LMFDB - Embedded newform 201.3.h.a.97.1

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			97.1
Character	$\chi$	$=$	201.97
Dual form			201.3.h.a.172.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.30238 + 1.90663i) q^{2} -1.73205i q^{3} +(5.27046 - 9.12871i) q^{4} +0.881143i q^{5} +(3.30238 + 5.71988i) q^{6} +(1.91999 + 1.10851i) q^{7} +24.9422i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-3.30238 + 1.90663i) q^{2} -1.73205i q^{3} +(5.27046 - 9.12871i) q^{4} +0.881143i q^{5} +(3.30238 + 5.71988i) q^{6} +(1.91999 + 1.10851i) q^{7} +24.9422i q^{8} -3.00000 q^{9} +(-1.68001 - 2.90987i) q^{10} +(-0.911496 - 0.526253i) q^{11} +(-15.8114 - 9.12871i) q^{12} +(6.16276 - 3.55807i) q^{13} -8.45404 q^{14} +1.52619 q^{15} +(-26.4737 - 45.8537i) q^{16} +(-0.806902 - 1.39760i) q^{17} +(9.90713 - 5.71988i) q^{18} +(-15.8829 - 27.5099i) q^{19} +(8.04370 + 4.64403i) q^{20} +(1.91999 - 3.32552i) q^{21} +4.01347 q^{22} +(2.03182 + 3.51921i) q^{23} +43.2012 q^{24} +24.2236 q^{25} +(-13.5678 + 23.5002i) q^{26} +5.19615i q^{27} +(20.2385 - 11.6847i) q^{28} +(22.2903 - 38.6080i) q^{29} +(-5.04004 + 2.90987i) q^{30} +(27.3175 + 15.7717i) q^{31} +(88.4497 + 51.0665i) q^{32} +(-0.911496 + 1.57876i) q^{33} +(5.32939 + 3.07692i) q^{34} +(-0.976754 + 1.69179i) q^{35} +(-15.8114 + 27.3861i) q^{36} +(-6.27741 - 10.8728i) q^{37} +(104.902 + 60.5654i) q^{38} +(-6.16276 - 10.6742i) q^{39} -21.9777 q^{40} +(-18.1180 - 10.4605i) q^{41} +14.6428i q^{42} -6.05549i q^{43} +(-9.60801 + 5.54719i) q^{44} -2.64343i q^{45} +(-13.4196 - 7.74783i) q^{46} +(44.8720 - 77.7206i) q^{47} +(-79.4210 + 45.8537i) q^{48} +(-22.0424 - 38.1786i) q^{49} +(-79.9954 + 46.1854i) q^{50} +(-2.42071 + 1.39760i) q^{51} -75.0107i q^{52} -85.2941i q^{53} +(-9.90713 - 17.1597i) q^{54} +(0.463704 - 0.803159i) q^{55} +(-27.6486 + 47.8888i) q^{56} +(-47.6486 + 27.5099i) q^{57} +169.997i q^{58} -46.9558 q^{59} +(8.04370 - 13.9321i) q^{60} +(24.3328 - 14.0486i) q^{61} -120.283 q^{62} +(-5.75997 - 3.32552i) q^{63} -177.670 q^{64} +(3.13517 + 5.43027i) q^{65} -6.95154i q^{66} +(66.3988 - 8.95554i) q^{67} -17.0110 q^{68} +(6.09545 - 3.51921i) q^{69} -7.44922i q^{70} +(-42.1944 + 73.0828i) q^{71} -74.8266i q^{72} +(59.3601 + 102.815i) q^{73} +(41.4608 + 23.9374i) q^{74} -41.9565i q^{75} -334.840 q^{76} +(-1.16671 - 2.02080i) q^{77} +(40.7035 + 23.5002i) q^{78} +(-58.2400 - 33.6249i) q^{79} +(40.4037 - 23.3271i) q^{80} +9.00000 q^{81} +79.7768 q^{82} +(5.15254 + 8.92447i) q^{83} +(-20.2385 - 35.0541i) q^{84} +(1.23148 - 0.710996i) q^{85} +(11.5456 + 19.9975i) q^{86} +(-66.8710 - 38.6080i) q^{87} +(13.1259 - 22.7347i) q^{88} +22.9401 q^{89} +(5.04004 + 8.72960i) q^{90} +15.7766 q^{91} +42.8344 q^{92} +(27.3175 - 47.3152i) q^{93} +342.217i q^{94} +(24.2402 - 13.9951i) q^{95} +(88.4497 - 153.199i) q^{96} +(76.5306 - 44.1850i) q^{97} +(145.585 + 84.0534i) q^{98} +(2.73449 + 1.57876i) 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 $

$2$	−3.30238	+	1.90663i	−1.65119	+	0.953314i	−0.674604	+	0.738180i	$0.735685\pi$
$2$	−3.30238	+	1.90663i	−1.65119	+	0.953314i	−0.976585	+	0.215134i	$0.930981\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	5.27046	−	9.12871i	1.31762	−	2.28218i
$5$			0.881143i			0.176229i	0.996110	+	0.0881143i	$0.0280841\pi$
$5$			0.881143i			0.176229i	−0.996110	+	0.0881143i	$0.971916\pi$
$6$	3.30238	+	5.71988i	0.550396	+	0.953314i
$7$	1.91999	+	1.10851i	0.274284	+	0.158358i	0.630833	−	0.775919i	$-0.282713\pi$
$7$	1.91999	+	1.10851i	0.274284	+	0.158358i	−0.356549	+	0.934277i	$0.616047\pi$
$8$			24.9422i			3.11778i
$9$	−3.00000			−0.333333
$10$	−1.68001	−	2.90987i	−0.168001	−	0.290987i
$11$	−0.911496	−	0.526253i	−0.0828633	−	0.0478411i	0.457996	−	0.888954i	$-0.348567\pi$
$11$	−0.911496	−	0.526253i	−0.0828633	−	0.0478411i	−0.540859	+	0.841113i	$0.681901\pi$
$12$	−15.8114	−	9.12871i	−1.31762	−	0.760725i
$13$	6.16276	−	3.55807i	0.474058	−	0.273698i	−0.243879	−	0.969806i	$-0.578420\pi$
$13$	6.16276	−	3.55807i	0.474058	−	0.273698i	0.717937	+	0.696108i	$0.245087\pi$
$14$	−8.45404			−0.603860
$15$	1.52619			0.101746
$16$	−26.4737	−	45.8537i	−1.65460	−	2.86586i
$17$	−0.806902	−	1.39760i	−0.0474648	−	0.0822115i	0.841317	−	0.540542i	$-0.181781\pi$
$17$	−0.806902	−	1.39760i	−0.0474648	−	0.0822115i	−0.888782	+	0.458331i	$0.848448\pi$
$18$	9.90713	−	5.71988i	0.550396	−	0.317771i
$19$	−15.8829	−	27.5099i	−0.835940	−	1.44789i	−0.893263	−	0.449535i	$-0.851590\pi$
$19$	−15.8829	−	27.5099i	−0.835940	−	1.44789i	0.0573227	−	0.998356i	$-0.481744\pi$
$20$	8.04370	+	4.64403i	0.402185	+	0.232202i
$21$	1.91999	−	3.32552i	0.0914281	−	0.158358i
$22$	4.01347			0.182431
$23$	2.03182	+	3.51921i	0.0883398	+	0.153009i	0.906809	−	0.421541i	$-0.138511\pi$
$23$	2.03182	+	3.51921i	0.0883398	+	0.153009i	−0.818470	+	0.574550i	$0.805177\pi$
$24$	43.2012			1.80005
$25$	24.2236			0.968943
$26$	−13.5678	+	23.5002i	−0.521840	+	0.903853i
$27$			5.19615i			0.192450i
$28$	20.2385	−	11.6847i	0.722803	−	0.417310i
$29$	22.2903	−	38.6080i	0.768632	−	1.33131i	−0.169673	−	0.985500i	$-0.554271\pi$
$29$	22.2903	−	38.6080i	0.768632	−	1.33131i	0.938305	−	0.345809i	$-0.112396\pi$
$30$	−5.04004	+	2.90987i	−0.168001	+	0.0969956i
$31$	27.3175	+	15.7717i	0.881208	+	0.508766i	0.871057	−	0.491183i	$-0.163435\pi$
$31$	27.3175	+	15.7717i	0.881208	+	0.508766i	0.0101517	+	0.999948i	$0.496769\pi$
$32$	88.4497	+	51.0665i	2.76405	+	1.59583i
$33$	−0.911496	+	1.57876i	−0.0276211	+	0.0478411i
$34$	5.32939	+	3.07692i	0.156747	+	0.0904978i
$35$	−0.976754	+	1.69179i	−0.0279072	+	0.0483368i
$36$	−15.8114	+	27.3861i	−0.439205	+	0.760725i
$37$	−6.27741	−	10.8728i	−0.169660	−	0.293859i	0.768640	−	0.639681i	$-0.220934\pi$
$37$	−6.27741	−	10.8728i	−0.169660	−	0.293859i	−0.938300	+	0.345822i	$0.887600\pi$
$38$	104.902	+	60.5654i	2.76059	+	1.59383i
$39$	−6.16276	−	10.6742i	−0.158019	−	0.273698i
$40$	−21.9777			−0.549442
$41$	−18.1180	−	10.4605i	−0.441903	−	0.255133i	0.262501	−	0.964932i	$-0.415453\pi$
$41$	−18.1180	−	10.4605i	−0.441903	−	0.255133i	−0.704405	+	0.709799i	$0.748786\pi$
$42$			14.6428i			0.348639i
$43$		−	6.05549i		−	0.140825i	−0.997518	−	0.0704126i	$-0.977568\pi$
$43$		−	6.05549i		−	0.140825i	0.997518	−	0.0704126i	$-0.0224316\pi$
$44$	−9.60801	+	5.54719i	−0.218364	+	0.126072i
$45$		−	2.64343i		−	0.0587429i
$46$	−13.4196	−	7.74783i	−0.291731	−	0.168431i
$47$	44.8720	−	77.7206i	0.954723	−	1.65363i	0.219723	−	0.975562i	$-0.429485\pi$
$47$	44.8720	−	77.7206i	0.954723	−	1.65363i	0.735000	−	0.678067i	$-0.237182\pi$
$48$	−79.4210	+	45.8537i	−1.65460	+	0.955286i
$49$	−22.0424	−	38.1786i	−0.449845	−	0.779155i
$50$	−79.9954	+	46.1854i	−1.59991	+	0.923707i
$51$	−2.42071	+	1.39760i	−0.0474648	+	0.0274038i
$52$		−	75.0107i		−	1.44251i
$53$		−	85.2941i		−	1.60932i	−0.593734	−	0.804661i	$-0.702347\pi$
$53$		−	85.2941i		−	1.60932i	0.593734	−	0.804661i	$-0.297653\pi$
$54$	−9.90713	−	17.1597i	−0.183465	−	0.317771i
$55$	0.463704	−	0.803159i	0.00843098	−	0.0146029i
$56$	−27.6486	+	47.8888i	−0.493725	+	0.855157i
$57$	−47.6486	+	27.5099i	−0.835940	+	0.482630i
$58$			169.997i			2.93099i
$59$	−46.9558			−0.795862			−0.397931	−	0.917415i	$-0.630272\pi$
$59$	−46.9558			−0.795862			−0.397931	+	0.917415i	$0.630272\pi$
$60$	8.04370	−	13.9321i	0.134062	−	0.232202i
$61$	24.3328	−	14.0486i	0.398899	−	0.230305i	−0.287110	−	0.957898i	$-0.592694\pi$
$61$	24.3328	−	14.0486i	0.398899	−	0.230305i	0.686009	+	0.727593i	$0.259361\pi$
$62$	−120.283			−1.94005
$63$	−5.75997	−	3.32552i	−0.0914281	−	0.0527861i
$64$	−177.670			−2.77609
$65$	3.13517	+	5.43027i	0.0482334	+	0.0835427i
$66$		−	6.95154i		−	0.105326i
$67$	66.3988	−	8.95554i	0.991027	−	0.133665i
$67$	66.3988	−	8.95554i	0.991027	−	0.133665i
$68$	−17.0110			−0.250162
$69$	6.09545	−	3.51921i	0.0883398	−	0.0510030i
$70$		−	7.44922i		−	0.106417i
$71$	−42.1944	+	73.0828i	−0.594287	+	1.02934i	0.399360	+	0.916794i	$0.369232\pi$
$71$	−42.1944	+	73.0828i	−0.594287	+	1.02934i	−0.993647	+	0.112541i	$0.964101\pi$
$72$		−	74.8266i		−	1.03926i
$73$	59.3601	+	102.815i	0.813152	+	1.40842i	0.910647	+	0.413185i	$0.135584\pi$
$73$	59.3601	+	102.815i	0.813152	+	1.40842i	−0.0974950	+	0.995236i	$0.531083\pi$
$74$	41.4608	+	23.9374i	0.560280	+	0.323478i
$75$		−	41.9565i		−	0.559420i
$76$	−334.840			−4.40579
$77$	−1.16671	−	2.02080i	−0.0151521	−	0.0262442i
