LMFDB - Embedded newform 231.2.y.b.214.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			214.2
Character	$\chi$	$=$	231.214
Dual form			231.2.y.b.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49404 + 1.65930i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.312065 - 2.96910i) q^{4} +(-1.00537 + 0.213698i) q^{5} +(-0.689977 + 2.12353i) q^{6} +(2.49708 + 0.874397i) q^{7} +(1.78011 + 1.29333i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-1.49404 + 1.65930i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.312065 - 2.96910i) q^{4} +(-1.00537 + 0.213698i) q^{5} +(-0.689977 + 2.12353i) q^{6} +(2.49708 + 0.874397i) q^{7} +(1.78011 + 1.29333i) q^{8} +(0.669131 - 0.743145i) q^{9} +(1.14748 - 1.98749i) q^{10} +(-0.216549 + 3.30955i) q^{11} +(-1.49273 - 2.58548i) q^{12} +(1.56619 + 4.82025i) q^{13} +(-5.18164 + 2.83703i) q^{14} +(-0.831533 + 0.604144i) q^{15} +(1.03484 - 0.219963i) q^{16} +(1.74191 + 1.93458i) q^{17} +(0.233393 + 2.22058i) q^{18} +(0.140718 - 1.33884i) q^{19} +(0.948233 + 2.91836i) q^{20} +(2.63685 - 0.216854i) q^{21} +(-5.16801 - 5.30393i) q^{22} +(0.946580 + 1.63952i) q^{23} +(2.15226 + 0.457476i) q^{24} +(-3.60262 + 1.60399i) q^{25} +(-10.3382 - 4.60287i) q^{26} +(0.309017 - 0.951057i) q^{27} +(1.81692 - 7.68697i) q^{28} +(3.25868 - 2.36757i) q^{29} +(0.239888 - 2.28238i) q^{30} +(-3.21210 - 0.682752i) q^{31} +(-3.38146 + 5.85686i) q^{32} +(1.14829 + 3.11150i) q^{33} -5.81254 q^{34} +(-2.69735 - 0.345471i) q^{35} +(-2.41528 - 1.75481i) q^{36} +(-7.36469 - 3.27897i) q^{37} +(2.01131 + 2.23379i) q^{38} +(3.39136 + 3.76649i) q^{39} +(-2.06605 - 0.919867i) q^{40} +(-0.828434 - 0.601893i) q^{41} +(-3.57974 + 4.69932i) q^{42} +9.19303 q^{43} +(9.89396 - 0.389839i) q^{44} +(-0.513916 + 0.890128i) q^{45} +(-4.13470 - 0.878858i) q^{46} +(1.03382 - 9.83610i) q^{47} +(0.855911 - 0.621855i) q^{48} +(5.47086 + 4.36689i) q^{49} +(2.72097 - 8.37428i) q^{50} +(2.37818 + 1.05883i) q^{51} +(13.8230 - 6.15442i) q^{52} +(11.9272 + 2.53519i) q^{53} +(1.11641 + 1.93367i) q^{54} +(-0.489532 - 3.37360i) q^{55} +(3.31421 + 4.78607i) q^{56} +(-0.416005 - 1.28033i) q^{57} +(-0.940093 + 8.94438i) q^{58} +(-0.645139 - 6.13808i) q^{59} +(2.05326 + 2.28037i) q^{60} +(3.41290 - 0.725434i) q^{61} +(5.93191 - 4.30978i) q^{62} +(2.32068 - 1.27061i) q^{63} +(-4.01240 - 12.3489i) q^{64} +(-2.60468 - 4.51144i) q^{65} +(-6.87852 - 2.74336i) q^{66} +(-0.556014 + 0.963044i) q^{67} +(5.20038 - 5.77561i) q^{68} +(1.53160 + 1.11277i) q^{69} +(4.60320 - 3.95958i) q^{70} +(-2.29639 + 7.06755i) q^{71} +(2.15226 - 0.457476i) q^{72} +(-1.15674 - 11.0057i) q^{73} +(16.4440 - 7.32133i) q^{74} +(-2.63876 + 2.93064i) q^{75} -4.01908 q^{76} +(-3.43460 + 8.07487i) q^{77} -11.3166 q^{78} +(-9.35663 + 10.3916i) q^{79} +(-0.993397 + 0.442289i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(2.23644 - 0.475370i) q^{82} +(1.44739 - 4.45461i) q^{83} +(-1.46673 - 7.76140i) q^{84} +(-2.16468 - 1.57273i) q^{85} +(-13.7348 + 15.2540i) q^{86} +(2.01397 - 3.48830i) q^{87} +(-4.66581 + 5.61130i) q^{88} +(-9.17730 - 15.8955i) q^{89} +(-0.709180 - 2.18263i) q^{90} +(-0.303894 + 13.4060i) q^{91} +(4.57252 - 3.32213i) q^{92} +(-3.21210 + 0.682752i) q^{93} +(14.7765 + 16.4110i) q^{94} +(0.144635 + 1.37611i) q^{95} +(-0.706917 + 6.72587i) q^{96} +(-2.19712 - 6.76203i) q^{97} +(-15.4197 + 2.55350i) q^{98} +(2.31457 + 2.37545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.49404	+	1.65930i	−1.05645	+	1.17330i	−0.0720411	+	0.997402i	$0.522951\pi$
$2$	−1.49404	+	1.65930i	−1.05645	+	1.17330i	−0.984407	+	0.175903i	$0.943715\pi$
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$4$	−0.312065	−	2.96910i	−0.156033	−	1.48455i
$5$	−1.00537	+	0.213698i	−0.449615	+	0.0955687i	−0.427154	−	0.904179i	$-0.640484\pi$
$5$	−1.00537	+	0.213698i	−0.449615	+	0.0955687i	−0.0224617	+	0.999748i	$0.507150\pi$
$6$	−0.689977	+	2.12353i	−0.281682	+	0.866928i
$7$	2.49708	+	0.874397i	0.943809	+	0.330491i
$7$	2.49708	+	0.874397i	0.943809	+	0.330491i
$8$	1.78011	+	1.29333i	0.629365	+	0.457260i
$9$	0.669131	−	0.743145i	0.223044	−	0.247715i
$10$	1.14748	−	1.98749i	0.362864	−	0.628499i
$11$	−0.216549	+	3.30955i	−0.0652919	+	0.997866i
$11$	−0.216549	+	3.30955i	−0.0652919	+	0.997866i
$12$	−1.49273	−	2.58548i	−0.430913	−	0.746364i
$13$	1.56619	+	4.82025i	0.434384	+	1.33690i	0.893717	+	0.448632i	$0.148088\pi$
$13$	1.56619	+	4.82025i	0.434384	+	1.33690i	−0.459333	+	0.888264i	$0.651912\pi$
$14$	−5.18164	+	2.83703i	−1.38485	+	0.758229i
$15$	−0.831533	+	0.604144i	−0.214701	+	0.155989i
$16$	1.03484	−	0.219963i	0.258711	−	0.0549908i
$17$	1.74191	+	1.93458i	0.422474	+	0.469205i	0.916380	−	0.400311i	$-0.131098\pi$
$17$	1.74191	+	1.93458i	0.422474	+	0.469205i	−0.493905	+	0.869516i	$0.664431\pi$
$18$	0.233393	+	2.22058i	0.0550112	+	0.523396i
$19$	0.140718	−	1.33884i	0.0322830	−	0.307152i	−0.966451	−	0.256851i	$-0.917315\pi$
$19$	0.140718	−	1.33884i	0.0322830	−	0.307152i	0.998734	−	0.0503013i	$-0.0160182\pi$
$20$	0.948233	+	2.91836i	0.212031	+	0.652565i
$21$	2.63685	−	0.216854i	0.575408	−	0.0473214i
$22$	−5.16801	−	5.30393i	−1.10182	−	1.13080i
$23$	0.946580	+	1.63952i	0.197376	+	0.341864i	0.947677	−	0.319232i	$-0.103425\pi$
$23$	0.946580	+	1.63952i	0.197376	+	0.341864i	−0.750301	+	0.661096i	$0.770091\pi$
$24$	2.15226	+	0.457476i	0.439328	+	0.0933820i
$25$	−3.60262	+	1.60399i	−0.720525	+	0.320798i
$26$	−10.3382	−	4.60287i	−2.02749	−	0.902697i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	1.81692	−	7.68697i	0.343366	−	1.45270i
$29$	3.25868	−	2.36757i	0.605121	−	0.439646i	−0.242572	−	0.970133i	$-0.577991\pi$
$29$	3.25868	−	2.36757i	0.605121	−	0.439646i	0.847693	+	0.530487i	$0.177991\pi$
$30$	0.239888	−	2.28238i	0.0437974	−	0.416704i
$31$	−3.21210	−	0.682752i	−0.576910	−	0.122626i	−0.0897892	−	0.995961i	$-0.528619\pi$
$31$	−3.21210	−	0.682752i	−0.576910	−	0.122626i	−0.487120	+	0.873335i	$0.661953\pi$
$32$	−3.38146	+	5.85686i	−0.597763	+	1.03536i
$33$	1.14829	+	3.11150i	0.199891	+	0.541643i
$34$	−5.81254			−0.996843
$35$	−2.69735	−	0.345471i	−0.455936	−	0.0583953i
$36$	−2.41528	−	1.75481i	−0.402547	−	0.292468i
$37$	−7.36469	−	3.27897i	−1.21075	−	0.539060i	−0.300762	−	0.953699i	$-0.597241\pi$
$37$	−7.36469	−	3.27897i	−1.21075	−	0.539060i	−0.909986	+	0.414639i	$0.863908\pi$
$38$	2.01131	+	2.23379i	0.326278	+	0.362368i
$39$	3.39136	+	3.76649i	0.543052	+	0.603120i
$40$	−2.06605	−	0.919867i	−0.326672	−	0.145444i
$41$	−0.828434	−	0.601893i	−0.129380	−	0.0939999i	0.521213	−	0.853426i	$-0.325480\pi$
$41$	−0.828434	−	0.601893i	−0.129380	−	0.0939999i	−0.650593	+	0.759427i	$0.725480\pi$
$42$	−3.57974	+	4.69932i	−0.552366	+	0.725121i
$43$	9.19303			1.40192			0.700962	−	0.713199i	$-0.252754\pi$
$43$	9.19303			1.40192			0.700962	+	0.713199i	$0.252754\pi$
$44$	9.89396	−	0.389839i	1.49157	−	0.0587705i
$45$	−0.513916	+	0.890128i	−0.0766100	+	0.132692i
$46$	−4.13470	−	0.878858i	−0.609628	−	0.129581i
$47$	1.03382	−	9.83610i	0.150798	−	1.43474i	−0.613406	−	0.789768i	$-0.710201\pi$
$47$	1.03382	−	9.83610i	0.150798	−	1.43474i	0.764204	−	0.644975i	$-0.223132\pi$
$48$	0.855911	−	0.621855i	0.123540	−	0.0897571i
$49$	5.47086	+	4.36689i	0.781551	+	0.623841i
$50$	2.72097	−	8.37428i	0.384803	−	1.18430i
$51$	2.37818	+	1.05883i	0.333011	+	0.148266i
$52$	13.8230	−	6.15442i	1.91691	−	0.853464i
$53$	11.9272	+	2.53519i	1.63832	+	0.348236i	0.932784	−	0.360437i	$-0.117372\pi$
$53$	11.9272	+	2.53519i	1.63832	+	0.348236i	0.705537	+	0.708673i	$0.250706\pi$
$54$	1.11641	+	1.93367i	0.151924	+	0.263140i
$55$	−0.489532	−	3.37360i	−0.0660085	−	0.454896i
$56$	3.31421	+	4.78607i	0.442880	+	0.639566i
$57$	−0.416005	−	1.28033i	−0.0551012	−	0.169584i
$58$	−0.940093	+	8.94438i	−0.123440	+	1.17446i
$59$	−0.645139	−	6.13808i	−0.0839899	−	0.799110i	−0.952725	−	0.303834i	$-0.901733\pi$
$59$	−0.645139	−	6.13808i	−0.0839899	−	0.799110i	0.868735	−	0.495277i	$-0.164933\pi$
$60$	2.05326	+	2.28037i	0.265074	+	0.294395i
$61$	3.41290	−	0.725434i	0.436977	−	0.0928823i	0.0158300	−	0.999875i	$-0.494961\pi$
$61$	3.41290	−	0.725434i	0.436977	−	0.0928823i	0.421147	+	0.906992i	$0.361628\pi$
$62$	5.93191	−	4.30978i	0.753353	−	0.547343i
$63$	2.32068	−	1.27061i	0.292378	−	0.160082i
$64$	−4.01240	−	12.3489i	−0.501550	−	1.54361i
$65$	−2.60468	−	4.51144i	−0.323071	−	0.559575i
$66$	−6.87852	−	2.74336i	−0.846687	−	0.337684i
$67$	−0.556014	+	0.963044i	−0.0679279	+	0.117655i	−0.897989	−	0.440018i	$-0.854972\pi$
$67$	−0.556014	+	0.963044i	−0.0679279	+	0.117655i	0.830061	+	0.557672i	$0.188305\pi$
$68$	5.20038	−	5.77561i	0.630639	−	0.700396i
$69$	1.53160	+	1.11277i	0.184383	+	0.133962i
$70$	4.60320	−	3.95958i	0.550188	−	0.473260i
$71$	−2.29639	+	7.06755i	−0.272531	+	0.838764i	0.717331	+	0.696732i	$0.245364\pi$
$71$	−2.29639	+	7.06755i	−0.272531	+	0.838764i	−0.989862	+	0.142032i	$0.954636\pi$
$72$	2.15226	−	0.457476i	0.253646	−	0.0539141i
$73$	−1.15674	−	11.0057i	−0.135386	−	1.28811i	−0.825495	−	0.564409i	$-0.809104\pi$
$73$	−1.15674	−	11.0057i	−0.135386	−	1.28811i	0.690109	−	0.723706i	$-0.257563\pi$
$74$	16.4440	−	7.32133i	1.91157	−	0.851088i
$75$	−2.63876	+	2.93064i	−0.304698	+	0.338401i
$76$	−4.01908			−0.461020
$77$	−3.43460	+	8.07487i	−0.391409	+	0.920217i
$78$	−11.3166			−1.28135
