LMFDB - Embedded newform 210.3.o.b.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(31,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("210.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.o (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.3
Root			$1.92573 - 3.33546i$ of defining polynomial
Character	$\chi$	$=$	210.61
Dual form			210.3.o.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(-2.67372 - 6.46925i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(-2.67372 - 6.46925i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(-0.578394 - 1.00181i) q^{11} +(3.00000 + 1.73205i) q^{12} -14.8176i q^{13} +(9.81379 + 1.29982i) q^{14} -3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(10.9271 - 6.30878i) q^{17} +(2.12132 + 3.67423i) q^{18} +(16.7162 + 9.65108i) q^{19} -4.47214i q^{20} +(9.61312 + 7.38837i) q^{21} +1.63595 q^{22} +(12.1504 - 21.0450i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(18.1477 + 10.4776i) q^{26} +5.19615i q^{27} +(-8.53135 + 11.1003i) q^{28} +49.0382 q^{29} +(2.73861 - 4.74342i) q^{30} +(-24.9581 + 14.4096i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(1.73518 + 1.00181i) q^{33} +17.8439i q^{34} +(2.05520 - 15.5170i) q^{35} -6.00000 q^{36} +(26.6579 - 46.1728i) q^{37} +(-23.6402 + 13.6487i) q^{38} +(12.8324 + 22.2264i) q^{39} +(5.47723 + 3.16228i) q^{40} -38.0398i q^{41} +(-15.8464 + 6.54925i) q^{42} -63.5774 q^{43} +(-1.15679 + 2.00362i) q^{44} +(5.80948 - 3.35410i) q^{45} +(17.1832 + 29.7622i) q^{46} +(21.8175 + 12.5964i) q^{47} -6.92820i q^{48} +(-34.7024 + 34.5940i) q^{49} -7.07107 q^{50} +(-10.9271 + 18.9263i) q^{51} +(-25.6648 + 14.8176i) q^{52} +(-10.4160 - 18.0411i) q^{53} +(-6.36396 - 3.67423i) q^{54} -2.58666i q^{55} +(-7.56243 - 18.2978i) q^{56} -33.4323 q^{57} +(-34.6752 + 60.0593i) q^{58} +(21.1419 - 12.2063i) q^{59} +(3.87298 + 6.70820i) q^{60} +(5.53376 + 3.19492i) q^{61} -40.7564i q^{62} +(-20.8182 - 2.75734i) q^{63} +8.00000 q^{64} +(16.5665 - 28.6941i) q^{65} +(-2.45392 + 1.41677i) q^{66} +(-62.2451 - 107.812i) q^{67} +(-21.8543 - 12.6176i) q^{68} +42.0901i q^{69} +(17.5511 + 13.4892i) q^{70} -118.973 q^{71} +(4.24264 - 7.34847i) q^{72} +(-34.2336 + 19.7648i) q^{73} +(37.7000 + 65.2983i) q^{74} +(-7.50000 - 4.33013i) q^{75} -38.6043i q^{76} +(-4.93448 + 6.42033i) q^{77} -36.2955 q^{78} +(46.4356 - 80.4288i) q^{79} +(-7.74597 + 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(46.5891 + 26.8982i) q^{82} -5.79665i q^{83} +(3.18391 - 24.0388i) q^{84} +28.2137 q^{85} +(44.9560 - 77.8661i) q^{86} +(-73.5573 + 42.4683i) q^{87} +(-1.63595 - 2.83354i) q^{88} +(131.622 + 75.9919i) q^{89} +9.48683i q^{90} +(-95.8586 + 39.6181i) q^{91} -48.6014 q^{92} +(24.9581 - 43.2287i) q^{93} +(-30.8546 + 17.8139i) q^{94} +(21.5805 + 37.3785i) q^{95} +(8.48528 + 4.89898i) q^{96} +144.310i q^{97} +(-17.8305 - 66.9632i) q^{98} -3.47036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	$ 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$		−	2.44949i		−	0.408248i
$7$	−2.67372	−	6.46925i	−0.381960	−	0.924179i
$7$	−2.67372	−	6.46925i	−0.381960	−	0.924179i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	−2.73861	+	1.58114i	−0.273861	+	0.158114i
$11$	−0.578394	−	1.00181i	−0.0525813	−	0.0910735i	0.838537	−	0.544845i	$-0.183412\pi$
$11$	−0.578394	−	1.00181i	−0.0525813	−	0.0910735i	−0.891118	+	0.453772i	$0.850078\pi$
$12$	3.00000	+	1.73205i	0.250000	+	0.144338i
$13$		−	14.8176i		−	1.13981i	−0.821710	−	0.569906i	$-0.806979\pi$
$13$		−	14.8176i		−	1.13981i	0.821710	−	0.569906i	$-0.193021\pi$
$14$	9.81379	+	1.29982i	0.700985	+	0.0928446i
$15$	−3.87298			−0.258199
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	10.9271	−	6.30878i	0.642772	−	0.371105i	−0.142909	−	0.989736i	$-0.545646\pi$
$17$	10.9271	−	6.30878i	0.642772	−	0.371105i	0.785682	+	0.618631i	$0.212312\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	16.7162	+	9.65108i	0.879798	+	0.507951i	0.870592	−	0.492006i	$-0.163736\pi$
$19$	16.7162	+	9.65108i	0.879798	+	0.507951i	0.00920603	+	0.999958i	$0.497070\pi$
$20$		−	4.47214i		−	0.223607i
$21$	9.61312	+	7.38837i	0.457768	+	0.351827i
$22$	1.63595			0.0743612
$23$	12.1504	−	21.0450i	0.528277	−	0.915002i	−0.471180	−	0.882037i	$-0.656172\pi$
$23$	12.1504	−	21.0450i	0.528277	−	0.915002i	0.999457	−	0.0329648i	$-0.0104949\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	18.1477	+	10.4776i	0.697990	+	0.402985i
$27$			5.19615i			0.192450i
$28$	−8.53135	+	11.1003i	−0.304691	+	0.396438i
$29$	49.0382			1.69097			0.845486	−	0.533998i	$-0.179311\pi$
$29$	49.0382			1.69097			0.845486	+	0.533998i	$0.179311\pi$
$30$	2.73861	−	4.74342i	0.0912871	−	0.158114i
$31$	−24.9581	+	14.4096i	−0.805100	+	0.464825i	−0.845251	−	0.534369i	$-0.820549\pi$
$31$	−24.9581	+	14.4096i	−0.805100	+	0.464825i	0.0401515	+	0.999194i	$0.487216\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	1.73518	+	1.00181i	0.0525813	+	0.0303578i
$34$			17.8439i			0.524822i
$35$	2.05520	−	15.5170i	0.0587201	−	0.443342i
$36$	−6.00000			−0.166667
$37$	26.6579	−	46.1728i	0.720484	−	1.24791i	−0.240322	−	0.970693i	$-0.577253\pi$
$37$	26.6579	−	46.1728i	0.720484	−	1.24791i	0.960806	−	0.277221i	$-0.0894136\pi$
$38$	−23.6402	+	13.6487i	−0.622111	+	0.359176i
$39$	12.8324	+	22.2264i	0.329036	+	0.569906i
$40$	5.47723	+	3.16228i	0.136931	+	0.0790569i
$41$		−	38.0398i		−	0.927800i	−0.885888	−	0.463900i	$-0.846450\pi$
$41$		−	38.0398i		−	0.927800i	0.885888	−	0.463900i	$-0.153550\pi$
$42$	−15.8464	+	6.54925i	−0.377294	+	0.155935i
$43$	−63.5774			−1.47854			−0.739272	−	0.673407i	$-0.764830\pi$
$43$	−63.5774			−1.47854			−0.739272	+	0.673407i	$0.764830\pi$
$44$	−1.15679	+	2.00362i	−0.0262906	+	0.0455367i
$45$	5.80948	−	3.35410i	0.129099	−	0.0745356i
$46$	17.1832	+	29.7622i	0.373548	+	0.647004i
$47$	21.8175	+	12.5964i	0.464203	+	0.268008i	0.713810	−	0.700340i	$-0.246968\pi$
$47$	21.8175	+	12.5964i	0.464203	+	0.268008i	−0.249607	+	0.968347i	$0.580301\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−34.7024	+	34.5940i	−0.708213	+	0.705999i
$50$	−7.07107			−0.141421
$51$	−10.9271	+	18.9263i	−0.214257	+	0.371105i
$52$	−25.6648	+	14.8176i	−0.493553	+	0.284953i
$53$	−10.4160	−	18.0411i	−0.196529	−	0.340397i	0.750872	−	0.660448i	$-0.229634\pi$
$53$	−10.4160	−	18.0411i	−0.196529	−	0.340397i	−0.947401	+	0.320050i	$0.896300\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$		−	2.58666i		−	0.0470301i
$56$	−7.56243	−	18.2978i	−0.135043	−	0.326747i
$57$	−33.4323			−0.586532
$58$	−34.6752	+	60.0593i	−0.597849	+	1.03550i
$59$	21.1419	−	12.2063i	0.358337	−	0.206886i	−0.310014	−	0.950732i	$-0.600334\pi$
$59$	21.1419	−	12.2063i	0.358337	−	0.206886i	0.668351	+	0.743846i	$0.267000\pi$
$60$	3.87298	+	6.70820i	0.0645497	+	0.111803i
$61$	5.53376	+	3.19492i	0.0907174	+	0.0523757i	0.544672	−	0.838649i	$-0.316654\pi$
$61$	5.53376	+	3.19492i	0.0907174	+	0.0523757i	−0.453955	+	0.891025i	$0.649987\pi$
$62$		−	40.7564i		−	0.657361i
$63$	−20.8182	−	2.75734i	−0.330447	−	0.0437674i
$64$	8.00000			0.125000
$65$	16.5665	−	28.6941i	0.254870	−	0.441448i
$66$	−2.45392	+	1.41677i	−0.0371806	+	0.0214662i
$67$	−62.2451	−	107.812i	−0.929031	−	1.60913i	−0.784946	−	0.619564i	$-0.787310\pi$
$67$	−62.2451	−	107.812i	−0.929031	−	1.60913i	−0.144085	−	0.989565i	$-0.546024\pi$
$68$	−21.8543	−	12.6176i	−0.321386	−	0.185552i
$69$			42.0901i			0.610001i
$70$	17.5511	+	13.4892i	0.250730	+	0.192704i
$71$	−118.973			−1.67567			−0.837835	−	0.545924i	$-0.816179\pi$
$71$	−118.973			−1.67567			−0.837835	+	0.545924i	$0.816179\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	−34.2336	+	19.7648i	−0.468953	+	0.270750i	−0.715801	−	0.698304i	$-0.753938\pi$
$73$	−34.2336	+	19.7648i	−0.468953	+	0.270750i	0.246848	+	0.969054i	$0.420605\pi$
$74$	37.7000	+	65.2983i	0.509459	+	0.882409i
$75$	−7.50000	−	4.33013i	−0.100000	−	0.0577350i
$76$		−	38.6043i		−	0.507951i
$77$	−4.93448	+	6.42033i	−0.0640842	+	0.0833809i
$78$	−36.2955			−0.465327
$79$	46.4356	−	80.4288i	0.587792	−	1.01809i	−0.406729	−	0.913549i	$-0.633331\pi$
$79$	46.4356	−	80.4288i	0.587792	−	1.01809i	0.994521	−	0.104537i	$-0.0333360\pi$
$80$	−7.74597	+	4.47214i	−0.0968246	+	0.0559017i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	46.5891	+	26.8982i	0.568159	+	0.328027i
$83$		−	5.79665i		−	0.0698392i	−0.999390	−	0.0349196i	$-0.988882\pi$
$83$		−	5.79665i		−	0.0698392i	0.999390	−	0.0349196i	$-0.0111175\pi$
$84$	3.18391	−	24.0388i	0.0379037	−	0.286176i
$85$	28.2137			0.331926
$86$	44.9560	−	77.8661i	0.522744	−	0.905420i
$87$	−73.5573	+	42.4683i	−0.845486	+	0.488142i
$88$	−1.63595	−	2.83354i	−0.0185903	−	0.0321993i
