LMFDB - Embedded newform 201.3.h.a.97.10

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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			97.10
Character	$\chi$	$=$	201.97
Dual form			201.3.h.a.172.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.82230 - 1.62946i) q^{2} -1.73205i q^{3} +(3.31026 - 5.73353i) q^{4} -4.04184i q^{5} +(-2.82230 - 4.88837i) q^{6} +(7.82069 + 4.51528i) q^{7} -8.54003i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(2.82230 - 1.62946i) q^{2} -1.73205i q^{3} +(3.31026 - 5.73353i) q^{4} -4.04184i q^{5} +(-2.82230 - 4.88837i) q^{6} +(7.82069 + 4.51528i) q^{7} -8.54003i q^{8} -3.00000 q^{9} +(-6.58601 - 11.4073i) q^{10} +(-3.39408 - 1.95957i) q^{11} +(-9.93077 - 5.73353i) q^{12} +(-11.9123 + 6.87758i) q^{13} +29.4298 q^{14} -7.00068 q^{15} +(-0.674573 - 1.16839i) q^{16} +(2.20601 + 3.82093i) q^{17} +(-8.46690 + 4.88837i) q^{18} +(-0.977337 - 1.69280i) q^{19} +(-23.1740 - 13.3795i) q^{20} +(7.82069 - 13.5458i) q^{21} -12.7721 q^{22} +(-12.0492 - 20.8698i) q^{23} -14.7918 q^{24} +8.66350 q^{25} +(-22.4134 + 38.8212i) q^{26} +5.19615i q^{27} +(51.7770 - 29.8934i) q^{28} +(-7.80127 + 13.5122i) q^{29} +(-19.7580 + 11.4073i) q^{30} +(30.3317 + 17.5120i) q^{31} +(25.7758 + 14.8817i) q^{32} +(-3.39408 + 5.87871i) q^{33} +(12.4521 + 7.18921i) q^{34} +(18.2500 - 31.6100i) q^{35} +(-9.93077 + 17.2006i) q^{36} +(19.2446 + 33.3326i) q^{37} +(-5.51668 - 3.18506i) q^{38} +(11.9123 + 20.6327i) q^{39} -34.5174 q^{40} +(19.8866 + 11.4816i) q^{41} -50.9739i q^{42} -14.4133i q^{43} +(-22.4705 + 12.9734i) q^{44} +12.1255i q^{45} +(-68.0129 - 39.2673i) q^{46} +(-6.24913 + 10.8238i) q^{47} +(-2.02372 + 1.16839i) q^{48} +(16.2754 + 28.1899i) q^{49} +(24.4510 - 14.1168i) q^{50} +(6.61804 - 3.82093i) q^{51} +91.0662i q^{52} -62.8612i q^{53} +(8.46690 + 14.6651i) q^{54} +(-7.92028 + 13.7183i) q^{55} +(38.5606 - 66.7889i) q^{56} +(-2.93201 + 1.69280i) q^{57} +50.8473i q^{58} -85.0717 q^{59} +(-23.1740 + 40.1386i) q^{60} +(-89.9035 + 51.9058i) q^{61} +114.140 q^{62} +(-23.4621 - 13.5458i) q^{63} +102.393 q^{64} +(27.7981 + 48.1477i) q^{65} +22.1220i q^{66} +(29.0180 + 60.3901i) q^{67} +29.2099 q^{68} +(-36.1476 + 20.8698i) q^{69} -118.951i q^{70} +(34.5015 - 59.7583i) q^{71} +25.6201i q^{72} +(-55.1214 - 95.4731i) q^{73} +(108.628 + 62.7163i) q^{74} -15.0056i q^{75} -12.9409 q^{76} +(-17.6960 - 30.6504i) q^{77} +(67.2403 + 38.8212i) q^{78} +(-87.0062 - 50.2331i) q^{79} +(-4.72247 + 2.72652i) q^{80} +9.00000 q^{81} +74.8348 q^{82} +(10.4614 + 18.1196i) q^{83} +(-51.7770 - 89.6803i) q^{84} +(15.4436 - 8.91636i) q^{85} +(-23.4858 - 40.6786i) q^{86} +(23.4038 + 13.5122i) q^{87} +(-16.7348 + 28.9855i) q^{88} +63.0209 q^{89} +(19.7580 + 34.2219i) q^{90} -124.217 q^{91} -159.544 q^{92} +(30.3317 - 52.5360i) q^{93} +40.7308i q^{94} +(-6.84202 + 3.95024i) q^{95} +(25.7758 - 44.6450i) q^{96} +(-57.6084 + 33.2602i) q^{97} +(91.8683 + 53.0402i) q^{98} +(10.1822 + 5.87871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * 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 $

$2$	2.82230	−	1.62946i	1.41115	−	0.814728i	0.415654	−	0.909523i	$-0.363553\pi$
$2$	2.82230	−	1.62946i	1.41115	−	0.814728i	0.995497	+	0.0947946i	$0.0302194\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.31026	−	5.73353i	0.827564	−	1.43338i
$5$		−	4.04184i		−	0.808369i	−0.914678	−	0.404184i	$-0.867555\pi$
$5$		−	4.04184i		−	0.808369i	0.914678	−	0.404184i	$-0.132445\pi$
$6$	−2.82230	−	4.88837i	−0.470384	−	0.814728i
$7$	7.82069	+	4.51528i	1.11724	+	0.645039i	0.940695	−	0.339253i	$-0.110174\pi$
$7$	7.82069	+	4.51528i	1.11724	+	0.645039i	0.176546	+	0.984292i	$0.443508\pi$
$8$		−	8.54003i		−	1.06750i
$9$	−3.00000			−0.333333
$10$	−6.58601	−	11.4073i	−0.658601	−	1.14073i
$11$	−3.39408	−	1.95957i	−0.308552	−	0.178143i	0.337726	−	0.941244i	$-0.390342\pi$
$11$	−3.39408	−	1.95957i	−0.308552	−	0.178143i	−0.646278	+	0.763102i	$0.723676\pi$
$12$	−9.93077	−	5.73353i	−0.827564	−	0.477794i
$13$	−11.9123	+	6.87758i	−0.916332	+	0.529044i	−0.882463	−	0.470382i	$-0.844116\pi$
$13$	−11.9123	+	6.87758i	−0.916332	+	0.529044i	−0.0338686	+	0.999426i	$0.510783\pi$
$14$	29.4298			2.10213
$15$	−7.00068			−0.466712
$16$	−0.674573	−	1.16839i	−0.0421608	−	0.0730247i
$17$	2.20601	+	3.82093i	0.129766	+	0.224760i	0.923586	−	0.383392i	$-0.125244\pi$
$17$	2.20601	+	3.82093i	0.129766	+	0.224760i	−0.793820	+	0.608153i	$0.791911\pi$
$18$	−8.46690	+	4.88837i	−0.470384	+	0.271576i
$19$	−0.977337	−	1.69280i	−0.0514388	−	0.0890946i	0.839160	−	0.543885i	$-0.183047\pi$
$19$	−0.977337	−	1.69280i	−0.0514388	−	0.0890946i	−0.890598	+	0.454791i	$0.849714\pi$
$20$	−23.1740	−	13.3795i	−1.15870	−	0.668977i
$21$	7.82069	−	13.5458i	0.372414	−	0.645039i
$22$	−12.7721			−0.580552
$23$	−12.0492	−	20.8698i	−0.523878	−	0.907383i	−0.999614	−	0.0277949i	$-0.991151\pi$
$23$	−12.0492	−	20.8698i	−0.523878	−	0.907383i	0.475736	−	0.879588i	$-0.342182\pi$
$24$	−14.7918			−0.616323
$25$	8.66350			0.346540
$26$	−22.4134	+	38.8212i	−0.862055	+	1.49312i
$27$			5.19615i			0.192450i
$28$	51.7770	−	29.8934i	1.84918	−	1.06762i
$29$	−7.80127	+	13.5122i	−0.269009	+	0.465938i	−0.968606	−	0.248600i	$-0.920030\pi$
$29$	−7.80127	+	13.5122i	−0.269009	+	0.465938i	0.699597	+	0.714538i	$0.253363\pi$
$30$	−19.7580	+	11.4073i	−0.658601	+	0.380243i
$31$	30.3317	+	17.5120i	0.978441	+	0.564903i	0.901799	−	0.432156i	$-0.142247\pi$
$31$	30.3317	+	17.5120i	0.978441	+	0.564903i	0.0766416	+	0.997059i	$0.475580\pi$
$32$	25.7758	+	14.8817i	0.805494	+	0.465052i
$33$	−3.39408	+	5.87871i	−0.102851	+	0.178143i
$34$	12.4521	+	7.18921i	0.366237	+	0.211447i
$35$	18.2500	−	31.6100i	0.521430	−	0.903143i
$36$	−9.93077	+	17.2006i	−0.275855	+	0.477794i
$37$	19.2446	+	33.3326i	0.520123	+	0.900880i	0.999726	+	0.0233942i	$0.00744730\pi$
$37$	19.2446	+	33.3326i	0.520123	+	0.900880i	−0.479603	+	0.877486i	$0.659219\pi$
$38$	−5.51668	−	3.18506i	−0.145176	−	0.0838172i
$39$	11.9123	+	20.6327i	0.305444	+	0.529044i
$40$	−34.5174			−0.862936
$41$	19.8866	+	11.4816i	0.485040	+	0.280038i	0.722515	−	0.691356i	$-0.242986\pi$
$41$	19.8866	+	11.4816i	0.485040	+	0.280038i	−0.237474	+	0.971394i	$0.576320\pi$
$42$		−	50.9739i		−	1.21366i
$43$		−	14.4133i		−	0.335192i	−0.985856	−	0.167596i	$-0.946400\pi$
$43$		−	14.4133i		−	0.335192i	0.985856	−	0.167596i	$-0.0536004\pi$
$44$	−22.4705	+	12.9734i	−0.510694	+	0.294849i
$45$			12.1255i			0.269456i
$46$	−68.0129	−	39.2673i	−1.47854	−	0.853636i
$47$	−6.24913	+	10.8238i	−0.132960	+	0.230294i	−0.924816	−	0.380414i	$-0.875782\pi$
$47$	−6.24913	+	10.8238i	−0.132960	+	0.230294i	0.791856	+	0.610708i	$0.209115\pi$
$48$	−2.02372	+	1.16839i	−0.0421608	+	0.0243416i
$49$	16.2754	+	28.1899i	0.332152	+	0.575304i
$50$	24.4510	−	14.1168i	0.489020	−	0.282336i
$51$	6.61804	−	3.82093i	0.129766	−	0.0749202i
$52$			91.0662i			1.75127i
$53$		−	62.8612i		−	1.18606i	−0.805180	−	0.593030i	$-0.797931\pi$
$53$		−	62.8612i		−	1.18606i	0.805180	−	0.593030i	$-0.202069\pi$
$54$	8.46690	+	14.6651i	0.156795	+	0.271576i
$55$	−7.92028	+	13.7183i	−0.144005	+	0.249424i
$56$	38.5606	−	66.7889i	0.688582	−	1.19266i
$57$	−2.93201	+	1.69280i	−0.0514388	+	0.0296982i
$58$			50.8473i			0.876678i
$59$	−85.0717			−1.44189			−0.720946	−	0.692991i	$-0.756293\pi$
$59$	−85.0717			−1.44189			−0.720946	+	0.692991i	$0.756293\pi$
$60$	−23.1740	+	40.1386i	−0.386234	+	0.668977i
$61$	−89.9035	+	51.9058i	−1.47383	+	0.850915i	−0.999566	−	0.0294691i	$-0.990618\pi$
$61$	−89.9035	+	51.9058i	−1.47383	+	0.850915i	−0.474262	+	0.880384i	$0.657285\pi$
$62$	114.140			1.84097
$63$	−23.4621	−	13.5458i	−0.372414	−	0.215013i
$64$	102.393			1.59989
$65$	27.7981	+	48.1477i	0.427663	+	0.740734i
$66$			22.1220i			0.335182i
$67$	29.0180	+	60.3901i	0.433104	+	0.901344i
$67$	29.0180	+	60.3901i	0.433104	+	0.901344i
$68$	29.2099			0.429557
$69$	−36.1476	+	20.8698i	−0.523878	+	0.302461i
$70$		−	118.951i		−	1.69929i
$71$	34.5015	−	59.7583i	0.485936	−	0.841666i	−0.513933	−	0.857830i	$-0.671812\pi$
$71$	34.5015	−	59.7583i	0.485936	−	0.841666i	0.999869	+	0.0161639i	$0.00514535\pi$
$72$			25.6201i			0.355834i
$73$	−55.1214	−	95.4731i	−0.755088	−	1.30785i	−0.945331	−	0.326113i	$-0.894261\pi$
$73$	−55.1214	−	95.4731i	−0.755088	−	1.30785i	0.190243	−	0.981737i	$-0.439072\pi$
$74$	108.628	+	62.7163i	1.46794	+	0.847518i
$75$		−	15.0056i		−	0.200075i