$79$	−9.35663	+	10.3916i	−1.05270	+	1.16915i	−0.0675061	+	0.997719i	$0.521504\pi$
$79$	−9.35663	+	10.3916i	−1.05270	+	1.16915i	−0.985197	+	0.171426i	$0.945162\pi$
$80$	−0.993397	+	0.442289i	−0.111065	+	0.0494494i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	2.23644	−	0.475370i	0.246974	−	0.0524958i
$83$	1.44739	−	4.45461i	0.158872	−	0.488957i	−0.839661	−	0.543111i	$-0.817246\pi$
$83$	1.44739	−	4.45461i	0.158872	−	0.488957i	0.998533	+	0.0541542i	$0.0172463\pi$
$84$	−1.46673	−	7.76140i	−0.160033	−	0.846838i
$85$	−2.16468	−	1.57273i	−0.234792	−	0.170587i
$86$	−13.7348	+	15.2540i	−1.48106	+	1.64488i
$87$	2.01397	−	3.48830i	0.215921	−	0.373985i
$88$	−4.66581	+	5.61130i	−0.497377	+	0.598166i
$89$	−9.17730	−	15.8955i	−0.972792	−	1.68492i	−0.687038	−	0.726621i	$-0.741089\pi$
$89$	−9.17730	−	15.8955i	−0.972792	−	1.68492i	−0.285754	−	0.958303i	$-0.592244\pi$
$90$	−0.709180	−	2.18263i	−0.0747542	−	0.230070i
$91$	−0.303894	+	13.4060i	−0.0318568	+	1.40533i
$92$	4.57252	−	3.32213i	0.476718	−	0.346356i
$93$	−3.21210	+	0.682752i	−0.333079	+	0.0707981i
$94$	14.7765	+	16.4110i	1.52408	+	1.69266i
$95$	0.144635	+	1.37611i	0.0148392	+	0.141185i
$96$	−0.706917	+	6.72587i	−0.0721494	+	0.686456i
$97$	−2.19712	−	6.76203i	−0.223083	−	0.686580i	−0.998481	−	0.0551061i	$-0.982450\pi$
$97$	−2.19712	−	6.76203i	−0.223083	−	0.686580i	0.775397	−	0.631474i	$-0.217550\pi$
$98$	−15.4197	+	2.55350i	−1.55762	+	0.257942i
$99$	2.31457	+	2.37545i	0.232623	+	0.238741i
$100$	5.88667	+	10.1960i	0.588667	+	1.01960i
$101$	−6.12292	−	1.30147i	−0.609253	−	0.129501i	−0.107055	−	0.994253i	$-0.534142\pi$
$101$	−6.12292	−	1.30147i	−0.609253	−	0.129501i	−0.502199	+	0.864752i	$0.667475\pi$
$102$	−5.31002	+	2.36417i	−0.525771	+	0.234088i
$103$	9.63859	+	4.29138i	0.949719	+	0.422842i	0.822330	−	0.569011i	$-0.192674\pi$
$103$	9.63859	+	4.29138i	0.949719	+	0.422842i	0.127389	+	0.991853i	$0.459340\pi$
$104$	−3.44616	+	10.6062i	−0.337923	+	1.04002i
$105$	−2.60467	+	0.781508i	−0.254190	+	0.0762674i
$106$	−22.0264	+	16.0031i	−2.13939	+	1.55436i
$107$	0.669658	−	6.37137i	0.0647383	−	0.615944i	−0.913267	−	0.407362i	$-0.866449\pi$
$107$	0.669658	−	6.37137i	0.0647383	−	0.615944i	0.978005	−	0.208582i	$-0.0668847\pi$
$108$	−2.92022	−	0.620711i	−0.280998	−	0.0597280i
$109$	0.0464491	−	0.0804522i	0.00444901	−	0.00770592i	−0.863792	−	0.503848i	$-0.831917\pi$
$109$	0.0464491	−	0.0804522i	0.00444901	−	0.00770592i	0.868241	+	0.496142i	$0.165250\pi$
$110$	6.32921	+	4.22802i	0.603466	+	0.403126i
$111$	−8.06166			−0.765179
$112$	2.77643	+	0.355599i	0.262348	+	0.0336010i
$113$	−9.18338	−	6.67212i	−0.863900	−	0.627660i	0.0650432	−	0.997882i	$-0.479281\pi$
$113$	−9.18338	−	6.67212i	−0.863900	−	0.627660i	−0.928943	+	0.370222i	$0.879281\pi$
$114$	2.74599	+	1.22259i	0.257185	+	0.114506i
$115$	−1.30203	−	1.44605i	−0.121415	−	0.134845i
$116$	−8.04647	−	8.93651i	−0.747096	−	0.829734i
$117$	4.63013	+	2.06147i	0.428056	+	0.190583i
$118$	11.1488	+	8.10009i	1.02633	+	0.745673i
$119$	2.65809	+	6.35393i	0.243667	+	0.582464i
$120$	−2.26158			−0.206453
$121$	−10.9062	−	1.43336i	−0.991474	−	0.130305i
$122$	−3.89531	+	6.74687i	−0.352664	+	0.610833i
$123$	−1.00162	−	0.212902i	−0.0903134	−	0.0191967i
$124$	−1.02478	+	9.75010i	−0.0920277	+	0.875585i
$125$	7.43687	−	5.40320i	0.665174	−	0.483277i
$126$	−1.35887	+	5.74906i	−0.121058	+	0.512167i
$127$	3.42572	−	10.5433i	0.303984	−	0.935566i	−0.676071	−	0.736837i	$-0.736319\pi$
$127$	3.42572	−	10.5433i	0.303984	−	0.935566i	0.980054	−	0.198729i	$-0.0636814\pi$
$128$	14.1288	+	6.29055i	1.24882	+	0.556012i
$129$	8.39825	−	3.73914i	0.739424	−	0.329213i
$130$	11.3774	+	2.41833i	0.997861	+	0.212102i
$131$	2.66318	+	4.61277i	0.232683	+	0.403019i	0.958597	−	0.284767i	$-0.0919161\pi$
$131$	2.66318	+	4.61277i	0.232683	+	0.403019i	−0.725914	+	0.687786i	$0.758583\pi$
$132$	8.88002	−	4.38037i	0.772907	−	0.381262i
$133$	1.52207	−	3.22016i	0.131980	−	0.279224i
$134$	−0.767274	−	2.36143i	−0.0662824	−	0.203996i
$135$	−0.107438	+	1.02220i	−0.00924676	+	0.0879770i
$136$	0.598740	+	5.69663i	0.0513415	+	0.488482i
$137$	−2.72980	−	3.03175i	−0.233222	−	0.259020i	0.615162	−	0.788401i	$-0.289091\pi$
$137$	−2.72980	−	3.03175i	−0.233222	−	0.259020i	−0.848384	+	0.529381i	$0.822424\pi$
$138$	−4.13470	+	0.878858i	−0.351969	+	0.0748133i
$139$	−15.9478	+	11.5867i	−1.35267	+	0.982774i	−0.353799	+	0.935321i	$0.615110\pi$
$139$	−15.9478	+	11.5867i	−1.35267	+	0.982774i	−0.998873	+	0.0474531i	$0.984890\pi$
$140$	−0.183989	+	8.11652i	−0.0155499	+	0.685971i
$141$	−3.05627	−	9.40622i	−0.257384	−	0.792146i
$142$	−8.29631	−	14.3696i	−0.696211	−	1.20587i
$143$	−16.2920	+	4.13957i	−1.36240	+	0.346168i
$144$	0.528982	−	0.916223i	0.0440818	−	0.0763520i
$145$	−2.77023	+	3.07666i	−0.230055	+	0.255502i
$146$	19.9900	+	14.5236i	1.65438	+	1.20198i
$147$	6.77405	+	1.76415i	0.558714	+	0.145505i
$148$	−7.43734	+	22.8898i	−0.611345	+	1.88153i
$149$	−4.68041	+	0.994852i	−0.383434	+	0.0815015i	−0.395596	−	0.918425i	$-0.629462\pi$
$149$	−4.68041	+	0.994852i	−0.383434	+	0.0815015i	0.0121618	+	0.999926i	$0.496129\pi$
$150$	−0.920398	−	8.75700i	−0.0751502	−	0.715006i
$151$	−5.02084	+	2.23542i	−0.408590	+	0.181916i	−0.600731	−	0.799451i	$-0.705124\pi$
$151$	−5.02084	+	2.23542i	−0.408590	+	0.181916i	0.192141	+	0.981367i	$0.438457\pi$
$152$	1.98206	−	2.20130i	0.160766	−	0.178549i
$153$	2.60324			0.210459
$154$	−8.26722	−	17.7633i	−0.666192	−	1.43140i
$155$	3.37525			0.271107
$156$	10.1248	−	11.2447i	0.810629	−	0.900295i
$157$	18.9942	−	8.45676i	1.51590	−	0.674923i	0.530894	−	0.847438i	$-0.321856\pi$
$157$	18.9942	−	8.45676i	1.51590	−	0.674923i	0.985007	+	0.172516i	$0.0551895\pi$
$158$	−3.26359	−	31.0510i	−0.259637	−	2.47028i
$159$	11.9272	−	2.53519i	0.945885	−	0.201054i
$160$	2.14802	−	6.61092i	0.169816	−	0.522639i
$161$	0.930094	+	4.92172i	0.0733017	+	0.387886i
$162$	1.80638	+	1.31241i	0.141923	+	0.103113i
$163$	−4.89610	+	5.43767i	−0.383492	+	0.425911i	−0.903725	−	0.428113i	$-0.859179\pi$
$163$	−4.89610	+	5.43767i	−0.383492	+	0.425911i	0.520233	+	0.854024i	$0.325845\pi$
$164$	−1.52856	+	2.64754i	−0.119360	+	0.206738i
$165$	−1.81938	−	2.88282i	−0.141638	−	0.224428i
$166$	5.22908	+	9.05704i	0.405856	+	0.702963i
$167$	1.84641	+	5.68265i	0.142879	+	0.439737i	0.996732	−	0.0807774i	$-0.0257403\pi$
$167$	1.84641	+	5.68265i	0.142879	+	0.439737i	−0.853853	+	0.520514i	$0.825740\pi$
$168$	4.97435	+	3.02428i	0.383780	+	0.233329i
$169$	−10.2646	+	7.45766i	−0.789584	+	0.573666i
$170$	5.84376	−	1.24213i	0.448196	−	0.0952670i
$171$	−0.900796	−	1.00044i	−0.0688856	−	0.0765052i
$172$	−2.86882	−	27.2950i	−0.218746	−	2.08123i
$173$	−0.154714	+	1.47200i	−0.0117627	+	0.111914i	−0.998828	−	0.0484057i	$-0.984586\pi$
$173$	−0.154714	+	1.47200i	−0.0117627	+	0.111914i	0.987065	+	0.160320i	$0.0512526\pi$
$174$	2.77919	+	8.55347i	0.210690	+	0.648437i
$175$	−10.3986	+	0.855178i	−0.786059	+	0.0646454i
$176$	0.503884	+	3.47250i	0.0379817	+	0.261750i
$177$	−3.08595	−	5.34502i	−0.231954	−	0.401756i
$178$	40.0868	+	8.52072i	3.00463	+	0.638655i
$179$	−4.93541	+	2.19738i	−0.368890	+	0.164240i	−0.582805	−	0.812612i	$-0.698045\pi$
$179$	−4.93541	+	2.19738i	−0.368890	+	0.164240i	0.213916	+	0.976852i	$0.431378\pi$
$180$	2.80326	+	1.24809i	0.208942	+	0.0930271i
$181$	7.70985	−	23.7285i	0.573068	−	1.76372i	−0.0695958	−	0.997575i	$-0.522171\pi$
$181$	7.70985	−	23.7285i	0.573068	−	1.76372i	0.642664	−	0.766148i	$-0.277829\pi$
$182$	−21.7907	−	20.5335i	−1.61523	−	1.52204i
$183$	2.82278	−	2.05087i	0.208666	−	0.151605i
$184$	−0.435423	+	4.14278i	−0.0320998	+	0.305409i
$185$	8.10496	+	1.72276i	0.595888	+	0.126660i
$186$	3.66612	−	6.34991i	0.268813	−	0.465598i
$187$	−6.77980	+	5.34599i	−0.495788	+	0.390937i
$188$	−29.5270			−2.15348
$189$	1.60324	−	2.10466i	0.116619	−	0.153092i
$190$	−2.49947	−	1.81597i	−0.181330	−	0.131744i
$191$	20.8770	+	9.29503i	1.51061	+	0.672565i	0.984101	−	0.177607i	$-0.0568357\pi$
$191$	20.8770	+	9.29503i	1.51061	+	0.672565i	0.526504	+	0.850172i	$0.323502\pi$
$192$	−8.68826	−	9.64929i	−0.627021	−	0.696378i
$193$	−4.91168	−	5.45497i	−0.353550	−	0.392657i	0.539967	−	0.841686i	$-0.318437\pi$
$193$	−4.91168	−	5.45497i	−0.353550	−	0.392657i	−0.893517	+	0.449029i	$0.851770\pi$
$194$	14.5028	+	6.45708i	1.04124	+	0.463592i
$195$	−4.21446	−	3.06199i	−0.301804	−	0.219273i
$196$	11.2585	−	17.6063i	0.804176	−	1.25759i
$197$	26.2782			1.87224			0.936121	−	0.351679i	$-0.114389\pi$
$197$	26.2782			1.87224			0.936121	+	0.351679i	$0.114389\pi$
$198$	−7.39966	+	0.291560i	−0.525871	+	0.0207202i
$199$	−6.06430	+	10.5037i	−0.429887	+	0.744586i	−0.996863	−	0.0791483i	$-0.974780\pi$
$199$	−6.06430	+	10.5037i	−0.429887	+	0.744586i	0.566976	+	0.823734i	$0.308113\pi$
$200$	−8.48756	−	1.80409i	−0.600161	−	0.127568i
$201$	−0.116239	+	1.10594i	−0.00819883	+	0.0780067i
$202$	11.3074	−	8.21534i	0.795589	−	0.578029i
$203$	10.2074	−	3.06264i	0.716418	−	0.214955i
$204$	2.40163	−	7.39147i	0.168148	−	0.517506i
$205$	0.961507	+	0.428090i	0.0671546	+	0.0298991i
$206$	−21.5212	+	9.58184i	−1.49945	+	0.667599i
$207$	1.85179	+	0.393610i	0.128708	+	0.0273578i
$208$	2.68104	+	4.64370i	0.185897	+	0.321983i
$209$	4.40050	+	0.755639i	0.304389	+	0.0522686i
$210$	2.59473	−	5.48955i	0.179053	−	0.378815i
$211$	5.52303	+	16.9981i	0.380221	+	1.17020i	0.939888	+	0.341483i	$0.110929\pi$
