LMFDB - Embedded newform 333.3.bb.b.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(82,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("333.82");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.bb (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 111)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			199.6
Character	$\chi$	$=$	333.199
Dual form			333.3.bb.b.82.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.81682 - 1.02271i) q^{2} +(10.0581 - 5.80704i) q^{4} +(-3.12011 - 0.836031i) q^{5} +(-4.42663 - 7.66714i) q^{7} +(21.2746 - 21.2746i) q^{8} +O(q^{10})$	\(q+(3.81682 - 1.02271i) q^{2} +(10.0581 - 5.80704i) q^{4} +(-3.12011 - 0.836031i) q^{5} +(-4.42663 - 7.66714i) q^{7} +(21.2746 - 21.2746i) q^{8} -12.7639 q^{10} +5.77622i q^{11} +(-1.44834 - 0.388081i) q^{13} +(-24.7369 - 24.7369i) q^{14} +(36.2154 - 62.7268i) q^{16} +(5.29921 + 19.7769i) q^{17} +(26.3729 + 7.06661i) q^{19} +(-36.2373 + 9.70974i) q^{20} +(5.90742 + 22.0468i) q^{22} +(-11.1157 + 11.1157i) q^{23} +(-12.6145 - 7.28298i) q^{25} -5.92494 q^{26} +(-89.0469 - 51.4112i) q^{28} +(21.3977 + 21.3977i) q^{29} +(26.1105 + 26.1105i) q^{31} +(42.9278 - 160.209i) q^{32} +(40.4523 + 70.0654i) q^{34} +(7.40160 + 27.6231i) q^{35} +(24.0158 - 28.1468i) q^{37} +107.888 q^{38} +(-84.1654 + 48.5929i) q^{40} +(-20.6541 + 11.9246i) q^{41} +(-22.8207 + 22.8207i) q^{43} +(33.5428 + 58.0978i) q^{44} +(-31.0584 + 53.7947i) q^{46} -59.8153 q^{47} +(-14.6900 + 25.4439i) q^{49} +(-55.5957 - 14.8968i) q^{50} +(-16.8211 + 4.50720i) q^{52} +(29.7974 - 51.6106i) q^{53} +(4.82910 - 18.0224i) q^{55} +(-257.290 - 68.9406i) q^{56} +(103.555 + 59.7874i) q^{58} +(3.02150 + 11.2764i) q^{59} +(-21.6834 + 80.9237i) q^{61} +(126.363 + 72.9554i) q^{62} -365.669i q^{64} +(4.19453 + 2.42171i) q^{65} +(-65.6658 + 37.9122i) q^{67} +(168.145 + 168.145i) q^{68} +(56.5012 + 97.8629i) q^{70} +(-24.9235 - 43.1687i) q^{71} -38.1995i q^{73} +(62.8779 - 131.993i) q^{74} +(306.298 - 82.0722i) q^{76} +(44.2871 - 25.5692i) q^{77} +(-53.2289 - 14.2626i) q^{79} +(-165.438 + 165.438i) q^{80} +(-66.6375 + 66.6375i) q^{82} +(36.7004 - 63.5669i) q^{83} -66.1365i q^{85} +(-63.7634 + 110.441i) q^{86} +(122.887 + 122.887i) q^{88} +(-51.9117 + 13.9097i) q^{89} +(3.43578 + 12.8225i) q^{91} +(-47.2533 + 176.352i) q^{92} +(-228.305 + 61.1740i) q^{94} +(-76.3786 - 44.0972i) q^{95} +(-49.5738 + 49.5738i) q^{97} +(-30.0474 + 112.139i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	$ 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} - 60 q^{10} + 28 q^{13} - 42 q^{14} + 26 q^{16} - 10 q^{17} + 60 q^{19} + 4 q^{20} - 64 q^{22} - 34 q^{23} - 162 q^{25} + 44 q^{26} - 48 q^{28} - 32 q^{29} + 90 q^{32} + 46 q^{34} + 30 q^{35} + 80 q^{37} + 284 q^{38} - 144 q^{40} + 30 q^{41} + 130 q^{43} + 16 q^{44} + 78 q^{46} + 56 q^{47} - 20 q^{49} - 70 q^{50} + 16 q^{52} + 190 q^{53} + 350 q^{55} - 376 q^{56} + 336 q^{58} + 258 q^{59} - 84 q^{61} + 474 q^{62} + 54 q^{65} - 372 q^{67} + 434 q^{68} + 102 q^{70} - 66 q^{71} + 416 q^{74} + 702 q^{76} - 198 q^{77} + 88 q^{79} - 900 q^{80} - 470 q^{82} - 166 q^{83} - 432 q^{86} + 530 q^{88} - 304 q^{89} + 524 q^{91} - 330 q^{92} - 344 q^{94} - 1080 q^{95} - 110 q^{97} - 926 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 - 60 * q^10 + 28 * q^13 - 42 * q^14 + 26 * q^16 - 10 * q^17 + 60 * q^19 + 4 * q^20 - 64 * q^22 - 34 * q^23 - 162 * q^25 + 44 * q^26 - 48 * q^28 - 32 * q^29 + 90 * q^32 + 46 * q^34 + 30 * q^35 + 80 * q^37 + 284 * q^38 - 144 * q^40 + 30 * q^41 + 130 * q^43 + 16 * q^44 + 78 * q^46 + 56 * q^47 - 20 * q^49 - 70 * q^50 + 16 * q^52 + 190 * q^53 + 350 * q^55 - 376 * q^56 + 336 * q^58 + 258 * q^59 - 84 * q^61 + 474 * q^62 + 54 * q^65 - 372 * q^67 + 434 * q^68 + 102 * q^70 - 66 * q^71 + 416 * q^74 + 702 * q^76 - 198 * q^77 + 88 * q^79 - 900 * q^80 - 470 * q^82 - 166 * q^83 - 432 * q^86 + 530 * q^88 - 304 * q^89 + 524 * q^91 - 330 * q^92 - 344 * q^94 - 1080 * q^95 - 110 * q^97 - 926 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	3.81682	−	1.02271i	1.90841	−	0.511357i	0.914010	−	0.405691i	$-0.132969\pi$
$2$	3.81682	−	1.02271i	1.90841	−	0.511357i	0.994402	−	0.105666i	$-0.0336976\pi$
$3$		0			0
$3$		0			0
$4$	10.0581	−	5.80704i	2.51452	−	1.45176i
$5$	−3.12011	−	0.836031i	−0.624022	−	0.167206i	−0.0670667	−	0.997748i	$-0.521364\pi$
$5$	−3.12011	−	0.836031i	−0.624022	−	0.167206i	−0.556956	+	0.830542i	$0.688031\pi$
$6$		0			0
$7$	−4.42663	−	7.66714i	−0.632375	−	1.09531i	−0.987065	−	0.160322i	$-0.948747\pi$
$7$	−4.42663	−	7.66714i	−0.632375	−	1.09531i	0.354690	−	0.934984i	$-0.384587\pi$
$8$	21.2746	−	21.2746i	2.65932	−	2.65932i
$9$		0			0
$10$	−12.7639			−1.27639
$11$			5.77622i			0.525111i	0.964917	+	0.262555i	$0.0845652\pi$
$11$			5.77622i			0.525111i	−0.964917	+	0.262555i	$0.915435\pi$
$12$		0			0
$13$	−1.44834	−	0.388081i	−0.111411	−	0.0298524i	0.202683	−	0.979244i	$-0.435034\pi$
$13$	−1.44834	−	0.388081i	−0.111411	−	0.0298524i	−0.314094	+	0.949392i	$0.601701\pi$
$14$	−24.7369	−	24.7369i	−1.76692	−	1.76692i
$15$		0			0
$16$	36.2154	−	62.7268i	2.26346	−	3.92043i
$17$	5.29921	+	19.7769i	0.311718	+	1.16335i	0.927006	+	0.375045i	$0.122373\pi$
$17$	5.29921	+	19.7769i	0.311718	+	1.16335i	−0.615288	+	0.788302i	$0.710960\pi$
$18$		0			0
$19$	26.3729	+	7.06661i	1.38805	+	0.371927i	0.874038	−	0.485857i	$-0.161492\pi$
$19$	26.3729	+	7.06661i	1.38805	+	0.371927i	0.514011	+	0.857784i	$0.328159\pi$
$20$	−36.2373	+	9.70974i	−1.81186	+	0.485487i
$21$		0			0
$22$	5.90742	+	22.0468i	0.268519	+	1.00213i
$23$	−11.1157	+	11.1157i	−0.483290	+	0.483290i	−0.906181	−	0.422891i	$-0.861015\pi$
$23$	−11.1157	+	11.1157i	−0.483290	+	0.483290i	0.422891	+	0.906181i	$0.361015\pi$
$24$		0			0
$25$	−12.6145	−	7.28298i	−0.504579	−	0.291319i
$26$	−5.92494			−0.227882
$27$		0			0
$28$	−89.0469	−	51.4112i	−3.18024	−	1.83612i
$29$	21.3977	+	21.3977i	0.737851	+	0.737851i	0.972162	−	0.234311i	$-0.0752833\pi$
$29$	21.3977	+	21.3977i	0.737851	+	0.737851i	−0.234311	+	0.972162i	$0.575283\pi$
$30$		0			0
$31$	26.1105	+	26.1105i	0.842273	+	0.842273i	0.989154	−	0.146881i	$-0.0469236\pi$
$31$	26.1105	+	26.1105i	0.842273	+	0.842273i	−0.146881	+	0.989154i	$0.546924\pi$
$32$	42.9278	−	160.209i	1.34149	−	5.00652i
$33$		0			0
$34$	40.4523	+	70.0654i	1.18977	+	2.06075i
$35$	7.40160	+	27.6231i	0.211474	+	0.789232i
$36$		0			0
$37$	24.0158	−	28.1468i	0.649076	−	0.760724i
$37$	24.0158	−	28.1468i	0.649076	−	0.760724i
$38$	107.888			2.83916
$39$		0			0
$40$	−84.1654	+	48.5929i	−2.10413	+	1.21482i
$41$	−20.6541	+	11.9246i	−0.503758	+	0.290845i	−0.730264	−	0.683165i	$-0.760603\pi$
$41$	−20.6541	+	11.9246i	−0.503758	+	0.290845i	0.226506	+	0.974010i	$0.427270\pi$
$42$		0			0
$43$	−22.8207	+	22.8207i	−0.530713	+	0.530713i	−0.920785	−	0.390072i	$-0.872450\pi$
$43$	−22.8207	+	22.8207i	−0.530713	+	0.530713i	0.390072	+	0.920785i	$0.372450\pi$
$44$	33.5428	+	58.0978i	0.762335	+	1.32040i
$45$		0			0
$46$	−31.0584	+	53.7947i	−0.675182	+	1.16945i
$47$	−59.8153			−1.27267			−0.636333	−	0.771414i	$-0.719550\pi$
$47$	−59.8153			−1.27267			−0.636333	+	0.771414i	$0.719550\pi$
$48$		0			0
$49$	−14.6900	+	25.4439i	−0.299797	+	0.519263i
$50$	−55.5957	−	14.8968i	−1.11191	−	0.297936i
$51$		0			0
$52$	−16.8211	+	4.50720i	−0.323483	+	0.0866770i
$53$	29.7974	−	51.6106i	0.562215	−	0.973784i	−0.435088	−	0.900388i	$-0.643283\pi$
$53$	29.7974	−	51.6106i	0.562215	−	0.973784i	0.997303	−	0.0733964i	$-0.0233838\pi$
$54$		0			0
$55$	4.82910	−	18.0224i	0.0878018	−	0.327681i
$56$	−257.290	−	68.9406i	−4.59446	−	1.23108i
$57$		0			0
$58$	103.555	+	59.7874i	1.78543	+	1.03082i
$59$	3.02150	+	11.2764i	0.0512118	+	0.191125i	0.986793	−	0.161987i	$-0.0517902\pi$
