LMFDB - Embedded newform 855.2.i.d.571.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(286,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("855.286");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.i (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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			571.13
Character	$\chi$	$=$	855.571
Dual form			855.2.i.d.286.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0983098 + 0.170278i) q^{2} +(0.994216 - 1.41829i) q^{3} +(0.980670 - 1.69857i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.339244 + 0.0298612i) q^{6} +(0.566167 + 0.980630i) q^{7} +0.778878 q^{8} +(-1.02307 - 2.82016i) q^{9} +O(q^{10})$	\(q+(0.0983098 + 0.170278i) q^{2} +(0.994216 - 1.41829i) q^{3} +(0.980670 - 1.69857i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.339244 + 0.0298612i) q^{6} +(0.566167 + 0.980630i) q^{7} +0.778878 q^{8} +(-1.02307 - 2.82016i) q^{9} +0.196620 q^{10} +(0.420339 + 0.728049i) q^{11} +(-1.43406 - 3.07962i) q^{12} +(-0.596003 + 1.03231i) q^{13} +(-0.111320 + 0.192811i) q^{14} +(-0.731164 - 1.57016i) q^{15} +(-1.88477 - 3.26452i) q^{16} +4.25355 q^{17} +(0.379633 - 0.451456i) q^{18} +1.00000 q^{19} +(-0.980670 - 1.69857i) q^{20} +(1.95371 + 0.171971i) q^{21} +(-0.0826469 + 0.143149i) q^{22} +(3.94693 - 6.83627i) q^{23} +(0.774372 - 1.10467i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.234372 q^{26} +(-5.01695 - 1.35285i) q^{27} +2.22089 q^{28} +(1.14685 + 1.98641i) q^{29} +(0.195482 - 0.278863i) q^{30} +(-4.69071 + 8.12455i) q^{31} +(1.14946 - 1.99092i) q^{32} +(1.45049 + 0.127676i) q^{33} +(0.418166 + 0.724285i) q^{34} +1.13233 q^{35} +(-5.79354 - 1.02789i) q^{36} -8.54624 q^{37} +(0.0983098 + 0.170278i) q^{38} +(0.871552 + 1.87164i) q^{39} +(0.389439 - 0.674528i) q^{40} +(-2.95188 + 5.11281i) q^{41} +(0.162786 + 0.349579i) q^{42} +(0.975886 + 1.69028i) q^{43} +1.64886 q^{44} +(-2.95387 - 0.524077i) q^{45} +1.55209 q^{46} +(-2.25497 - 3.90572i) q^{47} +(-6.50389 - 0.572491i) q^{48} +(2.85891 - 4.95178i) q^{49} +(0.0983098 - 0.170278i) q^{50} +(4.22895 - 6.03275i) q^{51} +(1.16896 + 2.02471i) q^{52} -3.93369 q^{53} +(-0.262857 - 0.987273i) q^{54} +0.840678 q^{55} +(0.440975 + 0.763791i) q^{56} +(0.994216 - 1.41829i) q^{57} +(-0.225494 + 0.390567i) q^{58} +(0.561004 - 0.971688i) q^{59} +(-3.38406 - 0.297875i) q^{60} +(4.41842 + 7.65293i) q^{61} -1.84457 q^{62} +(2.18631 - 2.59994i) q^{63} -7.08706 q^{64} +(0.596003 + 1.03231i) q^{65} +(0.120857 + 0.259538i) q^{66} +(-4.16976 + 7.22223i) q^{67} +(4.17133 - 7.22496i) q^{68} +(-5.77170 - 12.3946i) q^{69} +(0.111320 + 0.192811i) q^{70} +6.82749 q^{71} +(-0.796847 - 2.19656i) q^{72} -9.95404 q^{73} +(-0.840180 - 1.45523i) q^{74} +(-1.72538 - 0.151873i) q^{75} +(0.980670 - 1.69857i) q^{76} +(-0.475964 + 0.824394i) q^{77} +(-0.233016 + 0.332406i) q^{78} +(0.113548 + 0.196671i) q^{79} -3.76954 q^{80} +(-6.90665 + 5.77045i) q^{81} -1.16080 q^{82} +(8.07424 + 13.9850i) q^{83} +(2.20805 - 3.14986i) q^{84} +(2.12678 - 3.68368i) q^{85} +(-0.191878 + 0.332343i) q^{86} +(3.95752 + 0.348352i) q^{87} +(0.327393 + 0.567061i) q^{88} +13.8453 q^{89} +(-0.201156 - 0.554500i) q^{90} -1.34975 q^{91} +(-7.74126 - 13.4083i) q^{92} +(6.85936 + 14.7303i) q^{93} +(0.443371 - 0.767941i) q^{94} +(0.500000 - 0.866025i) q^{95} +(-1.68089 - 3.60967i) q^{96} +(-0.938006 - 1.62467i) q^{97} +1.12424 q^{98} +(1.62318 - 1.93027i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9 + 6 * q^10 - q^11 + 9 * q^12 - 11 * q^13 - 3 * q^14 + q^15 - 45 * q^16 - 30 * q^17 - 18 * q^18 + 46 * q^19 + 29 * q^20 - 2 * q^21 - 5 * q^22 + 13 * q^23 - 6 * q^24 - 23 * q^25 - 12 * q^26 + 23 * q^27 + 56 * q^28 + 2 * q^29 + 6 * q^30 - 16 * q^31 + 25 * q^32 + 19 * q^33 - 18 * q^34 - 20 * q^35 - 5 * q^36 + 58 * q^37 + 3 * q^38 + 32 * q^39 - 6 * q^40 + 14 * q^41 - 67 * q^42 - 34 * q^43 + 64 * q^44 - 7 * q^45 - 4 * q^46 + 22 * q^47 + 89 * q^48 - 61 * q^49 + 3 * q^50 - 38 * q^51 - 20 * q^52 - 70 * q^53 - 91 * q^54 - 2 * q^55 - 26 * q^56 + 2 * q^57 - 23 * q^58 - 15 * q^59 + 3 * q^60 - 32 * q^61 + 6 * q^62 - 31 * q^63 + 164 * q^64 + 11 * q^65 + 54 * q^66 - 16 * q^67 + 26 * q^68 - 19 * q^69 + 3 * q^70 + 50 * q^71 + 22 * q^72 + 82 * q^73 + 9 * q^74 - q^75 - 29 * q^76 + 18 * q^77 - 41 * q^78 - 11 * q^79 - 90 * q^80 + 8 * q^81 + 60 * q^82 + 26 * q^83 + 123 * q^84 - 15 * q^85 - 15 * q^86 - 26 * q^87 - 22 * q^88 + 40 * q^89 - 12 * q^90 + 116 * q^91 + 2 * q^92 + 42 * q^93 - 36 * q^94 + 23 * q^95 - 48 * q^96 - 50 * q^97 - 24 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.0983098	+	0.170278i	0.0695156	+	0.120404i	0.898688	−	0.438588i	$-0.144521\pi$
$2$	0.0983098	+	0.170278i	0.0695156	+	0.120404i	−0.829173	+	0.558993i	$0.811188\pi$
$3$	0.994216	−	1.41829i	0.574011	−	0.818848i
$3$	0.994216	−	1.41829i	0.574011	−	0.818848i
$4$	0.980670	−	1.69857i	0.490335	−	0.849285i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.339244	+	0.0298612i	0.138496	+	0.0121908i
$7$	0.566167	+	0.980630i	0.213991	+	0.370643i	0.952960	−	0.303096i	$-0.0980203\pi$
$7$	0.566167	+	0.980630i	0.213991	+	0.370643i	−0.738969	+	0.673739i	$0.764687\pi$
$8$	0.778878			0.275375
$9$	−1.02307	−	2.82016i	−0.341023	−	0.940055i
$10$	0.196620			0.0621766
$11$	0.420339	+	0.728049i	0.126737	+	0.219515i	0.922411	−	0.386211i	$-0.126216\pi$
$11$	0.420339	+	0.728049i	0.126737	+	0.219515i	−0.795674	+	0.605726i	$0.792883\pi$
$12$	−1.43406	−	3.07962i	−0.413978	−	0.889009i
$13$	−0.596003	+	1.03231i	−0.165301	+	0.286311i	−0.936762	−	0.349966i	$-0.886193\pi$
$13$	−0.596003	+	1.03231i	−0.165301	+	0.286311i	0.771461	+	0.636277i	$0.219526\pi$
$14$	−0.111320	+	0.192811i	−0.0297514	+	0.0515309i
$15$	−0.731164	−	1.57016i	−0.188786	−	0.405413i
$16$	−1.88477	−	3.26452i	−0.471192	−	0.816129i
$17$	4.25355			1.03164			0.515819	−	0.856698i	$-0.327488\pi$
$17$	4.25355			1.03164			0.515819	+	0.856698i	$0.327488\pi$
$18$	0.379633	−	0.451456i	0.0894804	−	0.106409i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−0.980670	−	1.69857i	−0.219285	−	0.379812i
$21$	1.95371	+	0.171971i	0.426334	+	0.0375271i
$22$	−0.0826469	+	0.143149i	−0.0176204	+	0.0305194i
$23$	3.94693	−	6.83627i	0.822991	−	1.42546i	−0.0804544	−	0.996758i	$-0.525637\pi$
$23$	3.94693	−	6.83627i	0.822991	−	1.42546i	0.903445	−	0.428704i	$-0.141030\pi$
$24$	0.774372	−	1.10467i	0.158068	−	0.225490i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.234372			−0.0459641
$27$	−5.01695	−	1.35285i	−0.965513	−	0.260355i
$28$	2.22089			0.419709
$29$	1.14685	+	1.98641i	0.212965	+	0.368867i	0.952641	−	0.304096i	$-0.0983545\pi$
$29$	1.14685	+	1.98641i	0.212965	+	0.368867i	−0.739676	+	0.672963i	$0.765021\pi$
$30$	0.195482	−	0.278863i	0.0356900	−	0.0509132i
$31$	−4.69071	+	8.12455i	−0.842477	+	1.45921i	0.0453176	+	0.998973i	$0.485570\pi$
$31$	−4.69071	+	8.12455i	−0.842477	+	1.45921i	−0.887794	+	0.460240i	$0.847763\pi$
$32$	1.14946	−	1.99092i	0.203198	−	0.351949i
$33$	1.45049	+	0.127676i	0.252498	+	0.0222256i
$34$	0.418166	+	0.724285i	0.0717149	+	0.124214i
$35$	1.13233			0.191399
$36$	−5.79354	−	1.02789i	−0.965591	−	0.171316i
$37$	−8.54624			−1.40499			−0.702497	−	0.711687i	$-0.747931\pi$
$37$	−8.54624			−1.40499			−0.702497	+	0.711687i	$0.747931\pi$
$38$	0.0983098	+	0.170278i	0.0159480	+	0.0276227i
$39$	0.871552	+	1.87164i	0.139560	+	0.299702i
$40$	0.389439	−	0.674528i	0.0615757	−	0.106652i
$41$	−2.95188	+	5.11281i	−0.461006	+	0.798486i	−0.999011	−	0.0444553i	$-0.985845\pi$
$41$	−2.95188	+	5.11281i	−0.461006	+	0.798486i	0.538005	+	0.842942i	$0.319178\pi$
$42$	0.162786	+	0.349579i	0.0251184	+	0.0539412i
$43$	0.975886	+	1.69028i	0.148821	+	0.257766i	0.930792	−	0.365549i	$-0.119119\pi$
$43$	0.975886	+	1.69028i	0.148821	+	0.257766i	−0.781971	+	0.623315i	$0.785785\pi$
$44$	1.64886			0.248574
$45$	−2.95387	−	0.524077i	−0.440337	−	0.0781248i
$46$	1.55209			0.228843
$47$	−2.25497	−	3.90572i	−0.328921	−	0.569707i	0.653377	−	0.757032i	$-0.273352\pi$
$47$	−2.25497	−	3.90572i	−0.328921	−	0.569707i	−0.982298	+	0.187325i	$0.940018\pi$
$48$	−6.50389	−	0.572491i	−0.938755	−	0.0826320i
$49$	2.85891	−	4.95178i	0.408416	−	0.707397i
$50$	0.0983098	−	0.170278i	0.0139031	−	0.0240809i
$51$	4.22895	−	6.03275i	0.592171	−	0.844754i
$52$	1.16896	+	2.02471i	0.162106	+	0.280776i
$53$	−3.93369			−0.540333			−0.270167	−	0.962814i	$-0.587079\pi$
$53$	−3.93369			−0.540333			−0.270167	+	0.962814i	$0.587079\pi$
$54$	−0.262857	−	0.987273i	−0.0357702	−	0.134351i
$55$	0.840678			0.113357
$56$	0.440975	+	0.763791i	0.0589277	+	0.102066i
$57$	0.994216	−	1.41829i	0.131687	−	0.187857i
$58$	−0.225494	+	0.390567i	−0.0296088	+	0.0512840i
$59$	0.561004	−	0.971688i	0.0730365	−	0.126503i	−0.827194	−	0.561916i	$-0.810064\pi$
$59$	0.561004	−	0.971688i	0.0730365	−	0.126503i	0.900231	+	0.435413i	$0.143398\pi$
$60$	−3.38406	−	0.297875i	−0.436880	−	0.0384555i
$61$	4.41842	+	7.65293i	0.565721	+	0.979858i	0.996982	+	0.0776306i	$0.0247355\pi$
$61$	4.41842	+	7.65293i	0.565721	+	0.979858i	−0.431261	+	0.902227i	$0.641931\pi$