$78$	40.7035	+	23.5002i	0.521840	+	0.301284i
$79$	−58.2400	−	33.6249i	−0.737215	−	0.425631i	0.0838410	−	0.996479i	$-0.473281\pi$
$79$	−58.2400	−	33.6249i	−0.737215	−	0.425631i	−0.821056	+	0.570848i	$0.806615\pi$
$80$	40.4037	−	23.3271i	0.505046	−	0.291589i
$81$	9.00000			0.111111
$82$	79.7768			0.972888
$83$	5.15254	+	8.92447i	0.0620788	+	0.107524i	0.895394	−	0.445274i	$-0.146894\pi$
$83$	5.15254	+	8.92447i	0.0620788	+	0.107524i	−0.833316	+	0.552797i	$0.813560\pi$
$84$	−20.2385	−	35.0541i	−0.240934	−	0.417310i
$85$	1.23148	−	0.710996i	0.0144880	−	0.00836466i
$86$	11.5456	+	19.9975i	0.134251	+	0.232529i
$87$	−66.8710	−	38.6080i	−0.768632	−	0.443770i
$88$	13.1259	−	22.7347i	0.149158	−	0.258349i
$89$	22.9401			0.257753			0.128877	−	0.991661i	$-0.458863\pi$
$89$	22.9401			0.257753			0.128877	+	0.991661i	$0.458863\pi$
$90$	5.04004	+	8.72960i	0.0560004	+	0.0969956i
$91$	15.7766			0.173369
$92$	42.8344			0.465592
$93$	27.3175	−	47.3152i	0.293736	−	0.508766i
$94$			342.217i			3.64060i
$95$	24.2402	−	13.9951i	0.255160	−	0.147317i
$96$	88.4497	−	153.199i	0.921351	−	1.59583i
$97$	76.5306	−	44.1850i	0.788975	−	0.455515i	−0.0506263	−	0.998718i	$-0.516122\pi$
$97$	76.5306	−	44.1850i	0.788975	−	0.455515i	0.839602	+	0.543203i	$0.182788\pi$
$98$	145.585	+	84.0534i	1.48556	+	0.857688i
$99$	2.73449	+	1.57876i	0.0276211	+	0.0159470i
$100$	127.669	−	221.130i	1.27669	−	2.21130i
$101$	−92.8431	−	53.6030i	−0.919239	−	0.530723i	−0.0358469	−	0.999357i	$-0.511413\pi$
$101$	−92.8431	−	53.6030i	−0.919239	−	0.530723i	−0.883392	+	0.468634i	$0.844746\pi$
$102$	5.32939	−	9.23077i	0.0522489	−	0.0904978i
$103$	−49.6136	+	85.9333i	−0.481685	+	0.834303i	−0.999779	−	0.0210204i	$-0.993308\pi$
$103$	−49.6136	+	85.9333i	−0.481685	+	0.834303i	0.518094	+	0.855324i	$0.326642\pi$
$104$	88.7461	+	153.713i	0.853328	+	1.47801i
$105$	2.93026	+	1.69179i	0.0279072	+	0.0161123i
$106$	162.624	+	281.673i	1.53419	+	2.65730i
$107$	−80.8274			−0.755396			−0.377698	−	0.925929i	$-0.623284\pi$
$107$	−80.8274			−0.755396			−0.377698	+	0.925929i	$0.623284\pi$
$108$	47.4341	+	27.3861i	0.439205	+	0.253575i
$109$			91.2109i			0.836798i	0.908263	+	0.418399i	$0.137409\pi$
$109$			91.2109i			0.836798i	−0.908263	+	0.418399i	$0.862591\pi$
$110$			3.53644i			0.0321495i
$111$	−18.8322	+	10.8728i	−0.169660	+	0.0979531i
$112$		−	117.385i		−	1.04808i
$113$	171.845	+	99.2149i	1.52075	+	0.878008i	0.999700	+	0.0244844i	$0.00779442\pi$
$113$	171.845	+	99.2149i	1.52075	+	0.878008i	0.521054	+	0.853524i	$0.325539\pi$
$114$	104.902	−	181.696i	0.920196	−	1.59383i
$115$	−3.10093	+	1.79032i	−0.0269646	+	0.0155680i
$116$	−234.961	−	406.964i	−2.02552	−	3.50831i
$117$	−18.4883	+	10.6742i	−0.158019	+	0.0912326i
$118$	155.066	−	89.5273i	1.31412	−	0.758706i
$119$		−	3.57783i		−	0.0300658i
$120$			38.0664i			0.317220i
$121$	−59.9461	−	103.830i	−0.495422	−	0.858097i
$122$	−53.5708	+	92.7874i	−0.439105	+	0.760552i
$123$	−18.1180	+	31.3814i	−0.147301	+	0.255133i
$124$	287.951	−	166.249i	2.32219	−	1.34072i
$125$			43.3730i			0.346984i
$126$	25.3621			0.201287
$127$	−1.48348	+	2.56945i	−0.0116809	+	0.0202319i	−0.871807	−	0.489850i	$-0.837052\pi$
$127$	−1.48348	+	2.56945i	−0.0116809	+	0.0202319i	0.860126	+	0.510082i	$0.170385\pi$
$128$	232.933	−	134.484i	1.81979	−	1.05066i
$129$	−10.4884			−0.0813055
$130$	−20.7070	−	11.9552i	−0.159285	−	0.0919631i
$131$	−237.269			−1.81121			−0.905606	−	0.424121i	$-0.860583\pi$
$131$	−237.269			−1.81121			−0.905606	+	0.424121i	$0.860583\pi$
$132$	9.60801	+	16.6416i	0.0727880	+	0.126072i
$133$		−	70.4251i		−	0.529512i
$134$	−202.199	+	156.172i	−1.50895	+	1.16547i
$135$	−4.57856			−0.0339152
$136$	34.8591	−	20.1259i	0.256317	−	0.147985i
$137$			23.0184i			0.168017i	0.996465	+	0.0840087i	$0.0267724\pi$
$137$			23.0184i			0.168017i	−0.996465	+	0.0840087i	$0.973228\pi$
$138$	−13.4196	+	23.2435i	−0.0972438	+	0.168431i
$139$			212.339i			1.52762i	0.645443	+	0.763809i	$0.276673\pi$
$139$			212.339i			1.52762i	−0.645443	+	0.763809i	$0.723327\pi$
$140$	10.2959	+	17.8330i	0.0735420	+	0.127379i
$141$	−134.616	−	77.7206i	−0.954723	−	0.551210i
$142$		−	321.796i		−	2.26617i
$143$	−7.48978			−0.0523761
$144$	79.4210	+	137.561i	0.551535	+	0.955286i
$145$	34.0192	+	19.6410i	0.234615	+	0.135455i
$146$	−392.059	−	226.355i	−2.68533	−	1.55038i
$147$	−66.1273	+	38.1786i	−0.449845	+	0.259718i
$148$	−132.339			−0.894185
$149$	202.807			1.36112			0.680562	−	0.732691i	$-0.261736\pi$
$149$	202.807			1.36112			0.680562	+	0.732691i	$0.261736\pi$
$150$	79.9954	+	138.556i	0.533303	+	0.923707i
$151$	27.6829	+	47.9482i	0.183330	+	0.317538i	0.943013	−	0.332757i	$-0.107979\pi$
$151$	27.6829	+	47.9482i	0.183330	+	0.317538i	−0.759682	+	0.650295i	$0.774645\pi$
$152$	686.158	−	396.154i	4.51420	−	2.60627i
$153$	2.42071	+	4.19279i	0.0158216	+	0.0274038i
$154$	7.70583	+	4.44896i	0.0500378	+	0.0288894i
$155$	−13.8972	+	24.0706i	−0.0896591	+	0.155294i
$156$	−129.922			−0.832835
$157$	96.3860	+	166.945i	0.613924	+	1.06335i	0.990572	+	0.136991i	$0.0437431\pi$
$157$	96.3860	+	166.945i	0.613924	+	1.06335i	−0.376649	+	0.926356i	$0.622924\pi$
$158$	256.440			1.62304
$159$	−147.734			−0.929143
$160$	−44.9969	+	77.9369i	−0.281230	+	0.487105i
$161$			9.00913i			0.0559573i
$162$	−29.7214	+	17.1597i	−0.183465	+	0.105924i
$163$	23.7328	−	41.1063i	0.145600	−	0.252186i	−0.783997	−	0.620765i	$-0.786822\pi$
$163$	23.7328	−	41.1063i	0.145600	−	0.252186i	0.929597	+	0.368579i	$0.120155\pi$
$164$	−190.981	+	110.263i	−1.16452	+	0.672334i
$165$	−1.39111	−	0.803159i	−0.00843098	−	0.00486763i
$166$	−34.0313	−	19.6480i	−0.205008	−	0.118361i
$167$	27.2052	−	47.1208i	0.162905	−	0.282161i	−0.773004	−	0.634401i	$-0.781247\pi$
$167$	27.2052	−	47.1208i	0.162905	−	0.282161i	0.935909	+	0.352241i	$0.114580\pi$
$168$	82.9459	+	47.8888i	0.493725	+	0.285052i
$169$	−59.1803	+	102.503i	−0.350179	+	0.606528i
$170$	−2.71121	+	4.69596i	−0.0159483	+	0.0276233i
$171$	47.6486	+	82.5298i	0.278647	+	0.482630i
$172$	−55.2788	−	31.9152i	−0.321388	−	0.185554i
$173$	70.2971	+	121.758i	0.406341	+	0.703804i	0.994477	−	0.104959i	$-0.0334710\pi$
$173$	70.2971	+	121.758i	0.406341	+	0.703804i	−0.588135	+	0.808763i	$0.700138\pi$
$174$	294.444			1.69221
$175$	46.5091	+	26.8520i	0.265766	+	0.153440i
$176$			55.7274i			0.316633i
$177$			81.3299i			0.459491i
$178$	−75.7567	+	43.7382i	−0.425600	+	0.245720i
$179$		−	240.028i		−	1.34094i	−0.741937	−	0.670470i	$-0.766093\pi$
$179$		−	240.028i		−	1.34094i	0.741937	−	0.670470i	$-0.233907\pi$
$180$	−24.1311	−	13.9321i	−0.134062	−	0.0774005i
$181$	−55.1865	+	95.5858i	−0.304898	+	0.528099i	−0.977239	−	0.212143i	$-0.931956\pi$
$181$	−55.1865	+	95.5858i	−0.304898	+	0.528099i	0.672341	+	0.740242i	$0.265289\pi$
$182$	−52.1002	+	30.0801i	−0.286265	+	0.165275i
$183$	−24.3328	−	42.1457i	−0.132966	−	0.230305i
$184$	−87.7768	+	50.6780i	−0.477048	+	0.275424i
$185$	9.58049	−	5.53130i	0.0517864	−	0.0298989i
$186$			208.337i			1.12009i
$187$			1.69854i			0.00908309i
$188$	−472.992	−	819.246i	−2.51592	−	4.35769i
$189$	−5.75997	+	9.97656i	−0.0304760	+	0.0527861i
$190$	−53.3668	+	92.4340i	−0.280878	+	0.486495i
$191$	99.6762	−	57.5481i	0.521865	−	0.301299i	−0.215833	−	0.976430i	$-0.569247\pi$
$191$	99.6762	−	57.5481i	0.521865	−	0.301299i	0.737697	+	0.675132i	$0.235913\pi$
$192$			307.733i			1.60278i
$193$	−199.491			−1.03363			−0.516816	−	0.856096i	$-0.672883\pi$
$193$	−199.491			−1.03363			−0.516816	+	0.856096i	$0.672883\pi$
$194$	−168.489	+	291.831i	−0.868498	+	1.50428i
$195$	9.40551	−	5.43027i	0.0482334	−	0.0278476i
$196$	−464.695			−2.37089
$197$	113.285	+	65.4049i	0.575049	+	0.332005i	0.759163	−	0.650900i	$-0.225608\pi$
$197$	113.285	+	65.4049i	0.575049	+	0.332005i	−0.184114	+	0.982905i	$0.558942\pi$
$198$	−12.0404			−0.0608102
$199$	−162.671	−	281.755i	−0.817444	−	1.41586i	−0.907559	−	0.419924i	$-0.862057\pi$
$199$	−162.671	−	281.755i	−0.817444	−	1.41586i	0.0901148	−	0.995931i	$-0.471277\pi$
$200$			604.190i			3.02095i
$201$	−15.5114	−	115.006i	−0.0771714	−	0.572169i
$202$	408.804			2.02378
$203$	85.5944	−	49.4180i	0.421648	−	0.243438i
$204$			29.4639i			0.144431i
$205$	9.21716	−	15.9646i	0.0449618	−	0.0778760i
$206$		−	378.379i		−	1.83679i
$207$	−6.09545	−	10.5576i	−0.0294466	−	0.0510030i
$208$	−326.302	−	188.390i	−1.56876	−	0.905723i
$209$			33.4336i			0.159969i
$210$	−12.9024			−0.0614402
