LMFDB - Embedded newform 287.2.e.d.165.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (of order $3$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.17
Character	$\chi$	$=$	287.165
Dual form			287.2.e.d.247.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38401 + 2.39717i) q^{2} +(1.42525 - 2.46860i) q^{3} +(-2.83094 + 4.90334i) q^{4} +(1.51053 + 2.61632i) q^{5} +7.89019 q^{6} +(1.12514 - 2.39459i) q^{7} -10.1361 q^{8} +(-2.56265 - 4.43864i) q^{9} +O(q^{10})$	\(q+(1.38401 + 2.39717i) q^{2} +(1.42525 - 2.46860i) q^{3} +(-2.83094 + 4.90334i) q^{4} +(1.51053 + 2.61632i) q^{5} +7.89019 q^{6} +(1.12514 - 2.39459i) q^{7} -10.1361 q^{8} +(-2.56265 - 4.43864i) q^{9} +(-4.18117 + 7.24200i) q^{10} +(0.404704 - 0.700968i) q^{11} +(8.06958 + 13.9769i) q^{12} -3.86586 q^{13} +(7.29743 - 0.616977i) q^{14} +8.61152 q^{15} +(-8.36658 - 14.4913i) q^{16} +(0.414002 - 0.717073i) q^{17} +(7.09344 - 12.2862i) q^{18} +(0.946033 + 1.63858i) q^{19} -17.1049 q^{20} +(-4.30768 - 6.19040i) q^{21} +2.24045 q^{22} +(0.237683 + 0.411679i) q^{23} +(-14.4465 + 25.0220i) q^{24} +(-2.06342 + 3.57395i) q^{25} +(-5.35037 - 9.26711i) q^{26} -6.05815 q^{27} +(8.55627 + 12.2959i) q^{28} -2.61064 q^{29} +(11.9184 + 20.6433i) q^{30} +(-0.224522 + 0.388883i) q^{31} +(13.0227 - 22.5559i) q^{32} +(-1.15360 - 1.99810i) q^{33} +2.29192 q^{34} +(7.96457 - 0.673382i) q^{35} +29.0189 q^{36} +(-1.62940 - 2.82220i) q^{37} +(-2.61863 + 4.53560i) q^{38} +(-5.50979 + 9.54324i) q^{39} +(-15.3110 - 26.5194i) q^{40} +1.00000 q^{41} +(8.87757 - 18.8938i) q^{42} -6.10120 q^{43} +(2.29139 + 3.96880i) q^{44} +(7.74193 - 13.4094i) q^{45} +(-0.657909 + 1.13953i) q^{46} +(2.83987 + 4.91879i) q^{47} -47.6977 q^{48} +(-4.46812 - 5.38850i) q^{49} -11.4231 q^{50} +(-1.18011 - 2.04401i) q^{51} +(10.9440 - 18.9556i) q^{52} +(6.50421 - 11.2656i) q^{53} +(-8.38451 - 14.5224i) q^{54} +2.44527 q^{55} +(-11.4046 + 24.2719i) q^{56} +5.39331 q^{57} +(-3.61315 - 6.25815i) q^{58} +(4.76477 - 8.25283i) q^{59} +(-24.3787 + 42.2252i) q^{60} +(5.85474 + 10.1407i) q^{61} -1.24296 q^{62} +(-13.5121 + 1.14241i) q^{63} +38.6274 q^{64} +(-5.83950 - 10.1143i) q^{65} +(3.19319 - 5.53077i) q^{66} +(-2.56678 + 4.44580i) q^{67} +(2.34403 + 4.05998i) q^{68} +1.35503 q^{69} +(12.6372 + 18.1605i) q^{70} -1.45987 q^{71} +(25.9754 + 44.9907i) q^{72} +(-4.37044 + 7.56982i) q^{73} +(4.51019 - 7.81188i) q^{74} +(5.88176 + 10.1875i) q^{75} -10.7127 q^{76} +(-1.22318 - 1.75779i) q^{77} -30.5023 q^{78} +(5.34420 + 9.25642i) q^{79} +(25.2760 - 43.7793i) q^{80} +(-0.946397 + 1.63921i) q^{81} +(1.38401 + 2.39717i) q^{82} -6.30118 q^{83} +(42.5484 - 3.59734i) q^{84} +2.50146 q^{85} +(-8.44410 - 14.6256i) q^{86} +(-3.72081 + 6.44463i) q^{87} +(-4.10213 + 7.10510i) q^{88} +(1.53772 + 2.66341i) q^{89} +42.8595 q^{90} +(-4.34963 + 9.25714i) q^{91} -2.69147 q^{92} +(0.639997 + 1.10851i) q^{93} +(-7.86078 + 13.6153i) q^{94} +(-2.85803 + 4.95025i) q^{95} +(-37.1210 - 64.2954i) q^{96} -15.8551 q^{97} +(6.73322 - 18.1685i) q^{98} -4.14846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) $ 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.38401	+	2.39717i	0.978640	+	1.69505i	0.667360	+	0.744735i	$0.267424\pi$
$2$	1.38401	+	2.39717i	0.978640	+	1.69505i	0.311280	+	0.950318i	$0.399242\pi$
$3$	1.42525	−	2.46860i	0.822866	−	1.42525i	−0.0806736	−	0.996741i	$-0.525707\pi$
$3$	1.42525	−	2.46860i	0.822866	−	1.42525i	0.903539	−	0.428505i	$-0.140960\pi$
$4$	−2.83094	+	4.90334i	−1.41547	+	2.45167i
$5$	1.51053	+	2.61632i	0.675531	+	1.17005i	0.976313	+	0.216361i	$0.0694188\pi$
$5$	1.51053	+	2.61632i	0.675531	+	1.17005i	−0.300782	+	0.953693i	$0.597248\pi$
$6$	7.89019			3.22116
$7$	1.12514	−	2.39459i	0.425263	−	0.905070i
$7$	1.12514	−	2.39459i	0.425263	−	0.905070i
$8$	−10.1361			−3.58367
$9$	−2.56265	−	4.43864i	−0.854217	−	1.47955i
$10$	−4.18117	+	7.24200i	−1.32220	+	2.29012i
$11$	0.404704	−	0.700968i	0.122023	−	0.211350i	−0.798542	−	0.601939i	$-0.794395\pi$
$11$	0.404704	−	0.700968i	0.122023	−	0.211350i	0.920565	+	0.390589i	$0.127729\pi$
$12$	8.06958	+	13.9769i	2.32949	+	4.03479i
$13$	−3.86586			−1.07220			−0.536098	−	0.844156i	$-0.680102\pi$
$13$	−3.86586			−1.07220			−0.536098	+	0.844156i	$0.680102\pi$
$14$	7.29743	−	0.616977i	1.95032	−	0.164894i
$15$	8.61152			2.22349
$16$	−8.36658	−	14.4913i	−2.09165	−	3.62284i
$17$	0.414002	−	0.717073i	0.100410	−	0.173916i	−0.811443	−	0.584431i	$-0.801318\pi$
$17$	0.414002	−	0.717073i	0.100410	−	0.173916i	0.911854	+	0.410515i	$0.134651\pi$
$18$	7.09344	−	12.2862i	1.67194	−	2.89589i
$19$	0.946033	+	1.63858i	0.217035	+	0.375915i	0.953900	−	0.300124i	$-0.0970282\pi$
$19$	0.946033	+	1.63858i	0.217035	+	0.375915i	−0.736865	+	0.676040i	$0.763695\pi$
$20$	−17.1049			−3.82478
$21$	−4.30768	−	6.19040i	−0.940013	−	1.35086i
$22$	2.24045			0.477665
$23$	0.237683	+	0.411679i	0.0495603	+	0.0858410i	0.889741	−	0.456465i	$-0.150885\pi$
$23$	0.237683	+	0.411679i	0.0495603	+	0.0858410i	−0.840181	+	0.542306i	$0.817551\pi$
$24$	−14.4465	+	25.0220i	−2.94888	+	5.10760i
$25$	−2.06342	+	3.57395i	−0.412684	+	0.714790i
$26$	−5.35037	−	9.26711i	−1.04929	−	1.81743i
$27$	−6.05815			−1.16589
$28$	8.55627	+	12.2959i	1.61698	+	2.32370i
$29$	−2.61064			−0.484784			−0.242392	−	0.970178i	$-0.577932\pi$
$29$	−2.61064			−0.484784			−0.242392	+	0.970178i	$0.577932\pi$
$30$	11.9184	+	20.6433i	2.17599	+	3.76893i
$31$	−0.224522	+	0.388883i	−0.0403253	+	0.0698454i	−0.885484	−	0.464671i	$-0.846173\pi$
$31$	−0.224522	+	0.388883i	−0.0403253	+	0.0698454i	0.845158	+	0.534516i	$0.179506\pi$
$32$	13.0227	−	22.5559i	2.30210	−	3.98736i
$33$	−1.15360	−	1.99810i	−0.200817	−	0.347825i
$34$	2.29192			0.393062
$35$	7.96457	−	0.673382i	1.34626	−	0.113822i
$36$	29.0189			4.83648
$37$	−1.62940	−	2.82220i	−0.267871	−	0.463967i	0.700441	−	0.713711i	$-0.252987\pi$
$37$	−1.62940	−	2.82220i	−0.267871	−	0.463967i	−0.968312	+	0.249744i	$0.919654\pi$
$38$	−2.61863	+	4.53560i	−0.424798	+	0.735771i
$39$	−5.50979	+	9.54324i	−0.882273	+	1.52814i
$40$	−15.3110	−	26.5194i	−2.42088	−	4.19308i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	8.87757	−	18.8938i	1.36984	−	2.91537i
$43$	−6.10120			−0.930425			−0.465212	−	0.885199i	$-0.654022\pi$
$43$	−6.10120			−0.930425			−0.465212	+	0.885199i	$0.654022\pi$
$44$	2.29139	+	3.96880i	0.345440	+	0.598319i
$45$	7.74193	−	13.4094i	1.15410	−	1.99896i
$46$	−0.657909	+	1.13953i	−0.0970034	+	0.168015i
$47$	2.83987	+	4.91879i	0.414237	+	0.717480i	0.995348	−	0.0963448i	$-0.0307151\pi$
$47$	2.83987	+	4.91879i	0.414237	+	0.717480i	−0.581111	+	0.813824i	$0.697382\pi$
$48$	−47.6977			−6.88458
$49$	−4.46812	−	5.38850i	−0.638303	−	0.769785i
$50$	−11.4231			−1.61548
$51$	−1.18011	−	2.04401i	−0.165248	−	0.286219i
$52$	10.9440	−	18.9556i	1.51766	−	2.62867i
$53$	6.50421	−	11.2656i	0.893422	−	1.54745i	0.0576769	−	0.998335i	$-0.481631\pi$
$53$	6.50421	−	11.2656i	0.893422	−	1.54745i	0.835745	−	0.549117i	$-0.185036\pi$
$54$	−8.38451	−	14.5224i	−1.14099	−	1.97625i
$55$	2.44527			0.329721
$56$	−11.4046	+	24.2719i	−1.52400	+	3.24347i
$57$	5.39331			0.714362
$58$	−3.61315	−	6.25815i	−0.474429	−	0.821735i
$59$	4.76477	−	8.25283i	0.620321	−	1.07443i	−0.369105	−	0.929388i	$-0.620336\pi$
$59$	4.76477	−	8.25283i	0.620321	−	1.07443i	0.989426	−	0.145039i	$-0.0463308\pi$
$60$	−24.3787	+	42.2252i	−3.14728	+	5.45125i
$61$	5.85474	+	10.1407i	0.749623	+	1.29839i	0.948003	+	0.318260i	$0.103099\pi$
$61$	5.85474	+	10.1407i	0.749623	+	1.29839i	−0.198380	+	0.980125i	$0.563568\pi$
$62$	−1.24296			−0.157856
$63$	−13.5121	+	1.14241i	−1.70236	+	0.143930i
$64$	38.6274			4.82842
$65$	−5.83950	−	10.1143i	−0.724301	−	1.25453i
$66$	3.19319	−	5.53077i	0.393055	−	0.680791i
$67$	−2.56678	+	4.44580i	−0.313583	+	0.543141i	−0.979135	−	0.203210i	$-0.934863\pi$
$67$	−2.56678	+	4.44580i	−0.313583	+	0.543141i	0.665553	+	0.746351i	$0.268196\pi$
$68$	2.34403	+	4.05998i	0.284256	+	0.492345i
$69$	1.35503			0.163126
$70$	12.6372	+	18.1605i	1.51044	+	2.17059i
$71$	−1.45987			−0.173255			−0.0866273	−	0.996241i	$-0.527609\pi$
$71$	−1.45987			−0.173255			−0.0866273	+	0.996241i	$0.527609\pi$
$72$	25.9754	+	44.9907i	3.06123	+	5.30220i
$73$	−4.37044	+	7.56982i	−0.511521	+	0.885981i	0.488389	+	0.872626i	$0.337585\pi$
$73$	−4.37044	+	7.56982i	−0.511521	+	0.885981i	−0.999911	+	0.0133552i	$0.995749\pi$