$59$	3.02150	+	11.2764i	0.0512118	+	0.191125i	−0.935581	+	0.353112i	$0.885124\pi$
$60$		0			0
$61$	−21.6834	+	80.9237i	−0.355466	+	1.32662i	0.524431	+	0.851453i	$0.324278\pi$
$61$	−21.6834	+	80.9237i	−0.355466	+	1.32662i	−0.879897	+	0.475165i	$0.842388\pi$
$62$	126.363	+	72.9554i	2.03811	+	1.17670i
$63$		0			0
$64$		−	365.669i		−	5.71357i
$65$	4.19453	+	2.42171i	0.0645312	+	0.0372571i
$66$		0			0
$67$	−65.6658	+	37.9122i	−0.980087	+	0.565853i	−0.902296	−	0.431116i	$-0.858120\pi$
$67$	−65.6658	+	37.9122i	−0.980087	+	0.565853i	−0.0777904	+	0.996970i	$0.524786\pi$
$68$	168.145	+	168.145i	2.47273	+	2.47273i
$69$		0			0
$70$	56.5012	+	97.8629i	0.807160	+	1.39804i
$71$	−24.9235	−	43.1687i	−0.351035	−	0.608010i	0.635396	−	0.772186i	$-0.280837\pi$
$71$	−24.9235	−	43.1687i	−0.351035	−	0.608010i	−0.986431	+	0.164176i	$0.947503\pi$
$72$		0			0
$73$		−	38.1995i		−	0.523281i	−0.965165	−	0.261640i	$-0.915737\pi$
$73$		−	38.1995i		−	0.523281i	0.965165	−	0.261640i	$-0.0842634\pi$
$74$	62.8779	−	131.993i	0.849702	−	1.78368i
$75$		0			0
$76$	306.298	−	82.0722i	4.03023	−	1.07990i
$77$	44.2871	−	25.5692i	0.575157	−	0.332067i
$78$		0			0
$79$	−53.2289	−	14.2626i	−0.673783	−	0.180540i	−0.0943248	−	0.995541i	$-0.530069\pi$
$79$	−53.2289	−	14.2626i	−0.673783	−	0.180540i	−0.579458	+	0.815002i	$0.696736\pi$
$80$	−165.438	+	165.438i	−2.06797	+	2.06797i
$81$		0			0
$82$	−66.6375	+	66.6375i	−0.812652	+	0.812652i
$83$	36.7004	−	63.5669i	0.442173	−	0.765866i	−0.555677	−	0.831398i	$-0.687541\pi$
$83$	36.7004	−	63.5669i	0.442173	−	0.765866i	0.997850	+	0.0655318i	$0.0208744\pi$
$84$		0			0
$85$		−	66.1365i		−	0.778076i
$86$	−63.7634	+	110.441i	−0.741435	+	1.28420i
$87$		0			0
$88$	122.887	+	122.887i	1.39644	+	1.39644i
$89$	−51.9117	+	13.9097i	−0.583278	+	0.156289i	−0.538379	−	0.842703i	$-0.680963\pi$
$89$	−51.9117	+	13.9097i	−0.583278	+	0.156289i	−0.0448988	+	0.998992i	$0.514297\pi$
$90$		0			0
$91$	3.43578	+	12.8225i	0.0377558	+	0.140906i
$92$	−47.2533	+	176.352i	−0.513623	+	1.91687i
$93$		0			0
$94$	−228.305	+	61.1740i	−2.42877	+	0.650788i
$95$	−76.3786	−	44.0972i	−0.803985	−	0.464181i
$96$		0			0
$97$	−49.5738	+	49.5738i	−0.511070	+	0.511070i	−0.914854	−	0.403784i	$-0.867695\pi$
$97$	−49.5738	+	49.5738i	−0.511070	+	0.511070i	0.403784	+	0.914854i	$0.367695\pi$
$98$	−30.0474	+	112.139i	−0.306606	+	1.14427i
$99$		0			0
$100$	−169.170			−1.69170
$101$		−	16.8205i		−	0.166540i	−0.996527	−	0.0832700i	$-0.973464\pi$
$101$		−	16.8205i		−	0.166540i	0.996527	−	0.0832700i	$-0.0265364\pi$
$102$		0			0
$103$	108.646	+	108.646i	1.05482	+	1.05482i	0.998408	+	0.0564096i	$0.0179653\pi$
$103$	108.646	+	108.646i	1.05482	+	1.05482i	0.0564096	+	0.998408i	$0.482035\pi$
$104$	−39.0690	+	22.5565i	−0.375664	+	0.216890i
$105$		0			0
$106$	60.9484	−	227.463i	0.574985	−	2.14587i
$107$	−42.1732	−	73.0462i	−0.394142	−	0.682674i	0.598849	−	0.800862i	$-0.295625\pi$
$107$	−42.1732	−	73.0462i	−0.394142	−	0.682674i	−0.992991	+	0.118187i	$0.962292\pi$
$108$		0			0
$109$	22.5291	+	84.0796i	0.206689	+	0.771372i	0.988928	+	0.148395i	$0.0474106\pi$
$109$	22.5291	+	84.0796i	0.206689	+	0.771372i	−0.782240	+	0.622978i	$0.785923\pi$
$110$		−	73.7273i		−	0.670248i
$111$		0			0
$112$	−641.247			−5.72542
$113$	73.2837	−	19.6363i	0.648528	−	0.173773i	0.0804649	−	0.996757i	$-0.474359\pi$
$113$	73.2837	−	19.6363i	0.648528	−	0.173773i	0.568063	+	0.822985i	$0.307693\pi$
$114$		0			0
$115$	43.9752	−	25.3891i	0.382393	−	0.220775i
$116$	339.477	+	90.9626i	2.92653	+	0.784161i
$117$		0			0
$118$	23.0650	+	39.9498i	0.195466	+	0.338558i
$119$	128.175	−	128.175i	1.07710	−	1.07710i
$120$		0			0
$121$	87.6353			0.724259
$122$			331.047i			2.71350i
$123$		0			0
$124$	414.246	+	110.997i	3.34069	+	0.895136i
$125$	90.3718	+	90.3718i	0.722975	+	0.722975i
$126$		0			0
$127$	50.1421	−	86.8486i	0.394819	−	0.683847i	−0.598259	−	0.801303i	$-0.704141\pi$
$127$	50.1421	−	86.8486i	0.394819	−	0.683847i	0.993078	+	0.117456i	$0.0374739\pi$
$128$	−202.263	−	754.858i	−1.58018	−	5.89732i
$129$		0			0
$130$	18.4865	+	4.95344i	0.142204	+	0.0381034i
$131$	−131.240	+	35.1656i	−1.00183	+	0.268440i	−0.722212	−	0.691672i	$-0.756874\pi$
$131$	−131.240	+	35.1656i	−1.00183	+	0.268440i	−0.279618	+	0.960111i	$0.590208\pi$
$132$		0			0
$133$	−62.5624	−	233.486i	−0.470394	−	1.75554i
$134$	−211.861	+	211.861i	−1.58106	+	1.58106i
$135$		0			0
$136$	533.484	+	308.007i	3.92268	+	2.26476i
$137$	−152.999			−1.11678			−0.558392	−	0.829577i	$-0.688582\pi$
$137$	−152.999			−1.11678			−0.558392	+	0.829577i	$0.688582\pi$
$138$		0			0
$139$	−23.2249	−	13.4089i	−0.167086	−	0.0964669i	0.414125	−	0.910220i	$-0.364088\pi$
$139$	−23.2249	−	13.4089i	−0.167086	−	0.0964669i	−0.581211	+	0.813753i	$0.697421\pi$
$140$	234.855	+	234.855i	1.67753	+	1.67753i
$141$		0			0
$142$	−139.278	−	139.278i	−0.980830	−	0.980830i
$143$	2.24164	−	8.36591i	0.0156758	−	0.0585029i
$144$		0			0
$145$	−48.8740	−	84.6523i	−0.337062	−	0.583809i
$146$	−39.0672	−	145.801i	−0.267583	−	0.998635i
$147$		0			0
$148$	78.1036	−	422.564i	0.527727	−	2.85516i
$149$	17.8007			0.119468			0.0597340	−	0.998214i	$-0.480975\pi$
$149$	17.8007			0.119468			0.0597340	+	0.998214i	$0.480975\pi$
$150$		0			0
$151$	55.7345	−	32.1783i	0.369103	−	0.213102i	−0.303964	−	0.952684i	$-0.598310\pi$
$151$	55.7345	−	32.1783i	0.369103	−	0.213102i	0.673066	+	0.739582i	$0.264977\pi$
$152$	711.413	−	410.734i	4.68035	−	2.70220i
$153$		0			0
$154$	142.886	−	142.886i	0.927831	−	0.927831i
$155$	−59.6384	−	103.297i	−0.384764	−	0.666430i
$156$		0			0
$157$	89.1203	−	154.361i	0.567645	−	0.983190i	−0.429153	−	0.903232i	$-0.641188\pi$
$157$	89.1203	−	154.361i	0.567645	−	0.983190i	0.996798	−	0.0799583i	$-0.0254787\pi$
$158$	−217.752			−1.37818
$159$		0			0
$160$	−267.879	+	463.980i	−1.67424	+	2.89988i
$161$	134.430	+	36.0205i	0.834971	+	0.223730i
$162$		0			0
$163$	−98.6502	+	26.4332i	−0.605216	+	0.162167i	−0.548398	−	0.836218i	$-0.684762\pi$
$163$	−98.6502	+	26.4332i	−0.605216	+	0.162167i	−0.0568178	+	0.998385i	$0.518095\pi$
$164$	−138.494	+	239.878i	−0.844474	+	1.46267i
$165$		0			0
$166$	75.0680	−	280.158i	0.452217	−	1.68770i
$167$	−109.143	−	29.2447i	−0.653549	−	0.175118i	−0.0832158	−	0.996532i	$-0.526519\pi$
$167$	−109.143	−	29.2447i	−0.653549	−	0.175118i	−0.570333	+	0.821414i	$0.693186\pi$
$168$		0			0
$169$	−144.411	−	83.3759i	−0.854504	−	0.493348i
$170$	−67.6387	−	252.431i	−0.397875	−	1.48489i
$171$		0			0
$172$	−97.0118	+	362.053i	−0.564022	+	2.10496i
$173$	11.0085	+	6.35575i	0.0636329	+	0.0367385i	0.531479	−	0.847072i	$-0.321636\pi$
$173$	11.0085	+	6.35575i	0.0636329	+	0.0367385i	−0.467846	+	0.883810i	$0.654970\pi$
$174$		0			0
$175$			128.956i			0.736892i
$176$	362.324	+	209.188i	2.05866	+	1.18857i
$177$		0			0
$178$	−183.912	+	106.182i	−1.03322	+	0.596527i
$179$	77.9841	+	77.9841i	0.435665	+	0.435665i	0.890550	−	0.454885i	$-0.150320\pi$
$179$	77.9841	+	77.9841i	0.435665	+	0.435665i	−0.454885	+	0.890550i	$0.650320\pi$
$180$		0			0
$181$	62.1863	+	107.710i	0.343571	+	0.595082i	0.985093	−	0.172022i	$-0.0550301\pi$
$181$	62.1863	+	107.710i	0.343571	+	0.595082i	−0.641522	+	0.767104i	$0.721697\pi$
$182$	26.2275	+	45.4274i	0.144107	+	0.249601i
$183$		0			0
$184$			472.963i			2.57045i
$185$	−98.4636	+	67.7432i	−0.532236	+	0.366179i
$186$		0			0
$187$	−114.236	+	30.6094i	−0.610886	+	0.163686i
$188$	−601.628	+	347.350i	−3.20015	+	1.84761i
$189$		0			0
$190$	−336.623	−	90.1977i	−1.77170	−	0.474725i
$191$	58.9780	−	58.9780i	0.308786	−	0.308786i	−0.535653	−	0.844438i	$-0.679934\pi$
$191$	58.9780	−	58.9780i	0.308786	−	0.308786i	0.844438	+	0.535653i	$0.179934\pi$
$192$		0			0
$193$	−134.637	+	134.637i	−0.697601	+	0.697601i	−0.963892	−	0.266292i	$-0.914202\pi$