$211$	−60.8446	−	105.386i	−0.288363	−	0.499459i	0.685056	−	0.728490i	$-0.259778\pi$
$211$	−60.8446	−	105.386i	−0.288363	−	0.499459i	−0.973419	+	0.229031i	$0.926444\pi$
$212$	−778.625	−	449.539i	−3.67276	−	2.12047i
$213$	126.583	+	73.0828i	0.594287	+	0.343112i
$214$	266.923	−	154.108i	1.24730	−	0.720130i
$215$	5.33575			0.0248174
$216$	−129.604			−0.600016
$217$	34.9662	+	60.5632i	0.161134	+	0.279093i
$218$	−173.905	−	301.213i	−0.797731	−	1.38171i
$219$	178.080	−	102.815i	0.813152	−	0.469474i
$220$	−4.88787	−	8.46603i	−0.0222176	−	0.0384820i
$221$	−9.94549	−	5.74203i	−0.0450022	−	0.0259820i
$222$	41.4608	−	71.8121i	0.186760	−	0.323478i
$223$	−125.386			−0.562271			−0.281136	−	0.959668i	$-0.590711\pi$
$223$	−125.386			−0.562271			−0.281136	+	0.959668i	$0.590711\pi$
$224$	113.215	+	196.094i	0.505425	+	0.875421i
$225$	−72.6708			−0.322981
$226$	−756.664			−3.34807
$227$	−206.854	+	358.282i	−0.911253	+	1.57834i	−0.0989566	+	0.995092i	$0.531550\pi$
$227$	−206.854	+	358.282i	−0.911253	+	1.57834i	−0.812296	+	0.583245i	$0.801783\pi$
$228$			579.960i			2.54368i
$229$	272.812	−	157.508i	1.19132	−	0.687809i	0.232715	−	0.972545i	$-0.425239\pi$
$229$	272.812	−	157.508i	1.19132	−	0.687809i	0.958606	+	0.284736i	$0.0919058\pi$
$230$	6.82695	−	11.8246i	0.0296824	−	0.0514114i
$231$	−3.50013	+	2.02080i	−0.0151521	+	0.00874805i
$232$	962.968	+	555.970i	4.15073	+	2.39642i
$233$	200.667	+	115.855i	0.861230	+	0.497231i	0.864424	−	0.502764i	$-0.167683\pi$
$233$	200.667	+	115.855i	0.861230	+	0.497231i	−0.00319401	+	0.999995i	$0.501017\pi$
$234$	40.7035	−	70.5005i	0.173947	−	0.301284i
$235$	68.4830	+	39.5387i	0.291417	+	0.168250i
$236$	−247.479	+	428.646i	−1.04864	+	1.81630i
$237$	−58.2400	+	100.875i	−0.245738	+	0.425631i
$238$	6.82159	+	11.8153i	0.0286621	+	0.0496443i
$239$	289.769	+	167.298i	1.21242	+	0.699992i	0.963286	−	0.268476i	$-0.0865201\pi$
$239$	289.769	+	167.298i	1.21242	+	0.699992i	0.249136	+	0.968469i	$0.419853\pi$
$240$	−40.4037	−	69.9813i	−0.168349	−	0.291589i
$241$	368.218			1.52787			0.763937	−	0.645291i	$-0.223264\pi$
$241$	368.218			1.52787			0.763937	+	0.645291i	$0.223264\pi$
$242$	395.929	+	228.590i	1.63607	+	0.944586i
$243$		−	15.5885i		−	0.0641500i
$244$		−	296.170i		−	1.21381i
$245$	33.6408	−	19.4225i	0.137309	−	0.0792757i
$246$		−	138.177i		−	0.561697i
$247$	−195.764	−	113.025i	−0.792569	−	0.457590i
$248$	−393.382	+	681.358i	−1.58622	+	2.74741i
$249$	15.4576	−	8.92447i	0.0620788	−	0.0358412i
$250$	−82.6962	−	143.234i	−0.330785	−	0.572936i
$251$	352.120	−	203.297i	1.40287	−	0.809947i	0.408184	−	0.912900i	$-0.366162\pi$
$251$	352.120	−	203.297i	1.40287	−	0.809947i	0.994686	+	0.102952i	$0.0328289\pi$
$252$	−60.7154	+	35.0541i	−0.240934	+	0.139103i
$253$		−	4.27699i		−	0.0169051i
$254$		−	11.3137i		−	0.0445423i
$255$	−1.23148	−	2.13299i	−0.00482934	−	0.00836466i
$256$	−157.483	+	272.768i	−0.615168	+	1.06550i
$257$	29.3774	−	50.8831i	0.114309	−	0.197989i	−0.803194	−	0.595717i	$-0.796868\pi$
$257$	29.3774	−	50.8831i	0.114309	−	0.197989i	0.917503	+	0.397728i	$0.130201\pi$
$258$	34.6367	−	19.9975i	0.134251	−	0.0775097i
$259$		−	27.8342i		−	0.107468i
$260$	66.0952			0.254212
$261$	−66.8710	+	115.824i	−0.256211	+	0.443770i
$262$	783.551	−	452.383i	2.99065	−	1.72665i
$263$	−292.476			−1.11208			−0.556038	−	0.831157i	$-0.687679\pi$
$263$	−292.476			−1.11208			−0.556038	+	0.831157i	$0.687679\pi$
$264$	−39.3777	−	22.7347i	−0.149158	−	0.0861164i
$265$	75.1563			0.283609
$266$	134.274	+	232.570i	0.504791	+	0.874324i
$267$		−	39.7333i		−	0.148814i
$268$	268.200	−	653.335i	1.00075	−	2.43782i
$269$	−95.6097			−0.355426			−0.177713	−	0.984082i	$-0.556870\pi$
$269$	−95.6097			−0.355426			−0.177713	+	0.984082i	$0.556870\pi$
$270$	15.1201	−	8.72960i	0.0560004	−	0.0323319i
$271$			190.456i			0.702789i	0.936227	+	0.351395i	$0.114292\pi$
$271$			190.456i			0.702789i	−0.936227	+	0.351395i	$0.885708\pi$
$272$	−42.7233	+	73.9990i	−0.157071	+	0.272055i
$273$		−	27.3258i		−	0.100095i
$274$	−43.8875	−	76.0154i	−0.160173	−	0.277428i
$275$	−22.0797	−	12.7477i	−0.0802898	−	0.0463554i
$276$		−	74.1914i		−	0.268809i
$277$	−272.909			−0.985232			−0.492616	−	0.870247i	$-0.663959\pi$
$277$	−272.909			−0.985232			−0.492616	+	0.870247i	$0.663959\pi$
$278$	−404.851	−	701.223i	−1.45630	−	2.52238i
$279$	−81.9524	−	47.3152i	−0.293736	−	0.169589i
$280$	−42.1969	−	24.3624i	−0.150703	−	0.0870086i
$281$	110.969	−	64.0677i	0.394906	−	0.227999i	−0.289378	−	0.957215i	$-0.593448\pi$
$281$	110.969	−	64.0677i	0.394906	−	0.227999i	0.684284	+	0.729216i	$0.260115\pi$
$282$	592.737			2.10190
$283$	44.0320			0.155590			0.0777950	−	0.996969i	$-0.475212\pi$
$283$	44.0320			0.155590			0.0777950	+	0.996969i	$0.475212\pi$
$284$	444.768	+	770.360i	1.56608	+	2.71254i
$285$	−24.2402	−	41.9852i	−0.0850533	−	0.147317i
$286$	24.7341	−	14.2802i	0.0864827	−	0.0499308i
$287$	−23.1910	−	40.1679i	−0.0808048	−	0.139958i
$288$	−265.349	−	153.199i	−0.921351	−	0.531942i
$289$	143.198	−	248.026i	0.495494	−	0.858221i
$290$	−149.792			−0.516525
$291$	−76.5306	−	132.555i	−0.262992	−	0.455515i
$292$	1251.42			4.28569
$293$	186.277			0.635759			0.317880	−	0.948131i	$-0.397029\pi$
$293$	186.277			0.635759			0.317880	+	0.948131i	$0.397029\pi$
$294$	145.585	−	252.160i	0.495186	−	0.857688i
$295$		−	41.3748i		−	0.140254i
$296$	271.192	−	156.573i	0.916188	−	0.528961i
$297$	2.73449	−	4.73627i	0.00920703	−	0.0159470i
$298$	−669.747	+	386.678i	−2.24747	+	1.29758i
$299$	25.0432	+	14.4587i	0.0837565	+	0.0483568i
$300$	−383.008	−	221.130i	−1.27669	−	0.737100i
$301$	6.71255	−	11.6265i	0.0223008	−	0.0386262i
$302$	−182.839	−	105.562i	−0.605426	−	0.349543i
$303$	−92.8431	+	160.809i	−0.306413	+	0.530723i
$304$	−840.955	+	1456.58i	−2.76630	+	4.79137i
$305$	12.3788	+	21.4407i	0.0405863	+	0.0702975i
$306$	−15.9882	−	9.23077i	−0.0522489	−	0.0301659i
$307$	−122.049	−	211.395i	−0.397553	−	0.688582i	0.595870	−	0.803081i	$-0.296807\pi$
$307$	−122.049	−	211.395i	−0.397553	−	0.688582i	−0.993423	+	0.114498i	$0.963474\pi$
$308$	−24.5964			−0.0798584
$309$	148.841	+	85.9333i	0.481685	+	0.278101i
$310$		−	105.987i		−	0.341893i
$311$			276.119i			0.887841i	0.896066	+	0.443921i	$0.146413\pi$
$311$			276.119i			0.887841i	−0.896066	+	0.443921i	$0.853587\pi$
$312$	266.238	−	153.713i	0.853328	−	0.492669i
$313$			454.047i			1.45063i	0.688418	+	0.725314i	$0.258305\pi$
$313$			454.047i			1.45063i	−0.688418	+	0.725314i	$0.741695\pi$
$314$	−636.606	−	367.545i	−2.02741	−	1.17052i
$315$	2.93026	−	5.07536i	0.00930242	−	0.0161123i
$316$	−613.903	+	354.437i	−1.94273	+	1.12164i
$317$	−142.630	−	247.043i	−0.449938	−	0.779315i	0.548444	−	0.836187i	$-0.315220\pi$
$317$	−142.630	−	247.043i	−0.449938	−	0.779315i	−0.998381	+	0.0568725i	$0.981887\pi$
$318$	487.872	−	281.673i	1.53419	−	0.885765i
$319$	−40.6351	+	23.4607i	−0.127383	+	0.0735445i
$320$		−	156.552i		−	0.489226i
$321$			139.997i			0.436128i
$322$	−17.1771	−	29.7515i	−0.0533449	−	0.0923961i
$323$	−25.6318	+	44.3956i	−0.0793555	+	0.137448i
$324$	47.4341	−	82.1584i	0.146402	−	0.253575i
$325$	149.284	−	86.1892i	0.459336	−	0.265198i
$326$			180.998i			0.555209i
$327$	157.982			0.483125
$328$	260.907	−	451.904i	0.795448	−	1.37776i
$329$	172.308	−	99.4818i	0.523731	−	0.302376i
$330$	6.12530			0.0185615
$331$	−382.346	−	220.747i	−1.15512	−	0.666911i	−0.204993	−	0.978763i	$-0.565717\pi$
$331$	−382.346	−	220.747i	−1.15512	−	0.666911i	−0.950130	+	0.311853i	$0.899050\pi$
$332$	108.625			0.327184
$333$	18.8322	+	32.6184i	0.0565533	+	0.0979531i
$334$			207.481i			0.621200i
$335$	7.89111	+	58.5068i	0.0235556	+	0.174647i
$336$	−203.317			−0.605110
$337$	−512.810	+	296.071i	−1.52169	+	0.878548i	−0.522019	+	0.852934i	$0.674821\pi$
$337$	−512.810	+	296.071i	−1.52169	+	0.878548i	−0.999672	+	0.0256143i	$0.991846\pi$
$338$		−	451.339i		−	1.33532i
$339$	171.845	−	297.645i	0.506918	−	0.878008i
$340$		−	14.9891i		−	0.0440856i
$341$	−16.5998	−	28.7518i	−0.0486799	−	0.0843160i
$342$	−314.707	−	181.696i	−0.920196	−	0.531276i
$343$		−	206.370i		−	0.601663i
$344$	151.037			0.439062
$345$	3.10093	+	5.37096i	0.00898819	+	0.0155680i
$346$	−464.295	−	268.061i	−1.34189	−	0.774742i
$347$	239.264	+	138.139i	0.689520	+	0.398095i	0.803432	−	0.595396i	$-0.203005\pi$
$347$	239.264	+	138.139i	0.689520	+	0.398095i	−0.113912	+	0.993491i	$0.536338\pi$
$348$	−704.882	+	406.964i	−2.02552	+	1.16944i
