LMFDB - Embedded newform 105.3.c.a.71.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(71,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$16$
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} + 46x^{14} + 823x^{12} + 7252x^{10} + 32831x^{8} + 71486x^{6} + 60809x^{4} + 15680x^{2} + 576 $ x^16 + 46x^14 + 823x^12 + 7252x^10 + 32831x^8 + 71486x^6 + 60809x^4 + 15680*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.16
Root			$3.73696i$ of defining polynomial
Character	$\chi$	$=$	105.71
Dual form			105.3.c.a.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.73696i q^{2} +(1.47033 + 2.61498i) q^{3} -9.96484 q^{4} -2.23607i q^{5} +(-9.77207 + 5.49456i) q^{6} -2.64575 q^{7} -22.2903i q^{8} +(-4.67625 + 7.68978i) q^{9} +O(q^{10})$	\(q+3.73696i q^{2} +(1.47033 + 2.61498i) q^{3} -9.96484 q^{4} -2.23607i q^{5} +(-9.77207 + 5.49456i) q^{6} -2.64575 q^{7} -22.2903i q^{8} +(-4.67625 + 7.68978i) q^{9} +8.35609 q^{10} +13.0941i q^{11} +(-14.6516 - 26.0579i) q^{12} +10.2615 q^{13} -9.88705i q^{14} +(5.84728 - 3.28776i) q^{15} +43.4386 q^{16} +21.6208i q^{17} +(-28.7363 - 17.4750i) q^{18} +21.6075 q^{19} +22.2821i q^{20} +(-3.89013 - 6.91859i) q^{21} -48.9321 q^{22} -33.9527i q^{23} +(58.2888 - 32.7742i) q^{24} -5.00000 q^{25} +38.3467i q^{26} +(-26.9843 - 0.921805i) q^{27} +26.3645 q^{28} +23.2697i q^{29} +(12.2862 + 21.8510i) q^{30} -7.46874 q^{31} +73.1668i q^{32} +(-34.2408 + 19.2527i) q^{33} -80.7961 q^{34} +5.91608i q^{35} +(46.5981 - 76.6273i) q^{36} +29.2021 q^{37} +80.7463i q^{38} +(15.0878 + 26.8336i) q^{39} -49.8427 q^{40} +6.98134i q^{41} +(25.8545 - 14.5372i) q^{42} +51.1167 q^{43} -130.481i q^{44} +(17.1949 + 10.4564i) q^{45} +126.880 q^{46} -43.1554i q^{47} +(63.8691 + 113.591i) q^{48} +7.00000 q^{49} -18.6848i q^{50} +(-56.5381 + 31.7898i) q^{51} -102.254 q^{52} -16.4853i q^{53} +(3.44475 - 100.839i) q^{54} +29.2793 q^{55} +58.9747i q^{56} +(31.7702 + 56.5032i) q^{57} -86.9580 q^{58} +32.7663i q^{59} +(-58.2671 + 32.7620i) q^{60} -15.5110 q^{61} -27.9104i q^{62} +(12.3722 - 20.3452i) q^{63} -99.6668 q^{64} -22.9454i q^{65} +(-71.9463 - 127.956i) q^{66} +34.1378 q^{67} -215.448i q^{68} +(88.7856 - 49.9217i) q^{69} -22.1081 q^{70} -127.596i q^{71} +(171.408 + 104.235i) q^{72} -78.3146 q^{73} +109.127i q^{74} +(-7.35165 - 13.0749i) q^{75} -215.315 q^{76} -34.6437i q^{77} +(-100.276 + 56.3824i) q^{78} +67.0191 q^{79} -97.1317i q^{80} +(-37.2653 - 71.9187i) q^{81} -26.0889 q^{82} -81.5990i q^{83} +(38.7645 + 68.9426i) q^{84} +48.3457 q^{85} +191.021i q^{86} +(-60.8499 + 34.2142i) q^{87} +291.872 q^{88} +139.828i q^{89} +(-39.0752 + 64.2564i) q^{90} -27.1494 q^{91} +338.333i q^{92} +(-10.9815 - 19.5306i) q^{93} +161.270 q^{94} -48.3159i q^{95} +(-191.330 + 107.579i) q^{96} +128.230 q^{97} +26.1587i q^{98} +(-100.691 - 61.2314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	$ 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) $ 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			3.73696i			1.86848i	0.356648	+	0.934239i	$0.383920\pi$
$2$			3.73696i			1.86848i	−0.356648	+	0.934239i	$0.616080\pi$
$3$	1.47033	+	2.61498i	0.490110	+	0.871660i
$3$	1.47033	+	2.61498i	0.490110	+	0.871660i
$4$	−9.96484			−2.49121
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	−9.77207	+	5.49456i	−1.62868	+	0.915760i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		−	22.2903i		−	2.78629i
$9$	−4.67625	+	7.68978i	−0.519584	+	0.854419i
$10$	8.35609			0.835609
$11$			13.0941i			1.19037i	0.803588	+	0.595186i	$0.202922\pi$
$11$			13.0941i			1.19037i	−0.803588	+	0.595186i	$0.797078\pi$
$12$	−14.6516	−	26.0579i	−1.22097	−	2.17149i
$13$	10.2615			0.789346			0.394673	−	0.918822i	$-0.370858\pi$
$13$	10.2615			0.789346			0.394673	+	0.918822i	$0.370858\pi$
$14$		−	9.88705i		−	0.706218i
$15$	5.84728	−	3.28776i	0.389818	−	0.219184i
$16$	43.4386			2.71491
$17$			21.6208i			1.27181i	0.771766	+	0.635907i	$0.219374\pi$
$17$			21.6208i			1.27181i	−0.771766	+	0.635907i	$0.780626\pi$
$18$	−28.7363	−	17.4750i	−1.59646	−	0.970831i
$19$	21.6075			1.13724			0.568619	−	0.822601i	$-0.307478\pi$
$19$	21.6075			1.13724			0.568619	+	0.822601i	$0.307478\pi$
$20$			22.2821i			1.11410i
$21$	−3.89013	−	6.91859i	−0.185244	−	0.329457i
$22$	−48.9321			−2.22419
$23$		−	33.9527i		−	1.47620i	−0.674689	−	0.738102i	$-0.735722\pi$
$23$		−	33.9527i		−	1.47620i	0.674689	−	0.738102i	$-0.264278\pi$
$24$	58.2888	−	32.7742i	2.42870	−	1.36559i
$25$	−5.00000			−0.200000
$26$			38.3467i			1.47487i
$27$	−26.9843	−	0.921805i	−0.999417	−	0.0341409i
$28$	26.3645			0.941588
$29$			23.2697i			0.802405i	0.915989	+	0.401202i	$0.131408\pi$
$29$			23.2697i			0.802405i	−0.915989	+	0.401202i	$0.868592\pi$
$30$	12.2862	+	21.8510i	0.409540	+	0.728367i
$31$	−7.46874			−0.240927			−0.120464	−	0.992718i	$-0.538438\pi$
$31$	−7.46874			−0.240927			−0.120464	+	0.992718i	$0.538438\pi$
$32$			73.1668i			2.28646i
$33$	−34.2408	+	19.2527i	−1.03760	+	0.583414i
$34$	−80.7961			−2.37636
$35$			5.91608i			0.169031i
$36$	46.5981	−	76.6273i	1.29439	−	2.12854i
$37$	29.2021			0.789246			0.394623	−	0.918843i	$-0.370875\pi$
$37$	29.2021			0.789246			0.394623	+	0.918843i	$0.370875\pi$
$38$			80.7463i			2.12490i
$39$	15.0878	+	26.8336i	0.386866	+	0.688041i
$40$	−49.8427			−1.24607
$41$			6.98134i			0.170277i	0.996369	+	0.0851383i	$0.0271332\pi$
$41$			6.98134i			0.170277i	−0.996369	+	0.0851383i	$0.972867\pi$
$42$	25.8545	−	14.5372i	0.615582	−	0.346125i
$43$	51.1167			1.18876			0.594380	−	0.804184i	$-0.297397\pi$
$43$	51.1167			1.18876			0.594380	+	0.804184i	$0.297397\pi$
$44$		−	130.481i		−	2.96547i
$45$	17.1949	+	10.4564i	0.382108	+	0.232365i
$46$	126.880			2.75825
$47$		−	43.1554i		−	0.918199i	−0.888385	−	0.459100i	$-0.848172\pi$
$47$		−	43.1554i		−	0.918199i	0.888385	−	0.459100i	$-0.151828\pi$
$48$	63.8691	+	113.591i	1.33061	+	2.36648i
$49$	7.00000			0.142857
$50$		−	18.6848i		−	0.373696i
$51$	−56.5381	+	31.7898i	−1.10859	+	0.623329i
$52$	−102.254			−1.96643
$53$		−	16.4853i		−	0.311044i	−0.987832	−	0.155522i	$-0.950294\pi$
$53$		−	16.4853i		−	0.311044i	0.987832	−	0.155522i	$-0.0497060\pi$
$54$	3.44475	−	100.839i	0.0637916	−	1.86739i
$55$	29.2793			0.532351
$56$			58.9747i			1.05312i
$57$	31.7702	+	56.5032i	0.557372	+	0.991285i
$58$	−86.9580			−1.49928
$59$			32.7663i			0.555361i	0.960674	+	0.277680i	$0.0895656\pi$
$59$			32.7663i			0.555361i	−0.960674	+	0.277680i	$0.910434\pi$
$60$	−58.2671	+	32.7620i	−0.971119	+	0.546033i
$61$	−15.5110			−0.254279			−0.127139	−	0.991885i	$-0.540580\pi$
$61$	−15.5110			−0.254279			−0.127139	+	0.991885i	$0.540580\pi$
$62$		−	27.9104i		−	0.450167i
$63$	12.3722	−	20.3452i	0.196384	−	0.322940i
$64$	−99.6668			−1.55729
$65$		−	22.9454i		−	0.353006i
$66$	−71.9463	−	127.956i	−1.09010	−	1.93873i
$67$	34.1378			0.509519			0.254759	−	0.967004i	$-0.418004\pi$
$67$	34.1378			0.509519			0.254759	+	0.967004i	$0.418004\pi$
$68$		−	215.448i		−	3.16836i
$69$	88.7856	−	49.9217i	1.28675	−	0.723502i
$70$	−22.1081			−0.315830
$71$		−	127.596i		−	1.79712i	−0.438850	−	0.898560i	$-0.644614\pi$
$71$		−	127.596i		−	1.79712i	0.438850	−	0.898560i	$-0.355386\pi$
$72$	171.408	+	104.235i	2.38066	+	1.44771i
$73$	−78.3146			−1.07280			−0.536402	−	0.843963i	$-0.680217\pi$
$73$	−78.3146			−1.07280			−0.536402	+	0.843963i	$0.680217\pi$