$74$	4.51019	−	7.81188i	0.524299	−	0.908113i
$75$	5.88176	+	10.1875i	0.679167	+	1.17635i
$76$	−10.7127			−1.22883
$77$	−1.22318	−	1.75779i	−0.139395	−	0.200318i
$78$	−30.5023			−3.45371
$79$	5.34420	+	9.25642i	0.601269	+	1.04143i	0.992629	+	0.121191i	$0.0386714\pi$
$79$	5.34420	+	9.25642i	0.601269	+	1.04143i	−0.391360	+	0.920238i	$0.627995\pi$
$80$	25.2760	−	43.7793i	2.82594	−	4.89468i
$81$	−0.946397	+	1.63921i	−0.105155	+	0.182134i
$82$	1.38401	+	2.39717i	0.152838	+	0.264723i
$83$	−6.30118			−0.691644			−0.345822	−	0.938300i	$-0.612400\pi$
$83$	−6.30118			−0.691644			−0.345822	+	0.938300i	$0.612400\pi$
$84$	42.5484	−	3.59734i	4.64241	−	0.392502i
$85$	2.50146			0.271321
$86$	−8.44410	−	14.6256i	−0.910551	−	1.57712i
$87$	−3.72081	+	6.44463i	−0.398913	+	0.690937i
$88$	−4.10213	+	7.10510i	−0.437289	+	0.757407i
$89$	1.53772	+	2.66341i	0.162998	+	0.282321i	0.935942	−	0.352153i	$-0.114550\pi$
$89$	1.53772	+	2.66341i	0.162998	+	0.282321i	−0.772945	+	0.634473i	$0.781217\pi$
$90$	42.8595			4.51779
$91$	−4.34963	+	9.25714i	−0.455965	+	0.970412i
$92$	−2.69147			−0.280605
$93$	0.639997	+	1.10851i	0.0663646	+	0.114947i
$94$	−7.86078	+	13.6153i	−0.810778	+	1.40431i
$95$	−2.85803	+	4.95025i	−0.293227	+	0.507885i
$96$	−37.1210	−	64.2954i	−3.78864	−	6.56212i
$97$	−15.8551			−1.60984			−0.804918	−	0.593386i	$-0.797791\pi$
$97$	−15.8551			−1.60984			−0.804918	+	0.593386i	$0.797791\pi$
$98$	6.73322	−	18.1685i	0.680158	−	1.83530i
$99$	−4.14846			−0.416936
$100$	−11.6828	−	20.2353i	−1.16828	−	2.02353i
$101$	−1.42946	+	2.47590i	−0.142237	+	0.246361i	−0.928339	−	0.371736i	$-0.878763\pi$
$101$	−1.42946	+	2.47590i	−0.142237	+	0.246361i	0.786102	+	0.618097i	$0.212096\pi$
$102$	3.26656	−	5.65784i	0.323437	−	0.560210i
$103$	4.87428	+	8.44249i	0.480277	+	0.831864i	0.999744	−	0.0226267i	$-0.00720292\pi$
$103$	4.87428	+	8.44249i	0.480277	+	0.831864i	−0.519467	+	0.854490i	$0.673870\pi$
$104$	39.1848			3.84239
$105$	9.68916	−	20.6211i	0.945566	−	2.01241i
$106$	36.0075			3.49735
$107$	7.44246	+	12.8907i	0.719489	+	1.24619i	0.961202	+	0.275844i	$0.0889574\pi$
$107$	7.44246	+	12.8907i	0.719489	+	1.24619i	−0.241713	+	0.970348i	$0.577709\pi$
$108$	17.1503	−	29.7051i	1.65028	−	2.85838i
$109$	4.87979	−	8.45204i	0.467399	−	0.809558i	−0.531907	−	0.846803i	$-0.678525\pi$
$109$	4.87979	−	8.45204i	0.467399	−	0.809558i	0.999306	+	0.0372440i	$0.0118579\pi$
$110$	3.38427	+	5.86173i	0.322678	+	0.558894i
$111$	−9.28917			−0.881689
$112$	−44.1144	+	3.72975i	−4.16842	+	0.352428i
$113$	−20.3338			−1.91284			−0.956420	−	0.291996i	$-0.905681\pi$
$113$	−20.3338			−1.91284			−0.956420	+	0.291996i	$0.905681\pi$
$114$	7.46438	+	12.9287i	0.699103	+	1.21088i
$115$	−0.718056	+	1.24371i	−0.0669590	+	0.115976i
$116$	7.39058	−	12.8009i	0.686198	−	1.18853i
$117$	9.90684	+	17.1591i	0.915887	+	1.58636i
$118$	26.3779			2.42828
$119$	−1.25128	−	1.79817i	−0.114705	−	0.164838i
$120$	−87.2876			−7.96823
$121$	5.17243	+	8.95891i	0.470221	+	0.814446i
$122$	−16.2060	+	28.0696i	−1.46722	+	2.54130i
$123$	1.42525	−	2.46860i	0.128510	−	0.222586i
$124$	−1.27122	−	2.20181i	−0.114159	−	0.197728i
$125$	2.63787			0.235939
$126$	−21.4393	−	30.8096i	−1.90996	−	2.74474i
$127$	7.82133			0.694031			0.347015	−	0.937859i	$-0.387195\pi$
$127$	7.82133			0.694031			0.347015	+	0.937859i	$0.387195\pi$
$128$	27.4152	+	47.4845i	2.42318	+	4.19708i
$129$	−8.69571	+	15.0614i	−0.765615	+	1.32608i
$130$	16.1638	−	27.9965i	1.41766	−	2.45546i
$131$	1.22626	+	2.12394i	0.107139	+	0.185570i	0.914610	−	0.404337i	$-0.132498\pi$
$131$	1.22626	+	2.12394i	0.107139	+	0.185570i	−0.807471	+	0.589907i	$0.799164\pi$
$132$	13.0632			1.13700
$133$	4.98814	−	0.421733i	0.432526	−	0.0365689i
$134$	−14.2098			−1.22754
$135$	−9.15103	−	15.8500i	−0.787595	−	1.36416i
$136$	−4.19638	+	7.26835i	−0.359837	+	0.623256i
$137$	−6.67878	+	11.5680i	−0.570607	+	0.988320i	0.425897	+	0.904772i	$0.359959\pi$
$137$	−6.67878	+	11.5680i	−0.570607	+	0.988320i	−0.996504	+	0.0835483i	$0.973375\pi$
$138$	1.87536	+	3.24822i	0.159642	+	0.276507i
$139$	−9.08568			−0.770638			−0.385319	−	0.922784i	$-0.625909\pi$
$139$	−9.08568			−0.770638			−0.385319	+	0.922784i	$0.625909\pi$
$140$	−19.2454	+	40.9593i	−1.62654	+	3.46169i
$141$	16.1900			1.36345
$142$	−2.02047	−	3.49955i	−0.169554	−	0.293676i
$143$	−1.56453	+	2.70984i	−0.130832	+	0.226608i
$144$	−42.8812	+	74.2725i	−3.57344	+	6.18937i
$145$	−3.94346	−	6.83028i	−0.327487	−	0.567224i
$146$	−24.1949			−2.00238
$147$	−19.6702	+	3.35007i	−1.62237	+	0.276309i
$148$	18.4509			1.51666
$149$	−1.47041	−	2.54682i	−0.120460	−	0.208643i	0.799489	−	0.600681i	$-0.205104\pi$
$149$	−1.47041	−	2.54682i	−0.120460	−	0.208643i	−0.919949	+	0.392037i	$0.871770\pi$
$150$	−16.2808	+	28.1991i	−1.32932	+	2.30245i
$151$	−0.959050	+	1.66112i	−0.0780464	+	0.135180i	−0.902407	−	0.430885i	$-0.858202\pi$
$151$	−0.959050	+	1.66112i	−0.0780464	+	0.135180i	0.824361	+	0.566065i	$0.191535\pi$
$152$	−9.58911	−	16.6088i	−0.777780	−	1.34715i
$153$	−4.24377			−0.343088
$154$	2.52082	−	5.36496i	0.203133	−	0.432321i
$155$	−1.35659			−0.108964
$156$	−31.1958	−	54.0327i	−2.49766	−	4.32608i
$157$	−5.25445	+	9.10098i	−0.419351	+	0.726337i	−0.995874	−	0.0907437i	$-0.971076\pi$
$157$	−5.25445	+	9.10098i	−0.419351	+	0.726337i	0.576523	+	0.817081i	$0.304409\pi$
$158$	−14.7928	+	25.6219i	−1.17685	+	2.03837i
$159$	−18.5402	−	32.1126i	−1.47033	−	2.54669i
$160$	78.6846			6.22057
$161$	1.25323	−	0.105957i	0.0987682	−	0.00835057i
$162$	−5.23927			−0.411636
$163$	−9.04376	−	15.6643i	−0.708362	−	1.22692i	−0.965464	−	0.260535i	$-0.916101\pi$
$163$	−9.04376	−	15.6643i	−0.708362	−	1.22692i	0.257103	−	0.966384i	$-0.417232\pi$
$164$	−2.83094	+	4.90334i	−0.221059	+	0.382886i
$165$	3.48512	−	6.03640i	0.271316	−	0.469933i
$166$	−8.72086	−	15.1050i	−0.676870	−	1.17237i
$167$	19.0456			1.47380			0.736898	−	0.676004i	$-0.236290\pi$
$167$	19.0456			1.47380			0.736898	+	0.676004i	$0.236290\pi$
$168$	43.6632	+	62.7467i	3.36869	+	4.84101i
$169$	1.94485			0.149604
$170$	3.46203	+	5.99641i	0.265525	+	0.459904i
$171$	4.84870	−	8.39819i	0.370789	−	0.642226i
$172$	17.2722	−	29.9162i	1.31699	−	2.28109i
$173$	2.31718	+	4.01346i	0.176172	+	0.305138i	0.940566	−	0.339611i	$-0.110295\pi$
$173$	2.31718	+	4.01346i	0.176172	+	0.305138i	−0.764395	+	0.644749i	$0.776962\pi$
$174$	−20.5985			−1.56157
$175$	6.23651	+	8.96224i	0.471436	+	0.677481i
$176$	−13.5440			−1.02091
$177$	−13.5819	−	23.5246i	−1.02088	−	1.76822i
$178$	−4.25642	+	7.37234i	−0.319032	+	0.552580i
$179$	5.39179	−	9.33885i	0.403001	−	0.698018i	−0.591086	−	0.806609i	$-0.701300\pi$
$179$	5.39179	−	9.33885i	0.403001	−	0.698018i	0.994087	+	0.108591i	$0.0346338\pi$
$180$	43.8339	+	75.9226i	3.26719	+	5.65894i
$181$	19.6683			1.46193			0.730965	−	0.682415i	$-0.239070\pi$
$181$	19.6683			1.46193			0.730965	+	0.682415i	$0.239070\pi$
$182$	−28.2108	+	2.38515i	−2.09113	+	0.176799i
$183$	33.3778			2.46736
$184$	−2.40919	−	4.17283i	−0.177608	−	0.307625i
$185$	4.92252	−	8.52605i	0.361911	−	0.626848i
$186$	−1.77152	+	3.06836i	−0.129894	+	0.224983i
$187$	−0.335097	−	0.580404i	−0.0245047	−	0.0424434i
$188$	−32.1580			−2.34536
$189$	−6.81626	+	14.5068i	−0.495810	+	1.05521i
$190$	−15.8221			−1.14786
$191$	−11.6115	−	20.1117i	−0.840177	−	1.45523i	−0.889745	−	0.456458i	$-0.849118\pi$
$191$	−11.6115	−	20.1117i	−0.840177	−	1.45523i	0.0495678	−	0.998771i	$-0.484216\pi$
$192$	55.0535	−	95.3555i	3.97315	−	6.88169i
$193$	7.38409	−	12.7896i	0.531518	−	0.920616i	−0.467805	−	0.883832i	$-0.654955\pi$
$193$	7.38409	−	12.7896i	0.531518	−	0.920616i	0.999323	−	0.0367848i	$-0.0117116\pi$
$194$	−21.9435	−	38.0072i	−1.57545	−	2.72876i
$195$	−33.2909			−2.38401
$196$	39.0706	−	6.65418i	2.79076	−	0.475299i
$197$	−22.0210			−1.56893			−0.784466	−	0.620172i	$-0.787063\pi$
$197$	−22.0210			−1.56893			−0.784466	+	0.620172i	$0.787063\pi$
$198$	−5.74149	−	9.94455i	−0.408030	−	0.706728i
$199$	3.57620	−	6.19416i	0.253510	−	0.439092i	−0.710980	−	0.703213i	$-0.751748\pi$
$199$	3.57620	−	6.19416i	0.253510	−	0.439092i	0.964490	+	0.264120i	$0.0850816\pi$
$200$	20.9151	−	36.2260i	1.47892	−	2.56157i
$201$	7.31659	+	12.6727i	0.516073	+	0.893864i
$202$	−7.91353			−0.556794
$203$	−2.93734	+	6.25142i	−0.206161	+	0.438764i
$204$	13.3633			0.935617
$205$	1.51053	+	2.61632i	0.105500	+	0.182732i
$206$	−13.4920	+	23.3689i	−0.940036	+	1.62819i
