LMFDB - Embedded newform 207.2.e.a.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(70,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, 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("207.70");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 11 x^{14} - 4 x^{13} + 77 x^{12} - 23 x^{11} + 282 x^{10} - 20 x^{9} + 714 x^{8} + \cdots + 1 $ x^16 - x^15 + 11x^14 - 4x^13 + 77x^12 - 23x^11 + 282x^10 - 20x^9 + 714x^8 - 43x^7 + 938x^6 + 178x^5 + 738x^4 - 55x^3 + 36x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			139.1
Root			$1.30401 + 2.25862i$ of defining polynomial
Character	$\chi$	$=$	207.139
Dual form			207.2.e.a.70.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30401 - 2.25862i) q^{2} +(1.44644 + 0.952792i) q^{3} +(-2.40091 + 4.15849i) q^{4} +(1.60524 - 2.78036i) q^{5} +(0.265817 - 4.50941i) q^{6} +(1.48649 + 2.57468i) q^{7} +7.30721 q^{8} +(1.18437 + 2.75631i) q^{9} +O(q^{10})$	\(q+(-1.30401 - 2.25862i) q^{2} +(1.44644 + 0.952792i) q^{3} +(-2.40091 + 4.15849i) q^{4} +(1.60524 - 2.78036i) q^{5} +(0.265817 - 4.50941i) q^{6} +(1.48649 + 2.57468i) q^{7} +7.30721 q^{8} +(1.18437 + 2.75631i) q^{9} -8.37303 q^{10} +(0.580275 + 1.00507i) q^{11} +(-7.43494 + 3.72744i) q^{12} +(3.21843 - 5.57448i) q^{13} +(3.87681 - 6.71483i) q^{14} +(4.97099 - 2.49216i) q^{15} +(-4.72689 - 8.18721i) q^{16} -4.73790 q^{17} +(4.68102 - 6.26932i) q^{18} -1.71414 q^{19} +(7.70807 + 13.3508i) q^{20} +(-0.303014 + 5.14043i) q^{21} +(1.51337 - 2.62124i) q^{22} +(0.500000 - 0.866025i) q^{23} +(10.5694 + 6.96225i) q^{24} +(-2.65360 - 4.59618i) q^{25} -16.7875 q^{26} +(-0.913068 + 5.11530i) q^{27} -14.2757 q^{28} +(-2.39541 - 4.14897i) q^{29} +(-12.1111 - 7.97776i) q^{30} +(-2.36989 + 4.10477i) q^{31} +(-5.02066 + 8.69603i) q^{32} +(-0.118286 + 2.00665i) q^{33} +(6.17829 + 10.7011i) q^{34} +9.54471 q^{35} +(-14.3057 - 1.69244i) q^{36} -2.59497 q^{37} +(2.23526 + 3.87158i) q^{38} +(9.96659 - 4.99666i) q^{39} +(11.7298 - 20.3167i) q^{40} +(-2.15592 + 3.73416i) q^{41} +(12.0054 - 6.01880i) q^{42} +(2.22924 + 3.86115i) q^{43} -5.57274 q^{44} +(9.56475 + 1.13156i) q^{45} -2.60803 q^{46} +(-0.161218 - 0.279239i) q^{47} +(0.963554 - 16.3461i) q^{48} +(-0.919310 + 1.59229i) q^{49} +(-6.92068 + 11.9870i) q^{50} +(-6.85309 - 4.51424i) q^{51} +(15.4543 + 26.7676i) q^{52} +11.6411 q^{53} +(12.7442 - 4.60815i) q^{54} +3.72593 q^{55} +(10.8621 + 18.8137i) q^{56} +(-2.47939 - 1.63322i) q^{57} +(-6.24729 + 10.8206i) q^{58} +(-2.50093 + 4.33174i) q^{59} +(-1.57125 + 26.6553i) q^{60} +(-0.431864 - 0.748011i) q^{61} +12.3615 q^{62} +(-5.33606 + 7.14661i) q^{63} +7.28048 q^{64} +(-10.3327 - 17.8968i) q^{65} +(4.68650 - 2.34953i) q^{66} +(-0.597357 + 1.03465i) q^{67} +(11.3753 - 19.7025i) q^{68} +(1.54836 - 0.776257i) q^{69} +(-12.4464 - 21.5579i) q^{70} -9.14295 q^{71} +(8.65447 + 20.1409i) q^{72} -8.15065 q^{73} +(3.38388 + 5.86105i) q^{74} +(0.540924 - 9.17642i) q^{75} +(4.11548 - 7.12822i) q^{76} +(-1.72515 + 2.98804i) q^{77} +(-24.2821 - 15.9950i) q^{78} +(1.90179 + 3.29399i) q^{79} -30.3512 q^{80} +(-6.19452 + 6.52901i) q^{81} +11.2454 q^{82} +(-0.0456526 - 0.0790727i) q^{83} +(-20.6489 - 13.6018i) q^{84} +(-7.60548 + 13.1731i) q^{85} +(5.81391 - 10.0700i) q^{86} +(0.488293 - 8.28356i) q^{87} +(4.24019 + 7.34422i) q^{88} -9.39887 q^{89} +(-9.91680 - 23.0787i) q^{90} +19.1367 q^{91} +(2.40091 + 4.15849i) q^{92} +(-7.33890 + 3.67929i) q^{93} +(-0.420462 + 0.728262i) q^{94} +(-2.75160 + 4.76592i) q^{95} +(-15.5476 + 7.79464i) q^{96} +(7.21929 + 12.5042i) q^{97} +4.79517 q^{98} +(-2.08301 + 2.78979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - q^{3} - 5 q^{4} - q^{6} + 7 q^{7} + 12 q^{8} + 5 q^{9}+O(q^{10}) $ 16 * q - q^2 - q^3 - 5 * q^4 - q^6 + 7 * q^7 + 12 * q^8 + 5 * q^9	\( 16 q - q^{2} - q^{3} - 5 q^{4} - q^{6} + 7 q^{7} + 12 q^{8} + 5 q^{9} - 20 q^{10} + 3 q^{11} - 17 q^{12} + 15 q^{13} + 5 q^{14} + q^{16} - 12 q^{17} + 23 q^{18} - 24 q^{19} + 7 q^{20} - 10 q^{21} + 17 q^{22} + 8 q^{23} + 18 q^{24} + 10 q^{25} - 52 q^{26} + 2 q^{27} - 40 q^{28} - 10 q^{29} - 45 q^{30} + 8 q^{31} - 13 q^{32} - 13 q^{33} + 15 q^{34} + 30 q^{35} + q^{36} - 38 q^{37} - 7 q^{38} + 9 q^{39} + 30 q^{40} - q^{41} + 41 q^{42} + 17 q^{43} - 12 q^{44} + 33 q^{45} - 2 q^{46} - 5 q^{47} - 20 q^{48} + 15 q^{49} - 7 q^{50} - 55 q^{51} + 39 q^{52} + 8 q^{53} + 59 q^{54} - 20 q^{55} + 24 q^{56} - 20 q^{57} + 4 q^{58} - 20 q^{59} + 6 q^{60} + 16 q^{61} + 78 q^{62} + 32 q^{63} - 8 q^{64} - 2 q^{65} - 28 q^{66} + 7 q^{67} + 24 q^{68} - 2 q^{69} - 16 q^{70} - 10 q^{71} + 33 q^{72} - 96 q^{73} - 21 q^{74} + 26 q^{75} + 6 q^{76} + 16 q^{77} - 30 q^{78} + 12 q^{79} - 94 q^{80} + 17 q^{81} - 16 q^{82} + 12 q^{83} - 59 q^{84} + 6 q^{85} + 19 q^{86} - 53 q^{87} + 7 q^{88} + 22 q^{89} + 21 q^{90} - 4 q^{91} + 5 q^{92} - 31 q^{93} + q^{94} - 4 q^{95} - 38 q^{96} + 43 q^{97} + 56 q^{98} + 2 q^{99}+O(q^{100}) \) 16 * q - q^2 - q^3 - 5 * q^4 - q^6 + 7 * q^7 + 12 * q^8 + 5 * q^9 - 20 * q^10 + 3 * q^11 - 17 * q^12 + 15 * q^13 + 5 * q^14 + q^16 - 12 * q^17 + 23 * q^18 - 24 * q^19 + 7 * q^20 - 10 * q^21 + 17 * q^22 + 8 * q^23 + 18 * q^24 + 10 * q^25 - 52 * q^26 + 2 * q^27 - 40 * q^28 - 10 * q^29 - 45 * q^30 + 8 * q^31 - 13 * q^32 - 13 * q^33 + 15 * q^34 + 30 * q^35 + q^36 - 38 * q^37 - 7 * q^38 + 9 * q^39 + 30 * q^40 - q^41 + 41 * q^42 + 17 * q^43 - 12 * q^44 + 33 * q^45 - 2 * q^46 - 5 * q^47 - 20 * q^48 + 15 * q^49 - 7 * q^50 - 55 * q^51 + 39 * q^52 + 8 * q^53 + 59 * q^54 - 20 * q^55 + 24 * q^56 - 20 * q^57 + 4 * q^58 - 20 * q^59 + 6 * q^60 + 16 * q^61 + 78 * q^62 + 32 * q^63 - 8 * q^64 - 2 * q^65 - 28 * q^66 + 7 * q^67 + 24 * q^68 - 2 * q^69 - 16 * q^70 - 10 * q^71 + 33 * q^72 - 96 * q^73 - 21 * q^74 + 26 * q^75 + 6 * q^76 + 16 * q^77 - 30 * q^78 + 12 * q^79 - 94 * q^80 + 17 * q^81 - 16 * q^82 + 12 * q^83 - 59 * q^84 + 6 * q^85 + 19 * q^86 - 53 * q^87 + 7 * q^88 + 22 * q^89 + 21 * q^90 - 4 * q^91 + 5 * q^92 - 31 * q^93 + q^94 - 4 * q^95 - 38 * q^96 + 43 * q^97 + 56 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.30401	−	2.25862i	−0.922077	−	1.59708i	−0.796195	−	0.605040i	$-0.793157\pi$
$2$	−1.30401	−	2.25862i	−0.922077	−	1.59708i	−0.125882	−	0.992045i	$-0.540176\pi$
$3$	1.44644	+	0.952792i	0.835102	+	0.550095i
$3$	1.44644	+	0.952792i	0.835102	+	0.550095i
$4$	−2.40091	+	4.15849i	−1.20045	+	2.07925i
$5$	1.60524	−	2.78036i	0.717886	−	1.24342i	−0.243950	−	0.969788i	$-0.578443\pi$
$5$	1.60524	−	2.78036i	0.717886	−	1.24342i	0.961836	−	0.273627i	$-0.0882235\pi$
$6$	0.265817	−	4.50941i	0.108519	−	1.84096i
$7$	1.48649	+	2.57468i	0.561841	+	0.973137i	0.997336	+	0.0729456i	$0.0232400\pi$
$7$	1.48649	+	2.57468i	0.561841	+	0.973137i	−0.435495	+	0.900191i	$0.643427\pi$
$8$	7.30721			2.58349
$9$	1.18437	+	2.75631i	0.394791	+	0.918771i
$10$	−8.37303			−2.64779
$11$	0.580275	+	1.00507i	0.174959	+	0.303039i	0.940147	−	0.340769i	$-0.110687\pi$
$11$	0.580275	+	1.00507i	0.174959	+	0.303039i	−0.765188	+	0.643807i	$0.777354\pi$
$12$	−7.43494	+	3.72744i	−2.14628	+	1.07602i
$13$	3.21843	−	5.57448i	0.892632	−	1.54608i	0.0559234	−	0.998435i	$-0.482190\pi$
$13$	3.21843	−	5.57448i	0.892632	−	1.54608i	0.836708	−	0.547649i	$-0.184477\pi$
$14$	3.87681	−	6.71483i	1.03612	−	1.79461i
$15$	4.97099	−	2.49216i	1.28350	−	0.643473i
$16$	−4.72689	−	8.18721i	−1.18172	−	2.04680i
$17$	−4.73790			−1.14911			−0.574555	−	0.818466i	$-0.694825\pi$
$17$	−4.73790			−1.14911			−0.574555	+	0.818466i	$0.694825\pi$
$18$	4.68102	−	6.26932i	1.10333	−	1.47769i
$19$	−1.71414			−0.393250			−0.196625	−	0.980479i	$-0.562998\pi$
$19$	−1.71414			−0.393250			−0.196625	+	0.980479i	$0.562998\pi$
$20$	7.70807	+	13.3508i	1.72358	+	2.98532i
$21$	−0.303014	+	5.14043i	−0.0661231	+	1.12173i
$22$	1.51337	−	2.62124i	0.322652	−	0.558850i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	10.5694	+	6.96225i	2.15748	+	1.42116i
$25$	−2.65360	−	4.59618i	−0.530721	−	0.919235i
$26$	−16.7875			−3.29230
$27$	−0.913068	+	5.11530i	−0.175720	+	0.984440i
$28$	−14.2757			−2.69785
$29$	−2.39541	−	4.14897i	−0.444816	−	0.770444i	0.553223	−	0.833033i	$-0.313398\pi$
$29$	−2.39541	−	4.14897i	−0.444816	−	0.770444i	−0.998039	+	0.0625888i	$0.980064\pi$
$30$	−12.1111	−	7.97776i	−2.21117	−	1.45653i
$31$	−2.36989	+	4.10477i	−0.425645	+	0.737239i	−0.996480	−	0.0838258i	$-0.973286\pi$
$31$	−2.36989	+	4.10477i	−0.425645	+	0.737239i	0.570835	+	0.821064i	$0.306619\pi$
$32$	−5.02066	+	8.69603i	−0.887535	+	1.53726i
$33$	−0.118286	+	2.00665i	−0.0205910	+	0.349313i
$34$	6.17829	+	10.7011i	1.05957	+	1.83523i
$35$	9.54471			1.61335
$36$	−14.3057	−	1.69244i	−2.38428	−	0.282073i
$37$	−2.59497			−0.426611			−0.213305	−	0.976986i	$-0.568423\pi$
$37$	−2.59497			−0.426611			−0.213305	+	0.976986i	$0.568423\pi$
$38$	2.23526	+	3.87158i	0.362607	+	0.628053i
$39$	9.96659	−	4.99666i	1.59593	−	0.800106i
$40$	11.7298	−	20.3167i	1.85465	−	3.21235i
$41$	−2.15592	+	3.73416i	−0.336698	+	0.583177i	−0.983809	−	0.179218i	$-0.942643\pi$
$41$	−2.15592	+	3.73416i	−0.336698	+	0.583177i	0.647112	+	0.762395i	$0.275977\pi$
$42$	12.0054	−	6.01880i	1.85248	−	0.928722i
$43$	2.22924	+	3.86115i	0.339955	+	0.588820i	0.984424	−	0.175811i	$-0.0562547\pi$
$43$	2.22924	+	3.86115i	0.339955	+	0.588820i	−0.644469	+	0.764631i	$0.722921\pi$
