LMFDB - Embedded newform 63.3.n.b.2.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(2,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("63.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.9
Character	$\chi$	$=$	63.2
Dual form			63.3.n.b.32.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86624 - 1.07747i) q^{2} +(2.05320 + 2.18732i) q^{3} +(0.321900 - 0.557548i) q^{4} -1.87862i q^{5} +(6.18854 + 1.86979i) q^{6} +(-3.79886 - 5.87951i) q^{7} +7.23243i q^{8} +(-0.568739 + 8.98201i) q^{9} +O(q^{10})$	\(q+(1.86624 - 1.07747i) q^{2} +(2.05320 + 2.18732i) q^{3} +(0.321900 - 0.557548i) q^{4} -1.87862i q^{5} +(6.18854 + 1.86979i) q^{6} +(-3.79886 - 5.87951i) q^{7} +7.23243i q^{8} +(-0.568739 + 8.98201i) q^{9} +(-2.02416 - 3.50595i) q^{10} -8.28911i q^{11} +(1.88046 - 0.440658i) q^{12} +(-7.80795 - 13.5238i) q^{13} +(-13.4246 - 6.87940i) q^{14} +(4.10914 - 3.85718i) q^{15} +(9.08036 + 15.7276i) q^{16} +(-12.1546 + 7.01745i) q^{17} +(8.61648 + 17.3754i) q^{18} +(2.57597 - 4.46172i) q^{19} +(-1.04742 - 0.604727i) q^{20} +(5.06054 - 20.3811i) q^{21} +(-8.93131 - 15.4695i) q^{22} +41.1362i q^{23} +(-15.8196 + 14.8496i) q^{24} +21.4708 q^{25} +(-29.1430 - 16.8257i) q^{26} +(-20.8143 + 17.1979i) q^{27} +(-4.50096 + 0.225432i) q^{28} +(9.94271 + 5.74042i) q^{29} +(3.51263 - 11.6259i) q^{30} +(6.78372 - 11.7498i) q^{31} +(8.83838 + 5.10284i) q^{32} +(18.1309 - 17.0192i) q^{33} +(-15.1222 + 26.1925i) q^{34} +(-11.0453 + 7.13661i) q^{35} +(4.82482 + 3.20841i) q^{36} +(27.3835 - 47.4297i) q^{37} -11.1022i q^{38} +(13.5495 - 44.8455i) q^{39} +13.5870 q^{40} +(-1.63319 + 0.942922i) q^{41} +(-12.5160 - 43.4887i) q^{42} +(-7.28633 + 12.6203i) q^{43} +(-4.62158 - 2.66827i) q^{44} +(16.8738 + 1.06844i) q^{45} +(44.3232 + 76.7700i) q^{46} +(19.4530 - 11.2312i) q^{47} +(-15.7576 + 52.1537i) q^{48} +(-20.1373 + 44.6709i) q^{49} +(40.0697 - 23.1342i) q^{50} +(-40.3052 - 12.1777i) q^{51} -10.0535 q^{52} +(28.3293 - 16.3560i) q^{53} +(-20.3142 + 54.5222i) q^{54} -15.5721 q^{55} +(42.5232 - 27.4750i) q^{56} +(15.0482 - 3.52632i) q^{57} +24.7406 q^{58} +(76.5400 + 44.1904i) q^{59} +(-0.827828 - 3.53267i) q^{60} +(-50.3250 - 87.1654i) q^{61} -29.2371i q^{62} +(54.9704 - 30.7775i) q^{63} -50.6502 q^{64} +(-25.4060 + 14.6681i) q^{65} +(15.4989 - 51.2976i) q^{66} +(-60.6144 + 104.987i) q^{67} +9.03568i q^{68} +(-89.9781 + 84.4609i) q^{69} +(-12.9237 + 25.2197i) q^{70} +8.97813i q^{71} +(-64.9618 - 4.11337i) q^{72} +(-21.3298 - 36.9443i) q^{73} -118.020i q^{74} +(44.0839 + 46.9635i) q^{75} +(-1.65841 - 2.87246i) q^{76} +(-48.7359 + 31.4892i) q^{77} +(-23.0332 - 98.2916i) q^{78} +(-6.15560 - 10.6618i) q^{79} +(29.5462 - 17.0585i) q^{80} +(-80.3531 - 10.2168i) q^{81} +(-2.03195 + 3.51944i) q^{82} +(1.14818 + 0.662903i) q^{83} +(-9.73447 - 9.38219i) q^{84} +(13.1831 + 22.8338i) q^{85} +31.4033i q^{86} +(7.85822 + 33.5341i) q^{87} +59.9505 q^{88} +(-133.917 - 77.3170i) q^{89} +(32.6417 - 16.1871i) q^{90} +(-49.8518 + 97.2818i) q^{91} +(22.9354 + 13.2418i) q^{92} +(39.6288 - 9.28642i) q^{93} +(24.2026 - 41.9202i) q^{94} +(-8.38186 - 4.83927i) q^{95} +(6.98541 + 29.8095i) q^{96} +(0.176137 - 0.305078i) q^{97} +(10.5508 + 105.064i) q^{98} +(74.4529 + 4.71434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) $ 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.86624	−	1.07747i	0.933120	−	0.538737i	0.0453229	−	0.998972i	$-0.485568\pi$
$2$	1.86624	−	1.07747i	0.933120	−	0.538737i	0.887797	+	0.460235i	$0.152235\pi$
$3$	2.05320	+	2.18732i	0.684400	+	0.729107i
$3$	2.05320	+	2.18732i	0.684400	+	0.729107i
$4$	0.321900	−	0.557548i	0.0804751	−	0.139387i
$5$		−	1.87862i		−	0.375723i	−0.982196	−	0.187862i	$-0.939844\pi$
$5$		−	1.87862i		−	0.375723i	0.982196	−	0.187862i	$-0.0601557\pi$
$6$	6.18854	+	1.86979i	1.03142	+	0.311632i
$7$	−3.79886	−	5.87951i	−0.542695	−	0.839930i
$7$	−3.79886	−	5.87951i	−0.542695	−	0.839930i
$8$			7.23243i			0.904054i
$9$	−0.568739	+	8.98201i	−0.0631932	+	0.998001i
$10$	−2.02416	−	3.50595i	−0.202416	−	0.350595i
$11$		−	8.28911i		−	0.753556i	−0.926304	−	0.376778i	$-0.877032\pi$
$11$		−	8.28911i		−	0.753556i	0.926304	−	0.376778i	$-0.122968\pi$
$12$	1.88046	−	0.440658i	0.156705	−	0.0367215i
$13$	−7.80795	−	13.5238i	−0.600611	−	1.04029i	−0.992729	−	0.120374i	$-0.961591\pi$
$13$	−7.80795	−	13.5238i	−0.600611	−	1.04029i	0.392117	−	0.919915i	$-0.371743\pi$
$14$	−13.4246	−	6.87940i	−0.958901	−	0.491386i
$15$	4.10914	−	3.85718i	0.273942	−	0.257145i
$16$	9.08036	+	15.7276i	0.567523	+	0.982978i
$17$	−12.1546	+	7.01745i	−0.714975	+	0.412791i	−0.812900	−	0.582403i	$-0.802113\pi$
$17$	−12.1546	+	7.01745i	−0.714975	+	0.412791i	0.0979253	+	0.995194i	$0.468779\pi$
$18$	8.61648	+	17.3754i	0.478693	+	0.965299i
$19$	2.57597	−	4.46172i	0.135578	−	0.234827i	−0.790240	−	0.612797i	$-0.790044\pi$
$19$	2.57597	−	4.46172i	0.135578	−	0.234827i	0.925818	+	0.377970i	$0.123378\pi$
$20$	−1.04742	−	0.604727i	−0.0523709	−	0.0302364i
$21$	5.06054	−	20.3811i	0.240978	−	0.970531i
$22$	−8.93131	−	15.4695i	−0.405968	−	0.703158i
$23$			41.1362i			1.78853i	0.447537	+	0.894266i	$0.352301\pi$
$23$			41.1362i			1.78853i	−0.447537	+	0.894266i	$0.647699\pi$
$24$	−15.8196	+	14.8496i	−0.659152	+	0.618735i
$25$	21.4708			0.858832
$26$	−29.1430	−	16.8257i	−1.12088	−	0.647143i
$27$	−20.8143	+	17.1979i	−0.770899	+	0.636958i
$28$	−4.50096	+	0.225432i	−0.160749	+	0.00805113i
$29$	9.94271	+	5.74042i	0.342852	+	0.197946i	0.661532	−	0.749917i	$-0.269906\pi$
$29$	9.94271	+	5.74042i	0.342852	+	0.197946i	−0.318681	+	0.947862i	$0.603240\pi$
$30$	3.51263	−	11.6259i	0.117088	−	0.387530i
$31$	6.78372	−	11.7498i	0.218830	−	0.379024i	−0.735621	−	0.677394i	$-0.763109\pi$
$31$	6.78372	−	11.7498i	0.218830	−	0.379024i	0.954450	+	0.298369i	$0.0964427\pi$
$32$	8.83838	+	5.10284i	0.276199	+	0.159464i
$33$	18.1309	−	17.0192i	0.549423	−	0.515734i
$34$	−15.1222	+	26.1925i	−0.444772	+	0.770367i
$35$	−11.0453	+	7.13661i	−0.315581	+	0.203903i
$36$	4.82482	+	3.20841i	0.134023	+	0.0891226i
$37$	27.3835	−	47.4297i	0.740096	−	1.28188i	−0.212356	−	0.977192i	$-0.568114\pi$
$37$	27.3835	−	47.4297i	0.740096	−	1.28188i	0.952451	−	0.304691i	$-0.0985531\pi$
$38$		−	11.1022i		−	0.292163i
$39$	13.5495	−	44.8455i	0.347423	−	1.14988i
$40$	13.5870			0.339674
$41$	−1.63319	+	0.942922i	−0.0398339	+	0.0229981i	−0.519785	−	0.854297i	$-0.673988\pi$
$41$	−1.63319	+	0.942922i	−0.0398339	+	0.0229981i	0.479951	+	0.877295i	$0.340655\pi$
$42$	−12.5160	−	43.4887i	−0.297999	−	1.03545i
$43$	−7.28633	+	12.6203i	−0.169449	+	0.293495i	−0.938226	−	0.346022i	$-0.887532\pi$
$43$	−7.28633	+	12.6203i	−0.169449	+	0.293495i	0.768777	+	0.639517i	$0.220866\pi$
$44$	−4.62158	−	2.66827i	−0.105036	−	0.0606425i
$45$	16.8738	+	1.06844i	0.374972	+	0.0237432i
$46$	44.3232	+	76.7700i	0.963548	+	1.66891i
$47$	19.4530	−	11.2312i	0.413894	−	0.238962i	−0.278568	−	0.960417i	$-0.589860\pi$
$47$	19.4530	−	11.2312i	0.413894	−	0.238962i	0.692461	+	0.721455i	$0.256526\pi$
$48$	−15.7576	+	52.1537i	−0.328283	+	1.08653i
$49$	−20.1373	+	44.6709i	−0.410965	+	0.911651i
$50$	40.0697	−	23.1342i	0.801393	−	0.462685i
$51$	−40.3052	−	12.1777i	−0.790298	−	0.238779i
$52$	−10.0535			−0.193337
$53$	28.3293	−	16.3560i	0.534516	−	0.308603i	−0.208338	−	0.978057i	$-0.566805\pi$
$53$	28.3293	−	16.3560i	0.534516	−	0.308603i	0.742853	+	0.669454i	$0.233472\pi$
$54$	−20.3142	+	54.5222i	−0.376188	+	1.00967i
$55$	−15.5721			−0.283128
$56$	42.5232	−	27.4750i	0.759342	−	0.490626i
$57$	15.0482	−	3.52632i	0.264003	−	0.0618653i
$58$	24.7406			0.426563
$59$	76.5400	+	44.1904i	1.29729	+	0.748989i	0.979935	−	0.199318i	$-0.0638728\pi$
$59$	76.5400	+	44.1904i	1.29729	+	0.748989i	0.317353	+	0.948308i	$0.397206\pi$
$60$	−0.827828	−	3.53267i	−0.0137971	−	0.0588778i
$61$	−50.3250	−	87.1654i	−0.825000	−	1.42894i	−0.901920	−	0.431904i	$-0.857842\pi$
$61$	−50.3250	−	87.1654i	−0.825000	−	1.42894i	0.0769202	−	0.997037i	$-0.475491\pi$
$62$		−	29.2371i		−	0.471567i
$63$	54.9704	−	30.7775i	0.872546	−	0.488532i
$64$	−50.6502			−0.791409
$65$	−25.4060	+	14.6681i	−0.390861	+	0.225664i
$66$	15.4989	−	51.2976i	0.234832	−	0.777236i
$67$	−60.6144	+	104.987i	−0.904693	+	1.56697i	−0.0833635	+	0.996519i	$0.526566\pi$
$67$	−60.6144	+	104.987i	−0.904693	+	1.56697i	−0.821329	+	0.570455i	$0.806767\pi$
$68$			9.03568i			0.132878i
$69$	−89.9781	+	84.4609i	−1.30403	+	1.22407i
$70$	−12.9237	+	25.2197i	−0.184625	+	0.360281i
$71$			8.97813i			0.126453i	0.997999	+	0.0632263i	$0.0201390\pi$
$71$			8.97813i			0.126453i	−0.997999	+	0.0632263i	$0.979861\pi$
$72$	−64.9618	−	4.11337i	−0.902247	−	0.0571301i
$73$	−21.3298	−	36.9443i	−0.292189	−	0.506086i	0.682138	−	0.731223i	$-0.261050\pi$
$73$	−21.3298	−	36.9443i	−0.292189	−	0.506086i	−0.974327	+	0.225137i	$0.927717\pi$
$74$		−	118.020i		−	1.59487i
$75$	44.0839	+	46.9635i	0.587785	+	0.626180i
$76$	−1.65841	−	2.87246i	−0.0218212	−	0.0377955i