$62$	−1.84457			−0.234261
$63$	2.18631	−	2.59994i	0.275449	−	0.327561i
$64$	−7.08706			−0.885883
$65$	0.596003	+	1.03231i	0.0739251	+	0.128042i
$66$	0.120857	+	0.259538i	0.0148765	+	0.0319469i
$67$	−4.16976	+	7.22223i	−0.509417	+	0.882336i	0.490524	+	0.871428i	$0.336806\pi$
$67$	−4.16976	+	7.22223i	−0.509417	+	0.882336i	−0.999941	+	0.0109081i	$0.996528\pi$
$68$	4.17133	−	7.22496i	0.505848	−	0.876155i
$69$	−5.77170	−	12.3946i	−0.694831	−	1.49213i
$70$	0.111320	+	0.192811i	0.0133052	+	0.0230453i
$71$	6.82749			0.810274			0.405137	−	0.914256i	$-0.367224\pi$
$71$	6.82749			0.810274			0.405137	+	0.914256i	$0.367224\pi$
$72$	−0.796847	−	2.19656i	−0.0939093	−	0.258867i
$73$	−9.95404			−1.16503			−0.582516	−	0.812819i	$-0.697932\pi$
$73$	−9.95404			−1.16503			−0.582516	+	0.812819i	$0.697932\pi$
$74$	−0.840180	−	1.45523i	−0.0976689	−	0.169167i
$75$	−1.72538	−	0.151873i	−0.199230	−	0.0175368i
$76$	0.980670	−	1.69857i	0.112491	−	0.194839i
$77$	−0.475964	+	0.824394i	−0.0542412	+	0.0939485i
$78$	−0.233016	+	0.332406i	−0.0263839	+	0.0376376i
$79$	0.113548	+	0.196671i	0.0127751	+	0.0221272i	0.872342	−	0.488896i	$-0.162600\pi$
$79$	0.113548	+	0.196671i	0.0127751	+	0.0221272i	−0.859567	+	0.511023i	$0.829267\pi$
$80$	−3.76954			−0.421447
$81$	−6.90665	+	5.77045i	−0.767406	+	0.641162i
$82$	−1.16080			−0.128188
$83$	8.07424	+	13.9850i	0.886263	+	1.53505i	0.844259	+	0.535935i	$0.180041\pi$
$83$	8.07424	+	13.9850i	0.886263	+	1.53505i	0.0420033	+	0.999117i	$0.486626\pi$
$84$	2.20805	−	3.14986i	0.240918	−	0.343678i
$85$	2.12678	−	3.68368i	0.230681	−	0.399552i
$86$	−0.191878	+	0.332343i	−0.0206908	+	0.0358375i
$87$	3.95752	+	0.348352i	0.424290	+	0.0373473i
$88$	0.327393	+	0.567061i	0.0349002	+	0.0604489i
$89$	13.8453			1.46760			0.733799	−	0.679366i	$-0.237745\pi$
$89$	13.8453			1.46760			0.733799	+	0.679366i	$0.237745\pi$
$90$	−0.201156	−	0.554500i	−0.0212037	−	0.0584494i
$91$	−1.34975			−0.141492
$92$	−7.74126	−	13.4083i	−0.807083	−	1.39791i
$93$	6.85936	+	14.7303i	0.711282	+	1.52746i
$94$	0.443371	−	0.767941i	0.0457302	−	0.0792070i
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$	−1.68089	−	3.60967i	−0.171555	−	0.368410i
$97$	−0.938006	−	1.62467i	−0.0952400	−	0.164961i	0.814469	−	0.580207i	$-0.197029\pi$
$97$	−0.938006	−	1.62467i	−0.0952400	−	0.164961i	−0.909709	+	0.415247i	$0.863695\pi$
$98$	1.12424			0.113565
$99$	1.62318	−	1.93027i	0.163136	−	0.194000i
$100$	−1.96134			−0.196134
$101$	3.87429	+	6.71047i	0.385507	+	0.667717i	0.991839	−	0.127494i	$-0.0406933\pi$
$101$	3.87429	+	6.71047i	0.385507	+	0.667717i	−0.606333	+	0.795211i	$0.707360\pi$
$102$	1.44299	+	0.127016i	0.142877	+	0.0125765i
$103$	−1.05012	+	1.81887i	−0.103472	+	0.179218i	−0.913113	−	0.407707i	$-0.866328\pi$
$103$	−1.05012	+	1.81887i	−0.103472	+	0.179218i	0.809641	+	0.586925i	$0.199662\pi$
$104$	−0.464213	+	0.804041i	−0.0455199	+	0.0788427i
$105$	1.12578	−	1.60597i	0.109865	−	0.156727i
$106$	−0.386720	−	0.669819i	−0.0375616	−	0.0650586i
$107$	−0.774260			−0.0748505			−0.0374252	−	0.999299i	$-0.511916\pi$
$107$	−0.774260			−0.0748505			−0.0374252	+	0.999299i	$0.511916\pi$
$108$	−7.21788	+	7.19495i	−0.694541	+	0.692335i
$109$	19.1893			1.83800			0.919002	−	0.394253i	$-0.128997\pi$
$109$	19.1893			1.83800			0.919002	+	0.394253i	$0.128997\pi$
$110$	0.0826469	+	0.143149i	0.00788008	+	0.0136487i
$111$	−8.49681	+	12.1210i	−0.806481	+	1.15048i
$112$	2.13419	−	3.69652i	0.201662	−	0.349289i
$113$	5.62481	−	9.74246i	0.529138	−	0.916494i	−0.470285	−	0.882515i	$-0.655849\pi$
$113$	5.62481	−	9.74246i	0.529138	−	0.916494i	0.999423	−	0.0339791i	$-0.0108180\pi$
$114$	0.339244	+	0.0298612i	0.0317731	+	0.00279676i
$115$	−3.94693	−	6.83627i	−0.368053	−	0.637486i
$116$	4.49874			0.417698
$117$	3.52103	+	0.624703i	0.325519	+	0.0577538i
$118$	0.220609			0.0203087
$119$	2.40822	+	4.17116i	0.220761	+	0.382370i
$120$	−0.569487	−	1.22296i	−0.0519868	−	0.111641i
$121$	5.14663	−	8.91422i	0.467875	−	0.810384i
$122$	−0.868749	+	1.50472i	−0.0786528	+	0.136231i
$123$	4.31662	+	9.26984i	0.389216	+	0.835834i
$124$	9.20009	+	15.9350i	0.826192	+	1.43101i
$125$	−1.00000			−0.0894427
$126$	0.657647	+	0.116680i	0.0585878	+	0.0103947i
$127$	6.47394			0.574470			0.287235	−	0.957860i	$-0.407264\pi$
$127$	6.47394			0.574470			0.287235	+	0.957860i	$0.407264\pi$
$128$	−2.99565	−	5.18862i	−0.264780	−	0.458613i
$129$	3.36755	+	0.296422i	0.296496	+	0.0260985i
$130$	−0.117186	+	0.202972i	−0.0102779	+	0.0178018i
$131$	9.13443	−	15.8213i	0.798079	−	1.38231i	−0.122787	−	0.992433i	$-0.539183\pi$
$131$	9.13443	−	15.8213i	0.798079	−	1.38231i	0.920866	−	0.389880i	$-0.127484\pi$
$132$	1.63932	−	2.33855i	0.142684	−	0.203545i
$133$	0.566167	+	0.980630i	0.0490929	+	0.0850314i
$134$	−1.63971			−0.141650
$135$	−3.68007	+	3.66839i	−0.316730	+	0.315724i
$136$	3.31300			0.284087
$137$	−2.92225	−	5.06149i	−0.249665	−	0.432432i	0.713768	−	0.700382i	$-0.246987\pi$
$137$	−2.92225	−	5.06149i	−0.249665	−	0.432432i	−0.963433	+	0.267950i	$0.913654\pi$
$138$	1.54311	−	2.20130i	0.131358	−	0.187387i
$139$	−5.01719	+	8.69003i	−0.425553	+	0.737079i	−0.996472	−	0.0839272i	$-0.973254\pi$
$139$	−5.01719	+	8.69003i	−0.425553	+	0.737079i	0.570919	+	0.821006i	$0.306587\pi$
$140$	1.11045	−	1.92335i	0.0938498	−	0.162553i
$141$	−7.78134	−	0.684937i	−0.655307	−	0.0576821i
$142$	0.671210	+	1.16257i	0.0563267	+	0.0975606i
$143$	−1.00209			−0.0837993
$144$	−7.27822	+	8.65519i	−0.606518	+	0.721266i
$145$	2.29371			0.190482
$146$	−0.978580	−	1.69495i	−0.0809879	−	0.140275i
$147$	−4.18066	−	8.97789i	−0.344815	−	0.740484i
$148$	−8.38105	+	14.5164i	−0.688918	+	1.19324i
$149$	1.13271	−	1.96191i	0.0927952	−	0.160726i	−0.815891	−	0.578206i	$-0.803753\pi$
$149$	1.13271	−	1.96191i	0.0927952	−	0.160726i	0.908686	+	0.417480i	$0.137086\pi$
$150$	−0.143761	−	0.308724i	−0.0117381	−	0.0252072i
$151$	−0.667185	−	1.15560i	−0.0542948	−	0.0940413i	0.837601	−	0.546283i	$-0.183958\pi$
$151$	−0.667185	−	1.15560i	−0.0542948	−	0.0940413i	−0.891895	+	0.452242i	$0.850624\pi$
$152$	0.778878			0.0631753
$153$	−4.35168	−	11.9957i	−0.351813	−	0.969796i
$154$	−0.187168			−0.0150824
$155$	4.69071	+	8.12455i	0.376767	+	0.652580i
$156$	4.03382	+	0.355068i	0.322964	+	0.0284282i
$157$	−7.48108	+	12.9576i	−0.597055	+	1.03413i	0.396198	+	0.918165i	$0.370329\pi$
$157$	−7.48108	+	12.9576i	−0.597055	+	1.03413i	−0.993253	+	0.115964i	$0.963004\pi$
$158$	−0.0223258	+	0.0386694i	−0.00177614	+	0.00307637i
$159$	−3.91093	+	5.57909i	−0.310157	+	0.442451i
$160$	−1.14946	−	1.99092i	−0.0908728	−	0.157396i
$161$	8.93847			0.704451
$162$	−1.66157	−	0.608756i	−0.130545	−	0.0478284i
$163$	11.7505			0.920371			0.460185	−	0.887823i	$-0.347783\pi$
$163$	11.7505			0.920371			0.460185	+	0.887823i	$0.347783\pi$
$164$	5.78964	+	10.0280i	0.452095	+	0.783052i
$165$	0.835816	−	1.19232i	0.0650682	−	0.0928222i
$166$	−1.58755	+	2.74972i	−0.123218	+	0.213420i
$167$	1.06750	−	1.84897i	0.0826059	−	0.143078i	−0.821763	−	0.569830i	$-0.807009\pi$
$167$	1.06750	−	1.84897i	0.0826059	−	0.143078i	0.904369	+	0.426752i	$0.140342\pi$
$168$	1.52170	+	0.133944i	0.117402	+	0.0103340i
$169$	5.78956	+	10.0278i	0.445351	+	0.771370i
$170$	0.836332			0.0641437
$171$	−1.02307	−	2.82016i	−0.0782362	−	0.215663i
$172$	3.82809			0.291889
$173$	0.966554	+	1.67412i	0.0734858	+	0.127281i	0.900427	−	0.435008i	$-0.143254\pi$
$173$	0.966554	+	1.67412i	0.0734858	+	0.127281i	−0.826941	+	0.562289i	$0.809921\pi$
$174$	0.329746	+	0.708123i	0.0249980	+	0.0536827i
$175$	0.566167	−	0.980630i	0.0427982	−	0.0741287i
$176$	1.58448	−	2.74441i	0.119435	−	0.206868i
$177$	−0.820372	−	1.76173i	−0.0616629	−	0.132420i
$178$	1.36113	+	2.35754i	0.102021	+	0.176705i
$179$	−7.70484			−0.575887			−0.287943	−	0.957647i	$-0.592971\pi$
$179$	−7.70484			−0.575887			−0.287943	+	0.957647i	$0.592971\pi$
$180$	−3.78695	+	4.50341i	−0.282263	+	0.335664i
$181$	−5.35970			−0.398384			−0.199192	−	0.979961i	$-0.563832\pi$
$181$	−5.35970			−0.398384			−0.199192	+	0.979961i	$0.563832\pi$
$182$	−0.132694	−	0.229832i	−0.00983590	−	0.0170363i
$183$	15.2469	+	1.34208i	1.12708	+	0.0992093i
$184$	3.07417	−	5.32462i	0.226631	−	0.392536i
$185$	−4.27312	+	7.40126i	−0.314166	+	0.544152i
$186$	−1.83390	+	2.61613i	−0.134468	+	0.191824i
$187$	1.78793	+	3.09679i	0.130747	+	0.226460i
$188$	−8.84551			−0.645125
$189$	−1.51379	−	5.68571i	−0.110112	−	0.413575i
$190$	0.196620			0.0142643
$191$	−1.58824	−	2.75091i	−0.114921	−	0.199049i	0.802827	−	0.596212i	$-0.203328\pi$
$191$	−1.58824	−	2.75091i	−0.114921	−	0.199049i	−0.917748	+	0.397163i	$0.869995\pi$
$192$	−7.04607	+	10.0515i	−0.508506	+	0.725403i
$193$	−12.2208	+	21.1671i	−0.879674	+	1.52364i	−0.0279753	+	0.999609i	$0.508906\pi$
$193$	−12.2208	+	21.1671i	−0.879674	+	1.52364i	−0.851699	+	0.524032i	$0.824427\pi$
$194$	0.184430	−	0.319443i	0.0132413	−	0.0229347i
$195$	2.05666	+	0.181034i	0.147281	+	0.0129641i
$196$	−5.60730	−	9.71212i	−0.400521	−	0.693723i
$197$	−24.4727			−1.74360			−0.871802	−	0.489858i	$-0.837049\pi$
$197$	−24.4727			−1.74360			−0.871802	+	0.489858i	$0.837049\pi$
