LMFDB - Embedded newform 220.3.p.a.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(41,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("220.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.p (of order $10$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} + 36 x^{13} + 396 x^{12} + 1918 x^{11} + 8573 x^{10} + 28624 x^{9} + \cdots + 121 $ x^16 - 2x^15 + 5x^14 + 36x^13 + 396x^12 + 1918x^11 + 8573x^10 + 28624x^9 + 80803x^8 + 170874x^7 + 284613x^6 + 345888x^5 + 305926x^4 + 174966x^3 + 69685x^2 + 4598*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5\cdot 11 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.4
Root			$-0.0370387 - 0.0269102i$ of defining polynomial
Character	$\chi$	$=$	220.41
Dual form			220.3.p.a.161.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.59415 + 4.90629i) q^{3} +(-1.80902 - 1.31433i) q^{5} +(-9.66012 - 3.13876i) q^{7} +(-14.2492 + 10.3527i) q^{9} +(-1.51124 + 10.8957i) q^{11} +(-1.96578 - 2.70567i) q^{13} +(3.56463 - 10.9708i) q^{15} +(-11.8653 + 16.3311i) q^{17} +(-5.26038 + 1.70920i) q^{19} -52.3990i q^{21} +34.6484 q^{23} +(1.54508 + 4.75528i) q^{25} +(-35.9469 - 26.1169i) q^{27} +(-42.6710 - 13.8647i) q^{29} +(35.0661 - 25.4770i) q^{31} +(-55.8666 + 9.95478i) q^{33} +(13.3500 + 18.3746i) q^{35} +(-18.3557 + 56.4930i) q^{37} +(10.1411 - 13.9580i) q^{39} +(31.4716 - 10.2257i) q^{41} +65.3574i q^{43} +39.3839 q^{45} +(21.2781 + 65.4871i) q^{47} +(43.8242 + 31.8401i) q^{49} +(-99.0403 - 32.1801i) q^{51} +(2.60431 - 1.89214i) q^{53} +(17.0544 - 17.7242i) q^{55} +(-16.7717 - 23.0842i) q^{57} +(20.4015 - 62.7894i) q^{59} +(-27.8545 + 38.3384i) q^{61} +(170.144 - 55.2831i) q^{63} +7.47829i q^{65} -31.6113 q^{67} +(55.2349 + 169.995i) q^{69} +(-3.04204 - 2.21017i) q^{71} +(21.3156 + 6.92587i) q^{73} +(-20.8677 + 15.1613i) q^{75} +(48.7978 - 100.510i) q^{77} +(-45.9740 - 63.2778i) q^{79} +(21.8480 - 67.2413i) q^{81} +(13.0450 - 17.9550i) q^{83} +(42.9289 - 13.9484i) q^{85} -231.459i q^{87} +68.2014 q^{89} +(10.4973 + 32.3072i) q^{91} +(180.898 + 131.430i) q^{93} +(11.7626 + 3.82189i) q^{95} +(-49.7040 + 36.1121i) q^{97} +(-91.2656 - 170.901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} - 20 q^{5} - 10 q^{7} - 19 q^{9} - 37 q^{11} + 35 q^{13} + 15 q^{15} + 55 q^{17} + 30 q^{19} + 72 q^{23} - 20 q^{25} - 25 q^{27} - 145 q^{29} - 80 q^{31} - 94 q^{33} + 44 q^{37} + 175 q^{39}+ \cdots - 70 q^{99}+O(q^{100}) $ 16 * q - q^3 - 20 * q^5 - 10 * q^7 - 19 * q^9 - 37 * q^11 + 35 * q^13 + 15 * q^15 + 55 * q^17 + 30 * q^19 + 72 * q^23 - 20 * q^25 - 25 * q^27 - 145 * q^29 - 80 * q^31 - 94 * q^33 + 44 * q^37 + 175 * q^39 + 35 * q^41 + 30 * q^45 + 2 * q^47 + 172 * q^49 - 460 * q^51 + 47 * q^53 + 85 * q^55 + 10 * q^57 + 98 * q^59 + 330 * q^61 + 90 * q^63 + 152 * q^67 - 317 * q^69 - 20 * q^71 - 495 * q^73 - 30 * q^75 - 204 * q^77 + 25 * q^79 + 57 * q^81 + 190 * q^83 - 25 * q^85 + 160 * q^89 - 119 * q^91 + 617 * q^93 - 90 * q^95 - 521 * q^97 - 70 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.59415	+	4.90629i	0.531384	+	1.63543i	0.751336	+	0.659920i	$0.229410\pi$
$3$	1.59415	+	4.90629i	0.531384	+	1.63543i	−0.219952	+	0.975511i	$0.570590\pi$
$4$		0			0
$5$	−1.80902	−	1.31433i	−0.361803	−	0.262866i
$5$	−1.80902	−	1.31433i	−0.361803	−	0.262866i
$6$		0			0
$7$	−9.66012	−	3.13876i	−1.38002	−	0.448395i	−0.477342	−	0.878718i	$-0.658400\pi$
$7$	−9.66012	−	3.13876i	−1.38002	−	0.448395i	−0.902675	+	0.430323i	$0.858400\pi$
$8$		0			0
$9$	−14.2492	+	10.3527i	−1.58325	+	1.15030i
$10$		0			0
$11$	−1.51124	+	10.8957i	−0.137386	+	0.990518i
$11$	−1.51124	+	10.8957i	−0.137386	+	0.990518i
$12$		0			0
$13$	−1.96578	−	2.70567i	−0.151214	−	0.208128i	0.726689	−	0.686967i	$-0.241058\pi$
$13$	−1.96578	−	2.70567i	−0.151214	−	0.208128i	−0.877903	+	0.478838i	$0.841058\pi$
$14$		0			0
$15$	3.56463	−	10.9708i	0.237642	−	0.731387i
$16$		0			0
$17$	−11.8653	+	16.3311i	−0.697956	+	0.960654i	0.302017	+	0.953303i	$0.402340\pi$
$17$	−11.8653	+	16.3311i	−0.697956	+	0.960654i	−0.999973	+	0.00735170i	$0.997660\pi$
$18$		0			0
$19$	−5.26038	+	1.70920i	−0.276862	+	0.0899579i	−0.444157	−	0.895949i	$-0.646497\pi$
$19$	−5.26038	+	1.70920i	−0.276862	+	0.0899579i	0.167295	+	0.985907i	$0.446497\pi$
$20$		0			0
$21$		−	52.3990i		−	2.49519i
$22$		0			0
$23$	34.6484			1.50645			0.753227	−	0.657761i	$-0.228496\pi$
$23$	34.6484			1.50645			0.753227	+	0.657761i	$0.228496\pi$
$24$		0			0
$25$	1.54508	+	4.75528i	0.0618034	+	0.190211i
$26$		0			0
$27$	−35.9469	−	26.1169i	−1.33137	−	0.967294i
$28$		0			0
$29$	−42.6710	−	13.8647i	−1.47142	−	0.478092i	−0.539880	−	0.841742i	$-0.681530\pi$
$29$	−42.6710	−	13.8647i	−1.47142	−	0.478092i	−0.931536	+	0.363650i	$0.881530\pi$
$30$		0			0
$31$	35.0661	−	25.4770i	1.13116	−	0.821838i	0.145299	−	0.989388i	$-0.453585\pi$
$31$	35.0661	−	25.4770i	1.13116	−	0.821838i	0.985864	+	0.167550i	$0.0535854\pi$
$32$		0			0
$33$	−55.8666	+	9.95478i	−1.69293	+	0.301660i
$34$		0			0
$35$	13.3500	+	18.3746i	0.381427	+	0.524989i
$36$		0			0
$37$	−18.3557	+	56.4930i	−0.496100	+	1.52684i	0.319136	+	0.947709i	$0.396607\pi$
$37$	−18.3557	+	56.4930i	−0.496100	+	1.52684i	−0.815236	+	0.579129i	$0.803393\pi$
$38$		0			0
$39$	10.1411	−	13.9580i	0.260027	−	0.357896i
$40$		0			0
$41$	31.4716	−	10.2257i	0.767599	−	0.249408i	0.101062	−	0.994880i	$-0.467776\pi$
$41$	31.4716	−	10.2257i	0.767599	−	0.249408i	0.666537	+	0.745472i	$0.267776\pi$
$42$		0			0
$43$			65.3574i			1.51994i	0.649958	+	0.759970i	$0.274787\pi$
$43$			65.3574i			1.51994i	−0.649958	+	0.759970i	$0.725213\pi$
$44$		0			0
$45$	39.3839			0.875199
$46$		0			0
$47$	21.2781	+	65.4871i	0.452725	+	1.39334i	0.873786	+	0.486311i	$0.161658\pi$
$47$	21.2781	+	65.4871i	0.452725	+	1.39334i	−0.421061	+	0.907032i	$0.638342\pi$
$48$		0			0
$49$	43.8242	+	31.8401i	0.894371	+	0.649798i
$50$		0			0
$51$	−99.0403	−	32.1801i	−1.94197	−	0.630983i
$52$		0			0
$53$	2.60431	−	1.89214i	0.0491380	−	0.0357008i	−0.562945	−	0.826494i	$-0.690332\pi$
$53$	2.60431	−	1.89214i	0.0491380	−	0.0357008i	0.612083	+	0.790793i	$0.290332\pi$
$54$		0			0
$55$	17.0544	−	17.7242i	0.310080	−	0.322259i
$56$		0			0
$57$	−16.7717	−	23.0842i	−0.294240	−	0.404986i
$58$		0			0
$59$	20.4015	−	62.7894i	0.345788	−	1.06423i	−0.615372	−	0.788237i	$-0.710994\pi$
$59$	20.4015	−	62.7894i	0.345788	−	1.06423i	0.961160	−	0.275991i	$-0.0890058\pi$
$60$		0			0
$61$	−27.8545	+	38.3384i	−0.456631	+	0.628499i	−0.973806	−	0.227381i	$-0.926984\pi$
$61$	−27.8545	+	38.3384i	−0.456631	+	0.628499i	0.517175	+	0.855880i	$0.326984\pi$
$62$		0			0
$63$	170.144	−	55.2831i	2.70070	−	0.877510i
$64$		0			0
$65$			7.47829i			0.115051i
$66$		0			0
$67$	−31.6113			−0.471810			−0.235905	−	0.971776i	$-0.575805\pi$
