LMFDB - Embedded newform 484.3.b.k.243.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,3,Mod(243,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("484.243");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	484.b (of order $2$, degree $1$, 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:	$13.1880447950$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + x^{18} - 2 x^{17} - 12 x^{16} - 4 x^{15} - 16 x^{14} - 80 x^{13} - 16 x^{12} + 512 x^{11} + \cdots + 1048576 $ x^20 + x^18 - 2x^17 - 12x^16 - 4x^15 - 16x^14 - 80x^13 - 16x^12 + 512x^11 + 320x^10 + 2048x^9 - 256x^8 - 5120x^7 - 4096x^6 - 4096x^5 - 49152x^4 - 32768x^3 + 65536x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			243.17
Root			$-1.74858 - 0.970805i$ of defining polynomial
Character	$\chi$	$=$	484.243
Dual form			484.3.b.k.243.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74858 - 0.970805i) q^{2} -1.09265i q^{3} +(2.11508 - 3.39506i) q^{4} -0.748181 q^{5} +(-1.06075 - 1.91059i) q^{6} -3.87834i q^{7} +(0.402437 - 7.98987i) q^{8} +7.80611 q^{9} +O(q^{10})$	\(q+(1.74858 - 0.970805i) q^{2} -1.09265i q^{3} +(2.11508 - 3.39506i) q^{4} -0.748181 q^{5} +(-1.06075 - 1.91059i) q^{6} -3.87834i q^{7} +(0.402437 - 7.98987i) q^{8} +7.80611 q^{9} +(-1.30826 + 0.726338i) q^{10} +(-3.70962 - 2.31104i) q^{12} -3.44211 q^{13} +(-3.76511 - 6.78159i) q^{14} +0.817502i q^{15} +(-7.05291 - 14.3616i) q^{16} +7.77228 q^{17} +(13.6496 - 7.57821i) q^{18} -19.1857i q^{19} +(-1.58246 + 2.54012i) q^{20} -4.23767 q^{21} -15.0061i q^{23} +(-8.73015 - 0.439723i) q^{24} -24.4402 q^{25} +(-6.01881 + 3.34162i) q^{26} -18.3632i q^{27} +(-13.1672 - 8.20297i) q^{28} -13.9769 q^{29} +(0.793635 + 1.42947i) q^{30} +55.6293i q^{31} +(-26.2749 - 18.2655i) q^{32} +(13.5905 - 7.54537i) q^{34} +2.90170i q^{35} +(16.5105 - 26.5022i) q^{36} +36.6774 q^{37} +(-18.6256 - 33.5478i) q^{38} +3.76103i q^{39} +(-0.301095 + 5.97787i) q^{40} -55.1896 q^{41} +(-7.40992 + 4.11396i) q^{42} -43.0444i q^{43} -5.84038 q^{45} +(-14.5680 - 26.2395i) q^{46} -48.5615i q^{47} +(-15.6923 + 7.70638i) q^{48} +33.9585 q^{49} +(-42.7357 + 23.7267i) q^{50} -8.49241i q^{51} +(-7.28032 + 11.6862i) q^{52} +92.4253 q^{53} +(-17.8271 - 32.1096i) q^{54} +(-30.9874 - 1.56078i) q^{56} -20.9634 q^{57} +(-24.4398 + 13.5689i) q^{58} +80.2261i q^{59} +(2.77547 + 1.72908i) q^{60} +77.7361 q^{61} +(54.0052 + 97.2724i) q^{62} -30.2747i q^{63} +(-63.6761 - 6.43083i) q^{64} +2.57532 q^{65} +57.7376i q^{67} +(16.4390 - 26.3874i) q^{68} -16.3965 q^{69} +(2.81698 + 5.07385i) q^{70} +98.2910i q^{71} +(3.14146 - 62.3698i) q^{72} -74.8240 q^{73} +(64.1334 - 35.6066i) q^{74} +26.7047i q^{75} +(-65.1368 - 40.5793i) q^{76} +(3.65123 + 6.57647i) q^{78} -75.6468i q^{79} +(5.27685 + 10.7451i) q^{80} +50.1904 q^{81} +(-96.5035 + 53.5783i) q^{82} +66.0432i q^{83} +(-8.96300 + 14.3872i) q^{84} -5.81507 q^{85} +(-41.7877 - 75.2667i) q^{86} +15.2719i q^{87} +46.7420 q^{89} +(-10.2124 + 5.66987i) q^{90} +13.3497i q^{91} +(-50.9468 - 31.7391i) q^{92} +60.7835 q^{93} +(-47.1437 - 84.9137i) q^{94} +14.3544i q^{95} +(-19.9578 + 28.7094i) q^{96} +107.299 q^{97} +(59.3792 - 32.9671i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{4} + 2 q^{5} + 3 q^{6} - 6 q^{8} - 30 q^{9}+O(q^{10}) $ 20 * q - 2 * q^4 + 2 * q^5 + 3 * q^6 - 6 * q^8 - 30 * q^9	$ 20 q - 2 q^{4} + 2 q^{5} + 3 q^{6} - 6 q^{8} - 30 q^{9} + 4 q^{10} - 25 q^{12} - 2 q^{13} + 12 q^{14} + 50 q^{16} + 10 q^{17} + 9 q^{18} - 18 q^{20} + 26 q^{21} - 27 q^{24} + 30 q^{25} - 72 q^{26} - 60 q^{28} + 14 q^{29} + 188 q^{30} - 10 q^{32} + 129 q^{34} - 23 q^{36} + 50 q^{37} - 95 q^{38} - 226 q^{40} + 50 q^{41} + 40 q^{42} + 72 q^{45} + 210 q^{46} + 163 q^{48} + 46 q^{49} + 176 q^{50} - 418 q^{52} - 230 q^{53} + 270 q^{54} - 428 q^{56} - 146 q^{57} - 28 q^{58} + 238 q^{60} - 26 q^{61} + 322 q^{62} + 34 q^{64} - 82 q^{65} - 297 q^{68} + 208 q^{69} - 322 q^{70} - 425 q^{72} + 42 q^{73} + 566 q^{74} - 183 q^{76} + 706 q^{78} - 90 q^{80} - 300 q^{81} - 185 q^{82} - 790 q^{84} + 142 q^{85} + 17 q^{86} - 44 q^{89} + 520 q^{90} + 474 q^{92} - 384 q^{93} + 524 q^{94} - 1067 q^{96} + 150 q^{97} + 326 q^{98}+O(q^{100}) $ 20 * q - 2 * q^4 + 2 * q^5 + 3 * q^6 - 6 * q^8 - 30 * q^9 + 4 * q^10 - 25 * q^12 - 2 * q^13 + 12 * q^14 + 50 * q^16 + 10 * q^17 + 9 * q^18 - 18 * q^20 + 26 * q^21 - 27 * q^24 + 30 * q^25 - 72 * q^26 - 60 * q^28 + 14 * q^29 + 188 * q^30 - 10 * q^32 + 129 * q^34 - 23 * q^36 + 50 * q^37 - 95 * q^38 - 226 * q^40 + 50 * q^41 + 40 * q^42 + 72 * q^45 + 210 * q^46 + 163 * q^48 + 46 * q^49 + 176 * q^50 - 418 * q^52 - 230 * q^53 + 270 * q^54 - 428 * q^56 - 146 * q^57 - 28 * q^58 + 238 * q^60 - 26 * q^61 + 322 * q^62 + 34 * q^64 - 82 * q^65 - 297 * q^68 + 208 * q^69 - 322 * q^70 - 425 * q^72 + 42 * q^73 + 566 * q^74 - 183 * q^76 + 706 * q^78 - 90 * q^80 - 300 * q^81 - 185 * q^82 - 790 * q^84 + 142 * q^85 + 17 * q^86 - 44 * q^89 + 520 * q^90 + 474 * q^92 - 384 * q^93 + 524 * q^94 - 1067 * q^96 + 150 * q^97 + 326 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.74858	−	0.970805i	0.874291	−	0.485403i
$2$	1.74858	−	0.970805i	0.874291	−	0.485403i
$3$		−	1.09265i		−	0.364218i	−0.983278	−	0.182109i	$-0.941708\pi$
$3$		−	1.09265i		−	0.364218i	0.983278	−	0.182109i	$-0.0582923\pi$
$4$	2.11508	−	3.39506i	0.528769	−	0.848766i
$5$	−0.748181			−0.149636			−0.0748181	−	0.997197i	$-0.523838\pi$
$5$	−0.748181			−0.149636			−0.0748181	+	0.997197i	$0.523838\pi$
$6$	−1.06075	−	1.91059i	−0.176792	−	0.318432i
$7$		−	3.87834i		−	0.554048i	−0.960863	−	0.277024i	$-0.910652\pi$
$7$		−	3.87834i		−	0.554048i	0.960863	−	0.277024i	$-0.0893482\pi$
$8$	0.402437	−	7.98987i	0.0503046	−	0.998734i
$9$	7.80611			0.867346
$10$	−1.30826	+	0.726338i	−0.130826	+	0.0726338i
$11$		0			0
$11$		0			0
$12$	−3.70962	−	2.31104i	−0.309135	−	0.192587i
$13$	−3.44211			−0.264778			−0.132389	−	0.991198i	$-0.542265\pi$
$13$	−3.44211			−0.264778			−0.132389	+	0.991198i	$0.542265\pi$
$14$	−3.76511	−	6.78159i	−0.268936	−	0.484399i
$15$			0.817502i			0.0545001i
$16$	−7.05291	−	14.3616i	−0.440807	−	0.897602i
$17$	7.77228			0.457193			0.228597	−	0.973521i	$-0.426586\pi$
$17$	7.77228			0.457193			0.228597	+	0.973521i	$0.426586\pi$
$18$	13.6496	−	7.57821i	0.758312	−	0.421012i
$19$		−	19.1857i		−	1.00978i	−0.863185	−	0.504888i	$-0.831534\pi$
$19$		−	19.1857i		−	1.00978i	0.863185	−	0.504888i	$-0.168466\pi$
$20$	−1.58246	+	2.54012i	−0.0791229	+	0.127006i
$21$	−4.23767			−0.201794
$22$		0			0
$23$		−	15.0061i		−	0.652441i	−0.945294	−	0.326220i	$-0.894225\pi$
$23$		−	15.0061i		−	0.652441i	0.945294	−	0.326220i	$-0.105775\pi$
$24$	−8.73015	−	0.439723i	−0.363756	−	0.0183218i
$25$	−24.4402			−0.977609
$26$	−6.01881	+	3.34162i	−0.231493	+	0.128524i
$27$		−	18.3632i		−	0.680120i
$28$	−13.1672	−	8.20297i	−0.470257	−	0.292963i
$29$	−13.9769			−0.481963			−0.240982	−	0.970530i	$-0.577469\pi$
$29$	−13.9769			−0.481963			−0.240982	+	0.970530i	$0.577469\pi$
$30$	0.793635	+	1.42947i	0.0264545	+	0.0476489i
$31$			55.6293i			1.79449i	0.441529	+	0.897247i	$0.354436\pi$
$31$			55.6293i			1.79449i	−0.441529	+	0.897247i	$0.645564\pi$
$32$	−26.2749	−	18.2655i	−0.821092	−	0.570796i
$33$		0			0
$34$	13.5905	−	7.54537i	0.399720	−	0.221923i
$35$			2.90170i			0.0829056i
$36$	16.5105	−	26.5022i	0.458625	−	0.736173i
$37$	36.6774			0.991281			0.495640	−	0.868528i	$-0.334933\pi$
$37$	36.6774			0.991281			0.495640	+	0.868528i	$0.334933\pi$
$38$	−18.6256	−	33.5478i	−0.490148	−	0.882838i
$39$			3.76103i			0.0964366i
$40$	−0.301095	+	5.97787i	−0.00752738	+	0.149447i
$41$	−55.1896			−1.34609			−0.673044	−	0.739603i	$-0.735013\pi$
$41$	−55.1896			−1.34609			−0.673044	+	0.739603i	$0.735013\pi$
$42$	−7.40992	+	4.11396i	−0.176427	+	0.0979513i
$43$		−	43.0444i		−	1.00103i	−0.865727	−	0.500517i	$-0.833143\pi$
$43$		−	43.0444i		−	1.00103i	0.865727	−	0.500517i	$-0.166857\pi$
$44$		0			0
$45$	−5.84038			−0.129786