$77$	−48.7359	+	31.4892i	−0.632934	+	0.408951i
$78$	−23.0332	−	98.2916i	−0.295297	−	1.26015i
$79$	−6.15560	−	10.6618i	−0.0779190	−	0.134960i	0.824433	−	0.565960i	$-0.191494\pi$
$79$	−6.15560	−	10.6618i	−0.0779190	−	0.134960i	−0.902352	+	0.431000i	$0.858161\pi$
$80$	29.5462	−	17.0585i	0.369328	−	0.213231i
$81$	−80.3531	−	10.2168i	−0.992013	−	0.126134i
$82$	−2.03195	+	3.51944i	−0.0247799	+	0.0429200i
$83$	1.14818	+	0.662903i	0.0138335	+	0.00798678i	0.506901	−	0.862004i	$-0.330791\pi$
$83$	1.14818	+	0.662903i	0.0138335	+	0.00798678i	−0.493067	+	0.869991i	$0.664124\pi$
$84$	−9.73447	−	9.38219i	−0.115887	−	0.111693i
$85$	13.1831	+	22.8338i	0.155095	+	0.268633i
$86$			31.4033i			0.365155i
$87$	7.85822	+	33.5341i	0.0903244	+	0.385450i
$88$	59.9505			0.681255
$89$	−133.917	−	77.3170i	−1.50468	−	0.868730i	−0.999985	−	0.00543494i	$-0.998270\pi$
$89$	−133.917	−	77.3170i	−1.50468	−	0.868730i	−0.504699	−	0.863295i	$-0.668397\pi$
$90$	32.6417	−	16.1871i	0.362685	−	0.179856i
$91$	−49.8518	+	97.2818i	−0.547821	+	1.06903i
$92$	22.9354	+	13.2418i	0.249298	+	0.143932i
$93$	39.6288	−	9.28642i	0.426116	−	0.0998540i
$94$	24.2026	−	41.9202i	0.257475	−	0.445960i
$95$	−8.38186	−	4.83927i	−0.0882301	−	0.0509397i
$96$	6.98541	+	29.8095i	0.0727647	+	0.310516i
$97$	0.176137	−	0.305078i	0.00181585	−	0.00314514i	−0.865116	−	0.501572i	$-0.832755\pi$
$97$	0.176137	−	0.305078i	0.00181585	−	0.00314514i	0.866932	+	0.498427i	$0.166089\pi$
$98$	10.5508	+	105.064i	0.107661	+	1.07208i
$99$	74.4529	+	4.71434i	0.752050	+	0.0476196i
$100$	6.91146	−	11.9710i	0.0691146	−	0.119710i
$101$			129.443i			1.28161i	0.767703	+	0.640806i	$0.221400\pi$
$101$			129.443i			1.28161i	−0.767703	+	0.640806i	$0.778600\pi$
$102$	−88.3403	+	20.7012i	−0.866082	+	0.202953i
$103$	129.275			1.25509			0.627547	−	0.778579i	$-0.284059\pi$
$103$	129.275			1.25509			0.627547	+	0.778579i	$0.284059\pi$
$104$	97.8097	−	56.4705i	0.940478	−	0.542985i
$105$	−38.2883	−	9.50682i	−0.364651	−	0.0905411i
$106$	35.2462	−	61.0483i	0.332512	−	0.575927i
$107$	28.4643	+	16.4339i	0.266021	+	0.153587i	0.627078	−	0.778956i	$-0.284251\pi$
$107$	28.4643	+	16.4339i	0.266021	+	0.153587i	−0.361057	+	0.932544i	$0.617584\pi$
$108$	2.88850	+	17.1409i	0.0267454	+	0.158712i
$109$	−24.8411	−	43.0261i	−0.227900	−	0.394735i	0.729285	−	0.684210i	$-0.239853\pi$
$109$	−24.8411	−	43.0261i	−0.227900	−	0.394735i	−0.957186	+	0.289475i	$0.906519\pi$
$110$	−29.0612	+	16.7785i	−0.264193	+	0.152532i
$111$	159.968	−	37.4861i	1.44115	−	0.337712i
$112$	57.9758	−	113.135i	0.517641	−	1.01014i
$113$	−64.2699	+	37.1062i	−0.568760	+	0.328374i	−0.756654	−	0.653816i	$-0.773167\pi$
$113$	−64.2699	+	37.1062i	−0.568760	+	0.328374i	0.187894	+	0.982189i	$0.439834\pi$
$114$	24.2840	−	22.7950i	0.213018	−	0.199956i
$115$	77.2792			0.671993
$116$	6.40112	−	3.69569i	0.0551821	−	0.0318594i
$117$	125.911	−	62.4396i	1.07616	−	0.533672i
$118$	190.456			1.61403
$119$	87.4327	+	44.8046i	0.734729	+	0.376510i
$120$	27.8968	+	29.7191i	0.232473	+	0.247659i
$121$	52.2906			0.432154
$122$	−187.837	−	108.448i	−1.53965	−	0.888916i
$123$	−5.41574	−	1.63630i	−0.0440304	−	0.0133033i
$124$	−4.36737	−	7.56450i	−0.0352207	−	0.0610040i
$125$		−	87.3008i		−	0.698406i
$126$	69.4259	−	116.667i	0.550999	−	0.925932i
$127$	−204.966			−1.61391			−0.806954	−	0.590614i	$-0.798885\pi$
$127$	−204.966			−1.61391			−0.806954	+	0.590614i	$0.798885\pi$
$128$	−129.879	+	74.9856i	−1.01468	+	0.585825i
$129$	−42.5649	+	9.97445i	−0.329960	+	0.0773213i
$130$	−31.6091	+	54.7485i	−0.243147	+	0.421142i
$131$			109.527i			0.836082i	0.908428	+	0.418041i	$0.137283\pi$
$131$			109.527i			0.836082i	−0.908428	+	0.418041i	$0.862717\pi$
$132$	−3.65267	−	15.5874i	−0.0276717	−	0.118086i
$133$	−36.0185	+	1.80399i	−0.270816	+	0.0135639i
$134$			261.242i			1.94957i
$135$	32.3082	+	39.1020i	0.239320	+	0.289645i
$136$	−50.7532	−	87.9072i	−0.373186	−	0.646376i
$137$		−	137.346i		−	1.00253i	−0.865295	−	0.501263i	$-0.832869\pi$
$137$		−	137.346i		−	1.00253i	0.865295	−	0.501263i	$-0.167131\pi$
$138$	−76.9163	+	254.573i	−0.557364	+	1.84473i
$139$	−108.758	−	188.374i	−0.782429	−	1.35521i	−0.930523	−	0.366234i	$-0.880647\pi$
$139$	−108.758	−	188.374i	−0.782429	−	1.35521i	0.148093	−	0.988973i	$-0.452686\pi$
$140$	0.423499	+	8.45559i	0.00302500	+	0.0603970i
$141$	64.5071	+	19.4900i	0.457497	+	0.138227i
$142$	9.67371	+	16.7553i	0.0681247	+	0.117995i
$143$	−112.100	+	64.7210i	−0.783916	+	0.452594i
$144$	−146.430	+	72.6150i	−1.01688	+	0.504271i
$145$	10.7841	−	18.6785i	0.0743728	−	0.128817i
$146$	−79.6131	−	45.9646i	−0.545295	−	0.314826i
$147$	−139.055	+	47.6717i	−0.945955	+	0.324297i
$148$	−17.6295	−	30.5353i	−0.119119	−	0.206319i
$149$		−	274.720i		−	1.84376i	−0.387478	−	0.921879i	$-0.626654\pi$
$149$		−	274.720i		−	1.84376i	0.387478	−	0.921879i	$-0.373346\pi$
$150$	132.873	+	40.1460i	0.885820	+	0.267640i
$151$	96.4577			0.638793			0.319396	−	0.947621i	$-0.396520\pi$
$151$	96.4577			0.638793			0.319396	+	0.947621i	$0.396520\pi$
$152$	32.2691	+	18.6306i	0.212297	+	0.122570i
$153$	−56.1180	−	113.164i	−0.366785	−	0.739632i
$154$	−57.0241	+	111.278i	−0.370286	+	0.722585i
$155$	−22.0733	−	12.7440i	−0.142408	−	0.0822194i
$156$	−20.6419	−	21.9903i	−0.132320	−	0.140963i
$157$	−51.1433	+	88.5828i	−0.325754	+	0.564222i	−0.981665	−	0.190616i	$-0.938951\pi$
$157$	−51.1433	+	88.5828i	−0.325754	+	0.564222i	0.655911	+	0.754838i	$0.272285\pi$
$158$	−22.9757	−	13.2650i	−0.145416	−	0.0839557i
$159$	93.9415	+	28.3833i	0.590827	+	0.178511i
$160$	9.58628	−	16.6039i	0.0599142	−	0.103774i
$161$	241.861	−	156.271i	1.50224	−	0.970627i
$162$	−160.966	+	67.5113i	−0.993620	+	0.416736i
$163$	40.2540	−	69.7220i	0.246957	−	0.427742i	−0.715723	−	0.698384i	$-0.753903\pi$
$163$	40.2540	−	69.7220i	0.246957	−	0.427742i	0.962680	+	0.270642i	$0.0872360\pi$
$164$			1.21411i			0.00740310i
$165$	−31.9726	−	34.0611i	−0.193773	−	0.206431i
$166$	2.85704			0.0172111
$167$	−129.516	+	74.7758i	−0.775542	+	0.447759i	−0.834848	−	0.550480i	$-0.814445\pi$
$167$	−129.516	+	74.7758i	−0.775542	+	0.447759i	0.0593059	+	0.998240i	$0.481111\pi$
$168$	147.405	+	36.6001i	0.877412	+	0.217857i
$169$	−37.4280	+	64.8272i	−0.221468	+	0.383593i
$170$	49.2056	+	28.4089i	0.289445	+	0.167111i
$171$	38.6102	+	25.6750i	0.225790	+	0.150146i
$172$	4.69094	+	8.12495i	0.0272729	+	0.0472381i
$173$	−128.773	+	74.3470i	−0.744352	+	0.429752i	−0.823649	−	0.567099i	$-0.808066\pi$
$173$	−128.773	+	74.3470i	−0.744352	+	0.429752i	0.0792976	+	0.996851i	$0.474732\pi$
$174$	50.7975	+	54.1157i	0.291939	+	0.311010i
$175$	−81.5646	−	126.238i	−0.466084	−	0.721359i
$176$	130.368	−	75.2682i	0.740729	−	0.427660i
$177$	60.4934	+	258.149i	0.341770	+	1.45847i
$178$	−333.228			−1.87207
$179$	107.003	−	61.7780i	0.597780	−	0.345129i	−0.170387	−	0.985377i	$-0.554502\pi$
$179$	107.003	−	61.7780i	0.597780	−	0.345129i	0.768168	+	0.640248i	$0.221169\pi$
$180$	6.02738	−	9.06399i	0.0334854	−	0.0503555i
$181$	312.835			1.72837			0.864185	−	0.503174i	$-0.167834\pi$
$181$	312.835			1.72837			0.864185	+	0.503174i	$0.167834\pi$
$182$	11.7833	+	235.265i	0.0647434	+	1.29267i
$183$	87.3314	−	289.045i	0.477221	−	1.57948i
$184$	−297.515			−1.61693
$185$	−89.1022	−	51.4432i	−0.481633	−	0.278071i
$186$	63.9510	−	60.0297i	0.343822	−	0.322740i
$187$	58.1684	+	100.751i	0.311061	+	0.538774i
$188$		−	14.4613i		−	0.0769218i
$189$	180.186	+	57.0454i	0.953363	+	0.301828i
$190$	−20.8567			−0.109772
$191$	257.120	−	148.448i	1.34618	−	0.777216i	0.358472	−	0.933541i	$-0.383298\pi$
$191$	257.120	−	148.448i	1.34618	−	0.777216i	0.987706	+	0.156325i	$0.0499646\pi$
$192$	−103.995	−	110.788i	−0.541641	−	0.577022i
$193$	−8.13342	+	14.0875i	−0.0421421	+	0.0729922i	−0.886327	−	0.463060i	$-0.846752\pi$
$193$	−8.13342	+	14.0875i	−0.0421421	+	0.0729922i	0.844185	+	0.536052i	$0.180085\pi$
$194$		−	0.759133i		−	0.00391306i
$195$	−84.2474	−	25.4543i	−0.432038	−	0.130535i
$196$	18.4240	+	25.6071i	0.0939999	+	0.130648i
$197$			14.3341i			0.0727620i	0.999338	+	0.0363810i	$0.0115830\pi$
$197$			14.3341i			0.0727620i	−0.999338	+	0.0363810i	$0.988417\pi$
$198$	144.027	−	71.4230i	0.727407	−	0.360722i
$199$	45.6835	+	79.1261i	0.229565	+	0.397619i	0.957679	−	0.287837i	$-0.0929362\pi$
$199$	45.6835	+	79.1261i	0.229565	+	0.397619i	−0.728114	+	0.685456i	$0.759603\pi$
$200$			155.286i			0.776431i
$201$	−354.094	+	82.9767i	−1.76166	+	0.412819i
$202$	139.471	+	241.571i	0.690451	+	1.19590i
$203$	−4.02010	−	80.2653i	−0.0198035	−	0.395396i
$204$	−19.7639	+	18.5521i	−0.0968820	+	0.0909415i
$205$	1.77139	+	3.06814i	0.00864092	+	0.0149665i
$206$	241.257	−	139.290i	1.17115	−	0.676165i
$207$	−369.486	−	23.3958i	−1.78496	−	0.113023i
$208$	141.798	−	245.601i	0.681721	−	1.18078i
$209$	−36.9837	−	21.3525i	−0.176955	−	0.102165i
$210$	−81.6986	+	23.5127i	−0.389041	+	0.111965i
$211$	86.8888	+	150.496i	0.411795	+	0.713251i	0.995086	−	0.0990128i	$-0.0315685\pi$