$74$			109.127i			1.47469i
$75$	−7.35165	−	13.0749i	−0.0980221	−	0.174332i
$76$	−215.315			−2.83310
$77$		−	34.6437i		−	0.449919i
$78$	−100.276	+	56.3824i	−1.28559	+	0.722851i
$79$	67.0191			0.848343			0.424171	−	0.905582i	$-0.360565\pi$
$79$	67.0191			0.848343			0.424171	+	0.905582i	$0.360565\pi$
$80$		−	97.1317i		−	1.21415i
$81$	−37.2653	−	71.9187i	−0.460065	−	0.887885i
$82$	−26.0889			−0.318158
$83$		−	81.5990i		−	0.983121i	−0.870844	−	0.491560i	$-0.836427\pi$
$83$		−	81.5990i		−	0.983121i	0.870844	−	0.491560i	$-0.163573\pi$
$84$	38.7645	+	68.9426i	0.461482	+	0.820745i
$85$	48.3457			0.568773
$86$			191.021i			2.22117i
$87$	−60.8499	+	34.2142i	−0.699425	+	0.393267i
$88$	291.872			3.31673
$89$			139.828i			1.57110i	0.618801	+	0.785548i	$0.287619\pi$
$89$			139.828i			1.57110i	−0.618801	+	0.785548i	$0.712381\pi$
$90$	−39.0752	+	64.2564i	−0.434169	+	0.713960i
$91$	−27.1494			−0.298345
$92$			338.333i			3.67753i
$93$	−10.9815	−	19.5306i	−0.118081	−	0.210007i
$94$	161.270			1.71563
$95$		−	48.3159i		−	0.508588i
$96$	−191.330	+	107.579i	−1.99302	+	1.12062i
$97$	128.230			1.32196			0.660979	−	0.750404i	$-0.270141\pi$
$97$	128.230			1.32196			0.660979	+	0.750404i	$0.270141\pi$
$98$			26.1587i			0.266925i
$99$	−100.691	−	61.2314i	−1.01708	−	0.618499i
$100$	49.8242			0.498242
$101$			80.2818i			0.794870i	0.917630	+	0.397435i	$0.130100\pi$
$101$			80.2818i			0.794870i	−0.917630	+	0.397435i	$0.869900\pi$
$102$	−118.797	−	211.280i	−1.16468	−	2.07138i
$103$	−69.3748			−0.673542			−0.336771	−	0.941587i	$-0.609335\pi$
$103$	−69.3748			−0.673542			−0.336771	+	0.941587i	$0.609335\pi$
$104$		−	228.732i		−	2.19935i
$105$	−15.4704	+	8.69859i	−0.147338	+	0.0828438i
$106$	61.6050			0.581179
$107$			18.9210i			0.176831i	0.996084	+	0.0884157i	$0.0281804\pi$
$107$			18.9210i			0.176831i	−0.996084	+	0.0884157i	$0.971820\pi$
$108$	268.894	+	9.18564i	2.48976	+	0.0850522i
$109$	107.724			0.988295			0.494148	−	0.869378i	$-0.335480\pi$
$109$	107.724			0.988295			0.494148	+	0.869378i	$0.335480\pi$
$110$			109.415i			0.994686i
$111$	42.9367	+	76.3629i	0.386818	+	0.687954i
$112$	−114.928			−1.02614
$113$		−	116.992i		−	1.03533i	−0.855583	−	0.517665i	$-0.826801\pi$
$113$		−	116.992i		−	1.03533i	0.855583	−	0.517665i	$-0.173199\pi$
$114$	−211.150	+	118.724i	−1.85219	+	1.04144i
$115$	−75.9205			−0.660178
$116$		−	231.879i		−	1.99896i
$117$	−47.9854	+	78.9086i	−0.410131	+	0.674432i
$118$	−122.446			−1.03768
$119$		−	57.2034i		−	0.480701i
$120$	−73.2852	−	130.338i	−0.610710	−	1.08615i
$121$	−50.4555			−0.416988
$122$		−	57.9639i		−	0.475114i
$123$	−18.2561	+	10.2649i	−0.148423	+	0.0834543i
$124$	74.4248			0.600200
$125$			11.1803i			0.0894427i
$126$	76.0292	+	46.2344i	0.603407	+	0.366940i
$127$	−150.788			−1.18731			−0.593653	−	0.804721i	$-0.702315\pi$
$127$	−150.788			−1.18731			−0.593653	+	0.804721i	$0.702315\pi$
$128$		−	79.7830i		−	0.623305i
$129$	75.1584	+	133.669i	0.582624	+	1.03620i
$130$	85.7459			0.659584
$131$			3.82738i			0.0292167i	0.999893	+	0.0146083i	$0.00465014\pi$
$131$			3.82738i			0.0292167i	−0.999893	+	0.0146083i	$0.995350\pi$
$132$	341.204	−	191.850i	2.58488	−	1.45341i
$133$	−57.1681			−0.429835
$134$			127.571i			0.952024i
$135$	−2.06122	+	60.3386i	−0.0152683	+	0.446953i
$136$	481.936			3.54364
$137$		−	88.7626i		−	0.647902i	−0.946074	−	0.323951i	$-0.894989\pi$
$137$		−	88.7626i		−	0.647902i	0.946074	−	0.323951i	$-0.105011\pi$
$138$	186.555	+	331.788i	1.35185	+	2.40426i
$139$	−27.4700			−0.197626			−0.0988130	−	0.995106i	$-0.531505\pi$
$139$	−27.4700			−0.197626			−0.0988130	+	0.995106i	$0.531505\pi$
$140$		−	58.9528i		−	0.421091i
$141$	112.850	−	63.4527i	0.800358	−	0.450019i
$142$	476.819			3.35788
$143$			134.365i			0.939616i
$144$	−203.130	+	334.033i	−1.41063	+	2.31967i
$145$	52.0327			0.358846
$146$		−	292.658i		−	2.00451i
$147$	10.2923	+	18.3049i	0.0700158	+	0.124523i
$148$	−290.994			−1.96618
$149$			61.4882i			0.412672i	0.978481	+	0.206336i	$0.0661541\pi$
$149$			61.4882i			0.412672i	−0.978481	+	0.206336i	$0.933846\pi$
$150$	48.8603	−	27.4728i	0.325736	−	0.183152i
$151$	−238.923			−1.58227			−0.791137	−	0.611639i	$-0.790511\pi$
$151$	−238.923			−1.58227			−0.791137	+	0.611639i	$0.790511\pi$
$152$		−	481.638i		−	3.16867i
$153$	−166.259	−	101.105i	−1.08666	−	0.660814i
$154$	129.462			0.840663
$155$			16.7006i			0.107746i
$156$	−150.347	−	267.393i	−0.963765	−	1.71405i
$157$	−126.588			−0.806292			−0.403146	−	0.915136i	$-0.632083\pi$
$157$	−126.588			−0.806292			−0.403146	+	0.915136i	$0.632083\pi$
$158$			250.447i			1.58511i
$159$	43.1089	−	24.2389i	0.271125	−	0.152446i
$160$	163.606			1.02254
$161$			89.8303i			0.557952i
$162$	268.757	−	139.259i	1.65899	−	0.859622i
$163$	−173.730			−1.06583			−0.532915	−	0.846169i	$-0.678903\pi$
$163$	−173.730			−1.06583			−0.532915	+	0.846169i	$0.678903\pi$
$164$		−	69.5679i		−	0.424194i
$165$	43.0503	+	76.5648i	0.260911	+	0.464029i
$166$	304.932			1.83694
$167$			96.1095i			0.575506i	0.957705	+	0.287753i	$0.0929082\pi$
$167$			96.1095i			0.575506i	−0.957705	+	0.287753i	$0.907092\pi$
$168$	−154.218	+	86.7123i	−0.917962	+	0.516144i
$169$	−63.7017			−0.376933
$170$			180.666i			1.06274i
$171$	−101.042	+	166.157i	−0.590890	+	0.971678i
$172$	−509.369			−2.96145
$173$		−	87.7337i		−	0.507131i	−0.967318	−	0.253566i	$-0.918397\pi$
$173$		−	87.7337i		−	0.507131i	0.967318	−	0.253566i	$-0.0816034\pi$
$174$	−127.857	−	227.394i	−0.734810	−	1.30686i
$175$	13.2288			0.0755929
$176$			568.790i			3.23176i
$177$	−85.6832	+	48.1773i	−0.484086	+	0.272188i
$178$	−522.529			−2.93556
$179$		−	229.013i		−	1.27940i	−0.768624	−	0.639701i	$-0.779058\pi$
$179$		−	229.013i		−	1.27940i	0.768624	−	0.639701i	$-0.220942\pi$
$180$	−171.344	−	104.197i	−0.951911	−	0.578870i
$181$	254.045			1.40357			0.701783	−	0.712391i	$-0.252388\pi$
$181$	254.045			1.40357			0.701783	+	0.712391i	$0.252388\pi$
$182$		−	101.456i		−	0.557450i
$183$	−22.8063	−	40.5610i	−0.124625	−	0.221645i
$184$	−756.816			−4.11313
$185$		−	65.2979i		−	0.352961i
$186$	72.9851	−	41.0375i	0.392393	−	0.220632i
$187$	−283.106			−1.51393
$188$			430.036i			2.28743i
$189$	71.3936	+	2.43887i	0.377744	+	0.0129041i
$190$	180.554			0.950285
$191$			84.5770i			0.442811i	0.975182	+	0.221406i	$0.0710645\pi$
$191$			84.5770i			0.442811i	−0.975182	+	0.221406i	$0.928936\pi$
$192$	−146.543	−	260.627i	−0.763246	−	1.35743i
$193$	325.676			1.68744			0.843720	−	0.536784i	$-0.180361\pi$
$193$	325.676			1.68744			0.843720	+	0.536784i	$0.180361\pi$
$194$			479.190i			2.47005i
$195$	60.0018	−	33.7373i	0.307701	−	0.173012i
$196$	−69.7539			−0.355887
$197$		−	277.493i		−	1.40859i	−0.709905	−	0.704297i	$-0.751262\pi$
$197$		−	277.493i		−	1.40859i	0.709905	−	0.704297i	$-0.248738\pi$
$198$	228.819	−	376.277i	1.15565	−	1.90039i
$199$	−151.689			−0.762256			−0.381128	−	0.924522i	$-0.624464\pi$
$199$	−151.689			−0.762256			−0.381128	+	0.924522i	$0.624464\pi$
$200$			111.452i			0.557258i
$201$	50.1938	+	89.2696i	0.249720	+	0.444127i
$202$	−300.010			−1.48520
$203$		−	61.5659i		−	0.303281i
$204$	563.393	−	316.780i	2.76173	−	1.55284i
$205$	15.6107			0.0761500
$206$		−	259.251i		−	1.25850i
$207$	261.088	+	158.771i	1.26130	+	0.767012i
$208$	445.745			2.14300
$209$			282.931i			1.35374i
$210$	−32.5063	−	57.8123i	−0.154792	−	0.275297i