$44$	−5.57274			−0.840122
$45$	9.56475	+	1.13156i	1.42583	+	0.168683i
$46$	−2.60803			−0.384533
$47$	−0.161218	−	0.279239i	−0.0235161	−	0.0407311i	0.854028	−	0.520227i	$-0.174153\pi$
$47$	−0.161218	−	0.279239i	−0.0235161	−	0.0407311i	−0.877544	+	0.479496i	$0.840819\pi$
$48$	0.963554	−	16.3461i	0.139077	−	2.35935i
$49$	−0.919310	+	1.59229i	−0.131330	+	0.227470i
$50$	−6.92068	+	11.9870i	−0.978731	+	1.69521i
$51$	−6.85309	−	4.51424i	−0.959624	−	0.632120i
$52$	15.4543	+	26.7676i	2.14313	+	3.71200i
$53$	11.6411			1.59902			0.799512	−	0.600650i	$-0.205091\pi$
$53$	11.6411			1.59902			0.799512	+	0.600650i	$0.205091\pi$
$54$	12.7442	−	4.60815i	1.73426	−	0.627090i
$55$	3.72593			0.502404
$56$	10.8621	+	18.8137i	1.45151	+	2.51409i
$57$	−2.47939	−	1.63322i	−0.328404	−	0.216325i
$58$	−6.24729	+	10.8206i	−0.820310	+	1.42082i
$59$	−2.50093	+	4.33174i	−0.325594	+	0.563945i	−0.981632	−	0.190782i	$-0.938897\pi$
$59$	−2.50093	+	4.33174i	−0.325594	+	0.563945i	0.656039	+	0.754727i	$0.272231\pi$
$60$	−1.57125	+	26.6553i	−0.202848	+	3.44118i
$61$	−0.431864	−	0.748011i	−0.0552946	−	0.0957730i	0.837053	−	0.547122i	$-0.184276\pi$
$61$	−0.431864	−	0.748011i	−0.0552946	−	0.0957730i	−0.892348	+	0.451349i	$0.850943\pi$
$62$	12.3615			1.56991
$63$	−5.33606	+	7.14661i	−0.672280	+	0.900389i
$64$	7.28048			0.910059
$65$	−10.3327	−	17.8968i	−1.28162	−	2.21982i
$66$	4.68650	−	2.34953i	0.576868	−	0.289208i
$67$	−0.597357	+	1.03465i	−0.0729787	+	0.126403i	−0.900206	−	0.435465i	$-0.856584\pi$
$67$	−0.597357	+	1.03465i	−0.0729787	+	0.126403i	0.827227	+	0.561868i	$0.189917\pi$
$68$	11.3753	−	19.7025i	1.37945	−	2.38928i
$69$	1.54836	−	0.776257i	0.186401	−	0.0934504i
$70$	−12.4464	−	21.5579i	−1.48763	−	2.57666i
$71$	−9.14295			−1.08507			−0.542534	−	0.840034i	$-0.682535\pi$
$71$	−9.14295			−1.08507			−0.542534	+	0.840034i	$0.682535\pi$
$72$	8.65447	+	20.1409i	1.01994	+	2.37363i
$73$	−8.15065			−0.953962			−0.476981	−	0.878914i	$-0.658269\pi$
$73$	−8.15065			−0.953962			−0.476981	+	0.878914i	$0.658269\pi$
$74$	3.38388	+	5.86105i	0.393368	+	0.681334i
$75$	0.540924	−	9.17642i	0.0624606	−	1.05960i
$76$	4.11548	−	7.12822i	0.472078	−	0.817663i
$77$	−1.72515	+	2.98804i	−0.196599	+	0.340519i
$78$	−24.2821	−	15.9950i	−2.74941	−	1.81108i
$79$	1.90179	+	3.29399i	0.213968	+	0.370603i	0.952953	−	0.303119i	$-0.0980279\pi$
$79$	1.90179	+	3.29399i	0.213968	+	0.370603i	−0.738985	+	0.673722i	$0.764695\pi$
$80$	−30.3512			−3.39337
$81$	−6.19452	+	6.52901i	−0.688280	+	0.725445i
$82$	11.2454			1.24184
$83$	−0.0456526	−	0.0790727i	−0.00501103	−	0.00867935i	0.863509	−	0.504333i	$-0.168262\pi$
$83$	−0.0456526	−	0.0790727i	−0.00501103	−	0.00867935i	−0.868520	+	0.495654i	$0.834928\pi$
$84$	−20.6489	−	13.6018i	−2.25298	−	1.48408i
$85$	−7.60548	+	13.1731i	−0.824930	+	1.42882i
$86$	5.81391	−	10.0700i	0.626930	−	1.08588i
$87$	0.488293	−	8.28356i	0.0523505	−	0.888091i
$88$	4.24019	+	7.34422i	0.452006	+	0.782897i
$89$	−9.39887			−0.996278			−0.498139	−	0.867097i	$-0.665983\pi$
$89$	−9.39887			−0.996278			−0.498139	+	0.867097i	$0.665983\pi$
$90$	−9.91680	−	23.0787i	−1.04532	−	2.43271i
$91$	19.1367			2.00607
$92$	2.40091	+	4.15849i	0.250312	+	0.433553i
$93$	−7.33890	+	3.67929i	−0.761008	+	0.381525i
$94$	−0.420462	+	0.728262i	−0.0433674	+	0.0751145i
$95$	−2.75160	+	4.76592i	−0.282309	+	0.488973i
$96$	−15.5476	+	7.79464i	−1.58682	+	0.795537i
$97$	7.21929	+	12.5042i	0.733007	+	1.26961i	0.955592	+	0.294693i	$0.0952173\pi$
$97$	7.21929	+	12.5042i	0.733007	+	1.26961i	−0.222585	+	0.974913i	$0.571449\pi$
$98$	4.79517			0.484386
$99$	−2.08301	+	2.78979i	−0.209351	+	0.280385i
$100$	25.4842			2.54842
$101$	−2.81080	−	4.86845i	−0.279685	−	0.484429i	0.691621	−	0.722260i	$-0.256897\pi$
$101$	−2.81080	−	4.86845i	−0.279685	−	0.484429i	−0.971306	+	0.237832i	$0.923563\pi$
$102$	−1.25942	+	21.3651i	−0.124701	+	2.11546i
$103$	−1.41944	+	2.45854i	−0.139861	+	0.242247i	−0.927444	−	0.373962i	$-0.877999\pi$
$103$	−1.41944	+	2.45854i	−0.139861	+	0.242247i	0.787583	+	0.616209i	$0.211332\pi$
$104$	23.5177	−	40.7339i	2.30610	−	3.99429i
$105$	13.8058	+	9.09413i	1.34731	+	0.887496i
$106$	−15.1801	−	26.2928i	−1.47442	−	2.55378i
$107$	−17.6357			−1.70491			−0.852456	−	0.522799i	$-0.824888\pi$
$107$	−17.6357			−1.70491			−0.852456	+	0.522799i	$0.824888\pi$
$108$	−19.0797	−	16.0783i	−1.83595	−	1.54714i
$109$	2.64839			0.253669			0.126835	−	0.991924i	$-0.459518\pi$
$109$	2.64839			0.253669			0.126835	+	0.991924i	$0.459518\pi$
$110$	−4.85866	−	8.41545i	−0.463255	−	0.802381i
$111$	−3.75347	−	2.47247i	−0.356264	−	0.234676i
$112$	14.0530	−	24.3404i	1.32788	−	2.29996i
$113$	−7.75724	+	13.4359i	−0.729740	+	1.26395i	0.227253	+	0.973836i	$0.427026\pi$
$113$	−7.75724	+	13.4359i	−0.729740	+	1.26395i	−0.956993	+	0.290111i	$0.906308\pi$
$114$	−0.455647	+	7.72974i	−0.0426752	+	0.723957i
$115$	−1.60524	−	2.78036i	−0.149690	−	0.259270i
$116$	23.0046			2.13592
$117$	19.1768	+	2.26873i	1.77290	+	0.209744i
$118$	13.0450			1.20089
$119$	−7.04285	−	12.1986i	−0.645617	−	1.11824i
$120$	36.3241	−	18.2107i	3.31592	−	1.66241i
$121$	4.82656	−	8.35985i	0.438778	−	0.759986i
$122$	−1.12631	+	1.95083i	−0.101972	+	0.176620i
$123$	−6.67628	+	3.34709i	−0.601980	+	0.301797i
$124$	−11.3798	−	19.7103i	−1.02193	−	1.77004i
$125$	−0.986287			−0.0882162
$126$	23.0998	+	2.73283i	2.05789	+	0.243460i
$127$	−12.4652			−1.10611			−0.553054	−	0.833146i	$-0.686538\pi$
$127$	−12.4652			−1.10611			−0.553054	+	0.833146i	$0.686538\pi$
$128$	0.547472	+	0.948249i	0.0483901	+	0.0838142i
$129$	−0.454419	+	7.70892i	−0.0400094	+	0.678733i
$130$	−26.9480	+	46.6753i	−2.36350	+	4.09370i
$131$	7.69245	−	13.3237i	0.672092	−	1.16410i	−0.305218	−	0.952283i	$-0.598729\pi$
$131$	7.69245	−	13.3237i	0.672092	−	1.16410i	0.977310	−	0.211815i	$-0.0679375\pi$
$132$	−8.06063	−	5.30967i	−0.701588	−	0.462147i
$133$	−2.54805	−	4.41335i	−0.220944	−	0.382686i
$134$	3.11585			0.269168
$135$	12.7567	+	10.7500i	1.09792	+	0.925209i
$136$	−34.6208			−2.96871
$137$	−2.84613	−	4.92963i	−0.243161	−	0.421167i	0.718452	−	0.695576i	$-0.244851\pi$
$137$	−2.84613	−	4.92963i	−0.243161	−	0.421167i	−0.961613	+	0.274409i	$0.911518\pi$
$138$	−3.77236	−	2.48491i	−0.321124	−	0.211530i
$139$	9.29194	−	16.0941i	0.788132	−	1.36509i	−0.138978	−	0.990296i	$-0.544382\pi$
$139$	9.29194	−	16.0941i	0.788132	−	1.36509i	0.927110	−	0.374790i	$-0.122285\pi$
$140$	−22.9160	+	39.6916i	−1.93675	+	3.35455i
$141$	0.0328636	−	0.557509i	0.00276761	−	0.0469508i
$142$	11.9225	+	20.6504i	1.00052	+	1.73295i
$143$	7.47029			0.624697
$144$	16.9681	−	22.7255i	1.41401	−	1.89379i
$145$	−15.3808			−1.27731
$146$	10.6286	+	18.4092i	0.879626	+	1.52356i
$147$	−2.84685	+	1.42724i	−0.234804	+	0.117717i
$148$	6.23029	−	10.7912i	0.512126	−	0.887029i
$149$	−0.865357	+	1.49884i	−0.0708928	+	0.122790i	−0.899293	−	0.437347i	$-0.855918\pi$
$149$	−0.865357	+	1.49884i	−0.0708928	+	0.122790i	0.828400	+	0.560137i	$0.189251\pi$
$150$	−21.4314	+	10.7444i	−1.74987	+	0.877280i
$151$	−4.02648	−	6.97407i	−0.327670	−	0.567542i	0.654379	−	0.756167i	$-0.272930\pi$
$151$	−4.02648	−	6.97407i	−0.327670	−	0.567542i	−0.982049	+	0.188625i	$0.939597\pi$
$152$	−12.5256			−1.01596
$153$	−5.61145	−	13.0591i	−0.453659	−	1.05577i
$154$	8.99846			0.725117
$155$	7.60850	+	13.1783i	0.611129	+	1.05851i
$156$	−3.15028	+	53.4425i	−0.252225	+	4.27882i
$157$	−0.269329	+	0.466491i	−0.0214948	+	0.0372301i	−0.876573	−	0.481269i	$-0.840176\pi$
$157$	−0.269329	+	0.466491i	−0.0214948	+	0.0372301i	0.855078	+	0.518500i	$0.173509\pi$
$158$	4.95992	−	8.59083i	0.394590	−	0.683449i
$159$	16.8381	+	11.0915i	1.33535	+	0.879615i
$160$	16.1187	+	27.9185i	1.27430	+	2.20715i
$161$	2.97298			0.234304
$162$	22.8243	+	5.47713i	1.79324	+	0.430324i
$163$	3.01163			0.235889			0.117944	−	0.993020i	$-0.462370\pi$
$163$	3.01163			0.235889			0.117944	+	0.993020i	$0.462370\pi$
$164$	−10.3523	−	17.9307i	−0.808379	−	1.40015i
$165$	5.38933	+	3.55003i	0.419558	+	0.276370i
$166$	−0.119063	+	0.206224i	−0.00924111	+	0.0160061i
$167$	−4.90755	+	8.50012i	−0.379757	+	0.657759i	−0.991027	−	0.133663i	$-0.957326\pi$
$167$	−4.90755	+	8.50012i	−0.379757	+	0.657759i	0.611269	+	0.791423i	$0.290659\pi$
$168$	−2.21419	+	37.5622i	−0.170828	+	2.89799i
$169$	−14.2166	−	24.6238i	−1.09358	−	1.89414i
$170$	39.6706			3.04260
$171$	−2.03018	−	4.72470i	−0.155252	−	0.361307i
$172$	−21.4088			−1.63240
$173$	7.57472	+	13.1198i	0.575895	+	0.997480i	0.995944	+	0.0899781i	$0.0286797\pi$
$173$	7.57472	+	13.1198i	0.575895	+	0.997480i	−0.420049	+	0.907502i	$0.637987\pi$
$174$	−19.3461	+	9.69901i	−1.46663	+	0.735280i
$175$	7.88912	−	13.6644i	0.596361	−	1.03293i
$176$	5.48579	−	9.50167i	0.413507	−	0.716215i
$177$	−7.74470	+	3.88273i	−0.582127	+	0.291844i
$178$	12.2563	+	21.2285i	0.918645	+	1.59114i
$179$	7.72994			0.577763			0.288881	−	0.957365i	$-0.406717\pi$
$179$	7.72994			0.577763			0.288881	+	0.957365i	$0.406717\pi$
$180$	−27.6697	+	37.0582i	−2.06237	+	2.76215i
$181$	−3.73899			−0.277917			−0.138958	−	0.990298i	$-0.544375\pi$
$181$	−3.73899			−0.277917			−0.138958	+	0.990298i	$0.544375\pi$
$182$	−24.9545	−	43.2224i	−1.84975	−	3.20386i
$183$	0.0880335	−	1.49343i	0.00650762	−	0.110397i
$184$	3.65360	−	6.32823i	0.269347	−	0.466523i