$207$	1.21820	−	2.10998i	0.0846705	−	0.146654i
$208$	32.3440	+	56.0215i	2.24265	+	3.88439i
$209$	1.53145			0.105933
$210$	62.8420	−	5.31311i	4.33651	−	0.366640i
$211$	17.5087			1.20535			0.602673	−	0.797988i	$-0.294102\pi$
$211$	17.5087			1.20535			0.602673	+	0.797988i	$0.294102\pi$
$212$	36.8261	+	63.7847i	2.52923	+	4.38075i
$213$	−2.08067	+	3.60383i	−0.142565	+	0.246930i
$214$	−20.6008	+	35.6816i	−1.40824	+	2.43915i
$215$	−9.21607	−	15.9627i	−0.628531	−	1.08865i
$216$	61.4062			4.17816
$217$	0.678597	+	0.975185i	0.0460662	+	0.0661999i
$218$	27.0146			1.82966
$219$	12.4579	+	21.5777i	0.841827	+	1.45809i
$220$	−6.92243	+	11.9900i	−0.466710	+	0.808366i
$221$	−1.60047	+	2.77210i	−0.107659	+	0.186472i
$222$	−12.8563	−	22.2677i	−0.862856	−	1.49451i
$223$	9.22671			0.617866			0.308933	−	0.951084i	$-0.400028\pi$
$223$	9.22671			0.617866			0.308933	+	0.951084i	$0.400028\pi$
$224$	−39.3598	−	56.5625i	−2.62984	−	3.77924i
$225$	21.1513			1.41009
$226$	−28.1420	−	48.7434i	−1.87198	−	3.24236i
$227$	−10.9427	+	18.9532i	−0.726290	+	1.25797i	0.232151	+	0.972680i	$0.425424\pi$
$227$	−10.9427	+	18.9532i	−0.726290	+	1.25797i	−0.958441	+	0.285291i	$0.907910\pi$
$228$	−15.2682	+	26.4452i	−1.01116	+	1.75138i
$229$	4.45733	+	7.72032i	0.294548	+	0.510173i	0.974880	−	0.222732i	$-0.0714974\pi$
$229$	4.45733	+	7.72032i	0.294548	+	0.510173i	−0.680331	+	0.732905i	$0.738164\pi$
$230$	−3.97517			−0.262115
$231$	−6.08260	+	0.514267i	−0.400206	+	0.0338363i
$232$	26.4618			1.73730
$233$	−0.268519	−	0.465088i	−0.0175912	−	0.0304689i	0.857096	−	0.515157i	$-0.172266\pi$
$233$	−0.268519	−	0.465088i	−0.0175912	−	0.0304689i	−0.874687	+	0.484688i	$0.838933\pi$
$234$	−27.4222	+	47.4967i	−1.79265	+	3.10496i
$235$	−8.57942	+	14.8600i	−0.559660	+	0.969359i
$236$	26.9776	+	46.7266i	1.75609	+	3.04164i
$237$	30.4672			1.97906
$238$	2.57874	−	5.48822i	0.167155	−	0.355748i
$239$	14.2066			0.918951			0.459476	−	0.888190i	$-0.348037\pi$
$239$	14.2066			0.918951			0.459476	+	0.888190i	$0.348037\pi$
$240$	−72.0490	−	124.793i	−4.65074	−	8.05533i
$241$	3.59363	−	6.22435i	0.231486	−	0.400945i	−0.726760	−	0.686892i	$-0.758975\pi$
$241$	3.59363	−	6.22435i	0.231486	−	0.400945i	0.958246	+	0.285946i	$0.0923080\pi$
$242$	−14.3173	+	24.7984i	−0.920354	+	1.59410i
$243$	−6.38952	−	11.0670i	−0.409888	−	0.709947i
$244$	−66.2978			−4.24428
$245$	7.34878	−	19.8295i	0.469497	−	1.26686i
$246$	7.89019			0.503060
$247$	−3.65723	−	6.33450i	−0.232704	−	0.403055i
$248$	2.27578	−	3.94177i	0.144512	−	0.250303i
$249$	−8.98072	+	15.5551i	−0.569130	+	0.985763i
$250$	3.65083	+	6.32342i	0.230899	+	0.399928i
$251$	7.54012			0.475928			0.237964	−	0.971274i	$-0.423520\pi$
$251$	7.54012			0.475928			0.237964	+	0.971274i	$0.423520\pi$
$252$	32.6503	−	69.4883i	2.05677	−	4.37735i
$253$	0.384765			0.0241900
$254$	10.8248	+	18.7490i	0.679206	+	1.17642i
$255$	3.56519	−	6.17509i	0.223261	−	0.386699i
$256$	−37.2582	+	64.5331i	−2.32864	+	4.03332i
$257$	−9.86848	−	17.0927i	−0.615579	−	1.06621i	−0.990283	−	0.139069i	$-0.955589\pi$
$257$	−9.86848	−	17.0927i	−0.615579	−	1.06621i	0.374704	−	0.927144i	$-0.377744\pi$
$258$	−48.1397			−2.99704
$259$	−8.59131	+	0.726371i	−0.533838	+	0.0451345i
$260$	66.1252			4.10091
$261$	6.69016	+	11.5877i	0.414111	+	0.717261i
$262$	−3.39430	+	5.87910i	−0.209700	+	0.363212i
$263$	−0.143376	+	0.248334i	−0.00884092	+	0.0153129i	−0.870412	−	0.492324i	$-0.836148\pi$
$263$	−0.143376	+	0.248334i	−0.00884092	+	0.0153129i	0.861571	+	0.507637i	$0.169481\pi$
$264$	11.6931	+	20.2530i	0.719660	+	1.24649i
$265$	39.2993			2.41414
$266$	7.91457	+	11.3737i	0.485274	+	0.697368i
$267$	8.76651			0.536501
$268$	−14.5328	−	25.1716i	−0.887734	−	1.53760i
$269$	9.10137	−	15.7640i	0.554920	−	0.961150i	−0.442990	−	0.896527i	$-0.646082\pi$
$269$	9.10137	−	15.7640i	0.554920	−	0.961150i	0.997910	−	0.0646231i	$-0.0205845\pi$
$270$	25.3302	−	43.8731i	1.54154	−	2.67003i
$271$	2.41084	+	4.17570i	0.146448	+	0.253656i	0.929912	−	0.367781i	$-0.119882\pi$
$271$	2.41084	+	4.17570i	0.146448	+	0.253656i	−0.783464	+	0.621437i	$0.786549\pi$
$272$	−13.8551			−0.840091
$273$	16.6529	+	23.9312i	1.00788	+	1.44838i
$274$	−36.9739			−2.23367
$275$	1.67015	+	2.89278i	0.100714	+	0.174441i
$276$	−3.83600	+	6.64415i	−0.230900	+	0.399931i
$277$	7.21834	−	12.5025i	0.433708	−	0.751204i	−0.563481	−	0.826129i	$-0.690538\pi$
$277$	7.21834	−	12.5025i	0.433708	−	0.751204i	0.997189	+	0.0749248i	$0.0238717\pi$
$278$	−12.5746	−	21.7799i	−0.754176	−	1.30627i
$279$	2.30148			0.137786
$280$	−80.7300	+	6.82549i	−4.82454	+	0.407901i
$281$	−4.23994			−0.252934			−0.126467	−	0.991971i	$-0.540364\pi$
$281$	−4.23994			−0.252934			−0.126467	+	0.991971i	$0.540364\pi$
$282$	22.4071	+	38.8102i	1.33432	+	2.31111i
$283$	11.2627	−	19.5076i	0.669498	−	1.15961i	−0.308546	−	0.951209i	$-0.599842\pi$
$283$	11.2627	−	19.5076i	0.669498	−	1.15961i	0.978045	−	0.208396i	$-0.0668243\pi$
$284$	4.13280	−	7.15823i	0.245237	−	0.424763i
$285$	8.14678	+	14.1106i	0.482574	+	0.835842i
$286$	−8.66126			−0.512151
$287$	1.12514	−	2.39459i	0.0664149	−	0.141348i
$288$	−133.490			−7.86598
$289$	8.15720	+	14.1287i	0.479836	+	0.831100i
$290$	10.9156	−	18.9063i	0.640983	−	1.11022i
$291$	−22.5973	+	39.1397i	−1.32468	+	2.29441i
$292$	−24.7449	−	42.8595i	−1.44809	−	2.50816i
$293$	13.5665			0.792565			0.396282	−	0.918129i	$-0.370300\pi$
$293$	13.5665			0.792565			0.396282	+	0.918129i	$0.370300\pi$
$294$	−35.2543	−	42.5163i	−2.05607	−	2.47960i
$295$	28.7894			1.67618
$296$	16.5158	+	28.6062i	0.959962	+	1.66270i
$297$	−2.45176	+	4.24656i	−0.142265	+	0.246411i
$298$	4.07010	−	7.04962i	0.235774	−	0.408373i
$299$	−0.918848	−	1.59149i	−0.0531383	−	0.0920383i
$300$	−66.6037			−3.84537
$301$	−6.86471	+	14.6099i	−0.395675	+	0.842099i
$302$	−5.30932			−0.305517
$303$	4.07467	+	7.05753i	0.234084	+	0.405445i
$304$	15.8301	−	27.4186i	0.907920	−	1.57256i
$305$	−17.6876	+	30.6358i	−1.01279	+	1.75420i
$306$	−5.87340	−	10.1730i	−0.335760	−	0.581553i
$307$	−26.6357			−1.52018			−0.760090	−	0.649817i	$-0.774845\pi$
$307$	−26.6357			−1.52018			−0.760090	+	0.649817i	$0.774845\pi$
$308$	12.0818	−	1.02148i	0.688423	−	0.0582042i
$309$	27.7882			1.58081
$310$	−1.87753	−	3.25197i	−0.106636	−	0.184700i
$311$	−4.71654	+	8.16928i	−0.267450	+	0.463237i	−0.968203	−	0.250167i	$-0.919514\pi$
$311$	−4.71654	+	8.16928i	−0.267450	+	0.463237i	0.700752	+	0.713405i	$0.252848\pi$
$312$	55.8480	−	96.7316i	3.16177	−	5.47635i
$313$	6.07734	+	10.5263i	0.343511	+	0.594979i	0.985082	−	0.172085i	$-0.0550502\pi$
$313$	6.07734	+	10.5263i	0.343511	+	0.594979i	−0.641571	+	0.767064i	$0.721717\pi$
$314$	−29.0888			−1.64157
$315$	−23.3993	−	33.6262i	−1.31840	−	1.89462i
$316$	−60.5165			−3.40432
$317$	−7.20004	−	12.4708i	−0.404394	−	0.700432i	0.589856	−	0.807508i	$-0.299184\pi$
$317$	−7.20004	−	12.4708i	−0.404394	−	0.700432i	−0.994251	+	0.107077i	$0.965851\pi$
$318$	51.3195	−	88.8879i	2.87785	−	4.98459i
$319$	−1.05654	+	1.82998i	−0.0591548	+	0.102459i
$320$	58.3479	+	101.062i	3.26175	+	5.64952i
$321$	42.4293			2.36817
$322$	1.98847	+	2.85755i	0.110813	+	0.159245i
$323$	1.56664			0.0871701
$324$	−5.35839	−	9.28100i	−0.297688	−	0.515611i
$325$	7.97689	−	13.8164i	0.442478	−	0.766394i
$326$	25.0332	−	43.3588i	1.38646	−	2.40142i
$327$	−13.9098	−	24.0925i	−0.769213	−	1.33232i
$328$	−10.1361			−0.559675
$329$	14.9737	−	1.26599i	0.825529	−	0.0697961i
$330$	19.2937			1.06208
$331$	2.38078	+	4.12363i	0.130859	+	0.226655i	0.924008	−	0.382373i	$-0.124893\pi$
$331$	2.38078	+	4.12363i	0.130859	+	0.226655i	−0.793149	+	0.609028i	$0.791560\pi$
$332$	17.8383	−	30.8968i	0.979002	−	1.69568i
$333$	−8.35115	+	14.4646i	−0.457640	+	0.792656i
$334$	26.3593	+	45.6556i	1.44231	+	2.49816i
$335$	−15.5088			−0.847339
$336$	−53.6666	+	114.217i	−2.92775	+	6.23102i
$337$	−8.79898			−0.479311			−0.239655	−	0.970858i	$-0.577034\pi$
$337$	−8.79898			−0.479311			−0.239655	+	0.970858i	$0.577034\pi$
$338$	2.69168	+	4.66212i	0.146408	+	0.253586i
$339$	−28.9806	+	50.1959i	−1.57401	+	2.72627i
$340$	−7.08148	+	12.2655i	−0.384047	+	0.665189i
$341$	0.181730	+	0.314765i	0.00984121	+	0.0170455i
$342$	26.8425			1.45148
$343$	−17.9305	+	4.63651i	−0.968156	+	0.250348i
$344$	61.8426			3.33433
$345$	2.04681	+	3.54518i	0.110197	+	0.190866i
$346$	−6.41397	+	11.1093i	−0.344817	+	0.597240i
$347$	13.0101	−	22.5341i	0.698416	−	1.20969i	−0.270599	−	0.962692i	$-0.587222\pi$