$198$	0.488257	+	0.0866268i	0.0346989	+	0.00615630i
$199$	8.26849			0.586137			0.293069	−	0.956091i	$-0.405324\pi$
$199$	8.26849			0.586137			0.293069	+	0.956091i	$0.405324\pi$
$200$	−0.389439	−	0.674528i	−0.0275375	−	0.0476963i
$201$	6.09755	+	13.0944i	0.430088	+	0.923605i
$202$	−0.761762	+	1.31941i	−0.0535974	+	0.0928335i
$203$	−1.29862	+	2.24928i	−0.0911454	+	0.157868i
$204$	−6.09985	−	13.0993i	−0.427075	−	0.917135i
$205$	2.95188	+	5.11281i	0.206168	+	0.357094i
$206$	−0.412949			−0.0287716
$207$	−23.3174	−	4.13699i	−1.62067	−	0.287540i
$208$	4.49331			0.311555
$209$	0.420339	+	0.728049i	0.0290755	+	0.0503602i
$210$	0.384137	+	0.0338129i	0.0265080	+	0.00233331i
$211$	2.07870	−	3.60042i	0.143104	−	0.247863i	−0.785560	−	0.618785i	$-0.787625\pi$
$211$	2.07870	−	3.60042i	0.143104	−	0.247863i	0.928664	+	0.370922i	$0.120958\pi$
$212$	−3.85765	+	6.68165i	−0.264944	+	0.458897i
$213$	6.78800	−	9.68334i	0.465106	−	0.663491i
$214$	−0.0761173	−	0.131839i	−0.00520327	−	0.00901233i
$215$	1.95177			0.133110
$216$	−3.90759	−	1.05370i	−0.265878	−	0.0716952i
$217$	−10.6229			−0.721130
$218$	1.88650	+	3.26751i	0.127770	+	0.221304i
$219$	−9.89647	+	14.1177i	−0.668741	+	0.953984i
$220$	0.824428	−	1.42795i	0.0555829	−	0.0962725i
$221$	−2.53513	+	4.39097i	−0.170531	+	0.295369i
$222$	−2.89926	−	0.255201i	−0.194585	−	0.0171280i
$223$	−7.02409	−	12.1661i	−0.470368	−	0.814701i	0.529058	−	0.848586i	$-0.322545\pi$
$223$	−7.02409	−	12.1661i	−0.470368	−	0.814701i	−0.999426	+	0.0338849i	$0.989212\pi$
$224$	2.60315			0.173930
$225$	−1.93080	+	2.29609i	−0.128720	+	0.153072i
$226$	2.21190			0.147133
$227$	−1.50997	−	2.61535i	−0.100220	−	0.173587i	0.811555	−	0.584276i	$-0.198621\pi$
$227$	−1.50997	−	2.61535i	−0.100220	−	0.173587i	−0.911775	+	0.410689i	$0.865288\pi$
$228$	−1.43406	−	3.07962i	−0.0949730	−	0.203953i
$229$	−13.1393	+	22.7580i	−0.868273	+	1.50389i	−0.00451189	+	0.999990i	$0.501436\pi$
$229$	−13.1393	+	22.7580i	−0.868273	+	1.50389i	−0.863761	+	0.503902i	$0.831897\pi$
$230$	0.776043	−	1.34415i	0.0511708	−	0.0886304i
$231$	0.696016	+	1.49468i	0.0457945	+	0.0983427i
$232$	0.893259	+	1.54717i	0.0586453	+	0.101577i
$233$	14.8891			0.975416			0.487708	−	0.873007i	$-0.337833\pi$
$233$	14.8891			0.975416			0.487708	+	0.873007i	$0.337833\pi$
$234$	0.239779	+	0.660967i	0.0156748	+	0.0432088i
$235$	−4.50993			−0.294196
$236$	−1.10032	−	1.90581i	−0.0716247	−	0.124058i
$237$	0.391827	+	0.0344897i	0.0254519	+	0.00224035i
$238$	−0.473504	+	0.820132i	−0.0306927	+	0.0531613i
$239$	−11.2699	+	19.5201i	−0.728992	+	1.26265i	0.228318	+	0.973587i	$0.426678\pi$
$239$	−11.2699	+	19.5201i	−0.728992	+	1.26265i	−0.957310	+	0.289065i	$0.906656\pi$
$240$	−3.74773	+	5.34628i	−0.241915	+	0.345101i
$241$	−5.35787	−	9.28010i	−0.345131	−	0.597784i	0.640247	−	0.768169i	$-0.278832\pi$
$241$	−5.35787	−	9.28010i	−0.345131	−	0.597784i	−0.985378	+	0.170385i	$0.945499\pi$
$242$	2.02386			0.130098
$243$	1.31745	+	15.5327i	0.0845145	+	0.996422i
$244$	17.3321			1.10957
$245$	−2.85891	−	4.95178i	−0.182649	−	0.316357i
$246$	−1.15408	+	1.64634i	−0.0735815	+	0.104967i
$247$	−0.596003	+	1.03231i	−0.0379228	+	0.0656841i
$248$	−3.65349	+	6.32803i	−0.231997	+	0.401830i
$249$	27.8623	+	2.45252i	1.76570	+	0.155422i
$250$	−0.0983098	−	0.170278i	−0.00621766	−	0.0107693i
$251$	30.6819			1.93662			0.968312	−	0.249745i	$-0.0803468\pi$
$251$	30.6819			1.93662			0.968312	+	0.249745i	$0.0803468\pi$
$252$	−2.27213	−	6.26328i	−0.143131	−	0.394550i
$253$	6.63619			0.417214
$254$	0.636452	+	1.10237i	0.0399346	+	0.0691687i
$255$	−3.11004	−	6.67875i	−0.194758	−	0.418240i
$256$	−6.49806	+	11.2550i	−0.406129	+	0.703436i
$257$	−4.06610	+	7.04270i	−0.253637	+	0.439311i	−0.964524	−	0.263994i	$-0.914960\pi$
$257$	−4.06610	+	7.04270i	−0.253637	+	0.439311i	0.710888	+	0.703306i	$0.248293\pi$
$258$	0.280589	+	0.602559i	0.0174687	+	0.0375137i
$259$	−4.83860	−	8.38070i	−0.300656	−	0.520751i
$260$	2.33793			0.144992
$261$	4.42869	−	5.26655i	0.274129	−	0.325991i
$262$	3.59202			0.221916
$263$	−5.16715	−	8.94976i	−0.318620	−	0.551866i	0.661580	−	0.749874i	$-0.269886\pi$
$263$	−5.16715	−	8.94976i	−0.318620	−	0.551866i	−0.980200	+	0.198008i	$0.936553\pi$
$264$	1.12975	+	0.0994442i	0.0695315	+	0.00612037i
$265$	−1.96684	+	3.40667i	−0.120822	+	0.209270i
$266$	−0.111320	+	0.192811i	−0.00682544	+	0.0118220i
$267$	13.7652	−	19.6366i	0.842417	−	1.20174i
$268$	8.17832	+	14.1653i	0.499570	+	0.865281i
$269$	−5.03384			−0.306919			−0.153459	−	0.988155i	$-0.549041\pi$
$269$	−5.03384			−0.306919			−0.153459	+	0.988155i	$0.549041\pi$
$270$	−0.986432	−	0.265996i	−0.0600323	−	0.0161880i
$271$	−5.05606			−0.307134			−0.153567	−	0.988138i	$-0.549076\pi$
$271$	−5.05606			−0.307134			−0.153567	+	0.988138i	$0.549076\pi$
$272$	−8.01696	−	13.8858i	−0.486100	−	0.841950i
$273$	−1.34194	+	1.91433i	−0.0812180	+	0.115861i
$274$	0.574572	−	0.995189i	0.0347112	−	0.0601215i
$275$	0.420339	−	0.728049i	0.0253474	−	0.0439030i
$276$	−26.7132	−	2.35138i	−1.60795	−	0.141536i
$277$	−1.94961	−	3.37683i	−0.117141	−	0.202894i	0.801493	−	0.598005i	$-0.204040\pi$
$277$	−1.94961	−	3.37683i	−0.117141	−	0.202894i	−0.918633	+	0.395111i	$0.870706\pi$
$278$	−1.97296			−0.118330
$279$	27.7115	+	4.91659i	1.65904	+	0.294349i
$280$	0.881949			0.0527066
$281$	11.8928	+	20.5989i	0.709465	+	1.22883i	0.965056	+	0.262044i	$0.0843965\pi$
$281$	11.8928	+	20.5989i	0.709465	+	1.22883i	−0.255591	+	0.966785i	$0.582270\pi$
$282$	−0.648353	−	1.39232i	−0.0386089	−	0.0829117i
$283$	11.3265	−	19.6182i	0.673293	−	1.16618i	−0.303671	−	0.952777i	$-0.598212\pi$
$283$	11.3265	−	19.6182i	0.673293	−	1.16618i	0.976965	−	0.213401i	$-0.0684542\pi$
$284$	6.69552	−	11.5970i	0.397306	−	0.688154i
$285$	−0.731164	−	1.57016i	−0.0433104	−	0.0930082i
$286$	−0.0985156	−	0.170634i	−0.00582535	−	0.0100898i
$287$	−6.68503			−0.394605
$288$	−6.79071	−	1.20481i	−0.400146	−	0.0709942i
$289$	1.09270			0.0642766
$290$	0.225494	+	0.390567i	0.0132415	+	0.0229349i
$291$	−3.23683	−	0.284915i	−0.189746	−	0.0167020i
$292$	−9.76163	+	16.9076i	−0.571256	+	0.989445i
$293$	−0.348467	+	0.603562i	−0.0203576	+	0.0352605i	−0.876025	−	0.482266i	$-0.839814\pi$
$293$	−0.348467	+	0.603562i	−0.0203576	+	0.0352605i	0.855667	+	0.517527i	$0.173147\pi$
$294$	1.11773	−	1.59449i	0.0651875	−	0.0929924i
$295$	−0.561004	−	0.971688i	−0.0326629	−	0.0565738i
$296$	−6.65647			−0.386900
$297$	−1.12388	−	4.22124i	−0.0652144	−	0.244941i
$298$	0.445426			0.0258028
$299$	4.70476	+	8.14888i	0.272083	+	0.471262i
$300$	−1.95000	+	2.78174i	−0.112583	+	0.160604i
$301$	−1.10503	+	1.91397i	−0.0636928	+	0.110319i
$302$	0.131182	−	0.227213i	0.00754866	−	0.0130747i
$303$	13.3693	+	1.17680i	0.768044	+	0.0676055i
$304$	−1.88477	−	3.26452i	−0.108099	−	0.187233i
$305$	8.83685			0.505996
$306$	1.61479	−	1.92029i	0.0923113	−	0.109776i
$307$	−10.0599			−0.574151			−0.287076	−	0.957908i	$-0.592683\pi$
$307$	−10.0599			−0.574151			−0.287076	+	0.957908i	$0.592683\pi$
$308$	0.933528	+	1.61692i	0.0531927	+	0.0921325i
$309$	1.53562	+	3.29772i	0.0873586	+	0.187601i
$310$	−0.922286	+	1.59745i	−0.0523823	+	0.0907289i
$311$	−7.54925	+	13.0757i	−0.428079	+	0.741454i	−0.996702	−	0.0811437i	$-0.974143\pi$
$311$	−7.54925	+	13.0757i	−0.428079	+	0.741454i	0.568624	+	0.822598i	$0.307476\pi$
$312$	0.678832	+	1.45778i	0.0384313	+	0.0825304i
$313$	−4.41737	−	7.65111i	−0.249685	−	0.432466i	0.713754	−	0.700397i	$-0.246994\pi$
$313$	−4.41737	−	7.65111i	−0.249685	−	0.432466i	−0.963438	+	0.267930i	$0.913660\pi$
$314$	−2.94185			−0.166018
$315$	−1.15846	−	3.19337i	−0.0652717	−	0.179926i
$316$	0.445412			0.0250564
$317$	−11.0290	−	19.1028i	−0.619450	−	1.07292i	−0.989586	−	0.143941i	$-0.954022\pi$
$317$	−11.0290	−	19.1028i	−0.619450	−	1.07292i	0.370136	−	0.928978i	$-0.379311\pi$
$318$	−1.33448	−	0.117465i	−0.0748338	−	0.00658709i
$319$	−0.964135	+	1.66993i	−0.0539812	+	0.0934982i
$320$	−3.54353	+	6.13758i	−0.198089	+	0.343101i
$321$	−0.769781	+	1.09812i	−0.0429650	+	0.0612912i
$322$	0.878740	+	1.52202i	0.0489703	+	0.0848190i
$323$	4.25355			0.236674
$324$	3.02837	+	17.3904i	0.168243	+	0.966131i
$325$	1.19201			0.0661206
$326$	1.15519	+	2.00085i	0.0639801	+	0.110817i
$327$	19.0783	−	27.2159i	1.05503	−	1.50505i
$328$	−2.29915	+	3.98225i	−0.126949	+	0.219883i
$329$	2.55337	−	4.42257i	0.140772	−	0.243824i
$330$	0.285195	+	0.0251037i	0.0156995	+	0.00138191i
$331$	−8.86834	−	15.3604i	−0.487448	−	0.844285i	0.512448	−	0.858718i	$-0.328739\pi$
$331$	−8.86834	−	15.3604i	−0.487448	−	0.844285i	−0.999896	+	0.0144336i	$0.995405\pi$
$332$	31.6727			1.73826
$333$	8.74341	+	24.1018i	0.479136	+	1.32077i
$334$	0.419784			0.0229696
$335$	4.16976	+	7.22223i	0.227818	+	0.394593i
$336$	−3.12088	−	6.70203i	−0.170258	−	0.365626i
$337$	−11.0452	+	19.1308i	−0.601669	+	1.04212i	0.390899	+	0.920433i	$0.372164\pi$
$337$	−11.0452	+	19.1308i	−0.601669	+	1.04212i	−0.992568	+	0.121688i	$0.961169\pi$
$338$	−1.13834	+	1.97167i	−0.0619176	+	0.107244i
$339$	−8.22532	−	17.6637i	−0.446738	−	0.959361i