$185$	−4.16556	+	7.21496i	−0.306258	+	0.530454i
$186$	17.8801	+	11.7779i	1.31104	+	0.863600i
$187$	−2.74929	−	4.76190i	−0.201048	−	0.348225i
$188$	1.54828			0.112920
$189$	−14.5275	+	5.25299i	−1.05672	+	0.382099i
$190$	14.3525			1.04124
$191$	−10.5459	−	18.2660i	−0.763072	−	1.32168i	−0.941260	−	0.337683i	$-0.890357\pi$
$191$	−10.5459	−	18.2660i	−0.763072	−	1.32168i	0.178188	−	0.983996i	$-0.442977\pi$
$192$	10.5308	+	6.93678i	0.759993	+	0.500619i
$193$	11.5463	−	19.9988i	0.831122	−	1.43955i	−0.0660273	−	0.997818i	$-0.521032\pi$
$193$	11.5463	−	19.9988i	0.831122	−	1.43955i	0.897149	−	0.441728i	$-0.145634\pi$
$194$	18.8281	−	32.6112i	1.35178	−	2.34135i
$195$	2.10628	−	35.7316i	0.150833	−	2.55879i
$196$	−4.41436	−	7.64589i	−0.315311	−	0.546135i
$197$	12.7284			0.906862			0.453431	−	0.891291i	$-0.350200\pi$
$197$	12.7284			0.906862			0.453431	+	0.891291i	$0.350200\pi$
$198$	9.01735	+	1.06680i	0.640835	+	0.0758143i
$199$	19.5735			1.38753			0.693763	−	0.720204i	$-0.255952\pi$
$199$	19.5735			1.38753			0.693763	+	0.720204i	$0.255952\pi$
$200$	−19.3904	−	33.5852i	−1.37111	−	2.37483i
$201$	−1.84985	+	0.927405i	−0.130478	+	0.0654141i
$202$	−7.33064	+	12.6970i	−0.515782	+	0.893361i
$203$	7.12151	−	12.3348i	0.499832	−	0.865734i
$204$	35.2260	−	17.6603i	2.46632	−	1.23647i
$205$	6.92154	+	11.9885i	0.483421	+	0.837310i
$206$	7.40386			0.515851
$207$	2.97922	+	0.352458i	0.207070	+	0.0244976i
$208$	−60.8527			−4.21937
$209$	−0.994670	−	1.72282i	−0.0688028	−	0.119170i
$210$	2.53715	−	43.0410i	0.175080	−	2.97011i
$211$	4.48997	−	7.77686i	0.309102	−	0.535381i	−0.669064	−	0.743205i	$-0.733305\pi$
$211$	4.48997	−	7.77686i	0.309102	−	0.535381i	0.978166	+	0.207824i	$0.0666381\pi$
$212$	−27.9491	+	48.4093i	−1.91955	+	3.32477i
$213$	−13.2247	−	8.71133i	−0.906143	−	0.596891i
$214$	22.9973	+	39.8324i	1.57206	+	2.72289i
$215$	14.3139			0.976197
$216$	−6.67198	+	37.3786i	−0.453971	+	2.54329i
$217$	−14.0913			−0.956579
$218$	−3.45353	−	5.98170i	−0.233903	−	0.405132i
$219$	−11.7894	−	7.76588i	−0.796656	−	0.524769i
$220$	−8.94560	+	15.4942i	−0.603112	+	1.04462i
$221$	−15.2486	+	26.4114i	−1.02573	+	1.77662i
$222$	−0.689788	+	11.7018i	−0.0462955	+	0.785373i
$223$	8.31701	+	14.4055i	0.556948	+	0.964662i	0.997749	+	0.0670575i	$0.0213611\pi$
$223$	8.31701	+	14.4055i	0.556948	+	0.964662i	−0.440801	+	0.897605i	$0.645306\pi$
$224$	−29.8526			−1.99461
$225$	9.52564	−	12.7578i	0.635043	−	0.850517i
$226$	40.4622			2.69151
$227$	−3.51367	−	6.08585i	−0.233210	−	0.403932i	0.725541	−	0.688179i	$-0.241590\pi$
$227$	−3.51367	−	6.08585i	−0.233210	−	0.403932i	−0.958751	+	0.284247i	$0.908256\pi$
$228$	12.7445	−	6.38934i	0.844026	−	0.423145i
$229$	−10.9762	+	19.0113i	−0.725326	+	1.25630i	0.233513	+	0.972354i	$0.424978\pi$
$229$	−10.9762	+	19.0113i	−0.725326	+	1.25630i	−0.958840	+	0.283948i	$0.908356\pi$
$230$	−4.18652	+	7.25126i	−0.276051	+	0.478134i
$231$	−5.34230	+	2.67831i	−0.351498	+	0.176220i
$232$	−17.5038	−	30.3174i	−1.14918	−	1.99043i
$233$	13.7997			0.904046			0.452023	−	0.892006i	$-0.350703\pi$
$233$	13.7997			0.904046			0.452023	+	0.892006i	$0.350703\pi$
$234$	−19.8827	−	46.2716i	−1.29977	−	3.02487i
$235$	−1.03518			−0.0675276
$236$	−12.0090	−	20.8002i	−0.781720	−	1.35398i
$237$	−0.387670	+	6.57657i	−0.0251819	+	0.427194i
$238$	−18.3679	+	31.8142i	−1.19062	+	2.06221i
$239$	0.474536	−	0.821920i	0.0306952	−	0.0531656i	−0.850270	−	0.526347i	$-0.823561\pi$
$239$	0.474536	−	0.821920i	0.0306952	−	0.0531656i	0.880965	+	0.473182i	$0.156895\pi$
$240$	−43.9012	−	28.9184i	−2.83381	−	1.86667i
$241$	6.48358	+	11.2299i	0.417644	+	0.723381i	0.995702	−	0.0926146i	$-0.0295225\pi$
$241$	6.48358	+	11.2299i	0.417644	+	0.723381i	−0.578058	+	0.815996i	$0.696189\pi$
$242$	−25.1756			−1.61835
$243$	−15.1808	+	3.54173i	−0.973848	+	0.227202i
$244$	4.14746			0.265514
$245$	2.95143	+	5.11203i	0.188560	+	0.326595i
$246$	16.2658	+	10.7145i	1.03707	+	0.683132i
$247$	−5.51683	+	9.55543i	−0.351027	+	0.607997i
$248$	−17.3173	+	29.9944i	−1.09965	+	1.90465i
$249$	0.00930607	−	0.157871i	0.000589748	−	0.0100047i
$250$	1.28613	+	2.22765i	0.0813421	+	0.140889i
$251$	21.4989			1.35700			0.678500	−	0.734600i	$-0.262630\pi$
$251$	21.4989			1.35700			0.678500	+	0.734600i	$0.262630\pi$
$252$	−16.9078	−	39.3483i	−1.06509	−	2.47871i
$253$	1.16055			0.0729631
$254$	16.2548	+	28.1541i	1.01992	+	1.76655i
$255$	−23.5521	+	11.8076i	−1.47489	+	0.739422i
$256$	8.70830	−	15.0832i	0.544269	−	0.942701i
$257$	−1.30007	+	2.25178i	−0.0810960	+	0.140462i	−0.903721	−	0.428122i	$-0.859175\pi$
$257$	−1.30007	+	2.25178i	−0.0810960	+	0.140462i	0.822625	+	0.568584i	$0.192509\pi$
$258$	18.0041	−	9.02618i	1.12089	−	0.561946i
$259$	−3.85740	−	6.68122i	−0.239687	−	0.415151i
$260$	99.2316			6.15408
$261$	8.59880	−	11.5164i	0.532252	−	0.712849i
$262$	−40.1242			−2.47888
$263$	6.51468	+	11.2838i	0.401712	+	0.695786i	0.993933	−	0.109990i	$-0.0350818\pi$
$263$	6.51468	+	11.2838i	0.401712	+	0.695786i	−0.592220	+	0.805776i	$0.701749\pi$
$264$	−0.864342	+	14.6630i	−0.0531966	+	0.902445i
$265$	18.6867	−	32.3664i	1.14792	−	1.98825i
$266$	−6.64538	+	11.5101i	−0.407455	+	0.705732i
$267$	−13.5949	−	8.95517i	−0.831994	−	0.548047i
$268$	−2.86840	−	4.96821i	−0.175215	−	0.303481i
$269$	−23.9547			−1.46054			−0.730271	−	0.683158i	$-0.760606\pi$
$269$	−23.9547			−1.46054			−0.730271	+	0.683158i	$0.760606\pi$
$270$	7.64515	−	42.8306i	0.465269	−	2.60659i
$271$	7.81616			0.474798			0.237399	−	0.971412i	$-0.423705\pi$
$271$	7.81616			0.474798			0.237399	+	0.971412i	$0.423705\pi$
$272$	22.3955	+	38.7902i	1.35793	+	2.35200i
$273$	27.6800	+	18.2333i	1.67527	+	1.10353i
$274$	−7.42278	+	12.8566i	−0.448426	+	0.776697i
$275$	3.07964	−	5.33409i	0.185709	−	0.321658i
$276$	−0.489413	+	8.30257i	−0.0294592	+	0.499756i
$277$	−11.7720	−	20.3897i	−0.707309	−	1.22510i	−0.965852	−	0.259096i	$-0.916575\pi$
$277$	−11.7720	−	20.3897i	−0.707309	−	1.22510i	0.258542	−	0.966000i	$-0.416758\pi$
$278$	−48.4673			−2.90688
$279$	−14.1209	−	1.67058i	−0.845394	−	0.100015i
$280$	69.7452			4.16807
$281$	4.94180	+	8.55945i	0.294803	+	0.510614i	0.974939	−	0.222472i	$-0.0714126\pi$
$281$	4.94180	+	8.55945i	0.294803	+	0.510614i	−0.680136	+	0.733086i	$0.738079\pi$
$282$	−1.30206	+	0.652774i	−0.0775363	+	0.0388721i
$283$	−0.200234	+	0.346815i	−0.0119027	+	0.0206160i	−0.871915	−	0.489657i	$-0.837122\pi$
$283$	−0.200234	+	0.346815i	−0.0119027	+	0.0206160i	0.860013	+	0.510273i	$0.170455\pi$
$284$	21.9514	−	38.0209i	1.30257	−	2.25612i
$285$	−8.52096	+	4.27190i	−0.504738	+	0.253046i
$286$	−9.74137	−	16.8725i	−0.576019	−	0.997695i
$287$	−12.8190			−0.756682
$288$	−29.9153	−	3.53915i	−1.76278	−	0.208546i
$289$	5.44772			0.320454
$290$	20.0568	+	34.7395i	1.17778	+	2.03997i
$291$	−1.47162	+	24.9650i	−0.0862677	+	1.46347i
$292$	19.5690	−	33.8944i	1.14519	−	1.98352i
$293$	−3.06704	+	5.31227i	−0.179178	+	0.310346i	−0.941599	−	0.336735i	$-0.890677\pi$
$293$	−3.06704	+	5.31227i	−0.179178	+	0.310346i	0.762421	+	0.647081i	$0.224011\pi$
$294$	6.93593	+	4.56880i	0.404512	+	0.266458i
$295$	8.02920	+	13.9070i	0.467478	+	0.809696i
$296$	−18.9620			−1.10214
$297$	−5.67104	+	2.05059i	−0.329067	+	0.118987i
$298$	4.51375			0.261475
$299$	−3.21843	−	5.57448i	−0.186127	−	0.322381i
$300$	36.8614	+	24.2812i	2.12819	+	1.40187i
$301$	−6.62748	+	11.4791i	−0.382002	+	0.661646i
$302$	−10.5012	+	18.1886i	−0.604275	+	1.04663i
$303$	0.572968	−	9.72002i	0.0329161	−	0.558401i
$304$	8.10254	+	14.0340i	0.464712	+	0.804905i
$305$	−2.77299			−0.158781
$306$	−22.1782	+	29.7034i	−1.26784	+	1.69803i
$307$	14.3572			0.819408			0.409704	−	0.912218i	$-0.365632\pi$
$307$	14.3572			0.819408			0.409704	+	0.912218i	$0.365632\pi$
$308$	−8.28383	−	14.3480i	−0.472015	−	0.817554i
$309$	−4.39560	+	2.20370i	−0.250057	+	0.125364i
$310$	19.8432	−	34.3694i	1.12702	−	1.95205i
$311$	7.42723	−	12.8643i	0.421160	−	0.729470i	−0.574894	−	0.818228i	$-0.694957\pi$
$311$	7.42723	−	12.8643i	0.421160	−	0.729470i	0.996053	+	0.0887583i	$0.0282899\pi$
$312$	72.8279	−	36.5116i	4.12307	−	2.06706i
$313$	16.9307	+	29.3248i	0.956979	+	1.65754i	0.729772	+	0.683690i	$0.239626\pi$
$313$	16.9307	+	29.3248i	0.956979	+	1.65754i	0.227207	+	0.973846i	$0.427041\pi$
$314$	1.40483			0.0792794
$315$	11.3045	+	26.3082i	0.636937	+	1.48230i
$316$	−18.2641			−1.02743
$317$	6.14337	+	10.6406i	0.345046	+	0.597637i	0.985362	−	0.170474i	$-0.0545300\pi$
$317$	6.14337	+	10.6406i	0.345046	+	0.597637i	−0.640316	+	0.768111i	$0.721197\pi$
$318$	3.09440	−	52.4944i	0.173525	−	2.94374i
$319$	2.77999	−	4.81509i	0.155650	−	0.269593i
$320$	11.6869	−	20.2423i	0.653319	−	1.13158i
$321$	−25.5090	−	16.8032i	−1.42378	−	0.937863i
$322$	−3.87681	−	6.71483i	−0.216046	−	0.374203i
$323$	8.12141			0.451887
$324$	−12.2784	−	41.4354i	−0.682132	−	2.30197i
$325$	−34.1618			−1.89495
$326$	−3.92721	−	6.80212i	−0.217508	−	0.376735i
$327$	3.83073	+	2.52336i	0.211840	+	0.139542i
$328$	−15.7537	+	27.2863i	−0.869854	+	1.50663i
$329$	0.479299	−	0.830171i	0.0264246	−	0.0457688i
$330$	0.990415	−	16.8017i	0.0545205	−	0.924905i
$331$	−7.77105	−	13.4599i	−0.427135	−	0.739820i	0.569482	−	0.822004i	$-0.307144\pi$
$331$	−7.77105	−	13.4599i	−0.427135	−	0.739820i	−0.996617	+	0.0821837i	$0.973811\pi$