$193$	−134.637	+	134.637i	−0.697601	+	0.697601i	0.266292	+	0.963892i	$0.414202\pi$
$194$	−138.515	+	239.914i	−0.713993	+	1.23667i
$195$		0			0
$196$			341.223i			1.74093i
$197$	83.0403	−	143.830i	0.421524	−	0.730101i	−0.574565	−	0.818459i	$-0.694829\pi$
$197$	83.0403	−	143.830i	0.421524	−	0.730101i	0.996089	+	0.0883578i	$0.0281619\pi$
$198$		0			0
$199$	45.0255	+	45.0255i	0.226259	+	0.226259i	0.811128	−	0.584869i	$-0.198854\pi$
$199$	45.0255	+	45.0255i	0.226259	+	0.226259i	−0.584869	+	0.811128i	$0.698854\pi$
$200$	−423.310	+	113.426i	−2.11655	+	0.567128i
$201$		0			0
$202$	−17.2026	−	64.2010i	−0.0851615	−	0.317827i
$203$	69.3395	−	258.779i	0.341574	−	1.27477i
$204$		0			0
$205$	74.4124	−	19.9387i	0.362987	−	0.0972622i
$206$	525.797	+	303.569i	2.55241	+	1.47364i
$207$		0			0
$208$	−76.7951	+	76.7951i	−0.369207	+	0.369207i
$209$	−40.8183	+	152.336i	−0.195303	+	0.728880i
$210$		0			0
$211$	−140.399			−0.665397			−0.332699	−	0.943033i	$-0.607959\pi$
$211$	−140.399			−0.665397			−0.332699	+	0.943033i	$0.607959\pi$
$212$		−	692.139i		−	3.26481i
$213$		0			0
$214$	−235.673	−	235.673i	−1.10128	−	1.10128i
$215$	90.2818	−	52.1242i	0.419915	−	0.242438i
$216$		0			0
$217$	84.6113	−	315.774i	0.389914	−	1.45518i
$218$	171.979	+	297.876i	0.788894	+	1.36640i
$219$		0			0
$220$	−56.0856	−	209.314i	−0.254935	−	0.951429i
$221$		−	30.7001i		−	0.138915i
$222$		0			0
$223$	188.879			0.846991			0.423495	−	0.905898i	$-0.360803\pi$
$223$	188.879			0.846991			0.423495	+	0.905898i	$0.360803\pi$
$224$	−1418.37	+	380.051i	−6.33200	+	1.69665i
$225$		0			0
$226$	259.629	−	149.897i	1.14880	−	0.663260i
$227$	−384.144	−	102.931i	−1.69227	−	0.453441i	−0.721292	−	0.692631i	$-0.756452\pi$
$227$	−384.144	−	102.931i	−1.69227	−	0.453441i	−0.970973	+	0.239189i	$0.923118\pi$
$228$		0			0
$229$	−73.6555	−	127.575i	−0.321640	−	0.557097i	0.659187	−	0.751979i	$-0.270901\pi$
$229$	−73.6555	−	127.575i	−0.321640	−	0.557097i	−0.980827	+	0.194883i	$0.937567\pi$
$230$	141.880	−	141.880i	0.616868	−	0.616868i
$231$		0			0
$232$	910.454			3.92437
$233$			270.171i			1.15953i	0.814782	+	0.579767i	$0.196856\pi$
$233$			270.171i			1.15953i	−0.814782	+	0.579767i	$0.803144\pi$
$234$		0			0
$235$	186.631	+	50.0075i	0.794173	+	0.212798i
$236$	95.8729	+	95.8729i	0.406241	+	0.406241i
$237$		0			0
$238$	358.134	−	620.306i	1.50477	−	2.60633i
$239$	−114.692	−	428.037i	−0.479884	−	1.79095i	−0.602071	−	0.798443i	$-0.705657\pi$
$239$	−114.692	−	428.037i	−0.479884	−	1.79095i	0.122187	−	0.992507i	$-0.461009\pi$
$240$		0			0
$241$	6.53045	+	1.74983i	0.0270973	+	0.00726070i	0.272342	−	0.962200i	$-0.412202\pi$
$241$	6.53045	+	1.74983i	0.0270973	+	0.00726070i	−0.245245	+	0.969461i	$0.578868\pi$
$242$	334.488	−	89.6259i	1.38218	−	0.370355i
$243$		0			0
$244$	251.833	+	939.855i	1.03210	+	3.85186i
$245$	67.1064	−	67.1064i	0.273904	−	0.273904i
$246$		0			0
$247$	−35.4545	−	20.4697i	−0.143540	−	0.0828731i
$248$	1110.98			4.47975
$249$		0			0
$250$	437.358	+	252.509i	1.74943	+	1.01003i
$251$	−30.1348	−	30.1348i	−0.120059	−	0.120059i	0.644525	−	0.764584i	$-0.277055\pi$
$251$	−30.1348	−	30.1348i	−0.120059	−	0.120059i	−0.764584	+	0.644525i	$0.777055\pi$
$252$		0			0
$253$	−64.2065	−	64.2065i	−0.253781	−	0.253781i
$254$	102.562	−	382.767i	0.403788	−	1.50696i
$255$		0			0
$256$	−812.671	−	1407.59i	−3.17450	−	5.49839i
$257$	19.9978	+	74.6328i	0.0778124	+	0.290400i	0.993856	−	0.110678i	$-0.0353023\pi$
$257$	19.9978	+	74.6328i	0.0778124	+	0.290400i	−0.916044	+	0.401078i	$0.868636\pi$
$258$		0			0
$259$	−322.114	−	59.5372i	−1.24368	−	0.229873i
$260$	56.2519			0.216354
$261$		0			0
$262$	−464.955	+	268.442i	−1.77464	+	1.02459i
$263$	−260.075	+	150.155i	−0.988879	+	0.570930i	−0.904939	−	0.425541i	$-0.860084\pi$
$263$	−260.075	+	150.155i	−0.988879	+	0.570930i	−0.0839403	+	0.996471i	$0.526751\pi$
$264$		0			0
$265$	−136.119	+	136.119i	−0.513657	+	0.513657i
$266$	−477.580	−	827.192i	−1.79541	−	3.10975i
$267$		0			0
$268$	−440.315	+	762.649i	−1.64297	+	2.84570i
$269$	−3.20939			−0.0119308			−0.00596542	−	0.999982i	$-0.501899\pi$
$269$	−3.20939			−0.0119308			−0.00596542	+	0.999982i	$0.501899\pi$
$270$		0			0
$271$	126.003	−	218.243i	0.464954	−	0.805324i	−0.534245	−	0.845330i	$-0.679404\pi$
$271$	126.003	−	218.243i	0.464954	−	0.805324i	0.999199	+	0.0400051i	$0.0127374\pi$
$272$	1432.46	+	383.825i	5.26638	+	1.41112i
$273$		0			0
$274$	−583.972	+	156.475i	−2.13128	+	0.571076i
$275$	42.0681	−	72.8640i	0.152975	−	0.264960i
$276$		0			0
$277$	46.4253	−	173.262i	0.167601	−	0.625494i	−0.830094	−	0.557624i	$-0.811713\pi$
$277$	46.4253	−	173.262i	0.167601	−	0.625494i	0.997694	−	0.0678697i	$-0.0216202\pi$
$278$	−102.359	−	27.4270i	−0.368197	−	0.0986581i
$279$		0			0
$280$	745.137	+	430.205i	2.66120	+	1.53645i
$281$	125.791	+	469.460i	0.447656	+	1.67067i	0.708827	+	0.705382i	$0.249225\pi$
$281$	125.791	+	469.460i	0.447656	+	1.67067i	−0.261171	+	0.965293i	$0.584109\pi$
$282$		0			0
$283$	8.80130	−	32.8469i	0.0311000	−	0.116067i	−0.948631	−	0.316385i	$-0.897531\pi$
$283$	8.80130	−	32.8469i	0.0311000	−	0.116067i	0.979731	+	0.200318i	$0.0641976\pi$
$284$	−501.365	−	289.463i	−1.76537	−	1.01924i
$285$		0			0
$286$		−	34.2238i		−	0.119664i
$287$	182.856	+	105.572i	0.637128	+	0.367846i
$288$		0			0
$289$	−112.763	+	65.1038i	−0.390184	+	0.225273i
$290$	−273.119	−	273.119i	−0.941789	−	0.941789i
$291$		0			0
$292$	−221.826	−	384.214i	−0.759678	−	1.31580i
$293$	−81.7243	−	141.551i	−0.278922	−	0.483108i	0.692195	−	0.721711i	$-0.256644\pi$
$293$	−81.7243	−	141.551i	−0.278922	−	0.483108i	−0.971117	+	0.238603i	$0.923311\pi$
$294$		0			0
$295$		−	37.7096i		−	0.127829i
$296$	−87.8851	−	1109.74i	−0.296909	−	3.74911i
$297$		0			0
$298$	67.9422	−	18.2051i	0.227994	−	0.0610908i
$299$	20.4130	−	11.7855i	0.0682709	−	0.0394162i
$300$		0			0
$301$	275.988	+	73.9507i	0.916903	+	0.245683i
$302$	179.820	−	179.820i	0.595429	−	0.595429i
$303$		0			0
$304$	1398.37	−	1398.37i	4.59991	−	4.59991i
$305$	135.309	−	234.363i	0.443638	−	0.768403i
$306$		0			0
$307$		−	79.1084i		−	0.257682i	−0.991665	−	0.128841i	$-0.958874\pi$
$307$		−	79.1084i		−	0.257682i	0.991665	−	0.128841i	$-0.0411257\pi$
$308$	296.962	−	514.354i	0.964164	−	1.66998i
$309$		0			0
$310$	−333.272	−	333.272i	−1.07507	−	1.07507i
$311$	442.182	−	118.482i	1.42181	−	0.380972i	0.535683	−	0.844419i	$-0.320054\pi$
$311$	442.182	−	118.482i	1.42181	−	0.380972i	0.886125	+	0.463447i	$0.153388\pi$
$312$		0			0
$313$	66.0855	+	246.635i	0.211136	+	0.787970i	0.987491	+	0.157674i	$0.0503996\pi$
$313$	66.0855	+	246.635i	0.211136	+	0.787970i	−0.776355	+	0.630296i	$0.782934\pi$
$314$	182.289	−	680.313i	0.580539	−	2.16660i
$315$		0			0
$316$	−618.205	+	165.647i	−1.95634	+	0.524201i
$317$	−95.3102	−	55.0274i	−0.300663	−	0.173588i	0.342078	−	0.939672i	$-0.388869\pi$
$317$	−95.3102	−	55.0274i	−0.300663	−	0.173588i	−0.642741	+	0.766084i	$0.722203\pi$
$318$		0			0
$319$	−123.598	+	123.598i	−0.387454	+	0.387454i
$320$	−305.710	+	1140.93i	−0.955345	+	3.56540i
$321$		0			0
$322$	549.935			1.70787
$323$			559.022i			1.73072i
$324$		0			0
$325$	15.4436	+	15.4436i	0.0475189	+	0.0475189i
$326$	−349.497	+	201.782i	−1.07208	+	0.618963i
$327$		0			0
$328$	−185.715	+	693.099i	−0.566205	+	2.11311i
$329$	264.780	+	458.613i	0.804803	+	1.39396i
$330$		0			0
$331$	−146.233	−	545.751i	−0.441793	−	1.64879i	−0.724268	−	0.689519i	$-0.757822\pi$
$331$	−146.233	−	545.751i	−0.441793	−	1.64879i	0.282475	−	0.959275i	$-0.408845\pi$
$332$		−	852.483i		−	2.56772i
$333$		0			0
$334$	−446.487			−1.33679
$335$	236.580	−	63.3915i	0.706210	−	0.189228i
$336$		0			0
$337$	348.133	−	200.995i	1.03304	−	0.596424i	0.115184	−	0.993344i	$-0.463254\pi$