$89$	131.622	+	75.9919i	1.47890	+	0.853842i	0.999715	−	0.0238738i	$-0.00759998\pi$
$89$	131.622	+	75.9919i	1.47890	+	0.853842i	0.479182	+	0.877715i	$0.340933\pi$
$90$			9.48683i			0.105409i
$91$	−95.8586	+	39.6181i	−1.05339	+	0.435363i
$92$	−48.6014			−0.528277
$93$	24.9581	−	43.2287i	0.268367	−	0.464825i
$94$	−30.8546	+	17.8139i	−0.328241	+	0.189510i
$95$	21.5805	+	37.3785i	0.227163	+	0.393458i
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$			144.310i			1.48773i	0.668331	+	0.743864i	$0.267009\pi$
$97$			144.310i			1.48773i	−0.668331	+	0.743864i	$0.732991\pi$
$98$	−17.8305	−	66.9632i	−0.181943	−	0.683298i
$99$	−3.47036			−0.0350542
$100$	5.00000	−	8.66025i	0.0500000	−	0.0866025i
$101$	−33.8480	+	19.5422i	−0.335129	+	0.193487i	−0.658116	−	0.752917i	$-0.728646\pi$
$101$	−33.8480	+	19.5422i	−0.335129	+	0.193487i	0.322987	+	0.946403i	$0.395313\pi$
$102$	−15.4533	−	26.7659i	−0.151503	−	0.262411i
$103$	32.7730	+	18.9215i	0.318185	+	0.183704i	0.650583	−	0.759435i	$-0.274525\pi$
$103$	32.7730	+	18.9215i	0.318185	+	0.183704i	−0.332398	+	0.943139i	$0.607858\pi$
$104$		−	41.9104i		−	0.402985i
$105$	10.3553	+	25.0553i	0.0986217	+	0.238622i
$106$	29.4609			0.277933
$107$	−41.5160	+	71.9079i	−0.388000	+	0.672036i	−0.992180	−	0.124811i	$-0.960167\pi$
$107$	−41.5160	+	71.9079i	−0.388000	+	0.672036i	0.604180	+	0.796848i	$0.293501\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	23.8962	+	41.3894i	0.219231	+	0.379719i	0.954573	−	0.297977i	$-0.0963118\pi$
$109$	23.8962	+	41.3894i	0.219231	+	0.379719i	−0.735342	+	0.677696i	$0.762978\pi$
$110$	3.16800	+	1.82904i	0.0288000	+	0.0166277i
$111$			92.3457i			0.831943i
$112$	27.7576	+	3.67646i	0.247836	+	0.0328255i
$113$	−16.2283			−0.143613			−0.0718064	−	0.997419i	$-0.522876\pi$
$113$	−16.2283			−0.143613			−0.0718064	+	0.997419i	$0.522876\pi$
$114$	23.6402	−	40.9461i	0.207370	−	0.359176i
$115$	47.0582	−	27.1690i	0.409201	−	0.236252i
$116$	−49.0382	−	84.9366i	−0.422743	−	0.732212i
$117$	−38.4972	−	22.2264i	−0.329036	−	0.189969i
$118$			34.5246i			0.292581i
$119$	−70.0292	−	53.8224i	−0.588481	−	0.452289i
$120$	−10.9545			−0.0912871
$121$	59.8309	−	103.630i	0.494470	−	0.856448i
$122$	−7.82592	+	4.51830i	−0.0641469	+	0.0370352i
$123$	32.9434	+	57.0597i	0.267833	+	0.463900i
$124$	49.9162	+	28.8191i	0.402550	+	0.232412i
$125$			11.1803i			0.0894427i
$126$	18.0977	−	23.5472i	0.143633	−	0.186883i
$127$	80.5643			0.634365			0.317182	−	0.948365i	$-0.397263\pi$
$127$	80.5643			0.634365			0.317182	+	0.948365i	$0.397263\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	95.3661	−	55.0597i	0.739272	−	0.426819i
$130$	23.4286	+	40.5796i	0.180220	+	0.312151i
$131$	107.981	+	62.3429i	0.824283	+	0.475900i	0.851891	−	0.523719i	$-0.175456\pi$
$131$	107.981	+	62.3429i	0.824283	+	0.475900i	−0.0276082	+	0.999619i	$0.508789\pi$
$132$		−	4.00723i		−	0.0303578i
$133$	17.7409	−	133.945i	0.133390	−	1.00711i
$134$	176.056			1.31385
$135$	−5.80948	+	10.0623i	−0.0430331	+	0.0745356i
$136$	30.9066	−	17.8439i	0.227254	−	0.131205i
$137$	38.0330	+	65.8750i	0.277613	+	0.480840i	0.970791	−	0.239927i	$-0.0771234\pi$
$137$	38.0330	+	65.8750i	0.277613	+	0.480840i	−0.693178	+	0.720766i	$0.743790\pi$
$138$	−51.5496	−	29.7622i	−0.373548	−	0.215668i
$139$			91.7680i			0.660201i	0.943946	+	0.330101i	$0.107083\pi$
$139$			91.7680i			0.660201i	−0.943946	+	0.330101i	$0.892917\pi$
$140$	−28.9314	+	11.9572i	−0.206653	+	0.0854089i
$141$	−43.6350			−0.309468
$142$	84.1263	−	145.711i	0.592439	−	1.02613i
$143$	−14.8444	+	8.57039i	−0.103807	+	0.0599328i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$	94.9620	+	54.8264i	0.654911	+	0.378113i
$146$		−	55.9032i		−	0.382898i
$147$	22.0944	−	81.9441i	0.150302	−	0.557443i
$148$	−106.632			−0.720484
$149$	49.4579	−	85.6637i	0.331933	−	0.574924i	−0.650958	−	0.759114i	$-0.725633\pi$
$149$	49.4579	−	85.6637i	0.331933	−	0.574924i	0.982891	+	0.184190i	$0.0589660\pi$
$150$	10.6066	−	6.12372i	0.0707107	−	0.0408248i
$151$	−48.8950	−	84.6886i	−0.323808	−	0.560852i	0.657462	−	0.753487i	$-0.271630\pi$
$151$	−48.8950	−	84.6886i	−0.323808	−	0.560852i	−0.981270	+	0.192635i	$0.938297\pi$
$152$	47.2804	+	27.2974i	0.311055	+	0.179588i
$153$		−	37.8527i		−	0.247403i
$154$	−4.37406	−	10.5833i	−0.0284030	−	0.0687230i
$155$	−64.4415			−0.415752
$156$	25.6648	−	44.4527i	0.164518	−	0.284953i
$157$	115.530	−	66.7013i	0.735860	−	0.424849i	−0.0847022	−	0.996406i	$-0.526994\pi$
$157$	115.530	−	66.7013i	0.735860	−	0.424849i	0.820562	+	0.571557i	$0.193661\pi$
$158$	65.6698	+	113.743i	0.415632	+	0.719895i
$159$	31.2480	+	18.0411i	0.196529	+	0.113466i
$160$		−	12.6491i		−	0.0790569i
$161$	−168.632	−	22.3352i	−1.04741	−	0.138728i
$162$	12.7279			0.0785674
$163$	16.3746	−	28.3616i	0.100458	−	0.173998i	−0.811416	−	0.584469i	$-0.801303\pi$
$163$	16.3746	−	28.3616i	0.100458	−	0.173998i	0.911873	+	0.410472i	$0.134636\pi$
$164$	−65.8869	+	38.0398i	−0.401749	+	0.231950i
$165$	2.24011	+	3.87999i	0.0135764	+	0.0235151i
$166$	7.09942	+	4.09885i	0.0427676	+	0.0246919i
$167$			171.659i			1.02790i	0.857821	+	0.513948i	$0.171818\pi$
$167$			171.659i			1.02790i	−0.857821	+	0.513948i	$0.828182\pi$
$168$	27.1900	+	20.8975i	0.161845	+	0.124390i
$169$	−50.5603			−0.299173
$170$	−19.9501	+	34.5546i	−0.117354	+	0.203262i
$171$	50.1485	−	28.9532i	0.293266	−	0.169317i
$172$	63.5774	+	110.119i	0.369636	+	0.640229i
$173$	175.336	+	101.230i	1.01350	+	0.585145i	0.912215	−	0.409712i	$-0.134371\pi$
$173$	175.336	+	101.230i	1.01350	+	0.585145i	0.101287	+	0.994857i	$0.467704\pi$
$174$		−	120.119i		−	0.690336i
$175$	21.3284	−	27.7507i	0.121876	−	0.158575i
$176$	4.62715			0.0262906
$177$	−21.1419	+	36.6188i	−0.119446	+	0.206886i
$178$	−186.141	+	107.469i	−1.04574	+	0.603757i
$179$	39.3459	+	68.1491i	0.219810	+	0.380721i	0.954750	−	0.297411i	$-0.0961230\pi$
$179$	39.3459	+	68.1491i	0.219810	+	0.380721i	−0.734940	+	0.678132i	$0.762790\pi$
$180$	−11.6190	−	6.70820i	−0.0645497	−	0.0372678i
$181$			58.1509i			0.321276i	0.987013	+	0.160638i	$0.0513551\pi$
$181$			58.1509i			0.321276i	−0.987013	+	0.160638i	$0.948645\pi$
$182$	19.2602	−	145.416i	0.105825	−	0.798992i
$183$	−11.0675			−0.0604783
$184$	34.3664	−	59.5244i	0.186774	−	0.323502i
$185$	103.246	−	59.6089i	0.558084	−	0.322210i
$186$	35.2961	+	61.1346i	0.189764	+	0.328681i
$187$	−12.6404	−	7.29793i	−0.0675956	−	0.0390263i
$188$		−	50.3854i		−	0.268008i
$189$	33.6152	−	13.8931i	0.177858	−	0.0735083i
$190$	−61.0388			−0.321257
$191$	−184.204	+	319.051i	−0.964419	+	1.67042i	−0.253251	+	0.967401i	$0.581500\pi$
$191$	−184.204	+	319.051i	−0.964419	+	1.67042i	−0.711168	+	0.703022i	$0.751834\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	−140.409	−	243.196i	−0.727510	−	1.26008i	−0.957932	−	0.286994i	$-0.907344\pi$
$193$	−140.409	−	243.196i	−0.727510	−	1.26008i	0.230422	−	0.973091i	$-0.425989\pi$
$194$	−176.742	−	102.042i	−0.911044	−	0.525991i
$195$			57.3882i			0.294298i
$196$	94.6209	+	25.5124i	0.482760	+	0.130165i
$197$	7.61779			0.0386690			0.0193345	−	0.999813i	$-0.493845\pi$
$197$	7.61779			0.0386690			0.0193345	+	0.999813i	$0.493845\pi$
$198$	2.45392	−	4.25031i	0.0123935	−	0.0214662i
$199$	−174.795	+	100.918i	−0.878366	+	0.507125i	−0.870119	−	0.492841i	$-0.835958\pi$
$199$	−174.795	+	100.918i	−0.878366	+	0.507125i	−0.00824641	+	0.999966i	$0.502625\pi$
$200$	7.07107	+	12.2474i	0.0353553	+	0.0612372i
$201$	186.735	+	107.812i	0.929031	+	0.536376i
$202$		−	55.2736i		−	0.273632i
$203$	−131.114	−	317.240i	−0.645884	−	1.56276i
$204$	43.7085			0.214257
$205$	42.5298	−	73.6638i	0.207462	−	0.359335i
$206$	−46.3481	+	26.7591i	−0.224991	+	0.129898i
$207$	−36.4511	−	63.1351i	−0.176092	−	0.305001i
$208$	51.3296	+	29.6351i	0.246777	+	0.142477i
$209$		−	22.3285i		−	0.106835i
$210$	−38.0086	−	5.03420i	−0.180994	−	0.0239724i
$211$	30.3818			0.143989			0.0719947	−	0.997405i	$-0.477064\pi$
$211$	30.3818			0.143989			0.0719947	+	0.997405i	$0.477064\pi$
$212$	−20.8320	+	36.0821i	−0.0982643	+	0.170199i
$213$	178.459	−	103.033i	0.837835	−	0.483724i
$214$	−58.7126	−	101.693i	−0.274358	−	0.475202i
$215$	−123.117	−	71.0817i	−0.572638	−	0.330613i
$216$			14.6969i			0.0680414i
$217$	159.950	+	122.933i	0.737097	+	0.566512i
$218$	−67.5886			−0.310039
$219$	34.2336	−	59.2943i	0.156318	−	0.270750i
$220$	−4.48022	+	2.58666i	−0.0203646	+	0.0117575i
$221$	−93.4808	−	161.914i	−0.422990	−	0.732640i
$222$	−113.100	−	65.2983i	−0.509459	−	0.294136i
$223$		−	16.7377i		−	0.0750569i	−0.999296	−	0.0375284i	$-0.988052\pi$
$223$		−	16.7377i		−	0.0750569i	0.999296	−	0.0375284i	$-0.0119485\pi$
$224$	−24.1303	+	31.3963i	−0.107725	+	0.140162i
$225$	15.0000			0.0666667
$226$	11.4751	−	19.8755i	0.0507748	−	0.0879446i
