0.962351i
$823$	−582.687	+	1009.24i	−0.708004	+	1.22630i	0.257593	+	0.966254i	$0.417071\pi$
$823$	−582.687	+	1009.24i	−0.708004	+	1.22630i	−0.965597	+	0.260045i	$0.916263\pi$
$824$	158.002	+	91.2226i	0.191750	+	0.110707i
$825$	−196.381	+	305.509i	−0.238037	+	0.370314i
$826$		0			0
$827$	−1250.89			−1.51257			−0.756283	−	0.654244i	$-0.772987\pi$
$827$	−1250.89			−1.51257			−0.756283	+	0.654244i	$0.772987\pi$
$828$	−37.3871	−	81.9082i	−0.0451535	−	0.0989229i
$829$		−	121.096i		−	0.146075i	−0.997329	−	0.0730374i	$-0.976731\pi$
$829$		−	121.096i		−	0.146075i	0.997329	−	0.0730374i	$-0.0232692\pi$
$830$	22.8908	+	39.6480i	0.0275793	+	0.0477687i
$831$	233.568	+	453.167i	0.281069	+	0.545327i
$832$	−1497.66	−	864.676i	−1.80008	−	1.03927i
$833$		0			0
$834$	40.2741	−	843.740i	0.0482902	−	1.01168i
$835$	65.8225	+	114.008i	0.0788294	+	0.136536i
$836$			78.4664i			0.0938593i
$837$	−35.3527	−	27.8183i	−0.0422374	−	0.0332357i
$838$			338.988i			0.404521i
$839$	−530.632	+	306.360i	−0.632457	+	0.365149i	−0.781703	−	0.623651i	$-0.785649\pi$
$839$	−530.632	+	306.360i	−0.632457	+	0.365149i	0.149246	+	0.988800i	$0.452315\pi$
$840$		0			0
$841$	−101.103	+	175.116i	−0.120218	+	0.208224i
$842$	−545.024	+	944.009i	−0.647297	+	1.12115i
$843$	313.121	+	607.514i	0.371437	+	0.720657i
$844$	71.0878	+	123.128i	0.0842272	+	0.145886i
$845$		−	1028.21i		−	1.21682i
$846$	−599.242	−	426.893i	−0.708324	−	0.504602i
$847$		0			0
$848$	10.4362	+	18.0761i	0.0123069	+	0.0213161i
$849$	−328.025	−	210.854i	−0.386367	−	0.248356i
$850$	−640.240	−	369.642i	−0.753223	−	0.434874i
$851$	169.036	−	292.779i	0.198632	−	0.344041i
$852$	126.670	−	197.060i	0.148674	−	0.231291i
$853$	1000.90	−	577.868i	1.17338	−	0.677453i	0.218909	−	0.975745i	$-0.429750\pi$
$853$	1000.90	−	577.868i	1.17338	−	0.677453i	0.954475	+	0.298292i	$0.0964169\pi$
$854$		0			0
$855$	132.177	−	185.541i	0.154593	−	0.217007i
$856$	1090.93			1.27445
$857$	−352.355	+	203.432i	−0.411149	+	0.237377i	−0.691283	−	0.722584i	$-0.742954\pi$
$857$	−352.355	+	203.432i	−0.411149	+	0.237377i	0.280134	+	0.959961i	$0.409621\pi$
$858$	686.252	−	353.703i	0.799827	−	0.412242i
$859$	−325.728	−	188.059i	−0.379194	−	0.218928i	0.298273	−	0.954480i	$-0.403589\pi$
$859$	−325.728	−	188.059i	−0.379194	−	0.218928i	−0.677468	+	0.735553i	$0.736923\pi$
$860$	10.2415	+	5.91290i	0.0119087	+	0.00687547i
$861$		0			0
$862$	401.849	+	696.024i	0.466183	+	0.807452i
$863$	−631.055			−0.731234			−0.365617	−	0.930765i	$-0.619142\pi$
$863$	−631.055			−0.731234			−0.365617	+	0.930765i	$0.619142\pi$
$864$	301.566	−	383.244i	0.349035	−	0.443569i