$46$	−14.5680	−	26.2395i	−0.316696	−	0.570423i
$47$		−	48.5615i		−	1.03322i	−0.856220	−	0.516611i	$-0.827193\pi$
$47$		−	48.5615i		−	1.03322i	0.856220	−	0.516611i	$-0.172807\pi$
$48$	−15.6923	+	7.70638i	−0.326922	+	0.160550i
$49$	33.9585			0.693031
$50$	−42.7357	+	23.7267i	−0.854715	+	0.474534i
$51$		−	8.49241i		−	0.166518i
$52$	−7.28032	+	11.6862i	−0.140006	+	0.224734i
$53$	92.4253			1.74387			0.871937	−	0.489618i	$-0.162864\pi$
$53$	92.4253			1.74387			0.871937	+	0.489618i	$0.162864\pi$
$54$	−17.8271	−	32.1096i	−0.330132	−	0.594623i
$55$		0			0
$56$	−30.9874	−	1.56078i	−0.553347	−	0.0278712i
$57$	−20.9634			−0.367778
$58$	−24.4398	+	13.5689i	−0.421376	+	0.233946i
$59$			80.2261i			1.35976i	0.733322	+	0.679882i	$0.237969\pi$
$59$			80.2261i			1.35976i	−0.733322	+	0.679882i	$0.762031\pi$
$60$	2.77547	+	1.72908i	0.0462578	+	0.0288180i
$61$	77.7361			1.27436			0.637181	−	0.770714i	$-0.280100\pi$
$61$	77.7361			1.27436			0.637181	+	0.770714i	$0.280100\pi$
$62$	54.0052	+	97.2724i	0.871052	+	1.56891i
$63$		−	30.2747i		−	0.480551i
$64$	−63.6761	−	6.43083i	−0.994939	−	0.100482i
$65$	2.57532			0.0396203
$66$		0			0
$67$			57.7376i			0.861755i	0.902411	+	0.430877i	$0.141796\pi$
$67$			57.7376i			0.861755i	−0.902411	+	0.430877i	$0.858204\pi$
$68$	16.4390	−	26.3874i	0.241749	−	0.388050i
$69$	−16.3965			−0.237630
$70$	2.81698	+	5.07385i	0.0402426	+	0.0724836i
$71$			98.2910i			1.38438i	0.721715	+	0.692190i	$0.243354\pi$
$71$			98.2910i			1.38438i	−0.721715	+	0.692190i	$0.756646\pi$
$72$	3.14146	−	62.3698i	0.0436315	−	0.866247i
$73$	−74.8240			−1.02499			−0.512493	−	0.858691i	$-0.671278\pi$
$73$	−74.8240			−1.02499			−0.512493	+	0.858691i	$0.671278\pi$
$74$	64.1334	−	35.6066i	0.866667	−	0.481170i
$75$			26.7047i			0.356062i
$76$	−65.1368	−	40.5793i	−0.857064	−	0.533938i
$77$		0			0
$78$	3.65123	+	6.57647i	0.0468106	+	0.0843137i
$79$		−	75.6468i		−	0.957555i	−0.877936	−	0.478777i	$-0.841080\pi$
$79$		−	75.6468i		−	0.957555i	0.877936	−	0.478777i	$-0.158920\pi$
$80$	5.27685	+	10.7451i	0.0659607	+	0.134314i
$81$	50.1904			0.619634
$82$	−96.5035	+	53.5783i	−1.17687	+	0.653394i
$83$			66.0432i			0.795701i	0.917450	+	0.397851i	$0.130244\pi$
$83$			66.0432i			0.795701i	−0.917450	+	0.397851i	$0.869756\pi$
$84$	−8.96300	+	14.3872i	−0.106702	+	0.171276i
$85$	−5.81507			−0.0684126
$86$	−41.7877	−	75.2667i	−0.485904	−	0.875194i
$87$			15.2719i			0.175539i
$88$		0			0
$89$	46.7420			0.525191			0.262596	−	0.964906i	$-0.415421\pi$
$89$	46.7420			0.525191			0.262596	+	0.964906i	$0.415421\pi$
$90$	−10.2124	+	5.66987i	−0.113471	+	0.0629986i
$91$			13.3497i			0.146700i
$92$	−50.9468	−	31.7391i	−0.553769	−	0.344990i
$93$	60.7835			0.653586
$94$	−47.1437	−	84.9137i	−0.501529	−	0.903337i
$95$			14.3544i			0.151099i
$96$	−19.9578	+	28.7094i	−0.207894	+	0.299056i
$97$	107.299			1.10618			0.553089	−	0.833122i	$-0.313449\pi$
$97$	107.299			1.10618			0.553089	+	0.833122i	$0.313449\pi$
$98$	59.3792	−	32.9671i	0.605910	−	0.336399i
$99$		0			0
$100$	−51.6929	+	82.9761i	−0.516929	+	0.829761i
$101$	72.4386			0.717214			0.358607	−	0.933489i	$-0.383252\pi$
$101$	72.4386			0.717214			0.358607	+	0.933489i	$0.383252\pi$
$102$	−8.24447	−	14.8497i	−0.0808281	−	0.145585i
$103$		−	20.9665i		−	0.203558i	−0.994807	−	0.101779i	$-0.967547\pi$
$103$		−	20.9665i		−	0.203558i	0.994807	−	0.101779i	$-0.0324534\pi$
$104$	−1.38523	+	27.5020i	−0.0133195	+	0.264442i
$105$	3.17055			0.0301957
$106$	161.613	−	89.7270i	1.52465	−	0.846481i
$107$		−	26.2544i		−	0.245368i	−0.992446	−	0.122684i	$-0.960850\pi$
$107$		−	26.2544i		−	0.245368i	0.992446	−	0.122684i	$-0.0391502\pi$
$108$	−62.3444	−	38.8396i	−0.577263	−	0.359626i
$109$	79.3568			0.728044			0.364022	−	0.931390i	$-0.381403\pi$
$109$	79.3568			0.728044			0.364022	+	0.931390i	$0.381403\pi$
$110$		0			0
$111$		−	40.0756i		−	0.361042i
$112$	−55.6992	+	27.3536i	−0.497315	+	0.244228i
$113$	−22.7482			−0.201311			−0.100656	−	0.994921i	$-0.532094\pi$
$113$	−22.7482			−0.201311			−0.100656	+	0.994921i	$0.532094\pi$
$114$	−36.6561	+	20.3513i	−0.321545	+	0.178520i
$115$			11.2273i			0.0976287i
$116$	−29.5623	+	47.4526i	−0.254847	+	0.409074i
$117$	−26.8695			−0.229654
$118$	77.8839	+	140.282i	0.660033	+	1.18883i
$119$		−	30.1435i		−	0.253307i
$120$	6.53173	+	0.328993i	0.0544311	+	0.00274160i
$121$		0			0
$122$	135.928	−	75.4666i	1.11416	−	0.618579i
$123$			60.3030i			0.490269i
$124$	188.865	+	117.660i	1.52311	+	0.948873i
$125$	36.9902			0.295922
$126$	−29.3909	−	52.9378i	−0.233261	−	0.420142i
$127$			88.8013i			0.699223i	0.936895	+	0.349612i	$0.113686\pi$
$127$			88.8013i			0.699223i	−0.936895	+	0.349612i	$0.886314\pi$
$128$	−117.586	+	50.5722i	−0.918640	+	0.395096i
$129$	−47.0326			−0.364594
$130$	4.50316	−	2.50013i	0.0346397	−	0.0192318i
$131$			170.654i			1.30271i	0.758775	+	0.651353i	$0.225798\pi$
$131$			170.654i			1.30271i	−0.758775	+	0.651353i	$0.774202\pi$
$132$		0			0
$133$	−74.4088			−0.559465
$134$	56.0519	+	100.959i	0.418298	+	0.753424i
$135$			13.7390i			0.101771i
$136$	3.12785	−	62.0995i	0.0229989	−	0.456614i
$137$	89.1693			0.650871			0.325435	−	0.945564i	$-0.394489\pi$
$137$	89.1693			0.650871			0.325435	+	0.945564i	$0.394489\pi$
$138$	−28.6706	+	15.9178i	−0.207758	+	0.115346i
$139$		−	179.148i		−	1.28884i	−0.764673	−	0.644419i	$-0.777099\pi$
$139$		−	179.148i		−	1.28884i	0.764673	−	0.644419i	$-0.222901\pi$
$140$	9.85145	+	6.13731i	0.0703675	+	0.0438379i
$141$	−53.0608			−0.376318
$142$	95.4214	+	171.870i	0.671982	+	1.21035i
$143$		0			0
$144$	−55.0558	−	112.108i	−0.382332	−	0.778531i
$145$	10.4573			0.0721191
$146$	−130.836	+	72.6395i	−0.896136	+	0.497531i
$147$		−	37.1048i		−	0.252414i
$148$	77.5754	−	124.522i	0.524158	−	0.841365i
$149$	118.471			0.795107			0.397553	−	0.917579i	$-0.369859\pi$
$149$	118.471			0.795107			0.397553	+	0.917579i	$0.369859\pi$
$150$	25.9250	+	46.6953i	0.172834	+	0.311302i
$151$			145.233i			0.961805i	0.876774	+	0.480902i	$0.159691\pi$
$151$			145.233i			0.961805i	−0.876774	+	0.480902i	$0.840309\pi$
$152$	−153.292	−	7.72105i	−1.00850	−	0.0507964i
$153$	60.6713			0.396544
$154$		0			0
$155$		−	41.6208i		−	0.268521i
$156$	12.7689	+	7.95486i	0.0818521	+	0.0509927i
$157$	88.7641			0.565376			0.282688	−	0.959212i	$-0.408774\pi$
$157$	88.7641			0.565376			0.282688	+	0.959212i	$0.408774\pi$
$158$	−73.4383	−	132.275i	−0.464800	−	0.837182i
$159$		−	100.989i		−	0.635149i
$160$	19.6584	+	13.6659i	0.122865	+	0.0854117i
$161$	−58.1989			−0.361484
$162$	87.7619	−	48.7250i	0.541740	−	0.300772i
$163$			22.7268i			0.139428i	0.997567	+	0.0697141i	$0.0222087\pi$
$163$			22.7268i			0.139428i	−0.997567	+	0.0697141i	$0.977791\pi$
$164$	−116.730	+	187.372i	−0.711769	+	1.14251i
$165$		0			0
$166$	64.1151	+	115.482i	0.386235	+	0.695674i
$167$			299.390i			1.79276i	0.443291	+	0.896378i	$0.353811\pi$
$167$			299.390i			1.79276i	−0.443291	+	0.896378i	$0.646189\pi$
$168$	−1.70540	+	33.8585i	−0.0101512	+	0.201539i
$169$	−157.152			−0.929893
$170$	−10.1681	+	5.64530i	−0.0598125	+	0.0332077i
$171$		−	149.766i		−	0.875825i
$172$	−146.139	−	91.0422i	−0.849643	−	0.529315i
$173$	47.0616			0.272033			0.136016	−	0.990707i	$-0.456570\pi$
$173$	47.0616			0.272033			0.136016	+	0.990707i	$0.456570\pi$
$174$	14.8261	+	26.7042i	0.0852073	+	0.153473i
$175$			94.7874i			0.541642i
$176$		0			0
$177$	87.6592			0.495250
$178$	81.7322	−	45.3774i	0.459170	−	0.254929i
$179$			91.2529i			0.509793i	0.966968	+	0.254896i	$0.0820413\pi$
$179$			91.2529i			0.509793i	−0.966968	+	0.254896i	$0.917959\pi$
$180$	−12.3528	+	19.8285i	−0.0686269	+	0.110158i
$181$	−20.0086			−0.110545			−0.0552723	−	0.998471i	$-0.517603\pi$
$181$	−20.0086			−0.110545			−0.0552723	+	0.998471i	$0.517603\pi$
$182$	12.9599	+	23.3430i	0.0712083	+	0.128258i
$183$		−	84.9386i		−	0.464145i
$184$	−119.897	−	6.03902i	−0.651615	−	0.0328208i
$185$	−27.4413			−0.148331
$186$	106.285	−	59.0090i	0.571424	−	0.317252i
$187$		0			0
$188$	−164.869	−	102.711i	−0.876964	−	0.546336i