$337$	348.133	−	200.995i	1.03304	−	0.596424i	0.917853	+	0.396920i	$0.129921\pi$
$338$	−636.462	−	170.539i	−1.88302	−	0.504555i
$339$		0			0
$340$	−384.057	−	665.207i	−1.12958	−	1.95649i
$341$	−150.820	+	150.820i	−0.442286	+	0.442286i
$342$		0			0
$343$	−173.700			−0.506415
$344$			971.000i			2.82268i
$345$		0			0
$346$	48.5176	+	13.0002i	0.140224	+	0.0375730i
$347$	−152.661	−	152.661i	−0.439946	−	0.439946i	0.452047	−	0.891994i	$-0.350694\pi$
$347$	−152.661	−	152.661i	−0.439946	−	0.439946i	−0.891994	+	0.452047i	$0.850694\pi$
$348$		0			0
$349$	−225.429	+	390.455i	−0.645928	+	1.11878i	0.338158	+	0.941089i	$0.390196\pi$
$349$	−225.429	+	390.455i	−0.645928	+	1.11878i	−0.984086	+	0.177692i	$0.943137\pi$
$350$	131.885	+	492.202i	0.376815	+	1.40629i
$351$		0			0
$352$	925.401	+	247.960i	2.62898	+	0.704433i
$353$	22.6347	−	6.06496i	0.0641210	−	0.0171812i	−0.226616	−	0.973984i	$-0.572766\pi$
$353$	22.6347	−	6.06496i	0.0641210	−	0.0171812i	0.290737	+	0.956803i	$0.406100\pi$
$354$		0			0
$355$	41.6736	+	155.528i	0.117390	+	0.438107i
$356$	−441.359	+	441.359i	−1.23977	+	1.23977i
$357$		0			0
$358$	377.407	+	217.896i	1.05421	+	0.608648i
$359$	−1.07021			−0.00298109			−0.00149054	−	0.999999i	$-0.500474\pi$
$359$	−1.07021			−0.00298109			−0.00149054	+	0.999999i	$0.500474\pi$
$360$		0			0
$361$	332.960	+	192.234i	0.922326	+	0.532505i
$362$	347.511	+	347.511i	0.959975	+	0.959975i
$363$		0			0
$364$	109.018	+	109.018i	0.299500	+	0.299500i
$365$	−31.9360	+	119.187i	−0.0874958	+	0.326539i
$366$		0			0
$367$	−16.3995	−	28.4047i	−0.0446852	−	0.0773970i	0.842818	−	0.538199i	$-0.180895\pi$
$367$	−16.3995	−	28.4047i	−0.0446852	−	0.0773970i	−0.887503	+	0.460802i	$0.847562\pi$
$368$	294.693	+	1099.81i	0.800796	+	2.98861i
$369$		0			0
$370$	−306.536	+	359.264i	−0.828476	+	0.970983i
$371$	−527.607			−1.42212
$372$		0			0
$373$	477.963	−	275.952i	1.28140	−	0.739818i	0.304297	−	0.952577i	$-0.401578\pi$
$373$	477.963	−	275.952i	1.28140	−	0.739818i	0.977105	+	0.212760i	$0.0682451\pi$
$374$	−404.713	+	233.661i	−1.08212	+	0.624762i
$375$		0			0
$376$	−1272.55	+	1272.55i	−3.38443	+	3.38443i
$377$	−22.6870	−	39.2951i	−0.0601778	−	0.104231i
$378$		0			0
$379$	75.2861	−	130.399i	0.198644	−	0.344062i	−0.749445	−	0.662067i	$-0.769680\pi$
$379$	75.2861	−	130.399i	0.198644	−	0.344062i	0.948089	+	0.318005i	$0.103013\pi$
$380$	−1024.30			−2.69552
$381$		0			0
$382$	164.791	−	285.426i	0.431390	−	0.747190i
$383$	−472.167	−	126.517i	−1.23281	−	0.330331i	−0.417137	−	0.908843i	$-0.636967\pi$
$383$	−472.167	−	126.517i	−1.23281	−	0.330331i	−0.815673	+	0.578513i	$0.803633\pi$
$384$		0			0
$385$	−159.557	+	42.7532i	−0.414434	+	0.111047i
$386$	−376.190	+	651.581i	−0.974586	+	1.68803i
$387$		0			0
$388$	−210.741	+	786.495i	−0.543146	+	2.02705i
$389$	241.856	+	64.8051i	0.621737	+	0.166594i	0.555917	−	0.831238i	$-0.312367\pi$
$389$	241.856	+	64.8051i	0.621737	+	0.166594i	0.0658198	+	0.997832i	$0.479034\pi$
$390$		0			0
$391$	−278.738	−	160.929i	−0.712884	−	0.411584i
$392$	228.784	+	853.833i	0.583632	+	2.17814i
$393$		0			0
$394$	169.853	−	633.900i	0.431099	−	1.60888i
$395$	154.156	+	89.0020i	0.390268	+	0.225322i
$396$		0			0
$397$			676.347i			1.70365i	0.523830	+	0.851823i	$0.324503\pi$
$397$			676.347i			1.70365i	−0.523830	+	0.851823i	$0.675497\pi$
$398$	217.902	+	125.806i	0.547493	+	0.316096i
$399$		0			0
$400$	−913.676	+	527.511i	−2.28419	+	1.31878i
$401$	450.431	+	450.431i	1.12327	+	1.12327i	0.991247	+	0.132023i	$0.0421474\pi$
$401$	450.431	+	450.431i	1.12327	+	1.12327i	0.132023	+	0.991247i	$0.457853\pi$
$402$		0			0
$403$	−27.6838	−	47.9497i	−0.0686942	−	0.118982i
$404$	−97.6776	−	169.183i	−0.241776	−	0.418769i
$405$		0			0
$406$		−	1058.63i		−	2.60745i
$407$	162.582	+	138.721i	0.399464	+	0.340837i
$408$		0			0
$409$	−344.146	+	92.2136i	−0.841432	+	0.225461i	−0.653695	−	0.756758i	$-0.726782\pi$
$409$	−344.146	+	92.2136i	−0.841432	+	0.225461i	−0.187737	+	0.982219i	$0.560115\pi$
$410$	263.627	−	152.205i	0.642994	−	0.371233i
$411$		0			0
$412$	1723.69	+	461.861i	4.18371	+	1.12102i
$413$	73.0825	−	73.0825i	0.176955	−	0.176955i
$414$		0			0
$415$	−167.653	+	167.653i	−0.403984	+	0.403984i
$416$	−124.348	+	215.377i	−0.298913	+	0.517733i
$417$		0			0
$418$			623.184i			1.49087i
$419$	−252.122	+	436.688i	−0.601723	+	1.04221i	0.390837	+	0.920460i	$0.372186\pi$
$419$	−252.122	+	436.688i	−0.601723	+	1.04221i	−0.992560	+	0.121755i	$0.961148\pi$
$420$		0			0
$421$	514.581	+	514.581i	1.22228	+	1.22228i	0.966818	+	0.255466i	$0.0822287\pi$
$421$	514.581	+	514.581i	1.22228	+	1.22228i	0.255466	+	0.966818i	$0.417771\pi$
$422$	−535.878	+	143.588i	−1.26985	+	0.340256i
$423$		0			0
$424$	−464.067	−	1731.92i	−1.09450	−	4.08472i
$425$	77.1880	−	288.069i	0.181619	−	0.677811i
$426$		0			0
$427$	716.438	−	191.969i	1.67784	−	0.449576i
$428$	−848.365	−	489.804i	−1.98216	−	1.14440i
$429$		0			0
$430$	291.281	−	291.281i	0.677399	−	0.677399i
$431$	−18.6399	+	69.5652i	−0.0432481	+	0.161404i	−0.984173	−	0.177212i	$-0.943292\pi$
$431$	−18.6399	+	69.5652i	−0.0432481	+	0.161404i	0.940925	+	0.338616i	$0.109959\pi$
$432$		0			0
$433$	−610.395			−1.40969			−0.704844	−	0.709363i	$-0.748983\pi$
$433$	−610.395			−1.40969			−0.704844	+	0.709363i	$0.748983\pi$
$434$		−	1291.79i		−	2.97646i
$435$		0			0
$436$	714.853	+	714.853i	1.63957	+	1.63957i
$437$	−371.703	+	214.603i	−0.850579	+	0.491082i
$438$		0			0
$439$	−34.5809	+	129.058i	−0.0787719	+	0.293981i	−0.994062	−	0.108814i	$-0.965295\pi$
$439$	−34.5809	+	129.058i	−0.0787719	+	0.293981i	0.915290	+	0.402795i	$0.131961\pi$
$440$	−280.683	−	486.157i	−0.637916	−	1.10490i
$441$		0			0
$442$	−31.3975	−	117.177i	−0.0710351	−	0.265106i
$443$			301.732i			0.681110i	0.940225	+	0.340555i	$0.110615\pi$
$443$			301.732i			0.681110i	−0.940225	+	0.340555i	$0.889385\pi$
$444$		0			0
$445$	173.599			0.390111
$446$	720.918	−	193.169i	1.61641	−	0.433115i
$447$		0			0
$448$	−2803.63	+	1618.68i	−6.25811	+	3.61312i
$449$	862.990	+	231.237i	1.92203	+	0.515005i	0.987083	+	0.160207i	$0.0512161\pi$
$449$	862.990	+	231.237i	1.92203	+	0.515005i	0.934943	+	0.354799i	$0.115451\pi$
$450$		0			0
$451$	−68.8793	−	119.302i	−0.152726	−	0.264529i
$452$	623.066	−	623.066i	1.37846	−	1.37846i
$453$		0			0
$454$	−1571.48			−3.46141
$455$		−	42.8800i		−	0.0942418i
$456$		0			0
$457$	258.719	+	69.3237i	0.566126	+	0.151693i	0.530519	−	0.847673i	$-0.321997\pi$
$457$	258.719	+	69.3237i	0.566126	+	0.151693i	0.0356066	+	0.999366i	$0.488664\pi$
$458$	−411.603	−	411.603i	−0.898697	−	0.898697i
$459$		0			0
$460$	294.871	−	510.732i	0.641024	−	1.11029i
$461$	−92.6889	−	345.920i	−0.201060	−	0.750368i	−0.990614	−	0.136687i	$-0.956355\pi$
$461$	−92.6889	−	345.920i	−0.201060	−	0.750368i	0.789554	−	0.613681i	$-0.210312\pi$
$462$		0			0
$463$	187.710	+	50.2967i	0.405421	+	0.108632i	0.455766	−	0.890100i	$-0.349365\pi$
$463$	187.710	+	50.2967i	0.405421	+	0.108632i	−0.0503452	+	0.998732i	$0.516032\pi$
$464$	2117.13	−	567.284i	4.56279	−	1.22260i
$465$		0			0
$466$	276.308	+	1031.20i	0.592936	+	2.21287i
$467$	68.5440	−	68.5440i	0.146775	−	0.146775i	−0.629901	−	0.776676i	$-0.716904\pi$
$467$	68.5440	−	68.5440i	0.146775	−	0.146775i	0.776676	+	0.629901i	$0.216904\pi$
$468$		0			0
$469$	581.356	+	335.646i	1.23956	+	0.715663i
$470$	763.479			1.62442
$471$		0			0
$472$	304.181	+	175.619i	0.644452	+	0.372075i
$473$	−131.817	−	131.817i	−0.278683	−	0.278683i
$474$		0			0
$475$	−281.215	−	281.215i	−0.592032	−	0.592032i
$476$	544.877	−	2033.51i	1.14470	−	4.27208i
$477$		0			0
$478$	−875.520	−	1516.44i	−1.83163	−	3.17248i
$479$	10.9392	+	40.8257i	0.0228376	+	0.0852311i	0.976404	−	0.215951i	$-0.0692853\pi$
$479$	10.9392	+	40.8257i	0.0228376	+	0.0852311i	−0.953566	+	0.301183i	$0.902619\pi$