$332$	0.438431			0.0240620
$333$	−3.07342	−	7.15256i	−0.168422	−	0.391958i
$334$	25.5981			1.40066
$335$	1.91780	+	3.32173i	0.104781	+	0.181486i
$336$	43.5181	−	21.8174i	2.37411	−	1.19024i
$337$	15.7950	−	27.3578i	0.860409	−	1.49027i	−0.0111247	−	0.999938i	$-0.503541\pi$
$337$	15.7950	−	27.3578i	0.860409	−	1.49027i	0.871534	−	0.490335i	$-0.163125\pi$
$338$	−37.0773	+	64.2197i	−2.01674	+	3.49309i
$339$	−24.0220	+	12.0432i	−1.30470	+	0.654099i
$340$	−36.5201	−	63.2547i	−1.98058	−	3.43047i
$341$	−5.50075			−0.297882
$342$	−8.02391	+	10.7465i	−0.433883	+	0.581103i
$343$	15.3447			0.828535
$344$	16.2895	+	28.2142i	0.878271	+	1.52121i
$345$	0.327221	−	5.55109i	0.0176170	−	0.298860i
$346$	19.7551	−	34.2168i	1.06204	−	1.83951i
$347$	11.2520	−	19.4891i	0.604040	−	1.04623i	−0.388162	−	0.921591i	$-0.626890\pi$
$347$	11.2520	−	19.4891i	0.604040	−	1.04623i	0.992202	−	0.124637i	$-0.0397767\pi$
$348$	33.2748	+	21.9186i	1.78372	+	1.17496i
$349$	−11.9510	−	20.6998i	−0.639724	−	1.10804i	−0.985493	−	0.169715i	$-0.945715\pi$
$349$	−11.9510	−	20.6998i	−0.639724	−	1.10804i	0.345769	−	0.938320i	$-0.387618\pi$
$350$	−41.1501			−2.19956
$351$	25.5765	+	21.5531i	1.36517	+	1.15042i
$352$	−11.6534			−0.621131
$353$	1.19270	+	2.06581i	0.0634809	+	0.109952i	0.896019	−	0.444015i	$-0.146446\pi$
$353$	1.19270	+	2.06581i	0.0634809	+	0.109952i	−0.832538	+	0.553968i	$0.813113\pi$
$354$	18.8688	+	12.4292i	1.00287	+	0.660604i
$355$	−14.6766	+	25.4207i	−0.778956	+	1.34919i
$356$	22.5658	−	39.0851i	1.19598	−	2.07151i
$357$	1.43565	−	24.3549i	0.0759827	−	1.28900i
$358$	−10.0800	−	17.4590i	−0.532742	−	0.922736i
$359$	−0.497590			−0.0262618			−0.0131309	−	0.999914i	$-0.504180\pi$
$359$	−0.497590			−0.0262618			−0.0131309	+	0.999914i	$0.504180\pi$
$360$	69.8916	+	8.26856i	3.68361	+	0.435791i
$361$	−16.0617			−0.845355
$362$	4.87570	+	8.44495i	0.256261	+	0.443857i
$363$	14.9465	−	7.49331i	0.784489	−	0.393297i
$364$	−45.9453	+	79.5797i	−2.40819	+	4.17111i
$365$	−13.0838	+	22.6618i	−0.684836	+	1.18617i
$366$	−3.48789	+	1.74862i	−0.182315	+	0.0914018i
$367$	10.1990	+	17.6653i	0.532386	+	0.922119i	0.999285	+	0.0378085i	$0.0120377\pi$
$367$	10.1990	+	17.6653i	0.532386	+	0.922119i	−0.466899	+	0.884310i	$0.654629\pi$
$368$	−9.45378			−0.492812
$369$	−12.8459	−	1.51974i	−0.668732	−	0.0791146i
$370$	21.7278			1.12957
$371$	17.3044	+	29.9720i	0.898397	+	1.55607i
$372$	2.31971	−	39.3524i	0.120271	−	2.04033i
$373$	17.9622	−	31.1114i	0.930045	−	1.61089i	0.146806	−	0.989165i	$-0.453101\pi$
$373$	17.9622	−	31.1114i	0.930045	−	1.61089i	0.783239	−	0.621720i	$-0.213566\pi$
$374$	−7.17021	+	12.4192i	−0.370763	+	0.642180i
$375$	−1.42660	−	0.939726i	−0.0736695	−	0.0485273i
$376$	−1.17806	−	2.04045i	−0.0607536	−	0.105228i
$377$	−30.8378			−1.58823
$378$	30.8086	+	25.9622i	1.58462	+	1.33535i
$379$	−37.2450			−1.91315			−0.956573	−	0.291492i	$-0.905848\pi$
$379$	−37.2450			−1.91315			−0.956573	+	0.291492i	$0.905848\pi$
$380$	−13.2127	−	22.8850i	−0.677797	−	1.17398i
$381$	−18.0302	−	11.8767i	−0.923713	−	0.608464i
$382$	−27.5039	+	47.6382i	−1.40722	+	2.43738i
$383$	15.3344	−	26.5600i	0.783552	−	1.35715i	−0.146308	−	0.989239i	$-0.546739\pi$
$383$	15.3344	−	26.5600i	0.783552	−	1.35715i	0.929860	−	0.367913i	$-0.119928\pi$
$384$	−0.111600	+	1.89321i	−0.00569504	+	0.0966126i
$385$	5.53855	+	9.59306i	0.282271	+	0.488908i
$386$	−60.2262			−3.06543
$387$	−8.00229	+	10.7175i	−0.406779	+	0.544802i
$388$	−69.3313			−3.51976
$389$	3.57923	+	6.19941i	0.181474	+	0.314322i	0.942383	−	0.334537i	$-0.108580\pi$
$389$	3.57923	+	6.19941i	0.181474	+	0.314322i	−0.760909	+	0.648859i	$0.775246\pi$
$390$	−83.4506	+	41.8372i	−4.22568	+	2.11851i
$391$	−2.36895	+	4.10314i	−0.119803	+	0.207505i
$392$	−6.71759	+	11.6352i	−0.339290	+	0.587667i
$393$	23.8214	−	11.9426i	1.20163	−	0.602426i
$394$	−16.5980	−	28.7486i	−0.836196	−	1.44833i
$395$	12.2113			0.614418
$396$	−6.60021	−	15.3602i	−0.331673	−	0.771880i
$397$	32.3003			1.62111			0.810553	−	0.585665i	$-0.199166\pi$
$397$	32.3003			1.62111			0.810553	+	0.585665i	$0.199166\pi$
$398$	−25.5241	−	44.2090i	−1.27941	−	2.21600i
$399$	0.519407	−	8.81140i	0.0260029	−	0.441122i
$400$	−25.0866	+	43.4513i	−1.25433	+	2.17256i
$401$	−4.54392	+	7.87030i	−0.226912	+	0.393024i	−0.956891	−	0.290446i	$-0.906196\pi$
$401$	−4.54392	+	7.87030i	−0.226912	+	0.393024i	0.729979	+	0.683470i	$0.239530\pi$
$402$	4.50688	+	2.96875i	0.224783	+	0.148068i
$403$	15.2547	+	26.4218i	0.759888	+	1.31617i
$404$	26.9939			1.34299
$405$	8.20930	+	27.7036i	0.407923	+	1.37660i
$406$	−37.1462			−1.84353
$407$	−1.50580	−	2.60812i	−0.0746396	−	0.129280i
$408$	−50.0769	−	32.9865i	−2.47918	−	1.63307i
$409$	17.0578	−	29.5450i	0.843453	−	1.46090i	−0.0435043	−	0.999053i	$-0.513852\pi$
$409$	17.0578	−	29.5450i	0.843453	−	1.46090i	0.886958	−	0.461851i	$-0.152814\pi$
$410$	18.0516	−	31.2662i	0.891503	−	1.54413i
$411$	0.580169	−	9.84218i	0.0286176	−	0.485479i
$412$	−6.81587	−	11.8054i	−0.335794	−	0.581612i
$413$	−14.8705			−0.731727
$414$	−3.08888	−	7.18854i	−0.151810	−	0.353298i
$415$	−0.293134			−0.0143894
$416$	32.3173	+	55.9752i	1.58448	+	2.74441i
$417$	28.7746	−	14.4259i	1.40910	−	0.706438i
$418$	−2.59413	+	4.49316i	−0.126883	+	0.219768i
$419$	−14.4981	+	25.1114i	−0.708278	+	1.22677i	0.257217	+	0.966354i	$0.417195\pi$
$419$	−14.4981	+	25.1114i	−0.708278	+	1.22677i	−0.965495	+	0.260421i	$0.916139\pi$
$420$	−70.9644	+	35.5774i	−3.46271	+	1.73600i
$421$	2.27354	+	3.93789i	0.110806	+	0.191921i	0.916095	−	0.400960i	$-0.131324\pi$
$421$	2.27354	+	3.93789i	0.110806	+	0.191921i	−0.805290	+	0.592882i	$0.797990\pi$
$422$	−23.4200			−1.14007
$423$	0.578726	−	0.775091i	0.0281386	−	0.0376862i
$424$	85.0638			4.13106
$425$	12.5725	+	21.7762i	0.609857	+	1.05630i
$426$	−2.43035	+	41.2293i	−0.117751	+	1.99757i
$427$	1.28392	−	2.22382i	0.0621335	−	0.107618i
$428$	42.3418	−	73.3381i	2.04667	−	3.54493i
$429$	10.8053	+	7.11764i	0.521686	+	0.343643i
$430$	−18.6655	−	32.3296i	−0.900129	−	1.55907i
$431$	5.64346			0.271836			0.135918	−	0.990720i	$-0.456602\pi$
$431$	5.64346			0.271836			0.135918	+	0.990720i	$0.456602\pi$
$432$	46.1960	−	16.7040i	2.22261	−	0.803671i
$433$	−8.32441			−0.400046			−0.200023	−	0.979791i	$-0.564102\pi$
$433$	−8.32441			−0.400046			−0.200023	+	0.979791i	$0.564102\pi$
$434$	18.3752	+	31.8268i	0.882039	+	1.52774i
$435$	−22.2475	−	14.6547i	−1.06668	−	0.702641i
$436$	−6.35853	+	11.0133i	−0.304518	+	0.527441i
$437$	−0.857068	+	1.48449i	−0.0409991	+	0.0710126i
$438$	−2.16658	+	36.7546i	−0.103523	+	1.75620i
$439$	5.52177	+	9.56399i	0.263540	+	0.456465i	0.967180	−	0.254092i	$-0.0817766\pi$
$439$	5.52177	+	9.56399i	0.263540	+	0.456465i	−0.703640	+	0.710557i	$0.748443\pi$
$440$	27.2261			1.29795
$441$	−5.47766	−	0.648037i	−0.260841	−	0.0308589i
$442$	79.5376			3.78322
$443$	−8.85047	−	15.3295i	−0.420499	−	0.728325i	0.575490	−	0.817809i	$-0.304812\pi$
$443$	−8.85047	−	15.3295i	−0.420499	−	0.728325i	−0.995988	+	0.0894841i	$0.971478\pi$
$444$	19.2935	−	9.67261i	0.915628	−	0.459042i
$445$	−15.0875	+	26.1322i	−0.715214	+	1.23879i
$446$	21.6910	−	37.5699i	1.02710	−	1.77899i
$447$	−2.67977	+	1.34348i	−0.126749	+	0.0635444i
$448$	10.8224	+	18.7449i	0.511308	+	0.885612i
$449$	15.9726			0.753793			0.376896	−	0.926255i	$-0.376991\pi$
$449$	15.9726			0.753793			0.376896	+	0.926255i	$0.376991\pi$
$450$	−41.2365	−	4.87850i	−1.94391	−	0.229975i
$451$	−5.00410			−0.235634
$452$	−37.2488	−	64.5169i	−1.75204	−	3.03462i
$453$	0.820779	−	13.9240i	0.0385636	−	0.654205i
$454$	−9.16375	+	15.8721i	−0.430076	+	0.744914i
$455$	30.7190	−	53.2068i	1.44013	−	2.49437i
$456$	−18.1175	−	11.9342i	−0.848427	−	0.558872i
$457$	−6.09316	−	10.5537i	−0.285026	−	0.493680i	0.687589	−	0.726100i	$-0.258669\pi$
$457$	−6.09316	−	10.5537i	−0.285026	−	0.493680i	−0.972615	+	0.232420i	$0.925336\pi$
$458$	57.2524			2.67523
$459$	4.32603	−	24.2358i	0.201922	−	1.13123i
$460$	15.4161			0.718781
$461$	−7.12207	−	12.3358i	−0.331708	−	0.574535i	0.651139	−	0.758958i	$-0.274291\pi$
$461$	−7.12207	−	12.3358i	−0.331708	−	0.574535i	−0.982847	+	0.184424i	$0.940958\pi$
$462$	13.0157	+	8.57366i	0.605547	+	0.398883i
$463$	−17.4350	+	30.1983i	−0.810273	+	1.40343i	0.102401	+	0.994743i	$0.467348\pi$
$463$	−17.4350	+	30.1983i	−0.810273	+	1.40343i	−0.912673	+	0.408690i	$0.865986\pi$
$464$	−22.6457	+	39.2235i	−1.05130	+	1.82090i
$465$	−1.55096	+	26.3109i	−0.0719238	+	1.22014i
$466$	−17.9950	−	31.1682i	−0.833600	−	1.44384i
$467$	6.73985			0.311883			0.155942	−	0.987766i	$-0.450159\pi$
$467$	6.73985			0.311883			0.155942	+	0.987766i	$0.450159\pi$
$468$	−55.4763	+	74.2998i	−2.56439	+	3.43451i
$469$	−3.55186			−0.164010
$470$	1.34989	+	2.33807i	0.0622657	+	0.107847i
$471$	−0.834037	+	0.418137i	−0.0384304	+	0.0192667i
$472$	−18.2748	+	31.6529i	−0.841167	+	1.45694i
$473$	−2.58714	+	4.48106i	−0.118957	+	0.206039i
$474$	15.3595	−	7.70034i	0.705485	−	0.353688i
$475$	4.54864	+	7.87847i	0.208706	+	0.361489i
$476$	67.6369			3.10013
$477$	13.7874	+	32.0864i	0.631281	+	1.46914i
$478$	−2.47520			−0.113213
$479$	−1.96115	−	3.39680i	−0.0896070	−	0.155204i	0.817738	−	0.575591i	$-0.195228\pi$
$479$	−1.96115	−	3.39680i	−0.0896070	−	0.155204i	−0.907345	+	0.420387i	$0.861894\pi$