$189$	−71.2188			−0.376819
$190$	13.9353	+	25.0999i	0.0733439	+	0.132104i
$191$		−	219.753i		−	1.15054i	−0.817963	−	0.575271i	$-0.804897\pi$
$191$		−	219.753i		−	1.15054i	0.817963	−	0.575271i	$-0.195103\pi$
$192$	−7.02667	+	69.5758i	−0.0365972	+	0.362374i
$193$	−89.8121			−0.465348			−0.232674	−	0.972555i	$-0.574747\pi$
$193$	−89.8121			−0.465348			−0.232674	+	0.972555i	$0.574747\pi$
$194$	187.621	−	104.167i	0.967121	−	0.536941i
$195$		−	2.81393i		−	0.0144304i
$196$	71.8248	−	115.291i	0.366453	−	0.588221i
$197$	113.348			0.575370			0.287685	−	0.957725i	$-0.407114\pi$
$197$	113.348			0.575370			0.287685	+	0.957725i	$0.407114\pi$
$198$		0			0
$199$			128.213i			0.644289i	0.946691	+	0.322144i	$0.104404\pi$
$199$			128.213i			0.644289i	−0.946691	+	0.322144i	$0.895596\pi$
$200$	−9.83564	+	195.274i	−0.0491782	+	0.976371i
$201$	63.0871			0.313866
$202$	126.665	−	70.3237i	0.627053	−	0.348137i
$203$			54.2073i			0.267031i
$204$	−28.8323	−	17.9621i	−0.141335	−	0.0880494i
$205$	41.2918			0.201423
$206$	−20.3544	−	36.6616i	−0.0988075	−	0.177969i
$207$		−	117.140i		−	0.565892i
$208$	24.2769	+	49.4343i	0.116716	+	0.237665i
$209$		0			0
$210$	5.54396	−	3.07798i	0.0263998	−	0.0146571i
$211$		−	287.917i		−	1.36453i	−0.731103	−	0.682267i	$-0.760994\pi$
$211$		−	287.917i		−	1.36453i	0.731103	−	0.682267i	$-0.239006\pi$
$212$	195.486	−	313.790i	0.922106	−	1.48014i
$213$	107.398			0.504216
$214$	−25.4879	−	45.9080i	−0.119102	−	0.214523i
$215$			32.2050i			0.149791i
$216$	−146.720	−	7.39004i	−0.679259	−	0.0342131i
$217$	215.749			0.994236
$218$	138.762	−	77.0400i	0.636522	−	0.353394i
$219$			81.7566i			0.373318i
$220$		0			0
$221$	−26.7530			−0.121055
$222$	−38.9056	−	70.0755i	−0.175251	−	0.315655i
$223$			153.839i			0.689862i	0.938628	+	0.344931i	$0.112098\pi$
$223$			153.839i			0.689862i	−0.938628	+	0.344931i	$0.887902\pi$
$224$	−70.8397	+	101.903i	−0.316249	+	0.454924i
$225$	−190.783			−0.847925
$226$	−39.7771	+	22.0841i	−0.176005	+	0.0977171i
$227$			323.043i			1.42310i	0.702637	+	0.711549i	$0.252006\pi$
$227$			323.043i			1.42310i	−0.702637	+	0.711549i	$0.747994\pi$
$228$	−44.3391	+	71.1719i	−0.194470	+	0.312158i
$229$	−285.133			−1.24512			−0.622561	−	0.782571i	$-0.713908\pi$
$229$	−285.133			−1.24512			−0.622561	+	0.782571i	$0.713908\pi$
$230$	10.8995	+	19.6319i	0.0473892	+	0.0853559i
$231$		0			0
$232$	−5.62483	+	111.674i	−0.0242450	+	0.481353i
$233$	195.030			0.837038			0.418519	−	0.908208i	$-0.362549\pi$
$233$	195.030			0.837038			0.418519	+	0.908208i	$0.362549\pi$
$234$	−46.9835	+	26.0850i	−0.200784	+	0.111474i
$235$			36.3327i			0.154607i
$236$	272.373	+	169.684i	1.15412	+	0.719001i
$237$	−82.6557			−0.348758
$238$	−29.2635	−	52.7084i	−0.122956	−	0.221464i
$239$		−	211.328i		−	0.884218i	−0.896961	−	0.442109i	$-0.854230\pi$
$239$		−	211.328i		−	0.884218i	0.896961	−	0.442109i	$-0.145770\pi$
$240$	11.7407	−	5.76577i	0.0489194	−	0.0240240i
$241$	−328.286			−1.36218			−0.681092	−	0.732198i	$-0.738495\pi$
$241$	−328.286			−1.36218			−0.681092	+	0.732198i	$0.738495\pi$
$242$		0			0
$243$		−	220.110i		−	0.905802i
$244$	164.418	−	263.919i	0.673843	−	1.08164i
$245$	−25.4071			−0.103702
$246$	58.5425	+	105.445i	0.237978	+	0.428637i
$247$			66.0394i			0.267366i
$248$	444.471	+	22.3873i	1.79222	+	0.0902713i
$249$	72.1623			0.289808
$250$	64.6804	−	35.9103i	0.258722	−	0.143641i
$251$		−	83.8863i		−	0.334209i	−0.985939	−	0.167104i	$-0.946558\pi$
$251$		−	83.8863i		−	0.334209i	0.985939	−	0.167104i	$-0.0534417\pi$
$252$	−102.785	−	64.0333i	−0.407876	−	0.254100i
$253$		0			0
$254$	86.2088	+	155.276i	0.339405	+	0.611324i
$255$			6.35385i			0.0249171i
$256$	−156.513	+	202.583i	−0.611378	+	0.791339i
$257$	−161.915			−0.630021			−0.315010	−	0.949088i	$-0.602008\pi$
$257$	−161.915			−0.630021			−0.315010	+	0.949088i	$0.602008\pi$
$258$	−82.2403	+	45.6595i	−0.318761	+	0.176975i
$259$		−	142.247i		−	0.549217i
$260$	5.44700	−	8.74337i	0.0209500	−	0.0336284i
$261$	−109.105			−0.418029
$262$	165.672	+	298.403i	0.632337	+	1.13894i
$263$		−	399.263i		−	1.51811i	−0.651027	−	0.759055i	$-0.725661\pi$
$263$		−	399.263i		−	1.51811i	0.651027	−	0.759055i	$-0.274339\pi$
$264$		0			0
$265$	−69.1508			−0.260947
$266$	−130.110	+	72.2364i	−0.489135	+	0.271566i
$267$		−	51.0728i		−	0.191284i
$268$	196.023	+	122.119i	0.731428	+	0.455669i
$269$	−63.7905			−0.237139			−0.118570	−	0.992946i	$-0.537831\pi$
$269$	−63.7905			−0.237139			−0.118570	+	0.992946i	$0.537831\pi$
$270$	13.3379	+	24.0238i	0.0493997	+	0.0889770i
$271$			170.795i			0.630240i	0.949052	+	0.315120i	$0.102045\pi$
$271$			170.795i			0.630240i	−0.949052	+	0.315120i	$0.897955\pi$
$272$	−54.8173	−	111.623i	−0.201534	−	0.410377i
$273$	14.5865			0.0534305
$274$	155.920	−	86.5660i	0.569050	−	0.315934i
$275$		0			0
$276$	−34.6798	+	55.6671i	−0.125652	+	0.201693i
$277$	−323.707			−1.16862			−0.584309	−	0.811531i	$-0.698634\pi$
$277$	−323.707			−1.16862			−0.584309	+	0.811531i	$0.698634\pi$
$278$	−173.918	−	313.256i	−0.625605	−	1.12682i
$279$			434.249i			1.55645i
$280$	23.1842	+	1.16775i	0.0828007	+	0.00417053i
$281$	−382.434			−1.36098			−0.680488	−	0.732759i	$-0.738232\pi$
$281$	−382.434			−1.36098			−0.680488	+	0.732759i	$0.738232\pi$
$282$	−92.7811	+	51.5117i	−0.329011	+	0.182666i
$283$			440.836i			1.55773i	0.627195	+	0.778863i	$0.284203\pi$
$283$			440.836i			1.55773i	−0.627195	+	0.778863i	$0.715797\pi$
$284$	333.704	+	207.893i	1.17502	+	0.732017i
$285$	15.6844			0.0550329
$286$		0			0
$287$			214.044i			0.745797i
$288$	−205.105	−	142.582i	−0.712170	−	0.495078i
$289$	−228.592			−0.790974
$290$	18.2854	−	10.1520i	0.0630531	−	0.0350068i
$291$		−	117.241i		−	0.402889i
$292$	−158.258	+	254.032i	−0.541981	+	0.869973i
$293$	522.768			1.78419			0.892096	−	0.451847i	$-0.149235\pi$
$293$	522.768			1.78419			0.892096	+	0.451847i	$0.149235\pi$
$294$	−36.0216	−	64.8808i	−0.122522	−	0.220683i
$295$		−	60.0236i		−	0.203470i
$296$	14.7603	−	293.048i	0.0498659	−	0.990026i
$297$		0			0
$298$	207.156	−	115.012i	0.695155	−	0.385947i
$299$			51.6528i			0.172752i
$300$	90.6641	+	56.4824i	0.302214	+	0.188275i
$301$	−166.941			−0.554621
$302$	140.992	+	253.951i	0.466862	+	0.840897i
$303$		−	79.1502i		−	0.261222i
$304$	−275.539	+	135.315i	−0.906377	+	0.445117i
$305$	−58.1607			−0.190691
$306$	106.089	−	58.9000i	0.346695	−	0.192484i
$307$		−	528.080i		−	1.72013i	−0.510183	−	0.860066i	$-0.670422\pi$
$307$		−	528.080i		−	1.72013i	0.510183	−	0.860066i	$-0.329578\pi$
$308$		0			0
$309$	−22.9091			−0.0741394
$310$	−40.4057	−	72.7774i	−0.130341	−	0.234766i
$311$		−	318.851i		−	1.02524i	−0.858615	−	0.512621i	$-0.828674\pi$
$311$		−	318.851i		−	1.02524i	0.858615	−	0.512621i	$-0.171326\pi$
$312$	30.0501	+	1.51358i	0.0963145	+	0.00485120i
$313$	−322.385			−1.02998			−0.514991	−	0.857195i	$-0.672205\pi$
$313$	−322.385			−1.02998			−0.514991	+	0.857195i	$0.672205\pi$
$314$	155.211	−	86.1726i	0.494303	−	0.274435i
$315$			22.6510i			0.0719078i
$316$	−256.826	−	159.999i	−0.812740	−	0.506325i
$317$	−362.536			−1.14365			−0.571823	−	0.820377i	$-0.693764\pi$
$317$	−362.536			−1.14365			−0.571823	+	0.820377i	$0.693764\pi$
$318$	−98.0404	−	176.587i	−0.308303	−	0.555305i
$319$		0			0
$320$	47.6412	+	4.81143i	0.148879	+	0.0150357i
$321$	−28.6869			−0.0893674
$322$	−101.765	+	56.4997i	−0.316042	+	0.175465i
$323$		−	149.117i		−	0.461663i
$324$	106.156	−	170.399i	0.327643	−	0.525924i
$325$	84.1259			0.258849
$326$	22.0633	+	39.7397i	0.0676788	+	0.121901i
$327$		−	86.7094i		−	0.265166i
$328$	−22.2103	+	440.958i	−0.0677143	+	1.34438i
$329$	−188.338			−0.572455
$330$		0			0
$331$		−	88.0333i		−	0.265962i	−0.991119	−	0.132981i	$-0.957545\pi$
$331$		−	88.0333i		−	0.265962i	0.991119	−	0.132981i	$-0.0424549\pi$
$332$	224.221	+	139.686i	0.675364	+	0.420742i
$333$	286.308			0.859783
$334$	290.649	+	523.508i	0.870208	+	1.56739i
$335$		−	43.1981i		−	0.128950i
$336$	29.8880	+	60.8599i	0.0889523	+	0.181131i
