LMFDB - Embedded newform 201.3.h.b.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(97,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("201.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.h (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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			97.3
Character	$\chi$	$=$	201.97
Dual form			201.3.h.b.172.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.78358 + 1.60710i) q^{2} +1.73205i q^{3} +(3.16555 - 5.48289i) q^{4} +6.80030i q^{5} +(-2.78358 - 4.82130i) q^{6} +(9.81487 + 5.66662i) q^{7} +7.49262i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-2.78358 + 1.60710i) q^{2} +1.73205i q^{3} +(3.16555 - 5.48289i) q^{4} +6.80030i q^{5} +(-2.78358 - 4.82130i) q^{6} +(9.81487 + 5.66662i) q^{7} +7.49262i q^{8} -3.00000 q^{9} +(-10.9288 - 18.9292i) q^{10} +(14.2778 + 8.24332i) q^{11} +(9.49665 + 5.48289i) q^{12} +(14.8562 - 8.57724i) q^{13} -36.4273 q^{14} -11.7785 q^{15} +(0.620797 + 1.07525i) q^{16} +(11.5774 + 20.0526i) q^{17} +(8.35074 - 4.82130i) q^{18} +(1.69094 + 2.92880i) q^{19} +(37.2853 + 21.5267i) q^{20} +(-9.81487 + 16.9999i) q^{21} -52.9914 q^{22} +(-20.3759 - 35.2921i) q^{23} -12.9776 q^{24} -21.2441 q^{25} +(-27.5690 + 47.7509i) q^{26} -5.19615i q^{27} +(62.1389 - 35.8759i) q^{28} +(3.45557 - 5.98522i) q^{29} +(32.7863 - 18.9292i) q^{30} +(-32.4604 - 18.7410i) q^{31} +(-29.4113 - 16.9806i) q^{32} +(-14.2778 + 24.7300i) q^{33} +(-64.4530 - 37.2120i) q^{34} +(-38.5347 + 66.7441i) q^{35} +(-9.49665 + 16.4487i) q^{36} +(-13.3240 - 23.0778i) q^{37} +(-9.41375 - 5.43503i) q^{38} +(14.8562 + 25.7317i) q^{39} -50.9521 q^{40} +(16.0419 + 9.26178i) q^{41} -63.0940i q^{42} -0.773007i q^{43} +(90.3945 - 52.1893i) q^{44} -20.4009i q^{45} +(113.436 + 65.4923i) q^{46} +(-7.84438 + 13.5869i) q^{47} +(-1.86239 + 1.07525i) q^{48} +(39.7212 + 68.7991i) q^{49} +(59.1347 - 34.1414i) q^{50} +(-34.7321 + 20.0526i) q^{51} -108.607i q^{52} -70.3521i q^{53} +(8.35074 + 14.4639i) q^{54} +(-56.0571 + 97.0937i) q^{55} +(-42.4578 + 73.5391i) q^{56} +(-5.07283 + 2.92880i) q^{57} +22.2138i q^{58} -5.22640 q^{59} +(-37.2853 + 64.5801i) q^{60} +(-15.8223 + 9.13503i) q^{61} +120.475 q^{62} +(-29.4446 - 16.9999i) q^{63} +104.192 q^{64} +(58.3278 + 101.027i) q^{65} -91.7838i q^{66} +(64.6341 - 17.6473i) q^{67} +146.595 q^{68} +(61.1277 - 35.2921i) q^{69} -247.717i q^{70} +(54.5452 - 94.4750i) q^{71} -22.4779i q^{72} +(-41.0503 - 71.1011i) q^{73} +(74.1768 + 42.8260i) q^{74} -36.7959i q^{75} +21.4110 q^{76} +(93.4235 + 161.814i) q^{77} +(-82.7069 - 47.7509i) q^{78} +(99.9083 + 57.6821i) q^{79} +(-7.31204 + 4.22161i) q^{80} +9.00000 q^{81} -59.5385 q^{82} +(-48.3092 - 83.6740i) q^{83} +(62.1389 + 107.628i) q^{84} +(-136.363 + 78.7295i) q^{85} +(1.24230 + 2.15173i) q^{86} +(10.3667 + 5.98522i) q^{87} +(-61.7641 + 106.978i) q^{88} -130.895 q^{89} +(32.7863 + 56.7876i) q^{90} +194.416 q^{91} -258.004 q^{92} +(32.4604 - 56.2231i) q^{93} -50.4268i q^{94} +(-19.9167 + 11.4989i) q^{95} +(29.4113 - 50.9418i) q^{96} +(-49.6133 + 28.6442i) q^{97} +(-221.134 - 127.672i) q^{98} +(-42.8335 - 24.7300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.78358	+	1.60710i	−1.39179	+	0.803551i	−0.993513	−	0.113715i	$-0.963725\pi$
$2$	−2.78358	+	1.60710i	−1.39179	+	0.803551i	−0.398277	+	0.917265i	$0.630392\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	3.16555	−	5.48289i	0.791387	−	1.37072i
$5$			6.80030i			1.36006i	0.733184	+	0.680030i	$0.238033\pi$
$5$			6.80030i			1.36006i	−0.733184	+	0.680030i	$0.761967\pi$
$6$	−2.78358	−	4.82130i	−0.463930	−	0.803551i
$7$	9.81487	+	5.66662i	1.40212	+	0.809517i	0.994611	−	0.103682i	$-0.0330623\pi$
$7$	9.81487	+	5.66662i	1.40212	+	0.809517i	0.407514	+	0.913199i	$0.366396\pi$
$8$			7.49262i			0.936577i
$9$	−3.00000			−0.333333
$10$	−10.9288	−	18.9292i	−1.09288	−	1.89292i
$11$	14.2778	+	8.24332i	1.29799	+	0.749393i	0.980056	−	0.198721i	$-0.0636789\pi$
$11$	14.2778	+	8.24332i	1.29799	+	0.749393i	0.317930	+	0.948114i	$0.397012\pi$
$12$	9.49665	+	5.48289i	0.791387	+	0.456908i
$13$	14.8562	−	8.57724i	1.14279	−	0.659788i	0.195667	−	0.980670i	$-0.437313\pi$
$13$	14.8562	−	8.57724i	1.14279	−	0.659788i	0.947119	+	0.320883i	$0.103980\pi$
$14$	−36.4273			−2.60195
$15$	−11.7785			−0.785231
$16$	0.620797	+	1.07525i	0.0387998	+	0.0672033i
$17$	11.5774	+	20.0526i	0.681021	+	1.17956i	0.974670	+	0.223649i	$0.0717970\pi$
$17$	11.5774	+	20.0526i	0.681021	+	1.17956i	−0.293649	+	0.955913i	$0.594870\pi$
$18$	8.35074	−	4.82130i	0.463930	−	0.267850i
$19$	1.69094	+	2.92880i	0.0889970	+	0.154147i	0.907087	−	0.420942i	$-0.138301\pi$
$19$	1.69094	+	2.92880i	0.0889970	+	0.154147i	−0.818090	+	0.575090i	$0.804967\pi$
$20$	37.2853	+	21.5267i	1.86427	+	1.07633i
$21$	−9.81487	+	16.9999i	−0.467375	+	0.809517i
$22$	−52.9914			−2.40870
$23$	−20.3759	−	35.2921i	−0.885909	−	1.53444i	−0.844668	−	0.535291i	$-0.820202\pi$
$23$	−20.3759	−	35.2921i	−0.885909	−	1.53444i	−0.0412415	−	0.999149i	$-0.513131\pi$
$24$	−12.9776			−0.540733
$25$	−21.2441			−0.849764
$26$	−27.5690	+	47.7509i	−1.06035	+	1.83657i
$27$		−	5.19615i		−	0.192450i
$28$	62.1389	−	35.8759i	2.21925	−	1.28128i
$29$	3.45557	−	5.98522i	0.119158	−	0.206387i	−0.800277	−	0.599631i	$-0.795314\pi$
$29$	3.45557	−	5.98522i	0.119158	−	0.206387i	0.919434	+	0.393244i	$0.128647\pi$
$30$	32.7863	−	18.9292i	1.09288	−	0.630973i
$31$	−32.4604	−	18.7410i	−1.04711	−	0.604549i	−0.125271	−	0.992123i	$-0.539980\pi$
$31$	−32.4604	−	18.7410i	−1.04711	−	0.604549i	−0.921839	+	0.387573i	$0.873313\pi$
$32$	−29.4113	−	16.9806i	−0.919102	−	0.530644i
$33$	−14.2778	+	24.7300i	−0.432662	+	0.749393i
$34$	−64.4530	−	37.2120i	−1.89568	−	1.09447i
$35$	−38.5347	+	66.7441i	−1.10099	+	1.90697i
$36$	−9.49665	+	16.4487i	−0.263796	+	0.456908i
$37$	−13.3240	−	23.0778i	−0.360108	−	0.623725i	0.627870	−	0.778318i	$-0.283927\pi$
$37$	−13.3240	−	23.0778i	−0.360108	−	0.623725i	−0.987978	+	0.154593i	$0.950593\pi$
$38$	−9.41375	−	5.43503i	−0.247730	−	0.143027i
$39$	14.8562	+	25.7317i	0.380929	+	0.659788i
$40$	−50.9521			−1.27380
$41$	16.0419	+	9.26178i	0.391265	+	0.225897i	0.682708	−	0.730691i	$-0.260802\pi$
$41$	16.0419	+	9.26178i	0.391265	+	0.225897i	−0.291443	+	0.956588i	$0.594135\pi$
$42$		−	63.0940i		−	1.50224i
$43$		−	0.773007i		−	0.0179769i	−0.999960	−	0.00898845i	$-0.997139\pi$
$43$		−	0.773007i		−	0.0179769i	0.999960	−	0.00898845i	$-0.00286115\pi$
$44$	90.3945	−	52.1893i	2.05442	−	1.18612i
$45$		−	20.4009i		−	0.453353i
$46$	113.436	+	65.4923i	2.46600	+	1.42375i
$47$	−7.84438	+	13.5869i	−0.166902	+	0.289082i	−0.937329	−	0.348446i	$-0.886710\pi$
$47$	−7.84438	+	13.5869i	−0.166902	+	0.289082i	0.770427	+	0.637528i	$0.220043\pi$
$48$	−1.86239	+	1.07525i	−0.0387998	+	0.0224011i
$49$	39.7212	+	68.7991i	0.810636	+	1.40406i
$50$	59.1347	−	34.1414i	1.18269	−	0.682828i
$51$	−34.7321	+	20.0526i	−0.681021	+	0.393188i
$52$		−	108.607i		−	2.08859i
$53$		−	70.3521i		−	1.32740i	−0.748000	−	0.663699i	$-0.768986\pi$
$53$		−	70.3521i		−	1.32740i	0.748000	−	0.663699i	$-0.231014\pi$
$54$	8.35074	+	14.4639i	0.154643	+	0.267850i
$55$	−56.0571	+	97.0937i	−1.01922	+	1.76534i
$56$	−42.4578	+	73.5391i	−0.758176	+	1.31320i
$57$	−5.07283	+	2.92880i	−0.0889970	+	0.0513824i
$58$			22.2138i			0.382997i
$59$	−5.22640			−0.0885831			−0.0442915	−	0.999019i	$-0.514103\pi$
$59$	−5.22640			−0.0885831			−0.0442915	+	0.999019i	$0.514103\pi$
$60$	−37.2853	+	64.5801i	−0.621422	+	1.07633i
$61$	−15.8223	+	9.13503i	−0.259383	+	0.149755i	−0.624053	−	0.781382i	$-0.714515\pi$
$61$	−15.8223	+	9.13503i	−0.259383	+	0.149755i	0.364670	+	0.931137i	$0.381182\pi$
$62$	120.475			1.94314
$63$	−29.4446	−	16.9999i	−0.467375	−	0.269839i
$64$	104.192			1.62800
$65$	58.3278	+	101.027i	0.897351	+	1.55426i
$66$		−	91.7838i		−	1.39066i
$67$	64.6341	−	17.6473i	0.964689	−	0.263393i
$67$	64.6341	−	17.6473i	0.964689	−	0.263393i
$68$	146.595			2.15580
$69$	61.1277	−	35.2921i	0.885909	−	0.511480i
$70$		−	247.717i		−	3.53881i
$71$	54.5452	−	94.4750i	0.768242	−	1.33063i	−0.170274	−	0.985397i	$-0.554465\pi$
$71$	54.5452	−	94.4750i	0.768242	−	1.33063i	0.938516	−	0.345237i	$-0.112201\pi$
$72$		−	22.4779i		−	0.312192i
$73$	−41.0503	−	71.1011i	−0.562332	−	0.973988i	−0.997292	−	0.0735384i	$-0.976571\pi$
$73$	−41.0503	−	71.1011i	−0.562332	−	0.973988i	0.434960	−	0.900450i	$-0.356762\pi$