$211$	5.52303	+	16.9981i	0.380221	+	1.17020i	−0.559667	+	0.828718i	$0.689071\pi$
$212$	3.80520	−	36.2041i	0.261342	−	2.48651i
$213$	0.776779	+	7.39056i	0.0532240	+	0.506393i
$214$	9.57155	+	10.6303i	0.654297	+	0.726671i
$215$	−9.24240	+	1.96453i	−0.630326	+	0.133980i
$216$	1.78011	−	1.29333i	0.121121	−	0.0879998i
$217$	−7.42388	−	4.51354i	−0.503966	−	0.306399i
$218$	0.0640976	+	0.197272i	0.00434124	+	0.0133610i
$219$	−5.53314	−	9.58368i	−0.373895	−	0.647605i
$220$	−9.86379	+	2.50625i	−0.665017	+	0.168972i
$221$	−6.59700	+	11.4263i	−0.443762	+	0.768619i
$222$	12.0445	−	13.3767i	0.808372	−	0.897788i
$223$	1.70719	+	1.24034i	0.114322	+	0.0830596i	0.643477	−	0.765465i	$-0.277491\pi$
$223$	1.70719	+	1.24034i	0.114322	+	0.0830596i	−0.529155	+	0.848525i	$0.677491\pi$
$224$	−13.5650	+	11.6683i	−0.906350	+	0.779623i
$225$	−1.21863	+	3.75055i	−0.0812419	+	0.250037i
$226$	24.7914	−	5.26958i	1.64910	−	0.350528i
$227$	1.18037	+	11.2305i	0.0783440	+	0.745393i	0.961219	+	0.275786i	$0.0889380\pi$
$227$	1.18037	+	11.2305i	0.0783440	+	0.745393i	−0.882875	+	0.469608i	$0.844395\pi$
$228$	−3.67161	+	1.63471i	−0.243158	+	0.108261i
$229$	18.6521	−	20.7153i	1.23257	−	1.36890i	0.326819	−	0.945087i	$-0.394023\pi$
$229$	18.6521	−	20.7153i	1.23257	−	1.36890i	0.905748	−	0.423817i	$-0.139310\pi$
$230$	4.34472			0.286482
$231$	0.146682	+	8.77374i	0.00965099	+	0.577270i
$232$	8.86285			0.581875
$233$	−4.59822	+	5.10684i	−0.301240	+	0.334560i	−0.874693	−	0.484678i	$-0.838937\pi$
$233$	−4.59822	+	5.10684i	−0.301240	+	0.334560i	0.573453	+	0.819238i	$0.305603\pi$
$234$	−10.3382	+	4.60287i	−0.675830	+	0.300899i
$235$	1.06259	+	10.1099i	0.0693156	+	0.659494i
$236$	−18.0233	+	3.83096i	−1.17321	+	0.249375i
$237$	−4.32107	+	13.2989i	−0.280683	+	0.863855i
$238$	−14.5144	−	5.08247i	−0.940829	−	0.329448i
$239$	−9.02995	−	6.56065i	−0.584099	−	0.424373i	0.256100	−	0.966650i	$-0.417562\pi$
$239$	−9.02995	−	6.56065i	−0.584099	−	0.424373i	−0.840200	+	0.542277i	$0.817562\pi$
$240$	−0.727618	+	0.808102i	−0.0469675	+	0.0521627i
$241$	−8.25275	+	14.2942i	−0.531606	+	0.920769i	0.467713	+	0.883880i	$0.345078\pi$
$241$	−8.25275	+	14.2942i	−0.531606	+	0.920769i	−0.999319	+	0.0368888i	$0.988255\pi$
$242$	18.6727	−	15.9552i	1.20033	−	1.02564i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−3.21893	−	9.90686i	−0.206071	−	0.634222i
$245$	−6.43344	−	3.22123i	−0.411017	−	0.205797i
$246$	1.84974	−	1.34391i	0.117935	−	0.0856848i
$247$	6.67395	−	1.41859i	0.424653	−	0.0902629i
$248$	−4.83487	−	5.36967i	−0.307015	−	0.340974i
$249$	−0.489596	−	4.65819i	−0.0310269	−	0.295201i
$250$	−2.14545	+	20.4126i	−0.135690	+	1.29101i
$251$	−7.05468	−	21.7121i	−0.445288	−	1.37045i	−0.882168	−	0.470935i	$-0.843917\pi$
$251$	−7.05468	−	21.7121i	−0.445288	−	1.37045i	0.436880	−	0.899520i	$-0.356083\pi$
$252$	−4.49677	−	6.49382i	−0.283270	−	0.409072i
$253$	−5.63107	+	2.77771i	−0.354022	+	0.174633i
$254$	12.3763	+	21.4365i	0.776561	+	1.34504i
$255$	−2.61722	−	0.556307i	−0.163897	−	0.0348373i
$256$	−7.82333	+	3.48317i	−0.488958	+	0.217698i
$257$	6.82073	+	3.03679i	0.425466	+	0.189430i	0.608288	−	0.793716i	$-0.291857\pi$
$257$	6.82073	+	3.03679i	0.425466	+	0.189430i	−0.182822	+	0.983146i	$0.558523\pi$
$258$	−6.34298	+	19.5217i	−0.394897	+	1.21537i
$259$	−15.5231	−	14.6275i	−0.964561	−	0.908911i
$260$	−12.5821	+	9.14143i	−0.780309	+	0.566927i
$261$	0.421035	−	4.00588i	0.0260614	−	0.247958i
$262$	−11.6329	−	2.47265i	−0.718682	−	0.152761i
$263$	−11.1744	+	19.3547i	−0.689045	+	1.19346i	0.283102	+	0.959090i	$0.408636\pi$
$263$	−11.1744	+	19.3547i	−0.689045	+	1.19346i	−0.972147	+	0.234371i	$0.924697\pi$
$264$	−1.98011	+	7.02393i	−0.121867	+	0.432293i
$265$	−12.5330			−0.769895
$266$	3.06919	+	7.33664i	0.188184	+	0.449838i
$267$	−14.8492	−	10.7886i	−0.908755	−	0.660249i
$268$	3.03289	+	1.35033i	0.185263	+	0.0824845i
$269$	−0.771020	−	0.856304i	−0.0470099	−	0.0522098i	0.719181	−	0.694823i	$-0.244517\pi$
$269$	−0.771020	−	0.856304i	−0.0470099	−	0.0522098i	−0.766191	+	0.642613i	$0.777850\pi$
$270$	−1.53562	−	1.70548i	−0.0934552	−	0.103792i
$271$	−6.54462	−	2.91385i	−0.397558	−	0.177004i	0.198213	−	0.980159i	$-0.436486\pi$
$271$	−6.54462	−	2.91385i	−0.397558	−	0.177004i	−0.595770	+	0.803155i	$0.703153\pi$
$272$	2.22814	+	1.61884i	0.135101	+	0.0981564i
$273$	5.17510	+	12.3706i	0.313212	+	0.748704i
$274$	9.10902			0.550296
$275$	−4.52834	−	12.2704i	−0.273069	−	0.739933i
$276$	2.82597	−	4.89473i	0.170104	−	0.294628i
$277$	−9.88954	−	2.10209i	−0.594205	−	0.126302i	−0.0990135	−	0.995086i	$-0.531569\pi$
$277$	−9.88954	−	2.10209i	−0.594205	−	0.126302i	−0.495191	+	0.868784i	$0.664902\pi$
$278$	4.60076	−	43.7733i	0.275935	−	2.62535i
$279$	−2.65670	+	1.93020i	−0.159052	+	0.115558i
$280$	−4.35478	−	4.10354i	−0.260248	−	0.245233i
$281$	−6.23152	+	19.1787i	−0.371742	+	1.14410i	0.573909	+	0.818919i	$0.305426\pi$
$281$	−6.23152	+	19.1787i	−0.371742	+	1.14410i	−0.945651	+	0.325184i	$0.894574\pi$
$282$	20.1740	+	8.98203i	1.20134	+	0.534872i
$283$	−1.79246	+	0.798054i	−0.106551	+	0.0474394i	−0.459320	−	0.888271i	$-0.651907\pi$
$283$	−1.79246	+	0.798054i	−0.106551	+	0.0474394i	0.352769	+	0.935710i	$0.385240\pi$
$284$	21.7009	+	4.61267i	1.28771	+	0.273712i
$285$	0.691843	+	1.19831i	0.0409812	+	0.0709816i
$286$	17.4721	−	33.2181i	1.03315	−	1.96423i
$287$	−1.54238	−	2.22736i	−0.0910436	−	0.131477i
$288$	2.08986	+	6.43191i	0.123146	+	0.379004i
$289$	1.06861	−	10.1672i	0.0628595	−	0.598068i
$290$	−0.966257	−	9.19332i	−0.0567405	−	0.539850i
$291$	−4.75753	−	5.28377i	−0.278891	−	0.309740i
$292$	−32.3159	+	6.86897i	−1.89115	+	0.401976i
$293$	22.6634	−	16.4659i	1.32401	−	0.961949i	0.324136	−	0.946011i	$-0.394927\pi$
$293$	22.6634	−	16.4659i	1.32401	−	0.961949i	0.999873	−	0.0159379i	$-0.00507341\pi$
$294$	−13.0480	+	8.60449i	−0.760974	+	0.501824i
$295$	1.96030	+	6.03318i	0.114133	+	0.351266i
$296$	−8.86920	−	15.3619i	−0.515512	−	0.892892i
$297$	3.08065	+	1.22866i	0.178757	+	0.0712939i
$298$	5.34198	−	9.25258i	0.309453	−	0.535988i
$299$	−6.42039	+	7.13056i	−0.371300	+	0.412371i
$300$	9.52483	+	6.92019i	0.549916	+	0.399537i
$301$	22.9558	+	8.03836i	1.32315	+	0.463323i
$302$	3.79211	−	11.6709i	0.218211	−	0.671586i
$303$	−6.12292	+	1.30147i	−0.351753	+	0.0747673i
$304$	−0.148875	−	1.41645i	−0.00853855	−	0.0812389i
$305$	−3.27621	+	1.45866i	−0.187595	+	0.0835227i
$306$	−3.88935	+	4.31956i	−0.222339	+	0.246933i
$307$	17.2450			0.984223			0.492111	−	0.870532i	$-0.336225\pi$
$307$	17.2450			0.984223			0.492111	+	0.870532i	$0.336225\pi$
$308$	25.0469	+	7.67779i	1.42718	+	0.437483i
$309$	10.5508			0.600211
$310$	−5.04277	+	5.60057i	−0.286410	+	0.318091i
$311$	27.4253	−	12.2105i	1.55515	−	0.692396i	0.564075	−	0.825724i	$-0.309233\pi$
$311$	27.4253	−	12.2105i	1.55515	−	0.692396i	0.991072	+	0.133328i	$0.0425663\pi$
$312$	1.16570	+	11.0909i	0.0659948	+	0.627899i
$313$	−26.7599	+	5.68800i	−1.51256	+	0.321505i	−0.888136	−	0.459581i	$-0.848000\pi$
$313$	−26.7599	+	5.68800i	−1.51256	+	0.321505i	−0.624424	+	0.781085i	$0.714666\pi$
$314$	−14.3458	+	44.1519i	−0.809581	+	2.49163i
$315$	−2.06162	+	1.77336i	−0.116159	+	0.0999174i
$316$	33.7736	+	24.5379i	1.89991	+	1.38037i
$317$	−17.1371	+	19.0327i	−0.962516	+	1.06898i	0.0350591	+	0.999385i	$0.488838\pi$
$317$	−17.1371	+	19.0327i	−0.962516	+	1.06898i	−0.997575	+	0.0695972i	$0.977829\pi$
$318$	−13.6130	+	23.5785i	−0.763381	+	1.32221i
$319$	7.12992	+	11.2974i	0.399199	+	0.632535i
$320$	6.67289	+	11.5578i	0.373026	+	0.646099i
$321$	−1.97971	−	6.09291i	−0.110497	−	0.340073i
$322$	−9.55623	−	5.80995i	−0.532548	−	0.323776i
$323$	2.83522	−	2.05991i	0.157756	−	0.114616i
$324$	−2.92022	+	0.620711i	−0.162234	+	0.0344840i
$325$	−13.3740	−	14.8534i	−0.741858	−	0.823917i
$326$	−1.70776	−	16.2482i	−0.0945840	−	0.899907i
$327$	0.00971050	−	0.0923892i	0.000536992	−	0.00510914i
$328$	−0.696262	−	2.14287i	−0.0384446	−	0.118320i
$329$	11.1822	−	23.6576i	0.616494	−	1.30429i
$330$	7.50171	+	1.28817i	0.412956	+	0.0709114i
$331$	6.59787	+	11.4279i	0.362652	+	0.628132i	0.988396	−	0.151897i	$-0.0485381\pi$
$331$	6.59787	+	11.4279i	0.362652	+	0.628132i	−0.625744	+	0.780028i	$0.715205\pi$
$332$	−13.6779	−	2.90732i	−0.750670	−	0.159560i
$333$	−7.36469	+	3.27897i	−0.403583	+	0.179687i
$334$	−12.1879	−	5.42638i	−0.666890	−	0.296918i
$335$	0.353199	−	1.08704i	0.0192973	−	0.0593911i
$336$	2.68103	−	0.804420i	0.146262	−	0.0438847i
$337$	17.5919	−	12.7813i	0.958292	−	0.696240i	0.00553877	−	0.999985i	$-0.498237\pi$
$337$	17.5919	−	12.7813i	0.958292	−	0.696240i	0.952754	+	0.303745i	$0.0982369\pi$
$338$	2.96122	−	28.1742i	0.161069	−	1.53247i
$339$	−11.1032	−	2.36006i	−0.603045	−	0.128181i
$340$	−3.99408	+	6.91794i	−0.216609	+	0.375178i
$341$	2.95518	−	10.4827i	0.160032	−	0.567672i
$342$	3.00586			0.162538
$343$	9.84280	+	15.6882i	0.531461	+	0.847083i
$344$	16.3646	+	11.8896i	0.882321	+	0.641044i
$345$	−1.77762	−	0.791448i	−0.0957039	−	0.0426101i
$346$	−2.21135	−	2.45596i	−0.118883	−	0.132033i
$347$	9.18671	+	10.2029i	0.493168	+	0.547719i	0.937428	−	0.348179i	$-0.113200\pi$
$347$	9.18671	+	10.2029i	0.493168	+	0.547719i	−0.444260	+	0.895898i	$0.646533\pi$
$348$	−10.9856	−	4.89111i	−0.588891	−	0.262191i
$349$	−18.6455	−	13.5467i	−0.998070	−	0.725140i	−0.0363964	−	0.999337i	$-0.511588\pi$