$337$	11.5855			0.0343783			0.0171892	−	0.999852i	$-0.494528\pi$
$337$	11.5855			0.0343783			0.0171892	+	0.999852i	$0.494528\pi$
$338$	−274.793	+	152.564i	−0.812997	+	0.451372i
$339$			24.8559i			0.0733212i
$340$	−12.2993	+	19.7425i	−0.0361745	+	0.0580663i
$341$		0			0
$342$	−145.394	−	261.878i	−0.425128	−	0.765726i
$343$		−	321.741i		−	0.938021i
$344$	−343.919	−	17.3227i	−0.999766	−	0.0503565i
$345$	12.2675			0.0355581
$346$	82.2911	−	45.6877i	0.237836	−	0.132045i
$347$		−	26.4687i		−	0.0762787i	−0.999272	−	0.0381393i	$-0.987857\pi$
$347$		−	26.4687i		−	0.0762787i	0.999272	−	0.0381393i	$-0.0121431\pi$
$348$	51.8492	+	32.3013i	0.148992	+	0.0928198i
$349$	289.758			0.830252			0.415126	−	0.909764i	$-0.363737\pi$
$349$	289.758			0.830252			0.415126	+	0.909764i	$0.363737\pi$
$350$	92.0201	+	165.744i	0.262915	+	0.473553i
$351$			63.2083i			0.180081i
$352$		0			0
$353$	217.033			0.614825			0.307413	−	0.951576i	$-0.400537\pi$
$353$	217.033			0.614825			0.307413	+	0.951576i	$0.400537\pi$
$354$	153.279	−	85.1000i	0.432992	−	0.240395i
$355$		−	73.5395i		−	0.207153i
$356$	98.8629	−	158.692i	0.277705	−	0.445764i
$357$	−32.9364			−0.0922589
$358$	88.5888	+	159.563i	0.247455	+	0.445707i
$359$			234.346i			0.652774i	0.945236	+	0.326387i	$0.105831\pi$
$359$			234.346i			0.652774i	−0.945236	+	0.326387i	$0.894169\pi$
$360$	−2.35038	+	46.6639i	−0.00652884	+	0.129622i
$361$	−7.09295			−0.0196481
$362$	−34.9866	+	19.4244i	−0.0966480	+	0.0536586i
$363$		0			0
$364$	45.3229	+	28.2355i	0.124514	+	0.0775701i
$365$	55.9819			0.153375
$366$	−82.4588	−	148.522i	−0.225297	−	0.405798i
$367$		−	283.781i		−	0.773245i	−0.922238	−	0.386623i	$-0.873642\pi$
$367$		−	283.781i		−	0.773245i	0.922238	−	0.386623i	$-0.126358\pi$
$368$	−215.513	+	105.837i	−0.585632	+	0.287601i
$369$	−430.816			−1.16752
$370$	−47.9834	+	26.6402i	−0.129685	+	0.0720004i
$371$		−	358.457i		−	0.966190i
$372$	128.562	−	206.364i	0.345596	−	0.554742i
$373$	−377.208			−1.01128			−0.505640	−	0.862744i	$-0.668744\pi$
$373$	−377.208			−1.01128			−0.505640	+	0.862744i	$0.668744\pi$
$374$		0			0
$375$		−	40.4175i		−	0.107780i
$376$	−388.000	−	19.5429i	−1.03191	−	0.0519758i
$377$	48.1101			0.127613
$378$	−124.532	+	69.1396i	−0.329450	+	0.182909i
$379$		−	404.837i		−	1.06817i	−0.845431	−	0.534085i	$-0.820656\pi$
$379$		−	404.837i		−	1.06817i	0.845431	−	0.534085i	$-0.179344\pi$
$380$	48.7341	+	30.3607i	0.128248	+	0.0798965i
$381$	97.0290			0.254669
$382$	−213.338	−	384.257i	−0.558476	−	1.00591i
$383$			180.382i			0.470971i	0.971878	+	0.235485i	$0.0756680\pi$
$383$			180.382i			0.470971i	−0.971878	+	0.235485i	$0.924332\pi$
$384$	55.2579	+	128.481i	0.143901	+	0.334585i
$385$		0			0
$386$	−157.044	+	87.1900i	−0.406849	+	0.225881i
$387$		−	336.010i		−	0.868242i
$388$	226.946	−	364.288i	0.584912	−	0.938886i
$389$	212.782			0.546996			0.273498	−	0.961873i	$-0.411819\pi$
$389$	212.782			0.546996			0.273498	+	0.961873i	$0.411819\pi$
$390$	−2.73178	−	4.92039i	−0.00700456	−	0.0126164i
$391$		−	116.632i		−	0.298291i
$392$	13.6661	−	271.324i	0.0348626	−	0.692153i
$393$	186.466			0.474468
$394$	198.198	−	110.039i	0.503040	−	0.279286i
$395$			56.5975i			0.143285i
$396$		0			0
$397$	−510.883			−1.28686			−0.643430	−	0.765505i	$-0.722489\pi$
$397$	−510.883			−1.28686			−0.643430	+	0.765505i	$0.722489\pi$
$398$	124.470	+	224.192i	0.312739	+	0.563296i
$399$			81.3030i			0.203767i
$400$	172.375	+	351.001i	0.430937	+	0.877504i
$401$	−27.4315			−0.0684076			−0.0342038	−	0.999415i	$-0.510890\pi$
$401$	−27.4315			−0.0684076			−0.0342038	+	0.999415i	$0.510890\pi$
$402$	110.313	−	61.2453i	0.274410	−	0.152351i
$403$		−	191.482i		−	0.475142i
$404$	153.213	−	245.934i	0.379240	−	0.608746i
$405$	−37.5515			−0.0927197
$406$	52.6247	+	94.7858i	0.129617	+	0.233463i
$407$		0			0
$408$	−67.8532	−	3.41765i	−0.166307	−	0.00837661i
$409$	−133.429			−0.326232			−0.163116	−	0.986607i	$-0.552154\pi$
$409$	−133.429			−0.326232			−0.163116	+	0.986607i	$0.552154\pi$
$410$	72.2020	−	40.0863i	0.176103	−	0.0977714i
$411$		−	97.4310i		−	0.237058i
$412$	−71.1825	−	44.3457i	−0.172773	−	0.107635i
$413$	311.144			0.753375
$414$	−113.720	−	204.828i	−0.274685	−	0.494754i
$415$		−	49.4122i		−	0.119066i
$416$	90.4412	+	62.8718i	0.217407	+	0.151134i
$417$	−195.747			−0.469417
$418$		0			0
$419$			302.402i			0.721723i	0.932619	+	0.360861i	$0.117517\pi$
$419$			302.402i			0.721723i	−0.932619	+	0.360861i	$0.882483\pi$
$420$	6.70595	−	10.7642i	0.0159665	−	0.0256291i
$421$	−104.074			−0.247208			−0.123604	−	0.992332i	$-0.539445\pi$
$421$	−104.074			−0.247208			−0.123604	+	0.992332i	$0.539445\pi$
$422$	−279.511	−	503.446i	−0.662348	−	1.19300i
$423$		−	379.076i		−	0.896161i
$424$	37.1953	−	738.466i	0.0877248	−	1.74167i
$425$	−189.956			−0.446956
$426$	187.794	−	104.262i	0.440831	−	0.244748i
$427$		−	301.487i		−	0.706058i
$428$	−89.1354	−	55.5300i	−0.208260	−	0.129743i
$429$		0			0
$430$	31.2648	+	56.3131i	0.0727088	+	0.130961i
$431$			335.743i			0.778986i	0.921029	+	0.389493i	$0.127350\pi$
$431$			335.743i			0.778986i	−0.921029	+	0.389493i	$0.872650\pi$
$432$	−263.726	+	129.514i	−0.610477	+	0.299802i
$433$	−639.297			−1.47644			−0.738219	−	0.674561i	$-0.764333\pi$
$433$	−639.297			−1.47644			−0.738219	+	0.674561i	$0.764333\pi$
$434$	377.255	−	209.450i	0.869252	−	0.482605i
$435$		−	11.4262i		−	0.0262670i
$436$	167.846	−	269.421i	0.384967	−	0.617939i
$437$	−287.904			−0.658819
$438$	79.3697	+	142.958i	0.181209	+	0.326388i
$439$			419.823i			0.956317i	0.878273	+	0.478159i	$0.158696\pi$
$439$			419.823i			0.956317i	−0.878273	+	0.478159i	$0.841304\pi$
$440$		0			0
$441$	265.084			0.601097
$442$	−46.7799	+	25.9720i	−0.105837	+	0.0587602i
$443$		−	250.477i		−	0.565411i	−0.959207	−	0.282705i	$-0.908768\pi$
$443$		−	250.477i		−	0.565411i	0.959207	−	0.282705i	$-0.0912319\pi$
$444$	−136.059	−	84.7630i	−0.306440	−	0.190908i
$445$	−34.9715			−0.0785876
$446$	149.348	+	269.000i	0.334861	+	0.603140i
$447$		−	129.448i		−	0.289592i
$448$	−24.9409	+	246.957i	−0.0556717	+	0.551244i
$449$	109.767			0.244469			0.122235	−	0.992501i	$-0.460994\pi$
$449$	109.767			0.244469			0.122235	+	0.992501i	$0.460994\pi$
$450$	−333.600	+	185.213i	−0.741333	+	0.411585i
$451$		0			0
$452$	−48.1141	+	77.2316i	−0.106447	+	0.170866i
$453$	158.689			0.350306
$454$	313.612	+	564.867i	0.690775	+	1.24420i
$455$		−	9.98796i		−	0.0219516i
$456$	−8.43642	+	167.495i	−0.0185009	+	0.367313i
$457$	−319.371			−0.698842			−0.349421	−	0.936966i	$-0.613622\pi$
$457$	−319.371			−0.698842			−0.349421	+	0.936966i	$0.613622\pi$
$458$	−498.578	+	276.809i	−1.08860	+	0.604385i
$459$		−	142.724i		−	0.310946i
$460$	38.1174	+	23.7466i	0.0828639	+	0.0516230i
$461$	635.144			1.37775			0.688876	−	0.724879i	$-0.258104\pi$
$461$	635.144			1.37775			0.688876	+	0.724879i	$0.258104\pi$
$462$		0			0
$463$		−	735.608i		−	1.58879i	−0.607404	−	0.794393i	$-0.707789\pi$
$463$		−	735.608i		−	1.58879i	0.607404	−	0.794393i	$-0.292211\pi$
$464$	98.5781	+	200.732i	0.212453	+	0.432611i
$465$	−45.4771			−0.0978001
$466$	341.026	−	189.336i	0.731815	−	0.406300i
$467$			293.335i			0.628127i	0.949402	+	0.314064i	$0.101691\pi$
$467$			293.335i			0.628127i	−0.949402	+	0.314064i	$0.898309\pi$
$468$	−56.8310	+	91.2236i	−0.121434	+	0.194922i
$469$	223.926			0.477454
$470$	35.2720	+	63.5308i	0.0750468	+	0.135172i
$471$		−	96.9883i		−	0.205920i
$472$	640.996	+	32.2859i	1.35804	+	0.0684023i
$473$		0			0
$474$	−144.530	+	80.2426i	−0.304916	+	0.169288i
$475$			468.904i			0.987166i
$476$	−102.339	−	63.7558i	−0.214998	−	0.133941i
$477$	721.482			1.51254
$478$	−205.158	−	369.525i	−0.429202	−	0.773064i
$479$		−	100.560i		−	0.209937i	−0.994476	−	0.104969i	$-0.966526\pi$
$479$		−	100.560i		−	0.209937i	0.994476	−	0.104969i	$-0.0334742\pi$
$480$	14.9321	−	21.4798i	0.0311085	−	0.0447496i
$481$	−126.248			−0.262469
$482$	−574.036	+	318.702i	−1.19095	+	0.661208i
$483$			63.5911i			0.131659i