$227$	−366.738	+	211.736i	−1.61558	+	0.932758i	−0.627541	+	0.778583i	$0.715939\pi$
$227$	−366.738	+	211.736i	−1.61558	+	0.932758i	−0.988044	+	0.154175i	$0.950728\pi$
$228$	33.4323	+	57.9065i	0.146633	+	0.253976i
$229$	−350.596	−	202.417i	−1.53099	−	0.883916i	−0.999317	−	0.0369660i	$-0.988231\pi$
$229$	−350.596	−	202.417i	−1.53099	−	0.883916i	−0.531672	−	0.846951i	$-0.678436\pi$
$230$			76.8456i			0.334111i
$231$	1.84155	−	13.9039i	0.00797209	−	0.0601900i
$232$	138.701			0.597849
$233$	−138.649	+	240.147i	−0.595061	+	1.03068i	0.398478	+	0.917178i	$0.369539\pi$
$233$	−138.649	+	240.147i	−0.595061	+	1.03068i	−0.993538	+	0.113497i	$0.963795\pi$
$234$	54.4432	−	31.4328i	0.232663	−	0.134328i
$235$	28.1663	+	48.7855i	0.119857	+	0.207598i
$236$	−42.2838	−	24.4125i	−0.179169	−	0.103443i
$237$			160.858i			0.678724i
$238$	115.437	−	47.7097i	0.485029	−	0.200461i
$239$	290.247			1.21442			0.607211	−	0.794541i	$-0.292288\pi$
$239$	290.247			1.21442			0.607211	+	0.794541i	$0.292288\pi$
$240$	7.74597	−	13.4164i	0.0322749	−	0.0559017i
$241$	−350.574	+	202.404i	−1.45466	+	0.839850i	−0.998741	−	0.0501703i	$-0.984024\pi$
$241$	−350.574	+	202.404i	−1.45466	+	0.839850i	−0.455922	+	0.890020i	$0.650690\pi$
$242$	84.6137	+	146.555i	0.349643	+	0.605600i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		−	12.7797i		−	0.0523757i
$245$	−105.878	+	28.1924i	−0.432156	+	0.115071i
$246$	−93.1781			−0.378773
$247$	143.005	−	247.693i	0.578970	−	1.00280i
$248$	−70.5922	+	40.7564i	−0.284646	+	0.164340i
$249$	5.02005	+	8.69498i	0.0201608	+	0.0349196i
$250$	−13.6931	−	7.90569i	−0.0547723	−	0.0316228i
$251$		−	155.805i		−	0.620739i	−0.950616	−	0.310369i	$-0.899547\pi$
$251$		−	155.805i		−	0.620739i	0.950616	−	0.310369i	$-0.100453\pi$
$252$	16.0423	+	38.8155i	0.0636600	+	0.154030i
$253$	−28.1108			−0.111110
$254$	−56.9676	+	98.6707i	−0.224282	+	0.388467i
$255$	−42.3206	+	24.4338i	−0.165963	+	0.0958189i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−22.4315	−	12.9508i	−0.0872821	−	0.0503923i	0.455724	−	0.890121i	$-0.349381\pi$
$257$	−22.4315	−	12.9508i	−0.0872821	−	0.0503923i	−0.543006	+	0.839729i	$0.682714\pi$
$258$			155.732i			0.603613i
$259$	−369.980	−	49.0033i	−1.42849	−	0.189202i
$260$	−66.2662			−0.254870
$261$	73.5573	−	127.405i	0.281829	−	0.488142i
$262$	−152.708	+	88.1662i	−0.582856	+	0.336512i
$263$	157.902	+	273.495i	0.600389	+	1.03990i	0.992762	+	0.120098i	$0.0383209\pi$
$263$	157.902	+	273.495i	0.600389	+	1.03990i	−0.392373	+	0.919806i	$0.628346\pi$
$264$	4.90784	+	2.83354i	0.0185903	+	0.0107331i
$265$		−	46.5818i		−	0.175781i
$266$	151.504	+	116.442i	0.569564	+	0.437751i
$267$	−263.244			−0.985931
$268$	−124.490	+	215.623i	−0.464516	+	0.804565i
$269$	−41.4157	+	23.9114i	−0.153962	+	0.0888899i	−0.575002	−	0.818152i	$-0.694999\pi$
$269$	−41.4157	+	23.9114i	−0.153962	+	0.0888899i	0.421040	+	0.907042i	$0.361665\pi$
$270$	−8.21584	−	14.2302i	−0.0304290	−	0.0527046i
$271$	294.580	+	170.076i	1.08701	+	0.627587i	0.932779	−	0.360448i	$-0.117376\pi$
$271$	294.580	+	170.076i	1.08701	+	0.627587i	0.154233	+	0.988035i	$0.450709\pi$
$272$			50.4703i			0.185552i
$273$	109.478	−	142.443i	0.401017	−	0.521769i
$274$	−107.573			−0.392604
$275$	2.89197	−	5.00904i	0.0105163	−	0.0182147i
$276$	72.9022	−	42.0901i	0.264138	−	0.152500i
$277$	−105.293	−	182.374i	−0.380121	−	0.658388i	0.610959	−	0.791663i	$-0.290784\pi$
$277$	−105.293	−	182.374i	−0.380121	−	0.658388i	−0.991079	+	0.133274i	$0.957451\pi$
$278$	−112.392	−	64.8898i	−0.404289	−	0.233416i
$279$			86.4574i			0.309883i
$280$	5.81299	−	43.8886i	0.0207607	−	0.156745i
$281$	471.785			1.67895			0.839476	−	0.543397i	$-0.182862\pi$
$281$	471.785			1.67895			0.839476	+	0.543397i	$0.182862\pi$
$282$	30.8546	−	53.4418i	0.109414	−	0.189510i
$283$	405.534	−	234.135i	1.43298	−	0.827333i	0.435636	−	0.900123i	$-0.356524\pi$
$283$	405.534	−	234.135i	1.43298	−	0.827333i	0.997347	+	0.0727901i	$0.0231903\pi$
$284$	118.973	+	206.067i	0.418917	+	0.725586i
$285$	−64.7414	−	37.3785i	−0.227163	−	0.131153i
$286$		−	24.2407i		−	0.0847578i
$287$	−246.089	+	101.708i	−0.857453	+	0.354383i
$288$	−16.9706			−0.0589256
$289$	−64.8985	+	112.408i	−0.224562	+	0.388953i
$290$	−134.297	+	77.5362i	−0.463092	+	0.267366i
$291$	−124.976	−	216.464i	−0.429470	−	0.743864i
$292$	68.4671	+	39.5295i	0.234476	+	0.135375i
$293$			63.5067i			0.216746i	0.994110	+	0.108373i	$0.0345642\pi$
$293$			63.5067i			0.216746i	−0.994110	+	0.108373i	$0.965436\pi$
$294$	84.7375	+	85.0032i	0.288223	+	0.289127i
$295$	54.5881			0.185044
$296$	75.3999	−	130.597i	0.254730	−	0.441204i
$297$	5.20555	−	3.00542i	0.0175271	−	0.0101193i
$298$	69.9441	+	121.147i	0.234712	+	0.406533i
$299$	−311.836	−	180.039i	−1.04293	−	0.602136i
$300$			17.3205i			0.0577350i
$301$	169.988	+	411.298i	0.564745	+	1.36644i
$302$	138.296			0.457934
$303$	33.8480	−	58.6265i	0.111710	−	0.193487i
$304$	−66.8646	+	38.6043i	−0.219949	+	0.126988i
$305$	7.14406	+	12.3739i	0.0234231	+	0.0405701i
$306$	46.3599	+	26.7659i	0.151503	+	0.0874703i
$307$			211.610i			0.689283i	0.938734	+	0.344642i	$0.112000\pi$
$307$			211.610i			0.689283i	−0.938734	+	0.344642i	$0.888000\pi$
$308$	16.0548	+	2.12644i	0.0521261	+	0.00690403i
$309$	−65.5460			−0.212123
$310$	45.5670	−	78.9244i	0.146990	−	0.254595i
$311$	58.3090	−	33.6647i	0.187489	−	0.108247i	−0.403318	−	0.915060i	$-0.632143\pi$
$311$	58.3090	−	33.6647i	0.187489	−	0.108247i	0.590806	+	0.806813i	$0.298810\pi$
$312$	36.2955	+	62.8656i	0.116332	+	0.201492i
$313$	−119.714	−	69.1168i	−0.382472	−	0.220821i	0.296421	−	0.955057i	$-0.404207\pi$
$313$	−119.714	−	69.1168i	−0.382472	−	0.220821i	−0.678893	+	0.734237i	$0.737540\pi$
$314$			188.660i			0.600827i
$315$	−37.2314	−	28.6150i	−0.118195	−	0.0908413i
$316$	−185.742			−0.587792
$317$	−9.91216	+	17.1684i	−0.0312686	+	0.0541589i	−0.881236	−	0.472676i	$-0.843288\pi$
$317$	−9.91216	+	17.1684i	−0.0312686	+	0.0541589i	0.849968	+	0.526835i	$0.176621\pi$
$318$	−44.1914	+	25.5139i	−0.138967	+	0.0802325i
$319$	−28.3634	−	49.1268i	−0.0889135	−	0.154003i
$320$	15.4919	+	8.94427i	0.0484123	+	0.0279508i
$321$		−	143.816i		−	0.448024i
$322$	146.596	−	190.738i	0.455267	−	0.592355i
$323$	243.546			0.754013
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$	64.1619	−	37.0439i	0.197421	−	0.113981i
$326$	23.1572	+	40.1094i	0.0710342	+	0.123035i
$327$	−71.6885	−	41.3894i	−0.219231	−	0.126573i
$328$		−	107.593i		−	0.328027i
$329$	23.1550	−	174.822i	0.0703799	−	0.531374i
$330$	−6.33599			−0.0192000
$331$	131.139	−	227.139i	0.396189	−	0.686220i	−0.597063	−	0.802194i	$-0.703666\pi$
$331$	131.139	−	227.139i	0.396189	−	0.686220i	0.993252	+	0.115974i	$0.0369991\pi$
$332$	−10.0401	+	5.79665i	−0.0302412	+	0.0174598i
$333$	−79.9737	−	138.519i	−0.240161	−	0.415972i
$334$	−210.238	−	121.381i	−0.629455	−	0.363416i
$335$		−	278.368i		−	0.830951i
$336$	−44.8203	+	18.5241i	−0.133394	+	0.0551312i
$337$	578.125			1.71550			0.857752	−	0.514063i	$-0.171860\pi$
$337$	578.125			1.71550			0.857752	+	0.514063i	$0.171860\pi$
$338$	35.7515	−	61.9235i	0.105774	−	0.183206i
$339$	24.3424	−	14.0541i	0.0718064	−	0.0414575i
$340$	−28.2137	−	48.8676i	−0.0829816	−	0.143728i
$341$	28.8712	+	16.6688i	0.0846664	+	0.0488822i
$342$			81.8921i			0.239451i
$343$	316.582	+	132.004i	0.922978	+	0.384852i
$344$	−179.824			−0.522744
$345$	−47.0582	+	81.5071i	−0.136400	+	0.236252i
$346$	−247.962	+	143.161i	−0.716654	+	0.413760i
$347$	−229.861	−	398.131i	−0.662423	−	1.14735i	−0.979977	−	0.199110i	$-0.936195\pi$
$347$	−229.861	−	398.131i	−0.662423	−	1.14735i	0.317554	−	0.948240i	$-0.397139\pi$
$348$	147.115	+	84.9366i	0.422743	+	0.244071i
$349$			389.147i			1.11504i	0.830165	+	0.557518i	$0.188246\pi$
$349$			389.147i			1.11504i	−0.830165	+	0.557518i	$0.811754\pi$
$350$	18.9061	+	45.7445i	0.0540173	+	0.130699i
$351$	76.9943			0.219357
$352$	−3.27189	+	5.66708i	−0.00929515	+	0.0160997i
$353$	559.415	−	322.978i	1.58475	−	0.914953i	0.590593	−	0.806970i	$-0.298894\pi$
$353$	559.415	−	322.978i	1.58475	−	0.914953i	0.994153	−	0.107983i	$-0.0344393\pi$
$354$	−29.8991	−	51.7868i	−0.0844608	−	0.146290i
$355$	−230.389	−	133.015i	−0.648984	−	0.374691i
$356$		−	303.968i		−	0.853842i
$357$	151.655	+	20.0866i	0.424805	+	0.0562649i
$358$	−111.287			−0.310858
$359$	33.0206	−	57.1934i	0.0919794	−	0.159313i	−0.816365	−	0.577537i	$-0.804014\pi$
$359$	33.0206	−	57.1934i	0.0919794	−	0.159313i	0.908344	+	0.418224i	$0.137347\pi$
$360$	16.4317	−	9.48683i	0.0456435	−	0.0263523i
$361$	5.78661	+	10.0227i	0.0160294	+	0.0277637i
$362$	−71.2200	−	41.1189i	−0.196740	−	0.113588i
$363$			207.260i			0.570965i
$364$	164.479	+	126.414i	0.451866	+	0.347291i
$365$	−88.3907			−0.242166