$349$	−18.6455	−	13.5467i	−0.998070	−	0.725140i	−0.961673	+	0.274197i	$0.911588\pi$
$350$	14.1169	−	18.5321i	0.754582	−	0.990581i
$351$	5.06831			0.270526
$352$	−18.6513	−	12.4594i	−0.994117	−	0.664088i
$353$	2.13324	−	3.69489i	0.113541	−	0.196659i	−0.803655	−	0.595096i	$-0.797114\pi$
$353$	2.13324	−	3.69489i	0.113541	−	0.196659i	0.917196	+	0.398437i	$0.130447\pi$
$354$	13.4795	+	2.86517i	0.716430	+	0.152282i
$355$	0.798397	−	7.59624i	0.0423745	−	0.403167i
$356$	−44.3316	+	32.2088i	−2.34957	+	1.70706i
$357$	5.01266	+	4.72346i	0.265298	+	0.249992i
$358$	3.72758	−	11.4723i	0.197009	−	0.606331i
$359$	14.3328	+	6.38140i	0.756459	+	0.336797i	0.748468	−	0.663171i	$-0.230790\pi$
$359$	14.3328	+	6.38140i	0.756459	+	0.336797i	0.00799080	+	0.999968i	$0.497456\pi$
$360$	−2.06605	+	0.919867i	−0.108891	+	0.0484812i
$361$	16.8121	+	3.57352i	0.884847	+	0.188080i
$362$	27.8539	+	48.2444i	1.46397	+	2.53567i
$363$	−10.5463	+	3.12652i	−0.553538	+	0.164100i
$364$	39.8987	−	3.28126i	2.09126	−	0.171985i
$365$	3.51484	+	10.8176i	0.183975	+	0.566218i
$366$	−0.814341	+	7.74793i	−0.0425663	+	0.404991i
$367$	1.40004	+	13.3205i	0.0730814	+	0.695323i	0.968316	+	0.249728i	$0.0803411\pi$
$367$	1.40004	+	13.3205i	0.0730814	+	0.695323i	−0.895235	+	0.445595i	$0.852992\pi$
$368$	1.34020	+	1.48844i	0.0698627	+	0.0775903i
$369$	−1.00162	+	0.212902i	−0.0521425	+	0.0110832i
$370$	−14.9677	+	10.8747i	−0.778136	+	0.565349i
$371$	27.5663	+	16.7597i	1.43117	+	0.870118i
$372$	3.02954	+	9.32398i	0.157075	+	0.483426i
$373$	−12.3967	−	21.4717i	−0.641877	−	1.11176i	−0.985013	−	0.172478i	$-0.944823\pi$
$373$	−12.3967	−	21.4717i	−0.641877	−	1.11176i	0.343137	−	0.939286i	$-0.388511\pi$
$374$	1.25870	−	19.2369i	0.0650858	−	0.994716i
$375$	4.59624	−	7.96092i	0.237349	−	0.411100i
$376$	14.5616	−	16.1723i	0.750958	−	0.834023i
$377$	16.5160	+	11.9996i	0.850616	+	0.618009i
$378$	1.09696	+	5.80473i	0.0564217	+	0.298563i
$379$	3.42758	−	10.5490i	0.176063	−	0.541865i	−0.823618	−	0.567145i	$-0.808048\pi$
$379$	3.42758	−	10.5490i	0.176063	−	0.541865i	0.999680	+	0.0252801i	$0.00804775\pi$
$380$	4.04066	−	0.858869i	0.207282	−	0.0440591i
$381$	−1.15879	−	11.0251i	−0.0593666	−	0.564835i
$382$	−46.6144	+	20.7541i	−2.38500	+	1.06187i
$383$	−1.82252	+	2.02412i	−0.0931266	+	0.103428i	−0.787907	−	0.615795i	$-0.788835\pi$
$383$	−1.82252	+	2.02412i	−0.0931266	+	0.103428i	0.694780	+	0.719222i	$0.255502\pi$
$384$	15.4659			0.789242
$385$	1.72746	−	8.85220i	0.0880396	−	0.451150i
$386$	16.3897			0.834214
$387$	6.15133	−	6.83175i	0.312690	−	0.347277i
$388$	−19.3915	+	8.63365i	−0.984455	+	0.438307i
$389$	2.29204	+	21.8073i	0.116211	+	1.10567i	0.884813	+	0.465946i	$0.154286\pi$
$389$	2.29204	+	21.8073i	0.116211	+	1.10567i	−0.768602	+	0.639727i	$0.779047\pi$
$390$	11.3774	−	2.41833i	0.576115	−	0.122457i
$391$	−1.52294	+	4.68713i	−0.0770185	+	0.237039i
$392$	4.09093	+	14.8492i	0.206623	+	0.749996i
$393$	4.30912	+	3.13076i	0.217366	+	0.157926i
$394$	−39.2607	+	43.6035i	−1.97793	+	2.19671i
$395$	7.18622	−	12.4469i	0.361578	−	0.626271i
$396$	6.33064	−	7.61350i	0.318127	−	0.382593i
$397$	−6.46252	−	11.1934i	−0.324344	−	0.561781i	0.657035	−	0.753860i	$-0.271810\pi$
$397$	−6.46252	−	11.1934i	−0.324344	−	0.561781i	−0.981379	+	0.192079i	$0.938477\pi$
$398$	−8.36846	−	25.7555i	−0.419473	−	1.29101i
$399$	0.0807189	−	3.56085i	0.00404100	−	0.178265i
$400$	−3.37534	+	2.45233i	−0.168767	+	0.122616i
$401$	−10.7671	+	2.28863i	−0.537685	+	0.114289i	−0.468747	−	0.883332i	$-0.655294\pi$
$401$	−10.7671	+	2.28863i	−0.537685	+	0.114289i	−0.0689382	+	0.997621i	$0.521961\pi$
$402$	−1.66142	−	1.84519i	−0.0828640	−	0.0920298i
$403$	−1.73973	−	16.5524i	−0.0866621	−	0.824535i
$404$	−1.95344	+	18.5857i	−0.0971871	+	0.924674i
$405$	0.317617	+	0.977526i	0.0157825	+	0.0485736i
$406$	−10.1684	+	21.5129i	−0.504651	+	1.06767i
$407$	12.4467	−	23.6637i	0.616962	−	1.17297i
$408$	2.86400	+	4.96060i	0.141789	+	0.245586i
$409$	−10.8632	−	2.30904i	−0.537149	−	0.114175i	−0.0686538	−	0.997641i	$-0.521870\pi$
$409$	−10.8632	−	2.30904i	−0.537149	−	0.114175i	−0.468495	+	0.883466i	$0.655204\pi$
$410$	−2.14687	+	0.955846i	−0.106026	+	0.0472059i
$411$	−3.72692	−	1.65933i	−0.183835	−	0.0818487i
$412$	9.73367	−	29.9571i	0.479543	−	1.47588i
$413$	3.75616	−	15.8914i	0.184828	−	0.781966i
$414$	−3.41977	+	2.48461i	−0.168073	+	0.122112i
$415$	−0.503222	+	4.78784i	−0.0247022	+	0.235026i
$416$	−33.5275	−	7.12649i	−1.64382	−	0.349405i
$417$	−9.85627	+	17.0716i	−0.482664	+	0.835998i
$418$	−7.82837	+	6.17280i	−0.382898	+	0.301922i
$419$	−35.9681			−1.75716			−0.878578	−	0.477599i	$-0.841507\pi$
$419$	−35.9681			−1.75716			−0.878578	+	0.477599i	$0.841507\pi$
$420$	3.13320	+	7.48965i	0.152885	+	0.365457i
$421$	16.1469	+	11.7314i	0.786953	+	0.571755i	0.907058	−	0.421006i	$-0.138323\pi$
$421$	16.1469	+	11.7314i	0.786953	+	0.571755i	−0.120105	+	0.992761i	$0.538323\pi$
$422$	−36.4567	−	16.2316i	−1.77469	−	0.790141i
$423$	−6.61789	−	7.34991i	−0.321773	−	0.357365i
$424$	17.9528	+	19.9386i	0.871867	+	0.968306i
$425$	−9.37848	−	4.17557i	−0.454923	−	0.202545i
$426$	−13.4237	−	9.75290i	−0.650381	−	0.472530i
$427$	9.15662	+	1.17276i	0.443120	+	0.0567538i
$428$	−19.1262			−0.924501
$429$	−13.1998	+	10.4082i	−0.637290	+	0.502514i
$430$	10.5488	−	18.2710i	0.508708	−	0.881108i
$431$	−14.1620	−	3.01022i	−0.682157	−	0.144997i	−0.146217	−	0.989253i	$-0.546710\pi$
$431$	−14.1620	−	3.01022i	−0.682157	−	0.144997i	−0.535941	+	0.844256i	$0.680043\pi$
$432$	0.110587	−	1.05217i	0.00532064	−	0.0506225i
$433$	−23.6623	+	17.1917i	−1.13714	+	0.826179i	−0.986718	−	0.162443i	$-0.948063\pi$
$433$	−23.6623	+	17.1917i	−1.13714	+	0.826179i	−0.150420	+	0.988622i	$0.548063\pi$
$434$	18.5809	−	5.57505i	0.891913	−	0.267611i
$435$	−1.27935	+	3.93742i	−0.0613399	+	0.188785i
$436$	−0.253366	−	0.112806i	−0.0121340	−	0.00540241i
$437$	2.32827	−	1.03661i	0.111376	−	0.0495879i
$438$	24.1690	+	5.13728i	1.15484	+	0.245469i
$439$	−9.92126	−	17.1841i	−0.473516	−	0.820154i	0.526025	−	0.850469i	$-0.323682\pi$
$439$	−9.92126	−	17.1841i	−0.473516	−	0.820154i	−0.999540	+	0.0303159i	$0.990349\pi$
$440$	3.49174	−	6.63851i	0.166462	−	0.316479i
$441$	6.90595	−	1.14362i	0.328855	−	0.0544582i
$442$	−9.10356	−	28.0179i	−0.433012	−	1.33268i
$443$	0.891676	−	8.48373i	0.0423648	−	0.403074i	−0.952705	−	0.303897i	$-0.901712\pi$
$443$	0.891676	−	8.48373i	0.0423648	−	0.403074i	0.995070	−	0.0991773i	$-0.0316211\pi$
$444$	2.51576	+	23.9359i	0.119393	+	1.13595i
$445$	12.6234	+	14.0197i	0.598408	+	0.664600i
$446$	−4.60872	+	0.979614i	−0.218229	+	0.0463860i
$447$	−3.87113	+	2.81254i	−0.183098	+	0.133029i
$448$	0.778541	−	34.3447i	0.0367826	−	1.62263i
$449$	−3.28407	−	10.1073i	−0.154985	−	0.476994i	0.843175	−	0.537640i	$-0.180684\pi$
$449$	−3.28407	−	10.1073i	−0.154985	−	0.476994i	−0.998159	+	0.0606458i	$0.980684\pi$
$450$	−4.40262	−	7.62556i	−0.207542	−	0.359472i
$451$	2.17139	−	2.61140i	0.102247	−	0.122966i
$452$	−16.9444	+	29.3485i	−0.796997	+	1.38044i
$453$	−3.67754	+	4.08432i	−0.172786	+	0.191898i
$454$	−20.3983	−	14.8202i	−0.957340	−	0.695548i
$455$	−2.55932	−	13.5430i	−0.119983	−	0.634905i
$456$	0.915351	−	2.81716i	0.0428653	−	0.131926i
$457$	−4.92526	+	1.04690i	−0.230394	+	0.0489718i	−0.321662	−	0.946855i	$-0.604241\pi$
$457$	−4.92526	+	1.04690i	−0.230394	+	0.0489718i	0.0912677	+	0.995826i	$0.470908\pi$
$458$	6.50585	+	61.8991i	0.303999	+	2.89235i
$459$	2.37818	−	1.05883i	0.111004	−	0.0494220i
$460$	−3.88714	+	4.31711i	−0.181239	+	0.201286i
$461$	15.3843			0.716519			0.358260	−	0.933622i	$-0.383370\pi$
$461$	15.3843			0.716519			0.358260	+	0.933622i	$0.383370\pi$
$462$	−14.7774	−	12.8650i	−0.687509	−	0.598532i
$463$	31.6955			1.47302			0.736508	−	0.676429i	$-0.236473\pi$
$463$	31.6955			1.47302			0.736508	+	0.676429i	$0.236473\pi$
$464$	2.85145	−	3.16685i	0.132375	−	0.147017i
$465$	3.08344	−	1.37284i	0.142991	−	0.0636638i
$466$	−1.60386	−	15.2597i	−0.0742973	−	0.706892i
$467$	−17.6587	+	3.75348i	−0.817149	+	0.173690i	−0.597480	−	0.801884i	$-0.703831\pi$
$467$	−17.6587	+	3.75348i	−0.817149	+	0.173690i	−0.219669	+	0.975574i	$0.570498\pi$
$468$	4.67580	−	14.3906i	0.216139	−	0.665207i
$469$	−2.23050	+	1.91863i	−0.102995	+	0.0885939i
$470$	−18.3629	−	13.3414i	−0.847016	−	0.615393i
$471$	13.9124	−	15.4513i	0.641049	−	0.711957i
$472$	6.79013	−	11.7609i	0.312541	−	0.541337i
$473$	−1.99074	+	30.4248i	−0.0915342	+	1.39893i
$474$	−15.6110	−	27.0391i	−0.717037	−	1.24195i
$475$	1.64054	+	5.04906i	0.0752731	+	0.231667i
$476$	18.0360	−	9.87499i	0.826677	−	0.452619i
$477$	9.86484	−	7.16723i	0.451680	−	0.328165i
$478$	24.3773	−	5.18155i	1.11499	−	0.236998i
$479$	4.32294	+	4.80111i	0.197520	+	0.219368i	0.833766	−	0.552118i	$-0.186180\pi$
$479$	4.32294	+	4.80111i	0.197520	+	0.219368i	−0.636246	+	0.771486i	$0.719514\pi$
$480$	−0.726592	−	6.91306i	−0.0331642	−	0.315536i
$481$	4.27093	−	40.6351i	0.194737	−	1.85280i
$482$	−11.3884	−	35.0500i	−0.518728	−	1.59648i
$483$	2.85153	+	4.11791i	0.129749	+	0.187371i
$484$	−0.852333	+	32.8290i	−0.0387424	+	1.49223i
$485$	3.65395	+	6.32883i	0.165917	+	0.287377i
$486$	2.18402	+	0.464228i	0.0990692	+	0.0210578i
$487$	4.00193	−	1.78177i	0.181345	−	0.0807398i	−0.314056	−	0.949404i	$-0.601688\pi$
$487$	4.00193	−	1.78177i	0.181345	−	0.0807398i	0.495401	+	0.868665i	$0.335021\pi$