$865$	−13.9657			−0.0161453
$866$	1107.73	−	639.550i	1.27914	−	0.738511i
$867$	655.977	+	31.3116i	0.756606	+	0.0361149i
$868$		0			0
$869$	−320.272	+	554.727i	−0.368552	+	0.638351i
$870$	339.661	−	175.066i	0.390415	−	0.201225i
$871$	−55.4403	+	32.0085i	−0.0636513	+	0.0367491i
$872$	898.732			1.03066
$873$	123.516	−	56.3789i	0.141484	−	0.0645806i
$874$		−	155.144i		−	0.177510i
$875$		0			0
$876$	−63.1180	−	40.5721i	−0.0720525	−	0.0463152i
$877$	609.906	−	1056.39i	0.695445	−	1.20455i	−0.274585	−	0.961563i	$-0.588540\pi$
$877$	609.906	−	1056.39i	0.695445	−	1.20455i	0.970030	−	0.242984i	$-0.0781262\pi$
$878$	−503.873	−	290.911i	−0.573888	−	0.331334i
$879$	−377.292	−	242.522i	−0.429229	−	0.275907i
$880$	125.352	−	72.3720i	0.142445	−	0.0822409i
$881$			543.964i			0.617439i	0.951153	+	0.308719i	$0.0999004\pi$
$881$			543.964i			0.617439i	−0.951153	+	0.308719i	$0.900100\pi$
$882$		0			0
$883$	1196.59			1.35514			0.677570	−	0.735458i	$-0.263033\pi$
$883$	1196.59			1.35514			0.677570	+	0.735458i	$0.263033\pi$
$884$	−325.217	−	563.292i	−0.367892	−	0.637208i
$885$	341.306	+	662.198i	0.385656	+	0.748246i
$886$	44.0362	−	76.2729i	0.0497022	−	0.0860868i
$887$	916.233	+	528.987i	1.03296	+	0.596378i	0.917830	−	0.396973i	$-0.129939\pi$
$887$	916.233	+	528.987i	1.03296	+	0.596378i	0.115126	+	0.993351i	$0.463273\pi$
$888$	1031.26	+	49.2249i	1.16133	+	0.0554334i
$889$		0			0
$890$	−54.7021			−0.0614631
$891$	164.265	+	475.207i	0.184360	+	0.533341i
$892$		−	354.931i		−	0.397904i
$893$	262.354	+	454.411i	0.293790	+	0.508858i
$894$	−1273.35	−	60.7808i	−1.42433	−	0.0679874i
$895$	521.532	+	301.106i	0.582717	+	0.336432i
$896$		0			0
$897$	561.578	−	289.445i	0.626062	−	0.322681i
$898$	−24.9794	−	43.2656i	−0.0278167	−	0.0481799i
$899$			53.8135i			0.0598593i
$900$	−204.589	−	19.5758i	−0.227321	−	0.0217509i
$901$			47.2984i			0.0524954i
$902$	291.963	−	168.565i	0.323684	−	0.186879i
$903$		0			0
$904$	831.077	−	1439.47i	0.919333	−	1.59233i
$905$	120.195	−	208.183i	0.132812	−	0.230037i
$906$	−232.049	+	360.998i	−0.256125	+	0.398453i
$907$	−46.8954	−	81.2252i	−0.0517038	−	0.0895537i	0.839015	−	0.544108i	$-0.183132\pi$
$907$	−46.8954	−	81.2252i	−0.0517038	−	0.0895537i	−0.890719	+	0.454554i	$0.849799\pi$
$908$			208.678i			0.229821i
$909$	−814.316	+	371.695i	−0.895837	+	0.408906i
$910$		0			0
$911$	357.105	+	618.525i	0.391993	+	0.678951i	0.992712	−	0.120509i	$-0.0384525\pi$
$911$	357.105	+	618.525i	0.391993	+	0.678951i	−0.600720	+	0.799460i	$0.705119\pi$
$912$	286.311	−	147.568i	0.313937	−	0.161807i
$913$	62.4069	+	36.0306i	0.0683537	+	0.0394640i