$349$	−390.420			−1.11868			−0.559342	−	0.828937i	$-0.688946\pi$
$349$	−390.420			−1.11868			−0.559342	+	0.828937i	$0.688946\pi$
$350$	−204.787			−0.585106
$351$	18.4883	+	32.0226i	0.0526732	+	0.0912326i
$352$	−53.7477	−	93.0938i	−0.152692	−	0.264471i
$353$	508.760	−	293.732i	1.44125	−	0.832103i	0.443312	−	0.896367i	$-0.353803\pi$
$353$	508.760	−	293.732i	1.44125	−	0.832103i	0.997933	+	0.0642638i	$0.0204699\pi$
$354$	−155.066	−	268.582i	−0.438039	−	0.758706i
$355$	−64.3964	−	37.1793i	−0.181398	−	0.104730i
$356$	120.905	−	209.413i	0.339620	−	0.588239i
$357$	−6.19698			−0.0173585
$358$	457.644	+	792.663i	1.27834	+	2.21414i
$359$	−354.290			−0.986881			−0.493441	−	0.869780i	$-0.664261\pi$
$359$	−354.290			−0.986881			−0.493441	+	0.869780i	$0.664261\pi$
$360$	65.9330			0.183147
$361$	−324.031	+	561.237i	−0.897592	+	1.55467i
$362$		−	420.881i		−	1.16265i
$363$	−179.838	+	103.830i	−0.495422	+	0.286032i
$364$	83.1499	−	144.020i	0.228434	−	0.395659i
$365$	−90.5945	+	52.3048i	−0.248204	+	0.143301i
$366$	160.712	+	92.7874i	0.439105	+	0.253517i
$367$	−280.242	−	161.798i	−0.763602	−	0.440866i	0.0669857	−	0.997754i	$-0.478662\pi$
$367$	−280.242	−	161.798i	−0.763602	−	0.440866i	−0.830587	+	0.556888i	$0.811995\pi$
$368$	107.579	−	186.333i	0.292335	−	0.506339i
$369$	54.3541	+	31.3814i	0.147301	+	0.0850443i
$370$	−21.0923	+	36.5329i	−0.0570061	+	0.0987375i
$371$	94.5491	−	163.764i	0.254849	−	0.441412i
$372$	−287.951	−	498.746i	−0.774062	−	1.34072i
$373$	−400.048	−	230.968i	−1.07251	−	0.619216i	−0.143647	−	0.989629i	$-0.545883\pi$
$373$	−400.048	−	230.968i	−1.07251	−	0.619216i	−0.928867	+	0.370413i	$0.879216\pi$
$374$	−3.23848	−	5.60921i	−0.00865903	−	0.0149979i
$375$	75.1243			0.200331
$376$	1938.52	+	1119.21i	5.15564	+	2.97661i
$377$		−	317.242i		−	0.841491i
$378$		−	43.9285i		−	0.116213i
$379$	288.690	−	166.675i	0.761715	−	0.439777i	−0.0681959	−	0.997672i	$-0.521724\pi$
$379$	288.690	−	166.675i	0.761715	−	0.439777i	0.829911	+	0.557895i	$0.188391\pi$
$380$		−	295.042i		−	0.776426i
$381$	4.45043	+	2.56945i	0.0116809	+	0.00674397i
$382$	−219.446	+	380.091i	−0.574465	+	0.995002i
$383$	−151.745	+	87.6099i	−0.396200	+	0.228746i	−0.684843	−	0.728690i	$-0.740129\pi$
$383$	−151.745	+	87.6099i	−0.396200	+	0.228746i	0.288643	+	0.957437i	$0.406796\pi$
$384$	−232.933	−	403.452i	−0.606597	−	1.05066i
$385$	1.78061	−	1.02804i	0.00462497	−	0.00267023i
$386$	658.795	−	380.355i	1.70672	−	0.985377i
$387$			18.1665i			0.0469418i
$388$		−	931.501i		−	2.40077i
$389$	36.3100	+	62.8907i	0.0933419	+	0.161673i	0.908915	−	0.416981i	$-0.136912\pi$
$389$	36.3100	+	62.8907i	0.0933419	+	0.161673i	−0.815574	+	0.578653i	$0.803578\pi$
$390$	−20.7070	+	35.8656i	−0.0530949	+	0.0919631i
$391$	3.27895	−	5.67931i	0.00838607	−	0.0145251i
$392$	952.259	−	549.787i	2.42923	−	1.40252i
$393$			410.961i			1.04570i
$394$	−498.812			−1.26602
$395$	29.6283	−	51.3178i	0.0750084	−	0.129918i
$396$	28.8240	−	16.6416i	0.0727880	−	0.0420241i
$397$	479.215			1.20709			0.603545	−	0.797329i	$-0.293754\pi$
$397$	479.215			1.20709			0.603545	+	0.797329i	$0.293754\pi$
$398$	1074.40	+	620.308i	2.69951	+	1.55856i
$399$	−121.980			−0.305714
$400$	−641.287	−	1110.74i	−1.60322	−	2.77686i
$401$			615.744i			1.53552i	0.640738	+	0.767760i	$0.278629\pi$
$401$			615.744i			1.53552i	−0.640738	+	0.767760i	$0.721371\pi$
$402$	270.498	+	350.219i	0.672882	+	0.871191i
$403$	224.468			0.556992
$404$	−978.652	+	565.025i	−2.42241	+	1.39858i
$405$			7.93029i			0.0195810i
$406$	−188.443	+	326.394i	−0.464146	+	0.803925i
$407$			13.2140i			0.0324669i
$408$	−34.8591	−	60.3778i	−0.0854390	−	0.147985i
$409$	161.245	+	93.0950i	0.394243	+	0.227616i	0.683997	−	0.729485i	$-0.260240\pi$
$409$	161.245	+	93.0950i	0.394243	+	0.227616i	−0.289754	+	0.957101i	$0.593574\pi$
$410$			70.2948i			0.171451i
$411$	39.8690			0.0970049
$412$	522.973	+	905.816i	1.26935	+	2.19858i
$413$	−90.1548	−	52.0509i	−0.218292	−	0.126031i
$414$	40.2589	+	23.2435i	0.0972438	+	0.0561437i
$415$	−7.86374	+	4.54013i	−0.0189488	+	0.0109401i
$416$	726.792			1.74710
$417$	367.782			0.881970
$418$	−63.7454	−	110.410i	−0.152501	−	0.264139i
$419$	30.2322	+	52.3636i	0.0721531	+	0.124973i	0.899845	−	0.436210i	$-0.143680\pi$
$419$	30.2322	+	52.3636i	0.0721531	+	0.124973i	−0.827692	+	0.561183i	$0.810346\pi$
$420$	30.8877	−	17.8330i	0.0735420	−	0.0424595i
$421$	111.932	+	193.871i	0.265871	+	0.460501i	0.967791	−	0.251754i	$-0.0810073\pi$
$421$	111.932	+	193.871i	0.265871	+	0.460501i	−0.701921	+	0.712255i	$0.747674\pi$
$422$	401.863	+	232.016i	0.952283	+	0.549801i
$423$	−134.616	+	233.162i	−0.318241	+	0.551210i
$424$	2127.42			5.01751
$425$	−19.5461	−	33.8548i	−0.0459907	−	0.0796583i
$426$	−557.367			−1.30837
$427$	62.2918			0.145882
$428$	−425.998	+	737.850i	−0.995322	+	1.72395i
$429$			12.9727i			0.0302393i
$430$	−17.6207	+	10.1733i	−0.0409783	+	0.0236588i
$431$	−277.268	+	480.242i	−0.643313	+	1.11425i	0.341375	+	0.939927i	$0.389107\pi$
$431$	−277.268	+	480.242i	−0.643313	+	1.11425i	−0.984688	+	0.174324i	$0.944226\pi$
$432$	238.263	−	137.561i	0.551535	−	0.318429i
$433$	−55.3666	−	31.9659i	−0.127867	−	0.0738243i	0.434702	−	0.900574i	$-0.356854\pi$
$433$	−55.3666	−	31.9659i	−0.127867	−	0.0738243i	−0.562569	+	0.826750i	$0.690187\pi$
$434$	−230.943	−	133.335i	−0.532127	−	0.307223i
$435$	34.0192	−	58.9229i	0.0782050	−	0.135455i
$436$	832.638	+	480.724i	1.90972	+	1.10258i
$437$	64.5421	−	111.790i	0.147694	−	0.255813i
$438$	−392.059	+	679.066i	−0.895112	+	1.55038i
$439$	−104.582	−	181.141i	−0.238227	−	0.412621i	0.721979	−	0.691915i	$-0.243233\pi$
$439$	−104.582	−	181.141i	−0.238227	−	0.412621i	−0.960206	+	0.279294i	$0.909900\pi$
$440$	20.0326	+	11.5658i	0.0455285	+	0.0262859i
$441$	66.1273	+	114.536i	0.149948	+	0.259718i
$442$	43.7917			0.0990761
$443$	−410.130	−	236.789i	−0.925801	−	0.534511i	−0.0403198	−	0.999187i	$-0.512838\pi$
$443$	−410.130	−	236.789i	−0.925801	−	0.534511i	−0.885481	+	0.464675i	$0.846171\pi$
$444$			229.219i			0.516258i
$445$			20.2135i			0.0454236i
$446$	414.073	−	239.065i	0.928415	−	0.536021i
$447$		−	351.273i		−	0.785845i
$448$	−341.124	−	196.948i	−0.761438	−	0.439616i
$449$	36.7343	−	63.6257i	0.0818137	−	0.141705i	−0.822215	−	0.569177i	$-0.807262\pi$
$449$	36.7343	−	63.6257i	0.0818137	−	0.141705i	0.904029	+	0.427471i	$0.140595\pi$
$450$	239.986	−	138.556i	0.533303	−	0.307902i
$451$	11.0097	+	19.0693i	0.0244117	+	0.0422823i
$452$	1811.41	−	1045.82i	4.00754	−	2.31375i
$453$	83.0487	−	47.9482i	0.183330	−	0.105846i
$454$		−	1577.58i		−	3.47484i
$455$			13.9014i			0.0305526i
$456$	−686.158	−	1188.46i	−1.50473	−	2.60627i
$457$	−92.4650	+	160.154i	−0.202330	+	0.350446i	−0.949279	−	0.314435i	$-0.898185\pi$
$457$	−92.4650	+	160.154i	−0.202330	+	0.350446i	0.746949	+	0.664882i	$0.231518\pi$
$458$	−600.620	+	1040.30i	−1.31140	+	2.27141i
$459$	7.26212	−	4.19279i	0.0158216	−	0.00913461i
$460$			37.7433i			0.0820506i
$461$	419.044			0.908989			0.454494	−	0.890750i	$-0.349820\pi$
$461$	419.044			0.908989			0.454494	+	0.890750i	$0.349820\pi$
$462$	7.70583	−	13.3469i	0.0166793	−	0.0288894i
$463$	251.667	−	145.300i	0.543557	−	0.313823i	−0.202962	−	0.979187i	$-0.565057\pi$
$463$	251.667	−	145.300i	0.543557	−	0.313823i	0.746519	+	0.665364i	$0.231724\pi$
$464$	−2360.43			−5.08713
$465$	41.6915	+	24.0706i	0.0896591	+	0.0517647i
$466$	−883.569			−1.89607
$467$	257.982	+	446.838i	0.552424	+	0.956826i	0.998099	+	0.0616315i	$0.0196304\pi$
$467$	257.982	+	446.838i	0.552424	+	0.956826i	−0.445675	+	0.895195i	$0.647036\pi$
$468$			225.032i			0.480838i
$469$	137.412	+	56.4090i	0.292990	+	0.120275i
$470$	−301.542			−0.641579
$471$	289.158	−	166.945i	0.613924	−	0.354449i
$472$		−	1171.18i		−	2.48132i
$473$	−3.18672	+	5.51955i	−0.00673724	+	0.0116692i
$474$		−	444.168i		−	0.937063i
$475$	−384.740	−	666.389i	−0.809979	−	1.40292i
$476$	−32.6609	−	18.8568i	−0.0686154	−	0.0396151i
$477$			255.882i			0.536441i
$478$	−1275.90			−2.66925
$479$	−170.814	−	295.858i	−0.356605	−	0.617658i	0.630786	−	0.775957i	$-0.282733\pi$
$479$	−170.814	−	295.858i	−0.356605	−	0.617658i	−0.987391	+	0.158298i	$0.949399\pi$
$480$	134.991	+	77.9369i	0.281230	+	0.162368i
$481$	−77.3723	−	44.6709i	−0.160857	−	0.0928710i
$482$	−1215.99	+	702.054i	−2.52281	+	1.45654i
$483$	15.6043			0.0323070
$484$	−1263.77			−2.61110