$366$	7.82592	−	13.5549i	0.0213823	−	0.0370352i
$367$	519.556	−	299.966i	1.41568	−	0.817346i	0.419768	−	0.907631i	$-0.362111\pi$
$367$	519.556	−	299.966i	1.41568	−	0.817346i	0.995916	+	0.0902858i	$0.0287781\pi$
$368$	48.6014	+	84.1802i	0.132069	+	0.228750i
$369$	−98.8303	−	57.0597i	−0.267833	−	0.154633i
$370$			168.599i			0.455674i
$371$	−88.8627	+	115.621i	−0.239522	+	0.311646i
$372$	−99.8324			−0.268367
$373$	−202.376	+	350.526i	−0.542564	+	0.939748i	0.456192	+	0.889881i	$0.349213\pi$
$373$	−202.376	+	350.526i	−0.542564	+	0.939748i	−0.998756	+	0.0498667i	$0.984120\pi$
$374$	17.8762	−	10.3208i	0.0477973	−	0.0275958i
$375$	−9.68246	−	16.7705i	−0.0258199	−	0.0447214i
$376$	61.7093	+	35.6279i	0.164120	+	0.0947550i
$377$		−	726.627i		−	1.92739i
$378$	−6.75409	+	50.9939i	−0.0178680	+	0.134905i
$379$	−239.675			−0.632388			−0.316194	−	0.948695i	$-0.602405\pi$
$379$	−239.675			−0.632388			−0.316194	+	0.948695i	$0.602405\pi$
$380$	43.1609	−	74.7569i	0.113581	−	0.196729i
$381$	−120.846	+	69.7707i	−0.317182	+	0.183125i
$382$	−260.504	−	451.206i	−0.681947	−	1.18117i
$383$	553.486	+	319.555i	1.44513	+	0.834347i	0.998186	−	0.0602133i	$-0.0191781\pi$
$383$	553.486	+	319.555i	1.44513	+	0.834347i	0.446947	+	0.894561i	$0.352511\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−16.7337	+	6.91600i	−0.0434642	+	0.0179636i
$386$	397.138			1.02885
$387$	−95.3661	+	165.179i	−0.246424	+	0.426819i
$388$	249.952	−	144.310i	0.644205	−	0.371932i
$389$	−260.797	−	451.714i	−0.670429	−	1.16122i	−0.977782	−	0.209622i	$-0.932777\pi$
$389$	−260.797	−	451.714i	−0.670429	−	1.16122i	0.307353	−	0.951596i	$-0.400557\pi$
$390$	−70.2859	−	40.5796i	−0.180220	−	0.104050i
$391$		−	306.616i		−	0.784184i
$392$	−98.1533	+	97.8465i	−0.250391	+	0.249608i
$393$	−215.962			−0.549522
$394$	−5.38659	+	9.32985i	−0.0136716	+	0.0236798i
$395$	179.844	−	103.833i	0.455302	−	0.262869i
$396$	3.47036	+	6.01085i	0.00876355	+	0.0151789i
$397$	125.712	+	72.5800i	0.316656	+	0.182821i	0.649901	−	0.760019i	$-0.274810\pi$
$397$	125.712	+	72.5800i	0.316656	+	0.182821i	−0.333245	+	0.942840i	$0.608144\pi$
$398$		−	285.439i		−	0.717182i
$399$	89.3887	+	216.282i	0.224032	+	0.542060i
$400$	−20.0000			−0.0500000
$401$	−107.021	+	185.366i	−0.266886	+	0.462260i	−0.968056	−	0.250734i	$-0.919328\pi$
$401$	−107.021	+	185.366i	−0.266886	+	0.462260i	0.701170	+	0.712994i	$0.252661\pi$
$402$	−264.084	+	152.469i	−0.656924	+	0.379275i
$403$	213.515	+	369.818i	0.529813	+	0.917663i
$404$	67.6960	+	39.0843i	0.167564	+	0.0967434i
$405$		−	20.1246i		−	0.0496904i
$406$	481.250	+	63.7410i	1.18535	+	0.156998i
$407$	−61.6751			−0.151536
$408$	−30.9066	+	53.5318i	−0.0757515	+	0.131205i
$409$	−479.754	+	276.986i	−1.17299	+	0.677228i	−0.954383	−	0.298585i	$-0.903486\pi$
$409$	−479.754	+	276.986i	−1.17299	+	0.677228i	−0.218610	+	0.975812i	$0.570152\pi$
$410$	60.1462	+	104.176i	0.146698	+	0.254089i
$411$	−114.099	−	65.8750i	−0.277613	−	0.160280i
$412$		−	75.6861i		−	0.183704i
$413$	−135.493	−	104.136i	−0.328070	−	0.252145i
$414$	103.099			0.249032
$415$	6.48085	−	11.2252i	0.0156165	−	0.0270486i
$416$	−72.5910	+	41.9104i	−0.174497	+	0.100746i
$417$	−79.4734	−	137.652i	−0.190584	−	0.330101i
$418$	27.3467	+	15.7886i	0.0654228	+	0.0377719i
$419$		−	268.003i		−	0.639626i	−0.947481	−	0.319813i	$-0.896380\pi$
$419$		−	268.003i		−	0.639626i	0.947481	−	0.319813i	$-0.103620\pi$
$420$	33.0418	−	42.9912i	0.0786709	−	0.102360i
$421$	−9.12915			−0.0216844			−0.0108422	−	0.999941i	$-0.503451\pi$
$421$	−9.12915			−0.0216844			−0.0108422	+	0.999941i	$0.503451\pi$
$422$	−21.4831	+	37.2099i	−0.0509079	+	0.0881751i
$423$	65.4526	−	37.7891i	0.154734	−	0.0893358i
$424$	−29.4609	−	51.0278i	−0.0694833	−	0.120349i
$425$	54.6357	+	31.5439i	0.128554	+	0.0742210i
$426$			291.422i			0.684089i
$427$	5.87299	−	44.3416i	0.0137541	−	0.103845i
$428$	166.064			0.388000
$429$	14.8444	−	25.7112i	0.0346022	−	0.0599328i
$430$	174.114	−	100.525i	0.404916	−	0.233778i
$431$	134.221	+	232.478i	0.311419	+	0.539393i	0.978670	−	0.205440i	$-0.0658626\pi$
$431$	134.221	+	232.478i	0.311419	+	0.539393i	−0.667251	+	0.744833i	$0.732529\pi$
$432$	−18.0000	−	10.3923i	−0.0416667	−	0.0240563i
$433$			472.254i			1.09066i	0.838223	+	0.545328i	$0.183595\pi$
$433$			472.254i			1.09066i	−0.838223	+	0.545328i	$0.816405\pi$
$434$	−263.663	+	108.971i	−0.607519	+	0.251086i
$435$	−189.924			−0.436607
$436$	47.7924	−	82.7788i	0.109616	−	0.189860i
$437$	406.215	−	234.528i	0.929553	−	0.536678i
$438$	48.4136	+	83.8548i	0.110533	+	0.191449i
$439$	475.788	+	274.696i	1.08380	+	0.625731i	0.931919	−	0.362667i	$-0.118134\pi$
$439$	475.788	+	274.696i	1.08380	+	0.625731i	0.151880	+	0.988399i	$0.451467\pi$
$440$		−	7.31617i		−	0.0166277i
$441$	37.8241	+	142.050i	0.0857689	+	0.322110i
$442$	264.404			0.598198
$443$	−235.405	+	407.734i	−0.531388	+	0.920392i	0.467940	+	0.883760i	$0.344996\pi$
$443$	−235.405	+	407.734i	−0.531388	+	0.920392i	−0.999329	+	0.0366317i	$0.988337\pi$
$444$	159.947	−	92.3457i	0.360242	−	0.207986i
$445$	169.923	+	294.315i	0.381850	+	0.661383i
$446$	20.4994	+	11.8353i	0.0459628	+	0.0265366i
$447$			171.327i			0.383283i
$448$	−21.3898	−	51.7540i	−0.0477450	−	0.115522i
$449$	559.525			1.24616			0.623079	−	0.782159i	$-0.285882\pi$
$449$	559.525			1.24616			0.623079	+	0.782159i	$0.285882\pi$
$450$	−10.6066	+	18.3712i	−0.0235702	+	0.0408248i
$451$	−38.1086	+	22.0020i	−0.0844980	+	0.0487849i
$452$	16.2283	+	28.1082i	0.0359032	+	0.0621862i
$453$	146.685	+	84.6886i	0.323808	+	0.186951i
$454$		−	598.880i		−	1.31912i
$455$	−229.924	−	30.4531i	−0.505327	−	0.0669299i
$456$	−94.5609			−0.207370
$457$	−313.689	+	543.325i	−0.686409	+	1.18890i	0.286583	+	0.958055i	$0.407481\pi$
$457$	−313.689	+	543.325i	−0.686409	+	1.18890i	−0.972992	+	0.230840i	$0.925853\pi$
$458$	495.818	−	286.261i	1.08257	−	0.625023i
$459$	32.7814	+	56.7790i	0.0714192	+	0.123702i
$460$	−94.1163	−	54.3381i	−0.204601	−	0.118126i
$461$		−	223.659i		−	0.485160i	−0.970131	−	0.242580i	$-0.922006\pi$
$461$		−	223.659i		−	0.485160i	0.970131	−	0.242580i	$-0.0779936\pi$
$462$	15.7265	+	12.0870i	0.0340401	+	0.0261623i
$463$	−397.204			−0.857893			−0.428946	−	0.903330i	$-0.641115\pi$
$463$	−397.204			−0.857893			−0.428946	+	0.903330i	$0.641115\pi$
$464$	−98.0764	+	169.873i	−0.211371	+	0.366106i
$465$	96.6623	−	55.8080i	0.207876	−	0.120017i
$466$	−196.079	−	339.620i	−0.420771	−	0.728797i
$467$	−289.014	−	166.862i	−0.618874	−	0.357307i	0.157557	−	0.987510i	$-0.449638\pi$
$467$	−289.014	−	166.862i	−0.618874	−	0.357307i	−0.776430	+	0.630203i	$0.782972\pi$
$468$			88.9054i			0.189969i
$469$	−531.035	+	690.937i	−1.13227	+	1.47321i
$470$	−79.6663			−0.169503
$471$	−115.530	+	200.104i	−0.245287	+	0.424849i
$472$	59.7983	−	34.5246i	0.126691	−	0.0731452i
$473$	36.7728	+	63.6924i	0.0777438	+	0.134656i
$474$	−197.009	−	113.743i	−0.415632	−	0.239965i
$475$			96.5108i			0.203181i
$476$	−23.1940	+	175.117i	−0.0487268	+	0.367892i
$477$	−62.4961			−0.131019
$478$	−205.235	+	355.478i	−0.429363	+	0.743678i
$479$	527.265	−	304.417i	1.10076	−	0.635526i	0.164341	−	0.986404i	$-0.447450\pi$
$479$	527.265	−	304.417i	1.10076	−	0.635526i	0.936421	+	0.350878i	$0.114117\pi$
$480$	10.9545	+	18.9737i	0.0228218	+	0.0395285i
$481$	−684.169	−	395.005i	−1.42239	−	0.821217i
$482$		−	572.484i		−	1.18773i
$483$	272.291	−	112.537i	0.563750	−	0.232996i
$484$	−239.324			−0.494470
$485$	−161.343	+	279.454i	−0.332666	+	0.576195i
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	159.238	+	275.809i	0.326978	+	0.566343i	0.981911	−	0.189344i	$-0.0606363\pi$
$487$	159.238	+	275.809i	0.326978	+	0.566343i	−0.654932	+	0.755687i	$0.727303\pi$
$488$	15.6518	+	9.03659i	0.0320734	+	0.0185176i
$489$			56.7232i			0.115998i
$490$	40.3387	−	149.609i	0.0823238	−	0.305324i
$491$	523.303			1.06579			0.532895	−	0.846181i	$-0.321104\pi$
$491$	523.303			1.06579			0.532895	+	0.846181i	$0.321104\pi$
$492$	65.8869	−	114.119i	0.133916	−	0.231950i
$493$	535.847	−	309.371i	1.08691	−	0.627528i
$494$	202.240	+	350.290i	0.409393	+	0.709090i
$495$	−6.72033	−	3.87999i	−0.0135764	−	0.00783836i
$496$		−	115.277i		−	0.232412i
$497$	318.100	+	769.663i	0.640039	+	1.54862i
$498$	−14.1988			−0.0285117
$499$	391.909	−	678.806i	0.785388	−	1.36033i	−0.143379	−	0.989668i	$-0.545797\pi$
$499$	391.909	−	678.806i	0.785388	−	1.36033i	0.928767	−	0.370664i	$-0.120870\pi$
$500$	19.3649	−	11.1803i	0.0387298	−	0.0223607i
$501$	−148.661	−	257.488i	−0.296728	−	0.513948i
$502$	190.822	+	110.171i	0.380123	+	0.219464i
$503$			58.0772i			0.115462i	0.998332	+	0.0577308i	$0.0183865\pi$
$503$			58.0772i			0.115462i	−0.998332	+	0.0577308i	$0.981613\pi$
$504$	−58.8827	−	7.79895i	−0.116831	−	0.0154741i