$480$	−3.28573	+	55.7402i	−0.149972	+	2.54418i
$481$	−8.35174	+	14.4656i	−0.380806	+	0.659576i
$482$	16.9094	−	29.2879i	0.770201	−	1.33403i
$483$	4.30024	+	2.83263i	0.195668	+	0.128889i
$484$	23.1762	+	40.1424i	1.05347	+	1.82466i
$485$	46.3548			2.10486
$486$	27.7954	+	29.6691i	1.26082	+	1.34582i
$487$	−5.94494			−0.269391			−0.134696	−	0.990887i	$-0.543006\pi$
$487$	−5.94494			−0.269391			−0.134696	+	0.990887i	$0.543006\pi$
$488$	−3.15572	−	5.46587i	−0.142853	−	0.247428i
$489$	4.35614	+	2.86946i	0.196991	+	0.129761i
$490$	7.69741	−	13.3323i	0.347734	−	0.602293i
$491$	−6.81264	+	11.7998i	−0.307450	+	0.532519i	−0.977804	−	0.209522i	$-0.932809\pi$
$491$	−6.81264	+	11.7998i	−0.307450	+	0.532519i	0.670354	+	0.742042i	$0.266142\pi$
$492$	2.11027	−	35.7993i	0.0951382	−	1.61396i
$493$	11.3492	+	19.6574i	0.511143	+	0.885325i
$494$	28.7761			1.29470
$495$	4.41289	+	10.2698i	0.198345	+	0.461594i
$496$	44.8089			2.01198
$497$	−13.5909	−	23.5401i	−0.609636	−	1.05592i
$498$	−0.368706	+	0.184848i	−0.0165221	+	0.00828322i
$499$	−12.1327	+	21.0144i	−0.543133	+	0.940733i	0.455589	+	0.890190i	$0.349429\pi$
$499$	−12.1327	+	21.0144i	−0.543133	+	0.940733i	−0.998722	+	0.0505432i	$0.983905\pi$
$500$	2.36798	−	4.10147i	0.105899	−	0.183423i
$501$	−15.1973	+	7.61904i	−0.678966	+	0.340394i
$502$	−28.0349	−	48.5579i	−1.25126	−	2.16725i
$503$	−31.2131			−1.39172			−0.695861	−	0.718177i	$-0.744977\pi$
$503$	−31.2131			−1.39172			−0.695861	+	0.718177i	$0.744977\pi$
$504$	−38.9917	+	52.2218i	−1.73683	+	2.32614i
$505$	−18.0481			−0.803128
$506$	−1.51337	−	2.62124i	−0.0672776	−	0.116528i
$507$	2.89798	−	49.1623i	0.128704	−	2.18338i
$508$	29.9278	−	51.8364i	1.32783	−	2.29987i
$509$	−4.11166	+	7.12160i	−0.182246	+	0.315659i	−0.942645	−	0.333797i	$-0.891670\pi$
$509$	−4.11166	+	7.12160i	−0.182246	+	0.315659i	0.760399	+	0.649456i	$0.225003\pi$
$510$	57.3811	+	37.7979i	2.54088	+	1.67372i
$511$	−12.1159	−	20.9853i	−0.535975	−	0.928335i
$512$	−43.2331			−1.91065
$513$	1.56512	−	8.76832i	0.0691019	−	0.387131i
$514$	6.78122			0.299107
$515$	4.55708	+	7.89309i	0.200809	+	0.347811i
$516$	−30.9665	−	20.3981i	−1.36322	−	0.897976i
$517$	0.187102	−	0.324070i	0.00822874	−	0.0142526i
$518$	−10.0602	+	17.4248i	−0.442021	+	0.765602i
$519$	−1.54407	+	26.1941i	−0.0677772	+	1.14979i
$520$	−75.5033	−	130.776i	−3.31104	−	5.73489i
$521$	8.60438			0.376965			0.188482	−	0.982077i	$-0.439643\pi$
$521$	8.60438			0.376965			0.188482	+	0.982077i	$0.439643\pi$
$522$	−37.2242	−	4.40382i	−1.62926	−	0.192750i
$523$	−1.51553			−0.0662696			−0.0331348	−	0.999451i	$-0.510549\pi$
$523$	−1.51553			−0.0662696			−0.0331348	+	0.999451i	$0.510549\pi$
$524$	36.9377	+	63.9779i	1.61363	+	2.79489i
$525$	24.4304	−	12.2480i	1.06623	−	0.534545i
$526$	16.9905	−	29.4284i	0.740820	−	1.28314i
$527$	11.2283	−	19.4480i	0.489113	−	0.847168i
$528$	16.9880	−	8.51677i	0.739307	−	0.370645i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−97.4711			−4.23388
$531$	−14.9017	−	1.76295i	−0.646678	−	0.0765055i
$532$	24.4705			1.06093
$533$	13.8773	+	24.0362i	0.601094	+	1.04113i
$534$	−2.49838	+	42.3833i	−0.108115	+	1.83411i
$535$	−28.3096	+	49.0337i	−1.22393	+	2.11991i
$536$	−4.36501	+	7.56042i	−0.188540	+	0.326560i
$537$	11.1809	+	7.36503i	0.482491	+	0.317824i
$538$	31.2372	+	54.1045i	1.34673	+	2.33261i
$539$	−2.13381			−0.0919097
$540$	−75.3312	+	27.2389i	−3.24174	+	1.17218i
$541$	−19.7783			−0.850336			−0.425168	−	0.905115i	$-0.639785\pi$
$541$	−19.7783			−0.850336			−0.425168	+	0.905115i	$0.639785\pi$
$542$	−10.1924	−	17.6537i	−0.437800	−	0.758293i
$543$	−5.40822	−	3.56248i	−0.232089	−	0.152881i
$544$	23.7874	−	41.2010i	1.01988	−	1.76648i
$545$	4.25130	−	7.36347i	0.182106	−	0.315416i
$546$	5.08685	−	86.2951i	0.217697	−	3.69309i
$547$	−2.02048	−	3.49958i	−0.0863897	−	0.149631i	0.819593	−	0.572946i	$-0.194200\pi$
$547$	−2.02048	−	3.49958i	−0.0863897	−	0.149631i	−0.905983	+	0.423315i	$0.860866\pi$
$548$	27.3331			1.16761
$549$	1.55026	−	2.07628i	0.0661636	−	0.0886134i
$550$	−16.0636			−0.684953
$551$	4.10606	+	7.11190i	0.174924	+	0.302977i
$552$	11.3142	−	5.67227i	0.481564	−	0.241428i
$553$	−5.65398	+	9.79298i	−0.240432	+	0.416440i
$554$	−30.7016	+	53.1768i	−1.30439	+	2.25927i
$555$	−12.8996	+	6.46709i	−0.547557	+	0.274513i
$556$	44.6182	+	77.2809i	1.89223	+	3.27744i
$557$	−9.69006			−0.410581			−0.205290	−	0.978701i	$-0.565814\pi$
$557$	−9.69006			−0.410581			−0.205290	+	0.978701i	$0.565814\pi$
$558$	14.6406	+	34.0721i	0.619787	+	1.44239i
$559$	28.6986			1.21382
$560$	−45.1168	−	78.1446i	−1.90653	−	3.30221i
$561$	0.560429	−	9.50730i	0.0236613	−	0.401399i
$562$	12.8884	−	22.3233i	0.543662	−	0.941651i
$563$	−19.7674	+	34.2381i	−0.833096	+	1.44297i	0.0624744	+	0.998047i	$0.480101\pi$
$563$	−19.7674	+	34.2381i	−0.833096	+	1.44297i	−0.895571	+	0.444919i	$0.853233\pi$
$564$	2.23950	+	1.47519i	0.0942998	+	0.0621167i
$565$	24.9045	+	43.1359i	1.04774	+	1.81474i
$566$	1.04443			0.0439007
$567$	−26.0182	−	6.24357i	−1.09266	−	0.262205i
$568$	−66.8094			−2.80326
$569$	−4.25150	−	7.36381i	−0.178232	−	0.308707i	0.763043	−	0.646348i	$-0.223704\pi$
$569$	−4.25150	−	7.36381i	−0.178232	−	0.308707i	−0.941275	+	0.337641i	$0.890371\pi$
$570$	20.7601	+	13.6750i	0.869543	+	0.572782i
$571$	7.16082	−	12.4029i	0.299671	−	0.519046i	−0.676390	−	0.736544i	$-0.736456\pi$
$571$	7.16082	−	12.4029i	0.299671	−	0.519046i	0.976061	+	0.217498i	$0.0697897\pi$
$572$	−17.9355	+	31.0652i	−0.749920	+	1.29890i
$573$	2.14972	−	36.4686i	0.0898060	−	1.52350i
$574$	16.7162	+	28.9532i	0.697719	+	1.20848i
$575$	−5.30721			−0.221326
$576$	8.62280	+	20.0673i	0.359284	+	0.836136i
$577$	16.9073			0.703859			0.351929	−	0.936027i	$-0.385526\pi$
$577$	16.9073			0.703859			0.351929	+	0.936027i	$0.385526\pi$
$578$	−7.10390	−	12.3043i	−0.295483	−	0.511792i
$579$	35.7558	−	17.9258i	1.48596	−	0.744972i
$580$	36.9280	−	63.9611i	1.53335	−	2.65584i
$581$	0.135724	−	0.235082i	0.00563080	−	0.00975283i
$582$	58.3054	−	29.2309i	2.41684	−	1.21166i
$583$	6.75502	+	11.7000i	0.279764	+	0.484566i
$584$	−59.5585			−2.46455
$585$	37.0914	−	49.6767i	1.53354	−	2.05388i
$586$	15.9979			0.660865
$587$	5.24011	+	9.07614i	0.216283	+	0.374612i	0.953669	−	0.300859i	$-0.0972734\pi$
$587$	5.24011	+	9.07614i	0.216283	+	0.374612i	−0.737386	+	0.675472i	$0.763940\pi$
$588$	0.899845	−	15.2653i	0.0371090	−	0.629529i
$589$	4.06232	−	7.03614i	0.167385	−	0.289919i
$590$	20.9404	−	36.2698i	0.862102	−	1.49321i
$591$	18.4109	+	12.1275i	0.757322	+	0.498860i
$592$	12.2662	+	21.2456i	0.504136	+	0.873189i
$593$	−14.0368			−0.576423			−0.288212	−	0.957567i	$-0.593061\pi$
$593$	−14.0368			−0.576423			−0.288212	+	0.957567i	$0.593061\pi$
$594$	12.0266	+	10.1347i	0.493458	+	0.415833i
$595$	−45.2219			−1.85392
$596$	−4.15528	−	7.19716i	−0.170207	−	0.294807i
$597$	28.3118	+	18.6494i	1.15873	+	0.763271i
$598$	−8.39376	+	14.5384i	−0.343246	+	0.594520i
$599$	11.7587	−	20.3667i	0.480449	−	0.832162i	−0.519299	−	0.854593i	$-0.673807\pi$
$599$	11.7587	−	20.3667i	0.480449	−	0.832162i	0.999748	+	0.0224300i	$0.00714030\pi$
$600$	3.95265	−	67.0540i	0.161366	−	2.73747i
$601$	5.83597	+	10.1082i	0.238054	+	0.412322i	0.960156	−	0.279465i	$-0.0901570\pi$
$601$	5.83597	+	10.1082i	0.238054	+	0.412322i	−0.722102	+	0.691787i	$0.756824\pi$
$602$	34.5693			1.40894
$603$	−3.55932	−	0.421087i	−0.144947	−	0.0171480i
$604$	38.6688			1.57341
$605$	−15.4956	−	26.8392i	−0.629986	−	1.09117i
$606$	−22.7010	+	11.3809i	−0.922164	+	0.462319i
$607$	−2.74470	+	4.75396i	−0.111404	+	0.192957i	−0.916336	−	0.400409i	$-0.868868\pi$
$607$	−2.74470	+	4.75396i	−0.111404	+	0.192957i	0.804933	+	0.593366i	$0.202201\pi$
$608$	8.60609	−	14.9062i	0.349023	−	0.604526i
$609$	22.0533	−	11.0562i	0.893646	−	0.448021i
$610$	3.61602	+	6.26312i	0.146408	+	0.253586i
$611$	−2.07548			−0.0839650
$612$	67.7789	+	8.01861i	2.73980	+	0.324133i
$613$	35.5993			1.43784			0.718920	−	0.695092i	$-0.244637\pi$
$613$	35.5993			1.43784			0.718920	+	0.695092i	$0.244637\pi$
$614$	−18.7220	−	32.4274i	−0.755558	−	1.30866i
$615$	−1.41092	+	23.9354i	−0.0568939	+	0.965167i
$616$	−12.6060	+	21.8342i	−0.507910	+	0.879727i
$617$	17.4370	−	30.2018i	0.701989	−	1.21588i	−0.265778	−	0.964034i	$-0.585629\pi$
$617$	17.4370	−	30.2018i	0.701989	−	1.21588i	0.967767	−	0.251846i	$-0.0810378\pi$
$618$	10.7092	+	7.05434i	0.430789	+	0.283767i
$619$	−22.1736	−	38.4058i	−0.891232	−	1.54366i	−0.838399	−	0.545056i	$-0.816508\pi$
$619$	−22.1736	−	38.4058i	−0.891232	−	1.54366i	−0.0528331	−	0.998603i	$-0.516825\pi$
$620$	−73.0692			−2.93453
$621$	3.97345	+	3.34839i	0.159449	+	0.134366i
$622$	−38.7409			−1.55337
$623$	−13.9713	−	24.1991i	−0.559749	−	0.969515i
$624$	−88.0197	−	57.9799i	−3.52361	−	2.32106i
$625$	11.6848	−	20.2387i	0.467392	−	0.809546i
$626$	44.1557	−	76.4800i	1.76482	−	3.05675i
$627$	0.202759	−	3.43967i	0.00809740	−	0.137367i
$628$	−1.29327	−	2.24000i	−0.0516070	−	0.0893859i
$629$	12.2947			0.490223
$630$	44.6790	−	59.8388i	1.78005	−	2.38404i
$631$	−20.3008			−0.808164			−0.404082	−	0.914723i	$-0.632409\pi$
$631$	−20.3008			−0.808164			−0.404082	+	0.914723i	$0.632409\pi$
$632$	13.8968	+	24.0699i	0.552783	+	0.957449i
$633$	13.9042	−	6.97075i	0.552643	−	0.277062i
$634$	16.0221	−	27.7511i	0.636318	−	1.10214i