$67$	−31.6113			−0.471810			−0.235905	+	0.971776i	$0.575805\pi$
$68$		0			0
$69$	55.2349	+	169.995i	0.800505	+	2.46370i
$70$		0			0
$71$	−3.04204	−	2.21017i	−0.0428456	−	0.0311292i	0.566156	−	0.824298i	$-0.308430\pi$
$71$	−3.04204	−	2.21017i	−0.0428456	−	0.0311292i	−0.609002	+	0.793169i	$0.708430\pi$
$72$		0			0
$73$	21.3156	+	6.92587i	0.291995	+	0.0948749i	0.451352	−	0.892346i	$-0.350942\pi$
$73$	21.3156	+	6.92587i	0.291995	+	0.0948749i	−0.159357	+	0.987221i	$0.550942\pi$
$74$		0			0
$75$	−20.8677	+	15.1613i	−0.278236	+	0.202150i
$76$		0			0
$77$	48.7978	−	100.510i	0.633737	−	1.30533i
$78$		0			0
$79$	−45.9740	−	63.2778i	−0.581949	−	0.800984i	0.411958	−	0.911203i	$-0.364845\pi$
$79$	−45.9740	−	63.2778i	−0.581949	−	0.800984i	−0.993907	+	0.110218i	$0.964845\pi$
$80$		0			0
$81$	21.8480	−	67.2413i	0.269729	−	0.830140i
$82$		0			0
$83$	13.0450	−	17.9550i	0.157169	−	0.216325i	−0.723169	−	0.690671i	$-0.757315\pi$
$83$	13.0450	−	17.9550i	0.157169	−	0.216325i	0.880339	+	0.474346i	$0.157315\pi$
$84$		0			0
$85$	42.9289	−	13.9484i	0.505046	−	0.164099i
$86$		0			0
$87$		−	231.459i		−	2.66045i
$88$		0			0
$89$	68.2014			0.766308			0.383154	−	0.923684i	$-0.374838\pi$
$89$	68.2014			0.766308			0.383154	+	0.923684i	$0.374838\pi$
$90$		0			0
$91$	10.4973	+	32.3072i	0.115354	+	0.355024i
$92$		0			0
$93$	180.898	+	131.430i	1.94514	+	1.41323i
$94$		0			0
$95$	11.7626	+	3.82189i	0.123816	+	0.0402304i
$96$		0			0
$97$	−49.7040	+	36.1121i	−0.512412	+	0.372289i	−0.813738	−	0.581232i	$-0.802571\pi$
$97$	−49.7040	+	36.1121i	−0.512412	+	0.372289i	0.301326	+	0.953521i	$0.402571\pi$
$98$		0			0
$99$	−91.2656	−	170.901i	−0.921875	−	1.72627i
$100$		0			0
$101$	−4.39224	−	6.04540i	−0.0434875	−	0.0598554i	0.786719	−	0.617311i	$-0.211778\pi$
$101$	−4.39224	−	6.04540i	−0.0434875	−	0.0598554i	−0.830207	+	0.557455i	$0.811778\pi$
$102$		0			0
$103$	−25.5387	+	78.6000i	−0.247948	+	0.763107i	0.747189	+	0.664612i	$0.231403\pi$
$103$	−25.5387	+	78.6000i	−0.247948	+	0.763107i	−0.995138	+	0.0984954i	$0.968597\pi$
$104$		0			0
$105$	−68.8695	+	94.7907i	−0.655900	+	0.902769i
$106$		0			0
$107$	150.340	−	48.8485i	1.40505	−	0.456528i	0.494228	−	0.869332i	$-0.335451\pi$
$107$	150.340	−	48.8485i	1.40505	−	0.456528i	0.910820	+	0.412804i	$0.135451\pi$
$108$		0			0
$109$			79.1292i			0.725956i	0.931798	+	0.362978i	$0.118240\pi$
$109$			79.1292i			0.725956i	−0.931798	+	0.362978i	$0.881760\pi$
$110$		0			0
$111$	−306.433			−2.76066
$112$		0			0
$113$	8.72182	+	26.8430i	0.0771843	+	0.237549i	0.982203	−	0.187823i	$-0.0601432\pi$
$113$	8.72182	+	26.8430i	0.0771843	+	0.237549i	−0.905019	+	0.425372i	$0.860143\pi$
$114$		0			0
$115$	−62.6796	−	45.5394i	−0.545040	−	0.395995i
$116$		0			0
$117$	56.0219	+	18.2026i	0.478820	+	0.155578i
$118$		0			0
$119$	165.879	−	120.518i	1.39394	−	1.01276i
$120$		0			0
$121$	−116.432	−	32.9321i	−0.962250	−	0.272166i
$122$		0			0
$123$	100.341	+	138.107i	0.815780	+	1.12282i
$124$		0			0
$125$	3.45492	−	10.6331i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−54.6099	+	75.1641i	−0.429999	+	0.591844i	−0.967953	−	0.251131i	$-0.919198\pi$
$127$	−54.6099	+	75.1641i	−0.429999	+	0.591844i	0.537954	+	0.842974i	$0.319198\pi$
$128$		0			0
$129$	−320.663	+	104.190i	−2.48576	+	0.807672i
$130$		0			0
$131$			156.944i			1.19804i	0.800733	+	0.599021i	$0.204444\pi$
$131$			156.944i			1.19804i	−0.800733	+	0.599021i	$0.795556\pi$
$132$		0			0
$133$	56.1806			0.422411
$134$		0			0
$135$	30.7023	+	94.4919i	0.227424	+	0.699940i
$136$		0			0
$137$	−2.76854	−	2.01146i	−0.0202083	−	0.0146822i	0.577635	−	0.816295i	$-0.303976\pi$
$137$	−2.76854	−	2.01146i	−0.0202083	−	0.0146822i	−0.597844	+	0.801613i	$0.703976\pi$
$138$		0			0
$139$	−107.150	−	34.8152i	−0.770864	−	0.250469i	−0.102929	−	0.994689i	$-0.532821\pi$
$139$	−107.150	−	34.8152i	−0.770864	−	0.250469i	−0.667935	+	0.744220i	$0.732821\pi$
$140$		0			0
$141$	−287.379	+	208.793i	−2.03815	+	1.48080i
$142$		0			0
$143$	32.4509	−	17.3297i	0.226930	−	0.121186i
$144$		0			0
$145$	58.9699	+	81.1651i	0.406689	+	0.559760i
$146$		0			0
$147$	−86.3546	+	265.772i	−0.587447	+	1.80797i
$148$		0			0
$149$	78.4143	−	107.928i	0.526271	−	0.724349i	−0.460286	−	0.887771i	$-0.652253\pi$
$149$	78.4143	−	107.928i	0.526271	−	0.724349i	0.986556	+	0.163421i	$0.0522530\pi$
$150$		0			0
$151$	238.890	−	77.6202i	1.58206	−	0.514041i	0.619470	−	0.785020i	$-0.287347\pi$
$151$	238.890	−	77.6202i	1.58206	−	0.514041i	0.962585	+	0.270979i	$0.0873475\pi$
$152$		0			0
$153$		−	355.543i		−	2.32381i
$154$		0			0
$155$	−96.9202			−0.625292
$156$		0			0
$157$	−73.1074	−	225.002i	−0.465653	−	1.43313i	−0.858160	−	0.513382i	$-0.828392\pi$
$157$	−73.1074	−	225.002i	−0.465653	−	1.43313i	0.392508	−	0.919749i	$-0.371608\pi$
$158$		0			0
$159$	13.4351	+	9.76116i	0.0844974	+	0.0613909i
$160$		0			0
$161$	−334.708	−	108.753i	−2.07893	−	0.675486i
$162$		0			0
$163$	−159.980	+	116.232i	−0.981471	+	0.713081i	−0.958037	−	0.286645i	$-0.907460\pi$
$163$	−159.980	+	116.232i	−0.981471	+	0.713081i	−0.0234342	+	0.999725i	$0.507460\pi$
$164$		0			0
$165$	114.148	+	55.4187i	0.691803	+	0.335871i
$166$		0			0
$167$	−2.44891	−	3.37064i	−0.0146641	−	0.0201834i	0.801622	−	0.597831i	$-0.203971\pi$
$167$	−2.44891	−	3.37064i	−0.0146641	−	0.0201834i	−0.816286	+	0.577648i	$0.803971\pi$
$168$		0			0
$169$	48.7675	−	150.091i	0.288565	−	0.888113i
$170$		0			0
$171$	57.2616	−	78.8138i	0.334863	−	0.460900i
$172$		0			0
$173$	−210.476	+	68.3878i	−1.21662	+	0.395305i	−0.845852	−	0.533418i	$-0.820907\pi$
$173$	−210.476	+	68.3878i	−1.21662	+	0.395305i	−0.370773	+	0.928724i	$0.620907\pi$
$174$		0			0
$175$		−	50.7862i		−	0.290207i
$176$		0			0
$177$	340.586			1.92422
$178$		0			0
$179$	−7.44534	−	22.9144i	−0.0415941	−	0.128013i	0.928103	−	0.372323i	$-0.121439\pi$
$179$	−7.44534	−	22.9144i	−0.0415941	−	0.128013i	−0.969697	+	0.244310i	$0.921439\pi$
$180$		0			0
$181$	44.3948	+	32.2547i	0.245275	+	0.178203i	0.703630	−	0.710566i	$-0.251561\pi$
$181$	44.3948	+	32.2547i	0.245275	+	0.178203i	−0.458355	+	0.888769i	$0.651561\pi$
$182$		0			0
$183$	−232.504	−	75.5451i	−1.27051	−	0.412815i
$184$		0			0
$185$	107.456	−	78.0714i	0.580844	−	0.422008i
$186$		0			0
$187$	−160.008	−	153.960i	−0.855656	−	0.823318i
$188$		0			0
$189$	265.276	+	365.121i	1.40358	+	1.93186i
$190$		0			0
$191$	70.6739	−	217.512i	0.370020	−	1.13881i	−0.576757	−	0.816916i	$-0.695682\pi$
$191$	70.6739	−	217.512i	0.370020	−	1.13881i	0.946777	−	0.321890i	$-0.104318\pi$
$192$		0			0
$193$	82.5205	−	113.580i	0.427567	−	0.588496i	−0.539825	−	0.841777i	$-0.681510\pi$
$193$	82.5205	−	113.580i	0.427567	−	0.588496i	0.967393	+	0.253281i	$0.0815097\pi$
$194$		0			0
$195$	−36.6907	+	11.9215i	−0.188157	+	0.0611360i