$484$		0			0
$485$	−80.2792			−0.165524
$486$	−213.684	−	384.880i	−0.439678	−	0.791934i
$487$			119.645i			0.245678i	0.992427	+	0.122839i	$0.0391998\pi$
$487$			119.645i			0.245678i	−0.992427	+	0.122839i	$0.960800\pi$
$488$	31.2839	−	621.102i	0.0641063	−	1.27275i
$489$	24.8325			0.0507822
$490$	−44.4264	+	24.6653i	−0.0906661	+	0.0503374i
$491$		−	279.148i		−	0.568529i	−0.958746	−	0.284265i	$-0.908251\pi$
$491$		−	279.148i		−	0.568529i	0.958746	−	0.284265i	$-0.0917494\pi$
$492$	204.733	+	127.545i	0.416123	+	0.259239i
$493$	−108.633			−0.220350
$494$	64.1114	+	115.475i	0.129780	+	0.233756i
$495$		0			0
$496$	798.928	−	392.349i	1.61074	−	0.791026i
$497$	381.206			0.767014
$498$	126.182	−	70.0555i	0.253377	−	0.140674i
$499$			169.097i			0.338873i	0.985541	+	0.169436i	$0.0541947\pi$
$499$			169.097i			0.338873i	−0.985541	+	0.169436i	$0.945805\pi$
$500$	78.2371	−	125.584i	0.156474	−	0.251168i
$501$	327.129			0.652953
$502$	−81.4373	−	146.682i	−0.162226	−	0.292195i
$503$			621.985i			1.23655i	0.785962	+	0.618275i	$0.212168\pi$
$503$			621.985i			1.23655i	−0.785962	+	0.618275i	$0.787832\pi$
$504$	−241.891	−	12.1837i	−0.479943	−	0.0241739i
$505$	−54.1971			−0.107321
$506$		0			0
$507$			171.712i			0.338683i
$508$	301.486	+	187.821i	0.593477	+	0.369727i
$509$	316.860			0.622514			0.311257	−	0.950326i	$-0.399250\pi$
$509$	316.860			0.622514			0.311257	+	0.950326i	$0.399250\pi$
$510$	6.16835	+	11.1102i	0.0120948	+	0.0217848i
$511$			290.193i			0.567892i
$512$	−77.0071	+	506.176i	−0.150405	+	0.988625i
$513$	−352.312			−0.686769
$514$	−283.122	+	157.188i	−0.550821	+	0.305814i
$515$			15.6867i			0.0304596i
$516$	−99.4775	+	159.679i	−0.192786	+	0.309455i
$517$		0			0
$518$	−138.094	−	248.731i	−0.266591	−	0.480176i
$519$		−	51.4220i		−	0.0990790i
$520$	1.03640	−	20.5765i	0.00199308	−	0.0395701i
$521$	−350.372			−0.672499			−0.336249	−	0.941773i	$-0.609158\pi$
$521$	−350.372			−0.672499			−0.336249	+	0.941773i	$0.609158\pi$
$522$	−190.780	+	105.920i	−0.365479	+	0.202912i
$523$			675.740i			1.29205i	0.763318	+	0.646023i	$0.223569\pi$
$523$			675.740i			1.29205i	−0.763318	+	0.646023i	$0.776431\pi$
$524$	579.383	+	360.947i	1.10569	+	0.688830i
$525$	103.570			0.197276
$526$	−387.606	−	698.144i	−0.736894	−	1.32727i
$527$			432.367i			0.820431i
$528$		0			0
$529$	303.816			0.574321
$530$	−120.916	+	67.1320i	−0.228143	+	0.126664i
$531$			626.253i			1.17939i
$532$	−157.380	+	252.623i	−0.295827	+	0.474855i
$533$	189.969			0.356414
$534$	−49.5817	−	89.3049i	−0.0928497	−	0.167238i
$535$			19.6430i			0.0367160i
$536$	461.316	+	23.2357i	0.860664	+	0.0433502i
$537$	99.7077			0.185675
$538$	−111.543	+	61.9281i	−0.207329	+	0.115108i
$539$		0			0
$540$	46.6449	+	29.0591i	0.0863794	+	0.0538131i
$541$	−379.994			−0.702392			−0.351196	−	0.936302i	$-0.614225\pi$
$541$	−379.994			−0.702392			−0.351196	+	0.936302i	$0.614225\pi$
$542$	165.809	+	298.649i	0.305920	+	0.551013i
$543$			21.8624i			0.0402622i
$544$	−204.216	−	141.964i	−0.375398	−	0.260964i
$545$	−59.3732			−0.108942
$546$	25.5058	−	14.1607i	0.0467138	−	0.0259353i
$547$			234.348i			0.428424i	0.976787	+	0.214212i	$0.0687183\pi$
$547$			234.348i			0.428424i	−0.976787	+	0.214212i	$0.931282\pi$
$548$	188.600	−	302.735i	0.344160	−	0.552437i
$549$	606.817			1.10531
$550$		0			0
$551$			268.158i			0.486675i
$552$	−6.59855	+	131.006i	−0.0119539	+	0.237329i
$553$	−293.384			−0.530532
$554$	−566.029	+	314.257i	−1.02171	+	0.567250i
$555$			29.9838i			0.0540249i
$556$	−608.220	−	378.912i	−1.09392	−	0.681497i
$557$	50.6330			0.0909030			0.0454515	−	0.998967i	$-0.485527\pi$
$557$	50.6330			0.0909030			0.0454515	+	0.998967i	$0.485527\pi$
$558$	421.571	+	759.319i	0.755503	+	1.36079i
$559$			148.164i			0.265051i
$560$	41.6731	−	20.4654i	0.0744163	−	0.0365454i
$561$		0			0
$562$	−668.717	+	371.269i	−1.18989	+	0.660621i
$563$			521.866i			0.926938i	0.886113	+	0.463469i	$0.153395\pi$
$563$			521.866i			0.926938i	−0.886113	+	0.463469i	$0.846605\pi$
$564$	−112.228	+	180.145i	−0.198985	+	0.319406i
$565$	17.0198			0.0301235
$566$	427.966	+	770.838i	0.756124	+	1.36190i
$567$		−	194.655i		−	0.343307i
$568$	785.333	+	39.5559i	1.38263	+	0.0696407i
$569$	−283.284			−0.497862			−0.248931	−	0.968521i	$-0.580079\pi$
$569$	−283.284			−0.497862			−0.248931	+	0.968521i	$0.580079\pi$
$570$	27.4254	−	15.2265i	0.0481148	−	0.0267131i
$571$		−	187.846i		−	0.328977i	−0.986379	−	0.164488i	$-0.947403\pi$
$571$		−	187.846i		−	0.328977i	0.986379	−	0.164488i	$-0.0525973\pi$
$572$		0			0
$573$	−240.114			−0.419047
$574$	207.795	+	374.273i	0.362012	+	0.652044i
$575$			366.753i			0.637832i
$576$	−497.063	−	50.1998i	−0.862956	−	0.0871524i
$577$	942.839			1.63404			0.817018	−	0.576612i	$-0.195626\pi$
$577$	942.839			1.63404			0.817018	+	0.576612i	$0.195626\pi$
$578$	−399.711	+	221.918i	−0.691542	+	0.383941i
$579$			98.1334i			0.169488i
$580$	22.1179	−	35.5031i	0.0381343	−	0.0612122i
$581$	256.138			0.440857
$582$	−113.818	−	205.005i	−0.195563	−	0.352242i
$583$		0			0
$584$	−30.1119	+	597.834i	−0.0515615	+	1.02369i
$585$	20.1032			0.0343645
$586$	914.103	−	507.506i	1.55990	−	0.866051i
$587$			30.8807i			0.0526077i	0.999654	+	0.0263038i	$0.00837374\pi$
$587$			30.8807i			0.0526077i	−0.999654	+	0.0263038i	$0.991626\pi$
$588$	−125.973	−	78.4795i	−0.214240	−	0.133469i
$589$	1067.29			1.81204
$590$	−58.2712	−	104.956i	−0.0987648	−	0.177892i
$591$		−	123.850i		−	0.209560i
$592$	−258.682	−	526.747i	−0.436964	−	0.889775i
$593$	313.027			0.527870			0.263935	−	0.964540i	$-0.414980\pi$
$593$	313.027			0.527870			0.263935	+	0.964540i	$0.414980\pi$
$594$		0			0
$595$			22.5528i			0.0379039i
$596$	250.575	−	402.216i	0.420428	−	0.674860i
$597$	140.093			0.234661
$598$	50.1448	+	90.3191i	0.0838541	+	0.151035i
$599$			907.116i			1.51438i	0.653192	+	0.757192i	$0.273429\pi$
$599$			907.116i			1.51438i	−0.653192	+	0.757192i	$0.726571\pi$
$600$	213.367	+	10.7469i	0.355612	+	0.0179116i
$601$	−1035.56			−1.72306			−0.861532	−	0.507703i	$-0.830495\pi$
$601$	−1035.56			−1.72306			−0.861532	+	0.507703i	$0.830495\pi$
$602$	−291.910	+	162.067i	−0.484900	+	0.269214i
$603$			450.706i			0.747439i
$604$	493.074	+	307.178i	0.816347	+	0.508572i
$605$		0			0
$606$	−76.8394	−	138.401i	−0.126798	−	0.228384i
$607$		−	494.406i		−	0.814507i	−0.913315	−	0.407253i	$-0.866487\pi$
$607$		−	494.406i		−	0.814507i	0.913315	−	0.407253i	$-0.133513\pi$
$608$	−350.437	+	504.104i	−0.576376	+	0.829119i
$609$	59.2297			0.0972573
$610$	−101.699	+	56.4627i	−0.166719	+	0.0925618i
$611$			167.154i			0.273574i
$612$	128.324	−	205.983i	0.209680	−	0.336573i
$613$	816.052			1.33124			0.665622	−	0.746289i	$-0.268166\pi$
$613$	816.052			1.33124			0.665622	+	0.746289i	$0.268166\pi$
$614$	−512.663	−	923.392i	−0.834956	−	1.50390i
$615$		−	45.1176i		−	0.0733619i
$616$		0			0
$617$	965.796			1.56531			0.782654	−	0.622457i	$-0.213865\pi$
$617$	965.796			1.56531			0.782654	+	0.622457i	$0.213865\pi$
$618$	−40.0584	+	22.2402i	−0.0648194	+	0.0359874i
$619$			1.94486i			0.00314193i	0.999999	+	0.00157097i	$0.000500055\pi$
$619$			1.94486i			0.00314193i	−0.999999	+	0.00157097i	$0.999500\pi$
$620$	−141.305	−	88.0311i	−0.227912	−	0.141986i
$621$	−275.561			−0.443738
$622$	−309.542	−	557.536i	−0.497655	−	0.896360i
$623$		−	181.281i		−	0.290981i
$624$	54.0145	−	26.5262i	0.0865617	−	0.0425100i
$625$	583.330			0.933328
$626$	−563.716	+	312.973i	−0.900504	+	0.499956i
$627$		0			0
$628$	187.743	−	301.360i	0.298953	−	0.479872i
$629$	285.067			0.453207
$630$	21.9897	+	39.6071i	0.0349042	+	0.0628684i
$631$		−	429.095i		−	0.680023i	−0.940421	−	0.340012i	$-0.889569\pi$
$631$		−	429.095i		−	0.680023i	0.940421	−	0.340012i	$-0.110431\pi$
$632$	−604.409	−	30.4431i	−0.956343	−	0.0481694i
$633$	−314.593			−0.496987
$634$	−633.924	+	351.952i	−0.999880	+	0.555129i
$635$		−	66.4394i		−	0.104629i
$636$	−342.863	−	213.599i	−0.539093	−	0.335847i
$637$	−116.889			−0.183499
$638$		0			0