$76$	−12.9409			−0.170276
$77$	−17.6960	−	30.6504i	−0.229818	−	0.398057i
$78$	67.2403	+	38.8212i	0.862055	+	0.497707i
$79$	−87.0062	−	50.2331i	−1.10134	−	0.635861i	−0.164771	−	0.986332i	$-0.552688\pi$
$79$	−87.0062	−	50.2331i	−1.10134	−	0.635861i	−0.936574	+	0.350470i	$0.886022\pi$
$80$	−4.72247	+	2.72652i	−0.0590308	+	0.0340815i
$81$	9.00000			0.111111
$82$	74.8348			0.912620
$83$	10.4614	+	18.1196i	0.126041	+	0.218309i	0.922139	−	0.386858i	$-0.126440\pi$
$83$	10.4614	+	18.1196i	0.126041	+	0.218309i	−0.796099	+	0.605167i	$0.793106\pi$
$84$	−51.7770	−	89.6803i	−0.616392	−	1.06762i
$85$	15.4436	−	8.91636i	0.181689	−	0.104898i
$86$	−23.4858	−	40.6786i	−0.273090	−	0.473007i
$87$	23.4038	+	13.5122i	0.269009	+	0.155313i
$88$	−16.7348	+	28.9855i	−0.190168	+	0.329381i
$89$	63.0209			0.708100			0.354050	−	0.935226i	$-0.384804\pi$
$89$	63.0209			0.708100			0.354050	+	0.935226i	$0.384804\pi$
$90$	19.7580	+	34.2219i	0.219534	+	0.380243i
$91$	−124.217			−1.36502
$92$	−159.544			−1.73417
$93$	30.3317	−	52.5360i	0.326147	−	0.564903i
$94$			40.7308i			0.433306i
$95$	−6.84202	+	3.95024i	−0.0720213	+	0.0415815i
$96$	25.7758	−	44.6450i	0.268498	−	0.465052i
$97$	−57.6084	+	33.2602i	−0.593901	+	0.342889i	−0.766638	−	0.642079i	$-0.778072\pi$
$97$	−57.6084	+	33.2602i	−0.593901	+	0.342889i	0.172738	+	0.984968i	$0.444739\pi$
$98$	91.8683	+	53.0402i	0.937432	+	0.541227i
$99$	10.1822	+	5.87871i	0.102851	+	0.0593809i
$100$	28.6784	−	49.6725i	0.286784	−	0.496725i
$101$	73.1701	+	42.2448i	0.724456	+	0.418265i	0.816391	−	0.577500i	$-0.195972\pi$
$101$	73.1701	+	42.2448i	0.724456	+	0.418265i	−0.0919344	+	0.995765i	$0.529305\pi$
$102$	12.4521	−	21.5676i	0.122079	−	0.211447i
$103$	−71.7243	+	124.230i	−0.696352	+	1.20612i	0.273370	+	0.961909i	$0.411862\pi$
$103$	−71.7243	+	124.230i	−0.696352	+	1.20612i	−0.969723	+	0.244209i	$0.921472\pi$
$104$	58.7347	+	101.731i	0.564756	+	0.978187i
$105$	−54.7501	−	31.6100i	−0.521430	−	0.301048i
$106$	−102.430	−	177.413i	−0.966317	−	1.67371i
$107$	2.33589			0.0218308			0.0109154	−	0.999940i	$-0.496525\pi$
$107$	2.33589			0.0218308			0.0109154	+	0.999940i	$0.496525\pi$
$108$	29.7923	+	17.2006i	0.275855	+	0.159265i
$109$		−	151.418i		−	1.38916i	−0.719418	−	0.694578i	$-0.755591\pi$
$109$		−	151.418i		−	1.38916i	0.719418	−	0.694578i	$-0.244409\pi$
$110$			51.6230i			0.469300i
$111$	57.7337	−	33.3326i	0.520123	−	0.300293i
$112$		−	12.1835i		−	0.108782i
$113$	105.226	+	60.7522i	0.931202	+	0.537630i	0.887192	−	0.461401i	$-0.152653\pi$
$113$	105.226	+	60.7522i	0.931202	+	0.537630i	0.0440108	+	0.999031i	$0.485986\pi$
$114$	−5.51668	+	9.55517i	−0.0483919	+	0.0838172i
$115$	−84.3525	+	48.7010i	−0.733500	+	0.423487i
$116$	51.6484	+	89.4576i	0.445245	+	0.771187i
$117$	35.7369	−	20.6327i	0.305444	−	0.176348i
$118$	−240.098	+	138.621i	−2.03473	+	1.17475i
$119$			39.8430i			0.334815i
$120$			59.7860i			0.498216i
$121$	−52.8202	−	91.4872i	−0.436530	−	0.756093i
$122$	−169.156	+	292.988i	−1.38653	+	2.40154i
$123$	19.8866	−	34.4447i	0.161680	−	0.280038i
$124$	200.811	−	115.938i	1.61944	−	0.934987i
$125$		−	136.063i		−	1.08850i
$126$	−88.2893			−0.700709
$127$	−106.733	+	184.867i	−0.840417	+	1.45564i	0.0491263	+	0.998793i	$0.484356\pi$
$127$	−106.733	+	184.867i	−0.840417	+	1.45564i	−0.889543	+	0.456852i	$0.848977\pi$
$128$	185.880	−	107.318i	1.45219	−	0.838421i
$129$	−24.9645			−0.193523
$130$	156.909	+	90.5915i	1.20699	+	0.696858i
$131$	−199.752			−1.52482			−0.762410	−	0.647094i	$-0.775984\pi$
$131$	−199.752			−1.52482			−0.762410	+	0.647094i	$0.775984\pi$
$132$	22.4705	+	38.9201i	0.170231	+	0.294849i
$133$		−	17.6518i		−	0.132720i
$134$	180.300	+	123.155i	1.34553	+	0.919070i
$135$	21.0020			0.155571
$136$	32.6308	−	18.8394i	0.239933	−	0.138525i
$137$		−	101.532i		−	0.741111i	−0.928810	−	0.370555i	$-0.879167\pi$
$137$		−	101.532i		−	0.741111i	0.928810	−	0.370555i	$-0.120833\pi$
$138$	−68.0129	+	117.802i	−0.492847	+	0.853636i
$139$			48.8623i			0.351528i	0.984432	+	0.175764i	$0.0562395\pi$
$139$			48.8623i			0.351528i	−0.984432	+	0.175764i	$0.943761\pi$
$140$	−120.825	−	209.274i	−0.863033	−	1.49482i
$141$	18.7474	+	10.8238i	0.132960	+	0.0767646i
$142$		−	224.875i		−	1.58362i
$143$	53.9084			0.376982
$144$	2.02372	+	3.50518i	0.0140536	+	0.0243416i
$145$	54.6142	+	31.5315i	0.376649	+	0.217459i
$146$	−311.138	−	179.636i	−2.13109	−	1.23038i
$147$	48.8263	−	28.1899i	0.332152	−	0.191768i
$148$	254.818			1.72174
$149$	−207.247			−1.39092			−0.695461	−	0.718564i	$-0.744800\pi$
$149$	−207.247			−1.39092			−0.695461	+	0.718564i	$0.744800\pi$
$150$	−24.4510	−	42.3504i	−0.163007	−	0.282336i
$151$	49.7696	+	86.2035i	0.329600	+	0.570884i	0.982432	−	0.186618i	$-0.0597528\pi$
$151$	49.7696	+	86.2035i	0.329600	+	0.570884i	−0.652833	+	0.757502i	$0.726419\pi$
$152$	−14.4565	+	8.34648i	−0.0951087	+	0.0549111i
$153$	−6.61804	−	11.4628i	−0.0432552	−	0.0749202i
$154$	−99.8869	−	57.6697i	−0.648616	−	0.374479i
$155$	70.7807	−	122.596i	0.456650	−	0.790941i
$156$	157.731			1.01110
$157$	−57.0092	−	98.7428i	−0.363116	−	0.628935i	0.625356	−	0.780340i	$-0.284954\pi$
$157$	−57.0092	−	98.7428i	−0.363116	−	0.628935i	−0.988472	+	0.151404i	$0.951620\pi$
$158$	−327.410			−2.07222
$159$	−108.879			−0.684773
$160$	60.1494	−	104.182i	0.375934	−	0.651136i
$161$		−	217.622i		−	1.35169i
$162$	25.4007	−	14.6651i	0.156795	−	0.0905254i
$163$	30.6246	−	53.0434i	0.187881	−	0.325420i	−0.756662	−	0.653806i	$-0.773171\pi$
$163$	30.6246	−	53.0434i	0.187881	−	0.325420i	0.944544	+	0.328386i	$0.106505\pi$
$164$	131.660	−	76.0138i	0.802804	−	0.463499i
$165$	23.7608	+	13.7183i	0.144005	+	0.0831413i
$166$	59.0503	+	34.0927i	0.355725	+	0.205378i
$167$	113.737	−	196.999i	0.681063	−	1.17964i	−0.293594	−	0.955930i	$-0.594851\pi$
$167$	113.737	−	196.999i	0.681063	−	1.17964i	0.974657	−	0.223705i	$-0.0718152\pi$
$168$	−115.682	−	66.7889i	−0.688582	−	0.397553i
$169$	10.1021	−	17.4973i	0.0597756	−	0.103534i
$170$	29.0576	−	50.3293i	0.170927	−	0.296055i
$171$	2.93201	+	5.07839i	0.0171463	+	0.0296982i
$172$	−82.6389	−	47.7116i	−0.480459	−	0.277393i
$173$	−152.016	−	263.300i	−0.878706	−	1.52196i	−0.852762	−	0.522299i	$-0.825074\pi$
$173$	−152.016	−	263.300i	−0.878706	−	1.52196i	−0.0259436	−	0.999663i	$-0.508259\pi$
$174$	88.0701			0.506150
$175$	67.7545	+	39.1181i	0.387169	+	0.223532i
$176$			5.28749i			0.0300426i
$177$			147.348i			0.832477i
$178$	177.864	−	102.690i	0.999236	−	0.576909i
$179$			231.441i			1.29296i	0.762929	+	0.646482i	$0.223761\pi$
$179$			231.441i			1.29296i	−0.762929	+	0.646482i	$0.776239\pi$
$180$	69.5221	+	40.1386i	0.386234	+	0.222992i
$181$	−14.5833	+	25.2591i	−0.0805710	+	0.139553i	−0.903495	−	0.428598i	$-0.859008\pi$
$181$	−14.5833	+	25.2591i	−0.0805710	+	0.139553i	0.822924	+	0.568151i	$0.192341\pi$
$182$	−350.577	+	202.406i	−1.92625	+	1.11212i
$183$	89.9035	+	155.717i	0.491276	+	0.850915i
$184$	−178.229	+	102.900i	−0.968634	+	0.559241i
$185$	134.725	−	77.7835i	0.728243	−	0.420451i
$186$		−	197.696i		−	1.06288i
$187$		−	17.2914i		−	0.0924671i
$188$	41.3725	+	71.6592i	0.220066	+	0.381166i
$189$	−23.4621	+	40.6375i	−0.124138	+	0.215013i
$190$	−12.8735	+	22.2975i	−0.0677552	+	0.117356i
$191$	114.789	−	66.2737i	0.600991	−	0.346982i	−0.168440	−	0.985712i	$-0.553873\pi$
$191$	114.789	−	66.2737i	0.600991	−	0.346982i	0.769431	+	0.638729i	$0.220540\pi$
$192$		−	177.349i		−	0.923695i
$193$	379.448			1.96605			0.983027	−	0.183460i	$-0.0587298\pi$
$193$	379.448			1.96605			0.983027	+	0.183460i	$0.0587298\pi$
$194$	−108.392	+	187.741i	−0.558722	+	0.967735i
$195$	83.3942	−	48.1477i	0.427663	−	0.246911i
$196$	215.503			1.09951
$197$	−10.2380	−	5.91090i	−0.0519694	−	0.0300046i	0.473790	−	0.880638i	$-0.342886\pi$
$197$	−10.2380	−	5.91090i	−0.0519694	−	0.0300046i	−0.525760	+	0.850633i	$0.676219\pi$
$198$	38.3164			0.193517
$199$	−9.48709	−	16.4321i	−0.0476738	−	0.0825735i	0.841204	−	0.540718i	$-0.181847\pi$
$199$	−9.48709	−	16.4321i	−0.0476738	−	0.0825735i	−0.888878	+	0.458145i	$0.848514\pi$
$200$		−	73.9865i		−	0.369933i
$201$	104.599	−	50.2606i	0.520391	−	0.250053i
$202$	275.344			1.36309
$203$	−122.023	+	70.4498i	−0.601096	+	0.347043i
$204$		−	50.5930i		−	0.248005i
$205$	46.4067	−	80.3787i	0.226374	−	0.392091i
$206$			467.487i			2.26935i
$207$	36.1476	+	62.6094i	0.174626	+	0.302461i
$208$	16.0714	+	9.27885i	0.0772665	+	0.0446099i