$914$	−99.9237	+	173.073i	−0.109326	+	0.189358i
$915$	−162.564	−	7.75965i	−0.177666	−	0.00848049i
$916$	287.057	−	165.733i	0.313382	−	0.180931i
$917$		0			0
$918$	−950.277	+	380.114i	−1.03516	+	0.414067i
$919$	1672.93			1.82038			0.910191	−	0.414189i	$-0.135935\pi$
$919$	1672.93			1.82038			0.910191	+	0.414189i	$0.135935\pi$
$920$	150.887	−	87.1147i	0.164008	−	0.0946898i
$921$	−1.51071	+	31.6493i	−0.00164029	+	0.0343640i
$922$	1106.58	+	638.885i	1.20020	+	0.692934i
$923$	1423.55	+	821.889i	1.54231	+	0.890454i
$924$		0			0
$925$	−385.848	−	668.309i	−0.417133	−	0.722496i
$926$	−199.103			−0.215014
$927$	−153.765	−	109.540i	−0.165873	−	0.118166i
$928$	−583.369			−0.628631
$929$	−600.433	+	346.660i	−0.646322	+	0.373154i	−0.787046	−	0.616895i	$-0.788390\pi$
$929$	−600.433	+	346.660i	−0.646322	+	0.373154i	0.140724	+	0.990049i	$0.455057\pi$
$930$	10.6585	−	16.5815i	0.0114608	−	0.0178296i
$931$		0			0
$932$	140.180	−	242.800i	0.150408	−	0.260515i
$933$	−1139.68	−	732.586i	−1.22153	−	0.785194i
$934$	146.059	−	84.3273i	0.156380	−	0.0902862i
$935$	327.999			0.350801
$936$	1571.42	+	1119.46i	1.67887	+	1.19601i
$937$		−	909.088i		−	0.970211i	−0.874456	−	0.485105i	$-0.838781\pi$
$937$		−	909.088i		−	0.970211i	0.874456	−	0.485105i	$-0.161219\pi$
$938$		0			0
$939$	451.991	−	232.962i	0.481354	−	0.248096i
$940$	−66.7160	+	115.555i	−0.0709744	+	0.122931i
$941$	−1095.81	−	632.664i	−1.16451	−	0.672332i	−0.212132	−	0.977241i	$-0.568041\pi$
$941$	−1095.81	−	632.664i	−1.16451	−	0.672332i	−0.952381	+	0.304909i	$0.901374\pi$
$942$	−59.9878	+	1256.74i	−0.0636814	+	1.33412i
$943$	238.921	−	137.941i	0.253362	−	0.146279i
$944$			1053.34i			1.11583i
$945$		0			0
$946$	−44.9745			−0.0475418
$947$	−489.835	−	848.420i	−0.517249	−	0.895902i	−0.999799	−	0.0200339i	$-0.993623\pi$
$947$	−489.835	−	848.420i	−0.517249	−	0.895902i	0.482550	−	0.875869i	$-0.339711\pi$
$948$	−362.069	−	17.2825i	−0.381929	−	0.0182305i
$949$	263.249	−	455.961i	0.277397	−	0.480465i
$950$	−306.693	−	177.069i	−0.322834	−	0.186389i
$951$	−228.254	−	442.856i	−0.240015	−	0.465674i
$952$		0			0
$953$	−307.846			−0.323029			−0.161514	−	0.986870i	$-0.551638\pi$
$953$	−307.846			−0.323029			−0.161514	+	0.986870i	$0.551638\pi$
$954$	−13.1922	−	28.9017i	−0.0138283	−	0.0302953i
$955$		−	283.878i		−	0.297254i
$956$	−256.536	−	444.334i	−0.268343	−	0.464784i
$957$	325.228	−	505.957i	0.339841	−	0.528691i
$958$	945.194	+	545.708i	0.986632	+	0.569633i
$959$		0			0
$960$	415.135	+	266.848i	0.432433	+	0.277967i
$961$	−479.112	−	829.846i	−0.498556	−	0.863524i
$962$			1640.45i			1.70525i