$505$	−87.3952			−0.173060
$506$	19.8773	−	34.4286i	0.0392833	−	0.0680406i
$507$	75.8404	−	43.7865i	0.149587	−	0.0863639i
$508$	−80.5643	−	139.541i	−0.158591	−	0.274688i
$509$	−811.110	−	468.295i	−1.59354	−	0.920029i	−0.992694	−	0.120662i	$-0.961498\pi$
$509$	−811.110	−	468.295i	−1.59354	−	0.920029i	−0.600843	−	0.799367i	$-0.705168\pi$
$510$		−	69.1092i		−	0.135508i
$511$	219.394	+	168.620i	0.429343	+	0.329981i
$512$	22.6274			0.0441942
$513$	−50.1485	+	86.8597i	−0.0977553	+	0.169317i
$514$	31.7229	−	18.3152i	0.0617178	−	0.0356328i
$515$	42.3098	+	73.2827i	0.0821549	+	0.142297i
$516$	−190.732	−	110.119i	−0.369636	−	0.213410i
$517$		−	29.1426i		−	0.0563687i
$518$	321.632	−	418.480i	0.620910	−	0.807876i
$519$	−350.672			−0.675668
$520$	46.8573	−	81.1592i	0.0901101	−	0.156075i
$521$	−607.133	+	350.528i	−1.16532	+	0.672799i	−0.952574	−	0.304308i	$-0.901575\pi$
$521$	−607.133	+	350.528i	−1.16532	+	0.672799i	−0.212749	+	0.977107i	$0.568242\pi$
$522$	104.026	+	180.178i	0.199283	+	0.345168i
$523$	−594.464	−	343.214i	−1.13664	−	0.656241i	−0.191046	−	0.981581i	$-0.561188\pi$
$523$	−594.464	−	343.214i	−1.13664	−	0.656241i	−0.945597	+	0.325340i	$0.894521\pi$
$524$		−	249.372i		−	0.475900i
$525$	−7.95977	+	60.0969i	−0.0151615	+	0.114470i
$526$	−446.615			−0.849078
$527$	−181.814	+	314.910i	−0.344997	+	0.597553i
$528$	−6.94073	+	4.00723i	−0.0131453	+	0.00758945i
$529$	−30.7626	−	53.2824i	−0.0581524	−	0.100723i
$530$	57.0509	+	32.9383i	0.107643	+	0.0621478i
$531$		−	73.2376i		−	0.137924i
$532$	−249.741	+	103.217i	−0.469438	+	0.194017i
$533$	−563.657			−1.05752
$534$	186.141	−	322.406i	0.348579	−	0.603757i
$535$	−160.791	+	92.8327i	−0.300544	+	0.173519i
$536$	−176.056	−	304.937i	−0.328462	−	0.568913i
$537$	−118.038	−	68.1491i	−0.219810	−	0.126907i
$538$		−	67.6316i		−	0.125709i
$539$	54.7282	+	14.7562i	0.101537	+	0.0273770i
$540$	23.2379			0.0430331
$541$	−398.250	+	689.789i	−0.736136	+	1.27503i	0.218087	+	0.975929i	$0.430018\pi$
$541$	−398.250	+	689.789i	−0.736136	+	1.27503i	−0.954223	+	0.299096i	$0.903315\pi$
$542$	−416.599	+	240.524i	−0.768634	+	0.443771i
$543$	−50.3602	−	87.2263i	−0.0927443	−	0.160638i
$544$	−61.8132	−	35.6879i	−0.113627	−	0.0656027i
$545$			106.867i			0.196086i
$546$	97.0440	+	234.805i	0.177736	+	0.430045i
$547$	−395.055			−0.722221			−0.361111	−	0.932523i	$-0.617602\pi$
$547$	−395.055			−0.722221			−0.361111	+	0.932523i	$0.617602\pi$
$548$	76.0659	−	131.750i	0.138806	−	0.240420i
$549$	16.6013	−	9.58476i	0.0302391	−	0.0174586i
$550$	4.08986	+	7.08385i	0.00743612	+	0.0128797i
$551$	819.730	+	473.271i	1.48771	+	0.858932i
$552$			119.049i			0.215668i
$553$	−644.470	−	85.3592i	−1.16541	−	0.154357i
$554$	297.815			0.537572
$555$	−103.246	+	178.827i	−0.186028	+	0.322210i
$556$	158.947	−	91.7680i	0.285876	−	0.165050i
$557$	20.8443	+	36.1034i	0.0374224	+	0.0648175i	0.884130	−	0.467241i	$-0.154752\pi$
$557$	20.8443	+	36.1034i	0.0374224	+	0.0648175i	−0.846708	+	0.532059i	$0.821419\pi$
$558$	−105.888	−	61.1346i	−0.189764	−	0.109560i
$559$			942.063i			1.68526i
$560$	49.6419	+	38.1534i	0.0886463	+	0.0681310i
$561$	25.2808			0.0450637
$562$	−333.603	+	577.817i	−0.593599	+	1.02814i
$563$	−640.642	+	369.875i	−1.13791	+	0.656972i	−0.945912	−	0.324424i	$-0.894830\pi$
$563$	−640.642	+	369.875i	−1.13791	+	0.656972i	−0.191996	+	0.981396i	$0.561496\pi$
$564$	43.6350	+	75.5781i	0.0773671	+	0.134004i
$565$	−31.4259	−	18.1437i	−0.0556210	−	0.0321128i
$566$			662.234i			1.17003i
$567$	−38.3911	+	49.9512i	−0.0677091	+	0.0880974i
$568$	−336.505			−0.592439
$569$	−2.38030	+	4.12281i	−0.00418331	+	0.00724570i	−0.868109	−	0.496373i	$-0.834665\pi$
$569$	−2.38030	+	4.12281i	−0.00418331	+	0.00724570i	0.863926	+	0.503618i	$0.167998\pi$
$570$	91.5582	−	52.8611i	0.160628	−	0.0927388i
$571$	−399.848	−	692.557i	−0.700260	−	1.21289i	−0.968375	−	0.249498i	$-0.919734\pi$
$571$	−399.848	−	692.557i	−0.700260	−	1.21289i	0.268116	−	0.963387i	$-0.413599\pi$
$572$	29.6887	+	17.1408i	0.0519033	+	0.0299664i
$573$		−	638.101i		−	1.11362i
$574$	49.4451	−	373.315i	0.0861412	−	0.650374i
$575$	121.504			0.211311
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−148.871	+	85.9510i	−0.258009	+	0.148962i	−0.623426	−	0.781882i	$-0.714260\pi$
$577$	−148.871	+	85.9510i	−0.258009	+	0.148962i	0.365417	+	0.930844i	$0.380926\pi$
$578$	−91.7804	−	158.968i	−0.158790	−	0.275032i
$579$	421.228	+	243.196i	0.727510	+	0.420028i
$580$		−	219.305i		−	0.378113i
$581$	−37.5000	+	15.4986i	−0.0645439	+	0.0266758i
$582$	353.485			0.607362
$583$	−12.0491	+	20.8697i	−0.0206675	+	0.0357971i
$584$	−96.8271	+	55.9032i	−0.165800	+	0.0957246i
$585$	−49.6996	−	86.0823i	−0.0849566	−	0.147149i
$586$	−77.7795	−	44.9060i	−0.132730	−	0.0766314i
$587$		−	724.352i		−	1.23399i	−0.786967	−	0.616994i	$-0.788350\pi$
$587$		−	724.352i		−	1.23399i	0.786967	−	0.616994i	$-0.211650\pi$
$588$	−164.026	+	43.6755i	−0.278955	+	0.0742781i
$589$	−556.271			−0.944433
$590$	−38.5996	+	66.8565i	−0.0654231	+	0.113316i
$591$	−11.4267	+	6.59720i	−0.0193345	+	0.0111628i
$592$	106.632	+	184.691i	0.180121	+	0.311979i
$593$	−894.293	−	516.320i	−1.50808	−	0.870692i	−0.999956	−	0.00940925i	$-0.997005\pi$
$593$	−894.293	−	516.320i	−1.50808	−	0.870692i	−0.508127	−	0.861282i	$-0.669662\pi$
$594$			8.50062i			0.0143108i
$595$	−75.4357	−	182.522i	−0.126783	−	0.306759i
$596$	−197.832			−0.331933
$597$	174.795	−	302.753i	0.292789	−	0.507125i
$598$	441.003	−	254.613i	0.737464	−	0.425775i
$599$	212.436	+	367.949i	0.354650	+	0.614272i	0.987058	−	0.160363i	$-0.0512666\pi$
$599$	212.436	+	367.949i	0.354650	+	0.614272i	−0.632408	+	0.774636i	$0.717933\pi$
$600$	−21.2132	−	12.2474i	−0.0353553	−	0.0204124i
$601$		−	749.418i		−	1.24695i	−0.781843	−	0.623476i	$-0.785720\pi$
$601$		−	749.418i		−	1.24695i	0.781843	−	0.623476i	$-0.214280\pi$
$602$	−623.935	−	82.6395i	−1.03644	−	0.137275i
$603$	−373.471			−0.619354
$604$	−97.7900	+	169.377i	−0.161904	+	0.280426i
$605$	231.724	−	133.786i	0.383015	−	0.221134i
$606$	47.8683	+	82.9104i	0.0789906	+	0.136816i
$607$	−205.133	−	118.434i	−0.337945	−	0.195113i	0.321418	−	0.946938i	$-0.395841\pi$
$607$	−205.133	−	118.434i	−0.337945	−	0.195113i	−0.659363	+	0.751825i	$0.729174\pi$
$608$		−	109.189i		−	0.179588i
$609$	471.410	+	362.312i	0.774072	+	0.594929i
$610$	−20.2064			−0.0331253
$611$	186.647	−	323.283i	0.305478	−	0.529104i
$612$	−65.5628	+	37.8527i	−0.107129	+	0.0618508i
$613$	469.189	+	812.659i	0.765398	+	1.32571i	0.940036	+	0.341075i	$0.110791\pi$
$613$	469.189	+	812.659i	0.765398	+	1.32571i	−0.174638	+	0.984633i	$0.555876\pi$
$614$	−259.168	−	149.631i	−0.422098	−	0.243698i
$615$			147.328i			0.239557i
$616$	−13.9568	+	18.1594i	−0.0226572	+	0.0294796i
$617$	225.176			0.364952			0.182476	−	0.983210i	$-0.441589\pi$
$617$	225.176			0.364952			0.182476	+	0.983210i	$0.441589\pi$
$618$	46.3481	−	80.2772i	0.0749969	−	0.129898i
$619$	916.115	−	528.919i	1.47999	−	0.854473i	0.480248	−	0.877133i	$-0.340547\pi$
$619$	916.115	−	528.919i	1.47999	−	0.854473i	0.999743	+	0.0226591i	$0.00721323\pi$
$620$	64.4415	+	111.616i	0.103938	+	0.180026i
$621$	109.353	+	63.1351i	0.176092	+	0.101667i
$622$			95.2182i			0.153084i
$623$	139.691	−	1054.68i	0.224222	−	1.69290i
$624$	−102.659			−0.164518
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	169.301	−	97.7460i	0.270449	−	0.156144i
$627$	19.3371	+	33.4928i	0.0308406	+	0.0534175i
$628$	−231.060	−	133.403i	−0.367930	−	0.212424i
$629$		−	672.716i		−	1.06950i
$630$	61.3727	−	25.3652i	0.0974170	−	0.0402621i
$631$	877.283			1.39031			0.695153	−	0.718862i	$-0.255336\pi$
$631$	877.283			1.39031			0.695153	+	0.718862i	$0.255336\pi$
$632$	131.340	−	227.487i	0.207816	−	0.359948i
$633$	−45.5726	+	26.3114i	−0.0719947	+	0.0415662i
$634$	−14.0179	−	24.2797i	−0.0221103	−	0.0382961i
$635$	156.012	+	90.0736i	0.245688	+	0.141848i
$636$		−	72.1643i		−	0.113466i
$637$	512.598	+	514.205i	0.804707	+	0.807230i
$638$	80.2238			0.125743
$639$	−178.459	+	309.100i	−0.279278	+	0.483724i
$640$	−21.9089	+	12.6491i	−0.0342327	+	0.0197642i
$641$	−26.8684	−	46.5374i	−0.0419163	−	0.0726012i	0.844306	−	0.535861i	$-0.180013\pi$
$641$	−26.8684	−	46.5374i	−0.0419163	−	0.0726012i	−0.886222	+	0.463260i	$0.846680\pi$
$642$	176.138	+	101.693i	0.274358	+	0.158401i
$643$		−	99.7799i		−	0.155179i	−0.996985	−	0.0775893i	$-0.975278\pi$
$643$		−	99.7799i		−	0.155179i	0.996985	−	0.0775893i	$-0.0247223\pi$
$644$	129.947	+	314.415i	0.201781	+	0.488222i
$645$	246.234			0.381759
$646$	−172.213	+	298.282i	−0.266584	+	0.461737i
$647$	−657.905	+	379.842i	−1.01685	+	0.587081i	−0.913191	−	0.407531i	$-0.866390\pi$