$211$	86.8888	+	150.496i	0.411795	+	0.713251i	−0.583291	+	0.812263i	$0.698235\pi$
$212$		−	21.0600i		−	0.0993394i
$213$	−19.6381	+	18.4339i	−0.0921974	+	0.0865442i
$214$	70.8282			0.330973
$215$	23.7087	+	13.6882i	0.110273	+	0.0636661i
$216$	−124.382	−	150.538i	−0.575844	−	0.696934i
$217$	−94.8532	+	4.75074i	−0.437112	+	0.0218928i
$218$	−92.7191	−	53.5314i	−0.425317	−	0.245557i
$219$	37.0147	−	122.509i	0.169017	−	0.559403i
$220$	−5.01266	+	8.68217i	−0.0227848	+	0.0394644i
$221$	189.805	+	109.584i	0.858844	+	0.495854i
$222$	258.148	−	242.319i	1.16283	−	1.09153i
$223$	−82.8319	+	143.469i	−0.371444	+	0.643359i	−0.989788	−	0.142548i	$-0.954470\pi$
$223$	−82.8319	+	143.469i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$224$	−3.57359	−	71.3503i	−0.0159535	−	0.318528i
$225$	−12.2113	+	192.851i	−0.0542723	+	0.857115i
$226$	−79.9620	+	138.498i	−0.353814	+	0.612824i
$227$			139.229i			0.613343i	0.951815	+	0.306671i	$0.0992152\pi$
$227$			139.229i			0.613343i	−0.951815	+	0.306671i	$0.900785\pi$
$228$	2.87793	−	9.52522i	0.0126225	−	0.0417773i
$229$	108.840			0.475282			0.237641	−	0.971353i	$-0.423626\pi$
$229$	108.840			0.475282			0.237641	+	0.971353i	$0.423626\pi$
$230$	144.221	−	83.2663i	0.627050	−	0.362027i
$231$	−168.942	−	41.9474i	−0.731349	−	0.181591i
$232$	−41.5172	+	71.9100i	−0.178954	+	0.309957i
$233$	−205.617	−	118.713i	−0.882475	−	0.509497i	−0.0110015	−	0.999939i	$-0.503502\pi$
$233$	−205.617	−	118.713i	−0.882475	−	0.509497i	−0.871474	+	0.490442i	$0.836835\pi$
$234$	167.704	−	252.193i	0.716682	−	1.07775i
$235$	−21.0991	−	36.5447i	−0.0897834	−	0.155509i
$236$	49.2765	−	28.4498i	0.208799	−	0.120550i
$237$	10.6821	−	35.3551i	0.0450722	−	0.149178i
$238$	211.446	−	10.5903i	0.888430	−	0.0444972i
$239$	103.240	−	59.6058i	0.431968	−	0.249397i	−0.268217	−	0.963359i	$-0.586434\pi$
$239$	103.240	−	59.6058i	0.431968	−	0.249397i	0.700185	+	0.713962i	$0.253101\pi$
$240$	97.9767	+	29.6025i	0.408236	+	0.123344i
$241$	421.256			1.74795			0.873975	−	0.485971i	$-0.161534\pi$
$241$	421.256			1.74795			0.873975	+	0.485971i	$0.161534\pi$
$242$	97.5868	−	56.3417i	0.403251	−	0.232817i
$243$	−142.633	−	196.735i	−0.586969	−	0.809609i
$244$	−64.7985			−0.265568
$245$	83.9195	+	37.8302i	0.342529	+	0.154409i
$246$	−11.8701	+	2.78159i	−0.0482526	+	0.0113073i
$247$	−80.4523			−0.325718
$248$	84.9793	+	49.0628i	0.342658	+	0.197834i
$249$	0.907466	+	3.87251i	0.00364444	+	0.0155523i
$250$	−94.0643	−	162.924i	−0.376257	−	0.651697i
$251$			324.926i			1.29453i	0.762266	+	0.647264i	$0.224087\pi$
$251$			324.926i			1.29453i	−0.762266	+	0.647264i	$0.775913\pi$
$252$	0.535044	−	40.5559i	0.00212319	−	0.160936i
$253$	340.983			1.34776
$254$	−382.516	+	220.846i	−1.50597	+	0.869472i
$255$	−22.8773	+	75.7180i	−0.0897148	+	0.296933i
$256$	−60.2897	+	104.425i	−0.235507	+	0.407910i
$257$			213.706i			0.831540i	0.909470	+	0.415770i	$0.136488\pi$
$257$			213.706i			0.831540i	−0.909470	+	0.415770i	$0.863512\pi$
$258$	−68.6891	+	64.4773i	−0.266237	+	0.249912i
$259$	−382.890	+	19.1771i	−1.47834	+	0.0740428i
$260$			18.8867i			0.0726412i
$261$	−57.2154	+	86.0407i	−0.219216	+	0.329658i
$262$	118.012	+	204.403i	0.450428	+	0.780164i
$263$			75.1954i			0.285914i	0.989729	+	0.142957i	$0.0456611\pi$
$263$			75.1954i			0.285914i	−0.989729	+	0.142957i	$0.954339\pi$
$264$	123.090	+	131.131i	0.466251	+	0.496708i
$265$	−30.7266	−	53.2200i	−0.115949	−	0.200830i
$266$	−65.2754	+	42.1757i	−0.245396	+	0.158555i
$267$	−105.841	−	451.666i	−0.396409	−	1.69163i
$268$	39.0236	+	67.5909i	0.145610	+	0.252205i
$269$	131.138	−	75.7123i	0.487500	−	0.281458i	−0.236037	−	0.971744i	$-0.575849\pi$
$269$	131.138	−	75.7123i	0.487500	−	0.281458i	0.723537	+	0.690286i	$0.242515\pi$
$270$	102.426	+	38.1625i	0.379356	+	0.141343i
$271$	−165.822	+	287.212i	−0.611890	+	1.05982i	0.379032	+	0.925384i	$0.376257\pi$
$271$	−165.822	+	287.212i	−0.611890	+	1.05982i	−0.990922	+	0.134440i	$0.957076\pi$
$272$	−220.736	−	127.442i	−0.811529	−	0.468537i
$273$	−315.142	+	90.6973i	−1.15437	+	0.332224i
$274$	−147.987	−	256.321i	−0.540098	−	0.935477i
$275$		−	177.974i		−	0.647178i
$276$	18.1270	+	77.3551i	0.0656776	+	0.280272i
$277$	100.917			0.364323			0.182161	−	0.983269i	$-0.441691\pi$
$277$	100.917			0.364323			0.182161	+	0.983269i	$0.441691\pi$
$278$	−405.936	−	234.367i	−1.46020	−	0.843047i
$279$	101.678	+	67.6140i	0.364438	+	0.242344i
$280$	−51.6150	−	79.8847i	−0.184339	−	0.285303i
$281$	−192.943	−	111.396i	−0.686630	−	0.396426i	0.115718	−	0.993282i	$-0.463083\pi$
$281$	−192.943	−	111.396i	−0.686630	−	0.396426i	−0.802348	+	0.596856i	$0.796416\pi$
$282$	141.386	−	33.1316i	0.501368	−	0.117488i
$283$	19.4781	−	33.7370i	0.0688271	−	0.119212i	−0.829558	−	0.558420i	$-0.811408\pi$
$283$	19.4781	−	33.7370i	0.0688271	−	0.119212i	0.898385	+	0.439208i	$0.144741\pi$
$284$	5.00574	+	2.89007i	0.0176258	+	0.0101763i
$285$	−6.62460	−	28.2698i	−0.0232442	−	0.0991922i
$286$	−139.470	+	241.570i	−0.487658	+	0.844649i
$287$	11.7482	+	6.02032i	0.0409344	+	0.0209767i
$288$	−50.8605	+	76.4842i	−0.176599	+	0.265570i
$289$	−46.0108	+	79.6931i	−0.159207	+	0.275755i
$290$		−	46.4782i		−	0.160269i
$291$	1.02895	−	0.241119i	0.00353591	−	0.000828587i
$292$	−27.4643			−0.0940558
$293$	−309.922	+	178.934i	−1.05775	+	0.610695i	−0.924810	−	0.380429i	$-0.875776\pi$
$293$	−309.922	+	178.934i	−1.05775	+	0.610695i	−0.132944	+	0.991124i	$0.542443\pi$
$294$	−208.146	+	238.795i	−0.707979	+	0.812229i
$295$	83.0167	−	143.789i	0.281413	−	0.487421i
$296$	343.032	+	198.050i	1.15889	+	0.669087i
$297$	142.555	+	172.532i	0.479983	+	0.580915i
$298$	−296.004	−	512.693i	−0.993301	−	1.72045i
$299$	556.316	−	321.189i	1.86059	−	1.07421i
$300$	40.3750	−	9.46128i	0.134583	−	0.0315376i
$301$	101.881	−	5.10272i	0.338475	−	0.0169526i
$302$	180.013	−	103.931i	0.596070	−	0.344141i
$303$	−283.133	+	265.772i	−0.934431	+	0.877135i
$304$	93.5631			0.307773
$305$	−163.750	+	94.5413i	−0.536886	+	0.309972i
$306$	−226.661	−	150.725i	−0.740721	−	0.492565i
$307$	−209.912			−0.683754			−0.341877	−	0.939745i	$-0.611063\pi$
$307$	−209.912			−0.683754			−0.341877	+	0.939745i	$0.611063\pi$
$308$	1.86863	+	37.3090i	0.00606698	+	0.121133i
$309$	265.427	+	282.765i	0.858986	+	0.915097i
$310$	−54.9254			−0.177179
$311$	−418.282	−	241.495i	−1.34496	−	0.776512i	−0.357427	−	0.933941i	$-0.616346\pi$
$311$	−418.282	−	241.495i	−1.34496	−	0.776512i	−0.987530	+	0.157429i	$0.949679\pi$
$312$	324.342	+	97.9960i	1.03956	+	0.314090i
$313$	−156.617	−	271.269i	−0.500374	−	0.866673i	−1.00000		0.000431965i	$-0.999863\pi$
$313$	−156.617	−	271.269i	−0.500374	−	0.866673i	0.499626	−	0.866241i	$-0.333471\pi$
$314$			220.422i			0.701982i
$315$	−57.8192	−	103.268i	−0.183553	−	0.327836i
$316$	−7.92596			−0.0250822
$317$	270.737	−	156.310i	0.854059	−	0.493091i	−0.00795927	−	0.999968i	$-0.502534\pi$
$317$	270.737	−	156.310i	0.854059	−	0.493091i	0.862018	+	0.506877i	$0.169200\pi$
$318$	205.900	−	48.2495i	0.647483	−	0.151728i
$319$	47.5830	−	82.4162i	0.149163	−	0.258358i
$320$			95.1523i			0.297351i
$321$	22.4967	+	96.0025i	0.0700833	+	0.299073i
$322$	282.992	−	552.238i	0.878858	−	1.71502i
$323$			72.3071i			0.223861i
$324$	−31.5621	+	41.5119i	−0.0974138	+	0.128123i
$325$	−167.643	−	290.366i	−0.515824	−	0.893434i
$326$		−	173.491i		−	0.532180i
$327$	43.1081	−	142.677i	0.131829	−	0.436320i
$328$	−6.81963	−	11.8119i	−0.0207915	−	0.0360120i
$329$	−139.933	−	71.7083i	−0.425329	−	0.217958i
$330$	−96.3684	−	29.1166i	−0.292026	−	0.0882320i
$331$	28.1126	+	48.6924i	0.0849323	+	0.147107i	0.905362	−	0.424640i	$-0.139599\pi$
$331$	28.1126	+	48.6924i	0.0849323	+	0.147107i	−0.820430	+	0.571747i	$0.806266\pi$
$332$	0.739200	−	0.426778i	0.00222651	−	0.00128547i
$333$	410.440	+	272.934i	1.23255	+	0.819623i
$334$	−161.138	+	279.099i	−0.482449	+	0.835627i
$335$	197.231	+	113.871i	0.588748	+	0.339914i
$336$	366.499	−	105.478i	1.09077	−	0.313922i
$337$	84.7809	+	146.845i	0.251575	+	0.435741i	0.963960	−	0.266048i	$-0.0857181\pi$
$337$	84.7809	+	146.845i	0.251575	+	0.435741i	−0.712384	+	0.701789i	$0.752385\pi$
$338$			161.311i			0.477251i
$339$	−213.122	−	64.3923i	−0.628679	−	0.189948i
$340$	16.9746			0.0499252
$341$	−97.3950	−	56.2310i	−0.285616	−	0.164900i
$342$	99.7199	+	6.31424i	0.291579	+	0.0184627i
$343$	339.142	−	51.3014i	0.988752	−	0.149567i
$344$	−91.2754	−	52.6979i	−0.265335	−	0.153191i
$345$	158.670	+	169.034i	0.459912	+	0.489954i
$346$	−160.214	+	277.499i	−0.463046	+	0.802020i
$347$	263.870	+	152.345i	0.760431	+	0.439035i	0.829450	−	0.558580i	$-0.188654\pi$
$347$	263.870	+	152.345i	0.760431	+	0.439035i	−0.0690194	+	0.997615i	$0.521987\pi$
$348$	21.2264	+	6.41331i	0.0609955	+	0.0184291i
$349$	56.9456	−	98.6327i	0.163168	−	0.282615i	−0.772835	−	0.634607i	$-0.781162\pi$
$349$	56.9456	−	98.6327i	0.163168	−	0.282615i	0.936003	+	0.351992i	$0.114495\pi$