$74$	74.1768	+	42.8260i	1.00239	+	0.578730i
$75$		−	36.7959i		−	0.490611i
$76$	21.4110			0.281724
$77$	93.4235	+	161.814i	1.21329	+	2.10148i
$78$	−82.7069	−	47.7509i	−1.06035	−	0.612191i
$79$	99.9083	+	57.6821i	1.26466	+	0.730153i	0.973973	−	0.226665i	$-0.0727822\pi$
$79$	99.9083	+	57.6821i	1.26466	+	0.730153i	0.290689	+	0.956818i	$0.406116\pi$
$80$	−7.31204	+	4.22161i	−0.0914005	+	0.0527701i
$81$	9.00000			0.111111
$82$	−59.5385			−0.726079
$83$	−48.3092	−	83.6740i	−0.582038	−	1.00812i	−0.995238	−	0.0974793i	$-0.968922\pi$
$83$	−48.3092	−	83.6740i	−0.582038	−	1.00812i	0.413199	−	0.910641i	$-0.364411\pi$
$84$	62.1389	+	107.628i	0.739749	+	1.28128i
$85$	−136.363	+	78.7295i	−1.60428	+	0.926229i
$86$	1.24230	+	2.15173i	0.0144454	+	0.0250201i
$87$	10.3667	+	5.98522i	0.119158	+	0.0687956i
$88$	−61.7641	+	106.978i	−0.701864	+	1.21566i
$89$	−130.895			−1.47074			−0.735368	−	0.677668i	$-0.762991\pi$
$89$	−130.895			−1.47074			−0.735368	+	0.677668i	$0.762991\pi$
$90$	32.7863	+	56.7876i	0.364292	+	0.630973i
$91$	194.416			2.13644
$92$	−258.004			−2.80439
$93$	32.4604	−	56.2231i	0.349037	−	0.604549i
$94$		−	50.4268i		−	0.536456i
$95$	−19.9167	+	11.4989i	−0.209650	+	0.121041i
$96$	29.4113	−	50.9418i	0.306367	−	0.530644i
$97$	−49.6133	+	28.6442i	−0.511477	+	0.295302i	−0.733441	−	0.679753i	$-0.762087\pi$
$97$	−49.6133	+	28.6442i	−0.511477	+	0.295302i	0.221963	+	0.975055i	$0.428753\pi$
$98$	−221.134	−	127.672i	−2.25647	−	1.30277i
$99$	−42.8335	−	24.7300i	−0.432662	−	0.249798i
$100$	−67.2492	+	116.479i	−0.672492	+	1.16479i
$101$	−47.3196	−	27.3200i	−0.468511	−	0.270495i	0.247105	−	0.968989i	$-0.420521\pi$
$101$	−47.3196	−	27.3200i	−0.468511	−	0.270495i	−0.715616	+	0.698494i	$0.753854\pi$
$102$	64.4530	−	111.636i	0.631892	−	1.09447i
$103$	−67.9445	+	117.683i	−0.659656	+	1.14256i	0.321049	+	0.947062i	$0.395964\pi$
$103$	−67.9445	+	117.683i	−0.659656	+	1.14256i	−0.980705	+	0.195494i	$0.937369\pi$
$104$	64.2660	+	111.312i	0.617942	+	1.07031i
$105$	−115.604	−	66.7441i	−1.10099	−	0.635658i
$106$	113.063	+	195.831i	1.06663	+	1.84746i
$107$	−104.370			−0.975422			−0.487711	−	0.873005i	$-0.662168\pi$
$107$	−104.370			−0.975422			−0.487711	+	0.873005i	$0.662168\pi$
$108$	−28.4899	−	16.4487i	−0.263796	−	0.152303i
$109$		−	120.352i		−	1.10415i	−0.833795	−	0.552074i	$-0.813837\pi$
$109$		−	120.352i		−	1.10415i	0.833795	−	0.552074i	$-0.186163\pi$
$110$		−	360.357i		−	3.27598i
$111$	39.9720	−	23.0778i	0.360108	−	0.207908i
$112$			14.0713i			0.125637i
$113$	−24.8672	−	14.3571i	−0.220063	−	0.127054i	0.385916	−	0.922534i	$-0.373885\pi$
$113$	−24.8672	−	14.3571i	−0.220063	−	0.127054i	−0.605980	+	0.795480i	$0.707219\pi$
$114$	9.41375	−	16.3051i	0.0825768	−	0.143027i
$115$	239.997	−	138.562i	2.08693	−	1.20489i
$116$	−21.8775	−	37.8930i	−0.188600	−	0.326664i
$117$	−44.5686	+	25.7317i	−0.380929	+	0.219929i
$118$	14.5481	−	8.39935i	0.123289	−	0.0711810i
$119$			262.418i			2.20519i
$120$		−	88.2516i		−	0.735430i
$121$	75.4047	+	130.605i	0.623179	+	1.07938i
$122$	29.3618	−	50.8562i	0.240671	−	0.416854i
$123$	−16.0419	+	27.7854i	−0.130422	+	0.225897i
$124$	−205.510	+	118.651i	−1.65734	+	0.956865i
$125$			25.5413i			0.204330i
$126$	109.282			0.867317
$127$	77.2649	−	133.827i	0.608385	−	1.05375i	−0.383121	−	0.923698i	$-0.625151\pi$
$127$	77.2649	−	133.827i	0.608385	−	1.05375i	0.991507	−	0.130056i	$-0.0415158\pi$
$128$	−172.381	+	99.5244i	−1.34673	+	0.777534i
$129$	1.33889			0.0103790
$130$	−324.720	−	187.477i	−2.49785	−	1.44213i
$131$	47.6405			0.363668			0.181834	−	0.983329i	$-0.441797\pi$
$131$	47.6405			0.363668			0.181834	+	0.983329i	$0.441797\pi$
$132$	90.3945	+	156.568i	0.684806	+	1.18612i
$133$			38.3277i			0.288178i
$134$	−151.553	+	152.996i	−1.13099	+	1.14176i
$135$	35.3354			0.261744
$136$	−150.246	+	86.7447i	−1.10475	+	0.637829i
$137$		−	248.742i		−	1.81563i	−0.419366	−	0.907817i	$-0.637748\pi$
$137$		−	248.742i		−	1.81563i	0.419366	−	0.907817i	$-0.362252\pi$
$138$	−113.436	+	196.477i	−0.822000	+	1.42375i
$139$			96.6902i			0.695613i	0.937566	+	0.347807i	$0.113073\pi$
$139$			96.6902i			0.695613i	−0.937566	+	0.347807i	$0.886927\pi$
$140$	243.967	+	422.563i	1.74262	+	3.01831i
$141$	−23.5331	−	13.5869i	−0.166902	−	0.0963607i
$142$			350.638i			2.46928i
$143$	282.820			1.97776
$144$	−1.86239	−	3.22576i	−0.0129333	−	0.0224011i
$145$	40.7013	+	23.4989i	0.280699	+	0.162061i
$146$	228.533	+	131.944i	1.56530	+	0.903725i
$147$	−119.164	+	68.7991i	−0.810636	+	0.468021i
$148$	−168.711			−1.13994
$149$	−66.1803			−0.444163			−0.222082	−	0.975028i	$-0.571285\pi$
$149$	−66.1803			−0.444163			−0.222082	+	0.975028i	$0.571285\pi$
$150$	59.1347	+	102.424i	0.394231	+	0.682828i
$151$	21.9853	+	38.0796i	0.145598	+	0.252183i	0.929596	−	0.368580i	$-0.120156\pi$
$151$	21.9853	+	38.0796i	0.145598	+	0.252183i	−0.783998	+	0.620763i	$0.786823\pi$
$152$	−21.9444	+	12.6696i	−0.144371	+	0.0833526i
$153$	−34.7321	−	60.1577i	−0.227007	−	0.393188i
$154$	−520.104	−	300.282i	−3.37730	−	1.94988i
$155$	127.445	−	220.741i	0.822224	−	1.42413i
$156$	188.112			1.20585
$157$	−45.5688	−	78.9275i	−0.290247	−	0.502723i	0.683621	−	0.729837i	$-0.260404\pi$
$157$	−45.5688	−	78.9275i	−0.290247	−	0.502723i	−0.973868	+	0.227115i	$0.927071\pi$
$158$	−370.804			−2.34686
$159$	121.853			0.766373
$160$	115.473	−	200.006i	0.721708	−	1.25003i
$161$		−	461.850i		−	2.86864i
$162$	−25.0522	+	14.4639i	−0.154643	+	0.0892834i
$163$	−112.468	+	194.800i	−0.689986	+	1.19509i	0.281856	+	0.959457i	$0.409050\pi$
$163$	−112.468	+	194.800i	−0.689986	+	1.19509i	−0.971842	+	0.235634i	$0.924283\pi$
$164$	101.563	−	58.6373i	0.619285	−	0.357544i
$165$	−168.171	−	97.0937i	−1.01922	−	0.588447i
$166$	268.945	+	155.275i	1.62015	+	0.935395i
$167$	−38.4494	+	66.5964i	−0.230236	+	0.398781i	−0.957878	−	0.287177i	$-0.907283\pi$
$167$	−38.4494	+	66.5964i	−0.230236	+	0.398781i	0.727641	+	0.685958i	$0.240617\pi$
$168$	−127.373	−	73.5391i	−0.758176	−	0.437733i
$169$	62.6380	−	108.492i	0.370639	−	0.641966i
$170$	253.053	−	438.300i	1.48854	−	2.57823i
$171$	−5.07283	−	8.78640i	−0.0296657	−	0.0513824i
$172$	−4.23831	−	2.44699i	−0.0246414	−	0.0142267i
$173$	18.5390	+	32.1105i	0.107162	+	0.185610i	0.914619	−	0.404316i	$-0.132490\pi$
$173$	18.5390	+	32.1105i	0.107162	+	0.185610i	−0.807458	+	0.589926i	$0.799157\pi$
$174$	−38.4754			−0.221123
$175$	−208.508	−	120.382i	−1.19148	−	0.687898i
$176$			20.4697i			0.116305i
$177$		−	9.05239i		−	0.0511435i
$178$	364.358	−	210.362i	2.04696	−	1.18181i
$179$			62.5481i			0.349431i	0.984619	+	0.174715i	$0.0559005\pi$
$179$			62.5481i			0.349431i	−0.984619	+	0.174715i	$0.944099\pi$
$180$	−111.856	−	64.5801i	−0.621422	−	0.358778i
$181$	56.5192	−	97.8941i	0.312261	−	0.540851i	−0.666591	−	0.745424i	$-0.732247\pi$
$181$	56.5192	−	97.8941i	0.312261	−	0.540851i	0.978851	+	0.204573i	$0.0655805\pi$
$182$	−541.172	+	312.446i	−2.97347	+	1.71674i
$183$	−15.8223	−	27.4051i	−0.0864608	−	0.149755i
$184$	264.430	−	152.669i	1.43712	−	0.829723i
$185$	156.936	−	90.6072i	0.848304	−	0.489769i
$186$			208.669i			1.12187i
$187$			381.743i			2.04141i
$188$	49.6635	+	86.0197i	0.264168	+	0.457552i
$189$	29.4446	−	50.9996i	0.155792	−	0.269839i
$190$	36.9599	−	64.0163i	0.194526	−	0.336928i
$191$	62.1550	−	35.8852i	0.325419	−	0.187881i	−0.328387	−	0.944543i	$-0.606505\pi$
$191$	62.1550	−	35.8852i	0.325419	−	0.187881i	0.653805	+	0.756663i	$0.273172\pi$
$192$			180.466i			0.939925i
$193$	−151.760			−0.786319			−0.393160	−	0.919470i	$-0.628618\pi$
$193$	−151.760			−0.786319			−0.393160	+	0.919470i	$0.628618\pi$
$194$	92.0684	−	159.467i	0.474579	−	0.821996i
$195$	−174.983	+	101.027i	−0.897351	+	0.518086i
$196$	502.957			2.56611
$197$	−125.610	−	72.5211i	−0.637616	−	0.368128i	0.146080	−	0.989273i	$-0.453334\pi$
$197$	−125.610	−	72.5211i	−0.637616	−	0.368128i	−0.783695	+	0.621145i	$0.786668\pi$
$198$	158.974			0.802900
$199$	77.7249	+	134.623i	0.390577	+	0.676500i	0.992526	−	0.122035i	$-0.0389421\pi$
$199$	77.7249	+	134.623i	0.390577	+	0.676500i	−0.601948	+	0.798535i	$0.705609\pi$
$200$		−	159.174i		−	0.795870i
$201$	30.5661	+	111.950i	0.152070	+	0.556963i
$202$	175.624			0.869425
$203$	67.8320	−	39.1628i	0.334148	−	0.192920i
$204$			253.909i			1.24465i
$205$	−62.9829	+	109.090i	−0.307234	+	0.532145i
$206$		−	436.775i		−	2.12027i