$639$			767.271i			1.20074i
$640$	87.9755	−	37.8372i	0.137462	−	0.0591206i
$641$	−281.133			−0.438586			−0.219293	−	0.975659i	$-0.570375\pi$
$641$	−281.133			−0.438586			−0.219293	+	0.975659i	$0.570375\pi$
$642$	−50.1615	+	27.8494i	−0.0781331	+	0.0433792i
$643$			625.100i			0.972162i	0.873914	+	0.486081i	$0.161574\pi$
$643$			625.100i			0.972162i	−0.873914	+	0.486081i	$0.838426\pi$
$644$	−123.095	+	197.589i	−0.191141	+	0.306815i
$645$	35.1889			0.0545564
$646$	−144.764	−	260.743i	−0.224092	−	0.403628i
$647$			7.49467i			0.0115837i	0.999983	+	0.00579186i	$0.00184362\pi$
$647$			7.49467i			0.0115837i	−0.999983	+	0.00579186i	$0.998156\pi$
$648$	20.1984	−	401.014i	0.0311704	−	0.618849i
$649$		0			0
$650$	147.101	−	81.6699i	0.226309	−	0.125646i
$651$		−	235.739i		−	0.362118i
$652$	77.1589	+	48.0689i	0.118342	+	0.0737253i
$653$	1094.24			1.67571			0.837855	−	0.545893i	$-0.183810\pi$
$653$	1094.24			1.67571			0.837855	+	0.545893i	$0.183810\pi$
$654$	−84.1779	−	151.618i	−0.128712	−	0.231832i
$655$		−	127.680i		−	0.194932i
$656$	389.247	+	792.612i	0.593365	+	1.20825i
$657$	−584.084			−0.889017
$658$	−329.324	+	182.839i	−0.500492	+	0.277871i
$659$			690.561i			1.04789i	0.851752	+	0.523946i	$0.175541\pi$
$659$			690.561i			1.04789i	−0.851752	+	0.523946i	$0.824459\pi$
$660$		0			0
$661$	−981.006			−1.48412			−0.742062	−	0.670331i	$-0.766152\pi$
$661$	−981.006			−1.48412			−0.742062	+	0.670331i	$0.766152\pi$
$662$	−85.4632	−	153.933i	−0.129098	−	0.232528i
$663$			29.2318i			0.0440902i
$664$	527.677	+	26.5782i	0.794694	+	0.0400274i
$665$	55.6712			0.0837161
$666$	500.632	−	277.949i	0.751700	−	0.417341i
$667$			209.740i			0.314452i
$668$	1016.45	+	633.233i	1.52163	+	0.947953i
$669$	168.093			0.251260
$670$	−41.9370	−	75.5355i	−0.0625925	−	0.112739i
$671$		0			0
$672$	111.345	+	77.4032i	0.165691	+	0.115183i
$673$	214.113			0.318147			0.159074	−	0.987267i	$-0.449149\pi$
$673$	214.113			0.318147			0.159074	+	0.987267i	$0.449149\pi$
$674$	20.2582	−	11.2473i	0.0300567	−	0.0166873i
$675$			448.802i			0.664891i
$676$	−332.388	+	533.541i	−0.491698	+	0.789261i
$677$	1123.63			1.65972			0.829860	−	0.557971i	$-0.188420\pi$
$677$	1123.63			1.65972			0.829860	+	0.557971i	$0.188420\pi$
$678$	24.1302	+	43.4625i	0.0355903	+	0.0641040i
$679$		−	416.142i		−	0.612876i
$680$	−2.34020	+	46.4617i	−0.00344147	+	0.0683260i
$681$	352.974			0.518317
$682$		0			0
$683$		−	87.6213i		−	0.128289i	−0.997941	−	0.0641445i	$-0.979568\pi$
$683$		−	87.6213i		−	0.128289i	0.997941	−	0.0641445i	$-0.0204318\pi$
$684$	−508.465	−	316.766i	−0.743370	−	0.463109i
$685$	−66.7147			−0.0973938
$686$	−312.348	−	562.590i	−0.455318	−	0.820103i
$687$			311.551i			0.453495i
$688$	−618.188	+	303.589i	−0.898529	+	0.441263i
$689$	−318.138			−0.461739
$690$	21.4508	−	11.9094i	0.0310881	−	0.0172600i
$691$		−	538.429i		−	0.779202i	−0.920984	−	0.389601i	$-0.872613\pi$
$691$		−	538.429i		−	0.779202i	0.920984	−	0.389601i	$-0.127387\pi$
$692$	99.5389	−	159.777i	0.143842	−	0.230892i
$693$		0			0
$694$	−25.6960	−	46.2827i	−0.0370259	−	0.0666898i
$695$			134.035i			0.192857i
$696$	122.021	+	6.14598i	0.175317	+	0.00883044i
$697$	−428.949			−0.615422
$698$	506.666	−	281.299i	0.725882	−	0.403007i
$699$		−	213.100i		−	0.304864i
$700$	321.809	+	200.483i	0.459728	+	0.286404i
$701$	−821.402			−1.17176			−0.585879	−	0.810399i	$-0.699251\pi$
$701$	−821.402			−1.17176			−0.585879	+	0.810399i	$0.699251\pi$
$702$	61.3629	+	110.525i	0.0874116	+	0.157443i
$703$		−	703.683i		−	1.00097i
$704$		0			0
$705$	39.6991			0.0563107
$706$	379.500	−	210.697i	0.537536	−	0.298438i
$707$		−	280.941i		−	0.397371i
$708$	185.406	−	297.609i	0.261873	−	0.420351i
$709$	710.138			1.00160			0.500802	−	0.865562i	$-0.333038\pi$
$709$	710.138			1.00160			0.500802	+	0.865562i	$0.333038\pi$
$710$	−71.3925	−	128.590i	−0.100553	−	0.181112i
$711$		−	590.508i		−	0.830531i
$712$	18.8107	−	373.463i	0.0264195	−	0.524526i
$713$	834.781			1.17080
$714$	−57.5920	+	31.9748i	−0.0806611	+	0.0447827i
$715$		0			0
$716$	309.809	+	193.007i	0.432695	+	0.269562i
$717$	−230.908			−0.322048
$718$	227.504	+	409.773i	0.316858	+	0.570714i
$719$			923.401i			1.28428i	0.766585	+	0.642142i	$0.221954\pi$
$719$			923.401i			1.28428i	−0.766585	+	0.642142i	$0.778046\pi$
$720$	41.1917	+	83.8774i	0.0572107	+	0.116496i
$721$	−81.3150			−0.112781
$722$	−12.4026	+	6.88587i	−0.0171781	+	0.00953722i
$723$			358.703i			0.496131i
$724$	−42.3196	+	67.9303i	−0.0584525	+	0.0938264i
$725$	341.599			0.471172
$726$		0			0
$727$		−	824.285i		−	1.13382i	−0.823781	−	0.566909i	$-0.808139\pi$
$727$		−	824.285i		−	1.13382i	0.823781	−	0.566909i	$-0.191861\pi$
$728$	106.662	+	5.37239i	0.146514	+	0.00737966i
$729$	211.210			0.289725
$730$	97.8889	−	54.3475i	0.134094	−	0.0744486i
$731$		−	334.554i		−	0.457666i
$732$	−288.372	−	179.651i	−0.393951	−	0.245426i
$733$	0.866025			0.00118148			0.000590740	−	1.00000i	$-0.499812\pi$
$733$	0.866025			0.00118148			0.000590740		1.00000i	$0.499812\pi$
$734$	−275.496	−	496.214i	−0.375335	−	0.676041i
$735$			27.7611i			0.0377702i
$736$	−274.094	+	394.285i	−0.372411	+	0.535714i
$737$		0			0
$738$	−753.317	+	418.238i	−1.02075	+	0.566718i
$739$			420.401i			0.568878i	0.958694	+	0.284439i	$0.0918074\pi$
$739$			420.401i			0.568878i	−0.958694	+	0.284439i	$0.908193\pi$
$740$	−58.0404	+	93.1650i	−0.0784330	+	0.125899i
$741$	72.1582			0.0973794
$742$	−347.991	−	626.790i	−0.468991	−	0.844731i
$743$			1385.51i			1.86476i	0.361484	+	0.932378i	$0.382270\pi$
$743$			1385.51i			1.86476i	−0.361484	+	0.932378i	$0.617730\pi$
$744$	24.4615	−	485.653i	0.0328784	−	0.652759i
$745$	−88.6377			−0.118977
$746$	−659.578	+	366.195i	−0.884153	+	0.490878i
$747$			515.540i			0.690148i
$748$		0			0
$749$	−101.823			−0.135946
$750$	−39.2375	−	70.6732i	−0.0523166	−	0.0942310i
$751$		−	1307.84i		−	1.74147i	−0.491752	−	0.870735i	$-0.663643\pi$
$751$		−	1307.84i		−	1.74147i	0.491752	−	0.870735i	$-0.336357\pi$
$752$	−697.422	+	342.500i	−0.927422	+	0.455452i
$753$	−91.6586			−0.121725
$754$	84.1245	−	46.7056i	0.111571	−	0.0619437i
$755$		−	108.660i		−	0.143921i
$756$	−150.633	+	241.792i	−0.199250	+	0.319831i
$757$	−33.5035			−0.0442583			−0.0221291	−	0.999755i	$-0.507044\pi$
$757$	−33.5035			−0.0442583			−0.0221291	+	0.999755i	$0.507044\pi$
$758$	−393.017	−	707.890i	−0.518493	−	0.933892i
$759$		0			0
$760$	114.690	+	5.77674i	0.150908	+	0.00760097i
$761$	−66.0526			−0.0867971			−0.0433986	−	0.999058i	$-0.513819\pi$
$761$	−66.0526			−0.0867971			−0.0433986	+	0.999058i	$0.513819\pi$
$762$	169.663	−	94.1962i	0.222655	−	0.123617i
$763$		−	307.772i		−	0.403371i
$764$	−746.077	−	464.795i	−0.976540	−	0.608370i
$765$	−45.3931			−0.0593374
$766$	175.116	+	315.412i	0.228610	+	0.411766i
$767$		−	276.147i		−	0.360035i
$768$	221.352	+	171.014i	0.288219	+	0.222675i
$769$	−1115.14			−1.45012			−0.725062	−	0.688684i	$-0.758189\pi$
$769$	−1115.14			−1.45012			−0.725062	+	0.688684i	$0.758189\pi$
$770$		0			0
$771$			176.917i			0.229465i
$772$	−189.959	+	304.918i	−0.246061	+	0.394971i
$773$	−170.401			−0.220441			−0.110221	−	0.993907i	$-0.535156\pi$
$773$	−170.401			−0.220441			−0.110221	+	0.993907i	$0.535156\pi$
$774$	−326.200	−	587.540i	−0.421447	−	0.759096i
$775$		−	1359.59i		−	1.75431i
$776$	43.1811	−	857.307i	0.0556458	−	1.10478i
$777$	−155.427			−0.200035
$778$	372.066	−	206.569i	0.478234	−	0.265513i
$779$			1058.85i			1.35925i
$780$	−9.55347	−	5.95167i	−0.0122480	−	0.00763035i
$781$		0			0
$782$	−113.227	−	203.940i	−0.144791	−	0.260793i
$783$			256.662i			0.327793i
$784$	−239.506	−	487.699i	−0.305493	−	0.622066i
$785$	−66.4116			−0.0846007
$786$	326.051	−	181.022i	0.414823	−	0.230308i
$787$		−	520.780i		−	0.661728i	−0.943678	−	0.330864i	$-0.892660\pi$
$787$		−	520.780i		−	0.661728i	0.943678	−	0.330864i	$-0.107340\pi$
$788$	239.739	−	384.823i	0.304238	−	0.488354i
$789$	−436.256			−0.552922
$790$	54.9452	+	98.9654i	0.0695508	+	0.125273i
$791$			88.2252i			0.111536i