$350$	−288.237	−	147.706i	−0.823535	−	0.422018i
$351$	395.096	+	147.207i	1.12563	+	0.419394i
$352$	42.2980	−	73.2623i	0.120165	−	0.208132i
$353$			274.642i			0.778023i	0.921233	+	0.389012i	$0.127183\pi$
$353$			274.642i			0.778023i	−0.921233	+	0.389012i	$0.872817\pi$
$354$	391.044	+	416.588i	1.10464	+	1.17680i
$355$	16.8665			0.0475112
$356$	−86.2158	+	49.7767i	−0.242179	+	0.139822i
$357$	81.5148	+	283.236i	0.228333	+	0.793379i
$358$	133.128	−	230.585i	0.371867	−	0.644093i
$359$	−114.579	−	66.1523i	−0.319162	−	0.184268i	0.331857	−	0.943330i	$-0.392325\pi$
$359$	−114.579	−	66.1523i	−0.319162	−	0.184268i	−0.651019	+	0.759061i	$0.725658\pi$
$360$	−7.72744	+	122.038i	−0.0214651	+	0.338995i
$361$	167.229	+	289.649i	0.463237	+	0.802351i
$362$	583.825	−	337.072i	1.61278	−	0.931137i
$363$	107.363	+	114.376i	0.295766	+	0.315086i
$364$	38.1920	+	59.1098i	0.104923	+	0.162390i
$365$	−69.4042	+	40.0705i	−0.190148	+	0.109782i
$366$	−148.457	−	633.524i	−0.405620	−	1.73094i
$367$	−135.136			−0.368217			−0.184108	−	0.982906i	$-0.558940\pi$
$367$	−135.136			−0.368217			−0.184108	+	0.982906i	$0.558940\pi$
$368$	−646.976	+	373.532i	−1.75809	+	1.01503i
$369$	−7.54048	−	15.2056i	−0.0204349	−	0.0412076i
$370$	−221.715			−0.599229
$371$	−203.784	−	104.429i	−0.549284	−	0.281479i
$372$	7.57891	−	25.0843i	0.0203734	−	0.0674308i
$373$	538.499			1.44370			0.721848	−	0.692051i	$-0.243293\pi$
$373$	538.499			1.44370			0.721848	+	0.692051i	$0.243293\pi$
$374$	217.113	+	125.350i	0.580515	+	0.335160i
$375$	190.955	−	179.246i	0.509213	−	0.477989i
$376$	81.2289	+	140.693i	0.216034	+	0.374182i
$377$		−	179.284i		−	0.475553i
$378$	397.734	−	87.6848i	1.05221	−	0.231970i
$379$	−147.000			−0.387863			−0.193932	−	0.981015i	$-0.562124\pi$
$379$	−147.000			−0.387863			−0.193932	+	0.981015i	$0.562124\pi$
$380$	−5.39625	+	3.11552i	−0.0142007	+	0.00819875i
$381$	−420.837	−	448.327i	−1.10456	−	1.17671i
$382$	319.898	−	554.080i	0.837430	−	1.45047i
$383$			365.002i			0.953009i	0.879172	+	0.476504i	$0.158096\pi$
$383$			365.002i			0.953009i	−0.879172	+	0.476504i	$0.841904\pi$
$384$	−430.685	−	130.126i	−1.12158	−	0.338870i
$385$	59.1562	+	91.5561i	0.153652	+	0.237808i
$386$			35.0542i			0.0908139i
$387$	−109.212	−	72.6235i	−0.282200	−	0.187658i
$388$	−0.113397	−	0.196410i	−0.000292261	−	0.000506211i
$389$			28.1868i			0.0724596i	0.999343	+	0.0362298i	$0.0115348\pi$
$389$			28.1868i			0.0724596i	−0.999343	+	0.0362298i	$0.988465\pi$
$390$	−184.652	+	43.2705i	−0.473467	+	0.110950i
$391$	−288.671	−	499.993i	−0.738290	−	1.27876i
$392$	−323.079	−	145.642i	−0.824182	−	0.371534i
$393$	−239.570	+	224.880i	−0.609593	+	0.572214i
$394$	15.4446	+	26.7509i	0.0391996	+	0.0678957i
$395$	−20.0295	+	11.5640i	−0.0507075	+	0.0292760i
$396$	26.5949	−	39.9935i	0.0671588	−	0.100994i
$397$	−113.780	+	197.074i	−0.286601	+	0.496407i	−0.972996	−	0.230822i	$-0.925859\pi$
$397$	−113.780	+	197.074i	−0.286601	+	0.496407i	0.686395	+	0.727229i	$0.259192\pi$
$398$	170.513	+	98.4456i	0.428424	+	0.247351i
$399$	−77.8991	−	75.0800i	−0.195236	−	0.188170i
$400$	194.963	+	337.685i	0.487407	+	0.844213i
$401$			309.562i			0.771976i	0.922504	+	0.385988i	$0.126139\pi$
$401$			309.562i			0.771976i	−0.922504	+	0.385988i	$0.873861\pi$
$402$	−571.419	+	536.382i	−1.42144	+	1.33428i
$403$	−211.868			−0.525726
$404$	72.1705	+	41.6677i	0.178640	+	0.103138i
$405$	−19.1935	+	150.953i	−0.0473914	+	0.372722i
$406$	−93.9863	−	145.463i	−0.231493	−	0.358283i
$407$	−393.150	−	226.985i	−0.965971	−	0.557703i
$408$	88.0746	−	291.505i	0.215869	−	0.714472i
$409$	241.845	−	418.888i	0.591308	−	1.02418i	−0.402749	−	0.915311i	$-0.631945\pi$
$409$	241.845	−	418.888i	0.591308	−	1.02418i	0.994057	−	0.108865i	$-0.0347216\pi$
$410$	6.61168	+	3.81725i	0.0161260	+	0.00931037i
$411$	300.420	−	281.999i	0.730949	−	0.686129i
$412$	41.6136	−	72.0768i	0.101004	−	0.174944i
$413$	−30.9472	−	617.891i	−0.0749326	−	1.49610i
$414$	−714.758	+	354.449i	−1.72647	+	0.856158i
$415$	1.24534	−	2.15699i	0.00300082	−	0.00519757i
$416$		−	159.371i		−	0.383103i
$417$	188.733	−	624.657i	0.452596	−	1.49798i
$418$	−92.0273			−0.220161
$419$	367.460	−	212.153i	0.876993	−	0.506332i	0.00732730	−	0.999973i	$-0.497668\pi$
$419$	367.460	−	212.153i	0.876993	−	0.506332i	0.869666	+	0.493641i	$0.164334\pi$
$420$	−17.6255	+	18.2873i	−0.0419656	+	0.0435413i
$421$	−141.405	+	244.921i	−0.335879	+	0.581760i	−0.983653	−	0.180072i	$-0.942367\pi$
$421$	−141.405	+	244.921i	−0.335879	+	0.581760i	0.647774	+	0.761833i	$0.275700\pi$
$422$	324.311	+	187.241i	0.768509	+	0.443699i
$423$	89.8150	+	181.115i	0.212329	+	0.428167i
$424$	118.293	+	204.890i	0.278994	+	0.483231i
$425$	−260.969	+	150.670i	−0.614044	+	0.354518i
$426$	−16.7873	+	55.5616i	−0.0394067	+	0.130426i
$427$	−321.312	+	627.016i	−0.752488	+	1.46842i
$428$	18.3253	−	10.5801i	0.0428162	−	0.0247199i
$429$	−371.729	−	112.313i	−0.866502	−	0.261803i
$430$	58.9948			0.137197
$431$	−487.196	+	281.283i	−1.13039	+	0.652629i	−0.944032	−	0.329854i	$-0.893001\pi$
$431$	−487.196	+	281.283i	−1.13039	+	0.652629i	−0.186354	+	0.982483i	$0.559667\pi$
$432$	−459.483	−	171.197i	−1.06362	−	0.396289i
$433$	−508.023			−1.17326			−0.586631	−	0.809854i	$-0.699546\pi$
$433$	−508.023			−1.17326			−0.586631	+	0.809854i	$0.699546\pi$
$434$	−171.900	+	111.068i	−0.396083	+	0.255917i
$435$	62.9977	−	14.7626i	0.144822	−	0.0339370i
$436$	−31.9855			−0.0733613
$437$	183.538	+	105.966i	0.419996	+	0.242485i
$438$	−62.9222	−	268.514i	−0.143658	−	0.613045i
$439$	176.926	+	306.445i	0.403021	+	0.698053i	0.994089	−	0.108569i	$-0.0346267\pi$
$439$	176.926	+	306.445i	0.403021	+	0.698053i	−0.591068	+	0.806622i	$0.701293\pi$
$440$		−	112.624i		−	0.255964i
$441$	−389.782	−	206.279i	−0.883859	−	0.467754i
$442$	472.294			1.06854
$443$	−410.091	+	236.766i	−0.925713	+	0.534460i	−0.885453	−	0.464729i	$-0.846152\pi$
$443$	−410.091	+	236.766i	−0.925713	+	0.534460i	−0.0402596	+	0.999189i	$0.512818\pi$
$444$	30.5934	−	101.256i	0.0689041	−	0.228055i
$445$	−145.249	+	251.579i	−0.326402	+	0.565345i
$446$			356.997i			0.800441i
$447$	600.900	−	564.055i	1.34430	−	1.26187i
$448$	192.413	+	297.798i	0.429494	+	0.664728i
$449$		−	216.879i		−	0.483028i	−0.970397	−	0.241514i	$-0.922356\pi$
$449$		−	216.879i		−	0.483028i	0.970397	−	0.241514i	$-0.0776439\pi$
$450$	185.003	+	373.064i	0.411117	+	0.829030i
$451$	7.81599	+	13.5377i	0.0173304	+	0.0300171i
$452$			47.7780i			0.105704i
$453$	198.047	+	210.984i	0.437190	+	0.465748i
$454$	150.015	+	259.834i	0.330430	+	0.572322i
$455$	182.755	+	93.6523i	0.401660	+	0.205829i
$456$	25.5039	+	108.835i	0.0559296	+	0.238673i
$457$	−14.1334	−	24.4797i	−0.0309264	−	0.0535661i	0.850148	−	0.526544i	$-0.176512\pi$
$457$	−14.1334	−	24.4797i	−0.0309264	−	0.0535661i	−0.881074	+	0.472978i	$0.843179\pi$
$458$	203.121	−	117.272i	0.443495	−	0.256052i
$459$	132.304	−	355.096i	0.288243	−	0.773629i
$460$	24.8762	−	43.0868i	0.0540787	−	0.0936670i
$461$	366.061	+	211.346i	0.794059	+	0.458450i	0.841390	−	0.540429i	$-0.181738\pi$
$461$	366.061	+	211.346i	0.794059	+	0.458450i	−0.0473303	+	0.998879i	$0.515071\pi$
$462$	−360.483	+	103.746i	−0.780266	+	0.224559i
$463$	−194.660	−	337.162i	−0.420433	−	0.728211i	0.575549	−	0.817767i	$-0.304788\pi$
$463$	−194.660	−	337.162i	−0.420433	−	0.728211i	−0.995982	+	0.0895564i	$0.971455\pi$
$464$			208.501i			0.449355i
$465$	−17.4456	−	74.4473i	−0.0375175	−	0.160102i
$466$	−511.640			−1.09794
$467$	219.298	+	126.612i	0.469589	+	0.271118i	0.716068	−	0.698031i	$-0.245940\pi$
$467$	219.298	+	126.612i	0.469589	+	0.271118i	−0.246478	+	0.969148i	$0.579273\pi$
$468$	5.71783	−	90.3009i	0.0122176	−	0.192951i
$469$	847.539	−	42.4492i	1.80712	−	0.0905099i
$470$	−78.7520	−	45.4675i	−0.167557	−	0.0967393i
$471$	−298.766	+	70.0114i	−0.634324	+	0.148644i
$472$	−319.604	+	553.570i	−0.677127	+	1.17282i
$473$	104.611	+	60.3972i	0.221165	+	0.127690i
$474$	−18.1588	−	77.4908i	−0.0383097	−	0.163483i
$475$	55.3082	−	95.7967i	0.116438	−	0.201677i
$476$	53.1254	−	34.3253i	0.111608	−	0.0721120i
$477$	130.797	+	263.757i	0.274208	+	0.552949i
$478$	128.447	−	222.478i	0.268719	−	0.465434i
$479$		−	385.897i		−	0.805631i	−0.915281	−	0.402816i	$-0.868032\pi$
$479$		−	385.897i		−	0.805631i	0.915281	−	0.402816i	$-0.131968\pi$
$480$	56.0006	−	13.1229i	0.116668	−	0.0273394i
$481$	−855.237			−1.77804
$482$	786.165	−	453.892i	1.63105	−	0.941685i
$483$	838.403	+	208.172i	1.73582	+	0.430997i
$484$	16.8324	−	29.1545i	0.0347776	−	0.0602366i
$485$	−0.573125	−	0.330894i	−0.00118170	−	0.000682256i
$486$	−478.165	−	213.471i	−0.983879	−	0.439241i
$487$	−197.660	−	342.358i	−0.405873	−	0.702993i	0.588549	−	0.808461i	$-0.299699\pi$
$487$	−197.660	−	342.358i	−0.405873	−	0.702993i	−0.994423	+	0.105468i	$0.966366\pi$
$488$	630.418	−	363.972i	1.29184	−	0.745844i
$489$	235.154	−	55.1048i	0.480887	−	0.112689i
$490$	197.375	−	19.8208i	0.402806	−	0.0404507i