$480$		0			0
$481$	−45.7062	+	31.4460i	−0.0950233	+	0.0653762i
$482$	26.7151			0.0554256
$483$		0			0
$484$	881.444	−	508.902i	1.82117	−	1.05145i
$485$	196.121	−	113.231i	0.404373	−	0.233465i
$486$		0			0
$487$	−12.7079	+	12.7079i	−0.0260943	+	0.0260943i	−0.720034	−	0.693939i	$-0.755874\pi$
$487$	−12.7079	+	12.7079i	−0.0260943	+	0.0260943i	0.693939	+	0.720034i	$0.255874\pi$
$488$	1260.31	+	2182.93i	2.58261	+	4.47321i
$489$		0			0
$490$	187.503	−	324.764i	0.382658	−	0.662784i
$491$	−565.567			−1.15187			−0.575933	−	0.817497i	$-0.695361\pi$
$491$	−565.567			−1.15187			−0.575933	+	0.817497i	$0.695361\pi$
$492$		0			0
$493$	−309.789	+	536.571i	−0.628376	+	1.08838i
$494$	−156.258	−	41.8692i	−0.316312	−	0.0847555i
$495$		0			0
$496$	2583.43	−	692.227i	5.20852	−	1.39562i
$497$	−220.654	+	382.184i	−0.443971	+	0.768981i
$498$		0			0
$499$	−242.728	+	905.875i	−0.486430	+	1.81538i	0.0871049	+	0.996199i	$0.472238\pi$
$499$	−242.728	+	905.875i	−0.486430	+	1.81538i	−0.573535	+	0.819181i	$0.694428\pi$
$500$	1433.76	+	384.175i	2.86752	+	0.768351i
$501$		0			0
$502$	−145.839	−	84.2000i	−0.290515	−	0.167729i
$503$	90.3544	+	337.207i	0.179631	+	0.670392i	0.995716	+	0.0924606i	$0.0294732\pi$
$503$	90.3544	+	337.207i	0.179631	+	0.670392i	−0.816085	+	0.577931i	$0.803860\pi$
$504$		0			0
$505$	−14.0625	+	52.4820i	−0.0278465	+	0.103925i
$506$	−310.730	−	179.400i	−0.614091	−	0.354546i
$507$		0			0
$508$		−	1164.71i		−	2.29273i
$509$	−479.850	−	277.042i	−0.942732	−	0.544286i	−0.0519161	−	0.998651i	$-0.516533\pi$
$509$	−479.850	−	277.042i	−0.942732	−	0.544286i	−0.890816	+	0.454365i	$0.849866\pi$
$510$		0			0
$511$	−292.881	+	169.095i	−0.573152	+	0.330910i
$512$	−2331.01	−	2331.01i	−4.55275	−	4.55275i
$513$		0			0
$514$	152.656	+	264.408i	0.296996	+	0.514413i
$515$	−248.157	−	429.820i	−0.481858	−	0.834602i
$516$		0			0
$517$		−	345.506i		−	0.668291i
$518$	−1290.34	+	102.188i	−2.49101	+	0.197274i
$519$		0			0
$520$	140.758	−	37.7159i	0.270688	−	0.0725306i
$521$	762.669	−	440.327i	1.46386	−	0.845158i	0.464670	−	0.885484i	$-0.346173\pi$
$521$	762.669	−	440.327i	1.46386	−	0.845158i	0.999187	+	0.0403263i	$0.0128397\pi$
$522$		0			0
$523$	300.352	+	80.4792i	0.574288	+	0.153880i	0.534262	−	0.845319i	$-0.320589\pi$
$523$	300.352	+	80.4792i	0.574288	+	0.153880i	0.0400254	+	0.999199i	$0.487256\pi$
$524$	−1115.81	+	1115.81i	−2.12942	+	2.12942i
$525$		0			0
$526$	−839.096	+	839.096i	−1.59524	+	1.59524i
$527$	−378.019	+	654.749i	−0.717304	+	1.24241i
$528$		0			0
$529$			281.884i			0.532862i
$530$	−380.332	+	658.754i	−0.717607	+	1.24293i
$531$		0			0
$532$	−1985.12	−	1985.12i	−3.73144	−	3.73144i
$533$	34.5418	−	9.25544i	0.0648064	−	0.0173648i
$534$		0			0
$535$	70.5163	+	263.170i	0.131806	+	0.491907i
$536$	−590.447	+	2203.58i	−1.10158	+	4.11116i
$537$		0			0
$538$	−12.2497	+	3.28230i	−0.0227689	+	0.00610092i
$539$	−146.969	−	84.8528i	−0.272671	−	0.157426i
$540$		0			0
$541$	−153.648	+	153.648i	−0.284008	+	0.284008i	−0.834705	−	0.550697i	$-0.814362\pi$
$541$	−153.648	+	153.648i	−0.284008	+	0.284008i	0.550697	+	0.834705i	$0.314362\pi$
$542$	257.729	−	961.860i	0.475516	−	1.77465i
$543$		0			0
$544$	3395.92			6.24249
$545$		−	281.173i		−	0.515913i
$546$		0			0
$547$	−576.856	−	576.856i	−1.05458	−	1.05458i	−0.998422	−	0.0561593i	$-0.982115\pi$
$547$	−576.856	−	576.856i	−1.05458	−	1.05458i	−0.0561593	−	0.998422i	$-0.517885\pi$
$548$	−1538.88	+	888.475i	−2.80818	+	1.62130i
$549$		0			0
$550$	86.0473	−	321.133i	0.156450	−	0.583878i
$551$	413.111	+	715.529i	0.749747	+	1.29860i
$552$		0			0
$553$	126.271	+	471.249i	0.228338	+	0.852167i
$554$		−	708.789i		−	1.27940i
$555$		0			0
$556$	−311.464			−0.560188
$557$	519.266	−	139.137i	0.932256	−	0.249797i	0.239439	−	0.970911i	$-0.423036\pi$
$557$	519.266	−	139.137i	0.932256	−	0.249797i	0.692816	+	0.721114i	$0.256370\pi$
$558$		0			0
$559$	41.9083	−	24.1957i	0.0749700	−	0.0432840i
$560$	2000.76	+	536.103i	3.57279	+	0.957327i
$561$		0			0
$562$	960.247	+	1663.20i	1.70862	+	2.95942i
$563$	338.672	−	338.672i	0.601549	−	0.601549i	−0.339174	−	0.940724i	$-0.610148\pi$
$563$	338.672	−	338.672i	0.601549	−	0.601549i	0.940724	+	0.339174i	$0.110148\pi$
$564$		0			0
$565$	−245.070			−0.433752
$566$		−	134.372i		−	0.237406i
$567$		0			0
$568$	−1448.63	−	388.160i	−2.55041	−	0.683381i
$569$	361.073	+	361.073i	0.634575	+	0.634575i	0.949212	−	0.314637i	$-0.101883\pi$
$569$	361.073	+	361.073i	0.634575	+	0.634575i	−0.314637	+	0.949212i	$0.601883\pi$
$570$		0			0
$571$	−110.817	+	191.941i	−0.194076	+	0.336149i	−0.946597	−	0.322419i	$-0.895504\pi$
$571$	−110.817	+	191.941i	−0.194076	+	0.336149i	0.752522	+	0.658568i	$0.228837\pi$
$572$	−26.0346	−	97.1624i	−0.0455150	−	0.169864i
$573$		0			0
$574$	805.898	+	215.940i	1.40400	+	0.376202i
$575$	221.174	−	59.2633i	0.384650	−	0.103067i
$576$		0			0
$577$	−2.70920	−	10.1109i	−0.00469533	−	0.0175232i	0.963538	−	0.267570i	$-0.0862207\pi$
$577$	−2.70920	−	10.1109i	−0.00469533	−	0.0175232i	−0.968234	+	0.250047i	$0.919554\pi$
$578$	−363.814	+	363.814i	−0.629436	+	0.629436i
$579$		0			0
$580$	−983.159	−	567.627i	−1.69510	−	0.978668i
$581$	−649.835			−1.11848
$582$		0			0
$583$	298.114	+	172.116i	0.511345	+	0.295225i
$584$	−812.679	−	812.679i	−1.39157	−	1.39157i
$585$		0			0
$586$	−456.693	−	456.693i	−0.779340	−	0.779340i
$587$	119.180	−	444.785i	0.203032	−	0.757726i	−0.787008	−	0.616942i	$-0.788371\pi$
$587$	119.180	−	444.785i	0.203032	−	0.757726i	0.990040	−	0.140783i	$-0.0449621\pi$
$588$		0			0
$589$	504.097	+	873.122i	0.855852	+	1.48238i
$590$	−38.5662	−	143.931i	−0.0653664	−	0.243951i
$591$		0			0
$592$	−895.818	−	2525.78i	−1.51321	−	4.26652i
$593$	−123.526			−0.208307			−0.104153	−	0.994561i	$-0.533213\pi$
$593$	−123.526			−0.208307			−0.104153	+	0.994561i	$0.533213\pi$
$594$		0			0
$595$	−507.078	+	292.761i	−0.852231	+	0.492036i
$596$	179.041	−	103.370i	0.300405	−	0.173439i
$597$		0			0
$598$	65.8597	−	65.8597i	0.110133	−	0.110133i
$599$	−590.899	−	1023.47i	−0.986475	−	1.70862i	−0.635189	−	0.772357i	$-0.719078\pi$
$599$	−590.899	−	1023.47i	−0.986475	−	1.70862i	−0.351286	−	0.936268i	$-0.614255\pi$
$600$		0			0
$601$	465.530	−	806.321i	0.774592	−	1.34163i	−0.160432	−	0.987047i	$-0.551289\pi$
$601$	465.530	−	806.321i	0.774592	−	1.34163i	0.935024	−	0.354586i	$-0.115378\pi$
$602$	1129.03			1.87546
$603$		0			0
$604$	373.722	−	647.306i	0.618745	−	1.07170i
$605$	−273.432	−	73.2659i	−0.451954	−	0.121101i
$606$		0			0
$607$	−280.846	+	75.2523i	−0.462678	+	0.123974i	−0.482626	−	0.875827i	$-0.660317\pi$
$607$	−280.846	+	75.2523i	−0.462678	+	0.123974i	0.0199474	+	0.999801i	$0.493650\pi$
$608$	2264.26	−	3921.82i	3.72412	−	6.45036i
$609$		0			0
$610$	276.766	−	1032.91i	0.453715	−	1.69329i
$611$	86.6328	+	23.2132i	0.141788	+	0.0379921i
$612$		0			0
$613$	771.729	+	445.558i	1.25894	+	0.726848i	0.972868	−	0.231360i	$-0.0743176\pi$
$613$	771.729	+	445.558i	1.25894	+	0.726848i	0.286070	+	0.958209i	$0.407651\pi$
$614$	−80.9054	−	301.943i	−0.131768	−	0.491764i
$615$		0			0
$616$	398.216	−	1486.16i	0.646455	−	2.41260i
$617$	381.058	+	220.004i	0.617598	+	0.356570i	0.775933	−	0.630815i	$-0.217279\pi$
$617$	381.058	+	220.004i	0.617598	+	0.356570i	−0.158335	+	0.987385i	$0.550613\pi$
$618$		0			0
$619$			765.578i			1.23680i	0.785864	+	0.618399i	$0.212219\pi$
$619$			765.578i			1.23680i	−0.785864	+	0.618399i	$0.787781\pi$
$620$	−1199.70	−	692.645i	−1.93500	−	1.11717i
$621$		0			0
$622$	1566.56	−	904.452i	2.51858	−	1.45410i
$623$	336.442	+	336.442i	0.540035	+	0.540035i
$624$		0			0
$625$	−24.3421	−	42.1618i	−0.0389474	−	0.0674588i
$626$	504.474	+	873.774i	0.805869	+	1.39581i
$627$		0			0
$628$		−	2070.10i		−	3.29634i