$792$		0			0
$793$	−267.576			−0.337423
$794$	−893.321	+	495.968i	−1.12509	+	0.624645i
$795$			75.5578i			0.0950413i
$796$	435.293	+	271.181i	0.546850	+	0.340680i
$797$	410.499			0.515055			0.257527	−	0.966271i	$-0.417092\pi$
$797$	410.499			0.515055			0.257527	+	0.966271i	$0.417092\pi$
$798$	78.9293	+	142.165i	0.0989089	+	0.178151i
$799$		−	377.433i		−	0.472382i
$800$	642.165	+	446.412i	0.802707	+	0.558015i
$801$	364.873			0.455522
$802$	−47.9662	+	26.6306i	−0.0598082	+	0.0332052i
$803$		0			0
$804$	133.434	−	214.185i	0.165963	−	0.266399i
$805$	43.5433			0.0540910
$806$	−185.892	−	334.822i	−0.230635	−	0.415412i
$807$			69.7008i			0.0863703i
$808$	29.1519	−	578.775i	0.0360791	−	0.716306i
$809$	−1315.28			−1.62581			−0.812907	−	0.582393i	$-0.802117\pi$
$809$	−1315.28			−1.62581			−0.812907	+	0.582393i	$0.802117\pi$
$810$	−65.6618	+	36.4551i	−0.0810639	+	0.0450064i
$811$		−	1017.54i		−	1.25468i	−0.778746	−	0.627339i	$-0.784144\pi$
$811$		−	1017.54i		−	1.25468i	0.778746	−	0.627339i	$-0.215856\pi$
$812$	184.037	+	114.652i	0.226647	+	0.141198i
$813$	186.620			0.229544
$814$		0			0
$815$		−	17.0038i		−	0.0208635i
$816$	−121.965	+	59.8962i	−0.149467	+	0.0734022i
$817$	−825.840			−1.01082
$818$	−233.311	+	129.533i	−0.285221	+	0.158354i
$819$			104.209i			0.127239i
$820$	87.3352	−	140.188i	0.106506	−	0.170961i
$821$	−3.29503			−0.00401343			−0.00200672	−	0.999998i	$-0.500639\pi$
$821$	−3.29503			−0.00401343			−0.00200672	+	0.999998i	$0.500639\pi$
$822$	−94.5865	−	170.366i	−0.115069	−	0.207258i
$823$			1168.59i			1.41992i	0.704242	+	0.709960i	$0.251287\pi$
$823$			1168.59i			1.41992i	−0.704242	+	0.709960i	$0.748713\pi$
$824$	−167.519	−	8.43767i	−0.203300	−	0.0102399i
$825$		0			0
$826$	544.060	−	302.060i	0.658668	−	0.365690i
$827$		−	1071.53i		−	1.29569i	−0.761773	−	0.647844i	$-0.775671\pi$
$827$		−	1071.53i		−	1.29569i	0.761773	−	0.647844i	$-0.224329\pi$
$828$	−397.696	−	247.759i	−0.480310	−	0.299226i
$829$	239.575			0.288992			0.144496	−	0.989505i	$-0.453844\pi$
$829$	239.575			0.288992			0.144496	+	0.989505i	$0.453844\pi$
$830$	−47.9697	−	86.4013i	−0.0577948	−	0.104098i
$831$			353.700i			0.425631i
$832$	219.180	+	22.1356i	0.263438	+	0.0266053i
$833$	263.935			0.316849
$834$	−342.280	+	190.032i	−0.410407	+	0.227856i
$835$		−	223.998i		−	0.268261i
$836$		0			0
$837$	1021.53			1.22047
$838$	293.573	+	528.774i	0.350326	+	0.630995i
$839$			869.050i			1.03582i	0.855436	+	0.517908i	$0.173289\pi$
$839$			869.050i			1.03582i	−0.855436	+	0.517908i	$0.826711\pi$
$840$	1.27594	−	25.3323i	0.00151898	−	0.0301575i
$841$	−645.645			−0.767711
$842$	−181.983	+	101.036i	−0.216131	+	0.119995i
$843$			417.868i			0.495691i
$844$	−977.495	−	608.965i	−1.15817	−	0.721523i
$845$	117.578			0.139146
$846$	−368.009	−	662.845i	−0.434999	−	0.783505i
$847$		0			0
$848$	−651.868	−	1327.38i	−0.768712	−	1.56530i
$849$	481.681			0.567351
$850$	−332.154	+	184.411i	−0.390770	+	0.216954i
$851$		−	550.386i		−	0.646752i
$852$	227.155	−	364.623i	0.266614	−	0.427961i
$853$	1302.18			1.52659			0.763295	−	0.646050i	$-0.223580\pi$
$853$	1302.18			1.52659			0.763295	+	0.646050i	$0.223580\pi$
$854$	−292.685	−	527.174i	−0.342722	−	0.617300i
$855$			112.052i			0.131055i
$856$	−209.769	−	10.5657i	−0.245058	−	0.0123431i
$857$	−676.267			−0.789110			−0.394555	−	0.918872i	$-0.629101\pi$
$857$	−676.267			−0.789110			−0.394555	+	0.918872i	$0.629101\pi$
$858$		0			0
$859$		−	745.506i		−	0.867877i	−0.900943	−	0.433938i	$-0.857124\pi$
$859$		−	745.506i		−	0.867877i	0.900943	−	0.433938i	$-0.142876\pi$
$860$	109.338	+	68.1160i	0.127137	+	0.0792047i
$861$	233.875			0.271632
$862$	325.941	+	587.074i	0.378122	+	0.681060i
$863$		−	1333.64i		−	1.54536i	−0.634797	−	0.772679i	$-0.718916\pi$
$863$		−	1333.64i		−	1.54536i	0.634797	−	0.772679i	$-0.281084\pi$
$864$	−335.413	+	482.493i	−0.388210	+	0.558441i
$865$	−35.2106			−0.0407059
$866$	−1117.86	+	620.633i	−1.29084	+	0.716667i
$867$			249.771i			0.288087i
$868$	456.326	−	732.483i	0.525721	−	0.843874i
$869$		0			0
$870$	−11.0926	−	19.9796i	−0.0127501	−	0.0229650i
$871$		−	198.739i		−	0.228173i
$872$	31.9361	−	634.051i	0.0366239	−	0.727122i
$873$	837.589			0.959438
$874$	−503.424	+	279.499i	−0.576000	+	0.319792i
$875$		−	143.461i		−	0.163955i
$876$	277.569	+	172.921i	0.316860	+	0.197399i
$877$	397.205			0.452913			0.226456	−	0.974021i	$-0.427286\pi$
$877$	397.205			0.452913			0.226456	+	0.974021i	$0.427286\pi$
$878$	407.567	+	734.095i	0.464199	+	0.836100i
$879$		−	571.204i		−	0.649834i
$880$		0			0
$881$	473.383			0.537325			0.268662	−	0.963234i	$-0.413418\pi$
$881$	473.383			0.537325			0.268662	+	0.963234i	$0.413418\pi$
$882$	463.521	−	257.345i	0.525534	−	0.291774i
$883$		−	1372.93i		−	1.55485i	−0.628976	−	0.777425i	$-0.716525\pi$
$883$		−	1372.93i		−	1.55485i	0.628976	−	0.777425i	$-0.283475\pi$
$884$	−56.5847	+	90.8283i	−0.0640099	+	0.102747i
$885$	−65.5849			−0.0741073
$886$	−243.164	−	437.979i	−0.274452	−	0.494333i
$887$			280.674i			0.316431i	0.987405	+	0.158215i	$0.0505740\pi$
$887$			280.674i			0.316431i	−0.987405	+	0.158215i	$0.949426\pi$
$888$	−320.199	−	16.1279i	−0.360585	−	0.0181621i
$889$	344.401			0.387403
$890$	−61.1505	+	33.9505i	−0.0687084	+	0.0381466i
$891$		0			0
$892$	522.294	+	325.381i	0.585531	+	0.364777i
$893$	−931.688			−1.04332
$894$	−125.668	−	226.350i	−0.140569	−	0.253187i
$895$		−	68.2736i		−	0.0762834i
$896$	196.136	+	456.038i	0.218902	+	0.508971i
$897$	56.4385			0.0629192
$898$	191.936	−	106.562i	0.213737	−	0.118666i
$899$		−	777.527i		−	0.864880i
$900$	−403.521	+	647.721i	−0.448356	+	0.719690i
$901$	718.356			0.797287
$902$		0			0
$903$			182.408i			0.202003i
$904$	−9.15471	+	181.755i	−0.0101269	+	0.201057i
$905$	14.9700			0.0165415
$906$	277.480	−	154.056i	0.306269	−	0.170039i
$907$			487.212i			0.537168i	0.963256	+	0.268584i	$0.0865557\pi$
$907$			487.212i			0.537168i	−0.963256	+	0.268584i	$0.913444\pi$
$908$	1096.75	+	683.260i	1.20788	+	0.752489i
$909$	565.464			0.622072
$910$	−9.69636	−	17.4648i	−0.0106553	−	0.0191920i
$911$		−	1067.99i		−	1.17233i	−0.810193	−	0.586163i	$-0.800638\pi$
$911$		−	1067.99i		−	1.17233i	0.810193	−	0.586163i	$-0.199362\pi$
$912$	147.853	+	301.068i	0.162119	+	0.330118i
$913$		0			0
$914$	−558.446	+	310.047i	−0.610991	+	0.339219i
$915$			63.5494i			0.0694529i
$916$	−603.078	+	968.045i	−0.658382	+	1.05682i
$917$	661.856			0.721762
$918$	−138.557	−	249.565i	−0.150934	−	0.271857i
$919$		−	290.602i		−	0.316215i	−0.987422	−	0.158108i	$-0.949461\pi$
$919$		−	290.602i		−	0.316215i	0.987422	−	0.158108i	$-0.0505393\pi$
$920$	89.7047	+	4.51828i	0.0975051	+	0.00491117i
$921$	−577.008			−0.626502
$922$	1110.60	−	616.601i	1.20456	−	0.668765i
$923$		−	338.328i		−	0.366553i
$924$		0			0
$925$	−896.403			−0.969085
$926$	−714.132	−	1286.27i	−0.771201	−	1.38906i
$927$		−	163.667i		−	0.176555i
$928$	367.243	+	255.295i	0.395736	+	0.275103i
$929$	−171.850			−0.184984			−0.0924918	−	0.995713i	$-0.529483\pi$
$929$	−171.850			−0.184984			−0.0924918	+	0.995713i	$0.529483\pi$
$930$	−79.5204	+	44.1494i	−0.0855058	+	0.0474724i
$931$		−	651.519i		−	0.699806i
$932$	412.503	−	662.139i	0.442600	−	0.710449i
$933$	−348.393			−0.373411
$934$	284.772	+	512.921i	0.304895	+	0.549166i
$935$		0			0
$936$	−10.8133	+	214.684i	−0.0115526	+	0.229363i
$937$	−858.691			−0.916426			−0.458213	−	0.888843i	$-0.651510\pi$
$937$	−858.691			−0.916426			−0.458213	+	0.888843i	$0.651510\pi$
$938$	391.552	−	217.388i	0.417433	−	0.231757i
$939$			352.254i			0.375138i
$940$	123.352	+	76.8465i	0.131226	+	0.0817516i
$941$	−933.772			−0.992318			−0.496159	−	0.868232i	$-0.665257\pi$
$941$	−933.772			−0.992318			−0.496159	+	0.868232i	$0.665257\pi$
$942$	−94.1567	−	169.592i	−0.0999540	−	0.180034i
$943$			828.182i			0.878242i
$944$	1152.18	−	565.827i	1.22053	−	0.599394i
$945$	53.2846			0.0563858
$946$		0			0
$947$			588.592i			0.621533i	0.950486	+	0.310767i	$0.100586\pi$