$196$		0			0
$197$		−	301.867i		−	1.53232i	−0.642651	−	0.766159i	$-0.722166\pi$
$197$		−	301.867i		−	1.53232i	0.642651	−	0.766159i	$-0.277834\pi$
$198$		0			0
$199$	169.860			0.853570			0.426785	−	0.904353i	$-0.359646\pi$
$199$	169.860			0.853570			0.426785	+	0.904353i	$0.359646\pi$
$200$		0			0
$201$	−50.3932	−	155.094i	−0.250712	−	0.771613i
$202$		0			0
$203$	368.689	+	267.868i	1.81620	+	1.31955i
$204$		0			0
$205$	−70.3726	−	22.8654i	−0.343281	−	0.111539i
$206$		0			0
$207$	−493.714	+	358.704i	−2.38509	+	1.73287i
$208$		0			0
$209$	−10.6732	−	59.8985i	−0.0510680	−	0.286596i
$210$		0			0
$211$	51.1528	+	70.4058i	0.242430	+	0.333677i	0.912842	−	0.408312i	$-0.133883\pi$
$211$	51.1528	+	70.4058i	0.242430	+	0.333677i	−0.670412	+	0.741989i	$0.733883\pi$
$212$		0			0
$213$	5.99428	−	18.4485i	0.0281421	−	0.0866126i
$214$		0			0
$215$	85.9011	−	118.233i	0.399540	−	0.549920i
$216$		0			0
$217$	−418.708	+	136.047i	−1.92953	+	0.626943i
$218$		0			0
$219$			115.622i			0.527952i
$220$		0			0
$221$	67.5112			0.305480
$222$		0			0
$223$	−7.20191	−	22.1652i	−0.0322956	−	0.0993956i	0.933609	−	0.358293i	$-0.116641\pi$
$223$	−7.20191	−	22.1652i	−0.0322956	−	0.0993956i	−0.965905	+	0.258897i	$0.916641\pi$
$224$		0			0
$225$	−71.2462	−	51.7634i	−0.316650	−	0.230060i
$226$		0			0
$227$	375.447	+	121.990i	1.65395	+	0.537401i	0.979591	−	0.201003i	$-0.0644199\pi$
$227$	375.447	+	121.990i	1.65395	+	0.537401i	0.674359	+	0.738403i	$0.264420\pi$
$228$		0			0
$229$	−347.641	+	252.576i	−1.51808	+	1.10295i	−0.555655	+	0.831413i	$0.687532\pi$
$229$	−347.641	+	252.576i	−1.51808	+	1.10295i	−0.962428	+	0.271538i	$0.912468\pi$
$230$		0			0
$231$	570.924	+	79.1877i	2.47153	+	0.342804i
$232$		0			0
$233$	−70.5095	−	97.0480i	−0.302616	−	0.416515i	0.630445	−	0.776234i	$-0.282873\pi$
$233$	−70.5095	−	97.0480i	−0.302616	−	0.416515i	−0.933061	+	0.359719i	$0.882873\pi$
$234$		0			0
$235$	47.5792	−	146.434i	0.202465	−	0.623122i
$236$		0			0
$237$	237.170	−	326.436i	1.00072	−	1.37737i
$238$		0			0
$239$	−196.634	+	63.8903i	−0.822736	+	0.267323i	−0.689983	−	0.723826i	$-0.742382\pi$
$239$	−196.634	+	63.8903i	−0.822736	+	0.267323i	−0.132754	+	0.991149i	$0.542382\pi$
$240$		0			0
$241$			314.829i			1.30634i	0.757209	+	0.653172i	$0.226562\pi$
$241$			314.829i			1.30634i	−0.757209	+	0.653172i	$0.773438\pi$
$242$		0			0
$243$	−35.1603			−0.144693
$244$		0			0
$245$	−37.4303	−	115.199i	−0.152777	−	0.470199i
$246$		0			0
$247$	14.9653	+	10.8729i	0.0605883	+	0.0440199i
$248$		0			0
$249$	108.888	+	35.3799i	0.437302	+	0.142088i
$250$		0			0
$251$	69.0557	−	50.1719i	0.275122	−	0.199888i	−0.441665	−	0.897180i	$-0.645612\pi$
$251$	69.0557	−	50.1719i	0.275122	−	0.199888i	0.716787	+	0.697292i	$0.245612\pi$
$252$		0			0
$253$	−52.3622	+	377.519i	−0.206965	+	1.49217i
$254$		0			0
$255$	136.870	+	188.386i	0.536746	+	0.738768i
$256$		0			0
$257$	−91.2434	+	280.818i	−0.355033	+	1.09268i	0.600958	+	0.799281i	$0.294786\pi$
$257$	−91.2434	+	280.818i	−0.355033	+	1.09268i	−0.955991	+	0.293397i	$0.905214\pi$
$258$		0			0
$259$	354.636	−	488.115i	1.36925	−	1.88461i
$260$		0			0
$261$	751.567	−	244.199i	2.87957	−	0.935628i
$262$		0			0
$263$		−	264.881i		−	1.00715i	−0.863951	−	0.503577i	$-0.832017\pi$
$263$		−	264.881i		−	1.00715i	0.863951	−	0.503577i	$-0.167983\pi$
$264$		0			0
$265$	−7.19814			−0.0271628
$266$		0			0
$267$	108.723	+	334.616i	0.407204	+	1.25324i
$268$		0			0
$269$	−72.6949	−	52.8159i	−0.270241	−	0.196342i	0.444409	−	0.895824i	$-0.353414\pi$
$269$	−72.6949	−	52.8159i	−0.270241	−	0.196342i	−0.714650	+	0.699483i	$0.753414\pi$
$270$		0			0
$271$	96.2743	+	31.2814i	0.355256	+	0.115430i	0.481207	−	0.876607i	$-0.340198\pi$
$271$	96.2743	+	31.2814i	0.355256	+	0.115430i	−0.125952	+	0.992036i	$0.540198\pi$
$272$		0			0
$273$	−141.774	+	103.005i	−0.519320	+	0.377308i
$274$		0			0
$275$	−54.1471	+	9.64838i	−0.196899	+	0.0350850i
$276$		0			0
$277$	151.909	+	209.085i	0.548410	+	0.754821i	0.989795	−	0.142496i	$-0.0455129\pi$
$277$	151.909	+	209.085i	0.548410	+	0.754821i	−0.441386	+	0.897318i	$0.645513\pi$
$278$		0			0
$279$	−235.910	+	726.055i	−0.845555	+	2.60235i
$280$		0			0
$281$	225.491	−	310.362i	0.802459	−	1.10449i	−0.189984	−	0.981787i	$-0.560844\pi$
$281$	225.491	−	310.362i	0.802459	−	1.10449i	0.992443	−	0.122703i	$-0.0391563\pi$
$282$		0			0
$283$	89.7763	−	29.1701i	0.317231	−	0.103075i	−0.146074	−	0.989274i	$-0.546664\pi$
$283$	89.7763	−	29.1701i	0.317231	−	0.103075i	0.463304	+	0.886199i	$0.346664\pi$
$284$		0			0
$285$			63.8032i			0.223871i
$286$		0			0
$287$	−336.115			−1.17113
$288$		0			0
$289$	−36.6154	−	112.691i	−0.126697	−	0.389933i
$290$		0			0
$291$	−256.412	−	186.294i	−0.881141	−	0.640187i
$292$		0			0
$293$	−6.26659	−	2.03614i	−0.0213877	−	0.00694928i	0.298304	−	0.954471i	$-0.403579\pi$
$293$	−6.26659	−	2.03614i	−0.0213877	−	0.00694928i	−0.319691	+	0.947522i	$0.603579\pi$
$294$		0			0
$295$	−119.433	+	86.7728i	−0.404856	+	0.294145i
$296$		0			0
$297$	338.887	−	352.197i	1.14103	−	1.18585i
$298$		0			0
$299$	−68.1114	−	93.7473i	−0.227797	−	0.313536i
$300$		0			0
$301$	205.141	−	631.360i	0.681533	−	2.09754i
$302$		0			0
$303$	22.6586	−	31.1869i	0.0747809	−	0.102927i
$304$		0			0
$305$	100.779	−	32.7449i	0.330421	−	0.107360i
$306$		0			0
$307$			598.880i			1.95075i	0.220557	+	0.975374i	$0.429213\pi$
$307$			598.880i			1.95075i	−0.220557	+	0.975374i	$0.570787\pi$
$308$		0			0
$309$	−426.347			−1.37976
$310$		0			0
$311$	113.489	+	349.284i	0.364918	+	1.12310i	0.950033	+	0.312151i	$0.101049\pi$
$311$	113.489	+	349.284i	0.364918	+	1.12310i	−0.585115	+	0.810950i	$0.698951\pi$
$312$		0			0
$313$	−301.571	−	219.104i	−0.963484	−	0.700012i	−0.00952693	−	0.999955i	$-0.503033\pi$
$313$	−301.571	−	219.104i	−0.963484	−	0.700012i	−0.953957	+	0.299942i	$0.903033\pi$
$314$		0			0
$315$	−380.453	−	123.617i	−1.20779	−	0.392434i
$316$		0			0
$317$	312.109	−	226.761i	0.984572	−	0.715333i	0.0258462	−	0.999666i	$-0.491772\pi$
$317$	312.109	−	226.761i	0.984572	−	0.715333i	0.958726	+	0.284333i	$0.0917720\pi$
$318$		0			0
$319$	215.551	−	443.978i	0.675710	−	1.39178i
$320$		0			0
$321$	479.330	+	659.741i	1.49324	+	2.05527i
$322$		0			0
$323$	34.5026	−	106.188i	0.106819	−	0.328755i
$324$		0			0
$325$	9.82892	−	13.5284i	0.0302428	−	0.0416257i
$326$		0			0
$327$	−388.231	+	126.144i	−1.18725	+	0.385761i
$328$		0			0
$329$		−	699.400i		−	2.12584i
$330$		0			0
$331$	−617.568			−1.86576			−0.932882	−	0.360182i	$-0.882715\pi$
$331$	−617.568			−1.86576			−0.932882	+	0.360182i	$0.882715\pi$
$332$		0			0
$333$	−323.299	−	995.013i	−0.970869	−	2.98803i
$334$		0			0
$335$	57.1854	+	41.5476i	0.170703	+	0.124023i
$336$		0			0