$635$	−20.0097	+	34.6577i	−0.794059	+	1.37535i
$636$	−86.5508	+	43.3914i	−3.43196	+	1.72058i
$637$	5.91747	+	10.2494i	0.234459	+	0.406094i
$638$	−14.5006			−0.574084
$639$	−10.8287	−	25.2008i	−0.428376	−	0.996929i
$640$	3.51530			0.138954
$641$	2.48124	+	4.29763i	0.0980031	+	0.169746i	0.910858	−	0.412720i	$-0.135421\pi$
$641$	2.48124	+	4.29763i	0.0980031	+	0.169746i	−0.812855	+	0.582466i	$0.802088\pi$
$642$	−4.68788	+	79.5268i	−0.185016	+	3.13867i
$643$	8.73157	−	15.1235i	0.344340	−	0.596414i	−0.640894	−	0.767629i	$-0.721436\pi$
$643$	8.73157	−	15.1235i	0.344340	−	0.596414i	0.985234	+	0.171216i	$0.0547695\pi$
$644$	−7.13785	+	12.3631i	−0.281271	+	0.487175i
$645$	20.7041	+	13.6381i	0.815224	+	0.537001i
$646$	−10.5904	−	18.3432i	−0.416675	−	0.721702i
$647$	23.7292			0.932891			0.466446	−	0.884550i	$-0.345534\pi$
$647$	23.7292			0.932891			0.466446	+	0.884550i	$0.345534\pi$
$648$	−45.2646	+	47.7088i	−1.77816	+	1.87418i
$649$	−5.80491			−0.227863
$650$	44.5474	+	77.1584i	1.74729	+	3.02640i
$651$	−20.3822	−	13.4261i	−0.798841	−	0.526209i
$652$	−7.23064	+	12.5238i	−0.283174	+	0.490471i
$653$	10.3786	−	17.9763i	0.406147	−	0.703468i	−0.588307	−	0.808638i	$-0.700205\pi$
$653$	10.3786	−	17.9763i	0.406147	−	0.703468i	0.994454	+	0.105170i	$0.0335387\pi$
$654$	0.703986	−	11.9427i	0.0275280	−	0.466995i
$655$	−24.6965	−	42.7755i	−0.964971	−	1.67138i
$656$	40.7631			1.59153
$657$	−9.65342	−	22.4657i	−0.376616	−	0.876472i
$658$	−2.50005			−0.0974622
$659$	21.4224	+	37.1046i	0.834497	+	1.44539i	0.894439	+	0.447190i	$0.147575\pi$
$659$	21.4224	+	37.1046i	0.834497	+	1.44539i	−0.0599421	+	0.998202i	$0.519092\pi$
$660$	−27.7021	+	13.8882i	−1.07830	+	0.540596i
$661$	14.0819	−	24.3906i	0.547724	−	0.948685i	−0.450706	−	0.892672i	$-0.648828\pi$
$661$	14.0819	−	24.3906i	0.547724	−	0.948685i	0.998430	−	0.0560130i	$-0.0178388\pi$
$662$	−20.2671	+	35.1037i	−0.787704	+	1.36434i
$663$	−47.2207	+	23.6737i	−1.83390	+	0.919409i
$664$	−0.333593	−	0.577800i	−0.0129459	−	0.0224230i
$665$	−16.3609			−0.634450
$666$	−12.1471	+	16.2687i	−0.470691	+	0.630400i
$667$	−4.79082			−0.185501
$668$	−23.5651	−	40.8160i	−0.911762	−	1.57922i
$669$	−1.69538	+	28.7610i	−0.0655473	+	1.11197i
$670$	5.00169	−	8.66318i	0.193232	−	0.334688i
$671$	0.501200	−	0.868104i	0.0193486	−	0.0335128i
$672$	−43.1800	−	28.4434i	−1.66571	−	1.09723i
$673$	−19.6398	−	34.0171i	−0.757058	−	1.31126i	−0.944345	−	0.328957i	$-0.893303\pi$
$673$	−19.6398	−	34.0171i	−0.757058	−	1.31126i	0.187287	−	0.982305i	$-0.440030\pi$
$674$	−82.3877			−3.17346
$675$	25.9338	−	9.37736i	0.998191	−	0.360935i
$676$	136.531			5.25118
$677$	22.3874	+	38.7761i	0.860418	+	1.49029i	0.871526	+	0.490350i	$0.163131\pi$
$677$	22.3874	+	38.7761i	0.860418	+	1.49029i	−0.0111071	+	0.999938i	$0.503536\pi$
$678$	58.5262	+	38.5521i	2.24768	+	1.48058i
$679$	−21.4628	+	37.1747i	−0.823667	+	1.42663i
$680$	−55.5748	+	96.2584i	−2.13120	+	3.69134i
$681$	0.716245	−	12.1506i	0.0274466	−	0.465613i
$682$	7.17306	+	12.4241i	0.274671	+	0.475743i
$683$	−26.0050			−0.995054			−0.497527	−	0.867449i	$-0.665758\pi$
$683$	−26.0050			−0.995054			−0.497527	+	0.867449i	$0.665758\pi$
$684$	24.5219	+	2.90107i	0.937617	+	0.110925i
$685$	−18.2749			−0.698247
$686$	−20.0097	−	34.6578i	−0.763974	−	1.32324i
$687$	−33.9902	+	17.0407i	−1.29681	+	0.650142i
$688$	21.0747	−	36.5025i	0.803466	−	1.39164i
$689$	37.4660	−	64.8930i	1.42734	−	2.47223i
$690$	−12.9645	+	6.49963i	−0.493550	+	0.247437i
$691$	9.91613	+	17.1752i	0.377227	+	0.653377i	0.990658	−	0.136372i	$-0.0435442\pi$
$691$	9.91613	+	17.1752i	0.377227	+	0.653377i	−0.613430	+	0.789749i	$0.710211\pi$
$692$	−72.7448			−2.76534
$693$	−10.2792	−	1.21608i	−0.390474	−	0.0461952i
$694$	−58.6912			−2.22789
$695$	−29.8316	−	51.6699i	−1.13158	−	1.95995i
$696$	3.56806	−	60.5297i	0.135247	−	2.29437i
$697$	10.2145	−	17.6921i	0.386903	−	0.670135i
$698$	−31.1686	+	53.9857i	−1.17975	+	2.04339i
$699$	19.9604	+	13.1482i	0.754971	+	0.497311i
$700$	37.8821	+	65.6137i	1.43181	+	2.47996i
$701$	13.9631			0.527381			0.263690	−	0.964607i	$-0.415060\pi$
$701$	13.9631			0.527381			0.263690	+	0.964607i	$0.415060\pi$
$702$	15.3281	−	85.8732i	0.578524	−	3.24107i
$703$	4.44814			0.167765
$704$	4.22468	+	7.31735i	0.159223	+	0.275783i
$705$	−1.49732	−	0.986310i	−0.0563924	−	0.0371466i
$706$	3.11059	−	5.38770i	0.117069	−	0.202769i
$707$	8.35645	−	14.4738i	0.314277	−	0.544343i
$708$	2.44798	−	41.5283i	0.0920007	−	1.56073i
$709$	−1.66024	−	2.87562i	−0.0623516	−	0.107996i	0.833165	−	0.553025i	$-0.186527\pi$
$709$	−1.66024	−	2.87562i	−0.0623516	−	0.107996i	−0.895516	+	0.445029i	$0.853193\pi$
$710$	76.5542			2.87303
$711$	−6.82684	+	9.14324i	−0.256027	+	0.342898i
$712$	−68.6795			−2.57387
$713$	2.36989	+	4.10477i	0.0887531	+	0.153725i
$714$	−56.8805	+	28.5165i	−2.12870	+	1.06720i
$715$	11.9916	−	20.7701i	0.448462	−	0.776758i
$716$	−18.5589	+	32.1449i	−0.693577	+	1.20131i
$717$	1.46951	−	0.736723i	0.0548797	−	0.0275134i
$718$	0.648865	+	1.12387i	0.0242154	+	0.0419424i
$719$	45.2541			1.68769			0.843847	−	0.536584i	$-0.180286\pi$
$719$	45.2541			1.68769			0.843847	+	0.536584i	$0.180286\pi$
$720$	−35.9472	−	83.6574i	−1.33967	−	3.11773i
$721$	−8.43992			−0.314319
$722$	20.9447	+	36.2773i	0.779482	+	1.35010i
$723$	−1.32165	+	22.4209i	−0.0491526	+	0.833841i
$724$	8.97696	−	15.5486i	0.333626	−	0.577858i
$725$	−12.7129	+	22.0194i	−0.472146	+	0.817782i
$726$	−36.4150	−	23.9871i	−1.35149	−	0.890246i
$727$	4.38613	+	7.59701i	0.162673	+	0.281757i	0.935826	−	0.352461i	$-0.114655\pi$
$727$	4.38613	+	7.59701i	0.162673	+	0.281757i	−0.773154	+	0.634219i	$0.781322\pi$
$728$	139.836			5.18265
$729$	−25.3326	−	9.34124i	−0.938245	−	0.345972i
$730$	68.2457			2.52589
$731$	−10.5619	−	18.2938i	−0.390646	−	0.676619i
$732$	5.99906	+	3.95167i	0.221731	+	0.146058i
$733$	−11.9182	+	20.6430i	−0.440210	+	0.762467i	−0.997705	−	0.0677140i	$-0.978429\pi$
$733$	−11.9182	+	20.6430i	−0.440210	+	0.762467i	0.557494	+	0.830181i	$0.311763\pi$
$734$	26.5994	−	46.0715i	0.981801	−	1.70053i
$735$	−0.601635	+	10.2063i	−0.0221916	+	0.376466i
$736$	5.02066	+	8.69603i	0.185064	+	0.320540i
$737$	−1.38652			−0.0510733
$738$	13.3187	+	30.9958i	0.490269	+	1.14097i
$739$	15.3419			0.564362			0.282181	−	0.959361i	$-0.408942\pi$
$739$	15.3419			0.564362			0.282181	+	0.959361i	$0.408942\pi$
$740$	−20.0022	−	34.6449i	−0.735297	−	1.27357i
$741$	−17.0841	+	8.56495i	−0.627600	+	0.314641i
$742$	45.1302	−	78.1679i	1.65678	−	2.86963i
$743$	−5.22365	+	9.04763i	−0.191637	+	0.331925i	−0.945793	−	0.324770i	$-0.894713\pi$
$743$	−5.22365	+	9.04763i	−0.191637	+	0.331925i	0.754156	+	0.656696i	$0.228046\pi$
$744$	−53.6268	+	26.8853i	−1.96606	+	0.985664i
$745$	2.77821	+	4.81201i	0.101786	+	0.176298i
$746$	−93.6916			−3.43029
$747$	0.163879	−	0.219485i	0.00599603	−	0.00803052i
$748$	26.4031			0.965393
$749$	−26.2154	−	45.4064i	−0.957889	−	1.65911i
$750$	−0.262172	+	4.44757i	−0.00957316	+	0.162402i
$751$	−13.9395	+	24.1439i	−0.508658	+	0.881022i	0.491292	+	0.870995i	$0.336525\pi$
$751$	−13.9395	+	24.1439i	−0.508658	+	0.881022i	−0.999950	+	0.0100265i	$0.996808\pi$
$752$	−1.52412	+	2.63986i	−0.0555791	+	0.0962658i
$753$	31.0969	+	20.4840i	1.13323	+	0.746479i
$754$	40.2130	+	69.6509i	1.46447	+	2.53654i
$755$	−25.8539			−0.940920
$756$	13.0347	−	73.0245i	0.474067	−	2.65588i
$757$	−9.30099			−0.338050			−0.169025	−	0.985612i	$-0.554062\pi$
$757$	−9.30099			−0.338050			−0.169025	+	0.985612i	$0.554062\pi$
$758$	48.5680	+	84.1222i	1.76407	+	3.05546i
$759$	1.67866	+	1.10576i	0.0609317	+	0.0401366i
$760$	−20.1065	+	34.8256i	−0.729341	+	1.26326i
$761$	−2.97267	+	5.14882i	−0.107759	+	0.186645i	−0.914862	−	0.403766i	$-0.867701\pi$
$761$	−2.97267	+	5.14882i	−0.107759	+	0.186645i	0.807103	+	0.590411i	$0.201034\pi$
$762$	−3.31346	+	56.2107i	−0.120034	+	2.03630i
$763$	3.93680	+	6.81874i	0.142522	+	0.246855i
$764$	101.279			3.66413
$765$	−45.3168	−	5.36123i	−1.63843	−	0.193836i
$766$	−79.9852			−2.88998
$767$	16.0982	+	27.8828i	0.581271	+	1.00679i
$768$	26.9672	−	13.5198i	0.973095	−	0.487852i
$769$	−14.2882	+	24.7478i	−0.515244	+	0.892429i	0.484599	+	0.874736i	$0.338965\pi$
$769$	−14.2882	+	24.7478i	−0.515244	+	0.892429i	−0.999843	+	0.0176928i	$0.994368\pi$
$770$	14.4447	−	25.0190i	0.520551	−	0.901621i
$771$	−4.02595	+	2.01837i	−0.144991	+	0.0726899i
$772$	55.4432	+	96.0305i	1.99545	+	3.45621i
$773$	28.3191			1.01857			0.509283	−	0.860599i	$-0.329911\pi$
$773$	28.3191			1.01857			0.509283	+	0.860599i	$0.329911\pi$
$774$	34.6419	+	4.09833i	1.24518	+	0.147311i
$775$	25.1550			0.903594
$776$	52.7528	+	91.3706i	1.89372	+	3.28001i
$777$	0.786313	−	13.3393i	0.0282088	−	0.478544i
$778$	9.33473	−	16.1682i	0.334666	−	0.579659i
$779$	3.69553	−	6.40085i	0.132406	−	0.229334i
$780$	143.532	+	94.5471i	5.13929	+	3.38533i
$781$	−5.30542	−	9.18926i	−0.189843	−	0.328818i
$782$	12.3566			0.441871
$783$	23.4104	−	8.46494i	0.836619	−	0.302512i
$784$	17.3819			0.620783
$785$	0.864676	+	1.49766i	0.0308616	+	0.0534539i
$786$	−58.0373	−	38.2301i	−2.07012	−	1.36362i
$787$	−26.1051	+	45.2154i	−0.930547	+	1.61175i	−0.148158	+	0.988964i	$0.547335\pi$
$787$	−26.1051	+	45.2154i	−0.930547	+	1.61175i	−0.782388	+	0.622791i	$0.785999\pi$
$788$	−30.5597	+	52.9310i	−1.08864	+	1.88559i