$485$	38.9333	+	67.4344i	0.0802748	+	0.139040i
$486$	29.7214	+	51.4790i	0.0611551	+	0.105924i
$487$	−737.538	+	425.818i	−1.51445	+	0.874369i	−0.514595	+	0.857434i	$0.672058\pi$
$487$	−737.538	+	425.818i	−1.51445	+	0.874369i	−0.999857	+	0.0169354i	$0.994609\pi$
$488$	350.403	+	606.915i	0.718038	+	1.24368i
$489$	−71.1983	−	41.1063i	−0.145600	−	0.0840621i
$490$	−74.0631	+	128.281i	−0.151149	+	0.261798i
$491$	570.860			1.16265			0.581324	−	0.813672i	$-0.302535\pi$
$491$	570.860			1.16265			0.581324	+	0.813672i	$0.302535\pi$
$492$	190.981	+	330.788i	0.388172	+	0.672334i
$493$	−71.9444			−0.145932
$494$	861.984			1.74491
$495$	−1.39111	+	2.40948i	−0.00281033	+	0.00486763i
$496$		−	1670.14i		−	3.36723i
$497$	−162.026	+	93.5455i	−0.326007	+	0.188220i
$498$	−34.0313	+	58.9439i	−0.0683359	+	0.118361i
$499$	−361.955	+	208.975i	−0.725361	+	0.418787i	−0.816722	−	0.577031i	$-0.804211\pi$
$499$	−361.955	+	208.975i	−0.725361	+	0.418787i	0.0913620	+	0.995818i	$0.470878\pi$
$500$	395.940	+	228.596i	0.791879	+	0.457192i
$501$	−81.6156	−	47.1208i	−0.162905	−	0.0940535i
$502$	−775.223	+	1342.73i	−1.54427	+	2.67475i
$503$	1.65934	+	0.958018i	0.00329888	+	0.00190461i	0.501649	−	0.865072i	$-0.332727\pi$
$503$	1.65934	+	0.958018i	0.00329888	+	0.00190461i	−0.498350	+	0.866976i	$0.666060\pi$
$504$	82.9459	−	143.666i	0.164575	−	0.285052i
$505$	47.2319	−	81.8081i	0.0935286	−	0.161996i
$506$	8.15463	+	14.1242i	0.0161159	+	0.0279135i
$507$	177.541	+	102.503i	0.350179	+	0.202176i
$508$	15.6372	+	27.0844i	0.0307819	+	0.0533158i
$509$	93.9867			0.184650			0.0923249	−	0.995729i	$-0.470570\pi$
$509$	93.9867			0.184650			0.0923249	+	0.995729i	$0.470570\pi$
$510$	8.13363	+	4.69596i	0.0159483	+	0.00920776i
$511$			263.204i			0.515077i
$512$		−	125.173i		−	0.244478i
$513$	142.946	−	82.5298i	0.278647	−	0.160877i
$514$			224.047i			0.435889i
$515$	−75.7195	−	43.7167i	−0.147028	−	0.0848868i
$516$	−55.2788	+	95.7456i	−0.107129	+	0.185554i
$517$	−81.8013	+	47.2280i	−0.158223	+	0.0913501i
$518$	53.0695	+	91.9191i	0.102451	+	0.177450i
$519$	210.891	−	121.758i	0.406341	−	0.234601i
$520$	−135.443	+	78.1981i	−0.260467	+	0.150381i
$521$		−	164.385i		−	0.315519i	−0.987478	−	0.157760i	$-0.949573\pi$
$521$		−	164.385i		−	0.315519i	0.987478	−	0.157760i	$-0.0504271\pi$
$522$		−	509.992i		−	0.976997i
$523$	155.301	+	268.990i	0.296943	+	0.514320i	0.975435	−	0.220287i	$-0.0706995\pi$
$523$	155.301	+	268.990i	0.296943	+	0.514320i	−0.678492	+	0.734608i	$0.737366\pi$
$524$	−1250.52	+	2165.96i	−2.38648	+	4.13350i
$525$	46.5091	−	80.5561i	0.0885887	−	0.153440i
$526$	965.866	−	557.643i	1.83625	−	1.06016i
$527$		−	50.9050i		−	0.0965939i
$528$	96.5226			0.182808
$529$	256.243	−	443.827i	0.484392	−	0.838992i
$530$	−248.195	+	143.295i	−0.468292	+	0.270368i
$531$	140.868			0.265287
$532$	−642.890	−	371.173i	−1.20844	−	0.697693i
$533$	−148.876			−0.279317
$534$	75.7567	+	131.214i	0.141867	+	0.245720i
$535$		−	71.2205i		−	0.133123i
$536$	223.371	+	1656.13i	0.416737	+	3.08980i
$537$	−415.741			−0.774192
$538$	315.739	−	182.292i	0.586876	−	0.338833i
$539$			46.3995i			0.0860845i
$540$	−24.1311	+	41.7963i	−0.0446872	+	0.0774005i
$541$			125.092i			0.231223i	0.993294	+	0.115612i	$0.0368828\pi$
$541$			125.092i			0.231223i	−0.993294	+	0.115612i	$0.963117\pi$
$542$	−363.129	−	628.957i	−0.669979	−	1.16044i
$543$	165.560	+	95.5858i	0.304898	+	0.176033i
$544$		−	164.823i		−	0.302983i
$545$	−80.3699			−0.147468
$546$	52.1002	+	90.2402i	0.0954217	+	0.165275i
$547$	337.348	+	194.768i	0.616724	+	0.356066i	0.775592	−	0.631234i	$-0.217451\pi$
$547$	337.348	+	194.768i	0.616724	+	0.356066i	−0.158868	+	0.987300i	$0.550785\pi$
$548$	210.128	+	121.318i	0.383446	+	0.221382i
$549$	−72.9985	+	42.1457i	−0.132966	+	0.0767682i
$550$	97.2207			0.176765
$551$	−1416.14			−2.57012
$552$	87.7768	+	152.034i	0.159016	+	0.275424i
$553$	−74.5468	−	129.119i	−0.134804	−	0.233488i
$554$	901.249	−	520.336i	1.62680	−	0.939235i
$555$	−9.58049	−	16.5939i	−0.0172621	−	0.0298989i
$556$	1938.38	+	1119.12i	3.48629	+	2.01281i
$557$	159.626	−	276.480i	0.286581	−	0.496373i	−0.686410	−	0.727215i	$-0.740815\pi$
$557$	159.626	−	276.480i	0.286581	−	0.496373i	0.972991	+	0.230841i	$0.0741479\pi$
$558$	360.850			0.646685
$559$	−21.5458	−	37.3185i	−0.0385436	−	0.0667594i
$560$	103.433			0.184702
$561$	2.94195			0.00524412
$562$	−244.307	+	423.151i	−0.434709	+	0.752938i
$563$			391.261i			0.694958i	0.937688	+	0.347479i	$0.112962\pi$
$563$			391.261i			0.694958i	−0.937688	+	0.347479i	$0.887038\pi$
$564$	−1418.98	+	819.246i	−2.51592	+	1.45256i
$565$	−87.4225	+	151.420i	−0.154730	+	0.268001i
$566$	−145.410	+	83.9526i	−0.256908	+	0.148326i
$567$	17.2799	+	9.97656i	0.0304760	+	0.0175954i
$568$	−1822.85	−	1052.42i	−3.20924	−	1.85285i
$569$	272.311	−	471.657i	0.478578	−	0.828922i	−0.521120	−	0.853483i	$-0.674486\pi$
$569$	272.311	−	471.657i	0.478578	−	0.828922i	0.999698	+	0.0245615i	$0.00781894\pi$
$570$	160.100	+	92.4340i	0.280878	+	0.162165i
$571$	488.946	−	846.879i	0.856297	−	1.48315i	−0.0191386	−	0.999817i	$-0.506092\pi$
$571$	488.946	−	846.879i	0.856297	−	1.48315i	0.875436	−	0.483334i	$-0.160574\pi$
$572$	−39.4746	+	68.3720i	−0.0690115	+	0.119531i
$573$	−99.6762	−	172.644i	−0.173955	−	0.301299i
$574$	153.171	+	88.4331i	0.266848	+	0.154065i
$575$	49.2179	+	85.2478i	0.0855963	+	0.148257i
$576$	533.009			0.925363
$577$	500.997	+	289.251i	0.868278	+	0.501301i	0.866776	−	0.498698i	$-0.166188\pi$
$577$	500.997	+	289.251i	0.868278	+	0.501301i	0.00150258	+	0.999999i	$0.499522\pi$
$578$			1092.10i			1.88945i
$579$			345.529i			0.596768i
$580$	358.593	−	207.034i	0.618264	−	0.356955i
$581$			22.8465i			0.0393228i
$582$	505.466	+	291.831i	0.868498	+	0.501428i
$583$	−44.8862	+	77.7453i	−0.0769918	+	0.133354i
$584$	−2564.43	+	1480.57i	−4.39114	+	2.53523i
$585$	−9.40551	−	16.2908i	−0.0160778	−	0.0278476i
$586$	−615.158	+	355.162i	−1.04976	+	0.606078i
$587$	−371.387	+	214.420i	−0.632686	+	0.365282i	−0.781792	−	0.623540i	$-0.785694\pi$
$587$	−371.387	+	214.420i	−0.632686	+	0.365282i	0.149105	+	0.988821i	$0.452361\pi$
$588$			804.875i			1.36884i
$589$		−	1002.00i		−	1.70119i
$590$	78.8864	+	136.635i	0.133706	+	0.231585i
$591$	113.285	−	196.215i	0.191683	−	0.332005i
$592$	−332.372	+	575.686i	−0.561440	+	0.972442i
$593$	−277.030	+	159.943i	−0.467166	+	0.269719i	−0.715053	−	0.699070i	$-0.753597\pi$
$593$	−277.030	+	159.943i	−0.467166	+	0.269719i	0.247886	+	0.968789i	$0.420264\pi$
$594$			20.8546i			0.0351088i
$595$	3.15258			0.00529845
$596$	1068.89	−	1851.37i	1.79344	−	3.10633i
$597$	−488.014	+	281.755i	−0.817444	+	0.471952i
$598$	−110.269			−0.184397
$599$	53.7337	+	31.0232i	0.0897057	+	0.0517916i	0.544182	−	0.838967i	$-0.316840\pi$
$599$	53.7337	+	31.0232i	0.0897057	+	0.0517916i	−0.454476	+	0.890759i	$0.650174\pi$
$600$	1046.49			1.74415
$601$	50.3568	+	87.2205i	0.0837883	+	0.145126i	0.904874	−	0.425679i	$-0.139965\pi$
$601$	50.3568	+	87.2205i	0.0837883	+	0.145126i	−0.821086	+	0.570805i	$0.806631\pi$
$602$			51.1933i			0.0850388i
$603$	−199.196	+	26.8666i	−0.330342	+	0.0445549i
$604$	583.607			0.966236
$605$	91.4889	−	52.8211i	0.151221	−	0.0873076i
$606$		−	708.069i		−	1.16843i
$607$	−292.734	+	507.030i	−0.482263	+	0.835304i	−0.999793	−	0.0203610i	$-0.993518\pi$
$607$	−292.734	+	507.030i	−0.482263	+	0.835304i	0.517530	+	0.855665i	$0.326852\pi$
$608$		−	3244.33i		−	5.33606i
$609$	−85.5944	−	148.254i	−0.140549	−	0.243438i
$610$	−81.7590	−	47.2036i	−0.134031	−	0.0773829i
$611$		−	638.631i		−	1.04522i
$612$	51.0330			0.0833872
$613$	−576.469	−	998.473i	−0.940406	−	1.62883i	−0.764698	−	0.644388i	$-0.777112\pi$
$613$	−576.469	−	998.473i	−0.940406	−	1.62883i	−0.175707	−	0.984442i	$-0.556221\pi$
$614$	806.102	+	465.403i	1.31287	+	0.757986i
$615$	−27.6515	−	15.9646i	−0.0449618	−	0.0259587i
$616$	50.4032	−	29.1003i	0.0818234	−	0.0472408i
$617$	462.961			0.750341			0.375171	−	0.926956i	$-0.377584\pi$
$617$	462.961			0.750341			0.375171	+	0.926956i	$0.377584\pi$
$618$	−655.371			−1.06047
$619$	−363.314	−	629.278i	−0.586936	−	1.01660i	−0.994631	−	0.103485i	$-0.967001\pi$
$619$	−363.314	−	629.278i	−0.586936	−	1.01660i	0.407695	−	0.913118i	$-0.366333\pi$
$620$	146.489	+	253.726i	0.236272	+	0.409236i
$621$	−18.2863	+	10.5576i	−0.0294466	+	0.0170010i
$622$	−526.455	−	911.848i	−0.846391	−	1.46599i
$623$	44.0447	+	25.4292i	0.0706978	+	0.0408174i