$211$	−220.598			−1.04549			−0.522745	−	0.852489i	$-0.675092\pi$
$211$	−220.598			−1.04549			−0.522745	+	0.852489i	$0.675092\pi$
$212$			164.274i			0.774876i
$213$	333.660	−	187.608i	1.56648	−	0.880787i
$214$	−70.7068			−0.330406
$215$		−	114.300i		−	0.531630i
$216$	−20.5473	+	601.488i	−0.0951266	+	2.78467i
$217$	19.7604			0.0910619
$218$			402.560i			1.84661i
$219$	−115.148	−	204.791i	−0.525792	−	0.935120i
$220$	−291.763			−1.32620
$221$			221.862i			1.00390i
$222$	−285.365	+	160.453i	−1.28543	+	0.722760i
$223$	214.732			0.962922			0.481461	−	0.876468i	$-0.340106\pi$
$223$	214.732			0.962922			0.481461	+	0.876468i	$0.340106\pi$
$224$		−	193.581i		−	0.864202i
$225$	23.3813	−	38.4489i	0.103917	−	0.170884i
$226$	437.195			1.93449
$227$		−	221.599i		−	0.976208i	−0.872786	−	0.488104i	$-0.837689\pi$
$227$		−	221.599i		−	0.976208i	0.872786	−	0.488104i	$-0.162311\pi$
$228$	−316.585	−	563.045i	−1.38853	−	2.46950i
$229$	−143.791			−0.627908			−0.313954	−	0.949438i	$-0.601654\pi$
$229$	−143.791			−0.627908			−0.313954	+	0.949438i	$0.601654\pi$
$230$		−	283.712i		−	1.23353i
$231$	90.5927	−	50.9378i	0.392176	−	0.220510i
$232$	518.690			2.23573
$233$			16.7638i			0.0719478i	0.999353	+	0.0359739i	$0.0114533\pi$
$233$			16.7638i			0.0719478i	−0.999353	+	0.0359739i	$0.988547\pi$
$234$	−294.878	−	179.319i	−1.26016	−	0.766321i
$235$	−96.4983			−0.410631
$236$		−	326.511i		−	1.38352i
$237$	98.5402	+	175.254i	0.415782	+	0.739467i
$238$	213.766			0.898178
$239$		−	80.9593i		−	0.338742i	−0.985552	−	0.169371i	$-0.945826\pi$
$239$		−	80.9593i		−	0.338742i	0.985552	−	0.169371i	$-0.0541736\pi$
$240$	253.998	−	142.816i	1.05832	−	0.595065i
$241$	−159.830			−0.663194			−0.331597	−	0.943421i	$-0.607587\pi$
$241$	−159.830			−0.663194			−0.331597	+	0.943421i	$0.607587\pi$
$242$		−	188.550i		−	0.779133i
$243$	133.274	−	203.192i	0.548452	−	0.836182i
$244$	154.565			0.633462
$245$		−	15.6525i		−	0.0638877i
$246$	−38.3594	−	68.2221i	−0.155932	−	0.277326i
$247$	221.725			0.897673
$248$			166.481i			0.671293i
$249$	213.380	−	119.978i	0.856947	−	0.481838i
$250$	−41.7804			−0.167122
$251$		−	99.5406i		−	0.396576i	−0.980144	−	0.198288i	$-0.936462\pi$
$251$		−	99.5406i		−	0.396576i	0.980144	−	0.198288i	$-0.0635382\pi$
$252$	−123.287	+	202.737i	−0.489234	+	0.804512i
$253$	444.580			1.75723
$254$		−	563.487i		−	2.21845i
$255$	71.0841	+	126.423i	0.278761	+	0.495777i
$256$	−100.522			−0.392663
$257$			81.1780i			0.315868i	0.987450	+	0.157934i	$0.0504833\pi$
$257$			81.1780i			0.315868i	−0.987450	+	0.157934i	$0.949517\pi$
$258$	−499.516	+	280.864i	−1.93611	+	1.08862i
$259$	−77.2615			−0.298307
$260$			228.647i			0.879412i
$261$	−178.939	−	108.815i	−0.685590	−	0.416917i
$262$	−14.3028			−0.0545907
$263$		−	297.941i		−	1.13286i	−0.824112	−	0.566428i	$-0.808325\pi$
$263$		−	297.941i		−	1.13286i	0.824112	−	0.566428i	$-0.191675\pi$
$264$	429.148	+	763.239i	1.62556	+	2.89106i
$265$	−36.8623			−0.139103
$266$		−	213.635i		−	0.803138i
$267$	−365.646	+	205.593i	−1.36946	+	0.770010i
$268$	−340.177			−1.26932
$269$			290.348i			1.07936i	0.841870	+	0.539681i	$0.181455\pi$
$269$			290.348i			1.07936i	−0.841870	+	0.539681i	$0.818545\pi$
$270$	−225.483	−	7.70269i	−0.835122	−	0.0285285i
$271$	422.723			1.55986			0.779931	−	0.625865i	$-0.215254\pi$
$271$	422.723			1.55986			0.779931	+	0.625865i	$0.215254\pi$
$272$			939.179i			3.45287i
$273$	−39.9185	−	70.9951i	−0.146222	−	0.260055i
$274$	331.702			1.21059
$275$		−	65.4705i		−	0.238075i
$276$	−884.734	+	497.461i	−3.20556	+	1.80240i
$277$	3.16548			0.0114277			0.00571387	−	0.999984i	$-0.498181\pi$
$277$	3.16548			0.0114277			0.00571387	+	0.999984i	$0.498181\pi$
$278$		−	102.654i		−	0.369260i
$279$	34.9257	−	57.4330i	0.125182	−	0.205853i
$280$	131.871			0.470969
$281$			156.543i			0.557091i	0.960423	+	0.278546i	$0.0898524\pi$
$281$			156.543i			0.557091i	−0.960423	+	0.278546i	$0.910148\pi$
$282$	237.120	+	421.717i	0.840850	+	1.49545i
$283$	501.692			1.77276			0.886382	−	0.462954i	$-0.153210\pi$
$283$	501.692			1.77276			0.886382	+	0.462954i	$0.153210\pi$
$284$			1271.47i			4.47700i
$285$	126.345	−	71.0403i	0.443316	−	0.249264i
$286$	−502.116			−1.75565
$287$		−	18.4709i		−	0.0643585i
$288$	−562.637	−	342.147i	−1.95360	−	1.18801i
$289$	−178.461			−0.617512
$290$			194.444i			0.670496i
$291$	188.540	+	335.319i	0.647905	+	1.15230i
$292$	780.392			2.67258
$293$			173.378i			0.591734i	0.955229	+	0.295867i	$0.0956086\pi$
$293$			173.378i			0.591734i	−0.955229	+	0.295867i	$0.904391\pi$
$294$	−68.4045	+	38.4619i	−0.232668	+	0.130823i
$295$	73.2677			0.248365
$296$		−	650.924i		−	2.19907i
$297$	12.0702	−	353.335i	0.0406405	−	1.18968i
$298$	−229.779			−0.771069
$299$		−	348.405i		−	1.16523i
$300$	73.2580	+	130.289i	0.244193	+	0.434298i
$301$	−135.242			−0.449309
$302$		−	892.846i		−	2.95644i
$303$	−209.936	+	118.041i	−0.692856	+	0.389574i
$304$	938.600			3.08750
$305$			34.6837i			0.113717i
$306$	377.823	−	621.304i	1.23472	−	2.03041i
$307$	−24.8109			−0.0808172			−0.0404086	−	0.999183i	$-0.512866\pi$
$307$	−24.8109			−0.0808172			−0.0404086	+	0.999183i	$0.512866\pi$
$308$			345.219i			1.12084i
$309$	−102.004	−	181.414i	−0.330110	−	0.587100i
$310$	−62.4095			−0.201321
$311$			255.231i			0.820680i	0.911933	+	0.410340i	$0.134590\pi$
$311$			255.231i			0.820680i	−0.911933	+	0.410340i	$0.865410\pi$
$312$	598.130	−	336.312i	1.91708	−	1.07792i
$313$	−517.647			−1.65382			−0.826911	−	0.562332i	$-0.809904\pi$
$313$	−517.647			−1.65382			−0.826911	+	0.562332i	$0.809904\pi$
$314$		−	473.053i		−	1.50654i
$315$	−45.4933	−	27.6651i	−0.144423	−	0.0878257i
$316$	−667.834			−2.11340
$317$		−	259.120i		−	0.817413i	−0.912666	−	0.408706i	$-0.865980\pi$
$317$		−	259.120i		−	0.817413i	0.912666	−	0.408706i	$-0.134020\pi$
$318$	90.5797	+	161.096i	0.284842	+	0.506591i
$319$	−304.696			−0.955161
$320$			222.862i			0.696443i
$321$	−49.4780	+	27.8201i	−0.154137	+	0.0866669i
$322$	−335.692			−1.04252
$323$			467.173i			1.44635i
$324$	371.342	+	716.658i	1.14612	+	2.21191i
$325$	−51.3075			−0.157869
$326$		−	649.222i		−	1.99148i
$327$	158.390	+	281.697i	0.484374	+	0.861458i
$328$	155.616			0.474440
$329$			114.178i			0.347047i
$330$	−286.119	+	160.877i	−0.867028	+	0.487506i
$331$	308.463			0.931913			0.465956	−	0.884808i	$-0.345710\pi$
$331$	308.463			0.931913			0.465956	+	0.884808i	$0.345710\pi$
$332$			813.121i			2.44916i
$333$	−136.556	+	224.558i	−0.410079	+	0.674347i
$334$	−359.157			−1.07532
$335$		−	76.3343i		−	0.227864i
$336$	−168.982	−	300.534i	−0.502922	−	0.894446i
$337$	395.297			1.17299			0.586494	−	0.809953i	$-0.300508\pi$
$337$	395.297			1.17299			0.586494	+	0.809953i	$0.300508\pi$
$338$		−	238.051i		−	0.704292i
$339$	305.933	−	172.017i	0.902456	−	0.507426i
$340$	−481.757			−1.41693
$341$		−	97.7965i		−	0.286793i
$342$	−620.921	−	377.590i	−1.81556	−	1.10407i
$343$	−18.5203			−0.0539949
$344$		−	1139.41i		−	3.31223i
$345$	−111.628	−	198.531i	−0.323560	−	0.575451i
$346$	327.857			0.947564
$347$			126.894i			0.365688i	0.983142	+	0.182844i	$0.0585304\pi$
$347$			126.894i			0.365688i	−0.983142	+	0.182844i	$0.941470\pi$
$348$	606.360	−	340.939i	1.74241	−	0.979710i
$349$	−264.985			−0.759269			−0.379635	−	0.925136i	$-0.623950\pi$
$349$	−264.985			−0.759269			−0.379635	+	0.925136i	$0.623950\pi$
$350$			49.4353i			0.141244i