$340$	−4.17133	−	7.22496i	−0.226222	−	0.391828i
$341$	−7.88676			−0.427092
$342$	0.379633	−	0.451456i	0.0205282	−	0.0244119i
$343$	14.4008			0.777571
$344$	0.760096	+	1.31652i	0.0409816	+	0.0709823i
$345$	−13.6199	−	1.19886i	−0.733270	−	0.0645446i
$346$	−0.190044	+	0.329165i	−0.0102168	+	0.0176960i
$347$	−0.599067	+	1.03761i	−0.0321596	+	0.0557021i	−0.881657	−	0.471890i	$-0.843572\pi$
$347$	−0.599067	+	1.03761i	−0.0321596	+	0.0557021i	0.849498	+	0.527592i	$0.176905\pi$
$348$	4.47272	−	6.38050i	0.239763	−	0.342031i
$349$	−3.97687	−	6.88814i	−0.212877	−	0.368714i	0.739737	−	0.672896i	$-0.234950\pi$
$349$	−3.97687	−	6.88814i	−0.212877	−	0.368714i	−0.952614	+	0.304183i	$0.901617\pi$
$350$	0.222639			0.0119006
$351$	4.38667	−	4.37274i	0.234143	−	0.233399i
$352$	1.93265			0.103011
$353$	−4.52044	−	7.82964i	−0.240599	−	0.416729i	0.720286	−	0.693677i	$-0.244010\pi$
$353$	−4.52044	−	7.82964i	−0.240599	−	0.416729i	−0.960885	+	0.276948i	$0.910677\pi$
$354$	0.219333	−	0.312887i	0.0116574	−	0.0166297i
$355$	3.41375	−	5.91278i	0.181183	−	0.313818i
$356$	13.5777	−	23.5172i	0.719615	−	1.24641i
$357$	8.31019	+	0.731487i	0.439822	+	0.0387144i
$358$	−0.757461	−	1.31196i	−0.0400331	−	0.0693393i
$359$	−32.8928			−1.73601			−0.868007	−	0.496551i	$-0.834599\pi$
$359$	−32.8928			−1.73601			−0.868007	+	0.496551i	$0.834599\pi$
$360$	−2.30070	−	0.408192i	−0.121258	−	0.0215136i
$361$	1.00000			0.0526316
$362$	−0.526911	−	0.912637i	−0.0276939	−	0.0479672i
$363$	−7.52606	−	16.1621i	−0.395016	−	0.848288i
$364$	−1.32366	+	2.29264i	−0.0693786	+	0.120167i
$365$	−4.97702	+	8.62045i	−0.260509	+	0.451215i
$366$	1.27040	+	2.72815i	0.0664046	+	0.142603i
$367$	−17.5092	−	30.3269i	−0.913975	−	1.58305i	−0.808395	−	0.588640i	$-0.799663\pi$
$367$	−17.5092	−	30.3269i	−0.913975	−	1.58305i	−0.105580	−	0.994411i	$-0.533670\pi$
$368$	−29.7562			−1.55115
$369$	17.4389	+	3.09403i	0.907835	+	0.161069i
$370$	−1.68036			−0.0873577
$371$	−2.22712	−	3.85749i	−0.115626	−	0.200271i
$372$	31.7473	+	2.79449i	1.64602	+	0.144888i
$373$	−2.21337	+	3.83367i	−0.114604	+	0.198500i	−0.917621	−	0.397456i	$-0.869893\pi$
$373$	−2.21337	+	3.83367i	−0.114604	+	0.198500i	0.803017	+	0.595956i	$0.203227\pi$
$374$	−0.351543	+	0.608890i	−0.0181779	+	0.0314850i
$375$	−0.994216	+	1.41829i	−0.0513411	+	0.0732400i
$376$	−1.75634	−	3.04207i	−0.0905764	−	0.156883i
$377$	−2.73411			−0.140814
$378$	0.819329	−	0.816726i	0.0421417	−	0.0420079i
$379$	19.8896			1.02166			0.510831	−	0.859681i	$-0.329338\pi$
$379$	19.8896			1.02166			0.510831	+	0.859681i	$0.329338\pi$
$380$	−0.980670	−	1.69857i	−0.0503073	−	0.0871348i
$381$	6.43650	−	9.18190i	0.329752	−	0.470403i
$382$	0.312278	−	0.540882i	0.0159776	−	0.0276739i
$383$	15.9079	−	27.5533i	0.812856	−	1.40791i	−0.0980018	−	0.995186i	$-0.531245\pi$
$383$	15.9079	−	27.5533i	0.812856	−	1.40791i	0.910857	−	0.412721i	$-0.135422\pi$
$384$	−10.3373	−	0.909916i	−0.527521	−	0.0464340i
$385$	0.475964	+	0.824394i	0.0242574	+	0.0420150i
$386$	−4.80571			−0.244604
$387$	3.76848	−	4.48144i	0.191563	−	0.227804i
$388$	−3.67950			−0.186798
$389$	7.38890	+	12.7980i	0.374632	+	0.648882i	0.990272	−	0.139146i	$-0.0444356\pi$
$389$	7.38890	+	12.7980i	0.374632	+	0.648882i	−0.615640	+	0.788028i	$0.711102\pi$
$390$	0.171364	+	0.368001i	0.00867736	+	0.0186345i
$391$	16.7884	−	29.0784i	0.849028	−	1.47056i
$392$	2.22674	−	3.85683i	0.112467	−	0.194799i
$393$	−13.3575	−	28.6850i	−0.673798	−	1.44697i
$394$	−2.40590	−	4.16715i	−0.121208	−	0.209938i
$395$	0.227096			0.0114264
$396$	−1.68690	−	4.65005i	−0.0847697	−	0.233674i
$397$	25.1011			1.25979			0.629894	−	0.776681i	$-0.283098\pi$
$397$	25.1011			1.25979			0.629894	+	0.776681i	$0.283098\pi$
$398$	0.812874	+	1.40794i	0.0407457	+	0.0705736i
$399$	1.95371	+	0.171971i	0.0978076	+	0.00860932i
$400$	−1.88477	+	3.26452i	−0.0942385	+	0.163226i
$401$	−19.9229	+	34.5075i	−0.994903	+	1.72322i	−0.410120	+	0.912031i	$0.634513\pi$
$401$	−19.9229	+	34.5075i	−0.994903	+	1.72322i	−0.584782	+	0.811190i	$0.698820\pi$
$402$	−1.63023	+	2.32558i	−0.0813084	+	0.115989i
$403$	−5.59136	−	9.68451i	−0.278525	−	0.482420i
$404$	15.1976			0.756110
$405$	1.54403	+	8.86656i	0.0767236	+	0.440583i
$406$	−0.510669			−0.0253441
$407$	−3.59232	−	6.22208i	−0.178065	−	0.308417i
$408$	3.29383	−	4.69878i	0.163069	−	0.232624i
$409$	−18.0611	+	31.2827i	−0.893062	+	1.54683i	−0.0568779	+	0.998381i	$0.518115\pi$
$409$	−18.0611	+	31.2827i	−0.893062	+	1.54683i	−0.836184	+	0.548448i	$0.815219\pi$
$410$	−0.580398	+	1.00528i	−0.0286638	+	0.0496472i
$411$	−10.0840	−	0.887623i	−0.497407	−	0.0437832i
$412$	2.05965	+	3.56742i	0.101472	+	0.175754i
$413$	1.27049			0.0625166
$414$	−1.58789	−	4.37714i	−0.0780407	−	0.215125i
$415$	16.1485			0.792698
$416$	1.37016	+	2.37319i	0.0671778	+	0.116355i
$417$	7.33678	+	15.7556i	0.359284	+	0.771554i
$418$	−0.0826469	+	0.143149i	−0.00404239	+	0.00700163i
$419$	10.4207	−	18.0491i	0.509083	−	0.881758i	−0.490862	−	0.871238i	$-0.663318\pi$
$419$	10.4207	−	18.0491i	0.509083	−	0.881758i	0.999945	−	0.0105202i	$-0.00334873\pi$
$420$	−1.62384	−	3.48715i	−0.0792351	−	0.170156i
$421$	−13.5755	−	23.5135i	−0.661630	−	1.14598i	−0.980187	−	0.198074i	$-0.936532\pi$
$421$	−13.5755	−	23.5135i	−0.661630	−	1.14598i	0.318557	−	0.947904i	$-0.396802\pi$
$422$	0.817428			0.0397918
$423$	−8.70777	+	10.3552i	−0.423386	+	0.503487i
$424$	−3.06386			−0.148794
$425$	−2.12678	−	3.68368i	−0.103164	−	0.178685i
$426$	2.31618	+	0.203877i	0.112219	+	0.00987789i
$427$	−5.00313	+	8.66568i	−0.242118	+	0.419361i
$428$	−0.759293	+	1.31513i	−0.0367018	+	0.0635694i
$429$	−0.996297	+	1.42126i	−0.0481017	+	0.0686188i
$430$	0.191878	+	0.332343i	0.00925320	+	0.0160270i
$431$	12.4188			0.598195			0.299097	−	0.954223i	$-0.403314\pi$
$431$	12.4188			0.598195			0.299097	+	0.954223i	$0.403314\pi$
$432$	5.03941	+	18.9277i	0.242459	+	0.910661i
$433$	−4.82404			−0.231829			−0.115914	−	0.993259i	$-0.536980\pi$
$433$	−4.82404			−0.231829			−0.115914	+	0.993259i	$0.536980\pi$
$434$	−1.04434	−	1.80884i	−0.0501297	−	0.0868273i
$435$	2.28044	−	3.25313i	0.109339	−	0.155976i
$436$	18.8184	−	32.5944i	0.901238	−	1.56099i
$437$	3.94693	−	6.83627i	0.188807	−	0.327023i
$438$	−3.37684	−	0.297240i	−0.161352	−	0.0142027i
$439$	6.27596	+	10.8703i	0.299535	+	0.518811i	0.976030	−	0.217637i	$-0.0698350\pi$
$439$	6.27596	+	10.8703i	0.299535	+	0.518811i	−0.676494	+	0.736448i	$0.736502\pi$
$440$	0.654785			0.0312157
$441$	−16.8897	−	2.99658i	−0.804271	−	0.142694i
$442$	−0.996913			−0.0474183
$443$	6.72949	+	11.6558i	0.319728	+	0.553785i	0.980431	−	0.196862i	$-0.0630752\pi$
$443$	6.72949	+	11.6558i	0.319728	+	0.553785i	−0.660703	+	0.750647i	$0.729742\pi$
$444$	12.2558	+	26.3191i	0.581636	+	1.24905i
$445$	6.92265	−	11.9904i	0.328165	−	0.568398i
$446$	1.38107	−	2.39209i	0.0653957	−	0.113269i
$447$	−1.65639	−	3.55707i	−0.0783447	−	0.168244i
$448$	−4.01246	−	6.94979i	−0.189571	−	0.328347i
$449$	11.9773			0.565245			0.282622	−	0.959231i	$-0.408796\pi$
$449$	11.9773			0.565245			0.282622	+	0.959231i	$0.408796\pi$
$450$	−0.580789	−	0.103044i	−0.0273786	−	0.00485754i
$451$	−4.96316			−0.233706
$452$	−11.0322	−	19.1083i	−0.518910	−	0.898778i
$453$	−2.30230	−	0.202655i	−0.108171	−	0.00952156i
$454$	0.296890	−	0.514229i	0.0139338	−	0.0241340i
$455$	−0.674874	+	1.16892i	−0.0316386	+	0.0547997i
$456$	0.774372	−	1.10467i	0.0362633	−	0.0517310i
$457$	−17.8102	−	30.8481i	−0.833125	−	1.44301i	−0.895548	−	0.444965i	$-0.853216\pi$
$457$	−17.8102	−	30.8481i	−0.833125	−	1.44301i	0.0624231	−	0.998050i	$-0.480117\pi$
$458$	−5.16691			−0.241434
$459$	−21.3399	−	5.75440i	−0.996060	−	0.268592i
$460$	−15.4825			−0.721877
$461$	18.2539	+	31.6166i	0.850167	+	1.47253i	0.881057	+	0.473010i	$0.156833\pi$
$461$	18.2539	+	31.6166i	0.850167	+	1.47253i	−0.0308896	+	0.999523i	$0.509834\pi$
$462$	−0.186085	+	0.265458i	−0.00865747	+	0.0123502i
$463$	9.96344	−	17.2572i	0.463040	−	0.802010i	−0.536070	−	0.844173i	$-0.680092\pi$
$463$	9.96344	−	17.2572i	0.463040	−	0.802010i	0.999111	+	0.0421638i	$0.0134251\pi$
$464$	4.32311	−	7.48785i	0.200695	−	0.347615i
$465$	16.1865	+	1.42479i	0.750632	+	0.0660728i
$466$	1.46374	+	2.53528i	0.0678065	+	0.117444i
$467$	−25.2050			−1.16635			−0.583174	−	0.812347i	$-0.698190\pi$
$467$	−25.2050			−1.16635			−0.583174	+	0.812347i	$0.698190\pi$
$468$	4.51407	−	5.36809i	0.208663	−	0.248140i
$469$	−9.44312			−0.436043
$470$	−0.443371	−	0.767941i	−0.0204512	−	0.0354225i
$471$	10.9398	+	23.4930i	0.504079	+	1.08250i
$472$	0.436954	−	0.756826i	0.0201124	−	0.0348357i
$473$	−0.820407	+	1.42099i	−0.0377223	+	0.0653370i
$474$	0.0326476	+	0.0701100i	0.00149955	+	0.00322026i
$475$	−0.500000	−	0.866025i	−0.0229416	−	0.0397360i
$476$	9.44668			0.432988
$477$	4.02444	+	11.0936i	0.184266	+	0.507943i
$478$	−4.43179			−0.202705
$479$	−2.25930	−	3.91322i	−0.103230	−	0.178800i	0.809784	−	0.586729i	$-0.199584\pi$
$479$	−2.25930	−	3.91322i	−0.103230	−	0.178800i	−0.913014	+	0.407929i	$0.866251\pi$
$480$	−3.96651	−	0.349144i	−0.181046	−	0.0159362i
$481$	5.09358	−	8.82235i	0.232247	−	0.402264i