$209$			7.66064i			0.0366538i
$210$	−206.028			−0.981088
$211$	−2.54221	−	4.40323i	−0.0120484	−	0.0208684i	0.859938	−	0.510398i	$-0.170502\pi$
$211$	−2.54221	−	4.40323i	−0.0120484	−	0.0208684i	−0.871987	+	0.489530i	$0.837169\pi$
$212$	−360.417	−	208.087i	−1.70008	−	0.981542i
$213$	−103.504	−	59.7583i	−0.485936	−	0.280555i
$214$	6.59259	−	3.80623i	0.0308065	−	0.0177861i
$215$	−58.2561			−0.270959
$216$	44.3753			0.205441
$217$	158.143	+	273.912i	0.728769	+	1.26227i
$218$	−246.729	−	427.347i	−1.13178	−	1.96031i
$219$	−165.364	+	95.4731i	−0.755088	+	0.435950i
$220$	52.4363	+	90.8223i	0.238347	+	0.412829i
$221$	−52.5574	−	30.3441i	−0.237816	−	0.137303i
$222$	108.628	−	188.149i	0.489315	−	0.847518i
$223$	−98.7411			−0.442785			−0.221393	−	0.975185i	$-0.571060\pi$
$223$	−98.7411			−0.442785			−0.221393	+	0.975185i	$0.571060\pi$
$224$	134.390	+	232.770i	0.599954	+	1.03915i
$225$	−25.9905			−0.115513
$226$	395.972			1.75209
$227$	−180.822	+	313.192i	−0.796571	+	1.37970i	0.125266	+	0.992123i	$0.460022\pi$
$227$	−180.822	+	313.192i	−0.796571	+	1.37970i	−0.921837	+	0.387578i	$0.873312\pi$
$228$			22.4144i			0.0983086i
$229$	−239.337	+	138.181i	−1.04514	+	0.603412i	−0.921285	−	0.388888i	$-0.872859\pi$
$229$	−239.337	+	138.181i	−1.04514	+	0.603412i	−0.123856	+	0.992300i	$0.539526\pi$
$230$	−158.712	+	274.898i	−0.690053	+	1.19521i
$231$	−53.0880	+	30.6504i	−0.229818	+	0.132686i
$232$	115.394	+	66.6230i	0.497390	+	0.287168i
$233$	105.271	+	60.7781i	0.451806	+	0.260850i	0.708593	−	0.705618i	$-0.249330\pi$
$233$	105.271	+	60.7781i	0.451806	+	0.260850i	−0.256787	+	0.966468i	$0.582664\pi$
$234$	67.2403	−	116.464i	0.287352	−	0.497707i
$235$	43.7482	+	25.2580i	0.186162	+	0.107481i
$236$	−281.609	+	487.761i	−1.19326	+	2.06679i
$237$	−87.0062	+	150.699i	−0.367115	+	0.635861i
$238$	64.9225	+	112.449i	0.272784	+	0.472475i
$239$	259.730	+	149.955i	1.08674	+	0.627428i	0.932706	−	0.360638i	$-0.117441\pi$
$239$	259.730	+	149.955i	1.08674	+	0.627428i	0.154032	+	0.988066i	$0.450774\pi$
$240$	4.72247	+	8.17955i	0.0196769	+	0.0340815i
$241$	185.903			0.771383			0.385691	−	0.922628i	$-0.373963\pi$
$241$	185.903			0.771383			0.385691	+	0.922628i	$0.373963\pi$
$242$	−298.149	−	172.136i	−1.23202	−	0.711307i
$243$		−	15.5885i		−	0.0641500i
$244$			687.286i			2.81675i
$245$	113.939	−	65.7828i	0.465057	−	0.268501i
$246$		−	129.618i		−	0.526901i
$247$	23.2847	+	13.4434i	0.0942699	+	0.0544268i
$248$	149.553	−	259.033i	0.603036	−	1.04449i
$249$	31.3841	−	18.1196i	0.126041	−	0.0727696i
$250$	−221.708	−	384.010i	−0.886832	−	1.53604i
$251$	150.808	−	87.0688i	0.600827	−	0.346888i	−0.168540	−	0.985695i	$-0.553905\pi$
$251$	150.808	−	87.0688i	0.600827	−	0.346888i	0.769367	+	0.638807i	$0.220572\pi$
$252$	−155.331	+	89.6803i	−0.616392	+	0.355874i
$253$			94.4450i			0.373300i
$254$			695.667i			2.73884i
$255$	−15.4436	−	26.7491i	−0.0605631	−	0.104898i
$256$	144.954	−	251.068i	0.566226	−	0.980733i
$257$	68.8559	−	119.262i	0.267922	−	0.464054i	−0.700403	−	0.713747i	$-0.746996\pi$
$257$	68.8559	−	119.262i	0.267922	−	0.464054i	0.968325	+	0.249693i	$0.0803298\pi$
$258$	−70.4573	+	40.6786i	−0.273090	+	0.157669i
$259$			347.578i			1.34200i
$260$	368.075			1.41567
$261$	23.4038	−	40.5366i	0.0896697	−	0.155313i
$262$	−563.759	+	325.486i	−2.15175	+	1.24231i
$263$	−273.578			−1.04022			−0.520111	−	0.854099i	$-0.674109\pi$
$263$	−273.578			−1.04022			−0.520111	+	0.854099i	$0.674109\pi$
$264$	50.2043	+	28.9855i	0.190168	+	0.109794i
$265$	−254.075			−0.958775
$266$	−28.7628	−	49.8186i	−0.108131	−	0.187288i
$267$		−	109.155i		−	0.408822i
$268$	442.305	+	33.5312i	1.65039	+	0.125116i
$269$	55.2408			0.205356			0.102678	−	0.994715i	$-0.467259\pi$
$269$	55.2408			0.205356			0.102678	+	0.994715i	$0.467259\pi$
$270$	59.2741	−	34.2219i	0.219534	−	0.126748i
$271$		−	81.6125i		−	0.301153i	−0.988598	−	0.150577i	$-0.951887\pi$
$271$		−	81.6125i		−	0.301153i	0.988598	−	0.150577i	$-0.0481130\pi$
$272$	2.97623	−	5.15499i	0.0109420	−	0.0189522i
$273$			215.149i			0.788093i
$274$	−165.442	−	286.554i	−0.603804	−	1.04582i
$275$	−29.4046	−	16.9767i	−0.106926	−	0.0617336i
$276$			276.338i			1.00122i
$277$	460.012			1.66069			0.830346	−	0.557248i	$-0.188143\pi$
$277$	460.012			1.66069			0.830346	+	0.557248i	$0.188143\pi$
$278$	79.6190	+	137.904i	0.286399	+	0.496058i
$279$	−90.9950	−	52.5360i	−0.326147	−	0.188301i
$280$	−269.950	−	155.856i	−0.964108	−	0.556628i
$281$	435.448	−	251.406i	1.54964	−	0.894683i	0.551467	−	0.834197i	$-0.314068\pi$
$281$	435.448	−	251.406i	1.54964	−	0.894683i	0.998169	−	0.0604858i	$-0.0192650\pi$
$282$	70.5477			0.250169
$283$	315.874			1.11616			0.558081	−	0.829787i	$-0.311538\pi$
$283$	315.874			1.11616			0.558081	+	0.829787i	$0.311538\pi$
$284$	−228.418	−	395.631i	−0.804287	−	1.39307i
$285$	6.84202	+	11.8507i	0.0240071	+	0.0415815i
$286$	152.146	−	87.8413i	0.531978	−	0.307138i
$287$	103.685	+	179.587i	0.361271	+	0.625740i
$288$	−77.3275	−	44.6450i	−0.268498	−	0.155017i
$289$	134.767	−	233.423i	0.466322	−	0.807693i
$290$	205.517			0.708679
$291$	57.6084	+	99.7806i	0.197967	+	0.342889i
$292$	−729.864			−2.49953
$293$	41.2234			0.140694			0.0703470	−	0.997523i	$-0.477589\pi$
$293$	41.2234			0.140694			0.0703470	+	0.997523i	$0.477589\pi$
$294$	91.8683	−	159.121i	0.312477	−	0.541227i
$295$			343.846i			1.16558i
$296$	284.661	−	164.349i	0.961692	−	0.555233i
$297$	10.1822	−	17.6361i	0.0342836	−	0.0593809i
$298$	−584.914	+	337.700i	−1.96280	+	1.13322i
$299$	287.067	+	165.738i	0.960092	+	0.554309i
$300$	−86.0352	−	49.6725i	−0.286784	−	0.165575i
$301$	65.0798	−	112.722i	0.216212	−	0.374490i
$302$	280.930	+	162.195i	0.930230	+	0.537069i
$303$	73.1701	−	126.734i	0.241485	−	0.418265i
$304$	−1.31857	+	2.28383i	−0.00433740	+	0.00751260i
$305$	209.795	+	363.376i	0.687853	+	1.19140i
$306$	−37.3562	−	21.5676i	−0.122079	−	0.0704824i
$307$	−271.955	−	471.041i	−0.885848	−	1.53433i	−0.844738	−	0.535180i	$-0.820244\pi$
$307$	−271.955	−	471.041i	−0.885848	−	1.53433i	−0.0411101	−	0.999155i	$-0.513089\pi$
$308$	−234.313			−0.760757
$309$	215.173	+	124.230i	0.696352	+	0.402039i
$310$		−	461.336i		−	1.48818i
$311$			77.8965i			0.250471i	0.992127	+	0.125235i	$0.0399686\pi$
$311$			77.8965i			0.250471i	−0.992127	+	0.125235i	$0.960031\pi$
$312$	176.204	−	101.731i	0.564756	−	0.326062i
$313$			220.571i			0.704700i	0.935868	+	0.352350i	$0.114617\pi$
$313$			220.571i			0.704700i	−0.935868	+	0.352350i	$0.885383\pi$
$314$	−321.794	−	185.788i	−1.02482	−	0.591681i
$315$	−54.7501	+	94.8300i	−0.173810	+	0.301048i
$316$	−576.026	+	332.569i	−1.82287	+	1.05243i
$317$	−0.998197	−	1.72893i	−0.00314889	−	0.00545403i	0.864447	−	0.502725i	$-0.167669\pi$
$317$	−0.998197	−	1.72893i	−0.00314889	−	0.00545403i	−0.867596	+	0.497271i	$0.834336\pi$
$318$	−307.289	+	177.413i	−0.966317	+	0.557904i
$319$	52.9562	−	30.5743i	0.166007	−	0.0958441i
$320$		−	413.856i		−	1.29330i
$321$		−	4.04588i		−	0.0126040i
$322$	−354.605	−	614.194i	−1.10126	−	1.90743i
$323$	4.31204	−	7.46867i	0.0133500	−	0.0231228i
$324$	29.7923	−	51.6018i	0.0919516	−	0.159265i
$325$	−103.202	+	59.5839i	−0.317546	+	0.183335i
$326$		−	199.606i		−	0.612288i
$327$	−262.264			−0.802029
$328$	98.0528	−	169.832i	0.298942	−	0.517782i
$329$	−97.7450	+	56.4331i	−0.297097	+	0.171529i
$330$	89.4136			0.270950
$331$	−153.282	−	88.4973i	−0.463087	−	0.267363i	0.250254	−	0.968180i	$-0.419486\pi$
$331$	−153.282	−	88.4973i	−0.463087	−	0.267363i	−0.713341	+	0.700817i	$0.752819\pi$
$332$	138.519			0.417227
$333$	−57.7337	−	99.9977i	−0.173374	−	0.300293i
$334$		−	741.321i		−	2.21952i
$335$	244.087	−	117.286i	0.728618	−	0.350108i
$336$	−21.1025			−0.0628050
$337$	143.431	−	82.8098i	0.425611	−	0.245726i	−0.271864	−	0.962336i	$-0.587640\pi$
$337$	143.431	−	82.8098i	0.425611	−	0.245726i	0.697475	+	0.716609i	$0.254307\pi$
$338$		−	65.8436i		−	0.194804i
$339$	105.226	−	182.257i	0.310401	−	0.537630i
$340$		−	118.062i		−	0.347241i
$341$	−68.6319	−	118.874i	−0.201267	−	0.348604i
$342$	16.5500	+	9.55517i	0.0483919	+	0.0279391i
$343$		−	148.545i		−	0.433075i
$344$	−123.090			−0.357819
$345$	84.3525	+	146.103i	0.244500	+	0.423487i
$346$	−858.070	−	495.407i	−2.47997	−	1.43181i
$347$	−376.654	−	217.461i	−1.08546	−	0.626690i	−0.153095	−	0.988212i	$-0.548924\pi$
$347$	−376.654	−	217.461i	−1.08546	−	0.626690i	−0.932364	+	0.361522i	$0.882257\pi$