$491$	561.238	−	324.031i	1.14305	−	0.659940i	0.195866	−	0.980631i	$-0.437248\pi$
$491$	561.238	−	324.031i	1.14305	−	0.659940i	0.947184	+	0.320690i	$0.103915\pi$
$492$	−2.65564	+	2.49281i	−0.00539765	+	0.00506668i
$493$	−161.133			−0.326841
$494$	−150.143	+	86.6852i	−0.303934	+	0.175476i
$495$	8.85644	−	139.868i	0.0178918	−	0.282563i
$496$	246.395			0.496763
$497$	52.7870	−	34.1067i	0.106211	−	0.0686252i
$498$	5.86608	+	6.24927i	0.0117793	+	0.0125487i
$499$	261.624			0.524296			0.262148	−	0.965028i	$-0.415569\pi$
$499$	261.624			0.524296			0.262148	+	0.965028i	$0.415569\pi$
$500$	−48.6744	−	28.1022i	−0.0973488	−	0.0562043i
$501$	−429.480	−	129.762i	−0.857246	−	0.259006i
$502$	350.100	+	606.390i	0.697410	+	1.20795i
$503$		−	39.6573i		−	0.0788416i	−0.999223	−	0.0394208i	$-0.987449\pi$
$503$		−	39.6573i		−	0.0788416i	0.999223	−	0.0394208i	$-0.0125513\pi$
$504$	222.596	+	397.570i	0.441660	+	0.788829i
$505$	243.173			0.481531
$506$	636.356	−	367.400i	1.25762	−	0.726087i
$507$	−218.645	+	51.2362i	−0.431253	+	0.101058i
$508$	−65.9787	+	114.279i	−0.129879	+	0.224958i
$509$		−	351.756i		−	0.691072i	−0.938405	−	0.345536i	$-0.887697\pi$
$509$		−	351.756i		−	0.691072i	0.938405	−	0.345536i	$-0.112303\pi$
$510$	38.8897	+	165.958i	0.0762543	+	0.325407i
$511$	−136.185	+	265.755i	−0.266508	+	0.520069i
$512$		−	340.042i		−	0.664146i
$513$	23.1150	+	137.169i	0.0450584	+	0.267385i
$514$	230.262	+	398.826i	0.447981	+	0.775927i
$515$		−	242.857i		−	0.471568i
$516$	−8.14043	+	26.9427i	−0.0157760	+	0.0522146i
$517$	−93.0967	−	161.248i	−0.180071	−	0.311892i
$518$	−693.901	+	448.343i	−1.33958	+	0.865526i
$519$	−427.017	−	129.018i	−0.822769	−	0.248590i
$520$	−106.086	−	183.747i	−0.204012	−	0.353359i
$521$	543.934	−	314.040i	1.04402	−	0.602765i	0.123050	−	0.992400i	$-0.460732\pi$
$521$	543.934	−	314.040i	1.04402	−	0.602765i	0.920969	+	0.389636i	$0.127399\pi$
$522$	−14.0710	+	222.221i	−0.0269559	+	0.425710i
$523$	71.0022	−	122.979i	0.135759	−	0.235142i	−0.790128	−	0.612942i	$-0.789986\pi$
$523$	71.0022	−	122.979i	0.135759	−	0.235142i	0.925887	+	0.377800i	$0.123319\pi$
$524$	61.0664	+	35.2567i	0.116539	+	0.0672838i
$525$	108.654	−	437.599i	0.206960	−	0.833523i
$526$	81.0211	+	140.333i	0.154032	+	0.266792i
$527$			190.418i			0.361324i
$528$	432.308	+	130.617i	0.818765	+	0.247380i
$529$	−1163.19			−2.19884
$530$	−114.686	−	66.2141i	−0.216389	−	0.124932i
$531$	−440.450	+	662.350i	−0.829472	+	1.24736i
$532$	−10.5886	+	20.6627i	−0.0199033	+	0.0388397i
$533$	25.5037	+	14.7246i	0.0478494	+	0.0276258i
$534$	−684.184	−	728.877i	−1.28124	−	1.36494i
$535$	30.8729	−	53.4734i	0.0577064	−	0.0999504i
$536$	−759.313	−	438.390i	−1.41663	−	0.817891i
$537$	354.826	+	107.206i	0.660757	+	0.199640i
$538$	163.156	−	282.595i	0.303264	−	0.525269i
$539$	370.282	+	166.920i	0.686980	+	0.309685i
$540$	32.2013	−	5.42639i	0.0596320	−	0.0100489i
$541$	30.1590	−	52.2370i	0.0557468	−	0.0965563i	−0.836805	−	0.547501i	$-0.815579\pi$
$541$	30.1590	−	52.2370i	0.0557468	−	0.0965563i	0.892552	+	0.450944i	$0.148913\pi$
$542$			714.676i			1.31859i
$543$	642.313	+	684.271i	1.18290	+	1.26017i
$544$	−143.236			−0.263301
$545$	−80.8296	+	46.6670i	−0.148311	+	0.0856275i
$546$	−490.407	+	508.820i	−0.898181	+	0.931905i
$547$	81.2758	−	140.774i	0.148585	−	0.257356i	−0.782120	−	0.623128i	$-0.785862\pi$
$547$	81.2758	−	140.774i	0.148585	−	0.257356i	0.930705	+	0.365772i	$0.119195\pi$
$548$	−76.5770	−	44.2118i	−0.139739	−	0.0806784i
$549$	811.542	−	402.445i	1.47822	−	0.733051i
$550$	−191.762	−	332.142i	−0.348659	−	0.603895i
$551$	51.2243	−	29.5744i	0.0929661	−	0.0536740i
$552$	−610.858	−	650.761i	−1.10663	−	1.17891i
$553$	−39.3020	+	76.6947i	−0.0710704	+	0.138688i
$554$	188.336	−	108.736i	0.339957	−	0.196274i
$555$	−70.4219	−	300.518i	−0.126886	−	0.541474i
$556$	−140.037			−0.251864
$557$	−24.9850	+	14.4251i	−0.0448564	+	0.0258979i	−0.522261	−	0.852786i	$-0.674911\pi$
$557$	−24.9850	+	14.4251i	−0.0448564	+	0.0258979i	0.477404	+	0.878684i	$0.341578\pi$
$558$	262.608	+	16.6283i	0.470624	+	0.0297998i
$559$	227.565			0.407093
$560$	−212.538	−	108.914i	−0.379532	−	0.194490i
$561$	−100.943	+	334.094i	−0.179933	+	0.595534i
$562$	−480.104			−0.854278
$563$	44.4673	+	25.6732i	0.0789828	+	0.0456007i	0.538971	−	0.842324i	$-0.318813\pi$
$563$	44.4673	+	25.6732i	0.0789828	+	0.0456007i	−0.459988	+	0.887925i	$0.652146\pi$
$564$	31.6315	−	29.6920i	0.0560842	−	0.0526453i
$565$	69.7084	+	120.738i	0.123378	+	0.213696i
$566$		−	83.9484i		−	0.148319i
$567$	245.180	+	511.249i	0.432417	+	0.901674i
$568$	−64.9338			−0.114320
$569$	−622.020	+	359.123i	−1.09318	+	0.631148i	−0.934422	−	0.356169i	$-0.884083\pi$
$569$	−622.020	+	359.123i	−1.09318	+	0.631148i	−0.158760	+	0.987317i	$0.550749\pi$
$570$	−42.8231	−	45.6204i	−0.0751282	−	0.0800357i
$571$	52.6345	−	91.1656i	0.0921795	−	0.159660i	−0.816248	−	0.577701i	$-0.803950\pi$
$571$	52.6345	−	91.1656i	0.0921795	−	0.159660i	0.908428	+	0.418041i	$0.137283\pi$
$572$			83.3348i			0.145690i
$573$	852.622	+	257.610i	1.48800	+	0.449580i
$574$	28.4117	−	1.42300i	0.0494977	−	0.00247910i
$575$			883.228i			1.53605i
$576$	28.8067	−	454.941i	0.0500117	−	0.789827i
$577$	4.08616	+	7.07744i	0.00708174	+	0.0122659i	0.869545	−	0.493854i	$-0.164412\pi$
$577$	4.08616	+	7.07744i	0.00708174	+	0.0122659i	−0.862463	+	0.506120i	$0.831079\pi$
$578$			198.302i			0.343083i
$579$	−47.5134	+	11.1341i	−0.0820611	+	0.0192298i
$580$	−6.94278	−	12.0253i	−0.0119703	−	0.0207332i
$581$	−0.464241	−	9.26902i	−0.000799037	−	0.0159536i
$582$	1.66047	−	1.55865i	0.00285303	−	0.00267810i
$583$	−135.576	−	234.825i	−0.232549	−	0.402788i
$584$	267.197	−	154.266i	0.457530	−	0.264155i
$585$	−117.300	−	236.539i	−0.200513	−	0.404340i
$586$	−385.593	+	667.866i	−0.658008	+	1.13970i
$587$	−303.721	−	175.354i	−0.517413	−	0.298728i	0.218463	−	0.975845i	$-0.429896\pi$
$587$	−303.721	−	175.354i	−0.517413	−	0.298728i	−0.735875	+	0.677117i	$0.763229\pi$
$588$	−18.1828	+	92.8756i	−0.0309231	+	0.157952i
$589$	−34.9494	−	60.5341i	−0.0593368	−	0.102774i
$590$		−	357.794i		−	0.606430i
$591$	−31.3533	+	29.4308i	−0.0530513	+	0.0497983i
$592$	994.610			1.68008
$593$	5.22685	+	3.01772i	0.00881424	+	0.00508891i	0.504401	−	0.863470i	$-0.331713\pi$
$593$	5.22685	+	3.01772i	0.00881424	+	0.00508891i	−0.495586	+	0.868559i	$0.665047\pi$
$594$	451.940	+	168.387i	0.760842	+	0.283479i
$595$	84.1707	−	164.253i	0.141463	−	0.276055i
$596$	−153.170	−	88.4325i	−0.256996	−	0.148377i
$597$	−79.2768	+	262.386i	−0.132792	+	0.439508i
$598$	692.146	−	1198.83i	1.15744	−	2.00474i
$599$	−58.7010	−	33.8910i	−0.0979983	−	0.0565793i	0.450200	−	0.892928i	$-0.351353\pi$
$599$	−58.7010	−	33.8910i	−0.0979983	−	0.0565793i	−0.548198	+	0.836348i	$0.684686\pi$
$600$	−339.661	+	318.834i	−0.566101	+	0.531389i
$601$	89.6906	−	155.349i	0.149236	−	0.258484i	−0.781710	−	0.623643i	$-0.785652\pi$
$601$	89.6906	−	155.349i	0.149236	−	0.258484i	0.930945	+	0.365159i	$0.118985\pi$
$602$	184.636	−	119.297i	0.306704	−	0.198168i
$603$	−908.523	−	604.150i	−1.50667	−	1.00191i
$604$	31.0498	−	53.7798i	0.0514069	−	0.0890394i
$605$		−	98.2339i		−	0.162370i
$606$	−242.031	+	801.062i	−0.399392	+	1.32188i
$607$	94.2012			0.155191			0.0775957	−	0.996985i	$-0.475276\pi$
$607$	94.2012			0.155191			0.0775957	+	0.996985i	$0.475276\pi$
$608$	45.5349	−	26.2896i	0.0748929	−	0.0432394i
$609$	167.312	−	173.594i	0.274732	−	0.285048i
$610$	−203.732	+	352.873i	−0.333986	+	0.578481i
$611$	−303.776	−	175.385i	−0.497178	−	0.287046i
$612$	−81.1586	−	5.13894i	−0.132612	−	0.00839696i
$613$	40.0164	+	69.3105i	0.0652797	+	0.113068i	0.896818	−	0.442400i	$-0.145873\pi$
$613$	40.0164	+	69.3105i	0.0652797	+	0.113068i	−0.831538	+	0.555467i	$0.812539\pi$
$614$	−391.747	+	226.175i	−0.638024	+	0.368364i
$615$	−3.07398	+	10.1741i	−0.00499834	+	0.0165432i
$616$	−227.744	−	352.479i	−0.369714	−	0.572207i
$617$	−624.576	+	360.599i	−1.01228	+	0.584439i	−0.911858	−	0.410506i	$-0.865352\pi$
$617$	−624.576	+	360.599i	−1.01228	+	0.584439i	−0.100421	+	0.994945i	$0.532019\pi$
$618$	800.022	+	241.717i	1.29453	+	0.391128i
$619$	295.008			0.476588			0.238294	−	0.971193i	$-0.423412\pi$
$619$	295.008			0.476588			0.238294	+	0.971193i	$0.423412\pi$
$620$	−14.2108	+	8.20461i	−0.0229206	+	0.0132332i
$621$	−707.455	−	856.220i	−1.13922	−	1.37878i
$622$	−1040.82			−1.67334
$623$	54.1462	+	1081.08i	0.0869121	+	1.73529i
$624$	828.348	−	194.111i	1.32748	−	0.311075i
$625$	372.765			0.596424
$626$	−584.570	−	337.502i	−0.933818	−	0.539140i
$627$	−29.2301	−	124.736i	−0.0466189	−	0.198941i
$628$	32.9261	+	57.0297i	0.0524301	+	0.0908116i
$629$			768.650i			1.22202i
$630$	−219.173	−	130.425i	−0.347894	−	0.207023i
$631$	−673.272			−1.06699			−0.533496	−	0.845803i	$-0.679122\pi$
$631$	−673.272			−1.06699			−0.533496	+	0.845803i	$0.679122\pi$
$632$	77.1109	−	44.5200i	0.122011	−	0.0704430i