$629$	683.921	+	325.803i	1.08731	+	0.517969i
$630$		0			0
$631$	−295.766	+	79.2502i	−0.468725	+	0.125595i	−0.485448	−	0.874266i	$-0.661343\pi$
$631$	−295.766	+	79.2502i	−0.468725	+	0.125595i	0.0167225	+	0.999860i	$0.494677\pi$
$632$	−1435.85	+	828.991i	−2.27192	+	1.31169i
$633$		0			0
$634$	−420.060	−	112.555i	−0.662554	−	0.177531i
$635$	−229.057	+	229.057i	−0.360720	+	0.360720i
$636$		0			0
$637$	31.1504	−	31.1504i	0.0489017	−	0.0489017i
$638$	−345.345	+	598.156i	−0.541294	+	0.937548i
$639$		0			0
$640$			2524.34i			3.94428i
$641$	404.003	−	699.754i	0.630270	−	1.09166i	−0.357226	−	0.934018i	$-0.616277\pi$
$641$	404.003	−	699.754i	0.630270	−	1.09166i	0.987496	−	0.157642i	$-0.0503893\pi$
$642$		0			0
$643$	−834.417	−	834.417i	−1.29769	−	1.29769i	−0.929913	−	0.367781i	$-0.880118\pi$
$643$	−834.417	−	834.417i	−1.29769	−	1.29769i	−0.367781	−	0.929913i	$-0.619882\pi$
$644$	1561.29	−	418.345i	2.42436	−	0.649604i
$645$		0			0
$646$	571.721	+	2133.69i	0.885016	+	3.30293i
$647$	−311.878	+	1163.95i	−0.482038	+	1.79899i	0.111007	+	0.993820i	$0.464593\pi$
$647$	−311.878	+	1163.95i	−0.482038	+	1.79899i	−0.593044	+	0.805170i	$0.702074\pi$
$648$		0			0
$649$	−65.1348	+	17.4528i	−0.100362	+	0.0268919i
$650$	74.7401	+	43.1512i	0.114985	+	0.0663865i
$651$		0			0
$652$	−838.734	+	838.734i	−1.28640	+	1.28640i
$653$	55.4522	−	206.950i	0.0849192	−	0.316923i	−0.910380	−	0.413774i	$-0.864210\pi$
$653$	55.4522	−	206.950i	0.0849192	−	0.316923i	0.995299	+	0.0968512i	$0.0308771\pi$
$654$		0			0
$655$	438.882			0.670049
$656$			1727.42i			2.63326i
$657$		0			0
$658$	1479.65	+	1479.65i	2.24871	+	2.24871i
$659$	720.838	−	416.176i	1.09384	−	0.631526i	0.159241	−	0.987240i	$-0.449095\pi$
$659$	720.838	−	416.176i	1.09384	−	0.631526i	0.934595	+	0.355713i	$0.115762\pi$
$660$		0			0
$661$	209.041	−	780.150i	0.316249	−	1.18026i	−0.606572	−	0.795028i	$-0.707456\pi$
$661$	209.041	−	780.150i	0.316249	−	1.18026i	0.922821	−	0.385229i	$-0.125877\pi$
$662$	−1116.29	−	1933.48i	−1.68625	−	2.92066i
$663$		0			0
$664$	−571.575	−	2133.15i	−0.860805	−	3.21257i
$665$			780.807i			1.17415i
$666$		0			0
$667$	−475.699			−0.713192
$668$	−1267.59	+	339.650i	−1.89759	+	0.508459i
$669$		0			0
$670$	838.154	−	483.909i	1.25098	−	0.722252i
$671$	−467.433	−	125.248i	−0.696621	−	0.186659i
$672$		0			0
$673$	−314.895	−	545.413i	−0.467897	−	0.810421i	0.531430	−	0.847102i	$-0.321655\pi$
$673$	−314.895	−	545.413i	−0.467897	−	0.810421i	−0.999327	+	0.0366809i	$0.988321\pi$
$674$	1123.20	−	1123.20i	1.66647	−	1.66647i
$675$		0			0
$676$	−1936.67			−2.86490
$677$		−	136.913i		−	0.202236i	−0.994874	−	0.101118i	$-0.967758\pi$
$677$		−	136.913i		−	0.202236i	0.994874	−	0.101118i	$-0.0322419\pi$
$678$		0			0
$679$	599.534	+	160.645i	0.882966	+	0.236590i
$680$	−1407.03	−	1407.03i	−2.06916	−	2.06916i
$681$		0			0
$682$	−421.407	+	729.898i	−0.617898	+	1.07023i
$683$	−54.7903	−	204.480i	−0.0802200	−	0.299385i	0.914146	−	0.405385i	$-0.132862\pi$
$683$	−54.7903	−	204.480i	−0.0802200	−	0.299385i	−0.994366	+	0.106000i	$0.966196\pi$
$684$		0			0
$685$	477.375	+	127.912i	0.696898	+	0.186733i
$686$	−662.983	+	177.646i	−0.966448	+	0.258959i
$687$		0			0
$688$	605.009	+	2257.93i	0.879374	+	3.28187i
$689$	−63.1857	+	63.1857i	−0.0917064	+	0.0917064i
$690$		0			0
$691$	−814.501	−	470.252i	−1.17873	−	0.680539i	−0.223008	−	0.974817i	$-0.571588\pi$
$691$	−814.501	−	470.252i	−1.17873	−	0.680539i	−0.955720	+	0.294278i	$0.904921\pi$
$692$	147.633			0.213342
$693$		0			0
$694$	−738.811	−	426.553i	−1.06457	−	0.614629i
$695$	61.2540	+	61.2540i	0.0881353	+	0.0881353i
$696$		0			0
$697$	−345.283	−	345.283i	−0.495384	−	0.495384i
$698$	−461.099	+	1720.85i	−0.660601	+	2.46540i
$699$		0			0
$700$	748.853	+	1297.05i	1.06979	+	1.85293i
$701$	−30.6462	−	114.373i	−0.0437178	−	0.163157i	0.940616	−	0.339473i	$-0.110249\pi$
$701$	−30.6462	−	114.373i	−0.0437178	−	0.163157i	−0.984334	+	0.176316i	$0.943582\pi$
$702$		0			0
$703$	832.269	−	572.603i	1.18388	−	0.814514i
$704$	2112.18			3.00026
$705$		0			0
$706$	80.1900	−	46.2977i	0.113584	−	0.0655775i
$707$	−128.965	+	74.4582i	−0.182412	+	0.105316i
$708$		0			0
$709$	−468.226	+	468.226i	−0.660404	+	0.660404i	−0.955475	−	0.295071i	$-0.904657\pi$
$709$	−468.226	+	468.226i	−0.660404	+	0.660404i	0.295071	+	0.955475i	$0.404657\pi$
$710$	318.122	+	551.003i	0.448059	+	0.776061i
$711$		0			0
$712$	−808.478	+	1400.32i	−1.13550	+	1.96675i
$713$	−580.470			−0.814124
$714$		0			0
$715$	−13.9883	+	24.2285i	−0.0195641	+	0.0338860i
$716$	1237.23	+	331.515i	1.72797	+	0.463009i
$717$		0			0
$718$	−4.08481	+	1.09452i	−0.00568915	+	0.00152440i
$719$	515.544	−	892.949i	0.717030	−	1.24193i	−0.245142	−	0.969487i	$-0.578834\pi$
$719$	515.544	−	892.949i	0.717030	−	1.24193i	0.962171	−	0.272445i	$-0.0878322\pi$
$720$		0			0
$721$	352.070	−	1313.94i	0.488307	−	1.82239i
$722$	1467.45	+	393.202i	2.03248	+	0.544601i
$723$		0			0
$724$	1250.95	+	722.238i	1.72783	+	0.997566i
$725$	−114.082	−	425.759i	−0.157354	−	0.587254i
$726$		0			0
$727$	180.254	−	672.718i	0.247943	−	0.925334i	−0.723939	−	0.689864i	$-0.757670\pi$
$727$	180.254	−	672.718i	0.247943	−	0.925334i	0.971882	−	0.235470i	$-0.0756630\pi$
$728$	345.888	+	199.699i	0.475121	+	0.274311i
$729$		0			0
$730$			487.576i			0.667912i
$731$	−572.253	−	330.391i	−0.782836	−	0.451971i
$732$		0			0
$733$	−106.774	+	61.6460i	−0.145667	+	0.0841009i	−0.571062	−	0.820907i	$-0.693468\pi$
$733$	−106.774	+	61.6460i	−0.145667	+	0.0841009i	0.425395	+	0.905008i	$0.360135\pi$
$734$	−91.6437	−	91.6437i	−0.124855	−	0.124855i
$735$		0			0
$736$	1303.66	+	2258.00i	1.77127	+	3.06793i
$737$	−218.989	−	379.300i	−0.297136	−	0.514654i
$738$		0			0
$739$		−	104.123i		−	0.140897i	−0.997515	−	0.0704487i	$-0.977557\pi$
$739$		−	104.123i		−	0.140897i	0.997515	−	0.0704487i	$-0.0224431\pi$
$740$	−596.969	+	1253.15i	−0.806714	+	1.69345i
$741$		0			0
$742$	−2013.78	+	539.592i	−2.71399	+	0.727213i
$743$	86.0318	−	49.6705i	0.115790	−	0.0668512i	−0.440987	−	0.897514i	$-0.645371\pi$
$743$	86.0318	−	49.6705i	0.115790	−	0.0668512i	0.556776	+	0.830662i	$0.312038\pi$
$744$		0			0
$745$	−55.5402	−	14.8820i	−0.0745507	−	0.0199758i
$746$	1542.08	−	1542.08i	2.06713	−	2.06713i
$747$		0			0
$748$	−971.244	+	971.244i	−1.29845	+	1.29845i
$749$	−373.370	+	646.696i	−0.498492	+	0.863413i
$750$		0			0
$751$		−	969.097i		−	1.29041i	−0.764010	−	0.645205i	$-0.776772\pi$
$751$		−	969.097i		−	1.29041i	0.764010	−	0.645205i	$-0.223228\pi$
$752$	−2166.23	+	3752.03i	−2.88063	+	4.98940i
$753$		0			0
$754$	−126.780	−	126.780i	−0.168143	−	0.168143i
$755$	−200.800	+	53.8042i	−0.265960	+	0.0712639i
$756$		0			0
$757$	−6.84610	−	25.5500i	−0.00904372	−	0.0337516i	0.961257	−	0.275655i	$-0.0888949\pi$
$757$	−6.84610	−	25.5500i	−0.00904372	−	0.0337516i	−0.970300	+	0.241904i	$0.922228\pi$
$758$	153.993	−	574.708i	0.203156	−	0.758190i
$759$		0			0
$760$	−2563.07	+	686.774i	−3.37247	+	0.903650i
$761$	−437.202	−	252.419i	−0.574510	−	0.331694i	0.184438	−	0.982844i	$-0.440953\pi$
$761$	−437.202	−	252.419i	−0.574510	−	0.331694i	−0.758949	+	0.651150i	$0.774287\pi$
$762$		0			0
$763$	544.922	−	544.922i	0.714184	−	0.714184i
$764$	250.719	−	935.695i	0.328166	−	1.22473i
$765$		0			0
$766$	−1931.57			−2.52163
$767$		−	17.5046i		−	0.0228221i
$768$		0			0
$769$	−914.097	−	914.097i	−1.18868	−	1.18868i	−0.977432	−	0.211251i	$-0.932246\pi$
$769$	−914.097	−	914.097i	−1.18868	−	1.18868i	−0.211251	−	0.977432i	$-0.567754\pi$
$770$	−565.278	+	326.363i	−0.734127	+	0.423848i
$771$		0			0
$772$	−572.349	+	2136.03i	−0.741384	+	2.76688i
$773$	365.202	+	632.548i	0.472447	+	0.818302i	0.999503	−	0.0315283i	$-0.0100374\pi$
$773$	365.202	+	632.548i	0.472447	+	0.818302i	−0.527056	+	0.849831i	$0.676704\pi$