$207$	61.1277	+	105.876i	0.295303	+	0.511480i
$208$	18.4454	+	10.6495i	0.0886798	+	0.0511993i
$209$			55.7559i			0.266775i
$210$	429.058			2.04313
$211$	−16.5350	−	28.6395i	−0.0783650	−	0.135732i	0.824180	−	0.566328i	$-0.191637\pi$
$211$	−16.5350	−	28.6395i	−0.0783650	−	0.135732i	−0.902545	+	0.430596i	$0.858303\pi$
$212$	−385.733	−	222.703i	−1.81949	−	1.05049i
$213$	163.635	+	94.4750i	0.768242	+	0.443545i
$214$	290.523	−	167.733i	1.35758	−	0.783801i
$215$	5.25668			0.0244497
$216$	38.9328			0.180244
$217$	−212.397	−	367.882i	−0.978786	−	1.69531i
$218$	193.418	+	335.010i	0.887239	+	1.53674i
$219$	123.151	−	71.1011i	0.562332	−	0.324663i
$220$	354.903	+	614.710i	1.61319	+	2.79413i
$221$	343.991	+	198.603i	1.55652	+	0.898658i
$222$	−74.1768	+	128.478i	−0.334130	+	0.578730i
$223$	−11.0522			−0.0495616			−0.0247808	−	0.999693i	$-0.507889\pi$
$223$	−11.0522			−0.0495616			−0.0247808	+	0.999693i	$0.507889\pi$
$224$	−192.445	−	333.325i	−0.859131	−	1.48806i
$225$	63.7323			0.283255
$226$	92.2930			0.408376
$227$	77.0061	−	133.378i	0.339234	−	0.587570i	−0.645055	−	0.764136i	$-0.723166\pi$
$227$	77.0061	−	133.378i	0.339234	−	0.587570i	0.984289	+	0.176566i	$0.0564989\pi$
$228$			37.0850i			0.162654i
$229$	−86.7614	+	50.0917i	−0.378871	+	0.218741i	−0.677327	−	0.735682i	$-0.736862\pi$
$229$	−86.7614	+	50.0917i	−0.378871	+	0.218741i	0.298456	+	0.954423i	$0.403528\pi$
$230$	−445.367	+	771.399i	−1.93638	+	3.35391i
$231$	−280.271	+	161.814i	−1.21329	+	0.700495i
$232$	44.8450	+	25.8913i	0.193297	+	0.111600i
$233$	383.256	+	221.273i	1.64488	+	0.949670i	0.979064	+	0.203551i	$0.0652483\pi$
$233$	383.256	+	221.273i	1.64488	+	0.949670i	0.665813	+	0.746119i	$0.268085\pi$
$234$	82.7069	−	143.253i	0.353448	−	0.612191i
$235$	−92.3947	−	53.3441i	−0.393169	−	0.226996i
$236$	−16.5444	+	28.6558i	−0.0701035	+	0.121423i
$237$	−99.9083	+	173.046i	−0.421554	+	0.730153i
$238$	−421.732	−	730.461i	−1.77198	−	3.06917i
$239$	63.5317	+	36.6801i	0.265823	+	0.153473i	0.626988	−	0.779029i	$-0.284288\pi$
$239$	63.5317	+	36.6801i	0.265823	+	0.153473i	−0.361165	+	0.932502i	$0.617621\pi$
$240$	−7.31204	−	12.6648i	−0.0304668	−	0.0527701i
$241$	−90.4804			−0.375437			−0.187719	−	0.982223i	$-0.560109\pi$
$241$	−90.4804			−0.375437			−0.187719	+	0.982223i	$0.560109\pi$
$242$	−419.790	−	242.366i	−1.73467	−	1.00151i
$243$			15.5885i			0.0641500i
$244$			115.670i			0.474055i
$245$	−467.855	+	270.116i	−1.90961	+	1.10251i
$246$		−	103.124i		−	0.419202i
$247$	50.2420	+	29.0072i	0.203409	+	0.117438i
$248$	140.419	−	243.214i	0.566207	−	0.980700i
$249$	144.928	−	83.6740i	0.582038	−	0.336040i
$250$	−41.0474	−	71.0962i	−0.164190	−	0.284385i
$251$	−209.770	+	121.111i	−0.835736	+	0.482512i	−0.855812	−	0.517286i	$-0.826942\pi$
$251$	−209.770	+	121.111i	−0.835736	+	0.482512i	0.0200768	+	0.999798i	$0.493609\pi$
$252$	−186.417	+	107.628i	−0.739749	+	0.427094i
$253$		−	671.861i		−	2.65558i
$254$			496.690i			1.95547i
$255$	−136.363	−	236.188i	−0.534759	−	0.926229i
$256$	111.508	−	193.137i	0.435578	−	0.754443i
$257$	−0.725648	+	1.25686i	−0.00282353	+	0.00489050i	−0.867434	−	0.497553i	$-0.834232\pi$
$257$	−0.725648	+	1.25686i	−0.00282353	+	0.00489050i	0.864610	+	0.502443i	$0.167565\pi$
$258$	−3.72690	+	2.15173i	−0.0144454	+	0.00834003i
$259$		−	302.008i		−	1.16605i
$260$	738.558			2.84061
$261$	−10.3667	+	17.9557i	−0.0397192	+	0.0687956i
$262$	−132.611	+	76.5630i	−0.506149	+	0.292225i
$263$	374.978			1.42577			0.712886	−	0.701280i	$-0.247388\pi$
$263$	374.978			1.42577			0.712886	+	0.701280i	$0.247388\pi$
$264$	−185.292	−	106.978i	−0.701864	−	0.405222i
$265$	478.415			1.80534
$266$	−61.5965	−	106.688i	−0.231566	−	0.401084i
$267$		−	226.718i		−	0.849130i
$268$	107.844	−	410.245i	0.402403	−	1.53077i
$269$	−241.762			−0.898745			−0.449372	−	0.893345i	$-0.648352\pi$
$269$	−241.762			−0.898745			−0.449372	+	0.893345i	$0.648352\pi$
$270$	−98.3590	+	56.7876i	−0.364292	+	0.210324i
$271$			200.316i			0.739175i	0.929196	+	0.369587i	$0.120501\pi$
$271$			200.316i			0.739175i	−0.929196	+	0.369587i	$0.879499\pi$
$272$	−14.3744	+	24.8972i	−0.0528470	+	0.0915337i
$273$			336.738i			1.23347i
$274$	399.753	+	692.393i	1.45895	+	2.52698i
$275$	−303.320	−	175.122i	−1.10298	−	0.636807i
$276$		−	446.876i		−	1.61911i
$277$	−266.542			−0.962244			−0.481122	−	0.876654i	$-0.659771\pi$
$277$	−266.542			−0.962244			−0.481122	+	0.876654i	$0.659771\pi$
$278$	−155.391	−	269.145i	−0.558960	−	0.968148i
$279$	97.3813	+	56.2231i	0.349037	+	0.201516i
$280$	−500.088	−	288.726i	−1.78603	−	1.03116i
$281$	130.414	−	75.2948i	0.464108	−	0.267953i	−0.249662	−	0.968333i	$-0.580319\pi$
$281$	130.414	−	75.2948i	0.464108	−	0.267953i	0.713770	+	0.700380i	$0.246986\pi$
$282$	87.3418			0.309723
$283$	98.8383			0.349252			0.174626	−	0.984635i	$-0.444128\pi$
$283$	98.8383			0.349252			0.174626	+	0.984635i	$0.444128\pi$
$284$	−345.331	−	598.130i	−1.21595	−	2.10609i
$285$	−19.9167	−	34.4968i	−0.0698832	−	0.121041i
$286$	−787.252	+	454.520i	−2.75263	+	1.58923i
$287$	104.966	+	181.807i	0.365735	+	0.633472i
$288$	88.2338	+	50.9418i	0.306367	+	0.176881i
$289$	−123.570	+	214.030i	−0.427579	+	0.740588i
$290$	−151.061			−0.520898
$291$	−49.6133	−	85.9327i	−0.170492	−	0.295302i
$292$	−519.786			−1.78009
$293$	320.171			1.09273			0.546367	−	0.837546i	$-0.316010\pi$
$293$	320.171			1.09273			0.546367	+	0.837546i	$0.316010\pi$
$294$	221.134	−	383.016i	0.752157	−	1.30277i
$295$		−	35.5411i		−	0.120478i
$296$	172.913	−	99.8316i	0.584167	−	0.337269i
$297$	42.8335	−	74.1899i	0.144221	−	0.249798i
$298$	184.218	−	106.358i	0.618182	−	0.356907i
$299$	−605.418	−	349.538i	−2.02481	−	1.16902i
$300$	−201.748	−	116.479i	−0.672492	−	0.388264i
$301$	4.38034	−	7.58697i	0.0145526	−	0.0252059i
$302$	−122.396	−	70.6652i	−0.405284	−	0.233991i
$303$	47.3196	−	81.9599i	0.156170	−	0.270495i
$304$	−2.09947	+	3.63638i	−0.00690614	+	0.0119618i
$305$	−62.1210	−	107.597i	−0.203675	−	0.352776i
$306$	193.359	+	111.636i	0.631892	+	0.364823i
$307$	−82.5486	−	142.978i	−0.268888	−	0.465727i	0.699687	−	0.714449i	$-0.253323\pi$
$307$	−82.5486	−	142.978i	−0.268888	−	0.465727i	−0.968575	+	0.248722i	$0.919989\pi$
$308$	1182.95			3.84074
$309$	−203.834	−	117.683i	−0.659656	−	0.380852i
$310$			819.266i			2.64279i
$311$			586.356i			1.88539i	0.333659	+	0.942694i	$0.391717\pi$
$311$			586.356i			1.88539i	−0.333659	+	0.942694i	$0.608283\pi$
$312$	−192.798	+	111.312i	−0.617942	+	0.356769i
$313$		−	231.647i		−	0.740085i	−0.929015	−	0.370042i	$-0.879343\pi$
$313$		−	231.647i		−	0.740085i	0.929015	−	0.370042i	$-0.120657\pi$
$314$	253.689	+	146.467i	0.807926	+	0.466456i
$315$	115.604	−	200.232i	0.366997	−	0.635658i
$316$	632.529	−	365.191i	2.00167	−	1.15567i
$317$	87.9007	+	152.249i	0.277289	+	0.480279i	0.970710	−	0.240254i	$-0.0772306\pi$
$317$	87.9007	+	152.249i	0.277289	+	0.480279i	−0.693421	+	0.720533i	$0.743897\pi$
$318$	−339.189	+	195.831i	−1.06663	+	0.615820i
$319$	98.6762	−	56.9707i	0.309330	−	0.178592i
$320$			708.536i			2.21417i
$321$		−	180.774i		−	0.563160i
$322$	742.240	+	1285.60i	2.30509	+	3.99254i
$323$	−39.1533	+	67.8155i	−0.121218	+	0.209955i
$324$	28.4899	−	49.3460i	0.0879319	−	0.152303i
$325$	−315.607	+	182.216i	−0.971098	+	0.560664i
$326$		−	722.988i		−	2.21775i
$327$	208.456			0.637480
$328$	−69.3950	+	120.196i	−0.211570	+	0.366450i
$329$	−153.983	+	88.9022i	−0.468034	+	0.270220i
$330$	624.157			1.89139
$331$	116.247	+	67.1151i	0.351198	+	0.202765i	0.665213	−	0.746654i	$-0.268341\pi$
$331$	116.247	+	67.1151i	0.351198	+	0.202765i	−0.314015	+	0.949418i	$0.601674\pi$
$332$	−611.700			−1.84247
$333$	39.9720	+	69.2335i	0.120036	+	0.207908i
$334$		−	247.168i		−	0.740025i
$335$	120.007	+	439.532i	0.358230	+	1.31203i
$336$	−24.3722			−0.0725363
$337$	−186.342	+	107.585i	−0.552943	+	0.319242i	−0.750308	−	0.661088i	$-0.770095\pi$
$337$	−186.342	+	107.585i	−0.552943	+	0.319242i	0.197365	+	0.980330i	$0.436762\pi$
$338$			402.663i			1.19131i
$339$	24.8672	−	43.0712i	0.0733545	−	0.127054i
$340$			996.888i			2.93202i
$341$	−308.977	−	535.163i	−0.906090	−	1.56939i
$342$	28.2413	+	16.3051i	0.0825768	+	0.0476757i
$343$			345.010i			1.00586i
$344$	5.79185			0.0168368
$345$	239.997	+	415.687i	0.695644	+	1.20489i
$346$	−103.210	−	59.5881i	−0.298294	−	0.172220i
$347$	65.3994	+	37.7584i	0.188471	+	0.108814i	0.591267	−	0.806476i	$-0.298628\pi$