$351$	−276.899	−	9.45910i	−0.788886	−	0.0269490i
$352$	−958.054			−2.72175
$353$			360.423i			1.02103i	0.859869	+	0.510514i	$0.170545\pi$
$353$			360.423i			1.02103i	−0.859869	+	0.510514i	$0.829455\pi$
$354$	−180.036	−	320.194i	−0.508577	−	0.904504i
$355$	−285.312			−0.803697
$356$		−	1393.36i		−	3.91393i
$357$	149.586	−	84.1079i	0.419008	−	0.235596i
$358$	855.811			2.39053
$359$			216.993i			0.604437i	0.953239	+	0.302219i	$0.0977273\pi$
$359$			216.993i			0.604437i	−0.953239	+	0.302219i	$0.902273\pi$
$360$	233.077	−	383.279i	0.647436	−	1.06466i
$361$	105.885			0.293309
$362$			949.357i			2.62253i
$363$	−74.1863	−	131.940i	−0.204370	−	0.363472i
$364$	270.539			0.743239
$365$			175.117i			0.479772i
$366$	151.575	−	85.2262i	0.414138	−	0.232858i
$367$	320.938			0.874491			0.437245	−	0.899342i	$-0.355954\pi$
$367$	320.938			0.874491			0.437245	+	0.899342i	$0.355954\pi$
$368$		−	1474.86i		−	4.00776i
$369$	−53.6849	−	32.6465i	−0.145488	−	0.0884729i
$370$	244.015			0.659501
$371$			43.6161i			0.117564i
$372$	109.429	+	194.619i	0.294164	+	0.523171i
$373$	347.774			0.932371			0.466185	−	0.884687i	$-0.345628\pi$
$373$	347.774			0.932371			0.466185	+	0.884687i	$0.345628\pi$
$374$		−	1057.95i		−	2.82875i
$375$	−29.2364	+	16.4388i	−0.0779637	+	0.0438368i
$376$	−961.947			−2.55837
$377$			238.782i			0.633375i
$378$	−9.11394	+	266.795i	−0.0241110	+	0.705806i
$379$	−433.539			−1.14390			−0.571951	−	0.820288i	$-0.693813\pi$
$379$	−433.539			−1.14390			−0.571951	+	0.820288i	$0.693813\pi$
$380$			481.460i			1.26700i
$381$	−221.708	−	394.307i	−0.581910	−	1.03493i
$382$	−316.060			−0.827383
$383$			512.700i			1.33864i	0.742974	+	0.669321i	$0.233415\pi$
$383$			512.700i			1.33864i	−0.742974	+	0.669321i	$0.766585\pi$
$384$	208.631	−	117.307i	0.543310	−	0.305488i
$385$	−77.4658			−0.201210
$386$			1217.04i			3.15294i
$387$	−239.035	+	393.076i	−0.617661	+	1.01570i
$388$	−1277.79			−3.29327
$389$			289.287i			0.743668i	0.928299	+	0.371834i	$0.121271\pi$
$389$			289.287i			0.743668i	−0.928299	+	0.371834i	$0.878729\pi$
$390$	126.075	+	224.224i	0.323269	+	0.574933i
$391$	734.086			1.87746
$392$		−	156.032i		−	0.398042i
$393$	−10.0085	+	5.62752i	−0.0254670	+	0.0143194i
$394$	1036.98			2.63193
$395$		−	149.859i		−	0.379390i
$396$	1003.37	+	610.160i	2.53375	+	1.54081i
$397$	−256.259			−0.645489			−0.322745	−	0.946486i	$-0.604606\pi$
$397$	−256.259			−0.645489			−0.322745	+	0.946486i	$0.604606\pi$
$398$		−	566.855i		−	1.42426i
$399$	−84.0560	−	149.494i	−0.210667	−	0.374670i
$400$	−217.193			−0.542983
$401$			172.152i			0.429307i	0.976690	+	0.214654i	$0.0688623\pi$
$401$			172.152i			0.429307i	−0.976690	+	0.214654i	$0.931138\pi$
$402$	−333.596	+	187.572i	−0.829842	+	0.466597i
$403$	−76.6405			−0.190175
$404$		−	799.995i		−	1.98019i
$405$	−160.815	+	83.3277i	−0.397074	+	0.205747i
$406$	230.069			0.566673
$407$			382.375i			0.939497i
$408$	708.605	+	1260.25i	1.73678	+	3.08885i
$409$	249.379			0.609728			0.304864	−	0.952396i	$-0.401389\pi$
$409$	249.379			0.609728			0.304864	+	0.952396i	$0.401389\pi$
$410$			58.3367i			0.142285i
$411$	232.112	−	130.510i	0.564750	−	0.317543i
$412$	691.309			1.67793
$413$		−	86.6915i		−	0.209907i
$414$	−593.322	+	975.676i	−1.43314	+	2.35671i
$415$	−182.461			−0.439665
$416$			750.801i			1.80481i
$417$	−40.3900	−	71.8336i	−0.0968585	−	0.172263i
$418$	−1057.30			−2.52943
$419$			228.286i			0.544836i	0.962179	+	0.272418i	$0.0878233\pi$
$419$			228.286i			0.544836i	−0.962179	+	0.272418i	$0.912177\pi$
$420$	154.160	−	86.6801i	0.367049	−	0.206381i
$421$	−515.136			−1.22360			−0.611801	−	0.791012i	$-0.709555\pi$
$421$	−515.136			−1.22360			−0.611801	+	0.791012i	$0.709555\pi$
$422$		−	824.367i		−	1.95348i
$423$	331.855	+	201.805i	0.784527	+	0.477082i
$424$	−367.464			−0.866659
$425$		−	108.104i		−	0.254363i
$426$	701.082	+	1246.87i	1.64573	+	2.92693i
$427$	41.0383			0.0961083
$428$		−	188.544i		−	0.440524i
$429$	−351.362	+	197.561i	−0.819026	+	0.460515i
$430$	427.135			0.993338
$431$		−	176.742i		−	0.410075i	−0.978754	−	0.205038i	$-0.934268\pi$
$431$		−	176.742i		−	0.410075i	0.978754	−	0.205038i	$-0.0657317\pi$
$432$	−1172.16	−	40.0419i	−2.71333	−	0.0926897i
$433$	22.1817			0.0512281			0.0256140	−	0.999672i	$-0.491846\pi$
$433$	22.1817			0.0512281			0.0256140	+	0.999672i	$0.491846\pi$
$434$			73.8439i			0.170147i
$435$	76.5053	+	136.065i	0.175874	+	0.312792i
$436$	−1073.45			−2.46205
$437$		−	733.633i		−	1.67879i
$438$	765.296	−	430.304i	1.74725	−	0.982430i
$439$	52.1005			0.118680			0.0593400	−	0.998238i	$-0.481100\pi$
$439$	52.1005			0.118680			0.0593400	+	0.998238i	$0.481100\pi$
$440$		−	652.645i		−	1.48328i
$441$	−32.7338	+	53.8284i	−0.0742263	+	0.122060i
$442$	−829.089			−1.87577
$443$		−	577.463i		−	1.30353i	−0.758422	−	0.651764i	$-0.774029\pi$
$443$		−	577.463i		−	1.30353i	0.758422	−	0.651764i	$-0.225971\pi$
$444$	−427.858	−	760.944i	−0.963643	−	1.71384i
$445$	312.664			0.702615
$446$			802.442i			1.79920i
$447$	−160.790	+	90.4080i	−0.359710	+	0.202255i
$448$	263.694			0.588602
$449$			272.682i			0.607310i	0.952782	+	0.303655i	$0.0982070\pi$
$449$			272.682i			0.607310i	−0.952782	+	0.303655i	$0.901793\pi$
$450$	143.682	+	87.3748i	0.319293	+	0.194166i
$451$	−91.4143			−0.202693
$452$			1165.81i			2.57922i
$453$	−351.296	−	624.780i	−0.775489	−	1.37921i
$454$	828.106			1.82402
$455$			60.7078i			0.133424i
$456$	1259.48	−	708.168i	2.76201	−	1.55300i
$457$	−527.189			−1.15359			−0.576793	−	0.816890i	$-0.695696\pi$
$457$	−527.189			−1.15359			−0.576793	+	0.816890i	$0.695696\pi$
$458$		−	537.340i		−	1.17323i
$459$	19.9302	−	583.422i	0.0434209	−	1.27107i
$460$	756.535			1.64464
$461$			218.757i			0.474528i	0.971445	+	0.237264i	$0.0762506\pi$
$461$			218.757i			0.474528i	−0.971445	+	0.237264i	$0.923749\pi$
$462$	190.352	+	338.541i	0.412018	+	0.732773i
$463$	335.972			0.725641			0.362820	−	0.931859i	$-0.381814\pi$
$463$	335.972			0.725641			0.362820	+	0.931859i	$0.381814\pi$
$464$			1010.81i			2.17846i
$465$	−43.6718	+	24.5554i	−0.0939179	+	0.0528074i
$466$	−62.6458			−0.134433
$467$		−	582.921i		−	1.24823i	−0.781334	−	0.624113i	$-0.785461\pi$
$467$		−	582.921i		−	1.24823i	0.781334	−	0.624113i	$-0.214539\pi$
$468$	478.166	−	786.311i	1.02172	−	1.68015i
$469$	−90.3200			−0.192580
$470$		−	360.610i		−	0.767255i
$471$	−186.126	−	331.025i	−0.395172	−	0.702813i
$472$	730.371			1.54740
$473$			669.327i			1.41507i
$474$	−654.915	+	368.240i	−1.38168	+	0.776879i
$475$	−108.038			−0.227447
$476$			570.022i			1.19753i
$477$	126.769	+	77.0896i	0.265762	+	0.161614i
$478$	302.541			0.632931
$479$		−	389.458i		−	0.813065i	−0.913636	−	0.406532i	$-0.866738\pi$
$479$		−	389.458i		−	0.813065i	0.913636	−	0.406532i	$-0.133262\pi$
$480$	240.555	+	427.827i	0.501156	+	0.891306i
$481$	299.657			0.622988
$482$		−	597.277i		−	1.23916i
$483$	−234.905	+	132.080i	−0.486345	+	0.273458i
$484$	502.781			1.03880
$485$		−	286.731i		−	0.591198i
$486$	759.321	+	498.038i	1.56239	+	1.02477i
$487$	128.363			0.263580			0.131790	−	0.991278i	$-0.457928\pi$
$487$	128.363			0.263580			0.131790	+	0.991278i	$0.457928\pi$
$488$			345.745i			0.708495i
$489$	−255.441	−	454.301i	−0.522374	−	0.929041i
$490$	58.4926			0.119373
$491$		−	703.343i		−	1.43247i	−0.697859	−	0.716235i	$-0.745864\pi$
$491$		−	703.343i		−	1.43247i	0.697859	−	0.716235i	$-0.254136\pi$