$488$	7.01357	+	3.12264i	0.317489	+	0.141355i
$489$	−2.26111	+	6.95899i	−0.102251	+	0.314696i
$490$	14.9568	−	5.86237i	0.675681	−	0.264835i
$491$	−33.0596	+	24.0192i	−1.49196	+	1.08397i	−0.518510	+	0.855071i	$0.673513\pi$
$491$	−33.0596	+	24.0192i	−1.49196	+	1.08397i	−0.973450	+	0.228901i	$0.926487\pi$
$492$	−0.319555	+	3.04036i	−0.0144067	+	0.137070i
$493$	10.2566	+	2.18010i	0.461932	+	0.0981867i
$494$	−7.61730	+	13.1936i	−0.342719	+	0.593606i
$495$	−2.83463	−	1.89358i	−0.127407	−	0.0851103i
$496$	−3.47420			−0.155996
$497$	−11.9141	+	15.6403i	−0.534421	+	0.701564i
$498$	8.46084	+	6.14716i	0.379139	+	0.275461i
$499$	30.3241	+	13.5011i	1.35749	+	0.604394i	0.950980	−	0.309252i	$-0.100079\pi$
$499$	30.3241	+	13.5011i	1.35749	+	0.604394i	0.406511	+	0.913646i	$0.366745\pi$
$500$	−18.3634	−	20.3947i	−0.821238	−	0.912077i
$501$	3.99812	+	4.44036i	0.178623	+	0.198381i
$502$	46.5669	+	20.7329i	2.07838	+	0.925356i
$503$	17.0117	+	12.3597i	0.758516	+	0.551094i	0.898455	−	0.439066i	$-0.144691\pi$
$503$	17.0117	+	12.3597i	0.758516	+	0.551094i	−0.139939	+	0.990160i	$0.544691\pi$
$504$	5.77438	+	0.739571i	0.257211	+	0.0329431i
$505$	6.43392			0.286306
$506$	3.80399	−	13.4937i	0.169108	−	0.599867i
$507$	−6.34387	+	10.9879i	−0.281741	+	0.487990i
$508$	−32.3732	−	6.88113i	−1.43633	−	0.305301i
$509$	−3.24941	+	30.9161i	−0.144028	+	1.37033i	0.648834	+	0.760930i	$0.275257\pi$
$509$	−3.24941	+	30.9161i	−0.144028	+	1.37033i	−0.792862	+	0.609401i	$0.791410\pi$
$510$	4.83332	−	3.51161i	0.214023	−	0.155497i
$511$	6.73484	−	28.4935i	0.297932	−	1.26048i
$512$	−3.64970	+	11.2326i	−0.161296	+	0.496417i
$513$	−1.22983	−	0.547557i	−0.0542984	−	0.0241752i
$514$	−15.2294	+	6.78058i	−0.671741	+	0.299078i
$515$	−10.6074	−	2.25468i	−0.467419	−	0.0993529i
$516$	−13.7227	−	23.7684i	−0.604108	−	1.04635i
$517$	32.3292	+	5.55146i	1.42184	+	0.244153i
$518$	47.4638	−	3.90341i	2.08544	−	0.171506i
$519$	0.457380	+	1.40767i	0.0200768	+	0.0617899i
$520$	1.19814	−	11.3996i	0.0525421	−	0.499905i
$521$	−3.05973	−	29.1114i	−0.134049	−	1.27539i	−0.830187	−	0.557486i	$-0.811766\pi$
$521$	−3.05973	−	29.1114i	−0.134049	−	1.27539i	0.696137	−	0.717909i	$-0.254901\pi$
$522$	6.01793	+	6.68359i	0.263398	+	0.292533i
$523$	9.16995	−	1.94913i	0.400974	−	0.0852296i	−0.00301064	−	0.999995i	$-0.500958\pi$
$523$	9.16995	−	1.94913i	0.400974	−	0.0852296i	0.403984	+	0.914766i	$0.367625\pi$
$524$	12.8647	−	9.34674i	0.561996	−	0.408314i
$525$	−9.15174	+	5.01073i	−0.399415	+	0.218686i
$526$	−15.4202	−	47.4585i	−0.672353	−	2.06929i
$527$	−4.27433	−	7.40335i	−0.186193	−	0.322495i
$528$	1.87271	+	2.96734i	0.0814994	+	0.129137i
$529$	9.70797	−	16.8147i	0.422086	−	0.731074i
$530$	18.7248	−	20.7960i	0.813354	−	0.903321i
$531$	−4.99317	−	3.62775i	−0.216685	−	0.157431i
$532$	−10.0360	−	3.51427i	−0.435115	−	0.152363i
$533$	1.60378	−	4.93594i	0.0694676	−	0.213799i
$534$	40.0868	−	8.52072i	1.73473	−	0.368728i
$535$	0.688296	+	6.54870i	0.0297576	+	0.283125i
$536$	−2.23530	+	0.995219i	−0.0965502	+	0.0429869i
$537$	−3.61496	+	4.01482i	−0.155997	+	0.173252i
$538$	2.57281			0.110922
$539$	−15.6371	+	17.1604i	−0.673539	+	0.739152i
$540$	3.06855			0.132049
$541$	26.2492	−	29.1527i	1.12854	−	1.25337i	0.164859	−	0.986317i	$-0.447283\pi$
$541$	26.2492	−	29.1527i	1.12854	−	1.25337i	0.963681	−	0.267055i	$-0.0860504\pi$
$542$	14.6129	−	6.50609i	0.627679	−	0.279461i
$543$	−2.60794	−	24.8129i	−0.111918	−	1.06482i
$544$	−17.2208	+	3.66038i	−0.738334	+	0.156938i
$545$	−0.0295061	+	0.0908103i	−0.00126390	+	0.00388989i
$546$	−28.2585	−	9.89519i	−1.20935	−	0.423475i
$547$	4.06399	+	2.95266i	0.173764	+	0.126247i	0.671268	−	0.741215i	$-0.265750\pi$
$547$	4.06399	+	2.95266i	0.173764	+	0.126247i	−0.497504	+	0.867462i	$0.665750\pi$
$548$	−8.14969	+	9.05115i	−0.348137	+	0.386646i
$549$	1.74457	−	3.02169i	0.0744566	−	0.128963i
$550$	27.1259	+	10.8186i	1.15665	+	0.461307i
$551$	−2.71125	−	4.69602i	−0.115503	−	0.200057i
$552$	1.28724	+	3.96172i	0.0547886	+	0.168622i
$553$	−32.4507	+	17.7673i	−1.37994	+	0.755541i
$554$	18.2634	−	13.2691i	0.775938	−	0.563752i
$555$	8.10496	−	1.72276i	0.344036	−	0.0731272i
$556$	39.3790	+	43.7348i	1.67004	+	1.85477i
$557$	0.999243	+	9.50716i	0.0423393	+	0.402831i	0.995082	+	0.0990533i	$0.0315814\pi$
$557$	0.999243	+	9.50716i	0.0423393	+	0.402831i	−0.952743	+	0.303778i	$0.901752\pi$
$558$	0.766428	−	7.29207i	0.0324455	−	0.308698i
$559$	14.3981	+	44.3126i	0.608973	+	1.87423i
$560$	−2.86733	+	0.235809i	−0.121167	+	0.00996474i
$561$	−4.01925	+	7.64140i	−0.169693	+	0.322620i
$562$	−22.5130	−	38.9937i	−0.949656	−	1.64485i
$563$	−24.7845	−	5.26811i	−1.04454	−	0.222024i	−0.346477	−	0.938059i	$-0.612622\pi$
$563$	−24.7845	−	5.26811i	−1.04454	−	0.222024i	−0.698065	+	0.716034i	$0.745955\pi$
$564$	−26.9743	+	12.0097i	−1.13582	+	0.505700i
$565$	10.6585	+	4.74548i	0.448407	+	0.199644i
$566$	1.35380	−	4.16656i	0.0569044	−	0.175134i
$567$	0.608591	−	2.57480i	0.0255584	−	0.108132i
$568$	−13.2285	+	9.61106i	−0.555055	+	0.403271i
$569$	3.56834	−	33.9505i	0.149593	−	1.42328i	−0.619928	−	0.784659i	$-0.712838\pi$
$569$	3.56834	−	33.9505i	0.149593	−	1.42328i	0.769521	−	0.638622i	$-0.220495\pi$
$570$	−3.02200	−	0.642346i	−0.126578	−	0.0269049i
$571$	22.6152	−	39.1707i	0.946416	−	1.63924i	0.193525	−	0.981095i	$-0.438008\pi$
$571$	22.6152	−	39.1707i	0.946416	−	1.63924i	0.752891	−	0.658145i	$-0.228659\pi$
$572$	17.3750	+	47.0808i	0.726484	+	1.96855i
$573$	22.8527			0.954686
$574$	6.00024	+	0.768498i	0.250445	+	0.0320765i
$575$	−6.03995	−	4.38828i	−0.251884	−	0.183004i
$576$	−11.8618	−	5.28123i	−0.494243	−	0.220051i
$577$	−0.613256	−	0.681090i	−0.0255302	−	0.0283541i	0.730244	−	0.683186i	$-0.239406\pi$
$577$	−0.613256	−	0.681090i	−0.0255302	−	0.0283541i	−0.755775	+	0.654832i	$0.772739\pi$
$578$	15.2738	+	16.9633i	0.635308	+	0.705581i
$579$	−6.70577	−	2.98560i	−0.278682	−	0.124077i
$580$	9.99940	+	7.26499i	0.415202	+	0.301662i
$581$	7.50935	−	9.85794i	0.311540	−	0.408976i
$582$	15.8753			0.658054
$583$	−10.9732	+	38.9245i	−0.454462	+	1.61209i
$584$	12.1748	−	21.0874i	0.503796	−	0.872601i
$585$	−5.09553	−	1.08309i	−0.210674	−	0.0447802i
$586$	−6.53814	+	62.2062i	−0.270088	+	2.56972i
$587$	0.0318255	−	0.0231226i	0.00131358	−	0.000954370i	−0.587128	−	0.809494i	$-0.699742\pi$
$587$	0.0318255	−	0.0231226i	0.00131358	−	0.000954370i	0.588442	+	0.808540i	$0.299742\pi$
$588$	3.12400	−	20.6634i	0.128831	−	0.852143i
$589$	−1.36610	+	4.20442i	−0.0562891	+	0.173240i
$590$	−12.9397	−	5.76111i	−0.532717	−	0.237181i
$591$	24.0063	−	10.6883i	0.987487	−	0.439658i
$592$	−8.34257	−	1.77327i	−0.342877	−	0.0728808i
$593$	−4.44625	−	7.70113i	−0.182586	−	0.316248i	0.760175	−	0.649719i	$-0.225113\pi$
$593$	−4.44625	−	7.70113i	−0.182586	−	0.316248i	−0.942760	+	0.333471i	$0.891780\pi$
$594$	−6.64134	+	3.27607i	−0.272497	+	0.134419i
$595$	−4.03019	−	5.82003i	−0.165222	−	0.238598i
$596$	4.41441	+	13.5862i	0.180821	+	0.556511i
$597$	−1.26778	+	12.0622i	−0.0518870	+	0.493671i
$598$	−2.23943	−	21.3067i	−0.0915770	−	0.871297i
$599$	−16.7013	−	18.5486i	−0.682396	−	0.757877i	0.298075	−	0.954542i	$-0.403655\pi$
$599$	−16.7013	−	18.5486i	−0.682396	−	0.757877i	−0.980471	+	0.196665i	$0.936989\pi$
$600$	−8.48756	+	1.80409i	−0.346503	+	0.0736515i
$601$	−22.5755	+	16.4021i	−0.920874	+	0.669054i	−0.943741	−	0.330685i	$-0.892720\pi$
$601$	−22.5755	+	16.4021i	−0.920874	+	0.669054i	0.0228677	+	0.999738i	$0.492720\pi$
$602$	−47.6350	+	26.0809i	−1.94146	+	1.06298i
$603$	0.343635	+	1.05760i	0.0139939	+	0.0430688i
$604$	8.20402	+	14.2098i	0.333817	+	0.578188i
$605$	11.2711	−	0.889582i	0.458235	−	0.0361667i
$606$	6.98838	−	12.1042i	0.283884	−	0.491701i
$607$	5.60803	−	6.22835i	0.227623	−	0.252801i	−0.618505	−	0.785781i	$-0.712261\pi$
$607$	5.60803	−	6.22835i	0.227623	−	0.252801i	0.846128	+	0.532980i	$0.178928\pi$
$608$	7.36559	+	5.35141i	0.298714	+	0.217028i
$609$	8.07922	−	6.94958i	0.327387	−	0.281611i
$610$	2.47443	−	7.61552i	0.100187	−	0.308343i
$611$	49.0316	−	10.4220i	1.98361	−	0.421628i
$612$	−0.812380	−	7.72928i	−0.0328385	−	0.312437i
$613$	−18.3669	+	8.17745i	−0.741830	+	0.330284i	−0.742618	−	0.669716i	$-0.766416\pi$
$613$	−18.3669	+	8.17745i	−0.741830	+	0.330284i	0.000787513		1.00000i	$0.499749\pi$
$614$	−25.7648	+	28.6147i	−1.03978	+	1.15479i
$615$	1.05250			0.0424409
$616$	−16.5574	+	9.93211i	−0.667118	+	0.400176i
$617$	−22.3648			−0.900374			−0.450187	−	0.892934i	$-0.648643\pi$
$617$	−22.3648			−0.900374			−0.450187	+	0.892934i	$0.648643\pi$
$618$	−15.7633	+	17.5069i	−0.634092	+	0.704231i
$619$	15.7813	−	7.02629i	0.634304	−	0.282410i	−0.0642870	−	0.997931i	$-0.520477\pi$
$619$	15.7813	−	7.02629i	0.634304	−	0.282410i	0.698591	+	0.715521i	$0.253811\pi$
$620$	−1.05330	−	10.0215i	−0.0423015	−	0.402472i
$621$	1.85179	−	0.393610i	0.0743098	−	0.0157950i
$622$	−20.7136	+	63.7500i	−0.830541	+	2.55614i
$623$	−9.01746	−	47.7171i	−0.361277	−	1.91175i
$624$	4.33802	+	3.15175i	0.173660	+	0.126171i
$625$	6.87164	−	7.63173i	0.274866	−	0.305269i
$626$	30.5424	−	52.9010i	1.22072	−	2.11435i
$627$	4.32740	−	1.09953i	0.172820	−	0.0439111i
$628$	−31.0364	−	53.7566i	−1.23849	−	2.14512i
$629$	−6.48516	−	19.9593i	−0.258580	−	0.795828i
$630$	0.137605	−	6.07032i	0.00548231	−	0.241847i