$482$	1.05346	−	1.82465i	0.0479839	−	0.0831106i
$483$	8.88677	−	12.6773i	0.404362	−	0.576838i
$484$	−10.0943	−	17.4838i	−0.458832	−	0.794720i
$485$	−1.87601			−0.0851853
$486$	−2.51535	+	1.75135i	−0.114099	+	0.0794428i
$487$	−21.0129			−0.952187			−0.476094	−	0.879395i	$-0.657948\pi$
$487$	−21.0129			−0.952187			−0.476094	+	0.879395i	$0.657948\pi$
$488$	3.44141	+	5.96070i	0.155785	+	0.269828i
$489$	11.6825	−	16.6656i	0.528303	−	0.753644i
$490$	0.562118	−	0.973617i	0.0253939	−	0.0439835i
$491$	3.53236	−	6.11823i	0.159413	−	0.276112i	−0.775244	−	0.631662i	$-0.782373\pi$
$491$	3.53236	−	6.11823i	0.159413	−	0.276112i	0.934657	+	0.355550i	$0.115706\pi$
$492$	19.9787	+	1.75858i	0.900708	+	0.0792830i
$493$	4.87820	+	8.44929i	0.219703	+	0.380537i
$494$	−0.234372			−0.0105449
$495$	−0.860073	−	2.37085i	−0.0386574	−	0.106562i
$496$	35.3636			1.58787
$497$	3.86550	+	6.69524i	0.173391	+	0.300323i
$498$	2.32152	+	4.98542i	0.104030	+	0.223402i
$499$	−1.69697	+	2.93924i	−0.0759669	+	0.131579i	−0.901506	−	0.432766i	$-0.857538\pi$
$499$	−1.69697	+	2.93924i	−0.0759669	+	0.131579i	0.825539	+	0.564344i	$0.190871\pi$
$500$	−0.980670	+	1.69857i	−0.0438569	+	0.0759624i
$501$	−1.56104	−	3.35230i	−0.0697421	−	0.149770i
$502$	3.01633	+	5.22444i	0.134625	+	0.233178i
$503$	−35.7792			−1.59531			−0.797657	−	0.603111i	$-0.793928\pi$
$503$	−35.7792			−1.59531			−0.797657	+	0.603111i	$0.793928\pi$
$504$	1.70287	−	2.02503i	0.0758517	−	0.0902021i
$505$	7.74859			0.344808
$506$	0.652403	+	1.12999i	0.0290028	+	0.0502344i
$507$	19.9784	+	1.75856i	0.887271	+	0.0781002i
$508$	6.34880	−	10.9965i	0.281683	−	0.487889i
$509$	−14.2757	+	24.7262i	−0.632758	+	1.09597i	0.354227	+	0.935159i	$0.384744\pi$
$509$	−14.2757	+	24.7262i	−0.632758	+	1.09597i	−0.986985	+	0.160810i	$0.948589\pi$
$510$	0.831494	−	1.18616i	0.0368192	−	0.0525240i
$511$	−5.63565	−	9.76123i	−0.249307	−	0.431812i
$512$	−14.5379			−0.642490
$513$	−5.01695	−	1.35285i	−0.221504	−	0.0597296i
$514$	−1.59895			−0.0705268
$515$	1.05012	+	1.81887i	0.0462739	+	0.0801488i
$516$	3.80595	−	5.42933i	0.167548	−	0.239013i
$517$	1.89570	−	3.28345i	0.0833728	−	0.144406i
$518$	0.951364	−	1.64781i	0.0418005	−	0.0724006i
$519$	3.33535	+	0.293587i	0.146405	+	0.0128870i
$520$	0.464213	+	0.804041i	0.0203571	+	0.0352595i
$521$	14.6467			0.641685			0.320842	−	0.947133i	$-0.396034\pi$
$521$	14.6467			0.641685			0.320842	+	0.947133i	$0.396034\pi$
$522$	1.33216	+	0.236353i	0.0583071	+	0.0103449i
$523$	32.4473			1.41882			0.709410	−	0.704796i	$-0.248962\pi$
$523$	32.4473			1.41882			0.709410	+	0.704796i	$0.248962\pi$
$524$	−17.9157	−	31.0310i	−0.782652	−	1.35559i
$525$	−0.827922	−	1.77794i	−0.0361335	−	0.0775959i
$526$	1.01596	−	1.75970i	0.0442981	−	0.0767265i
$527$	−19.9522	+	34.5582i	−0.869131	+	1.50538i
$528$	−2.31704	−	4.97579i	−0.100836	−	0.216543i
$529$	−19.6564	−	34.0459i	−0.854628	−	1.48026i
$530$	−0.773440			−0.0335961
$531$	−3.31427	−	0.588019i	−0.143827	−	0.0255178i
$532$	2.22089			0.0962879
$533$	−3.51866	−	6.09450i	−0.152410	−	0.263982i
$534$	4.69693	+	0.413437i	0.203256	+	0.0178912i
$535$	−0.387130	+	0.670528i	−0.0167371	+	0.0289895i
$536$	−3.24773	+	5.62523i	−0.140281	+	0.242973i
$537$	−7.66027	+	10.9277i	−0.330565	+	0.471564i
$538$	−0.494876	−	0.857151i	−0.0213356	−	0.0369544i
$539$	4.80685			0.207046
$540$	2.62207	+	9.84834i	0.112836	+	0.423805i
$541$	−2.11702			−0.0910177			−0.0455089	−	0.998964i	$-0.514491\pi$
$541$	−2.11702			−0.0910177			−0.0455089	+	0.998964i	$0.514491\pi$
$542$	−0.497061	−	0.860934i	−0.0213506	−	0.0369803i
$543$	−5.32870	+	7.60159i	−0.228676	+	0.326216i
$544$	4.88929	−	8.46850i	0.209627	−	0.363084i
$545$	9.59466	−	16.6184i	0.410990	−	0.711856i
$546$	−0.457894	−	0.0403051i	−0.0195960	−	0.00172490i
$547$	4.87432	+	8.44258i	0.208411	+	0.360979i	0.951214	−	0.308531i	$-0.0998375\pi$
$547$	4.87432	+	8.44258i	0.208411	+	0.360979i	−0.742803	+	0.669510i	$0.766504\pi$
$548$	−11.4631			−0.489678
$549$	17.0622	−	20.2902i	0.728196	−	0.865963i
$550$	0.165294			0.00704816
$551$	1.14685	+	1.98641i	0.0488576	+	0.0846239i
$552$	−4.49545	−	9.65388i	−0.191339	−	0.410896i
$553$	−0.128574	+	0.222697i	−0.00546753	+	0.00947004i
$554$	0.383332	−	0.663950i	0.0162862	−	0.0282086i
$555$	6.24870	+	13.4190i	0.265243	+	0.569603i
$556$	9.84043	+	17.0441i	0.417327	+	0.722832i
$557$	0.847731			0.0359195			0.0179597	−	0.999839i	$-0.494283\pi$
$557$	0.847731			0.0359195			0.0179597	+	0.999839i	$0.494283\pi$
$558$	1.88713	+	5.20200i	0.0798885	+	0.220218i
$559$	−2.32652			−0.0984015
$560$	−2.13419	−	3.69652i	−0.0901859	−	0.156207i
$561$	6.16973	+	0.543078i	0.260486	+	0.0229288i
$562$	−2.33836	+	4.05015i	−0.0986376	+	0.170845i
$563$	6.25816	−	10.8394i	0.263750	−	0.456828i	−0.703485	−	0.710710i	$-0.748374\pi$
$563$	6.25816	−	10.8394i	0.263750	−	0.456828i	0.967235	+	0.253881i	$0.0817073\pi$
$564$	−8.79435	+	12.5455i	−0.370309	+	0.528259i
$565$	−5.62481	−	9.74246i	−0.236638	−	0.409869i
$566$	4.45404			0.187217
$567$	−9.56900	−	3.50583i	−0.401860	−	0.147231i
$568$	5.31778			0.223129
$569$	−18.2364	−	31.5864i	−0.764510	−	1.32417i	−0.940505	−	0.339780i	$-0.889647\pi$
$569$	−18.2364	−	31.5864i	−0.764510	−	1.32417i	0.175995	−	0.984391i	$-0.443686\pi$
$570$	0.195482	−	0.278863i	0.00818785	−	0.0116803i
$571$	13.0246	−	22.5593i	0.545063	−	0.944077i	−0.453540	−	0.891236i	$-0.649839\pi$
$571$	13.0246	−	22.5593i	0.545063	−	0.944077i	0.998603	−	0.0528409i	$-0.0168276\pi$
$572$	−0.982723	+	1.70213i	−0.0410897	+	0.0711695i
$573$	−5.48062	−	0.482420i	−0.228956	−	0.0201534i
$574$	−0.657204	−	1.13831i	−0.0274312	−	0.0475122i
$575$	−7.89385			−0.329196
$576$	7.25057	+	19.9867i	0.302107	+	0.832779i
$577$	11.5979			0.482826			0.241413	−	0.970423i	$-0.422389\pi$
$577$	11.5979			0.482826			0.241413	+	0.970423i	$0.422389\pi$
$578$	0.107423	+	0.186063i	0.00446822	+	0.00773919i
$579$	17.8708	+	38.3773i	0.742687	+	1.59490i
$580$	2.24937	−	3.89603i	0.0934001	−	0.161774i
$581$	−9.14273	+	15.8357i	−0.379305	+	0.656975i
$582$	−0.269698	−	0.579170i	−0.0111793	−	0.0240074i
$583$	−1.65348	−	2.86392i	−0.0684803	−	0.118611i
$584$	−7.75298			−0.320821
$585$	2.30152	−	2.73695i	0.0951563	−	0.113159i
$586$	−0.137031			−0.00566069
$587$	−16.7930	−	29.0864i	−0.693123	−	1.20052i	−0.970809	−	0.239853i	$-0.922901\pi$
$587$	−16.7930	−	29.0864i	−0.693123	−	1.20052i	0.277686	−	0.960672i	$-0.410432\pi$
$588$	−19.3494	−	1.70319i	−0.797957	−	0.0702385i
$589$	−4.69071	+	8.12455i	−0.193277	+	0.334766i
$590$	0.110304	−	0.191053i	0.00454116	−	0.00786552i
$591$	−24.3311	+	34.7092i	−1.00085	+	1.42775i
$592$	16.1077	+	27.8993i	0.662022	+	1.14666i
$593$	−39.1388			−1.60724			−0.803618	−	0.595145i	$-0.797095\pi$
$593$	−39.1388			−1.60724			−0.803618	+	0.595145i	$0.797095\pi$
$594$	0.608294	−	0.606362i	0.0249586	−	0.0248793i
$595$	4.81644			0.197455
$596$	−2.22163	−	3.84798i	−0.0910015	−	0.157619i
$597$	8.22066	−	11.7271i	0.336449	−	0.479957i
$598$	−0.925048	+	1.60223i	−0.0378280	+	0.0655201i
$599$	−0.155250	+	0.268900i	−0.00634333	+	0.0109870i	−0.869180	−	0.494496i	$-0.835352\pi$
$599$	−0.155250	+	0.268900i	−0.00634333	+	0.0109870i	0.862836	+	0.505483i	$0.168686\pi$
$600$	−1.34386	−	0.118290i	−0.0548628	−	0.00482919i
$601$	−13.8900	−	24.0583i	−0.566587	−	0.981357i	−0.996900	−	0.0786776i	$-0.974930\pi$
$601$	−13.8900	−	24.0583i	−0.566587	−	0.981357i	0.430313	−	0.902680i	$-0.358403\pi$
$602$	−0.434541			−0.0177106
$603$	24.6338	+	4.37055i	1.00317	+	0.177983i
$604$	−2.61716			−0.106491
$605$	−5.14663	−	8.91422i	−0.209240	−	0.362415i
$606$	1.11395	+	2.39218i	0.0452510	+	0.0971755i
$607$	−1.23436	+	2.13797i	−0.0501010	+	0.0867774i	−0.889988	−	0.455983i	$-0.849288\pi$
$607$	−1.23436	+	2.13797i	−0.0501010	+	0.0867774i	0.839887	+	0.542761i	$0.182621\pi$
$608$	1.14946	−	1.99092i	0.0466168	−	0.0807426i
$609$	1.89901	+	4.07809i	0.0769518	+	0.165252i
$610$	0.868749	+	1.50472i	0.0351746	+	0.0609242i
$611$	5.37587			0.217484
$612$	−24.6431	−	4.37220i	−0.996140	−	0.176736i
$613$	−21.2105			−0.856683			−0.428341	−	0.903617i	$-0.640902\pi$
$613$	−21.2105			−0.856683			−0.428341	+	0.903617i	$0.640902\pi$
$614$	−0.988991	−	1.71298i	−0.0399124	−	0.0691304i
$615$	10.1862	+	0.896622i	0.410748	+	0.0361553i
$616$	−0.370718	+	0.642102i	−0.0149366	+	0.0258710i
$617$	−21.4497	+	37.1519i	−0.863531	+	1.49568i	0.00496705	+	0.999988i	$0.498419\pi$
$617$	−21.4497	+	37.1519i	−0.863531	+	1.49568i	−0.868498	+	0.495692i	$0.834914\pi$
$618$	−0.410561	+	0.585680i	−0.0165152	+	0.0235595i
$619$	12.3354	+	21.3655i	0.495800	+	0.858751i	0.999988	−	0.00484287i	$-0.00154154\pi$
$619$	12.3354	+	21.3655i	0.495800	+	0.858751i	−0.504188	+	0.863594i	$0.668208\pi$
$620$	18.4002			0.738969
$621$	−29.0500	+	28.9577i	−1.16573	+	1.16203i
$622$	−2.96866			−0.119033
$623$	7.83875	+	13.5771i	0.314053	+	0.543956i
$624$	4.46732	−	6.37280i	0.178836	−	0.255116i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.868542	−	1.50436i	0.0347139	−	0.0601263i
$627$	1.45049	+	0.127676i	0.0579270	+	0.00509890i