$492$	181.919	−	102.288i	0.369753	−	0.207902i
$493$	−503.111			−1.02051
$494$			828.578i			1.67728i
$495$	−136.917	+	225.151i	−0.276601	+	0.454851i
$496$	−324.432			−0.654096
$497$			337.586i			0.679248i
$498$	448.351	+	797.391i	0.900303	+	1.60119i
$499$	710.959			1.42477			0.712384	−	0.701790i	$-0.247616\pi$
$499$	710.959			1.42477			0.712384	+	0.701790i	$0.247616\pi$
$500$		−	111.410i		−	0.222821i
$501$	−251.325	+	141.313i	−0.501646	+	0.282061i
$502$	371.979			0.740994
$503$		−	222.890i		−	0.443122i	−0.975147	−	0.221561i	$-0.928885\pi$
$503$		−	222.890i		−	0.443122i	0.975147	−	0.221561i	$-0.0711151\pi$
$504$	−453.502	−	275.781i	−0.899805	−	0.547184i
$505$	179.516			0.355477
$506$			1661.38i			3.28335i
$507$	−93.6626	−	166.579i	−0.184739	−	0.328558i
$508$	1502.58			2.95783
$509$			13.3352i			0.0261987i	0.999914	+	0.0130994i	$0.00416978\pi$
$509$			13.3352i			0.0261987i	−0.999914	+	0.0130994i	$0.995830\pi$
$510$	−472.437	+	265.638i	−0.926348	+	0.520859i
$511$	207.201			0.405481
$512$		−	694.777i		−	1.35699i
$513$	−583.063	−	19.9179i	−1.13657	−	0.0388264i
$514$	−303.358			−0.590192
$515$			155.127i			0.301217i
$516$	−748.941	−	1331.99i	−1.45144	−	2.58138i
$517$	565.081			1.09300
$518$		−	288.723i		−	0.557380i
$519$	229.422	−	128.998i	0.442046	−	0.248550i
$520$	−511.460			−0.983578
$521$		−	615.359i		−	1.18111i	−0.806997	−	0.590556i	$-0.798909\pi$
$521$		−	615.359i		−	1.18111i	0.806997	−	0.590556i	$-0.201091\pi$
$522$	406.638	−	668.687i	0.778999	−	1.28101i
$523$	680.178			1.30053			0.650266	−	0.759707i	$-0.274657\pi$
$523$	680.178			1.30053			0.650266	+	0.759707i	$0.274657\pi$
$524$		−	38.1392i		−	0.0727848i
$525$	19.4506	+	34.5930i	0.0370489	+	0.0658913i
$526$	1113.39			2.11671
$527$		−	161.481i		−	0.306415i
$528$	−1487.37	+	836.309i	−2.81700	+	1.58392i
$529$	−623.785			−1.17918
$530$		−	137.753i		−	0.259911i
$531$	−251.965	−	153.224i	−0.474511	−	0.288557i
$532$	569.671			1.07081
$533$			71.6389i			0.134407i
$534$	−768.291	−	1366.40i	−1.43875	−	2.55881i
$535$	42.3086			0.0790814
$536$		−	760.942i		−	1.41967i
$537$	598.864	−	336.725i	1.11520	−	0.627048i
$538$	−1085.02			−2.01676
$539$			91.6587i			0.170053i
$540$	20.5397	−	601.265i	0.0380365	−	1.11345i
$541$	943.869			1.74467			0.872337	−	0.488905i	$-0.162603\pi$
$541$	943.869			1.74467			0.872337	+	0.488905i	$0.162603\pi$
$542$			1579.70i			2.91457i
$543$	373.531	+	664.324i	0.687902	+	1.22343i
$544$	−1581.93			−2.90796
$545$		−	240.879i		−	0.441979i
$546$	265.305	−	149.174i	0.485907	−	0.273212i
$547$	−845.426			−1.54557			−0.772785	−	0.634668i	$-0.781137\pi$
$547$	−845.426			−1.54557			−0.772785	+	0.634668i	$0.781137\pi$
$548$			884.504i			1.61406i
$549$	72.5334	−	119.276i	0.132119	−	0.217261i
$550$	244.660			0.444837
$551$			502.801i			0.912525i
$552$	−1112.77	−	1979.06i	−2.01589	−	3.58525i
$553$	−177.316			−0.320643
$554$			11.8293i			0.0213525i
$555$	170.753	−	96.0095i	0.307663	−	0.172990i
$556$	273.734			0.492328
$557$		−	551.899i		−	0.990842i	−0.868653	−	0.495421i	$-0.835014\pi$
$557$		−	551.899i		−	0.990842i	0.868653	−	0.495421i	$-0.164986\pi$
$558$	214.624	+	130.516i	0.384632	+	0.233900i
$559$	524.534			0.938343
$560$			256.986i			0.458904i
$561$	−416.259	−	740.316i	−0.741994	−	1.31964i
$562$	−584.993			−1.04091
$563$		−	263.433i		−	0.467909i	−0.972248	−	0.233955i	$-0.924833\pi$
$563$		−	263.433i		−	0.467909i	0.972248	−	0.233955i	$-0.0751667\pi$
$564$	−1124.54	+	632.295i	−1.99386	+	1.12109i
$565$	−261.603			−0.463014
$566$			1874.80i			3.31237i
$567$	98.5947	+	190.279i	0.173888	+	0.335589i
$568$	−2844.15			−5.00730
$569$		−	254.373i		−	0.447053i	−0.974698	−	0.223526i	$-0.928243\pi$
$569$		−	254.373i		−	0.447053i	0.974698	−	0.223526i	$-0.0717569\pi$
$570$	265.474	+	472.146i	0.465745	+	0.828326i
$571$	−794.913			−1.39214			−0.696071	−	0.717973i	$-0.745070\pi$
$571$	−794.913			−1.39214			−0.696071	+	0.717973i	$0.745070\pi$
$572$		−	1338.93i		−	2.34078i
$573$	−221.167	+	124.356i	−0.385981	+	0.217026i
$574$	69.0249			0.120252
$575$			169.763i			0.295241i
$576$	466.067	−	766.415i	0.809145	−	1.33058i
$577$	−50.8397			−0.0881104			−0.0440552	−	0.999029i	$-0.514028\pi$
$577$	−50.8397			−0.0881104			−0.0440552	+	0.999029i	$0.514028\pi$
$578$		−	666.900i		−	1.15381i
$579$	478.851	+	851.636i	0.827031	+	1.47087i
$580$	−518.498			−0.893961
$581$			215.891i			0.371585i
$582$	−1253.07	+	704.567i	−2.15304	+	1.21060i
$583$	215.861			0.370259
$584$			1745.66i			2.98914i
$585$	176.445	+	107.299i	0.301615	+	0.183416i
$586$	−647.907			−1.10564
$587$			1064.94i			1.81421i	0.420904	+	0.907105i	$0.361713\pi$
$587$			1064.94i			1.81421i	−0.420904	+	0.907105i	$0.638287\pi$
$588$	−102.561	−	182.405i	−0.174424	−	0.310213i
$589$	−161.381			−0.273991
$590$			273.798i			0.464064i
$591$	725.640	−	408.007i	1.22782	−	0.690367i
$592$	1268.50			2.14273
$593$		−	331.267i		−	0.558629i	−0.960200	−	0.279314i	$-0.909893\pi$
$593$		−	331.267i		−	0.558629i	0.960200	−	0.279314i	$-0.0901072\pi$
$594$	1320.40	+	45.1059i	2.22289	+	0.0759358i
$595$	−127.911			−0.214976
$596$		−	612.720i		−	1.02805i
$597$	−223.033	−	396.664i	−0.373589	−	0.664428i
$598$	1301.97			2.17722
$599$		−	54.5928i		−	0.0911398i	−0.998961	−	0.0455699i	$-0.985490\pi$
$599$		−	54.5928i		−	0.0911398i	0.998961	−	0.0455699i	$-0.0145104\pi$
$600$	−291.444	+	163.871i	−0.485740	+	0.273118i
$601$	−136.822			−0.227657			−0.113829	−	0.993500i	$-0.536311\pi$
$601$	−136.822			−0.227657			−0.113829	+	0.993500i	$0.536311\pi$
$602$		−	505.393i		−	0.839524i
$603$	−159.637	+	262.512i	−0.264738	+	0.435343i
$604$	2380.83			3.94178
$605$			112.822i			0.186483i
$606$	−441.113	−	784.520i	−0.727910	−	1.29459i
$607$	651.001			1.07249			0.536244	−	0.844063i	$-0.319843\pi$
$607$	651.001			1.07249			0.536244	+	0.844063i	$0.319843\pi$
$608$			1580.95i			2.60025i
$609$	160.994	−	90.5223i	0.264358	−	0.148641i
$610$	−129.611			−0.212478
$611$		−	442.839i		−	0.724777i
$612$	1656.75	+	1007.49i	2.70710	+	1.64623i
$613$	−442.652			−0.722108			−0.361054	−	0.932545i	$-0.617583\pi$
$613$	−442.652			−0.722108			−0.361054	+	0.932545i	$0.617583\pi$
$614$		−	92.7172i		−	0.151005i
$615$	22.9530	+	40.8218i	0.0373219	+	0.0663769i
$616$	−772.220			−1.25360
$617$			536.750i			0.869936i	0.900446	+	0.434968i	$0.143240\pi$
$617$			536.750i			0.869936i	−0.900446	+	0.434968i	$0.856760\pi$
$618$	677.936	−	381.184i	1.09698	−	0.616803i
$619$	−220.199			−0.355734			−0.177867	−	0.984055i	$-0.556920\pi$
$619$	−220.199			−0.355734			−0.177867	+	0.984055i	$0.556920\pi$
$620$		−	166.419i		−	0.268418i
$621$	−31.2978	+	916.188i	−0.0503990	+	1.47534i
$622$	−953.789			−1.53342
$623$		−	369.949i		−	0.593818i
$624$	655.393	+	1165.61i	1.05031	+	1.86797i
$625$	25.0000			0.0400000
$626$		−	1934.42i		−	3.09013i
$627$	−739.859	+	416.002i	−1.18000	+	0.663480i
$628$	1261.43			2.00864
$629$			631.374i			1.00377i
$630$	103.383	−	170.007i	0.164100	−	0.269852i
$631$	−519.388			−0.823119			−0.411560	−	0.911383i	$-0.635016\pi$
$631$	−519.388			−0.823119			−0.411560	+	0.911383i	$0.635016\pi$
$632$		−	1493.88i		−	2.36373i
$633$	−324.353	−	576.861i	−0.512406	−	0.911313i
$634$	968.319			1.52732
$635$			337.172i			0.530979i
$636$	−429.573	+	241.537i	−0.675429	+	0.379775i
$637$	71.8305			0.112764
$638$		−	1138.64i		−	1.78470i