$631$	−31.1456	+	22.6286i	−1.23989	+	0.900830i	−0.997591	−	0.0693729i	$-0.977900\pi$
$631$	−31.1456	+	22.6286i	−1.23989	+	0.900830i	−0.242295	+	0.970203i	$0.577900\pi$
$632$	−30.0956	+	6.39701i	−1.19714	+	0.254459i
$633$	11.9593	+	13.2822i	0.475340	+	0.527918i
$634$	−5.97742	−	56.8714i	−0.237394	−	2.25865i
$635$	−1.19104	+	11.3320i	−0.0472650	+	0.449696i
$636$	−11.2493	−	34.6218i	−0.446064	−	1.37284i
$637$	−12.4810	+	33.2103i	−0.494517	+	1.31584i
$638$	−29.3983	−	5.04818i	−1.16389	−	0.199859i
$639$	3.71563	+	6.43566i	0.146988	+	0.254591i
$640$	−15.5490	−	3.30504i	−0.614627	−	0.130643i
$641$	−16.9821	+	7.56090i	−0.670751	+	0.298638i	−0.713712	−	0.700439i	$-0.752988\pi$
$641$	−16.9821	+	7.56090i	−0.670751	+	0.298638i	0.0429611	+	0.999077i	$0.486321\pi$
$642$	13.0678	+	5.81814i	0.515744	+	0.229624i
$643$	−2.98936	+	9.20029i	−0.117889	+	0.362824i	−0.992539	−	0.121931i	$-0.961091\pi$
$643$	−2.98936	+	9.20029i	−0.117889	+	0.362824i	0.874650	+	0.484755i	$0.161091\pi$
$644$	14.3228	−	4.29744i	0.564399	−	0.169343i
$645$	−7.64430	+	5.55391i	−0.300994	+	0.218685i
$646$	−0.817931	+	7.78209i	−0.0321811	+	0.306182i
$647$	20.8973	+	4.44186i	0.821557	+	0.174627i	0.599468	−	0.800399i	$-0.295379\pi$
$647$	20.8973	+	4.44186i	0.821557	+	0.174627i	0.222090	+	0.975026i	$0.428712\pi$
$648$	1.10017	−	1.90555i	0.0432188	−	0.0748571i
$649$	20.4540	−	0.805923i	0.802889	−	0.0316352i
$650$	44.6277			1.75044
$651$	−8.61787	−	1.10376i	−0.337761	−	0.0432597i
$652$	17.6729	+	12.8401i	0.692124	+	0.502858i
$653$	29.2356	+	13.0165i	1.14408	+	0.509376i	0.889164	−	0.457588i	$-0.151287\pi$
$653$	29.2356	+	13.0165i	1.14408	+	0.509376i	0.254913	+	0.966964i	$0.417953\pi$
$654$	0.138794	+	0.154146i	0.00542727	+	0.00602759i
$655$	−3.66322	−	4.06842i	−0.143134	−	0.158966i
$656$	−0.989695	−	0.440641i	−0.0386411	−	0.0172041i
$657$	−8.95281	−	6.50460i	−0.349282	−	0.253769i
$658$	22.5485	+	53.9001i	0.879031	+	2.10125i
$659$	−33.3651			−1.29972			−0.649860	−	0.760054i	$-0.725173\pi$
$659$	−33.3651			−1.29972			−0.649860	+	0.760054i	$0.725173\pi$
$660$	−7.99164	+	6.30154i	−0.311074	+	0.245287i
$661$	−13.3562	+	23.1336i	−0.519495	+	0.899792i	0.480248	+	0.877133i	$0.340547\pi$
$661$	−13.3562	+	23.1336i	−0.519495	+	0.899792i	−0.999743	+	0.0226592i	$0.992787\pi$
$662$	−28.8198	−	6.12584i	−1.12011	−	0.238087i
$663$	−1.37915	+	13.1217i	−0.0535617	+	0.509606i
$664$	8.33778	−	6.05775i	0.323569	−	0.235086i
$665$	−0.842099	+	3.56272i	−0.0326552	+	0.138156i
$666$	5.56236	−	17.1192i	0.215537	−	0.663355i
$667$	6.96628	+	3.10159i	0.269736	+	0.120094i
$668$	16.2962	−	7.25552i	0.630518	−	0.280725i
$669$	2.06409	+	0.438735i	0.0798022	+	0.0169625i
$670$	1.27603	+	2.21014i	0.0492972	+	0.0853853i
$671$	1.66180	+	11.4522i	0.0641531	+	0.442109i
$672$	−7.64631	+	16.1769i	−0.294963	+	0.624039i
$673$	0.507396	+	1.56161i	0.0195587	+	0.0601954i	0.960359	−	0.278764i	$-0.0899249\pi$
$673$	0.507396	+	1.56161i	0.0195587	+	0.0601954i	−0.940801	+	0.338960i	$0.889925\pi$
$674$	−5.07507	+	48.2861i	−0.195485	+	1.85991i
$675$	0.412215	+	3.92196i	0.0158661	+	0.150956i
$676$	25.3458	+	28.1493i	0.974838	+	1.08267i
$677$	−0.483086	+	0.102683i	−0.0185665	+	0.00394643i	−0.217186	−	0.976130i	$-0.569688\pi$
$677$	−0.483086	+	0.102683i	−0.0185665	+	0.00394643i	0.198619	+	0.980077i	$0.436354\pi$
$678$	20.5048	−	14.8976i	0.787481	−	0.572139i
$679$	0.426315	−	18.8065i	0.0163604	−	0.721728i
$680$	−1.81931	−	5.59927i	−0.0697675	−	0.214722i
$681$	5.64617	+	9.77946i	0.216362	+	0.374750i
$682$	12.9789	+	20.5652i	0.496987	+	0.787482i
$683$	12.6490	−	21.9087i	0.484000	−	0.838312i	−0.515831	−	0.856690i	$-0.672517\pi$
$683$	12.6490	−	21.9087i	0.484000	−	0.838312i	0.999831	+	0.0183779i	$0.00585018\pi$
$684$	−2.68929	+	2.98676i	−0.102828	+	0.114202i
$685$	3.39234	+	2.46468i	0.129614	+	0.0941704i
$686$	−40.7370	−	7.10664i	−1.55535	−	0.271333i
$687$	8.61390	−	26.5108i	0.328641	−	1.01145i
$688$	9.51335	−	2.02213i	0.362693	−	0.0770928i
$689$	6.45996	+	61.4624i	0.246105	+	2.34153i
$690$	3.96910	−	1.76716i	0.151101	−	0.0672745i
$691$	−1.03073	+	1.14475i	−0.0392110	+	0.0435482i	−0.762431	−	0.647069i	$-0.775994\pi$
$691$	−1.03073	+	1.14475i	−0.0392110	+	0.0435482i	0.723220	+	0.690617i	$0.242661\pi$
$692$	4.41881			0.167978
$693$	3.70260	+	7.95555i	0.140650	+	0.302206i
$694$	−30.6550			−1.16365
$695$	13.5574	−	15.0570i	0.514260	−	0.571144i
$696$	8.09662	−	3.60485i	0.306901	−	0.136641i
$697$	−0.278643	−	2.65111i	−0.0105544	−	0.100418i
$698$	50.3353	−	10.6991i	1.90522	−	0.404967i
$699$	−2.12355	+	6.53560i	−0.0803199	+	0.247199i
$700$	5.78414	+	30.6076i	0.218620	+	1.15686i
$701$	6.24771	+	4.53922i	0.235973	+	0.171444i	0.699487	−	0.714645i	$-0.253412\pi$
$701$	6.24771	+	4.53922i	0.235973	+	0.171444i	−0.463515	+	0.886089i	$0.653412\pi$
$702$	−7.57227	+	8.40986i	−0.285797	+	0.317410i
$703$	−5.42638	+	9.39877i	−0.204660	+	0.354481i
$704$	41.7382	−	10.6051i	1.57307	−	0.399694i
$705$	5.08277	+	8.80362i	0.191428	+	0.331563i
$706$	2.94378	+	9.06002i	0.110791	+	0.340979i
$707$	−14.1514	−	8.60374i	−0.532220	−	0.323577i
$708$	−14.9069	+	10.8305i	−0.560235	+	0.407034i
$709$	−19.6765	+	4.18237i	−0.738967	+	0.157072i	−0.561991	−	0.827143i	$-0.689965\pi$
$709$	−19.6765	+	4.18237i	−0.738967	+	0.157072i	−0.176975	+	0.984215i	$0.556631\pi$
$710$	11.4116	+	12.6739i	0.428271	+	0.475643i
$711$	1.46165	+	13.9067i	0.0548161	+	0.521541i
$712$	4.22152	−	40.1651i	0.158208	−	1.50525i
$713$	−1.92112	−	5.91259i	−0.0719464	−	0.221428i
$714$	−15.3268	+	1.26047i	−0.573591	+	0.0471720i
$715$	15.4949	−	7.64337i	0.579475	−	0.285846i
$716$	8.06442	+	13.9680i	0.301382	+	0.522008i
$717$	−10.9177	−	2.32064i	−0.407730	−	0.0866657i
$718$	−32.0026	+	14.2485i	−1.19433	+	0.531748i
$719$	−19.0573	−	8.48487i	−0.710718	−	0.316432i	0.0193438	−	0.999813i	$-0.493842\pi$
$719$	−19.0573	−	8.48487i	−0.710718	−	0.316432i	−0.730062	+	0.683381i	$0.760509\pi$
$720$	−0.336028	+	1.03419i	−0.0125230	+	0.0385419i
$721$	20.3160	+	19.1439i	0.756608	+	0.712956i
$722$	−31.0476	+	22.5574i	−1.15547	+	0.839499i
$723$	−1.72529	+	16.4151i	−0.0641644	+	0.610483i
$724$	−72.8582	−	15.4865i	−2.70775	−	0.575551i
$725$	−7.94223	+	13.7563i	−0.294967	+	0.510898i
$726$	10.5688	−	22.1707i	0.392246	−	0.822832i
$727$	−41.6247			−1.54378			−0.771888	−	0.635758i	$-0.780687\pi$
$727$	−41.6247			−1.54378			−0.771888	+	0.635758i	$0.780687\pi$
$728$	−17.8794	+	23.4712i	−0.662653	+	0.869901i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−23.2010	−	10.3297i	−0.858706	−	0.382321i
$731$	16.0134	+	17.7847i	0.592276	+	0.657790i
$732$	−6.97013	−	7.74111i	−0.257623	−	0.286120i
$733$	45.6839	+	20.3398i	1.68738	+	0.751268i	0.999681	+	0.0252675i	$0.00804374\pi$
$733$	45.6839	+	20.3398i	1.68738	+	0.751268i	0.687694	+	0.726000i	$0.258623\pi$
$734$	−24.1944	−	17.5783i	−0.893032	−	0.648826i
$735$	−7.18743	−	0.326023i	−0.265112	−	0.0120256i
$736$	−12.8033			−0.471935
$737$	−3.06684	−	2.04870i	−0.112968	−	0.0754648i
$738$	1.14320	−	1.98008i	0.0420818	−	0.0728879i
$739$	−3.78631	−	0.804805i	−0.139282	−	0.0296052i	0.137743	−	0.990468i	$-0.456015\pi$
$739$	−3.78631	−	0.804805i	−0.139282	−	0.0296052i	−0.277025	+	0.960863i	$0.589348\pi$
$740$	2.58578	−	24.6021i	0.0950552	−	0.904389i
$741$	5.51996	−	4.01049i	0.202781	−	0.147329i
$742$	−68.9947	+	20.7013i	−2.53288	+	0.759967i
$743$	−2.87081	+	8.83546i	−0.105320	+	0.324141i	−0.989805	−	0.142426i	$-0.954510\pi$
$743$	−2.87081	+	8.83546i	−0.105320	+	0.324141i	0.884485	+	0.466568i	$0.154510\pi$
$744$	−6.60091	−	2.93892i	−0.242001	−	0.107746i
$745$	4.49295	−	2.00039i	0.164609	−	0.0732887i
$746$	54.1493	+	11.5098i	1.98255	+	0.421403i
$747$	−2.34193	−	4.05634i	−0.0856866	−	0.148414i
$748$	17.9885	+	18.4616i	0.657726	+	0.675024i
$749$	7.24330	−	15.3243i	0.264665	−	0.559938i
$750$	6.34260	+	19.5205i	0.231599	+	0.712788i
$751$	2.26247	−	21.5260i	0.0825589	−	0.785495i	−0.872407	−	0.488780i	$-0.837442\pi$
$751$	2.26247	−	21.5260i	0.0825589	−	0.785495i	0.954966	−	0.296715i	$-0.0958912\pi$
$752$	−1.09374	−	10.4062i	−0.0398846	−	0.379477i
$753$	−15.2759	−	16.9656i	−0.556684	−	0.618260i
$754$	−44.5865	+	9.47715i	−1.62374	+	0.345138i
$755$	4.57010	−	3.32037i	0.166323	−	0.120841i
$756$	−6.74928	−	4.10340i	−0.245469	−	0.149239i
$757$	3.03614	+	9.34428i	0.110350	+	0.339624i	0.990949	−	0.134239i	$-0.0428591\pi$
$757$	3.03614	+	9.34428i	0.110350	+	0.339624i	−0.880599	+	0.473863i	$0.842859\pi$
$758$	12.3830	+	21.4480i	0.449772	+	0.779028i
$759$	−4.01444	+	4.82793i	−0.145715	+	0.175243i
$760$	−1.52229	+	2.63668i	−0.0552193	+	0.0956426i
$761$	−22.2450	+	24.7055i	−0.806379	+	0.895575i	−0.996275	−	0.0862293i	$-0.972518\pi$
$761$	−22.2450	+	24.7055i	−0.806379	+	0.895575i	0.189896	+	0.981804i	$0.439185\pi$
$762$	20.0253	+	14.5493i	0.725442	+	0.527064i
$763$	0.186334	−	0.160281i	0.00674576	−	0.00580256i
$764$	21.0829	−	64.8866i	0.762753	−	2.34751i
$765$	−2.61722	+	0.556307i	−0.0946257	+	0.0201133i
$766$	−0.635696	−	6.04824i	−0.0229686	−	0.218532i
$767$	28.5767	−	12.7232i	1.03184	−	0.459406i
$768$	−5.73024	+	6.36407i	−0.206772	+	0.229644i
$769$	2.47573			0.0892770			0.0446385	−	0.999003i	$-0.485786\pi$
$769$	2.47573			0.0892770			0.0446385	+	0.999003i	$0.485786\pi$
$770$	12.1076	+	16.0920i	0.436327	+	0.579914i
$771$	7.46622			0.268889
$772$	−14.6636	+	16.2856i	−0.527754	+	0.586130i