$347$	65.3994	+	37.7584i	0.188471	+	0.108814i	−0.402796	+	0.915290i	$0.631961\pi$
$348$	65.6326	−	37.8930i	0.188600	−	0.108888i
$349$	−300.812			−0.861926			−0.430963	−	0.902369i	$-0.641826\pi$
$349$	−300.812			−0.861926			−0.430963	+	0.902369i	$0.641826\pi$
$350$	773.866			2.21104
$351$	−44.5686	−	77.1951i	−0.126976	−	0.219929i
$352$	−279.953	−	484.893i	−0.795321	−	1.37754i
$353$	−106.939	+	61.7410i	−0.302942	+	0.174904i	−0.643764	−	0.765224i	$-0.722628\pi$
$353$	−106.939	+	61.7410i	−0.302942	+	0.174904i	0.340822	+	0.940128i	$0.389295\pi$
$354$	14.5481	+	25.1981i	0.0410964	+	0.0711810i
$355$	642.458	+	370.924i	1.80974	+	1.04485i
$356$	−414.356	+	717.686i	−1.16392	+	2.01597i
$357$	−454.521			−1.27317
$358$	−100.521	−	174.108i	−0.280785	−	0.486335i
$359$	711.012			1.98053			0.990267	−	0.139182i	$-0.0444475\pi$
$359$	711.012			1.98053			0.990267	+	0.139182i	$0.0444475\pi$
$360$	152.856			0.424601
$361$	174.781	−	302.730i	0.484159	−	0.838588i
$362$			363.328i			1.00367i
$363$	−226.214	+	130.605i	−0.623179	+	0.359793i
$364$	615.433	−	1065.96i	1.69075	−	2.92846i
$365$	483.509	−	279.154i	1.32468	−	0.764806i
$366$	88.0855	+	50.8562i	0.240671	+	0.138951i
$367$	−557.359	−	321.792i	−1.51869	−	0.876816i	−0.999758	−	0.0220009i	$-0.992996\pi$
$367$	−557.359	−	321.792i	−1.51869	−	0.876816i	−0.518932	−	0.854815i	$-0.673670\pi$
$368$	25.2986	−	43.8185i	0.0687463	−	0.119072i
$369$	−48.1256	−	27.7854i	−0.130422	−	0.0752991i
$370$	−291.230	+	504.425i	−0.787108	+	1.36331i
$371$	398.658	−	690.497i	1.07455	−	1.86118i
$372$	−205.510	−	355.954i	−0.552446	−	0.956865i
$373$	−418.723	−	241.750i	−1.12258	−	0.648122i	−0.180522	−	0.983571i	$-0.557779\pi$
$373$	−418.723	−	241.750i	−1.12258	−	0.648122i	−0.942059	+	0.335449i	$0.891112\pi$
$374$	−613.500	−	1062.61i	−1.64037	−	2.84121i
$375$	−44.2388			−0.117970
$376$	−101.801	−	58.7749i	−0.270748	−	0.156316i
$377$		−	118.557i		−	0.314475i
$378$			189.282i			0.500746i
$379$	−142.198	+	82.0983i	−0.375194	+	0.216618i	−0.675725	−	0.737154i	$-0.736169\pi$
$379$	−142.198	+	82.0983i	−0.375194	+	0.216618i	0.300531	+	0.953772i	$0.402836\pi$
$380$			145.602i			0.383162i
$381$	231.795	+	133.827i	0.608385	+	0.351251i
$382$	−115.342	+	199.779i	−0.301943	+	0.522981i
$383$	290.875	−	167.937i	0.759464	−	0.438477i	−0.0696390	−	0.997572i	$-0.522185\pi$
$383$	290.875	−	167.937i	0.759464	−	0.438477i	0.829103	+	0.559095i	$0.188851\pi$
$384$	−172.381	−	298.573i	−0.448910	−	0.777534i
$385$	−1100.39	+	635.308i	−2.85815	+	1.65015i
$386$	422.435	−	243.893i	1.09439	−	0.631847i
$387$			2.31902i			0.00599230i
$388$			362.699i			0.934791i
$389$	1.45179	+	2.51458i	0.00373211	+	0.00646421i	0.867885	−	0.496764i	$-0.165479\pi$
$389$	1.45179	+	2.51458i	0.00373211	+	0.00646421i	−0.864153	+	0.503229i	$0.832145\pi$
$390$	324.720	−	562.432i	0.832616	−	1.44213i
$391$	471.798	−	817.179i	1.20665	−	2.08997i
$392$	−515.485	+	297.616i	−1.31501	+	0.759223i
$393$			82.5157i			0.209964i
$394$	466.195			1.18324
$395$	−392.255	+	679.406i	−0.993052	+	1.72002i
$396$	−271.183	+	156.568i	−0.684806	+	0.395373i
$397$	359.797			0.906289			0.453145	−	0.891437i	$-0.350302\pi$
$397$	359.797			0.906289			0.453145	+	0.891437i	$0.350302\pi$
$398$	−432.707	−	249.824i	−1.08720	−	0.627697i
$399$	−66.3856			−0.166380
$400$	−13.1883	−	22.8428i	−0.0329707	−	0.0571069i
$401$			396.737i			0.989369i	0.869073	+	0.494685i	$0.164716\pi$
$401$			396.737i			0.989369i	−0.869073	+	0.494685i	$0.835284\pi$
$402$	−264.997	−	262.498i	−0.659198	−	0.652980i
$403$	−642.985			−1.59550
$404$	−299.585	+	172.965i	−0.741547	+	0.428132i
$405$			61.2027i			0.151118i
$406$	−125.877	+	218.026i	−0.310042	+	0.537009i
$407$		−	439.336i		−	1.07945i
$408$	−150.246	−	260.234i	−0.368251	−	0.637829i
$409$	−332.938	−	192.222i	−0.814028	−	0.469979i	0.0343246	−	0.999411i	$-0.489072\pi$
$409$	−332.938	−	192.222i	−0.814028	−	0.469979i	−0.848353	+	0.529431i	$0.822405\pi$
$410$		−	404.880i		−	0.987512i
$411$	430.834			1.04826
$412$	430.163	+	745.065i	1.04409	+	1.80841i
$413$	−51.2965	−	29.6160i	−0.124205	−	0.0717095i
$414$	−340.308	−	196.477i	−0.822000	−	0.474582i
$415$	569.008	−	328.517i	1.37110	−	0.791607i
$416$	−582.587			−1.40045
$417$	−167.472			−0.401612
$418$	−89.6054	−	155.201i	−0.214367	−	0.371295i
$419$	346.009	+	599.305i	0.825797	+	1.43032i	0.901309	+	0.433177i	$0.142607\pi$
$419$	346.009	+	599.305i	0.825797	+	1.43032i	−0.0755124	+	0.997145i	$0.524059\pi$
$420$	−731.901	+	422.563i	−1.74262	+	1.00610i
$421$	240.035	+	415.752i	0.570153	+	0.987535i	0.996550	+	0.0829982i	$0.0264496\pi$
$421$	240.035	+	415.752i	0.570153	+	0.987535i	−0.426396	+	0.904536i	$0.640217\pi$
$422$	92.0531	+	53.1469i	0.218135	+	0.125941i
$423$	23.5331	−	40.7606i	0.0556339	−	0.0963607i
$424$	527.121			1.24321
$425$	−245.950	−	425.999i	−0.578707	−	1.00235i
$426$	−607.323			−1.42564
$427$	−207.059			−0.484916
$428$	−330.389	+	572.250i	−0.771937	+	1.33703i
$429$			489.858i			1.14186i
$430$	−14.6324	+	8.44802i	−0.0340288	+	0.0196465i
$431$	101.699	−	176.148i	0.235960	−	0.408696i	−0.723591	−	0.690229i	$-0.757510\pi$
$431$	101.699	−	176.148i	0.235960	−	0.408696i	0.959551	+	0.281534i	$0.0908431\pi$
$432$	5.58718	−	3.22576i	0.0129333	−	0.00746703i
$433$	340.885	+	196.810i	0.787264	+	0.454527i	0.838998	−	0.544134i	$-0.183142\pi$
$433$	340.885	+	196.810i	0.787264	+	0.454527i	−0.0517347	+	0.998661i	$0.516475\pi$
$434$	1182.45	+	682.686i	2.72453	+	1.57301i
$435$	−40.7013	+	70.4967i	−0.0935662	+	0.162061i
$436$	−659.878	−	380.981i	−1.51348	−	0.873809i
$437$	68.9090	−	119.354i	0.157687	−	0.273121i
$438$	−228.533	+	395.832i	−0.521766	+	0.903725i
$439$	110.091	+	190.684i	0.250778	+	0.434359i	0.963740	−	0.266843i	$-0.0859804\pi$
$439$	110.091	+	190.684i	0.250778	+	0.434359i	−0.712963	+	0.701202i	$0.752647\pi$
$440$	−727.486	−	420.014i	−1.65338	−	0.954578i
$441$	−119.164	−	206.397i	−0.270212	−	0.468021i
$442$	−1276.70			−2.88847
$443$	−584.626	−	337.534i	−1.31970	−	0.761927i	−0.336017	−	0.941856i	$-0.609080\pi$
$443$	−584.626	−	337.534i	−1.31970	−	0.761927i	−0.983680	+	0.179929i	$0.942413\pi$
$444$		−	292.216i		−	0.658144i
$445$		−	890.129i		−	2.00029i
$446$	30.7648	−	17.7621i	0.0689794	−	0.0398253i
$447$		−	114.628i		−	0.256438i
$448$	1022.63	+	590.416i	2.28266	+	1.31789i
$449$	−52.5589	+	91.0347i	−0.117058	+	0.202750i	−0.918600	−	0.395188i	$-0.870680\pi$
$449$	−52.5589	+	91.0347i	−0.117058	+	0.202750i	0.801543	+	0.597937i	$0.204013\pi$
$450$	−177.404	+	102.424i	−0.394231	+	0.227609i
$451$	152.696	+	264.477i	0.338571	+	0.586423i
$452$	−157.436	+	90.8960i	−0.348311	+	0.201097i
$453$	−65.9559	+	38.0796i	−0.145598	+	0.0840610i
$454$			495.026i			1.09037i
$455$			1322.09i			2.90568i
$456$	−21.9444	−	38.0088i	−0.0481236	−	0.0833526i
$457$	−123.339	+	213.629i	−0.269888	+	0.467460i	−0.968833	−	0.247716i	$-0.920320\pi$
$457$	−123.339	+	213.629i	−0.269888	+	0.467460i	0.698945	+	0.715176i	$0.253653\pi$
$458$	161.005	−	278.869i	0.351539	−	0.608883i
$459$	104.196	−	60.1577i	0.227007	−	0.131063i
$460$		−	1754.50i		−	3.81414i
$461$	1.23362			0.00267597			0.00133799	−	0.999999i	$-0.499574\pi$
$461$	1.23362			0.00267597			0.00133799	+	0.999999i	$0.499574\pi$
$462$	520.104	−	900.846i	1.12577	−	1.94988i
$463$	365.044	−	210.758i	0.788433	−	0.455202i	−0.0509779	−	0.998700i	$-0.516234\pi$
$463$	365.044	−	210.758i	0.788433	−	0.455202i	0.839410	+	0.543498i	$0.182900\pi$
$464$	8.58083			0.0184932
$465$	382.334	+	220.741i	0.822224	+	0.474711i
$466$	−1422.43			−3.05243
$467$	54.0189	+	93.5635i	0.115672	+	0.200350i	0.918048	−	0.396469i	$-0.129764\pi$
$467$	54.0189	+	93.5635i	0.115672	+	0.200350i	−0.802376	+	0.596819i	$0.796431\pi$
$468$			325.820i			0.696197i
$469$	734.377	+	193.051i	1.56584	+	0.411622i
$470$	342.918			0.729612
$471$	136.706	−	78.9275i	0.290247	−	0.167574i
$472$		−	39.1594i		−	0.0829649i
$473$	6.37214	−	11.0369i	0.0134718	−	0.0233338i
$474$		−	642.251i		−	1.35496i
$475$	−35.9225	−	62.2197i	−0.0756264	−	0.130989i
$476$	1438.81	+	830.697i	3.02271	+	1.74516i
$477$			211.056i			0.442466i
$478$	−235.794			−0.493293
$479$	120.613	+	208.908i	0.251802	+	0.436134i	0.964022	−	0.265822i	$-0.0856434\pi$
$479$	120.613	+	208.908i	0.251802	+	0.436134i	−0.712220	+	0.701956i	$0.752310\pi$
$480$	346.420	+	200.006i	0.721708	+	0.416678i
$481$	−395.888	−	228.566i	−0.823052	−	0.475190i