$647$	−657.905	+	379.842i	−1.01685	+	0.587081i	−0.103663	+	0.994612i	$0.533056\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	−24.4567	−	14.1201i	−0.0376836	−	0.0217567i
$650$			104.776i			0.161194i
$651$	−346.388	−	45.8787i	−0.532086	−	0.0704742i
$652$	−65.4983			−0.100458
$653$	−574.896	+	995.749i	−0.880392	+	1.52488i	−0.0294854	+	0.999565i	$0.509387\pi$
$653$	−574.896	+	995.749i	−0.880392	+	1.52488i	−0.850906	+	0.525318i	$0.823946\pi$
$654$	101.383	−	58.5334i	0.155020	−	0.0895007i
$655$	139.403	+	241.453i	0.212829	+	0.368631i
$656$	131.774	+	76.0796i	0.200875	+	0.115975i
$657$			118.589i			0.180500i
$658$	197.740	+	151.977i	0.300516	+	0.230968i
$659$	213.700			0.324280			0.162140	−	0.986768i	$-0.448160\pi$
$659$	213.700			0.324280			0.162140	+	0.986768i	$0.448160\pi$
$660$	4.48022	−	7.75997i	0.00678821	−	0.0117575i
$661$	665.936	−	384.479i	1.00747	−	0.581662i	0.0970187	−	0.995283i	$-0.469069\pi$
$661$	665.936	−	384.479i	1.00747	−	0.581662i	0.910449	+	0.413621i	$0.135736\pi$
$662$	185.458	+	321.223i	0.280148	+	0.485231i
$663$	280.442	+	161.914i	0.422990	+	0.244213i
$664$		−	16.3954i		−	0.0246919i
$665$	184.111	−	239.549i	0.276858	−	0.360224i
$666$	226.200			0.339639
$667$	595.832	−	1032.01i	0.893301	−	1.54724i
$668$	297.322	−	171.659i	0.445092	−	0.256974i
$669$	14.4953	+	25.1065i	0.0216671	+	0.0375284i
$670$	340.930	+	196.836i	0.508851	+	0.293785i
$671$		−	7.39169i		−	0.0110159i
$672$	9.00545	−	67.9919i	0.0134010	−	0.101178i
$673$	−1299.78			−1.93133			−0.965664	−	0.259796i	$-0.916345\pi$
$673$	−1299.78			−1.93133			−0.965664	+	0.259796i	$0.916345\pi$
$674$	−408.796	+	708.056i	−0.606523	+	1.05053i
$675$	−22.5000	+	12.9904i	−0.0333333	+	0.0192450i
$676$	50.5603	+	87.5730i	0.0747933	+	0.129546i
$677$	1073.60	+	619.840i	1.58581	+	0.915569i	0.993986	+	0.109504i	$0.0349261\pi$
$677$	1073.60	+	619.840i	1.58581	+	0.915569i	0.591826	+	0.806066i	$0.298407\pi$
$678$			39.7509i			0.0586297i
$679$	933.575	−	385.844i	1.37493	−	0.568253i
$680$	79.8005			0.117354
$681$	366.738	−	635.208i	0.538528	−	0.932758i
$682$	−40.8301	+	23.5733i	−0.0598682	+	0.0345649i
$683$	233.043	+	403.643i	0.341205	+	0.590985i	0.984657	−	0.174502i	$-0.0558316\pi$
$683$	233.043	+	403.643i	0.341205	+	0.590985i	−0.643452	+	0.765487i	$0.722498\pi$
$684$	−100.297	−	57.9065i	−0.146633	−	0.0846586i
$685$			170.089i			0.248304i
$686$	−385.528	+	294.391i	−0.561995	+	0.429141i
$687$	701.193			1.02066
$688$	127.155	−	220.239i	0.184818	−	0.320114i
$689$	−267.325	+	154.340i	−0.387989	+	0.224006i
$690$	−66.5503	−	115.268i	−0.0964497	−	0.167056i
$691$	−93.9272	−	54.2289i	−0.135929	−	0.0784788i	0.430493	−	0.902594i	$-0.358340\pi$
$691$	−93.9272	−	54.2289i	−0.135929	−	0.0784788i	−0.566423	+	0.824115i	$0.691673\pi$
$692$		−	404.921i		−	0.585145i
$693$	9.27879	+	22.4507i	0.0133893	+	0.0323963i
$694$	650.145			0.936808
$695$	−102.600	+	177.708i	−0.147626	+	0.255695i
$696$	−208.051	+	120.119i	−0.298924	+	0.172584i
$697$	−239.985	−	415.666i	−0.344311	−	0.596364i
$698$	−476.606	−	275.169i	−0.682817	−	0.394224i
$699$		−	480.295i		−	0.687117i
$700$	−69.3940	−	9.19115i	−0.0991342	−	0.0131302i
$701$	528.400			0.753780			0.376890	−	0.926258i	$-0.376993\pi$
$701$	528.400			0.753780			0.376890	+	0.926258i	$0.376993\pi$
$702$	−54.4432	+	94.2984i	−0.0775544	+	0.134328i
$703$	891.235	−	514.555i	1.26776	−	0.731942i
$704$	−4.62715	−	8.01446i	−0.00657266	−	0.0113842i
$705$	−84.4989	−	48.7855i	−0.119857	−	0.0691992i
$706$			913.521i			1.29394i
$707$	216.923	+	166.721i	0.306822	+	0.235815i
$708$	84.5675			0.119446
$709$	466.779	−	808.484i	0.658362	−	1.14032i	−0.322678	−	0.946509i	$-0.604583\pi$
$709$	466.779	−	808.484i	0.658362	−	1.14032i	0.981040	−	0.193808i	$-0.0620837\pi$
$710$	325.820	−	188.112i	0.458901	−	0.264947i
$711$	−139.307	−	241.286i	−0.195931	−	0.339362i
$712$	372.283	+	214.938i	0.522869	+	0.301879i
$713$			700.326i			0.982224i
$714$	−131.837	+	171.536i	−0.184646	+	0.240246i
$715$	−38.3280			−0.0536055
$716$	78.6918	−	136.298i	0.109905	−	0.190361i
$717$	−435.370	+	251.361i	−0.607211	+	0.350573i
$718$	46.6982	+	80.8836i	0.0650392	+	0.112651i
$719$	557.452	+	321.845i	0.775316	+	0.447629i	0.834768	−	0.550602i	$-0.185602\pi$
$719$	557.452	+	321.845i	0.775316	+	0.447629i	−0.0594517	+	0.998231i	$0.518935\pi$
$720$			26.8328i			0.0372678i
$721$	34.7821	−	262.608i	0.0482414	−	0.364227i
$722$	−16.3670			−0.0226690
$723$	350.574	−	607.211i	0.484887	−	0.839850i
$724$	100.720	−	58.1509i	0.139116	−	0.0803189i
$725$	122.595	+	212.342i	0.169097	+	0.292885i
$726$	−253.841	−	146.555i	−0.349643	−	0.201867i
$727$			317.353i			0.436524i	0.975890	+	0.218262i	$0.0700388\pi$
$727$			317.353i			0.436524i	−0.975890	+	0.218262i	$0.929961\pi$
$728$	−271.129	+	112.057i	−0.372430	+	0.153924i
$729$	−27.0000			−0.0370370
$730$	62.5016	−	108.256i	0.0856187	−	0.148296i
$731$	−694.719	+	401.096i	−0.950368	+	0.548695i
$732$	11.0675	+	19.1695i	0.0151196	+	0.0261879i
$733$	−727.023	−	419.747i	−0.991846	−	0.572643i	−0.0860205	−	0.996293i	$-0.527415\pi$
$733$	−727.023	−	419.747i	−0.991846	−	0.572643i	−0.905826	+	0.423651i	$0.860748\pi$
$734$			848.431i			1.15590i
$735$	134.402	−	133.982i	0.182860	−	0.182288i
$736$	−137.466			−0.186774
$737$	−72.0044	+	124.715i	−0.0976993	+	0.169220i
$738$	139.767	−	80.6946i	0.189386	−	0.109342i
$739$	459.403	+	795.709i	0.621654	+	1.07674i	0.989178	+	0.146723i	$0.0468725\pi$
$739$	459.403	+	795.709i	0.621654	+	1.07674i	−0.367523	+	0.930014i	$0.619794\pi$
$740$	−206.491	−	119.218i	−0.279042	−	0.161105i
$741$			495.386i			0.668537i
$742$	−78.7703	−	190.590i	−0.106160	−	0.256860i
$743$	−1034.18			−1.39190			−0.695952	−	0.718088i	$-0.745017\pi$
$743$	−1034.18			−1.39190			−0.695952	+	0.718088i	$0.745017\pi$
$744$	70.5922	−	122.269i	0.0948819	−	0.164340i
$745$	191.550	−	110.591i	0.257114	−	0.148445i
$746$	−286.203	−	495.719i	−0.383651	−	0.664502i
$747$	−15.0601	−	8.69498i	−0.0201608	−	0.0116399i
$748$			29.1917i			0.0390263i
$749$	576.193	+	76.3160i	0.769283	+	0.101891i
$750$	27.3861			0.0365148
$751$	340.948	−	590.540i	0.453992	−	0.786338i	−0.544637	−	0.838672i	$-0.683333\pi$
$751$	340.948	−	590.540i	0.453992	−	0.786338i	0.998630	+	0.0523339i	$0.0166660\pi$
$752$	−87.2701	+	50.3854i	−0.116051	+	0.0670019i
$753$	134.931	+	233.708i	0.179192	+	0.310369i
$754$	889.932	+	513.803i	1.18028	+	0.681436i
$755$		−	218.665i		−	0.289623i
$756$	−57.6787	−	44.3302i	−0.0762946	−	0.0586378i
$757$	183.172			0.241971			0.120985	−	0.992654i	$-0.461395\pi$
$757$	183.172			0.241971			0.120985	+	0.992654i	$0.461395\pi$
$758$	169.476	−	293.541i	0.223583	−	0.387257i
$759$	42.1662	−	24.3447i	0.0555549	−	0.0320747i
$760$	61.0388	+	105.722i	0.0803142	+	0.139108i
$761$	−673.743	−	388.985i	−0.885338	−	0.511150i	−0.0129235	−	0.999916i	$-0.504114\pi$
$761$	−673.743	−	388.985i	−0.885338	−	0.511150i	−0.872415	+	0.488766i	$0.837447\pi$
$762$		−	197.341i		−	0.258978i
$763$	203.867	−	265.254i	0.267191	−	0.347646i
$764$	736.816			0.964419
$765$	42.3206	−	73.3014i	0.0553210	−	0.0958189i
$766$	−782.747	+	451.919i	−1.02186	+	0.589973i
$767$	−180.867	−	313.271i	−0.235811	−	0.408437i
$768$	24.0000	+	13.8564i	0.0312500	+	0.0180422i
$769$		−	302.546i		−	0.393428i	−0.980461	−	0.196714i	$-0.936973\pi$
$769$		−	302.546i		−	0.393428i	0.980461	−	0.196714i	$-0.0630271\pi$
$770$	3.36220	−	25.3849i	0.00436649	−	0.0329674i
$771$	44.8630			0.0581881
$772$	−280.819	+	486.393i	−0.363755	+	0.630042i
$773$	−110.995	+	64.0833i	−0.143591	+	0.0829020i	−0.570074	−	0.821593i	$-0.693086\pi$
$773$	−110.995	+	64.0833i	−0.143591	+	0.0829020i	0.426484	+	0.904495i	$0.359752\pi$
$774$	−134.868	−	233.598i	−0.174248	−	0.301807i
$775$	−124.790	−	72.0478i	−0.161020	−	0.0929649i
$776$			408.169i			0.525991i
$777$	597.407	−	246.907i	0.768864	−	0.317769i
$778$	737.645			0.948130
$779$	367.125	−	635.879i	0.471277	−	0.816277i
$780$	99.3993	−	57.3882i	0.127435	−	0.0735746i
$781$	68.8130	+	119.188i	0.0881089	+	0.152609i
$782$	375.526	+	216.810i	0.480213	+	0.277251i
$783$			254.810i			0.325428i
$784$	−50.4321	−	189.401i	−0.0643267	−	0.241582i
$785$	298.297			0.379996
$786$	152.708	−	264.499i	0.194285	−	0.336512i
$787$	−466.311	+	269.225i	−0.592518	+	0.342090i	−0.766092	−	0.642731i	$-0.777801\pi$
$787$	−466.311	+	269.225i	−0.592518	+	0.342090i	0.173575	+	0.984821i	$0.444468\pi$
$788$	−7.61779	−	13.1944i	−0.00966725	−	0.0167442i
$789$	−473.707	−	273.495i	−0.600389	−	0.346635i
$790$			293.684i			0.371752i
$791$	43.3898	+	104.985i	0.0548544	+	0.132724i
$792$	−9.81567			−0.0123935
$793$	47.3409	−	81.9969i	0.0596985	−	0.103401i
$794$	−177.784	+	102.644i	−0.223909	+	0.129274i
$795$	40.3411	+	69.8727i	0.0507435	+	0.0878903i
$796$	349.589	+	201.836i	0.439183	+	0.253562i