$639$	981.181	+	596.669i	1.53549	+	0.933755i
$640$	−178.400			−0.278750
$641$		−	865.234i		−	1.34982i	−0.737901	−	0.674909i	$-0.764183\pi$
$641$		−	865.234i		−	1.34982i	0.737901	−	0.674909i	$-0.235817\pi$
$642$	−103.962	−	184.897i	−0.161935	−	0.288002i
$643$	−1049.23			−1.63177			−0.815883	−	0.578217i	$-0.803749\pi$
$643$	−1049.23			−1.63177			−0.815883	+	0.578217i	$0.803749\pi$
$644$		−	895.145i		−	1.38998i
$645$	298.893	−	168.059i	0.463401	−	0.260557i
$646$	−1745.80			−2.70248
$647$			808.756i			1.25001i	0.780621	+	0.625005i	$0.214903\pi$
$647$			808.756i			1.25001i	−0.780621	+	0.625005i	$0.785097\pi$
$648$	−1603.09	+	830.655i	−2.47391	+	1.28188i
$649$	−429.045			−0.661087
$650$		−	191.734i		−	0.294975i
$651$	29.0544	+	51.6732i	0.0446304	+	0.0793751i
$652$	1731.19			2.65520
$653$			628.543i			0.962547i	0.876570	+	0.481274i	$0.159826\pi$
$653$			628.543i			0.962547i	−0.876570	+	0.481274i	$0.840174\pi$
$654$	−1052.69	+	591.897i	−1.60961	+	0.905041i
$655$	8.55829			0.0130661
$656$			303.260i			0.462286i
$657$	366.219	−	602.222i	0.557411	−	0.916624i
$658$	−426.679			−0.648449
$659$			16.9190i			0.0256737i	0.999918	+	0.0128369i	$0.00408621\pi$
$659$			16.9190i			0.0256737i	−0.999918	+	0.0128369i	$0.995914\pi$
$660$	−428.989	−	762.956i	−0.649983	−	1.15599i
$661$	−731.023			−1.10593			−0.552967	−	0.833203i	$-0.686505\pi$
$661$	−731.023			−1.10593			−0.552967	+	0.833203i	$0.686505\pi$
$662$			1152.71i			1.74126i
$663$	−580.165	+	326.211i	−0.875061	+	0.492022i
$664$	−1818.87			−2.73926
$665$			127.832i			0.192228i
$666$	−839.162	−	510.305i	−1.26000	−	0.766224i
$667$	790.070			1.18451
$668$		−	957.716i		−	1.43371i
$669$	315.726	+	561.519i	0.471938	+	0.839341i
$670$	285.258			0.425758
$671$		−	203.103i		−	0.302687i
$672$	506.211	−	284.629i	0.753291	−	0.423554i
$673$	1076.89			1.60013			0.800064	−	0.599914i	$-0.204799\pi$
$673$	1076.89			1.60013			0.800064	+	0.599914i	$0.204799\pi$
$674$			1477.21i			2.19170i
$675$	134.921	+	4.60903i	0.199883	+	0.00682819i
$676$	634.777			0.939020
$677$		−	489.988i		−	0.723763i	−0.932224	−	0.361882i	$-0.882134\pi$
$677$		−	489.988i		−	0.723763i	0.932224	−	0.361882i	$-0.117866\pi$
$678$	642.821	+	1143.26i	0.948114	+	1.68622i
$679$	−339.265			−0.499653
$680$		−	1077.64i		−	1.58477i
$681$	579.478	−	325.824i	0.850922	−	0.478449i
$682$	365.461			0.535867
$683$		−	641.762i		−	0.939623i	−0.882767	−	0.469811i	$-0.844322\pi$
$683$		−	641.762i		−	0.939623i	0.882767	−	0.469811i	$-0.155678\pi$
$684$	1006.87	−	1655.73i	1.47203	−	2.42065i
$685$	−198.479			−0.289751
$686$		−	69.2094i		−	0.100888i
$687$	−211.420	−	376.011i	−0.307744	−	0.547323i
$688$	2220.44			3.22738
$689$		−	169.164i		−	0.245521i
$690$	741.900	−	417.150i	1.07522	−	0.604565i
$691$	−1174.09			−1.69912			−0.849559	−	0.527494i	$-0.823132\pi$
$691$	−1174.09			−1.69912			−0.849559	+	0.527494i	$0.823132\pi$
$692$			874.252i			1.26337i
$693$	266.403	+	162.003i	0.384419	+	0.233770i
$694$	−474.197			−0.683280
$695$			61.4248i			0.0883810i
$696$	762.646	+	1356.36i	1.09576	+	1.94880i
$697$	−150.942			−0.216560
$698$		−	990.237i		−	1.41868i
$699$	−43.8371	+	24.6484i	−0.0627141	+	0.0352624i
$700$	−131.822			−0.188318
$701$		−	149.228i		−	0.212878i	−0.994319	−	0.106439i	$-0.966055\pi$
$701$		−	149.228i		−	0.212878i	0.994319	−	0.106439i	$-0.0339450\pi$
$702$	35.3482	−	1034.76i	0.0503536	−	1.47402i
$703$	630.985			0.897560
$704$		−	1305.05i		−	1.85376i
$705$	−141.884	−	252.341i	−0.201255	−	0.357931i
$706$	−1346.89			−1.90777
$707$		−	212.406i		−	0.300432i
$708$	853.819	−	480.079i	1.20596	−	0.678077i
$709$	−1041.49			−1.46895			−0.734476	−	0.678634i	$-0.762572\pi$
$709$	−1041.49			−1.46895			−0.734476	+	0.678634i	$0.762572\pi$
$710$		−	1066.20i		−	1.50169i
$711$	−313.398	+	515.362i	−0.440785	+	0.724841i
$712$	3116.80			4.37753
$713$			253.584i			0.355658i
$714$	314.307	+	558.995i	0.440206	+	0.782907i
$715$	300.449			0.420209
$716$			2282.08i			3.18726i
$717$	211.707	−	119.037i	0.295268	−	0.166021i
$718$	−810.893			−1.12938
$719$		−	1178.89i		−	1.63962i	−0.572634	−	0.819811i	$-0.694078\pi$
$719$		−	1178.89i		−	1.63962i	0.572634	−	0.819811i	$-0.305922\pi$
$720$	746.921	+	454.213i	1.03739	+	0.630851i
$721$	183.549			0.254575
$722$			395.686i			0.548041i
$723$	−235.003	−	417.952i	−0.325038	−	0.578080i
$724$	−2531.52			−3.49658
$725$		−	116.349i		−	0.160481i
$726$	493.055	−	277.231i	0.679139	−	0.381861i
$727$	−398.248			−0.547796			−0.273898	−	0.961759i	$-0.588313\pi$
$727$	−398.248			−0.547796			−0.273898	+	0.961759i	$0.588313\pi$
$728$			605.168i			0.831275i
$729$	727.301	+	49.7485i	0.997669	+	0.0682421i
$730$	−654.404			−0.896444
$731$			1105.19i			1.51188i
$732$	227.261	+	404.184i	0.310466	+	0.552163i
$733$	−1241.03			−1.69309			−0.846543	−	0.532320i	$-0.821320\pi$
$733$	−1241.03			−1.69309			−0.846543	+	0.532320i	$0.821320\pi$
$734$			1199.33i			1.63397i
$735$	40.9309	−	23.0143i	0.0556883	−	0.0313120i
$736$	2484.21			3.37529
$737$			447.003i			0.606517i
$738$	121.999	−	200.618i	0.165310	−	0.271840i
$739$	872.289			1.18036			0.590182	−	0.807270i	$-0.299056\pi$
$739$	872.289			1.18036			0.590182	+	0.807270i	$0.299056\pi$
$740$			650.683i			0.879301i
$741$	326.010	+	579.808i	0.439959	+	0.782466i
$742$	−162.991			−0.219665
$743$			731.727i			0.984828i	0.870361	+	0.492414i	$0.163885\pi$
$743$			731.727i			0.984828i	−0.870361	+	0.492414i	$0.836115\pi$
$744$	−435.344	+	244.782i	−0.585140	+	0.329008i
$745$	137.492			0.184553
$746$			1299.62i			1.74211i
$747$	627.478	+	381.578i	0.839997	+	0.510814i
$748$	2821.10			3.77152
$749$		−	50.0602i		−	0.0668360i
$750$	−61.4311	−	109.255i	−0.0819081	−	0.145673i
$751$	1429.48			1.90343			0.951717	−	0.306978i	$-0.0993179\pi$
$751$	1429.48			1.90343			0.951717	+	0.306978i	$0.0993179\pi$
$752$		−	1874.61i		−	2.49283i
$753$	260.297	−	146.358i	0.345680	−	0.194366i
$754$	−892.319			−1.18345
$755$			534.249i			0.707615i
$756$	−711.426	−	24.3029i	−0.941040	−	0.0321467i
$757$	−490.187			−0.647539			−0.323769	−	0.946136i	$-0.604950\pi$
$757$	−490.187			−0.647539			−0.323769	+	0.946136i	$0.604950\pi$
$758$		−	1620.11i		−	2.13735i
$759$	653.680	+	1162.57i	0.861238	+	1.53171i
$760$	−1076.98			−1.41707
$761$			1191.76i			1.56605i	0.621991	+	0.783024i	$0.286324\pi$
$761$			1191.76i			1.56605i	−0.621991	+	0.783024i	$0.713676\pi$
$762$	1473.51	−	828.512i	1.93374	−	1.08729i
$763$	−285.011			−0.373540
$764$		−	842.796i		−	1.10314i
$765$	−226.077	+	371.767i	−0.295525	+	0.485970i
$766$	−1915.94			−2.50122
$767$			336.231i			0.438372i
$768$	−147.800	−	262.862i	−0.192448	−	0.342268i
$769$	793.768			1.03221			0.516104	−	0.856526i	$-0.327382\pi$
$769$	793.768			1.03221			0.516104	+	0.856526i	$0.327382\pi$
$770$		−	289.486i		−	0.375956i
$771$	−212.279	+	119.358i	−0.275329	+	0.154810i
$772$	−3245.31			−4.20376
$773$			1182.36i			1.52957i	0.644286	+	0.764785i	$0.277155\pi$
$773$			1182.36i			1.52957i	−0.644286	+	0.764785i	$0.722845\pi$
$774$	−1468.91	−	893.262i	−1.89781	−	1.15408i
$775$	37.3437			0.0481854
$776$		−	2858.29i		−	3.68336i
$777$	−113.600	−	202.037i	−0.146203	−	0.260022i
$778$	−1081.05			−1.38953
$779$			150.849i			0.193645i
$780$	−597.908	+	336.187i	−0.766549	+	0.431009i
$781$	1670.75			2.13924
$782$			2743.25i			3.50799i
$783$	21.4502	−	627.917i	0.0273949	−	0.801937i
$784$	304.070			0.387845