$963$	−1123.75	−	107.525i	−1.16693	−	0.111656i
$964$			6.71395i			0.00696468i
$965$	548.336	−	316.582i	0.568224	−	0.328064i
$966$		0			0
$967$	28.5677	−	49.4807i	0.0295426	−	0.0511693i	−0.850876	−	0.525366i	$-0.823928\pi$
$967$	28.5677	−	49.4807i	0.0295426	−	0.0511693i	0.880419	+	0.474197i	$0.157262\pi$
$968$	−358.632	+	621.168i	−0.370487	+	0.641703i
$969$	729.076	+	34.8008i	0.752401	+	0.0359142i
$970$	29.7469	+	51.5232i	0.0306669	+	0.0531167i
$971$			1757.15i			1.80963i	0.425808	+	0.904813i	$0.359990\pi$
$971$			1757.15i			1.80963i	−0.425808	+	0.904813i	$0.640010\pi$
$972$	−196.448	+	205.829i	−0.202107	+	0.211759i
$973$		0			0
$974$	530.173	+	918.287i	0.544326	+	0.942800i
$975$	68.7587	−	1440.49i	0.0705217	−	1.47743i
$976$	−199.286	−	115.058i	−0.204186	−	0.117887i
$977$	−262.748	+	455.093i	−0.268934	+	0.465807i	−0.968587	−	0.248676i	$-0.920005\pi$
$977$	−262.748	+	455.093i	−0.268934	+	0.465807i	0.699653	+	0.714483i	$0.253338\pi$
$978$	−408.204	−	791.992i	−0.417386	−	0.809808i
$979$	−74.5669	+	43.0512i	−0.0761664	+	0.0439747i
$980$		0			0
$981$	−925.771	−	88.5810i	−0.943701	−	0.0902967i
$982$	−1321.22			−1.34544
$983$	1303.53	−	752.592i	1.32607	−	0.765607i	0.341381	−	0.939925i	$-0.389105\pi$
$983$	1303.53	−	752.592i	1.32607	−	0.765607i	0.984689	+	0.174318i	$0.0557720\pi$
$984$	708.724	+	455.566i	0.720247	+	0.462973i
$985$	23.7359	+	13.7039i	0.0240973	+	0.0139126i
$986$	1060.31	+	612.169i	1.07536	+	0.620861i
$987$		0			0
$988$	−155.788	−	269.833i	−0.157680	−	0.273110i
$989$	−36.8039			−0.0372132
$990$	−200.424	+	91.4839i	−0.202449	+	0.0924080i
$991$	183.562			0.185229			0.0926143	−	0.995702i	$-0.470478\pi$
$991$	183.562			0.185229			0.0926143	+	0.995702i	$0.470478\pi$
$992$	−26.0613	+	15.0465i	−0.0262714	+	0.0151678i
$993$	118.250	+	229.428i	0.119084	+	0.231045i
$994$		0			0
$995$	−310.167	+	537.226i	−0.311726	+	0.539925i
$996$	−1.94429	+	40.7328i	−0.00195210	+	0.0408964i
$997$	−518.220	+	299.195i	−0.519780	+	0.300095i	−0.736845	−	0.676062i	$-0.763685\pi$
$997$	−518.220	+	299.195i	−0.519780	+	0.300095i	0.217065	+	0.976157i	$0.430352\pi$
$998$	391.497			0.392281
$999$	−1057.43	−	152.349i	−1.05849	−	0.152502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.l.b.391.5		28
7.2	even	3		441.3.k.b.31.5		28
7.3	odd	6		441.3.t.a.166.10		28
7.4	even	3		63.3.t.a.40.10	yes	28
7.5	odd	6		63.3.k.a.31.5	✓	28
7.6	odd	2		441.3.l.a.391.5		28
9.7	even	3		441.3.l.a.97.5		28
21.5	even	6		189.3.k.a.10.10		28
21.11	odd	6		189.3.t.a.145.5		28
63.11	odd	6		189.3.k.a.19.10		28
63.16	even	3		441.3.t.a.178.10		28
63.25	even	3		63.3.k.a.61.5	yes	28