$789$	−1.32799	+	22.5284i	−0.0472776	+	0.802032i
$790$	−15.9237	−	27.5807i	−0.566541	−	0.981278i
$791$	−46.1243			−1.63999
$792$	−15.2210	+	20.3856i	−0.540855	+	0.724370i
$793$	−5.55970			−0.197431
$794$	−42.1201	−	72.9541i	−1.49479	−	2.58905i
$795$	57.8677	−	29.0114i	2.05236	−	1.02893i
$796$	−46.9940	+	81.3961i	−1.66566	+	2.88501i
$797$	10.0566	−	17.4185i	0.356223	−	0.616996i	−0.631104	−	0.775699i	$-0.717398\pi$
$797$	10.0566	−	17.4185i	0.356223	−	0.616996i	0.987326	+	0.158702i	$0.0507310\pi$
$798$	−20.5789	+	10.3171i	−0.728486	+	0.365220i
$799$	0.763837	+	1.32300i	0.0270226	+	0.0468045i
$800$	53.2914			1.88413
$801$	−11.1318	−	25.9062i	−0.393322	−	0.915351i
$802$	23.7013			0.836923
$803$	−4.72962	−	8.19194i	−0.166905	−	0.289087i
$804$	0.584709	−	9.91919i	0.0206211	−	0.349823i
$805$	4.77236	−	8.26596i	0.168203	−	0.291337i
$806$	39.7846	−	68.9089i	1.40135	−	2.42721i
$807$	−34.6490	−	22.8238i	−1.21970	−	0.803437i
$808$	−20.5391	−	35.5748i	−0.722563	−	1.25152i
$809$	−0.925066			−0.0325236			−0.0162618	−	0.999868i	$-0.505177\pi$
$809$	−0.925066			−0.0325236			−0.0162618	+	0.999868i	$0.505177\pi$
$810$	51.8669	−	54.6676i	1.82242	−	1.92082i
$811$	−37.0990			−1.30272			−0.651360	−	0.758768i	$-0.725801\pi$
$811$	−37.0990			−1.30272			−0.651360	+	0.758768i	$0.725801\pi$
$812$	34.1961	+	59.2295i	1.20005	+	2.07855i
$813$	11.3056	+	7.44718i	0.396505	+	0.261184i
$814$	−3.92716	+	6.80204i	−0.137647	+	0.238412i
$815$	4.83439	−	8.37341i	0.169341	−	0.293308i
$816$	−4.56522	+	77.4460i	−0.159815	+	2.71115i
$817$	−3.82122	−	6.61854i	−0.133687	−	0.231553i
$818$	−88.9744			−3.11092
$819$	22.6650	+	52.7466i	0.791978	+	1.84312i
$820$	−66.4718			−2.32130
$821$	24.6875	+	42.7601i	0.861601	+	1.49234i	0.870383	+	0.492375i	$0.163871\pi$
$821$	24.6875	+	42.7601i	0.861601	+	1.49234i	−0.00878180	+	0.999961i	$0.502795\pi$
$822$	−22.9863	+	11.5240i	−0.801739	+	0.401944i
$823$	10.3990	−	18.0115i	0.362485	−	0.627842i	−0.625884	−	0.779916i	$-0.715262\pi$
$823$	10.3990	−	18.0115i	0.362485	−	0.627842i	0.988369	+	0.152074i	$0.0485951\pi$
$824$	−10.3721	+	17.9650i	−0.361330	+	0.625842i
$825$	9.53679	−	4.78118i	0.332028	−	0.166459i
$826$	19.3913	+	33.5867i	0.674709	+	1.16863i
$827$	1.88619			0.0655893			0.0327947	−	0.999462i	$-0.489559\pi$
$827$	1.88619			0.0655893			0.0327947	+	0.999462i	$0.489559\pi$
$828$	−8.61853	+	11.5429i	−0.299515	+	0.401142i
$829$	0.759943			0.0263939			0.0131970	−	0.999913i	$-0.495799\pi$
$829$	0.759943			0.0263939			0.0131970	+	0.999913i	$0.495799\pi$
$830$	0.382251	+	0.662078i	0.0132681	+	0.0229811i
$831$	2.39966	−	40.7086i	0.0832433	−	1.41217i
$832$	23.4317	−	40.5849i	0.812348	−	1.40703i
$833$	4.35560	−	7.54412i	0.150913	−	0.261388i
$834$	−70.1050	−	46.1793i	−2.42754	−	1.59906i
$835$	15.7556	+	27.2895i	0.545245	+	0.944392i
$836$	9.55244			0.330378
$837$	−18.8333	−	15.8706i	−0.650973	−	0.548570i
$838$	75.6229			2.61235
$839$	−2.80890	−	4.86515i	−0.0969739	−	0.167964i	0.813457	−	0.581625i	$-0.197583\pi$
$839$	−2.80890	−	4.86515i	−0.0969739	−	0.167964i	−0.910431	+	0.413662i	$0.864250\pi$
$840$	100.882	+	66.4527i	3.48077	+	2.29284i
$841$	3.02403	−	5.23778i	0.104277	−	0.180613i
$842$	5.92947	−	10.2701i	0.204343	−	0.353932i
$843$	−1.00736	+	17.0892i	−0.0346954	+	0.588584i
$844$	21.5600	+	37.3430i	0.742126	+	1.28540i
$845$	−91.2842			−3.14027
$846$	−2.50530	−	0.296391i	−0.0861341	−	0.0101901i
$847$	28.6986			0.986094
$848$	−55.0261	−	95.3080i	−1.88960	−	3.27289i
$849$	−0.620069	+	0.310866i	−0.0212807	+	0.0106689i
$850$	32.7895	−	56.7930i	1.12467	−	1.94799i
$851$	−1.29749	+	2.24731i	−0.0444773	+	0.0770369i
$852$	67.9773	−	34.0798i	2.32886	−	1.16756i
$853$	−2.43391	−	4.21566i	−0.0833356	−	0.144341i	0.821345	−	0.570431i	$-0.193224\pi$
$853$	−2.43391	−	4.21566i	−0.0833356	−	0.144341i	−0.904681	+	0.426090i	$0.859891\pi$
$854$	−6.69703			−0.229167
$855$	−16.3953	−	1.93965i	−0.560707	−	0.0663347i
$856$	−128.868			−4.40462
$857$	9.76372	+	16.9113i	0.333522	+	0.577678i	0.983200	−	0.182532i	$-0.0584294\pi$
$857$	9.76372	+	16.9113i	0.333522	+	0.577678i	−0.649677	+	0.760210i	$0.725096\pi$
$858$	1.98573	−	33.6866i	0.0677918	−	1.15004i
$859$	−6.04749	+	10.4746i	−0.206338	+	0.357387i	−0.950558	−	0.310547i	$-0.899488\pi$
$859$	−6.04749	+	10.4746i	−0.206338	+	0.357387i	0.744220	+	0.667934i	$0.232821\pi$
$860$	−34.3662	+	59.5241i	−1.17188	+	2.02975i
$861$	−18.5419	−	12.2138i	−0.631906	−	0.416247i
$862$	−7.35915	−	12.7464i	−0.250654	−	0.434145i
$863$	−11.6847			−0.397752			−0.198876	−	0.980025i	$-0.563729\pi$
$863$	−11.6847			−0.397752			−0.198876	+	0.980025i	$0.563729\pi$
$864$	−39.8986	−	33.6223i	−1.35738	−	1.14385i
$865$	48.6370			1.65371
$866$	10.8551	+	18.8017i	0.368873	+	0.638907i
$867$	7.87979	+	5.19054i	0.267612	+	0.176280i
$868$	33.8319	−	58.5985i	1.14833	−	1.98896i
$869$	−2.20712	+	3.82284i	−0.0748714	+	0.129681i
$870$	−4.08849	+	69.3585i	−0.138613	+	2.35147i
$871$	3.84510	+	6.65991i	0.130286	+	0.225662i
$872$	19.3523			0.655352
$873$	−25.9151	+	34.7082i	−0.877092	+	1.17470i
$874$	4.47052			0.151217
$875$	−1.46611	−	2.53937i	−0.0495634	−	0.0858464i
$876$	60.5997	−	30.3811i	2.04747	−	1.02648i
$877$	4.45789	−	7.72128i	0.150532	−	0.260729i	−0.780891	−	0.624667i	$-0.785235\pi$
$877$	4.45789	−	7.72128i	0.150532	−	0.260729i	0.931423	+	0.363938i	$0.118568\pi$
$878$	14.4009	−	24.9432i	0.486008	−	0.841791i
$879$	−9.49778	+	4.76162i	−0.320352	+	0.160606i
$880$	−17.6120	−	30.5050i	−0.593702	−	1.02832i
$881$	0.306690			0.0103327			0.00516633	−	0.999987i	$-0.498355\pi$
$881$	0.306690			0.0103327			0.00516633	+	0.999987i	$0.498355\pi$
$882$	5.67928	+	13.2170i	0.191231	+	0.445039i
$883$	51.2396			1.72435			0.862175	−	0.506610i	$-0.169102\pi$
$883$	51.2396			1.72435			0.862175	+	0.506610i	$0.169102\pi$
$884$	−73.2210	−	126.822i	−2.46269	−	4.26550i
$885$	−1.63671	+	27.7658i	−0.0550176	+	0.933337i
$886$	−23.0823	+	39.9797i	−0.775464	+	1.34314i
$887$	−0.955363	+	1.65474i	−0.0320780	+	0.0555607i	−0.881619	−	0.471962i	$-0.843546\pi$
$887$	−0.955363	+	1.65474i	−0.0320780	+	0.0555607i	0.849541	+	0.527523i	$0.176879\pi$
$888$	−27.4274	−	18.0669i	−0.920403	−	0.606284i
$889$	−18.5294	−	32.0939i	−0.621456	−	1.07639i
$890$	78.6970			2.63793
$891$	−10.1566	−	2.43728i	−0.340259	−	0.0816518i
$892$	−79.8734			−2.67436
$893$	0.276350	+	0.478653i	0.00924771	+	0.0160175i
$894$	6.52887	+	4.30067i	0.218358	+	0.143836i
$895$	12.4084	−	21.4920i	0.414768	−	0.718399i
$896$	−1.62762	+	2.81913i	−0.0543751	+	0.0941805i
$897$	0.656062	−	11.1296i	0.0219053	−	0.371608i
$898$	−20.8285	−	36.0760i	−0.695055	−	1.20387i
$899$	22.7074			0.757335
$900$	30.1828	+	70.2425i	1.00609	+	2.34142i
$901$	−55.1543			−1.83746
$902$	6.52541	+	11.3023i	0.217272	+	0.376327i
$903$	−20.5235	+	10.2893i	−0.682979	+	0.342405i
$904$	−56.6838	+	98.1792i	−1.88527	+	3.26539i
$905$	−6.00198	+	10.3957i	−0.199513	+	0.345566i
$906$	−32.5193	+	16.3032i	−1.08038	+	0.541639i
$907$	−10.1643	−	17.6050i	−0.337499	−	0.584565i	0.646463	−	0.762945i	$-0.276248\pi$
$907$	−10.1643	−	17.6050i	−0.337499	−	0.584565i	−0.983962	+	0.178381i	$0.942914\pi$
$908$	33.7440			1.11983
$909$	10.0899	−	13.5135i	0.334662	−	0.448215i
$910$	−160.232			−5.31164
$911$	13.1453	+	22.7683i	0.435523	+	0.754348i	0.997338	−	0.0729146i	$-0.0232301\pi$
$911$	13.1453	+	22.7683i	0.435523	+	0.754348i	−0.561815	+	0.827263i	$0.689897\pi$
$912$	−1.65166	+	28.0194i	−0.0546920	+	0.927814i
$913$	0.0529821	−	0.0917678i	0.00175345	−	0.00303707i
$914$	−15.8911	+	27.5243i	−0.525632	+	0.910421i
$915$	−4.01096	−	2.64208i	−0.132598	−	0.0873445i
$916$	−52.7055	−	91.2887i	−1.74144	−	3.01626i
$917$	45.7390			1.51043
$918$	−60.3806	+	21.8330i	−1.99286	+	0.720596i
$919$	−21.2514			−0.701019			−0.350509	−	0.936559i	$-0.613992\pi$
$919$	−21.2514			−0.701019			−0.350509	+	0.936559i	$0.613992\pi$
$920$	−11.7298	−	20.3167i	−0.386721	−	0.669821i
$921$	20.7668	+	13.6794i	0.684290	+	0.450752i
$922$	−18.5746	+	32.1721i	−0.611720	+	1.05953i
$923$	−29.4259	+	50.9672i	−0.968567	+	1.67761i
$924$	1.68862	−	28.6463i	0.0555515	−	0.942394i
$925$	6.88603	+	11.9270i	0.226411	+	0.392156i
$926$	90.9419			2.98854
$927$	−8.45764	−	1.00058i	−0.277785	−	0.0328635i
$928$	48.1061			1.57916
$929$	−13.6857	−	23.7044i	−0.449015	−	0.777716i	0.549308	−	0.835620i	$-0.314892\pi$
$929$	−13.6857	−	23.7044i	−0.449015	−	0.777716i	−0.998322	+	0.0579042i	$0.981558\pi$
$930$	61.4488	−	30.8068i	2.01499	−	1.01020i
$931$	1.57582	−	2.72941i	0.0516455	−	0.0894527i
$932$	−33.1317	+	57.3858i	−1.08526	+	1.87973i
$933$	23.0001	−	11.5309i	0.752989	−	0.377504i
$934$	−8.78887	−	15.2228i	−0.287580	−	0.498104i
$935$	−17.6531			−0.577317
$936$	140.129	+	16.5780i	4.58027	+	0.541870i
$937$	−51.2264			−1.67349			−0.836746	−	0.547591i	$-0.815545\pi$
$937$	−51.2264			−1.67349			−0.836746	+	0.547591i	$0.815545\pi$
$938$	4.63168	+	8.02230i	0.151230	+	0.261937i
$939$	−3.45124	+	58.5480i	−0.112627	+	1.91064i
$940$	2.48537	−	4.30478i	0.0810637	−	0.140406i
$941$	−23.5119	+	40.7238i	−0.766466	+	1.32756i	0.173002	+	0.984921i	$0.444653\pi$
$941$	−23.5119	+	40.7238i	−0.766466	+	1.32756i	−0.939468	+	0.342636i	$0.888680\pi$
$942$	2.03201	+	1.33852i	0.0662064	+	0.0436112i
$943$	2.15592	+	3.73416i	0.0702063	+	0.121601i