$785$			283.059i			0.360585i
$786$	−21.0298	−	37.4014i	−0.0267554	−	0.0475845i
$787$	−1417.70			−1.80139			−0.900696	−	0.434450i	$-0.856943\pi$
$787$	−1417.70			−1.80139			−0.900696	+	0.434450i	$0.856943\pi$
$788$			2765.17i			3.50910i
$789$	779.110	−	438.072i	0.987465	−	0.555224i
$790$	560.017			0.708883
$791$			309.532i			0.391318i
$792$	−1364.87	+	2244.43i	−1.72332	+	2.83387i
$793$	−159.166			−0.200714
$794$		−	957.629i		−	1.20608i
$795$	−54.1998	−	96.3943i	−0.0681759	−	0.121251i
$796$	1511.56			1.89894
$797$		−	636.801i		−	0.798997i	−0.916734	−	0.399499i	$-0.869184\pi$
$797$		−	636.801i		−	0.798997i	0.916734	−	0.399499i	$-0.130816\pi$
$798$	558.651	−	314.114i	0.700063	−	0.393626i
$799$	933.055			1.16778
$800$		−	365.834i		−	0.457293i
$801$	−1075.24	−	653.869i	−1.34237	−	0.816316i
$802$	−643.325			−0.802151
$803$		−	1025.46i		−	1.27704i
$804$	−500.173	−	889.557i	−0.622106	−	1.10641i
$805$	200.867			0.249524
$806$		−	286.402i		−	0.355337i
$807$	−759.255	+	426.908i	−0.940837	+	0.529006i
$808$	1789.51			2.21474
$809$		−	275.068i		−	0.340009i	−0.985443	−	0.170005i	$-0.945622\pi$
$809$		−	275.068i		−	0.340009i	0.985443	−	0.170005i	$-0.0543783\pi$
$810$	−311.392	−	600.959i	−0.384434	−	0.741924i
$811$	−113.237			−0.139626			−0.0698131	−	0.997560i	$-0.522240\pi$
$811$	−113.237			−0.139626			−0.0698131	+	0.997560i	$0.522240\pi$
$812$			613.495i			0.755535i
$813$	621.542	+	1105.41i	0.764505	+	1.35967i
$814$	−1428.92			−1.75543
$815$			388.472i			0.476653i
$816$	−2455.94	+	1380.90i	−3.00973	+	1.69228i
$817$	1104.50			1.35190
$818$			931.918i			1.13926i
$819$	126.957	−	208.772i	0.155015	−	0.254911i
$820$	−155.558			−0.189705
$821$		−	1170.08i		−	1.42518i	−0.701579	−	0.712592i	$-0.747521\pi$
$821$		−	1170.08i		−	1.42518i	0.701579	−	0.712592i	$-0.252479\pi$
$822$	487.711	+	867.394i	0.593323	+	1.05522i
$823$	−725.581			−0.881630			−0.440815	−	0.897598i	$-0.645311\pi$
$823$	−725.581			−0.881630			−0.440815	+	0.897598i	$0.645311\pi$
$824$			1546.39i			1.87668i
$825$	171.204	−	96.2633i	0.207520	−	0.116683i
$826$	323.962			0.392206
$827$		−	998.577i		−	1.20747i	−0.797185	−	0.603735i	$-0.793679\pi$
$827$		−	998.577i		−	1.20747i	0.797185	−	0.603735i	$-0.206321\pi$
$828$	−2601.70	−	1582.13i	−3.14215	−	1.91079i
$829$	−689.724			−0.831995			−0.415998	−	0.909366i	$-0.636568\pi$
$829$	−689.724			−0.831995			−0.415998	+	0.909366i	$0.636568\pi$
$830$		−	681.848i		−	0.821504i
$831$	4.65431	+	8.27768i	0.00560085	+	0.00996111i
$832$	−1022.73			−1.22924
$833$			151.346i			0.181688i
$834$	268.439	−	150.936i	0.321869	−	0.180978i
$835$	214.907			0.257374
$836$		−	2819.36i		−	3.37244i
$837$	201.539	+	6.88473i	0.240787	+	0.00822548i
$838$	−853.095			−1.01801
$839$		−	1092.33i		−	1.30194i	−0.759105	−	0.650969i	$-0.774363\pi$
$839$		−	1092.33i		−	1.30194i	0.759105	−	0.650969i	$-0.225637\pi$
$840$	193.895	+	344.841i	0.230827	+	0.410525i
$841$	299.519			0.356146
$842$		−	1925.04i		−	2.28627i
$843$	−409.356	+	230.170i	−0.485595	+	0.273036i
$844$	2198.23			2.60454
$845$			142.441i			0.168570i
$846$	−754.138	+	1240.13i	−0.891416	+	1.46587i
$847$	133.493			0.157607
$848$		−	716.100i		−	0.844458i
$849$	737.654	+	1311.92i	0.868850	+	1.54525i
$850$	403.981			0.475271
$851$		−	991.489i		−	1.16509i
$852$	−3324.87	+	1869.48i	−3.90243	+	2.19423i
$853$	−1203.90			−1.41137			−0.705685	−	0.708525i	$-0.749361\pi$
$853$	−1203.90			−1.41137			−0.705685	+	0.708525i	$0.749361\pi$
$854$			153.358i			0.179576i
$855$	371.538	+	225.937i	0.434548	+	0.264254i
$856$	421.755			0.492704
$857$		−	1387.00i		−	1.61844i	−0.587505	−	0.809220i	$-0.699890\pi$
$857$		−	1387.00i		−	1.61844i	0.587505	−	0.809220i	$-0.300110\pi$
$858$	−738.277	−	1313.02i	−0.860463	−	1.53033i
$859$	376.641			0.438465			0.219232	−	0.975673i	$-0.429645\pi$
$859$	376.641			0.438465			0.219232	+	0.975673i	$0.429645\pi$
$860$			1138.98i			1.32440i
$861$	48.3010	−	27.1583i	0.0560987	−	0.0315427i
$862$	660.479			0.766216
$863$			805.783i			0.933700i	0.884337	+	0.466850i	$0.154611\pi$
$863$			805.783i			0.933700i	−0.884337	+	0.466850i	$0.845389\pi$
$864$	67.4456	−	1974.35i	0.0780620	−	2.28513i
$865$	−196.179			−0.226796
$866$			82.8922i			0.0957185i
$867$	−262.397	−	466.672i	−0.302649	−	0.538261i
$868$	−196.910			−0.226854
$869$			877.555i			1.00984i
$870$	−508.467	+	285.897i	−0.584445	+	0.328617i
$871$	350.304			0.402186
$872$		−	2401.21i		−	2.75368i
$873$	−599.636	+	986.059i	−0.686868	+	1.12951i
$874$	2741.55			3.13679
$875$		−	29.5804i		−	0.0338062i
$876$	1147.43	+	2040.71i	1.30986	+	2.32958i
$877$	−387.086			−0.441375			−0.220688	−	0.975345i	$-0.570830\pi$
$877$	−387.086			−0.441375			−0.220688	+	0.975345i	$0.570830\pi$
$878$			194.697i			0.221751i
$879$	−453.381	+	254.923i	−0.515791	+	0.290015i
$880$	1271.85			1.44529
$881$		−	1259.44i		−	1.42955i	−0.699352	−	0.714777i	$-0.746528\pi$
$881$		−	1259.44i		−	1.42955i	0.699352	−	0.714777i	$-0.253472\pi$
$882$	−201.154	−	122.325i	−0.228066	−	0.138690i
$883$	248.902			0.281882			0.140941	−	0.990018i	$-0.454987\pi$
$883$	248.902			0.281882			0.140941	+	0.990018i	$0.454987\pi$
$884$		−	2210.82i		−	2.50093i
$885$	107.728	+	191.594i	0.121726	+	0.216490i
$886$	2157.95			2.43561
$887$		−	487.117i		−	0.549173i	−0.961562	−	0.274587i	$-0.911459\pi$
$887$		−	487.117i		−	0.549173i	0.961562	−	0.274587i	$-0.0885410\pi$
$888$	1702.15	−	957.074i	1.91684	−	1.07779i
$889$	398.947			0.448759
$890$			1168.41i			1.31282i
$891$	941.711	−	487.955i	1.05691	−	0.547649i
$892$	−2139.76			−2.39884
$893$		−	932.480i		−	1.04421i
$894$	−337.851	−	600.867i	−0.377909	−	0.672110i
$895$	−512.088			−0.572166
$896$			211.086i			0.235587i
$897$	911.073	−	512.271i	1.01569	−	0.571094i
$898$	−1019.00			−1.13474
$899$		−	173.796i		−	0.193321i
$900$	−232.991	+	383.137i	−0.258878	+	0.425707i
$901$	356.427			0.395590
$902$		−	341.611i		−	0.378727i
$903$	−198.851	−	353.655i	−0.220211	−	0.391645i
$904$	−2607.80			−2.88473
$905$		−	568.063i		−	0.627694i
$906$	2334.78	−	1312.78i	2.57702	−	1.44898i
$907$	482.964			0.532485			0.266243	−	0.963906i	$-0.414218\pi$
$907$	482.964			0.532485			0.266243	+	0.963906i	$0.414218\pi$
$908$			2208.20i			2.43194i
$909$	−617.349	−	375.418i	−0.679152	−	0.413001i
$910$	−226.862			−0.249299
$911$		−	1029.67i		−	1.13026i	−0.825001	−	0.565132i	$-0.808825\pi$
$911$		−	1029.67i		−	1.13026i	0.825001	−	0.565132i	$-0.191175\pi$
$912$	1380.05	+	2454.42i	1.51322	+	2.69125i
$913$	1068.47			1.17028
$914$		−	1970.08i		−	2.15545i
$915$	−90.6971	+	50.9965i	−0.0991225	+	0.0557338i
$916$	1432.85			1.56425
$917$		−	10.1263i		−	0.0110429i
$918$	2180.22	+	74.4783i	2.37497	+	0.0811311i
$919$	90.9717			0.0989899			0.0494949	−	0.998774i	$-0.484239\pi$
$919$	90.9717			0.0989899			0.0494949	+	0.998774i	$0.484239\pi$
$920$			1692.29i			1.83945i
$921$	−36.4802	−	64.8800i	−0.0396093	−	0.0704452i
$922$	−817.487			−0.886645
$923$		−	1309.32i		−	1.41855i
$924$	−902.742	+	507.586i	−0.976993	+	0.549336i
$925$	−146.010			−0.157849
$926$			1255.51i			1.35584i
$927$	324.414	−	533.477i	0.349962	−	0.575487i
$928$	−1702.57			−1.83467
$929$			1079.33i			1.16182i	0.813968	+	0.580910i	$0.197303\pi$
$929$			1079.33i			1.16182i	−0.813968	+	0.580910i	$0.802697\pi$
$930$	−91.7626	−	163.200i	−0.0986694	−	0.175483i
$931$	151.253			0.162462
$932$		−	167.049i		−	0.179237i