$347$	13.0101	−	22.5341i	0.698416	−	1.20969i	0.969015	−	0.247000i	$-0.0794448\pi$
$348$	−21.0668	−	36.4887i	−1.12930	−	1.95600i
$349$	−14.7488			−0.789488			−0.394744	−	0.918791i	$-0.629167\pi$
$349$	−14.7488			−0.789488			−0.394744	+	0.918791i	$0.629167\pi$
$350$	−12.8526	+	27.3537i	−0.687002	+	1.46212i
$351$	23.4199			1.25006
$352$	−10.5406	−	18.2569i	−0.561818	−	0.973097i
$353$	−5.52696	+	9.57297i	−0.294170	+	0.509518i	−0.974792	−	0.223118i	$-0.928377\pi$
$353$	−5.52696	+	9.57297i	−0.294170	+	0.509518i	0.680621	+	0.732635i	$0.261710\pi$
$354$	37.5950	−	65.1164i	1.99815	−	3.46090i
$355$	−2.20518	−	3.81948i	−0.117039	−	0.202717i
$356$	−17.4128			−0.922875
$357$	−6.22235	+	0.526082i	−0.329322	+	0.0278432i
$358$	29.8490			1.57757
$359$	−11.8770	−	20.5716i	−0.626845	−	1.08573i	−0.988181	−	0.153291i	$-0.951013\pi$
$359$	−11.8770	−	20.5716i	−0.626845	−	1.08573i	0.361337	−	0.932435i	$-0.382321\pi$
$360$	−78.4733	+	135.920i	−4.13591	+	7.16360i
$361$	7.71004	−	13.3542i	0.405792	−	0.702852i
$362$	27.2210	+	47.1481i	1.43070	+	2.47805i
$363$	29.4879			1.54771
$364$	−33.0773	−	47.5341i	−1.73372	−	2.49146i
$365$	−26.4068			−1.38219
$366$	46.1951	+	80.0122i	2.41465	+	4.18230i
$367$	−10.5665	+	18.3017i	−0.551567	+	0.955342i	0.446595	+	0.894736i	$0.352637\pi$
$367$	−10.5665	+	18.3017i	−0.551567	+	0.955342i	−0.998162	+	0.0606060i	$0.980697\pi$
$368$	3.97719	−	6.88869i	0.207325	−	0.359098i
$369$	−2.56265	−	4.43864i	−0.133406	−	0.231066i
$370$	27.2512			1.41672
$371$	−19.6584	−	28.2503i	−1.02061	−	1.46668i
$372$	−7.24718			−0.375749
$373$	−4.45809	−	7.72164i	−0.230831	−	0.399811i	0.727222	−	0.686403i	$-0.240811\pi$
$373$	−4.45809	−	7.72164i	−0.230831	−	0.399811i	−0.958053	+	0.286591i	$0.907478\pi$
$374$	0.927551	−	1.60657i	0.0479625	−	0.0830735i
$375$	3.75962	−	6.51185i	0.194146	−	0.336270i
$376$	−28.7853	−	49.8575i	−1.48449	−	2.57121i
$377$	10.0924			0.519784
$378$	−44.2089	+	3.73774i	−2.27386	+	0.192249i
$379$	2.48486			0.127639			0.0638194	−	0.997961i	$-0.479672\pi$
$379$	2.48486			0.127639			0.0638194	+	0.997961i	$0.479672\pi$
$380$	−16.1818	−	28.0277i	−0.830110	−	1.43779i
$381$	11.1473	−	19.3077i	0.571094	−	0.989165i
$382$	32.1407	−	55.6693i	1.64446	−	2.84829i
$383$	6.07611	+	10.5241i	0.310475	+	0.537758i	0.978465	−	0.206412i	$-0.0661786\pi$
$383$	6.07611	+	10.5241i	0.310475	+	0.537758i	−0.667990	+	0.744170i	$0.732845\pi$
$384$	156.294			7.97582
$385$	2.75128	−	5.85543i	0.140218	−	0.298420i
$386$	40.8785			2.08066
$387$	15.6352	+	27.0810i	0.794784	+	1.37661i
$388$	44.8847	−	77.7426i	2.27868	−	3.94678i
$389$	16.5051	−	28.5878i	0.836844	−	1.44946i	−0.0556756	−	0.998449i	$-0.517731\pi$
$389$	16.5051	−	28.5878i	0.836844	−	1.44946i	0.892520	−	0.451008i	$-0.148935\pi$
$390$	−46.0748	−	79.8039i	−2.33309	−	4.04103i
$391$	0.393605			0.0199055
$392$	45.2895	+	54.6185i	2.28746	+	2.75865i
$393$	6.99088			0.352643
$394$	−30.4772	−	52.7881i	−1.53542	−	2.65942i
$395$	−16.1452	+	27.9643i	−0.812352	+	1.40703i
$396$	11.7440	−	20.3413i	0.590160	−	1.02219i
$397$	−8.55970	−	14.8258i	−0.429599	−	0.744088i	0.567238	−	0.823554i	$-0.308012\pi$
$397$	−8.55970	−	14.8258i	−0.429599	−	0.744088i	−0.996838	+	0.0794660i	$0.974678\pi$
$398$	19.7979			0.992380
$399$	6.06823	−	12.9148i	0.303792	−	0.646548i
$400$	69.0551			3.45276
$401$	−7.76580	−	13.4508i	−0.387805	−	0.671699i	0.604349	−	0.796720i	$-0.293433\pi$
$401$	−7.76580	−	13.4508i	−0.387805	−	0.671699i	−0.992154	+	0.125021i	$0.960100\pi$
$402$	−20.2524	+	35.0782i	−1.01010	+	1.74954i
$403$	0.867968	−	1.50337i	0.0432366	−	0.0748880i
$404$	−8.09345	−	14.0183i	−0.402664	−	0.697435i
$405$	−5.71826			−0.284142
$406$	−19.0510	+	1.61071i	−0.945485	+	0.0799381i
$407$	−2.63770			−0.130746
$408$	11.9617	+	20.7184i	0.592195	+	1.02571i
$409$	−0.554215	+	0.959928i	−0.0274041	+	0.0474654i	−0.879402	−	0.476080i	$-0.842057\pi$
$409$	−0.554215	+	0.959928i	−0.0274041	+	0.0474654i	0.851998	+	0.523545i	$0.175391\pi$
$410$	−4.18117	+	7.24200i	−0.206493	+	0.357657i
$411$	19.0378	+	32.9744i	0.939066	+	1.62651i
$412$	−55.1952			−2.71927
$413$	−14.4011	−	20.6953i	−0.708632	−	1.01835i
$414$	6.74396			0.331448
$415$	−9.51814	−	16.4859i	−0.467227	−	0.809261i
$416$	−50.3437	+	87.1979i	−2.46830	+	4.27523i
$417$	−12.9493	+	22.4289i	−0.634131	+	1.09835i
$418$	2.11954	+	3.67115i	0.103670	+	0.179562i
$419$	−5.74205			−0.280518			−0.140259	−	0.990115i	$-0.544793\pi$
$419$	−5.74205			−0.280518			−0.140259	+	0.990115i	$0.544793\pi$
$420$	73.6825	+	105.886i	3.59534	+	5.16672i
$421$	−24.9380			−1.21541			−0.607703	−	0.794165i	$-0.707909\pi$
$421$	−24.9380			−1.21541			−0.607703	+	0.794165i	$0.707909\pi$
$422$	24.2321	+	41.9712i	1.17960	+	2.04313i
$423$	14.5552	−	25.2103i	0.707696	−	1.22577i
$424$	−65.9276	+	114.190i	−3.20173	+	5.54555i
$425$	1.70852	+	2.95924i	0.0828754	+	0.143544i
$426$	−11.5186			−0.558080
$427$	30.8703	−	2.60999i	1.49392	−	0.126306i
$428$	−84.2766			−4.07367
$429$	4.45967	+	7.72438i	0.215315	+	0.372936i
$430$	25.5102	−	44.1849i	1.23021	−	2.13079i
$431$	−7.94627	+	13.7633i	−0.382758	+	0.662957i	−0.991455	−	0.130446i	$-0.958359\pi$
$431$	−7.94627	+	13.7633i	−0.382758	+	0.662957i	0.608697	+	0.793403i	$0.291692\pi$
$432$	50.6860	+	87.7907i	2.43863	+	4.22383i
$433$	6.34096			0.304727			0.152364	−	0.988325i	$-0.451312\pi$
$433$	6.34096			0.304727			0.152364	+	0.988325i	$0.451312\pi$
$434$	−1.39850	+	2.97637i	−0.0671301	+	0.142870i
$435$	−22.4816			−1.07791
$436$	27.6288	+	47.8545i	1.32318	+	2.29181i
$437$	−0.449711	+	0.778923i	−0.0215126	+	0.0372609i
$438$	−34.4836	+	59.7274i	−1.64769	+	2.85388i
$439$	15.1863	+	26.3035i	0.724803	+	1.25540i	0.959055	+	0.283220i	$0.0914026\pi$
$439$	15.1863	+	26.3035i	0.724803	+	1.25540i	−0.234252	+	0.972176i	$0.575264\pi$
$440$	−24.7856			−1.18161
$441$	−12.4674	+	33.6412i	−0.593684	+	1.60196i
$442$	−8.86025			−0.421439
$443$	−14.6735	−	25.4152i	−0.697157	−	1.20751i	−0.969448	−	0.245297i	$-0.921115\pi$
$443$	−14.6735	−	25.4152i	−0.697157	−	1.20751i	0.272291	−	0.962215i	$-0.412219\pi$
$444$	26.2971	−	45.5479i	1.24801	−	2.16161i
$445$	−4.64555	+	8.04633i	−0.220220	+	0.381432i
$446$	12.7698	+	22.1180i	0.604668	+	1.04732i
$447$	−8.38275			−0.396491
$448$	43.4612	−	92.4968i	2.05335	−	4.37006i
$449$	35.1178			1.65731			0.828656	−	0.559758i	$-0.189106\pi$
$449$	35.1178			1.65731			0.828656	+	0.559758i	$0.189106\pi$
$450$	29.2735	+	50.7032i	1.37997	+	2.39017i
$451$	0.404704	−	0.700968i	0.0190568	−	0.0330073i
$452$	57.5637	−	99.7033i	2.70757	−	4.68965i
$453$	2.73376	+	4.73502i	0.128443	+	0.222471i
$454$	−60.5788			−2.84310
$455$	−30.7899	+	2.60320i	−1.44345	+	0.122040i
$456$	−54.6674			−2.56003
$457$	−2.45068	−	4.24471i	−0.114638	−	0.198559i	0.802997	−	0.595983i	$-0.203238\pi$
$457$	−2.45068	−	4.24471i	−0.114638	−	0.198559i	−0.917635	+	0.397424i	$0.869904\pi$
$458$	−12.3379	+	21.3699i	−0.576514	+	0.998551i
$459$	−2.50809	+	4.34413i	−0.117067	+	0.202767i
$460$	−4.06555	−	7.04174i	−0.189557	−	0.328323i
$461$	1.55339			0.0723486			0.0361743	−	0.999345i	$-0.488483\pi$
$461$	1.55339			0.0723486			0.0361743	+	0.999345i	$0.488483\pi$
$462$	−9.65114	−	13.8693i	−0.449012	−	0.645257i
$463$	−6.30847			−0.293179			−0.146590	−	0.989197i	$-0.546830\pi$
$463$	−6.30847			−0.293179			−0.146590	+	0.989197i	$0.546830\pi$
$464$	21.8422	+	37.8317i	1.01400	+	1.75629i
$465$	−1.93347	+	3.34887i	−0.0896627	+	0.155300i
$466$	0.743262	−	1.28737i	0.0344310	−	0.0596362i
$467$	−10.5031	−	18.1919i	−0.486024	−	0.841819i	0.513847	−	0.857882i	$-0.328220\pi$
$467$	−10.5031	−	18.1919i	−0.486024	−	0.841819i	−0.999871	+	0.0160631i	$0.994887\pi$
$468$	−112.183			−5.18565
$469$	7.75788	+	11.1485i	0.358225	+	0.514792i
$470$	−47.4959			−2.19082
$471$	14.9778	+	25.9423i	0.690139	+	1.19536i
$472$	−48.2964	+	83.6518i	−2.22302	+	3.85039i
$473$	−2.46918	+	4.27675i	−0.113533	+	0.196645i
$474$	42.1667	+	73.0349i	1.93678	+	3.35461i
$475$	−7.80825			−0.358267
$476$	12.3594	−	1.04495i	0.566490	−	0.0478951i
$477$	−66.6721			−3.05270
$478$	19.6621	+	34.0557i	0.899322	+	1.55767i
$479$	0.255136	−	0.441909i	0.0116575	−	0.0201913i	−0.860138	−	0.510062i	$-0.829623\pi$
$479$	0.255136	−	0.441909i	0.0116575	−	0.0201913i	0.871795	+	0.489870i	$0.162956\pi$
$480$	112.145	−	194.241i	5.11869	−	8.86583i
$481$	6.29902	+	10.9102i	0.287211	+	0.497463i
$482$	19.8944			0.906165