$947$			588.592i			0.621533i	−0.950486	+	0.310767i	$0.899414\pi$
$948$	−174.823	+	280.621i	−0.184413	+	0.296014i
$949$	257.552			0.271393
$950$	455.214	+	819.917i	0.479173	+	0.863070i
$951$			396.126i			0.416536i
$952$	−240.843	−	12.1309i	−0.252986	−	0.0127425i
$953$	14.8762			0.0156099			0.00780495	−	0.999970i	$-0.497516\pi$
$953$	14.8762			0.0156099			0.00780495	+	0.999970i	$0.497516\pi$
$954$	1261.57	−	700.419i	1.32240	−	0.734191i
$955$			164.415i			0.172163i
$956$	−717.473	−	446.975i	−0.750494	−	0.467547i
$957$		0			0
$958$	−97.6240	−	175.837i	−0.101904	−	0.183546i
$959$		−	345.829i		−	0.360614i
$960$	5.25722	−	52.0553i	0.00547627	−	0.0542243i
$961$	−2133.62			−2.22021
$962$	−220.754	+	122.562i	−0.229474	+	0.127403i
$963$		−	204.945i		−	0.212819i
$964$	−694.350	+	1114.55i	−0.720280	+	1.15618i
$965$	67.1957			0.0696328
$966$	61.7346	+	111.194i	0.0639074	+	0.115108i
$967$		−	974.002i		−	1.00724i	−0.863925	−	0.503621i	$-0.832001\pi$
$967$		−	974.002i		−	1.00724i	0.863925	−	0.503621i	$-0.167999\pi$
$968$		0			0
$969$	−162.933			−0.168146
$970$	−140.375	+	77.9355i	−0.144716	+	0.0803458i
$971$			429.666i			0.442499i	0.975217	+	0.221249i	$0.0710135\pi$
$971$			429.666i			0.442499i	−0.975217	+	0.221249i	$0.928987\pi$
$972$	−747.287	−	465.549i	−0.768813	−	0.478960i
$973$	−694.798			−0.714078
$974$	116.152	+	209.209i	0.119253	+	0.214794i
$975$		−	91.9204i		−	0.0942773i
$976$	−548.266	−	1116.42i	−0.561748	−	1.14387i
$977$	−319.706			−0.327232			−0.163616	−	0.986524i	$-0.552316\pi$
$977$	−319.706			−0.327232			−0.163616	+	0.986524i	$0.552316\pi$
$978$	43.4217	−	24.1075i	0.0443984	−	0.0246498i
$979$		0			0
$980$	−53.7379	+	86.2587i	−0.0548346	+	0.0880191i
$981$	619.468			0.631466
$982$	−270.998	−	488.113i	−0.275966	−	0.497060i
$983$			296.460i			0.301587i	0.988565	+	0.150793i	$0.0481829\pi$
$983$			296.460i			0.301587i	−0.988565	+	0.150793i	$0.951817\pi$
$984$	481.813	+	24.2681i	0.489648	+	0.0246627i
$985$	−84.8047			−0.0860961
$986$	−189.953	+	105.461i	−0.192650	+	0.106959i
$987$			205.788i			0.208498i
$988$	224.208	+	139.678i	0.226931	+	0.141375i
$989$	−645.931			−0.653115
$990$		0			0
$991$			418.812i			0.422616i	0.977420	+	0.211308i	$0.0677723\pi$
$991$			418.812i			0.422616i	−0.977420	+	0.211308i	$0.932228\pi$
$992$	1016.10	−	1461.66i	1.02429	−	1.47344i
$993$	−96.1898			−0.0968679
$994$	666.569	−	370.076i	0.670593	−	0.372310i
$995$		−	95.9269i		−	0.0964089i
$996$	152.629	−	244.995i	0.153242	−	0.245979i
$997$	1536.75			1.54138			0.770689	−	0.637212i	$-0.219912\pi$
$997$	1536.75			1.54138			0.770689	+	0.637212i	$0.219912\pi$
$998$	164.161	+	295.681i	0.164490	+	0.296273i
$999$		−	673.516i		−	0.674190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.3.b.k.243.17		20
4.3	odd	2	inner	484.3.b.k.243.18		20
11.2	odd	10		44.3.h.a.15.10	yes	40
11.6	odd	10		44.3.h.a.3.7	✓	40
11.10	odd	2		484.3.b.j.243.4		20
33.2	even	10		396.3.s.a.235.1		40
33.17	even	10		396.3.s.a.91.4		40
44.35	even	10		44.3.h.a.15.7	yes	40
44.39	even	10		44.3.h.a.3.10	yes	40
44.43	even	2		484.3.b.j.243.3		20
132.35	odd	10		396.3.s.a.235.4		40
132.83	odd	10		396.3.s.a.91.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.h.a.3.7	✓	40	11.6	odd	10
44.3.h.a.3.10	yes	40	44.39	even	10
44.3.h.a.15.7	yes	40	44.35	even	10
44.3.h.a.15.10	yes	40	11.2	odd	10
396.3.s.a.91.1		40	132.83	odd	10
396.3.s.a.91.4		40	33.17	even	10
396.3.s.a.235.1		40	33.2	even	10
396.3.s.a.235.4		40	132.35	odd	10
484.3.b.j.243.3		20	44.43	even	2
484.3.b.j.243.4		20	11.10	odd	2
484.3.b.k.243.17		20	1.1	even	1	trivial
484.3.b.k.243.18		20	4.3	odd	2	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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	484.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74858 - 0.970805i) q^{2} -1.09265i q^{3} +(2.11508 - 3.39506i) q^{4} -0.748181 q^{5} +(-1.06075 - 1.91059i) q^{6} -3.87834i q^{7} +(0.402437 - 7.98987i) q^{8} +7.80611 q^{9} +O(q^{10})\)	\(q+(1.74858 - 0.970805i) q^{2} -1.09265i q^{3} +(2.11508 - 3.39506i) q^{4} -0.748181 q^{5} +(-1.06075 - 1.91059i) q^{6} -3.87834i q^{7} +(0.402437 - 7.98987i) q^{8} +7.80611 q^{9} +(-1.30826 + 0.726338i) q^{10} +(-3.70962 - 2.31104i) q^{12} -3.44211 q^{13} +(-3.76511 - 6.78159i) q^{14} +0.817502i q^{15} +(-7.05291 - 14.3616i) q^{16} +7.77228 q^{17} +(13.6496 - 7.57821i) q^{18} -19.1857i q^{19} +(-1.58246 + 2.54012i) q^{20} -4.23767 q^{21} -15.0061i q^{23} +(-8.73015 - 0.439723i) q^{24} -24.4402 q^{25} +(-6.01881 + 3.34162i) q^{26} -18.3632i q^{27} +(-13.1672 - 8.20297i) q^{28} -13.9769 q^{29} +(0.793635 + 1.42947i) q^{30} +55.6293i q^{31} +(-26.2749 - 18.2655i) q^{32} +(13.5905 - 7.54537i) q^{34} +2.90170i q^{35} +(16.5105 - 26.5022i) q^{36} +36.6774 q^{37} +(-18.6256 - 33.5478i) q^{38} +3.76103i q^{39} +(-0.301095 + 5.97787i) q^{40} -55.1896 q^{41} +(-7.40992 + 4.11396i) q^{42} -43.0444i q^{43} -5.84038 q^{45} +(-14.5680 - 26.2395i) q^{46} -48.5615i q^{47} +(-15.6923 + 7.70638i) q^{48} +33.9585 q^{49} +(-42.7357 + 23.7267i) q^{50} -8.49241i q^{51} +(-7.28032 + 11.6862i) q^{52} +92.4253 q^{53} +(-17.8271 - 32.1096i) q^{54} +(-30.9874 - 1.56078i) q^{56} -20.9634 q^{57} +(-24.4398 + 13.5689i) q^{58} +80.2261i q^{59} +(2.77547 + 1.72908i) q^{60} +77.7361 q^{61} +(54.0052 + 97.2724i) q^{62} -30.2747i q^{63} +(-63.6761 - 6.43083i) q^{64} +2.57532 q^{65} +57.7376i q^{67} +(16.4390 - 26.3874i) q^{68} -16.3965 q^{69} +(2.81698 + 5.07385i) q^{70} +98.2910i q^{71} +(3.14146 - 62.3698i) q^{72} -74.8240 q^{73} +(64.1334 - 35.6066i) q^{74} +26.7047i q^{75} +(-65.1368 - 40.5793i) q^{76} +(3.65123 + 6.57647i) q^{78} -75.6468i q^{79} +(5.27685 + 10.7451i) q^{80} +50.1904 q^{81} +(-96.5035 + 53.5783i) q^{82} +66.0432i q^{83} +(-8.96300 + 14.3872i) q^{84} -5.81507 q^{85} +(-41.7877 - 75.2667i) q^{86} +15.2719i q^{87} +46.7420 q^{89} +(-10.2124 + 5.66987i) q^{90} +13.3497i q^{91} +(-50.9468 - 31.7391i) q^{92} +60.7835 q^{93} +(-47.1437 - 84.9137i) q^{94} +14.3544i q^{95} +(-19.9578 + 28.7094i) q^{96} +107.299 q^{97} +(59.3792 - 32.9671i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{4} + 2 q^{5} + 3 q^{6} - 6 q^{8} - 30 q^{9}+O(q^{10}) \) 20 * q - 2 * q^4 + 2 * q^5 + 3 * q^6 - 6 * q^8 - 30 * q^9	\( 20 q - 2 q^{4} + 2 q^{5} + 3 q^{6} - 6 q^{8} - 30 q^{9} + 4 q^{10} - 25 q^{12} - 2 q^{13} + 12 q^{14} + 50 q^{16} + 10 q^{17} + 9 q^{18} - 18 q^{20} + 26 q^{21} - 27 q^{24} + 30 q^{25} - 72 q^{26} - 60 q^{28} + 14 q^{29} + 188 q^{30} - 10 q^{32} + 129 q^{34} - 23 q^{36} + 50 q^{37} - 95 q^{38} - 226 q^{40} + 50 q^{41} + 40 q^{42} + 72 q^{45} + 210 q^{46} + 163 q^{48} + 46 q^{49} + 176 q^{50} - 418 q^{52} - 230 q^{53} + 270 q^{54} - 428 q^{56} - 146 q^{57} - 28 q^{58} + 238 q^{60} - 26 q^{61} + 322 q^{62} + 34 q^{64} - 82 q^{65} - 297 q^{68} + 208 q^{69} - 322 q^{70} - 425 q^{72} + 42 q^{73} + 566 q^{74} - 183 q^{76} + 706 q^{78} - 90 q^{80} - 300 q^{81} - 185 q^{82} - 790 q^{84} + 142 q^{85} + 17 q^{86} - 44 q^{89} + 520 q^{90} + 474 q^{92} - 384 q^{93} + 524 q^{94} - 1067 q^{96} + 150 q^{97} + 326 q^{98}+O(q^{100}) \) 20 * q - 2 * q^4 + 2 * q^5 + 3 * q^6 - 6 * q^8 - 30 * q^9 + 4 * q^10 - 25 * q^12 - 2 * q^13 + 12 * q^14 + 50 * q^16 + 10 * q^17 + 9 * q^18 - 18 * q^20 + 26 * q^21 - 27 * q^24 + 30 * q^25 - 72 * q^26 - 60 * q^28 + 14 * q^29 + 188 * q^30 - 10 * q^32 + 129 * q^34 - 23 * q^36 + 50 * q^37 - 95 * q^38 - 226 * q^40 + 50 * q^41 + 40 * q^42 + 72 * q^45 + 210 * q^46 + 163 * q^48 + 46 * q^49 + 176 * q^50 - 418 * q^52 - 230 * q^53 + 270 * q^54 - 428 * q^56 - 146 * q^57 - 28 * q^58 + 238 * q^60 - 26 * q^61 + 322 * q^62 + 34 * q^64 - 82 * q^65 - 297 * q^68 + 208 * q^69 - 322 * q^70 - 425 * q^72 + 42 * q^73 + 566 * q^74 - 183 * q^76 + 706 * q^78 - 90 * q^80 - 300 * q^81 - 185 * q^82 - 790 * q^84 + 142 * q^85 + 17 * q^86 - 44 * q^89 + 520 * q^90 + 474 * q^92 - 384 * q^93 + 524 * q^94 - 1067 * q^96 + 150 * q^97 + 326 * q^98

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