63.34	odd	6	inner	441.3.l.b.97.5		28
63.47	even	6		189.3.t.a.73.5		28
63.52	odd	6		441.3.k.b.313.5		28
63.61	odd	6		63.3.t.a.52.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.5	✓	28	7.5	odd	6
63.3.k.a.61.5	yes	28	63.25	even	3
63.3.t.a.40.10	yes	28	7.4	even	3
63.3.t.a.52.10	yes	28	63.61	odd	6
189.3.k.a.10.10		28	21.5	even	6
189.3.k.a.19.10		28	63.11	odd	6
189.3.t.a.73.5		28	63.47	even	6
189.3.t.a.145.5		28	21.11	odd	6
441.3.k.b.31.5		28	7.2	even	3
441.3.k.b.313.5		28	63.52	odd	6
441.3.l.a.97.5		28	9.7	even	3
441.3.l.a.391.5		28	7.6	odd	2
441.3.l.b.97.5		28	63.34	odd	6	inner
441.3.l.b.391.5		28	1.1	even	1	trivial
441.3.t.a.166.10		28	7.3	odd	6
441.3.t.a.178.10		28	63.16	even	3

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.840995 - 1.45665i) q^{2} +(-2.99659 - 0.143035i) q^{3} +(0.585454 - 1.01404i) q^{4} +(-2.03050 - 1.17231i) q^{5} +(2.31176 + 4.48526i) q^{6} -8.69742 q^{8} +(8.95908 + 0.857237i) q^{9} +O(q^{10})\)	\(q+(-0.840995 - 1.45665i) q^{2} +(-2.99659 - 0.143035i) q^{3} +(0.585454 - 1.01404i) q^{4} +(-2.03050 - 1.17231i) q^{5} +(2.31176 + 4.48526i) q^{6} -8.69742 q^{8} +(8.95908 + 0.857237i) q^{9} +3.94363i q^{10} +(3.10369 + 5.37574i) q^{11} +(-1.89941 + 2.95491i) q^{12} +(-21.3461 - 12.3242i) q^{13} +(5.91690 + 3.80337i) q^{15} +(4.97267 + 8.61292i) q^{16} +22.5368i q^{17} +(-6.28585 - 13.7711i) q^{18} +10.7958i q^{19} +(-2.37753 + 1.37267i) q^{20} +(5.22037 - 9.04195i) q^{22} +(4.27197 - 7.39927i) q^{23} +(26.0626 + 1.24404i) q^{24} +(-9.75137 - 16.8899i) q^{25} +41.4583i q^{26} +(-26.7241 - 3.85025i) q^{27} +(16.1494 + 27.9715i) q^{29} +(0.564079 - 11.8174i) q^{30} +(1.44290 + 0.833060i) q^{31} +(-9.03085 + 15.6419i) q^{32} +(-8.53154 - 16.5528i) q^{33} +(32.8282 - 18.9534i) q^{34} +(6.11440 - 8.58296i) q^{36} +39.5686 q^{37} +(15.7256 - 9.07919i) q^{38} +(62.2027 + 39.9837i) q^{39} +(17.6601 + 10.1961i) q^{40} +(27.9638 + 16.1449i) q^{41} +(-2.15380 - 3.73049i) q^{43} +7.26826 q^{44} +(-17.1865 - 12.2435i) q^{45} -14.3708 q^{46} +(42.0916 - 24.3016i) q^{47} +(-13.6691 - 26.5206i) q^{48} +(-16.4017 + 28.4086i) q^{50} +(3.22356 - 67.5336i) q^{51} +(-24.9943 + 14.4305i) q^{52} +2.09872 q^{53} +(16.8664 + 42.1656i) q^{54} -14.5539i q^{55} +(1.54418 - 32.3505i) q^{57} +(27.1631 - 47.0478i) q^{58} +(91.7236 + 52.9566i) q^{59} +(7.32082 - 3.77325i) q^{60} +(-20.0381 + 11.5690i) q^{61} -2.80240i q^{62} +70.1610 q^{64} +(28.8955 + 50.0485i) q^{65} +(-16.9366 + 26.3483i) q^{66} +(1.29860 - 2.24925i) q^{67} +(22.8531 + 13.1943i) q^{68} +(-13.8597 + 21.5615i) q^{69} -66.6892 q^{71} +(-77.9209 - 