$482$	251.860	−	145.411i	0.522530	−	0.301683i
$483$	799.948			1.65621
$484$	954.788			1.97270
$485$	−194.790	−	337.385i	−0.401628	−	0.695640i
$486$	−25.0522	−	43.3917i	−0.0515478	−	0.0892834i
$487$	−365.377	+	210.951i	−0.750261	+	0.433163i	−0.825788	−	0.563980i	$-0.809269\pi$
$487$	−365.377	+	210.951i	−0.750261	+	0.433163i	0.0755273	+	0.997144i	$0.475936\pi$
$488$	−68.4453	−	118.551i	−0.140257	−	0.242932i
$489$	−337.403	−	194.800i	−0.689986	−	0.398364i
$490$	868.207	−	1503.78i	1.77185	−	3.06894i
$491$	−606.351			−1.23493			−0.617466	−	0.786598i	$-0.711841\pi$
$491$	−606.351			−1.23493			−0.617466	+	0.786598i	$0.711841\pi$
$492$	101.563	+	175.912i	0.206428	+	0.357544i
$493$	160.025			0.324595
$494$	−186.470			−0.377470
$495$	168.171	−	291.281i	0.339740	−	0.588447i
$496$		−	46.5375i		−	0.0938257i
$497$	1070.71	−	618.173i	2.15434	−	1.24381i
$498$	−268.945	+	465.826i	−0.540050	+	0.935395i
$499$	266.956	−	154.127i	0.534983	−	0.308872i	−0.208060	−	0.978116i	$-0.566715\pi$
$499$	266.956	−	154.127i	0.534983	−	0.308872i	0.743043	+	0.669244i	$0.233382\pi$
$500$	140.040	+	80.8521i	0.280080	+	0.161704i
$501$	−115.348	−	66.5964i	−0.230236	−	0.132927i
$502$	389.274	−	674.242i	0.775446	−	1.34311i
$503$	596.189	+	344.210i	1.18527	+	0.684314i	0.957227	−	0.289338i	$-0.0934351\pi$
$503$	596.189	+	344.210i	1.18527	+	0.684314i	0.228040	+	0.973652i	$0.426768\pi$
$504$	127.373	−	220.617i	0.252725	−	0.437733i
$505$	185.784	−	321.787i	0.367889	−	0.637203i
$506$	1079.75	+	1870.18i	2.13389	+	3.69601i
$507$	187.914	+	108.492i	0.370639	+	0.213989i
$508$	−489.172	−	847.270i	−0.962937	−	1.66786i
$509$	−968.452			−1.90266			−0.951328	−	0.308179i	$-0.900280\pi$
$509$	−968.452			−1.90266			−0.951328	+	0.308179i	$0.900280\pi$
$510$	759.158	+	438.300i	1.48854	+	0.859411i
$511$		−	930.465i		−	1.82087i
$512$		−	79.3772i		−	0.155034i
$513$	15.2185	−	8.78640i	0.0296657	−	0.0171275i
$514$		−	4.66476i		−	0.00907541i
$515$	−800.282	−	462.043i	−1.55395	−	0.897171i
$516$	4.23831	−	7.34097i	0.00821378	−	0.0142267i
$517$	−224.002	+	129.327i	−0.433272	+	0.250150i
$518$	485.358	+	840.664i	0.936984	+	1.62290i
$519$	−55.6170	+	32.1105i	−0.107162	+	0.0618699i
$520$	−756.955	+	437.028i	−1.45568	+	0.840439i
$521$		−	309.480i		−	0.594012i	−0.954876	−	0.297006i	$-0.904012\pi$
$521$		−	309.480i		−	0.594012i	0.954876	−	0.297006i	$-0.0959881\pi$
$522$		−	66.6414i		−	0.127666i
$523$	−105.945	−	183.502i	−0.202571	−	0.350864i	0.746785	−	0.665066i	$-0.231596\pi$
$523$	−105.945	−	183.502i	−0.202571	−	0.350864i	−0.949356	+	0.314202i	$0.898263\pi$
$524$	150.808	−	261.207i	0.287802	−	0.498488i
$525$	208.508	−	361.147i	0.397158	−	0.687898i
$526$	−1043.78	+	602.627i	−1.98438	+	1.14568i
$527$		−	867.886i		−	1.64684i
$528$	−35.4546			−0.0671489
$529$	−565.856	+	980.091i	−1.06967	+	1.85272i
$530$	−1331.71	+	768.862i	−2.51266	+	1.45068i
$531$	15.6792			0.0295277
$532$	210.147	+	121.328i	0.395013	+	0.228061i
$533$	317.762			0.596177
$534$	364.358	+	631.087i	0.682319	+	1.18181i
$535$		−	709.749i		−	1.32663i
$536$	132.225	+	484.279i	0.246688	+	0.903506i
$537$	−108.337			−0.201744
$538$	672.965	−	388.536i	1.25086	−	0.722187i
$539$			1309.74i			2.42994i
$540$	111.856	−	193.740i	0.207141	−	0.358778i
$541$			892.800i			1.65028i	0.564930	+	0.825139i	$0.308903\pi$
$541$			892.800i			1.65028i	−0.564930	+	0.825139i	$0.691097\pi$
$542$	−321.929	−	557.597i	−0.593964	−	1.02878i
$543$	169.557	+	97.8941i	0.312261	+	0.180284i
$544$		−	786.362i		−	1.44552i
$545$	818.431			1.50171
$546$	−541.172	−	937.338i	−0.991158	−	1.71674i
$547$	84.4185	+	48.7390i	0.154330	+	0.0891024i	0.575176	−	0.818030i	$-0.304933\pi$
$547$	84.4185	+	48.7390i	0.154330	+	0.0891024i	−0.420846	+	0.907132i	$0.638267\pi$
$548$	−1363.82	−	787.405i	−2.48873	−	1.43687i
$549$	47.4670	−	27.4051i	0.0864608	−	0.0499182i
$550$	1125.75			2.04683
$551$	23.3727			0.0424186
$552$	264.430	+	458.007i	0.479041	+	0.829723i
$553$	653.725	+	1132.28i	1.18214	+	2.04753i
$554$	741.940	−	428.360i	1.33924	−	0.773212i
$555$	156.936	+	271.822i	0.282768	+	0.489769i
$556$	530.142	+	306.078i	0.953493	+	0.550499i
$557$	121.049	−	209.662i	0.217322	−	0.376414i	−0.736666	−	0.676257i	$-0.763601\pi$
$557$	121.049	−	209.662i	0.217322	−	0.376414i	0.953989	+	0.299843i	$0.0969344\pi$
$558$	−361.425			−0.647715
$559$	−6.63026	−	11.4840i	−0.0118609	−	0.0205437i
$560$	−95.6890			−0.170873
$561$	−661.199			−1.17861
$562$	−242.013	+	419.178i	−0.430628	+	0.745869i
$563$			580.795i			1.03161i	0.856707	+	0.515804i	$0.172507\pi$
$563$			580.795i			1.03161i	−0.856707	+	0.515804i	$0.827493\pi$
$564$	−148.991	+	86.0197i	−0.264168	+	0.152517i
$565$	97.6324	−	169.104i	0.172801	−	0.299300i
$566$	−275.124	+	158.843i	−0.486086	+	0.280642i
$567$	88.3339	+	50.9996i	0.155792	+	0.0899464i
$568$	707.865	+	408.686i	1.24624	+	0.719518i
$569$	−136.627	+	236.645i	−0.240118	+	0.415896i	−0.960748	−	0.277424i	$-0.910519\pi$
$569$	−136.627	+	236.645i	−0.240118	+	0.415896i	0.720630	+	0.693320i	$0.243853\pi$
$570$	110.880	+	64.0163i	0.194526	+	0.112309i
$571$	535.822	−	928.070i	0.938392	−	1.62534i	0.169920	−	0.985458i	$-0.445649\pi$
$571$	535.822	−	928.070i	0.938392	−	1.62534i	0.768471	−	0.639884i	$-0.221018\pi$
$572$	895.280	−	1550.67i	1.56517	−	2.71096i
$573$	62.1550	+	107.656i	0.108473	+	0.187881i
$574$	−584.363	−	337.382i	−1.01805	−	0.587774i
$575$	432.868	+	749.749i	0.752814	+	1.30391i
$576$	−312.576			−0.542666
$577$	50.9787	+	29.4325i	0.0883512	+	0.0510096i	0.543525	−	0.839393i	$-0.317089\pi$
$577$	50.9787	+	29.4325i	0.0883512	+	0.0510096i	−0.455173	+	0.890403i	$0.650423\pi$
$578$		−	794.359i		−	1.37432i
$579$		−	262.855i		−	0.453982i
$580$	257.684	−	148.774i	0.444283	−	0.256507i
$581$		−	1095.00i		−	1.88468i
$582$	276.205	+	159.467i	0.474579	+	0.273999i
$583$	579.935	−	1004.48i	0.994742	−	1.72294i
$584$	532.734	−	307.574i	0.912215	−	0.526668i
$585$	−174.983	−	303.080i	−0.299117	−	0.518086i
$586$	−891.223	+	514.548i	−1.52086	+	0.878068i
$587$	165.196	−	95.3762i	0.281425	−	0.162481i	−0.352643	−	0.935758i	$-0.614717\pi$
$587$	165.196	−	95.3762i	0.281425	−	0.162481i	0.634068	+	0.773277i	$0.281384\pi$
$588$			871.147i			1.48154i
$589$		−	126.760i		−	0.215212i
$590$	57.1181	+	98.9315i	0.0968104	+	0.167681i
$591$	125.610	−	217.563i	0.212539	−	0.368128i
$592$	16.5430	−	28.6533i	0.0279443	−	0.0484009i
$593$	−126.224	+	72.8755i	−0.212857	+	0.122893i	−0.602638	−	0.798014i	$-0.705884\pi$
$593$	−126.224	+	72.8755i	−0.212857	+	0.122893i	0.389782	+	0.920907i	$0.372551\pi$
$594$			275.351i			0.463555i
$595$	−1784.52			−2.99919
$596$	−209.497	+	362.859i	−0.351505	+	0.608824i
$597$	−233.175	+	134.623i	−0.390577	+	0.225500i
$598$	2246.97			3.75748
$599$	795.482	+	459.272i	1.32802	+	0.766730i	0.984993	−	0.172596i	$-0.0552156\pi$
$599$	795.482	+	459.272i	1.32802	+	0.766730i	0.343023	+	0.939327i	$0.388549\pi$
$600$	275.697			0.459496
$601$	523.024	+	905.904i	0.870256	+	1.50733i	0.861731	+	0.507365i	$0.169380\pi$
$601$	523.024	+	905.904i	0.870256	+	1.50733i	0.00852498	+	0.999964i	$0.497286\pi$
$602$			28.1586i			0.0467750i
$603$	−193.902	+	52.9420i	−0.321563	+	0.0877977i
$604$	278.382			0.460897
$605$	−888.151	+	512.774i	−1.46802	+	0.847561i
$606$			304.189i			0.501963i
$607$	−202.335	+	350.455i	−0.333337	+	0.577356i	−0.983164	−	0.182726i	$-0.941508\pi$
$607$	−202.335	+	350.455i	−0.333337	+	0.577356i	0.649827	+	0.760082i	$0.274841\pi$
$608$		−	114.853i		−	0.188903i
$609$	67.8320	+	117.488i	0.111383	+	0.192920i
$610$	345.837	+	199.669i	0.566947	+	0.327327i
$611$			269.132i			0.440479i
$612$	−439.784			−0.718602
$613$	−80.8320	−	140.005i	−0.131863	−	0.228393i	0.792532	−	0.609831i	$-0.208763\pi$
$613$	−80.8320	−	140.005i	−0.131863	−	0.228393i	−0.924395	+	0.381437i	$0.875429\pi$
$614$	459.561	+	265.328i	0.748471	+	0.432130i
$615$	−188.949	−	109.090i	−0.307234	−	0.177382i
$616$	−1212.41	+	699.987i	−1.96820	+	1.13634i
$617$	−551.295			−0.893510			−0.446755	−	0.894656i	$-0.647420\pi$
$617$	−551.295			−0.893510			−0.446755	+	0.894656i	$0.647420\pi$
$618$	756.516			1.22414
$619$	342.641	+	593.471i	0.553539	+	0.958758i	0.998016	+	0.0629674i	$0.0200564\pi$
$619$	342.641	+	593.471i	0.553539	+	0.958758i	−0.444476	+	0.895791i	$0.646610\pi$
$620$	−806.865	−	1397.53i	−1.30139	−	2.25408i
$621$	−183.383	+	105.876i	−0.295303	+	0.170493i