$483$	1.52459	−	3.24473i	0.0693714	−	0.147640i
$484$	−58.5714			−2.66234
$485$	−23.9496	−	41.4819i	−1.08749	−	1.88360i
$486$	17.6863	−	30.6335i	0.802266	−	1.38956i
$487$	−5.47275	+	9.47909i	−0.247994	+	0.429538i	−0.962969	−	0.269612i	$-0.913105\pi$
$487$	−5.47275	+	9.47909i	−0.247994	+	0.429538i	0.714975	+	0.699150i	$0.246438\pi$
$488$	−59.3445	−	102.788i	−2.68640	−	4.65298i
$489$	−51.5583			−2.33155
$490$	57.7055	−	9.82792i	2.60687	−	0.443980i
$491$	1.52841			0.0689760			0.0344880	−	0.999405i	$-0.489020\pi$
$491$	1.52841			0.0689760			0.0344880	+	0.999405i	$0.489020\pi$
$492$	8.06958	+	13.9769i	0.363805	+	0.630128i
$493$	−1.08081	+	1.87202i	−0.0486773	+	0.0843116i
$494$	10.1232	−	17.5340i	0.455466	−	0.788891i
$495$	−6.26638	−	10.8537i	−0.281653	−	0.487837i
$496$	7.51392			0.337385
$497$	−1.64256	+	3.49579i	−0.0736787	+	0.156808i
$498$	−49.7175			−2.22789
$499$	14.7952	+	25.6260i	0.662324	+	1.14718i	0.980004	+	0.198980i	$0.0637629\pi$
$499$	14.7952	+	25.6260i	0.662324	+	1.14718i	−0.317680	+	0.948198i	$0.602904\pi$
$500$	−7.46767	+	12.9344i	−0.333964	+	0.578443i
$501$	27.1447	−	47.0160i	1.21274	−	2.10052i
$502$	10.4356	+	18.0749i	0.465762	+	0.806724i
$503$	29.9673			1.33618			0.668088	−	0.744082i	$-0.267113\pi$
$503$	29.9673			1.33618			0.668088	+	0.744082i	$0.267113\pi$
$504$	136.960	−	11.5796i	6.10069	−	0.515796i
$505$	−8.63700			−0.384341
$506$	0.532517	+	0.922346i	0.0236732	+	0.0410033i
$507$	2.77188	−	4.80104i	0.123104	−	0.213222i
$508$	−22.1417	+	38.3506i	−0.982381	+	1.70153i
$509$	4.97317	+	8.61379i	0.220432	+	0.381799i	0.954939	−	0.296802i	$-0.0959200\pi$
$509$	4.97317	+	8.61379i	0.220432	+	0.381799i	−0.734507	+	0.678601i	$0.762587\pi$
$510$	19.7370			0.873967
$511$	13.2093	+	18.9825i	0.584344	+	0.839737i
$512$	−96.6013			−4.26922
$513$	−5.73120	−	9.92674i	−0.253039	−	0.438276i
$514$	27.3160	−	47.3128i	1.20486	−	2.08688i
$515$	−14.7255	+	25.5053i	−0.648884	+	1.12390i
$516$	−49.2341	−	85.2760i	−2.16741	−	3.75407i
$517$	4.59722			0.202185
$518$	−13.6317	−	19.5895i	−0.598941	−	0.860714i
$519$	13.2102			0.579862
$520$	59.1900	+	102.520i	2.59565	+	4.49580i
$521$	15.9602	−	27.6439i	0.699230	−	1.21110i	−0.269504	−	0.962999i	$-0.586860\pi$
$521$	15.9602	−	27.6439i	0.699230	−	1.21110i	0.968734	−	0.248102i	$-0.0798069\pi$
$522$	−18.5184	+	32.0749i	−0.810531	+	1.40388i
$523$	−6.78625	−	11.7541i	−0.296742	−	0.513972i	0.678646	−	0.734465i	$-0.262567\pi$
$523$	−6.78625	−	11.7541i	−0.296742	−	0.513972i	−0.975389	+	0.220493i	$0.929234\pi$
$524$	−13.8859			−0.606607
$525$	31.0127	−	2.62204i	1.35351	−	0.114435i
$526$	−0.793731			−0.0346083
$527$	0.185905	+	0.321997i	0.00809814	+	0.0140264i
$528$	−19.3035	+	33.4346i	−0.840075	+	1.45505i
$529$	11.3870	−	19.7229i	0.495088	−	0.857517i
$530$	54.3905	+	94.2070i	2.36257	+	4.09209i
$531$	−48.8418			−2.11955
$532$	−12.0532	+	25.6524i	−0.522574	+	1.11217i
$533$	−3.86586			−0.167449
$534$	12.1329	+	21.0148i	0.525042	+	0.909399i
$535$	−22.4841	+	38.9437i	−0.972075	+	1.68368i
$536$	26.0173	−	45.0632i	1.12377	−	1.94644i
$537$	−15.3692	−	26.6203i	−0.663231	−	1.14875i
$538$	50.3854			2.17227
$539$	−5.58543	+	0.951264i	−0.240581	+	0.0409738i
$540$	103.624			4.45927
$541$	1.92858	+	3.34039i	0.0829159	+	0.143615i	0.904501	−	0.426471i	$-0.140243\pi$
$541$	1.92858	+	3.34039i	0.0829159	+	0.143615i	−0.821585	+	0.570086i	$0.806910\pi$
$542$	−6.67324	+	11.5584i	−0.286640	+	0.496475i
$543$	28.0321	−	48.5530i	1.20297	−	2.08361i
$544$	−10.7828	−	18.6764i	−0.462309	−	0.800743i
$545$	29.4843			1.26297
$546$	−34.3194	+	73.0406i	−1.46873	+	3.12585i
$547$	3.96156			0.169384			0.0846920	−	0.996407i	$-0.473009\pi$
$547$	3.96156			0.169384			0.0846920	+	0.996407i	$0.473009\pi$
$548$	−37.8145	−	65.4966i	−1.61535	−	2.79788i
$549$	30.0073	−	51.9742i	1.28068	−	2.21820i
$550$	−4.62299	+	8.00725i	−0.197125	+	0.341430i
$551$	−2.46975	−	4.27774i	−0.105215	−	0.182238i
$552$	−13.7347			−0.584589
$553$	28.1783	−	2.38240i	1.19826	−	0.101310i
$554$	39.9609			1.69777
$555$	−14.0316	−	24.3034i	−0.595608	−	1.03162i
$556$	25.7210	−	44.5502i	1.09082	−	1.88935i
$557$	3.58904	−	6.21641i	0.152073	−	0.263398i	−0.779917	−	0.625883i	$-0.784739\pi$
$557$	3.58904	−	6.21641i	0.152073	−	0.263398i	0.931989	+	0.362486i	$0.118072\pi$
$558$	3.18526	+	5.51704i	0.134843	+	0.233555i
$559$	23.5864			0.997597
$560$	−76.3945	−	109.784i	−3.22826	−	4.63920i
$561$	−1.91038			−0.0806563
$562$	−5.86811	−	10.1639i	−0.247531	−	0.428736i
$563$	12.4742	−	21.6059i	0.525723	−	0.910580i	−0.473828	−	0.880618i	$-0.657128\pi$
$563$	12.4742	−	21.6059i	0.525723	−	0.910580i	0.999551	−	0.0299620i	$-0.00953864\pi$
$564$	−45.8330	+	79.3851i	−1.92992	+	3.34272i
$565$	−30.7148	−	53.1996i	−1.29218	−	2.23812i
$566$	62.3506			2.62079
$567$	2.86040	+	4.11057i	0.120126	+	0.172628i
$568$	14.7974			0.620886
$569$	17.8763	+	30.9626i	0.749412	+	1.29802i	0.948105	+	0.317958i	$0.102997\pi$
$569$	17.8763	+	30.9626i	0.749412	+	1.29802i	−0.198693	+	0.980062i	$0.563670\pi$
$570$	−22.5504	+	39.0584i	−0.944531	+	1.63598i
$571$	−16.4613	+	28.5118i	−0.688883	+	1.19318i	0.283317	+	0.959026i	$0.408565\pi$
$571$	−16.4613	+	28.5118i	−0.688883	+	1.19318i	−0.972200	+	0.234154i	$0.924768\pi$
$572$	−8.85817	−	15.3428i	−0.370379	−	0.641515i
$573$	−66.1968			−2.76541
$574$	7.29743	−	0.616977i	0.304589	−	0.0257521i
$575$	−1.96176			−0.0818110
$576$	−98.9885	−	171.453i	−4.12452	−	7.14388i
$577$	6.51889	−	11.2910i	0.271385	−	0.470052i	−0.697832	−	0.716262i	$-0.745852\pi$
$577$	6.51889	−	11.2910i	0.271385	−	0.470052i	0.969217	+	0.246209i	$0.0791851\pi$
$578$	−22.5792	+	39.1084i	−0.939172	+	1.62669i
$579$	−21.0483	−	36.4567i	−0.874736	−	1.51509i
$580$	44.6549			1.85419
$581$	−7.08970	+	15.0887i	−0.294130	+	0.625986i
$582$	−125.099			−5.18554
$583$	−5.26456	−	9.11848i	−0.218036	−	0.377649i
$584$	44.2994	−	76.7288i	1.83312	−	3.17506i
$585$	−29.9292	+	51.8389i	−1.23742	+	2.14327i
$586$	18.7761	+	32.5212i	0.775635	+	1.34344i
$587$	20.5144			0.846721			0.423360	−	0.905961i	$-0.360850\pi$
$587$	20.5144			0.846721			0.423360	+	0.905961i	$0.360850\pi$
$588$	39.2587	−	105.933i	1.61900	−	4.36862i
$589$	−0.849619			−0.0350079
$590$	39.8447	+	69.0130i	1.64038	+	2.84122i
$591$	−31.3854	+	54.3610i	−1.29102	+	2.23611i
$592$	−27.2650	+	47.2244i	−1.12058	+	1.94091i
$593$	12.9121	+	22.3644i	0.530236	+	0.918396i	0.999378	+	0.0352733i	$0.0112302\pi$
$593$	12.9121	+	22.3644i	0.530236	+	0.918396i	−0.469141	+	0.883123i	$0.655436\pi$
$594$	−13.5730			−0.556906
$595$	2.81449	−	5.98996i	0.115383	−	0.245564i
$596$	16.6505			0.682032
$597$	−10.1939	−	17.6564i	−0.417210	−	0.722628i
$598$	2.54338	−	4.40527i	0.104007	−	0.180145i
$599$	−4.06584	+	7.04224i	−0.166126	+	0.287738i	−0.937054	−	0.349183i	$-0.886459\pi$
$599$	−4.06584	+	7.04224i	−0.166126	+	0.287738i	0.770929	+	0.636921i	$0.219792\pi$
$600$	−59.6183	−	103.262i	−2.43391	−	4.21565i
$601$	−16.8215			−0.686163			−0.343082	−	0.939306i	$-0.611471\pi$
$601$	−16.8215			−0.686163			−0.343082	+	0.939306i	$0.611471\pi$
$602$	−44.5231	+	3.76430i	−1.81463	+	0.153422i
$603$	26.3111			1.07147
$604$	−5.43003	−	9.40509i	−0.220945	−	0.382688i
$605$	−15.6263	+	27.0655i	−0.635297	+	1.10037i
$606$	−11.2787	+	19.5353i	−0.458167	+	0.793569i
$607$	−1.22922	−	2.12907i	−0.0498924	−	0.0864161i	0.840001	−	0.542585i	$-0.182554\pi$
$607$	−1.22922	−	2.12907i	−0.0498924	−	0.0864161i	−0.889893	+	0.456169i	$0.849221\pi$
$608$	49.2794			1.99854
$609$	11.2458	+	16.1609i	0.455703	+	0.654873i
$610$	−97.9188			−3.96462
$611$	−10.9785	−	19.0153i	−0.444143	−	0.769278i
$612$	12.0139	−	20.8086i	0.485632	−	0.841139i
$613$	−11.4554	+	19.8413i	−0.462678	+	0.801381i	−0.999093	−	0.0425726i	$-0.986445\pi$
$613$	−11.4554	+	19.8413i	−0.462678	+	0.801381i	0.536416	+	0.843954i	$0.319778\pi$
$614$	−36.8640	−	63.8503i	−1.48771	−	2.57679i
$615$	8.61152			0.347250
$616$	12.3983	+	17.8172i	0.499543	+	0.717874i
$617$	−31.6529			−1.27430			−0.637149	−	0.770741i	$-0.719886\pi$
$617$	−31.6529			−1.27430			−0.637149	+	0.770741i	$0.719886\pi$
$618$	38.4590	+	66.6129i	1.54705	+	2.67956i
$619$	−2.30198	+	3.98714i	−0.0925243	+	0.160257i	−0.908573	−	0.417727i	$-0.862827\pi$
$619$	−2.30198	+	3.98714i	−0.0925243	+	0.160257i	0.816048	+	0.577984i	$0.196160\pi$
$620$	3.84043	−	6.65181i	0.154235	−	0.267143i
$621$	−1.43992	−	2.49401i	−0.0577819	−	0.100081i