$774$		0			0
$775$	−139.208	−	519.532i	−0.179623	−	0.670363i
$776$			2109.33i			2.71820i
$777$		0			0
$778$	989.398			1.27172
$779$	−628.975	+	168.533i	−0.807414	+	0.216346i
$780$		0			0
$781$	249.352	−	143.963i	0.319273	−	0.184332i
$782$	−1228.48	−	329.170i	−1.57094	−	0.420933i
$783$		0			0
$784$	1064.01	+	1842.92i	1.35715	+	2.35066i
$785$	−407.116	+	407.116i	−0.518619	+	0.518619i
$786$		0			0
$787$	799.741			1.01619			0.508095	−	0.861301i	$-0.330350\pi$
$787$	799.741			1.01619			0.508095	+	0.861301i	$0.330350\pi$
$788$		−	1928.87i		−	2.44781i
$789$		0			0
$790$	679.410	+	182.047i	0.860013	+	0.230440i
$791$	−474.954	−	474.954i	−0.600447	−	0.600447i
$792$		0			0
$793$	62.8098	−	108.790i	0.0792054	−	0.137188i
$794$	691.711	+	2581.50i	0.871172	+	3.25126i
$795$		0			0
$796$	714.335	+	191.406i	0.897406	+	0.240459i
$797$	−348.317	+	93.3312i	−0.437035	+	0.117103i	−0.470627	−	0.882333i	$-0.655972\pi$
$797$	−348.317	+	93.3312i	−0.437035	+	0.117103i	0.0335917	+	0.999436i	$0.489305\pi$
$798$		0			0
$799$	−316.974	−	1182.96i	−0.396713	−	1.48055i
$800$	−1708.31	+	1708.31i	−2.13539	+	2.13539i
$801$		0			0
$802$	2179.88	+	1258.55i	2.71805	+	1.56927i
$803$	220.649			0.274780
$804$		0			0
$805$	−389.323	−	224.776i	−0.483631	−	0.279225i
$806$	−154.703	−	154.703i	−0.191939	−	0.191939i
$807$		0			0
$808$	−357.850	−	357.850i	−0.442884	−	0.442884i
$809$	−172.656	+	644.362i	−0.213419	+	0.796492i	0.773298	+	0.634043i	$0.218606\pi$
$809$	−172.656	+	644.362i	−0.213419	+	0.796492i	−0.986717	+	0.162449i	$0.948061\pi$
$810$		0			0
$811$	48.3136	+	83.6817i	0.0595729	+	0.103183i	0.894274	−	0.447520i	$-0.147693\pi$
$811$	48.3136	+	83.6817i	0.0595729	+	0.103183i	−0.834701	+	0.550704i	$0.814359\pi$
$812$	−805.315	−	3005.48i	−0.991767	−	3.70133i
$813$		0			0
$814$	762.418	+	363.197i	0.936632	+	0.446188i
$815$	329.899			0.404784
$816$		0			0
$817$	−763.112	+	440.583i	−0.934042	+	0.539269i
$818$	−1219.24	+	703.926i	−1.49051	+	0.860545i
$819$		0			0
$820$	632.662	−	632.662i	0.771539	−	0.771539i
$821$	−236.138	−	409.003i	−0.287622	−	0.498176i	0.685619	−	0.727960i	$-0.259531\pi$
$821$	−236.138	−	409.003i	−0.287622	−	0.498176i	−0.973242	+	0.229784i	$0.926198\pi$
$822$		0			0
$823$	557.252	−	965.189i	0.677099	−	1.17277i	−0.298752	−	0.954331i	$-0.596570\pi$
$823$	557.252	−	965.189i	0.677099	−	1.17277i	0.975851	−	0.218439i	$-0.0700964\pi$
$824$	4622.81			5.61020
$825$		0			0
$826$	204.201	−	353.686i	0.247216	−	0.428191i
$827$	−873.241	−	233.984i	−1.05591	−	0.282931i	−0.311220	−	0.950338i	$-0.600738\pi$
$827$	−873.241	−	233.984i	−1.05591	−	0.282931i	−0.744694	+	0.667407i	$0.767404\pi$
$828$		0			0
$829$	900.504	−	241.289i	1.08625	−	0.291061i	0.329098	−	0.944296i	$-0.393255\pi$
$829$	900.504	−	241.289i	1.08625	−	0.291061i	0.757155	+	0.653235i	$0.226589\pi$
$830$	−468.441	+	811.364i	−0.564387	+	0.977547i
$831$		0			0
$832$	−141.909	+	529.611i	−0.170564	+	0.636552i
$833$	−581.047	−	155.691i	−0.697535	−	0.186904i
$834$		0			0
$835$	316.088	+	182.493i	0.378548	+	0.218555i
$836$	474.067	+	1769.24i	0.567066	+	2.11632i
$837$		0			0
$838$	−515.698	+	1924.61i	−0.615391	+	2.29667i
$839$	907.669	+	524.043i	1.08185	+	0.624604i	0.931394	−	0.364013i	$-0.118594\pi$
$839$	907.669	+	524.043i	1.08185	+	0.624604i	0.150453	+	0.988617i	$0.451927\pi$
$840$		0			0
$841$			74.7214i			0.0888482i
$842$	2490.34	+	1437.80i	2.95764	+	1.70760i
$843$		0			0
$844$	−1412.15	+	815.303i	−1.67316	+	0.965998i
$845$	380.874	+	380.874i	0.450739	+	0.450739i
$846$		0			0
$847$	−387.929	−	671.912i	−0.458003	−	0.793285i
$848$	−2158.25	−	3738.19i	−2.54510	−	4.40824i
$849$		0			0
$850$		−	1178.45i		−	1.38641i
$851$	45.9187	+	579.822i	0.0539585	+	0.681342i
$852$		0			0
$853$	−1477.35	+	395.855i	−1.73195	+	0.464073i	−0.980630	−	0.195870i	$-0.937247\pi$
$853$	−1477.35	+	395.855i	−1.73195	+	0.464073i	−0.751316	+	0.659943i	$0.770580\pi$
$854$	2538.19	−	1465.42i	2.97212	−	1.71595i
$855$		0			0
$856$	−2451.25	−	656.809i	−2.86361	−	0.767301i
$857$	782.483	−	782.483i	0.913049	−	0.913049i	−0.0834623	−	0.996511i	$-0.526598\pi$
$857$	782.483	−	782.483i	0.913049	−	0.913049i	0.996511	+	0.0834623i	$0.0265978\pi$
$858$		0			0
$859$	165.015	−	165.015i	0.192101	−	0.192101i	−0.604502	−	0.796603i	$-0.706628\pi$
$859$	165.015	−	165.015i	0.192101	−	0.192101i	0.796603	+	0.604502i	$0.206628\pi$
$860$	605.375	−	1048.54i	0.703925	−	1.21923i
$861$		0			0
$862$			284.582i			0.330141i
$863$	408.922	−	708.274i	0.473838	−	0.820711i	−0.525714	−	0.850662i	$-0.676202\pi$
$863$	408.922	−	708.274i	0.473838	−	0.820711i	0.999551	+	0.0299506i	$0.00953500\pi$
$864$		0			0
$865$	−29.0341	−	29.0341i	−0.0335654	−	0.0335654i
$866$	−2329.77	+	624.260i	−2.69026	+	0.720854i
$867$		0			0
$868$	−982.683	−	3667.42i	−1.13212	−	4.22514i
$869$	82.3841	−	307.462i	0.0948033	−	0.353811i
$870$		0			0
$871$	109.819	−	29.4260i	0.126084	−	0.0337841i
$872$	2268.06	+	1309.46i	2.60098	+	1.50168i
$873$		0			0
$874$	−1199.25	+	1199.25i	−1.37214	+	1.37214i
$875$	292.851	−	1092.94i	0.334687	−	1.24907i
$876$		0			0
$877$	−248.750			−0.283638			−0.141819	−	0.989893i	$-0.545295\pi$
$877$	−248.750			−0.283638			−0.141819	+	0.989893i	$0.545295\pi$
$878$			527.956i			0.601317i
$879$		0			0
$880$	−955.604	−	955.604i	−1.08591	−	1.08591i
$881$	−260.672	+	150.499i	−0.295882	+	0.170828i	−0.640592	−	0.767882i	$-0.721311\pi$
$881$	−260.672	+	150.499i	−0.295882	+	0.170828i	0.344709	+	0.938709i	$0.387977\pi$
$882$		0			0
$883$	−339.376	+	1266.57i	−0.384344	+	1.43439i	0.454854	+	0.890566i	$0.349692\pi$
$883$	−339.376	+	1266.57i	−0.384344	+	1.43439i	−0.839198	+	0.543826i	$0.816975\pi$
$884$	−178.277	−	308.785i	−0.201671	−	0.349304i
$885$		0			0
$886$	308.586	+	1151.66i	0.348291	+	1.29984i
$887$		−	1196.69i		−	1.34915i	−0.738208	−	0.674573i	$-0.764328\pi$
$887$		−	1196.69i		−	1.34915i	0.738208	−	0.674573i	$-0.235672\pi$
$888$		0			0
$889$	−887.840			−0.998696
$890$	662.598	−	177.543i	0.744493	−	0.199486i
$891$		0			0
$892$	1899.76	−	1096.83i	2.12978	−	1.22963i
$893$	−1577.51	−	422.691i	−1.76652	−	0.473339i
$894$		0			0
$895$	−178.122	−	308.516i	−0.199019	−	0.344711i
$896$	−4892.25	+	4892.25i	−5.46010	+	5.46010i
$897$		0			0
$898$	3530.37			3.93137
$899$			1117.41i			1.24294i
$900$		0			0
$901$	1178.60	+	315.805i	1.30810	+	0.350505i
$902$	−384.913	−	384.913i	−0.426732	−	0.426732i
$903$		0			0
$904$	1141.33	−	1976.84i	1.26253	−	2.18677i
$905$	−103.979	−	388.057i	−0.114894	−	0.428792i
$906$		0			0
$907$	834.053	+	223.484i	0.919573	+	0.246399i	0.687403	−	0.726276i	$-0.258751\pi$
$907$	834.053	+	223.484i	0.919573	+	0.246399i	0.232170	+	0.972675i	$0.425417\pi$
$908$	−4461.49	+	1195.45i	−4.91353	+	1.31658i
$909$		0			0
$910$	−43.8540	−	163.666i	−0.0481913	−	0.179852i
$911$	227.768	−	227.768i	0.250020	−	0.250020i	−0.570959	−	0.820979i	$-0.693428\pi$
$911$	227.768	−	227.768i	0.250020	−	0.250020i	0.820979	+	0.570959i	$0.193428\pi$
$912$		0			0
$913$	367.176	+	211.989i	0.402165	+	0.232190i
$914$	1058.39			1.15797
$915$		0			0
$916$	−1481.67	−	855.442i	−1.61754	−	0.933889i
$917$	850.569	+	850.569i	0.927556	+	0.927556i
$918$		0			0
$919$	851.550	+	851.550i	0.926606	+	0.926606i	0.997485	−	0.0708794i	$-0.0225805\pi$
$919$	851.550	+	851.550i	0.926606	+	0.926606i	−0.0708794	+	0.997485i	$0.522581\pi$
$920$	395.412	−	1475.70i	0.429795	−	1.60402i
$921$		0			0
$922$	−707.554	−	1225.52i	−0.767412	−	1.32920i
$923$	19.3446	+	72.1952i	0.0209584	+	0.0782180i
$924$		0			0
$925$	−507.939	+	180.151i	−0.549124	+	0.194758i
$926$	767.894			0.829259
$927$		0			0
$928$	4346.65	−	2509.54i	4.68389	−	2.70425i
$929$	−199.308	+	115.071i	−0.214541	+	0.123865i	−0.603420	−	0.797424i	$-0.706196\pi$