$624$	−326.302	+	565.171i	−0.522919	+	0.905723i
$625$	567.372			0.907795
$626$	−865.698	−	1499.43i	−1.38290	−	2.39526i
$627$	57.9087			0.0923583
$628$	2031.99			3.23566
$629$	−10.1305	+	17.5466i	−0.0161057	+	0.0278960i
$630$			22.3477i			0.0354725i
$631$	74.0778	−	42.7688i	0.117397	−	0.0677795i	−0.440151	−	0.897924i	$-0.645075\pi$
$631$	74.0778	−	42.7688i	0.117397	−	0.0677795i	0.557549	+	0.830144i	$0.311742\pi$
$632$	838.678	−	1452.63i	1.32702	−	2.29847i
$633$	−182.534	+	105.386i	−0.288363	+	0.166486i
$634$	942.038	+	543.886i	1.48586	+	0.857864i
$635$	−2.26406	−	1.30715i	−0.00356545	−	0.00205851i
$636$	−778.625	+	1348.62i	−1.22425	+	2.12047i
$637$	−271.684	−	156.857i	−0.426506	−	0.246243i
$638$	89.4616	−	154.952i	0.140222	−	0.242872i
$639$	126.583	−	219.248i	0.198096	−	0.343112i
$640$	118.500	+	205.248i	0.185156	+	0.320699i
$641$	−323.464	−	186.752i	−0.504624	−	0.291345i	0.225997	−	0.974128i	$-0.427436\pi$
$641$	−323.464	−	186.752i	−0.504624	−	0.291345i	−0.730621	+	0.682783i	$0.760769\pi$
$642$	−266.923	−	462.323i	−0.415767	−	0.720130i
$643$	715.781			1.11319			0.556595	−	0.830784i	$-0.312108\pi$
$643$	715.781			1.11319			0.556595	+	0.830784i	$0.312108\pi$
$644$	82.2417	+	47.4823i	0.127704	+	0.0737302i
$645$		−	9.24179i		−	0.0143284i
$646$		−	195.481i		−	0.302603i
$647$	−98.7589	+	57.0185i	−0.152641	+	0.0881275i	−0.574375	−	0.818592i	$-0.694755\pi$
$647$	−98.7589	+	57.0185i	−0.152641	+	0.0881275i	0.421734	+	0.906720i	$0.361422\pi$
$648$			224.480i			0.346420i
$649$	42.8001	+	24.7106i	0.0659477	+	0.0380749i
$650$	−328.662	+	569.259i	−0.505633	+	0.875782i
$651$	104.899	−	60.5632i	0.161134	−	0.0930310i
$652$	−250.165	−	433.299i	−0.383689	−	0.664569i
$653$	543.079	−	313.547i	0.831668	−	0.480164i	−0.0227557	−	0.999741i	$-0.507244\pi$
$653$	543.079	−	313.547i	0.831668	−	0.480164i	0.854423	+	0.519578i	$0.173911\pi$
$654$	−521.716	+	301.213i	−0.797731	+	0.460570i
$655$		−	209.068i		−	0.319187i
$656$			1107.71i			1.68858i
$657$	−178.080	−	308.444i	−0.271051	−	0.469474i
$658$	−379.350	+	657.053i	−0.576519	+	0.998561i
$659$	48.0823	−	83.2810i	0.0729625	−	0.126375i	−0.827236	−	0.561855i	$-0.810088\pi$
$659$	48.0823	−	83.2810i	0.0729625	−	0.126375i	0.900198	+	0.435480i	$0.143421\pi$
$660$	−14.6636	+	8.46603i	−0.0222176	+	0.0128273i
$661$			1284.37i			1.94307i	0.236899	+	0.971534i	$0.423869\pi$
$661$			1284.37i			1.94307i	−0.236899	+	0.971534i	$0.576131\pi$
$662$	1683.53			2.54310
$663$	−9.94549	+	17.2261i	−0.0150007	+	0.0259820i
$664$	−222.596	+	128.516i	−0.335235	+	0.193548i
$665$	62.0546			0.0933151
$666$	−124.382	−	71.8121i	−0.186760	−	0.107826i
$667$	181.159			0.271603
$668$	−286.768	−	496.697i	−0.429293	−	0.743558i
$669$			217.176i			0.324627i
$670$	−137.610	−	178.166i	−0.205388	−	0.265920i
$671$	−29.5724			−0.0440721
$672$	339.645	−	196.094i	0.505425	−	0.291807i
$673$		−	231.048i		−	0.343310i	−0.985157	−	0.171655i	$-0.945088\pi$
$673$		−	231.048i		−	0.343310i	0.985157	−	0.171655i	$-0.0549115\pi$
$674$	1128.99	−	1955.47i	1.67507	−	2.90130i
$675$			125.869i			0.186473i
$676$	623.815	+	1080.48i	0.922803	+	1.59834i
$677$	−812.504	−	469.099i	−1.20015	−	0.692909i	−0.239564	−	0.970880i	$-0.577005\pi$
$677$	−812.504	−	469.099i	−1.20015	−	0.692909i	−0.960589	+	0.277971i	$0.910338\pi$
$678$			1310.58i			1.93301i
$679$	195.917			0.288538
$680$	17.7338	+	30.7159i	0.0260791	+	0.0451704i
$681$	620.563	+	358.282i	0.911253	+	0.526112i
$682$	109.638	+	63.2994i	0.160759	+	0.0928144i
$683$	−212.351	+	122.601i	−0.310909	+	0.179503i	−0.647333	−	0.762207i	$-0.724116\pi$
$683$	−212.351	+	122.601i	−0.310909	+	0.179503i	0.336424	+	0.941711i	$0.390782\pi$
$684$	1004.52			1.46860
$685$	−20.2825			−0.0296095
$686$	393.472	+	681.513i	0.573574	+	0.993459i
$687$	−272.812	−	472.525i	−0.397107	−	0.687809i
$688$	−277.667	+	160.311i	−0.403585	+	0.233010i
$689$	−303.482	−	525.647i	−0.440468	−	0.762913i
$690$	−20.4809	−	11.8246i	−0.0296824	−	0.0171371i
$691$	−144.921	+	251.010i	−0.209726	+	0.363256i	−0.951628	−	0.307252i	$-0.900591\pi$
$691$	−144.921	+	251.010i	−0.209726	+	0.363256i	0.741902	+	0.670508i	$0.233924\pi$
$692$	1481.99			2.14161
$693$	3.50013	+	6.06240i	0.00505069	+	0.00874805i
$694$	−1053.52			−1.51804
$695$	−187.101			−0.269210
$696$	962.968	−	1667.91i	1.38358	−	2.39642i
$697$			33.7622i			0.0484394i
$698$	1289.32	−	744.386i	1.84716	−	1.06646i
$699$	200.667	−	347.565i	0.287077	−	0.497231i
$700$	490.248	−	283.045i	0.700355	−	0.404350i
$701$	−649.206	−	374.819i	−0.926114	−	0.534692i	−0.0405336	−	0.999178i	$-0.512906\pi$
$701$	−649.206	−	374.819i	−0.926114	−	0.534692i	−0.885580	+	0.464486i	$0.846239\pi$
$702$	−122.111	−	70.5005i	−0.173947	−	0.100428i
$703$	−199.407	+	345.382i	−0.283651	+	0.491298i
$704$	161.945	+	93.4991i	0.230036	+	0.132811i
$705$	68.4830	−	118.616i	0.0971389	−	0.168250i
$706$	−1120.08	+	1940.03i	−1.58651	+	2.74792i
$707$	−118.839	−	205.835i	−0.168089	−	0.291138i
$708$	742.437	+	428.646i	1.04864	+	0.605432i
$709$	409.227	+	708.803i	0.577190	+	0.999722i	0.995800	+	0.0915558i	$0.0291840\pi$
$709$	409.227	+	708.803i	0.577190	+	0.999722i	−0.418610	+	0.908166i	$0.637483\pi$
$710$	283.548			0.399364
$711$	174.720	+	100.875i	0.245738	+	0.141877i
$712$			572.176i			0.803618i
$713$			128.181i			0.179777i
$714$	20.4648	−	11.8153i	0.0286621	−	0.0165481i
$715$		−	6.59957i		−	0.00923016i
$716$	−2191.15	−	1265.06i	−3.06026	−	1.76684i
$717$	289.769	−	501.894i	0.404141	−	0.699992i
$718$	1170.00	−	675.500i	1.62953	−	0.940808i
$719$	571.172	+	989.299i	0.794398	+	1.37594i	0.923221	+	0.384270i	$0.125547\pi$
$719$	571.172	+	989.299i	0.794398	+	1.37594i	−0.128823	+	0.991668i	$0.541120\pi$
$720$	−121.211	+	69.9813i	−0.168349	+	0.0971962i
$721$	−190.515	+	109.994i	−0.264238	+	0.152558i
$722$		−	2471.22i		−	3.42275i
$723$		−	637.772i		−	0.882118i
$724$	581.717	+	1007.56i	0.803476	+	1.39166i
$725$	539.952	−	935.224i	0.744761	−	1.28996i
$726$	395.929	−	685.770i	0.545357	−	0.944586i
$727$	484.138	−	279.517i	0.665940	−	0.384480i	−0.128597	−	0.991697i	$-0.541047\pi$
$727$	484.138	−	279.517i	0.665940	−	0.384480i	0.794536	+	0.607217i	$0.207714\pi$
$728$			393.503i			0.540526i
$729$	−27.0000			−0.0370370
$730$	199.451	−	345.460i	0.273221	−	0.473233i
$731$	−8.46312	+	4.88618i	−0.0115775	+	0.00668425i
$732$	−512.981			−0.700794
$733$	−280.375	−	161.875i	−0.382503	−	0.220838i	0.296403	−	0.955063i	$-0.404213\pi$
$733$	−280.375	−	161.875i	−0.382503	−	0.220838i	−0.678907	+	0.734224i	$0.737546\pi$
$734$	1233.95			1.68113
$735$	−33.6408	−	58.2676i	−0.0457698	−	0.0792757i
$736$			415.031i			0.563900i
$737$	−65.2351	−	26.7796i	−0.0885144	−	0.0363359i
$738$	−239.330			−0.324296
$739$	1186.45	−	684.997i	1.60548	−	0.926925i	0.615117	−	0.788436i	$-0.289109\pi$
$739$	1186.45	−	684.997i	1.60548	−	0.926925i	0.990364	−	0.138489i	$-0.0442245\pi$
$740$		−	116.610i		−	0.157581i
$741$	−195.764	+	339.074i	−0.264190	+	0.457590i
$742$			721.080i			0.971806i
$743$	227.709	+	394.403i	0.306472	+	0.530825i	0.977588	−	0.210527i	$-0.0675181\pi$
$743$	227.709	+	394.403i	0.306472	+	0.530825i	−0.671116	+	0.741352i	$0.734185\pi$
$744$	1180.15	+	681.358i	1.58622	+	0.915803i
$745$			178.702i			0.239869i
$746$	1761.48			2.36123
$747$	−15.4576	−	26.7734i	−0.0206929	−	0.0358412i
$748$	15.5054	+	8.95207i	0.0207292	+	0.0119680i
$749$	−155.188	−	89.5978i	−0.207193	−	0.119623i
$750$	−248.089	+	143.234i	−0.330785	+	0.190979i
$751$	847.002			1.12783			0.563916	−	0.825832i	$-0.309294\pi$
$751$	847.002			1.12783			0.563916	+	0.825832i	$0.309294\pi$
$752$	−4751.70			−6.31876
$753$	−352.120	−	609.890i	−0.467623	−	0.809947i
$754$	604.863	+	1047.65i	0.802205	+	1.38946i
$755$	−42.2492	+	24.3926i	−0.0559592	+	0.0323081i
$756$	60.7154	+	105.162i	0.0803114	+	0.139103i
$757$	820.780	+	473.877i	1.08425	+	0.625994i	0.932041	−	0.362354i	$-0.118027\pi$
$757$	820.780	+	473.877i	1.08425	+	0.625994i	0.152213	+	0.988348i	$0.451360\pi$
$758$	−635.576	+	1100.85i	−0.838490	+	1.45231i
$759$	−7.40797			−0.00976017
$760$	349.068	+	604.604i	0.459300	+	0.795531i
$761$	132.104			0.173592			0.0867960	−	0.996226i	$-0.472337\pi$
$761$	132.104			0.173592			0.0867960	+	0.996226i	$0.472337\pi$
$762$	−19.5960			−0.0257165
$763$	−101.108	+	175.124i	−0.132514	+	0.229521i
$764$		−	1213.22i		−	1.58798i
$765$	−3.69445	+	2.13299i	−0.00482934	+	0.00278822i