$622$	−26.1108			−1.04695
$623$	8.10791	−	0.685501i	0.324837	−	0.0274640i
$624$	184.393			7.38161
$625$	14.3017	+	24.7713i	0.572068	+	0.990851i
$626$	−16.8221	+	29.1368i	−0.672348	+	1.16454i
$627$	2.18270	−	3.78054i	0.0871685	−	0.150980i
$628$	−29.7501	−	51.5287i	−1.18716	−	2.05622i
$629$	−2.69830			−0.107588
$630$	48.2229	−	102.631i	1.92125	−	4.08892i
$631$	−5.46440			−0.217534			−0.108767	−	0.994067i	$-0.534690\pi$
$631$	−5.46440			−0.217534			−0.108767	+	0.994067i	$0.534690\pi$
$632$	−54.1695	−	93.8243i	−2.15475	−	3.73213i
$633$	24.9541	−	43.2218i	0.991838	−	1.71791i
$634$	19.9298	−	34.5194i	0.791513	−	1.37094i
$635$	11.8144	+	20.4631i	0.468839	+	0.812054i
$636$	209.945			8.32486
$637$	17.2731	+	20.8312i	0.684386	+	0.825360i
$638$	−5.84902			−0.231565
$639$	3.74113	+	6.47983i	0.147997	+	0.256338i
$640$	−82.8231	+	143.454i	−3.27387	+	5.67051i
$641$	−18.4768	+	32.0027i	−0.729789	+	1.26403i	0.227183	+	0.973852i	$0.427048\pi$
$641$	−18.4768	+	32.0027i	−0.729789	+	1.26403i	−0.956972	+	0.290180i	$0.906285\pi$
$642$	58.7224	+	101.710i	2.31759	+	4.01418i
$643$	21.6513			0.853843			0.426922	−	0.904289i	$-0.359598\pi$
$643$	21.6513			0.853843			0.426922	+	0.904289i	$0.359598\pi$
$644$	−3.02828	+	6.44496i	−0.119331	+	0.253967i
$645$	−52.5406			−2.06879
$646$	2.16824	+	3.75549i	0.0853081	+	0.147758i
$647$	8.97436	−	15.5440i	0.352818	−	0.611099i	−0.633924	−	0.773396i	$-0.718557\pi$
$647$	8.97436	−	15.5440i	0.352818	−	0.611099i	0.986742	+	0.162296i	$0.0518900\pi$
$648$	9.59281	−	16.6152i	0.376841	−	0.652708i
$649$	−3.85664	−	6.67990i	−0.151387	−	0.262209i
$650$	44.1602			1.73211
$651$	3.37451	−	0.285305i	0.132257	−	0.0111820i
$652$	102.409			4.01066
$653$	−17.6573	−	30.5833i	−0.690982	−	1.19682i	−0.971516	−	0.236972i	$-0.923845\pi$
$653$	−17.6573	−	30.5833i	−0.690982	−	1.19682i	0.280534	−	0.959844i	$-0.409488\pi$
$654$	38.5024	−	66.6882i	1.50556	−	2.60771i
$655$	−3.70461	+	6.41657i	−0.144751	+	0.250716i
$656$	−8.36658	−	14.4913i	−0.326660	−	0.565792i
$657$	44.7996			1.74780
$658$	23.7585	+	34.1424i	0.926203	+	1.33101i
$659$	−5.81071			−0.226353			−0.113177	−	0.993575i	$-0.536103\pi$
$659$	−5.81071			−0.226353			−0.113177	+	0.993575i	$0.536103\pi$
$660$	19.7323	+	34.1774i	0.768080	+	1.33035i
$661$	−18.3436	+	31.7720i	−0.713482	+	1.23579i	0.250060	+	0.968230i	$0.419550\pi$
$661$	−18.3436	+	31.7720i	−0.713482	+	1.23579i	−0.963542	+	0.267557i	$0.913784\pi$
$662$	−6.59002	+	11.4143i	−0.256129	+	0.443628i
$663$	4.56213	+	7.90185i	0.177179	+	0.306882i
$664$	63.8696			2.47862
$665$	8.63813	+	12.4135i	0.334972	+	0.481376i
$666$	−46.2322			−1.79146
$667$	−0.620505	−	1.07475i	−0.0240261	−	0.0416144i
$668$	−53.9171	+	93.3872i	−2.08612	+	3.61326i
$669$	13.1503	−	22.7770i	0.508421	−	0.880611i
$670$	−21.4643	−	37.1773i	−0.829239	−	1.43628i
$671$	9.47775			0.365885
$672$	−195.727	+	16.5482i	−7.55035	+	0.638361i
$673$	−45.8608			−1.76780			−0.883902	−	0.467672i	$-0.845093\pi$
$673$	−45.8608			−1.76780			−0.883902	+	0.467672i	$0.845093\pi$
$674$	−12.1778	−	21.0926i	−0.469073	−	0.812458i
$675$	12.5005	−	21.6515i	0.481145	−	0.833367i
$676$	−5.50575	+	9.53623i	−0.211759	+	0.366778i
$677$	9.94509	+	17.2254i	0.382221	+	0.662026i	0.991379	−	0.131023i	$-0.0418261\pi$
$677$	9.94509	+	17.2254i	0.382221	+	0.662026i	−0.609159	+	0.793048i	$0.708493\pi$
$678$	−160.437			−6.16155
$679$	−17.8391	+	37.9663i	−0.684604	+	1.45701i
$680$	−25.3551			−0.972323
$681$	31.1920	+	54.0261i	1.19528	+	2.07028i
$682$	−0.503029	+	0.871272i	−0.0192620	+	0.0333627i
$683$	4.24912	−	7.35969i	0.162588	−	0.281611i	−0.773208	−	0.634152i	$-0.781349\pi$
$683$	4.24912	−	7.35969i	0.162588	−	0.281611i	0.935796	+	0.352542i	$0.114683\pi$
$684$	27.4528	+	47.5496i	1.04968	+	1.81810i
$685$	−40.3541			−1.54185
$686$	−35.9304	−	36.5655i	−1.37183	−	1.39608i
$687$	25.4111			0.969496
$688$	51.0462	+	88.4147i	1.94612	+	3.37078i
$689$	−25.1443	+	43.5513i	−0.957923	+	1.65917i
$690$	−5.66560	+	9.81310i	−0.215686	+	0.373578i
$691$	−15.6192	−	27.0533i	−0.594183	−	1.02915i	−0.993662	−	0.112412i	$-0.964142\pi$
$691$	−15.6192	−	27.0533i	−0.594183	−	1.02915i	0.399479	−	0.916742i	$-0.369191\pi$
$692$	−26.2392			−0.997463
$693$	−4.66759	+	9.93385i	−0.177307	+	0.377356i
$694$	72.0239			2.73399
$695$	−13.7242	−	23.7711i	−0.520590	−	0.901687i
$696$	37.7146	−	65.3236i	1.42957	−	2.47609i
$697$	0.414002	−	0.717073i	0.0156814	−	0.0271611i
$698$	−20.4125	−	35.3555i	−0.772624	−	1.33822i
$699$	−1.53082			−0.0579009
$700$	−61.6000	+	5.20811i	−2.32826	+	0.196848i
$701$	20.3738			0.769508			0.384754	−	0.923019i	$-0.374286\pi$
$701$	20.3738			0.769508			0.384754	+	0.923019i	$0.374286\pi$
$702$	32.4133	+	56.1415i	1.22336	+	2.11892i
$703$	3.08293	−	5.33979i	0.116275	−	0.201394i
$704$	15.6327	−	27.0766i	0.589178	−	1.02049i
$705$	24.4556	+	42.3583i	0.921050	+	1.59531i
$706$	−30.5974			−1.15155
$707$	4.32042	+	6.20871i	0.162486	+	0.233503i
$708$	153.799			5.78011
$709$	−24.0062	−	41.5799i	−0.901571	−	1.56157i	−0.825455	−	0.564469i	$-0.809081\pi$
$709$	−24.0062	−	41.5799i	−0.901571	−	1.56157i	−0.0761168	−	0.997099i	$-0.524252\pi$
$710$	6.10396	−	10.5724i	0.229078	−	0.396774i
$711$	27.3906	−	47.4419i	1.02723	−	1.77921i
$712$	−15.5865	−	26.9967i	−0.584130	−	1.01174i
$713$	−0.213460			−0.00799413
$714$	−9.87288	−	14.1879i	−0.369483	−	0.530970i
$715$	−9.45308			−0.353525
$716$	30.5277	+	52.8755i	1.14087	+	1.97605i
$717$	20.2480	−	35.0705i	0.756174	−	1.30973i
$718$	32.8757	−	56.9424i	1.22691	−	2.12507i
$719$	1.66575	+	2.88517i	0.0621221	+	0.107599i	0.895414	−	0.445235i	$-0.146880\pi$
$719$	1.66575	+	2.88517i	0.0621221	+	0.107599i	−0.833292	+	0.552834i	$0.813547\pi$
$720$	−259.094			−9.65587
$721$	25.7006	−	2.17291i	0.957139	−	0.0809233i
$722$	42.6830			1.58850
$723$	−10.2436	−	17.7424i	−0.380964	−	0.659848i
$724$	−55.6797	+	96.4401i	−2.06932	+	3.58417i
$725$	5.38685	−	9.33031i	0.200063	−	0.346519i
$726$	40.8115	+	70.6875i	1.51466	+	2.62346i
$727$	32.9605			1.22244			0.611219	−	0.791461i	$-0.290679\pi$
$727$	32.9605			1.22244			0.611219	+	0.791461i	$0.290679\pi$
$728$	44.0884	−	93.8316i	1.63403	−	3.47763i
$729$	−42.1049			−1.55944
$730$	−36.5471	−	63.3015i	−1.35267	−	2.34289i
$731$	−2.52591	+	4.37501i	−0.0934242	+	0.161815i
$732$	−94.4906	+	163.663i	−3.49247	+	6.04914i
$733$	17.8857	+	30.9789i	0.660623	+	1.14423i	0.980452	+	0.196757i	$0.0630410\pi$
$733$	17.8857	+	30.9789i	0.660623	+	1.14423i	−0.319830	+	0.947475i	$0.603626\pi$
$734$	−58.4964			−2.15914
$735$	−38.4773	−	46.4031i	−1.41926	−	1.71161i
$736$	12.3811			0.456372
$737$	2.07757	+	3.59846i	0.0765284	+	0.132551i
$738$	7.09344	−	12.2862i	0.261113	−	0.452261i
$739$	−9.59562	+	16.6201i	−0.352980	+	0.611380i	−0.986770	−	0.162125i	$-0.948165\pi$
$739$	−9.59562	+	16.6201i	−0.352980	+	0.611380i	0.633790	+	0.773505i	$0.281498\pi$
$740$	27.8707	+	48.2735i	1.02455	+	1.77457i
$741$	−20.8498			−0.765936
$742$	40.5134	−	86.2231i	1.48729	−	3.16535i
$743$	5.15568			0.189144			0.0945718	−	0.995518i	$-0.469852\pi$
$743$	5.15568			0.189144			0.0945718	+	0.995518i	$0.469852\pi$
$744$	−6.48710	−	11.2360i	−0.237828	−	0.411931i
$745$	4.44219	−	7.69410i	0.162749	−	0.281890i
$746$	12.3400	−	21.3736i	0.451801	−	0.782542i
$747$	16.1477	+	27.9687i	0.590814	+	1.02332i
$748$	3.79456			0.138743
$749$	39.2418	−	3.31778i	1.43386	−	0.121229i
$750$	20.8133			0.759995
$751$	−9.99905	−	17.3189i	−0.364871	−	0.631974i	0.623885	−	0.781516i	$-0.285553\pi$
$751$	−9.99905	−	17.3189i	−0.364871	−	0.631974i	−0.988755	+	0.149542i	$0.952220\pi$
$752$	47.5200	−	82.3070i	1.73287	−	3.00143i
$753$	10.7465	−	18.6135i	0.391625	−	0.678315i
$754$	13.9679	+	24.1931i	0.508681	+	0.881061i
$755$	−5.79471			−0.210891
$756$	−51.8352	−	74.4903i	−1.88523	−	2.70918i
$757$	−1.81127			−0.0658319			−0.0329159	−	0.999458i	$-0.510479\pi$
$757$	−1.81127			−0.0658319			−0.0329159	+	0.999458i	$0.510479\pi$
$758$	3.43906	+	5.95663i	0.124912	+	0.216355i
$759$	0.548384	−	0.949829i	0.0199051	−	0.0344766i
$760$	28.9693	−	50.1764i	1.05083	−	1.82009i
$761$	−11.8601	−	20.5424i	−0.429930	−	0.744660i	0.566937	−	0.823761i	$-0.308128\pi$
$761$	−11.8601	−	20.5424i	−0.429930	−	0.744660i	−0.996867	+	0.0791010i	$0.974795\pi$
$762$	61.7118			2.23558
$763$	−14.7487	−	21.1948i	−0.533940	−	0.767304i
$764$	131.486			4.75698
$765$	−6.41035	−	11.1031i	−0.231767	−	0.401432i
$766$	−16.8187	+	29.1309i	−0.607686	+	1.05254i