$337$	−162.510	−	52.8027i	−0.482225	−	0.156685i	0.0578087	−	0.998328i	$-0.481589\pi$
$337$	−162.510	−	52.8027i	−0.482225	−	0.156685i	−0.540034	+	0.841643i	$0.681589\pi$
$338$		0			0
$339$	−117.796	+	85.5837i	−0.347480	+	0.252459i
$340$		0			0
$341$	224.596	+	420.571i	0.658639	+	1.23335i
$342$		0			0
$343$	−30.8643	−	42.4811i	−0.0899834	−	0.123851i
$344$		0			0
$345$	123.509	−	380.121i	0.357997	−	1.10180i
$346$		0			0
$347$	249.062	−	342.805i	0.717758	−	0.987910i	−0.281837	−	0.959462i	$-0.590944\pi$
$347$	249.062	−	342.805i	0.717758	−	0.987910i	0.999595	−	0.0284473i	$-0.00905628\pi$
$348$		0			0
$349$	272.056	−	88.3964i	0.779530	−	0.253285i	0.107891	−	0.994163i	$-0.465590\pi$
$349$	272.056	−	88.3964i	0.779530	−	0.253285i	0.671640	+	0.740878i	$0.265590\pi$
$350$		0			0
$351$			148.601i			0.423364i
$352$		0			0
$353$	124.306			0.352142			0.176071	−	0.984377i	$-0.443661\pi$
$353$	124.306			0.352142			0.176071	+	0.984377i	$0.443661\pi$
$354$		0			0
$355$	2.59821	+	7.99647i	0.00731891	+	0.0225253i
$356$		0			0
$357$	855.735	+	621.728i	2.39702	+	1.74153i
$358$		0			0
$359$	270.229	+	87.8027i	0.752726	+	0.244576i	0.660154	−	0.751130i	$-0.270491\pi$
$359$	270.229	+	87.8027i	0.752726	+	0.244576i	0.0925724	+	0.995706i	$0.470491\pi$
$360$		0			0
$361$	−267.305	+	194.208i	−0.740457	+	0.537973i
$362$		0			0
$363$	−24.0362	−	623.750i	−0.0662154	−	1.71832i
$364$		0			0
$365$	−29.4575	−	40.5447i	−0.0807054	−	0.111081i
$366$		0			0
$367$	−83.0950	+	255.740i	−0.226417	+	0.696839i	0.771728	+	0.635953i	$0.219393\pi$
$367$	−83.0950	+	255.740i	−0.226417	+	0.696839i	−0.998145	+	0.0608865i	$0.980607\pi$
$368$		0			0
$369$	−342.582	+	471.524i	−0.928408	+	1.27784i
$370$		0			0
$371$	−31.0970	+	10.1040i	−0.0838193	+	0.0272345i
$372$		0			0
$373$			556.864i			1.49293i	0.665423	+	0.746466i	$0.268251\pi$
$373$			556.864i			1.49293i	−0.665423	+	0.746466i	$0.731749\pi$
$374$		0			0
$375$	57.6769			0.153805
$376$		0			0
$377$	46.3689	+	142.709i	0.122994	+	0.378538i
$378$		0			0
$379$	490.846	+	356.621i	1.29511	+	0.940951i	0.999895	−	0.0144801i	$-0.00460933\pi$
$379$	490.846	+	356.621i	1.29511	+	0.940951i	0.295213	+	0.955431i	$0.404609\pi$
$380$		0			0
$381$	−455.834	−	148.109i	−1.19641	−	0.388739i
$382$		0			0
$383$	−551.513	+	400.697i	−1.43998	+	1.04621i	−0.451934	+	0.892051i	$0.649266\pi$
$383$	−551.513	+	400.697i	−1.43998	+	1.04621i	−0.988047	+	0.154156i	$0.950734\pi$
$384$		0			0
$385$	−220.379	+	117.688i	−0.572414	+	0.305684i
$386$		0			0
$387$	−676.625	−	931.294i	−1.74838	−	2.40645i
$388$		0			0
$389$	−40.2985	+	124.026i	−0.103595	+	0.318833i	−0.989398	−	0.145228i	$-0.953608\pi$
$389$	−40.2985	+	124.026i	−0.103595	+	0.318833i	0.885803	+	0.464061i	$0.153608\pi$
$390$		0			0
$391$	−411.113	+	565.848i	−1.05144	+	1.44718i
$392$		0			0
$393$	−770.011	+	250.192i	−1.95932	+	0.636621i
$394$		0			0
$395$			174.895i			0.442773i
$396$		0			0
$397$	47.4096			0.119420			0.0597098	−	0.998216i	$-0.480982\pi$
$397$	47.4096			0.119420			0.0597098	+	0.998216i	$0.480982\pi$
$398$		0			0
$399$	89.5604	+	275.639i	0.224462	+	0.690824i
$400$		0			0
$401$	306.275	+	222.522i	0.763778	+	0.554918i	0.900067	−	0.435752i	$-0.143517\pi$
$401$	306.275	+	222.522i	0.763778	+	0.554918i	−0.136289	+	0.990669i	$0.543517\pi$
$402$		0			0
$403$	−137.865	−	44.7949i	−0.342096	−	0.111154i
$404$		0			0
$405$	−127.901	+	92.9252i	−0.315804	+	0.229445i
$406$		0			0
$407$	−587.790	−	285.373i	−1.44420	−	0.701161i
$408$		0			0
$409$	−0.977980	−	1.34607i	−0.00239115	−	0.00329113i	0.807820	−	0.589430i	$-0.200647\pi$
$409$	−0.977980	−	1.34607i	−0.00239115	−	0.00329113i	−0.810211	+	0.586138i	$0.800647\pi$
$410$		0			0
$411$	5.45536	−	16.7899i	0.0132734	−	0.0408513i
$412$		0			0
$413$	−394.162	+	542.518i	−0.954388	+	1.31360i
$414$		0			0
$415$	−47.1974	+	15.3354i	−0.113729	+	0.0369527i
$416$		0			0
$417$		−	581.210i		−	1.39379i
$418$		0			0
$419$	230.024			0.548983			0.274491	−	0.961590i	$-0.411491\pi$
$419$	230.024			0.548983			0.274491	+	0.961590i	$0.411491\pi$
$420$		0			0
$421$	56.9804	+	175.368i	0.135345	+	0.416550i	0.995644	−	0.0932408i	$-0.0297226\pi$
$421$	56.9804	+	175.368i	0.135345	+	0.416550i	−0.860298	+	0.509791i	$0.829723\pi$
$422$		0			0
$423$	−981.164	−	712.857i	−2.31954	−	1.68524i
$424$		0			0
$425$	−95.9919	−	31.1897i	−0.225863	−	0.0733875i
$426$		0			0
$427$	389.413	−	282.925i	0.911974	−	0.662588i
$428$		0			0
$429$	136.756	+	131.588i	0.318779	+	0.306731i
$430$		0			0
$431$	−57.2541	−	78.8035i	−0.132840	−	0.182839i	0.737415	−	0.675440i	$-0.236046\pi$
$431$	−57.2541	−	78.8035i	−0.132840	−	0.182839i	−0.870255	+	0.492601i	$0.836046\pi$
$432$		0			0
$433$	95.9227	−	295.220i	0.221530	−	0.681800i	−0.777095	−	0.629383i	$-0.783308\pi$
$433$	95.9227	−	295.220i	0.221530	−	0.681800i	0.998625	−	0.0524170i	$-0.0166925\pi$
$434$		0			0
$435$	−304.213	+	418.713i	−0.699340	+	0.962559i
$436$		0			0
$437$	−182.264	+	59.2211i	−0.417080	+	0.135517i
$438$		0			0
$439$		−	124.229i		−	0.282982i	−0.989940	−	0.141491i	$-0.954810\pi$
$439$		−	124.229i		−	0.282982i	0.989940	−	0.141491i	$-0.0451896\pi$
$440$		0			0
$441$	−954.092			−2.16347
$442$		0			0
$443$	104.077	+	320.315i	0.234936	+	0.723060i	0.997130	+	0.0757105i	$0.0241225\pi$
$443$	104.077	+	320.315i	0.234936	+	0.723060i	−0.762193	+	0.647349i	$0.775878\pi$
$444$		0			0
$445$	−123.378	−	89.6390i	−0.277253	−	0.201436i
$446$		0			0
$447$	654.531	+	212.670i	1.46428	+	0.475772i
$448$		0			0
$449$	−163.977	+	119.136i	−0.365204	+	0.265336i	−0.755220	−	0.655472i	$-0.772470\pi$
$449$	−163.977	+	119.136i	−0.365204	+	0.265336i	0.390015	+	0.920808i	$0.372470\pi$
$450$		0			0
$451$	63.8553	+	358.358i	0.141586	+	0.794586i
$452$		0			0
$453$	761.655	+	1048.33i	1.68136	+	2.31419i
$454$		0			0
$455$	23.4726	−	72.2411i	0.0515881	−	0.158772i
$456$		0			0
$457$	480.313	−	661.095i	1.05101	−	1.44660i	0.163087	−	0.986612i	$-0.447855\pi$
$457$	480.313	−	661.095i	1.05101	−	1.44660i	0.887927	−	0.459985i	$-0.152145\pi$
$458$		0			0
$459$	853.038	−	277.169i	1.85847	−	0.603853i
$460$		0			0
$461$			572.857i			1.24264i	0.783557	+	0.621320i	$0.213403\pi$
$461$			572.857i			1.24264i	−0.783557	+	0.621320i	$0.786597\pi$
$462$		0			0
$463$	809.225			1.74779			0.873893	−	0.486119i	$-0.161588\pi$
$463$	809.225			1.74779			0.873893	+	0.486119i	$0.161588\pi$
$464$		0			0
$465$	−154.505	−	475.519i	−0.332270	−	1.02262i
$466$		0			0
$467$	647.652	+	470.547i	1.38683	+	1.00759i	0.996204	+	0.0870466i	$0.0277429\pi$
$467$	647.652	+	470.547i	1.38683	+	1.00759i	0.390630	+	0.920548i	$0.372257\pi$
$468$		0			0
$469$	305.369	+	99.2203i	0.651106	+	0.211557i
$470$		0			0
$471$	987.379	−	717.373i	2.09635	−	1.52309i
$472$		0			0
$473$	−712.115	−	98.7710i	−1.50553	−	0.208818i
$474$		0			0