$628$	14.6729	+	25.4143i	0.585514	+	1.01414i
$629$	−36.3519			−1.44944
$630$	0.429871	−	0.511199i	0.0171265	−	0.0203667i
$631$	−15.0408			−0.598764			−0.299382	−	0.954133i	$-0.596780\pi$
$631$	−15.0408			−0.598764			−0.299382	+	0.954133i	$0.596780\pi$
$632$	0.0884399	+	0.153182i	0.00351795	+	0.00609327i
$633$	−3.03975	−	6.52779i	−0.120819	−	0.259456i
$634$	2.16852	−	3.75598i	0.0861228	−	0.149169i
$635$	3.23697	−	5.60660i	0.128455	−	0.222491i
$636$	5.64115	+	12.1142i	0.223686	+	0.480361i
$637$	3.40784	+	5.90255i	0.135023	+	0.233867i
$638$	−0.379136			−0.0150101
$639$	−6.98501	−	19.2547i	−0.276323	−	0.761702i
$640$	−5.99130			−0.236827
$641$	−16.2195	−	28.0930i	−0.640633	−	1.10961i	−0.985292	−	0.170880i	$-0.945339\pi$
$641$	−16.2195	−	28.0930i	−0.640633	−	1.10961i	0.344659	−	0.938728i	$-0.387994\pi$
$642$	−0.262663	−	0.0231203i	−0.0103665	−	0.000912487i
$643$	19.6181	−	33.9795i	0.773661	−	1.34002i	−0.161883	−	0.986810i	$-0.551757\pi$
$643$	19.6181	−	33.9795i	0.773661	−	1.34002i	0.935544	−	0.353210i	$-0.114910\pi$
$644$	8.76570	−	15.1826i	0.345417	−	0.598280i
$645$	1.94048	−	2.76817i	0.0764064	−	0.108997i
$646$	0.418166	+	0.724285i	0.0164525	+	0.0284966i
$647$	−0.466894			−0.0183555			−0.00917774	−	0.999958i	$-0.502921\pi$
$647$	−0.466894			−0.0183555			−0.00917774	+	0.999958i	$0.502921\pi$
$648$	−5.37944	+	4.49448i	−0.211324	+	0.176560i
$649$	0.943248			0.0370257
$650$	0.117186	+	0.202972i	0.00459641	+	0.00796121i
$651$	−10.5615	+	15.0663i	−0.413936	+	0.590496i
$652$	11.5234	−	19.9591i	0.451290	−	0.781658i
$653$	−5.07710	+	8.79379i	−0.198682	+	0.344128i	−0.948101	−	0.317968i	$-0.896999\pi$
$653$	−5.07710	+	8.79379i	−0.198682	+	0.344128i	0.749419	+	0.662096i	$0.230333\pi$
$654$	6.50985	+	0.573017i	0.254555	+	0.0224067i
$655$	−9.13443	−	15.8213i	−0.356912	−	0.618189i
$656$	22.2545			0.868890
$657$	10.1837	+	28.0720i	0.397303	+	1.09519i
$658$	1.00409			0.0391434
$659$	−9.55129	−	16.5433i	−0.372065	−	0.644436i	0.617818	−	0.786321i	$-0.288017\pi$
$659$	−9.55129	−	16.5433i	−0.372065	−	0.644436i	−0.989883	+	0.141885i	$0.954684\pi$
$660$	−1.20558	−	2.58897i	−0.0469273	−	0.100775i
$661$	−9.74398	+	16.8771i	−0.378997	+	0.656442i	−0.990917	−	0.134478i	$-0.957064\pi$
$661$	−9.74398	+	16.8771i	−0.378997	+	0.656442i	0.611920	+	0.790920i	$0.290398\pi$
$662$	1.74369	−	3.02016i	0.0677704	−	0.117382i
$663$	3.70719	+	7.96111i	0.143975	+	0.309184i
$664$	6.28884	+	10.8926i	0.244054	+	0.422715i
$665$	1.13233			0.0439100
$666$	−3.24444	+	3.85825i	−0.125719	+	0.149504i
$667$	18.1062			0.701074
$668$	−2.09374	−	3.62646i	−0.0810091	−	0.140312i
$669$	−24.2384	−	2.13354i	−0.937112	−	0.0824874i
$670$	−0.819856	+	1.42003i	−0.0316738	+	0.0548607i
$671$	−3.71447	+	6.43366i	−0.143396	+	0.248369i
$672$	2.58809	−	3.69201i	0.0998377	−	0.142422i
$673$	−22.7959	−	39.4837i	−0.878718	−	1.52198i	−0.852749	−	0.522321i	$-0.825066\pi$
$673$	−22.7959	−	39.4837i	−0.878718	−	1.52198i	−0.0259689	−	0.999663i	$-0.508267\pi$
$674$	−4.34340			−0.167301
$675$	1.33688	+	5.02123i	0.0514565	+	0.193267i
$676$	22.7106			0.873485
$677$	12.2524	+	21.2218i	0.470897	+	0.815618i	0.999446	−	0.0332848i	$-0.0105968\pi$
$677$	12.2524	+	21.2218i	0.470897	+	0.815618i	−0.528548	+	0.848903i	$0.677264\pi$
$678$	2.19910	−	3.13710i	0.0844561	−	0.120480i
$679$	1.06214	−	1.83967i	0.0407610	−	0.0706002i
$680$	1.65650	−	2.86914i	0.0635238	−	0.110026i
$681$	−5.21055	−	0.458648i	−0.199669	−	0.0175754i
$682$	−0.775346	−	1.34294i	−0.0296895	−	0.0514238i
$683$	28.9302			1.10698			0.553492	−	0.832854i	$-0.313295\pi$
$683$	28.9302			1.10698			0.553492	+	0.832854i	$0.313295\pi$
$684$	−5.79354	−	1.02789i	−0.221522	−	0.0393025i
$685$	−5.84451			−0.223307
$686$	1.41574	+	2.45214i	0.0540533	+	0.0936230i
$687$	19.2140	+	41.2617i	0.733061	+	1.57423i
$688$	3.67864	−	6.37159i	0.140247	−	0.242915i
$689$	2.34449	−	4.06077i	0.0893179	−	0.154703i
$690$	−1.13483	−	2.43702i	−0.0432022	−	0.0927758i
$691$	−9.86480	−	17.0863i	−0.375274	−	0.649994i	0.615094	−	0.788454i	$-0.289118\pi$
$691$	−9.86480	−	17.0863i	−0.375274	−	0.649994i	−0.990368	+	0.138460i	$0.955785\pi$
$692$	3.79148			0.144131
$693$	2.81187	+	0.498884i	0.106814	+	0.0189510i
$694$	−0.235577			−0.00894237
$695$	5.01719	+	8.69003i	0.190313	+	0.329632i
$696$	3.08242	+	0.271324i	0.116839	+	0.0102845i
$697$	−12.5560	+	21.7476i	−0.475591	+	0.823749i
$698$	0.781931	−	1.35434i	0.0295965	−	0.0512627i
$699$	14.8029	−	21.1170i	0.559899	−	0.798717i
$700$	−1.11045	−	1.92335i	−0.0419709	−	0.0726958i
$701$	1.10195			0.0416201			0.0208100	−	0.999783i	$-0.493375\pi$
$701$	1.10195			0.0416201			0.0208100	+	0.999783i	$0.493375\pi$
$702$	1.17583	+	0.317069i	0.0443789	+	0.0119670i
$703$	−8.54624			−0.322328
$704$	−2.97897	−	5.15973i	−0.112274	−	0.194465i
$705$	−4.48384	+	6.39637i	−0.168871	+	0.240901i
$706$	0.888808	−	1.53946i	0.0334507	−	0.0579384i
$707$	−4.38700	+	7.59850i	−0.164990	+	0.285771i
$708$	−3.79694	−	0.334218i	−0.142698	−	0.0125607i
$709$	−15.7970	−	27.3612i	−0.593268	−	1.02757i	−0.993789	−	0.111283i	$-0.964504\pi$
$709$	−15.7970	−	27.3612i	−0.593268	−	1.02757i	0.400521	−	0.916288i	$-0.368829\pi$
$710$	1.34242			0.0503801
$711$	0.438476	−	0.521432i	0.0164442	−	0.0195552i
$712$	10.7838			0.404140
$713$	37.0278	+	64.1340i	1.38670	+	2.40184i
$714$	0.692417	+	1.48695i	0.0259131	+	0.0556478i
$715$	−0.501047	+	0.867838i	−0.0187381	+	0.0324553i
$716$	−7.55591	+	13.0872i	−0.282378	+	0.489092i
$717$	16.4804	+	35.3912i	0.615470	+	1.32171i
$718$	−3.23368	−	5.60090i	−0.120680	−	0.209024i
$719$	−21.1572			−0.789030			−0.394515	−	0.918890i	$-0.629087\pi$
$719$	−21.1572			−0.789030			−0.394515	+	0.918890i	$0.629087\pi$
$720$	3.85650	+	10.6307i	0.143723	+	0.396183i
$721$	−2.37818			−0.0885680
$722$	0.0983098	+	0.170278i	0.00365871	+	0.00633708i
$723$	−18.4887	−	1.62743i	−0.687603	−	0.0605248i
$724$	−5.25610	+	9.10383i	−0.195341	+	0.338341i
$725$	1.14685	−	1.98641i	0.0425931	−	0.0737734i
$726$	2.01215	−	2.87041i	0.0746779	−	0.106531i
$727$	13.7296	+	23.7804i	0.509203	+	0.881966i	0.999943	+	0.0106598i	$0.00339319\pi$
$727$	13.7296	+	23.7804i	0.509203	+	0.881966i	−0.490740	+	0.871306i	$0.663273\pi$
$728$	−1.05129			−0.0389634
$729$	23.3396	+	13.5743i	0.864430	+	0.502753i
$730$	−1.95716			−0.0724378
$731$	4.15098	+	7.18971i	0.153530	+	0.265921i
$732$	17.2318	−	24.5818i	0.636906	−	0.908571i
$733$	−3.48023	+	6.02794i	−0.128545	+	0.222647i	−0.923113	−	0.384528i	$-0.874364\pi$
$733$	−3.48023	+	6.02794i	−0.128545	+	0.222647i	0.794568	+	0.607175i	$0.207697\pi$
$734$	3.44266	−	5.96286i	0.127071	−	0.220093i
$735$	−9.86541	−	0.868382i	−0.363891	−	0.0320308i
$736$	−9.07367	−	15.7161i	−0.334460	−	0.579301i
$737$	−7.01085			−0.258248
$738$	1.18758	+	3.27363i	0.0437153	+	0.120504i
$739$	−4.18362			−0.153897			−0.0769484	−	0.997035i	$-0.524518\pi$
$739$	−4.18362			−0.153897			−0.0769484	+	0.997035i	$0.524518\pi$
$740$	8.38105	+	14.5164i	0.308093	+	0.533633i
$741$	0.871552	+	1.87164i	0.0320172	+	0.0687564i
$742$	0.437896	−	0.758459i	0.0160757	−	0.0278439i
$743$	−8.30048	+	14.3769i	−0.304515	+	0.527436i	−0.977153	−	0.212536i	$-0.931828\pi$
$743$	−8.30048	+	14.3769i	−0.304515	+	0.527436i	0.672638	+	0.739972i	$0.265161\pi$
$744$	5.34260	+	11.4731i	0.195869	+	0.420625i
$745$	−1.13271	−	1.96191i	−0.0414993	−	0.0718788i
$746$	−0.870385			−0.0318670
$747$	31.1795	−	37.0783i	1.14080	−	1.35662i
$748$	7.01350			0.256439
$749$	−0.438360	−	0.759262i	−0.0160173	−	0.0277428i
$750$	−0.339244	−	0.0298612i	−0.0123874	−	0.00109038i
$751$	−23.7249	+	41.0927i	−0.865733	+	1.49949i	0.000583727		1.00000i	$0.499814\pi$
$751$	−23.7249	+	41.0927i	−0.865733	+	1.49949i	−0.866317	+	0.499494i	$0.833519\pi$
$752$	−8.50018	+	14.7227i	−0.309970	+	0.536883i
$753$	30.5044	−	43.5157i	1.11164	−	1.58580i
$754$	−0.268790	−	0.465558i	−0.00978876	−	0.0169546i
$755$	−1.33437			−0.0485627
$756$	−11.1421	−	3.00452i	−0.405235	−	0.109273i
$757$	35.5056			1.29047			0.645237	−	0.763983i	$-0.276759\pi$
$757$	35.5056			1.29047			0.645237	+	0.763983i	$0.276759\pi$
$758$	1.95535	+	3.38676i	0.0710214	+	0.123013i
$759$	6.59780	−	9.41201i	0.239485	−	0.341634i
$760$	0.389439	−	0.674528i	0.0141264	−	0.0244677i
$761$	−15.1929	+	26.3149i	−0.550743	+	0.953915i	0.447478	+	0.894295i	$0.352322\pi$
$761$	−15.1929	+	26.3149i	−0.550743	+	0.953915i	−0.998221	+	0.0596199i	$0.981011\pi$
$762$	2.19624	+	0.193320i	0.0795615	+	0.00700324i
$763$	10.8644	+	18.8176i	0.393316	+	0.681244i
$764$	−6.23014			−0.225399
$765$	−12.5644	−	2.22919i	−0.454268	−	0.0805965i
$766$	6.25561			0.226024
$767$	0.668720	+	1.15826i	0.0241461	+	0.0418222i
$768$	9.50230	+	20.4060i	0.342885	+	0.736337i
$769$	−9.04622	+	15.6685i	−0.326215	+	0.565021i	−0.981757	−	0.190137i	$-0.939107\pi$
$769$	−9.04622	+	15.6685i	−0.326215	+	0.565021i	0.655543	+	0.755158i	$0.272440\pi$
$770$	−0.0935839	+	0.162092i	−0.00337253	+	0.00584140i
$771$	5.94598	+	12.7689i	0.214139	+	0.459859i
$772$	23.9692	+	41.5159i	0.862670	+	1.49419i
$773$	−5.49300			−0.197570			−0.0987848	−	0.995109i	$-0.531496\pi$
$773$	−5.49300			−0.197570			−0.0987848	+	0.995109i	$0.531496\pi$