$348$	154.945	−	89.4576i	0.445245	−	0.257062i
$349$	592.323			1.69720			0.848600	−	0.529035i	$-0.177446\pi$
$349$	592.323			1.69720			0.848600	+	0.529035i	$0.177446\pi$
$350$	254.965			0.728471
$351$	−35.7369	−	61.8982i	−0.101815	−	0.176348i
$352$	−58.3234	−	101.019i	−0.165691	−	0.286986i
$353$	−495.070	+	285.829i	−1.40246	+	0.809713i	−0.994645	−	0.103350i	$-0.967044\pi$
$353$	−495.070	+	285.829i	−1.40246	+	0.809713i	−0.407819	+	0.913063i	$0.633710\pi$
$354$	240.098	+	415.862i	0.678243	+	1.17475i
$355$	−241.534	−	139.450i	−0.680377	−	0.392816i
$356$	208.615	−	361.332i	0.585998	−	1.01498i
$357$	69.0102			0.193306
$358$	377.123	+	653.195i	1.05342	+	1.82457i
$359$	485.484			1.35232			0.676162	−	0.736753i	$-0.263642\pi$
$359$	485.484			1.35232			0.676162	+	0.736753i	$0.263642\pi$
$360$	103.552			0.287645
$361$	178.590	−	309.326i	0.494708	−	0.856860i
$362$			95.0517i			0.262574i
$363$	−158.461	+	91.4872i	−0.436530	+	0.252031i
$364$	−411.189	+	712.200i	−1.12964	+	1.95659i
$365$	−385.887	+	222.792i	−1.05723	+	0.610389i
$366$	507.469	+	292.988i	1.38653	+	0.800513i
$367$	108.867	+	62.8543i	0.296640	+	0.171265i	0.640932	−	0.767597i	$-0.278548\pi$
$367$	108.867	+	62.8543i	0.296640	+	0.171265i	−0.344293	+	0.938862i	$0.611881\pi$
$368$	−16.2561	+	28.1564i	−0.0441742	+	0.0765120i
$369$	−59.6599	−	34.4447i	−0.161680	−	0.0933460i
$370$	253.490	−	439.057i	0.685107	−	1.18664i
$371$	283.836	−	491.618i	0.765056	−	1.32512i
$372$	−200.811	−	347.815i	−0.539815	−	0.934987i
$373$	500.193	+	288.787i	1.34100	+	0.774227i	0.986954	−	0.161000i	$-0.0514720\pi$
$373$	500.193	+	288.787i	1.34100	+	0.774227i	0.354047	+	0.935228i	$0.384805\pi$
$374$	−28.1755	−	48.8014i	−0.0753356	−	0.130485i
$375$	−235.667			−0.628446
$376$	92.4356	+	53.3677i	0.245839	+	0.141935i
$377$		−	214.615i		−	0.569271i
$378$			152.922i			0.404555i
$379$	36.4230	−	21.0288i	0.0961028	−	0.0554850i	−0.451178	−	0.892434i	$-0.648996\pi$
$379$	36.4230	−	21.0288i	0.0961028	−	0.0554850i	0.547281	+	0.836949i	$0.315663\pi$
$380$			52.3053i			0.137645i
$381$	320.199	+	184.867i	0.840417	+	0.485215i
$382$	215.980	−	374.088i	0.565393	−	0.979289i
$383$	−362.516	+	209.299i	−0.946516	+	0.546471i	−0.891997	−	0.452041i	$-0.850696\pi$
$383$	−362.516	+	209.299i	−0.946516	+	0.546471i	−0.0545191	+	0.998513i	$0.517363\pi$
$384$	−185.880	−	321.954i	−0.484062	−	0.838421i
$385$	−123.884	+	71.5245i	−0.321777	+	0.185778i
$386$	1070.92	−	618.295i	2.77440	−	1.60180i
$387$			43.2398i			0.111731i
$388$			440.399i			1.13505i
$389$	−126.119	−	218.445i	−0.324213	−	0.561554i	0.657139	−	0.753769i	$-0.271766\pi$
$389$	−126.119	−	218.445i	−0.324213	−	0.561554i	−0.981353	+	0.192215i	$0.938433\pi$
$390$	156.909	−	271.775i	0.402331	−	0.696858i
$391$	53.1614	−	92.0782i	0.135963	−	0.235494i
$392$	240.742	−	138.993i	0.614138	−	0.354573i
$393$			345.980i			0.880356i
$394$	−38.5262			−0.0977823
$395$	−203.034	+	351.665i	−0.514010	+	0.890292i
$396$	67.4116	−	38.9201i	0.170231	−	0.0982830i
$397$	−140.858			−0.354805			−0.177403	−	0.984138i	$-0.556769\pi$
$397$	−140.858			−0.354805			−0.177403	+	0.984138i	$0.556769\pi$
$398$	−53.5509	−	30.9176i	−0.134550	−	0.0776824i
$399$	−30.5738			−0.0766260
$400$	−5.84416	−	10.1224i	−0.0146104	−	0.0253060i
$401$		−	383.320i		−	0.955910i	−0.878384	−	0.477955i	$-0.841378\pi$
$401$		−	383.320i		−	0.955910i	0.878384	−	0.477955i	$-0.158622\pi$
$402$	213.311	−	312.289i	0.530626	−	0.776839i
$403$	−481.760			−1.19543
$404$	484.424	−	279.682i	1.19907	−	0.692282i
$405$		−	36.3766i		−	0.0898187i
$406$	−229.590	+	397.661i	−0.565492	+	0.979460i
$407$		−	150.844i		−	0.370625i
$408$	−32.6308	−	56.5182i	−0.0799775	−	0.138525i
$409$	−473.150	−	273.173i	−1.15685	−	0.667905i	−0.206299	−	0.978489i	$-0.566142\pi$
$409$	−473.150	−	273.173i	−1.15685	−	0.667905i	−0.950546	+	0.310584i	$0.899475\pi$
$410$		−	302.471i		−	0.737733i
$411$	−175.859			−0.427881
$412$	474.852	+	822.467i	1.15255	+	1.99628i
$413$	−665.319	−	384.122i	−1.61094	−	0.930078i
$414$	204.039	+	117.802i	0.492847	+	0.284545i
$415$	73.2367	−	42.2833i	0.176474	−	0.101887i
$416$	−409.399			−0.984133
$417$	84.6320			0.202955
$418$	12.4827	+	21.6206i	0.0298629	+	0.0517240i
$419$	283.394	+	490.853i	0.676359	+	1.17149i	0.976070	+	0.217457i	$0.0697763\pi$
$419$	283.394	+	490.853i	0.676359	+	1.17149i	−0.299711	+	0.954030i	$0.596890\pi$
$420$	−362.474	+	209.274i	−0.863033	+	0.498272i
$421$	129.442	+	224.201i	0.307464	+	0.532544i	0.977807	−	0.209508i	$-0.0671862\pi$
$421$	129.442	+	224.201i	0.307464	+	0.532544i	−0.670343	+	0.742052i	$0.733853\pi$
$422$	−14.3498	−	8.28483i	−0.0340041	−	0.0196323i
$423$	18.7474	−	32.4714i	0.0443201	−	0.0767646i
$424$	−536.837			−1.26612
$425$	19.1118	+	33.1026i	0.0449689	+	0.0778885i
$426$	−389.494			−0.914306
$427$	−937.476			−2.19549
$428$	7.73240	−	13.3929i	0.0180664	−	0.0312919i
$429$		−	93.3720i		−	0.217650i
$430$	−164.416	+	94.9259i	−0.382364	+	0.220758i
$431$	32.5483	−	56.3753i	0.0755181	−	0.130801i	−0.825793	−	0.563973i	$-0.809272\pi$
$431$	32.5483	−	56.3753i	0.0755181	−	0.130801i	0.901311	+	0.433172i	$0.142606\pi$
$432$	6.07116	−	3.50518i	0.0140536	−	0.00811385i
$433$	215.622	+	124.489i	0.497971	+	0.287504i	0.727875	−	0.685709i	$-0.240508\pi$
$433$	215.622	+	124.489i	0.497971	+	0.287504i	−0.229904	+	0.973213i	$0.573841\pi$
$434$	892.654	+	515.374i	2.05681	+	1.18750i
$435$	54.6142	−	94.5945i	0.125550	−	0.217459i
$436$	−868.160	−	501.232i	−1.99119	−	1.14962i
$437$	−23.5522	+	40.7937i	−0.0538953	+	0.0933494i
$438$	−311.138	+	538.908i	−0.710362	+	1.23038i
$439$	62.5066	+	108.265i	0.142384	+	0.246616i	0.928394	−	0.371598i	$-0.121190\pi$
$439$	62.5066	+	108.265i	0.142384	+	0.246616i	−0.786010	+	0.618214i	$0.787857\pi$
$440$	117.155	+	67.6394i	0.266261	+	0.153726i
$441$	−48.8263	−	84.5696i	−0.110717	−	0.191768i
$442$	−197.777			−0.447460
$443$	−469.591	−	271.119i	−1.06002	−	0.612006i	−0.134586	−	0.990902i	$-0.542970\pi$
$443$	−469.591	−	271.119i	−1.06002	−	0.612006i	−0.925439	+	0.378896i	$0.876304\pi$
$444$		−	441.357i		−	0.994048i
$445$		−	254.721i		−	0.572406i
$446$	−278.677	+	160.894i	−0.624837	+	0.360750i
$447$			358.963i			0.803049i
$448$	800.782	+	462.332i	1.78746	+	1.03199i
$449$	−144.155	+	249.684i	−0.321058	+	0.556089i	−0.980707	−	0.195485i	$-0.937372\pi$
$449$	−144.155	+	249.684i	−0.321058	+	0.556089i	0.659648	+	0.751574i	$0.270705\pi$
$450$	−73.3530	+	42.3504i	−0.163007	+	0.0941120i
$451$	−44.9978	−	77.9386i	−0.0997735	−	0.172813i
$452$	696.649	−	402.211i	1.54126	−	0.889847i
$453$	149.309	−	86.2035i	0.329600	−	0.190295i
$454$			1178.56i			2.59596i
$455$			502.064i			1.10344i
$456$	14.4565	+	25.0394i	0.0317029	+	0.0549111i
$457$	314.736	−	545.139i	0.688701	−	1.19287i	−0.283557	−	0.958955i	$-0.591515\pi$
$457$	314.736	−	545.139i	0.688701	−	1.19287i	0.972258	−	0.233910i	$-0.0751521\pi$
$458$	−450.321	+	779.979i	−0.983234	+	1.70301i
$459$	−19.8541	+	11.4628i	−0.0432552	+	0.0249734i
$460$			644.851i			1.40185i
$461$	609.483			1.32209			0.661044	−	0.750347i	$-0.270114\pi$
$461$	609.483			1.32209			0.661044	+	0.750347i	$0.270114\pi$
$462$	−99.8869	+	173.009i	−0.216205	+	0.374479i
$463$	122.587	−	70.7757i	0.264767	−	0.152863i	−0.361740	−	0.932279i	$-0.617817\pi$
$463$	122.587	−	70.7757i	0.264767	−	0.152863i	0.626507	+	0.779416i	$0.284484\pi$
$464$	21.0501			0.0453666
$465$	−212.342	−	122.596i	−0.456650	−	0.263647i
$466$	396.141			0.850088
$467$	54.2233	+	93.9175i	0.116110	+	0.201108i	0.918223	−	0.396064i	$-0.129624\pi$
$467$	54.2233	+	93.9175i	0.116110	+	0.201108i	−0.802113	+	0.597172i	$0.796291\pi$
$468$		−	273.198i		−	0.583757i
$469$	−45.7374	+	603.316i	−0.0975212	+	1.28639i
$470$	164.627			0.350271
$471$	−171.028	+	98.7428i	−0.363116	+	0.209645i
$472$			726.514i			1.53923i
$473$	−28.2438	+	48.9197i	−0.0597120	+	0.103424i
$474$			567.091i			1.19640i
$475$	−8.46716	−	14.6655i	−0.0178256	−	0.0308748i
$476$	228.441	+	131.891i	0.479919	+	0.277081i
$477$			188.584i			0.395354i
$478$	977.383			2.04473
$479$	293.901	+	509.051i	0.613571	+	1.06274i	0.990633	+	0.136549i	$0.0436010\pi$
$479$	293.901	+	509.051i	0.613571	+	1.06274i	−0.377062	+	0.926188i	$0.623066\pi$
$480$	−180.448	−	104.182i	−0.375934	−	0.217045i
$481$	−458.494	−	264.712i	−0.953210	−	0.550336i
$482$	524.675	−	302.921i	1.08854	−	0.628467i
$483$	−376.932			−0.780397