$475$	−16.2555	−	22.3737i	−0.0342220	−	0.0471026i
$476$		0			0
$477$	−17.5207	+	53.9232i	−0.0367311	+	0.113047i
$478$		0			0
$479$	−389.858	+	536.594i	−0.813900	+	1.12024i	0.176810	+	0.984245i	$0.443422\pi$
$479$	−389.858	+	536.594i	−0.813900	+	1.12024i	−0.990710	+	0.135992i	$0.956578\pi$
$480$		0			0
$481$	188.935	−	61.3886i	0.392796	−	0.127627i
$482$		0			0
$483$		−	1815.54i		−	3.75889i
$484$		0			0
$485$	137.378			0.283255
$486$		0			0
$487$	−76.5765	−	235.678i	−0.157241	−	0.483939i	0.841140	−	0.540818i	$-0.181885\pi$
$487$	−76.5765	−	235.678i	−0.157241	−	0.483939i	−0.998381	+	0.0568789i	$0.981885\pi$
$488$		0			0
$489$	−825.301	−	599.616i	−1.68773	−	1.22621i
$490$		0			0
$491$	−793.666	−	257.878i	−1.61643	−	0.525209i	−0.645332	−	0.763902i	$-0.723281\pi$
$491$	−793.666	−	257.878i	−1.61643	−	0.525209i	−0.971095	+	0.238693i	$0.923281\pi$
$492$		0			0
$493$	732.728	−	532.358i	1.48626	−	1.07983i
$494$		0			0
$495$	−59.5187	+	429.115i	−0.120240	+	0.866900i
$496$		0			0
$497$	22.4493	+	30.8987i	0.0451695	+	0.0621705i
$498$		0			0
$499$	162.360	−	499.693i	0.325371	−	1.00139i	−0.645902	−	0.763420i	$-0.723518\pi$
$499$	162.360	−	499.693i	0.325371	−	1.00139i	0.971273	−	0.237969i	$-0.0764815\pi$
$500$		0			0
$501$	12.6334	−	17.3884i	0.0252164	−	0.0347073i
$502$		0			0
$503$	311.917	−	101.348i	0.620114	−	0.201487i	0.0179231	−	0.999839i	$-0.494295\pi$
$503$	311.917	−	101.348i	0.620114	−	0.201487i	0.602191	+	0.798352i	$0.294295\pi$
$504$		0			0
$505$			16.7091i			0.0330873i
$506$		0			0
$507$	814.133			1.60579
$508$		0			0
$509$	−121.378	−	373.562i	−0.238463	−	0.733914i	−0.996643	−	0.0818689i	$-0.973911\pi$
$509$	−121.378	−	373.562i	−0.238463	−	0.733914i	0.758180	−	0.652045i	$-0.226089\pi$
$510$		0			0
$511$	−184.173	−	133.809i	−0.360416	−	0.261858i
$512$		0			0
$513$	233.733	+	75.9445i	0.455620	+	0.148040i
$514$		0			0
$515$	149.506	−	108.623i	0.290303	−	0.210918i
$516$		0			0
$517$	−745.684	+	132.872i	−1.44233	+	0.257006i
$518$		0			0
$519$	−671.061	−	923.637i	−1.29299	−	1.77965i
$520$		0			0
$521$	−28.6933	+	88.3090i	−0.0550736	+	0.169499i	−0.974810	−	0.223038i	$-0.928403\pi$
$521$	−28.6933	+	88.3090i	−0.0550736	+	0.169499i	0.919736	+	0.392537i	$0.128403\pi$
$522$		0			0
$523$	−200.411	+	275.843i	−0.383196	+	0.527424i	−0.956428	−	0.291969i	$-0.905689\pi$
$523$	−200.411	+	275.843i	−0.383196	+	0.527424i	0.573232	+	0.819393i	$0.305689\pi$
$524$		0			0
$525$	249.172	−	80.9609i	0.474614	−	0.154211i
$526$		0			0
$527$			874.959i			1.66026i
$528$		0			0
$529$	671.515			1.26940
$530$		0			0
$531$	359.333	+	1105.91i	0.676709	+	2.08270i
$532$		0			0
$533$	−89.5338	−	65.0501i	−0.167981	−	0.122045i
$534$		0			0
$535$	−336.171	−	109.229i	−0.628357	−	0.204165i
$536$		0			0
$537$	100.556	−	73.0580i	0.187255	−	0.136048i
$538$		0			0
$539$	−413.149	+	429.377i	−0.766511	+	0.796617i
$540$		0			0
$541$	109.740	+	151.045i	0.202847	+	0.279195i	0.898306	−	0.439371i	$-0.144799\pi$
$541$	109.740	+	151.045i	0.202847	+	0.279195i	−0.695458	+	0.718566i	$0.744799\pi$
$542$		0			0
$543$	−87.4791	+	269.233i	−0.161103	+	0.495825i
$544$		0			0
$545$	104.002	−	143.146i	0.190829	−	0.262653i
$546$		0			0
$547$	76.6547	−	24.9066i	0.140137	−	0.0455331i	−0.238109	−	0.971238i	$-0.576528\pi$
$547$	76.6547	−	24.9066i	0.140137	−	0.0455331i	0.378245	+	0.925705i	$0.376528\pi$
$548$		0			0
$549$		−	834.663i		−	1.52033i
$550$		0			0
$551$	248.163			0.450387
$552$		0			0
$553$	245.500	+	755.572i	0.443942	+	1.36631i
$554$		0			0
$555$	554.342	+	402.753i	0.998815	+	0.725682i
$556$		0			0
$557$	−23.1601	−	7.52516i	−0.0415800	−	0.0135102i	0.288153	−	0.957584i	$-0.406959\pi$
$557$	−23.1601	−	7.52516i	−0.0415800	−	0.0135102i	−0.329733	+	0.944074i	$0.606959\pi$
$558$		0			0
$559$	176.836	−	128.479i	0.316343	−	0.229837i
$560$		0			0
$561$	500.299	−	1030.48i	0.891799	−	1.83686i
$562$		0			0
$563$	187.899	+	258.621i	0.333746	+	0.459363i	0.942602	−	0.333919i	$-0.108371\pi$
$563$	187.899	+	258.621i	0.333746	+	0.459363i	−0.608855	+	0.793281i	$0.708371\pi$
$564$		0			0
$565$	19.5026	−	60.0228i	0.0345179	−	0.106235i
$566$		0			0
$567$	−422.109	+	580.983i	−0.744460	+	1.02466i
$568$		0			0
$569$	−707.744	+	229.960i	−1.24384	+	0.404148i	−0.855709	−	0.517457i	$-0.826879\pi$
$569$	−707.744	+	229.960i	−1.24384	+	0.404148i	−0.388129	+	0.921605i	$0.626879\pi$
$570$		0			0
$571$			265.828i			0.465549i	0.972531	+	0.232774i	$0.0747804\pi$
$571$			265.828i			0.465549i	−0.972531	+	0.232774i	$0.925220\pi$
$572$		0			0
$573$	1179.84			2.05906
$574$		0			0
$575$	53.5348	+	164.763i	0.0931040	+	0.286545i
$576$		0			0
$577$	−178.202	−	129.471i	−0.308843	−	0.224387i	0.422557	−	0.906336i	$-0.361133\pi$
$577$	−178.202	−	129.471i	−0.308843	−	0.224387i	−0.731400	+	0.681949i	$0.761133\pi$
$578$		0			0
$579$	688.806	+	223.807i	1.18965	+	0.386540i
$580$		0			0
$581$	−182.373	+	132.502i	−0.313895	+	0.228058i
$582$		0			0
$583$	16.6805	+	31.2353i	0.0286114	+	0.0535768i
$584$		0			0
$585$	−77.4203	−	106.560i	−0.132342	−	0.182154i
$586$		0			0
$587$	−139.600	+	429.644i	−0.237819	+	0.731932i	0.758916	+	0.651189i	$0.225729\pi$
$587$	−139.600	+	429.644i	−0.237819	+	0.731932i	−0.996735	+	0.0807430i	$0.974271\pi$
$588$		0			0
$589$	−140.915	+	193.953i	−0.239245	+	0.329293i
$590$		0			0
$591$	1481.05	−	481.221i	2.50600	−	0.814249i
$592$		0			0
$593$			337.627i			0.569353i	0.958624	+	0.284677i	$0.0918863\pi$
$593$			337.627i			0.569353i	−0.958624	+	0.284677i	$0.908114\pi$
$594$		0			0
$595$	−458.479			−0.770553
$596$		0			0
$597$	270.783	+	833.385i	0.453573	+	1.39595i
$598$		0			0
$599$	533.497	+	387.608i	0.890646	+	0.647093i	0.936046	−	0.351876i	$-0.114456\pi$
$599$	533.497	+	387.608i	0.890646	+	0.647093i	−0.0454000	+	0.998969i	$0.514456\pi$
$600$		0			0
$601$	563.792	+	183.187i	0.938090	+	0.304804i	0.737867	−	0.674946i	$-0.235833\pi$
$601$	563.792	+	183.187i	0.938090	+	0.304804i	0.200223	+	0.979750i	$0.435833\pi$
$602$		0			0
$603$	450.437	−	327.262i	0.746993	−	0.542722i
$604$		0			0
$605$	167.344	+	212.605i	0.276602	+	0.351413i
$606$		0			0
$607$	−361.851	−	498.046i	−0.596131	−	0.820503i	0.399217	−	0.916857i	$-0.369282\pi$
$607$	−361.851	−	498.046i	−0.596131	−	0.820503i	−0.995347	+	0.0963532i	$0.969282\pi$
$608$		0			0
$609$	−726.495	+	2235.92i	−1.19293	+	3.67146i
$610$		0			0
$611$	135.359	−	186.305i	0.221536	−	0.304918i
$612$		0			0
$613$	−445.660	+	144.804i	−0.727015	+	0.236221i	−0.649062	−	0.760736i	$-0.724838\pi$
$613$	−445.660	+	144.804i	−0.727015	+	0.236221i	−0.0779528	+	0.996957i	$0.524838\pi$
$614$		0			0
$615$		−	381.719i		−	0.620682i
$616$		0			0
$617$	−94.7516			−0.153568			−0.0767841	−	0.997048i	$-0.524465\pi$
$617$	−94.7516			−0.153568			−0.0767841	+	0.997048i	$0.524465\pi$
$618$		0			0