7.45575i) q^{72} +21.3604i q^{73} +(-33.2770 - 57.6375i) q^{74} +(26.8050 + 52.0068i) q^{75} +(10.9473 + 6.32042i) q^{76} +(5.93001 - 124.233i) q^{78} +(51.5954 + 89.3659i) q^{79} -23.3181i q^{80} +(79.5303 + 15.3601i) q^{81} -54.3111i q^{82} +(10.0537 - 5.80449i) q^{83} +(26.4202 - 45.7611i) q^{85} +(-3.62267 + 6.27465i) q^{86} +(-44.3920 - 86.1290i) q^{87} +(-26.9940 - 46.7551i) q^{88} +13.8710i q^{89} +(-3.38063 + 35.3313i) q^{90} +(-5.00208 - 8.66386i) q^{92} +(-4.20463 - 2.70272i) q^{93} +(-70.7976 - 40.8750i) q^{94} +(12.6560 - 21.9208i) q^{95} +(29.2991 - 45.5806i) q^{96} +(13.0649 - 7.54303i) q^{97} +(23.1979 + 50.8223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9	\( 28 q + q^{2} - 23 q^{4} + 3 q^{5} - 12 q^{6} - 16 q^{8} + 6 q^{9} + 7 q^{11} + 27 q^{12} - 15 q^{13} - 18 q^{15} - 27 q^{16} + 9 q^{18} - 108 q^{20} - 10 q^{22} + 34 q^{23} + 120 q^{24} + 31 q^{25} + 81 q^{27} + 70 q^{29} + 33 q^{30} + 45 q^{31} + 153 q^{32} - 111 q^{33} - 12 q^{34} - 174 q^{36} - 18 q^{37} - 87 q^{38} - 9 q^{39} + 102 q^{40} + 234 q^{41} + 30 q^{43} - 102 q^{44} + 3 q^{45} + 44 q^{46} - 111 q^{47} - 147 q^{48} + 241 q^{50} - 6 q^{51} + 219 q^{52} - 296 q^{53} + 207 q^{54} + 189 q^{57} + 17 q^{58} + 42 q^{59} - 489 q^{60} + 120 q^{61} - 48 q^{64} + 114 q^{65} - 705 q^{66} - 34 q^{67} + 18 q^{68} - 78 q^{69} - 350 q^{71} + 177 q^{72} + 359 q^{74} + 387 q^{75} - 72 q^{76} - 375 q^{78} - 82 q^{79} + 438 q^{81} - 738 q^{83} + 3 q^{85} + 17 q^{86} + 564 q^{87} + 25 q^{88} + 543 q^{90} + 288 q^{92} - 30 q^{93} - 3 q^{94} + 507 q^{95} - 813 q^{96} + 57 q^{97} - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 23 * q^4 + 3 * q^5 - 12 * q^6 - 16 * q^8 + 6 * q^9 + 7 * q^11 + 27 * q^12 - 15 * q^13 - 18 * q^15 - 27 * q^16 + 9 * q^18 - 108 * q^20 - 10 * q^22 + 34 * q^23 + 120 * q^24 + 31 * q^25 + 81 * q^27 + 70 * q^29 + 33 * q^30 + 45 * q^31 + 153 * q^32 - 111 * q^33 - 12 * q^34 - 174 * q^36 - 18 * q^37 - 87 * q^38 - 9 * q^39 + 102 * q^40 + 234 * q^41 + 30 * q^43 - 102 * q^44 + 3 * q^45 + 44 * q^46 - 111 * q^47 - 147 * q^48 + 241 * q^50 - 6 * q^51 + 219 * q^52 - 296 * q^53 + 207 * q^54 + 189 * q^57 + 17 * q^58 + 42 * q^59 - 489 * q^60 + 120 * q^61 - 48 * q^64 + 114 * q^65 - 705 * q^66 - 34 * q^67 + 18 * q^68 - 78 * q^69 - 350 * q^71 + 177 * q^72 + 359 * q^74 + 387 * q^75 - 72 * q^76 - 375 * q^78 - 82 * q^79 + 438 * q^81 - 738 * q^83 + 3 * q^85 + 17 * q^86 + 564 * q^87 + 25 * q^88 + 543 * q^90 + 288 * q^92 - 30 * q^93 - 3 * q^94 + 507 * q^95 - 813 * q^96 + 57 * q^97 - 162 * q^99

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