$622$	−942.333	−	1632.17i	−1.51500	−	2.62406i
$623$	−1284.72	−	741.735i	−2.06215	−	1.19059i
$624$	−18.4454	+	31.9484i	−0.0295599	+	0.0511993i
$625$	−704.791			−1.12767
$626$	372.280	+	644.807i	0.594696	+	1.03004i
$627$	−96.5721			−0.154022
$628$	−577.001			−0.918791
$629$	308.513	−	534.361i	0.490482	−	0.849540i
$630$			743.150i			1.17960i
$631$	−451.547	+	260.701i	−0.715606	+	0.413155i	−0.813133	−	0.582078i	$-0.802240\pi$
$631$	−451.547	+	260.701i	−0.715606	+	0.413155i	0.0975275	+	0.995233i	$0.468907\pi$
$632$	−432.190	+	748.575i	−0.683845	+	1.18445i
$633$	49.6051	−	28.6395i	0.0783650	−	0.0452441i
$634$	−489.358	−	282.531i	−0.771857	−	0.445632i
$635$	910.062	+	525.425i	1.43317	+	0.827441i
$636$	385.733	−	668.109i	0.606498	−	1.05049i
$637$	1180.21	+	681.396i	1.85277	+	1.06970i
$638$	−183.115	+	317.165i	−0.287015	+	0.497124i
$639$	−163.635	+	283.425i	−0.256081	+	0.443545i
$640$	−676.796	−	1172.24i	−1.05749	−	1.83163i
$641$	599.562	+	346.158i	0.935355	+	0.540027i	0.888501	−	0.458874i	$-0.151747\pi$
$641$	599.562	+	346.158i	0.935355	+	0.540027i	0.0468537	+	0.998902i	$0.485081\pi$
$642$	290.523	+	503.200i	0.452528	+	0.783801i
$643$	312.843			0.486536			0.243268	−	0.969959i	$-0.421781\pi$
$643$	312.843			0.486536			0.243268	+	0.969959i	$0.421781\pi$
$644$	−2532.27	−	1462.01i	−3.93210	−	2.27020i
$645$			9.10484i			0.0141160i
$646$		−	251.693i		−	0.389618i
$647$	−285.962	+	165.100i	−0.441981	+	0.255178i	−0.704438	−	0.709766i	$-0.748801\pi$
$647$	−285.962	+	165.100i	−0.441981	+	0.255178i	0.262456	+	0.964944i	$0.415467\pi$
$648$			67.4336i			0.104064i
$649$	−74.6218	−	43.0829i	−0.114980	−	0.0663835i
$650$	585.678	−	1014.42i	0.901043	−	1.56065i
$651$	637.190	−	367.882i	0.978786	−	0.565103i
$652$	712.044	+	1233.30i	1.09209	+	1.89156i
$653$	1017.16	−	587.257i	1.55767	−	0.899321i	0.560191	−	0.828363i	$-0.310728\pi$
$653$	1017.16	−	587.257i	1.55767	−	0.899321i	0.997479	−	0.0709581i	$-0.0226057\pi$
$654$	−580.254	+	335.010i	−0.887239	+	0.512248i
$655$			323.970i			0.494610i
$656$			22.9988i			0.0350591i
$657$	123.151	+	213.303i	0.187444	+	0.324663i
$658$	285.750	−	494.933i	0.434270	−	0.752178i
$659$	−563.305	+	975.673i	−0.854788	+	1.48054i	0.0220535	+	0.999757i	$0.492980\pi$
$659$	−563.305	+	975.673i	−0.854788	+	1.48054i	−0.876842	+	0.480780i	$0.840354\pi$
$660$	−1064.71	+	614.710i	−1.61319	+	0.931378i
$661$			958.202i			1.44963i	0.688946	+	0.724813i	$0.258074\pi$
$661$			958.202i			1.44963i	−0.688946	+	0.724813i	$0.741926\pi$
$662$	−431.443			−0.651726
$663$	−343.991	+	595.810i	−0.518841	+	0.898658i
$664$	626.937	−	361.962i	0.944182	−	0.545124i
$665$	−260.640			−0.391940
$666$	−222.531	−	128.478i	−0.334130	−	0.192910i
$667$	−281.642			−0.422251
$668$	243.427	+	421.628i	0.364412	+	0.631180i
$669$		−	19.1431i		−	0.0286144i
$670$	−1040.42	−	1030.61i	−1.55287	−	1.53822i
$671$	−301.212			−0.448900
$672$	577.336	−	333.325i	0.859131	−	0.496019i
$673$		−	67.6336i		−	0.100496i	−0.998737	−	0.0502479i	$-0.983999\pi$
$673$		−	67.6336i		−	0.100496i	0.998737	−	0.0502479i	$-0.0160011\pi$
$674$	345.799	−	598.941i	0.513054	−	0.888636i
$675$			110.388i			0.163537i
$676$	−396.568	−	686.875i	−0.586638	−	1.01609i
$677$	−385.373	−	222.495i	−0.569237	−	0.328649i	0.187608	−	0.982244i	$-0.439927\pi$
$677$	−385.373	−	222.495i	−0.569237	−	0.328649i	−0.756845	+	0.653595i	$0.773260\pi$
$678$			159.856i			0.235776i
$679$	−649.264			−0.956207
$680$	−589.890	−	1021.72i	−0.867485	−	1.50253i
$681$	231.018	+	133.378i	0.339234	+	0.195857i
$682$	1720.12	+	993.114i	2.52217	+	1.45618i
$683$	−805.498	+	465.054i	−1.17935	+	0.680900i	−0.955865	−	0.293807i	$-0.905078\pi$
$683$	−805.498	+	465.054i	−1.17935	+	0.680900i	−0.223488	+	0.974707i	$0.571744\pi$
$684$	−64.2331			−0.0939081
$685$	1691.52			2.46937
$686$	−554.467	−	960.364i	−0.808260	−	1.39995i
$687$	−86.7614	−	150.275i	−0.126290	−	0.218741i
$688$	0.831178	−	0.479881i	0.00120811	−	0.000697501i
$689$	−603.426	−	1045.17i	−0.875800	−	1.51693i
$690$	−1336.10	−	771.399i	−1.93638	−	1.11797i
$691$	−470.697	+	815.271i	−0.681182	+	1.17984i	0.293438	+	0.955978i	$0.405200\pi$
$691$	−470.697	+	815.271i	−0.681182	+	1.17984i	−0.974620	+	0.223864i	$0.928133\pi$
$692$	234.744			0.339226
$693$	−280.271	−	485.443i	−0.404431	−	0.700495i
$694$	−242.726			−0.349749
$695$	−657.523			−0.946076
$696$	−44.8450	+	77.6738i	−0.0644324	+	0.111600i
$697$			428.908i			0.615363i
$698$	837.335	−	483.436i	1.19962	−	0.692602i
$699$	−383.256	+	663.819i	−0.548292	+	0.949670i
$700$	−1320.09	+	762.152i	−1.88584	+	1.08879i
$701$	−692.304	−	399.702i	−0.987594	−	0.570188i	−0.0830401	−	0.996546i	$-0.526463\pi$
$701$	−692.304	−	399.702i	−0.987594	−	0.570188i	−0.904554	+	0.426358i	$0.859796\pi$
$702$	248.121	+	143.253i	0.353448	+	0.204064i
$703$	45.0602	−	78.0466i	0.0640970	−	0.111019i
$704$	1487.64	+	858.887i	2.11312	+	1.22001i
$705$	92.3947	−	160.032i	0.131056	−	0.226996i
$706$	198.448	−	343.722i	0.281088	−	0.486859i
$707$	−309.624	−	536.284i	−0.437940	−	0.758535i
$708$	−49.6333	−	28.6558i	−0.0701035	−	0.0404743i
$709$	−213.454	−	369.713i	−0.301063	−	0.521457i	0.675314	−	0.737531i	$-0.264008\pi$
$709$	−213.454	−	369.713i	−0.301063	−	0.521457i	−0.976377	+	0.216073i	$0.930675\pi$
$710$	−2384.45			−3.35838
$711$	−299.725	−	173.046i	−0.421554	−	0.243384i
$712$		−	980.750i		−	1.37746i
$713$			1527.46i			2.14230i
$714$	1265.20	−	730.461i	1.77198	−	1.02306i
$715$			1923.26i			2.68987i
$716$	342.945	+	197.999i	0.478973	+	0.276535i
$717$	−63.5317	+	110.040i	−0.0886077	+	0.153473i
$718$	−1979.16	+	1142.67i	−2.75649	+	1.59146i
$719$	−277.432	−	480.526i	−0.385858	−	0.668325i	0.606030	−	0.795442i	$-0.292761\pi$
$719$	−277.432	−	480.526i	−0.385858	−	0.668325i	−0.991888	+	0.127117i	$0.959428\pi$
$720$	21.9361	−	12.6648i	0.0304668	−	0.0175900i
$721$	−1333.73	+	770.032i	−1.84984	+	1.06800i
$722$			1123.57i			1.55619i
$723$		−	156.717i		−	0.216759i
$724$	−357.828	−	619.777i	−0.494238	−	0.856045i
$725$	−73.4104	+	127.151i	−0.101256	+	0.175380i
$726$	419.790	−	727.098i	0.578223	−	1.00151i
$727$	1130.73	−	652.830i	1.55534	−	0.897978i	0.557652	−	0.830075i	$-0.311702\pi$
$727$	1130.73	−	652.830i	1.55534	−	0.897978i	0.997692	−	0.0679030i	$-0.0216308\pi$
$728$			1456.68i			2.00094i
$729$	−27.0000			−0.0370370
$730$	−897.258	+	1554.10i	−1.22912	+	2.12890i
$731$	15.5008	−	8.94937i	0.0212049	−	0.0122426i
$732$	−200.345			−0.273696
$733$	−1014.46	−	585.697i	−1.38398	−	0.799041i	−0.391352	−	0.920241i	$-0.627993\pi$
$733$	−1014.46	−	585.697i	−1.38398	−	0.799041i	−0.992628	+	0.121200i	$0.961326\pi$
$734$	2068.61			2.81826
$735$	−467.855	−	810.348i	−0.636537	−	1.10251i
$736$			1383.98i			1.88041i
$737$	1068.31	+	280.834i	1.44954	+	0.381050i
$738$	178.616			0.242026
$739$	1144.11	−	660.552i	1.54819	−	0.893845i	0.549905	−	0.835227i	$-0.314664\pi$
$739$	1144.11	−	660.552i	1.54819	−	0.893845i	0.998281	−	0.0586176i	$-0.0186693\pi$
$740$		−	1147.29i		−	1.55039i
$741$	−50.2420	+	87.0217i	−0.0678030	+	0.117438i
$742$			2562.74i			3.45382i
$743$	−290.026	−	502.339i	−0.390344	−	0.676095i	0.602151	−	0.798382i	$-0.294311\pi$
$743$	−290.026	−	502.339i	−0.390344	−	0.676095i	−0.992495	+	0.122287i	$0.960977\pi$
$744$	421.258	+	243.214i	0.566207	+	0.326900i
$745$		−	450.046i		−	0.604088i
$746$	1554.06			2.08320
$747$	144.928	+	251.022i	0.194013	+	0.336040i
$748$	2093.06	+	1208.43i	2.79820	+	1.61554i
$749$	−1024.38	−	591.426i	−1.36766	−	0.789621i
$750$	123.142	−	71.0962i	0.164190	−	0.0947949i
$751$	−1493.65			−1.98889			−0.994443	−	0.105278i	$-0.966427\pi$
$751$	−1493.65			−1.98889			−0.994443	+	0.105278i	$0.966427\pi$
$752$	−19.4791			−0.0259030
$753$	−209.770	−	363.332i	−0.278579	−	0.482512i
$754$	190.533	+	330.013i	0.252696	+	0.437683i
$755$	−258.953	+	149.507i	−0.342984	+	0.198022i
$756$	−186.417	−	322.883i	−0.246583	−	0.427094i
$757$	−784.724	−	453.061i	−1.03662	−	0.598495i	−0.117749	−	0.993043i	$-0.537568\pi$
$757$	−784.724	−	453.061i	−1.03662	−	0.598495i	−0.918875	+	0.394548i	$0.870901\pi$
$758$	263.880	−	457.054i	0.348127	−	0.602974i
$759$	1163.70			1.53320
$760$	−86.1570	−	149.228i	−0.113364	−	0.196353i
$761$	−244.482			−0.321264			−0.160632	−	0.987014i	$-0.551353\pi$
$761$	−244.482			−0.321264			−0.160632	+	0.987014i	$0.551353\pi$
$762$	−860.293			−1.12899
$763$	681.990	−	1181.24i	0.893827	−	1.54815i
$764$		−	454.385i		−	0.594745i