$619$	−4.71805	−	14.5207i	−0.00762205	−	0.0234583i	0.947173	−	0.320723i	$-0.103926\pi$
$619$	−4.71805	−	14.5207i	−0.00762205	−	0.0234583i	−0.954795	+	0.297264i	$0.903926\pi$
$620$		0			0
$621$	−1245.50	−	904.911i	−2.00564	−	1.45718i
$622$		0			0
$623$	−658.834	−	214.068i	−1.05752	−	0.343608i
$624$		0			0
$625$	−20.2254	+	14.6946i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	276.865	−	147.853i	0.441571	−	0.235810i
$628$		0			0
$629$	−704.799	−	970.073i	−1.12051	−	1.54225i
$630$		0			0
$631$	297.044	−	914.207i	0.470751	−	1.44882i	−0.380853	−	0.924636i	$-0.624369\pi$
$631$	297.044	−	914.207i	0.470751	−	1.44882i	0.851603	−	0.524187i	$-0.175631\pi$
$632$		0			0
$633$	−263.886	+	363.208i	−0.416882	+	0.573788i
$634$		0			0
$635$	197.581	−	64.1978i	0.311151	−	0.101099i
$636$		0			0
$637$		−	181.165i		−	0.284403i
$638$		0			0
$639$	66.2280			0.103643
$640$		0			0
$641$	48.7450	+	150.022i	0.0760452	+	0.234043i	0.981852	−	0.189647i	$-0.0607345\pi$
$641$	48.7450	+	150.022i	0.0760452	+	0.234043i	−0.905807	+	0.423690i	$0.860734\pi$
$642$		0			0
$643$	724.751	+	526.563i	1.12714	+	0.818915i	0.985276	−	0.170971i	$-0.0546903\pi$
$643$	724.751	+	526.563i	1.12714	+	0.818915i	0.141864	+	0.989886i	$0.454690\pi$
$644$		0			0
$645$	717.024	+	232.975i	1.11166	+	0.361202i
$646$		0			0
$647$	136.729	−	99.3394i	0.211328	−	0.153539i	−0.477087	−	0.878856i	$-0.658307\pi$
$647$	136.729	−	99.3394i	0.211328	−	0.153539i	0.688414	+	0.725318i	$0.258307\pi$
$648$		0			0
$649$	653.303	+	317.179i	1.00663	+	0.488719i
$650$		0			0
$651$	−1334.97	−	1837.43i	−2.05064	−	2.82247i
$652$		0			0
$653$	40.7174	−	125.315i	0.0623543	−	0.191907i	−0.915027	−	0.403394i	$-0.867831\pi$
$653$	40.7174	−	125.315i	0.0623543	−	0.191907i	0.977381	+	0.211487i	$0.0678305\pi$
$654$		0			0
$655$	206.275	−	283.914i	0.314924	−	0.433456i
$656$		0			0
$657$	−375.433	+	121.986i	−0.571435	+	0.185670i
$658$		0			0
$659$			956.323i			1.45117i	0.688131	+	0.725586i	$0.258431\pi$
$659$			956.323i			1.45117i	−0.688131	+	0.725586i	$0.741569\pi$
$660$		0			0
$661$	−649.628			−0.982795			−0.491398	−	0.870935i	$-0.663514\pi$
$661$	−649.628			−0.982795			−0.491398	+	0.870935i	$0.663514\pi$
$662$		0			0
$663$	107.623	+	331.230i	0.162327	+	0.499592i
$664$		0			0
$665$	−101.632	−	73.8398i	−0.152830	−	0.111037i
$666$		0			0
$667$	−1478.49	−	480.389i	−2.21662	−	0.720223i
$668$		0			0
$669$	97.2681	−	70.6694i	0.145393	−	0.105634i
$670$		0			0
$671$	−375.629	−	361.433i	−0.559805	−	0.538648i
$672$		0			0
$673$	−445.913	−	613.747i	−0.662576	−	0.911957i	0.336987	−	0.941509i	$-0.390592\pi$
$673$	−445.913	−	613.747i	−0.662576	−	0.911957i	−0.999563	+	0.0295518i	$0.990592\pi$
$674$		0			0
$675$	68.6524	−	211.290i	0.101707	−	0.313023i
$676$		0			0
$677$	83.2729	−	114.615i	0.123003	−	0.169299i	−0.743075	−	0.669208i	$-0.766633\pi$
$677$	83.2729	−	114.615i	0.123003	−	0.169299i	0.866078	+	0.499909i	$0.166633\pi$
$678$		0			0
$679$	593.493	−	192.838i	0.874070	−	0.284003i
$680$		0			0
$681$			2036.52i			2.99049i
$682$		0			0
$683$	101.169			0.148124			0.0740621	−	0.997254i	$-0.476404\pi$
$683$	101.169			0.148124			0.0740621	+	0.997254i	$0.476404\pi$
$684$		0			0
$685$	2.36462	+	7.27755i	0.00345200	+	0.0106242i
$686$		0			0
$687$	−1793.40	−	1302.98i	−2.61049	−	1.89663i
$688$		0			0
$689$	−10.2390	−	3.32686i	−0.0148607	−	0.00482854i
$690$		0			0
$691$	510.040	−	370.566i	0.738118	−	0.536274i	−0.154003	−	0.988070i	$-0.549217\pi$
$691$	510.040	−	370.566i	0.738118	−	0.536274i	0.892121	+	0.451796i	$0.149217\pi$
$692$		0			0
$693$	345.219	+	1937.38i	0.498152	+	2.79565i
$694$		0			0
$695$	148.078	+	203.812i	0.213062	+	0.293254i
$696$		0			0
$697$	−206.421	+	635.297i	−0.296156	+	0.911474i
$698$		0			0
$699$	363.743	−	500.649i	0.520376	−	0.716237i
$700$		0			0
$701$	248.103	−	80.6134i	0.353927	−	0.114998i	−0.126657	−	0.991947i	$-0.540425\pi$
$701$	248.103	−	80.6134i	0.353927	−	0.114998i	0.480584	+	0.876949i	$0.340425\pi$
$702$		0			0
$703$		−	328.548i		−	0.467351i
$704$		0			0
$705$	794.295			1.12666
$706$		0			0
$707$	23.4545	+	72.1854i	0.0331746	+	0.102101i
$708$		0			0
$709$	516.303	+	375.116i	0.728213	+	0.529077i	0.888997	−	0.457912i	$-0.151403\pi$
$709$	516.303	+	375.116i	0.728213	+	0.529077i	−0.160785	+	0.986989i	$0.551403\pi$
$710$		0			0
$711$	1310.19	+	425.706i	1.84274	+	0.598743i
$712$		0			0
$713$	1214.98	−	882.738i	1.70405	−	1.23806i
$714$		0			0
$715$	−81.4811	−	11.3015i	−0.113960	−	0.0158063i
$716$		0			0
$717$	−626.929	−	862.893i	−0.874378	−	1.20348i
$718$		0			0
$719$	278.327	−	856.602i	0.387103	−	1.19138i	−0.547841	−	0.836583i	$-0.684550\pi$
$719$	278.327	−	856.602i	0.387103	−	1.19138i	0.934943	−	0.354797i	$-0.115450\pi$
$720$		0			0
$721$	493.413	−	679.125i	0.684346	−	0.941921i
$722$		0			0
$723$	−1544.64	+	501.885i	−2.13644	+	0.694170i
$724$		0			0
$725$		−	224.335i		−	0.309428i
$726$		0			0
$727$	−356.679			−0.490618			−0.245309	−	0.969445i	$-0.578889\pi$
$727$	−356.679			−0.490618			−0.245309	+	0.969445i	$0.578889\pi$
$728$		0			0
$729$	−252.683	−	777.679i	−0.346616	−	1.06677i
$730$		0			0
$731$	−1067.36	−	775.483i	−1.46014	−	1.06085i
$732$		0			0
$733$	−174.799	−	56.7957i	−0.238471	−	0.0774838i	0.187343	−	0.982294i	$-0.440012\pi$
$733$	−174.799	−	56.7957i	−0.238471	−	0.0774838i	−0.425814	+	0.904811i	$0.640012\pi$
$734$		0			0
$735$	505.529	−	367.288i	0.687794	−	0.499712i
$736$		0			0
$737$	47.7723	−	344.427i	0.0648200	−	0.467336i
$738$		0			0
$739$	367.548	+	505.886i	0.497358	+	0.684555i	0.981724	−	0.190311i	$-0.0609496\pi$
$739$	367.548	+	505.886i	0.497358	+	0.684555i	−0.484366	+	0.874866i	$0.660950\pi$
$740$		0			0
$741$	−29.4888	+	90.7572i	−0.0397960	+	0.122479i
$742$		0			0
$743$	−281.333	+	387.221i	−0.378644	+	0.521159i	−0.955225	−	0.295881i	$-0.904387\pi$
$743$	−281.333	+	387.221i	−0.378644	+	0.521159i	0.576580	+	0.817040i	$0.304387\pi$
$744$		0			0
$745$	−283.706	+	92.1816i	−0.380813	+	0.123734i
$746$		0			0
$747$			390.896i			0.523288i
$748$		0			0
$749$	−1605.63			−2.14369
$750$		0			0
$751$	−224.079	−	689.645i	−0.298374	−	0.918302i	−0.982067	−	0.188532i	$-0.939627\pi$
$751$	−224.079	−	689.645i	−0.298374	−	0.918302i	0.683693	−	0.729770i	$-0.260373\pi$
$752$		0			0
$753$	356.243	+	258.826i	0.473099	+	0.343726i
$754$		0			0
$755$	−534.175	−	173.564i	−0.707517	−	0.229886i
$756$		0			0
$757$	−449.589	+	326.646i	−0.593909	+	0.431500i	−0.843712	−	0.536796i	$-0.819634\pi$
$757$	−449.589	+	326.646i	−0.593909	+	0.431500i	0.249802	+	0.968297i	$0.419634\pi$
$758$		0			0
$759$	−1935.69	+	344.918i	−2.55032	+	0.454437i
$760$		0			0
$761$	−601.445	−	827.818i	−0.790335	−	1.08780i	−0.994066	−	0.108776i	$-0.965307\pi$
$761$	−601.445	−	827.818i	−0.790335	−	1.08780i	0.203732	−	0.979027i	$-0.434693\pi$