$484$	−699.393			−1.44503
$485$	134.433	+	232.844i	0.277181	+	0.480091i
$486$	−25.4007	−	43.9953i	−0.0522648	−	0.0905254i
$487$	−50.7967	+	29.3275i	−0.104305	+	0.0602207i	−0.551245	−	0.834343i	$-0.685847\pi$
$487$	−50.7967	+	29.3275i	−0.104305	+	0.0602207i	0.446940	+	0.894564i	$0.352514\pi$
$488$	443.277	+	767.778i	0.908354	+	1.57332i
$489$	−91.8739	−	53.0434i	−0.187881	−	0.108473i
$490$	214.380	−	371.317i	0.437511	−	0.757791i
$491$	−796.350			−1.62189			−0.810947	−	0.585120i	$-0.801047\pi$
$491$	−796.350			−1.62189			−0.810947	+	0.585120i	$0.801047\pi$
$492$	−131.660	−	228.041i	−0.267601	−	0.463499i
$493$	−68.8388			−0.139632
$494$	87.6218			0.177372
$495$	23.7608	−	41.1550i	0.0480017	−	0.0831413i
$496$		−	47.2525i		−	0.0952670i
$497$	539.651	−	311.567i	1.08582	−	0.626896i
$498$	59.0503	−	102.278i	0.118575	−	0.205378i
$499$	714.778	−	412.677i	1.43242	−	0.827008i	0.435116	−	0.900375i	$-0.356707\pi$
$499$	714.778	−	412.677i	1.43242	−	0.827008i	0.997305	+	0.0733661i	$0.0233741\pi$
$500$	−780.119	−	450.402i	−1.56024	−	0.900804i
$501$	−341.212	−	196.999i	−0.681063	−	0.393212i
$502$	283.750	−	491.469i	0.565238	−	0.979021i
$503$	−351.637	−	203.018i	−0.699079	−	0.403613i	0.107925	−	0.994159i	$-0.465579\pi$
$503$	−351.637	−	203.018i	−0.699079	−	0.403613i	−0.807004	+	0.590546i	$0.798913\pi$
$504$	−115.682	+	200.367i	−0.229527	+	0.397553i
$505$	170.747	−	295.742i	0.338112	−	0.585628i
$506$	153.894	+	266.552i	0.304138	+	0.526783i
$507$	−30.3062	−	17.4973i	−0.0597756	−	0.0345115i
$508$	706.627	+	1223.91i	1.39100	+	2.40928i
$509$	−536.214			−1.05346			−0.526732	−	0.850031i	$-0.676583\pi$
$509$	−536.214			−1.05346			−0.526732	+	0.850031i	$0.676583\pi$
$510$	−87.1729	−	50.3293i	−0.170927	−	0.0986850i
$511$		−	995.553i		−	1.94825i
$512$		−	86.2421i		−	0.168442i
$513$	8.79603	−	5.07839i	0.0171463	−	0.00989940i
$514$		−	448.791i		−	0.873134i
$515$	502.119	+	289.898i	0.974988	+	0.562910i
$516$	−82.6389	+	143.135i	−0.160153	+	0.277393i
$517$	42.4200	−	24.4912i	0.0820504	−	0.0473718i
$518$	566.363	+	980.970i	1.09337	+	1.89376i
$519$	−456.048	+	263.300i	−0.878706	+	0.507321i
$520$	411.183	−	237.396i	0.790736	−	0.456531i
$521$		−	201.807i		−	0.387345i	−0.981066	−	0.193673i	$-0.937960\pi$
$521$		−	201.807i		−	0.387345i	0.981066	−	0.193673i	$-0.0620400\pi$
$522$		−	152.542i		−	0.292226i
$523$	−263.687	−	456.720i	−0.504182	−	0.873269i	−0.999988	−	0.00483613i	$-0.998461\pi$
$523$	−263.687	−	456.720i	−0.504182	−	0.873269i	0.495806	−	0.868433i	$-0.334873\pi$
$524$	−661.229	+	1145.28i	−1.26189	+	2.18565i
$525$	67.7545	−	117.354i	0.129056	−	0.223532i
$526$	−772.120	+	445.784i	−1.46791	+	0.847498i
$527$			154.527i			0.293220i
$528$	9.15820			0.0173451
$529$	−25.8661	+	44.8014i	−0.0488962	+	0.0846907i
$530$	−717.077	+	414.005i	−1.35298	+	0.781141i
$531$	255.215			0.480631
$532$	−101.207	−	58.4319i	−0.190239	−	0.109834i
$533$	−315.861			−0.592610
$534$	−177.864	−	308.070i	−0.333079	−	0.576909i
$535$		−	9.44131i		−	0.0176473i
$536$	515.733	−	247.814i	0.962188	−	0.462340i
$537$	400.867			0.746494
$538$	155.906	−	90.0126i	0.289789	−	0.167310i
$539$		−	127.571i		−	0.236682i
$540$	69.5221	−	120.416i	0.128745	−	0.222992i
$541$			261.832i			0.483978i	0.970279	+	0.241989i	$0.0777997\pi$
$541$			261.832i			0.483978i	−0.970279	+	0.241989i	$0.922200\pi$
$542$	−132.984	−	230.335i	−0.245358	−	0.424973i
$543$	43.7500	+	25.2591i	0.0805710	+	0.0465177i
$544$			131.317i			0.241391i
$545$	−612.008			−1.12295
$546$	350.577	+	607.217i	0.642082	+	1.11212i
$547$	347.428	+	200.587i	0.635151	+	0.366705i	0.782744	−	0.622344i	$-0.213819\pi$
$547$	347.428	+	200.587i	0.635151	+	0.366705i	−0.147593	+	0.989048i	$0.547153\pi$
$548$	−582.138	−	336.098i	−1.06230	−	0.613317i
$549$	269.710	−	155.717i	0.491276	−	0.283638i
$550$	−110.651			−0.201184
$551$	30.4979			0.0553500
$552$	178.229	+	308.701i	0.322878	+	0.559241i
$553$	−453.632	−	785.714i	−0.820311	−	1.42082i
$554$	1298.29	−	749.569i	2.34349	−	1.35301i
$555$	−134.725	−	233.350i	−0.242748	−	0.420451i
$556$	280.154	+	161.747i	0.503874	+	0.290912i
$557$	238.623	−	413.308i	0.428408	−	0.742024i	−0.568324	−	0.822805i	$-0.692408\pi$
$557$	238.623	−	413.308i	0.428408	−	0.742024i	0.996732	+	0.0807806i	$0.0257413\pi$
$558$	−342.420			−0.613656
$559$	99.1283	+	171.695i	0.177331	+	0.307147i
$560$	−49.2439			−0.0879356
$561$	−29.9495			−0.0533859
$562$	819.310	−	1419.09i	1.45785	−	2.52506i
$563$		−	828.704i		−	1.47194i	−0.677013	−	0.735971i	$-0.736726\pi$
$563$		−	828.704i		−	1.47194i	0.677013	−	0.735971i	$-0.263274\pi$
$564$	124.117	−	71.6592i	0.220066	−	0.127055i
$565$	245.551	−	425.307i	0.434603	−	0.752755i
$566$	891.491	−	514.702i	1.57507	−	0.909368i
$567$	70.3862	+	40.6375i	0.124138	+	0.0716710i
$568$	−510.338	−	294.644i	−0.898482	−	0.518739i
$569$	446.808	−	773.894i	0.785251	−	1.36009i	−0.143598	−	0.989636i	$-0.545867\pi$
$569$	446.808	−	773.894i	0.785251	−	1.36009i	0.928849	−	0.370459i	$-0.120799\pi$
$570$	38.6205	+	22.2975i	0.0677552	+	0.0391185i
$571$	−307.256	+	532.183i	−0.538101	+	0.932019i	0.460905	+	0.887449i	$0.347525\pi$
$571$	−307.256	+	532.183i	−0.538101	+	0.932019i	−0.999006	+	0.0445693i	$0.985808\pi$
$572$	178.451	−	309.085i	0.311976	−	0.540359i
$573$	−114.789	−	198.821i	−0.200330	−	0.346982i
$574$	585.260	+	337.900i	1.01962	+	0.588676i
$575$	−104.388	−	180.806i	−0.181545	−	0.314445i
$576$	−307.178			−0.533296
$577$	−176.336	−	101.807i	−0.305608	−	0.176443i	0.339352	−	0.940660i	$-0.389792\pi$
$577$	−176.336	−	101.807i	−0.305608	−	0.176443i	−0.644959	+	0.764217i	$0.723126\pi$
$578$		−	878.388i		−	1.51970i
$579$		−	657.224i		−	1.13510i
$580$	361.574	−	208.755i	0.623403	−	0.359922i
$581$			188.944i			0.325205i
$582$	325.176	+	187.741i	0.558722	+	0.322578i
$583$	−123.181	+	213.356i	−0.211288	+	0.365962i
$584$	−815.342	+	470.738i	−1.39613	+	0.806059i
$585$	−83.3942	−	144.443i	−0.142554	−	0.246911i
$586$	116.345	−	67.1717i	0.198541	−	0.114627i
$587$	123.981	−	71.5804i	0.211211	−	0.121943i	−0.390663	−	0.920534i	$-0.627754\pi$
$587$	123.981	−	71.5804i	0.211211	−	0.121943i	0.601874	+	0.798591i	$0.294421\pi$
$588$		−	373.263i		−	0.634801i
$589$		−	68.4604i		−	0.116232i
$590$	560.283	+	970.438i	0.949632	+	1.64481i
$591$	−10.2380	+	17.7327i	−0.0173231	+	0.0300046i
$592$	25.9637	−	44.9705i	0.0438576	−	0.0759636i
$593$	−55.2918	+	31.9227i	−0.0932408	+	0.0538326i	−0.545895	−	0.837853i	$-0.683810\pi$
$593$	−55.2918	+	31.9227i	−0.0932408	+	0.0538326i	0.452655	+	0.891686i	$0.350477\pi$
$594$		−	66.3660i		−	0.111727i
$595$	161.039			0.270654
$596$	−686.042	+	1188.26i	−1.15108	+	1.99372i
$597$	−28.4613	+	16.4321i	−0.0476738	+	0.0275245i
$598$	1080.25			1.80645
$599$	180.990	+	104.495i	0.302154	+	0.174449i	0.643410	−	0.765522i	$-0.277519\pi$
$599$	180.990	+	104.495i	0.302154	+	0.174449i	−0.341256	+	0.939970i	$0.610852\pi$
$600$	−128.148			−0.213581
$601$	351.220	+	608.330i	0.584392	+	1.01220i	0.994951	+	0.100363i	$0.0320003\pi$
$601$	351.220	+	608.330i	0.584392	+	1.01220i	−0.410559	+	0.911834i	$0.634666\pi$
$602$		−	424.179i		−	0.704616i
$603$	−87.0539	−	181.170i	−0.144368	−	0.300448i
$604$	659.001			1.09106
$605$	−369.777	+	213.491i	−0.611202	+	0.352877i
$606$		−	476.910i		−	0.786980i
$607$	−324.060	+	561.289i	−0.533872	+	0.924694i	0.465345	+	0.885129i	$0.345930\pi$
$607$	−324.060	+	561.289i	−0.533872	+	0.924694i	−0.999217	+	0.0395642i	$0.987403\pi$
$608$		−	58.1776i		−	0.0956869i
$609$	122.023	+	211.349i	0.200365	+	0.347043i
$610$	1184.21	+	683.704i	1.94133	+	1.12083i
$611$		−	171.915i		−	0.281367i
$612$	−87.6297			−0.143186
$613$	521.988	+	904.110i	0.851530	+	1.47489i	0.879827	+	0.475294i	$0.157658\pi$
$613$	521.988	+	904.110i	0.851530	+	1.47489i	−0.0282969	+	0.999600i	$0.509008\pi$
$614$	−1535.08	−	886.279i	−2.50013	−	1.44345i
$615$	−139.220	−	80.3787i	−0.226374	−	0.130697i
$616$	−261.755	+	151.124i	−0.424927	+	0.245332i
$617$	−508.426			−0.824030			−0.412015	−	0.911177i	$-0.635175\pi$
$617$	−508.426			−0.824030			−0.412015	+	0.911177i	$0.635175\pi$
$618$	809.710			1.31021
$619$	−165.273	−	286.260i	−0.266999	−	0.462456i	0.701086	−	0.713076i	$-0.252699\pi$
$619$	−165.273	−	286.260i	−0.266999	−	0.462456i	−0.968085	+	0.250620i	$0.919365\pi$
$620$	−468.605	−	811.647i	−0.755814	−	1.30911i
$621$	108.443	−	62.6094i	0.174626	−	0.100820i
$622$	126.929	+	219.847i	0.204066	+	0.353452i