$797$			207.481i			0.260328i	0.991492	+	0.130164i	$0.0415504\pi$
$797$			207.481i			0.260328i	−0.991492	+	0.130164i	$0.958450\pi$
$798$	−328.098	−	43.4561i	−0.411150	−	0.0544563i
$799$	317.871			0.397836
$800$	14.1421	−	24.4949i	0.0176777	−	0.0306186i
$801$	394.866	−	227.976i	0.492966	−	0.284614i
$802$	−151.351	−	262.148i	−0.188717	−	0.326867i
$803$	39.6010	+	22.8636i	0.0493163	+	0.0284728i
$804$		−	431.247i		−	0.536376i
$805$	−301.584	−	231.789i	−0.374638	−	0.287936i
$806$	−603.911			−0.749269
$807$	41.4157	−	71.7341i	0.0513206	−	0.0888899i
$808$	−95.7366	+	55.2736i	−0.118486	+	0.0684079i
$809$	−722.858	−	1252.03i	−0.893520	−	1.54762i	−0.835625	−	0.549300i	$-0.814894\pi$
$809$	−722.858	−	1252.03i	−0.893520	−	1.54762i	−0.0578954	−	0.998323i	$-0.518439\pi$
$810$	24.6475	+	14.2302i	0.0304290	+	0.0175682i
$811$		−	207.868i		−	0.256310i	−0.991754	−	0.128155i	$-0.959094\pi$
$811$		−	207.868i		−	0.256310i	0.991754	−	0.128155i	$-0.0409055\pi$
$812$	−418.362	+	544.337i	−0.515224	+	0.670366i
$813$	−589.161			−0.724675
$814$	43.6109	−	75.5363i	0.0535760	−	0.0927964i
$815$	63.4185	−	36.6147i	0.0778141	−	0.0449260i
$816$	−43.7085	−	75.7054i	−0.0535644	−	0.0927762i
$817$	−1062.77	−	613.591i	−1.30082	−	0.751029i
$818$		−	783.435i		−	0.957745i
$819$	−40.8571	+	308.475i	−0.0498866	+	0.376648i
$820$	−170.119			−0.207462
$821$	−307.642	+	532.851i	−0.374716	+	0.649027i	−0.990285	−	0.139056i	$-0.955593\pi$
$821$	−307.642	+	532.851i	−0.374716	+	0.649027i	0.615568	+	0.788083i	$0.288926\pi$
$822$	161.360	−	93.1613i	0.196302	−	0.113335i
$823$	167.804	+	290.645i	0.203893	+	0.353153i	0.949779	−	0.312920i	$-0.101307\pi$
$823$	167.804	+	290.645i	0.203893	+	0.353153i	−0.745886	+	0.666073i	$0.767974\pi$
$824$	92.6961	+	53.5181i	0.112495	+	0.0649492i
$825$			10.0181i			0.0121431i
$826$	223.348	−	92.3091i	0.270397	−	0.111754i
$827$	−1453.38			−1.75741			−0.878707	−	0.477362i	$-0.841593\pi$
$827$	−1453.38			−1.75741			−0.878707	+	0.477362i	$0.841593\pi$
$828$	−72.9022	+	126.270i	−0.0880461	+	0.152500i
$829$	−11.2468	+	6.49333i	−0.0135667	+	0.00783273i	−0.506768	−	0.862082i	$-0.669160\pi$
$829$	−11.2468	+	6.49333i	−0.0135667	+	0.00783273i	0.493201	+	0.869915i	$0.335827\pi$
$830$	9.16531	+	15.8748i	0.0110425	+	0.0191262i
$831$	315.880	+	182.374i	0.380121	+	0.219463i
$832$		−	118.541i		−	0.142477i
$833$	−160.952	+	596.943i	−0.193220	+	0.716618i
$834$	224.785			0.269526
$835$	−191.920	+	332.416i	−0.229845	+	0.398103i
$836$	−38.6741	+	22.3285i	−0.0462609	+	0.0267087i
$837$	−74.8743	−	129.686i	−0.0894555	−	0.154942i
$838$	328.236	+	189.507i	0.391689	+	0.226142i
$839$			940.714i			1.12123i	0.828076	+	0.560616i	$0.189436\pi$
$839$			940.714i			1.12123i	−0.828076	+	0.560616i	$0.810564\pi$
$840$	29.2892	+	70.8671i	0.0348680	+	0.0843656i
$841$	1563.74			1.85939
$842$	6.45529	−	11.1809i	0.00766661	−	0.0132790i
$843$	−707.678	+	408.578i	−0.839476	+	0.484671i
$844$	−30.3818	−	52.6228i	−0.0359973	−	0.0623492i
$845$	−97.9096	−	56.5281i	−0.115869	−	0.0668972i
$846$			106.884i			0.126340i
$847$	−830.381	−	109.983i	−0.980379	−	0.129850i
$848$	83.3281			0.0982643
$849$	−405.534	+	702.406i	−0.477661	+	0.827333i
$850$	−77.2665	+	44.6098i	−0.0909018	+	0.0524822i
$851$	−647.806	−	1122.03i	−0.761230	−	1.31849i
$852$	−356.918	−	206.067i	−0.418917	−	0.241862i
$853$		−	1176.97i		−	1.37980i	−0.723903	−	0.689902i	$-0.757654\pi$
$853$		−	1176.97i		−	1.37980i	0.723903	−	0.689902i	$-0.242346\pi$
$854$	50.1543	+	38.5472i	0.0587287	+	0.0451372i
$855$	129.483			0.151442
$856$	−117.425	+	203.386i	−0.137179	+	0.237601i
$857$	415.523	−	239.902i	0.484858	−	0.279933i	−0.237581	−	0.971368i	$-0.576355\pi$
$857$	415.523	−	239.902i	0.484858	−	0.279933i	0.722439	+	0.691435i	$0.243021\pi$
$858$	20.9931	+	36.3611i	0.0244675	+	0.0423789i
$859$	1185.54	+	684.470i	1.38014	+	0.796821i	0.992175	−	0.124855i	$-0.0398465\pi$
$859$	1185.54	+	684.470i	1.38014	+	0.796821i	0.387960	+	0.921676i	$0.373180\pi$
$860$			284.327i			0.330613i
$861$	281.052	−	365.681i	0.326425	−	0.424717i
$862$	−379.635			−0.440412
$863$	−42.7677	+	74.0758i	−0.0495570	+	0.0858352i	−0.889740	−	0.456468i	$-0.849114\pi$
$863$	−42.7677	+	74.0758i	−0.0495570	+	0.0858352i	0.840183	+	0.542303i	$0.182448\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$	226.358	+	392.063i	0.261685	+	0.453252i
$866$	−578.391	−	333.934i	−0.667888	−	0.385605i
$867$		−	224.815i		−	0.259302i
$868$	52.9762	−	399.975i	0.0610324	−	0.460800i
$869$	−107.432			−0.123627
$870$	134.297	−	232.609i	0.154364	−	0.267366i
$871$	−1597.51	+	922.321i	−1.83411	+	1.05892i
$872$	67.5886	+	117.067i	0.0775099	+	0.134251i
$873$	374.927	+	216.464i	0.429470	+	0.247955i
$874$			663.346i			0.758977i
$875$	72.3284	−	29.8931i	0.0826611	−	0.0341636i
$876$	−136.934			−0.156318
$877$	236.635	−	409.863i	0.269823	−	0.467347i	−0.698993	−	0.715128i	$-0.746368\pi$
$877$	236.635	−	409.863i	0.269823	−	0.467347i	0.968816	+	0.247781i	$0.0797015\pi$
$878$	−672.865	+	388.479i	−0.766361	+	0.442459i
$879$	−54.9984	−	95.2601i	−0.0625693	−	0.108373i
$880$	8.96044	+	5.17331i	0.0101823	+	0.00587877i
$881$		−	442.658i		−	0.502449i	−0.967929	−	0.251225i	$-0.919167\pi$
$881$		−	442.658i		−	0.502449i	0.967929	−	0.251225i	$-0.0808333\pi$
$882$	−200.721	−	54.1200i	−0.227575	−	0.0613605i
$883$	432.227			0.489498			0.244749	−	0.969586i	$-0.421294\pi$
$883$	432.227			0.489498			0.244749	+	0.969586i	$0.421294\pi$
$884$	−186.962	+	323.827i	−0.211495	+	0.366320i
$885$	−81.8822	+	47.2747i	−0.0925222	+	0.0534177i
$886$	−332.913	−	576.622i	−0.375748	−	0.650815i
$887$	451.613	+	260.739i	0.509146	+	0.293956i	0.732483	−	0.680786i	$-0.238362\pi$
$887$	451.613	+	260.739i	0.509146	+	0.293956i	−0.223337	+	0.974741i	$0.571695\pi$
$888$			261.193i			0.294136i
$889$	−215.407	−	521.191i	−0.242302	−	0.586266i
$890$	−480.615			−0.540017
$891$	−5.20555	+	9.01627i	−0.00584237	+	0.0101193i
$892$	−28.9905	+	16.7377i	−0.0325006	+	0.0187642i
$893$	243.137	+	421.125i	0.272270	+	0.471585i
$894$	−209.832	−	121.147i	−0.234712	−	0.135511i
$895$			175.960i			0.196604i
$896$	78.5103	+	10.3986i	0.0876231	+	0.0116056i
$897$	623.673			0.695287
$898$	−395.644	+	685.275i	−0.440583	+	0.763113i
$899$	−1223.90	+	706.619i	−1.36140	+	0.786005i
$900$	−15.0000	−	25.9808i	−0.0166667	−	0.0288675i
$901$	−227.634	−	131.425i	−0.252646	−	0.145865i
$902$		−	62.2311i		−	0.0689923i
$903$	−611.177	−	469.733i	−0.676830	−	0.520192i
$904$	−45.9004			−0.0507748
$905$	−65.0147	+	112.609i	−0.0718394	+	0.124430i
$906$	−207.444	+	119.768i	−0.228967	+	0.132194i
$907$	−633.871	−	1097.90i	−0.698865	−	1.21047i	−0.968860	−	0.247608i	$-0.920355\pi$
$907$	−633.871	−	1097.90i	−0.698865	−	1.21047i	0.269995	−	0.962862i	$-0.412978\pi$
$908$	733.475	+	423.472i	0.807792	+	0.466379i
$909$			117.253i			0.128991i
$910$	199.878	−	260.064i	0.219646	−	0.285785i
$911$	789.834			0.866997			0.433498	−	0.901154i	$-0.357279\pi$
$911$	789.834			0.866997			0.433498	+	0.901154i	$0.357279\pi$
$912$	66.8646	−	115.813i	0.0733165	−	0.126988i
$913$	−5.80713	+	3.35275i	−0.00636049	+	0.00367223i
$914$	−443.623	−	768.378i	−0.485364	−	0.840676i
$915$	−21.4322	−	12.3739i	−0.0234231	−	0.0135234i
$916$			809.668i			0.883916i
$917$	114.601	−	865.244i	0.124973	−	0.943560i
$918$	−92.7198			−0.101002
$919$	506.816	−	877.831i	0.551486	−	0.955202i	−0.446681	−	0.894693i	$-0.647394\pi$
$919$	506.816	−	877.831i	0.551486	−	0.955202i	0.998168	−	0.0605090i	$-0.0192724\pi$
$920$	133.101	−	76.8456i	0.144675	−	0.0835279i
$921$	−183.260	−	317.415i	−0.198979	−	0.344642i
$922$	273.925	+	158.151i	0.297098	+	0.171530i
$923$			1762.88i			1.90995i
$924$	−25.9238	+	10.7142i	−0.0280561	+	0.0115955i
$925$	266.579			0.288194
$926$	280.866	−	486.474i	0.303311	−	0.525350i
$927$	98.3191	−	56.7645i	0.106062	−	0.0612347i
$928$	−138.701	−	240.237i	−0.149462	−	0.258876i
$929$	546.568	+	315.561i	0.588340	+	0.339678i	0.764441	−	0.644694i	$-0.223015\pi$
$929$	546.568	+	315.561i	0.588340	+	0.339678i	−0.176101	+	0.984372i	$0.556348\pi$
$930$			157.849i			0.169730i
$931$	−913.960	+	243.362i	−0.981697	+	0.261399i
$932$	554.596			0.595061
$933$	−58.3090	+	100.994i	−0.0624963	+	0.108247i
$934$	408.727	−	235.979i	0.437610	−	0.252654i
$935$	−16.3187	−	28.2647i	−0.0174531	−	0.0302297i
$936$	−108.886	−	62.8656i	−0.116332	−	0.0671641i
$937$			867.113i			0.925414i	0.886511	+	0.462707i	$0.153122\pi$
$937$			867.113i			0.925414i	−0.886511	+	0.462707i	$0.846878\pi$
$938$	−470.724	−	1138.95i	−0.501838	−	1.21423i
$939$	239.428			0.254982
$940$	56.3326	−	97.5709i	0.0599283	−	0.103799i
$941$	−1151.28	+	664.692i	−1.22346	+	0.706367i	−0.965655	−	0.259829i	$-0.916334\pi$
$941$	−1151.28	+	664.692i	−1.22346	+	0.706367i	−0.257809	+	0.966196i	$0.583001\pi$