$773$	−26.9385	+	11.9938i	−0.968910	+	0.431387i	−0.829290	−	0.558818i	$-0.811255\pi$
$773$	−26.9385	+	11.9938i	−0.968910	+	0.431387i	−0.139620	+	0.990205i	$0.544588\pi$
$774$	2.14558	+	20.4139i	0.0771214	+	0.733761i
$775$	12.6671	−	2.69248i	0.455016	−	0.0967166i
$776$	4.83440	−	14.8788i	0.173545	−	0.534116i
$777$	−20.1306	−	7.04909i	−0.722183	−	0.252885i
$778$	−39.6093	−	28.7779i	−1.42006	−	1.03174i
$779$	−0.922417	+	1.02445i	−0.0330490	+	0.0367046i
$780$	−7.77616	+	13.4687i	−0.278431	+	0.482257i
$781$	−22.8931	−	9.13047i	−0.819180	−	0.326714i
$782$	−5.50204	−	9.52981i	−0.196752	−	0.340785i
$783$	−1.24470	−	3.83080i	−0.0444821	−	0.136902i
$784$	6.62204	+	3.31566i	0.236502	+	0.118417i
$785$	−17.2890	+	12.5612i	−0.617071	+	0.448328i
$786$	−11.6329	+	2.47265i	−0.414931	+	0.0881964i
$787$	−16.4180	−	18.2341i	−0.585240	−	0.649975i	0.375697	−	0.926743i	$-0.377403\pi$
$787$	−16.4180	−	18.2341i	−0.585240	−	0.649975i	−0.960937	+	0.276768i	$0.910737\pi$
$788$	−8.20050	−	78.0225i	−0.292131	−	2.77944i
$789$	−2.33609	+	22.2264i	−0.0831671	+	0.791282i
$790$	9.91665	+	30.5203i	0.352819	+	1.08586i
$791$	−17.0976	−	24.6908i	−0.607921	−	0.877903i
$792$	1.04797	+	7.22206i	0.0372380	+	0.256625i
$793$	8.84203	+	15.3148i	0.313990	+	0.543846i
$794$	28.2285	+	6.00016i	1.00179	+	0.212938i
$795$	−11.4494	+	5.09762i	−0.406070	+	0.180794i
$796$	33.0790	+	14.7277i	1.17245	+	0.522009i
$797$	−5.49479	+	16.9112i	−0.194635	+	0.599026i	0.805345	+	0.592806i	$0.201980\pi$
$797$	−5.49479	+	16.9112i	−0.194635	+	0.599026i	−0.999981	+	0.00622010i	$0.998020\pi$
$798$	5.78793	+	5.45400i	0.204890	+	0.193069i
$799$	20.8296	−	15.1336i	0.736897	−	0.535387i
$800$	2.78777	−	26.5239i	0.0985626	−	0.937761i
$801$	−17.9535	−	3.81614i	−0.634356	−	0.134837i
$802$	12.2891	−	21.2853i	0.433942	−	0.751609i
$803$	36.6742	−	1.44503i	1.29421	−	0.0509940i
$804$	3.31991			0.117084
$805$	−1.98685	−	4.74939i	−0.0700273	−	0.167394i
$806$	30.0647	+	21.8433i	1.05898	+	0.769397i
$807$	−1.05265	−	0.468671i	−0.0370551	−	0.0164980i
$808$	−9.21626	−	10.2357i	−0.324227	−	0.360091i
$809$	−8.32774	−	9.24889i	−0.292788	−	0.325174i	0.578747	−	0.815507i	$-0.303542\pi$
$809$	−8.32774	−	9.24889i	−0.292788	−	0.325174i	−0.871535	+	0.490333i	$0.836875\pi$
$810$	−2.09655	−	0.933442i	−0.0736651	−	0.0327978i
$811$	22.4462	+	16.3081i	0.788191	+	0.572654i	0.907426	−	0.420212i	$-0.138044\pi$
$811$	22.4462	+	16.3081i	0.788191	+	0.572654i	−0.119235	+	0.992866i	$0.538044\pi$
$812$	−12.2786	−	29.3510i	−0.430896	−	1.03002i
$813$	−7.16398			−0.251252
$814$	20.6694	+	56.0076i	0.724461	+	1.96306i
$815$	3.76038	−	6.51317i	0.131720	−	0.228146i
$816$	2.69395	+	0.572616i	0.0943070	+	0.0200456i
$817$	1.29363	−	12.3080i	0.0452582	−	0.430603i
$818$	20.0614	−	14.5755i	0.701432	−	0.509620i
$819$	9.75928	+	9.19623i	0.341017	+	0.321342i
$820$	0.970991	−	2.98840i	0.0339085	−	0.104360i
$821$	−29.9706	−	13.3438i	−1.04598	−	0.465700i	−0.189500	−	0.981881i	$-0.560687\pi$
$821$	−29.9706	−	13.3438i	−1.04598	−	0.465700i	−0.856480	+	0.516181i	$0.827353\pi$
$822$	8.32151	−	3.70497i	0.290246	−	0.129226i
$823$	0.642109	+	0.136484i	0.0223825	+	0.00475755i	0.219089	−	0.975705i	$-0.429691\pi$
$823$	0.642109	+	0.136484i	0.0223825	+	0.00475755i	−0.196707	+	0.980462i	$0.563025\pi$
$824$	11.6076	+	20.1050i	0.404371	+	0.700390i
$825$	−9.12767	−	9.36772i	−0.317785	−	0.326142i
$826$	20.7568	+	29.9751i	0.722222	+	1.04297i
$827$	6.33848	+	19.5078i	0.220411	+	0.678354i	0.998725	+	0.0504794i	$0.0160749\pi$
$827$	6.33848	+	19.5078i	0.220411	+	0.678354i	−0.778315	+	0.627875i	$0.783925\pi$
$828$	0.590789	−	5.62098i	0.0205313	−	0.195343i
$829$	0.879970	+	8.37236i	0.0305626	+	0.290784i	0.999118	+	0.0419866i	$0.0133687\pi$
$829$	0.879970	+	8.37236i	0.0305626	+	0.290784i	−0.968556	+	0.248797i	$0.919965\pi$
$830$	−7.19264	−	7.98824i	−0.249660	−	0.277276i
$831$	−9.88954	+	2.10209i	−0.343064	+	0.0729206i
$832$	53.2405	−	38.6815i	1.84578	−	1.34104i
$833$	1.08162	+	18.1905i	0.0374759	+	0.630265i
$834$	−13.6012	−	41.8602i	−0.470971	−	1.44950i
$835$	−3.07069	−	5.31860i	−0.106266	−	0.184058i
$836$	0.870326	−	13.3013i	0.0301009	−	0.460036i
$837$	−1.64193	+	2.84390i	−0.0567533	+	0.0982997i
$838$	53.7379	−	59.6820i	1.85634	−	2.06168i
$839$	−31.8742	−	23.1580i	−1.10042	−	0.799503i	−0.119293	−	0.992859i	$-0.538063\pi$
$839$	−31.8742	−	23.1580i	−1.10042	−	0.799503i	−0.981129	+	0.193356i	$0.938063\pi$
$840$	−5.64735	−	1.97752i	−0.194852	−	0.0682308i
$841$	−3.94789	+	12.1504i	−0.136134	+	0.418978i
$842$	−43.5902	+	9.26539i	−1.50222	+	0.319306i
$843$	2.10788	+	20.0552i	0.0725993	+	0.690737i
$844$	48.7457	−	21.7030i	1.67789	−	0.747047i
$845$	8.72603	−	9.69124i	0.300185	−	0.333389i
$846$	22.0832			0.759235
$847$	−25.9804	−	13.1156i	−0.892697	−	0.450657i
$848$	12.9004			0.443002
$849$	−1.31290	+	1.45812i	−0.0450584	+	0.0500425i
$850$	20.9404	−	9.32327i	0.718250	−	0.319786i
$851$	−1.59531	−	15.1784i	−0.0546867	−	0.520309i
$852$	21.7009	−	4.61267i	0.743461	−	0.158027i
$853$	8.34555	−	25.6850i	0.285746	−	0.879436i	−0.700428	−	0.713723i	$-0.747007\pi$
$853$	8.34555	−	25.6850i	0.285746	−	0.879436i	0.986174	−	0.165713i	$-0.0529925\pi$
$854$	−15.6263	+	13.4415i	−0.534723	+	0.459957i
$855$	1.11943	+	0.813310i	0.0382835	+	0.0278146i
$856$	9.43234	−	10.4757i	0.322391	−	0.358051i
$857$	7.07983	−	12.2626i	0.241842	−	0.418883i	−0.719397	−	0.694599i	$-0.755582\pi$
$857$	7.07983	−	12.2626i	0.241842	−	0.418883i	0.961239	+	0.275716i	$0.0889150\pi$
$858$	2.45059	−	37.4528i	0.0836618	−	1.27862i
$859$	−8.62094	−	14.9319i	−0.294143	−	0.509470i	0.680642	−	0.732616i	$-0.261701\pi$
$859$	−8.62094	−	14.9319i	−0.294143	−	0.509470i	−0.974785	+	0.223146i	$0.928367\pi$
$860$	8.71713	+	26.8286i	0.297252	+	0.914846i
$861$	−2.31498	−	1.40745i	−0.0788943	−	0.0479658i
$862$	26.1534	−	19.0016i	0.890790	−	0.647197i
$863$	−20.9304	+	4.44889i	−0.712479	+	0.151442i	−0.549872	−	0.835249i	$-0.685323\pi$
$863$	−20.9304	+	4.44889i	−0.712479	+	0.151442i	−0.162607	+	0.986691i	$0.551990\pi$
$864$	4.52527	+	5.02583i	0.153953	+	0.170982i
$865$	−0.159020	−	1.51297i	−0.00540684	−	0.0514426i
$866$	6.82632	−	64.9481i	0.231968	−	2.20703i
$867$	−3.15913	−	9.72280i	−0.107290	−	0.330204i
$868$	−11.0844	+	23.4508i	−0.376230	+	0.795971i
$869$	−32.3653	−	33.2165i	−1.09792	−	1.12679i
$870$	−4.62198	−	8.00550i	−0.156700	−	0.271412i
$871$	−5.51293	−	1.17181i	−0.186799	−	0.0397053i
$872$	0.186736	−	0.0831400i	0.00632366	−	0.00281548i
$873$	−6.49532	−	2.89190i	−0.219833	−	0.0978761i
$874$	−1.75848	+	5.41205i	−0.0594815	+	0.183065i
$875$	23.2950	−	6.98947i	0.787516	−	0.236287i
$876$	−26.7282	+	19.4192i	−0.903063	+	0.656114i
$877$	−1.70357	+	16.2083i	−0.0575253	+	0.547317i	0.927367	+	0.374152i	$0.122066\pi$
$877$	−1.70357	+	16.2083i	−0.0575253	+	0.547317i	−0.984893	+	0.173165i	$0.944601\pi$
$878$	43.3365	+	9.21145i	1.46254	+	0.310871i
$879$	14.0067	−	24.2604i	0.472436	−	0.818282i
$880$	−1.24866	−	3.38347i	−0.0420922	−	0.114057i
$881$	36.6728			1.23554			0.617769	−	0.786359i	$-0.288036\pi$
$881$	36.6728			1.23554			0.617769	+	0.786359i	$0.288036\pi$
$882$	−8.42017	+	13.1677i	−0.283522	+	0.443379i
$883$	6.10529	+	4.43575i	0.205459	+	0.149275i	0.685757	−	0.727831i	$-0.259471\pi$
$883$	6.10529	+	4.43575i	0.205459	+	0.149275i	−0.480298	+	0.877106i	$0.659471\pi$
$884$	35.9847	+	16.0214i	1.21030	+	0.538858i
$885$	4.24474	+	4.71426i	0.142685	+	0.158468i
$886$	12.7449	+	14.1546i	0.428173	+	0.475534i
$887$	11.2521	+	5.00974i	0.377807	+	0.168210i	0.586849	−	0.809696i	$-0.300368\pi$
$887$	11.2521	+	5.00974i	0.377807	+	0.168210i	−0.209043	+	0.977907i	$0.567035\pi$
$888$	−14.3507	−	10.4264i	−0.481577	−	0.349886i
$889$	17.7733	−	23.3320i	0.596099	−	0.782532i
$890$	−42.1230			−1.41197
$891$	3.31405	−	0.130579i	0.111025	−	0.00437458i
$892$	3.14995	−	5.45588i	0.105468	−	0.182676i
$893$	−13.0235	−	2.76824i	−0.435816	−	0.0926355i
$894$	1.11678	−	10.6254i	0.0373506	−	0.355368i
$895$	4.49234	−	3.26387i	0.150162	−	0.109099i
$896$	29.7804	+	28.0622i	0.994893	+	0.937494i
$897$	−2.96505	+	9.12550i	−0.0990003	+	0.304691i
$898$	21.6777	+	9.65152i	0.723393	+	0.322075i
$899$	−12.0836	+	5.37999i	−0.403012	+	0.179433i
$900$	11.5161	+	2.44781i	0.383869	+	0.0815938i
$901$	15.8714	+	27.4901i	0.528754	+	0.915829i
$902$	1.08896	+	7.50455i	0.0362585	+	0.249874i
$903$	24.2406	−	1.99354i	0.806677	−	0.0663410i
$904$	−7.71822	−	23.7542i	−0.256704	−	0.790054i
$905$	−2.68052	+	25.5035i	−0.0891036	+	0.847765i
$906$	−1.28272	−	12.2043i	−0.0426157	−	0.405461i
$907$	1.01594	+	1.12831i	0.0337337	+	0.0374650i	0.759776	−	0.650185i	$-0.225309\pi$
$907$	1.01594	+	1.12831i	0.0337337	+	0.0374650i	−0.726042	+	0.687651i	$0.758642\pi$
$908$	32.9761	−	7.00928i	1.09435	−	0.232611i
$909$	−5.06421	+	3.67936i	−0.167969	+	0.122037i
$910$	26.2956	+	15.9871i	0.871692	+	0.529968i
$911$	−4.72572	−	14.5443i	−0.156570	−	0.481873i	0.841747	−	0.539873i	$-0.181528\pi$
$911$	−4.72572	−	14.5443i	−0.156570	−	0.481873i	−0.998317	+	0.0579998i	$0.981528\pi$
$912$	−0.712125	−	1.23344i	−0.0235808	−	0.0408432i
$913$	14.4293	+	5.75485i	0.477540	+	0.190458i
$914$	5.62144	−	9.73662i	0.185941	−	0.322059i
$915$	−2.39967	+	2.66511i	−0.0793307	+	0.0881057i
$916$	−67.3264	−	48.9155i	−2.22453	−	1.61621i
$917$	2.61680	+	13.8471i	0.0864143	+	0.457273i
$918$	−1.79617	+	5.52806i	−0.0592826	+	0.182453i