$766$	334.079	−	578.642i	0.436134	−	0.755407i
$767$	−289.378	+	167.072i	−0.377285	+	0.217826i
$768$	472.449	+	272.768i	0.615168	+	0.355167i
$769$	−936.602	−	540.747i	−1.21795	−	0.703183i	−0.253469	−	0.967343i	$-0.581572\pi$
$769$	−936.602	−	540.747i	−1.21795	−	0.703183i	−0.964479	+	0.264161i	$0.914905\pi$
$770$	−3.92017	+	6.78994i	−0.00509113	+	0.00881810i
$771$	−88.1321	−	50.8831i	−0.114309	−	0.0659962i
$772$	−1051.41	+	1821.10i	−1.36193	+	2.35893i
$773$	−248.861	+	431.041i	−0.321942	+	0.557620i	−0.980889	−	0.194569i	$-0.937669\pi$
$773$	−248.861	+	431.041i	−0.321942	+	0.557620i	0.658946	+	0.752190i	$0.271002\pi$
$774$	−34.6367	−	59.9925i	−0.0447502	−	0.0775097i
$775$	661.727	+	382.048i	0.853841	+	0.492965i
$776$	1102.07	+	1908.84i	1.42019	+	2.45985i
$777$	−48.2103			−0.0620467
$778$	−239.818	−	138.459i	−0.308250	−	0.177968i
$779$			664.568i			0.853104i
$780$		−	114.480i		−	0.146769i
$781$	76.9200	−	44.4098i	0.0984892	−	0.0568627i
$782$			25.0070i			0.0319782i
$783$	200.613	+	115.824i	0.256211	+	0.147923i
$784$	−1167.09	+	2021.46i	−1.48863	+	2.57839i
$785$	−147.103	+	84.9299i	−0.187392	+	0.108191i
$786$	−783.551	−	1357.15i	−0.996884	−	1.72665i
$787$	−167.884	+	96.9279i	−0.213321	+	0.123161i	−0.602854	−	0.797851i	$-0.705970\pi$
$787$	−167.884	+	96.9279i	−0.213321	+	0.123161i	0.389533	+	0.921013i	$0.372637\pi$
$788$	1194.12	−	689.428i	1.51539	−	0.874909i
$789$			506.584i			0.642058i
$790$			225.961i			0.286026i
$791$	219.961	+	380.983i	0.278079	+	0.481648i
$792$	−39.3777	+	68.2042i	−0.0497193	+	0.0861164i
$793$	99.9717	−	173.156i	0.126068	−	0.218356i
$794$	−1582.55	+	913.685i	−1.99313	+	1.15074i
$795$		−	130.175i		−	0.163742i
$796$	−3429.41			−4.30831
$797$	372.837	−	645.773i	0.467801	−	0.810255i	−0.531522	−	0.847044i	$-0.678380\pi$
$797$	372.837	−	645.773i	0.467801	−	0.810255i	0.999323	+	0.0367894i	$0.0117131\pi$
$798$	402.823	−	232.570i	0.504791	−	0.291441i
$799$	−144.829			−0.181263
$800$	2142.57	+	1237.01i	2.67821	+	1.54627i
$801$	−68.8202			−0.0859178
$802$	−1173.99	−	2033.42i	−1.46383	−	2.53543i
$803$		−	124.954i		−	0.155609i
$804$	−1131.61	−	464.536i	−1.40747	−	0.577780i
$805$	−7.93833			−0.00986128
$806$	−741.277	+	427.977i	−0.919699	+	0.530989i
$807$			165.601i			0.205206i
$808$	1336.98	−	2315.71i	1.65468	−	2.86598i
$809$		−	284.782i		−	0.352017i	−0.984389	−	0.176008i	$-0.943681\pi$
$809$		−	284.782i		−	0.352017i	0.984389	−	0.176008i	$-0.0563186\pi$
$810$	−15.1201	−	26.1888i	−0.0186668	−	0.0323319i
$811$	623.695	+	360.090i	0.769044	+	0.444008i	0.832534	−	0.553975i	$-0.186890\pi$
$811$	623.695	+	360.090i	0.769044	+	0.444008i	−0.0634893	+	0.997983i	$0.520223\pi$
$812$		−	1041.82i		−	1.28303i
$813$	329.879			0.405756
$814$	−25.1942	−	43.6377i	−0.0309511	−	0.0536089i
$815$	36.2206	+	20.9120i	0.0444424	+	0.0256589i
$816$	128.170	+	73.9990i	0.157071	+	0.0906850i
$817$	−166.586	+	96.1784i	−0.203900	+	0.117721i
$818$	−709.990			−0.867958
$819$	−47.3298			−0.0577897
$820$	−97.1573	−	168.281i	−0.118485	−	0.205221i
$821$	−239.152	−	414.224i	−0.291294	−	0.504536i	0.682822	−	0.730585i	$-0.260752\pi$
$821$	−239.152	−	414.224i	−0.291294	−	0.504536i	−0.974116	+	0.226049i	$0.927419\pi$
$822$	−131.663	+	76.0154i	−0.160173	+	0.0924762i
$823$	−178.664	−	309.455i	−0.217089	−	0.376009i	0.736828	−	0.676080i	$-0.236323\pi$
$823$	−178.664	−	309.455i	−0.217089	−	0.376009i	−0.953917	+	0.300072i	$0.902989\pi$
$824$	−2143.37	−	1237.47i	−2.60117	−	1.50179i
$825$	−22.0797	+	38.2432i	−0.0267633	+	0.0463554i
$826$	396.967			0.480589
$827$	−327.086	−	566.530i	−0.395510	−	0.685043i	0.597657	−	0.801752i	$-0.296099\pi$
$827$	−327.086	−	566.530i	−0.395510	−	0.685043i	−0.993166	+	0.116710i	$0.962765\pi$
$828$	−128.503			−0.155197
$829$	696.011			0.839579			0.419790	−	0.907621i	$-0.362104\pi$
$829$	696.011			0.839579			0.419790	+	0.907621i	$0.362104\pi$
$830$	17.3127	−	29.9864i	0.0208586	−	0.0361282i
$831$			472.693i			0.568824i
$832$	−1094.94	+	632.161i	−1.31603	+	0.759809i
$833$	−35.5722	+	61.6128i	−0.0427037	+	0.0739649i
$834$	−1214.55	+	701.223i	−1.45630	+	0.840795i
$835$	41.5202	+	23.9717i	0.0497248	+	0.0287086i
$836$	305.205	+	176.210i	0.365078	+	0.210778i
$837$	−81.9524	+	141.946i	−0.0979120	+	0.169589i
$838$	−199.676	−	115.283i	−0.238277	−	0.137569i
$839$	−549.332	+	951.470i	−0.654746	+	1.13405i	0.327212	+	0.944951i	$0.393891\pi$
$839$	−549.332	+	951.470i	−0.654746	+	1.13405i	−0.981957	+	0.189102i	$0.939442\pi$
$840$	−42.1969	+	73.0872i	−0.0502344	+	0.0870086i
$841$	−573.217	−	992.842i	−0.681590	−	1.18055i
$842$	−739.280	−	426.824i	−0.878005	−	0.506916i
$843$	−110.969	−	192.203i	−0.131635	−	0.227999i
$844$	−1282.72			−1.51981
$845$	−90.3200	−	52.1463i	−0.106888	−	0.0617116i
$846$		−	1026.65i		−	1.21353i
$847$		−	265.803i		−	0.313817i
$848$	−3911.05	+	2258.05i	−4.61209	+	2.66279i
$849$		−	76.2656i		−	0.0898300i
$850$	129.097	+	74.5341i	0.151879	+	0.0876872i
$851$	25.5091	−	44.1830i	0.0299754	−	0.0519190i
$852$	1334.30	−	770.360i	1.56608	−	0.904179i
$853$	429.599	+	744.088i	0.503633	+	0.872319i	0.999991	+	0.00420060i	$0.00133710\pi$
$853$	429.599	+	744.088i	0.503633	+	0.872319i	−0.496358	+	0.868118i	$0.665330\pi$
$854$	−205.711	+	118.767i	−0.240879	+	0.139072i
$855$	−72.7206	+	41.9852i	−0.0850533	+	0.0491055i
$856$		−	2016.01i		−	2.35516i
$857$			850.912i			0.992897i	0.868066	+	0.496448i	$0.165363\pi$
$857$			850.912i			0.992897i	−0.868066	+	0.496448i	$0.834637\pi$
$858$	−24.7341	−	42.8406i	−0.0288276	−	0.0499308i
$859$	−106.561	+	184.568i	−0.124052	+	0.214864i	−0.921362	−	0.388706i	$-0.872922\pi$
$859$	−106.561	+	184.568i	−0.124052	+	0.214864i	0.797310	+	0.603570i	$0.206256\pi$
$860$	28.1219	−	48.7085i	0.0326998	−	0.0566378i
$861$	−69.5729	+	40.1679i	−0.0808048	+	0.0466527i
$862$		−	2114.59i		−	2.45312i
$863$	−1477.00			−1.71147			−0.855737	−	0.517410i	$-0.826896\pi$
$863$	−1477.00			−1.71147			−0.855737	+	0.517410i	$0.826896\pi$
$864$	−265.349	+	459.598i	−0.307117	+	0.531942i
$865$	−107.286	+	61.9418i	−0.124030	+	0.0716090i
$866$	243.788			0.281511
$867$	−429.593	−	248.026i	−0.495494	−	0.286074i
$868$	737.152			0.849253
$869$	35.3903	+	61.2979i	0.0407254	+	0.0705384i
$870$			259.448i			0.298216i
$871$	377.335	−	291.442i	0.433221	−	0.334607i
$872$	−2275.00			−2.60895
$873$	−229.592	+	132.555i	−0.262992	+	0.151838i
$874$			492.231i			0.563193i
$875$	−48.0793	+	83.2758i	−0.0549478	+	0.0951724i
$876$		−	2167.52i		−	2.47434i
$877$	568.670	+	984.965i	0.648427	+	1.12311i	0.983499	+	0.180915i	$0.0579060\pi$
$877$	568.670	+	984.965i	0.648427	+	1.12311i	−0.335072	+	0.942192i	$0.608761\pi$
$878$	690.736	+	398.797i	0.786715	+	0.454210i
$879$		−	322.642i		−	0.367056i
$880$	−49.1038			−0.0557998
$881$	−193.814	−	335.696i	−0.219994	−	0.381040i	0.734812	−	0.678271i	$-0.237270\pi$
$881$	−193.814	−	335.696i	−0.219994	−	0.381040i	−0.954806	+	0.297231i	$0.903937\pi$
$882$	−436.754	−	252.160i	−0.495186	−	0.285896i
$883$	1058.66	+	611.215i	1.19893	+	0.692203i	0.960317	−	0.278912i	$-0.0899736\pi$
$883$	1058.66	+	611.215i	1.19893	+	0.692203i	0.238614	+	0.971115i	$0.423307\pi$
$884$	−104.835	+	60.5263i	−0.118591	+	0.0684686i
$885$	−71.6633			−0.0809755
$886$	1805.87			2.03823
$887$	154.015	+	266.762i	0.173636	+	0.300746i	0.939688	−	0.342032i	$-0.111115\pi$
$887$	154.015	+	266.762i	0.173636	+	0.300746i	−0.766053	+	0.642778i	$0.777782\pi$
$888$	−271.192	−	469.718i	−0.305396	−	0.528961i
$889$	−5.69652	+	3.28889i	−0.00640778	+	0.00369953i
$890$	−38.5396	−	66.7525i	−0.0433029	−	0.0750028i
$891$	−8.20347	−	4.73627i	−0.00920703	−	0.00531568i
$892$	−660.844	+	1144.62i	−0.740857	+	1.28320i
$893$	−2850.78			−3.19237
$894$	669.747	+	1160.04i	0.749157	+	1.29758i
$895$	211.499			0.236312
$896$	596.306			0.665520
$897$	25.0432	−	43.3761i	0.0279188	−	0.0483568i
$898$			280.155i			0.311976i
$899$	1217.83	−	703.115i	1.35465	−	0.782107i
$900$	−383.008	+	663.390i	−0.425565	+	0.737100i
$901$	−119.207	+	68.8240i	−0.132305	+	0.0763862i
$902$	−72.7162	−	41.9827i	−0.0806167	−	0.0465441i
$903$	−20.1376	−	11.6265i	−0.0223008	−	0.0128754i
$904$	−2474.64	+	4286.20i	−2.73743	+	4.74137i
$905$	−84.2248	−	48.6272i	−0.0930661	−	0.0537317i
$906$	−182.839	+	316.686i	−0.201809	+	0.349543i
$907$	749.090	−	1297.46i	0.825899	−	1.43050i	−0.0753314	−	0.997159i	$-0.524001\pi$
$907$	749.090	−	1297.46i	0.825899	−	1.43050i	0.901230	−	0.433340i	$-0.142665\pi$