$765$	409.090	−	236.188i	0.534759	−	0.308743i
$766$	−539.783	+	934.931i	−0.704677	+	1.22054i
$767$	−77.6445	+	44.8281i	−0.101231	+	0.0584460i
$768$	334.524	+	193.137i	0.435578	+	0.251481i
$769$	−1269.32	−	732.841i	−1.65061	−	0.952979i	−0.976822	−	0.214053i	$-0.931333\pi$
$769$	−1269.32	−	732.841i	−1.65061	−	0.952979i	−0.673787	−	0.738926i	$-0.735333\pi$
$770$	2042.01	−	3536.86i	2.65196	−	4.59333i
$771$	−2.17694	−	1.25686i	−0.00282353	−	0.00163017i
$772$	−480.402	+	832.081i	−0.622283	+	1.07783i
$773$	341.531	−	591.550i	0.441826	−	0.765265i	−0.555999	−	0.831183i	$-0.687664\pi$
$773$	341.531	−	591.550i	0.441826	−	0.765265i	0.997825	+	0.0659182i	$0.0209976\pi$
$774$	−3.72690	−	6.45518i	−0.00481512	−	0.00834003i
$775$	689.592	+	398.136i	0.889797	+	0.513724i
$776$	−214.620	−	371.734i	−0.276573	−	0.479038i
$777$	523.093			0.673222
$778$	−8.08236	−	4.66636i	−0.0103886	−	0.00599789i
$779$			62.6446i			0.0804167i
$780$			1279.22i			1.64003i
$781$	1557.58	−	899.266i	1.99433	−	1.15143i
$782$			3032.91i			3.87840i
$783$	−31.1001	−	17.9557i	−0.0397192	−	0.0229319i
$784$	−49.3176	+	85.4206i	−0.0629051	+	0.108955i
$785$	536.731	−	309.882i	0.683733	−	0.394754i
$786$	−132.611	−	229.689i	−0.168716	−	0.292225i
$787$	−1053.73	+	608.369i	−1.33892	+	0.773023i	−0.986647	−	0.162876i	$-0.947923\pi$
$787$	−1053.73	+	608.369i	−1.33892	+	0.773023i	−0.352269	+	0.935899i	$0.614590\pi$
$788$	−795.251	+	459.138i	−1.00920	+	0.582663i
$789$			649.481i			0.823169i
$790$		−	2521.58i		−	3.19187i
$791$	−162.712	−	281.826i	−0.205704	−	0.356290i
$792$	185.292	−	320.935i	0.233955	−	0.405222i
$793$	−156.707	+	271.424i	−0.197612	+	0.342275i
$794$	−1001.52	+	578.230i	−1.26137	+	0.728249i
$795$			828.639i			1.04231i
$796$	984.168			1.23639
$797$	26.9413	−	46.6637i	0.0338034	−	0.0585491i	−0.848629	−	0.528989i	$-0.822571\pi$
$797$	26.9413	−	46.6637i	0.0338034	−	0.0585491i	0.882432	+	0.470440i	$0.155905\pi$
$798$	184.790	−	106.688i	0.231566	−	0.133695i
$799$	−363.269			−0.454654
$800$	624.816	+	360.738i	0.781020	+	0.450922i
$801$	392.686			0.490245
$802$	−637.597	−	1104.35i	−0.795008	−	1.37699i
$803$		−	1353.56i		−	1.68563i
$804$	710.566	+	186.792i	0.883788	+	0.232328i
$805$	3140.72			3.90152
$806$	1789.80	−	1033.34i	2.22060	−	1.28206i
$807$		−	418.745i		−	0.518890i
$808$	204.698	−	354.548i	0.253339	−	0.438797i
$809$			225.703i			0.278990i	0.990223	+	0.139495i	$0.0445480\pi$
$809$			225.703i			0.278990i	−0.990223	+	0.139495i	$0.955452\pi$
$810$	−98.3590	−	170.363i	−0.121431	−	0.210324i
$811$	902.051	+	520.799i	1.11227	+	0.642169i	0.939416	−	0.342778i	$-0.111368\pi$
$811$	902.051	+	520.799i	1.11227	+	0.642169i	0.172853	+	0.984948i	$0.444701\pi$
$812$		−	495.887i		−	0.610698i
$813$	−346.958			−0.426763
$814$	706.057	+	1222.93i	0.867392	+	1.50237i
$815$	−1324.70	−	764.814i	−1.62540	−	0.938423i
$816$	−43.1231	−	24.8972i	−0.0528470	−	0.0305112i
$817$	2.26398	−	1.30711i	0.00277109	−	0.00159989i
$818$	1235.68			1.51061
$819$	−583.247			−0.712146
$820$	398.751	+	690.657i	0.486282	+	0.842265i
$821$	−663.627	−	1149.43i	−0.808315	−	1.40004i	−0.914030	−	0.405646i	$-0.867047\pi$
$821$	−663.627	−	1149.43i	−0.808315	−	1.40004i	0.105715	−	0.994396i	$-0.466287\pi$
$822$	−1199.26	+	692.393i	−1.45895	+	0.842327i
$823$	413.401	+	716.032i	0.502310	+	0.870027i	0.999996	+	0.00266982i	$0.000849831\pi$
$823$	413.401	+	716.032i	0.502310	+	0.870027i	−0.497686	+	0.867357i	$0.665817\pi$
$824$	−881.757	−	509.082i	−1.07009	−	0.617818i
$825$	303.320	−	525.366i	0.367661	−	0.636807i
$826$	190.384			0.230489
$827$	200.826	+	347.840i	0.242836	+	0.420605i	0.961521	−	0.274731i	$-0.0885889\pi$
$827$	200.826	+	347.840i	0.242836	+	0.420605i	−0.718685	+	0.695336i	$0.755256\pi$
$828$	774.011			0.934796
$829$	915.170			1.10394			0.551972	−	0.833863i	$-0.313875\pi$
$829$	915.170			1.10394			0.551972	+	0.833863i	$0.313875\pi$
$830$	−1055.92	+	1828.91i	−1.27219	+	2.20350i
$831$		−	461.664i		−	0.555552i
$832$	1547.90	−	893.678i	1.86045	−	1.07413i
$833$	−919.732	+	1593.02i	−1.10412	+	1.91239i
$834$	466.173	−	269.145i	0.558960	−	0.322716i
$835$	−452.875	−	261.468i	−0.542366	−	0.313135i
$836$	305.704	+	176.498i	0.365674	+	0.211122i
$837$	−97.3813	+	168.669i	−0.116346	+	0.201516i
$838$	−1926.29	−	1112.14i	−2.29867	−	1.32714i
$839$	−97.9570	+	169.666i	−0.116754	+	0.202225i	−0.918480	−	0.395468i	$-0.870582\pi$
$839$	−97.9570	+	169.666i	−0.116754	+	0.202225i	0.801725	+	0.597693i	$0.203916\pi$
$840$	500.088	−	866.178i	0.595343	−	1.03116i
$841$	396.618	+	686.963i	0.471603	+	0.816840i
$842$	−1336.31	−	771.520i	−1.58707	−	0.916294i
$843$	130.414	+	225.884i	0.154703	+	0.267953i
$844$	−209.370			−0.248068
$845$	737.780	+	425.958i	0.873113	+	0.504092i
$846$			151.281i			0.178819i
$847$			1709.16i			2.01790i
$848$	75.6462	−	43.6744i	0.0892055	−	0.0515028i
$849$			171.193i			0.201641i
$850$	1369.25	+	790.534i	1.61088	+	0.930041i
$851$	−542.977	+	940.464i	−0.638046	+	1.10513i
$852$	1035.99	−	598.130i	1.21595	−	0.702031i
$853$	154.090	+	266.891i	0.180644	+	0.312885i	0.942100	−	0.335332i	$-0.108848\pi$
$853$	154.090	+	266.891i	0.180644	+	0.312885i	−0.761456	+	0.648217i	$0.775515\pi$
$854$	576.365	−	332.765i	0.674901	−	0.389654i
$855$	59.7501	−	34.4968i	0.0698832	−	0.0403471i
$856$		−	782.006i		−	0.913558i
$857$		−	816.318i		−	0.952529i	−0.879302	−	0.476265i	$-0.841990\pi$
$857$		−	816.318i		−	0.952529i	0.879302	−	0.476265i	$-0.158010\pi$
$858$	−787.252	−	1363.56i	−0.917543	−	1.58923i
$859$	212.191	−	367.525i	0.247021	−	0.427852i	−0.715677	−	0.698431i	$-0.753882\pi$
$859$	212.191	−	367.525i	0.247021	−	0.427852i	0.962698	+	0.270579i	$0.0872151\pi$
$860$	16.6403	−	28.8218i	0.0193492	−	0.0335137i
$861$	−314.898	+	181.807i	−0.365735	+	0.211157i
$862$			653.762i			0.758425i
$863$	1106.57			1.28224			0.641119	−	0.767442i	$-0.278471\pi$
$863$	1106.57			1.28224			0.641119	+	0.767442i	$0.278471\pi$
$864$	−88.2338	+	152.825i	−0.102122	+	0.176881i
$865$	−218.361	+	126.071i	−0.252440	+	0.145747i
$866$	−1265.18			−1.46094
$867$	−370.711	−	214.030i	−0.427579	−	0.246863i
$868$	−2689.41			−3.09840
$869$	950.983	+	1647.15i	1.09434	+	1.89546i
$870$		−	261.644i		−	0.300741i
$871$	808.853	−	816.555i	0.928649	−	0.937491i
$872$	901.753			1.03412
$873$	148.840	−	85.9327i	0.170492	−	0.0984338i
$874$			442.975i			0.506836i
$875$	−144.733	+	250.684i	−0.165409	+	0.286496i
$876$		−	900.296i		−	1.02774i
$877$	392.140	+	679.207i	0.447138	+	0.774466i	0.998198	−	0.0599993i	$-0.0191099\pi$
$877$	392.140	+	679.207i	0.447138	+	0.774466i	−0.551060	+	0.834466i	$0.685777\pi$
$878$	−612.896	−	353.856i	−0.698060	−	0.403025i
$879$			554.553i			0.630891i
$880$	−139.200			−0.158182
$881$	−90.0678	−	156.002i	−0.102234	−	0.177074i	0.810371	−	0.585917i	$-0.199266\pi$
$881$	−90.0678	−	156.002i	−0.102234	−	0.177074i	−0.912605	+	0.408843i	$0.865932\pi$
$882$	663.403	+	383.016i	0.752157	+	0.434258i
$883$	−810.408	−	467.889i	−0.917789	−	0.529886i	−0.0348602	−	0.999392i	$-0.511099\pi$
$883$	−810.408	−	467.889i	−0.917789	−	0.529886i	−0.882929	+	0.469506i	$0.844432\pi$
$884$	2177.84	−	1257.38i	2.46362	−	1.42237i
$885$	61.5590			0.0695582
$886$	2169.80			2.44899
$887$	621.001	+	1075.60i	0.700114	+	1.21263i	0.968426	+	0.249300i	$0.0802006\pi$
$887$	621.001	+	1075.60i	0.700114	+	1.21263i	−0.268313	+	0.963332i	$0.586466\pi$
$888$	172.913	+	299.495i	0.194722	+	0.337269i
$889$	1516.69	−	875.662i	1.70606	−	0.984997i
$890$	1430.53	+	2477.74i	1.60733	+	2.78398i
$891$	128.501	+	74.1899i	0.144221	+	0.0832659i
$892$	−34.9864	+	60.5983i	−0.0392224	+	0.0679353i
$893$	−53.0576			−0.0594150
$894$	184.218	+	319.075i	0.206061	+	0.356907i
$895$	−425.346			−0.475247
$896$	−2255.87			−2.51771
$897$	605.418	−	1048.61i	0.674936	−	1.16902i
$898$		−	337.870i		−	0.376247i
$899$	−224.338	+	129.522i	−0.249542	+	0.144073i
$900$	201.748	−	349.437i	0.224164	−	0.388264i
$901$	1410.74	−	814.491i	1.56575	−	0.903985i
$902$	−850.082	−	490.795i	−0.942441	−	0.544119i
$903$	13.1410	+	7.58697i	0.0145526	+	0.00840195i
$904$	107.572	−	186.320i	0.118996	−	0.206106i
$905$	665.709	+	384.347i	0.735590	+	0.424693i
$906$	122.396	−	211.996i	0.135095	−	0.233991i
$907$	−95.8075	+	165.944i	−0.105631	+	0.182959i	−0.913996	−	0.405723i	$-0.867020\pi$
$907$	−95.8075	+	165.944i	−0.105631	+	0.182959i	0.808365	+	0.588682i	$0.200353\pi$