$623$	492.867	+	284.557i	0.791119	+	0.456753i
$624$	16.0714	−	27.8366i	0.0257555	−	0.0446099i
$625$	−333.356			−0.533370
$626$	359.411	+	622.518i	0.574139	+	0.994438i
$627$	13.2686			0.0211621
$628$	−754.860			−1.20201
$629$	−84.9075	+	147.064i	−0.134988	+	0.233806i
$630$			356.852i			0.566431i
$631$	−446.655	+	257.876i	−0.707852	+	0.408678i	−0.810265	−	0.586063i	$-0.800677\pi$
$631$	−446.655	+	257.876i	−0.707852	+	0.408678i	0.102413	+	0.994742i	$0.467344\pi$
$632$	−428.992	+	743.035i	−0.678784	+	1.17569i
$633$	−7.62662	+	4.40323i	−0.0120484	+	0.00695613i
$634$	−5.63443	−	3.25304i	−0.00888711	−	0.00513098i
$635$	747.203	+	431.398i	1.17670	+	0.679366i
$636$	−360.417	+	624.260i	−0.566693	+	0.981542i
$637$	−387.756	−	223.871i	−0.608722	−	0.351446i
$638$	99.6389	−	172.580i	0.156174	−	0.270501i
$639$	−103.504	+	179.275i	−0.161979	+	0.280555i
$640$	−433.762	−	751.298i	−0.677753	−	1.17390i
$641$	−424.027	−	244.812i	−0.661508	−	0.381922i	0.131343	−	0.991337i	$-0.458071\pi$
$641$	−424.027	−	244.812i	−0.661508	−	0.381922i	−0.792851	+	0.609415i	$0.791404\pi$
$642$	−6.59259	−	11.4187i	−0.0102688	−	0.0177861i
$643$	−53.4468			−0.0831210			−0.0415605	−	0.999136i	$-0.513233\pi$
$643$	−53.4468			−0.0831210			−0.0415605	+	0.999136i	$0.513233\pi$
$644$	−1247.74	−	720.384i	−1.93749	−	1.11861i
$645$			100.903i			0.156438i
$646$		−	28.1051i		−	0.0435064i
$647$	−1000.71	+	577.762i	−1.54670	+	0.892986i	−0.548307	+	0.836277i	$0.684727\pi$
$647$	−1000.71	+	577.762i	−1.54670	+	0.892986i	−0.998391	+	0.0567089i	$0.981939\pi$
$648$		−	76.8602i		−	0.118611i
$649$	288.740	+	166.704i	0.444899	+	0.256863i
$650$	−194.179	+	336.327i	−0.298736	+	0.517427i
$651$	474.429	−	273.912i	0.728769	−	0.420755i
$652$	−202.751	−	351.175i	−0.310967	−	0.538611i
$653$	−461.837	+	266.642i	−0.707254	+	0.408333i	−0.810043	−	0.586370i	$-0.800557\pi$
$653$	−461.837	+	266.642i	−0.707254	+	0.408333i	0.102789	+	0.994703i	$0.467223\pi$
$654$	−740.187	+	427.347i	−1.13178	+	0.653436i
$655$			807.364i			1.23262i
$656$		−	30.9806i		−	0.0472265i
$657$	165.364	+	286.419i	0.251696	+	0.435950i
$658$	−183.911	+	318.542i	−0.279499	+	0.484107i
$659$	−331.620	+	574.383i	−0.503217	+	0.871598i	0.496776	+	0.867879i	$0.334517\pi$
$659$	−331.620	+	574.383i	−0.503217	+	0.871598i	−0.999993	+	0.00371910i	$0.998816\pi$
$660$	157.309	−	90.8223i	0.238347	−	0.137610i
$661$			850.702i			1.28699i	0.765449	+	0.643496i	$0.222517\pi$
$661$			850.702i			1.28699i	−0.765449	+	0.643496i	$0.777483\pi$
$662$	−576.810			−0.871314
$663$	−52.5574	+	91.0322i	−0.0792722	+	0.137303i
$664$	154.742	−	89.3404i	0.233045	−	0.134549i
$665$	−71.3457			−0.107287
$666$	−325.884	−	188.149i	−0.489315	−	0.282506i
$667$	375.996			0.563712
$668$	−753.000	−	1304.24i	−1.12725	−	1.95245i
$669$			171.025i			0.255642i
$670$	497.775	−	728.746i	0.742948	−	1.08768i
$671$	406.852			0.606337
$672$	403.169	−	232.770i	0.599954	−	0.346384i
$673$		−	404.640i		−	0.601248i	−0.953743	−	0.300624i	$-0.902805\pi$
$673$		−	404.640i		−	0.601248i	0.953743	−	0.300624i	$-0.0971950\pi$
$674$	269.870	−	467.428i	0.400400	−	0.693514i
$675$			45.0169i			0.0666917i
$676$	−66.8810	−	115.841i	−0.0989363	−	0.171363i
$677$	−245.870	−	141.953i	−0.363176	−	0.209680i	0.307297	−	0.951614i	$-0.400575\pi$
$677$	−245.870	−	141.953i	−0.363176	−	0.209680i	−0.670473	+	0.741934i	$0.733909\pi$
$678$		−	685.844i		−	1.01157i
$679$	−600.716			−0.884707
$680$	−76.1460	−	131.889i	−0.111979	−	0.193954i
$681$	542.465	+	313.192i	0.796571	+	0.459900i
$682$	−387.400	−	223.666i	−0.568035	−	0.327955i
$683$	−657.184	+	379.425i	−0.962202	+	0.555527i	−0.896850	−	0.442335i	$-0.854150\pi$
$683$	−657.184	+	379.425i	−0.962202	+	0.555527i	−0.0653518	+	0.997862i	$0.520817\pi$
$684$	38.8228			0.0567585
$685$	−410.377			−0.599091
$686$	−242.047	−	419.238i	−0.352839	−	0.611134i
$687$	239.337	+	414.544i	0.348380	+	0.603412i
$688$	−16.8404	+	9.72279i	−0.0244773	+	0.0141320i
$689$	432.333	+	748.822i	0.627479	+	1.08683i
$690$	476.136	+	274.898i	0.690053	+	0.398402i
$691$	509.288	−	882.112i	0.737030	−	1.27657i	−0.216797	−	0.976217i	$-0.569561\pi$
$691$	509.288	−	882.112i	0.737030	−	1.27657i	0.953827	−	0.300356i	$-0.0971056\pi$
$692$	−2012.85			−2.90874
$693$	53.0880	+	91.9511i	0.0766061	+	0.132686i
$694$	−1417.38			−2.04233
$695$	197.494			0.284164
$696$	115.394	−	199.869i	0.165797	−	0.287168i
$697$			101.314i			0.145357i
$698$	1671.71	−	965.164i	2.39501	−	1.38276i
$699$	105.271	−	182.334i	0.150602	−	0.260850i
$700$	448.570	−	258.982i	0.640814	−	0.369974i
$701$	180.692	+	104.322i	0.257763	+	0.148819i	0.623314	−	0.781972i	$-0.285786\pi$
$701$	180.692	+	104.322i	0.257763	+	0.148819i	−0.365551	+	0.930791i	$0.619119\pi$
$702$	−201.721	−	116.464i	−0.287352	−	0.165902i
$703$	37.6168	−	65.1543i	0.0535090	−	0.0926803i
$704$	−347.529	−	200.646i	−0.493649	−	0.285008i
$705$	43.7482	−	75.7740i	0.0620541	−	0.107481i
$706$	−931.491	+	1613.39i	−1.31939	+	2.28525i
$707$	381.494	+	660.766i	0.539595	+	0.934606i
$708$	844.827	+	487.761i	1.19326	+	0.688928i
$709$	102.006	+	176.679i	0.143873	+	0.249195i	0.928952	−	0.370201i	$-0.120711\pi$
$709$	102.006	+	176.679i	0.143873	+	0.249195i	−0.785079	+	0.619396i	$0.787378\pi$
$710$	−908.908			−1.28015
$711$	261.019	+	150.699i	0.367115	+	0.211954i
$712$		−	538.200i		−	0.755899i
$713$		−	844.021i		−	1.18376i
$714$	194.768	−	112.449i	0.272784	−	0.157492i
$715$		−	217.889i		−	0.304740i
$716$	1326.97	+	766.128i	1.85331	+	1.07001i
$717$	259.730	−	449.866i	0.362246	−	0.627428i
$718$	1370.18	−	791.075i	1.90833	−	1.10178i
$719$	465.401	+	806.098i	0.647289	+	1.12114i	0.983768	+	0.179446i	$0.0574306\pi$
$719$	465.401	+	806.098i	0.647289	+	1.12114i	−0.336479	+	0.941691i	$0.609236\pi$
$720$	14.1674	−	8.17955i	0.0196769	−	0.0113605i
$721$	−1121.87	+	647.710i	−1.55599	+	0.898350i
$722$		−	1164.02i		−	1.61221i
$723$		−	321.994i		−	0.445358i
$724$	96.5492	+	167.228i	0.133355	+	0.230978i
$725$	−67.5863	+	117.063i	−0.0932225	+	0.161466i
$726$	−298.149	+	516.409i	−0.410673	+	0.711307i
$727$	−449.733	+	259.653i	−0.618615	+	0.357157i	−0.776329	−	0.630327i	$-0.782921\pi$
$727$	−449.733	+	259.653i	−0.618615	+	0.357157i	0.157715	+	0.987485i	$0.449587\pi$
$728$			1060.81i			1.45716i
$729$	−27.0000			−0.0370370
$730$	−726.060	+	1257.57i	−0.994603	+	1.72270i
$731$	55.0720	−	31.7959i	0.0753379	−	0.0434964i
$732$	1190.41			1.62625
$733$	−277.178	−	160.029i	−0.378142	−	0.218320i	0.298868	−	0.954295i	$-0.403391\pi$
$733$	−277.178	−	160.029i	−0.378142	−	0.218320i	−0.677009	+	0.735974i	$0.736724\pi$
$734$	409.673			0.558138
$735$	−113.939	−	197.348i	−0.155019	−	0.268501i
$736$		−	717.249i		−	0.974523i
$737$	19.8494	−	261.831i	0.0269328	−	0.355266i
$738$	−224.504			−0.304207
$739$	810.566	−	467.980i	1.09684	−	0.633262i	0.161452	−	0.986881i	$-0.448382\pi$
$739$	810.566	−	467.980i	1.09684	−	0.633262i	0.935390	+	0.353619i	$0.115049\pi$
$740$		−	1029.93i		−	1.39180i
$741$	23.2847	−	40.3302i	0.0314233	−	0.0544268i
$742$		−	1849.99i		−	2.49325i
$743$	414.586	+	718.084i	0.557989	+	0.966466i	0.997664	+	0.0683090i	$0.0217604\pi$
$743$	414.586	+	718.084i	0.557989	+	0.966466i	−0.439675	+	0.898157i	$0.644906\pi$
$744$	−448.659	−	259.033i	−0.603036	−	0.348163i
$745$			837.661i			1.12438i
$746$	1882.26			2.52314
$747$	−31.3841	−	54.3589i	−0.0420136	−	0.0727696i
$748$	−99.1406	−	57.2388i	−0.132541	−	0.0765225i
$749$	18.2683	+	10.5472i	0.0243902	+	0.0140817i
$750$	−665.124	+	384.010i	−0.886832	+	0.512013i
$751$	−138.625			−0.184587			−0.0922933	−	0.995732i	$-0.529420\pi$
$751$	−138.625			−0.184587			−0.0922933	+	0.995732i	$0.529420\pi$
$752$	16.8620			0.0224228
$753$	−150.808	−	261.206i	−0.200276	−	0.346888i
$754$	−349.706	−	605.709i	−0.463801	−	0.803327i
$755$	348.421	−	201.161i	0.461485	−	0.266438i
$756$	155.331	+	269.041i	0.205464	+	0.355874i
$757$	−1126.68	−	650.492i	−1.48836	−	0.859302i	−0.488443	−	0.872596i	$-0.662435\pi$
$757$	−1126.68	−	650.492i	−1.48836	−	0.859302i	−0.999912	+	0.0132933i	$0.995768\pi$
$758$	68.5311	−	118.699i	0.0904104	−	0.156595i
$759$	163.583			0.215525
$760$	33.7352	+	58.4310i	0.0443884	+	0.0768829i
$761$	−776.781			−1.02074			−0.510369	−	0.859956i	$-0.670491\pi$
$761$	−776.781			−1.02074			−0.510369	+	0.859956i	$0.670491\pi$
$762$	1204.93			1.58127
$763$	683.694	−	1184.19i	0.896060	−	1.55202i
$764$		−	877.531i		−	1.14860i