$774$	1.13357	+	0.201118i	0.0407453	+	0.00722905i
$775$	9.38143			0.336991
$776$	−0.730591	−	1.26542i	−0.0262267	−	0.0454260i
$777$	−16.6968	−	1.46971i	−0.598996	−	0.0527254i
$778$	−1.45280	+	2.51633i	−0.0520855	+	0.0902148i
$779$	−2.95188	+	5.11281i	−0.105762	+	0.183185i
$780$	2.32441	−	3.31585i	0.0832271	−	0.118727i
$781$	2.86986	+	4.97075i	0.102692	+	0.177867i
$782$	6.60188			0.236083
$783$	−3.06641	−	11.5172i	−0.109584	−	0.411592i
$784$	−21.5535			−0.769769
$785$	7.48108	+	12.9576i	0.267011	+	0.462477i
$786$	3.57124	−	5.09451i	0.127382	−	0.181715i
$787$	5.60823	−	9.71373i	0.199912	−	0.346257i	−0.748588	−	0.663036i	$-0.769268\pi$
$787$	5.60823	−	9.71373i	0.199912	−	0.346257i	0.948500	+	0.316778i	$0.102601\pi$
$788$	−23.9996	+	41.5685i	−0.854951	+	1.48082i
$789$	−17.8306	−	1.56950i	−0.634785	−	0.0558757i
$790$	0.0223258	+	0.0386694i	0.000794315	+	0.00137579i
$791$	12.7383			0.452923
$792$	1.26426	−	1.50344i	0.0449235	−	0.0534226i
$793$	−10.5336			−0.374058
$794$	2.46769	+	4.27416i	0.0875749	+	0.151684i
$795$	2.87617	+	6.17651i	0.102007	+	0.219058i
$796$	8.10866	−	14.0446i	0.287404	−	0.497798i
$797$	8.52842	−	14.7717i	0.302092	−	0.523239i	−0.674517	−	0.738259i	$-0.735648\pi$
$797$	8.52842	−	14.7717i	0.302092	−	0.523239i	0.976610	+	0.215020i	$0.0689816\pi$
$798$	0.162786	+	0.349579i	0.00576255	+	0.0123750i
$799$	−9.59161	−	16.6132i	−0.339327	−	0.587731i
$800$	−2.29892			−0.0812791
$801$	−14.1647	−	39.0460i	−0.500486	−	1.37962i
$802$	−7.83447			−0.276645
$803$	−4.18407	−	7.24703i	−0.147653	−	0.255742i
$804$	28.2214	+	2.48413i	0.995292	+	0.0876085i
$805$	4.46924	−	7.74095i	0.157520	−	0.272833i
$806$	1.09937	−	1.90417i	0.0387237	−	0.0670714i
$807$	−5.00473	+	7.13943i	−0.176175	+	0.251320i
$808$	3.01760	+	5.22664i	0.106159	+	0.183872i
$809$	−24.7585			−0.870462			−0.435231	−	0.900319i	$-0.643333\pi$
$809$	−24.7585			−0.870462			−0.435231	+	0.900319i	$0.643333\pi$
$810$	−1.35798	+	1.13458i	−0.0477147	+	0.0398652i
$811$	21.8137			0.765982			0.382991	−	0.923752i	$-0.374894\pi$
$811$	21.8137			0.765982			0.382991	+	0.923752i	$0.374894\pi$
$812$	2.54704	+	4.41160i	0.0893836	+	0.154817i
$813$	−5.02682	+	7.17094i	−0.176298	+	0.251496i
$814$	0.706321	−	1.22338i	0.0247565	−	0.0428796i
$815$	5.87525	−	10.1762i	0.205801	−	0.356458i
$816$	−27.6646	−	2.43512i	−0.968455	−	0.0852463i
$817$	0.975886	+	1.69028i	0.0341419	+	0.0591356i
$818$	−7.10232			−0.248327
$819$	1.38089	+	3.80651i	0.0482521	+	0.133010i
$820$	11.5793			0.404366
$821$	10.1620	+	17.6011i	0.354655	+	0.614281i	0.987059	−	0.160358i	$-0.0512649\pi$
$821$	10.1620	+	17.6011i	0.354655	+	0.614281i	−0.632404	+	0.774639i	$0.717932\pi$
$822$	−0.840213	−	1.80434i	−0.0293058	−	0.0629336i
$823$	3.36752	−	5.83272i	0.117384	−	0.203316i	−0.801346	−	0.598201i	$-0.795882\pi$
$823$	3.36752	−	5.83272i	0.117384	−	0.203316i	0.918730	+	0.394885i	$0.129216\pi$
$824$	−0.817917	+	1.41667i	−0.0284935	+	0.0493522i
$825$	−0.614674	−	1.32000i	−0.0214002	−	0.0459565i
$826$	0.124901	+	0.216336i	0.00434588	+	0.00752728i
$827$	29.1337			1.01308			0.506538	−	0.862217i	$-0.330925\pi$
$827$	29.1337			1.01308			0.506538	+	0.862217i	$0.330925\pi$
$828$	−29.8936	+	35.5492i	−1.03888	+	1.23542i
$829$	−31.1381			−1.08147			−0.540736	−	0.841192i	$-0.681854\pi$
$829$	−31.1381			−1.08147			−0.540736	+	0.841192i	$0.681854\pi$
$830$	1.58755	+	2.74972i	0.0551048	+	0.0954443i
$831$	−6.72764	−	0.592187i	−0.233379	−	0.0205427i
$832$	4.22391	−	7.31603i	0.146438	−	0.253638i
$833$	12.1605	−	21.0626i	0.421337	−	0.729777i
$834$	−1.96155	+	2.79822i	−0.0679228	+	0.0968944i
$835$	−1.06750	−	1.84897i	−0.0369425	−	0.0639862i
$836$	1.64886			0.0570269
$837$	34.5243	−	34.4147i	1.19334	−	1.18955i
$838$	4.09782			0.141557
$839$	−8.01090	−	13.8753i	−0.276567	−	0.479028i	0.693962	−	0.720011i	$-0.255863\pi$
$839$	−8.01090	−	13.8753i	−0.276567	−	0.479028i	−0.970529	+	0.240983i	$0.922530\pi$
$840$	0.876848	−	1.25086i	0.0302541	−	0.0431587i
$841$	11.8695	−	20.5585i	0.409291	−	0.708914i
$842$	2.66921	−	4.62321i	0.0919872	−	0.159326i
$843$	41.0392	+	3.61239i	1.41346	+	0.124417i
$844$	−4.07705	−	7.06165i	−0.140338	−	0.243072i
$845$	11.5791			0.398334
$846$	−2.61932	−	0.464721i	−0.0900540	−	0.0159774i
$847$	11.6554			0.400485
$848$	7.41409	+	12.8416i	0.254601	+	0.440982i
$849$	−16.5631	−	35.5690i	−0.568445	−	1.22072i
$850$	0.418166	−	0.724285i	0.0143430	−	0.0248428i
$851$	−33.7314	+	58.4245i	−1.15630	+	2.00276i
$852$	−9.79104	−	21.0261i	−0.335436	−	0.720341i
$853$	−10.9211	−	18.9160i	−0.373933	−	0.647671i	0.616234	−	0.787563i	$-0.288658\pi$
$853$	−10.9211	−	18.9160i	−0.373933	−	0.647671i	−0.990167	+	0.139893i	$0.955324\pi$
$854$	−1.96743			−0.0673240
$855$	−2.95387	−	0.524077i	−0.101020	−	0.0179231i
$856$	−0.603053			−0.0206119
$857$	−17.7449	−	30.7351i	−0.606155	−	1.04989i	−0.991868	−	0.127272i	$-0.959378\pi$
$857$	−17.7449	−	30.7351i	−0.606155	−	1.04989i	0.385713	−	0.922619i	$-0.373955\pi$
$858$	−0.339954	−	0.0299237i	−0.0116058	−	0.00102158i
$859$	8.55245	−	14.8133i	0.291806	−	0.505423i	−0.682431	−	0.730950i	$-0.739077\pi$
$859$	8.55245	−	14.8133i	0.291806	−	0.505423i	0.974237	+	0.225527i	$0.0724105\pi$
$860$	1.91405	−	3.31522i	0.0652684	−	0.113048i
$861$	−6.64636	+	9.48128i	−0.226507	+	0.323121i
$862$	1.22090	+	2.11465i	0.0415838	+	0.0720253i
$863$	−31.8857			−1.08540			−0.542700	−	0.839926i	$-0.682598\pi$
$863$	−31.8857			−1.08540			−0.542700	+	0.839926i	$0.682598\pi$
$864$	−8.46020	+	8.43333i	−0.287822	+	0.286908i
$865$	1.93311			0.0657277
$866$	−0.474251	−	0.821426i	−0.0161157	−	0.0279132i
$867$	1.08638	−	1.54976i	0.0368955	−	0.0526327i
$868$	−10.4176	+	18.0438i	−0.353595	+	0.612445i
$869$	−0.0954573	+	0.165337i	−0.00323817	+	0.00560867i
$870$	0.778126	+	0.0684929i	0.0263809	+	0.00232213i
$871$	−4.97038	−	8.60894i	−0.168415	−	0.291703i
$872$	14.9461			0.506140
$873$	−3.62220	+	4.30748i	−0.122593	+	0.145786i
$874$	1.55209			0.0525001
$875$	−0.566167	−	0.980630i	−0.0191399	−	0.0331513i
$876$	14.2747	+	30.6546i	0.482298	+	1.03572i
$877$	−27.9659	+	48.4384i	−0.944342	+	1.63565i	−0.187278	+	0.982307i	$0.559967\pi$
$877$	−27.9659	+	48.4384i	−0.944342	+	1.63565i	−0.757064	+	0.653341i	$0.773367\pi$
$878$	−1.23398	+	2.13731i	−0.0416447	+	0.0721308i
$879$	0.509573	+	1.09430i	0.0171875	+	0.0369097i
$880$	−1.58448	−	2.74441i	−0.0534130	−	0.0925140i
$881$	−12.3650			−0.416589			−0.208294	−	0.978066i	$-0.566791\pi$
$881$	−12.3650			−0.416589			−0.208294	+	0.978066i	$0.566791\pi$
$882$	−1.15017	−	3.17053i	−0.0387283	−	0.106757i
$883$	−25.9946			−0.874787			−0.437394	−	0.899270i	$-0.644098\pi$
$883$	−25.9946			−0.874787			−0.437394	+	0.899270i	$0.644098\pi$
$884$	4.97225	+	8.61219i	0.167235	+	0.289659i
$885$	−1.93589	−	0.170403i	−0.0650742	−	0.00572803i
$886$	−1.32315	+	2.29176i	−0.0444521	+	0.0769933i
$887$	20.5788	−	35.6435i	0.690969	−	1.19679i	−0.280552	−	0.959839i	$-0.590517\pi$
$887$	20.5788	−	35.6435i	0.690969	−	1.19679i	0.971521	−	0.236954i	$-0.0761492\pi$
$888$	−6.61797	+	9.44079i	−0.222085	+	0.316812i
$889$	3.66533	+	6.34854i	0.122931	+	0.212923i
$890$	2.72226			0.0912503
$891$	−7.10431	−	2.60283i	−0.238003	−	0.0871982i
$892$	−27.5533			−0.922551
$893$	−2.25497	−	3.90572i	−0.0754596	−	0.130700i
$894$	0.442850	−	0.631742i	0.0148111	−	0.0211286i
$895$	−3.85242	+	6.67259i	−0.128772	+	0.223040i
$896$	3.39207	−	5.87525i	0.113321	−	0.196278i
$897$	16.2350	+	1.42905i	0.542070	+	0.0477146i
$898$	1.17749	+	2.03947i	0.0392933	+	0.0680580i
$899$	−21.5183			−0.717674
$900$	2.00659	+	5.53130i	0.0668863	+	0.184377i
$901$	−16.7321			−0.557428
$902$	−0.487928	−	0.845116i	−0.0162462	−	0.0281393i
$903$	1.61592	+	3.47014i	0.0537743	+	0.115479i
$904$	4.38104	−	7.58819i	0.145711	−	0.252379i
$905$	−2.67985	+	4.64164i	−0.0890813	+	0.154293i
$906$	−0.191831	−	0.411952i	−0.00637315	−	0.0136862i
$907$	24.1101	+	41.7600i	0.800564	+	1.38662i	0.919245	+	0.393685i	$0.128800\pi$
$907$	24.1101	+	41.7600i	0.800564	+	1.38662i	−0.118682	+	0.992932i	$0.537867\pi$
$908$	−5.92314			−0.196566
$909$	14.9610	−	17.7914i	0.496224	−	0.590105i
$910$	−0.265387			−0.00879750
$911$	−2.57332	−	4.45712i	−0.0852578	−	0.147671i	0.820243	−	0.572015i	$-0.193838\pi$
$911$	−2.57332	−	4.45712i	−0.0852578	−	0.147671i	−0.905501	+	0.424344i	$0.860505\pi$
$912$	−6.50389	−	0.572491i	−0.215365	−	0.0189571i
$913$	−6.78784	+	11.7569i	−0.224645	+	0.389096i
$914$	3.50183	−	6.06535i	0.115830	−	0.200624i
$915$	8.78573	−	12.5332i	0.290447	−	0.414334i
$916$	25.7707	+	44.6362i	0.851489	+	1.47482i
$917$	20.6865			0.683127
$918$	−1.11807	−	4.19942i	−0.0369019	−	0.138601i
$919$	−22.9141			−0.755867			−0.377934	−	0.925833i	$-0.623365\pi$
$919$	−22.9141			−0.755867			−0.377934	+	0.925833i	$0.623365\pi$
$920$	−3.07417	−	5.32462i	−0.101352	−	0.175548i
$921$	−10.0018	+	14.2679i	−0.329569	+	0.470143i
$922$	−3.58907	+	6.21645i	−0.118200	+	0.204728i
$923$	−4.06921	+	7.04807i	−0.133940	+	0.231990i
$924$	3.22138	+	0.283555i	0.105976	+	0.00932829i
$925$	4.27312	+	7.40126i	0.140499	+	0.243352i