$908$	−487.533	−	844.432i	−0.536931	−	0.929991i
$909$	141.959	+	81.9599i	0.156170	+	0.0901649i
$910$	−2124.73	−	3680.13i	−2.33486	−	4.04410i
$911$	−151.188			−0.165958			−0.0829790	−	0.996551i	$-0.526443\pi$
$911$	−151.188			−0.165958			−0.0829790	+	0.996551i	$0.526443\pi$
$912$	−6.29840	−	3.63638i	−0.00690614	−	0.00398726i
$913$		−	1592.91i		−	1.74470i
$914$		−	792.872i		−	0.867474i
$915$	186.363	−	107.597i	0.203675	−	0.117592i
$916$			634.271i			0.692435i
$917$	467.585	+	269.960i	0.509907	+	0.294395i
$918$	−193.359	+	334.908i	−0.210631	+	0.364823i
$919$	−337.561	+	194.891i	−0.367314	+	0.212069i	−0.672284	−	0.740293i	$-0.734687\pi$
$919$	−337.561	+	194.891i	−0.367314	+	0.212069i	0.304971	+	0.952362i	$0.401353\pi$
$920$	1038.20	+	1798.21i	1.12847	+	1.95457i
$921$	247.646	−	142.978i	0.268888	−	0.155242i
$922$	−3.43389	+	1.98256i	−0.00372439	+	0.00215028i
$923$		−	1871.39i		−	2.02751i
$924$			2048.92i			2.21745i
$925$	283.056	+	490.268i	0.306007	+	0.530019i
$926$	−677.420	+	1173.33i	−0.731555	+	1.26709i
$927$	203.834	−	353.050i	0.219885	−	0.380852i
$928$	−203.265	+	117.355i	−0.219036	+	0.126460i
$929$		−	708.991i		−	0.763177i	−0.924332	−	0.381588i	$-0.875377\pi$
$929$		−	708.991i		−	0.763177i	0.924332	−	0.381588i	$-0.124623\pi$
$930$	−1419.01			−1.52582
$931$	−134.332	+	232.671i	−0.144288	+	0.249915i
$932$	2426.43	−	1400.90i	2.60347	−	1.50311i
$933$	−1015.60			−1.08853
$934$	−300.732	−	173.628i	−0.321983	−	0.185897i
$935$	−2595.97			−2.77644
$936$	−192.798	−	333.936i	−0.205981	−	0.356769i
$937$		−	453.304i		−	0.483782i	−0.970303	−	0.241891i	$-0.922232\pi$
$937$		−	453.304i		−	0.483782i	0.970303	−	0.241891i	$-0.0777677\pi$
$938$	−2354.45	+	642.845i	−2.51007	+	0.685336i
$939$	401.224			0.427288
$940$	−584.960	+	337.727i	−0.622298	+	0.359284i
$941$		−	809.567i		−	0.860327i	−0.902751	−	0.430163i	$-0.858456\pi$
$941$		−	809.567i		−	0.860327i	0.902751	−	0.430163i	$-0.141544\pi$
$942$	−253.689	+	439.402i	−0.269309	+	0.466456i
$943$		−	754.869i		−	0.800498i
$944$	−3.24454	−	5.61970i	−0.00343701	−	0.00595307i
$945$	346.813	+	200.232i	0.366997	+	0.211886i
$946$			40.9627i			0.0433010i
$947$	−1086.01			−1.14679			−0.573395	−	0.819279i	$-0.694374\pi$
$947$	−1086.01			−1.14679			−0.573395	+	0.819279i	$0.694374\pi$
$948$	632.529	+	1095.57i	0.667225	+	1.15567i
$949$	−1219.70	−	704.196i	−1.28525	−	0.742040i
$950$	199.987	+	115.462i	0.210512	+	0.121539i
$951$	−263.702	+	152.249i	−0.277289	+	0.160093i
$952$	−1966.20			−2.06533
$953$	−997.180			−1.04636			−0.523179	−	0.852223i	$-0.675254\pi$
$953$	−997.180			−1.04636			−0.523179	+	0.852223i	$0.675254\pi$
$954$	−339.189	−	587.492i	−0.355544	−	0.615820i
$955$	244.030	+	422.673i	0.255529	+	0.442589i
$956$	402.226	−	232.225i	0.420738	−	0.242913i
$957$	98.6762	+	170.912i	0.103110	+	0.178592i
$958$	−671.474	−	387.675i	−0.700912	−	0.404672i
$959$	1409.53	−	2441.37i	1.46979	−	2.54575i
$960$	−1227.22			−1.27835
$961$	221.953	+	384.433i	0.230960	+	0.400035i
$962$	1469.32			1.52736
$963$	313.111			0.325141
$964$	−286.420	+	496.094i	−0.297116	+	0.514621i
$965$		−	1032.01i		−	1.06944i
$966$	−2226.72	+	1285.60i	−2.30509	+	1.33085i
$967$	62.3061	−	107.917i	0.0644324	−	0.111600i	−0.832010	−	0.554761i	$-0.812810\pi$
$967$	62.3061	−	107.917i	0.0644324	−	0.111600i	0.896442	+	0.443161i	$0.146143\pi$
$968$	−978.571	+	564.978i	−1.01092	+	0.583655i
$969$	−117.460	−	67.8155i	−0.121218	−	0.0699850i
$970$	1084.42	+	626.093i	1.11796	+	0.645457i
$971$	761.387	−	1318.76i	0.784127	−	1.35815i	−0.145392	−	0.989374i	$-0.546444\pi$
$971$	761.387	−	1318.76i	0.784127	−	1.35815i	0.929519	−	0.368774i	$-0.120222\pi$
$972$	85.4698	+	49.3460i	0.0879319	+	0.0507675i
$973$	−547.907	+	949.003i	−0.563111	+	0.975337i
$974$	678.038	−	1174.40i	0.696137	−	1.20575i
$975$	−315.607	−	546.647i	−0.323699	−	0.560664i
$976$	−19.6449	−	11.3420i	−0.0201280	−	0.0116209i
$977$	226.051	+	391.532i	0.231373	+	0.400749i	0.958212	−	0.286058i	$-0.0923450\pi$
$977$	226.051	+	391.532i	0.231373	+	0.400749i	−0.726840	+	0.686807i	$0.759012\pi$
$978$	1252.25			1.28042
$979$	−1868.91	−	1079.01i	−1.90899	−	1.10216i
$980$			3420.26i			3.49006i
$981$			361.057i			0.368049i
$982$	1687.83	−	974.468i	1.71877	−	0.992330i
$983$			670.533i			0.682130i	0.940040	+	0.341065i	$0.110788\pi$
$983$			670.533i			0.682130i	−0.940040	+	0.341065i	$0.889212\pi$
$984$	−208.185	−	120.196i	−0.211570	−	0.122150i
$985$	493.166	−	854.188i	0.500676	−	0.867196i
$986$	−445.444	+	257.177i	−0.451768	+	0.260829i
$987$	−153.983	−	266.707i	−0.156011	−	0.270220i
$988$	318.087	−	183.648i	0.321950	−	0.185878i
$989$	−27.2811	+	15.7507i	−0.0275845	+	0.0159259i
$990$			1081.07i			1.09199i
$991$		−	1498.42i		−	1.51202i	−0.654558	−	0.756012i	$-0.727145\pi$
$991$		−	1498.42i		−	1.51202i	0.654558	−	0.756012i	$-0.272855\pi$
$992$	636.468	+	1102.40i	0.641601	+	1.11129i
$993$	−116.247	+	201.345i	−0.117066	+	0.202765i
$994$	−1986.93	+	3441.47i	−1.99893	+	3.46224i
$995$	−915.480	+	528.553i	−0.920080	+	0.531209i
$996$		−	1059.50i		−	1.06375i
$997$	314.997			0.315945			0.157972	−	0.987444i	$-0.449504\pi$
$997$	314.997			0.315945			0.157972	+	0.987444i	$0.449504\pi$
$998$	−495.396	+	858.052i	−0.496389	+	0.859771i
$999$	−119.916	+	69.2335i	−0.120036	+	0.0693028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.b.97.3	✓	24
67.38	odd	6	inner	201.3.h.b.172.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.b.97.3	✓	24	1.1	even	1	trivial
201.3.h.b.172.3	yes	24	67.38	odd	6	inner

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.78358 + 1.60710i) q^{2} +1.73205i q^{3} +(3.16555 - 5.48289i) q^{4} +6.80030i q^{5} +(-2.78358 - 4.82130i) q^{6} +(9.81487 + 5.66662i) q^{7} +7.49262i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-2.78358 + 1.60710i) q^{2} +1.73205i q^{3} +(3.16555 - 5.48289i) q^{4} +6.80030i q^{5} +(-2.78358 - 4.82130i) q^{6} +(9.81487 + 5.66662i) q^{7} +7.49262i q^{8} -3.00000 q^{9} +(-10.9288 - 18.9292i) q^{10} +(14.2778 + 8.24332i) q^{11} +(9.49665 + 5.48289i) q^{12} +(14.8562 - 8.57724i) q^{13} -36.4273 q^{14} -11.7785 q^{15} +(0.620797 + 1.07525i) q^{16} +(11.5774 + 20.0526i) q^{17} +(8.35074 - 4.82130i) q^{18} +(1.69094 + 2.92880i) q^{19} +(37.2853 + 21.5267i) q^{20} +(-9.81487 + 16.9999i) q^{21} -52.9914 q^{22} +(-20.3759 - 35.2921i) q^{23} -12.9776 q^{24} -21.2441 q^{25} +(-27.5690 + 47.7509i) q^{26} -5.19615i q^{27} +(62.1389 - 35.8759i) q^{28} +(3.45557 - 5.98522i) q^{29} +(32.7863 - 18.9292i) q^{30} +(-32.4604 - 18.7410i) q^{31} +(-29.4113 - 16.9806i) q^{32} +(-14.2778 + 24.7300i) q^{33} +(-64.4530 - 37.2120i) q^{34} +(-38.5347 + 66.7441i) q^{35} +(-9.49665 + 16.4487i) q^{36} +(-13.3240 - 23.0778i) q^{37} +(-9.41375 - 5.43503i) q^{38} +(14.8562 + 25.7317i) q^{39} -50.9521 q^{40} +(16.0419 + 9.26178i) q^{41} -63.0940i q^{42} -0.773007i q^{43} +(90.3945 - 52.1893i) q^{44} -20.4009i q^{45} +(113.436 + 65.4923i) q^{46} +(-7.84438 + 13.5869i) q^{47} +(-1.86239 + 1.07525i) q^{48} +(39.7212 + 68.7991i) q^{49} +(59.1347 - 34.1414i) q^{50} +(-34.7321 + 20.0526i) q^{51} -108.607i q^{52} -70.3521i q^{53} +(8.35074 + 14.4639i) q^{54} +(-56.0571 + 97.0937i) q^{55} +(-42.4578 + 73.5391i) q^{56} +(-5.07283 + 2.92880i) q^{57} +22.2138i q^{58} -5.22640 q^{59} +(-37.2853 + 64.5801i) q^{60} +(-15.8223 + 9.13503i) q^{61} +120.475 q^{62} +(-29.4446 - 16.9999i) q^{63} +104.192 q^{64} +(58.3278 + 101.027i) q^{65} -91.7838i q^{66} +(64.6341 - 17.6473i) q^{67} +146.595 q^{68} +(61.1277 - 35.2921i) q^{69} -247.717i q^{70} +(54.5452 - 94.4750i) q^{71} -22.4779i q^{72} +(-41.0503 - 71.1011i) q^{73} +(74.1768 + 42.8260i) q^{74} -36.7959i q^{75} +21.4110 q^{76} +(93.4235 + 161.814i) q^{77} +(-82.7069 - 47.7509i) q^{78} +(99.9083 + 57.6821i) q^{79} +(-7.31204 + 4.22161i) q^{80} +9.00000 q^{81} -59.5385 q^{82} +(-48.3092 - 83.6740i) q^{83} +(62.1389 + 107.628i) q^{84} +(-136.363 + 78.7295i) q^{85} +(1.24230 + 2.15173i) q^{86} +(10.3667 + 5.98522i) q^{87} +(-61.7641 + 106.978i) q^{88} -130.895 q^{89} +(32.7863 + 56.7876i) q^{90} +194.416 q^{91} -258.004 q^{92} +(32.4604 - 56.2231i) q^{93} -50.4268i q^{94} +(-19.9167 + 11.4989i) q^{95} +(29.4113 - 50.9418i) q^{96} +(-49.6133 + 28.6442i) q^{97} +(-221.134 - 127.672i) q^{98} +(-42.8335 - 24.7300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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