$765$	−46.3308	+	26.7491i	−0.0605631	+	0.0349661i
$766$	−682.086	+	1181.41i	−0.890451	+	1.54231i
$767$	1013.40	−	585.087i	1.32125	−	0.762825i
$768$	−434.862	−	251.068i	−0.566226	−	0.326911i
$769$	1052.02	+	607.384i	1.36804	+	0.789836i	0.990677	−	0.136232i	$-0.0434991\pi$
$769$	1052.02	+	607.384i	1.36804	+	0.789836i	0.377359	+	0.926067i	$0.376832\pi$
$770$	−233.092	+	403.727i	−0.302717	+	0.524321i
$771$	−206.568	−	119.262i	−0.267922	−	0.154685i
$772$	1256.07	−	2175.58i	1.62704	−	2.81811i
$773$	399.602	−	692.130i	0.516949	−	0.895382i	−0.482857	−	0.875699i	$-0.660401\pi$
$773$	399.602	−	692.130i	0.516949	−	0.895382i	0.999806	−	0.0196830i	$-0.00626568\pi$
$774$	70.4573	+	122.036i	0.0910302	+	0.157669i
$775$	262.778	+	151.715i	0.339069	+	0.195761i
$776$	284.043	+	491.977i	0.366035	+	0.633991i
$777$	602.023			0.774804
$778$	−711.892	−	411.011i	−0.915028	−	0.528292i
$779$		−	44.8854i		−	0.0576193i
$780$		−	637.525i		−	0.817340i
$781$	−234.201	+	135.216i	−0.299874	+	0.173132i
$782$		−	346.497i		−	0.443090i
$783$	−70.2114	−	40.5366i	−0.0896697	−	0.0517709i
$784$	21.9579	−	38.0322i	0.0280076	−	0.0485105i
$785$	−399.103	+	230.422i	−0.508411	+	0.293532i
$786$	563.759	+	976.459i	0.717251	+	1.24231i
$787$	590.039	−	340.659i	0.749732	−	0.432858i	−0.0758649	−	0.997118i	$-0.524172\pi$
$787$	590.039	−	340.659i	0.749732	−	0.432858i	0.825597	+	0.564260i	$0.190838\pi$
$788$	−67.7807	+	39.1332i	−0.0860161	+	0.0496614i
$789$			473.851i			0.600572i
$790$			1323.34i			1.67512i
$791$	548.626	+	950.248i	0.693585	+	1.20132i
$792$	50.2043	−	86.9565i	0.0633893	−	0.109794i
$793$	713.972	−	1236.64i	0.900343	−	1.55944i
$794$	−397.543	+	229.521i	−0.500683	+	0.289070i
$795$			440.071i			0.553549i
$796$	−125.619			−0.157813
$797$	493.720	−	855.147i	0.619473	−	1.07296i	−0.370110	−	0.928988i	$-0.620680\pi$
$797$	493.720	−	855.147i	0.619473	−	1.07296i	0.989582	−	0.143970i	$-0.0459868\pi$
$798$	−86.2884	+	49.8186i	−0.108131	+	0.0624294i
$799$	−55.1427			−0.0690146
$800$	223.309	+	128.927i	0.279136	+	0.161159i
$801$	−189.063			−0.236033
$802$	−624.603	−	1081.84i	−0.778807	−	1.34893i
$803$			432.057i			0.538054i
$804$	58.0778	−	766.095i	0.0722360	−	0.952855i
$805$	−879.593			−1.09266
$806$	−1359.67	+	785.007i	−1.68694	+	0.973954i
$807$		−	95.6800i		−	0.118563i
$808$	360.771	−	624.874i	0.446499	−	0.773359i
$809$			603.716i			0.746250i	0.927781	+	0.373125i	$0.121714\pi$
$809$			603.716i			0.746250i	−0.927781	+	0.373125i	$0.878286\pi$
$810$	−59.2741	−	102.666i	−0.0731779	−	0.126748i
$811$	1320.61	+	762.452i	1.62837	+	0.940138i	0.984580	+	0.174933i	$0.0559709\pi$
$811$	1320.61	+	762.452i	1.62837	+	0.940138i	0.643787	+	0.765205i	$0.277362\pi$
$812$			932.827i			1.14880i
$813$	−141.357			−0.173871
$814$	−245.794	−	425.728i	−0.301958	−	0.523007i
$815$	−214.393	−	123.780i	−0.263059	−	0.151877i
$816$	−8.92870	−	5.15499i	−0.0109420	−	0.00631739i
$817$	−24.3987	+	14.0866i	−0.0298638	+	0.0172419i
$818$	−1780.50			−2.17664
$819$	372.650			0.455006
$820$	−307.236	−	532.148i	−0.374678	−	0.648961i
$821$	570.870	+	988.777i	0.695336	+	1.20436i	0.970067	+	0.242836i	$0.0780776\pi$
$821$	570.870	+	988.777i	0.695336	+	1.20436i	−0.274732	+	0.961521i	$0.588589\pi$
$822$	−496.327	+	286.554i	−0.603804	+	0.348606i
$823$	602.783	+	1044.05i	0.732421	+	1.26859i	0.955845	+	0.293870i	$0.0949432\pi$
$823$	602.783	+	1044.05i	0.732421	+	1.26859i	−0.223424	+	0.974721i	$0.571723\pi$
$824$	1060.93	+	612.527i	1.28753	+	0.743359i
$825$	−29.4046	+	50.9302i	−0.0356419	+	0.0617336i
$826$	−2503.64			−3.03104
$827$	−501.754	−	869.064i	−0.606716	−	1.05086i	−0.991778	−	0.127973i	$-0.959153\pi$
$827$	−501.754	−	869.064i	−0.606716	−	1.05086i	0.385061	−	0.922891i	$-0.374180\pi$
$828$	478.631			0.578057
$829$	−2.88962			−0.00348567			−0.00174283	−	0.999998i	$-0.500555\pi$
$829$	−2.88962			−0.00348567			−0.00174283	+	0.999998i	$0.500555\pi$
$830$	137.797	−	238.672i	0.166021	−	0.287557i
$831$		−	796.763i		−	0.958801i
$832$	−1219.73	+	704.214i	−1.46603	+	0.846411i
$833$	−71.8077	+	124.375i	−0.0862037	+	0.149309i
$834$	238.857	−	137.904i	0.286399	−	0.165353i
$835$	−796.239	−	459.709i	−0.953580	−	0.550550i
$836$	43.9225	+	25.3587i	0.0525389	+	0.0303334i
$837$	−90.9950	+	157.608i	−0.108716	+	0.188301i
$838$	1599.65	+	923.557i	1.90889	+	1.10210i
$839$	483.224	−	836.969i	0.575953	−	0.997579i	−0.419985	−	0.907531i	$-0.637965\pi$
$839$	483.224	−	836.969i	0.575953	−	0.997579i	0.995937	−	0.0900480i	$-0.0287021\pi$
$840$	−269.950	+	467.567i	−0.321369	+	0.556628i
$841$	298.780	+	517.503i	0.355268	+	0.615342i
$842$	730.651	+	421.842i	0.867757	+	0.501000i
$843$	−435.448	−	754.217i	−0.516545	−	0.894683i
$844$	−33.6614			−0.0398832
$845$	−70.7214	−	40.8310i	−0.0836940	−	0.0483207i
$846$		−	122.192i		−	0.144435i
$847$		−	953.991i		−	1.12632i
$848$	−73.4467	+	42.4045i	−0.0866117	+	0.0500053i
$849$		−	547.109i		−	0.644416i
$850$	107.879	+	62.2837i	0.126916	+	0.0732749i
$851$	463.763	−	803.261i	0.544962	−	0.943902i
$852$	−685.253	+	395.631i	−0.804287	+	0.464355i
$853$	−220.322	−	381.609i	−0.258291	−	0.447373i	0.707493	−	0.706720i	$-0.249826\pi$
$853$	−220.322	−	381.609i	−0.258291	−	0.447373i	−0.965784	+	0.259347i	$0.916493\pi$
$854$	−2645.84	+	1527.58i	−3.09817	+	1.78873i
$855$	20.5261	−	11.8507i	0.0240071	−	0.0138605i
$856$		−	19.9486i		−	0.0233044i
$857$			1440.04i			1.68033i	0.542331	+	0.840165i	$0.317542\pi$
$857$			1440.04i			1.68033i	−0.542331	+	0.840165i	$0.682458\pi$
$858$	−152.146	−	263.524i	−0.177326	−	0.307138i
$859$	−7.73250	+	13.3931i	−0.00900175	+	0.0155915i	−0.870491	−	0.492184i	$-0.836199\pi$
$859$	−7.73250	+	13.3931i	−0.00900175	+	0.0155915i	0.861489	+	0.507775i	$0.169532\pi$
$860$	−192.843	+	334.014i	−0.224236	+	0.388388i
$861$	311.054	−	179.587i	0.361271	−	0.208580i
$862$		−	212.144i		−	0.246107i
$863$	512.321			0.593651			0.296826	−	0.954932i	$-0.404072\pi$
$863$	512.321			0.593651			0.296826	+	0.954932i	$0.404072\pi$
$864$	−77.3275	+	133.935i	−0.0894994	+	0.155017i
$865$	−1064.22	+	614.425i	−1.23031	+	0.710318i
$866$	811.399			0.936950
$867$	−404.301	−	233.423i	−0.466322	−	0.269231i
$868$	2093.97			2.41241
$869$	196.870	+	340.990i	0.226548	+	0.392393i
$870$		−	355.966i		−	0.409156i
$871$	−761.008	−	519.812i	−0.873717	−	0.596799i
$872$	−1293.11			−1.48293
$873$	172.825	−	99.7806i	0.197967	−	0.114296i
$874$			153.509i			0.175640i
$875$	614.360	−	1064.10i	0.702126	−	1.21612i
$876$			1264.16i			1.44311i
$877$	725.922	+	1257.33i	0.827734	+	1.43368i	0.899812	+	0.436278i	$0.143703\pi$
$877$	725.922	+	1257.33i	0.827734	+	1.43368i	−0.0720784	+	0.997399i	$0.522963\pi$
$878$	352.825	+	203.703i	0.401850	+	0.232008i
$879$		−	71.4010i		−	0.0812298i
$880$	21.3712			0.0242855
$881$	−183.275	−	317.441i	−0.208030	−	0.360319i	0.743064	−	0.669221i	$-0.233372\pi$
$881$	−183.275	−	317.441i	−0.208030	−	0.360319i	−0.951094	+	0.308902i	$0.900039\pi$
$882$	−275.605	−	159.121i	−0.312477	−	0.180409i
$883$	−727.244	−	419.874i	−0.823606	−	0.475509i	0.0280526	−	0.999606i	$-0.491069\pi$
$883$	−727.244	−	419.874i	−0.823606	−	0.475509i	−0.851658	+	0.524097i	$0.824403\pi$
$884$	−347.957	+	200.893i	−0.393617	+	0.227255i
$885$	595.559			0.672949
$886$	−1767.10			−1.99447
$887$	758.125	+	1313.11i	0.854707	+	1.48040i	0.876916	+	0.480643i	$0.159597\pi$
$887$	758.125	+	1313.11i	0.854707	+	1.48040i	−0.0222089	+	0.999753i	$0.507070\pi$
$888$	−284.661	−	493.047i	−0.320564	−	0.555233i
$889$	−1669.45	+	963.857i	−1.87790	+	1.08420i
$890$	−415.056	−	718.899i	−0.466355	−	0.807751i
$891$	−30.5467	−	17.6361i	−0.0342836	−	0.0197936i
$892$	−326.858	+	566.135i	−0.366433	+	0.634681i
$893$	24.4300			0.0273572
$894$	584.914	+	1013.10i	0.654266	+	1.13322i
$895$	935.447			1.04519
$896$	1938.28			2.16326
$897$	287.067	−	497.215i	0.320031	−	0.554309i
$898$			939.579i			1.04630i
$899$	−473.251	+	273.231i	−0.526419	+	0.303928i
$900$	−86.0352	+	149.017i	−0.0955947	+	0.165575i
$901$	240.188	−	138.673i	0.266580	−	0.153910i
$902$	−253.995	−	146.644i	−0.281591	−	0.162577i
$903$	−195.240	−	112.722i	−0.216212	−	0.124830i
$904$	518.825	−	898.632i	0.573922	−	0.994062i
$905$	102.093	+	58.9436i	0.112810	+	0.0651311i
$906$	280.930	−	486.584i	0.310077	−	0.537069i
$907$	−170.863	+	295.943i	−0.188383	+	0.326288i	−0.944711	−	0.327904i	$-0.893658\pi$
$907$	−170.863	+	295.943i	−0.188383	+	0.326288i	0.756329	+	0.654192i	$0.226991\pi$