$933$	−667.426	+	375.275i	−0.715354	+	0.402224i
$934$	2178.35			2.33228
$935$			633.043i			0.677052i
$936$	1758.90	+	1069.61i	1.87916	+	1.14274i
$937$	−363.968			−0.388440			−0.194220	−	0.980958i	$-0.562217\pi$
$937$	−363.968			−0.388440			−0.194220	+	0.980958i	$0.562217\pi$
$938$		−	337.522i		−	0.359831i
$939$	−761.112	−	1353.64i	−0.810556	−	1.44157i
$940$	961.590			1.02297
$941$			1666.39i			1.77087i	0.464766	+	0.885433i	$0.346138\pi$
$941$			1666.39i			1.77087i	−0.464766	+	0.885433i	$0.653862\pi$
$942$	1237.03	−	695.545i	1.31319	−	0.738370i
$943$	237.035			0.251363
$944$			1423.32i			1.50776i
$945$	5.45347	−	159.641i	0.00577087	−	0.168932i
$946$	−2501.25			−2.64402
$947$			1846.42i			1.94976i	0.222734	+	0.974879i	$0.428502\pi$
$947$			1846.42i			1.94976i	−0.222734	+	0.974879i	$0.571498\pi$
$948$	−981.937	−	1746.37i	−1.03580	−	1.84217i
$949$	−803.625			−0.846812
$950$		−	403.732i		−	0.424981i
$951$	677.593	−	380.992i	0.712506	−	0.400622i
$952$	−1275.08			−1.33937
$953$			133.619i			0.140209i	0.997540	+	0.0701046i	$0.0223333\pi$
$953$			133.619i			0.140209i	−0.997540	+	0.0701046i	$0.977667\pi$
$954$	−288.081	+	473.728i	−0.301971	+	0.496571i
$955$	189.120			0.198031
$956$			806.746i			0.843876i
$957$	−448.004	−	796.775i	−0.468134	−	0.832576i
$958$	1455.39			1.51919
$959$			234.844i			0.244884i
$960$	−582.779	+	327.681i	−0.607062	+	0.341334i
$961$	−905.218			−0.941954
$962$			1119.81i			1.16404i
$963$	−145.498	−	88.4793i	−0.151088	−	0.0918788i
$964$	1592.68			1.65215
$965$		−	728.233i		−	0.754646i
$966$	−493.578	−	877.828i	−0.510951	−	0.908725i
$967$	946.468			0.978768			0.489384	−	0.872068i	$-0.337222\pi$
$967$	946.468			0.978768			0.489384	+	0.872068i	$0.337222\pi$
$968$			1124.67i			1.16185i
$969$	−1221.65	+	686.898i	−1.26073	+	0.708873i
$970$	1071.50			1.10464
$971$		−	561.947i		−	0.578730i	−0.957219	−	0.289365i	$-0.906556\pi$
$971$		−	561.947i		−	0.578730i	0.957219	−	0.289365i	$-0.0934441\pi$
$972$	−1328.05	+	2024.78i	−1.36631	+	2.08310i
$973$	72.6788			0.0746956
$974$			479.688i			0.492493i
$975$	−75.4390	−	134.168i	−0.0773733	−	0.137608i
$976$	−673.776			−0.690345
$977$			403.696i			0.413200i	0.978426	+	0.206600i	$0.0662398\pi$
$977$			403.696i			0.413200i	−0.978426	+	0.206600i	$0.933760\pi$
$978$	1697.70	−	954.571i	1.73589	−	0.976044i
$979$	−1830.92			−1.87019
$980$			155.974i			0.159158i
$981$	−503.746	+	828.375i	−0.513502	+	0.844419i
$982$	2628.36			2.67654
$983$			1212.94i			1.23392i	0.786995	+	0.616959i	$0.211636\pi$
$983$			1212.94i			1.23392i	−0.786995	+	0.616959i	$0.788364\pi$
$984$	228.807	+	406.934i	0.232528	+	0.413550i
$985$	−620.494			−0.629943
$986$		−	1880.10i		−	1.90680i
$987$	−298.574	+	167.880i	−0.302507	+	0.170091i
$988$	−2209.46			−2.23629
$989$		−	1735.55i		−	1.75485i
$990$	−841.380	−	511.655i	−0.849879	−	0.516823i
$991$	−925.326			−0.933730			−0.466865	−	0.884329i	$-0.654617\pi$
$991$	−925.326			−0.933730			−0.466865	+	0.884329i	$0.654617\pi$
$992$		−	546.464i		−	0.550871i
$993$	453.543	+	806.625i	0.456740	+	0.812312i
$994$	−1261.54			−1.26916
$995$			339.187i			0.340891i
$996$	−2126.30	+	1195.56i	−2.13484	+	1.20036i
$997$	−795.648			−0.798043			−0.399021	−	0.916942i	$-0.630650\pi$
$997$	−795.648			−0.798043			−0.399021	+	0.916942i	$0.630650\pi$
$998$			2656.82i			2.66215i
$999$	−787.997	−	26.9187i	−0.788786	−	0.0269456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.c.a.71.16	yes	16
3.2	odd	2	inner	105.3.c.a.71.1	✓	16
4.3	odd	2		1680.3.l.a.1121.7		16
5.2	odd	4		525.3.f.b.449.2		32
5.3	odd	4		525.3.f.b.449.32		32
5.4	even	2		525.3.c.b.176.1		16
12.11	even	2		1680.3.l.a.1121.8		16
15.2	even	4		525.3.f.b.449.31		32
15.8	even	4		525.3.f.b.449.1		32
15.14	odd	2		525.3.c.b.176.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.c.a.71.1	✓	16	3.2	odd	2	inner
105.3.c.a.71.16	yes	16	1.1	even	1	trivial
525.3.c.b.176.1		16	5.4	even	2
525.3.c.b.176.16		16	15.14	odd	2
525.3.f.b.449.1		32	15.8	even	4
525.3.f.b.449.2		32	5.2	odd	4
525.3.f.b.449.31		32	15.2	even	4
525.3.f.b.449.32		32	5.3	odd	4
1680.3.l.a.1121.7		16	4.3	odd	2
1680.3.l.a.1121.8		16	12.11	even	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.73696i q^{2} +(1.47033 + 2.61498i) q^{3} -9.96484 q^{4} -2.23607i q^{5} +(-9.77207 + 5.49456i) q^{6} -2.64575 q^{7} -22.2903i q^{8} +(-4.67625 + 7.68978i) q^{9} +O(q^{10})\)	\(q+3.73696i q^{2} +(1.47033 + 2.61498i) q^{3} -9.96484 q^{4} -2.23607i q^{5} +(-9.77207 + 5.49456i) q^{6} -2.64575 q^{7} -22.2903i q^{8} +(-4.67625 + 7.68978i) q^{9} +8.35609 q^{10} +13.0941i q^{11} +(-14.6516 - 26.0579i) q^{12} +10.2615 q^{13} -9.88705i q^{14} +(5.84728 - 3.28776i) q^{15} +43.4386 q^{16} +21.6208i q^{17} +(-28.7363 - 17.4750i) q^{18} +21.6075 q^{19} +22.2821i q^{20} +(-3.89013 - 6.91859i) q^{21} -48.9321 q^{22} -33.9527i q^{23} +(58.2888 - 32.7742i) q^{24} -5.00000 q^{25} +38.3467i q^{26} +(-26.9843 - 0.921805i) q^{27} +26.3645 q^{28} +23.2697i q^{29} +(12.2862 + 21.8510i) q^{30} -7.46874 q^{31} +73.1668i q^{32} +(-34.2408 + 19.2527i) q^{33} -80.7961 q^{34} +5.91608i q^{35} +(46.5981 - 76.6273i) q^{36} +29.2021 q^{37} +80.7463i q^{38} +(15.0878 + 26.8336i) q^{39} -49.8427 q^{40} +6.98134i q^{41} +(25.8545 - 14.5372i) q^{42} +51.1167 q^{43} -130.481i q^{44} +(17.1949 + 10.4564i) q^{45} +126.880 q^{46} -43.1554i q^{47} +(63.8691 + 113.591i) q^{48} +7.00000 q^{49} -18.6848i q^{50} +(-56.5381 + 31.7898i) q^{51} -102.254 q^{52} -16.4853i q^{53} +(3.44475 - 100.839i) q^{54} +29.2793 q^{55} +58.9747i q^{56} +(31.7702 + 56.5032i) q^{57} -86.9580 q^{58} +32.7663i q^{59} +(-58.2671 + 32.7620i) q^{60} -15.5110 q^{61} -27.9104i q^{62} +(12.3722 - 20.3452i) q^{63} -99.6668 q^{64} -22.9454i q^{65} +(-71.9463 - 127.956i) q^{66} +34.1378 q^{67} -215.448i q^{68} +(88.7856 - 49.9217i) q^{69} -22.1081 q^{70} -127.596i q^{71} +(171.408 + 104.235i) q^{72} -78.3146 q^{73} +109.127i q^{74} +(-7.35165 - 13.0749i) q^{75} -215.315 q^{76} -34.6437i q^{77} +(-100.276 + 56.3824i) q^{78} +67.0191 q^{79} -97.1317i q^{80} +(-37.2653 - 71.9187i) q^{81} -26.0889 q^{82} -81.5990i q^{83} +(38.7645 + 68.9426i) q^{84} +48.3457 q^{85} +191.021i q^{86} +(-60.8499 + 34.2142i) q^{87} +291.872 q^{88} +139.828i q^{89} +(-39.0752 + 64.2564i) q^{90} -27.1494 q^{91} +338.333i q^{92} +(-10.9815 - 19.5306i) q^{93} +161.270 q^{94} -48.3159i q^{95} +(-191.330 + 107.579i) q^{96} +128.230 q^{97} +26.1587i q^{98} +(-100.691 - 61.2314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9	\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 28 * q^4 - 28 * q^6 + 22 * q^9 - 20 * q^10 + 12 * q^12 + 10 * q^15 + 92 * q^16 - 52 * q^18 - 16 * q^19 - 14 * q^21 + 16 * q^22 + 128 * q^24 - 80 * q^25 - 148 * q^27 + 112 * q^28 + 80 * q^30 - 72 * q^31 - 4 * q^33 - 176 * q^34 - 76 * q^36 - 40 * q^37 + 90 * q^39 - 60 * q^40 + 280 * q^43 + 40 * q^45 + 72 * q^46 - 172 * q^48 + 112 * q^49 + 38 * q^51 - 88 * q^52 + 208 * q^54 + 80 * q^55 - 36 * q^57 - 24 * q^58 - 80 * q^60 - 56 * q^61 - 56 * q^63 - 44 * q^64 - 260 * q^66 - 120 * q^67 + 60 * q^69 + 376 * q^72 - 208 * q^73 - 40 * q^75 + 144 * q^76 - 228 * q^78 - 204 * q^79 + 458 * q^81 - 384 * q^82 - 84 * q^84 + 100 * q^85 - 324 * q^87 + 168 * q^88 - 160 * q^90 - 28 * q^91 + 108 * q^93 + 984 * q^94 + 40 * q^96 + 728 * q^97 - 166 * q^99

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