$908$	2180.44	+	3776.63i	2.40136	+	4.15928i
$909$	278.529	+	160.809i	0.306413	+	0.176908i
$910$	−26.5049	−	45.9078i	−0.0291262	−	0.0504481i
$911$	771.207			0.846550			0.423275	−	0.906001i	$-0.360880\pi$
$911$	771.207			0.846550			0.423275	+	0.906001i	$0.360880\pi$
$912$	2522.87	+	1456.58i	2.76630	+	1.59712i
$913$		−	10.8462i		−	0.0118797i
$914$		−	705.185i		−	0.771537i
$915$	37.1364	−	21.4407i	0.0405863	−	0.0234325i
$916$		−	3320.57i		−	3.62507i
$917$	−455.554	−	263.014i	−0.496787	−	0.286820i
$918$	−15.9882	+	27.6923i	−0.0174163	+	0.0301659i
$919$	−78.3208	+	45.2185i	−0.0852239	+	0.0492041i	−0.542006	−	0.840374i	$-0.682335\pi$
$919$	−78.3208	+	45.2185i	−0.0852239	+	0.0492041i	0.456782	+	0.889578i	$0.349002\pi$
$920$	−44.6546	−	77.3440i	−0.0485376	−	0.0840695i
$921$	−366.147	+	211.395i	−0.397553	+	0.229527i
$922$	−1383.84	+	798.961i	−1.50091	+	0.866552i
$923$			600.522i			0.650620i
$924$			42.6022i			0.0461063i
$925$	−152.061	−	263.378i	−0.164391	−	0.284733i
$926$	−554.066	+	959.670i	−0.598343	+	1.03636i
$927$	148.841	−	257.800i	0.160562	−	0.278101i
$928$	3943.15	−	2276.58i	4.24908	−	2.45321i
$929$		−	1567.69i		−	1.68751i	−0.536730	−	0.843754i	$-0.680341\pi$
$929$		−	1567.69i		−	1.68751i	0.536730	−	0.843754i	$-0.319659\pi$
$930$	−183.575			−0.197392
$931$	−700.194	+	1212.77i	−0.752088	+	1.30265i
$932$	2115.21	−	1221.22i	2.26954	−	1.31032i
$933$	478.251			0.512595
$934$	−1703.91	−	983.751i	−1.82431	−	1.05327i
$935$	−1.49665			−0.00160070
$936$	−266.238	−	461.138i	−0.284443	−	0.492669i
$937$			886.522i			0.946128i	0.881028	+	0.473064i	$0.156852\pi$
$937$			886.522i			0.946128i	−0.881028	+	0.473064i	$0.843148\pi$
$938$	−561.338	+	75.7105i	−0.598442	+	0.0807148i
$939$	786.432			0.837520
$940$	721.873	−	416.774i	0.767950	−	0.443376i
$941$			998.005i			1.06058i	0.847817	+	0.530289i	$0.177917\pi$
$941$			998.005i			1.06058i	−0.847817	+	0.530289i	$0.822083\pi$
$942$	−636.606	+	1102.63i	−0.675802	+	1.17052i
$943$		−	85.0149i		−	0.0901536i
$944$	1243.09	+	2153.10i	1.31684	+	2.28083i
$945$	−8.79078	−	5.07536i	−0.00930242	−	0.00537075i
$946$		−	24.3035i		−	0.0256908i
$947$	−87.8228			−0.0927379			−0.0463689	−	0.998924i	$-0.514765\pi$
$947$	−87.8228			−0.0927379			−0.0463689	+	0.998924i	$0.514765\pi$
$948$	613.903	+	1063.31i	0.647577	+	1.12164i
$949$	731.644	+	422.415i	0.770963	+	0.445116i
$950$	2541.11	+	1467.11i	2.67485	+	1.54433i
$951$	−427.891	+	247.043i	−0.449938	+	0.259772i
$952$	89.2389			0.0937384
$953$	1272.41			1.33517			0.667583	−	0.744535i	$-0.267329\pi$
$953$	1272.41			1.33517			0.667583	+	0.744535i	$0.267329\pi$
$954$	−487.872	−	845.020i	−0.511397	−	0.885765i
$955$	50.7081	+	87.8290i	0.0530975	+	0.0919675i
$956$	3054.43	−	1763.48i	3.19501	−	1.84464i
$957$	40.6351	+	70.3821i	0.0424609	+	0.0735445i
$958$	1128.18	+	651.357i	1.17764	+	0.679914i
$959$	−25.5161	+	44.1951i	−0.0266069	+	0.0460846i
$960$	−271.157			−0.282455
$961$	16.9957	+	29.4374i	0.0176855	+	0.0306321i
$962$	340.683			0.354141
$963$	242.482			0.251799
$964$	1940.68	−	3361.35i	2.01315	−	3.48688i
$965$		−	175.780i		−	0.182156i
$966$	−51.5312	+	29.7515i	−0.0533449	+	0.0307987i
$967$	−795.327	+	1377.55i	−0.822468	+	1.42456i	0.0813710	+	0.996684i	$0.474070\pi$
$967$	−795.327	+	1377.55i	−0.822468	+	1.42456i	−0.903839	+	0.427873i	$0.859263\pi$
$968$	2589.74	−	1495.19i	2.67535	−	1.54462i
$969$	76.8955	+	44.3956i	0.0793555	+	0.0458159i
$970$	−257.145	−	148.463i	−0.265098	−	0.153054i
$971$	−315.021	+	545.633i	−0.324430	+	0.561929i	−0.981397	−	0.191990i	$-0.938506\pi$
$971$	−315.021	+	545.633i	−0.324430	+	0.561929i	0.656967	+	0.753919i	$0.271839\pi$
$972$	−142.302	−	82.1584i	−0.146402	−	0.0845251i
$973$	−235.379	+	407.689i	−0.241911	+	0.419002i
$974$	1623.75	−	2812.42i	1.66710	−	2.88750i
$975$	−149.284	−	258.568i	−0.153112	−	0.265198i
$976$	−1288.36	−	743.835i	−1.32004	−	0.762126i
$977$	793.875	+	1375.03i	0.812564	+	1.40740i	0.911064	+	0.412266i	$0.135262\pi$
$977$	793.875	+	1375.03i	0.812564	+	1.40740i	−0.0984995	+	0.995137i	$0.531404\pi$
$978$	313.498			0.320550
$979$	−20.9098	−	12.0723i	−0.0213583	−	0.0123312i
$980$		−	409.463i		−	0.417819i
$981$		−	273.633i		−	0.278933i
$982$	−1885.19	+	1088.42i	−1.91975	+	1.10837i
$983$			578.367i			0.588369i	0.955749	+	0.294184i	$0.0950480\pi$
$983$			578.367i			0.588369i	−0.955749	+	0.294184i	$0.904952\pi$
$984$	−782.720	−	451.904i	−0.795448	−	0.459252i
$985$	−57.6311	+	99.8200i	−0.0585088	+	0.101340i
$986$	237.588	−	137.171i	0.240961	−	0.139119i
$987$	−172.308	−	298.446i	−0.174577	−	0.302376i
$988$	−2063.54	+	1191.38i	−2.08860	+	1.20585i
$989$	21.3105	−	12.3036i	0.0215475	−	0.0124405i
$990$		−	10.6093i		−	0.0107165i
$991$			1365.26i			1.37766i	0.724925	+	0.688828i	$0.241874\pi$
$991$			1365.26i			1.37766i	−0.724925	+	0.688828i	$0.758126\pi$
$992$	1610.81	+	2790.01i	1.62380	+	2.81251i
$993$	−382.346	+	662.242i	−0.385041	+	0.666911i
$994$	356.713	−	617.845i	0.358866	−	0.621575i
$995$	248.267	−	143.337i	0.249514	−	0.144057i
$996$		−	188.144i		−	0.188900i
$997$	530.351			0.531947			0.265974	−	0.963980i	$-0.414307\pi$
$997$	530.351			0.531947			0.265974	+	0.963980i	$0.414307\pi$
$998$	796.874	−	1380.23i	0.798471	−	1.38299i
$999$	56.4967	−	32.6184i	0.0565533	−	0.0326510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.a.97.1	✓	22
67.38	odd	6	inner	201.3.h.a.172.1	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.1	✓	22	1.1	even	1	trivial
201.3.h.a.172.1	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)

\(f(q)\)	\(=\)	\(q+(-3.30238 + 1.90663i) q^{2} -1.73205i q^{3} +(5.27046 - 9.12871i) q^{4} +0.881143i q^{5} +(3.30238 + 5.71988i) q^{6} +(1.91999 + 1.10851i) q^{7} +24.9422i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-3.30238 + 1.90663i) q^{2} -1.73205i q^{3} +(5.27046 - 9.12871i) q^{4} +0.881143i q^{5} +(3.30238 + 5.71988i) q^{6} +(1.91999 + 1.10851i) q^{7} +24.9422i q^{8} -3.00000 q^{9} +(-1.68001 - 2.90987i) q^{10} +(-0.911496 - 0.526253i) q^{11} +(-15.8114 - 9.12871i) q^{12} +(6.16276 - 3.55807i) q^{13} -8.45404 q^{14} +1.52619 q^{15} +(-26.4737 - 45.8537i) q^{16} +(-0.806902 - 1.39760i) q^{17} +(9.90713 - 5.71988i) q^{18} +(-15.8829 - 27.5099i) q^{19} +(8.04370 + 4.64403i) q^{20} +(1.91999 - 3.32552i) q^{21} +4.01347 q^{22} +(2.03182 + 3.51921i) q^{23} +43.2012 q^{24} +24.2236 q^{25} +(-13.5678 + 23.5002i) q^{26} +5.19615i q^{27} +(20.2385 - 11.6847i) q^{28} +(22.2903 - 38.6080i) q^{29} +(-5.04004 + 2.90987i) q^{30} +(27.3175 + 15.7717i) q^{31} +(88.4497 + 51.0665i) q^{32} +(-0.911496 + 1.57876i) q^{33} +(5.32939 + 3.07692i) q^{34} +(-0.976754 + 1.69179i) q^{35} +(-15.8114 + 27.3861i) q^{36} +(-6.27741 - 10.8728i) q^{37} +(104.902 + 60.5654i) q^{38} +(-6.16276 - 10.6742i) q^{39} -21.9777 q^{40} +(-18.1180 - 10.4605i) q^{41} +14.6428i q^{42} -6.05549i q^{43} +(-9.60801 + 5.54719i) q^{44} -2.64343i q^{45} +(-13.4196 - 7.74783i) q^{46} +(44.8720 - 77.7206i) q^{47} +(-79.4210 + 45.8537i) q^{48} +(-22.0424 - 38.1786i) q^{49} +(-79.9954 + 46.1854i) q^{50} +(-2.42071 + 1.39760i) q^{51} -75.0107i q^{52} -85.2941i q^{53} +(-9.90713 - 17.1597i) q^{54} +(0.463704 - 0.803159i) q^{55} +(-27.6486 + 47.8888i) q^{56} +(-47.6486 + 27.5099i) q^{57} +169.997i q^{58} -46.9558 q^{59} +(8.04370 - 13.9321i) q^{60} +(24.3328 - 14.0486i) q^{61} -120.283 q^{62} +(-5.75997 - 3.32552i) q^{63} -177.670 q^{64} +(3.13517 + 5.43027i) q^{65} -6.95154i q^{66} +(66.3988 - 8.95554i) q^{67} -17.0110 q^{68} +(6.09545 - 3.51921i) q^{69} -7.44922i q^{70} +(-42.1944 + 73.0828i) q^{71} -74.8266i q^{72} +(59.3601 + 102.815i) q^{73} +(41.4608 + 23.9374i) q^{74} -41.9565i q^{75} -334.840 q^{76} +(-1.16671 - 2.02080i) q^{77} +(40.7035 + 23.5002i) q^{78} +(-58.2400 - 33.6249i) q^{79} +(40.4037 - 23.3271i) q^{80} +9.00000 q^{81} +79.7768 q^{82} +(5.15254 + 8.92447i) q^{83} +(-20.2385 - 35.0541i) q^{84} +(1.23148 - 0.710996i) q^{85} +(11.5456 + 19.9975i) q^{86} +(-66.8710 - 38.6080i) q^{87} +(13.1259 - 22.7347i) q^{88} +22.9401 q^{89} +(5.04004 + 8.72960i) q^{90} +15.7766 q^{91} +42.8344 q^{92} +(27.3175 - 47.3152i) q^{93} +342.217i q^{94} +(24.2402 - 13.9951i) q^{95} +(88.4497 - 153.199i) q^{96} +(76.5306 - 44.1850i) q^{97} +(145.585 + 84.0534i) q^{98} +(2.73449 + 1.57876i) 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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