$633$	−150.783	+	499.052i	−0.238203	+	0.788392i
$634$	336.840	−	583.424i	0.531293	−	0.920226i
$635$			385.053i			0.606383i
$636$	46.0649	−	43.2403i	0.0724290	−	0.0679879i
$637$	761.349	−	76.4564i	1.19521	−	0.120026i
$638$		−	205.078i		−	0.321439i
$639$	−80.6417	−	5.10621i	−0.126200	−	0.00799094i
$640$	140.869	+	243.993i	0.220108	+	0.381238i
$641$			726.037i			1.13266i	0.824178	+	0.566331i	$0.191638\pi$
$641$			726.037i			1.13266i	−0.824178	+	0.566331i	$0.808362\pi$
$642$	145.424	+	154.924i	0.226518	+	0.241315i
$643$	320.110	+	554.447i	0.497839	+	0.862282i	0.999997	−	0.00249385i	$-0.000793817\pi$
$643$	320.110	+	554.447i	0.497839	+	0.862282i	−0.502158	+	0.864776i	$0.667460\pi$
$644$	−9.27340	−	185.153i	−0.0143997	−	0.287504i
$645$	18.7382	+	79.9631i	0.0290514	+	0.123974i
$646$	77.9090	+	134.942i	0.120602	+	0.208889i
$647$	−802.987	+	463.605i	−1.24109	+	0.716545i	−0.969317	−	0.245815i	$-0.920944\pi$
$647$	−802.987	+	463.605i	−1.24109	+	0.716545i	−0.271776	+	0.962360i	$0.587611\pi$
$648$	73.8926	−	581.148i	0.114032	−	0.896834i
$649$	366.299	−	634.448i	0.564405	−	0.977579i
$650$	−625.723	−	361.262i	−0.962651	−	0.555787i
$651$	−205.144	−	197.720i	−0.315121	−	0.303718i
$652$	−25.9156	−	44.8871i	−0.0397478	−	0.0688452i
$653$		−	1193.86i		−	1.82827i	−0.405413	−	0.914134i	$-0.632872\pi$
$653$		−	1193.86i		−	1.82827i	0.405413	−	0.914134i	$-0.367128\pi$
$654$	−73.2805	−	312.717i	−0.112050	−	0.478160i
$655$	205.759			0.314135
$656$	−29.6599	−	17.1242i	−0.0452133	−	0.0261039i
$657$	343.965	−	170.573i	0.523539	−	0.259624i
$658$	−338.413	+	16.9495i	−0.514305	+	0.0257591i
$659$	−516.282	−	298.076i	−0.783433	−	0.452315i	0.0542125	−	0.998529i	$-0.482735\pi$
$659$	−516.282	−	298.076i	−0.783433	−	0.452315i	−0.837646	+	0.546214i	$0.816068\pi$
$660$	−29.2827	+	6.86196i	−0.0443677	+	0.0103969i
$661$	−106.001	+	183.598i	−0.160364	+	0.277758i	−0.934999	−	0.354650i	$-0.884600\pi$
$661$	−106.001	+	183.598i	−0.160364	+	0.277758i	0.774635	+	0.632408i	$0.217933\pi$
$662$	104.930	+	60.5811i	0.158504	+	0.0915123i
$663$	150.012	+	640.161i	0.226263	+	0.965552i
$664$	−4.79440	+	8.30415i	−0.00722049	+	0.0125062i
$665$	3.38901	+	67.6649i	0.00509626	+	0.101752i
$666$	1060.06	+	67.1227i	1.59168	+	0.100785i
$667$	−236.139	+	409.005i	−0.354032	+	0.613201i
$668$			96.2815i			0.144134i
$669$	−483.883	+	113.391i	−0.723293	+	0.169493i
$670$	490.773			0.732497
$671$	−722.524	+	417.149i	−1.07679	+	0.621683i
$672$	148.729	−	154.313i	0.221322	−	0.229633i
$673$	346.329	−	599.859i	0.514604	−	0.891321i	−0.485252	−	0.874374i	$-0.661272\pi$
$673$	346.329	−	599.859i	0.514604	−	0.891321i	0.999856	−	0.0169467i	$-0.00539457\pi$
$674$	316.443	+	182.698i	0.469500	+	0.271066i
$675$	−446.899	+	369.252i	−0.662073	+	0.547040i
$676$	24.0962	+	41.7358i	0.0356453	+	0.0617394i
$677$	−82.2238	+	47.4719i	−0.121453	+	0.0701210i	−0.559496	−	0.828833i	$-0.689005\pi$
$677$	−82.2238	+	47.4719i	−0.121453	+	0.0701210i	0.438043	+	0.898954i	$0.355672\pi$
$678$	−467.118	+	109.462i	−0.688965	+	0.161449i
$679$	−2.46283	+	0.123351i	−0.00362715	+	0.000181666i
$680$	−165.144	+	95.3459i	−0.242859	+	0.140215i
$681$	−304.538	+	285.864i	−0.447192	+	0.419772i
$682$	−242.350			−0.355352
$683$	620.015	−	357.966i	0.907782	−	0.524108i	0.0280655	−	0.999606i	$-0.491065\pi$
$683$	620.015	−	357.966i	0.907782	−	0.524108i	0.879717	+	0.475498i	$0.157732\pi$
$684$	26.7437	−	13.2622i	0.0390989	−	0.0193892i
$685$	−258.021			−0.376672
$686$	577.644	−	461.157i	0.842047	−	0.672241i
$687$	223.470	+	238.067i	0.325283	+	0.346532i
$688$	−264.650			−0.384666
$689$	−442.388	−	255.413i	−0.642072	−	0.370701i
$690$	478.246	+	144.496i	0.693110	+	0.209415i
$691$	−186.265	−	322.620i	−0.269558	−	0.466888i	0.699190	−	0.714936i	$-0.253544\pi$
$691$	−186.265	−	322.620i	−0.269558	−	0.466888i	−0.968748	+	0.248048i	$0.920211\pi$
$692$			95.7294i			0.138337i
$693$	−255.118	−	455.656i	−0.368136	−	0.657512i
$694$	656.592			0.946098
$695$	−353.882	+	204.314i	−0.509183	+	0.293977i
$696$	−242.533	+	56.8341i	−0.348467	+	0.0816581i
$697$	13.2338	−	22.9216i	0.0189868	−	0.0328862i
$698$		−	245.430i		−	0.351618i
$699$	−162.509	−	693.491i	−0.232488	−	0.992119i
$700$	−96.6393	+	4.84020i	−0.138056	+	0.00691457i
$701$			404.972i			0.577706i	0.957374	+	0.288853i	$0.0932738\pi$
$701$			404.972i			0.577706i	−0.957374	+	0.288853i	$0.906726\pi$
$702$	895.956	−	150.982i	1.27629	−	0.215074i
$703$	−141.079	−	244.355i	−0.200681	−	0.347589i
$704$			419.845i			0.596371i
$705$	36.6143	−	121.184i	0.0519352	−	0.171892i
$706$	295.920	+	512.548i	0.419150	+	0.725989i
$707$	761.060	−	491.735i	1.07646	−	0.695524i
$708$	163.403	+	49.3703i	0.230796	+	0.0697321i
$709$	−88.9344	−	154.039i	−0.125436	−	0.217262i	0.796467	−	0.604682i	$-0.206700\pi$
$709$	−88.9344	−	154.039i	−0.125436	−	0.217262i	−0.921903	+	0.387420i	$0.873366\pi$
$710$	31.4769	−	18.1732i	0.0443336	−	0.0255960i
$711$	99.2655	−	49.2259i	0.139614	−	0.0692347i
$712$	559.190	−	968.545i	0.785379	−	1.36032i
$713$	483.340	+	279.057i	0.677897	+	0.391384i
$714$	457.306	+	440.757i	0.640485	+	0.617306i
$715$	121.586	+	210.593i	0.170050	+	0.294535i
$716$		−	79.5455i		−	0.111097i
$717$	342.350	+	103.437i	0.477476	+	0.144264i
$718$	−285.110			−0.397088
$719$	635.474	+	366.891i	0.883831	+	0.510280i	0.871920	−	0.489649i	$-0.162875\pi$
$719$	635.474	+	366.891i	0.883831	+	0.510280i	0.0119111	+	0.999929i	$0.496208\pi$
$720$	136.416	+	275.086i	0.189466	+	0.382064i
$721$	−491.097	−	760.071i	−0.681133	−	1.05419i
$722$	624.178	+	360.369i	0.864512	+	0.499126i
$723$	864.923	+	921.422i	1.19630	+	1.27444i
$724$	100.702	−	174.421i	0.139091	−	0.240912i
$725$	213.478	+	123.251i	0.294452	+	0.170002i
$726$	323.603	+	97.7726i	0.445734	+	0.134673i
$727$	571.120	−	989.209i	0.785585	−	1.36067i	−0.143064	−	0.989713i	$-0.545696\pi$
$727$	571.120	−	989.209i	0.785585	−	1.36067i	0.928649	−	0.370959i	$-0.120971\pi$
$728$	−703.584	−	360.550i	−0.966462	−	0.495260i
$729$	137.468	−	715.922i	0.188570	−	0.982060i
$730$	−86.3499	+	149.562i	−0.118288	+	0.204880i
$731$		−	204.526i		−	0.279789i
$732$	−133.044	−	141.735i	−0.181755	−	0.193627i
$733$	−555.720			−0.758145			−0.379072	−	0.925367i	$-0.623757\pi$
$733$	−555.720			−0.758145			−0.379072	+	0.925367i	$0.623757\pi$
$734$	−252.195	+	145.605i	−0.343590	+	0.198372i
$735$	89.5567	+	261.232i	0.121846	+	0.355417i
$736$	−209.911	+	363.577i	−0.285206	+	0.493991i
$737$	870.251	+	502.440i	1.18080	+	0.681737i
$738$	−30.4560	−	20.2526i	−0.0412683	−	0.0274426i
$739$	711.251	+	1231.92i	0.962451	+	1.66701i	0.716312	+	0.697780i	$0.245829\pi$
$739$	711.251	+	1231.92i	0.962451	+	1.66701i	0.246139	+	0.969235i	$0.420838\pi$
$740$	−57.3641	+	33.1192i	−0.0775190	+	0.0447556i
$741$	−165.185	−	175.975i	−0.222921	−	0.237483i
$742$	−492.829	+	24.6834i	−0.664191	+	0.0332661i
$743$	710.228	−	410.050i	0.955892	−	0.551884i	0.0609855	−	0.998139i	$-0.480576\pi$
$743$	710.228	−	410.050i	0.955892	−	0.551884i	0.894906	+	0.446254i	$0.147242\pi$
$744$	67.1634	+	286.613i	0.0902734	+	0.385232i
$745$	−516.093			−0.692743
$746$	1004.97	−	580.219i	1.34714	−	0.777773i
$747$	−6.60722	+	9.93596i	−0.00884500	+	0.0133012i
$748$	74.8978			0.100131
$749$	−11.5089	−	229.786i	−0.0153656	−	0.306790i
$750$	163.235	−	540.265i	0.217646	−	0.720353i
$751$	536.431			0.714289			0.357145	−	0.934049i	$-0.383750\pi$
$751$	536.431			0.714289			0.357145	+	0.934049i	$0.383750\pi$
$752$	353.281	+	203.967i	0.469788	+	0.271232i
$753$	−710.718	+	667.139i	−0.943849	+	0.885975i
$754$	−193.173	−	334.586i	−0.256198	−	0.443748i
$755$		−	181.207i		−	0.240009i
$756$	89.8073	−	82.0991i	0.118793	−	0.108597i
$757$	−668.336			−0.882874			−0.441437	−	0.897292i	$-0.645531\pi$
$757$	−668.336			−0.882874			−0.441437	+	0.897292i	$0.645531\pi$
$758$	−274.338	+	158.389i	−0.361923	+	0.208956i
$759$	700.106	+	745.839i	0.922406	+	0.982660i
$760$	34.9997	−	60.6212i	0.0460522	−	0.0797648i
$761$		−	858.678i		−	1.12836i	−0.825653	−	0.564178i	$-0.809193\pi$
$761$		−	858.678i		−	1.12836i	0.825653	−	0.564178i	$-0.190807\pi$
$762$	−1268.44	−	383.245i	−1.66462	−	0.502946i
$763$	−158.604	+	309.504i	−0.207870	+	0.405641i
$764$		−	191.142i		−	0.250186i
$765$	−212.591	+	105.424i	−0.277897	+	0.137809i
$766$	393.281	+	681.182i	0.513421	+	0.889271i
$767$		−	1380.14i		−	1.79941i
$768$	−352.198	+	82.5322i	−0.458590	+	0.107464i
$769$	482.278	+	835.330i	0.627150	+	1.08626i	0.988121	+	0.153678i	$0.0491119\pi$
$769$	482.278	+	835.330i	0.627150	+	1.08626i	−0.360971	+	0.932577i	$0.617555\pi$
$770$	209.049	+	107.126i	0.271492	+	0.139125i
$771$	−467.443	+	438.781i	−0.606282	+	0.569106i
$772$	5.23630	+	9.06954i	0.00678277	+	0.0117481i
$773$	−5.75452	+	3.32237i	−0.00744440	+	0.00429803i	−0.503718	−	0.863868i	$-0.668035\pi$
$773$	−5.75452	+	3.32237i	−0.00744440	+	0.00429803i	0.496273	+	0.868166i	$0.334701\pi$
$774$	−282.065	−	17.8603i	−0.364425	−	0.0230753i