$929$	−199.308	+	115.071i	−0.214541	+	0.123865i	0.388879	+	0.921289i	$0.372862\pi$
$930$		0			0
$931$	−567.221	+	567.221i	−0.609260	+	0.609260i
$932$	1568.90	+	2717.41i	1.68337	+	2.91568i
$933$		0			0
$934$	191.519	−	331.721i	0.205053	−	0.355162i
$935$	382.019			0.408576
$936$		0			0
$937$	69.0112	−	119.531i	0.0736513	−	0.127568i	−0.826848	−	0.562426i	$-0.809868\pi$
$937$	69.0112	−	119.531i	0.0736513	−	0.127568i	0.900499	+	0.434858i	$0.143201\pi$
$938$	2562.20	+	686.540i	2.73156	+	0.731919i
$939$		0			0
$940$	2167.54	−	580.792i	2.30590	−	0.617863i
$941$	727.171	−	1259.50i	0.772765	−	1.33847i	−0.163278	−	0.986580i	$-0.552207\pi$
$941$	727.171	−	1259.50i	0.772765	−	1.33847i	0.936042	−	0.351887i	$-0.114460\pi$
$942$		0			0
$943$	97.0336	−	362.134i	0.102899	−	0.384024i
$944$	816.756	+	218.849i	0.865208	+	0.231832i
$945$		0			0
$946$	−637.934	−	368.311i	−0.674349	−	0.389335i
$947$	−359.108	−	1340.21i	−0.379206	−	1.41521i	−0.847102	−	0.531431i	$-0.821655\pi$
$947$	−359.108	−	1340.21i	−0.379206	−	1.41521i	0.467896	−	0.883783i	$-0.345012\pi$
$948$		0			0
$949$	−14.8245	+	55.3257i	−0.0156212	+	0.0582990i
$950$	−1360.95	−	785.746i	−1.43258	−	0.827101i
$951$		0			0
$952$		−	5453.73i		−	5.72871i
$953$	−567.577	−	327.691i	−0.595569	−	0.343852i	0.171728	−	0.985144i	$-0.445065\pi$
$953$	−567.577	−	327.691i	−0.595569	−	0.343852i	−0.767296	+	0.641293i	$0.778398\pi$
$954$		0			0
$955$	−233.326	+	134.711i	−0.244320	+	0.141058i
$956$	−3639.22	−	3639.22i	−3.80671	−	3.80671i
$957$		0			0
$958$	83.5061	+	144.637i	0.0871671	+	0.150978i
$959$	677.271	+	1173.07i	0.706227	+	1.22322i
$960$		0			0
$961$			402.511i			0.418846i
$962$	−142.292	+	166.768i	−0.147913	+	0.173356i
$963$		0			0
$964$	75.8452	−	20.3227i	0.0786776	−	0.0210816i
$965$	532.643	−	307.522i	0.551962	−	0.318675i
$966$		0			0
$967$	870.300	+	233.196i	0.900000	+	0.241154i	0.679016	−	0.734123i	$-0.262407\pi$
$967$	870.300	+	233.196i	0.900000	+	0.241154i	0.220984	+	0.975277i	$0.429073\pi$
$968$	1864.41	−	1864.41i	1.92604	−	1.92604i
$969$		0			0
$970$	632.757	−	632.757i	0.652327	−	0.652327i
$971$	267.203	−	462.808i	0.275183	−	0.476631i	−0.694998	−	0.719011i	$-0.744595\pi$
$971$	267.203	−	462.808i	0.275183	−	0.476631i	0.970181	+	0.242381i	$0.0779283\pi$
$972$		0			0
$973$			237.425i			0.244013i
$974$	−35.5074	+	61.5006i	−0.0364552	+	0.0631423i
$975$		0			0
$976$	4290.81	+	4290.81i	4.39633	+	4.39633i
$977$	1461.26	−	391.545i	1.49567	−	0.400762i	0.584020	−	0.811740i	$-0.301479\pi$
$977$	1461.26	−	391.545i	1.49567	−	0.400762i	0.911646	+	0.410977i	$0.134812\pi$
$978$		0			0
$979$	−80.3455	−	299.854i	−0.0820690	−	0.306286i
$980$	285.273	−	1064.65i	0.291095	−	1.08638i
$981$		0			0
$982$	−2158.67	+	578.413i	−2.19824	+	0.589016i
$983$	−310.433	−	179.229i	−0.315802	−	0.182328i	0.333718	−	0.942673i	$-0.391697\pi$
$983$	−310.433	−	179.229i	−0.315802	−	0.182328i	−0.649520	+	0.760345i	$0.725030\pi$
$984$		0			0
$985$	−379.341	+	379.341i	−0.385118	+	0.385118i
$986$	−633.652	+	2364.82i	−0.642649	+	2.39840i
$987$		0			0
$988$	−475.473			−0.481248
$989$		−	507.334i		−	0.512976i
$990$		0			0
$991$	147.397	+	147.397i	0.148735	+	0.148735i	0.777553	−	0.628818i	$-0.216461\pi$
$991$	147.397	+	147.397i	0.148735	+	0.148735i	−0.628818	+	0.777553i	$0.716461\pi$
$992$	5303.99	−	3062.26i	5.34676	−	3.08695i
$993$		0			0
$994$	−451.332	+	1684.39i	−0.454056	+	1.69456i
$995$	−102.842	−	178.127i	−0.103359	−	0.179022i
$996$		0			0
$997$	−209.412	−	781.537i	−0.210042	−	0.783888i	−0.987853	−	0.155390i	$-0.950337\pi$
$997$	−209.412	−	781.537i	−0.210042	−	0.783888i	0.777811	−	0.628498i	$-0.216330\pi$
$998$			3705.81i			3.71323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bb.b.199.6		24
3.2	odd	2		111.3.l.b.88.1	yes	24
37.8	odd	12	inner	333.3.bb.b.82.6		24
111.8	even	12		111.3.l.b.82.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.l.b.82.1	✓	24	111.8	even	12
111.3.l.b.88.1	yes	24	3.2	odd	2
333.3.bb.b.82.6		24	37.8	odd	12	inner
333.3.bb.b.199.6		24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.81682 - 1.02271i) q^{2} +(10.0581 - 5.80704i) q^{4} +(-3.12011 - 0.836031i) q^{5} +(-4.42663 - 7.66714i) q^{7} +(21.2746 - 21.2746i) q^{8} +O(q^{10})\)	\(q+(3.81682 - 1.02271i) q^{2} +(10.0581 - 5.80704i) q^{4} +(-3.12011 - 0.836031i) q^{5} +(-4.42663 - 7.66714i) q^{7} +(21.2746 - 21.2746i) q^{8} -12.7639 q^{10} +5.77622i q^{11} +(-1.44834 - 0.388081i) q^{13} +(-24.7369 - 24.7369i) q^{14} +(36.2154 - 62.7268i) q^{16} +(5.29921 + 19.7769i) q^{17} +(26.3729 + 7.06661i) q^{19} +(-36.2373 + 9.70974i) q^{20} +(5.90742 + 22.0468i) q^{22} +(-11.1157 + 11.1157i) q^{23} +(-12.6145 - 7.28298i) q^{25} -5.92494 q^{26} +(-89.0469 - 51.4112i) q^{28} +(21.3977 + 21.3977i) q^{29} +(26.1105 + 26.1105i) q^{31} +(42.9278 - 160.209i) q^{32} +(40.4523 + 70.0654i) q^{34} +(7.40160 + 27.6231i) q^{35} +(24.0158 - 28.1468i) q^{37} +107.888 q^{38} +(-84.1654 + 48.5929i) q^{40} +(-20.6541 + 11.9246i) q^{41} +(-22.8207 + 22.8207i) q^{43} +(33.5428 + 58.0978i) q^{44} +(-31.0584 + 53.7947i) q^{46} -59.8153 q^{47} +(-14.6900 + 25.4439i) q^{49} +(-55.5957 - 14.8968i) q^{50} +(-16.8211 + 4.50720i) q^{52} +(29.7974 - 51.6106i) q^{53} +(4.82910 - 18.0224i) q^{55} +(-257.290 - 68.9406i) q^{56} +(103.555 + 59.7874i) q^{58} +(3.02150 + 11.2764i) q^{59} +(-21.6834 + 80.9237i) q^{61} +(126.363 + 72.9554i) q^{62} -365.669i q^{64} +(4.19453 + 2.42171i) q^{65} +(-65.6658 + 37.9122i) q^{67} +(168.145 + 168.145i) q^{68} +(56.5012 + 97.8629i) q^{70} +(-24.9235 - 43.1687i) q^{71} -38.1995i q^{73} +(62.8779 - 131.993i) q^{74} +(306.298 - 82.0722i) q^{76} +(44.2871 - 25.5692i) q^{77} +(-53.2289 - 14.2626i) q^{79} +(-165.438 + 165.438i) q^{80} +(-66.6375 + 66.6375i) q^{82} +(36.7004 - 63.5669i) q^{83} -66.1365i q^{85} +(-63.7634 + 110.441i) q^{86} +(122.887 + 122.887i) q^{88} +(-51.9117 + 13.9097i) q^{89} +(3.43578 + 12.8225i) q^{91} +(-47.2533 + 176.352i) q^{92} +(-228.305 + 61.1740i) q^{94} +(-76.3786 - 44.0972i) q^{95} +(-49.5738 + 49.5738i) q^{97} +(-30.0474 + 112.139i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8}+O(q^{10}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8	\( 24 q + 4 q^{2} + 18 q^{4} - 8 q^{5} + 36 q^{8} - 60 q^{10} + 28 q^{13} - 42 q^{14} + 26 q^{16} - 10 q^{17} + 60 q^{19} + 4 q^{20} - 64 q^{22} - 34 q^{23} - 162 q^{25} + 44 q^{26} - 48 q^{28} - 32 q^{29} + 90 q^{32} + 46 q^{34} + 30 q^{35} + 80 q^{37} + 284 q^{38} - 144 q^{40} + 30 q^{41} + 130 q^{43} + 16 q^{44} + 78 q^{46} + 56 q^{47} - 20 q^{49} - 70 q^{50} + 16 q^{52} + 190 q^{53} + 350 q^{55} - 376 q^{56} + 336 q^{58} + 258 q^{59} - 84 q^{61} + 474 q^{62} + 54 q^{65} - 372 q^{67} + 434 q^{68} + 102 q^{70} - 66 q^{71} + 416 q^{74} + 702 q^{76} - 198 q^{77} + 88 q^{79} - 900 q^{80} - 470 q^{82} - 166 q^{83} - 432 q^{86} + 530 q^{88} - 304 q^{89} + 524 q^{91} - 330 q^{92} - 344 q^{94} - 1080 q^{95} - 110 q^{97} - 926 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 18 * q^4 - 8 * q^5 + 36 * q^8 - 60 * q^10 + 28 * q^13 - 42 * q^14 + 26 * q^16 - 10 * q^17 + 60 * q^19 + 4 * q^20 - 64 * q^22 - 34 * q^23 - 162 * q^25 + 44 * q^26 - 48 * q^28 - 32 * q^29 + 90 * q^32 + 46 * q^34 + 30 * q^35 + 80 * q^37 + 284 * q^38 - 144 * q^40 + 30 * q^41 + 130 * q^43 + 16 * q^44 + 78 * q^46 + 56 * q^47 - 20 * q^49 - 70 * q^50 + 16 * q^52 + 190 * q^53 + 350 * q^55 - 376 * q^56 + 336 * q^58 + 258 * q^59 - 84 * q^61 + 474 * q^62 + 54 * q^65 - 372 * q^67 + 434 * q^68 + 102 * q^70 - 66 * q^71 + 416 * q^74 + 702 * q^76 - 198 * q^77 + 88 * q^79 - 900 * q^80 - 470 * q^82 - 166 * q^83 - 432 * q^86 + 530 * q^88 - 304 * q^89 + 524 * q^91 - 330 * q^92 - 344 * q^94 - 1080 * q^95 - 110 * q^97 - 926 * q^98

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