$767$	−18.4199	+	31.9042i	−0.665105	+	1.15200i
$768$	106.204	+	183.951i	3.83231	+	6.63776i
$769$	−47.0762			−1.69761			−0.848806	−	0.528704i	$-0.822678\pi$
$769$	−47.0762			−1.69761			−0.848806	+	0.528704i	$0.822678\pi$
$770$	17.8442	−	1.50868i	0.643061	−	0.0543690i
$771$	−56.2600			−2.02615
$772$	41.8078	+	72.4133i	1.50470	+	2.60621i
$773$	13.2379	−	22.9287i	0.476134	−	0.824688i	−0.523492	−	0.852030i	$-0.675371\pi$
$773$	13.2379	−	22.9287i	0.476134	−	0.824688i	0.999626	+	0.0273423i	$0.00870442\pi$
$774$	−43.2785	+	74.9606i	−1.55561	+	2.69440i
$775$	−0.926565	−	1.60486i	−0.0332832	−	0.0576482i
$776$	160.709			5.76912
$777$	−10.4516	+	22.2438i	−0.374950	+	0.797990i
$778$	91.3729			3.27588
$779$	0.946033	+	1.63858i	0.0338951	+	0.0587081i
$780$	94.2446	−	163.236i	3.37450	−	5.84480i
$781$	−0.590815	+	1.02332i	−0.0211410	+	0.0366173i
$782$	0.544751	+	0.943537i	0.0194803	+	0.0337408i
$783$	15.8157			0.565206
$784$	−40.7037	+	109.832i	−1.45370	+	3.92259i
$785$	−31.7481			−1.13314
$786$	9.67542	+	16.7583i	0.345111	+	0.597749i
$787$	−25.3695	+	43.9412i	−0.904324	+	1.56633i	−0.0825008	+	0.996591i	$0.526291\pi$
$787$	−25.3695	+	43.9412i	−0.904324	+	1.56633i	−0.821823	+	0.569743i	$0.807043\pi$
$788$	62.3402	−	107.976i	2.22078	−	3.84650i
$789$	0.408691	+	0.707873i	0.0145498	+	0.0252010i
$790$	−89.3800			−3.18000
$791$	−22.8783	+	48.6910i	−0.813459	+	1.73125i
$792$	42.0493			1.49416
$793$	−22.6336	−	39.2026i	−0.803743	−	1.39212i
$794$	23.6934	−	41.0381i	0.840846	−	1.45639i
$795$	56.0112	−	97.0142i	1.98651	−	3.44074i
$796$	20.2480	+	35.0706i	0.717672	+	1.24305i
$797$	18.9700			0.671953			0.335976	−	0.941870i	$-0.390934\pi$
$797$	18.9700			0.671953			0.335976	+	0.941870i	$0.390934\pi$
$798$	39.3574	−	3.32755i	1.39324	−	0.117794i
$799$	4.70284			0.166375
$800$	53.7424	+	93.0846i	1.90008	+	3.29104i
$801$	7.88127	−	13.6508i	0.278471	−	0.482326i
$802$	21.4958	−	37.2318i	0.759043	−	1.31470i
$803$	3.53747	+	6.12707i	0.124835	+	0.216220i
$804$	−82.8514			−2.92194
$805$	2.17026	+	3.11880i	0.0764916	+	0.109923i
$806$	4.80509			0.169252
$807$	−25.9434	−	44.9352i	−0.913250	−	1.58179i
$808$	14.4892	−	25.0961i	0.509729	−	0.882877i
$809$	−21.7714	+	37.7092i	−0.765443	+	1.32579i	0.174569	+	0.984645i	$0.444147\pi$
$809$	−21.7714	+	37.7092i	−0.765443	+	1.32579i	−0.940012	+	0.341142i	$0.889186\pi$
$810$	−7.91410	−	13.7076i	−0.278073	−	0.481637i
$811$	32.9946			1.15860			0.579298	−	0.815116i	$-0.303327\pi$
$811$	32.9946			1.15860			0.579298	+	0.815116i	$0.303327\pi$
$812$	−22.3374	−	32.1002i	−0.783888	−	1.12650i
$813$	13.7442			0.482029
$814$	−3.65058	−	6.32300i	−0.127953	−	0.221621i
$815$	27.3218	−	47.3227i	0.957041	−	1.65764i
$816$	−19.7470	+	34.2027i	−0.691282	+	1.19734i
$817$	−5.77194	−	9.99729i	−0.201935	−	0.349761i
$818$	−3.06814			−0.107275
$819$	52.2357	−	4.41638i	1.82526	−	0.154321i
$820$	−17.1049			−0.597330
$821$	−17.3802	−	30.1034i	−0.606573	−	1.05062i	−0.991801	−	0.127794i	$-0.959210\pi$
$821$	−17.3802	−	30.1034i	−0.606573	−	1.05062i	0.385228	−	0.922822i	$-0.374123\pi$
$822$	−52.6969	+	91.2736i	−1.83801	+	3.18353i
$823$	−10.7856	+	18.6811i	−0.375961	+	0.651183i	−0.990470	−	0.137726i	$-0.956021\pi$
$823$	−10.7856	+	18.6811i	−0.375961	+	0.651183i	0.614510	+	0.788909i	$0.289354\pi$
$824$	−49.4063	−	85.5743i	−1.72115	−	2.98112i
$825$	9.52149			0.331496
$826$	29.6788	−	63.1642i	1.03266	−	2.19776i
$827$	−1.59470			−0.0554532			−0.0277266	−	0.999616i	$-0.508827\pi$
$827$	−1.59470			−0.0554532			−0.0277266	+	0.999616i	$0.508827\pi$
$828$	6.89728	+	11.9464i	0.239697	+	0.415168i
$829$	−18.0669	+	31.2928i	−0.627489	+	1.08684i	0.360565	+	0.932734i	$0.382584\pi$
$829$	−18.0669	+	31.2928i	−0.627489	+	1.08684i	−0.988054	+	0.154109i	$0.950749\pi$
$830$	26.3463	−	45.6331i	0.914494	−	1.58395i
$831$	−20.5758	−	35.6383i	−0.713767	−	1.23628i
$832$	−149.328			−5.17701
$833$	−5.71375	+	0.973119i	−0.197970	+	0.0337166i
$834$	−71.6878			−2.48234
$835$	28.7691	+	49.8295i	0.995595	+	1.72442i
$836$	−4.33545	+	7.50922i	−0.149945	+	0.259712i
$837$	1.36018	−	2.35591i	0.0470149	−	0.0814321i
$838$	−7.94703	−	13.7647i	−0.274526	−	0.475493i
$839$	3.43446			0.118571			0.0592853	−	0.998241i	$-0.481118\pi$
$839$	3.43446			0.118571			0.0592853	+	0.998241i	$0.481118\pi$
$840$	−98.2107	+	209.018i	−3.38859	+	7.21180i
$841$	−22.1845			−0.764984
$842$	−34.5144	−	59.7806i	−1.18944	−	2.06018i
$843$	−6.04296	+	10.4667i	−0.208131	+	0.360493i
$844$	−49.5660	+	85.8508i	−1.70613	+	2.95511i
$845$	2.93775	+	5.08834i	0.101062	+	0.175044i
$846$	80.5777			2.77032
$847$	27.2726	−	2.30582i	0.937098	−	0.0792290i
$848$	−217.672			−7.47489
$849$	−32.1042	−	55.6062i	−1.10181	−	1.90840i
$850$	−4.72920	+	8.19122i	−0.162210	+	0.280957i
$851$	0.774560	−	1.34158i	0.0265516	−	0.0459887i
$852$	−11.7805	−	20.4045i	−0.403594	−	0.699045i
$853$	5.93145			0.203089			0.101544	−	0.994831i	$-0.467622\pi$
$853$	5.93145			0.203089			0.101544	+	0.994831i	$0.467622\pi$
$854$	48.9812	+	70.3890i	1.67610	+	2.40866i
$855$	29.2965			1.00192
$856$	−75.4377	−	130.662i	−2.57841	−	4.46594i
$857$	−7.76117	+	13.4427i	−0.265117	+	0.459195i	−0.967594	−	0.252511i	$-0.918744\pi$
$857$	−7.76117	+	13.4427i	−0.265117	+	0.459195i	0.702478	+	0.711706i	$0.252077\pi$
$858$	−12.3444	+	21.3812i	−0.421431	+	0.729941i
$859$	10.3059	+	17.8504i	0.351634	+	0.609048i	0.986536	−	0.163545i	$-0.0522928\pi$
$859$	10.3059	+	17.8504i	0.351634	+	0.609048i	−0.634902	+	0.772593i	$0.718959\pi$
$860$	104.361			3.55867
$861$	−4.30768	−	6.19040i	−0.146805	−	0.210968i
$862$	−43.9907			−1.49833
$863$	14.8204	+	25.6696i	0.504491	+	0.873805i	0.999987	+	0.00519395i	$0.00165329\pi$
$863$	14.8204	+	25.6696i	0.504491	+	0.873805i	−0.495495	+	0.868611i	$0.665013\pi$
$864$	−78.8932	+	136.647i	−2.68400	+	4.64882i
$865$	−7.00034	+	12.1249i	−0.238019	+	0.412260i
$866$	8.77593	+	15.2004i	0.298218	+	0.516529i
$867$	46.5041			1.57936
$868$	−6.70273	+	0.566696i	−0.227505	+	0.0192349i
$869$	8.65127			0.293474
$870$	−31.1147	−	53.8922i	−1.05489	−	1.82712i
$871$	9.92282	−	17.1868i	0.336222	−	0.582353i
$872$	−49.4622	+	85.6710i	−1.67500	+	2.90119i
$873$	40.6309	+	70.3749i	1.37515	+	2.38183i
$874$	−2.48961			−0.0842124
$875$	2.96798	−	6.31662i	0.100336	−	0.213541i
$876$	−141.070			−4.76633
$877$	12.8490	+	22.2551i	0.433880	+	0.751502i	0.997204	−	0.0747341i	$-0.0238108\pi$
$877$	12.8490	+	22.2551i	0.433880	+	0.751502i	−0.563323	+	0.826237i	$0.690477\pi$
$878$	−42.0359	+	72.8083i	−1.41864	+	2.45716i
$879$	19.3356	−	33.4903i	0.652174	−	1.12960i
$880$	−20.4586	−	35.4353i	−0.689659	−	1.19452i
$881$	3.71565			0.125183			0.0625917	−	0.998039i	$-0.480063\pi$
$881$	3.71565			0.125183			0.0625917	+	0.998039i	$0.480063\pi$
$882$	−97.8985	+	16.6733i	−3.29641	+	0.561418i
$883$	−11.8979			−0.400395			−0.200198	−	0.979756i	$-0.564158\pi$
$883$	−11.8979			−0.400395			−0.200198	+	0.979756i	$0.564158\pi$
$884$	−9.06169	−	15.6953i	−0.304778	−	0.527890i
$885$	41.0319	−	71.0694i	1.37927	−	2.38897i
$886$	40.6163	−	70.3495i	1.36453	−	2.36344i
$887$	4.90467	+	8.49513i	0.164683	+	0.285239i	0.936543	−	0.350554i	$-0.114007\pi$
$887$	4.90467	+	8.49513i	0.164683	+	0.285239i	−0.771860	+	0.635793i	$0.780673\pi$
$888$	94.1563			3.15968
$889$	8.80009	−	18.7289i	0.295146	−	0.628147i
$890$	−25.7179			−0.862065
$891$	0.766021	+	1.32679i	0.0256627	+	0.0444491i
$892$	−26.1203	+	45.2416i	−0.874571	+	1.51480i
$893$	−5.37321	+	9.30667i	−0.179808	+	0.311436i
$894$	−11.6018	−	20.0949i	−0.388021	−	0.672073i
$895$	32.5779			1.08896
$896$	144.552	−	12.2215i	4.82914	−	0.408290i
$897$	−5.23834			−0.174903
$898$	48.6033	+	84.1833i	1.62191	+	2.80923i
$899$	0.586146	−	1.01523i	0.0195491	−	0.0338600i
$900$	−59.8781	+	103.712i	−1.99594	+	3.45706i
$901$	−5.38551	−	9.32798i	−0.179417	−	0.310760i
$902$	2.24045			0.0745988
$903$	26.2820	+	37.7689i	0.874611	+	1.25687i
$904$	206.106			6.85498
$905$	29.7096	+	51.4585i	0.987579	+	1.71054i
$906$	−7.56709	+	13.1066i	−0.251400	+	0.435437i
$907$	11.1977	−	19.3950i	0.371814	−	0.644001i	−0.618031	−	0.786154i	$-0.712069\pi$
$907$	11.1977	−	19.3950i	0.371814	−	0.644001i	0.989845	+	0.142153i	$0.0454026\pi$
$908$	−61.9561	−	107.311i	−2.05608	−	3.56124i
$909$	14.6528			0.486004
$910$	−48.8537	−	70.2057i	−1.61948	−	2.32730i
$911$	−26.3926			−0.874425			−0.437213	−	0.899358i	$-0.644034\pi$
$911$	−26.3926			−0.874425			−0.437213	+	0.899358i	$0.644034\pi$