$919$	18.3544	−	3.90134i	0.605454	−	0.128693i	0.105023	−	0.994470i	$-0.466508\pi$
$919$	18.3544	−	3.90134i	0.605454	−	0.128693i	0.500431	+	0.865776i	$0.333175\pi$
$920$	−0.447542	−	4.25807i	−0.0147550	−	0.140385i
$921$	15.7541	−	7.01416i	0.519114	−	0.231125i
$922$	−22.9849	+	25.5273i	−0.756966	+	0.840696i
$923$	−37.6639			−1.23972
$924$	26.0043	−	3.17349i	0.855480	−	0.104400i
$925$	31.7917			1.04530
$926$	−47.3545	+	52.5925i	−1.55617	+	1.72830i
$927$	9.63859	−	4.29138i	0.316573	−	0.140947i
$928$	2.84742	+	27.0914i	0.0934713	+	0.889320i
$929$	−34.0162	+	7.23037i	−1.11604	+	0.237221i	−0.728778	−	0.684750i	$-0.759911\pi$
$929$	−34.0162	+	7.23037i	−1.11604	+	0.237221i	−0.387258	+	0.921971i	$0.626578\pi$
$930$	−2.32885	+	7.16745i	−0.0763659	+	0.235030i
$931$	6.61643	−	6.71013i	0.216845	−	0.219916i
$932$	16.5977	+	12.0589i	0.543675	+	0.395003i
$933$	20.0878	−	22.3098i	0.657645	−	0.730389i
$934$	20.1548	−	34.9091i	0.659484	−	1.14226i
$935$	5.67378	−	6.82353i	0.185553	−	0.223153i
$936$	5.57600	+	9.65791i	0.182257	+	0.315679i
$937$	−2.05971	−	6.33914i	−0.0672878	−	0.207091i	0.911759	−	0.410725i	$-0.134725\pi$
$937$	−2.05971	−	6.33914i	−0.0672878	−	0.207091i	−0.979047	+	0.203635i	$0.934725\pi$
$938$	0.148877	−	6.56758i	0.00486100	−	0.214439i
$939$	−22.1329	+	16.0805i	−0.722279	+	0.524767i
$940$	29.6856	−	6.30987i	0.968237	−	0.205805i
$941$	−31.7077	−	35.2150i	−1.03364	−	1.14798i	−0.988840	−	0.148979i	$-0.952401\pi$
$941$	−31.7077	−	35.2150i	−1.03364	−	1.14798i	−0.0448011	−	0.998996i	$-0.514265\pi$
$942$	4.85263	+	46.1697i	0.158107	+	1.50429i
$943$	0.202639	−	1.92798i	0.00659882	−	0.0627836i
$944$	−2.01777	−	6.21006i	−0.0656728	−	0.202120i
$945$	−1.16209	+	2.45858i	−0.0378028	+	0.0799775i
$946$	−47.5097	−	48.7592i	−1.54467	−	1.58530i
$947$	9.06351	+	15.6985i	0.294524	+	0.510131i	0.974874	−	0.222756i	$-0.0715054\pi$
$947$	9.06351	+	15.6985i	0.294524	+	0.510131i	−0.680350	+	0.732888i	$0.738172\pi$
$948$	40.8342	+	8.67957i	1.32623	+	0.281899i
$949$	51.2383	−	22.8128i	1.66327	−	0.740534i
$950$	−10.8290	−	4.82137i	−0.351338	−	0.156426i
$951$	−7.91424	+	24.3575i	−0.256637	+	0.789847i
$952$	−3.48601	+	14.7485i	−0.112982	+	0.478002i
$953$	35.0699	−	25.4797i	1.13602	−	0.825370i	0.149464	−	0.988767i	$-0.452245\pi$
$953$	35.0699	−	25.4797i	1.13602	−	0.825370i	0.986560	+	0.163398i	$0.0522453\pi$
$954$	−2.84590	+	27.0769i	−0.0921394	+	0.876648i
$955$	−22.9754	−	4.88358i	−0.743468	−	0.158029i
$956$	−16.6613	+	28.8582i	−0.538865	+	0.933341i
$957$	11.1086	+	7.42073i	0.359090	+	0.239878i
$958$	−14.4252			−0.466056
$959$	−4.16558	−	9.95745i	−0.134514	−	0.321543i
$960$	10.7970	+	7.84445i	0.348470	+	0.253178i
$961$	−18.4685	−	8.22270i	−0.595758	−	0.265249i
$962$	61.0451	+	67.7974i	1.96817	+	2.18588i
$963$	−4.28676	−	4.76093i	−0.138139	−	0.153419i
$964$	45.0163	+	20.0425i	1.44988	+	0.645527i
$965$	6.10377	+	4.43465i	0.196487	+	0.142756i
$966$	−11.0932	−	1.42079i	−0.356917	−	0.0457131i
$967$	−48.3991			−1.55641			−0.778205	−	0.628011i	$-0.783869\pi$
$967$	−48.3991			−1.55641			−0.778205	+	0.628011i	$0.783869\pi$
$968$	−17.5605	−	16.6568i	−0.564415	−	0.535371i
$969$	1.75226	−	3.03501i	0.0562908	−	0.0974986i
$970$	−15.9606	−	3.39253i	−0.512464	−	0.108928i
$971$	5.78816	−	55.0707i	0.185751	−	1.76730i	−0.363453	−	0.931613i	$-0.618402\pi$
$971$	5.78816	−	55.0707i	0.185751	−	1.76730i	0.549204	−	0.835689i	$-0.314931\pi$
$972$	−2.41528	+	1.75481i	−0.0774703	+	0.0562855i
$973$	−49.9544	+	14.9884i	−1.60146	+	0.480505i
$974$	−3.02255	+	9.30246i	−0.0968488	+	0.298070i
$975$	−18.2592	−	8.12952i	−0.584763	−	0.260353i
$976$	3.37225	−	1.50142i	0.107943	−	0.0480594i
$977$	13.6340	+	2.89801i	0.436192	+	0.0927154i	0.420774	−	0.907166i	$-0.361759\pi$
$977$	13.6340	+	2.89801i	0.436192	+	0.0927154i	0.0154182	+	0.999881i	$0.495092\pi$
$978$	−8.16887	−	14.1489i	−0.261212	−	0.452432i
$979$	54.5944	−	26.9305i	1.74484	−	0.860704i
$980$	−7.55650	+	20.1068i	−0.241384	+	0.642287i
$981$	−0.0287071	−	0.0883514i	−0.000916547	−	0.00282084i
$982$	9.53734	−	90.7417i	0.304349	−	2.89568i
$983$	0.969245	+	9.22175i	0.0309141	+	0.294128i	0.999045	+	0.0436848i	$0.0139097\pi$
$983$	0.969245	+	9.22175i	0.0309141	+	0.294128i	−0.968131	+	0.250443i	$0.919424\pi$
$984$	−1.50765	−	1.67442i	−0.0480622	−	0.0533785i
$985$	−26.4193	+	5.61559i	−0.841789	+	0.178928i
$986$	−18.9412	+	13.7616i	−0.603211	+	0.438258i
$987$	0.593018	−	26.1605i	0.0188760	−	0.832698i
$988$	−6.29465	−	19.3729i	−0.200260	−	0.616336i
$989$	8.70193	+	15.0722i	0.276705	+	0.479268i
$990$	7.37710	−	1.87442i	0.234460	−	0.0595730i
$991$	−10.8473	+	18.7881i	−0.344576	+	0.596823i	−0.985277	−	0.170968i	$-0.945311\pi$
$991$	−10.8473	+	18.7881i	−0.344576	+	0.596823i	0.640701	+	0.767791i	$0.278644\pi$
$992$	14.8603	−	16.5041i	0.471817	−	0.524005i
$993$	10.6756	+	7.75627i	0.338779	+	0.246138i
$994$	−8.15182	−	43.1365i	−0.258560	−	1.36821i
$995$	3.85226	−	11.8560i	0.122125	−	0.375861i
$996$	−13.6779	+	2.90732i	−0.433400	+	0.0921220i
$997$	1.02189	+	9.72262i	0.0323635	+	0.307918i	0.998714	+	0.0506909i	$0.0161423\pi$
$997$	1.02189	+	9.72262i	0.0323635	+	0.307918i	−0.966351	+	0.257228i	$0.917191\pi$
$998$	−67.7080	+	30.1455i	−2.14326	+	0.954240i
$999$	−5.39430	+	5.99098i	−0.170668	+	0.189546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.214.2	yes	64
3.2	odd	2		693.2.by.c.676.7		64
7.2	even	3	inner	231.2.y.b.16.7	✓	64
11.9	even	5	inner	231.2.y.b.130.7	yes	64
21.2	odd	6		693.2.by.c.478.2		64
33.20	odd	10		693.2.by.c.361.2		64
77.9	even	15	inner	231.2.y.b.163.2	yes	64
231.86	odd	30		693.2.by.c.163.7		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.16.7	✓	64	7.2	even	3	inner
231.2.y.b.130.7	yes	64	11.9	even	5	inner
231.2.y.b.163.2	yes	64	77.9	even	15	inner
231.2.y.b.214.2	yes	64	1.1	even	1	trivial
693.2.by.c.163.7		64	231.86	odd	30
693.2.by.c.361.2		64	33.20	odd	10
693.2.by.c.478.2		64	21.2	odd	6
693.2.by.c.676.7		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49404 + 1.65930i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.312065 - 2.96910i) q^{4} +(-1.00537 + 0.213698i) q^{5} +(-0.689977 + 2.12353i) q^{6} +(2.49708 + 0.874397i) q^{7} +(1.78011 + 1.29333i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-1.49404 + 1.65930i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.312065 - 2.96910i) q^{4} +(-1.00537 + 0.213698i) q^{5} +(-0.689977 + 2.12353i) q^{6} +(2.49708 + 0.874397i) q^{7} +(1.78011 + 1.29333i) q^{8} +(0.669131 - 0.743145i) q^{9} +(1.14748 - 1.98749i) q^{10} +(-0.216549 + 3.30955i) q^{11} +(-1.49273 - 2.58548i) q^{12} +(1.56619 + 4.82025i) q^{13} +(-5.18164 + 2.83703i) q^{14} +(-0.831533 + 0.604144i) q^{15} +(1.03484 - 0.219963i) q^{16} +(1.74191 + 1.93458i) q^{17} +(0.233393 + 2.22058i) q^{18} +(0.140718 - 1.33884i) q^{19} +(0.948233 + 2.91836i) q^{20} +(2.63685 - 0.216854i) q^{21} +(-5.16801 - 5.30393i) q^{22} +(0.946580 + 1.63952i) q^{23} +(2.15226 + 0.457476i) q^{24} +(-3.60262 + 1.60399i) q^{25} +(-10.3382 - 4.60287i) q^{26} +(0.309017 - 0.951057i) q^{27} +(1.81692 - 7.68697i) q^{28} +(3.25868 - 2.36757i) q^{29} +(0.239888 - 2.28238i) q^{30} +(-3.21210 - 0.682752i) q^{31} +(-3.38146 + 5.85686i) q^{32} +(1.14829 + 3.11150i) q^{33} -5.81254 q^{34} +(-2.69735 - 0.345471i) q^{35} +(-2.41528 - 1.75481i) q^{36} +(-7.36469 - 3.27897i) q^{37} +(2.01131 + 2.23379i) q^{38} +(3.39136 + 3.76649i) q^{39} +(-2.06605 - 0.919867i) q^{40} +(-0.828434 - 0.601893i) q^{41} +(-3.57974 + 4.69932i) q^{42} +9.19303 q^{43} +(9.89396 - 0.389839i) q^{44} +(-0.513916 + 0.890128i) q^{45} +(-4.13470 - 0.878858i) q^{46} +(1.03382 - 9.83610i) q^{47} +(0.855911 - 0.621855i) q^{48} +(5.47086 + 4.36689i) q^{49} +(2.72097 - 8.37428i) q^{50} +(2.37818 + 1.05883i) q^{51} +(13.8230 - 6.15442i) q^{52} +(11.9272 + 2.53519i) q^{53} +(1.11641 + 1.93367i) q^{54} +(-0.489532 - 3.37360i) q^{55} +(3.31421 + 4.78607i) q^{56} +(-0.416005 - 1.28033i) q^{57} +(-0.940093 + 8.94438i) q^{58} +(-0.645139 - 6.13808i) q^{59} +(2.05326 + 2.28037i) q^{60} +(3.41290 - 0.725434i) q^{61} +(5.93191 - 4.30978i) q^{62} +(2.32068 - 1.27061i) q^{63} +(-4.01240 - 12.3489i) q^{64} +(-2.60468 - 4.51144i) q^{65} +(-6.87852 - 2.74336i) q^{66} +(-0.556014 + 0.963044i) q^{67} +(5.20038 - 5.77561i) q^{68} +(1.53160 + 1.11277i) q^{69} +(4.60320 - 3.95958i) q^{70} +(-2.29639 + 7.06755i) q^{71} +(2.15226 - 0.457476i) q^{72} +(-1.15674 - 11.0057i) q^{73} +(16.4440 - 7.32133i) q^{74} +(-2.63876 + 2.93064i) q^{75} -4.01908 q^{76} +(-3.43460 + 8.07487i) q^{77} -11.3166 q^{78} +(-9.35663 + 10.3916i) q^{79} +(-0.993397 + 0.442289i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(2.23644 - 0.475370i) q^{82} +(1.44739 - 4.45461i) q^{83} +(-1.46673 - 7.76140i) q^{84} +(-2.16468 - 1.57273i) q^{85} +(-13.7348 + 15.2540i) q^{86} +(2.01397 - 3.48830i) q^{87} +(-4.66581 + 5.61130i) q^{88} +(-9.17730 - 15.8955i) q^{89} +(-0.709180 - 2.18263i) q^{90} +(-0.303894 + 13.4060i) q^{91} +(4.57252 - 3.32213i) q^{92} +(-3.21210 + 0.682752i) q^{93} +(14.7765 + 16.4110i) q^{94} +(0.144635 + 1.37611i) q^{95} +(-0.706917 + 6.72587i) q^{96} +(-2.19712 - 6.76203i) q^{97} +(-15.4197 + 2.55350i) q^{98} +(2.31457 + 2.37545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

L-functions

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