$762$		0			0
$763$	248.368	−	764.397i	0.325515	−	1.00183i
$764$		0			0
$765$	−467.301	+	643.184i	−0.610850	+	0.840763i
$766$		0			0
$767$	−209.992	+	68.2307i	−0.273784	+	0.0889579i
$768$		0			0
$769$			500.191i			0.650443i	0.945638	+	0.325222i	$0.105439\pi$
$769$			500.191i			0.650443i	−0.945638	+	0.325222i	$0.894561\pi$
$770$		0			0
$771$	−1523.23			−1.97566
$772$		0			0
$773$	−233.354	−	718.189i	−0.301881	−	0.929094i	−0.980823	−	0.194902i	$-0.937561\pi$
$773$	−233.354	−	718.189i	−0.301881	−	0.929094i	0.678942	−	0.734192i	$-0.262439\pi$
$774$		0			0
$775$	175.330	+	127.385i	0.226233	+	0.164368i
$776$		0			0
$777$	2960.18	+	961.820i	3.80975	+	1.23786i
$778$		0			0
$779$	−148.075	+	107.582i	−0.190083	+	0.138103i
$780$		0			0
$781$	28.6786	−	29.8050i	0.0367204	−	0.0381626i
$782$		0			0
$783$	1171.79	+	1612.83i	1.49654	+	2.05981i
$784$		0			0
$785$	−163.473	+	503.119i	−0.208246	+	0.640916i
$786$		0			0
$787$	−823.732	+	1133.77i	−1.04667	+	1.44062i	−0.155015	+	0.987912i	$0.549543\pi$
$787$	−823.732	+	1133.77i	−1.04667	+	1.44062i	−0.891658	+	0.452710i	$0.850457\pi$
$788$		0			0
$789$	1299.59	−	422.261i	1.64713	−	0.535185i
$790$		0			0
$791$		−	286.682i		−	0.362430i
$792$		0			0
$793$	158.487			0.199858
$794$		0			0
$795$	−11.4749	−	35.3162i	−0.0144339	−	0.0444229i
$796$		0			0
$797$	−53.7259	−	39.0341i	−0.0674101	−	0.0489763i	0.553570	−	0.832803i	$-0.313265\pi$
$797$	−53.7259	−	39.0341i	−0.0674101	−	0.0489763i	−0.620980	+	0.783826i	$0.713265\pi$
$798$		0			0
$799$	−1321.95	−	429.527i	−1.65450	−	0.537581i
$800$		0			0
$801$	−971.819	+	706.068i	−1.21326	+	0.881483i
$802$		0			0
$803$	−107.675	+	221.782i	−0.134091	+	0.276192i
$804$		0			0
$805$	462.555	+	636.652i	0.574603	+	0.790873i
$806$		0			0
$807$	143.244	−	440.859i	0.177502	−	0.546294i
$808$		0			0
$809$	−3.74766	+	5.15822i	−0.00463246	+	0.00637604i	−0.811327	−	0.584593i	$-0.801254\pi$
$809$	−3.74766	+	5.15822i	−0.00463246	+	0.00637604i	0.806694	+	0.590969i	$0.201254\pi$
$810$		0			0
$811$	−639.496	+	207.785i	−0.788527	+	0.256208i	−0.675477	−	0.737381i	$-0.736062\pi$
$811$	−639.496	+	207.785i	−0.788527	+	0.256208i	−0.113050	+	0.993589i	$0.536062\pi$
$812$		0			0
$813$			522.217i			0.642334i
$814$		0			0
$815$	442.173			0.542544
$816$		0			0
$817$	−111.709	−	343.805i	−0.136731	−	0.420814i
$818$		0			0
$819$	−484.044	−	351.679i	−0.591019	−	0.429400i
$820$		0			0
$821$	−75.7555	−	24.6145i	−0.0922723	−	0.0299811i	0.262517	−	0.964927i	$-0.415447\pi$
$821$	−75.7555	−	24.6145i	−0.0922723	−	0.0299811i	−0.354789	+	0.934946i	$0.615447\pi$
$822$		0			0
$823$	559.800	−	406.718i	0.680194	−	0.494190i	−0.193228	−	0.981154i	$-0.561896\pi$
$823$	559.800	−	406.718i	0.680194	−	0.494190i	0.873422	+	0.486964i	$0.161896\pi$
$824$		0			0
$825$	−133.656	−	250.281i	−0.162008	−	0.303370i
$826$		0			0
$827$	617.430	+	849.819i	0.746590	+	1.02759i	0.998212	+	0.0597676i	$0.0190360\pi$
$827$	617.430	+	849.819i	0.746590	+	1.02759i	−0.251622	+	0.967826i	$0.580964\pi$
$828$		0			0
$829$	102.939	−	316.813i	0.124172	−	0.382163i	−0.869577	−	0.493797i	$-0.835608\pi$
$829$	102.939	−	316.813i	0.124172	−	0.382163i	0.993749	+	0.111634i	$0.0356085\pi$
$830$		0			0
$831$	−783.668	+	1078.63i	−0.943042	+	1.29799i
$832$		0			0
$833$	−1039.97	+	337.907i	−1.24846	+	0.405650i
$834$		0			0
$835$			9.31621i			0.0111571i
$836$		0			0
$837$	−1925.90			−2.30095
$838$		0			0
$839$	9.21153	+	28.3502i	0.0109792	+	0.0337904i	0.956396	−	0.292073i	$-0.0943450\pi$
$839$	9.21153	+	28.3502i	0.0109792	+	0.0337904i	−0.945417	+	0.325863i	$0.894345\pi$
$840$		0			0
$841$	948.206	+	688.912i	1.12747	+	0.819158i
$842$		0			0
$843$	1882.19	+	611.562i	2.23273	+	0.725459i
$844$		0			0
$845$	−285.490	+	207.421i	−0.337858	+	0.245468i
$846$		0			0
$847$	1021.38	+	683.581i	1.20588	+	0.807061i
$848$		0			0
$849$	286.234	+	393.968i	0.337143	+	0.464037i
$850$		0			0
$851$	−635.996	+	1957.39i	−0.747351	+	2.30011i
$852$		0			0
$853$	317.699	−	437.275i	0.372449	−	0.512632i	−0.581115	−	0.813821i	$-0.697383\pi$
$853$	317.699	−	437.275i	0.372449	−	0.512632i	0.953564	+	0.301189i	$0.0973835\pi$
$854$		0			0
$855$	−207.174	+	67.3150i	−0.242309	+	0.0787310i
$856$		0			0
$857$		−	273.436i		−	0.319062i	−0.987193	−	0.159531i	$-0.949002\pi$
$857$		−	273.436i		−	0.319062i	0.987193	−	0.159531i	$-0.0509981\pi$
$858$		0			0
$859$	−275.966			−0.321264			−0.160632	−	0.987014i	$-0.551353\pi$
$859$	−275.966			−0.321264			−0.160632	+	0.987014i	$0.551353\pi$
$860$		0			0
$861$	−535.818	−	1649.08i	−0.622321	−	1.91531i
$862$		0			0
$863$	29.8179	+	21.6639i	0.0345514	+	0.0251031i	0.604927	−	0.796281i	$-0.293202\pi$
$863$	29.8179	+	21.6639i	0.0345514	+	0.0251031i	−0.570376	+	0.821384i	$0.693202\pi$
$864$		0			0
$865$	470.639	+	152.920i	0.544091	+	0.176786i
$866$		0			0
$867$	494.523	−	359.292i	0.570384	−	0.414408i
$868$		0			0
$869$	758.933	−	405.290i	0.873341	−	0.466387i
$870$		0			0
$871$	62.1410	+	85.5297i	0.0713444	+	0.0981971i
$872$		0			0
$873$	334.388	−	1029.14i	0.383033	−	1.17885i
$874$		0			0
$875$	−66.7498	+	91.8732i	−0.0762854	+	0.104998i
$876$		0			0
$877$	426.669	−	138.633i	0.486509	−	0.158076i	−0.0554835	−	0.998460i	$-0.517670\pi$
$877$	426.669	−	138.633i	0.486509	−	0.158076i	0.541993	+	0.840383i	$0.317670\pi$
$878$		0			0
$879$		−	33.9916i		−	0.0386708i
$880$		0			0
$881$	710.818			0.806831			0.403415	−	0.915017i	$-0.367823\pi$
$881$	710.818			0.806831			0.403415	+	0.915017i	$0.367823\pi$
$882$		0			0
$883$	−396.461	−	1220.18i	−0.448993	−	1.38186i	−0.878045	−	0.478578i	$-0.841152\pi$
$883$	−396.461	−	1220.18i	−0.448993	−	1.38186i	0.429052	−	0.903280i	$-0.358848\pi$
$884$		0			0
$885$	−616.127	−	447.642i	−0.696188	−	0.505810i
$886$		0			0
$887$	973.403	+	316.278i	1.09741	+	0.356570i	0.801105	−	0.598523i	$-0.204246\pi$
$887$	973.403	+	316.278i	1.09741	+	0.356570i	0.296305	+	0.955093i	$0.404246\pi$
$888$		0			0
$889$	763.461	−	554.687i	0.858786	−	0.623944i
$890$		0			0
$891$	699.623	+	339.667i	0.785211	+	0.381220i
$892$		0			0
$893$	−223.861	−	308.119i	−0.250684	−	0.345038i
$894$		0			0
$895$	−16.6483	+	51.2381i	−0.0186014	+	0.0572493i
$896$		0			0
$897$	351.372	−	483.622i	0.391719	−	0.539155i
$898$		0			0
$899$	−1849.53	+	600.950i	−2.05732	+	0.668465i
$900$		0			0
$901$			64.9821i			0.0721222i
$902$		0			0
$903$	3424.67			3.79254
$904$		0			0
$905$	−37.9177	−	116.699i	−0.0418980	−	0.128949i
$906$		0			0
$907$	−1249.82	−	908.047i	−1.37797	−	1.00115i	−0.997066	−	0.0765405i	$-0.975613\pi$
$907$	−1249.82	−	908.047i	−1.37797	−	1.00115i	−0.380905	−	0.924614i	$-0.624387\pi$
$908$		0			0
$909$	125.172	+	40.6709i	0.137703	+	0.0447425i
$910$		0			0
$911$	304.683	−	221.365i	0.334449	−	0.242991i	−0.407867	−	0.913041i	$-0.633727\pi$