$908$	1197.13	+	2073.49i	1.31843	+	2.28358i
$909$	−219.510	−	126.734i	−0.241485	−	0.139422i
$910$	818.092	+	1416.98i	0.899002	+	1.55712i
$911$	−1359.95			−1.49281			−0.746405	−	0.665493i	$-0.768222\pi$
$911$	−1359.95			−1.49281			−0.746405	+	0.665493i	$0.768222\pi$
$912$	3.95571	+	2.28383i	0.00433740	+	0.00250420i
$913$		−	81.9992i		−	0.0898129i
$914$		−	2051.40i		−	2.24442i
$915$	629.385	−	363.376i	0.687853	−	0.397132i
$916$			1829.66i			1.99745i
$917$	−1562.19	−	901.933i	−1.70359	−	0.983570i
$918$	−37.3562	+	64.7029i	−0.0406930	+	0.0704824i
$919$	388.426	−	224.258i	0.422662	−	0.244024i	−0.273554	−	0.961857i	$-0.588199\pi$
$919$	388.426	−	224.258i	0.422662	−	0.244024i	0.696215	+	0.717833i	$0.254866\pi$
$920$	415.907	+	720.373i	0.452073	+	0.783014i
$921$	−815.866	+	471.041i	−0.885848	+	0.511445i
$922$	1720.14	−	993.126i	1.86567	−	1.07714i
$923$			949.146i			1.02833i
$924$			405.842i			0.439223i
$925$	166.725	+	288.777i	0.180243	+	0.312191i
$926$	230.652	−	399.501i	0.249084	−	0.431426i
$927$	215.173	−	372.690i	0.232117	−	0.402039i
$928$	−402.168	+	232.192i	−0.433371	+	0.250207i
$929$		−	1045.55i		−	1.12546i	−0.826641	−	0.562729i	$-0.809751\pi$
$929$		−	1045.55i		−	1.12546i	0.826641	−	0.562729i	$-0.190249\pi$
$930$	−799.058			−0.859202
$931$	31.8132	−	55.1020i	0.0341710	−	0.0591858i
$932$	696.947	−	402.382i	0.747797	−	0.431741i
$933$	134.921			0.144609
$934$	306.069	+	176.709i	0.327697	+	0.189196i
$935$	−69.8890			−0.0747475
$936$	−176.204	−	305.194i	−0.188252	−	0.326062i
$937$		−	889.830i		−	0.949658i	−0.880078	−	0.474829i	$-0.842510\pi$
$937$		−	889.830i		−	0.949658i	0.880078	−	0.474829i	$-0.157490\pi$
$938$	853.992	+	1777.27i	0.910439	+	1.89474i
$939$	382.040			0.406859
$940$	289.635	−	167.221i	0.308123	−	0.177895i
$941$			1673.22i			1.77813i	0.457783	+	0.889064i	$0.348644\pi$
$941$			1673.22i			1.77813i	−0.457783	+	0.889064i	$0.651356\pi$
$942$	−321.794	+	557.364i	−0.341607	+	0.591681i
$943$		−	553.374i		−	0.586823i
$944$	57.3870	+	99.3973i	0.0607914	+	0.105294i
$945$	164.250	+	94.8300i	0.173810	+	0.100349i
$946$			184.088i			0.194596i
$947$	1039.30			1.09747			0.548735	−	0.835996i	$-0.315110\pi$
$947$	1039.30			1.09747			0.548735	+	0.835996i	$0.315110\pi$
$948$	576.026	+	997.706i	0.607622	+	1.05243i
$949$	1313.25	+	758.203i	1.38382	+	0.798950i
$950$	−47.7937	−	27.5937i	−0.0503092	−	0.0290460i
$951$	−2.99459	+	1.72893i	−0.00314889	+	0.00181801i
$952$	340.261			0.357417
$953$	−121.490			−0.127482			−0.0637411	−	0.997966i	$-0.520303\pi$
$953$	−121.490			−0.127482			−0.0637411	+	0.997966i	$0.520303\pi$
$954$	307.289	+	532.240i	0.322106	+	0.557904i
$955$	−267.868	−	463.961i	−0.280490	−	0.485823i
$956$	1719.55	−	992.782i	1.79869	−	1.03847i
$957$	−52.9562	−	91.7228i	−0.0553356	−	0.0958441i
$958$	1658.95	+	957.797i	1.73168	+	0.999788i
$959$	458.446	−	794.052i	0.478046	−	0.828000i
$960$	−716.819			−0.746686
$961$	132.840	+	230.085i	0.138231	+	0.239422i
$962$	−1725.35			−1.79350
$963$	−7.00768			−0.00727692
$964$	615.388	−	1065.88i	0.638369	−	1.10569i
$965$		−	1533.67i		−	1.58930i
$966$	−1063.82	+	614.194i	−1.10126	+	0.635812i
$967$	−764.955	+	1324.94i	−0.791060	+	1.37016i	0.134251	+	0.990947i	$0.457137\pi$
$967$	−764.955	+	1324.94i	−0.791060	+	1.37016i	−0.925311	+	0.379208i	$0.876196\pi$
$968$	−781.303	+	451.086i	−0.807131	+	0.465998i
$969$	−12.9361	−	7.46867i	−0.0133500	−	0.00770760i
$970$	758.818	+	438.104i	0.782287	+	0.451654i
$971$	135.695	−	235.030i	0.139747	−	0.242050i	−0.787654	−	0.616118i	$-0.788704\pi$
$971$	135.695	−	235.030i	0.139747	−	0.242050i	0.927401	+	0.374069i	$0.122038\pi$
$972$	−89.3769	−	51.6018i	−0.0919516	−	0.0530883i
$973$	−220.627	+	382.137i	−0.226749	+	0.392741i
$974$	−95.5757	+	165.542i	−0.0981270	+	0.169961i
$975$	103.202	+	178.752i	0.105849	+	0.183335i
$976$	121.293	+	70.0285i	0.124276	+	0.0717505i
$977$	−328.506	−	568.988i	−0.336239	−	0.582383i	0.647483	−	0.762080i	$-0.275822\pi$
$977$	−328.506	−	568.988i	−0.336239	−	0.582383i	−0.983722	+	0.179697i	$0.942488\pi$
$978$	−345.728			−0.353505
$979$	−213.898	−	123.494i	−0.218486	−	0.126143i
$980$		−	871.031i		−	0.888807i
$981$			454.254i			0.463052i
$982$	−2247.54	+	1297.62i	−2.28874	+	1.32140i
$983$			270.977i			0.275663i	0.990456	+	0.137832i	$0.0440133\pi$
$983$			270.977i			0.275663i	−0.990456	+	0.137832i	$0.955987\pi$
$984$	−294.158	−	169.832i	−0.298942	−	0.172594i
$985$	−23.8909	+	41.3803i	−0.0242548	+	0.0420105i
$986$	−194.284	+	112.170i	−0.197042	+	0.113763i
$987$	97.7450	+	169.299i	0.0990324	+	0.171529i
$988$	154.157	−	89.0023i	0.156029	−	0.0900833i
$989$	−300.802	+	173.668i	−0.304148	+	0.175600i
$990$		−	154.869i		−	0.156433i
$991$			233.900i			0.236024i	0.993012	+	0.118012i	$0.0376522\pi$
$991$			233.900i			0.236024i	−0.993012	+	0.118012i	$0.962348\pi$
$992$	521.216	+	902.772i	0.525419	+	0.910052i
$993$	−153.282	+	265.492i	−0.154362	+	0.267363i
$994$	1015.37	−	1758.67i	1.02150	−	1.76929i
$995$	−66.4161	+	38.3453i	−0.0667498	+	0.0385380i
$996$		−	239.923i		−	0.240886i
$997$	1197.16			1.20076			0.600382	−	0.799713i	$-0.295015\pi$
$997$	1197.16			1.20076			0.600382	+	0.799713i	$0.295015\pi$
$998$	1344.88	−	2329.40i	1.34757	−	2.33407i
$999$	−173.201	+	99.9977i	−0.173374	+	0.100098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.a.97.10	✓	22
67.38	odd	6	inner	201.3.h.a.172.10	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.10	✓	22	1.1	even	1	trivial
201.3.h.a.172.10	yes	22	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)

\(f(q)\)	\(=\)	\(q+(2.82230 - 1.62946i) q^{2} -1.73205i q^{3} +(3.31026 - 5.73353i) q^{4} -4.04184i q^{5} +(-2.82230 - 4.88837i) q^{6} +(7.82069 + 4.51528i) q^{7} -8.54003i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(2.82230 - 1.62946i) q^{2} -1.73205i q^{3} +(3.31026 - 5.73353i) q^{4} -4.04184i q^{5} +(-2.82230 - 4.88837i) q^{6} +(7.82069 + 4.51528i) q^{7} -8.54003i q^{8} -3.00000 q^{9} +(-6.58601 - 11.4073i) q^{10} +(-3.39408 - 1.95957i) q^{11} +(-9.93077 - 5.73353i) q^{12} +(-11.9123 + 6.87758i) q^{13} +29.4298 q^{14} -7.00068 q^{15} +(-0.674573 - 1.16839i) q^{16} +(2.20601 + 3.82093i) q^{17} +(-8.46690 + 4.88837i) q^{18} +(-0.977337 - 1.69280i) q^{19} +(-23.1740 - 13.3795i) q^{20} +(7.82069 - 13.5458i) q^{21} -12.7721 q^{22} +(-12.0492 - 20.8698i) q^{23} -14.7918 q^{24} +8.66350 q^{25} +(-22.4134 + 38.8212i) q^{26} +5.19615i q^{27} +(51.7770 - 29.8934i) q^{28} +(-7.80127 + 13.5122i) q^{29} +(-19.7580 + 11.4073i) q^{30} +(30.3317 + 17.5120i) q^{31} +(25.7758 + 14.8817i) q^{32} +(-3.39408 + 5.87871i) q^{33} +(12.4521 + 7.18921i) q^{34} +(18.2500 - 31.6100i) q^{35} +(-9.93077 + 17.2006i) q^{36} +(19.2446 + 33.3326i) q^{37} +(-5.51668 - 3.18506i) q^{38} +(11.9123 + 20.6327i) q^{39} -34.5174 q^{40} +(19.8866 + 11.4816i) q^{41} -50.9739i q^{42} -14.4133i q^{43} +(-22.4705 + 12.9734i) q^{44} +12.1255i q^{45} +(-68.0129 - 39.2673i) q^{46} +(-6.24913 + 10.8238i) q^{47} +(-2.02372 + 1.16839i) q^{48} +(16.2754 + 28.1899i) q^{49} +(24.4510 - 14.1168i) q^{50} +(6.61804 - 3.82093i) q^{51} +91.0662i q^{52} -62.8612i q^{53} +(8.46690 + 14.6651i) q^{54} +(-7.92028 + 13.7183i) q^{55} +(38.5606 - 66.7889i) q^{56} +(-2.93201 + 1.69280i) q^{57} +50.8473i q^{58} -85.0717 q^{59} +(-23.1740 + 40.1386i) q^{60} +(-89.9035 + 51.9058i) q^{61} +114.140 q^{62} +(-23.4621 - 13.5458i) q^{63} +102.393 q^{64} +(27.7981 + 48.1477i) q^{65} +22.1220i q^{66} +(29.0180 + 60.3901i) q^{67} +29.2099 q^{68} +(-36.1476 + 20.8698i) q^{69} -118.951i q^{70} +(34.5015 - 59.7583i) q^{71} +25.6201i q^{72} +(-55.1214 - 95.4731i) q^{73} +(108.628 + 62.7163i) q^{74} -15.0056i q^{75} -12.9409 q^{76} +(-17.6960 - 30.6504i) q^{77} +(67.2403 + 38.8212i) q^{78} +(-87.0062 - 50.2331i) q^{79} +(-4.72247 + 2.72652i) q^{80} +9.00000 q^{81} +74.8348 q^{82} +(10.4614 + 18.1196i) q^{83} +(-51.7770 - 89.6803i) q^{84} +(15.4436 - 8.91636i) q^{85} +(-23.4858 - 40.6786i) q^{86} +(23.4038 + 13.5122i) q^{87} +(-16.7348 + 28.9855i) q^{88} +63.0209 q^{89} +(19.7580 + 34.2219i) q^{90} -124.217 q^{91} -159.544 q^{92} +(30.3317 - 52.5360i) q^{93} +40.7308i q^{94} +(-6.84202 + 3.95024i) q^{95} +(25.7758 - 44.6450i) q^{96} +(-57.6084 + 33.2602i) q^{97} +(91.8683 + 53.0402i) q^{98} +(10.1822 + 5.87871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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