$775$	145.652	−	252.277i	0.187938	−	0.325518i
$776$	2.20646	+	1.27390i	0.00284338	+	0.00164162i
$777$	−828.095	−	798.128i	−1.06576	−	1.02719i
$778$	30.3705	+	52.6033i	0.0390366	+	0.0676135i
$779$			9.71578i			0.0124721i
$780$	−41.3113	+	38.7782i	−0.0529632	+	0.0497156i
$781$	74.4208			0.0952891
$782$	−1077.46	−	622.072i	−1.37783	−	0.795488i
$783$	−305.673	+	51.5105i	−0.390387	+	0.0657860i
$784$	−885.422	+	88.9161i	−1.12936	+	0.113413i
$785$	166.413	+	96.0787i	0.211991	+	0.122393i
$786$	−204.792	+	677.811i	−0.260550	+	0.862355i
$787$	−746.114	+	1292.31i	−0.948048	+	1.64207i	−0.198517	+	0.980097i	$0.563612\pi$
$787$	−746.114	+	1292.31i	−0.948048	+	1.64207i	−0.749531	+	0.661969i	$0.769721\pi$
$788$	7.99196	+	4.61416i	0.0101421	+	0.00585553i
$789$	−164.476	+	154.391i	−0.208462	+	0.195680i
$790$	−24.9198	+	43.1624i	−0.0315441	+	0.0546360i
$791$	462.319	+	236.914i	0.584474	+	0.299512i
$792$	−34.0962	+	538.476i	−0.0430507	+	0.679894i
$793$	−785.869	+	1361.17i	−0.991008	+	1.71648i
$794$			490.382i			0.617609i
$795$	53.3213	−	176.480i	0.0670708	−	0.221987i
$796$	58.8222			0.0738972
$797$	−795.162	+	459.087i	−0.997694	+	0.576019i	−0.907565	−	0.419911i	$-0.862061\pi$
$797$	−795.162	+	459.087i	−0.997694	+	0.576019i	−0.0901291	+	0.995930i	$0.528728\pi$
$798$	−226.275	−	56.1831i	−0.283553	−	0.0704049i
$799$	−157.629	+	273.021i	−0.197282	+	0.341703i
$800$	189.767	+	109.562i	0.237209	+	0.136953i
$801$	770.626	−	1158.87i	0.962080	−	1.44678i
$802$	333.545	+	577.718i	0.415892	+	0.720346i
$803$	−306.236	+	176.805i	−0.381364	+	0.220181i
$804$	−67.7196	+	224.135i	−0.0842284	+	0.278775i
$805$	−293.573	−	454.364i	−0.364687	−	0.564427i
$806$	−395.396	+	228.282i	−0.490566	+	0.283228i
$807$	434.859	+	131.387i	0.538858	+	0.162810i
$808$	−936.186			−1.15865
$809$	221.806	−	128.060i	0.274173	−	0.158294i	−0.356610	−	0.934253i	$-0.616067\pi$
$809$	221.806	−	128.060i	0.274173	−	0.158294i	0.630782	+	0.775960i	$0.282734\pi$
$810$	126.828	+	302.394i	0.156578	+	0.373326i
$811$	768.635			0.947762			0.473881	−	0.880589i	$-0.342853\pi$
$811$	768.635			0.947762			0.473881	+	0.880589i	$0.342853\pi$
$812$	−46.0458	−	23.5960i	−0.0567067	−	0.0290592i
$813$	−968.691	+	226.998i	−1.19150	+	0.279211i
$814$	−978.283			−1.20182
$815$	−130.981	−	75.6219i	−0.160713	−	0.0927876i
$816$	−174.459	−	744.484i	−0.213797	−	0.912358i
$817$	37.5388	+	65.0191i	0.0459471	+	0.0795827i
$818$		−	1042.33i		−	1.27424i
$819$	−845.434	−	503.097i	−1.03228	−	0.614282i
$820$	2.28084			0.00278152
$821$	941.392	−	543.513i	1.14664	−	0.662013i	0.198574	−	0.980086i	$-0.436369\pi$
$821$	941.392	−	543.513i	1.14664	−	0.662013i	0.948066	+	0.318072i	$0.103035\pi$
$822$	256.809	−	849.972i	0.312420	−	1.03403i
$823$	445.550	−	771.715i	0.541373	−	0.937685i	−0.457453	−	0.889234i	$-0.651238\pi$
$823$	445.550	−	771.715i	0.541373	−	0.937685i	0.998826	−	0.0484512i	$-0.0154285\pi$
$824$			934.970i			1.13467i
$825$	389.286	−	365.416i	0.471862	−	0.442929i
$826$	−723.516	−	1119.79i	−0.875927	−	1.35567i
$827$		−	593.193i		−	0.717283i	−0.933475	−	0.358642i	$-0.883240\pi$
$827$		−	593.193i		−	0.717283i	0.933475	−	0.358642i	$-0.116760\pi$
$828$	−131.982	+	198.475i	−0.159399	+	0.239704i
$829$	−580.373	−	1005.24i	−0.700088	−	1.21259i	−0.968435	−	0.249266i	$-0.919811\pi$
$829$	−580.373	−	1005.24i	−0.700088	−	1.21259i	0.268347	−	0.963322i	$-0.413523\pi$
$830$		−	5.36729i		−	0.00646661i
$831$	207.204	+	220.739i	0.249343	+	0.265630i
$832$	395.474	+	684.981i	0.475329	+	0.823294i
$833$	−68.7158	−	684.268i	−0.0824919	−	0.821451i
$834$	−320.832	−	1369.11i	−0.384690	−	1.64162i
$835$	140.475	+	243.310i	0.168234	+	0.291389i
$836$	−23.8101	+	13.7468i	−0.0284810	+	0.0164435i
$837$	60.8723	+	361.228i	0.0727267	+	0.431575i
$838$	457.179	−	791.857i	0.545560	−	0.944937i
$839$	−683.513	−	394.626i	−0.814675	−	0.470353i	0.0339016	−	0.999425i	$-0.489207\pi$
$839$	−683.513	−	394.626i	−0.814675	−	0.470353i	−0.848577	+	0.529072i	$0.822540\pi$
$840$	68.7575	−	276.918i	0.0818541	−	0.329664i
$841$	−354.595	−	614.177i	−0.421635	−	0.730293i
$842$			609.442i			0.723803i
$843$	−152.493	−	650.746i	−0.180893	−	0.771941i
$844$	111.878			0.132557
$845$	121.786	+	70.3129i	0.144125	+	0.0832105i
$846$	362.763	+	241.230i	0.428798	+	0.285142i
$847$	−198.645	−	307.443i	−0.234527	−	0.362979i
$848$	514.481	+	297.036i	0.606700	+	0.350278i
$849$	113.786	−	26.6640i	0.134023	−	0.0314064i
$850$	−324.687	+	562.374i	−0.381984	+	0.661616i
$851$	1951.08	+	1126.46i	2.29269	+	1.32368i
$852$	3.95629	+	16.8830i	0.00464353	+	0.0198158i
$853$	−526.183	+	911.376i	−0.616862	+	1.06844i	0.373193	+	0.927754i	$0.378263\pi$
$853$	−526.183	+	911.376i	−0.616862	+	1.06844i	−0.990055	+	0.140682i	$0.955070\pi$
$854$	75.9475	+	1516.37i	0.0889315	+	1.77561i
$855$	48.2334	−	72.5337i	0.0564134	−	0.0848347i
$856$	−118.857	+	205.866i	−0.138851	+	0.240498i
$857$		−	336.463i		−	0.392606i	−0.980543	−	0.196303i	$-0.937106\pi$
$857$		−	336.463i		−	0.392606i	0.980543	−	0.196303i	$-0.0628935\pi$
$858$	−814.751	+	190.925i	−0.949593	+	0.222523i
$859$	652.375			0.759459			0.379729	−	0.925098i	$-0.376017\pi$
$859$	652.375			0.759459			0.379729	+	0.925098i	$0.376017\pi$
$860$	15.2637	−	8.81248i	0.0177484	−	0.0102471i
$861$	10.9530	+	38.0580i	0.0127213	+	0.0442021i
$862$	−606.150	+	1049.88i	−0.703191	+	1.21796i
$863$	−1441.38	−	832.183i	−1.67020	−	0.964291i	−0.967523	−	0.252782i	$-0.918654\pi$
$863$	−1441.38	−	832.183i	−1.67020	−	0.964291i	−0.702677	−	0.711509i	$-0.748012\pi$
$864$	−271.722	+	45.7892i	−0.314493	+	0.0529968i
$865$	139.670	+	241.915i	0.161468	+	0.279670i
$866$	−948.092	+	547.381i	−1.09479	+	0.632080i
$867$	−268.784	+	62.9854i	−0.310016	+	0.0726476i
$868$	−27.8845	+	54.4145i	−0.0321250	+	0.0626895i
$869$	−88.3770	+	51.0245i	−0.101700	+	0.0587163i
$870$	101.663	−	95.4289i	0.116854	−	0.109688i
$871$	1893.10			2.17347
$872$	311.184	−	179.662i	0.356862	−	0.206034i
$873$	2.64004	+	1.75558i	0.00302410	+	0.00201097i
$874$	456.702			0.522542
$875$	−513.286	+	331.644i	−0.586613	+	0.379022i
$876$	−56.3897	−	60.0732i	−0.0643718	−	0.0685767i
$877$	746.423			0.851110			0.425555	−	0.904933i	$-0.360079\pi$
$877$	746.423			0.851110			0.425555	+	0.904933i	$0.360079\pi$
$878$	660.374	+	381.267i	0.752134	+	0.434245i
$879$	−1027.72	−	310.512i	−1.16919	−	0.353256i
$880$	−141.400	−	244.912i	−0.160682	−	0.278309i
$881$		−	746.281i		−	0.847084i	−0.905876	−	0.423542i	$-0.860787\pi$
$881$		−	746.281i		−	0.847084i	0.905876	−	0.423542i	$-0.139213\pi$
$882$	−949.687	+	35.0131i	−1.07674	+	0.0396974i
$883$	762.699			0.863759			0.431879	−	0.901931i	$-0.357851\pi$
$883$	762.699			0.863759			0.431879	+	0.901931i	$0.357851\pi$
$884$	122.196	−	70.5501i	0.138231	−	0.0798078i
$885$	484.963	−	113.644i	0.547981	−	0.128411i
$886$	−510.218	+	883.724i	−0.575867	+	0.997431i
$887$		−	1258.60i		−	1.41894i	−0.704738	−	0.709468i	$-0.748936\pi$
$887$		−	1258.60i		−	1.41894i	0.704738	−	0.709468i	$-0.251064\pi$
$888$	271.115	+	1156.96i	0.305310	+	1.30288i
$889$	778.639	+	1205.10i	0.875859	+	1.35557i
$890$			626.008i			0.703380i
$891$	−84.6885	+	666.056i	−0.0950489	+	0.747537i
$892$	53.3273	+	92.3655i	0.0597839	+	0.103549i
$893$		−	115.725i		−	0.129591i
$894$	513.670	−	1700.12i	0.574575	−	1.90170i
$895$	−116.057	−	201.017i	−0.129673	−	0.224600i
$896$	934.271	+	478.764i	1.04271	+	0.534335i
$897$	1844.77	+	557.376i	2.05660	+	0.621378i
$898$	−233.682	−	404.749i	−0.260225	−	0.450723i
$899$	134.897	−	77.8829i	0.150052	−	0.0866328i
$900$	103.593	+	68.8872i	0.115103	+	0.0765413i
$901$	−229.554	+	397.599i	−0.254777	+	0.441287i
$902$	29.1730	+	16.8431i	0.0323426	+	0.0186730i
$903$	220.343	+	212.369i	0.244012	+	0.235182i
$904$	−268.368	−	464.828i	−0.296868	−	0.514190i
$905$		−	587.697i		−	0.649389i
$906$	596.933	+	180.356i	0.658866	+	0.199068i
$907$	261.720			0.288556			0.144278	−	0.989537i	$-0.453914\pi$
$907$	261.720			0.288556			0.144278	+	0.989537i	$0.453914\pi$
$908$	77.6267	+	44.8178i	0.0854920	+	0.0493588i
$909$	−1162.66	−	73.6191i	−1.27905	−	0.0809891i
$910$	441.973	−	22.1363i	0.485685	−	0.0243256i
$911$	848.904	+	490.115i	0.931838	+	0.537997i	0.887392	−	0.461015i	$-0.152515\pi$
$911$	848.904	+	490.115i	0.931838	+	0.537997i	0.0444454	+	0.999012i	$0.485848\pi$
$912$	192.104	+	204.652i	0.210640	+	0.224400i
$913$	5.49488	−	9.51741i	0.00601849	−	0.0104243i
$914$	−52.7525	−	30.4567i	−0.0577161	−	0.0333224i
$915$	−543.004	−	164.062i	−0.593447	−	0.179303i
$916$	35.0355	−	60.6833i	0.0382484	−	0.0662482i
$917$	643.963	−	416.077i	0.702250	−	0.453737i
$918$	−135.696	−	805.247i	−0.147817	−	0.877176i
$919$	536.421	−	929.108i	0.583700	−	1.01100i	−0.411336	−	0.911484i	$-0.634938\pi$
$919$	536.421	−	929.108i	0.583700	−	1.01100i	0.995036	−	0.0995147i	$-0.0317290\pi$
$920$			558.917i			0.607518i
$921$	−430.992	−	459.146i	−0.467961	−	0.498530i
$922$	910.878			0.987937
$923$	121.418	−	70.1008i	0.131547	−	0.0759488i