$911$	304.683	−	221.365i	0.334449	−	0.242991i	0.742316	+	0.670050i	$0.233727\pi$
$912$		0			0
$913$	175.918	+	169.269i	0.192681	+	0.185399i
$914$		0			0
$915$	321.312	+	442.249i	0.351161	+	0.483332i
$916$		0			0
$917$	492.609	−	1516.09i	0.537196	−	1.65332i
$918$		0			0
$919$	832.306	−	1145.57i	0.905664	−	1.24654i	−0.0629614	−	0.998016i	$-0.520054\pi$
$919$	832.306	−	1145.57i	0.905664	−	1.24654i	0.968626	−	0.248524i	$-0.0799455\pi$
$920$		0			0
$921$	−2938.28	+	954.705i	−3.19031	+	1.03660i
$922$		0			0
$923$			12.5755i			0.0136246i
$924$		0			0
$925$	−297.001			−0.321082
$926$		0			0
$927$	−449.814	−	1384.38i	−0.485236	−	1.49340i
$928$		0			0
$929$	647.408	+	470.370i	0.696887	+	0.506318i	0.878917	−	0.476975i	$-0.158267\pi$
$929$	647.408	+	470.370i	0.696887	+	0.506318i	−0.182030	+	0.983293i	$0.558267\pi$
$930$		0			0
$931$	−284.953	−	92.5868i	−0.306072	−	0.0994487i
$932$		0			0
$933$	−1532.77	+	1113.62i	−1.64284	+	1.19360i
$934$		0			0
$935$	87.1020	+	488.820i	0.0931572	+	0.522802i
$936$		0			0
$937$	−560.986	−	772.131i	−0.598705	−	0.824046i	0.396884	−	0.917869i	$-0.370091\pi$
$937$	−560.986	−	772.131i	−0.598705	−	0.824046i	−0.995589	+	0.0938225i	$0.970091\pi$
$938$		0			0
$939$	594.239	−	1828.88i	0.632842	−	1.94769i
$940$		0			0
$941$	514.157	−	707.676i	0.546394	−	0.752047i	−0.443123	−	0.896461i	$-0.646130\pi$
$941$	514.157	−	707.676i	0.546394	−	0.752047i	0.989517	+	0.144414i	$0.0461296\pi$
$942$		0			0
$943$	1090.44	−	354.306i	1.15635	−	0.375722i
$944$		0			0
$945$		−	1009.17i		−	1.06790i
$946$		0			0
$947$	614.074			0.648441			0.324221	−	0.945982i	$-0.394898\pi$
$947$	614.074			0.648441			0.324221	+	0.945982i	$0.394898\pi$
$948$		0			0
$949$	−23.1628	−	71.2878i	−0.0244076	−	0.0751189i
$950$		0			0
$951$	1610.10	+	1169.81i	1.69306	+	1.23008i
$952$		0			0
$953$	582.761	+	189.351i	0.611502	+	0.198689i	0.598364	−	0.801225i	$-0.295818\pi$
$953$	582.761	+	189.351i	0.611502	+	0.198689i	0.0131383	+	0.999914i	$0.495818\pi$
$954$		0			0
$955$	−413.732	+	300.594i	−0.433227	+	0.314758i
$956$		0			0
$957$	2521.91	+	349.791i	2.63522	+	0.365508i
$958$		0			0
$959$	20.4309	+	28.1208i	0.0213044	+	0.0293230i
$960$		0			0
$961$	283.586	−	872.789i	0.295095	−	0.908209i
$962$		0			0
$963$	−1636.52	+	2252.48i	−1.69940	+	2.33902i
$964$		0			0
$965$	−298.562	+	97.0087i	−0.309391	+	0.100527i
$966$		0			0
$967$			200.077i			0.206905i	0.994634	+	0.103452i	$0.0329890\pi$
$967$			200.077i			0.206905i	−0.994634	+	0.103452i	$0.967011\pi$
$968$		0			0
$969$	575.992			0.594419
$970$		0			0
$971$	292.370	+	899.821i	0.301102	+	0.926695i	0.981103	+	0.193485i	$0.0619790\pi$
$971$	292.370	+	899.821i	0.301102	+	0.926695i	−0.680002	+	0.733211i	$0.738021\pi$
$972$		0			0
$973$	925.806	+	672.637i	0.951496	+	0.691302i
$974$		0			0
$975$	82.0429	+	26.6573i	0.0841465	+	0.0273409i
$976$		0			0
$977$	277.738	−	201.789i	0.284277	−	0.206539i	−0.436504	−	0.899702i	$-0.643783\pi$
$977$	277.738	−	201.789i	0.284277	−	0.206539i	0.720781	+	0.693163i	$0.243783\pi$
$978$		0			0
$979$	−103.069	+	743.102i	−0.105280	+	0.759042i
$980$		0			0
$981$	−819.200	−	1127.53i	−0.835066	−	1.14937i
$982$		0			0
$983$	−60.4947	+	186.184i	−0.0615409	+	0.189404i	−0.977100	−	0.212779i	$-0.931748\pi$
$983$	−60.4947	+	186.184i	−0.0615409	+	0.189404i	0.915559	+	0.402183i	$0.131748\pi$
$984$		0			0
$985$	−396.752	+	546.082i	−0.402794	+	0.554398i
$986$		0			0
$987$	3431.46	−	1114.95i	3.47666	−	1.12963i
$988$		0			0
$989$			2264.53i			2.28972i
$990$		0			0
$991$	−1157.74			−1.16826			−0.584130	−	0.811660i	$-0.698564\pi$
$991$	−1157.74			−1.16826			−0.584130	+	0.811660i	$0.698564\pi$
$992$		0			0
$993$	−984.497	−	3029.97i	−0.991437	−	3.05133i
$994$		0			0
$995$	−307.280	−	223.252i	−0.308824	−	0.224374i
$996$		0			0
$997$	−1397.23	−	453.989i	−1.40144	−	0.455355i	−0.491782	−	0.870718i	$-0.663654\pi$
$997$	−1397.23	−	453.989i	−1.40144	−	0.455355i	−0.909655	+	0.415364i	$0.863654\pi$
$998$		0			0
$999$	2135.25	−	1551.35i	2.13739	−	1.55291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.p.a.41.4	✓	16
11.2	odd	10		2420.3.f.c.241.16		16
11.7	odd	10	inner	220.3.p.a.161.4	yes	16
11.9	even	5		2420.3.f.c.241.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.p.a.41.4	✓	16	1.1	even	1	trivial
220.3.p.a.161.4	yes	16	11.7	odd	10	inner
2420.3.f.c.241.15		16	11.9	even	5
2420.3.f.c.241.16		16	11.2	odd	10

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59415 + 4.90629i) q^{3} +(-1.80902 - 1.31433i) q^{5} +(-9.66012 - 3.13876i) q^{7} +(-14.2492 + 10.3527i) q^{9} +(-1.51124 + 10.8957i) q^{11} +(-1.96578 - 2.70567i) q^{13} +(3.56463 - 10.9708i) q^{15} +(-11.8653 + 16.3311i) q^{17} +(-5.26038 + 1.70920i) q^{19} -52.3990i q^{21} +34.6484 q^{23} +(1.54508 + 4.75528i) q^{25} +(-35.9469 - 26.1169i) q^{27} +(-42.6710 - 13.8647i) q^{29} +(35.0661 - 25.4770i) q^{31} +(-55.8666 + 9.95478i) q^{33} +(13.3500 + 18.3746i) q^{35} +(-18.3557 + 56.4930i) q^{37} +(10.1411 - 13.9580i) q^{39} +(31.4716 - 10.2257i) q^{41} +65.3574i q^{43} +39.3839 q^{45} +(21.2781 + 65.4871i) q^{47} +(43.8242 + 31.8401i) q^{49} +(-99.0403 - 32.1801i) q^{51} +(2.60431 - 1.89214i) q^{53} +(17.0544 - 17.7242i) q^{55} +(-16.7717 - 23.0842i) q^{57} +(20.4015 - 62.7894i) q^{59} +(-27.8545 + 38.3384i) q^{61} +(170.144 - 55.2831i) q^{63} +7.47829i q^{65} -31.6113 q^{67} +(55.2349 + 169.995i) q^{69} +(-3.04204 - 2.21017i) q^{71} +(21.3156 + 6.92587i) q^{73} +(-20.8677 + 15.1613i) q^{75} +(48.7978 - 100.510i) q^{77} +(-45.9740 - 63.2778i) q^{79} +(21.8480 - 67.2413i) q^{81} +(13.0450 - 17.9550i) q^{83} +(42.9289 - 13.9484i) q^{85} -231.459i q^{87} +68.2014 q^{89} +(10.4973 + 32.3072i) q^{91} +(180.898 + 131.430i) q^{93} +(11.7626 + 3.82189i) q^{95} +(-49.7040 + 36.1121i) q^{97} +(-91.2656 - 170.901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} - 20 q^{5} - 10 q^{7} - 19 q^{9} - 37 q^{11} + 35 q^{13} + 15 q^{15} + 55 q^{17} + 30 q^{19} + 72 q^{23} - 20 q^{25} - 25 q^{27} - 145 q^{29} - 80 q^{31} - 94 q^{33} + 44 q^{37} + 175 q^{39}+ \cdots - 70 q^{99}+O(q^{100}) \) 16 * q - q^3 - 20 * q^5 - 10 * q^7 - 19 * q^9 - 37 * q^11 + 35 * q^13 + 15 * q^15 + 55 * q^17 + 30 * q^19 + 72 * q^23 - 20 * q^25 - 25 * q^27 - 145 * q^29 - 80 * q^31 - 94 * q^33 + 44 * q^37 + 175 * q^39 + 35 * q^41 + 30 * q^45 + 2 * q^47 + 172 * q^49 - 460 * q^51 + 47 * q^53 + 85 * q^55 + 10 * q^57 + 98 * q^59 + 330 * q^61 + 90 * q^63 + 152 * q^67 - 317 * q^69 - 20 * q^71 - 495 * q^73 - 30 * q^75 - 204 * q^77 + 25 * q^79 + 57 * q^81 + 190 * q^83 - 25 * q^85 + 160 * q^89 - 119 * q^91 + 617 * q^93 - 90 * q^95 - 521 * q^97 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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