$926$	3.91802			0.128754
$927$	6.20385	+	1.10069i	0.203761	+	0.0361514i
$928$	5.27305			0.173096
$929$	9.17626	+	15.8937i	0.301063	+	0.521457i	0.976377	−	0.216074i	$-0.0693252\pi$
$929$	9.17626	+	15.8937i	0.301063	+	0.521457i	−0.675314	+	0.737530i	$0.735992\pi$
$930$	1.34869	+	2.89627i	0.0442251	+	0.0949725i
$931$	2.85891	−	4.95178i	0.0936970	−	0.162288i
$932$	14.6013	−	25.2901i	0.478281	−	0.828406i
$933$	11.0395	+	23.7070i	0.361416	+	0.776134i
$934$	−2.47790	−	4.29185i	−0.0810794	−	0.140434i
$935$	3.57587			0.116943
$936$	2.74245	+	0.486567i	0.0896398	+	0.0159039i
$937$	−18.0297			−0.589004			−0.294502	−	0.955651i	$-0.595154\pi$
$937$	−18.0297			−0.589004			−0.294502	+	0.955651i	$0.595154\pi$
$938$	−0.928351	−	1.60795i	−0.0303117	−	0.0525015i
$939$	−15.2433	−	1.34176i	−0.497446	−	0.0437866i
$940$	−4.42276	+	7.66044i	−0.144254	+	0.249856i
$941$	25.5415	−	44.2391i	0.832628	−	1.44215i	−0.0633183	−	0.997993i	$-0.520168\pi$
$941$	25.5415	−	44.2391i	0.832628	−	1.44215i	0.895947	−	0.444161i	$-0.146498\pi$
$942$	−2.92484	+	4.17239i	−0.0952963	+	0.135944i
$943$	23.3017	+	40.3597i	0.758808	+	1.31429i
$944$	−4.22945			−0.137657
$945$	−5.68087	−	1.53187i	−0.184799	−	0.0498318i
$946$	−0.322616			−0.0104892
$947$	3.05498	+	5.29138i	0.0992735	+	0.171947i	0.911384	−	0.411557i	$-0.135015\pi$
$947$	3.05498	+	5.29138i	0.0992735	+	0.171947i	−0.812111	+	0.583503i	$0.801681\pi$
$948$	0.442836	−	0.631722i	0.0143826	−	0.0205174i
$949$	5.93264	−	10.2756i	0.192582	−	0.333561i
$950$	0.0983098	−	0.170278i	0.00318959	−	0.00552454i
$951$	−38.0584	−	3.35001i	−1.23413	−	0.108632i
$952$	1.87571	+	3.24882i	0.0607921	+	0.105295i
$953$	34.1359			1.10577			0.552885	−	0.833258i	$-0.313527\pi$
$953$	34.1359			1.10577			0.552885	+	0.833258i	$0.313527\pi$
$954$	−1.49336	+	1.77589i	−0.0483492	+	0.0574964i
$955$	−3.17647			−0.102788
$956$	22.1042	+	38.2856i	0.714901	+	1.23824i
$957$	1.40988	+	3.02769i	0.0455750	+	0.0978714i
$958$	0.444222	−	0.769416i	0.0143522	−	0.0248587i
$959$	3.30897	−	5.73130i	0.106852	−	0.185073i
$960$	5.18181	+	11.1278i	0.167242	+	0.359149i
$961$	−28.5056	−	49.3731i	−0.919535	−	1.59268i
$962$	2.00300			0.0645792
$963$	0.792122	+	2.18354i	0.0255258	+	0.0703636i
$964$	−21.0172			−0.676919
$965$	12.2208	+	21.1671i	0.393402	+	0.681393i
$966$	3.03232	+	0.266914i	0.0975633	+	0.00858781i
$967$	7.68071	−	13.3034i	0.246995	−	0.427808i	−0.715696	−	0.698412i	$-0.753890\pi$
$967$	7.68071	−	13.3034i	0.246995	−	0.427808i	0.962691	+	0.270604i	$0.0872235\pi$
$968$	4.00859	−	6.94309i	0.128841	−	0.223159i
$969$	4.22895	−	6.03275i	0.135853	−	0.193800i
$970$	−0.184430	−	0.319443i	−0.00592170	−	0.0102567i
$971$	26.4881			0.850043			0.425022	−	0.905183i	$-0.360266\pi$
$971$	26.4881			0.850043			0.425022	+	0.905183i	$0.360266\pi$
$972$	27.6754	+	12.9947i	0.887687	+	0.416804i
$973$	−11.3623			−0.364258
$974$	−2.06578	−	3.57803i	−0.0661918	−	0.114648i
$975$	1.18511	−	1.69061i	0.0379539	−	0.0541427i
$976$	16.6554	−	28.8480i	0.533127	−	0.923403i
$977$	−18.7759	+	32.5208i	−0.600695	+	1.04043i	0.392021	+	0.919956i	$0.371776\pi$
$977$	−18.7759	+	32.5208i	−0.600695	+	1.04043i	−0.992716	+	0.120478i	$0.961557\pi$
$978$	3.98628	+	0.350885i	0.127467	+	0.0112201i
$979$	5.81972	+	10.0801i	0.185999	+	0.322160i
$980$	−11.2146			−0.358237
$981$	−19.6320	−	54.1170i	−0.626802	−	1.72782i
$982$	1.38906			0.0443268
$983$	6.67405	+	11.5598i	0.212869	+	0.368700i	0.952611	−	0.304190i	$-0.0983859\pi$
$983$	6.67405	+	11.5598i	0.212869	+	0.368700i	−0.739742	+	0.672890i	$0.765053\pi$
$984$	3.36212	+	7.22007i	0.107180	+	0.230167i
$985$	−12.2363	+	21.1939i	−0.389882	+	0.675295i
$986$	−0.959151	+	1.66130i	−0.0305456	+	0.0529065i
$987$	−3.73387	−	8.01841i	−0.118850	−	0.255229i
$988$	1.16896	+	2.02471i	0.0371897	+	0.0644145i
$989$	15.4070			0.489914
$990$	0.319149	−	0.379529i	0.0101432	−	0.0120622i
$991$	35.6425			1.13222			0.566111	−	0.824329i	$-0.308448\pi$
$991$	35.6425			1.13222			0.566111	+	0.824329i	$0.308448\pi$
$992$	10.7836	+	18.6777i	0.342379	+	0.593018i
$993$	−30.6025	−	2.69372i	−0.971141	−	0.0854827i
$994$	−0.760034	+	1.31642i	−0.0241068	+	0.0417542i
$995$	4.13424	−	7.16072i	0.131064	−	0.227010i
$996$	31.4895	−	44.9209i	0.997782	−	1.42337i
$997$	19.7964	+	34.2884i	0.626958	+	1.08592i	0.988159	+	0.153435i	$0.0490336\pi$
$997$	19.7964	+	34.2884i	0.626958	+	1.08592i	−0.361201	+	0.932488i	$0.617633\pi$
$998$	−0.667316			−0.0211235
$999$	42.8761	+	11.5617i	1.35654	+	0.365797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.i.d.571.13	yes	46
9.4	even	3		7695.2.a.w.1.11		23
9.5	odd	6		7695.2.a.x.1.13		23
9.7	even	3	inner	855.2.i.d.286.13	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.i.d.286.13	✓	46	9.7	even	3	inner
855.2.i.d.571.13	yes	46	1.1	even	1	trivial
7695.2.a.w.1.11		23	9.4	even	3
7695.2.a.x.1.13		23	9.5	odd	6

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0983098 + 0.170278i) q^{2} +(0.994216 - 1.41829i) q^{3} +(0.980670 - 1.69857i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.339244 + 0.0298612i) q^{6} +(0.566167 + 0.980630i) q^{7} +0.778878 q^{8} +(-1.02307 - 2.82016i) q^{9} +O(q^{10})\)	\(q+(0.0983098 + 0.170278i) q^{2} +(0.994216 - 1.41829i) q^{3} +(0.980670 - 1.69857i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.339244 + 0.0298612i) q^{6} +(0.566167 + 0.980630i) q^{7} +0.778878 q^{8} +(-1.02307 - 2.82016i) q^{9} +0.196620 q^{10} +(0.420339 + 0.728049i) q^{11} +(-1.43406 - 3.07962i) q^{12} +(-0.596003 + 1.03231i) q^{13} +(-0.111320 + 0.192811i) q^{14} +(-0.731164 - 1.57016i) q^{15} +(-1.88477 - 3.26452i) q^{16} +4.25355 q^{17} +(0.379633 - 0.451456i) q^{18} +1.00000 q^{19} +(-0.980670 - 1.69857i) q^{20} +(1.95371 + 0.171971i) q^{21} +(-0.0826469 + 0.143149i) q^{22} +(3.94693 - 6.83627i) q^{23} +(0.774372 - 1.10467i) q^{24} +(-0.500000 - 0.866025i) q^{25} -0.234372 q^{26} +(-5.01695 - 1.35285i) q^{27} +2.22089 q^{28} +(1.14685 + 1.98641i) q^{29} +(0.195482 - 0.278863i) q^{30} +(-4.69071 + 8.12455i) q^{31} +(1.14946 - 1.99092i) q^{32} +(1.45049 + 0.127676i) q^{33} +(0.418166 + 0.724285i) q^{34} +1.13233 q^{35} +(-5.79354 - 1.02789i) q^{36} -8.54624 q^{37} +(0.0983098 + 0.170278i) q^{38} +(0.871552 + 1.87164i) q^{39} +(0.389439 - 0.674528i) q^{40} +(-2.95188 + 5.11281i) q^{41} +(0.162786 + 0.349579i) q^{42} +(0.975886 + 1.69028i) q^{43} +1.64886 q^{44} +(-2.95387 - 0.524077i) q^{45} +1.55209 q^{46} +(-2.25497 - 3.90572i) q^{47} +(-6.50389 - 0.572491i) q^{48} +(2.85891 - 4.95178i) q^{49} +(0.0983098 - 0.170278i) q^{50} +(4.22895 - 6.03275i) q^{51} +(1.16896 + 2.02471i) q^{52} -3.93369 q^{53} +(-0.262857 - 0.987273i) q^{54} +0.840678 q^{55} +(0.440975 + 0.763791i) q^{56} +(0.994216 - 1.41829i) q^{57} +(-0.225494 + 0.390567i) q^{58} +(0.561004 - 0.971688i) q^{59} +(-3.38406 - 0.297875i) q^{60} +(4.41842 + 7.65293i) q^{61} -1.84457 q^{62} +(2.18631 - 2.59994i) q^{63} -7.08706 q^{64} +(0.596003 + 1.03231i) q^{65} +(0.120857 + 0.259538i) q^{66} +(-4.16976 + 7.22223i) q^{67} +(4.17133 - 7.22496i) q^{68} +(-5.77170 - 12.3946i) q^{69} +(0.111320 + 0.192811i) q^{70} +6.82749 q^{71} +(-0.796847 - 2.19656i) q^{72} -9.95404 q^{73} +(-0.840180 - 1.45523i) q^{74} +(-1.72538 - 0.151873i) q^{75} +(0.980670 - 1.69857i) q^{76} +(-0.475964 + 0.824394i) q^{77} +(-0.233016 + 0.332406i) q^{78} +(0.113548 + 0.196671i) q^{79} -3.76954 q^{80} +(-6.90665 + 5.77045i) q^{81} -1.16080 q^{82} +(8.07424 + 13.9850i) q^{83} +(2.20805 - 3.14986i) q^{84} +(2.12678 - 3.68368i) q^{85} +(-0.191878 + 0.332343i) q^{86} +(3.95752 + 0.348352i) q^{87} +(0.327393 + 0.567061i) q^{88} +13.8453 q^{89} +(-0.201156 - 0.554500i) q^{90} -1.34975 q^{91} +(-7.74126 - 13.4083i) q^{92} +(6.85936 + 14.7303i) q^{93} +(0.443371 - 0.767941i) q^{94} +(0.500000 - 0.866025i) q^{95} +(-1.68089 - 3.60967i) q^{96} +(-0.938006 - 1.62467i) q^{97} +1.12424 q^{98} +(1.62318 - 1.93027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9 + 6 * q^10 - q^11 + 9 * q^12 - 11 * q^13 - 3 * q^14 + q^15 - 45 * q^16 - 30 * q^17 - 18 * q^18 + 46 * q^19 + 29 * q^20 - 2 * q^21 - 5 * q^22 + 13 * q^23 - 6 * q^24 - 23 * q^25 - 12 * q^26 + 23 * q^27 + 56 * q^28 + 2 * q^29 + 6 * q^30 - 16 * q^31 + 25 * q^32 + 19 * q^33 - 18 * q^34 - 20 * q^35 - 5 * q^36 + 58 * q^37 + 3 * q^38 + 32 * q^39 - 6 * q^40 + 14 * q^41 - 67 * q^42 - 34 * q^43 + 64 * q^44 - 7 * q^45 - 4 * q^46 + 22 * q^47 + 89 * q^48 - 61 * q^49 + 3 * q^50 - 38 * q^51 - 20 * q^52 - 70 * q^53 - 91 * q^54 - 2 * q^55 - 26 * q^56 + 2 * q^57 - 23 * q^58 - 15 * q^59 + 3 * q^60 - 32 * q^61 + 6 * q^62 - 31 * q^63 + 164 * q^64 + 11 * q^65 + 54 * q^66 - 16 * q^67 + 26 * q^68 - 19 * q^69 + 3 * q^70 + 50 * q^71 + 22 * q^72 + 82 * q^73 + 9 * q^74 - q^75 - 29 * q^76 + 18 * q^77 - 41 * q^78 - 11 * q^79 - 90 * q^80 + 8 * q^81 + 60 * q^82 + 26 * q^83 + 123 * q^84 - 15 * q^85 - 15 * q^86 - 26 * q^87 - 22 * q^88 + 40 * q^89 - 12 * q^90 + 116 * q^91 + 2 * q^92 + 42 * q^93 - 36 * q^94 + 23 * q^95 - 48 * q^96 - 50 * q^97 - 24 * q^98 - 29 * q^99

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