$924$	−77.7701	+	80.6902i	−0.0841668	+	0.0873270i
$925$	587.946	−	1018.35i	0.635618	−	1.10092i
$926$	−726.566	−	419.483i	−0.784628	−	0.453005i
$927$	−73.5235	+	1161.15i	−0.0793134	+	1.25259i
$928$	58.5849	+	101.472i	0.0631303	+	0.109345i
$929$	−949.406	+	548.140i	−1.02197	+	0.590032i	−0.914673	−	0.404195i	$-0.867552\pi$
$929$	−949.406	+	548.140i	−1.02197	+	0.590032i	−0.107293	+	0.994227i	$0.534218\pi$
$930$	−112.773	−	120.139i	−0.121261	−	0.129182i
$931$	147.436	+	204.918i	0.158363	+	0.220105i
$932$	−132.376	+	76.4275i	−0.142035	+	0.0820037i
$933$	−330.589	−	1410.75i	−0.354329	−	1.51206i
$934$	545.684			0.584244
$935$	189.272	−	109.276i	0.202430	−	0.116873i
$936$	451.590	+	910.645i	0.482468	+	0.972911i
$937$	29.4033			0.0313803			0.0156901	−	0.999877i	$-0.495005\pi$
$937$	29.4033			0.0313803			0.0156901	+	0.999877i	$0.495005\pi$
$938$	1535.97	−	992.422i	1.63750	−	1.05802i
$939$	271.785	−	899.541i	0.289441	−	0.957977i
$940$	−27.1672			−0.0289013
$941$	253.466	+	146.339i	0.269358	+	0.155514i	0.628596	−	0.777732i	$-0.283630\pi$
$941$	253.466	+	146.339i	0.269358	+	0.155514i	−0.359238	+	0.933246i	$0.616963\pi$
$942$	−482.134	+	452.571i	−0.511820	+	0.480436i
$943$	−38.7883	−	67.1832i	−0.0411328	−	0.0712442i
$944$			1605.06i			1.70027i
$945$	107.166	−	338.499i	0.113404	−	0.358200i
$946$	260.306			0.275164
$947$	−207.970	+	120.071i	−0.219609	+	0.126791i	−0.605769	−	0.795640i	$-0.707135\pi$
$947$	−207.970	+	120.071i	−0.219609	+	0.126791i	0.386160	+	0.922432i	$0.373801\pi$
$948$	−16.2736	−	17.3366i	−0.0171662	−	0.0182876i
$949$	−333.084	+	576.918i	−0.350984	+	0.607922i
$950$		−	238.373i		−	0.250919i
$951$	897.777	+	271.252i	0.944034	+	0.285229i
$952$	−324.047	+	632.352i	−0.340385	+	0.664235i
$953$			1250.22i			1.31188i	0.754813	+	0.655941i	$0.227728\pi$
$953$			1250.22i			1.31188i	−0.754813	+	0.655941i	$0.772272\pi$
$954$	528.290	+	351.303i	0.553763	+	0.368242i
$955$	−278.877	−	483.030i	−0.292018	−	0.505790i
$956$		−	76.7486i		−	0.0802809i
$957$	277.968	−	65.1377i	0.290458	−	0.0680645i
$958$	−415.794	−	720.177i	−0.434023	−	0.751750i
$959$	−807.528	+	521.759i	−0.842052	+	0.544066i
$960$	−208.128	+	195.367i	−0.216801	+	0.203507i
$961$	388.462	+	672.836i	0.404227	+	0.700142i
$962$	−1596.08	+	921.495i	−1.65912	+	0.957895i
$963$	−163.798	+	246.320i	−0.170091	+	0.255784i
$964$	135.602	−	234.870i	0.140666	−	0.243642i
$965$	26.4650	+	15.2796i	0.0274249	+	0.0158338i
$966$	1788.96	−	514.859i	1.85193	−	0.532981i
$967$	−261.683	−	453.248i	−0.270613	−	0.468715i	0.698406	−	0.715702i	$-0.253893\pi$
$967$	−261.683	−	453.248i	−0.270613	−	0.468715i	−0.969019	+	0.246986i	$0.920560\pi$
$968$			378.188i			0.390690i
$969$	−158.159	+	148.461i	−0.163218	+	0.153210i
$970$	−1.42612			−0.00147023
$971$	−884.396	−	510.606i	−0.910809	−	0.525856i	−0.0301178	−	0.999546i	$-0.509588\pi$
$971$	−884.396	−	510.606i	−0.910809	−	0.525856i	−0.880691	+	0.473690i	$0.842922\pi$
$972$	−155.603	+	16.1959i	−0.160085	+	0.0166624i
$973$	−694.390	+	1355.05i	−0.713659	+	1.39265i
$974$	−737.763	−	425.948i	−0.757457	−	0.437318i
$975$	290.919	−	962.868i	0.298378	−	0.987557i
$976$	913.938	−	1582.99i	0.936412	−	1.62191i
$977$	−1309.53	−	756.057i	−1.34036	−	0.773855i	−0.353497	−	0.935436i	$-0.615008\pi$
$977$	−1309.53	−	756.057i	−1.34036	−	0.773855i	−0.986860	+	0.161580i	$0.948341\pi$
$978$	379.480	−	356.211i	0.388016	−	0.364224i
$979$	−640.889	+	1110.05i	−0.654637	+	1.13386i
$980$	48.1059	−	34.6116i	0.0490876	−	0.0353179i
$981$	400.589	−	198.653i	0.408348	−	0.202500i
$982$	698.269	−	1209.44i	0.711068	−	1.23161i
$983$		−	1748.95i		−	1.77920i	−0.456741	−	0.889600i	$-0.650983\pi$
$983$		−	1748.95i		−	1.77920i	0.456741	−	0.889600i	$-0.349017\pi$
$984$	11.8344	−	39.1690i	0.0120269	−	0.0398059i
$985$	26.9283			0.0273384
$986$	−300.712	+	173.616i	−0.304982	+	0.176081i
$987$	−130.462	−	453.310i	−0.132180	−	0.459281i
$988$	−25.8976	+	44.8560i	−0.0262122	+	0.0454008i
$989$	−519.151	−	299.732i	−0.524925	−	0.303066i
$990$	−134.176	−	270.571i	−0.135532	−	0.273304i
$991$	−173.941	−	301.275i	−0.175521	−	0.304011i	0.764820	−	0.644243i	$-0.222828\pi$
$991$	−173.941	−	301.275i	−0.175521	−	0.304011i	−0.940341	+	0.340232i	$0.889494\pi$
$992$	119.914	−	69.2325i	0.120881	−	0.0697908i
$993$	−48.7851	+	161.466i	−0.0491290	+	0.162605i
$994$	61.7642	−	120.528i	0.0621370	−	0.121255i
$995$	148.648	−	85.8218i	0.149395	−	0.0862530i
$996$	2.45123	+	0.740608i	0.00246107	+	0.000743582i
$997$	−619.044			−0.620907			−0.310453	−	0.950589i	$-0.600481\pi$
$997$	−619.044			−0.620907			−0.310453	+	0.950589i	$0.600481\pi$
$998$	488.253	−	281.893i	0.489231	−	0.282458i
$999$	245.720	+	1458.15i	0.245966	+	1.45961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.n.b.2.9	yes	22
3.2	odd	2		189.3.n.b.170.3		22
7.2	even	3		441.3.r.g.344.3		22
7.3	odd	6		441.3.j.f.263.9		22
7.4	even	3		63.3.j.b.11.9	✓	22
7.5	odd	6		441.3.r.f.344.3		22
7.6	odd	2		441.3.n.f.128.9		22
9.4	even	3		189.3.j.b.44.9		22
9.5	odd	6		63.3.j.b.23.3	yes	22
21.11	odd	6		189.3.j.b.116.3		22
63.4	even	3		189.3.n.b.179.3		22
63.5	even	6		441.3.r.f.50.3		22
63.23	odd	6		441.3.r.g.50.3		22
63.32	odd	6	inner	63.3.n.b.32.9	yes	22
63.41	even	6		441.3.j.f.275.3		22
63.59	even	6		441.3.n.f.410.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.9	✓	22	7.4	even	3
63.3.j.b.23.3	yes	22	9.5	odd	6
63.3.n.b.2.9	yes	22	1.1	even	1	trivial
63.3.n.b.32.9	yes	22	63.32	odd	6	inner
189.3.j.b.44.9		22	9.4	even	3
189.3.j.b.116.3		22	21.11	odd	6
189.3.n.b.170.3		22	3.2	odd	2
189.3.n.b.179.3		22	63.4	even	3
441.3.j.f.263.9		22	7.3	odd	6
441.3.j.f.275.3		22	63.41	even	6
441.3.n.f.128.9		22	7.6	odd	2
441.3.n.f.410.9		22	63.59	even	6
441.3.r.f.50.3		22	63.5	even	6
441.3.r.f.344.3		22	7.5	odd	6
441.3.r.g.50.3		22	63.23	odd	6
441.3.r.g.344.3		22	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86624 - 1.07747i) q^{2} +(2.05320 + 2.18732i) q^{3} +(0.321900 - 0.557548i) q^{4} -1.87862i q^{5} +(6.18854 + 1.86979i) q^{6} +(-3.79886 - 5.87951i) q^{7} +7.23243i q^{8} +(-0.568739 + 8.98201i) q^{9} +O(q^{10})\)	\(q+(1.86624 - 1.07747i) q^{2} +(2.05320 + 2.18732i) q^{3} +(0.321900 - 0.557548i) q^{4} -1.87862i q^{5} +(6.18854 + 1.86979i) q^{6} +(-3.79886 - 5.87951i) q^{7} +7.23243i q^{8} +(-0.568739 + 8.98201i) q^{9} +(-2.02416 - 3.50595i) q^{10} -8.28911i q^{11} +(1.88046 - 0.440658i) q^{12} +(-7.80795 - 13.5238i) q^{13} +(-13.4246 - 6.87940i) q^{14} +(4.10914 - 3.85718i) q^{15} +(9.08036 + 15.7276i) q^{16} +(-12.1546 + 7.01745i) q^{17} +(8.61648 + 17.3754i) q^{18} +(2.57597 - 4.46172i) q^{19} +(-1.04742 - 0.604727i) q^{20} +(5.06054 - 20.3811i) q^{21} +(-8.93131 - 15.4695i) q^{22} +41.1362i q^{23} +(-15.8196 + 14.8496i) q^{24} +21.4708 q^{25} +(-29.1430 - 16.8257i) q^{26} +(-20.8143 + 17.1979i) q^{27} +(-4.50096 + 0.225432i) q^{28} +(9.94271 + 5.74042i) q^{29} +(3.51263 - 11.6259i) q^{30} +(6.78372 - 11.7498i) q^{31} +(8.83838 + 5.10284i) q^{32} +(18.1309 - 17.0192i) q^{33} +(-15.1222 + 26.1925i) q^{34} +(-11.0453 + 7.13661i) q^{35} +(4.82482 + 3.20841i) q^{36} +(27.3835 - 47.4297i) q^{37} -11.1022i q^{38} +(13.5495 - 44.8455i) q^{39} +13.5870 q^{40} +(-1.63319 + 0.942922i) q^{41} +(-12.5160 - 43.4887i) q^{42} +(-7.28633 + 12.6203i) q^{43} +(-4.62158 - 2.66827i) q^{44} +(16.8738 + 1.06844i) q^{45} +(44.3232 + 76.7700i) q^{46} +(19.4530 - 11.2312i) q^{47} +(-15.7576 + 52.1537i) q^{48} +(-20.1373 + 44.6709i) q^{49} +(40.0697 - 23.1342i) q^{50} +(-40.3052 - 12.1777i) q^{51} -10.0535 q^{52} +(28.3293 - 16.3560i) q^{53} +(-20.3142 + 54.5222i) q^{54} -15.5721 q^{55} +(42.5232 - 27.4750i) q^{56} +(15.0482 - 3.52632i) q^{57} +24.7406 q^{58} +(76.5400 + 44.1904i) q^{59} +(-0.827828 - 3.53267i) q^{60} +(-50.3250 - 87.1654i) q^{61} -29.2371i q^{62} +(54.9704 - 30.7775i) q^{63} -50.6502 q^{64} +(-25.4060 + 14.6681i) q^{65} +(15.4989 - 51.2976i) q^{66} +(-60.6144 + 104.987i) q^{67} +9.03568i q^{68} +(-89.9781 + 84.4609i) q^{69} +(-12.9237 + 25.2197i) q^{70} +8.97813i q^{71} +(-64.9618 - 4.11337i) q^{72} +(-21.3298 - 36.9443i) q^{73} -118.020i q^{74} +(44.0839 + 46.9635i) q^{75} +(-1.65841 - 2.87246i) q^{76} +(-48.7359 + 31.4892i) q^{77} +(-23.0332 - 98.2916i) q^{78} +(-6.15560 - 10.6618i) q^{79} +(29.5462 - 17.0585i) q^{80} +(-80.3531 - 10.2168i) q^{81} +(-2.03195 + 3.51944i) q^{82} +(1.14818 + 0.662903i) q^{83} +(-9.73447 - 9.38219i) q^{84} +(13.1831 + 22.8338i) q^{85} +31.4033i q^{86} +(7.85822 + 33.5341i) q^{87} +59.9505 q^{88} +(-133.917 - 77.3170i) q^{89} +(32.6417 - 16.1871i) q^{90} +(-49.8518 + 97.2818i) q^{91} +(22.9354 + 13.2418i) q^{92} +(39.6288 - 9.28642i) q^{93} +(24.2026 - 41.9202i) q^{94} +(-8.38186 - 4.83927i) q^{95} +(6.98541 + 29.8095i) q^{96} +(0.176137 - 0.305078i) q^{97} +(10.5508 + 105.064i) q^{98} +(74.4529 + 4.71434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

Introduction

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