$944$	47.2865			1.53905
$945$	−8.71497	+	48.8241i	−0.283498	+	1.58825i
$946$	13.4947			0.438750
$947$	28.4595	+	49.2933i	0.924810	+	1.60182i	0.791867	+	0.610694i	$0.209110\pi$
$947$	28.4595	+	49.2933i	0.924810	+	1.60182i	0.132943	+	0.991124i	$0.457557\pi$
$948$	−26.4178	−	17.4018i	−0.858012	−	0.565186i
$949$	−26.2323	+	45.4357i	−0.851537	+	1.47490i
$950$	11.8630	−	20.5473i	0.384886	−	0.666642i
$951$	−1.25230	+	21.2444i	−0.0406085	+	0.688896i
$952$	−51.4636	−	89.1375i	−1.66794	−	2.88896i
$953$	0.150027			0.00485984			0.00242992	−	0.999997i	$-0.499227\pi$
$953$	0.150027			0.00485984			0.00242992	+	0.999997i	$0.499227\pi$
$954$	54.4921	−	72.9816i	1.76425	−	2.36287i
$955$	−67.7147			−2.19120
$956$	2.27863	+	3.94670i	0.0736962	+	0.127646i
$957$	8.60886	−	4.31598i	0.278285	−	0.139516i
$958$	−5.11472	+	8.85896i	−0.165249	+	0.286220i
$959$	8.46148	−	14.6557i	0.273235	−	0.473258i
$960$	36.1912	−	18.1441i	1.16807	−	0.585599i
$961$	4.26724	+	7.39107i	0.137653	+	0.238422i
$962$	43.5631			1.40453
$963$	−20.8873	−	48.6096i	−0.673084	−	1.56642i
$964$	−62.2659			−2.00545
$965$	−37.0693	−	64.2058i	−1.19330	−	2.06686i
$966$	0.790269	−	13.4064i	0.0254265	−	0.431344i
$967$	−16.0423	+	27.7861i	−0.515886	+	0.893542i	0.483943	+	0.875099i	$0.339204\pi$
$967$	−16.0423	+	27.7861i	−0.515886	+	0.893542i	−0.999830	+	0.0184423i	$0.994129\pi$
$968$	35.2687	−	61.0872i	1.13358	−	1.96342i
$969$	11.7471	+	7.73802i	0.377372	+	0.248581i
$970$	−60.4473	−	104.698i	−1.94085	−	3.36164i
$971$	10.8639			0.348638			0.174319	−	0.984689i	$-0.444228\pi$
$971$	10.8639			0.348638			0.174319	+	0.984689i	$0.444228\pi$
$972$	21.7194	−	71.6325i	0.696650	−	2.29761i
$973$	55.2495			1.77122
$974$	7.75229	+	13.4274i	0.248399	+	0.430240i
$975$	−49.4129	−	32.5491i	−1.58248	−	1.04240i
$976$	−4.08275	+	7.07153i	−0.130686	+	0.226354i
$977$	21.3593	−	36.9955i	0.683346	−	1.18359i	−0.290608	−	0.956842i	$-0.593858\pi$
$977$	21.3593	−	36.9955i	0.683346	−	1.18359i	0.973954	−	0.226747i	$-0.0728091\pi$
$978$	0.800542	−	13.5807i	0.0255985	−	0.434262i
$979$	−5.45393	−	9.44648i	−0.174308	−	0.301911i
$980$	−28.3444			−0.905430
$981$	3.13668	+	7.29978i	0.100146	+	0.233064i
$982$	35.5351			1.13397
$983$	−21.8617	−	37.8656i	−0.697280	−	1.20772i	−0.969406	−	0.245463i	$-0.921060\pi$
$983$	−21.8617	−	37.8656i	−0.697280	−	1.20772i	0.272126	−	0.962262i	$-0.412273\pi$
$984$	−48.7850	+	24.4579i	−1.55521	+	0.779689i
$985$	20.4322	−	35.3896i	0.651023	−	1.12761i
$986$	29.5991	−	51.2671i	0.942626	−	1.63268i
$987$	1.48426	−	0.744119i	0.0472445	−	0.0236856i
$988$	−26.4908	−	45.8834i	−0.842784	−	1.45974i
$989$	4.45847			0.141771
$990$	17.4411	−	23.3590i	0.554316	−	0.742398i
$991$	48.2749			1.53350			0.766751	−	0.641944i	$-0.221872\pi$
$991$	48.2749			1.53350			0.766751	+	0.641944i	$0.221872\pi$
$992$	−23.7968	−	41.2173i	−0.755550	−	1.30865i
$993$	1.58409	−	26.8731i	0.0502696	−	0.852791i
$994$	−35.4455	+	61.3934i	−1.12426	+	1.94728i
$995$	31.4201	−	54.4213i	0.996085	−	1.72527i
$996$	0.634164	+	0.417733i	0.0200942	+	0.0132364i
$997$	−20.6550	−	35.7755i	−0.654150	−	1.13302i	−0.982106	−	0.188328i	$-0.939693\pi$
$997$	−20.6550	−	35.7755i	−0.654150	−	1.13302i	0.327956	−	0.944693i	$-0.393640\pi$
$998$	63.2847			2.00324
$999$	2.36939	−	13.2741i	0.0749641	−	0.419973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.e.a.139.1	yes	16
3.2	odd	2		621.2.e.a.415.8		16
9.2	odd	6		621.2.e.a.208.8		16
9.4	even	3		1863.2.a.f.1.8		8
9.5	odd	6		1863.2.a.e.1.1		8
9.7	even	3	inner	207.2.e.a.70.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.e.a.70.1	✓	16	9.7	even	3	inner
207.2.e.a.139.1	yes	16	1.1	even	1	trivial
621.2.e.a.208.8		16	9.2	odd	6
621.2.e.a.415.8		16	3.2	odd	2
1863.2.a.e.1.1		8	9.5	odd	6
1863.2.a.f.1.8		8	9.4	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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30401 - 2.25862i) q^{2} +(1.44644 + 0.952792i) q^{3} +(-2.40091 + 4.15849i) q^{4} +(1.60524 - 2.78036i) q^{5} +(0.265817 - 4.50941i) q^{6} +(1.48649 + 2.57468i) q^{7} +7.30721 q^{8} +(1.18437 + 2.75631i) q^{9} +O(q^{10})\)	\(q+(-1.30401 - 2.25862i) q^{2} +(1.44644 + 0.952792i) q^{3} +(-2.40091 + 4.15849i) q^{4} +(1.60524 - 2.78036i) q^{5} +(0.265817 - 4.50941i) q^{6} +(1.48649 + 2.57468i) q^{7} +7.30721 q^{8} +(1.18437 + 2.75631i) q^{9} -8.37303 q^{10} +(0.580275 + 1.00507i) q^{11} +(-7.43494 + 3.72744i) q^{12} +(3.21843 - 5.57448i) q^{13} +(3.87681 - 6.71483i) q^{14} +(4.97099 - 2.49216i) q^{15} +(-4.72689 - 8.18721i) q^{16} -4.73790 q^{17} +(4.68102 - 6.26932i) q^{18} -1.71414 q^{19} +(7.70807 + 13.3508i) q^{20} +(-0.303014 + 5.14043i) q^{21} +(1.51337 - 2.62124i) q^{22} +(0.500000 - 0.866025i) q^{23} +(10.5694 + 6.96225i) q^{24} +(-2.65360 - 4.59618i) q^{25} -16.7875 q^{26} +(-0.913068 + 5.11530i) q^{27} -14.2757 q^{28} +(-2.39541 - 4.14897i) q^{29} +(-12.1111 - 7.97776i) q^{30} +(-2.36989 + 4.10477i) q^{31} +(-5.02066 + 8.69603i) q^{32} +(-0.118286 + 2.00665i) q^{33} +(6.17829 + 10.7011i) q^{34} +9.54471 q^{35} +(-14.3057 - 1.69244i) q^{36} -2.59497 q^{37} +(2.23526 + 3.87158i) q^{38} +(9.96659 - 4.99666i) q^{39} +(11.7298 - 20.3167i) q^{40} +(-2.15592 + 3.73416i) q^{41} +(12.0054 - 6.01880i) q^{42} +(2.22924 + 3.86115i) q^{43} -5.57274 q^{44} +(9.56475 + 1.13156i) q^{45} -2.60803 q^{46} +(-0.161218 - 0.279239i) q^{47} +(0.963554 - 16.3461i) q^{48} +(-0.919310 + 1.59229i) q^{49} +(-6.92068 + 11.9870i) q^{50} +(-6.85309 - 4.51424i) q^{51} +(15.4543 + 26.7676i) q^{52} +11.6411 q^{53} +(12.7442 - 4.60815i) q^{54} +3.72593 q^{55} +(10.8621 + 18.8137i) q^{56} +(-2.47939 - 1.63322i) q^{57} +(-6.24729 + 10.8206i) q^{58} +(-2.50093 + 4.33174i) q^{59} +(-1.57125 + 26.6553i) q^{60} +(-0.431864 - 0.748011i) q^{61} +12.3615 q^{62} +(-5.33606 + 7.14661i) q^{63} +7.28048 q^{64} +(-10.3327 - 17.8968i) q^{65} +(4.68650 - 2.34953i) q^{66} +(-0.597357 + 1.03465i) q^{67} +(11.3753 - 19.7025i) q^{68} +(1.54836 - 0.776257i) q^{69} +(-12.4464 - 21.5579i) q^{70} -9.14295 q^{71} +(8.65447 + 20.1409i) q^{72} -8.15065 q^{73} +(3.38388 + 5.86105i) q^{74} +(0.540924 - 9.17642i) q^{75} +(4.11548 - 7.12822i) q^{76} +(-1.72515 + 2.98804i) q^{77} +(-24.2821 - 15.9950i) q^{78} +(1.90179 + 3.29399i) q^{79} -30.3512 q^{80} +(-6.19452 + 6.52901i) q^{81} +11.2454 q^{82} +(-0.0456526 - 0.0790727i) q^{83} +(-20.6489 - 13.6018i) q^{84} +(-7.60548 + 13.1731i) q^{85} +(5.81391 - 10.0700i) q^{86} +(0.488293 - 8.28356i) q^{87} +(4.24019 + 7.34422i) q^{88} -9.39887 q^{89} +(-9.91680 - 23.0787i) q^{90} +19.1367 q^{91} +(2.40091 + 4.15849i) q^{92} +(-7.33890 + 3.67929i) q^{93} +(-0.420462 + 0.728262i) q^{94} +(-2.75160 + 4.76592i) q^{95} +(-15.5476 + 7.79464i) q^{96} +(7.21929 + 12.5042i) q^{97} +4.79517 q^{98} +(-2.08301 + 2.78979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - q^{3} - 5 q^{4} - q^{6} + 7 q^{7} + 12 q^{8} + 5 q^{9}+O(q^{10}) \) 16 * q - q^2 - q^3 - 5 * q^4 - q^6 + 7 * q^7 + 12 * q^8 + 5 * q^9	\( 16 q - q^{2} - q^{3} - 5 q^{4} - q^{6} + 7 q^{7} + 12 q^{8} + 5 q^{9} - 20 q^{10} + 3 q^{11} - 17 q^{12} + 15 q^{13} + 5 q^{14} + q^{16} - 12 q^{17} + 23 q^{18} - 24 q^{19} + 7 q^{20} - 10 q^{21} + 17 q^{22} + 8 q^{23} + 18 q^{24} + 10 q^{25} - 52 q^{26} + 2 q^{27} - 40 q^{28} - 10 q^{29} - 45 q^{30} + 8 q^{31} - 13 q^{32} - 13 q^{33} + 15 q^{34} + 30 q^{35} + q^{36} - 38 q^{37} - 7 q^{38} + 9 q^{39} + 30 q^{40} - q^{41} + 41 q^{42} + 17 q^{43} - 12 q^{44} + 33 q^{45} - 2 q^{46} - 5 q^{47} - 20 q^{48} + 15 q^{49} - 7 q^{50} - 55 q^{51} + 39 q^{52} + 8 q^{53} + 59 q^{54} - 20 q^{55} + 24 q^{56} - 20 q^{57} + 4 q^{58} - 20 q^{59} + 6 q^{60} + 16 q^{61} + 78 q^{62} + 32 q^{63} - 8 q^{64} - 2 q^{65} - 28 q^{66} + 7 q^{67} + 24 q^{68} - 2 q^{69} - 16 q^{70} - 10 q^{71} + 33 q^{72} - 96 q^{73} - 21 q^{74} + 26 q^{75} + 6 q^{76} + 16 q^{77} - 30 q^{78} + 12 q^{79} - 94 q^{80} + 17 q^{81} - 16 q^{82} + 12 q^{83} - 59 q^{84} + 6 q^{85} + 19 q^{86} - 53 q^{87} + 7 q^{88} + 22 q^{89} + 21 q^{90} - 4 q^{91} + 5 q^{92} - 31 q^{93} + q^{94} - 4 q^{95} - 38 q^{96} + 43 q^{97} + 56 q^{98} + 2 q^{99}+O(q^{100}) \) 16 * q - q^2 - q^3 - 5 * q^4 - q^6 + 7 * q^7 + 12 * q^8 + 5 * q^9 - 20 * q^10 + 3 * q^11 - 17 * q^12 + 15 * q^13 + 5 * q^14 + q^16 - 12 * q^17 + 23 * q^18 - 24 * q^19 + 7 * q^20 - 10 * q^21 + 17 * q^22 + 8 * q^23 + 18 * q^24 + 10 * q^25 - 52 * q^26 + 2 * q^27 - 40 * q^28 - 10 * q^29 - 45 * q^30 + 8 * q^31 - 13 * q^32 - 13 * q^33 + 15 * q^34 + 30 * q^35 + q^36 - 38 * q^37 - 7 * q^38 + 9 * q^39 + 30 * q^40 - q^41 + 41 * q^42 + 17 * q^43 - 12 * q^44 + 33 * q^45 - 2 * q^46 - 5 * q^47 - 20 * q^48 + 15 * q^49 - 7 * q^50 - 55 * q^51 + 39 * q^52 + 8 * q^53 + 59 * q^54 - 20 * q^55 + 24 * q^56 - 20 * q^57 + 4 * q^58 - 20 * q^59 + 6 * q^60 + 16 * q^61 + 78 * q^62 + 32 * q^63 - 8 * q^64 - 2 * q^65 - 28 * q^66 + 7 * q^67 + 24 * q^68 - 2 * q^69 - 16 * q^70 - 10 * q^71 + 33 * q^72 - 96 * q^73 - 21 * q^74 + 26 * q^75 + 6 * q^76 + 16 * q^77 - 30 * q^78 + 12 * q^79 - 94 * q^80 + 17 * q^81 - 16 * q^82 + 12 * q^83 - 59 * q^84 + 6 * q^85 + 19 * q^86 - 53 * q^87 + 7 * q^88 + 22 * q^89 + 21 * q^90 - 4 * q^91 + 5 * q^92 - 31 * q^93 + q^94 - 4 * q^95 - 38 * q^96 + 43 * q^97 + 56 * q^98 + 2 * q^99

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