$912$	−45.1236	−	78.1564i	−1.49419	−	2.58802i
$913$	−2.55011	+	4.41692i	−0.0843964	+	0.146179i
$914$	6.78352	−	11.7494i	0.224379	−	0.388635i
$915$	50.4183	+	87.3270i	1.66678	+	2.88694i
$916$	−50.4737			−1.66770
$917$	6.46569	−	0.546655i	0.213516	−	0.0180521i
$918$	−13.8848			−0.458267
$919$	25.1788	+	43.6109i	0.830571	+	1.43859i	0.897586	+	0.440839i	$0.145319\pi$
$919$	25.1788	+	43.6109i	0.830571	+	1.43859i	−0.0670152	+	0.997752i	$0.521348\pi$
$920$	7.27831	−	12.6064i	0.239959	−	0.415621i
$921$	−37.9624	+	65.7529i	−1.25090	+	2.16663i
$922$	2.14990	+	3.72374i	0.0708032	+	0.122635i
$923$	5.64364			0.185763
$924$	14.6979	−	31.2809i	0.483525	−	1.02907i
$925$	13.4485			0.442185
$926$	−8.73095	−	15.1225i	−0.286917	−	0.496955i
$927$	24.9821	−	43.2703i	0.820521	−	1.42118i
$928$	−33.9975	+	58.8854i	−1.11602	+	1.93301i
$929$	−9.58186	−	16.5963i	−0.314371	−	0.544506i	0.664933	−	0.746903i	$-0.268460\pi$
$929$	−9.58186	−	16.5963i	−0.314371	−	0.544506i	−0.979304	+	0.202397i	$0.935127\pi$
$930$	−10.7037			−0.350990
$931$	4.60247	−	12.4191i	0.150840	−	0.407018i
$932$	3.04064			0.0995995
$933$	13.4444	+	23.2865i	0.440151	+	0.762364i
$934$	29.0726	−	50.3553i	0.951286	−	1.64767i
$935$	1.01235	−	1.75344i	0.0331073	−	0.0573436i
$936$	−100.417	−	173.927i	−3.28223	−	5.68500i
$937$	4.86054			0.158787			0.0793935	−	0.996843i	$-0.474702\pi$
$937$	4.86054			0.158787			0.0793935	+	0.996843i	$0.474702\pi$
$938$	−15.9880	+	34.0266i	−0.522026	+	1.11101i
$939$	34.6468			1.13066
$940$	−48.5757	−	84.1356i	−1.58436	−	2.74420i
$941$	−7.97137	+	13.8068i	−0.259859	+	0.450089i	−0.966204	−	0.257779i	$-0.917009\pi$
$941$	−7.97137	+	13.8068i	−0.259859	+	0.450089i	0.706345	+	0.707868i	$0.250343\pi$
$942$	−41.4586	+	71.8084i	−1.35079	+	2.33965i
$943$	0.237683	+	0.411679i	0.00774002	+	0.0134061i
$944$	−159.459			−5.18996
$945$	−48.2506	+	4.07945i	−1.56959	+	0.132704i
$946$	−13.6694			−0.444432
$947$	16.3953	+	28.3975i	0.532775	+	0.922794i	0.999267	+	0.0382686i	$0.0121843\pi$
$947$	16.3953	+	28.3975i	0.532775	+	0.922794i	−0.466492	+	0.884525i	$0.654482\pi$
$948$	−86.2508	+	149.391i	−2.80130	+	4.85199i
$949$	16.8955	−	29.2639i	0.548451	−	0.949945i
$950$	−10.8067	−	18.7177i	−0.350614	−	0.607282i
$951$	−41.0473			−1.33105
$952$	12.6832	+	18.2265i	0.411065	+	0.590725i
$953$	−18.3086			−0.593074			−0.296537	−	0.955021i	$-0.595832\pi$
$953$	−18.3086			−0.593074			−0.296537	+	0.955021i	$0.595832\pi$
$954$	−92.2745	−	159.824i	−2.98750	−	5.17450i
$955$	35.0790	−	60.7587i	1.13513	−	1.96610i
$956$	−40.2182	+	69.6599i	−1.30075	+	2.25296i
$957$	3.01165	+	5.21633i	0.0973529	+	0.168620i
$958$	1.41244			0.0456338
$959$	20.1860	+	29.0085i	0.651841	+	0.936735i
$960$	332.641			10.7359
$961$	15.3992	+	26.6722i	0.496748	+	0.860392i
$962$	−17.4358	+	30.1996i	−0.562151	+	0.973675i
$963$	38.1448	−	66.0687i	1.22920	−	2.12904i
$964$	20.3467	+	35.2415i	0.655323	+	1.13505i
$965$	44.6156			1.43623
$966$	9.88821	−	0.836020i	0.318148	−	0.0268985i
$967$	21.3394			0.686230			0.343115	−	0.939293i	$-0.388518\pi$
$967$	21.3394			0.686230			0.343115	+	0.939293i	$0.388518\pi$
$968$	−52.4285	−	90.8087i	−1.68511	−	2.91870i
$969$	2.23284	−	3.86740i	0.0717293	−	0.124239i
$970$	66.2927	−	114.822i	2.12853	−	3.68672i
$971$	18.8333	+	32.6202i	0.604389	+	1.04683i	0.992148	+	0.125071i	$0.0399159\pi$
$971$	18.8333	+	32.6202i	0.604389	+	1.04683i	−0.387759	+	0.921761i	$0.626751\pi$
$972$	72.3535			2.32074
$973$	−10.2227	+	21.7565i	−0.327723	+	0.697481i
$974$	−30.2973			−0.970787
$975$	−22.7380	−	39.3834i	−0.728200	−	1.26128i
$976$	97.9684	−	169.686i	3.13589	−	5.43153i
$977$	7.77560	−	13.4677i	0.248764	−	0.430871i	−0.714419	−	0.699718i	$-0.753309\pi$
$977$	7.77560	−	13.4677i	0.248764	−	0.430871i	0.963183	+	0.268847i	$0.0866425\pi$
$978$	−71.3570	−	123.594i	−2.28174	−	3.95210i
$979$	2.48928			0.0795578
$980$	76.4269	+	92.1698i	2.44137	+	2.94426i
$981$	−50.0207			−1.59704
$982$	2.11532	+	3.66385i	0.0675027	+	0.116918i
$983$	11.1820	−	19.3679i	0.356652	−	0.617739i	−0.630747	−	0.775988i	$-0.717252\pi$
$983$	11.1820	−	19.3679i	0.356652	−	0.617739i	0.987399	+	0.158249i	$0.0505850\pi$
$984$	−14.4465	+	25.0220i	−0.460537	+	0.797674i
$985$	−33.2635	−	57.6140i	−1.05986	−	1.83574i
$986$	−5.98340			−0.190550
$987$	18.2160	−	38.7685i	0.579823	−	1.23401i
$988$	41.4136			1.31754
$989$	−1.45015	−	2.51174i	−0.0461121	−	0.0798686i
$990$	17.3454	−	30.0431i	0.551273	−	0.954834i
$991$	7.58636	−	13.1400i	0.240989	−	0.417404i	−0.720008	−	0.693966i	$-0.755862\pi$
$991$	7.58636	−	13.1400i	0.240989	−	0.417404i	0.960996	+	0.276562i	$0.0891951\pi$
$992$	5.84774	+	10.1286i	0.185666	+	0.321583i
$993$	13.5728			0.430719
$994$	−10.6533	+	0.900706i	−0.337902	+	0.0285687i
$995$	21.6079			0.685016
$996$	−50.8478	−	88.0710i	−1.61117	−	2.79064i
$997$	9.07659	−	15.7211i	0.287458	−	0.497893i	−0.685744	−	0.727843i	$-0.740523\pi$
$997$	9.07659	−	15.7211i	0.287458	−	0.497893i	0.973202	+	0.229950i	$0.0738563\pi$
$998$	−40.9532	+	70.9331i	−1.29635	+	2.24535i
$999$	9.87113	+	17.0973i	0.312309	+	0.540935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.d.165.17	✓	34
7.2	even	3	inner	287.2.e.d.247.17	yes	34
7.3	odd	6		2009.2.a.r.1.1		17
7.4	even	3		2009.2.a.s.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.17	✓	34	1.1	even	1	trivial
287.2.e.d.247.17	yes	34	7.2	even	3	inner
2009.2.a.r.1.1		17	7.3	odd	6
2009.2.a.s.1.1		17	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38401 + 2.39717i) q^{2} +(1.42525 - 2.46860i) q^{3} +(-2.83094 + 4.90334i) q^{4} +(1.51053 + 2.61632i) q^{5} +7.89019 q^{6} +(1.12514 - 2.39459i) q^{7} -10.1361 q^{8} +(-2.56265 - 4.43864i) q^{9} +O(q^{10})\)	\(q+(1.38401 + 2.39717i) q^{2} +(1.42525 - 2.46860i) q^{3} +(-2.83094 + 4.90334i) q^{4} +(1.51053 + 2.61632i) q^{5} +7.89019 q^{6} +(1.12514 - 2.39459i) q^{7} -10.1361 q^{8} +(-2.56265 - 4.43864i) q^{9} +(-4.18117 + 7.24200i) q^{10} +(0.404704 - 0.700968i) q^{11} +(8.06958 + 13.9769i) q^{12} -3.86586 q^{13} +(7.29743 - 0.616977i) q^{14} +8.61152 q^{15} +(-8.36658 - 14.4913i) q^{16} +(0.414002 - 0.717073i) q^{17} +(7.09344 - 12.2862i) q^{18} +(0.946033 + 1.63858i) q^{19} -17.1049 q^{20} +(-4.30768 - 6.19040i) q^{21} +2.24045 q^{22} +(0.237683 + 0.411679i) q^{23} +(-14.4465 + 25.0220i) q^{24} +(-2.06342 + 3.57395i) q^{25} +(-5.35037 - 9.26711i) q^{26} -6.05815 q^{27} +(8.55627 + 12.2959i) q^{28} -2.61064 q^{29} +(11.9184 + 20.6433i) q^{30} +(-0.224522 + 0.388883i) q^{31} +(13.0227 - 22.5559i) q^{32} +(-1.15360 - 1.99810i) q^{33} +2.29192 q^{34} +(7.96457 - 0.673382i) q^{35} +29.0189 q^{36} +(-1.62940 - 2.82220i) q^{37} +(-2.61863 + 4.53560i) q^{38} +(-5.50979 + 9.54324i) q^{39} +(-15.3110 - 26.5194i) q^{40} +1.00000 q^{41} +(8.87757 - 18.8938i) q^{42} -6.10120 q^{43} +(2.29139 + 3.96880i) q^{44} +(7.74193 - 13.4094i) q^{45} +(-0.657909 + 1.13953i) q^{46} +(2.83987 + 4.91879i) q^{47} -47.6977 q^{48} +(-4.46812 - 5.38850i) q^{49} -11.4231 q^{50} +(-1.18011 - 2.04401i) q^{51} +(10.9440 - 18.9556i) q^{52} +(6.50421 - 11.2656i) q^{53} +(-8.38451 - 14.5224i) q^{54} +2.44527 q^{55} +(-11.4046 + 24.2719i) q^{56} +5.39331 q^{57} +(-3.61315 - 6.25815i) q^{58} +(4.76477 - 8.25283i) q^{59} +(-24.3787 + 42.2252i) q^{60} +(5.85474 + 10.1407i) q^{61} -1.24296 q^{62} +(-13.5121 + 1.14241i) q^{63} +38.6274 q^{64} +(-5.83950 - 10.1143i) q^{65} +(3.19319 - 5.53077i) q^{66} +(-2.56678 + 4.44580i) q^{67} +(2.34403 + 4.05998i) q^{68} +1.35503 q^{69} +(12.6372 + 18.1605i) q^{70} -1.45987 q^{71} +(25.9754 + 44.9907i) q^{72} +(-4.37044 + 7.56982i) q^{73} +(4.51019 - 7.81188i) q^{74} +(5.88176 + 10.1875i) q^{75} -10.7127 q^{76} +(-1.22318 - 1.75779i) q^{77} -30.5023 q^{78} +(5.34420 + 9.25642i) q^{79} +(25.2760 - 43.7793i) q^{80} +(-0.946397 + 1.63921i) q^{81} +(1.38401 + 2.39717i) q^{82} -6.30118 q^{83} +(42.5484 - 3.59734i) q^{84} +2.50146 q^{85} +(-8.44410 - 14.6256i) q^{86} +(-3.72081 + 6.44463i) q^{87} +(-4.10213 + 7.10510i) q^{88} +(1.53772 + 2.66341i) q^{89} +42.8595 q^{90} +(-4.34963 + 9.25714i) q^{91} -2.69147 q^{92} +(0.639997 + 1.10851i) q^{93} +(-7.86078 + 13.6153i) q^{94} +(-2.85803 + 4.95025i) q^{95} +(-37.1210 - 64.2954i) q^{96} -15.8551 q^{97} +(6.73322 - 18.1685i) q^{98} -4.14846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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