$942$	−163.384	−	282.990i	−0.173444	−	0.300414i
$943$	−800.550	−	462.197i	−0.848939	−	0.490135i
$944$			97.6502i			0.103443i
$945$	80.6285	+	10.6791i	0.0853212	+	0.0113007i
$946$	−104.009			−0.109946
$947$	770.741	−	1334.96i	0.813877	−	1.40968i	−0.0962547	−	0.995357i	$-0.530686\pi$
$947$	770.741	−	1334.96i	0.813877	−	1.40968i	0.910132	−	0.414319i	$-0.135980\pi$
$948$	278.613	−	160.858i	0.293896	−	0.169681i
$949$	292.866	+	507.258i	0.308604	+	0.534519i
$950$	−118.201	−	68.2434i	−0.124422	−	0.0718352i
$951$		−	34.3367i		−	0.0361059i
$952$	−198.073	−	152.233i	−0.208059	−	0.159908i
$953$	−114.779			−0.120439			−0.0602196	−	0.998185i	$-0.519180\pi$
$953$	−114.779			−0.120439			−0.0602196	+	0.998185i	$0.519180\pi$
$954$	44.1914	−	76.5418i	0.0463222	−	0.0802325i
$955$	−713.419	+	411.893i	−0.747036	+	0.431301i
$956$	−290.247	−	502.722i	−0.303605	−	0.525860i
$957$	85.0902	+	49.1268i	0.0889135	+	0.0513342i
$958$			861.020i			0.898769i
$959$	324.472	−	422.176i	0.338345	−	0.440225i
$960$	−30.9839			−0.0322749
$961$	−65.2290	+	112.980i	−0.0678761	+	0.117565i
$962$	967.561	−	558.622i	1.00578	−	0.580688i
$963$	124.548	+	215.724i	0.129333	+	0.224012i
$964$	701.147	+	404.808i	0.727331	+	0.419925i
$965$		−	627.930i		−	0.650705i
$966$	−54.7097	+	413.063i	−0.0566353	+	0.427602i
$967$	−881.904			−0.912000			−0.456000	−	0.889980i	$-0.650718\pi$
$967$	−881.904			−0.912000			−0.456000	+	0.889980i	$0.650718\pi$
$968$	169.227	−	293.110i	0.174822	−	0.302800i
$969$	−365.319	+	210.917i	−0.377007	+	0.217665i
$970$	−228.174	−	395.208i	−0.235230	−	0.407431i
$971$	407.102	+	235.041i	0.419261	+	0.242060i	0.694761	−	0.719241i	$-0.255510\pi$
$971$	407.102	+	235.041i	0.419261	+	0.242060i	−0.275500	+	0.961301i	$0.588843\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	593.670	−	245.362i	0.610144	−	0.252171i
$974$	−450.394			−0.462417
$975$	−64.1619	+	111.132i	−0.0658071	+	0.113981i
$976$	−22.1350	+	12.7797i	−0.0226794	+	0.0130939i
$977$	527.971	+	914.472i	0.540400	+	0.936000i	0.998881	+	0.0472957i	$0.0150603\pi$
$977$	527.971	+	914.472i	0.540400	+	0.936000i	−0.458481	+	0.888704i	$0.651606\pi$
$978$	−69.4715	−	40.1094i	−0.0710342	−	0.0410116i
$979$		−	175.813i		−	0.179584i
$980$	154.709	+	155.194i	0.157866	+	0.158361i
$981$	143.377			0.146154
$982$	−370.031	+	640.913i	−0.376814	+	0.652661i
$983$	−128.137	+	73.9799i	−0.130353	+	0.0752593i	−0.563758	−	0.825940i	$-0.690645\pi$
$983$	−128.137	+	73.9799i	−0.130353	+	0.0752593i	0.433406	+	0.901199i	$0.357312\pi$
$984$	93.1781	+	161.389i	0.0946932	+	0.164013i
$985$	14.7518	+	8.51695i	0.0149764	+	0.00864665i
$986$			875.034i			0.887458i
$987$	116.668	+	282.286i	0.118205	+	0.286004i
$988$	−572.022			−0.578970
$989$	−772.489	+	1337.99i	−0.781081	+	1.35287i
$990$	9.50399	−	5.48713i	0.00959999	−	0.00554255i
$991$	653.220	+	1131.41i	0.659153	+	1.14169i	0.980835	+	0.194839i	$0.0624183\pi$
$991$	653.220	+	1131.41i	0.659153	+	1.14169i	−0.321682	+	0.946848i	$0.604248\pi$
$992$	141.184	+	81.5128i	0.142323	+	0.0821702i
$993$			454.278i			0.457480i
$994$	−1167.57	−	154.643i	−1.17462	−	0.155577i
$995$	−451.318			−0.453586
$996$	10.0401	−	17.3900i	0.0100804	−	0.0174598i
$997$	−306.223	+	176.798i	−0.307145	+	0.177330i	−0.645648	−	0.763635i	$-0.723413\pi$
$997$	−306.223	+	176.798i	−0.307145	+	0.177330i	0.338503	+	0.940965i	$0.390079\pi$
$998$	554.242	+	959.976i	0.555353	+	0.961900i
$999$	239.921	+	138.519i	0.240161	+	0.138657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.b.61.3	yes	16
3.2	odd	2		630.3.v.c.271.5		16
5.2	odd	4		1050.3.q.e.649.6		32
5.3	odd	4		1050.3.q.e.649.14		32
5.4	even	2		1050.3.p.i.901.8		16
7.2	even	3		1470.3.f.d.391.10		16
7.3	odd	6	inner	210.3.o.b.31.3	✓	16
7.5	odd	6		1470.3.f.d.391.16		16
21.17	even	6		630.3.v.c.451.5		16
35.3	even	12		1050.3.q.e.199.6		32
35.17	even	12		1050.3.q.e.199.13		32
35.24	odd	6		1050.3.p.i.451.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.3	✓	16	7.3	odd	6	inner
210.3.o.b.61.3	yes	16	1.1	even	1	trivial
630.3.v.c.271.5		16	3.2	odd	2
630.3.v.c.451.5		16	21.17	even	6
1050.3.p.i.451.8		16	35.24	odd	6
1050.3.p.i.901.8		16	5.4	even	2
1050.3.q.e.199.6		32	35.3	even	12
1050.3.q.e.199.13		32	35.17	even	12
1050.3.q.e.649.6		32	5.2	odd	4
1050.3.q.e.649.14		32	5.3	odd	4
1470.3.f.d.391.10		16	7.2	even	3
1470.3.f.d.391.16		16	7.5	odd	6

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(-2.67372 - 6.46925i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} -2.44949i q^{6} +(-2.67372 - 6.46925i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(-0.578394 - 1.00181i) q^{11} +(3.00000 + 1.73205i) q^{12} -14.8176i q^{13} +(9.81379 + 1.29982i) q^{14} -3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(10.9271 - 6.30878i) q^{17} +(2.12132 + 3.67423i) q^{18} +(16.7162 + 9.65108i) q^{19} -4.47214i q^{20} +(9.61312 + 7.38837i) q^{21} +1.63595 q^{22} +(12.1504 - 21.0450i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(18.1477 + 10.4776i) q^{26} +5.19615i q^{27} +(-8.53135 + 11.1003i) q^{28} +49.0382 q^{29} +(2.73861 - 4.74342i) q^{30} +(-24.9581 + 14.4096i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(1.73518 + 1.00181i) q^{33} +17.8439i q^{34} +(2.05520 - 15.5170i) q^{35} -6.00000 q^{36} +(26.6579 - 46.1728i) q^{37} +(-23.6402 + 13.6487i) q^{38} +(12.8324 + 22.2264i) q^{39} +(5.47723 + 3.16228i) q^{40} -38.0398i q^{41} +(-15.8464 + 6.54925i) q^{42} -63.5774 q^{43} +(-1.15679 + 2.00362i) q^{44} +(5.80948 - 3.35410i) q^{45} +(17.1832 + 29.7622i) q^{46} +(21.8175 + 12.5964i) q^{47} -6.92820i q^{48} +(-34.7024 + 34.5940i) q^{49} -7.07107 q^{50} +(-10.9271 + 18.9263i) q^{51} +(-25.6648 + 14.8176i) q^{52} +(-10.4160 - 18.0411i) q^{53} +(-6.36396 - 3.67423i) q^{54} -2.58666i q^{55} +(-7.56243 - 18.2978i) q^{56} -33.4323 q^{57} +(-34.6752 + 60.0593i) q^{58} +(21.1419 - 12.2063i) q^{59} +(3.87298 + 6.70820i) q^{60} +(5.53376 + 3.19492i) q^{61} -40.7564i q^{62} +(-20.8182 - 2.75734i) q^{63} +8.00000 q^{64} +(16.5665 - 28.6941i) q^{65} +(-2.45392 + 1.41677i) q^{66} +(-62.2451 - 107.812i) q^{67} +(-21.8543 - 12.6176i) q^{68} +42.0901i q^{69} +(17.5511 + 13.4892i) q^{70} -118.973 q^{71} +(4.24264 - 7.34847i) q^{72} +(-34.2336 + 19.7648i) q^{73} +(37.7000 + 65.2983i) q^{74} +(-7.50000 - 4.33013i) q^{75} -38.6043i q^{76} +(-4.93448 + 6.42033i) q^{77} -36.2955 q^{78} +(46.4356 - 80.4288i) q^{79} +(-7.74597 + 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(46.5891 + 26.8982i) q^{82} -5.79665i q^{83} +(3.18391 - 24.0388i) q^{84} +28.2137 q^{85} +(44.9560 - 77.8661i) q^{86} +(-73.5573 + 42.4683i) q^{87} +(-1.63595 - 2.83354i) q^{88} +(131.622 + 75.9919i) q^{89} +9.48683i q^{90} +(-95.8586 + 39.6181i) q^{91} -48.6014 q^{92} +(24.9581 - 43.2287i) q^{93} +(-30.8546 + 17.8139i) q^{94} +(21.5805 + 37.3785i) q^{95} +(8.48528 + 4.89898i) q^{96} +144.310i q^{97} +(-17.8305 - 66.9632i) q^{98} -3.47036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9	\( 16 q - 24 q^{3} - 16 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} + 48 q^{12} + 8 q^{14} - 32 q^{16} + 12 q^{17} - 72 q^{19} - 24 q^{21} - 48 q^{22} - 12 q^{23} + 40 q^{25} + 32 q^{28} + 72 q^{29} + 120 q^{31} + 12 q^{33} - 20 q^{35} - 96 q^{36} + 44 q^{37} - 72 q^{38} + 36 q^{39} - 24 q^{42} - 56 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} - 40 q^{49} - 12 q^{51} - 72 q^{52} + 32 q^{53} + 16 q^{56} + 144 q^{57} - 88 q^{58} + 132 q^{59} + 96 q^{61} + 60 q^{63} + 128 q^{64} + 20 q^{65} + 72 q^{66} - 164 q^{67} - 24 q^{68} - 136 q^{71} - 348 q^{73} - 112 q^{74} - 120 q^{75} + 96 q^{77} + 280 q^{79} - 72 q^{81} + 264 q^{82} - 24 q^{84} + 120 q^{85} - 88 q^{86} - 108 q^{87} + 48 q^{88} - 300 q^{89} - 272 q^{91} + 48 q^{92} - 120 q^{93} + 200 q^{95} + 384 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 - 16 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 + 48 * q^12 + 8 * q^14 - 32 * q^16 + 12 * q^17 - 72 * q^19 - 24 * q^21 - 48 * q^22 - 12 * q^23 + 40 * q^25 + 32 * q^28 + 72 * q^29 + 120 * q^31 + 12 * q^33 - 20 * q^35 - 96 * q^36 + 44 * q^37 - 72 * q^38 + 36 * q^39 - 24 * q^42 - 56 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 - 40 * q^49 - 12 * q^51 - 72 * q^52 + 32 * q^53 + 16 * q^56 + 144 * q^57 - 88 * q^58 + 132 * q^59 + 96 * q^61 + 60 * q^63 + 128 * q^64 + 20 * q^65 + 72 * q^66 - 164 * q^67 - 24 * q^68 - 136 * q^71 - 348 * q^73 - 112 * q^74 - 120 * q^75 + 96 * q^77 + 280 * q^79 - 72 * q^81 + 264 * q^82 - 24 * q^84 + 120 * q^85 - 88 * q^86 - 108 * q^87 + 48 * q^88 - 300 * q^89 - 272 * q^91 + 48 * q^92 - 120 * q^93 + 200 * q^95 + 384 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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